LMFDB - Embedded newform 40.6.k.a.3.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(3,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("40.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.k (of order $4$, 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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.6
Character	$\chi$	$=$	40.3
Dual form			40.6.k.a.27.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.60651 - 3.28330i) q^{2} +(11.5932 + 11.5932i) q^{3} +(10.4398 + 30.2491i) q^{4} +(-48.9682 + 26.9650i) q^{5} +(-15.3402 - 91.4681i) q^{6} +(-75.8554 - 75.8554i) q^{7} +(51.2259 - 173.620i) q^{8} +25.8041i q^{9} +O(q^{10})$	\(q+(-4.60651 - 3.28330i) q^{2} +(11.5932 + 11.5932i) q^{3} +(10.4398 + 30.2491i) q^{4} +(-48.9682 + 26.9650i) q^{5} +(-15.3402 - 91.4681i) q^{6} +(-75.8554 - 75.8554i) q^{7} +(51.2259 - 173.620i) q^{8} +25.8041i q^{9} +(314.107 + 36.5629i) q^{10} -570.121 q^{11} +(-229.653 + 471.715i) q^{12} +(-373.587 + 373.587i) q^{13} +(100.372 + 598.485i) q^{14} +(-880.309 - 255.087i) q^{15} +(-806.020 + 631.592i) q^{16} +(120.205 - 120.205i) q^{17} +(84.7226 - 118.867i) q^{18} +1018.64i q^{19} +(-1326.89 - 1199.74i) q^{20} -1758.81i q^{21} +(2626.27 + 1871.88i) q^{22} +(-785.825 + 785.825i) q^{23} +(2606.68 - 1418.94i) q^{24} +(1670.77 - 2640.86i) q^{25} +(2947.53 - 494.333i) q^{26} +(2517.99 - 2517.99i) q^{27} +(1502.64 - 3086.48i) q^{28} -6337.75 q^{29} +(3217.62 + 4065.38i) q^{30} +2427.71i q^{31} +(5786.64 - 263.026i) q^{32} +(-6609.52 - 6609.52i) q^{33} +(-948.396 + 159.056i) q^{34} +(5759.95 + 1669.06i) q^{35} +(-780.551 + 269.390i) q^{36} +(6307.89 + 6307.89i) q^{37} +(3344.52 - 4692.39i) q^{38} -8662.14 q^{39} +(2173.23 + 9883.17i) q^{40} -18431.2 q^{41} +(-5774.72 + 8101.99i) q^{42} +(15967.9 + 15967.9i) q^{43} +(-5951.97 - 17245.7i) q^{44} +(-695.808 - 1263.58i) q^{45} +(6200.01 - 1039.81i) q^{46} +(1022.27 + 1022.27i) q^{47} +(-16666.5 - 2022.17i) q^{48} -5298.91i q^{49} +(-16367.2 + 6679.48i) q^{50} +2787.12 q^{51} +(-15200.9 - 7400.50i) q^{52} +(23324.9 - 23324.9i) q^{53} +(-19866.5 + 3331.82i) q^{54} +(27917.8 - 15373.3i) q^{55} +(-17055.8 + 9284.26i) q^{56} +(-11809.3 + 11809.3i) q^{57} +(29194.9 + 20808.8i) q^{58} +25583.1i q^{59} +(-1474.11 - 29291.6i) q^{60} -561.671i q^{61} +(7970.91 - 11183.3i) q^{62} +(1957.38 - 1957.38i) q^{63} +(-27519.8 - 17787.7i) q^{64} +(8220.11 - 28367.7i) q^{65} +(8745.74 + 52147.9i) q^{66} +(-24390.4 + 24390.4i) q^{67} +(4891.02 + 2381.18i) q^{68} -18220.4 q^{69} +(-21053.2 - 26600.2i) q^{70} +63763.0i q^{71} +(4480.11 + 1321.84i) q^{72} +(-7254.89 - 7254.89i) q^{73} +(-8346.62 - 49768.0i) q^{74} +(49985.6 - 11246.4i) q^{75} +(-30813.1 + 10634.5i) q^{76} +(43246.8 + 43246.8i) q^{77} +(39902.2 + 28440.4i) q^{78} +28160.2 q^{79} +(22438.5 - 52662.3i) q^{80} +64653.5 q^{81} +(84903.2 + 60515.1i) q^{82} +(-71722.4 - 71722.4i) q^{83} +(53202.6 - 18361.7i) q^{84} +(-2644.90 + 9127.57i) q^{85} +(-21128.8 - 125984. i) q^{86} +(-73474.7 - 73474.7i) q^{87} +(-29204.9 + 98984.4i) q^{88} -25944.6i q^{89} +(-943.472 + 8105.24i) q^{90} +56677.3 q^{91} +(-31974.4 - 15566.6i) q^{92} +(-28144.9 + 28144.9i) q^{93} +(-1352.68 - 8065.54i) q^{94} +(-27467.8 - 49881.2i) q^{95} +(70135.0 + 64036.4i) q^{96} +(-72884.3 + 72884.3i) q^{97} +(-17397.9 + 24409.5i) q^{98} -14711.4i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	−4.60651	−	3.28330i	−0.814323	−	0.580412i
$2$	−4.60651	−	3.28330i	−0.814323	−	0.580412i
$3$	11.5932	+	11.5932i	0.743703	+	0.743703i	0.973289	−	0.229585i	$-0.0737369\pi$
$3$	11.5932	+	11.5932i	0.743703	+	0.743703i	−0.229585	+	0.973289i	$0.573737\pi$
$4$	10.4398	+	30.2491i	0.326245	+	0.945285i
$5$	−48.9682	+	26.9650i	−0.875970	+	0.482365i
$5$	−48.9682	+	26.9650i	−0.875970	+	0.482365i
$6$	−15.3402	−	91.4681i	−0.173961	−	1.03727i
$7$	−75.8554	−	75.8554i	−0.585115	−	0.585115i	0.351189	−	0.936305i	$-0.385777\pi$
$7$	−75.8554	−	75.8554i	−0.585115	−	0.585115i	−0.936305	+	0.351189i	$0.885777\pi$
$8$	51.2259	−	173.620i	0.282986	−	0.959124i
$9$			25.8041i			0.106190i
$10$	314.107	+	36.5629i	0.993293	+	0.115622i
$11$	−570.121			−1.42064			−0.710322	−	0.703877i	$-0.751451\pi$
$11$	−570.121			−1.42064			−0.710322	+	0.703877i	$0.751451\pi$
$12$	−229.653	+	471.715i	−0.460383	+	0.945641i
$13$	−373.587	+	373.587i	−0.613104	+	0.613104i	−0.943753	−	0.330650i	$-0.892732\pi$
$13$	−373.587	+	373.587i	−0.613104	+	0.613104i	0.330650	+	0.943753i	$0.392732\pi$
$14$	100.372	+	598.485i	0.136865	+	0.816081i
$15$	−880.309	−	255.087i	−1.01020	−	0.292725i
$16$	−806.020	+	631.592i	−0.787129	+	0.616789i
$17$	120.205	−	120.205i	0.100879	−	0.100879i	−0.654866	−	0.755745i	$-0.727275\pi$
$17$	120.205	−	120.205i	0.100879	−	0.100879i	0.755745	+	0.654866i	$0.227275\pi$
$18$	84.7226	−	118.867i	0.0616337	−	0.0864727i
$19$			1018.64i			0.647349i	0.946169	+	0.323674i	$0.104918\pi$
$19$			1018.64i			0.647349i	−0.946169	+	0.323674i	$0.895082\pi$
$20$	−1326.89	−	1199.74i	−0.741753	−	0.670673i
$21$		−	1758.81i		−	0.870305i
$22$	2626.27	+	1871.88i	1.15686	+	0.824558i
$23$	−785.825	+	785.825i	−0.309746	+	0.309746i	−0.844811	−	0.535065i	$-0.820287\pi$
$23$	−785.825	+	785.825i	−0.309746	+	0.309746i	0.535065	+	0.844811i	$0.320287\pi$
$24$	2606.68	−	1418.94i	0.923761	−	0.502846i
$25$	1670.77	−	2640.86i	0.534648	−	0.845075i
$26$	2947.53	−	494.333i	0.855117	−	0.143412i
$27$	2517.99	−	2517.99i	0.664730	−	0.664730i
$28$	1502.64	−	3086.48i	0.362210	−	0.743992i
$29$	−6337.75			−1.39939			−0.699697	−	0.714440i	$-0.746682\pi$
$29$	−6337.75			−1.39939			−0.699697	+	0.714440i	$0.746682\pi$
$30$	3217.62	+	4065.38i	0.652727	+	0.824704i
$31$			2427.71i			0.453725i	0.973927	+	0.226863i	$0.0728468\pi$
$31$			2427.71i			0.453725i	−0.973927	+	0.226863i	$0.927153\pi$
$32$	5786.64	−	263.026i	0.998969	−	0.0454071i
$33$	−6609.52	−	6609.52i	−1.05654	−	1.05654i
$34$	−948.396	+	159.056i	−0.140699	+	0.0235968i
$35$	5759.95	+	1669.06i	0.794783	+	0.230304i
$36$	−780.551	+	269.390i	−0.100380	+	0.0346438i
$37$	6307.89	+	6307.89i	0.757494	+	0.757494i	0.975866	−	0.218371i	$-0.0700744\pi$
$37$	6307.89	+	6307.89i	0.757494	+	0.757494i	−0.218371	+	0.975866i	$0.570074\pi$
$38$	3344.52	−	4692.39i	0.375729	−	0.527151i
$39$	−8662.14			−0.911934
$40$	2173.23	+	9883.17i	0.214761	+	0.976667i
$41$	−18431.2			−1.71235			−0.856176	−	0.516685i	$-0.827166\pi$
$41$	−18431.2			−1.71235			−0.856176	+	0.516685i	$0.827166\pi$
$42$	−5774.72	+	8101.99i	−0.505135	+	0.708709i
$43$	15967.9	+	15967.9i	1.31697	+	1.31697i	0.916159	+	0.400815i	$0.131273\pi$
$43$	15967.9	+	15967.9i	1.31697	+	1.31697i	0.400815	+	0.916159i	$0.368727\pi$
$44$	−5951.97	−	17245.7i	−0.463478	−	1.34291i
$45$	−695.808	−	1263.58i	−0.0512222	−	0.0930190i
$46$	6200.01	−	1039.81i	0.432014	−	0.0724533i
$47$	1022.27	+	1022.27i	0.0675028	+	0.0675028i	0.740052	−	0.672549i	$-0.234801\pi$
$47$	1022.27	+	1022.27i	0.0675028	+	0.0675028i	−0.672549	+	0.740052i	$0.734801\pi$
$48$	−16666.5	−	2022.17i	−1.04410	−	0.126682i
$49$		−	5298.91i		−	0.315280i
$50$	−16367.2	+	6679.48i	−0.925867	+	0.377849i
$51$	2787.12			0.150048
$52$	−15200.9	−	7400.50i	−0.779580	−	0.379536i
$53$	23324.9	−	23324.9i	1.14059	−	1.14059i	0.152251	−	0.988342i	$-0.451348\pi$
$53$	23324.9	−	23324.9i	1.14059	−	1.14059i	0.988342	−	0.152251i	$-0.0486523\pi$
$54$	−19866.5	+	3331.82i	−0.927122	+	0.155488i
$55$	27917.8	−	15373.3i	1.24444	−	0.685269i
$56$	−17055.8	+	9284.26i	−0.726778	+	0.395619i
$57$	−11809.3	+	11809.3i	−0.481436	+	0.481436i
$58$	29194.9	+	20808.8i	1.13956	+	0.812224i
$59$			25583.1i			0.956804i	0.878141	+	0.478402i	$0.158784\pi$
$59$			25583.1i			0.956804i	−0.878141	+	0.478402i	$0.841216\pi$
$60$	−1474.11	−	29291.6i	−0.0528631	−	1.05043i
$61$		−	561.671i		−	0.0193267i	−0.999953	−	0.00966334i	$-0.996924\pi$
$61$		−	561.671i		−	0.0193267i	0.999953	−	0.00966334i	$-0.00307598\pi$
$62$	7970.91	−	11183.3i	0.263347	−	0.369479i
$63$	1957.38	−	1957.38i	0.0621332	−	0.0621332i
$64$	−27519.8	−	17787.7i	−0.839838	−	0.542837i
$65$	8220.11	−	28367.7i	0.241321	−	0.832800i
$66$	8745.74	+	52147.9i	0.247137	+	1.47359i
$67$	−24390.4	+	24390.4i	−0.663792	+	0.663792i	−0.956272	−	0.292480i	$-0.905520\pi$
$67$	−24390.4	+	24390.4i	−0.663792	+	0.663792i	0.292480	+	0.956272i	$0.405520\pi$
$68$	4891.02	+	2381.18i	0.128271	+	0.0624482i
$69$	−18220.4			−0.460719
$70$	−21053.2	−	26600.2i	−0.513539	−	0.648844i
$71$			63763.0i			1.50114i	0.660788	+	0.750572i	$0.270222\pi$
$71$			63763.0i			1.50114i	−0.660788	+	0.750572i	$0.729778\pi$
$72$	4480.11	+	1321.84i	0.101849	+	0.0300502i
$73$	−7254.89	−	7254.89i	−0.159340	−	0.159340i	0.622934	−	0.782274i	$-0.285940\pi$
$73$	−7254.89	−	7254.89i	−0.159340	−	0.159340i	−0.782274	+	0.622934i	$0.785940\pi$
$74$	−8346.62	−	49768.0i	−0.177187	−	1.05650i
$75$	49985.6	−	11246.4i	1.02610	−	0.230866i
$76$	−30813.1	+	10634.5i	−0.611929	+	0.211194i
$77$	43246.8	+	43246.8i	0.831241	+	0.831241i
$78$	39902.2	+	28440.4i	0.742609	+	0.529297i
$79$	28160.2			0.507654			0.253827	−	0.967250i	$-0.418311\pi$
$79$	28160.2			0.507654			0.253827	+	0.967250i	$0.418311\pi$
$80$	22438.5	−	52662.3i	0.391984	−	0.919972i
$81$	64653.5			1.09491
$82$	84903.2	+	60515.1i	1.39441	+	0.993868i
$83$	−71722.4	−	71722.4i	−1.14277	−	1.14277i	−0.987941	−	0.154831i	$-0.950517\pi$
$83$	−71722.4	−	71722.4i	−1.14277	−	1.14277i	−0.154831	−	0.987941i	$-0.549483\pi$
$84$	53202.6	−	18361.7i	0.822686	−	0.283932i
$85$	−2644.90	+	9127.57i	−0.0397065	+	0.137028i
$86$	−21128.8	−	125984.i	−0.308056	−	1.83683i
$87$	−73474.7	−	73474.7i	−1.04073	−	1.04073i
$88$	−29204.9	+	98984.4i	−0.402022	+	1.36257i
$89$		−	25944.6i		−	0.347194i	−0.984817	−	0.173597i	$-0.944461\pi$
$89$		−	25944.6i		−	0.347194i	0.984817	−	0.173597i	$-0.0555391\pi$
$90$	−943.472	+	8105.24i	−0.0122779	+	0.105477i
$91$	56677.3			0.717473
$92$	−31974.4	−	15566.6i	−0.393852	−	0.191746i
$93$	−28144.9	+	28144.9i	−0.337437	+	0.337437i
$94$	−1352.68	−	8065.54i	−0.0157897	−	0.0941486i
$95$	−27467.8	−	49881.2i	−0.312258	−	0.567058i
$96$	70135.0	+	64036.4i	0.776706	+	0.709167i
$97$	−72884.3	+	72884.3i	−0.786510	+	0.786510i	−0.980920	−	0.194410i	$-0.937721\pi$
$97$	−72884.3	+	72884.3i	−0.786510	+	0.786510i	0.194410	+	0.980920i	$0.437721\pi$
$98$	−17397.9	+	24409.5i	−0.182992	+	0.256740i
$99$		−	14711.4i		−	0.150858i
$100$	97326.3	+	22969.3i	0.973263	+	0.229693i
$101$		−	117380.i		−	1.14497i	−0.819917	−	0.572483i	$-0.805980\pi$
$101$		−	117380.i		−	1.14497i	0.819917	−	0.572483i	$-0.194020\pi$
$102$	−12838.9	−	9150.97i	−0.122188	−	0.0870897i
$103$	12501.4	−	12501.4i	0.116109	−	0.116109i	−0.646665	−	0.762774i	$-0.723837\pi$
$103$	12501.4	−	12501.4i	0.116109	−	0.116109i	0.762774	+	0.646665i	$0.223837\pi$
$104$	45724.9	+	83999.6i	0.414543	+	0.761542i
$105$	47426.4	+	86125.9i	0.419805	+	0.762361i
$106$	−184029.	+	30863.7i	−1.59082	+	0.266798i
$107$	−37722.9	+	37722.9i	−0.318526	+	0.318526i	−0.848201	−	0.529675i	$-0.822314\pi$
$107$	−37722.9	+	37722.9i	−0.318526	+	0.318526i	0.529675	+	0.848201i	$0.322314\pi$
$108$	102455.	+	49879.7i	0.845224	+	0.411495i
$109$	−209518.			−1.68910			−0.844548	−	0.535480i	$-0.820131\pi$
$109$	−209518.			−1.68910			−0.844548	+	0.535480i	$0.820131\pi$
$110$	−179079.	−	20845.3i	−1.41112	−	0.164258i
$111$			146257.i			1.12670i
$112$	109051.	+	13231.3i	0.821454	+	0.0996684i
$113$	−80425.4	−	80425.4i	−0.592512	−	0.592512i	0.345797	−	0.938309i	$-0.387609\pi$
$113$	−80425.4	−	80425.4i	−0.592512	−	0.592512i	−0.938309	+	0.345797i	$0.887609\pi$
$114$	93173.4	−	15626.2i	0.671475	−	0.112613i
$115$	17290.7	−	59670.3i	0.121918	−	0.420740i
$116$	−66165.0	−	191711.i	−0.456545	−	1.32283i
$117$	−9640.08	−	9640.08i	−0.0651052	−	0.0651052i
$118$	83997.0	−	117849.i	0.555340	−	0.779148i
$119$	−18236.4			−0.118052
$120$	−89382.8	+	139772.i	−0.566632	+	0.886069i
$121$	163987.			1.01823
$122$	−1844.14	+	2587.34i	−0.0112174	+	0.0157382i
$123$	−213676.	−	213676.i	−1.27348	−	1.27348i
$124$	−73436.1	+	25344.9i	−0.428900	+	0.148025i
$125$	−10604.0	+	174371.i	−0.0607007	+	0.998156i
$126$	−15443.4	+	2590.01i	−0.0866593	+	0.0145337i
$127$	−77805.1	−	77805.1i	−0.428054	−	0.428054i	0.459911	−	0.887965i	$-0.347881\pi$
$127$	−77805.1	−	77805.1i	−0.428054	−	0.428054i	−0.887965	+	0.459911i	$0.847881\pi$
$128$	68367.9	+	172295.i	0.368831	+	0.929496i
$129$			370238.i			1.95888i
$130$	−131006.	+	103687.i	−0.679880	+	0.538103i
$131$	−134502.			−0.684781			−0.342390	−	0.939558i	$-0.611237\pi$
$131$	−134502.			−0.684781			−0.342390	+	0.939558i	$0.611237\pi$
$132$	130930.	−	268934.i	0.654039	−	1.34342i
$133$	77269.7	−	77269.7i	0.378774	−	0.378774i
$134$	192436.	−	32273.5i	0.925814	−	0.155269i
$135$	−55403.9	+	191199.i	−0.261641	+	0.902926i
$136$	−14712.4	−	27027.6i	−0.0682082	−	0.125303i
$137$	99849.0	−	99849.0i	0.454509	−	0.454509i	−0.442339	−	0.896848i	$-0.645851\pi$
$137$	99849.0	−	99849.0i	0.454509	−	0.454509i	0.896848	+	0.442339i	$0.145851\pi$
$138$	83932.6	+	59823.2i	0.375174	+	0.267407i
$139$			87569.1i			0.384427i	0.981353	+	0.192214i	$0.0615666\pi$
$139$			87569.1i			0.384427i	−0.981353	+	0.192214i	$0.938433\pi$
$140$	9645.27	+	191658.i	0.0415905	+	0.826432i
$141$			23702.8i			0.100404i
$142$	209353.	−	293725.i	0.871282	−	1.22242i
$143$	212990.	−	212990.i	0.871002	−	0.871002i
$144$	−16297.6	−	20798.6i	−0.0654966	−	0.0835849i
$145$	310348.	−	170898.i	1.22583	−	0.675019i
$146$	9599.70	+	57239.7i	0.0372714	+	0.222236i
$147$	61431.2	−	61431.2i	0.234475	−	0.234475i
$148$	−124955.	+	256661.i	−0.468920	+	0.963177i
$149$	341100.			1.25868			0.629341	−	0.777130i	$-0.283325\pi$
$149$	341100.			1.25868			0.629341	+	0.777130i	$0.283325\pi$
$150$	−267184.	−	112311.i	−0.969578	−	0.407563i
$151$		−	224116.i		−	0.799892i	−0.916539	−	0.399946i	$-0.869029\pi$
$151$		−	224116.i		−	0.799892i	0.916539	−	0.399946i	$-0.130971\pi$
$152$	176857.	+	52180.9i	0.620888	+	0.183190i
$153$	3101.78	+	3101.78i	0.0107123	+	0.0107123i
$154$	−57224.3	−	341209.i	−0.194437	−	1.15936i
$155$	−65463.3	−	118881.i	−0.218861	−	0.397450i
$156$	−90431.3	−	262022.i	−0.297514	−	0.862038i
$157$	−29808.0	−	29808.0i	−0.0965124	−	0.0965124i	0.657202	−	0.753714i	$-0.271740\pi$
$157$	−29808.0	−	29808.0i	−0.0965124	−	0.0965124i	−0.753714	+	0.657202i	$0.771740\pi$
$158$	−129720.	−	92458.5i	−0.413395	−	0.294648i
$159$	540821.			1.69653
$160$	−276269.	+	168917.i	−0.853164	+	0.521643i
$161$	119218.			0.362475
$162$	−297827.	−	212277.i	−0.891613	−	0.635500i
$163$	125534.	+	125534.i	0.370076	+	0.370076i	0.867505	−	0.497429i	$-0.165722\pi$
$163$	125534.	+	125534.i	0.370076	+	0.370076i	−0.497429	+	0.867505i	$0.665722\pi$
$164$	−192418.	−	557526.i	−0.558646	−	1.61866i
$165$	501882.	+	145430.i	1.43513	+	0.415859i
$166$	94903.4	+	565876.i	0.267308	+	1.59386i
$167$	63530.2	+	63530.2i	0.176274	+	0.176274i	0.789730	−	0.613455i	$-0.210221\pi$
$167$	63530.2	+	63530.2i	0.176274	+	0.176274i	−0.613455	+	0.789730i	$0.710221\pi$
$168$	−305365.	−	90096.7i	−0.834730	−	0.246284i
$169$			92158.0i			0.248208i
$170$	42152.3	−	33362.2i	0.111866	−	0.0885386i
$171$	−26285.2			−0.0687417
$172$	−316313.	+	649718.i	−0.815260	+	1.67457i
$173$	−399899.	+	399899.i	−1.01586	+	1.01586i	−0.0159894	+	0.999872i	$0.505090\pi$
$173$	−399899.	+	399899.i	−1.01586	+	1.01586i	−0.999872	+	0.0159894i	$0.994910\pi$
$174$	97222.1	+	579702.i	0.243440	+	1.45155i
$175$	−327061.	+	73586.3i	−0.807297	+	0.181636i
$176$	459529.	−	360084.i	1.11823	−	0.876237i
$177$	−296590.	+	296590.i	−0.711578	+	0.711578i
$178$	−85184.1	+	119514.i	−0.201516	+	0.282728i
$179$			560510.i			1.30753i	0.756699	+	0.653763i	$0.226811\pi$
$179$			560510.i			1.30753i	−0.756699	+	0.653763i	$0.773189\pi$
$180$	30958.1	−	34239.2i	0.0712185	−	0.0787665i
$181$		−	739824.i		−	1.67854i	−0.543715	−	0.839270i	$-0.682983\pi$
$181$		−	739824.i		−	1.67854i	0.543715	−	0.839270i	$-0.317017\pi$
$182$	−261084.	−	186089.i	−0.584255	−	0.416429i
$183$	6511.56	−	6511.56i	0.0143733	−	0.0143733i
$184$	96180.4	+	176690.i	0.209431	+	0.384739i
$185$	−478978.	−	138794.i	−1.02893	−	0.298154i
$186$	222058.	−	37241.5i	0.470635	−	0.0789305i
$187$	−68531.5	+	68531.5i	−0.143313	+	0.143313i
$188$	−20250.5	+	41595.2i	−0.0417870	+	0.0858319i
$189$	−382007.			−0.777887
$190$	−37244.6	+	319963.i	−0.0748478	+	0.643007i
$191$			624674.i			1.23900i	0.784998	+	0.619498i	$0.212664\pi$
$191$			624674.i			1.23900i	−0.784998	+	0.619498i	$0.787336\pi$
$192$	−112827.	−	525258.i	−0.220881	−	1.02830i
$193$	−524568.	−	524568.i	−1.01370	−	1.01370i	−0.999905	−	0.0137938i	$-0.995609\pi$
$193$	−524568.	−	524568.i	−1.01370	−	1.01370i	−0.0137938	−	0.999905i	$-0.504391\pi$
$194$	575043.	−	96440.8i	1.09697	−	0.183974i
$195$	424170.	−	233575.i	0.798827	−	0.439885i
$196$	160287.	−	55319.7i	0.298029	−	0.102858i
$197$	−209313.	−	209313.i	−0.384265	−	0.384265i	0.488371	−	0.872636i	$-0.337591\pi$
$197$	−209313.	−	209313.i	−0.384265	−	0.384265i	−0.872636	+	0.488371i	$0.837591\pi$
$198$	−48302.1	+	67768.4i	−0.0875595	+	0.122847i
$199$	−435549.			−0.779658			−0.389829	−	0.920887i	$-0.627466\pi$
$199$	−435549.			−0.779658			−0.389829	+	0.920887i	$0.627466\pi$
$200$	−372919.	−	425360.i	−0.659234	−	0.751938i
$201$	−565525.			−0.987329
$202$	−385396.	+	540714.i	−0.664551	+	0.932372i
$203$	480753.	+	480753.i	0.818807	+	0.818807i
$204$	29097.1	+	84308.0i	0.0489524	+	0.141838i
$205$	902541.	−	496997.i	1.49997	−	0.825979i
$206$	−98633.4	+	16541.9i	−0.161941	+	0.0271592i
$207$	−20277.5	−	20277.5i	−0.0328919	−	0.0328919i
$208$	65164.0	−	537074.i	0.104436	−	0.860747i
$209$		−	580750.i		−	0.919652i
$210$	64307.3	−	552455.i	0.100626	−	0.864468i
$211$	815482.			1.26098			0.630490	−	0.776198i	$-0.282854\pi$
$211$	815482.			1.26098			0.630490	+	0.776198i	$0.282854\pi$
$212$	949067.	+	462050.i	1.45030	+	0.706073i
$213$	−739216.	+	739216.i	−1.11641	+	1.11641i
$214$	297627.	−	49915.1i	0.444260	−	0.0745071i
$215$	−1.21250e6	−	351345.i	−1.78889	−	0.518368i
$216$	−308188.	−	566160.i	−0.449449	−	0.825667i
$217$	184155.	−	184155.i	0.265482	−	0.265482i
$218$	965144.	+	687910.i	1.37547	+	0.980370i
$219$		−	168215.i		−	0.237003i
$220$	756487.	+	683994.i	1.05377	+	0.952787i
$221$			89814.3i			0.123699i
$222$	480206.	−	673734.i	0.653951	−	0.917500i
$223$	850803.	−	850803.i	1.14569	−	1.14569i	0.158298	−	0.987391i	$-0.449399\pi$
$223$	850803.	−	850803.i	1.14569	−	1.14569i	0.987391	−	0.158298i	$-0.0506005\pi$
$224$	−458900.	−	418996.i	−0.611080	−	0.557944i
$225$	68145.0	+	43112.8i	0.0897382	+	0.0567740i
$226$	106419.	+	634541.i	0.138596	+	0.826397i
$227$	−166062.	+	166062.i	−0.213897	+	0.213897i	−0.805921	−	0.592023i	$-0.798329\pi$
$227$	−166062.	+	166062.i	−0.213897	+	0.213897i	0.592023	+	0.805921i	$0.298329\pi$
$228$	−480509.	−	233934.i	−0.612160	−	0.298028i
$229$	−763112.			−0.961612			−0.480806	−	0.876827i	$-0.659656\pi$
$229$	−763112.			−0.961612			−0.480806	+	0.876827i	$0.659656\pi$
$230$	−275565.	+	218101.i	−0.343483	+	0.271856i
$231$			1.00274e6i			1.23639i
$232$	−324657.	+	1.10036e6i	−0.396008	+	1.34219i
$233$	333510.	+	333510.i	0.402457	+	0.402457i	0.879098	−	0.476641i	$-0.158146\pi$
$233$	333510.	+	333510.i	0.402457	+	0.402457i	−0.476641	+	0.879098i	$0.658146\pi$
$234$	12755.8	+	76058.4i	0.0152289	+	0.0908045i
$235$	−77624.5	−	22493.3i	−0.0916915	−	0.0265695i
$236$	−773866.	+	267083.i	−0.904452	+	0.312152i
$237$	326467.	+	326467.i	0.377544	+	0.377544i
$238$	84006.3	+	59875.7i	0.0961323	+	0.0685186i
$239$	374083.			0.423617			0.211809	−	0.977311i	$-0.432065\pi$
$239$	374083.			0.423617			0.211809	+	0.977311i	$0.432065\pi$
$240$	870657.	−	350390.i	0.975706	−	0.392667i
$241$	−315848.			−0.350296			−0.175148	−	0.984542i	$-0.556040\pi$
$241$	−315848.			−0.350296			−0.175148	+	0.984542i	$0.556040\pi$
$242$	−755406.	−	538418.i	−0.829167	−	0.590991i
$243$	137668.	+	137668.i	0.149561	+	0.149561i
$244$	16990.1	−	5863.75i	0.0182692	−	0.00630523i
$245$	142885.	+	259478.i	0.152080	+	0.276176i
$246$	282737.	+	1.68586e6i	0.297882	+	1.77617i
$247$	−380552.	−	380552.i	−0.396892	−	0.396892i
$248$	421499.	+	124362.i	0.435179	+	0.128398i
$249$		−	1.66298e6i		−	1.69977i
$250$	621359.	−	768424.i	0.628771	−	0.777590i
$251$	−795235.			−0.796730			−0.398365	−	0.917227i	$-0.630422\pi$
$251$	−795235.			−0.796730			−0.398365	+	0.917227i	$0.630422\pi$
$252$	79643.8	+	38774.3i	0.0790042	+	0.0384630i
$253$	448015.	−	448015.i	0.440039	−	0.440039i
$254$	102952.	+	613867.i	0.100127	+	0.597022i
$255$	−136480.	+	75154.8i	−0.131438	+	0.0723780i
$256$	250759.	−	1.01815e6i	0.239143	−	0.970984i
$257$	810885.	−	810885.i	0.765820	−	0.765820i	−0.211548	−	0.977368i	$-0.567850\pi$
$257$	810885.	−	810885.i	0.765820	−	0.765820i	0.977368	+	0.211548i	$0.0678505\pi$
$258$	1.21560e6	−	1.70551e6i	1.13695	−	1.59516i
$259$		−	956975.i		−	0.886443i
$260$	943915.	−	47502.9i	0.865963	−	0.0435799i
$261$		−	163540.i		−	0.148601i
$262$	619586.	+	441612.i	0.557633	+	0.397455i
$263$	−181631.	+	181631.i	−0.161920	+	0.161920i	−0.783417	−	0.621497i	$-0.786525\pi$
$263$	−181631.	+	181631.i	−0.161920	+	0.161920i	0.621497	+	0.783417i	$0.286525\pi$
$264$	−1.48612e6	+	808966.i	−1.31234	+	0.714366i
$265$	−513223.	+	1.77114e6i	−0.448943	+	1.54931i
$266$	−609643.	+	102244.i	−0.528289	+	0.0885996i
$267$	300781.	−	300781.i	0.258210	−	0.258210i
$268$	−992420.	−	483157.i	−0.844031	−	0.410914i
$269$	−438410.			−0.369402			−0.184701	−	0.982795i	$-0.559132\pi$
$269$	−438410.			−0.369402			−0.184701	+	0.982795i	$0.559132\pi$
$270$	882984.	−	698854.i	0.737129	−	0.583414i
$271$		−	63769.8i		−	0.0527463i	−0.999652	−	0.0263732i	$-0.991604\pi$
$271$		−	63769.8i		−	0.0527463i	0.999652	−	0.0263732i	$-0.00839581\pi$
$272$	−20967.1	+	172808.i	−0.0171837	+	0.141626i
$273$	657070.	+	657070.i	0.533587	+	0.533587i
$274$	−787790.	+	132121.i	−0.633920	+	0.106315i
$275$	−952543.	+	1.50561e6i	−0.759544	+	1.20055i
$276$	−190218.	−	551152.i	−0.150307	−	0.435511i
$277$	607033.	+	607033.i	0.475349	+	0.475349i	0.903641	−	0.428291i	$-0.140884\pi$
$277$	607033.	+	607033.i	0.475349	+	0.475349i	−0.428291	+	0.903641i	$0.640884\pi$
$278$	287516.	−	403388.i	0.223126	−	0.313048i
$279$	−62644.9			−0.0481809
$280$	584841.	−	914543.i	0.445803	−	0.697123i
$281$	1.53941e6			1.16302			0.581511	−	0.813539i	$-0.302462\pi$
$281$	1.53941e6			1.16302			0.581511	+	0.813539i	$0.302462\pi$
$282$	77823.5	−	109187.i	0.0582757	−	0.0817615i
$283$	−72147.0	−	72147.0i	−0.0535491	−	0.0535491i	0.679825	−	0.733374i	$-0.262056\pi$
$283$	−72147.0	−	72147.0i	−0.0535491	−	0.0535491i	−0.733374	+	0.679825i	$0.762056\pi$
$284$	−1.92877e6	+	665675.i	−1.41901	+	0.489741i
$285$	259843.	−	896721.i	0.189495	−	0.653951i
$286$	−1.68045e6	+	281829.i	−1.21482	+	0.203737i
$287$	1.39810e6	+	1.39810e6i	1.00192	+	1.00192i
$288$	6787.14	+	149319.i	0.00482176	+	0.106080i
$289$			1.39096e6i			0.979647i
$290$	−1.99073e6	−	231726.i	−1.39001	−	0.161801i
$291$	−1.68992e6			−1.16986
$292$	143714.	−	295194.i	0.0986376	−	0.202605i
$293$	−723501.	+	723501.i	−0.492346	+	0.492346i	−0.909045	−	0.416699i	$-0.863187\pi$
$293$	−723501.	+	723501.i	−0.492346	+	0.492346i	0.416699	+	0.909045i	$0.363187\pi$
$294$	−484681.	+	81286.1i	−0.327030	+	0.0548464i
$295$	−689849.	−	1.25276e6i	−0.461529	−	0.838132i
$296$	1.41830e6	−	772048.i	0.940891	−	0.512171i
$297$	−1.43556e6	+	1.43556e6i	−0.944344	+	0.944344i
$298$	−1.57128e6	−	1.11993e6i	−1.02497	−	0.730553i
$299$		−	587149.i		−	0.379813i
$300$	862035.	+	1.39461e6i	0.552995	+	0.894643i
$301$		−	2.42251e6i		−	1.54116i
$302$	−735842.	+	1.03239e6i	−0.464266	+	0.651370i
$303$	1.36081e6	−	1.36081e6i	0.851515	−	0.851515i
$304$	−643367.	−	821047.i	−0.399278	−	0.509547i
$305$	15145.5	+	27504.0i	0.00932252	+	0.0169296i
$306$	−4104.29	−	24472.5i	−0.00250573	−	0.0149408i
$307$	923308.	−	923308.i	0.559114	−	0.559114i	−0.369941	−	0.929055i	$-0.620622\pi$
$307$	923308.	−	923308.i	0.559114	−	0.559114i	0.929055	+	0.369941i	$0.120622\pi$
$308$	−856688.	+	1.75967e6i	−0.514572	+	1.05695i
$309$	289861.			0.172701
$310$	−88764.2	+	762561.i	−0.0524606	+	0.450682i
$311$			1.85222e6i			1.08590i	0.839764	+	0.542952i	$0.182693\pi$
$311$			1.85222e6i			1.08590i	−0.839764	+	0.542952i	$0.817307\pi$
$312$	−443726.	+	1.50392e6i	−0.258064	+	0.874658i
$313$	228542.	+	228542.i	0.131858	+	0.131858i	0.769955	−	0.638098i	$-0.220278\pi$
$313$	228542.	+	228542.i	0.131858	+	0.131858i	−0.638098	+	0.769955i	$0.720278\pi$
$314$	39442.0	+	235179.i	0.0225754	+	0.134609i
$315$	−43068.6	+	148630.i	−0.0244559	+	0.0843977i
$316$	293988.	+	851822.i	0.165620	+	0.479878i
$317$	2.16668e6	+	2.16668e6i	1.21101	+	1.21101i	0.970697	+	0.240309i	$0.0772487\pi$
$317$	2.16668e6	+	2.16668e6i	1.21101	+	1.21101i	0.240309	+	0.970697i	$0.422751\pi$
$318$	−2.49130e6	−	1.77568e6i	−1.38152	−	0.984683i
$319$	3.61328e6			1.98804
$320$	1.82724e6	+	128958.i	0.997519	+	0.0704003i
$321$	−874657.			−0.473778
$322$	−549180.	−	391430.i	−0.295172	−	0.210385i
$323$	122446.	+	122446.i	0.0653039	+	0.0653039i
$324$	674972.	+	1.95571e6i	0.357210	+	1.03501i
$325$	362412.	+	1.61077e6i	0.190324	+	0.845913i
$326$	−166107.	−	990437.i	−0.0865651	−	0.516158i
$327$	−2.42898e6	−	2.42898e6i	−1.25619	−	1.25619i
$328$	−944152.	+	3.20002e6i	−0.484571	+	1.64236i
$329$		−	155090.i		−	0.0789939i
$330$	−1.83443e6	−	2.31776e6i	−0.927293	−	1.17161i
$331$	261939.			0.131410			0.0657052	−	0.997839i	$-0.479070\pi$
$331$	261939.			0.131410			0.0657052	+	0.997839i	$0.479070\pi$
$332$	1.42077e6	−	2.91831e6i	0.707422	−	1.45307i
$333$	−162769.	+	162769.i	−0.0804381	+	0.0804381i
$334$	−84063.5	−	501241.i	−0.0412326	−	0.245856i
$335$	536667.	−	1.85204e6i	0.261272	−	0.901652i
$336$	1.11085e6	+	1.41764e6i	0.536794	+	0.685042i
$337$	657466.	−	657466.i	0.315354	−	0.315354i	−0.531626	−	0.846979i	$-0.678419\pi$
$337$	657466.	−	657466.i	0.315354	−	0.315354i	0.846979	+	0.531626i	$0.178419\pi$
$338$	302583.	−	424526.i	0.144063	−	0.202122i
$339$		−	1.86477e6i		−	0.881307i
$340$	−303713.	+	15284.5i	−0.142484	+	0.00717057i
$341$		−	1.38409e6i		−	0.644582i
$342$	121083.	+	86302.2i	0.0559780	+	0.0398985i
$343$	−1.67685e6	+	1.67685e6i	−0.769591	+	0.769591i
$344$	3.59032e6	−	1.95438e6i	1.63583	−	0.890457i
$345$	892223.	−	491315.i	0.403576	−	0.222235i
$346$	3.15512e6	−	529148.i	1.41686	−	0.237622i
$347$	588905.	−	588905.i	0.262556	−	0.262556i	−0.563536	−	0.826092i	$-0.690559\pi$
$347$	588905.	−	588905.i	0.262556	−	0.262556i	0.826092	+	0.563536i	$0.190559\pi$
$348$	1.45548e6	−	2.98961e6i	0.644256	−	1.32332i
$349$	−2.40028e6			−1.05487			−0.527434	−	0.849596i	$-0.676846\pi$
$349$	−2.40028e6			−1.05487			−0.527434	+	0.849596i	$0.676846\pi$
$350$	1.74821e6	+	734864.i	0.762824	+	0.320654i
$351$			1.88138e6i			0.815096i
$352$	−3.29909e6	+	149956.i	−1.41918	+	0.0645072i
$353$	2.67685e6	+	2.67685e6i	1.14337	+	1.14337i	0.987829	+	0.155542i	$0.0497125\pi$
$353$	2.67685e6	+	2.67685e6i	1.14337	+	1.14337i	0.155542	+	0.987829i	$0.450287\pi$
$354$	2.34004e6	−	392449.i	0.992463	−	0.166446i
$355$	−1.71937e6	−	3.12236e6i	−0.724100	−	1.31496i
$356$	784803.	−	270858.i	0.328198	−	0.113270i
$357$	−211418.	−	211418.i	−0.0877955	−	0.0877955i
$358$	1.84032e6	−	2.58199e6i	0.758903	−	1.06475i
$359$	−567415.			−0.232362			−0.116181	−	0.993228i	$-0.537065\pi$
$359$	−567415.			−0.232362			−0.116181	+	0.993228i	$0.537065\pi$
$360$	−255026.	+	56078.2i	−0.103712	+	0.0228054i
$361$	1.43846e6			0.580940
$362$	−2.42907e6	+	3.40800e6i	−0.974244	+	1.36687i
$363$	1.90113e6	+	1.90113e6i	0.757260	+	0.757260i
$364$	591701.	+	1.71444e6i	0.234072	+	0.678216i
$365$	550887.	+	159631.i	0.216437	+	0.0627169i
$366$	−51375.0	+	8616.12i	−0.0200470	+	0.00336209i
$367$	−754935.	−	754935.i	−0.292580	−	0.292580i	0.545519	−	0.838099i	$-0.316333\pi$
$367$	−754935.	−	754935.i	−0.292580	−	0.292580i	−0.838099	+	0.545519i	$0.816333\pi$
$368$	137070.	−	1.12971e6i	0.0527621	−	0.434858i
$369$		−	475599.i		−	0.181834i
$370$	1.75072e6	+	2.21198e6i	0.664831	+	0.839997i
$371$	−3.53865e6			−1.33476
$372$	−1.14519e6	−	557531.i	−0.429061	−	0.208887i
$373$	−2.13280e6	+	2.13280e6i	−0.793740	+	0.793740i	−0.982100	−	0.188360i	$-0.939683\pi$
$373$	−2.13280e6	+	2.13280e6i	−0.793740	+	0.793740i	0.188360	+	0.982100i	$0.439683\pi$
$374$	540700.	−	90681.1i	0.199884	−	0.0335226i
$375$	−2.14445e6	+	1.89858e6i	−0.787475	+	0.697189i
$376$	229854.	−	125120.i	0.0838459	−	0.0456413i
$377$	2.36770e6	−	2.36770e6i	0.857973	−	0.857973i
$378$	1.75972e6	+	1.25424e6i	0.633452	+	0.451495i
$379$			594036.i			0.212429i	0.994343	+	0.106215i	$0.0338731\pi$
$379$			594036.i			0.212429i	−0.994343	+	0.106215i	$0.966127\pi$
$380$	1.22210e6	−	1.35163e6i	0.434159	−	0.480173i
$381$		−	1.80402e6i		−	0.636691i
$382$	2.05100e6	−	2.87757e6i	0.719128	−	1.00894i
$383$	−1.07098e6	+	1.07098e6i	−0.373065	+	0.373065i	−0.868592	−	0.495527i	$-0.834975\pi$
$383$	−1.07098e6	+	1.07098e6i	−0.373065	+	0.373065i	0.495527	+	0.868592i	$0.334975\pi$
$384$	−1.20485e6	+	2.79005e6i	−0.416969	+	0.965571i
$385$	−3.28387e6	−	951567.i	−1.12910	−	0.327180i
$386$	694111.	+	4.13875e6i	0.237116	+	1.41384i
$387$	−412038.	+	412038.i	−0.139849	+	0.139849i
$388$	−2.96558e6	−	1.44379e6i	−1.00007	−	0.486882i
$389$	−453123.			−0.151824			−0.0759122	−	0.997115i	$-0.524187\pi$
$389$	−453123.			−0.151824			−0.0759122	+	0.997115i	$0.524187\pi$
$390$	−2.72084e6	−	316713.i	−0.905818	−	0.105440i
$391$			188920.i			0.0624938i
$392$	−919996.	−	271441.i	−0.302392	−	0.0892197i
$393$	−1.55931e6	−	1.55931e6i	−0.509274	−	0.509274i
$394$	276964.	+	1.65144e6i	0.0898840	+	0.535947i
$395$	−1.37896e6	+	759341.i	−0.444690	+	0.244875i
$396$	445008.	−	153585.i	0.142604	−	0.0492165i
$397$	−1.77341e6	−	1.77341e6i	−0.564721	−	0.564721i	0.365924	−	0.930645i	$-0.380753\pi$
$397$	−1.77341e6	−	1.77341e6i	−0.564721	−	0.564721i	−0.930645	+	0.365924i	$0.880753\pi$
$398$	2.00636e6	+	1.43004e6i	0.634893	+	0.452522i
$399$	1.79160e6			0.563391
$400$	321269.	+	3.18383e6i	0.100396	+	0.994948i
$401$	−2.32162e6			−0.720993			−0.360497	−	0.932761i	$-0.617393\pi$
$401$	−2.32162e6			−0.720993			−0.360497	+	0.932761i	$0.617393\pi$
$402$	2.60510e6	+	1.85679e6i	0.804005	+	0.573057i
$403$	−906962.	−	906962.i	−0.278180	−	0.278180i
$404$	3.55066e6	−	1.22543e6i	1.08232	−	0.373539i
$405$	−3.16597e6	+	1.74338e6i	−0.959112	+	0.528148i
$406$	−636134.	−	3.79305e6i	−0.191529	−	1.14202i
$407$	−3.59626e6	−	3.59626e6i	−1.07613	−	1.07613i
$408$	142773.	−	483900.i	0.0424615	−	0.143915i
$409$			786623.i			0.232519i	0.993219	+	0.116260i	$0.0370904\pi$
$409$			786623.i			0.232519i	−0.993219	+	0.116260i	$0.962910\pi$
$410$	−5.78935e6	−	673896.i	−1.70087	−	0.197986i
$411$	2.31514e6			0.676040
$412$	508667.	+	247643.i	0.147636	+	0.0718759i
$413$	1.94062e6	−	1.94062e6i	0.559841	−	0.559841i
$414$	26831.3	+	159986.i	0.00769379	+	0.0458754i
$415$	5.44612e6	+	1.57812e6i	1.55227	+	0.449801i
$416$	−2.06355e6	+	2.26008e6i	−0.584632	+	0.640310i
$417$	−1.01521e6	+	1.01521e6i	−0.285900	+	0.285900i
$418$	−1.90678e6	+	2.67523e6i	−0.533777	+	0.748894i
$419$			6.98085e6i			1.94255i	0.237950	+	0.971277i	$0.423525\pi$
$419$			6.98085e6i			1.94255i	−0.237950	+	0.971277i	$0.576475\pi$
$420$	−2.11011e6	+	2.33375e6i	−0.583690	+	0.645552i
$421$			203905.i			0.0560690i	0.999607	+	0.0280345i	$0.00892482\pi$
$421$			203905.i			0.0560690i	−0.999607	+	0.0280345i	$0.991075\pi$
$422$	−3.75652e6	−	2.67747e6i	−1.02685	−	0.731887i
$423$	−26378.8	+	26378.8i	−0.00716810	+	0.00716810i
$424$	−2.85483e6	−	5.24452e6i	−0.771199	−	1.41674i
$425$	−116609.	−	518281.i	−0.0313156	−	0.139185i
$426$	5.83228e6	−	978134.i	1.55709	−	0.261141i
$427$	−42605.8	+	42605.8i	−0.0113083	+	0.0113083i
$428$	−1.53491e6	−	747264.i	−0.405016	−	0.197181i
$429$	4.93846e6			1.29553
$430$	4.43180e6	+	5.59947e6i	1.15587	+	1.46041i
$431$		−	5.73366e6i		−	1.48675i	−0.668874	−	0.743376i	$-0.733223\pi$
$431$		−	5.73366e6i		−	1.48675i	0.668874	−	0.743376i	$-0.266777\pi$
$432$	−439208.	+	3.61990e6i	−0.113230	+	0.933226i
$433$	−113631.	−	113631.i	−0.0291258	−	0.0291258i	0.692394	−	0.721520i	$-0.256556\pi$
$433$	−113631.	−	113631.i	−0.0291258	−	0.0291258i	−0.721520	+	0.692394i	$0.756556\pi$
$434$	−1.45295e6	+	243675.i	−0.370276	+	0.0620993i
$435$	5.57917e6	+	1.61668e6i	1.41367	+	0.409638i
$436$	−2.18733e6	−	6.33772e6i	−0.551059	−	1.59668i
$437$	−800476.	−	800476.i	−0.200514	−	0.200514i
$438$	−552300.	+	774882.i	−0.137559	+	0.192997i
$439$	−5.86078e6			−1.45142			−0.725711	−	0.687999i	$-0.758489\pi$
$439$	−5.86078e6			−1.45142			−0.725711	+	0.687999i	$0.758489\pi$
$440$	−1.23900e6	−	5.63460e6i	−0.305099	−	1.38750i
$441$	136733.			0.0334795
$442$	294887.	−	413730.i	0.0717961	−	0.100731i
$443$	−1.78245e6	−	1.78245e6i	−0.431527	−	0.431527i	0.457621	−	0.889148i	$-0.348702\pi$
$443$	−1.78245e6	−	1.78245e6i	−0.431527	−	0.431527i	−0.889148	+	0.457621i	$0.848702\pi$
$444$	−4.42415e6	+	1.52690e6i	−1.06506	+	0.367581i
$445$	699598.	+	1.27046e6i	0.167474	+	0.304132i
$446$	−6.71267e6	+	1.12579e6i	−1.59793	+	0.267990i
$447$	3.95443e6	+	3.95443e6i	0.936086	+	0.936086i
$448$	738235.	+	3.43682e6i	0.173780	+	0.809025i
$449$		−	3.13103e6i		−	0.732946i	−0.930429	−	0.366473i	$-0.880565\pi$
$449$		−	3.13103e6i		−	0.732946i	0.930429	−	0.366473i	$-0.119435\pi$
$450$	−172358.	−	422340.i	−0.0401236	−	0.0983175i
$451$	1.05080e7			2.43264
$452$	1.59317e6	−	3.27243e6i	0.366789	−	0.753397i
$453$	2.59822e6	−	2.59822e6i	0.594882	−	0.594882i
$454$	1.31020e6	−	219734.i	0.298330	−	0.0500331i
$455$	−2.77538e6	+	1.52830e6i	−0.628485	+	0.346084i
$456$	1.44539e6	+	2.65528e6i	0.325517	+	0.597996i
$457$	−3.84103e6	+	3.84103e6i	−0.860315	+	0.860315i	−0.991374	−	0.131060i	$-0.958162\pi$
$457$	−3.84103e6	+	3.84103e6i	−0.860315	+	0.860315i	0.131060	+	0.991374i	$0.458162\pi$
$458$	3.51528e6	+	2.50553e6i	0.783063	+	0.558131i
$459$		−	605352.i		−	0.134115i
$460$	1.98549e6	−	99920.2i	0.437494	−	0.0220170i
$461$			5.45953e6i			1.19647i	0.801319	+	0.598237i	$0.204132\pi$
$461$			5.45953e6i			1.19647i	−0.801319	+	0.598237i	$0.795868\pi$
$462$	3.29229e6	−	4.61911e6i	0.717617	−	1.00682i
$463$	−150397.	+	150397.i	−0.0326051	+	0.0326051i	−0.723221	−	0.690616i	$-0.757339\pi$
$463$	−150397.	+	150397.i	−0.0326051	+	0.0326051i	0.690616	+	0.723221i	$0.257339\pi$
$464$	5.10835e6	−	4.00287e6i	1.10150	−	0.863131i
$465$	619278.	−	2.13714e6i	0.132817	−	0.458352i
$466$	−441302.	−	2.63133e6i	−0.0941394	−	0.561321i
$467$	−632068.	+	632068.i	−0.134113	+	0.134113i	−0.770977	−	0.636863i	$-0.780232\pi$
$467$	−632068.	+	632068.i	−0.134113	+	0.134113i	0.636863	+	0.770977i	$0.280232\pi$
$468$	190963.	−	392245.i	0.0403028	−	0.0827833i
$469$	3.70029e6			0.776790
$470$	283726.	+	358480.i	0.0592453	+	0.0748549i
$471$		−	691138.i		−	0.143553i
$472$	4.44174e6	+	1.31052e6i	0.917694	+	0.270762i
$473$	−9.10364e6	−	9.10364e6i	−1.87095	−	1.87095i
$474$	−431982.	−	2.57576e6i	−0.0883120	−	0.526574i
$475$	2.69010e6	+	1.70192e6i	0.547058	+	0.346104i
$476$	−190385.	−	551636.i	−0.0385138	−	0.111593i
$477$	601879.	+	601879.i	0.121119	+	0.121119i
$478$	−1.72322e6	−	1.22823e6i	−0.344961	−	0.245872i
$479$	6.58795e6			1.31193			0.655966	−	0.754790i	$-0.272261\pi$
$479$	6.58795e6			1.31193			0.655966	+	0.754790i	$0.272261\pi$
$480$	−5.16113e6	−	1.24455e6i	−1.02245	−	0.246553i
$481$	−4.71309e6			−0.928845
$482$	1.45496e6	+	1.03703e6i	0.285255	+	0.203316i
$483$	1.38212e6	+	1.38212e6i	0.269574	+	0.269574i
$484$	1.71199e6	+	4.96045e6i	0.332192	+	0.962516i
$485$	1.60369e6	−	5.53434e6i	0.309574	−	1.06834i
$486$	−182163.	−	1.08618e6i	−0.0349841	−	0.208598i
$487$	6.69914e6	+	6.69914e6i	1.27996	+	1.27996i	0.940688	+	0.339272i	$0.110181\pi$
$487$	6.69914e6	+	6.69914e6i	1.27996	+	1.27996i	0.339272	+	0.940688i	$0.389819\pi$
$488$	−97517.3	−	28772.1i	−0.0185367	−	0.00546918i
$489$			2.91067e6i			0.550454i
$490$	193743.	−	1.66442e6i	0.0364533	−	0.313165i
$491$	−3.16982e6			−0.593378			−0.296689	−	0.954974i	$-0.595882\pi$
$491$	−3.16982e6			−0.593378			−0.296689	+	0.954974i	$0.595882\pi$
$492$	4.23277e6	−	8.69425e6i	0.788337	−	1.61927i
$493$	−761830.	+	761830.i	−0.141169	+	0.141169i
$494$	503549.	+	3.00249e6i	0.0928376	+	0.553559i
$495$	396695.	+	720393.i	0.0727685	+	0.132147i
$496$	−1.53332e6	−	1.95678e6i	−0.279853	−	0.357140i
$497$	4.83677e6	−	4.83677e6i	0.878343	−	0.878343i
$498$	−5.46008e6	+	7.66054e6i	−0.986564	+	1.38416i
$499$		−	1.26756e6i		−	0.227886i	−0.993487	−	0.113943i	$-0.963652\pi$
$499$		−	1.26756e6i		−	0.227886i	0.993487	−	0.113943i	$-0.0363482\pi$
$500$	−5.38527e6	+	1.49964e6i	−0.963345	+	0.268264i
$501$			1.47304e6i			0.262192i
$502$	3.66326e6	+	2.61100e6i	0.648796	+	0.462431i
$503$	1.10664e6	−	1.10664e6i	0.195023	−	0.195023i	−0.602840	−	0.797862i	$-0.705964\pi$
$503$	1.10664e6	−	1.10664e6i	0.195023	−	0.195023i	0.797862	+	0.602840i	$0.205964\pi$
$504$	−239572.	−	440109.i	−0.0420106	−	0.0771763i
$505$	3.16517e6	+	5.74791e6i	0.552291	+	1.00296i
$506$	−3.53476e6	+	592816.i	−0.613738	+	0.102930i
$507$	−1.06840e6	+	1.06840e6i	−0.184593	+	0.184593i
$508$	1.54126e6	−	3.16581e6i	0.264983	−	0.544284i
$509$	−3.15635e6			−0.539997			−0.269998	−	0.962861i	$-0.587023\pi$
$509$	−3.15635e6			−0.539997			−0.269998	+	0.962861i	$0.587023\pi$
$510$	875454.	+	101905.i	0.149042	+	0.0173489i
$511$			1.10065e6i			0.186464i
$512$	−4.49802e6	+	3.86680e6i	−0.758310	+	0.651894i
$513$	2.56494e6	+	2.56494e6i	0.430312	+	0.430312i
$514$	−6.39773e6	+	1.07297e6i	−1.06812	+	0.179134i
$515$	−275070.	+	949269.i	−0.0457009	+	0.157714i
$516$	−1.11994e7	+	3.86523e6i	−1.85170	+	0.639073i
$517$	−582819.	−	582819.i	−0.0958975	−	0.0958975i
$518$	−3.14204e6	+	4.40831e6i	−0.514502	+	0.721852i
$519$	−9.27220e6			−1.51100
$520$	−4.50412e6	−	2.88034e6i	−0.730468	−	0.467127i
$521$	9.90035e6			1.59792			0.798962	−	0.601381i	$-0.205383\pi$
$521$	9.90035e6			1.59792			0.798962	+	0.601381i	$0.205383\pi$
$522$	−536951.	+	753347.i	−0.0862498	+	0.121009i
$523$	−3.15331e6	−	3.15331e6i	−0.504095	−	0.504095i	0.408613	−	0.912708i	$-0.366013\pi$
$523$	−3.15331e6	−	3.15331e6i	−0.504095	−	0.504095i	−0.912708	+	0.408613i	$0.866013\pi$
$524$	−1.40418e6	−	4.06858e6i	−0.223406	−	0.647313i
$525$	−4.64478e6	−	2.93858e6i	−0.735473	−	0.465306i
$526$	1.43303e6	−	240335.i	0.225836	−	0.0378750i
$527$	291823.	+	291823.i	0.0457713	+	0.0457713i
$528$	9.50192e6	+	1.15288e6i	1.48329	+	0.179970i
$529$			5.20130e6i			0.808114i
$530$	8.17935e6	−	6.47370e6i	1.26482	−	1.00107i
$531$	−660148.			−0.101603
$532$	3.14402e6	+	1.53066e6i	0.481622	+	0.234476i
$533$	6.88565e6	−	6.88565e6i	1.04985	−	1.04985i
$534$	−2.37311e6	+	397995.i	−0.360134	+	0.0603983i
$535$	830024.	−	2.86442e6i	0.125374	−	0.432666i
$536$	2.98524e6	+	5.48408e6i	0.448815	+	0.824502i
$537$	−6.49809e6	+	6.49809e6i	−0.972412	+	0.972412i
$538$	2.01954e6	+	1.43943e6i	0.300813	+	0.214405i
$539$			3.02102e6i			0.447900i
$540$	−6.36202e6	+	320171.i	−0.938882	+	0.0472496i
$541$			1.03364e7i			1.51837i	0.650876	+	0.759184i	$0.274402\pi$
$541$			1.03364e7i			1.51837i	−0.650876	+	0.759184i	$0.725598\pi$
$542$	−209376.	+	293756.i	−0.0306146	+	0.0429525i
$543$	8.57691e6	−	8.57691e6i	1.24834	−	1.24834i
$544$	663967.	−	727202.i	0.0961943	−	0.105356i
$545$	1.02597e7	−	5.64965e6i	1.47960	−	0.814761i
$546$	−869438.	−	5.18416e6i	−0.124812	−	0.744212i
$547$	−6.28342e6	+	6.28342e6i	−0.897899	+	0.897899i	−0.995250	−	0.0973509i	$-0.968963\pi$
$547$	−6.28342e6	+	6.28342e6i	−0.897899	+	0.897899i	0.0973509	+	0.995250i	$0.468963\pi$
$548$	4.06275e6	+	1.97794e6i	0.577922	+	0.281359i
$549$	14493.4			0.00205229
$550$	9.33127e6	−	3.80811e6i	1.31533	−	0.536788i
$551$		−	6.45591e6i		−	0.905896i
$552$	−933358.	+	3.16343e6i	−0.130377	+	0.441887i
$553$	−2.13610e6	−	2.13610e6i	−0.297036	−	0.297036i
$554$	−803229.	−	4.78938e6i	−0.111190	−	0.662986i
$555$	−3.94383e6	−	7.16195e6i	−0.543482	−	0.986958i
$556$	−2.64889e6	+	914207.i	−0.363393	+	0.125417i
$557$	−8.18985e6	−	8.18985e6i	−1.11850	−	1.11850i	−0.991961	−	0.126544i	$-0.959612\pi$
$557$	−8.18985e6	−	8.18985e6i	−1.11850	−	1.11850i	−0.126544	−	0.991961i	$-0.540388\pi$
$558$	288574.	+	205682.i	0.0392348	+	0.0279648i
$559$	−1.19308e7			−1.61488
$560$	−5.69680e6	+	2.29264e6i	−0.767646	+	0.308934i
$561$	−1.58900e6			−0.213165
$562$	−7.09130e6	−	5.05434e6i	−0.947076	−	0.675031i
$563$	−5.64038e6	−	5.64038e6i	−0.749959	−	0.749959i	0.224512	−	0.974471i	$-0.427921\pi$
$563$	−5.64038e6	−	5.64038e6i	−0.749959	−	0.749959i	−0.974471	+	0.224512i	$0.927921\pi$
$564$	−716989.	+	247453.i	−0.0949106	+	0.0327563i
$565$	6.10696e6	+	1.76962e6i	0.804830	+	0.233216i
$566$	95465.2	+	569226.i	0.0125258	+	0.0746868i
$567$	−4.90432e6	−	4.90432e6i	−0.640651	−	0.640651i
$568$	1.10705e7	+	3.26631e6i	1.43978	+	0.424803i
$569$		−	446954.i		−	0.0578738i	−0.999581	−	0.0289369i	$-0.990788\pi$
$569$		−	446954.i		−	0.0578738i	0.999581	−	0.0289369i	$-0.00921219\pi$
$570$	−4.14118e6	+	3.27761e6i	−0.533871	+	0.422542i
$571$	−3.03616e6			−0.389704			−0.194852	−	0.980833i	$-0.562423\pi$
$571$	−3.03616e6			−0.389704			−0.194852	+	0.980833i	$0.562423\pi$
$572$	8.66634e6	+	4.21918e6i	1.10750	+	0.539185i
$573$	−7.24197e6	+	7.24197e6i	−0.921446	+	0.921446i
$574$	−1.84998e6	−	1.10308e7i	−0.234362	−	1.39742i
$575$	762318.	+	3.38819e6i	0.0961538	+	0.427364i
$576$	458995.	−	710124.i	0.0576437	−	0.0891821i
$577$	−1.86814e6	+	1.86814e6i	−0.233598	+	0.233598i	−0.814193	−	0.580594i	$-0.802820\pi$
$577$	−1.86814e6	+	1.86814e6i	−0.233598	+	0.233598i	0.580594	+	0.814193i	$0.302820\pi$
$578$	4.56694e6	−	6.40746e6i	0.568598	−	0.797749i
$579$		−	1.21628e7i		−	1.50778i
$580$	8.40949e6	+	7.60362e6i	1.03801	+	0.938535i
$581$			1.08811e7i			1.33731i
$582$	7.78464e6	+	5.54853e6i	0.952645	+	0.679001i
$583$	−1.32980e7	+	1.32980e7i	−1.62038	+	1.62038i
$584$	−1.63123e6	+	887956.i	−0.197917	+	0.107736i
$585$	732003.	+	212113.i	0.0884348	+	0.0256258i
$586$	5.70829e6	−	957340.i	0.686692	−	0.115165i
$587$	−2.52291e6	+	2.52291e6i	−0.302208	+	0.302208i	−0.841877	−	0.539669i	$-0.818549\pi$
$587$	−2.52291e6	+	2.52291e6i	−0.302208	+	0.302208i	0.539669	+	0.841877i	$0.318549\pi$
$588$	2.49957e6	+	1.21691e6i	0.298142	+	0.145149i
$589$	−2.47297e6			−0.293718
$590$	−935392.	+	8.03582e6i	−0.110628	+	0.950387i
$591$		−	4.85321e6i		−	0.571558i
$592$	−9.06829e6	−	1.10027e6i	−1.06346	−	0.129031i
$593$	4.59347e6	+	4.59347e6i	0.536419	+	0.536419i	0.922475	−	0.386057i	$-0.126163\pi$
$593$	4.59347e6	+	4.59347e6i	0.536419	+	0.536419i	−0.386057	+	0.922475i	$0.626163\pi$
$594$	1.13263e7	−	1.89954e6i	1.31711	−	0.220893i
$595$	893006.	−	491746.i	0.103410	−	0.0569440i
$596$	3.56103e6	+	1.03180e7i	0.410638	+	1.18981i
$597$	−5.04940e6	−	5.04940e6i	−0.579834	−	0.579834i
$598$	−1.92779e6	+	2.70471e6i	−0.220448	+	0.309291i
$599$	−5.28076e6			−0.601352			−0.300676	−	0.953726i	$-0.597212\pi$
$599$	−5.28076e6			−0.601352			−0.300676	+	0.953726i	$0.597212\pi$
$600$	607959.	−	9.25460e6i	0.0689439	−	1.04949i
$601$	7.37217e6			0.832548			0.416274	−	0.909239i	$-0.363336\pi$
$601$	7.37217e6			0.832548			0.416274	+	0.909239i	$0.363336\pi$
$602$	−7.95383e6	+	1.11593e7i	−0.894509	+	1.25501i
$603$	−629372.	−	629372.i	−0.0704878	−	0.0704878i
$604$	6.77932e6	−	2.33974e6i	0.756126	−	0.260961i
$605$	−8.03014e6	+	4.42191e6i	−0.891938	+	0.491158i
$606$	−1.07366e7	+	1.80063e6i	−1.18764	+	0.199179i
$607$	9.09980e6	+	9.09980e6i	1.00244	+	1.00244i	0.999997	+	0.00244749i	$0.000779062\pi$
$607$	9.09980e6	+	9.09980e6i	1.00244	+	1.00244i	0.00244749	+	0.999997i	$0.499221\pi$
$608$	267930.	+	5.89453e6i	0.0293942	+	0.646681i
$609$			1.11469e7i			1.21790i
$610$	20536.3	−	176425.i	0.00223459	−	0.0191971i
$611$	−763816.			−0.0827725
$612$	−61444.2	+	126208.i	−0.00663135	+	0.0136210i
$613$	3.92586e6	−	3.92586e6i	0.421972	−	0.421972i	−0.463910	−	0.885882i	$-0.653554\pi$
$613$	3.92586e6	−	3.92586e6i	0.421972	−	0.421972i	0.885882	+	0.463910i	$0.153554\pi$
$614$	−7.28473e6	+	1.22173e6i	−0.779816	+	0.130783i
$615$	1.62251e7	+	4.70155e6i	1.72981	+	0.501249i
$616$	9.72386e6	−	5.29315e6i	1.03249	−	0.562034i
$617$	4.37860e6	−	4.37860e6i	0.463044	−	0.463044i	−0.436608	−	0.899652i	$-0.643820\pi$
$617$	4.37860e6	−	4.37860e6i	0.463044	−	0.463044i	0.899652	+	0.436608i	$0.143820\pi$
$618$	−1.33525e6	−	951703.i	−0.140634	−	0.100237i
$619$		−	8.50734e6i		−	0.892416i	−0.894929	−	0.446208i	$-0.852774\pi$
$619$		−	8.50734e6i		−	0.892416i	0.894929	−	0.446208i	$-0.147226\pi$
$620$	2.91261e6	−	3.22130e6i	0.304301	−	0.336552i
$621$			3.95740e6i			0.411795i
$622$	6.08140e6	−	8.53226e6i	0.630271	−	0.884276i
$623$	−1.96804e6	+	1.96804e6i	−0.203149	+	0.203149i
$624$	6.98185e6	−	5.47094e6i	0.717810	−	0.562471i
$625$	−4.18265e6	−	8.82456e6i	−0.428304	−	0.903635i
$626$	−302408.	−	1.80315e6i	−0.0308431	−	0.183907i
$627$	6.73274e6	−	6.73274e6i	0.683948	−	0.683948i
$628$	590474.	−	1.21285e6i	0.0597451	−	0.122718i
$629$	1.51648e6			0.152831
$630$	686394.	−	543259.i	0.0689005	−	0.0545325i
$631$		−	1.29241e7i		−	1.29219i	−0.763255	−	0.646097i	$-0.776400\pi$
$631$		−	1.29241e7i		−	1.29219i	0.763255	−	0.646097i	$-0.223600\pi$
$632$	1.44253e6	−	4.88918e6i	0.143659	−	0.486904i
$633$	9.45403e6	+	9.45403e6i	0.937795	+	0.937795i
$634$	−2.86696e6	−	1.70947e7i	−0.283268	−	1.68903i
$635$	5.90799e6	+	1.71196e6i	0.581441	+	0.168484i
$636$	5.64608e6	+	1.63594e7i	0.553483	+	1.60370i
$637$	1.97960e6	+	1.97960e6i	0.193299	+	0.193299i
$638$	−1.66446e7	−	1.18635e7i	−1.61891	−	1.15388i
$639$	−1.64534e6			−0.159406
$640$	−7.99380e6	−	6.59344e6i	−0.771442	−	0.636300i
$641$	−1.32292e7			−1.27171			−0.635856	−	0.771807i	$-0.719353\pi$
$641$	−1.32292e7			−1.27171			−0.635856	+	0.771807i	$0.719353\pi$
$642$	4.02912e6	+	2.87177e6i	0.385809	+	0.274986i
$643$	−1.30647e6	−	1.30647e6i	−0.124616	−	0.124616i	0.642048	−	0.766664i	$-0.278085\pi$
$643$	−1.30647e6	−	1.30647e6i	−0.124616	−	0.124616i	−0.766664	+	0.642048i	$0.778085\pi$
$644$	1.24462e6	+	3.60625e6i	0.118256	+	0.342642i
$645$	−9.98349e6	−	1.81299e7i	−0.944894	−	1.71592i
$646$	−162021.	−	966078.i	−0.0152753	−	0.0910816i
$647$	4.43306e6	+	4.43306e6i	0.416335	+	0.416335i	0.883939	−	0.467603i	$-0.154882\pi$
$647$	4.43306e6	+	4.43306e6i	0.416335	+	0.416335i	−0.467603	+	0.883939i	$0.654882\pi$
$648$	3.31194e6	−	1.12251e7i	0.309845	−	1.05016i
$649$		−	1.45854e7i		−	1.35928i
$650$	3.61920e6	−	8.60994e6i	0.335992	−	0.799313i
$651$	4.26989e6			0.394879
$652$	−2.48673e6	+	5.10783e6i	−0.229092	+	0.470563i
$653$	1.18262e7	−	1.18262e7i	1.08533	−	1.08533i	0.0893303	−	0.996002i	$-0.471527\pi$
$653$	1.18262e7	−	1.18262e7i	1.08533	−	1.08533i	0.996002	−	0.0893303i	$-0.0284727\pi$
$654$	3.21403e6	+	1.91642e7i	0.293837	+	1.75205i
$655$	6.58634e6	−	3.62686e6i	0.599848	−	0.330314i
$656$	1.48559e7	−	1.16410e7i	1.34784	−	1.05616i
$657$	187206.	−	187206.i	0.0169202	−	0.0169202i
$658$	−509207.	+	714423.i	−0.0458490	+	0.0643266i
$659$			2.06175e7i			1.84936i	0.380740	+	0.924682i	$0.375669\pi$
$659$			2.06175e7i			1.84936i	−0.380740	+	0.924682i	$0.624331\pi$
$660$	840422.	+	1.66998e7i	0.0750996	+	1.49228i
$661$			1.97452e6i			0.175775i	0.996130	+	0.0878876i	$0.0280116\pi$
$661$			1.97452e6i			0.175775i	−0.996130	+	0.0878876i	$0.971988\pi$
$662$	−1.20662e6	−	860024.i	−0.107010	−	0.0762721i
$663$	−1.04123e6	+	1.04123e6i	−0.0919950	+	0.0919950i
$664$	−1.61265e7	+	8.77840e6i	−1.41945	+	0.772672i
$665$	−1.70018e6	+	5.86734e6i	−0.149087	+	0.514502i
$666$	1.28422e6	−	215377.i	0.112190	−	0.0188154i
$667$	4.98036e6	−	4.98036e6i	0.433457	−	0.433457i
$668$	−1.25849e6	+	2.58498e6i	−0.109121	+	0.224138i
$669$	1.97270e7			1.70411
$670$	−8.55298e6	+	6.76941e6i	−0.736089	+	0.582591i
$671$			320220.i			0.0274563i
$672$	−462613.	−	1.01776e7i	−0.0395180	−	0.869407i
$673$	1.02682e6	+	1.02682e6i	0.0873889	+	0.0873889i	0.749450	−	0.662061i	$-0.230318\pi$
$673$	1.02682e6	+	1.02682e6i	0.0873889	+	0.0873889i	−0.662061	+	0.749450i	$0.730318\pi$
$674$	−5.18728e6	+	869961.i	−0.439835	+	0.0737650i
$675$	−2.44267e6	−	1.08567e7i	−0.206350	−	0.917143i
$676$	−2.78770e6	+	962114.i	−0.234628	+	0.0809766i
$677$	8.46734e6	+	8.46734e6i	0.710028	+	0.710028i	0.966541	−	0.256513i	$-0.0825737\pi$
$677$	8.46734e6	+	8.46734e6i	0.710028	+	0.710028i	−0.256513	+	0.966541i	$0.582574\pi$
$678$	−6.12262e6	+	8.59010e6i	−0.511521	+	0.717668i
$679$	1.10573e7			0.920399
$680$	1.44924e6	+	926775.i	0.120190	+	0.0768603i
$681$	−3.85037e6			−0.318152
$682$	−4.54438e6	+	6.37582e6i	−0.374123	+	0.524898i
$683$	5.01535e6	+	5.01535e6i	0.411386	+	0.411386i	0.882221	−	0.470835i	$-0.156047\pi$
$683$	5.01535e6	+	5.01535e6i	0.411386	+	0.411386i	−0.470835	+	0.882221i	$0.656047\pi$
$684$	−274413.	−	795103.i	−0.0224266	−	0.0649805i
$685$	−2.19700e6	+	7.58186e6i	−0.178897	+	0.617376i
$686$	1.32301e7	−	2.21882e6i	1.07337	−	0.180016i
$687$	−8.84691e6	−	8.84691e6i	−0.715154	−	0.715154i
$688$	−2.29557e7	−	2.78525e6i	−1.84892	−	0.224333i
$689$			1.74278e7i			1.39860i
$690$	−5.72317e6	−	666192.i	−0.457629	−	0.0532693i
$691$	−1.11672e7			−0.889715			−0.444857	−	0.895601i	$-0.646746\pi$
$691$	−1.11672e7			−0.889715			−0.444857	+	0.895601i	$0.646746\pi$
$692$	−1.62715e7	−	7.92171e6i	−1.29170	−	0.628859i
$693$	−1.11594e6	+	1.11594e6i	−0.0882691	+	0.0882691i
$694$	−4.64635e6	+	779242.i	−0.366196	+	0.0614149i
$695$	−2.36130e6	−	4.28810e6i	−0.185434	−	0.336747i
$696$	−1.65205e7	+	8.99287e6i	−1.29271	+	0.703680i
$697$	−2.21552e6	+	2.21552e6i	−0.172740	+	0.172740i
$698$	1.10569e7	+	7.88084e6i	0.859003	+	0.612257i
$699$			7.73290e6i			0.598617i
$700$	−5.64038e6	−	9.12508e6i	−0.435074	−	0.703868i
$701$		−	4.47239e6i		−	0.343751i	−0.985119	−	0.171876i	$-0.945017\pi$
$701$		−	4.47239e6i		−	0.343751i	0.985119	−	0.171876i	$-0.0549827\pi$
$702$	6.17715e6	−	8.66660e6i	0.473091	−	0.663752i
$703$	−6.42549e6	+	6.42549e6i	−0.490363	+	0.490363i
$704$	1.56896e7	+	1.01411e7i	1.19311	+	0.771178i
$705$	−639147.	−	1.16068e6i	−0.0484315	−	0.0879511i
$706$	−3.54202e6	−	2.11198e7i	−0.267448	−	1.59470i
$707$	−8.90394e6	+	8.90394e6i	−0.669937	+	0.669937i
$708$	−1.20679e7	−	5.87523e6i	−0.904793	−	0.440496i
$709$	−2.91189e6			−0.217550			−0.108775	−	0.994066i	$-0.534693\pi$
$709$	−2.91189e6			−0.217550			−0.108775	+	0.994066i	$0.534693\pi$
$710$	−2.33136e6	+	2.00284e7i	−0.173565	+	1.49108i
$711$			726648.i			0.0539076i
$712$	−4.50451e6	−	1.32904e6i	−0.333002	−	0.0982510i
$713$	−1.90776e6	−	1.90776e6i	−0.140540	−	0.140540i
$714$	279750.	+	1.66805e6i	0.0205364	+	0.122451i
$715$	−4.68646e6	+	1.61730e7i	−0.342831	+	1.18311i
$716$	−1.69549e7	+	5.85163e6i	−1.23599	+	0.426574i
$717$	4.33682e6	+	4.33682e6i	0.315046	+	0.315046i
$718$	2.61380e6	+	1.86300e6i	0.189218	+	0.134865i
$719$	4.58157e6			0.330515			0.165258	−	0.986250i	$-0.447154\pi$
$719$	4.58157e6			0.330515			0.165258	+	0.986250i	$0.447154\pi$
$720$	1.35890e6	+	579004.i	0.0976915	+	0.0416246i
$721$	−1.89659e6			−0.135874
$722$	−6.62630e6	−	4.72291e6i	−0.473073	−	0.337184i
$723$	−3.66169e6	−	3.66169e6i	−0.260517	−	0.260517i
$724$	2.23790e7	−	7.72364e6i	1.58670	−	0.547615i
$725$	−1.05889e7	+	1.67371e7i	−0.748183	+	1.18259i
$726$	−2.51558e6	−	1.49995e7i	−0.177132	−	1.05618i
$727$	1.49733e6	+	1.49733e6i	0.105071	+	0.105071i	0.757688	−	0.652617i	$-0.226329\pi$
$727$	1.49733e6	+	1.49733e6i	0.105071	+	0.105071i	−0.652617	+	0.757688i	$0.726329\pi$
$728$	2.90334e6	−	9.84031e6i	0.203035	−	0.688145i
$729$		−	1.25188e7i		−	0.872455i
$730$	−2.01355e6	−	2.54407e6i	−0.139848	−	0.176694i
$731$	3.83885e6			0.265710
$732$	264948.	+	128989.i	0.0182761	+	0.00889767i
$733$	−2.27068e6	+	2.27068e6i	−0.156097	+	0.156097i	−0.780835	−	0.624737i	$-0.785206\pi$
$733$	−2.27068e6	+	2.27068e6i	−0.156097	+	0.156097i	0.624737	+	0.780835i	$0.285206\pi$
$734$	998934.	+	5.95630e6i	0.0684379	+	0.408071i
$735$	−1.35168e6	+	4.66467e6i	−0.0922904	+	0.318495i
$736$	−4.34060e6	+	4.75398e6i	−0.295362	+	0.323492i
$737$	1.39055e7	−	1.39055e7i	0.943012	−	0.943012i
$738$	−1.56154e6	+	2.19085e6i	−0.105539	+	0.148072i
$739$		−	3.43953e6i		−	0.231680i	−0.993268	−	0.115840i	$-0.963044\pi$
$739$		−	3.43953e6i		−	0.231680i	0.993268	−	0.115840i	$-0.0369560\pi$
$740$	−802068.	−	1.59377e7i	−0.0538433	−	1.06990i
$741$		−	8.82363e6i		−	0.590340i
$742$	1.63008e7	+	1.16184e7i	1.08692	+	0.774709i
$743$	2.61358e6	−	2.61358e6i	0.173686	−	0.173686i	−0.614911	−	0.788597i	$-0.710808\pi$
$743$	2.61358e6	−	2.61358e6i	0.173686	−	0.173686i	0.788597	+	0.614911i	$0.210808\pi$
$744$	3.44477e6	+	6.32827e6i	0.228154	+	0.419134i
$745$	−1.67030e7	+	9.19777e6i	−1.10257	+	0.607144i
$746$	1.68274e7	−	2.82213e6i	1.10706	−	0.185665i
$747$	1.85073e6	−	1.85073e6i	0.121351	−	0.121351i
$748$	−2.78847e6	−	1.35756e6i	−0.182227	−	0.0887166i
$749$	5.72297e6			0.372750
$750$	1.61120e7	−	1.70495e6i	1.04592	−	0.110677i
$751$		−	3.75344e6i		−	0.242845i	−0.992601	−	0.121422i	$-0.961254\pi$
$751$		−	3.75344e6i		−	0.242845i	0.992601	−	0.121422i	$-0.0387456\pi$
$752$	−1.46963e6	−	178313.i	−0.0947684	−	0.0114984i
$753$	−9.21931e6	−	9.21931e6i	−0.592531	−	0.592531i
$754$	−1.86807e7	+	3.13295e6i	−1.19665	+	0.200690i
$755$	6.04330e6	+	1.09746e7i	0.385840	+	0.700681i
$756$	−3.98809e6	−	1.15554e7i	−0.253782	−	0.735326i
$757$	903047.	+	903047.i	0.0572757	+	0.0572757i	0.735164	−	0.677889i	$-0.237105\pi$
$757$	903047.	+	903047.i	0.0572757	+	0.0572757i	−0.677889	+	0.735164i	$0.737105\pi$
$758$	1.95040e6	−	2.73643e6i	0.123296	−	0.172986i
$759$	1.03878e7			0.654517
$760$	−1.00674e7	+	2.21375e6i	−0.632244	+	0.139025i
$761$	−3.74081e6			−0.234155			−0.117078	−	0.993123i	$-0.537353\pi$
$761$	−3.74081e6			−0.234155			−0.117078	+	0.993123i	$0.537353\pi$
$762$	−5.92314e6	+	8.31022e6i	−0.369543	+	0.518472i
$763$	1.58930e7	+	1.58930e7i	0.988316	+	0.988316i
$764$	−1.88959e7	+	6.52150e6i	−1.17121	+	0.404216i
$765$	−235529.	−	68249.2i	−0.0145509	−	0.00421642i
$766$	8.44984e6	−	1.41713e6i	0.520327	−	0.0872644i
$767$	−9.55752e6	−	9.55752e6i	−0.586620	−	0.586620i
$768$	1.47107e7	−	8.89651e6i	0.899976	−	0.544273i
$769$		−	1.53331e7i		−	0.935007i	−0.883991	−	0.467503i	$-0.845154\pi$
$769$		−	1.53331e7i		−	0.935007i	0.883991	−	0.467503i	$-0.154846\pi$
$770$	1.20029e7	+	1.51653e7i	0.729556	+	0.921775i
$771$	1.88015e7			1.13909
$772$	1.03913e7	−	2.13441e7i	0.627520	−	1.28895i
$773$	2.38468e6	−	2.38468e6i	0.143543	−	0.143543i	−0.631684	−	0.775226i	$-0.717636\pi$
$773$	2.38468e6	−	2.38468e6i	0.143543	−	0.143543i	0.775226	+	0.631684i	$0.217636\pi$
$774$	3.25090e6	−	545210.i	0.195052	−	0.0327123i
$775$	6.41124e6	+	4.05616e6i	0.383432	+	0.242583i
$776$	8.92060e6	+	1.63877e7i	0.531790	+	0.976932i
$777$	1.10944e7	−	1.10944e7i	0.659251	−	0.659251i
$778$	2.08731e6	+	1.48774e6i	0.123634	+	0.0881207i
$779$		−	1.87748e7i		−	1.10849i
$780$	1.14937e7	+	1.03923e7i	0.676430	+	0.611609i
$781$		−	3.63526e7i		−	2.13259i
$782$	620283.	−	870264.i	0.0362721	−	0.0508902i
$783$	−1.59584e7	+	1.59584e7i	−0.930219	+	0.930219i
$784$	3.34675e6	+	4.27102e6i	0.194461	+	0.248166i
$785$	2.26341e6	+	655870.i	0.131096	+	0.0379878i
$786$	2.06329e6	+	1.23027e7i	0.119125	+	0.710302i
$787$	1.25982e7	−	1.25982e7i	0.725056	−	0.725056i	−0.244574	−	0.969631i	$-0.578648\pi$
$787$	1.25982e7	−	1.25982e7i	0.725056	−	0.725056i	0.969631	+	0.244574i	$0.0786482\pi$
$788$	4.14634e6	−	8.51673e6i	0.237875	−	0.488604i
$789$	−4.21137e6			−0.240841
$790$	8.84532e6	+	1.02962e6i	0.504250	+	0.0586960i
$791$			1.22014e7i			0.693376i
$792$	−2.55420e6	−	753607.i	−0.144691	−	0.0426906i
$793$	209833.	+	209833.i	0.0118493	+	0.0118493i
$794$	2.34659e6	+	1.39919e7i	0.132095	+	0.787636i
$795$	−2.64830e7	+	1.45832e7i	−1.48611	+	0.818345i
$796$	−4.54705e6	−	1.31750e7i	−0.254359	−	0.736999i
$797$	−7.47193e6	−	7.47193e6i	−0.416665	−	0.416665i	0.467388	−	0.884053i	$-0.345195\pi$
$797$	−7.47193e6	−	7.47193e6i	−0.416665	−	0.416665i	−0.884053	+	0.467388i	$0.845195\pi$
$798$	−8.25304e6	−	5.88238e6i	−0.458782	−	0.326998i
$799$	245765.			0.0136192
$800$	8.97356e6	−	1.57212e7i	0.495724	−	0.868480i
$801$	669478.			0.0368684
$802$	1.06946e7	+	7.62260e6i	0.587121	+	0.418473i
$803$	4.13616e6	+	4.13616e6i	0.226365	+	0.226365i
$804$	−5.90399e6	−	1.71066e7i	−0.322111	−	0.933307i
$805$	−5.83790e6	+	3.21472e6i	−0.317517	+	0.174845i
$806$	1.20010e6	+	7.15576e6i	0.0650697	+	0.387988i
$807$	−5.08257e6	−	5.08257e6i	−0.274726	−	0.274726i
$808$	−2.03796e7	−	6.01292e6i	−1.09816	−	0.324009i
$809$		−	1.93743e7i		−	1.04077i	−0.853932	−	0.520384i	$-0.825789\pi$
$809$		−	1.93743e7i		−	1.04077i	0.853932	−	0.520384i	$-0.174211\pi$
$810$	2.03081e7	+	2.36392e6i	1.08757	+	0.126596i
$811$	1.01979e7			0.544451			0.272225	−	0.962233i	$-0.412240\pi$
$811$	1.01979e7			0.544451			0.272225	+	0.962233i	$0.412240\pi$
$812$	−9.52337e6	+	1.95613e7i	−0.506875	+	1.04114i
$813$	739296.	−	739296.i	0.0392276	−	0.0392276i
$814$	4.75858e6	+	2.83738e7i	0.251719	+	1.50092i
$815$	−9.53218e6	−	2.76214e6i	−0.502687	−	0.145664i
$816$	−2.24648e6	+	1.76032e6i	−0.118107	+	0.0925480i
$817$	−1.62656e7	+	1.62656e7i	−0.852542	+	0.852542i
$818$	2.58272e6	−	3.62359e6i	0.134957	−	0.189346i
$819$			1.46250e6i			0.0761882i
$820$	2.44561e7	+	2.21125e7i	1.27014	+	1.14843i
$821$			2.27277e7i			1.17679i	0.808575	+	0.588393i	$0.200239\pi$
$821$			2.27277e7i			1.17679i	−0.808575	+	0.588393i	$0.799761\pi$
$822$	−1.06647e7	−	7.60130e6i	−0.550515	−	0.392381i
$823$	5.40655e6	−	5.40655e6i	0.278241	−	0.278241i	−0.554166	−	0.832406i	$-0.686963\pi$
$823$	5.40655e6	−	5.40655e6i	0.278241	−	0.278241i	0.832406	+	0.554166i	$0.186963\pi$
$824$	−1.53009e6	−	2.81088e6i	−0.0785054	−	0.144220i
$825$	−2.84978e7	+	6.41180e6i	−1.45773	+	0.327978i
$826$	−1.53111e7	+	2.56783e6i	−0.780829	+	0.130953i
$827$	2.60998e7	−	2.60998e7i	1.32701	−	1.32701i	0.419044	−	0.907966i	$-0.362365\pi$
$827$	2.60998e7	−	2.60998e7i	1.32701	−	1.32701i	0.907966	−	0.419044i	$-0.137635\pi$
$828$	401683.	−	825070.i	0.0203614	−	0.0418230i
$829$	390079.			0.0197136			0.00985681	−	0.999951i	$-0.496862\pi$
$829$	390079.			0.0197136			0.00985681	+	0.999951i	$0.496862\pi$
$830$	−1.99061e7	−	2.51509e7i	−1.00298	−	1.26724i
$831$			1.40749e7i			0.707038i
$832$	1.69263e7	−	3.63580e6i	0.847723	−	0.182093i
$833$	−636956.	−	636956.i	−0.0318051	−	0.0318051i
$834$	8.00978e6	−	1.34332e6i	0.398754	−	0.0668753i
$835$	−4.82406e6	−	1.39787e6i	−0.239440	−	0.0693825i
$836$	1.75672e7	−	6.06293e6i	0.869333	−	0.300032i
$837$	6.11296e6	+	6.11296e6i	0.301605	+	0.301605i
$838$	2.29203e7	−	3.21573e7i	1.12748	−	1.58187i
$839$	−4.33875e6			−0.212794			−0.106397	−	0.994324i	$-0.533931\pi$
$839$	−4.33875e6			−0.212794			−0.106397	+	0.994324i	$0.533931\pi$
$840$	1.73826e7	−	3.82230e6i	0.849998	−	0.186908i
$841$	1.96559e7			0.958303
$842$	669482.	−	939290.i	0.0325431	−	0.0456583i
$843$	1.78466e7	+	1.78466e7i	0.864944	+	0.864944i
$844$	8.51349e6	+	2.46676e7i	0.411388	+	1.19199i
$845$	−2.48504e6	−	4.51281e6i	−0.119727	−	0.217423i
$846$	208124.	−	34904.6i	0.00999760	−	0.00167670i
$847$	−1.24393e7	−	1.24393e7i	−0.595781	−	0.595781i
$848$	−4.06852e6	+	3.35322e7i	−0.194288	+	1.60130i
$849$		−	1.67283e6i		−	0.0796493i
$850$	−1.16451e6	+	2.77033e6i	−0.0552836	+	0.131518i
$851$	−9.91379e6			−0.469262
$852$	−3.00779e7	−	1.46433e7i	−1.41954	−	0.691101i
$853$	−8.78804e6	+	8.78804e6i	−0.413542	+	0.413542i	−0.882970	−	0.469429i	$-0.844460\pi$
$853$	−8.78804e6	+	8.78804e6i	−0.413542	+	0.413542i	0.469429	+	0.882970i	$0.344460\pi$
$854$	336152.	−	56376.2i	0.0157721	−	0.00264515i
$855$	1.28714e6	−	708780.i	0.0602157	−	0.0331586i
$856$	4.61706e6	+	8.48184e6i	0.215368	+	0.395645i
$857$	−1.60816e7	+	1.60816e7i	−0.747956	+	0.747956i	−0.974095	−	0.226139i	$-0.927390\pi$
$857$	−1.60816e7	+	1.60816e7i	−0.747956	+	0.747956i	0.226139	+	0.974095i	$0.427390\pi$
$858$	−2.27491e7	−	1.62145e7i	−1.05498	−	0.751943i
$859$		−	8.59975e6i		−	0.397652i	−0.980035	−	0.198826i	$-0.936287\pi$
$859$		−	8.59975e6i		−	0.397652i	0.980035	−	0.198826i	$-0.0637128\pi$
$860$	−2.03037e6	−	4.03449e7i	−0.0936116	−	1.86013i
$861$			3.24169e7i			1.49027i
$862$	−1.88253e7	+	2.64121e7i	−0.862928	+	1.21070i
$863$	−1.81516e7	+	1.81516e7i	−0.829634	+	0.829634i	−0.987466	−	0.157832i	$-0.949550\pi$
$863$	−1.81516e7	+	1.81516e7i	−0.829634	+	0.829634i	0.157832	+	0.987466i	$0.449550\pi$
$864$	1.39084e7	−	1.52330e7i	0.633861	−	0.694228i
$865$	8.79904e6	−	3.03656e7i	0.399848	−	1.37988i
$866$	150357.	+	896528.i	0.00681286	+	0.0406227i
$867$	−1.61256e7	+	1.61256e7i	−0.728567	+	0.728567i
$868$	7.49308e6	+	3.64798e6i	0.337568	+	0.164344i
$869$	−1.60547e7			−0.721196
$870$	−2.03925e7	−	2.57654e7i	−0.913422	−	1.15409i
$871$		−	1.82239e7i		−	0.813946i
$872$	−1.07327e7	+	3.63764e7i	−0.477990	+	1.62005i
$873$	−1.88071e6	−	1.88071e6i	−0.0835192	−	0.0835192i
$874$	1.05919e6	+	6.31560e6i	0.0469026	+	0.279664i
$875$	1.40313e7	−	1.24226e7i	0.619553	−	0.548520i
$876$	5.08835e6	−	1.75613e6i	0.224035	−	0.0773209i
$877$	−1.50023e7	−	1.50023e7i	−0.658657	−	0.658657i	0.296405	−	0.955062i	$-0.404212\pi$
$877$	−1.50023e7	−	1.50023e7i	−0.658657	−	0.658657i	−0.955062	+	0.296405i	$0.904212\pi$
$878$	2.69977e7	+	1.92427e7i	1.18193	+	0.842422i
$879$	−1.67754e7			−0.732319
$880$	−1.27926e7	+	3.00239e7i	−0.556869	+	1.30695i
$881$	−3.24105e7			−1.40685			−0.703423	−	0.710772i	$-0.748346\pi$
$881$	−3.24105e7			−1.40685			−0.703423	+	0.710772i	$0.748346\pi$
$882$	−629864.	−	448937.i	−0.0272631	−	0.0194319i
$883$	−3.31227e6	−	3.31227e6i	−0.142963	−	0.142963i	0.632003	−	0.774966i	$-0.282233\pi$
$883$	−3.31227e6	−	3.31227e6i	−0.142963	−	0.142963i	−0.774966	+	0.632003i	$0.782233\pi$
$884$	−2.71680e6	+	937646.i	−0.116930	+	0.0403560i
$885$	6.52592e6	−	2.25210e7i	0.280081	−	0.966562i
$886$	2.35855e6	+	1.40632e7i	0.100939	+	0.601866i
$887$	2.77149e7	+	2.77149e7i	1.18278	+	1.18278i	0.979021	+	0.203758i	$0.0653154\pi$
$887$	2.77149e7	+	2.77149e7i	1.18278	+	1.18278i	0.203758	+	0.979021i	$0.434685\pi$
$888$	2.53931e7	+	7.49215e6i	1.08065	+	0.318841i
$889$			1.18039e7i			0.500922i
$890$	948611.	−	8.14939e6i	0.0401433	−	0.344866i
$891$	−3.68603e7			−1.55548
$892$	3.46183e7	+	1.68538e7i	1.45678	+	0.709228i
$893$	−1.04133e6	+	1.04133e6i	−0.0436979	+	0.0436979i
$894$	−5.23253e6	−	3.11997e7i	−0.218961	−	1.30559i
$895$	−1.51142e7	−	2.74472e7i	−0.630705	−	1.14535i
$896$	7.88343e6	−	1.82556e7i	0.328054	−	0.759671i
$897$	6.80693e6	−	6.80693e6i	0.282468	−	0.282468i
$898$	−1.02801e7	+	1.44231e7i	−0.425410	+	0.596855i
$899$		−	1.53862e7i		−	0.634940i
$900$	−592702.	+	2.51142e6i	−0.0243910	+	0.103350i
$901$		−	5.60755e6i		−	0.230124i
$902$	−4.84051e7	−	3.45009e7i	−1.98096	−	1.41193i
$903$	2.80846e7	−	2.80846e7i	1.14617	−	1.14617i
$904$	−1.80833e7	+	9.84360e6i	−0.735965	+	0.400620i
$905$	1.99494e7	+	3.62278e7i	0.809669	+	1.47035i
$906$	−2.04995e7	+	3.43798e6i	−0.829703	+	0.139150i
$907$	−3.16986e7	+	3.16986e7i	−1.27944	+	1.27944i	−0.338465	+	0.940979i	$0.609908\pi$
$907$	−3.16986e7	+	3.16986e7i	−1.27944	+	1.27944i	−0.940979	+	0.338465i	$0.890092\pi$
$908$	−6.75688e6	−	3.28957e6i	−0.271977	−	0.132411i
$909$	3.02889e6			0.121583
$910$	1.78027e7	+	2.07229e6i	0.712661	+	0.0829557i
$911$		−	6.13974e6i		−	0.245106i	−0.992462	−	0.122553i	$-0.960892\pi$
$911$		−	6.13974e6i		−	0.245106i	0.992462	−	0.122553i	$-0.0391082\pi$
$912$	2.05988e6	−	1.69772e7i	0.0820076	−	0.675896i
$913$	4.08904e7	+	4.08904e7i	1.62347	+	1.62347i
$914$	3.03050e7	−	5.08247e6i	1.19991	−	0.201238i
$915$	−143275.	+	494444.i	−0.00565741	+	0.0195238i
$916$	−7.96677e6	−	2.30835e7i	−0.313721	−	0.908998i
$917$	1.02027e7	+	1.02027e7i	0.400676	+	0.400676i
$918$	−1.98755e6	+	2.78856e6i	−0.0778417	+	0.109213i
$919$	3.41663e7			1.33447			0.667235	−	0.744848i	$-0.267478\pi$
$919$	3.41663e7			1.33447			0.667235	+	0.744848i	$0.267478\pi$
$920$	−9.47422e6	−	6.05867e6i	−0.369040	−	0.235998i
$921$	2.14082e7			0.831630
$922$	1.79253e7	−	2.51494e7i	0.694447	−	0.974317i
$923$	−2.38210e7	−	2.38210e7i	−0.920357	−	0.920357i
$924$	−3.03319e7	+	1.04684e7i	−1.16874	+	0.403367i
$925$	2.71973e7	−	6.11919e6i	1.04513	−	0.235147i
$926$	1.18660e6	−	199006.i	0.0454755	−	0.00762672i
$927$	322586.	+	322586.i	0.0123295	+	0.0123295i
$928$	−3.66743e7	+	1.66699e6i	−1.39795	+	0.0635424i
$929$			2.60571e7i			0.990572i	0.868730	+	0.495286i	$0.164937\pi$
$929$			2.60571e7i			0.990572i	−0.868730	+	0.495286i	$0.835063\pi$
$930$	−9.86957e6	+	7.81145e6i	−0.374189	+	0.296159i
$931$	5.39770e6			0.204096
$932$	−6.60660e6	+	1.35702e7i	−0.249137	+	0.511736i
$933$	−2.14731e7	+	2.14731e7i	−0.807590	+	0.807590i
$934$	4.98690e6	−	836355.i	0.187052	−	0.0313707i
$935$	1.50791e6	−	5.20382e6i	0.0564088	−	0.194667i
$936$	−2.16753e6	+	1.17989e6i	−0.0808679	+	0.0440202i
$937$	1.38135e7	−	1.38135e7i	0.513990	−	0.513990i	−0.401756	−	0.915747i	$-0.631600\pi$
$937$	1.38135e7	−	1.38135e7i	0.513990	−	0.513990i	0.915747	+	0.401756i	$0.131600\pi$
$938$	−1.70454e7	−	1.21492e7i	−0.632558	−	0.450858i
$939$			5.29906e6i			0.196126i
$940$	−129985.	−	2.58290e6i	−0.00479816	−	0.0953428i
$941$		−	5.20322e7i		−	1.91557i	−0.287485	−	0.957785i	$-0.592819\pi$
$941$		−	5.20322e7i		−	1.91557i	0.287485	−	0.957785i	$-0.407181\pi$
$942$	−2.26922e6	+	3.18373e6i	−0.0833199	+	0.116899i
$943$	1.44837e7	−	1.44837e7i	0.530395	−	0.530395i
$944$	−1.61581e7	−	2.06205e7i	−0.590146	−	0.753128i
$945$	1.87062e7	−	1.03008e7i	0.681406	−	0.375226i
$946$	1.20460e7	+	7.18260e7i	0.437637	+	2.60948i
$947$	1.15837e7	−	1.15837e7i	0.419730	−	0.419730i	−0.465380	−	0.885111i	$-0.654082\pi$
$947$	1.15837e7	−	1.15837e7i	0.419730	−	0.419730i	0.885111	+	0.465380i	$0.154082\pi$
$948$	−6.46707e6	+	1.32836e7i	−0.233715	+	0.480059i
$949$	5.42067e6			0.195383
$950$	−6.80401e6	−	1.66723e7i	−0.244600	−	0.599359i
$951$			5.02374e7i			1.80126i
$952$	−934177.	+	3.16621e6i	−0.0334070	+	0.113226i
$953$	1.61748e6	+	1.61748e6i	0.0576908	+	0.0576908i	0.735364	−	0.677673i	$-0.237011\pi$
$953$	1.61748e6	+	1.61748e6i	0.0576908	+	0.0576908i	−0.677673	+	0.735364i	$0.737011\pi$
$954$	−796408.	−	4.74871e6i	−0.0283312	−	0.168929i
$955$	−1.68444e7	−	3.05892e7i	−0.597649	−	1.08532i
$956$	3.90537e6	+	1.13157e7i	0.138203	+	0.400439i
$957$	4.18895e7	+	4.18895e7i	1.47851	+	1.47851i
$958$	−3.03474e7	−	2.16302e7i	−1.06834	−	0.761460i
$959$	−1.51482e7			−0.531880
$960$	1.96885e7	+	2.26786e7i	0.689501	+	0.794215i
$961$	2.27354e7			0.794134
$962$	2.17109e7	+	1.54745e7i	0.756380	+	0.539112i
$963$	−973405.	−	973405.i	−0.0338242	−	0.0338242i
$964$	−3.29740e6	−	9.55413e6i	−0.114282	−	0.331130i
$965$	3.98322e7	+	1.15422e7i	1.37694	+	0.398997i
$966$	−1.82883e6	−	1.09047e7i	−0.0630565	−	0.375984i
$967$	8.43066e6	+	8.43066e6i	0.289932	+	0.289932i	0.837053	−	0.547122i	$-0.184276\pi$
$967$	8.43066e6	+	8.43066e6i	0.289932	+	0.289932i	−0.547122	+	0.837053i	$0.684276\pi$
$968$	8.40036e6	−	2.84714e7i	0.288144	−	0.976607i
$969$			2.83908e6i			0.0971335i
$970$	−2.55583e7	+	2.02286e7i	−0.872173	+	0.690297i
$971$	−3.67122e7			−1.24957			−0.624787	−	0.780795i	$-0.714814\pi$
$971$	−3.67122e7			−1.24957			−0.624787	+	0.780795i	$0.714814\pi$
$972$	−2.72711e6	+	5.60158e6i	−0.0925843	+	0.190171i
$973$	6.64259e6	−	6.64259e6i	0.224934	−	0.224934i
$974$	−8.86433e6	−	5.28549e7i	−0.299398	−	1.78521i
$975$	−1.44725e7	+	2.28755e7i	−0.487564	+	0.770653i
$976$	354747.	+	452718.i	0.0119205	+	0.0152126i
$977$	1.13558e7	−	1.13558e7i	0.380612	−	0.380612i	−0.490711	−	0.871323i	$-0.663263\pi$
$977$	1.13558e7	−	1.13558e7i	0.380612	−	0.380612i	0.871323	+	0.490711i	$0.163263\pi$
$978$	9.55661e6	−	1.34080e7i	0.319490	−	0.448247i
$979$			1.47916e7i			0.493239i
$980$	−6.35729e6	+	7.03106e6i	−0.211450	+	0.233860i
$981$		−	5.40641e6i		−	0.179364i
$982$	1.46018e7	+	1.04075e7i	0.483202	+	0.344404i
$983$	3.63764e7	−	3.63764e7i	1.20070	−	1.20070i	0.226750	−	0.973953i	$-0.427190\pi$
$983$	3.63764e7	−	3.63764e7i	1.20070	−	1.20070i	0.973953	−	0.226750i	$-0.0728100\pi$
$984$	−4.80441e7	+	2.61527e7i	−1.58180	+	0.861050i
$985$	1.58938e7	+	4.60555e6i	0.521960	+	0.151249i
$986$	6.01070e6	−	1.00806e6i	0.196894	−	0.0330212i
$987$	1.79799e6	−	1.79799e6i	0.0587480	−	0.0587480i
$988$	7.53848e6	−	1.54843e7i	0.245692	−	0.504660i
$989$	−2.50960e7			−0.815856
$990$	537893.	−	4.62097e6i	0.0174425	−	0.149846i
$991$			6.12387e6i			0.198081i	0.995083	+	0.0990403i	$0.0315773\pi$
$991$			6.12387e6i			0.198081i	−0.995083	+	0.0990403i	$0.968423\pi$
$992$	638551.	+	1.40483e7i	0.0206023	+	0.453257i
$993$	3.03670e6	+	3.03670e6i	0.0977303	+	0.0977303i
$994$	−3.81612e7	+	6.40003e6i	−1.22506	+	0.205455i
$995$	2.13280e7	−	1.17446e7i	0.682957	−	0.376080i
$996$	5.03038e7	−	1.73613e7i	1.60676	−	0.554540i
$997$	−2.69679e7	−	2.69679e7i	−0.859229	−	0.859229i	0.132018	−	0.991247i	$-0.457854\pi$
$997$	−2.69679e7	−	2.69679e7i	−0.859229	−	0.859229i	−0.991247	+	0.132018i	$0.957854\pi$
$998$	−4.16179e6	+	5.83904e6i	−0.132268	+	0.185573i
$999$	3.17664e7			1.00706

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.k.a.3.6	✓	56
4.3	odd	2		160.6.o.a.143.6		56
5.2	odd	4	inner	40.6.k.a.27.21	yes	56
8.3	odd	2	inner	40.6.k.a.3.21	yes	56
8.5	even	2		160.6.o.a.143.5		56
20.7	even	4		160.6.o.a.47.5		56
40.27	even	4	inner	40.6.k.a.27.6	yes	56
40.37	odd	4		160.6.o.a.47.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.6	✓	56	1.1	even	1	trivial
40.6.k.a.3.21	yes	56	8.3	odd	2	inner
40.6.k.a.27.6	yes	56	40.27	even	4	inner
40.6.k.a.27.21	yes	56	5.2	odd	4	inner
160.6.o.a.47.5		56	20.7	even	4
160.6.o.a.47.6		56	40.37	odd	4
160.6.o.a.143.5		56	8.5	even	2
160.6.o.a.143.6		56	4.3	odd	2

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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.60651 - 3.28330i) q^{2} +(11.5932 + 11.5932i) q^{3} +(10.4398 + 30.2491i) q^{4} +(-48.9682 + 26.9650i) q^{5} +(-15.3402 - 91.4681i) q^{6} +(-75.8554 - 75.8554i) q^{7} +(51.2259 - 173.620i) q^{8} +25.8041i q^{9} +O(q^{10})\)	\(q+(-4.60651 - 3.28330i) q^{2} +(11.5932 + 11.5932i) q^{3} +(10.4398 + 30.2491i) q^{4} +(-48.9682 + 26.9650i) q^{5} +(-15.3402 - 91.4681i) q^{6} +(-75.8554 - 75.8554i) q^{7} +(51.2259 - 173.620i) q^{8} +25.8041i q^{9} +(314.107 + 36.5629i) q^{10} -570.121 q^{11} +(-229.653 + 471.715i) q^{12} +(-373.587 + 373.587i) q^{13} +(100.372 + 598.485i) q^{14} +(-880.309 - 255.087i) q^{15} +(-806.020 + 631.592i) q^{16} +(120.205 - 120.205i) q^{17} +(84.7226 - 118.867i) q^{18} +1018.64i q^{19} +(-1326.89 - 1199.74i) q^{20} -1758.81i q^{21} +(2626.27 + 1871.88i) q^{22} +(-785.825 + 785.825i) q^{23} +(2606.68 - 1418.94i) q^{24} +(1670.77 - 2640.86i) q^{25} +(2947.53 - 494.333i) q^{26} +(2517.99 - 2517.99i) q^{27} +(1502.64 - 3086.48i) q^{28} -6337.75 q^{29} +(3217.62 + 4065.38i) q^{30} +2427.71i q^{31} +(5786.64 - 263.026i) q^{32} +(-6609.52 - 6609.52i) q^{33} +(-948.396 + 159.056i) q^{34} +(5759.95 + 1669.06i) q^{35} +(-780.551 + 269.390i) q^{36} +(6307.89 + 6307.89i) q^{37} +(3344.52 - 4692.39i) q^{38} -8662.14 q^{39} +(2173.23 + 9883.17i) q^{40} -18431.2 q^{41} +(-5774.72 + 8101.99i) q^{42} +(15967.9 + 15967.9i) q^{43} +(-5951.97 - 17245.7i) q^{44} +(-695.808 - 1263.58i) q^{45} +(6200.01 - 1039.81i) q^{46} +(1022.27 + 1022.27i) q^{47} +(-16666.5 - 2022.17i) q^{48} -5298.91i q^{49} +(-16367.2 + 6679.48i) q^{50} +2787.12 q^{51} +(-15200.9 - 7400.50i) q^{52} +(23324.9 - 23324.9i) q^{53} +(-19866.5 + 3331.82i) q^{54} +(27917.8 - 15373.3i) q^{55} +(-17055.8 + 9284.26i) q^{56} +(-11809.3 + 11809.3i) q^{57} +(29194.9 + 20808.8i) q^{58} +25583.1i q^{59} +(-1474.11 - 29291.6i) q^{60} -561.671i q^{61} +(7970.91 - 11183.3i) q^{62} +(1957.38 - 1957.38i) q^{63} +(-27519.8 - 17787.7i) q^{64} +(8220.11 - 28367.7i) q^{65} +(8745.74 + 52147.9i) q^{66} +(-24390.4 + 24390.4i) q^{67} +(4891.02 + 2381.18i) q^{68} -18220.4 q^{69} +(-21053.2 - 26600.2i) q^{70} +63763.0i q^{71} +(4480.11 + 1321.84i) q^{72} +(-7254.89 - 7254.89i) q^{73} +(-8346.62 - 49768.0i) q^{74} +(49985.6 - 11246.4i) q^{75} +(-30813.1 + 10634.5i) q^{76} +(43246.8 + 43246.8i) q^{77} +(39902.2 + 28440.4i) q^{78} +28160.2 q^{79} +(22438.5 - 52662.3i) q^{80} +64653.5 q^{81} +(84903.2 + 60515.1i) q^{82} +(-71722.4 - 71722.4i) q^{83} +(53202.6 - 18361.7i) q^{84} +(-2644.90 + 9127.57i) q^{85} +(-21128.8 - 125984. i) q^{86} +(-73474.7 - 73474.7i) q^{87} +(-29204.9 + 98984.4i) q^{88} -25944.6i q^{89} +(-943.472 + 8105.24i) q^{90} +56677.3 q^{91} +(-31974.4 - 15566.6i) q^{92} +(-28144.9 + 28144.9i) q^{93} +(-1352.68 - 8065.54i) q^{94} +(-27467.8 - 49881.2i) q^{95} +(70135.0 + 64036.4i) q^{96} +(-72884.3 + 72884.3i) q^{97} +(-17397.9 + 24409.5i) q^{98} -14711.4i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Introduction

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