LMFDB - Embedded newform 950.2.bb.c.143.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.4
Character	$\chi$	$=$	950.143
Dual form			950.2.bb.c.857.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 - 0.819152i) q^{2} +(-0.218924 + 2.50231i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.92421 + 1.61460i) q^{6} +(-0.801272 - 2.99039i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-3.25922 - 0.574689i) q^{9} +O(q^{10})$	\(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	$0.285991\pi$
$3$	−0.218924	+	2.50231i	−0.126396	+	1.44471i	−0.749205	+	0.662338i	$0.769564\pi$
$4$	−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	$-0.884402\pi$
$7$	−0.801272	−	2.99039i	−0.302852	−	1.13026i	0.631926	−	0.775029i	$-0.282265\pi$
$8$	−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	−0.101232	−	0.994863i	$-0.532278\pi$
$13$	−0.101567	+	0.00888598i	−0.0281697	+	0.00246453i	0.0730622	+	0.997327i	$0.476723\pi$
$14$	−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	$-0.882205\pi$
$17$	−6.56000	−	4.59336i	−1.59103	−	1.11405i	−0.658730	−	0.752379i	$-0.728906\pi$
$18$	−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	−0.222241	−	0.974992i	$-0.571337\pi$
$23$	−5.33288	−	2.48676i	−1.11198	−	0.518526i	−0.889741	+	0.456466i	$0.849115\pi$
$24$	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	0.939271	−	0.343177i	$-0.111503\pi$
$37$	3.62590	+	3.62590i	0.596094	+	0.596094i	−0.343177	+	0.939271i	$0.611503\pi$
$38$	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	0.890471	−	0.455039i	$-0.150375\pi$
$43$	−0.199956	−	0.428806i	−0.0304929	−	0.0653923i	−0.920964	+	0.389647i	$0.872597\pi$
$44$	−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	0.980894	−	0.194541i	$-0.0623217\pi$
$47$	3.17143	+	4.52927i	0.462600	+	0.660662i	−0.518294	+	0.855202i	$0.673433\pi$
$48$	−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	$-0.681710\pi$
$53$	3.28738	−	7.04981i	0.451556	−	0.968366i	0.991912	−	0.126929i	$-0.0405120\pi$
$54$	−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	−0.360087	−	0.932919i	$-0.617253\pi$
$67$	3.22023	−	2.25483i	0.393414	−	0.275471i	0.753500	+	0.657448i	$0.228364\pi$
$68$	−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	−0.627879	−	0.778311i	$-0.716077\pi$
$73$	−11.8024	−	1.03258i	−1.38137	−	0.120854i	−0.753492	+	0.657457i	$0.771632\pi$
$74$	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	−0.742210	−	0.670168i	$-0.766222\pi$
$83$	−9.56503	+	2.56294i	−1.04990	+	0.281319i	−0.307689	+	0.951487i	$0.599555\pi$
$84$	−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	−0.779753	−	0.626087i	$-0.784656\pi$
$97$	0.741294	−	1.05868i	0.0752670	−	0.107492i	0.855020	+	0.518594i	$0.173544\pi$
$98$	−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	0.310794	−	0.950477i	$-0.399405\pi$
$103$	1.06271	+	0.284752i	0.104712	+	0.0280575i	−0.206083	+	0.978535i	$0.566072\pi$
$104$	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	−0.961589	−	0.274493i	$-0.911490\pi$
$107$	−17.1412	+	4.59297i	−1.65710	+	0.444019i	−0.695514	+	0.718513i	$0.744823\pi$
$108$	−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	$-0.409512\pi$
$113$	13.1849	−	13.1849i	1.24033	−	1.24033i	0.959865	−	0.280462i	$-0.0904876\pi$
$114$	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	$0.269063\pi$
$127$	1.57769	+	18.0330i	0.139997	+	1.60017i	−0.523521	+	0.852013i	$0.675382\pi$
$128$	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	−0.942579	−	0.333984i	$-0.891607\pi$
$137$	−0.946374	+	2.02951i	−0.0808542	+	0.173392i	0.861725	+	0.507376i	$0.169385\pi$
$138$	−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	0.210139	−	0.977672i	$-0.432608\pi$
$157$	13.7097	−	6.39294i	1.09415	−	0.510212i	0.884014	+	0.467460i	$0.154831\pi$
$158$	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	$0.417971\pi$
$163$	−5.73685	+	21.4102i	−0.449344	+	1.67698i	−0.704204	+	0.709998i	$0.748696\pi$
$164$	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	−0.158698	−	0.987327i	$-0.550730\pi$
$167$	−13.1431	−	6.12873i	−1.01704	−	0.474255i	−0.858346	+	0.513072i	$0.828508\pi$
$168$	−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	0.934976	−	0.354712i	$-0.115421\pi$
$173$	12.1196	+	8.48623i	0.921436	+	0.645196i	−0.0135397	+	0.999908i	$0.504310\pi$
$174$	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	$-0.862454\pi$
$193$	0.818630	−	9.35699i	0.0589263	−	0.673531i	0.967009	−	0.254741i	$-0.0819901\pi$
$194$	−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	$-0.662691\pi$
$197$	−7.04077	−	26.2765i	−0.501634	−	1.87212i	−0.0124888	−	0.999922i	$-0.503975\pi$
$198$	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	0.0847387	−	0.996403i	$-0.472994\pi$
$223$	13.4772	−	6.28450i	0.902497	−	0.420841i	0.817758	+	0.575562i	$0.195217\pi$
$224$	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	0.417094	−	0.908863i	$-0.363049\pi$
$227$	−7.40925	−	7.40925i	−0.491769	−	0.491769i	−0.908863	+	0.417094i	$0.863049\pi$
$228$	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	$-0.685732\pi$
$233$	−12.7625	−	27.3693i	−0.836100	−	1.79302i	−0.285156	−	0.958481i	$-0.592046\pi$
$234$	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	−0.325518	−	0.945536i	$-0.605539\pi$
$257$	7.24068	−	5.06998i	0.451661	−	0.316257i	0.777179	+	0.629279i	$0.216650\pi$
$258$	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	0.366565	−	0.930392i	$-0.380534\pi$
$263$	9.17898	+	0.803057i	0.566000	+	0.0495186i	0.199435	+	0.979911i	$0.436089\pi$
$264$	−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	0.996848	−	0.0793400i	$-0.0252813\pi$
$277$	30.2987	+	8.11851i	1.82047	+	0.487794i	0.823625	+	0.567134i	$0.191948\pi$
$278$	−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	−0.656693	−	0.754158i	$-0.728045\pi$
$283$	4.65291	−	6.64504i	0.276587	−	0.395007i	0.933279	+	0.359152i	$0.116934\pi$
$284$	−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	0.709027	−	0.705181i	$-0.249134\pi$
$293$	16.6118	+	4.45112i	0.970472	+	0.260037i	0.261445	+	0.965218i	$0.415801\pi$
$294$	−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	0.527729	−	0.849413i	$-0.323044\pi$
$307$	15.7682	+	1.37954i	0.899941	+	0.0787346i	0.372212	+	0.928148i	$0.378599\pi$
$308$	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	$-0.360179\pi$
$313$	25.1437	−	17.6058i	1.42121	−	0.995138i	0.995935	−	0.0900718i	$-0.0287097\pi$
$314$	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	$-0.992129\pi$
$317$	−0.346847	−	3.96448i	−0.0194809	−	0.222667i	0.980213	−	0.197943i	$-0.0634262\pi$
$318$	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	0.988643	−	0.150285i	$-0.0480191\pi$
$337$	4.36966	+	9.37077i	0.238031	+	0.510458i	−0.750612	+	0.660743i	$0.770241\pi$
$338$	−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	−0.604287	−	0.796767i	$-0.706542\pi$
$347$	−7.12249	+	3.32127i	−0.382355	+	0.178295i	0.221931	+	0.975062i	$0.428764\pi$
$348$	−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	−0.941410	−	0.337265i	$-0.890498\pi$
$353$	0.798642	−	2.98057i	0.0425074	−	0.158640i	0.983917	+	0.178625i	$0.0571649\pi$
$354$	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	0.479626	−	0.877473i	$-0.340772\pi$
$367$	21.1561	−	1.85092i	1.10434	−	0.0966170i	0.624711	+	0.780856i	$0.285217\pi$
$368$	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	0.997857	−	0.0654301i	$-0.0208419\pi$
$373$	1.95010	+	7.27788i	0.100972	+	0.376834i	−0.896885	+	0.442264i	$0.854175\pi$
$374$	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	$0.180858\pi$
$383$	−1.57806	+	18.0373i	−0.0806349	+	0.921661i	−0.923516	+	0.383561i	$0.874698\pi$
$384$	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	0.479390	−	0.877602i	$-0.340858\pi$
$397$	−3.61287	−	2.52976i	−0.181325	−	0.126965i	−0.660715	+	0.750637i	$0.729747\pi$
$398$	−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	−0.995112	−	0.0987536i	$-0.968514\pi$
$433$	−5.82261	+	12.4866i	−0.279817	+	0.600069i	0.715295	+	0.698822i	$0.246292\pi$
$434$	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	$0.0606026\pi$
$443$	1.00563	+	11.4944i	0.0477790	+	0.546117i	−0.934152	+	0.356876i	$0.883842\pi$
$444$	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	$-0.470611\pi$
$457$	23.2575	−	23.2575i	1.08794	−	1.08794i	0.995741	−	0.0921986i	$-0.0293895\pi$
$458$	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	−0.989263	−	0.146145i	$-0.953313\pi$
$463$	−38.1486	+	10.2219i	−1.77292	+	0.475052i	−0.783655	+	0.621197i	$0.786647\pi$
$464$	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	0.486636	−	0.873605i	$-0.338224\pi$
$467$	10.1843	+	2.72887i	0.471273	+	0.126277i	−0.0153633	+	0.999882i	$0.504890\pi$
$468$	−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	0.759380	−	0.650647i	$-0.225502\pi$
$487$	38.4502	−	10.3027i	1.74235	−	0.466860i	0.982966	+	0.183786i	$0.0588355\pi$
$488$	−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	−0.281641	−	0.959520i	$-0.590879\pi$
$503$	11.7450	−	8.22396i	0.523685	−	0.366688i	0.805327	+	0.592831i	$0.201990\pi$
$504$	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	$-0.874708\pi$
$523$	−22.1388	−	31.6175i	−0.968063	−	1.38254i	−0.0445350	−	0.999008i	$-0.514181\pi$
$524$	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	−0.0570093	−	0.998374i	$-0.518156\pi$
$547$	−20.0775	−	9.36230i	−0.858453	−	0.400303i	−0.801443	+	0.598071i	$0.795934\pi$
$548$	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	−0.264463	−	0.964396i	$-0.585195\pi$
$557$	−8.43594	+	0.738049i	−0.357442	+	0.0312721i	−0.0929794	+	0.995668i	$0.529639\pi$
$558$	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	$-0.881527\pi$
$563$	−7.27563	−	27.1530i	−0.306631	−	1.14436i	0.624901	−	0.780704i	$-0.285139\pi$
$564$	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	$-0.966331\pi$
$577$	−4.46823	−	16.6757i	−0.186015	−	0.694217i	0.808396	−	0.588639i	$-0.200336\pi$
$578$	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	0.935042	−	0.354538i	$-0.115362\pi$
$587$	22.3307	+	15.6361i	0.921688	+	0.645373i	−0.0133539	+	0.999911i	$0.504251\pi$
$588$	−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	0.553780	−	0.832663i	$-0.313185\pi$
$593$	6.62087	+	3.08736i	0.271887	+	0.126783i	−0.281894	+	0.959446i	$0.590963\pi$
$594$	−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	0.988780	−	0.149376i	$-0.0477265\pi$
$607$	20.6807	+	20.6807i	0.839404	+	0.839404i	−0.149376	+	0.988780i	$0.547727\pi$
$608$	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	$0.0317636\pi$
$613$	10.6897	+	22.9240i	0.431751	+	0.925893i	−0.563274	+	0.826270i	$0.690459\pi$
$614$	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	$0.0155927\pi$
$617$	17.4672	+	24.9458i	0.703204	+	1.00428i	−0.295596	+	0.955313i	$0.595518\pi$
$618$	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	0.993137	−	0.116960i	$-0.0373148\pi$
$643$	49.4692	+	4.32800i	1.95088	+	0.170679i	0.957739	+	0.287639i	$0.0928704\pi$
$644$	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	−0.869790	−	0.493422i	$-0.835746\pi$
$647$	−9.57339	+	9.57339i	−0.376369	+	0.376369i	0.493422	+	0.869790i	$0.335746\pi$
$648$	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	−0.190970	−	0.981596i	$-0.561163\pi$
$653$	3.43555	−	0.920552i	0.134443	−	0.0360240i	0.325413	+	0.945572i	$0.394497\pi$
$654$	−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	0.264154	−	0.964480i	$-0.414907\pi$
$673$	0.277010	+	0.0742246i	0.0106779	+	0.00286115i	−0.253476	+	0.967342i	$0.581574\pi$
$674$	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	0.109435	−	0.993994i	$-0.465096\pi$
$677$	18.2448	−	4.88869i	0.701206	−	0.187888i	0.591771	+	0.806106i	$0.298429\pi$
$678$	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	$-0.387016\pi$
$683$	33.5879	−	33.5879i	1.28521	−	1.28521i	0.937664	−	0.347542i	$-0.112984\pi$
$684$	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	−0.195735	−	0.980657i	$-0.562709\pi$
$727$	11.5853	−	5.40233i	0.429676	−	0.200361i	0.625411	+	0.780296i	$0.284931\pi$
$728$	−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	−0.992669	−	0.120861i	$-0.961434\pi$
$733$	−1.96454	+	7.33176i	−0.0725619	+	0.270805i	0.920107	+	0.391666i	$0.128101\pi$
$734$	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	0.670589	−	0.741829i	$-0.266042\pi$
$743$	5.52934	+	3.87168i	0.202852	+	0.142038i	−0.467737	+	0.883868i	$0.654931\pi$
$744$	−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	$-0.868373\pi$
$757$	1.53708	−	17.5689i	0.0558662	−	0.638553i	0.971578	−	0.236718i	$-0.0760718\pi$
$758$	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	−0.449826	−	0.893116i	$-0.648514\pi$
$773$	−20.5110	+	1.79448i	−0.737729	+	0.0645430i	−0.287904	+	0.957659i	$0.592958\pi$
$774$	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	−0.979434	−	0.201764i	$-0.935333\pi$
$787$	−0.851073	+	3.17625i	−0.0303375	+	0.113221i	0.949097	+	0.314985i	$0.101999\pi$
$788$	−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	0.660913	−	0.750462i	$-0.270169\pi$
$797$	−2.52806	−	2.52806i	−0.0895486	−	0.0895486i	−0.750462	+	0.660913i	$0.770169\pi$
$798$	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	0.990417	−	0.138110i	$-0.0441027\pi$
$823$	−0.256353	−	2.93012i	−0.00893589	−	0.102138i	−0.999353	+	0.0359723i	$0.988547\pi$
$824$	−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	−0.852180	−	0.523249i	$-0.824720\pi$
$827$	−18.7485	+	13.1278i	−0.651950	+	0.456500i	0.200230	+	0.979749i	$0.435831\pi$
$828$	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	$-0.587265\pi$
$853$	21.2172	−	30.3013i	0.726464	−	1.03750i	0.997195	−	0.0748434i	$-0.0238457\pi$
$854$	−20.9720			−0.717647
$855$		0			0
$856$	17.7459			0.606542
$857$	10.2557	−	14.6467i	0.350328	−	0.500321i	−0.604855	−	0.796336i	$-0.706769\pi$
$857$	10.2557	−	14.6467i	0.350328	−	0.500321i	0.955183	+	0.296015i	$0.0956578\pi$
$858$	−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	0.0534624	−	0.998570i	$-0.482974\pi$
$863$	−11.7367	−	3.14485i	−0.399523	−	0.107052i	−0.452985	+	0.891518i	$0.649641\pi$
$864$	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	−0.843308	−	0.537431i	$-0.819395\pi$
$877$	−52.3321	−	4.57846i	−1.76713	−	0.154604i	−0.923820	+	0.382827i	$0.874951\pi$
$878$	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	−0.294964	−	0.955508i	$-0.595308\pi$
$883$	14.9182	−	10.4458i	0.502037	−	0.351530i	0.797001	+	0.603979i	$0.206419\pi$
$884$	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	$0.124374\pi$
$887$	2.38807	+	27.2958i	0.0801837	+	0.916503i	−0.844447	+	0.535639i	$0.820071\pi$
$888$	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	0.911287	−	0.411772i	$-0.135090\pi$
$907$	0.303791	+	0.651481i	0.0100872	+	0.0216321i	−0.901200	+	0.433404i	$0.857312\pi$
$908$	−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	−0.496434	−	0.868075i	$-0.665357\pi$
$937$	−25.5470	+	2.23508i	−0.834586	+	0.0730168i	−0.338152	+	0.941091i	$0.609802\pi$
$938$	−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	$0.138422\pi$
$947$	−1.82725	+	20.8855i	−0.0593775	+	0.678688i	−0.966305	+	0.257401i	$0.917134\pi$
$948$	−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	$-0.876582\pi$
$953$	1.59261	−	18.2036i	0.0515897	−	0.589673i	0.977360	−	0.211585i	$-0.0678626\pi$
$954$	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	0.952693	−	0.303936i	$-0.0983009\pi$
$967$	30.8767	+	21.6201i	0.992926	+	0.695254i	0.0402338	+	0.999190i	$0.487190\pi$
$968$	−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	−0.996505	−	0.0835366i	$-0.973378\pi$
$977$	−2.86746	+	10.7015i	−0.0917380	+	0.342371i	0.904767	+	0.425908i	$0.140045\pi$
$978$	−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	−0.600926	−	0.799304i	$-0.705202\pi$
$983$	−11.7539	+	5.48094i	−0.374892	+	0.174815i	0.226035	+	0.974119i	$0.427424\pi$
$984$	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	0.997625	−	0.0688846i	$-0.0219440\pi$
$997$	18.6827	+	26.6816i	0.591687	+	0.845016i	−0.405938	+	0.913901i	$0.633055\pi$
$998$	−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.143.4	yes	72
5.2	odd	4	inner	950.2.bb.c.257.6	yes	72
5.3	odd	4	inner	950.2.bb.c.257.1	yes	72
5.4	even	2	inner	950.2.bb.c.143.3	✓	72
19.2	odd	18	inner	950.2.bb.c.743.6	yes	72
95.2	even	36	inner	950.2.bb.c.857.4	yes	72
95.59	odd	18	inner	950.2.bb.c.743.1	yes	72
95.78	even	36	inner	950.2.bb.c.857.3	yes	72

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