LMFDB - Embedded newform 675.2.u.c.49.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(49,675)] 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("675.49"); 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, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [60] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.9
Character	$\chi$	$=$	675.49
Dual form			675.2.u.c.124.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36249 + 1.62376i) q^{2} +(1.71592 + 0.235856i) q^{3} +(-0.432902 + 2.45511i) q^{4} +(1.95495 + 3.10759i) q^{6} +(0.0622407 - 0.0109747i) q^{7} +(-0.904959 + 0.522478i) q^{8} +(2.88874 + 0.809420i) q^{9} +(-1.08697 - 0.395623i) q^{11} +(-1.32188 + 4.11066i) q^{12} +(-3.95386 + 4.71203i) q^{13} +(0.102623 + 0.0861109i) q^{14} +(2.60389 + 0.947740i) q^{16} +(-1.79428 - 1.03593i) q^{17} +(2.62160 + 5.79345i) q^{18} +(-0.296045 - 0.512766i) q^{19} +(0.109388 - 0.00415183i) q^{21} +(-0.838589 - 2.30400i) q^{22} +(7.34532 + 1.29518i) q^{23} +(-1.67606 + 0.683089i) q^{24} -13.0383 q^{26} +(4.76594 + 2.07023i) q^{27} +0.157559i q^{28} +(1.76698 - 1.48267i) q^{29} +(1.49057 - 8.45346i) q^{31} +(2.72368 + 7.48326i) q^{32} +(-1.77183 - 0.935225i) q^{33} +(-0.762600 - 4.32492i) q^{34} +(-3.23776 + 6.74178i) q^{36} +(-3.75919 - 2.17037i) q^{37} +(0.429247 - 1.17935i) q^{38} +(-7.89587 + 7.15291i) q^{39} +(-5.08956 - 4.27065i) q^{41} +(0.155783 + 0.171963i) q^{42} +(3.77698 - 10.3772i) q^{43} +(1.44185 - 2.49735i) q^{44} +(7.90491 + 13.6917i) q^{46} +(-5.81510 + 1.02536i) q^{47} +(4.24453 + 2.24039i) q^{48} +(-6.57409 + 2.39277i) q^{49} +(-2.83450 - 2.20076i) q^{51} +(-9.85691 - 11.7470i) q^{52} -0.617222i q^{53} +(3.13202 + 10.5594i) q^{54} +(-0.0505913 + 0.0424511i) q^{56} +(-0.387050 - 0.949687i) q^{57} +(4.81500 + 0.849014i) q^{58} +(-10.3506 + 3.76730i) q^{59} +(-2.06979 - 11.7384i) q^{61} +(15.7573 - 9.09747i) q^{62} +(0.188681 + 0.0186757i) q^{63} +(-5.66899 + 9.81898i) q^{64} +(-0.895535 - 4.15127i) q^{66} +(3.03089 - 3.61207i) q^{67} +(3.32006 - 3.95669i) q^{68} +(12.2985 + 3.95486i) q^{69} +(-1.42779 + 2.47301i) q^{71} +(-3.03710 + 0.776814i) q^{72} +(2.52392 - 1.45719i) q^{73} +(-1.59772 - 9.06114i) q^{74} +(1.38705 - 0.504846i) q^{76} +(-0.0719954 - 0.0126947i) q^{77} +(-22.3727 - 3.07517i) q^{78} +(3.93760 - 3.30404i) q^{79} +(7.68968 + 4.67641i) q^{81} -14.0830i q^{82} +(2.15868 + 2.57261i) q^{83} +(-0.0371612 + 0.270358i) q^{84} +(21.9962 - 8.00594i) q^{86} +(3.38169 - 2.12739i) q^{87} +(1.19036 - 0.209893i) q^{88} +(-5.76784 - 9.99019i) q^{89} +(-0.194378 + 0.336673i) q^{91} +(-6.35961 + 17.4729i) q^{92} +(4.55150 - 14.1539i) q^{93} +(-9.58798 - 8.04527i) q^{94} +(2.90864 + 13.4830i) q^{96} +(4.40371 - 12.0991i) q^{97} +(-12.8425 - 7.41460i) q^{98} +(-2.81974 - 2.02267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{9} - 12 q^{11} + 18 q^{14} + 24 q^{16} - 48 q^{19} - 72 q^{21} - 90 q^{24} - 36 q^{26} - 36 q^{29} + 24 q^{31} + 138 q^{34} - 84 q^{36} - 12 q^{39} - 150 q^{41} - 24 q^{44} + 60 q^{46} + 72 q^{49}+ \cdots - 246 q^{99}+O(q^{100}) $ 60 * q + 6 * q^9 - 12 * q^11 + 18 * q^14 + 24 * q^16 - 48 * q^19 - 72 * q^21 - 90 * q^24 - 36 * q^26 - 36 * q^29 + 24 * q^31 + 138 * q^34 - 84 * q^36 - 12 * q^39 - 150 * q^41 - 24 * q^44 + 60 * q^46 + 72 * q^49 + 42 * q^51 - 36 * q^54 + 60 * q^56 + 54 * q^59 - 24 * q^61 - 54 * q^64 + 156 * q^66 + 234 * q^69 + 24 * q^71 - 60 * q^76 - 108 * q^79 - 54 * q^81 - 90 * q^84 + 36 * q^86 - 18 * q^89 + 102 * q^91 - 30 * q^94 - 30 * q^96 - 246 * 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 $

$2$	1.36249	+	1.62376i	0.963429	+	1.14817i	0.988913	+	0.148495i	$0.0474429\pi$
$2$	1.36249	+	1.62376i	0.963429	+	1.14817i	−0.0254839	+	0.999675i	$0.508113\pi$
$3$	1.71592	+	0.235856i	0.990685	+	0.136172i
$3$	1.71592	+	0.235856i	0.990685	+	0.136172i
$4$	−0.432902	+	2.45511i	−0.216451	+	1.22755i
$5$		0			0
$5$		0			0
$6$	1.95495	+	3.10759i	0.798107	+	1.26867i
$7$	0.0622407	−	0.0109747i	0.0235248	−	0.00414805i	−0.161873	−	0.986812i	$-0.551754\pi$
$7$	0.0622407	−	0.0109747i	0.0235248	−	0.00414805i	0.185398	+	0.982663i	$0.440643\pi$
$8$	−0.904959	+	0.522478i	−0.319951	+	0.184724i
$9$	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	$0.666904\pi$
$12$	−1.32188	+	4.11066i	−0.381593	+	1.18665i
$13$	−3.95386	+	4.71203i	−1.09660	+	1.30688i	−0.148504	+	0.988912i	$0.547446\pi$
$13$	−3.95386	+	4.71203i	−1.09660	+	1.30688i	−0.948101	+	0.317970i	$0.896999\pi$
$14$	0.102623	+	0.0861109i	0.0274271	+	0.0230141i
$15$		0			0
$16$	2.60389	+	0.947740i	0.650973	+	0.236935i
$17$	−1.79428	−	1.03593i	−0.435176	−	0.251249i	0.266373	−	0.963870i	$-0.414175\pi$
$17$	−1.79428	−	1.03593i	−0.435176	−	0.251249i	−0.701549	+	0.712621i	$0.747508\pi$
$18$	2.62160	+	5.79345i	0.617916	+	1.36553i
$19$	−0.296045	−	0.512766i	−0.0679175	−	0.117636i	0.830067	−	0.557664i	$-0.188302\pi$
$19$	−0.296045	−	0.512766i	−0.0679175	−	0.117636i	−0.897984	+	0.440027i	$0.854969\pi$
$20$		0			0
$21$	0.109388	−	0.00415183i	0.0238705	−	0.000906005i
$22$	−0.838589	−	2.30400i	−0.178788	−	0.491216i
$23$	7.34532	+	1.29518i	1.53161	+	0.270063i	0.874982	−	0.484155i	$-0.160873\pi$
$23$	7.34532	+	1.29518i	1.53161	+	0.270063i	0.656624	+	0.754218i	$0.271984\pi$
$24$	−1.67606	+	0.683089i	−0.342125	+	0.139435i
$25$		0			0
$26$	−13.0383			−2.55702
$27$	4.76594	+	2.07023i	0.917205	+	0.398415i
$28$			0.157559i			0.0297758i
$29$	1.76698	−	1.48267i	0.328120	−	0.275325i	−0.463814	−	0.885933i	$-0.653519\pi$
$29$	1.76698	−	1.48267i	0.328120	−	0.275325i	0.791933	+	0.610608i	$0.209075\pi$
$30$		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	$-0.224615\pi$
$32$	2.72368	+	7.48326i	0.481484	+	1.32287i
$33$	−1.77183	−	0.935225i	−0.308437	−	0.162802i
$34$	−0.762600	−	4.32492i	−0.130785	−	0.741717i
$35$		0			0
$36$	−3.23776	+	6.74178i	−0.539626	+	1.12363i
$37$	−3.75919	−	2.17037i	−0.618007	−	0.356807i	0.158085	−	0.987425i	$-0.449468\pi$
$37$	−3.75919	−	2.17037i	−0.618007	−	0.356807i	−0.776093	+	0.630619i	$0.782801\pi$
$38$	0.429247	−	1.17935i	0.0696331	−	0.191315i
$39$	−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	$0.895845\pi$
$42$	0.155783	+	0.171963i	0.0240378	+	0.0265345i
$43$	3.77698	−	10.3772i	0.575985	−	1.58251i	−0.218902	−	0.975747i	$-0.570247\pi$
$43$	3.77698	−	10.3772i	0.575985	−	1.58251i	0.794886	−	0.606758i	$-0.207530\pi$
$44$	1.44185	−	2.49735i	0.217367	−	0.376490i
$45$		0			0
$46$	7.90491	+	13.6917i	1.16552	+	2.01873i
$47$	−5.81510	+	1.02536i	−0.848219	+	0.149564i	−0.580830	−	0.814025i	$-0.697272\pi$
$47$	−5.81510	+	1.02536i	−0.848219	+	0.149564i	−0.267389	+	0.963589i	$0.586161\pi$
$48$	4.24453	+	2.24039i	0.612646	+	0.323372i
$49$	−6.57409	+	2.39277i	−0.939156	+	0.341825i
$50$		0			0
$51$	−2.83450	−	2.20076i	−0.396910	−	0.308168i
$52$	−9.85691	−	11.7470i	−1.36691	−	1.62902i
$53$		−	0.617222i		−	0.0847820i	−0.999101	−	0.0423910i	$-0.986502\pi$
$53$		−	0.617222i		−	0.0847820i	0.999101	−	0.0423910i	$-0.0134975\pi$
$54$	3.13202	+	10.5594i	0.426214	+	1.43695i
$55$		0			0
$56$	−0.0505913	+	0.0424511i	−0.00676054	+	0.00567277i
$57$	−0.387050	−	0.949687i	−0.0512661	−	0.125789i
$58$	4.81500	+	0.849014i	0.632240	+	0.111481i
$59$	−10.3506	+	3.76730i	−1.34753	+	0.490460i	−0.912175	−	0.409800i	$-0.865599\pi$
$59$	−10.3506	+	3.76730i	−1.34753	+	0.490460i	−0.435353	+	0.900260i	$0.643376\pi$
$60$		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	$-0.331862\pi$
$62$	15.7573	−	9.09747i	2.00118	−	1.15538i
$63$	0.188681	+	0.0186757i	0.0237715	+	0.00235292i
$64$	−5.66899	+	9.81898i	−0.708624	+	1.22737i
$65$		0			0
$66$	−0.895535	−	4.15127i	−0.110233	−	0.510986i
$67$	3.03089	−	3.61207i	0.370282	−	0.441285i	−0.548440	−	0.836190i	$-0.684778\pi$
$67$	3.03089	−	3.61207i	0.370282	−	0.441285i	0.918722	+	0.394905i	$0.129223\pi$
$68$	3.32006	−	3.95669i	0.402616	−	0.479819i
$69$	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	$0.220865\pi$
$72$	−3.03710	+	0.776814i	−0.357926	+	0.0915484i
$73$	2.52392	−	1.45719i	0.295403	−	0.170551i	−0.344973	−	0.938613i	$-0.612112\pi$
$73$	2.52392	−	1.45719i	0.295403	−	0.170551i	0.640376	+	0.768062i	$0.278779\pi$
$74$	−1.59772	−	9.06114i	−0.185732	−	1.05334i
$75$		0			0
$76$	1.38705	−	0.504846i	0.159106	−	0.0579098i
$77$	−0.0719954	−	0.0126947i	−0.00820464	−	0.00144670i
$78$	−22.3727	−	3.07517i	−2.53321	−	0.348194i
$79$	3.93760	−	3.30404i	0.443014	−	0.371733i	−0.393822	−	0.919187i	$-0.628847\pi$
$79$	3.93760	−	3.30404i	0.443014	−	0.371733i	0.836836	+	0.547454i	$0.184403\pi$
$80$		0			0
$81$	7.68968	+	4.67641i	0.854409	+	0.519602i
$82$		−	14.0830i		−	1.55520i
$83$	2.15868	+	2.57261i	0.236946	+	0.282381i	0.871393	−	0.490585i	$-0.163217\pi$
$83$	2.15868	+	2.57261i	0.236946	+	0.282381i	−0.634448	+	0.772966i	$0.718772\pi$
$84$	−0.0371612	+	0.270358i	−0.00405462	+	0.0294984i
$85$		0			0
$86$	21.9962	−	8.00594i	2.37191	−	0.863303i
$87$	3.38169	−	2.12739i	0.362555	−	0.228080i
$88$	1.19036	−	0.209893i	0.126893	−	0.0223747i
$89$	−5.76784	−	9.99019i	−0.611390	−	1.05896i	−0.991006	−	0.133814i	$-0.957277\pi$
$89$	−5.76784	−	9.99019i	−0.611390	−	1.05896i	0.379617	−	0.925144i	$-0.376056\pi$
$90$		0			0
$91$	−0.194378	+	0.336673i	−0.0203764	+	0.0352929i
$92$	−6.35961	+	17.4729i	−0.663035	+	1.82167i
$93$	4.55150	−	14.1539i	0.471969	−	1.46769i
$94$	−9.58798	−	8.04527i	−0.988924	−	0.829806i
$95$		0			0
$96$	2.90864	+	13.4830i	0.296862	+	1.37611i
$97$	4.40371	−	12.0991i	0.447129	−	1.22848i	−0.487585	−	0.873075i	$-0.662122\pi$
$97$	4.40371	−	12.0991i	0.447129	−	1.22848i	0.934714	−	0.355401i	$-0.115656\pi$
$98$	−12.8425	−	7.41460i	−1.29728	−	0.748987i
$99$	−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	$0.795931\pi$
$102$	−0.288498	−	7.60107i	−0.0285656	−	0.752618i
$103$	4.85061	+	13.3270i	0.477945	+	1.31314i	0.911234	+	0.411888i	$0.135131\pi$
$103$	4.85061	+	13.3270i	0.477945	+	1.31314i	−0.433289	+	0.901255i	$0.642647\pi$
$104$	1.11615	−	6.33000i	0.109448	−	0.620708i
$105$		0			0
$106$	1.00222	−	0.840962i	0.0973442	−	0.0816814i
$107$			20.5665i			1.98824i	0.108303	+	0.994118i	$0.465458\pi$
$107$			20.5665i			1.98824i	−0.108303	+	0.994118i	$0.534542\pi$
$108$	−7.14581	+	10.8047i	−0.687606	+	1.03968i
$109$	−2.72255			−0.260773			−0.130386	−	0.991463i	$-0.541622\pi$
$109$	−2.72255			−0.260773			−0.130386	+	0.991463i	$0.541622\pi$
$110$		0			0
$111$	−5.93857	−	4.61081i	−0.563664	−	0.437638i
$112$	0.172469	+	0.0304110i	0.0162968	+	0.00287357i
$113$	5.22307	+	14.3503i	0.491345	+	1.34996i	0.899450	+	0.437024i	$0.143968\pi$
$113$	5.22307	+	14.3503i	0.491345	+	1.34996i	−0.408105	+	0.912935i	$0.633810\pi$
$114$	1.01471	−	1.92242i	0.0950362	−	0.180051i
$115$		0			0
$116$	2.87519	+	4.97997i	0.266955	+	0.462379i
$117$	−15.2357	+	10.4115i	−1.40854	+	0.962545i
$118$	−20.2198	−	11.6739i	−1.86138	−	1.07467i
$119$	−0.123046	−	0.0447851i	−0.0112796	−	0.00410545i
$120$		0			0
$121$	−7.40151	−	6.21061i	−0.672865	−	0.564600i
$122$	16.2402	−	19.3543i	1.47032	−	1.75226i
$123$	−7.72600	−	8.52848i	−0.696630	−	0.768988i
$124$	20.1089	+	7.31904i	1.80583	+	0.657269i
$125$		0			0
$126$	0.226751	+	0.331817i	0.0202006	+	0.0295606i
$127$	−5.18376	+	2.99285i	−0.459984	+	0.265572i	−0.712038	−	0.702141i	$-0.752227\pi$
$127$	−5.18376	+	2.99285i	−0.459984	+	0.265572i	0.252053	+	0.967713i	$0.418894\pi$
$128$	−7.98255	+	1.40754i	−0.705565	+	0.124410i
$129$	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	$-0.00984418\pi$
$132$	3.06311	−	3.94518i	0.266609	−	0.343384i
$133$	−0.0240535	−	0.0286659i	−0.00208571	−	0.00248565i
$134$	9.99470			0.863410
$135$		0			0
$136$	2.16500			0.185647
$137$	2.38282	+	2.83974i	0.203578	+	0.242615i	0.858168	−	0.513369i	$-0.171603\pi$
$137$	2.38282	+	2.83974i	0.203578	+	0.242615i	−0.654589	+	0.755985i	$0.727158\pi$
$138$	10.3349	+	25.3583i	0.879765	+	2.15864i
$139$	1.10921	−	6.29062i	0.0940816	−	0.533563i	−0.900943	−	0.433937i	$-0.857124\pi$
$139$	1.10921	−	6.29062i	0.0940816	−	0.533563i	0.995025	−	0.0996265i	$-0.0317648\pi$
$140$		0			0
$141$	−10.2201	+	0.387903i	−0.860685	+	0.0326673i
$142$	−5.96094	+	1.05107i	−0.500231	+	0.0882042i
$143$	6.16191	−	3.55758i	0.515284	−	0.297500i
$144$	6.75486	+	4.84542i	0.562905	+	0.403785i
$145$		0			0
$146$	5.80495	+	2.11283i	0.480421	+	0.174859i
$147$	−11.8450	+	2.55526i	−0.976955	+	0.210754i
$148$	6.95586	−	8.28967i	0.571768	−	0.681406i
$149$	11.2316	+	9.42447i	0.920132	+	0.772083i	0.974019	−	0.226464i	$-0.0727167\pi$
$149$	11.2316	+	9.42447i	0.920132	+	0.772083i	−0.0538872	+	0.998547i	$0.517161\pi$
$150$		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	$0.771551\pi$
$152$	0.535818	+	0.309355i	0.0434606	+	0.0250920i
$153$	−4.34471	−	4.44485i	−0.351249	−	0.359345i
$154$	−0.0774802	−	0.134200i	−0.00624353	−	0.0108141i
$155$		0			0
$156$	−14.1430	−	22.4817i	−1.13235	−	1.79998i
$157$	7.81218	+	21.4638i	0.623480	+	1.71300i	0.698304	+	0.715801i	$0.253938\pi$
$157$	7.81218	+	21.4638i	0.623480	+	1.71300i	−0.0748243	+	0.997197i	$0.523840\pi$
$158$	10.7299	+	1.89197i	0.853626	+	0.150517i
$159$	0.145576	−	1.05910i	0.0115449	−	0.0839923i
$160$		0			0
$161$	0.471392			0.0371509
$162$	2.88378	+	18.8578i	0.226571	+	1.48161i
$163$			4.08982i			0.320340i	0.987089	+	0.160170i	$0.0512042\pi$
$163$			4.08982i			0.320340i	−0.987089	+	0.160170i	$0.948796\pi$
$164$	12.6882	−	10.6466i	0.990781	−	0.831364i
$165$		0			0
$166$	−1.23611	+	7.01034i	−0.0959408	+	0.544108i
$167$	−2.50261	−	6.87588i	−0.193658	−	0.532071i	0.804419	−	0.594063i	$-0.202477\pi$
$167$	−2.50261	−	6.87588i	−0.193658	−	0.532071i	−0.998077	+	0.0619917i	$0.980255\pi$
$168$	−0.0968228	+	0.0609103i	−0.00747004	+	0.00469933i
$169$	−4.31277	−	24.4590i	−0.331752	−	1.88146i
$170$		0			0
$171$	−0.440156	−	1.72087i	−0.0336596	−	0.131598i
$172$	23.8420	+	13.7652i	1.81794	+	1.04959i
$173$	−6.42229	+	17.6451i	−0.488277	+	1.34153i	0.413961	+	0.910294i	$0.364145\pi$
$173$	−6.42229	+	17.6451i	−0.488277	+	1.34153i	−0.902239	+	0.431237i	$0.858077\pi$
$174$	8.06189	+	2.59249i	0.611170	+	0.196536i
$175$		0			0
$176$	−2.45540	−	2.06032i	−0.185082	−	0.155303i
$177$	−18.6492	+	4.02312i	−1.40176	+	0.302396i
$178$	8.36300	−	22.9772i	0.626833	−	1.72221i
$179$	−5.41651	+	9.38167i	−0.404849	+	0.701219i	−0.994304	−	0.106582i	$-0.966009\pi$
$179$	−5.41651	+	9.38167i	−0.404849	+	0.701219i	0.589455	+	0.807801i	$0.299343\pi$
$180$		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	$0.630385\pi$
$182$	−0.811514	+	0.143092i	−0.0601534	+	0.0106067i
$183$	−0.783022	−	20.6303i	−0.0578826	−	1.52503i
$184$	−7.32392	+	2.66569i	−0.539927	+	0.196517i
$185$		0			0
$186$	29.1839	−	11.8940i	2.13987	−	0.872114i
$187$	1.54048	+	1.83588i	0.112651	+	0.134253i
$188$		−	14.7206i		−	1.07361i
$189$	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	$0.265146\pi$
$192$	−12.0434	+	15.5115i	−0.869157	+	1.11945i
$193$	−0.543795	−	0.0958856i	−0.0391432	−	0.00690200i	0.154042	−	0.988064i	$-0.450771\pi$
$193$	−0.543795	−	0.0958856i	−0.0391432	−	0.00690200i	−0.193185	+	0.981162i	$0.561882\pi$
$194$	25.6460	−	9.33439i	1.84128	−	0.670170i
$195$		0			0
$196$	−3.02858	−	17.1759i	−0.216327	−	1.22685i
$197$	12.8472	−	7.41735i	0.915327	−	0.528464i	0.0331858	−	0.999449i	$-0.489435\pi$
$197$	12.8472	−	7.41735i	0.915327	−	0.528464i	0.882141	+	0.470985i	$0.156101\pi$
$198$	−0.557561	−	7.33445i	−0.0396242	−	0.521237i
$199$	−2.77326	+	4.80343i	−0.196591	+	0.340506i	−0.947421	−	0.319990i	$-0.896321\pi$
$199$	−2.77326	+	4.80343i	−0.196591	+	0.340506i	0.750830	+	0.660496i	$0.229654\pi$
$200$		0			0
$201$	6.05268	−	5.48316i	0.426923	−	0.386752i
$202$	−12.3188	+	14.6810i	−0.866750	+	1.03295i
$203$	0.0937061	−	0.111675i	0.00657688	−	0.00783802i
$204$	6.63016	−	6.00630i	0.464204	−	0.420525i
$205$		0			0
$206$	−15.0308	+	26.0341i	−1.04725	+	1.81388i
$207$	20.1704	+	9.68689i	1.40194	+	0.673286i
$208$	−14.7612	+	8.52239i	−1.02351	+	0.590922i
$209$	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	$0.420513\pi$
$212$	1.51535	+	0.267197i	0.104074	+	0.0183511i
$213$	−3.03325	+	3.90673i	−0.207835	+	0.267685i
$214$	−33.3950	+	28.0217i	−2.28283	+	1.91552i
$215$		0			0
$216$	−5.39463	+	0.616629i	−0.367058	+	0.0419563i
$217$		−	0.542508i		−	0.0368279i
$218$	−3.70946	−	4.42076i	−0.251236	−	0.299412i
$219$	4.67453	−	1.90513i	0.315875	−	0.128737i
$220$		0			0
$221$	11.9757	−	4.35878i	0.805569	−	0.293203i
$222$	−0.604433	−	15.9250i	−0.0405669	−	1.06882i
$223$	−11.3092	+	1.99412i	−0.757321	+	0.133536i	−0.538959	−	0.842332i	$-0.681182\pi$
$223$	−11.3092	+	1.99412i	−0.757321	+	0.133536i	−0.218361	+	0.975868i	$0.570071\pi$
$224$	0.251651	+	0.435872i	0.0168141	+	0.0291229i
$225$		0			0
$226$	−16.1850	+	28.0332i	−1.07661	+	1.86474i
$227$	7.10252	−	19.5140i	0.471411	−	1.29519i	−0.445208	−	0.895427i	$-0.646870\pi$
$227$	7.10252	−	19.5140i	0.471411	−	1.29519i	0.916618	−	0.399763i	$-0.130908\pi$
$228$	2.49914	−	0.539129i	0.165510	−	0.0357047i
$229$	9.01009	+	7.56037i	0.595404	+	0.499603i	0.889965	−	0.456030i	$-0.150729\pi$
$229$	9.01009	+	7.56037i	0.595404	+	0.499603i	−0.294561	+	0.955633i	$0.595173\pi$
$230$		0			0
$231$	−0.120544	−	0.0387637i	−0.00793122	−	0.00255046i
$232$	−0.824380	+	2.26496i	−0.0541232	+	0.148702i
$233$	−6.93110	−	4.00167i	−0.454072	−	0.262158i	0.255477	−	0.966815i	$-0.417768\pi$
$233$	−6.93110	−	4.00167i	−0.454072	−	0.262158i	−0.709548	+	0.704657i	$0.751101\pi$
$234$	−37.6644	−	10.5535i	−2.46220	−	0.689902i
$235$		0			0
$236$	−4.76834	−	27.0426i	−0.310393	−	1.76032i
$237$	7.53587	−	4.74074i	0.489507	−	0.307944i
$238$	−0.0949295	−	0.260817i	−0.00615337	−	0.0169062i
$239$	0.910140	−	5.16166i	0.0588720	−	0.333880i	−0.941119	−	0.338075i	$-0.890224\pi$
$239$	0.910140	−	5.16166i	0.0588720	−	0.333880i	0.999991	+	0.00419508i	$0.00133534\pi$
$240$		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	$0.265713\pi$
$242$		−	20.4802i		−	1.31652i
$243$	12.0919	+	9.83800i	0.775695	+	0.631108i
$244$	29.7150			1.90231
$245$		0			0
$246$	3.32155	−	24.1652i	0.211775	−	1.54072i
$247$	3.58669	+	0.632430i	0.228216	+	0.0402406i
$248$	3.06784	+	8.42883i	0.194808	+	0.535231i
$249$	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	$0.672008\pi$
$252$	−0.127531	+	0.455147i	−0.00803371	+	0.0286715i
$253$	−7.47172	−	4.31380i	−0.469743	−	0.271206i
$254$	−11.9225	−	4.33944i	−0.748084	−	0.272280i
$255$		0			0
$256$	4.20911	+	3.53186i	0.263069	+	0.220741i
$257$	−6.10495	+	7.27559i	−0.380816	+	0.453839i	−0.922072	−	0.387019i	$-0.873505\pi$
$257$	−6.10495	+	7.27559i	−0.380816	+	0.453839i	0.541255	+	0.840858i	$0.317949\pi$
$258$	39.6318	−	8.54960i	2.46737	−	0.532275i
$259$	−0.257794	−	0.0938294i	−0.0160185	−	0.00583027i
$260$		0			0
$261$	6.30445	−	2.85283i	0.390236	−	0.176586i
$262$	8.57294	−	4.94959i	0.529638	−	0.305787i
$263$	−2.44889	+	0.431805i	−0.151005	+	0.0266262i	−0.248640	−	0.968596i	$-0.579983\pi$
$263$	−2.44889	+	0.431805i	−0.151005	+	0.0266262i	0.0976346	+	0.995222i	$0.468872\pi$
$264$	2.09207	−	0.0794046i	0.128758	−	0.00488701i
$265$		0			0
$266$	0.0137736	−	0.0781142i	0.000844516	−	0.00478949i
$267$	−7.54088	−	18.5027i	−0.461495	−	1.13235i
$268$	7.55595	+	9.00483i	0.461553	+	0.550057i
$269$	19.1404			1.16701			0.583506	−	0.812109i	$-0.301680\pi$
$269$	19.1404			1.16701			0.583506	+	0.812109i	$0.301680\pi$
$270$		0			0
$271$	−14.2245			−0.864077			−0.432039	−	0.901855i	$-0.642206\pi$
$271$	−14.2245			−0.864077			−0.432039	+	0.901855i	$0.642206\pi$
$272$	−3.69032	−	4.39795i	−0.223758	−	0.266665i
$273$	−0.412943	+	0.531857i	−0.0249925	+	0.0321895i
$274$	−1.36446	+	7.73826i	−0.0824303	+	0.467485i
$275$		0			0
$276$	−15.0337	+	28.4821i	−0.904919	+	1.71442i
$277$	13.2973	−	2.34467i	0.798956	−	0.140877i	0.240758	−	0.970585i	$-0.422604\pi$
$277$	13.2973	−	2.34467i	0.798956	−	0.140877i	0.558198	+	0.829708i	$0.311493\pi$
$278$	11.7257	−	6.76985i	0.703263	−	0.406029i
$279$	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	$0.653144\pi$
$282$	−14.5546	−	16.0664i	−0.866717	−	0.956740i
$283$	−0.817538	+	0.974304i	−0.0485976	+	0.0579163i	−0.789796	−	0.613370i	$-0.789813\pi$
$283$	−0.817538	+	0.974304i	−0.0485976	+	0.0579163i	0.741198	+	0.671286i	$0.234258\pi$
$284$	−5.45342	−	4.57596i	−0.323601	−	0.271533i
$285$		0			0
$286$	14.1722	+	5.15826i	0.838020	+	0.305014i
$287$	−0.363647	−	0.209952i	−0.0214654	−	0.0123931i
$288$	1.81092	+	23.8218i	0.106710	+	1.40371i
$289$	−6.35371	−	11.0049i	−0.373748	−	0.647350i
$290$		0			0
$291$	10.4100	−	19.7224i	0.610248	−	1.15615i
$292$	2.48494	+	6.82732i	0.145420	+	0.399538i
$293$	−28.8865	−	5.09348i	−1.68757	−	0.297564i	−0.754244	−	0.656595i	$-0.771996\pi$
$293$	−28.8865	−	5.09348i	−1.68757	−	0.297564i	−0.933326	+	0.359031i	$0.883107\pi$
$294$	−20.2878	−	15.7518i	−1.18321	−	0.918664i
$295$		0			0
$296$	4.53589			0.263643
$297$	−4.36138	−	4.13578i	−0.253073	−	0.239982i
$298$			31.0783i			1.80032i
$299$	−35.1453	+	29.4904i	−2.03251	+	1.70548i
$300$		0			0
$301$	0.121196	−	0.687335i	0.00698560	−	0.0396173i
$302$	−8.60503	−	23.6421i	−0.495164	−	1.36045i
$303$	0.593952	+	15.6489i	0.0341217	+	0.899003i
$304$	−0.284902	−	1.61576i	−0.0163403	−	0.0926702i
$305$		0			0
$306$	1.29772	−	13.1108i	0.0741858	−	0.749497i
$307$	−15.5189	−	8.95982i	−0.885708	−	0.511364i	−0.0131717	−	0.999913i	$-0.504193\pi$
$307$	−15.5189	−	8.95982i	−0.885708	−	0.511364i	−0.872536	+	0.488550i	$0.837526\pi$
$308$	0.0623339	−	0.171261i	0.00355180	−	0.00975850i
$309$	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	$0.542724\pi$
$312$	3.40819	−	10.5985i	0.192951	−	0.600023i
$313$	1.96214	−	5.39093i	0.110907	−	0.304713i	−0.871806	−	0.489851i	$-0.837051\pi$
$313$	1.96214	−	5.39093i	0.110907	−	0.304713i	0.982713	+	0.185138i	$0.0592732\pi$
$314$	−24.2080	+	41.9294i	−1.36613	+	2.36621i
$315$		0			0
$316$	6.40717	+	11.0975i	0.360432	+	0.624286i
$317$	1.03017	−	0.181646i	0.0578599	−	0.0102023i	−0.144643	−	0.989484i	$-0.546203\pi$
$317$	1.03017	−	0.181646i	0.0578599	−	0.0102023i	0.202503	+	0.979282i	$0.435092\pi$
$318$	1.91807	−	1.20664i	0.107560	−	0.0676651i
$319$	−2.50723	+	0.912555i	−0.140378	+	0.0510933i
$320$		0			0
$321$	−4.85073	+	35.2904i	−0.270742	+	1.96972i
$322$	0.642270	+	0.765427i	0.0357923	+	0.0426556i
$323$			1.22673i			0.0682568i
$324$	−14.8100	+	16.8546i	−0.822776	+	0.936365i
$325$		0			0
$326$	−6.64089	+	5.57236i	−0.367805	+	0.308625i
$327$	−4.67167	−	0.642130i	−0.258344	−	0.0355099i
$328$	6.83717	+	1.20558i	0.377519	+	0.0665668i
$329$	−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	$0.946292\pi$
$332$	−7.25053	+	4.18610i	−0.397925	+	0.229742i
$333$	−9.10260	−	9.31241i	−0.498819	−	0.510317i
$334$	7.75496	−	13.4320i	0.424333	−	0.734966i
$335$		0			0
$336$	0.288770	+	0.0928608i	0.0157537	+	0.00506597i
$337$	−14.0775	+	16.7769i	−0.766851	+	0.913898i	−0.998260	−	0.0589586i	$-0.981222\pi$
$337$	−14.0775	+	16.7769i	−0.766851	+	0.913898i	0.231409	+	0.972857i	$0.425666\pi$
$338$	33.8393	−	40.3281i	1.84061	−	2.19356i
$339$	5.57775	+	25.8558i	0.302942	+	1.40429i
$340$		0			0
$341$	−4.96459	+	8.59892i	−0.268848	+	0.465658i
$342$	2.19457	−	3.05939i	0.118669	−	0.165433i
$343$	−0.766051	+	0.442280i	−0.0413629	+	0.0238809i
$344$	2.00384	+	11.3643i	0.108040	+	0.612723i
$345$		0			0
$346$	−37.4017	+	13.6131i	−2.01073	+	0.731845i
$347$	−28.3773	−	5.00368i	−1.52337	−	0.268611i	−0.651615	−	0.758550i	$-0.725908\pi$
$347$	−28.3773	−	5.00368i	−1.52337	−	0.268611i	−0.871757	+	0.489939i	$0.837019\pi$
$348$	3.75903	+	9.22335i	0.201505	+	0.494424i
$349$	−13.1242	+	11.0125i	−0.702521	+	0.589485i	−0.922490	−	0.386022i	$-0.873849\pi$
$349$	−13.1242	+	11.0125i	−0.702521	+	0.589485i	0.219969	+	0.975507i	$0.429404\pi$
$350$		0			0
$351$	−28.5988	+	14.2719i	−1.52649	+	0.761775i
$352$		−	9.21160i		−	0.490980i
$353$	−1.56036	−	1.85957i	−0.0830497	−	0.0989747i	0.722919	−	0.690932i	$-0.242800\pi$
$353$	−1.56036	−	1.85957i	−0.0830497	−	0.0989747i	−0.805969	+	0.591958i	$0.798355\pi$
$354$	−31.9421	−	24.8004i	−1.69770	−	1.31813i
$355$		0			0
$356$	27.0239	−	9.83590i	1.43226	−	0.521301i
$357$	−0.200574	−	0.105869i	−0.0106155	−	0.00560317i
$358$	−22.6135	+	3.98738i	−1.19516	+	0.210739i
$359$	4.55147	+	7.88338i	0.240217	+	0.416069i	0.960776	−	0.277325i	$-0.0894479\pi$
$359$	4.55147	+	7.88338i	0.240217	+	0.416069i	−0.720559	+	0.693394i	$0.756115\pi$
$360$		0			0
$361$	9.32471	−	16.1509i	0.490774	−	0.850046i
$362$	−11.6115	+	31.9024i	−0.610289	+	1.67676i
$363$	−11.2356	−	12.4026i	−0.589714	−	0.650967i
$364$	−0.742421	−	0.622965i	−0.0389134	−	0.0326523i
$365$		0			0
$366$	32.4317	−	29.3801i	1.69523	−	1.53572i
$367$	−5.10194	+	14.0175i	−0.266319	+	0.731706i	0.732389	+	0.680887i	$0.238405\pi$
$367$	−5.10194	+	14.0175i	−0.266319	+	0.731706i	−0.998708	+	0.0508190i	$0.983817\pi$
$368$	17.8989	+	10.3340i	0.933047	+	0.538695i
$369$	−11.2457	−	16.4564i	−0.585427	−	0.856686i
$370$		0			0
$371$	−0.00677384	−	0.0384164i	−0.000351680	−	0.00199448i
$372$	32.7790	+	17.3017i	1.69951	+	0.897050i
$373$	−6.70266	−	18.4154i	−0.347050	−	0.953513i	−0.983294	−	0.182025i	$-0.941735\pi$
$373$	−6.70266	−	18.4154i	−0.347050	−	0.953513i	0.636243	−	0.771488i	$-0.280487\pi$
$374$	−0.882119	+	5.00274i	−0.0456133	+	0.258686i
$375$		0			0
$376$	4.72670	−	3.96617i	0.243761	−	0.204540i
$377$			14.1883i			0.730737i
$378$	0.310826	+	0.622852i	0.0159871	+	0.0320360i
$379$	−7.13880			−0.366696			−0.183348	−	0.983048i	$-0.558693\pi$
$379$	−7.13880			−0.366696			−0.183348	+	0.983048i	$0.558693\pi$
$380$		0			0
$381$	−9.60079	+	3.91285i	−0.491863	+	0.200461i
$382$	2.28916	+	0.403641i	0.117124	+	0.0206521i
$383$	11.7974	+	32.4131i	0.602820	+	1.65623i	0.745532	+	0.666470i	$0.232195\pi$
$383$	11.7974	+	32.4131i	0.602820	+	1.65623i	−0.142712	+	0.989764i	$0.545582\pi$
$384$	−14.0294	+	0.532485i	−0.715934	+	0.0271733i
$385$		0			0
$386$	−0.585222	−	1.01363i	−0.0297870	−	0.0515926i
$387$	19.3102	−	26.9198i	0.981595	−	1.36841i
$388$	27.7982	+	16.0493i	1.41124	+	0.814780i
$389$	−9.11176	−	3.31641i	−0.461985	−	0.168149i	0.100533	−	0.994934i	$-0.467945\pi$
$389$	−9.11176	−	3.31641i	−0.461985	−	0.168149i	−0.562518	+	0.826785i	$0.690167\pi$
$390$		0			0
$391$	−11.8378	−	9.93313i	−0.598666	−	0.502340i
$392$	4.69911	−	5.60019i	0.237341	−	0.282852i
$393$	2.47630	−	7.70059i	0.124913	−	0.388443i
$394$	29.5483	+	10.7547i	1.48862	+	0.541813i
$395$		0			0
$396$	6.18654	−	6.04715i	0.310885	−	0.303881i
$397$	17.4381	−	10.0679i	0.875193	−	0.505293i	0.00612241	−	0.999981i	$-0.498051\pi$
$397$	17.4381	−	10.0679i	0.875193	−	0.505293i	0.869070	+	0.494688i	$0.164718\pi$
$398$	−11.5782	+	2.04154i	−0.580361	+	0.102333i
$399$	−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	$0.962614\pi$
$402$	17.1501	+	2.35731i	0.855368	+	0.117572i
$403$	33.9395	+	40.4475i	1.69064	+	2.01483i
$404$	−22.5400			−1.12141
$405$		0			0
$406$	0.309007			0.0153357
$407$	3.22747	+	3.84634i	0.159980	+	0.190656i
$408$	3.71496	+	0.510629i	0.183918	+	0.0252799i
$409$	−0.783389	+	4.44282i	−0.0387361	+	0.219683i	−0.998031	−	0.0627230i	$-0.980022\pi$
$409$	−0.783389	+	4.44282i	−0.0387361	+	0.219683i	0.959295	+	0.282406i	$0.0911326\pi$
$410$		0			0
$411$	3.41896	+	5.43476i	0.168645	+	0.268077i
$412$	−34.8189	+	6.13952i	−1.71541	+	0.302472i
$413$	−0.602881	+	0.348074i	−0.0296658	+	0.0171276i
$414$	11.7529	+	45.9502i	0.577624	+	2.25833i
$415$		0			0
$416$	−46.0304	−	16.7537i	−2.25683	−	0.821418i
$417$	3.38699	−	10.5326i	0.165862	−	0.515782i
$418$	−0.933154	+	1.11209i	−0.0456421	+	0.0543941i
$419$	−16.6030	−	13.9316i	−0.811111	−	0.680603i	0.139762	−	0.990185i	$-0.455366\pi$
$419$	−16.6030	−	13.9316i	−0.811111	−	0.680603i	−0.950873	+	0.309582i	$0.899811\pi$
$420$		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	$0.446965\pi$
$422$	−5.28955	−	3.05393i	−0.257491	−	0.148663i
$423$	−17.6283	−	1.74486i	−0.857116	−	0.0848380i
$424$	0.322485	+	0.558561i	0.0156613	+	0.0271261i
$425$		0			0
$426$	−10.4764	+	0.397631i	−0.507582	+	0.0192653i
$427$	−0.257651	−	0.707890i	−0.0124686	−	0.0342572i
$428$	−50.4929	−	8.90326i	−2.44067	−	0.430355i
$429$	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	$0.404476\pi$
$432$	10.4480	+	9.90752i	0.502678	+	0.476676i
$433$		−	34.5905i		−	1.66231i	−0.556039	−	0.831156i	$-0.687679\pi$
$433$		−	34.5905i		−	1.66231i	0.556039	−	0.831156i	$-0.312321\pi$
$434$	0.880902	−	0.739165i	0.0422847	−	0.0354810i
$435$		0			0
$436$	1.17860	−	6.68415i	0.0564445	−	0.320113i
$437$	−1.51043	−	4.14986i	−0.0722535	−	0.198515i
$438$	9.46248	+	4.99457i	0.452135	+	0.238650i
$439$	−5.53151	−	31.3708i	−0.264005	−	1.49724i	−0.771854	−	0.635799i	$-0.780671\pi$
$439$	−5.53151	−	31.3708i	−0.264005	−	1.49724i	0.507850	−	0.861446i	$-0.330441\pi$
$440$		0			0
$441$	−20.9276	+	1.59091i	−0.996554	+	0.0757575i
$442$	23.3944	+	13.5067i	1.11276	+	0.642450i
$443$	0.638551	−	1.75440i	0.0303385	−	0.0833543i	−0.923599	−	0.383361i	$-0.874767\pi$
$443$	0.638551	−	1.75440i	0.0303385	−	0.0833543i	0.953937	+	0.300006i	$0.0969888\pi$
$444$	13.8908	−	12.5838i	0.659230	−	0.597201i
$445$		0			0
$446$	−18.6467	−	15.6464i	−0.882947	−	0.740880i
$447$	17.0498	+	18.8207i	0.806426	+	0.890187i
$448$	−0.245082	+	0.673356i	−0.0115790	+	0.0318131i
$449$	11.2063	−	19.4098i	0.528856	−	0.916006i	−0.470577	−	0.882359i	$-0.655954\pi$
$449$	11.2063	−	19.4098i	0.528856	−	0.916006i	0.999434	−	0.0336474i	$-0.0107123\pi$
$450$		0			0
$451$	3.84261	+	6.65560i	0.180942	+	0.313400i
$452$	−37.4925	+	6.61094i	−1.76350	+	0.310953i
$453$	−18.1814	−	9.59664i	−0.854235	−	0.450890i
$454$	41.3632	−	15.0550i	1.94127	−	0.706565i
$455$		0			0
$456$	0.846456	+	0.657203i	0.0396389	+	0.0307763i
$457$	−10.2686	−	12.2376i	−0.480345	−	0.572453i	0.470390	−	0.882459i	$-0.344113\pi$
$457$	−10.2686	−	12.2376i	−0.480345	−	0.572453i	−0.950735	+	0.310006i	$0.899669\pi$
$458$			24.9312i			1.16496i
$459$	−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	$0.0814516\pi$
$462$	−0.101298	−	0.248550i	−0.00471280	−	0.0115636i
$463$	35.3386	+	6.23114i	1.64232	+	0.289586i	0.917019	−	0.398844i	$-0.130588\pi$
$463$	35.3386	+	6.23114i	1.64232	+	0.289586i	0.725303	+	0.688429i	$0.241699\pi$
$464$	6.00621	−	2.18608i	0.278831	−	0.101486i
$465$		0			0
$466$	−2.94584	−	16.7067i	−0.136463	−	0.773923i
$467$	−9.02009	+	5.20775i	−0.417400	+	0.240986i	−0.693964	−	0.720009i	$-0.744137\pi$
$467$	−9.02009	+	5.20775i	−0.417400	+	0.240986i	0.276564	+	0.960995i	$0.410804\pi$
$468$	−18.9658	−	41.9125i	−0.876695	−	1.93740i
$469$	0.149003	−	0.258081i	0.00688033	−	0.0119171i
$470$		0			0
$471$	8.34269	+	38.6727i	0.384411	+	1.78194i
$472$	7.39850	−	8.81719i	0.340544	−	0.405844i
$473$	−8.21091	+	9.78538i	−0.377538	+	0.449932i
$474$	17.9654	+	5.77718i	0.825178	+	0.265355i
$475$		0			0
$476$	0.163219	−	0.282704i	0.00748114	−	0.0129577i
$477$	0.499592	−	1.78300i	0.0228747	−	0.0816378i
$478$	9.62135	−	5.55489i	0.440070	−	0.254075i
$479$	1.11318	+	6.31318i	0.0508627	+	0.288457i	0.999620	−	0.0275476i	$-0.00876978\pi$
$479$	1.11318	+	6.31318i	0.0508627	+	0.288457i	−0.948758	+	0.316004i	$0.897659\pi$
$480$		0			0
$481$	25.0902	−	9.13208i	1.14401	−	0.416387i
$482$	2.45594	+	0.433048i	0.111865	+	0.0197248i
$483$	0.808870	+	0.111181i	0.0368049	+	0.00505891i
$484$	18.4518	−	15.4829i	0.838720	−	0.703769i
$485$		0			0
$486$	0.500605	+	33.0385i	0.0227079	+	1.49866i
$487$			15.0810i			0.683385i	0.939812	+	0.341692i	$0.111000\pi$
$487$			15.0810i			0.683385i	−0.939812	+	0.341692i	$0.889000\pi$
$488$	8.00613	+	9.54133i	0.362420	+	0.431916i
$489$	−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	$0.563279\pi$
$492$	24.2829	−	15.2762i	1.09476	−	0.688703i
$493$	−4.70639	+	0.829863i	−0.211965	+	0.0373752i
$494$	3.85993	+	6.68560i	0.173667	+	0.300799i
$495$		0			0
$496$	11.8930	−	20.5992i	0.534010	−	0.924933i
$497$	−0.0617263	+	0.169592i	−0.00276880	+	0.00760723i
$498$	−3.77450	+	11.7376i	−0.169139	+	0.525975i
$499$	2.92703	+	2.45607i	0.131032	+	0.109949i	0.705948	−	0.708263i	$-0.250521\pi$
$499$	2.92703	+	2.45607i	0.131032	+	0.109949i	−0.574917	+	0.818212i	$0.694965\pi$
$500$		0			0
$501$	−2.67256	−	12.3887i	−0.119401	−	0.553486i
$502$	−11.1503	+	30.6351i	−0.497660	+	1.36731i
$503$	−7.37530	−	4.25813i	−0.328848	−	0.189861i	0.326481	−	0.945204i	$-0.394137\pi$
$503$	−7.37530	−	4.25813i	−0.328848	−	0.189861i	−0.655330	+	0.755343i	$0.727470\pi$
$504$	−0.180506	+	0.0816808i	−0.00804037	+	0.00363835i
$505$		0			0
$506$	−3.17561	−	18.0098i	−0.141173	−	0.800633i
$507$	−1.63156	−	42.9867i	−0.0724602	−	1.90911i
$508$	−5.10370	−	14.0223i	−0.226440	−	0.622139i
$509$	−2.56080	+	14.5230i	−0.113506	+	0.643722i	0.873974	+	0.485973i	$0.161535\pi$
$509$	−2.56080	+	14.5230i	−0.113506	+	0.643722i	−0.987479	+	0.157749i	$0.949576\pi$
$510$		0			0
$511$	0.141098	−	0.118396i	0.00624183	−	0.00523752i
$512$			27.8581i			1.23117i
$513$	−0.349393	−	3.05669i	−0.0154261	−	0.134956i
$514$	−20.1318			−0.887974
$515$		0			0
$516$	37.6643	+	29.2432i	1.65808	+	1.28736i
$517$	6.72647	+	1.18606i	0.295830	+	0.0521628i
$518$	−0.198887	−	0.546437i	−0.00873859	−	0.0240091i
$519$	−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	$0.834434\pi$
$522$	13.2221	+	6.34994i	0.578715	+	0.277929i
$523$	−1.13662	−	0.656230i	−0.0497011	−	0.0286949i	0.474944	−	0.880016i	$-0.342468\pi$
$523$	−1.13662	−	0.656230i	−0.0497011	−	0.0286949i	−0.524645	+	0.851321i	$0.675802\pi$
$524$	10.9405	+	3.98201i	0.477937	+	0.173955i
$525$		0			0
$526$	−4.03774	−	3.38807i	−0.176054	−	0.147727i
$527$	−11.4317	+	13.6237i	−0.497972	+	0.593459i
$528$	−3.72732	−	4.11446i	−0.162211	−	0.179059i
$529$	30.6634	+	11.1606i	1.33319	+	0.485242i
$530$		0			0
$531$	−32.9494	+	2.50480i	−1.42988	+	0.108699i
$532$	0.0807907	−	0.0466445i	0.00350272	−	0.00202230i
$533$	40.2469	−	7.09661i	1.74328	−	0.307388i
$534$	19.7695	−	37.4544i	0.855511	−	1.62081i
$535$		0			0
$536$	−0.855600	+	4.85235i	−0.0369563	+	0.209590i
$537$	−11.5070	+	14.8207i	−0.496564	+	0.639558i
$538$	26.0787	+	31.0794i	1.12433	+	1.33993i
$539$	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	$0.365180\pi$
$542$	−19.3808	−	23.0972i	−0.832477	−	0.992108i
$543$	10.4701	+	25.6900i	0.449314	+	1.10246i
$544$	2.86506	−	16.2486i	0.122839	−	0.696652i
$545$		0			0
$546$	−1.42624	+	0.0541329i	−0.0610374	+	0.00231668i
$547$	30.7920	−	5.42945i	1.31657	−	0.232147i	0.529131	−	0.848540i	$-0.322518\pi$
$547$	30.7920	−	5.42945i	1.31657	−	0.232147i	0.787438	+	0.616394i	$0.211407\pi$
$548$	−8.00340	+	4.62076i	−0.341888	+	0.197389i
$549$	3.52218	−	35.5845i	0.150323	−	1.51871i
$550$		0			0
$551$	−1.28337	−	0.467108i	−0.0546733	−	0.0198995i
$552$	−13.1960	+	2.84671i	−0.561657	+	0.121164i
$553$	0.208818	−	0.248860i	0.00887984	−	0.0105826i
$554$	21.9246	+	18.3970i	0.931489	+	0.781612i
$555$		0			0
$556$	14.9640	+	5.44644i	0.634614	+	0.230981i
$557$	31.9837	+	18.4658i	1.35519	+	0.782422i	0.988972	−	0.148105i	$-0.0473175\pi$
$557$	31.9837	+	18.4658i	1.35519	+	0.782422i	0.366223	+	0.930527i	$0.380651\pi$
$558$	52.8824	−	13.5260i	2.23869	−	0.572601i
$559$	33.9639	+	58.8272i	1.43652	+	2.48813i
$560$		0			0
$561$	2.21034	+	3.51354i	0.0933205	+	0.148342i
$562$	−3.20019	−	8.79244i	−0.134992	−	0.370887i
$563$	−32.9458	−	5.80924i	−1.38850	−	0.244830i	−0.571091	−	0.820887i	$-0.693480\pi$
$563$	−32.9458	−	5.80924i	−1.38850	−	0.244830i	−0.817410	+	0.576056i	$0.804591\pi$
$564$	3.47194	−	25.2593i	0.146195	−	1.06361i
$565$		0			0
$566$	−2.69592			−0.113318
$567$	0.529933	+	0.206671i	0.0222551	+	0.00867938i
$568$		−	2.98397i		−	0.125204i
$569$	18.5935	−	15.6018i	0.779481	−	0.654062i	−0.163637	−	0.986521i	$-0.552323\pi$
$569$	18.5935	−	15.6018i	0.779481	−	0.654062i	0.943118	+	0.332459i	$0.107878\pi$
$570$		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	$0.813716\pi$
$572$	6.06674	+	16.6682i	0.253663	+	0.696934i
$573$	1.60773	−	1.01141i	0.0671640	−	0.0422522i
$574$	−0.154556	−	0.876533i	−0.00645106	−	0.0365858i
$575$		0			0
$576$	−24.3239	+	23.7759i	−1.01350	+	0.990663i
$577$	−15.1290	−	8.73471i	−0.629827	−	0.363631i	0.150858	−	0.988555i	$-0.451796\pi$
$577$	−15.1290	−	8.73471i	−0.629827	−	0.363631i	−0.780685	+	0.624925i	$0.785130\pi$
$578$	9.21248	−	25.3111i	0.383189	−	1.05280i
$579$	−0.910491	−	0.292789i	−0.0378387	−	0.0121679i
$580$		0			0
$581$	0.162591	+	0.136430i	0.00674542	+	0.00566008i
$582$	46.2080	−	9.96826i	1.91538	−	0.413198i
$583$	−0.244188	+	0.670900i	−0.0101132	+	0.0277858i
$584$	−1.52270	+	2.63739i	−0.0630096	+	0.109136i
$585$		0			0
$586$	−31.0872	−	53.8446i	−1.28420	−	2.22430i
$587$	−11.2489	+	1.98349i	−0.464294	+	0.0818675i	−0.400901	−	0.916121i	$-0.631303\pi$
$587$	−11.2489	+	1.98349i	−0.464294	+	0.0818675i	−0.0633922	+	0.997989i	$0.520192\pi$
$588$	−1.14574	−	30.1868i	−0.0472495	−	1.24488i
$589$	−4.77592	+	1.73829i	−0.196788	+	0.0716251i
$590$		0			0
$591$	23.7942	−	9.69746i	0.978763	−	0.398900i
$592$	−7.73159	−	9.21415i	−0.317766	−	0.378699i
$593$			21.5568i			0.885230i	0.896712	+	0.442615i	$0.145949\pi$
$593$			21.5568i			0.885230i	−0.896712	+	0.442615i	$0.854051\pi$
$594$	0.773148	−	12.7168i	0.0317227	−	0.521777i
$595$		0			0
$596$	−28.0003	+	23.4950i	−1.14694	+	0.962394i
$597$	−5.89161	+	7.58820i	−0.241127	+	0.310564i
$598$	−95.7707	−	16.8870i	−3.91635	−	0.690559i
$599$	−9.12886	+	3.32263i	−0.372995	+	0.135759i	−0.521714	−	0.853120i	$-0.674707\pi$
$599$	−9.12886	+	3.32263i	−0.372995	+	0.135759i	0.148719	+	0.988880i	$0.452485\pi$
$600$		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	$-0.222755\pi$
$602$	1.28119	−	0.739697i	0.0522175	−	0.0301478i
$603$	11.6791	−	7.98109i	0.475611	−	0.325015i
$604$	14.7953	−	25.6261i	0.602011	−	1.04271i
$605$		0			0
$606$	−24.6007	+	22.2859i	−0.999335	+	0.905304i
$607$	0.295294	−	0.351918i	0.0119856	−	0.0142839i	−0.760018	−	0.649902i	$-0.774810\pi$
$607$	0.295294	−	0.351918i	0.0119856	−	0.0142839i	0.772004	+	0.635618i	$0.219255\pi$
$608$	3.03082	−	3.61199i	0.122916	−	0.146486i
$609$	0.187131	−	0.169523i	0.00758293	−	0.00686943i
$610$		0			0
$611$	18.1606	−	31.4551i	0.734699	−	1.27254i
$612$	12.7934	−	8.74255i	0.517144	−	0.353396i
$613$	24.5986	−	14.2020i	0.993527	−	0.573613i	0.0872001	−	0.996191i	$-0.472208\pi$
$613$	24.5986	−	14.2020i	0.993527	−	0.573613i	0.906327	+	0.422578i	$0.138875\pi$
$614$	−6.59579	−	37.4066i	−0.266184	−	1.50961i
$615$		0			0
$616$	0.0717856	−	0.0261278i	0.00289233	−	0.00105272i
$617$	−12.4327	−	2.19222i	−0.500520	−	0.0882553i	−0.0823125	−	0.996607i	$-0.526231\pi$
$617$	−12.4327	−	2.19222i	−0.500520	−	0.0882553i	−0.418208	+	0.908351i	$0.637342\pi$
$618$	−31.9319	+	41.1273i	−1.28449	+	1.65438i
$619$	6.34778	−	5.32642i	0.255139	−	0.214087i	−0.506243	−	0.862391i	$-0.668966\pi$
$619$	6.34778	−	5.32642i	0.255139	−	0.214087i	0.761381	+	0.648304i	$0.224521\pi$
$620$		0			0
$621$	32.3260	+	21.3792i	1.29720	+	0.857919i
$622$			39.9597i			1.60224i
$623$	−0.468634	−	0.558496i	−0.0187754	−	0.0223757i
$624$	−27.3391	+	11.1422i	−1.09444	+	0.446045i
$625$		0			0
$626$	11.4270	−	4.15908i	0.456714	−	0.166230i
$627$	0.0449920	+	1.18540i	0.00179681	+	0.0473405i
$628$	−56.0778	+	9.88804i	−2.23775	+	0.394576i
$629$	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	$-0.0302191\pi$
$632$	−1.83708	+	5.04733i	−0.0730750	+	0.200772i
$633$	−4.87870	+	1.05246i	−0.193911	+	0.0418316i
$634$	1.69854	+	1.42525i	0.0674578	+	0.0566038i
$635$		0			0
$636$	2.53719	+	0.815892i	0.100606	+	0.0323522i
$637$	14.7182	−	40.4380i	0.583158	−	1.60221i
$638$	−4.89785	−	2.82778i	−0.193908	−	0.111953i
$639$	−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	$0.981108\pi$
$642$	−63.9121	+	40.2065i	−2.52241	+	1.58682i
$643$	4.76353	+	13.0877i	0.187855	+	0.516128i	0.997490	−	0.0708056i	$-0.0225570\pi$
$643$	4.76353	+	13.0877i	0.187855	+	0.516128i	−0.809635	+	0.586934i	$0.800335\pi$
$644$	−0.204067	+	1.15732i	−0.00804135	+	0.0456048i
$645$		0			0
$646$	−1.99191	+	1.67141i	−0.0783705	+	0.0657606i
$647$		−	12.0852i		−	0.475119i	−0.971373	−	0.237559i	$-0.923653\pi$
$647$		−	12.0852i		−	0.475119i	0.971373	−	0.237559i	$-0.0763474\pi$
$648$	−9.40217	−	0.214273i	−0.369352	−	0.00841744i
$649$	12.7411			0.500133
$650$		0			0
$651$	0.127954	−	0.930899i	0.00501491	−	0.0364848i
$652$	−10.0410	−	1.77049i	−0.393234	−	0.0693378i
$653$	−8.18336	−	22.4836i	−0.320240	−	0.879851i	−0.990474	−	0.137701i	$-0.956029\pi$
$653$	−8.18336	−	22.4836i	−0.320240	−	0.879851i	0.670234	−	0.742150i	$-0.266194\pi$
$654$	−5.32246	−	8.46056i	−0.208125	−	0.330834i
$655$		0			0
$656$	−9.20521	−	15.9439i	−0.359403	−	0.622504i
$657$	8.47044	−	2.16653i	0.330463	−	0.0845242i
$658$	−0.685057	−	0.395518i	−0.0267063	−	0.0154189i
$659$	−12.1165	−	4.41004i	−0.471991	−	0.171791i	0.0950632	−	0.995471i	$-0.469695\pi$
$659$	−12.1165	−	4.41004i	−0.471991	−	0.171791i	−0.567054	+	0.823681i	$0.691917\pi$
$660$		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	$0.840606\pi$
$662$	0.287678	−	0.342842i	0.0111809	−	0.0133249i
$663$	21.5773	−	4.65477i	0.837992	−	0.180776i
$664$	−3.29765	−	1.20025i	−0.127974	−	0.0465786i
$665$		0			0
$666$	2.71885	−	27.4685i	0.105353	−	1.06438i
$667$	14.8994	−	8.60215i	0.576905	−	0.333076i
$668$	17.9644	−	3.16761i	0.695064	−	0.122558i
$669$	−19.8760	+	0.754393i	−0.768450	+	0.0291665i
$670$		0			0
$671$	−2.39418	+	13.5781i	−0.0924264	+	0.524176i
$672$	0.329009	+	0.807273i	0.0126918	+	0.0311412i
$673$	−18.2991	−	21.8080i	−0.705378	−	0.840637i	0.287746	−	0.957707i	$-0.407094\pi$
$673$	−18.2991	−	21.8080i	−0.705378	−	0.840637i	−0.993124	+	0.117070i	$0.962650\pi$
$674$	−46.4222			−1.78812
$675$		0			0
$676$	61.9164			2.38140
$677$	12.1627	+	14.4949i	0.467450	+	0.557085i	0.947334	−	0.320247i	$-0.103766\pi$
$677$	12.1627	+	14.4949i	0.467450	+	0.557085i	−0.479884	+	0.877332i	$0.659321\pi$
$678$	−34.3838	+	44.2853i	−1.32050	+	1.70076i
$679$	0.141306	−	0.801385i	0.00542282	−	0.0307544i
$680$		0			0
$681$	16.7898	−	31.8093i	0.643388	−	1.21893i
$682$	−20.7268	+	3.65469i	−0.793670	+	0.139945i
$683$	−37.3592	+	21.5693i	−1.42951	+	0.825328i	−0.997082	−	0.0763404i	$-0.975676\pi$
$683$	−37.3592	+	21.5693i	−1.42951	+	0.825328i	−0.432428	+	0.901668i	$0.642343\pi$
$684$	4.41547	−	0.335662i	0.168830	−	0.0128344i
$685$		0			0
$686$	−1.76190	−	0.641278i	−0.0672695	−	0.0244841i
$687$	13.6774	+	15.0981i	0.521826	+	0.576027i
$688$	19.6697	−	23.4415i	0.749901	−	0.893698i
$689$	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	$0.359397\pi$
$692$	−40.5404	−	23.4060i	−1.54111	−	0.889762i
$693$	−0.197701	−	0.0949464i	−0.00751004	−	0.00360671i
$694$	−30.5391	−	52.8953i	−1.15925	−	2.00788i
$695$		0			0
$696$	−1.94877	+	3.69206i	−0.0738681	+	0.139947i
$697$	4.70801	+	12.9351i	0.178328	+	0.489953i
$698$	−35.7632	−	6.30602i	−1.35366	−	0.238687i
$699$	−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	$0.594432\pi$
$702$	−62.1398	−	26.9923i	−2.34532	−	1.01876i
$703$			2.57011i			0.0969336i
$704$	10.0466	−	8.43012i	0.378646	−	0.317722i
$705$		0			0
$706$	0.893502	−	5.06730i	0.0336274	−	0.190710i
$707$	0.195438	+	0.536962i	0.00735021	+	0.0201945i
$708$	−1.80391	−	47.5275i	−0.0677950	−	1.78619i
$709$	−7.54820	−	42.8080i	−0.283479	−	1.60769i	−0.710669	−	0.703526i	$-0.751608\pi$
$709$	−7.54820	−	42.8080i	−0.283479	−	1.60769i	0.427191	−	0.904162i	$-0.359503\pi$
$710$		0			0
$711$	14.0491	−	6.35734i	0.526881	−	0.238419i
$712$	10.4393	+	6.02714i	0.391230	+	0.225877i
$713$	21.8975	−	60.1629i	0.820068	−	2.25312i
$714$	−0.101376	−	0.469930i	−0.00379390	−	0.0175867i
$715$		0			0
$716$	−20.6882	−	17.3595i	−0.773154	−	0.648753i
$717$	2.77913	−	8.64232i	0.103789	−	0.322753i
$718$	−6.59934	+	18.1315i	−0.246285	+	0.676663i
$719$	17.5213	−	30.3477i	0.653433	−	1.13178i	−0.328851	−	0.944382i	$-0.606661\pi$
$719$	17.5213	−	30.3477i	0.653433	−	1.13178i	0.982284	−	0.187397i	$-0.0600052\pi$
$720$		0			0
$721$	0.448165	+	0.776245i	0.0166905	+	0.0289089i
$722$	38.9300	−	6.86441i	1.44882	−	0.255467i
$723$	1.72486	−	1.08510i	0.0641483	−	0.0403551i
$724$	−37.5211	+	13.6566i	−1.39446	+	0.507542i
$725$		0			0
$726$	4.83038	−	35.1423i	0.179272	−	1.30425i
$727$	2.42271	+	2.88728i	0.0898534	+	0.107083i	0.809098	−	0.587674i	$-0.199956\pi$
$727$	2.42271	+	2.88728i	0.0898534	+	0.107083i	−0.719244	+	0.694757i	$0.755512\pi$
$728$		−	0.406233i		−	0.0150560i
$729$	18.4283	+	19.7331i	0.682531	+	0.730857i
$730$		0			0
$731$	−17.5270	+	14.7069i	−0.648258	+	0.543953i
$732$	50.9885	+	7.00848i	1.88459	+	0.259041i
$733$	−1.64628	−	0.290284i	−0.0608068	−	0.0107219i	0.143162	−	0.989699i	$-0.454273\pi$
$733$	−1.64628	−	0.290284i	−0.0608068	−	0.0107219i	−0.203969	+	0.978977i	$0.565384\pi$
$734$	−29.7123	+	10.8144i	−1.09670	+	0.399167i
$735$		0			0
$736$	10.3142	+	58.4946i	0.380186	+	2.15614i
$737$	−4.72349	+	2.72711i	−0.173992	+	0.100454i
$738$	11.3990	−	40.6820i	0.419604	−	1.49753i
$739$	−22.4813	+	38.9388i	−0.826989	+	1.43239i	0.0734007	+	0.997303i	$0.476615\pi$
$739$	−22.4813	+	38.9388i	−0.826989	+	1.43239i	−0.900390	+	0.435084i	$0.856719\pi$
$740$		0			0
$741$	6.00530	+	1.93114i	0.220610	+	0.0709423i
$742$	0.0531495	−	0.0633412i	0.00195118	−	0.00232533i
$743$	0.0666964	−	0.0794857i	0.00244685	−	0.00291605i	−0.764820	−	0.644244i	$-0.777172\pi$
$743$	0.0666964	−	0.0794857i	0.00244685	−	0.00291605i	0.767266	+	0.641328i	$0.221616\pi$
$744$	3.27617	+	15.1867i	0.120110	+	0.556773i
$745$		0			0
$746$	20.7698	−	35.9744i	0.760437	−	1.31712i
$747$	4.15354	+	9.17889i	0.151970	+	0.335838i
$748$	−5.17415	+	2.98730i	−0.189186	+	0.109226i
$749$	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	$0.528299\pi$
$752$	−16.1137	−	2.84127i	−0.587605	−	0.103611i
$753$	10.0541	+	24.6694i	0.366393	+	0.899002i
$754$	−23.0384	+	19.3315i	−0.839010	+	0.704013i
$755$		0			0
$756$	−0.326182	+	0.750915i	−0.0118631	+	0.0273105i
$757$		−	10.9327i		−	0.397356i	−0.980065	−	0.198678i	$-0.936335\pi$
$757$		−	10.9327i		−	0.397356i	0.980065	−	0.198678i	$-0.0636648\pi$
$758$	−9.72658	−	11.5917i	−0.353285	−	0.421029i
$759$	−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	$0.222919\pi$
$762$	−19.4345	−	10.2581i	−0.704039	−	0.371612i
$763$	−0.169453	+	0.0298792i	−0.00613462	+	0.00108170i
$764$	1.36693	+	2.36760i	0.0494539	+	0.0856566i
$765$		0			0
$766$	−36.5572	+	63.3189i	−1.32086	+	2.28780i
$767$	23.1731	−	63.6675i	0.836732	−	2.29890i
$768$	6.38947	+	7.05313i	0.230560	+	0.254508i
$769$	−14.3237	−	12.0190i	−0.516525	−	0.433416i	0.346893	−	0.937905i	$-0.387237\pi$
$769$	−14.3237	−	12.0190i	−0.516525	−	0.433416i	−0.863418	+	0.504489i	$0.831681\pi$
$770$		0			0
$771$	−12.1916	+	11.0444i	−0.439069	+	0.397755i
$772$	0.470819	−	1.29357i	0.0169452	−	0.0465564i
$773$	26.7246	+	15.4294i	0.961216	+	0.554959i	0.896547	−	0.442948i	$-0.146067\pi$
$773$	26.7246	+	15.4294i	0.961216	+	0.554959i	0.0646692	+	0.997907i	$0.479401\pi$
$774$	70.0214	−	5.32299i	2.51687	−	0.191331i
$775$		0			0
$776$	2.33634	+	13.2500i	0.0838696	+	0.475648i
$777$	−0.420223	−	0.221806i	−0.0150754	−	0.00795724i
$778$	−7.02968	−	19.3139i	−0.252026	−	0.692436i
$779$	−0.683101	+	3.87406i	−0.0244746	+	0.138802i
$780$		0			0
$781$	2.53035	−	2.12321i	0.0905429	−	0.0759745i
$782$		−	32.7556i		−	1.17134i
$783$	11.4908	−	3.40827i	0.410647	−	0.121802i
$784$	−19.3860			−0.692356
$785$		0			0
$786$	15.8778	−	6.47110i	0.566344	−	0.230816i
$787$	−37.7923	−	6.66381i	−1.34715	−	0.237539i	−0.546897	−	0.837200i	$-0.684191\pi$
$787$	−37.7923	−	6.66381i	−1.34715	−	0.237539i	−0.800254	+	0.599661i	$0.795302\pi$
$788$	12.6488	+	34.7523i	0.450595	+	1.23800i
$789$	−4.30393	+	0.163356i	−0.153224	+	0.00581562i
$790$		0			0
$791$	0.482578	+	0.835849i	0.0171585	+	0.0297194i
$792$	3.60855	+	0.357177i	0.128224	+	0.0126917i
$793$	63.4953	+	36.6590i	2.25478	+	1.30180i
$794$	40.1071	+	14.5978i	1.42335	+	0.518056i
$795$		0			0
$796$	−10.5924	−	8.88807i	−0.375437	−	0.315029i
$797$	23.8010	−	28.3650i	0.843076	−	1.00474i	−0.156778	−	0.987634i	$-0.550111\pi$
$797$	23.8010	−	28.3650i	0.843076	−	1.00474i	0.999854	−	0.0171048i	$-0.00544488\pi$
$798$	0.0420582	−	0.130789i	0.00148884	−	0.00462988i
$799$	11.4961	+	4.18424i	0.406703	+	0.148028i
$800$		0			0
$801$	−8.57555	−	33.5277i	−0.303002	−	1.18464i
$802$	−21.1628	+	12.2183i	−0.747283	+	0.431444i
$803$	−3.31991	+	0.585390i	−0.117157	+	0.0206580i
$804$	10.8415	+	17.2337i	0.382351	+	0.607784i
$805$		0			0
$806$	−19.4346	+	110.219i	−0.684554	+	3.88230i
$807$	32.8434	+	4.51439i	1.15614	+	0.158914i
$808$	−6.07296	−	7.23747i	−0.213646	−	0.254613i
$809$	34.2586			1.20447			0.602234	−	0.798320i	$-0.294278\pi$
$809$	34.2586			1.20447			0.602234	+	0.798320i	$0.294278\pi$
$810$		0			0
$811$	−28.6218			−1.00505			−0.502524	−	0.864563i	$-0.667595\pi$
$811$	−28.6218			−1.00505			−0.502524	+	0.864563i	$0.667595\pi$
$812$	0.233608	+	0.278403i	0.00819802	+	0.00977002i
$813$	−24.4081	−	3.35494i	−0.856029	−	0.117663i
$814$	−1.84813	+	10.4812i	−0.0647768	+	0.367368i
$815$		0			0
$816$	−5.29500	−	8.41691i	−0.185362	−	0.294651i
$817$	−6.43922	+	1.13541i	−0.225280	+	0.0397229i
$818$	−8.28143	+	4.78129i	−0.289553	+	0.167174i
$819$	−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	$0.493868\pi$
$822$	−4.16643	+	12.9564i	−0.145321	+	0.451906i
$823$	−33.9324	+	40.4390i	−1.18281	+	1.40962i	−0.291287	+	0.956636i	$0.594084\pi$
$823$	−33.9324	+	40.4390i	−1.18281	+	1.40962i	−0.891521	+	0.452980i	$0.850361\pi$
$824$	−11.3526	−	9.52600i	−0.395488	−	0.331854i
$825$		0			0
$826$	−1.38661	−	0.504685i	−0.0482463	−	0.0175602i
$827$	19.9595	+	11.5236i	0.694058	+	0.400715i	0.805131	−	0.593098i	$-0.202095\pi$
$827$	19.9595	+	11.5236i	0.694058	+	0.400715i	−0.111072	+	0.993812i	$0.535428\pi$
$828$	−32.5142	+	45.3271i	−1.12995	+	1.57522i
$829$	22.7628	+	39.4264i	0.790586	+	1.36934i	0.925605	+	0.378492i	$0.123557\pi$
$829$	22.7628	+	39.4264i	0.790586	+	1.36934i	−0.135018	+	0.990843i	$0.543109\pi$
$830$		0			0
$831$	23.3700	−	0.887009i	0.810697	−	0.0307700i
$832$	−23.8529	−	65.5354i	−0.826951	−	2.27203i
$833$	14.2745	+	2.51698i	0.494582	+	0.0872081i
$834$	21.7171	−	8.85092i	0.752001	−	0.306482i
$835$		0			0
$836$	−1.70741			−0.0590520
$837$	24.6046	−	37.2029i	0.850458	−	1.28592i
$838$		−	45.9410i		−	1.58701i
$839$	11.6668	−	9.78962i	0.402783	−	0.337975i	−0.418785	−	0.908085i	$-0.637544\pi$
$839$	11.6668	−	9.78962i	0.402783	−	0.337975i	0.821568	+	0.570110i	$0.193099\pi$
$840$		0			0
$841$	−4.11190	+	23.3197i	−0.141790	+	0.804129i
$842$	14.6706	+	40.3071i	0.505582	+	1.38908i
$843$	−6.76159	−	3.56896i	−0.232882	−	0.122922i
$844$	−1.24741	−	7.07443i	−0.0429377	−	0.243512i
$845$		0			0
$846$	−21.1852	−	31.0014i	−0.728362	−	1.06585i
$847$	−0.528835	−	0.305323i	−0.0181710	−	0.0104910i
$848$	0.584966	−	1.60718i	0.0200878	−	0.0551908i
$849$	−1.63262	+	1.47900i	−0.0560315	+	0.0507592i
$850$		0			0
$851$	−24.8015	−	20.8109i	−0.850183	−	0.713389i
$852$	−8.27834	−	9.13819i	−0.283611	−	0.313069i
$853$	−1.83847	+	5.05116i	−0.0629481	+	0.172948i	−0.967179	−	0.254095i	$-0.918223\pi$
$853$	−1.83847	+	5.05116i	−0.0629481	+	0.172948i	0.904231	+	0.427043i	$0.140445\pi$
$854$	0.798394	−	1.38286i	0.0273205	−	0.0473205i
$855$		0			0
$856$	−10.7455	−	18.6118i	−0.367275	−	0.636139i
$857$	18.3455	−	3.23480i	0.626670	−	0.110499i	0.148710	−	0.988881i	$-0.452488\pi$
$857$	18.3455	−	3.23480i	0.626670	−	0.110499i	0.477959	+	0.878382i	$0.341377\pi$
$858$	23.1017	+	12.1938i	0.788680	+	0.416288i
$859$	17.0674	−	6.21203i	0.582333	−	0.211952i	−0.0340211	−	0.999421i	$-0.510831\pi$
$859$	17.0674	−	6.21203i	0.582333	−	0.211952i	0.616354	+	0.787469i	$0.288609\pi$
$860$		0			0
$861$	−0.574470	−	0.446028i	−0.0195779	−	0.0152006i
$862$	16.7234	+	19.9302i	0.569602	+	0.678825i
$863$		−	5.04898i		−	0.171869i	−0.996301	−	0.0859346i	$-0.972612\pi$
$863$		−	5.04898i		−	0.171869i	0.996301	−	0.0859346i	$-0.0273876\pi$
$864$	−2.51114	+	41.3034i	−0.0854306	+	1.40517i
$865$		0			0
$866$	56.1666	−	47.1294i	1.90862	−	1.60152i
$867$	−8.30685	−	20.3821i	−0.282116	−	0.692214i
$868$	1.33192	+	0.234853i	0.0452082	+	0.00797142i
$869$	−5.58719	+	2.03357i	−0.189532	+	0.0689841i
$870$		0			0
$871$	5.03648	+	28.5633i	0.170654	+	0.967830i
$872$	2.46379	−	1.42247i	0.0834346	−	0.0481710i
$873$	22.5144	−	31.3867i	0.761998	−	1.06228i
$874$	4.68042	−	8.10673i	0.158318	−	0.274214i
$875$		0			0
$876$	2.65368	+	12.3012i	0.0896597	+	0.415619i
$877$	28.9444	−	34.4946i	0.977382	−	1.16480i	−0.00893847	−	0.999960i	$-0.502845\pi$
$877$	28.9444	−	34.4946i	0.977382	−	1.16480i	0.986321	−	0.164839i	$-0.0527103\pi$
$878$	43.4019	−	51.7243i	1.46474	−	1.74561i
$879$	−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	$0.196521\pi$
$882$	−31.0970	−	31.8138i	−1.04709	−	1.07123i
$883$	17.6251	−	10.1759i	0.593132	−	0.342445i	−0.173203	−	0.984886i	$-0.555412\pi$
$883$	17.6251	−	10.1759i	0.593132	−	0.342445i	0.766335	+	0.642441i	$0.222078\pi$
$884$	5.51700	+	31.2884i	0.185557	+	1.05234i
$885$		0			0
$886$	3.71875	−	1.35351i	0.124934	−	0.0454722i
$887$	−29.0270	−	5.11824i	−0.974630	−	0.171854i	−0.336417	−	0.941713i	$-0.609215\pi$
$887$	−29.0270	−	5.11824i	−0.974630	−	0.171854i	−0.638213	+	0.769860i	$0.720326\pi$
$888$	7.78321	+	1.06982i	0.261187	+	0.0359007i
$889$	−0.289795	+	0.243167i	−0.00971942	+	0.00815556i
$890$		0			0
$891$	−6.50832	−	8.12532i	−0.218037	−	0.272208i
$892$		−	28.6286i		−	0.958556i
$893$	2.24730	+	2.67823i	0.0752031	+	0.0896236i
$894$	−7.33001	+	53.3277i	−0.245152	+	1.78355i
$895$		0			0
$896$	−0.481392	+	0.175213i	−0.0160822	+	0.00585344i
$897$	−67.2620	+	42.3139i	−2.24581	+	1.41282i
$898$	46.7853	−	8.24952i	1.56125	−	0.275290i
$899$	−9.89989	−	17.1471i	−0.330180	−	0.571888i
$900$		0			0
$901$	−0.639397	+	1.10747i	−0.0213014	+	0.0368951i
$902$	−5.57154	+	15.3077i	−0.185512	+	0.509690i
$903$	0.370074	−	1.15082i	0.0123153	−	0.0382970i
$904$	−12.2244	−	10.2575i	−0.406576	−	0.341158i
$905$		0			0
$906$	−9.18938	−	42.5975i	−0.305297	−	1.41521i
$907$	−18.1861	+	49.9658i	−0.603859	+	1.65909i	0.139521	+	0.990219i	$0.455444\pi$
$907$	−18.1861	+	49.9658i	−0.603859	+	1.65909i	−0.743380	+	0.668870i	$0.766778\pi$
$908$	44.8343	+	25.8851i	1.48788	+	0.859027i
$909$	−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	$0.901164\pi$
$912$	−0.107781	−	2.83971i	−0.00356899	−	0.0940321i
$913$	−1.32862	−	3.65036i	−0.0439710	−	0.120809i
$914$	5.88005	−	33.3474i	0.194495	−	1.10303i
$915$		0			0
$916$	−22.4620	+	18.8479i	−0.742165	+	0.622751i
$917$		−	0.295158i		−	0.00974698i
$918$	5.31906	−	22.1910i	0.175555	−	0.732414i
$919$	−5.96363			−0.196722			−0.0983609	−	0.995151i	$-0.531360\pi$
$919$	−5.96363			−0.196722			−0.0983609	+	0.995151i	$0.531360\pi$
$920$		0			0
$921$	−24.5158	−	19.0345i	−0.807824	−	0.627209i
$922$	51.8483	+	9.14225i	1.70753	+	0.301084i
$923$	−6.00761	−	16.5058i	−0.197743	−	0.543294i
$924$	0.147353	−	0.279168i	0.00484755	−	0.00918394i
$925$		0			0
$926$	38.0307	+	65.8712i	1.24977	+	2.16466i
$927$	3.22508	+	42.4243i	0.105925	+	1.39340i
$928$	15.9079	+	9.18443i	0.522202	+	0.301494i
$929$	5.31666	+	1.93510i	0.174434	+	0.0634887i	0.427761	−	0.903892i	$-0.359303\pi$
$929$	5.31666	+	1.93510i	0.174434	+	0.0634887i	−0.253327	+	0.967381i	$0.581525\pi$
$930$		0			0
$931$	3.17316	+	2.66260i	0.103996	+	0.0872632i
$932$	12.8250	−	15.2843i	0.420098	−	0.500653i
$933$	21.9222	+	24.1992i	0.717699	+	0.792245i
$934$	−20.7460	−	7.55091i	−0.678829	−	0.247073i
$935$		0			0
$936$	8.34790	−	17.3823i	0.272860	−	0.568159i
$937$	4.93110	−	2.84697i	0.161092	−	0.0930065i	−0.417287	−	0.908775i	$-0.637019\pi$
$937$	4.93110	−	2.84697i	0.161092	−	0.0930065i	0.578379	+	0.815768i	$0.303686\pi$
$938$	0.622077	−	0.109689i	0.0203115	−	0.00358147i
$939$	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	$0.0608977\pi$
$942$	−51.4282	+	66.2378i	−1.67562	+	2.15814i
$943$	−31.8532	−	37.9612i	−1.03728	−	1.23619i
$944$	−30.5222			−0.993412
$945$		0			0
$946$	−27.0764			−0.880330
$947$	6.58349	+	7.84590i	0.213935	+	0.254958i	0.862330	−	0.506346i	$-0.169004\pi$
$947$	6.58349	+	7.84590i	0.213935	+	0.254958i	−0.648396	+	0.761304i	$0.724560\pi$
$948$	8.37675	+	20.5536i	0.272064	+	0.667551i
$949$	−3.11293	+	17.6543i	−0.101050	+	0.573083i
$950$		0			0
$951$	1.81052	−	0.0687183i	0.0587102	−	0.00222834i
$952$	0.134751	−	0.0237602i	0.00436731	−	0.000770074i
$953$	−14.6696	+	8.46948i	−0.475194	+	0.274353i	−0.718411	−	0.695618i	$-0.755130\pi$
$953$	−14.6696	+	8.46948i	−0.475194	+	0.274353i	0.243217	+	0.969972i	$0.421797\pi$
$954$	3.57585	−	1.61811i	0.115772	−	0.0523881i
$955$		0			0
$956$	12.2784	+	4.46898i	0.397113	+	0.144537i
$957$	−4.51742	+	0.974524i	−0.146028	+	0.0315019i
$958$	−8.73437	+	10.4092i	−0.282195	+	0.336306i
$959$	0.179474	+	0.150597i	0.00579552	+	0.00486302i
$960$		0			0
$961$	−40.1088	−	14.5984i	−1.29383	−	0.470916i
$962$	49.0135	+	28.2980i	1.58026	+	0.912363i
$963$	−16.6469	+	59.4113i	−0.536439	+	1.91450i
$964$	1.46652	+	2.54009i	0.0472334	+	0.0818107i
$965$		0			0
$966$	0.921551	+	1.46489i	0.0296504	+	0.0471322i
$967$	10.1584	+	27.9101i	0.326673	+	0.897528i	0.988947	+	0.148266i	$0.0473692\pi$
$967$	10.1584	+	27.9101i	0.326673	+	0.897528i	−0.662274	+	0.749262i	$0.730409\pi$
$968$	9.94297	+	1.75321i	0.319579	+	0.0563504i
$969$	−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	$0.164900\pi$
$972$	−29.3879	+	25.4280i	−0.942619	+	0.815604i
$973$		−	0.403706i		−	0.0129422i
$974$	−24.4879	+	20.5478i	−0.784642	+	0.658393i
$975$		0			0
$976$	5.73541	−	32.5271i	0.183586	−	1.04117i
$977$	13.3499	+	36.6787i	0.427103	+	1.17345i	0.947563	+	0.319569i	$0.103538\pi$
$977$	13.3499	+	36.6787i	0.427103	+	1.17345i	−0.520460	+	0.853886i	$0.674240\pi$
$978$	−12.7095	+	7.99542i	−0.406405	+	0.255665i
$979$	2.31709	+	13.1409i	0.0740546	+	0.419985i
$980$		0			0
$981$	−7.86474	−	2.20369i	−0.251102	−	0.0703583i
$982$	−42.3734	−	24.4643i	−1.35219	−	0.780686i
$983$	1.57885	−	4.33786i	0.0503575	−	0.138356i	−0.911964	−	0.410270i	$-0.865434\pi$
$983$	1.57885	−	4.33786i	0.0503575	−	0.138356i	0.962322	+	0.271914i	$0.0876566\pi$
$984$	11.4477	+	3.68126i	0.364938	+	0.117354i
$985$		0			0
$986$	−7.75993	−	6.51135i	−0.247126	−	0.207364i
$987$	−0.631847	+	0.136306i	−0.0201119	+	0.00433866i
$988$	−3.10537	+	8.53193i	−0.0987950	+	0.271437i
$989$	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	$0.870866\pi$
$992$	67.3193	−	11.8702i	2.13739	−	0.376879i
$993$	−0.0138704	−	0.365444i	−0.000440164	−	0.0115970i
$994$	−0.359478	+	0.130839i	−0.0114019	+	0.00414997i
$995$		0			0
$996$	−13.4286	+	5.47291i	−0.425502	+	0.173416i
$997$	28.1225	+	33.5151i	0.890648	+	1.06143i	0.997741	+	0.0671838i	$0.0214014\pi$
$997$	28.1225	+	33.5151i	0.890648	+	1.06143i	−0.107093	+	0.994249i	$0.534154\pi$
$998$			8.09917i			0.256375i
$999$	−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.u.c.49.9		60
5.2	odd	4		675.2.l.d.76.1		30
5.3	odd	4		135.2.k.a.76.5	yes	30
5.4	even	2	inner	675.2.u.c.49.2		60
15.8	even	4		405.2.k.a.361.1		30
27.16	even	9	inner	675.2.u.c.124.2		60
135.23	even	36		3645.2.a.g.1.3		15
135.38	even	36		405.2.k.a.46.1		30
135.43	odd	36		135.2.k.a.16.5	✓	30
135.58	odd	36		3645.2.a.h.1.13		15
135.97	odd	36		675.2.l.d.151.1		30
135.124	even	18	inner	675.2.u.c.124.9		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.a.16.5	✓	30	135.43	odd	36
135.2.k.a.76.5	yes	30	5.3	odd	4
405.2.k.a.46.1		30	135.38	even	36
405.2.k.a.361.1		30	15.8	even	4
675.2.l.d.76.1		30	5.2	odd	4
675.2.l.d.151.1		30	135.97	odd	36
675.2.u.c.49.2		60	5.4	even	2	inner
675.2.u.c.49.9		60	1.1	even	1	trivial
675.2.u.c.124.2		60	27.16	even	9	inner
675.2.u.c.124.9		60	135.124	even	18	inner
3645.2.a.g.1.3		15	135.23	even	36
3645.2.a.h.1.13		15	135.58	odd	36

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36249 + 1.62376i) q^{2} +(1.71592 + 0.235856i) q^{3} +(-0.432902 + 2.45511i) q^{4} +(1.95495 + 3.10759i) q^{6} +(0.0622407 - 0.0109747i) q^{7} +(-0.904959 + 0.522478i) q^{8} +(2.88874 + 0.809420i) q^{9} +(-1.08697 - 0.395623i) q^{11} +(-1.32188 + 4.11066i) q^{12} +(-3.95386 + 4.71203i) q^{13} +(0.102623 + 0.0861109i) q^{14} +(2.60389 + 0.947740i) q^{16} +(-1.79428 - 1.03593i) q^{17} +(2.62160 + 5.79345i) q^{18} +(-0.296045 - 0.512766i) q^{19} +(0.109388 - 0.00415183i) q^{21} +(-0.838589 - 2.30400i) q^{22} +(7.34532 + 1.29518i) q^{23} +(-1.67606 + 0.683089i) q^{24} -13.0383 q^{26} +(4.76594 + 2.07023i) q^{27} +0.157559i q^{28} +(1.76698 - 1.48267i) q^{29} +(1.49057 - 8.45346i) q^{31} +(2.72368 + 7.48326i) q^{32} +(-1.77183 - 0.935225i) q^{33} +(-0.762600 - 4.32492i) q^{34} +(-3.23776 + 6.74178i) q^{36} +(-3.75919 - 2.17037i) q^{37} +(0.429247 - 1.17935i) q^{38} +(-7.89587 + 7.15291i) q^{39} +(-5.08956 - 4.27065i) q^{41} +(0.155783 + 0.171963i) q^{42} +(3.77698 - 10.3772i) q^{43} +(1.44185 - 2.49735i) q^{44} +(7.90491 + 13.6917i) q^{46} +(-5.81510 + 1.02536i) q^{47} +(4.24453 + 2.24039i) q^{48} +(-6.57409 + 2.39277i) q^{49} +(-2.83450 - 2.20076i) q^{51} +(-9.85691 - 11.7470i) q^{52} -0.617222i q^{53} +(3.13202 + 10.5594i) q^{54} +(-0.0505913 + 0.0424511i) q^{56} +(-0.387050 - 0.949687i) q^{57} +(4.81500 + 0.849014i) q^{58} +(-10.3506 + 3.76730i) q^{59} +(-2.06979 - 11.7384i) q^{61} +(15.7573 - 9.09747i) q^{62} +(0.188681 + 0.0186757i) q^{63} +(-5.66899 + 9.81898i) q^{64} +(-0.895535 - 4.15127i) q^{66} +(3.03089 - 3.61207i) q^{67} +(3.32006 - 3.95669i) q^{68} +(12.2985 + 3.95486i) q^{69} +(-1.42779 + 2.47301i) q^{71} +(-3.03710 + 0.776814i) q^{72} +(2.52392 - 1.45719i) q^{73} +(-1.59772 - 9.06114i) q^{74} +(1.38705 - 0.504846i) q^{76} +(-0.0719954 - 0.0126947i) q^{77} +(-22.3727 - 3.07517i) q^{78} +(3.93760 - 3.30404i) q^{79} +(7.68968 + 4.67641i) q^{81} -14.0830i q^{82} +(2.15868 + 2.57261i) q^{83} +(-0.0371612 + 0.270358i) q^{84} +(21.9962 - 8.00594i) q^{86} +(3.38169 - 2.12739i) q^{87} +(1.19036 - 0.209893i) q^{88} +(-5.76784 - 9.99019i) q^{89} +(-0.194378 + 0.336673i) q^{91} +(-6.35961 + 17.4729i) q^{92} +(4.55150 - 14.1539i) q^{93} +(-9.58798 - 8.04527i) q^{94} +(2.90864 + 13.4830i) q^{96} +(4.40371 - 12.0991i) q^{97} +(-12.8425 - 7.41460i) q^{98} +(-2.81974 - 2.02267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{9} - 12 q^{11} + 18 q^{14} + 24 q^{16} - 48 q^{19} - 72 q^{21} - 90 q^{24} - 36 q^{26} - 36 q^{29} + 24 q^{31} + 138 q^{34} - 84 q^{36} - 12 q^{39} - 150 q^{41} - 24 q^{44} + 60 q^{46} + 72 q^{49}+ \cdots - 246 q^{99}+O(q^{100}) \) 60 * q + 6 * q^9 - 12 * q^11 + 18 * q^14 + 24 * q^16 - 48 * q^19 - 72 * q^21 - 90 * q^24 - 36 * q^26 - 36 * q^29 + 24 * q^31 + 138 * q^34 - 84 * q^36 - 12 * q^39 - 150 * q^41 - 24 * q^44 + 60 * q^46 + 72 * q^49 + 42 * q^51 - 36 * q^54 + 60 * q^56 + 54 * q^59 - 24 * q^61 - 54 * q^64 + 156 * q^66 + 234 * q^69 + 24 * q^71 - 60 * q^76 - 108 * q^79 - 54 * q^81 - 90 * q^84 + 36 * q^86 - 18 * q^89 + 102 * q^91 - 30 * q^94 - 30 * q^96 - 246 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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