LMFDB - Embedded newform 950.2.bb.b.257.3

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:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			257.3
Character	$\chi$	$=$	950.257
Dual form			950.2.bb.b.743.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.819152 + 0.573576i) q^{2} +(-1.52626 - 0.133530i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-1.17365 - 0.984808i) q^{6} +(-3.99264 + 1.06982i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-0.642788 - 0.113341i) q^{9} +O(q^{10})$	\(q+(0.819152 + 0.573576i) q^{2} +(-1.52626 - 0.133530i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-1.17365 - 0.984808i) q^{6} +(-3.99264 + 1.06982i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-0.642788 - 0.113341i) q^{9} +(1.83060 + 3.17069i) q^{11} +(-0.396534 - 1.47988i) q^{12} +(-0.542815 - 6.20441i) q^{13} +(-3.88421 - 1.41374i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(1.30468 - 1.86328i) q^{17} +(-0.461531 - 0.461531i) q^{18} +(4.31176 + 0.639298i) q^{19} +(6.23666 - 1.09969i) q^{21} +(-0.319095 + 3.64727i) q^{22} +(3.36517 - 7.21662i) q^{23} +(0.524005 - 1.43969i) q^{24} +(3.11405 - 5.39370i) q^{26} +(5.40558 + 1.44842i) q^{27} +(-2.37087 - 3.38595i) q^{28} +(1.32695 - 7.52553i) q^{29} +(-5.27806 - 3.04729i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(-2.37059 - 5.08374i) q^{33} +(2.13747 - 0.777974i) q^{34} +(-0.113341 - 0.642788i) q^{36} +(-5.80894 + 5.80894i) q^{37} +(3.16530 + 2.99681i) q^{38} +9.54201i q^{39} +(-3.86168 - 4.60217i) q^{41} +(5.73953 + 2.67638i) q^{42} +(-2.65485 + 1.23798i) q^{43} +(-2.35338 + 2.80464i) q^{44} +(6.89587 - 3.98133i) q^{46} +(4.79838 - 3.35986i) q^{47} +(1.25501 - 0.878770i) q^{48} +(8.73447 - 5.04285i) q^{49} +(-2.24009 + 2.66963i) q^{51} +(5.64458 - 2.63211i) q^{52} +(-8.85215 - 4.12783i) q^{53} +(3.59721 + 4.28699i) q^{54} -4.13348i q^{56} +(-6.49550 - 1.55149i) q^{57} +(5.40344 - 5.40344i) q^{58} +(1.07520 + 6.09774i) q^{59} +(2.57823 - 0.938398i) q^{61} +(-2.57568 - 5.52356i) q^{62} +(2.68767 - 0.235141i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(0.974042 - 5.52407i) q^{66} +(-6.39502 - 9.13304i) q^{67} +(2.19714 + 0.588721i) q^{68} +(-6.09975 + 10.5651i) q^{69} +(2.18904 - 6.01434i) q^{71} +(0.275844 - 0.591550i) q^{72} +(-0.304351 + 3.47874i) q^{73} +(-8.09028 + 1.42653i) q^{74} +(0.873966 + 4.27038i) q^{76} +(-10.7010 - 10.7010i) q^{77} +(-5.47307 + 7.81636i) q^{78} +(6.41146 - 5.37985i) q^{79} +(-6.21688 - 2.26276i) q^{81} +(-0.523606 - 5.98484i) q^{82} +(2.46535 + 9.20081i) q^{83} +(3.16643 + 5.48442i) q^{84} +(-2.88480 - 0.508669i) q^{86} +(-3.03016 + 11.3087i) q^{87} +(-3.53645 + 0.947589i) q^{88} +(0.289299 + 0.242751i) q^{89} +(8.80489 + 24.1912i) q^{91} +(7.93236 + 0.693992i) q^{92} +(7.64878 + 5.35573i) q^{93} +5.85774 q^{94} +1.53209 q^{96} +(11.7855 + 8.25227i) q^{97} +(10.0473 + 0.879026i) q^{98} +(-0.817319 - 2.24556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{6}+O(q^{10}) $ 48 * q - 48 * q^6	$ 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) $ 48 * q - 48 * q^6 - 12 * q^11 + 36 * q^21 - 72 * q^31 + 48 * q^36 + 96 * q^41 + 72 * q^46 - 48 * q^51 - 108 * q^61 + 24 * q^66 - 60 * q^71 - 48 * q^76 - 168 * q^81 - 48 * q^86 + 252 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$3$	−1.52626	−	0.133530i	−0.881186	−	0.0770938i	−0.362425	−	0.932013i	$-0.618051\pi$
$3$	−1.52626	−	0.133530i	−0.881186	−	0.0770938i	−0.518761	+	0.854919i	$0.673607\pi$
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$		0			0
$5$		0			0
$6$	−1.17365	−	0.984808i	−0.479140	−	0.402046i
$7$	−3.99264	+	1.06982i	−1.50908	+	0.404356i	−0.916128	−	0.400885i	$-0.868703\pi$
$7$	−3.99264	+	1.06982i	−1.50908	+	0.404356i	−0.592948	+	0.805241i	$0.702036\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	−0.642788	−	0.113341i	−0.214263	−	0.0377803i
$10$		0			0
$11$	1.83060	+	3.17069i	0.551947	+	0.956000i	0.998134	+	0.0610605i	$0.0194483\pi$
$11$	1.83060	+	3.17069i	0.551947	+	0.956000i	−0.446187	+	0.894940i	$0.647218\pi$
$12$	−0.396534	−	1.47988i	−0.114469	−	0.427206i
$13$	−0.542815	−	6.20441i	−0.150550	−	1.72079i	−0.577393	−	0.816467i	$-0.695930\pi$
$13$	−0.542815	−	6.20441i	−0.150550	−	1.72079i	0.426843	−	0.904326i	$-0.359626\pi$
$14$	−3.88421	−	1.41374i	−1.03810	−	0.377837i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	1.30468	−	1.86328i	0.316432	−	0.451912i	−0.629156	−	0.777279i	$-0.716599\pi$
$17$	1.30468	−	1.86328i	0.316432	−	0.451912i	0.945588	+	0.325368i	$0.105488\pi$
$18$	−0.461531	−	0.461531i	−0.108784	−	0.108784i
$19$	4.31176	+	0.639298i	0.989186	+	0.146665i
$19$	4.31176	+	0.639298i	0.989186	+	0.146665i
$20$		0			0
$21$	6.23666	−	1.09969i	1.36095	−	0.239972i
$22$	−0.319095	+	3.64727i	−0.0680312	+	0.777601i
$23$	3.36517	−	7.21662i	0.701686	−	1.50477i	−0.154440	−	0.988002i	$-0.549357\pi$
$23$	3.36517	−	7.21662i	0.701686	−	1.50477i	0.856125	−	0.516768i	$-0.172865\pi$
$24$	0.524005	−	1.43969i	0.106962	−	0.293876i
$25$		0			0
$26$	3.11405	−	5.39370i	0.610716	−	1.05779i
$27$	5.40558	+	1.44842i	1.04030	+	0.278749i
$28$	−2.37087	−	3.38595i	−0.448052	−	0.639885i
$29$	1.32695	−	7.52553i	0.246409	−	1.39746i	−0.570788	−	0.821097i	$-0.693362\pi$
$29$	1.32695	−	7.52553i	0.246409	−	1.39746i	0.817197	−	0.576358i	$-0.195527\pi$
$30$		0			0
$31$	−5.27806	−	3.04729i	−0.947968	−	0.547309i	−0.0555186	−	0.998458i	$-0.517681\pi$
$31$	−5.27806	−	3.04729i	−0.947968	−	0.547309i	−0.892449	+	0.451148i	$0.851015\pi$
$32$	−0.996195	+	0.0871557i	−0.176104	+	0.0154071i
$33$	−2.37059	−	5.08374i	−0.412666	−	0.884966i
$34$	2.13747	−	0.777974i	0.366572	−	0.133421i
$35$		0			0
$36$	−0.113341	−	0.642788i	−0.0188901	−	0.107131i
$37$	−5.80894	+	5.80894i	−0.954984	+	0.954984i	−0.999030	−	0.0440453i	$-0.985975\pi$
$37$	−5.80894	+	5.80894i	−0.954984	+	0.954984i	0.0440453	+	0.999030i	$0.485975\pi$
$38$	3.16530	+	2.99681i	0.513480	+	0.486146i
$39$			9.54201i			1.52794i
$40$		0			0
$41$	−3.86168	−	4.60217i	−0.603093	−	0.718738i	0.374973	−	0.927036i	$-0.377652\pi$
$41$	−3.86168	−	4.60217i	−0.603093	−	0.718738i	−0.978065	+	0.208298i	$0.933208\pi$
$42$	5.73953	+	2.67638i	0.885628	+	0.412975i
$43$	−2.65485	+	1.23798i	−0.404861	+	0.188790i	−0.614372	−	0.789016i	$-0.710591\pi$
$43$	−2.65485	+	1.23798i	−0.404861	+	0.188790i	0.209511	+	0.977806i	$0.432813\pi$
$44$	−2.35338	+	2.80464i	−0.354785	+	0.422816i
$45$		0			0
$46$	6.89587	−	3.98133i	1.01674	−	0.587015i
$47$	4.79838	−	3.35986i	0.699915	−	0.490086i	−0.168640	−	0.985678i	$-0.553938\pi$
$47$	4.79838	−	3.35986i	0.699915	−	0.490086i	0.868556	+	0.495592i	$0.165049\pi$
$48$	1.25501	−	0.878770i	0.181146	−	0.126840i
$49$	8.73447	−	5.04285i	1.24778	−	0.720407i
$50$		0			0
$51$	−2.24009	+	2.66963i	−0.313675	+	0.373823i
$52$	5.64458	−	2.63211i	0.782762	−	0.365008i
$53$	−8.85215	−	4.12783i	−1.21594	−	0.567001i	−0.294546	−	0.955637i	$-0.595168\pi$
$53$	−8.85215	−	4.12783i	−1.21594	−	0.567001i	−0.921391	+	0.388637i	$0.872946\pi$
$54$	3.59721	+	4.28699i	0.489518	+	0.583385i
$55$		0			0
$56$		−	4.13348i		−	0.552360i
$57$	−6.49550	−	1.55149i	−0.860350	−	0.205499i
$58$	5.40344	−	5.40344i	0.709507	−	0.709507i
$59$	1.07520	+	6.09774i	0.139979	+	0.793858i	0.971263	+	0.238010i	$0.0764951\pi$
$59$	1.07520	+	6.09774i	0.139979	+	0.793858i	−0.831284	+	0.555848i	$0.812394\pi$
$60$		0			0
$61$	2.57823	−	0.938398i	0.330108	−	0.120150i	−0.171649	−	0.985158i	$-0.554909\pi$
$61$	2.57823	−	0.938398i	0.330108	−	0.120150i	0.501757	+	0.865009i	$0.332687\pi$
$62$	−2.57568	−	5.52356i	−0.327112	−	0.701493i
$63$	2.68767	−	0.235141i	0.338615	−	0.0296250i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$		0			0
$66$	0.974042	−	5.52407i	0.119896	−	0.679966i
$67$	−6.39502	−	9.13304i	−0.781276	−	1.11578i	−0.990446	−	0.137899i	$-0.955965\pi$
$67$	−6.39502	−	9.13304i	−0.781276	−	1.11578i	0.209170	−	0.977879i	$-0.432924\pi$
$68$	2.19714	+	0.588721i	0.266442	+	0.0713929i
$69$	−6.09975	+	10.5651i	−0.734324	+	1.27189i
$70$		0			0
$71$	2.18904	−	6.01434i	0.259791	−	0.713771i	−0.739388	−	0.673279i	$-0.764885\pi$
$71$	2.18904	−	6.01434i	0.259791	−	0.713771i	0.999180	−	0.0404920i	$-0.0128925\pi$
$72$	0.275844	−	0.591550i	0.0325086	−	0.0697149i
$73$	−0.304351	+	3.47874i	−0.0356216	+	0.407156i	0.957361	+	0.288895i	$0.0932877\pi$
$73$	−0.304351	+	3.47874i	−0.0356216	+	0.407156i	−0.992982	+	0.118262i	$0.962268\pi$
$74$	−8.09028	+	1.42653i	−0.940476	+	0.165831i
$75$		0			0
$76$	0.873966	+	4.27038i	0.100251	+	0.489847i
$77$	−10.7010	−	10.7010i	−1.21949	−	1.21949i
$78$	−5.47307	+	7.81636i	−0.619703	+	0.885028i
$79$	6.41146	−	5.37985i	0.721345	−	0.605280i	−0.206412	−	0.978465i	$-0.566179\pi$
$79$	6.41146	−	5.37985i	0.721345	−	0.605280i	0.927757	+	0.373185i	$0.121734\pi$
$80$		0			0
$81$	−6.21688	−	2.26276i	−0.690765	−	0.251418i
$82$	−0.523606	−	5.98484i	−0.0578226	−	0.660916i
$83$	2.46535	+	9.20081i	0.270607	+	1.00992i	0.958728	+	0.284324i	$0.0917692\pi$
$83$	2.46535	+	9.20081i	0.270607	+	1.00992i	−0.688121	+	0.725596i	$0.741564\pi$
$84$	3.16643	+	5.48442i	0.345486	+	0.598400i
$85$		0			0
$86$	−2.88480	−	0.508669i	−0.311076	−	0.0548512i
$87$	−3.03016	+	11.3087i	−0.324867	+	1.21242i
$88$	−3.53645	+	0.947589i	−0.376987	+	0.101013i
$89$	0.289299	+	0.242751i	0.0306657	+	0.0257316i	0.657992	−	0.753025i	$-0.271406\pi$
$89$	0.289299	+	0.242751i	0.0306657	+	0.0257316i	−0.627326	+	0.778757i	$0.715851\pi$
$90$		0			0
$91$	8.80489	+	24.1912i	0.923003	+	2.53593i
$92$	7.93236	+	0.693992i	0.827006	+	0.0723537i
$93$	7.64878	+	5.35573i	0.793142	+	0.555364i
$94$	5.85774			0.604179
$95$		0			0
$96$	1.53209			0.156368
$97$	11.7855	+	8.25227i	1.19663	+	0.837891i	0.990075	−	0.140543i	$-0.0448849\pi$
$97$	11.7855	+	8.25227i	1.19663	+	0.837891i	0.206558	+	0.978434i	$0.433774\pi$
$98$	10.0473	+	0.879026i	1.01493	+	0.0887951i
$99$	−0.817319	−	2.24556i	−0.0821436	−	0.225688i
$100$		0			0
$101$	−6.52975	−	5.47911i	−0.649734	−	0.545192i	0.257256	−	0.966343i	$-0.417182\pi$
$101$	−6.52975	−	5.47911i	−0.649734	−	0.545192i	−0.906990	+	0.421152i	$0.861626\pi$
$102$	−3.36621	+	0.901973i	−0.333304	+	0.0893086i
$103$	1.81938	−	6.79001i	0.179269	−	0.669040i	−0.816516	−	0.577322i	$-0.804098\pi$
$103$	1.81938	−	6.79001i	0.179269	−	0.669040i	0.995785	−	0.0917174i	$-0.0292356\pi$
$104$	6.13349	+	1.08150i	0.601438	+	0.106050i
$105$		0			0
$106$	−4.88363	−	8.45870i	−0.474341	−	0.821582i
$107$	2.82923	+	10.5588i	0.273512	+	1.02076i	0.956832	+	0.290641i	$0.0938686\pi$
$107$	2.82923	+	10.5588i	0.273512	+	1.02076i	−0.683320	+	0.730119i	$0.739465\pi$
$108$	0.487747	+	5.57497i	0.0469335	+	0.536452i
$109$	−10.2018	−	3.71314i	−0.977153	−	0.355655i	−0.196421	−	0.980520i	$-0.562932\pi$
$109$	−10.2018	−	3.71314i	−0.977153	−	0.355655i	−0.780733	+	0.624865i	$0.785154\pi$
$110$		0			0
$111$	9.64162	−	8.09028i	0.915142	−	0.767895i
$112$	2.37087	−	3.38595i	0.224026	−	0.319942i
$113$	−6.50873	−	6.50873i	−0.612290	−	0.612290i	0.331252	−	0.943542i	$-0.392529\pi$
$113$	−6.50873	−	6.50873i	−0.612290	−	0.612290i	−0.943542	+	0.331252i	$0.892529\pi$
$114$	−4.43091	−	4.99657i	−0.414992	−	0.467972i
$115$		0			0
$116$	7.52553	−	1.32695i	0.698728	−	0.123205i
$117$	−0.354297	+	4.04964i	−0.0327548	+	0.374389i
$118$	−2.61677	+	5.61168i	−0.240893	+	0.516597i
$119$	−3.21574	+	8.83518i	−0.294787	+	0.809920i
$120$		0			0
$121$	−1.20220	+	2.08227i	−0.109291	+	0.189297i
$122$	2.65020	+	0.710120i	0.239938	+	0.0642912i
$123$	5.27939	+	7.53975i	0.476027	+	0.679837i
$124$	1.05831	−	6.00199i	0.0950393	−	0.538994i
$125$		0			0
$126$	2.33649	+	1.34897i	0.208151	+	0.120176i
$127$	−18.8921	+	1.65284i	−1.67640	+	0.146666i	−0.885299	−	0.465022i	$-0.846047\pi$
$127$	−18.8921	+	1.65284i	−1.67640	+	0.146666i	−0.791099	+	0.611688i	$0.790491\pi$
$128$	−0.422618	−	0.906308i	−0.0373545	−	0.0801070i
$129$	4.21730	−	1.53497i	0.371313	−	0.135147i
$130$		0			0
$131$	−1.40733	−	7.98137i	−0.122959	−	0.697336i	−0.982499	−	0.186267i	$-0.940361\pi$
$131$	−1.40733	−	7.98137i	−0.122959	−	0.697336i	0.859540	−	0.511068i	$-0.170750\pi$
$132$	3.96636	−	3.96636i	0.345228	−	0.345228i
$133$	−17.8993	+	2.06034i	−1.55206	+	0.178654i
$134$		−	11.1494i		−	0.963160i
$135$		0			0
$136$	1.46211	+	1.74248i	0.125375	+	0.149416i
$137$	0.342498	+	0.159709i	0.0292616	+	0.0136449i	0.437194	−	0.899367i	$-0.355972\pi$
$137$	0.342498	+	0.159709i	0.0292616	+	0.0136449i	−0.407932	+	0.913012i	$0.633750\pi$
$138$	−11.0565	+	5.15574i	−0.941193	+	0.438885i
$139$	8.52927	−	10.1648i	0.723443	−	0.862166i	−0.271518	−	0.962433i	$-0.587526\pi$
$139$	8.52927	−	10.1648i	0.723443	−	0.862166i	0.994960	+	0.100268i	$0.0319700\pi$
$140$		0			0
$141$	−7.77221	+	4.48729i	−0.654538	+	0.377898i
$142$	5.24284	−	3.67108i	0.439970	−	0.308070i
$143$	18.6786	−	13.0789i	1.56198	−	1.09371i
$144$	0.565258	−	0.326352i	0.0471048	−	0.0271960i
$145$		0			0
$146$	−2.24464	+	2.67505i	−0.185767	+	0.221389i
$147$	−14.0044	+	6.53037i	−1.15507	+	0.538616i
$148$	−7.44540	−	3.47184i	−0.612008	−	0.285384i
$149$	3.84545	+	4.58283i	0.315032	+	0.375440i	0.900204	−	0.435469i	$-0.143418\pi$
$149$	3.84545	+	4.58283i	0.315032	+	0.375440i	−0.585172	+	0.810909i	$0.698973\pi$
$150$		0			0
$151$			1.82405i			0.148439i	0.997242	+	0.0742196i	$0.0236466\pi$
$151$			1.82405i			0.148439i	−0.997242	+	0.0742196i	$0.976353\pi$
$152$	−1.73348	+	3.99938i	−0.140604	+	0.324393i
$153$	−1.04982	+	1.04982i	−0.0848728	+	0.0848728i
$154$	−2.62791	−	14.9036i	−0.211763	−	1.20097i
$155$		0			0
$156$	−8.96656	+	3.26356i	−0.717899	+	0.261294i
$157$	−0.159944	−	0.343002i	−0.0127650	−	0.0273745i	0.899822	−	0.436257i	$-0.143696\pi$
$157$	−0.159944	−	0.343002i	−0.0127650	−	0.0273745i	−0.912587	+	0.408883i	$0.865918\pi$
$158$	8.33771	−	0.729455i	0.663313	−	0.0580323i
$159$	12.9595	+	7.48216i	1.02775	+	0.593374i
$160$		0			0
$161$	−5.71538	+	32.4135i	−0.450435	+	2.55454i
$162$	−3.79471	−	5.41940i	−0.298140	−	0.425788i
$163$	10.9906	+	2.94493i	0.860852	+	0.230665i	0.662128	−	0.749391i	$-0.269654\pi$
$163$	10.9906	+	2.94493i	0.860852	+	0.230665i	0.198724	+	0.980055i	$0.436320\pi$
$164$	3.00385	−	5.20283i	0.234561	−	0.406272i
$165$		0			0
$166$	−3.25787	+	8.95093i	−0.252860	+	0.694727i
$167$	−0.196415	+	0.421213i	−0.0151990	+	0.0325945i	−0.913761	−	0.406253i	$-0.866835\pi$
$167$	−0.196415	+	0.421213i	−0.0151990	+	0.0325945i	0.898562	+	0.438847i	$0.144613\pi$
$168$	−0.551946	+	6.30877i	−0.0425835	+	0.486732i
$169$	−25.3975	+	4.47826i	−1.95365	+	0.344482i
$170$		0			0
$171$	−2.69909	−	0.899632i	−0.206404	−	0.0687966i
$172$	−2.07133	−	2.07133i	−0.157938	−	0.157938i
$173$	−0.815805	+	1.16509i	−0.0620245	+	0.0885802i	−0.848966	−	0.528447i	$-0.822774\pi$
$173$	−0.815805	+	1.16509i	−0.0620245	+	0.0885802i	0.786942	+	0.617028i	$0.211663\pi$
$174$	−8.96857	+	7.52553i	−0.679906	+	0.570509i
$175$		0			0
$176$	−3.44040	−	1.25220i	−0.259330	−	0.0943885i
$177$	−0.826794	−	9.45029i	−0.0621456	−	0.710328i
$178$	0.0977439	+	0.364785i	0.00732622	+	0.0273418i
$179$	−4.21754	−	7.30500i	−0.315234	−	0.546001i	0.664253	−	0.747508i	$-0.268750\pi$
$179$	−4.21754	−	7.30500i	−0.315234	−	0.546001i	−0.979487	+	0.201506i	$0.935416\pi$
$180$		0			0
$181$	−6.24543	−	1.10124i	−0.464219	−	0.0818543i	−0.0633532	−	0.997991i	$-0.520179\pi$
$181$	−6.24543	−	1.10124i	−0.464219	−	0.0818543i	−0.400866	+	0.916137i	$0.631291\pi$
$182$	−6.66298	+	24.8666i	−0.493893	+	1.84323i
$183$	−4.06035	+	1.08797i	−0.300149	+	0.0804248i
$184$	6.09975	+	5.11830i	0.449680	+	0.377326i
$185$		0			0
$186$	3.19359	+	8.77432i	0.234165	+	0.643364i
$187$	8.29624	+	0.725827i	0.606681	+	0.0530777i
$188$	4.79838	+	3.35986i	0.349958	+	0.245043i
$189$	−23.1321			−1.68261
$190$		0			0
$191$	−10.2856			−0.744243			−0.372122	−	0.928184i	$-0.621370\pi$
$191$	−10.2856			−0.744243			−0.372122	+	0.928184i	$0.621370\pi$
$192$	1.25501	+	0.878770i	0.0905728	+	0.0634198i
$193$	−19.3637	−	1.69410i	−1.39383	−	0.121944i	−0.634636	−	0.772811i	$-0.718850\pi$
$193$	−19.3637	−	1.69410i	−1.39383	−	0.121944i	−0.759192	+	0.650867i	$0.774405\pi$
$194$	4.92078	+	13.5197i	0.353291	+	0.970660i
$195$		0			0
$196$	7.72609	+	6.48296i	0.551864	+	0.463069i
$197$	20.8758	−	5.59366i	1.48734	−	0.398532i	0.578503	−	0.815681i	$-0.303637\pi$
$197$	20.8758	−	5.59366i	1.48734	−	0.398532i	0.908838	+	0.417149i	$0.136971\pi$
$198$	0.618495	−	2.30825i	0.0439545	−	0.164040i
$199$	−3.46309	−	0.610637i	−0.245492	−	0.0432869i	0.0495480	−	0.998772i	$-0.484222\pi$
$199$	−3.46309	−	0.610637i	−0.245492	−	0.0432869i	−0.295040	+	0.955485i	$0.595333\pi$
$200$		0			0
$201$	8.54092	+	14.7933i	0.602430	+	1.04344i
$202$	−2.20617	−	8.23353i	−0.155225	−	0.579309i
$203$	2.75295	+	31.4663i	0.193219	+	2.20850i
$204$	−3.27479	−	1.19193i	−0.229281	−	0.0834515i
$205$		0			0
$206$	5.38494	−	4.51850i	0.375186	−	0.314819i
$207$	−2.98103	+	4.25735i	−0.207196	+	0.295906i
$208$	4.40394	+	4.40394i	0.305358	+	0.305358i
$209$	5.86610	+	14.8416i	0.405766	+	1.02661i
$210$		0			0
$211$	6.10693	−	1.07682i	0.420419	−	0.0741311i	0.0405631	−	0.999177i	$-0.487085\pi$
$211$	6.10693	−	1.07682i	0.420419	−	0.0741311i	0.379855	+	0.925046i	$0.375974\pi$
$212$	0.851274	−	9.73010i	0.0584657	−	0.668266i
$213$	−4.14414	+	8.88714i	−0.283952	+	0.608937i
$214$	−3.73872	+	10.2721i	−0.255574	+	0.702184i
$215$		0			0
$216$	−2.79813	+	4.84651i	−0.190389	+	0.329763i
$217$	24.3335	+	6.52013i	1.65186	+	0.442615i
$218$	−6.22704	−	8.89313i	−0.421748	−	0.602319i
$219$	0.929036	−	5.26882i	0.0627784	−	0.356034i
$220$		0			0
$221$	−12.2687	−	7.08336i	−0.825285	−	0.476478i
$222$	12.5383	−	1.09696i	0.841519	−	0.0736233i
$223$	2.62597	+	5.63140i	0.175848	+	0.377107i	0.974401	−	0.224818i	$-0.0721787\pi$
$223$	2.62597	+	5.63140i	0.175848	+	0.377107i	−0.798553	+	0.601924i	$0.794401\pi$
$224$	3.88421	−	1.41374i	0.259524	−	0.0944591i
$225$		0			0
$226$	−1.59839	−	9.06490i	−0.106323	−	0.602988i
$227$	−7.05994	+	7.05994i	−0.468585	+	0.468585i	−0.901456	−	0.432871i	$-0.857500\pi$
$227$	−7.05994	+	7.05994i	−0.468585	+	0.468585i	0.432871	+	0.901456i	$0.357500\pi$
$228$	−0.763672	−	6.63441i	−0.0505754	−	0.439375i
$229$		−	24.8729i		−	1.64365i	−0.569741	−	0.821824i	$-0.692957\pi$
$229$		−	24.8729i		−	1.64365i	0.569741	−	0.821824i	$-0.307043\pi$
$230$		0			0
$231$	14.9036	+	17.7614i	0.980586	+	1.16862i
$232$	6.92566	+	3.22949i	0.454692	+	0.212026i
$233$	−0.171137	+	0.0798023i	−0.0112115	+	0.00522803i	−0.428216	−	0.903676i	$-0.640858\pi$
$233$	−0.171137	+	0.0798023i	−0.0112115	+	0.00522803i	0.417004	+	0.908904i	$0.363080\pi$
$234$	−2.61300	+	3.11405i	−0.170817	+	0.203572i
$235$		0			0
$236$	−5.36226	+	3.09590i	−0.349053	+	0.201526i
$237$	−10.5039	+	7.35492i	−0.682303	+	0.477753i
$238$	−7.70184	+	5.39288i	−0.499236	+	0.349569i
$239$	−18.7432	+	10.8214i	−1.21240	+	0.699978i	−0.963281	−	0.268495i	$-0.913474\pi$
$239$	−18.7432	+	10.8214i	−1.21240	+	0.699978i	−0.249117	+	0.968473i	$0.580140\pi$
$240$		0			0
$241$	−1.59052	+	1.89551i	−0.102454	+	0.122100i	−0.814835	−	0.579693i	$-0.803173\pi$
$241$	−1.59052	+	1.89551i	−0.102454	+	0.122100i	0.712381	+	0.701793i	$0.247617\pi$
$242$	−2.17913	+	1.01614i	−0.140080	+	0.0653202i
$243$	−6.02940	−	2.81155i	−0.386786	−	0.180361i
$244$	1.76361	+	2.10179i	0.112904	+	0.134553i
$245$		0			0
$246$			9.20434i			0.586847i
$247$	1.62598	−	27.0989i	0.103458	−	1.72426i
$248$	4.30952	−	4.30952i	0.273655	−	0.273655i
$249$	−2.53418	−	14.3720i	−0.160597	−	0.910790i
$250$		0			0
$251$	−10.1984	+	3.71191i	−0.643716	+	0.234294i	−0.643190	−	0.765706i	$-0.722390\pi$
$251$	−10.1984	+	3.71191i	−0.643716	+	0.234294i	−0.000525892		1.00000i	$0.500167\pi$
$252$	1.14020	+	2.44516i	0.0718258	+	0.154031i
$253$	29.0420	−	2.54084i	1.82585	−	0.159742i
$254$	−16.4235	−	9.48211i	−1.03050	−	0.594960i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−2.19355	−	3.13272i	−0.136830	−	0.195413i	0.744889	−	0.667188i	$-0.232502\pi$
$257$	−2.19355	−	3.13272i	−0.136830	−	0.195413i	−0.881719	+	0.471775i	$0.843614\pi$
$258$	4.33504	+	1.16157i	0.269888	+	0.0723162i
$259$	16.9785	−	29.4076i	1.05499	−	1.82730i
$260$		0			0
$261$	−1.70590	+	4.68692i	−0.105592	+	0.290113i
$262$	3.42511	−	7.34517i	0.211604	−	0.453786i
$263$	−2.01299	+	23.0086i	−0.124126	+	1.41877i	0.637349	+	0.770575i	$0.280031\pi$
$263$	−2.01299	+	23.0086i	−0.124126	+	1.41877i	−0.761475	+	0.648194i	$0.775525\pi$
$264$	5.52407	−	0.974042i	0.339983	−	0.0599482i
$265$		0			0
$266$	−15.8440	−	8.57886i	−0.971456	−	0.526003i
$267$	−0.409131	−	0.409131i	−0.0250384	−	0.0250384i
$268$	6.39502	−	9.13304i	0.390638	−	0.557889i
$269$	10.7847	−	9.04946i	0.657556	−	0.551755i	−0.251797	−	0.967780i	$-0.581022\pi$
$269$	10.7847	−	9.04946i	0.657556	−	0.551755i	0.909353	+	0.416025i	$0.136577\pi$
$270$		0			0
$271$	−6.75133	−	2.45728i	−0.410114	−	0.149269i	0.128720	−	0.991681i	$-0.458913\pi$
$271$	−6.75133	−	2.45728i	−0.410114	−	0.149269i	−0.538835	+	0.842412i	$0.681135\pi$
$272$	0.198248	+	2.26599i	0.0120206	+	0.137396i
$273$	−10.2083	−	38.0978i	−0.617833	−	2.30578i
$274$	0.188952	+	0.327275i	0.0114150	+	0.0197714i
$275$		0			0
$276$	−12.0142	−	2.11842i	−0.723168	−	0.127514i
$277$	6.31328	−	23.5615i	0.379328	−	1.41567i	−0.467589	−	0.883946i	$-0.654877\pi$
$277$	6.31328	−	23.5615i	0.379328	−	1.41567i	0.846917	−	0.531726i	$-0.178456\pi$
$278$	12.8170	−	3.43432i	0.768715	−	0.205977i
$279$	3.04729	+	2.55698i	0.182436	+	0.153082i
$280$		0			0
$281$	−3.19392	−	8.77521i	−0.190533	−	0.523485i	0.807237	−	0.590227i	$-0.200962\pi$
$281$	−3.19392	−	8.77521i	−0.190533	−	0.523485i	−0.997770	+	0.0667418i	$0.978740\pi$
$282$	−8.94042	−	0.782186i	−0.532394	−	0.0465785i
$283$	6.37341	+	4.46271i	0.378860	+	0.265280i	0.747459	−	0.664308i	$-0.231274\pi$
$283$	6.37341	+	4.46271i	0.378860	+	0.265280i	−0.368599	+	0.929588i	$0.620163\pi$
$284$	6.40033			0.379790
$285$		0			0
$286$	22.8024			1.34833
$287$	20.3418	+	14.2435i	1.20074	+	0.840766i
$288$	0.650220	+	0.0568869i	0.0383146	+	0.00335209i
$289$	4.04473	+	11.1128i	0.237925	+	0.653694i
$290$		0			0
$291$	−16.8857	−	14.1688i	−0.989860	−	0.830591i
$292$	−3.37304	+	0.903805i	−0.197392	+	0.0528912i
$293$	−1.20205	+	4.48611i	−0.0702245	+	0.262081i	−0.992108	−	0.125386i	$-0.959983\pi$
$293$	−1.20205	+	4.48611i	−0.0702245	+	0.262081i	0.921884	+	0.387467i	$0.126650\pi$
$294$	−15.2174	−	2.68324i	−0.887499	−	0.156490i
$295$		0			0
$296$	−4.10754	−	7.11447i	−0.238746	−	0.413520i
$297$	5.30296	+	19.7909i	0.307709	+	1.14839i
$298$	0.521406	+	5.95969i	0.0302042	+	0.345236i
$299$	−46.6015	−	16.9616i	−2.69504	−	0.980913i
$300$		0			0
$301$	9.27546	−	7.78303i	0.534628	−	0.448606i
$302$	−1.04623	+	1.49418i	−0.0602039	+	0.0859801i
$303$	9.23446	+	9.23446i	0.530506	+	0.530506i
$304$	−3.71393	+	2.28182i	−0.213009	+	0.130871i
$305$		0			0
$306$	−1.46211	+	0.257810i	−0.0835834	+	0.0147380i
$307$	2.15056	−	24.5810i	0.122739	−	1.40291i	−0.645994	−	0.763342i	$-0.723557\pi$
$307$	2.15056	−	24.5810i	0.122739	−	1.40291i	0.768733	−	0.639570i	$-0.220887\pi$
$308$	6.39570	−	13.7156i	0.364429	−	0.781520i
$309$	−3.68351	+	10.1204i	−0.209548	+	0.575728i
$310$		0			0
$311$	−12.6886	+	21.9772i	−0.719502	+	1.24621i	0.241696	+	0.970352i	$0.422296\pi$
$311$	−12.6886	+	21.9772i	−0.719502	+	1.24621i	−0.961197	+	0.275862i	$0.911037\pi$
$312$	−9.21687	−	2.46965i	−0.521803	−	0.139817i
$313$	−3.16157	−	4.51519i	−0.178703	−	0.255214i	0.719800	−	0.694181i	$-0.244233\pi$
$313$	−3.16157	−	4.51519i	−0.178703	−	0.255214i	−0.898503	+	0.438967i	$0.855344\pi$
$314$	0.0657190	−	0.372711i	0.00370874	−	0.0210333i
$315$		0			0
$316$	7.24825	+	4.18478i	0.407746	+	0.235412i
$317$	32.3581	−	2.83096i	1.81741	−	0.159003i	0.872989	−	0.487740i	$-0.162179\pi$
$317$	32.3581	−	2.83096i	1.81741	−	0.159003i	0.944421	+	0.328738i	$0.106623\pi$
$318$	6.32420	+	13.5623i	0.354643	+	0.760535i
$319$	26.2903	−	9.56887i	1.47197	−	0.535754i
$320$		0			0
$321$	−2.90821	−	16.4933i	−0.162321	−	0.920566i
$322$	−23.2734	+	23.2734i	−1.29698	+	1.29698i
$323$	6.81667	−	7.19994i	0.379290	−	0.400615i
$324$		−	6.61587i		−	0.367548i
$325$		0			0
$326$	7.31385	+	8.71630i	0.405077	+	0.482751i
$327$	15.0747	+	7.02947i	0.833635	+	0.388730i
$328$	5.44483	−	2.53897i	0.300640	−	0.140191i
$329$	−15.5637	+	18.5481i	−0.858056	+	1.02259i
$330$		0			0
$331$	−3.46608	+	2.00114i	−0.190513	+	0.109993i	−0.592223	−	0.805774i	$-0.701749\pi$
$331$	−3.46608	+	2.00114i	−0.190513	+	0.109993i	0.401710	+	0.915767i	$0.368416\pi$
$332$	−7.80274	+	5.46354i	−0.428231	+	0.299850i
$333$	4.39231	−	3.07553i	0.240697	−	0.168538i
$334$	−0.402492	+	0.232379i	−0.0220234	+	0.0127152i
$335$		0			0
$336$	−4.07069	+	4.85126i	−0.222074	+	0.264658i
$337$	8.93644	−	4.16713i	0.486799	−	0.226998i	−0.163693	−	0.986511i	$-0.552341\pi$
$337$	8.93644	−	4.16713i	0.486799	−	0.226998i	0.650492	+	0.759513i	$0.274563\pi$
$338$	−23.3730	−	10.8990i	−1.27133	−	0.592829i
$339$	9.06490	+	10.8031i	0.492338	+	0.586745i
$340$		0			0
$341$		−	22.3135i		−	1.20834i
$342$	−1.69496	−	2.28507i	−0.0916528	−	0.123562i
$343$	−9.01892	+	9.01892i	−0.486976	+	0.486976i
$344$	−0.508669	−	2.88480i	−0.0274256	−	0.155538i
$345$		0			0
$346$	−1.33654	+	0.486460i	−0.0718527	+	0.0261522i
$347$	−14.0821	−	30.1992i	−0.755969	−	1.62118i	−0.783370	−	0.621556i	$-0.786501\pi$
$347$	−14.0821	−	30.1992i	−0.755969	−	1.62118i	0.0274014	−	0.999625i	$-0.491277\pi$
$348$	−11.6631	+	1.02039i	−0.625207	+	0.0546985i
$349$	16.2073	+	9.35730i	0.867558	+	0.500885i	0.866536	−	0.499115i	$-0.166341\pi$
$349$	16.2073	+	9.35730i	0.867558	+	0.500885i	0.00102184	+	0.999999i	$0.499675\pi$
$350$		0			0
$351$	6.05236	−	34.3246i	0.323051	−	1.83211i
$352$	−2.09998	−	2.99908i	−0.111929	−	0.159852i
$353$	−4.77769	−	1.28018i	−0.254291	−	0.0681370i	0.129422	−	0.991590i	$-0.458688\pi$
$353$	−4.77769	−	1.28018i	−0.254291	−	0.0681370i	−0.383712	+	0.923453i	$0.625355\pi$
$354$	4.74320	−	8.21546i	0.252098	−	0.436647i
$355$		0			0
$356$	−0.129165	+	0.354878i	−0.00684574	+	0.0188085i
$357$	6.08782	−	13.0554i	0.322202	−	0.690964i
$358$	0.735166	−	8.40299i	0.0388547	−	0.444112i
$359$	2.24525	−	0.395898i	0.118500	−	0.0208947i	−0.114084	−	0.993471i	$-0.536393\pi$
$359$	2.24525	−	0.395898i	0.118500	−	0.0208947i	0.232583	+	0.972576i	$0.425282\pi$
$360$		0			0
$361$	18.1826	+	5.51301i	0.956979	+	0.290158i
$362$	−4.48431	−	4.48431i	−0.235690	−	0.235690i
$363$	2.11291	−	3.01755i	0.110899	−	0.158381i
$364$	−19.7209	+	16.5478i	−1.03365	+	0.867339i
$365$		0			0
$366$	−3.95007	−	1.43771i	−0.206474	−	0.0751503i
$367$	2.95120	+	33.7324i	0.154051	+	1.76082i	0.543165	+	0.839626i	$0.317226\pi$
$367$	2.95120	+	33.7324i	0.154051	+	1.76082i	−0.389114	+	0.921190i	$0.627219\pi$
$368$	2.06089	+	7.69134i	0.107431	+	0.400939i
$369$	1.96063	+	3.39590i	0.102066	+	0.176784i
$370$		0			0
$371$	39.7595	+	7.01067i	2.06421	+	0.363976i
$372$	−2.41671	+	9.01927i	−0.125300	+	0.467627i
$373$	21.3499	−	5.72069i	1.10546	−	0.296206i	0.340471	−	0.940255i	$-0.389413\pi$
$373$	21.3499	−	5.72069i	1.10546	−	0.296206i	0.764984	+	0.644049i	$0.222747\pi$
$374$	6.37956	+	5.35309i	0.329879	+	0.276802i
$375$		0			0
$376$	2.00346	+	5.50447i	0.103321	+	0.283871i
$377$	−47.4117	−	4.14799i	−2.44183	−	0.213632i
$378$	−18.9487	−	13.2680i	−0.974616	−	0.682433i
$379$	14.2951			0.734288			0.367144	−	0.930164i	$-0.380336\pi$
$379$	14.2951			0.734288			0.367144	+	0.930164i	$0.380336\pi$
$380$		0			0
$381$	29.0549			1.48853
$382$	−8.42551	−	5.89960i	−0.431087	−	0.301850i
$383$	−0.865789	−	0.0757467i	−0.0442397	−	0.00387048i	0.0650144	−	0.997884i	$-0.479291\pi$
$383$	−0.865789	−	0.0757467i	−0.0442397	−	0.00387048i	−0.109254	+	0.994014i	$0.534846\pi$
$384$	0.524005	+	1.43969i	0.0267405	+	0.0734690i
$385$		0			0
$386$	−14.8901	−	12.4943i	−0.757886	−	0.635942i
$387$	1.84682	−	0.494854i	0.0938792	−	0.0251549i
$388$	−3.72373	+	13.8972i	−0.189044	+	0.705521i
$389$	−7.53956	−	1.32943i	−0.382271	−	0.0674047i	−0.0207893	−	0.999784i	$-0.506618\pi$
$389$	−7.53956	−	1.32943i	−0.382271	−	0.0674047i	−0.361482	+	0.932379i	$0.617729\pi$
$390$		0			0
$391$	−9.05611	−	15.6856i	−0.457987	−	0.793257i
$392$	2.61037	+	9.74203i	0.131844	+	0.492047i
$393$	1.08220	+	12.3696i	0.0545896	+	0.623962i
$394$	20.3089	+	7.39182i	1.02315	+	0.372395i
$395$		0			0
$396$	1.83060	−	1.53606i	0.0919912	−	0.0771897i
$397$	12.1958	−	17.4173i	0.612087	−	0.874151i	−0.386758	−	0.922181i	$-0.626405\pi$
$397$	12.1958	−	17.4173i	0.612087	−	0.874151i	0.998846	+	0.0480296i	$0.0152942\pi$
$398$	−2.48655	−	2.48655i	−0.124640	−	0.124640i
$399$	27.5940	−	0.754521i	1.38143	−	0.0377733i
$400$		0			0
$401$	11.1259	−	1.96180i	0.555601	−	0.0979674i	0.111204	−	0.993798i	$-0.464529\pi$
$401$	11.1259	−	1.96180i	0.555601	−	0.0979674i	0.444397	+	0.895830i	$0.353418\pi$
$402$	−1.48878	+	17.0168i	−0.0742536	+	0.848723i
$403$	−16.0416	+	34.4013i	−0.799089	+	1.71365i
$404$	2.91537	−	8.00992i	0.145045	−	0.398509i
$405$		0			0
$406$	−15.7933	+	27.3547i	−0.783806	+	1.35759i
$407$	−29.0522	−	7.78452i	−1.44007	−	0.385864i
$408$	−1.99889	−	2.85471i	−0.0989597	−	0.141329i
$409$	5.47207	−	31.0336i	0.270576	−	1.53451i	−0.482095	−	0.876119i	$-0.660124\pi$
$409$	5.47207	−	31.0336i	0.270576	−	1.53451i	0.752672	−	0.658396i	$-0.228765\pi$
$410$		0			0
$411$	−0.501414	−	0.289492i	−0.0247329	−	0.0142796i
$412$	7.00279	−	0.612664i	0.345002	−	0.0301838i
$413$	−10.8164	−	23.1958i	−0.532239	−	1.14139i
$414$	−4.88383	+	1.77757i	−0.240027	+	0.0873627i
$415$		0			0
$416$	1.08150	+	6.13349i	0.0530249	+	0.300719i
$417$	−14.3752	+	14.3752i	−0.703955	+	0.703955i
$418$	−3.70755	+	15.5222i	−0.181342	+	0.759214i
$419$			18.2686i			0.892479i	0.894914	+	0.446239i	$0.147237\pi$
$419$			18.2686i			0.892479i	−0.894914	+	0.446239i	$0.852763\pi$
$420$		0			0
$421$	−2.42659	−	2.89189i	−0.118265	−	0.140942i	0.703664	−	0.710533i	$-0.251546\pi$
$421$	−2.42659	−	2.89189i	−0.118265	−	0.140942i	−0.821928	+	0.569591i	$0.807102\pi$
$422$	5.62014	+	2.62072i	0.273584	+	0.127574i
$423$	−3.46515	+	1.61582i	−0.168481	+	0.0785641i
$424$	6.27828	−	7.48216i	0.304900	−	0.363366i
$425$		0			0
$426$	−8.49214	+	4.90294i	−0.411445	+	0.237548i
$427$	−9.29001	+	6.50494i	−0.449575	+	0.314796i
$428$	−8.95440	+	6.26994i	−0.432827	+	0.303069i
$429$	−30.2548	+	17.4676i	−1.46072	+	0.843344i
$430$		0			0
$431$	23.2119	−	27.6629i	1.11808	−	1.33247i	0.180949	−	0.983492i	$-0.442083\pi$
$431$	23.2119	−	27.6629i	1.11808	−	1.33247i	0.937129	−	0.348982i	$-0.113473\pi$
$432$	−5.07194	+	2.36508i	−0.244024	+	0.113790i
$433$	10.9741	+	5.11731i	0.527382	+	0.245922i	0.668026	−	0.744138i	$-0.267139\pi$
$433$	10.9741	+	5.11731i	0.527382	+	0.245922i	−0.140644	+	0.990060i	$0.544917\pi$
$434$	16.1930	+	19.2981i	0.777289	+	0.926337i
$435$		0			0
$436$		−	10.8565i		−	0.519932i
$437$	19.1234	−	28.9650i	0.914795	−	1.38559i
$438$	3.78310	−	3.78310i	0.180763	−	0.180763i
$439$	3.01712	+	17.1110i	0.143999	+	0.816661i	0.968165	+	0.250312i	$0.0805333\pi$
$439$	3.01712	+	17.1110i	0.143999	+	0.816661i	−0.824166	+	0.566349i	$0.808356\pi$
$440$		0			0
$441$	−6.18597	+	2.25151i	−0.294570	+	0.107215i
$442$	−5.98712	−	12.8394i	−0.284778	−	0.610708i
$443$	−20.3382	+	1.77937i	−0.966299	+	0.0845402i	−0.559369	−	0.828919i	$-0.688956\pi$
$443$	−20.3382	+	1.77937i	−0.966299	+	0.0845402i	−0.406930	+	0.913459i	$0.633401\pi$
$444$	10.9000	+	6.29312i	0.517291	+	0.298658i
$445$		0			0
$446$	−1.07897	+	6.11917i	−0.0510909	+	0.289751i
$447$	−5.25721	−	7.50807i	−0.248657	−	0.355119i
$448$	3.99264	+	1.06982i	0.188634	+	0.0505445i
$449$	4.44673	−	7.70195i	0.209854	−	0.363478i	−0.741814	−	0.670605i	$-0.766034\pi$
$449$	4.44673	−	7.70195i	0.209854	−	0.363478i	0.951668	+	0.307128i	$0.0993678\pi$
$450$		0			0
$451$	7.52288	−	20.6689i	0.354238	−	0.973262i
$452$	3.89009	−	8.34233i	0.182975	−	0.392390i
$453$	0.243566	−	2.78397i	0.0114437	−	0.130803i
$454$	−9.83258	+	1.73375i	−0.461466	+	0.0813688i
$455$		0			0
$456$	3.17978	−	5.87262i	0.148907	−	0.275010i
$457$	−16.2697	−	16.2697i	−0.761063	−	0.761063i	0.215452	−	0.976514i	$-0.430878\pi$
$457$	−16.2697	−	16.2697i	−0.761063	−	0.761063i	−0.976514	+	0.215452i	$0.930878\pi$
$458$	14.2665	−	20.3747i	0.666631	−	0.952047i
$459$	9.75137	−	8.18237i	0.455155	−	0.381920i
$460$		0			0
$461$	−16.9357	−	6.16411i	−0.788776	−	0.287091i	−0.0839491	−	0.996470i	$-0.526753\pi$
$461$	−16.9357	−	6.16411i	−0.788776	−	0.287091i	−0.704827	+	0.709379i	$0.748976\pi$
$462$	2.02078	+	23.0977i	0.0940154	+	1.07460i
$463$	−5.39296	−	20.1268i	−0.250632	−	0.935372i	−0.970468	−	0.241228i	$-0.922450\pi$
$463$	−5.39296	−	20.1268i	−0.250632	−	0.935372i	0.719836	−	0.694144i	$-0.244217\pi$
$464$	3.82081	+	6.61784i	0.177377	+	0.307225i
$465$		0			0
$466$	−0.185960	−	0.0327897i	−0.00861442	−	0.00151895i
$467$	−8.31642	+	31.0373i	−0.384838	+	1.43623i	0.453584	+	0.891213i	$0.350145\pi$
$467$	−8.31642	+	31.0373i	−0.384838	+	1.43623i	−0.838422	+	0.545021i	$0.816522\pi$
$468$	−3.92659	+	1.05213i	−0.181507	+	0.0486346i
$469$	35.3038	+	29.6234i	1.63018	+	1.36788i
$470$		0			0
$471$	0.198315	+	0.544867i	0.00913789	+	0.0251061i
$472$	−6.16824	−	0.539651i	−0.283916	−	0.0248395i
$473$	−8.78523	−	6.15148i	−0.403945	−	0.282846i
$474$	−12.8229			−0.588976
$475$		0			0
$476$	−9.40221			−0.430949
$477$	5.22220	+	3.65663i	0.239108	+	0.167425i
$478$	−21.5604	−	1.88629i	−0.986152	−	0.0862771i
$479$	13.3397	+	36.6506i	0.609508	+	1.67461i	0.731303	+	0.682053i	$0.238913\pi$
$479$	13.3397	+	36.6506i	0.609508	+	1.67461i	−0.121795	+	0.992555i	$0.538865\pi$
$480$		0			0
$481$	39.1942	+	32.8879i	1.78710	+	1.49956i
$482$	−2.39010	+	0.640424i	−0.108866	+	0.0291705i
$483$	13.0513	−	48.7082i	0.593856	−	2.21630i
$484$	−2.36787	−	0.417520i	−0.107631	−	0.0189782i
$485$		0			0
$486$	−3.32635	−	5.76141i	−0.150886	−	0.261343i
$487$	5.68091	+	21.2014i	0.257426	+	0.960729i	0.966724	+	0.255820i	$0.0823454\pi$
$487$	5.68091	+	21.2014i	0.257426	+	0.960729i	−0.709298	+	0.704909i	$0.750988\pi$
$488$	0.239129	+	2.73325i	0.0108248	+	0.123728i
$489$	−16.3813	−	5.96230i	−0.740788	−	0.269625i
$490$		0			0
$491$	−11.9289	+	10.0095i	−0.538344	+	0.451725i	−0.870971	−	0.491334i	$-0.836509\pi$
$491$	−11.9289	+	10.0095i	−0.538344	+	0.451725i	0.332627	+	0.943059i	$0.392065\pi$
$492$	−5.27939	+	7.53975i	−0.238013	+	0.339918i
$493$	−12.2909	−	12.2909i	−0.553555	−	0.553555i
$494$	16.8752	−	21.2655i	0.759253	−	0.956782i
$495$		0			0
$496$	6.00199	−	1.05831i	0.269497	−	0.0475196i
$497$	−2.30576	+	26.3550i	−0.103428	+	1.18218i
$498$	6.16758	−	13.2264i	0.276376	−	0.592690i
$499$	4.83433	−	13.2822i	0.216414	−	0.594594i	−0.783217	−	0.621749i	$-0.786423\pi$
$499$	4.83433	−	13.2822i	0.216414	−	0.594594i	0.999631	+	0.0271550i	$0.00864476\pi$
$500$		0			0
$501$	0.356025	−	0.616653i	0.0159060	−	0.0275500i
$502$	−10.4831	−	2.80894i	−0.467883	−	0.125369i
$503$	14.0622	+	20.0829i	0.627001	+	0.895450i	0.999469	−	0.0325949i	$-0.0103771\pi$
$503$	14.0622	+	20.0829i	0.627001	+	0.895450i	−0.372468	+	0.928045i	$0.621488\pi$
$504$	−0.468492	+	2.65695i	−0.0208683	+	0.118350i
$505$		0			0
$506$	25.2472	+	14.5765i	1.12237	+	0.648003i
$507$	39.3611	−	3.44365i	1.74809	−	0.152938i
$508$	−8.01463	−	17.1874i	−0.355592	−	0.762568i
$509$	−16.9399	+	6.16563i	−0.750849	+	0.273287i	−0.688963	−	0.724797i	$-0.741934\pi$
$509$	−16.9399	+	6.16563i	−0.750849	+	0.273287i	−0.0618860	+	0.998083i	$0.519712\pi$
$510$		0			0
$511$	−2.50648	−	14.2150i	−0.110880	−	0.628833i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	22.3816	+	9.70102i	0.988172	+	0.428311i
$514$		−	3.82434i		−	0.168684i
$515$		0			0
$516$	2.88480	+	3.43798i	0.126996	+	0.151348i
$517$	19.4370	+	9.06362i	0.854838	+	0.398618i
$518$	30.7754	−	14.3508i	1.35219	−	0.630539i
$519$	1.40071	−	1.66930i	0.0614841	−	0.0732739i
$520$		0			0
$521$	9.10986	−	5.25958i	0.399110	−	0.230426i	−0.286990	−	0.957934i	$-0.592655\pi$
$521$	9.10986	−	5.25958i	0.399110	−	0.230426i	0.686100	+	0.727507i	$0.259321\pi$
$522$	−4.08570	+	2.86083i	−0.178826	+	0.125215i
$523$	21.7371	−	15.2205i	0.950496	−	0.665544i	0.00807293	−	0.999967i	$-0.497430\pi$
$523$	21.7371	−	15.2205i	0.950496	−	0.665544i	0.942423	+	0.334423i	$0.108541\pi$
$524$	7.01870	−	4.05225i	0.306613	−	0.177023i
$525$		0			0
$526$	−14.8461	+	17.6929i	−0.647321	+	0.771448i
$527$	−12.5641	+	5.85876i	−0.547303	+	0.255211i
$528$	5.08374	+	2.37059i	0.221241	+	0.103167i
$529$	−25.9712	−	30.9513i	−1.12918	−	1.34571i
$530$		0			0
$531$		−	4.04141i		−	0.175382i
$532$	−8.05799	−	16.1151i	−0.349358	−	0.698679i
$533$	−26.4575	+	26.4575i	−1.14600	+	1.14600i
$534$	−0.100473	−	0.569809i	−0.00434788	−	0.0246580i
$535$		0			0
$536$	10.4770	−	3.81331i	0.452537	−	0.164710i
$537$	5.46162	+	11.7125i	0.235686	+	0.505431i
$538$	14.0249	−	1.22702i	0.604656	−	0.0529005i
$539$	31.9787	+	18.4629i	1.37742	+	0.795253i
$540$		0			0
$541$	−6.58833	+	37.3643i	−0.283254	+	1.60642i	0.428200	+	0.903684i	$0.359148\pi$
$541$	−6.58833	+	37.3643i	−0.283254	+	1.60642i	−0.711455	+	0.702732i	$0.751963\pi$
$542$	−4.12093	−	5.88529i	−0.177009	−	0.252795i
$543$	9.38509	+	2.51473i	0.402753	+	0.107917i
$544$	−1.13732	+	1.96990i	−0.0487623	+	0.0844587i
$545$		0			0
$546$	13.4899	−	37.0631i	0.577313	−	1.58616i
$547$	4.95925	−	10.6352i	0.212042	−	0.454726i	−0.771304	−	0.636467i	$-0.780395\pi$
$547$	4.95925	−	10.6352i	0.212042	−	0.454726i	0.983347	+	0.181740i	$0.0581730\pi$
$548$	−0.0329366	+	0.376467i	−0.00140698	+	0.0160819i
$549$	−1.76361	+	0.310972i	−0.0752691	+	0.0132720i
$550$		0			0
$551$	10.5326	−	31.6000i	0.448702	−	1.34620i
$552$	−8.62636	−	8.62636i	−0.367162	−	0.367162i
$553$	−19.8431	+	28.3389i	−0.843816	+	1.20509i
$554$	18.6858	−	15.6793i	0.793885	−	0.666149i
$555$		0			0
$556$	12.4690	+	4.53833i	0.528801	+	0.192468i
$557$	2.43709	+	27.8560i	0.103263	+	1.18030i	0.854207	+	0.519933i	$0.174043\pi$
$557$	2.43709	+	27.8560i	0.103263	+	1.18030i	−0.750944	+	0.660366i	$0.770401\pi$
$558$	1.02957	+	3.84241i	0.0435852	+	0.162662i
$559$	9.12202	+	15.7998i	0.385820	+	0.668260i
$560$		0			0
$561$	−12.5653	−	2.21560i	−0.530507	−	0.0935427i
$562$	2.41695	−	9.02019i	0.101953	−	0.380494i
$563$	−23.4272	+	6.27730i	−0.987338	+	0.264556i	−0.716132	−	0.697965i	$-0.754089\pi$
$563$	−23.4272	+	6.27730i	−0.987338	+	0.264556i	−0.271206	+	0.962521i	$0.587422\pi$
$564$	−6.87492	−	5.76874i	−0.289486	−	0.242908i
$565$		0			0
$566$	2.66109	+	7.31127i	0.111854	+	0.307316i
$567$	27.2425	+	2.38341i	1.14408	+	0.100094i
$568$	5.24284	+	3.67108i	0.219985	+	0.154035i
$569$	−14.9059			−0.624889			−0.312444	−	0.949936i	$-0.601148\pi$
$569$	−14.9059			−0.624889			−0.312444	+	0.949936i	$0.601148\pi$
$570$		0			0
$571$	21.4399			0.897231			0.448615	−	0.893725i	$-0.351917\pi$
$571$	21.4399			0.897231			0.448615	+	0.893725i	$0.351917\pi$
$572$	18.6786	+	13.0789i	0.780991	+	0.546856i
$573$	15.6986	+	1.37345i	0.655817	+	0.0573765i
$574$	8.49330	+	23.3352i	0.354504	+	0.973991i
$575$		0			0
$576$	0.500000	+	0.419550i	0.0208333	+	0.0174812i
$577$	−7.24579	+	1.94150i	−0.301646	+	0.0808258i	−0.406467	−	0.913665i	$-0.633240\pi$
$577$	−7.24579	+	1.94150i	−0.301646	+	0.0808258i	0.104821	+	0.994491i	$0.466573\pi$
$578$	−3.06079	+	11.4230i	−0.127312	+	0.475136i
$579$	29.3278	+	5.17127i	1.21882	+	0.214911i
$580$		0			0
$581$	−19.6865	−	34.0980i	−0.816734	−	1.41463i
$582$	−5.70509	−	21.2917i	−0.236484	−	0.882568i
$583$	−3.11668	−	35.6239i	−0.129080	−	1.47539i
$584$	−3.28144	−	1.19435i	−0.135787	−	0.0494224i
$585$		0			0
$586$	−3.55779	+	2.98534i	−0.146971	+	0.123323i
$587$	−9.37249	+	13.3853i	−0.386844	+	0.552470i	−0.964593	−	0.263744i	$-0.915042\pi$
$587$	−9.37249	+	13.3853i	−0.386844	+	0.552470i	0.577749	+	0.816215i	$0.303931\pi$
$588$	−10.9263	−	10.9263i	−0.450595	−	0.450595i
$589$	−20.8096	−	16.5134i	−0.857445	−	0.680425i
$590$		0			0
$591$	−32.6088	+	5.74982i	−1.34135	+	0.236516i
$592$	0.715992	−	8.18382i	0.0294271	−	0.336353i
$593$	16.6832	−	35.7772i	0.685097	−	1.46920i	−0.188263	−	0.982119i	$-0.560286\pi$
$593$	16.6832	−	35.7772i	0.685097	−	1.46920i	0.873359	−	0.487076i	$-0.161937\pi$
$594$	−7.00767	+	19.2534i	−0.287528	+	0.789977i
$595$		0			0
$596$	−2.99123	+	5.18096i	−0.122526	+	0.212220i
$597$	5.20404	+	1.39442i	0.212987	+	0.0570697i
$598$	−28.4450	−	40.6236i	−1.16320	−	1.66122i
$599$	0.324751	−	1.84175i	0.0132690	−	0.0752521i	−0.977454	−	0.211147i	$-0.932280\pi$
$599$	0.324751	−	1.84175i	0.0132690	−	0.0752521i	0.990723	+	0.135895i	$0.0433911\pi$
$600$		0			0
$601$	3.10902	+	1.79499i	0.126820	+	0.0732194i	0.562068	−	0.827091i	$-0.310006\pi$
$601$	3.10902	+	1.79499i	0.126820	+	0.0732194i	−0.435248	+	0.900311i	$0.643339\pi$
$602$	12.0622	−	1.05530i	0.491617	−	0.0430110i
$603$	3.07549	+	6.59542i	0.125244	+	0.268586i
$604$	−1.71405	+	0.623862i	−0.0697436	+	0.0253846i
$605$		0			0
$606$	2.26776	+	12.8611i	0.0921214	+	0.522446i
$607$	2.60850	−	2.60850i	0.105876	−	0.105876i	−0.652184	−	0.758060i	$-0.726147\pi$
$607$	2.60850	−	2.60850i	0.105876	−	0.105876i	0.758060	+	0.652184i	$0.226147\pi$
$608$	−4.35107	−	0.261071i	−0.176459	−	0.0105878i
$609$		−	48.3934i		−	1.96100i
$610$		0			0
$611$	−23.4506	−	27.9473i	−0.948708	−	1.13063i
$612$	−1.34557	−	0.627448i	−0.0543913	−	0.0253631i
$613$	−14.9434	+	6.96824i	−0.603560	+	0.281444i	−0.700281	−	0.713867i	$-0.746942\pi$
$613$	−14.9434	+	6.96824i	−0.603560	+	0.281444i	0.0967217	+	0.995311i	$0.469164\pi$
$614$	15.8607	−	18.9021i	0.640087	−	0.762825i
$615$		0			0
$616$	13.1060	−	7.56676i	0.528056	−	0.304873i
$617$	−0.261183	+	0.182882i	−0.0105148	+	0.00736256i	−0.578822	−	0.815454i	$-0.696487\pi$
$617$	−0.261183	+	0.182882i	−0.0105148	+	0.00736256i	0.568307	+	0.822816i	$0.307599\pi$
$618$	−8.82216	+	6.17735i	−0.354879	+	0.248489i
$619$	13.5452	−	7.82034i	0.544429	−	0.314326i	−0.202443	−	0.979294i	$-0.564888\pi$
$619$	13.5452	−	7.82034i	0.544429	−	0.314326i	0.746872	+	0.664968i	$0.231555\pi$
$620$		0			0
$621$	28.6434	−	34.1359i	1.14942	−	1.36982i
$622$	−22.9995	+	10.7248i	−0.922195	+	0.430026i
$623$	−1.41477	−	0.659718i	−0.0566815	−	0.0264310i
$624$	−6.13349	−	7.30960i	−0.245536	−	0.292618i
$625$		0			0
$626$		−	5.51203i		−	0.220305i
$627$	−6.97138	−	23.4354i	−0.278410	−	0.935919i
$628$	0.267612	−	0.267612i	0.0106789	−	0.0106789i
$629$	3.24486	+	18.4025i	0.129381	+	0.733756i
$630$		0			0
$631$	−18.3557	+	6.68092i	−0.730728	+	0.265963i	−0.680473	−	0.732773i	$-0.738226\pi$
$631$	−18.3557	+	6.68092i	−0.730728	+	0.265963i	−0.0502551	+	0.998736i	$0.516003\pi$
$632$	3.53713	+	7.58540i	0.140699	+	0.301731i
$633$	−9.46455	+	0.828041i	−0.376182	+	0.0329117i
$634$	28.1300	+	16.2408i	1.11718	+	0.645006i
$635$		0			0
$636$	−2.59853	+	14.7370i	−0.103038	+	0.584359i
$637$	−36.0291	−	51.4549i	−1.42752	−	2.03872i
$638$	27.0242	+	7.24111i	1.06990	+	0.286678i
$639$	−2.08876	+	3.61784i	−0.0826300	+	0.143119i
$640$		0			0
$641$	6.78311	−	18.6364i	0.267917	−	0.736095i	−0.730659	−	0.682743i	$-0.760787\pi$
$641$	6.78311	−	18.6364i	0.267917	−	0.736095i	0.998576	−	0.0533527i	$-0.0169908\pi$
$642$	7.07789	−	15.1786i	0.279342	−	0.599051i
$643$	0.732946	−	8.37761i	0.0289046	−	0.330381i	−0.967951	−	0.251139i	$-0.919195\pi$
$643$	0.732946	−	8.37761i	0.0289046	−	0.330381i	0.996855	−	0.0792412i	$-0.0252497\pi$
$644$	−32.4135	+	5.71538i	−1.27727	+	0.225217i
$645$		0			0
$646$	9.71360	−	1.98796i	0.382177	−	0.0782153i
$647$	12.6447	+	12.6447i	0.497113	+	0.497113i	0.910538	−	0.413425i	$-0.135668\pi$
$647$	12.6447	+	12.6447i	0.497113	+	0.497113i	−0.413425	+	0.910538i	$0.635668\pi$
$648$	3.79471	−	5.41940i	0.149070	−	0.212894i
$649$	−17.3658	+	14.5716i	−0.681667	+	0.571987i
$650$		0			0
$651$	−36.2685	−	13.2007i	−1.42148	−	0.517375i
$652$	0.991687	+	11.3350i	0.0388374	+	0.443914i
$653$	−8.24323	−	30.7641i	−0.322582	−	1.20389i	−0.916720	−	0.399531i	$-0.869173\pi$
$653$	−8.24323	−	30.7641i	−0.322582	−	1.20389i	0.594137	−	0.804364i	$-0.297494\pi$
$654$	8.31657	+	14.4047i	0.325204	+	0.563269i
$655$		0			0
$656$	5.91644	+	1.04323i	0.230998	+	0.0407312i
$657$	0.589917	−	2.20160i	0.0230148	−	0.0858925i
$658$	−23.3878	+	6.26675i	−0.911753	+	0.244303i
$659$	1.60393	+	1.34585i	0.0624801	+	0.0524270i	0.673493	−	0.739194i	$-0.264793\pi$
$659$	1.60393	+	1.34585i	0.0624801	+	0.0524270i	−0.611013	+	0.791621i	$0.709238\pi$
$660$		0			0
$661$	1.65737	+	4.55359i	0.0644643	+	0.177114i	0.967743	−	0.251941i	$-0.0810688\pi$
$661$	1.65737	+	4.55359i	0.0644643	+	0.177114i	−0.903278	+	0.429055i	$0.858847\pi$
$662$	−3.98706	−	0.348823i	−0.154961	−	0.0135574i
$663$	17.7794	+	12.4493i	0.690496	+	0.483490i
$664$	−9.52538			−0.369657
$665$		0			0
$666$	5.36202			0.207774
$667$	−49.8435	−	34.9008i	−1.92995	−	1.35136i
$668$	−0.462989	−	0.0405063i	−0.0179136	−	0.00156723i
$669$	−3.25594	−	8.94562i	−0.125882	−	0.345858i
$670$		0			0
$671$	7.69508	+	6.45694i	0.297065	+	0.249267i
$672$	−6.11708	+	1.63907i	−0.235971	+	0.0632284i
$673$	5.86065	−	21.8723i	0.225912	−	0.843114i	−0.756126	−	0.654426i	$-0.772910\pi$
$673$	5.86065	−	21.8723i	0.225912	−	0.843114i	0.982037	−	0.188687i	$-0.0604232\pi$
$674$	9.71047	+	1.71222i	0.374033	+	0.0659521i
$675$		0			0
$676$	−12.8946	−	22.3342i	−0.495948	−	0.859007i
$677$	−10.0753	−	37.6017i	−0.387227	−	1.44515i	−0.834627	−	0.550816i	$-0.814317\pi$
$677$	−10.0753	−	37.6017i	−0.387227	−	1.44515i	0.447400	−	0.894334i	$-0.352350\pi$
$678$	1.22911	+	14.0488i	0.0472038	+	0.539542i
$679$	−55.8836	−	20.3400i	−2.14462	−	0.780576i
$680$		0			0
$681$	11.7180	−	9.83258i	0.449035	−	0.376785i
$682$	12.7985	−	18.2781i	0.490079	−	0.699906i
$683$	12.1271	+	12.1271i	0.464031	+	0.464031i	0.899974	−	0.435943i	$-0.143585\pi$
$683$	12.1271	+	12.1271i	0.464031	+	0.464031i	−0.435943	+	0.899974i	$0.643585\pi$
$684$	−0.0777656	−	2.84401i	−0.00297344	−	0.108743i
$685$		0			0
$686$	−12.5609	+	2.21483i	−0.479578	+	0.0845625i
$687$	−3.32129	+	37.9625i	−0.126715	+	1.44836i
$688$	1.23798	−	2.65485i	0.0471975	−	0.101215i
$689$	−20.8056	+	57.1630i	−0.792631	+	2.17774i
$690$		0			0
$691$	−12.3728	+	21.4304i	−0.470684	+	0.815249i	−0.999438	−	0.0335262i	$-0.989326\pi$
$691$	−12.3728	+	21.4304i	−0.470684	+	0.815249i	0.528753	+	0.848775i	$0.322660\pi$
$692$	−1.37385	−	0.368122i	−0.0522259	−	0.0139939i
$693$	5.66562	+	8.09134i	0.215219	+	0.307365i
$694$	5.78616	−	32.8149i	0.219640	−	1.24564i
$695$		0			0
$696$	−10.1391	−	5.85382i	−0.384322	−	0.221888i
$697$	−13.6134	+	1.19102i	−0.515644	+	0.0451130i
$698$	7.90913	+	16.9612i	0.299365	+	0.641990i
$699$	0.271855	−	0.0989471i	0.0102825	−	0.00374252i
$700$		0			0
$701$	0.399610	+	2.26630i	0.0150931	+	0.0855970i	0.991424	−	0.130686i	$-0.0417178\pi$
$701$	0.399610	+	2.26630i	0.0150931	+	0.0855970i	−0.976331	+	0.216283i	$0.930607\pi$
$702$	24.6456	−	24.6456i	0.930188	−	0.930188i
$703$	−28.7604	+	21.3331i	−1.08472	+	0.804594i
$704$		−	3.66120i		−	0.137987i
$705$		0			0
$706$	−3.17937	−	3.78903i	−0.119657	−	0.142602i
$707$	31.9326	+	14.8904i	1.20095	+	0.560012i
$708$	8.59759	−	4.00912i	0.323117	−	0.150672i
$709$	−8.58743	+	10.2341i	−0.322508	+	0.384350i	−0.902801	−	0.430058i	$-0.858493\pi$
$709$	−8.58743	+	10.2341i	−0.322508	+	0.384350i	0.580294	+	0.814407i	$0.302938\pi$
$710$		0			0
$711$	−4.73096	+	2.73142i	−0.177425	+	0.102436i
$712$	−0.309356	+	0.216613i	−0.0115936	+	0.00811792i
$713$	−39.7527	+	27.8351i	−1.48875	+	1.04243i
$714$	12.4751	−	7.20251i	0.466869	−	0.269547i
$715$		0			0
$716$	5.42197	−	6.46165i	0.202628	−	0.241483i
$717$	30.0520	−	14.0135i	1.12231	−	0.523343i
$718$	2.06628	+	0.963521i	0.0771128	+	0.0359583i
$719$	−20.2864	−	24.1764i	−0.756557	−	0.901629i	0.241068	−	0.970508i	$-0.422502\pi$
$719$	−20.2864	−	24.1764i	−0.756557	−	0.901629i	−0.997625	+	0.0688789i	$0.978058\pi$
$720$		0			0
$721$			29.0565i			1.08212i
$722$	11.7322	+	14.9451i	0.436627	+	0.556199i
$723$	2.68065	−	2.68065i	0.0996946	−	0.0996946i
$724$	−1.10124	−	6.24543i	−0.0409272	−	0.232109i
$725$		0			0
$726$	3.46160	−	1.25992i	0.128472	−	0.0467599i
$727$	8.96872	+	19.2335i	0.332631	+	0.713330i	0.999493	−	0.0318518i	$-0.0101405\pi$
$727$	8.96872	+	19.2335i	0.332631	+	0.713330i	−0.666861	+	0.745182i	$0.732363\pi$
$728$	−25.6458	+	2.24372i	−0.950497	+	0.0831577i
$729$	26.0155	+	15.0201i	0.963538	+	0.556299i
$730$		0			0
$731$	−1.15704	+	6.56190i	−0.0427947	+	0.242701i
$732$	−2.41107	−	3.44337i	−0.0891159	−	0.127271i
$733$	41.0435	+	10.9976i	1.51597	+	0.406204i	0.918414	−	0.395620i	$-0.129470\pi$
$733$	41.0435	+	10.9976i	1.51597	+	0.406204i	0.597560	+	0.801824i	$0.296137\pi$
$734$	−16.9306	+	29.3247i	−0.624920	+	1.08239i
$735$		0			0
$736$	−2.72339	+	7.48246i	−0.100386	+	0.275807i
$737$	17.2513	−	36.9956i	0.635461	−	1.36275i
$738$	−0.341760	+	3.90633i	−0.0125803	+	0.143794i
$739$	19.8303	−	3.49661i	0.729468	−	0.128625i	0.203434	−	0.979089i	$-0.434790\pi$
$739$	19.8303	−	3.49661i	0.729468	−	0.128625i	0.526034	+	0.850464i	$0.323679\pi$
$740$		0			0
$741$	−6.10019	+	41.1429i	−0.224096	+	1.51142i
$742$	28.5479	+	28.5479i	1.04803	+	1.04803i
$743$	−20.4293	+	29.1760i	−0.749477	+	1.07036i	0.245415	+	0.969418i	$0.421076\pi$
$743$	−20.4293	+	29.1760i	−0.749477	+	1.07036i	−0.994892	+	0.100946i	$0.967813\pi$
$744$	−7.15289	+	6.00199i	−0.262238	+	0.220044i
$745$		0			0
$746$	20.7701	+	7.55969i	0.760446	+	0.276780i
$747$	−0.541869	−	6.19359i	−0.0198260	−	0.226612i
$748$	2.15543	+	8.04416i	0.0788102	+	0.294124i
$749$	−22.5922	−	39.1308i	−0.825500	−	1.42981i
$750$		0			0
$751$	−1.31326	−	0.231563i	−0.0479216	−	0.00844987i	0.149636	−	0.988741i	$-0.452190\pi$
$751$	−1.31326	−	0.231563i	−0.0479216	−	0.00844987i	−0.197558	+	0.980291i	$0.563301\pi$
$752$	−1.51609	+	5.65814i	−0.0552863	+	0.206331i
$753$	16.0610	−	4.30354i	0.585296	−	0.156830i
$754$	−36.4582	−	30.5921i	−1.32773	−	1.11410i
$755$		0			0
$756$	−7.91164	−	21.7370i	−0.287744	−	0.790569i
$757$	33.4589	+	2.92727i	1.21608	+	0.106393i	0.677079	−	0.735910i	$-0.263245\pi$
$757$	33.4589	+	2.92727i	1.21608	+	0.106393i	0.539004	+	0.842303i	$0.318801\pi$
$758$	11.7098	+	8.19931i	0.425320	+	0.297812i
$759$	−44.6649			−1.62123
$760$		0			0
$761$	31.5263			1.14283			0.571414	−	0.820662i	$-0.306395\pi$
$761$	31.5263			1.14283			0.571414	+	0.820662i	$0.306395\pi$
$762$	23.8004	+	16.6652i	0.862196	+	0.603716i
$763$	44.7045	+	3.91113i	1.61841	+	0.141593i
$764$	−3.51790	−	9.66535i	−0.127273	−	0.349680i
$765$		0			0
$766$	−0.665766	−	0.558644i	−0.0240551	−	0.0201846i
$767$	37.2492	−	9.98089i	1.34499	−	0.360389i
$768$	−0.396534	+	1.47988i	−0.0143087	+	0.0534007i
$769$	41.2590	+	7.27508i	1.48784	+	0.262346i	0.857706	−	0.514141i	$-0.171889\pi$
$769$	41.2590	+	7.27508i	1.48784	+	0.262346i	0.630133	+	0.776487i	$0.283000\pi$
$770$		0			0
$771$	2.92961	+	5.07424i	0.105508	+	0.182744i
$772$	−5.03083	−	18.7753i	−0.181064	−	0.675738i
$773$	−0.973760	−	11.1301i	−0.0350237	−	0.400323i	−0.993391	−	0.114783i	$-0.963383\pi$
$773$	−0.973760	−	11.1301i	−0.0350237	−	0.400323i	0.958367	−	0.285540i	$-0.0921729\pi$
$774$	1.79666	+	0.653932i	0.0645797	+	0.0235051i
$775$		0			0
$776$	−11.0214	+	9.24804i	−0.395645	+	0.331985i
$777$	−29.8403	+	42.6164i	−1.07052	+	1.52886i
$778$	−5.41352	−	5.41352i	−0.194084	−	0.194084i
$779$	−13.7085	−	22.3122i	−0.491157	−	0.799419i
$780$		0			0
$781$	23.0769	−	4.06908i	0.825756	−	0.145603i
$782$	1.57858	−	18.0433i	0.0564501	−	0.645227i
$783$	18.0731	−	38.7578i	0.645879	−	1.38509i
$784$	−3.44951	+	9.47745i	−0.123197	+	0.338481i
$785$		0			0
$786$	−6.20840	+	10.7533i	−0.221446	+	0.383557i
$787$	14.0432	+	3.76285i	0.500585	+	0.134131i	0.500271	−	0.865869i	$-0.333234\pi$
$787$	14.0432	+	3.76285i	0.500585	+	0.134131i	0.000313276		1.00000i	$0.499900\pi$
$788$	12.3963	+	17.7037i	0.441599	+	0.630669i
$789$	6.14468	−	34.8482i	0.218757	−	1.24063i
$790$		0			0
$791$	32.9502	+	19.0238i	1.17158	+	0.676409i
$792$	2.38059	−	0.208274i	0.0845905	−	0.00740071i
$793$	−7.22170	−	15.4870i	−0.256450	−	0.549959i
$794$	19.9804	−	7.27226i	0.709076	−	0.258083i
$795$		0			0
$796$	−0.610637	−	3.46309i	−0.0216434	−	0.122746i
$797$	−35.4793	+	35.4793i	−1.25674	+	1.25674i	−0.304102	+	0.952640i	$0.598356\pi$
$797$	−35.4793	+	35.4793i	−1.25674	+	1.25674i	−0.952640	+	0.304102i	$0.901644\pi$
$798$	23.0365	+	15.2092i	0.815482	+	0.538400i
$799$		−	13.3243i		−	0.471379i
$800$		0			0
$801$	−0.158444	−	0.188827i	−0.00559836	−	0.00667187i
$802$	10.2390	+	4.77454i	0.361553	+	0.168595i
$803$	−11.5872	+	5.40319i	−0.408903	+	0.190674i
$804$	−10.9800	+	13.0854i	−0.387235	+	0.461488i
$805$		0			0
$806$	−32.8723	+	18.9788i	−1.15788	+	0.668501i
$807$	−17.6687	+	12.3717i	−0.621966	+	0.435505i
$808$	6.98244	−	4.88915i	0.245641	−	0.172000i
$809$	−30.2930	+	17.4897i	−1.06505	+	0.614904i	−0.926824	−	0.375497i	$-0.877472\pi$
$809$	−30.2930	+	17.4897i	−1.06505	+	0.614904i	−0.138222	+	0.990401i	$0.544139\pi$
$810$		0			0
$811$	19.7125	−	23.4925i	0.692201	−	0.824933i	−0.299419	−	0.954122i	$-0.596793\pi$
$811$	19.7125	−	23.4925i	0.692201	−	0.824933i	0.991620	+	0.129189i	$0.0412374\pi$
$812$	−28.6271	+	13.3490i	−1.00461	+	0.468459i
$813$	9.97616	+	4.65196i	0.349879	+	0.163151i
$814$	−19.3332	−	23.0404i	−0.677628	−	0.807565i
$815$		0			0
$816$		−	3.48496i		−	0.121998i
$817$	−12.2385	+	3.64063i	−0.428172	+	0.127369i
$818$	22.2826	−	22.2826i	0.779094	−	0.779094i
$819$	−2.91782	−	16.5478i	−0.101957	−	0.578226i
$820$		0			0
$821$	−41.5756	+	15.1323i	−1.45100	+	0.528120i	−0.942870	−	0.333161i	$-0.891885\pi$
$821$	−41.5756	+	15.1323i	−1.45100	+	0.528120i	−0.508128	+	0.861281i	$0.669662\pi$
$822$	−0.244689	−	0.524737i	−0.00853451	−	0.0183023i
$823$	6.44288	−	0.563679i	0.224585	−	0.0196486i	0.0256921	−	0.999670i	$-0.491821\pi$
$823$	6.44288	−	0.563679i	0.224585	−	0.0196486i	0.198893	+	0.980021i	$0.436265\pi$
$824$	6.08776	+	3.51477i	0.212077	+	0.122443i
$825$		0			0
$826$	4.44430	−	25.2049i	0.154637	−	0.876991i
$827$	−6.13372	−	8.75987i	−0.213291	−	0.304610i	0.698223	−	0.715880i	$-0.253974\pi$
$827$	−6.13372	−	8.75987i	−0.213291	−	0.304610i	−0.911514	+	0.411270i	$0.865085\pi$
$828$	−5.02017	−	1.34515i	−0.174463	−	0.0467472i
$829$	−13.9465	+	24.1561i	−0.484383	+	0.838975i	−0.999839	−	0.0179405i	$-0.994289\pi$
$829$	−13.9465	+	24.1561i	−0.484383	+	0.838975i	0.515456	+	0.856916i	$0.327622\pi$
$830$		0			0
$831$	−12.7819	+	35.1179i	−0.443398	+	1.21823i
$832$	−2.63211	+	5.64458i	−0.0912520	+	0.195691i
$833$	1.99947	−	22.8541i	0.0692776	−	0.791847i
$834$	−20.0207	+	3.53019i	−0.693261	+	0.122241i
$835$		0			0
$836$	−11.9402	+	10.5884i	−0.412960	+	0.366209i
$837$	−24.1172	−	24.1172i	−0.833613	−	0.833613i
$838$	−10.4784	+	14.9648i	−0.361971	+	0.516949i
$839$	31.4993	−	26.4310i	1.08748	−	0.912501i	0.0909559	−	0.995855i	$-0.471008\pi$
$839$	31.4993	−	26.4310i	1.08748	−	0.912501i	0.996520	+	0.0833543i	$0.0265633\pi$
$840$		0			0
$841$	−27.6217	−	10.0535i	−0.952471	−	0.346671i
$842$	−0.329022	−	3.76073i	−0.0113388	−	0.129603i
$843$	3.70299	+	13.8197i	0.127538	+	0.475977i
$844$	3.10057	+	5.37035i	0.106726	+	0.184855i
$845$		0			0
$846$	−3.76528	−	0.663921i	−0.129453	−	0.0228261i
$847$	2.57229	−	9.59990i	0.0883848	−	0.329856i
$848$	9.43446	−	2.52796i	0.323981	−	0.0868103i
$849$	−9.13156	−	7.66229i	−0.313394	−	0.262969i
$850$		0			0
$851$	22.3729	+	61.4690i	0.766933	+	2.10713i
$852$	−9.76856	−	0.854638i	−0.334665	−	0.0292794i
$853$	33.4537	+	23.4246i	1.14543	+	0.802042i	0.982805	−	0.184645i	$-0.0591137\pi$
$853$	33.4537	+	23.4246i	1.14543	+	0.802042i	0.162629	+	0.986687i	$0.448003\pi$
$854$	−11.3410			−0.388081
$855$		0			0
$856$	−10.9313			−0.373624
$857$	−17.3858	−	12.1737i	−0.593888	−	0.415845i	0.237620	−	0.971358i	$-0.423633\pi$
$857$	−17.3858	−	12.1737i	−0.593888	−	0.415845i	−0.831507	+	0.555514i	$0.812522\pi$
$858$	−34.8023	−	3.04481i	−1.18813	−	0.103948i
$859$	10.6856	+	29.3583i	0.364587	+	1.00169i	0.977387	+	0.211456i	$0.0678206\pi$
$859$	10.6856	+	29.3583i	0.364587	+	1.00169i	−0.612801	+	0.790238i	$0.709957\pi$
$860$		0			0
$861$	−29.1449	−	24.4555i	−0.993256	−	0.833441i
$862$	34.8809	−	9.34630i	1.18805	−	0.318336i
$863$	−5.28319	+	19.7172i	−0.179842	+	0.671180i	0.815834	+	0.578286i	$0.196278\pi$
$863$	−5.28319	+	19.7172i	−0.179842	+	0.671180i	−0.995676	+	0.0928935i	$0.970388\pi$
$864$	−5.51125	−	0.971782i	−0.187496	−	0.0330607i
$865$		0			0
$866$	6.05430	+	10.4864i	0.205733	+	0.356341i
$867$	−4.68941	−	17.5011i	−0.159261	−	0.594369i
$868$	2.19561	+	25.0960i	0.0745240	+	0.851813i
$869$	28.7947	+	10.4804i	0.976792	+	0.355523i
$870$		0			0
$871$	−53.1937	+	44.6349i	−1.80240	+	1.51239i
$872$	6.22704	−	8.89313i	0.210874	−	0.301159i
$873$	−6.64023	−	6.64023i	−0.224738	−	0.224738i
$874$	32.2786	−	12.7580i	1.09184	−	0.431547i
$875$		0			0
$876$	5.26882	−	0.929036i	0.178017	−	0.0313892i
$877$	0.603351	−	6.89634i	0.0203737	−	0.232873i	−0.979180	−	0.202995i	$-0.934933\pi$
$877$	0.603351	−	6.89634i	0.0203737	−	0.232873i	0.999554	−	0.0298780i	$-0.00951187\pi$
$878$	−7.34296	+	15.7470i	−0.247813	+	0.531436i
$879$	2.43367	−	6.68646i	0.0820857	−	0.225529i
$880$		0			0
$881$	−18.4419	+	31.9423i	−0.621323	+	1.07616i	0.367917	+	0.929859i	$0.380071\pi$
$881$	−18.4419	+	31.9423i	−0.621323	+	1.07616i	−0.989240	+	0.146304i	$0.953262\pi$
$882$	−6.35866	−	1.70380i	−0.214107	−	0.0573699i
$883$	−20.4537	−	29.2109i	−0.688323	−	0.983027i	−0.999466	−	0.0326637i	$-0.989601\pi$
$883$	−20.4537	−	29.2109i	−0.688323	−	0.983027i	0.311144	−	0.950363i	$-0.399288\pi$
$884$	2.46003	−	13.9515i	0.0827396	−	0.469240i
$885$		0			0
$886$	−17.6807	−	10.2080i	−0.593995	−	0.342943i
$887$	0.942805	−	0.0824848i	0.0316563	−	0.00276957i	−0.0713166	−	0.997454i	$-0.522720\pi$
$887$	0.942805	−	0.0824848i	0.0316563	−	0.00276957i	0.102973	+	0.994684i	$0.467165\pi$
$888$	5.31918	+	11.4070i	0.178500	+	0.382794i
$889$	73.6609	−	26.8104i	2.47051	−	0.899191i
$890$		0			0
$891$	−4.20611	−	23.8540i	−0.140910	−	0.799140i
$892$	−4.39365	+	4.39365i	−0.147110	+	0.147110i
$893$	22.8374	−	11.4193i	0.764225	−	0.382133i
$894$		−	9.16566i		−	0.306545i
$895$		0			0
$896$	2.65695	+	3.16643i	0.0887626	+	0.105783i
$897$	68.8611	+	32.1105i	2.29921	+	1.07214i
$898$	8.06020	−	3.75854i	0.268973	−	0.125424i
$899$	−29.9362	+	35.6766i	−0.998428	+	1.18988i
$900$		0			0
$901$	−19.2405	+	11.1085i	−0.640995	+	0.370079i
$902$	18.0176	−	12.6161i	0.599920	−	0.420069i
$903$	−15.1960	+	10.6404i	−0.505692	+	0.354089i
$904$	7.97154	−	4.60237i	0.265129	−	0.153073i
$905$		0			0
$906$	1.79634	−	2.14079i	0.0596794	−	0.0711231i
$907$	−44.9298	+	20.9511i	−1.49187	+	0.695670i	−0.985970	−	0.166923i	$-0.946617\pi$
$907$	−44.9298	+	20.9511i	−1.49187	+	0.695670i	−0.505899	+	0.862593i	$0.668839\pi$
$908$	−9.04881	−	4.21953i	−0.300295	−	0.140030i
$909$	3.57623	+	4.26199i	0.118616	+	0.141361i
$910$		0			0
$911$			46.8406i			1.55190i	0.630796	+	0.775949i	$0.282729\pi$
$911$			46.8406i			1.55190i	−0.630796	+	0.775949i	$0.717271\pi$
$912$	5.97312	−	2.98672i	0.197790	−	0.0989002i
$913$	−24.6599	+	24.6599i	−0.816123	+	0.816123i
$914$	−3.99543	−	22.6592i	−0.132157	−	0.749500i
$915$		0			0
$916$	23.3729	−	8.50704i	0.772262	−	0.281080i
$917$	14.1576	+	30.3611i	0.467526	+	1.00261i
$918$	12.6811	−	1.10945i	0.418538	−	0.0366173i
$919$	−32.2684	−	18.6302i	−1.06444	−	0.614552i	−0.137780	−	0.990463i	$-0.543997\pi$
$919$	−32.2684	−	18.6302i	−1.06444	−	0.614552i	−0.926656	+	0.375910i	$0.877330\pi$
$920$		0			0
$921$	−6.56462	+	37.2298i	−0.216312	+	1.22676i
$922$	−10.3374	−	14.7633i	−0.340443	−	0.486203i
$923$	−38.5037	−	10.3170i	−1.26736	−	0.339589i
$924$	−11.5930	+	20.0796i	−0.381380	+	0.660570i
$925$		0			0
$926$	7.12661	−	19.5802i	0.234195	−	0.643445i
$927$	−1.93906	+	4.15832i	−0.0636870	+	0.136577i
$928$	−0.666011	+	7.61254i	−0.0218629	+	0.249894i
$929$	21.0778	−	3.71659i	0.691541	−	0.121937i	0.183177	−	0.983080i	$-0.441362\pi$
$929$	21.0778	−	3.71659i	0.691541	−	0.121937i	0.508364	+	0.861143i	$0.330251\pi$
$930$		0			0
$931$	40.8848	−	16.1596i	1.33995	−	0.529611i
$932$	−0.133522	−	0.133522i	−0.00437365	−	0.00437365i
$933$	22.3006	−	31.8486i	0.730090	−	1.04268i
$934$	−24.6147	+	20.6542i	−0.805417	+	0.675825i
$935$		0			0
$936$	−3.81995	−	1.39035i	−0.124859	−	0.0454450i
$937$	2.91251	+	33.2901i	0.0951476	+	1.08754i	0.882270	+	0.470744i	$0.156015\pi$
$937$	2.91251	+	33.2901i	0.0951476	+	1.08754i	−0.787122	+	0.616797i	$0.788430\pi$
$938$	11.9279	+	44.5155i	0.389459	+	1.45348i
$939$	4.22246	+	7.31352i	0.137795	+	0.238668i
$940$		0			0
$941$	17.3581	+	3.06070i	0.565858	+	0.0997761i	0.449257	−	0.893403i	$-0.351689\pi$
$941$	17.3581	+	3.06070i	0.565858	+	0.0997761i	0.116602	+	0.993179i	$0.462800\pi$
$942$	−0.150072	+	0.560078i	−0.00488962	+	0.0182483i
$943$	−46.2073	+	12.3812i	−1.50472	+	0.403188i
$944$	−4.74320	−	3.98001i	−0.154378	−	0.129538i
$945$		0			0
$946$	−3.66809	−	10.0780i	−0.119260	−	0.327664i
$947$	−14.8232	−	1.29687i	−0.481691	−	0.0421425i	−0.156275	−	0.987714i	$-0.549949\pi$
$947$	−14.8232	−	1.29687i	−0.481691	−	0.0421425i	−0.325416	+	0.945571i	$0.605504\pi$
$948$	−10.5039	−	7.35492i	−0.341151	−	0.238877i
$949$	21.7487			0.705994
$950$		0			0
$951$	−49.7648			−1.61373
$952$	−7.70184	−	5.39288i	−0.249618	−	0.174784i
$953$	−12.3463	−	1.08016i	−0.399936	−	0.0349899i	−0.114586	−	0.993413i	$-0.536554\pi$
$953$	−12.3463	−	1.08016i	−0.399936	−	0.0349899i	−0.285350	+	0.958423i	$0.592110\pi$
$954$	2.18042	+	5.99066i	0.0705938	+	0.193955i
$955$		0			0
$956$	−16.5794	−	13.9117i	−0.536215	−	0.449937i
$957$	−41.4035	+	11.0940i	−1.33838	+	0.358619i
$958$	−10.0947	+	37.6738i	−0.326143	+	1.21718i
$959$	−1.53833	−	0.271249i	−0.0496753	−	0.00875910i
$960$		0			0
$961$	3.07194	+	5.32076i	0.0990950	+	0.171638i
$962$	13.2423	+	49.4210i	0.426950	+	1.59340i
$963$	−0.621847	−	7.10775i	−0.0200388	−	0.229044i
$964$	−2.32518	−	0.846298i	−0.0748892	−	0.0272574i
$965$		0			0
$966$	38.6289	−	32.4135i	1.24287	−	1.04289i
$967$	−10.7550	+	15.3597i	−0.345857	+	0.493935i	−0.953964	−	0.299920i	$-0.903040\pi$
$967$	−10.7550	+	15.3597i	−0.345857	+	0.493935i	0.608108	+	0.793855i	$0.291929\pi$
$968$	−1.70017	−	1.70017i	−0.0546454	−	0.0546454i
$969$	−11.3654	+	10.0787i	−0.365110	+	0.323776i
$970$		0			0
$971$	31.4795	−	5.55069i	1.01023	−	0.178130i	0.356045	−	0.934469i	$-0.384125\pi$
$971$	31.4795	−	5.55069i	1.01023	−	0.178130i	0.654180	+	0.756339i	$0.273014\pi$
$972$	0.579821	−	6.62739i	0.0185978	−	0.212574i
$973$	−23.1797	+	49.7091i	−0.743109	+	1.59360i
$974$	−7.50712	+	20.6256i	−0.240543	+	0.660888i
$975$		0			0
$976$	−1.37185	+	2.37611i	−0.0439117	+	0.0760573i
$977$	10.6920	+	2.86491i	0.342067	+	0.0916567i	0.425763	−	0.904835i	$-0.360006\pi$
$977$	10.6920	+	2.86491i	0.342067	+	0.0916567i	−0.0836957	+	0.996491i	$0.526672\pi$
$978$	−9.99893	−	14.2800i	−0.319731	−	0.456623i
$979$	−0.240097	+	1.36166i	−0.00767355	+	0.0435188i
$980$		0			0
$981$	6.13673	+	3.54304i	0.195931	+	0.113121i
$982$	−15.5128	+	1.35720i	−0.495034	+	0.0433099i
$983$	4.74633	+	10.1785i	0.151384	+	0.324645i	0.967345	−	0.253462i	$-0.0815694\pi$
$983$	4.74633	+	10.1785i	0.151384	+	0.324645i	−0.815961	+	0.578107i	$0.803792\pi$
$984$	−8.64925	+	3.14807i	−0.275728	+	0.100357i
$985$		0			0
$986$	−3.01835	−	17.1179i	−0.0961237	−	0.545145i
$987$	26.2310	−	26.2310i	0.834943	−	0.834943i
$988$	26.0208	−	7.74047i	0.827832	−	0.246257i
$989$			23.3251i			0.741695i
$990$		0			0
$991$	8.91656	+	10.6263i	0.283244	+	0.337557i	0.888842	−	0.458214i	$-0.151511\pi$
$991$	8.91656	+	10.6263i	0.283244	+	0.337557i	−0.605598	+	0.795771i	$0.707066\pi$
$992$	5.52356	+	2.57568i	0.175373	+	0.0817779i
$993$	5.55736	−	2.59144i	0.176357	−	0.0822368i
$994$	−17.0054	+	20.2662i	−0.539378	+	0.642805i
$995$		0			0
$996$	12.6385	−	7.29687i	0.400468	−	0.231210i
$997$	27.1075	−	18.9809i	0.858504	−	0.601131i	−0.0592666	−	0.998242i	$-0.518876\pi$
$997$	27.1075	−	18.9809i	0.858504	−	0.601131i	0.917770	+	0.397111i	$0.129987\pi$
$998$	11.5784	−	8.10730i	0.366508	−	0.256632i
$999$	−39.8145	+	22.9869i	−1.25967	+	0.727273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.b.257.3	yes	48
5.2	odd	4	inner	950.2.bb.b.143.1	✓	48
5.3	odd	4	inner	950.2.bb.b.143.4	yes	48
5.4	even	2	inner	950.2.bb.b.257.2	yes	48
19.2	odd	18	inner	950.2.bb.b.857.4	yes	48
95.2	even	36	inner	950.2.bb.b.743.2	yes	48
95.59	odd	18	inner	950.2.bb.b.857.1	yes	48
95.78	even	36	inner	950.2.bb.b.743.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.b.143.1	✓	48	5.2	odd	4	inner
950.2.bb.b.143.4	yes	48	5.3	odd	4	inner
950.2.bb.b.257.2	yes	48	5.4	even	2	inner
950.2.bb.b.257.3	yes	48	1.1	even	1	trivial
950.2.bb.b.743.2	yes	48	95.2	even	36	inner
950.2.bb.b.743.3	yes	48	95.78	even	36	inner
950.2.bb.b.857.1	yes	48	95.59	odd	18	inner
950.2.bb.b.857.4	yes	48	19.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.819152 + 0.573576i) q^{2} +(-1.52626 - 0.133530i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-1.17365 - 0.984808i) q^{6} +(-3.99264 + 1.06982i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-0.642788 - 0.113341i) q^{9} +O(q^{10})\)	\(q+(0.819152 + 0.573576i) q^{2} +(-1.52626 - 0.133530i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-1.17365 - 0.984808i) q^{6} +(-3.99264 + 1.06982i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-0.642788 - 0.113341i) q^{9} +(1.83060 + 3.17069i) q^{11} +(-0.396534 - 1.47988i) q^{12} +(-0.542815 - 6.20441i) q^{13} +(-3.88421 - 1.41374i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(1.30468 - 1.86328i) q^{17} +(-0.461531 - 0.461531i) q^{18} +(4.31176 + 0.639298i) q^{19} +(6.23666 - 1.09969i) q^{21} +(-0.319095 + 3.64727i) q^{22} +(3.36517 - 7.21662i) q^{23} +(0.524005 - 1.43969i) q^{24} +(3.11405 - 5.39370i) q^{26} +(5.40558 + 1.44842i) q^{27} +(-2.37087 - 3.38595i) q^{28} +(1.32695 - 7.52553i) q^{29} +(-5.27806 - 3.04729i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(-2.37059 - 5.08374i) q^{33} +(2.13747 - 0.777974i) q^{34} +(-0.113341 - 0.642788i) q^{36} +(-5.80894 + 5.80894i) q^{37} +(3.16530 + 2.99681i) q^{38} +9.54201i q^{39} +(-3.86168 - 4.60217i) q^{41} +(5.73953 + 2.67638i) q^{42} +(-2.65485 + 1.23798i) q^{43} +(-2.35338 + 2.80464i) q^{44} +(6.89587 - 3.98133i) q^{46} +(4.79838 - 3.35986i) q^{47} +(1.25501 - 0.878770i) q^{48} +(8.73447 - 5.04285i) q^{49} +(-2.24009 + 2.66963i) q^{51} +(5.64458 - 2.63211i) q^{52} +(-8.85215 - 4.12783i) q^{53} +(3.59721 + 4.28699i) q^{54} -4.13348i q^{56} +(-6.49550 - 1.55149i) q^{57} +(5.40344 - 5.40344i) q^{58} +(1.07520 + 6.09774i) q^{59} +(2.57823 - 0.938398i) q^{61} +(-2.57568 - 5.52356i) q^{62} +(2.68767 - 0.235141i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(0.974042 - 5.52407i) q^{66} +(-6.39502 - 9.13304i) q^{67} +(2.19714 + 0.588721i) q^{68} +(-6.09975 + 10.5651i) q^{69} +(2.18904 - 6.01434i) q^{71} +(0.275844 - 0.591550i) q^{72} +(-0.304351 + 3.47874i) q^{73} +(-8.09028 + 1.42653i) q^{74} +(0.873966 + 4.27038i) q^{76} +(-10.7010 - 10.7010i) q^{77} +(-5.47307 + 7.81636i) q^{78} +(6.41146 - 5.37985i) q^{79} +(-6.21688 - 2.26276i) q^{81} +(-0.523606 - 5.98484i) q^{82} +(2.46535 + 9.20081i) q^{83} +(3.16643 + 5.48442i) q^{84} +(-2.88480 - 0.508669i) q^{86} +(-3.03016 + 11.3087i) q^{87} +(-3.53645 + 0.947589i) q^{88} +(0.289299 + 0.242751i) q^{89} +(8.80489 + 24.1912i) q^{91} +(7.93236 + 0.693992i) q^{92} +(7.64878 + 5.35573i) q^{93} +5.85774 q^{94} +1.53209 q^{96} +(11.7855 + 8.25227i) q^{97} +(10.0473 + 0.879026i) q^{98} +(-0.817319 - 2.24556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{6}+O(q^{10}) \) 48 * q - 48 * q^6	\( 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) \) 48 * q - 48 * q^6 - 12 * q^11 + 36 * q^21 - 72 * q^31 + 48 * q^36 + 96 * q^41 + 72 * q^46 - 48 * q^51 - 108 * q^61 + 24 * q^66 - 60 * q^71 - 48 * q^76 - 168 * q^81 - 48 * q^86 + 252 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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