LMFDB - Embedded newform 637.2.bd.b.97.2

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			97.2
Character	$\chi$	$=$	637.97
Dual form			637.2.bd.b.440.2

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$

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	−0.968212	−	0.250130i	$-0.919527\pi$
$2$	−0.360315	−	1.34471i	−0.254781	−	0.950856i	0.713431	−	0.700725i	$-0.247140\pi$
$3$	1.25446	+	0.724265i	0.724265	+	0.418155i	0.816320	−	0.577599i	$-0.196010\pi$
$3$	1.25446	+	0.724265i	0.724265	+	0.418155i	−0.0920554	+	0.995754i	$0.529344\pi$
$4$	0.0536242	−	0.0309600i	0.0268121	−	0.0154800i
$5$	−0.470766	−	0.470766i	−0.210533	−	0.210533i	0.593961	−	0.804494i	$-0.297563\pi$
$5$	−0.470766	−	0.470766i	−0.210533	−	0.210533i	−0.804494	+	0.593961i	$0.797563\pi$
$6$	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	0.524283	−	0.851544i	$-0.324333\pi$
$11$	4.65687	−	1.24780i	1.40410	−	0.376227i	0.879815	+	0.475317i	$0.157667\pi$
$12$	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	0.836259	−	0.548334i	$-0.184738\pi$
$17$	−0.233952	−	0.405217i	−0.0567417	−	0.0982794i	−0.893001	+	0.450055i	$0.851404\pi$
$18$	−0.887691	+	0.887691i	−0.209231	+	0.209231i
$19$	−0.873976	+	3.26172i	−0.200504	+	0.748290i	0.790269	+	0.612760i	$0.209941\pi$
$19$	−0.873976	+	3.26172i	−0.200504	+	0.748290i	−0.990773	+	0.135531i	$0.956726\pi$
$20$	−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	−0.283663	−	0.958924i	$-0.591550\pi$
$23$	−6.02331	−	3.47756i	−1.25595	−	0.725122i	−0.972284	+	0.233802i	$0.924883\pi$
$24$	−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	−0.990318	−	0.138817i	$-0.955670\pi$
$29$	−2.01911	+	3.49720i	−0.374940	+	0.649414i	0.615378	+	0.788232i	$0.289003\pi$
$30$	−1.16269	+	0.671280i	−0.212277	+	0.122558i
$31$	3.00205	+	3.00205i	0.539184	+	0.539184i	0.923289	−	0.384105i	$-0.125490\pi$
$31$	3.00205	+	3.00205i	0.539184	+	0.539184i	−0.384105	+	0.923289i	$0.625490\pi$
$32$	−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	0.0194074	−	0.999812i	$-0.493822\pi$
$37$	3.26109	−	0.873807i	0.536120	−	0.143653i	0.516713	+	0.856159i	$0.327155\pi$
$38$	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	0.0402801	−	0.999188i	$-0.487175\pi$
$41$	3.68025	−	0.986119i	0.574758	−	0.154006i	0.534478	+	0.845182i	$0.320508\pi$
$42$		0			0
$43$	3.42191	−	1.97564i	0.521836	−	0.301282i	−0.215849	−	0.976427i	$-0.569252\pi$
$43$	3.42191	−	1.97564i	0.521836	−	0.301282i	0.737686	+	0.675144i	$0.235919\pi$
$44$	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	0.0305229	−	0.999534i	$-0.490283\pi$
$47$	7.06171	−	7.06171i	1.03006	−	1.03006i	0.999534	−	0.0305229i	$-0.00971724\pi$
$48$	−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	−0.147962	−	0.988993i	$-0.547271\pi$
$59$	−5.91907	−	1.58601i	−0.770598	−	0.206481i	−0.622635	+	0.782512i	$0.713938\pi$
$60$	−0.0422244	−	0.0422244i	−0.00545114	−	0.00545114i
$61$	−4.21802	+	2.43528i	−0.540062	+	0.311805i	−0.745104	−	0.666948i	$-0.767600\pi$
$61$	−4.21802	+	2.43528i	−0.540062	+	0.311805i	0.205042	+	0.978753i	$0.434267\pi$
$62$	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	0.940558	+	0.339633i	$0.110303\pi$
$67$	2.42145	+	9.03697i	0.295827	+	1.10404i	−0.644731	+	0.764409i	$0.723031\pi$
$68$	−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	0.443617	−	0.896216i	$-0.353695\pi$
$71$	3.19935	+	0.857263i	0.379693	+	0.101738i	−0.0639244	+	0.997955i	$0.520362\pi$
$72$	−0.669954	+	2.50030i	−0.0789548	+	0.294663i
$73$	−0.0824857	+	0.0824857i	−0.00965422	+	0.00965422i	−0.711917	−	0.702263i	$-0.752173\pi$
$73$	−0.0824857	+	0.0824857i	−0.00965422	+	0.00965422i	0.702263	+	0.711917i	$0.252173\pi$
$74$	−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	0.946828	+	0.321741i	$0.104268\pi$
$83$	11.5572	+	11.5572i	1.26857	+	1.26857i	0.321741	+	0.946828i	$0.395732\pi$
$84$		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	0.962059	+	0.272842i	$0.0879636\pi$
$89$	2.50295	+	9.34114i	0.265312	+	0.990159i	−0.696747	+	0.717317i	$0.745370\pi$
$90$	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	0.176705	+	0.984264i	$0.443456\pi$
$97$	−4.61378	+	17.2188i	−0.468458	+	1.74831i	−0.645163	+	0.764045i	$0.723210\pi$
$98$		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	0.443413	+	0.896317i	$0.353767\pi$
$101$	−5.57293	+	9.65259i	−0.554527	+	0.960469i	−0.997940	+	0.0641517i	$0.979566\pi$
$102$	−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	−0.748089	−	0.663598i	$-0.769028\pi$
$107$	2.07553	−	3.59492i	0.200649	−	0.347534i	0.948738	+	0.316065i	$0.102362\pi$
$108$	−0.174980	−	0.303074i	−0.0168375	−	0.0291633i
$109$	−4.34964	+	4.34964i	−0.416620	+	0.416620i	−0.884037	−	0.467417i	$-0.845185\pi$
$109$	−4.34964	+	4.34964i	−0.416620	+	0.416620i	0.467417	+	0.884037i	$0.345185\pi$
$110$	−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	0.838743	−	0.544528i	$-0.183291\pi$
$113$	−0.554932	−	0.961171i	−0.0522036	−	0.0904194i	−0.890946	+	0.454109i	$0.849958\pi$
$114$	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	0.999309	+	0.0371647i	$0.0118326\pi$
$127$	17.2552	+	9.96228i	1.53115	+	0.884009i	0.531840	+	0.846845i	$0.321501\pi$
$128$	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	$0.108272\pi$
$131$			7.63701i			0.667249i	−0.942706	+	0.333625i	$0.891728\pi$
$132$	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	−0.653018	−	0.757343i	$-0.726497\pi$
$137$	3.40822	−	12.7196i	0.291184	−	1.08671i	0.944201	−	0.329369i	$-0.106836\pi$
$138$	−9.91752	+	9.91752i	−0.844236	+	0.844236i
$139$	−14.9082	+	8.60724i	−1.26449	+	0.730056i	−0.973941	−	0.226802i	$-0.927173\pi$
$139$	−14.9082	+	8.60724i	−1.26449	+	0.730056i	−0.290554	+	0.956859i	$0.593839\pi$
$140$		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	0.106854	−	0.994275i	$-0.465922\pi$
$149$	−3.63443	−	0.973843i	−0.297744	−	0.0797804i	−0.404599	+	0.914494i	$0.632589\pi$
$150$	−8.87592	−	2.37829i	−0.724716	−	0.194187i
$151$	−5.34620	−	5.34620i	−0.435067	−	0.435067i	0.455281	−	0.890348i	$-0.349539\pi$
$151$	−5.34620	−	5.34620i	−0.435067	−	0.435067i	−0.890348	+	0.455281i	$0.849539\pi$
$152$	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	$0.441569\pi$
$157$			24.6389i			1.96640i	−0.182537	+	0.983199i	$0.558431\pi$
$158$	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	0.351828	+	0.936065i	$0.385560\pi$
$163$	−5.37364	+	20.0547i	−0.420896	+	1.57081i	−0.772724	+	0.634742i	$0.781107\pi$
$164$	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	−0.885571	−	0.464503i	$-0.846233\pi$
$167$	−4.53457	−	16.9233i	−0.350896	−	1.30956i	0.534676	−	0.845057i	$-0.320434\pi$
$168$		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	0.956340	−	0.292257i	$-0.0944063\pi$
$173$	2.96030	+	5.12740i	0.225068	+	0.389829i	−0.731272	+	0.682086i	$0.761073\pi$
$174$	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	0.372992	−	0.927835i	$-0.378332\pi$
$179$	−3.26505	−	1.88508i	−0.244041	−	0.140897i	−0.617033	+	0.786938i	$0.711665\pi$
$180$	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	0.982840	−	0.184459i	$-0.0590534\pi$
$191$	4.58382	+	7.93941i	0.331674	+	0.574476i	−0.651167	+	0.758935i	$0.725720\pi$
$192$	−5.96223	+	10.3269i	−0.430287	+	0.745278i
$193$	24.5455	−	6.57695i	1.76682	−	0.473419i	0.778742	−	0.627345i	$-0.215858\pi$
$193$	24.5455	−	6.57695i	1.76682	−	0.473419i	0.988082	+	0.153926i	$0.0491917\pi$
$194$	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	0.951422	−	0.307889i	$-0.0996225\pi$
$197$	−0.371638	−	1.38697i	−0.0264781	−	0.0988175i	−0.977900	+	0.209071i	$0.932956\pi$
$198$	−3.02619	+	5.24152i	−0.215062	+	0.372499i
$199$	−5.50792	−	9.53999i	−0.390446	−	0.676272i	0.602062	−	0.798449i	$-0.294346\pi$
$199$	−5.50792	−	9.53999i	−0.390446	−	0.676272i	−0.992508	+	0.122177i	$0.961012\pi$
$200$	−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	−0.127792	−	0.991801i	$-0.540789\pi$
$211$	11.5485	−	20.0025i	0.795029	−	1.37703i	0.922821	−	0.385229i	$-0.125878\pi$
$212$	−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	−0.376613	−	0.926371i	$-0.622911\pi$
$223$	−3.57776	+	0.958657i	−0.239584	+	0.0641964i	0.137029	+	0.990567i	$0.456245\pi$
$224$		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	−0.372433	−	0.928059i	$-0.621476\pi$
$227$	6.23954	−	23.2863i	0.414133	−	1.54556i	0.786566	−	0.617506i	$-0.211857\pi$
$228$	−0.0783894	+	0.292553i	−0.00519147	+	0.0193748i
$229$	−13.1839	+	13.1839i	−0.871216	+	0.871216i	−0.992605	−	0.121389i	$-0.961265\pi$
$229$	−13.1839	+	13.1839i	−0.871216	+	0.871216i	0.121389	+	0.992605i	$0.461265\pi$
$230$	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	$-0.952670\pi$
$233$		−	4.52263i		−	0.296288i	0.988966	−	0.148144i	$-0.0473299\pi$
$234$	−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	−0.968998	−	0.247067i	$-0.920533\pi$
$239$	−11.1608	+	11.1608i	−0.721931	+	0.721931i	0.247067	+	0.968998i	$0.420533\pi$
$240$	3.60714	+	0.966531i	0.232840	+	0.0623893i
$241$	7.31049	+	1.95884i	0.470910	+	0.126180i	0.486467	−	0.873699i	$-0.338285\pi$
$241$	7.31049	+	1.95884i	0.470910	+	0.126180i	−0.0155569	+	0.999879i	$0.504952\pi$
$242$	−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	−0.977874	−	0.209197i	$-0.932915\pi$
$251$	−10.6165	−	18.3883i	−0.670106	−	1.16066i	0.307767	−	0.951462i	$-0.400418\pi$
$252$		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	−0.140403	−	0.990094i	$-0.544840\pi$
$257$	12.6205	−	21.8594i	0.787245	−	1.36355i	0.927648	−	0.373455i	$-0.121827\pi$
$258$	−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	−0.870674	−	0.491860i	$-0.836317\pi$
$263$	−0.152018	+	0.263302i	−0.00937381	+	0.0162359i	0.861300	+	0.508096i	$0.169650\pi$
$264$	−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	−0.892210	−	0.451622i	$-0.850846\pi$
$269$	−15.5352	+	8.96926i	−0.947199	+	0.546865i	−0.0549891	+	0.998487i	$0.517512\pi$
$270$	4.53654	+	2.61917i	0.276085	+	0.159398i
$271$	−3.36065	−	12.5421i	−0.204145	−	0.761879i	−0.989708	−	0.143098i	$-0.954293\pi$
$271$	−3.36065	−	12.5421i	−0.204145	−	0.761879i	0.785563	−	0.618781i	$-0.212373\pi$
$272$	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	−0.329572	−	0.944130i	$-0.606904\pi$
$277$	5.38051	−	3.10644i	0.323283	−	0.186648i	0.652855	+	0.757483i	$0.273571\pi$
$278$	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	0.756779	−	0.653671i	$-0.226772\pi$
$281$	1.72841	+	1.72841i	0.103108	+	0.103108i	−0.653671	+	0.756779i	$0.726772\pi$
$282$	−10.0695	−	17.4409i	−0.599631	−	1.03859i
$283$	−9.00809	+	15.6025i	−0.535475	+	0.927471i	0.463665	+	0.886011i	$0.346534\pi$
$283$	−9.00809	+	15.6025i	−0.535475	+	0.927471i	−0.999140	+	0.0414599i	$0.986799\pi$
$284$	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	0.384532	−	0.923111i	$-0.374363\pi$
$293$	4.38187	+	1.17412i	0.255992	+	0.0685927i	−0.128541	+	0.991704i	$0.541029\pi$
$294$		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	−0.296691	−	0.954973i	$-0.595883\pi$
$307$	11.5340	−	11.5340i	0.658282	−	0.658282i	0.954973	+	0.296691i	$0.0958832\pi$
$308$		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	$-0.934893\pi$
$313$		−	7.18694i		−	0.406230i	0.979155	−	0.203115i	$-0.0651065\pi$
$314$	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	−0.869685	−	0.493606i	$-0.835678\pi$
$317$	−6.69590	+	6.69590i	−0.376079	+	0.376079i	0.493606	+	0.869685i	$0.335678\pi$
$318$	−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	0.0978341	−	0.995203i	$-0.468809\pi$
$331$	−5.73166	−	1.53579i	−0.315040	−	0.0844148i	−0.412875	+	0.910788i	$0.635475\pi$
$332$	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	$-0.856039\pi$
$337$		−	16.0448i		−	0.874014i	0.899458	−	0.437007i	$-0.143961\pi$
$338$	−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	−0.990266	−	0.139187i	$-0.955551\pi$
$347$	−11.4687	−	19.8644i	−0.615673	−	1.06638i	0.374593	−	0.927189i	$-0.377782\pi$
$348$	−0.181100	+	0.313674i	−0.00970798	+	0.0168147i
$349$	−3.69715	−	13.7979i	−0.197904	−	0.738587i	−0.991496	−	0.130137i	$-0.958458\pi$
$349$	−3.69715	−	13.7979i	−0.197904	−	0.738587i	0.793592	−	0.608450i	$-0.208208\pi$
$350$		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	−0.376381	−	0.926465i	$-0.622832\pi$
$353$	−4.49235	+	1.20372i	−0.239104	+	0.0640677i	0.137277	+	0.990533i	$0.456165\pi$
$354$	−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	0.959612	−	0.281326i	$-0.0907741\pi$
$359$	12.8517	+	12.8517i	0.678287	+	0.678287i	−0.281326	+	0.959612i	$0.590774\pi$
$360$	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	0.130746	−	0.991416i	$-0.458263\pi$
$367$	−12.6911	−	7.32723i	−0.662472	−	0.382478i	−0.793218	+	0.608937i	$0.791596\pi$
$368$	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	0.930569	−	0.366115i	$-0.119312\pi$
$373$	2.86259	+	4.95816i	0.148220	+	0.256724i	−0.782350	+	0.622839i	$0.785979\pi$
$374$	−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	0.958267	−	0.285875i	$-0.0922840\pi$
$379$	−0.283332	−	1.05741i	−0.0145538	−	0.0543156i	−0.972821	+	0.231559i	$0.925617\pi$
$380$	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	−0.962472	−	0.271381i	$-0.912520\pi$
$383$	0.131981	−	0.492561i	0.00674393	−	0.0251687i	0.969216	+	0.246213i	$0.0791862\pi$
$384$	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	$0.174611\pi$
$389$			20.5695i			1.04291i	−0.853277	+	0.521457i	$0.825389\pi$
$390$	−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	0.890045	−	0.455874i	$-0.150673\pi$
$397$	28.5505	+	7.65009i	1.43291	+	0.383947i	0.542864	+	0.839820i	$0.317340\pi$
$398$	−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	−0.0957844	−	0.995402i	$-0.530536\pi$
$401$	6.38727	−	1.71146i	0.318965	−	0.0854664i	0.414749	+	0.909936i	$0.363869\pi$
$402$	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	−0.948945	−	0.315441i	$-0.897848\pi$
$409$	0.618563	−	2.30851i	0.0305860	−	0.114148i	0.979531	+	0.201293i	$0.0645142\pi$
$410$	−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	0.786093	−	0.618108i	$-0.212101\pi$
$419$	13.1791	+	7.60897i	0.643842	+	0.371722i	−0.142251	+	0.989831i	$0.545434\pi$
$420$		0			0
$421$	−15.0076	+	15.0076i	−0.731425	+	0.731425i	−0.970902	−	0.239477i	$-0.923024\pi$
$421$	−15.0076	+	15.0076i	−0.731425	+	0.731425i	0.239477	+	0.970902i	$0.423024\pi$
$422$	−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	−0.854037	−	0.520213i	$-0.825853\pi$
$431$	−7.77536	−	29.0180i	−0.374526	−	1.39775i	0.479511	−	0.877536i	$-0.340814\pi$
$432$	18.9536	+	10.9428i	0.911903	+	0.526488i
$433$	−7.75396	−	13.4302i	−0.372631	−	0.645417i	0.617338	−	0.786698i	$-0.288211\pi$
$433$	−7.75396	−	13.4302i	−0.372631	−	0.645417i	−0.989969	+	0.141281i	$0.954878\pi$
$434$		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	−0.985253	−	0.171103i	$-0.945267\pi$
$439$	−7.21696	+	12.5001i	−0.344447	+	0.596599i	0.640806	+	0.767703i	$0.278600\pi$
$440$	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	0.553804	+	0.832647i	$0.313176\pi$
$449$	−7.24956	+	27.0557i	−0.342128	+	1.27684i	−0.895932	+	0.444191i	$0.853491\pi$
$450$	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	−0.986770	−	0.162128i	$-0.948164\pi$
$457$	−4.55910	−	17.0148i	−0.213266	−	0.795919i	0.773504	−	0.633791i	$-0.218502\pi$
$458$	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	−0.925757	−	0.378118i	$-0.876571\pi$
$461$	1.39627	−	5.21097i	0.0650310	−	0.242699i	0.990788	+	0.135419i	$0.0432381\pi$
$462$		0			0
$463$	−19.4789	−	19.4789i	−0.905259	−	0.905259i	0.0906259	−	0.995885i	$-0.471113\pi$
$463$	−19.4789	−	19.4789i	−0.905259	−	0.905259i	−0.995885	+	0.0906259i	$0.971113\pi$
$464$	−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	0.866068	+	0.499927i	$0.166640\pi$
$479$	8.01018	+	29.8944i	0.365994	+	1.36591i	−0.500073	+	0.865983i	$0.666694\pi$
$480$			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	0.134260	−	0.990946i	$-0.457134\pi$
$487$	−5.40538	−	1.44837i	−0.244941	−	0.0656318i	−0.379201	+	0.925314i	$0.623801\pi$
$488$	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	0.745915	−	0.666041i	$-0.232013\pi$
$491$	12.0113	+	6.93474i	0.542063	+	0.312960i	−0.203851	+	0.979002i	$0.565346\pi$
$492$	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	−0.836851	−	0.547430i	$-0.815606\pi$
$499$	−6.46517	+	6.46517i	−0.289421	+	0.289421i	0.547430	+	0.836851i	$0.315606\pi$
$500$	−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	−0.970434	−	0.241369i	$-0.922404\pi$
$503$	−27.9587	+	16.1420i	−1.24662	+	0.719736i	−0.276185	+	0.961104i	$0.589070\pi$
$504$		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	0.00914032	−	0.999958i	$-0.497091\pi$
$509$	11.6648	−	3.12559i	0.517035	−	0.138539i	0.507895	+	0.861419i	$0.330424\pi$
$510$	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	$-0.916996\pi$
$521$		−	11.7697i		−	0.515641i	0.966193	−	0.257821i	$-0.0830043\pi$
$522$	−1.31209	−	4.89678i	−0.0574286	−	0.214326i
$523$	−13.2762	−	7.66503i	−0.580529	−	0.335168i	0.180815	−	0.983517i	$-0.442127\pi$
$523$	−13.2762	−	7.66503i	−0.580529	−	0.335168i	−0.761344	+	0.648349i	$0.775460\pi$
$524$	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	0.440779	−	0.897616i	$-0.354702\pi$
$541$	−10.6257	−	10.6257i	−0.456836	−	0.456836i	−0.897616	+	0.440779i	$0.854702\pi$
$542$	−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	−0.309453	−	0.950915i	$-0.600146\pi$
$557$	−2.40703	+	0.644961i	−0.101989	+	0.0273279i	0.207464	+	0.978243i	$0.433479\pi$
$558$	−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	0.580011	−	0.814609i	$-0.303048\pi$
$563$	−9.85804	−	17.0746i	−0.415467	−	0.719609i	−0.995477	+	0.0949995i	$0.969715\pi$
$564$	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	0.986290	+	0.165023i	$0.0527700\pi$
$569$	38.6991	+	22.3429i	1.62235	+	0.936664i	0.636059	+	0.771640i	$0.280563\pi$
$570$	−1.17336	−	4.37906i	−0.0491468	−	0.183418i
$571$		−	27.5399i		−	1.15251i	−0.817270	−	0.576255i	$-0.804514\pi$
$571$		−	27.5399i		−	1.15251i	0.817270	−	0.576255i	$-0.195486\pi$
$572$	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	0.382436	−	0.923982i	$-0.375085\pi$
$577$	−13.0084	−	13.0084i	−0.541546	−	0.541546i	−0.923982	+	0.382436i	$0.875085\pi$
$578$	−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	−0.649927	−	0.759997i	$-0.725200\pi$
$587$	−20.1767	+	5.40633i	−0.832781	+	0.223143i	−0.182855	+	0.983140i	$0.558534\pi$
$588$		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	−0.823919	−	0.566707i	$-0.808217\pi$
$593$	−6.26353	+	6.26353i	−0.257212	+	0.257212i	0.566707	+	0.823919i	$0.308217\pi$
$594$	−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	0.971693	−	0.236248i	$-0.0759177\pi$
$601$	30.7163	+	17.7340i	1.25294	+	0.723387i	0.281250	+	0.959635i	$0.409251\pi$
$602$		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	0.0252989	−	0.999680i	$-0.491946\pi$
$607$	22.2647	−	12.8545i	0.903697	−	0.521749i	0.878398	+	0.477930i	$0.158613\pi$
$608$	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	−0.613941	−	0.789352i	$-0.710417\pi$
$613$	−11.8082	−	44.0688i	−0.476928	−	1.77992i	0.137013	−	0.990569i	$-0.456250\pi$
$614$	−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	0.889769	−	0.456411i	$-0.150865\pi$
$617$	35.5733	+	9.53183i	1.43213	+	0.383737i	0.542357	+	0.840148i	$0.317532\pi$
$618$	−3.90000	+	14.5550i	−0.156881	+	0.585489i
$619$	−3.75724	+	3.75724i	−0.151016	+	0.151016i	−0.778572	−	0.627556i	$-0.784056\pi$
$619$	−3.75724	+	3.75724i	−0.151016	+	0.151016i	0.627556	+	0.778572i	$0.284056\pi$
$620$	−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	0.860455	+	0.509526i	$0.170179\pi$
$631$	−3.50380	+	13.0763i	−0.139484	+	0.520561i	−0.999939	+	0.0110350i	$0.996487\pi$
$632$	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	−0.819386	−	0.573241i	$-0.805686\pi$
$641$	−18.5489	+	10.7092i	−0.732638	+	0.422989i	0.0867484	+	0.996230i	$0.472352\pi$
$642$	−5.91911	−	5.91911i	−0.233609	−	0.233609i
$643$	−3.68080	+	13.7369i	−0.145157	+	0.541732i	0.854592	+	0.519300i	$0.173807\pi$
$643$	−3.68080	+	13.7369i	−0.145157	+	0.541732i	−0.999748	+	0.0224315i	$0.992859\pi$
$644$		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	−0.590288	−	0.807193i	$-0.700986\pi$
$647$	10.2738	−	17.7948i	0.403906	−	0.699585i	0.994193	+	0.107608i	$0.0343191\pi$
$648$	−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	−0.0216997	−	0.999765i	$-0.506908\pi$
$653$	21.8478	−	37.8415i	0.854972	−	1.48085i	0.876671	−	0.481090i	$-0.159759\pi$
$654$	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	0.717848	−	0.696200i	$-0.245127\pi$
$659$	−6.26381	−	10.8492i	−0.244003	−	0.422626i	−0.961851	+	0.273574i	$0.911794\pi$
$660$	−0.249321	−	0.143945i	−0.00970480	−	0.00560307i
$661$	−5.95454	−	22.2227i	−0.231605	−	0.864361i	−0.979650	−	0.200713i	$-0.935674\pi$
$661$	−5.95454	−	22.2227i	−0.231605	−	0.864361i	0.748045	−	0.663648i	$-0.230993\pi$
$662$			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	0.249027	−	0.968497i	$-0.419889\pi$
$673$	−12.0684	−	6.96769i	−0.465202	−	0.268585i	−0.714229	+	0.699912i	$0.753223\pi$
$674$	−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	$0.467361\pi$
$677$			51.7651i			1.98949i	−0.102360	+	0.994747i	$0.532639\pi$
$678$	−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	0.667942	+	0.744213i	$0.267175\pi$
$683$	−7.38605	+	27.5651i	−0.282620	+	1.05475i	−0.950561	+	0.310537i	$0.899491\pi$
$684$	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	0.102386	−	0.994745i	$-0.467352\pi$
$691$	18.0966	−	4.84897i	0.688427	−	0.184463i	0.586041	+	0.810281i	$0.300686\pi$
$692$	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	$0.124116\pi$
$701$			20.1282i			0.760231i	−0.924939	+	0.380115i	$0.875884\pi$
$702$	−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	−0.983702	−	0.179809i	$-0.942452\pi$
$709$	−1.11532	+	4.16243i	−0.0418867	+	0.156323i	0.941815	+	0.336132i	$0.109119\pi$
$710$	−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	−0.993711	−	0.111973i	$-0.964283\pi$
$719$	−15.9230	−	27.5794i	−0.593827	−	1.02854i	0.399884	−	0.916566i	$-0.369050\pi$
$720$	−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	0.887088	−	0.461601i	$-0.152725\pi$
$733$	11.5196	+	11.5196i	0.425487	+	0.425487i	−0.461601	+	0.887088i	$0.652725\pi$
$734$	−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	−0.677727	−	0.735313i	$-0.737035\pi$
$739$	−24.3845	+	6.53382i	−0.897000	+	0.240350i	−0.219273	+	0.975664i	$0.570368\pi$
$740$	−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	0.994289	−	0.106721i	$-0.0340352\pi$
$743$	2.17652	+	8.12290i	0.0798489	+	0.298000i	−0.914440	+	0.404721i	$0.867369\pi$
$744$	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	−0.149211	−	0.988805i	$-0.547673\pi$
$751$	−29.6007	−	17.0900i	−1.08015	−	0.623623i	−0.930936	+	0.365183i	$0.881007\pi$
$752$	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	−0.962476	−	0.271368i	$-0.912524\pi$
$757$	−6.77459	+	11.7339i	−0.246227	+	0.426477i	0.716249	+	0.697845i	$0.245857\pi$
$758$	−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	0.591174	−	0.806544i	$-0.298665\pi$
$761$	19.3069	+	5.17326i	0.699873	+	0.187531i	0.108700	+	0.994075i	$0.465331\pi$
$762$	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	0.334936	−	0.942241i	$-0.391285\pi$
$769$	30.3963	−	8.14467i	1.09612	−	0.293704i	0.761184	+	0.648536i	$0.224619\pi$
$770$		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	0.522142	+	0.852859i	$0.325133\pi$
$773$	−9.91105	+	36.9885i	−0.356476	+	1.33039i	−0.878617	+	0.477527i	$0.841533\pi$
$774$	−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	0.619888	−	0.784690i	$-0.287178\pi$
$787$	21.4436	+	5.74579i	0.764381	+	0.204815i	0.144494	+	0.989506i	$0.453845\pi$
$788$	−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	0.998836	+	0.0482334i	$0.0153591\pi$
$797$	15.2784	+	26.4630i	0.541189	+	0.937367i	−0.457647	+	0.889134i	$0.651308\pi$
$798$		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	−0.999438	−	0.0335223i	$-0.989328\pi$
$809$	−13.3877	+	23.1882i	−0.470688	+	0.815255i	0.528750	+	0.848778i	$0.322661\pi$
$810$	2.54027	+	4.39987i	0.0892559	+	0.154596i
$811$	−7.94016	−	7.94016i	−0.278817	−	0.278817i	0.553820	−	0.832637i	$-0.313170\pi$
$811$	−7.94016	−	7.94016i	−0.278817	−	0.278817i	−0.832637	+	0.553820i	$0.813170\pi$
$812$		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	0.994933	−	0.100539i	$-0.0320568\pi$
$821$	2.37896	+	8.87838i	0.0830261	+	0.309858i	−0.911907	+	0.410397i	$0.865390\pi$
$822$	−22.9972	−	13.2774i	−0.802119	−	0.463104i
$823$	29.9975	−	17.3191i	1.04565	−	0.603705i	0.124220	−	0.992255i	$-0.460357\pi$
$823$	29.9975	−	17.3191i	1.04565	−	0.603705i	0.921428	+	0.388550i	$0.127024\pi$
$824$	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	0.303482	−	0.952837i	$-0.401851\pi$
$827$	−18.6739	−	18.6739i	−0.649355	−	0.649355i	−0.952837	+	0.303482i	$0.901851\pi$
$828$	0.194176	+	0.336323i	0.00674809	+	0.0116880i
$829$	16.3278	−	28.2806i	0.567089	−	0.982228i	−0.429763	−	0.902942i	$-0.641403\pi$
$829$	16.3278	−	28.2806i	0.567089	−	0.982228i	0.996852	−	0.0792856i	$-0.0252639\pi$
$830$	−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	−0.479058	−	0.877783i	$-0.659022\pi$
$839$	−38.6060	−	10.3444i	−1.33283	−	0.357130i	−0.853768	+	0.520654i	$0.825688\pi$
$840$		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	−0.273436	−	0.961890i	$-0.588160\pi$
$853$	20.1071	−	20.1071i	0.688454	−	0.688454i	0.961890	+	0.273436i	$0.0881603\pi$
$854$		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	$-0.929534\pi$
$859$		−	12.8706i		−	0.439141i	0.975597	−	0.219570i	$-0.0704656\pi$
$860$	−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	−0.864042	−	0.503419i	$-0.832075\pi$
$863$	−10.5940	+	10.5940i	−0.360623	+	0.360623i	0.503419	+	0.864042i	$0.332075\pi$
$864$	−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	−0.0578858	−	0.998323i	$-0.518436\pi$
$877$	−17.9811	−	4.81802i	−0.607178	−	0.162693i	−0.549292	+	0.835630i	$0.685103\pi$
$878$	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	−0.927762	−	0.373173i	$-0.878270\pi$
$881$	−4.17631	+	7.23358i	−0.140703	+	0.243705i	0.787058	+	0.616879i	$0.211603\pi$
$882$		0			0
$883$		−	44.6713i		−	1.50331i	−0.659557	−	0.751655i	$-0.729256\pi$
$883$		−	44.6713i		−	1.50331i	0.659557	−	0.751655i	$-0.270744\pi$
$884$	−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	0.527977	−	0.849259i	$-0.322951\pi$
$887$	1.68229	+	0.971270i	0.0564858	+	0.0326121i	−0.471491	+	0.881871i	$0.656284\pi$
$888$	−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	0.999996	−	0.00273135i	$-0.000869417\pi$
$907$	45.1033	+	26.0404i	1.49763	+	0.864656i	0.497633	+	0.867388i	$0.334203\pi$
$908$	−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	0.798022	−	0.602628i	$-0.205880\pi$
$919$	−3.72510	−	6.45206i	−0.122880	−	0.212834i	−0.920902	+	0.389794i	$0.872546\pi$
$920$	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	−0.999903	−	0.0139191i	$-0.995569\pi$
$929$	−3.87096	+	14.4466i	−0.127002	+	0.473978i	0.872901	+	0.487897i	$0.162236\pi$
$930$	−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	$0.00428071\pi$
$937$			0.823290i			0.0268957i	−0.999910	+	0.0134479i	$0.995719\pi$
$938$		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	0.933539	−	0.358475i	$-0.116703\pi$
$941$	17.6405	+	17.6405i	0.575064	+	0.575064i	−0.358475	+	0.933539i	$0.616703\pi$
$942$	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	−0.447171	−	0.894449i	$-0.647568\pi$
$947$	−11.9157	+	3.19280i	−0.387207	+	0.103752i	0.0599632	+	0.998201i	$0.480902\pi$
$948$	−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	−0.761249	−	0.648460i	$-0.775414\pi$
$953$	−17.9140	+	10.3426i	−0.580291	+	0.335031i	0.180958	+	0.983491i	$0.442080\pi$
$954$	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	−0.596793	−	0.802395i	$-0.703559\pi$
$967$	6.39351	−	6.39351i	0.205601	−	0.205601i	0.802395	+	0.596793i	$0.203559\pi$
$968$	−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	−0.720420	−	0.693538i	$-0.756051\pi$
$971$	−14.9575	+	8.63569i	−0.480008	+	0.277133i	0.240412	+	0.970671i	$0.422717\pi$
$972$	−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	−0.707761	−	0.706452i	$-0.750295\pi$
$977$	−14.0046	−	52.2660i	−0.448048	−	1.67214i	0.259714	−	0.965686i	$-0.416372\pi$
$978$	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	−0.143574	−	0.989640i	$-0.545860\pi$
$983$	26.5265	−	26.5265i	0.846065	−	0.846065i	0.989640	+	0.143574i	$0.0458596\pi$
$984$	−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	0.444425	+	0.895816i	$0.353408\pi$
$991$	−17.4270	+	30.1845i	−0.553587	+	0.958841i	−0.998012	+	0.0630250i	$0.979925\pi$
$992$	−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	−0.276491	−	0.961016i	$-0.589172\pi$
$997$	13.1836	−	7.61153i	0.417528	−	0.241060i	0.694019	+	0.719957i	$0.255838\pi$
$998$	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.97.2		28
7.2	even	3		91.2.ba.a.45.2	yes	28
7.3	odd	6		91.2.w.a.19.6	✓	28
7.4	even	3		637.2.x.a.19.6		28
7.5	odd	6		637.2.bb.a.227.2		28
7.6	odd	2		637.2.bd.a.97.2		28
13.11	odd	12		637.2.bd.a.440.2		28
21.2	odd	6		819.2.et.b.136.6		28
21.17	even	6		819.2.gh.b.19.2		28
91.11	odd	12		637.2.bb.a.362.2		28
91.24	even	12		91.2.ba.a.89.2	yes	28
91.37	odd	12		91.2.w.a.24.6	yes	28
91.76	even	12	inner	637.2.bd.b.440.2		28
91.89	even	12		637.2.x.a.570.6		28
273.128	even	12		819.2.gh.b.388.2		28
273.206	odd	12		819.2.et.b.271.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.6	✓	28	7.3	odd	6
91.2.w.a.24.6	yes	28	91.37	odd	12
91.2.ba.a.45.2	yes	28	7.2	even	3
91.2.ba.a.89.2	yes	28	91.24	even	12
637.2.x.a.19.6		28	7.4	even	3
637.2.x.a.570.6		28	91.89	even	12
637.2.bb.a.227.2		28	7.5	odd	6
637.2.bb.a.362.2		28	91.11	odd	12
637.2.bd.a.97.2		28	7.6	odd	2
637.2.bd.a.440.2		28	13.11	odd	12
637.2.bd.b.97.2		28	1.1	even	1	trivial
637.2.bd.b.440.2		28	91.76	even	12	inner
819.2.et.b.136.6		28	21.2	odd	6
819.2.et.b.271.6		28	273.206	odd	12
819.2.gh.b.19.2		28	21.17	even	6
819.2.gh.b.388.2		28	273.128	even	12

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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