LMFDB - Embedded newform 43.7.d.a.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, degree $2$, 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:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	43.37
Dual form			43.7.d.a.7.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-12.8196i q^{2} +(-27.1856 - 15.6956i) q^{3} -100.343 q^{4} +(-154.521 - 89.2129i) q^{5} +(-201.212 + 348.509i) q^{6} +(237.672 - 137.220i) q^{7} +465.907i q^{8} +(128.203 + 222.054i) q^{9} +O(q^{10})$	\(q-12.8196i q^{2} +(-27.1856 - 15.6956i) q^{3} -100.343 q^{4} +(-154.521 - 89.2129i) q^{5} +(-201.212 + 348.509i) q^{6} +(237.672 - 137.220i) q^{7} +465.907i q^{8} +(128.203 + 222.054i) q^{9} +(-1143.68 + 1980.91i) q^{10} +1248.81 q^{11} +(2727.89 + 1574.95i) q^{12} +(-1134.17 - 1964.44i) q^{13} +(-1759.11 - 3046.86i) q^{14} +(2800.50 + 4850.61i) q^{15} -449.209 q^{16} +(-125.974 - 218.194i) q^{17} +(2846.65 - 1643.52i) q^{18} +(5838.49 + 3370.86i) q^{19} +(15505.2 + 8951.91i) q^{20} -8614.98 q^{21} -16009.3i q^{22} +(6606.78 - 11443.3i) q^{23} +(7312.68 - 12665.9i) q^{24} +(8105.39 + 14038.9i) q^{25} +(-25183.4 + 14539.7i) q^{26} +14835.3i q^{27} +(-23848.7 + 13769.1i) q^{28} +(-21385.7 + 12347.0i) q^{29} +(62183.0 - 35901.4i) q^{30} +(-9219.56 + 15968.7i) q^{31} +35576.7i q^{32} +(-33949.7 - 19600.9i) q^{33} +(-2797.17 + 1614.94i) q^{34} -48967.1 q^{35} +(-12864.3 - 22281.6i) q^{36} +(-61805.5 - 35683.4i) q^{37} +(43213.2 - 74847.4i) q^{38} +71205.9i q^{39} +(41564.9 - 71992.5i) q^{40} +101877. q^{41} +110441. i q^{42} +(-62823.1 - 48730.0i) q^{43} -125310. q^{44} -45749.4i q^{45} +(-146699. - 84696.5i) q^{46} +826.733 q^{47} +(12212.0 + 7050.60i) q^{48} +(-21166.0 + 36660.5i) q^{49} +(179974. - 103908. i) q^{50} +7908.96i q^{51} +(113806. + 197118. i) q^{52} +(123261. - 213495. i) q^{53} +190183. q^{54} +(-192968. - 111410. i) q^{55} +(63931.6 + 110733. i) q^{56} +(-105815. - 183277. i) q^{57} +(158285. + 274157. i) q^{58} +287368. q^{59} +(-281011. - 486725. i) q^{60} +(-373160. + 215444. i) q^{61} +(204713. + 118191. i) q^{62} +(60940.4 + 35184.0i) q^{63} +427331. q^{64} +404731. i q^{65} +(-251276. + 435223. i) q^{66} +(-68734.6 + 119052. i) q^{67} +(12640.7 + 21894.3i) q^{68} +(-359218. + 207395. i) q^{69} +627741. i q^{70} +(90467.6 - 52231.5i) q^{71} +(-103456. + 59730.6i) q^{72} +(286616. - 165478. i) q^{73} +(-457449. + 792324. i) q^{74} -508875. i q^{75} +(-585853. - 338242. i) q^{76} +(296808. - 171362. i) q^{77} +912834. q^{78} +(-419278. - 726211. i) q^{79} +(69412.4 + 40075.2i) q^{80} +(326308. - 565183. i) q^{81} -1.30603e6i q^{82} +(-89773.6 + 155492. i) q^{83} +864454. q^{84} +44954.1i q^{85} +(-624702. + 805370. i) q^{86} +775176. q^{87} +581831. i q^{88} +(-450443. - 260063. i) q^{89} -586491. q^{90} +(-539121. - 311261. i) q^{91} +(-662945. + 1.14825e6i) q^{92} +(501277. - 289413. i) q^{93} -10598.4i q^{94} +(-601448. - 1.04174e6i) q^{95} +(558398. - 967173. i) q^{96} +1.59060e6 q^{97} +(469975. + 271340. i) q^{98} +(160102. + 277304. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) $ 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	12.8196i		−	1.60246i	−0.598360	−	0.801228i	$-0.704181\pi$
$2$		−	12.8196i		−	1.60246i	0.598360	−	0.801228i	$-0.295819\pi$
$3$	−27.1856	−	15.6956i	−1.00687	−	0.581318i	−0.0965980	−	0.995323i	$-0.530796\pi$
$3$	−27.1856	−	15.6956i	−1.00687	−	0.581318i	−0.910274	+	0.414005i	$0.864129\pi$
$4$	−100.343			−1.56786
$5$	−154.521	−	89.2129i	−1.23617	−	0.713703i	−0.267861	−	0.963458i	$-0.586317\pi$
$5$	−154.521	−	89.2129i	−1.23617	−	0.713703i	−0.968309	+	0.249754i	$0.919650\pi$
$6$	−201.212	+	348.509i	−0.931536	+	1.61347i
$7$	237.672	−	137.220i	0.692920	−	0.400058i	−0.111785	−	0.993732i	$-0.535657\pi$
$7$	237.672	−	137.220i	0.692920	−	0.400058i	0.804705	+	0.593675i	$0.202323\pi$
$8$			465.907i			0.909974i
$9$	128.203	+	222.054i	0.175861	+	0.304601i
$10$	−1143.68	+	1980.91i	−1.14368	+	1.98091i
$11$	1248.81			0.938252			0.469126	−	0.883131i	$-0.344569\pi$
$11$	1248.81			0.938252			0.469126	+	0.883131i	$0.344569\pi$
$12$	2727.89	+	1574.95i	1.57864	+	0.911427i
$13$	−1134.17	−	1964.44i	−0.516236	−	0.894147i	−0.999822	−	0.0188506i	$-0.993999\pi$
$13$	−1134.17	−	1964.44i	−0.516236	−	0.894147i	0.483586	−	0.875297i	$-0.339334\pi$
$14$	−1759.11	−	3046.86i	−0.641074	−	1.11037i
$15$	2800.50	+	4850.61i	0.829777	+	1.43722i
$16$	−449.209			−0.109670
$17$	−125.974	−	218.194i	−0.0256410	−	0.0444115i	0.852920	−	0.522041i	$-0.174829\pi$
$17$	−125.974	−	218.194i	−0.0256410	−	0.0444115i	−0.878561	+	0.477630i	$0.841496\pi$
$18$	2846.65	−	1643.52i	0.488109	−	0.281810i
$19$	5838.49	+	3370.86i	0.851217	+	0.491450i	0.861061	−	0.508501i	$-0.169800\pi$
$19$	5838.49	+	3370.86i	0.851217	+	0.491450i	−0.00984455	+	0.999952i	$0.503134\pi$
$20$	15505.2	+	8951.91i	1.93814	+	1.11899i
$21$	−8614.98			−0.930243
$22$		−	16009.3i		−	1.50351i
$23$	6606.78	−	11443.3i	0.543008	−	0.940517i	−0.455721	−	0.890122i	$-0.650619\pi$
$23$	6606.78	−	11443.3i	0.543008	−	0.940517i	0.998729	−	0.0503949i	$-0.0160480\pi$
$24$	7312.68	−	12665.9i	0.528984	−	0.916228i
$25$	8105.39	+	14038.9i	0.518745	+	0.898492i
$26$	−25183.4	+	14539.7i	−1.43283	+	0.827245i
$27$			14835.3i			0.753710i
$28$	−23848.7	+	13769.1i	−1.08640	+	0.627235i
$29$	−21385.7	+	12347.0i	−0.876858	+	0.506254i	−0.869621	−	0.493720i	$-0.835637\pi$
$29$	−21385.7	+	12347.0i	−0.876858	+	0.506254i	−0.00723686	+	0.999974i	$0.502304\pi$
$30$	62183.0	−	35901.4i	2.30307	−	1.32968i
$31$	−9219.56	+	15968.7i	−0.309475	+	0.536026i	−0.978248	−	0.207441i	$-0.933486\pi$
$31$	−9219.56	+	15968.7i	−0.309475	+	0.536026i	0.668773	+	0.743467i	$0.266820\pi$
$32$			35576.7i			1.08572i
$33$	−33949.7	−	19600.9i	−0.944700	−	0.545423i
$34$	−2797.17	+	1614.94i	−0.0711675	+	0.0410886i
$35$	−48967.1			−1.14209
$36$	−12864.3	−	22281.6i	−0.275726	−	0.477572i
$37$	−61805.5	−	35683.4i	−1.22017	−	0.704468i	−0.255219	−	0.966883i	$-0.582148\pi$
$37$	−61805.5	−	35683.4i	−1.22017	−	0.704468i	−0.964955	+	0.262415i	$0.915481\pi$
$38$	43213.2	−	74847.4i	0.787527	−	1.36404i
$39$			71205.9i			1.20039i
$40$	41564.9	−	71992.5i	0.649451	−	1.12488i
$41$	101877.			1.47817			0.739085	−	0.673612i	$-0.235258\pi$
$41$	101877.			1.47817			0.739085	+	0.673612i	$0.235258\pi$
$42$			110441.i			1.49067i
$43$	−62823.1	−	48730.0i	−0.790158	−	0.612903i
$43$	−62823.1	−	48730.0i	−0.790158	−	0.612903i
$44$	−125310.			−1.47105
$45$		−	45749.4i		−	0.502052i
$46$	−146699.	−	84696.5i	−1.50714	−	0.870146i
$47$	826.733			0.00796291			0.00398145	−	0.999992i	$-0.498733\pi$
$47$	826.733			0.00796291			0.00398145	+	0.999992i	$0.498733\pi$
$48$	12212.0	+	7050.60i	0.110424	+	0.0637532i
$49$	−21166.0	+	36660.5i	−0.179908	+	0.311609i
$50$	179974.	−	103908.i	1.43979	−	0.831265i
$51$			7908.96i			0.0596223i
$52$	113806.	+	197118.i	0.809387	+	1.40190i
$53$	123261.	−	213495.i	0.827942	−	1.43404i	−0.0717085	−	0.997426i	$-0.522845\pi$
$53$	123261.	−	213495.i	0.827942	−	1.43404i	0.899650	−	0.436611i	$-0.143822\pi$
$54$	190183.			1.20779
$55$	−192968.	−	111410.i	−1.15984	−	0.669634i
$56$	63931.6	+	110733.i	0.364042	+	0.630539i
$57$	−105815.	−	183277.i	−0.571378	−	0.989655i
$58$	158285.	+	274157.i	0.811250	+	1.40513i
$59$	287368.			1.39921			0.699605	−	0.714530i	$-0.253359\pi$
$59$	287368.			1.39921			0.699605	+	0.714530i	$0.253359\pi$
$60$	−281011.	−	486725.i	−1.30098	−	2.25336i
$61$	−373160.	+	215444.i	−1.64401	+	0.949172i	−0.664627	+	0.747175i	$0.731410\pi$
$61$	−373160.	+	215444.i	−1.64401	+	0.949172i	−0.979386	+	0.201996i	$0.935257\pi$
$62$	204713.	+	118191.i	0.858957	+	0.495919i
$63$	60940.4	+	35184.0i	0.243716	+	0.140709i
$64$	427331.			1.63014
$65$			404731.i			1.47376i
$66$	−251276.	+	435223.i	−0.874016	+	1.51384i
$67$	−68734.6	+	119052.i	−0.228534	+	0.395833i	−0.957374	−	0.288851i	$-0.906727\pi$
$67$	−68734.6	+	119052.i	−0.228534	+	0.395833i	0.728840	+	0.684684i	$0.240060\pi$
$68$	12640.7	+	21894.3i	0.0402016	+	0.0696311i
$69$	−359218.	+	207395.i	−1.09348	+	0.631321i
$70$			627741.i			1.83015i
$71$	90467.6	−	52231.5i	0.252766	−	0.145934i	−0.368264	−	0.929721i	$-0.620048\pi$
$71$	90467.6	−	52231.5i	0.252766	−	0.145934i	0.621030	+	0.783787i	$0.286715\pi$
$72$	−103456.	+	59730.6i	−0.277179	+	0.160029i
$73$	286616.	−	165478.i	0.736770	−	0.425375i	−0.0841235	−	0.996455i	$-0.526809\pi$
$73$	286616.	−	165478.i	0.736770	−	0.425375i	0.820894	+	0.571081i	$0.193476\pi$
$74$	−457449.	+	792324.i	−1.12888	+	1.95527i
$75$		−	508875.i		−	1.20622i
$76$	−585853.	−	338242.i	−1.33459	−	0.770526i
$77$	296808.	−	171362.i	0.650134	−	0.375355i
$78$	912834.			1.92357
$79$	−419278.	−	726211.i	−0.850395	−	1.47293i	−0.880852	−	0.473391i	$-0.843030\pi$
$79$	−419278.	−	726211.i	−0.850395	−	1.47293i	0.0304572	−	0.999536i	$-0.490304\pi$
$80$	69412.4	+	40075.2i	0.135571	+	0.0782720i
$81$	326308.	−	565183.i	0.614007	−	1.06349i
$82$		−	1.30603e6i		−	2.36870i
$83$	−89773.6	+	155492.i	−0.157005	+	0.271941i	−0.933787	−	0.357828i	$-0.883517\pi$
$83$	−89773.6	+	155492.i	−0.157005	+	0.271941i	0.776782	+	0.629769i	$0.216851\pi$
$84$	864454.			1.45849
$85$			44954.1i			0.0732003i
$86$	−624702.	+	805370.i	−0.982149	+	1.26619i
$87$	775176.			1.17718
$88$			581831.i			0.853785i
$89$	−450443.	−	260063.i	−0.638954	−	0.368900i	0.145257	−	0.989394i	$-0.453599\pi$
$89$	−450443.	−	260063.i	−0.638954	−	0.368900i	−0.784212	+	0.620493i	$0.786932\pi$
$90$	−586491.			−0.804515
$91$	−539121.	−	311261.i	−0.715421	−	0.413049i
$92$	−662945.	+	1.14825e6i	−0.851362	+	1.47460i
$93$	501277.	−	289413.i	0.623203	−	0.359806i
$94$		−	10598.4i		−	0.0127602i
$95$	−601448.	−	1.04174e6i	−0.701499	−	1.21503i
$96$	558398.	−	967173.i	0.631146	−	1.09318i
$97$	1.59060e6			1.74280			0.871398	−	0.490577i	$-0.163214\pi$
$97$	1.59060e6			1.74280			0.871398	+	0.490577i	$0.163214\pi$
$98$	469975.	+	271340.i	0.499340	+	0.288294i
$99$	160102.	+	277304.i	0.165002	+	0.285792i
$100$	−813321.	−	1.40871e6i	−0.813321	−	1.40871i
$101$	127750.	+	221269.i	0.123993	+	0.214761i	0.921339	−	0.388761i	$-0.127097\pi$
$101$	127750.	+	221269.i	0.123993	+	0.214761i	−0.797346	+	0.603522i	$0.793763\pi$
$102$	101390.			0.0955421
$103$	−55531.9	−	96184.0i	−0.0508195	−	0.0880220i	0.839497	−	0.543365i	$-0.182850\pi$
$103$	−55531.9	−	96184.0i	−0.0508195	−	0.0880220i	−0.890316	+	0.455343i	$0.849517\pi$
$104$	915246.	−	528418.i	0.813651	−	0.469761i
$105$	1.33120e6	+	768567.i	1.14994	+	0.663917i
$106$	−2.73693e6	−	1.58017e6i	−2.29798	−	1.32674i
$107$	−1.27758e6			−1.04289			−0.521443	−	0.853286i	$-0.674606\pi$
$107$	−1.27758e6			−1.04289			−0.521443	+	0.853286i	$0.674606\pi$
$108$		−	1.48862e6i		−	1.18171i
$109$	−867637.	+	1.50279e6i	−0.669975	+	1.16043i	0.307936	+	0.951407i	$0.400362\pi$
$109$	−867637.	+	1.50279e6i	−0.669975	+	1.16043i	−0.977911	+	0.209023i	$0.932972\pi$
$110$	−1.42824e6	+	2.47378e6i	−1.07306	+	1.85859i
$111$	1.12014e6	+	1.94015e6i	0.819040	+	1.41862i
$112$	−106764.	+	61640.3i	−0.0759927	+	0.0438744i
$113$		−	78335.7i		−	0.0542906i	−0.999631	−	0.0271453i	$-0.991358\pi$
$113$		−	78335.7i		−	0.0542906i	0.999631	−	0.0271453i	$-0.00864167\pi$
$114$	−2.34955e6	+	1.35651e6i	−1.58588	+	0.915607i
$115$	−2.04178e6	+	1.17882e6i	−1.34250	+	0.775093i
$116$	2.14591e6	−	1.23894e6i	1.37479	−	0.793737i
$117$	290808.	−	503695.i	0.181572	−	0.314492i
$118$		−	3.68396e6i		−	2.24217i
$119$	−59881.0	−	34572.3i	−0.0355343	−	0.0205158i
$120$	−2.25993e6	+	1.30477e6i	−1.30783	+	0.755076i
$121$	−212025.			−0.119683
$122$	2.76191e6	+	4.78377e6i	1.52100	+	2.63446i
$123$	−2.76958e6	−	1.59902e6i	−1.48833	−	0.859287i
$124$	925120.	−	1.60235e6i	0.485213	−	0.840414i
$125$		−	104518.i		−	0.0535131i
$126$	451046.	−	781234.i	0.225480	−	0.390544i
$127$	−3.26576e6			−1.59431			−0.797155	−	0.603774i	$-0.793663\pi$
$127$	−3.26576e6			−1.59431			−0.797155	+	0.603774i	$0.793663\pi$
$128$		−	3.20132e6i		−	1.52651i
$129$	943035.	+	2.31080e6i	0.439297	+	1.07645i
$130$	5.18850e6			2.36163
$131$		−	422176.i		−	0.187793i	−0.995582	−	0.0938965i	$-0.970068\pi$
$131$		−	422176.i		−	0.187793i	0.995582	−	0.0938965i	$-0.0299323\pi$
$132$	3.40662e6	+	1.96681e6i	1.48116	+	0.855148i
$133$	1.85019e6			0.786433
$134$	1.52620e6	+	881153.i	0.634304	+	0.366216i
$135$	1.32350e6	−	2.29237e6i	0.537926	−	0.931715i
$136$	101658.	−	58692.2i	0.0404133	−	0.0233326i
$137$			2.92378e6i			1.13706i	0.822663	+	0.568529i	$0.192487\pi$
$137$			2.92378e6i			1.13706i	−0.822663	+	0.568529i	$0.807513\pi$
$138$	2.65872e6	+	4.60504e6i	1.01166	+	1.75225i
$139$	−304791.	+	527913.i	−0.113490	+	0.196571i	−0.917175	−	0.398484i	$-0.869536\pi$
$139$	−304791.	+	527913.i	−0.113490	+	0.196571i	0.803685	+	0.595055i	$0.202870\pi$
$140$	4.91351e6			1.79064
$141$	−22475.2	−	12976.1i	−0.00801763	−	0.00462898i
$142$	−669589.	−	1.15976e6i	−0.233853	−	0.405046i
$143$	−1.41637e6	−	2.45322e6i	−0.484360	−	0.838936i
$144$	−57589.9	−	99748.7i	−0.0192867	−	0.0334056i
$145$	4.40606e6			1.44526
$146$	−2.12137e6	−	3.67432e6i	−0.681644	−	1.18064i
$147$	1.15082e6	−	664425.i	0.362288	−	0.209167i
$148$	6.20176e6	+	3.58059e6i	1.91307	+	1.10451i
$149$	−2.34530e6	−	1.35406e6i	−0.708988	−	0.409334i	0.101698	−	0.994815i	$-0.467572\pi$
$149$	−2.34530e6	−	1.35406e6i	−0.708988	−	0.409334i	−0.810686	+	0.585481i	$0.800906\pi$
$150$	−6.52360e6			−1.93292
$151$			4.41037e6i			1.28099i	0.767964	+	0.640493i	$0.221270\pi$
$151$			4.41037e6i			1.28099i	−0.767964	+	0.640493i	$0.778730\pi$
$152$	−1.57050e6	+	2.72019e6i	−0.447207	+	0.774585i
$153$	32300.5	−	55946.2i	0.00901853	−	0.0156205i
$154$	−2.19680e6	−	3.80497e6i	−0.601489	−	1.04181i
$155$	2.84924e6	−	1.64501e6i	0.765126	−	0.441746i
$156$		−	7.14503e6i		−	1.88205i
$157$	−3.21701e6	+	1.85734e6i	−0.831292	+	0.479947i	−0.854295	−	0.519789i	$-0.826011\pi$
$157$	−3.21701e6	+	1.85734e6i	−0.831292	+	0.479947i	0.0230028	+	0.999735i	$0.492677\pi$
$158$	−9.30976e6	+	5.37499e6i	−2.36030	+	1.36272i
$159$	−6.70186e6	+	3.86932e6i	−1.66726	+	0.962595i
$160$	3.17390e6	−	5.49736e6i	0.774879	−	1.34213i
$161$		−	3.62632e6i		−	0.868938i
$162$	−7.24544e6	−	4.18316e6i	−1.70420	−	0.983919i
$163$	4.85171e6	−	2.80114e6i	1.12029	−	0.646802i	0.178818	−	0.983882i	$-0.442773\pi$
$163$	4.85171e6	−	2.80114e6i	1.12029	−	0.646802i	0.941476	+	0.337080i	$0.109439\pi$
$164$	−1.02227e7			−2.31757
$165$	3.49730e6	+	6.05750e6i	0.778540	+	1.34847i
$166$	1.99336e6	+	1.15087e6i	0.435774	+	0.251594i
$167$	−2.06323e6	+	3.57362e6i	−0.442995	+	0.767290i	−0.997910	−	0.0646173i	$-0.979417\pi$
$167$	−2.06323e6	+	3.57362e6i	−0.442995	+	0.767290i	0.554915	+	0.831907i	$0.312751\pi$
$168$		−	4.01378e6i		−	0.846497i
$169$	−159284.	+	275887.i	−0.0329998	+	0.0571573i
$170$	576296.			0.117300
$171$			1.72862e6i			0.345708i
$172$	6.30387e6	+	4.88973e6i	1.23886	+	0.960947i
$173$	2.10733e6			0.407001			0.203500	−	0.979075i	$-0.434768\pi$
$173$	2.10733e6			0.407001			0.203500	+	0.979075i	$0.434768\pi$
$174$		−	9.93748e6i		−	1.88638i
$175$	3.85284e6	+	2.22444e6i	0.718898	+	0.415056i
$176$	−560978.			−0.102898
$177$	−7.81227e6	−	4.51042e6i	−1.40883	−	0.813386i
$178$	−3.33392e6	+	5.77452e6i	−0.591146	+	1.02390i
$179$	2.23434e6	−	1.29000e6i	0.389574	−	0.224921i	−0.292401	−	0.956296i	$-0.594454\pi$
$179$	2.23434e6	−	1.29000e6i	0.389574	−	0.224921i	0.681976	+	0.731375i	$0.261121\pi$
$180$			4.59064e6i			0.787148i
$181$	−1.25865e6	−	2.18004e6i	−0.212260	−	0.367645i	0.740161	−	0.672429i	$-0.234749\pi$
$181$	−1.25865e6	−	2.18004e6i	−0.212260	−	0.367645i	−0.952422	+	0.304784i	$0.901416\pi$
$182$	−3.99026e6	+	6.91133e6i	−0.661892	+	1.14643i
$183$	1.35261e7			2.20708
$184$	5.33150e6	+	3.07814e6i	0.855846	+	0.494123i
$185$	6.36684e6	+	1.10277e7i	1.00556	+	1.74169i
$186$	−3.71017e6	−	6.42620e6i	−0.576573	−	0.998654i
$187$	−157318.	−	272483.i	−0.0240577	−	0.0416692i
$188$	−82957.0			−0.0124847
$189$	2.03569e6	+	3.52593e6i	0.301528	+	0.522261i
$190$	−1.33547e7	+	7.71035e6i	−1.94703	+	1.12412i
$191$	529684.	+	305813.i	0.0760181	+	0.0438891i	0.537527	−	0.843246i	$-0.319359\pi$
$191$	529684.	+	305813.i	0.0760181	+	0.0438891i	−0.461509	+	0.887135i	$0.652692\pi$
$192$	−1.16172e7	−	6.70722e6i	−1.64134	−	0.947630i
$193$	1.05603e7			1.46894			0.734472	−	0.678640i	$-0.237430\pi$
$193$	1.05603e7			1.46894			0.734472	+	0.678640i	$0.237430\pi$
$194$		−	2.03909e7i		−	2.79275i
$195$	6.35249e6	−	1.10028e7i	0.856722	−	1.48389i
$196$	2.12386e6	−	3.67864e6i	0.282071	−	0.488561i
$197$	−5.91981e6	−	1.02534e7i	−0.774299	−	1.34113i	−0.935188	−	0.354153i	$-0.884769\pi$
$197$	−5.91981e6	−	1.02534e7i	−0.774299	−	1.34113i	0.160888	−	0.986973i	$-0.448564\pi$
$198$	3.55494e6	−	2.05245e6i	0.457970	−	0.264409i
$199$		−	5.52654e6i		−	0.701285i	−0.936509	−	0.350642i	$-0.885963\pi$
$199$		−	5.52654e6i		−	0.701285i	0.936509	−	0.350642i	$-0.114037\pi$
$200$	−6.54084e6	+	3.77635e6i	−0.817605	+	0.472044i
$201$	3.73718e6	−	2.15766e6i	0.460210	−	0.265702i
$202$	2.83659e6	−	1.63771e6i	0.344146	−	0.198693i
$203$	−3.38851e6	+	5.86908e6i	−0.405062	+	0.701587i
$204$		−	793610.i		−	0.0934796i
$205$	−1.57422e7	−	9.08874e6i	−1.82727	−	1.05497i
$206$	−1.23304e6	+	711898.i	−0.141051	+	0.0814360i
$207$	3.38803e6			0.381977
$208$	509480.	+	882445.i	0.0566157	+	0.0980613i
$209$	7.29119e6	+	4.20957e6i	0.798656	+	0.461104i
$210$	9.85276e6	−	1.70655e7i	1.06390	−	1.84273i
$211$		−	1.26231e7i		−	1.34375i	−0.740662	−	0.671877i	$-0.765488\pi$
$211$		−	1.26231e7i		−	1.34375i	0.740662	−	0.671877i	$-0.234512\pi$
$212$	−1.23684e7	+	2.14228e7i	−1.29810	+	2.24837i
$213$	−3.27922e6			−0.339337
$214$			1.63781e7i			1.67118i
$215$	5.36016e6	+	1.31345e7i	0.539340	+	1.32159i
$216$	−6.91186e6			−0.685857
$217$			5.06042e6i			0.495231i
$218$	1.92652e7	+	1.11228e7i	1.85954	+	1.07360i
$219$	−1.03891e7			−0.989112
$220$	1.93631e7	+	1.11793e7i	1.81847	+	1.04989i
$221$	−285753.	+	494938.i	−0.0264736	+	0.0458537i
$222$	2.48720e7	−	1.43599e7i	2.27327	−	1.31248i
$223$			2.48592e6i			0.224167i	0.993699	+	0.112084i	$0.0357525\pi$
$223$			2.48592e6i			0.224167i	−0.993699	+	0.112084i	$0.964248\pi$
$224$	4.88183e6	+	8.45558e6i	0.434349	+	0.752314i
$225$	−2.07827e6	+	3.59967e6i	−0.182454	+	0.316020i
$226$	−1.00424e6			−0.0869982
$227$	−9.30334e6	−	5.37129e6i	−0.795356	−	0.459199i	0.0464888	−	0.998919i	$-0.485197\pi$
$227$	−9.30334e6	−	5.37129e6i	−0.795356	−	0.459199i	−0.841845	+	0.539720i	$0.818530\pi$
$228$	1.06178e7	+	1.83906e7i	0.895842	+	1.55164i
$229$	−4.93688e6	−	8.55093e6i	−0.411099	−	0.712044i	0.583911	−	0.811817i	$-0.301522\pi$
$229$	−4.93688e6	−	8.55093e6i	−0.411099	−	0.712044i	−0.995010	+	0.0997734i	$0.968188\pi$
$230$	1.51120e7	+	2.61748e7i	1.24205	+	2.15130i
$231$	−1.07585e7			−0.872803
$232$	−5.75256e6	−	9.96373e6i	−0.460678	−	0.797918i
$233$	−4.36594e6	+	2.52068e6i	−0.345152	+	0.199273i	−0.662548	−	0.749020i	$-0.730525\pi$
$233$	−4.36594e6	+	2.52068e6i	−0.345152	+	0.199273i	0.317396	+	0.948293i	$0.397192\pi$
$234$	−6.45718e6	−	3.72806e6i	−0.503959	−	0.290961i
$235$	−127748.	−	73755.3i	−0.00984351	−	0.00568315i
$236$	−2.88355e7			−2.19377
$237$			2.63233e7i			1.97740i
$238$	−443205.	+	767653.i	−0.0328756	+	0.0569422i
$239$	1.16405e7	−	2.01619e7i	0.852664	−	1.47686i	−0.0261310	−	0.999659i	$-0.508319\pi$
$239$	1.16405e7	−	2.01619e7i	0.852664	−	1.47686i	0.878795	−	0.477199i	$-0.158348\pi$
$240$	−1.25801e6	−	2.17894e6i	−0.0910018	−	0.157620i
$241$	−4.38536e6	+	2.53189e6i	−0.313295	+	0.180881i	−0.648400	−	0.761300i	$-0.724562\pi$
$241$	−4.38536e6	+	2.53189e6i	−0.313295	+	0.180881i	0.335105	+	0.942181i	$0.391228\pi$
$242$			2.71809e6i			0.191786i
$243$	−8.37576e6	+	4.83575e6i	−0.583721	+	0.337011i
$244$	3.74440e7	−	2.16183e7i	2.57759	−	1.48817i
$245$	6.54119e6	−	3.77656e6i	0.444793	−	0.256802i
$246$	−2.04988e7	+	3.55050e7i	−1.37697	+	2.38498i
$247$		−	1.52925e7i		−	1.01482i
$248$	−7.43994e6	−	4.29545e6i	−0.487769	−	0.281614i
$249$	4.88109e6	−	2.81810e6i	0.316169	−	0.182540i
$250$	−1.33988e6			−0.0857524
$251$	−7.52918e6	−	1.30409e7i	−0.476131	−	0.824683i	0.523495	−	0.852029i	$-0.324628\pi$
$251$	−7.52918e6	−	1.30409e7i	−0.476131	−	0.824683i	−0.999626	+	0.0273458i	$0.991294\pi$
$252$	−6.11496e6	−	3.53047e6i	−0.382113	−	0.220613i
$253$	8.25063e6	−	1.42905e7i	0.509478	−	0.882443i
$254$			4.18659e7i			2.55481i
$255$	705581.	−	1.22210e6i	0.0425526	−	0.0737033i
$256$	−1.36906e7			−0.816025
$257$		−	8.42306e6i		−	0.496216i	−0.968732	−	0.248108i	$-0.920191\pi$
$257$		−	8.42306e6i		−	0.496216i	0.968732	−	0.248108i	$-0.0798088\pi$
$258$	2.96236e7	−	1.20894e7i	1.72496	−	0.703954i
$259$	−1.95859e7			−1.12731
$260$		−	4.06120e7i		−	2.31065i
$261$	−5.48342e6	−	3.16585e6i	−0.308411	−	0.178061i
$262$	−5.41214e6			−0.300930
$263$	6.70832e6	+	3.87305e6i	0.368762	+	0.212905i	0.672918	−	0.739717i	$-0.265041\pi$
$263$	6.70832e6	+	3.87305e6i	0.368762	+	0.212905i	−0.304155	+	0.952622i	$0.598374\pi$
$264$	9.13217e6	−	1.58174e7i	0.496321	−	0.859653i
$265$	−3.80930e7	+	2.19930e7i	−2.04695	+	1.18181i
$266$		−	2.37188e7i		−	1.26022i
$267$	8.16370e6	+	1.41399e7i	0.428897	+	0.742871i
$268$	6.89705e6	−	1.19460e7i	0.358310	−	0.620611i
$269$	−2.74015e7			−1.40773			−0.703863	−	0.710336i	$-0.748543\pi$
$269$	−2.74015e7			−1.40773			−0.703863	+	0.710336i	$0.748543\pi$
$270$	−2.93873e7	−	1.69668e7i	−1.49303	−	0.862002i
$271$	1.13081e7	+	1.95862e7i	0.568176	+	0.984109i	0.996746	+	0.0806011i	$0.0256840\pi$
$271$	1.13081e7	+	1.95862e7i	0.568176	+	0.984109i	−0.428571	+	0.903508i	$0.640983\pi$
$272$	56588.8	+	98014.6i	0.00281205	+	0.00487062i
$273$	9.77086e6	+	1.69236e7i	0.480225	+	0.831774i
$274$	3.74818e7			1.82208
$275$	1.01221e7	+	1.75320e7i	0.486714	+	0.843013i
$276$	3.60451e7	−	2.08106e7i	1.71443	−	0.989824i
$277$	2.16077e7	+	1.24752e7i	1.01664	+	0.586960i	0.913130	−	0.407668i	$-0.133658\pi$
$277$	2.16077e7	+	1.24752e7i	1.01664	+	0.586960i	0.103514	+	0.994628i	$0.466991\pi$
$278$	6.76766e6	+	3.90731e6i	0.314995	+	0.181863i
$279$	−4.72790e6			−0.217699
$280$		−	2.28141e7i		−	1.03927i
$281$	7.44081e6	−	1.28879e7i	0.335352	−	0.580847i	−0.648200	−	0.761470i	$-0.724478\pi$
$281$	7.44081e6	−	1.28879e7i	0.335352	−	0.580847i	0.983552	+	0.180623i	$0.0578113\pi$
$282$	−166348.	+	288124.i	−0.00741774	+	0.0128479i
$283$	−1.70377e7	−	2.95102e7i	−0.751714	−	1.30201i	−0.946992	−	0.321258i	$-0.895894\pi$
$283$	−1.70377e7	−	2.95102e7i	−0.751714	−	1.30201i	0.195278	−	0.980748i	$-0.437439\pi$
$284$	−9.07781e6	+	5.24107e6i	−0.396302	+	0.228805i
$285$			3.77603e7i			1.63118i
$286$	−3.14494e7	+	1.81573e7i	−1.34436	+	0.776165i
$287$	2.42132e7	−	1.39795e7i	1.02425	−	0.591353i
$288$	−7.89995e6	+	4.56104e6i	−0.330710	+	0.190935i
$289$	1.20370e7	−	2.08488e7i	0.498685	−	0.863748i
$290$		−	5.64841e7i		−	2.31597i
$291$	−4.32414e7	−	2.49654e7i	−1.75477	−	1.01312i
$292$	−2.87600e7	+	1.66046e7i	−1.15515	+	0.666929i
$293$	4.32143e7			1.71801			0.859003	−	0.511971i	$-0.171084\pi$
$293$	4.32143e7			1.71801			0.859003	+	0.511971i	$0.171084\pi$
$294$	−8.51769e6	−	1.47531e7i	−0.335181	−	0.580551i
$295$	−4.44045e7	−	2.56370e7i	−1.72966	−	0.998621i
$296$	1.66251e7	−	2.87956e7i	0.641048	−	1.11033i
$297$			1.85265e7i			0.707171i
$298$	−1.73585e7	+	3.00659e7i	−0.655940	+	1.13612i
$299$	−2.99729e7			−1.12128
$300$			5.10622e7i			1.89119i
$301$	−2.16180e7	−	2.96117e6i	−0.792713	−	0.108584i
$302$	5.65394e7			2.05272
$303$		−	8.02043e6i		−	0.288317i
$304$	−2.62270e6	−	1.51422e6i	−0.0933531	−	0.0538974i
$305$	7.68815e7			2.70971
$306$	−717210.	−	414081.i	−0.0250312	−	0.0144518i
$307$	−1.42630e7	+	2.47043e7i	−0.492942	+	0.853801i	−0.999967	−	0.00813035i	$-0.997412\pi$
$307$	−1.42630e7	+	2.47043e7i	−0.492942	+	0.853801i	0.507025	+	0.861932i	$0.330745\pi$
$308$	−2.97826e7	+	1.71950e7i	−1.01932	+	0.588505i
$309$			3.48642e6i			0.118169i
$310$	−2.10884e7	−	3.65262e7i	−0.707878	−	1.22608i
$311$	−2.85337e6	+	4.94218e6i	−0.0948587	+	0.164300i	−0.909550	−	0.415595i	$-0.863573\pi$
$311$	−2.85337e6	+	4.94218e6i	−0.0948587	+	0.164300i	0.814691	+	0.579895i	$0.196907\pi$
$312$	−3.31753e7			−1.09232
$313$	−1.48449e7	−	8.57073e6i	−0.484112	−	0.279502i	0.238017	−	0.971261i	$-0.423503\pi$
$313$	−1.48449e7	−	8.57073e6i	−0.484112	−	0.279502i	−0.722128	+	0.691759i	$0.756836\pi$
$314$	2.38105e7	+	4.12409e7i	0.769093	+	1.33211i
$315$	−6.27773e6	−	1.08733e7i	−0.200850	−	0.347882i
$316$	4.20717e7	+	7.28703e7i	1.33330	+	2.30935i
$317$	−1.01432e7			−0.318418			−0.159209	−	0.987245i	$-0.550894\pi$
$317$	−1.01432e7			−0.318418			−0.159209	+	0.987245i	$0.550894\pi$
$318$	4.96033e7	+	8.59155e7i	1.54252	+	2.67171i
$319$	−2.67067e7	+	1.54191e7i	−0.822714	+	0.474994i
$320$	−6.60318e7	−	3.81235e7i	−2.01513	−	1.16344i
$321$	3.47317e7	+	2.00524e7i	1.05005	+	0.606248i
$322$	−4.64881e7			−1.39243
$323$		−	1.69856e6i		−	0.0504051i
$324$	−3.27428e7	+	5.67122e7i	−0.962678	+	1.66741i
$325$	1.83858e7	−	3.18451e7i	0.535590	−	0.927669i
$326$	−3.59096e7	−	6.21972e7i	−1.03647	−	1.79522i
$327$	4.71744e7	−	2.72361e7i	1.34916	−	0.778937i
$328$			4.74651e7i			1.34510i
$329$	196491.	−	113444.i	0.00551766	−	0.00318562i
$330$	7.76550e7	−	4.48341e7i	2.16087	−	1.24758i
$331$	−1.89354e7	+	1.09323e7i	−0.522143	+	0.301459i	−0.737811	−	0.675007i	$-0.764140\pi$
$331$	−1.89354e7	+	1.09323e7i	−0.522143	+	0.301459i	0.215668	+	0.976467i	$0.430807\pi$
$332$	9.00817e6	−	1.56026e7i	0.246163	−	0.426366i
$333$		−	1.82989e7i		−	0.495555i
$334$	4.58126e7	+	2.64499e7i	1.22955	+	0.709879i
$335$	2.12419e7	−	1.22640e7i	0.565015	−	0.326211i
$336$	3.86993e6			0.102020
$337$	−7.71788e6	−	1.33678e7i	−0.201655	−	0.349276i	0.747407	−	0.664366i	$-0.231299\pi$
$337$	−7.71788e6	−	1.33678e7i	−0.201655	−	0.349276i	−0.949062	+	0.315090i	$0.897965\pi$
$338$	3.53678e6	+	2.04196e6i	0.0915920	+	0.0528807i
$339$	−1.22952e6	+	2.12960e6i	−0.0315601	+	0.0546637i
$340$		−	4.51084e6i		−	0.114768i
$341$	−1.15135e7	+	1.99420e7i	−0.290365	+	0.502927i
$342$	2.21602e7			0.553982
$343$			4.39051e7i			1.08801i
$344$	2.27036e7	−	2.92697e7i	0.557725	−	0.719023i
$345$	7.40091e7			1.80230
$346$		−	2.70153e7i		−	0.652200i
$347$	−5.77909e7	−	3.33656e7i	−1.38316	−	0.798566i	−0.390625	−	0.920550i	$-0.627741\pi$
$347$	−5.77909e7	−	3.33656e7i	−1.38316	−	0.798566i	−0.992532	+	0.121984i	$0.961074\pi$
$348$	−7.77836e7			−1.84565
$349$	−536016.	−	309469.i	−0.0126096	−	0.00728016i	0.493682	−	0.869643i	$-0.335651\pi$
$349$	−536016.	−	309469.i	−0.0126096	−	0.00728016i	−0.506292	+	0.862362i	$0.668984\pi$
$350$	2.85165e7	−	4.93920e7i	0.665108	−	1.15200i
$351$	2.91431e7	−	1.68257e7i	0.673928	−	0.389093i
$352$			4.44287e7i			1.01867i
$353$	2.56412e7	+	4.44118e7i	0.582927	+	1.00966i	0.995130	+	0.0985670i	$0.0314259\pi$
$353$	2.56412e7	+	4.44118e7i	0.582927	+	1.00966i	−0.412204	+	0.911092i	$0.635241\pi$
$354$	−5.78219e7	+	1.00150e8i	−1.30341	+	2.25758i
$355$	−1.86389e7			−0.416615
$356$	4.51989e7	+	2.60956e7i	1.00179	+	0.578385i
$357$	1.08527e6	+	1.87973e6i	0.0238524	+	0.0413135i
$358$	−1.65373e7	−	2.86434e7i	−0.360425	−	0.624275i
$359$	−1.57501e7	−	2.72801e7i	−0.340409	−	0.589606i	0.644099	−	0.764942i	$-0.277232\pi$
$359$	−1.57501e7	−	2.72801e7i	−0.340409	−	0.589606i	−0.984509	+	0.175336i	$0.943899\pi$
$360$	2.13150e7			0.456854
$361$	−797593.	−	1.38147e6i	−0.0169535	−	0.0293644i
$362$	−2.79474e7	+	1.61354e7i	−0.589135	+	0.340137i
$363$	5.76402e6	+	3.32786e6i	0.120505	+	0.0695737i
$364$	5.40971e7	+	3.12330e7i	1.12168	+	0.647603i
$365$	−5.90511e7			−1.21437
$366$		−	1.73399e8i		−	3.53675i
$367$	−1.54846e7	+	2.68201e7i	−0.313257	+	0.542577i	−0.979065	−	0.203546i	$-0.934753\pi$
$367$	−1.54846e7	+	2.68201e7i	−0.313257	+	0.542577i	0.665808	+	0.746123i	$0.268087\pi$
$368$	−2.96782e6	+	5.14042e6i	−0.0595518	+	0.103147i
$369$	1.30609e7	+	2.26222e7i	0.259953	+	0.450252i
$370$	1.41371e8	−	8.16207e7i	2.79097	−	1.61137i
$371$		−	6.76556e7i		−	1.32490i
$372$	−5.02998e7	+	2.90406e7i	−0.977096	+	0.564127i
$373$	3.85960e7	−	2.22834e7i	0.743731	−	0.429393i	−0.0796934	−	0.996819i	$-0.525394\pi$
$373$	3.85960e7	−	2.22834e7i	0.743731	−	0.429393i	0.823424	+	0.567426i	$0.192061\pi$
$374$	−3.49314e6	+	2.01676e6i	−0.0667730	+	0.0385514i
$375$	−1.64047e6	+	2.84137e6i	−0.0311081	+	0.0538809i
$376$			385180.i			0.00724604i
$377$	4.85101e7	+	2.80073e7i	0.905332	+	0.522694i
$378$	4.52011e7	−	2.60969e7i	0.836900	−	0.483184i
$379$	6.36338e7			1.16888			0.584441	−	0.811436i	$-0.301314\pi$
$379$	6.36338e7			1.16888			0.584441	+	0.811436i	$0.301314\pi$
$380$	6.03512e7	+	1.04531e8i	1.09985	+	1.90500i
$381$	8.87815e7	+	5.12580e7i	1.60527	+	0.926802i
$382$	3.92042e6	−	6.79036e6i	0.0703303	−	0.121816i
$383$		−	5.19796e7i		−	0.925202i	−0.886567	−	0.462601i	$-0.846916\pi$
$383$		−	5.19796e7i		−	0.925202i	0.886567	−	0.462601i	$-0.153084\pi$
$384$	−5.02467e7	+	8.70298e7i	−0.887388	+	1.53700i
$385$	−6.11508e7			−1.07157
$386$		−	1.35379e8i		−	2.35392i
$387$	2.76659e6	−	2.01975e7i	0.0477323	−	0.348469i
$388$	−1.59606e8			−2.73246
$389$			3.06400e7i			0.520523i	0.965538	+	0.260261i	$0.0838087\pi$
$389$			3.06400e7i			0.520523i	−0.965538	+	0.260261i	$0.916191\pi$
$390$	−1.41052e8	−	8.14366e7i	−2.37786	−	1.37286i
$391$	−3.32914e6			−0.0556931
$392$	−1.70804e7	−	9.86137e6i	−0.283556	−	0.163711i
$393$	−6.62629e6	+	1.14771e7i	−0.109167	+	0.189084i
$394$	−1.31445e8	+	7.58898e7i	−2.14909	+	1.24078i
$395$			1.49620e8i			2.42772i
$396$	−1.60651e7	−	2.78256e7i	−0.258701	−	0.448083i
$397$	2.07871e7	−	3.60044e7i	0.332218	−	0.575418i	−0.650729	−	0.759310i	$-0.725536\pi$
$397$	2.07871e7	−	3.60044e7i	0.332218	−	0.575418i	0.982946	+	0.183892i	$0.0588697\pi$
$398$	−7.08483e7			−1.12378
$399$	−5.02985e7	−	2.90399e7i	−0.791838	−	0.457168i
$400$	−3.64101e6	−	6.30642e6i	−0.0568908	−	0.0985378i
$401$	3.56807e7	+	6.18008e7i	0.553351	+	0.958432i	0.998030	+	0.0627417i	$0.0199844\pi$
$401$	3.56807e7	+	6.18008e7i	0.553351	+	0.958432i	−0.444679	+	0.895690i	$0.646682\pi$
$402$	−2.76604e7	−	4.79093e7i	−0.425776	−	0.737465i
$403$	4.18262e7			0.639048
$404$	−1.28188e7	−	2.22028e7i	−0.194403	−	0.336716i
$405$	−1.00843e8	+	5.82219e7i	−1.51803	+	0.876438i
$406$	7.52395e7	+	4.34395e7i	1.12426	+	0.649093i
$407$	−7.71836e7	−	4.45620e7i	−1.14483	−	0.660969i
$408$	−3.68484e6			−0.0542547
$409$		−	5.23395e7i		−	0.764996i	−0.923956	−	0.382498i	$-0.875064\pi$
$409$		−	5.23395e7i		−	0.764996i	0.923956	−	0.382498i	$-0.124936\pi$
$410$	−1.16514e8	+	2.01809e8i	−1.69055	+	2.92812i
$411$	4.58904e7	−	7.94845e7i	0.660992	−	1.14487i
$412$	5.57224e6	+	9.65141e6i	0.0796780	+	0.138006i
$413$	6.82993e7	−	3.94326e7i	0.969541	−	0.559765i
$414$		−	4.34334e7i		−	0.612100i
$415$	2.77439e7	−	1.60179e7i	0.388171	−	0.224110i
$416$	6.98884e7	−	4.03501e7i	0.970790	−	0.560486i
$417$	1.65718e7	−	9.56775e6i	0.228540	−	0.131948i
$418$	5.39652e7	−	9.34705e7i	0.738899	−	1.27981i
$419$			1.62920e6i			0.0221479i	0.999939	+	0.0110739i	$0.00352502\pi$
$419$			1.62920e6i			0.0221479i	−0.999939	+	0.0110739i	$0.996475\pi$
$420$	−1.33577e8	−	7.71205e7i	−1.80295	−	1.04093i
$421$	−6.38306e7	+	3.68526e7i	−0.855427	+	0.493881i	−0.862478	−	0.506094i	$-0.831089\pi$
$421$	−6.38306e7	+	3.68526e7i	−0.855427	+	0.493881i	0.00705150	+	0.999975i	$0.497755\pi$
$422$	−1.61824e8			−2.15331
$423$	105990.	+	183579.i	0.00140037	+	0.00242551i
$424$	9.94688e7	+	5.74283e7i	1.30494	+	0.753405i
$425$	2.04214e6	−	3.53709e6i	0.0266023	−	0.0460765i
$426$			4.20384e7i			0.543772i
$427$	−5.91263e7	+	1.02410e8i	−0.759447	+	1.31540i
$428$	1.28196e8			1.63510
$429$			8.89229e7i			1.12627i
$430$	1.68379e8	−	6.87154e7i	2.11779	−	0.864268i
$431$	3.06752e7			0.383138			0.191569	−	0.981479i	$-0.438642\pi$
$431$	3.06752e7			0.383138			0.191569	+	0.981479i	$0.438642\pi$
$432$		−	6.66414e6i		−	0.0826595i
$433$	−1.29255e8	−	7.46253e7i	−1.59215	−	0.919226i	−0.992938	−	0.118633i	$-0.962149\pi$
$433$	−1.29255e8	−	7.46253e7i	−1.59215	−	0.919226i	−0.599209	−	0.800593i	$-0.704518\pi$
$434$	6.48728e7			0.793585
$435$	−1.19781e8	−	6.91557e7i	−1.45519	−	0.840157i
$436$	8.70614e7	−	1.50795e8i	1.05043	−	1.81939i
$437$	7.71473e7	−	4.45410e7i	0.924435	−	0.533723i
$438$			1.33184e8i			1.58501i
$439$	7.59919e7	+	1.31622e8i	0.898201	+	1.55573i	0.829792	+	0.558073i	$0.188459\pi$
$439$	7.59919e7	+	1.31622e8i	0.898201	+	1.55573i	0.0684096	+	0.997657i	$0.478208\pi$
$440$	5.19068e7	−	8.99052e7i	0.609349	−	1.05542i
$441$	−1.08542e7			−0.126555
$442$	6.34493e6	+	3.66325e6i	0.0734784	+	0.0424228i
$443$	−5.03329e7	−	8.71792e7i	−0.578950	−	1.00277i	−0.995600	−	0.0937040i	$-0.970129\pi$
$443$	−5.03329e7	−	8.71792e7i	−0.578950	−	1.00277i	0.416650	−	0.909067i	$-0.363204\pi$
$444$	−1.12399e8	−	1.94681e8i	−1.28414	−	2.22420i
$445$	4.64020e7	+	8.03707e7i	0.526571	+	0.912048i
$446$	3.18686e7			0.359218
$447$	4.25055e7	+	7.36216e7i	0.475907	+	0.824295i
$448$	1.01565e8	−	5.86383e7i	1.12956	−	0.652150i
$449$	−2.20118e7	−	1.27085e7i	−0.243174	−	0.140396i	0.373461	−	0.927646i	$-0.378171\pi$
$449$	−2.20118e7	−	1.27085e7i	−0.243174	−	0.140396i	−0.616635	+	0.787249i	$0.711504\pi$
$450$	4.61465e7	+	2.66427e7i	0.506408	+	0.292375i
$451$	1.27225e8			1.38690
$452$			7.86045e6i			0.0851201i
$453$	6.92234e7	−	1.19898e8i	0.744660	−	1.28979i
$454$	−6.88580e7	+	1.19266e8i	−0.735846	+	1.27452i
$455$	5.55371e7	+	9.61930e7i	0.589588	+	1.02120i
$456$	8.53901e7	−	4.93000e7i	0.900560	−	0.519939i
$457$			5.36683e7i			0.562302i	0.959664	+	0.281151i	$0.0907162\pi$
$457$			5.36683e7i			0.562302i	−0.959664	+	0.281151i	$0.909284\pi$
$458$	−1.09620e8	+	6.32890e7i	−1.14102	+	0.658767i
$459$	3.23697e6	−	1.86886e6i	0.0334734	−	0.0193259i
$460$	2.04878e8	−	1.18287e8i	2.10486	−	1.21524i
$461$	−4.61402e6	+	7.99171e6i	−0.0470952	+	0.0815712i	−0.888612	−	0.458660i	$-0.848330\pi$
$461$	−4.61402e6	+	7.99171e6i	−0.0470952	+	0.0815712i	0.841517	+	0.540231i	$0.181663\pi$
$462$			1.37920e8i			1.39863i
$463$	−1.55014e8	−	8.94973e7i	−1.56181	−	0.901710i	−0.997074	−	0.0764371i	$-0.975646\pi$
$463$	−1.55014e8	−	8.94973e7i	−1.56181	−	0.901710i	−0.564734	−	0.825273i	$-0.691021\pi$
$464$	9.60664e6	−	5.54640e6i	0.0961652	−	0.0555210i
$465$	−1.03277e8			−1.02718
$466$	3.23142e7	+	5.59698e7i	0.319327	+	0.553090i
$467$	8.89394e7	+	5.13492e7i	0.873260	+	0.504177i	0.868430	−	0.495812i	$-0.165129\pi$
$467$	8.89394e7	+	5.13492e7i	0.873260	+	0.504177i	0.00482972	+	0.999988i	$0.498463\pi$
$468$	−2.91806e7	+	5.05423e7i	−0.284680	+	0.493080i
$469$			3.77270e7i			0.365707i
$470$	−945516.	+	1.63768e6i	−0.00910700	+	0.0157738i
$471$	1.16608e8			1.11601
$472$			1.33887e8i			1.27324i
$473$	−7.84544e7	−	6.08548e7i	−0.741368	−	0.575057i
$474$	3.37455e8			3.16869
$475$			1.09288e8i			1.01975i
$476$	6.00865e6	+	3.46910e6i	0.0557129	+	0.0321659i
$477$	6.32099e7			0.582412
$478$	−2.58469e8	−	1.49227e8i	−2.36660	−	1.36636i
$479$	−3.61921e6	+	6.26866e6i	−0.0329312	+	0.0570385i	−0.882021	−	0.471210i	$-0.843818\pi$
$479$	−3.61921e6	+	6.26866e6i	−0.0329312	+	0.0570385i	0.849090	+	0.528248i	$0.177151\pi$
$480$	−1.72569e8	+	9.96325e7i	−1.56041	+	0.900902i
$481$			1.61884e8i			1.45469i
$482$	3.24579e7	+	5.62187e7i	0.289854	+	0.502042i
$483$	−5.69173e7	+	9.85836e7i	−0.505129	+	0.874910i
$484$	2.12753e7			0.187646
$485$	−2.45782e8	−	1.41902e8i	−2.15439	−	1.24384i
$486$	6.19925e7	+	1.07374e8i	0.540046	+	0.935387i
$487$	4.75316e7	+	8.23272e7i	0.411525	+	0.712781i	0.995057	−	0.0993086i	$-0.0316631\pi$
$487$	4.75316e7	+	8.23272e7i	0.411525	+	0.712781i	−0.583532	+	0.812090i	$0.698330\pi$
$488$	−1.00377e8	−	1.73858e8i	−0.863721	−	1.49601i
$489$	−1.75862e8			−1.50399
$490$	−4.84141e7	−	8.38557e7i	−0.411513	−	0.712761i
$491$	2.88084e7	−	1.66325e7i	0.243374	−	0.140512i	−0.373352	−	0.927690i	$-0.621792\pi$
$491$	2.88084e7	−	1.66325e7i	0.243374	−	0.140512i	0.616727	+	0.787177i	$0.288458\pi$
$492$	2.77909e8	+	1.60451e8i	2.33349	+	1.34724i
$493$	5.38809e6	+	3.11082e6i	0.0449670	+	0.0259617i
$494$	−1.96045e8			−1.62620
$495$		−	5.71325e7i		−	0.471051i
$496$	4.14151e6	−	7.17330e6i	0.0339401	−	0.0587860i
$497$	1.43344e7	−	2.48279e7i	0.116764	−	0.202242i
$498$	−3.61270e7	−	6.25738e7i	−0.292512	−	0.506646i
$499$	2.87932e7	−	1.66238e7i	0.231733	−	0.133791i	−0.379638	−	0.925135i	$-0.623951\pi$
$499$	2.87932e7	−	1.66238e7i	0.231733	−	0.133791i	0.611372	+	0.791344i	$0.290618\pi$
$500$			1.04877e7i			0.0839012i
$501$	1.12180e8	−	6.47673e7i	0.892079	−	0.515042i
$502$	−1.67180e8	+	9.65213e7i	−1.32152	+	0.762978i
$503$	1.25027e8	−	7.21844e7i	0.982427	−	0.567204i	0.0794247	−	0.996841i	$-0.474692\pi$
$503$	1.25027e8	−	7.21844e7i	0.982427	−	0.567204i	0.903002	+	0.429637i	$0.141358\pi$
$504$	−1.63924e7	+	2.83925e7i	−0.128042	+	0.221775i
$505$		−	4.55877e7i		−	0.353976i
$506$	−1.83199e8	−	1.05770e8i	−1.41407	−	0.816416i
$507$	8.66043e6	−	5.00010e6i	0.0664532	−	0.0383668i
$508$	3.27697e8			2.49966
$509$	1.33310e7	+	2.30899e7i	0.101090	+	0.175093i	0.912134	−	0.409892i	$-0.134434\pi$
$509$	1.33310e7	+	2.30899e7i	0.101090	+	0.175093i	−0.811044	+	0.584985i	$0.801100\pi$
$510$	−1.56669e7	−	9.04530e6i	−0.118106	−	0.0681887i
$511$	4.54137e7	−	7.86588e7i	0.340349	−	0.589501i
$512$		−	2.93759e7i		−	0.218868i
$513$	−5.00076e7	+	8.66157e7i	−0.370411	+	0.641571i
$514$	−1.07981e8			−0.795164
$515$			1.98166e7i			0.145080i
$516$	−9.46271e7	−	2.31873e8i	−0.688758	−	1.68772i
$517$	1.03244e6			0.00747122
$518$			2.51084e8i			1.80647i
$519$	−5.72890e7	−	3.30758e7i	−0.409798	−	0.236597i
$520$	−1.88567e8			−1.34108
$521$	−1.12740e8	−	6.50907e7i	−0.797198	−	0.460262i	0.0452925	−	0.998974i	$-0.485578\pi$
$521$	−1.12740e8	−	6.50907e7i	−0.797198	−	0.460262i	−0.842490	+	0.538711i	$0.818911\pi$
$522$	−4.05851e7	+	7.02954e7i	−0.285335	+	0.494215i
$523$	2.16635e7	−	1.25074e7i	0.151434	−	0.0874306i	−0.422368	−	0.906424i	$-0.638801\pi$
$523$	2.16635e7	−	1.25074e7i	0.151434	−	0.0874306i	0.573802	+	0.818994i	$0.305468\pi$
$524$			4.23624e7i			0.294433i
$525$	−6.98278e7	−	1.20945e8i	−0.482559	−	0.835816i
$526$	4.96511e7	−	8.59983e7i	0.341171	−	0.590925i
$527$	4.64571e6			0.0317409
$528$	1.52505e7	+	8.80489e6i	0.103605	+	0.0598166i
$529$	−1.32811e7	−	2.30035e7i	−0.0897153	−	0.155391i
$530$	2.81943e8	+	4.88339e8i	1.89380	+	3.28015i
$531$	3.68415e7	+	6.38113e7i	0.246067	+	0.426201i
$532$	−1.85654e8			−1.23302
$533$	−1.15546e8	−	2.00131e8i	−0.763085	−	1.32170i
$534$	1.81269e8	−	1.04656e8i	1.19042	−	0.687288i
$535$	1.97413e8	+	1.13977e8i	1.28918	+	0.744311i
$536$	−5.54671e7	−	3.20239e7i	−0.360198	−	0.207960i
$537$	−8.09890e7			−0.523002
$538$			3.51278e8i			2.25582i
$539$	−2.64324e7	+	4.57822e7i	−0.168799	+	0.292368i
$540$	−1.32804e8	+	2.30023e8i	−0.843393	+	1.46080i
$541$	−1.70474e7	−	2.95269e7i	−0.107663	−	0.186477i	0.807160	−	0.590332i	$-0.201003\pi$
$541$	−1.70474e7	−	2.95269e7i	−0.107663	−	0.186477i	−0.914823	+	0.403855i	$0.867670\pi$
$542$	2.51089e8	−	1.44966e8i	1.57699	−	0.910476i
$543$			7.90209e7i			0.493563i
$544$	7.76262e6	−	4.48175e6i	0.0482183	−	0.0278388i
$545$	2.68137e8	−	1.54809e8i	1.65641	−	0.956326i
$546$	2.16955e8	−	1.25259e8i	1.33288	−	0.769539i
$547$	−4.41213e7	+	7.64204e7i	−0.269579	+	0.466925i	−0.968753	−	0.248027i	$-0.920218\pi$
$547$	−4.41213e7	+	7.64204e7i	−0.269579	+	0.466925i	0.699174	+	0.714952i	$0.253551\pi$
$548$		−	2.93381e8i		−	1.78275i
$549$	−9.56804e7	−	5.52411e7i	−0.578237	−	0.333845i
$550$	2.24754e8	−	1.29762e8i	1.35089	−	0.779937i
$551$	−1.66480e8			−0.995195
$552$	−9.66265e7	−	1.67362e8i	−0.574485	−	0.995038i
$553$	−1.99301e8	−	1.15066e8i	−1.17851	−	0.680414i
$554$	1.59928e8	−	2.77003e8i	0.940576	−	1.62913i
$555$		−	3.99725e8i		−	2.33821i
$556$	3.05837e7	−	5.29725e7i	0.177937	−	0.308195i
$557$	3.16403e8			1.83094			0.915472	−	0.402382i	$-0.131818\pi$
$557$	3.16403e8			1.83094			0.915472	+	0.402382i	$0.131818\pi$
$558$			6.06099e7i			0.348852i
$559$	−2.44752e7	+	1.78681e8i	−0.140117	+	1.02292i
$560$	2.19965e7			0.125253
$561$			9.87682e6i			0.0559408i
$562$	−1.65218e8	−	9.53885e7i	−0.930782	−	0.537387i
$563$	−1.46146e8			−0.818958			−0.409479	−	0.912320i	$-0.634290\pi$
$563$	−1.46146e8			−0.818958			−0.409479	+	0.912320i	$0.634290\pi$
$564$	2.25523e6	+	1.30206e6i	0.0125705	+	0.00725761i
$565$	−6.98856e6	+	1.21045e7i	−0.0387474	+	0.0671124i
$566$	−3.78310e8	+	2.18418e8i	−2.08641	+	1.20459i
$567$		−	1.79104e8i		−	0.982553i
$568$	2.43350e7	+	4.21495e7i	0.132796	+	0.230010i
$569$	1.04276e8	−	1.80612e8i	0.566042	−	0.980414i	−0.430910	−	0.902395i	$-0.641807\pi$
$569$	1.04276e8	−	1.80612e8i	0.566042	−	0.980414i	0.996952	−	0.0780186i	$-0.0248593\pi$
$570$	4.84074e8			2.61389
$571$	−1.80519e8	−	1.04223e8i	−0.969651	−	0.559828i	−0.0705212	−	0.997510i	$-0.522466\pi$
$571$	−1.80519e8	−	1.04223e8i	−0.969651	−	0.559828i	−0.899130	+	0.437682i	$0.855800\pi$
$572$	1.42123e8	+	2.46164e8i	0.759410	+	1.31534i
$573$	−9.59984e6	−	1.66274e7i	−0.0510270	−	0.0883814i
$574$	−1.79213e8	−	3.10405e8i	−0.947617	−	1.64132i
$575$	2.14202e8			1.12673
$576$	5.47852e7	+	9.48907e7i	0.286679	+	0.496542i
$577$	2.46994e8	−	1.42602e8i	1.28576	−	0.742333i	0.307863	−	0.951431i	$-0.400386\pi$
$577$	2.46994e8	−	1.42602e8i	1.28576	−	0.742333i	0.977895	+	0.209098i	$0.0670528\pi$
$578$	−2.67274e8	−	1.54311e8i	−1.38412	−	0.799120i
$579$	−2.87088e8	−	1.65750e8i	−1.47904	−	0.853923i
$580$	−4.42118e8			−2.26597
$581$			4.92749e7i			0.251245i
$582$	−3.20048e8	+	5.54339e8i	−1.62348	+	2.81194i
$583$	1.53931e8	−	2.66616e8i	0.776818	−	1.34549i
$584$	7.70973e7	+	1.33536e8i	0.387080	+	0.670442i
$585$	−8.98721e7	+	5.18877e7i	−0.448908	+	0.259177i
$586$		−	5.53992e8i		−	2.75303i
$587$	−2.08701e6	+	1.20493e6i	−0.0103183	+	0.00595729i	−0.505150	−	0.863031i	$-0.668563\pi$
$587$	−2.08701e6	+	1.20493e6i	−0.0103183	+	0.00595729i	0.494832	+	0.868989i	$0.335230\pi$
$588$	−1.15477e8	+	6.66705e7i	−0.568018	+	0.327946i
$589$	−1.07657e8	+	6.21556e7i	−0.526860	+	0.304183i
$590$	−3.28657e8	+	5.69250e8i	−1.60025	+	2.77171i
$591$			3.71659e8i			1.80046i
$592$	2.77636e7	+	1.60293e7i	0.133817	+	0.0772591i
$593$	−2.55275e8	+	1.47383e8i	−1.22418	+	0.706778i	−0.965805	−	0.259268i	$-0.916519\pi$
$593$	−2.55275e8	+	1.47383e8i	−1.22418	+	0.706778i	−0.258370	+	0.966046i	$0.583185\pi$
$594$	2.37503e8			1.13321
$595$	6.16859e6	+	1.06843e7i	0.0292843	+	0.0507219i
$596$	2.35334e8	+	1.35870e8i	1.11160	+	0.641780i
$597$	−8.67423e7	+	1.50242e8i	−0.407669	+	0.706104i
$598$			3.84241e8i			1.79680i
$599$	4.03059e7	−	6.98119e7i	0.187537	−	0.324824i	−0.756891	−	0.653541i	$-0.773283\pi$
$599$	4.03059e7	−	6.98119e7i	0.187537	−	0.324824i	0.944429	+	0.328716i	$0.106616\pi$
$600$	2.37088e8			1.09763
$601$		−	2.64593e7i		−	0.121886i	−0.998141	−	0.0609431i	$-0.980589\pi$
$601$		−	2.64593e7i		−	0.121886i	0.998141	−	0.0609431i	$-0.0194108\pi$
$602$	−3.79612e7	+	2.77135e8i	−0.174000	+	1.27029i
$603$	−3.52479e7			−0.160761
$604$		−	4.42551e8i		−	2.00841i
$605$	3.27624e7	+	1.89154e7i	0.147948	+	0.0854179i
$606$	−1.02819e8			−0.462014
$607$	2.95865e8	+	1.70818e8i	1.32290	+	0.763777i	0.984190	−	0.177114i	$-0.0566761\pi$
$607$	2.95865e8	+	1.70818e8i	1.32290	+	0.763777i	0.338710	+	0.940891i	$0.390009\pi$
$608$	−1.19924e8	+	2.07714e8i	−0.533575	+	0.924179i
$609$	1.84237e8	−	1.06369e8i	0.815691	−	0.470939i
$610$		−	9.85593e8i		−	4.34218i
$611$	−937657.	−	1.62407e6i	−0.00411074	−	0.00712001i
$612$	−3.24114e6	+	5.61382e6i	−0.0141398	+	0.0244909i
$613$	−4.27790e8			−1.85716			−0.928580	−	0.371132i	$-0.878970\pi$
$613$	−4.27790e8			−1.85716			−0.928580	+	0.371132i	$0.878970\pi$
$614$	3.16700e8	+	1.82847e8i	1.36818	+	0.789918i
$615$	2.85306e8	+	4.94165e8i	1.22655	+	2.12445i
$616$	7.98386e7	+	1.38285e8i	0.341563	+	0.591605i
$617$	1.89799e8	+	3.28742e8i	0.808052	+	1.39959i	0.914211	+	0.405238i	$0.132811\pi$
$617$	1.89799e8	+	3.28742e8i	0.808052	+	1.39959i	−0.106159	+	0.994349i	$0.533855\pi$
$618$	4.46947e7			0.189361
$619$	−8.91897e6	−	1.54481e7i	−0.0376048	−	0.0651334i	0.846610	−	0.532213i	$-0.178639\pi$
$619$	−8.91897e6	−	1.54481e7i	−0.0376048	−	0.0651334i	−0.884215	+	0.467080i	$0.845306\pi$
$620$	−2.85901e8	+	1.65065e8i	−1.19961	+	0.692597i
$621$	1.69764e8	+	9.80134e7i	0.708878	+	0.409271i
$622$	6.33570e7	+	3.65792e7i	0.263283	+	0.152007i
$623$	−1.42743e8			−0.590326
$624$		−	3.19863e7i		−	0.131647i
$625$	1.17322e8	−	2.03208e8i	0.480552	−	0.832341i
$626$	−1.09874e8	+	1.90307e8i	−0.447890	+	0.775767i
$627$	−1.32143e8	−	2.28879e8i	−0.536096	−	0.928546i
$628$	3.22805e8	−	1.86372e8i	1.30335	−	0.752490i
$629$			1.79808e7i			0.0722531i
$630$	−1.39392e8	+	8.04782e7i	−0.557465	+	0.321852i
$631$	−2.77570e8	+	1.60255e8i	−1.10480	+	0.637858i	−0.937478	−	0.348045i	$-0.886846\pi$
$631$	−2.77570e8	+	1.60255e8i	−1.10480	+	0.637858i	−0.167324	+	0.985902i	$0.553512\pi$
$632$	3.38346e8	−	1.95344e8i	1.34033	−	0.773837i
$633$	−1.98128e8	+	3.43167e8i	−0.781149	+	1.35299i
$634$			1.30032e8i			0.510251i
$635$	5.04629e8	+	2.91348e8i	1.97084	+	1.13786i
$636$	6.72486e8	−	3.88260e8i	2.61404	−	1.50922i
$637$	9.60233e7			0.371500
$638$	1.97668e8	+	3.42371e8i	0.761157	+	1.31836i
$639$	2.31964e7	+	1.33925e7i	0.0889035	+	0.0513284i
$640$	−2.85600e8	+	4.94673e8i	−1.08948	+	1.88703i
$641$		−	1.32790e8i		−	0.504186i	−0.967703	−	0.252093i	$-0.918881\pi$
$641$		−	1.32790e8i		−	0.504186i	0.967703	−	0.252093i	$-0.0811189\pi$
$642$	2.57064e8	−	4.45248e8i	0.971485	−	1.68266i
$643$	1.50916e6			0.00567679			0.00283839	−	0.999996i	$-0.499097\pi$
$643$	1.50916e6			0.00567679			0.00283839	+	0.999996i	$0.499097\pi$
$644$			3.63877e8i			1.36237i
$645$	6.04342e7	−	4.41199e8i	0.225218	−	1.64420i
$646$	−2.17750e7			−0.0807719
$647$		−	2.81487e8i		−	1.03931i	−0.854376	−	0.519655i	$-0.826060\pi$
$647$		−	2.81487e8i		−	1.03931i	0.854376	−	0.519655i	$-0.173940\pi$
$648$	2.63322e8	+	1.52029e8i	0.967749	+	0.558730i
$649$	3.58870e8			1.31281
$650$	−4.08243e8	−	2.35699e8i	−1.48655	−	0.858259i
$651$	7.94263e7	−	1.37570e8i	0.287886	−	0.498634i
$652$	−4.86836e8	+	2.81075e8i	−1.75647	+	1.01410i
$653$			4.14602e8i			1.48899i	0.667628	+	0.744495i	$0.267310\pi$
$653$			4.14602e8i			1.48899i	−0.667628	+	0.744495i	$0.732690\pi$
$654$	−3.49158e8	−	6.04759e8i	−1.24821	−	2.16197i
$655$	−3.76635e7	+	6.52351e7i	−0.134028	+	0.232144i
$656$	−4.57640e7			−0.162111
$657$	7.34901e7	+	4.24295e7i	0.259139	+	0.149614i
$658$	−1.45431e6	−	2.51894e6i	−0.00510482	−	0.00884180i
$659$	−3.48578e7	−	6.03755e7i	−0.121799	−	0.210962i	0.798678	−	0.601759i	$-0.205533\pi$
$659$	−3.48578e7	−	6.03755e7i	−0.121799	−	0.210962i	−0.920477	+	0.390796i	$0.872200\pi$
$660$	−3.50930e8	−	6.07829e8i	−1.22064	−	2.11422i
$661$	−1.63295e8			−0.565416			−0.282708	−	0.959206i	$-0.591233\pi$
$661$	−1.63295e8			−0.565416			−0.282708	+	0.959206i	$0.591233\pi$
$662$	1.40149e8	+	2.42744e8i	0.483075	+	0.836711i
$663$	1.55367e7	−	8.97011e6i	0.0533111	−	0.0307792i
$664$	−7.24450e7	−	4.18261e7i	−0.247459	−	0.142871i
$665$	−2.85894e8	−	1.65061e8i	−0.972166	−	0.561280i
$666$	−2.34585e8			−0.794105
$667$			3.26296e8i			1.09960i
$668$	2.07031e8	−	3.58589e8i	0.694555	−	1.20300i
$669$	3.90180e7	−	6.75811e7i	0.130313	−	0.225708i
$670$	−1.57221e8	−	2.72314e8i	−0.522739	−	0.905410i
$671$	−4.66007e8	+	2.69049e8i	−1.54250	+	0.890562i
$672$		−	3.06493e8i		−	1.00998i
$673$	−5.72770e7	+	3.30689e7i	−0.187904	+	0.108486i	−0.591001	−	0.806671i	$-0.701267\pi$
$673$	−5.72770e7	+	3.30689e7i	−0.187904	+	0.108486i	0.403097	+	0.915157i	$0.367934\pi$
$674$	−1.71370e8	+	9.89404e7i	−0.559699	+	0.323142i
$675$	−2.08272e8	+	1.20246e8i	−0.677203	+	0.390983i
$676$	1.59830e7	−	2.76834e7i	0.0517391	−	0.0896148i
$677$		−	2.64211e8i		−	0.851500i	−0.904841	−	0.425750i	$-0.860010\pi$
$677$		−	2.64211e8i		−	0.851500i	0.904841	−	0.425750i	$-0.139990\pi$
$678$	2.73007e7	+	1.57621e7i	0.0875961	+	0.0505736i
$679$	3.78041e8	−	2.18262e8i	1.20762	−	0.697219i
$680$	−2.09444e7			−0.0666103
$681$	1.68611e8	+	2.92043e8i	0.533881	+	0.924710i
$682$	2.55649e8	+	1.47599e8i	0.805918	+	0.465297i
$683$	1.42292e8	−	2.46458e8i	0.446601	−	0.773535i	−0.551561	−	0.834134i	$-0.685968\pi$
$683$	1.42292e8	−	2.46458e8i	0.446601	−	0.773535i	0.998162	+	0.0605991i	$0.0193011\pi$
$684$		−	1.73455e8i		−	0.542023i
$685$	2.60839e8	−	4.51786e8i	0.811522	−	1.40560i
$686$	5.62848e8			1.74349
$687$			3.09949e8i			0.955917i
$688$	2.82207e7	+	2.18900e7i	0.0866568	+	0.0672171i
$689$	−5.59198e8			−1.70965
$690$		−	9.48770e8i		−	2.88811i
$691$	4.57650e8	+	2.64224e8i	1.38707	+	0.800827i	0.992984	−	0.118246i	$-0.0377271\pi$
$691$	4.57650e8	+	2.64224e8i	1.38707	+	0.800827i	0.394088	+	0.919073i	$0.371060\pi$
$692$	−2.11457e8			−0.638121
$693$	7.61032e7	+	4.39382e7i	0.228667	+	0.132021i
$694$	−4.27735e8	+	7.40859e8i	−1.27967	+	2.21645i
$695$	9.41934e7	−	5.43826e7i	0.280586	−	0.161996i
$696$			3.61160e8i			1.07120i
$697$	−1.28339e7	−	2.22289e7i	−0.0379017	−	0.0656477i
$698$	−3.96728e6	+	6.87153e6i	−0.0116661	+	0.0202063i
$699$	1.58254e8			0.463365
$700$	−3.86606e8	−	2.23207e8i	−1.12713	−	0.650750i
$701$	−1.70383e8	−	2.95111e8i	−0.494620	−	0.856706i	0.505361	−	0.862908i	$-0.331359\pi$
$701$	−1.70383e8	−	2.95111e8i	−0.494620	−	0.856706i	−0.999981	+	0.00620169i	$0.998026\pi$
$702$	−2.15700e8	−	3.73603e8i	−0.623504	−	1.07994i
$703$	−2.40567e8	−	4.16675e8i	−0.692422	−	1.19931i
$704$	5.33657e8			1.52948
$705$	2.31526e6	+	4.01016e6i	0.00660744	+	0.0114444i
$706$	5.69344e8	−	3.28711e8i	1.61793	−	0.934114i
$707$	6.07249e7	+	3.50596e7i	0.171834	+	0.0992084i
$708$	7.83908e8	+	4.52589e8i	2.20885	+	1.27528i
$709$	−2.28094e8			−0.639993			−0.319996	−	0.947419i	$-0.603682\pi$
$709$	−2.28094e8			−0.639993			−0.319996	+	0.947419i	$0.603682\pi$
$710$			2.38944e8i			0.667607i
$711$	1.07505e8	−	1.86205e8i	0.299103	−	0.518062i
$712$	1.21165e8	−	2.09864e8i	0.335690	−	0.581432i
$713$	1.21823e8	+	2.11004e8i	0.336094	+	0.582132i
$714$	2.40975e7	−	1.39127e7i	0.0662030	−	0.0382223i
$715$			5.05433e8i			1.38276i
$716$	−2.24201e8	+	1.29442e8i	−0.610799	+	0.352645i
$717$	−6.32907e8	+	3.65409e8i	−1.71705	+	0.991338i
$718$	−3.49721e8	+	2.01911e8i	−0.944817	+	0.545490i
$719$	1.43750e7	−	2.48982e7i	0.0386741	−	0.0669855i	−0.846040	−	0.533119i	$-0.821020\pi$
$719$	1.43750e7	−	2.48982e7i	0.0386741	−	0.0669855i	0.884715	+	0.466133i	$0.154353\pi$
$720$			2.05511e7i			0.0550601i
$721$	−2.63967e7	−	1.52401e7i	−0.0704277	−	0.0406615i
$722$	−1.77100e7	+	1.02249e7i	−0.0470551	+	0.0271672i
$723$	1.58958e8			0.420598
$724$	1.26297e8	+	2.18752e8i	0.332795	+	0.576418i
$725$	−3.46679e8	−	2.00155e8i	−0.909731	−	0.525234i
$726$	4.26620e7	−	7.38927e7i	0.111489	−	0.193104i
$727$			6.00857e8i			1.56375i	0.623434	+	0.781876i	$0.285737\pi$
$727$			6.00857e8i			1.56375i	−0.623434	+	0.781876i	$0.714263\pi$
$728$	1.45019e8	−	2.51180e8i	0.375863	−	0.651014i
$729$	−1.72158e8			−0.444371
$730$			7.57014e8i			1.94597i
$731$	−2.71850e6	+	1.98463e7i	−0.00695948	+	0.0508076i
$732$	−1.35725e9			−3.46040
$733$		−	5.49758e8i		−	1.39592i	−0.716138	−	0.697959i	$-0.754092\pi$
$733$		−	5.49758e8i		−	1.39592i	0.716138	−	0.697959i	$-0.245908\pi$
$734$	3.43823e8	+	1.98507e8i	0.869455	+	0.501980i
$735$	−2.37101e8			−0.597134
$736$	4.07114e8	+	2.35047e8i	1.02113	+	0.589552i
$737$	−8.58368e7	+	1.48674e8i	−0.214423	+	0.371391i
$738$	2.90008e8	−	1.67436e8i	0.721508	−	0.416563i
$739$			7.25658e8i			1.79804i	0.437910	+	0.899019i	$0.355719\pi$
$739$			7.25658e8i			1.79804i	−0.437910	+	0.899019i	$0.644281\pi$
$740$	−6.38869e8	−	1.10655e9i	−1.57658	−	2.73072i
$741$	−2.40025e8	+	4.15735e8i	−0.589932	+	1.02179i
$742$	−8.67321e8			−2.12309
$743$	2.35578e7	+	1.36011e7i	0.0574339	+	0.0331595i	0.528442	−	0.848969i	$-0.322776\pi$
$743$	2.35578e7	+	1.36011e7i	0.0574339	+	0.0331595i	−0.471008	+	0.882129i	$0.656110\pi$
$744$	1.34839e8	+	2.33548e8i	0.327414	+	0.567098i
$745$	2.41599e8	+	4.18461e8i	0.584287	+	1.01201i
$746$	−2.85665e8	−	4.94787e8i	−0.688083	−	1.19180i
$747$	−4.60370e7			−0.110445
$748$	1.57858e7	+	2.73419e7i	0.0377192	+	0.0653316i
$749$	−3.03644e8	+	1.75309e8i	−0.722636	+	0.417214i
$750$	3.64254e7	+	2.10302e7i	0.0863417	+	0.0498494i
$751$	−4.16717e8	−	2.40592e8i	−0.983834	−	0.568017i	−0.0804086	−	0.996762i	$-0.525622\pi$
$751$	−4.16717e8	−	2.40592e8i	−0.983834	−	0.568017i	−0.903425	+	0.428745i	$0.858956\pi$
$752$	−371376.			−0.000873293
$753$			4.72699e8i			1.10713i
$754$	3.59044e8	−	6.21882e8i	0.837593	−	1.45075i
$755$	3.93462e8	−	6.81497e8i	0.914244	−	1.58352i
$756$	−2.04268e8	−	3.53803e8i	−0.472754	−	0.818834i
$757$	4.25537e8	−	2.45684e8i	0.980957	−	0.566356i	0.0783983	−	0.996922i	$-0.475019\pi$
$757$	4.25537e8	−	2.45684e8i	0.980957	−	0.566356i	0.902559	+	0.430566i	$0.141686\pi$
$758$		−	8.15763e8i		−	1.87308i
$759$	−4.48596e8	+	2.58997e8i	−1.02596	+	0.592338i
$760$	4.85353e8	−	2.80219e8i	1.10565	−	0.638346i
$761$	3.70362e8	−	2.13829e8i	0.840374	−	0.485190i	−0.0170173	−	0.999855i	$-0.505417\pi$
$761$	3.70362e8	−	2.13829e8i	0.840374	−	0.485190i	0.857391	+	0.514665i	$0.172084\pi$
$762$	6.57109e8	−	1.13815e9i	1.48516	−	2.57237i
$763$			4.76228e8i			1.07211i
$764$	−5.31502e7	−	3.06863e7i	−0.119186	−	0.0688120i
$765$	−9.98224e6	+	5.76325e6i	−0.0222969	+	0.0128731i
$766$	−6.66359e8			−1.48259
$767$	−3.25925e8	−	5.64518e8i	−0.722323	−	1.25110i
$768$	3.72187e8	+	2.14882e8i	0.821633	+	0.474370i
$769$	2.97935e8	−	5.16038e8i	0.655152	−	1.13476i	−0.326703	−	0.945127i	$-0.605938\pi$
$769$	2.97935e8	−	5.16038e8i	0.655152	−	1.13476i	0.981856	−	0.189630i	$-0.0607288\pi$
$770$			7.83931e8i			1.71714i
$771$	−1.32205e8	+	2.28986e8i	−0.288459	+	0.499626i
$772$	−1.05966e9			−2.30310
$773$		−	7.29317e8i		−	1.57898i	−0.613760	−	0.789492i	$-0.710344\pi$
$773$		−	7.29317e8i		−	1.57898i	0.613760	−	0.789492i	$-0.289656\pi$
$774$	−2.58924e8	−	3.54667e7i	−0.558406	−	0.0764889i
$775$	−2.98912e8			−0.642153
$776$			7.41072e8i			1.58590i
$777$	5.32453e8	+	3.07412e8i	1.13506	+	0.655326i
$778$	3.92793e8			0.834114
$779$	5.94808e8	+	3.43412e8i	1.25824	+	0.726447i
$780$	−6.37429e8	+	1.10406e9i	−1.34322	+	2.32653i
$781$	1.12977e8	−	6.52274e7i	0.237158	−	0.136923i
$782$			4.26783e7i			0.0892456i
$783$	−1.83172e8	−	3.17263e8i	−0.381569	−	0.660897i
$784$	9.50795e6	−	1.64682e7i	0.0197305	−	0.0341743i
$785$	6.62796e8			1.37016
$786$	1.47132e8	+	8.49467e7i	0.302998	+	0.174936i
$787$	−2.79087e8	−	4.83393e8i	−0.572552	−	0.991690i	−0.996303	−	0.0859110i	$-0.972620\pi$
$787$	−2.79087e8	−	4.83393e8i	−0.572552	−	0.991690i	0.423750	−	0.905779i	$-0.360713\pi$
$788$	5.94012e8	+	1.02886e9i	1.21399	+	2.10270i
$789$	−1.21580e8	−	2.10582e8i	−0.247531	−	0.428737i
$790$	1.91807e9			3.89031
$791$	−1.07492e7	−	1.86182e7i	−0.0217194	−	0.0376190i
$792$	−1.29198e8	+	7.45924e7i	−0.260064	+	0.150148i
$793$	8.46454e8	+	4.88701e8i	1.69740	+	0.979994i
$794$	−4.61563e8	−	2.66484e8i	−0.922082	−	0.532364i
$795$	1.38077e9			2.74803
$796$			5.54551e8i			1.09952i
$797$	−3.97117e7	+	6.87827e7i	−0.0784410	+	0.135864i	−0.902577	−	0.430527i	$-0.858328\pi$
$797$	−3.97117e7	+	6.87827e7i	−0.0784410	+	0.135864i	0.824136	+	0.566391i	$0.191661\pi$
$798$	−3.72281e8	+	6.44809e8i	−0.732591	+	1.26889i
$799$	−104147.	−	180388.i	−0.000204177	−	0.000353645i
$800$	−4.99460e8	+	2.88363e8i	−0.975507	+	0.563209i
$801$		−	1.33364e8i		−	0.259501i
$802$	7.92264e8	−	4.57414e8i	1.53584	−	0.886720i
$803$	3.57930e8	−	2.06651e8i	0.691276	−	0.399109i
$804$	−3.75000e8	+	2.16507e8i	−0.721545	+	0.416584i
$805$	−3.23515e8	+	5.60344e8i	−0.620164	+	1.07416i
$806$		−	5.36197e8i		−	1.02405i
$807$	7.44926e8	+	4.30083e8i	1.41740	+	0.818336i
$808$	−1.03091e8	+	5.95194e7i	−0.195427	+	0.112830i
$809$	3.71225e8			0.701118			0.350559	−	0.936541i	$-0.385992\pi$
$809$	3.71225e8			0.701118			0.350559	+	0.936541i	$0.385992\pi$
$810$	7.46383e8	+	1.29277e9i	1.40445	+	2.43258i
$811$	3.36002e8	+	1.93991e8i	0.629911	+	0.363679i	0.780718	−	0.624884i	$-0.214854\pi$
$811$	3.36002e8	+	1.93991e8i	0.629911	+	0.363679i	−0.150807	+	0.988563i	$0.548187\pi$
$812$	3.40014e8	−	5.88922e8i	0.635081	−	1.09999i
$813$		−	7.09951e8i		−	1.32116i
$814$	−5.71268e8	+	9.89466e8i	−1.05917	+	1.83454i
$815$	−9.99590e8			−1.84650
$816$		−	3.55278e6i		−	0.00653879i
$817$	−2.02531e8	−	4.96278e8i	−0.371385	−	0.910036i
$818$	−6.70973e8			−1.22587
$819$		−	1.59619e8i		−	0.290557i
$820$	1.57962e9	+	9.11993e8i	2.86491	+	1.65405i
$821$	2.06100e7			0.0372434			0.0186217	−	0.999827i	$-0.494072\pi$
$821$	2.06100e7			0.0372434			0.0186217	+	0.999827i	$0.494072\pi$
$822$	−1.01896e9	−	5.88298e8i	−1.83461	−	1.05921i
$823$	3.69902e8	−	6.40688e8i	0.663570	−	1.14934i	−0.316101	−	0.948725i	$-0.602374\pi$
$823$	3.69902e8	−	6.40688e8i	0.663570	−	1.14934i	0.979671	−	0.200611i	$-0.0642928\pi$
$824$	4.48128e7	−	2.58727e7i	0.0800977	−	0.0462444i
$825$		−	6.35491e8i		−	1.13174i
$826$	−5.05512e8	−	8.75572e8i	−0.896998	−	1.55365i
$827$	2.71344e8	−	4.69981e8i	0.479737	−	0.830929i	−0.519993	−	0.854171i	$-0.674065\pi$
$827$	2.71344e8	−	4.69981e8i	0.479737	−	0.830929i	0.999730	+	0.0232417i	$0.00739874\pi$
$828$	−3.39966e8			−0.598887
$829$	1.55326e8	+	8.96776e7i	0.272635	+	0.157406i	0.630084	−	0.776527i	$-0.283020\pi$
$829$	1.55326e8	+	8.96776e7i	0.272635	+	0.157406i	−0.357450	+	0.933932i	$0.616354\pi$
$830$	−2.05344e8	−	3.55666e8i	−0.359127	−	0.622026i
$831$	−3.91611e8	−	6.78290e8i	−0.682420	−	1.18199i
$832$	−4.84667e8	−	8.39468e8i	−0.841537	−	1.45759i
$833$	1.06655e7			0.0184521
$834$	−1.22655e8	−	2.12445e8i	−0.211440	−	0.366225i
$835$	6.37627e8	−	3.68134e8i	1.09523	−	0.632334i
$836$	−7.31621e8	−	4.22402e8i	−1.25218	−	0.722948i
$837$	−2.36901e8	−	1.36775e8i	−0.404008	−	0.233254i
$838$	2.08858e7			0.0354910
$839$			3.24666e8i			0.549732i	0.961482	+	0.274866i	$0.0886336\pi$
$839$			3.24666e8i			0.549732i	−0.961482	+	0.274866i	$0.911366\pi$
$840$	−3.58081e8	+	6.20214e8i	−0.604147	+	1.04641i
$841$	7.48684e6	−	1.29676e7i	0.0125867	−	0.0218007i
$842$	4.72437e8	+	8.18286e8i	0.791422	+	1.37078i
$843$	−4.04565e8	+	2.33576e8i	−0.675314	+	0.389893i
$844$			1.26665e9i			2.10682i
$845$	4.92255e7	−	2.84203e7i	0.0815867	−	0.0471041i
$846$	2.35342e6	−	1.35875e6i	0.00388677	−	0.00224403i
$847$	−5.03924e7	+	2.90940e7i	−0.0829305	+	0.0478800i
$848$	−5.53702e7	+	9.59039e7i	−0.0908005	+	0.157271i
$849$			1.06967e9i			1.74794i
$850$	−4.53442e7	−	2.61795e7i	−0.0738355	−	0.0426290i
$851$	−8.16670e8	+	4.71505e8i	−1.32513	+	0.765064i
$852$	3.29047e8			0.532034
$853$	−1.08230e8	−	1.87459e8i	−0.174381	−	0.302037i	0.765566	−	0.643358i	$-0.222459\pi$
$853$	−1.08230e8	−	1.87459e8i	−0.174381	−	0.302037i	−0.939947	+	0.341321i	$0.889126\pi$
$854$	1.31286e9	+	7.57978e8i	2.10787	+	1.21698i
$855$	1.54215e8	−	2.67108e8i	0.246733	−	0.427355i
$856$		−	5.95233e8i		−	0.948998i
$857$	−1.79089e7	+	3.10191e7i	−0.0284529	+	0.0492818i	−0.879901	−	0.475157i	$-0.842391\pi$
$857$	−1.79089e7	+	3.10191e7i	−0.0284529	+	0.0492818i	0.851448	+	0.524438i	$0.175725\pi$
$858$	1.13996e9			1.80479
$859$			7.85671e8i			1.23954i	0.784783	+	0.619771i	$0.212775\pi$
$859$			7.85671e8i			1.23954i	−0.784783	+	0.619771i	$0.787225\pi$
$860$	−5.37856e8	−	1.31795e9i	−0.845611	−	2.07207i
$861$	−8.77668e8			−1.37506
$862$		−	3.93245e8i		−	0.613961i
$863$	2.23304e8	+	1.28925e8i	0.347428	+	0.200588i	0.663552	−	0.748130i	$-0.269048\pi$
$863$	2.23304e8	+	1.28925e8i	0.347428	+	0.200588i	−0.316124	+	0.948718i	$0.602382\pi$
$864$	−5.27791e8			−0.818315
$865$	−3.25628e8	−	1.88001e8i	−0.503122	−	0.290478i
$866$	−9.56670e8	+	1.65700e9i	−1.47302	+	2.55134i
$867$	−6.54468e8	+	3.77857e8i	−1.00422	+	0.579789i
$868$		−	5.07779e8i		−	0.776453i
$869$	−5.23600e8	−	9.06902e8i	−0.797885	−	1.38198i
$870$	−8.86551e8	+	1.53555e9i	−1.34631	+	2.33188i
$871$	3.11827e8			0.471911
$872$	−7.00160e8	−	4.04238e8i	−1.05596	−	0.609659i
$873$	2.03920e8	+	3.53200e8i	0.306490	+	0.530857i
$874$	−5.71000e8	−	9.89000e8i	−0.855267	−	1.48137i
$875$	−1.43419e7	−	2.48409e7i	−0.0214083	−	0.0370803i
$876$	1.04247e9			1.55079
$877$	1.70711e7	+	2.95680e7i	0.0253083	+	0.0438352i	0.878402	−	0.477922i	$-0.158610\pi$
$877$	1.70711e7	+	2.95680e7i	0.0253083	+	0.0438352i	−0.853094	+	0.521757i	$0.825277\pi$
$878$	1.68734e9	−	9.74189e8i	2.49299	−	1.43933i
$879$	−1.17480e9	−	6.78274e8i	−1.72981	−	0.998708i
$880$	8.66831e7	+	5.00465e7i	0.127200	+	0.0734388i
$881$	−1.31455e8			−0.192243			−0.0961214	−	0.995370i	$-0.530644\pi$
$881$	−1.31455e8			−0.192243			−0.0961214	+	0.995370i	$0.530644\pi$
$882$			1.39146e8i			0.202799i
$883$	−2.76070e8	+	4.78168e8i	−0.400994	+	0.694542i	−0.993846	−	0.110770i	$-0.964668\pi$
$883$	−2.76070e8	+	4.78168e8i	−0.400994	+	0.694542i	0.592852	+	0.805311i	$0.298002\pi$
$884$	2.86733e7	−	4.96637e7i	0.0415070	−	0.0718922i
$885$	8.04775e8	+	1.39391e9i	1.16103	+	2.01097i
$886$	−1.11761e9	+	6.45250e8i	−1.60690	+	0.927741i
$887$			5.34710e8i			0.766209i	0.923705	+	0.383104i	$0.125145\pi$
$887$			5.34710e8i			0.766209i	−0.923705	+	0.383104i	$0.874855\pi$
$888$	−9.03927e8	+	5.21883e8i	−1.29091	+	0.745305i
$889$	−7.76178e8	+	4.48127e8i	−1.10473	+	0.637816i
$890$	1.03032e9	−	5.94857e8i	1.46152	−	0.843806i
$891$	4.07498e8	−	7.05808e8i	0.576093	−	0.997823i
$892$		−	2.49445e8i		−	0.351463i
$893$	4.82688e6	+	2.78680e6i	0.00677816	+	0.00391337i
$894$	9.43803e8	−	5.44905e8i	1.32090	−	0.762620i
$895$	−4.60338e8			−0.642107
$896$	−4.39285e8	−	7.60864e8i	−0.610692	−	1.05775i
$897$	8.14829e8	+	4.70442e8i	1.12899	+	0.651821i
$898$	−1.62919e8	+	2.82184e8i	−0.224979	+	0.389675i
$899$		−	4.55337e8i		−	0.626691i
$900$	2.08540e8	−	3.61202e8i	0.286063	−	0.495476i
$901$	−6.21111e7			−0.0849170
$902$		−	1.63098e9i		−	2.22244i
$903$	5.41220e8	+	4.19808e8i	0.735039	+	0.570148i
$904$	3.64971e7			0.0494030
$905$			4.49151e8i			0.605963i
$906$	−1.53705e9	−	8.87419e8i	−2.06683	−	1.19328i
$907$	5.25767e8			0.704647			0.352323	−	0.935878i	$-0.385392\pi$
$907$	5.25767e8			0.704647			0.352323	+	0.935878i	$0.385392\pi$
$908$	9.33527e8	+	5.38972e8i	1.24701	+	0.719961i
$909$	−3.27558e7	+	5.67347e7i	−0.0436110	+	0.0755365i
$910$	1.23316e9	−	7.11965e8i	1.63642	−	0.944789i
$911$		−	8.90951e8i		−	1.17842i	−0.807982	−	0.589208i	$-0.799440\pi$
$911$		−	8.90951e8i		−	1.17842i	0.807982	−	0.589208i	$-0.200560\pi$
$912$	4.75331e7	+	8.23298e7i	0.0626631	+	0.108536i
$913$	−1.12111e8	+	1.94181e8i	−0.147311	+	0.255149i
$914$	6.88009e8			0.901064
$915$	−2.09007e9	−	1.20670e9i	−2.72833	−	1.57520i
$916$	4.95382e8	+	8.58027e8i	0.644546	+	1.11639i
$917$	−5.79308e7	−	1.00339e8i	−0.0751280	−	0.130125i
$918$	−2.39582e7	−	4.14967e7i	−0.0309689	−	0.0536397i
$919$	−1.26333e9			−1.62768			−0.813840	−	0.581089i	$-0.802627\pi$
$919$	−1.26333e9			−1.62768			−0.813840	+	0.581089i	$0.802627\pi$
$920$	−5.49220e8	−	9.51277e8i	−0.705314	−	1.22164i
$921$	7.75496e8	−	4.47733e8i	0.992660	−	0.573113i
$922$	1.02451e8	+	5.91500e7i	0.130714	+	0.0754679i
$923$	−2.05211e8	−	1.18479e8i	−0.260974	−	0.150673i
$924$	1.07954e9			1.36843
$925$		−	1.15691e9i		−	1.46176i
$926$	−1.14732e9	+	1.98722e9i	−1.44495	+	2.50273i
$927$	1.42387e7	−	2.46621e7i	0.0178744	−	0.0309593i
$928$	−4.39267e8	−	7.60833e8i	−0.549648	−	0.952018i
$929$	−7.81725e8	+	4.51329e8i	−0.975005	+	0.562919i	−0.900758	−	0.434320i	$-0.856989\pi$
$929$	−7.81725e8	+	4.51329e8i	−0.975005	+	0.562919i	−0.0742467	+	0.997240i	$0.523655\pi$
$930$			1.32398e9i			1.64601i
$931$	−2.47155e8	+	1.42695e8i	−0.306281	+	0.176831i
$932$	4.38092e8	−	2.52933e8i	0.541150	−	0.312433i
$933$	1.55141e8	−	8.95707e7i	0.191021	−	0.110286i
$934$	6.58278e8	−	1.14017e9i	0.807921	−	1.39936i
$935$			5.61393e7i			0.0686803i
$936$	2.34675e8	+	1.35489e8i	0.286180	+	0.165226i
$937$	3.64020e8	−	2.10167e8i	0.442493	−	0.255473i	−0.262162	−	0.965024i	$-0.584435\pi$
$937$	3.64020e8	−	2.10167e8i	0.442493	−	0.255473i	0.704655	+	0.709551i	$0.251102\pi$
$938$	4.83647e8			0.586030
$939$	2.69045e8	+	4.66000e8i	0.324959	+	0.562846i
$940$	1.28186e7	+	7.40084e6i	0.0154333	+	0.00891040i
$941$	−3.87783e8	+	6.71660e8i	−0.465393	+	0.806084i	−0.999219	−	0.0395098i	$-0.987420\pi$
$941$	−3.87783e8	+	6.71660e8i	−0.465393	+	0.806084i	0.533826	+	0.845594i	$0.320754\pi$
$942$		−	1.49488e9i		−	1.78835i
$943$	6.73078e8	−	1.16581e9i	0.802658	−	1.39024i
$944$	−1.29088e8			−0.153452
$945$		−	7.26441e8i		−	0.860805i
$946$	−7.80136e8	+	1.00576e9i	−0.921503	+	1.18801i
$947$	9.68852e8			1.14079			0.570397	−	0.821369i	$-0.306789\pi$
$947$	9.68852e8			1.14079			0.570397	+	0.821369i	$0.306789\pi$
$948$		−	2.64136e9i		−	3.10029i
$949$	−6.50144e8	−	3.75361e8i	−0.760695	−	0.439188i
$950$	1.40104e9			1.63410
$951$	2.75749e8	+	1.59204e8i	0.320606	+	0.185102i
$952$	1.61075e7	−	2.78990e7i	0.0186688	−	0.0323353i
$953$	2.35531e8	−	1.35984e8i	0.272125	−	0.157112i	−0.357728	−	0.933826i	$-0.616448\pi$
$953$	2.35531e8	−	1.35984e8i	0.272125	−	0.157112i	0.629853	+	0.776714i	$0.283115\pi$
$954$		−	8.10329e8i		−	0.933289i
$955$	−5.45650e7	−	9.45094e7i	−0.0626476	−	0.108509i
$956$	−1.16805e9	+	2.02311e9i	−1.33686	+	2.31551i
$957$	9.68050e8			1.10449
$958$	8.03620e7	+	4.63970e7i	0.0914017	+	0.0527708i
$959$	4.01200e8	+	6.94898e8i	0.454888	+	0.787890i
$960$	1.19674e9	+	2.07282e9i	1.35265	+	2.34286i
$961$	2.73751e8	+	4.74151e8i	0.308451	+	0.534253i
$962$	2.07530e9			2.33107
$963$	−1.63789e8	−	2.83692e8i	−0.183403	−	0.317664i
$964$	4.40041e8	−	2.54058e8i	0.491204	−	0.283597i
$965$	−1.63179e9	−	9.42116e8i	−1.81586	−	1.04839i
$966$	1.26381e9	+	7.29659e8i	1.40200	+	0.809447i
$967$	−5.71119e8			−0.631608			−0.315804	−	0.948824i	$-0.602274\pi$
$967$	−5.71119e8			−0.631608			−0.315804	+	0.948824i	$0.602274\pi$
$968$		−	9.87839e7i		−	0.108908i
$969$	−2.66600e7	+	4.61764e7i	−0.0293014	+	0.0507515i
$970$	−1.81914e9	+	3.15084e9i	−1.99320	+	3.45232i
$971$	2.76610e8	+	4.79102e8i	0.302141	+	0.523324i	0.976621	−	0.214970i	$-0.0689653\pi$
$971$	2.76610e8	+	4.79102e8i	0.302141	+	0.523324i	−0.674480	+	0.738293i	$0.735632\pi$
$972$	8.40450e8	−	4.85234e8i	0.915194	−	0.528388i
$973$			1.67293e8i			0.181610i
$974$	1.05540e9	−	6.09338e8i	1.14220	−	0.659450i
$975$	−9.99656e8	+	5.77152e8i	−1.07854	+	0.622696i
$976$	1.67627e8	−	9.67793e7i	0.180299	−	0.104096i
$977$	4.67995e8	−	8.10591e8i	0.501831	−	0.869196i	−0.498167	−	0.867081i	$-0.665993\pi$
$977$	4.67995e8	−	8.10591e8i	0.501831	−	0.869196i	0.999998	−	0.00211533i	$-0.000673332\pi$
$978$			2.25449e9i			2.41008i
$979$	−5.62519e8	−	3.24771e8i	−0.599500	−	0.346122i
$980$	−6.56364e8	+	3.78952e8i	−0.697375	+	0.402630i
$981$	−4.44934e8			−0.471291
$982$	−2.13223e8	−	3.69313e8i	−0.225164	−	0.389996i
$983$	−6.09293e8	−	3.51775e8i	−0.641454	−	0.370344i	0.143720	−	0.989618i	$-0.454093\pi$
$983$	−6.09293e8	−	3.51775e8i	−0.641454	−	0.370344i	−0.785174	+	0.619275i	$0.787427\pi$
$984$	7.44993e8	−	1.29037e9i	0.781928	−	1.35434i
$985$			2.11249e9i			2.21048i
$986$	3.98795e7	−	6.90734e7i	0.0416025	−	0.0720577i
$987$	−7.12229e6			−0.00740744
$988$			1.53450e9i			1.59109i
$989$	−9.72690e8	+	3.96954e8i	−1.00551	+	0.410347i
$990$	−7.32419e8			−0.754838
$991$			1.19291e9i			1.22570i	0.790198	+	0.612852i	$0.209978\pi$
$991$			1.19291e9i			1.22570i	−0.790198	+	0.612852i	$0.790022\pi$
$992$	−5.68115e8	−	3.28002e8i	−0.581971	−	0.336001i
$993$	6.86358e8			0.700975
$994$	−3.18285e8	−	1.83762e8i	−0.324083	−	0.187109i
$995$	−4.93039e8	+	8.53968e8i	−0.500509	+	0.866907i
$996$	−4.89784e8	+	2.82777e8i	−0.495709	+	0.286198i
$997$			5.74759e8i			0.579963i	0.957032	+	0.289981i	$0.0936491\pi$
$997$			5.74759e8i			0.579963i	−0.957032	+	0.289981i	$0.906351\pi$
$998$	−2.13111e8	−	3.69119e8i	−0.214395	−	0.371343i
$999$	5.29374e8	−	9.16902e8i	0.530965	−	0.919658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.d.a.37.3	yes	42
43.7	odd	6	inner	43.7.d.a.7.19	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.d.a.7.19	✓	42	43.7	odd	6	inner
43.7.d.a.37.3	yes	42	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-12.8196i q^{2} +(-27.1856 - 15.6956i) q^{3} -100.343 q^{4} +(-154.521 - 89.2129i) q^{5} +(-201.212 + 348.509i) q^{6} +(237.672 - 137.220i) q^{7} +465.907i q^{8} +(128.203 + 222.054i) q^{9} +O(q^{10})\)	\(q-12.8196i q^{2} +(-27.1856 - 15.6956i) q^{3} -100.343 q^{4} +(-154.521 - 89.2129i) q^{5} +(-201.212 + 348.509i) q^{6} +(237.672 - 137.220i) q^{7} +465.907i q^{8} +(128.203 + 222.054i) q^{9} +(-1143.68 + 1980.91i) q^{10} +1248.81 q^{11} +(2727.89 + 1574.95i) q^{12} +(-1134.17 - 1964.44i) q^{13} +(-1759.11 - 3046.86i) q^{14} +(2800.50 + 4850.61i) q^{15} -449.209 q^{16} +(-125.974 - 218.194i) q^{17} +(2846.65 - 1643.52i) q^{18} +(5838.49 + 3370.86i) q^{19} +(15505.2 + 8951.91i) q^{20} -8614.98 q^{21} -16009.3i q^{22} +(6606.78 - 11443.3i) q^{23} +(7312.68 - 12665.9i) q^{24} +(8105.39 + 14038.9i) q^{25} +(-25183.4 + 14539.7i) q^{26} +14835.3i q^{27} +(-23848.7 + 13769.1i) q^{28} +(-21385.7 + 12347.0i) q^{29} +(62183.0 - 35901.4i) q^{30} +(-9219.56 + 15968.7i) q^{31} +35576.7i q^{32} +(-33949.7 - 19600.9i) q^{33} +(-2797.17 + 1614.94i) q^{34} -48967.1 q^{35} +(-12864.3 - 22281.6i) q^{36} +(-61805.5 - 35683.4i) q^{37} +(43213.2 - 74847.4i) q^{38} +71205.9i q^{39} +(41564.9 - 71992.5i) q^{40} +101877. q^{41} +110441. i q^{42} +(-62823.1 - 48730.0i) q^{43} -125310. q^{44} -45749.4i q^{45} +(-146699. - 84696.5i) q^{46} +826.733 q^{47} +(12212.0 + 7050.60i) q^{48} +(-21166.0 + 36660.5i) q^{49} +(179974. - 103908. i) q^{50} +7908.96i q^{51} +(113806. + 197118. i) q^{52} +(123261. - 213495. i) q^{53} +190183. q^{54} +(-192968. - 111410. i) q^{55} +(63931.6 + 110733. i) q^{56} +(-105815. - 183277. i) q^{57} +(158285. + 274157. i) q^{58} +287368. q^{59} +(-281011. - 486725. i) q^{60} +(-373160. + 215444. i) q^{61} +(204713. + 118191. i) q^{62} +(60940.4 + 35184.0i) q^{63} +427331. q^{64} +404731. i q^{65} +(-251276. + 435223. i) q^{66} +(-68734.6 + 119052. i) q^{67} +(12640.7 + 21894.3i) q^{68} +(-359218. + 207395. i) q^{69} +627741. i q^{70} +(90467.6 - 52231.5i) q^{71} +(-103456. + 59730.6i) q^{72} +(286616. - 165478. i) q^{73} +(-457449. + 792324. i) q^{74} -508875. i q^{75} +(-585853. - 338242. i) q^{76} +(296808. - 171362. i) q^{77} +912834. q^{78} +(-419278. - 726211. i) q^{79} +(69412.4 + 40075.2i) q^{80} +(326308. - 565183. i) q^{81} -1.30603e6i q^{82} +(-89773.6 + 155492. i) q^{83} +864454. q^{84} +44954.1i q^{85} +(-624702. + 805370. i) q^{86} +775176. q^{87} +581831. i q^{88} +(-450443. - 260063. i) q^{89} -586491. q^{90} +(-539121. - 311261. i) q^{91} +(-662945. + 1.14825e6i) q^{92} +(501277. - 289413. i) q^{93} -10598.4i q^{94} +(-601448. - 1.04174e6i) q^{95} +(558398. - 967173. i) q^{96} +1.59060e6 q^{97} +(469975. + 271340. i) q^{98} +(160102. + 277304. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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