LMFDB - Embedded newform 950.2.bb.b.307.4

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			307.4
Character	$\chi$	$=$	950.307
Dual form			950.2.bb.b.393.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 - 0.0871557i) q^{2} +(-1.70330 - 0.794263i) q^{3} +(0.984808 - 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(1.00792 - 3.76160i) q^{7} +(0.965926 - 0.258819i) q^{8} +(0.342020 + 0.407604i) q^{9} +O(q^{10})$	\(q+(0.996195 - 0.0871557i) q^{2} +(-1.70330 - 0.794263i) q^{3} +(0.984808 - 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(1.00792 - 3.76160i) q^{7} +(0.965926 - 0.258819i) q^{8} +(0.342020 + 0.407604i) q^{9} +(-1.56588 + 2.71219i) q^{11} +(-1.81535 - 0.486421i) q^{12} +(0.684531 + 1.46798i) q^{13} +(0.676236 - 3.83513i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-0.551728 - 6.30628i) q^{17} +(0.376244 + 0.376244i) q^{18} +(-2.70709 - 3.41638i) q^{19} +(-4.70448 + 5.60658i) q^{21} +(-1.32354 + 2.83834i) q^{22} +(0.0240279 + 0.0168245i) q^{23} +(-1.85083 - 0.326352i) q^{24} +(0.809869 + 1.40273i) q^{26} +(1.20044 + 4.48011i) q^{27} +(0.339410 - 3.87947i) q^{28} +(-0.496737 + 0.416812i) q^{29} +(-6.55008 + 3.78169i) q^{31} +(0.906308 - 0.422618i) q^{32} +(4.82136 - 3.37595i) q^{33} +(-1.09926 - 6.23420i) q^{34} +(0.407604 + 0.342020i) q^{36} +(4.88201 - 4.88201i) q^{37} +(-2.99455 - 3.16744i) q^{38} -3.04411i q^{39} +(-2.29280 - 6.29940i) q^{41} +(-4.19793 + 5.99527i) q^{42} +(-2.28848 - 3.26829i) q^{43} +(-1.07113 + 2.94289i) q^{44} +(0.0254029 + 0.0146663i) q^{46} +(-13.3033 - 1.16389i) q^{47} +(-1.87223 - 0.163799i) q^{48} +(-7.07153 - 4.08275i) q^{49} +(-4.06908 + 11.1797i) q^{51} +(0.929044 + 1.32681i) q^{52} +(0.168784 - 0.241049i) q^{53} +(1.58634 + 4.35844i) q^{54} -3.89429i q^{56} +(1.89749 + 7.96927i) q^{57} +(-0.458520 + 0.458520i) q^{58} +(5.17755 + 4.34448i) q^{59} +(-0.0829556 - 0.470464i) q^{61} +(-6.19556 + 4.33818i) q^{62} +(1.87797 - 0.875711i) q^{63} +(0.866025 - 0.500000i) q^{64} +(4.50878 - 3.78331i) q^{66} +(0.685803 - 7.83877i) q^{67} +(-1.63842 - 6.11467i) q^{68} +(-0.0275637 - 0.0477418i) q^{69} +(-5.21131 - 0.918895i) q^{71} +(0.435862 + 0.305194i) q^{72} +(2.70149 - 5.79337i) q^{73} +(4.43794 - 5.28893i) q^{74} +(-3.25921 - 2.89440i) q^{76} +(8.62387 + 8.62387i) q^{77} +(-0.265312 - 3.03253i) q^{78} +(11.2679 - 4.10117i) q^{79} +(1.79086 - 10.1565i) q^{81} +(-2.83310 - 6.07560i) q^{82} +(-12.7675 - 3.42105i) q^{83} +(-3.65944 + 6.33833i) q^{84} +(-2.56462 - 3.05640i) q^{86} +(1.17715 - 0.315417i) q^{87} +(-0.810560 + 3.02505i) q^{88} +(3.79474 + 1.38117i) q^{89} +(6.21190 - 1.09533i) q^{91} +(0.0265845 + 0.0123965i) q^{92} +(14.1604 - 1.23888i) q^{93} -13.3541 q^{94} -1.87939 q^{96} +(8.38333 - 0.733447i) q^{97} +(-7.40046 - 3.45089i) 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.996195	−	0.0871557i	0.704416	−	0.0616284i
$2$	0.996195	−	0.0871557i	0.704416	−	0.0616284i
$3$	−1.70330	−	0.794263i	−0.983402	−	0.458568i	−0.136687	−	0.990614i	$-0.543645\pi$
$3$	−1.70330	−	0.794263i	−0.983402	−	0.458568i	−0.846715	+	0.532047i	$0.821423\pi$
$4$	0.984808	−	0.173648i	0.492404	−	0.0868241i
$5$		0			0
$5$		0			0
$6$	−1.76604	−	0.642788i	−0.720985	−	0.262417i
$7$	1.00792	−	3.76160i	0.380957	−	1.42175i	−0.463486	−	0.886104i	$-0.653402\pi$
$7$	1.00792	−	3.76160i	0.380957	−	1.42175i	0.844443	−	0.535646i	$-0.179932\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$	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	$0.323182\pi$
$12$	−1.81535	−	0.486421i	−0.524045	−	0.140418i
$13$	0.684531	+	1.46798i	0.189855	+	0.407145i	0.978076	−	0.208247i	$-0.0667757\pi$
$13$	0.684531	+	1.46798i	0.189855	+	0.407145i	−0.788222	+	0.615392i	$0.788998\pi$
$14$	0.676236	−	3.83513i	0.180732	−	1.02498i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	−0.551728	−	6.30628i	−0.133814	−	1.52950i	−0.705313	−	0.708896i	$-0.749194\pi$
$17$	−0.551728	−	6.30628i	−0.133814	−	1.52950i	0.571500	−	0.820602i	$-0.306362\pi$
$18$	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
$22$	−1.32354	+	2.83834i	−0.282180	+	0.605136i
$23$	0.0240279	+	0.0168245i	0.00501017	+	0.00350816i	0.576079	−	0.817394i	$-0.304582\pi$
$23$	0.0240279	+	0.0168245i	0.00501017	+	0.00350816i	−0.571069	+	0.820902i	$0.693471\pi$
$24$	−1.85083	−	0.326352i	−0.377800	−	0.0666163i
$25$		0			0
$26$	0.809869	+	1.40273i	0.158828	+	0.275099i
$27$	1.20044	+	4.48011i	0.231025	+	0.862198i
$28$	0.339410	−	3.87947i	0.0641424	−	0.733151i
$29$	−0.496737	+	0.416812i	−0.0922418	+	0.0774001i	−0.687742	−	0.725955i	$-0.741398\pi$
$29$	−0.496737	+	0.416812i	−0.0922418	+	0.0774001i	0.595501	+	0.803355i	$0.296954\pi$
$30$		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	$0.571011\pi$
$32$	0.906308	−	0.422618i	0.160214	−	0.0747091i
$33$	4.82136	−	3.37595i	0.839290	−	0.587677i
$34$	−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	−0.180903	−	0.983501i	$-0.557902\pi$
$37$	4.88201	−	4.88201i	0.802598	−	0.802598i	0.983501	+	0.180903i	$0.0579021\pi$
$38$	−2.99455	−	3.16744i	−0.485780	−	0.513827i
$39$		−	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	$-0.286474\pi$
$42$	−4.19793	+	5.99527i	−0.647755	+	0.925090i
$43$	−2.28848	−	3.26829i	−0.348990	−	0.498409i	0.605830	−	0.795594i	$-0.292841\pi$
$43$	−2.28848	−	3.26829i	−0.348990	−	0.498409i	−0.954820	+	0.297185i	$0.903952\pi$
$44$	−1.07113	+	2.94289i	−0.161478	+	0.443658i
$45$		0			0
$46$	0.0254029	+	0.0146663i	0.00374545	+	0.00216244i
$47$	−13.3033	−	1.16389i	−1.94049	−	0.169771i	−0.950480	−	0.310787i	$-0.899407\pi$
$47$	−13.3033	−	1.16389i	−1.94049	−	0.169771i	−0.990007	+	0.141016i	$0.954963\pi$
$48$	−1.87223	−	0.163799i	−0.270234	−	0.0236424i
$49$	−7.07153	−	4.08275i	−1.01022	−	0.583250i
$50$		0			0
$51$	−4.06908	+	11.1797i	−0.569786	+	1.56547i
$52$	0.929044	+	1.32681i	0.128835	+	0.183996i
$53$	0.168784	−	0.241049i	0.0231843	−	0.0331106i	−0.807393	−	0.590015i	$-0.799122\pi$
$53$	0.168784	−	0.241049i	0.0231843	−	0.0331106i	0.830577	+	0.556904i	$0.188011\pi$
$54$	1.58634	+	4.35844i	0.215874	+	0.593109i
$55$		0			0
$56$		−	3.89429i		−	0.520396i
$57$	1.89749	+	7.96927i	0.251329	+	1.05556i
$58$	−0.458520	+	0.458520i	−0.0602066	+	0.0602066i
$59$	5.17755	+	4.34448i	0.674060	+	0.565603i	0.914264	−	0.405119i	$-0.132770\pi$
$59$	5.17755	+	4.34448i	0.674060	+	0.565603i	−0.240204	+	0.970722i	$0.577214\pi$
$60$		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	$0.954181\pi$
$62$	−6.19556	+	4.33818i	−0.786837	+	0.550949i
$63$	1.87797	−	0.875711i	0.236602	−	0.110329i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$		0			0
$66$	4.50878	−	3.78331i	0.554992	−	0.465694i
$67$	0.685803	−	7.83877i	0.0837842	−	0.957658i	−0.831679	−	0.555256i	$-0.812620\pi$
$67$	0.685803	−	7.83877i	0.0837842	−	0.957658i	0.915463	−	0.402401i	$-0.131824\pi$
$68$	−1.63842	−	6.11467i	−0.198688	−	0.741512i
$69$	−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	$0.657226\pi$
$72$	0.435862	+	0.305194i	0.0513668	+	0.0359674i
$73$	2.70149	−	5.79337i	0.316186	−	0.678063i	−0.682414	−	0.730966i	$-0.739070\pi$
$73$	2.70149	−	5.79337i	0.316186	−	0.678063i	0.998600	+	0.0529031i	$0.0168475\pi$
$74$	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
$78$	−0.265312	−	3.03253i	−0.0300407	−	0.343366i
$79$	11.2679	−	4.10117i	1.26773	−	0.461417i	0.381377	−	0.924420i	$-0.375450\pi$
$79$	11.2679	−	4.10117i	1.26773	−	0.461417i	0.886357	+	0.463003i	$0.153228\pi$
$80$		0			0
$81$	1.79086	−	10.1565i	0.198984	−	1.12850i
$82$	−2.83310	−	6.07560i	−0.312864	−	0.670938i
$83$	−12.7675	−	3.42105i	−1.40142	−	0.375509i	−0.522564	−	0.852600i	$-0.675025\pi$
$83$	−12.7675	−	3.42105i	−1.40142	−	0.375509i	−0.878854	+	0.477091i	$0.841691\pi$
$84$	−3.65944	+	6.33833i	−0.399277	+	0.691568i
$85$		0			0
$86$	−2.56462	−	3.05640i	−0.276550	−	0.329580i
$87$	1.17715	−	0.315417i	0.126204	−	0.0338162i
$88$	−0.810560	+	3.02505i	−0.0864060	+	0.322471i
$89$	3.79474	+	1.38117i	0.402241	+	0.146404i	0.535215	−	0.844716i	$-0.320230\pi$
$89$	3.79474	+	1.38117i	0.402241	+	0.146404i	−0.132974	+	0.991120i	$0.542453\pi$
$90$		0			0
$91$	6.21190	−	1.09533i	0.651185	−	0.114821i
$92$	0.0265845	+	0.0123965i	0.00277162	+	0.00129243i
$93$	14.1604	−	1.23888i	1.46837	−	0.128465i
$94$	−13.3541			−1.37737
$95$		0			0
$96$	−1.87939			−0.191814
$97$	8.38333	−	0.733447i	0.851199	−	0.0744702i	0.346798	−	0.937940i	$-0.387269\pi$
$97$	8.38333	−	0.733447i	0.851199	−	0.0744702i	0.504401	+	0.863470i	$0.331713\pi$
$98$	−7.40046	−	3.45089i	−0.747559	−	0.348592i
$99$	−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	$0.502812\pi$
$102$	−3.07922	+	11.4918i	−0.304888	+	1.13786i
$103$	13.2891	−	3.56081i	1.30941	−	0.350857i	0.464412	−	0.885619i	$-0.346266\pi$
$103$	13.2891	−	3.56081i	1.30941	−	0.350857i	0.845002	+	0.534763i	$0.179599\pi$
$104$	1.04115	+	1.24079i	0.102093	+	0.121670i
$105$		0			0
$106$	0.147133	−	0.254842i	0.0142909	−	0.0247525i
$107$	−1.57944	−	0.423208i	−0.152690	−	0.0409131i	0.181664	−	0.983361i	$-0.441852\pi$
$107$	−1.57944	−	0.423208i	−0.152690	−	0.0409131i	−0.334354	+	0.942447i	$0.608518\pi$
$108$	1.96017	+	4.20360i	0.188617	+	0.404491i
$109$	−1.42174	+	8.06307i	−0.136178	+	0.772302i	0.837855	+	0.545893i	$0.183810\pi$
$109$	−1.42174	+	8.06307i	−0.136178	+	0.772302i	−0.974032	+	0.226409i	$0.927302\pi$
$110$		0			0
$111$	−12.1931	+	4.43794i	−1.15732	+	0.421230i
$112$	−0.339410	−	3.87947i	−0.0320712	−	0.366576i
$113$	10.7410	+	10.7410i	1.01043	+	1.01043i	0.999945	+	0.0104800i	$0.00333596\pi$
$113$	10.7410	+	10.7410i	1.01043	+	1.01043i	0.0104800	+	0.999945i	$0.496664\pi$
$114$	2.58484	+	7.77356i	0.242092	+	0.728061i
$115$		0			0
$116$	−0.416812	+	0.496737i	−0.0387000	+	0.0461209i
$117$	−0.364231	+	0.781097i	−0.0336732	+	0.0722124i
$118$	5.53649	+	3.87670i	0.509676	+	0.356879i
$119$	−24.2778	−	4.28083i	−2.22554	−	0.392423i
$120$		0			0
$121$	0.596031	+	1.03236i	0.0541846	+	0.0938505i
$122$	−0.123644	−	0.461444i	−0.0111942	−	0.0417772i
$123$	−1.09806	+	12.5509i	−0.0990086	+	1.13167i
$124$	−5.79388	+	4.86165i	−0.520306	+	0.436589i
$125$		0			0
$126$	1.79450	−	1.03605i	0.159867	−	0.0922991i
$127$	5.43978	−	2.53661i	0.482702	−	0.225088i	−0.166006	−	0.986125i	$-0.553087\pi$
$127$	5.43978	−	2.53661i	0.482702	−	0.225088i	0.648709	+	0.761037i	$0.275309\pi$
$128$	0.819152	−	0.573576i	0.0724035	−	0.0506975i
$129$	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
$133$	−15.5796	+	6.73956i	−1.35092	+	0.584394i
$134$		−	7.86871i		−	0.679753i
$135$		0			0
$136$	−2.16511	−	5.94860i	−0.185657	−	0.510088i
$137$	−4.75319	+	6.78826i	−0.406093	+	0.579960i	−0.969154	−	0.246454i	$-0.920734\pi$
$137$	−4.75319	+	6.78826i	−0.406093	+	0.579960i	0.563062	+	0.826415i	$0.309623\pi$
$138$	−0.0316198	−	0.0451578i	−0.00269166	−	0.00384408i
$139$	0.759848	−	2.08767i	0.0644495	−	0.177074i	−0.903288	−	0.429035i	$-0.858854\pi$
$139$	0.759848	−	2.08767i	0.0644495	−	0.177074i	0.967737	+	0.251962i	$0.0810758\pi$
$140$		0			0
$141$	21.7351	+	12.5488i	1.83043	+	1.05680i
$142$	−5.27157	−	0.461202i	−0.442380	−	0.0387032i
$143$	−5.05333	−	0.442109i	−0.422581	−	0.0369711i
$144$	0.460802	+	0.266044i	0.0384002	+	0.0221704i
$145$		0			0
$146$	2.18629	−	6.00678i	0.180939	−	0.497125i
$147$	8.80217	+	12.5708i	0.725991	+	1.03682i
$148$	3.96009	−	5.65559i	0.325517	−	0.464887i
$149$	7.06188	+	19.4024i	0.578532	+	1.58950i	0.790656	+	0.612261i	$0.209740\pi$
$149$	7.06188	+	19.4024i	0.578532	+	1.58950i	−0.212124	+	0.977243i	$0.568038\pi$
$150$		0			0
$151$			8.61268i			0.700890i	0.936583	+	0.350445i	$0.113970\pi$
$151$			8.61268i			0.700890i	−0.936583	+	0.350445i	$0.886030\pi$
$152$	−3.49907	−	2.59932i	−0.283812	−	0.210833i
$153$	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
$157$	16.5057	−	11.5574i	1.31729	−	0.922380i	0.317629	−	0.948215i	$-0.397113\pi$
$157$	16.5057	−	11.5574i	1.31729	−	0.922380i	0.999666	+	0.0258354i	$0.00822458\pi$
$158$	10.8675	−	5.06762i	0.864575	−	0.403158i
$159$	−0.478947	+	0.276520i	−0.0379830	+	0.0219295i
$160$		0			0
$161$	0.0875053	−	0.0734257i	0.00689638	−	0.00578675i
$162$	0.898850	−	10.2739i	0.0706203	−	0.807194i
$163$	4.24265	+	15.8338i	0.332310	+	1.24020i	0.906756	+	0.421656i	$0.138551\pi$
$163$	4.24265	+	15.8338i	0.332310	+	1.24020i	−0.574446	+	0.818542i	$0.694782\pi$
$164$	−3.35184	−	5.80556i	−0.261735	−	0.453338i
$165$		0			0
$166$	−13.0171	−	2.29527i	−1.01032	−	0.178147i
$167$	−16.3681	−	11.4611i	−1.26660	−	0.886885i	−0.269504	−	0.962999i	$-0.586860\pi$
$167$	−16.3681	−	11.4611i	−1.26660	−	0.886885i	−0.997099	+	0.0761147i	$0.975748\pi$
$168$	−3.09309	+	6.63315i	−0.238637	+	0.511759i
$169$	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
$173$	−0.0351104	−	0.401314i	−0.00266939	−	0.0305113i	0.994743	−	0.102401i	$-0.0326525\pi$
$173$	−0.0351104	−	0.401314i	−0.00266939	−	0.0305113i	−0.997413	+	0.0718899i	$0.977097\pi$
$174$	1.14518	−	0.416812i	0.0868160	−	0.0315985i
$175$		0			0
$176$	−0.543825	+	3.08418i	−0.0409923	+	0.232479i
$177$	−5.36827	−	11.5123i	−0.403504	−	0.865317i
$178$	3.90067	+	1.04518i	0.292368	+	0.0783397i
$179$	8.88327	−	15.3863i	0.663966	−	1.15002i	−0.315598	−	0.948893i	$-0.602205\pi$
$179$	8.88327	−	15.3863i	0.663966	−	1.15002i	0.979564	−	0.201131i	$-0.0644616\pi$
$180$		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	$0.943839\pi$
$182$	6.09280	−	1.63256i	0.451629	−	0.121014i
$183$	−0.232374	+	0.867231i	−0.0171776	+	0.0641076i
$184$	0.0275637	+	0.0100324i	0.00203202	+	0.000739596i
$185$		0			0
$186$	13.9986	−	2.46832i	1.02642	−	0.180986i
$187$	17.9677	+	8.37850i	1.31393	+	0.612697i
$188$	−13.3033	+	1.16389i	−0.970243	+	0.0848853i
$189$	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	$0.397606\pi$
$192$	−1.87223	+	0.163799i	−0.135117	+	0.0118212i
$193$	−15.2767	−	7.12362i	−1.09964	−	0.512769i	−0.213853	−	0.976866i	$-0.568601\pi$
$193$	−15.2767	−	7.12362i	−1.09964	−	0.512769i	−0.885785	+	0.464097i	$0.846379\pi$
$194$	8.28751	−	1.46131i	0.595008	−	0.104916i
$195$		0			0
$196$	−7.67306	−	2.79277i	−0.548076	−	0.199483i
$197$	3.01010	−	11.2338i	0.214461	−	0.800378i	−0.771895	−	0.635750i	$-0.780691\pi$
$197$	3.01010	−	11.2338i	0.214461	−	0.800378i	0.986356	−	0.164628i	$-0.0526424\pi$
$198$	−1.60960	+	0.431290i	−0.114389	+	0.0306504i
$199$	−4.98476	−	5.94060i	−0.353360	−	0.421118i	0.559858	−	0.828588i	$-0.310856\pi$
$199$	−4.98476	−	5.94060i	−0.353360	−	0.421118i	−0.913219	+	0.407470i	$0.866411\pi$
$200$		0			0
$201$	−7.39417	+	12.8071i	−0.521544	+	0.903341i
$202$	6.47885	+	1.73600i	0.455850	+	0.122145i
$203$	1.06721	+	2.28864i	0.0749034	+	0.160631i
$204$	−2.06593	+	11.7165i	−0.144644	+	0.820316i
$205$		0			0
$206$	12.9282	−	4.70548i	0.900750	−	0.327846i
$207$	0.00136029	+	0.0155482i	9.45468e−5	+	0.00108068i
$208$	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	$-0.124503\pi$
$212$	0.124362	−	0.266696i	0.00854125	−	0.0183168i
$213$	8.14659	+	5.70430i	0.558195	+	0.390852i
$214$	−1.61031	−	0.283941i	−0.110079	−	0.0194098i
$215$		0			0
$216$	2.31908	+	4.01676i	0.157793	+	0.273306i
$217$	7.62326	+	28.4504i	0.517500	+	1.93134i
$218$	−0.713584	+	8.15630i	−0.0483300	+	0.552414i
$219$	−9.20292	+	7.72217i	−0.621876	+	0.521816i
$220$		0			0
$221$	8.87983	−	5.12677i	0.597322	−	0.344864i
$222$	−11.7599	+	5.48375i	−0.789276	+	0.368045i
$223$	−22.9748	+	16.0871i	−1.53851	+	1.07727i	−0.572122	+	0.820169i	$0.693880\pi$
$223$	−22.9748	+	16.0871i	−1.53851	+	1.07727i	−0.966384	+	0.257105i	$0.917232\pi$
$224$	−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	−0.328204	−	0.944607i	$-0.606443\pi$
$227$	9.28705	−	9.28705i	0.616403	−	0.616403i	0.944607	+	0.328204i	$0.106443\pi$
$228$	3.25251	+	7.51870i	0.215403	+	0.497938i
$229$			6.90731i			0.456448i	0.973609	+	0.228224i	$0.0732919\pi$
$229$			6.90731i			0.456448i	−0.973609	+	0.228224i	$0.926708\pi$
$230$		0			0
$231$	−7.83943	−	21.5387i	−0.515797	−	1.41714i
$232$	−0.371933	+	0.531175i	−0.0244186	+	0.0348733i
$233$	13.9812	+	19.9672i	0.915940	+	1.30810i	0.951154	+	0.308718i	$0.0998998\pi$
$233$	13.9812	+	19.9672i	0.915940	+	1.30810i	−0.0352142	+	0.999380i	$0.511211\pi$
$234$	−0.294768	+	0.809869i	−0.0192696	+	0.0529428i
$235$		0			0
$236$	5.85330	+	3.37941i	0.381018	+	0.219981i
$237$	−22.4500	−	1.96412i	−1.45828	−	0.127583i
$238$	−24.5585	−	2.14859i	−1.59189	−	0.139272i
$239$	9.82220	+	5.67085i	0.635345	+	0.366817i	0.782819	−	0.622249i	$-0.213781\pi$
$239$	9.82220	+	5.67085i	0.635345	+	0.366817i	−0.147474	+	0.989066i	$0.547114\pi$
$240$		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	$-0.221285\pi$
$242$	0.683738	+	0.976480i	0.0439524	+	0.0627705i
$243$	−3.13626	+	4.47905i	−0.201191	+	0.287331i
$244$	−0.163391	−	0.448912i	−0.0104600	−	0.0287386i
$245$		0			0
$246$			12.5988i			0.803271i
$247$	3.16209	−	6.31258i	0.201199	−	0.401660i
$248$	−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	$0.689022\pi$
$252$	1.69737	−	1.18851i	0.106924	−	0.0748693i
$253$	−0.0832562	+	0.0388230i	−0.00523427	+	0.00244078i
$254$	5.19800	−	3.00107i	0.326151	−	0.188304i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−0.550772	+	6.29536i	−0.0343562	+	0.392694i	0.959475	+	0.281793i	$0.0909291\pi$
$257$	−0.550772	+	6.29536i	−0.0343562	+	0.392694i	−0.993831	+	0.110901i	$0.964626\pi$
$258$	1.94074	+	7.24295i	0.120825	+	0.450926i
$259$	−13.4435	−	23.2848i	−0.835338	−	1.44685i
$260$		0			0
$261$	−0.339788	−	0.0599139i	−0.0210324	−	0.00370858i
$262$	16.2727	+	11.3943i	1.00533	+	0.703941i
$263$	5.17359	−	11.0948i	0.319017	−	0.684135i	−0.679767	−	0.733428i	$-0.737919\pi$
$263$	5.17359	−	11.0948i	0.319017	−	0.684135i	0.998784	+	0.0492932i	$0.0156969\pi$
$264$	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
$268$	−0.685803	−	7.83877i	−0.0418921	−	0.478829i
$269$	14.0112	−	5.09967i	0.854279	−	0.310932i	0.122495	−	0.992469i	$-0.460910\pi$
$269$	14.0112	−	5.09967i	0.854279	−	0.310932i	0.731784	+	0.681537i	$0.238688\pi$
$270$		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	$-0.267194\pi$
$272$	−2.67533	−	5.73726i	−0.162216	−	0.347873i
$273$	−11.4507	−	3.06821i	−0.693029	−	0.185697i
$274$	−4.14347	+	7.17670i	−0.250316	+	0.433560i
$275$		0			0
$276$	−0.0354352	−	0.0422301i	−0.00213295	−	0.00254195i
$277$	−21.7246	+	5.82108i	−1.30530	+	0.349755i	−0.843453	−	0.537203i	$-0.819481\pi$
$277$	−21.7246	+	5.82108i	−1.30530	+	0.349755i	−0.461850	+	0.886958i	$0.652814\pi$
$278$	0.575005	−	2.14595i	0.0344865	−	0.128705i
$279$	−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	$0.399859\pi$
$282$	22.7461	+	10.6067i	1.35451	+	0.631619i
$283$	−18.2106	+	1.59322i	−1.08251	+	0.0947071i	−0.614423	−	0.788977i	$-0.710611\pi$
$283$	−18.2106	+	1.59322i	−1.08251	+	0.0947071i	−0.468084	+	0.883684i	$0.655056\pi$
$284$	−5.29170			−0.314005
$285$		0			0
$286$	−5.07264			−0.299951
$287$	−26.0068	+	2.27530i	−1.53513	+	0.134306i
$288$	0.482236	+	0.224870i	0.0284160	+	0.0132506i
$289$	−22.7230	+	4.00669i	−1.33665	+	0.235687i
$290$		0			0
$291$	−14.8619	−	5.40929i	−0.871220	−	0.317098i
$292$	1.65444	−	6.17447i	0.0968190	−	0.361333i
$293$	25.3496	−	6.79240i	1.48094	−	0.396816i	0.574272	−	0.818665i	$-0.305285\pi$
$293$	25.3496	−	6.79240i	1.48094	−	0.396816i	0.906666	+	0.421848i	$0.138619\pi$
$294$	9.86430	+	11.7558i	0.575297	+	0.685613i
$295$		0			0
$296$	3.45210	−	5.97922i	0.200649	−	0.347535i
$297$	−14.0307	−	3.75950i	−0.814141	−	0.218148i
$298$	8.72604	+	18.7130i	0.505486	+	1.08402i
$299$	−0.00825025	+	0.0467895i	−0.000477124	+	0.00270591i
$300$		0			0
$301$	−14.6006	+	5.31417i	−0.841563	+	0.306304i
$302$	0.750645	+	8.57991i	0.0431947	+	0.493718i
$303$	−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
$307$	−1.46662	+	3.14518i	−0.0837046	+	0.179505i	−0.943705	−	0.330788i	$-0.892685\pi$
$307$	−1.46662	+	3.14518i	−0.0837046	+	0.179505i	0.860000	+	0.510293i	$0.170463\pi$
$308$	9.99037	+	6.99534i	0.569254	+	0.398596i
$309$	−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	$0.966235\pi$
$312$	−0.787874	−	2.94039i	−0.0446046	−	0.166467i
$313$	0.569406	−	6.50834i	0.0321847	−	0.367873i	−0.962974	−	0.269594i	$-0.913111\pi$
$313$	0.569406	−	6.50834i	0.0321847	−	0.367873i	0.995159	−	0.0982792i	$-0.0313338\pi$
$314$	15.4356	−	12.9520i	0.871079	−	0.730922i
$315$		0			0
$316$	10.3845	−	5.99550i	0.584175	−	0.337273i
$317$	−7.84916	+	3.66012i	−0.440853	+	0.205573i	−0.630355	−	0.776307i	$-0.717090\pi$
$317$	−7.84916	+	3.66012i	−0.440853	+	0.205573i	0.189502	+	0.981880i	$0.439313\pi$
$318$	−0.453024	+	0.317211i	−0.0254043	+	0.0177883i
$319$	−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
$323$	−20.0511	+	18.9566i	−1.11567	+	1.05477i
$324$		−	10.3131i		−	0.572953i
$325$		0			0
$326$	5.60651	+	15.4038i	0.310516	+	0.853136i
$327$	8.82584	−	12.6046i	0.488070	−	0.697036i
$328$	−3.84508	−	5.49134i	−0.212309	−	0.303208i
$329$	−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	$0.749653\pi$
$332$	−13.1676	−	1.15202i	−0.722667	−	0.0632252i
$333$	3.65967	+	0.320180i	0.200549	+	0.0175457i
$334$	−17.3047	−	9.99089i	−0.946873	−	0.546677i
$335$		0			0
$336$	−2.50320	+	6.87749i	−0.136561	+	0.375198i
$337$	7.90612	+	11.2911i	0.430674	+	0.615066i	0.974569	−	0.224087i	$-0.0719401\pi$
$337$	7.90612	+	11.2911i	0.430674	+	0.615066i	−0.543896	+	0.839153i	$0.683051\pi$
$338$	5.95169	−	8.49989i	0.323729	−	0.462333i
$339$	−9.76396	−	26.8263i	−0.530305	−	1.45700i
$340$		0			0
$341$		−	23.6867i		−	1.28271i
$342$	0.266865	−	2.30392i	0.0144304	−	0.124582i
$343$	−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
$347$	−15.5115	+	10.8612i	−0.832698	+	0.583062i	−0.910312	−	0.413922i	$-0.864159\pi$
$347$	−15.5115	+	10.8612i	−0.832698	+	0.583062i	0.0776140	+	0.996983i	$0.475270\pi$
$348$	1.10450	−	0.515035i	0.0592072	−	0.0276088i
$349$	−4.72687	+	2.72906i	−0.253024	+	0.146083i	−0.621148	−	0.783693i	$-0.713333\pi$
$349$	−4.72687	+	2.72906i	−0.253024	+	0.146083i	0.368124	+	0.929777i	$0.380000\pi$
$350$		0			0
$351$	−5.75499	+	4.82901i	−0.307178	+	0.257753i
$352$	−0.272951	+	3.11985i	−0.0145483	+	0.166288i
$353$	−4.42630	−	16.5192i	−0.235588	−	0.879226i	−0.977883	−	0.209153i	$-0.932929\pi$
$353$	−4.42630	−	16.5192i	−0.235588	−	0.879226i	0.742295	−	0.670073i	$-0.233737\pi$
$354$	−6.35121	−	11.0006i	−0.337563	−	0.584676i
$355$		0			0
$356$	3.97692	+	0.701239i	0.210776	+	0.0371656i
$357$	37.9523	+	26.5745i	2.00865	+	1.40647i
$358$	7.50846	−	16.1019i	0.396834	−	0.851014i
$359$	−2.08887	+	2.48942i	−0.110247	+	0.131387i	−0.818346	−	0.574726i	$-0.805109\pi$
$359$	−2.08887	+	2.48942i	−0.110247	+	0.131387i	0.708099	+	0.706113i	$0.249553\pi$
$360$		0			0
$361$	−4.34330	+	18.4969i	−0.228595	+	0.973522i
$362$	−9.48177	−	9.48177i	−0.498351	−	0.498351i
$363$	−0.195259	−	2.23182i	−0.0102484	−	0.117140i
$364$	5.92733	−	2.15737i	0.310677	−	0.113077i
$365$		0			0
$366$	−0.155905	+	0.884184i	−0.00814931	+	0.0462170i
$367$	−12.8977	−	27.6591i	−0.673252	−	1.44379i	−0.884585	−	0.466380i	$-0.845558\pi$
$367$	−12.8977	−	27.6591i	−0.673252	−	1.44379i	0.211333	−	0.977414i	$-0.432220\pi$
$368$	0.0283332	+	0.00759186i	0.00147697	+	0.000395753i
$369$	1.78348	−	3.08907i	0.0928442	−	0.160811i
$370$		0			0
$371$	−0.736609	−	0.877856i	−0.0382428	−	0.0455760i
$372$	13.7302	−	3.67898i	0.711875	−	0.190746i
$373$	6.40932	−	23.9199i	0.331862	−	1.23853i	−0.575370	−	0.817893i	$-0.695142\pi$
$373$	6.40932	−	23.9199i	0.331862	−	1.23853i	0.907231	−	0.420632i	$-0.138192\pi$
$374$	18.6296	+	6.78062i	0.963314	+	0.350618i
$375$		0			0
$376$	−13.1512	+	2.31892i	−0.678224	+	0.119589i
$377$	−0.951905	−	0.443881i	−0.0490256	−	0.0228610i
$378$	17.9936	−	1.57424i	0.925491	−	0.0809699i
$379$	2.41856			0.124233			0.0621165	−	0.998069i	$-0.480215\pi$
$379$	2.41856			0.124233			0.0621165	+	0.998069i	$0.480215\pi$
$380$		0			0
$381$	−11.2803			−0.577908
$382$	8.70563	−	0.761644i	0.445419	−	0.0389691i
$383$	−5.85531	−	2.73038i	−0.299192	−	0.139516i	0.267225	−	0.963634i	$-0.413893\pi$
$383$	−5.85531	−	2.73038i	−0.299192	−	0.139516i	−0.566418	+	0.824118i	$0.691671\pi$
$384$	−1.85083	+	0.326352i	−0.0944499	+	0.0166541i
$385$		0			0
$386$	−15.8394	−	5.76506i	−0.806203	−	0.293434i
$387$	0.549460	−	2.05061i	0.0279306	−	0.104239i
$388$	8.12861	−	2.17805i	0.412668	−	0.110574i
$389$	−1.44246	−	1.71905i	−0.0731354	−	0.0871594i	0.728236	−	0.685326i	$-0.240340\pi$
$389$	−1.44246	−	1.71905i	−0.0731354	−	0.0871594i	−0.801372	+	0.598167i	$0.795896\pi$
$390$		0			0
$391$	0.0928434	−	0.160810i	0.00469529	−	0.00813249i
$392$	−7.88727	−	2.11339i	−0.398367	−	0.106742i
$393$	−15.7783	−	33.8366i	−0.795909	−	1.70683i
$394$	2.01955	−	11.4534i	0.101743	−	0.577016i
$395$		0			0
$396$	−1.56588	+	0.569934i	−0.0786885	+	0.0286403i
$397$	−1.26359	−	14.4429i	−0.0634178	−	0.724869i	−0.959634	−	0.281251i	$-0.909251\pi$
$397$	−1.26359	−	14.4429i	−0.0634178	−	0.724869i	0.896216	−	0.443617i	$-0.146305\pi$
$398$	−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	$0.238879\pi$
$402$	−6.24982	+	13.4028i	−0.311713	+	0.668470i
$403$	−10.0352	−	7.02671i	−0.499888	−	0.350025i
$404$	6.60550	+	1.16473i	0.328636	+	0.0579474i
$405$		0			0
$406$	1.26262	+	2.18692i	0.0626626	+	0.108535i
$407$	5.59627	+	20.8856i	0.277397	+	1.03526i
$408$	−1.03691	+	11.8519i	−0.0513347	+	0.586758i
$409$	−27.6318	+	23.1858i	−1.36630	+	1.14646i	−0.392325	+	0.919827i	$0.628329\pi$
$409$	−27.6318	+	23.1858i	−1.36630	+	1.14646i	−0.973979	+	0.226638i	$0.927227\pi$
$410$		0			0
$411$	13.4878	−	7.78718i	0.665303	−	0.384113i
$412$	12.4689	−	5.81434i	0.614298	−	0.286452i
$413$	21.5607	−	15.0970i	1.06093	−	0.742874i
$414$	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
$418$	13.2798	−	3.16194i	0.649536	−	0.154655i
$419$		−	7.30395i		−	0.356821i	−0.983956	−	0.178411i	$-0.942904\pi$
$419$		−	7.30395i		−	0.356821i	0.983956	−	0.178411i	$-0.0570956\pi$
$420$		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	$0.772619\pi$
$422$	14.7685	−	21.0917i	0.718921	−	1.02673i
$423$	−4.07559	−	5.82055i	−0.198162	−	0.283005i
$424$	0.100645	−	0.276520i	0.00488776	−	0.0134290i
$425$		0			0
$426$	8.61275	+	4.97258i	0.417289	+	0.240922i
$427$	−1.85331	−	0.162144i	−0.0896879	−	0.00784668i
$428$	−1.62893	−	0.142513i	−0.0787373	−	0.00688862i
$429$	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	$0.869972\pi$
$432$	2.66034	+	3.79935i	0.127996	+	0.182797i
$433$	−10.4346	+	14.9022i	−0.501457	+	0.716155i	−0.987472	−	0.157796i	$-0.949561\pi$
$433$	−10.4346	+	14.9022i	−0.501457	+	0.716155i	0.486015	+	0.873951i	$0.338450\pi$
$434$	10.0739	+	27.6777i	0.483561	+	1.32857i
$435$		0			0
$436$			8.18746i			0.392108i
$437$	−0.00756683	−	0.127634i	−0.000361970	−	0.00610557i
$438$	−8.49487	+	8.49487i	−0.405900	+	0.405900i
$439$	28.4376	+	23.8620i	1.35725	+	1.13887i	0.976820	+	0.214062i	$0.0686693\pi$
$439$	28.4376	+	23.8620i	1.35725	+	1.13887i	0.380432	+	0.924809i	$0.375775\pi$
$440$		0			0
$441$	−0.754462	−	4.27877i	−0.0359267	−	0.203751i
$442$	8.39921	−	5.88119i	0.399510	−	0.279740i
$443$	17.2828	−	8.05911i	0.821132	−	0.382900i	0.0337992	−	0.999429i	$-0.489239\pi$
$443$	17.2828	−	8.05911i	0.821132	−	0.382900i	0.787332	+	0.616529i	$0.211462\pi$
$444$	−11.2373	+	6.48783i	−0.533296	+	0.307899i
$445$		0			0
$446$	−21.4853	+	18.0283i	−1.01736	+	0.853664i
$447$	3.38205	−	38.6571i	0.159966	−	1.82842i
$448$	−1.00792	−	3.76160i	−0.0476196	−	0.177719i
$449$	−5.70099	−	9.87440i	−0.269046	−	0.466002i	0.699570	−	0.714564i	$-0.253375\pi$
$449$	−5.70099	−	9.87440i	−0.269046	−	0.466002i	−0.968616	+	0.248563i	$0.920042\pi$
$450$		0			0
$451$	20.6754	+	3.64563i	0.973567	+	0.171666i
$452$	12.4429	+	8.71264i	0.585266	+	0.409808i
$453$	6.84073	−	14.6700i	0.321405	−	0.689256i
$454$	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	$-0.0750932\pi$
$457$	15.7889	+	15.7889i	0.738571	+	0.738571i	−0.233730	+	0.972302i	$0.575093\pi$
$458$	0.602012	+	6.88103i	0.0281302	+	0.321529i
$459$	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	$-0.00659344\pi$
$462$	−9.68682	−	20.7735i	−0.450672	−	0.966469i
$463$	22.4433	+	6.01367i	1.04303	+	0.279479i	0.739368	−	0.673301i	$-0.235124\pi$
$463$	22.4433	+	6.01367i	1.04303	+	0.279479i	0.303661	+	0.952780i	$0.401791\pi$
$464$	−0.324222	+	0.561570i	−0.0150516	+	0.0260702i
$465$		0			0
$466$	15.6683	+	18.6727i	0.725819	+	0.864997i
$467$	−35.1421	+	9.41628i	−1.62618	+	0.435734i	−0.952809	−	0.303571i	$-0.901821\pi$
$467$	−35.1421	+	9.41628i	−1.62618	+	0.435734i	−0.673371	+	0.739304i	$0.735154\pi$
$468$	−0.223062	+	0.832478i	−0.0103110	+	0.0384813i
$469$	−28.7950	−	10.4805i	−1.32963	−	0.483946i
$470$		0			0
$471$	−37.2937	+	6.57589i	−1.71840	+	0.303001i
$472$	6.12556	+	2.85640i	0.281952	+	0.131476i
$473$	12.4477	−	1.08903i	0.572345	−	0.0500737i
$474$	−22.5357			−1.03510
$475$		0			0
$476$	−24.6523			−1.12994
$477$	0.155980	−	0.0136465i	0.00714184	−	0.000624830i
$478$	10.2791	+	4.79321i	0.470154	+	0.219236i
$479$	−37.1809	+	6.55600i	−1.69884	+	0.299551i	−0.937289	−	0.348553i	$-0.886673\pi$
$479$	−37.1809	+	6.55600i	−1.69884	+	0.299551i	−0.761551	+	0.648105i	$0.775562\pi$
$480$		0			0
$481$	10.5086	+	3.82481i	0.479151	+	0.174397i
$482$	6.94743	−	25.9282i	0.316447	−	1.18100i
$483$	−0.207367	+	0.0555639i	−0.00943553	+	0.00252824i
$484$	0.766242	+	0.913172i	0.0348292	+	0.0415078i
$485$		0			0
$486$	−2.73396	+	4.73535i	−0.124015	+	0.214800i
$487$	−11.2798	−	3.02241i	−0.511137	−	0.136959i	−0.00597286	−	0.999982i	$-0.501901\pi$
$487$	−11.2798	−	3.02241i	−0.511137	−	0.136959i	−0.505164	+	0.863024i	$0.668568\pi$
$488$	−0.201894	−	0.432963i	−0.00913931	−	0.0195993i
$489$	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	$0.239490\pi$
$492$	1.09806	+	12.5509i	0.0495043	+	0.565837i
$493$	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
$497$	−8.70908	+	18.6767i	−0.390656	+	0.837763i
$498$	20.3490	+	14.2485i	0.911861	+	0.638492i
$499$	−33.7600	−	5.95279i	−1.51130	−	0.266484i	−0.644295	−	0.764777i	$-0.722849\pi$
$499$	−33.7600	−	5.95279i	−1.51130	−	0.266484i	−0.867008	+	0.498294i	$0.833960\pi$
$500$		0			0
$501$	18.7767	+	32.5222i	0.838882	+	1.45299i
$502$	5.89687	+	22.0074i	0.263190	+	0.982239i
$503$	−3.33314	+	38.0979i	−0.148617	+	1.69870i	0.446274	+	0.894896i	$0.352751\pi$
$503$	−3.33314	+	38.0979i	−0.148617	+	1.69870i	−0.594892	+	0.803806i	$0.702805\pi$
$504$	1.58733	−	1.33193i	0.0707052	−	0.0593287i
$505$		0			0
$506$	−0.0795557	+	0.0459315i	−0.00353668	+	0.00204191i
$507$	−17.6742	+	8.24162i	−0.784940	+	0.366023i
$508$	4.91666	−	3.44268i	0.218141	−	0.152744i
$509$	−2.71535	−	15.3995i	−0.120356	−	0.682570i	−0.983958	−	0.178398i	$-0.942909\pi$
$509$	−2.71535	−	15.3995i	−0.120356	−	0.682570i	0.863603	−	0.504173i	$-0.168202\pi$
$510$		0			0
$511$	−19.0694	−	16.0012i	−0.843583	−	0.707850i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	12.0561	−	16.2293i	0.532288	−	0.716539i
$514$			6.31941i			0.278737i
$515$		0			0
$516$	2.56462	+	7.04624i	0.112901	+	0.310193i
$517$	23.9881	−	34.2585i	1.05499	−	1.50669i
$518$	−15.4217	−	22.0245i	−0.677592	−	0.967702i
$519$	−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	$0.694533\pi$
$522$	−0.343717	−	0.0300714i	−0.0150441	−	0.00131619i
$523$	33.2076	+	2.90529i	1.45207	+	0.127039i	0.785710	−	0.618595i	$-0.212298\pi$
$523$	33.2076	+	2.90529i	1.45207	+	0.127039i	0.666356	+	0.745634i	$0.267853\pi$
$524$	17.2039	+	9.93266i	0.751555	+	0.433910i
$525$		0			0
$526$	4.18693	−	11.5035i	0.182559	−	0.501576i
$527$	27.4623	+	39.2202i	1.19627	+	1.70846i
$528$	3.37595	−	4.82136i	0.146919	−	0.209823i
$529$	−7.86617	−	21.6121i	−0.342007	−	0.939657i
$530$		0			0
$531$			3.59629i			0.156066i
$532$	−14.1726	+	9.34254i	−0.614458	+	0.405050i
$533$	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
$537$	−27.3516	+	19.1518i	−1.18031	+	0.826461i
$538$	13.5134	−	6.30142i	0.582606	−	0.271673i
$539$	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	$0.505872\pi$
$542$	2.43602	−	27.8438i	0.104636	−	1.19599i
$543$	6.52254	+	24.3424i	0.279909	+	1.04463i
$544$	−3.16518	−	5.48226i	−0.135706	−	0.235050i
$545$		0			0
$546$	−11.6746	−	2.05854i	−0.499625	−	0.0880974i
$547$	22.0696	+	15.4533i	0.943628	+	0.660735i	0.940693	−	0.339260i	$-0.110177\pi$
$547$	22.0696	+	15.4533i	0.943628	+	0.660735i	0.00293537	+	0.999996i	$0.499066\pi$
$548$	−3.50221	+	7.51052i	−0.149607	+	0.320833i
$549$	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
$553$	−4.06987	−	46.5188i	−0.173068	−	1.97818i
$554$	−21.1346	+	7.69236i	−0.897922	+	0.326817i
$555$		0			0
$556$	0.385785	−	2.18790i	0.0163609	−	0.0927875i
$557$	1.07869	+	2.31325i	0.0457054	+	0.0980156i	0.927835	−	0.372992i	$-0.121668\pi$
$557$	1.07869	+	2.31325i	0.0457054	+	0.0980156i	−0.882129	+	0.471008i	$0.843890\pi$
$558$	−3.88726	−	1.04159i	−0.164561	−	0.0440940i
$559$	3.23125	−	5.59669i	0.136667	−	0.236715i
$560$		0			0
$561$	−23.9498	−	28.5422i	−1.01116	−	1.20505i
$562$	4.52118	−	1.21145i	0.190714	−	0.0511017i
$563$	8.99598	−	33.5735i	0.379136	−	1.41495i	−0.468072	−	0.883690i	$-0.655051\pi$
$563$	8.99598	−	33.5735i	0.379136	−	1.41495i	0.847207	−	0.531263i	$-0.178282\pi$
$564$	23.5840	+	8.58387i	0.993065	+	0.361446i
$565$		0			0
$566$	−18.0024	+	3.17432i	−0.756699	+	0.133426i
$567$	−36.3995	−	16.9734i	−1.52864	−	0.712814i
$568$	−5.27157	+	0.461202i	−0.221190	+	0.0193516i
$569$	8.01662			0.336074			0.168037	−	0.985781i	$-0.446257\pi$
$569$	8.01662			0.336074			0.168037	+	0.985781i	$0.446257\pi$
$570$		0			0
$571$	−3.98332			−0.166697			−0.0833484	−	0.996520i	$-0.526561\pi$
$571$	−3.98332			−0.166697			−0.0833484	+	0.996520i	$0.526561\pi$
$572$	−5.05333	+	0.442109i	−0.211291	+	0.0184855i
$573$	−14.8849	−	6.94097i	−0.621828	−	0.289963i
$574$	−25.7095	+	4.53328i	−1.07309	+	0.189215i
$575$		0			0
$576$	0.500000	+	0.181985i	0.0208333	+	0.00758271i
$577$	11.5140	−	42.9708i	0.479334	−	1.78890i	−0.124986	−	0.992158i	$-0.539889\pi$
$577$	11.5140	−	42.9708i	0.479334	−	1.78890i	0.604320	−	0.796741i	$-0.293445\pi$
$578$	−22.2874	+	5.97188i	−0.927032	+	0.248398i
$579$	20.3627	+	24.2673i	0.846246	+	1.00852i
$580$		0			0
$581$	−25.7372	+	44.5782i	−1.06776	+	1.84941i
$582$	−15.2768	−	4.09340i	−0.633243	−	0.169677i
$583$	0.389474	+	0.835229i	0.0161304	+	0.0345917i
$584$	1.11001	−	6.29517i	0.0459325	−	0.260496i
$585$		0			0
$586$	24.6611	−	8.97591i	1.01874	−	0.370792i
$587$	3.01529	+	34.4649i	0.124454	+	1.42252i	0.759732	+	0.650237i	$0.225330\pi$
$587$	3.01529	+	34.4649i	0.124454	+	1.42252i	−0.635277	+	0.772284i	$0.719114\pi$
$588$	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
$592$	2.91784	−	6.25734i	0.119923	−	0.257175i
$593$	−7.41648	−	5.19308i	−0.304559	−	0.213254i	0.411299	−	0.911500i	$-0.365075\pi$
$593$	−7.41648	−	5.19308i	−0.304559	−	0.213254i	−0.715858	+	0.698246i	$0.753964\pi$
$594$	−14.3049	−	2.52234i	−0.586938	−	0.103493i
$595$		0			0
$596$	10.3238	+	17.8813i	0.422879	+	0.732447i
$597$	3.77215	+	14.0778i	0.154384	+	0.576168i
$598$	−0.00414088	+	0.0473305i	−0.000169333	+	0.00193549i
$599$	−4.22725	+	3.54709i	−0.172721	+	0.144930i	−0.725050	−	0.688696i	$-0.758184\pi$
$599$	−4.22725	+	3.54709i	−0.172721	+	0.144930i	0.552329	+	0.833626i	$0.313739\pi$
$600$		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	$0.103792\pi$
$602$	−14.0819	+	6.56648i	−0.573933	+	0.267630i
$603$	3.42967	−	2.40148i	0.139667	−	0.0977958i
$604$	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	−0.885657	−	0.464340i	$-0.846292\pi$
$607$	−10.3802	+	10.3802i	−0.421318	+	0.421318i	0.464340	+	0.885657i	$0.346292\pi$
$608$	−3.89728	−	1.95222i	−0.158056	−	0.0791732i
$609$		−	4.74588i		−	0.192313i
$610$		0			0
$611$	−7.39796	−	20.3257i	−0.299289	−	0.822291i
$612$	1.93199	−	2.75917i	0.0780960	−	0.111533i
$613$	−13.8031	−	19.7129i	−0.557502	−	0.796195i	0.437160	−	0.899384i	$-0.355984\pi$
$613$	−13.8031	−	19.7129i	−0.557502	−	0.796195i	−0.994662	+	0.103189i	$0.967095\pi$
$614$	−1.18692	+	3.26104i	−0.0479003	+	0.131605i
$615$		0			0
$616$	10.5620	+	6.09800i	0.425557	+	0.245695i
$617$	−18.8394	−	1.64823i	−0.758445	−	0.0663553i	−0.298629	−	0.954369i	$-0.596529\pi$
$617$	−18.8394	−	1.64823i	−0.758445	−	0.0663553i	−0.459816	+	0.888014i	$0.652085\pi$
$618$	−25.7580	−	2.25353i	−1.03614	−	0.0906504i
$619$	−14.9536	−	8.63346i	−0.601035	−	0.347008i	0.168413	−	0.985716i	$-0.446136\pi$
$619$	−14.9536	−	8.63346i	−0.601035	−	0.347008i	−0.769449	+	0.638709i	$0.779469\pi$
$620$		0			0
$621$	−0.0465317	+	0.127845i	−0.00186725	+	0.00513024i
$622$	−8.20331	−	11.7155i	−0.328923	−	0.469750i
$623$	9.02018	−	12.8822i	0.361386	−	0.516113i
$624$	−1.04115	−	2.86053i	−0.0416793	−	0.114513i
$625$		0			0
$626$		−	6.53320i		−	0.261119i
$627$	−24.5854	−	7.33257i	−0.981846	−	0.292835i
$628$	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	$0.860744\pi$
$632$	9.82246	−	6.87776i	0.390716	−	0.273583i
$633$	−43.8569	+	20.4508i	−1.74316	+	0.812847i
$634$	−7.50029	+	4.33030i	−0.297875	+	0.171978i
$635$		0			0
$636$	−0.423654	+	0.355488i	−0.0167990	+	0.0140960i
$637$	1.15272	−	13.1756i	0.0456724	−	0.522038i
$638$	−0.525603	−	1.96158i	−0.0208088	−	0.0776596i
$639$	−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	$0.606673\pi$
$642$	2.51732	+	1.76265i	0.0993507	+	0.0695661i
$643$	−0.168288	+	0.360894i	−0.00663662	+	0.0142323i	−0.909598	−	0.415489i	$-0.863610\pi$
$643$	−0.168288	+	0.360894i	−0.00663662	+	0.0142323i	0.902962	+	0.429721i	$0.141388\pi$
$644$	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	$-0.112571\pi$
$647$	15.0528	+	15.0528i	0.591787	+	0.591787i	−0.346327	+	0.938114i	$0.612571\pi$
$648$	−0.898850	−	10.2739i	−0.0353102	−	0.403597i
$649$	−19.8905	+	7.23954i	−0.780769	+	0.284177i
$650$		0			0
$651$	9.61237	−	54.5144i	0.376738	−	2.13659i
$652$	6.92770	+	14.8565i	0.271310	+	0.581826i
$653$	7.66830	+	2.05471i	0.300084	+	0.0804072i	0.405719	−	0.913998i	$-0.367021\pi$
$653$	7.66830	+	2.05471i	0.300084	+	0.0804072i	−0.105636	+	0.994405i	$0.533688\pi$
$654$	7.69369	−	13.3259i	0.300847	−	0.521083i
$655$		0			0
$656$	−4.30905	−	5.13532i	−0.168240	−	0.200501i
$657$	3.28537	−	0.880311i	0.128174	−	0.0343442i
$658$	−13.4598	+	50.2328i	−0.524719	+	1.95828i
$659$	17.9446	+	6.53131i	0.699024	+	0.254424i	0.666994	−	0.745063i	$-0.267581\pi$
$659$	17.9446	+	6.53131i	0.699024	+	0.254424i	0.0320298	+	0.999487i	$0.489803\pi$
$660$		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	$0.0980050\pi$
$662$	−8.50047	−	3.96383i	−0.330380	−	0.154059i
$663$	−19.1970	+	1.67952i	−0.745551	+	0.0652273i
$664$	−13.2179			−0.512955
$665$		0			0
$666$	3.67365			0.142351
$667$	−0.0189483	+	0.00165776i	−0.000733679	+	6.41886e-5i
$668$	−18.1096	−	8.44466i	−0.700683	−	0.326734i
$669$	51.9104	−	9.15320i	2.00697	−	0.353883i
$670$		0			0
$671$	1.40589	+	0.511701i	0.0542736	+	0.0197540i
$672$	−1.89426	+	7.06949i	−0.0730728	+	0.272711i
$673$	0.775055	−	0.207675i	0.0298762	−	0.00800530i	−0.243850	−	0.969813i	$-0.578410\pi$
$673$	0.775055	−	0.207675i	0.0298762	−	0.00800530i	0.273726	+	0.961808i	$0.411744\pi$
$674$	8.86011	+	10.5591i	0.341279	+	0.406720i
$675$		0			0
$676$	5.18822	−	8.98627i	0.199547	−	0.345626i
$677$	41.8561	+	11.2153i	1.60866	+	0.431040i	0.947644	−	0.319330i	$-0.103458\pi$
$677$	41.8561	+	11.2153i	1.60866	+	0.431040i	0.661019	+	0.750370i	$0.270124\pi$
$678$	−12.0649	−	25.8732i	−0.463348	−	0.993654i
$679$	5.69077	−	32.2740i	0.218392	−	1.23856i
$680$		0			0
$681$	−23.1950	+	8.44229i	−0.888834	+	0.323509i
$682$	−2.06443	−	23.5966i	−0.0790512	−	0.903560i
$683$	−6.91468	−	6.91468i	−0.264583	−	0.264583i	0.562330	−	0.826913i	$-0.309905\pi$
$683$	−6.91468	−	6.91468i	−0.264583	−	0.264583i	−0.826913	+	0.562330i	$0.809905\pi$
$684$	0.0650496	−	2.31841i	0.00248723	−	0.0886466i
$685$		0			0
$686$	−2.91748	+	3.47692i	−0.111390	+	0.132749i
$687$	5.48622	−	11.7652i	0.209312	−	0.448872i
$688$	−3.26829	−	2.28848i	−0.124602	−	0.0872475i
$689$	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	$0.901857\pi$
$692$	−0.104264	−	0.389120i	−0.00396354	−	0.0147921i
$693$	−0.565584	+	6.46466i	−0.0214848	+	0.245572i
$694$	−14.5058	+	12.1718i	−0.550633	+	0.462036i
$695$		0			0
$696$	1.05541	−	0.609339i	0.0400050	−	0.0230969i
$697$	−38.4608	+	17.9346i	−1.45681	+	0.679320i
$698$	−4.47103	+	3.13065i	−0.169231	+	0.118497i
$699$	−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
$703$	−29.8949	−	3.46275i	−1.12751	−	0.130600i
$704$			3.13176i			0.118033i
$705$		0			0
$706$	−5.84919	−	16.0705i	−0.220137	−	0.604822i
$707$	14.9821	−	21.3967i	0.563461	−	0.804706i
$708$	−7.28580	−	10.4052i	−0.273817	−	0.391052i
$709$	−8.82228	+	24.2390i	−0.331328	+	0.910315i	0.656439	+	0.754379i	$0.272062\pi$
$709$	−8.82228	+	24.2390i	−0.331328	+	0.910315i	−0.987767	+	0.155937i	$0.950160\pi$
$710$		0			0
$711$	5.52549	+	3.19014i	0.207222	+	0.119640i
$712$	4.02291	+	0.351959i	0.150765	+	0.0131902i
$713$	−0.221010	−	0.0193359i	−0.00827689	−	0.000724134i
$714$	40.1240	+	23.1656i	1.50160	+	0.866950i
$715$		0			0
$716$	6.07651	−	16.6951i	0.227090	−	0.623924i
$717$	−12.2260	−	17.4606i	−0.456589	−	0.652077i
$718$	−1.86396	+	2.66201i	−0.0695623	+	0.0993452i
$719$	1.77083	+	4.86532i	0.0660408	+	0.181446i	0.968323	−	0.249700i	$-0.0803319\pi$
$719$	1.77083	+	4.86532i	0.0660408	+	0.181446i	−0.902283	+	0.431145i	$0.858110\pi$
$720$		0			0
$721$		−	53.5772i		−	1.99532i
$722$	−2.71466	+	18.8051i	−0.101029	+	0.699852i
$723$	−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
$727$	36.8172	−	25.7797i	1.36548	−	0.956117i	0.365799	−	0.930694i	$-0.380796\pi$
$727$	36.8172	−	25.7797i	1.36548	−	0.956117i	0.999677	−	0.0254229i	$-0.00809324\pi$
$728$	5.71675	−	2.66576i	0.211877	−	0.0987998i
$729$	−17.8948	+	10.3316i	−0.662770	+	0.382651i
$730$		0			0
$731$	−19.3481	+	16.2350i	−0.715616	+	0.600473i
$732$	−0.0782505	+	0.894407i	−0.00289222	+	0.0330582i
$733$	8.31879	+	31.0462i	0.307262	+	1.14672i	0.930981	+	0.365068i	$0.118954\pi$
$733$	8.31879	+	31.0462i	0.307262	+	1.14672i	−0.623719	+	0.781648i	$0.714379\pi$
$734$	−15.2592	−	26.4298i	−0.563228	−	0.975540i
$735$		0			0
$736$	0.0288871	+	0.00509357i	0.00106479	+	0.000187751i
$737$	20.1863	+	14.1346i	0.743572	+	0.520655i
$738$	1.50746	−	3.23276i	0.0554904	−	0.119000i
$739$	32.1725	−	38.3417i	1.18349	−	1.41042i	0.292575	−	0.956243i	$-0.405488\pi$
$739$	32.1725	−	38.3417i	1.18349	−	1.41042i	0.890910	−	0.454180i	$-0.150068\pi$
$740$		0			0
$741$	−10.3998	+	8.24070i	−0.382048	+	0.302730i
$742$	−0.810316	−	0.810316i	−0.0297476	−	0.0297476i
$743$	3.47931	+	39.7687i	0.127643	+	1.45897i	0.742242	+	0.670131i	$0.233762\pi$
$743$	3.47931	+	39.7687i	0.127643	+	1.45897i	−0.614599	+	0.788840i	$0.710682\pi$
$744$	13.3573	−	4.86165i	0.489701	−	0.178237i
$745$		0			0
$746$	4.30017	−	24.3875i	0.157440	−	0.892889i
$747$	−2.97232	−	6.37416i	−0.108751	−	0.233218i
$748$	19.1497	+	5.13114i	0.700182	+	0.187613i
$749$	−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	$0.771191\pi$
$752$	−12.8991	+	3.45630i	−0.470382	+	0.126038i
$753$	11.0825	−	41.3604i	0.403868	−	1.50726i
$754$	−0.986970	−	0.359228i	−0.0359433	−	0.0130823i
$755$		0			0
$756$	17.7879	−	3.13649i	0.646940	−	0.114073i
$757$	0.380410	+	0.177388i	0.0138262	+	0.00644727i	0.429519	−	0.903058i	$-0.358683\pi$
$757$	0.380410	+	0.177388i	0.0138262	+	0.00644727i	−0.415693	+	0.909505i	$0.636461\pi$
$758$	2.40935	−	0.210791i	0.0875117	−	0.00765628i
$759$	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	$0.536996\pi$
$762$	−11.2374	+	0.983144i	−0.407088	+	0.0356156i
$763$	28.8970	+	13.4749i	1.04614	+	0.487824i
$764$	8.60612	−	1.51749i	0.311358	−	0.0549009i
$765$		0			0
$766$	−6.07100	−	2.20966i	−0.219354	−	0.0798383i
$767$	−2.83342	+	10.5745i	−0.102309	+	0.381822i
$768$	−1.81535	+	0.486421i	−0.0655057	+	0.0175522i
$769$	12.6226	+	15.0430i	0.455183	+	0.542466i	0.944011	−	0.329915i	$-0.107020\pi$
$769$	12.6226	+	15.0430i	0.455183	+	0.542466i	−0.488828	+	0.872380i	$0.662575\pi$
$770$		0			0
$771$	5.93830	−	10.2854i	0.213863	−	0.370421i
$772$	−16.2816	−	4.36263i	−0.585986	−	0.157015i
$773$	6.20181	+	13.2998i	0.223063	+	0.478361i	0.985709	−	0.168455i	$-0.0538778\pi$
$773$	6.20181	+	13.2998i	0.223063	+	0.478361i	−0.762646	+	0.646816i	$0.776100\pi$
$774$	0.368647	−	2.09070i	0.0132507	−	0.0751486i
$775$		0			0
$776$	7.90785	−	2.87822i	0.283875	−	0.103322i
$777$	4.40407	+	50.3387i	0.157995	+	1.80589i
$778$	−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
$782$	0.0784746	−	0.168289i	0.00280625	−	0.00601802i
$783$	−2.46367	−	1.72508i	−0.0880444	−	0.0616494i
$784$	−8.04145	−	1.41792i	−0.287195	−	0.0506402i
$785$		0			0
$786$	−18.6673	−	32.3327i	−0.665840	−	1.15327i
$787$	−6.36949	−	23.7713i	−0.227048	−	0.847354i	−0.981574	−	0.191084i	$-0.938800\pi$
$787$	−6.36949	−	23.7713i	−0.227048	−	0.847354i	0.754526	−	0.656270i	$-0.227867\pi$
$788$	1.01363	−	11.5859i	0.0361092	−	0.412730i
$789$	−17.6244	+	14.7886i	−0.627444	+	0.526488i
$790$		0			0
$791$	51.2292	−	29.5772i	1.82150	−	1.05164i
$792$	−1.51025	+	0.704241i	−0.0536644	+	0.0250241i
$793$	0.633847	−	0.443825i	0.0225086	−	0.0157607i
$794$	−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	−0.146506	−	0.989210i	$-0.546803\pi$
$797$	23.7905	−	23.7905i	0.842704	−	0.842704i	0.989210	+	0.146506i	$0.0468027\pi$
$798$	31.8463	−	1.88802i	1.12735	−	0.0668351i
$799$			84.5365i			2.99069i
$800$		0			0
$801$	0.734906	+	2.01914i	0.0259666	+	0.0713427i
$802$	−1.20151	+	1.71593i	−0.0424267	+	0.0605916i
$803$	11.4825	+	16.3987i	0.405208	+	0.578697i
$804$	−5.05791	+	13.8965i	−0.178379	+	0.490091i
$805$		0			0
$806$	−10.6094	−	6.12535i	−0.373701	−	0.215756i
$807$	−27.9158	−	2.44232i	−0.982683	−	0.0859736i
$808$	6.68188	+	0.584588i	0.235068	+	0.0205657i
$809$	4.89923	+	2.82857i	0.172248	+	0.0994472i	0.583645	−	0.812009i	$-0.301626\pi$
$809$	4.89923	+	2.82857i	0.172248	+	0.0994472i	−0.411398	+	0.911456i	$0.634959\pi$
$810$		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	$0.883277\pi$
$812$	1.44841	+	2.06855i	0.0508294	+	0.0725918i
$813$	−30.1294	+	43.0293i	−1.05669	+	1.50910i
$814$	7.39527	+	20.3183i	0.259204	+	0.712158i
$815$		0			0
$816$			11.8972i			0.416485i
$817$	−4.97058	+	16.6659i	−0.173899	+	0.583065i
$818$	−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	$0.605978\pi$
$822$	12.7578	−	8.93308i	0.444978	−	0.311577i
$823$	−43.5776	+	20.3206i	−1.51902	+	0.708331i	−0.990103	−	0.140342i	$-0.955180\pi$
$823$	−43.5776	+	20.3206i	−1.51902	+	0.708331i	−0.528918	+	0.848673i	$0.677402\pi$
$824$	11.9147	−	6.87895i	0.415068	−	0.239639i
$825$		0			0
$826$	20.1629	−	16.9187i	0.701557	−	0.588676i
$827$	2.47030	−	28.2356i	0.0859007	−	0.981849i	−0.823881	−	0.566762i	$-0.808196\pi$
$827$	2.47030	−	28.2356i	0.0859007	−	0.981849i	0.909782	−	0.415087i	$-0.136249\pi$
$828$	0.00403954	+	0.0150758i	0.000140384	+	0.000523920i
$829$	−5.95974	−	10.3226i	−0.206990	−	0.358518i	0.743775	−	0.668430i	$-0.233034\pi$
$829$	−5.95974	−	10.3226i	−0.206990	−	0.358518i	−0.950765	+	0.309913i	$0.899700\pi$
$830$		0			0
$831$	41.6270	+	7.33996i	1.44402	+	0.254620i
$832$	1.32681	+	0.929044i	0.0459989	+	0.0322088i
$833$	−21.8454	+	46.8476i	−0.756898	+	1.62317i
$834$	−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
$838$	−0.636581	−	7.27616i	−0.0219903	−	0.251351i
$839$	−14.8033	+	5.38796i	−0.511066	+	0.186013i	−0.584665	−	0.811275i	$-0.698774\pi$
$839$	−14.8033	+	5.38796i	−0.511066	+	0.186013i	0.0735985	+	0.997288i	$0.476552\pi$
$840$		0			0
$841$	−4.96278	+	28.1453i	−0.171130	+	0.970529i
$842$	6.19491	+	13.2850i	0.213491	+	0.457833i
$843$	−8.49703	−	2.27677i	−0.292653	−	0.0784162i
$844$	12.8741	−	22.2986i	0.443144	−	0.767548i
$845$		0			0
$846$	−4.56738	−	5.44319i	−0.157030	−	0.187141i
$847$	4.48405	−	1.20150i	0.154074	−	0.0412840i
$848$	0.0761618	−	0.284240i	0.00261541	−	0.00976083i
$849$	32.2836	+	11.7503i	1.10797	+	0.403268i
$850$		0			0
$851$	0.199442	−	0.0351671i	0.00683679	−	0.00120551i
$852$	9.01337	+	4.20300i	0.308793	+	0.143992i
$853$	9.58289	−	0.838394i	0.328112	−	0.0287061i	0.0780902	−	0.996946i	$-0.475118\pi$
$853$	9.58289	−	0.838394i	0.328112	−	0.0287061i	0.250022	+	0.968240i	$0.419562\pi$
$854$	−1.86039			−0.0636612
$855$		0			0
$856$	−1.63515			−0.0558883
$857$	−27.1477	+	2.37512i	−0.927348	+	0.0811324i	−0.540813	−	0.841143i	$-0.681883\pi$
$857$	−27.1477	+	2.37512i	−0.927348	+	0.0811324i	−0.386534	+	0.922275i	$0.626328\pi$
$858$	8.64023	+	4.02901i	0.294973	+	0.137548i
$859$	24.3714	−	4.29734i	0.831542	−	0.146623i	0.258357	−	0.966049i	$-0.416819\pi$
$859$	24.3714	−	4.29734i	0.831542	−	0.146623i	0.573185	+	0.819426i	$0.305708\pi$
$860$		0			0
$861$	46.1045	+	16.7807i	1.57124	+	0.571884i
$862$	−7.38443	+	27.5591i	−0.251515	+	0.938666i
$863$	30.5143	−	8.17628i	1.03872	−	0.278324i	0.301136	−	0.953581i	$-0.402634\pi$
$863$	30.5143	−	8.17628i	1.03872	−	0.278324i	0.737582	+	0.675257i	$0.235967\pi$
$864$	2.98135	+	3.55303i	0.101428	+	0.120877i
$865$		0			0
$866$	−9.09612	+	15.7549i	−0.309099	+	0.535375i
$867$	41.8866	+	11.2235i	1.42254	+	0.381169i
$868$	12.4478	+	26.6944i	0.422506	+	0.906067i
$869$	−6.52101	+	36.9825i	−0.221210	+	1.25454i
$870$		0			0
$871$	11.9766	−	4.35913i	0.405812	−	0.147704i
$872$	0.713584	+	8.15630i	0.0241650	+	0.276207i
$873$	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
$877$	0.722132	−	1.54862i	0.0243847	−	0.0522931i	−0.893738	−	0.448589i	$-0.851927\pi$
$877$	0.722132	−	1.54862i	0.0243847	−	0.0522931i	0.918123	+	0.396296i	$0.129705\pi$
$878$	30.4091	+	21.2927i	1.02626	+	0.718593i
$879$	−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	$-0.408264\pi$
$882$	−1.12451	−	4.19673i	−0.0378642	−	0.141311i
$883$	2.21101	−	25.2720i	0.0744064	−	0.850469i	−0.863674	−	0.504051i	$-0.831842\pi$
$883$	2.21101	−	25.2720i	0.0744064	−	0.850469i	0.938080	−	0.346418i	$-0.112602\pi$
$884$	7.85467	−	6.59085i	0.264181	−	0.221674i
$885$		0			0
$886$	16.5147	−	9.53474i	0.554821	−	0.320326i
$887$	−8.56224	+	3.99264i	−0.287492	+	0.134060i	−0.561015	−	0.827806i	$-0.689589\pi$
$887$	−8.56224	+	3.99264i	−0.287492	+	0.134060i	0.273523	+	0.961866i	$0.411811\pi$
$888$	−10.6290	+	7.44253i	−0.356687	+	0.249755i
$889$	−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
$893$	32.0370	+	48.5999i	1.07208	+	1.62633i
$894$		−	38.8047i		−	1.29782i
$895$		0			0
$896$	−1.33193	−	3.65944i	−0.0444965	−	0.122253i
$897$	0.0512158	−	0.0731438i	0.00171005	−	0.00244220i
$898$	−6.53990	−	9.33995i	−0.218239	−	0.311678i
$899$	1.67741	−	4.60866i	0.0559449	−	0.153707i
$900$		0			0
$901$	−1.61325	−	0.931408i	−0.0537450	−	0.0310297i
$902$	20.9145	+	1.82978i	0.696375	+	0.0609250i
$903$	29.0900	+	2.54505i	0.968056	+	0.0846939i
$904$	13.1549	+	7.59501i	0.437527	+	0.252606i
$905$		0			0
$906$	5.53612	−	15.2104i	0.183925	−	0.505331i
$907$	19.3512	+	27.6363i	0.642545	+	0.917650i	0.999867	−	0.0163318i	$-0.00519882\pi$
$907$	19.3512	+	27.6363i	0.642545	+	0.917650i	−0.357321	+	0.933981i	$0.616310\pi$
$908$	7.53328	−	10.7586i	0.250001	−	0.357038i
$909$	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	$-0.00820757\pi$
$912$	4.50871	+	6.83968i	0.149298	+	0.226484i
$913$	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
$917$	63.3707	−	44.3726i	2.09268	−	1.46531i
$918$	26.6103	−	12.4086i	0.878271	−	0.409545i
$919$	1.73927	−	1.00417i	0.0573732	−	0.0331245i	−0.471039	−	0.882112i	$-0.656121\pi$
$919$	1.73927	−	1.00417i	0.0573732	−	0.0331245i	0.528412	+	0.848988i	$0.322788\pi$
$920$		0			0
$921$	4.99620	−	4.19231i	0.164631	−	0.138141i
$922$	0.726102	−	8.29938i	0.0239129	−	0.273326i
$923$	−2.21838	−	8.27912i	−0.0730190	−	0.272511i
$924$	−11.4605	−	19.8501i	−0.377022	−	0.653022i
$925$		0			0
$926$	22.8820	+	4.03472i	0.751950	+	0.132589i
$927$	5.99654	+	4.19882i	0.196952	+	0.137907i
$928$	−0.274045	+	0.587691i	−0.00899595	+	0.0192919i
$929$	−2.12800	+	2.53605i	−0.0698173	+	0.0832050i	−0.799823	−	0.600236i	$-0.795073\pi$
$929$	−2.12800	+	2.53605i	−0.0698173	+	0.0832050i	0.730005	+	0.683441i	$0.239518\pi$
$930$		0			0
$931$	5.19506	+	35.2114i	0.170261	+	1.15401i
$932$	17.2361	+	17.2361i	0.564587	+	0.564587i
$933$	2.34266	+	26.7767i	0.0766953	+	0.876631i
$934$	−34.1876	+	12.4433i	−1.11865	+	0.407157i
$935$		0			0
$936$	−0.149658	+	0.848752i	−0.00489172	+	0.0277423i
$937$	−19.7619	−	42.3794i	−0.645592	−	1.38448i	−0.907775	−	0.419458i	$-0.862220\pi$
$937$	−19.7619	−	42.3794i	−0.645592	−	1.38448i	0.262183	−	0.965018i	$-0.415558\pi$
$938$	−29.5989	−	7.93100i	−0.966438	−	0.258956i
$939$	−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	$0.806666\pi$
$942$	−36.5787	+	9.80122i	−1.19180	+	0.319341i
$943$	0.0508934	−	0.189937i	0.00165732	−	0.00618520i
$944$	6.35121	+	2.31165i	0.206714	+	0.0752378i
$945$		0			0
$946$	12.3054	−	2.16978i	0.400083	−	0.0705455i
$947$	−7.19045	−	3.35296i	−0.233658	−	0.108957i	0.302263	−	0.953225i	$-0.402258\pi$
$947$	−7.19045	−	3.35296i	−0.233658	−	0.108957i	−0.535921	+	0.844268i	$0.680036\pi$
$948$	−22.4500	+	1.96412i	−0.729141	+	0.0637916i
$949$	10.3538			0.336099
$950$		0			0
$951$	16.2766			0.527805
$952$	−24.5585	+	2.14859i	−0.795945	+	0.0696362i
$953$	−4.22198	−	1.96874i	−0.136763	−	0.0637738i	0.353032	−	0.935611i	$-0.385151\pi$
$953$	−4.22198	−	1.96874i	−0.136763	−	0.0637738i	−0.489795	+	0.871837i	$0.662928\pi$
$954$	0.154197	−	0.0271891i	0.00499232	−	0.000880281i
$955$		0			0
$956$	10.6577	+	3.87909i	0.344695	+	0.125459i
$957$	−0.987811	+	3.68656i	−0.0319314	+	0.119170i
$958$	−36.4681	+	9.77159i	−1.17823	+	0.315706i
$959$	20.7439	+	24.7216i	0.669855	+	0.798302i
$960$		0			0
$961$	13.1024	−	22.6939i	0.422656	−	0.732062i
$962$	10.8020	+	2.89438i	0.348269	+	0.0933184i
$963$	−0.367697	−	0.788530i	−0.0118489	−	0.0254100i
$964$	4.66121	−	26.4350i	0.150127	−	0.851414i
$965$		0			0
$966$	−0.201735	+	0.0734257i	−0.00649073	+	0.00236243i
$967$	−1.86629	−	21.3318i	−0.0600158	−	0.685983i	−0.965294	−	0.261165i	$-0.915893\pi$
$967$	−1.86629	−	21.3318i	−0.0600158	−	0.685983i	0.905278	−	0.424819i	$-0.139662\pi$
$968$	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	$0.386033\pi$
$972$	−2.31084	+	4.95561i	−0.0741202	+	0.158951i
$973$	−7.08709	−	4.96244i	−0.227202	−	0.159088i
$974$	−11.5003	−	2.02781i	−0.368493	−	0.0649753i
$975$		0			0
$976$	−0.238861	−	0.413719i	−0.00764576	−	0.0132428i
$977$	1.53806	+	5.74010i	0.0492068	+	0.183642i	0.986155	−	0.165826i	$-0.0530290\pi$
$977$	1.53806	+	5.74010i	0.0492068	+	0.183642i	−0.936948	+	0.349468i	$0.886362\pi$
$978$	2.68505	−	30.6903i	0.0858585	−	0.981368i
$979$	−9.68810	+	8.12928i	−0.309633	+	0.259813i
$980$		0			0
$981$	−3.77280	+	2.17823i	−0.120456	+	0.0695454i
$982$	18.1669	−	8.47134i	0.579728	−	0.270331i
$983$	−29.4427	+	20.6160i	−0.939076	+	0.657548i	−0.939535	−	0.342452i	$-0.888743\pi$
$983$	−29.4427	+	20.6160i	−0.939076	+	0.657548i	0.000459562		1.00000i	$0.499854\pi$
$984$	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
$988$	2.01789	−	6.76577i	0.0641975	−	0.215248i
$989$		−	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	$0.809664\pi$
$992$	−4.33818	+	6.19556i	−0.137737	+	0.196709i
$993$	10.1105	+	14.4393i	0.320848	+	0.458219i
$994$	−7.04816	+	19.3647i	−0.223554	+	0.614210i
$995$		0			0
$996$	21.5134	+	12.4208i	0.681679	+	0.393567i
$997$	−1.70329	−	0.149019i	−0.0539439	−	0.00471948i	0.0601519	−	0.998189i	$-0.480842\pi$
$997$	−1.70329	−	0.149019i	−0.0539439	−	0.00471948i	−0.114096	+	0.993470i	$0.536397\pi$
$998$	−34.1503	−	2.98776i	−1.08101	−	0.0945760i
$999$	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.307.4	yes	48
5.2	odd	4	inner	950.2.bb.b.193.4	yes	48
5.3	odd	4	inner	950.2.bb.b.193.1	✓	48
5.4	even	2	inner	950.2.bb.b.307.1	yes	48
19.13	odd	18	inner	950.2.bb.b.507.1	yes	48
95.13	even	36	inner	950.2.bb.b.393.4	yes	48
95.32	even	36	inner	950.2.bb.b.393.1	yes	48
95.89	odd	18	inner	950.2.bb.b.507.4	yes	48

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

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