LMFDB - Embedded newform 930.2.j.g.497.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.8
Character	$\chi$	$=$	930.497
Dual form			930.2.j.g.683.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.853874 + 1.50695i) q^{3} -1.00000i q^{4} +(-2.20708 - 0.358875i) q^{5} +(-1.66935 - 0.461795i) q^{6} +(-1.72132 - 1.72132i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.54180 + 2.57349i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.853874 + 1.50695i) q^{3} -1.00000i q^{4} +(-2.20708 - 0.358875i) q^{5} +(-1.66935 - 0.461795i) q^{6} +(-1.72132 - 1.72132i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.54180 + 2.57349i) q^{9} +(1.81441 - 1.30688i) q^{10} -0.339931i q^{11} +(1.50695 - 0.853874i) q^{12} +(2.77436 - 2.77436i) q^{13} +2.43431 q^{14} +(-1.34376 - 3.63240i) q^{15} -1.00000 q^{16} +(-0.287410 + 0.287410i) q^{17} +(-0.729516 - 2.90995i) q^{18} -5.47806i q^{19} +(-0.358875 + 2.20708i) q^{20} +(1.12415 - 4.06373i) q^{21} +(0.240367 + 0.240367i) q^{22} +(3.99600 + 3.99600i) q^{23} +(-0.461795 + 1.66935i) q^{24} +(4.74242 + 1.58413i) q^{25} +3.92354i q^{26} +(-5.19463 - 0.125978i) q^{27} +(-1.72132 + 1.72132i) q^{28} +6.27134 q^{29} +(3.51868 + 1.61831i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.512259 - 0.290258i) q^{33} -0.406459i q^{34} +(3.18135 + 4.41683i) q^{35} +(2.57349 + 1.54180i) q^{36} +(0.324010 + 0.324010i) q^{37} +(3.87357 + 3.87357i) q^{38} +(6.54978 + 1.81187i) q^{39} +(-1.30688 - 1.81441i) q^{40} -8.78665i q^{41} +(2.07860 + 3.66839i) q^{42} +(6.31498 - 6.31498i) q^{43} -0.339931 q^{44} +(4.32644 - 5.12659i) q^{45} -5.65120 q^{46} +(2.27627 - 2.27627i) q^{47} +(-0.853874 - 1.50695i) q^{48} -1.07412i q^{49} +(-4.47355 + 2.23325i) q^{50} +(-0.678525 - 0.187701i) q^{51} +(-2.77436 - 2.77436i) q^{52} +(7.53540 + 7.53540i) q^{53} +(3.76223 - 3.58407i) q^{54} +(-0.121993 + 0.750255i) q^{55} -2.43431i q^{56} +(8.25516 - 4.67757i) q^{57} +(-4.43451 + 4.43451i) q^{58} +0.628713 q^{59} +(-3.63240 + 1.34376i) q^{60} -11.4778 q^{61} +(-0.707107 + 0.707107i) q^{62} +(7.08373 - 1.77587i) q^{63} +1.00000i q^{64} +(-7.11889 + 5.12759i) q^{65} +(-0.156978 + 0.567465i) q^{66} +(0.339602 + 0.339602i) q^{67} +(0.287410 + 0.287410i) q^{68} +(-2.60969 + 9.43385i) q^{69} +(-5.37273 - 0.873613i) q^{70} +1.05992i q^{71} +(-2.90995 + 0.729516i) q^{72} +(6.50142 - 6.50142i) q^{73} -0.458220 q^{74} +(1.66222 + 8.49924i) q^{75} -5.47806 q^{76} +(-0.585129 + 0.585129i) q^{77} +(-5.91258 + 3.35021i) q^{78} +3.87570i q^{79} +(2.20708 + 0.358875i) q^{80} +(-4.24571 - 7.93561i) q^{81} +(6.21310 + 6.21310i) q^{82} +(-6.20369 - 6.20369i) q^{83} +(-4.06373 - 1.12415i) q^{84} +(0.737482 - 0.531193i) q^{85} +8.93072i q^{86} +(5.35494 + 9.45060i) q^{87} +(0.240367 - 0.240367i) q^{88} -13.1527 q^{89} +(0.565795 + 6.68430i) q^{90} -9.55112 q^{91} +(3.99600 - 3.99600i) q^{92} +(0.853874 + 1.50695i) q^{93} +3.21914i q^{94} +(-1.96594 + 12.0905i) q^{95} +(1.66935 + 0.461795i) q^{96} +(0.395402 + 0.395402i) q^{97} +(0.759520 + 0.759520i) q^{98} +(0.874809 + 0.524105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 - 8 * q^7	$ 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.853874	+	1.50695i	0.492984	+	0.870038i
$3$	0.853874	+	1.50695i	0.492984	+	0.870038i
$4$		−	1.00000i		−	0.500000i
$5$	−2.20708	−	0.358875i	−0.987037	−	0.160494i
$5$	−2.20708	−	0.358875i	−0.987037	−	0.160494i
$6$	−1.66935	−	0.461795i	−0.681511	−	0.188527i
$7$	−1.72132	−	1.72132i	−0.650597	−	0.650597i	0.302540	−	0.953137i	$-0.402166\pi$
$7$	−1.72132	−	1.72132i	−0.650597	−	0.650597i	−0.953137	+	0.302540i	$0.902166\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.54180	+	2.57349i	−0.513933	+	0.857830i
$10$	1.81441	−	1.30688i	0.573765	−	0.413272i
$11$		−	0.339931i		−	0.102493i	−0.998686	−	0.0512465i	$-0.983681\pi$
$11$		−	0.339931i		−	0.102493i	0.998686	−	0.0512465i	$-0.0163194\pi$
$12$	1.50695	−	0.853874i	0.435019	−	0.246492i
$13$	2.77436	−	2.77436i	0.769469	−	0.769469i	−0.208544	−	0.978013i	$-0.566872\pi$
$13$	2.77436	−	2.77436i	0.769469	−	0.769469i	0.978013	+	0.208544i	$0.0668723\pi$
$14$	2.43431			0.650597
$15$	−1.34376	−	3.63240i	−0.346958	−	0.937881i
$16$	−1.00000			−0.250000
$17$	−0.287410	+	0.287410i	−0.0697072	+	0.0697072i	−0.741101	−	0.671394i	$-0.765696\pi$
$17$	−0.287410	+	0.287410i	−0.0697072	+	0.0697072i	0.671394	+	0.741101i	$0.265696\pi$
$18$	−0.729516	−	2.90995i	−0.171949	−	0.685882i
$19$		−	5.47806i		−	1.25675i	−0.777909	−	0.628376i	$-0.783720\pi$
$19$		−	5.47806i		−	1.25675i	0.777909	−	0.628376i	$-0.216280\pi$
$20$	−0.358875	+	2.20708i	−0.0802468	+	0.493518i
$21$	1.12415	−	4.06373i	0.245310	−	0.886779i
$22$	0.240367	+	0.240367i	0.0512465	+	0.0512465i
$23$	3.99600	+	3.99600i	0.833223	+	0.833223i	0.987956	−	0.154733i	$-0.0494517\pi$
$23$	3.99600	+	3.99600i	0.833223	+	0.833223i	−0.154733	+	0.987956i	$0.549452\pi$
$24$	−0.461795	+	1.66935i	−0.0942635	+	0.340756i
$25$	4.74242	+	1.58413i	0.948484	+	0.316826i
$26$			3.92354i			0.769469i
$27$	−5.19463	−	0.125978i	−0.999706	−	0.0242444i
$28$	−1.72132	+	1.72132i	−0.325299	+	0.325299i
$29$	6.27134			1.16456			0.582280	−	0.812989i	$-0.302161\pi$
$29$	6.27134			1.16456			0.582280	+	0.812989i	$0.302161\pi$
$30$	3.51868	+	1.61831i	0.642419	+	0.295461i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.512259	−	0.290258i	0.0891728	−	0.0505274i
$34$		−	0.406459i		−	0.0697072i
$35$	3.18135	+	4.41683i	0.537747	+	0.746580i
$36$	2.57349	+	1.54180i	0.428915	+	0.256966i
$37$	0.324010	+	0.324010i	0.0532669	+	0.0532669i	0.733238	−	0.679972i	$-0.238008\pi$
$37$	0.324010	+	0.324010i	0.0532669	+	0.0532669i	−0.679972	+	0.733238i	$0.738008\pi$
$38$	3.87357	+	3.87357i	0.628376	+	0.628376i
$39$	6.54978	+	1.81187i	1.04880	+	0.290131i
$40$	−1.30688	−	1.81441i	−0.206636	−	0.286883i
$41$		−	8.78665i		−	1.37224i	−0.727486	−	0.686122i	$-0.759312\pi$
$41$		−	8.78665i		−	1.37224i	0.727486	−	0.686122i	$-0.240688\pi$
$42$	2.07860	+	3.66839i	0.320734	+	0.566045i
$43$	6.31498	−	6.31498i	0.963025	−	0.963025i	−0.0363157	−	0.999340i	$-0.511562\pi$
$43$	6.31498	−	6.31498i	0.963025	−	0.963025i	0.999340	+	0.0363157i	$0.0115622\pi$
$44$	−0.339931			−0.0512465
$45$	4.32644	−	5.12659i	0.644947	−	0.764227i
$46$	−5.65120			−0.833223
$47$	2.27627	−	2.27627i	0.332029	−	0.332029i	−0.521328	−	0.853356i	$-0.674563\pi$
$47$	2.27627	−	2.27627i	0.332029	−	0.332029i	0.853356	+	0.521328i	$0.174563\pi$
$48$	−0.853874	−	1.50695i	−0.123246	−	0.217510i
$49$		−	1.07412i		−	0.153446i
$50$	−4.47355	+	2.23325i	−0.632655	+	0.315829i
$51$	−0.678525	−	0.187701i	−0.0950125	−	0.0262834i
$52$	−2.77436	−	2.77436i	−0.384735	−	0.384735i
$53$	7.53540	+	7.53540i	1.03507	+	1.03507i	0.999362	+	0.0357049i	$0.0113676\pi$
$53$	7.53540	+	7.53540i	1.03507	+	1.03507i	0.0357049	+	0.999362i	$0.488632\pi$
$54$	3.76223	−	3.58407i	0.511975	−	0.487731i
$55$	−0.121993	+	0.750255i	−0.0164495	+	0.101164i
$56$		−	2.43431i		−	0.325299i
$57$	8.25516	−	4.67757i	1.09342	−	0.619559i
$58$	−4.43451	+	4.43451i	−0.582280	+	0.582280i
$59$	0.628713			0.0818514			0.0409257	−	0.999162i	$-0.486969\pi$
$59$	0.628713			0.0818514			0.0409257	+	0.999162i	$0.486969\pi$
$60$	−3.63240	+	1.34376i	−0.468940	+	0.173479i
$61$	−11.4778			−1.46958			−0.734789	−	0.678296i	$-0.762719\pi$
$61$	−11.4778			−1.46958			−0.734789	+	0.678296i	$0.762719\pi$
$62$	−0.707107	+	0.707107i	−0.0898027	+	0.0898027i
$63$	7.08373	−	1.77587i	0.892466	−	0.223739i
$64$			1.00000i			0.125000i
$65$	−7.11889	+	5.12759i	−0.882990	+	0.636000i
$66$	−0.156978	+	0.567465i	−0.0193227	+	0.0698501i
$67$	0.339602	+	0.339602i	0.0414889	+	0.0414889i	0.727547	−	0.686058i	$-0.240660\pi$
$67$	0.339602	+	0.339602i	0.0414889	+	0.0414889i	−0.686058	+	0.727547i	$0.740660\pi$
$68$	0.287410	+	0.287410i	0.0348536	+	0.0348536i
$69$	−2.60969	+	9.43385i	−0.314170	+	1.13570i
$70$	−5.37273	−	0.873613i	−0.642164	−	0.104417i
$71$			1.05992i			0.125789i	0.998020	+	0.0628945i	$0.0200332\pi$
$71$			1.05992i			0.125789i	−0.998020	+	0.0628945i	$0.979967\pi$
$72$	−2.90995	+	0.729516i	−0.342941	+	0.0859743i
$73$	6.50142	−	6.50142i	0.760933	−	0.760933i	−0.215558	−	0.976491i	$-0.569157\pi$
$73$	6.50142	−	6.50142i	0.760933	−	0.760933i	0.976491	+	0.215558i	$0.0691570\pi$
$74$	−0.458220			−0.0532669
$75$	1.66222	+	8.49924i	0.191937	+	0.981407i
$76$	−5.47806			−0.628376
$77$	−0.585129	+	0.585129i	−0.0666817	+	0.0666817i
$78$	−5.91258	+	3.35021i	−0.669468	+	0.379336i
$79$			3.87570i			0.436051i	0.975943	+	0.218025i	$0.0699615\pi$
$79$			3.87570i			0.436051i	−0.975943	+	0.218025i	$0.930038\pi$
$80$	2.20708	+	0.358875i	0.246759	+	0.0401234i
$81$	−4.24571	−	7.93561i	−0.471746	−	0.881735i
$82$	6.21310	+	6.21310i	0.686122	+	0.686122i
$83$	−6.20369	−	6.20369i	−0.680943	−	0.680943i	0.279269	−	0.960213i	$-0.409908\pi$
$83$	−6.20369	−	6.20369i	−0.680943	−	0.680943i	−0.960213	+	0.279269i	$0.909908\pi$
$84$	−4.06373	−	1.12415i	−0.443389	−	0.122655i
$85$	0.737482	−	0.531193i	0.0799911	−	0.0576160i
$86$			8.93072i			0.963025i
$87$	5.35494	+	9.45060i	0.574110	+	1.01321i
$88$	0.240367	−	0.240367i	0.0256233	−	0.0256233i
$89$	−13.1527			−1.39419			−0.697093	−	0.716981i	$-0.745523\pi$
$89$	−13.1527			−1.39419			−0.697093	+	0.716981i	$0.745523\pi$
$90$	0.565795	+	6.68430i	0.0596401	+	0.704587i
$91$	−9.55112			−1.00123
$92$	3.99600	−	3.99600i	0.416612	−	0.416612i
$93$	0.853874	+	1.50695i	0.0885426	+	0.156263i
$94$			3.21914i			0.332029i
$95$	−1.96594	+	12.0905i	−0.201701	+	1.24046i
$96$	1.66935	+	0.461795i	0.170378	+	0.0471317i
$97$	0.395402	+	0.395402i	0.0401470	+	0.0401470i	0.726895	−	0.686748i	$-0.240963\pi$
$97$	0.395402	+	0.395402i	0.0401470	+	0.0401470i	−0.686748	+	0.726895i	$0.740963\pi$
$98$	0.759520	+	0.759520i	0.0767231	+	0.0767231i
$99$	0.874809	+	0.524105i	0.0879216	+	0.0526745i
$100$	1.58413	−	4.74242i	0.158413	−	0.474242i
$101$		−	0.645235i		−	0.0642033i	−0.999485	−	0.0321016i	$-0.989780\pi$
$101$		−	0.645235i		−	0.0642033i	0.999485	−	0.0321016i	$-0.0102200\pi$
$102$	0.612514	−	0.347065i	0.0606479	−	0.0343646i
$103$	8.06425	−	8.06425i	0.794595	−	0.794595i	−0.187643	−	0.982237i	$-0.560085\pi$
$103$	8.06425	−	8.06425i	0.794595	−	0.794595i	0.982237	+	0.187643i	$0.0600847\pi$
$104$	3.92354			0.384735
$105$	−3.93947	+	8.56556i	−0.384453	+	0.835913i
$106$	−10.6567			−1.03507
$107$	10.0184	−	10.0184i	0.968519	−	0.968519i	−0.0310007	−	0.999519i	$-0.509869\pi$
$107$	10.0184	−	10.0184i	0.968519	−	0.968519i	0.999519	+	0.0310007i	$0.00986941\pi$
$108$	−0.125978	+	5.19463i	−0.0121222	+	0.499853i
$109$		−	2.02266i		−	0.193735i	−0.995297	−	0.0968676i	$-0.969118\pi$
$109$		−	2.02266i		−	0.193735i	0.995297	−	0.0968676i	$-0.0308824\pi$
$110$	−0.444249	−	0.616772i	−0.0423575	−	0.0588069i
$111$	−0.211603	+	0.764931i	−0.0200845	+	0.0726040i
$112$	1.72132	+	1.72132i	0.162649	+	0.162649i
$113$	6.79548	+	6.79548i	0.639265	+	0.639265i	0.950374	−	0.311109i	$-0.100700\pi$
$113$	6.79548	+	6.79548i	0.639265	+	0.639265i	−0.311109	+	0.950374i	$0.600700\pi$
$114$	−2.52974	+	9.14482i	−0.236932	+	0.856491i
$115$	−7.38543	−	10.2536i	−0.688695	−	0.956149i
$116$		−	6.27134i		−	0.582280i
$117$	2.86229	+	11.4173i	0.264618	+	1.05553i
$118$	−0.444567	+	0.444567i	−0.0409257	+	0.0409257i
$119$	0.989449			0.0907026
$120$	1.61831	−	3.51868i	0.147731	−	0.321210i
$121$	10.8844			0.989495
$122$	8.11601	−	8.11601i	0.734789	−	0.734789i
$123$	13.2410	−	7.50269i	1.19391	−	0.676495i
$124$		−	1.00000i		−	0.0898027i
$125$	−9.89840	−	5.19824i	−0.885340	−	0.464945i
$126$	−3.75322	+	6.26468i	−0.334363	+	0.558102i
$127$	8.53144	+	8.53144i	0.757043	+	0.757043i	0.975783	−	0.218740i	$-0.0701947\pi$
$127$	8.53144	+	8.53144i	0.757043	+	0.757043i	−0.218740	+	0.975783i	$0.570195\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	14.9085	+	4.12416i	1.31262	+	0.363112i
$130$	1.40806	−	8.65957i	0.123495	−	0.759495i
$131$		−	10.2520i		−	0.895721i	−0.894103	−	0.447860i	$-0.852186\pi$
$131$		−	10.2520i		−	0.895721i	0.894103	−	0.447860i	$-0.147814\pi$
$132$	−0.290258	−	0.512259i	−0.0252637	−	0.0445864i
$133$	−9.42948	+	9.42948i	−0.817640	+	0.817640i
$134$	−0.480269			−0.0414889
$135$	11.4198	+	2.14226i	0.982856	+	0.184377i
$136$	−0.406459			−0.0348536
$137$	−10.3401	+	10.3401i	−0.883417	+	0.883417i	−0.993880	−	0.110463i	$-0.964767\pi$
$137$	−10.3401	+	10.3401i	−0.883417	+	0.883417i	0.110463	+	0.993880i	$0.464767\pi$
$138$	−4.82541	−	8.51607i	−0.410766	−	0.724936i
$139$		−	14.5644i		−	1.23533i	−0.786440	−	0.617667i	$-0.788078\pi$
$139$		−	14.5644i		−	1.23533i	0.786440	−	0.617667i	$-0.211922\pi$
$140$	4.41683	−	3.18135i	0.373290	−	0.268873i
$141$	5.37388	+	1.48658i	0.452563	+	0.125193i
$142$	−0.749475	−	0.749475i	−0.0628945	−	0.0628945i
$143$	−0.943091	−	0.943091i	−0.0788652	−	0.0788652i
$144$	1.54180	−	2.57349i	0.128483	−	0.214458i
$145$	−13.8414	−	2.25063i	−1.14946	−	0.186904i
$146$			9.19439i			0.760933i
$147$	1.61865	−	0.917166i	0.133504	−	0.0756466i
$148$	0.324010	−	0.324010i	0.0266335	−	0.0266335i
$149$	−16.0970			−1.31871			−0.659357	−	0.751830i	$-0.729172\pi$
$149$	−16.0970			−1.31871			−0.659357	+	0.751830i	$0.729172\pi$
$150$	−7.18523	−	4.83450i	−0.586672	−	0.394735i
$151$	−7.93645			−0.645859			−0.322929	−	0.946423i	$-0.604668\pi$
$151$	−7.93645			−0.645859			−0.322929	+	0.946423i	$0.604668\pi$
$152$	3.87357	−	3.87357i	0.314188	−	0.314188i
$153$	−0.296519	−	1.18278i	−0.0239721	−	0.0956218i
$154$		−	0.827498i		−	0.0666817i
$155$	−2.20708	−	0.358875i	−0.177277	−	0.0288255i
$156$	1.81187	−	6.54978i	0.145066	−	0.524402i
$157$	10.2455	+	10.2455i	0.817678	+	0.817678i	0.985771	−	0.168093i	$-0.0537610\pi$
$157$	10.2455	+	10.2455i	0.817678	+	0.817678i	−0.168093	+	0.985771i	$0.553761\pi$
$158$	−2.74053	−	2.74053i	−0.218025	−	0.218025i
$159$	−4.92120	+	17.7898i	−0.390276	+	1.41082i
$160$	−1.81441	+	1.30688i	−0.143441	+	0.103318i
$161$		−	13.7568i		−	1.08419i
$162$	8.61350	+	2.60915i	0.676740	+	0.204994i
$163$	−3.74266	+	3.74266i	−0.293148	+	0.293148i	−0.838322	−	0.545175i	$-0.816463\pi$
$163$	−3.74266	+	3.74266i	−0.293148	+	0.293148i	0.545175	+	0.838322i	$0.316463\pi$
$164$	−8.78665			−0.686122
$165$	−1.23476	+	0.456786i	−0.0961262	+	0.0355608i
$166$	8.77334			0.680943
$167$	4.44965	−	4.44965i	0.344324	−	0.344324i	−0.513666	−	0.857990i	$-0.671713\pi$
$167$	4.44965	−	4.44965i	0.344324	−	0.344324i	0.857990	+	0.513666i	$0.171713\pi$
$168$	3.66839	−	2.07860i	0.283022	−	0.160367i
$169$		−	2.39416i		−	0.184166i
$170$	−0.145868	+	0.897089i	−0.0111876	+	0.0688036i
$171$	14.0977	+	8.44606i	1.07808	+	0.645887i
$172$	−6.31498	−	6.31498i	−0.481512	−	0.481512i
$173$	−9.03997	−	9.03997i	−0.687296	−	0.687296i	0.274337	−	0.961634i	$-0.411542\pi$
$173$	−9.03997	−	9.03997i	−0.687296	−	0.687296i	−0.961634	+	0.274337i	$0.911542\pi$
$174$	−10.4691	−	2.89607i	−0.793660	−	0.219551i
$175$	−5.43642	−	10.8900i	−0.410955	−	0.823207i
$176$			0.339931i			0.0256233i
$177$	0.536841	+	0.947439i	0.0403515	+	0.0712138i
$178$	9.30038	−	9.30038i	0.697093	−	0.697093i
$179$	−21.7538			−1.62595			−0.812977	−	0.582296i	$-0.802154\pi$
$179$	−21.7538			−1.62595			−0.812977	+	0.582296i	$0.802154\pi$
$180$	−5.12659	−	4.32644i	−0.382114	−	0.322474i
$181$	22.0926			1.64213			0.821066	−	0.570833i	$-0.193379\pi$
$181$	22.0926			1.64213			0.821066	+	0.570833i	$0.193379\pi$
$182$	6.75366	−	6.75366i	0.500615	−	0.500615i
$183$	−9.80056	−	17.2964i	−0.724478	−	1.27859i
$184$			5.65120i			0.416612i
$185$	−0.598838	−	0.831396i	−0.0440274	−	0.0611254i
$186$	−1.66935	−	0.461795i	−0.122403	−	0.0338604i
$187$	0.0976996	+	0.0976996i	0.00714450	+	0.00714450i
$188$	−2.27627	−	2.27627i	−0.166014	−	0.166014i
$189$	8.72476	+	9.15845i	0.634633	+	0.666179i
$190$	−7.15916	−	9.93942i	−0.519380	−	0.721081i
$191$		−	13.6016i		−	0.984174i	−0.870546	−	0.492087i	$-0.836234\pi$
$191$		−	13.6016i		−	0.984174i	0.870546	−	0.492087i	$-0.163766\pi$
$192$	−1.50695	+	0.853874i	−0.108755	+	0.0616230i
$193$	18.2354	−	18.2354i	1.31261	−	1.31261i	0.393128	−	0.919484i	$-0.371393\pi$
$193$	18.2354	−	18.2354i	1.31261	−	1.31261i	0.919484	−	0.393128i	$-0.128607\pi$
$194$	−0.559184			−0.0401470
$195$	−13.8057	−	6.34950i	−0.988644	−	0.454697i
$196$	−1.07412			−0.0767231
$197$	−6.55380	+	6.55380i	−0.466939	+	0.466939i	−0.900921	−	0.433983i	$-0.857108\pi$
$197$	−6.55380	+	6.55380i	−0.466939	+	0.466939i	0.433983	+	0.900921i	$0.357108\pi$
$198$	−0.989182	+	0.247985i	−0.0702981	+	0.0176235i
$199$			5.07211i			0.359553i	0.983708	+	0.179776i	$0.0575374\pi$
$199$			5.07211i			0.359553i	−0.983708	+	0.179776i	$0.942463\pi$
$200$	2.23325	+	4.47355i	0.157914	+	0.316327i
$201$	−0.221786	+	0.801740i	−0.0156436	+	0.0565503i
$202$	0.456250	+	0.456250i	0.0321016	+	0.0321016i
$203$	−10.7950	−	10.7950i	−0.757659	−	0.757659i
$204$	−0.187701	+	0.678525i	−0.0131417	+	0.0475062i
$205$	−3.15331	+	19.3929i	−0.220236	+	1.35446i
$206$			11.4046i			0.794595i
$207$	−16.4447	+	4.12264i	−1.14299	+	0.286543i
$208$	−2.77436	+	2.77436i	−0.192367	+	0.192367i
$209$	−1.86216			−0.128808
$210$	−3.27114	−	8.84239i	−0.225730	−	0.610183i
$211$	16.7604			1.15383			0.576916	−	0.816803i	$-0.304256\pi$
$211$	16.7604			1.15383			0.576916	+	0.816803i	$0.304256\pi$
$212$	7.53540	−	7.53540i	0.517534	−	0.517534i
$213$	−1.59724	+	0.905036i	−0.109441	+	0.0620120i
$214$			14.1682i			0.968519i
$215$	−16.2039	+	11.6714i	−1.10510	+	0.795982i
$216$	−3.58407	−	3.76223i	−0.243865	−	0.255988i
$217$	−1.72132	−	1.72132i	−0.116851	−	0.116851i
$218$	1.43023	+	1.43023i	0.0968676	+	0.0968676i
$219$	15.3487	+	4.24592i	1.03717	+	0.286913i
$220$	0.750255	+	0.121993i	0.0505822	+	0.00822474i
$221$			1.59476i			0.107275i
$222$	−0.391262	−	0.690514i	−0.0262598	−	0.0463443i
$223$	1.80926	−	1.80926i	0.121157	−	0.121157i	−0.643928	−	0.765086i	$-0.722697\pi$
$223$	1.80926	−	1.80926i	0.121157	−	0.121157i	0.765086	+	0.643928i	$0.222697\pi$
$224$	−2.43431			−0.162649
$225$	−11.3886	+	9.76216i	−0.759240	+	0.650811i
$226$	−9.61026			−0.639265
$227$	−1.05321	+	1.05321i	−0.0699043	+	0.0699043i	−0.741195	−	0.671290i	$-0.765740\pi$
$227$	−1.05321	+	1.05321i	−0.0699043	+	0.0699043i	0.671290	+	0.741195i	$0.265740\pi$
$228$	−4.67757	−	8.25516i	−0.309780	−	0.546711i
$229$			14.7360i			0.973785i	0.873462	+	0.486892i	$0.161870\pi$
$229$			14.7360i			0.973785i	−0.873462	+	0.486892i	$0.838130\pi$
$230$	12.4727	+	2.02807i	0.822422	+	0.133727i
$231$	−1.38139	−	0.382134i	−0.0908886	−	0.0251426i
$232$	4.43451	+	4.43451i	0.291140	+	0.291140i
$233$	−2.46841	−	2.46841i	−0.161711	−	0.161711i	0.621613	−	0.783324i	$-0.286478\pi$
$233$	−2.46841	−	2.46841i	−0.161711	−	0.161711i	−0.783324	+	0.621613i	$0.786478\pi$
$234$	−10.0972	−	6.04931i	−0.660074	−	0.395456i
$235$	−5.84082	+	4.20702i	−0.381013	+	0.274436i
$236$		−	0.628713i		−	0.0409257i
$237$	−5.84049	+	3.30936i	−0.379381	+	0.214966i
$238$	−0.699646	+	0.699646i	−0.0453513	+	0.0453513i
$239$	12.9412			0.837099			0.418549	−	0.908194i	$-0.362539\pi$
$239$	12.9412			0.837099			0.418549	+	0.908194i	$0.362539\pi$
$240$	1.34376	+	3.63240i	0.0867395	+	0.234470i
$241$	−28.5727			−1.84053			−0.920264	−	0.391297i	$-0.872026\pi$
$241$	−28.5727			−1.84053			−0.920264	+	0.391297i	$0.872026\pi$
$242$	−7.69647	+	7.69647i	−0.494748	+	0.494748i
$243$	8.33327	−	13.1741i	0.534580	−	0.845118i
$244$			11.4778i			0.734789i
$245$	−0.385476	+	2.37068i	−0.0246271	+	0.151457i
$246$	−4.05763	+	14.6680i	−0.258705	+	0.935200i
$247$	−15.1981	−	15.1981i	−0.967033	−	0.967033i
$248$	0.707107	+	0.707107i	0.0449013	+	0.0449013i
$249$	4.05148	−	14.6458i	0.256752	−	0.928141i
$250$	10.6749	−	3.32351i	0.675142	−	0.210197i
$251$			8.53466i			0.538703i	0.963042	+	0.269351i	$0.0868093\pi$
$251$			8.53466i			0.538703i	−0.963042	+	0.269351i	$0.913191\pi$
$252$	−1.77587	−	7.08373i	−0.111869	−	0.446233i
$253$	1.35836	−	1.35836i	0.0853996	−	0.0853996i
$254$	−12.0653			−0.757043
$255$	1.43020	+	0.657776i	0.0895625	+	0.0411916i
$256$	1.00000			0.0625000
$257$	2.86454	−	2.86454i	0.178685	−	0.178685i	−0.612097	−	0.790783i	$-0.709674\pi$
$257$	2.86454	−	2.86454i	0.178685	−	0.178685i	0.790783	+	0.612097i	$0.209674\pi$
$258$	−13.4582	+	7.62571i	−0.837868	+	0.474756i
$259$		−	1.11545i		−	0.0693107i
$260$	5.12759	+	7.11889i	0.318000	+	0.441495i
$261$	−9.66915	+	16.1392i	−0.598505	+	0.998994i
$262$	7.24925	+	7.24925i	0.447860	+	0.447860i
$263$	−19.0136	−	19.0136i	−1.17243	−	1.17243i	−0.981629	−	0.190799i	$-0.938892\pi$
$263$	−19.0136	−	19.0136i	−1.17243	−	1.17243i	−0.190799	−	0.981629i	$-0.561108\pi$
$264$	0.567465	+	0.156978i	0.0349251	+	0.00966135i
$265$	−13.9270	−	19.3355i	−0.855528	−	1.18777i
$266$		−	13.3353i		−	0.817640i
$267$	−11.2308	−	19.8205i	−0.687312	−	1.21299i
$268$	0.339602	−	0.339602i	0.0207445	−	0.0207445i
$269$	3.66288			0.223330			0.111665	−	0.993746i	$-0.464382\pi$
$269$	3.66288			0.223330			0.111665	+	0.993746i	$0.464382\pi$
$270$	−9.58979	+	6.56017i	−0.583616	+	0.399240i
$271$	−28.9175			−1.75661			−0.878306	−	0.478099i	$-0.841326\pi$
$271$	−28.9175			−1.75661			−0.878306	+	0.478099i	$0.841326\pi$
$272$	0.287410	−	0.287410i	0.0174268	−	0.0174268i
$273$	−8.15545	−	14.3931i	−0.493590	−	0.871108i
$274$		−	14.6232i		−	0.883417i
$275$	0.538495	−	1.61209i	0.0324725	−	0.0972129i
$276$	9.43385	+	2.60969i	0.567851	+	0.157085i
$277$	−4.44274	−	4.44274i	−0.266938	−	0.266938i	0.560927	−	0.827865i	$-0.310445\pi$
$277$	−4.44274	−	4.44274i	−0.266938	−	0.266938i	−0.827865	+	0.560927i	$0.810445\pi$
$278$	10.2986	+	10.2986i	0.617667	+	0.617667i
$279$	−1.54180	+	2.57349i	−0.0923051	+	0.154071i
$280$	−0.873613	+	5.37273i	−0.0522084	+	0.321082i
$281$		−	23.3736i		−	1.39435i	−0.716899	−	0.697177i	$-0.754439\pi$
$281$		−	23.3736i		−	1.39435i	0.716899	−	0.697177i	$-0.245561\pi$
$282$	−4.85108	+	2.74874i	−0.288878	+	0.163685i
$283$	4.91267	−	4.91267i	0.292028	−	0.292028i	−0.545853	−	0.837881i	$-0.683794\pi$
$283$	4.91267	−	4.91267i	0.292028	−	0.292028i	0.837881	+	0.545853i	$0.183794\pi$
$284$	1.05992			0.0628945
$285$	−19.8985	+	7.36121i	−1.17868	+	0.436041i
$286$	1.33373			0.0788652
$287$	−15.1246	+	15.1246i	−0.892779	+	0.892779i
$288$	0.729516	+	2.90995i	0.0429872	+	0.171470i
$289$			16.8348i			0.990282i
$290$	11.3788	−	8.19589i	0.668184	−	0.481279i
$291$	−0.258228	+	0.933476i	−0.0151376	+	0.0547213i
$292$	−6.50142	−	6.50142i	−0.380467	−	0.380467i
$293$	20.4203	+	20.4203i	1.19297	+	1.19297i	0.976230	+	0.216737i	$0.0695413\pi$
$293$	20.4203	+	20.4203i	1.19297	+	1.19297i	0.216737	+	0.976230i	$0.430459\pi$
$294$	−0.496025	+	1.79309i	−0.0289288	+	0.104575i
$295$	−1.38762	−	0.225629i	−0.0807904	−	0.0131366i
$296$			0.458220i			0.0266335i
$297$	−0.0428237	+	1.76581i	−0.00248489	+	0.102463i
$298$	11.3823	−	11.3823i	0.659357	−	0.659357i
$299$	22.1727			1.28228
$300$	8.49924	−	1.66222i	0.490704	−	0.0959683i
$301$	−21.7402			−1.25308
$302$	5.61191	−	5.61191i	0.322929	−	0.322929i
$303$	0.972337	−	0.550949i	0.0558593	−	0.0316512i
$304$			5.47806i			0.314188i
$305$	25.3324	+	4.11908i	1.45053	+	0.235858i
$306$	1.04602	+	0.626679i	0.0597970	+	0.0358248i
$307$	−9.27310	−	9.27310i	−0.529244	−	0.529244i	0.391103	−	0.920347i	$-0.372094\pi$
$307$	−9.27310	−	9.27310i	−0.529244	−	0.529244i	−0.920347	+	0.391103i	$0.872094\pi$
$308$	0.585129	+	0.585129i	0.0333408	+	0.0333408i
$309$	19.0383	+	5.26658i	1.08305	+	0.299605i
$310$	1.81441	−	1.30688i	0.103051	−	0.0742258i
$311$		−	5.57480i		−	0.316118i	−0.987430	−	0.158059i	$-0.949476\pi$
$311$		−	5.57480i		−	0.316118i	0.987430	−	0.158059i	$-0.0505236\pi$
$312$	3.35021	+	5.91258i	0.189668	+	0.334734i
$313$	−15.7491	+	15.7491i	−0.890190	+	0.890190i	−0.994541	−	0.104350i	$-0.966724\pi$
$313$	−15.7491	+	15.7491i	−0.890190	+	0.890190i	0.104350	+	0.994541i	$0.466724\pi$
$314$	−14.4893			−0.817678
$315$	−16.2717	+	1.37732i	−0.916805	+	0.0776033i
$316$	3.87570			0.218025
$317$	−2.62308	+	2.62308i	−0.147327	+	0.147327i	−0.776923	−	0.629596i	$-0.783220\pi$
$317$	−2.62308	+	2.62308i	−0.147327	+	0.147327i	0.629596	+	0.776923i	$0.283220\pi$
$318$	−9.09945	−	16.0591i	−0.510272	−	0.900548i
$319$		−	2.13182i		−	0.119359i
$320$	0.358875	−	2.20708i	0.0200617	−	0.123380i
$321$	23.6518	+	6.54280i	1.32011	+	0.365184i
$322$	9.72751	+	9.72751i	0.542093	+	0.542093i
$323$	1.57445	+	1.57445i	0.0876047	+	0.0876047i
$324$	−7.93561	+	4.24571i	−0.440867	+	0.235873i
$325$	17.5521	−	8.76223i	0.973617	−	0.486041i
$326$		−	5.29292i		−	0.293148i
$327$	3.04804	−	1.72709i	0.168557	−	0.0955085i
$328$	6.21310	−	6.21310i	0.343061	−	0.343061i
$329$	−7.83638			−0.432034
$330$	0.550113	−	1.19611i	0.0302827	−	0.0658435i
$331$	9.40872			0.517150			0.258575	−	0.965991i	$-0.416747\pi$
$331$	9.40872			0.517150			0.258575	+	0.965991i	$0.416747\pi$
$332$	−6.20369	+	6.20369i	−0.340472	+	0.340472i
$333$	−1.33340	+	0.334279i	−0.0730696	+	0.0183184i
$334$			6.29275i			0.344324i
$335$	−0.627654	−	0.871403i	−0.0342924	−	0.0476098i
$336$	−1.12415	+	4.06373i	−0.0613276	+	0.221695i
$337$	−3.73170	−	3.73170i	−0.203278	−	0.203278i	0.598125	−	0.801403i	$-0.295913\pi$
$337$	−3.73170	−	3.73170i	−0.203278	−	0.203278i	−0.801403	+	0.598125i	$0.795913\pi$
$338$	1.69293	+	1.69293i	0.0920831	+	0.0920831i
$339$	−4.43797	+	16.0429i	−0.241037	+	0.871333i
$340$	−0.531193	−	0.737482i	−0.0288080	−	0.0399956i
$341$		−	0.339931i		−	0.0184083i
$342$	−15.9409	+	3.99633i	−0.861984	+	0.216097i
$343$	−13.8981	+	13.8981i	−0.750429	+	0.750429i
$344$	8.93072			0.481512
$345$	9.14538	−	19.8847i	0.492371	−	1.07056i
$346$	12.7845			0.687296
$347$	8.71885	−	8.71885i	0.468052	−	0.468052i	−0.433231	−	0.901283i	$-0.642627\pi$
$347$	8.71885	−	8.71885i	0.468052	−	0.468052i	0.901283	+	0.433231i	$0.142627\pi$
$348$	9.45060	−	5.35494i	0.506606	−	0.287055i
$349$		−	10.4115i		−	0.557316i	−0.960390	−	0.278658i	$-0.910110\pi$
$349$		−	10.4115i		−	0.557316i	0.960390	−	0.278658i	$-0.0898897\pi$
$350$	11.5445	+	3.85627i	0.617081	+	0.206126i
$351$	−14.7613	+	14.0623i	−0.787899	+	0.750588i
$352$	−0.240367	−	0.240367i	−0.0128116	−	0.0128116i
$353$	17.0031	+	17.0031i	0.904985	+	0.904985i	0.995862	−	0.0908769i	$-0.0289670\pi$
$353$	17.0031	+	17.0031i	0.904985	+	0.904985i	−0.0908769	+	0.995862i	$0.528967\pi$
$354$	−1.04954	−	0.290336i	−0.0557827	−	0.0154312i
$355$	0.380378	−	2.33932i	0.0201883	−	0.124158i
$356$			13.1527i			0.697093i
$357$	0.844865	+	1.49105i	0.0447150	+	0.0789148i
$358$	15.3822	−	15.3822i	0.812977	−	0.812977i
$359$	−15.0677			−0.795241			−0.397620	−	0.917550i	$-0.630164\pi$
$359$	−15.0677			−0.795241			−0.397620	+	0.917550i	$0.630164\pi$
$360$	6.68430	−	0.565795i	0.352294	−	0.0298200i
$361$	−11.0091			−0.579428
$362$	−15.6219	+	15.6219i	−0.821066	+	0.821066i
$363$	9.29394	+	16.4023i	0.487806	+	0.860899i
$364$			9.55112i			0.500615i
$365$	−16.6823	+	12.0160i	−0.873194	+	0.628944i
$366$	19.1605	+	5.30037i	1.00153	+	0.277055i
$367$	8.60055	+	8.60055i	0.448945	+	0.448945i	0.895004	−	0.446059i	$-0.147173\pi$
$367$	8.60055	+	8.60055i	0.448945	+	0.448945i	−0.446059	+	0.895004i	$0.647173\pi$
$368$	−3.99600	−	3.99600i	−0.208306	−	0.208306i
$369$	22.6124	+	13.5473i	1.17715	+	0.705242i
$370$	1.01133	+	0.164443i	0.0525764	+	0.00854900i
$371$		−	25.9417i		−	1.34682i
$372$	1.50695	−	0.853874i	0.0781317	−	0.0442713i
$373$	−4.74466	+	4.74466i	−0.245669	+	0.245669i	−0.819191	−	0.573521i	$-0.805577\pi$
$373$	−4.74466	+	4.74466i	−0.245669	+	0.245669i	0.573521	+	0.819191i	$0.305577\pi$
$374$	−0.138168			−0.00714450
$375$	−0.618493	−	19.3550i	−0.0319389	−	0.999490i
$376$	3.21914			0.166014
$377$	17.3990	−	17.3990i	0.896093	−	0.896093i
$378$	−12.6453	−	0.306669i	−0.650406	−	0.0157734i
$379$		−	21.3833i		−	1.09839i	−0.835695	−	0.549194i	$-0.814935\pi$
$379$		−	21.3833i		−	1.09839i	0.835695	−	0.549194i	$-0.185065\pi$
$380$	12.0905	+	1.96594i	0.620231	+	0.100850i
$381$	−5.57168	+	20.1412i	−0.285446	+	1.03187i
$382$	9.61775	+	9.61775i	0.492087	+	0.492087i
$383$	−4.44916	−	4.44916i	−0.227342	−	0.227342i	0.584240	−	0.811581i	$-0.301393\pi$
$383$	−4.44916	−	4.44916i	−0.227342	−	0.227342i	−0.811581	+	0.584240i	$0.801393\pi$
$384$	0.461795	−	1.66935i	0.0235659	−	0.0851889i
$385$	1.50142	−	1.08144i	0.0765193	−	0.0551153i
$386$			25.7887i			1.31261i
$387$	6.51511	+	25.9880i	0.331182	+	1.32104i
$388$	0.395402	−	0.395402i	0.0200735	−	0.0200735i
$389$	23.8313			1.20829			0.604147	−	0.796873i	$-0.293514\pi$
$389$	23.8313			1.20829			0.604147	+	0.796873i	$0.293514\pi$
$390$	14.2518	−	5.27231i	0.721670	−	0.266974i
$391$	−2.29698			−0.116163
$392$	0.759520	−	0.759520i	0.0383616	−	0.0383616i
$393$	15.4492	−	8.75391i	0.779311	−	0.441576i
$394$		−	9.26847i		−	0.466939i
$395$	1.39089	−	8.55399i	0.0699833	−	0.430398i
$396$	0.524105	−	0.874809i	0.0263373	−	0.0439608i
$397$	16.3146	+	16.3146i	0.818808	+	0.818808i	0.985935	−	0.167127i	$-0.0534490\pi$
$397$	16.3146	+	16.3146i	0.818808	+	0.818808i	−0.167127	+	0.985935i	$0.553449\pi$
$398$	−3.58653	−	3.58653i	−0.179776	−	0.179776i
$399$	−22.2614	−	6.15817i	−1.11446	−	0.308294i
$400$	−4.74242	−	1.58413i	−0.237121	−	0.0792066i
$401$			39.7685i			1.98594i	0.118351	+	0.992972i	$0.462239\pi$
$401$			39.7685i			1.98594i	−0.118351	+	0.992972i	$0.537761\pi$
$402$	−0.410089	−	0.723742i	−0.0204534	−	0.0360970i
$403$	2.77436	−	2.77436i	0.138201	−	0.138201i
$404$	−0.645235			−0.0321016
$405$	6.52274	+	19.0382i	0.324118	+	0.946017i
$406$	15.2664			0.757659
$407$	0.110141	−	0.110141i	0.00545949	−	0.00545949i
$408$	−0.347065	−	0.612514i	−0.0171823	−	0.0303240i
$409$		−	4.30094i		−	0.212668i	−0.994330	−	0.106334i	$-0.966089\pi$
$409$		−	4.30094i		−	0.212668i	0.994330	−	0.106334i	$-0.0339113\pi$
$410$	−11.4831	−	15.9425i	−0.567110	−	0.787346i
$411$	−24.4112	−	6.75290i	−1.20412	−	0.333096i
$412$	−8.06425	−	8.06425i	−0.397297	−	0.397297i
$413$	−1.08221	−	1.08221i	−0.0532523	−	0.0532523i
$414$	8.71301	−	14.5433i	0.428221	−	0.714764i
$415$	11.4657	+	15.9184i	0.562829	+	0.781403i
$416$		−	3.92354i		−	0.192367i
$417$	21.9478	−	12.4361i	1.07479	−	0.609000i
$418$	1.31675	−	1.31675i	0.0644042	−	0.0644042i
$419$	−2.31109			−0.112904			−0.0564520	−	0.998405i	$-0.517979\pi$
$419$	−2.31109			−0.112904			−0.0564520	+	0.998405i	$0.517979\pi$
$420$	8.56556	+	3.93947i	0.417956	+	0.192226i
$421$	37.7374			1.83921			0.919604	−	0.392848i	$-0.128510\pi$
$421$	37.7374			1.83921			0.919604	+	0.392848i	$0.128510\pi$
$422$	−11.8514	+	11.8514i	−0.576916	+	0.576916i
$423$	2.34841	+	9.36753i	0.114184	+	0.455465i
$424$			10.6567i			0.517534i
$425$	−1.81831	+	0.907724i	−0.0882012	+	0.0440311i
$426$	0.489465	−	1.76938i	0.0237146	−	0.0857267i
$427$	19.7569	+	19.7569i	0.956103	+	0.956103i
$428$	−10.0184	−	10.0184i	−0.484259	−	0.484259i
$429$	0.615911	−	2.22647i	0.0297364	−	0.107495i
$430$	3.20501	−	19.7108i	0.154559	−	0.950541i
$431$		−	29.4393i		−	1.41804i	−0.705189	−	0.709019i	$-0.749138\pi$
$431$		−	29.4393i		−	1.41804i	0.705189	−	0.709019i	$-0.250862\pi$
$432$	5.19463	+	0.125978i	0.249927	+	0.00606111i
$433$	−19.4601	+	19.4601i	−0.935195	+	0.935195i	−0.998024	−	0.0628292i	$-0.979988\pi$
$433$	−19.4601	+	19.4601i	−0.935195	+	0.935195i	0.0628292	+	0.998024i	$0.479988\pi$
$434$	2.43431			0.116851
$435$	−8.42720	−	22.7800i	−0.404053	−	1.09222i
$436$	−2.02266			−0.0968676
$437$	21.8903	−	21.8903i	1.04716	−	1.04716i
$438$	−13.8555	+	7.85085i	−0.662041	+	0.375128i
$439$			38.7272i			1.84835i	0.381972	+	0.924174i	$0.375245\pi$
$439$			38.7272i			1.84835i	−0.381972	+	0.924174i	$0.624755\pi$
$440$	−0.616772	+	0.444249i	−0.0294035	+	0.0211787i
$441$	2.76425	+	1.65608i	0.131631	+	0.0788611i
$442$	−1.12767	−	1.12767i	−0.0536376	−	0.0536376i
$443$	3.55781	+	3.55781i	0.169036	+	0.169036i	0.786556	−	0.617519i	$-0.211862\pi$
$443$	3.55781	+	3.55781i	0.169036	+	0.169036i	−0.617519	+	0.786556i	$0.711862\pi$
$444$	0.764931	+	0.211603i	0.0363020	+	0.0100423i
$445$	29.0291	+	4.72018i	1.37611	+	0.223758i
$446$			2.55868i			0.121157i
$447$	−13.7448	−	24.2573i	−0.650106	−	1.14733i
$448$	1.72132	−	1.72132i	0.0813247	−	0.0813247i
$449$	2.93691			0.138601			0.0693007	−	0.997596i	$-0.477923\pi$
$449$	2.93691			0.138601			0.0693007	+	0.997596i	$0.477923\pi$
$450$	1.15007	−	14.9558i	0.0542148	−	0.705025i
$451$	−2.98685			−0.140645
$452$	6.79548	−	6.79548i	0.319632	−	0.319632i
$453$	−6.77672	−	11.9598i	−0.318398	−	0.561922i
$454$		−	1.48947i		−	0.0699043i
$455$	21.0801	+	3.42765i	0.988250	+	0.160691i
$456$	9.14482	+	2.52974i	0.428246	+	0.118466i
$457$	27.5939	+	27.5939i	1.29079	+	1.29079i	0.934299	+	0.356492i	$0.116027\pi$
$457$	27.5939	+	27.5939i	1.29079	+	1.29079i	0.356492	+	0.934299i	$0.383973\pi$
$458$	−10.4200	−	10.4200i	−0.486892	−	0.486892i
$459$	1.52920	−	1.45678i	0.0713767	−	0.0679967i
$460$	−10.2536	+	7.38543i	−0.478075	+	0.344348i
$461$			32.5644i			1.51667i	0.651863	+	0.758337i	$0.273988\pi$
$461$			32.5644i			1.51667i	−0.651863	+	0.758337i	$0.726012\pi$
$462$	1.24700	−	0.706579i	0.0580156	−	0.0328730i
$463$	2.46255	−	2.46255i	0.114445	−	0.114445i	−0.647565	−	0.762010i	$-0.724213\pi$
$463$	2.46255	−	2.46255i	0.114445	−	0.114445i	0.762010	+	0.647565i	$0.224213\pi$
$464$	−6.27134			−0.291140
$465$	−1.34376	−	3.63240i	−0.0623155	−	0.168448i
$466$	3.49086			0.161711
$467$	9.31980	−	9.31980i	0.431269	−	0.431269i	−0.457791	−	0.889060i	$-0.651359\pi$
$467$	9.31980	−	9.31980i	0.431269	−	0.431269i	0.889060	+	0.457791i	$0.151359\pi$
$468$	11.4173	−	2.86229i	0.527765	−	0.132309i
$469$		−	1.16912i		−	0.0539852i
$470$	1.15527	−	7.10490i	0.0532885	−	0.327725i
$471$	−6.69108	+	24.1878i	−0.308309	+	1.11451i
$472$	0.444567	+	0.444567i	0.0204629	+	0.0204629i
$473$	−2.14665	−	2.14665i	−0.0987033	−	0.0987033i
$474$	1.78978	−	6.46992i	0.0822073	−	0.297173i
$475$	8.67796	−	25.9792i	0.398172	−	1.19201i
$476$		−	0.989449i		−	0.0453513i
$477$	−31.0104	+	7.77422i	−1.41987	+	0.355957i
$478$	−9.15083	+	9.15083i	−0.418549	+	0.418549i
$479$	3.84425			0.175648			0.0878242	−	0.996136i	$-0.472009\pi$
$479$	3.84425			0.175648			0.0878242	+	0.996136i	$0.472009\pi$
$480$	−3.51868	−	1.61831i	−0.160605	−	0.0738653i
$481$	1.79784			0.0819746
$482$	20.2039	−	20.2039i	0.920264	−	0.920264i
$483$	20.7308	−	11.7466i	0.943283	−	0.534487i
$484$		−	10.8844i		−	0.494748i
$485$	−0.730786	−	1.01459i	−0.0331833	−	0.0460700i
$486$	3.42298	+	15.2080i	0.155269	+	0.689849i
$487$	−22.8502	−	22.8502i	−1.03544	−	1.03544i	−0.999348	−	0.0360931i	$-0.988509\pi$
$487$	−22.8502	−	22.8502i	−1.03544	−	1.03544i	−0.0360931	−	0.999348i	$-0.511491\pi$
$488$	−8.11601	−	8.11601i	−0.367394	−	0.367394i
$489$	−8.83576	−	2.44424i	−0.399567	−	0.110533i
$490$	−1.40375	−	1.94890i	−0.0634150	−	0.0880421i
$491$			22.9542i			1.03591i	0.855408	+	0.517955i	$0.173307\pi$
$491$			22.9542i			1.03591i	−0.855408	+	0.517955i	$0.826693\pi$
$492$	−7.50269	−	13.2410i	−0.338247	−	0.596953i
$493$	−1.80245	+	1.80245i	−0.0811782	+	0.0811782i
$494$	21.4934			0.967033
$495$	−1.74269	−	1.47069i	−0.0783279	−	0.0661026i
$496$	−1.00000			−0.0449013
$497$	1.82446	−	1.82446i	0.0818380	−	0.0818380i
$498$	7.49133	+	13.2210i	0.335694	+	0.592447i
$499$			4.02401i			0.180139i	0.995935	+	0.0900697i	$0.0287090\pi$
$499$			4.02401i			0.180139i	−0.995935	+	0.0900697i	$0.971291\pi$
$500$	−5.19824	+	9.89840i	−0.232472	+	0.442670i
$501$	10.5048	+	2.90596i	0.469322	+	0.129829i
$502$	−6.03491	−	6.03491i	−0.269351	−	0.269351i
$503$	17.6851	+	17.6851i	0.788539	+	0.788539i	0.981255	−	0.192716i	$-0.0617295\pi$
$503$	17.6851	+	17.6851i	0.788539	+	0.788539i	−0.192716	+	0.981255i	$0.561730\pi$
$504$	6.26468	+	3.75322i	0.279051	+	0.167182i
$505$	−0.231558	+	1.42409i	−0.0103042	+	0.0633710i
$506$			1.92102i			0.0853996i
$507$	3.60788	−	2.04431i	0.160232	−	0.0907910i
$508$	8.53144	−	8.53144i	0.378521	−	0.378521i
$509$	27.9548			1.23907			0.619536	−	0.784968i	$-0.287321\pi$
$509$	27.9548			1.23907			0.619536	+	0.784968i	$0.287321\pi$
$510$	−1.47642	+	0.546185i	−0.0653770	+	0.0241855i
$511$	−22.3820			−0.990122
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.690114	+	28.4565i	−0.0304693	+	1.25638i
$514$			4.05108i			0.178685i
$515$	−20.6925	+	14.9044i	−0.911822	+	0.656767i
$516$	4.12416	−	14.9085i	0.181556	−	0.656312i
$517$	−0.773776	−	0.773776i	−0.0340306	−	0.0340306i
$518$	0.788742	+	0.788742i	0.0346553	+	0.0346553i
$519$	5.90379	−	21.3418i	0.259148	−	0.936800i
$520$	−8.65957	−	1.40806i	−0.379747	−	0.0617475i
$521$		−	45.3925i		−	1.98868i	−0.106230	−	0.994342i	$-0.533878\pi$
$521$		−	45.3925i		−	1.98868i	0.106230	−	0.994342i	$-0.466122\pi$
$522$	−4.57505	−	18.2493i	−0.200244	−	0.798750i
$523$	−29.5729	+	29.5729i	−1.29313	+	1.29313i	−0.360293	+	0.932839i	$0.617323\pi$
$523$	−29.5729	+	29.5729i	−1.29313	+	1.29313i	−0.932839	+	0.360293i	$0.882677\pi$
$524$	−10.2520			−0.447860
$525$	11.7687	−	17.4911i	0.513628	−	0.763374i
$526$	26.8893			1.17243
$527$	−0.287410	+	0.287410i	−0.0125198	+	0.0125198i
$528$	−0.512259	+	0.290258i	−0.0222932	+	0.0126319i
$529$			8.93602i			0.388523i
$530$	23.5201	+	3.82441i	1.02165	+	0.166122i
$531$	−0.969348	+	1.61799i	−0.0420661	+	0.0702146i
$532$	9.42948	+	9.42948i	0.408820	+	0.408820i
$533$	−24.3773	−	24.3773i	−1.05590	−	1.05590i
$534$	21.9566	+	6.07386i	0.950153	+	0.262842i
$535$	−25.7069	+	18.5161i	−1.11140	+	0.800523i
$536$			0.480269i			0.0207445i
$537$	−18.5750	−	32.7819i	−0.801570	−	1.41464i
$538$	−2.59005	+	2.59005i	−0.111665	+	0.111665i
$539$	−0.365128			−0.0157272
$540$	2.14226	−	11.4198i	0.0921883	−	0.491428i
$541$	37.5056			1.61249			0.806246	−	0.591580i	$-0.201496\pi$
$541$	37.5056			1.61249			0.806246	+	0.591580i	$0.201496\pi$
$542$	20.4477	−	20.4477i	0.878306	−	0.878306i
$543$	18.8643	+	33.2925i	0.809546	+	1.42872i
$544$			0.406459i			0.0174268i
$545$	−0.725880	+	4.46417i	−0.0310933	+	0.191224i
$546$	15.9442	+	4.41066i	0.682349	+	0.188759i
$547$	9.77768	+	9.77768i	0.418063	+	0.418063i	0.884536	−	0.466472i	$-0.154475\pi$
$547$	9.77768	+	9.77768i	0.418063	+	0.418063i	−0.466472	+	0.884536i	$0.654475\pi$
$548$	10.3401	+	10.3401i	0.441708	+	0.441708i
$549$	17.6964	−	29.5379i	0.755264	−	1.26065i
$550$	0.759149	+	1.52070i	0.0323702	+	0.0648427i
$551$		−	34.3548i		−	1.46356i
$552$	−8.51607	+	4.82541i	−0.362468	+	0.205383i
$553$	6.67132	−	6.67132i	0.283693	−	0.283693i
$554$	6.28298			0.266938
$555$	0.741540	−	1.61233i	0.0314766	−	0.0684394i
$556$	−14.5644			−0.617667
$557$	−15.5465	+	15.5465i	−0.658728	+	0.658728i	−0.955079	−	0.296351i	$-0.904230\pi$
$557$	−15.5465	+	15.5465i	−0.658728	+	0.658728i	0.296351	+	0.955079i	$0.404230\pi$
$558$	−0.729516	−	2.90995i	−0.0308829	−	0.123188i
$559$		−	35.0400i		−	1.48204i
$560$	−3.18135	−	4.41683i	−0.134437	−	0.186645i
$561$	−0.0638053	+	0.230652i	−0.00269386	+	0.00973812i
$562$	16.5277	+	16.5277i	0.697177	+	0.697177i
$563$	15.8739	+	15.8739i	0.669004	+	0.669004i	0.957486	−	0.288481i	$-0.0931503\pi$
$563$	15.8739	+	15.8739i	0.669004	+	0.669004i	−0.288481	+	0.957486i	$0.593150\pi$
$564$	1.48658	−	5.37388i	0.0625964	−	0.226281i
$565$	−12.5595	−	17.4369i	−0.528380	−	0.733576i
$566$			6.94756i			0.292028i
$567$	−6.35149	+	20.9679i	−0.266738	+	0.880571i
$568$	−0.749475	+	0.749475i	−0.0314473	+	0.0314473i
$569$	−24.5152			−1.02773			−0.513866	−	0.857871i	$-0.671787\pi$
$569$	−24.5152			−1.02773			−0.513866	+	0.857871i	$0.671787\pi$
$570$	8.86519	−	19.2755i	0.371322	−	0.807362i
$571$	16.5492			0.692561			0.346281	−	0.938131i	$-0.387445\pi$
$571$	16.5492			0.692561			0.346281	+	0.938131i	$0.387445\pi$
$572$	−0.943091	+	0.943091i	−0.0394326	+	0.0394326i
$573$	20.4969	−	11.6140i	0.856269	−	0.485182i
$574$		−	21.3895i		−	0.892779i
$575$	12.6205	+	25.2809i	0.526312	+	1.05429i
$576$	−2.57349	−	1.54180i	−0.107229	−	0.0642416i
$577$	6.13326	+	6.13326i	0.255331	+	0.255331i	0.823152	−	0.567821i	$-0.192213\pi$
$577$	6.13326	+	6.13326i	0.255331	+	0.255331i	−0.567821	+	0.823152i	$0.692213\pi$
$578$	−11.9040	−	11.9040i	−0.495141	−	0.495141i
$579$	43.0505	+	11.9091i	1.78912	+	0.494925i
$580$	−2.25063	+	13.8414i	−0.0934522	+	0.574732i
$581$			21.3570i			0.886040i
$582$	−0.477472	−	0.842662i	−0.0197919	−	0.0349295i
$583$	2.56152	−	2.56152i	0.106087	−	0.106087i
$584$	9.19439			0.380467
$585$	−2.21992	−	26.2261i	−0.0917824	−	1.08432i
$586$	−28.8787			−1.19297
$587$	−7.53706	+	7.53706i	−0.311088	+	0.311088i	−0.845331	−	0.534243i	$-0.820597\pi$
$587$	−7.53706	+	7.53706i	−0.311088	+	0.311088i	0.534243	+	0.845331i	$0.320597\pi$
$588$	−0.917166	−	1.61865i	−0.0378233	−	0.0667521i
$589$		−	5.47806i		−	0.225719i
$590$	1.14074	−	0.821652i	0.0469635	−	0.0338269i
$591$	−15.4724	−	4.28013i	−0.636448	−	0.176061i
$592$	−0.324010	−	0.324010i	−0.0133167	−	0.0133167i
$593$	−8.68375	−	8.68375i	−0.356599	−	0.356599i	0.505959	−	0.862558i	$-0.331139\pi$
$593$	−8.68375	−	8.68375i	−0.356599	−	0.356599i	−0.862558	+	0.505959i	$0.831139\pi$
$594$	−1.21834	−	1.27890i	−0.0499890	−	0.0524739i
$595$	−2.18379	−	0.355088i	−0.0895269	−	0.0145572i
$596$			16.0970i			0.659357i
$597$	−7.64343	+	4.33095i	−0.312825	+	0.177254i
$598$	−15.6785	+	15.6785i	−0.641140	+	0.641140i
$599$	−32.7513			−1.33818			−0.669090	−	0.743181i	$-0.733316\pi$
$599$	−32.7513			−1.33818			−0.669090	+	0.743181i	$0.733316\pi$
$600$	−4.83450	+	7.18523i	−0.197368	+	0.293336i
$601$	−25.4174			−1.03680			−0.518398	−	0.855140i	$-0.673471\pi$
$601$	−25.4174			−1.03680			−0.518398	+	0.855140i	$0.673471\pi$
$602$	15.3726	−	15.3726i	0.626541	−	0.626541i
$603$	−1.39756	+	0.350364i	−0.0569130	+	0.0142679i
$604$			7.93645i			0.322929i
$605$	−24.0229	−	3.90615i	−0.976668	−	0.158808i
$606$	−0.297966	+	1.07713i	−0.0121040	+	0.0437552i
$607$	5.98470	+	5.98470i	0.242911	+	0.242911i	0.818053	−	0.575142i	$-0.195053\pi$
$607$	5.98470	+	5.98470i	0.242911	+	0.242911i	−0.575142	+	0.818053i	$0.695053\pi$
$608$	−3.87357	−	3.87357i	−0.157094	−	0.157094i
$609$	7.04995	−	25.4851i	0.285678	−	1.03271i
$610$	−20.8253	+	15.0001i	−0.843192	+	0.607335i
$611$		−	12.6304i		−	0.510972i
$612$	−1.18278	+	0.296519i	−0.0478109	+	0.0119861i
$613$	−12.5860	+	12.5860i	−0.508344	+	0.508344i	−0.914018	−	0.405674i	$-0.867037\pi$
$613$	−12.5860	+	12.5860i	−0.508344	+	0.508344i	0.405674	+	0.914018i	$0.367037\pi$
$614$	13.1141			0.529244
$615$	−31.9166	+	11.8072i	−1.28700	+	0.476111i
$616$	−0.827498			−0.0333408
$617$	−20.0248	+	20.0248i	−0.806169	+	0.806169i	−0.984052	−	0.177883i	$-0.943075\pi$
$617$	−20.0248	+	20.0248i	−0.806169	+	0.806169i	0.177883	+	0.984052i	$0.443075\pi$
$618$	−17.1861	+	9.73807i	−0.691328	+	0.391723i
$619$			8.26964i			0.332385i	0.986093	+	0.166192i	$0.0531473\pi$
$619$			8.26964i			0.332385i	−0.986093	+	0.166192i	$0.946853\pi$
$620$	−0.358875	+	2.20708i	−0.0144128	+	0.0886385i
$621$	−20.2543	−	21.2611i	−0.812778	−	0.853180i
$622$	3.94198	+	3.94198i	0.158059	+	0.158059i
$623$	22.6400	+	22.6400i	0.907053	+	0.907053i
$624$	−6.54978	−	1.81187i	−0.262201	−	0.0725329i
$625$	19.9811	+	15.0252i	0.799242	+	0.601009i
$626$		−	22.2726i		−	0.890190i
$627$	−1.59005	−	2.80618i	−0.0635005	−	0.112068i
$628$	10.2455	−	10.2455i	0.408839	−	0.408839i
$629$	−0.186248			−0.00742618
$630$	10.5319	−	12.4797i	0.419601	−	0.497204i
$631$	−36.2340			−1.44245			−0.721226	−	0.692700i	$-0.756421\pi$
$631$	−36.2340			−1.44245			−0.721226	+	0.692700i	$0.756421\pi$
$632$	−2.74053	+	2.74053i	−0.109013	+	0.109013i
$633$	14.3113	+	25.2571i	0.568822	+	1.00388i
$634$		−	3.70959i		−	0.147327i
$635$	−15.7679	−	21.8913i	−0.625729	−	0.868730i
$636$	17.7898	+	4.92120i	0.705410	+	0.195138i
$637$	−2.98001	−	2.98001i	−0.118072	−	0.118072i
$638$	1.50743	+	1.50743i	0.0596796	+	0.0596796i
$639$	−2.72769	−	1.63418i	−0.107906	−	0.0646472i
$640$	1.30688	+	1.81441i	0.0516590	+	0.0717207i
$641$			45.3737i			1.79215i	0.443901	+	0.896076i	$0.353594\pi$
$641$			45.3737i			1.79215i	−0.443901	+	0.896076i	$0.646406\pi$
$642$	−21.3508	+	12.0979i	−0.842648	+	0.477464i
$643$	32.1520	−	32.1520i	1.26795	−	1.26795i	0.320803	−	0.947146i	$-0.396047\pi$
$643$	32.1520	−	32.1520i	1.26795	−	1.26795i	0.947146	−	0.320803i	$-0.103953\pi$
$644$	−13.7568			−0.542093
$645$	−31.4243	−	14.4527i	−1.23733	−	0.569073i
$646$	−2.22661			−0.0876047
$647$	−13.2630	+	13.2630i	−0.521424	+	0.521424i	−0.918001	−	0.396577i	$-0.870198\pi$
$647$	−13.2630	+	13.2630i	−0.521424	+	0.521424i	0.396577	+	0.918001i	$0.370198\pi$
$648$	2.60915	−	8.61350i	0.102497	−	0.338370i
$649$		−	0.213719i		−	0.00838920i
$650$	−6.21540	+	18.6071i	−0.243788	+	0.729829i
$651$	1.12415	−	4.06373i	0.0440590	−	0.159270i
$652$	3.74266	+	3.74266i	0.146574	+	0.146574i
$653$	26.7007	+	26.7007i	1.04488	+	1.04488i	0.998944	+	0.0459355i	$0.0146269\pi$
$653$	26.7007	+	26.7007i	1.04488	+	1.04488i	0.0459355	+	0.998944i	$0.485373\pi$
$654$	−0.934052	+	3.37653i	−0.0365243	+	0.132033i
$655$	−3.67918	+	22.6270i	−0.143757	+	0.884109i
$656$			8.78665i			0.343061i
$657$	6.70746	+	26.7552i	0.261683	+	1.04382i
$658$	5.54116	−	5.54116i	0.216017	−	0.216017i
$659$	−20.4388			−0.796184			−0.398092	−	0.917345i	$-0.630328\pi$
$659$	−20.4388			−0.796184			−0.398092	+	0.917345i	$0.630328\pi$
$660$	0.456786	+	1.23476i	0.0177804	+	0.0480631i
$661$	34.7022			1.34976			0.674879	−	0.737928i	$-0.264196\pi$
$661$	34.7022			1.34976			0.674879	+	0.737928i	$0.264196\pi$
$662$	−6.65297	+	6.65297i	−0.258575	+	0.258575i
$663$	−2.40322	+	1.36172i	−0.0933335	+	0.0528849i
$664$		−	8.77334i		−	0.340472i
$665$	24.1956	−	17.4276i	0.938267	−	0.675815i
$666$	0.706482	−	1.17922i	0.0273756	−	0.0456940i
$667$	25.0603	+	25.0603i	0.970338	+	0.970338i
$668$	−4.44965	−	4.44965i	−0.172162	−	0.172162i
$669$	4.27135	+	1.18159i	0.165140	+	0.0456828i
$670$	1.05999	+	0.172356i	0.0409511	+	0.00665871i
$671$			3.90165i			0.150621i
$672$	−2.07860	−	3.66839i	−0.0801836	−	0.141511i
$673$	−20.6241	+	20.6241i	−0.795002	+	0.795002i	−0.982303	−	0.187301i	$-0.940026\pi$
$673$	−20.6241	+	20.6241i	−0.795002	+	0.795002i	0.187301	+	0.982303i	$0.440026\pi$
$674$	5.27742			0.203278
$675$	−24.4355	−	8.82641i	−0.940524	−	0.339729i
$676$	−2.39416			−0.0920831
$677$	−17.3257	+	17.3257i	−0.665880	+	0.665880i	−0.956760	−	0.290880i	$-0.906052\pi$
$677$	−17.3257	+	17.3257i	−0.665880	+	0.665880i	0.290880	+	0.956760i	$0.406052\pi$
$678$	−8.20595	−	14.4822i	−0.315148	−	0.556185i
$679$		−	1.36123i		−	0.0522391i
$680$	0.897089	+	0.145868i	0.0344018	+	0.00559378i
$681$	−2.48645	−	0.687830i	−0.0952811	−	0.0263577i
$682$	0.240367	+	0.240367i	0.00920414	+	0.00920414i
$683$	−20.3143	−	20.3143i	−0.777304	−	0.777304i	0.202067	−	0.979372i	$-0.435234\pi$
$683$	−20.3143	−	20.3143i	−0.777304	−	0.777304i	−0.979372	+	0.202067i	$0.935234\pi$
$684$	8.44606	−	14.0977i	0.322943	−	0.539040i
$685$	26.5323	−	19.1107i	1.01375	−	0.730182i
$686$		−	19.6549i		−	0.750429i
$687$	−22.2065	+	12.5827i	−0.847230	+	0.480061i
$688$	−6.31498	+	6.31498i	−0.240756	+	0.240756i
$689$	41.8119			1.59291
$690$	7.59387	+	20.5274i	0.289094	+	0.781464i
$691$	38.8687			1.47864			0.739318	−	0.673356i	$-0.235148\pi$
$691$	38.8687			1.47864			0.739318	+	0.673356i	$0.235148\pi$
$692$	−9.03997	+	9.03997i	−0.343648	+	0.343648i
$693$	−0.603673	−	2.40798i	−0.0229317	−	0.0914715i
$694$			12.3303i			0.468052i
$695$	−5.22679	+	32.1448i	−0.198263	+	1.21932i
$696$	−2.89607	+	10.4691i	−0.109775	+	0.396830i
$697$	2.52537	+	2.52537i	0.0956553	+	0.0956553i
$698$	7.36206	+	7.36206i	0.278658	+	0.278658i
$699$	1.61206	−	5.82748i	0.0609737	−	0.220415i
$700$	−10.8900	+	5.43642i	−0.411604	+	0.205477i
$701$		−	11.0159i		−	0.416065i	−0.978122	−	0.208032i	$-0.933294\pi$
$701$		−	11.0159i		−	0.416065i	0.978122	−	0.208032i	$-0.0667059\pi$
$702$	0.494279	−	20.3813i	0.0186554	−	0.769243i
$703$	1.77495	−	1.77495i	0.0669434	−	0.0669434i
$704$	0.339931			0.0128116
$705$	−11.3271	−	5.20956i	−0.426603	−	0.196203i
$706$	−24.0461			−0.904985
$707$	−1.11065	+	1.11065i	−0.0417705	+	0.0417705i
$708$	0.947439	−	0.536841i	0.0356069	−	0.0201757i
$709$			1.44528i			0.0542787i	0.999632	+	0.0271394i	$0.00863979\pi$
$709$			1.44528i			0.0542787i	−0.999632	+	0.0271394i	$0.991360\pi$
$710$	1.38518	+	1.92312i	0.0519851	+	0.0721734i
$711$	−9.97408	−	5.97555i	−0.374057	−	0.224101i
$712$	−9.30038	−	9.30038i	−0.348546	−	0.348546i
$713$	3.99600	+	3.99600i	0.149651	+	0.149651i
$714$	−1.65174	−	0.456922i	−0.0618149	−	0.0170999i
$715$	1.74303	+	2.41993i	0.0651855	+	0.0905003i
$716$			21.7538i			0.812977i
$717$	11.0502	+	19.5018i	0.412676	+	0.728308i
$718$	10.6544	−	10.6544i	0.397620	−	0.397620i
$719$	−5.37476			−0.200445			−0.100222	−	0.994965i	$-0.531955\pi$
$719$	−5.37476			−0.200445			−0.100222	+	0.994965i	$0.531955\pi$
$720$	−4.32644	+	5.12659i	−0.161237	+	0.191057i
$721$	−27.7623			−1.03392
$722$	7.78463	−	7.78463i	0.289714	−	0.289714i
$723$	−24.3975	−	43.0576i	−0.907352	−	1.60133i
$724$		−	22.0926i		−	0.821066i
$725$	29.7413	+	9.93463i	1.10457	+	0.368963i
$726$	−18.1700	−	5.02638i	−0.674352	−	0.186547i
$727$	−4.43498	−	4.43498i	−0.164484	−	0.164484i	0.620066	−	0.784550i	$-0.287106\pi$
$727$	−4.43498	−	4.43498i	−0.164484	−	0.164484i	−0.784550	+	0.620066i	$0.787106\pi$
$728$	−6.75366	−	6.75366i	−0.250307	−	0.250307i
$729$	26.9683	+	1.30881i	0.998824	+	0.0484746i
$730$	3.29963	−	20.2928i	0.122125	−	0.751069i
$731$			3.62998i			0.134260i
$732$	−17.2964	+	9.80056i	−0.639294	+	0.362239i
$733$	−15.2541	+	15.2541i	−0.563422	+	0.563422i	−0.930278	−	0.366856i	$-0.880434\pi$
$733$	−15.2541	+	15.2541i	−0.563422	+	0.563422i	0.366856	+	0.930278i	$0.380434\pi$
$734$	−12.1630			−0.448945
$735$	−3.90164	+	1.44337i	−0.143914	+	0.0532394i
$736$	5.65120			0.208306
$737$	0.115441	−	0.115441i	0.00425233	−	0.00425233i
$738$	−25.5687	+	6.41001i	−0.941197	+	0.235956i
$739$		−	13.0021i		−	0.478291i	−0.970984	−	0.239145i	$-0.923133\pi$
$739$		−	13.0021i		−	0.478291i	0.970984	−	0.239145i	$-0.0768672\pi$
$740$	−0.831396	+	0.598838i	−0.0305627	+	0.0220137i
$741$	9.92553	−	35.8801i	0.364623	−	1.31809i
$742$	18.3435	+	18.3435i	0.673412	+	0.673412i
$743$	−6.27884	−	6.27884i	−0.230348	−	0.230348i	0.582490	−	0.812838i	$-0.302079\pi$
$743$	−6.27884	−	6.27884i	−0.230348	−	0.230348i	−0.812838	+	0.582490i	$0.802079\pi$
$744$	−0.461795	+	1.66935i	−0.0169302	+	0.0612015i
$745$	35.5273	+	5.77679i	1.30162	+	0.211645i
$746$		−	6.70997i		−	0.245669i
$747$	25.5300	−	6.40030i	0.934093	−	0.234175i
$748$	0.0976996	−	0.0976996i	0.00357225	−	0.00357225i
$749$	−34.4898			−1.26023
$750$	14.1234	+	13.2487i	0.515714	+	0.483775i
$751$	−37.8482			−1.38110			−0.690550	−	0.723285i	$-0.742631\pi$
$751$	−37.8482			−1.38110			−0.690550	+	0.723285i	$0.742631\pi$
$752$	−2.27627	+	2.27627i	−0.0830072	+	0.0830072i
$753$	−12.8613	+	7.28752i	−0.468692	+	0.265572i
$754$			24.6059i			0.896093i
$755$	17.5164	+	2.84819i	0.637486	+	0.103656i
$756$	9.15845	−	8.72476i	0.333090	−	0.317316i
$757$	−6.11361	−	6.11361i	−0.222203	−	0.222203i	0.587223	−	0.809425i	$-0.300221\pi$
$757$	−6.11361	−	6.11361i	−0.222203	−	0.222203i	−0.809425	+	0.587223i	$0.800221\pi$
$758$	15.1203	+	15.1203i	0.549194	+	0.549194i
$759$	3.20686	+	0.887115i	0.116402	+	0.0322002i
$760$	−9.93942	+	7.15916i	−0.360541	+	0.259690i
$761$			9.06260i			0.328519i	0.986417	+	0.164260i	$0.0525235\pi$
$761$			9.06260i			0.328519i	−0.986417	+	0.164260i	$0.947477\pi$
$762$	−10.3022	−	18.1818i	−0.373210	−	0.658656i
$763$	−3.48164	+	3.48164i	−0.126044	+	0.126044i
$764$	−13.6016			−0.492087
$765$	0.229973	+	2.71690i	0.00831468	+	0.0982296i
$766$	6.29206			0.227342
$767$	1.74428	−	1.74428i	0.0629821	−	0.0629821i
$768$	0.853874	+	1.50695i	0.0308115	+	0.0543774i
$769$		−	16.3442i		−	0.589386i	−0.955592	−	0.294693i	$-0.904783\pi$
$769$		−	16.3442i		−	0.589386i	0.955592	−	0.294693i	$-0.0952173\pi$
$770$	−0.296968	+	1.82636i	−0.0107020	+	0.0658173i
$771$	6.76269	+	1.87077i	0.243552	+	0.0673740i
$772$	−18.2354	−	18.2354i	−0.656306	−	0.656306i
$773$	9.73290	+	9.73290i	0.350068	+	0.350068i	0.860135	−	0.510067i	$-0.170379\pi$
$773$	9.73290	+	9.73290i	0.350068	+	0.350068i	−0.510067	+	0.860135i	$0.670379\pi$
$774$	−22.9831	−	13.7694i	−0.826112	−	0.494930i
$775$	4.74242	+	1.58413i	0.170353	+	0.0569037i
$776$			0.559184i			0.0200735i
$777$	1.68093	−	0.952453i	0.0603029	−	0.0341691i
$778$	−16.8513	+	16.8513i	−0.604147	+	0.604147i
$779$	−48.1338			−1.72457
$780$	−6.34950	+	13.8057i	−0.227348	+	0.494322i
$781$	0.360299			0.0128925
$782$	1.62421	−	1.62421i	0.0580817	−	0.0580817i
$783$	−32.5773	−	0.790050i	−1.16422	−	0.0282341i
$784$			1.07412i			0.0383616i
$785$	−18.9358	−	26.2894i	−0.675846	−	0.938310i
$786$	−4.73432	+	17.1142i	−0.168868	+	0.610444i
$787$	14.1056	+	14.1056i	0.502810	+	0.502810i	0.912310	−	0.409500i	$-0.134297\pi$
$787$	14.1056	+	14.1056i	0.502810	+	0.502810i	−0.409500	+	0.912310i	$0.634297\pi$
$788$	6.55380	+	6.55380i	0.233469	+	0.233469i
$789$	12.4173	−	44.8877i	0.442069	−	1.59805i
$790$	5.06508	+	7.03209i	0.180207	+	0.250191i
$791$		−	23.3944i		−	0.831808i
$792$	0.247985	+	0.989182i	0.00881177	+	0.0351490i
$793$	−31.8435	+	31.8435i	−1.13079	+	1.13079i
$794$	−23.0724			−0.818808
$795$	17.2458	−	37.4974i	0.611645	−	1.32989i
$796$	5.07211			0.179776
$797$	11.5853	−	11.5853i	0.410371	−	0.410371i	−0.471497	−	0.881868i	$-0.656286\pi$
$797$	11.5853	−	11.5853i	0.410371	−	0.410371i	0.881868	+	0.471497i	$0.156286\pi$
$798$	20.0956	−	11.3867i	0.711378	−	0.403084i
$799$			1.30845i			0.0462896i
$800$	4.47355	−	2.23325i	0.158164	−	0.0789572i
$801$	20.2788	−	33.8484i	0.716518	−	1.19597i
$802$	−28.1206	−	28.1206i	−0.992972	−	0.992972i
$803$	−2.21003	−	2.21003i	−0.0779903	−	0.0779903i
$804$	0.801740	+	0.221786i	0.0282752	+	0.00782178i
$805$	−4.93696	+	30.3623i	−0.174005	+	1.07013i
$806$			3.92354i			0.138201i
$807$	3.12763	+	5.51977i	0.110098	+	0.194305i
$808$	0.456250	−	0.456250i	0.0160508	−	0.0160508i
$809$	−25.3543			−0.891408			−0.445704	−	0.895180i	$-0.647047\pi$
$809$	−25.3543			−0.891408			−0.445704	+	0.895180i	$0.647047\pi$
$810$	−18.0743	−	8.84978i	−0.635067	−	0.310950i
$811$	−1.41662			−0.0497443			−0.0248722	−	0.999691i	$-0.507918\pi$
$811$	−1.41662			−0.0497443			−0.0248722	+	0.999691i	$0.507918\pi$
$812$	−10.7950	+	10.7950i	−0.378830	+	0.378830i
$813$	−24.6919	−	43.5772i	−0.865982	−	1.52832i
$814$			0.155763i			0.00545949i
$815$	9.60350	−	6.91721i	0.336396	−	0.242299i
$816$	0.678525	+	0.187701i	0.0237531	+	0.00657084i
$817$	−34.5938	−	34.5938i	−1.21028	−	1.21028i
$818$	3.04123	+	3.04123i	0.106334	+	0.106334i
$819$	14.7259	−	24.5797i	0.514565	−	0.858885i
$820$	19.3929	+	3.15331i	0.677228	+	0.110118i
$821$		−	2.80000i		−	0.0977208i	−0.998806	−	0.0488604i	$-0.984441\pi$
$821$		−	2.80000i		−	0.0977208i	0.998806	−	0.0488604i	$-0.0155589\pi$
$822$	22.0364	−	12.4863i	0.768607	−	0.435511i
$823$	17.5215	−	17.5215i	0.610761	−	0.610761i	−0.332383	−	0.943144i	$-0.607853\pi$
$823$	17.5215	−	17.5215i	0.610761	−	0.610761i	0.943144	+	0.332383i	$0.107853\pi$
$824$	11.4046			0.397297
$825$	2.88915	−	0.565040i	0.100587	−	0.0196722i
$826$	1.53048			0.0532523
$827$	31.5700	−	31.5700i	1.09780	−	1.09780i	0.103130	−	0.994668i	$-0.467114\pi$
$827$	31.5700	−	31.5700i	1.09780	−	1.09780i	0.994668	−	0.103130i	$-0.0328857\pi$
$828$	4.12264	+	16.4447i	0.143272	+	0.571493i
$829$			30.3483i			1.05404i	0.849853	+	0.527020i	$0.176691\pi$
$829$			30.3483i			1.05404i	−0.849853	+	0.527020i	$0.823309\pi$
$830$	−19.3635	−	3.14853i	−0.672116	−	0.109287i
$831$	2.90145	−	10.4885i	0.100650	−	0.363843i
$832$	2.77436	+	2.77436i	0.0961837	+	0.0961837i
$833$	0.308714	+	0.308714i	0.0106963	+	0.0106963i
$834$	−6.72576	+	24.3131i	−0.232894	+	0.841894i
$835$	−11.4176	+	8.22387i	−0.395122	+	0.284599i
$836$			1.86216i			0.0644042i
$837$	−5.19463	−	0.125978i	−0.179553	−	0.00435443i
$838$	1.63419	−	1.63419i	0.0564520	−	0.0564520i
$839$	21.7362			0.750417			0.375209	−	0.926940i	$-0.377571\pi$
$839$	21.7362			0.750417			0.375209	+	0.926940i	$0.377571\pi$
$840$	−8.84239	+	3.27114i	−0.305091	+	0.112865i
$841$	10.3298			0.356199
$842$	−26.6844	+	26.6844i	−0.919604	+	0.919604i
$843$	35.2229	−	19.9581i	1.21314	−	0.687395i
$844$		−	16.7604i		−	0.576916i
$845$	−0.859203	+	5.28411i	−0.0295575	+	0.181779i
$846$	−8.28442	−	4.96326i	−0.284824	−	0.170640i
$847$	−18.7356	−	18.7356i	−0.643763	−	0.643763i
$848$	−7.53540	−	7.53540i	−0.258767	−	0.258767i
$849$	11.5979	+	3.20835i	0.398040	+	0.110110i
$850$	0.643885	−	1.92760i	0.0220851	−	0.0661161i
$851$			2.58949i			0.0887665i
$852$	0.905036	+	1.59724i	0.0310060	+	0.0547207i
$853$	−9.57823	+	9.57823i	−0.327952	+	0.327952i	−0.851807	−	0.523855i	$-0.824493\pi$
$853$	−9.57823	+	9.57823i	−0.327952	+	0.327952i	0.523855	+	0.851807i	$0.324493\pi$
$854$	−27.9405			−0.956103
$855$	−28.0838	−	23.7005i	−0.960445	−	0.810539i
$856$	14.1682			0.484259
$857$	6.81335	−	6.81335i	0.232740	−	0.232740i	−0.581096	−	0.813835i	$-0.697376\pi$
$857$	6.81335	−	6.81335i	0.232740	−	0.232740i	0.813835	+	0.581096i	$0.197376\pi$
$858$	1.13884	+	2.00987i	0.0388793	+	0.0686158i
$859$		−	11.2558i		−	0.384043i	−0.981391	−	0.192021i	$-0.938496\pi$
$859$		−	11.2558i		−	0.384043i	0.981391	−	0.192021i	$-0.0615043\pi$
$860$	11.6714	+	16.2039i	0.397991	+	0.552550i
$861$	−35.7066	−	9.87754i	−1.21688	−	0.336626i
$862$	20.8167	+	20.8167i	0.709019	+	0.709019i
$863$	29.2586	+	29.2586i	0.995973	+	0.995973i	0.999992	−	0.00401921i	$-0.00127936\pi$
$863$	29.2586	+	29.2586i	0.995973	+	0.995973i	−0.00401921	+	0.999992i	$0.501279\pi$
$864$	−3.76223	+	3.58407i	−0.127994	+	0.121933i
$865$	16.7077	+	23.1962i	0.568080	+	0.788693i
$866$		−	27.5208i		−	0.935195i
$867$	−25.3692	+	14.3748i	−0.861583	+	0.488193i
$868$	−1.72132	+	1.72132i	−0.0584254	+	0.0584254i
$869$	1.31747			0.0446921
$870$	22.0668	+	10.1490i	0.748136	+	0.344082i
$871$	1.88435			0.0638489
$872$	1.43023	−	1.43023i	0.0484338	−	0.0484338i
$873$	−1.62720	+	0.407934i	−0.0550722	+	0.0138065i
$874$			30.9576i			1.04716i
$875$	8.09047	+	25.9861i	0.273508	+	0.878491i
$876$	4.24592	−	15.3487i	0.143456	−	0.518584i
$877$	0.389742	+	0.389742i	0.0131607	+	0.0131607i	0.713656	−	0.700496i	$-0.247038\pi$
$877$	0.389742	+	0.389742i	0.0131607	+	0.0131607i	−0.700496	+	0.713656i	$0.747038\pi$
$878$	−27.3843	−	27.3843i	−0.924174	−	0.924174i
$879$	−13.3360	+	48.2087i	−0.449813	+	1.62604i
$880$	0.121993	−	0.750255i	0.00411237	−	0.0252911i
$881$		−	17.5314i		−	0.590649i	−0.955397	−	0.295324i	$-0.904572\pi$
$881$		−	17.5314i		−	0.590649i	0.955397	−	0.295324i	$-0.0954277\pi$
$882$	−3.12565	+	0.783591i	−0.105246	+	0.0263849i
$883$	16.1865	−	16.1865i	0.544719	−	0.544719i	−0.380190	−	0.924908i	$-0.624141\pi$
$883$	16.1865	−	16.1865i	0.544719	−	0.544719i	0.924908	+	0.380190i	$0.124141\pi$
$884$	1.59476			0.0536376
$885$	−0.844841	−	2.28373i	−0.0283990	−	0.0767668i
$886$	−5.03150			−0.169036
$887$	28.8585	−	28.8585i	0.968975	−	0.968975i	−0.0305579	−	0.999533i	$-0.509728\pi$
$887$	28.8585	−	28.8585i	0.968975	−	0.968975i	0.999533	+	0.0305579i	$0.00972840\pi$
$888$	−0.690514	+	0.391262i	−0.0231721	+	0.0131299i
$889$		−	29.3707i		−	0.985060i
$890$	−23.8644	+	17.1890i	−0.799935	+	0.576177i
$891$	−2.69756	+	1.44325i	−0.0903716	+	0.0483506i
$892$	−1.80926	−	1.80926i	−0.0605786	−	0.0605786i
$893$	−12.4696	−	12.4696i	−0.417278	−	0.417278i
$894$	26.8715	+	7.43350i	0.898719	+	0.248613i
$895$	48.0124	+	7.80688i	1.60488	+	0.260955i
$896$			2.43431i			0.0813247i
$897$	18.9327	+	33.4131i	0.632144	+	1.11563i
$898$	−2.07671	+	2.07671i	−0.0693007	+	0.0693007i
$899$	6.27134			0.209161
$900$	9.76216	+	11.3886i	0.325405	+	0.379620i
$901$	−4.33150			−0.144303
$902$	2.11202	−	2.11202i	0.0703227	−	0.0703227i
$903$	−18.5634	−	32.7614i	−0.617750	−	1.09023i
$904$			9.61026i			0.319632i
$905$	−48.7603	−	7.92849i	−1.62085	−	0.263552i
$906$	13.2487	+	3.66501i	0.440160	+	0.121762i
$907$	−27.8020	−	27.8020i	−0.923151	−	0.923151i	0.0741002	−	0.997251i	$-0.476392\pi$
$907$	−27.8020	−	27.8020i	−0.923151	−	0.923151i	−0.997251	+	0.0741002i	$0.976392\pi$
$908$	1.05321	+	1.05321i	0.0349521	+	0.0349521i
$909$	1.66051	+	0.994822i	0.0550755	+	0.0329962i
$910$	−17.3296	+	12.4822i	−0.574471	+	0.413780i
$911$		−	27.3543i		−	0.906288i	−0.891437	−	0.453144i	$-0.850302\pi$
$911$		−	27.3543i		−	0.906288i	0.891437	−	0.453144i	$-0.149698\pi$
$912$	−8.25516	+	4.67757i	−0.273356	+	0.154890i
$913$	−2.10883	+	2.10883i	−0.0697919	+	0.0697919i
$914$	−39.0237			−1.29079
$915$	15.4234	+	41.6918i	0.509882	+	1.37829i
$916$	14.7360			0.486892
$917$	−17.6469	+	17.6469i	−0.582754	+	0.582754i
$918$	−0.0512049	+	2.11140i	−0.00169001	+	0.0696867i
$919$		−	3.24404i		−	0.107011i	−0.998568	−	0.0535056i	$-0.982961\pi$
$919$		−	3.24404i		−	0.107011i	0.998568	−	0.0535056i	$-0.0170395\pi$
$920$	2.02807	−	12.4727i	0.0668635	−	0.411211i
$921$	6.05604	−	21.8922i	0.199553	−	0.721371i
$922$	−23.0265	−	23.0265i	−0.758337	−	0.758337i
$923$	2.94059	+	2.94059i	0.0967908	+	0.0967908i
$924$	−0.382134	+	1.38139i	−0.0125713	+	0.0454443i
$925$	1.02332	+	2.04987i	0.0336465	+	0.0673992i
$926$			3.48258i			0.114445i
$927$	8.31983	+	33.1867i	0.273259	+	1.09000i
$928$	4.43451	−	4.43451i	0.145570	−	0.145570i
$929$	−27.5398			−0.903551			−0.451775	−	0.892132i	$-0.649209\pi$
$929$	−27.5398			−0.903551			−0.451775	+	0.892132i	$0.649209\pi$
$930$	3.51868	+	1.61831i	0.115382	+	0.0530664i
$931$	−5.88411			−0.192844
$932$	−2.46841	+	2.46841i	−0.0808554	+	0.0808554i
$933$	8.40094	−	4.76017i	0.275035	−	0.155841i
$934$			13.1802i			0.431269i
$935$	−0.180569	−	0.250693i	−0.00590524	−	0.00819853i
$936$	−6.04931	+	10.0972i	−0.197728	+	0.330037i
$937$	−16.3010	−	16.3010i	−0.532529	−	0.532529i	0.388795	−	0.921324i	$-0.372891\pi$
$937$	−16.3010	−	16.3010i	−0.532529	−	0.532529i	−0.921324	+	0.388795i	$0.872891\pi$
$938$	0.826696	+	0.826696i	0.0269926	+	0.0269926i
$939$	−37.1808	−	10.2854i	−1.21335	−	0.335650i
$940$	4.20702	+	5.84082i	0.137218	+	0.190506i
$941$		−	36.8373i		−	1.20086i	−0.799677	−	0.600431i	$-0.794996\pi$
$941$		−	36.8373i		−	1.20086i	0.799677	−	0.600431i	$-0.205004\pi$
$942$	−12.3720	−	21.8346i	−0.403102	−	0.711411i
$943$	35.1115	−	35.1115i	1.14339	−	1.14339i
$944$	−0.628713			−0.0204629
$945$	−15.9695	−	23.3445i	−0.519488	−	0.759398i
$946$	3.03583			0.0987033
$947$	6.05124	−	6.05124i	0.196639	−	0.196639i	−0.601919	−	0.798557i	$-0.705597\pi$
$947$	6.05124	−	6.05124i	0.196639	−	0.196639i	0.798557	+	0.601919i	$0.205597\pi$
$948$	3.30936	+	5.84049i	0.107483	+	0.189690i
$949$		−	36.0745i		−	1.17103i
$950$	12.2339	+	24.5063i	0.396919	+	0.795091i
$951$	−6.19262	−	1.71307i	−0.200809	−	0.0555501i
$952$	0.699646	+	0.699646i	0.0226757	+	0.0226757i
$953$	26.6654	+	26.6654i	0.863777	+	0.863777i	0.991775	−	0.127997i	$-0.0408548\pi$
$953$	26.6654	+	26.6654i	0.863777	+	0.863777i	−0.127997	+	0.991775i	$0.540855\pi$
$954$	16.4304	−	27.4248i	0.531955	−	0.887912i
$955$	−4.88125	+	30.0197i	−0.157954	+	0.971416i
$956$		−	12.9412i		−	0.418549i
$957$	3.21255	−	1.82031i	0.103847	−	0.0588422i
$958$	−2.71830	+	2.71830i	−0.0878242	+	0.0878242i
$959$	35.5973			1.14950
$960$	3.63240	−	1.34376i	0.117235	−	0.0433698i
$961$	1.00000			0.0322581
$962$	−1.27127	+	1.27127i	−0.0409873	+	0.0409873i
$963$	10.3359	+	41.2288i	0.333071	+	1.32858i
$964$			28.5727i			0.920264i
$965$	−46.7912	+	33.7028i	−1.50626	+	1.08493i
$966$	−6.35281	+	22.9649i	−0.204398	+	0.738885i
$967$	16.0301	+	16.0301i	0.515493	+	0.515493i	0.916204	−	0.400711i	$-0.131237\pi$
$967$	16.0301	+	16.0301i	0.515493	+	0.515493i	−0.400711	+	0.916204i	$0.631237\pi$
$968$	7.69647	+	7.69647i	0.247374	+	0.247374i
$969$	−1.02824	+	3.71700i	−0.0330317	+	0.119407i
$970$	1.23416	+	0.200677i	0.0396266	+	0.00644334i
$971$		−	3.18491i		−	0.102209i	−0.998693	−	0.0511043i	$-0.983726\pi$
$971$		−	3.18491i		−	0.102209i	0.998693	−	0.0511043i	$-0.0162741\pi$
$972$	−13.1741	−	8.33327i	−0.422559	−	0.267290i
$973$	−25.0699	+	25.0699i	−0.803705	+	0.803705i
$974$	32.3151			1.03544
$975$	28.1916	+	18.9684i	0.902852	+	0.607474i
$976$	11.4778			0.367394
$977$	−38.4313	+	38.4313i	−1.22953	+	1.22953i	−0.265385	+	0.964143i	$0.585499\pi$
$977$	−38.4313	+	38.4313i	−1.22953	+	1.22953i	−0.964143	+	0.265385i	$0.914501\pi$
$978$	7.97617	−	4.51949i	0.255050	−	0.144517i
$979$			4.47101i			0.142894i
$980$	2.37068	+	0.385476i	0.0757286	+	0.0123136i
$981$	5.20529	+	3.11853i	0.166192	+	0.0995670i
$982$	−16.2311	−	16.2311i	−0.517955	−	0.517955i
$983$	−0.539182	−	0.539182i	−0.0171972	−	0.0171972i	0.698456	−	0.715653i	$-0.253871\pi$
$983$	−0.539182	−	0.539182i	−0.0171972	−	0.0171972i	−0.715653	+	0.698456i	$0.753871\pi$
$984$	14.6680	+	4.05763i	0.467600	+	0.129353i
$985$	16.8168	−	12.1128i	0.535827	−	0.385945i
$986$		−	2.54905i		−	0.0811782i
$987$	−6.69128	−	11.8090i	−0.212986	−	0.375886i
$988$	−15.1981	+	15.1981i	−0.483516	+	0.483516i
$989$	50.4693			1.60483
$990$	2.27220	−	0.192331i	0.0722153	−	0.00611269i
$991$	50.8751			1.61610			0.808051	−	0.589112i	$-0.200523\pi$
$991$	50.8751			1.61610			0.808051	+	0.589112i	$0.200523\pi$
$992$	0.707107	−	0.707107i	0.0224507	−	0.0224507i
$993$	8.03386	+	14.1785i	0.254947	+	0.449940i
$994$			2.58017i			0.0818380i
$995$	1.82025	−	11.1946i	0.0577059	−	0.354892i
$996$	−14.6458	−	4.05148i	−0.464071	−	0.128376i
$997$	−34.7729	−	34.7729i	−1.10127	−	1.10127i	−0.994258	−	0.107012i	$-0.965872\pi$
$997$	−34.7729	−	34.7729i	−1.10127	−	1.10127i	−0.107012	−	0.994258i	$-0.534128\pi$
$998$	−2.84541	−	2.84541i	−0.0900697	−	0.0900697i
$999$	−1.64229	−	1.72393i	−0.0519599	−	0.0545427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.g.497.8	✓	40
3.2	odd	2	inner	930.2.j.g.497.13	yes	40
5.3	odd	4	inner	930.2.j.g.683.13	yes	40
15.8	even	4	inner	930.2.j.g.683.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.8	✓	40	1.1	even	1	trivial
930.2.j.g.497.13	yes	40	3.2	odd	2	inner
930.2.j.g.683.8	yes	40	15.8	even	4	inner
930.2.j.g.683.13	yes	40	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.853874 + 1.50695i) q^{3} -1.00000i q^{4} +(-2.20708 - 0.358875i) q^{5} +(-1.66935 - 0.461795i) q^{6} +(-1.72132 - 1.72132i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.54180 + 2.57349i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.853874 + 1.50695i) q^{3} -1.00000i q^{4} +(-2.20708 - 0.358875i) q^{5} +(-1.66935 - 0.461795i) q^{6} +(-1.72132 - 1.72132i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.54180 + 2.57349i) q^{9} +(1.81441 - 1.30688i) q^{10} -0.339931i q^{11} +(1.50695 - 0.853874i) q^{12} +(2.77436 - 2.77436i) q^{13} +2.43431 q^{14} +(-1.34376 - 3.63240i) q^{15} -1.00000 q^{16} +(-0.287410 + 0.287410i) q^{17} +(-0.729516 - 2.90995i) q^{18} -5.47806i q^{19} +(-0.358875 + 2.20708i) q^{20} +(1.12415 - 4.06373i) q^{21} +(0.240367 + 0.240367i) q^{22} +(3.99600 + 3.99600i) q^{23} +(-0.461795 + 1.66935i) q^{24} +(4.74242 + 1.58413i) q^{25} +3.92354i q^{26} +(-5.19463 - 0.125978i) q^{27} +(-1.72132 + 1.72132i) q^{28} +6.27134 q^{29} +(3.51868 + 1.61831i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.512259 - 0.290258i) q^{33} -0.406459i q^{34} +(3.18135 + 4.41683i) q^{35} +(2.57349 + 1.54180i) q^{36} +(0.324010 + 0.324010i) q^{37} +(3.87357 + 3.87357i) q^{38} +(6.54978 + 1.81187i) q^{39} +(-1.30688 - 1.81441i) q^{40} -8.78665i q^{41} +(2.07860 + 3.66839i) q^{42} +(6.31498 - 6.31498i) q^{43} -0.339931 q^{44} +(4.32644 - 5.12659i) q^{45} -5.65120 q^{46} +(2.27627 - 2.27627i) q^{47} +(-0.853874 - 1.50695i) q^{48} -1.07412i q^{49} +(-4.47355 + 2.23325i) q^{50} +(-0.678525 - 0.187701i) q^{51} +(-2.77436 - 2.77436i) q^{52} +(7.53540 + 7.53540i) q^{53} +(3.76223 - 3.58407i) q^{54} +(-0.121993 + 0.750255i) q^{55} -2.43431i q^{56} +(8.25516 - 4.67757i) q^{57} +(-4.43451 + 4.43451i) q^{58} +0.628713 q^{59} +(-3.63240 + 1.34376i) q^{60} -11.4778 q^{61} +(-0.707107 + 0.707107i) q^{62} +(7.08373 - 1.77587i) q^{63} +1.00000i q^{64} +(-7.11889 + 5.12759i) q^{65} +(-0.156978 + 0.567465i) q^{66} +(0.339602 + 0.339602i) q^{67} +(0.287410 + 0.287410i) q^{68} +(-2.60969 + 9.43385i) q^{69} +(-5.37273 - 0.873613i) q^{70} +1.05992i q^{71} +(-2.90995 + 0.729516i) q^{72} +(6.50142 - 6.50142i) q^{73} -0.458220 q^{74} +(1.66222 + 8.49924i) q^{75} -5.47806 q^{76} +(-0.585129 + 0.585129i) q^{77} +(-5.91258 + 3.35021i) q^{78} +3.87570i q^{79} +(2.20708 + 0.358875i) q^{80} +(-4.24571 - 7.93561i) q^{81} +(6.21310 + 6.21310i) q^{82} +(-6.20369 - 6.20369i) q^{83} +(-4.06373 - 1.12415i) q^{84} +(0.737482 - 0.531193i) q^{85} +8.93072i q^{86} +(5.35494 + 9.45060i) q^{87} +(0.240367 - 0.240367i) q^{88} -13.1527 q^{89} +(0.565795 + 6.68430i) q^{90} -9.55112 q^{91} +(3.99600 - 3.99600i) q^{92} +(0.853874 + 1.50695i) q^{93} +3.21914i q^{94} +(-1.96594 + 12.0905i) q^{95} +(1.66935 + 0.461795i) q^{96} +(0.395402 + 0.395402i) q^{97} +(0.759520 + 0.759520i) q^{98} +(0.874809 + 0.524105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 - 8 * q^7	\( 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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