LMFDB - Embedded newform 950.2.bb.b.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.4
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.b.507.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 + 0.996195i) q^{2} +(-0.794263 + 1.70330i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(3.76160 + 1.00792i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(-0.342020 - 0.407604i) q^{9} +O(q^{10})$	\(q+(0.0871557 + 0.996195i) q^{2} +(-0.794263 + 1.70330i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(3.76160 + 1.00792i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(-0.342020 - 0.407604i) q^{9} +(-1.56588 + 2.71219i) q^{11} +(0.486421 - 1.81535i) q^{12} +(1.46798 - 0.684531i) q^{13} +(-0.676236 + 3.83513i) q^{14} +(0.939693 - 0.342020i) q^{16} +(6.30628 - 0.551728i) q^{17} +(0.376244 - 0.376244i) q^{18} +(2.70709 + 3.41638i) q^{19} +(-4.70448 + 5.60658i) q^{21} +(-2.83834 - 1.32354i) q^{22} +(0.0168245 - 0.0240279i) q^{23} +(1.85083 + 0.326352i) q^{24} +(0.809869 + 1.40273i) q^{26} +(-4.48011 + 1.20044i) q^{27} +(-3.87947 - 0.339410i) q^{28} +(0.496737 - 0.416812i) q^{29} +(-6.55008 + 3.78169i) q^{31} +(0.422618 + 0.906308i) q^{32} +(-3.37595 - 4.82136i) q^{33} +(1.09926 + 6.23420i) q^{34} +(0.407604 + 0.342020i) q^{36} +(4.88201 + 4.88201i) q^{37} +(-3.16744 + 2.99455i) q^{38} +3.04411i q^{39} +(-2.29280 - 6.29940i) q^{41} +(-5.99527 - 4.19793i) q^{42} +(-3.26829 + 2.28848i) q^{43} +(1.07113 - 2.94289i) q^{44} +(0.0254029 + 0.0146663i) q^{46} +(1.16389 - 13.3033i) q^{47} +(-0.163799 + 1.87223i) q^{48} +(7.07153 + 4.08275i) q^{49} +(-4.06908 + 11.1797i) q^{51} +(-1.32681 + 0.929044i) q^{52} +(-0.241049 - 0.168784i) q^{53} +(-1.58634 - 4.35844i) q^{54} -3.89429i q^{56} +(-7.96927 + 1.89749i) q^{57} +(0.458520 + 0.458520i) q^{58} +(-5.17755 - 4.34448i) q^{59} +(-0.0829556 - 0.470464i) q^{61} +(-4.33818 - 6.19556i) q^{62} +(-0.875711 - 1.87797i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(4.50878 - 3.78331i) q^{66} +(7.83877 + 0.685803i) q^{67} +(-6.11467 + 1.63842i) q^{68} +(0.0275637 + 0.0477418i) q^{69} +(-5.21131 - 0.918895i) q^{71} +(-0.305194 + 0.435862i) q^{72} +(-5.79337 - 2.70149i) q^{73} +(-4.43794 + 5.28893i) q^{74} +(-3.25921 - 2.89440i) q^{76} +(-8.62387 + 8.62387i) q^{77} +(-3.03253 + 0.265312i) q^{78} +(-11.2679 + 4.10117i) q^{79} +(1.79086 - 10.1565i) q^{81} +(6.07560 - 2.83310i) q^{82} +(-3.42105 + 12.7675i) q^{83} +(3.65944 - 6.33833i) q^{84} +(-2.56462 - 3.05640i) q^{86} +(0.315417 + 1.17715i) q^{87} +(3.02505 + 0.810560i) q^{88} +(-3.79474 - 1.38117i) q^{89} +(6.21190 - 1.09533i) q^{91} +(-0.0123965 + 0.0265845i) q^{92} +(-1.23888 - 14.1604i) q^{93} +13.3541 q^{94} -1.87939 q^{96} +(0.733447 + 8.38333i) q^{97} +(-3.45089 + 7.40046i) q^{98} +(1.64106 - 0.289363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{6}+O(q^{10}) $ 48 * q - 48 * q^6	$ 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) $ 48 * q - 48 * q^6 - 12 * q^11 + 36 * q^21 - 72 * q^31 + 48 * q^36 + 96 * q^41 + 72 * q^46 - 48 * q^51 - 108 * q^61 + 24 * q^66 - 60 * q^71 - 48 * q^76 - 168 * q^81 - 48 * q^86 + 252 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.0871557	+	0.996195i	0.0616284	+	0.704416i
$2$	0.0871557	+	0.996195i	0.0616284	+	0.704416i
$3$	−0.794263	+	1.70330i	−0.458568	+	0.983402i	0.532047	+	0.846715i	$0.321423\pi$
$3$	−0.794263	+	1.70330i	−0.458568	+	0.983402i	−0.990614	+	0.136687i	$0.956355\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	−1.76604	−	0.642788i	−0.720985	−	0.262417i
$7$	3.76160	+	1.00792i	1.42175	+	0.380957i	0.886104	−	0.463486i	$-0.153402\pi$
$7$	3.76160	+	1.00792i	1.42175	+	0.380957i	0.535646	+	0.844443i	$0.320068\pi$
$8$	−0.258819	−	0.965926i	−0.0915064	−	0.341506i
$9$	−0.342020	−	0.407604i	−0.114007	−	0.135868i
$10$		0			0
$11$	−1.56588	+	2.71219i	−0.472131	+	0.817755i	−0.999491	−	0.0318867i	$-0.989848\pi$
$11$	−1.56588	+	2.71219i	−0.472131	+	0.817755i	0.527360	+	0.849642i	$0.323182\pi$
$12$	0.486421	−	1.81535i	0.140418	−	0.524045i
$13$	1.46798	−	0.684531i	0.407145	−	0.189855i	−0.208247	−	0.978076i	$-0.566776\pi$
$13$	1.46798	−	0.684531i	0.407145	−	0.189855i	0.615392	+	0.788222i	$0.288998\pi$
$14$	−0.676236	+	3.83513i	−0.180732	+	1.02498i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	6.30628	−	0.551728i	1.52950	−	0.133814i	0.708896	−	0.705313i	$-0.249194\pi$
$17$	6.30628	−	0.551728i	1.52950	−	0.133814i	0.820602	+	0.571500i	$0.193638\pi$
$18$	0.376244	−	0.376244i	0.0886815	−	0.0886815i
$19$	2.70709	+	3.41638i	0.621050	+	0.783771i
$19$	2.70709	+	3.41638i	0.621050	+	0.783771i
$20$		0			0
$21$	−4.70448	+	5.60658i	−1.02660	+	1.22346i
$22$	−2.83834	−	1.32354i	−0.605136	−	0.282180i
$23$	0.0168245	−	0.0240279i	0.00350816	−	0.00501017i	−0.817394	−	0.576079i	$-0.804582\pi$
$23$	0.0168245	−	0.0240279i	0.00350816	−	0.00501017i	0.820902	+	0.571069i	$0.193471\pi$
$24$	1.85083	+	0.326352i	0.377800	+	0.0666163i
$25$		0			0
$26$	0.809869	+	1.40273i	0.158828	+	0.275099i
$27$	−4.48011	+	1.20044i	−0.862198	+	0.231025i
$28$	−3.87947	−	0.339410i	−0.733151	−	0.0641424i
$29$	0.496737	−	0.416812i	0.0922418	−	0.0774001i	−0.595501	−	0.803355i	$-0.703046\pi$
$29$	0.496737	−	0.416812i	0.0922418	−	0.0774001i	0.687742	+	0.725955i	$0.258602\pi$
$30$		0			0
$31$	−6.55008	+	3.78169i	−1.17643	+	0.679211i	−0.955186	−	0.296007i	$-0.904345\pi$
$31$	−6.55008	+	3.78169i	−1.17643	+	0.679211i	−0.221243	+	0.975219i	$0.571011\pi$
$32$	0.422618	+	0.906308i	0.0747091	+	0.160214i
$33$	−3.37595	−	4.82136i	−0.587677	−	0.839290i
$34$	1.09926	+	6.23420i	0.188521	+	1.06916i
$35$		0			0
$36$	0.407604	+	0.342020i	0.0679340	+	0.0570034i
$37$	4.88201	+	4.88201i	0.802598	+	0.802598i	0.983501	−	0.180903i	$-0.0579021\pi$
$37$	4.88201	+	4.88201i	0.802598	+	0.802598i	−0.180903	+	0.983501i	$0.557902\pi$
$38$	−3.16744	+	2.99455i	−0.513827	+	0.485780i
$39$			3.04411i			0.487448i
$40$		0			0
$41$	−2.29280	−	6.29940i	−0.358074	−	0.983801i	−0.979697	−	0.200484i	$-0.935748\pi$
$41$	−2.29280	−	6.29940i	−0.358074	−	0.983801i	0.621622	−	0.783317i	$-0.286474\pi$
$42$	−5.99527	−	4.19793i	−0.925090	−	0.647755i
$43$	−3.26829	+	2.28848i	−0.498409	+	0.348990i	−0.795594	−	0.605830i	$-0.792841\pi$
$43$	−3.26829	+	2.28848i	−0.498409	+	0.348990i	0.297185	+	0.954820i	$0.403952\pi$
$44$	1.07113	−	2.94289i	0.161478	−	0.443658i
$45$		0			0
$46$	0.0254029	+	0.0146663i	0.00374545	+	0.00216244i
$47$	1.16389	−	13.3033i	0.169771	−	1.94049i	−0.141016	−	0.990007i	$-0.545037\pi$
$47$	1.16389	−	13.3033i	0.169771	−	1.94049i	0.310787	−	0.950480i	$-0.399407\pi$
$48$	−0.163799	+	1.87223i	−0.0236424	+	0.270234i
$49$	7.07153	+	4.08275i	1.01022	+	0.583250i
$50$		0			0
$51$	−4.06908	+	11.1797i	−0.569786	+	1.56547i
$52$	−1.32681	+	0.929044i	−0.183996	+	0.128835i
$53$	−0.241049	−	0.168784i	−0.0331106	−	0.0231843i	0.556904	−	0.830577i	$-0.311989\pi$
$53$	−0.241049	−	0.168784i	−0.0331106	−	0.0231843i	−0.590015	+	0.807393i	$0.700878\pi$
$54$	−1.58634	−	4.35844i	−0.215874	−	0.593109i
$55$		0			0
$56$		−	3.89429i		−	0.520396i
$57$	−7.96927	+	1.89749i	−1.05556	+	0.251329i
$58$	0.458520	+	0.458520i	0.0602066	+	0.0602066i
$59$	−5.17755	−	4.34448i	−0.674060	−	0.565603i	0.240204	−	0.970722i	$-0.422786\pi$
$59$	−5.17755	−	4.34448i	−0.674060	−	0.565603i	−0.914264	+	0.405119i	$0.867230\pi$
$60$		0			0
$61$	−0.0829556	−	0.470464i	−0.0106214	−	0.0602368i	0.979036	−	0.203685i	$-0.0652920\pi$
$61$	−0.0829556	−	0.470464i	−0.0106214	−	0.0602368i	−0.989658	+	0.143449i	$0.954181\pi$
$62$	−4.33818	−	6.19556i	−0.550949	−	0.786837i
$63$	−0.875711	−	1.87797i	−0.110329	−	0.236602i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	4.50878	−	3.78331i	0.554992	−	0.465694i
$67$	7.83877	+	0.685803i	0.957658	+	0.0837842i	0.555256	−	0.831679i	$-0.312620\pi$
$67$	7.83877	+	0.685803i	0.957658	+	0.0837842i	0.402401	+	0.915463i	$0.368176\pi$
$68$	−6.11467	+	1.63842i	−0.741512	+	0.198688i
$69$	0.0275637	+	0.0477418i	0.00331828	+	0.00574743i
$70$		0			0
$71$	−5.21131	−	0.918895i	−0.618469	−	0.109053i	−0.144369	−	0.989524i	$-0.546115\pi$
$71$	−5.21131	−	0.918895i	−0.618469	−	0.109053i	−0.474100	+	0.880471i	$0.657226\pi$
$72$	−0.305194	+	0.435862i	−0.0359674	+	0.0513668i
$73$	−5.79337	−	2.70149i	−0.678063	−	0.316186i	0.0529031	−	0.998600i	$-0.483153\pi$
$73$	−5.79337	−	2.70149i	−0.678063	−	0.316186i	−0.730966	+	0.682414i	$0.760930\pi$
$74$	−4.43794	+	5.28893i	−0.515900	+	0.614825i
$75$		0			0
$76$	−3.25921	−	2.89440i	−0.373857	−	0.332010i
$77$	−8.62387	+	8.62387i	−0.982781	+	0.982781i
$78$	−3.03253	+	0.265312i	−0.343366	+	0.0300407i
$79$	−11.2679	+	4.10117i	−1.26773	+	0.461417i	−0.886357	−	0.463003i	$-0.846772\pi$
$79$	−11.2679	+	4.10117i	−1.26773	+	0.461417i	−0.381377	+	0.924420i	$0.624550\pi$
$80$		0			0
$81$	1.79086	−	10.1565i	0.198984	−	1.12850i
$82$	6.07560	−	2.83310i	0.670938	−	0.312864i
$83$	−3.42105	+	12.7675i	−0.375509	+	1.40142i	0.477091	+	0.878854i	$0.341691\pi$
$83$	−3.42105	+	12.7675i	−0.375509	+	1.40142i	−0.852600	+	0.522564i	$0.824975\pi$
$84$	3.65944	−	6.33833i	0.399277	−	0.691568i
$85$		0			0
$86$	−2.56462	−	3.05640i	−0.276550	−	0.329580i
$87$	0.315417	+	1.17715i	0.0338162	+	0.126204i
$88$	3.02505	+	0.810560i	0.322471	+	0.0864060i
$89$	−3.79474	−	1.38117i	−0.402241	−	0.146404i	0.132974	−	0.991120i	$-0.457547\pi$
$89$	−3.79474	−	1.38117i	−0.402241	−	0.146404i	−0.535215	+	0.844716i	$0.679770\pi$
$90$		0			0
$91$	6.21190	−	1.09533i	0.651185	−	0.114821i
$92$	−0.0123965	+	0.0265845i	−0.00129243	+	0.00277162i
$93$	−1.23888	−	14.1604i	−0.128465	−	1.46837i
$94$	13.3541			1.37737
$95$		0			0
$96$	−1.87939			−0.191814
$97$	0.733447	+	8.38333i	0.0744702	+	0.851199i	0.937940	+	0.346798i	$0.112731\pi$
$97$	0.733447	+	8.38333i	0.0744702	+	0.851199i	−0.863470	+	0.504401i	$0.831713\pi$
$98$	−3.45089	+	7.40046i	−0.348592	+	0.747559i
$99$	1.64106	−	0.289363i	0.164933	−	0.0290821i
$100$		0			0
$101$	6.30289	+	2.29407i	0.627161	+	0.228268i	0.635995	−	0.771693i	$-0.280590\pi$
$101$	6.30289	+	2.29407i	0.627161	+	0.228268i	−0.00883393	+	0.999961i	$0.502812\pi$
$102$	−11.4918	−	3.07922i	−1.13786	−	0.304888i
$103$	−3.56081	−	13.2891i	−0.350857	−	1.30941i	−0.885619	−	0.464412i	$-0.846266\pi$
$103$	−3.56081	−	13.2891i	−0.350857	−	1.30941i	0.534763	−	0.845002i	$-0.320401\pi$
$104$	−1.04115	−	1.24079i	−0.102093	−	0.121670i
$105$		0			0
$106$	0.147133	−	0.254842i	0.0142909	−	0.0247525i
$107$	0.423208	−	1.57944i	0.0409131	−	0.152690i	−0.942447	−	0.334354i	$-0.891482\pi$
$107$	0.423208	−	1.57944i	0.0409131	−	0.152690i	0.983361	+	0.181664i	$0.0581485\pi$
$108$	4.20360	−	1.96017i	0.404491	−	0.188617i
$109$	1.42174	−	8.06307i	0.136178	−	0.772302i	−0.837855	−	0.545893i	$-0.816190\pi$
$109$	1.42174	−	8.06307i	0.136178	−	0.772302i	0.974032	−	0.226409i	$-0.0726985\pi$
$110$		0			0
$111$	−12.1931	+	4.43794i	−1.15732	+	0.421230i
$112$	3.87947	−	0.339410i	0.366576	−	0.0320712i
$113$	10.7410	−	10.7410i	1.01043	−	1.01043i	0.0104800	−	0.999945i	$-0.496664\pi$
$113$	10.7410	−	10.7410i	1.01043	−	1.01043i	0.999945	−	0.0104800i	$-0.00333596\pi$
$114$	−2.58484	−	7.77356i	−0.242092	−	0.728061i
$115$		0			0
$116$	−0.416812	+	0.496737i	−0.0387000	+	0.0461209i
$117$	−0.781097	−	0.364231i	−0.0722124	−	0.0336732i
$118$	3.87670	−	5.53649i	0.356879	−	0.509676i
$119$	24.2778	+	4.28083i	2.22554	+	0.392423i
$120$		0			0
$121$	0.596031	+	1.03236i	0.0541846	+	0.0938505i
$122$	0.461444	−	0.123644i	0.0417772	−	0.0111942i
$123$	12.5509	+	1.09806i	1.13167	+	0.0990086i
$124$	5.79388	−	4.86165i	0.520306	−	0.436589i
$125$		0			0
$126$	1.79450	−	1.03605i	0.159867	−	0.0922991i
$127$	2.53661	+	5.43978i	0.225088	+	0.482702i	0.986125	−	0.166006i	$-0.0530872\pi$
$127$	2.53661	+	5.43978i	0.225088	+	0.482702i	−0.761037	+	0.648709i	$0.775309\pi$
$128$	−0.573576	−	0.819152i	−0.0506975	−	0.0724035i
$129$	−1.30209	−	7.38453i	−0.114643	−	0.650172i
$130$		0			0
$131$	15.2177	+	12.7692i	1.32958	+	1.11565i	0.984176	+	0.177194i	$0.0567020\pi$
$131$	15.2177	+	12.7692i	1.32958	+	1.11565i	0.345402	+	0.938455i	$0.387742\pi$
$132$	4.16188	+	4.16188i	0.362245	+	0.362245i
$133$	6.73956	+	15.5796i	0.584394	+	1.35092i
$134$			7.86871i			0.679753i
$135$		0			0
$136$	−2.16511	−	5.94860i	−0.185657	−	0.510088i
$137$	−6.78826	−	4.75319i	−0.579960	−	0.406093i	0.246454	−	0.969154i	$-0.420734\pi$
$137$	−6.78826	−	4.75319i	−0.579960	−	0.406093i	−0.826415	+	0.563062i	$0.809623\pi$
$138$	−0.0451578	+	0.0316198i	−0.00384408	+	0.00269166i
$139$	−0.759848	+	2.08767i	−0.0644495	+	0.177074i	−0.967737	−	0.251962i	$-0.918924\pi$
$139$	−0.759848	+	2.08767i	−0.0644495	+	0.177074i	0.903288	+	0.429035i	$0.141146\pi$
$140$		0			0
$141$	21.7351	+	12.5488i	1.83043	+	1.05680i
$142$	0.461202	−	5.27157i	0.0387032	−	0.442380i
$143$	−0.442109	+	5.05333i	−0.0369711	+	0.422581i
$144$	−0.460802	−	0.266044i	−0.0384002	−	0.0221704i
$145$		0			0
$146$	2.18629	−	6.00678i	0.180939	−	0.497125i
$147$	−12.5708	+	8.80217i	−1.03682	+	0.725991i
$148$	−5.65559	−	3.96009i	−0.464887	−	0.325517i
$149$	−7.06188	−	19.4024i	−0.578532	−	1.58950i	−0.790656	−	0.612261i	$-0.790260\pi$
$149$	−7.06188	−	19.4024i	−0.578532	−	1.58950i	0.212124	−	0.977243i	$-0.431962\pi$
$150$		0			0
$151$			8.61268i			0.700890i	0.936583	+	0.350445i	$0.113970\pi$
$151$			8.61268i			0.700890i	−0.936583	+	0.350445i	$0.886030\pi$
$152$	2.59932	−	3.49907i	0.210833	−	0.283812i
$153$	−2.38176	−	2.38176i	−0.192554	−	0.192554i
$154$	−9.34267	−	7.83943i	−0.752854	−	0.631720i
$155$		0			0
$156$	−0.528605	−	2.99787i	−0.0423222	−	0.240021i
$157$	11.5574	+	16.5057i	0.922380	+	1.31729i	0.948215	+	0.317629i	$0.102887\pi$
$157$	11.5574	+	16.5057i	0.922380	+	1.31729i	−0.0258354	+	0.999666i	$0.508225\pi$
$158$	−5.06762	−	10.8675i	−0.403158	−	0.864575i
$159$	0.478947	−	0.276520i	0.0379830	−	0.0219295i
$160$		0			0
$161$	0.0875053	−	0.0734257i	0.00689638	−	0.00578675i
$162$	10.2739	+	0.898850i	0.807194	+	0.0706203i
$163$	15.8338	−	4.24265i	1.24020	−	0.332310i	0.421656	−	0.906756i	$-0.361449\pi$
$163$	15.8338	−	4.24265i	1.24020	−	0.332310i	0.818542	+	0.574446i	$0.194782\pi$
$164$	3.35184	+	5.80556i	0.261735	+	0.453338i
$165$		0			0
$166$	−13.0171	−	2.29527i	−1.01032	−	0.178147i
$167$	11.4611	−	16.3681i	0.886885	−	1.26660i	−0.0761147	−	0.997099i	$-0.524252\pi$
$167$	11.4611	−	16.3681i	0.886885	−	1.26660i	0.962999	−	0.269504i	$-0.0868596\pi$
$168$	6.63315	+	3.09309i	0.511759	+	0.238637i
$169$	−6.66985	+	7.94882i	−0.513065	+	0.611448i
$170$		0			0
$171$	0.466649	−	2.27189i	0.0356855	−	0.173736i
$172$	2.82124	−	2.82124i	0.215118	−	0.215118i
$173$	−0.401314	+	0.0351104i	−0.0305113	+	0.00266939i	−0.102401	−	0.994743i	$-0.532653\pi$
$173$	−0.401314	+	0.0351104i	−0.0305113	+	0.00266939i	0.0718899	+	0.997413i	$0.477097\pi$
$174$	−1.14518	+	0.416812i	−0.0868160	+	0.0315985i
$175$		0			0
$176$	−0.543825	+	3.08418i	−0.0409923	+	0.232479i
$177$	11.5123	−	5.36827i	0.865317	−	0.403504i
$178$	1.04518	−	3.90067i	0.0783397	−	0.292368i
$179$	−8.88327	+	15.3863i	−0.663966	+	1.15002i	0.315598	+	0.948893i	$0.397795\pi$
$179$	−8.88327	+	15.3863i	−0.663966	+	1.15002i	−0.979564	+	0.201131i	$0.935538\pi$
$180$		0			0
$181$	−8.61930	−	10.2721i	−0.640668	−	0.763518i	0.343808	−	0.939040i	$-0.388283\pi$
$181$	−8.61930	−	10.2721i	−0.640668	−	0.763518i	−0.984475	+	0.175522i	$0.943839\pi$
$182$	1.63256	+	6.09280i	0.121014	+	0.451629i
$183$	0.867231	+	0.232374i	0.0641076	+	0.0171776i
$184$	−0.0275637	−	0.0100324i	−0.00203202	−	0.000739596i
$185$		0			0
$186$	13.9986	−	2.46832i	1.02642	−	0.180986i
$187$	−8.37850	+	17.9677i	−0.612697	+	1.31393i
$188$	1.16389	+	13.3033i	0.0848853	+	0.970243i
$189$	−18.0623			−1.31384
$190$		0			0
$191$	8.73888			0.632323			0.316162	−	0.948705i	$-0.397606\pi$
$191$	8.73888			0.632323			0.316162	+	0.948705i	$0.397606\pi$
$192$	−0.163799	−	1.87223i	−0.0118212	−	0.135117i
$193$	−7.12362	+	15.2767i	−0.512769	+	1.09964i	0.464097	+	0.885785i	$0.346379\pi$
$193$	−7.12362	+	15.2767i	−0.512769	+	1.09964i	−0.976866	+	0.213853i	$0.931399\pi$
$194$	−8.28751	+	1.46131i	−0.595008	+	0.104916i
$195$		0			0
$196$	−7.67306	−	2.79277i	−0.548076	−	0.199483i
$197$	11.2338	+	3.01010i	0.800378	+	0.214461i	0.635750	−	0.771895i	$-0.280691\pi$
$197$	11.2338	+	3.01010i	0.800378	+	0.214461i	0.164628	+	0.986356i	$0.447358\pi$
$198$	0.431290	+	1.60960i	0.0306504	+	0.114389i
$199$	4.98476	+	5.94060i	0.353360	+	0.421118i	0.913219	−	0.407470i	$-0.133589\pi$
$199$	4.98476	+	5.94060i	0.353360	+	0.421118i	−0.559858	+	0.828588i	$0.689144\pi$
$200$		0			0
$201$	−7.39417	+	12.8071i	−0.521544	+	0.903341i
$202$	−1.73600	+	6.47885i	−0.122145	+	0.455850i
$203$	2.28864	−	1.06721i	0.160631	−	0.0749034i
$204$	2.06593	−	11.7165i	0.144644	−	0.820316i
$205$		0			0
$206$	12.9282	−	4.70548i	0.900750	−	0.327846i
$207$	−0.0155482	+	0.00136029i	−0.00108068	+	9.45468e-5i
$208$	1.14533	−	1.14533i	0.0794142	−	0.0794142i
$209$	−13.5048	+	1.99249i	−0.934150	+	0.137824i
$210$		0			0
$211$	16.5506	−	19.7242i	1.13939	−	1.35787i	0.214914	−	0.976633i	$-0.431053\pi$
$211$	16.5506	−	19.7242i	1.13939	−	1.35787i	0.924476	−	0.381240i	$-0.124503\pi$
$212$	0.266696	+	0.124362i	0.0183168	+	0.00854125i
$213$	5.70430	−	8.14659i	0.390852	−	0.558195i
$214$	1.61031	+	0.283941i	0.110079	+	0.0194098i
$215$		0			0
$216$	2.31908	+	4.01676i	0.157793	+	0.273306i
$217$	−28.4504	+	7.62326i	−1.93134	+	0.517500i
$218$	8.15630	+	0.713584i	0.552414	+	0.0483300i
$219$	9.20292	−	7.72217i	0.621876	−	0.521816i
$220$		0			0
$221$	8.87983	−	5.12677i	0.597322	−	0.344864i
$222$	−5.48375	−	11.7599i	−0.368045	−	0.789276i
$223$	16.0871	+	22.9748i	1.07727	+	1.53851i	0.820169	+	0.572122i	$0.193880\pi$
$223$	16.0871	+	22.9748i	1.07727	+	1.53851i	0.257105	+	0.966384i	$0.417232\pi$
$224$	0.676236	+	3.83513i	0.0451830	+	0.256245i
$225$		0			0
$226$	11.6362	+	9.76396i	0.774031	+	0.649489i
$227$	9.28705	+	9.28705i	0.616403	+	0.616403i	0.944607	−	0.328204i	$-0.106443\pi$
$227$	9.28705	+	9.28705i	0.616403	+	0.616403i	−0.328204	+	0.944607i	$0.606443\pi$
$228$	7.51870	−	3.25251i	0.497938	−	0.215403i
$229$		−	6.90731i		−	0.456448i	−0.973609	−	0.228224i	$-0.926708\pi$
$229$		−	6.90731i		−	0.456448i	0.973609	−	0.228224i	$-0.0732919\pi$
$230$		0			0
$231$	−7.83943	−	21.5387i	−0.515797	−	1.41714i
$232$	−0.531175	−	0.371933i	−0.0348733	−	0.0244186i
$233$	19.9672	−	13.9812i	1.30810	−	0.915940i	0.308718	−	0.951154i	$-0.400100\pi$
$233$	19.9672	−	13.9812i	1.30810	−	0.915940i	0.999380	+	0.0352142i	$0.0112113\pi$
$234$	0.294768	−	0.809869i	0.0192696	−	0.0529428i
$235$		0			0
$236$	5.85330	+	3.37941i	0.381018	+	0.219981i
$237$	1.96412	−	22.4500i	0.127583	−	1.45828i
$238$	−2.14859	+	24.5585i	−0.139272	+	1.59189i
$239$	−9.82220	−	5.67085i	−0.635345	−	0.366817i	0.147474	−	0.989066i	$-0.452886\pi$
$239$	−9.82220	−	5.67085i	−0.635345	−	0.366817i	−0.782819	+	0.622249i	$0.786219\pi$
$240$		0			0
$241$	9.18078	−	25.2240i	0.591386	−	1.62482i	−0.176548	−	0.984292i	$-0.556493\pi$
$241$	9.18078	−	25.2240i	0.591386	−	1.62482i	0.767935	−	0.640528i	$-0.221285\pi$
$242$	−0.976480	+	0.683738i	−0.0627705	+	0.0439524i
$243$	4.47905	+	3.13626i	0.287331	+	0.201191i
$244$	0.163391	+	0.448912i	0.0104600	+	0.0287386i
$245$		0			0
$246$			12.5988i			0.803271i
$247$	6.31258	+	3.16209i	0.401660	+	0.201199i
$248$	5.34812	+	5.34812i	0.339606	+	0.339606i
$249$	−19.0297	−	15.9678i	−1.20596	−	1.01192i
$250$		0			0
$251$	3.95636	+	22.4376i	0.249723	+	1.41625i	0.809263	+	0.587447i	$0.199867\pi$
$251$	3.95636	+	22.4376i	0.249723	+	1.41625i	−0.559540	+	0.828803i	$0.689022\pi$
$252$	1.18851	+	1.69737i	0.0748693	+	0.106924i
$253$	0.0388230	+	0.0832562i	0.00244078	+	0.00523427i
$254$	−5.19800	+	3.00107i	−0.326151	+	0.188304i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−6.29536	−	0.550772i	−0.392694	−	0.0343562i	−0.110901	−	0.993831i	$-0.535374\pi$
$257$	−6.29536	−	0.550772i	−0.392694	−	0.0343562i	−0.281793	+	0.959475i	$0.590929\pi$
$258$	7.24295	−	1.94074i	0.450926	−	0.120825i
$259$	13.4435	+	23.2848i	0.835338	+	1.44685i
$260$		0			0
$261$	−0.339788	−	0.0599139i	−0.0210324	−	0.00370858i
$262$	−11.3943	+	16.2727i	−0.703941	+	1.00533i
$263$	−11.0948	−	5.17359i	−0.684135	−	0.319017i	0.0492932	−	0.998784i	$-0.484303\pi$
$263$	−11.0948	−	5.17359i	−0.684135	−	0.319017i	−0.733428	+	0.679767i	$0.762081\pi$
$264$	−3.78331	+	4.50878i	−0.232847	+	0.277496i
$265$		0			0
$266$	−14.9329	+	8.07177i	−0.915594	+	0.494912i
$267$	5.36657	−	5.36657i	0.328429	−	0.328429i
$268$	−7.83877	+	0.685803i	−0.478829	+	0.0418921i
$269$	−14.0112	+	5.09967i	−0.854279	+	0.310932i	−0.731784	−	0.681537i	$-0.761312\pi$
$269$	−14.0112	+	5.09967i	−0.854279	+	0.310932i	−0.122495	+	0.992469i	$0.539090\pi$
$270$		0			0
$271$	4.85349	−	27.5255i	0.294829	−	1.67206i	−0.373070	−	0.927803i	$-0.621695\pi$
$271$	4.85349	−	27.5255i	0.294829	−	1.67206i	0.667898	−	0.744253i	$-0.267194\pi$
$272$	5.73726	−	2.67533i	0.347873	−	0.162216i
$273$	−3.06821	+	11.4507i	−0.185697	+	0.693029i
$274$	4.14347	−	7.17670i	0.250316	−	0.433560i
$275$		0			0
$276$	−0.0354352	−	0.0422301i	−0.00213295	−	0.00254195i
$277$	−5.82108	−	21.7246i	−0.349755	−	1.30530i	−0.886958	−	0.461850i	$-0.847186\pi$
$277$	−5.82108	−	21.7246i	−0.349755	−	1.30530i	0.537203	−	0.843453i	$-0.319481\pi$
$278$	−2.14595	−	0.575005i	−0.128705	−	0.0344865i
$279$	3.78169	+	1.37642i	0.226404	+	0.0824043i
$280$		0			0
$281$	4.60956	−	0.812789i	0.274983	−	0.0484869i	−0.0344560	−	0.999406i	$-0.510970\pi$
$281$	4.60956	−	0.812789i	0.274983	−	0.0484869i	0.309439	+	0.950919i	$0.399859\pi$
$282$	−10.6067	+	22.7461i	−0.631619	+	1.35451i
$283$	1.59322	+	18.2106i	0.0947071	+	1.08251i	0.883684	+	0.468084i	$0.155056\pi$
$283$	1.59322	+	18.2106i	0.0947071	+	1.08251i	−0.788977	+	0.614423i	$0.789389\pi$
$284$	5.29170			0.314005
$285$		0			0
$286$	−5.07264			−0.299951
$287$	−2.27530	−	26.0068i	−0.134306	−	1.53513i
$288$	0.224870	−	0.482236i	0.0132506	−	0.0284160i
$289$	22.7230	−	4.00669i	1.33665	−	0.235687i
$290$		0			0
$291$	−14.8619	−	5.40929i	−0.871220	−	0.317098i
$292$	6.17447	+	1.65444i	0.361333	+	0.0968190i
$293$	−6.79240	−	25.3496i	−0.396816	−	1.48094i	−0.818665	−	0.574272i	$-0.805285\pi$
$293$	−6.79240	−	25.3496i	−0.396816	−	1.48094i	0.421848	−	0.906666i	$-0.361381\pi$
$294$	−9.86430	−	11.7558i	−0.575297	−	0.685613i
$295$		0			0
$296$	3.45210	−	5.97922i	0.200649	−	0.347535i
$297$	3.75950	−	14.0307i	0.218148	−	0.814141i
$298$	18.7130	−	8.72604i	1.08402	−	0.505486i
$299$	0.00825025	−	0.0467895i	0.000477124	−	0.00270591i
$300$		0			0
$301$	−14.6006	+	5.31417i	−0.841563	+	0.306304i
$302$	−8.57991	+	0.750645i	−0.493718	+	0.0431947i
$303$	−8.91364	+	8.91364i	−0.512075	+	0.512075i
$304$	3.71231	+	2.28447i	0.212915	+	0.131023i
$305$		0			0
$306$	2.16511	−	2.58028i	0.123771	−	0.147505i
$307$	−3.14518	−	1.46662i	−0.179505	−	0.0837046i	0.330788	−	0.943705i	$-0.392685\pi$
$307$	−3.14518	−	1.46662i	−0.179505	−	0.0837046i	−0.510293	+	0.860000i	$0.670463\pi$
$308$	6.99534	−	9.99037i	0.398596	−	0.569254i
$309$	25.4636	+	4.48991i	1.44857	+	0.255422i
$310$		0			0
$311$	−7.15102	−	12.3859i	−0.405497	−	0.702341i	0.588882	−	0.808219i	$-0.299568\pi$
$311$	−7.15102	−	12.3859i	−0.405497	−	0.702341i	−0.994379	+	0.105878i	$0.966235\pi$
$312$	2.94039	−	0.787874i	0.166467	−	0.0446046i
$313$	−6.50834	−	0.569406i	−0.367873	−	0.0321847i	−0.0982792	−	0.995159i	$-0.531334\pi$
$313$	−6.50834	−	0.569406i	−0.367873	−	0.0321847i	−0.269594	+	0.962974i	$0.586889\pi$
$314$	−15.4356	+	12.9520i	−0.871079	+	0.730922i
$315$		0			0
$316$	10.3845	−	5.99550i	0.584175	−	0.337273i
$317$	−3.66012	−	7.84916i	−0.205573	−	0.440853i	0.776307	−	0.630355i	$-0.217090\pi$
$317$	−3.66012	−	7.84916i	−0.205573	−	0.440853i	−0.981880	+	0.189502i	$0.939313\pi$
$318$	0.317211	+	0.453024i	0.0177883	+	0.0254043i
$319$	0.352640	+	1.99992i	0.0197441	+	0.111974i
$320$		0			0
$321$	2.35412	+	1.97534i	0.131394	+	0.110253i
$322$	0.0807728	+	0.0807728i	0.00450129	+	0.00450129i
$323$	18.9566	+	20.0511i	1.05477	+	1.11567i
$324$			10.3131i			0.572953i
$325$		0			0
$326$	5.60651	+	15.4038i	0.310516	+	0.853136i
$327$	12.6046	+	8.82584i	0.697036	+	0.488070i
$328$	−5.49134	+	3.84508i	−0.303208	+	0.212309i
$329$	17.7867	−	48.8686i	0.980613	−	2.69421i
$330$		0			0
$331$	−8.12265	−	4.68961i	−0.446461	−	0.257764i	0.259873	−	0.965643i	$-0.416319\pi$
$331$	−8.12265	−	4.68961i	−0.446461	−	0.257764i	−0.706334	+	0.707878i	$0.749653\pi$
$332$	1.15202	−	13.1676i	0.0632252	−	0.722667i
$333$	0.320180	−	3.65967i	0.0175457	−	0.200549i
$334$	17.3047	+	9.99089i	0.946873	+	0.546677i
$335$		0			0
$336$	−2.50320	+	6.87749i	−0.136561	+	0.375198i
$337$	−11.2911	+	7.90612i	−0.615066	+	0.430674i	−0.839153	−	0.543896i	$-0.816949\pi$
$337$	−11.2911	+	7.90612i	−0.615066	+	0.430674i	0.224087	+	0.974569i	$0.428060\pi$
$338$	−8.49989	−	5.95169i	−0.462333	−	0.323729i
$339$	9.76396	+	26.8263i	0.530305	+	1.45700i
$340$		0			0
$341$		−	23.6867i		−	1.28271i
$342$	2.30392	+	0.266865i	0.124582	+	0.0144304i
$343$	3.20941	+	3.20941i	0.173292	+	0.173292i
$344$	3.05640	+	2.56462i	0.164790	+	0.138275i
$345$		0			0
$346$	−0.0699536	−	0.396726i	−0.00376073	−	0.0213281i
$347$	−10.8612	−	15.5115i	−0.583062	−	0.832698i	0.413922	−	0.910312i	$-0.364159\pi$
$347$	−10.8612	−	15.5115i	−0.583062	−	0.832698i	−0.996983	+	0.0776140i	$0.975270\pi$
$348$	−0.515035	−	1.10450i	−0.0276088	−	0.0592072i
$349$	4.72687	−	2.72906i	0.253024	−	0.146083i	−0.368124	−	0.929777i	$-0.620000\pi$
$349$	4.72687	−	2.72906i	0.253024	−	0.146083i	0.621148	+	0.783693i	$0.286667\pi$
$350$		0			0
$351$	−5.75499	+	4.82901i	−0.307178	+	0.257753i
$352$	−3.11985	−	0.272951i	−0.166288	−	0.0145483i
$353$	−16.5192	+	4.42630i	−0.879226	+	0.235588i	−0.670073	−	0.742295i	$-0.733737\pi$
$353$	−16.5192	+	4.42630i	−0.879226	+	0.235588i	−0.209153	+	0.977883i	$0.567071\pi$
$354$	6.35121	+	11.0006i	0.337563	+	0.584676i
$355$		0			0
$356$	3.97692	+	0.701239i	0.210776	+	0.0371656i
$357$	−26.5745	+	37.9523i	−1.40647	+	2.00865i
$358$	−16.1019	−	7.50846i	−0.851014	−	0.396834i
$359$	2.08887	−	2.48942i	0.110247	−	0.131387i	−0.708099	−	0.706113i	$-0.750447\pi$
$359$	2.08887	−	2.48942i	0.110247	−	0.131387i	0.818346	+	0.574726i	$0.194891\pi$
$360$		0			0
$361$	−4.34330	+	18.4969i	−0.228595	+	0.973522i
$362$	9.48177	−	9.48177i	0.498351	−	0.498351i
$363$	−2.23182	+	0.195259i	−0.117140	+	0.0102484i
$364$	−5.92733	+	2.15737i	−0.310677	+	0.113077i
$365$		0			0
$366$	−0.155905	+	0.884184i	−0.00814931	+	0.0462170i
$367$	27.6591	−	12.8977i	1.44379	−	0.673252i	0.466380	−	0.884585i	$-0.345558\pi$
$367$	27.6591	−	12.8977i	1.44379	−	0.673252i	0.977414	+	0.211333i	$0.0677803\pi$
$368$	0.00759186	−	0.0283332i	0.000395753	−	0.00147697i
$369$	−1.78348	+	3.08907i	−0.0928442	+	0.160811i
$370$		0			0
$371$	−0.736609	−	0.877856i	−0.0382428	−	0.0455760i
$372$	3.67898	+	13.7302i	0.190746	+	0.711875i
$373$	−23.9199	−	6.40932i	−1.23853	−	0.331862i	−0.420632	−	0.907231i	$-0.638192\pi$
$373$	−23.9199	−	6.40932i	−1.23853	−	0.331862i	−0.817893	+	0.575370i	$0.804858\pi$
$374$	−18.6296	−	6.78062i	−0.963314	−	0.350618i
$375$		0			0
$376$	−13.1512	+	2.31892i	−0.678224	+	0.119589i
$377$	0.443881	−	0.951905i	0.0228610	−	0.0490256i
$378$	−1.57424	−	17.9936i	−0.0809699	−	0.925491i
$379$	−2.41856			−0.124233			−0.0621165	−	0.998069i	$-0.519785\pi$
$379$	−2.41856			−0.124233			−0.0621165	+	0.998069i	$0.519785\pi$
$380$		0			0
$381$	−11.2803			−0.577908
$382$	0.761644	+	8.70563i	0.0389691	+	0.445419i
$383$	−2.73038	+	5.85531i	−0.139516	+	0.299192i	−0.963634	−	0.267225i	$-0.913893\pi$
$383$	−2.73038	+	5.85531i	−0.139516	+	0.299192i	0.824118	+	0.566418i	$0.191671\pi$
$384$	1.85083	−	0.326352i	0.0944499	−	0.0166541i
$385$		0			0
$386$	−15.8394	−	5.76506i	−0.806203	−	0.293434i
$387$	2.05061	+	0.549460i	0.104239	+	0.0279306i
$388$	−2.17805	−	8.12861i	−0.110574	−	0.412668i
$389$	1.44246	+	1.71905i	0.0731354	+	0.0871594i	0.801372	−	0.598167i	$-0.204104\pi$
$389$	1.44246	+	1.71905i	0.0731354	+	0.0871594i	−0.728236	+	0.685326i	$0.759660\pi$
$390$		0			0
$391$	0.0928434	−	0.160810i	0.00469529	−	0.00813249i
$392$	2.11339	−	7.88727i	0.106742	−	0.398367i
$393$	−33.8366	+	15.7783i	−1.70683	+	0.795909i
$394$	−2.01955	+	11.4534i	−0.101743	+	0.577016i
$395$		0			0
$396$	−1.56588	+	0.569934i	−0.0786885	+	0.0286403i
$397$	14.4429	−	1.26359i	0.724869	−	0.0634178i	0.281251	−	0.959634i	$-0.409251\pi$
$397$	14.4429	−	1.26359i	0.724869	−	0.0634178i	0.443617	+	0.896216i	$0.353695\pi$
$398$	−5.48355	+	5.48355i	−0.274865	+	0.274865i
$399$	−31.8897	−	0.894756i	−1.59648	−	0.0447938i
$400$		0			0
$401$	−1.34649	+	1.60468i	−0.0672405	+	0.0801340i	−0.798616	−	0.601841i	$-0.794434\pi$
$401$	−1.34649	+	1.60468i	−0.0672405	+	0.0801340i	0.731376	+	0.681975i	$0.238879\pi$
$402$	−13.4028	−	6.24982i	−0.668470	−	0.311713i
$403$	−7.02671	+	10.0352i	−0.350025	+	0.499888i
$404$	−6.60550	−	1.16473i	−0.328636	−	0.0579474i
$405$		0			0
$406$	1.26262	+	2.18692i	0.0626626	+	0.108535i
$407$	−20.8856	+	5.59627i	−1.03526	+	0.277397i
$408$	11.8519	+	1.03691i	0.586758	+	0.0513347i
$409$	27.6318	−	23.1858i	1.36630	−	1.14646i	0.392325	−	0.919827i	$-0.371671\pi$
$409$	27.6318	−	23.1858i	1.36630	−	1.14646i	0.973979	−	0.226638i	$-0.0727734\pi$
$410$		0			0
$411$	13.4878	−	7.78718i	0.665303	−	0.384113i
$412$	5.81434	+	12.4689i	0.286452	+	0.614298i
$413$	−15.0970	−	21.5607i	−0.742874	−	1.06093i
$414$	−0.00271023	−	0.0153705i	−0.000133201	−	0.000755418i
$415$		0			0
$416$	1.24079	+	1.04115i	0.0608348	+	0.0510465i
$417$	−2.95241	−	2.95241i	−0.144580	−	0.144580i
$418$	−3.16194	−	13.2798i	−0.154655	−	0.649536i
$419$			7.30395i			0.356821i	0.983956	+	0.178411i	$0.0570956\pi$
$419$			7.30395i			0.356821i	−0.983956	+	0.178411i	$0.942904\pi$
$420$		0			0
$421$	5.01347	+	13.7744i	0.244342	+	0.671323i	0.999869	+	0.0162059i	$0.00515871\pi$
$421$	5.01347	+	13.7744i	0.244342	+	0.671323i	−0.755527	+	0.655118i	$0.772619\pi$
$422$	21.0917	+	14.7685i	1.02673	+	0.718921i
$423$	−5.82055	+	4.07559i	−0.283005	+	0.198162i
$424$	−0.100645	+	0.276520i	−0.00488776	+	0.0134290i
$425$		0			0
$426$	8.61275	+	4.97258i	0.417289	+	0.240922i
$427$	0.162144	−	1.85331i	0.00784668	−	0.0896879i
$428$	−0.142513	+	1.62893i	−0.00688862	+	0.0787373i
$429$	−8.25620	−	4.76672i	−0.398613	−	0.230139i
$430$		0			0
$431$	−9.75827	+	26.8106i	−0.470039	+	1.29142i	0.447681	+	0.894193i	$0.352250\pi$
$431$	−9.75827	+	26.8106i	−0.470039	+	1.29142i	−0.917720	+	0.397228i	$0.869972\pi$
$432$	−3.79935	+	2.66034i	−0.182797	+	0.127996i
$433$	14.9022	+	10.4346i	0.716155	+	0.501457i	0.873951	−	0.486015i	$-0.161550\pi$
$433$	14.9022	+	10.4346i	0.716155	+	0.501457i	−0.157796	+	0.987472i	$0.550439\pi$
$434$	−10.0739	−	27.6777i	−0.483561	−	1.32857i
$435$		0			0
$436$			8.18746i			0.392108i
$437$	0.127634	−	0.00756683i	0.00610557	−	0.000361970i
$438$	8.49487	+	8.49487i	0.405900	+	0.405900i
$439$	−28.4376	−	23.8620i	−1.35725	−	1.13887i	−0.976820	−	0.214062i	$-0.931331\pi$
$439$	−28.4376	−	23.8620i	−1.35725	−	1.13887i	−0.380432	−	0.924809i	$-0.624225\pi$
$440$		0			0
$441$	−0.754462	−	4.27877i	−0.0359267	−	0.203751i
$442$	5.88119	+	8.39921i	0.279740	+	0.399510i
$443$	−8.05911	−	17.2828i	−0.382900	−	0.821132i	−0.999429	−	0.0337992i	$-0.989239\pi$
$443$	−8.05911	−	17.2828i	−0.382900	−	0.821132i	0.616529	−	0.787332i	$-0.288538\pi$
$444$	11.2373	−	6.48783i	0.533296	−	0.307899i
$445$		0			0
$446$	−21.4853	+	18.0283i	−1.01736	+	0.853664i
$447$	38.6571	+	3.38205i	1.82842	+	0.159966i
$448$	−3.76160	+	1.00792i	−0.177719	+	0.0476196i
$449$	5.70099	+	9.87440i	0.269046	+	0.466002i	0.968616	−	0.248563i	$-0.0799582\pi$
$449$	5.70099	+	9.87440i	0.269046	+	0.466002i	−0.699570	+	0.714564i	$0.746625\pi$
$450$		0			0
$451$	20.6754	+	3.64563i	0.973567	+	0.171666i
$452$	−8.71264	+	12.4429i	−0.409808	+	0.585266i
$453$	−14.6700	−	6.84073i	−0.689256	−	0.321405i
$454$	−8.44229	+	10.0611i	−0.396216	+	0.472192i
$455$		0			0
$456$	3.89544	+	7.20661i	0.182420	+	0.337481i
$457$	−15.7889	+	15.7889i	−0.738571	+	0.738571i	−0.972302	−	0.233730i	$-0.924907\pi$
$457$	−15.7889	+	15.7889i	−0.738571	+	0.738571i	0.233730	+	0.972302i	$0.424907\pi$
$458$	6.88103	−	0.602012i	0.321529	−	0.0281302i
$459$	−27.5905	+	10.0421i	−1.28782	+	0.468727i
$460$		0			0
$461$	1.44668	−	8.20452i	0.0673785	−	0.382122i	−0.932407	−	0.361410i	$-0.882295\pi$
$461$	1.44668	−	8.20452i	0.0673785	−	0.382122i	0.999785	−	0.0207124i	$-0.00659344\pi$
$462$	20.7735	−	9.68682i	0.966469	−	0.450672i
$463$	6.01367	−	22.4433i	0.279479	−	1.04303i	−0.673301	−	0.739368i	$-0.735124\pi$
$463$	6.01367	−	22.4433i	0.279479	−	1.04303i	0.952780	−	0.303661i	$-0.0982091\pi$
$464$	0.324222	−	0.561570i	0.0150516	−	0.0260702i
$465$		0			0
$466$	15.6683	+	18.6727i	0.725819	+	0.864997i
$467$	−9.41628	−	35.1421i	−0.435734	−	1.62618i	−0.739304	−	0.673371i	$-0.764846\pi$
$467$	−9.41628	−	35.1421i	−0.435734	−	1.62618i	0.303571	−	0.952809i	$-0.401821\pi$
$468$	0.832478	+	0.223062i	0.0384813	+	0.0103110i
$469$	28.7950	+	10.4805i	1.32963	+	0.483946i
$470$		0			0
$471$	−37.2937	+	6.57589i	−1.71840	+	0.303001i
$472$	−2.85640	+	6.12556i	−0.131476	+	0.281952i
$473$	−1.08903	−	12.4477i	−0.0500737	−	0.572345i
$474$	22.5357			1.03510
$475$		0			0
$476$	−24.6523			−1.12994
$477$	0.0136465	+	0.155980i	0.000624830	+	0.00714184i
$478$	4.79321	−	10.2791i	0.219236	−	0.470154i
$479$	37.1809	−	6.55600i	1.69884	−	0.299551i	0.761551	−	0.648105i	$-0.224438\pi$
$479$	37.1809	−	6.55600i	1.69884	−	0.299551i	0.937289	+	0.348553i	$0.113327\pi$
$480$		0			0
$481$	10.5086	+	3.82481i	0.479151	+	0.174397i
$482$	25.9282	+	6.94743i	1.18100	+	0.316447i
$483$	0.0555639	+	0.207367i	0.00252824	+	0.00943553i
$484$	−0.766242	−	0.913172i	−0.0348292	−	0.0415078i
$485$		0			0
$486$	−2.73396	+	4.73535i	−0.124015	+	0.214800i
$487$	3.02241	−	11.2798i	0.136959	−	0.511137i	−0.863024	−	0.505164i	$-0.831432\pi$
$487$	3.02241	−	11.2798i	0.136959	−	0.511137i	0.999982	−	0.00597286i	$-0.00190123\pi$
$488$	−0.432963	+	0.201894i	−0.0195993	+	0.00913931i
$489$	−5.34967	+	30.3395i	−0.241921	+	1.37200i
$490$		0			0
$491$	18.8360	−	6.85576i	0.850059	−	0.309396i	0.119995	−	0.992775i	$-0.461712\pi$
$491$	18.8360	−	6.85576i	0.850059	−	0.309396i	0.730064	+	0.683378i	$0.239490\pi$
$492$	−12.5509	+	1.09806i	−0.565837	+	0.0495043i
$493$	2.90260	−	2.90260i	0.130726	−	0.130726i
$494$	−2.59988	+	6.56415i	−0.116974	+	0.295335i
$495$		0			0
$496$	−4.86165	+	5.79388i	−0.218294	+	0.260153i
$497$	−18.6767	−	8.70908i	−0.837763	−	0.390656i
$498$	14.2485	−	20.3490i	0.638492	−	0.911861i
$499$	33.7600	+	5.95279i	1.51130	+	0.266484i	0.867008	−	0.498294i	$-0.166040\pi$
$499$	33.7600	+	5.95279i	1.51130	+	0.266484i	0.644295	+	0.764777i	$0.277151\pi$
$500$		0			0
$501$	18.7767	+	32.5222i	0.838882	+	1.45299i
$502$	−22.0074	+	5.89687i	−0.982239	+	0.263190i
$503$	38.0979	+	3.33314i	1.69870	+	0.148617i	0.894896	−	0.446274i	$-0.147249\pi$
$503$	38.0979	+	3.33314i	1.69870	+	0.148617i	0.803806	+	0.594892i	$0.202805\pi$
$504$	−1.58733	+	1.33193i	−0.0707052	+	0.0593287i
$505$		0			0
$506$	−0.0795557	+	0.0459315i	−0.00353668	+	0.00204191i
$507$	−8.24162	−	17.6742i	−0.366023	−	0.784940i
$508$	−3.44268	−	4.91666i	−0.152744	−	0.218141i
$509$	2.71535	+	15.3995i	0.120356	+	0.682570i	0.983958	+	0.178398i	$0.0570914\pi$
$509$	2.71535	+	15.3995i	0.120356	+	0.682570i	−0.863603	+	0.504173i	$0.831798\pi$
$510$		0			0
$511$	−19.0694	−	16.0012i	−0.843583	−	0.707850i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−16.2293	−	12.0561i	−0.716539	−	0.532288i
$514$		−	6.31941i		−	0.278737i
$515$		0			0
$516$	2.56462	+	7.04624i	0.112901	+	0.310193i
$517$	34.2585	+	23.9881i	1.50669	+	1.05499i
$518$	−22.0245	+	15.4217i	−0.967702	+	0.677592i
$519$	0.258945	−	0.711445i	0.0113664	−	0.0312290i
$520$		0			0
$521$	−3.45662	−	1.99568i	−0.151437	−	0.0874324i	0.422367	−	0.906425i	$-0.361200\pi$
$521$	−3.45662	−	1.99568i	−0.151437	−	0.0874324i	−0.573804	+	0.818993i	$0.694533\pi$
$522$	0.0300714	−	0.343717i	0.00131619	−	0.0150441i
$523$	2.90529	−	33.2076i	0.127039	−	1.45207i	−0.618595	−	0.785710i	$-0.712298\pi$
$523$	2.90529	−	33.2076i	0.127039	−	1.45207i	0.745634	−	0.666356i	$-0.232147\pi$
$524$	−17.2039	−	9.93266i	−0.751555	−	0.433910i
$525$		0			0
$526$	4.18693	−	11.5035i	0.182559	−	0.501576i
$527$	−39.2202	+	27.4623i	−1.70846	+	1.19627i
$528$	−4.82136	−	3.37595i	−0.209823	−	0.146919i
$529$	7.86617	+	21.6121i	0.342007	+	0.939657i
$530$		0			0
$531$			3.59629i			0.156066i
$532$	−9.34254	−	14.1726i	−0.405050	−	0.614458i
$533$	−7.67792	−	7.67792i	−0.332568	−	0.332568i
$534$	5.81387	+	4.87842i	0.251591	+	0.211110i
$535$		0			0
$536$	−1.36639	−	7.74917i	−0.0590189	−	0.334713i
$537$	−19.1518	−	27.3516i	−0.826461	−	1.18031i
$538$	−6.30142	−	13.5134i	−0.271673	−	0.582606i
$539$	−22.1464	+	12.7862i	−0.953911	+	0.550741i
$540$		0			0
$541$	−23.4057	+	19.6397i	−1.00629	+	0.844378i	−0.987843	−	0.155452i	$-0.950317\pi$
$541$	−23.4057	+	19.6397i	−1.00629	+	0.844378i	−0.0184466	+	0.999830i	$0.505872\pi$
$542$	27.8438	+	2.43602i	1.19599	+	0.104636i
$543$	24.3424	−	6.52254i	1.04463	−	0.279909i
$544$	3.16518	+	5.48226i	0.135706	+	0.235050i
$545$		0			0
$546$	−11.6746	−	2.05854i	−0.499625	−	0.0880974i
$547$	−15.4533	+	22.0696i	−0.660735	+	0.943628i	0.339260	+	0.940693i	$0.389823\pi$
$547$	−15.4533	+	22.0696i	−0.660735	+	0.943628i	−0.999996	+	0.00293537i	$0.999066\pi$
$548$	7.51052	+	3.50221i	0.320833	+	0.149607i
$549$	−0.163391	+	0.194721i	−0.00697334	+	0.00831050i
$550$		0			0
$551$	2.76870	+	0.568694i	0.117951	+	0.0242272i
$552$	0.0389810	−	0.0389810i	0.00165914	−	0.00165914i
$553$	−46.5188	+	4.06987i	−1.97818	+	0.173068i
$554$	21.1346	−	7.69236i	0.897922	−	0.326817i
$555$		0			0
$556$	0.385785	−	2.18790i	0.0163609	−	0.0927875i
$557$	−2.31325	+	1.07869i	−0.0980156	+	0.0457054i	−0.471008	−	0.882129i	$-0.656110\pi$
$557$	−2.31325	+	1.07869i	−0.0980156	+	0.0457054i	0.372992	+	0.927835i	$0.378332\pi$
$558$	−1.04159	+	3.88726i	−0.0440940	+	0.164561i
$559$	−3.23125	+	5.59669i	−0.136667	+	0.236715i
$560$		0			0
$561$	−23.9498	−	28.5422i	−1.01116	−	1.20505i
$562$	1.21145	+	4.52118i	0.0511017	+	0.190714i
$563$	−33.5735	−	8.99598i	−1.41495	−	0.379136i	−0.531263	−	0.847207i	$-0.678282\pi$
$563$	−33.5735	−	8.99598i	−1.41495	−	0.379136i	−0.883690	+	0.468072i	$0.844949\pi$
$564$	−23.5840	−	8.58387i	−0.993065	−	0.361446i
$565$		0			0
$566$	−18.0024	+	3.17432i	−0.756699	+	0.133426i
$567$	16.9734	−	36.3995i	0.712814	−	1.52864i
$568$	0.461202	+	5.27157i	0.0193516	+	0.221190i
$569$	−8.01662			−0.336074			−0.168037	−	0.985781i	$-0.553743\pi$
$569$	−8.01662			−0.336074			−0.168037	+	0.985781i	$0.553743\pi$
$570$		0			0
$571$	−3.98332			−0.166697			−0.0833484	−	0.996520i	$-0.526561\pi$
$571$	−3.98332			−0.166697			−0.0833484	+	0.996520i	$0.526561\pi$
$572$	−0.442109	−	5.05333i	−0.0184855	−	0.211291i
$573$	−6.94097	+	14.8849i	−0.289963	+	0.621828i
$574$	25.7095	−	4.53328i	1.07309	−	0.189215i
$575$		0			0
$576$	0.500000	+	0.181985i	0.0208333	+	0.00758271i
$577$	42.9708	+	11.5140i	1.78890	+	0.479334i	0.992158	−	0.124986i	$-0.0398887\pi$
$577$	42.9708	+	11.5140i	1.78890	+	0.479334i	0.796741	+	0.604320i	$0.206555\pi$
$578$	5.97188	+	22.2874i	0.248398	+	0.927032i
$579$	−20.3627	−	24.2673i	−0.846246	−	1.00852i
$580$		0			0
$581$	−25.7372	+	44.5782i	−1.06776	+	1.84941i
$582$	4.09340	−	15.2768i	0.169677	−	0.633243i
$583$	0.835229	−	0.389474i	0.0345917	−	0.0161304i
$584$	−1.11001	+	6.29517i	−0.0459325	+	0.260496i
$585$		0			0
$586$	24.6611	−	8.97591i	1.01874	−	0.370792i
$587$	−34.4649	+	3.01529i	−1.42252	+	0.124454i	−0.772284	−	0.635277i	$-0.780886\pi$
$587$	−34.4649	+	3.01529i	−1.42252	+	0.124454i	−0.650237	+	0.759732i	$0.725330\pi$
$588$	10.8513	−	10.8513i	0.447502	−	0.447502i
$589$	−30.6514	−	12.1402i	−1.26297	−	0.500227i
$590$		0			0
$591$	−14.0497	+	16.7438i	−0.577928	+	0.688748i
$592$	6.25734	+	2.91784i	0.257175	+	0.119923i
$593$	−5.19308	+	7.41648i	−0.213254	+	0.304559i	−0.911500	−	0.411299i	$-0.865075\pi$
$593$	−5.19308	+	7.41648i	−0.213254	+	0.304559i	0.698246	+	0.715858i	$0.253964\pi$
$594$	14.3049	+	2.52234i	0.586938	+	0.103493i
$595$		0			0
$596$	10.3238	+	17.8813i	0.422879	+	0.732447i
$597$	−14.0778	+	3.77215i	−0.576168	+	0.154384i
$598$	0.0473305	+	0.00414088i	0.00193549	+	0.000169333i
$599$	4.22725	−	3.54709i	0.172721	−	0.144930i	−0.552329	−	0.833626i	$-0.686261\pi$
$599$	4.22725	−	3.54709i	0.172721	−	0.144930i	0.725050	+	0.688696i	$0.241816\pi$
$600$		0			0
$601$	28.0345	−	16.1857i	1.14355	−	0.660229i	0.196243	−	0.980555i	$-0.437126\pi$
$601$	28.0345	−	16.1857i	1.14355	−	0.660229i	0.947307	+	0.320326i	$0.103792\pi$
$602$	−6.56648	−	14.0819i	−0.267630	−	0.573933i
$603$	−2.40148	−	3.42967i	−0.0977958	−	0.139667i
$604$	−1.49558	−	8.48183i	−0.0608541	−	0.345121i
$605$		0			0
$606$	−9.65659	−	8.10284i	−0.392272	−	0.329156i
$607$	−10.3802	−	10.3802i	−0.421318	−	0.421318i	0.464340	−	0.885657i	$-0.346292\pi$
$607$	−10.3802	−	10.3802i	−0.421318	−	0.421318i	−0.885657	+	0.464340i	$0.846292\pi$
$608$	−1.95222	+	3.89728i	−0.0791732	+	0.158056i
$609$			4.74588i			0.192313i
$610$		0			0
$611$	−7.39796	−	20.3257i	−0.299289	−	0.822291i
$612$	2.75917	+	1.93199i	0.111533	+	0.0780960i
$613$	−19.7129	+	13.8031i	−0.796195	+	0.557502i	−0.899384	−	0.437160i	$-0.855984\pi$
$613$	−19.7129	+	13.8031i	−0.796195	+	0.557502i	0.103189	+	0.994662i	$0.467095\pi$
$614$	1.18692	−	3.26104i	0.0479003	−	0.131605i
$615$		0			0
$616$	10.5620	+	6.09800i	0.425557	+	0.245695i
$617$	1.64823	−	18.8394i	0.0663553	−	0.758445i	−0.888014	−	0.459816i	$-0.847915\pi$
$617$	1.64823	−	18.8394i	0.0663553	−	0.758445i	0.954369	−	0.298629i	$-0.0965292\pi$
$618$	−2.25353	+	25.7580i	−0.0906504	+	1.03614i
$619$	14.9536	+	8.63346i	0.601035	+	0.347008i	0.769449	−	0.638709i	$-0.220531\pi$
$619$	14.9536	+	8.63346i	0.601035	+	0.347008i	−0.168413	+	0.985716i	$0.553864\pi$
$620$		0			0
$621$	−0.0465317	+	0.127845i	−0.00186725	+	0.00513024i
$622$	11.7155	−	8.20331i	0.469750	−	0.328923i
$623$	−12.8822	−	9.02018i	−0.516113	−	0.361386i
$624$	1.04115	+	2.86053i	0.0416793	+	0.114513i
$625$		0			0
$626$		−	6.53320i		−	0.261119i
$627$	7.33257	−	24.5854i	0.292835	−	0.981846i
$628$	−14.2480	−	14.2480i	−0.568556	−	0.568556i
$629$	33.4809	+	28.0938i	1.33497	+	1.12017i
$630$		0			0
$631$	2.26764	+	12.8604i	0.0902734	+	0.511966i	0.996094	+	0.0883035i	$0.0281445\pi$
$631$	2.26764	+	12.8604i	0.0902734	+	0.511966i	−0.905820	+	0.423662i	$0.860744\pi$
$632$	6.87776	+	9.82246i	0.273583	+	0.390716i
$633$	20.4508	+	43.8569i	0.812847	+	1.74316i
$634$	7.50029	−	4.33030i	0.297875	−	0.171978i
$635$		0			0
$636$	−0.423654	+	0.355488i	−0.0167990	+	0.0140960i
$637$	13.1756	+	1.15272i	0.522038	+	0.0456724i
$638$	−1.96158	+	0.525603i	−0.0776596	+	0.0208088i
$639$	1.40783	+	2.43843i	0.0556928	+	0.0964628i
$640$		0			0
$641$	−7.97365	−	1.40597i	−0.314940	−	0.0555325i	0.0139437	−	0.999903i	$-0.495561\pi$
$641$	−7.97365	−	1.40597i	−0.314940	−	0.0555325i	−0.328884	+	0.944370i	$0.606673\pi$
$642$	−1.76265	+	2.51732i	−0.0695661	+	0.0993507i
$643$	0.360894	+	0.168288i	0.0142323	+	0.00663662i	0.429721	−	0.902962i	$-0.358612\pi$
$643$	0.360894	+	0.168288i	0.0142323	+	0.00663662i	−0.415489	+	0.909598i	$0.636390\pi$
$644$	−0.0734257	+	0.0875053i	−0.00289338	+	0.00344819i
$645$		0			0
$646$	−18.3226	+	20.6320i	−0.720893	+	0.811756i
$647$	−15.0528	+	15.0528i	−0.591787	+	0.591787i	−0.938114	−	0.346327i	$-0.887429\pi$
$647$	−15.0528	+	15.0528i	−0.591787	+	0.591787i	0.346327	+	0.938114i	$0.387429\pi$
$648$	−10.2739	+	0.898850i	−0.403597	+	0.0353102i
$649$	19.8905	−	7.23954i	0.780769	−	0.284177i
$650$		0			0
$651$	9.61237	−	54.5144i	0.376738	−	2.13659i
$652$	−14.8565	+	6.92770i	−0.581826	+	0.271310i
$653$	2.05471	−	7.66830i	0.0804072	−	0.300084i	−0.913998	−	0.405719i	$-0.867021\pi$
$653$	2.05471	−	7.66830i	0.0804072	−	0.300084i	0.994405	+	0.105636i	$0.0336877\pi$
$654$	−7.69369	+	13.3259i	−0.300847	+	0.521083i
$655$		0			0
$656$	−4.30905	−	5.13532i	−0.168240	−	0.200501i
$657$	0.880311	+	3.28537i	0.0343442	+	0.128174i
$658$	50.2328	+	13.4598i	1.95828	+	0.524719i
$659$	−17.9446	−	6.53131i	−0.699024	−	0.254424i	−0.0320298	−	0.999487i	$-0.510197\pi$
$659$	−17.9446	−	6.53131i	−0.699024	−	0.254424i	−0.666994	+	0.745063i	$0.732419\pi$
$660$		0			0
$661$	44.8594	−	7.90992i	1.74483	−	0.307660i	0.791854	−	0.610711i	$-0.209116\pi$
$661$	44.8594	−	7.90992i	1.74483	−	0.307660i	0.952975	+	0.303050i	$0.0980050\pi$
$662$	3.96383	−	8.50047i	0.154059	−	0.330380i
$663$	1.67952	+	19.1970i	0.0652273	+	0.745551i
$664$	13.2179			0.512955
$665$		0			0
$666$	3.67365			0.142351
$667$	−0.00165776	−	0.0189483i	−6.41886e−5	−	0.000733679i
$668$	−8.44466	+	18.1096i	−0.326734	+	0.700683i
$669$	−51.9104	+	9.15320i	−2.00697	+	0.353883i
$670$		0			0
$671$	1.40589	+	0.511701i	0.0542736	+	0.0197540i
$672$	−7.06949	−	1.89426i	−0.272711	−	0.0730728i
$673$	−0.207675	−	0.775055i	−0.00800530	−	0.0298762i	0.961808	−	0.273726i	$-0.0882562\pi$
$673$	−0.207675	−	0.775055i	−0.00800530	−	0.0298762i	−0.969813	+	0.243850i	$0.921590\pi$
$674$	−8.86011	−	10.5591i	−0.341279	−	0.406720i
$675$		0			0
$676$	5.18822	−	8.98627i	0.199547	−	0.345626i
$677$	−11.2153	+	41.8561i	−0.431040	+	1.60866i	0.319330	+	0.947644i	$0.396542\pi$
$677$	−11.2153	+	41.8561i	−0.431040	+	1.60866i	−0.750370	+	0.661019i	$0.770124\pi$
$678$	−25.8732	+	12.0649i	−0.993654	+	0.463348i
$679$	−5.69077	+	32.2740i	−0.218392	+	1.23856i
$680$		0			0
$681$	−23.1950	+	8.44229i	−0.888834	+	0.323509i
$682$	23.5966	−	2.06443i	0.903560	−	0.0790512i
$683$	−6.91468	+	6.91468i	−0.264583	+	0.264583i	−0.826913	−	0.562330i	$-0.809905\pi$
$683$	−6.91468	+	6.91468i	−0.264583	+	0.264583i	0.562330	+	0.826913i	$0.309905\pi$
$684$	−0.0650496	+	2.31841i	−0.00248723	+	0.0886466i
$685$		0			0
$686$	−2.91748	+	3.47692i	−0.111390	+	0.132749i
$687$	11.7652	+	5.48622i	0.448872	+	0.209312i
$688$	−2.28848	+	3.26829i	−0.0872475	+	0.124602i
$689$	−0.469394	−	0.0827668i	−0.0178825	−	0.00315316i
$690$		0			0
$691$	−5.61528	−	9.72594i	−0.213615	−	0.369992i	0.739228	−	0.673455i	$-0.235191\pi$
$691$	−5.61528	−	9.72594i	−0.213615	−	0.369992i	−0.952843	+	0.303463i	$0.901857\pi$
$692$	0.389120	−	0.104264i	0.0147921	−	0.00396354i
$693$	6.46466	+	0.565584i	0.245572	+	0.0214848i
$694$	14.5058	−	12.1718i	0.550633	−	0.462036i
$695$		0			0
$696$	1.05541	−	0.609339i	0.0400050	−	0.0230969i
$697$	−17.9346	−	38.4608i	−0.679320	−	1.45681i
$698$	3.13065	+	4.47103i	0.118497	+	0.169231i
$699$	7.95499	+	45.1150i	0.300885	+	1.70641i
$700$		0			0
$701$	4.09358	+	3.43492i	0.154612	+	0.129735i	0.716812	−	0.697266i	$-0.245600\pi$
$701$	4.09358	+	3.43492i	0.154612	+	0.129735i	−0.562200	+	0.827001i	$0.690045\pi$
$702$	−5.31221	−	5.31221i	−0.200496	−	0.200496i
$703$	−3.46275	+	29.8949i	−0.130600	+	1.12751i
$704$		−	3.13176i		−	0.118033i
$705$		0			0
$706$	−5.84919	−	16.0705i	−0.220137	−	0.604822i
$707$	21.3967	+	14.9821i	0.804706	+	0.563461i
$708$	−10.4052	+	7.28580i	−0.391052	+	0.273817i
$709$	8.82228	−	24.2390i	0.331328	−	0.910315i	−0.656439	−	0.754379i	$-0.727938\pi$
$709$	8.82228	−	24.2390i	0.331328	−	0.910315i	0.987767	−	0.155937i	$-0.0498395\pi$
$710$		0			0
$711$	5.52549	+	3.19014i	0.207222	+	0.119640i
$712$	−0.351959	+	4.02291i	−0.0131902	+	0.150765i
$713$	−0.0193359	+	0.221010i	−0.000724134	+	0.00827689i
$714$	−40.1240	−	23.1656i	−1.50160	−	0.866950i
$715$		0			0
$716$	6.07651	−	16.6951i	0.227090	−	0.623924i
$717$	17.4606	−	12.2260i	0.652077	−	0.456589i
$718$	2.66201	+	1.86396i	0.0993452	+	0.0695623i
$719$	−1.77083	−	4.86532i	−0.0660408	−	0.181446i	0.902283	−	0.431145i	$-0.141890\pi$
$719$	−1.77083	−	4.86532i	−0.0660408	−	0.181446i	−0.968323	+	0.249700i	$0.919668\pi$
$720$		0			0
$721$		−	53.5772i		−	1.99532i
$722$	−18.8051	−	2.71466i	−0.699852	−	0.101029i
$723$	35.6721	+	35.6721i	1.32666	+	1.32666i
$724$	10.2721	+	8.61930i	0.381759	+	0.320334i
$725$		0			0
$726$	−0.389031	−	2.20631i	−0.0144383	−	0.0818837i
$727$	25.7797	+	36.8172i	0.956117	+	1.36548i	0.930694	+	0.365799i	$0.119204\pi$
$727$	25.7797	+	36.8172i	0.956117	+	1.36548i	0.0254229	+	0.999677i	$0.491907\pi$
$728$	−2.66576	−	5.71675i	−0.0987998	−	0.211877i
$729$	17.8948	−	10.3316i	0.662770	−	0.382651i
$730$		0			0
$731$	−19.3481	+	16.2350i	−0.715616	+	0.600473i
$732$	−0.894407	−	0.0782505i	−0.0330582	−	0.00289222i
$733$	31.0462	−	8.31879i	1.14672	−	0.307262i	0.365068	−	0.930981i	$-0.381046\pi$
$733$	31.0462	−	8.31879i	1.14672	−	0.307262i	0.781648	+	0.623719i	$0.214379\pi$
$734$	15.2592	+	26.4298i	0.563228	+	0.975540i
$735$		0			0
$736$	0.0288871	+	0.00509357i	0.00106479	+	0.000187751i
$737$	−14.1346	+	20.1863i	−0.520655	+	0.743572i
$738$	−3.23276	−	1.50746i	−0.119000	−	0.0554904i
$739$	−32.1725	+	38.3417i	−1.18349	+	1.41042i	−0.292575	+	0.956243i	$0.594512\pi$
$739$	−32.1725	+	38.3417i	−1.18349	+	1.41042i	−0.890910	+	0.454180i	$0.849932\pi$
$740$		0			0
$741$	−10.3998	+	8.24070i	−0.382048	+	0.302730i
$742$	0.810316	−	0.810316i	0.0297476	−	0.0297476i
$743$	39.7687	−	3.47931i	1.45897	−	0.127643i	0.670131	−	0.742242i	$-0.266238\pi$
$743$	39.7687	−	3.47931i	1.45897	−	0.127643i	0.788840	+	0.614599i	$0.210682\pi$
$744$	−13.3573	+	4.86165i	−0.489701	+	0.178237i
$745$		0			0
$746$	4.30017	−	24.3875i	0.157440	−	0.892889i
$747$	6.37416	−	2.97232i	0.233218	−	0.108751i
$748$	5.13114	−	19.1497i	0.187613	−	0.700182i
$749$	3.18388	−	5.51464i	0.116336	−	0.201501i
$750$		0			0
$751$	0.728959	+	0.868740i	0.0266001	+	0.0317008i	0.779180	−	0.626800i	$-0.215636\pi$
$751$	0.728959	+	0.868740i	0.0266001	+	0.0317008i	−0.752580	+	0.658500i	$0.771191\pi$
$752$	−3.45630	−	12.8991i	−0.126038	−	0.470382i
$753$	−41.3604	−	11.0825i	−1.50726	−	0.403868i
$754$	0.986970	+	0.359228i	0.0359433	+	0.0130823i
$755$		0			0
$756$	17.7879	−	3.13649i	0.646940	−	0.114073i
$757$	−0.177388	+	0.380410i	−0.00644727	+	0.0138262i	−0.909505	−	0.415693i	$-0.863539\pi$
$757$	−0.177388	+	0.380410i	−0.00644727	+	0.0138262i	0.903058	+	0.429519i	$0.141317\pi$
$758$	−0.210791	−	2.40935i	−0.00765628	−	0.0875117i
$759$	−0.172646			−0.00626666
$760$		0			0
$761$	−6.39812			−0.231932			−0.115966	−	0.993253i	$-0.536996\pi$
$761$	−6.39812			−0.231932			−0.115966	+	0.993253i	$0.536996\pi$
$762$	−0.983144	−	11.2374i	−0.0356156	−	0.407088i
$763$	13.4749	−	28.8970i	0.487824	−	1.04614i
$764$	−8.60612	+	1.51749i	−0.311358	+	0.0549009i
$765$		0			0
$766$	−6.07100	−	2.20966i	−0.219354	−	0.0798383i
$767$	−10.5745	−	2.83342i	−0.381822	−	0.102309i
$768$	0.486421	+	1.81535i	0.0175522	+	0.0655057i
$769$	−12.6226	−	15.0430i	−0.455183	−	0.542466i	0.488828	−	0.872380i	$-0.337425\pi$
$769$	−12.6226	−	15.0430i	−0.455183	−	0.542466i	−0.944011	+	0.329915i	$0.892980\pi$
$770$		0			0
$771$	5.93830	−	10.2854i	0.213863	−	0.370421i
$772$	4.36263	−	16.2816i	0.157015	−	0.585986i
$773$	13.2998	−	6.20181i	0.478361	−	0.223063i	−0.168455	−	0.985709i	$-0.553878\pi$
$773$	13.2998	−	6.20181i	0.478361	−	0.223063i	0.646816	+	0.762646i	$0.276100\pi$
$774$	−0.368647	+	2.09070i	−0.0132507	+	0.0751486i
$775$		0			0
$776$	7.90785	−	2.87822i	0.283875	−	0.103322i
$777$	−50.3387	+	4.40407i	−1.80589	+	0.157995i
$778$	−1.58679	+	1.58679i	−0.0568892	+	0.0568892i
$779$	15.3143	−	24.8861i	0.548693	−	0.891638i
$780$		0			0
$781$	10.6525	−	12.6952i	0.381177	−	0.454269i
$782$	0.168289	+	0.0784746i	0.00601802	+	0.00280625i
$783$	−1.72508	+	2.46367i	−0.0616494	+	0.0880444i
$784$	8.04145	+	1.41792i	0.287195	+	0.0506402i
$785$		0			0
$786$	−18.6673	−	32.3327i	−0.665840	−	1.15327i
$787$	23.7713	−	6.36949i	0.847354	−	0.227048i	0.191084	−	0.981574i	$-0.438800\pi$
$787$	23.7713	−	6.36949i	0.847354	−	0.227048i	0.656270	+	0.754526i	$0.272133\pi$
$788$	−11.5859	−	1.01363i	−0.412730	−	0.0361092i
$789$	17.6244	−	14.7886i	0.627444	−	0.526488i
$790$		0			0
$791$	51.2292	−	29.5772i	1.82150	−	1.05164i
$792$	−0.704241	−	1.51025i	−0.0250241	−	0.0536644i
$793$	−0.443825	−	0.633847i	−0.0157607	−	0.0225086i
$794$	2.51756	+	14.2778i	0.0893450	+	0.506701i
$795$		0			0
$796$	−5.94060	−	4.98476i	−0.210559	−	0.176680i
$797$	23.7905	+	23.7905i	0.842704	+	0.842704i	0.989210	−	0.146506i	$-0.0468027\pi$
$797$	23.7905	+	23.7905i	0.842704	+	0.842704i	−0.146506	+	0.989210i	$0.546803\pi$
$798$	−1.88802	−	31.8463i	−0.0668351	−	1.12735i
$799$		−	84.5365i		−	2.99069i
$800$		0			0
$801$	0.734906	+	2.01914i	0.0259666	+	0.0713427i
$802$	−1.71593	−	1.20151i	−0.0605916	−	0.0424267i
$803$	16.3987	−	11.4825i	0.578697	−	0.405208i
$804$	5.05791	−	13.8965i	0.178379	−	0.490091i
$805$		0			0
$806$	−10.6094	−	6.12535i	−0.373701	−	0.215756i
$807$	2.44232	−	27.9158i	0.0859736	−	0.982683i
$808$	0.584588	−	6.68188i	0.0205657	−	0.235068i
$809$	−4.89923	−	2.82857i	−0.172248	−	0.0994472i	0.411398	−	0.911456i	$-0.365041\pi$
$809$	−4.89923	−	2.82857i	−0.172248	−	0.0994472i	−0.583645	+	0.812009i	$0.698374\pi$
$810$		0			0
$811$	−12.7827	+	35.1202i	−0.448862	+	1.23324i	0.484655	+	0.874705i	$0.338945\pi$
$811$	−12.7827	+	35.1202i	−0.448862	+	1.23324i	−0.933517	+	0.358533i	$0.883277\pi$
$812$	−2.06855	+	1.44841i	−0.0725918	+	0.0508294i
$813$	43.0293	+	30.1294i	1.50910	+	1.05669i
$814$	−7.39527	−	20.3183i	−0.259204	−	0.712158i
$815$		0			0
$816$			11.8972i			0.416485i
$817$	−16.6659	−	4.97058i	−0.583065	−	0.173899i
$818$	25.5059	+	25.5059i	0.891791	+	0.891791i
$819$	−2.57106	−	2.15737i	−0.0898400	−	0.0753847i
$820$		0			0
$821$	8.69704	+	49.3234i	0.303529	+	1.72140i	0.630350	+	0.776311i	$0.282911\pi$
$821$	8.69704	+	49.3234i	0.303529	+	1.72140i	−0.326822	+	0.945086i	$0.605978\pi$
$822$	8.93308	+	12.7578i	0.311577	+	0.444978i
$823$	20.3206	+	43.5776i	0.708331	+	1.51902i	0.848673	+	0.528918i	$0.177402\pi$
$823$	20.3206	+	43.5776i	0.708331	+	1.51902i	−0.140342	+	0.990103i	$0.544820\pi$
$824$	−11.9147	+	6.87895i	−0.415068	+	0.239639i
$825$		0			0
$826$	20.1629	−	16.9187i	0.701557	−	0.588676i
$827$	28.2356	+	2.47030i	0.981849	+	0.0859007i	0.566762	−	0.823881i	$-0.308196\pi$
$827$	28.2356	+	2.47030i	0.981849	+	0.0859007i	0.415087	+	0.909782i	$0.363751\pi$
$828$	0.0150758	−	0.00403954i	0.000523920	−	0.000140384i
$829$	5.95974	+	10.3226i	0.206990	+	0.358518i	0.950765	−	0.309913i	$-0.100300\pi$
$829$	5.95974	+	10.3226i	0.206990	+	0.358518i	−0.743775	+	0.668430i	$0.766966\pi$
$830$		0			0
$831$	41.6270	+	7.33996i	1.44402	+	0.254620i
$832$	−0.929044	+	1.32681i	−0.0322088	+	0.0459989i
$833$	46.8476	+	21.8454i	1.62317	+	0.756898i
$834$	2.68385	−	3.19849i	0.0929342	−	0.110755i
$835$		0			0
$836$	12.9537	−	4.30731i	0.448012	−	0.148972i
$837$	24.8054	−	24.8054i	0.857400	−	0.857400i
$838$	−7.27616	+	0.636581i	−0.251351	+	0.0219903i
$839$	14.8033	−	5.38796i	0.511066	−	0.186013i	−0.0735985	−	0.997288i	$-0.523448\pi$
$839$	14.8033	−	5.38796i	0.511066	−	0.186013i	0.584665	+	0.811275i	$0.301226\pi$
$840$		0			0
$841$	−4.96278	+	28.1453i	−0.171130	+	0.970529i
$842$	−13.2850	+	6.19491i	−0.457833	+	0.213491i
$843$	−2.27677	+	8.49703i	−0.0784162	+	0.292653i
$844$	−12.8741	+	22.2986i	−0.443144	+	0.767548i
$845$		0			0
$846$	−4.56738	−	5.44319i	−0.157030	−	0.187141i
$847$	1.20150	+	4.48405i	0.0412840	+	0.154074i
$848$	−0.284240	−	0.0761618i	−0.00976083	−	0.00261541i
$849$	−32.2836	−	11.7503i	−1.10797	−	0.403268i
$850$		0			0
$851$	0.199442	−	0.0351671i	0.00683679	−	0.00120551i
$852$	−4.20300	+	9.01337i	−0.143992	+	0.308793i
$853$	−0.838394	−	9.58289i	−0.0287061	−	0.328112i	−0.996946	−	0.0780902i	$-0.975118\pi$
$853$	−0.838394	−	9.58289i	−0.0287061	−	0.328112i	0.968240	−	0.250022i	$-0.0804378\pi$
$854$	1.86039			0.0636612
$855$		0			0
$856$	−1.63515			−0.0558883
$857$	−2.37512	−	27.1477i	−0.0811324	−	0.927348i	−0.922275	−	0.386534i	$-0.873672\pi$
$857$	−2.37512	−	27.1477i	−0.0811324	−	0.927348i	0.841143	−	0.540813i	$-0.181883\pi$
$858$	4.02901	−	8.64023i	0.137548	−	0.294973i
$859$	−24.3714	+	4.29734i	−0.831542	+	0.146623i	−0.573185	−	0.819426i	$-0.694292\pi$
$859$	−24.3714	+	4.29734i	−0.831542	+	0.146623i	−0.258357	+	0.966049i	$0.583181\pi$
$860$		0			0
$861$	46.1045	+	16.7807i	1.57124	+	0.571884i
$862$	−27.5591	−	7.38443i	−0.938666	−	0.251515i
$863$	−8.17628	−	30.5143i	−0.278324	−	1.03872i	−0.953581	−	0.301136i	$-0.902634\pi$
$863$	−8.17628	−	30.5143i	−0.278324	−	1.03872i	0.675257	−	0.737582i	$-0.264033\pi$
$864$	−2.98135	−	3.55303i	−0.101428	−	0.120877i
$865$		0			0
$866$	−9.09612	+	15.7549i	−0.309099	+	0.535375i
$867$	−11.2235	+	41.8866i	−0.381169	+	1.42254i
$868$	26.6944	−	12.4478i	0.906067	−	0.422506i
$869$	6.52101	−	36.9825i	0.221210	−	1.25454i
$870$		0			0
$871$	11.9766	−	4.35913i	0.405812	−	0.147704i
$872$	−8.15630	+	0.713584i	−0.276207	+	0.0241650i
$873$	3.16622	−	3.16622i	0.107160	−	0.107160i
$874$	0.0186621	+	0.126489i	0.000631254	+	0.00427855i
$875$		0			0
$876$	−7.72217	+	9.20292i	−0.260908	+	0.310938i
$877$	1.54862	+	0.722132i	0.0522931	+	0.0243847i	0.448589	−	0.893738i	$-0.351927\pi$
$877$	1.54862	+	0.722132i	0.0522931	+	0.0243847i	−0.396296	+	0.918123i	$0.629705\pi$
$878$	21.2927	−	30.4091i	0.718593	−	1.02626i
$879$	48.5729	+	8.56472i	1.63832	+	0.288881i
$880$		0			0
$881$	−20.4268	−	35.3803i	−0.688197	−	1.19199i	−0.972421	−	0.233234i	$-0.925069\pi$
$881$	−20.4268	−	35.3803i	−0.688197	−	1.19199i	0.284224	−	0.958758i	$-0.408264\pi$
$882$	4.19673	−	1.12451i	0.141311	−	0.0378642i
$883$	−25.2720	−	2.21101i	−0.850469	−	0.0744064i	−0.346418	−	0.938080i	$-0.612602\pi$
$883$	−25.2720	−	2.21101i	−0.850469	−	0.0744064i	−0.504051	+	0.863674i	$0.668158\pi$
$884$	−7.85467	+	6.59085i	−0.264181	+	0.221674i
$885$		0			0
$886$	16.5147	−	9.53474i	0.554821	−	0.320326i
$887$	−3.99264	−	8.56224i	−0.134060	−	0.287492i	0.827806	−	0.561015i	$-0.189589\pi$
$887$	−3.99264	−	8.56224i	−0.134060	−	0.287492i	−0.961866	+	0.273523i	$0.911811\pi$
$888$	7.44253	+	10.6290i	0.249755	+	0.356687i
$889$	4.05886	+	23.0189i	0.136130	+	0.772030i
$890$		0			0
$891$	24.7420	+	20.7610i	0.828887	+	0.695519i
$892$	−19.8322	−	19.8322i	−0.664033	−	0.664033i
$893$	48.5999	−	32.0370i	1.62633	−	1.07208i
$894$			38.8047i			1.29782i
$895$		0			0
$896$	−1.33193	−	3.65944i	−0.0444965	−	0.122253i
$897$	0.0731438	+	0.0512158i	0.00244220	+	0.00171005i
$898$	−9.33995	+	6.53990i	−0.311678	+	0.218239i
$899$	−1.67741	+	4.60866i	−0.0559449	+	0.153707i
$900$		0			0
$901$	−1.61325	−	0.931408i	−0.0537450	−	0.0310297i
$902$	−1.82978	+	20.9145i	−0.0609250	+	0.696375i
$903$	2.54505	−	29.0900i	0.0846939	−	0.968056i
$904$	−13.1549	−	7.59501i	−0.437527	−	0.252606i
$905$		0			0
$906$	5.53612	−	15.2104i	0.183925	−	0.505331i
$907$	−27.6363	+	19.3512i	−0.917650	+	0.642545i	−0.933981	−	0.357321i	$-0.883690\pi$
$907$	−27.6363	+	19.3512i	−0.917650	+	0.642545i	0.0163318	+	0.999867i	$0.494801\pi$
$908$	−10.7586	−	7.53328i	−0.357038	−	0.250001i
$909$	−1.22065	−	3.35370i	−0.0404863	−	0.111235i
$910$		0			0
$911$		−	1.55634i		−	0.0515640i	−0.999668	−	0.0257820i	$-0.991792\pi$
$911$		−	1.55634i		−	0.0515640i	0.999668	−	0.0257820i	$-0.00820757\pi$
$912$	−6.83968	+	4.50871i	−0.226484	+	0.149298i
$913$	−29.2710	−	29.2710i	−0.968727	−	0.968727i
$914$	−17.1049	−	14.3527i	−0.565779	−	0.474745i
$915$		0			0
$916$	1.19944	+	6.80238i	0.0396307	+	0.224757i
$917$	44.3726	+	63.3707i	1.46531	+	2.09268i
$918$	−12.4086	−	26.6103i	−0.409545	−	0.878271i
$919$	−1.73927	+	1.00417i	−0.0573732	+	0.0331245i	−0.528412	−	0.848988i	$-0.677212\pi$
$919$	−1.73927	+	1.00417i	−0.0573732	+	0.0331245i	0.471039	+	0.882112i	$0.343879\pi$
$920$		0			0
$921$	4.99620	−	4.19231i	0.164631	−	0.138141i
$922$	8.29938	+	0.726102i	0.273326	+	0.0239129i
$923$	−8.27912	+	2.21838i	−0.272511	+	0.0730190i
$924$	11.4605	+	19.8501i	0.377022	+	0.653022i
$925$		0			0
$926$	22.8820	+	4.03472i	0.751950	+	0.132589i
$927$	−4.19882	+	5.99654i	−0.137907	+	0.196952i
$928$	0.587691	+	0.274045i	0.0192919	+	0.00899595i
$929$	2.12800	−	2.53605i	0.0698173	−	0.0832050i	−0.730005	−	0.683441i	$-0.760482\pi$
$929$	2.12800	−	2.53605i	0.0698173	−	0.0832050i	0.799823	+	0.600236i	$0.204927\pi$
$930$		0			0
$931$	5.19506	+	35.2114i	0.170261	+	1.15401i
$932$	−17.2361	+	17.2361i	−0.564587	+	0.564587i
$933$	26.7767	−	2.34266i	0.876631	−	0.0766953i
$934$	34.1876	−	12.4433i	1.11865	−	0.407157i
$935$		0			0
$936$	−0.149658	+	0.848752i	−0.00489172	+	0.0277423i
$937$	42.3794	−	19.7619i	1.38448	−	0.645592i	0.419458	−	0.907775i	$-0.362220\pi$
$937$	42.3794	−	19.7619i	1.38448	−	0.645592i	0.965018	+	0.262183i	$0.0844424\pi$
$938$	−7.93100	+	29.5989i	−0.258956	+	0.966438i
$939$	6.13920	−	10.6334i	0.200345	−	0.347008i
$940$		0			0
$941$	−3.57407	−	4.25941i	−0.116511	−	0.138853i	0.704636	−	0.709569i	$-0.251110\pi$
$941$	−3.57407	−	4.25941i	−0.116511	−	0.138853i	−0.821148	+	0.570716i	$0.806666\pi$
$942$	−9.80122	−	36.5787i	−0.319341	−	1.19180i
$943$	−0.189937	−	0.0508934i	−0.00618520	−	0.00165732i
$944$	−6.35121	−	2.31165i	−0.206714	−	0.0752378i
$945$		0			0
$946$	12.3054	−	2.16978i	0.400083	−	0.0705455i
$947$	3.35296	−	7.19045i	0.108957	−	0.233658i	−0.844268	−	0.535921i	$-0.819964\pi$
$947$	3.35296	−	7.19045i	0.108957	−	0.233658i	0.953225	+	0.302263i	$0.0977421\pi$
$948$	1.96412	+	22.4500i	0.0637916	+	0.729141i
$949$	−10.3538			−0.336099
$950$		0			0
$951$	16.2766			0.527805
$952$	−2.14859	−	24.5585i	−0.0696362	−	0.795945i
$953$	−1.96874	+	4.22198i	−0.0637738	+	0.136763i	−0.935611	−	0.353032i	$-0.885151\pi$
$953$	−1.96874	+	4.22198i	−0.0637738	+	0.136763i	0.871837	+	0.489795i	$0.162928\pi$
$954$	−0.154197	+	0.0271891i	−0.00499232	+	0.000880281i
$955$		0			0
$956$	10.6577	+	3.87909i	0.344695	+	0.125459i
$957$	−3.68656	−	0.987811i	−0.119170	−	0.0319314i
$958$	9.77159	+	36.4681i	0.315706	+	1.17823i
$959$	−20.7439	−	24.7216i	−0.669855	−	0.798302i
$960$		0			0
$961$	13.1024	−	22.6939i	0.422656	−	0.732062i
$962$	−2.89438	+	10.8020i	−0.0933184	+	0.348269i
$963$	−0.788530	+	0.367697i	−0.0254100	+	0.0118489i
$964$	−4.66121	+	26.4350i	−0.150127	+	0.851414i
$965$		0			0
$966$	−0.201735	+	0.0734257i	−0.00649073	+	0.00236243i
$967$	21.3318	−	1.86629i	0.685983	−	0.0600158i	0.261165	−	0.965294i	$-0.415893\pi$
$967$	21.3318	−	1.86629i	0.685983	−	0.0600158i	0.424819	+	0.905278i	$0.360338\pi$
$968$	0.842915	−	0.842915i	0.0270923	−	0.0270923i
$969$	−49.2095	+	16.3630i	−1.58084	+	0.525655i
$970$		0			0
$971$	−19.7178	+	23.4987i	−0.632774	+	0.754111i	−0.983210	−	0.182476i	$-0.941589\pi$
$971$	−19.7178	+	23.4987i	−0.632774	+	0.754111i	0.350436	+	0.936587i	$0.386033\pi$
$972$	−4.95561	−	2.31084i	−0.158951	−	0.0741202i
$973$	−4.96244	+	7.08709i	−0.159088	+	0.227202i
$974$	11.5003	+	2.02781i	0.368493	+	0.0649753i
$975$		0			0
$976$	−0.238861	−	0.413719i	−0.00764576	−	0.0132428i
$977$	−5.74010	+	1.53806i	−0.183642	+	0.0492068i	−0.349468	−	0.936948i	$-0.613638\pi$
$977$	−5.74010	+	1.53806i	−0.183642	+	0.0492068i	0.165826	+	0.986155i	$0.446971\pi$
$978$	−30.6903	−	2.68505i	−0.981368	−	0.0858585i
$979$	9.68810	−	8.12928i	0.309633	−	0.259813i
$980$		0			0
$981$	−3.77280	+	2.17823i	−0.120456	+	0.0695454i
$982$	8.47134	+	18.1669i	0.270331	+	0.579728i
$983$	20.6160	+	29.4427i	0.657548	+	0.939076i	1.00000		0.000459562i	$-0.000146283\pi$
$983$	20.6160	+	29.4427i	0.657548	+	0.939076i	−0.342452	+	0.939535i	$0.611257\pi$
$984$	−2.18776	−	12.4074i	−0.0697432	−	0.395534i
$985$		0			0
$986$	3.14453	+	2.63858i	0.100142	+	0.0840294i
$987$	69.1106	+	69.1106i	2.19981	+	2.19981i
$988$	−6.76577	−	2.01789i	−0.215248	−	0.0641975i
$989$			0.117033i			0.00372143i
$990$		0			0
$991$	5.30438	+	14.5737i	0.168499	+	0.462948i	0.994987	−	0.100007i	$-0.0318866\pi$
$991$	5.30438	+	14.5737i	0.168499	+	0.462948i	−0.826488	+	0.562955i	$0.809664\pi$
$992$	−6.19556	−	4.33818i	−0.196709	−	0.137737i
$993$	14.4393	−	10.1105i	0.458219	−	0.320848i
$994$	7.04816	−	19.3647i	0.223554	−	0.614210i
$995$		0			0
$996$	21.5134	+	12.4208i	0.681679	+	0.393567i
$997$	0.149019	−	1.70329i	0.00471948	−	0.0539439i	−0.993470	−	0.114096i	$-0.963603\pi$
$997$	0.149019	−	1.70329i	0.00471948	−	0.0539439i	0.998189	+	0.0601519i	$0.0191585\pi$
$998$	−2.98776	+	34.1503i	−0.0945760	+	1.08101i
$999$	−27.7325	−	16.0114i	−0.877419	−	0.506578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.b.193.4	yes	48
5.2	odd	4	inner	950.2.bb.b.307.1	yes	48
5.3	odd	4	inner	950.2.bb.b.307.4	yes	48
5.4	even	2	inner	950.2.bb.b.193.1	✓	48
19.13	odd	18	inner	950.2.bb.b.393.1	yes	48
95.13	even	36	inner	950.2.bb.b.507.1	yes	48
95.32	even	36	inner	950.2.bb.b.507.4	yes	48
95.89	odd	18	inner	950.2.bb.b.393.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.b.193.1	✓	48	5.4	even	2	inner
950.2.bb.b.193.4	yes	48	1.1	even	1	trivial
950.2.bb.b.307.1	yes	48	5.2	odd	4	inner
950.2.bb.b.307.4	yes	48	5.3	odd	4	inner
950.2.bb.b.393.1	yes	48	19.13	odd	18	inner
950.2.bb.b.393.4	yes	48	95.89	odd	18	inner
950.2.bb.b.507.1	yes	48	95.13	even	36	inner
950.2.bb.b.507.4	yes	48	95.32	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0871557 + 0.996195i) q^{2} +(-0.794263 + 1.70330i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(3.76160 + 1.00792i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(-0.342020 - 0.407604i) q^{9} +O(q^{10})\)	\(q+(0.0871557 + 0.996195i) q^{2} +(-0.794263 + 1.70330i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(3.76160 + 1.00792i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(-0.342020 - 0.407604i) q^{9} +(-1.56588 + 2.71219i) q^{11} +(0.486421 - 1.81535i) q^{12} +(1.46798 - 0.684531i) q^{13} +(-0.676236 + 3.83513i) q^{14} +(0.939693 - 0.342020i) q^{16} +(6.30628 - 0.551728i) q^{17} +(0.376244 - 0.376244i) q^{18} +(2.70709 + 3.41638i) q^{19} +(-4.70448 + 5.60658i) q^{21} +(-2.83834 - 1.32354i) q^{22} +(0.0168245 - 0.0240279i) q^{23} +(1.85083 + 0.326352i) q^{24} +(0.809869 + 1.40273i) q^{26} +(-4.48011 + 1.20044i) q^{27} +(-3.87947 - 0.339410i) q^{28} +(0.496737 - 0.416812i) q^{29} +(-6.55008 + 3.78169i) q^{31} +(0.422618 + 0.906308i) q^{32} +(-3.37595 - 4.82136i) q^{33} +(1.09926 + 6.23420i) q^{34} +(0.407604 + 0.342020i) q^{36} +(4.88201 + 4.88201i) q^{37} +(-3.16744 + 2.99455i) q^{38} +3.04411i q^{39} +(-2.29280 - 6.29940i) q^{41} +(-5.99527 - 4.19793i) q^{42} +(-3.26829 + 2.28848i) q^{43} +(1.07113 - 2.94289i) q^{44} +(0.0254029 + 0.0146663i) q^{46} +(1.16389 - 13.3033i) q^{47} +(-0.163799 + 1.87223i) q^{48} +(7.07153 + 4.08275i) q^{49} +(-4.06908 + 11.1797i) q^{51} +(-1.32681 + 0.929044i) q^{52} +(-0.241049 - 0.168784i) q^{53} +(-1.58634 - 4.35844i) q^{54} -3.89429i q^{56} +(-7.96927 + 1.89749i) q^{57} +(0.458520 + 0.458520i) q^{58} +(-5.17755 - 4.34448i) q^{59} +(-0.0829556 - 0.470464i) q^{61} +(-4.33818 - 6.19556i) q^{62} +(-0.875711 - 1.87797i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(4.50878 - 3.78331i) q^{66} +(7.83877 + 0.685803i) q^{67} +(-6.11467 + 1.63842i) q^{68} +(0.0275637 + 0.0477418i) q^{69} +(-5.21131 - 0.918895i) q^{71} +(-0.305194 + 0.435862i) q^{72} +(-5.79337 - 2.70149i) q^{73} +(-4.43794 + 5.28893i) q^{74} +(-3.25921 - 2.89440i) q^{76} +(-8.62387 + 8.62387i) q^{77} +(-3.03253 + 0.265312i) q^{78} +(-11.2679 + 4.10117i) q^{79} +(1.79086 - 10.1565i) q^{81} +(6.07560 - 2.83310i) q^{82} +(-3.42105 + 12.7675i) q^{83} +(3.65944 - 6.33833i) q^{84} +(-2.56462 - 3.05640i) q^{86} +(0.315417 + 1.17715i) q^{87} +(3.02505 + 0.810560i) q^{88} +(-3.79474 - 1.38117i) q^{89} +(6.21190 - 1.09533i) q^{91} +(-0.0123965 + 0.0265845i) q^{92} +(-1.23888 - 14.1604i) q^{93} +13.3541 q^{94} -1.87939 q^{96} +(0.733447 + 8.38333i) q^{97} +(-3.45089 + 7.40046i) q^{98} +(1.64106 - 0.289363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{6}+O(q^{10}) \) 48 * q - 48 * q^6	\( 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) \) 48 * q - 48 * q^6 - 12 * q^11 + 36 * q^21 - 72 * q^31 + 48 * q^36 + 96 * q^41 + 72 * q^46 - 48 * q^51 - 108 * q^61 + 24 * q^66 - 60 * q^71 - 48 * q^76 - 168 * q^81 - 48 * q^86 + 252 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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