LMFDB - Embedded newform 950.2.bb.c.143.3

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:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.3
Character	$\chi$	$=$	950.143
Dual form			950.2.bb.c.857.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 + 0.819152i) q^{2} +(0.218924 - 2.50231i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.92421 + 1.61460i) q^{6} +(0.801272 + 2.99039i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-3.25922 - 0.574689i) q^{9} +O(q^{10})$	\(q+(-0.573576 + 0.819152i) q^{2} +(0.218924 - 2.50231i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.92421 + 1.61460i) q^{6} +(0.801272 + 2.99039i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-3.25922 - 0.574689i) q^{9} +(-1.10915 - 1.92111i) q^{11} +(-2.42628 + 0.650120i) q^{12} +(0.101567 - 0.00888598i) q^{13} +(-2.90917 - 1.05885i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(6.56000 + 4.59336i) q^{17} +(2.34017 - 2.34017i) q^{18} +(4.26892 - 0.881100i) q^{19} +(7.65831 - 1.35037i) q^{21} +(2.20986 + 0.193338i) q^{22} +(5.33288 + 2.48676i) q^{23} +(0.859111 - 2.36039i) q^{24} +(-0.0509776 + 0.0882957i) q^{26} +(-0.201214 + 0.750940i) q^{27} +(2.53599 - 1.77572i) q^{28} +(1.07941 - 6.12163i) q^{29} +(-2.35091 - 1.35730i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(-5.05003 + 2.35487i) q^{33} +(-7.52533 + 2.73899i) q^{34} +(0.574689 + 3.25922i) q^{36} +(-3.62590 - 3.62590i) q^{37} +(-1.72680 + 4.00227i) q^{38} -0.256098i q^{39} +(0.277083 + 0.330215i) q^{41} +(-3.28647 + 7.04786i) q^{42} +(0.199956 + 0.428806i) q^{43} +(-1.42590 + 1.69932i) q^{44} +(-5.09585 + 2.94209i) q^{46} +(-3.17143 - 4.52927i) q^{47} +(1.44075 + 2.05761i) q^{48} +(-2.23821 + 1.29223i) q^{49} +(12.9302 - 15.4096i) q^{51} +(-0.0430881 - 0.0924027i) q^{52} +(-3.28738 + 7.04981i) q^{53} +(-0.499722 - 0.595546i) q^{54} +3.09588i q^{56} +(-1.27022 - 10.8751i) q^{57} +(4.39542 + 4.39542i) q^{58} +(-0.900432 - 5.10660i) q^{59} +(6.36564 - 2.31690i) q^{61} +(2.46026 - 1.14724i) q^{62} +(-0.892982 - 10.2068i) q^{63} +(0.866025 + 0.500000i) q^{64} +(0.967584 - 5.48744i) q^{66} +(-3.22023 + 2.25483i) q^{67} +(2.07270 - 7.73541i) q^{68} +(7.39015 - 12.8001i) q^{69} +(4.27837 - 11.7547i) q^{71} +(-2.99943 - 1.39866i) q^{72} +(11.8024 + 1.03258i) q^{73} +(5.04989 - 0.890432i) q^{74} +(-2.28802 - 3.71012i) q^{76} +(4.85613 - 4.85613i) q^{77} +(0.209783 + 0.146892i) q^{78} +(-9.47813 + 7.95310i) q^{79} +(-7.49471 - 2.72785i) q^{81} +(-0.429424 + 0.0375698i) q^{82} +(9.56503 - 2.56294i) q^{83} +(-3.88823 - 6.73460i) q^{84} +(-0.465947 - 0.0821591i) q^{86} +(-15.0819 - 4.04119i) q^{87} +(-0.574139 - 2.14272i) q^{88} +(11.4725 + 9.62654i) q^{89} +(0.107955 + 0.296605i) q^{91} +(0.512840 - 5.86179i) q^{92} +(-3.91106 + 5.58558i) q^{93} +5.52921 q^{94} -2.51187 q^{96} +(-0.741294 + 1.05868i) q^{97} +(0.225251 - 2.57463i) q^{98} +(2.51093 + 6.89874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{6}+O(q^{10}) $ 72 * q + 24 * q^6	$ 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) $ 72 * q + 24 * q^6 + 24 * q^21 + 12 * q^26 + 36 * q^31 - 24 * q^36 + 48 * q^41 - 36 * q^46 + 156 * q^51 + 168 * q^61 - 36 * q^66 - 84 * q^71 - 48 * q^76 - 60 * q^81 - 60 * q^86 - 264 * q^91 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$3$	0.218924	−	2.50231i	0.126396	−	1.44471i	−0.622809	−	0.782374i	$-0.714009\pi$
$3$	0.218924	−	2.50231i	0.126396	−	1.44471i	0.749205	−	0.662338i	$-0.230436\pi$
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$		0			0
$5$		0			0
$6$	1.92421	+	1.61460i	0.785554	+	0.659158i
$7$	0.801272	+	2.99039i	0.302852	+	1.13026i	0.934778	+	0.355232i	$0.115598\pi$
$7$	0.801272	+	2.99039i	0.302852	+	1.13026i	−0.631926	+	0.775029i	$0.717735\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	−3.25922	−	0.574689i	−1.08641	−	0.191563i
$10$		0			0
$11$	−1.10915	−	1.92111i	−0.334422	−	0.579236i	0.648952	−	0.760830i	$-0.275208\pi$
$11$	−1.10915	−	1.92111i	−0.334422	−	0.579236i	−0.983374	+	0.181594i	$0.941874\pi$
$12$	−2.42628	+	0.650120i	−0.700407	+	0.187674i
$13$	0.101567	−	0.00888598i	0.0281697	−	0.00246453i	−0.0730622	−	0.997327i	$-0.523277\pi$
$13$	0.101567	−	0.00888598i	0.0281697	−	0.00246453i	0.101232	+	0.994863i	$0.467722\pi$
$14$	−2.90917	−	1.05885i	−0.777509	−	0.282990i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	6.56000	+	4.59336i	1.59103	+	1.11405i	0.932304	+	0.361675i	$0.117795\pi$
$17$	6.56000	+	4.59336i	1.59103	+	1.11405i	0.658730	+	0.752379i	$0.271094\pi$
$18$	2.34017	−	2.34017i	0.551584	−	0.551584i
$19$	4.26892	−	0.881100i	0.979357	−	0.202138i
$19$	4.26892	−	0.881100i	0.979357	−	0.202138i
$20$		0			0
$21$	7.65831	−	1.35037i	1.67118	−	0.294674i
$22$	2.20986	+	0.193338i	0.471144	+	0.0412198i
$23$	5.33288	+	2.48676i	1.11198	+	0.518526i	0.889741	−	0.456466i	$-0.150885\pi$
$23$	5.33288	+	2.48676i	1.11198	+	0.518526i	0.222241	+	0.974992i	$0.428663\pi$
$24$	0.859111	−	2.36039i	0.175365	−	0.481812i
$25$		0			0
$26$	−0.0509776	+	0.0882957i	−0.00999752	+	0.0173162i
$27$	−0.201214	+	0.750940i	−0.0387236	+	0.144518i
$28$	2.53599	−	1.77572i	0.479258	−	0.335580i
$29$	1.07941	−	6.12163i	0.200441	−	1.13676i	−0.704013	−	0.710187i	$-0.748610\pi$
$29$	1.07941	−	6.12163i	0.200441	−	1.13676i	0.904454	−	0.426571i	$-0.140278\pi$
$30$		0			0
$31$	−2.35091	−	1.35730i	−0.422236	−	0.243778i	0.273797	−	0.961787i	$-0.411720\pi$
$31$	−2.35091	−	1.35730i	−0.422236	−	0.243778i	−0.696034	+	0.718009i	$0.745054\pi$
$32$	−0.0871557	−	0.996195i	−0.0154071	−	0.176104i
$33$	−5.05003	+	2.35487i	−0.879098	+	0.409930i
$34$	−7.52533	+	2.73899i	−1.29058	+	0.469734i
$35$		0			0
$36$	0.574689	+	3.25922i	0.0957815	+	0.543204i
$37$	−3.62590	−	3.62590i	−0.596094	−	0.596094i	0.343177	−	0.939271i	$-0.388497\pi$
$37$	−3.62590	−	3.62590i	−0.596094	−	0.596094i	−0.939271	+	0.343177i	$0.888497\pi$
$38$	−1.72680	+	4.00227i	−0.280123	+	0.649254i
$39$		−	0.256098i		−	0.0410085i
$40$		0			0
$41$	0.277083	+	0.330215i	0.0432731	+	0.0515709i	0.787247	−	0.616638i	$-0.211506\pi$
$41$	0.277083	+	0.330215i	0.0432731	+	0.0515709i	−0.743974	+	0.668209i	$0.767061\pi$
$42$	−3.28647	+	7.04786i	−0.507113	+	1.08751i
$43$	0.199956	+	0.428806i	0.0304929	+	0.0653923i	0.920964	−	0.389647i	$-0.127403\pi$
$43$	0.199956	+	0.428806i	0.0304929	+	0.0653923i	−0.890471	+	0.455039i	$0.849625\pi$
$44$	−1.42590	+	1.69932i	−0.214962	+	0.256182i
$45$		0			0
$46$	−5.09585	+	2.94209i	−0.751342	+	0.433788i
$47$	−3.17143	−	4.52927i	−0.462600	−	0.660662i	0.518294	−	0.855202i	$-0.326567\pi$
$47$	−3.17143	−	4.52927i	−0.462600	−	0.660662i	−0.980894	+	0.194541i	$0.937678\pi$
$48$	1.44075	+	2.05761i	0.207954	+	0.296990i
$49$	−2.23821	+	1.29223i	−0.319744	+	0.184604i
$50$		0			0
$51$	12.9302	−	15.4096i	1.81059	−	2.15777i
$52$	−0.0430881	−	0.0924027i	−0.00597524	−	0.0128140i
$53$	−3.28738	+	7.04981i	−0.451556	+	0.968366i	0.540355	+	0.841437i	$0.318290\pi$
$53$	−3.28738	+	7.04981i	−0.451556	+	0.968366i	−0.991912	+	0.126929i	$0.959488\pi$
$54$	−0.499722	−	0.595546i	−0.0680036	−	0.0810435i
$55$		0			0
$56$			3.09588i			0.413704i
$57$	−1.27022	−	10.8751i	−0.168245	−	1.44044i
$58$	4.39542	+	4.39542i	0.577147	+	0.577147i
$59$	−0.900432	−	5.10660i	−0.117226	−	0.664823i	−0.985624	−	0.168955i	$-0.945961\pi$
$59$	−0.900432	−	5.10660i	−0.117226	−	0.664823i	0.868398	−	0.495869i	$-0.165150\pi$
$60$		0			0
$61$	6.36564	−	2.31690i	0.815036	−	0.296649i	0.0993337	−	0.995054i	$-0.468329\pi$
$61$	6.36564	−	2.31690i	0.815036	−	0.296649i	0.715703	+	0.698405i	$0.246107\pi$
$62$	2.46026	−	1.14724i	0.312454	−	0.145700i
$63$	−0.892982	−	10.2068i	−0.112505	−	1.28594i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	0.967584	−	5.48744i	0.119101	−	0.675458i
$67$	−3.22023	+	2.25483i	−0.393414	+	0.275471i	−0.753500	−	0.657448i	$-0.771636\pi$
$67$	−3.22023	+	2.25483i	−0.393414	+	0.275471i	0.360087	+	0.932919i	$0.382747\pi$
$68$	2.07270	−	7.73541i	0.251351	−	0.938056i
$69$	7.39015	−	12.8001i	0.889670	−	1.54095i
$70$		0			0
$71$	4.27837	−	11.7547i	0.507749	−	1.39503i	−0.375805	−	0.926699i	$-0.622634\pi$
$71$	4.27837	−	11.7547i	0.507749	−	1.39503i	0.883554	−	0.468329i	$-0.155144\pi$
$72$	−2.99943	−	1.39866i	−0.353486	−	0.164833i
$73$	11.8024	+	1.03258i	1.38137	+	0.120854i	0.753492	−	0.657457i	$-0.228368\pi$
$73$	11.8024	+	1.03258i	1.38137	+	0.120854i	0.627879	+	0.778311i	$0.283923\pi$
$74$	5.04989	−	0.890432i	0.587038	−	0.103511i
$75$		0			0
$76$	−2.28802	−	3.71012i	−0.262454	−	0.425580i
$77$	4.85613	−	4.85613i	0.553407	−	0.553407i
$78$	0.209783	+	0.146892i	0.0237533	+	0.0166322i
$79$	−9.47813	+	7.95310i	−1.06637	+	0.894794i	−0.994719	−	0.102636i	$-0.967272\pi$
$79$	−9.47813	+	7.95310i	−1.06637	+	0.894794i	−0.0716544	+	0.997430i	$0.522828\pi$
$80$		0			0
$81$	−7.49471	−	2.72785i	−0.832745	−	0.303095i
$82$	−0.429424	+	0.0375698i	−0.0474220	+	0.00414889i
$83$	9.56503	−	2.56294i	1.04990	−	0.281319i	0.307689	−	0.951487i	$-0.400445\pi$
$83$	9.56503	−	2.56294i	1.04990	−	0.281319i	0.742210	+	0.670168i	$0.233778\pi$
$84$	−3.88823	−	6.73460i	−0.424240	−	0.734805i
$85$		0			0
$86$	−0.465947	−	0.0821591i	−0.0502444	−	0.00885944i
$87$	−15.0819	−	4.04119i	−1.61695	−	0.433261i
$88$	−0.574139	−	2.14272i	−0.0612035	−	0.228414i
$89$	11.4725	+	9.62654i	1.21608	+	1.02041i	0.999020	+	0.0442531i	$0.0140908\pi$
$89$	11.4725	+	9.62654i	1.21608	+	1.02041i	0.217059	+	0.976159i	$0.430354\pi$
$90$		0			0
$91$	0.107955	+	0.296605i	0.0113168	+	0.0310927i
$92$	0.512840	−	5.86179i	0.0534673	−	0.611134i
$93$	−3.91106	+	5.58558i	−0.405558	+	0.579197i
$94$	5.52921			0.570295
$95$		0			0
$96$	−2.51187			−0.256367
$97$	−0.741294	+	1.05868i	−0.0752670	+	0.107492i	−0.855020	−	0.518594i	$-0.826456\pi$
$97$	−0.741294	+	1.05868i	−0.0752670	+	0.107492i	0.779753	+	0.626087i	$0.215344\pi$
$98$	0.225251	−	2.57463i	0.0227537	−	0.260077i
$99$	2.51093	+	6.89874i	0.252358	+	0.693349i
$100$		0			0
$101$	7.85564	+	6.59166i	0.781665	+	0.655895i	0.943667	−	0.330895i	$-0.107351\pi$
$101$	7.85564	+	6.59166i	0.781665	+	0.655895i	−0.162002	+	0.986790i	$0.551795\pi$
$102$	5.20635	+	19.4304i	0.515505	+	1.92389i
$103$	−1.06271	−	0.284752i	−0.104712	−	0.0280575i	0.206083	−	0.978535i	$-0.433928\pi$
$103$	−1.06271	−	0.284752i	−0.104712	−	0.0280575i	−0.310794	+	0.950477i	$0.600595\pi$
$104$	0.100406	+	0.0177043i	0.00984564	+	0.00173605i
$105$		0			0
$106$	−3.88930	−	6.73647i	−0.377762	−	0.654304i
$107$	17.1412	−	4.59297i	1.65710	−	0.444019i	0.695514	−	0.718513i	$-0.255177\pi$
$107$	17.1412	−	4.59297i	1.65710	−	0.444019i	0.961589	+	0.274493i	$0.0885101\pi$
$108$	0.774472	−	0.0677575i	0.0745236	−	0.00651997i
$109$	−14.6385	−	5.32797i	−1.40211	−	0.510327i	−0.473307	−	0.880898i	$-0.656940\pi$
$109$	−14.6385	−	5.32797i	−1.40211	−	0.510327i	−0.928804	+	0.370571i	$0.879162\pi$
$110$		0			0
$111$	−9.86693	+	8.27934i	−0.936527	+	0.785840i
$112$	−2.53599	−	1.77572i	−0.239629	−	0.167790i
$113$	−13.1849	+	13.1849i	−1.24033	+	1.24033i	−0.280462	+	0.959865i	$0.590488\pi$
$113$	−13.1849	+	13.1849i	−1.24033	+	1.24033i	−0.959865	+	0.280462i	$0.909512\pi$
$114$	9.63690	+	5.19718i	0.902579	+	0.486760i
$115$		0			0
$116$	−6.12163	+	1.07941i	−0.568379	+	0.100221i
$117$	−0.336137	−	0.0294082i	−0.0310759	−	0.00271878i
$118$	4.69955	+	2.19144i	0.432629	+	0.201738i
$119$	−8.47959	+	23.2975i	−0.777323	+	2.13568i
$120$		0			0
$121$	3.03956	−	5.26468i	0.276324	−	0.478607i
$122$	−1.75328	+	6.54334i	−0.158735	+	0.592407i
$123$	0.886961	−	0.621057i	0.0799746	−	0.0559988i
$124$	−0.471385	+	2.67336i	−0.0423317	+	0.240075i
$125$		0			0
$126$	8.87314	+	5.12291i	0.790482	+	0.456385i
$127$	−1.57769	−	18.0330i	−0.139997	−	1.60017i	−0.663518	−	0.748160i	$-0.730937\pi$
$127$	−1.57769	−	18.0330i	−0.139997	−	1.60017i	0.523521	−	0.852013i	$-0.324618\pi$
$128$	−0.906308	+	0.422618i	−0.0801070	+	0.0373545i
$129$	1.11678	−	0.406476i	0.0983272	−	0.0357882i
$130$		0			0
$131$	0.577009	+	3.27238i	0.0504135	+	0.285909i	0.999584	−	0.0288544i	$-0.00918591\pi$
$131$	0.577009	+	3.27238i	0.0504135	+	0.285909i	−0.949170	+	0.314763i	$0.898075\pi$
$132$	3.94007	+	3.94007i	0.342939	+	0.342939i
$133$	6.05540	+	12.0597i	0.525070	+	1.04571i
$134$		−	3.93117i		−	0.339602i
$135$		0			0
$136$	5.14763	+	6.13470i	0.441405	+	0.526046i
$137$	0.946374	−	2.02951i	0.0808542	−	0.173392i	−0.861725	−	0.507376i	$-0.830615\pi$
$137$	0.946374	−	2.02951i	0.0808542	−	0.173392i	0.942579	+	0.333984i	$0.108393\pi$
$138$	6.24643	+	13.3955i	0.531731	+	1.14030i
$139$	1.64823	−	1.96428i	0.139801	−	0.166608i	−0.691601	−	0.722280i	$-0.743094\pi$
$139$	1.64823	−	1.96428i	0.139801	−	0.166608i	0.831402	+	0.555671i	$0.187539\pi$
$140$		0			0
$141$	−12.0280	+	6.94434i	−1.01294	+	0.584819i
$142$	7.17493	+	10.2469i	0.602107	+	0.859897i
$143$	−0.129724	−	0.185266i	−0.0108481	−	0.0154927i
$144$	2.86611	−	1.65475i	0.238843	−	0.137896i
$145$		0			0
$146$	−7.61544	+	9.07573i	−0.630258	+	0.751112i
$147$	2.74357	+	5.88360i	0.226286	+	0.485271i
$148$	−2.16710	+	4.64736i	−0.178134	+	0.382010i
$149$	3.20204	+	3.81605i	0.262322	+	0.312623i	0.881088	−	0.472952i	$-0.156812\pi$
$149$	3.20204	+	3.81605i	0.262322	+	0.312623i	−0.618766	+	0.785575i	$0.712367\pi$
$150$		0			0
$151$			17.2663i			1.40511i	0.711629	+	0.702555i	$0.247958\pi$
$151$			17.2663i			1.40511i	−0.711629	+	0.702555i	$0.752042\pi$
$152$	4.35150	+	0.253800i	0.352954	+	0.0205859i
$153$	−18.7408	−	18.7408i	−1.51510	−	1.51510i
$154$	1.19255	+	6.76326i	0.0960981	+	0.544999i
$155$		0			0
$156$	−0.240654	+	0.0875908i	−0.0192677	+	0.00701287i
$157$	−13.7097	+	6.39294i	−1.09415	+	0.510212i	−0.884014	−	0.467460i	$-0.845169\pi$
$157$	−13.7097	+	6.39294i	−1.09415	+	0.510212i	−0.210139	+	0.977672i	$0.567392\pi$
$158$	−1.07836	−	12.3257i	−0.0857899	−	0.980583i
$159$	16.9211	+	9.76943i	1.34193	+	0.774766i
$160$		0			0
$161$	−3.16330	+	17.9400i	−0.249303	+	1.41387i
$162$	6.53331	−	4.57467i	0.513305	−	0.359420i
$163$	5.73685	−	21.4102i	0.449344	−	1.67698i	−0.254859	−	0.966978i	$-0.582029\pi$
$163$	5.73685	−	21.4102i	0.449344	−	1.67698i	0.704204	−	0.709998i	$-0.251304\pi$
$164$	0.215532	−	0.373313i	0.0168302	−	0.0291508i
$165$		0			0
$166$	−3.38684	+	9.30525i	−0.262869	+	0.722228i
$167$	13.1431	+	6.12873i	1.01704	+	0.474255i	0.858346	−	0.513072i	$-0.171492\pi$
$167$	13.1431	+	6.12873i	1.01704	+	0.474255i	0.158698	+	0.987327i	$0.449270\pi$
$168$	7.74686	+	0.677762i	0.597683	+	0.0522905i
$169$	−12.7923	+	2.25562i	−0.984020	+	0.173509i
$170$		0			0
$171$	−14.4197	+	0.418403i	−1.10270	+	0.0319961i
$172$	0.334557	−	0.334557i	0.0255097	−	0.0255097i
$173$	−12.1196	−	8.48623i	−0.921436	−	0.645196i	0.0135397	−	0.999908i	$-0.495690\pi$
$173$	−12.1196	−	8.48623i	−0.921436	−	0.645196i	−0.934976	+	0.354712i	$0.884579\pi$
$174$	11.9610	−	10.0365i	0.906760	−	0.760862i
$175$		0			0
$176$	2.08452	+	0.758705i	0.157127	+	0.0571895i
$177$	−12.9755	+	1.13521i	−0.975295	+	0.0853272i
$178$	−14.4659	+	3.87614i	−1.08427	+	0.290529i
$179$	0.489628	+	0.848061i	0.0365965	+	0.0633871i	0.883744	−	0.467972i	$-0.155015\pi$
$179$	0.489628	+	0.848061i	0.0365965	+	0.0633871i	−0.847147	+	0.531359i	$0.821682\pi$
$180$		0			0
$181$	5.96573	+	1.05192i	0.443429	+	0.0781886i	0.390905	−	0.920431i	$-0.372162\pi$
$181$	5.96573	+	1.05192i	0.443429	+	0.0781886i	0.0525245	+	0.998620i	$0.483273\pi$
$182$	−0.304885	−	0.0816938i	−0.0225996	−	0.00605555i
$183$	−4.40403	−	16.4360i	−0.325555	−	1.21499i
$184$	4.50754	+	3.78228i	0.332301	+	0.278833i
$185$		0			0
$186$	−2.33214	−	6.40751i	−0.171001	−	0.469821i
$187$	1.54831	−	17.6972i	0.113223	−	1.29415i
$188$	−3.17143	+	4.52927i	−0.231300	+	0.330331i
$189$	−2.40683			−0.175071
$190$		0			0
$191$	−3.11639			−0.225494			−0.112747	−	0.993624i	$-0.535965\pi$
$191$	−3.11639			−0.225494			−0.112747	+	0.993624i	$0.535965\pi$
$192$	1.44075	−	2.05761i	0.103977	−	0.148495i
$193$	−0.818630	+	9.35699i	−0.0589263	+	0.673531i	0.908083	+	0.418790i	$0.137546\pi$
$193$	−0.818630	+	9.35699i	−0.0589263	+	0.673531i	−0.967009	+	0.254741i	$0.918010\pi$
$194$	−0.442029	−	1.21447i	−0.0317359	−	0.0871936i
$195$		0			0
$196$	1.97981	+	1.66126i	0.141415	+	0.118661i
$197$	7.04077	+	26.2765i	0.501634	+	1.87212i	0.489145	+	0.872202i	$0.337309\pi$
$197$	7.04077	+	26.2765i	0.501634	+	1.87212i	0.0124888	+	0.999922i	$0.496025\pi$
$198$	−7.09133	−	1.90012i	−0.503959	−	0.135035i
$199$	−5.11238	−	0.901450i	−0.362407	−	0.0639021i	−0.0105200	−	0.999945i	$-0.503349\pi$
$199$	−5.11238	−	0.901450i	−0.362407	−	0.0639021i	−0.351887	+	0.936043i	$0.614460\pi$
$200$		0			0
$201$	4.93730	+	8.55166i	0.348250	+	0.603188i
$202$	−9.90538	+	2.65414i	−0.696940	+	0.186745i
$203$	19.1709	−	1.67724i	1.34554	−	0.117719i
$204$	−18.9027	−	6.88000i	−1.32345	−	0.481697i
$205$		0			0
$206$	0.842800	−	0.707193i	0.0587207	−	0.0492725i
$207$	−15.9519	−	11.1697i	−1.10874	−	0.776345i
$208$	−0.0720932	+	0.0720932i	−0.00499876	+	0.00499876i
$209$	−6.42757	−	7.22378i	−0.444604	−	0.499679i
$210$		0			0
$211$	−16.0196	+	2.82468i	−1.10283	+	0.194459i	−0.695292	−	0.718727i	$-0.744725\pi$
$211$	−16.0196	+	2.82468i	−1.10283	+	0.194459i	−0.407541	+	0.913187i	$0.633614\pi$
$212$	7.74900	+	0.677950i	0.532204	+	0.0465618i
$213$	−28.4773	−	13.2792i	−1.95124	−	0.909876i
$214$	−6.06945	+	16.6757i	−0.414899	+	1.13993i
$215$		0			0
$216$	−0.388715	+	0.673274i	−0.0264487	+	0.0458105i
$217$	2.17513	−	8.11771i	0.147658	−	0.551066i
$218$	12.7607	−	8.93514i	0.864263	−	0.605164i
$219$	5.16768	−	29.3073i	0.349199	−	1.98041i
$220$		0			0
$221$	0.707097	+	0.408243i	0.0475645	+	0.0274614i
$222$	−1.12260	−	12.8313i	−0.0753438	−	0.861184i
$223$	−13.4772	+	6.28450i	−0.902497	+	0.420841i	−0.817758	−	0.575562i	$-0.804783\pi$
$223$	−13.4772	+	6.28450i	−0.902497	+	0.420841i	−0.0847387	+	0.996403i	$0.527006\pi$
$224$	2.90917	−	1.05885i	0.194377	−	0.0707476i
$225$		0			0
$226$	−3.23788	−	18.3629i	−0.215381	−	1.22148i
$227$	7.40925	+	7.40925i	0.491769	+	0.491769i	0.908863	−	0.417094i	$-0.136951\pi$
$227$	7.40925	+	7.40925i	0.491769	+	0.491769i	−0.417094	+	0.908863i	$0.636951\pi$
$228$	−9.78478	+	4.91311i	−0.648013	+	0.325379i
$229$			10.5985i			0.700371i	0.936680	+	0.350186i	$0.113882\pi$
$229$			10.5985i			0.700371i	−0.936680	+	0.350186i	$0.886118\pi$
$230$		0			0
$231$	−11.0884	−	13.2147i	−0.729565	−	0.869462i
$232$	2.62702	−	5.63367i	0.172472	−	0.369868i
$233$	12.7625	+	27.3693i	0.836100	+	1.79302i	0.550944	+	0.834542i	$0.314268\pi$
$233$	12.7625	+	27.3693i	0.836100	+	1.79302i	0.285156	+	0.958481i	$0.407954\pi$
$234$	0.216890	−	0.258479i	0.0141785	−	0.0168973i
$235$		0			0
$236$	−4.49067	+	2.59269i	−0.292318	+	0.168770i
$237$	17.8262	+	25.4584i	1.15793	+	1.65370i
$238$	−14.2205	−	20.3090i	−0.921778	−	1.31643i
$239$	18.3390	−	10.5880i	1.18625	−	0.684881i	0.228797	−	0.973474i	$-0.426521\pi$
$239$	18.3390	−	10.5880i	1.18625	−	0.684881i	0.957452	+	0.288593i	$0.0931876\pi$
$240$		0			0
$241$	5.67569	−	6.76403i	0.365603	−	0.435709i	−0.551612	−	0.834101i	$-0.685987\pi$
$241$	5.67569	−	6.76403i	0.365603	−	0.435709i	0.917215	+	0.398392i	$0.130432\pi$
$242$	2.56915	+	5.50956i	0.165151	+	0.354168i
$243$	−9.45238	+	20.2707i	−0.606370	+	1.30037i
$244$	−4.35435	−	5.18931i	−0.278759	−	0.332212i
$245$		0			0
$246$			1.08278i			0.0690355i
$247$	0.425752	−	0.127424i	0.0270900	−	0.00810782i
$248$	−1.91951	−	1.91951i	−0.121889	−	0.121889i
$249$	−4.31927	−	24.4958i	−0.273723	−	1.55236i
$250$		0			0
$251$	15.0642	−	5.48293i	0.950846	−	0.346080i	0.180406	−	0.983592i	$-0.442259\pi$
$251$	15.0642	−	5.48293i	0.950846	−	0.346080i	0.770440	+	0.637513i	$0.220037\pi$
$252$	−9.28586	+	4.33007i	−0.584954	+	0.272769i
$253$	−1.13764	−	13.0032i	−0.0715225	−	0.817506i
$254$	15.6767	+	9.05096i	0.983645	+	0.567908i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−7.24068	+	5.06998i	−0.451661	+	0.316257i	−0.777179	−	0.629279i	$-0.783350\pi$
$257$	−7.24068	+	5.06998i	−0.451661	+	0.316257i	0.325518	+	0.945536i	$0.394461\pi$
$258$	−0.307595	+	1.14796i	−0.0191500	+	0.0714689i
$259$	7.93751	−	13.7482i	0.493213	−	0.854270i
$260$		0			0
$261$	−7.03606	+	19.3314i	−0.435521	+	1.19659i
$262$	−3.01153	−	1.40430i	−0.186053	−	0.0867581i
$263$	−9.17898	−	0.803057i	−0.566000	−	0.0495186i	−0.199435	−	0.979911i	$-0.563911\pi$
$263$	−9.17898	−	0.803057i	−0.566000	−	0.0495186i	−0.366565	+	0.930392i	$0.619466\pi$
$264$	−5.48744	+	0.967584i	−0.337729	+	0.0595507i
$265$		0			0
$266$	−13.3520	−	1.95688i	−0.818662	−	0.119984i
$267$	26.6002	−	26.6002i	1.62791	−	1.62791i
$268$	3.22023	+	2.25483i	0.196707	+	0.137736i
$269$	−10.7252	+	8.99948i	−0.653925	+	0.548708i	−0.908259	−	0.418408i	$-0.862588\pi$
$269$	−10.7252	+	8.99948i	−0.653925	+	0.548708i	0.254334	+	0.967116i	$0.418144\pi$
$270$		0			0
$271$	−3.56004	−	1.29575i	−0.216257	−	0.0787111i	0.231620	−	0.972806i	$-0.425597\pi$
$271$	−3.56004	−	1.29575i	−0.216257	−	0.0787111i	−0.447877	+	0.894095i	$0.647820\pi$
$272$	−7.97781	+	0.697968i	−0.483726	+	0.0423205i
$273$	0.765833	−	0.205204i	0.0463503	−	0.0124195i
$274$	1.11966	+	1.93930i	0.0676409	+	0.117157i
$275$		0			0
$276$	−14.5558	−	2.56657i	−0.876154	−	0.154490i
$277$	−30.2987	−	8.11851i	−1.82047	−	0.487794i	−0.823625	−	0.567134i	$-0.808052\pi$
$277$	−30.2987	−	8.11851i	−1.82047	−	0.487794i	−0.996848	+	0.0793400i	$0.974719\pi$
$278$	0.663661	+	2.47682i	0.0398038	+	0.148550i
$279$	6.88212	+	5.77479i	0.412022	+	0.345727i
$280$		0			0
$281$	−4.93036	−	13.5460i	−0.294121	−	0.808090i	−0.995453	−	0.0952551i	$-0.969633\pi$
$281$	−4.93036	−	13.5460i	−0.294121	−	0.808090i	0.701332	−	0.712834i	$-0.252589\pi$
$282$	1.21048	−	13.8358i	0.0720829	−	0.823912i
$283$	−4.65291	+	6.64504i	−0.276587	+	0.395007i	−0.933279	−	0.359152i	$-0.883066\pi$
$283$	−4.65291	+	6.64504i	−0.276587	+	0.395007i	0.656693	+	0.754158i	$0.271955\pi$
$284$	−12.5091			−0.742279
$285$		0			0
$286$	0.226167			0.0133736
$287$	−0.765451	+	1.09318i	−0.0451832	+	0.0645282i
$288$	−0.288442	+	3.29691i	−0.0169966	+	0.194272i
$289$	16.1203	+	44.2902i	0.948253	+	2.60530i
$290$		0			0
$291$	2.48686	+	2.08672i	0.145782	+	0.122326i
$292$	−3.06636	−	11.4438i	−0.179445	−	0.669699i
$293$	−16.6118	−	4.45112i	−0.970472	−	0.260037i	−0.261445	−	0.965218i	$-0.584199\pi$
$293$	−16.6118	−	4.45112i	−0.970472	−	0.260037i	−0.709027	+	0.705181i	$0.750866\pi$
$294$	−6.39321	−	1.12730i	−0.372860	−	0.0657452i
$295$		0			0
$296$	−2.56390	−	4.44080i	−0.149023	−	0.258116i
$297$	1.66581	−	0.446353i	0.0966603	−	0.0259000i
$298$	−4.96254	+	0.434166i	−0.287472	+	0.0251506i
$299$	0.563743	+	0.205186i	0.0326021	+	0.0118662i
$300$		0			0
$301$	−1.12208	+	0.941535i	−0.0646755	+	0.0542692i
$302$	−14.1437	−	9.90353i	−0.813879	−	0.569884i
$303$	18.2142	−	18.2142i	1.04638	−	1.04638i
$304$	−2.70382	+	3.41897i	−0.155075	+	0.196091i
$305$		0			0
$306$	26.1008	−	4.60227i	1.49208	−	0.263094i
$307$	−15.7682	−	1.37954i	−0.899941	−	0.0787346i	−0.372212	−	0.928148i	$-0.621401\pi$
$307$	−15.7682	−	1.37954i	−0.899941	−	0.0787346i	−0.527729	+	0.849413i	$0.676956\pi$
$308$	−6.22416	−	2.90237i	−0.354654	−	0.165378i
$309$	−0.945192	+	2.59689i	−0.0537701	+	0.147732i
$310$		0			0
$311$	−7.72997	+	13.3887i	−0.438327	+	0.759204i	−0.997561	−	0.0698059i	$-0.977762\pi$
$311$	−7.72997	+	13.3887i	−0.438327	+	0.759204i	0.559234	+	0.829010i	$0.311095\pi$
$312$	0.0662831	−	0.247372i	0.00375254	−	0.0140047i
$313$	−25.1437	+	17.6058i	−1.42121	+	0.995138i	−0.425270	+	0.905067i	$0.639821\pi$
$313$	−25.1437	+	17.6058i	−1.42121	+	0.995138i	−0.995935	+	0.0900718i	$0.971290\pi$
$314$	2.62677	−	14.8972i	0.148237	−	0.840696i
$315$		0			0
$316$	10.7152	+	6.18641i	0.602776	+	0.348013i
$317$	0.346847	+	3.96448i	0.0194809	+	0.222667i	0.999694	+	0.0247239i	$0.00787067\pi$
$317$	0.346847	+	3.96448i	0.0194809	+	0.222667i	−0.980213	+	0.197943i	$0.936574\pi$
$318$	−17.7082	+	8.25748i	−0.993028	+	0.463056i
$319$	−12.9575	+	4.71616i	−0.725483	+	0.264054i
$320$		0			0
$321$	−7.74044	−	43.8982i	−0.432029	−	2.45016i
$322$	−12.8812	−	12.8812i	−0.717839	−	0.717839i
$323$	32.0513	+	13.8287i	1.78338	+	0.769448i
$324$			7.97570i			0.443095i
$325$		0			0
$326$	14.2477	+	16.9797i	0.789106	+	0.940420i
$327$	−16.5370	+	35.4636i	−0.914496	+	1.96114i
$328$	0.182176	+	0.390677i	0.0100590	+	0.0215715i
$329$	11.0031	−	13.1130i	0.606620	−	0.722942i
$330$		0			0
$331$	13.2412	−	7.64483i	0.727804	−	0.420198i	−0.0898141	−	0.995959i	$-0.528627\pi$
$331$	13.2412	−	7.64483i	0.727804	−	0.420198i	0.817618	+	0.575761i	$0.195294\pi$
$332$	−5.67981	−	8.11161i	−0.311720	−	0.445182i
$333$	9.73384	+	13.9014i	0.533411	+	0.761790i
$334$	−12.5589	+	7.25091i	−0.687195	+	0.396752i
$335$		0			0
$336$	−4.99861	+	5.95711i	−0.272696	+	0.324987i
$337$	−4.36966	−	9.37077i	−0.238031	−	0.510458i	0.750612	−	0.660743i	$-0.229759\pi$
$337$	−4.36966	−	9.37077i	−0.238031	−	0.510458i	−0.988643	+	0.150285i	$0.951981\pi$
$338$	5.48964	−	11.7726i	0.298597	−	0.640344i
$339$	30.1062	+	35.8791i	1.63514	+	1.94869i
$340$		0			0
$341$			6.02181i			0.326099i
$342$	7.92807	−	12.0519i	0.428701	−	0.651694i
$343$	9.66613	+	9.66613i	0.521922	+	0.521922i
$344$	0.0821591	+	0.465947i	0.00442972	+	0.0251222i
$345$		0			0
$346$	13.9030	−	5.06029i	0.747432	−	0.272043i
$347$	7.12249	−	3.32127i	0.382355	−	0.178295i	−0.221931	−	0.975062i	$-0.571236\pi$
$347$	7.12249	−	3.32127i	0.382355	−	0.178295i	0.604287	+	0.796767i	$0.293458\pi$
$348$	1.36085	+	15.5545i	0.0729490	+	0.833811i
$349$	−25.6229	−	14.7934i	−1.37156	−	0.791873i	−0.380440	−	0.924806i	$-0.624227\pi$
$349$	−25.6229	−	14.7934i	−1.37156	−	0.791873i	−0.991125	+	0.132932i	$0.957561\pi$
$350$		0			0
$351$	−0.0137639	+	0.0780588i	−0.000734661	+	0.00416647i
$352$	−1.81713	+	1.27237i	−0.0968533	+	0.0678174i
$353$	−0.798642	+	2.98057i	−0.0425074	+	0.158640i	−0.983917	−	0.178625i	$-0.942835\pi$
$353$	−0.798642	+	2.98057i	−0.0425074	+	0.158640i	0.941410	+	0.337265i	$0.109502\pi$
$354$	6.51251	−	11.2800i	0.346136	−	0.599525i
$355$		0			0
$356$	5.12218	−	14.0731i	0.271475	−	0.745871i
$357$	56.4412	+	26.3190i	2.98719	+	1.39295i
$358$	−0.975530	−	0.0853478i	−0.0515584	−	0.00451077i
$359$	−20.5407	+	3.62189i	−1.08410	+	0.191156i	−0.687027	−	0.726632i	$-0.741085\pi$
$359$	−20.5407	+	3.62189i	−1.08410	+	0.191156i	−0.397071	+	0.917788i	$0.629973\pi$
$360$		0			0
$361$	17.4473	−	7.52269i	0.918280	−	0.395931i
$362$	−4.28349	+	4.28349i	−0.225135	+	0.225135i
$363$	−12.5084	−	8.75851i	−0.656523	−	0.459702i
$364$	0.241795	−	0.202890i	0.0126735	−	0.0106343i
$365$		0			0
$366$	15.9897	+	5.81976i	0.835793	+	0.304204i
$367$	−21.1561	+	1.85092i	−1.10434	+	0.0966170i	−0.624711	−	0.780856i	$-0.714783\pi$
$367$	−21.1561	+	1.85092i	−1.10434	+	0.0966170i	−0.479626	+	0.877473i	$0.659228\pi$
$368$	−5.68368	+	1.52294i	−0.296282	+	0.0793886i
$369$	−0.713305	−	1.23548i	−0.0371332	−	0.0643165i
$370$		0			0
$371$	−23.7158	−	4.18173i	−1.23126	−	0.217104i
$372$	6.58639	+	1.76482i	0.341488	+	0.0915015i
$373$	−1.95010	−	7.27788i	−0.100972	−	0.376834i	0.896885	−	0.442264i	$-0.145825\pi$
$373$	−1.95010	−	7.27788i	−0.100972	−	0.376834i	−0.997857	+	0.0654301i	$0.979158\pi$
$374$	13.6086	+	11.4190i	0.703686	+	0.590462i
$375$		0			0
$376$	−1.89110	−	5.19576i	−0.0975262	−	0.267951i
$377$	0.0552358	−	0.631348i	0.00284479	−	0.0325161i
$378$	1.38050	−	1.97156i	0.0710053	−	0.101406i
$379$	7.75392			0.398292			0.199146	−	0.979970i	$-0.436183\pi$
$379$	7.75392			0.398292			0.199146	+	0.979970i	$0.436183\pi$
$380$		0			0
$381$	−45.4697			−2.32948
$382$	1.78749	−	2.55279i	0.0914557	−	0.130612i
$383$	1.57806	−	18.0373i	0.0806349	−	0.921661i	−0.842881	−	0.538100i	$-0.819142\pi$
$383$	1.57806	−	18.0373i	0.0806349	−	0.921661i	0.923516	−	0.383561i	$-0.125302\pi$
$384$	0.859111	+	2.36039i	0.0438413	+	0.120453i
$385$		0			0
$386$	−7.19525	−	6.03753i	−0.366229	−	0.307302i
$387$	−0.405270	−	1.51249i	−0.0206010	−	0.0768841i
$388$	1.24837	+	0.334500i	0.0633764	+	0.0169816i
$389$	1.74500	+	0.307690i	0.0884748	+	0.0156005i	0.217710	−	0.976013i	$-0.430141\pi$
$389$	1.74500	+	0.307690i	0.0884748	+	0.0156005i	−0.129235	+	0.991614i	$0.541252\pi$
$390$		0			0
$391$	23.5611	+	40.8090i	1.19154	+	2.06380i
$392$	−2.49640	+	0.668908i	−0.126087	+	0.0337849i
$393$	8.31484	−	0.727454i	0.419428	−	0.0366952i
$394$	−25.5629	−	9.30413i	−1.28784	−	0.468735i
$395$		0			0
$396$	5.62390	−	4.71901i	0.282612	−	0.237139i
$397$	3.61287	+	2.52976i	0.181325	+	0.126965i	0.660715	−	0.750637i	$-0.270253\pi$
$397$	3.61287	+	2.52976i	0.181325	+	0.126965i	−0.479390	+	0.877602i	$0.659142\pi$
$398$	3.67076	−	3.67076i	0.183999	−	0.183999i
$399$	31.5029	−	12.5123i	1.57712	−	0.626401i
$400$		0			0
$401$	13.0863	−	2.30747i	0.653499	−	0.115230i	0.162938	−	0.986636i	$-0.447903\pi$
$401$	13.0863	−	2.30747i	0.653499	−	0.115230i	0.490561	+	0.871407i	$0.336792\pi$
$402$	−9.83703	−	0.860629i	−0.490626	−	0.0429243i
$403$	−0.250836	−	0.116967i	−0.0124951	−	0.00582654i
$404$	3.50735	−	9.63637i	0.174497	−	0.479427i
$405$		0			0
$406$	−9.62209	+	16.6659i	−0.477536	+	0.827117i
$407$	−2.94407	+	10.9874i	−0.145932	+	0.544626i
$408$	16.4779	−	11.5379i	0.815777	−	0.571213i
$409$	6.43391	−	36.4885i	0.318136	−	1.80424i	−0.235933	−	0.971769i	$-0.575814\pi$
$409$	6.43391	−	36.4885i	0.318136	−	1.80424i	0.554069	−	0.832471i	$-0.313074\pi$
$410$		0			0
$411$	−4.87128	−	2.81243i	−0.240282	−	0.138727i
$412$	0.0958885	+	1.09601i	0.00472409	+	0.0539966i
$413$	14.5492	−	6.78442i	0.715921	−	0.333840i
$414$	18.2993	−	6.66040i	0.899362	−	0.327341i
$415$		0			0
$416$	−0.0177043	−	0.100406i	−0.000868026	−	0.00492282i
$417$	−4.55442	−	4.55442i	−0.223031	−	0.223031i
$418$	9.60407	−	1.12177i	0.469751	−	0.0548674i
$419$		−	39.6074i		−	1.93495i	−0.252968	−	0.967475i	$-0.581407\pi$
$419$		−	39.6074i		−	1.93495i	0.252968	−	0.967475i	$-0.418593\pi$
$420$		0			0
$421$	7.10249	+	8.46441i	0.346154	+	0.412530i	0.910830	−	0.412783i	$-0.135443\pi$
$421$	7.10249	+	8.46441i	0.346154	+	0.412530i	−0.564676	+	0.825313i	$0.690999\pi$
$422$	6.87461	−	14.7426i	0.334651	−	0.717661i
$423$	7.73347	+	16.5845i	0.376014	+	0.806365i
$424$	−4.99999	+	5.95876i	−0.242821	+	0.289383i
$425$		0			0
$426$	27.2116	−	15.7106i	1.31841	−	0.761183i
$427$	12.0290	+	17.1793i	0.582126	+	0.831363i
$428$	−10.1786	−	14.5366i	−0.492002	−	0.702652i
$429$	−0.491992	+	0.284052i	−0.0237536	+	0.0137142i
$430$		0			0
$431$	11.1305	−	13.2648i	0.536137	−	0.638943i	−0.428180	−	0.903693i	$-0.640845\pi$
$431$	11.1305	−	13.2648i	0.536137	−	0.638943i	0.964317	+	0.264750i	$0.0852895\pi$
$432$	−0.328556	−	0.704591i	−0.0158077	−	0.0338996i
$433$	5.82261	−	12.4866i	0.279817	−	0.600069i	−0.715295	−	0.698822i	$-0.753708\pi$
$433$	5.82261	−	12.4866i	0.279817	−	0.600069i	0.995112	+	0.0987536i	$0.0314856\pi$
$434$	5.40203	+	6.43789i	0.259306	+	0.309029i
$435$		0			0
$436$			15.5779i			0.746048i
$437$	24.9567	+	5.91698i	1.19384	+	0.283048i
$438$	21.0431	+	21.0431i	1.00548	+	1.00548i
$439$	5.05582	+	28.6730i	0.241301	+	1.36849i	0.828928	+	0.559355i	$0.188951\pi$
$439$	5.05582	+	28.6730i	0.241301	+	1.36849i	−0.587627	+	0.809132i	$0.699938\pi$
$440$		0			0
$441$	8.03745	−	2.92539i	0.382736	−	0.139304i
$442$	−0.739987	+	0.345062i	−0.0351976	+	0.0164129i
$443$	−1.00563	−	11.4944i	−0.0477790	−	0.546117i	−0.981931	−	0.189241i	$-0.939397\pi$
$443$	−1.00563	−	11.4944i	−0.0477790	−	0.546117i	0.934152	−	0.356876i	$-0.116158\pi$
$444$	11.1547	+	6.44018i	0.529379	+	0.305637i
$445$		0			0
$446$	2.58222	−	14.6445i	0.122271	−	0.693436i
$447$	10.2500	−	7.17709i	0.484806	−	0.339465i
$448$	−0.801272	+	2.99039i	−0.0378566	+	0.141283i
$449$	−12.6098	+	21.8408i	−0.595093	+	1.03073i	0.398440	+	0.917194i	$0.369552\pi$
$449$	−12.6098	+	21.8408i	−0.595093	+	1.03073i	−0.993534	+	0.113538i	$0.963782\pi$
$450$		0			0
$451$	0.327051	−	0.898565i	0.0154002	−	0.0423118i
$452$	16.8992	+	7.88023i	0.794871	+	0.370655i
$453$	43.2057	+	3.78001i	2.02998	+	0.177600i
$454$	−10.3191	+	1.81953i	−0.484298	+	0.0853948i
$455$		0			0
$456$	1.58774	−	10.8333i	0.0743525	−	0.507314i
$457$	−23.2575	+	23.2575i	−1.08794	+	1.08794i	−0.0921986	+	0.995741i	$0.529389\pi$
$457$	−23.2575	+	23.2575i	−1.08794	+	1.08794i	−0.995741	+	0.0921986i	$0.970611\pi$
$458$	−8.68182	−	6.07907i	−0.405675	−	0.284056i
$459$	−4.76930	+	4.00192i	−0.222612	+	0.186794i
$460$		0			0
$461$	−12.5663	−	4.57375i	−0.585270	−	0.213021i	0.0323777	−	0.999476i	$-0.489692\pi$
$461$	−12.5663	−	4.57375i	−0.585270	−	0.213021i	−0.617648	+	0.786455i	$0.711914\pi$
$462$	17.1849	−	1.50348i	0.799513	−	0.0699484i
$463$	38.1486	−	10.2219i	1.77292	−	0.475052i	0.783655	−	0.621197i	$-0.213353\pi$
$463$	38.1486	−	10.2219i	1.77292	−	0.475052i	0.989263	+	0.146145i	$0.0466865\pi$
$464$	3.10803	+	5.38327i	0.144287	+	0.249912i
$465$		0			0
$466$	−29.7399	−	5.24395i	−1.37767	−	0.242921i
$467$	−10.1843	−	2.72887i	−0.471273	−	0.126277i	0.0153633	−	0.999882i	$-0.495110\pi$
$467$	−10.1843	−	2.72887i	−0.471273	−	0.126277i	−0.486636	+	0.873605i	$0.661776\pi$
$468$	0.0873309	+	0.325923i	0.00403687	+	0.0150658i
$469$	−9.32309	−	7.82300i	−0.430500	−	0.361233i
$470$		0			0
$471$	12.9958	+	35.7055i	0.598813	+	1.64522i
$472$	0.451936	−	5.16565i	0.0208020	−	0.237768i
$473$	0.602002	−	0.859748i	0.0276801	−	0.0395312i
$474$	−31.0790			−1.42750
$475$		0			0
$476$	24.7927			1.13637
$477$	14.7658	−	21.0877i	0.676077	−	0.965539i
$478$	−1.84561	+	21.0954i	−0.0844162	+	0.964882i
$479$	−0.777924	−	2.13733i	−0.0355442	−	0.0976570i	0.920651	−	0.390387i	$-0.127659\pi$
$479$	−0.777924	−	2.13733i	−0.0355442	−	0.0976570i	−0.956195	+	0.292730i	$0.905436\pi$
$480$		0			0
$481$	−0.400492	−	0.336052i	−0.0182608	−	0.0153227i
$482$	2.28532	+	8.52894i	0.104094	+	0.388483i
$483$	44.1989	+	11.8431i	2.01112	+	0.538877i
$484$	−5.98677	−	1.05563i	−0.272126	−	0.0479831i
$485$		0			0
$486$	−11.1831	−	19.3697i	−0.507276	−	0.878629i
$487$	−38.4502	+	10.3027i	−1.74235	+	0.466860i	−0.982966	−	0.183786i	$-0.941165\pi$
$487$	−38.4502	+	10.3027i	−1.74235	+	0.466860i	−0.759380	+	0.650647i	$0.774498\pi$
$488$	6.74839	−	0.590408i	0.305485	−	0.0267265i
$489$	−52.3191	−	19.0426i	−2.36595	−	0.861136i
$490$		0			0
$491$	−8.05134	+	6.75587i	−0.363352	+	0.304888i	−0.806125	−	0.591745i	$-0.798439\pi$
$491$	−8.05134	+	6.75587i	−0.363352	+	0.304888i	0.442773	+	0.896634i	$0.353995\pi$
$492$	−0.886961	−	0.621057i	−0.0399873	−	0.0279994i
$493$	35.1998	−	35.1998i	1.58532	−	1.58532i
$494$	−0.139822	+	0.421844i	−0.00629087	+	0.0189796i
$495$		0			0
$496$	2.67336	−	0.471385i	0.120037	−	0.0211658i
$497$	38.5793	+	3.37525i	1.73052	+	0.151401i
$498$	22.5432	+	10.5121i	1.01019	+	0.471057i
$499$	4.42658	−	12.1619i	0.198161	−	0.544443i	−0.800318	−	0.599576i	$-0.795336\pi$
$499$	4.42658	−	12.1619i	0.198161	−	0.544443i	0.998479	+	0.0551328i	$0.0175582\pi$
$500$		0			0
$501$	18.2134	−	31.5465i	0.813713	−	1.40939i
$502$	−4.14913	+	15.4848i	−0.185185	+	0.691119i
$503$	−11.7450	+	8.22396i	−0.523685	+	0.366688i	−0.805327	−	0.592831i	$-0.798010\pi$
$503$	−11.7450	+	8.22396i	−0.523685	+	0.366688i	0.281641	+	0.959520i	$0.409121\pi$
$504$	1.77917	−	10.0902i	0.0792504	−	0.449451i
$505$		0			0
$506$	11.3041	+	6.52645i	0.502531	+	0.290136i
$507$	2.84374	+	32.5041i	0.126295	+	1.44356i
$508$	−16.4059	+	7.65020i	−0.727895	+	0.339423i
$509$	−8.08628	+	2.94317i	−0.358418	+	0.130454i	−0.514952	−	0.857219i	$-0.672190\pi$
$509$	−8.08628	+	2.94317i	−0.358418	+	0.130454i	0.156534	+	0.987673i	$0.449968\pi$
$510$		0			0
$511$	6.36915	+	36.1212i	0.281755	+	1.59791i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.197311	+	3.38299i	−0.00871151	+	0.149363i
$514$		−	8.83924i		−	0.389882i
$515$		0			0
$516$	−0.763924	−	0.910410i	−0.0336299	−	0.0400786i
$517$	−5.18362	+	11.1163i	−0.227975	+	0.488894i
$518$	6.70907	+	14.3877i	0.294780	+	0.632157i
$519$	−23.8885	+	28.4692i	−1.04859	+	1.24966i
$520$		0			0
$521$	13.0222	−	7.51836i	0.570512	−	0.329385i	−0.186842	−	0.982390i	$-0.559825\pi$
$521$	13.0222	−	7.51836i	0.570512	−	0.329385i	0.757354	+	0.653005i	$0.226492\pi$
$522$	−11.7997	−	16.8517i	−0.516457	−	0.737577i
$523$	22.1388	+	31.6175i	0.968063	+	1.38254i	0.923528	+	0.383530i	$0.125292\pi$
$523$	22.1388	+	31.6175i	0.968063	+	1.38254i	0.0445350	+	0.999008i	$0.485819\pi$
$524$	2.87768	−	1.66143i	0.125712	−	0.0725799i
$525$		0			0
$526$	5.92267	−	7.05837i	0.258241	−	0.307759i
$527$	−9.18742	−	19.7025i	−0.400210	−	0.858254i
$528$	2.35487	−	5.05003i	0.102483	−	0.219775i
$529$	7.47149	+	8.90418i	0.324848	+	0.387138i
$530$		0			0
$531$			17.1610i			0.744726i
$532$	9.26136	−	9.81488i	0.401531	−	0.425529i
$533$	0.0310768	+	0.0310768i	0.00134609	+	0.00134609i
$534$	6.53237	+	37.0469i	0.282683	+	1.60318i
$535$		0			0
$536$	−3.69409	+	1.34454i	−0.159561	+	0.0580753i
$537$	2.22931	−	1.03954i	0.0962017	−	0.0448596i
$538$	−1.22024	−	13.9474i	−0.0526083	−	0.601316i
$539$	4.96503	+	2.86656i	0.213859	+	0.123471i
$540$		0			0
$541$	−1.34147	+	7.60787i	−0.0576744	+	0.327088i	−0.999970	−	0.00769303i	$-0.997551\pi$
$541$	−1.34147	+	7.60787i	−0.0576744	+	0.327088i	0.942296	+	0.334781i	$0.108662\pi$
$542$	3.10337	−	2.17300i	0.133301	−	0.0933385i
$543$	3.93828	−	14.6978i	0.169008	−	0.630745i
$544$	4.00414	−	6.93538i	0.171676	−	0.297352i
$545$		0			0
$546$	−0.271170	+	0.745034i	−0.0116050	+	0.0318845i
$547$	20.0775	+	9.36230i	0.858453	+	0.400303i	0.801443	−	0.598071i	$-0.204066\pi$
$547$	20.0775	+	9.36230i	0.858453	+	0.400303i	0.0570093	+	0.998374i	$0.481844\pi$
$548$	−2.23079	−	0.195169i	−0.0952946	−	0.00833720i
$549$	−22.0785	+	3.89304i	−0.942289	+	0.166151i
$550$		0			0
$551$	−0.785864	−	27.0838i	−0.0334789	−	1.15381i
$552$	10.4513	−	10.4513i	0.444835	−	0.444835i
$553$	−31.3774	−	21.9707i	−1.33430	−	0.934289i
$554$	24.0289	−	20.1627i	1.02089	−	0.856629i
$555$		0			0
$556$	−2.40955	−	0.877005i	−0.102188	−	0.0371933i
$557$	8.43594	−	0.738049i	0.357442	−	0.0312721i	0.0929794	−	0.995668i	$-0.470361\pi$
$557$	8.43594	−	0.738049i	0.357442	−	0.0312721i	0.264463	+	0.964396i	$0.414805\pi$
$558$	−8.67785	+	2.32522i	−0.367363	+	0.0984346i
$559$	0.0241193	+	0.0417758i	0.00102014	+	0.00176693i
$560$		0			0
$561$	−43.9450	−	7.74869i	−1.85536	−	0.327150i
$562$	13.9242	+	3.73098i	0.587357	+	0.157382i
$563$	7.27563	+	27.1530i	0.306631	+	1.14436i	0.931532	+	0.363659i	$0.118473\pi$
$563$	7.27563	+	27.1530i	0.306631	+	1.14436i	−0.624901	+	0.780704i	$0.714861\pi$
$564$	10.6393	+	8.92747i	0.447997	+	0.375914i
$565$		0			0
$566$	−2.77450	−	7.62287i	−0.116621	−	0.320413i
$567$	2.15203	−	24.5978i	0.0903769	−	1.03301i
$568$	7.17493	−	10.2469i	0.301053	−	0.429949i
$569$	−24.3153			−1.01935			−0.509675	−	0.860367i	$-0.670234\pi$
$569$	−24.3153			−1.01935			−0.509675	+	0.860367i	$0.670234\pi$
$570$		0			0
$571$	−12.5657			−0.525859			−0.262930	−	0.964815i	$-0.584689\pi$
$571$	−12.5657			−0.525859			−0.262930	+	0.964815i	$0.584689\pi$
$572$	−0.129724	+	0.185266i	−0.00542405	+	0.00774634i
$573$	−0.682252	+	7.79818i	−0.0285015	+	0.325773i
$574$	−0.456434	−	1.25404i	−0.0190512	−	0.0523427i
$575$		0			0
$576$	−2.53523	−	2.12731i	−0.105634	−	0.0886378i
$577$	4.46823	+	16.6757i	0.186015	+	0.694217i	0.994411	+	0.105578i	$0.0336693\pi$
$577$	4.46823	+	16.6757i	0.186015	+	0.694217i	−0.808396	+	0.588639i	$0.799664\pi$
$578$	−45.5266	−	12.1988i	−1.89366	−	0.507404i
$579$	23.2349	+	4.09694i	0.965610	+	0.170263i
$580$		0			0
$581$	15.3284	+	26.5495i	0.635928	+	1.10146i
$582$	−3.13575	+	0.840220i	−0.129981	+	0.0348283i
$583$	17.1896	−	1.50390i	0.711922	−	0.0622851i
$584$	11.1330	+	4.05209i	0.460688	+	0.167677i
$585$		0			0
$586$	13.1743	−	11.0545i	0.544224	−	0.456659i
$587$	−22.3307	−	15.6361i	−0.921688	−	0.645373i	0.0133539	−	0.999911i	$-0.495749\pi$
$587$	−22.3307	−	15.6361i	−0.921688	−	0.645373i	−0.935042	+	0.354538i	$0.884638\pi$
$588$	4.59042	−	4.59042i	0.189306	−	0.189306i
$589$	−11.2318	−	3.72281i	−0.462797	−	0.153396i
$590$		0			0
$591$	67.2935	−	11.8657i	2.76808	−	0.488088i
$592$	5.10828	+	0.446917i	0.209949	+	0.0183682i
$593$	−6.62087	−	3.08736i	−0.271887	−	0.126783i	0.281894	−	0.959446i	$-0.409037\pi$
$593$	−6.62087	−	3.08736i	−0.271887	−	0.126783i	−0.553780	+	0.832663i	$0.686815\pi$
$594$	−0.589840	+	1.62057i	−0.0242014	+	0.0664929i
$595$		0			0
$596$	2.49075	−	4.31410i	0.102025	−	0.176713i
$597$	−3.37493	+	12.5954i	−0.138127	+	0.515496i
$598$	−0.491428	+	0.344101i	−0.0200960	+	0.0140714i
$599$	3.45728	−	19.6072i	0.141261	−	0.801129i	−0.829033	−	0.559199i	$-0.811109\pi$
$599$	3.45728	−	19.6072i	0.141261	−	0.801129i	0.970294	−	0.241929i	$-0.0777802\pi$
$600$		0			0
$601$	13.8740	+	8.01016i	0.565933	+	0.326741i	0.755523	−	0.655122i	$-0.227383\pi$
$601$	13.8740	+	8.01016i	0.565933	+	0.326741i	−0.189591	+	0.981863i	$0.560716\pi$
$602$	−0.127663	−	1.45920i	−0.00520316	−	0.0594724i
$603$	11.7913	−	5.49836i	0.480178	−	0.223911i
$604$	16.2250	−	5.90542i	0.660186	−	0.240288i
$605$		0			0
$606$	4.47296	+	25.3674i	0.181702	+	1.03048i
$607$	−20.6807	−	20.6807i	−0.839404	−	0.839404i	0.149376	−	0.988780i	$-0.452273\pi$
$607$	−20.6807	−	20.6807i	−0.839404	−	0.839404i	−0.988780	+	0.149376i	$0.952273\pi$
$608$	−1.24981	−	4.17588i	−0.0506864	−	0.169354i
$609$		−	48.3389i		−	1.95879i
$610$		0			0
$611$	−0.362360	−	0.431844i	−0.0146595	−	0.0174705i
$612$	−11.2008	+	24.0203i	−0.452767	+	0.970962i
$613$	−10.6897	−	22.9240i	−0.431751	−	0.925893i	−0.995025	−	0.0996229i	$-0.968236\pi$
$613$	−10.6897	−	22.9240i	−0.431751	−	0.925893i	0.563274	−	0.826270i	$-0.309541\pi$
$614$	10.1743	−	12.1253i	0.410603	−	0.489338i
$615$		0			0
$616$	5.94752	−	3.43380i	0.239632	−	0.138352i
$617$	−17.4672	−	24.9458i	−0.703204	−	1.00428i	−0.998800	−	0.0489664i	$-0.984407\pi$
$617$	−17.4672	−	24.9458i	−0.703204	−	1.00428i	0.295596	−	0.955313i	$-0.404482\pi$
$618$	−1.58511	−	2.26377i	−0.0637625	−	0.0910623i
$619$	13.5933	−	7.84808i	0.546360	−	0.315441i	−0.201293	−	0.979531i	$-0.564514\pi$
$619$	13.5933	−	7.84808i	0.546360	−	0.315441i	0.747653	+	0.664090i	$0.231181\pi$
$620$		0			0
$621$	−2.94046	+	3.50430i	−0.117996	+	0.140623i
$622$	−6.53366	−	14.0115i	−0.261976	−	0.561809i
$623$	−19.5945	+	42.0206i	−0.785039	+	1.68352i
$624$	0.164617	+	0.196183i	0.00658995	+	0.00785359i
$625$		0			0
$626$		−	30.6948i		−	1.22681i
$627$	−19.4833	+	14.5023i	−0.778088	+	0.579167i
$628$	10.6964	+	10.6964i	0.426832	+	0.426832i
$629$	−7.13083	−	40.4410i	−0.284325	−	1.61249i
$630$		0			0
$631$	−15.8774	+	5.77892i	−0.632071	+	0.230055i	−0.638133	−	0.769927i	$-0.720293\pi$
$631$	−15.8774	+	5.77892i	−0.632071	+	0.230055i	0.00606138	+	0.999982i	$0.498071\pi$
$632$	−11.2136	+	5.22898i	−0.446053	+	0.207998i
$633$	3.56117	+	40.7044i	0.141544	+	1.61785i
$634$	−3.44645	−	1.98981i	−0.136876	−	0.0790255i
$635$		0			0
$636$	3.39289	−	19.2420i	0.134537	−	0.762996i
$637$	−0.215846	+	0.151137i	−0.00855212	+	0.00598826i
$638$	3.56889	−	13.3193i	0.141294	−	0.527315i
$639$	−20.6995	+	35.8525i	−0.818858	+	1.41830i
$640$		0			0
$641$	3.61897	−	9.94303i	0.142941	−	0.392726i	−0.847477	−	0.530832i	$-0.821879\pi$
$641$	3.61897	−	9.94303i	0.142941	−	0.392726i	0.990417	+	0.138106i	$0.0441016\pi$
$642$	40.3990	+	18.8384i	1.59442	+	0.743491i
$643$	−49.4692	−	4.32800i	−1.95088	−	0.170679i	−0.957739	−	0.287639i	$-0.907130\pi$
$643$	−49.4692	−	4.32800i	−1.95088	−	0.170679i	−0.993137	+	0.116960i	$0.962685\pi$
$644$	17.9400	−	3.16330i	0.706933	−	0.124651i
$645$		0			0
$646$	−29.7117	+	18.3231i	−1.16899	+	0.720913i
$647$	9.57339	−	9.57339i	0.376369	−	0.376369i	−0.493422	−	0.869790i	$-0.664254\pi$
$647$	9.57339	−	9.57339i	0.376369	−	0.376369i	0.869790	+	0.493422i	$0.164254\pi$
$648$	−6.53331	−	4.57467i	−0.256653	−	0.179710i
$649$	−8.81162	+	7.39383i	−0.345886	+	0.290233i
$650$		0			0
$651$	−19.8369	−	7.22003i	−0.777468	−	0.282975i
$652$	−22.0811	+	1.93185i	−0.864763	+	0.0756570i
$653$	−3.43555	+	0.920552i	−0.134443	+	0.0360240i	−0.325413	−	0.945572i	$-0.605503\pi$
$653$	−3.43555	+	0.920552i	−0.134443	+	0.0360240i	0.190970	+	0.981596i	$0.438837\pi$
$654$	−19.5649	−	33.8874i	−0.765048	−	1.32510i
$655$		0			0
$656$	−0.424516	−	0.0748536i	−0.0165746	−	0.00292254i
$657$	−37.8734	−	10.1481i	−1.47758	−	0.395917i
$658$	4.43041	+	16.5345i	0.172715	+	0.644582i
$659$	3.47522	+	2.91606i	0.135376	+	0.113594i	0.707961	−	0.706251i	$-0.249615\pi$
$659$	3.47522	+	2.91606i	0.135376	+	0.113594i	−0.572586	+	0.819845i	$0.694060\pi$
$660$		0			0
$661$	−5.63415	−	15.4797i	−0.219143	−	0.602090i	0.780594	−	0.625039i	$-0.214917\pi$
$661$	−5.63415	−	15.4797i	−0.219143	−	0.602090i	−0.999737	+	0.0229485i	$0.992695\pi$
$662$	−1.33258	+	15.2315i	−0.0517923	+	0.591988i
$663$	1.17635	−	1.68001i	0.0456857	−	0.0652460i
$664$	9.90245			0.384289
$665$		0			0
$666$	−16.9704			−0.657591
$667$	20.9794	−	29.9617i	0.812325	−	1.16012i
$668$	1.26392	−	14.4466i	0.0489024	−	0.558957i
$669$	12.7753	+	35.0999i	0.493922	+	1.35704i
$670$		0			0
$671$	−11.5115	−	9.65928i	−0.444396	−	0.372892i
$672$	−2.01269	−	7.51147i	−0.0776413	−	0.289761i
$673$	−0.277010	−	0.0742246i	−0.0106779	−	0.00286115i	0.253476	−	0.967342i	$-0.418426\pi$
$673$	−0.277010	−	0.0742246i	−0.0106779	−	0.00286115i	−0.264154	+	0.964480i	$0.585093\pi$
$674$	10.1824	+	1.79543i	0.392212	+	0.0691576i
$675$		0			0
$676$	6.49480	+	11.2493i	0.249800	+	0.432666i
$677$	−18.2448	+	4.88869i	−0.701206	+	0.187888i	−0.591771	−	0.806106i	$-0.701571\pi$
$677$	−18.2448	+	4.88869i	−0.701206	+	0.187888i	−0.109435	+	0.993994i	$0.534904\pi$
$678$	−46.6587	+	4.08210i	−1.79191	+	0.156772i
$679$	−3.75984	−	1.36847i	−0.144289	−	0.0525170i
$680$		0			0
$681$	20.1623	−	16.9182i	0.772622	−	0.648307i
$682$	−4.93278	−	3.45397i	−0.188886	−	0.132259i
$683$	−33.5879	+	33.5879i	−1.28521	+	1.28521i	−0.347542	+	0.937664i	$0.612984\pi$
$683$	−33.5879	+	33.5879i	−1.28521	+	1.28521i	−0.937664	+	0.347542i	$0.887016\pi$
$684$	5.32500	+	13.4070i	0.203607	+	0.512629i
$685$		0			0
$686$	−13.4623	+	2.37377i	−0.513993	+	0.0906308i
$687$	26.5209	+	2.32028i	1.01183	+	0.0885240i
$688$	−0.428806	−	0.199956i	−0.0163481	−	0.00762324i
$689$	−0.271245	+	0.745241i	−0.0103336	+	0.0283914i
$690$		0			0
$691$	0.376062	−	0.651359i	0.0143061	−	0.0247789i	−0.858784	−	0.512338i	$-0.828779\pi$
$691$	0.376062	−	0.651359i	0.0143061	−	0.0247789i	0.873090	+	0.487559i	$0.162113\pi$
$692$	−3.82930	+	14.2912i	−0.145568	+	0.543268i
$693$	−18.6180	+	13.0364i	−0.707238	+	0.495213i
$694$	−1.36467	+	7.73941i	−0.0518020	+	0.293784i
$695$		0			0
$696$	−13.5221	−	7.80698i	−0.512553	−	0.295923i
$697$	0.300869	+	3.43895i	0.0113962	+	0.130260i
$698$	26.8148	−	12.5039i	1.01495	−	0.473281i
$699$	71.2806	−	25.9440i	2.69608	−	0.981293i
$700$		0			0
$701$	0.344279	+	1.95250i	0.0130032	+	0.0737450i	0.990619	−	0.136654i	$-0.0436348\pi$
$701$	0.344279	+	1.95250i	0.0130032	+	0.0737450i	−0.977616	+	0.210399i	$0.932524\pi$
$702$	−0.0560474	−	0.0560474i	−0.00211537	−	0.00211537i
$703$	−18.6734	−	12.2839i	−0.704282	−	0.463295i
$704$		−	2.21830i		−	0.0836055i
$705$		0			0
$706$	−1.98346	−	2.36380i	−0.0746485	−	0.0889626i
$707$	−13.4171	+	28.7731i	−0.504603	+	1.08212i
$708$	5.50461	+	11.8047i	0.206876	+	0.443647i
$709$	11.9715	−	14.2671i	0.449599	−	0.535811i	−0.492871	−	0.870102i	$-0.664053\pi$
$709$	11.9715	−	14.2671i	0.449599	−	0.535811i	0.942470	+	0.334292i	$0.108497\pi$
$710$		0			0
$711$	35.4619	−	20.4739i	1.32993	−	0.767833i
$712$	8.59002	+	12.2678i	0.321925	+	0.459756i
$713$	−9.16185	−	13.0845i	−0.343114	−	0.490017i
$714$	−53.9326	+	31.1380i	−2.01838	+	1.16531i
$715$		0			0
$716$	0.629454	−	0.750154i	0.0235238	−	0.0280346i
$717$	−22.4797	−	48.2078i	−0.839518	−	1.80035i
$718$	8.81481	−	18.9034i	0.328966	−	0.705469i
$719$	−12.3045	−	14.6640i	−0.458881	−	0.546873i	0.486141	−	0.873881i	$-0.338404\pi$
$719$	−12.3045	−	14.6640i	−0.458881	−	0.546873i	−0.945022	+	0.327007i	$0.893960\pi$
$720$		0			0
$721$		−	3.40608i		−	0.126849i
$722$	−3.84515	+	18.6068i	−0.143102	+	0.692475i
$723$	−15.6832	−	15.6832i	−0.583263	−	0.583263i
$724$	−1.05192	−	5.96573i	−0.0390943	−	0.221715i
$725$		0			0
$726$	14.3491	−	5.22264i	0.532545	−	0.193831i
$727$	−11.5853	+	5.40233i	−0.429676	+	0.200361i	−0.625411	−	0.780296i	$-0.715069\pi$
$727$	−11.5853	+	5.40233i	−0.429676	+	0.200361i	0.195735	+	0.980657i	$0.437291\pi$
$728$	0.0275099	+	0.314440i	0.00101958	+	0.0116539i
$729$	27.9328	+	16.1270i	1.03455	+	0.597297i
$730$		0			0
$731$	−0.657953	+	3.73144i	−0.0243353	+	0.138012i
$732$	−13.9386	+	9.75989i	−0.515184	+	0.360736i
$733$	1.96454	−	7.33176i	0.0725619	−	0.270805i	−0.920107	−	0.391666i	$-0.871899\pi$
$733$	1.96454	−	7.33176i	0.0725619	−	0.270805i	0.992669	+	0.120861i	$0.0385656\pi$
$734$	10.6184	−	18.3917i	0.391934	−	0.678849i
$735$		0			0
$736$	2.01251	−	5.52932i	0.0741820	−	0.203813i
$737$	7.90349	+	3.68546i	0.291129	+	0.135756i
$738$	1.42118	+	0.124337i	0.0523144	+	0.00457692i
$739$	−42.6996	+	7.52908i	−1.57073	+	0.276962i	−0.890134	−	0.455698i	$-0.849390\pi$
$739$	−42.6996	+	7.52908i	−1.57073	+	0.276962i	−0.680594	+	0.732660i	$0.738278\pi$
$740$		0			0
$741$	−0.225648	−	1.09326i	−0.00828940	−	0.0401620i
$742$	17.0283	−	17.0283i	0.625127	−	0.625127i
$743$	−5.52934	−	3.87168i	−0.202852	−	0.142038i	0.467737	−	0.883868i	$-0.345069\pi$
$743$	−5.52934	−	3.87168i	−0.202852	−	0.142038i	−0.670589	+	0.741829i	$0.733958\pi$
$744$	−5.22345	+	4.38299i	−0.191501	+	0.160688i
$745$		0			0
$746$	7.08022	+	2.57699i	0.259225	+	0.0943503i
$747$	−32.6475	+	2.85628i	−1.19451	+	0.104506i
$748$	−17.1595	+	4.59787i	−0.627413	+	0.168115i
$749$	27.4695	+	47.5786i	1.00372	+	1.73849i
$750$		0			0
$751$	31.6882	+	5.58749i	1.15632	+	0.203890i	0.718733	−	0.695286i	$-0.244722\pi$
$751$	31.6882	+	5.58749i	1.15632	+	0.203890i	0.437587	+	0.899176i	$0.355833\pi$
$752$	5.34081	+	1.43107i	0.194759	+	0.0521856i
$753$	−10.4221	−	38.8958i	−0.379802	−	1.41744i
$754$	0.485488	+	0.407373i	0.0176804	+	0.0148356i
$755$		0			0
$756$	0.823184	+	2.26168i	0.0299389	+	0.0822565i
$757$	−1.53708	+	17.5689i	−0.0558662	+	0.638553i	0.915712	+	0.401835i	$0.131627\pi$
$757$	−1.53708	+	17.5689i	−0.0558662	+	0.638553i	−0.971578	+	0.236718i	$0.923928\pi$
$758$	−4.44747	+	6.35164i	−0.161539	+	0.230702i
$759$	−32.7872			−1.19010
$760$		0			0
$761$	−27.9924			−1.01472			−0.507361	−	0.861733i	$-0.669379\pi$
$761$	−27.9924			−1.01472			−0.507361	+	0.861733i	$0.669379\pi$
$762$	26.0804	−	37.2466i	0.944792	−	1.34930i
$763$	4.20329	−	48.0439i	0.152169	−	1.73930i
$764$	1.06587	+	2.92844i	0.0385617	+	0.105947i
$765$		0			0
$766$	13.8701	+	11.6384i	0.501148	+	0.420513i
$767$	−0.136832	−	0.510662i	−0.00494070	−	0.0184389i
$768$	−2.42628	−	0.650120i	−0.0875509	−	0.0234592i
$769$	−11.1265	−	1.96191i	−0.401233	−	0.0707482i	−0.0306095	−	0.999531i	$-0.509745\pi$
$769$	−11.1265	−	1.96191i	−0.401233	−	0.0707482i	−0.370623	+	0.928783i	$0.620856\pi$
$770$		0			0
$771$	11.1015	+	19.2284i	0.399812	+	0.692494i
$772$	9.07268	−	2.43102i	0.326533	−	0.0874942i
$773$	20.5110	−	1.79448i	0.737729	−	0.0645430i	0.287904	−	0.957659i	$-0.407042\pi$
$773$	20.5110	−	1.79448i	0.737729	−	0.0645430i	0.449826	+	0.893116i	$0.351486\pi$
$774$	1.47141	+	0.535550i	0.0528888	+	0.0192499i
$775$		0			0
$776$	−0.990042	+	0.830743i	−0.0355404	+	0.0298220i
$777$	−32.6645	−	22.8719i	−1.17183	−	0.820526i
$778$	−1.25293	+	1.25293i	−0.0449199	+	0.0449199i
$779$	1.47380	+	1.16552i	0.0528043	+	0.0417591i
$780$		0			0
$781$	−27.3274	+	4.81856i	−0.977852	+	0.172422i
$782$	−46.9429	−	4.10697i	−1.67867	−	0.146865i
$783$	4.37978	+	2.04233i	0.156521	+	0.0729868i
$784$	0.883938	−	2.42860i	0.0315692	−	0.0867357i
$785$		0			0
$786$	−4.17330	+	7.22837i	−0.148857	+	0.257827i
$787$	0.851073	−	3.17625i	0.0303375	−	0.113221i	−0.949097	−	0.314985i	$-0.898001\pi$
$787$	0.851073	−	3.17625i	0.0303375	−	0.113221i	0.979434	+	0.201764i	$0.0646673\pi$
$788$	22.2838	−	15.6033i	0.793826	−	0.555843i
$789$	−4.01900	+	22.7929i	−0.143080	+	0.811448i
$790$		0			0
$791$	−49.9925	−	28.8632i	−1.77753	−	1.02626i
$792$	0.639852	+	7.31355i	0.0227362	+	0.259876i
$793$	0.625952	−	0.291886i	0.0222282	−	0.0103652i
$794$	−4.14452	+	1.50848i	−0.147083	+	0.0535340i
$795$		0			0
$796$	0.901450	+	5.11238i	0.0319510	+	0.181203i
$797$	2.52806	+	2.52806i	0.0895486	+	0.0895486i	0.750462	−	0.660913i	$-0.229831\pi$
$797$	2.52806	+	2.52806i	0.0895486	+	0.0895486i	−0.660913	+	0.750462i	$0.729831\pi$
$798$	−7.81980	+	32.9824i	−0.276818	+	1.16757i
$799$		−	44.2795i		−	1.56650i
$800$		0			0
$801$	−31.8591	−	37.9682i	−1.12568	−	1.34154i
$802$	−5.61583	+	12.0432i	−0.198302	+	0.425260i
$803$	−11.1070	−	23.8190i	−0.391958	−	0.840556i
$804$	6.34727	−	7.56439i	0.223851	−	0.266775i
$805$		0			0
$806$	0.239688	−	0.138384i	0.00844264	−	0.00487436i
$807$	20.1715	+	28.8079i	0.710071	+	1.01409i
$808$	5.88192	+	8.40025i	0.206925	+	0.295520i
$809$	−37.2695	+	21.5176i	−1.31033	+	0.756517i	−0.982150	−	0.188099i	$-0.939767\pi$
$809$	−37.2695	+	21.5176i	−1.31033	+	0.756517i	−0.328176	+	0.944617i	$0.606434\pi$
$810$		0			0
$811$	19.5841	−	23.3394i	0.687689	−	0.819556i	−0.303385	−	0.952868i	$-0.598117\pi$
$811$	19.5841	−	23.3394i	0.687689	−	0.819556i	0.991074	+	0.133312i	$0.0425612\pi$
$812$	−8.13294	−	17.4411i	−0.285410	−	0.612064i
$813$	−4.02175	+	8.62467i	−0.141049	+	0.302480i
$814$	−7.31171	−	8.71376i	−0.256275	−	0.305417i
$815$		0			0
$816$			20.1158i			0.704193i
$817$	1.23142	+	1.65436i	0.0430818	+	0.0578786i
$818$	26.1993	+	26.1993i	0.916037	+	0.916037i
$819$	−0.181395	−	1.02874i	−0.00633846	−	0.0359472i
$820$		0			0
$821$	21.7276	−	7.90819i	0.758298	−	0.275998i	0.0662047	−	0.997806i	$-0.478911\pi$
$821$	21.7276	−	7.90819i	0.758298	−	0.275998i	0.692093	+	0.721808i	$0.256689\pi$
$822$	5.09786	−	2.37717i	0.177808	−	0.0829134i
$823$	0.256353	+	2.93012i	0.00893589	+	0.102138i	0.999353	−	0.0359723i	$-0.0114528\pi$
$823$	0.256353	+	2.93012i	0.00893589	+	0.102138i	−0.990417	+	0.138110i	$0.955897\pi$
$824$	−0.952799	−	0.550099i	−0.0331923	−	0.0191636i
$825$		0			0
$826$	−2.78763	+	15.8094i	−0.0969940	+	0.550080i
$827$	18.7485	−	13.1278i	0.651950	−	0.456500i	−0.200230	−	0.979749i	$-0.564169\pi$
$827$	18.7485	−	13.1278i	0.651950	−	0.456500i	0.852180	+	0.523249i	$0.175280\pi$
$828$	−5.04017	+	18.8102i	−0.175158	+	0.653698i
$829$	−6.70018	+	11.6050i	−0.232707	+	0.403060i	−0.958604	−	0.284744i	$-0.908092\pi$
$829$	−6.70018	+	11.6050i	−0.232707	+	0.403060i	0.725897	+	0.687803i	$0.241425\pi$
$830$		0			0
$831$	−26.9482	+	74.0395i	−0.934822	+	2.56840i
$832$	0.0924027	+	0.0430881i	0.00320349	+	0.00149381i
$833$	−20.6183	−	1.80387i	−0.714383	−	0.0625004i
$834$	6.34307	−	1.11845i	0.219642	−	0.0387289i
$835$		0			0
$836$	−4.58977	+	8.51062i	−0.158741	+	0.294346i
$837$	1.49229	−	1.49229i	0.0515810	−	0.0515810i
$838$	32.4445	+	22.7179i	1.12078	+	0.784776i
$839$	12.9503	−	10.8666i	0.447095	−	0.375157i	−0.391262	−	0.920279i	$-0.627961\pi$
$839$	12.9503	−	10.8666i	0.447095	−	0.375157i	0.838356	+	0.545122i	$0.183517\pi$
$840$		0			0
$841$	−9.05812	−	3.29689i	−0.312349	−	0.113686i
$842$	−11.0075	+	0.963028i	−0.379342	+	0.0331881i
$843$	−34.9758	+	9.37175i	−1.20463	+	0.322780i
$844$	8.13335	+	14.0874i	0.279962	+	0.484908i
$845$		0			0
$846$	−18.0209	−	3.17758i	−0.619573	−	0.109247i
$847$	18.1790	+	4.87104i	0.624636	+	0.167371i
$848$	−2.01325	−	7.51355i	−0.0691353	−	0.258017i
$849$	15.6093	+	13.0978i	0.535711	+	0.449515i
$850$		0			0
$851$	−10.3197	−	28.3532i	−0.353756	−	0.971935i
$852$	−2.73854	+	31.3017i	−0.0938210	+	1.07238i
$853$	−21.2172	+	30.3013i	−0.726464	+	1.03750i	0.270731	+	0.962655i	$0.412735\pi$
$853$	−21.2172	+	30.3013i	−0.726464	+	1.03750i	−0.997195	+	0.0748434i	$0.976154\pi$
$854$	−20.9720			−0.717647
$855$		0			0
$856$	17.7459			0.606542
$857$	−10.2557	+	14.6467i	−0.350328	+	0.500321i	−0.955183	−	0.296015i	$-0.904342\pi$
$857$	−10.2557	+	14.6467i	−0.350328	+	0.500321i	0.604855	+	0.796336i	$0.293231\pi$
$858$	0.0495135	−	0.565942i	0.00169036	−	0.0193209i
$859$	−1.84874	−	5.07938i	−0.0630783	−	0.173306i	0.904150	−	0.427216i	$-0.140506\pi$
$859$	−1.84874	−	5.07938i	−0.0630783	−	0.173306i	−0.967228	+	0.253910i	$0.918283\pi$
$860$		0			0
$861$	2.56790	+	2.15472i	0.0875137	+	0.0734327i
$862$	4.48170	+	16.7259i	0.152647	+	0.569688i
$863$	11.7367	+	3.14485i	0.399523	+	0.107052i	0.452985	−	0.891518i	$-0.350359\pi$
$863$	11.7367	+	3.14485i	0.399523	+	0.107052i	−0.0534624	+	0.998570i	$0.517026\pi$
$864$	0.765619	+	0.134999i	0.0260469	+	0.00459277i
$865$		0			0
$866$	6.88873	+	11.9316i	0.234089	+	0.405453i
$867$	114.357	−	30.6419i	3.88377	−	1.04065i
$868$	−8.37209	+	0.732463i	−0.284167	+	0.0248614i
$869$	25.7915	+	9.38732i	0.874915	+	0.318443i
$870$		0			0
$871$	−0.307033	+	0.257631i	−0.0104034	+	0.00872951i
$872$	−12.7607	−	8.93514i	−0.432132	−	0.302582i
$873$	3.02445	−	3.02445i	0.102362	−	0.102362i
$874$	−19.1615	+	17.0495i	−0.648147	+	0.576708i
$875$		0			0
$876$	−29.3073	+	5.16768i	−0.990203	+	0.174600i
$877$	52.3321	+	4.57846i	1.76713	+	0.154604i	0.923820	−	0.382827i	$-0.125049\pi$
$877$	52.3321	+	4.57846i	1.76713	+	0.154604i	0.843308	+	0.537431i	$0.180605\pi$
$878$	−26.3874	−	12.3047i	−0.890532	−	0.415262i
$879$	−14.7748	+	40.5935i	−0.498342	+	1.36918i
$880$		0			0
$881$	−0.0675398	+	0.116982i	−0.00227548	+	0.00394124i	−0.867161	−	0.498028i	$-0.834058\pi$
$881$	−0.0675398	+	0.116982i	−0.00227548	+	0.00394124i	0.864885	+	0.501969i	$0.167391\pi$
$882$	−2.21375	+	8.26183i	−0.0745409	+	0.278190i
$883$	−14.9182	+	10.4458i	−0.502037	+	0.351530i	−0.797001	−	0.603979i	$-0.793581\pi$
$883$	−14.9182	+	10.4458i	−0.502037	+	0.351530i	0.294964	+	0.955508i	$0.404692\pi$
$884$	0.141781	−	0.804081i	0.00476862	−	0.0270442i
$885$		0			0
$886$	9.99249	+	5.76917i	0.335704	+	0.193819i
$887$	−2.38807	−	27.2958i	−0.0801837	−	0.916503i	−0.924631	−	0.380865i	$-0.875626\pi$
$887$	−2.38807	−	27.2958i	−0.0801837	−	0.916503i	0.844447	−	0.535639i	$-0.179929\pi$
$888$	−11.6736	+	5.44347i	−0.391739	+	0.182671i
$889$	52.6616	−	19.1673i	1.76621	−	0.642849i
$890$		0			0
$891$	3.07228	+	17.4237i	0.102925	+	0.583717i
$892$	10.5150	+	10.5150i	0.352067	+	0.352067i
$893$	−17.5293	−	16.5407i	−0.586596	−	0.553514i
$894$			12.5129i			0.418493i
$895$		0			0
$896$	−1.98999	−	2.37158i	−0.0664810	−	0.0792289i
$897$	0.636855	−	1.36574i	0.0212640	−	0.0456008i
$898$	−10.6583	−	22.8567i	−0.355671	−	0.762739i
$899$	−10.8465	+	12.9263i	−0.361750	+	0.431117i
$900$		0			0
$901$	−53.9476	+	31.1466i	−1.79725	+	1.03764i
$902$	0.548472	+	0.783300i	0.0182621	+	0.0260810i
$903$	2.11037	+	3.01392i	0.0702286	+	0.100297i
$904$	−16.1481	+	9.32310i	−0.537077	+	0.310082i
$905$		0			0
$906$	−27.8781	+	33.2239i	−0.926189	+	1.10379i
$907$	−0.303791	−	0.651481i	−0.0100872	−	0.0216321i	0.901200	−	0.433404i	$-0.142688\pi$
$907$	−0.303791	−	0.651481i	−0.0100872	−	0.0216321i	−0.911287	+	0.411772i	$0.864910\pi$
$908$	4.42831	−	9.49653i	0.146958	−	0.315154i
$909$	−21.8151	−	25.9983i	−0.723562	−	0.862308i
$910$		0			0
$911$			22.7653i			0.754247i	0.926163	+	0.377123i	$0.123087\pi$
$911$			22.7653i			0.754247i	−0.926163	+	0.377123i	$0.876913\pi$
$912$	7.96340	+	7.51430i	0.263695	+	0.248823i
$913$	−15.5328	−	15.5328i	−0.514059	−	0.514059i
$914$	−5.71147	−	32.3914i	−0.188919	−	1.07141i
$915$		0			0
$916$	9.95937	−	3.62491i	0.329067	−	0.119771i
$917$	−9.32334	+	4.34755i	−0.307884	+	0.143569i
$918$	−0.542621	−	6.20219i	−0.0179092	−	0.204703i
$919$	40.8735	+	23.5983i	1.34829	+	0.778436i	0.988007	−	0.154406i	$-0.0493465\pi$
$919$	40.8735	+	23.5983i	1.34829	+	0.778436i	0.360284	+	0.932843i	$0.382680\pi$
$920$		0			0
$921$	−6.90409	+	39.1551i	−0.227498	+	1.29020i
$922$	10.9543	−	7.67030i	0.360761	−	0.252608i
$923$	0.330089	−	1.23191i	0.0108650	−	0.0405488i
$924$	−8.62527	+	14.9394i	−0.283750	+	0.491470i
$925$		0			0
$926$	−13.5079	+	37.1126i	−0.443896	+	1.21960i
$927$	3.29996	+	1.53880i	0.108385	+	0.0505407i
$928$	−6.19241	−	0.541766i	−0.203276	−	0.0177843i
$929$	25.4212	−	4.48244i	0.834043	−	0.147064i	0.259710	−	0.965687i	$-0.416373\pi$
$929$	25.4212	−	4.48244i	0.834043	−	0.147064i	0.574332	+	0.818622i	$0.305262\pi$
$930$		0			0
$931$	−8.41615	+	7.48851i	−0.275828	+	0.245426i
$932$	21.3537	−	21.3537i	0.699464	−	0.699464i
$933$	31.8105	+	22.2739i	1.04143	+	0.729216i
$934$	8.07683	−	6.77726i	0.264282	−	0.221759i
$935$		0			0
$936$	−0.317072	−	0.115405i	−0.0103638	−	0.00377212i
$937$	25.5470	−	2.23508i	0.834586	−	0.0730168i	0.338152	−	0.941091i	$-0.390198\pi$
$937$	25.5470	−	2.23508i	0.834586	−	0.0730168i	0.496434	+	0.868075i	$0.334643\pi$
$938$	11.7557	−	3.14994i	0.383838	−	0.102849i
$939$	38.5507	+	66.7717i	1.25805	+	2.17901i
$940$		0			0
$941$	32.2865	+	5.69299i	1.05251	+	0.185586i	0.673031	−	0.739614i	$-0.264992\pi$
$941$	32.2865	+	5.69299i	1.05251	+	0.185586i	0.379480	+	0.925200i	$0.376103\pi$
$942$	−36.7023	−	9.83436i	−1.19583	−	0.320421i
$943$	0.656485	+	2.45003i	0.0213781	+	0.0797841i
$944$	3.97223	+	3.33310i	0.129285	+	0.108483i
$945$		0			0
$946$	0.358970	+	0.986262i	0.0116711	+	0.0320661i
$947$	1.82725	−	20.8855i	0.0593775	−	0.678688i	−0.906927	−	0.421287i	$-0.861578\pi$
$947$	1.82725	−	20.8855i	0.0593775	−	0.678688i	0.966305	−	0.257401i	$-0.0828661\pi$
$948$	17.8262	−	25.4584i	0.578967	−	0.826850i
$949$	1.20792			0.0392106
$950$		0			0
$951$	9.99630			0.324152
$952$	−14.2205	+	20.3090i	−0.460889	+	0.658217i
$953$	−1.59261	+	18.2036i	−0.0515897	+	0.589673i	0.925770	+	0.378088i	$0.123418\pi$
$953$	−1.59261	+	18.2036i	−0.0515897	+	0.589673i	−0.977360	+	0.211585i	$0.932137\pi$
$954$	8.80473	+	24.1908i	0.285064	+	0.783206i
$955$		0			0
$956$	−16.2218	−	13.6117i	−0.524649	−	0.440233i
$957$	8.96459	+	33.4563i	0.289784	+	1.08149i
$958$	2.19700	+	0.588683i	0.0709817	+	0.0190195i
$959$	6.82731	+	1.20384i	0.220465	+	0.0388740i
$960$		0			0
$961$	−11.8155	−	20.4650i	−0.381144	−	0.660161i
$962$	0.504991	−	0.135312i	0.0162816	−	0.00436263i
$963$	−58.5066	+	5.11866i	−1.88535	+	0.164947i
$964$	−8.29731	−	3.01997i	−0.267238	−	0.0972668i
$965$		0			0
$966$	−35.0527	+	29.4127i	−1.12780	+	0.946338i
$967$	−30.8767	−	21.6201i	−0.992926	−	0.695254i	−0.0402338	−	0.999190i	$-0.512810\pi$
$967$	−30.8767	−	21.6201i	−0.992926	−	0.695254i	−0.952693	+	0.303936i	$0.901699\pi$
$968$	4.29859	−	4.29859i	0.138162	−	0.138162i
$969$	41.6205	−	77.1751i	1.33704	−	2.47922i
$970$		0			0
$971$	10.0346	−	1.76938i	0.322027	−	0.0567820i	−0.0102981	−	0.999947i	$-0.503278\pi$
$971$	10.0346	−	1.76938i	0.322027	−	0.0567820i	0.332325	+	0.943165i	$0.392167\pi$
$972$	22.2811	+	1.94935i	0.714667	+	0.0625253i
$973$	7.19465	+	3.35492i	0.230650	+	0.107554i
$974$	13.6147	−	37.4060i	0.436242	−	1.19857i
$975$		0			0
$976$	−3.38708	+	5.86660i	−0.108418	+	0.187785i
$977$	2.86746	−	10.7015i	0.0917380	−	0.342371i	−0.904767	−	0.425908i	$-0.859955\pi$
$977$	2.86746	−	10.7015i	0.0917380	−	0.342371i	0.996505	+	0.0835366i	$0.0266215\pi$
$978$	45.6078	−	31.9349i	1.45838	−	1.02117i
$979$	5.76892	−	32.7171i	0.184375	−	1.04564i
$980$		0			0
$981$	44.6481	+	25.7776i	1.42550	+	0.823015i
$982$	−0.916031	−	10.4703i	−0.0292317	−	0.334120i
$983$	11.7539	−	5.48094i	0.374892	−	0.174815i	−0.226035	−	0.974119i	$-0.572576\pi$
$983$	11.7539	−	5.48094i	0.374892	−	0.174815i	0.600926	+	0.799304i	$0.294798\pi$
$984$	1.01748	−	0.370332i	0.0324361	−	0.0118058i
$985$		0			0
$986$	8.64421	+	49.0237i	0.275288	+	1.56123i
$987$	−30.4039	−	30.4039i	−0.967768	−	0.967768i
$988$	−0.265356	−	0.356495i	−0.00844209	−	0.0113416i
$989$			2.78401i			0.0885265i
$990$		0			0
$991$	8.83684	+	10.5313i	0.280711	+	0.334539i	0.887915	−	0.460007i	$-0.152153\pi$
$991$	8.83684	+	10.5313i	0.280711	+	0.334539i	−0.607204	+	0.794546i	$0.707709\pi$
$992$	−1.14724	+	2.46026i	−0.0364249	+	0.0781134i
$993$	−16.2309	−	34.8074i	−0.515073	−	1.10458i
$994$	−24.8930	+	29.6664i	−0.789559	+	0.940959i
$995$		0			0
$996$	−21.5412	+	12.4368i	−0.682560	+	0.394076i
$997$	−18.6827	−	26.6816i	−0.591687	−	0.845016i	0.405938	−	0.913901i	$-0.366945\pi$
$997$	−18.6827	−	26.6816i	−0.591687	−	0.845016i	−0.997625	+	0.0688846i	$0.978056\pi$
$998$	7.42349	+	10.6018i	0.234986	+	0.335595i
$999$	3.45241	−	1.99325i	0.109229	−	0.0630636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.c.143.3	✓	72
5.2	odd	4	inner	950.2.bb.c.257.1	yes	72
5.3	odd	4	inner	950.2.bb.c.257.6	yes	72
5.4	even	2	inner	950.2.bb.c.143.4	yes	72
19.2	odd	18	inner	950.2.bb.c.743.1	yes	72
95.2	even	36	inner	950.2.bb.c.857.3	yes	72
95.59	odd	18	inner	950.2.bb.c.743.6	yes	72
95.78	even	36	inner	950.2.bb.c.857.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.c.143.3	✓	72	1.1	even	1	trivial
950.2.bb.c.143.4	yes	72	5.4	even	2	inner
950.2.bb.c.257.1	yes	72	5.2	odd	4	inner
950.2.bb.c.257.6	yes	72	5.3	odd	4	inner
950.2.bb.c.743.1	yes	72	19.2	odd	18	inner
950.2.bb.c.743.6	yes	72	95.59	odd	18	inner
950.2.bb.c.857.3	yes	72	95.2	even	36	inner
950.2.bb.c.857.4	yes	72	95.78	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)

\(f(q)\)	\(=\)	\(q+(-0.573576 + 0.819152i) q^{2} +(0.218924 - 2.50231i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.92421 + 1.61460i) q^{6} +(0.801272 + 2.99039i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-3.25922 - 0.574689i) q^{9} +O(q^{10})\)	\(q+(-0.573576 + 0.819152i) q^{2} +(0.218924 - 2.50231i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.92421 + 1.61460i) q^{6} +(0.801272 + 2.99039i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-3.25922 - 0.574689i) q^{9} +(-1.10915 - 1.92111i) q^{11} +(-2.42628 + 0.650120i) q^{12} +(0.101567 - 0.00888598i) q^{13} +(-2.90917 - 1.05885i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(6.56000 + 4.59336i) q^{17} +(2.34017 - 2.34017i) q^{18} +(4.26892 - 0.881100i) q^{19} +(7.65831 - 1.35037i) q^{21} +(2.20986 + 0.193338i) q^{22} +(5.33288 + 2.48676i) q^{23} +(0.859111 - 2.36039i) q^{24} +(-0.0509776 + 0.0882957i) q^{26} +(-0.201214 + 0.750940i) q^{27} +(2.53599 - 1.77572i) q^{28} +(1.07941 - 6.12163i) q^{29} +(-2.35091 - 1.35730i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(-5.05003 + 2.35487i) q^{33} +(-7.52533 + 2.73899i) q^{34} +(0.574689 + 3.25922i) q^{36} +(-3.62590 - 3.62590i) q^{37} +(-1.72680 + 4.00227i) q^{38} -0.256098i q^{39} +(0.277083 + 0.330215i) q^{41} +(-3.28647 + 7.04786i) q^{42} +(0.199956 + 0.428806i) q^{43} +(-1.42590 + 1.69932i) q^{44} +(-5.09585 + 2.94209i) q^{46} +(-3.17143 - 4.52927i) q^{47} +(1.44075 + 2.05761i) q^{48} +(-2.23821 + 1.29223i) q^{49} +(12.9302 - 15.4096i) q^{51} +(-0.0430881 - 0.0924027i) q^{52} +(-3.28738 + 7.04981i) q^{53} +(-0.499722 - 0.595546i) q^{54} +3.09588i q^{56} +(-1.27022 - 10.8751i) q^{57} +(4.39542 + 4.39542i) q^{58} +(-0.900432 - 5.10660i) q^{59} +(6.36564 - 2.31690i) q^{61} +(2.46026 - 1.14724i) q^{62} +(-0.892982 - 10.2068i) q^{63} +(0.866025 + 0.500000i) q^{64} +(0.967584 - 5.48744i) q^{66} +(-3.22023 + 2.25483i) q^{67} +(2.07270 - 7.73541i) q^{68} +(7.39015 - 12.8001i) q^{69} +(4.27837 - 11.7547i) q^{71} +(-2.99943 - 1.39866i) q^{72} +(11.8024 + 1.03258i) q^{73} +(5.04989 - 0.890432i) q^{74} +(-2.28802 - 3.71012i) q^{76} +(4.85613 - 4.85613i) q^{77} +(0.209783 + 0.146892i) q^{78} +(-9.47813 + 7.95310i) q^{79} +(-7.49471 - 2.72785i) q^{81} +(-0.429424 + 0.0375698i) q^{82} +(9.56503 - 2.56294i) q^{83} +(-3.88823 - 6.73460i) q^{84} +(-0.465947 - 0.0821591i) q^{86} +(-15.0819 - 4.04119i) q^{87} +(-0.574139 - 2.14272i) q^{88} +(11.4725 + 9.62654i) q^{89} +(0.107955 + 0.296605i) q^{91} +(0.512840 - 5.86179i) q^{92} +(-3.91106 + 5.58558i) q^{93} +5.52921 q^{94} -2.51187 q^{96} +(-0.741294 + 1.05868i) q^{97} +(0.225251 - 2.57463i) q^{98} +(2.51093 + 6.89874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{6}+O(q^{10}) \) 72 * q + 24 * q^6	\( 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) \) 72 * q + 24 * q^6 + 24 * q^21 + 12 * q^26 + 36 * q^31 - 24 * q^36 + 48 * q^41 - 36 * q^46 + 156 * q^51 + 168 * q^61 - 36 * q^66 - 84 * q^71 - 48 * q^76 - 60 * q^81 - 60 * q^86 - 264 * q^91 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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