LMFDB - Embedded newform 637.2.bd.b.440.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(97,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

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

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

chi := DirichletCharacter("637.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bd (of order $12$, degree $4$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			440.2
Character	$\chi$	$=$	637.440
Dual form			637.2.bd.b.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.360315 + 1.34471i) q^{2} +(1.25446 - 0.724265i) q^{3} +(0.0536242 + 0.0309600i) q^{4} +(-0.470766 + 0.470766i) q^{5} +(0.521927 + 1.94786i) q^{6} +(-2.02975 + 2.02975i) q^{8} +(-0.450880 + 0.780947i) q^{9} +O(q^{10})$	\(q+(-0.360315 + 1.34471i) q^{2} +(1.25446 - 0.724265i) q^{3} +(0.0536242 + 0.0309600i) q^{4} +(-0.470766 + 0.470766i) q^{5} +(0.521927 + 1.94786i) q^{6} +(-2.02975 + 2.02975i) q^{8} +(-0.450880 + 0.780947i) q^{9} +(-0.463421 - 0.802669i) q^{10} +(4.65687 + 1.24780i) q^{11} +0.0896929 q^{12} +(3.60544 + 0.0282257i) q^{13} +(-0.249600 + 0.931519i) q^{15} +(-1.93616 - 3.35353i) q^{16} +(-0.233952 + 0.405217i) q^{17} +(-0.887691 - 0.887691i) q^{18} +(-0.873976 - 3.26172i) q^{19} +(-0.0398194 + 0.0106696i) q^{20} +(-3.35587 + 5.81255i) q^{22} +(-6.02331 + 3.47756i) q^{23} +(-1.07617 + 4.01633i) q^{24} +4.55676i q^{25} +(-1.33705 + 4.83811i) q^{26} +5.65182i q^{27} +(-2.01911 - 3.49720i) q^{29} +(-1.16269 - 0.671280i) q^{30} +(3.00205 - 3.00205i) q^{31} +(-0.338214 + 0.0906241i) q^{32} +(6.74561 - 1.80748i) q^{33} +(-0.460604 - 0.460604i) q^{34} +(-0.0483562 + 0.0279185i) q^{36} +(3.26109 + 0.873807i) q^{37} +4.70099 q^{38} +(4.54334 - 2.57589i) q^{39} -1.91108i q^{40} +(3.68025 + 0.986119i) q^{41} +(3.42191 + 1.97564i) q^{43} +(0.211089 + 0.211089i) q^{44} +(-0.155384 - 0.579902i) q^{45} +(-2.50603 - 9.35265i) q^{46} +(7.06171 + 7.06171i) q^{47} +(-4.85769 - 2.80459i) q^{48} +(-6.12753 - 1.64187i) q^{50} +0.677773i q^{51} +(0.192465 + 0.113138i) q^{52} -4.40103 q^{53} +(-7.60007 - 2.03643i) q^{54} +(-2.77972 + 1.60487i) q^{55} +(-3.45872 - 3.45872i) q^{57} +(5.43025 - 1.45503i) q^{58} +(-5.91907 + 1.58601i) q^{59} +(-0.0422244 + 0.0422244i) q^{60} +(-4.21802 - 2.43528i) q^{61} +(2.95521 + 5.11858i) q^{62} -8.23211i q^{64} +(-1.71061 + 1.68403i) q^{65} +9.72217i q^{66} +(2.42145 - 9.03697i) q^{67} +(-0.0250910 + 0.0144863i) q^{68} +(-5.03735 + 8.72495i) q^{69} +(3.19935 - 0.857263i) q^{71} +(-0.669954 - 2.50030i) q^{72} +(-0.0824857 - 0.0824857i) q^{73} +(-2.35004 + 4.07039i) q^{74} +(3.30030 + 5.71629i) q^{75} +(0.0541165 - 0.201966i) q^{76} +(1.82680 + 7.03762i) q^{78} -0.389839 q^{79} +(2.49021 + 0.667250i) q^{80} +(2.74077 + 4.74716i) q^{81} +(-2.65209 + 4.59356i) q^{82} +(11.5572 - 11.5572i) q^{83} +(-0.0806256 - 0.300899i) q^{85} +(-3.88964 + 3.88964i) q^{86} +(-5.06581 - 2.92474i) q^{87} +(-11.9850 + 6.91955i) q^{88} +(2.50295 - 9.34114i) q^{89} +0.835790 q^{90} -0.430661 q^{92} +(1.59168 - 5.94024i) q^{93} +(-12.0404 + 6.95154i) q^{94} +(1.94695 + 1.12407i) q^{95} +(-0.358641 + 0.358641i) q^{96} +(-4.61378 - 17.2188i) q^{97} +(-3.07416 + 3.07416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$

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 $

$2$	−0.360315	+	1.34471i	−0.254781	+	0.950856i	0.713431	+	0.700725i	$0.247140\pi$
$2$	−0.360315	+	1.34471i	−0.254781	+	0.950856i	−0.968212	+	0.250130i	$0.919527\pi$
$3$	1.25446	−	0.724265i	0.724265	−	0.418155i	−0.0920554	−	0.995754i	$-0.529344\pi$
$3$	1.25446	−	0.724265i	0.724265	−	0.418155i	0.816320	+	0.577599i	$0.196010\pi$
$4$	0.0536242	+	0.0309600i	0.0268121	+	0.0154800i
$5$	−0.470766	+	0.470766i	−0.210533	+	0.210533i	−0.804494	−	0.593961i	$-0.797563\pi$
$5$	−0.470766	+	0.470766i	−0.210533	+	0.210533i	0.593961	+	0.804494i	$0.297563\pi$
$6$	0.521927	+	1.94786i	0.213076	+	0.795210i
$7$		0			0
$7$		0			0
$8$	−2.02975	+	2.02975i	−0.717625	+	0.717625i
$9$	−0.450880	+	0.780947i	−0.150293	+	0.260316i
$10$	−0.463421	−	0.802669i	−0.146547	−	0.253826i
$11$	4.65687	+	1.24780i	1.40410	+	0.376227i	0.879815	−	0.475317i	$-0.157667\pi$
$11$	4.65687	+	1.24780i	1.40410	+	0.376227i	0.524283	+	0.851544i	$0.324333\pi$
$12$	0.0896929			0.0258921
$13$	3.60544	+	0.0282257i	0.999969	+	0.00782840i
$13$	3.60544	+	0.0282257i	0.999969	+	0.00782840i
$14$		0			0
$15$	−0.249600	+	0.931519i	−0.0644463	+	0.240517i
$16$	−1.93616	−	3.35353i	−0.484041	−	0.838383i
$17$	−0.233952	+	0.405217i	−0.0567417	+	0.0982794i	−0.893001	−	0.450055i	$-0.851404\pi$
$17$	−0.233952	+	0.405217i	−0.0567417	+	0.0982794i	0.836259	+	0.548334i	$0.184738\pi$
$18$	−0.887691	−	0.887691i	−0.209231	−	0.209231i
$19$	−0.873976	−	3.26172i	−0.200504	−	0.748290i	−0.990773	−	0.135531i	$-0.956726\pi$
$19$	−0.873976	−	3.26172i	−0.200504	−	0.748290i	0.790269	−	0.612760i	$-0.209941\pi$
$20$	−0.0398194	+	0.0106696i	−0.00890388	+	0.00238579i
$21$		0			0
$22$	−3.35587	+	5.81255i	−0.715475	+	1.23924i
$23$	−6.02331	+	3.47756i	−1.25595	+	0.725122i	−0.972284	−	0.233802i	$-0.924883\pi$
$23$	−6.02331	+	3.47756i	−1.25595	+	0.725122i	−0.283663	+	0.958924i	$0.591550\pi$
$24$	−1.07617	+	4.01633i	−0.219673	+	0.819829i
$25$			4.55676i			0.911352i
$26$	−1.33705	+	4.83811i	−0.262217	+	0.948832i
$27$			5.65182i			1.08769i
$28$		0			0
$29$	−2.01911	−	3.49720i	−0.374940	−	0.649414i	0.615378	−	0.788232i	$-0.289003\pi$
$29$	−2.01911	−	3.49720i	−0.374940	−	0.649414i	−0.990318	+	0.138817i	$0.955670\pi$
$30$	−1.16269	−	0.671280i	−0.212277	−	0.122558i
$31$	3.00205	−	3.00205i	0.539184	−	0.539184i	−0.384105	−	0.923289i	$-0.625490\pi$
$31$	3.00205	−	3.00205i	0.539184	−	0.539184i	0.923289	+	0.384105i	$0.125490\pi$
$32$	−0.338214	+	0.0906241i	−0.0597883	+	0.0160202i
$33$	6.74561	−	1.80748i	1.17426	−	0.314642i
$34$	−0.460604	−	0.460604i	−0.0789929	−	0.0789929i
$35$		0			0
$36$	−0.0483562	+	0.0279185i	−0.00805937	+	0.00465308i
$37$	3.26109	+	0.873807i	0.536120	+	0.143653i	0.516713	−	0.856159i	$-0.327155\pi$
$37$	3.26109	+	0.873807i	0.536120	+	0.143653i	0.0194074	+	0.999812i	$0.493822\pi$
$38$	4.70099			0.762601
$39$	4.54334	−	2.57589i	0.727516	−	0.412472i
$40$		−	1.91108i		−	0.302168i
$41$	3.68025	+	0.986119i	0.574758	+	0.154006i	0.534478	−	0.845182i	$-0.320508\pi$
$41$	3.68025	+	0.986119i	0.574758	+	0.154006i	0.0402801	+	0.999188i	$0.487175\pi$
$42$		0			0
$43$	3.42191	+	1.97564i	0.521836	+	0.301282i	0.737686	−	0.675144i	$-0.235919\pi$
$43$	3.42191	+	1.97564i	0.521836	+	0.301282i	−0.215849	+	0.976427i	$0.569252\pi$
$44$	0.211089	+	0.211089i	0.0318228	+	0.0318228i
$45$	−0.155384	−	0.579902i	−0.0231633	−	0.0864468i
$46$	−2.50603	−	9.35265i	−0.369495	−	1.37897i
$47$	7.06171	+	7.06171i	1.03006	+	1.03006i	0.999534	+	0.0305229i	$0.00971724\pi$
$47$	7.06171	+	7.06171i	1.03006	+	1.03006i	0.0305229	+	0.999534i	$0.490283\pi$
$48$	−4.85769	−	2.80459i	−0.701148	−	0.404808i
$49$		0			0
$50$	−6.12753	−	1.64187i	−0.866564	−	0.232195i
$51$			0.677773i			0.0949072i
$52$	0.192465	+	0.113138i	0.0266901	+	0.0156894i
$53$	−4.40103			−0.604528			−0.302264	−	0.953224i	$-0.597742\pi$
$53$	−4.40103			−0.604528			−0.302264	+	0.953224i	$0.597742\pi$
$54$	−7.60007	−	2.03643i	−1.03424	−	0.277123i
$55$	−2.77972	+	1.60487i	−0.374817	+	0.216401i
$56$		0			0
$57$	−3.45872	−	3.45872i	−0.458119	−	0.458119i
$58$	5.43025	−	1.45503i	0.713027	−	0.191055i
$59$	−5.91907	+	1.58601i	−0.770598	+	0.206481i	−0.622635	−	0.782512i	$-0.713938\pi$
$59$	−5.91907	+	1.58601i	−0.770598	+	0.206481i	−0.147962	+	0.988993i	$0.547271\pi$
$60$	−0.0422244	+	0.0422244i	−0.00545114	+	0.00545114i
$61$	−4.21802	−	2.43528i	−0.540062	−	0.311805i	0.205042	−	0.978753i	$-0.434267\pi$
$61$	−4.21802	−	2.43528i	−0.540062	−	0.311805i	−0.745104	+	0.666948i	$0.767600\pi$
$62$	2.95521	+	5.11858i	0.375312	+	0.650060i
$63$		0			0
$64$		−	8.23211i		−	1.02901i
$65$	−1.71061	+	1.68403i	−0.212175	+	0.208878i
$66$			9.72217i			1.19672i
$67$	2.42145	−	9.03697i	0.295827	−	1.10404i	−0.644731	−	0.764409i	$-0.723031\pi$
$67$	2.42145	−	9.03697i	0.295827	−	1.10404i	0.940558	−	0.339633i	$-0.110303\pi$
$68$	−0.0250910	+	0.0144863i	−0.00304273	+	0.00175672i
$69$	−5.03735	+	8.72495i	−0.606426	+	1.05036i
$70$		0			0
$71$	3.19935	−	0.857263i	0.379693	−	0.101738i	−0.0639244	−	0.997955i	$-0.520362\pi$
$71$	3.19935	−	0.857263i	0.379693	−	0.101738i	0.443617	+	0.896216i	$0.353695\pi$
$72$	−0.669954	−	2.50030i	−0.0789548	−	0.294663i
$73$	−0.0824857	−	0.0824857i	−0.00965422	−	0.00965422i	0.702263	−	0.711917i	$-0.252173\pi$
$73$	−0.0824857	−	0.0824857i	−0.00965422	−	0.00965422i	−0.711917	+	0.702263i	$0.752173\pi$
$74$	−2.35004	+	4.07039i	−0.273187	+	0.473173i
$75$	3.30030	+	5.71629i	0.381086	+	0.660060i
$76$	0.0541165	−	0.201966i	0.00620759	−	0.0231670i
$77$		0			0
$78$	1.82680	+	7.03762i	0.206844	+	0.796853i
$79$	−0.389839			−0.0438604			−0.0219302	−	0.999760i	$-0.506981\pi$
$79$	−0.389839			−0.0438604			−0.0219302	+	0.999760i	$0.506981\pi$
$80$	2.49021	+	0.667250i	0.278414	+	0.0746008i
$81$	2.74077	+	4.74716i	0.304530	+	0.527462i
$82$	−2.65209	+	4.59356i	−0.292875	+	0.507274i
$83$	11.5572	−	11.5572i	1.26857	−	1.26857i	0.321741	−	0.946828i	$-0.395732\pi$
$83$	11.5572	−	11.5572i	1.26857	−	1.26857i	0.946828	−	0.321741i	$-0.104268\pi$
$84$		0			0
$85$	−0.0806256	−	0.300899i	−0.00874507	−	0.0326371i
$86$	−3.88964	+	3.88964i	−0.419430	+	0.419430i
$87$	−5.06581	−	2.92474i	−0.543111	−	0.313565i
$88$	−11.9850	+	6.91955i	−1.27761	+	0.737626i
$89$	2.50295	−	9.34114i	0.265312	−	0.990159i	−0.696747	−	0.717317i	$-0.745370\pi$
$89$	2.50295	−	9.34114i	0.265312	−	0.990159i	0.962059	−	0.272842i	$-0.0879636\pi$
$90$	0.835790			0.0881000
$91$		0			0
$92$	−0.430661			−0.0448995
$93$	1.59168	−	5.94024i	0.165050	−	0.615974i
$94$	−12.0404	+	6.95154i	−1.24187	+	0.716997i
$95$	1.94695	+	1.12407i	0.199752	+	0.115327i
$96$	−0.358641	+	0.358641i	−0.0366037	+	0.0366037i
$97$	−4.61378	−	17.2188i	−0.468458	−	1.74831i	−0.645163	−	0.764045i	$-0.723210\pi$
$97$	−4.61378	−	17.2188i	−0.468458	−	1.74831i	0.176705	−	0.984264i	$-0.443456\pi$
$98$		0			0
$99$	−3.07416	+	3.07416i	−0.308964	+	0.308964i
$100$	−0.141077	+	0.244353i	−0.0141077	+	0.0244353i
$101$	−5.57293	−	9.65259i	−0.554527	−	0.960469i	−0.997940	−	0.0641517i	$-0.979566\pi$
$101$	−5.57293	−	9.65259i	−0.554527	−	0.960469i	0.443413	−	0.896317i	$-0.353767\pi$
$102$	−0.911410	−	0.244212i	−0.0902430	−	0.0241805i
$103$	−7.47232			−0.736270			−0.368135	−	0.929772i	$-0.620003\pi$
$103$	−7.47232			−0.736270			−0.368135	+	0.929772i	$0.620003\pi$
$104$	−7.37544	+	7.26085i	−0.723221	+	0.711985i
$105$		0			0
$106$	1.58576	−	5.91812i	0.154022	−	0.574819i
$107$	2.07553	+	3.59492i	0.200649	+	0.347534i	0.948738	−	0.316065i	$-0.102362\pi$
$107$	2.07553	+	3.59492i	0.200649	+	0.347534i	−0.748089	+	0.663598i	$0.769028\pi$
$108$	−0.174980	+	0.303074i	−0.0168375	+	0.0291633i
$109$	−4.34964	−	4.34964i	−0.416620	−	0.416620i	0.467417	−	0.884037i	$-0.345185\pi$
$109$	−4.34964	−	4.34964i	−0.416620	−	0.416620i	−0.884037	+	0.467417i	$0.845185\pi$
$110$	−1.15652	−	4.31618i	−0.110270	−	0.411532i
$111$	4.72379	−	1.26574i	0.448363	−	0.120138i
$112$		0			0
$113$	−0.554932	+	0.961171i	−0.0522036	+	0.0904194i	−0.890946	−	0.454109i	$-0.849958\pi$
$113$	−0.554932	+	0.961171i	−0.0522036	+	0.0904194i	0.838743	+	0.544528i	$0.183291\pi$
$114$	5.89722	−	3.40476i	0.552325	−	0.318885i
$115$	1.19845	−	4.47269i	0.111756	−	0.417080i
$116$		−	0.250046i		−	0.0232162i
$117$	−1.64766	+	2.80293i	−0.152327	+	0.259131i
$118$		−	8.53092i		−	0.785335i
$119$		0			0
$120$	−1.38413	−	2.39738i	−0.126353	−	0.218849i
$121$	10.6031	+	6.12170i	0.963918	+	0.556519i
$122$	4.79456	−	4.79456i	0.434079	−	0.434079i
$123$	5.33095	−	1.42842i	0.480675	−	0.128797i
$124$	0.253926	−	0.0680392i	0.0228032	−	0.00611010i
$125$	−4.49900	−	4.49900i	−0.402403	−	0.402403i
$126$		0			0
$127$	17.2552	−	9.96228i	1.53115	−	0.884009i	0.531840	−	0.846845i	$-0.321501\pi$
$127$	17.2552	−	9.96228i	1.53115	−	0.884009i	0.999309	−	0.0371647i	$-0.0118326\pi$
$128$	10.3934	+	2.78490i	0.918655	+	0.246153i
$129$	5.72355			0.503931
$130$	−1.64818	−	2.90706i	−0.144555	−	0.254966i
$131$		−	7.63701i		−	0.667249i	−0.942706	−	0.333625i	$-0.891728\pi$
$131$		−	7.63701i		−	0.667249i	0.942706	−	0.333625i	$-0.108272\pi$
$132$	0.417688	+	0.111919i	0.0363550	+	0.00974131i
$133$		0			0
$134$	11.2797	+	6.51231i	0.974414	+	0.562578i
$135$	−2.66068	−	2.66068i	−0.228995	−	0.228995i
$136$	−0.347625	−	1.29735i	−0.0298086	−	0.111247i
$137$	3.40822	+	12.7196i	0.291184	+	1.08671i	0.944201	+	0.329369i	$0.106836\pi$
$137$	3.40822	+	12.7196i	0.291184	+	1.08671i	−0.653018	+	0.757343i	$0.726497\pi$
$138$	−9.91752	−	9.91752i	−0.844236	−	0.844236i
$139$	−14.9082	−	8.60724i	−1.26449	−	0.730056i	−0.290554	−	0.956859i	$-0.593839\pi$
$139$	−14.9082	−	8.60724i	−1.26449	−	0.730056i	−0.973941	+	0.226802i	$0.927173\pi$
$140$		0			0
$141$	13.9732	+	3.74411i	1.17676	+	0.315311i
$142$			4.61109i			0.386954i
$143$	16.7548	+	4.63032i	1.40111	+	0.387207i
$144$	3.49191			0.290992
$145$	2.59689	+	0.695836i	0.215660	+	0.0577860i
$146$	0.140640	−	0.0811987i	0.0116395	−	0.00672006i
$147$		0			0
$148$	0.147821	+	0.147821i	0.0121508	+	0.0121508i
$149$	−3.63443	+	0.973843i	−0.297744	+	0.0797804i	−0.404599	−	0.914494i	$-0.632589\pi$
$149$	−3.63443	+	0.973843i	−0.297744	+	0.0797804i	0.106854	+	0.994275i	$0.465922\pi$
$150$	−8.87592	+	2.37829i	−0.724716	+	0.194187i
$151$	−5.34620	+	5.34620i	−0.435067	+	0.435067i	−0.890348	−	0.455281i	$-0.849539\pi$
$151$	−5.34620	+	5.34620i	−0.435067	+	0.435067i	0.455281	+	0.890348i	$0.349539\pi$
$152$	8.39443	+	4.84653i	0.680879	+	0.393105i
$153$	−0.210968	−	0.365408i	−0.0170558	−	0.0295415i
$154$		0			0
$155$			2.82653i			0.227032i
$156$	0.323382	+	0.00253164i	0.0258913	+	0.000202694i
$157$		−	24.6389i		−	1.96640i	−0.182537	−	0.983199i	$-0.558431\pi$
$157$		−	24.6389i		−	1.96640i	0.182537	−	0.983199i	$-0.441569\pi$
$158$	0.140465	−	0.524222i	0.0111748	−	0.0417049i
$159$	−5.52093	+	3.18751i	−0.437838	+	0.252786i
$160$	0.116557	−	0.201882i	0.00921463	−	0.0159602i
$161$		0			0
$162$	−7.37111	+	1.97508i	−0.579129	+	0.155177i
$163$	−5.37364	−	20.0547i	−0.420896	−	1.57081i	−0.772724	−	0.634742i	$-0.781107\pi$
$163$	−5.37364	−	20.0547i	−0.420896	−	1.57081i	0.351828	−	0.936065i	$-0.385560\pi$
$164$	0.166820	+	0.166820i	0.0130265	+	0.0130265i
$165$	−2.32470	+	4.02651i	−0.180978	+	0.313463i
$166$	11.3769	+	19.7054i	0.883018	+	1.52943i
$167$	−4.53457	+	16.9233i	−0.350896	+	1.30956i	0.534676	+	0.845057i	$0.320434\pi$
$167$	−4.53457	+	16.9233i	−0.350896	+	1.30956i	−0.885571	+	0.464503i	$0.846233\pi$
$168$		0			0
$169$	12.9984	+	0.203532i	0.999877	+	0.0156563i
$170$	0.433673			0.0332612
$171$	2.94129	+	0.788117i	0.224926	+	0.0602688i
$172$	0.122332	+	0.211884i	0.00932769	+	0.0161560i
$173$	2.96030	−	5.12740i	0.225068	−	0.389829i	−0.731272	−	0.682086i	$-0.761073\pi$
$173$	2.96030	−	5.12740i	0.225068	−	0.389829i	0.956340	+	0.292257i	$0.0944063\pi$
$174$	5.75823	−	5.75823i	0.436530	−	0.436530i
$175$		0			0
$176$	−4.83190	−	18.0329i	−0.364218	−	1.35928i
$177$	−6.27657	+	6.27657i	−0.471776	+	0.471776i
$178$	11.6593	+	6.73150i	0.873902	+	0.504548i
$179$	−3.26505	+	1.88508i	−0.244041	+	0.140897i	−0.617033	−	0.786938i	$-0.711665\pi$
$179$	−3.26505	+	1.88508i	−0.244041	+	0.140897i	0.372992	+	0.927835i	$0.378332\pi$
$180$	0.00962139	−	0.0359075i	0.000717136	−	0.00267639i
$181$	5.68899			0.422859			0.211430	−	0.977393i	$-0.432188\pi$
$181$	5.68899			0.422859			0.211430	+	0.977393i	$0.432188\pi$
$182$		0			0
$183$	−7.05514			−0.521531
$184$	5.16724	−	19.2844i	0.380934	−	1.42167i
$185$	−1.94657	+	1.12385i	−0.143115	+	0.0826273i
$186$	7.41441	+	4.28071i	0.543651	+	0.313877i
$187$	−1.59511	+	1.59511i	−0.116646	+	0.116646i
$188$	0.160049	+	0.597309i	0.0116727	+	0.0435633i
$189$		0			0
$190$	−2.21307	+	2.21307i	−0.160553	+	0.160553i
$191$	4.58382	−	7.93941i	0.331674	−	0.574476i	−0.651167	−	0.758935i	$-0.725720\pi$
$191$	4.58382	−	7.93941i	0.331674	−	0.574476i	0.982840	+	0.184459i	$0.0590534\pi$
$192$	−5.96223	−	10.3269i	−0.430287	−	0.745278i
$193$	24.5455	+	6.57695i	1.76682	+	0.473419i	0.988082	−	0.153926i	$-0.0491917\pi$
$193$	24.5455	+	6.57695i	1.76682	+	0.473419i	0.778742	+	0.627345i	$0.215858\pi$
$194$	24.8168			1.78174
$195$	−0.926209	+	3.35149i	−0.0663272	+	0.240005i
$196$		0			0
$197$	−0.371638	+	1.38697i	−0.0264781	+	0.0988175i	−0.977900	−	0.209071i	$-0.932956\pi$
$197$	−0.371638	+	1.38697i	−0.0264781	+	0.0988175i	0.951422	+	0.307889i	$0.0996225\pi$
$198$	−3.02619	−	5.24152i	−0.215062	−	0.372499i
$199$	−5.50792	+	9.53999i	−0.390446	+	0.676272i	−0.992508	−	0.122177i	$-0.961012\pi$
$199$	−5.50792	+	9.53999i	−0.390446	+	0.676272i	0.602062	+	0.798449i	$0.294346\pi$
$200$	−9.24908	−	9.24908i	−0.654009	−	0.654009i
$201$	−3.50754	−	13.0903i	−0.247403	−	0.923321i
$202$	14.9880	−	4.01602i	1.05455	−	0.282566i
$203$		0			0
$204$	−0.0209838	+	0.0363450i	−0.00146916	+	0.00254466i
$205$	−2.19677	+	1.26830i	−0.153429	+	0.0885822i
$206$	2.69239	−	10.0481i	0.187588	−	0.700086i
$207$		−	6.27185i		−	0.435924i
$208$	−6.88607	−	12.1456i	−0.477463	−	0.842147i
$209$		−	16.2800i		−	1.12611i
$210$		0			0
$211$	11.5485	+	20.0025i	0.795029	+	1.37703i	0.922821	+	0.385229i	$0.125878\pi$
$211$	11.5485	+	20.0025i	0.795029	+	1.37703i	−0.127792	+	0.991801i	$0.540789\pi$
$212$	−0.236002	−	0.136256i	−0.0162087	−	0.00935808i
$213$	3.39258	−	3.39258i	0.232456	−	0.232456i
$214$	−5.58197	+	1.49569i	−0.381576	+	0.102243i
$215$	−2.54098	+	0.680855i	−0.173294	+	0.0464339i
$216$	−11.4718	−	11.4718i	−0.780556	−	0.780556i
$217$		0			0
$218$	7.41625	−	4.28178i	0.502292	−	0.289998i
$219$	−0.163217	−	0.0437338i	−0.0110292	−	0.00295526i
$220$	−0.198747			−0.0133995
$221$	−0.854937	+	1.45438i	−0.0575093	+	0.0978322i
$222$			6.80821i			0.456937i
$223$	−3.57776	−	0.958657i	−0.239584	−	0.0641964i	0.137029	−	0.990567i	$-0.456245\pi$
$223$	−3.57776	−	0.958657i	−0.239584	−	0.0641964i	−0.376613	+	0.926371i	$0.622911\pi$
$224$		0			0
$225$	−3.55859	−	2.05455i	−0.237239	−	0.136970i
$226$	−1.09255	−	1.09255i	−0.0726753	−	0.0726753i
$227$	6.23954	+	23.2863i	0.414133	+	1.54556i	0.786566	+	0.617506i	$0.211857\pi$
$227$	6.23954	+	23.2863i	0.414133	+	1.54556i	−0.372433	+	0.928059i	$0.621476\pi$
$228$	−0.0783894	−	0.292553i	−0.00519147	−	0.0193748i
$229$	−13.1839	−	13.1839i	−0.871216	−	0.871216i	0.121389	−	0.992605i	$-0.461265\pi$
$229$	−13.1839	−	13.1839i	−0.871216	−	0.871216i	−0.992605	+	0.121389i	$0.961265\pi$
$230$	5.58266	+	3.22315i	0.368110	+	0.212528i
$231$		0			0
$232$	11.1967	+	3.00016i	0.735102	+	0.196970i
$233$			4.52263i			0.296288i	0.988966	+	0.148144i	$0.0473299\pi$
$233$			4.52263i			0.296288i	−0.988966	+	0.148144i	$0.952670\pi$
$234$	−3.17546	−	3.22557i	−0.207586	−	0.210862i
$235$	−6.64883			−0.433722
$236$	−0.366509	−	0.0982057i	−0.0238577	−	0.00639264i
$237$	−0.489040	+	0.282347i	−0.0317665	+	0.0183404i
$238$		0			0
$239$	−11.1608	−	11.1608i	−0.721931	−	0.721931i	0.247067	−	0.968998i	$-0.420533\pi$
$239$	−11.1608	−	11.1608i	−0.721931	−	0.721931i	−0.968998	+	0.247067i	$0.920533\pi$
$240$	3.60714	−	0.966531i	0.232840	−	0.0623893i
$241$	7.31049	−	1.95884i	0.470910	−	0.126180i	−0.0155569	−	0.999879i	$-0.504952\pi$
$241$	7.31049	−	1.95884i	0.470910	−	0.126180i	0.486467	+	0.873699i	$0.338285\pi$
$242$	−12.0524	+	12.0524i	−0.774757	+	0.774757i
$243$	−7.80745	−	4.50763i	−0.500848	−	0.289165i
$244$	−0.150792	−	0.261180i	−0.00965348	−	0.0167203i
$245$		0			0
$246$			7.68328i			0.489868i
$247$	−3.05900	−	11.7846i	−0.194640	−	0.749837i
$248$			12.1868i			0.773864i
$249$	6.12762	−	22.8686i	0.388322	−	1.44924i
$250$	7.67092	−	4.42881i	0.485151	−	0.280102i
$251$	−10.6165	+	18.3883i	−0.670106	+	1.16066i	0.307767	+	0.951462i	$0.400418\pi$
$251$	−10.6165	+	18.3883i	−0.670106	+	1.16066i	−0.977874	+	0.209197i	$0.932915\pi$
$252$		0			0
$253$	−32.3891	+	8.67863i	−2.03628	+	0.545621i
$254$	7.17911	+	26.7928i	0.450458	+	1.68113i
$255$	−0.319072	−	0.319072i	−0.0199811	−	0.0199811i
$256$	0.742320	−	1.28574i	0.0463950	−	0.0803584i
$257$	12.6205	+	21.8594i	0.787245	+	1.36355i	0.927648	+	0.373455i	$0.121827\pi$
$257$	12.6205	+	21.8594i	0.787245	+	1.36355i	−0.140403	+	0.990094i	$0.544840\pi$
$258$	−2.06228	+	7.69653i	−0.128392	+	0.479165i
$259$		0			0
$260$	−0.143868	+	0.0373446i	−0.00892229	+	0.00231601i
$261$	3.64151			0.225404
$262$	10.2696	+	2.75173i	0.634458	+	0.170002i
$263$	−0.152018	−	0.263302i	−0.00937381	−	0.0162359i	0.861300	−	0.508096i	$-0.169650\pi$
$263$	−0.152018	−	0.263302i	−0.00937381	−	0.0162359i	−0.870674	+	0.491860i	$0.836317\pi$
$264$	−10.0232	+	17.3606i	−0.616884	+	1.06847i
$265$	2.07186	−	2.07186i	0.127273	−	0.127273i
$266$		0			0
$267$	−3.62560	−	13.5309i	−0.221883	−	0.828079i
$268$	0.409633	−	0.409633i	0.0250223	−	0.0250223i
$269$	−15.5352	−	8.96926i	−0.947199	−	0.546865i	−0.0549891	−	0.998487i	$-0.517512\pi$
$269$	−15.5352	−	8.96926i	−0.947199	−	0.546865i	−0.892210	+	0.451622i	$0.850846\pi$
$270$	4.53654	−	2.61917i	0.276085	−	0.159398i
$271$	−3.36065	+	12.5421i	−0.204145	+	0.761879i	0.785563	+	0.618781i	$0.212373\pi$
$271$	−3.36065	+	12.5421i	−0.204145	+	0.761879i	−0.989708	+	0.143098i	$0.954293\pi$
$272$	1.81188			0.109861
$273$		0			0
$274$	−18.3323			−1.10749
$275$	−5.68594	+	21.2202i	−0.342875	+	1.27963i
$276$	−0.540248	+	0.311913i	−0.0325191	+	0.0187749i
$277$	5.38051	+	3.10644i	0.323283	+	0.186648i	0.652855	−	0.757483i	$-0.273571\pi$
$277$	5.38051	+	3.10644i	0.323283	+	0.186648i	−0.329572	+	0.944130i	$0.606904\pi$
$278$	16.9459	−	16.9459i	1.01635	−	1.01635i
$279$	0.990877	+	3.69801i	0.0593223	+	0.221394i
$280$		0			0
$281$	1.72841	−	1.72841i	0.103108	−	0.103108i	−0.653671	−	0.756779i	$-0.726772\pi$
$281$	1.72841	−	1.72841i	0.103108	−	0.103108i	0.756779	+	0.653671i	$0.226772\pi$
$282$	−10.0695	+	17.4409i	−0.599631	+	1.03859i
$283$	−9.00809	−	15.6025i	−0.535475	−	0.927471i	−0.999140	−	0.0414599i	$-0.986799\pi$
$283$	−9.00809	−	15.6025i	−0.535475	−	0.927471i	0.463665	−	0.886011i	$-0.346534\pi$
$284$	0.198103	+	0.0530817i	0.0117553	+	0.00314982i
$285$	3.25650			0.192898
$286$	−12.2635	+	20.8621i	−0.725154	+	1.23360i
$287$		0			0
$288$	0.0817212	−	0.304988i	0.00481547	−	0.0179716i
$289$	8.39053	+	14.5328i	0.493561	+	0.854872i
$290$	−1.87140	+	3.24136i	−0.109892	+	0.190339i
$291$	−18.2588	−	18.2588i	−1.07035	−	1.07035i
$292$	−0.00186948	−	0.00697698i	−0.000109403	−	0.000408297i
$293$	4.38187	−	1.17412i	0.255992	−	0.0685927i	−0.128541	−	0.991704i	$-0.541029\pi$
$293$	4.38187	−	1.17412i	0.255992	−	0.0685927i	0.384532	+	0.923111i	$0.374363\pi$
$294$		0			0
$295$	2.03986	−	3.53314i	0.118765	−	0.205707i
$296$	−8.39282	+	4.84559i	−0.487823	+	0.281644i
$297$	−7.05236	+	26.3198i	−0.409219	+	1.52723i
$298$		−	5.23816i		−	0.303438i
$299$	−21.8149	+	12.3681i	−1.26159	+	0.715267i
$300$			0.408709i			0.0235968i
$301$		0			0
$302$	−5.26279	−	9.11542i	−0.302839	−	0.524533i
$303$	−13.9821	−	8.07256i	−0.803249	−	0.463756i
$304$	−9.24613	+	9.24613i	−0.530302	+	0.530302i
$305$	3.13215	−	0.839256i	0.179346	−	0.0480557i
$306$	0.567384	−	0.152030i	0.0324352	−	0.00869098i
$307$	11.5340	+	11.5340i	0.658282	+	0.658282i	0.954973	−	0.296691i	$-0.0958832\pi$
$307$	11.5340	+	11.5340i	0.658282	+	0.658282i	−0.296691	+	0.954973i	$0.595883\pi$
$308$		0			0
$309$	−9.37376	+	5.41194i	−0.533254	+	0.307875i
$310$	−3.80087	−	1.01844i	−0.215875	−	0.0578434i
$311$	−10.8487			−0.615173			−0.307587	−	0.951520i	$-0.599521\pi$
$311$	−10.8487			−0.615173			−0.307587	+	0.951520i	$0.599521\pi$
$312$	−3.99344	+	14.4503i	−0.226084	+	0.818084i
$313$			7.18694i			0.406230i	0.979155	+	0.203115i	$0.0651065\pi$
$313$			7.18694i			0.406230i	−0.979155	+	0.203115i	$0.934893\pi$
$314$	33.1322	+	8.87776i	1.86976	+	0.501001i
$315$		0			0
$316$	−0.0209048	−	0.0120694i	−0.00117599	−	0.000678958i
$317$	−6.69590	−	6.69590i	−0.376079	−	0.376079i	0.493606	−	0.869685i	$-0.335678\pi$
$317$	−6.69590	−	6.69590i	−0.376079	−	0.376079i	−0.869685	+	0.493606i	$0.835678\pi$
$318$	−2.29702	−	8.57258i	−0.128810	−	0.480726i
$319$	−5.03891	−	18.8055i	−0.282125	−	1.05290i
$320$	3.87540	+	3.87540i	0.216641	+	0.216641i
$321$	5.20734	+	3.00646i	0.290646	+	0.167804i
$322$		0			0
$323$	1.52617	+	0.408937i	0.0849185	+	0.0227538i
$324$			0.339417i			0.0188565i
$325$	−0.128618	+	16.4291i	−0.00713442	+	0.911324i
$326$	28.9040			1.60085
$327$	−8.60675	−	2.30617i	−0.475955	−	0.127532i
$328$	−9.47156	+	5.46841i	−0.522979	+	0.301942i
$329$		0			0
$330$	−4.57687	−	4.57687i	−0.251948	−	0.251948i
$331$	−5.73166	+	1.53579i	−0.315040	+	0.0844148i	−0.412875	−	0.910788i	$-0.635475\pi$
$331$	−5.73166	+	1.53579i	−0.315040	+	0.0844148i	0.0978341	+	0.995203i	$0.468809\pi$
$332$	0.977557	−	0.261936i	0.0536504	−	0.0143756i
$333$	−2.15276	+	2.15276i	−0.117970	+	0.117970i
$334$	−21.1230	−	12.1954i	−1.15580	−	0.667302i
$335$	3.11436	+	5.39424i	0.170156	+	0.294719i
$336$		0			0
$337$			16.0448i			0.874014i	0.899458	+	0.437007i	$0.143961\pi$
$337$			16.0448i			0.874014i	−0.899458	+	0.437007i	$0.856039\pi$
$338$	−4.95721	+	17.4058i	−0.269637	+	0.946750i
$339$			1.60767i			0.0873168i
$340$	0.00499233	−	0.0186316i	0.000270747	−	0.00101044i
$341$	17.7261	−	10.2342i	0.959922	−	0.554211i
$342$	−2.11958	+	3.67122i	−0.114614	+	0.198517i
$343$		0			0
$344$	−10.9557	+	2.93557i	−0.590691	+	0.158275i
$345$	−1.73600	−	6.47883i	−0.0934629	−	0.348808i
$346$	5.82823	+	5.82823i	0.313328	+	0.313328i
$347$	−11.4687	+	19.8644i	−0.615673	+	1.06638i	0.374593	+	0.927189i	$0.377782\pi$
$347$	−11.4687	+	19.8644i	−0.615673	+	1.06638i	−0.990266	+	0.139187i	$0.955551\pi$
$348$	−0.181100	−	0.313674i	−0.00970798	−	0.0168147i
$349$	−3.69715	+	13.7979i	−0.197904	+	0.738587i	0.793592	+	0.608450i	$0.208208\pi$
$349$	−3.69715	+	13.7979i	−0.197904	+	0.738587i	−0.991496	+	0.130137i	$0.958458\pi$
$350$		0			0
$351$	−0.159526	+	20.3773i	−0.00851489	+	1.08766i
$352$	−1.68810			−0.0899759
$353$	−4.49235	−	1.20372i	−0.239104	−	0.0640677i	0.137277	−	0.990533i	$-0.456165\pi$
$353$	−4.49235	−	1.20372i	−0.239104	−	0.0640677i	−0.376381	+	0.926465i	$0.622832\pi$
$354$	−6.17865	−	10.7017i	−0.328391	−	0.568790i
$355$	−1.10257	+	1.90972i	−0.0585186	+	0.101357i
$356$	0.423420	−	0.423420i	0.0224412	−	0.0224412i
$357$		0			0
$358$	−1.35844	−	5.06977i	−0.0717959	−	0.267946i
$359$	12.8517	−	12.8517i	0.678287	−	0.678287i	−0.281326	−	0.959612i	$-0.590774\pi$
$359$	12.8517	−	12.8517i	0.678287	−	0.678287i	0.959612	+	0.281326i	$0.0907741\pi$
$360$	1.49245	+	0.861666i	0.0786590	+	0.0454138i
$361$	6.57949	−	3.79867i	0.346289	−	0.199930i
$362$	−2.04983	+	7.65006i	−0.107736	+	0.402078i
$363$	17.7349			0.930843
$364$		0			0
$365$	0.0776629			0.00406506
$366$	2.54207	−	9.48714i	0.132876	−	0.495901i
$367$	−12.6911	+	7.32723i	−0.662472	+	0.382478i	−0.793218	−	0.608937i	$-0.791596\pi$
$367$	−12.6911	+	7.32723i	−0.662472	+	0.382478i	0.130746	+	0.991416i	$0.458263\pi$
$368$	23.3242	+	13.4663i	1.21586	+	0.701977i
$369$	−2.42946	+	2.42946i	−0.126472	+	0.126472i
$370$	−0.809882	−	3.02252i	−0.0421038	−	0.157133i
$371$		0			0
$372$	0.269262	−	0.269262i	0.0139606	−	0.0139606i
$373$	2.86259	−	4.95816i	0.148220	−	0.256724i	−0.782350	−	0.622839i	$-0.785979\pi$
$373$	2.86259	−	4.95816i	0.148220	−	0.256724i	0.930569	+	0.366115i	$0.119312\pi$
$374$	−1.57023	−	2.71971i	−0.0811945	−	0.140633i
$375$	−8.90230	−	2.38536i	−0.459713	−	0.123180i
$376$	−28.6670			−1.47839
$377$	−7.18108	−	12.6660i	−0.369844	−	0.652330i
$378$		0			0
$379$	−0.283332	+	1.05741i	−0.0145538	+	0.0543156i	−0.972821	−	0.231559i	$-0.925617\pi$
$379$	−0.283332	+	1.05741i	−0.0145538	+	0.0543156i	0.958267	+	0.285875i	$0.0922840\pi$
$380$	0.0696023	+	0.120555i	0.00357052	+	0.00618433i
$381$	14.4307	−	24.9946i	0.739305	−	1.28051i
$382$	9.02461	+	9.02461i	0.461739	+	0.461739i
$383$	0.131981	+	0.492561i	0.00674393	+	0.0251687i	0.969216	−	0.246213i	$-0.0791862\pi$
$383$	0.131981	+	0.492561i	0.00674393	+	0.0251687i	−0.962472	+	0.271381i	$0.912520\pi$
$384$	15.0551	−	4.03401i	0.768280	−	0.205860i
$385$		0			0
$386$	−17.6882	+	30.6369i	−0.900306	+	1.55938i
$387$	−3.08574	+	1.78155i	−0.156857	+	0.0905615i
$388$	0.285685	−	1.06619i	0.0145034	−	0.0541276i
$389$		−	20.5695i		−	1.04291i	−0.853277	−	0.521457i	$-0.825389\pi$
$389$		−	20.5695i		−	1.04291i	0.853277	−	0.521457i	$-0.174611\pi$
$390$	−4.17307	−	2.45308i	−0.211311	−	0.124216i
$391$		−	3.25433i		−	0.164578i
$392$		0			0
$393$	−5.53122	−	9.58036i	−0.279013	−	0.483265i
$394$	−1.73117	−	0.999492i	−0.0872151	−	0.0503537i
$395$	0.183523	−	0.183523i	0.00923405	−	0.00923405i
$396$	−0.260025	+	0.0696735i	−0.0130667	+	0.00350122i
$397$	28.5505	−	7.65009i	1.43291	−	0.383947i	0.542864	−	0.839820i	$-0.317340\pi$
$397$	28.5505	−	7.65009i	1.43291	−	0.383947i	0.890045	+	0.455874i	$0.150673\pi$
$398$	−10.8440	−	10.8440i	−0.543559	−	0.543559i
$399$		0			0
$400$	15.2812	−	8.82263i	0.764062	−	0.441131i
$401$	6.38727	+	1.71146i	0.318965	+	0.0854664i	0.414749	−	0.909936i	$-0.363869\pi$
$401$	6.38727	+	1.71146i	0.318965	+	0.0854664i	−0.0957844	+	0.995402i	$0.530536\pi$
$402$	18.8666			0.940978
$403$	10.9084	−	10.7390i	0.543388	−	0.534946i
$404$		−	0.690151i		−	0.0343363i
$405$	−3.52507	−	0.944538i	−0.175162	−	0.0469345i
$406$		0			0
$407$	14.0961	+	8.13841i	0.698719	+	0.403406i
$408$	−1.37571	−	1.37571i	−0.0681078	−	0.0681078i
$409$	0.618563	+	2.30851i	0.0305860	+	0.114148i	0.979531	−	0.201293i	$-0.0645142\pi$
$409$	0.618563	+	2.30851i	0.0305860	+	0.114148i	−0.948945	+	0.315441i	$0.897848\pi$
$410$	−0.913977	−	3.41101i	−0.0451381	−	0.168458i
$411$	13.4879	+	13.4879i	0.665308	+	0.665308i
$412$	−0.400697	−	0.231343i	−0.0197409	−	0.0113974i
$413$		0			0
$414$	8.43384	+	2.25984i	0.414501	+	0.111065i
$415$			10.8815i			0.534151i
$416$	−1.22197	+	0.317194i	−0.0599119	+	0.0155517i
$417$	−24.9357			−1.22111
$418$	21.8919	+	5.86591i	1.07077	+	0.286911i
$419$	13.1791	−	7.60897i	0.643842	−	0.371722i	−0.142251	−	0.989831i	$-0.545434\pi$
$419$	13.1791	−	7.60897i	0.643842	−	0.371722i	0.786093	+	0.618108i	$0.212101\pi$
$420$		0			0
$421$	−15.0076	−	15.0076i	−0.731425	−	0.731425i	0.239477	−	0.970902i	$-0.423024\pi$
$421$	−15.0076	−	15.0076i	−0.731425	−	0.731425i	−0.970902	+	0.239477i	$0.923024\pi$
$422$	−31.0587	+	8.32216i	−1.51192	+	0.405116i
$423$	−8.69881	+	2.33084i	−0.422951	+	0.113329i
$424$	8.93299	−	8.93299i	0.433824	−	0.433824i
$425$	−1.84647	−	1.06606i	−0.0895671	−	0.0517116i
$426$	3.33965	+	5.78445i	0.161807	+	0.280257i
$427$		0			0
$428$			0.257033i			0.0124241i
$429$	24.3719	−	6.32637i	1.17669	−	0.305440i
$430$		−	3.66222i		−	0.176608i
$431$	−7.77536	+	29.0180i	−0.374526	+	1.39775i	0.479511	+	0.877536i	$0.340814\pi$
$431$	−7.77536	+	29.0180i	−0.374526	+	1.39775i	−0.854037	+	0.520213i	$0.825853\pi$
$432$	18.9536	−	10.9428i	0.911903	−	0.526488i
$433$	−7.75396	+	13.4302i	−0.372631	+	0.645417i	−0.989969	−	0.141281i	$-0.954878\pi$
$433$	−7.75396	+	13.4302i	−0.372631	+	0.645417i	0.617338	+	0.786698i	$0.288211\pi$
$434$		0			0
$435$	3.76168	−	1.00794i	0.180359	−	0.0483270i
$436$	−0.0985813	−	0.367911i	−0.00472119	−	0.0176197i
$437$	16.6071	+	16.6071i	0.794424	+	0.794424i
$438$	0.117619	−	0.203722i	0.00562005	−	0.00973420i
$439$	−7.21696	−	12.5001i	−0.344447	−	0.596599i	0.640806	−	0.767703i	$-0.278600\pi$
$439$	−7.21696	−	12.5001i	−0.344447	−	0.596599i	−0.985253	+	0.171103i	$0.945267\pi$
$440$	2.38465	−	8.89962i	0.113684	−	0.424273i
$441$		0			0
$442$	−1.64768	−	1.67368i	−0.0783721	−	0.0796088i
$443$	−12.4771			−0.592805			−0.296403	−	0.955063i	$-0.595787\pi$
$443$	−12.4771			−0.592805			−0.296403	+	0.955063i	$0.595787\pi$
$444$	0.292497	+	0.0783743i	0.0138813	+	0.00371948i
$445$	3.21919	+	5.57580i	0.152604	+	0.264318i
$446$	2.57824	−	4.46564i	0.122083	−	0.211454i
$447$	−3.85394	+	3.85394i	−0.182285	+	0.182285i
$448$		0			0
$449$	−7.24956	−	27.0557i	−0.342128	−	1.27684i	−0.895932	−	0.444191i	$-0.853491\pi$
$449$	−7.24956	−	27.0557i	−0.342128	−	1.27684i	0.553804	−	0.832647i	$-0.313176\pi$
$450$	4.04499	−	4.04499i	0.190683	−	0.190683i
$451$	15.9079	+	9.18445i	0.749075	+	0.432479i
$452$	−0.0595156	+	0.0343614i	−0.00279938	+	0.00161622i
$453$	−2.83455	+	10.5787i	−0.133179	+	0.497030i
$454$	−33.5616			−1.57512
$455$		0			0
$456$	14.0407			0.657515
$457$	−4.55910	+	17.0148i	−0.213266	+	0.795919i	0.773504	+	0.633791i	$0.218502\pi$
$457$	−4.55910	+	17.0148i	−0.213266	+	0.795919i	−0.986770	+	0.162128i	$0.948164\pi$
$458$	22.4789	−	12.9782i	1.05037	−	0.606431i
$459$	−2.29021	−	1.32225i	−0.106898	−	0.0617175i
$460$	0.202740	−	0.202740i	0.00945282	−	0.00945282i
$461$	1.39627	+	5.21097i	0.0650310	+	0.242699i	0.990788	−	0.135419i	$-0.0432381\pi$
$461$	1.39627	+	5.21097i	0.0650310	+	0.242699i	−0.925757	+	0.378118i	$0.876571\pi$
$462$		0			0
$463$	−19.4789	+	19.4789i	−0.905259	+	0.905259i	−0.995885	−	0.0906259i	$-0.971113\pi$
$463$	−19.4789	+	19.4789i	−0.905259	+	0.905259i	0.0906259	+	0.995885i	$0.471113\pi$
$464$	−7.81866	+	13.5423i	−0.362972	+	0.628686i
$465$	2.04715	+	3.54577i	0.0949345	+	0.164431i
$466$	−6.08165	−	1.62957i	−0.281727	−	0.0754885i
$467$	−9.59610			−0.444055			−0.222027	−	0.975040i	$-0.571267\pi$
$467$	−9.59610			−0.444055			−0.222027	+	0.975040i	$0.571267\pi$
$468$	−0.175133	+	0.0992935i	−0.00809554	+	0.00458984i
$469$		0			0
$470$	2.39567	−	8.94077i	0.110504	−	0.412407i
$471$	−17.8451	−	30.9086i	−0.822259	−	1.42419i
$472$	8.79503	−	15.2334i	0.404824	−	0.701176i
$473$	13.4702	+	13.4702i	0.619359	+	0.619359i
$474$	−0.203468	−	0.759352i	−0.00934558	−	0.0348782i
$475$	14.8629	−	3.98250i	0.681956	−	0.182729i
$476$		0			0
$477$	1.98434	−	3.43697i	0.0908565	−	0.157368i
$478$	19.0295	−	10.9867i	0.870387	−	0.502518i
$479$	8.01018	−	29.8944i	0.365994	−	1.36591i	−0.500073	−	0.865983i	$-0.666694\pi$
$479$	8.01018	−	29.8944i	0.365994	−	1.36591i	0.866068	−	0.499927i	$-0.166640\pi$
$480$		−	0.337672i		−	0.0154126i
$481$	11.7330	+	3.24251i	0.534979	+	0.147846i
$482$			10.5363i			0.479916i
$483$		0			0
$484$	0.379055	+	0.656543i	0.0172298	+	0.0298429i
$485$	10.2781	+	5.93404i	0.466703	+	0.269451i
$486$	8.87461	−	8.87461i	0.402561	−	0.402561i
$487$	−5.40538	+	1.44837i	−0.244941	+	0.0656318i	−0.379201	−	0.925314i	$-0.623801\pi$
$487$	−5.40538	+	1.44837i	−0.244941	+	0.0656318i	0.134260	+	0.990946i	$0.457134\pi$
$488$	13.5045	−	3.61853i	0.611322	−	0.163803i
$489$	−21.2660	−	21.2660i	−0.961680	−	0.961680i
$490$		0			0
$491$	12.0113	−	6.93474i	0.542063	−	0.312960i	−0.203851	−	0.979002i	$-0.565346\pi$
$491$	12.0113	−	6.93474i	0.542063	−	0.312960i	0.745915	+	0.666041i	$0.232013\pi$
$492$	0.330092	+	0.0884479i	0.0148817	+	0.00398754i
$493$	1.88950			0.0850988
$494$	16.9491	+	0.132689i	0.762577	+	0.00596994i
$495$		−	2.89442i		−	0.130094i
$496$	−15.8799	−	4.25501i	−0.713030	−	0.191056i
$497$		0			0
$498$	28.5438	+	16.4798i	1.27908	+	0.738477i
$499$	−6.46517	−	6.46517i	−0.289421	−	0.289421i	0.547430	−	0.836851i	$-0.315606\pi$
$499$	−6.46517	−	6.46517i	−0.289421	−	0.289421i	−0.836851	+	0.547430i	$0.815606\pi$
$500$	−0.101966	−	0.380544i	−0.00456008	−	0.0170184i
$501$	6.56846	+	24.5138i	0.293457	+	1.09520i
$502$	−20.9017	−	20.9017i	−0.932888	−	0.932888i
$503$	−27.9587	−	16.1420i	−1.24662	−	0.719736i	−0.276185	−	0.961104i	$-0.589070\pi$
$503$	−27.9587	−	16.1420i	−1.24662	−	0.719736i	−0.970434	+	0.241369i	$0.922404\pi$
$504$		0			0
$505$	7.16766	+	1.92057i	0.318957	+	0.0854642i
$506$		−	46.6810i		−	2.07523i
$507$	16.4534	−	9.15897i	0.730723	−	0.406764i
$508$	1.23373			0.0547378
$509$	11.6648	+	3.12559i	0.517035	+	0.138539i	0.507895	−	0.861419i	$-0.330424\pi$
$509$	11.6648	+	3.12559i	0.517035	+	0.138539i	0.00914032	+	0.999958i	$0.497091\pi$
$510$	0.544027	−	0.314094i	0.0240899	−	0.0139083i
$511$		0			0
$512$	16.6785	+	16.6785i	0.737091	+	0.737091i
$513$	18.4347	−	4.93955i	0.813910	−	0.218087i
$514$	−33.9419	+	9.09471i	−1.49711	+	0.401150i
$515$	3.51771	−	3.51771i	0.155009	−	0.155009i
$516$	0.306921	+	0.177201i	0.0135114	+	0.00780084i
$517$	24.0738	+	41.6971i	1.05877	+	1.83384i
$518$		0			0
$519$		−	8.57618i		−	0.376452i
$520$	0.0539414	−	6.89027i	0.00236549	−	0.302158i
$521$			11.7697i			0.515641i	0.966193	+	0.257821i	$0.0830043\pi$
$521$			11.7697i			0.515641i	−0.966193	+	0.257821i	$0.916996\pi$
$522$	−1.31209	+	4.89678i	−0.0574286	+	0.214326i
$523$	−13.2762	+	7.66503i	−0.580529	+	0.335168i	−0.761344	−	0.648349i	$-0.775460\pi$
$523$	−13.2762	+	7.66503i	−0.580529	+	0.335168i	0.180815	+	0.983517i	$0.442127\pi$
$524$	0.236442	−	0.409529i	0.0103290	−	0.0178904i
$525$		0			0
$526$	0.408840	−	0.109548i	0.0178263	−	0.00477654i
$527$	0.514145	+	1.91881i	0.0223965	+	0.0835849i
$528$	−19.1220	−	19.1220i	−0.832180	−	0.832180i
$529$	12.6869	−	21.9743i	0.551603	−	0.955404i
$530$	2.03953	+	3.53257i	0.0885916	+	0.153445i
$531$	1.43020	−	5.33758i	0.0620654	−	0.231631i
$532$		0			0
$533$	13.2411	+	3.65927i	0.573535	+	0.158501i
$534$	19.5016			0.843916
$535$	−2.66945	−	0.715277i	−0.115410	−	0.0309241i
$536$	13.4279	+	23.2577i	0.579995	+	1.00458i
$537$	−2.73059	+	4.72952i	−0.117834	+	0.204094i
$538$	17.6586	−	17.6586i	0.761318	−	0.761318i
$539$		0			0
$540$	−0.0603024	−	0.225052i	−0.00259500	−	0.00968469i
$541$	−10.6257	+	10.6257i	−0.456836	+	0.456836i	−0.897616	−	0.440779i	$-0.854702\pi$
$541$	−10.6257	+	10.6257i	−0.456836	+	0.456836i	0.440779	+	0.897616i	$0.354702\pi$
$542$	−15.6547	−	9.03822i	−0.672425	−	0.388225i
$543$	7.13663	−	4.12034i	0.306262	−	0.176821i
$544$	0.0424034	−	0.158252i	0.00181803	−	0.00678498i
$545$	4.09532			0.175424
$546$		0			0
$547$	20.0277			0.856322			0.428161	−	0.903702i	$-0.359162\pi$
$547$	20.0277			0.856322			0.428161	+	0.903702i	$0.359162\pi$
$548$	−0.211036	+	0.787599i	−0.00901503	+	0.0336446i
$549$	3.80364	−	2.19603i	0.162336	−	0.0937245i
$550$	−26.4864	−	15.2919i	−1.12938	−	0.652049i
$551$	−9.64225	+	9.64225i	−0.410774	+	0.410774i
$552$	−7.48490	−	27.9340i	−0.318579	−	1.18895i
$553$		0			0
$554$	−6.11594	+	6.11594i	−0.259841	+	0.259841i
$555$	−1.62794	+	2.81967i	−0.0691020	+	0.119688i
$556$	−0.532959	−	0.923113i	−0.0226025	−	0.0391487i
$557$	−2.40703	−	0.644961i	−0.101989	−	0.0273279i	0.207464	−	0.978243i	$-0.433479\pi$
$557$	−2.40703	−	0.644961i	−0.101989	−	0.0273279i	−0.309453	+	0.950915i	$0.600146\pi$
$558$	−5.32978			−0.225628
$559$	12.2817	+	7.21964i	0.519462	+	0.305358i
$560$		0			0
$561$	−0.845727	+	3.15630i	−0.0357066	+	0.133259i
$562$	1.70144	+	2.94698i	0.0717710	+	0.124311i
$563$	−9.85804	+	17.0746i	−0.415467	+	0.719609i	−0.995477	−	0.0949995i	$-0.969715\pi$
$563$	−9.85804	+	17.0746i	−0.415467	+	0.719609i	0.580011	+	0.814609i	$0.303048\pi$
$564$	0.633386	+	0.633386i	0.0266703	+	0.0266703i
$565$	−0.191243	−	0.713730i	−0.00804567	−	0.0300268i
$566$	24.2266	−	6.49150i	1.01832	−	0.272858i
$567$		0			0
$568$	−4.75385	+	8.23391i	−0.199467	+	0.345487i
$569$	38.6991	−	22.3429i	1.62235	−	0.936664i	0.636059	−	0.771640i	$-0.280563\pi$
$569$	38.6991	−	22.3429i	1.62235	−	0.936664i	0.986290	−	0.165023i	$-0.0527700\pi$
$570$	−1.17336	+	4.37906i	−0.0491468	+	0.183418i
$571$			27.5399i			1.15251i	0.817270	+	0.576255i	$0.195486\pi$
$571$			27.5399i			1.15251i	−0.817270	+	0.576255i	$0.804514\pi$
$572$	0.755110	+	0.767027i	0.0315727	+	0.0320710i
$573$		−	13.2796i		−	0.554763i
$574$		0			0
$575$	−15.8464	−	27.4468i	−0.660841	−	1.14461i
$576$	6.42884	+	3.71169i	0.267868	+	0.154654i
$577$	−13.0084	+	13.0084i	−0.541546	+	0.541546i	−0.923982	−	0.382436i	$-0.875085\pi$
$577$	−13.0084	+	13.0084i	−0.541546	+	0.541546i	0.382436	+	0.923982i	$0.375085\pi$
$578$	−22.5657	+	6.04647i	−0.938610	+	0.251500i
$579$	35.5549	−	9.52691i	1.47761	−	0.395925i
$580$	0.117713	+	0.117713i	0.00488778	+	0.00488778i
$581$		0			0
$582$	31.1318	−	17.9740i	1.29046	−	0.745045i
$583$	−20.4950	−	5.49162i	−0.848816	−	0.227440i
$584$	0.334851			0.0138562
$585$	−0.543861	−	2.09519i	−0.0224859	−	0.0866254i
$586$			6.31541i			0.260887i
$587$	−20.1767	−	5.40633i	−0.832781	−	0.223143i	−0.182855	−	0.983140i	$-0.558534\pi$
$587$	−20.1767	−	5.40633i	−0.832781	−	0.223143i	−0.649927	+	0.759997i	$0.725200\pi$
$588$		0			0
$589$	−12.4156	−	7.16813i	−0.511574	−	0.295358i
$590$	4.01607	+	4.01607i	0.165339	+	0.165339i
$591$	0.538328	+	2.00907i	0.0221439	+	0.0826420i
$592$	−3.38367	−	12.6280i	−0.139068	−	0.519008i
$593$	−6.26353	−	6.26353i	−0.257212	−	0.257212i	0.566707	−	0.823919i	$-0.308217\pi$
$593$	−6.26353	−	6.26353i	−0.257212	−	0.257212i	−0.823919	+	0.566707i	$0.808217\pi$
$594$	−32.8514	−	18.9668i	−1.34791	−	0.778217i
$595$		0			0
$596$	−0.225044	−	0.0603003i	−0.00921815	−	0.00247000i
$597$			15.9568i			0.653067i
$598$	−8.77137	−	33.7911i	−0.358688	−	1.38182i
$599$	−36.2754			−1.48217			−0.741087	−	0.671409i	$-0.765689\pi$
$599$	−36.2754			−1.48217			−0.741087	+	0.671409i	$0.765689\pi$
$600$	−18.3014	−	4.90385i	−0.747153	−	0.200199i
$601$	30.7163	−	17.7340i	1.25294	−	0.723387i	0.281250	−	0.959635i	$-0.409251\pi$
$601$	30.7163	−	17.7340i	1.25294	−	0.723387i	0.971693	+	0.236248i	$0.0759177\pi$
$602$		0			0
$603$	5.96562	+	5.96562i	0.242939	+	0.242939i
$604$	−0.452204	+	0.121168i	−0.0183999	+	0.00493024i
$605$	−7.87347	+	2.10969i	−0.320102	+	0.0857711i
$606$	15.8932	−	15.8932i	0.645618	−	0.645618i
$607$	22.2647	+	12.8545i	0.903697	+	0.521749i	0.878398	−	0.477930i	$-0.158613\pi$
$607$	22.2647	+	12.8545i	0.903697	+	0.521749i	0.0252989	+	0.999680i	$0.491946\pi$
$608$	0.591182	+	1.02396i	0.0239756	+	0.0415269i
$609$		0			0
$610$			4.51424i			0.182776i
$611$	25.2613	+	25.6599i	1.02196	+	1.03809i
$612$		−	0.0261263i		−	0.00105609i
$613$	−11.8082	+	44.0688i	−0.476928	+	1.77992i	0.137013	+	0.990569i	$0.456250\pi$
$613$	−11.8082	+	44.0688i	−0.476928	+	1.77992i	−0.613941	+	0.789352i	$0.710417\pi$
$614$	−19.6659	+	11.3541i	−0.793649	+	0.458214i
$615$	−1.83718	+	3.18208i	−0.0740821	+	0.128314i
$616$		0			0
$617$	35.5733	−	9.53183i	1.43213	−	0.383737i	0.542357	−	0.840148i	$-0.317532\pi$
$617$	35.5733	−	9.53183i	1.43213	−	0.383737i	0.889769	+	0.456411i	$0.150865\pi$
$618$	−3.90000	−	14.5550i	−0.156881	−	0.585489i
$619$	−3.75724	−	3.75724i	−0.151016	−	0.151016i	0.627556	−	0.778572i	$-0.284056\pi$
$619$	−3.75724	−	3.75724i	−0.151016	−	0.151016i	−0.778572	+	0.627556i	$0.784056\pi$
$620$	−0.0875091	+	0.151570i	−0.00351445	+	0.00608721i
$621$	−19.6545	−	34.0427i	−0.788710	−	1.36609i
$622$	3.90895	−	14.5884i	0.156734	−	0.584941i
$623$		0			0
$624$	−17.4350	−	10.2489i	−0.697957	−	0.410284i
$625$	−18.5478			−0.741914
$626$	−9.66437	−	2.58956i	−0.386266	−	0.103500i
$627$	−11.7910	−	20.4226i	−0.470887	−	0.815601i
$628$	0.762819	−	1.32124i	0.0304398	−	0.0527233i
$629$	−1.11702	+	1.11702i	−0.0445385	+	0.0445385i
$630$		0			0
$631$	−3.50380	−	13.0763i	−0.139484	−	0.520561i	−0.999939	−	0.0110350i	$-0.996487\pi$
$631$	−3.50380	−	13.0763i	−0.139484	−	0.520561i	0.860455	−	0.509526i	$-0.170179\pi$
$632$	0.791277	−	0.791277i	0.0314753	−	0.0314753i
$633$	28.9743	+	16.7283i	1.15162	+	0.664890i
$634$	11.4167	−	6.59143i	0.453415	−	0.261779i
$635$	−3.43325	+	12.8131i	−0.136244	+	0.508471i
$636$	−0.394741			−0.0156525
$637$		0			0
$638$	27.1035			1.07304
$639$	−0.773046	+	2.88505i	−0.0305812	+	0.114131i
$640$	−6.20389	+	3.58182i	−0.245230	+	0.141584i
$641$	−18.5489	−	10.7092i	−0.732638	−	0.422989i	0.0867484	−	0.996230i	$-0.472352\pi$
$641$	−18.5489	−	10.7092i	−0.732638	−	0.422989i	−0.819386	+	0.573241i	$0.805686\pi$
$642$	−5.91911	+	5.91911i	−0.233609	+	0.233609i
$643$	−3.68080	−	13.7369i	−0.145157	−	0.541732i	−0.999748	−	0.0224315i	$-0.992859\pi$
$643$	−3.68080	−	13.7369i	−0.145157	−	0.541732i	0.854592	−	0.519300i	$-0.173807\pi$
$644$		0			0
$645$	−2.69445	+	2.69445i	−0.106094	+	0.106094i
$646$	−1.09980	+	1.90492i	−0.0432712	+	0.0749480i
$647$	10.2738	+	17.7948i	0.403906	+	0.699585i	0.994193	−	0.107608i	$-0.0343191\pi$
$647$	10.2738	+	17.7948i	0.403906	+	0.699585i	−0.590288	+	0.807193i	$0.700986\pi$
$648$	−15.1986	−	4.07246i	−0.597059	−	0.159981i
$649$	−29.5434			−1.15968
$650$	−22.0461	−	6.09261i	−0.864720	−	0.238972i
$651$		0			0
$652$	0.332736	−	1.24179i	0.0130309	−	0.0486321i
$653$	21.8478	+	37.8415i	0.854972	+	1.48085i	0.876671	+	0.481090i	$0.159759\pi$
$653$	21.8478	+	37.8415i	0.854972	+	1.48085i	−0.0216997	+	0.999765i	$0.506908\pi$
$654$	6.20228	−	10.7427i	0.242528	−	0.420072i
$655$	3.59525	+	3.59525i	0.140478	+	0.140478i
$656$	−3.81857	−	14.2511i	−0.149090	−	0.556413i
$657$	0.101608	−	0.0272258i	0.00396411	−	0.00106218i
$658$		0			0
$659$	−6.26381	+	10.8492i	−0.244003	+	0.422626i	−0.961851	−	0.273574i	$-0.911794\pi$
$659$	−6.26381	+	10.8492i	−0.244003	+	0.422626i	0.717848	+	0.696200i	$0.245127\pi$
$660$	−0.249321	+	0.143945i	−0.00970480	+	0.00560307i
$661$	−5.95454	+	22.2227i	−0.231605	+	0.864361i	0.748045	+	0.663648i	$0.230993\pi$
$661$	−5.95454	+	22.2227i	−0.231605	+	0.864361i	−0.979650	+	0.200713i	$0.935674\pi$
$662$		−	8.26081i		−	0.321065i
$663$	−0.0191306	+	2.44367i	−0.000742971	+	0.0949043i
$664$			46.9165i			1.82071i
$665$		0			0
$666$	−2.11917	−	3.67051i	−0.0821163	−	0.142230i
$667$	24.3235	+	14.0432i	0.941809	+	0.543754i
$668$	−0.767106	+	0.767106i	−0.0296802	+	0.0296802i
$669$	−5.18249	+	1.38864i	−0.200367	+	0.0536881i
$670$	−8.37585	+	2.24430i	−0.323587	+	0.0867050i
$671$	−16.6040	−	16.6040i	−0.640991	−	0.640991i
$672$		0			0
$673$	−12.0684	+	6.96769i	−0.465202	+	0.268585i	−0.714229	−	0.699912i	$-0.753223\pi$
$673$	−12.0684	+	6.96769i	−0.465202	+	0.268585i	0.249027	+	0.968497i	$0.419889\pi$
$674$	−21.5756	−	5.78116i	−0.831061	−	0.222682i
$675$	−25.7540			−0.991271
$676$	0.690728	+	0.413344i	0.0265665	+	0.0158979i
$677$		−	51.7651i		−	1.98949i	−0.102360	−	0.994747i	$-0.532639\pi$
$677$		−	51.7651i		−	1.98949i	0.102360	−	0.994747i	$-0.467361\pi$
$678$	−2.16186	−	0.579268i	−0.0830257	−	0.0222467i
$679$		0			0
$680$	0.774399	+	0.447100i	0.0296969	+	0.0171455i
$681$	24.6927	+	24.6927i	0.946227	+	0.946227i
$682$	7.37505	+	27.5240i	0.282405	+	1.05395i
$683$	−7.38605	−	27.5651i	−0.282620	−	1.05475i	−0.950561	−	0.310537i	$-0.899491\pi$
$683$	−7.38605	−	27.5651i	−0.282620	−	1.05475i	0.667942	−	0.744213i	$-0.267175\pi$
$684$	0.133324	+	0.133324i	0.00509779	+	0.00509779i
$685$	−7.59245	−	4.38350i	−0.290092	−	0.167485i
$686$		0			0
$687$	−26.0873	−	6.99008i	−0.995294	−	0.266688i
$688$		−	15.3007i		−	0.583332i
$689$	−15.8677	−	0.124222i	−0.604509	−	0.00473248i
$690$	9.33767			0.355479
$691$	18.0966	+	4.84897i	0.688427	+	0.184463i	0.586041	−	0.810281i	$-0.300686\pi$
$691$	18.0966	+	4.84897i	0.688427	+	0.184463i	0.102386	+	0.994745i	$0.467352\pi$
$692$	0.317488	−	0.183302i	0.0120691	−	0.00696809i
$693$		0			0
$694$	−22.5796	−	22.5796i	−0.857108	−	0.857108i
$695$	11.0703	−	2.96627i	0.419919	−	0.112517i
$696$	16.2188	−	4.34582i	0.614773	−	0.164728i
$697$	−1.26059	+	1.26059i	−0.0477483	+	0.0477483i
$698$	−17.2221	−	9.94320i	−0.651867	−	0.376356i
$699$	3.27559	+	5.67348i	0.123894	+	0.214591i
$700$		0			0
$701$		−	20.1282i		−	0.760231i	−0.924939	−	0.380115i	$-0.875884\pi$
$701$		−	20.1282i		−	0.760231i	0.924939	−	0.380115i	$-0.124116\pi$
$702$	−27.3441	−	7.55676i	−1.03204	−	0.285211i
$703$		−	11.4005i		−	0.429977i
$704$	10.2720	−	38.3358i	0.387142	−	1.44484i
$705$	−8.34072	+	4.81552i	−0.314130	+	0.181363i
$706$	3.23732	−	5.60721i	0.121838	−	0.211030i
$707$		0			0
$708$	−0.530899	+	0.142254i	−0.0199524	+	0.00534623i
$709$	−1.11532	−	4.16243i	−0.0418867	−	0.156323i	0.941815	−	0.336132i	$-0.109119\pi$
$709$	−1.11532	−	4.16243i	−0.0418867	−	0.156323i	−0.983702	+	0.179809i	$0.942452\pi$
$710$	−2.17075	−	2.17075i	−0.0814666	−	0.0814666i
$711$	0.175771	−	0.304444i	0.00659192	−	0.0114175i
$712$	13.8798	+	24.0406i	0.520168	+	0.900958i
$713$	−7.64247	+	28.5221i	−0.286213	+	1.06816i
$714$		0			0
$715$	−10.0674	+	5.70781i	−0.376500	+	0.213460i
$716$	−0.233448			−0.00872435
$717$	−22.0842	−	5.91744i	−0.824749	−	0.220991i
$718$	12.6512	+	21.9125i	0.472138	+	0.817767i
$719$	−15.9230	+	27.5794i	−0.593827	+	1.02854i	0.399884	+	0.916566i	$0.369050\pi$
$719$	−15.9230	+	27.5794i	−0.593827	+	1.02854i	−0.993711	+	0.111973i	$0.964283\pi$
$720$	−1.64387	+	1.64387i	−0.0612635	+	0.0612635i
$721$		0			0
$722$	2.73743	+	10.2162i	0.101877	+	0.380209i
$723$	7.75203	−	7.75203i	0.288301	−	0.288301i
$724$	0.305068	+	0.176131i	0.0113377	+	0.00654585i
$725$	15.9359	−	9.20060i	0.591845	−	0.341702i
$726$	−6.39016	+	23.8484i	−0.237161	+	0.885098i
$727$	−49.3169			−1.82906			−0.914531	−	0.404516i	$-0.867440\pi$
$727$	−49.3169			−1.82906			−0.914531	+	0.404516i	$0.867440\pi$
$728$		0			0
$729$	−29.5035			−1.09272
$730$	−0.0279831	+	0.104434i	−0.00103570	+	0.00386529i
$731$	−1.60112	+	0.924410i	−0.0592197	+	0.0341905i
$732$	−0.378327	−	0.218427i	−0.0139834	−	0.00807329i
$733$	11.5196	−	11.5196i	0.425487	−	0.425487i	−0.461601	−	0.887088i	$-0.652725\pi$
$733$	11.5196	−	11.5196i	0.425487	−	0.425487i	0.887088	+	0.461601i	$0.152725\pi$
$734$	−5.28022	−	19.7061i	−0.194896	−	0.727364i
$735$		0			0
$736$	1.72202	−	1.72202i	0.0634744	−	0.0634744i
$737$	22.5527	−	39.0625i	0.830741	−	1.43888i
$738$	−2.39155	−	4.14229i	−0.0880343	−	0.152480i
$739$	−24.3845	−	6.53382i	−0.897000	−	0.240350i	−0.219273	−	0.975664i	$-0.570368\pi$
$739$	−24.3845	−	6.53382i	−0.897000	−	0.240350i	−0.677727	+	0.735313i	$0.737035\pi$
$740$	−0.139178			−0.00511628
$741$	−12.3726	−	12.5678i	−0.454519	−	0.461691i
$742$		0			0
$743$	2.17652	−	8.12290i	0.0798489	−	0.298000i	−0.914440	−	0.404721i	$-0.867369\pi$
$743$	2.17652	−	8.12290i	0.0798489	−	0.298000i	0.994289	+	0.106721i	$0.0340352\pi$
$744$	8.82649	+	15.2879i	0.323595	+	0.560483i
$745$	1.25252	−	2.16942i	0.0458886	−	0.0794814i
$746$	5.63587	+	5.63587i	0.206344	+	0.206344i
$747$	3.81465	+	14.2365i	0.139571	+	0.520886i
$748$	−0.134921	+	0.0361521i	−0.00493321	+	0.00132185i
$749$		0			0
$750$	6.41526	−	11.1116i	0.234252	−	0.405737i
$751$	−29.6007	+	17.0900i	−1.08015	+	0.623623i	−0.930936	−	0.365183i	$-0.881007\pi$
$751$	−29.6007	+	17.0900i	−1.08015	+	0.623623i	−0.149211	+	0.988805i	$0.547673\pi$
$752$	10.0091	−	37.3543i	0.364993	−	1.36217i
$753$			30.7566i			1.12083i
$754$	19.6195	−	5.09276i	0.714501	−	0.185467i
$755$		−	5.03362i		−	0.183192i
$756$		0			0
$757$	−6.77459	−	11.7339i	−0.246227	−	0.426477i	0.716249	−	0.697845i	$-0.245857\pi$
$757$	−6.77459	−	11.7339i	−0.246227	−	0.426477i	−0.962476	+	0.271368i	$0.912524\pi$
$758$	−1.31983	−	0.762002i	−0.0479382	−	0.0276771i
$759$	−34.3453	+	34.3453i	−1.24666	+	1.24666i
$760$	−6.23340	+	1.67023i	−0.226109	+	0.0605857i
$761$	19.3069	−	5.17326i	0.699873	−	0.187531i	0.108700	−	0.994075i	$-0.465331\pi$
$761$	19.3069	−	5.17326i	0.699873	−	0.187531i	0.591174	+	0.806544i	$0.298665\pi$
$762$	28.4110	+	28.4110i	1.02922	+	1.02922i
$763$		0			0
$764$	0.491608	−	0.283830i	0.0177857	−	0.0102686i
$765$	0.271339	+	0.0727049i	0.00981027	+	0.00262865i
$766$	−0.709908			−0.0256500
$767$	−21.3856	+	5.55120i	−0.772190	+	0.200442i
$768$		−	2.15054i		−	0.0776011i
$769$	30.3963	+	8.14467i	1.09612	+	0.293704i	0.761184	−	0.648536i	$-0.224619\pi$
$769$	30.3963	+	8.14467i	1.09612	+	0.293704i	0.334936	+	0.942241i	$0.391285\pi$
$770$		0			0
$771$	31.6639	+	18.2812i	1.14035	+	0.658381i
$772$	1.11261	+	1.11261i	0.0400438	+	0.0400438i
$773$	−9.91105	−	36.9885i	−0.356476	−	1.33039i	−0.878617	−	0.477527i	$-0.841533\pi$
$773$	−9.91105	−	36.9885i	−0.356476	−	1.33039i	0.522142	−	0.852859i	$-0.325133\pi$
$774$	−1.28384	−	4.79136i	−0.0461467	−	0.172222i
$775$	13.6796	+	13.6796i	0.491386	+	0.491386i
$776$	44.3148	+	25.5852i	1.59081	+	0.918453i
$777$		0			0
$778$	27.6601	+	7.41149i	0.991661	+	0.265715i
$779$		−	12.8658i		−	0.460965i
$780$	−0.153429	+	0.151046i	−0.00549365	+	0.00540830i
$781$	15.9686			0.571403
$782$	4.37614	+	1.17258i	0.156490	+	0.0419315i
$783$	19.7656	−	11.4116i	0.706363	−	0.407819i
$784$		0			0
$785$	11.5992	+	11.5992i	0.413992	+	0.413992i
$786$	14.8758	−	3.98596i	0.530603	−	0.142175i
$787$	21.4436	−	5.74579i	0.764381	−	0.204815i	0.144494	−	0.989506i	$-0.453845\pi$
$787$	21.4436	−	5.74579i	0.764381	−	0.204815i	0.619888	+	0.784690i	$0.287178\pi$
$788$	−0.0628693	+	0.0628693i	−0.00223963	+	0.00223963i
$789$	−0.381401	−	0.220202i	−0.0135782	−	0.00783940i
$790$	0.180660	+	0.312912i	0.00642759	+	0.0111329i
$791$		0			0
$792$		−	12.4795i		−	0.443441i
$793$	−15.1391	−	8.89930i	−0.537605	−	0.316023i
$794$			41.1487i			1.46031i
$795$	1.09850	−	4.09964i	0.0389596	−	0.145399i
$796$	−0.590716	+	0.341050i	−0.0209374	+	0.0120882i
$797$	15.2784	−	26.4630i	0.541189	−	0.937367i	−0.457647	−	0.889134i	$-0.651308\pi$
$797$	15.2784	−	26.4630i	0.541189	−	0.937367i	0.998836	−	0.0482334i	$-0.0153591\pi$
$798$		0			0
$799$	−4.51362	+	1.20942i	−0.159681	+	0.0427863i
$800$	−0.412952	−	1.54116i	−0.0146001	−	0.0544882i
$801$	6.16641	+	6.16641i	0.217879	+	0.217879i
$802$	−4.60285	+	7.97238i	−0.162532	+	0.281514i
$803$	−0.281199	−	0.487050i	−0.00992329	−	0.0171876i
$804$	0.217187	−	0.810552i	0.00765959	−	0.0285860i
$805$		0			0
$806$	10.5104	+	18.5381i	0.370212	+	0.652978i
$807$	−25.9845			−0.914697
$808$	30.9040	+	8.28071i	1.08720	+	0.291314i
$809$	−13.3877	−	23.1882i	−0.470688	−	0.815255i	0.528750	−	0.848778i	$-0.322661\pi$
$809$	−13.3877	−	23.1882i	−0.470688	−	0.815255i	−0.999438	+	0.0335223i	$0.989328\pi$
$810$	2.54027	−	4.39987i	0.0892559	−	0.154596i
$811$	−7.94016	+	7.94016i	−0.278817	+	0.278817i	−0.832637	−	0.553820i	$-0.813170\pi$
$811$	−7.94016	+	7.94016i	−0.278817	+	0.278817i	0.553820	+	0.832637i	$0.313170\pi$
$812$		0			0
$813$	4.86800	+	18.1676i	0.170728	+	0.637167i
$814$	−16.0229	+	16.0229i	−0.561601	+	0.561601i
$815$	11.9708	+	6.91135i	0.419319	+	0.242094i
$816$	2.27293	−	1.31228i	0.0795686	−	0.0459389i
$817$	3.45332	−	12.8880i	0.120817	−	0.450893i
$818$	−3.32716			−0.116331
$819$		0			0
$820$	−0.157067			−0.00548500
$821$	2.37896	−	8.87838i	0.0830261	−	0.309858i	−0.911907	−	0.410397i	$-0.865390\pi$
$821$	2.37896	−	8.87838i	0.0830261	−	0.309858i	0.994933	+	0.100539i	$0.0320568\pi$
$822$	−22.9972	+	13.2774i	−0.802119	+	0.463104i
$823$	29.9975	+	17.3191i	1.04565	+	0.603705i	0.921428	−	0.388550i	$-0.127024\pi$
$823$	29.9975	+	17.3191i	1.04565	+	0.603705i	0.124220	+	0.992255i	$0.460357\pi$
$824$	15.1669	−	15.1669i	0.528366	−	0.528366i
$825$	8.23625	+	30.7381i	0.286750	+	1.07016i
$826$		0			0
$827$	−18.6739	+	18.6739i	−0.649355	+	0.649355i	−0.952837	−	0.303482i	$-0.901851\pi$
$827$	−18.6739	+	18.6739i	−0.649355	+	0.649355i	0.303482	+	0.952837i	$0.401851\pi$
$828$	0.194176	−	0.336323i	0.00674809	−	0.0116880i
$829$	16.3278	+	28.2806i	0.567089	+	0.982228i	0.996852	+	0.0792856i	$0.0252639\pi$
$829$	16.3278	+	28.2806i	0.567089	+	0.982228i	−0.429763	+	0.902942i	$0.641403\pi$
$830$	−14.6325	−	3.92076i	−0.507901	−	0.136092i
$831$	8.99953			0.312190
$832$	0.232357	−	29.6804i	0.00805552	−	1.02898i
$833$		0			0
$834$	8.98470	−	33.5313i	0.311115	−	1.16110i
$835$	−5.83217	−	10.1016i	−0.201831	−	0.349581i
$836$	0.504027	−	0.873000i	0.0174321	−	0.0301933i
$837$	16.9670	+	16.9670i	0.586466	+	0.586466i
$838$	5.48325	+	20.4638i	0.189416	+	0.706909i
$839$	−38.6060	+	10.3444i	−1.33283	+	0.357130i	−0.853768	−	0.520654i	$-0.825688\pi$
$839$	−38.6060	+	10.3444i	−1.33283	+	0.357130i	−0.479058	+	0.877783i	$0.659022\pi$
$840$		0			0
$841$	6.34638	−	10.9922i	0.218841	−	0.379043i
$842$	25.5883	−	14.7734i	0.881833	−	0.509126i
$843$	0.916400	−	3.42005i	0.0315625	−	0.117793i
$844$			1.43016i			0.0492281i
$845$	−6.21502	+	6.02339i	−0.213803	+	0.207211i
$846$		−	12.5372i		−	0.431039i
$847$		0			0
$848$	8.52111	+	14.7590i	0.292616	+	0.506826i
$849$	−22.6007	−	13.0485i	−0.775652	−	0.447823i
$850$	2.09886	−	2.09886i	0.0719903	−	0.0719903i
$851$	−22.6813	+	6.07744i	−0.777505	+	0.208332i
$852$	0.286959	−	0.0768904i	0.00983105	−	0.00263422i
$853$	20.1071	+	20.1071i	0.688454	+	0.688454i	0.961890	−	0.273436i	$-0.0881603\pi$
$853$	20.1071	+	20.1071i	0.688454	+	0.688454i	−0.273436	+	0.961890i	$0.588160\pi$
$854$		0			0
$855$	−1.75568	+	1.01364i	−0.0600429	+	0.0346658i
$856$	−11.5096	−	3.08398i	−0.393389	−	0.105408i
$857$	−13.3280			−0.455276			−0.227638	−	0.973746i	$-0.573100\pi$
$857$	−13.3280			−0.455276			−0.227638	+	0.973746i	$0.573100\pi$
$858$	−0.274415	+	35.0527i	−0.00936837	+	1.19668i
$859$			12.8706i			0.439141i	0.975597	+	0.219570i	$0.0704656\pi$
$859$			12.8706i			0.439141i	−0.975597	+	0.219570i	$0.929534\pi$
$860$	−0.157338	−	0.0421585i	−0.00536517	−	0.00143759i
$861$		0			0
$862$	−36.2193	−	20.9112i	−1.23364	−	0.712240i
$863$	−10.5940	−	10.5940i	−0.360623	−	0.360623i	0.503419	−	0.864042i	$-0.332075\pi$
$863$	−10.5940	−	10.5940i	−0.360623	−	0.360623i	−0.864042	+	0.503419i	$0.832075\pi$
$864$	−0.512191	−	1.91152i	−0.0174251	−	0.0650313i
$865$	1.02019	+	3.80741i	0.0346876	+	0.129456i
$866$	−15.2660	−	15.2660i	−0.518759	−	0.518759i
$867$	21.0512	+	12.1539i	0.714938	+	0.412769i
$868$		0			0
$869$	−1.81543	−	0.486443i	−0.0615842	−	0.0165014i
$870$			5.42155i			0.183808i
$871$	8.98547	−	32.5139i	0.304461	−	1.10169i
$872$	17.6574			0.597954
$873$	15.5273	+	4.16052i	0.525518	+	0.140812i
$874$	−28.3155	+	16.3480i	−0.957787	+	0.552978i
$875$		0			0
$876$	−0.00739838	−	0.00739838i	−0.000249968	−	0.000249968i
$877$	−17.9811	+	4.81802i	−0.607178	+	0.162693i	−0.549292	−	0.835630i	$-0.685103\pi$
$877$	−17.9811	+	4.81802i	−0.607178	+	0.162693i	−0.0578858	+	0.998323i	$0.518436\pi$
$878$	19.4095	−	5.20076i	0.655038	−	0.175517i
$879$	4.64652	−	4.64652i	0.156723	−	0.156723i
$880$	10.7640	+	6.21458i	0.362853	+	0.209494i
$881$	−4.17631	−	7.23358i	−0.140703	−	0.243705i	0.787058	−	0.616879i	$-0.211603\pi$
$881$	−4.17631	−	7.23358i	−0.140703	−	0.243705i	−0.927762	+	0.373173i	$0.878270\pi$
$882$		0			0
$883$			44.6713i			1.50331i	0.659557	+	0.751655i	$0.270744\pi$
$883$			44.6713i			1.50331i	−0.659557	+	0.751655i	$0.729256\pi$
$884$	−0.0908729	+	0.0515212i	−0.00305639	+	0.00173285i
$885$		−	5.90959i		−	0.198649i
$886$	4.49569	−	16.7781i	0.151036	−	0.563672i
$887$	1.68229	−	0.971270i	0.0564858	−	0.0326121i	−0.471491	−	0.881871i	$-0.656284\pi$
$887$	1.68229	−	0.971270i	0.0564858	−	0.0326121i	0.527977	+	0.849259i	$0.322951\pi$
$888$	−7.01899	+	12.1572i	−0.235542	+	0.407971i
$889$		0			0
$890$	−8.65777	+	2.31984i	−0.290209	+	0.0777613i
$891$	6.83989	+	25.5268i	0.229145	+	0.855181i
$892$	−0.162175	−	0.162175i	−0.00543000	−	0.00543000i
$893$	16.8616	−	29.2051i	0.564251	−	0.977312i
$894$	−3.79382	−	6.57108i	−0.126884	−	0.219770i
$895$	0.649644	−	2.42450i	0.0217152	−	0.0810422i
$896$		0			0
$897$	−18.4081	+	31.3151i	−0.614630	+	1.04558i
$898$	38.9943			1.30126
$899$	−16.5602	−	4.43730i	−0.552315	−	0.147992i
$900$	−0.127218	−	0.220347i	−0.00424059	−	0.00734492i
$901$	1.02963	−	1.78337i	0.0343019	−	0.0594127i
$902$	−18.0823	+	18.0823i	−0.602075	+	0.602075i
$903$		0			0
$904$	−0.824563	−	3.07731i	−0.0274246	−	0.102350i
$905$	−2.67818	+	2.67818i	−0.0890258	+	0.0890258i
$906$	−13.2040	−	7.62331i	−0.438672	−	0.253267i
$907$	45.1033	−	26.0404i	1.49763	−	0.864656i	0.497633	−	0.867388i	$-0.334203\pi$
$907$	45.1033	−	26.0404i	1.49763	−	0.864656i	0.999996	+	0.00273135i	$0.000869417\pi$
$908$	−0.386352	+	1.44188i	−0.0128215	+	0.0478506i
$909$	10.0509			0.333367
$910$		0			0
$911$	−48.8065			−1.61703			−0.808516	−	0.588474i	$-0.799729\pi$
$911$	−48.8065			−1.61703			−0.808516	+	0.588474i	$0.799729\pi$
$912$	−4.90229	+	18.2956i	−0.162331	+	0.605828i
$913$	68.2415	−	39.3992i	2.25846	−	1.30392i
$914$	−21.2373	−	12.2614i	−0.702468	−	0.405570i
$915$	3.32132	−	3.32132i	0.109800	−	0.109800i
$916$	−0.298803	−	1.11515i	−0.00987273	−	0.0368455i
$917$		0			0
$918$	2.60325	−	2.60325i	0.0859200	−	0.0859200i
$919$	−3.72510	+	6.45206i	−0.122880	+	0.212834i	−0.920902	−	0.389794i	$-0.872546\pi$
$919$	−3.72510	+	6.45206i	−0.122880	+	0.212834i	0.798022	+	0.602628i	$0.205880\pi$
$920$	6.64588	+	11.5110i	0.219108	+	0.379507i
$921$	22.8227	+	6.11533i	0.752035	+	0.201507i
$922$	−7.51035			−0.247340
$923$	11.5593	−	3.00051i	0.380478	−	0.0987629i
$924$		0			0
$925$	−3.98173	+	14.8600i	−0.130918	+	0.488594i
$926$	−19.1750	−	33.2120i	−0.630128	−	1.09141i
$927$	3.36912	−	5.83549i	0.110656	−	0.191663i
$928$	0.999823	+	0.999823i	0.0328208	+	0.0328208i
$929$	−3.87096	−	14.4466i	−0.127002	−	0.473978i	0.872901	−	0.487897i	$-0.162236\pi$
$929$	−3.87096	−	14.4466i	−0.127002	−	0.473978i	−0.999903	+	0.0139191i	$0.995569\pi$
$930$	−5.50567	+	1.47524i	−0.180538	+	0.0483750i
$931$		0			0
$932$	−0.140021	+	0.242523i	−0.00458653	+	0.00794410i
$933$	−13.6093	+	7.85733i	−0.445548	+	0.257238i
$934$	3.45762	−	12.9040i	0.113137	−	0.422232i
$935$		−	1.50185i		−	0.0491157i
$936$	−2.34491	−	9.03360i	−0.0766457	−	0.295272i
$937$		−	0.823290i		−	0.0268957i	−0.999910	−	0.0134479i	$-0.995719\pi$
$937$		−	0.823290i		−	0.0268957i	0.999910	−	0.0134479i	$-0.00428071\pi$
$938$		0			0
$939$	5.20525	+	9.01576i	0.169867	+	0.294218i
$940$	−0.356538	−	0.205848i	−0.0116290	−	0.00671401i
$941$	17.6405	−	17.6405i	0.575064	−	0.575064i	−0.358475	−	0.933539i	$-0.616703\pi$
$941$	17.6405	−	17.6405i	0.575064	−	0.575064i	0.933539	+	0.358475i	$0.116703\pi$
$942$	47.9931	−	12.8597i	1.56370	−	0.418992i
$943$	−25.5966	+	6.85858i	−0.833539	+	0.223346i
$944$	16.7790	+	16.7790i	0.546111	+	0.546111i
$945$		0			0
$946$	−22.9670	+	13.2600i	−0.746722	+	0.431120i
$947$	−11.9157	−	3.19280i	−0.387207	−	0.103752i	0.0599632	−	0.998201i	$-0.480902\pi$
$947$	−11.9157	−	3.19280i	−0.387207	−	0.103752i	−0.447171	+	0.894449i	$0.647568\pi$
$948$	−0.0349658			−0.00113564
$949$	−0.295069	−	0.299725i	−0.00957834	−	0.00972950i
$950$			21.4213i			0.694998i
$951$	−13.2494	−	3.55016i	−0.429640	−	0.115122i
$952$		0			0
$953$	−17.9140	−	10.3426i	−0.580291	−	0.335031i	0.180958	−	0.983491i	$-0.442080\pi$
$953$	−17.9140	−	10.3426i	−0.580291	−	0.335031i	−0.761249	+	0.648460i	$0.775414\pi$
$954$	3.90676	+	3.90676i	0.126486	+	0.126486i
$955$	1.57970	+	5.89551i	0.0511178	+	0.190774i
$956$	−0.252951	−	0.944026i	−0.00818102	−	0.0305320i
$957$	−19.9413	−	19.9413i	−0.644610	−	0.644610i
$958$	37.3132	+	21.5428i	1.20553	+	0.696016i
$959$		0			0
$960$	7.66836	+	2.05473i	0.247495	+	0.0663161i
$961$			12.9754i			0.418562i
$962$	−8.58782	+	14.6092i	−0.276882	+	0.471020i
$963$	−3.74325			−0.120625
$964$	0.452665	+	0.121291i	0.0145794	+	0.00390653i
$965$	−14.6514	+	8.45899i	−0.471645	+	0.272304i
$966$		0			0
$967$	6.39351	+	6.39351i	0.205601	+	0.205601i	0.802395	−	0.596793i	$-0.203559\pi$
$967$	6.39351	+	6.39351i	0.205601	+	0.205601i	−0.596793	+	0.802395i	$0.703559\pi$
$968$	−33.9472	+	9.09612i	−1.09110	+	0.292360i
$969$	2.21071	−	0.592357i	0.0710181	−	0.0190292i
$970$	−11.6829	+	11.6829i	−0.375116	+	0.375116i
$971$	−14.9575	−	8.63569i	−0.480008	−	0.277133i	0.240412	−	0.970671i	$-0.422717\pi$
$971$	−14.9575	−	8.63569i	−0.480008	−	0.277133i	−0.720420	+	0.693538i	$0.756051\pi$
$972$	−0.279112	−	0.483437i	−0.00895253	−	0.0155062i
$973$		0			0
$974$		−	7.79056i		−	0.249626i
$975$	11.7377	+	20.7029i	0.375907	+	0.663023i
$976$			18.8604i			0.603706i
$977$	−14.0046	+	52.2660i	−0.448048	+	1.67214i	0.259714	+	0.965686i	$0.416372\pi$
$977$	−14.0046	+	52.2660i	−0.448048	+	1.67214i	−0.707761	+	0.706452i	$0.750295\pi$
$978$	36.2591	−	20.9342i	1.15944	−	0.669401i
$979$	23.3118	−	40.3773i	0.745049	−	1.29046i
$980$		0			0
$981$	5.35800	−	1.43567i	0.171068	−	0.0458375i
$982$	4.99738	+	18.6505i	0.159473	+	0.595161i
$983$	26.5265	+	26.5265i	0.846065	+	0.846065i	0.989640	−	0.143574i	$-0.0458596\pi$
$983$	26.5265	+	26.5265i	0.846065	+	0.846065i	−0.143574	+	0.989640i	$0.545860\pi$
$984$	−7.92115	+	13.7198i	−0.252517	+	0.437372i
$985$	−0.477984	−	0.827893i	−0.0152298	−	0.0263789i
$986$	−0.680815	+	2.54083i	−0.0216816	+	0.0809167i
$987$		0			0
$988$	0.200815	−	0.726648i	0.00638876	−	0.0231177i
$989$	−27.4817			−0.873866
$990$	3.89216	+	1.04290i	0.123701	+	0.0331456i
$991$	−17.4270	−	30.1845i	−0.553587	−	0.958841i	−0.998012	−	0.0630250i	$-0.979925\pi$
$991$	−17.4270	−	30.1845i	−0.553587	−	0.958841i	0.444425	−	0.895816i	$-0.353408\pi$
$992$	−0.743276	+	1.28739i	−0.0235990	+	0.0408748i
$993$	−6.07784	+	6.07784i	−0.192874	+	0.192874i
$994$		0			0
$995$	−1.89816	−	7.08404i	−0.0601758	−	0.224579i
$996$	1.03660	−	1.03660i	0.0328459	−	0.0328459i
$997$	13.1836	+	7.61153i	0.417528	+	0.241060i	0.694019	−	0.719957i	$-0.255838\pi$
$997$	13.1836	+	7.61153i	0.417528	+	0.241060i	−0.276491	+	0.961016i	$0.589172\pi$
$998$	11.0233	−	6.36431i	0.348936	−	0.201459i
$999$	−4.93860	+	18.4311i	−0.156250	+	0.583134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bd.b.440.2		28
7.2	even	3		637.2.x.a.570.6		28
7.3	odd	6		637.2.bb.a.362.2		28
7.4	even	3		91.2.ba.a.89.2	yes	28
7.5	odd	6		91.2.w.a.24.6	yes	28
7.6	odd	2		637.2.bd.a.440.2		28
13.6	odd	12		637.2.bd.a.97.2		28
21.5	even	6		819.2.gh.b.388.2		28
21.11	odd	6		819.2.et.b.271.6		28
91.6	even	12	inner	637.2.bd.b.97.2		28
91.19	even	12		91.2.ba.a.45.2	yes	28
91.32	odd	12		91.2.w.a.19.6	✓	28
91.45	even	12		637.2.x.a.19.6		28
91.58	odd	12		637.2.bb.a.227.2		28
273.32	even	12		819.2.gh.b.19.2		28
273.110	odd	12		819.2.et.b.136.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.6	✓	28	91.32	odd	12
91.2.w.a.24.6	yes	28	7.5	odd	6
91.2.ba.a.45.2	yes	28	91.19	even	12
91.2.ba.a.89.2	yes	28	7.4	even	3
637.2.x.a.19.6		28	91.45	even	12
637.2.x.a.570.6		28	7.2	even	3
637.2.bb.a.227.2		28	91.58	odd	12
637.2.bb.a.362.2		28	7.3	odd	6
637.2.bd.a.97.2		28	13.6	odd	12
637.2.bd.a.440.2		28	7.6	odd	2
637.2.bd.b.97.2		28	91.6	even	12	inner
637.2.bd.b.440.2		28	1.1	even	1	trivial
819.2.et.b.136.6		28	273.110	odd	12
819.2.et.b.271.6		28	21.11	odd	6
819.2.gh.b.19.2		28	273.32	even	12
819.2.gh.b.388.2		28	21.5	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.360315 + 1.34471i) q^{2} +(1.25446 - 0.724265i) q^{3} +(0.0536242 + 0.0309600i) q^{4} +(-0.470766 + 0.470766i) q^{5} +(0.521927 + 1.94786i) q^{6} +(-2.02975 + 2.02975i) q^{8} +(-0.450880 + 0.780947i) q^{9} +O(q^{10})\)	\(q+(-0.360315 + 1.34471i) q^{2} +(1.25446 - 0.724265i) q^{3} +(0.0536242 + 0.0309600i) q^{4} +(-0.470766 + 0.470766i) q^{5} +(0.521927 + 1.94786i) q^{6} +(-2.02975 + 2.02975i) q^{8} +(-0.450880 + 0.780947i) q^{9} +(-0.463421 - 0.802669i) q^{10} +(4.65687 + 1.24780i) q^{11} +0.0896929 q^{12} +(3.60544 + 0.0282257i) q^{13} +(-0.249600 + 0.931519i) q^{15} +(-1.93616 - 3.35353i) q^{16} +(-0.233952 + 0.405217i) q^{17} +(-0.887691 - 0.887691i) q^{18} +(-0.873976 - 3.26172i) q^{19} +(-0.0398194 + 0.0106696i) q^{20} +(-3.35587 + 5.81255i) q^{22} +(-6.02331 + 3.47756i) q^{23} +(-1.07617 + 4.01633i) q^{24} +4.55676i q^{25} +(-1.33705 + 4.83811i) q^{26} +5.65182i q^{27} +(-2.01911 - 3.49720i) q^{29} +(-1.16269 - 0.671280i) q^{30} +(3.00205 - 3.00205i) q^{31} +(-0.338214 + 0.0906241i) q^{32} +(6.74561 - 1.80748i) q^{33} +(-0.460604 - 0.460604i) q^{34} +(-0.0483562 + 0.0279185i) q^{36} +(3.26109 + 0.873807i) q^{37} +4.70099 q^{38} +(4.54334 - 2.57589i) q^{39} -1.91108i q^{40} +(3.68025 + 0.986119i) q^{41} +(3.42191 + 1.97564i) q^{43} +(0.211089 + 0.211089i) q^{44} +(-0.155384 - 0.579902i) q^{45} +(-2.50603 - 9.35265i) q^{46} +(7.06171 + 7.06171i) q^{47} +(-4.85769 - 2.80459i) q^{48} +(-6.12753 - 1.64187i) q^{50} +0.677773i q^{51} +(0.192465 + 0.113138i) q^{52} -4.40103 q^{53} +(-7.60007 - 2.03643i) q^{54} +(-2.77972 + 1.60487i) q^{55} +(-3.45872 - 3.45872i) q^{57} +(5.43025 - 1.45503i) q^{58} +(-5.91907 + 1.58601i) q^{59} +(-0.0422244 + 0.0422244i) q^{60} +(-4.21802 - 2.43528i) q^{61} +(2.95521 + 5.11858i) q^{62} -8.23211i q^{64} +(-1.71061 + 1.68403i) q^{65} +9.72217i q^{66} +(2.42145 - 9.03697i) q^{67} +(-0.0250910 + 0.0144863i) q^{68} +(-5.03735 + 8.72495i) q^{69} +(3.19935 - 0.857263i) q^{71} +(-0.669954 - 2.50030i) q^{72} +(-0.0824857 - 0.0824857i) q^{73} +(-2.35004 + 4.07039i) q^{74} +(3.30030 + 5.71629i) q^{75} +(0.0541165 - 0.201966i) q^{76} +(1.82680 + 7.03762i) q^{78} -0.389839 q^{79} +(2.49021 + 0.667250i) q^{80} +(2.74077 + 4.74716i) q^{81} +(-2.65209 + 4.59356i) q^{82} +(11.5572 - 11.5572i) q^{83} +(-0.0806256 - 0.300899i) q^{85} +(-3.88964 + 3.88964i) q^{86} +(-5.06581 - 2.92474i) q^{87} +(-11.9850 + 6.91955i) q^{88} +(2.50295 - 9.34114i) q^{89} +0.835790 q^{90} -0.430661 q^{92} +(1.59168 - 5.94024i) q^{93} +(-12.0404 + 6.95154i) q^{94} +(1.94695 + 1.12407i) q^{95} +(-0.358641 + 0.358641i) q^{96} +(-4.61378 - 17.2188i) q^{97} +(-3.07416 + 3.07416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

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