LMFDB - Embedded newform 675.2.l.d.76.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.76"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [30,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			76.1
Character	$\chi$	$=$	675.76
Dual form			675.2.l.d.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.62376 + 1.36249i) q^{2} +(0.235856 - 1.71592i) q^{3} +(0.432902 - 2.45511i) q^{4} +(1.95495 + 3.10759i) q^{6} +(0.0109747 + 0.0622407i) q^{7} +(0.522478 + 0.904959i) q^{8} +(-2.88874 - 0.809420i) q^{9} +(-1.08697 - 0.395623i) q^{11} +(-4.11066 - 1.32188i) q^{12} +(4.71203 + 3.95386i) q^{13} +(-0.102623 - 0.0861109i) q^{14} +(2.60389 + 0.947740i) q^{16} +(1.03593 - 1.79428i) q^{17} +(5.79345 - 2.62160i) q^{18} +(0.296045 + 0.512766i) q^{19} +(0.109388 - 0.00415183i) q^{21} +(2.30400 - 0.838589i) q^{22} +(1.29518 - 7.34532i) q^{23} +(1.67606 - 0.683089i) q^{24} -13.0383 q^{26} +(-2.07023 + 4.76594i) q^{27} +0.157559 q^{28} +(-1.76698 + 1.48267i) q^{29} +(1.49057 - 8.45346i) q^{31} +(-7.48326 + 2.72368i) q^{32} +(-0.935225 + 1.77183i) q^{33} +(0.762600 + 4.32492i) q^{34} +(-3.23776 + 6.74178i) q^{36} +(2.17037 - 3.75919i) q^{37} +(-1.17935 - 0.429247i) q^{38} +(7.89587 - 7.15291i) q^{39} +(-5.08956 - 4.27065i) q^{41} +(-0.171963 + 0.155783i) q^{42} +(-10.3772 - 3.77698i) q^{43} +(-1.44185 + 2.49735i) q^{44} +(7.90491 + 13.6917i) q^{46} +(-1.02536 - 5.81510i) q^{47} +(2.24039 - 4.24453i) q^{48} +(6.57409 - 2.39277i) q^{49} +(-2.83450 - 2.20076i) q^{51} +(11.7470 - 9.85691i) q^{52} -0.617222 q^{53} +(-3.13202 - 10.5594i) q^{54} +(-0.0505913 + 0.0424511i) q^{56} +(0.949687 - 0.387050i) q^{57} +(0.849014 - 4.81500i) q^{58} +(10.3506 - 3.76730i) q^{59} +(-2.06979 - 11.7384i) q^{61} +(9.09747 + 15.7573i) q^{62} +(0.0186757 - 0.188681i) q^{63} +(5.66899 - 9.81898i) q^{64} +(-0.895535 - 4.15127i) q^{66} +(3.61207 + 3.03089i) q^{67} +(-3.95669 - 3.32006i) q^{68} +(-12.2985 - 3.95486i) q^{69} +(-1.42779 + 2.47301i) q^{71} +(-0.776814 - 3.03710i) q^{72} +(-1.45719 - 2.52392i) q^{73} +(1.59772 + 9.06114i) q^{74} +(1.38705 - 0.504846i) q^{76} +(0.0126947 - 0.0719954i) q^{77} +(-3.07517 + 22.3727i) q^{78} +(-3.93760 + 3.30404i) q^{79} +(7.68968 + 4.67641i) q^{81} +14.0830 q^{82} +(2.57261 - 2.15868i) q^{83} +(0.0371612 - 0.270358i) q^{84} +(21.9962 - 8.00594i) q^{86} +(2.12739 + 3.38169i) q^{87} +(-0.209893 - 1.19036i) q^{88} +(5.76784 + 9.99019i) q^{89} +(-0.194378 + 0.336673i) q^{91} +(-17.4729 - 6.35961i) q^{92} +(-14.1539 - 4.55150i) q^{93} +(9.58798 + 8.04527i) q^{94} +(2.90864 + 13.4830i) q^{96} +(12.0991 + 4.40371i) q^{97} +(-7.41460 + 12.8425i) q^{98} +(2.81974 + 2.02267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 9 q^{8} - 3 q^{9} - 6 q^{11} - 3 q^{12} - 3 q^{13} - 9 q^{14} + 12 q^{16} + 12 q^{17} - 6 q^{18} + 24 q^{19} - 36 q^{21} + 51 q^{22} - 18 q^{23} + 45 q^{24} - 18 q^{26} + 9 q^{27} + 60 q^{28}+ \cdots + 123 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 + 9 * q^8 - 3 * q^9 - 6 * q^11 - 3 * q^12 - 3 * q^13 - 9 * q^14 + 12 * q^16 + 12 * q^17 - 6 * q^18 + 24 * q^19 - 36 * q^21 + 51 * q^22 - 18 * q^23 + 45 * q^24 - 18 * q^26 + 9 * q^27 + 60 * q^28 + 18 * q^29 + 12 * q^31 - 36 * q^32 - 27 * q^33 - 69 * q^34 - 42 * q^36 - 24 * q^37 + 24 * q^38 + 6 * q^39 - 75 * q^41 + 18 * q^42 - 6 * q^43 + 12 * q^44 + 30 * q^46 - 45 * q^47 + 27 * q^48 - 36 * q^49 + 21 * q^51 - 30 * q^52 - 36 * q^53 + 18 * q^54 + 30 * q^56 - 30 * q^57 - 27 * q^58 - 27 * q^59 - 12 * q^61 - 36 * q^62 - 18 * q^63 + 27 * q^64 + 78 * q^66 + 30 * q^67 - 69 * q^68 - 117 * q^69 + 12 * q^71 - 9 * q^72 - 21 * q^73 - 30 * q^76 + 36 * q^77 - 66 * q^78 + 54 * q^79 - 27 * q^81 + 48 * q^82 + 87 * q^83 + 45 * q^84 + 18 * q^86 + 27 * q^87 + 18 * q^88 + 9 * q^89 + 51 * q^91 - 24 * q^92 - 36 * q^93 + 15 * q^94 - 15 * q^96 + 75 * q^97 + 15 * q^98 + 123 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	−1.62376	+	1.36249i	−1.14817	+	0.963429i	−0.999675	−	0.0254839i	$-0.991887\pi$
$2$	−1.62376	+	1.36249i	−1.14817	+	0.963429i	−0.148495	+	0.988913i	$0.547443\pi$
$3$	0.235856	−	1.71592i	0.136172	−	0.990685i
$3$	0.235856	−	1.71592i	0.136172	−	0.990685i
$4$	0.432902	−	2.45511i	0.216451	−	1.22755i
$5$		0			0
$5$		0			0
$6$	1.95495	+	3.10759i	0.798107	+	1.26867i
$7$	0.0109747	+	0.0622407i	0.00414805	+	0.0235248i	0.986812	−	0.161873i	$-0.0517536\pi$
$7$	0.0109747	+	0.0622407i	0.00414805	+	0.0235248i	−0.982663	+	0.185398i	$0.940643\pi$
$8$	0.522478	+	0.904959i	0.184724	+	0.319951i
$9$	−2.88874	−	0.809420i	−0.962915	−	0.269807i
$10$		0			0
$11$	−1.08697	−	0.395623i	−0.327733	−	0.119285i	0.172913	−	0.984937i	$-0.444682\pi$
$11$	−1.08697	−	0.395623i	−0.327733	−	0.119285i	−0.500646	+	0.865652i	$0.666904\pi$
$12$	−4.11066	−	1.32188i	−1.18665	−	0.381593i
$13$	4.71203	+	3.95386i	1.30688	+	1.09660i	0.988912	+	0.148504i	$0.0474457\pi$
$13$	4.71203	+	3.95386i	1.30688	+	1.09660i	0.317970	+	0.948101i	$0.396999\pi$
$14$	−0.102623	−	0.0861109i	−0.0274271	−	0.0230141i
$15$		0			0
$16$	2.60389	+	0.947740i	0.650973	+	0.236935i
$17$	1.03593	−	1.79428i	0.251249	−	0.435176i	−0.712621	−	0.701549i	$-0.752492\pi$
$17$	1.03593	−	1.79428i	0.251249	−	0.435176i	0.963870	+	0.266373i	$0.0858253\pi$
$18$	5.79345	−	2.62160i	1.36553	−	0.617916i
$19$	0.296045	+	0.512766i	0.0679175	+	0.117636i	0.897984	−	0.440027i	$-0.145031\pi$
$19$	0.296045	+	0.512766i	0.0679175	+	0.117636i	−0.830067	+	0.557664i	$0.811698\pi$
$20$		0			0
$21$	0.109388	−	0.00415183i	0.0238705	−	0.000906005i
$22$	2.30400	−	0.838589i	0.491216	−	0.178788i
$23$	1.29518	−	7.34532i	0.270063	−	1.53161i	−0.484155	−	0.874982i	$-0.660873\pi$
$23$	1.29518	−	7.34532i	0.270063	−	1.53161i	0.754218	−	0.656624i	$-0.228016\pi$
$24$	1.67606	−	0.683089i	0.342125	−	0.139435i
$25$		0			0
$26$	−13.0383			−2.55702
$27$	−2.07023	+	4.76594i	−0.398415	+	0.917205i
$28$	0.157559			0.0297758
$29$	−1.76698	+	1.48267i	−0.328120	+	0.275325i	−0.791933	−	0.610608i	$-0.790925\pi$
$29$	−1.76698	+	1.48267i	−0.328120	+	0.275325i	0.463814	+	0.885933i	$0.346481\pi$
$30$		0			0
$31$	1.49057	−	8.45346i	0.267715	−	1.51829i	−0.493476	−	0.869759i	$-0.664274\pi$
$31$	1.49057	−	8.45346i	0.267715	−	1.51829i	0.761191	−	0.648528i	$-0.224615\pi$
$32$	−7.48326	+	2.72368i	−1.32287	+	0.481484i
$33$	−0.935225	+	1.77183i	−0.162802	+	0.308437i
$34$	0.762600	+	4.32492i	0.130785	+	0.741717i
$35$		0			0
$36$	−3.23776	+	6.74178i	−0.539626	+	1.12363i
$37$	2.17037	−	3.75919i	0.356807	−	0.618007i	−0.630619	−	0.776093i	$-0.717199\pi$
$37$	2.17037	−	3.75919i	0.356807	−	0.618007i	0.987425	+	0.158085i	$0.0505321\pi$
$38$	−1.17935	−	0.429247i	−0.191315	−	0.0696331i
$39$	7.89587	−	7.15291i	1.26435	−	1.14538i
$40$		0			0
$41$	−5.08956	−	4.27065i	−0.794856	−	0.666963i	0.152086	−	0.988367i	$-0.451401\pi$
$41$	−5.08956	−	4.27065i	−0.794856	−	0.666963i	−0.946942	+	0.321404i	$0.895845\pi$
$42$	−0.171963	+	0.155783i	−0.0265345	+	0.0240378i
$43$	−10.3772	−	3.77698i	−1.58251	−	0.575985i	−0.606758	−	0.794886i	$-0.707530\pi$
$43$	−10.3772	−	3.77698i	−1.58251	−	0.575985i	−0.975747	+	0.218902i	$0.929753\pi$
$44$	−1.44185	+	2.49735i	−0.217367	+	0.376490i
$45$		0			0
$46$	7.90491	+	13.6917i	1.16552	+	2.01873i
$47$	−1.02536	−	5.81510i	−0.149564	−	0.848219i	−0.963589	−	0.267389i	$-0.913839\pi$
$47$	−1.02536	−	5.81510i	−0.149564	−	0.848219i	0.814025	−	0.580830i	$-0.197272\pi$
$48$	2.24039	−	4.24453i	0.323372	−	0.612646i
$49$	6.57409	−	2.39277i	0.939156	−	0.341825i
$50$		0			0
$51$	−2.83450	−	2.20076i	−0.396910	−	0.308168i
$52$	11.7470	−	9.85691i	1.62902	−	1.36691i
$53$	−0.617222			−0.0847820			−0.0423910	−	0.999101i	$-0.513498\pi$
$53$	−0.617222			−0.0847820			−0.0423910	+	0.999101i	$0.513498\pi$
$54$	−3.13202	−	10.5594i	−0.426214	−	1.43695i
$55$		0			0
$56$	−0.0505913	+	0.0424511i	−0.00676054	+	0.00567277i
$57$	0.949687	−	0.387050i	0.125789	−	0.0512661i
$58$	0.849014	−	4.81500i	0.111481	−	0.632240i
$59$	10.3506	−	3.76730i	1.34753	−	0.490460i	0.435353	−	0.900260i	$-0.356624\pi$
$59$	10.3506	−	3.76730i	1.34753	−	0.490460i	0.912175	+	0.409800i	$0.134401\pi$
$60$		0			0
$61$	−2.06979	−	11.7384i	−0.265010	−	1.50295i	−0.769007	−	0.639241i	$-0.779249\pi$
$61$	−2.06979	−	11.7384i	−0.265010	−	1.50295i	0.503997	−	0.863705i	$-0.331862\pi$
$62$	9.09747	+	15.7573i	1.15538	+	2.00118i
$63$	0.0186757	−	0.188681i	0.00235292	−	0.0237715i
$64$	5.66899	−	9.81898i	0.708624	−	1.22737i
$65$		0			0
$66$	−0.895535	−	4.15127i	−0.110233	−	0.510986i
$67$	3.61207	+	3.03089i	0.441285	+	0.370282i	0.836190	−	0.548440i	$-0.184778\pi$
$67$	3.61207	+	3.03089i	0.441285	+	0.370282i	−0.394905	+	0.918722i	$0.629223\pi$
$68$	−3.95669	−	3.32006i	−0.479819	−	0.402616i
$69$	−12.2985	−	3.95486i	−1.48056	−	0.476109i
$70$		0			0
$71$	−1.42779	+	2.47301i	−0.169448	+	0.293493i	−0.938226	−	0.346023i	$-0.887532\pi$
$71$	−1.42779	+	2.47301i	−0.169448	+	0.293493i	0.768778	+	0.639516i	$0.220865\pi$
$72$	−0.776814	−	3.03710i	−0.0915484	−	0.357926i
$73$	−1.45719	−	2.52392i	−0.170551	−	0.295403i	0.768062	−	0.640376i	$-0.221221\pi$
$73$	−1.45719	−	2.52392i	−0.170551	−	0.295403i	−0.938613	+	0.344973i	$0.887888\pi$
$74$	1.59772	+	9.06114i	0.185732	+	1.05334i
$75$		0			0
$76$	1.38705	−	0.504846i	0.159106	−	0.0579098i
$77$	0.0126947	−	0.0719954i	0.00144670	−	0.00820464i
$78$	−3.07517	+	22.3727i	−0.348194	+	2.53321i
$79$	−3.93760	+	3.30404i	−0.443014	+	0.371733i	−0.836836	−	0.547454i	$-0.815597\pi$
$79$	−3.93760	+	3.30404i	−0.443014	+	0.371733i	0.393822	+	0.919187i	$0.371153\pi$
$80$		0			0
$81$	7.68968	+	4.67641i	0.854409	+	0.519602i
$82$	14.0830			1.55520
$83$	2.57261	−	2.15868i	0.282381	−	0.236946i	−0.490585	−	0.871393i	$-0.663217\pi$
$83$	2.57261	−	2.15868i	0.282381	−	0.236946i	0.772966	+	0.634448i	$0.218772\pi$
$84$	0.0371612	−	0.270358i	0.00405462	−	0.0294984i
$85$		0			0
$86$	21.9962	−	8.00594i	2.37191	−	0.863303i
$87$	2.12739	+	3.38169i	0.228080	+	0.362555i
$88$	−0.209893	−	1.19036i	−0.0223747	−	0.126893i
$89$	5.76784	+	9.99019i	0.611390	+	1.05896i	0.991006	+	0.133814i	$0.0427225\pi$
$89$	5.76784	+	9.99019i	0.611390	+	1.05896i	−0.379617	+	0.925144i	$0.623944\pi$
$90$		0			0
$91$	−0.194378	+	0.336673i	−0.0203764	+	0.0352929i
$92$	−17.4729	−	6.35961i	−1.82167	−	0.663035i
$93$	−14.1539	−	4.55150i	−1.46769	−	0.471969i
$94$	9.58798	+	8.04527i	0.988924	+	0.829806i
$95$		0			0
$96$	2.90864	+	13.4830i	0.296862	+	1.37611i
$97$	12.0991	+	4.40371i	1.22848	+	0.447129i	0.873075	−	0.487585i	$-0.162122\pi$
$97$	12.0991	+	4.40371i	1.22848	+	0.447129i	0.355401	+	0.934714i	$0.384344\pi$
$98$	−7.41460	+	12.8425i	−0.748987	+	1.29728i
$99$	2.81974	+	2.02267i	0.283395	+	0.203286i
$100$		0			0
$101$	1.57002	+	8.90402i	0.156223	+	0.885983i	0.957659	+	0.287903i	$0.0929582\pi$
$101$	1.57002	+	8.90402i	0.156223	+	0.885983i	−0.801437	+	0.598080i	$0.795931\pi$
$102$	7.60107	−	0.288498i	0.752618	−	0.0285656i
$103$	13.3270	−	4.85061i	1.31314	−	0.477945i	0.411888	−	0.911234i	$-0.364869\pi$
$103$	13.3270	−	4.85061i	1.31314	−	0.477945i	0.901255	+	0.433289i	$0.142647\pi$
$104$	−1.11615	+	6.33000i	−0.109448	+	0.620708i
$105$		0			0
$106$	1.00222	−	0.840962i	0.0973442	−	0.0816814i
$107$	−20.5665			−1.98824			−0.994118	−	0.108303i	$-0.965458\pi$
$107$	−20.5665			−1.98824			−0.994118	+	0.108303i	$0.965458\pi$
$108$	10.8047	+	7.14581i	1.03968	+	0.687606i
$109$	2.72255			0.260773			0.130386	−	0.991463i	$-0.458378\pi$
$109$	2.72255			0.260773			0.130386	+	0.991463i	$0.458378\pi$
$110$		0			0
$111$	−5.93857	−	4.61081i	−0.563664	−	0.437638i
$112$	−0.0304110	+	0.172469i	−0.00287357	+	0.0162968i
$113$	14.3503	−	5.22307i	1.34996	−	0.491345i	0.437024	−	0.899450i	$-0.356032\pi$
$113$	14.3503	−	5.22307i	1.34996	−	0.491345i	0.912935	+	0.408105i	$0.133810\pi$
$114$	−1.01471	+	1.92242i	−0.0950362	+	0.180051i
$115$		0			0
$116$	2.87519	+	4.97997i	0.266955	+	0.462379i
$117$	−10.4115	−	15.2357i	−0.962545	−	1.40854i
$118$	−11.6739	+	20.2198i	−1.07467	+	1.86138i
$119$	0.123046	+	0.0447851i	0.0112796	+	0.00410545i
$120$		0			0
$121$	−7.40151	−	6.21061i	−0.672865	−	0.564600i
$122$	19.3543	+	16.2402i	1.75226	+	1.47032i
$123$	−8.52848	+	7.72600i	−0.768988	+	0.696630i
$124$	−20.1089	−	7.31904i	−1.80583	−	0.657269i
$125$		0			0
$126$	0.226751	+	0.331817i	0.0202006	+	0.0295606i
$127$	−2.99285	−	5.18376i	−0.265572	−	0.459984i	0.702141	−	0.712038i	$-0.252227\pi$
$127$	−2.99285	−	5.18376i	−0.265572	−	0.459984i	−0.967713	+	0.252053i	$0.918894\pi$
$128$	1.40754	+	7.98255i	0.124410	+	0.705565i
$129$	−8.92852	+	16.9156i	−0.786112	+	1.48933i
$130$		0			0
$131$	0.810965	−	4.59921i	0.0708543	−	0.401835i	−0.928668	−	0.370913i	$-0.879045\pi$
$131$	0.810965	−	4.59921i	0.0708543	−	0.401835i	0.999522	−	0.0309215i	$-0.00984418\pi$
$132$	3.94518	+	3.06311i	0.343384	+	0.266609i
$133$	−0.0286659	+	0.0240535i	−0.00248565	+	0.00208571i
$134$	−9.99470			−0.863410
$135$		0			0
$136$	2.16500			0.185647
$137$	−2.83974	+	2.38282i	−0.242615	+	0.203578i	−0.755985	−	0.654589i	$-0.772842\pi$
$137$	−2.83974	+	2.38282i	−0.242615	+	0.203578i	0.513369	+	0.858168i	$0.328397\pi$
$138$	25.3583	−	10.3349i	2.15864	−	0.879765i
$139$	−1.10921	+	6.29062i	−0.0940816	+	0.533563i	0.900943	+	0.433937i	$0.142876\pi$
$139$	−1.10921	+	6.29062i	−0.0940816	+	0.533563i	−0.995025	+	0.0996265i	$0.968235\pi$
$140$		0			0
$141$	−10.2201	+	0.387903i	−0.860685	+	0.0326673i
$142$	−1.05107	−	5.96094i	−0.0882042	−	0.500231i
$143$	−3.55758	−	6.16191i	−0.297500	−	0.515284i
$144$	−6.75486	−	4.84542i	−0.562905	−	0.403785i
$145$		0			0
$146$	5.80495	+	2.11283i	0.480421	+	0.174859i
$147$	−2.55526	−	11.8450i	−0.210754	−	0.976955i
$148$	−8.28967	−	6.95586i	−0.681406	−	0.571768i
$149$	−11.2316	−	9.42447i	−0.920132	−	0.772083i	0.0538872	−	0.998547i	$-0.482839\pi$
$149$	−11.2316	−	9.42447i	−0.920132	−	0.772083i	−0.974019	+	0.226464i	$0.927283\pi$
$150$		0			0
$151$	−11.1537	−	4.05962i	−0.907676	−	0.330367i	−0.154352	−	0.988016i	$-0.549329\pi$
$151$	−11.1537	−	4.05962i	−0.907676	−	0.330367i	−0.753325	+	0.657649i	$0.771551\pi$
$152$	−0.309355	+	0.535818i	−0.0250920	+	0.0434606i
$153$	−4.44485	+	4.34471i	−0.359345	+	0.351249i
$154$	0.0774802	+	0.134200i	0.00624353	+	0.0108141i
$155$		0			0
$156$	−14.1430	−	22.4817i	−1.13235	−	1.79998i
$157$	−21.4638	+	7.81218i	−1.71300	+	0.623480i	−0.997197	−	0.0748243i	$-0.976160\pi$
$157$	−21.4638	+	7.81218i	−1.71300	+	0.623480i	−0.715801	+	0.698304i	$0.753938\pi$
$158$	1.89197	−	10.7299i	0.150517	−	0.853626i
$159$	−0.145576	+	1.05910i	−0.0115449	+	0.0839923i
$160$		0			0
$161$	0.471392			0.0371509
$162$	−18.8578	+	2.88378i	−1.48161	+	0.226571i
$163$	4.08982			0.320340			0.160170	−	0.987089i	$-0.448796\pi$
$163$	4.08982			0.320340			0.160170	+	0.987089i	$0.448796\pi$
$164$	−12.6882	+	10.6466i	−0.990781	+	0.831364i
$165$		0			0
$166$	−1.23611	+	7.01034i	−0.0959408	+	0.544108i
$167$	6.87588	−	2.50261i	0.532071	−	0.193658i	−0.0619917	−	0.998077i	$-0.519745\pi$
$167$	6.87588	−	2.50261i	0.532071	−	0.193658i	0.594063	+	0.804419i	$0.297523\pi$
$168$	0.0609103	+	0.0968228i	0.00469933	+	0.00747004i
$169$	4.31277	+	24.4590i	0.331752	+	1.88146i
$170$		0			0
$171$	−0.440156	−	1.72087i	−0.0336596	−	0.131598i
$172$	−13.7652	+	23.8420i	−1.04959	+	1.81794i
$173$	17.6451	+	6.42229i	1.34153	+	0.488277i	0.910294	−	0.413961i	$-0.135855\pi$
$173$	17.6451	+	6.42229i	1.34153	+	0.488277i	0.431237	+	0.902239i	$0.358077\pi$
$174$	−8.06189	−	2.59249i	−0.611170	−	0.196536i
$175$		0			0
$176$	−2.45540	−	2.06032i	−0.185082	−	0.155303i
$177$	−4.02312	−	18.6492i	−0.302396	−	1.40176i
$178$	−22.9772	−	8.36300i	−1.72221	−	0.626833i
$179$	5.41651	−	9.38167i	0.404849	−	0.701219i	−0.589455	−	0.807801i	$-0.700657\pi$
$179$	5.41651	−	9.38167i	0.404849	−	0.701219i	0.994304	+	0.106582i	$0.0339908\pi$
$180$		0			0
$181$	8.00831	+	13.8708i	0.595253	+	1.03101i	0.993511	+	0.113735i	$0.0362815\pi$
$181$	8.00831	+	13.8708i	0.595253	+	1.03101i	−0.398258	+	0.917273i	$0.630385\pi$
$182$	−0.143092	−	0.811514i	−0.0106067	−	0.0601534i
$183$	−20.6303	+	0.783022i	−1.52503	+	0.0578826i
$184$	7.32392	−	2.66569i	0.539927	−	0.196517i
$185$		0			0
$186$	29.1839	−	11.8940i	2.13987	−	0.872114i
$187$	−1.83588	+	1.54048i	−0.134253	+	0.112651i
$188$	−14.7206			−1.07361
$189$	−0.319356	−	0.0765476i	−0.0232297	−	0.00556802i
$190$		0			0
$191$	0.840063	−	0.704896i	0.0607848	−	0.0510045i	−0.611889	−	0.790944i	$-0.709590\pi$
$191$	0.840063	−	0.704896i	0.0607848	−	0.0510045i	0.672674	+	0.739939i	$0.265146\pi$
$192$	−15.5115	−	12.0434i	−1.11945	−	0.869157i
$193$	−0.0958856	+	0.543795i	−0.00690200	+	0.0391432i	−0.988064	−	0.154042i	$-0.950771\pi$
$193$	−0.0958856	+	0.543795i	−0.00690200	+	0.0391432i	0.981162	+	0.193185i	$0.0618819\pi$
$194$	−25.6460	+	9.33439i	−1.84128	+	0.670170i
$195$		0			0
$196$	−3.02858	−	17.1759i	−0.216327	−	1.22685i
$197$	7.41735	+	12.8472i	0.528464	+	0.915327i	0.999449	+	0.0331858i	$0.0105653\pi$
$197$	7.41735	+	12.8472i	0.528464	+	0.915327i	−0.470985	+	0.882141i	$0.656101\pi$
$198$	−7.33445	+	0.557561i	−0.521237	+	0.0396242i
$199$	2.77326	−	4.80343i	0.196591	−	0.340506i	−0.750830	−	0.660496i	$-0.770346\pi$
$199$	2.77326	−	4.80343i	0.196591	−	0.340506i	0.947421	+	0.319990i	$0.103679\pi$
$200$		0			0
$201$	6.05268	−	5.48316i	0.426923	−	0.386752i
$202$	−14.6810	−	12.3188i	−1.03295	−	0.866750i
$203$	−0.111675	−	0.0937061i	−0.00783802	−	0.00657688i
$204$	−6.63016	+	6.00630i	−0.464204	+	0.420525i
$205$		0			0
$206$	−15.0308	+	26.0341i	−1.04725	+	1.81388i
$207$	−9.68689	+	20.1704i	−0.673286	+	1.40194i
$208$	8.52239	+	14.7612i	0.590922	+	1.02351i
$209$	−0.118929	−	0.674481i	−0.00822651	−	0.0466549i
$210$		0			0
$211$	−2.70774	+	0.985537i	−0.186409	+	0.0678471i	−0.433538	−	0.901135i	$-0.642735\pi$
$211$	−2.70774	+	0.985537i	−0.186409	+	0.0678471i	0.247129	+	0.968982i	$0.420513\pi$
$212$	−0.267197	+	1.51535i	−0.0183511	+	0.104074i
$213$	3.90673	+	3.03325i	0.267685	+	0.207835i
$214$	33.3950	−	28.0217i	2.28283	−	1.91552i
$215$		0			0
$216$	−5.39463	+	0.616629i	−0.367058	+	0.0419563i
$217$	0.542508			0.0368279
$218$	−4.42076	+	3.70946i	−0.299412	+	0.251236i
$219$	−4.67453	+	1.90513i	−0.315875	+	0.128737i
$220$		0			0
$221$	11.9757	−	4.35878i	0.805569	−	0.293203i
$222$	15.9250	−	0.604433i	1.06882	−	0.0405669i
$223$	1.99412	+	11.3092i	0.133536	+	0.757321i	0.975868	+	0.218361i	$0.0700712\pi$
$223$	1.99412	+	11.3092i	0.133536	+	0.757321i	−0.842332	+	0.538959i	$0.818818\pi$
$224$	−0.251651	−	0.435872i	−0.0168141	−	0.0291229i
$225$		0			0
$226$	−16.1850	+	28.0332i	−1.07661	+	1.86474i
$227$	19.5140	+	7.10252i	1.29519	+	0.471411i	0.895427	−	0.445208i	$-0.146870\pi$
$227$	19.5140	+	7.10252i	1.29519	+	0.471411i	0.399763	+	0.916618i	$0.369092\pi$
$228$	−0.539129	−	2.49914i	−0.0357047	−	0.165510i
$229$	−9.01009	−	7.56037i	−0.595404	−	0.499603i	0.294561	−	0.955633i	$-0.404827\pi$
$229$	−9.01009	−	7.56037i	−0.595404	−	0.499603i	−0.889965	+	0.456030i	$0.849271\pi$
$230$		0			0
$231$	−0.120544	−	0.0387637i	−0.00793122	−	0.00255046i
$232$	−2.26496	−	0.824380i	−0.148702	−	0.0541232i
$233$	−4.00167	+	6.93110i	−0.262158	+	0.454072i	−0.966815	−	0.255477i	$-0.917768\pi$
$233$	−4.00167	+	6.93110i	−0.262158	+	0.454072i	0.704657	+	0.709548i	$0.251101\pi$
$234$	37.6644	+	10.5535i	2.46220	+	0.689902i
$235$		0			0
$236$	−4.76834	−	27.0426i	−0.310393	−	1.76032i
$237$	4.74074	+	7.53587i	0.307944	+	0.489507i
$238$	−0.260817	+	0.0949295i	−0.0169062	+	0.00615337i
$239$	−0.910140	+	5.16166i	−0.0588720	+	0.333880i	−0.999991	−	0.00419508i	$-0.998665\pi$
$239$	−0.910140	+	5.16166i	−0.0588720	+	0.333880i	0.941119	+	0.338075i	$0.109776\pi$
$240$		0			0
$241$	0.901265	−	0.756251i	0.0580556	−	0.0487144i	−0.613298	−	0.789851i	$-0.710158\pi$
$241$	0.901265	−	0.756251i	0.0580556	−	0.0487144i	0.671354	+	0.741137i	$0.265713\pi$
$242$	20.4802			1.31652
$243$	9.83800	−	12.0919i	0.631108	−	0.775695i
$244$	−29.7150			−1.90231
$245$		0			0
$246$	3.32155	−	24.1652i	0.211775	−	1.54072i
$247$	−0.632430	+	3.58669i	−0.0402406	+	0.228216i
$248$	8.42883	−	3.06784i	0.535231	−	0.194808i
$249$	−3.09734	−	4.92352i	−0.196286	−	0.312016i
$250$		0			0
$251$	7.69016	+	13.3198i	0.485399	+	0.840735i	0.999859	−	0.0167787i	$-0.00534107\pi$
$251$	7.69016	+	13.3198i	0.485399	+	0.840735i	−0.514460	+	0.857514i	$0.672008\pi$
$252$	−0.455147	−	0.127531i	−0.0286715	−	0.00803371i
$253$	−4.31380	+	7.47172i	−0.271206	+	0.469743i
$254$	11.9225	+	4.33944i	0.748084	+	0.272280i
$255$		0			0
$256$	4.20911	+	3.53186i	0.263069	+	0.220741i
$257$	−7.27559	−	6.10495i	−0.453839	−	0.380816i	0.387019	−	0.922072i	$-0.373505\pi$
$257$	−7.27559	−	6.10495i	−0.453839	−	0.380816i	−0.840858	+	0.541255i	$0.817949\pi$
$258$	−8.54960	−	39.6318i	−0.532275	−	2.46737i
$259$	0.257794	+	0.0938294i	0.0160185	+	0.00583027i
$260$		0			0
$261$	6.30445	−	2.85283i	0.390236	−	0.176586i
$262$	4.94959	+	8.57294i	0.305787	+	0.529638i
$263$	0.431805	+	2.44889i	0.0266262	+	0.151005i	0.995222	−	0.0976346i	$-0.0311277\pi$
$263$	0.431805	+	2.44889i	0.0266262	+	0.151005i	−0.968596	+	0.248640i	$0.920017\pi$
$264$	−2.09207	+	0.0794046i	−0.128758	+	0.00488701i
$265$		0			0
$266$	0.0137736	−	0.0781142i	0.000844516	−	0.00478949i
$267$	18.5027	−	7.54088i	1.13235	−	0.461495i
$268$	9.00483	−	7.55595i	0.550057	−	0.461553i
$269$	−19.1404			−1.16701			−0.583506	−	0.812109i	$-0.698320\pi$
$269$	−19.1404			−1.16701			−0.583506	+	0.812109i	$0.698320\pi$
$270$		0			0
$271$	−14.2245			−0.864077			−0.432039	−	0.901855i	$-0.642206\pi$
$271$	−14.2245			−0.864077			−0.432039	+	0.901855i	$0.642206\pi$
$272$	4.39795	−	3.69032i	0.266665	−	0.223758i
$273$	0.531857	+	0.412943i	0.0321895	+	0.0249925i
$274$	1.36446	−	7.73826i	0.0824303	−	0.467485i
$275$		0			0
$276$	−15.0337	+	28.4821i	−0.904919	+	1.71442i
$277$	2.34467	+	13.2973i	0.140877	+	0.798956i	0.970585	+	0.240758i	$0.0773959\pi$
$277$	2.34467	+	13.2973i	0.140877	+	0.798956i	−0.829708	+	0.558198i	$0.811493\pi$
$278$	−6.76985	−	11.7257i	−0.406029	−	0.703263i
$279$	−11.1483	+	23.2134i	−0.667431	+	1.38975i
$280$		0			0
$281$	−4.14803	−	1.50976i	−0.247451	−	0.0900648i	0.215317	−	0.976544i	$-0.430921\pi$
$281$	−4.14803	−	1.50976i	−0.247451	−	0.0900648i	−0.462768	+	0.886479i	$0.653144\pi$
$282$	16.0664	−	14.5546i	0.956740	−	0.866717i
$283$	0.974304	+	0.817538i	0.0579163	+	0.0485976i	0.671286	−	0.741198i	$-0.265742\pi$
$283$	0.974304	+	0.817538i	0.0579163	+	0.0485976i	−0.613370	+	0.789796i	$0.710187\pi$
$284$	5.45342	+	4.57596i	0.323601	+	0.271533i
$285$		0			0
$286$	14.1722	+	5.15826i	0.838020	+	0.305014i
$287$	0.209952	−	0.363647i	0.0123931	−	0.0214654i
$288$	23.8218	−	1.81092i	1.40371	−	0.106710i
$289$	6.35371	+	11.0049i	0.373748	+	0.647350i
$290$		0			0
$291$	10.4100	−	19.7224i	0.610248	−	1.15615i
$292$	−6.82732	+	2.48494i	−0.399538	+	0.145420i
$293$	−5.09348	+	28.8865i	−0.297564	+	1.68757i	0.359031	+	0.933326i	$0.383107\pi$
$293$	−5.09348	+	28.8865i	−0.297564	+	1.68757i	−0.656595	+	0.754244i	$0.728004\pi$
$294$	20.2878	+	15.7518i	1.18321	+	0.918664i
$295$		0			0
$296$	4.53589			0.263643
$297$	4.13578	−	4.36138i	0.239982	−	0.253073i
$298$	31.0783			1.80032
$299$	35.1453	−	29.4904i	2.03251	−	1.70548i
$300$		0			0
$301$	0.121196	−	0.687335i	0.00698560	−	0.0396173i
$302$	23.6421	−	8.60503i	1.36045	−	0.495164i
$303$	15.6489	−	0.593952i	0.899003	−	0.0341217i
$304$	0.284902	+	1.61576i	0.0163403	+	0.0926702i
$305$		0			0
$306$	1.29772	−	13.1108i	0.0741858	−	0.749497i
$307$	8.95982	−	15.5189i	0.511364	−	0.885708i	−0.488550	−	0.872536i	$-0.662474\pi$
$307$	8.95982	−	15.5189i	0.511364	−	0.885708i	0.999913	−	0.0131717i	$-0.00419281\pi$
$308$	−0.171261	−	0.0623339i	−0.00975850	−	0.00355180i
$309$	−5.18000	−	24.0120i	−0.294680	−	1.36599i
$310$		0			0
$311$	14.4414	+	12.1178i	0.818895	+	0.687135i	0.952713	−	0.303871i	$-0.0982792\pi$
$311$	14.4414	+	12.1178i	0.818895	+	0.687135i	−0.133818	+	0.991006i	$0.542724\pi$
$312$	10.5985	+	3.40819i	0.600023	+	0.192951i
$313$	−5.39093	−	1.96214i	−0.304713	−	0.110907i	0.185138	−	0.982713i	$-0.440727\pi$
$313$	−5.39093	−	1.96214i	−0.304713	−	0.110907i	−0.489851	+	0.871806i	$0.662949\pi$
$314$	24.2080	−	41.9294i	1.36613	−	2.36621i
$315$		0			0
$316$	6.40717	+	11.0975i	0.360432	+	0.624286i
$317$	0.181646	+	1.03017i	0.0102023	+	0.0578599i	0.989484	−	0.144643i	$-0.0462035\pi$
$317$	0.181646	+	1.03017i	0.0102023	+	0.0578599i	−0.979282	+	0.202503i	$0.935092\pi$
$318$	−1.20664	−	1.91807i	−0.0676651	−	0.107560i
$319$	2.50723	−	0.912555i	0.140378	−	0.0510933i
$320$		0			0
$321$	−4.85073	+	35.2904i	−0.270742	+	1.96972i
$322$	−0.765427	+	0.642270i	−0.0426556	+	0.0357923i
$323$	1.22673			0.0682568
$324$	14.8100	−	16.8546i	0.822776	−	0.936365i
$325$		0			0
$326$	−6.64089	+	5.57236i	−0.367805	+	0.308625i
$327$	0.642130	−	4.67167i	0.0355099	−	0.258344i
$328$	1.20558	−	6.83717i	0.0665668	−	0.377519i
$329$	0.350683	−	0.127638i	0.0193338	−	0.00703692i
$330$		0			0
$331$	−0.0366642	−	0.207933i	−0.00201525	−	0.0114290i	0.983784	−	0.179360i	$-0.0574026\pi$
$331$	−0.0366642	−	0.207933i	−0.00201525	−	0.0114290i	−0.985799	+	0.167931i	$0.946292\pi$
$332$	−4.18610	−	7.25053i	−0.229742	−	0.397925i
$333$	−9.31241	+	9.10260i	−0.510317	+	0.498819i
$334$	−7.75496	+	13.4320i	−0.424333	+	0.734966i
$335$		0			0
$336$	0.288770	+	0.0928608i	0.0157537	+	0.00506597i
$337$	−16.7769	−	14.0775i	−0.913898	−	0.766851i	0.0589586	−	0.998260i	$-0.481222\pi$
$337$	−16.7769	−	14.0775i	−0.913898	−	0.766851i	−0.972857	+	0.231409i	$0.925666\pi$
$338$	−40.3281	−	33.8393i	−2.19356	−	1.84061i
$339$	−5.57775	−	25.8558i	−0.302942	−	1.40429i
$340$		0			0
$341$	−4.96459	+	8.59892i	−0.268848	+	0.465658i
$342$	3.05939	+	2.19457i	0.165433	+	0.118669i
$343$	0.442280	+	0.766051i	0.0238809	+	0.0413629i
$344$	−2.00384	−	11.3643i	−0.108040	−	0.612723i
$345$		0			0
$346$	−37.4017	+	13.6131i	−2.01073	+	0.731845i
$347$	5.00368	−	28.3773i	0.268611	−	1.52337i	−0.489939	−	0.871757i	$-0.662981\pi$
$347$	5.00368	−	28.3773i	0.268611	−	1.52337i	0.758550	−	0.651615i	$-0.225908\pi$
$348$	9.22335	−	3.75903i	0.494424	−	0.201505i
$349$	13.1242	−	11.0125i	0.702521	−	0.589485i	−0.219969	−	0.975507i	$-0.570596\pi$
$349$	13.1242	−	11.0125i	0.702521	−	0.589485i	0.922490	+	0.386022i	$0.126151\pi$
$350$		0			0
$351$	−28.5988	+	14.2719i	−1.52649	+	0.761775i
$352$	9.21160			0.490980
$353$	−1.85957	+	1.56036i	−0.0989747	+	0.0830497i	−0.690932	−	0.722919i	$-0.742800\pi$
$353$	−1.85957	+	1.56036i	−0.0989747	+	0.0830497i	0.591958	+	0.805969i	$0.298355\pi$
$354$	31.9421	+	24.8004i	1.69770	+	1.31813i
$355$		0			0
$356$	27.0239	−	9.83590i	1.43226	−	0.521301i
$357$	0.105869	−	0.200574i	0.00560317	−	0.0106155i
$358$	3.98738	+	22.6135i	0.210739	+	1.19516i
$359$	−4.55147	−	7.88338i	−0.240217	−	0.416069i	0.720559	−	0.693394i	$-0.243885\pi$
$359$	−4.55147	−	7.88338i	−0.240217	−	0.416069i	−0.960776	+	0.277325i	$0.910552\pi$
$360$		0			0
$361$	9.32471	−	16.1509i	0.490774	−	0.850046i
$362$	−31.9024	−	11.6115i	−1.67676	−	0.610289i
$363$	−12.4026	+	11.2356i	−0.650967	+	0.589714i
$364$	0.742421	+	0.622965i	0.0389134	+	0.0326523i
$365$		0			0
$366$	32.4317	−	29.3801i	1.69523	−	1.53572i
$367$	−14.0175	−	5.10194i	−0.731706	−	0.266319i	−0.0508190	−	0.998708i	$-0.516183\pi$
$367$	−14.0175	−	5.10194i	−0.731706	−	0.266319i	−0.680887	+	0.732389i	$0.738405\pi$
$368$	10.3340	−	17.8989i	0.538695	−	0.933047i
$369$	11.2457	+	16.4564i	0.585427	+	0.856686i
$370$		0			0
$371$	−0.00677384	−	0.0384164i	−0.000351680	−	0.00199448i
$372$	−17.3017	+	32.7790i	−0.897050	+	1.69951i
$373$	−18.4154	+	6.70266i	−0.953513	+	0.347050i	−0.771488	−	0.636243i	$-0.780487\pi$
$373$	−18.4154	+	6.70266i	−0.953513	+	0.347050i	−0.182025	+	0.983294i	$0.558265\pi$
$374$	0.882119	−	5.00274i	0.0456133	−	0.258686i
$375$		0			0
$376$	4.72670	−	3.96617i	0.243761	−	0.204540i
$377$	−14.1883			−0.730737
$378$	0.622852	−	0.310826i	0.0320360	−	0.0159871i
$379$	7.13880			0.366696			0.183348	−	0.983048i	$-0.441307\pi$
$379$	7.13880			0.366696			0.183348	+	0.983048i	$0.441307\pi$
$380$		0			0
$381$	−9.60079	+	3.91285i	−0.491863	+	0.200461i
$382$	−0.403641	+	2.28916i	−0.0206521	+	0.117124i
$383$	32.4131	−	11.7974i	1.65623	−	0.602820i	0.666470	−	0.745532i	$-0.267805\pi$
$383$	32.4131	−	11.7974i	1.65623	−	0.602820i	0.989764	+	0.142712i	$0.0455823\pi$
$384$	14.0294	−	0.532485i	0.715934	−	0.0271733i
$385$		0			0
$386$	−0.585222	−	1.01363i	−0.0297870	−	0.0515926i
$387$	26.9198	+	19.3102i	1.36841	+	0.981595i
$388$	16.0493	−	27.7982i	0.814780	−	1.41124i
$389$	9.11176	+	3.31641i	0.461985	+	0.168149i	0.562518	−	0.826785i	$-0.309833\pi$
$389$	9.11176	+	3.31641i	0.461985	+	0.168149i	−0.100533	+	0.994934i	$0.532055\pi$
$390$		0			0
$391$	−11.8378	−	9.93313i	−0.598666	−	0.502340i
$392$	5.60019	+	4.69911i	0.282852	+	0.237341i
$393$	−7.70059	−	2.47630i	−0.388443	−	0.124913i
$394$	−29.5483	−	10.7547i	−1.48862	−	0.541813i
$395$		0			0
$396$	6.18654	−	6.04715i	0.310885	−	0.303881i
$397$	10.0679	+	17.4381i	0.505293	+	0.875193i	0.999981	+	0.00612241i	$0.00194884\pi$
$397$	10.0679	+	17.4381i	0.505293	+	0.875193i	−0.494688	+	0.869070i	$0.664718\pi$
$398$	2.04154	+	11.5782i	0.102333	+	0.580361i
$399$	0.0345128	+	0.0548615i	0.00172780	+	0.00274651i
$400$		0			0
$401$	−2.00191	+	11.3534i	−0.0999706	+	0.566962i	0.893140	+	0.449779i	$0.148497\pi$
$401$	−2.00191	+	11.3534i	−0.0999706	+	0.566962i	−0.993110	+	0.117182i	$0.962614\pi$
$402$	−2.35731	+	17.1501i	−0.117572	+	0.855368i
$403$	40.4475	−	33.9395i	2.01483	−	1.69064i
$404$	22.5400			1.12141
$405$		0			0
$406$	0.309007			0.0153357
$407$	−3.84634	+	3.22747i	−0.190656	+	0.159980i
$408$	0.510629	−	3.71496i	0.0252799	−	0.183918i
$409$	0.783389	−	4.44282i	0.0387361	−	0.219683i	−0.959295	−	0.282406i	$-0.908867\pi$
$409$	0.783389	−	4.44282i	0.0387361	−	0.219683i	0.998031	+	0.0627230i	$0.0199785\pi$
$410$		0			0
$411$	3.41896	+	5.43476i	0.168645	+	0.268077i
$412$	−6.13952	−	34.8189i	−0.302472	−	1.71541i
$413$	0.348074	+	0.602881i	0.0171276	+	0.0296658i
$414$	−11.7529	−	45.9502i	−0.577624	−	2.25833i
$415$		0			0
$416$	−46.0304	−	16.7537i	−2.25683	−	0.821418i
$417$	10.5326	+	3.38699i	0.515782	+	0.165862i
$418$	1.11209	+	0.933154i	0.0543941	+	0.0456421i
$419$	16.6030	+	13.9316i	0.811111	+	0.680603i	0.950873	−	0.309582i	$-0.100189\pi$
$419$	16.6030	+	13.9316i	0.811111	+	0.680603i	−0.139762	+	0.990185i	$0.544634\pi$
$420$		0			0
$421$	19.0158	+	6.92118i	0.926773	+	0.337318i	0.760930	−	0.648834i	$-0.224743\pi$
$421$	19.0158	+	6.92118i	0.926773	+	0.337318i	0.165843	+	0.986152i	$0.446965\pi$
$422$	3.05393	−	5.28955i	0.148663	−	0.257491i
$423$	−1.74486	+	17.6283i	−0.0848380	+	0.857116i
$424$	−0.322485	−	0.558561i	−0.0156613	−	0.0271261i
$425$		0			0
$426$	−10.4764	+	0.397631i	−0.507582	+	0.0192653i
$427$	0.707890	−	0.257651i	0.0342572	−	0.0124686i
$428$	−8.90326	+	50.4929i	−0.430355	+	2.44067i
$429$	−11.4124	+	4.65118i	−0.550996	+	0.224561i
$430$		0			0
$431$	12.2741			0.591224			0.295612	−	0.955308i	$-0.404476\pi$
$431$	12.2741			0.591224			0.295612	+	0.955308i	$0.404476\pi$
$432$	−9.90752	+	10.4480i	−0.476676	+	0.502678i
$433$	−34.5905			−1.66231			−0.831156	−	0.556039i	$-0.812321\pi$
$433$	−34.5905			−1.66231			−0.831156	+	0.556039i	$0.812321\pi$
$434$	−0.880902	+	0.739165i	−0.0422847	+	0.0354810i
$435$		0			0
$436$	1.17860	−	6.68415i	0.0564445	−	0.320113i
$437$	4.14986	−	1.51043i	0.198515	−	0.0722535i
$438$	4.99457	−	9.46248i	0.238650	−	0.452135i
$439$	5.53151	+	31.3708i	0.264005	+	1.49724i	0.771854	+	0.635799i	$0.219329\pi$
$439$	5.53151	+	31.3708i	0.264005	+	1.49724i	−0.507850	+	0.861446i	$0.669559\pi$
$440$		0			0
$441$	−20.9276	+	1.59091i	−0.996554	+	0.0757575i
$442$	−13.5067	+	23.3944i	−0.642450	+	1.11276i
$443$	−1.75440	−	0.638551i	−0.0833543	−	0.0303385i	0.300006	−	0.953937i	$-0.403011\pi$
$443$	−1.75440	−	0.638551i	−0.0833543	−	0.0303385i	−0.383361	+	0.923599i	$0.625233\pi$
$444$	−13.8908	+	12.5838i	−0.659230	+	0.597201i
$445$		0			0
$446$	−18.6467	−	15.6464i	−0.882947	−	0.740880i
$447$	−18.8207	+	17.0498i	−0.890187	+	0.806426i
$448$	0.673356	+	0.245082i	0.0318131	+	0.0115790i
$449$	−11.2063	+	19.4098i	−0.528856	+	0.916006i	0.470577	+	0.882359i	$0.344046\pi$
$449$	−11.2063	+	19.4098i	−0.528856	+	0.916006i	−0.999434	+	0.0336474i	$0.989288\pi$
$450$		0			0
$451$	3.84261	+	6.65560i	0.180942	+	0.313400i
$452$	−6.61094	−	37.4925i	−0.310953	−	1.76350i
$453$	−9.59664	+	18.1814i	−0.450890	+	0.854235i
$454$	−41.3632	+	15.0550i	−1.94127	+	0.706565i
$455$		0			0
$456$	0.846456	+	0.657203i	0.0396389	+	0.0307763i
$457$	12.2376	−	10.2686i	0.572453	−	0.480345i	−0.310006	−	0.950735i	$-0.600331\pi$
$457$	12.2376	−	10.2686i	0.572453	−	0.480345i	0.882459	+	0.470390i	$0.155887\pi$
$458$	24.9312			1.16496
$459$	6.40681	+	8.65173i	0.299044	+	0.403828i
$460$		0			0
$461$	19.0270	−	15.9655i	0.886174	−	0.743588i	−0.0812651	−	0.996693i	$-0.525896\pi$
$461$	19.0270	−	15.9655i	0.886174	−	0.743588i	0.967439	+	0.253104i	$0.0814516\pi$
$462$	0.248550	−	0.101298i	0.0115636	−	0.00471280i
$463$	6.23114	−	35.3386i	0.289586	−	1.64232i	−0.398844	−	0.917019i	$-0.630588\pi$
$463$	6.23114	−	35.3386i	0.289586	−	1.64232i	0.688429	−	0.725303i	$-0.258301\pi$
$464$	−6.00621	+	2.18608i	−0.278831	+	0.101486i
$465$		0			0
$466$	−2.94584	−	16.7067i	−0.136463	−	0.773923i
$467$	−5.20775	−	9.02009i	−0.240986	−	0.417400i	0.720009	−	0.693964i	$-0.244137\pi$
$467$	−5.20775	−	9.02009i	−0.240986	−	0.417400i	−0.960995	+	0.276564i	$0.910804\pi$
$468$	−41.9125	+	18.9658i	−1.93740	+	0.876695i
$469$	−0.149003	+	0.258081i	−0.00688033	+	0.0119171i
$470$		0			0
$471$	8.34269	+	38.6727i	0.384411	+	1.78194i
$472$	8.81719	+	7.39850i	0.405844	+	0.340544i
$473$	9.78538	+	8.21091i	0.449932	+	0.377538i
$474$	−17.9654	−	5.77718i	−0.825178	−	0.265355i
$475$		0			0
$476$	0.163219	−	0.282704i	0.00748114	−	0.0129577i
$477$	1.78300	+	0.499592i	0.0816378	+	0.0228747i
$478$	−5.55489	−	9.62135i	−0.254075	−	0.440070i
$479$	−1.11318	−	6.31318i	−0.0508627	−	0.288457i	0.948758	−	0.316004i	$-0.102341\pi$
$479$	−1.11318	−	6.31318i	−0.0508627	−	0.288457i	−0.999620	+	0.0275476i	$0.991230\pi$
$480$		0			0
$481$	25.0902	−	9.13208i	1.14401	−	0.416387i
$482$	−0.433048	+	2.45594i	−0.0197248	+	0.111865i
$483$	0.111181	−	0.808870i	0.00505891	−	0.0368049i
$484$	−18.4518	+	15.4829i	−0.838720	+	0.703769i
$485$		0			0
$486$	0.500605	+	33.0385i	0.0227079	+	1.49866i
$487$	−15.0810			−0.683385			−0.341692	−	0.939812i	$-0.611000\pi$
$487$	−15.0810			−0.683385			−0.341692	+	0.939812i	$0.611000\pi$
$488$	9.54133	−	8.00613i	0.431916	−	0.362420i
$489$	0.964611	−	7.01780i	0.0436212	−	0.317356i
$490$		0			0
$491$	−21.6911	+	7.89490i	−0.978904	+	0.356292i	−0.781414	−	0.624013i	$-0.785501\pi$
$491$	−21.6911	+	7.89490i	−0.978904	+	0.356292i	−0.197490	+	0.980305i	$0.563279\pi$
$492$	15.2762	+	24.2829i	0.688703	+	1.09476i
$493$	0.829863	+	4.70639i	0.0373752	+	0.211965i
$494$	−3.85993	−	6.68560i	−0.173667	−	0.300799i
$495$		0			0
$496$	11.8930	−	20.5992i	0.534010	−	0.924933i
$497$	−0.169592	−	0.0617263i	−0.00760723	−	0.00276880i
$498$	11.7376	+	3.77450i	0.525975	+	0.169139i
$499$	−2.92703	−	2.45607i	−0.131032	−	0.109949i	0.574917	−	0.818212i	$-0.305035\pi$
$499$	−2.92703	−	2.45607i	−0.131032	−	0.109949i	−0.705948	+	0.708263i	$0.749479\pi$
$500$		0			0
$501$	−2.67256	−	12.3887i	−0.119401	−	0.553486i
$502$	−30.6351	−	11.1503i	−1.36731	−	0.497660i
$503$	−4.25813	+	7.37530i	−0.189861	+	0.328848i	−0.945204	−	0.326481i	$-0.894137\pi$
$503$	−4.25813	+	7.37530i	−0.189861	+	0.328848i	0.755343	+	0.655330i	$0.227470\pi$
$504$	0.180506	−	0.0816808i	0.00804037	−	0.00363835i
$505$		0			0
$506$	−3.17561	−	18.0098i	−0.141173	−	0.800633i
$507$	42.9867	−	1.63156i	1.90911	−	0.0724602i
$508$	−14.0223	+	5.10370i	−0.622139	+	0.226440i
$509$	2.56080	−	14.5230i	0.113506	−	0.643722i	−0.873974	−	0.485973i	$-0.838465\pi$
$509$	2.56080	−	14.5230i	0.113506	−	0.643722i	0.987479	−	0.157749i	$-0.0504236\pi$
$510$		0			0
$511$	0.141098	−	0.118396i	0.00624183	−	0.00523752i
$512$	−27.8581			−1.23117
$513$	−3.05669	+	0.349393i	−0.134956	+	0.0154261i
$514$	20.1318			0.887974
$515$		0			0
$516$	37.6643	+	29.2432i	1.65808	+	1.28736i
$517$	−1.18606	+	6.72647i	−0.0521628	+	0.295830i
$518$	−0.546437	+	0.198887i	−0.0240091	+	0.00873859i
$519$	15.1818	−	28.7628i	0.666408	−	1.26255i
$520$		0			0
$521$	−0.0788938	−	0.136648i	−0.00345640	−	0.00598666i	0.864292	−	0.502990i	$-0.167767\pi$
$521$	−0.0788938	−	0.136648i	−0.00345640	−	0.00598666i	−0.867748	+	0.497004i	$0.834434\pi$
$522$	−6.34994	+	13.2221i	−0.277929	+	0.578715i
$523$	−0.656230	+	1.13662i	−0.0286949	+	0.0497011i	−0.880016	−	0.474944i	$-0.842468\pi$
$523$	−0.656230	+	1.13662i	−0.0286949	+	0.0497011i	0.851321	+	0.524645i	$0.175802\pi$
$524$	−10.9405	−	3.98201i	−0.477937	−	0.173955i
$525$		0			0
$526$	−4.03774	−	3.38807i	−0.176054	−	0.147727i
$527$	−13.6237	−	11.4317i	−0.593459	−	0.497972i
$528$	−4.11446	+	3.72732i	−0.179059	+	0.162211i
$529$	−30.6634	−	11.1606i	−1.33319	−	0.485242i
$530$		0			0
$531$	−32.9494	+	2.50480i	−1.42988	+	0.108699i
$532$	0.0466445	+	0.0807907i	0.00202230	+	0.00350272i
$533$	−7.09661	−	40.2469i	−0.307388	−	1.74328i
$534$	−19.7695	+	37.4544i	−0.855511	+	1.62081i
$535$		0			0
$536$	−0.855600	+	4.85235i	−0.0369563	+	0.209590i
$537$	−14.8207	−	11.5070i	−0.639558	−	0.496564i
$538$	31.0794	−	26.0787i	1.33993	−	1.12433i
$539$	−8.09246			−0.348567
$540$		0			0
$541$	19.1191			0.821995			0.410998	−	0.911636i	$-0.365180\pi$
$541$	19.1191			0.821995			0.410998	+	0.911636i	$0.365180\pi$
$542$	23.0972	−	19.3808i	0.992108	−	0.832477i
$543$	25.6900	−	10.4701i	1.10246	−	0.449314i
$544$	−2.86506	+	16.2486i	−0.122839	+	0.696652i
$545$		0			0
$546$	−1.42624	+	0.0541329i	−0.0610374	+	0.00231668i
$547$	5.42945	+	30.7920i	0.232147	+	1.31657i	0.848540	+	0.529131i	$0.177482\pi$
$547$	5.42945	+	30.7920i	0.232147	+	1.31657i	−0.616394	+	0.787438i	$0.711407\pi$
$548$	4.62076	+	8.00340i	0.197389	+	0.341888i
$549$	−3.52218	+	35.5845i	−0.150323	+	1.51871i
$550$		0			0
$551$	−1.28337	−	0.467108i	−0.0546733	−	0.0198995i
$552$	−2.84671	−	13.1960i	−0.121164	−	0.561657i
$553$	−0.248860	−	0.208818i	−0.0105826	−	0.00887984i
$554$	−21.9246	−	18.3970i	−0.931489	−	0.781612i
$555$		0			0
$556$	14.9640	+	5.44644i	0.634614	+	0.230981i
$557$	−18.4658	+	31.9837i	−0.782422	+	1.35519i	0.148105	+	0.988972i	$0.452682\pi$
$557$	−18.4658	+	31.9837i	−0.782422	+	1.35519i	−0.930527	+	0.366223i	$0.880651\pi$
$558$	−13.5260	−	52.8824i	−0.572601	−	2.23869i
$559$	−33.9639	−	58.8272i	−1.43652	−	2.48813i
$560$		0			0
$561$	2.21034	+	3.51354i	0.0933205	+	0.148342i
$562$	8.79244	−	3.20019i	0.370887	−	0.134992i
$563$	−5.80924	+	32.9458i	−0.244830	+	1.38850i	0.576056	+	0.817410i	$0.304591\pi$
$563$	−5.80924	+	32.9458i	−0.244830	+	1.38850i	−0.820887	+	0.571091i	$0.806520\pi$
$564$	−3.47194	+	25.2593i	−0.146195	+	1.06361i
$565$		0			0
$566$	−2.69592			−0.113318
$567$	−0.206671	+	0.529933i	−0.00867938	+	0.0222551i
$568$	−2.98397			−0.125204
$569$	−18.5935	+	15.6018i	−0.779481	+	0.654062i	−0.943118	−	0.332459i	$-0.892122\pi$
$569$	−18.5935	+	15.6018i	−0.779481	+	0.654062i	0.163637	+	0.986521i	$0.447677\pi$
$570$		0			0
$571$	−5.71582	+	32.4160i	−0.239200	+	1.35657i	0.594387	+	0.804179i	$0.297395\pi$
$571$	−5.71582	+	32.4160i	−0.239200	+	1.35657i	−0.833586	+	0.552389i	$0.813716\pi$
$572$	−16.6682	+	6.06674i	−0.696934	+	0.253663i
$573$	−1.01141	−	1.60773i	−0.0422522	−	0.0671640i
$574$	0.154556	+	0.876533i	0.00645106	+	0.0365858i
$575$		0			0
$576$	−24.3239	+	23.7759i	−1.01350	+	0.990663i
$577$	8.73471	−	15.1290i	0.363631	−	0.629827i	−0.624925	−	0.780685i	$-0.714870\pi$
$577$	8.73471	−	15.1290i	0.363631	−	0.629827i	0.988555	+	0.150858i	$0.0482036\pi$
$578$	−25.3111	−	9.21248i	−1.05280	−	0.383189i
$579$	0.910491	+	0.292789i	0.0378387	+	0.0121679i
$580$		0			0
$581$	0.162591	+	0.136430i	0.00674542	+	0.00566008i
$582$	9.96826	+	46.2080i	0.413198	+	1.91538i
$583$	0.670900	+	0.244188i	0.0277858	+	0.0101132i
$584$	1.52270	−	2.63739i	0.0630096	−	0.109136i
$585$		0			0
$586$	−31.0872	−	53.8446i	−1.28420	−	2.22430i
$587$	−1.98349	−	11.2489i	−0.0818675	−	0.464294i	−0.997989	−	0.0633922i	$-0.979808\pi$
$587$	−1.98349	−	11.2489i	−0.0818675	−	0.464294i	0.916121	−	0.400901i	$-0.131303\pi$
$588$	−30.1868	+	1.14574i	−1.24488	+	0.0472495i
$589$	4.77592	−	1.73829i	0.196788	−	0.0716251i
$590$		0			0
$591$	23.7942	−	9.69746i	0.978763	−	0.398900i
$592$	9.21415	−	7.73159i	0.378699	−	0.317766i
$593$	21.5568			0.885230			0.442615	−	0.896712i	$-0.354051\pi$
$593$	21.5568			0.885230			0.442615	+	0.896712i	$0.354051\pi$
$594$	−0.773148	+	12.7168i	−0.0317227	+	0.521777i
$595$		0			0
$596$	−28.0003	+	23.4950i	−1.14694	+	0.962394i
$597$	−7.58820	−	5.89161i	−0.310564	−	0.241127i
$598$	−16.8870	+	95.7707i	−0.690559	+	3.91635i
$599$	9.12886	−	3.32263i	0.372995	−	0.135759i	−0.148719	−	0.988880i	$-0.547515\pi$
$599$	9.12886	−	3.32263i	0.372995	−	0.135759i	0.521714	+	0.853120i	$0.325293\pi$
$600$		0			0
$601$	−4.26938	−	24.2129i	−0.174152	−	0.987663i	−0.939118	−	0.343594i	$-0.888356\pi$
$601$	−4.26938	−	24.2129i	−0.174152	−	0.987663i	0.764967	−	0.644070i	$-0.222755\pi$
$602$	0.739697	+	1.28119i	0.0301478	+	0.0522175i
$603$	−7.98109	−	11.6791i	−0.325015	−	0.475611i
$604$	−14.7953	+	25.6261i	−0.602011	+	1.04271i
$605$		0			0
$606$	−24.6007	+	22.2859i	−0.999335	+	0.905304i
$607$	0.351918	+	0.295294i	0.0142839	+	0.0119856i	0.649902	−	0.760018i	$-0.274810\pi$
$607$	0.351918	+	0.295294i	0.0142839	+	0.0119856i	−0.635618	+	0.772004i	$0.719255\pi$
$608$	−3.61199	−	3.03082i	−0.146486	−	0.122916i
$609$	−0.187131	+	0.169523i	−0.00758293	+	0.00686943i
$610$		0			0
$611$	18.1606	−	31.4551i	0.734699	−	1.27254i
$612$	8.74255	+	12.7934i	0.353396	+	0.517144i
$613$	−14.2020	−	24.5986i	−0.573613	−	0.993527i	−0.996191	−	0.0872001i	$-0.972208\pi$
$613$	−14.2020	−	24.5986i	−0.573613	−	0.993527i	0.422578	−	0.906327i	$-0.361125\pi$
$614$	6.59579	+	37.4066i	0.266184	+	1.50961i
$615$		0			0
$616$	0.0717856	−	0.0261278i	0.00289233	−	0.00105272i
$617$	2.19222	−	12.4327i	0.0882553	−	0.500520i	−0.908351	−	0.418208i	$-0.862658\pi$
$617$	2.19222	−	12.4327i	0.0882553	−	0.500520i	0.996607	−	0.0823125i	$-0.0262306\pi$
$618$	41.1273	+	31.9319i	1.65438	+	1.28449i
$619$	−6.34778	+	5.32642i	−0.255139	+	0.214087i	−0.761381	−	0.648304i	$-0.775479\pi$
$619$	−6.34778	+	5.32642i	−0.255139	+	0.214087i	0.506243	+	0.862391i	$0.331034\pi$
$620$		0			0
$621$	32.3260	+	21.3792i	1.29720	+	0.857919i
$622$	−39.9597			−1.60224
$623$	−0.558496	+	0.468634i	−0.0223757	+	0.0187754i
$624$	27.3391	−	11.1422i	1.09444	−	0.446045i
$625$		0			0
$626$	11.4270	−	4.15908i	0.456714	−	0.166230i
$627$	−1.18540	+	0.0449920i	−0.0473405	+	0.00179681i
$628$	9.88804	+	56.0778i	0.394576	+	2.23775i
$629$	−4.49669	−	7.78850i	−0.179295	−	0.310548i
$630$		0			0
$631$	14.5655	−	25.2281i	0.579842	−	1.00432i	−0.415655	−	0.909522i	$-0.636448\pi$
$631$	14.5655	−	25.2281i	0.579842	−	1.00432i	0.995497	−	0.0947935i	$-0.0302191\pi$
$632$	−5.04733	−	1.83708i	−0.200772	−	0.0730750i
$633$	1.05246	+	4.87870i	0.0418316	+	0.193911i
$634$	−1.69854	−	1.42525i	−0.0674578	−	0.0566038i
$635$		0			0
$636$	2.53719	+	0.815892i	0.100606	+	0.0323522i
$637$	40.4380	+	14.7182i	1.60221	+	0.583158i
$638$	−2.82778	+	4.89785i	−0.111953	+	0.193908i
$639$	6.12624	−	5.98821i	0.242350	−	0.236890i
$640$		0			0
$641$	−1.01054	−	5.73104i	−0.0399138	−	0.226362i	0.958325	−	0.285679i	$-0.0922190\pi$
$641$	−1.01054	−	5.73104i	−0.0399138	−	0.226362i	−0.998239	+	0.0593164i	$0.981108\pi$
$642$	−40.2065	−	63.9121i	−1.58682	−	2.52241i
$643$	13.0877	−	4.76353i	0.516128	−	0.187855i	−0.0708056	−	0.997490i	$-0.522557\pi$
$643$	13.0877	−	4.76353i	0.516128	−	0.187855i	0.586934	+	0.809635i	$0.300335\pi$
$644$	0.204067	−	1.15732i	0.00804135	−	0.0456048i
$645$		0			0
$646$	−1.99191	+	1.67141i	−0.0783705	+	0.0657606i
$647$	12.0852			0.475119			0.237559	−	0.971373i	$-0.423653\pi$
$647$	12.0852			0.475119			0.237559	+	0.971373i	$0.423653\pi$
$648$	−0.214273	+	9.40217i	−0.00841744	+	0.369352i
$649$	−12.7411			−0.500133
$650$		0			0
$651$	0.127954	−	0.930899i	0.00501491	−	0.0364848i
$652$	1.77049	−	10.0410i	0.0693378	−	0.393234i
$653$	−22.4836	+	8.18336i	−0.879851	+	0.320240i	−0.742150	−	0.670234i	$-0.766194\pi$
$653$	−22.4836	+	8.18336i	−0.879851	+	0.320240i	−0.137701	+	0.990474i	$0.543971\pi$
$654$	5.32246	+	8.46056i	0.208125	+	0.330834i
$655$		0			0
$656$	−9.20521	−	15.9439i	−0.359403	−	0.622504i
$657$	2.16653	+	8.47044i	0.0845242	+	0.330463i
$658$	−0.395518	+	0.685057i	−0.0154189	+	0.0267063i
$659$	12.1165	+	4.41004i	0.471991	+	0.171791i	0.567054	−	0.823681i	$-0.308083\pi$
$659$	12.1165	+	4.41004i	0.471991	+	0.171791i	−0.0950632	+	0.995471i	$0.530305\pi$
$660$		0			0
$661$	−14.3143	−	12.0111i	−0.556761	−	0.467178i	0.320462	−	0.947261i	$-0.396162\pi$
$661$	−14.3143	−	12.0111i	−0.556761	−	0.467178i	−0.877223	+	0.480083i	$0.840606\pi$
$662$	0.342842	+	0.287678i	0.0133249	+	0.0111809i
$663$	−4.65477	−	21.5773i	−0.180776	−	0.837992i
$664$	3.29765	+	1.20025i	0.127974	+	0.0465786i
$665$		0			0
$666$	2.71885	−	27.4685i	0.105353	−	1.06438i
$667$	8.60215	+	14.8994i	0.333076	+	0.576905i
$668$	−3.16761	−	17.9644i	−0.122558	−	0.695064i
$669$	19.8760	−	0.754393i	0.768450	−	0.0291665i
$670$		0			0
$671$	−2.39418	+	13.5781i	−0.0924264	+	0.524176i
$672$	−0.807273	+	0.329009i	−0.0311412	+	0.0126918i
$673$	−21.8080	+	18.2991i	−0.840637	+	0.705378i	−0.957707	−	0.287746i	$-0.907094\pi$
$673$	−21.8080	+	18.2991i	−0.840637	+	0.705378i	0.117070	+	0.993124i	$0.462650\pi$
$674$	46.4222			1.78812
$675$		0			0
$676$	61.9164			2.38140
$677$	−14.4949	+	12.1627i	−0.557085	+	0.467450i	−0.877332	−	0.479884i	$-0.840679\pi$
$677$	−14.4949	+	12.1627i	−0.557085	+	0.467450i	0.320247	+	0.947334i	$0.396234\pi$
$678$	44.2853	+	34.3838i	1.70076	+	1.32050i
$679$	−0.141306	+	0.801385i	−0.00542282	+	0.0307544i
$680$		0			0
$681$	16.7898	−	31.8093i	0.643388	−	1.21893i
$682$	−3.65469	−	20.7268i	−0.139945	−	0.793670i
$683$	21.5693	+	37.3592i	0.825328	+	1.42951i	0.901668	+	0.432428i	$0.142343\pi$
$683$	21.5693	+	37.3592i	0.825328	+	1.42951i	−0.0763404	+	0.997082i	$0.524324\pi$
$684$	−4.41547	+	0.335662i	−0.168830	+	0.0128344i
$685$		0			0
$686$	−1.76190	−	0.641278i	−0.0672695	−	0.0244841i
$687$	−15.0981	+	13.6774i	−0.576027	+	0.521826i
$688$	−23.4415	−	19.6697i	−0.893698	−	0.749901i
$689$	−2.90837	−	2.44041i	−0.110800	−	0.0929723i
$690$		0			0
$691$	35.1209	+	12.7830i	1.33606	+	0.486287i	0.908570	−	0.417732i	$-0.137175\pi$
$691$	35.1209	+	12.7830i	1.33606	+	0.486287i	0.427492	+	0.904019i	$0.359397\pi$
$692$	23.4060	−	40.5404i	0.889762	−	1.54111i
$693$	−0.0949464	+	0.197701i	−0.00360671	+	0.00751004i
$694$	30.5391	+	52.8953i	1.15925	+	2.00788i
$695$		0			0
$696$	−1.94877	+	3.69206i	−0.0738681	+	0.139947i
$697$	−12.9351	+	4.70801i	−0.489953	+	0.178328i
$698$	−6.30602	+	35.7632i	−0.238687	+	1.35366i
$699$	10.9494	+	8.50129i	0.414144	+	0.321548i
$700$		0			0
$701$	−15.4800			−0.584670			−0.292335	−	0.956316i	$-0.594432\pi$
$701$	−15.4800			−0.584670			−0.292335	+	0.956316i	$0.594432\pi$
$702$	26.9923	−	62.1398i	1.01876	−	2.34532i
$703$	2.57011			0.0969336
$704$	−10.0466	+	8.43012i	−0.378646	+	0.317722i
$705$		0			0
$706$	0.893502	−	5.06730i	0.0336274	−	0.190710i
$707$	−0.536962	+	0.195438i	−0.0201945	+	0.00735021i
$708$	−47.5275	+	1.80391i	−1.78619	+	0.0677950i
$709$	7.54820	+	42.8080i	0.283479	+	1.60769i	0.710669	+	0.703526i	$0.248392\pi$
$709$	7.54820	+	42.8080i	0.283479	+	1.60769i	−0.427191	+	0.904162i	$0.640497\pi$
$710$		0			0
$711$	14.0491	−	6.35734i	0.526881	−	0.238419i
$712$	−6.02714	+	10.4393i	−0.225877	+	0.391230i
$713$	−60.1629	−	21.8975i	−2.25312	−	0.820068i
$714$	0.101376	+	0.469930i	0.00379390	+	0.0175867i
$715$		0			0
$716$	−20.6882	−	17.3595i	−0.773154	−	0.648753i
$717$	8.64232	+	2.77913i	0.322753	+	0.103789i
$718$	18.1315	+	6.59934i	0.676663	+	0.246285i
$719$	−17.5213	+	30.3477i	−0.653433	+	1.13178i	0.328851	+	0.944382i	$0.393339\pi$
$719$	−17.5213	+	30.3477i	−0.653433	+	1.13178i	−0.982284	+	0.187397i	$0.939995\pi$
$720$		0			0
$721$	0.448165	+	0.776245i	0.0166905	+	0.0289089i
$722$	6.86441	+	38.9300i	0.255467	+	1.44882i
$723$	−1.08510	−	1.72486i	−0.0403551	−	0.0641483i
$724$	37.5211	−	13.6566i	1.39446	−	0.507542i
$725$		0			0
$726$	4.83038	−	35.1423i	0.179272	−	1.30425i
$727$	−2.88728	+	2.42271i	−0.107083	+	0.0898534i	−0.694757	−	0.719244i	$-0.744488\pi$
$727$	−2.88728	+	2.42271i	−0.107083	+	0.0898534i	0.587674	+	0.809098i	$0.300044\pi$
$728$	−0.406233			−0.0150560
$729$	−18.4283	−	19.7331i	−0.682531	−	0.730857i
$730$		0			0
$731$	−17.5270	+	14.7069i	−0.648258	+	0.543953i
$732$	−7.00848	+	50.9885i	−0.259041	+	1.88459i
$733$	−0.290284	+	1.64628i	−0.0107219	+	0.0608068i	−0.989699	−	0.143162i	$-0.954273\pi$
$733$	−0.290284	+	1.64628i	−0.0107219	+	0.0608068i	0.978977	+	0.203969i	$0.0653841\pi$
$734$	29.7123	−	10.8144i	1.09670	−	0.399167i
$735$		0			0
$736$	10.3142	+	58.4946i	0.380186	+	2.15614i
$737$	−2.72711	−	4.72349i	−0.100454	−	0.173992i
$738$	−40.6820	−	11.3990i	−1.49753	−	0.419604i
$739$	22.4813	−	38.9388i	0.826989	−	1.43239i	−0.0734007	−	0.997303i	$-0.523385\pi$
$739$	22.4813	−	38.9388i	0.826989	−	1.43239i	0.900390	−	0.435084i	$-0.143281\pi$
$740$		0			0
$741$	6.00530	+	1.93114i	0.220610	+	0.0709423i
$742$	0.0633412	+	0.0531495i	0.00232533	+	0.00195118i
$743$	−0.0794857	−	0.0666964i	−0.00291605	−	0.00244685i	0.641328	−	0.767266i	$-0.278384\pi$
$743$	−0.0794857	−	0.0666964i	−0.00291605	−	0.00244685i	−0.644244	+	0.764820i	$0.722828\pi$
$744$	−3.27617	−	15.1867i	−0.120110	−	0.556773i
$745$		0			0
$746$	20.7698	−	35.9744i	0.760437	−	1.31712i
$747$	−9.17889	+	4.15354i	−0.335838	+	0.151970i
$748$	2.98730	+	5.17415i	0.109226	+	0.189186i
$749$	−0.225711	−	1.28007i	−0.00824731	−	0.0467728i
$750$		0			0
$751$	−21.8427	+	7.95008i	−0.797050	+	0.290102i	−0.708263	−	0.705948i	$-0.750521\pi$
$751$	−21.8427	+	7.95008i	−0.797050	+	0.290102i	−0.0887866	+	0.996051i	$0.528299\pi$
$752$	2.84127	−	16.1137i	0.103611	−	0.587605i
$753$	24.6694	−	10.0541i	0.899002	−	0.366393i
$754$	23.0384	−	19.3315i	0.839010	−	0.704013i
$755$		0			0
$756$	−0.326182	+	0.750915i	−0.0118631	+	0.0273105i
$757$	10.9327			0.397356			0.198678	−	0.980065i	$-0.436335\pi$
$757$	10.9327			0.397356			0.198678	+	0.980065i	$0.436335\pi$
$758$	−11.5917	+	9.72658i	−0.421029	+	0.353285i
$759$	11.8034	+	9.16437i	0.428437	+	0.332646i
$760$		0			0
$761$	25.8243	−	9.39926i	0.936129	−	0.340723i	0.171493	−	0.985185i	$-0.445141\pi$
$761$	25.8243	−	9.39926i	0.936129	−	0.340723i	0.764636	+	0.644462i	$0.222919\pi$
$762$	10.2581	−	19.4345i	0.371612	−	0.704039i
$763$	0.0298792	+	0.169453i	0.00108170	+	0.00613462i
$764$	−1.36693	−	2.36760i	−0.0494539	−	0.0856566i
$765$		0			0
$766$	−36.5572	+	63.3189i	−1.32086	+	2.28780i
$767$	63.6675	+	23.1731i	2.29890	+	0.836732i
$768$	7.05313	−	6.38947i	0.254508	−	0.230560i
$769$	14.3237	+	12.0190i	0.516525	+	0.433416i	0.863418	−	0.504489i	$-0.168319\pi$
$769$	14.3237	+	12.0190i	0.516525	+	0.433416i	−0.346893	+	0.937905i	$0.612763\pi$
$770$		0			0
$771$	−12.1916	+	11.0444i	−0.439069	+	0.397755i
$772$	1.29357	+	0.470819i	0.0465564	+	0.0169452i
$773$	15.4294	−	26.7246i	0.554959	−	0.961216i	−0.442948	−	0.896547i	$-0.646067\pi$
$773$	15.4294	−	26.7246i	0.554959	−	0.961216i	0.997907	−	0.0646692i	$-0.0205992\pi$
$774$	−70.0214	+	5.32299i	−2.51687	+	0.191331i
$775$		0			0
$776$	2.33634	+	13.2500i	0.0838696	+	0.475648i
$777$	0.221806	−	0.420223i	0.00795724	−	0.0150754i
$778$	−19.3139	+	7.02968i	−0.692436	+	0.252026i
$779$	0.683101	−	3.87406i	0.0244746	−	0.138802i
$780$		0			0
$781$	2.53035	−	2.12321i	0.0905429	−	0.0759745i
$782$	32.7556			1.17134
$783$	−3.40827	−	11.4908i	−0.121802	−	0.410647i
$784$	19.3860			0.692356
$785$		0			0
$786$	15.8778	−	6.47110i	0.566344	−	0.230816i
$787$	6.66381	−	37.7923i	0.237539	−	1.34715i	−0.599661	−	0.800254i	$-0.704698\pi$
$787$	6.66381	−	37.7923i	0.237539	−	1.34715i	0.837200	−	0.546897i	$-0.184191\pi$
$788$	34.7523	−	12.6488i	1.23800	−	0.450595i
$789$	4.30393	−	0.163356i	0.153224	−	0.00581562i
$790$		0			0
$791$	0.482578	+	0.835849i	0.0171585	+	0.0297194i
$792$	−0.357177	+	3.60855i	−0.0126917	+	0.128224i
$793$	36.6590	−	63.4953i	1.30180	−	2.25478i
$794$	−40.1071	−	14.5978i	−1.42335	−	0.518056i
$795$		0			0
$796$	−10.5924	−	8.88807i	−0.375437	−	0.315029i
$797$	28.3650	+	23.8010i	1.00474	+	0.843076i	0.987634	−	0.156778i	$-0.0501107\pi$
$797$	28.3650	+	23.8010i	1.00474	+	0.843076i	0.0171048	+	0.999854i	$0.494555\pi$
$798$	−0.130789	−	0.0420582i	−0.00462988	−	0.00148884i
$799$	−11.4961	−	4.18424i	−0.406703	−	0.148028i
$800$		0			0
$801$	−8.57555	−	33.5277i	−0.303002	−	1.18464i
$802$	−12.2183	−	21.1628i	−0.431444	−	0.747283i
$803$	0.585390	+	3.31991i	0.0206580	+	0.117157i
$804$	−10.8415	−	17.2337i	−0.382351	−	0.607784i
$805$		0			0
$806$	−19.4346	+	110.219i	−0.684554	+	3.88230i
$807$	−4.51439	+	32.8434i	−0.158914	+	1.15614i
$808$	−7.23747	+	6.07296i	−0.254613	+	0.213646i
$809$	−34.2586			−1.20447			−0.602234	−	0.798320i	$-0.705722\pi$
$809$	−34.2586			−1.20447			−0.602234	+	0.798320i	$0.705722\pi$
$810$		0			0
$811$	−28.6218			−1.00505			−0.502524	−	0.864563i	$-0.667595\pi$
$811$	−28.6218			−1.00505			−0.502524	+	0.864563i	$0.667595\pi$
$812$	−0.278403	+	0.233608i	−0.00977002	+	0.00819802i
$813$	−3.35494	+	24.4081i	−0.117663	+	0.856029i
$814$	1.84813	−	10.4812i	0.0647768	−	0.367368i
$815$		0			0
$816$	−5.29500	−	8.41691i	−0.185362	−	0.294651i
$817$	−1.13541	−	6.43922i	−0.0397229	−	0.225280i
$818$	4.78129	+	8.28143i	0.167174	+	0.289553i
$819$	0.834018	−	0.815228i	0.0291430	−	0.0284864i
$820$		0			0
$821$	19.3893	+	7.05712i	0.676690	+	0.246295i	0.657426	−	0.753519i	$-0.271645\pi$
$821$	19.3893	+	7.05712i	0.676690	+	0.246295i	0.0192644	+	0.999814i	$0.493868\pi$
$822$	−12.9564	−	4.16643i	−0.451906	−	0.145321i
$823$	40.4390	+	33.9324i	1.40962	+	1.18281i	0.956636	+	0.291287i	$0.0940836\pi$
$823$	40.4390	+	33.9324i	1.40962	+	1.18281i	0.452980	+	0.891521i	$0.350361\pi$
$824$	11.3526	+	9.52600i	0.395488	+	0.331854i
$825$		0			0
$826$	−1.38661	−	0.504685i	−0.0482463	−	0.0175602i
$827$	−11.5236	+	19.9595i	−0.400715	+	0.694058i	−0.993812	−	0.111072i	$-0.964572\pi$
$827$	−11.5236	+	19.9595i	−0.400715	+	0.694058i	0.593098	+	0.805131i	$0.297905\pi$
$828$	45.3271	+	32.5142i	1.57522	+	1.12995i
$829$	−22.7628	−	39.4264i	−0.790586	−	1.36934i	−0.925605	−	0.378492i	$-0.876443\pi$
$829$	−22.7628	−	39.4264i	−0.790586	−	1.36934i	0.135018	−	0.990843i	$-0.456891\pi$
$830$		0			0
$831$	23.3700	−	0.887009i	0.810697	−	0.0307700i
$832$	65.5354	−	23.8529i	2.27203	−	0.826951i
$833$	2.51698	−	14.2745i	0.0872081	−	0.494582i
$834$	−21.7171	+	8.85092i	−0.752001	+	0.306482i
$835$		0			0
$836$	−1.70741			−0.0590520
$837$	37.2029	+	24.6046i	1.28592	+	0.850458i
$838$	−45.9410			−1.58701
$839$	−11.6668	+	9.78962i	−0.402783	+	0.337975i	−0.821568	−	0.570110i	$-0.806901\pi$
$839$	−11.6668	+	9.78962i	−0.402783	+	0.337975i	0.418785	+	0.908085i	$0.362456\pi$
$840$		0			0
$841$	−4.11190	+	23.3197i	−0.141790	+	0.804129i
$842$	−40.3071	+	14.6706i	−1.38908	+	0.505582i
$843$	−3.56896	+	6.76159i	−0.122922	+	0.232882i
$844$	1.24741	+	7.07443i	0.0429377	+	0.243512i
$845$		0			0
$846$	−21.1852	−	31.0014i	−0.728362	−	1.06585i
$847$	0.305323	−	0.528835i	0.0104910	−	0.0181710i
$848$	−1.60718	−	0.584966i	−0.0551908	−	0.0200878i
$849$	1.63262	−	1.47900i	0.0560315	−	0.0507592i
$850$		0			0
$851$	−24.8015	−	20.8109i	−0.850183	−	0.713389i
$852$	9.13819	−	8.27834i	0.313069	−	0.283611i
$853$	5.05116	+	1.83847i	0.172948	+	0.0629481i	0.427043	−	0.904231i	$-0.359555\pi$
$853$	5.05116	+	1.83847i	0.172948	+	0.0629481i	−0.254095	+	0.967179i	$0.581777\pi$
$854$	−0.798394	+	1.38286i	−0.0273205	+	0.0473205i
$855$		0			0
$856$	−10.7455	−	18.6118i	−0.367275	−	0.636139i
$857$	3.23480	+	18.3455i	0.110499	+	0.626670i	0.988881	+	0.148710i	$0.0475122\pi$
$857$	3.23480	+	18.3455i	0.110499	+	0.626670i	−0.878382	+	0.477959i	$0.841377\pi$
$858$	12.1938	−	23.1017i	0.416288	−	0.788680i
$859$	−17.0674	+	6.21203i	−0.582333	+	0.211952i	−0.616354	−	0.787469i	$-0.711391\pi$
$859$	−17.0674	+	6.21203i	−0.582333	+	0.211952i	0.0340211	+	0.999421i	$0.489169\pi$
$860$		0			0
$861$	−0.574470	−	0.446028i	−0.0195779	−	0.0152006i
$862$	−19.9302	+	16.7234i	−0.678825	+	0.569602i
$863$	−5.04898			−0.171869			−0.0859346	−	0.996301i	$-0.527388\pi$
$863$	−5.04898			−0.171869			−0.0859346	+	0.996301i	$0.527388\pi$
$864$	2.51114	−	41.3034i	0.0854306	−	1.40517i
$865$		0			0
$866$	56.1666	−	47.1294i	1.90862	−	1.60152i
$867$	20.3821	−	8.30685i	0.692214	−	0.282116i
$868$	0.234853	−	1.33192i	0.00797142	−	0.0452082i
$869$	5.58719	−	2.03357i	0.189532	−	0.0689841i
$870$		0			0
$871$	5.03648	+	28.5633i	0.170654	+	0.967830i
$872$	1.42247	+	2.46379i	0.0481710	+	0.0834346i
$873$	−31.3867	−	22.5144i	−1.06228	−	0.761998i
$874$	−4.68042	+	8.10673i	−0.158318	+	0.274214i
$875$		0			0
$876$	2.65368	+	12.3012i	0.0896597	+	0.415619i
$877$	34.4946	+	28.9444i	1.16480	+	0.977382i	0.999960	−	0.00893847i	$-0.00284524\pi$
$877$	34.4946	+	28.9444i	1.16480	+	0.977382i	0.164839	+	0.986321i	$0.447290\pi$
$878$	−51.7243	−	43.4019i	−1.74561	−	1.46474i
$879$	48.3656	+	15.5531i	1.63133	+	0.524592i
$880$		0			0
$881$	−2.77972	+	4.81462i	−0.0936512	+	0.162209i	−0.909045	−	0.416698i	$-0.863187\pi$
$881$	−2.77972	+	4.81462i	−0.0936512	+	0.162209i	0.815394	+	0.578907i	$0.196521\pi$
$882$	31.8138	−	31.0970i	1.07123	−	1.04709i
$883$	−10.1759	−	17.6251i	−0.342445	−	0.593132i	0.642441	−	0.766335i	$-0.277922\pi$
$883$	−10.1759	−	17.6251i	−0.342445	−	0.593132i	−0.984886	+	0.173203i	$0.944588\pi$
$884$	−5.51700	−	31.2884i	−0.185557	−	1.05234i
$885$		0			0
$886$	3.71875	−	1.35351i	0.124934	−	0.0454722i
$887$	5.11824	−	29.0270i	0.171854	−	0.974630i	−0.769860	−	0.638213i	$-0.779674\pi$
$887$	5.11824	−	29.0270i	0.171854	−	0.974630i	0.941713	−	0.336417i	$-0.109215\pi$
$888$	1.06982	−	7.78321i	0.0359007	−	0.261187i
$889$	0.289795	−	0.243167i	0.00971942	−	0.00815556i
$890$		0			0
$891$	−6.50832	−	8.12532i	−0.218037	−	0.272208i
$892$	28.6286			0.958556
$893$	2.67823	−	2.24730i	0.0896236	−	0.0752031i
$894$	7.33001	−	53.3277i	0.245152	−	1.78355i
$895$		0			0
$896$	−0.481392	+	0.175213i	−0.0160822	+	0.00585344i
$897$	−42.3139	−	67.2620i	−1.41282	−	2.24581i
$898$	−8.24952	−	46.7853i	−0.275290	−	1.56125i
$899$	9.89989	+	17.1471i	0.330180	+	0.571888i
$900$		0			0
$901$	−0.639397	+	1.10747i	−0.0213014	+	0.0368951i
$902$	−15.3077	−	5.57154i	−0.509690	−	0.185512i
$903$	−1.15082	−	0.370074i	−0.0382970	−	0.0123153i
$904$	12.2244	+	10.2575i	0.406576	+	0.341158i
$905$		0			0
$906$	−9.18938	−	42.5975i	−0.305297	−	1.41521i
$907$	−49.9658	−	18.1861i	−1.65909	−	0.603859i	−0.668870	−	0.743380i	$-0.733222\pi$
$907$	−49.9658	−	18.1861i	−1.65909	−	0.603859i	−0.990219	+	0.139521i	$0.955444\pi$
$908$	25.8851	−	44.8343i	0.859027	−	1.48788i
$909$	2.67171	−	26.9922i	0.0886150	−	0.895276i
$910$		0			0
$911$	1.42089	+	8.05828i	0.0470763	+	0.266983i	0.999257	−	0.0385540i	$-0.0122752\pi$
$911$	1.42089	+	8.05828i	0.0470763	+	0.266983i	−0.952180	+	0.305537i	$0.901164\pi$
$912$	2.83971	−	0.107781i	0.0940321	−	0.00356899i
$913$	−3.65036	+	1.32862i	−0.120809	+	0.0439710i
$914$	−5.88005	+	33.3474i	−0.194495	+	1.10303i
$915$		0			0
$916$	−22.4620	+	18.8479i	−0.742165	+	0.622751i
$917$	0.295158			0.00974698
$918$	−22.1910	−	5.31906i	−0.732414	−	0.175555i
$919$	5.96363			0.196722			0.0983609	−	0.995151i	$-0.468640\pi$
$919$	5.96363			0.196722			0.0983609	+	0.995151i	$0.468640\pi$
$920$		0			0
$921$	−24.5158	−	19.0345i	−0.807824	−	0.627209i
$922$	−9.14225	+	51.8483i	−0.301084	+	1.70753i
$923$	−16.5058	+	6.00761i	−0.543294	+	0.197743i
$924$	−0.147353	+	0.279168i	−0.00484755	+	0.00918394i
$925$		0			0
$926$	38.0307	+	65.8712i	1.24977	+	2.16466i
$927$	−42.4243	+	3.22508i	−1.39340	+	0.105925i
$928$	9.18443	−	15.9079i	0.301494	−	0.522202i
$929$	−5.31666	−	1.93510i	−0.174434	−	0.0634887i	0.253327	−	0.967381i	$-0.418475\pi$
$929$	−5.31666	−	1.93510i	−0.174434	−	0.0634887i	−0.427761	+	0.903892i	$0.640697\pi$
$930$		0			0
$931$	3.17316	+	2.66260i	0.103996	+	0.0872632i
$932$	15.2843	+	12.8250i	0.500653	+	0.420098i
$933$	24.1992	−	21.9222i	0.792245	−	0.717699i
$934$	20.7460	+	7.55091i	0.678829	+	0.247073i
$935$		0			0
$936$	8.34790	−	17.3823i	0.272860	−	0.568159i
$937$	2.84697	+	4.93110i	0.0930065	+	0.161092i	0.908775	−	0.417287i	$-0.137019\pi$
$937$	2.84697	+	4.93110i	0.0930065	+	0.161092i	−0.815768	+	0.578379i	$0.803686\pi$
$938$	−0.109689	−	0.622077i	−0.00358147	−	0.0203115i
$939$	−4.63835	+	8.78761i	−0.151367	+	0.286773i
$940$		0			0
$941$	−0.178790	+	1.01397i	−0.00582839	+	0.0330545i	−0.987583	−	0.157096i	$-0.949787\pi$
$941$	−0.178790	+	1.01397i	−0.00582839	+	0.0330545i	0.981755	+	0.190151i	$0.0608977\pi$
$942$	−66.2378	−	51.4282i	−2.15814	−	1.67562i
$943$	−37.9612	+	31.8532i	−1.23619	+	1.03728i
$944$	30.5222			0.993412
$945$		0			0
$946$	−27.0764			−0.880330
$947$	−7.84590	+	6.58349i	−0.254958	+	0.213935i	−0.761304	−	0.648396i	$-0.775440\pi$
$947$	−7.84590	+	6.58349i	−0.254958	+	0.213935i	0.506346	+	0.862330i	$0.330996\pi$
$948$	20.5536	−	8.37675i	0.667551	−	0.272064i
$949$	3.11293	−	17.6543i	0.101050	−	0.573083i
$950$		0			0
$951$	1.81052	−	0.0687183i	0.0587102	−	0.00222834i
$952$	0.0237602	+	0.134751i	0.000770074	+	0.00436731i
$953$	8.46948	+	14.6696i	0.274353	+	0.475194i	0.969972	−	0.243217i	$-0.0782029\pi$
$953$	8.46948	+	14.6696i	0.274353	+	0.475194i	−0.695618	+	0.718411i	$0.744870\pi$
$954$	−3.57585	+	1.61811i	−0.115772	+	0.0523881i
$955$		0			0
$956$	12.2784	+	4.46898i	0.397113	+	0.144537i
$957$	−0.974524	−	4.51742i	−0.0315019	−	0.146028i
$958$	10.4092	+	8.73437i	0.336306	+	0.282195i
$959$	−0.179474	−	0.150597i	−0.00579552	−	0.00486302i
$960$		0			0
$961$	−40.1088	−	14.5984i	−1.29383	−	0.470916i
$962$	−28.2980	+	49.0135i	−0.912363	+	1.58026i
$963$	59.4113	+	16.6469i	1.91450	+	0.536439i
$964$	−1.46652	−	2.54009i	−0.0472334	−	0.0818107i
$965$		0			0
$966$	0.921551	+	1.46489i	0.0296504	+	0.0471322i
$967$	−27.9101	+	10.1584i	−0.897528	+	0.326673i	−0.749262	−	0.662274i	$-0.769591\pi$
$967$	−27.9101	+	10.1584i	−0.897528	+	0.326673i	−0.148266	+	0.988947i	$0.547369\pi$
$968$	1.75321	−	9.94297i	0.0563504	−	0.319579i
$969$	0.289331	−	2.10496i	0.00929465	−	0.0676210i
$970$		0			0
$971$	54.1443			1.73757			0.868787	−	0.495187i	$-0.164900\pi$
$971$	54.1443			1.73757			0.868787	+	0.495187i	$0.164900\pi$
$972$	−25.4280	−	29.3879i	−0.815604	−	0.942619i
$973$	−0.403706			−0.0129422
$974$	24.4879	−	20.5478i	0.784642	−	0.658393i
$975$		0			0
$976$	5.73541	−	32.5271i	0.183586	−	1.04117i
$977$	−36.6787	+	13.3499i	−1.17345	+	0.427103i	−0.853886	−	0.520460i	$-0.825760\pi$
$977$	−36.6787	+	13.3499i	−1.17345	+	0.427103i	−0.319569	+	0.947563i	$0.603538\pi$
$978$	7.99542	+	12.7095i	0.255665	+	0.406405i
$979$	−2.31709	−	13.1409i	−0.0740546	−	0.419985i
$980$		0			0
$981$	−7.86474	−	2.20369i	−0.251102	−	0.0703583i
$982$	24.4643	−	42.3734i	0.780686	−	1.35219i
$983$	−4.33786	−	1.57885i	−0.138356	−	0.0503575i	0.271914	−	0.962322i	$-0.412343\pi$
$983$	−4.33786	−	1.57885i	−0.138356	−	0.0503575i	−0.410270	+	0.911964i	$0.634566\pi$
$984$	−11.4477	−	3.68126i	−0.364938	−	0.117354i
$985$		0			0
$986$	−7.75993	−	6.51135i	−0.247126	−	0.207364i
$987$	−0.136306	−	0.631847i	−0.00433866	−	0.0201119i
$988$	8.53193	+	3.10537i	0.271437	+	0.0987950i
$989$	−41.1835	+	71.3319i	−1.30956	+	2.26822i
$990$		0			0
$991$	−3.70329	−	6.41429i	−0.117639	−	0.203757i	0.801193	−	0.598407i	$-0.204199\pi$
$991$	−3.70329	−	6.41429i	−0.117639	−	0.203757i	−0.918832	+	0.394650i	$0.870866\pi$
$992$	11.8702	+	67.3193i	0.376879	+	2.13739i
$993$	−0.365444	+	0.0138704i	−0.0115970	+	0.000440164i
$994$	0.359478	−	0.130839i	0.0114019	−	0.00414997i
$995$		0			0
$996$	−13.4286	+	5.47291i	−0.425502	+	0.173416i
$997$	−33.5151	+	28.1225i	−1.06143	+	0.890648i	−0.994249	−	0.107093i	$-0.965846\pi$
$997$	−33.5151	+	28.1225i	−1.06143	+	0.890648i	−0.0671838	+	0.997741i	$0.521401\pi$
$998$	8.09917			0.256375
$999$	13.4229	+	18.1262i	0.424682	+	0.573489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.d.76.1		30
5.2	odd	4		675.2.u.c.49.2		60
5.3	odd	4		675.2.u.c.49.9		60
5.4	even	2		135.2.k.a.76.5	yes	30
15.14	odd	2		405.2.k.a.361.1		30
27.16	even	9	inner	675.2.l.d.151.1		30
135.4	even	18		3645.2.a.h.1.13		15
135.43	odd	36		675.2.u.c.124.2		60
135.97	odd	36		675.2.u.c.124.9		60
135.104	odd	18		3645.2.a.g.1.3		15
135.119	odd	18		405.2.k.a.46.1		30
135.124	even	18		135.2.k.a.16.5	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.a.16.5	✓	30	135.124	even	18
135.2.k.a.76.5	yes	30	5.4	even	2
405.2.k.a.46.1		30	135.119	odd	18
405.2.k.a.361.1		30	15.14	odd	2
675.2.l.d.76.1		30	1.1	even	1	trivial
675.2.l.d.151.1		30	27.16	even	9	inner
675.2.u.c.49.2		60	5.2	odd	4
675.2.u.c.49.9		60	5.3	odd	4
675.2.u.c.124.2		60	135.43	odd	36
675.2.u.c.124.9		60	135.97	odd	36
3645.2.a.g.1.3		15	135.104	odd	18
3645.2.a.h.1.13		15	135.4	even	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.62376 + 1.36249i) q^{2} +(0.235856 - 1.71592i) q^{3} +(0.432902 - 2.45511i) q^{4} +(1.95495 + 3.10759i) q^{6} +(0.0109747 + 0.0622407i) q^{7} +(0.522478 + 0.904959i) q^{8} +(-2.88874 - 0.809420i) q^{9} +(-1.08697 - 0.395623i) q^{11} +(-4.11066 - 1.32188i) q^{12} +(4.71203 + 3.95386i) q^{13} +(-0.102623 - 0.0861109i) q^{14} +(2.60389 + 0.947740i) q^{16} +(1.03593 - 1.79428i) q^{17} +(5.79345 - 2.62160i) q^{18} +(0.296045 + 0.512766i) q^{19} +(0.109388 - 0.00415183i) q^{21} +(2.30400 - 0.838589i) q^{22} +(1.29518 - 7.34532i) q^{23} +(1.67606 - 0.683089i) q^{24} -13.0383 q^{26} +(-2.07023 + 4.76594i) q^{27} +0.157559 q^{28} +(-1.76698 + 1.48267i) q^{29} +(1.49057 - 8.45346i) q^{31} +(-7.48326 + 2.72368i) q^{32} +(-0.935225 + 1.77183i) q^{33} +(0.762600 + 4.32492i) q^{34} +(-3.23776 + 6.74178i) q^{36} +(2.17037 - 3.75919i) q^{37} +(-1.17935 - 0.429247i) q^{38} +(7.89587 - 7.15291i) q^{39} +(-5.08956 - 4.27065i) q^{41} +(-0.171963 + 0.155783i) q^{42} +(-10.3772 - 3.77698i) q^{43} +(-1.44185 + 2.49735i) q^{44} +(7.90491 + 13.6917i) q^{46} +(-1.02536 - 5.81510i) q^{47} +(2.24039 - 4.24453i) q^{48} +(6.57409 - 2.39277i) q^{49} +(-2.83450 - 2.20076i) q^{51} +(11.7470 - 9.85691i) q^{52} -0.617222 q^{53} +(-3.13202 - 10.5594i) q^{54} +(-0.0505913 + 0.0424511i) q^{56} +(0.949687 - 0.387050i) q^{57} +(0.849014 - 4.81500i) q^{58} +(10.3506 - 3.76730i) q^{59} +(-2.06979 - 11.7384i) q^{61} +(9.09747 + 15.7573i) q^{62} +(0.0186757 - 0.188681i) q^{63} +(5.66899 - 9.81898i) q^{64} +(-0.895535 - 4.15127i) q^{66} +(3.61207 + 3.03089i) q^{67} +(-3.95669 - 3.32006i) q^{68} +(-12.2985 - 3.95486i) q^{69} +(-1.42779 + 2.47301i) q^{71} +(-0.776814 - 3.03710i) q^{72} +(-1.45719 - 2.52392i) q^{73} +(1.59772 + 9.06114i) q^{74} +(1.38705 - 0.504846i) q^{76} +(0.0126947 - 0.0719954i) q^{77} +(-3.07517 + 22.3727i) q^{78} +(-3.93760 + 3.30404i) q^{79} +(7.68968 + 4.67641i) q^{81} +14.0830 q^{82} +(2.57261 - 2.15868i) q^{83} +(0.0371612 - 0.270358i) q^{84} +(21.9962 - 8.00594i) q^{86} +(2.12739 + 3.38169i) q^{87} +(-0.209893 - 1.19036i) q^{88} +(5.76784 + 9.99019i) q^{89} +(-0.194378 + 0.336673i) q^{91} +(-17.4729 - 6.35961i) q^{92} +(-14.1539 - 4.55150i) q^{93} +(9.58798 + 8.04527i) q^{94} +(2.90864 + 13.4830i) q^{96} +(12.0991 + 4.40371i) q^{97} +(-7.41460 + 12.8425i) q^{98} +(2.81974 + 2.02267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 9 q^{8} - 3 q^{9} - 6 q^{11} - 3 q^{12} - 3 q^{13} - 9 q^{14} + 12 q^{16} + 12 q^{17} - 6 q^{18} + 24 q^{19} - 36 q^{21} + 51 q^{22} - 18 q^{23} + 45 q^{24} - 18 q^{26} + 9 q^{27} + 60 q^{28}+ \cdots + 123 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 + 9 * q^8 - 3 * q^9 - 6 * q^11 - 3 * q^12 - 3 * q^13 - 9 * q^14 + 12 * q^16 + 12 * q^17 - 6 * q^18 + 24 * q^19 - 36 * q^21 + 51 * q^22 - 18 * q^23 + 45 * q^24 - 18 * q^26 + 9 * q^27 + 60 * q^28 + 18 * q^29 + 12 * q^31 - 36 * q^32 - 27 * q^33 - 69 * q^34 - 42 * q^36 - 24 * q^37 + 24 * q^38 + 6 * q^39 - 75 * q^41 + 18 * q^42 - 6 * q^43 + 12 * q^44 + 30 * q^46 - 45 * q^47 + 27 * q^48 - 36 * q^49 + 21 * q^51 - 30 * q^52 - 36 * q^53 + 18 * q^54 + 30 * q^56 - 30 * q^57 - 27 * q^58 - 27 * q^59 - 12 * q^61 - 36 * q^62 - 18 * q^63 + 27 * q^64 + 78 * q^66 + 30 * q^67 - 69 * q^68 - 117 * q^69 + 12 * q^71 - 9 * q^72 - 21 * q^73 - 30 * q^76 + 36 * q^77 - 66 * q^78 + 54 * q^79 - 27 * q^81 + 48 * q^82 + 87 * q^83 + 45 * q^84 + 18 * q^86 + 27 * q^87 + 18 * q^88 + 9 * q^89 + 51 * q^91 - 24 * q^92 - 36 * q^93 + 15 * q^94 - 15 * q^96 + 75 * q^97 + 15 * q^98 + 123 * q^99

Introduction

L-functions

Modular forms

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Database

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