LMFDB - Embedded newform 38.7.f.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,7,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, 7, names="a")

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

chi := DirichletCharacter("38.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
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:	$8.74205517755$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ 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			38.7.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)

$f(q)$	$=$	$q+(3.63616 - 4.33340i) q^{2} +(-1.10346 - 3.03174i) q^{3} +(-5.55674 - 31.5138i) q^{4} +(-30.9885 + 175.744i) q^{5} +(-17.1501 - 6.24213i) q^{6} +(294.726 + 510.481i) q^{7} +(-156.767 - 90.5097i) q^{8} +(550.473 - 461.901i) q^{9} +O(q^{10})$	\(q+(3.63616 - 4.33340i) q^{2} +(-1.10346 - 3.03174i) q^{3} +(-5.55674 - 31.5138i) q^{4} +(-30.9885 + 175.744i) q^{5} +(-17.1501 - 6.24213i) q^{6} +(294.726 + 510.481i) q^{7} +(-156.767 - 90.5097i) q^{8} +(550.473 - 461.901i) q^{9} +(648.892 + 773.320i) q^{10} +(340.172 - 589.195i) q^{11} +(-89.4101 + 51.6210i) q^{12} +(-485.188 + 1333.04i) q^{13} +(3283.79 + 579.021i) q^{14} +(567.006 - 99.9785i) q^{15} +(-962.245 + 350.229i) q^{16} +(813.855 + 682.906i) q^{17} -4064.96i q^{18} +(3113.19 + 6111.79i) q^{19} +5710.58 q^{20} +(1222.43 - 1456.83i) q^{21} +(-1316.30 - 3616.51i) q^{22} +(62.3548 + 353.632i) q^{23} +(-101.415 + 575.152i) q^{24} +(-15243.1 - 5548.05i) q^{25} +(4012.40 + 6949.67i) q^{26} +(-4044.66 - 2335.19i) q^{27} +(14449.5 - 12124.6i) q^{28} +(13033.7 + 15532.9i) q^{29} +(1628.48 - 2820.60i) q^{30} +(-33239.2 + 19190.7i) q^{31} +(-1981.19 + 5443.28i) q^{32} +(-2161.65 - 381.158i) q^{33} +(5918.61 - 1043.61i) q^{34} +(-98847.3 + 35977.5i) q^{35} +(-17615.1 - 14780.8i) q^{36} -71197.2i q^{37} +(37804.9 + 8732.73i) q^{38} +4576.83 q^{39} +(20764.6 - 24746.2i) q^{40} +(-24335.7 - 66861.7i) q^{41} +(-1868.10 - 10594.5i) q^{42} +(25300.3 - 143485. i) q^{43} +(-20458.0 - 7446.12i) q^{44} +(64118.3 + 111056. i) q^{45} +(1759.16 + 1015.65i) q^{46} +(-31258.5 + 26229.0i) q^{47} +(2123.60 + 2530.81i) q^{48} +(-114903. + 199017. i) q^{49} +(-79468.4 + 45881.1i) q^{50} +(1172.33 - 3220.96i) q^{51} +(44705.4 + 7882.77i) q^{52} +(165360. - 29157.4i) q^{53} +(-24826.3 + 9036.05i) q^{54} +(93006.4 + 78041.6i) q^{55} -106702. i q^{56} +(15094.1 - 16182.5i) q^{57} +114703. q^{58} +(242346. - 288817. i) q^{59} +(-6301.41 - 17313.0i) q^{60} +(58721.6 + 333027. i) q^{61} +(-37702.1 + 213819. i) q^{62} +(398030. + 144871. i) q^{63} +(16384.0 + 28377.9i) q^{64} +(-219240. - 126578. i) q^{65} +(-9511.82 + 7981.36i) q^{66} +(-182860. - 217925. i) q^{67} +(16998.6 - 29442.4i) q^{68} +(1003.31 - 579.263i) q^{69} +(-203519. + 559165. i) q^{70} +(-88479.5 - 15601.3i) q^{71} +(-128103. + 22588.0i) q^{72} +(59877.8 - 21793.7i) q^{73} +(-308526. - 258884. i) q^{74} +52335.3i q^{75} +(175307. - 132070. i) q^{76} +401030. q^{77} +(16642.1 - 19833.2i) q^{78} +(6711.86 + 18440.7i) q^{79} +(-31732.2 - 179962. i) q^{80} +(88349.5 - 501055. i) q^{81} +(-378227. - 137663. i) q^{82} +(-278853. - 482988. i) q^{83} +(-52703.0 - 30428.1i) q^{84} +(-145237. + 121868. i) q^{85} +(-529784. - 631371. i) q^{86} +(32709.6 - 56654.8i) q^{87} +(-106656. + 61577.7i) q^{88} +(3441.94 - 9456.64i) q^{89} +(714395. + 125967. i) q^{90} +(-823491. + 145204. i) q^{91} +(10797.8 - 3930.08i) q^{92} +(94859.3 + 79596.4i) q^{93} +230828. i q^{94} +(-1.17059e6 + 357730. i) q^{95} +18688.8 q^{96} +(-187751. + 223753. i) q^{97} +(444618. + 1.22158e6i) q^{98} +(-84894.7 - 481462. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 240 * q^6 + 432 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9} - 3360 q^{11} + 9660 q^{13} + 2496 q^{14} - 37464 q^{15} + 7704 q^{17} + 46704 q^{19} + 21504 q^{20} + 78732 q^{21} - 20304 q^{22} - 54120 q^{23} + 7680 q^{24} - 41328 q^{25} - 25536 q^{26} - 124830 q^{27} + 65280 q^{28} - 21840 q^{29} + 30780 q^{31} - 54582 q^{33} - 70560 q^{34} - 56796 q^{35} - 22080 q^{36} + 52080 q^{38} + 496344 q^{39} + 83394 q^{41} + 38880 q^{42} - 294384 q^{43} - 8448 q^{44} - 391824 q^{45} + 738720 q^{46} + 639264 q^{47} + 61440 q^{48} - 85530 q^{49} - 689472 q^{50} - 215478 q^{51} - 456960 q^{52} - 1189428 q^{53} - 907200 q^{54} - 316512 q^{55} + 517776 q^{57} + 440640 q^{58} + 957390 q^{59} + 586752 q^{60} + 1390404 q^{61} + 978384 q^{62} + 2002152 q^{63} + 983040 q^{64} - 878940 q^{65} - 976992 q^{66} - 2920854 q^{67} - 78144 q^{68} - 2667600 q^{69} - 643392 q^{70} + 1585980 q^{71} + 706560 q^{72} + 1734648 q^{73} - 1167552 q^{74} - 411264 q^{76} - 1481400 q^{77} - 2170608 q^{78} + 4991952 q^{79} + 40002 q^{81} + 2299392 q^{82} - 30672 q^{83} + 1313280 q^{84} + 815976 q^{85} - 1424976 q^{86} - 125892 q^{87} - 6804636 q^{89} - 2283456 q^{90} - 3838704 q^{91} - 244992 q^{92} - 3271128 q^{93} - 4631640 q^{95} + 2112390 q^{97} + 7177728 q^{98} + 21467982 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 240 * q^6 + 432 * q^7 + 690 * q^9 - 3360 * q^11 + 9660 * q^13 + 2496 * q^14 - 37464 * q^15 + 7704 * q^17 + 46704 * q^19 + 21504 * q^20 + 78732 * q^21 - 20304 * q^22 - 54120 * q^23 + 7680 * q^24 - 41328 * q^25 - 25536 * q^26 - 124830 * q^27 + 65280 * q^28 - 21840 * q^29 + 30780 * q^31 - 54582 * q^33 - 70560 * q^34 - 56796 * q^35 - 22080 * q^36 + 52080 * q^38 + 496344 * q^39 + 83394 * q^41 + 38880 * q^42 - 294384 * q^43 - 8448 * q^44 - 391824 * q^45 + 738720 * q^46 + 639264 * q^47 + 61440 * q^48 - 85530 * q^49 - 689472 * q^50 - 215478 * q^51 - 456960 * q^52 - 1189428 * q^53 - 907200 * q^54 - 316512 * q^55 + 517776 * q^57 + 440640 * q^58 + 957390 * q^59 + 586752 * q^60 + 1390404 * q^61 + 978384 * q^62 + 2002152 * q^63 + 983040 * q^64 - 878940 * q^65 - 976992 * q^66 - 2920854 * q^67 - 78144 * q^68 - 2667600 * q^69 - 643392 * q^70 + 1585980 * q^71 + 706560 * q^72 + 1734648 * q^73 - 1167552 * q^74 - 411264 * q^76 - 1481400 * q^77 - 2170608 * q^78 + 4991952 * q^79 + 40002 * q^81 + 2299392 * q^82 - 30672 * q^83 + 1313280 * q^84 + 815976 * q^85 - 1424976 * q^86 - 125892 * q^87 - 6804636 * q^89 - 2283456 * q^90 - 3838704 * q^91 - 244992 * q^92 - 3271128 * q^93 - 4631640 * q^95 + 2112390 * q^97 + 7177728 * q^98 + 21467982 * 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 $

$2$	3.63616	−	4.33340i	0.454519	−	0.541675i
$2$	3.63616	−	4.33340i	0.454519	−	0.541675i
$3$	−1.10346	−	3.03174i	−0.0408690	−	0.112287i	0.917579	−	0.397552i	$-0.130140\pi$
$3$	−1.10346	−	3.03174i	−0.0408690	−	0.112287i	−0.958448	+	0.285266i	$0.907918\pi$
$4$	−5.55674	−	31.5138i	−0.0868241	−	0.492404i
$5$	−30.9885	+	175.744i	−0.247908	+	1.40596i	0.565733	+	0.824588i	$0.308593\pi$
$5$	−30.9885	+	175.744i	−0.247908	+	1.40596i	−0.813641	+	0.581368i	$0.802518\pi$
$6$	−17.1501	−	6.24213i	−0.0793986	−	0.0288987i
$7$	294.726	+	510.481i	0.859260	+	1.48828i	0.872636	+	0.488372i	$0.162409\pi$
$7$	294.726	+	510.481i	0.859260	+	1.48828i	−0.0133755	+	0.999911i	$0.504258\pi$
$8$	−156.767	−	90.5097i	−0.306186	−	0.176777i
$9$	550.473	−	461.901i	0.755106	−	0.633610i
$10$	648.892	+	773.320i	0.648892	+	0.773320i
$11$	340.172	−	589.195i	0.255576	−	0.442671i	−0.709476	−	0.704730i	$-0.751068\pi$
$11$	340.172	−	589.195i	0.255576	−	0.442671i	0.965052	+	0.262059i	$0.0844015\pi$
$12$	−89.4101	+	51.6210i	−0.0517420	+	0.0298732i
$13$	−485.188	+	1333.04i	−0.220841	+	0.606757i	−0.999793	−	0.0203269i	$-0.993529\pi$
$13$	−485.188	+	1333.04i	−0.220841	+	0.606757i	0.778952	+	0.627084i	$0.215752\pi$
$14$	3283.79	+	579.021i	1.19672	+	0.211013i
$15$	567.006	−	99.9785i	0.168002	−	0.0296233i
$16$	−962.245	+	350.229i	−0.234923	+	0.0855050i
$17$	813.855	+	682.906i	0.165653	+	0.139000i	0.721846	−	0.692054i	$-0.243294\pi$
$17$	813.855	+	682.906i	0.165653	+	0.139000i	−0.556193	+	0.831053i	$0.687738\pi$
$18$		−	4064.96i		−	0.697010i
$19$	3113.19	+	6111.79i	0.453883	+	0.891061i
$19$	3113.19	+	6111.79i	0.453883	+	0.891061i
$20$	5710.58			0.713823
$21$	1222.43	−	1456.83i	0.131997	−	0.157308i
$22$	−1316.30	−	3616.51i	−0.123620	−	0.339642i
$23$	62.3548	+	353.632i	0.00512491	+	0.0290648i	0.987263	−	0.159097i	$-0.0508582\pi$
$23$	62.3548	+	353.632i	0.00512491	+	0.0290648i	−0.982138	+	0.188162i	$0.939747\pi$
$24$	−101.415	+	575.152i	−0.00733614	+	0.0416053i
$25$	−15243.1	−	5548.05i	−0.975561	−	0.355075i
$26$	4012.40	+	6949.67i	0.228288	+	0.395407i
$27$	−4044.66	−	2335.19i	−0.205490	−	0.118640i
$28$	14449.5	−	12124.6i	0.658231	−	0.552322i
$29$	13033.7	+	15532.9i	0.534408	+	0.636883i	0.963924	−	0.266176i	$-0.0857603\pi$
$29$	13033.7	+	15532.9i	0.534408	+	0.636883i	−0.429516	+	0.903059i	$0.641316\pi$
$30$	1628.48	−	2820.60i	0.0603139	−	0.104467i
$31$	−33239.2	+	19190.7i	−1.11575	+	0.644177i	−0.940312	−	0.340314i	$-0.889466\pi$
$31$	−33239.2	+	19190.7i	−1.11575	+	0.644177i	−0.175435	+	0.984491i	$0.556133\pi$
$32$	−1981.19	+	5443.28i	−0.0604612	+	0.166116i
$33$	−2161.65	−	381.158i	−0.0601512	−	0.0106063i
$34$	5918.61	−	1043.61i	0.150585	−	0.0265523i
$35$	−98847.3	+	35977.5i	−2.30548	+	0.839125i
$36$	−17615.1	−	14780.8i	−0.377553	−	0.316805i
$37$		−	71197.2i		−	1.40559i	−0.711394	−	0.702794i	$-0.751936\pi$
$37$		−	71197.2i		−	1.40559i	0.711394	−	0.702794i	$-0.248064\pi$
$38$	37804.9	+	8732.73i	0.688965	+	0.159147i
$39$	4576.83			0.0771562
$40$	20764.6	−	24746.2i	0.324446	−	0.386660i
$41$	−24335.7	−	66861.7i	−0.353095	−	0.970121i	−0.981370	−	0.192129i	$-0.938461\pi$
$41$	−24335.7	−	66861.7i	−0.353095	−	0.970121i	0.628275	−	0.777992i	$-0.283761\pi$
$42$	−1868.10	−	10594.5i	−0.0252146	−	0.142999i
$43$	25300.3	−	143485.i	0.318215	−	1.80469i	−0.235382	−	0.971903i	$-0.575634\pi$
$43$	25300.3	−	143485.i	0.318215	−	1.80469i	0.553597	−	0.832785i	$-0.313255\pi$
$44$	−20458.0	−	7446.12i	−0.240163	−	0.0874122i
$45$	64118.3	+	111056.i	0.703630	+	1.21872i
$46$	1759.16	+	1015.65i	0.0180731	+	0.0104345i
$47$	−31258.5	+	26229.0i	−0.301075	+	0.252632i	−0.780792	−	0.624792i	$-0.785184\pi$
$47$	−31258.5	+	26229.0i	−0.301075	+	0.252632i	0.479717	+	0.877424i	$0.340739\pi$
$48$	2123.60	+	2530.81i	0.0192021	+	0.0228842i
$49$	−114903.	+	199017.i	−0.976656	+	1.69162i
$50$	−79468.4	+	45881.1i	−0.635747	+	0.367049i
$51$	1172.33	−	3220.96i	0.00883772	−	0.0242814i
$52$	44705.4	+	7882.77i	0.317944	+	0.0560620i
$53$	165360.	−	29157.4i	1.11072	−	0.195849i	0.411955	−	0.911204i	$-0.364846\pi$
$53$	165360.	−	29157.4i	1.11072	−	0.195849i	0.698761	+	0.715355i	$0.253735\pi$
$54$	−24826.3	+	9036.05i	−0.157664	+	0.0573849i
$55$	93006.4	+	78041.6i	0.559016	+	0.469071i
$56$		−	106702.i		−	0.607589i
$57$	15094.1	−	16182.5i	0.0815045	−	0.0873818i
$58$	114703.			0.587883
$59$	242346.	−	288817.i	1.17999	−	1.40626i	0.285974	−	0.958237i	$-0.407683\pi$
$59$	242346.	−	288817.i	1.17999	−	1.40626i	0.894021	−	0.448026i	$-0.147873\pi$
$60$	−6301.41	−	17313.0i	−0.0291732	−	0.0801527i
$61$	58721.6	+	333027.i	0.258707	+	1.46720i	0.786375	+	0.617750i	$0.211955\pi$
$61$	58721.6	+	333027.i	0.258707	+	1.46720i	−0.527668	+	0.849451i	$0.676933\pi$
$62$	−37702.1	+	213819.i	−0.158194	+	0.897163i
$63$	398030.	+	144871.i	1.59182	+	0.579376i
$64$	16384.0	+	28377.9i	0.0625000	+	0.108253i
$65$	−219240.	−	126578.i	−0.798325	−	0.460913i
$66$	−9511.82	+	7981.36i	−0.0330850	+	0.0277616i
$67$	−182860.	−	217925.i	−0.607989	−	0.724573i	0.370967	−	0.928646i	$-0.379026\pi$
$67$	−182860.	−	217925.i	−0.607989	−	0.724573i	−0.978956	+	0.204074i	$0.934582\pi$
$68$	16998.6	−	29442.4i	0.0540613	−	0.0936369i
$69$	1003.31	−	579.263i	0.00305414	−	0.00176331i
$70$	−203519.	+	559165.i	−0.593351	+	1.63022i
$71$	−88479.5	−	15601.3i	−0.247211	−	0.0435899i	0.0486695	−	0.998815i	$-0.484502\pi$
$71$	−88479.5	−	15601.3i	−0.247211	−	0.0435899i	−0.295880	+	0.955225i	$0.595613\pi$
$72$	−128103.	+	22588.0i	−0.343211	+	0.0605173i
$73$	59877.8	−	21793.7i	0.153921	−	0.0560225i	−0.263911	−	0.964547i	$-0.585012\pi$
$73$	59877.8	−	21793.7i	0.153921	−	0.0560225i	0.417831	+	0.908525i	$0.362790\pi$
$74$	−308526.	−	258884.i	−0.761372	−	0.638867i
$75$			52335.3i			0.124054i
$76$	175307.	−	132070.i	0.399354	−	0.300860i
$77$	401030.			0.878426
$78$	16642.1	−	19833.2i	0.0350690	−	0.0417936i
$79$	6711.86	+	18440.7i	0.0136132	+	0.0374021i	0.946313	−	0.323251i	$-0.104776\pi$
$79$	6711.86	+	18440.7i	0.0136132	+	0.0374021i	−0.932700	+	0.360653i	$0.882554\pi$
$80$	−31732.2	−	179962.i	−0.0619770	−	0.351489i
$81$	88349.5	−	501055.i	0.166245	−	0.942824i
$82$	−378227.	−	137663.i	−0.685979	−	0.249676i
$83$	−278853.	−	482988.i	−0.487687	−	0.844699i	0.512213	−	0.858859i	$-0.328826\pi$
$83$	−278853.	−	482988.i	−0.487687	−	0.844699i	−0.999900	+	0.0141597i	$0.995493\pi$
$84$	−52703.0	−	30428.1i	−0.0889196	−	0.0513378i
$85$	−145237.	+	121868.i	−0.236494	+	0.198442i
$86$	−529784.	−	631371.i	−0.832920	−	0.992635i
$87$	32709.6	−	56654.8i	0.0496727	−	0.0860357i
$88$	−106656.	+	61577.7i	−0.156508	+	0.0903598i
$89$	3441.94	−	9456.64i	0.00488239	−	0.0134143i	−0.937227	−	0.348719i	$-0.886617\pi$
$89$	3441.94	−	9456.64i	0.00488239	−	0.0134143i	0.942110	+	0.335304i	$0.108839\pi$
$90$	714395.	+	125967.i	0.979966	+	0.172794i
$91$	−823491.	+	145204.i	−1.09279	+	0.192688i
$92$	10797.8	−	3930.08i	0.0138667	−	0.00504705i
$93$	94859.3	+	79596.4i	0.117932	+	0.0989566i
$94$			230828.i			0.277911i
$95$	−1.17059e6	+	357730.i	−1.36531	+	0.417239i
$96$	18688.8			0.0211236
$97$	−187751.	+	223753.i	−0.205715	+	0.245162i	−0.859031	−	0.511924i	$-0.828933\pi$
$97$	−187751.	+	223753.i	−0.205715	+	0.245162i	0.653316	+	0.757086i	$0.273377\pi$
$98$	444618.	+	1.22158e6i	0.472398	+	1.29790i
$99$	−84894.7	−	481462.i	−0.0874933	−	0.496199i
$100$	−90138.2	+	511199.i	−0.0901382	+	0.511199i
$101$	1.70397e6	+	620194.i	1.65386	+	0.601954i	0.989380	−	0.145355i	$-0.0464324\pi$
$101$	1.70397e6	+	620194.i	1.65386	+	0.601954i	0.664476	+	0.747309i	$0.268655\pi$
$102$	−9694.92	−	16792.1i	−0.00913574	−	0.0158236i
$103$	−1.04988e6	−	606148.i	−0.960789	−	0.554712i	−0.0643731	−	0.997926i	$-0.520505\pi$
$103$	−1.04988e6	−	606148.i	−0.960789	−	0.554712i	−0.896416	+	0.443214i	$0.853838\pi$
$104$	196715.	−	165064.i	0.174879	−	0.146741i
$105$	218149.	+	259979.i	0.188445	+	0.224580i
$106$	474924.	−	822592.i	0.398755	−	0.690664i
$107$	693954.	−	400654.i	0.566473	−	0.327053i	−0.189266	−	0.981926i	$-0.560611\pi$
$107$	693954.	−	400654.i	0.566473	−	0.327053i	0.755739	+	0.654872i	$0.227278\pi$
$108$	−51115.6	+	140439.i	−0.0405772	+	0.111485i
$109$	−148261.	−	26142.4i	−0.114485	−	0.0201867i	0.116112	−	0.993236i	$-0.462957\pi$
$109$	−148261.	−	26142.4i	−0.114485	−	0.0201867i	−0.230597	+	0.973049i	$0.574068\pi$
$110$	676371.	−	119263.i	0.508168	−	0.0896037i
$111$	−215851.	+	78563.5i	−0.157829	+	0.0574449i
$112$	−462384.	−	387986.i	−0.329116	−	0.276161i
$113$			1.35895e6i			0.941819i	0.882181	+	0.470910i	$0.156074\pi$
$113$			1.35895e6i			0.941819i	−0.882181	+	0.470910i	$0.843926\pi$
$114$	−15240.9	−	124251.i	−0.0102872	−	0.0838657i
$115$	−64081.1			−0.0421344
$116$	417078.	−	497054.i	0.267204	−	0.318442i
$117$	348652.	+	957914.i	0.217688	+	0.598093i
$118$	−370351.	−	2.10037e6i	−0.225407	−	1.27835i
$119$	−108746.	+	616728.i	−0.0645314	+	0.365976i
$120$	−97937.1	−	35646.2i	−0.0566765	−	0.0206286i
$121$	654347.	+	1.13336e6i	0.369362	+	0.639753i
$122$	1.65666e6	+	956472.i	0.912333	+	0.526736i
$123$	−175854.	+	147559.i	−0.0945010	+	0.0792957i
$124$	789473.	+	940858.i	0.414069	+	0.493468i
$125$	53216.6	−	92173.9i	0.0272469	−	0.0471930i
$126$	2.07509e6	−	1.19805e6i	1.03735	−	0.598913i
$127$	1.25152e6	−	3.43852e6i	0.610978	−	1.67865i	−0.117071	−	0.993124i	$-0.537351\pi$
$127$	1.25152e6	−	3.43852e6i	0.610978	−	1.67865i	0.728049	−	0.685525i	$-0.240427\pi$
$128$	182548.	+	32188.1i	0.0870455	+	0.0153485i
$129$	−462928.	+	81626.7i	−0.215647	+	0.0380245i
$130$	−1.34570e6	+	489797.i	−0.612519	+	0.222939i
$131$	1.34297e6	+	1.12688e6i	0.597381	+	0.501262i	0.890603	−	0.454782i	$-0.150283\pi$
$131$	1.34297e6	+	1.12688e6i	0.597381	+	0.501262i	−0.293222	+	0.956044i	$0.594727\pi$
$132$			70240.0i			0.0305396i
$133$	−2.20241e6	+	3.39053e6i	−0.936146	+	1.44116i
$134$	−1.60926e6			−0.668826
$135$	535735.	−	638464.i	0.217745	−	0.259498i
$136$	−65776.4	−	180719.i	−0.0261489	−	0.0718435i
$137$	−687698.	−	3.90013e6i	−0.267446	−	1.51676i	−0.761979	−	0.647602i	$-0.775772\pi$
$137$	−687698.	−	3.90013e6i	−0.267446	−	1.51676i	0.494533	−	0.869159i	$-0.335339\pi$
$138$	1138.02	−	6454.05i	0.000433026	−	0.00245581i
$139$	−2.41296e6	−	878246.i	−0.898474	−	0.327018i	−0.148833	−	0.988862i	$-0.547552\pi$
$139$	−2.41296e6	−	878246.i	−0.898474	−	0.327018i	−0.749641	+	0.661844i	$0.769774\pi$
$140$	1.68306e6	+	2.91514e6i	0.613359	+	1.06237i
$141$	114012.	+	65824.9i	0.0406718	+	0.0234819i
$142$	−389332.	+	326688.i	−0.135974	+	0.114096i
$143$	620376.	+	739335.i	0.212152	+	0.252833i
$144$	−367919.	+	637254.i	−0.123215	+	0.213415i
$145$	−3.13372e6	+	1.80926e6i	−1.02791	+	0.593466i
$146$	123284.	−	338720.i	0.0396139	−	0.108838i
$147$	730159.	+	128747.i	0.229861	+	0.0405307i
$148$	−2.24370e6	+	395624.i	−0.692117	+	0.122039i
$149$	3.64957e6	−	1.32833e6i	1.10327	−	0.401558i	0.274751	−	0.961515i	$-0.411405\pi$
$149$	3.64957e6	−	1.32833e6i	1.10327	−	0.401558i	0.828522	+	0.559957i	$0.189182\pi$
$150$	226790.	+	190299.i	0.0671970	+	0.0563850i
$151$		−	1.36202e6i		−	0.395596i	−0.980243	−	0.197798i	$-0.936621\pi$
$151$		−	1.36202e6i		−	0.395596i	0.980243	−	0.197798i	$-0.0633790\pi$
$152$	65130.0	−	1.23990e6i	0.0185460	−	0.353067i
$153$	763440.			0.213158
$154$	1.45821e6	−	1.73783e6i	0.399262	−	0.475821i
$155$	−2.34262e6	−	6.43630e6i	−0.629081	−	1.72839i
$156$	−25432.3	−	144234.i	−0.00669902	−	0.0379920i
$157$	−1.18411e6	+	6.71543e6i	−0.305980	+	1.73530i	0.312874	+	0.949795i	$0.398708\pi$
$157$	−1.18411e6	+	6.71543e6i	−0.305980	+	1.73530i	−0.618854	+	0.785506i	$0.712403\pi$
$158$	104316.	+	37968.0i	0.0264473	+	0.00962601i
$159$	−270866.	−	469154.i	−0.0673851	−	0.116714i
$160$	−895232.	−	516863.i	−0.218563	−	0.126187i
$161$	−162145.	+	136055.i	−0.0388530	+	0.0326016i
$162$	−1.85002e6	−	2.20477e6i	−0.435142	−	0.518583i
$163$	−2.60458e6	+	4.51126e6i	−0.601415	+	1.04168i	0.391192	+	0.920309i	$0.372063\pi$
$163$	−2.60458e6	+	4.51126e6i	−0.601415	+	1.04168i	−0.992607	+	0.121372i	$0.961271\pi$
$164$	−1.97184e6	+	1.13844e6i	−0.447034	+	0.258095i
$165$	133973.	−	368087.i	0.0298239	−	0.0819405i
$166$	−3.10693e6	−	547836.i	−0.679216	−	0.119764i
$167$	−3.27731e6	+	577878.i	−0.703668	+	0.124076i	−0.514022	−	0.857777i	$-0.671845\pi$
$167$	−3.27731e6	+	577878.i	−0.703668	+	0.124076i	−0.189646	+	0.981853i	$0.560734\pi$
$168$	−323494.	+	117742.i	−0.0682241	+	0.0248315i
$169$	2.15595e6	+	1.80906e6i	0.446662	+	0.374794i
$170$			1.07250e6i			0.218299i
$171$	4.53677e6	+	1.92639e6i	0.907315	+	0.385261i
$172$	−4.66236e6			−0.916264
$173$	6.06398e6	−	7.22677e6i	1.17117	−	1.39574i	0.269674	−	0.962952i	$-0.413084\pi$
$173$	6.06398e6	−	7.22677e6i	1.17117	−	1.39574i	0.901494	−	0.432792i	$-0.142472\pi$
$174$	−126571.	−	347750.i	−0.0240262	−	0.0660114i
$175$	−1.66038e6	−	9.41649e6i	−0.309809	−	1.75701i
$176$	−120976.	+	686088.i	−0.0221902	+	0.125847i
$177$	−1.14304e6	−	416032.i	−0.206130	−	0.0750251i
$178$	−28464.0	−	49301.1i	−0.00504703	−	0.00874172i
$179$	1.02121e6	+	589596.i	0.178056	+	0.102801i	0.586379	−	0.810037i	$-0.300553\pi$
$179$	1.02121e6	+	589596.i	0.178056	+	0.102801i	−0.408323	+	0.912837i	$0.633886\pi$
$180$	3.14352e6	−	2.63772e6i	0.539012	−	0.452285i
$181$	−4.30990e6	−	5.13634e6i	−0.726828	−	0.866200i	0.268447	−	0.963295i	$-0.413490\pi$
$181$	−4.30990e6	−	5.13634e6i	−0.726828	−	0.866200i	−0.995275	+	0.0970941i	$0.969045\pi$
$182$	−2.36512e6	+	4.09650e6i	−0.392318	+	0.679515i
$183$	944853.	−	545511.i	0.154174	−	0.0890123i
$184$	22231.9	−	61081.6i	0.00356881	−	0.00980521i
$185$	1.25125e7	+	2.20629e6i	1.97619	+	0.348456i
$186$	689846.	−	121639.i	0.107205	−	0.0189031i
$187$	679215.	−	247214.i	0.103868	−	0.0378049i
$188$	1.00027e6	+	839328.i	0.150538	+	0.126316i
$189$		−	2.75296e6i		−	0.407770i
$190$	−2.70624e6	+	6.37338e6i	−0.394554	+	0.929200i
$191$	−3.87100e6			−0.555550			−0.277775	−	0.960646i	$-0.589597\pi$
$191$	−3.87100e6			−0.555550			−0.277775	+	0.960646i	$0.589597\pi$
$192$	67955.3	−	80986.0i	0.00960107	−	0.0114421i
$193$	3.61567e6	+	9.93397e6i	0.502941	+	1.38182i	0.888390	+	0.459090i	$0.151824\pi$
$193$	3.61567e6	+	9.93397e6i	0.502941	+	1.38182i	−0.385449	+	0.922729i	$0.625953\pi$
$194$	286919.	+	1.62720e6i	0.0392965	+	0.222862i
$195$	−141829.	+	804353.i	−0.0191276	+	0.108478i
$196$	6.91028e6	+	2.51514e6i	0.917756	+	0.334036i
$197$	−317451.	−	549842.i	−0.0415220	−	0.0719182i	0.844518	−	0.535528i	$-0.179887\pi$
$197$	−317451.	−	549842.i	−0.0415220	−	0.0719182i	−0.886040	+	0.463610i	$0.846554\pi$
$198$	−2.39506e6	−	1.38279e6i	−0.308546	−	0.178139i
$199$	−4.99212e6	+	4.18888e6i	−0.633469	+	0.531544i	−0.902005	−	0.431726i	$-0.857905\pi$
$199$	−4.99212e6	+	4.18888e6i	−0.633469	+	0.531544i	0.268536	+	0.963270i	$0.413460\pi$
$200$	1.88747e6	+	2.24940e6i	0.235934	+	0.281176i
$201$	−458911.	+	794857.i	−0.0565119	+	0.0978815i
$202$	8.88345e6	−	5.12886e6i	1.07777	−	0.622253i
$203$	−4.08790e6	+	1.12314e7i	−0.488666	+	1.34260i
$204$	−108019.	−	19046.7i	−0.0127236	−	0.00224351i
$205$	1.25047e7	−	2.20492e6i	1.45148	−	0.255935i
$206$	−6.44421e6	+	2.34550e6i	−0.737171	+	0.268308i
$207$	197668.	+	165863.i	0.0222856	+	0.0186998i
$208$		−	1.45264e6i		−	0.161424i
$209$	4.66005e6	+	244785.i	0.510449	+	0.0268130i
$210$	1.91982e6			0.207301
$211$	1.52994e6	−	1.82331e6i	0.162864	−	0.194094i	−0.678440	−	0.734656i	$-0.737344\pi$
$211$	1.52994e6	−	1.82331e6i	0.162864	−	0.194094i	0.841305	+	0.540561i	$0.181788\pi$
$212$	−1.83773e6	−	5.04911e6i	−0.192874	−	0.529916i
$213$	50334.7	+	285462.i	0.00520869	+	0.0295400i
$214$	787128.	−	4.46402e6i	0.0803163	−	0.455497i
$215$	2.44327e7	+	8.89279e6i	2.45842	+	0.894793i
$216$	422714.	+	732162.i	0.0419455	+	0.0726518i
$217$	−1.95929e7	−	1.13120e7i	−1.91743	−	1.10703i
$218$	−652385.	+	547416.i	−0.0629701	+	0.0528382i
$219$	−132146.	−	157485.i	−0.0125812	−	0.0149936i
$220$	1.94258e6	−	3.36465e6i	0.182436	−	0.315988i
$221$	−1.30522e6	+	753567.i	−0.120922	+	0.0698144i
$222$	−444422.	+	1.22104e6i	−0.0406197	+	0.111602i
$223$	3.71816e6	+	655612.i	0.335284	+	0.0591197i	0.338756	−	0.940874i	$-0.389994\pi$
$223$	3.71816e6	+	655612.i	0.335284	+	0.0591197i	−0.00347153	+	0.999994i	$0.501105\pi$
$224$	−3.36260e6	+	592917.i	−0.299179	+	0.0527533i
$225$	−1.09536e7	+	3.98678e6i	−0.961631	+	0.350005i
$226$	5.88887e6	+	4.94135e6i	0.510160	+	0.428075i
$227$			1.75027e6i			0.149633i	0.997197	+	0.0748167i	$0.0238372\pi$
$227$			1.75027e6i			0.149633i	−0.997197	+	0.0748167i	$0.976163\pi$
$228$	−593847.	−	385750.i	−0.0501037	−	0.0325463i
$229$	−1.62643e7			−1.35434			−0.677171	−	0.735826i	$-0.736794\pi$
$229$	−1.62643e7			−1.35434			−0.677171	+	0.735826i	$0.736794\pi$
$230$	−233009.	+	277689.i	−0.0191509	+	0.0228231i
$231$	−442522.	−	1.21582e6i	−0.0359004	−	0.0986355i
$232$	−637375.	−	3.61473e6i	−0.0510424	−	0.289476i
$233$	317892.	−	1.80286e6i	0.0251311	−	0.142526i	−0.969660	−	0.244456i	$-0.921391\pi$
$233$	317892.	−	1.80286e6i	0.0251311	−	0.142526i	0.994792	+	0.101930i	$0.0325018\pi$
$234$	5.41878e6	+	1.97227e6i	0.422916	+	0.153929i
$235$	−3.64095e6	−	6.30631e6i	−0.280550	−	0.485928i
$236$	−1.04484e7	−	6.03238e6i	−0.794901	−	0.458937i
$237$	48501.0	−	40697.2i	0.00364339	−	0.00305717i
$238$	2.27711e6	+	2.71376e6i	0.168909	+	0.201298i
$239$	−1.99867e6	+	3.46181e6i	−0.146402	+	0.253576i	−0.929895	−	0.367824i	$-0.880103\pi$
$239$	−1.99867e6	+	3.46181e6i	−0.146402	+	0.253576i	0.783493	+	0.621401i	$0.213436\pi$
$240$	−510584.	+	294786.i	−0.0369346	+	0.0213242i
$241$	−4.16588e6	+	1.14457e7i	−0.297616	+	0.817692i	0.697282	+	0.716797i	$0.254393\pi$
$241$	−4.16588e6	+	1.14457e7i	−0.297616	+	0.817692i	−0.994897	+	0.100895i	$0.967829\pi$
$242$	7.29062e6	+	1.28553e6i	0.514420	+	0.0907062i
$243$	−4.96954e6	+	876264.i	−0.346336	+	0.0610683i
$244$	1.01686e7	−	3.70109e6i	0.699993	−	0.254777i
$245$	−3.14155e7	−	2.63607e7i	−2.13622	−	1.79250i
$246$			1.29859e6i			0.0872303i
$247$	−9.65777e6	+	1.18465e6i	−0.640893	+	0.0786136i
$248$	6.94776e6			0.455502
$249$	−1.15659e6	+	1.37837e6i	−0.0749171	+	0.0892827i
$250$	−205923.	−	565768.i	−0.0131790	−	0.0362091i
$251$	−2.11484e6	−	1.19938e7i	−0.133738	−	0.758468i	−0.975730	−	0.218977i	$-0.929728\pi$
$251$	−2.11484e6	−	1.19938e7i	−0.133738	−	0.758468i	0.841992	−	0.539491i	$-0.181383\pi$
$252$	2.35370e6	−	1.33485e7i	0.147078	−	0.834123i
$253$	229569.	+	83556.4i	0.0141760	+	0.00515963i
$254$	−1.03498e7	−	1.79263e7i	−0.631581	−	1.09393i
$255$	529737.	+	305844.i	0.0319477	+	0.0184450i
$256$	803256.	−	674012.i	0.0478778	−	0.0401742i
$257$	−5.20532e6	−	6.20346e6i	−0.306653	−	0.365455i	0.590605	−	0.806961i	$-0.298889\pi$
$257$	−5.20532e6	−	6.20346e6i	−0.306653	−	0.365455i	−0.897259	+	0.441505i	$0.854445\pi$
$258$	−1.32956e6	+	2.30286e6i	−0.0774191	+	0.134094i
$259$	3.63448e7	−	2.09837e7i	2.09191	−	1.20776i
$260$	−2.77071e6	+	7.61246e6i	−0.157642	+	0.433117i
$261$	1.43494e7	+	2.53018e6i	0.807071	+	0.142308i
$262$	9.76647e6	−	1.72209e6i	0.543043	−	0.0957531i
$263$	−2.19448e7	+	7.98726e6i	−1.20633	+	0.439067i	−0.865428	−	0.501034i	$-0.832953\pi$
$263$	−2.19448e7	+	7.98726e6i	−1.20633	+	0.439067i	−0.340898	+	0.940100i	$0.610731\pi$
$264$	304378.	+	255404.i	0.0165425	+	0.0138808i
$265$			2.99647e7i			1.61017i
$266$	6.68420e6	+	2.18724e7i	0.355144	+	1.16212i
$267$	−32468.1			−0.00170578
$268$	−5.85153e6	+	6.97359e6i	−0.303994	+	0.362286i
$269$	−8.81958e6	−	2.42316e7i	−0.453097	−	1.24487i	−0.930533	−	0.366207i	$-0.880656\pi$
$269$	−8.81958e6	−	2.42316e7i	−0.453097	−	1.24487i	0.477436	−	0.878666i	$-0.341566\pi$
$270$	−818705.	−	4.64311e6i	−0.0415945	−	0.235894i
$271$	−3.70545e6	+	2.10146e7i	−0.186180	+	1.05588i	0.738250	+	0.674527i	$0.235652\pi$
$271$	−3.70545e6	+	2.10146e7i	−0.186180	+	1.05588i	−0.924430	+	0.381352i	$0.875459\pi$
$272$	−1.02230e6	−	372087.i	−0.0508010	−	0.0184901i
$273$	1.34891e6	+	2.33638e6i	0.0662973	+	0.114830i
$274$	−1.94014e7	−	1.12014e7i	−0.943151	−	0.544528i
$275$	−8.45417e6	+	7.09389e6i	−0.406512	+	0.341104i
$276$	−23830.0	−	28399.4i	−0.00113343	−	0.00135077i
$277$	−1.02150e7	+	1.76929e7i	−0.480618	+	0.832455i	−0.999753	−	0.0222378i	$-0.992921\pi$
$277$	−1.02150e7	+	1.76929e7i	−0.480618	+	0.832455i	0.519135	+	0.854692i	$0.326254\pi$
$278$	−1.25797e7	+	7.26289e6i	−0.585512	+	0.338045i
$279$	−9.43308e6	+	2.59172e7i	−0.434351	+	1.19337i
$280$	1.87523e7	+	3.30654e6i	0.854243	+	0.150626i
$281$	3.47226e7	−	6.12253e6i	1.56492	−	0.275938i	0.677020	−	0.735965i	$-0.263271\pi$
$281$	3.47226e7	−	6.12253e6i	1.56492	−	0.275938i	0.887905	+	0.460027i	$0.152160\pi$
$282$	699812.	−	254711.i	0.0312057	−	0.0113579i
$283$	7.83673e6	+	6.57580e6i	0.345761	+	0.290128i	0.799085	−	0.601218i	$-0.205318\pi$
$283$	7.83673e6	+	6.57580e6i	0.345761	+	0.290128i	−0.453324	+	0.891346i	$0.649762\pi$
$284$			2.87502e6i			0.125512i
$285$	2.37624e6	+	3.15417e6i	0.102649	+	0.136254i
$286$	5.45962e6			0.233380
$287$	2.69593e7	−	3.21288e7i	1.14041	−	1.35909i
$288$	1.42367e6	+	3.91149e6i	0.0595979	+	0.163744i
$289$	−3.99544e6	−	2.26593e7i	−0.165528	−	0.938756i
$290$	−3.55447e6	+	2.01584e7i	−0.145741	+	0.826537i
$291$	885535.	+	322308.i	0.0359358	+	0.0130795i
$292$	−1.01953e6	−	1.76588e6i	−0.0409497	−	0.0709270i
$293$	1.51057e6	+	872129.i	0.0600535	+	0.0346719i	0.529726	−	0.848169i	$-0.322295\pi$
$293$	1.51057e6	+	872129.i	0.0600535	+	0.0346719i	−0.469673	+	0.882841i	$0.655628\pi$
$294$	3.21288e6	−	2.69593e6i	0.126431	−	0.106088i
$295$	4.32480e7	+	5.15410e7i	1.68461	+	2.00764i
$296$	−6.44404e6	+	1.11614e7i	−0.248475	+	0.430371i
$297$	−2.75176e6	+	1.58873e6i	−0.105037	+	0.0606430i
$298$	7.51420e6	−	2.06451e7i	0.283945	−	0.780132i
$299$	−501661.	−	88456.3i	−0.0187671	−	0.00330914i
$300$	1.64929e6	−	290814.i	0.0610847	−	0.0107709i
$301$	8.07032e7	−	2.93736e7i	2.95931	−	1.07710i
$302$	−5.90217e6	−	4.95251e6i	−0.214285	−	0.179806i
$303$		−	5.85035e6i		−	0.210307i
$304$	−5.13617e6	−	4.79071e6i	−0.182818	−	0.170522i
$305$	−6.03473e7			−2.12695
$306$	2.77599e6	−	3.30829e6i	0.0968842	−	0.115462i
$307$	−9.84543e6	−	2.70501e7i	−0.340267	−	0.934876i	−0.985317	−	0.170735i	$-0.945386\pi$
$307$	−9.84543e6	−	2.70501e7i	−0.340267	−	0.934876i	0.645050	−	0.764140i	$-0.276836\pi$
$308$	−2.22842e6	−	1.26380e7i	−0.0762685	−	0.432540i
$309$	−679180.	+	3.85182e6i	−0.0230202	+	0.130554i
$310$	−3.64092e7	−	1.32519e7i	−1.22215	−	0.444828i
$311$	−887492.	−	1.53718e6i	−0.0295042	−	0.0511027i	0.850896	−	0.525334i	$-0.176059\pi$
$311$	−887492.	−	1.53718e6i	−0.0295042	−	0.0511027i	−0.880400	+	0.474231i	$0.842726\pi$
$312$	−717497.	−	414247.i	−0.0236242	−	0.0136394i
$313$	3.72717e7	−	3.12747e7i	1.21548	−	1.01991i	0.216427	−	0.976299i	$-0.430560\pi$
$313$	3.72717e7	−	3.12747e7i	1.21548	−	1.01991i	0.999049	−	0.0436067i	$-0.0138849\pi$
$314$	2.47950e7	+	2.95496e7i	0.800895	+	0.954470i
$315$	−3.77947e7	+	6.54623e7i	−1.20920	+	2.09440i
$316$	543841.	−	313987.i	0.0172350	−	0.00995061i
$317$	4.11342e6	−	1.13015e7i	0.129129	−	0.354780i	−0.858233	−	0.513261i	$-0.828437\pi$
$317$	4.11342e6	−	1.13015e7i	0.129129	−	0.354780i	0.987362	+	0.158481i	$0.0506596\pi$
$318$	−3.01795e6	−	532145.i	−0.0938491	−	0.0165481i
$319$	1.35856e7	−	2.39551e6i	0.418512	−	0.0737949i
$320$	−5.49498e6	+	2.00001e6i	−0.167693	+	0.0610354i
$321$	−1.98043e6	−	1.66178e6i	−0.0598749	−	0.0502410i
$322$			1.19736e6i			0.0358638i
$323$	−1.64009e6	+	7.10012e6i	−0.0486699	+	0.210697i
$324$	−1.62811e7			−0.478684
$325$	1.47916e7	−	1.76279e7i	0.430888	−	0.513513i
$326$	1.00784e7	+	2.76903e7i	0.290898	+	0.799236i
$327$	84343.4	+	478335.i	0.00241217	+	0.0136801i
$328$	−2.23659e6	+	1.26843e7i	−0.0633819	+	0.359457i
$329$	−2.26021e7	−	8.22649e6i	−0.634689	−	0.231008i
$330$	−1.10792e6	−	1.91898e6i	−0.0308296	−	0.0533984i
$331$	2.88624e7	+	1.66637e7i	0.795881	+	0.459502i	0.842029	−	0.539433i	$-0.181361\pi$
$331$	2.88624e7	+	1.66637e7i	0.795881	+	0.459502i	−0.0461479	+	0.998935i	$0.514695\pi$
$332$	−1.36713e7	+	1.14716e7i	−0.373590	+	0.313479i
$333$	−3.28861e7	−	3.91921e7i	−0.890593	−	1.06137i
$334$	−9.41262e6	+	1.63031e7i	−0.252622	+	0.437554i
$335$	4.39656e7	−	2.53836e7i	1.16944	−	0.675178i
$336$	−666049.	+	1.82996e6i	−0.0175585	+	0.0482417i
$337$	−1.09236e7	−	1.92613e6i	−0.285415	−	0.0503263i	0.0291080	−	0.999576i	$-0.490733\pi$
$337$	−1.09236e7	−	1.92613e6i	−0.285415	−	0.0503263i	−0.314523	+	0.949250i	$0.601844\pi$
$338$	1.56787e7	−	2.76459e6i	0.406033	−	0.0715946i
$339$	4.11998e6	−	1.49955e6i	0.105754	−	0.0384912i
$340$	4.64759e6	+	3.89979e6i	0.118247	+	0.0992211i
$341$			2.61125e7i			0.658545i
$342$	2.48442e7	−	1.26550e7i	0.621079	−	0.316361i
$343$	−6.61108e7			−1.63829
$344$	−1.69531e7	+	2.02039e7i	−0.416460	+	0.496317i
$345$	70711.1	+	194277.i	0.00172199	+	0.00473113i
$346$	−9.26692e6	−	5.25553e7i	−0.223721	−	1.26879i
$347$	3.78324e6	−	2.14558e7i	0.0905473	−	0.513519i	−0.905474	−	0.424402i	$-0.860484\pi$
$347$	3.78324e6	−	2.14558e7i	0.0905473	−	0.513519i	0.996021	−	0.0891173i	$-0.0284046\pi$
$348$	−1.96717e6	−	715991.i	−0.0466771	−	0.0169891i
$349$	3.05395e6	+	5.28961e6i	0.0718433	+	0.124436i	0.899709	−	0.436490i	$-0.143779\pi$
$349$	3.05395e6	+	5.28961e6i	0.0718433	+	0.124436i	−0.827866	+	0.560926i	$0.810445\pi$
$350$	−4.68428e7	−	2.70447e7i	−1.09254	−	0.630781i
$351$	5.07533e6	−	4.25871e6i	0.117366	−	0.0984820i
$352$	2.53321e6	+	3.01896e6i	0.0580822	+	0.0692196i
$353$	−1.25658e7	+	2.17646e7i	−0.285670	+	0.494796i	−0.972772	−	0.231766i	$-0.925550\pi$
$353$	−1.25658e7	+	2.17646e7i	−0.285670	+	0.494796i	0.687101	+	0.726562i	$0.258883\pi$
$354$	−5.95909e6	+	3.44049e6i	−0.134329	+	0.0775550i
$355$	5.48369e6	−	1.50663e7i	0.122571	−	0.336761i
$356$	−317141.	−	55920.6i	−0.00702915	−	0.00123943i
$357$	1.98975e6	−	350847.i	0.0437315	−	0.00771105i
$358$	6.26823e6	−	2.28145e6i	0.136614	−	0.0497235i
$359$	1.82257e6	+	1.52932e6i	0.0393913	+	0.0330533i	0.662271	−	0.749265i	$-0.269593\pi$
$359$	1.82257e6	+	1.52932e6i	0.0393913	+	0.0330533i	−0.622879	+	0.782318i	$0.714037\pi$
$360$		−	2.32133e7i		−	0.497542i
$361$	−2.76620e7	+	3.80543e7i	−0.587980	+	0.808876i
$362$	−3.79293e7			−0.799557
$363$	2.71401e6	−	3.23443e6i	0.0567403	−	0.0676204i
$364$	9.15186e6	+	2.51445e7i	0.189760	+	0.521362i
$365$	1.97460e6	+	1.11985e7i	0.0406071	+	0.230294i
$366$	1.07171e6	−	6.07799e6i	0.0218593	−	0.123970i
$367$	−3.65290e7	−	1.32955e7i	−0.738991	−	0.268971i	−0.0550254	−	0.998485i	$-0.517524\pi$
$367$	−3.65290e7	−	1.32955e7i	−0.738991	−	0.268971i	−0.683966	+	0.729514i	$0.739746\pi$
$368$	−183853.	−	318442.i	−0.00368915	−	0.00638979i
$369$	−4.42796e7	−	2.55649e7i	−0.881302	−	0.508820i
$370$	5.50582e7	−	4.61993e7i	1.08697	−	0.912075i
$371$	6.36203e7	+	7.58197e7i	1.24587	+	1.48477i
$372$	1.98128e6	−	3.43168e6i	0.0384873	−	0.0666619i
$373$	1.31344e7	−	7.58313e6i	0.253095	−	0.146124i	−0.368086	−	0.929792i	$-0.619987\pi$
$373$	1.31344e7	−	7.58313e6i	0.253095	−	0.146124i	0.621180	+	0.783668i	$0.286653\pi$
$374$	1.39845e6	−	3.84222e6i	0.0267321	−	0.0734459i
$375$	−338170.	−	59628.5i	−0.00641270	−	0.00113073i
$376$	7.27429e6	−	1.28265e6i	0.136844	−	0.0241294i
$377$	−2.70299e7	+	9.83808e6i	−0.504453	+	0.183606i
$378$	−1.19297e7	−	1.00102e7i	−0.220879	−	0.185339i
$379$			5.11780e7i			0.940081i	0.882645	+	0.470041i	$0.155761\pi$
$379$			5.11780e7i			0.940081i	−0.882645	+	0.470041i	$0.844239\pi$
$380$	1.77781e7	+	3.49019e7i	0.323992	+	0.636059i
$381$	−1.18057e7			−0.213460
$382$	−1.40756e7	+	1.67746e7i	−0.252508	+	0.300928i
$383$	−3.56258e7	−	9.78812e7i	−0.634116	−	1.74222i	−0.669463	−	0.742845i	$-0.733476\pi$
$383$	−3.56258e7	−	9.78812e7i	−0.634116	−	1.74222i	0.0353471	−	0.999375i	$-0.488746\pi$
$384$	−103849.	−	588955.i	−0.00183403	−	0.0104013i
$385$	−1.24273e7	+	7.04789e7i	−0.217769	+	1.23503i
$386$	5.61950e7	+	2.04533e7i	0.977093	+	0.355633i
$387$	−5.23489e7	−	9.06710e7i	−0.903181	−	1.56436i
$388$	8.09458e6	+	4.67341e6i	0.138580	+	0.0800090i
$389$	1.38097e7	−	1.15877e7i	0.234604	−	0.196856i	−0.517905	−	0.855438i	$-0.673288\pi$
$389$	1.38097e7	−	1.15877e7i	0.234604	−	0.196856i	0.752509	+	0.658582i	$0.228843\pi$
$390$	2.96987e6	+	3.53935e6i	0.0500661	+	0.0596664i
$391$	−190749.	+	330387.i	−0.00319104	+	0.00552705i
$392$	3.60260e7	−	2.07996e7i	0.598077	−	0.345300i
$393$	1.93450e6	−	5.31500e6i	0.0318707	−	0.0875640i
$394$	−3.53699e6	−	623666.i	−0.0578289	−	0.0101968i
$395$	−3.44884e6	+	608123.i	−0.0559605	+	0.00986734i
$396$	−1.47010e7	+	5.35072e6i	−0.236734	+	0.0861641i
$397$	−1.30681e7	−	1.09654e7i	−0.208853	−	0.175248i	0.532361	−	0.846518i	$-0.321305\pi$
$397$	−1.30681e7	−	1.09654e7i	−0.208853	−	0.175248i	−0.741214	+	0.671269i	$0.765749\pi$
$398$			3.68643e7i			0.584732i
$399$	1.27095e7	+	2.93582e6i	0.200082	+	0.0462180i
$400$	1.66107e7			0.259543
$401$	−5.12465e7	+	6.10732e7i	−0.794752	+	0.947148i	−0.999498	−	0.0316669i	$-0.989918\pi$
$401$	−5.12465e7	+	6.10732e7i	−0.794752	+	0.947148i	0.204747	+	0.978815i	$0.434363\pi$
$402$	1.77576e6	+	4.87887e6i	0.0273342	+	0.0751002i
$403$	−9.45473e6	−	5.36204e7i	−0.144455	−	0.819247i
$404$	1.00762e7	−	5.71449e7i	0.152810	−	0.866629i
$405$	8.53199e7	+	3.10539e7i	1.28435	+	0.467467i
$406$	3.38060e7	+	5.85537e7i	0.505144	+	0.874936i
$407$	−4.19490e7	−	2.42193e7i	−0.622213	−	0.359235i
$408$	−475311.	+	398834.i	−0.00699838	+	0.00587234i
$409$	−6.15858e7	−	7.33950e7i	−0.900141	−	1.07275i	−0.996996	−	0.0774474i	$-0.975323\pi$
$409$	−6.15858e7	−	7.33950e7i	−0.900141	−	1.07275i	0.0968558	−	0.995298i	$-0.469121\pi$
$410$	3.59143e7	−	6.22053e7i	0.521093	−	0.902560i
$411$	−1.10653e7	+	6.38856e6i	−0.159382	+	0.0920191i
$412$	−1.32682e7	+	3.64540e7i	−0.189723	+	0.521258i
$413$	2.18861e8	+	3.85911e7i	3.10684	+	0.547820i
$414$	1.43750e6	−	253470.i	0.0202585	−	0.00357212i
$415$	9.35237e7	−	3.40398e7i	1.30851	−	0.476259i
$416$	−6.29488e6	−	5.28203e6i	−0.0874395	−	0.0733705i
$417$			8.28458e6i			0.114252i
$418$	1.80054e7	−	1.93038e7i	0.246533	−	0.264310i
$419$	4.43672e7			0.603143			0.301572	−	0.953444i	$-0.402489\pi$
$419$	4.43672e7			0.603143			0.301572	+	0.953444i	$0.402489\pi$
$420$	6.98076e6	−	8.31934e6i	0.0942225	−	0.112290i
$421$	3.75411e6	+	1.03143e7i	0.0503108	+	0.138228i	0.962303	−	0.271980i	$-0.0876784\pi$
$421$	3.75411e6	+	1.03143e7i	0.0503108	+	0.138228i	−0.911992	+	0.410208i	$0.865456\pi$
$422$	−2.33804e6	−	1.32597e7i	−0.0311110	−	0.176439i
$423$	−5.09174e6	+	2.88767e7i	−0.0672737	+	0.381528i
$424$	−2.85621e7	−	1.03957e7i	−0.374707	−	0.136382i
$425$	−8.61692e6	−	1.49249e7i	−0.112250	−	0.194422i
$426$	1.42005e6	+	819865.i	0.0183685	+	0.0106051i
$427$	−1.52697e8	+	1.28128e8i	−1.96131	+	1.64574i
$428$	−1.64823e7	−	1.96428e7i	−0.210226	−	0.250537i
$429$	1.55691e6	−	2.69665e6i	0.0197193	−	0.0341548i
$430$	1.27377e8	−	7.35413e7i	1.60209	−	0.924966i
$431$	−4.93614e7	+	1.35619e8i	−0.616532	+	1.69391i	0.0987859	+	0.995109i	$0.468504\pi$
$431$	−4.93614e7	+	1.35619e8i	−0.616532	+	1.69391i	−0.715318	+	0.698799i	$0.753718\pi$
$432$	4.70981e6	+	830466.i	0.0584187	+	0.0103008i
$433$	5.94745e7	−	1.04870e7i	0.732601	−	0.129177i	0.205111	−	0.978739i	$-0.434244\pi$
$433$	5.94745e7	−	1.04870e7i	0.732601	−	0.129177i	0.527490	+	0.849561i	$0.323133\pi$
$434$	−1.20262e8	+	4.37719e7i	−1.47116	+	0.535459i
$435$	8.94314e6	+	7.50419e6i	0.108648	+	0.0911666i
$436$			4.81754e6i			0.0581253i
$437$	−1.96720e6	+	1.48202e6i	−0.0235724	+	0.0177587i
$438$	−1.16295e6			−0.0138401
$439$	2.17229e7	−	2.58884e7i	0.256758	−	0.305993i	−0.622231	−	0.782833i	$-0.713774\pi$
$439$	2.17229e7	−	2.58884e7i	0.256758	−	0.305993i	0.878990	+	0.476841i	$0.158218\pi$
$440$	−7.51684e6	−	2.06524e7i	−0.0882424	−	0.242444i
$441$	2.86756e7	+	1.62627e8i	0.334346	+	1.89617i
$442$	−1.48046e6	+	8.39612e6i	−0.0171447	+	0.0972325i
$443$	1.16213e8	+	4.22982e7i	1.33673	+	0.486532i	0.908783	−	0.417270i	$-0.137013\pi$
$443$	1.16213e8	+	4.22982e7i	1.33673	+	0.486532i	0.427952	+	0.903802i	$0.359235\pi$
$444$	3.67527e6	+	6.36575e6i	0.0419894	+	0.0727278i
$445$	1.55529e6	+	897949.i	0.0176495	+	0.0101899i
$446$	1.63608e7	−	1.37284e7i	0.184417	−	0.154744i
$447$	−8.05433e6	−	9.59878e6i	−0.0901793	−	0.107471i
$448$	−9.65759e6	+	1.67274e7i	−0.107408	+	0.186035i
$449$	−1.10030e8	+	6.35259e7i	−1.21555	+	0.701798i	−0.963963	−	0.266037i	$-0.914286\pi$
$449$	−1.10030e8	+	6.35259e7i	−1.21555	+	0.701798i	−0.251587	+	0.967835i	$0.580952\pi$
$450$	−2.25526e7	+	6.19628e7i	−0.247491	+	0.679976i
$451$	−4.76729e7	−	8.40602e6i	−0.519687	−	0.0916348i
$452$	4.28257e7	−	7.55133e6i	0.463756	−	0.0817726i
$453$	−4.12928e6	+	1.50294e6i	−0.0444201	+	0.0161676i
$454$	7.58464e6	+	6.36427e6i	0.0810527	+	0.0680113i
$455$		−	1.49224e8i		−	1.58418i
$456$	−3.83093e6	+	1.17073e6i	−0.0404026	+	0.0123470i
$457$	−2.95265e7			−0.309360			−0.154680	−	0.987965i	$-0.549435\pi$
$457$	−2.95265e7			−0.309360			−0.154680	+	0.987965i	$0.549435\pi$
$458$	−5.91394e7	+	7.04796e7i	−0.615575	+	0.733613i
$459$	−1.69706e6	−	4.66263e6i	−0.0175493	−	0.0482162i
$460$	356082.	+	2.01944e6i	0.00365828	+	0.0207471i
$461$	−2.65596e6	+	1.50627e7i	−0.0271093	+	0.153744i	−0.995358	−	0.0962461i	$-0.969316\pi$
$461$	−2.65596e6	+	1.50627e7i	−0.0271093	+	0.153744i	0.968248	+	0.249991i	$0.0804275\pi$
$462$	−6.87771e6	−	2.50328e6i	−0.0697458	−	0.0253854i
$463$	−6.40656e7	−	1.10965e8i	−0.645478	−	1.11800i	−0.984191	−	0.177111i	$-0.943325\pi$
$463$	−6.40656e7	−	1.10965e8i	−0.645478	−	1.11800i	0.338712	−	0.940890i	$-0.390009\pi$
$464$	−1.79817e7	−	1.03817e7i	−0.180002	−	0.103924i
$465$	−1.69282e7	+	1.42044e7i	−0.168365	+	0.141275i
$466$	−6.65659e6	−	7.93302e6i	−0.0657800	−	0.0783936i
$467$	6.74117e7	−	1.16760e8i	0.661888	−	1.14642i	−0.318231	−	0.948013i	$-0.603089\pi$
$467$	6.74117e7	−	1.16760e8i	0.661888	−	1.14642i	0.980119	−	0.198410i	$-0.0635779\pi$
$468$	2.82502e7	−	1.63102e7i	0.275603	−	0.159119i
$469$	5.73526e7	−	1.57575e8i	0.555948	−	1.52745i
$470$	−4.05668e7	−	7.15303e6i	−0.390731	−	0.0688964i
$471$	2.16660e7	−	3.82031e6i	0.207356	−	0.0365625i
$472$	−6.41327e7	+	2.33424e7i	−0.609893	+	0.221983i
$473$	−7.59344e7	−	6.37165e7i	−0.717555	−	0.602100i
$474$		−	358156.i		−	0.00336308i
$475$	−1.35462e7	−	1.10435e8i	−0.126397	−	1.03045i
$476$	2.00397e7			0.185811
$477$	7.75583e7	−	9.24304e7i	0.714617	−	0.851647i
$478$	7.73390e6	+	2.12487e7i	0.0708133	+	0.194558i
$479$	−1.16091e7	−	6.58385e7i	−0.105631	−	0.599064i	−0.990966	−	0.134111i	$-0.957182\pi$
$479$	−1.16091e7	−	6.58385e7i	−0.105631	−	0.599064i	0.885335	−	0.464953i	$-0.153929\pi$
$480$	−579137.	+	3.28445e6i	−0.00523670	+	0.0296988i
$481$	9.49090e7	+	3.45441e7i	0.852849	+	0.310412i
$482$	3.44509e7	+	5.96706e7i	0.307651	+	0.532868i
$483$	591405.	+	341448.i	0.00524860	+	0.00303028i
$484$	3.20806e7	−	2.69188e7i	0.282947	−	0.237421i
$485$	−3.35052e7	−	3.99299e7i	−0.293688	−	0.350004i
$486$	−1.42728e7	+	2.47212e7i	−0.124337	+	0.215358i
$487$	−1.22013e8	+	7.04443e7i	−1.05638	+	0.609901i	−0.924428	−	0.381356i	$-0.875457\pi$
$487$	−1.22013e8	+	7.04443e7i	−1.05638	+	0.609901i	−0.131951	+	0.991256i	$0.542124\pi$
$488$	2.09365e7	−	5.75226e7i	0.180154	−	0.494970i
$489$	1.65510e7	+	2.91839e6i	0.141546	+	0.0249584i
$490$	−2.28463e8	+	4.02843e7i	−1.94191	+	0.342411i
$491$	−8.95961e7	+	3.26103e7i	−0.756910	+	0.275493i	−0.691511	−	0.722366i	$-0.743054\pi$
$491$	−8.95961e7	+	3.26103e7i	−0.756910	+	0.275493i	−0.0653998	+	0.997859i	$0.520832\pi$
$492$	5.62732e6	+	4.72188e6i	0.0472505	+	0.0396479i
$493$			2.15423e7i			0.179785i
$494$	−2.99836e7	+	4.61585e7i	−0.248715	+	0.382888i
$495$	8.72450e7			0.719324
$496$	2.52631e7	−	3.01074e7i	0.207034	−	0.246734i
$497$	−1.81131e7	−	4.97652e7i	−0.147544	−	0.405375i
$498$	1.76749e6	+	1.00239e7i	0.0143110	+	0.0811615i
$499$	−1.04230e7	+	5.91120e7i	−0.0838866	+	0.475745i	0.913705	+	0.406379i	$0.133209\pi$
$499$	−1.04230e7	+	5.91120e7i	−0.0838866	+	0.475745i	−0.997591	+	0.0693657i	$0.977902\pi$
$500$	−3.20046e6	−	1.16487e6i	−0.0256037	−	0.00931899i
$501$	5.36836e6	+	9.29828e6i	0.0426902	+	0.0739417i
$502$	−5.96640e7	−	3.44470e7i	−0.471630	−	0.272296i
$503$	−8.95303e7	+	7.51248e7i	−0.703503	+	0.590309i	−0.922768	−	0.385356i	$-0.874079\pi$
$503$	−8.95303e7	+	7.51248e7i	−0.703503	+	0.590309i	0.219265	+	0.975665i	$0.429634\pi$
$504$	−4.92859e7	−	5.87367e7i	−0.384974	−	0.458794i
$505$	−1.61799e8	+	2.80244e8i	−1.25633	+	2.17602i
$506$	1.19683e6	−	690992.i	0.00923809	−	0.00533362i
$507$	3.10558e6	−	8.53251e6i	0.0238297	−	0.0654716i
$508$	−1.15315e8	−	2.03332e7i	−0.879621	−	0.155101i
$509$	5.50853e7	−	9.71302e6i	0.417717	−	0.0736548i	0.0391605	−	0.999233i	$-0.487532\pi$
$509$	5.50853e7	−	9.71302e6i	0.417717	−	0.0736548i	0.378557	+	0.925578i	$0.376421\pi$
$510$	3.25155e6	−	1.18347e6i	0.0245121	−	0.00892166i
$511$	2.87728e7	+	2.41433e7i	0.215635	+	0.180939i
$512$		−	5.93164e6i		−	0.0441942i
$513$	1.68038e6	−	3.19900e7i	0.0124467	−	0.236953i
$514$	−4.58094e7			−0.337338
$515$	1.39061e8	−	1.65727e8i	1.01809	−	1.21331i
$516$	5.14474e6	+	1.41351e7i	0.0374468	+	0.102884i
$517$	4.82073e6	+	2.73397e7i	0.0348852	+	0.197844i
$518$	4.12246e7	−	2.33797e8i	0.296598	−	1.68209i
$519$	−2.86010e7	−	1.04099e7i	−0.204588	−	0.0744639i
$520$	2.29131e7	+	3.96867e7i	0.162957	+	0.282250i
$521$	2.29355e8	+	1.32418e8i	1.62179	+	0.936340i	0.986441	+	0.164114i	$0.0524765\pi$
$521$	2.29355e8	+	1.32418e8i	1.62179	+	0.936340i	0.635348	+	0.772226i	$0.280857\pi$
$522$	6.31409e7	−	5.29815e7i	0.443914	−	0.372488i
$523$	−2.27096e7	−	2.70642e7i	−0.158746	−	0.189187i	0.680808	−	0.732461i	$-0.261629\pi$
$523$	−2.27096e7	−	2.70642e7i	−0.158746	−	0.189187i	−0.839555	+	0.543275i	$0.817184\pi$
$524$	2.80499e7	−	4.85838e7i	0.194956	−	0.337674i
$525$	−2.67162e7	+	1.54246e7i	−0.184627	+	0.106595i
$526$	−4.51827e7	+	1.24139e8i	−0.310467	+	0.853001i
$527$	−4.01573e7	−	7.08082e6i	−0.274368	−	0.0483784i
$528$	2.21353e6	−	390305.i	0.0150378	−	0.00265157i
$529$	1.38987e8	−	5.05872e7i	0.938874	−	0.341722i
$530$	1.29849e8	+	1.08956e8i	0.872189	+	0.731854i
$531$		−	2.70926e8i		−	1.80953i
$532$	1.19087e8	+	5.05662e7i	0.790913	+	0.335835i
$533$	1.00937e8			0.666605
$534$	−118059.	+	140697.i	−0.000775311	+	0.000923980i
$535$	4.89082e7	+	1.34374e8i	0.319389	+	0.877515i
$536$	8.94226e6	+	5.07141e7i	0.0580702	+	0.329332i
$537$	660634.	−	3.74664e6i	0.00426617	−	0.0241946i
$538$	−1.37075e8	−	4.98911e7i	−0.880259	−	0.320388i
$539$	7.81733e7	+	1.35400e8i	0.499220	+	0.864675i
$540$	−2.30974e7	−	1.33353e7i	−0.146684	−	0.0846878i
$541$	1.22363e8	−	1.02675e8i	0.772783	−	0.648442i	−0.168637	−	0.985678i	$-0.553937\pi$
$541$	1.22363e8	−	1.02675e8i	0.772783	−	0.648442i	0.941420	+	0.337236i	$0.109492\pi$
$542$	7.75913e7	+	9.24697e7i	0.487321	+	0.580766i
$543$	−1.08162e7	+	1.87343e7i	−0.0675580	+	0.117014i
$544$	−5.32965e6	+	3.07708e6i	−0.0331056	+	0.0191136i
$545$	9.18876e6	−	2.52459e7i	0.0567633	−	0.155956i
$546$	1.50293e7	+	2.65008e6i	0.0923341	+	0.0162810i
$547$	−1.88076e8	+	3.31629e7i	−1.14914	+	0.202624i	−0.715598	−	0.698512i	$-0.753846\pi$
$547$	−1.88076e8	+	3.31629e7i	−1.14914	+	0.202624i	−0.433537	+	0.901136i	$0.642735\pi$
$548$	−1.19087e8	+	4.33440e7i	−0.723638	+	0.263383i
$549$	1.86150e8	+	1.56198e8i	1.12498	+	0.943973i
$550$			6.24298e7i			0.375236i
$551$	−5.43578e7	+	1.28016e8i	−0.324943	+	0.765261i
$552$	−209716.			−0.00124685
$553$	−7.43545e6	+	8.86123e6i	−0.0439675	+	0.0523985i
$554$	3.95272e7	+	1.08600e8i	0.232470	+	0.638706i
$555$	−7.11819e6	−	4.03692e7i	−0.0416381	−	0.236141i
$556$	−1.42687e7	+	8.09218e7i	−0.0830157	+	0.470805i
$557$	−2.74608e8	−	9.99491e7i	−1.58909	−	0.578380i	−0.611932	−	0.790911i	$-0.709607\pi$
$557$	−2.74608e8	−	9.99491e7i	−1.58909	−	0.578380i	−0.977154	+	0.212531i	$0.931829\pi$
$558$	7.80094e7	+	1.35116e8i	0.448998	+	0.777687i
$559$	1.78997e8	+	1.03344e8i	1.02473	+	0.591629i
$560$	8.25150e7	−	6.92383e7i	0.469860	−	0.394260i
$561$	−1.49898e6	−	1.78641e6i	−0.00848998	−	0.0101180i
$562$	9.97254e7	−	1.72730e8i	0.561820	−	0.973100i
$563$	−1.98236e8	+	1.14452e8i	−1.11085	+	0.641352i	−0.939051	−	0.343779i	$-0.888293\pi$
$563$	−1.98236e8	+	1.14452e8i	−1.11085	+	0.641352i	−0.171804	+	0.985131i	$0.554960\pi$
$564$	1.44086e6	−	3.95873e6i	0.00803128	−	0.0220658i
$565$	−2.38828e8	−	4.21118e7i	−1.32416	−	0.233485i
$566$	5.69912e7	−	1.00491e7i	0.314310	−	0.0554213i
$567$	2.81818e8	−	1.02573e8i	1.54604	−	0.562711i
$568$	1.24586e7	+	1.04540e7i	0.0679869	+	0.0570478i
$569$			1.92603e8i			1.04550i	0.852485	+	0.522752i	$0.175095\pi$
$569$			1.92603e8i			1.04550i	−0.852485	+	0.522752i	$0.824905\pi$
$570$	2.23087e7	+	1.17184e6i	0.120462	+	0.00632765i
$571$	8.35238e7			0.448644			0.224322	−	0.974515i	$-0.427983\pi$
$571$	8.35238e7			0.448644			0.224322	+	0.974515i	$0.427983\pi$
$572$	1.98520e7	−	2.36587e7i	0.106076	−	0.126416i
$573$	4.27151e6	+	1.17359e7i	0.0227048	+	0.0623809i
$574$	−4.11989e7	−	2.33651e8i	−0.217846	−	1.23547i
$575$	1.01148e6	−	5.73641e6i	0.00532053	−	0.0301742i
$576$	2.21267e7	+	8.05348e6i	0.115784	+	0.0421421i
$577$	1.18655e8	+	2.05517e8i	0.617675	+	1.06984i	0.989909	+	0.141705i	$0.0452585\pi$
$577$	1.18655e8	+	2.05517e8i	0.617675	+	1.06984i	−0.372234	+	0.928139i	$0.621408\pi$
$578$	−1.12720e8	−	6.50789e7i	−0.583737	−	0.337021i
$579$	2.61275e7	−	2.19235e7i	0.134605	−	0.112947i
$580$	7.44299e7	+	8.87021e7i	0.381473	+	0.454622i
$581$	1.64371e8	−	2.84698e8i	0.838100	−	1.45163i
$582$	4.61664e6	−	2.66542e6i	0.0234184	−	0.0135206i
$583$	3.90714e7	−	1.07348e8i	0.197176	−	0.541736i
$584$	−1.13594e7	−	2.00297e6i	−0.0570319	−	0.0100563i
$585$	−1.79152e8	+	3.15894e7i	−0.894859	+	0.157788i
$586$	9.27196e6	−	3.37472e6i	0.0460764	−	0.0167704i
$587$	−1.16970e8	−	9.81496e7i	−0.578310	−	0.485260i	0.306082	−	0.952005i	$-0.400982\pi$
$587$	−1.16970e8	−	9.81496e7i	−0.578310	−	0.485260i	−0.884392	+	0.466745i	$0.845426\pi$
$588$		−	2.37255e7i		−	0.116704i
$589$	−2.20769e8	−	1.43407e8i	−1.08042	−	0.701817i
$590$	3.80605e8			1.85318
$591$	−1.31668e6	+	1.56916e6i	−0.00637849	+	0.00760159i
$592$	2.49353e7	+	6.85092e7i	0.120185	+	0.330205i
$593$	2.74118e7	+	1.55460e8i	0.131454	+	0.745513i	0.977264	+	0.212028i	$0.0680068\pi$
$593$	2.74118e7	+	1.55460e8i	0.131454	+	0.745513i	−0.845809	+	0.533485i	$0.820882\pi$
$594$	−3.12123e6	+	1.77014e7i	−0.0148925	+	0.0844593i
$595$	−1.05017e8	−	3.82229e7i	−0.498548	−	0.181457i
$596$	−6.21407e7	−	1.07631e8i	−0.293520	−	0.508391i
$597$	1.82082e7	+	1.05125e7i	0.0855745	+	0.0494065i
$598$	−2.20743e6	+	1.85226e6i	−0.0103225	+	0.00866159i
$599$	−5.84553e7	−	6.96644e7i	−0.271984	−	0.324138i	0.612712	−	0.790306i	$-0.290079\pi$
$599$	−5.84553e7	−	6.96644e7i	−0.271984	−	0.324138i	−0.884696	+	0.466168i	$0.845634\pi$
$600$	4.73685e6	−	8.20447e6i	0.0219299	−	0.0379836i
$601$	8.63590e6	−	4.98594e6i	0.0397818	−	0.0229680i	−0.479977	−	0.877281i	$-0.659355\pi$
$601$	8.63590e6	−	4.98594e6i	0.0397818	−	0.0229680i	0.519759	+	0.854313i	$0.326022\pi$
$602$	1.66162e8	−	4.56526e8i	0.761626	−	2.09255i
$603$	−2.01319e8	−	3.54980e7i	−0.918192	−	0.161902i
$604$	−4.29224e7	+	7.56838e6i	−0.194793	+	0.0343473i
$605$	−2.19459e8	+	7.98766e7i	−0.991032	+	0.360706i
$606$	−2.53519e7	−	2.12728e7i	−0.113918	−	0.0955887i
$607$			2.69928e8i			1.20693i	0.797390	+	0.603465i	$0.206214\pi$
$607$			2.69928e8i			1.20693i	−0.797390	+	0.603465i	$0.793786\pi$
$608$	−3.94360e7	+	4.83732e6i	−0.175462	+	0.0215226i
$609$	3.85616e7			0.170727
$610$	−2.19432e8	+	2.61509e8i	−0.966742	+	1.15212i
$611$	−1.97982e7	−	5.43950e7i	−0.0867963	−	0.238471i
$612$	−4.24224e6	−	2.40589e7i	−0.0185072	−	0.104960i
$613$	1.97185e7	−	1.11829e8i	0.0856036	−	0.485482i	−0.911621	−	0.411032i	$-0.865169\pi$
$613$	1.97185e7	−	1.11829e8i	0.0856036	−	0.485482i	0.997225	−	0.0744506i	$-0.0237203\pi$
$614$	−1.53018e8	−	5.56942e7i	−0.661057	−	0.240605i
$615$	−2.04832e7	−	3.54779e7i	−0.0880587	−	0.152522i
$616$	−6.28685e7	−	3.62971e7i	−0.268962	−	0.155285i
$617$	−2.83299e8	+	2.37716e8i	−1.20612	+	1.01205i	−0.206682	+	0.978408i	$0.566266\pi$
$617$	−2.83299e8	+	2.37716e8i	−1.20612	+	1.01205i	−0.999434	+	0.0336431i	$0.989289\pi$
$618$	1.42219e7	+	1.69490e7i	0.0602549	+	0.0718089i
$619$	1.34671e8	−	2.33257e8i	0.567808	−	0.983472i	−0.428975	−	0.903317i	$-0.641125\pi$
$619$	1.34671e8	−	2.33257e8i	0.567808	−	0.983472i	0.996782	−	0.0801554i	$-0.0255417\pi$
$620$	−1.89815e8	+	1.09590e8i	−0.796445	+	0.459828i
$621$	573592.	−	1.57593e6i	0.00239513	−	0.00658056i
$622$	−9.88828e6	−	1.74357e6i	−0.0410913	−	0.00724550i
$623$	5.84186e6	−	1.03008e6i	0.0241595	−	0.00425997i
$624$	−4.40403e6	+	1.60294e6i	−0.0181258	+	0.00659725i
$625$	−1.79611e8	−	1.50712e8i	−0.735688	−	0.617316i
$626$		−	2.75233e8i		−	1.12196i
$627$	−4.40007e6	−	1.43982e7i	−0.0178508	−	0.0584124i
$628$	2.18209e8			0.881035
$629$	4.86210e7	−	5.79442e7i	0.195376	−	0.232840i
$630$	1.46247e8	+	4.01811e8i	0.584879	+	1.60694i
$631$	2.66753e7	+	1.51283e8i	0.106175	+	0.602147i	0.990745	+	0.135739i	$0.0433410\pi$
$631$	2.66753e7	+	1.51283e8i	0.106175	+	0.602147i	−0.884570	+	0.466408i	$0.845548\pi$
$632$	616860.	−	3.49838e6i	0.00244363	−	0.0138585i
$633$	−7.21602e6	−	2.62642e6i	−0.0284503	−	0.0103551i
$634$	−3.40170e7	−	5.89192e7i	−0.133484	−	0.231201i
$635$	5.65517e8	+	3.26502e8i	2.20864	+	1.27516i
$636$	−1.32797e7	+	1.11430e7i	−0.0516200	+	0.0433143i
$637$	−2.09549e8	−	2.49731e8i	−0.810714	−	0.966172i
$638$	3.90187e7	−	6.75824e7i	0.150249	−	0.260239i
$639$	−5.59118e7	+	3.22807e7i	−0.214290	+	0.123720i
$640$	−1.13138e7	+	3.10843e7i	−0.0431586	+	0.118577i
$641$	2.74860e7	+	4.84653e6i	0.104361	+	0.0184016i	0.225585	−	0.974224i	$-0.427571\pi$
$641$	2.74860e7	+	4.84653e6i	0.104361	+	0.0184016i	−0.121224	+	0.992625i	$0.538682\pi$
$642$	−1.44023e7	+	2.53952e6i	−0.0544286	+	0.00959724i
$643$	1.25886e8	−	4.58187e7i	0.473526	−	0.172349i	−0.0942231	−	0.995551i	$-0.530037\pi$
$643$	1.25886e8	−	4.58187e7i	0.473526	−	0.172349i	0.567749	+	0.823202i	$0.307814\pi$
$644$	5.18863e6	+	4.35378e6i	0.0194265	+	0.0163008i
$645$		−	8.38865e7i		−	0.312617i
$646$	2.48041e7	+	3.29243e7i	0.0920079	+	0.122129i
$647$	−2.90688e8			−1.07328			−0.536641	−	0.843811i	$-0.680307\pi$
$647$	−2.90688e8			−1.07328			−0.536641	+	0.843811i	$0.680307\pi$
$648$	−5.92007e7	+	7.05526e7i	−0.217571	+	0.259291i
$649$	−8.77301e7	−	2.41037e8i	−0.320933	−	0.881757i
$650$	−2.26044e7	−	1.28196e8i	−0.0823100	−	0.466803i
$651$	−1.26749e7	+	7.18830e7i	−0.0459412	+	0.260545i
$652$	1.56640e8	+	5.70123e7i	0.565145	+	0.205696i
$653$	9.22934e7	+	1.59857e8i	0.331460	+	0.574106i	0.982798	−	0.184682i	$-0.0591255\pi$
$653$	9.22934e7	+	1.59857e8i	0.331460	+	0.574106i	−0.651338	+	0.758787i	$0.725792\pi$
$654$	2.37951e6	+	1.37381e6i	0.00850655	+	0.00491126i
$655$	−2.39660e8	+	2.01099e8i	−0.852848	+	0.715624i
$656$	4.68338e7	+	5.58143e7i	0.165900	+	0.197712i
$657$	2.28945e7	−	3.96545e7i	0.0807301	−	0.139829i
$658$	−1.17833e8	+	6.80312e7i	−0.413610	+	0.238798i
$659$	−4.43568e7	+	1.21869e8i	−0.154990	+	0.425832i	−0.992749	−	0.120209i	$-0.961643\pi$
$659$	−4.43568e7	+	1.21869e8i	−0.154990	+	0.425832i	0.837759	+	0.546041i	$0.183866\pi$
$660$	−1.23443e7	−	2.17663e6i	−0.0429373	−	0.00757100i
$661$	−2.63298e8	+	4.64265e7i	−0.911681	+	0.160754i	−0.609767	−	0.792581i	$-0.708737\pi$
$661$	−2.63298e8	+	4.64265e7i	−0.911681	+	0.160754i	−0.301915	+	0.953335i	$0.597626\pi$
$662$	1.77159e8	−	6.44805e7i	0.610644	−	0.222256i
$663$	3.72488e6	+	3.12554e6i	0.0127812	+	0.0107247i
$664$			1.00956e8i			0.344847i
$665$	−5.27617e8	−	4.92129e8i	−1.79413	−	1.67346i
$666$	−2.89414e8			−0.979709
$667$	−4.68023e6	+	5.57768e6i	−0.0157721	+	0.0187965i
$668$	3.64223e7	+	1.00069e8i	0.122191	+	0.335716i
$669$	−2.11521e6	−	1.19959e7i	−0.00706438	−	0.0400641i
$670$	4.98687e7	−	2.82819e8i	0.165807	−	0.940339i
$671$	2.16193e8	+	7.86878e7i	0.715606	+	0.260459i
$672$	5.50807e6	+	9.54026e6i	0.0181506	+	0.0314378i
$673$	2.85604e8	+	1.64894e8i	0.936957	+	0.540952i	0.889005	−	0.457897i	$-0.151397\pi$
$673$	2.85604e8	+	1.64894e8i	0.936957	+	0.540952i	0.0479517	+	0.998850i	$0.484731\pi$
$674$	−4.80666e7	+	4.03327e7i	−0.156987	+	0.131728i
$675$	4.86977e7	+	5.80356e7i	0.158342	+	0.188705i
$676$	4.50303e7	−	7.79948e7i	0.145769	−	0.252479i
$677$	4.41747e8	−	2.55043e8i	1.42367	−	0.821954i	0.427055	−	0.904225i	$-0.359551\pi$
$677$	4.41747e8	−	2.55043e8i	1.42367	−	0.821954i	0.996610	+	0.0822718i	$0.0262176\pi$
$678$	8.48273e6	−	2.33061e7i	0.0272174	−	0.0747792i
$679$	−1.69556e8	−	2.98974e7i	−0.541633	−	0.0955045i
$680$	3.37987e7	−	5.95962e6i	0.107491	−	0.0189536i
$681$	5.30638e6	−	1.93136e6i	0.0168018	−	0.00611537i
$682$	1.13156e8	+	9.49491e7i	0.356717	+	0.299321i
$683$			3.93499e8i			1.23504i	0.786554	+	0.617521i	$0.211863\pi$
$683$			3.93499e8i			1.23504i	−0.786554	+	0.617521i	$0.788137\pi$
$684$	3.54982e7	−	1.53675e8i	0.110927	−	0.480215i
$685$	7.06737e8			2.19880
$686$	−2.40389e8	+	2.86484e8i	−0.744633	+	0.887419i
$687$	1.79470e7	+	4.93090e7i	0.0553506	+	0.152074i
$688$	2.59075e7	+	1.46929e8i	0.0795538	+	0.451172i
$689$	−4.13626e7	+	2.34579e8i	−0.126459	+	0.717186i
$690$	1.09900e6	+	400003.i	0.00334541	+	0.00121763i
$691$	−1.31330e8	−	2.27471e8i	−0.398044	−	0.689433i	0.595440	−	0.803399i	$-0.296978\pi$
$691$	−1.31330e8	−	2.27471e8i	−0.398044	−	0.689433i	−0.993485	+	0.113967i	$0.963644\pi$
$692$	−2.61439e8	−	1.50942e8i	−0.788955	−	0.455504i
$693$	2.20756e8	−	1.85236e8i	0.663305	−	0.556579i
$694$	−7.92203e7	−	9.44110e7i	−0.237005	−	0.282452i
$695$	2.29121e8	−	3.96849e8i	0.682512	−	1.18215i
$696$	−1.02556e7	+	5.92108e6i	−0.0304182	+	0.0175620i
$697$	2.58545e7	−	7.10347e7i	0.0763551	−	0.209784i
$698$	3.40266e7	+	5.99981e6i	0.100058	+	0.0176430i
$699$	−5.81657e6	+	1.02562e6i	−0.0170308	+	0.00300299i
$700$	−2.87523e8	+	1.04650e8i	−0.838261	+	0.305102i
$701$	−4.50851e7	−	3.78309e7i	−0.130882	−	0.109823i	0.574997	−	0.818156i	$-0.305003\pi$
$701$	−4.50851e7	−	3.78309e7i	−0.130882	−	0.109823i	−0.705879	+	0.708333i	$0.749448\pi$
$702$		−	3.74788e7i		−	0.108336i
$703$	4.35142e8	−	2.21650e8i	1.25246	−	0.637973i
$704$	2.22935e7			0.0638940
$705$	−1.51014e7	+	1.79972e7i	−0.0430974	+	0.0513614i
$706$	4.86235e7	+	1.33592e8i	0.138176	+	0.379635i
$707$	1.85607e8	+	1.05263e9i	0.525215	+	2.97864i
$708$	−6.75919e6	+	3.83333e7i	−0.0190456	+	0.108013i
$709$	4.73133e8	+	1.72206e8i	1.32753	+	0.483181i	0.905863	−	0.423570i	$-0.139223\pi$
$709$	4.73133e8	+	1.72206e8i	1.32753	+	0.483181i	0.421666	+	0.906751i	$0.361445\pi$
$710$	−4.53489e7	−	7.85465e7i	−0.126704	−	0.219458i
$711$	1.22125e7	+	7.05087e6i	0.0339778	+	0.0196171i
$712$	−1.39550e6	+	1.17096e6i	−0.00386625	+	0.00324417i
$713$	−8.85905e6	−	1.05578e7i	−0.0244410	−	0.0291276i
$714$	5.71469e6	−	9.89814e6i	0.0157000	−	0.0271931i
$715$	−1.49159e8	+	8.61167e7i	−0.408066	+	0.235597i
$716$	1.29058e7	−	3.54585e7i	0.0351598	−	0.0966009i
$717$	1.27008e7	+	2.23949e6i	0.0344566	+	0.00607562i
$718$	1.32543e7	−	2.33709e6i	0.0358083	−	0.00631396i
$719$	1.38330e8	−	5.03481e7i	0.372161	−	0.135456i	−0.149167	−	0.988812i	$-0.547659\pi$
$719$	1.38330e8	−	5.03481e7i	0.372161	−	0.135456i	0.521328	+	0.853357i	$0.325437\pi$
$720$	−1.00593e8	−	8.44072e7i	−0.269506	−	0.226142i
$721$		−	7.14591e8i		−	1.90657i
$722$	6.43210e7	+	2.58242e8i	0.170900	+	0.686144i
$723$	3.92972e7			0.103979
$724$	−1.37917e8	+	1.64363e8i	−0.363414	+	0.433100i
$725$	−1.12497e8	−	3.09082e8i	−0.295207	−	0.811074i
$726$	−4.14753e6	−	2.35218e7i	−0.0108388	−	0.0614696i
$727$	5.00308e7	−	2.83739e8i	0.130207	−	0.738441i	−0.847871	−	0.530202i	$-0.822116\pi$
$727$	5.00308e7	−	2.83739e8i	0.130207	−	0.738441i	0.978078	−	0.208238i	$-0.0667729\pi$
$728$	1.42239e8	+	5.17707e7i	0.368658	+	0.134181i
$729$	−1.77312e8	−	3.07113e8i	−0.457673	−	0.792712i
$730$	5.57077e7	+	3.21629e7i	0.143201	+	0.0826773i
$731$	1.18578e8	−	9.94985e7i	0.303565	−	0.254721i
$732$	−2.24415e7	−	2.67447e7i	−0.0572160	−	0.0681874i
$733$	−9.92113e7	+	1.71839e8i	−0.251912	+	0.436325i	−0.964052	−	0.265713i	$-0.914393\pi$
$733$	−9.92113e7	+	1.71839e8i	−0.251912	+	0.436325i	0.712140	+	0.702037i	$0.247726\pi$
$734$	−1.90440e8	+	1.09950e8i	−0.481581	+	0.278041i
$735$	−4.52530e7	+	1.24332e8i	−0.113969	+	0.313127i
$736$	−2.04845e6	−	361198.i	−0.00513798	−	0.000905965i
$737$	−1.90604e8	+	3.36086e7i	−0.476135	+	0.0839554i
$738$	−2.71790e8	+	9.89236e7i	−0.676184	+	0.246111i
$739$	5.18946e8	+	4.35448e8i	1.28585	+	1.07895i	0.992410	+	0.122975i	$0.0392435\pi$
$739$	5.18946e8	+	4.35448e8i	1.28585	+	1.07895i	0.293437	+	0.955978i	$0.405201\pi$
$740$		−	4.06577e8i		−	1.00334i
$741$	1.42485e7	+	2.79726e7i	0.0350199	+	0.0687509i
$742$	5.59890e8			1.37054
$743$	−4.10692e7	+	4.89444e7i	−0.100127	+	0.119326i	−0.813781	−	0.581172i	$-0.802594\pi$
$743$	−4.10692e7	+	4.89444e7i	−0.100127	+	0.119326i	0.713654	+	0.700498i	$0.247039\pi$
$744$	−7.66660e6	−	2.10638e7i	−0.0186159	−	0.0511467i
$745$	1.20353e8	+	6.82555e8i	0.291063	+	1.65070i
$746$	1.48979e7	−	8.44900e7i	0.0358845	−	0.203511i
$747$	−3.76594e8	−	1.37069e8i	−0.903465	−	0.328834i
$748$	−1.15649e7	−	2.00310e7i	−0.0276336	−	0.0478627i
$749$	4.09053e8	+	2.36167e8i	0.973496	+	0.562048i
$750$	−1.48803e6	+	1.24861e6i	−0.00352719	+	0.00295966i
$751$	−4.86214e8	−	5.79448e8i	−1.14791	−	1.36803i	−0.918847	−	0.394615i	$-0.870878\pi$
$751$	−4.86214e8	−	5.79448e8i	−1.14791	−	1.36803i	−0.229063	−	0.973412i	$-0.573566\pi$
$752$	2.08922e7	−	3.61864e7i	0.0491282	−	0.0850925i
$753$	−3.40286e7	+	1.96464e7i	−0.0797000	+	0.0460148i
$754$	−5.56526e7	+	1.52904e8i	−0.129829	+	0.356702i
$755$	2.39367e8	+	4.22069e7i	0.556191	+	0.0980714i
$756$	−8.67565e7	+	1.52975e7i	−0.200788	+	0.0354043i
$757$	−2.76054e8	+	1.00475e8i	−0.636365	+	0.231618i	−0.639999	−	0.768376i	$-0.721065\pi$
$757$	−2.76054e8	+	1.00475e8i	−0.636365	+	0.231618i	0.00363440	+	0.999993i	$0.498843\pi$
$758$	2.21775e8	+	1.86091e8i	0.509219	+	0.427285i
$759$		−	788196.i		−	0.00180264i
$760$	2.15888e8	+	4.98689e7i	0.491798	+	0.113603i
$761$	−3.05431e8			−0.693041			−0.346520	−	0.938042i	$-0.612637\pi$
$761$	−3.05431e8			−0.693041			−0.346520	+	0.938042i	$0.612637\pi$
$762$	−4.29273e7	+	5.11588e7i	−0.0970217	+	0.115626i
$763$	−3.03512e7	−	8.33892e7i	−0.0683285	−	0.187731i
$764$	2.15102e7	+	1.21990e8i	0.0482352	+	0.273555i
$765$	−2.36579e7	+	1.34170e8i	−0.0528434	+	0.299690i
$766$	−5.53700e8	−	2.01530e8i	−1.23194	−	0.448388i
$767$	2.67422e8	+	4.63189e8i	0.592668	+	1.02653i
$768$	−2.92979e6	−	1.69152e6i	−0.00646775	−	0.00373415i
$769$	−1.56895e7	+	1.31650e7i	−0.0345008	+	0.0289496i	−0.659875	−	0.751375i	$-0.729391\pi$
$769$	−1.56895e7	+	1.31650e7i	−0.0345008	+	0.0289496i	0.625374	+	0.780325i	$0.284946\pi$
$770$	2.60226e8	+	3.10125e8i	0.570004	+	0.679304i
$771$	−1.30634e7	+	2.26264e7i	−0.0285031	+	0.0493689i
$772$	2.92966e8	−	1.69144e8i	0.636745	−	0.367625i
$773$	−8.66344e7	+	2.38026e8i	−0.187565	+	0.515331i	−0.997459	−	0.0712458i	$-0.977303\pi$
$773$	−8.66344e7	+	2.38026e8i	−0.187565	+	0.515331i	0.809894	+	0.586577i	$0.199525\pi$
$774$	−5.83263e8	−	1.02845e8i	−1.25789	−	0.221799i
$775$	6.13141e8	−	1.08113e8i	1.31721	−	0.232260i
$776$	4.96849e7	−	1.80838e7i	0.106326	−	0.0386995i
$777$	−1.03722e8	−	8.70333e7i	−0.221110	−	0.185533i
$778$		−	1.01978e8i		−	0.216554i
$779$	3.32883e8	−	3.56887e8i	0.704173	−	0.754951i
$780$	2.61364e7			0.0550758
$781$	−3.92905e7	+	4.68245e7i	−0.0824772	+	0.0982925i
$782$	738108.	+	2.02793e6i	0.00154347	+	0.00424066i
$783$	−1.64445e7	−	9.32617e7i	−0.0342560	−	0.194275i
$784$	4.08630e7	−	2.31745e8i	0.0847973	−	0.480909i
$785$	−1.14351e9	−	4.16202e8i	−2.36390	−	0.860390i
$786$	−1.59979e7	−	2.77091e7i	−0.0329454	−	0.0570631i
$787$	−4.63179e8	−	2.67417e8i	−0.950221	−	0.548610i	−0.0570715	−	0.998370i	$-0.518176\pi$
$787$	−4.63179e8	−	2.67417e8i	−0.950221	−	0.548610i	−0.893150	+	0.449760i	$0.851510\pi$
$788$	−1.55636e7	+	1.30594e7i	−0.0318077	+	0.0266898i
$789$	4.84306e7	+	5.77173e7i	0.0986026	+	0.117510i
$790$	−9.90527e6	+	1.71564e7i	−0.0200902	+	0.0347973i
$791$	−6.93717e8	+	4.00518e8i	−1.40169	+	0.809268i
$792$	−3.02682e7	+	8.31612e7i	−0.0609272	+	0.167396i
$793$	−4.72430e8	−	8.33022e7i	−0.947367	−	0.167046i
$794$	−9.50352e7	+	1.67573e7i	−0.189855	+	0.0334766i
$795$	9.08450e7	−	3.30649e7i	0.180801	−	0.0658060i
$796$	1.59748e8	+	1.34044e8i	0.316735	+	0.265772i
$797$		−	3.27363e8i		−	0.646628i	−0.946292	−	0.323314i	$-0.895203\pi$
$797$		−	3.27363e8i		−	0.646628i	0.946292	−	0.323314i	$-0.104797\pi$
$798$	5.89357e7	−	4.44001e7i	0.115976	−	0.0873727i
$799$	−4.33518e7			−0.0849899
$800$	6.03992e7	−	7.19810e7i	0.117967	−	0.140588i
$801$	−2.47334e6	−	6.79546e6i	−0.00481268	−	0.0132227i
$802$	7.83145e7	+	4.44144e8i	0.151817	+	0.860994i
$803$	7.52798e6	−	4.26933e7i	0.0145389	−	0.0824542i
$804$	2.75990e7	+	1.00452e7i	0.0531038	+	0.0193282i
$805$	−1.88864e7	−	3.27122e7i	−0.0362044	−	0.0627078i
$806$	−2.66738e8	−	1.54001e8i	−0.509424	−	0.294116i
$807$	−6.37318e7	+	5.34774e7i	−0.121265	+	0.101753i
$808$	−2.10993e8	−	2.51452e8i	−0.399976	−	0.476673i
$809$	−1.16638e8	+	2.02024e8i	−0.220291	+	0.381555i	−0.954896	−	0.296940i	$-0.904034\pi$
$809$	−1.16638e8	+	2.02024e8i	−0.220291	+	0.381555i	0.734605	+	0.678495i	$0.237367\pi$
$810$	4.44805e8	−	2.56808e8i	0.836980	−	0.483230i
$811$	1.65482e8	−	4.54658e8i	0.310233	−	0.852359i	−0.682376	−	0.731002i	$-0.739053\pi$
$811$	1.65482e8	−	4.54658e8i	0.310233	−	0.852359i	0.992609	−	0.121357i	$-0.0387246\pi$
$812$	3.76660e8	+	6.64154e7i	0.703529	+	0.124051i
$813$	6.77997e7	−	1.19549e7i	0.126170	−	0.0222472i
$814$	−2.57485e8	+	9.37169e7i	−0.477396	+	0.173758i
$815$	−7.12117e8	−	5.97537e8i	−1.31546	−	1.10380i
$816$			3.50994e6i			0.00645994i
$817$	9.55716e8	−	2.92066e8i	1.75252	−	0.535569i
$818$	−5.41986e8			−0.990211
$819$	−3.86240e8	+	4.60302e8i	−0.703081	+	0.837899i
$820$	−1.38971e8	−	3.81819e8i	−0.252047	−	0.692494i
$821$	−5.33266e7	−	3.02430e8i	−0.0963639	−	0.546507i	−0.994321	−	0.106424i	$-0.966060\pi$
$821$	−5.33266e7	−	3.02430e8i	−0.0963639	−	0.546507i	0.897957	−	0.440083i	$-0.145051\pi$
$822$	−1.25510e7	+	7.11803e7i	−0.0225976	+	0.128158i
$823$	8.74144e8	+	3.18162e8i	1.56813	+	0.570754i	0.972582	−	0.232562i	$-0.0747107\pi$
$823$	8.74144e8	+	3.18162e8i	1.56813	+	0.570754i	0.595553	+	0.803316i	$0.296933\pi$
$824$	1.09725e8	+	1.90049e8i	0.196120	+	0.339690i
$825$	3.08357e7	+	1.78030e7i	0.0549151	+	0.0317053i
$826$	9.63045e8	−	8.08090e8i	1.70886	−	1.43390i
$827$	1.00408e8	+	1.19661e8i	0.177521	+	0.211561i	0.847466	−	0.530849i	$-0.178127\pi$
$827$	1.00408e8	+	1.19661e8i	0.177521	+	0.211561i	−0.669945	+	0.742410i	$0.733682\pi$
$828$	4.12859e6	−	7.15092e6i	0.00727295	−	0.0125971i
$829$	−9.20565e8	+	5.31488e8i	−1.61581	+	0.932889i	−0.627824	+	0.778355i	$0.716054\pi$
$829$	−9.20565e8	+	5.31488e8i	−1.61581	+	0.932889i	−0.987987	+	0.154534i	$0.950612\pi$
$830$	1.92558e8	−	5.29050e8i	0.336766	−	0.925257i
$831$	6.49123e7	+	1.14458e7i	0.113116	+	0.0199454i
$832$	−4.57784e7	+	8.07196e6i	−0.0794859	+	0.0140155i
$833$	−2.29424e8	+	8.35035e7i	−0.396921	+	0.144467i
$834$	3.59004e7	+	3.01240e7i	0.0618872	+	0.0519296i
$835$		−	5.93876e8i		−	1.02009i
$836$	−1.81806e7	−	1.48216e8i	−0.0311164	−	0.253675i
$837$	1.79255e8			0.305700
$838$	1.61326e8	−	1.92261e8i	0.274140	−	0.326708i
$839$	−1.86708e7	−	5.12976e7i	−0.0316138	−	0.0868583i	0.922882	−	0.385084i	$-0.125827\pi$
$839$	−1.86708e7	−	5.12976e7i	−0.0316138	−	0.0868583i	−0.954495	+	0.298226i	$0.903605\pi$
$840$	−1.06679e7	−	6.05009e7i	−0.0179988	−	0.102076i
$841$	3.18946e7	−	1.80883e8i	0.0536204	−	0.304096i
$842$	5.83467e7	+	2.12365e7i	0.0977418	+	0.0355751i
$843$	−5.68770e7	−	9.85139e7i	−0.0949411	−	0.164443i
$844$	−6.59609e7	−	3.80826e7i	−0.109713	−	0.0633430i
$845$	−3.84742e8	+	3.22837e8i	−0.637674	+	0.535072i
$846$	1.06620e8	+	1.27065e8i	0.176087	+	0.209852i
$847$	−3.85706e8	+	6.68063e8i	−0.634755	+	1.09943i
$848$	−1.48905e8	+	8.59704e7i	−0.244187	+	0.140981i
$849$	1.12886e7	−	3.10151e7i	0.0184466	−	0.0506815i
$850$	−9.60082e7	−	1.69288e7i	−0.156333	−	0.0275658i
$851$	2.51776e7	−	4.43949e6i	0.0408531	−	0.00720351i
$852$	8.71632e6	−	3.17248e6i	0.0140933	−	0.00512956i
$853$	1.53741e8	+	1.29004e8i	0.247709	+	0.207852i	0.758185	−	0.652040i	$-0.226086\pi$
$853$	1.53741e8	+	1.29004e8i	0.247709	+	0.207852i	−0.510476	+	0.859892i	$0.670531\pi$
$854$			1.12759e9i			1.81041i
$855$	−4.79139e8	+	7.37616e8i	−0.766591	+	1.18014i
$856$	−1.45052e8			−0.231262
$857$	−2.15078e7	+	2.56320e7i	−0.0341706	+	0.0407230i	−0.782859	−	0.622199i	$-0.786239\pi$
$857$	−2.15078e7	+	2.56320e7i	−0.0341706	+	0.0407230i	0.748688	+	0.662922i	$0.230684\pi$
$858$	−6.02448e6	−	1.65521e7i	−0.00953802	−	0.0262055i
$859$	−1.33550e7	−	7.57402e7i	−0.0210701	−	0.119494i	0.972459	−	0.233075i	$-0.0748789\pi$
$859$	−1.33550e7	−	7.57402e7i	−0.0210701	−	0.119494i	−0.993529	+	0.113581i	$0.963768\pi$
$860$	1.44480e8	−	8.19384e8i	0.227149	−	1.28823i
$861$	−1.27155e8	−	4.62805e7i	−0.199215	−	0.0725084i
$862$	4.08207e8	+	7.07036e8i	0.637322	+	1.10387i
$863$	3.73046e8	+	2.15378e8i	0.580403	+	0.335096i	0.761294	−	0.648407i	$-0.224565\pi$
$863$	3.73046e8	+	2.15378e8i	0.580403	+	0.335096i	−0.180890	+	0.983503i	$0.557898\pi$
$864$	2.07243e7	−	1.73898e7i	0.0321321	−	0.0269621i
$865$	1.08215e9	+	1.28966e9i	1.67201	+	1.99263i
$866$	1.70814e8	−	2.95859e8i	0.263009	−	0.455545i
$867$	−6.42882e7	+	3.71168e7i	−0.0986448	+	0.0569526i
$868$	−2.47611e8	+	6.80306e8i	−0.378627	+	1.04027i
$869$	1.31483e7	+	2.31841e6i	0.0200360	+	0.00353289i
$870$	6.50373e7	−	1.14678e7i	0.0987654	−	0.0174150i
$871$	3.79225e8	−	1.38027e8i	0.573908	−	0.208886i
$872$	2.08763e7	+	1.75173e7i	0.0314851	+	0.0264191i
$873$			2.09892e8i			0.315466i
$874$	−730854.	+	1.39135e7i	−0.00109470	+	0.0208403i
$875$	6.27373e7			0.0936487
$876$	−4.22866e6	+	5.03953e6i	−0.00629058	+	0.00749682i
$877$	1.66254e7	+	4.56779e7i	0.0246475	+	0.0677185i	0.951406	−	0.307939i	$-0.0996392\pi$
$877$	1.66254e7	+	4.56779e7i	0.0246475	+	0.0677185i	−0.926759	+	0.375657i	$0.877417\pi$
$878$	−3.31968e7	−	1.88268e8i	−0.0490470	−	0.278159i
$879$	977208.	−	5.54202e6i	0.00143887	−	0.00816021i
$880$	−1.16827e8	−	4.25217e7i	−0.171434	−	0.0623968i
$881$	−4.82460e8	−	8.35645e8i	−0.705560	−	1.22206i	−0.966489	−	0.256707i	$-0.917362\pi$
$881$	−4.82460e8	−	8.35645e8i	−0.705560	−	1.22206i	0.260930	−	0.965358i	$-0.415971\pi$
$882$	8.08998e8	+	4.67075e8i	1.17908	+	0.680739i
$883$	−5.04759e8	+	4.23543e8i	−0.733165	+	0.615198i	−0.930992	−	0.365038i	$-0.881056\pi$
$883$	−5.04759e8	+	4.23543e8i	−0.733165	+	0.615198i	0.197827	+	0.980237i	$0.436611\pi$
$884$	3.10006e7	+	3.69450e7i	0.0448758	+	0.0534809i
$885$	1.08536e8	−	1.87990e8i	0.156583	−	0.271210i
$886$	6.05865e8	−	3.49796e8i	0.871114	−	0.502938i
$887$	4.06729e8	−	1.11748e9i	0.582820	−	1.60128i	−0.200520	−	0.979690i	$-0.564263\pi$
$887$	4.06729e8	−	1.11748e9i	0.582820	−	1.60128i	0.783340	−	0.621594i	$-0.213515\pi$
$888$	4.09492e7	+	7.22045e6i	0.0584799	+	0.0103116i
$889$	2.12415e9	−	3.74545e8i	3.02329	−	0.533088i
$890$	9.54646e6	−	3.47463e6i	0.0135417	−	0.00492877i
$891$	−2.65165e8	−	2.22500e8i	−0.374872	−	0.314555i
$892$		−	1.20817e8i		−	0.170228i
$893$	−2.57620e8	−	1.09390e8i	−0.361763	−	0.153611i
$894$	−7.08822e7			−0.0992029
$895$	−1.35264e8	+	1.61201e8i	−0.188674	+	0.224853i
$896$	3.73702e7	+	1.02674e8i	0.0519519	+	0.142737i
$897$	285387.	+	1.61851e6i	0.000395419	+	0.00224253i
$898$	−1.24803e8	+	7.07795e8i	−0.172344	+	0.977414i
$899$	−7.31317e8	−	2.66178e8i	−1.00653	−	0.366347i
$900$	1.86505e8	+	3.23036e8i	0.255837	+	0.443122i
$901$	1.54491e8	+	8.91954e7i	0.211217	+	0.121946i
$902$	−2.09773e8	+	1.76020e8i	−0.285844	+	0.239852i
$903$	−1.78106e8	−	2.12258e8i	−0.241888	−	0.288271i
$904$	1.22998e8	−	2.13039e8i	0.166492	−	0.288372i
$905$	1.03624e9	−	5.98274e8i	1.39803	−	0.807151i
$906$	−8.50189e6	+	2.33587e7i	−0.0114322	+	0.0314098i
$907$	2.91023e8	+	5.13152e7i	0.390036	+	0.0687739i	0.365228	−	0.930918i	$-0.380991\pi$
$907$	2.91023e8	+	5.13152e7i	0.390036	+	0.0687739i	0.0248088	+	0.999692i	$0.492102\pi$
$908$	5.51579e7	−	9.72582e6i	0.0736801	−	0.0129918i
$909$	1.22446e9	−	4.45666e8i	1.63024	−	0.593359i
$910$	−6.46646e8	−	5.42601e8i	−0.858109	−	0.720039i
$911$			1.26981e9i			1.67951i	0.542963	+	0.839757i	$0.317302\pi$
$911$			1.26981e9i			1.67951i	−0.542963	+	0.839757i	$0.682698\pi$
$912$	−8.85661e6	+	2.08579e7i	−0.0116757	+	0.0274971i
$913$	−3.79432e8			−0.498565
$914$	−1.07363e8	+	1.27950e8i	−0.140610	+	0.167573i
$915$	6.65910e7	+	1.82957e8i	0.0869265	+	0.238829i
$916$	9.03764e7	+	5.12550e8i	0.117589	+	0.666883i
$917$	−1.79445e8	+	1.01768e9i	−0.232714	+	1.31979i
$918$	−2.63758e7	−	9.60001e6i	−0.0340940	−	0.0124092i
$919$	−1.05528e8	−	1.82780e8i	−0.135963	−	0.235495i	0.790002	−	0.613104i	$-0.210079\pi$
$919$	−1.05528e8	−	1.82780e8i	−0.135963	−	0.235495i	−0.925965	+	0.377610i	$0.876746\pi$
$920$	1.00458e7	+	5.79996e6i	0.0129010	+	0.00744838i
$921$	−7.11448e7	+	5.96976e7i	−0.0910677	+	0.0764148i
$922$	5.56152e7	+	6.62796e7i	0.0709579	+	0.0845643i
$923$	6.37265e7	−	1.10377e8i	0.0810429	−	0.140370i
$924$	−3.58562e7	+	2.07016e7i	−0.0454515	+	0.0262414i
$925$	−3.95006e8	+	1.08527e9i	−0.499089	+	1.37124i
$926$	−7.13808e8	−	1.25864e8i	−0.898976	−	0.158514i
$927$	−8.57911e8	+	1.51273e8i	−1.07697	+	0.189899i
$928$	−1.10372e8	+	4.01723e7i	−0.138107	+	0.0502670i
$929$	5.49022e8	+	4.60684e8i	0.684767	+	0.574588i	0.917395	−	0.397978i	$-0.130288\pi$
$929$	5.49022e8	+	4.60684e8i	0.684767	+	0.574588i	−0.232628	+	0.972566i	$0.574732\pi$
$930$			1.25006e8i			0.155411i
$931$	−1.57406e9	−	8.26829e7i	−1.95062	−	0.102463i
$932$	−5.85814e7			−0.0723622
$933$	−3.68102e6	+	4.38687e6i	−0.00453235	+	0.00540144i
$934$	−2.60851e8	−	7.16681e8i	−0.320148	−	0.879600i
$935$	2.23987e7	+	1.27029e8i	0.0274023	+	0.155406i
$936$	3.20432e7	−	1.81726e8i	0.0390758	−	0.221610i
$937$	5.74564e8	+	2.09124e8i	0.698424	+	0.254206i	0.666738	−	0.745292i	$-0.267690\pi$
$937$	5.74564e8	+	2.09124e8i	0.698424	+	0.254206i	0.0316863	+	0.999498i	$0.489912\pi$
$938$	−4.74292e8	−	8.21498e8i	−0.574695	−	0.995401i
$939$	−1.35945e8	−	7.84877e7i	−0.164197	−	0.0947992i
$940$	−1.78504e8	+	1.49783e8i	−0.214914	+	0.180334i
$941$	−1.33732e8	−	1.59375e8i	−0.160497	−	0.191272i	0.679803	−	0.733395i	$-0.262065\pi$
$941$	−1.33732e8	−	1.59375e8i	−0.160497	−	0.191272i	−0.840299	+	0.542123i	$0.817621\pi$
$942$	6.22262e7	−	1.07779e8i	0.0744424	−	0.128938i
$943$	2.21270e7	−	1.27750e7i	0.0263868	−	0.0152344i
$944$	−1.32044e8	+	3.62789e8i	−0.156966	+	0.431259i
$945$	4.83818e8	+	8.53102e7i	0.573307	+	0.101089i
$946$	−5.52218e8	+	9.73710e7i	−0.652285	+	0.115015i
$947$	8.43444e8	−	3.06988e8i	0.993130	−	0.361470i	0.206199	−	0.978510i	$-0.433891\pi$
$947$	8.43444e8	−	3.06988e8i	0.993130	−	0.361470i	0.786932	+	0.617040i	$0.211668\pi$
$948$	−1.55203e6	−	1.30231e6i	−0.00182170	−	0.00152858i
$949$			9.03938e7i			0.105764i
$950$	−5.27815e8	−	3.42857e8i	−0.615618	−	0.399892i
$951$	−3.88023e7			−0.0451144
$952$	7.28676e7	−	8.68402e7i	0.0844547	−	0.100649i
$953$	1.89535e8	+	5.20743e8i	0.218983	+	0.601651i	0.999731	−	0.0231954i	$-0.00738397\pi$
$953$	1.89535e8	+	5.20743e8i	0.218983	+	0.601651i	−0.780748	+	0.624846i	$0.785162\pi$
$954$	−1.18524e8	−	6.72183e8i	−0.136509	−	0.774180i
$955$	1.19957e8	−	6.80307e8i	0.137725	−	0.781079i
$956$	1.20201e8	+	4.37496e7i	0.137573	+	0.0500726i
$957$	−2.22538e7	−	3.85447e7i	−0.0253903	−	0.0439774i
$958$	−3.27517e8	−	1.89092e8i	−0.372510	−	0.215069i
$959$	1.78826e9	−	1.50053e9i	2.02756	−	1.70133i
$960$	1.21270e7	+	1.44524e7i	0.0137069	+	0.0163353i
$961$	2.92811e8	−	5.07164e8i	0.329927	−	0.571450i
$962$	4.94797e8	−	2.85671e8i	0.555779	−	0.320879i
$963$	1.96940e8	−	5.41088e8i	0.220523	−	0.605883i
$964$	3.83846e8	+	6.76823e7i	0.428475	+	0.0755517i
$965$	−1.85789e9	+	3.27595e8i	−2.06746	+	0.364549i
$966$	3.63007e6	−	1.32124e6i	0.00402702	−	0.00146572i
$967$	−7.15761e8	−	6.00594e8i	−0.791568	−	0.664205i	0.154565	−	0.987983i	$-0.450602\pi$
$967$	−7.15761e8	−	6.00594e8i	−0.791568	−	0.664205i	−0.946133	+	0.323778i	$0.895047\pi$
$968$		−	2.36899e8i		−	0.261178i
$969$	2.33355e7	−	2.86239e6i	0.0256475	−	0.00314599i
$970$	−2.94862e8			−0.323075
$971$	5.54426e8	−	6.60739e8i	0.605600	−	0.721726i	−0.372924	−	0.927862i	$-0.621645\pi$
$971$	5.54426e8	−	6.60739e8i	0.605600	−	0.721726i	0.978523	+	0.206136i	$0.0660891\pi$
$972$	5.52289e7	+	1.51740e8i	0.0601406	+	0.165235i
$973$	−2.62835e8	−	1.49061e9i	−0.285328	−	1.61818i
$974$	−1.38395e8	+	7.84878e8i	−0.149777	+	0.849426i
$975$	−6.97653e7	−	2.53925e7i	−0.0752706	−	0.0273963i
$976$	−1.73140e8	−	2.99887e8i	−0.186229	−	0.322559i
$977$	−1.00077e9	−	5.77794e8i	−1.07312	−	0.619568i	−0.144090	−	0.989565i	$-0.546026\pi$
$977$	−1.00077e9	−	5.77794e8i	−1.07312	−	0.619568i	−0.929033	+	0.369997i	$0.879359\pi$
$978$	7.28286e7	−	6.11105e7i	0.0778548	−	0.0653279i
$979$	−4.40096e6	−	5.24486e6i	−0.00469028	−	0.00558966i
$980$	−6.56161e8	+	1.13650e9i	−0.697159	+	1.20751i
$981$	−9.36887e7	+	5.40912e7i	−0.0992385	+	0.0572954i
$982$	−1.84472e8	+	5.06832e8i	−0.194803	+	0.535217i
$983$	6.03635e7	+	1.06437e7i	0.0635497	+	0.0112055i	0.205333	−	0.978692i	$-0.434172\pi$
$983$	6.03635e7	+	1.06437e7i	0.0635497	+	0.0112055i	−0.141783	+	0.989898i	$0.545283\pi$
$984$	4.09236e7	−	7.21594e6i	0.0429525	−	0.00757369i
$985$	1.06469e8	−	3.87515e7i	0.111408	−	0.0405490i
$986$	9.33516e7	+	7.83313e7i	0.0973848	+	0.0817156i
$987$			7.76013e7i			0.0807082i
$988$	9.09985e7	+	2.97771e8i	0.0943546	+	0.308753i
$989$	5.23186e7			0.0540838
$990$	3.17236e8	−	3.78068e8i	0.326947	−	0.389640i
$991$	−1.71384e8	−	4.70874e8i	−0.176096	−	0.483819i	0.819973	−	0.572402i	$-0.193988\pi$
$991$	−1.71384e8	−	4.70874e8i	−0.176096	−	0.483819i	−0.996069	+	0.0885828i	$0.971766\pi$
$992$	−3.86069e7	−	2.18951e8i	−0.0395485	−	0.224291i
$993$	1.86714e7	−	1.05891e8i	0.0190691	−	0.108146i
$994$	−2.81514e8	−	1.02463e8i	−0.286643	−	0.104330i
$995$	−5.81475e8	−	1.00714e9i	−0.590285	−	1.02240i
$996$	4.98646e7	+	2.87893e7i	0.0504678	+	0.0291376i
$997$	−1.34494e9	+	1.12854e9i	−1.35712	+	1.13876i	−0.380262	+	0.924879i	$0.624166\pi$
$997$	−1.34494e9	+	1.12854e9i	−1.35712	+	1.13876i	−0.976860	+	0.213881i	$0.931389\pi$
$998$	2.18256e8	+	2.60108e8i	0.219571	+	0.261674i
$999$	−1.66259e8	+	2.87969e8i	−0.166759	+	0.288834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.7.f.a.3.8	✓	60
19.13	odd	18	inner	38.7.f.a.13.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.f.a.3.8	✓	60	1.1	even	1	trivial
38.7.f.a.13.8	yes	60	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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	38.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(3.63616 - 4.33340i) q^{2} +(-1.10346 - 3.03174i) q^{3} +(-5.55674 - 31.5138i) q^{4} +(-30.9885 + 175.744i) q^{5} +(-17.1501 - 6.24213i) q^{6} +(294.726 + 510.481i) q^{7} +(-156.767 - 90.5097i) q^{8} +(550.473 - 461.901i) q^{9} +O(q^{10})\)	\(q+(3.63616 - 4.33340i) q^{2} +(-1.10346 - 3.03174i) q^{3} +(-5.55674 - 31.5138i) q^{4} +(-30.9885 + 175.744i) q^{5} +(-17.1501 - 6.24213i) q^{6} +(294.726 + 510.481i) q^{7} +(-156.767 - 90.5097i) q^{8} +(550.473 - 461.901i) q^{9} +(648.892 + 773.320i) q^{10} +(340.172 - 589.195i) q^{11} +(-89.4101 + 51.6210i) q^{12} +(-485.188 + 1333.04i) q^{13} +(3283.79 + 579.021i) q^{14} +(567.006 - 99.9785i) q^{15} +(-962.245 + 350.229i) q^{16} +(813.855 + 682.906i) q^{17} -4064.96i q^{18} +(3113.19 + 6111.79i) q^{19} +5710.58 q^{20} +(1222.43 - 1456.83i) q^{21} +(-1316.30 - 3616.51i) q^{22} +(62.3548 + 353.632i) q^{23} +(-101.415 + 575.152i) q^{24} +(-15243.1 - 5548.05i) q^{25} +(4012.40 + 6949.67i) q^{26} +(-4044.66 - 2335.19i) q^{27} +(14449.5 - 12124.6i) q^{28} +(13033.7 + 15532.9i) q^{29} +(1628.48 - 2820.60i) q^{30} +(-33239.2 + 19190.7i) q^{31} +(-1981.19 + 5443.28i) q^{32} +(-2161.65 - 381.158i) q^{33} +(5918.61 - 1043.61i) q^{34} +(-98847.3 + 35977.5i) q^{35} +(-17615.1 - 14780.8i) q^{36} -71197.2i q^{37} +(37804.9 + 8732.73i) q^{38} +4576.83 q^{39} +(20764.6 - 24746.2i) q^{40} +(-24335.7 - 66861.7i) q^{41} +(-1868.10 - 10594.5i) q^{42} +(25300.3 - 143485. i) q^{43} +(-20458.0 - 7446.12i) q^{44} +(64118.3 + 111056. i) q^{45} +(1759.16 + 1015.65i) q^{46} +(-31258.5 + 26229.0i) q^{47} +(2123.60 + 2530.81i) q^{48} +(-114903. + 199017. i) q^{49} +(-79468.4 + 45881.1i) q^{50} +(1172.33 - 3220.96i) q^{51} +(44705.4 + 7882.77i) q^{52} +(165360. - 29157.4i) q^{53} +(-24826.3 + 9036.05i) q^{54} +(93006.4 + 78041.6i) q^{55} -106702. i q^{56} +(15094.1 - 16182.5i) q^{57} +114703. q^{58} +(242346. - 288817. i) q^{59} +(-6301.41 - 17313.0i) q^{60} +(58721.6 + 333027. i) q^{61} +(-37702.1 + 213819. i) q^{62} +(398030. + 144871. i) q^{63} +(16384.0 + 28377.9i) q^{64} +(-219240. - 126578. i) q^{65} +(-9511.82 + 7981.36i) q^{66} +(-182860. - 217925. i) q^{67} +(16998.6 - 29442.4i) q^{68} +(1003.31 - 579.263i) q^{69} +(-203519. + 559165. i) q^{70} +(-88479.5 - 15601.3i) q^{71} +(-128103. + 22588.0i) q^{72} +(59877.8 - 21793.7i) q^{73} +(-308526. - 258884. i) q^{74} +52335.3i q^{75} +(175307. - 132070. i) q^{76} +401030. q^{77} +(16642.1 - 19833.2i) q^{78} +(6711.86 + 18440.7i) q^{79} +(-31732.2 - 179962. i) q^{80} +(88349.5 - 501055. i) q^{81} +(-378227. - 137663. i) q^{82} +(-278853. - 482988. i) q^{83} +(-52703.0 - 30428.1i) q^{84} +(-145237. + 121868. i) q^{85} +(-529784. - 631371. i) q^{86} +(32709.6 - 56654.8i) q^{87} +(-106656. + 61577.7i) q^{88} +(3441.94 - 9456.64i) q^{89} +(714395. + 125967. i) q^{90} +(-823491. + 145204. i) q^{91} +(10797.8 - 3930.08i) q^{92} +(94859.3 + 79596.4i) q^{93} +230828. i q^{94} +(-1.17059e6 + 357730. i) q^{95} +18688.8 q^{96} +(-187751. + 223753. i) q^{97} +(444618. + 1.22158e6i) q^{98} +(-84894.7 - 481462. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9}+O(q^{10}) \) 60 * q + 30 * q^3 - 240 * q^6 + 432 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9} - 3360 q^{11} + 9660 q^{13} + 2496 q^{14} - 37464 q^{15} + 7704 q^{17} + 46704 q^{19} + 21504 q^{20} + 78732 q^{21} - 20304 q^{22} - 54120 q^{23} + 7680 q^{24} - 41328 q^{25} - 25536 q^{26} - 124830 q^{27} + 65280 q^{28} - 21840 q^{29} + 30780 q^{31} - 54582 q^{33} - 70560 q^{34} - 56796 q^{35} - 22080 q^{36} + 52080 q^{38} + 496344 q^{39} + 83394 q^{41} + 38880 q^{42} - 294384 q^{43} - 8448 q^{44} - 391824 q^{45} + 738720 q^{46} + 639264 q^{47} + 61440 q^{48} - 85530 q^{49} - 689472 q^{50} - 215478 q^{51} - 456960 q^{52} - 1189428 q^{53} - 907200 q^{54} - 316512 q^{55} + 517776 q^{57} + 440640 q^{58} + 957390 q^{59} + 586752 q^{60} + 1390404 q^{61} + 978384 q^{62} + 2002152 q^{63} + 983040 q^{64} - 878940 q^{65} - 976992 q^{66} - 2920854 q^{67} - 78144 q^{68} - 2667600 q^{69} - 643392 q^{70} + 1585980 q^{71} + 706560 q^{72} + 1734648 q^{73} - 1167552 q^{74} - 411264 q^{76} - 1481400 q^{77} - 2170608 q^{78} + 4991952 q^{79} + 40002 q^{81} + 2299392 q^{82} - 30672 q^{83} + 1313280 q^{84} + 815976 q^{85} - 1424976 q^{86} - 125892 q^{87} - 6804636 q^{89} - 2283456 q^{90} - 3838704 q^{91} - 244992 q^{92} - 3271128 q^{93} - 4631640 q^{95} + 2112390 q^{97} + 7177728 q^{98} + 21467982 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 240 * q^6 + 432 * q^7 + 690 * q^9 - 3360 * q^11 + 9660 * q^13 + 2496 * q^14 - 37464 * q^15 + 7704 * q^17 + 46704 * q^19 + 21504 * q^20 + 78732 * q^21 - 20304 * q^22 - 54120 * q^23 + 7680 * q^24 - 41328 * q^25 - 25536 * q^26 - 124830 * q^27 + 65280 * q^28 - 21840 * q^29 + 30780 * q^31 - 54582 * q^33 - 70560 * q^34 - 56796 * q^35 - 22080 * q^36 + 52080 * q^38 + 496344 * q^39 + 83394 * q^41 + 38880 * q^42 - 294384 * q^43 - 8448 * q^44 - 391824 * q^45 + 738720 * q^46 + 639264 * q^47 + 61440 * q^48 - 85530 * q^49 - 689472 * q^50 - 215478 * q^51 - 456960 * q^52 - 1189428 * q^53 - 907200 * q^54 - 316512 * q^55 + 517776 * q^57 + 440640 * q^58 + 957390 * q^59 + 586752 * q^60 + 1390404 * q^61 + 978384 * q^62 + 2002152 * q^63 + 983040 * q^64 - 878940 * q^65 - 976992 * q^66 - 2920854 * q^67 - 78144 * q^68 - 2667600 * q^69 - 643392 * q^70 + 1585980 * q^71 + 706560 * q^72 + 1734648 * q^73 - 1167552 * q^74 - 411264 * q^76 - 1481400 * q^77 - 2170608 * q^78 + 4991952 * q^79 + 40002 * q^81 + 2299392 * q^82 - 30672 * q^83 + 1313280 * q^84 + 815976 * q^85 - 1424976 * q^86 - 125892 * q^87 - 6804636 * q^89 - 2283456 * q^90 - 3838704 * q^91 - 244992 * q^92 - 3271128 * q^93 - 4631640 * q^95 + 2112390 * q^97 + 7177728 * q^98 + 21467982 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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