LMFDB - Embedded newform 38.9.f.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,9,Mod(3,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	38.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.4803871823$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.8
Character	$\chi$	$=$	38.3
Dual form			38.9.f.a.13.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.27231 - 8.66680i) q^{2} +(-42.9893 - 118.112i) q^{3} +(-22.2270 - 126.055i) q^{4} +(-164.500 + 932.925i) q^{5} +(-1336.29 - 486.369i) q^{6} +(512.177 + 887.116i) q^{7} +(-1254.14 - 724.077i) q^{8} +(-7076.39 + 5937.80i) q^{9} +O(q^{10})$	\(q+(7.27231 - 8.66680i) q^{2} +(-42.9893 - 118.112i) q^{3} +(-22.2270 - 126.055i) q^{4} +(-164.500 + 932.925i) q^{5} +(-1336.29 - 486.369i) q^{6} +(512.177 + 887.116i) q^{7} +(-1254.14 - 724.077i) q^{8} +(-7076.39 + 5937.80i) q^{9} +(6889.19 + 8210.21i) q^{10} +(-12280.8 + 21270.9i) q^{11} +(-13933.2 + 8044.31i) q^{12} +(11858.9 - 32582.0i) q^{13} +(11413.2 + 2012.45i) q^{14} +(117262. - 20676.4i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(74611.5 + 62606.4i) q^{17} +104511. i q^{18} +(-96099.9 - 88024.8i) q^{19} +121257. q^{20} +(82761.1 - 98630.9i) q^{21} +(95041.4 + 261124. i) q^{22} +(60877.2 + 345252. i) q^{23} +(-31607.8 + 179257. i) q^{24} +(-476222. - 173331. i) q^{25} +(-196140. - 339725. i) q^{26} +(291353. + 168213. i) q^{27} +(100442. - 84280.6i) q^{28} +(392133. + 467326. i) q^{29} +(673565. - 1.16665e6i) q^{30} +(-1.40185e6 + 809357. i) q^{31} +(-63398.2 + 174185. i) q^{32} +(3.04030e6 + 536087. i) q^{33} +(1.08520e6 - 191349. i) q^{34} +(-911867. + 331892. i) q^{35} +(905779. + 760038. i) q^{36} +399475. i q^{37} +(-1.46176e6 + 192735. i) q^{38} -4.35813e6 q^{39} +(881816. - 1.05091e6i) q^{40} +(368407. + 1.01219e6i) q^{41} +(-252950. - 1.43455e6i) q^{42} +(-2525.89 + 14325.0i) q^{43} +(2.95428e6 + 1.07527e6i) q^{44} +(-4.37546e6 - 7.57852e6i) q^{45} +(3.43495e6 + 1.98317e6i) q^{46} +(-5.62488e6 + 4.71983e6i) q^{47} +(1.32372e6 + 1.57755e6i) q^{48} +(2.35775e6 - 4.08374e6i) q^{49} +(-4.96546e6 + 2.86681e6i) q^{50} +(4.18709e6 - 1.15039e7i) q^{51} +(-4.37072e6 - 770676. i) q^{52} +(-2.53300e6 + 446637. i) q^{53} +(3.57668e6 - 1.30180e6i) q^{54} +(-1.78240e7 - 1.49561e7i) q^{55} -1.48342e6i q^{56} +(-6.26554e6 + 1.51347e7i) q^{57} +6.90193e6 q^{58} +(1.41316e6 - 1.68413e6i) q^{59} +(-5.21274e6 - 1.43219e7i) q^{60} +(310457. + 1.76069e6i) q^{61} +(-3.18013e6 + 1.80354e7i) q^{62} +(-8.89189e6 - 3.23638e6i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(2.84458e7 + 1.64232e7i) q^{65} +(2.67562e7 - 2.24511e7i) q^{66} +(6.19152e6 + 7.37877e6i) q^{67} +(6.23349e6 - 1.07967e7i) q^{68} +(3.81614e7 - 2.20325e7i) q^{69} +(-3.75493e6 + 1.03166e7i) q^{70} +(-4.20799e7 - 7.41983e6i) q^{71} +(1.31742e7 - 2.32297e6i) q^{72} +(6.16418e6 - 2.24358e6i) q^{73} +(3.46217e6 + 2.90511e6i) q^{74} +6.36990e7i q^{75} +(-8.95999e6 + 1.40704e7i) q^{76} -2.51597e7 q^{77} +(-3.16937e7 + 3.77711e7i) q^{78} +(1.85098e7 + 5.08553e7i) q^{79} +(-2.69517e6 - 1.52850e7i) q^{80} +(-3.18152e6 + 1.80433e7i) q^{81} +(1.14516e7 + 4.16805e6i) q^{82} +(5.70350e6 + 9.87876e6i) q^{83} +(-1.42725e7 - 8.24022e6i) q^{84} +(-7.06807e7 + 5.93082e7i) q^{85} +(105783. + 126067. i) q^{86} +(3.83393e7 - 6.64057e7i) q^{87} +(3.08036e7 - 1.77845e7i) q^{88} +(2.66628e7 - 7.32555e7i) q^{89} +(-9.75012e7 - 1.71921e7i) q^{90} +(3.49778e7 - 6.16754e6i) q^{91} +(4.21678e7 - 1.53478e7i) q^{92} +(1.55859e8 + 1.30782e8i) q^{93} +8.30738e7i q^{94} +(9.79290e7 - 7.51740e7i) q^{95} +2.32988e7 q^{96} +(4.33270e7 - 5.16351e7i) q^{97} +(-1.82467e7 - 5.01324e7i) q^{98} +(-3.93989e7 - 2.23442e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 168 q^{3} - 2688 q^{6} - 6570 q^{7} - 2856 q^{9}+O(q^{10}) $ 84 * q - 168 * q^3 - 2688 * q^6 - 6570 * q^7 - 2856 * q^9	\( 84 q - 168 q^{3} - 2688 q^{6} - 6570 q^{7} - 2856 q^{9} - 20970 q^{11} + 62208 q^{12} - 101310 q^{13} - 142848 q^{14} + 331518 q^{15} + 29178 q^{17} - 319212 q^{19} - 428544 q^{20} - 186138 q^{21} + 1238016 q^{22} + 1989360 q^{23} + 344064 q^{24} - 272916 q^{25} - 695808 q^{26} - 6975648 q^{27} - 489984 q^{28} + 1676430 q^{29} - 3498768 q^{31} + 6273750 q^{33} + 2740224 q^{34} + 10942362 q^{35} + 365568 q^{36} + 5830272 q^{38} - 23638704 q^{39} + 430488 q^{41} + 4230144 q^{42} - 20999118 q^{43} + 700416 q^{44} + 49897728 q^{45} + 12003840 q^{46} - 22431150 q^{47} - 5505024 q^{48} - 59138004 q^{49} - 24993792 q^{50} + 6061860 q^{51} - 2857728 q^{52} + 69029982 q^{53} + 63262080 q^{54} + 20438670 q^{55} - 50408076 q^{57} - 31266816 q^{58} - 85956678 q^{59} - 9106176 q^{60} + 29908896 q^{61} - 39755520 q^{62} - 29288274 q^{63} + 88080384 q^{64} + 199314810 q^{65} + 117652224 q^{66} + 64371642 q^{67} + 25820928 q^{68} - 186304482 q^{69} - 187792896 q^{70} - 168095268 q^{71} + 23396352 q^{72} + 104437176 q^{73} + 33624576 q^{74} + 6617088 q^{76} - 277281288 q^{77} + 30777600 q^{78} + 199146114 q^{79} + 245855040 q^{81} - 69199872 q^{82} - 14372262 q^{83} - 348399360 q^{84} - 386680068 q^{85} - 155904768 q^{86} + 36917496 q^{87} + 292036248 q^{89} + 694869504 q^{90} + 285753588 q^{91} + 95143680 q^{92} + 529006800 q^{93} - 166014666 q^{95} + 251818254 q^{97} - 595464192 q^{98} - 1180902678 q^{99}+O(q^{100}) \) 84 * q - 168 * q^3 - 2688 * q^6 - 6570 * q^7 - 2856 * q^9 - 20970 * q^11 + 62208 * q^12 - 101310 * q^13 - 142848 * q^14 + 331518 * q^15 + 29178 * q^17 - 319212 * q^19 - 428544 * q^20 - 186138 * q^21 + 1238016 * q^22 + 1989360 * q^23 + 344064 * q^24 - 272916 * q^25 - 695808 * q^26 - 6975648 * q^27 - 489984 * q^28 + 1676430 * q^29 - 3498768 * q^31 + 6273750 * q^33 + 2740224 * q^34 + 10942362 * q^35 + 365568 * q^36 + 5830272 * q^38 - 23638704 * q^39 + 430488 * q^41 + 4230144 * q^42 - 20999118 * q^43 + 700416 * q^44 + 49897728 * q^45 + 12003840 * q^46 - 22431150 * q^47 - 5505024 * q^48 - 59138004 * q^49 - 24993792 * q^50 + 6061860 * q^51 - 2857728 * q^52 + 69029982 * q^53 + 63262080 * q^54 + 20438670 * q^55 - 50408076 * q^57 - 31266816 * q^58 - 85956678 * q^59 - 9106176 * q^60 + 29908896 * q^61 - 39755520 * q^62 - 29288274 * q^63 + 88080384 * q^64 + 199314810 * q^65 + 117652224 * q^66 + 64371642 * q^67 + 25820928 * q^68 - 186304482 * q^69 - 187792896 * q^70 - 168095268 * q^71 + 23396352 * q^72 + 104437176 * q^73 + 33624576 * q^74 + 6617088 * q^76 - 277281288 * q^77 + 30777600 * q^78 + 199146114 * q^79 + 245855040 * q^81 - 69199872 * q^82 - 14372262 * q^83 - 348399360 * q^84 - 386680068 * q^85 - 155904768 * q^86 + 36917496 * q^87 + 292036248 * q^89 + 694869504 * q^90 + 285753588 * q^91 + 95143680 * q^92 + 529006800 * q^93 - 166014666 * q^95 + 251818254 * q^97 - 595464192 * q^98 - 1180902678 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	7.27231	−	8.66680i	0.454519	−	0.541675i
$2$	7.27231	−	8.66680i	0.454519	−	0.541675i
$3$	−42.9893	−	118.112i	−0.530732	−	1.45818i	−0.858201	−	0.513313i	$-0.828418\pi$
$3$	−42.9893	−	118.112i	−0.530732	−	1.45818i	0.327469	−	0.944862i	$-0.393804\pi$
$4$	−22.2270	−	126.055i	−0.0868241	−	0.492404i
$5$	−164.500	+	932.925i	−0.263200	+	1.49268i	0.510913	+	0.859633i	$0.329308\pi$
$5$	−164.500	+	932.925i	−0.263200	+	1.49268i	−0.774113	+	0.633048i	$0.781804\pi$
$6$	−1336.29	−	486.369i	−1.03109	−	0.375285i
$7$	512.177	+	887.116i	0.213318	+	0.369478i	0.952751	−	0.303752i	$-0.0982396\pi$
$7$	512.177	+	887.116i	0.213318	+	0.369478i	−0.739433	+	0.673230i	$0.764906\pi$
$8$	−1254.14	−	724.077i	−0.306186	−	0.176777i
$9$	−7076.39	+	5937.80i	−1.07855	+	0.905014i
$10$	6889.19	+	8210.21i	0.688919	+	0.821021i
$11$	−12280.8	+	21270.9i	−0.838794	+	1.45283i	0.0521090	+	0.998641i	$0.483406\pi$
$11$	−12280.8	+	21270.9i	−0.838794	+	1.45283i	−0.890903	+	0.454193i	$0.849928\pi$
$12$	−13933.2	+	8044.31i	−0.671931	+	0.387939i
$13$	11858.9	−	32582.0i	0.415212	−	1.14079i	−0.539170	−	0.842197i	$-0.681262\pi$
$13$	11858.9	−	32582.0i	0.415212	−	1.14079i	0.954382	−	0.298588i	$-0.0965157\pi$
$14$	11413.2	+	2012.45i	0.297094	+	0.0523857i
$15$	117262.	−	20676.4i	2.31628	−	0.408422i
$16$	−15395.9	+	5603.66i	−0.234923	+	0.0855050i
$17$	74611.5	+	62606.4i	0.893326	+	0.749589i	0.968874	−	0.247553i	$-0.0796264\pi$
$17$	74611.5	+	62606.4i	0.893326	+	0.749589i	−0.0755487	+	0.997142i	$0.524071\pi$
$18$			104511.i			0.995573i
$19$	−96099.9	−	88024.8i	−0.737409	−	0.675446i
$19$	−96099.9	−	88024.8i	−0.737409	−	0.675446i
$20$	121257.			0.757854
$21$	82761.1	−	98630.9i	0.425549	−	0.507149i
$22$	95041.4	+	261124.i	0.405716	+	1.11470i
$23$	60877.2	+	345252.i	0.217542	+	1.23374i	0.876440	+	0.481511i	$0.159912\pi$
$23$	60877.2	+	345252.i	0.217542	+	1.23374i	−0.658898	+	0.752232i	$0.728977\pi$
$24$	−31607.8	+	179257.i	−0.0952685	+	0.540294i
$25$	−476222.	−	173331.i	−1.21913	−	0.443727i
$26$	−196140.	−	339725.i	−0.429213	−	0.743419i
$27$	291353.	+	168213.i	0.548232	+	0.316522i
$28$	100442.	−	84280.6i	0.163411	−	0.137118i
$29$	392133.	+	467326.i	0.554423	+	0.660735i	0.968356	−	0.249572i	$-0.0802898\pi$
$29$	392133.	+	467326.i	0.554423	+	0.660735i	−0.413933	+	0.910307i	$0.635845\pi$
$30$	673565.	−	1.16665e6i	0.831562	−	1.44031i
$31$	−1.40185e6	+	809357.i	−1.51794	+	0.876382i	−0.518161	+	0.855283i	$0.673383\pi$
$31$	−1.40185e6	+	809357.i	−1.51794	+	0.876382i	−0.999777	+	0.0210986i	$0.993284\pi$
$32$	−63398.2	+	174185.i	−0.0604612	+	0.166116i
$33$	3.04030e6	+	536087.i	2.56366	+	0.452043i
$34$	1.08520e6	−	191349.i	0.812068	−	0.143189i
$35$	−911867.	+	331892.i	−0.607658	+	0.221169i
$36$	905779.	+	760038.i	0.539277	+	0.452507i
$37$			399475.i			0.213149i	0.994305	+	0.106574i	$0.0339882\pi$
$37$			399475.i			0.213149i	−0.994305	+	0.106574i	$0.966012\pi$
$38$	−1.46176e6	+	192735.i	−0.701039	+	0.0924328i
$39$	−4.35813e6			−1.88383
$40$	881816.	−	1.05091e6i	0.344459	−	0.410511i
$41$	368407.	+	1.01219e6i	0.130374	+	0.358201i	0.987654	−	0.156650i	$-0.0500695\pi$
$41$	368407.	+	1.01219e6i	0.130374	+	0.358201i	−0.857280	+	0.514851i	$0.827847\pi$
$42$	−252950.	−	1.43455e6i	−0.0812900	−	0.461018i
$43$	−2525.89	+	14325.0i	−0.000738823	+	0.00419007i	−0.985175	−	0.171553i	$-0.945122\pi$
$43$	−2525.89	+	14325.0i	−0.000738823	+	0.00419007i	0.984436	+	0.175743i	$0.0562327\pi$
$44$	2.95428e6	+	1.07527e6i	0.788209	+	0.286885i
$45$	−4.37546e6	−	7.57852e6i	−1.06702	−	1.84814i
$46$	3.43495e6	+	1.98317e6i	0.767165	+	0.442923i
$47$	−5.62488e6	+	4.71983e6i	−1.15271	+	0.967242i	−0.999780	−	0.0209940i	$-0.993317\pi$
$47$	−5.62488e6	+	4.71983e6i	−1.15271	+	0.967242i	−0.152935	+	0.988236i	$0.548872\pi$
$48$	1.32372e6	+	1.57755e6i	0.249363	+	0.297179i
$49$	2.35775e6	−	4.08374e6i	0.408991	−	0.708393i
$50$	−4.96546e6	+	2.86681e6i	−0.794473	+	0.458689i
$51$	4.18709e6	−	1.15039e7i	0.618916	−	1.70046i
$52$	−4.37072e6	−	770676.i	−0.597777	−	0.105404i
$53$	−2.53300e6	+	446637.i	−0.321020	+	0.0566045i	−0.331836	−	0.943337i	$-0.607668\pi$
$53$	−2.53300e6	+	446637.i	−0.321020	+	0.0566045i	0.0108162	+	0.999942i	$0.496557\pi$
$54$	3.57668e6	−	1.30180e6i	0.420634	−	0.153098i
$55$	−1.78240e7	−	1.49561e7i	−1.94785	−	1.63444i
$56$		−	1.48342e6i		−	0.150839i
$57$	−6.26554e6	+	1.51347e7i	−0.593552	+	1.43375i
$58$	6.90193e6			0.609900
$59$	1.41316e6	−	1.68413e6i	0.116622	−	0.138985i	−0.704575	−	0.709630i	$-0.748862\pi$
$59$	1.41316e6	−	1.68413e6i	0.116622	−	0.138985i	0.821197	+	0.570645i	$0.193307\pi$
$60$	−5.21274e6	−	1.43219e7i	−0.402218	−	1.10508i
$61$	310457.	+	1.76069e6i	0.0224224	+	0.127164i	0.993964	−	0.109704i	$-0.0349903\pi$
$61$	310457.	+	1.76069e6i	0.0224224	+	0.127164i	−0.971542	+	0.236868i	$0.923879\pi$
$62$	−3.18013e6	+	1.80354e7i	−0.215218	+	1.22056i
$63$	−8.89189e6	−	3.23638e6i	−0.564458	−	0.205446i
$64$	1.04858e6	+	1.81619e6i	0.0625000	+	0.108253i
$65$	2.84458e7	+	1.64232e7i	1.59354	+	0.920033i
$66$	2.67562e7	−	2.24511e7i	1.41010	−	1.18321i
$67$	6.19152e6	+	7.37877e6i	0.307255	+	0.366172i	0.897471	−	0.441073i	$-0.145402\pi$
$67$	6.19152e6	+	7.37877e6i	0.307255	+	0.366172i	−0.590217	+	0.807245i	$0.700958\pi$
$68$	6.23349e6	−	1.07967e7i	0.291538	−	0.504959i
$69$	3.81614e7	−	2.20325e7i	1.68356	−	0.972002i
$70$	−3.75493e6	+	1.03166e7i	−0.156390	+	0.429679i
$71$	−4.20799e7	−	7.41983e6i	−1.65593	−	0.291985i	−0.733944	−	0.679210i	$-0.762322\pi$
$71$	−4.20799e7	−	7.41983e6i	−1.65593	−	0.291985i	−0.921985	+	0.387226i	$0.873433\pi$
$72$	1.31742e7	−	2.32297e6i	0.490224	−	0.0864397i
$73$	6.16418e6	−	2.24358e6i	0.217062	−	0.0790042i	−0.231200	−	0.972906i	$-0.574265\pi$
$73$	6.16418e6	−	2.24358e6i	0.217062	−	0.0790042i	0.448262	+	0.893902i	$0.352043\pi$
$74$	3.46217e6	+	2.90511e6i	0.115457	+	0.0968803i
$75$			6.36990e7i			2.01320i
$76$	−8.95999e6	+	1.40704e7i	−0.268567	+	0.421748i
$77$	−2.51597e7			−0.715720
$78$	−3.16937e7	+	3.77711e7i	−0.856238	+	1.02042i
$79$	1.85098e7	+	5.08553e7i	0.475219	+	1.30565i	0.913509	+	0.406819i	$0.133362\pi$
$79$	1.85098e7	+	5.08553e7i	0.475219	+	1.30565i	−0.438290	+	0.898834i	$0.644416\pi$
$80$	−2.69517e6	−	1.52850e7i	−0.0658000	−	0.373170i
$81$	−3.18152e6	+	1.80433e7i	−0.0739085	+	0.419156i
$82$	1.14516e7	+	4.16805e6i	0.253286	+	0.0921887i
$83$	5.70350e6	+	9.87876e6i	0.120179	+	0.208156i	0.919838	−	0.392298i	$-0.128320\pi$
$83$	5.70350e6	+	9.87876e6i	0.120179	+	0.208156i	−0.799659	+	0.600454i	$0.794986\pi$
$84$	−1.42725e7	−	8.24022e6i	−0.286670	−	0.165509i
$85$	−7.06807e7	+	5.93082e7i	−1.35402	+	1.13616i
$86$	105783.	+	126067.i	0.00193385	+	0.00230467i
$87$	3.83393e7	−	6.64057e7i	0.669218	−	1.15912i
$88$	3.08036e7	−	1.77845e7i	0.513655	−	0.296559i
$89$	2.66628e7	−	7.32555e7i	0.424958	−	1.16756i	−0.523877	−	0.851794i	$-0.675515\pi$
$89$	2.66628e7	−	7.32555e7i	0.424958	−	1.16756i	0.948836	−	0.315770i	$-0.102263\pi$
$90$	−9.75012e7	−	1.71921e7i	−1.48607	−	0.262035i
$91$	3.49778e7	−	6.16754e6i	0.510067	−	0.0899386i
$92$	4.21678e7	−	1.53478e7i	0.588612	−	0.214237i
$93$	1.55859e8	+	1.30782e8i	2.08354	+	1.74830i
$94$			8.30738e7i			1.06403i
$95$	9.79290e7	−	7.51740e7i	1.20231	−	0.922939i
$96$	2.32988e7			0.274315
$97$	4.33270e7	−	5.16351e7i	0.489409	−	0.583255i	−0.463658	−	0.886014i	$-0.653463\pi$
$97$	4.33270e7	−	5.16351e7i	0.489409	−	0.583255i	0.953067	+	0.302759i	$0.0979078\pi$
$98$	−1.82467e7	−	5.01324e7i	−0.197825	−	0.543518i
$99$	−3.93989e7	−	2.23442e8i	−0.410151	−	2.32608i
$100$	−1.12643e7	+	6.38830e7i	−0.112643	+	0.638830i
$101$	−1.68013e8	−	6.11517e7i	−1.61457	−	0.587656i	−0.632234	−	0.774777i	$-0.717862\pi$
$101$	−1.68013e8	−	6.11517e7i	−1.61457	−	0.587656i	−0.982337	+	0.187121i	$0.940084\pi$
$102$	−6.92525e7	−	1.19949e8i	−0.639786	−	1.10814i
$103$	2.86292e7	+	1.65291e7i	0.254367	+	0.146859i	0.621762	−	0.783206i	$-0.286417\pi$
$103$	2.86292e7	+	1.65291e7i	0.254367	+	0.146859i	−0.367395	+	0.930065i	$0.619750\pi$
$104$	−3.84645e7	+	3.22756e7i	−0.328796	+	0.275893i
$105$	7.84011e7	+	9.34348e7i	0.645007	+	0.768690i
$106$	−1.45499e7	+	2.52011e7i	−0.115249	+	0.199616i
$107$	5.48199e7	−	3.16503e7i	0.418218	−	0.241458i	−0.276097	−	0.961130i	$-0.589041\pi$
$107$	5.48199e7	−	3.16503e7i	0.418218	−	0.241458i	0.694315	+	0.719672i	$0.255708\pi$
$108$	1.47282e7	−	4.04655e7i	0.108257	−	0.297433i
$109$	−1.41266e8	−	2.49090e7i	−1.00076	−	0.176462i	−0.350820	−	0.936443i	$-0.614097\pi$
$109$	−1.41266e8	−	2.49090e7i	−1.00076	−	0.176462i	−0.649945	+	0.759981i	$0.725208\pi$
$110$	−2.59244e8	+	4.57116e7i	−1.77067	+	0.312217i
$111$	4.71829e7	−	1.71732e7i	0.310808	−	0.113125i
$112$	−1.28565e7	−	1.07879e7i	−0.0817056	−	0.0685591i
$113$		−	1.05038e7i		−	0.0644218i	−0.999481	−	0.0322109i	$-0.989745\pi$
$113$		−	1.05038e7i		−	0.0644218i	0.999481	−	0.0322109i	$-0.0102548\pi$
$114$	8.56045e7	+	1.64366e8i	0.506848	+	0.973181i
$115$	−3.32109e8			−1.89884
$116$	5.01930e7	−	5.98177e7i	0.277211	−	0.330368i
$117$	1.09547e8	+	3.00978e8i	0.584599	+	1.60617i
$118$	−4.31915e6	−	2.44951e7i	−0.0222777	−	0.126343i
$119$	−1.73249e7	+	9.82546e7i	−0.0863941	+	0.489965i
$120$	−1.62034e8	−	5.89754e7i	−0.781412	−	0.284411i
$121$	−1.94456e8	−	3.36808e8i	−0.907152	−	1.57123i
$122$	1.75173e7	+	1.01136e7i	0.0790729	+	0.0456527i
$123$	1.03714e8	−	8.70267e7i	0.453126	−	0.380218i
$124$	1.33183e8	+	1.58721e8i	0.563327	+	0.671348i
$125$	5.50202e7	−	9.52978e7i	0.225363	−	0.390340i
$126$	−9.27137e7	+	5.35283e7i	−0.367842	+	0.212374i
$127$	−7.41836e7	+	2.03818e8i	−0.285163	+	0.783479i	0.711563	+	0.702622i	$0.247988\pi$
$127$	−7.41836e7	+	2.03818e8i	−0.285163	+	0.783479i	−0.996726	+	0.0808562i	$0.974235\pi$
$128$	2.33661e7	+	4.12008e6i	0.0870455	+	0.0153485i
$129$	1.80055e6	−	317485.i	0.00650198	−	0.00114647i
$130$	3.49203e8	−	1.27099e8i	1.22266	−	0.445010i
$131$	−1.05694e8	−	8.86877e7i	−0.358893	−	0.301147i	0.445457	−	0.895304i	$-0.353041\pi$
$131$	−1.05694e8	−	8.86877e7i	−0.358893	−	0.301147i	−0.804349	+	0.594157i	$0.797486\pi$
$132$		−	3.95162e8i		−	1.30161i
$133$	2.88681e7	−	1.30336e8i	0.0922597	−	0.416541i
$134$	1.08977e8			0.337999
$135$	−2.04857e8	+	2.44140e8i	−0.616761	+	0.735027i
$136$	−4.82412e7	−	1.32542e8i	−0.141014	−	0.387433i
$137$	−6.09308e6	−	3.45555e7i	−0.0172963	−	0.0980924i	0.974938	−	0.222479i	$-0.0714149\pi$
$137$	−6.09308e6	−	3.45555e7i	−0.0172963	−	0.0980924i	−0.992234	+	0.124386i	$0.960304\pi$
$138$	8.65703e7	−	4.90965e8i	0.238700	−	1.35374i
$139$	5.98522e8	+	2.17844e8i	1.60332	+	0.583562i	0.980104	−	0.198485i	$-0.0636022\pi$
$139$	5.98522e8	+	2.17844e8i	1.60332	+	0.583562i	0.623219	+	0.782047i	$0.285824\pi$
$140$	6.21048e7	+	1.07569e8i	0.161664	+	0.280010i
$141$	7.99280e8	+	4.61464e8i	2.02219	+	1.16751i
$142$	−3.70325e8	+	3.10739e8i	−0.910813	+	0.764263i
$143$	5.47413e8	+	6.52381e8i	1.30909	+	1.56012i
$144$	7.56742e7	−	1.31072e8i	0.175994	−	0.304831i
$145$	−5.00486e8	+	2.88956e8i	−1.13219	+	0.653671i
$146$	2.53832e7	−	6.97398e7i	0.0558644	−	0.153486i
$147$	−5.83698e8	−	1.02922e8i	−1.25003	−	0.220413i
$148$	5.03560e7	−	8.87912e6i	0.104955	−	0.0185065i
$149$	3.76756e8	−	1.37128e8i	0.764391	−	0.278215i	0.0697424	−	0.997565i	$-0.477782\pi$
$149$	3.76756e8	−	1.37128e8i	0.764391	−	0.278215i	0.694648	+	0.719350i	$0.255560\pi$
$150$	5.52067e8	+	4.63239e8i	1.09050	+	0.915040i
$151$		−	8.02448e8i		−	1.54351i	−0.635921	−	0.771754i	$-0.719380\pi$
$151$		−	8.02448e8i		−	1.54351i	0.635921	−	0.771754i	$-0.280620\pi$
$152$	5.67858e7	+	1.79979e8i	0.106381	+	0.337169i
$153$	−8.99725e8			−1.64189
$154$	−1.82970e8	+	2.18055e8i	−0.325309	+	0.387688i
$155$	−5.24466e8	−	1.44096e9i	−0.908637	−	2.49646i
$156$	9.68681e7	+	5.49366e8i	0.163562	+	0.927606i
$157$	2.97144e7	−	1.68519e8i	0.0489068	−	0.277364i	−0.950541	−	0.310600i	$-0.899470\pi$
$157$	2.97144e7	−	1.68519e8i	0.0489068	−	0.277364i	0.999448	+	0.0332358i	$0.0105812\pi$
$158$	5.75362e8	+	2.09415e8i	0.923236	+	0.336030i
$159$	1.61645e8	+	2.79978e8i	0.252915	+	0.438062i
$160$	−1.52073e8	−	8.77992e7i	−0.232044	−	0.133971i
$161$	−2.75099e8	+	2.30835e8i	−0.409435	+	0.343557i
$162$	1.33241e8	+	1.58790e8i	0.193454	+	0.230549i
$163$	5.51768e8	−	9.55690e8i	0.781639	−	1.35384i	−0.149347	−	0.988785i	$-0.547717\pi$
$163$	5.51768e8	−	9.55690e8i	0.781639	−	1.35384i	0.930986	−	0.365054i	$-0.118949\pi$
$164$	1.19403e8	−	6.89376e7i	0.165060	−	0.0952973i
$165$	−1.00026e9	+	2.74819e9i	−1.34951	+	3.70775i
$166$	1.27095e8	+	2.24103e7i	0.167377	+	0.0295131i
$167$	−3.96485e8	+	6.99110e7i	−0.509754	+	0.0898834i	−0.422609	−	0.906312i	$-0.638886\pi$
$167$	−3.96485e8	+	6.99110e7i	−0.509754	+	0.0898834i	−0.0871453	+	0.996196i	$0.527774\pi$
$168$	−1.75210e8	+	6.37714e7i	−0.219949	+	0.0800550i
$169$	−2.96066e8	−	2.48429e8i	−0.362945	−	0.304547i
$170$			1.04388e9i			1.24985i
$171$	1.20271e9	+	5.22764e7i	1.40662	+	0.0611394i
$172$	1.86189e6			0.00212735
$173$	5.72996e8	−	6.82870e8i	0.639686	−	0.762348i	−0.344634	−	0.938737i	$-0.611997\pi$
$173$	5.72996e8	−	6.82870e8i	0.639686	−	0.762348i	0.984321	+	0.176389i	$0.0564415\pi$
$174$	−2.96709e8	−	8.15202e8i	−0.323694	−	0.889341i
$175$	−9.01455e7	−	5.11240e8i	−0.0961151	−	0.545096i
$176$	6.98790e7	−	3.96303e8i	0.0728276	−	0.413026i
$177$	−2.59667e8	−	9.45112e7i	−0.264560	−	0.0962920i
$178$	−4.40991e8	−	7.63819e8i	−0.439288	−	0.760870i
$179$	5.43048e8	+	3.13529e8i	0.528964	+	0.305398i	0.740595	−	0.671952i	$-0.234544\pi$
$179$	5.43048e8	+	3.13529e8i	0.528964	+	0.305398i	−0.211630	+	0.977350i	$0.567877\pi$
$180$	−8.58060e8	+	7.19998e8i	−0.817386	+	0.685869i
$181$	3.03004e8	+	3.61106e8i	0.282315	+	0.336449i	0.888502	−	0.458872i	$-0.151746\pi$
$181$	3.03004e8	+	3.61106e8i	0.282315	+	0.336449i	−0.606188	+	0.795322i	$0.707302\pi$
$182$	2.00917e8	−	3.47998e8i	0.183118	−	0.317170i
$183$	1.94613e8	−	1.12360e8i	0.173527	−	0.100186i
$184$	1.73641e8	−	4.77074e8i	0.151489	−	0.416212i
$185$	−3.72681e8	−	6.57136e7i	−0.318163	−	0.0561007i
$186$	2.26692e9	−	3.99719e8i	1.89402	−	0.333966i
$187$	−2.24799e9	+	8.18200e8i	−1.83835	+	0.669103i
$188$	7.19984e8	+	6.04139e8i	0.576357	+	0.483621i
$189$			3.44619e8i			0.270079i
$190$	6.06524e7	−	1.39542e9i	0.0465408	−	1.07076i
$191$	−3.97547e8			−0.298713			−0.149357	−	0.988783i	$-0.547720\pi$
$191$	−3.97547e8			−0.298713			−0.149357	+	0.988783i	$0.547720\pi$
$192$	1.69436e8	−	2.01926e8i	0.124681	−	0.148589i
$193$	2.88100e8	+	7.91548e8i	0.207641	+	0.570490i	0.999174	−	0.0406370i	$-0.0129387\pi$
$193$	2.88100e8	+	7.91548e8i	0.207641	+	0.570490i	−0.791533	+	0.611127i	$0.790716\pi$
$194$	−1.32424e8	−	7.51014e8i	−0.0934888	−	0.530201i
$195$	7.16912e8	−	4.06581e9i	0.495824	−	2.81196i
$196$	−5.67183e8	−	2.06438e8i	−0.384326	−	0.139883i
$197$	−8.88486e6	−	1.53890e7i	−0.00589910	−	0.0102175i	0.863061	−	0.505100i	$-0.168544\pi$
$197$	−8.88486e6	−	1.53890e7i	−0.00589910	−	0.0102175i	−0.868960	+	0.494883i	$0.835211\pi$
$198$	−2.22305e9	−	1.28348e9i	−1.44640	−	0.835081i
$199$	−9.82679e8	+	8.24565e8i	−0.626613	+	0.525791i	−0.899874	−	0.436149i	$-0.856342\pi$
$199$	−9.82679e8	+	8.24565e8i	−0.626613	+	0.525791i	0.273262	+	0.961940i	$0.411898\pi$
$200$	4.71744e8	+	5.62202e8i	0.294840	+	0.351376i
$201$	6.05353e8	−	1.04850e9i	0.370873	−	0.642370i
$202$	−1.75183e9	+	1.01142e9i	−1.05217	+	0.607472i
$203$	−2.13731e8	+	5.87221e8i	−0.125859	+	0.345794i
$204$	−1.54320e9	−	2.72108e8i	−0.891048	−	0.157116i
$205$	−1.00490e9	+	1.77191e8i	−0.568994	+	0.100329i
$206$	3.51455e8	−	1.27919e8i	0.195164	−	0.0710340i
$207$	−2.48083e9	−	2.08166e9i	−1.35119	−	1.13378i
$208$			5.68082e8i			0.303500i
$209$	3.05255e9	−	9.63122e8i	1.59985	−	0.504773i
$210$	1.37994e9			0.709549
$211$	−1.24201e9	+	1.48017e9i	−0.626606	+	0.746760i	−0.982191	−	0.187884i	$-0.939837\pi$
$211$	−1.24201e9	+	1.48017e9i	−0.626606	+	0.746760i	0.355585	+	0.934644i	$0.384282\pi$
$212$	1.12602e8	+	3.09371e8i	0.0557446	+	0.153157i
$213$	9.32616e8	+	5.28913e9i	0.453090	+	2.56960i
$214$	1.24361e8	−	7.05283e8i	0.0592963	−	0.336286i
$215$	−1.29487e7	−	4.71293e6i	−0.00605998	−	0.00220565i
$216$	−2.43598e8	−	4.21924e8i	−0.111907	−	0.193829i
$217$	−1.43599e9	−	8.29068e8i	−0.647608	−	0.373896i
$218$	−1.24321e9	+	1.04318e9i	−0.550452	+	0.461884i
$219$	−5.29988e8	−	6.31615e8i	−0.230404	−	0.274585i
$220$	−1.48913e9	+	2.57924e9i	−0.635683	+	1.10104i
$221$	2.92465e9	−	1.68855e9i	1.22604	−	0.707854i
$222$	1.94292e8	−	5.33814e8i	0.0799915	−	0.219775i
$223$	1.01525e9	+	1.79016e8i	0.410538	+	0.0723890i	0.375103	−	0.926983i	$-0.377607\pi$
$223$	1.01525e9	+	1.79016e8i	0.410538	+	0.0723890i	0.0354349	+	0.999372i	$0.488718\pi$
$224$	−1.86993e8	+	3.29720e7i	−0.0742736	+	0.0130964i
$225$	4.39914e9	−	1.60116e9i	1.71648	−	0.624746i
$226$	−9.10345e7	−	7.63870e7i	−0.0348957	−	0.0292810i
$227$		−	2.88581e9i		−	1.08684i	−0.839462	−	0.543418i	$-0.817130\pi$
$227$		−	2.88581e9i		−	1.08684i	0.839462	−	0.543418i	$-0.182870\pi$
$228$	2.04707e9	+	4.53406e8i	0.757520	+	0.167783i
$229$	3.52783e9			1.28282			0.641410	−	0.767199i	$-0.278350\pi$
$229$	3.52783e9			1.28282			0.641410	+	0.767199i	$0.278350\pi$
$230$	−2.41520e9	+	2.87832e9i	−0.863061	+	1.02856i
$231$	1.08160e9	+	2.97167e9i	0.379856	+	1.04365i
$232$	−1.53409e8	−	8.70026e8i	−0.0529540	−	0.300317i
$233$	−1.00311e9	+	5.68892e9i	−0.340350	+	1.93022i	0.0258114	+	0.999667i	$0.491783\pi$
$233$	−1.00311e9	+	5.68892e9i	−0.340350	+	1.93022i	−0.366161	+	0.930552i	$0.619328\pi$
$234$	3.40518e9	+	1.23938e9i	1.13573	+	0.413374i
$235$	−3.47796e9	−	6.02400e9i	−1.14039	−	1.97521i
$236$	−2.43704e8	−	1.40703e8i	−0.0785625	−	0.0453581i
$237$	5.21091e9	−	4.37247e9i	1.65166	−	1.38590i
$238$	7.25561e8	+	8.64690e8i	0.226134	+	0.269496i
$239$	6.41838e8	−	1.11170e9i	0.196713	−	0.340717i	−0.750748	−	0.660589i	$-0.770307\pi$
$239$	6.41838e8	−	1.11170e9i	0.196713	−	0.340717i	0.947461	+	0.319872i	$0.103640\pi$
$240$	−1.68949e9	+	9.75426e8i	−0.509225	+	0.294001i
$241$	−2.27436e9	+	6.24875e9i	−0.674204	+	1.85236i	−0.178314	+	0.983974i	$0.557064\pi$
$241$	−2.27436e9	+	6.24875e9i	−0.674204	+	1.85236i	−0.495890	+	0.868386i	$0.665158\pi$
$242$	−4.33319e9	−	7.64059e8i	−1.26342	−	0.222774i
$243$	4.44166e9	−	7.83184e8i	1.27385	−	0.224615i
$244$	2.15044e8	−	7.82695e7i	0.0606691	−	0.0220818i
$245$	3.42198e9	+	2.87138e9i	0.949758	+	0.796941i
$246$		−	1.53176e9i		−	0.418263i
$247$	−4.00766e9	+	2.08725e9i	−1.07672	+	0.560772i
$248$	2.34415e9			0.619696
$249$	9.21612e8	−	1.09833e9i	0.239746	−	0.285718i
$250$	−4.25803e8	−	1.16988e9i	−0.109006	−	0.299490i
$251$	9.59313e8	+	5.44053e9i	0.241694	+	1.37071i	0.828047	+	0.560658i	$0.189452\pi$
$251$	9.59313e8	+	5.44053e9i	0.241694	+	1.37071i	−0.586354	+	0.810055i	$0.699437\pi$
$252$	−2.10324e8	+	1.19281e9i	−0.0521538	+	0.295779i
$253$	−8.09146e9	−	2.94505e9i	−1.97490	−	0.718804i
$254$	1.22696e9	+	2.12516e9i	0.294779	+	0.510572i
$255$	1.00435e10	+	5.79864e9i	2.37534	+	1.37140i
$256$	2.05633e8	−	1.72547e8i	0.0478778	−	0.0401742i
$257$	2.52697e9	+	3.01152e9i	0.579252	+	0.690325i	0.973502	−	0.228678i	$-0.0734402\pi$
$257$	2.52697e9	+	3.01152e9i	0.579252	+	0.690325i	−0.394251	+	0.919003i	$0.628996\pi$
$258$	1.03426e7	−	1.79138e7i	0.00233426	−	0.00404305i
$259$	−3.54381e8	+	2.04602e8i	−0.0787538	+	0.0454685i
$260$	1.43797e9	−	3.95078e9i	0.314670	−	0.864548i
$261$	−5.54977e9	−	9.78575e8i	−1.19595	−	0.210878i
$262$	−1.53728e9	+	2.71063e8i	−0.326247	+	0.0575262i
$263$	−8.42940e9	+	3.06805e9i	−1.76187	+	0.641268i	−0.999979	−	0.00643823i	$-0.997951\pi$
$263$	−8.42940e9	+	3.06805e9i	−1.76187	+	0.641268i	−0.761890	+	0.647706i	$0.775728\pi$
$264$	−3.42479e9	−	2.87374e9i	−0.705048	−	0.591605i
$265$		−	2.43657e9i		−	0.494079i
$266$	−9.19659e8	−	1.19804e9i	−0.183696	−	0.239301i
$267$	−9.79859e9			−1.92805
$268$	7.92515e8	−	9.44483e8i	0.153627	−	0.183086i
$269$	1.93227e9	+	5.30886e9i	0.369027	+	1.01389i	0.975732	+	0.218966i	$0.0702684\pi$
$269$	1.93227e9	+	5.30886e9i	0.369027	+	1.01389i	−0.606706	+	0.794927i	$0.707509\pi$
$270$	6.26123e8	+	3.55092e9i	0.117816	+	0.668168i
$271$	1.00903e9	−	5.72252e9i	0.187081	−	1.06099i	−0.736172	−	0.676794i	$-0.763369\pi$
$271$	1.00903e9	−	5.72252e9i	0.187081	−	1.06099i	0.923253	−	0.384193i	$-0.125520\pi$
$272$	−1.49954e9	−	5.45787e8i	−0.273957	−	0.0997120i
$273$	−2.23213e9	−	3.86617e9i	−0.401855	−	0.696034i
$274$	−3.43797e8	−	1.98491e8i	−0.0609958	−	0.0352159i
$275$	9.53529e9	−	8.00106e9i	1.66726	−	1.39900i
$276$	−3.62553e9	−	4.32073e9i	−0.624791	−	0.744597i
$277$	−3.07697e9	+	5.32947e9i	−0.522642	+	0.905242i	0.477011	+	0.878897i	$0.341720\pi$
$277$	−3.07697e9	+	5.32947e9i	−0.522642	+	0.905242i	−0.999653	+	0.0263448i	$0.991613\pi$
$278$	6.24065e9	−	3.60304e9i	1.04484	−	0.603240i
$279$	5.11423e9	−	1.40512e10i	0.844040	−	2.31898i
$280$	1.38392e9	+	2.44023e8i	0.225154	+	0.0397007i
$281$	1.29774e9	−	2.28826e8i	0.208143	−	0.0367012i	−0.0686043	−	0.997644i	$-0.521855\pi$
$281$	1.29774e9	−	2.28826e8i	0.208143	−	0.0367012i	0.276747	+	0.960943i	$0.410743\pi$
$282$	9.81203e9	−	3.57129e9i	1.55154	−	0.564714i
$283$	1.99276e8	+	1.67213e8i	0.0310677	+	0.0260689i	0.658189	−	0.752852i	$-0.271323\pi$
$283$	1.99276e8	+	1.67213e8i	0.0310677	+	0.0260689i	−0.627122	+	0.778921i	$0.715767\pi$
$284$			5.46932e9i			0.840737i
$285$	−1.30889e10	−	8.33494e9i	−1.98391	−	1.26335i
$286$	9.63502e9			1.44009
$287$	−7.09241e8	+	8.45240e8i	−0.104536	+	0.124581i
$288$	−5.85645e8	−	1.60905e9i	−0.0851265	−	0.233883i
$289$	4.35975e8	+	2.47254e9i	0.0624985	+	0.354447i
$290$	−1.13537e9	+	6.43899e9i	−0.160526	+	0.910386i
$291$	−7.96134e9	−	2.89769e9i	−1.11023	−	0.404092i
$292$	−4.19826e8	−	7.27161e8i	−0.0577482	−	0.100023i
$293$	−4.36347e9	−	2.51925e9i	−0.592054	−	0.341823i	0.173855	−	0.984771i	$-0.444378\pi$
$293$	−4.36347e9	−	2.51925e9i	−0.592054	−	0.341823i	−0.765909	+	0.642948i	$0.777711\pi$
$294$	−5.13684e9	+	4.31032e9i	−0.687553	+	0.576926i
$295$	1.33871e9	+	1.59541e9i	0.176766	+	0.210661i
$296$	2.89251e8	−	5.00997e8i	0.0376797	−	0.0652632i
$297$	−7.15609e9	+	4.13157e9i	−0.919708	+	0.530993i
$298$	1.55143e9	−	4.26251e9i	0.196728	−	0.540506i
$299$	1.19709e10	+	2.11080e9i	1.49776	+	0.264096i
$300$	8.02961e9	−	1.41584e9i	0.991309	−	0.174795i
$301$	−1.40017e7	+	5.09619e6i	−0.00170574	+	0.000620840i
$302$	−6.95466e9	−	5.83565e9i	−0.836080	−	0.701554i
$303$			2.24732e10i			2.66622i
$304$	1.97281e9	+	8.16713e8i	0.230989	+	0.0956258i
$305$	−1.69366e9			−0.195716
$306$	−6.54308e9	+	7.79774e9i	−0.746271	+	0.889371i
$307$	−4.51818e9	−	1.24136e10i	−0.508639	−	1.39747i	−0.882642	−	0.470046i	$-0.844237\pi$
$307$	−4.51818e9	−	1.24136e10i	−0.508639	−	1.39747i	0.374003	−	0.927428i	$-0.377985\pi$
$308$	5.59225e8	+	3.17152e9i	0.0621418	+	0.352423i
$309$	7.21535e8	−	4.09203e9i	0.0791450	−	0.448854i
$310$	−1.63026e10	−	5.93366e9i	−1.76526	−	0.642504i
$311$	6.08226e9	+	1.05348e10i	0.650165	+	1.12612i	0.983083	+	0.183163i	$0.0586335\pi$
$311$	6.08226e9	+	1.05348e10i	0.650165	+	1.12612i	−0.332918	+	0.942956i	$0.608033\pi$
$312$	5.46570e9	+	3.15562e9i	0.576803	+	0.333017i
$313$	−7.48148e8	+	6.27770e8i	−0.0779489	+	0.0654069i	−0.680930	−	0.732349i	$-0.738424\pi$
$313$	−7.48148e8	+	6.27770e8i	−0.0779489	+	0.0654069i	0.602981	+	0.797756i	$0.293980\pi$
$314$	−1.24443e9	−	1.48305e9i	−0.128012	−	0.152559i
$315$	4.48202e9	−	7.76308e9i	0.455230	−	0.788482i
$316$	5.99917e9	−	3.46362e9i	0.601648	−	0.347362i
$317$	4.90644e9	−	1.34803e10i	0.485880	−	1.33494i	−0.418500	−	0.908217i	$-0.637444\pi$
$317$	4.90644e9	−	1.34803e10i	0.485880	−	1.33494i	0.904380	−	0.426728i	$-0.140334\pi$
$318$	3.60205e9	+	6.35139e8i	0.352242	+	0.0621098i
$319$	−1.47562e10	+	2.60191e9i	−1.42499	+	0.251263i
$320$	−1.86686e9	+	6.79481e8i	−0.178037	+	0.0648003i
$321$	−6.09495e9	−	5.11427e9i	−0.574050	−	0.481686i
$322$			4.06293e9i			0.377934i
$323$	−1.65923e9	−	1.25841e10i	−0.152439	−	1.15615i
$324$	2.34517e9			0.212811
$325$	−1.12949e10	+	1.34607e10i	−1.01239	+	1.20652i
$326$	−4.27015e9	−	1.17321e10i	−0.378071	−	1.03874i
$327$	3.13087e9	+	1.77561e10i	0.273826	+	1.55294i
$328$	2.70870e8	−	1.53618e9i	0.0234027	−	0.132723i
$329$	−7.06798e9	−	2.57253e9i	−0.603270	−	0.219572i
$330$	1.65438e10	+	2.86547e10i	1.39502	+	2.41624i
$331$	1.69327e10	+	9.77608e9i	1.41063	+	0.814428i	0.995448	−	0.0953102i	$-0.0303843\pi$
$331$	1.69327e10	+	9.77608e9i	1.41063	+	0.814428i	0.415183	+	0.909738i	$0.363718\pi$
$332$	1.11850e9	−	9.38532e8i	0.0920626	−	0.0772497i
$333$	−2.37200e9	−	2.82684e9i	−0.192903	−	0.229893i
$334$	−2.27746e9	+	3.94467e9i	−0.183006	+	0.316975i
$335$	−7.90235e9	+	4.56242e9i	−0.627447	+	0.362257i
$336$	−7.21491e8	+	1.98228e9i	−0.0566074	+	0.155528i
$337$	7.90712e9	+	1.39424e9i	0.613054	+	0.108098i	0.471550	−	0.881840i	$-0.343695\pi$
$337$	7.90712e9	+	1.39424e9i	0.613054	+	0.108098i	0.141505	+	0.989938i	$0.454806\pi$
$338$	−4.30616e9	+	7.59293e8i	−0.329931	+	0.0581758i
$339$	−1.24063e9	+	4.51552e8i	−0.0939383	+	0.0341908i
$340$	9.04713e9	+	7.59145e9i	0.677010	+	0.568079i
$341$		−	3.97582e10i		−	2.94042i
$342$	9.19959e9	−	1.00435e10i	0.672456	−	0.734145i
$343$	1.07355e10			0.775617
$344$	1.35402e7	−	1.61366e7i	0.000966924	−	0.00115234i
$345$	1.42771e10	+	3.92261e10i	1.00778	+	2.76884i
$346$	−1.75129e9	−	9.93208e9i	−0.122195	−	0.693004i
$347$	−2.25295e9	+	1.27771e10i	−0.155394	+	0.881282i	0.803031	+	0.595937i	$0.203219\pi$
$347$	−2.25295e9	+	1.27771e10i	−0.155394	+	0.881282i	−0.958425	+	0.285345i	$0.907892\pi$
$348$	−9.22296e9	−	3.35688e9i	−0.628859	−	0.228886i
$349$	3.19118e9	+	5.52729e9i	0.215105	+	0.372572i	0.953305	−	0.302009i	$-0.0976574\pi$
$349$	3.19118e9	+	5.52729e9i	0.215105	+	0.372572i	−0.738200	+	0.674582i	$0.764324\pi$
$350$	−5.08639e9	−	2.93663e9i	−0.338951	−	0.195694i
$351$	8.93581e9	−	7.49804e9i	0.588716	−	0.493991i
$352$	−2.92650e9	−	3.48767e9i	−0.190624	−	0.227177i
$353$	6.29408e9	−	1.09017e10i	0.405353	−	0.702092i	−0.589009	−	0.808126i	$-0.700482\pi$
$353$	6.29408e9	−	1.09017e10i	0.405353	−	0.702092i	0.994362	+	0.106034i	$0.0338153\pi$
$354$	−2.70749e9	+	1.56317e9i	−0.172407	+	0.0995391i
$355$	1.38443e10	−	3.80369e10i	0.871680	−	2.39492i
$356$	−9.82689e9	−	1.73275e9i	−0.611809	−	0.107879i
$357$	1.23499e10	−	2.17761e9i	0.760307	−	0.134063i
$358$	6.66651e9	−	2.42641e9i	0.405851	−	0.147718i
$359$	5.96544e8	+	5.00560e8i	0.0359141	+	0.0301355i	0.660568	−	0.750766i	$-0.270316\pi$
$359$	5.96544e8	+	5.00560e8i	0.0359141	+	0.0301355i	−0.624654	+	0.780902i	$0.714760\pi$
$360$			1.26727e10i			0.754499i
$361$	1.48682e9	+	1.69184e10i	0.0875448	+	0.996161i
$362$	5.33317e9			0.310564
$363$	−3.14216e10	+	3.74468e10i	−1.80968	+	2.15669i
$364$	−1.55490e9	−	4.27206e9i	−0.0885722	−	0.243350i
$365$	1.07908e9	+	6.11979e9i	0.0607973	+	0.344798i
$366$	4.41484e8	−	2.50378e9i	0.0246032	−	0.139531i
$367$	3.25374e10	+	1.18427e10i	1.79357	+	0.652807i	0.998955	+	0.0456954i	$0.0145504\pi$
$367$	3.25374e10	+	1.18427e10i	1.79357	+	0.652807i	0.794617	+	0.607111i	$0.207672\pi$
$368$	−2.87194e9	−	4.97434e9i	−0.156597	−	0.271234i
$369$	−8.61718e9	−	4.97513e9i	−0.464793	−	0.268348i
$370$	−3.27978e9	+	2.75206e9i	−0.175000	+	0.146842i
$371$	−1.69356e9	−	2.01831e9i	−0.0893935	−	0.106535i
$372$	1.30214e10	−	2.25538e10i	0.679966	−	1.17774i
$373$	−1.86100e10	+	1.07445e10i	−0.961415	+	0.555073i	−0.896608	−	0.442825i	$-0.853976\pi$
$373$	−1.86100e10	+	1.07445e10i	−0.961415	+	0.555073i	−0.0648067	+	0.997898i	$0.520643\pi$
$374$	−9.25688e9	+	2.54331e10i	−0.473127	+	1.29991i
$375$	−1.36211e10	−	2.40177e9i	−0.688791	−	0.121452i
$376$	1.04719e10	−	1.84648e9i	0.523931	−	0.0923832i
$377$	1.98766e10	−	7.23450e9i	0.983960	−	0.358132i
$378$	2.98674e9	+	2.50617e9i	0.146295	+	0.122756i
$379$		−	2.70906e10i		−	1.31299i	−0.754330	−	0.656496i	$-0.772038\pi$
$379$		−	2.70906e10i		−	1.31299i	0.754330	−	0.656496i	$-0.227962\pi$
$380$	−1.16527e10	−	1.06736e10i	−0.558848	−	0.511890i
$381$	2.72625e10			1.29379
$382$	−2.89108e9	+	3.44546e9i	−0.135771	+	0.161806i
$383$	1.07744e9	+	2.96024e9i	0.0500724	+	0.137573i	0.962208	−	0.272316i	$-0.0877897\pi$
$383$	1.07744e9	+	2.96024e9i	0.0500724	+	0.137573i	−0.912135	+	0.409889i	$0.865567\pi$
$384$	−5.17862e8	−	2.93694e9i	−0.0238171	−	0.135074i
$385$	4.13878e9	−	2.34722e10i	0.188377	−	1.06834i
$386$	8.95534e9	+	3.25948e9i	0.403397	+	0.146825i
$387$	−6.71849e7	−	1.16368e8i	−0.00299521	−	0.00518786i
$388$	−7.47191e9	−	4.31391e9i	−0.329689	−	0.190346i
$389$	2.32988e10	−	1.95500e10i	1.01750	−	0.853786i	0.0281905	−	0.999603i	$-0.491025\pi$
$389$	2.32988e10	−	1.95500e10i	1.01750	−	0.853786i	0.989312	+	0.145817i	$0.0465810\pi$
$390$	−3.00240e10	−	3.57812e10i	−1.29781	−	1.54667i
$391$	−1.70729e10	+	2.95711e10i	−0.730465	+	1.26520i
$392$	−5.91389e9	+	3.41439e9i	−0.250455	+	0.144600i
$393$	−5.93139e9	+	1.62964e10i	−0.248649	+	0.683157i
$394$	−1.97987e8	−	3.49105e7i	−0.00821584	−	0.00144867i
$395$	−5.04891e10	+	8.90258e9i	−2.07400	+	0.365702i
$396$	−2.72904e10	+	9.93290e9i	−1.10976	+	0.403920i
$397$	1.27399e10	+	1.06901e10i	0.512867	+	0.430347i	0.862137	−	0.506675i	$-0.169126\pi$
$397$	1.27399e10	+	1.06901e10i	0.512867	+	0.430347i	−0.349269	+	0.937022i	$0.613570\pi$
$398$			1.45132e10i			0.578403i
$399$	−1.66353e10	+	2.19338e9i	−0.656356	+	0.0865412i
$400$	8.30317e9			0.324342
$401$	8.60993e9	−	1.02609e10i	0.332983	−	0.396834i	−0.573410	−	0.819268i	$-0.694380\pi$
$401$	8.60993e9	−	1.02609e10i	0.332983	−	0.396834i	0.906393	+	0.422434i	$0.138824\pi$
$402$	−4.68485e9	−	1.28715e10i	−0.179387	−	0.492862i
$403$	9.74612e9	+	5.52730e10i	0.369498	+	2.09553i
$404$	−3.97408e9	+	2.25382e10i	−0.149180	+	0.846044i
$405$	−1.63097e10	−	5.93624e9i	−0.606213	−	0.220644i
$406$	3.53501e9	+	6.12282e9i	0.130103	+	0.225345i
$407$	−8.49722e9	−	4.90587e9i	−0.309670	−	0.178788i
$408$	−1.35809e10	+	1.13958e10i	−0.490105	+	0.411247i
$409$	−1.07143e10	−	1.27689e10i	−0.382888	−	0.456309i	0.539835	−	0.841771i	$-0.318487\pi$
$409$	−1.07143e10	−	1.27689e10i	−0.382888	−	0.456309i	−0.922724	+	0.385462i	$0.874042\pi$
$410$	−5.77227e9	+	9.99787e9i	−0.204273	+	0.353811i
$411$	−3.81949e9	+	2.20519e9i	−0.133856	+	0.0772819i
$412$	1.44724e9	−	3.97626e9i	0.0502286	−	0.138002i
$413$	2.21781e9	+	3.91060e8i	0.0762296	+	0.0134413i
$414$	−3.60827e10	+	6.36236e9i	−1.22828	+	0.216579i
$415$	−1.01544e10	+	3.69589e9i	−0.342342	+	0.124602i
$416$	4.92346e9	+	4.13127e9i	0.164398	+	0.137946i
$417$		−	8.00578e10i		−	2.64764i
$418$	1.38519e10	−	3.34600e10i	0.453738	−	1.09603i
$419$	4.58902e9			0.148890			0.0744448	−	0.997225i	$-0.476282\pi$
$419$	4.58902e9			0.148890			0.0744448	+	0.997225i	$0.476282\pi$
$420$	1.00353e10	−	1.19596e10i	0.322504	−	0.384345i
$421$	1.99226e9	+	5.47370e9i	0.0634189	+	0.174242i	0.967355	−	0.253426i	$-0.0815575\pi$
$421$	1.99226e9	+	5.47370e9i	0.0634189	+	0.174242i	−0.903936	+	0.427668i	$0.859335\pi$
$422$	3.79605e9	+	2.15285e10i	0.119697	+	0.678834i
$423$	1.17784e10	−	6.67988e10i	0.367897	−	2.08645i
$424$	3.50014e9	+	1.27395e9i	0.108298	+	0.0394174i
$425$	−2.46800e10	−	4.27470e10i	−0.756466	−	1.31024i
$426$	5.26221e10	+	3.03814e10i	1.59783	+	0.922506i
$427$	−1.40293e9	+	1.17720e9i	−0.0422011	+	0.0354109i
$428$	−5.20816e9	−	6.20685e9i	−0.155206	−	0.184968i
$429$	5.35213e10	−	9.27016e10i	1.58015	−	2.73689i
$430$	−1.35013e8	+	7.79497e7i	−0.00394913	+	0.00228003i
$431$	−1.15230e10	+	3.16592e10i	−0.333931	+	0.917469i	0.653147	+	0.757231i	$0.273448\pi$
$431$	−1.15230e10	+	3.16592e10i	−0.333931	+	0.917469i	−0.987078	+	0.160238i	$0.948774\pi$
$432$	−5.42825e9	−	9.57148e8i	−0.155857	−	0.0274817i
$433$	−1.16416e10	+	2.05273e9i	−0.331178	+	0.0583955i	−0.336765	−	0.941589i	$-0.609333\pi$
$433$	−1.16416e10	+	2.05273e9i	−0.331178	+	0.0583955i	0.00558707	+	0.999984i	$0.498222\pi$
$434$	−1.76283e10	+	6.41618e9i	−0.496881	+	0.180850i
$435$	5.56447e10	+	4.66915e10i	1.55406	+	1.30401i
$436$			1.83610e10i			0.508101i
$437$	2.45404e10	−	3.85374e10i	0.672910	−	1.05671i
$438$	−9.32833e9			−0.253459
$439$	2.76868e10	−	3.29959e10i	0.745444	−	0.888386i	−0.251391	−	0.967886i	$-0.580888\pi$
$439$	2.76868e10	−	3.29959e10i	0.745444	−	0.888386i	0.996835	+	0.0794999i	$0.0253323\pi$
$440$	1.15244e10	+	3.16630e10i	0.307473	+	0.844776i
$441$	7.56408e9	+	4.28980e10i	0.199987	+	1.13418i
$442$	6.63465e9	−	3.76270e10i	0.173832	−	0.985849i
$443$	7.74626e9	+	2.81941e9i	0.201130	+	0.0732054i	0.440621	−	0.897693i	$-0.354758\pi$
$443$	7.74626e9	+	2.81941e9i	0.201130	+	0.0732054i	−0.239491	+	0.970899i	$0.576981\pi$
$444$	−3.21350e9	−	5.56595e9i	−0.0826889	−	0.143221i
$445$	6.39559e10	+	3.69250e10i	1.63095	+	0.941630i
$446$	8.93471e9	−	7.49711e9i	0.225809	−	0.189476i
$447$	−3.23930e10	−	3.86045e10i	−0.811374	−	0.966958i
$448$	−1.07411e9	+	1.86042e9i	−0.0266648	+	0.0461847i
$449$	−4.22198e10	+	2.43756e10i	−1.03880	+	0.599751i	−0.919493	−	0.393107i	$-0.871400\pi$
$449$	−4.22198e10	+	2.43756e10i	−1.03880	+	0.599751i	−0.119306	+	0.992858i	$0.538067\pi$
$450$	1.81150e10	−	4.97706e10i	0.441762	−	1.21373i
$451$	−2.60546e10	−	4.59412e9i	−0.629764	−	0.111044i
$452$	−1.32406e9	+	2.33468e8i	−0.0317216	+	0.00559337i
$453$	−9.47789e10	+	3.44967e10i	−2.25071	+	0.819190i
$454$	−2.50107e10	−	2.09865e10i	−0.588712	−	0.493988i
$455$			3.36463e10i			0.785039i
$456$	1.88165e10	−	1.44443e10i	0.435192	−	0.334069i
$457$	2.46766e10			0.565745			0.282872	−	0.959158i	$-0.408713\pi$
$457$	2.46766e10			0.565745			0.282872	+	0.959158i	$0.408713\pi$
$458$	2.56555e10	−	3.05750e10i	0.583066	−	0.694871i
$459$	1.12071e10	+	3.07912e10i	0.252488	+	0.693706i
$460$	7.38177e9	+	4.18641e10i	0.164865	+	0.934997i
$461$	−1.01825e10	+	5.77479e10i	−0.225450	+	1.27859i	0.636372	+	0.771383i	$0.280434\pi$
$461$	−1.01825e10	+	5.77479e10i	−0.225450	+	1.27859i	−0.861822	+	0.507211i	$0.830677\pi$
$462$	3.36206e10	+	1.22369e10i	0.737969	+	0.268599i
$463$	−7.86858e9	−	1.36288e10i	−0.171227	−	0.296574i	0.767622	−	0.640903i	$-0.221440\pi$
$463$	−7.86858e9	−	1.36288e10i	−0.171227	−	0.296574i	−0.938849	+	0.344329i	$0.888107\pi$
$464$	−8.65598e9	−	4.99753e9i	−0.186743	−	0.107816i
$465$	−1.47648e11	+	1.23892e11i	−3.15803	+	2.64991i
$466$	4.20099e10	+	5.00654e10i	0.890856	+	1.06168i
$467$	1.33771e10	−	2.31698e10i	0.281251	−	0.487141i	−0.690442	−	0.723388i	$-0.742584\pi$
$467$	1.33771e10	−	2.31698e10i	0.281251	−	0.487141i	0.971693	+	0.236246i	$0.0759173\pi$
$468$	3.55050e10	−	2.04988e10i	0.740128	−	0.427313i
$469$	−3.37467e9	+	9.27184e9i	−0.0697494	+	0.191635i
$470$	−7.75017e10	−	1.36656e10i	−1.58825	−	0.280052i
$471$	−2.11815e10	+	3.73488e9i	−0.430402	+	0.0758914i
$472$	−2.99174e9	+	1.08890e9i	−0.0602775	+	0.0219392i
$473$	−2.73687e8	−	2.29651e8i	−0.00546776	−	0.00458799i
$474$		−	7.69599e10i		−	1.52458i
$475$	3.05075e10	+	5.85764e10i	0.599283	+	1.15066i
$476$	1.27706e10			0.248762
$477$	1.52725e10	−	1.82010e10i	0.295010	−	0.351579i
$478$	−4.96720e9	−	1.36473e10i	−0.0951482	−	0.261417i
$479$	−4.12112e9	−	2.33720e10i	−0.0782840	−	0.443970i	−0.998605	−	0.0528060i	$-0.983183\pi$
$479$	−4.12112e9	−	2.33720e10i	−0.0782840	−	0.443970i	0.920321	−	0.391164i	$-0.127928\pi$
$480$	−3.83265e9	+	2.17361e10i	−0.0721996	+	0.409464i
$481$	1.30157e10	+	4.73732e9i	0.243157	+	0.0885019i
$482$	3.76169e10	+	6.51543e10i	0.696938	+	1.20713i
$483$	3.90908e10	+	2.25691e10i	0.718267	+	0.414692i
$484$	−3.81343e10	+	3.19984e10i	−0.694919	+	0.583106i
$485$	4.10444e10	+	4.89149e10i	0.741801	+	0.884044i
$486$	2.55134e10	−	4.41905e10i	0.457323	−	0.792107i
$487$	−5.26800e10	+	3.04148e10i	−0.936547	+	0.540716i	−0.888876	−	0.458147i	$-0.848513\pi$
$487$	−5.26800e10	+	3.04148e10i	−0.936547	+	0.540716i	−0.0476709	+	0.998863i	$0.515180\pi$
$488$	8.85519e8	−	2.43294e9i	0.0156142	−	0.0428995i
$489$	−1.36599e11	−	2.40861e10i	−2.38898	−	0.421241i
$490$	4.97714e10	−	8.77604e9i	0.863367	−	0.152235i
$491$	3.01345e10	−	1.09681e10i	0.518487	−	0.188714i	−0.0695035	−	0.997582i	$-0.522141\pi$
$491$	3.01345e10	−	1.09681e10i	0.518487	−	0.188714i	0.587990	+	0.808868i	$0.299919\pi$
$492$	−1.32754e10	−	1.11394e10i	−0.226563	−	0.190109i
$493$			5.94179e10i			1.00584i
$494$	−1.10552e10	+	4.99127e10i	−0.185634	+	0.838114i
$495$	2.14936e11			3.58005
$496$	1.70474e10	−	2.03163e10i	0.281664	−	0.335674i
$497$	−1.49701e10	−	4.11301e10i	−0.245358	−	0.674115i
$498$	−2.81680e9	−	1.59749e10i	−0.0457971	−	0.259729i
$499$	9.08036e7	−	5.14973e8i	0.00146454	−	0.00830581i	−0.984067	−	0.177800i	$-0.943102\pi$
$499$	9.08036e7	−	5.14973e8i	0.00146454	−	0.00830581i	0.985531	+	0.169494i	$0.0542132\pi$
$500$	−1.32357e10	−	4.81741e9i	−0.211772	−	0.0770786i
$501$	2.53020e10	+	4.38243e10i	0.401609	+	0.695607i
$502$	5.41285e10	+	3.12511e10i	0.852336	+	0.492096i
$503$	7.07220e10	−	5.93428e10i	1.10480	−	0.927035i	0.107059	−	0.994253i	$-0.465857\pi$
$503$	7.07220e10	−	5.93428e10i	1.10480	−	0.927035i	0.997738	+	0.0672175i	$0.0214121\pi$
$504$	8.80827e9	+	1.04973e10i	0.136511	+	0.162688i
$505$	8.46881e10	−	1.46684e11i	1.30214	−	2.25537i
$506$	−8.43678e10	+	4.87097e10i	−1.28699	+	0.743043i
$507$	−1.66148e10	+	4.56487e10i	−0.251457	+	0.690871i
$508$	2.73412e10	+	4.82099e9i	0.410547	+	0.0723905i
$509$	4.60394e9	−	8.11800e8i	0.0685897	−	0.0120942i	−0.139248	−	0.990258i	$-0.544469\pi$
$509$	4.60394e9	−	8.11800e8i	0.0685897	−	0.0120942i	0.207838	+	0.978163i	$0.433357\pi$
$510$	1.23295e11	−	4.48758e10i	1.82249	−	0.663334i
$511$	5.14747e9	+	4.31924e9i	0.0754936	+	0.0633467i
$512$		−	3.03700e9i		−	0.0441942i
$513$	−1.31921e10	−	4.18115e10i	−0.190478	−	0.603707i
$514$	4.44772e10			0.637213
$515$	−2.01299e10	+	2.39899e10i	−0.286162	+	0.341035i
$516$	−8.00413e7	−	2.19912e8i	−0.00112906	−	0.00310206i
$517$	−3.13174e10	−	1.77610e11i	−0.438352	−	2.48602i
$518$	−8.03924e8	+	4.55928e9i	−0.0111660	+	0.0633253i
$519$	−1.05288e11	−	3.83217e10i	−1.45114	−	0.528172i
$520$	−2.37833e10	−	4.11939e10i	−0.325281	−	0.563403i
$521$	1.26907e10	+	7.32696e9i	0.172240	+	0.0994427i	0.583642	−	0.812011i	$-0.301627\pi$
$521$	1.26907e10	+	7.32696e9i	0.172240	+	0.0994427i	−0.411402	+	0.911454i	$0.634961\pi$
$522$	−4.88408e10	+	4.09823e10i	−0.657810	+	0.551968i
$523$	−6.52321e10	−	7.77406e10i	−0.871876	−	1.03906i	−0.998887	−	0.0471600i	$-0.984983\pi$
$523$	−6.52321e10	−	7.77406e10i	−0.871876	−	1.03906i	0.127011	−	0.991901i	$-0.459462\pi$
$524$	−8.83030e9	+	1.52945e10i	−0.117125	+	0.202867i
$525$	−5.65085e10	+	3.26252e10i	−0.743834	+	0.429453i
$526$	−3.47110e10	+	9.53678e10i	−0.453445	+	1.24583i
$527$	−1.55265e11	−	2.73774e10i	−2.01294	−	0.354936i
$528$	−4.98123e10	+	8.78325e9i	−0.640916	+	0.113011i
$529$	−4.19046e10	+	1.52520e10i	−0.535105	+	0.194762i
$530$	−2.11173e10	−	1.77195e10i	−0.267630	−	0.224568i
$531$			2.03086e10i			0.255448i
$532$	−1.70712e10	−	7.42006e8i	−0.213117	−	0.00926320i
$533$	3.73480e10			0.462763
$534$	−7.12584e10	+	8.49225e10i	−0.876337	+	1.04438i
$535$	2.05095e10	+	5.63493e10i	0.250345	+	0.687818i
$536$	−2.42223e9	−	1.37371e10i	−0.0293465	−	0.166432i
$537$	1.36863e10	−	7.76190e10i	0.164585	−	0.933407i
$538$	6.00629e10	+	2.18611e10i	0.716930	+	0.260941i
$539$	5.79101e10	+	1.00303e11i	0.686118	+	1.18839i
$540$	3.53285e10	+	2.03969e10i	0.415480	+	0.239877i
$541$	−9.82083e9	+	8.24065e9i	−0.114646	+	0.0961994i	−0.698308	−	0.715797i	$-0.746064\pi$
$541$	−9.82083e9	+	8.24065e9i	−0.114646	+	0.0961994i	0.583662	+	0.811996i	$0.301619\pi$
$542$	−4.22579e10	−	5.03610e10i	−0.489679	−	0.583576i
$543$	2.96251e10	−	5.13121e10i	0.340769	−	0.590229i
$544$	−1.56353e10	+	9.02706e9i	−0.178530	+	0.103074i
$545$	4.64765e10	−	1.27693e11i	0.526802	−	1.44738i
$546$	−4.97401e10	−	8.77053e9i	−0.559676	−	0.0986859i
$547$	−4.48682e10	+	7.91147e9i	−0.501175	+	0.0883707i	−0.418520	−	0.908208i	$-0.637451\pi$
$547$	−4.48682e10	+	7.91147e9i	−0.501175	+	0.0883707i	−0.0826549	+	0.996578i	$0.526340\pi$
$548$	−4.22048e9	+	1.53613e9i	−0.0467994	+	0.0170336i
$549$	−1.26515e10	−	1.06159e10i	−0.139269	−	0.116860i
$550$		−	1.40827e11i		−	1.53898i
$551$	3.45234e9	−	7.94274e10i	0.0374547	−	0.861715i
$552$	−6.38129e10			−0.687309
$553$	−3.56343e10	+	4.24673e10i	−0.381037	+	0.454102i
$554$	2.38128e10	+	6.54250e10i	0.252796	+	0.694552i
$555$	8.25971e9	+	4.68431e10i	0.0870548	+	0.493712i
$556$	1.41571e10	−	8.02890e10i	0.148141	−	0.840150i
$557$	−8.97163e10	−	3.26541e10i	−0.932075	−	0.339247i	−0.169043	−	0.985609i	$-0.554068\pi$
$557$	−8.97163e10	−	3.26541e10i	−0.932075	−	0.339247i	−0.763032	+	0.646361i	$0.776290\pi$
$558$	−8.45869e10	−	1.46509e11i	−0.872502	−	1.51122i
$559$	4.36783e8	+	2.52177e8i	0.00447320	+	0.00258260i
$560$	1.21792e10	−	1.02196e10i	0.123842	−	0.103916i
$561$	1.93279e11	+	2.30341e11i	1.95134	+	2.32552i
$562$	7.45436e9	−	1.29113e10i	0.0747249	−	0.129427i
$563$	6.52681e10	−	3.76826e10i	0.649632	−	0.375065i	−0.138683	−	0.990337i	$-0.544287\pi$
$563$	6.52681e10	−	3.76826e10i	0.649632	−	0.375065i	0.788315	+	0.615271i	$0.210954\pi$
$564$	4.04045e10	−	1.11010e11i	0.399313	−	1.09710i
$565$	9.79927e9	+	1.72788e9i	0.0961612	+	0.0169558i
$566$	2.89840e9	−	5.11066e8i	0.0282418	−	0.00497979i
$567$	−1.76360e10	+	6.41898e9i	−0.170635	+	0.0621060i
$568$	4.74015e10	+	3.97746e10i	0.455406	+	0.382131i
$569$			5.77161e10i			0.550615i	0.961356	+	0.275307i	$0.0887796\pi$
$569$			5.77161e10i			0.550615i	−0.961356	+	0.275307i	$0.911220\pi$
$570$	−1.67424e11	+	5.28244e10i	−1.58605	+	0.500420i
$571$	−1.40870e11			−1.32518			−0.662591	−	0.748981i	$-0.730543\pi$
$571$	−1.40870e11			−1.32518			−0.662591	+	0.748981i	$0.730543\pi$
$572$	7.00689e10	−	8.35048e10i	0.654547	−	0.780059i
$573$	1.70903e10	+	4.69551e10i	0.158537	+	0.435576i
$574$	2.16771e9	+	1.22937e10i	0.0199689	+	0.113249i
$575$	3.08517e10	−	1.74969e11i	0.282233	−	1.60062i
$576$	−1.82043e10	−	6.62582e9i	−0.165380	−	0.0601935i
$577$	5.11346e10	+	8.85677e10i	0.461330	+	0.799046i	0.999028	−	0.0440912i	$-0.0140392\pi$
$577$	5.11346e10	+	8.85677e10i	0.461330	+	0.799046i	−0.537698	+	0.843138i	$0.680706\pi$
$578$	2.45995e10	+	1.42025e10i	0.220402	+	0.127249i
$579$	8.11063e10	−	6.80562e10i	0.721672	−	0.605555i
$580$	4.75487e10	+	5.66663e10i	0.420171	+	0.500741i
$581$	−5.84240e9	+	1.01193e10i	−0.0512728	+	0.0888071i
$582$	−8.30111e10	+	4.79265e10i	−0.723509	+	0.417718i
$583$	2.16069e10	−	5.93644e10i	0.187033	−	0.513869i
$584$	−9.35527e9	−	1.64959e9i	−0.0804275	−	0.0141815i
$585$	−2.98811e11	+	5.26884e10i	−2.55137	+	0.449875i
$586$	−5.35664e10	+	1.94966e10i	−0.454257	+	0.165336i
$587$	1.18787e11	+	9.96737e10i	1.00049	+	0.839515i	0.987053	−	0.160395i	$-0.0512767\pi$
$587$	1.18787e11	+	9.96737e10i	1.00049	+	0.839515i	0.0134419	+	0.999910i	$0.495721\pi$
$588$			7.58659e10i			0.634655i
$589$	2.05961e11	+	4.56183e10i	1.71129	+	0.379033i
$590$	2.35626e10			0.194453
$591$	−1.43568e9	+	1.71097e9i	−0.0117681	+	0.0140247i
$592$	−2.23852e9	−	6.15029e9i	−0.0182253	−	0.0500736i
$593$	1.10450e10	+	6.26391e10i	0.0893193	+	0.506555i	0.996341	+	0.0854706i	$0.0272394\pi$
$593$	1.10450e10	+	6.26391e10i	0.0893193	+	0.506555i	−0.907021	+	0.421085i	$0.861650\pi$
$594$	−1.62338e10	+	9.20664e10i	−0.130399	+	0.739530i
$595$	−8.88143e10	−	3.23258e10i	−0.708623	−	0.257918i
$596$	−2.56599e10	−	4.44442e10i	−0.203362	−	0.352233i
$597$	1.39636e11	+	8.06189e10i	1.09926	+	0.634657i
$598$	1.05350e11	−	8.83993e10i	0.823816	−	0.691264i
$599$	−7.04332e10	−	8.39390e10i	−0.547104	−	0.652014i	0.419660	−	0.907681i	$-0.362149\pi$
$599$	−7.04332e10	−	8.39390e10i	−0.547104	−	0.652014i	−0.966765	+	0.255668i	$0.917705\pi$
$600$	4.61230e10	−	7.98874e10i	0.355887	−	0.616415i
$601$	2.61879e10	−	1.51196e10i	0.200725	−	0.115889i	−0.396268	−	0.918135i	$-0.629695\pi$
$601$	2.61879e10	−	1.51196e10i	0.200725	−	0.115889i	0.596994	+	0.802246i	$0.296362\pi$
$602$	−5.76568e7	+	1.58411e8i	−0.000439000	+	0.00120614i
$603$	−8.76273e10	−	1.54511e10i	−0.662781	−	0.116866i
$604$	−1.01153e11	+	1.78360e10i	−0.760029	+	0.134014i
$605$	3.46204e11	−	1.26008e11i	2.58411	−	0.940540i
$606$	1.94771e11	+	1.63432e11i	1.44422	+	1.21185i
$607$			5.43139e10i			0.400088i	0.979787	+	0.200044i	$0.0641086\pi$
$607$			5.43139e10i			0.400088i	−0.979787	+	0.200044i	$0.935891\pi$
$608$	2.14252e10	−	1.11586e10i	0.156787	−	0.0816570i
$609$	7.85461e10			0.571025
$610$	−1.23168e10	+	1.46786e10i	−0.0889569	+	0.106015i
$611$	8.70768e10	+	2.39241e11i	0.624795	+	1.71661i
$612$	1.99981e10	+	1.13415e11i	0.142556	+	0.808473i
$613$	4.08032e9	−	2.31407e10i	0.0288970	−	0.163883i	−0.966944	−	0.254987i	$-0.917929\pi$
$613$	4.08032e9	−	2.31407e10i	0.0288970	−	0.163883i	0.995841	+	0.0911046i	$0.0290398\pi$
$614$	−1.40444e11	−	5.11173e10i	−0.988163	−	0.359662i
$615$	6.41284e10	+	1.11074e11i	0.448281	+	0.776445i
$616$	3.15538e10	+	1.82176e10i	0.219144	+	0.126523i
$617$	−1.95334e11	+	1.63904e11i	−1.34783	+	1.13097i	−0.368296	+	0.929708i	$0.620059\pi$
$617$	−1.95334e11	+	1.63904e11i	−1.34783	+	1.13097i	−0.979538	+	0.201259i	$0.935497\pi$
$618$	−3.02176e10	−	3.60119e10i	−0.207160	−	0.246884i
$619$	6.50070e10	−	1.12595e11i	0.442790	−	0.766935i	−0.555105	−	0.831780i	$-0.687322\pi$
$619$	6.50070e10	−	1.12595e11i	0.442790	−	0.766935i	0.997895	+	0.0648454i	$0.0206554\pi$
$620$	−1.69983e11	+	9.81399e10i	−1.15038	+	0.664169i
$621$	−4.03390e10	+	1.10830e11i	−0.271243	+	0.745234i
$622$	1.35535e11	+	2.38985e10i	0.905503	+	0.159665i
$623$	7.86423e10	−	1.38668e10i	0.522040	−	0.0920498i
$624$	6.70975e10	−	2.44215e10i	0.442556	−	0.161077i
$625$	−7.17935e10	−	6.02419e10i	−0.470506	−	0.394801i
$626$			1.10494e10i			0.0719517i
$627$	−2.44984e11	−	3.19140e11i	−1.58514	−	2.06496i
$628$	−2.19032e10			−0.140821
$629$	−2.50097e10	+	2.98054e10i	−0.159774	+	0.190411i
$630$	−3.46865e10	−	9.53003e10i	−0.220190	−	0.604968i
$631$	2.78087e10	+	1.57711e11i	0.175414	+	0.994820i	0.937665	+	0.347540i	$0.112983\pi$
$631$	2.78087e10	+	1.57711e11i	0.175414	+	0.994820i	−0.762252	+	0.647281i	$0.775906\pi$
$632$	1.36093e10	−	7.71821e10i	0.0853036	−	0.483781i
$633$	2.28219e11	+	8.30649e10i	1.42147	+	0.517372i
$634$	−8.11502e10	−	1.40556e11i	−0.502265	−	0.869948i
$635$	−1.77944e11	−	1.02736e11i	−1.09443	−	0.631869i
$636$	3.16998e10	−	2.65993e10i	0.193744	−	0.162571i
$637$	−1.05096e11	−	1.25249e11i	−0.638306	−	0.760704i
$638$	−8.47611e10	+	1.46811e11i	−0.511581	+	0.886084i
$639$	3.41832e11	−	1.97357e11i	2.05026	−	1.18372i
$640$	−7.68745e9	+	2.11211e10i	−0.0458207	+	0.125891i
$641$	−4.95123e10	−	8.73036e9i	−0.293279	−	0.0517130i	0.0250728	−	0.999686i	$-0.492018\pi$
$641$	−4.95123e10	−	8.73036e9i	−0.293279	−	0.0517130i	−0.318352	+	0.947973i	$0.603129\pi$
$642$	−8.86488e10	+	1.56312e10i	−0.521834	+	0.0920135i
$643$	−1.34116e11	+	4.88143e10i	−0.784580	+	0.285564i	−0.703081	−	0.711110i	$-0.748193\pi$
$643$	−1.34116e11	+	4.88143e10i	−0.784580	+	0.285564i	−0.0814988	+	0.996673i	$0.525971\pi$
$644$	3.52126e10	+	2.95469e10i	0.204718	+	0.171778i
$645$			1.73200e9i			0.0100071i
$646$	−1.21131e11	−	7.71355e10i	−0.695543	−	0.442919i
$647$	−5.50601e10			−0.314210			−0.157105	−	0.987582i	$-0.550216\pi$
$647$	−5.50601e10			−0.314210			−0.157105	+	0.987582i	$0.550216\pi$
$648$	1.70548e10	−	2.03251e10i	0.0967268	−	0.115274i
$649$	1.84685e10	+	5.07417e10i	0.104100	+	0.286013i
$650$	3.45216e10	+	1.95781e11i	0.193391	+	1.09678i
$651$	−3.61909e10	+	2.05249e11i	−0.201500	+	1.14276i
$652$	−1.32734e11	−	4.83113e10i	−0.734500	−	0.267336i
$653$	1.07953e11	+	1.86980e11i	0.593721	+	1.02836i	0.993726	+	0.111842i	$0.0356752\pi$
$653$	1.07953e11	+	1.86980e11i	0.593721	+	1.02836i	−0.400005	+	0.916513i	$0.630992\pi$
$654$	1.76657e11	+	1.01993e11i	0.965651	+	0.557519i
$655$	1.00126e11	−	8.40154e10i	0.543976	−	0.456450i
$656$	−1.13439e10	−	1.35192e10i	−0.0612560	−	0.0730020i
$657$	−3.02983e10	+	5.24781e10i	−0.162613	+	0.281655i
$658$	−7.36962e10	+	4.25485e10i	−0.393135	+	0.226976i
$659$	3.71103e10	−	1.01960e11i	0.196767	−	0.540614i	−0.801592	−	0.597871i	$-0.796013\pi$
$659$	3.71103e10	−	1.01960e11i	0.196767	−	0.540614i	0.998359	+	0.0572575i	$0.0182356\pi$
$660$	3.68657e11	+	6.50041e10i	1.94288	+	0.342582i
$661$	1.05216e11	−	1.85524e10i	0.551158	−	0.0971840i	0.108868	−	0.994056i	$-0.465277\pi$
$661$	1.05216e11	−	1.85524e10i	0.551158	−	0.0971840i	0.442290	+	0.896872i	$0.354166\pi$
$662$	2.07867e11	−	7.56574e10i	1.08231	−	0.393930i
$663$	−3.25167e11	−	2.72847e11i	−1.68287	−	1.41210i
$664$		−	1.65191e10i		−	0.0849795i
$665$	1.16845e11	+	4.83721e10i	0.597481	+	0.247348i
$666$	−4.17497e10			−0.212205
$667$	−1.37473e11	+	1.63834e11i	−0.694568	+	0.827753i
$668$	1.76253e10	+	4.84251e10i	0.0885179	+	0.243201i
$669$	−2.25009e10	−	1.27609e11i	−0.112330	−	0.637056i
$670$	−1.79267e10	+	1.01667e11i	−0.0889614	+	0.504525i
$671$	−4.12642e10	−	1.50189e10i	−0.203556	−	0.0740882i
$672$	1.19331e10	+	2.06688e10i	0.0585163	+	0.101353i
$673$	2.08357e10	+	1.20295e10i	0.101566	+	0.0586391i	0.549923	−	0.835216i	$-0.314657\pi$
$673$	2.08357e10	+	1.20295e10i	0.101566	+	0.0586391i	−0.448357	+	0.893855i	$0.647991\pi$
$674$	6.95867e10	−	5.83901e10i	0.337199	−	0.282944i
$675$	−1.09592e11	−	1.30607e11i	−0.527916	−	0.629146i
$676$	−2.47351e10	+	4.28425e10i	−0.118448	+	0.205158i
$677$	2.13588e11	−	1.23315e11i	1.01677	−	0.587032i	0.103603	−	0.994619i	$-0.466963\pi$
$677$	2.13588e11	−	1.23315e11i	1.01677	−	0.587032i	0.913167	+	0.407587i	$0.133630\pi$
$678$	−5.10872e9	+	1.40361e10i	−0.0241765	+	0.0664244i
$679$	6.79975e10	+	1.19898e10i	0.319900	+	0.0564069i
$680$	1.31587e11	−	2.32024e10i	0.615429	−	0.108517i
$681$	−3.40849e11	+	1.24059e11i	−1.58480	+	0.576819i
$682$	−3.44576e11	−	2.89134e11i	−1.59275	−	1.33648i
$683$		−	4.29204e11i		−	1.97233i	−0.165752	−	0.986167i	$-0.553005\pi$
$683$		−	4.29204e11i		−	1.97233i	0.165752	−	0.986167i	$-0.446995\pi$
$684$	−2.01430e10	−	1.52771e11i	−0.0920236	−	0.697936i
$685$	3.32401e10			0.150973
$686$	7.80722e10	−	9.30428e10i	0.352533	−	0.420132i
$687$	−1.51659e11	−	4.16680e11i	−0.680834	−	1.87058i
$688$	−4.13841e7	−	2.34701e8i	−0.000184706	−	0.00104752i
$689$	−1.54862e10	+	8.78268e10i	−0.0687178	+	0.389718i
$690$	4.43792e11	+	1.61527e11i	1.95787	+	0.712606i
$691$	1.99569e11	+	3.45664e11i	0.875349	+	1.51615i	0.856390	+	0.516329i	$0.172702\pi$
$691$	1.99569e11	+	3.45664e11i	0.875349	+	1.51615i	0.0189592	+	0.999820i	$0.493965\pi$
$692$	−9.88154e10	−	5.70511e10i	−0.430924	−	0.248794i
$693$	1.78040e11	−	1.49394e11i	0.771943	−	0.647737i
$694$	9.43526e10	+	1.12445e11i	0.406739	+	0.484733i
$695$	−3.01689e11	+	5.22541e11i	−1.29307	+	2.23966i
$696$	−9.61657e10	+	5.55213e10i	−0.409811	+	0.236604i
$697$	−3.58822e10	+	9.85856e10i	−0.152037	+	0.417717i
$698$	7.11112e10	+	1.25388e10i	0.299582	+	0.0528245i
$699$	7.15054e11	−	1.26083e11i	2.99523	−	0.528140i
$700$	−6.24410e10	+	2.27267e10i	−0.260062	+	0.0946549i
$701$	1.99774e11	+	1.67631e11i	0.827309	+	0.694195i	0.954671	−	0.297662i	$-0.0962067\pi$
$701$	1.99774e11	+	1.67631e11i	0.827309	+	0.694195i	−0.127363	+	0.991856i	$0.540651\pi$
$702$		−	1.31973e11i		−	0.543421i
$703$	3.51637e10	−	3.83895e10i	0.143971	−	0.157178i
$704$	−5.15094e10			−0.209699
$705$	−5.61993e11	+	6.69758e11i	−2.27496	+	2.71120i
$706$	−4.87101e10	−	1.33830e11i	−0.196065	−	0.538684i
$707$	−3.18037e10	−	1.80368e11i	−0.127292	−	0.721906i
$708$	−6.14203e9	+	3.48332e10i	−0.0244444	+	0.138631i
$709$	−3.25936e11	−	1.18631e11i	−1.28987	−	0.469476i	−0.396189	−	0.918169i	$-0.629667\pi$
$709$	−3.25936e11	−	1.18631e11i	−1.28987	−	0.469476i	−0.893686	+	0.448693i	$0.851890\pi$
$710$	−2.28978e11	−	3.96602e11i	−0.901074	−	1.56071i
$711$	−4.32951e11	−	2.49965e11i	−1.69418	−	0.978138i
$712$	−8.64816e10	+	7.25667e10i	−0.336514	+	0.282369i
$713$	−3.64773e11	−	4.34719e11i	−1.41145	−	1.68210i
$714$	7.09391e10	−	1.22870e11i	0.272956	−	0.472774i
$715$	−6.98673e11	+	4.03379e11i	−2.67331	+	1.54344i
$716$	2.74517e10	−	7.54230e10i	0.104452	−	0.286980i
$717$	−1.58897e11	−	2.80178e10i	−0.601228	−	0.106013i
$718$	8.67651e9	−	1.52990e9i	0.0326473	−	0.00575660i
$719$	−1.82983e11	+	6.66002e10i	−0.684691	+	0.249207i	−0.660860	−	0.750509i	$-0.729808\pi$
$719$	−1.82983e11	+	6.66002e10i	−0.684691	+	0.249207i	−0.0238304	+	0.999716i	$0.507586\pi$
$720$	1.09832e11	+	9.21597e10i	0.408693	+	0.342934i
$721$			3.38632e10i			0.125310i
$722$	1.57441e11	+	1.10150e11i	0.579386	+	0.405354i
$723$	8.35827e11			3.05889
$724$	3.87845e10	−	4.62215e10i	0.141157	−	0.168225i
$725$	−1.05740e11	−	2.90519e11i	−0.382727	−	1.05153i
$726$	9.60363e10	+	5.44649e11i	0.345692	+	1.96052i
$727$	−4.53329e10	+	2.57096e11i	−0.162284	+	0.920359i	0.789536	+	0.613704i	$0.210321\pi$
$727$	−4.53329e10	+	2.57096e11i	−0.162284	+	0.920359i	−0.951821	+	0.306656i	$0.900790\pi$
$728$	−4.83328e10	−	1.75917e10i	−0.172075	−	0.0626300i
$729$	−2.23343e11	−	3.86842e11i	−0.790793	−	1.36969i
$730$	6.08865e10	+	3.51528e10i	0.214402	+	0.123785i
$731$	−1.08530e9	+	9.10674e8i	−0.00380084	+	0.00318928i
$732$	−1.84892e10	−	2.20345e10i	−0.0643981	−	0.0767467i
$733$	4.99967e9	−	8.65969e9i	0.0173191	−	0.0299976i	−0.857236	−	0.514924i	$-0.827820\pi$
$733$	4.99967e9	−	8.65969e9i	0.0173191	−	0.0299976i	0.874555	+	0.484926i	$0.161154\pi$
$734$	3.39260e11	−	1.95872e11i	1.16882	−	0.674820i
$735$	1.92037e11	−	5.27616e11i	0.658013	−	1.80788i
$736$	−6.39972e10	−	1.12844e10i	−0.218097	−	0.0384564i
$737$	−2.32990e11	+	4.10825e10i	−0.789710	+	0.139247i
$738$	−1.05785e11	+	3.85027e10i	−0.356615	+	0.129797i
$739$	−1.95602e11	−	1.64129e11i	−0.655836	−	0.550311i	0.253000	−	0.967466i	$-0.418583\pi$
$739$	−1.95602e11	−	1.64129e11i	−0.655836	−	0.550311i	−0.908835	+	0.417155i	$0.863027\pi$
$740$			4.84390e10i			0.161536i
$741$	4.18816e11	+	3.83624e11i	1.38915	+	1.27243i
$742$	−2.98084e10			−0.0983385
$743$	−3.34943e11	+	3.99169e11i	−1.09904	+	1.30979i	−0.152109	+	0.988364i	$0.548606\pi$
$743$	−3.34943e11	+	3.99169e11i	−1.09904	+	1.30979i	−0.946935	+	0.321426i	$0.895838\pi$
$744$	−1.00773e11	−	2.76873e11i	−0.328893	−	0.903625i
$745$	6.59539e10	+	3.74043e11i	0.214099	+	1.21422i
$746$	−4.22173e10	+	2.39426e11i	−0.136312	+	0.773066i
$747$	−9.90183e10	−	3.60397e10i	−0.318004	−	0.115744i
$748$	1.53104e11	+	2.65185e11i	0.489082	+	0.847114i
$749$	5.61549e10	+	3.24211e10i	0.178427	+	0.103015i
$750$	−1.19873e11	+	1.00585e11i	−0.378857	+	0.317899i
$751$	2.48151e9	+	2.95735e9i	0.00780112	+	0.00929701i	0.769931	−	0.638127i	$-0.220291\pi$
$751$	2.48151e9	+	2.95735e9i	0.00780112	+	0.00929701i	−0.762130	+	0.647424i	$0.775846\pi$
$752$	6.01519e10	−	1.04186e11i	0.188095	−	0.325790i
$753$	6.01353e11	−	3.47191e11i	1.87047	−	1.07991i
$754$	8.18491e10	−	2.24878e11i	0.253238	−	0.695765i
$755$	7.48624e11	+	1.32003e11i	2.30396	+	0.406251i
$756$	4.34410e10	−	7.65983e9i	0.132988	−	0.0234494i
$757$	−4.34419e11	+	1.58116e11i	−1.32290	+	0.481495i	−0.904385	−	0.426717i	$-0.859670\pi$
$757$	−4.34419e11	+	1.58116e11i	−1.32290	+	0.481495i	−0.418511	+	0.908212i	$0.637448\pi$
$758$	−2.34789e11	−	1.97011e11i	−0.711215	−	0.596780i
$759$			1.08231e12i			3.26124i
$760$	−1.77248e11	+	2.33704e10i	−0.531285	+	0.0700506i
$761$	−5.89797e9			−0.0175859			−0.00879294	−	0.999961i	$-0.502799\pi$
$761$	−5.89797e9			−0.0175859			−0.00879294	+	0.999961i	$0.502799\pi$
$762$	1.98261e11	−	2.36278e11i	0.588055	−	0.700816i
$763$	−5.02560e10	−	1.38077e11i	−0.148283	−	0.407403i
$764$	8.83626e9	+	5.01129e10i	0.0259355	+	0.147088i
$765$	1.48005e11	−	8.39376e11i	0.432145	−	2.45082i
$766$	3.34913e10	+	1.21899e10i	0.0972786	+	0.0354065i
$767$	−3.81140e10	−	6.60153e10i	−0.110129	−	0.190749i
$768$	−2.92200e10	−	1.68701e10i	−0.0839914	−	0.0484924i
$769$	9.44488e10	−	7.92519e10i	0.270079	−	0.226623i	−0.497682	−	0.867360i	$-0.665815\pi$
$769$	9.44488e10	−	7.92519e10i	0.270079	−	0.226623i	0.767761	+	0.640736i	$0.221371\pi$
$770$	−1.73330e11	−	2.06567e11i	−0.493073	−	0.587622i
$771$	2.47065e11	−	4.27929e11i	0.699188	−	1.21103i
$772$	9.33753e10	−	5.39103e10i	0.262883	−	0.151776i
$773$	−3.88005e10	+	1.06603e11i	−0.108672	+	0.298575i	−0.982094	−	0.188389i	$-0.939673\pi$
$773$	−3.88005e10	+	1.06603e11i	−0.108672	+	0.298575i	0.873422	+	0.486964i	$0.161896\pi$
$774$	−1.49713e9	−	2.63984e8i	−0.00417152	−	0.000735552i
$775$	8.07877e11	−	1.42451e11i	2.23944	−	0.394873i
$776$	−9.17259e10	+	3.33855e10i	−0.252956	+	0.0920685i
$777$	3.94006e10	+	3.30610e10i	0.108098	+	0.0907052i
$778$		−	3.44100e11i		−	0.939218i
$779$	5.36940e10	−	1.29700e11i	0.145806	−	0.352202i
$780$	−5.28452e11			−1.42767
$781$	6.74601e11	−	8.03959e11i	1.81319	−	2.16087i
$782$	1.32127e11	+	3.63017e11i	0.353318	+	0.970733i
$783$	3.56389e10	+	2.02118e11i	0.0948151	+	0.537723i
$784$	−1.34158e10	+	7.60850e10i	−0.0355102	+	0.201389i
$785$	1.52328e11	+	5.54427e10i	0.401144	+	0.146004i
$786$	9.81024e10	+	1.69918e11i	0.257033	+	0.445195i
$787$	−4.10181e11	−	2.36818e11i	−1.06924	−	0.617327i	−0.141268	−	0.989971i	$-0.545118\pi$
$787$	−4.10181e11	−	2.36818e11i	−1.06924	−	0.617327i	−0.927974	+	0.372644i	$0.878451\pi$
$788$	−1.74239e9	+	1.46204e9i	−0.00451897	+	0.00379187i
$789$	7.24749e11	+	8.63722e11i	1.87016	+	2.22877i
$790$	−2.90015e11	+	5.02321e11i	−0.744582	+	1.28965i
$791$	9.31810e9	−	5.37981e9i	0.0238024	−	0.0137423i
$792$	−1.12378e11	+	3.08756e11i	−0.285614	+	0.784719i
$793$	6.10484e10	+	1.07645e10i	0.154377	+	0.0272207i
$794$	1.85298e11	−	3.26730e10i	0.466217	−	0.0822065i
$795$	−2.87789e11	+	1.04747e11i	−0.720454	+	0.262224i
$796$	1.25783e11	+	1.05544e11i	0.313306	+	0.262895i
$797$		−	3.57903e11i		−	0.887017i	−0.896270	−	0.443508i	$-0.853734\pi$
$797$		−	3.57903e11i		−	0.887017i	0.896270	−	0.443508i	$-0.146266\pi$
$798$	−1.01968e11	+	1.60126e11i	−0.251449	+	0.394866i
$799$	−7.15172e11			−1.75478
$800$	6.03832e10	−	7.19619e10i	0.147420	−	0.175688i
$801$	2.46300e11	+	6.76704e11i	0.598321	+	1.64387i
$802$	−2.63153e10	−	1.49241e11i	−0.0636078	−	0.360738i
$803$	−2.79780e10	+	1.58671e11i	−0.0672905	+	0.381624i
$804$	−1.45625e11	−	5.30030e10i	−0.348506	−	0.126846i
$805$	−1.70098e11	−	2.94619e11i	−0.405057	−	0.701580i
$806$	5.49917e11	+	3.17495e11i	1.30304	+	0.752309i
$807$	5.43974e11	−	4.56449e11i	1.28258	−	1.07621i
$808$	1.66433e11	+	1.98347e11i	0.390476	+	0.465351i
$809$	−4.00388e11	+	6.93493e11i	−0.934732	+	1.61900i	−0.159621	+	0.987178i	$0.551027\pi$
$809$	−4.00388e11	+	6.93493e11i	−0.934732	+	1.61900i	−0.775111	+	0.631825i	$0.782306\pi$
$810$	−1.70057e11	+	9.81826e10i	−0.395053	+	0.228084i
$811$	−5.18564e10	+	1.42474e11i	−0.119872	+	0.329346i	−0.985087	−	0.172054i	$-0.944960\pi$
$811$	−5.18564e10	+	1.42474e11i	−0.119872	+	0.329346i	0.865215	+	0.501401i	$0.167182\pi$
$812$	7.87729e10	+	1.38898e10i	0.181198	+	0.0319501i
$813$	−7.19277e11	+	1.26828e11i	−1.64640	+	0.290304i
$814$	−1.04313e11	+	3.79667e10i	−0.237596	+	0.0864779i
$815$	8.00822e11	+	6.71970e11i	1.81512	+	1.52307i
$816$			2.00577e11i			0.452397i
$817$	1.50369e9	−	1.15429e9i	0.00337498	−	0.00259076i
$818$	−1.88583e11			−0.421201
$819$	−2.10895e11	+	2.51335e11i	−0.468739	+	0.558622i
$820$	4.46718e10	+	1.22735e11i	0.0988048	+	0.271464i
$821$	5.50426e10	+	3.12162e11i	0.121151	+	0.687081i	0.983520	+	0.180800i	$0.0578688\pi$
$821$	5.50426e10	+	3.12162e11i	0.121151	+	0.687081i	−0.862369	+	0.506280i	$0.831020\pi$
$822$	−8.66464e9	+	4.91396e10i	−0.0189786	+	0.107633i
$823$	−4.52869e10	−	1.64831e10i	−0.0987128	−	0.0359285i	0.292192	−	0.956360i	$-0.405615\pi$
$823$	−4.52869e10	−	1.64831e10i	−0.0987128	−	0.0359285i	−0.390904	+	0.920431i	$0.627838\pi$
$824$	−2.39367e10	−	4.14595e10i	−0.0519224	−	0.0899322i
$825$	−1.35494e12	−	7.82274e11i	−2.92485	−	1.68866i
$826$	1.95178e10	−	1.63774e10i	0.0419287	−	0.0351824i
$827$	1.94149e10	+	2.31378e10i	0.0415062	+	0.0494651i	0.786398	−	0.617720i	$-0.211943\pi$
$827$	1.94149e10	+	2.31378e10i	0.0415062	+	0.0494651i	−0.744892	+	0.667185i	$0.767499\pi$
$828$	−2.07263e11	+	3.58991e11i	−0.440962	+	0.763769i
$829$	2.78899e11	−	1.61022e11i	0.590512	−	0.340933i	−0.174788	−	0.984606i	$-0.555924\pi$
$829$	2.78899e11	−	1.61022e11i	0.590512	−	0.340933i	0.765300	+	0.643674i	$0.222591\pi$
$830$	−4.18142e10	+	1.14884e11i	−0.0881072	+	0.242073i
$831$	7.61752e11	+	1.34317e11i	1.59738	+	0.281662i
$832$	7.16099e10	−	1.26267e10i	0.149444	−	0.0263511i
$833$	4.31584e11	−	1.57084e11i	0.896365	−	0.326250i
$834$	−6.93845e11	−	5.82205e11i	−1.43416	−	1.20340i
$835$		−	3.81391e11i		−	0.784557i
$836$	−1.89256e11	−	3.63384e11i	−0.387457	−	0.743944i
$837$	−5.44577e11			−1.10958
$838$	3.33728e10	−	3.97722e10i	0.0676732	−	0.0806498i
$839$	1.80423e11	+	4.95707e11i	0.364119	+	1.00041i	0.977558	+	0.210666i	$0.0675634\pi$
$839$	1.80423e11	+	4.95707e11i	0.364119	+	1.00041i	−0.613439	+	0.789742i	$0.710214\pi$
$840$	−3.06718e10	−	1.73949e11i	−0.0616059	−	0.349385i
$841$	2.22417e10	−	1.26139e11i	0.0444616	−	0.252154i
$842$	6.19279e10	+	2.25399e10i	0.123208	+	0.0448439i
$843$	−8.28161e10	−	1.43442e11i	−0.163985	−	0.284030i
$844$	2.14189e11	+	1.23662e11i	0.422112	+	0.243706i
$845$	2.80468e11	−	2.35341e11i	0.550119	−	0.461605i
$846$	−4.93276e11	−	5.87863e11i	−0.962960	−	1.14761i
$847$	1.99192e11	−	3.45010e11i	0.387024	−	0.670345i
$848$	3.64951e10	−	2.10705e10i	0.0705751	−	0.0407465i
$849$	1.11831e10	−	3.07253e10i	0.0215244	−	0.0591379i
$850$	−5.49961e11	−	9.69729e10i	−1.05355	−	0.185770i
$851$	−1.37920e11	+	2.43189e10i	−0.262971	+	0.0463689i
$852$	6.45994e11	−	2.35122e11i	1.22594	−	0.446206i
$853$	−1.30136e11	−	1.09197e11i	−0.245810	−	0.206259i	0.511555	−	0.859250i	$-0.329069\pi$
$853$	−1.30136e11	−	1.09197e11i	−0.245810	−	0.206259i	−0.757366	+	0.652991i	$0.773514\pi$
$854$			2.07198e10i			0.0389542i
$855$	−2.46616e11	+	1.11344e12i	−0.461485	+	2.08355i
$856$	−9.16689e10			−0.170737
$857$	2.65241e11	−	3.16102e11i	0.491720	−	0.586009i	−0.461934	−	0.886914i	$-0.652844\pi$
$857$	2.65241e11	−	3.16102e11i	0.491720	−	0.586009i	0.953654	+	0.300905i	$0.0972887\pi$
$858$	−4.14203e11	−	1.13801e12i	−0.764300	−	2.09990i
$859$	−1.53539e11	−	8.70761e11i	−0.281997	−	1.59929i	−0.715818	−	0.698287i	$-0.753946\pi$
$859$	−1.53539e11	−	8.70761e11i	−0.281997	−	1.59929i	0.433820	−	0.900999i	$-0.357165\pi$
$860$	−3.06281e8	+	1.73700e9i	−0.000559919	+	0.00317546i
$861$	1.30323e11	+	4.74337e10i	0.237142	+	0.0863126i
$862$	1.90585e11	+	3.30103e11i	0.345192	+	0.597890i
$863$	3.32732e11	+	1.92103e11i	0.599862	+	0.346331i	0.768987	−	0.639264i	$-0.220761\pi$
$863$	3.32732e11	+	1.92103e11i	0.599862	+	0.346331i	−0.169125	+	0.985595i	$0.554094\pi$
$864$	−4.77714e10	+	4.00849e10i	−0.0857260	+	0.0719327i
$865$	5.42809e11	+	6.46894e11i	0.969577	+	1.15550i
$866$	−6.68707e10	+	1.15824e11i	−0.118895	+	0.205933i
$867$	2.73294e11	−	1.57787e11i	0.483676	−	0.279250i
$868$	−7.25908e10	+	1.99442e11i	−0.127880	+	0.351348i
$869$	−1.30906e12	−	2.30822e11i	−2.29551	−	0.404760i
$870$	8.09332e11	−	1.42707e11i	1.41270	−	0.249097i
$871$	3.13839e11	−	1.14228e11i	0.545299	−	0.198473i
$872$	1.59131e11	+	1.33527e11i	0.275226	+	0.230942i
$873$			6.22658e11i			1.07199i
$874$	−1.55530e11	−	4.92943e11i	−0.266544	−	0.844795i
$875$	1.12720e11			0.192296
$876$	−6.78385e10	+	8.08468e10i	−0.115202	+	0.137292i
$877$	−1.66881e11	−	4.58503e11i	−0.282104	−	0.775075i	−0.997111	−	0.0759574i	$-0.975799\pi$
$877$	−1.66881e11	−	4.58503e11i	−0.282104	−	0.775075i	0.715007	−	0.699117i	$-0.246424\pi$
$878$	−8.46215e10	−	4.79913e11i	−0.142398	−	0.807577i
$879$	−1.09972e11	+	6.23680e11i	−0.184215	+	1.04474i
$880$	3.58226e11	+	1.30384e11i	0.597347	+	0.217417i
$881$	−4.88033e11	−	8.45298e11i	−0.810113	−	1.40316i	−0.912784	−	0.408442i	$-0.866072\pi$
$881$	−4.88033e11	−	8.45298e11i	−0.810113	−	1.40316i	0.102671	−	0.994715i	$-0.467261\pi$
$882$	4.26797e11	+	2.46411e11i	0.705257	+	0.407180i
$883$	2.94893e11	−	2.47444e11i	0.485089	−	0.407038i	−0.367173	−	0.930153i	$-0.619674\pi$
$883$	2.94893e11	−	2.47444e11i	0.485089	−	0.407038i	0.852262	+	0.523114i	$0.175230\pi$
$884$	−2.77856e11	−	3.31136e11i	−0.455000	−	0.542248i
$885$	1.30887e11	−	2.26703e11i	0.213365	−	0.369560i
$886$	8.07685e10	−	4.66317e10i	0.131071	−	0.0756739i
$887$	−2.28491e11	+	6.27774e11i	−0.369126	+	1.01417i	0.606568	+	0.795031i	$0.292546\pi$
$887$	−2.28491e11	+	6.27774e11i	−0.369126	+	1.01417i	−0.975695	+	0.219135i	$0.929677\pi$
$888$	−7.16086e10	−	1.26265e10i	−0.115163	−	0.0203064i
$889$	−2.18805e11	+	3.85813e10i	−0.350308	+	0.0617688i
$890$	7.85129e11	−	2.85764e11i	1.25136	−	0.455456i
$891$	−3.44726e11	−	2.89260e11i	−0.546970	−	0.458962i
$892$		−	1.31957e11i		−	0.208436i
$893$	9.56013e11	+	4.15534e10i	1.50334	+	0.0653433i
$894$	−5.70149e11			−0.892562
$895$	−3.81831e11	+	4.55048e11i	−0.595084	+	0.709194i
$896$	8.31259e9	+	2.28387e10i	0.0128975	+	0.0354355i
$897$	−2.65311e11	−	1.50465e12i	−0.409813	−	2.32416i
$898$	−9.57770e10	+	5.43178e11i	−0.147284	+	0.835290i
$899$	−9.27944e11	−	3.37744e11i	−1.42064	−	0.517069i
$900$	−2.99614e11	−	5.18946e11i	−0.456659	−	0.790956i
$901$	−2.16953e11	−	1.25258e11i	−0.329206	−	0.190067i
$902$	−2.29293e11	+	1.92400e11i	−0.346390	+	0.290656i
$903$	1.20384e9	+	1.43469e9i	0.00181059	+	0.00215777i
$904$	−7.60557e9	+	1.31732e10i	−0.0113883	+	0.0197251i
$905$	−3.86729e11	+	2.23278e11i	−0.576517	+	0.332852i
$906$	−3.90285e11	+	1.07230e12i	−0.579255	+	1.59149i
$907$	4.56026e11	+	8.04097e10i	0.673846	+	0.118817i	0.500092	−	0.865972i	$-0.333299\pi$
$907$	4.56026e11	+	8.04097e10i	0.673846	+	0.118817i	0.173753	+	0.984789i	$0.444410\pi$
$908$	−3.63772e11	+	6.41428e10i	−0.535162	+	0.0943635i
$909$	1.55203e12	−	5.64894e11i	2.27324	−	0.827392i
$910$	2.91606e11	+	2.44686e11i	0.425236	+	0.356816i
$911$		−	6.79254e11i		−	0.986186i	−0.869977	−	0.493093i	$-0.835866\pi$
$911$		−	6.79254e11i		−	0.986186i	0.869977	−	0.493093i	$-0.164134\pi$
$912$	1.16540e10	−	2.68123e11i	0.0168460	−	0.387574i
$913$	−2.80174e11			−0.403222
$914$	1.79456e11	−	2.13867e11i	0.257142	−	0.306450i
$915$	7.28094e10	+	2.00042e11i	0.103873	+	0.285389i
$916$	−7.84129e10	−	4.44702e11i	−0.111380	−	0.631665i
$917$	2.45423e10	−	1.39187e11i	0.0347087	−	0.196843i
$918$	3.48362e11	+	1.26793e11i	0.490524	+	0.178536i
$919$	−1.64474e10	−	2.84877e10i	−0.0230587	−	0.0399389i	0.854266	−	0.519836i	$-0.174007\pi$
$919$	−1.64474e10	−	2.84877e10i	−0.0230587	−	0.0399389i	−0.877324	+	0.479898i	$0.840674\pi$
$920$	4.16510e11	+	2.40472e11i	0.581399	+	0.335671i
$921$	−1.27196e12	+	1.06730e12i	−1.76781	+	1.48337i
$922$	4.26439e11	+	5.08210e11i	0.590111	+	0.703266i
$923$	−7.40773e11	+	1.28306e12i	−1.02065	+	1.76782i
$924$	3.50555e11	−	2.02393e11i	0.480915	−	0.277656i
$925$	6.92413e10	−	1.90239e11i	0.0945798	−	0.259856i
$926$	−1.75341e11	−	3.09173e10i	−0.238473	−	0.0420492i
$927$	−3.00738e11	+	5.30282e10i	−0.407257	+	0.0718105i
$928$	−1.06262e11	+	3.86761e10i	−0.143280	+	0.0521495i
$929$	−3.31457e11	−	2.78125e11i	−0.445004	−	0.373403i	0.392574	−	0.919721i	$-0.371585\pi$
$929$	−3.31457e11	−	2.78125e11i	−0.445004	−	0.373403i	−0.837578	+	0.546318i	$0.816029\pi$
$930$			2.18062e12i			2.91506i
$931$	−5.86050e11	+	1.84907e11i	−0.780075	+	0.246124i
$932$	7.39416e11			0.979998
$933$	9.82814e11	−	1.17127e12i	1.29701	−	1.54572i
$934$	−1.03526e11	−	2.84435e11i	−0.136038	−	0.373762i
$935$	−3.93526e11	−	2.23180e12i	−0.514905	−	2.92017i
$936$	8.05443e10	−	4.56789e11i	0.104938	−	0.595131i
$937$	7.22849e11	+	2.63095e11i	0.937754	+	0.341315i	0.765279	−	0.643699i	$-0.222601\pi$
$937$	7.22849e11	+	2.63095e11i	0.937754	+	0.341315i	0.172476	+	0.985014i	$0.444823\pi$
$938$	5.58155e10	+	9.66753e10i	0.0721014	+	0.124883i
$939$	1.06310e11	+	6.13779e10i	0.136745	+	0.0789496i
$940$	−6.82054e11	+	5.72311e11i	−0.873589	+	0.733028i
$941$	8.63205e11	+	1.02873e12i	1.10092	+	1.31203i	0.946025	+	0.324094i	$0.105059\pi$
$941$	8.63205e11	+	1.02873e12i	1.10092	+	1.31203i	0.154895	+	0.987931i	$0.450496\pi$
$942$	−1.21669e11	+	2.10738e11i	−0.154517	+	0.267632i
$943$	−3.27033e11	+	1.88813e11i	−0.413566	+	0.238772i
$944$	−1.23195e10	+	3.38476e10i	−0.0155134	+	0.0426226i
$945$	−3.21503e11	−	5.66897e10i	−0.403142	−	0.0710849i
$946$	−3.98067e9	+	7.01900e8i	−0.00497041	+	0.000876417i
$947$	1.81563e10	−	6.60837e9i	0.0225750	−	0.00821664i	−0.330708	−	0.943733i	$-0.607288\pi$
$947$	1.81563e10	−	6.60837e9i	0.0225750	−	0.00821664i	0.353283	+	0.935517i	$0.385065\pi$
$948$	−6.66996e11	−	5.59676e11i	−0.825829	−	0.692952i
$949$		−	2.27448e11i		−	0.280425i
$950$	7.29531e11	+	1.61584e11i	0.895672	+	0.198382i
$951$	−1.80312e12			−2.20446
$952$	9.28718e10	−	1.10680e11i	0.113067	−	0.134748i
$953$	5.51428e11	+	1.51504e12i	0.668525	+	1.83676i	0.533269	+	0.845946i	$0.320963\pi$
$953$	5.51428e11	+	1.51504e12i	0.668525	+	1.83676i	0.135256	+	0.990811i	$0.456814\pi$
$954$	−4.66786e10	−	2.64727e11i	−0.0563539	−	0.319599i
$955$	6.53964e10	−	3.70881e11i	0.0786213	−	0.445884i
$956$	−1.54401e11	−	5.61975e10i	−0.184850	−	0.0672799i
$957$	9.41675e11	+	1.63103e12i	1.12267	+	1.94453i
$958$	−2.32531e11	−	1.34252e11i	−0.276069	−	0.159389i
$959$	2.75341e10	−	2.31038e10i	0.0325534	−	0.0273155i
$960$	1.60510e11	+	1.91288e11i	0.188980	+	0.225218i
$961$	8.83672e11	−	1.53057e12i	1.03609	−	1.79456i
$962$	1.35712e11	−	7.83531e10i	0.158459	−	0.0914863i
$963$	−1.99994e11	+	5.49479e11i	−0.232548	+	0.638919i
$964$	8.38241e11	+	1.47805e11i	0.970646	+	0.171151i
$965$	−7.85848e11	+	1.38566e11i	−0.906210	+	0.159789i
$966$	4.79882e11	−	1.74663e11i	0.551094	−	0.200582i
$967$	6.78383e11	+	5.69231e11i	0.775834	+	0.651002i	0.942196	−	0.335063i	$-0.108757\pi$
$967$	6.78383e11	+	5.69231e11i	0.775834	+	0.651002i	−0.166362	+	0.986065i	$0.553202\pi$
$968$			5.63205e11i			0.641453i
$969$	−1.41501e12	+	7.36959e11i	−1.60496	+	0.835888i
$970$	7.22423e11			0.816028
$971$	−5.75153e11	+	6.85440e11i	−0.647003	+	0.771068i	−0.985459	−	0.169914i	$-0.945651\pi$
$971$	−5.75153e11	+	6.85440e11i	−0.647003	+	0.771068i	0.338456	+	0.940982i	$0.390095\pi$
$972$	−1.97449e11	−	5.42487e11i	−0.221203	−	0.607749i
$973$	1.13296e11	+	6.42534e11i	0.126405	+	0.716877i
$974$	−1.19506e11	+	6.77753e11i	−0.132787	+	0.753070i
$975$	2.07544e12	+	7.55398e11i	2.29663	+	0.835906i
$976$	−1.46461e10	−	2.53677e10i	−0.0161407	−	0.0279565i
$977$	−1.27097e12	−	7.33796e11i	−1.39495	−	0.805373i	−0.401090	−	0.916039i	$-0.631368\pi$
$977$	−1.27097e12	−	7.33796e11i	−1.39495	−	0.805373i	−0.993858	+	0.110666i	$0.964702\pi$
$978$	−1.20214e12	+	1.00871e12i	−1.31401	+	1.10259i
$979$	1.23077e12	+	1.46678e12i	1.33982	+	1.59674i
$980$	2.85893e11	−	4.95181e11i	0.309955	−	0.536858i
$981$	1.14756e12	−	6.62544e11i	1.23908	−	0.715383i
$982$	1.24089e11	−	3.40933e11i	0.133441	−	0.366626i
$983$	1.89081e11	+	3.33401e10i	0.202504	+	0.0357070i	0.273980	−	0.961735i	$-0.411660\pi$
$983$	1.89081e11	+	3.33401e10i	0.202504	+	0.0357070i	−0.0714758	+	0.997442i	$0.522771\pi$
$984$	−1.93086e11	+	3.40463e10i	−0.205954	+	0.0363153i
$985$	1.58184e10	−	5.75742e9i	0.0168042	−	0.00611622i
$986$	5.14963e11	+	4.32105e11i	0.544839	+	0.457174i
$987$			9.45406e11i			0.996207i
$988$	3.52187e11	+	4.58794e11i	0.369612	+	0.481493i
$989$	−5.09951e9			−0.00533020
$990$	1.56308e12	−	1.86281e12i	1.62720	−	1.93922i
$991$	6.13817e10	+	1.68645e11i	0.0636420	+	0.174855i	0.967438	−	0.253109i	$-0.0814532\pi$
$991$	6.13817e10	+	1.68645e11i	0.0636420	+	0.174855i	−0.903796	+	0.427964i	$0.859231\pi$
$992$	−5.21033e10	−	2.95493e11i	−0.0538045	−	0.305141i
$993$	4.26750e11	−	2.42022e12i	0.438911	−	2.48919i
$994$	−4.65334e11	−	1.69368e11i	−0.476671	−	0.173494i
$995$	−6.07607e11	−	1.05241e12i	−0.619913	−	1.07372i
$996$	−1.58936e11	−	9.17615e10i	−0.161504	−	0.0932445i
$997$	−3.68519e11	+	3.09224e11i	−0.372975	+	0.312963i	−0.809937	−	0.586517i	$-0.800499\pi$
$997$	−3.68519e11	+	3.09224e11i	−0.372975	+	0.312963i	0.436962	+	0.899480i	$0.356054\pi$
$998$	−3.80281e9	−	4.53202e9i	−0.00383339	−	0.00456846i
$999$	−6.71968e10	+	1.16388e11i	−0.0674663	+	0.116855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.9.f.a.3.8	✓	84
19.13	odd	18	inner	38.9.f.a.13.8	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.9.f.a.3.8	✓	84	1.1	even	1	trivial
38.9.f.a.13.8	yes	84	19.13	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	38.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.27231 - 8.66680i) q^{2} +(-42.9893 - 118.112i) q^{3} +(-22.2270 - 126.055i) q^{4} +(-164.500 + 932.925i) q^{5} +(-1336.29 - 486.369i) q^{6} +(512.177 + 887.116i) q^{7} +(-1254.14 - 724.077i) q^{8} +(-7076.39 + 5937.80i) q^{9} +O(q^{10})\)	\(q+(7.27231 - 8.66680i) q^{2} +(-42.9893 - 118.112i) q^{3} +(-22.2270 - 126.055i) q^{4} +(-164.500 + 932.925i) q^{5} +(-1336.29 - 486.369i) q^{6} +(512.177 + 887.116i) q^{7} +(-1254.14 - 724.077i) q^{8} +(-7076.39 + 5937.80i) q^{9} +(6889.19 + 8210.21i) q^{10} +(-12280.8 + 21270.9i) q^{11} +(-13933.2 + 8044.31i) q^{12} +(11858.9 - 32582.0i) q^{13} +(11413.2 + 2012.45i) q^{14} +(117262. - 20676.4i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(74611.5 + 62606.4i) q^{17} +104511. i q^{18} +(-96099.9 - 88024.8i) q^{19} +121257. q^{20} +(82761.1 - 98630.9i) q^{21} +(95041.4 + 261124. i) q^{22} +(60877.2 + 345252. i) q^{23} +(-31607.8 + 179257. i) q^{24} +(-476222. - 173331. i) q^{25} +(-196140. - 339725. i) q^{26} +(291353. + 168213. i) q^{27} +(100442. - 84280.6i) q^{28} +(392133. + 467326. i) q^{29} +(673565. - 1.16665e6i) q^{30} +(-1.40185e6 + 809357. i) q^{31} +(-63398.2 + 174185. i) q^{32} +(3.04030e6 + 536087. i) q^{33} +(1.08520e6 - 191349. i) q^{34} +(-911867. + 331892. i) q^{35} +(905779. + 760038. i) q^{36} +399475. i q^{37} +(-1.46176e6 + 192735. i) q^{38} -4.35813e6 q^{39} +(881816. - 1.05091e6i) q^{40} +(368407. + 1.01219e6i) q^{41} +(-252950. - 1.43455e6i) q^{42} +(-2525.89 + 14325.0i) q^{43} +(2.95428e6 + 1.07527e6i) q^{44} +(-4.37546e6 - 7.57852e6i) q^{45} +(3.43495e6 + 1.98317e6i) q^{46} +(-5.62488e6 + 4.71983e6i) q^{47} +(1.32372e6 + 1.57755e6i) q^{48} +(2.35775e6 - 4.08374e6i) q^{49} +(-4.96546e6 + 2.86681e6i) q^{50} +(4.18709e6 - 1.15039e7i) q^{51} +(-4.37072e6 - 770676. i) q^{52} +(-2.53300e6 + 446637. i) q^{53} +(3.57668e6 - 1.30180e6i) q^{54} +(-1.78240e7 - 1.49561e7i) q^{55} -1.48342e6i q^{56} +(-6.26554e6 + 1.51347e7i) q^{57} +6.90193e6 q^{58} +(1.41316e6 - 1.68413e6i) q^{59} +(-5.21274e6 - 1.43219e7i) q^{60} +(310457. + 1.76069e6i) q^{61} +(-3.18013e6 + 1.80354e7i) q^{62} +(-8.89189e6 - 3.23638e6i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(2.84458e7 + 1.64232e7i) q^{65} +(2.67562e7 - 2.24511e7i) q^{66} +(6.19152e6 + 7.37877e6i) q^{67} +(6.23349e6 - 1.07967e7i) q^{68} +(3.81614e7 - 2.20325e7i) q^{69} +(-3.75493e6 + 1.03166e7i) q^{70} +(-4.20799e7 - 7.41983e6i) q^{71} +(1.31742e7 - 2.32297e6i) q^{72} +(6.16418e6 - 2.24358e6i) q^{73} +(3.46217e6 + 2.90511e6i) q^{74} +6.36990e7i q^{75} +(-8.95999e6 + 1.40704e7i) q^{76} -2.51597e7 q^{77} +(-3.16937e7 + 3.77711e7i) q^{78} +(1.85098e7 + 5.08553e7i) q^{79} +(-2.69517e6 - 1.52850e7i) q^{80} +(-3.18152e6 + 1.80433e7i) q^{81} +(1.14516e7 + 4.16805e6i) q^{82} +(5.70350e6 + 9.87876e6i) q^{83} +(-1.42725e7 - 8.24022e6i) q^{84} +(-7.06807e7 + 5.93082e7i) q^{85} +(105783. + 126067. i) q^{86} +(3.83393e7 - 6.64057e7i) q^{87} +(3.08036e7 - 1.77845e7i) q^{88} +(2.66628e7 - 7.32555e7i) q^{89} +(-9.75012e7 - 1.71921e7i) q^{90} +(3.49778e7 - 6.16754e6i) q^{91} +(4.21678e7 - 1.53478e7i) q^{92} +(1.55859e8 + 1.30782e8i) q^{93} +8.30738e7i q^{94} +(9.79290e7 - 7.51740e7i) q^{95} +2.32988e7 q^{96} +(4.33270e7 - 5.16351e7i) q^{97} +(-1.82467e7 - 5.01324e7i) q^{98} +(-3.93989e7 - 2.23442e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 168 q^{3} - 2688 q^{6} - 6570 q^{7} - 2856 q^{9}+O(q^{10}) \) 84 * q - 168 * q^3 - 2688 * q^6 - 6570 * q^7 - 2856 * q^9	\( 84 q - 168 q^{3} - 2688 q^{6} - 6570 q^{7} - 2856 q^{9} - 20970 q^{11} + 62208 q^{12} - 101310 q^{13} - 142848 q^{14} + 331518 q^{15} + 29178 q^{17} - 319212 q^{19} - 428544 q^{20} - 186138 q^{21} + 1238016 q^{22} + 1989360 q^{23} + 344064 q^{24} - 272916 q^{25} - 695808 q^{26} - 6975648 q^{27} - 489984 q^{28} + 1676430 q^{29} - 3498768 q^{31} + 6273750 q^{33} + 2740224 q^{34} + 10942362 q^{35} + 365568 q^{36} + 5830272 q^{38} - 23638704 q^{39} + 430488 q^{41} + 4230144 q^{42} - 20999118 q^{43} + 700416 q^{44} + 49897728 q^{45} + 12003840 q^{46} - 22431150 q^{47} - 5505024 q^{48} - 59138004 q^{49} - 24993792 q^{50} + 6061860 q^{51} - 2857728 q^{52} + 69029982 q^{53} + 63262080 q^{54} + 20438670 q^{55} - 50408076 q^{57} - 31266816 q^{58} - 85956678 q^{59} - 9106176 q^{60} + 29908896 q^{61} - 39755520 q^{62} - 29288274 q^{63} + 88080384 q^{64} + 199314810 q^{65} + 117652224 q^{66} + 64371642 q^{67} + 25820928 q^{68} - 186304482 q^{69} - 187792896 q^{70} - 168095268 q^{71} + 23396352 q^{72} + 104437176 q^{73} + 33624576 q^{74} + 6617088 q^{76} - 277281288 q^{77} + 30777600 q^{78} + 199146114 q^{79} + 245855040 q^{81} - 69199872 q^{82} - 14372262 q^{83} - 348399360 q^{84} - 386680068 q^{85} - 155904768 q^{86} + 36917496 q^{87} + 292036248 q^{89} + 694869504 q^{90} + 285753588 q^{91} + 95143680 q^{92} + 529006800 q^{93} - 166014666 q^{95} + 251818254 q^{97} - 595464192 q^{98} - 1180902678 q^{99}+O(q^{100}) \) 84 * q - 168 * q^3 - 2688 * q^6 - 6570 * q^7 - 2856 * q^9 - 20970 * q^11 + 62208 * q^12 - 101310 * q^13 - 142848 * q^14 + 331518 * q^15 + 29178 * q^17 - 319212 * q^19 - 428544 * q^20 - 186138 * q^21 + 1238016 * q^22 + 1989360 * q^23 + 344064 * q^24 - 272916 * q^25 - 695808 * q^26 - 6975648 * q^27 - 489984 * q^28 + 1676430 * q^29 - 3498768 * q^31 + 6273750 * q^33 + 2740224 * q^34 + 10942362 * q^35 + 365568 * q^36 + 5830272 * q^38 - 23638704 * q^39 + 430488 * q^41 + 4230144 * q^42 - 20999118 * q^43 + 700416 * q^44 + 49897728 * q^45 + 12003840 * q^46 - 22431150 * q^47 - 5505024 * q^48 - 59138004 * q^49 - 24993792 * q^50 + 6061860 * q^51 - 2857728 * q^52 + 69029982 * q^53 + 63262080 * q^54 + 20438670 * q^55 - 50408076 * q^57 - 31266816 * q^58 - 85956678 * q^59 - 9106176 * q^60 + 29908896 * q^61 - 39755520 * q^62 - 29288274 * q^63 + 88080384 * q^64 + 199314810 * q^65 + 117652224 * q^66 + 64371642 * q^67 + 25820928 * q^68 - 186304482 * q^69 - 187792896 * q^70 - 168095268 * q^71 + 23396352 * q^72 + 104437176 * q^73 + 33624576 * q^74 + 6617088 * q^76 - 277281288 * q^77 + 30777600 * q^78 + 199146114 * q^79 + 245855040 * q^81 - 69199872 * q^82 - 14372262 * q^83 - 348399360 * q^84 - 386680068 * q^85 - 155904768 * q^86 + 36917496 * q^87 + 292036248 * q^89 + 694869504 * q^90 + 285753588 * q^91 + 95143680 * q^92 + 529006800 * q^93 - 166014666 * q^95 + 251818254 * q^97 - 595464192 * q^98 - 1180902678 * q^99

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