LMFDB - Embedded newform 950.2.bb.e.193.9

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:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.9
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.e.507.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 + 0.996195i) q^{2} +(0.715886 - 1.53522i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(1.59177 + 0.579359i) q^{6} +(4.29599 + 1.15111i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(0.0839459 + 0.100043i) q^{9} +O(q^{10})$	\(q+(0.0871557 + 0.996195i) q^{2} +(0.715886 - 1.53522i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(1.59177 + 0.579359i) q^{6} +(4.29599 + 1.15111i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(0.0839459 + 0.100043i) q^{9} +(-2.39629 + 4.15050i) q^{11} +(-0.438422 + 1.63621i) q^{12} +(1.29075 - 0.601887i) q^{13} +(-0.772307 + 4.37997i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-3.30863 + 0.289468i) q^{17} +(-0.0923458 + 0.0923458i) q^{18} +(3.03200 + 3.13161i) q^{19} +(4.84265 - 5.77124i) q^{21} +(-4.34356 - 2.02543i) q^{22} +(-3.06066 + 4.37107i) q^{23} +(-1.66820 - 0.294148i) q^{24} +(0.712093 + 1.23338i) q^{26} +(5.12232 - 1.37252i) q^{27} +(-4.43061 - 0.387628i) q^{28} +(0.247532 - 0.207704i) q^{29} +(5.17258 - 2.98639i) q^{31} +(0.422618 + 0.906308i) q^{32} +(4.65647 + 6.65013i) q^{33} +(-0.576733 - 3.27081i) q^{34} +(-0.100043 - 0.0839459i) q^{36} +(-4.13942 - 4.13942i) q^{37} +(-2.85543 + 3.29340i) q^{38} -2.41247i q^{39} +(-1.30827 - 3.59444i) q^{41} +(6.17134 + 4.32122i) q^{42} +(8.76587 - 6.13793i) q^{43} +(1.63916 - 4.50356i) q^{44} +(-4.62120 - 2.66805i) q^{46} +(-0.495618 + 5.66494i) q^{47} +(0.147636 - 1.68749i) q^{48} +(11.0683 + 6.39029i) q^{49} +(-1.92421 + 5.28671i) q^{51} +(-1.16663 + 0.816880i) q^{52} +(-2.35536 - 1.64924i) q^{53} +(1.81374 + 4.98320i) q^{54} -4.44754i q^{56} +(6.97829 - 2.41292i) q^{57} +(0.228487 + 0.228487i) q^{58} +(0.122827 + 0.103064i) q^{59} +(0.661018 + 3.74882i) q^{61} +(3.42585 + 4.89262i) q^{62} +(0.245471 + 0.526414i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-6.21899 + 5.21835i) q^{66} +(-13.7568 - 1.20357i) q^{67} +(3.20810 - 0.859608i) q^{68} +(4.51949 + 7.82799i) q^{69} +(10.2922 + 1.81479i) q^{71} +(0.0749072 - 0.106979i) q^{72} +(8.21012 + 3.82844i) q^{73} +(3.76289 - 4.48444i) q^{74} +(-3.52974 - 2.55753i) q^{76} +(-15.0721 + 15.0721i) q^{77} +(2.40329 - 0.210261i) q^{78} +(-7.14978 + 2.60231i) q^{79} +(1.49184 - 8.46064i) q^{81} +(3.46674 - 1.61657i) q^{82} +(1.28270 - 4.78710i) q^{83} +(-3.76691 + 6.52448i) q^{84} +(6.87857 + 8.19756i) q^{86} +(-0.141667 - 0.528708i) q^{87} +(4.62928 + 1.24041i) q^{88} +(11.2576 + 4.09744i) q^{89} +(6.23789 - 1.09991i) q^{91} +(2.25513 - 4.83615i) q^{92} +(-0.881797 - 10.0790i) q^{93} -5.68658 q^{94} +1.69393 q^{96} +(-0.0458389 - 0.523941i) q^{97} +(-5.40131 + 11.5831i) q^{98} +(-0.616387 + 0.108686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^7	$ 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) $ 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

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
$3$	0.715886	−	1.53522i	0.413317	−	0.886361i	−0.583901	−	0.811825i	$-0.698474\pi$
$3$	0.715886	−	1.53522i	0.413317	−	0.886361i	0.997218	−	0.0745367i	$-0.0237478\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	1.59177	+	0.579359i	0.649839	+	0.236522i
$7$	4.29599	+	1.15111i	1.62373	+	0.435078i	0.952095	−	0.305803i	$-0.0989249\pi$
$7$	4.29599	+	1.15111i	1.62373	+	0.435078i	0.671637	+	0.740881i	$0.265592\pi$
$8$	−0.258819	−	0.965926i	−0.0915064	−	0.341506i
$9$	0.0839459	+	0.100043i	0.0279820	+	0.0333476i
$10$		0			0
$11$	−2.39629	+	4.15050i	−0.722509	+	1.25142i	0.237482	+	0.971392i	$0.423678\pi$
$11$	−2.39629	+	4.15050i	−0.722509	+	1.25142i	−0.959991	+	0.280031i	$0.909655\pi$
$12$	−0.438422	+	1.63621i	−0.126561	+	0.472334i
$13$	1.29075	−	0.601887i	0.357990	−	0.166933i	−0.235299	−	0.971923i	$-0.575607\pi$
$13$	1.29075	−	0.601887i	0.357990	−	0.166933i	0.593289	+	0.804990i	$0.297829\pi$
$14$	−0.772307	+	4.37997i	−0.206408	+	1.17060i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	−3.30863	+	0.289468i	−0.802461	+	0.0702063i	−0.481005	−	0.876718i	$-0.659728\pi$
$17$	−3.30863	+	0.289468i	−0.802461	+	0.0702063i	−0.321457	+	0.946924i	$0.604172\pi$
$18$	−0.0923458	+	0.0923458i	−0.0217661	+	0.0217661i
$19$	3.03200	+	3.13161i	0.695589	+	0.718440i
$19$	3.03200	+	3.13161i	0.695589	+	0.718440i
$20$		0			0
$21$	4.84265	−	5.77124i	1.05675	−	1.25939i
$22$	−4.34356	−	2.02543i	−0.926049	−	0.431824i
$23$	−3.06066	+	4.37107i	−0.638192	+	0.911432i	−0.999781	−	0.0209052i	$-0.993345\pi$
$23$	−3.06066	+	4.37107i	−0.638192	+	0.911432i	0.361590	+	0.932337i	$0.382234\pi$
$24$	−1.66820	−	0.294148i	−0.340519	−	0.0600427i
$25$		0			0
$26$	0.712093	+	1.23338i	0.139653	+	0.241886i
$27$	5.12232	−	1.37252i	0.985791	−	0.264142i
$28$	−4.43061	−	0.387628i	−0.837307	−	0.0732549i
$29$	0.247532	−	0.207704i	0.0459655	−	0.0385696i	−0.619516	−	0.784984i	$-0.712671\pi$
$29$	0.247532	−	0.207704i	0.0459655	−	0.0385696i	0.665481	+	0.746415i	$0.268226\pi$
$30$		0			0
$31$	5.17258	−	2.98639i	0.929023	−	0.536372i	0.0425205	−	0.999096i	$-0.486461\pi$
$31$	5.17258	−	2.98639i	0.929023	−	0.536372i	0.886502	+	0.462724i	$0.153128\pi$
$32$	0.422618	+	0.906308i	0.0747091	+	0.160214i
$33$	4.65647	+	6.65013i	0.810587	+	1.15764i
$34$	−0.576733	−	3.27081i	−0.0989088	−	0.560940i
$35$		0			0
$36$	−0.100043	−	0.0839459i	−0.0166738	−	0.0139910i
$37$	−4.13942	−	4.13942i	−0.680516	−	0.680516i	0.279600	−	0.960116i	$-0.409798\pi$
$37$	−4.13942	−	4.13942i	−0.680516	−	0.680516i	−0.960116	+	0.279600i	$0.909798\pi$
$38$	−2.85543	+	3.29340i	−0.463213	+	0.534260i
$39$		−	2.41247i		−	0.386305i
$40$		0			0
$41$	−1.30827	−	3.59444i	−0.204317	−	0.561357i	0.794637	−	0.607085i	$-0.207661\pi$
$41$	−1.30827	−	3.59444i	−0.204317	−	0.561357i	−0.998954	+	0.0457282i	$0.985439\pi$
$42$	6.17134	+	4.32122i	0.952259	+	0.666779i
$43$	8.76587	−	6.13793i	1.33678	−	0.936025i	0.336798	−	0.941577i	$-0.390656\pi$
$43$	8.76587	−	6.13793i	1.33678	−	0.936025i	0.999985	+	0.00555167i	$0.00176716\pi$
$44$	1.63916	−	4.50356i	0.247113	−	0.678937i
$45$		0			0
$46$	−4.62120	−	2.66805i	−0.681358	−	0.393382i
$47$	−0.495618	+	5.66494i	−0.0722933	+	0.826316i	0.870332	+	0.492465i	$0.163904\pi$
$47$	−0.495618	+	5.66494i	−0.0722933	+	0.826316i	−0.942626	+	0.333851i	$0.891652\pi$
$48$	0.147636	−	1.68749i	0.0213094	−	0.243568i
$49$	11.0683	+	6.39029i	1.58119	+	0.912899i
$50$		0			0
$51$	−1.92421	+	5.28671i	−0.269443	+	0.740288i
$52$	−1.16663	+	0.816880i	−0.161782	+	0.113281i
$53$	−2.35536	−	1.64924i	−0.323533	−	0.226541i	0.400514	−	0.916291i	$-0.368832\pi$
$53$	−2.35536	−	1.64924i	−0.323533	−	0.226541i	−0.724048	+	0.689750i	$0.757720\pi$
$54$	1.81374	+	4.98320i	0.246819	+	0.678128i
$55$		0			0
$56$		−	4.44754i		−	0.594327i
$57$	6.97829	−	2.41292i	0.924296	−	0.319599i
$58$	0.228487	+	0.228487i	0.0300018	+	0.0300018i
$59$	0.122827	+	0.103064i	0.0159907	+	0.0134178i	0.650748	−	0.759294i	$-0.274455\pi$
$59$	0.122827	+	0.103064i	0.0159907	+	0.0134178i	−0.634757	+	0.772712i	$0.718900\pi$
$60$		0			0
$61$	0.661018	+	3.74882i	0.0846347	+	0.479987i	0.997435	+	0.0715807i	$0.0228043\pi$
$61$	0.661018	+	3.74882i	0.0846347	+	0.479987i	−0.912800	+	0.408407i	$0.866085\pi$
$62$	3.42585	+	4.89262i	0.435083	+	0.621363i
$63$	0.245471	+	0.526414i	0.0309264	+	0.0663219i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	−6.21899	+	5.21835i	−0.765504	+	0.642334i
$67$	−13.7568	−	1.20357i	−1.68067	−	0.147039i	−0.793525	−	0.608538i	$-0.791756\pi$
$67$	−13.7568	−	1.20357i	−1.68067	−	0.147039i	−0.887141	+	0.461499i	$0.847312\pi$
$68$	3.20810	−	0.859608i	0.389039	−	0.104243i
$69$	4.51949	+	7.82799i	0.544083	+	0.942379i
$70$		0			0
$71$	10.2922	+	1.81479i	1.22146	+	0.215376i	0.746953	−	0.664877i	$-0.231516\pi$
$71$	10.2922	+	1.81479i	1.22146	+	0.215376i	0.474505	+	0.880253i	$0.342627\pi$
$72$	0.0749072	−	0.106979i	0.00882790	−	0.0126075i
$73$	8.21012	+	3.82844i	0.960922	+	0.448085i	0.838806	−	0.544430i	$-0.183254\pi$
$73$	8.21012	+	3.82844i	0.960922	+	0.448085i	0.122116	+	0.992516i	$0.461032\pi$
$74$	3.76289	−	4.48444i	0.437427	−	0.521305i
$75$		0			0
$76$	−3.52974	−	2.55753i	−0.404889	−	0.293369i
$77$	−15.0721	+	15.0721i	−1.71763	+	1.71763i
$78$	2.40329	−	0.210261i	0.272119	−	0.0238074i
$79$	−7.14978	+	2.60231i	−0.804413	+	0.292782i	−0.711314	−	0.702874i	$-0.751900\pi$
$79$	−7.14978	+	2.60231i	−0.804413	+	0.292782i	−0.0930991	+	0.995657i	$0.529677\pi$
$80$		0			0
$81$	1.49184	−	8.46064i	0.165760	−	0.940071i
$82$	3.46674	−	1.61657i	0.382837	−	0.178520i
$83$	1.28270	−	4.78710i	0.140794	−	0.525452i	−0.859112	−	0.511787i	$-0.828984\pi$
$83$	1.28270	−	4.78710i	0.140794	−	0.525452i	0.999907	−	0.0136648i	$-0.00434976\pi$
$84$	−3.76691	+	6.52448i	−0.411004	+	0.711879i
$85$		0			0
$86$	6.87857	+	8.19756i	0.741735	+	0.883965i
$87$	−0.141667	−	0.528708i	−0.0151883	−	0.0566835i
$88$	4.62928	+	1.24041i	0.493483	+	0.132228i
$89$	11.2576	+	4.09744i	1.19331	+	0.434328i	0.860883	−	0.508803i	$-0.169912\pi$
$89$	11.2576	+	4.09744i	1.19331	+	0.434328i	0.332423	+	0.943130i	$0.392134\pi$
$90$		0			0
$91$	6.23789	−	1.09991i	0.653909	−	0.115302i
$92$	2.25513	−	4.83615i	0.235114	−	0.504203i
$93$	−0.881797	−	10.0790i	−0.0914381	−	1.04514i
$94$	−5.68658			−0.586526
$95$		0			0
$96$	1.69393			0.172886
$97$	−0.0458389	−	0.523941i	−0.00465424	−	0.0531982i	0.993512	−	0.113724i	$-0.0362779\pi$
$97$	−0.0458389	−	0.523941i	−0.00465424	−	0.0531982i	−0.998167	+	0.0605256i	$0.980722\pi$
$98$	−5.40131	+	11.5831i	−0.545614	+	1.17007i
$99$	−0.616387	+	0.108686i	−0.0619492	+	0.0109233i
$100$		0			0
$101$	−1.43282	−	0.521503i	−0.142571	−	0.0518915i	0.269749	−	0.962931i	$-0.413059\pi$
$101$	−1.43282	−	0.521503i	−0.142571	−	0.0518915i	−0.412320	+	0.911039i	$0.635281\pi$
$102$	−5.43430	−	1.45612i	−0.538076	−	0.144177i
$103$	−4.28162	−	15.9792i	−0.421881	−	1.57448i	−0.770641	−	0.637269i	$-0.780064\pi$
$103$	−4.28162	−	15.9792i	−0.421881	−	1.57448i	0.348760	−	0.937212i	$-0.386603\pi$
$104$	−0.915449	−	1.09099i	−0.0897672	−	0.106980i
$105$		0			0
$106$	1.43768	−	2.49014i	0.139640	−	0.241864i
$107$	1.05049	−	3.92047i	0.101554	−	0.379006i	−0.896377	−	0.443292i	$-0.853810\pi$
$107$	1.05049	−	3.92047i	0.101554	−	0.379006i	0.997931	+	0.0642864i	$0.0204771\pi$
$108$	−4.80616	+	2.24115i	−0.462473	+	0.215655i
$109$	−0.00462595	+	0.0262351i	−0.000443085	+	0.00251286i	−0.985028	−	0.172392i	$-0.944851\pi$
$109$	−0.00462595	+	0.0262351i	−0.000443085	+	0.00251286i	0.984585	+	0.174904i	$0.0559617\pi$
$110$		0			0
$111$	−9.31828	+	3.39158i	−0.884452	+	0.321914i
$112$	4.43061	−	0.387628i	0.418653	−	0.0366274i
$113$	6.33461	−	6.33461i	0.595910	−	0.595910i	−0.343312	−	0.939222i	$-0.611549\pi$
$113$	6.33461	−	6.33461i	0.595910	−	0.595910i	0.939222	+	0.343312i	$0.111549\pi$
$114$	3.01194	+	6.74143i	0.282094	+	0.631393i
$115$		0			0
$116$	−0.207704	+	0.247532i	−0.0192848	+	0.0229827i
$117$	0.168568	+	0.0786045i	0.0155841	+	0.00726699i
$118$	−0.0919667	+	0.131342i	−0.00846622	+	0.0120910i
$119$	−14.5471	−	2.56504i	−1.33353	−	0.235137i
$120$		0			0
$121$	−5.98443	−	10.3653i	−0.544039	−	0.942304i
$122$	−3.67694	+	0.985234i	−0.332895	+	0.0891989i
$123$	−6.45484	−	0.564725i	−0.582013	−	0.0509196i
$124$	−4.57542	+	3.83923i	−0.410885	+	0.344773i
$125$		0			0
$126$	−0.503017	+	0.290417i	−0.0448123	+	0.0258724i
$127$	−5.25221	−	11.2634i	−0.466058	−	0.999465i	−0.989112	−	0.147166i	$-0.952985\pi$
$127$	−5.25221	−	11.2634i	−0.466058	−	0.999465i	0.523054	−	0.852300i	$-0.324793\pi$
$128$	−0.573576	−	0.819152i	−0.0506975	−	0.0724035i
$129$	−3.14772	−	17.8516i	−0.277142	−	1.57175i
$130$		0			0
$131$	−17.2748	−	14.4953i	−1.50931	−	1.26646i	−0.865084	−	0.501626i	$-0.832735\pi$
$131$	−17.2748	−	14.4953i	−1.50931	−	1.26646i	−0.644226	−	0.764835i	$-0.722820\pi$
$132$	−5.74051	−	5.74051i	−0.499647	−	0.499647i
$133$	9.42063	+	16.9435i	0.816872	+	1.46919i
$134$		−	13.8094i		−	1.19295i
$135$		0			0
$136$	1.13594	+	3.12097i	0.0974062	+	0.267621i
$137$	−5.76008	−	4.03325i	−0.492116	−	0.344584i	0.301030	−	0.953615i	$-0.402670\pi$
$137$	−5.76008	−	4.03325i	−0.492116	−	0.344584i	−0.793146	+	0.609031i	$0.791558\pi$
$138$	−7.40430	+	5.18455i	−0.630296	+	0.441338i
$139$	−2.87925	+	7.91069i	−0.244215	+	0.670976i	0.755657	+	0.654968i	$0.227318\pi$
$139$	−2.87925	+	7.91069i	−0.244215	+	0.670976i	−0.999872	+	0.0160078i	$0.994904\pi$
$140$		0			0
$141$	8.34214	+	4.81634i	0.702535	+	0.405609i
$142$	−0.910861	+	10.4112i	−0.0764377	+	0.873687i
$143$	−0.594884	+	6.79956i	−0.0497467	+	0.568608i
$144$	0.113100	+	0.0652983i	0.00942500	+	0.00544153i
$145$		0			0
$146$	−3.09832	+	8.51255i	−0.256418	+	0.704504i
$147$	17.7342	−	12.4176i	1.46269	−	1.02419i
$148$	4.79533	+	3.35773i	0.394174	+	0.276004i
$149$	−2.28842	−	6.28739i	−0.187475	−	0.515083i	0.809974	−	0.586466i	$-0.199481\pi$
$149$	−2.28842	−	6.28739i	−0.187475	−	0.515083i	−0.997449	+	0.0713827i	$0.977259\pi$
$150$		0			0
$151$		−	1.44444i		−	0.117547i	−0.998271	−	0.0587734i	$-0.981281\pi$
$151$		−	1.44444i		−	0.117547i	0.998271	−	0.0587734i	$-0.0187190\pi$
$152$	2.24016	−	3.73921i	0.181701	−	0.303290i
$153$	−0.306705	−	0.306705i	−0.0247957	−	0.0247957i
$154$	−16.3284	−	13.7011i	−1.31578	−	1.10407i
$155$		0			0
$156$	0.418922	+	2.37582i	0.0335406	+	0.190218i
$157$	7.66033	+	10.9401i	0.611361	+	0.873113i	0.998810	−	0.0487777i	$-0.0155326\pi$
$157$	7.66033	+	10.9401i	0.611361	+	0.873113i	−0.387449	+	0.921891i	$0.626644\pi$
$158$	−3.21555	−	6.89577i	−0.255815	−	0.548598i
$159$	−4.21812	+	2.43533i	−0.334519	+	0.193135i
$160$		0			0
$161$	−18.1801	+	15.2549i	−1.43280	+	1.20226i
$162$	8.55846	+	0.748768i	0.672416	+	0.0588288i
$163$	−12.1365	+	3.25198i	−0.950607	+	0.254715i	−0.700620	−	0.713535i	$-0.747093\pi$
$163$	−12.1365	+	3.25198i	−0.950607	+	0.254715i	−0.249987	+	0.968249i	$0.580426\pi$
$164$	1.91256	+	3.31265i	0.149346	+	0.258675i
$165$		0			0
$166$	4.88067	+	0.860595i	0.378814	+	0.0667951i
$167$	−0.231824	+	0.331079i	−0.0179391	+	0.0256197i	−0.828021	−	0.560696i	$-0.810533\pi$
$167$	−0.231824	+	0.331079i	−0.0179391	+	0.0256197i	0.810082	+	0.586316i	$0.199422\pi$
$168$	−6.82796	−	3.18393i	−0.526789	−	0.245646i
$169$	−7.05247	+	8.40480i	−0.542498	+	0.646523i
$170$		0			0
$171$	−0.0587709	+	0.566216i	−0.00449432	+	0.0432996i
$172$	−7.56686	+	7.56686i	−0.576967	+	0.576967i
$173$	−15.8338	+	1.38527i	−1.20382	+	0.105320i	−0.671357	−	0.741134i	$-0.734288\pi$
$173$	−15.8338	+	1.38527i	−1.20382	+	0.105320i	−0.532461	+	0.846454i	$0.678733\pi$
$174$	0.514349	−	0.187208i	0.0389927	−	0.0141922i
$175$		0			0
$176$	−0.832224	+	4.71977i	−0.0627312	+	0.355766i
$177$	0.246156	−	0.114785i	0.0185022	−	0.00862774i
$178$	−3.10068	+	11.5719i	−0.232406	+	0.867351i
$179$	11.8264	−	20.4839i	0.883947	−	1.53104i	0.0370309	−	0.999314i	$-0.488210\pi$
$179$	11.8264	−	20.4839i	0.883947	−	1.53104i	0.846916	−	0.531727i	$-0.178457\pi$
$180$		0			0
$181$	−13.8901	−	16.5536i	−1.03245	−	1.23042i	−0.972666	−	0.232209i	$-0.925405\pi$
$181$	−13.8901	−	16.5536i	−1.03245	−	1.23042i	−0.0597791	−	0.998212i	$-0.519040\pi$
$182$	1.63939	+	6.11829i	0.121520	+	0.453518i
$183$	6.22849	+	1.66892i	0.460423	+	0.123370i
$184$	5.01429	+	1.82505i	0.369658	+	0.134545i
$185$		0			0
$186$	9.96378	−	1.75688i	0.730579	−	0.128821i
$187$	6.72701	−	14.4261i	0.491928	−	1.05494i
$188$	−0.495618	−	5.66494i	−0.0361467	−	0.413158i
$189$	23.5854			1.71558
$190$		0			0
$191$	15.5082			1.12213			0.561065	−	0.827772i	$-0.310392\pi$
$191$	15.5082			1.12213			0.561065	+	0.827772i	$0.310392\pi$
$192$	0.147636	+	1.68749i	0.0106547	+	0.121784i
$193$	−7.50527	+	16.0951i	−0.540241	+	1.15855i	0.426898	+	0.904300i	$0.359606\pi$
$193$	−7.50527	+	16.0951i	−0.540241	+	1.15855i	−0.967138	+	0.254250i	$0.918171\pi$
$194$	0.517952	−	0.0913290i	0.0371868	−	0.00655704i
$195$		0			0
$196$	−12.0098	−	4.37122i	−0.857844	−	0.312230i
$197$	−5.99067	−	1.60519i	−0.426817	−	0.114365i	0.0390145	−	0.999239i	$-0.487578\pi$
$197$	−5.99067	−	1.60519i	−0.426817	−	0.114365i	−0.465832	+	0.884873i	$0.654245\pi$
$198$	−0.161994	−	0.604569i	−0.0115124	−	0.0429648i
$199$	−10.1137	−	12.0530i	−0.716939	−	0.854415i	0.277390	−	0.960757i	$-0.410530\pi$
$199$	−10.1137	−	12.0530i	−0.716939	−	0.854415i	−0.994330	+	0.106342i	$0.966086\pi$
$200$		0			0
$201$	−11.6961	+	20.2582i	−0.824978	+	1.42890i
$202$	0.394640	−	1.47282i	0.0277668	−	0.103627i
$203$	1.30248	−	0.607357i	0.0914163	−	0.0426281i
$204$	0.976945	−	5.54053i	0.0683999	−	0.387915i
$205$		0			0
$206$	15.5453	−	5.65801i	1.08309	−	0.394213i
$207$	−0.694225	+	0.0607368i	−0.0482520	+	0.00422150i
$208$	1.00705	−	1.00705i	0.0698265	−	0.0698265i
$209$	−20.2633	+	5.08007i	−1.40164	+	0.351396i
$210$		0			0
$211$	2.32781	−	2.77417i	0.160253	−	0.190982i	−0.679943	−	0.733265i	$-0.737995\pi$
$211$	2.32781	−	2.77417i	0.160253	−	0.190982i	0.840196	+	0.542283i	$0.182440\pi$
$212$	2.60596	+	1.21518i	0.178978	+	0.0834590i
$213$	10.1541	−	14.5016i	0.695750	−	0.993634i
$214$	3.99710	+	0.704797i	0.273236	+	0.0481789i
$215$		0			0
$216$	−2.65151	−	4.59255i	−0.180412	−	0.312483i
$217$	25.6590	−	6.87531i	1.74185	−	0.466727i
$218$	−0.0265384	−	0.00232181i	−0.00179741	−	0.000157253i
$219$	11.7550	−	9.86364i	0.794331	−	0.666523i
$220$		0			0
$221$	−4.09639	+	2.36505i	−0.275553	+	0.159091i
$222$	−4.19081	−	8.98723i	−0.281269	−	0.603183i
$223$	8.67348	+	12.3870i	0.580819	+	0.829496i	0.996805	−	0.0798754i	$-0.0254522\pi$
$223$	8.67348	+	12.3870i	0.580819	+	0.829496i	−0.415986	+	0.909371i	$0.636563\pi$
$224$	0.772307	+	4.37997i	0.0516019	+	0.292649i
$225$		0			0
$226$	6.86260	+	5.75841i	0.456493	+	0.383043i
$227$	4.85572	+	4.85572i	0.322286	+	0.322286i	0.849643	−	0.527358i	$-0.176817\pi$
$227$	4.85572	+	4.85572i	0.322286	+	0.322286i	−0.527358	+	0.849643i	$0.676817\pi$
$228$	−6.45327	+	3.58803i	−0.427378	+	0.237623i
$229$			11.3734i			0.751576i	0.926706	+	0.375788i	$0.122628\pi$
$229$			11.3734i			0.751576i	−0.926706	+	0.375788i	$0.877372\pi$
$230$		0			0
$231$	12.3491	+	33.9290i	0.812514	+	2.23236i
$232$	−0.264692	−	0.185339i	−0.0173779	−	0.0121681i
$233$	−1.60396	+	1.12311i	−0.105079	+	0.0735772i	−0.624935	−	0.780677i	$-0.714875\pi$
$233$	−1.60396	+	1.12311i	−0.105079	+	0.0735772i	0.519856	+	0.854254i	$0.325986\pi$
$234$	−0.0636137	+	0.174777i	−0.00415856	+	0.0114255i
$235$		0			0
$236$	−0.138858	−	0.0801696i	−0.00903887	−	0.00521859i
$237$	−1.12331	+	12.8395i	−0.0729667	+	0.834013i
$238$	1.28742	−	14.7153i	0.0834509	−	0.953849i
$239$	7.61511	+	4.39658i	0.492580	+	0.284391i	0.725644	−	0.688070i	$-0.241542\pi$
$239$	7.61511	+	4.39658i	0.492580	+	0.284391i	−0.233064	+	0.972461i	$0.574875\pi$
$240$		0			0
$241$	−3.07397	+	8.44566i	−0.198012	+	0.544033i	−0.998466	−	0.0553606i	$-0.982369\pi$
$241$	−3.07397	+	8.44566i	−0.198012	+	0.544033i	0.800455	+	0.599393i	$0.204591\pi$
$242$	9.80432	−	6.86506i	0.630246	−	0.441303i
$243$	1.11095	+	0.777897i	0.0712676	+	0.0499021i
$244$	−1.30195	−	3.57708i	−0.0833489	−	0.228999i
$245$		0			0
$246$		−	6.47950i		−	0.413118i
$247$	5.79843	+	2.21720i	0.368946	+	0.141077i
$248$	−4.22339	−	4.22339i	−0.268186	−	0.268186i
$249$	−6.43099	−	5.39625i	−0.407548	−	0.341973i
$250$		0			0
$251$	−2.59867	−	14.7378i	−0.164026	−	0.930240i	−0.950063	−	0.312059i	$-0.898981\pi$
$251$	−2.59867	−	14.7378i	−0.164026	−	0.930240i	0.786036	−	0.618180i	$-0.212130\pi$
$252$	−0.333152	−	0.475791i	−0.0209866	−	0.0299720i
$253$	−10.8079	−	23.1776i	−0.679487	−	1.45717i
$254$	10.7628	−	6.21389i	0.675317	−	0.389894i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−13.9309	−	1.21879i	−0.868983	−	0.0760262i	−0.356063	−	0.934462i	$-0.615881\pi$
$257$	−13.9309	−	1.21879i	−0.868983	−	0.0760262i	−0.512921	+	0.858436i	$0.671437\pi$
$258$	17.5094	−	4.69162i	1.09008	−	0.292087i
$259$	−13.0180	−	22.5478i	−0.808898	−	1.40105i
$260$		0			0
$261$	0.0415585	+	0.00732789i	0.00257241	+	0.000453585i
$262$	12.9346	−	18.4725i	0.799099	−	1.14123i
$263$	−16.4858	−	7.68748i	−1.01656	−	0.474030i	−0.158380	−	0.987378i	$-0.550627\pi$
$263$	−16.4858	−	7.68748i	−1.01656	−	0.474030i	−0.858180	+	0.513348i	$0.828405\pi$
$264$	5.21835	−	6.21899i	0.321167	−	0.382752i
$265$		0			0
$266$	−16.0580	+	10.8615i	−0.984578	+	0.665962i
$267$	14.3497	−	14.3497i	0.878185	−	0.878185i
$268$	13.7568	−	1.20357i	0.840333	−	0.0735196i
$269$	4.78473	−	1.74150i	0.291730	−	0.106181i	−0.192009	−	0.981393i	$-0.561500\pi$
$269$	4.78473	−	1.74150i	0.291730	−	0.106181i	0.483740	+	0.875212i	$0.339278\pi$
$270$		0			0
$271$	1.59484	−	9.04481i	0.0968799	−	0.549433i	−0.897275	−	0.441472i	$-0.854457\pi$
$271$	1.59484	−	9.04481i	0.0968799	−	0.549433i	0.994155	−	0.107961i	$-0.0344323\pi$
$272$	−3.01009	+	1.40363i	−0.182514	+	0.0851075i
$273$	2.77702	−	10.3640i	0.168073	−	0.627256i
$274$	3.51588	−	6.08968i	0.212402	−	0.367891i
$275$		0			0
$276$	−5.81015	−	6.92426i	−0.349730	−	0.416792i
$277$	−2.40587	−	8.97883i	−0.144555	−	0.539486i	−0.999775	−	0.0212207i	$-0.993245\pi$
$277$	−2.40587	−	8.97883i	−0.144555	−	0.539486i	0.855220	−	0.518265i	$-0.173422\pi$
$278$	−8.13153	−	2.17884i	−0.487697	−	0.130678i
$279$	0.732984	+	0.266784i	0.0438826	+	0.0159720i
$280$		0			0
$281$	−5.46236	+	0.963162i	−0.325857	+	0.0574574i	−0.334184	−	0.942508i	$-0.608461\pi$
$281$	−5.46236	+	0.963162i	−0.325857	+	0.0574574i	0.00832661	+	0.999965i	$0.497350\pi$
$282$	−4.07094	+	8.73017i	−0.242421	+	0.519874i
$283$	−1.36643	−	15.6184i	−0.0812259	−	0.928417i	−0.922040	−	0.387093i	$-0.873479\pi$
$283$	−1.36643	−	15.6184i	−0.0812259	−	0.928417i	0.840815	−	0.541323i	$-0.182076\pi$
$284$	−10.4510			−0.620150
$285$		0			0
$286$	−6.82553			−0.403602
$287$	−1.48273	−	16.9476i	−0.0875226	−	1.00039i
$288$	−0.0551925	+	0.118361i	−0.00325225	+	0.00697448i
$289$	−5.87848	+	1.03653i	−0.345793	+	0.0609726i
$290$		0			0
$291$	−0.837182	−	0.304709i	−0.0490765	−	0.0178624i
$292$	−8.75019	−	2.34461i	−0.512066	−	0.137208i
$293$	4.80708	+	17.9403i	0.280832	+	1.04808i	0.951831	+	0.306622i	$0.0991989\pi$
$293$	4.80708	+	17.9403i	0.280832	+	1.04808i	−0.670999	+	0.741458i	$0.734134\pi$
$294$	13.9160	+	16.5844i	0.811597	+	0.967223i
$295$		0			0
$296$	−2.92701	+	5.06973i	−0.170129	+	0.294672i
$297$	−6.57792	+	24.5491i	−0.381690	+	1.42449i
$298$	6.06401	−	2.82770i	0.351279	−	0.163804i
$299$	−1.31966	+	7.48414i	−0.0763177	+	0.432819i
$300$		0			0
$301$	44.7235	−	16.2780i	2.57782	−	0.938250i
$302$	1.43894	−	0.125891i	0.0828019	−	0.00724423i
$303$	−1.82636	+	1.82636i	−0.104921	+	0.104921i
$304$	3.92022	+	1.90574i	0.224840	+	0.109302i
$305$		0			0
$306$	0.278807	−	0.332269i	0.0159383	−	0.0189946i
$307$	−23.0656	−	10.7556i	−1.31642	−	0.613857i	−0.367692	−	0.929948i	$-0.619852\pi$
$307$	−23.0656	−	10.7556i	−1.31642	−	0.613857i	−0.948729	+	0.316090i	$0.897630\pi$
$308$	12.2259	−	17.4604i	0.696635	−	0.994898i
$309$	−27.5969	−	4.86607i	−1.56993	−	0.276821i
$310$		0			0
$311$	−0.929277	−	1.60956i	−0.0526945	−	0.0912695i	0.838475	−	0.544940i	$-0.183448\pi$
$311$	−0.929277	−	1.60956i	−0.0526945	−	0.0912695i	−0.891169	+	0.453671i	$0.850114\pi$
$312$	−2.33027	+	0.624394i	−0.131926	+	0.0353494i
$313$	−4.68953	−	0.410281i	−0.265068	−	0.0231904i	−0.0461529	−	0.998934i	$-0.514696\pi$
$313$	−4.68953	−	0.410281i	−0.265068	−	0.0231904i	−0.218915	+	0.975744i	$0.570252\pi$
$314$	−10.2308	+	8.58467i	−0.577358	+	0.484461i
$315$		0			0
$316$	6.58927	−	3.80432i	0.370675	−	0.214010i
$317$	−4.20236	−	9.01199i	−0.236028	−	0.506164i	0.752241	−	0.658888i	$-0.228973\pi$
$317$	−4.20236	−	9.01199i	−0.236028	−	0.506164i	−0.988269	+	0.152725i	$0.951195\pi$
$318$	−2.79370	−	3.98982i	−0.156663	−	0.223738i
$319$	0.268916	+	1.52510i	0.0150564	+	0.0853891i
$320$		0			0
$321$	−5.26676	−	4.41934i	−0.293962	−	0.246663i
$322$	−16.7814	−	16.7814i	−0.935191	−	0.935191i
$323$	−10.9383	−	9.48367i	−0.608622	−	0.527686i
$324$			8.59115i			0.477286i
$325$		0			0
$326$	−4.29737	−	11.8069i	−0.238009	−	0.653925i
$327$	0.0369650	+	0.0258832i	0.00204417	+	0.00143134i
$328$	−3.13336	+	2.19400i	−0.173011	+	0.121143i
$329$	−8.65012	+	23.7660i	−0.476897	+	1.31026i
$330$		0			0
$331$	19.4416	+	11.2246i	1.06861	+	0.616960i	0.927800	−	0.373078i	$-0.121697\pi$
$331$	19.4416	+	11.2246i	1.06861	+	0.616960i	0.140805	+	0.990037i	$0.455031\pi$
$332$	−0.431941	+	4.93711i	−0.0237058	+	0.270959i
$333$	0.0666319	−	0.761606i	0.00365141	−	0.0417358i
$334$	−0.350024	−	0.202086i	−0.0191525	−	0.0110577i
$335$		0			0
$336$	2.57672	−	7.07948i	0.140572	−	0.386217i
$337$	−4.18562	+	2.93080i	−0.228005	+	0.159651i	−0.681997	−	0.731355i	$-0.738888\pi$
$337$	−4.18562	+	2.93080i	−0.228005	+	0.159651i	0.453992	+	0.891006i	$0.349999\pi$
$338$	−8.98748	−	6.29310i	−0.488855	−	0.342300i
$339$	−5.19018	−	14.2599i	−0.281892	−	0.774491i
$340$		0			0
$341$			28.6251i			1.55013i
$342$	−0.569183	−	0.00919827i	−0.0307779	−	0.000497385i
$343$	18.1792	+	18.1792i	0.981587	+	0.981587i
$344$	−8.19756	−	6.87857i	−0.441983	−	0.370867i
$345$		0			0
$346$	−2.76001	−	15.6528i	−0.148379	−	0.841498i
$347$	13.3890	+	19.1215i	0.718761	+	1.02650i	0.997805	+	0.0662190i	$0.0210936\pi$
$347$	13.3890	+	19.1215i	0.718761	+	1.02650i	−0.279044	+	0.960278i	$0.590018\pi$
$348$	0.231324	+	0.496076i	0.0124003	+	0.0265925i
$349$	14.2919	−	8.25144i	0.765028	−	0.441689i	−0.0660700	−	0.997815i	$-0.521046\pi$
$349$	14.2919	−	8.25144i	0.765028	−	0.441689i	0.831098	+	0.556126i	$0.187713\pi$
$350$		0			0
$351$	5.78554	−	4.85464i	0.308809	−	0.259122i
$352$	−4.77435	−	0.417701i	−0.254474	−	0.0222636i
$353$	9.83848	−	2.63621i	0.523650	−	0.140311i	0.0126954	−	0.999919i	$-0.495959\pi$
$353$	9.83848	−	2.63621i	0.523650	−	0.140311i	0.510954	+	0.859608i	$0.329292\pi$
$354$	0.135802	+	0.235215i	0.00721778	+	0.0125016i
$355$		0			0
$356$	−11.7981	−	2.08033i	−0.625299	−	0.110257i
$357$	−14.3519	+	20.4967i	−0.759586	+	1.08480i
$358$	21.4367	+	9.99611i	1.13297	+	0.528311i
$359$	7.38619	−	8.80252i	0.389828	−	0.464579i	−0.535062	−	0.844813i	$-0.679712\pi$
$359$	7.38619	−	8.80252i	0.389828	−	0.464579i	0.924891	+	0.380233i	$0.124156\pi$
$360$		0			0
$361$	−0.613937	+	18.9901i	−0.0323125	+	0.999478i
$362$	15.2800	−	15.2800i	0.803100	−	0.803100i
$363$	−20.1973	+	1.76703i	−1.06008	+	0.0927452i
$364$	−5.95213	+	2.16640i	−0.311976	+	0.113550i
$365$		0			0
$366$	−1.11972	+	6.35025i	−0.0585287	+	0.331933i
$367$	−5.00283	+	2.33286i	−0.261146	+	0.121774i	−0.548782	−	0.835965i	$-0.684908\pi$
$367$	−5.00283	+	2.33286i	−0.261146	+	0.121774i	0.287636	+	0.957740i	$0.407131\pi$
$368$	−1.38108	+	5.15427i	−0.0719940	+	0.268685i
$369$	0.249774	−	0.432622i	0.0130027	−	0.0225214i
$370$		0			0
$371$	−8.22015	−	9.79639i	−0.426769	−	0.508603i
$372$	2.61860	+	9.77274i	0.135768	+	0.506693i
$373$	20.4418	+	5.47737i	1.05844	+	0.283607i	0.745734	−	0.666243i	$-0.232099\pi$
$373$	20.4418	+	5.47737i	1.05844	+	0.283607i	0.312703	+	0.949851i	$0.398765\pi$
$374$	14.9575	+	5.44409i	0.773435	+	0.281507i
$375$		0			0
$376$	5.60019	−	0.987464i	0.288808	−	0.0509246i
$377$	0.194487	−	0.417080i	0.0100166	−	0.0214807i
$378$	2.05560	+	23.4956i	0.105729	+	1.20848i
$379$	18.2787			0.938913			0.469456	−	0.882956i	$-0.344450\pi$
$379$	18.2787			0.938913			0.469456	+	0.882956i	$0.344450\pi$
$380$		0			0
$381$	−21.0518			−1.07852
$382$	1.35162	+	15.4491i	0.0691551	+	0.790447i
$383$	−8.86026	+	19.0009i	−0.452738	+	0.970900i	0.538962	+	0.842330i	$0.318817\pi$
$383$	−8.86026	+	19.0009i	−0.452738	+	0.970900i	−0.991700	+	0.128570i	$0.958961\pi$
$384$	−1.66820	+	0.294148i	−0.0851298	+	0.0150107i
$385$		0			0
$386$	−16.6880	−	6.07393i	−0.849396	−	0.309155i
$387$	1.34991	+	0.361709i	0.0686200	+	0.0183867i
$388$	0.136124	+	0.508022i	0.00691065	+	0.0257909i
$389$	4.95257	+	5.90225i	0.251105	+	0.299256i	0.876842	−	0.480779i	$-0.159646\pi$
$389$	4.95257	+	5.90225i	0.251105	+	0.299256i	−0.625737	+	0.780034i	$0.715201\pi$
$390$		0			0
$391$	8.86131	−	15.3482i	0.448136	−	0.776194i
$392$	3.30786	−	12.3451i	0.167072	−	0.623521i
$393$	−34.6204	+	16.1437i	−1.74637	+	0.814344i
$394$	1.07697	−	6.10777i	0.0542567	−	0.307705i
$395$		0			0
$396$	0.588149	−	0.214069i	0.0295556	−	0.0107574i
$397$	27.0549	−	2.36699i	1.35785	−	0.118796i	0.615142	−	0.788417i	$-0.289099\pi$
$397$	27.0549	−	2.36699i	1.35785	−	0.118796i	0.742703	+	0.669621i	$0.233543\pi$
$398$	11.1257	−	11.1257i	0.557680	−	0.557680i
$399$	32.7562	−	2.33314i	1.63986	−	0.116803i
$400$		0			0
$401$	−7.24488	+	8.63411i	−0.361792	+	0.431167i	−0.915980	−	0.401225i	$-0.868585\pi$
$401$	−7.24488	+	8.63411i	−0.361792	+	0.431167i	0.554187	+	0.832392i	$0.313029\pi$
$402$	−21.2005	−	9.88595i	−1.05738	−	0.493067i
$403$	4.87905	−	6.96800i	0.243043	−	0.347101i
$404$	1.50161	+	0.264774i	0.0747077	+	0.0131730i
$405$		0			0
$406$	0.718565	+	1.24459i	0.0356618	+	0.0617680i
$407$	27.0999	−	7.26140i	1.34329	−	0.359934i
$408$	5.60460	+	0.490339i	0.277469	+	0.0242754i
$409$	−7.33517	+	6.15494i	−0.362701	+	0.304342i	−0.805866	−	0.592098i	$-0.798300\pi$
$409$	−7.33517	+	6.15494i	−0.362701	+	0.304342i	0.443165	+	0.896440i	$0.353855\pi$
$410$		0			0
$411$	−10.3155	+	5.95565i	−0.508826	+	0.293771i
$412$	6.99134	+	14.9930i	0.344439	+	0.738651i
$413$	0.409025	+	0.584149i	0.0201268	+	0.0287441i
$414$	−0.121011	−	0.686289i	−0.00594738	−	0.0337293i
$415$		0			0
$416$	1.09099	+	0.915449i	0.0534902	+	0.0448836i
$417$	10.0835	+	10.0835i	0.493789	+	0.493789i
$418$	−6.82680	−	19.7434i	−0.333910	−	0.965683i
$419$			24.9800i			1.22035i	0.792266	+	0.610175i	$0.208901\pi$
$419$			24.9800i			1.22035i	−0.792266	+	0.610175i	$0.791099\pi$
$420$		0			0
$421$	−13.8212	−	37.9733i	−0.673602	−	1.85071i	−0.500333	−	0.865833i	$-0.666789\pi$
$421$	−13.8212	−	37.9733i	−0.673602	−	1.85071i	−0.173270	−	0.984874i	$-0.555433\pi$
$422$	2.96650	+	2.07717i	0.144407	+	0.101115i
$423$	−0.608342	+	0.425966i	−0.0295786	+	0.0207112i
$424$	−0.983432	+	2.70196i	−0.0477597	+	0.131219i
$425$		0			0
$426$	15.3314	+	8.85160i	0.742810	+	0.428861i
$427$	−1.47557	+	16.8658i	−0.0714077	+	0.816193i
$428$	−0.353745	+	4.04332i	−0.0170989	+	0.195441i
$429$	10.0130	+	5.78099i	0.483431	+	0.279109i
$430$		0			0
$431$	0.137309	−	0.377252i	0.00661392	−	0.0181716i	−0.936342	−	0.351090i	$-0.885811\pi$
$431$	0.137309	−	0.377252i	0.00661392	−	0.0181716i	0.942956	+	0.332918i	$0.108033\pi$
$432$	4.34398	−	3.04168i	0.209000	−	0.146343i
$433$	20.3380	+	14.2408i	0.977383	+	0.684371i	0.949016	−	0.315227i	$-0.102081\pi$
$433$	20.3380	+	14.2408i	0.977383	+	0.684371i	0.0283663	+	0.999598i	$0.490969\pi$
$434$	9.08548	+	24.9621i	0.436117	+	1.19822i
$435$		0			0
$436$		−	0.0266398i		−	0.00127581i
$437$	−22.9684	+	3.66832i	−1.09873	+	0.175479i
$438$	10.8506	+	10.8506i	0.518463	+	0.518463i
$439$	16.0777	+	13.4908i	0.767347	+	0.643881i	0.940028	−	0.341097i	$-0.110799\pi$
$439$	16.0777	+	13.4908i	0.767347	+	0.643881i	−0.172681	+	0.984978i	$0.555243\pi$
$440$		0			0
$441$	0.289836	+	1.64374i	0.0138017	+	0.0782735i
$442$	−2.71308	−	3.87468i	−0.129048	−	0.184300i
$443$	−6.20498	−	13.3066i	−0.294808	−	0.632217i	0.701990	−	0.712187i	$-0.252295\pi$
$443$	−6.20498	−	13.3066i	−0.294808	−	0.632217i	−0.996797	+	0.0799701i	$0.974518\pi$
$444$	8.58777	−	4.95815i	0.407558	−	0.235304i
$445$		0			0
$446$	−11.5839	+	9.72007i	−0.548515	+	0.460259i
$447$	−11.2908	−	0.987816i	−0.534036	−	0.0467221i
$448$	−4.29599	+	1.15111i	−0.202966	+	0.0543847i
$449$	−10.9056	−	18.8891i	−0.514668	−	0.891432i	−0.999855	−	0.0170211i	$-0.994582\pi$
$449$	−10.9056	−	18.8891i	−0.514668	−	0.891432i	0.485187	−	0.874411i	$-0.338752\pi$
$450$		0			0
$451$	18.0537	+	3.18336i	0.850116	+	0.149898i
$452$	−5.13838	+	7.33837i	−0.241689	+	0.345168i
$453$	−2.21754	−	1.03405i	−0.104189	−	0.0485841i
$454$	−4.41404	+	5.26045i	−0.207161	+	0.246885i
$455$		0			0
$456$	−4.13682	−	6.11600i	−0.193724	−	0.286408i
$457$	−23.4401	+	23.4401i	−1.09648	+	1.09648i	−0.101663	+	0.994819i	$0.532416\pi$
$457$	−23.4401	+	23.4401i	−1.09648	+	1.09648i	−0.994819	+	0.101663i	$0.967584\pi$
$458$	−11.3301	+	0.991258i	−0.529422	+	0.0463184i
$459$	−16.5506	+	6.02391i	−0.772514	+	0.281172i
$460$		0			0
$461$	3.54353	−	20.0963i	0.165038	−	0.935979i	−0.783986	−	0.620778i	$-0.786817\pi$
$461$	3.54353	−	20.0963i	0.165038	−	0.935979i	0.949025	−	0.315201i	$-0.102072\pi$
$462$	−32.7236	+	15.2593i	−1.52244	+	0.709925i
$463$	6.78191	−	25.3104i	0.315182	−	1.17627i	−0.608638	−	0.793448i	$-0.708284\pi$
$463$	6.78191	−	25.3104i	0.315182	−	1.17627i	0.923820	−	0.382827i	$-0.125049\pi$
$464$	0.161565	−	0.279838i	0.00750045	−	0.0129912i
$465$		0			0
$466$	−1.25863	−	1.49997i	−0.0583048	−	0.0694850i
$467$	6.92760	+	25.8541i	0.320571	+	1.19639i	0.918690	+	0.394980i	$0.129248\pi$
$467$	6.92760	+	25.8541i	0.320571	+	1.19639i	−0.598119	+	0.801407i	$0.704085\pi$
$468$	−0.179656	−	0.0481388i	−0.00830462	−	0.00222522i
$469$	−57.7138	−	21.0061i	−2.66498	−	0.969972i
$470$		0			0
$471$	22.2794	−	3.92846i	1.02658	−	0.181014i
$472$	0.0677622	−	0.145317i	0.00311901	−	0.00668874i
$473$	4.46988	+	51.0910i	0.205525	+	2.34917i
$474$	−12.8885			−0.591989
$475$		0			0
$476$	14.7715			0.677049
$477$	−0.0327281	−	0.374084i	−0.00149852	−	0.0171281i
$478$	−3.71615	+	7.96932i	−0.169973	+	0.364508i
$479$	32.1223	−	5.66402i	1.46770	−	0.258796i	0.618051	−	0.786138i	$-0.287923\pi$
$479$	32.1223	−	5.66402i	1.46770	−	0.258796i	0.849653	+	0.527343i	$0.176812\pi$
$480$		0			0
$481$	−7.83442	−	2.85150i	−0.357219	−	0.130017i
$482$	−8.68143	−	2.32618i	−0.395428	−	0.105955i
$483$	10.4048	+	38.8314i	0.473436	+	1.76689i
$484$	7.69344	+	9.16868i	0.349702	+	0.416758i
$485$		0			0
$486$	−0.678111	+	1.17452i	−0.0307597	+	0.0532774i
$487$	−5.52726	+	20.6280i	−0.250464	+	0.934744i	0.720094	+	0.693877i	$0.244099\pi$
$487$	−5.52726	+	20.6280i	−0.250464	+	0.934744i	−0.970558	+	0.240868i	$0.922568\pi$
$488$	3.45000	−	1.60876i	0.156174	−	0.0728252i
$489$	−3.69587	+	20.9603i	−0.167133	+	0.947860i
$490$		0			0
$491$	−22.8924	+	8.33216i	−1.03312	+	0.376025i	−0.802268	−	0.596963i	$-0.796374\pi$
$491$	−22.8924	+	8.33216i	−1.03312	+	0.376025i	−0.230853	+	0.972989i	$0.574152\pi$
$492$	6.45484	−	0.564725i	0.291007	−	0.0254598i
$493$	−0.758867	+	0.758867i	−0.0341777	+	0.0341777i
$494$	−1.70340	+	5.96961i	−0.0766396	+	0.268586i
$495$		0			0
$496$	3.83923	−	4.57542i	0.172387	−	0.205442i
$497$	42.1261	+	19.6437i	1.88961	+	0.881141i
$498$	4.81521	−	6.87684i	0.215775	−	0.308158i
$499$	5.63797	+	0.994126i	0.252390	+	0.0445032i	0.298412	−	0.954437i	$-0.403543\pi$
$499$	5.63797	+	0.994126i	0.252390	+	0.0445032i	−0.0460215	+	0.998940i	$0.514654\pi$
$500$		0			0
$501$	0.342320	+	0.592916i	0.0152937	+	0.0264895i
$502$	14.4552	−	3.87326i	0.645167	−	0.172872i
$503$	−12.4497	−	1.08921i	−0.555106	−	0.0485655i	−0.193849	−	0.981031i	$-0.562097\pi$
$503$	−12.4497	−	1.08921i	−0.555106	−	0.0485655i	−0.361258	+	0.932466i	$0.617653\pi$
$504$	0.444944	−	0.373353i	0.0198194	−	0.0166304i
$505$		0			0
$506$	22.1475	−	12.7868i	0.984575	−	0.568445i
$507$	7.85448	+	16.8440i	0.348830	+	0.748068i
$508$	7.12829	+	10.1802i	0.316267	+	0.451676i
$509$	3.15829	+	17.9115i	0.139989	+	0.793915i	0.971255	+	0.238041i	$0.0765052\pi$
$509$	3.15829	+	17.9115i	0.139989	+	0.793915i	−0.831267	+	0.555874i	$0.812384\pi$
$510$		0			0
$511$	30.8637	+	25.8977i	1.36533	+	1.14565i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	19.8291	+	11.8796i	0.875475	+	0.524498i
$514$		−	13.9841i		−	0.616811i
$515$		0			0
$516$	6.19980	+	17.0338i	0.272931	+	0.749872i
$517$	−22.3247	−	15.6319i	−0.981838	−	0.687491i
$518$	21.3274	−	14.9336i	0.937073	−	0.656145i
$519$	−9.20847	+	25.3000i	−0.404207	+	1.11055i
$520$		0			0
$521$	16.9493	+	9.78567i	0.742561	+	0.428718i	0.823000	−	0.568042i	$-0.192299\pi$
$521$	16.9493	+	9.78567i	0.742561	+	0.428718i	−0.0804386	+	0.996760i	$0.525632\pi$
$522$	−0.00367794	+	0.0420391i	−0.000160979	+	0.00184000i
$523$	1.86071	−	21.2680i	0.0813630	−	0.929983i	−0.840333	−	0.542070i	$-0.817641\pi$
$523$	1.86071	−	21.2680i	0.0813630	−	0.929983i	0.921696	−	0.387913i	$-0.126804\pi$
$524$	19.5295	+	11.2754i	0.853150	+	0.492566i
$525$		0			0
$526$	6.22139	−	17.0931i	0.271265	−	0.745295i
$527$	−16.2497	+	11.3782i	−0.707848	+	0.495641i
$528$	6.65013	+	4.65647i	0.289410	+	0.202647i
$529$	−1.87219	−	5.14381i	−0.0813997	−	0.223644i
$530$		0			0
$531$			0.0209398i			0.000908708i
$532$	−12.2197	−	15.0502i	−0.529792	−	0.652510i
$533$	−3.85210	−	3.85210i	−0.166853	−	0.166853i
$534$	15.5457	+	13.0444i	0.672729	+	0.564487i
$535$		0			0
$536$	2.39798	+	13.5996i	0.103577	+	0.587413i
$537$	−22.9810	−	32.8203i	−0.991705	−	1.41630i
$538$	2.15189	+	4.61475i	0.0927746	+	0.198956i
$539$	−53.0458	+	30.6260i	−2.28484	+	1.31916i
$540$		0			0
$541$	−8.39604	+	7.04512i	−0.360974	+	0.302893i	−0.805179	−	0.593032i	$-0.797931\pi$
$541$	−8.39604	+	7.04512i	−0.360974	+	0.302893i	0.444205	+	0.895925i	$0.353486\pi$
$542$	9.14939	+	0.800468i	0.393000	+	0.0343830i
$543$	−35.3572	+	9.47394i	−1.51732	+	0.406566i
$544$	−1.66064	−	2.87630i	−0.0711991	−	0.123321i
$545$		0			0
$546$	10.5666	+	1.86317i	0.452207	+	0.0797363i
$547$	16.2464	−	23.2022i	0.694645	−	0.992057i	−0.304571	−	0.952489i	$-0.598513\pi$
$547$	16.2464	−	23.2022i	0.694645	−	0.992057i	0.999217	−	0.0395671i	$-0.0125979\pi$
$548$	6.37293	+	2.97175i	0.272238	+	0.126947i
$549$	−0.319553	+	0.380828i	−0.0136382	+	0.0162534i
$550$		0			0
$551$	1.40096	+	0.145414i	0.0596830	+	0.00619485i
$552$	6.39153	−	6.39153i	0.272041	−	0.272041i
$553$	−33.7109	+	2.94932i	−1.43353	+	0.125418i
$554$	8.73498	−	3.17927i	0.371114	−	0.135074i
$555$		0			0
$556$	1.46184	−	8.29048i	0.0619957	−	0.351595i
$557$	−16.7187	+	7.79604i	−0.708392	+	0.330329i	−0.743204	−	0.669065i	$-0.766695\pi$
$557$	−16.7187	+	7.79604i	−0.708392	+	0.330329i	0.0348115	+	0.999394i	$0.488917\pi$
$558$	−0.201885	+	0.753447i	−0.00854649	+	0.0318959i
$559$	7.62022	−	13.1986i	0.322301	−	0.558241i
$560$		0			0
$561$	−17.3315	−	20.6549i	−0.731738	−	0.872052i
$562$	−1.43557	−	5.35763i	−0.0605560	−	0.225998i
$563$	−27.9700	−	7.49454i	−1.17880	−	0.315857i	−0.384347	−	0.923189i	$-0.625573\pi$
$563$	−27.9700	−	7.49454i	−1.17880	−	0.315857i	−0.794448	+	0.607332i	$0.792240\pi$
$564$	−9.05175	−	3.29457i	−0.381147	−	0.138726i
$565$		0			0
$566$	15.4399	−	2.72246i	0.648986	−	0.114434i
$567$	16.1480	−	34.6295i	0.678153	−	1.45430i
$568$	−0.910861	−	10.4112i	−0.0382189	−	0.436844i
$569$	−20.4117			−0.855701			−0.427851	−	0.903850i	$-0.640729\pi$
$569$	−20.4117			−0.855701			−0.427851	+	0.903850i	$0.640729\pi$
$570$		0			0
$571$	−18.2707			−0.764606			−0.382303	−	0.924037i	$-0.624869\pi$
$571$	−18.2707			−0.764606			−0.382303	+	0.924037i	$0.624869\pi$
$572$	−0.594884	−	6.79956i	−0.0248734	−	0.284304i
$573$	11.1021	−	23.8085i	0.463796	−	0.994613i
$574$	16.7539	−	2.95417i	0.699295	−	0.123305i
$575$		0			0
$576$	−0.122721	−	0.0446667i	−0.00511336	−	0.00186111i
$577$	−3.45553	−	0.925905i	−0.143855	−	0.0385459i	0.186173	−	0.982517i	$-0.440392\pi$
$577$	−3.45553	−	0.925905i	−0.143855	−	0.0385459i	−0.330028	+	0.943971i	$0.607058\pi$
$578$	−1.54493	−	5.76577i	−0.0642607	−	0.239824i
$579$	19.3366	+	23.0445i	0.803603	+	0.957697i
$580$		0			0
$581$	11.0209	−	19.0888i	0.457225	−	0.791937i
$582$	0.230585	−	0.860554i	0.00955804	−	0.0356711i
$583$	12.4893	−	5.82386i	0.517254	−	0.241199i
$584$	1.57306	−	8.92124i	0.0650935	−	0.369164i
$585$		0			0
$586$	−17.4530	+	6.35238i	−0.720978	+	0.262414i
$587$	−24.8886	+	2.17747i	−1.02726	+	0.0898739i	−0.588310	−	0.808636i	$-0.700206\pi$
$587$	−24.8886	+	2.17747i	−1.02726	+	0.0898739i	−0.438954	+	0.898510i	$0.644651\pi$
$588$	−15.3085	+	15.3085i	−0.631310	+	0.631310i
$589$	25.0355	+	7.14375i	1.03157	+	0.294353i
$590$		0			0
$591$	−6.75297	+	8.04787i	−0.277780	+	0.331045i
$592$	−5.30554	−	2.47402i	−0.218057	−	0.101681i
$593$	8.64055	−	12.3400i	0.354825	−	0.506743i	−0.601570	−	0.798820i	$-0.705458\pi$
$593$	8.64055	−	12.3400i	0.354825	−	0.506743i	0.956395	+	0.292078i	$0.0943466\pi$
$594$	−25.0290	−	4.41329i	−1.02695	−	0.181080i
$595$		0			0
$596$	3.34545	+	5.79449i	0.137035	+	0.237351i
$597$	−25.7443	+	6.89816i	−1.05364	+	0.282323i
$598$	−7.57068	−	0.662349i	−0.309588	−	0.0270854i
$599$	−3.36904	+	2.82696i	−0.137655	+	0.115507i	−0.709016	−	0.705193i	$-0.750860\pi$
$599$	−3.36904	+	2.82696i	−0.137655	+	0.115507i	0.571360	+	0.820699i	$0.306416\pi$
$600$		0			0
$601$	−36.2698	+	20.9404i	−1.47947	+	0.854175i	−0.999730	−	0.0232332i	$-0.992604\pi$
$601$	−36.2698	+	20.9404i	−1.47947	+	0.854175i	−0.479744	+	0.877408i	$0.659271\pi$
$602$	20.1140	+	43.1346i	0.819785	+	1.75803i
$603$	−1.03442	−	1.47731i	−0.0421249	−	0.0601607i
$604$	0.250824	+	1.42250i	0.0102059	+	0.0578805i
$605$		0			0
$606$	−1.97858	−	1.66023i	−0.0803745	−	0.0674422i
$607$	13.0240	+	13.0240i	0.528629	+	0.528629i	0.920163	−	0.391535i	$-0.128056\pi$
$607$	13.0240	+	13.0240i	0.528629	+	0.528629i	−0.391535	+	0.920163i	$0.628056\pi$
$608$	−1.55682	+	4.07140i	−0.0631375	+	0.165117i
$609$		−	2.43440i		−	0.0986468i
$610$		0			0
$611$	2.76993	+	7.61033i	0.112060	+	0.307881i
$612$	0.355305	+	0.248787i	0.0143623	+	0.0100566i
$613$	28.6179	−	20.0385i	1.15587	−	0.809346i	0.171448	−	0.985193i	$-0.445155\pi$
$613$	28.6179	−	20.0385i	1.15587	−	0.809346i	0.984417	+	0.175848i	$0.0562666\pi$
$614$	8.70442	−	23.9152i	0.351282	−	0.965139i
$615$		0			0
$616$	18.4595	+	10.6576i	0.743754	+	0.429407i
$617$	2.35778	−	26.9495i	0.0949206	−	1.08495i	−0.788079	−	0.615574i	$-0.788924\pi$
$617$	2.35778	−	26.9495i	0.0949206	−	1.08495i	0.883000	−	0.469373i	$-0.155520\pi$
$618$	2.44233	−	27.9159i	0.0982449	−	1.12294i
$619$	−31.1755	−	17.9992i	−1.25305	−	0.723449i	−0.281336	−	0.959609i	$-0.590778\pi$
$619$	−31.1755	−	17.9992i	−1.25305	−	0.723449i	−0.971714	+	0.236160i	$0.924111\pi$
$620$		0			0
$621$	−9.67828	+	26.5909i	−0.388376	+	1.06705i
$622$	1.52244	−	1.06602i	0.0610442	−	0.0427436i
$623$	43.6461	+	30.5613i	1.74864	+	1.22441i
$624$	−0.825115	−	2.26698i	−0.0330310	−	0.0907520i
$625$		0			0
$626$		−	4.70744i		−	0.188147i
$627$	−6.70717	+	34.7454i	−0.267859	+	1.38760i
$628$	−9.44367	−	9.44367i	−0.376844	−	0.376844i
$629$	14.8940	+	12.4976i	0.593864	+	0.498311i
$630$		0			0
$631$	3.01054	+	17.0736i	0.119848	+	0.679691i	0.984235	+	0.176864i	$0.0565954\pi$
$631$	3.01054	+	17.0736i	0.119848	+	0.679691i	−0.864387	+	0.502826i	$0.832294\pi$
$632$	4.36413	+	6.23263i	0.173596	+	0.247921i
$633$	−2.59253	−	5.55970i	−0.103044	−	0.220978i
$634$	8.61143	−	4.97181i	0.342004	−	0.197456i
$635$		0			0
$636$	3.73115	−	3.13080i	0.147950	−	0.124144i
$637$	18.1327	+	1.58640i	0.718442	+	0.0628556i
$638$	−1.49586	+	0.400814i	−0.0592215	+	0.0158684i
$639$	0.682430	+	1.18200i	0.0269965	+	0.0467593i
$640$		0			0
$641$	22.5681	+	3.97937i	0.891388	+	0.157176i	0.600541	−	0.799594i	$-0.294952\pi$
$641$	22.5681	+	3.97937i	0.891388	+	0.157176i	0.290847	+	0.956770i	$0.406063\pi$
$642$	3.94349	−	5.63189i	0.155637	−	0.222273i
$643$	−13.1790	−	6.14546i	−0.519728	−	0.242353i	0.145009	−	0.989430i	$-0.453679\pi$
$643$	−13.1790	−	6.14546i	−0.519728	−	0.242353i	−0.664737	+	0.747077i	$0.731457\pi$
$644$	15.2549	−	18.1801i	0.601129	−	0.716398i
$645$		0			0
$646$	8.49425	−	11.7232i	0.334202	−	0.461243i
$647$	29.3260	−	29.3260i	1.15292	−	1.15292i	0.166960	−	0.985964i	$-0.446605\pi$
$647$	29.3260	−	29.3260i	1.15292	−	1.15292i	0.985964	−	0.166960i	$-0.0533951\pi$
$648$	−8.55846	+	0.748768i	−0.336208	+	0.0294144i
$649$	−0.722096	+	0.262821i	−0.0283448	+	0.0103166i
$650$		0			0
$651$	7.81380	−	44.3143i	0.306247	−	1.73681i
$652$	11.3875	−	5.31006i	0.445967	−	0.207958i
$653$	3.88208	−	14.4881i	0.151918	−	0.566964i	−0.847432	−	0.530904i	$-0.821852\pi$
$653$	3.88208	−	14.4881i	0.151918	−	0.566964i	0.999350	−	0.0360603i	$-0.0114809\pi$
$654$	−0.0225630	+	0.0390802i	−0.000882282	+	0.00152816i
$655$		0			0
$656$	−2.45874	−	2.93021i	−0.0959977	−	0.114406i
$657$	0.306198	+	1.14275i	0.0119459	+	0.0445828i
$658$	−24.4295	−	6.54586i	−0.952360	−	0.255184i
$659$	39.7090	+	14.4529i	1.54684	+	0.563005i	0.967675	−	0.252202i	$-0.0811546\pi$
$659$	39.7090	+	14.4529i	1.54684	+	0.563005i	0.579170	+	0.815207i	$0.303377\pi$
$660$		0			0
$661$	15.1726	−	2.67534i	0.590146	−	0.104059i	0.129403	−	0.991592i	$-0.458694\pi$
$661$	15.1726	−	2.67534i	0.590146	−	0.104059i	0.460743	+	0.887534i	$0.347583\pi$
$662$	−9.48744	+	20.3459i	−0.368740	+	0.790765i
$663$	0.698334	+	7.98199i	0.0271210	+	0.309995i
$664$	−4.95597			−0.192329
$665$		0			0
$666$	0.764516			0.0296244
$667$	0.150278	+	1.71769i	0.00581880	+	0.0665092i
$668$	0.170811	−	0.366305i	0.00660887	−	0.0141728i
$669$	25.2261	−	4.44803i	0.975296	−	0.171971i
$670$		0			0
$671$	−17.1435	−	6.23971i	−0.661816	−	0.240881i
$672$	7.27711	+	1.94990i	0.280721	+	0.0752189i
$673$	−4.09227	−	15.2726i	−0.157746	−	0.588714i	−0.998855	−	0.0478488i	$-0.984763\pi$
$673$	−4.09227	−	15.2726i	−0.157746	−	0.588714i	0.841109	−	0.540866i	$-0.181903\pi$
$674$	−3.28445	−	3.91425i	−0.126512	−	0.150771i
$675$		0			0
$676$	5.48585	−	9.50176i	0.210994	−	0.365452i
$677$	0.441692	−	1.64842i	0.0169756	−	0.0633537i	−0.956918	−	0.290357i	$-0.906226\pi$
$677$	0.441692	−	1.64842i	0.0169756	−	0.0633537i	0.973894	+	0.227003i	$0.0728927\pi$
$678$	13.7533	−	6.41326i	0.528192	−	0.246300i
$679$	0.406189	−	2.30361i	0.0155881	−	0.0884045i
$680$		0			0
$681$	10.9308	−	3.97847i	0.418868	−	0.152455i
$682$	−28.5161	+	2.49484i	−1.09194	+	0.0955323i
$683$	29.8378	−	29.8378i	1.14171	−	1.14171i	0.153575	−	0.988137i	$-0.450921\pi$
$683$	29.8378	−	29.8378i	1.14171	−	1.14171i	0.988137	−	0.153575i	$-0.0490786\pi$
$684$	−0.0404443	−	0.567819i	−0.00154643	−	0.0217111i
$685$		0			0
$686$	−16.5256	+	19.6945i	−0.630952	+	0.751939i
$687$	17.4607	+	8.14207i	0.666168	+	0.310639i
$688$	6.13793	−	8.76587i	0.234006	−	0.334196i
$689$	−4.03284	−	0.711098i	−0.153639	−	0.0270907i
$690$		0			0
$691$	−8.52118	−	14.7591i	−0.324161	−	0.561464i	0.657181	−	0.753733i	$-0.271749\pi$
$691$	−8.52118	−	14.7591i	−0.324161	−	0.561464i	−0.981342	+	0.192269i	$0.938415\pi$
$692$	15.3527	−	4.11373i	0.583620	−	0.156381i
$693$	−2.77310	−	0.242615i	−0.105341	−	0.00921618i
$694$	−17.8818	+	15.0046i	−0.678785	+	0.569568i
$695$		0			0
$696$	−0.474027	+	0.273680i	−0.0179679	+	0.0103738i
$697$	5.36906	+	11.5140i	0.203367	+	0.436123i
$698$	9.46566	+	13.5184i	0.358280	+	0.511678i
$699$	0.575965	+	3.26646i	0.0217850	+	0.123549i
$700$		0			0
$701$	26.0039	+	21.8198i	0.982153	+	0.824124i	0.984413	−	0.175873i	$-0.0562749\pi$
$701$	26.0039	+	21.8198i	0.982153	+	0.824124i	−0.00226004	+	0.999997i	$0.500719\pi$
$702$	5.34041	+	5.34041i	0.201561	+	0.201561i
$703$	0.412314	−	25.5137i	0.0155507	−	0.962269i
$704$		−	4.79258i		−	0.180627i
$705$		0			0
$706$	3.48366	+	9.57128i	0.131109	+	0.360220i
$707$	−5.55506	−	3.88970i	−0.208920	−	0.146287i
$708$	−0.222485	+	0.155785i	−0.00836148	+	0.00585477i
$709$	10.6981	−	29.3928i	0.401776	−	1.10387i	−0.559631	−	0.828742i	$-0.689057\pi$
$709$	10.6981	−	29.3928i	0.401776	−	1.10387i	0.961407	−	0.275129i	$-0.0887206\pi$
$710$		0			0
$711$	−0.860537	−	0.496831i	−0.0322727	−	0.0186326i
$712$	1.04414	−	11.9345i	0.0391306	−	0.447265i
$713$	−2.77777	+	31.7501i	−0.104028	+	1.18905i
$714$	−21.6696	−	12.5109i	−0.810963	−	0.468210i
$715$		0			0
$716$	−8.08974	+	22.2264i	−0.302328	+	0.830638i
$717$	12.2013	−	8.54343i	0.455665	−	0.319060i
$718$	9.41277	+	6.59090i	0.351282	+	0.245970i
$719$	−15.7438	−	43.2557i	−0.587145	−	1.61317i	−0.775698	−	0.631104i	$-0.782602\pi$
$719$	−15.7438	−	43.2557i	−0.587145	−	1.61317i	0.188554	−	0.982063i	$-0.439620\pi$
$720$		0			0
$721$		−	73.5753i		−	2.74009i
$722$	−18.9713	+	1.04349i	−0.706040	+	0.0388348i
$723$	10.7654	+	10.7654i	0.400368	+	0.400368i
$724$	16.5536	+	13.8901i	0.615210	+	0.516223i
$725$		0			0
$726$	−3.52062	−	19.9664i	−0.130662	−	0.741023i
$727$	−0.794674	−	1.13491i	−0.0294728	−	0.0420916i	0.804145	−	0.594433i	$-0.202623\pi$
$727$	−0.794674	−	1.13491i	−0.0294728	−	0.0420916i	−0.833618	+	0.552341i	$0.813735\pi$
$728$	−2.67692	−	5.74066i	−0.0992131	−	0.212763i
$729$	24.3100	−	14.0354i	0.900372	−	0.519830i
$730$		0			0
$731$	−27.2263	+	22.8456i	−1.00700	+	0.844974i
$732$	−6.42367	−	0.561998i	−0.237426	−	0.0207721i
$733$	18.9180	−	5.06907i	0.698753	−	0.187230i	0.108081	−	0.994142i	$-0.465529\pi$
$733$	18.9180	−	5.06907i	0.698753	−	0.187230i	0.590672	+	0.806912i	$0.298863\pi$
$734$	−2.76001	−	4.78047i	−0.101874	−	0.176450i
$735$		0			0
$736$	−5.25503	−	0.926603i	−0.193703	−	0.0341551i
$737$	37.9608	−	54.2137i	1.39830	−	1.99699i
$738$	0.452745	+	0.211118i	0.0166658	+	0.00777137i
$739$	8.43050	−	10.0471i	0.310121	−	0.369588i	−0.588361	−	0.808598i	$-0.700227\pi$
$739$	8.43050	−	10.0471i	0.310121	−	0.369588i	0.898482	+	0.439011i	$0.144671\pi$
$740$		0			0
$741$	7.55492	−	7.31462i	0.277537	−	0.268709i
$742$	9.04268	−	9.04268i	0.331967	−	0.331967i
$743$	27.1591	−	2.37611i	0.996370	−	0.0871710i	0.422710	−	0.906265i	$-0.361079\pi$
$743$	27.1591	−	2.37611i	0.996370	−	0.0871710i	0.573659	+	0.819094i	$0.305523\pi$
$744$	−9.50732	+	3.46038i	−0.348555	+	0.126864i
$745$		0			0
$746$	−3.67490	+	20.8414i	−0.134548	+	0.763059i
$747$	0.586592	−	0.273532i	0.0214623	−	0.0100080i
$748$	−4.11974	+	15.3751i	−0.150633	+	0.562169i
$749$	9.02575	−	15.6331i	0.329794	−	0.571220i
$750$		0			0
$751$	−26.4784	−	31.5557i	−0.966211	−	1.15149i	−0.988422	−	0.151732i	$-0.951515\pi$
$751$	−26.4784	−	31.5557i	−0.966211	−	1.15149i	0.0222110	−	0.999753i	$-0.492929\pi$
$752$	1.47179	+	5.49281i	0.0536708	+	0.200302i
$753$	−24.4861	−	6.56103i	−0.892324	−	0.239097i
$754$	0.432443	+	0.157397i	0.0157487	+	0.00573204i
$755$		0			0
$756$	−23.2270	+	4.09555i	−0.844759	+	0.148954i
$757$	−7.12388	+	15.2772i	−0.258922	+	0.555260i	−0.992198	−	0.124671i	$-0.960212\pi$
$757$	−7.12388	+	15.2772i	−0.258922	+	0.555260i	0.733276	+	0.679931i	$0.237990\pi$
$758$	1.59309	+	18.2091i	0.0578637	+	0.661385i
$759$	−43.3201			−1.57242
$760$		0			0
$761$	43.9450			1.59300			0.796502	−	0.604636i	$-0.206681\pi$
$761$	43.9450			1.59300			0.796502	+	0.604636i	$0.206681\pi$
$762$	−1.83479	−	20.9717i	−0.0664673	−	0.759725i
$763$	−0.0500724	+	0.107381i	−0.00181274	+	0.00388744i
$764$	−15.2725	+	2.69296i	−0.552541	+	0.0974280i
$765$		0			0
$766$	−19.7008	−	7.17051i	−0.711819	−	0.259081i
$767$	0.220572	+	0.0591020i	0.00796439	+	0.00213405i
$768$	−0.438422	−	1.63621i	−0.0158202	−	0.0590417i
$769$	22.9008	+	27.2921i	0.825824	+	0.984179i	1.00000		0.000535705i	$-0.000170520\pi$
$769$	22.9008	+	27.2921i	0.825824	+	0.984179i	−0.174176	+	0.984715i	$0.555726\pi$
$770$		0			0
$771$	−11.8440	+	20.5145i	−0.426552	+	0.738810i
$772$	4.59636	−	17.1538i	0.165427	−	0.617381i
$773$	−14.2068	+	6.62473i	−0.510982	+	0.238275i	−0.660969	−	0.750413i	$-0.729855\pi$
$773$	−14.2068	+	6.62473i	−0.510982	+	0.238275i	0.149987	+	0.988688i	$0.452077\pi$
$774$	−0.242679	+	1.37630i	−0.00872293	+	0.0494702i
$775$		0			0
$776$	−0.494224	+	0.179883i	−0.0177416	+	0.00645742i
$777$	−43.9353	+	3.84384i	−1.57617	+	0.137897i
$778$	−5.44814	+	5.44814i	−0.195325	+	0.195325i
$779$	7.28970	−	14.9953i	0.261181	−	0.537264i
$780$		0			0
$781$	−32.1954	+	38.3689i	−1.15204	+	1.37295i
$782$	16.0621	+	7.48990i	0.574381	+	0.267838i
$783$	0.982858	−	1.40367i	0.0351245	−	0.0501630i
$784$	12.5864	+	2.21932i	0.449515	+	0.0792616i
$785$		0			0
$786$	−19.0997	−	33.0816i	−0.681263	−	1.17998i
$787$	−19.8817	+	5.32728i	−0.708705	+	0.189897i	−0.595126	−	0.803632i	$-0.702898\pi$
$787$	−19.8817	+	5.32728i	−0.708705	+	0.189897i	−0.113579	+	0.993529i	$0.536231\pi$
$788$	6.17839	+	0.540539i	0.220096	+	0.0192559i
$789$	−23.6040	+	19.8061i	−0.840324	+	0.705115i
$790$		0			0
$791$	34.5052	−	19.9216i	1.22686	−	0.708331i
$792$	0.264515	+	0.567254i	0.00939913	+	0.0201565i
$793$	3.10958	+	4.44094i	0.110424	+	0.157702i
$794$	4.71597	+	26.7456i	0.167364	+	0.949167i
$795$		0			0
$796$	12.0530	+	10.1137i	0.427207	+	0.358470i
$797$	−19.7495	−	19.7495i	−0.699563	−	0.699563i	0.264753	−	0.964316i	$-0.414709\pi$
$797$	−19.7495	−	19.7495i	−0.699563	−	0.699563i	−0.964316	+	0.264753i	$0.914709\pi$
$798$	5.17915	+	32.4282i	0.183340	+	1.14795i
$799$		−	18.8867i		−	0.668162i
$800$		0			0
$801$	0.535112	+	1.47021i	0.0189073	+	0.0519473i
$802$	−9.23269	−	6.46480i	−0.326018	−	0.228280i
$803$	−35.5638	+	24.9020i	−1.25502	+	0.878774i
$804$	8.00059	−	21.9814i	0.282159	−	0.775226i
$805$		0			0
$806$	7.36672	+	4.25318i	0.259482	+	0.149812i
$807$	0.751733	−	8.59235i	0.0264623	−	0.302465i
$808$	−0.132893	+	1.51897i	−0.00467515	+	0.0534372i
$809$	11.6091	+	6.70251i	0.408154	+	0.235648i	0.689996	−	0.723813i	$-0.257612\pi$
$809$	11.6091	+	6.70251i	0.408154	+	0.235648i	−0.281842	+	0.959461i	$0.590945\pi$
$810$		0			0
$811$	9.51193	−	26.1338i	0.334009	−	0.917683i	−0.653048	−	0.757316i	$-0.726510\pi$
$811$	9.51193	−	26.1338i	0.334009	−	0.917683i	0.987058	−	0.160366i	$-0.0512676\pi$
$812$	−1.17723	+	0.824304i	−0.0413126	+	0.0289274i
$813$	−12.7441	−	8.92350i	−0.446954	−	0.312961i
$814$	9.59568	+	26.3639i	0.336328	+	0.924054i
$815$		0			0
$816$			5.62600i			0.196950i
$817$	45.7997	+	8.84106i	1.60233	+	0.309310i
$818$	−6.77082	−	6.77082i	−0.236736	−	0.236736i
$819$	0.633684	+	0.531724i	0.0221427	+	0.0185799i
$820$		0			0
$821$	−0.697502	−	3.95573i	−0.0243430	−	0.138056i	0.970214	−	0.242249i	$-0.0778851\pi$
$821$	−0.697502	−	3.95573i	−0.0243430	−	0.138056i	−0.994557	+	0.104193i	$0.966774\pi$
$822$	−6.83205	−	9.75717i	−0.238295	−	0.340320i
$823$	−12.4093	−	26.6119i	−0.432562	−	0.927633i	−0.994913	−	0.100734i	$-0.967881\pi$
$823$	−12.4093	−	26.6119i	−0.432562	−	0.927633i	0.562351	−	0.826899i	$-0.309897\pi$
$824$	−14.3266	+	8.27146i	−0.499091	+	0.288150i
$825$		0			0
$826$	−0.546277	+	0.458381i	−0.0190074	+	0.0159491i
$827$	−48.3363	−	4.22887i	−1.68082	−	0.147052i	−0.793611	−	0.608426i	$-0.791801\pi$
$827$	−48.3363	−	4.22887i	−1.68082	−	0.147052i	−0.887206	+	0.461374i	$0.847357\pi$
$828$	0.673131	−	0.180365i	0.0233929	−	0.00626811i
$829$	−3.36973	−	5.83654i	−0.117035	−	0.202711i	0.801556	−	0.597920i	$-0.204006\pi$
$829$	−3.36973	−	5.83654i	−0.117035	−	0.202711i	−0.918592	+	0.395208i	$0.870672\pi$
$830$		0			0
$831$	−15.5068	−	2.73427i	−0.537926	−	0.0948509i
$832$	−0.816880	+	1.16663i	−0.0283202	+	0.0404455i
$833$	−38.4707	−	17.9392i	−1.33293	−	0.621556i
$834$	−9.16625	+	10.9239i	−0.317401	+	0.378264i
$835$		0			0
$836$	19.0733	−	8.52158i	0.659664	−	0.294725i
$837$	22.3967	−	22.3967i	0.774144	−	0.774144i
$838$	−24.8849	+	2.17715i	−0.859635	+	0.0752083i
$839$	12.1910	−	4.43714i	0.420878	−	0.153187i	−0.122894	−	0.992420i	$-0.539218\pi$
$839$	12.1910	−	4.43714i	0.420878	−	0.153187i	0.543773	+	0.839233i	$0.316995\pi$
$840$		0			0
$841$	−5.01767	+	28.4566i	−0.173023	+	0.981262i
$842$	36.6242	−	17.0782i	1.26215	−	0.588553i
$843$	−2.43176	+	9.07546i	−0.0837543	+	0.312575i
$844$	−1.81071	+	3.13625i	−0.0623273	+	0.107954i
$845$		0			0
$846$	−0.477365	−	0.568902i	−0.0164121	−	0.0195592i
$847$	−13.7774	−	51.4181i	−0.473399	−	1.76675i
$848$	−2.77739	−	0.744199i	−0.0953759	−	0.0255559i
$849$	−24.9559	−	9.08321i	−0.856485	−	0.311735i
$850$		0			0
$851$	30.7630	−	5.42436i	1.05454	−	0.185944i
$852$	−7.48170	+	16.0445i	−0.256319	+	0.549677i
$853$	−0.496886	−	5.67943i	−0.0170130	−	0.194460i	−0.999945	−	0.0104904i	$-0.996661\pi$
$853$	−0.496886	−	5.67943i	−0.0170130	−	0.194460i	0.982932	−	0.183970i	$-0.0588948\pi$
$854$	−16.9302			−0.579340
$855$		0			0
$856$	−4.05877			−0.138726
$857$	4.02616	+	46.0192i	0.137531	+	1.57199i	0.680826	+	0.732445i	$0.261621\pi$
$857$	4.02616	+	46.0192i	0.137531	+	1.57199i	−0.543295	+	0.839542i	$0.682824\pi$
$858$	−4.88631	+	10.4787i	−0.166816	+	0.357738i
$859$	−24.0660	+	4.24349i	−0.821122	+	0.144786i	−0.568399	−	0.822753i	$-0.692437\pi$
$859$	−24.0660	+	4.24349i	−0.821122	+	0.144786i	−0.252723	+	0.967539i	$0.581326\pi$
$860$		0			0
$861$	−27.0799	−	9.85627i	−0.922879	−	0.335901i
$862$	0.387784	+	0.103906i	0.0132080	+	0.00353907i
$863$	4.31769	+	16.1138i	0.146976	+	0.548522i	0.999659	+	0.0260938i	$0.00830687\pi$
$863$	4.31769	+	16.1138i	0.146976	+	0.548522i	−0.852684	+	0.522428i	$0.825026\pi$
$864$	3.40871	+	4.06235i	0.115967	+	0.138204i
$865$		0			0
$866$	−12.4141	+	21.5018i	−0.421847	+	0.730661i
$867$	−2.61701	+	9.76682i	−0.0888783	+	0.331698i
$868$	−24.0753	+	11.2265i	−0.817169	+	0.381052i
$869$	6.33209	−	35.9110i	0.214801	−	1.21820i
$870$		0			0
$871$	−18.4811	+	6.72656i	−0.626207	+	0.227921i
$872$	0.0265384	−	0.00232181i	0.000898704	−	7.86264e-5i
$873$	0.0485686	−	0.0485686i	0.00164380	−	0.00164380i
$874$	−5.65619	−	22.5613i	−0.191323	−	0.763147i
$875$		0			0
$876$	−9.86364	+	11.7550i	−0.333261	+	0.397166i
$877$	29.9631	+	13.9720i	1.01178	+	0.471802i	0.856543	−	0.516075i	$-0.172608\pi$
$877$	29.9631	+	13.9720i	1.01178	+	0.471802i	0.155239	+	0.987877i	$0.450385\pi$
$878$	−12.0382	+	17.1923i	−0.406269	+	0.580213i
$879$	30.9836	+	5.46325i	1.04505	+	0.184271i
$880$		0			0
$881$	14.9569	+	25.9062i	0.503912	+	0.872802i	0.999990	+	0.00452339i	$0.00143985\pi$
$881$	14.9569	+	25.9062i	0.503912	+	0.872802i	−0.496078	+	0.868278i	$0.665227\pi$
$882$	−1.61223	+	0.431995i	−0.0542865	+	0.0145460i
$883$	−15.5984	−	1.36468i	−0.524928	−	0.0459253i	−0.178388	−	0.983960i	$-0.557088\pi$
$883$	−15.5984	−	1.36468i	−0.524928	−	0.0459253i	−0.346540	+	0.938035i	$0.612644\pi$
$884$	3.62347	−	3.04046i	0.121871	−	0.102262i
$885$		0			0
$886$	12.7152	−	7.34112i	0.427175	−	0.246630i
$887$	19.7890	+	42.4376i	0.664450	+	1.42492i	0.892401	+	0.451244i	$0.149020\pi$
$887$	19.7890	+	42.4376i	0.664450	+	1.42492i	−0.227951	+	0.973673i	$0.573203\pi$
$888$	5.68776	+	8.12296i	0.190869	+	0.272589i
$889$	−9.59806	−	54.4333i	−0.321909	−	1.82564i
$890$		0			0
$891$	31.5410	+	26.4660i	1.05666	+	0.886645i
$892$	−10.6927	−	10.6927i	−0.358018	−	0.358018i
$893$	−19.2431	+	15.6240i	−0.643945	+	0.522838i
$894$		−	11.3339i		−	0.379063i
$895$		0			0
$896$	−1.52115	−	4.17932i	−0.0508180	−	0.139621i
$897$	10.5451	+	7.38376i	0.352091	+	0.246537i
$898$	17.8667	−	12.5104i	0.596221	−	0.417478i
$899$	0.660093	−	1.81359i	0.0220153	−	0.0604866i
$900$		0			0
$901$	8.27042	+	4.77493i	0.275528	+	0.159076i
$902$	−1.59776	+	18.2625i	−0.0531995	+	0.608074i
$903$	7.02654	−	80.3138i	0.233829	−	2.67267i
$904$	−7.75828	−	4.47925i	−0.258037	−	0.148977i
$905$		0			0
$906$	0.836849	−	2.29922i	0.0278024	−	0.0763866i
$907$	4.86551	−	3.40686i	0.161556	−	0.113123i	−0.490003	−	0.871721i	$-0.663004\pi$
$907$	4.86551	−	3.40686i	0.161556	−	0.113123i	0.651559	+	0.758598i	$0.274115\pi$
$908$	−5.62514	−	3.93877i	−0.186677	−	0.130713i
$909$	−0.0681065	−	0.187121i	−0.00225895	−	0.00620642i
$910$		0			0
$911$		−	29.5092i		−	0.977683i	−0.872373	−	0.488842i	$-0.837420\pi$
$911$		−	29.5092i		−	0.977683i	0.872373	−	0.488842i	$-0.162580\pi$
$912$	5.73217	−	4.65412i	0.189811	−	0.154113i
$913$	16.7951	+	16.7951i	0.555837	+	0.555837i
$914$	−25.3939	−	21.3080i	−0.839954	−	0.704805i
$915$		0			0
$916$	−1.97497	−	11.2006i	−0.0652549	−	0.370079i
$917$	−57.5269	−	82.1569i	−1.89971	−	2.71306i
$918$	−7.44347	−	15.9626i	−0.245671	−	0.526843i
$919$	8.64974	−	4.99393i	0.285329	−	0.164735i	−0.350505	−	0.936561i	$-0.613990\pi$
$919$	8.64974	−	4.99393i	0.285329	−	0.164735i	0.635833	+	0.771826i	$0.280657\pi$
$920$		0			0
$921$	−33.0246	+	27.7110i	−1.08820	+	0.913107i
$922$	20.3287	+	1.77853i	0.669490	+	0.0585728i
$923$	14.3769	−	3.85229i	0.473223	−	0.126800i
$924$	−18.0532	−	31.2691i	−0.593908	−	1.02868i
$925$		0			0
$926$	25.8052	+	4.55015i	0.848011	+	0.149527i
$927$	1.23918	−	1.76974i	0.0407001	−	0.0581258i
$928$	0.292855	+	0.136560i	0.00961343	+	0.00448282i
$929$	13.5105	−	16.1011i	0.443264	−	0.528261i	−0.497436	−	0.867500i	$-0.665725\pi$
$929$	13.5105	−	16.1011i	0.443264	−	0.528261i	0.940700	+	0.339239i	$0.110170\pi$
$930$		0			0
$931$	13.5472	+	54.0370i	0.443993	+	1.77099i
$932$	1.38457	−	1.38457i	0.0453531	−	0.0453531i
$933$	−3.13628	+	0.274389i	−0.102677	+	0.00898310i
$934$	−25.1520	+	9.15457i	−0.822998	+	0.299547i
$935$		0			0
$936$	0.0322975	−	0.183168i	0.00105568	−	0.00598705i
$937$	−9.56413	+	4.45983i	−0.312446	+	0.145696i	−0.572516	−	0.819894i	$-0.694032\pi$
$937$	−9.56413	+	4.45983i	−0.312446	+	0.145696i	0.260069	+	0.965590i	$0.416255\pi$
$938$	15.8961	−	59.3250i	0.519026	−	1.93703i
$939$	−3.98704	+	6.90576i	−0.130112	+	0.225361i
$940$		0			0
$941$	−26.6265	−	31.7322i	−0.867998	−	1.03444i	−0.999072	−	0.0430672i	$-0.986287\pi$
$941$	−26.6265	−	31.7322i	−0.867998	−	1.03444i	0.131074	−	0.991373i	$-0.458157\pi$
$942$	5.85528	+	21.8522i	0.190775	+	0.711984i
$943$	19.7157	+	5.28281i	0.642033	+	0.172032i
$944$	0.150669	+	0.0548392i	0.00490387	+	0.00178486i
$945$		0			0
$946$	−50.5070	+	8.90575i	−1.64212	+	0.289551i
$947$	18.6402	−	39.9740i	0.605725	−	1.29898i	−0.329242	−	0.944246i	$-0.606793\pi$
$947$	18.6402	−	39.9740i	0.605725	−	1.29898i	0.934967	−	0.354736i	$-0.115429\pi$
$948$	−1.12331	−	12.8395i	−0.0364833	−	0.417006i
$949$	12.9015			0.418801
$950$		0			0
$951$	−16.8438			−0.546198
$952$	1.28742	+	14.7153i	0.0417255	+	0.476924i
$953$	0.446311	−	0.957116i	0.0144574	−	0.0310040i	−0.898946	−	0.438058i	$-0.855666\pi$
$953$	0.446311	−	0.957116i	0.0144574	−	0.0310040i	0.913404	+	0.407054i	$0.133444\pi$
$954$	0.369808	−	0.0652071i	0.0119730	−	0.00211116i
$955$		0			0
$956$	−8.26287	−	3.00744i	−0.267240	−	0.0972676i
$957$	2.53388	+	0.678951i	0.0819087	+	0.0219474i
$958$	8.44211	+	31.5064i	0.272752	+	1.01792i
$959$	−20.1025	−	23.9573i	−0.649144	−	0.773620i
$960$		0			0
$961$	2.33706	−	4.04791i	0.0753891	−	0.130578i
$962$	2.15783	−	8.05313i	0.0695712	−	0.259643i
$963$	0.480399	−	0.224014i	0.0154806	−	0.00721874i
$964$	1.56069	−	8.85114i	0.0502666	−	0.285076i
$965$		0			0
$966$	−37.7768	+	13.7496i	−1.21545	+	0.442387i
$967$	46.1144	−	4.03448i	1.48294	−	0.129740i	0.683263	−	0.730173i	$-0.260560\pi$
$967$	46.1144	−	4.03448i	1.48294	−	0.129740i	0.799676	+	0.600432i	$0.205005\pi$
$968$	−8.46326	+	8.46326i	−0.272020	+	0.272020i
$969$	−22.3901	+	10.0035i	−0.719274	+	0.321358i
$970$		0			0
$971$	−4.93723	+	5.88396i	−0.158443	+	0.188825i	−0.839426	−	0.543474i	$-0.817109\pi$
$971$	−4.93723	+	5.88396i	−0.158443	+	0.188825i	0.680982	+	0.732300i	$0.261553\pi$
$972$	−1.22915	−	0.573164i	−0.0394251	−	0.0183842i
$973$	−21.4753	+	30.6699i	−0.688466	+	0.983232i
$974$	−21.0312	−	3.70838i	−0.673885	−	0.118824i
$975$		0			0
$976$	1.90333	+	3.29666i	0.0609240	+	0.105523i
$977$	−43.1053	+	11.5500i	−1.37906	+	0.369518i	−0.870780	−	0.491673i	$-0.836385\pi$
$977$	−43.1053	+	11.5500i	−1.37906	+	0.369518i	−0.508281	+	0.861191i	$0.669719\pi$
$978$	−21.2027	−	1.85500i	−0.677988	−	0.0593162i
$979$	−43.9830	+	36.9061i	−1.40570	+	1.17952i
$980$		0			0
$981$	−0.00301296	+	0.00173953i	−9.61964e−5	+	5.55390e-5i
$982$	−10.2957	−	22.0791i	−0.328548	−	0.704573i
$983$	22.1179	+	31.5876i	0.705450	+	1.00749i	0.998676	+	0.0514439i	$0.0163823\pi$
$983$	22.1179	+	31.5876i	0.705450	+	1.00749i	−0.293226	+	0.956043i	$0.594729\pi$
$984$	1.12515	+	6.38106i	0.0358686	+	0.203421i
$985$		0			0
$986$	−0.822119	−	0.689840i	−0.0261816	−	0.0219690i
$987$	30.2936	+	30.2936i	0.964257	+	0.964257i
$988$	−6.09536	−	1.17663i	−0.193919	−	0.0374337i
$989$			57.1024i			1.81575i
$990$		0			0
$991$	14.6445	+	40.2354i	0.465198	+	1.27812i	0.921529	+	0.388310i	$0.126941\pi$
$991$	14.6445	+	40.2354i	0.465198	+	1.27812i	−0.456331	+	0.889810i	$0.650837\pi$
$992$	4.89262	+	3.42585i	0.155341	+	0.108771i
$993$	31.1502	−	21.8116i	0.988522	−	0.692171i
$994$	−15.8974	+	43.6779i	−0.504236	+	1.38538i
$995$		0			0
$996$	7.27034	+	4.19753i	0.230370	+	0.133004i
$997$	−1.09498	+	12.5157i	−0.0346784	+	0.396376i	0.958942	+	0.283602i	$0.0915294\pi$
$997$	−1.09498	+	12.5157i	−0.0346784	+	0.396376i	−0.993621	+	0.112775i	$0.964026\pi$
$998$	−0.498962	+	5.70316i	−0.0157944	+	0.180530i
$999$	−26.8849	−	15.5220i	−0.850599	−	0.491094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.e.193.9		120
5.2	odd	4	inner	950.2.bb.e.307.2		120
5.3	odd	4		190.2.r.a.117.9	yes	120
5.4	even	2		190.2.r.a.3.2	✓	120
19.13	odd	18	inner	950.2.bb.e.393.2		120
95.13	even	36		190.2.r.a.127.2	yes	120
95.32	even	36	inner	950.2.bb.e.507.9		120
95.89	odd	18		190.2.r.a.13.9	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.r.a.3.2	✓	120	5.4	even	2
190.2.r.a.13.9	yes	120	95.89	odd	18
190.2.r.a.117.9	yes	120	5.3	odd	4
190.2.r.a.127.2	yes	120	95.13	even	36
950.2.bb.e.193.9		120	1.1	even	1	trivial
950.2.bb.e.307.2		120	5.2	odd	4	inner
950.2.bb.e.393.2		120	19.13	odd	18	inner
950.2.bb.e.507.9		120	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)

\(f(q)\)	\(=\)	\(q+(0.0871557 + 0.996195i) q^{2} +(0.715886 - 1.53522i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(1.59177 + 0.579359i) q^{6} +(4.29599 + 1.15111i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(0.0839459 + 0.100043i) q^{9} +O(q^{10})\)	\(q+(0.0871557 + 0.996195i) q^{2} +(0.715886 - 1.53522i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(1.59177 + 0.579359i) q^{6} +(4.29599 + 1.15111i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(0.0839459 + 0.100043i) q^{9} +(-2.39629 + 4.15050i) q^{11} +(-0.438422 + 1.63621i) q^{12} +(1.29075 - 0.601887i) q^{13} +(-0.772307 + 4.37997i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-3.30863 + 0.289468i) q^{17} +(-0.0923458 + 0.0923458i) q^{18} +(3.03200 + 3.13161i) q^{19} +(4.84265 - 5.77124i) q^{21} +(-4.34356 - 2.02543i) q^{22} +(-3.06066 + 4.37107i) q^{23} +(-1.66820 - 0.294148i) q^{24} +(0.712093 + 1.23338i) q^{26} +(5.12232 - 1.37252i) q^{27} +(-4.43061 - 0.387628i) q^{28} +(0.247532 - 0.207704i) q^{29} +(5.17258 - 2.98639i) q^{31} +(0.422618 + 0.906308i) q^{32} +(4.65647 + 6.65013i) q^{33} +(-0.576733 - 3.27081i) q^{34} +(-0.100043 - 0.0839459i) q^{36} +(-4.13942 - 4.13942i) q^{37} +(-2.85543 + 3.29340i) q^{38} -2.41247i q^{39} +(-1.30827 - 3.59444i) q^{41} +(6.17134 + 4.32122i) q^{42} +(8.76587 - 6.13793i) q^{43} +(1.63916 - 4.50356i) q^{44} +(-4.62120 - 2.66805i) q^{46} +(-0.495618 + 5.66494i) q^{47} +(0.147636 - 1.68749i) q^{48} +(11.0683 + 6.39029i) q^{49} +(-1.92421 + 5.28671i) q^{51} +(-1.16663 + 0.816880i) q^{52} +(-2.35536 - 1.64924i) q^{53} +(1.81374 + 4.98320i) q^{54} -4.44754i q^{56} +(6.97829 - 2.41292i) q^{57} +(0.228487 + 0.228487i) q^{58} +(0.122827 + 0.103064i) q^{59} +(0.661018 + 3.74882i) q^{61} +(3.42585 + 4.89262i) q^{62} +(0.245471 + 0.526414i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-6.21899 + 5.21835i) q^{66} +(-13.7568 - 1.20357i) q^{67} +(3.20810 - 0.859608i) q^{68} +(4.51949 + 7.82799i) q^{69} +(10.2922 + 1.81479i) q^{71} +(0.0749072 - 0.106979i) q^{72} +(8.21012 + 3.82844i) q^{73} +(3.76289 - 4.48444i) q^{74} +(-3.52974 - 2.55753i) q^{76} +(-15.0721 + 15.0721i) q^{77} +(2.40329 - 0.210261i) q^{78} +(-7.14978 + 2.60231i) q^{79} +(1.49184 - 8.46064i) q^{81} +(3.46674 - 1.61657i) q^{82} +(1.28270 - 4.78710i) q^{83} +(-3.76691 + 6.52448i) q^{84} +(6.87857 + 8.19756i) q^{86} +(-0.141667 - 0.528708i) q^{87} +(4.62928 + 1.24041i) q^{88} +(11.2576 + 4.09744i) q^{89} +(6.23789 - 1.09991i) q^{91} +(2.25513 - 4.83615i) q^{92} +(-0.881797 - 10.0790i) q^{93} -5.68658 q^{94} +1.69393 q^{96} +(-0.0458389 - 0.523941i) q^{97} +(-5.40131 + 11.5831i) q^{98} +(-0.616387 + 0.108686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^7	\( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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