LMFDB - Embedded newform 867.2.i.g.329.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(65,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.65"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.i (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,16,0,8,0,0,24,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			329.1
Character	$\chi$	$=$	867.329
Dual form			867.2.i.g.224.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.556851 + 1.34436i) q^{2} +(-1.69855 - 0.339031i) q^{3} +(-0.0830021 - 0.0830021i) q^{4} +(-2.53714 - 1.69526i) q^{5} +(1.40162 - 2.09466i) q^{6} +(1.19824 + 1.79329i) q^{7} +(-2.53091 + 1.04834i) q^{8} +(2.77012 + 1.15172i) q^{9} +(3.69185 - 2.46681i) q^{10} +(-1.61618 - 0.321478i) q^{11} +(0.112843 + 0.169123i) q^{12} +(-3.12551 + 3.12551i) q^{13} +(-3.07806 + 0.612265i) q^{14} +(3.73470 + 3.73965i) q^{15} -4.22099i q^{16} +(-3.09087 + 3.08269i) q^{18} +(-0.797694 - 0.330416i) q^{19} +(0.0698774 + 0.351298i) q^{20} +(-1.42728 - 3.45222i) q^{21} +(1.33215 - 1.99371i) q^{22} +(-0.149554 + 0.751858i) q^{23} +(4.65429 - 0.922593i) q^{24} +(1.64974 + 3.98282i) q^{25} +(-2.46136 - 5.94226i) q^{26} +(-4.31470 - 2.89540i) q^{27} +(0.0493905 - 0.248303i) q^{28} +(4.43981 - 6.64464i) q^{29} +(-7.10709 + 2.93834i) q^{30} +(-0.563512 - 2.83296i) q^{31} +(0.612694 + 0.253786i) q^{32} +(2.63616 + 1.09398i) q^{33} -6.58114i q^{35} +(-0.134330 - 0.325520i) q^{36} +(-2.33589 + 0.464638i) q^{37} +(0.888394 - 0.888394i) q^{38} +(6.36847 - 4.24918i) q^{39} +(8.19848 + 1.63078i) q^{40} +(-2.56055 + 1.71091i) q^{41} +(5.43581 + 0.00359897i) q^{42} +(10.5751 - 4.38037i) q^{43} +(0.107463 + 0.160829i) q^{44} +(-5.07570 - 7.61814i) q^{45} +(-0.927487 - 0.619727i) q^{46} +(2.21238 + 2.21238i) q^{47} +(-1.43105 + 7.16954i) q^{48} +(0.898671 - 2.16958i) q^{49} -6.27299 q^{50} +0.518848 q^{52} +(2.43710 - 5.88369i) q^{53} +(6.29511 - 4.18819i) q^{54} +(3.55548 + 3.55548i) q^{55} +(-4.91261 - 3.28250i) q^{56} +(1.24290 + 0.831669i) q^{57} +(6.46046 + 9.66877i) q^{58} +(5.62864 - 2.33146i) q^{59} +(0.000410749 - 0.620386i) q^{60} +(4.86125 - 3.24818i) q^{61} +(4.12231 + 0.819979i) q^{62} +(1.25389 + 6.34765i) q^{63} +(5.28702 - 5.28702i) q^{64} +(13.2284 - 2.63129i) q^{65} +(-2.93865 + 2.93476i) q^{66} -7.19481i q^{67} +(0.508927 - 1.22636i) q^{69} +(8.84742 + 3.66472i) q^{70} +(-0.424222 - 2.13271i) q^{71} +(-8.21831 - 0.0108825i) q^{72} +(-6.98874 + 10.4594i) q^{73} +(0.676105 - 3.39901i) q^{74} +(-1.45186 - 7.32431i) q^{75} +(0.0387851 + 0.0936354i) q^{76} +(-1.36006 - 3.28348i) q^{77} +(2.16613 + 10.9277i) q^{78} +(1.16236 - 5.84360i) q^{79} +(-7.15567 + 10.7092i) q^{80} +(6.34708 + 6.38079i) q^{81} +(-0.874225 - 4.39502i) q^{82} +(-11.9985 - 4.96993i) q^{83} +(-0.168074 + 0.405009i) q^{84} +16.6560i q^{86} +(-9.79395 + 9.78099i) q^{87} +(4.42742 - 0.880669i) q^{88} +(-3.42023 + 3.42023i) q^{89} +(13.0679 - 2.58139i) q^{90} +(-9.35006 - 1.85984i) q^{91} +(0.0748190 - 0.0499925i) q^{92} +(-0.00331239 + 5.00297i) q^{93} +(-4.20619 + 1.74226i) q^{94} +(1.46372 + 2.19061i) q^{95} +(-0.954647 - 0.638789i) q^{96} +(2.94959 + 1.97085i) q^{97} +(2.41627 + 2.41627i) q^{98} +(-4.10675 - 2.75191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 8 q^{6} + 24 q^{9} + 16 q^{10} + 16 q^{12} + 16 q^{13} + 16 q^{15} + 16 q^{18} + 32 q^{19} - 16 q^{21} - 16 q^{22} - 24 q^{24} - 24 q^{27} + 8 q^{30} - 32 q^{31} - 24 q^{36} - 16 q^{37}+ \cdots + 96 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 + 8 * q^6 + 24 * q^9 + 16 * q^10 + 16 * q^12 + 16 * q^13 + 16 * q^15 + 16 * q^18 + 32 * q^19 - 16 * q^21 - 16 * q^22 - 24 * q^24 - 24 * q^27 + 8 * q^30 - 32 * q^31 - 24 * q^36 - 16 * q^37 + 64 * q^39 - 16 * q^40 - 24 * q^42 - 32 * q^43 - 40 * q^45 + 40 * q^48 - 64 * q^49 - 96 * q^52 + 88 * q^54 + 48 * q^55 + 24 * q^57 + 64 * q^58 + 48 * q^60 + 32 * q^61 + 80 * q^63 - 16 * q^64 + 120 * q^66 + 80 * q^69 - 64 * q^72 - 48 * q^73 - 16 * q^75 + 32 * q^76 - 88 * q^78 + 32 * q^79 - 48 * q^81 - 96 * q^82 - 56 * q^87 - 128 * q^88 - 8 * q^90 - 64 * q^91 - 56 * q^93 - 48 * q^94 - 16 * q^96 - 128 * q^97 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{15}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.556851	+	1.34436i	−0.393753	+	0.950605i	0.595361	+	0.803458i	$0.297009\pi$
$2$	−0.556851	+	1.34436i	−0.393753	+	0.950605i	−0.989115	+	0.147147i	$0.952991\pi$
$3$	−1.69855	−	0.339031i	−0.980656	−	0.195740i
$3$	−1.69855	−	0.339031i	−0.980656	−	0.195740i
$4$	−0.0830021	−	0.0830021i	−0.0415010	−	0.0415010i
$5$	−2.53714	−	1.69526i	−1.13464	−	0.758144i	−0.161165	−	0.986928i	$-0.551525\pi$
$5$	−2.53714	−	1.69526i	−1.13464	−	0.758144i	−0.973477	+	0.228784i	$0.926525\pi$
$6$	1.40162	−	2.09466i	0.572208	−	0.855143i
$7$	1.19824	+	1.79329i	0.452891	+	0.677800i	0.985714	−	0.168427i	$-0.0538688\pi$
$7$	1.19824	+	1.79329i	0.452891	+	0.677800i	−0.532823	+	0.846227i	$0.678869\pi$
$8$	−2.53091	+	1.04834i	−0.894813	+	0.370644i
$9$	2.77012	+	1.15172i	0.923372	+	0.383906i
$10$	3.69185	−	2.46681i	1.16746	−	0.780075i
$11$	−1.61618	−	0.321478i	−0.487296	−	0.0969292i	−0.0546734	−	0.998504i	$-0.517412\pi$
$11$	−1.61618	−	0.321478i	−0.487296	−	0.0969292i	−0.432623	+	0.901575i	$0.642412\pi$
$12$	0.112843	+	0.169123i	0.0325748	+	0.0488216i
$13$	−3.12551	+	3.12551i	−0.866861	+	0.866861i	−0.992124	−	0.125262i	$-0.960023\pi$
$13$	−3.12551	+	3.12551i	−0.866861	+	0.866861i	0.125262	+	0.992124i	$0.460023\pi$
$14$	−3.07806	+	0.612265i	−0.822647	+	0.163635i
$15$	3.73470	+	3.73965i	0.964295	+	0.965572i
$16$		−	4.22099i		−	1.05525i
$17$		0			0
$17$		0			0
$18$	−3.09087	+	3.08269i	−0.728524	+	0.726597i
$19$	−0.797694	−	0.330416i	−0.183004	−	0.0758025i	0.289300	−	0.957238i	$-0.406577\pi$
$19$	−0.797694	−	0.330416i	−0.183004	−	0.0758025i	−0.472304	+	0.881436i	$0.656577\pi$
$20$	0.0698774	+	0.351298i	0.0156251	+	0.0785525i
$21$	−1.42728	−	3.45222i	−0.311458	−	0.753337i
$22$	1.33215	−	1.99371i	0.284016	−	0.425060i
$23$	−0.149554	+	0.751858i	−0.0311841	+	0.156773i	−0.993240	−	0.116080i	$-0.962967\pi$
$23$	−0.149554	+	0.751858i	−0.0311841	+	0.156773i	0.962056	+	0.272853i	$0.0879672\pi$
$24$	4.65429	−	0.922593i	0.950053	−	0.188323i
$25$	1.64974	+	3.98282i	0.329947	+	0.796563i
$26$	−2.46136	−	5.94226i	−0.482713	−	1.16537i
$27$	−4.31470	−	2.89540i	−0.830364	−	0.557221i
$28$	0.0493905	−	0.248303i	0.00933393	−	0.0469248i
$29$	4.43981	−	6.64464i	0.824451	−	1.23388i	−0.145204	−	0.989402i	$-0.546384\pi$
$29$	4.43981	−	6.64464i	0.824451	−	1.23388i	0.969655	−	0.244477i	$-0.0786163\pi$
$30$	−7.10709	+	2.93834i	−1.29757	+	0.536466i
$31$	−0.563512	−	2.83296i	−0.101210	−	0.508815i	−0.997820	−	0.0659948i	$-0.978978\pi$
$31$	−0.563512	−	2.83296i	−0.101210	−	0.508815i	0.896610	−	0.442820i	$-0.146022\pi$
$32$	0.612694	+	0.253786i	0.108310	+	0.0448635i
$33$	2.63616	+	1.09398i	0.458897	+	0.190437i
$34$		0			0
$35$		−	6.58114i		−	1.11242i
$36$	−0.134330	−	0.325520i	−0.0223884	−	0.0542534i
$37$	−2.33589	+	0.464638i	−0.384018	+	0.0763860i	−0.383324	−	0.923614i	$-0.625221\pi$
$37$	−2.33589	+	0.464638i	−0.384018	+	0.0763860i	−0.000693887		1.00000i	$0.500221\pi$
$38$	0.888394	−	0.888394i	0.144117	−	0.144117i
$39$	6.36847	−	4.24918i	1.01977	−	0.680414i
$40$	8.19848	+	1.63078i	1.29629	+	0.257849i
$41$	−2.56055	+	1.71091i	−0.399891	+	0.267199i	−0.739213	−	0.673471i	$-0.764802\pi$
$41$	−2.56055	+	1.71091i	−0.399891	+	0.267199i	0.339322	+	0.940670i	$0.389802\pi$
$42$	5.43581	+	0.00359897i	0.838764	+	0.000555333i
$43$	10.5751	−	4.38037i	1.61269	−	0.668000i	0.619557	−	0.784952i	$-0.287312\pi$
$43$	10.5751	−	4.38037i	1.61269	−	0.668000i	0.993138	+	0.116952i	$0.0373124\pi$
$44$	0.107463	+	0.160829i	0.0162006	+	0.0242459i
$45$	−5.07570	−	7.61814i	−0.756640	−	1.13564i
$46$	−0.927487	−	0.619727i	−0.136751	−	0.0913738i
$47$	2.21238	+	2.21238i	0.322708	+	0.322708i	0.849805	−	0.527097i	$-0.176719\pi$
$47$	2.21238	+	2.21238i	0.322708	+	0.322708i	−0.527097	+	0.849805i	$0.676719\pi$
$48$	−1.43105	+	7.16954i	−0.206554	+	1.03483i
$49$	0.898671	−	2.16958i	0.128382	−	0.309940i
$50$	−6.27299			−0.887135
$51$		0			0
$52$	0.518848			0.0719513
$53$	2.43710	−	5.88369i	0.334762	−	0.808187i	−0.663439	−	0.748230i	$-0.730904\pi$
$53$	2.43710	−	5.88369i	0.334762	−	0.808187i	0.998201	−	0.0599567i	$-0.0190963\pi$
$54$	6.29511	−	4.18819i	0.856655	−	0.569941i
$55$	3.55548	+	3.55548i	0.479420	+	0.479420i
$56$	−4.91261	−	3.28250i	−0.656475	−	0.438642i
$57$	1.24290	+	0.831669i	0.164626	+	0.110157i
$58$	6.46046	+	9.66877i	0.848301	+	1.26957i
$59$	5.62864	−	2.33146i	0.732786	−	0.303530i	0.0150898	−	0.999886i	$-0.495197\pi$
$59$	5.62864	−	2.33146i	0.732786	−	0.303530i	0.717696	+	0.696356i	$0.245197\pi$
$60$	0.000410749	−	0.620386i	5.30274e−5	−	0.0800915i
$61$	4.86125	−	3.24818i	0.622419	−	0.415887i	−0.203978	−	0.978976i	$-0.565387\pi$
$61$	4.86125	−	3.24818i	0.622419	−	0.415887i	0.826397	+	0.563089i	$0.190387\pi$
$62$	4.12231	+	0.819979i	0.523534	+	0.104137i
$63$	1.25389	+	6.34765i	0.157975	+	0.799729i
$64$	5.28702	−	5.28702i	0.660877	−	0.660877i
$65$	13.2284	−	2.63129i	1.64078	−	0.326372i
$66$	−2.93865	+	2.93476i	−0.361723	+	0.361244i
$67$		−	7.19481i		−	0.878985i	−0.898246	−	0.439493i	$-0.855158\pi$
$67$		−	7.19481i		−	0.878985i	0.898246	−	0.439493i	$-0.144842\pi$
$68$		0			0
$69$	0.508927	−	1.22636i	0.0612676	−	0.147637i
$70$	8.84742	+	3.66472i	1.05747	+	0.438018i
$71$	−0.424222	−	2.13271i	−0.0503459	−	0.253106i	0.947413	−	0.320012i	$-0.103687\pi$
$71$	−0.424222	−	2.13271i	−0.0503459	−	0.253106i	−0.997759	+	0.0669064i	$0.978687\pi$
$72$	−8.21831	−	0.0108825i	−0.968537	−	0.00128251i
$73$	−6.98874	+	10.4594i	−0.817970	+	1.22418i	0.153765	+	0.988107i	$0.450860\pi$
$73$	−6.98874	+	10.4594i	−0.817970	+	1.22418i	−0.971736	+	0.236072i	$0.924140\pi$
$74$	0.676105	−	3.39901i	0.0785956	−	0.395127i
$75$	−1.45186	−	7.32431i	−0.167646	−	0.845738i
$76$	0.0387851	+	0.0936354i	0.00444895	+	0.0107407i
$77$	−1.36006	−	3.28348i	−0.154994	−	0.374187i
$78$	2.16613	+	10.9277i	0.245266	+	1.23732i
$79$	1.16236	−	5.84360i	0.130776	−	0.657456i	−0.858667	−	0.512534i	$-0.828707\pi$
$79$	1.16236	−	5.84360i	0.130776	−	0.657456i	0.989443	−	0.144922i	$-0.0462932\pi$
$80$	−7.15567	+	10.7092i	−0.800028	+	1.19733i
$81$	6.34708	+	6.38079i	0.705232	+	0.708977i
$82$	−0.874225	−	4.39502i	−0.0965420	−	0.485349i
$83$	−11.9985	−	4.96993i	−1.31700	−	0.545521i	−0.390084	−	0.920779i	$-0.627554\pi$
$83$	−11.9985	−	4.96993i	−1.31700	−	0.545521i	−0.926920	+	0.375258i	$0.877554\pi$
$84$	−0.168074	+	0.405009i	−0.0183384	+	0.0441901i
$85$		0			0
$86$			16.6560i			1.79606i
$87$	−9.79395	+	9.78099i	−1.05002	+	1.04863i
$88$	4.42742	−	0.880669i	0.471965	−	0.0938796i
$89$	−3.42023	+	3.42023i	−0.362544	+	0.362544i	−0.864749	−	0.502205i	$-0.832522\pi$
$89$	−3.42023	+	3.42023i	−0.362544	+	0.362544i	0.502205	+	0.864749i	$0.332522\pi$
$90$	13.0679	−	2.58139i	1.37748	−	0.272102i
$91$	−9.35006	−	1.85984i	−0.980152	−	0.194964i
$92$	0.0748190	−	0.0499925i	0.00780042	−	0.00521208i
$93$	−0.00331239	+	5.00297i	−0.000343479	+	0.518783i
$94$	−4.20619	+	1.74226i	−0.433836	+	0.179701i
$95$	1.46372	+	2.19061i	0.150174	+	0.224752i
$96$	−0.954647	−	0.638789i	−0.0974333	−	0.0651962i
$97$	2.94959	+	1.97085i	0.299486	+	0.200110i	0.696229	−	0.717820i	$-0.254860\pi$
$97$	2.94959	+	1.97085i	0.299486	+	0.200110i	−0.396744	+	0.917929i	$0.629860\pi$
$98$	2.41627	+	2.41627i	0.244080	+	0.244080i
$99$	−4.10675	−	2.75191i	−0.412744	−	0.276578i
$100$	0.193650	−	0.467514i	0.0193650	−	0.0467514i
$101$	−3.73948			−0.372092			−0.186046	−	0.982541i	$-0.559567\pi$
$101$	−3.73948			−0.372092			−0.186046	+	0.982541i	$0.559567\pi$
$102$		0			0
$103$	9.33404			0.919710			0.459855	−	0.887994i	$-0.347901\pi$
$103$	9.33404			0.919710			0.459855	+	0.887994i	$0.347901\pi$
$104$	4.63380	−	11.1870i	0.454382	−	1.09698i
$105$	−2.23121	+	11.1784i	−0.217744	+	1.09090i
$106$	6.55268	+	6.55268i	0.636453	+	0.636453i
$107$	1.57145	+	1.05001i	0.151918	+	0.101508i	0.629206	−	0.777239i	$-0.283380\pi$
$107$	1.57145	+	1.05001i	0.151918	+	0.101508i	−0.477288	+	0.878747i	$0.658380\pi$
$108$	0.117805	+	0.598453i	0.0113357	+	0.0575862i
$109$	−2.33508	−	3.49469i	−0.223660	−	0.334730i	0.702621	−	0.711564i	$-0.252013\pi$
$109$	−2.33508	−	3.49469i	−0.223660	−	0.334730i	−0.926281	+	0.376834i	$0.877013\pi$
$110$	−6.75970	+	2.79996i	−0.644513	+	0.266966i
$111$	4.12515	+	0.00273120i	0.391542	+	0.000259234i
$112$	7.56945	−	5.05774i	0.715246	−	0.477912i
$113$	16.1688	+	3.21617i	1.52103	+	0.302552i	0.883705	−	0.468043i	$-0.155041\pi$
$113$	16.1688	+	3.21617i	1.52103	+	0.302552i	0.637325	+	0.770595i	$0.280041\pi$
$114$	−1.81017	+	1.20778i	−0.169538	+	0.113119i
$115$	1.65403	−	1.65403i	0.154239	−	0.154239i
$116$	−0.920032	+	0.183006i	−0.0854228	+	0.0169917i
$117$	−12.2577	+	5.05832i	−1.13323	+	0.467642i
$118$			8.86518i			0.816106i
$119$		0			0
$120$	−13.3726	−	5.54949i	−1.22075	−	0.506597i
$121$	−7.65399	−	3.17039i	−0.695817	−	0.288217i
$122$	1.65973	+	8.34401i	0.150265	+	0.755431i
$123$	4.92927	−	2.03795i	0.444457	−	0.183756i
$124$	−0.188369	+	0.281914i	−0.0169161	+	0.0253167i
$125$	−0.410177	+	2.06210i	−0.0366873	+	0.184440i
$126$	−9.23175	−	1.84902i	−0.822430	−	0.164724i
$127$	−4.71179	−	11.3753i	−0.418104	−	1.00939i	−0.982896	−	0.184159i	$-0.941044\pi$
$127$	−4.71179	−	11.3753i	−0.418104	−	1.00939i	0.564792	−	0.825233i	$-0.308956\pi$
$128$	4.67113	+	11.2771i	0.412874	+	0.996766i
$129$	−19.4474	+	3.85495i	−1.71225	+	0.339410i
$130$	−3.82886	+	19.2490i	−0.335813	+	1.68825i
$131$	1.95921	−	2.93217i	0.171177	−	0.256185i	−0.735955	−	0.677030i	$-0.763267\pi$
$131$	1.95921	−	2.93217i	0.171177	−	0.256185i	0.907132	+	0.420846i	$0.138267\pi$
$132$	−0.128004	−	0.309609i	−0.0111413	−	0.0269480i
$133$	−0.363296	−	1.82641i	−0.0315018	−	0.158370i
$134$	9.67240	+	4.00644i	0.835568	+	0.346103i
$135$	6.03852	+	14.6606i	0.519713	+	1.26178i
$136$		0			0
$137$		−	14.6484i		−	1.25150i	−0.780025	−	0.625748i	$-0.784794\pi$
$137$		−	14.6484i		−	1.25150i	0.780025	−	0.625748i	$-0.215206\pi$
$138$	1.36527	+	1.36708i	0.116220	+	0.116374i
$139$	−4.94769	+	0.984156i	−0.419657	+	0.0834750i	−0.400402	−	0.916340i	$-0.631130\pi$
$139$	−4.94769	+	0.984156i	−0.419657	+	0.0834750i	−0.0192553	+	0.999815i	$0.506130\pi$
$140$	−0.546249	+	0.546249i	−0.0461664	+	0.0461664i
$141$	−3.00776	−	4.50789i	−0.253299	−	0.379633i
$142$	3.10335	+	0.617296i	0.260428	+	0.0518023i
$143$	6.05617	−	4.04660i	0.506442	−	0.338394i
$144$	4.86139	−	11.6926i	0.405116	−	0.974385i
$145$	−22.5288	+	9.33173i	−1.87091	+	0.774958i
$146$	−10.1695	−	15.2197i	−0.841632	−	1.25959i
$147$	−2.26199	+	3.38046i	−0.186566	+	0.278816i
$148$	0.232450	+	0.155318i	0.0191073	+	0.0127671i
$149$	−4.44785	−	4.44785i	−0.364382	−	0.364382i	0.501041	−	0.865423i	$-0.332950\pi$
$149$	−4.44785	−	4.44785i	−0.364382	−	0.364382i	−0.865423	+	0.501041i	$0.832950\pi$
$150$	10.6550	+	2.12674i	0.869974	+	0.173647i
$151$	5.82179	−	14.0551i	0.473771	−	1.14378i	−0.488713	−	0.872445i	$-0.662533\pi$
$151$	5.82179	−	14.0551i	0.473771	−	1.14378i	0.962484	−	0.271339i	$-0.0874665\pi$
$152$	2.36528			0.191850
$153$		0			0
$154$	5.17153			0.416734
$155$	−3.37291	+	8.14291i	−0.270918	+	0.654055i
$156$	−0.881287	−	0.175906i	−0.0705594	−	0.0140837i
$157$	−1.74527	−	1.74527i	−0.139287	−	0.139287i	0.634025	−	0.773312i	$-0.281402\pi$
$157$	−1.74527	−	1.74527i	−0.139287	−	0.139287i	−0.773312	+	0.634025i	$0.781402\pi$
$158$	7.20863	+	4.81665i	0.573488	+	0.383192i
$159$	−6.13429	+	9.16747i	−0.486481	+	0.727027i
$160$	−1.12425	−	1.68257i	−0.0888801	−	0.133018i
$161$	−1.52750	+	0.632711i	−0.120384	+	0.0498646i
$162$	−12.1125	+	4.97960i	−0.951644	+	0.391235i
$163$	0.923662	−	0.617171i	0.0723468	−	0.0483406i	−0.518871	−	0.854853i	$-0.673647\pi$
$163$	0.923662	−	0.617171i	0.0723468	−	0.0483406i	0.591218	+	0.806512i	$0.298647\pi$
$164$	0.354540	+	0.0705224i	0.0276849	+	0.00550688i
$165$	−4.83372	−	7.24455i	−0.376305	−	0.563988i
$166$	13.3627	−	13.3627i	1.03715	−	1.03715i
$167$	−19.4786	+	3.87453i	−1.50730	+	0.299820i	−0.878497	−	0.477747i	$-0.841453\pi$
$167$	−19.4786	+	3.87453i	−1.50730	+	0.299820i	−0.628800	+	0.777567i	$0.716453\pi$
$168$	7.23142	+	7.24100i	0.557916	+	0.558655i
$169$		−	6.53766i		−	0.502897i
$170$		0			0
$171$	−1.82916	−	1.83401i	−0.139879	−	0.140250i
$172$	−1.24134	−	0.514179i	−0.0946511	−	0.0392058i
$173$	−2.27012	−	11.4127i	−0.172594	−	0.867689i	−0.965910	−	0.258879i	$-0.916647\pi$
$173$	−2.27012	−	11.4127i	−0.172594	−	0.867689i	0.793316	−	0.608811i	$-0.208353\pi$
$174$	−7.69538	−	18.6131i	−0.583385	−	1.41106i
$175$	−5.16557	+	7.73082i	−0.390480	+	0.584395i
$176$	−1.35695	+	6.82187i	−0.102284	+	0.514217i
$177$	−10.3509	+	2.05181i	−0.778024	+	0.154223i
$178$	−2.69345	−	6.50257i	−0.201883	−	0.487389i
$179$	0.324004	+	0.782216i	0.0242172	+	0.0584656i	0.935526	−	0.353259i	$-0.114927\pi$
$179$	0.324004	+	0.782216i	0.0242172	+	0.0584656i	−0.911308	+	0.411725i	$0.864927\pi$
$180$	−0.211028	+	1.05361i	−0.0157291	+	0.0785318i
$181$	0.279729	−	1.40629i	0.0207921	−	0.104529i	−0.968996	−	0.247078i	$-0.920530\pi$
$181$	0.279729	−	1.40629i	0.0207921	−	0.104529i	0.989788	+	0.142549i	$0.0455298\pi$
$182$	7.70689	−	11.5342i	0.571272	−	0.854970i
$183$	−9.35828	+	3.86907i	−0.691784	+	0.286010i
$184$	−0.409694	−	2.05967i	−0.0302030	−	0.151841i
$185$	6.71416	+	2.78110i	0.493635	+	0.204470i
$186$	−6.72393	−	2.79036i	−0.493023	−	0.204599i
$187$		0			0
$188$		−	0.367264i		−	0.0267855i
$189$	0.0222598	−	11.2069i	0.00161916	−	0.815181i
$190$	−3.76004	+	0.747918i	−0.272782	+	0.0542596i
$191$	−0.509849	+	0.509849i	−0.0368914	+	0.0368914i	−0.725312	−	0.688420i	$-0.758304\pi$
$191$	−0.509849	+	0.509849i	−0.0368914	+	0.0368914i	0.688420	+	0.725312i	$0.258304\pi$
$192$	−10.7727	+	7.18778i	−0.777453	+	0.518733i
$193$	−11.3982	−	2.26724i	−0.820460	−	0.163200i	−0.233025	−	0.972471i	$-0.574862\pi$
$193$	−11.3982	−	2.26724i	−0.820460	−	0.163200i	−0.587435	+	0.809271i	$0.699862\pi$
$194$	−4.29202	+	2.86783i	−0.308149	+	0.205898i
$195$	−23.3612	−	0.0154671i	−1.67293	−	0.00110762i
$196$	−0.254671	+	0.105488i	−0.0181908	+	0.00753488i
$197$	12.9248	+	19.3433i	0.920852	+	1.37815i	0.925738	+	0.378165i	$0.123445\pi$
$197$	12.9248	+	19.3433i	0.920852	+	1.37815i	−0.00488610	+	0.999988i	$0.501555\pi$
$198$	5.98641	−	3.98853i	0.425435	−	0.283453i
$199$	−20.0507	−	13.3975i	−1.42136	−	0.949720i	−0.999064	−	0.0432612i	$-0.986225\pi$
$199$	−20.0507	−	13.3975i	−1.42136	−	0.949720i	−0.422293	−	0.906459i	$-0.638775\pi$
$200$	−8.35068	−	8.35068i	−0.590482	−	0.590482i
$201$	−2.43926	+	12.2207i	−0.172052	+	0.861982i
$202$	2.08233	−	5.02720i	0.146512	−	0.353712i
$203$	17.2357			1.20971
$204$		0			0
$205$	9.39691			0.656309
$206$	−5.19767	+	12.5483i	−0.362139	+	0.874281i
$207$	−1.28021	+	1.91049i	−0.0889808	+	0.132788i
$208$	13.1927	+	13.1927i	0.914753	+	0.914753i
$209$	1.18299	+	0.790451i	0.0818294	+	0.0546767i
$210$	−13.7853	−	9.22424i	−0.951275	−	0.636533i
$211$	−8.67243	−	12.9792i	−0.597035	−	0.893525i	0.402728	−	0.915320i	$-0.368062\pi$
$211$	−8.67243	−	12.9792i	−0.597035	−	0.893525i	−0.999762	+	0.0217944i	$0.993062\pi$
$212$	−0.690643	+	0.286074i	−0.0474336	+	0.0196476i
$213$	−0.00249363	+	3.76633i	−0.000170861	+	0.258065i
$214$	−2.28665	+	1.52789i	−0.156312	+	0.104444i
$215$	−34.2564	−	6.81403i	−2.33627	−	0.464713i
$216$	13.9555	+	2.80475i	0.949551	+	0.190839i
$217$	4.40510	−	4.40510i	0.299038	−	0.299038i
$218$	5.99840	−	1.19316i	0.406263	−	0.0808107i
$219$	15.4168	−	15.3964i	1.04177	−	1.04039i
$220$		−	0.590224i		−	0.0397929i
$221$		0			0
$222$	−2.30077	+	5.54415i	−0.154417	+	0.372099i
$223$	2.24695	+	0.930718i	0.150467	+	0.0623255i	0.456646	−	0.889648i	$-0.349051\pi$
$223$	2.24695	+	0.930718i	0.150467	+	0.0623255i	−0.306179	+	0.951974i	$0.599051\pi$
$224$	0.279041	+	1.40283i	0.0186442	+	0.0937307i
$225$	−0.0171254	+	12.9329i	−0.00114169	+	0.862193i
$226$	−13.3273	+	19.9457i	−0.886518	+	1.32677i
$227$	0.273987	−	1.37743i	0.0181852	−	0.0914231i	−0.970627	−	0.240590i	$-0.922659\pi$
$227$	0.273987	−	1.37743i	0.0181852	−	0.0914231i	0.988812	+	0.149167i	$0.0476591\pi$
$228$	−0.0341329	−	0.172193i	−0.00226051	−	0.0114038i
$229$	4.16234	+	10.0488i	0.275055	+	0.664043i	0.999685	−	0.0250960i	$-0.00798914\pi$
$229$	4.16234	+	10.0488i	0.275055	+	0.664043i	−0.724630	+	0.689139i	$0.757989\pi$
$230$	1.30256	+	3.14466i	0.0858884	+	0.207353i
$231$	1.19693	+	6.03825i	0.0787520	+	0.397287i
$232$	−4.27093	+	21.4714i	−0.280400	+	1.40967i
$233$	−7.96478	+	11.9201i	−0.521790	+	0.780914i	−0.994983	−	0.100045i	$-0.968101\pi$
$233$	−7.96478	+	11.9201i	−0.521790	+	0.780914i	0.473193	+	0.880959i	$0.343101\pi$
$234$	0.0255506	−	19.2955i	0.00167030	−	1.26139i
$235$	−1.86255	−	9.36366i	−0.121499	−	0.610818i
$236$	−0.660704	−	0.273673i	−0.0430082	−	0.0178146i
$237$	−3.95549	+	9.53155i	−0.256937	+	0.619140i
$238$		0			0
$239$			23.7093i			1.53362i	0.641872	+	0.766812i	$0.278158\pi$
$239$			23.7093i			1.53362i	−0.641872	+	0.766812i	$0.721842\pi$
$240$	15.7850	−	15.7641i	1.01892	−	1.01757i
$241$	2.76030	−	0.549058i	0.177807	−	0.0353679i	−0.105384	−	0.994432i	$-0.533607\pi$
$241$	2.76030	−	0.549058i	0.177807	−	0.0353679i	0.283191	+	0.959064i	$0.408607\pi$
$242$	8.52427	−	8.52427i	0.547961	−	0.547961i
$243$	−8.61753	−	12.9899i	−0.552815	−	0.833304i
$244$	−0.673099	−	0.133888i	−0.0430908	−	0.00857128i
$245$	−5.95806	+	3.98105i	−0.380646	+	0.254340i
$246$	−0.00513881	+	7.76154i	−0.000327638	+	0.494858i
$247$	3.52592	−	1.46048i	0.224349	−	0.0929284i
$248$	4.39610	+	6.57923i	0.279153	+	0.417782i
$249$	18.6950	+	12.5095i	1.18475	+	0.792758i
$250$	−2.54379	−	1.69971i	−0.160883	−	0.107499i
$251$	−10.7058	−	10.7058i	−0.675745	−	0.675745i	0.283289	−	0.959034i	$-0.408574\pi$
$251$	−10.7058	−	10.7058i	−0.675745	−	0.675745i	−0.959034	+	0.283289i	$0.908574\pi$
$252$	0.422793	−	0.630944i	0.0266334	−	0.0397457i
$253$	0.483411	−	1.16706i	0.0303918	−	0.0733723i
$254$	17.9162			1.12416
$255$		0			0
$256$	−2.80767			−0.175479
$257$	−7.61319	+	18.3799i	−0.474898	+	1.14650i	0.487075	+	0.873360i	$0.338064\pi$
$257$	−7.61319	+	18.3799i	−0.474898	+	1.14650i	−0.961973	+	0.273145i	$0.911936\pi$
$258$	5.64690	−	28.2910i	0.351561	−	1.76132i
$259$	−3.63218	−	3.63218i	−0.225693	−	0.225693i
$260$	−1.31639	−	0.879583i	−0.0816389	−	0.0545494i
$261$	19.9515	−	13.2930i	1.23497	−	0.822817i
$262$	2.85090	+	4.26667i	0.176129	+	0.263596i
$263$	−0.121128	+	0.0501727i	−0.00746905	+	0.00309378i	−0.386415	−	0.922325i	$-0.626287\pi$
$263$	−0.121128	+	0.0501727i	−0.00746905	+	0.00309378i	0.378946	+	0.925419i	$0.376287\pi$
$264$	−7.81875	−	0.00517669i	−0.481211	−	0.000318603i
$265$	−16.1577	+	10.7962i	−0.992557	+	0.663205i
$266$	2.65765	+	0.528640i	0.162951	+	0.0324130i
$267$	6.96898	−	4.64985i	0.426495	−	0.284566i
$268$	−0.597184	+	0.597184i	−0.0364788	+	0.0364788i
$269$	5.83131	−	1.15992i	0.355541	−	0.0707216i	−0.0140883	−	0.999901i	$-0.504485\pi$
$269$	5.83131	−	1.15992i	0.355541	−	0.0707216i	0.369630	+	0.929179i	$0.379485\pi$
$270$	−23.0716	−	0.0458262i	−1.40409	−	0.00278890i
$271$			6.87483i			0.417616i	0.977957	+	0.208808i	$0.0669584\pi$
$271$			6.87483i			0.417616i	−0.977957	+	0.208808i	$0.933042\pi$
$272$		0			0
$273$	15.2510	+	6.32899i	0.923030	+	0.383048i
$274$	19.6927	+	8.15697i	1.18968	+	0.492781i
$275$	−1.38588	−	6.96730i	−0.0835718	−	0.420144i
$276$	−0.144033	+	0.0595485i	−0.00866974	+	0.00358440i
$277$	4.60979	−	6.89904i	0.276975	−	0.414523i	−0.666736	−	0.745294i	$-0.732309\pi$
$277$	4.60979	−	6.89904i	0.276975	−	0.414523i	0.943711	+	0.330771i	$0.107309\pi$
$278$	1.43207	−	7.19949i	0.0858897	−	0.431797i
$279$	1.70179	−	8.49665i	0.101883	−	0.508681i
$280$	6.89927	+	16.6563i	0.412310	+	0.995404i
$281$	5.07041	+	12.2411i	0.302475	+	0.730240i	0.999908	+	0.0135893i	$0.00432576\pi$
$281$	5.07041	+	12.2411i	0.302475	+	0.730240i	−0.697432	+	0.716651i	$0.745674\pi$
$282$	7.73509	−	1.53328i	0.460618	−	0.0913056i
$283$	2.73771	−	13.7634i	0.162740	−	0.818149i	−0.810032	−	0.586385i	$-0.800550\pi$
$283$	2.73771	−	13.7634i	0.162740	−	0.818149i	0.972772	−	0.231763i	$-0.0744495\pi$
$284$	−0.141808	+	0.212231i	−0.00841475	+	0.0125936i
$285$	−1.74351	−	4.21709i	−0.103276	−	0.249799i
$286$	2.06770	+	10.3950i	0.122266	+	0.614670i
$287$	−6.13631	−	2.54174i	−0.362215	−	0.150034i
$288$	1.40494	+	1.40867i	0.0827870	+	0.0830066i
$289$		0			0
$290$		−	35.4832i		−	2.08364i
$291$	−4.34183	−	4.34759i	−0.254523	−	0.254860i
$292$	1.44823	−	0.288071i	0.0847513	−	0.0168581i
$293$	18.6721	−	18.6721i	1.09083	−	1.09083i	0.0953949	−	0.995440i	$-0.469589\pi$
$293$	18.6721	−	18.6721i	1.09083	−	1.09083i	0.995440	−	0.0953949i	$-0.0304114\pi$
$294$	−3.28496	−	4.92334i	−0.191583	−	0.287135i
$295$	−18.2331	−	3.62678i	−1.06157	−	0.211159i
$296$	5.42484	−	3.62476i	0.315312	−	0.210685i
$297$	6.04252	+	6.06657i	0.350622	+	0.352018i
$298$	8.45629	−	3.50271i	0.489860	−	0.202907i
$299$	−1.88251	−	2.81737i	−0.108868	−	0.162933i
$300$	−0.487426	+	0.728440i	−0.0281415	+	0.0420565i
$301$	20.5268	+	13.7156i	1.18315	+	0.790552i
$302$	15.6531	+	15.6531i	0.900738	+	0.900738i
$303$	6.35167	+	1.26780i	0.364894	+	0.0728331i
$304$	−1.39468	+	3.36705i	−0.0799904	+	0.193114i
$305$	−17.8402			−1.02152
$306$		0			0
$307$	−24.4315			−1.39438			−0.697189	−	0.716887i	$-0.745566\pi$
$307$	−24.4315			−1.39438			−0.697189	+	0.716887i	$0.745566\pi$
$308$	−0.159648	+	0.385424i	−0.00909677	+	0.0219616i
$309$	−15.8543	−	3.16453i	−0.901919	−	0.180024i
$310$	−9.06879	−	9.06879i	−0.515073	−	0.515073i
$311$	19.4033	+	12.9649i	1.10026	+	0.735169i	0.966710	−	0.255873i	$-0.0823629\pi$
$311$	19.4033	+	12.9649i	1.10026	+	0.735169i	0.133548	+	0.991042i	$0.457363\pi$
$312$	−11.6635	+	17.4306i	−0.660314	+	0.986814i
$313$	−0.897040	−	1.34251i	−0.0507037	−	0.0758834i	0.805252	−	0.592933i	$-0.202030\pi$
$313$	−0.897040	−	1.34251i	−0.0507037	−	0.0758834i	−0.855955	+	0.517050i	$0.827030\pi$
$314$	3.31812	−	1.37441i	0.187252	−	0.0775624i
$315$	7.57963	−	18.2305i	0.427064	−	1.02717i
$316$	−0.581510	+	0.388552i	−0.0327125	+	0.0218578i
$317$	−23.9165	−	4.75728i	−1.34328	−	0.267195i	−0.529472	−	0.848327i	$-0.677610\pi$
$317$	−23.9165	−	4.75728i	−1.34328	−	0.267195i	−0.813809	+	0.581132i	$0.802610\pi$
$318$	−8.90847	−	13.3516i	−0.499562	−	0.748720i
$319$	−9.31162	+	9.31162i	−0.521351	+	0.521351i
$320$	−22.3768	+	4.45101i	−1.25090	+	0.248819i
$321$	−2.31319	−	2.31626i	−0.129110	−	0.129281i
$322$		−	2.40583i		−	0.134072i
$323$		0			0
$324$	0.00279782	−	1.05644i	0.000155435	−	0.0586911i
$325$	−17.6046	−	7.29207i	−0.976529	−	0.404491i
$326$	0.315357	+	1.58540i	0.0174660	+	0.0878074i
$327$	2.78143	+	6.72755i	0.153813	+	0.372034i
$328$	4.68693	−	7.01448i	0.258792	−	0.387310i
$329$	−1.31648	+	6.61839i	−0.0725798	+	0.364883i
$330$	12.4309	−	2.46411i	0.684301	−	0.135645i
$331$	−11.6584	−	28.1459i	−0.640804	−	1.54704i	−0.825597	−	0.564260i	$-0.809161\pi$
$331$	−11.6584	−	28.1459i	−0.640804	−	1.54704i	0.184793	−	0.982777i	$-0.440839\pi$
$332$	0.583384	+	1.40841i	0.0320173	+	0.0772967i
$333$	−7.00582	−	1.40319i	−0.383917	−	0.0768944i
$334$	5.63791	−	28.3437i	0.308493	−	1.55090i
$335$	−12.1971	+	18.2542i	−0.666397	+	0.997334i
$336$	−14.5718	+	6.02453i	−0.794956	+	0.328665i
$337$	3.36062	+	16.8950i	0.183065	+	0.920329i	0.957667	+	0.287880i	$0.0929504\pi$
$337$	3.36062	+	16.8950i	0.183065	+	0.920329i	−0.774602	+	0.632449i	$0.782050\pi$
$338$	8.78896	+	3.64051i	0.478057	+	0.198018i
$339$	−26.3730	−	10.9445i	−1.43239	−	0.594425i
$340$		0			0
$341$			4.75973i			0.257754i
$342$	3.48413	−	1.43777i	0.188400	−	0.0777459i
$343$	19.7748	−	3.93346i	1.06774	−	0.212387i
$344$	−22.1727	+	22.1727i	−1.19547	+	1.19547i
$345$	−3.37022	+	2.24868i	−0.181447	+	0.121065i
$346$	16.6068	+	3.30331i	0.892789	+	0.177587i
$347$	−16.8245	+	11.2418i	−0.903188	+	0.603491i	−0.918079	−	0.396398i	$-0.870260\pi$
$347$	−16.8245	+	11.2418i	−0.903188	+	0.603491i	0.0148907	+	0.999889i	$0.495260\pi$
$348$	1.62476	+	0.00107573i	0.0870963	+	5.76652e-5i
$349$	−7.02410	+	2.90948i	−0.375992	+	0.155741i	−0.562673	−	0.826680i	$-0.690227\pi$
$349$	−7.02410	+	2.90948i	−0.375992	+	0.155741i	0.186681	+	0.982421i	$0.440227\pi$
$350$	−7.51653	−	11.2493i	−0.401776	−	0.601300i
$351$	22.5353	−	4.43603i	1.20284	−	0.236778i
$352$	−0.908636	−	0.607131i	−0.0484304	−	0.0323602i
$353$	8.44344	+	8.44344i	0.449399	+	0.449399i	0.895155	−	0.445756i	$-0.147065\pi$
$353$	8.44344	+	8.44344i	0.449399	+	0.449399i	−0.445756	+	0.895155i	$0.647065\pi$
$354$	3.00557	−	15.0579i	0.159744	−	0.800319i
$355$	−2.53919	+	6.13014i	−0.134766	+	0.325354i
$356$	0.567772			0.0300919
$357$		0			0
$358$	−1.23200			−0.0651133
$359$	8.80076	−	21.2469i	0.464487	−	1.12137i	−0.502049	−	0.864839i	$-0.667420\pi$
$359$	8.80076	−	21.2469i	0.464487	−	1.12137i	0.966536	−	0.256531i	$-0.0825795\pi$
$360$	20.8325	+	13.9598i	1.09797	+	0.735746i
$361$	−12.9079	−	12.9079i	−0.679363	−	0.679363i
$362$	1.73479	+	1.15915i	0.0911786	+	0.0609236i
$363$	11.9258	+	7.97999i	0.625942	+	0.418841i
$364$	0.621703	+	0.930445i	0.0325861	+	0.0487685i
$365$	35.4628	−	14.6892i	1.85621	−	0.768866i
$366$	0.00975609	−	14.7354i	0.000509959	−	0.770231i
$367$	13.6449	−	9.11720i	0.712256	−	0.475914i	−0.145903	−	0.989299i	$-0.546609\pi$
$367$	13.6449	−	9.11720i	0.712256	−	0.475914i	0.858159	+	0.513385i	$0.171609\pi$
$368$	3.17358	+	0.631265i	0.165434	+	0.0329070i
$369$	−9.06352	+	1.79037i	−0.471828	+	0.0932031i
$370$	−7.47758	+	7.47758i	−0.388741	+	0.388741i
$371$	13.4714	−	2.67963i	0.699400	−	0.139119i
$372$	0.415531	−	0.414982i	0.0215443	−	0.0215158i
$373$		−	1.61824i		−	0.0837894i	−0.999122	−	0.0418947i	$-0.986661\pi$
$373$		−	1.61824i		−	0.0837894i	0.999122	−	0.0418947i	$-0.0133394\pi$
$374$		0			0
$375$	1.39582	−	3.36351i	0.0720798	−	0.173691i
$376$	−7.91865	−	3.28001i	−0.408373	−	0.169154i
$377$	6.89124	+	34.6446i	0.354917	+	1.78429i
$378$	15.0537	+	6.27050i	0.774278	+	0.322520i
$379$	8.62771	−	12.9123i	0.443176	−	0.663260i	−0.540884	−	0.841097i	$-0.681910\pi$
$379$	8.62771	−	12.9123i	0.443176	−	0.663260i	0.984060	+	0.177838i	$0.0569102\pi$
$380$	0.0603334	−	0.303317i	0.00309504	−	0.0155598i
$381$	4.14663	+	20.9189i	0.212438	+	1.07171i
$382$	−0.401510	−	0.969330i	−0.0205430	−	0.0495952i
$383$	−8.47433	−	20.4588i	−0.433018	−	1.04540i	−0.978309	−	0.207151i	$-0.933581\pi$
$383$	−8.47433	−	20.4588i	−0.433018	−	1.04540i	0.545291	−	0.838247i	$-0.316419\pi$
$384$	−4.11084	−	20.7384i	−0.209781	−	1.05830i
$385$	−2.11569	+	10.6363i	−0.107826	+	0.542076i
$386$	9.39509	−	14.0607i	0.478197	−	0.715673i
$387$	34.3393	+	0.0454712i	1.74557	+	0.00231143i
$388$	−0.0812372	−	0.408407i	−0.00412419	−	0.0207337i
$389$	14.0162	+	5.80572i	0.710652	+	0.294362i	0.708574	−	0.705636i	$-0.249339\pi$
$389$	14.0162	+	5.80572i	0.710652	+	0.294362i	0.00207747	+	0.999998i	$0.499339\pi$
$390$	13.0295	−	31.3972i	0.659774	−	1.58986i
$391$		0			0
$392$			6.43314i			0.324922i
$393$	−4.32191	+	4.31619i	−0.218011	+	0.217723i
$394$	−33.2015	+	6.60419i	−1.67267	+	0.332714i
$395$	−12.8555	+	12.8555i	−0.646831	+	0.646831i
$396$	0.112454	+	0.569283i	0.00565103	+	0.0286076i
$397$	36.9140	+	7.34266i	1.85266	+	0.368517i	0.990432	−	0.138000i	$-0.0440675\pi$
$397$	36.9140	+	7.34266i	1.85266	+	0.368517i	0.862230	+	0.506518i	$0.169068\pi$
$398$	29.1762	−	19.4949i	1.46247	−	0.977193i
$399$	−0.00213550	+	3.22541i	−0.000106909	+	0.161473i
$400$	16.8114	−	6.96352i	0.840571	−	0.348176i
$401$	−1.96330	−	2.93829i	−0.0980426	−	0.146731i	0.779205	−	0.626769i	$-0.215623\pi$
$401$	−1.96330	−	2.93829i	−0.0980426	−	0.146731i	−0.877248	+	0.480038i	$0.840623\pi$
$402$	−15.0707	−	10.0844i	−0.751658	−	0.502962i
$403$	10.6157	+	7.09320i	0.528807	+	0.353338i
$404$	0.310384	+	0.310384i	0.0154422	+	0.0154422i
$405$	−5.28632	−	26.9489i	−0.262679	−	1.33910i
$406$	−9.59773	+	23.1710i	−0.476327	+	1.14996i
$407$	3.92459			0.194535
$408$		0			0
$409$	12.2079			0.603641			0.301820	−	0.953365i	$-0.402406\pi$
$409$	12.2079			0.603641			0.301820	+	0.953365i	$0.402406\pi$
$410$	−5.23268	+	12.6328i	−0.258424	+	0.623890i
$411$	−4.96626	+	24.8810i	−0.244967	+	1.22729i
$412$	−0.774744	−	0.774744i	−0.0381689	−	0.0381689i
$413$	10.9254	+	7.30014i	0.537605	+	0.359216i
$414$	−1.85550	−	2.78492i	−0.0911926	−	0.136871i
$415$	22.0164	+	32.9499i	1.08074	+	1.61745i
$416$	−2.70819	+	1.12177i	−0.132780	+	0.0549993i
$417$	8.73753	+	0.00578500i	0.427879	+	0.000283293i
$418$	−1.72140	+	1.15020i	−0.0841965	+	0.0562583i
$419$	30.7895	+	6.12442i	1.50417	+	0.299198i	0.877305	−	0.479933i	$-0.159339\pi$
$419$	30.7895	+	6.12442i	1.50417	+	0.299198i	0.626862	+	0.779130i	$0.284339\pi$
$420$	1.11302	−	0.742633i	0.0543100	−	0.0362368i
$421$	−10.7245	+	10.7245i	−0.522682	+	0.522682i	−0.918380	−	0.395699i	$-0.870502\pi$
$421$	−10.7245	+	10.7245i	−0.522682	+	0.522682i	0.395699	+	0.918380i	$0.370502\pi$
$422$	22.2780	−	4.43136i	1.08447	−	0.215715i
$423$	3.58050	+	8.67658i	0.174090	+	0.421870i
$424$			17.4460i			0.847253i
$425$		0			0
$426$	−5.06191	−	2.10064i	−0.245250	−	0.101776i
$427$	11.6499	+	4.82553i	0.563776	+	0.233524i
$428$	−0.0432806	−	0.217586i	−0.00209205	−	0.0105174i
$429$	−11.6586	+	4.82011i	−0.562883	+	0.232717i
$430$	28.2362	−	42.2585i	1.36167	−	2.03789i
$431$	2.23450	−	11.2336i	0.107632	−	0.541102i	−0.888915	−	0.458072i	$-0.848540\pi$
$431$	2.23450	−	11.2336i	0.107632	−	0.541102i	0.996547	−	0.0830303i	$-0.0264598\pi$
$432$	−12.2215	+	18.2123i	−0.588005	+	0.876239i
$433$	10.2528	+	24.7526i	0.492720	+	1.18953i	0.953330	+	0.301930i	$0.0976307\pi$
$433$	10.2528	+	24.7526i	0.492720	+	1.18953i	−0.460610	+	0.887603i	$0.652369\pi$
$434$	3.46905	+	8.37502i	0.166520	+	0.402014i
$435$	41.4299	−	8.21241i	1.98641	−	0.393755i
$436$	−0.0962502	+	0.483882i	−0.00460955	+	0.0231738i
$437$	0.367724	−	0.550338i	0.0175906	−	0.0263262i
$438$	12.1134	+	29.2991i	0.578799	+	1.39997i
$439$	−1.66341	−	8.36252i	−0.0793902	−	0.399121i	−0.999963	−	0.00855138i	$-0.997278\pi$
$439$	−1.66341	−	8.36252i	−0.0793902	−	0.399121i	0.920573	−	0.390570i	$-0.127722\pi$
$440$	−12.7259	−	5.27126i	−0.606685	−	0.251297i
$441$	4.98817	−	4.97498i	0.237532	−	0.236904i
$442$		0			0
$443$			18.8773i			0.896886i	0.893811	+	0.448443i	$0.148021\pi$
$443$			18.8773i			0.896886i	−0.893811	+	0.448443i	$0.851979\pi$
$444$	−0.342169	−	0.342622i	−0.0162386	−	0.0162601i
$445$	14.4758	−	2.87941i	0.686217	−	0.136497i
$446$	−2.50244	+	2.50244i	−0.118494	+	0.118494i
$447$	6.04691	+	9.06283i	0.286009	+	0.428657i
$448$	15.8163	+	3.14605i	0.747248	+	0.148637i
$449$	22.6698	−	15.1475i	1.06985	−	0.714853i	0.109598	−	0.993976i	$-0.465044\pi$
$449$	22.6698	−	15.1475i	1.06985	−	0.714853i	0.960255	+	0.279123i	$0.0900437\pi$
$450$	−17.3769	−	7.22473i	−0.819156	−	0.340577i
$451$	4.68833	−	1.94197i	0.220765	−	0.0914438i
$452$	−1.07509	−	1.60899i	−0.0505681	−	0.0756805i
$453$	−14.6537	+	21.8994i	−0.688490	+	1.02892i
$454$	1.69919	+	1.13536i	0.0797468	+	0.0532851i
$455$	20.5695	+	20.5695i	0.964311	+	0.964311i
$456$	−4.01754	−	0.801903i	−0.188138	−	0.0375526i
$457$	−4.03405	+	9.73907i	−0.188705	+	0.455574i	−0.989711	−	0.143082i	$-0.954299\pi$
$457$	−4.03405	+	9.73907i	−0.188705	+	0.455574i	0.801006	+	0.598657i	$0.204299\pi$
$458$	−15.8270			−0.739546
$459$		0			0
$460$	−0.274576			−0.0128022
$461$	3.78349	−	9.13414i	0.176215	−	0.425419i	−0.810952	−	0.585112i	$-0.801050\pi$
$461$	3.78349	−	9.13414i	0.176215	−	0.425419i	0.987167	+	0.159693i	$0.0510504\pi$
$462$	−8.78408	−	1.75331i	−0.408672	−	0.0815713i
$463$	16.2123	+	16.2123i	0.753448	+	0.753448i	0.975121	−	0.221673i	$-0.0711518\pi$
$463$	16.2123	+	16.2123i	0.753448	+	0.753448i	−0.221673	+	0.975121i	$0.571152\pi$
$464$	−28.0469	−	18.7404i	−1.30205	−	0.870000i
$465$	8.48974	−	12.6876i	0.393702	−	0.588373i
$466$	−11.5897	−	17.3453i	−0.536884	−	0.803504i
$467$	−23.8791	+	9.89105i	−1.10499	+	0.457703i	−0.859211	−	0.511621i	$-0.829045\pi$
$467$	−23.8791	+	9.89105i	−1.10499	+	0.457703i	−0.245783	+	0.969325i	$0.579045\pi$
$468$	1.43727	+	0.597567i	0.0664378	+	0.0276226i
$469$	12.9024	−	8.62109i	0.595776	−	0.398085i
$470$	13.6253	+	2.71024i	0.628487	+	0.125014i
$471$	2.37271	+	3.55611i	0.109329	+	0.163857i
$472$	−11.8014	+	11.8014i	−0.543205	+	0.543205i
$473$	−18.4995	+	3.67978i	−0.850608	+	0.169196i
$474$	−10.6112	−	10.6253i	−0.487388	−	0.488034i
$475$		−	3.72217i		−	0.170785i
$476$		0			0
$477$	13.5274	−	13.4916i	0.619378	−	0.617740i
$478$	−31.8737	−	13.2025i	−1.45787	−	0.603870i
$479$	−1.69040	−	8.49821i	−0.0772363	−	0.388293i	−0.999996	−	0.00291662i	$-0.999072\pi$
$479$	−1.69040	−	8.49821i	−0.0772363	−	0.388293i	0.922759	−	0.385376i	$-0.125928\pi$
$480$	1.33916	+	3.23907i	0.0611238	+	0.147843i
$481$	5.84863	−	8.75309i	0.266675	−	0.399107i
$482$	−0.798947	+	4.01658i	−0.0363910	+	0.182950i
$483$	2.80904	−	0.556819i	0.127816	−	0.0253361i
$484$	0.372148	+	0.898446i	0.0169158	+	0.0408384i
$485$	−4.14240	−	10.0006i	−0.188097	−	0.454106i
$486$	22.2618	−	4.35159i	1.00982	−	0.197392i
$487$	7.57282	−	38.0711i	0.343157	−	1.72517i	−0.295207	−	0.955433i	$-0.595389\pi$
$487$	7.57282	−	38.0711i	0.343157	−	1.72517i	0.638364	−	0.769735i	$-0.279611\pi$
$488$	−8.89820	+	13.3171i	−0.402802	+	0.602836i
$489$	−1.77812	+	0.735143i	−0.0804094	+	0.0332443i
$490$	−2.03420	−	10.2266i	−0.0918958	−	0.461992i
$491$	−11.7073	−	4.84934i	−0.528345	−	0.218848i	0.102533	−	0.994730i	$-0.467305\pi$
$491$	−11.7073	−	4.84934i	−0.528345	−	0.218848i	−0.630878	+	0.775882i	$0.717305\pi$
$492$	−0.578293	−	0.239986i	−0.0260715	−	0.0108194i
$493$		0			0
$494$			5.55337i			0.249858i
$495$	5.75417	+	13.9440i	0.258631	+	0.626736i
$496$	−11.9579	+	2.37857i	−0.536926	+	0.106801i
$497$	3.31625	−	3.31625i	0.148754	−	0.148754i
$498$	−27.2276	+	18.1668i	−1.22010	+	0.814076i
$499$	−36.4030	−	7.24100i	−1.62962	−	0.324152i	−0.706221	−	0.707991i	$-0.749602\pi$
$499$	−36.4030	−	7.24100i	−1.62962	−	0.324152i	−0.923400	+	0.383839i	$0.874602\pi$
$500$	0.205204	−	0.137113i	0.00917700	−	0.00613187i
$501$	34.3988	+	0.0227750i	1.53683	+	0.00101751i
$502$	20.3540	−	8.43090i	0.908444	−	0.376290i
$503$	−17.7500	−	26.5648i	−0.791433	−	1.18446i	−0.979329	−	0.202275i	$-0.935167\pi$
$503$	−17.7500	−	26.5648i	−0.791433	−	1.18446i	0.187895	−	0.982189i	$-0.439833\pi$
$504$	−9.82797	−	14.7509i	−0.437773	−	0.657055i
$505$	9.48756	+	6.33939i	0.422191	+	0.282099i
$506$	1.29976	+	1.29976i	0.0577812	+	0.0577812i
$507$	−2.21647	+	11.1045i	−0.0984369	+	0.493169i
$508$	−0.553083	+	1.33526i	−0.0245391	+	0.0592426i
$509$	2.30289			0.102074			0.0510369	−	0.998697i	$-0.483747\pi$
$509$	2.30289			0.102074			0.0510369	+	0.998697i	$0.483747\pi$
$510$		0			0
$511$	−27.1309			−1.20020
$512$	−7.77882	+	18.7797i	−0.343778	+	0.829954i
$513$	2.48512	+	3.73529i	0.109721	+	0.164917i
$514$	−20.4697	−	20.4697i	−0.902880	−	0.902880i
$515$	−23.6817	−	15.8236i	−1.04354	−	0.697272i
$516$	1.93415	+	1.29421i	0.0851461	+	0.0569744i
$517$	−2.86437	−	4.28683i	−0.125975	−	0.188534i
$518$	6.90554	−	2.86037i	0.303412	−	0.125677i
$519$	−0.0133441	+	20.1546i	−0.000585740	+	0.884688i
$520$	−30.7215	+	20.5274i	−1.34723	+	0.900187i
$521$	2.69976	+	0.537016i	0.118279	+	0.0235271i	0.253875	−	0.967237i	$-0.418295\pi$
$521$	2.69976	+	0.537016i	0.118279	+	0.0235271i	−0.135596	+	0.990764i	$0.543295\pi$
$522$	6.76053	+	34.2243i	0.295900	+	1.49795i
$523$	−29.8001	+	29.8001i	−1.30307	+	1.30307i	−0.376755	+	0.926313i	$0.622960\pi$
$523$	−29.8001	+	29.8001i	−1.30307	+	1.30307i	−0.926313	+	0.376755i	$0.877040\pi$
$524$	−0.405995	+	0.0807574i	−0.0177360	+	0.00352790i
$525$	11.3949	−	11.3799i	0.497316	−	0.496658i
$526$		−	0.190778i		−	0.00831830i
$527$		0			0
$528$	4.61767	−	11.1272i	0.200958	−	0.484249i
$529$	20.7063	+	8.57683i	0.900274	+	0.372906i
$530$	−5.51655	−	27.7336i	−0.239624	−	1.20467i
$531$	18.2772	+	0.0242021i	0.793161	+	0.00105028i
$532$	−0.121442	+	0.181750i	−0.00526516	+	0.00787987i
$533$	2.65558	−	13.3505i	0.115026	−	0.578275i
$534$	2.37038	+	11.9581i	0.102576	+	0.517477i
$535$	−2.20694	−	5.32803i	−0.0954144	−	0.230351i
$536$	7.54259	+	18.2094i	0.325790	+	0.786527i
$537$	−0.285141	−	1.43848i	−0.0123047	−	0.0620749i
$538$	−1.68783	+	8.48527i	−0.0727674	+	0.365826i
$539$	−2.14988	+	3.21753i	−0.0926021	+	0.138589i
$540$	0.715648	−	1.71807i	0.0307966	−	0.0739339i
$541$	2.85545	+	14.3553i	0.122765	+	0.617184i	0.992356	+	0.123410i	$0.0393829\pi$
$541$	2.85545	+	14.3553i	0.122765	+	0.617184i	−0.869590	+	0.493774i	$0.835617\pi$
$542$	−9.24223	−	3.82826i	−0.396988	−	0.164438i
$543$	−0.951908	+	2.29381i	−0.0408503	+	0.0984369i
$544$		0			0
$545$			12.8251i			0.549365i
$546$	−17.0009	+	16.9784i	−0.727573	+	0.726610i
$547$	26.9003	−	5.35079i	1.15017	−	0.228783i	0.417052	−	0.908883i	$-0.363063\pi$
$547$	26.9003	−	5.35079i	1.15017	−	0.228783i	0.733120	+	0.680099i	$0.238063\pi$
$548$	−1.21585	+	1.21585i	−0.0519384	+	0.0519384i
$549$	17.2072	−	3.39905i	0.734386	−	0.145068i
$550$	10.1383	+	2.01663i	0.432297	+	0.0859893i
$551$	−5.73710	+	3.83341i	−0.244409	+	0.163309i
$552$	−0.00240823	+	3.63734i	−0.000102501	+	0.154816i
$553$	11.8721	−	4.91757i	0.504851	−	0.209116i
$554$	6.70781	+	10.0389i	0.284987	+	0.426514i
$555$	−10.4614	−	7.00013i	−0.444063	−	0.297139i
$556$	0.492355	+	0.328981i	0.0208805	+	0.0139519i
$557$	−31.0707	−	31.0707i	−1.31651	−	1.31651i	−0.916522	−	0.399984i	$-0.869016\pi$
$557$	−31.0707	−	31.0707i	−1.31651	−	1.31651i	−0.399984	−	0.916522i	$-0.630984\pi$
$558$	10.4749	+	7.01918i	0.443438	+	0.297146i
$559$	−19.3619	+	46.7436i	−0.818919	+	1.97705i
$560$	−27.7789			−1.17387
$561$		0			0
$562$	−19.2798			−0.813270
$563$	14.0437	−	33.9044i	0.591870	−	1.42890i	−0.289825	−	0.957080i	$-0.593597\pi$
$563$	14.0437	−	33.9044i	0.591870	−	1.42890i	0.881695	−	0.471821i	$-0.156403\pi$
$564$	−0.124514	+	0.623814i	−0.00524298	+	0.0262673i
$565$	−35.5701	−	35.5701i	−1.49645	−	1.49645i
$566$	16.9784	+	11.3446i	0.713657	+	0.476850i
$567$	−3.83729	+	19.0279i	−0.161151	+	0.799095i
$568$	3.30947	+	4.95297i	0.138862	+	0.207822i
$569$	−22.8578	+	9.46803i	−0.958251	+	0.396920i	−0.806326	−	0.591472i	$-0.798547\pi$
$569$	−22.8578	+	9.46803i	−0.958251	+	0.396920i	−0.151925	+	0.988392i	$0.548547\pi$
$570$	6.64016	+	0.00439636i	0.278126	+	0.000184143i
$571$	−1.63874	+	1.09497i	−0.0685792	+	0.0458232i	−0.589387	−	0.807851i	$-0.700631\pi$
$571$	−1.63874	+	1.09497i	−0.0685792	+	0.0458232i	0.520808	+	0.853674i	$0.325631\pi$
$572$	−0.838551	−	0.166798i	−0.0350616	−	0.00697418i
$573$	1.03886	−	0.693147i	0.0433989	−	0.0289566i
$574$	6.83402	−	6.83402i	0.285247	−	0.285247i
$575$	−3.24124	+	0.644722i	−0.135169	+	0.0268868i
$576$	20.7348	−	8.55649i	0.863951	−	0.356520i
$577$		−	26.8179i		−	1.11645i	−0.829691	−	0.558223i	$-0.811483\pi$
$577$		−	26.8179i		−	1.11645i	0.829691	−	0.558223i	$-0.188517\pi$
$578$		0			0
$579$	18.5917	+	7.71536i	0.772644	+	0.320639i
$580$	2.64449	+	1.09538i	0.109806	+	0.0454833i
$581$	−5.46450	−	27.4719i	−0.226706	−	1.13973i
$582$	8.26247	−	3.41602i	0.342490	−	0.141599i
$583$	−5.83027	+	8.72562i	−0.241465	+	0.361378i
$584$	6.72291	−	33.7984i	0.278196	−	1.39859i
$585$	39.6748	+	7.94643i	1.64035	+	0.328544i
$586$	14.7044	+	35.4995i	0.607433	+	1.46647i
$587$	−17.1080	−	41.3023i	−0.706122	−	1.70473i	−0.709471	−	0.704735i	$-0.751066\pi$
$587$	−17.1080	−	41.3023i	−0.706122	−	1.70473i	0.00334911	−	0.999994i	$-0.498934\pi$
$588$	0.468335	−	0.0928353i	0.0193138	−	0.00382846i
$589$	−0.486546	+	2.44603i	−0.0200478	+	0.100787i
$590$	15.0288	−	22.4922i	0.618726	−	0.925988i
$591$	−15.3953	−	37.2374i	−0.633280	−	1.53174i
$592$	1.96123	+	9.85977i	0.0806061	+	0.405234i
$593$	20.3889	+	8.44534i	0.837270	+	0.346809i	0.759777	−	0.650184i	$-0.225308\pi$
$593$	20.3889	+	8.44534i	0.837270	+	0.346809i	0.0774935	+	0.996993i	$0.475308\pi$
$594$	−11.5204	+	4.74513i	−0.472689	+	0.194695i
$595$		0			0
$596$			0.738361i			0.0302444i
$597$	29.5149	+	29.5540i	1.20796	+	1.20956i
$598$	4.83584	−	0.961908i	0.197752	−	0.0393353i
$599$	16.9345	−	16.9345i	0.691926	−	0.691926i	−0.270729	−	0.962655i	$-0.587265\pi$
$599$	16.9345	−	16.9345i	0.691926	−	0.691926i	0.962655	+	0.270729i	$0.0872649\pi$
$600$	11.3529	+	17.0151i	0.463479	+	0.694641i
$601$	2.58716	+	0.514619i	0.105533	+	0.0209917i	0.247574	−	0.968869i	$-0.420367\pi$
$601$	2.58716	+	0.514619i	0.105533	+	0.0209917i	−0.142041	+	0.989861i	$0.545367\pi$
$602$	−29.8690	+	19.9578i	−1.21737	+	0.813421i
$603$	8.28640	−	19.9304i	0.337448	−	0.811630i
$604$	−1.64982	+	0.683377i	−0.0671302	+	0.0278062i
$605$	14.0446	+	21.0192i	0.570994	+	0.854553i
$606$	−5.24131	+	7.83295i	−0.212914	+	0.318192i
$607$	−30.1592	−	20.1517i	−1.22412	−	0.817934i	−0.236025	−	0.971747i	$-0.575845\pi$
$607$	−30.1592	−	20.1517i	−1.22412	−	0.817934i	−0.988100	+	0.153813i	$0.950845\pi$
$608$	−0.404887	−	0.404887i	−0.0164203	−	0.0164203i
$609$	−29.2756	−	5.84344i	−1.18631	−	0.236788i
$610$	9.93432	−	23.9836i	0.402229	−	0.971066i
$611$	−13.8296			−0.559487
$612$		0			0
$613$	−25.0887			−1.01333			−0.506663	−	0.862144i	$-0.669121\pi$
$613$	−25.0887			−1.01333			−0.506663	+	0.862144i	$0.669121\pi$
$614$	13.6047	−	32.8447i	0.549041	−	1.32550i
$615$	−15.9611	−	3.18584i	−0.643613	−	0.128466i
$616$	6.88440	+	6.88440i	0.277380	+	0.277380i
$617$	−8.20652	−	5.48342i	−0.330382	−	0.220754i	0.379304	−	0.925272i	$-0.376163\pi$
$617$	−8.20652	−	5.48342i	−0.330382	−	0.220754i	−0.709686	+	0.704518i	$0.751163\pi$
$618$	13.0827	−	19.5517i	0.526265	−	0.786484i
$619$	−17.9502	−	26.8643i	−0.721478	−	1.07977i	−0.993089	−	0.117361i	$-0.962557\pi$
$619$	−17.9502	−	26.8643i	−0.721478	−	1.07977i	0.271611	−	0.962407i	$-0.412443\pi$
$620$	0.955837	−	0.395921i	0.0383873	−	0.0159006i
$621$	2.82221	−	2.81102i	0.113251	−	0.112802i
$622$	−28.2341	+	18.8655i	−1.13209	+	0.756436i
$623$	−10.2317	−	2.03521i	−0.409925	−	0.0815391i
$624$	−17.9357	−	26.8812i	−0.718004	−	1.07611i
$625$	19.7780	−	19.7780i	0.791122	−	0.791122i
$626$	2.30434	−	0.458362i	0.0920999	−	0.0183198i
$627$	−1.74138	−	1.74369i	−0.0695441	−	0.0696362i
$628$			0.289721i			0.0115611i
$629$		0			0
$630$	20.2876	+	20.3414i	0.808279	+	0.810422i
$631$	−3.56930	−	1.47845i	−0.142092	−	0.0588563i	0.310504	−	0.950572i	$-0.399502\pi$
$631$	−3.56930	−	1.47845i	−0.142092	−	0.0588563i	−0.452596	+	0.891716i	$0.649502\pi$
$632$	3.18423	+	16.0082i	0.126662	+	0.636772i
$633$	10.3302	+	24.9860i	0.410587	+	0.993104i
$634$	19.7134	−	29.5032i	0.782919	−	1.17172i
$635$	−7.32959	+	36.8483i	−0.290866	+	1.46228i
$636$	1.27008	−	0.251760i	0.0503618	−	0.00998293i
$637$	3.97225	+	9.58987i	0.157386	+	0.379964i
$638$	−7.33297	−	17.7033i	−0.290315	−	0.700882i
$639$	1.28114	−	6.39644i	0.0506810	−	0.253039i
$640$	7.26634	−	36.5304i	0.287227	−	1.44399i
$641$	20.7897	−	31.1140i	0.821145	−	1.22893i	−0.149583	−	0.988749i	$-0.547793\pi$
$641$	20.7897	−	31.1140i	0.821145	−	1.22893i	0.970728	−	0.240181i	$-0.0772068\pi$
$642$	4.40198	−	1.81995i	0.173732	−	0.0718276i
$643$	8.28711	+	41.6621i	0.326812	+	1.64299i	0.699206	+	0.714920i	$0.253537\pi$
$643$	8.28711	+	41.6621i	0.326812	+	1.64299i	−0.372395	+	0.928075i	$0.621463\pi$
$644$	0.179302	+	0.0742693i	0.00706549	+	0.00292662i
$645$	55.8760	+	23.1879i	2.20011	+	0.913024i
$646$		0			0
$647$		−	48.3331i		−	1.90017i	−0.311989	−	0.950086i	$-0.600995\pi$
$647$		−	48.3331i		−	1.90017i	0.311989	−	0.950086i	$-0.399005\pi$
$648$	−22.7531	−	9.49533i	−0.893828	−	0.373012i
$649$	−9.84639	+	1.95857i	−0.386505	+	0.0768806i
$650$	19.6063	−	19.6063i	0.769023	−	0.769023i
$651$	−8.97574	+	5.98880i	−0.351787	+	0.234720i
$652$	−0.127892	−	0.0254394i	−0.00500865	−	0.000996282i
$653$	5.37976	−	3.59464i	0.210526	−	0.140669i	−0.445837	−	0.895114i	$-0.647094\pi$
$653$	5.37976	−	3.59464i	0.210526	−	0.140669i	0.656363	+	0.754445i	$0.272094\pi$
$654$	−10.5931	−	0.00701353i	−0.414222	−	0.000274251i
$655$	−9.94158	+	4.11794i	−0.388450	+	0.160901i
$656$	7.22172	+	10.8081i	0.281961	+	0.421984i
$657$	−31.4059	+	20.9247i	−1.22526	+	0.816349i
$658$	−8.16440	−	5.45528i	−0.318281	−	0.212669i
$659$	−17.7005	−	17.7005i	−0.689515	−	0.689515i	0.272610	−	0.962125i	$-0.412113\pi$
$659$	−17.7005	−	17.7005i	−0.689515	−	0.689515i	−0.962125	+	0.272610i	$0.912113\pi$
$660$	−0.200104	+	1.00252i	−0.00778904	+	0.0390231i
$661$	9.53615	−	23.0223i	0.370913	−	0.895464i	−0.622683	−	0.782474i	$-0.713957\pi$
$661$	9.53615	−	23.0223i	0.370913	−	0.895464i	0.993596	−	0.112990i	$-0.0360427\pi$
$662$	44.3302			1.72294
$663$		0			0
$664$	35.5773			1.38067
$665$	−2.17451	+	5.24974i	−0.0843240	+	0.203576i
$666$	5.78760	−	8.63697i	0.224265	−	0.334676i
$667$	4.33184	+	4.33184i	0.167729	+	0.167729i
$668$	1.93835	+	1.29517i	0.0749972	+	0.0501115i
$669$	−3.50101	−	2.34265i	−0.135357	−	0.0905723i
$670$	−17.7482	−	26.5621i	−0.685674	−	1.02618i
$671$	−8.90086	+	3.68686i	−0.343614	+	0.142329i
$672$	0.00164024	−	2.47738i	6.32736e−5	−	0.0955670i
$673$	−15.6174	+	10.4352i	−0.602006	+	0.402248i	−0.818891	−	0.573949i	$-0.805411\pi$
$673$	−15.6174	+	10.4352i	−0.602006	+	0.402248i	0.216884	+	0.976197i	$0.430411\pi$
$674$	−24.5843	−	4.89012i	−0.946952	−	0.188360i
$675$	4.41374	−	21.9613i	0.169885	−	0.845291i
$676$	−0.542640	+	0.542640i	−0.0208708	+	0.0208708i
$677$	9.72023	−	1.93347i	0.373579	−	0.0743095i	−0.00473017	−	0.999989i	$-0.501506\pi$
$677$	9.72023	−	1.93347i	0.373579	−	0.0743095i	0.378309	+	0.925679i	$0.376506\pi$
$678$	29.3992	−	29.3603i	1.12907	−	1.12758i
$679$			7.65102i			0.293619i
$680$		0			0
$681$	−0.932371	+	2.24673i	−0.0357285	+	0.0860950i
$682$	−6.39878	−	2.65046i	−0.245022	−	0.101491i
$683$	−0.465840	−	2.34194i	−0.0178249	−	0.0896118i	0.970849	−	0.239693i	$-0.0770466\pi$
$683$	−0.465840	−	2.34194i	−0.0178249	−	0.0896118i	−0.988674	+	0.150081i	$0.952047\pi$
$684$	−0.000402615		0.304050i	−1.53944e−5		0.0116257i
$685$	−24.8328	+	37.1650i	−0.948814	+	1.42000i
$686$	−5.72366	+	28.7748i	−0.218530	+	1.09863i
$687$	−3.66308	−	18.4795i	−0.139755	−	0.705037i
$688$	−18.4895	−	44.6375i	−0.704905	−	1.70179i
$689$	10.7724	+	26.0068i	0.410394	+	0.990779i
$690$	−1.14632	−	5.78297i	−0.0436398	−	0.220154i
$691$	−6.36078	+	31.9778i	−0.241975	+	1.21649i	0.648412	+	0.761290i	$0.275433\pi$
$691$	−6.36078	+	31.9778i	−0.241975	+	1.21649i	−0.890388	+	0.455203i	$0.849567\pi$
$692$	−0.758850	+	1.13570i	−0.0288472	+	0.0431728i
$693$	0.0141184	−	10.6620i	0.000536313	−	0.405017i
$694$	−5.74423	−	28.8782i	−0.218048	−	1.09620i
$695$	14.2214	+	5.89068i	0.539447	+	0.223446i
$696$	14.5338	−	35.0222i	0.550904	−	1.32751i
$697$		0			0
$698$		−	11.0631i		−	0.418743i
$699$	17.5698	−	17.5466i	0.664552	−	0.663673i
$700$	1.07043	−	0.212921i	0.0404583	−	0.00804766i
$701$	−31.7150	+	31.7150i	−1.19786	+	1.19786i	−0.223051	+	0.974807i	$0.571602\pi$
$701$	−31.7150	+	31.7150i	−1.19786	+	1.19786i	−0.974807	+	0.223051i	$0.928398\pi$
$702$	−6.58518	+	32.7657i	−0.248542	+	1.23666i
$703$	2.01685	+	0.401176i	0.0760669	+	0.0151307i
$704$	−10.2444	+	6.84510i	−0.386101	+	0.257985i
$705$	−0.0109483	+	16.5361i	−0.000412337	+	0.622784i
$706$	−16.0527	+	6.64926i	−0.604153	+	0.250248i
$707$	−4.48078	−	6.70596i	−0.168517	−	0.252204i
$708$	1.02945	+	0.688845i	0.0386892	+	0.0258884i
$709$	32.8306	+	21.9367i	1.23298	+	0.823849i	0.989284	−	0.146003i	$-0.0466409\pi$
$709$	32.8306	+	21.9367i	1.23298	+	0.823849i	0.243693	+	0.969852i	$0.421641\pi$
$710$	−6.82716	−	6.82716i	−0.256219	−	0.256219i
$711$	9.95007	−	14.8487i	0.373157	−	0.556871i
$712$	5.07074	−	12.2419i	0.190034	−	0.458783i
$713$	2.21426			0.0829248
$714$		0			0
$715$	−22.2254			−0.831182
$716$	0.0380325	−	0.0918186i	0.00142134	−	0.00343142i
$717$	8.03817	−	40.2713i	0.300191	−	1.50396i
$718$	23.6628	+	23.6628i	0.883086	+	0.883086i
$719$	−36.5410	−	24.4159i	−1.36275	−	0.910560i	−0.362975	−	0.931799i	$-0.618239\pi$
$719$	−36.5410	−	24.4159i	−1.36275	−	0.910560i	−0.999774	+	0.0212393i	$0.993239\pi$
$720$	−32.1561	+	21.4245i	−1.19839	+	0.798442i
$721$	11.1844	+	16.7386i	0.416529	+	0.623379i
$722$	24.5406	−	10.1650i	0.913307	−	0.378304i
$723$	−4.87465	−	0.00322743i	−0.181290	−	0.000120030i
$724$	−0.139943	+	0.0935070i	−0.00520094	+	0.00347516i
$725$	33.7889	+	6.72103i	1.25489	+	0.249613i
$726$	−17.3689	+	11.5889i	−0.644619	+	0.430103i
$727$	0.0802760	−	0.0802760i	0.00297727	−	0.00297727i	−0.705617	−	0.708594i	$-0.749330\pi$
$727$	0.0802760	−	0.0802760i	0.00297727	−	0.00297727i	0.708594	+	0.705617i	$0.249330\pi$
$728$	25.6139	−	5.09492i	0.949315	−	0.188830i
$729$	10.2333	+	24.9856i	0.379010	+	0.925392i
$730$			55.8544i			2.06726i
$731$		0			0
$732$	1.09790	+	0.455616i	0.0405795	+	0.0168400i
$733$	−7.54651	−	3.12587i	−0.278737	−	0.115457i	0.238936	−	0.971035i	$-0.423201\pi$
$733$	−7.54651	−	3.12587i	−0.278737	−	0.115457i	−0.517673	+	0.855579i	$0.673201\pi$
$734$	4.65863	+	23.4205i	0.171953	+	0.864467i
$735$	11.4697	−	4.74203i	0.423068	−	0.174912i
$736$	−0.282442	+	0.422704i	−0.0104109	+	0.0155811i
$737$	−2.31297	+	11.6281i	−0.0851993	+	0.428326i
$738$	2.64013	−	13.1816i	0.0971846	−	0.485221i
$739$	4.49550	+	10.8531i	0.165370	+	0.399237i	0.984741	−	0.174025i	$-0.0556775\pi$
$739$	4.49550	+	10.8531i	0.165370	+	0.399237i	−0.819372	+	0.573263i	$0.805677\pi$
$740$	−0.326452	−	0.788126i	−0.0120006	−	0.0289721i
$741$	−6.48409	+	1.28530i	−0.238199	+	0.0472168i
$742$	−3.89919	+	19.6025i	−0.143144	+	0.719632i
$743$	22.8030	−	34.1272i	0.836563	−	1.25200i	−0.128951	−	0.991651i	$-0.541161\pi$
$743$	22.8030	−	34.1272i	0.836563	−	1.25200i	0.965513	−	0.260354i	$-0.0838391\pi$
$744$	−5.23642	−	12.6655i	−0.191976	−	0.464341i
$745$	3.74454	+	18.8251i	0.137189	+	0.689697i
$746$	2.17550	+	0.901121i	0.0796507	+	0.0329924i
$747$	−27.5132	−	27.5862i	−1.00666	−	1.00933i
$748$		0			0
$749$			4.07622i			0.148942i
$750$	3.74449	+	3.74945i	0.136730	+	0.136911i
$751$	−1.65656	+	0.329510i	−0.0604487	+	0.0120240i	−0.225222	−	0.974307i	$-0.572311\pi$
$751$	−1.65656	+	0.329510i	−0.0604487	+	0.0120240i	0.164773	+	0.986331i	$0.447311\pi$
$752$	9.33841	−	9.33841i	0.340537	−	0.340537i
$753$	14.5547	+	21.8139i	0.530403	+	0.794944i
$754$	−50.4121	−	10.0276i	−1.83590	−	0.365184i
$755$	−38.5977	+	25.7901i	−1.40471	+	0.938599i
$756$	−0.932042	+	0.928347i	−0.0338980	+	0.0337637i
$757$	−50.2881	+	20.8300i	−1.82775	+	0.757080i	−0.857715	+	0.514126i	$0.828116\pi$
$757$	−50.2881	+	20.8300i	−1.82775	+	0.757080i	−0.970038	+	0.242954i	$0.921884\pi$
$758$	12.5544	+	18.7890i	0.455996	+	0.682446i
$759$	−1.21677	+	1.81841i	−0.0441658	+	0.0660041i
$760$	−6.00104	−	4.00977i	−0.217681	−	0.145450i
$761$	24.1395	+	24.1395i	0.875055	+	0.875055i	0.993018	−	0.117963i	$-0.0376365\pi$
$761$	24.1395	+	24.1395i	0.875055	+	0.875055i	−0.117963	+	0.993018i	$0.537636\pi$
$762$	−30.4315	−	6.07415i	−1.10242	−	0.220043i
$763$	3.46901	−	8.37493i	0.125587	−	0.303193i
$764$	0.0846370			0.00306206
$765$		0			0
$766$	32.2229			1.16426
$767$	−10.3054	+	24.8794i	−0.372106	+	0.898343i
$768$	4.76895	+	0.951887i	0.172085	+	0.0343483i
$769$	−31.3211	−	31.3211i	−1.12947	−	1.12947i	−0.990264	−	0.139204i	$-0.955546\pi$
$769$	−31.3211	−	31.3211i	−1.12947	−	1.12947i	−0.139204	−	0.990264i	$-0.544454\pi$
$770$	−13.1209	−	8.76709i	−0.472843	−	0.315944i
$771$	19.1627	−	28.6379i	0.690128	−	1.03137i
$772$	0.757888	+	1.13426i	0.0272770	+	0.0408229i
$773$	−12.8222	+	5.31114i	−0.461184	+	0.191028i	−0.601164	−	0.799126i	$-0.705296\pi$
$773$	−12.8222	+	5.31114i	−0.461184	+	0.191028i	0.139980	+	0.990154i	$0.455296\pi$
$774$	−19.1830	+	46.1390i	−0.689520	+	1.65843i
$775$	10.3535	−	6.91801i	0.371910	−	0.248502i
$776$	−9.53128	−	1.89589i	−0.342153	−	0.0680584i
$777$	4.93801	+	7.40085i	0.177150	+	0.265504i
$778$	−15.6099	+	15.6099i	−0.559643	+	0.559643i
$779$	2.60785	−	0.518733i	0.0934359	−	0.0185856i
$780$	1.93774	+	1.94031i	0.0693822	+	0.0694742i
$781$			3.58322i			0.128218i
$782$		0			0
$783$	−38.3954	+	15.8146i	−1.37214	+	0.565168i
$784$	−9.15778	−	3.79328i	−0.327064	−	0.135474i
$785$	1.46930	+	7.38666i	0.0524415	+	0.263641i
$786$	−3.39584	−	8.21367i	−0.121126	−	0.292972i
$787$	13.2993	−	19.9038i	0.474070	−	0.709495i	−0.514960	−	0.857214i	$-0.672193\pi$
$787$	13.2993	−	19.9038i	0.474070	−	0.709495i	0.989029	+	0.147719i	$0.0471931\pi$
$788$	0.532750	−	2.67832i	0.0189784	−	0.0954111i
$789$	0.222751	−	0.0441546i	0.00793015	−	0.00157195i
$790$	−10.1238	−	24.4410i	−0.360189	−	0.869572i
$791$	13.6065	+	32.8490i	0.483792	+	1.16798i
$792$	13.2788	+	2.65959i	0.471840	+	0.0945045i
$793$	−5.04166	+	25.3461i	−0.179034	+	0.900067i
$794$	−30.4268	+	45.5369i	−1.07981	+	1.61604i
$795$	31.1048	−	12.8599i	1.10317	−	0.456094i
$796$	0.552234	+	2.77627i	0.0195734	+	0.0984022i
$797$	−43.2651	−	17.9210i	−1.53253	−	0.634795i	−0.552476	−	0.833529i	$-0.686317\pi$
$797$	−43.2651	−	17.9210i	−1.53253	−	0.634795i	−0.980053	+	0.198734i	$0.936317\pi$
$798$	−4.33492	−	1.79895i	−0.153455	−	0.0636820i
$799$		0			0
$800$			2.85893i			0.101078i
$801$	−13.4136	+	5.53529i	−0.473945	+	0.195580i
$802$	5.04338	−	1.00319i	0.178088	−	0.0354239i
$803$	14.6575	−	14.6575i	0.517252	−	0.517252i
$804$	1.21681	−	0.811880i	0.0429135	−	0.0286328i
$805$	4.94809	+	0.984236i	0.174397	+	0.0346897i
$806$	−15.4472	+	10.3215i	−0.544104	+	0.363559i
$807$	−10.2980	−	0.00681816i	−0.362507	−	0.000240011i
$808$	9.46429	−	3.92024i	0.332952	−	0.137913i
$809$	−6.50898	−	9.74138i	−0.228844	−	0.342489i	0.699223	−	0.714904i	$-0.253530\pi$
$809$	−6.50898	−	9.74138i	−0.228844	−	0.342489i	−0.928066	+	0.372415i	$0.878530\pi$
$810$	39.1727	+	7.89983i	1.37639	+	0.277572i
$811$	−15.6548	−	10.4602i	−0.549716	−	0.367308i	0.249479	−	0.968380i	$-0.419741\pi$
$811$	−15.6548	−	10.4602i	−0.549716	−	0.367308i	−0.799195	+	0.601072i	$0.794741\pi$
$812$	−1.43060	−	1.43060i	−0.0502042	−	0.0502042i
$813$	2.33078	−	11.6772i	0.0817440	−	0.409538i
$814$	−2.18541	+	5.27605i	−0.0765987	+	0.184926i
$815$	−3.38972			−0.118737
$816$		0			0
$817$	−9.88307			−0.345765
$818$	−6.79797	+	16.4118i	−0.237686	+	0.573824i
$819$	−23.7587	−	15.9206i	−0.830197	−	0.556311i
$820$	−0.779963	−	0.779963i	−0.0272375	−	0.0272375i
$821$	25.1885	+	16.8304i	0.879086	+	0.587386i	0.911139	−	0.412100i	$-0.135205\pi$
$821$	25.1885	+	16.8304i	0.879086	+	0.587386i	−0.0320530	+	0.999486i	$0.510205\pi$
$822$	−30.6834	−	20.5314i	−1.07021	−	0.716116i
$823$	−12.7499	−	19.0816i	−0.444434	−	0.665142i	0.539845	−	0.841765i	$-0.318483\pi$
$823$	−12.7499	−	19.0816i	−0.444434	−	0.665142i	−0.984279	+	0.176622i	$0.943483\pi$
$824$	−23.6236	+	9.78523i	−0.822968	+	0.340884i
$825$	−0.00814639	+	12.3041i	−0.000283621	+	0.428375i
$826$	−15.8978	+	10.6226i	−0.553156	+	0.369607i
$827$	17.1729	+	3.41591i	0.597161	+	0.118783i	0.484411	−	0.874841i	$-0.339034\pi$
$827$	17.1729	+	3.41591i	0.597161	+	0.118783i	0.112750	+	0.993623i	$0.464034\pi$
$828$	0.264835	−	0.0523144i	0.00920364	−	0.00181805i
$829$	31.1358	−	31.1358i	1.08139	−	1.08139i	0.0850121	−	0.996380i	$-0.472907\pi$
$829$	31.1358	−	31.1358i	1.08139	−	1.08139i	0.996380	−	0.0850121i	$-0.0270929\pi$
$830$	−56.5564	+	11.2498i	−1.96310	+	0.390485i
$831$	−10.1689	+	10.1555i	−0.352756	+	0.352289i
$832$			33.0493i			1.14578i
$833$		0			0
$834$	−4.87328	+	11.7432i	−0.168748	+	0.406632i
$835$	55.9881	+	23.1910i	1.93755	+	0.802559i
$836$	−0.0325818	−	0.163800i	−0.00112687	−	0.00566514i
$837$	−5.77119	+	13.8550i	−0.199481	+	0.478898i
$838$	−25.3786	+	37.9818i	−0.876690	+	1.31206i
$839$	3.85845	−	19.3977i	0.133209	−	0.669684i	−0.855253	−	0.518211i	$-0.826598\pi$
$839$	3.85845	−	19.3977i	0.133209	−	0.669684i	0.988461	−	0.151473i	$-0.0484018\pi$
$840$	−6.07172	−	30.6306i	−0.209494	−	1.05685i
$841$	−13.3415	−	32.2093i	−0.460053	−	1.11067i
$842$	−8.44564	−	20.3896i	−0.291056	−	0.702671i
$843$	−4.46223	−	22.5110i	−0.153687	−	0.775321i
$844$	−0.357471	+	1.79713i	−0.0123047	+	0.0618598i
$845$	−11.0830	+	16.5869i	−0.381268	+	0.570608i
$846$	−13.6582	−	0.0180859i	−0.469580	−	0.000621805i
$847$	−3.48588	−	17.5247i	−0.119776	−	0.602156i
$848$	−24.8350	−	10.2870i	−0.852837	−	0.353257i
$849$	−9.31634	+	22.4496i	−0.319736	+	0.770468i
$850$		0			0
$851$		−	1.82575i		−	0.0625858i
$852$	0.312820	−	0.312406i	0.0107170	−	0.0107029i
$853$	−6.05663	+	1.20474i	−0.207375	+	0.0412495i	−0.297685	−	0.954664i	$-0.596214\pi$
$853$	−6.05663	+	1.20474i	−0.207375	+	0.0412495i	0.0903095	+	0.995914i	$0.471214\pi$
$854$	−12.9745	+	12.9745i	−0.443977	+	0.443977i
$855$	1.53170	+	7.75403i	0.0523831	+	0.265182i
$856$	−5.07796	−	1.01007i	−0.173561	−	0.0345235i
$857$	21.6208	−	14.4466i	0.738554	−	0.493486i	−0.128494	−	0.991710i	$-0.541014\pi$
$857$	21.6208	−	14.4466i	0.738554	−	0.493486i	0.867048	+	0.498224i	$0.166014\pi$
$858$	0.0121542	−	18.3574i	0.000414937	−	0.626712i
$859$	−3.03380	+	1.25664i	−0.103512	+	0.0428761i	−0.433838	−	0.900991i	$-0.642841\pi$
$859$	−3.03380	+	1.25664i	−0.103512	+	0.0428761i	0.330326	+	0.943867i	$0.392841\pi$
$860$	2.27778	+	3.40893i	0.0776715	+	0.116244i
$861$	9.56107	+	6.39766i	0.325840	+	0.218032i
$862$	13.8577	+	9.25940i	0.471994	+	0.315376i
$863$	10.3922	+	10.3922i	0.353754	+	0.353754i	0.861504	−	0.507750i	$-0.169523\pi$
$863$	10.3922	+	10.3922i	0.353754	+	0.353754i	−0.507750	+	0.861504i	$0.669523\pi$
$864$	−1.90878	−	2.86901i	−0.0649379	−	0.0976056i
$865$	−13.5878	+	32.8040i	−0.462000	+	1.11537i
$866$	−38.9856			−1.32479
$867$		0			0
$868$	−0.731265			−0.0248208
$869$	−3.75718	+	9.07062i	−0.127453	+	0.307700i
$870$	−12.0299	+	60.2698i	−0.407851	+	2.04334i
$871$	22.4875	+	22.4875i	0.761958	+	0.761958i
$872$	9.57349	+	6.39680i	0.324199	+	0.216623i
$873$	5.90084	+	8.85659i	0.199713	+	0.299750i
$874$	0.535083	+	0.800809i	0.0180995	+	0.0270878i
$875$	−4.18943	+	1.73532i	−0.141629	+	0.0586644i
$876$	−2.55755	−	0.00169332i	−0.0864117	−	5.72119e-5i
$877$	−11.0888	+	7.40929i	−0.374442	+	0.250194i	−0.728524	−	0.685020i	$-0.759793\pi$
$877$	−11.0888	+	7.40929i	−0.374442	+	0.250194i	0.354082	+	0.935214i	$0.384793\pi$
$878$	12.1685	+	2.42046i	0.410667	+	0.0816867i
$879$	−38.0458	+	25.3850i	−1.28325	+	0.856214i
$880$	15.0076	−	15.0076i	0.505907	−	0.505907i
$881$	19.3402	−	3.84700i	0.651587	−	0.129609i	0.141781	−	0.989898i	$-0.454717\pi$
$881$	19.3402	−	3.84700i	0.651587	−	0.129609i	0.509806	+	0.860289i	$0.329717\pi$
$882$	3.91048	+	9.47622i	0.131673	+	0.319081i
$883$			44.5932i			1.50068i	0.661051	+	0.750341i	$0.270111\pi$
$883$			44.5932i			1.50068i	−0.661051	+	0.750341i	$0.729889\pi$
$884$		0			0
$885$	29.7401	+	12.3418i	0.999702	+	0.414866i
$886$	−25.3778	−	10.5118i	−0.852584	−	0.353152i
$887$	3.26124	+	16.3954i	0.109502	+	0.550502i	0.996120	+	0.0880011i	$0.0280479\pi$
$887$	3.26124	+	16.3954i	0.109502	+	0.550502i	−0.886619	+	0.462501i	$0.846952\pi$
$888$	−10.4432	+	4.31764i	−0.350452	+	0.144890i
$889$	14.7533	−	22.0799i	0.494810	−	0.740536i
$890$	−4.18990	+	21.0640i	−0.140446	+	0.706068i
$891$	−8.20674	−	12.3529i	−0.274936	−	0.413839i
$892$	−0.109250	−	0.263753i	−0.00365797	−	0.00883111i
$893$	−1.03380	−	2.49580i	−0.0345947	−	0.0835189i
$894$	−15.5509	+	3.08257i	−0.520101	+	0.103097i
$895$	0.504016	−	2.53386i	0.0168474	−	0.0846976i
$896$	−14.6260	+	21.8894i	−0.488620	+	0.731272i
$897$	2.24235	+	5.42367i	0.0748699	+	0.181091i
$898$	7.73992	+	38.9112i	0.258284	+	1.29848i
$899$	−21.3259	−	8.83348i	−0.711259	−	0.294613i
$900$	1.07488	−	1.07204i	0.0358293	−	0.0357345i
$901$		0			0
$902$			7.38418i			0.245866i
$903$	−30.2157	−	30.2557i	−1.00552	−	1.00685i
$904$	−44.2934	+	8.81050i	−1.47318	+	0.293033i
$905$	−3.09374	+	3.09374i	−0.102839	+	0.102839i
$906$	−21.2807	−	31.8945i	−0.707004	−	1.05962i
$907$	9.03651	+	1.79747i	0.300052	+	0.0596841i	0.342821	−	0.939401i	$-0.388618\pi$
$907$	9.03651	+	1.79747i	0.300052	+	0.0596841i	−0.0427682	+	0.999085i	$0.513618\pi$
$908$	−0.137071	+	0.0915878i	−0.00454886	+	0.00303945i
$909$	−10.3588	−	4.30683i	−0.343579	−	0.142848i
$910$	−39.1068	+	16.1986i	−1.29638	+	0.536978i
$911$	1.11409	+	1.66735i	0.0369113	+	0.0552417i	0.849466	−	0.527643i	$-0.176924\pi$
$911$	1.11409	+	1.66735i	0.0369113	+	0.0552417i	−0.812555	+	0.582884i	$0.801924\pi$
$912$	3.51046	−	5.24626i	0.116243	−	0.173721i
$913$	17.7940	+	11.8895i	0.588894	+	0.393486i
$914$	−10.8464	−	10.8464i	−0.358768	−	0.358768i
$915$	30.3023	+	6.04837i	1.00176	+	0.199953i
$916$	0.488587	−	1.17955i	0.0161434	−	0.0389735i
$917$	7.60583			0.251167
$918$		0			0
$919$	4.18774			0.138141			0.0690703	−	0.997612i	$-0.477997\pi$
$919$	4.18774			0.138141			0.0690703	+	0.997612i	$0.477997\pi$
$920$	−2.45223	+	5.92020i	−0.0808475	+	0.195183i
$921$	41.4980	+	8.28303i	1.36741	+	0.272935i
$922$	10.1727	+	10.1727i	0.335021	+	0.335021i
$923$	7.99172	+	5.33990i	0.263051	+	0.175765i
$924$	0.401840	−	0.600534i	0.0132196	−	0.0197561i
$925$	−5.70418	−	8.53690i	−0.187552	−	0.280692i
$926$	−30.8229	+	12.7673i	−1.01290	+	0.419558i
$927$	25.8564	+	10.7502i	0.849234	+	0.353083i
$928$	4.40656	−	2.94437i	0.144652	−	0.0966536i
$929$	23.9833	+	4.77057i	0.786866	+	0.156517i	0.572139	−	0.820157i	$-0.306114\pi$
$929$	23.9833	+	4.77057i	0.786866	+	0.156517i	0.214727	+	0.976674i	$0.431114\pi$
$930$	12.3292	+	18.4784i	0.404289	+	0.605929i
$931$	−1.43373	+	1.43373i	−0.0469885	+	0.0469885i
$932$	1.65049	−	0.328303i	0.0540636	−	0.0107539i
$933$	−28.5619	−	28.5997i	−0.935073	−	0.936312i
$934$		−	37.6099i		−	1.23063i
$935$		0			0
$936$	25.7205	−	25.6524i	0.840699	−	0.838476i
$937$	−46.7545	−	19.3663i	−1.52740	−	0.632671i	−0.548345	−	0.836252i	$-0.684742\pi$
$937$	−46.7545	−	19.3663i	−1.52740	−	0.632671i	−0.979058	+	0.203582i	$0.934742\pi$
$938$	4.40513	+	22.1461i	0.143832	+	0.723095i
$939$	1.06851	+	2.58445i	0.0348695	+	0.0843403i
$940$	−0.622608	+	0.931798i	−0.0203072	+	0.0303919i
$941$	−0.703081	+	3.53463i	−0.0229198	+	0.115226i	−0.990552	−	0.137141i	$-0.956209\pi$
$941$	−0.703081	+	3.53463i	−0.0229198	+	0.115226i	0.967632	+	0.252366i	$0.0812088\pi$
$942$	−6.10194	+	1.20955i	−0.198812	+	0.0394093i
$943$	−0.903419	−	2.18105i	−0.0294194	−	0.0710246i
$944$	−9.84105	−	23.7584i	−0.320299	−	0.773270i
$945$	−19.0551	+	28.3957i	−0.619861	+	0.923711i
$946$	5.35453	−	26.9191i	0.174091	−	0.875214i
$947$	−14.8925	+	22.2883i	−0.483943	+	0.724271i	−0.990436	−	0.137972i	$-0.955941\pi$
$947$	−14.8925	+	22.2883i	−0.483943	+	0.724271i	0.506493	+	0.862244i	$0.330941\pi$
$948$	1.11945	−	0.462824i	0.0363581	−	0.0150318i
$949$	−10.8476	−	54.5344i	−0.352127	−	1.77026i
$950$	5.00393	+	2.07269i	0.162349	+	0.0672471i
$951$	39.0103	+	16.1889i	1.26500	+	0.524960i
$952$		0			0
$953$		−	24.2594i		−	0.785838i	−0.919573	−	0.392919i	$-0.871465\pi$
$953$		−	24.2594i		−	0.785838i	0.919573	−	0.392919i	$-0.128535\pi$
$954$	10.6048	+	25.6985i	0.343344	+	0.832021i
$955$	2.15788	−	0.429230i	0.0698275	−	0.0138895i
$956$	1.96792	−	1.96792i	0.0636470	−	0.0636470i
$957$	18.9731	−	12.6593i	0.613315	−	0.409217i
$958$	12.3659	+	2.45974i	0.399525	+	0.0794705i
$959$	26.2688	−	17.5522i	0.848264	−	0.566792i
$960$	39.5170	+	0.0261636i	1.27541	+	0.000844428i
$961$	20.9321	−	8.67037i	0.675230	−	0.279689i
$962$	8.51048	+	12.7368i	0.274389	+	0.410652i
$963$	3.14378	+	4.71851i	0.101307	+	0.152052i
$964$	−0.274684	−	0.183538i	−0.00884697	−	0.00591135i
$965$	25.0752	+	25.0752i	0.807200	+	0.807200i
$966$	−0.815652	+	4.08642i	−0.0262432	+	0.131478i
$967$	5.07976	−	12.2636i	0.163354	−	0.394372i	−0.820914	−	0.571051i	$-0.806536\pi$
$967$	5.07976	−	12.2636i	0.163354	−	0.394372i	0.984268	+	0.176680i	$0.0565357\pi$
$968$	22.6952			0.729452
$969$		0			0
$970$	15.7512			0.505739
$971$	5.91933	−	14.2905i	0.189960	−	0.458605i	−0.799991	−	0.600012i	$-0.795163\pi$
$971$	5.91933	−	14.2905i	0.189960	−	0.458605i	0.989952	+	0.141407i	$0.0451626\pi$
$972$	−0.362918	+	1.79346i	−0.0116406	+	0.0575254i
$973$	−7.69338	−	7.69338i	−0.246638	−	0.246638i
$974$	46.9643	+	31.3806i	1.50483	+	1.00550i
$975$	27.4300	+	18.3544i	0.878464	+	0.587812i
$976$	−13.7105	−	20.5193i	−0.438863	−	0.656805i
$977$	18.6618	−	7.72995i	0.597042	−	0.247303i	−0.0636347	−	0.997973i	$-0.520269\pi$
$977$	18.6618	−	7.72995i	0.597042	−	0.247303i	0.660677	+	0.750670i	$0.270269\pi$
$978$	0.00185371	−	2.79980i	5.92750e−5	−	0.0895277i
$979$	6.62723	−	4.42817i	0.211807	−	0.141525i
$980$	0.824966	+	0.164096i	0.0263526	+	0.00524185i
$981$	−2.44353	−	12.3700i	−0.0780159	−	0.394945i
$982$	13.0385	−	13.0385i	0.416075	−	0.416075i
$983$	25.5849	−	5.08915i	0.816031	−	0.162319i	0.230608	−	0.973047i	$-0.425929\pi$
$983$	25.5849	−	5.08915i	0.816031	−	0.162319i	0.585423	+	0.810728i	$0.300929\pi$
$984$	−10.3391	+	10.3254i	−0.329598	+	0.329162i
$985$		−	70.9874i		−	2.26185i
$986$		0			0
$987$	4.47994	−	10.7953i	0.142598	−	0.343618i
$988$	−0.413882	−	0.171435i	−0.0131673	−	0.00545409i
$989$	1.71186	+	8.60611i	0.0544340	+	0.273658i
$990$	−21.9499	−	0.0290655i	−0.697615	−	0.000923762i
$991$	−20.0616	+	30.0243i	−0.637278	+	0.953754i	0.362485	+	0.931990i	$0.381928\pi$
$991$	−20.0616	+	30.0243i	−0.637278	+	0.953754i	−0.999763	+	0.0217647i	$0.993072\pi$
$992$	0.373707	−	1.87875i	0.0118652	−	0.0596504i
$993$	10.2600	+	51.7596i	0.325592	+	1.64254i
$994$	2.61157	+	6.30488i	0.0828339	+	0.199979i
$995$	28.1592	+	67.9824i	0.892707	+	2.15519i
$996$	−0.513408	−	2.59004i	−0.0162680	−	0.0820685i
$997$	−2.88218	+	14.4897i	−0.0912797	+	0.458894i	0.907929	+	0.419124i	$0.137663\pi$
$997$	−2.88218	+	14.4897i	−0.0912797	+	0.458894i	−0.999209	+	0.0397704i	$0.987337\pi$
$998$	30.0056	−	44.9065i	0.949809	−	1.42149i
$999$	11.4240	+	4.75858i	0.361439	+	0.150555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.i.g.329.1		32
3.2	odd	2	inner	867.2.i.g.329.4		32
17.2	even	8		867.2.i.c.653.1		32
17.3	odd	16	inner	867.2.i.g.224.4		32
17.4	even	4		867.2.i.b.827.4		32
17.5	odd	16		867.2.i.b.65.1		32
17.6	odd	16		51.2.i.a.29.1	✓	32
17.7	odd	16		867.2.i.d.158.4		32
17.8	even	8		867.2.i.h.503.4		32
17.9	even	8		51.2.i.a.44.4	yes	32
17.10	odd	16		867.2.i.c.158.4		32
17.11	odd	16		867.2.i.h.131.1		32
17.12	odd	16		867.2.i.i.65.1		32
17.13	even	4		867.2.i.i.827.4		32
17.14	odd	16		867.2.i.f.224.4		32
17.15	even	8		867.2.i.d.653.1		32
17.16	even	2		867.2.i.f.329.1		32
51.2	odd	8		867.2.i.c.653.4		32
51.5	even	16		867.2.i.b.65.4		32
51.8	odd	8		867.2.i.h.503.1		32
51.11	even	16		867.2.i.h.131.4		32
51.14	even	16		867.2.i.f.224.1		32
51.20	even	16	inner	867.2.i.g.224.1		32
51.23	even	16		51.2.i.a.29.4	yes	32
51.26	odd	8		51.2.i.a.44.1	yes	32
51.29	even	16		867.2.i.i.65.4		32
51.32	odd	8		867.2.i.d.653.4		32
51.38	odd	4		867.2.i.b.827.1		32
51.41	even	16		867.2.i.d.158.1		32
51.44	even	16		867.2.i.c.158.1		32
51.47	odd	4		867.2.i.i.827.1		32
51.50	odd	2		867.2.i.f.329.4		32
68.23	even	16		816.2.cj.c.641.4		32
68.43	odd	8		816.2.cj.c.401.3		32
204.23	odd	16		816.2.cj.c.641.3		32
204.179	even	8		816.2.cj.c.401.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.1	✓	32	17.6	odd	16
51.2.i.a.29.4	yes	32	51.23	even	16
51.2.i.a.44.1	yes	32	51.26	odd	8
51.2.i.a.44.4	yes	32	17.9	even	8
816.2.cj.c.401.3		32	68.43	odd	8
816.2.cj.c.401.4		32	204.179	even	8
816.2.cj.c.641.3		32	204.23	odd	16
816.2.cj.c.641.4		32	68.23	even	16
867.2.i.b.65.1		32	17.5	odd	16
867.2.i.b.65.4		32	51.5	even	16
867.2.i.b.827.1		32	51.38	odd	4
867.2.i.b.827.4		32	17.4	even	4
867.2.i.c.158.1		32	51.44	even	16
867.2.i.c.158.4		32	17.10	odd	16
867.2.i.c.653.1		32	17.2	even	8
867.2.i.c.653.4		32	51.2	odd	8
867.2.i.d.158.1		32	51.41	even	16
867.2.i.d.158.4		32	17.7	odd	16
867.2.i.d.653.1		32	17.15	even	8
867.2.i.d.653.4		32	51.32	odd	8
867.2.i.f.224.1		32	51.14	even	16
867.2.i.f.224.4		32	17.14	odd	16
867.2.i.f.329.1		32	17.16	even	2
867.2.i.f.329.4		32	51.50	odd	2
867.2.i.g.224.1		32	51.20	even	16	inner
867.2.i.g.224.4		32	17.3	odd	16	inner
867.2.i.g.329.1		32	1.1	even	1	trivial
867.2.i.g.329.4		32	3.2	odd	2	inner
867.2.i.h.131.1		32	17.11	odd	16
867.2.i.h.131.4		32	51.11	even	16
867.2.i.h.503.1		32	51.8	odd	8
867.2.i.h.503.4		32	17.8	even	8
867.2.i.i.65.1		32	17.12	odd	16
867.2.i.i.65.4		32	51.29	even	16
867.2.i.i.827.1		32	51.47	odd	4
867.2.i.i.827.4		32	17.13	even	4

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.556851 + 1.34436i) q^{2} +(-1.69855 - 0.339031i) q^{3} +(-0.0830021 - 0.0830021i) q^{4} +(-2.53714 - 1.69526i) q^{5} +(1.40162 - 2.09466i) q^{6} +(1.19824 + 1.79329i) q^{7} +(-2.53091 + 1.04834i) q^{8} +(2.77012 + 1.15172i) q^{9} +(3.69185 - 2.46681i) q^{10} +(-1.61618 - 0.321478i) q^{11} +(0.112843 + 0.169123i) q^{12} +(-3.12551 + 3.12551i) q^{13} +(-3.07806 + 0.612265i) q^{14} +(3.73470 + 3.73965i) q^{15} -4.22099i q^{16} +(-3.09087 + 3.08269i) q^{18} +(-0.797694 - 0.330416i) q^{19} +(0.0698774 + 0.351298i) q^{20} +(-1.42728 - 3.45222i) q^{21} +(1.33215 - 1.99371i) q^{22} +(-0.149554 + 0.751858i) q^{23} +(4.65429 - 0.922593i) q^{24} +(1.64974 + 3.98282i) q^{25} +(-2.46136 - 5.94226i) q^{26} +(-4.31470 - 2.89540i) q^{27} +(0.0493905 - 0.248303i) q^{28} +(4.43981 - 6.64464i) q^{29} +(-7.10709 + 2.93834i) q^{30} +(-0.563512 - 2.83296i) q^{31} +(0.612694 + 0.253786i) q^{32} +(2.63616 + 1.09398i) q^{33} -6.58114i q^{35} +(-0.134330 - 0.325520i) q^{36} +(-2.33589 + 0.464638i) q^{37} +(0.888394 - 0.888394i) q^{38} +(6.36847 - 4.24918i) q^{39} +(8.19848 + 1.63078i) q^{40} +(-2.56055 + 1.71091i) q^{41} +(5.43581 + 0.00359897i) q^{42} +(10.5751 - 4.38037i) q^{43} +(0.107463 + 0.160829i) q^{44} +(-5.07570 - 7.61814i) q^{45} +(-0.927487 - 0.619727i) q^{46} +(2.21238 + 2.21238i) q^{47} +(-1.43105 + 7.16954i) q^{48} +(0.898671 - 2.16958i) q^{49} -6.27299 q^{50} +0.518848 q^{52} +(2.43710 - 5.88369i) q^{53} +(6.29511 - 4.18819i) q^{54} +(3.55548 + 3.55548i) q^{55} +(-4.91261 - 3.28250i) q^{56} +(1.24290 + 0.831669i) q^{57} +(6.46046 + 9.66877i) q^{58} +(5.62864 - 2.33146i) q^{59} +(0.000410749 - 0.620386i) q^{60} +(4.86125 - 3.24818i) q^{61} +(4.12231 + 0.819979i) q^{62} +(1.25389 + 6.34765i) q^{63} +(5.28702 - 5.28702i) q^{64} +(13.2284 - 2.63129i) q^{65} +(-2.93865 + 2.93476i) q^{66} -7.19481i q^{67} +(0.508927 - 1.22636i) q^{69} +(8.84742 + 3.66472i) q^{70} +(-0.424222 - 2.13271i) q^{71} +(-8.21831 - 0.0108825i) q^{72} +(-6.98874 + 10.4594i) q^{73} +(0.676105 - 3.39901i) q^{74} +(-1.45186 - 7.32431i) q^{75} +(0.0387851 + 0.0936354i) q^{76} +(-1.36006 - 3.28348i) q^{77} +(2.16613 + 10.9277i) q^{78} +(1.16236 - 5.84360i) q^{79} +(-7.15567 + 10.7092i) q^{80} +(6.34708 + 6.38079i) q^{81} +(-0.874225 - 4.39502i) q^{82} +(-11.9985 - 4.96993i) q^{83} +(-0.168074 + 0.405009i) q^{84} +16.6560i q^{86} +(-9.79395 + 9.78099i) q^{87} +(4.42742 - 0.880669i) q^{88} +(-3.42023 + 3.42023i) q^{89} +(13.0679 - 2.58139i) q^{90} +(-9.35006 - 1.85984i) q^{91} +(0.0748190 - 0.0499925i) q^{92} +(-0.00331239 + 5.00297i) q^{93} +(-4.20619 + 1.74226i) q^{94} +(1.46372 + 2.19061i) q^{95} +(-0.954647 - 0.638789i) q^{96} +(2.94959 + 1.97085i) q^{97} +(2.41627 + 2.41627i) q^{98} +(-4.10675 - 2.75191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 8 q^{6} + 24 q^{9} + 16 q^{10} + 16 q^{12} + 16 q^{13} + 16 q^{15} + 16 q^{18} + 32 q^{19} - 16 q^{21} - 16 q^{22} - 24 q^{24} - 24 q^{27} + 8 q^{30} - 32 q^{31} - 24 q^{36} - 16 q^{37}+ \cdots + 96 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 + 8 * q^6 + 24 * q^9 + 16 * q^10 + 16 * q^12 + 16 * q^13 + 16 * q^15 + 16 * q^18 + 32 * q^19 - 16 * q^21 - 16 * q^22 - 24 * q^24 - 24 * q^27 + 8 * q^30 - 32 * q^31 - 24 * q^36 - 16 * q^37 + 64 * q^39 - 16 * q^40 - 24 * q^42 - 32 * q^43 - 40 * q^45 + 40 * q^48 - 64 * q^49 - 96 * q^52 + 88 * q^54 + 48 * q^55 + 24 * q^57 + 64 * q^58 + 48 * q^60 + 32 * q^61 + 80 * q^63 - 16 * q^64 + 120 * q^66 + 80 * q^69 - 64 * q^72 - 48 * q^73 - 16 * q^75 + 32 * q^76 - 88 * q^78 + 32 * q^79 - 48 * q^81 - 96 * q^82 - 56 * q^87 - 128 * q^88 - 8 * q^90 - 64 * q^91 - 56 * q^93 - 48 * q^94 - 16 * q^96 - 128 * q^97 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more