LMFDB - Embedded newform 950.2.bb.a.507.2

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:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			507.2
Character	$\chi$	$=$	950.507
Dual form			950.2.bb.a.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 - 0.996195i) q^{2} +(1.01913 + 2.18554i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(2.26604 - 0.824773i) q^{6} +(1.01230 - 0.271245i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.80958 + 2.15657i) q^{9} +O(q^{10})$	\(q+(0.0871557 - 0.996195i) q^{2} +(1.01913 + 2.18554i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(2.26604 - 0.824773i) q^{6} +(1.01230 - 0.271245i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.80958 + 2.15657i) q^{9} +(0.152704 + 0.264490i) q^{11} +(-0.624135 - 2.32931i) q^{12} +(2.92437 + 1.36365i) q^{13} +(-0.181985 - 1.03209i) q^{14} +(0.939693 + 0.342020i) q^{16} +(1.96212 + 0.171663i) q^{17} +(1.99065 + 1.99065i) q^{18} +(-1.55007 + 4.07398i) q^{19} +(1.62449 + 1.93599i) q^{21} +(0.276793 - 0.129071i) q^{22} +(-0.601114 - 0.858480i) q^{23} +(-2.37484 + 0.418748i) q^{24} +(1.61334 - 2.79439i) q^{26} +(0.430438 + 0.115336i) q^{27} +(-1.04402 + 0.0913401i) q^{28} +(2.09602 + 1.75877i) q^{29} +(3.31521 + 1.91404i) q^{31} +(0.422618 - 0.906308i) q^{32} +(-0.422429 + 0.603291i) q^{33} +(0.342020 - 1.93969i) q^{34} +(2.15657 - 1.80958i) q^{36} +(-0.822014 + 0.822014i) q^{37} +(3.92338 + 1.89924i) q^{38} +7.78106i q^{39} +(-2.48886 + 6.83807i) q^{41} +(2.07020 - 1.44957i) q^{42} +(-5.48065 - 3.83759i) q^{43} +(-0.104455 - 0.286989i) q^{44} +(-0.907604 + 0.524005i) q^{46} +(0.0499299 + 0.570701i) q^{47} +(0.210174 + 2.40230i) q^{48} +(-5.11100 + 2.95084i) q^{49} +(1.62449 + 4.46324i) q^{51} +(-2.64314 - 1.85075i) q^{52} +(9.03307 - 6.32502i) q^{53} +(0.152412 - 0.418748i) q^{54} +1.04801i q^{56} +(-10.4836 + 0.764198i) q^{57} +(1.93476 - 1.93476i) q^{58} +(5.85327 - 4.91147i) q^{59} +(-2.34864 + 13.3198i) q^{61} +(2.19569 - 3.13577i) q^{62} +(-1.24688 + 2.67394i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(0.564178 + 0.473401i) q^{66} +(-5.65843 + 0.495049i) q^{67} +(-1.90250 - 0.509774i) q^{68} +(1.26363 - 2.18866i) q^{69} +(-1.34730 + 0.237565i) q^{71} +(-1.61474 - 2.30608i) q^{72} +(13.4454 - 6.26968i) q^{73} +(0.747243 + 0.890530i) q^{74} +(2.23396 - 3.74292i) q^{76} +(0.226324 + 0.226324i) q^{77} +(7.75145 + 0.678164i) q^{78} +(2.32099 + 0.844770i) q^{79} +(1.65317 + 9.37560i) q^{81} +(6.59514 + 3.07536i) q^{82} +(-1.92749 - 7.19347i) q^{83} +(-1.26363 - 2.18866i) q^{84} +(-4.30066 + 5.12533i) q^{86} +(-1.70774 + 6.37335i) q^{87} +(-0.295001 + 0.0790452i) q^{88} +(-7.69475 + 2.80066i) q^{89} +(3.33022 + 0.587208i) q^{91} +(0.442908 + 0.949820i) q^{92} +(-0.804560 + 9.19617i) q^{93} +0.572881 q^{94} +2.41147 q^{96} +(-1.12124 + 12.8159i) q^{97} +(2.49416 + 5.34873i) q^{98} +(-0.846723 - 0.149300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 36 q^{6}+O(q^{10}) $ 24 * q + 36 * q^6	$ 24 q + 36 q^{6} + 12 q^{11} - 12 q^{21} + 12 q^{26} + 108 q^{31} - 36 q^{36} - 84 q^{41} - 36 q^{46} - 12 q^{51} - 12 q^{61} - 60 q^{66} - 24 q^{71} + 72 q^{76} - 216 q^{81} + 12 q^{86} - 12 q^{91} - 24 q^{96}+O(q^{100}) $ 24 * q + 36 * q^6 + 12 * q^11 - 12 * q^21 + 12 * q^26 + 108 * q^31 - 36 * q^36 - 84 * q^41 - 36 * q^46 - 12 * q^51 - 12 * q^61 - 60 * q^66 - 24 * q^71 + 72 * q^76 - 216 * q^81 + 12 * q^86 - 12 * q^91 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$3$	1.01913	+	2.18554i	0.588397	+	1.26182i	0.944849	+	0.327507i	$0.106209\pi$
$3$	1.01913	+	2.18554i	0.588397	+	1.26182i	−0.356452	+	0.934314i	$0.616014\pi$
$4$	−0.984808	−	0.173648i	−0.492404	−	0.0868241i
$5$		0			0
$5$		0			0
$6$	2.26604	−	0.824773i	0.925109	−	0.336712i
$7$	1.01230	−	0.271245i	0.382614	−	0.102521i	−0.0623853	−	0.998052i	$-0.519871\pi$
$7$	1.01230	−	0.271245i	0.382614	−	0.102521i	0.444999	+	0.895531i	$0.353204\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	−1.80958	+	2.15657i	−0.603193	+	0.718858i
$10$		0			0
$11$	0.152704	+	0.264490i	0.0460419	+	0.0797469i	0.888128	−	0.459596i	$-0.152006\pi$
$11$	0.152704	+	0.264490i	0.0460419	+	0.0797469i	−0.842086	+	0.539343i	$0.818673\pi$
$12$	−0.624135	−	2.32931i	−0.180172	−	0.672412i
$13$	2.92437	+	1.36365i	0.811073	+	0.378210i	0.783486	−	0.621410i	$-0.213440\pi$
$13$	2.92437	+	1.36365i	0.811073	+	0.378210i	0.0275876	+	0.999619i	$0.491217\pi$
$14$	−0.181985	−	1.03209i	−0.0486376	−	0.275837i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	1.96212	+	0.171663i	0.475884	+	0.0416345i	0.322575	−	0.946544i	$-0.395451\pi$
$17$	1.96212	+	0.171663i	0.475884	+	0.0416345i	0.153309	+	0.988178i	$0.451007\pi$
$18$	1.99065	+	1.99065i	0.469201	+	0.469201i
$19$	−1.55007	+	4.07398i	−0.355609	+	0.934635i
$19$	−1.55007	+	4.07398i	−0.355609	+	0.934635i
$20$		0			0
$21$	1.62449	+	1.93599i	0.354492	+	0.422467i
$22$	0.276793	−	0.129071i	0.0590125	−	0.0275180i
$23$	−0.601114	−	0.858480i	−0.125341	−	0.179005i	0.751577	−	0.659645i	$-0.229293\pi$
$23$	−0.601114	−	0.858480i	−0.125341	−	0.179005i	−0.876918	+	0.480640i	$0.840405\pi$
$24$	−2.37484	+	0.418748i	−0.484762	+	0.0854766i
$25$		0			0
$26$	1.61334	−	2.79439i	0.316402	−	0.548025i
$27$	0.430438	+	0.115336i	0.0828379	+	0.0221963i
$28$	−1.04402	+	0.0913401i	−0.197302	+	0.0172617i
$29$	2.09602	+	1.75877i	0.389221	+	0.326595i	0.816310	−	0.577614i	$-0.196016\pi$
$29$	2.09602	+	1.75877i	0.389221	+	0.326595i	−0.427088	+	0.904210i	$0.640461\pi$
$30$		0			0
$31$	3.31521	+	1.91404i	0.595429	+	0.343771i	0.767241	−	0.641359i	$-0.221629\pi$
$31$	3.31521	+	1.91404i	0.595429	+	0.343771i	−0.171812	+	0.985130i	$0.554962\pi$
$32$	0.422618	−	0.906308i	0.0747091	−	0.160214i
$33$	−0.422429	+	0.603291i	−0.0735354	+	0.105019i
$34$	0.342020	−	1.93969i	0.0586560	−	0.332655i
$35$		0			0
$36$	2.15657	−	1.80958i	0.359429	−	0.301597i
$37$	−0.822014	+	0.822014i	−0.135138	+	0.135138i	−0.771440	−	0.636302i	$-0.780463\pi$
$37$	−0.822014	+	0.822014i	−0.135138	+	0.135138i	0.636302	+	0.771440i	$0.280463\pi$
$38$	3.92338	+	1.89924i	0.636456	+	0.308097i
$39$			7.78106i			1.24597i
$40$		0			0
$41$	−2.48886	+	6.83807i	−0.388694	+	1.06793i	0.578896	+	0.815401i	$0.303484\pi$
$41$	−2.48886	+	6.83807i	−0.388694	+	1.06793i	−0.967590	+	0.252526i	$0.918739\pi$
$42$	2.07020	−	1.44957i	0.319439	−	0.223674i
$43$	−5.48065	−	3.83759i	−0.835791	−	0.585227i	0.0754269	−	0.997151i	$-0.475968\pi$
$43$	−5.48065	−	3.83759i	−0.835791	−	0.585227i	−0.911218	+	0.411924i	$0.864857\pi$
$44$	−0.104455	−	0.286989i	−0.0157473	−	0.0432652i
$45$		0			0
$46$	−0.907604	+	0.524005i	−0.133819	+	0.0772604i
$47$	0.0499299	+	0.570701i	0.00728302	+	0.0832453i	0.998966	−	0.0454570i	$-0.0144744\pi$
$47$	0.0499299	+	0.570701i	0.00728302	+	0.0832453i	−0.991683	+	0.128702i	$0.958919\pi$
$48$	0.210174	+	2.40230i	0.0303360	+	0.346742i
$49$	−5.11100	+	2.95084i	−0.730143	+	0.421548i
$50$		0			0
$51$	1.62449	+	4.46324i	0.227473	+	0.624978i
$52$	−2.64314	−	1.85075i	−0.366538	−	0.256653i
$53$	9.03307	−	6.32502i	1.24079	−	0.868809i	0.245850	−	0.969308i	$-0.420933\pi$
$53$	9.03307	−	6.32502i	1.24079	−	0.868809i	0.994937	+	0.100499i	$0.0320439\pi$
$54$	0.152412	−	0.418748i	0.0207406	−	0.0569844i
$55$		0			0
$56$			1.04801i			0.140046i
$57$	−10.4836	+	0.764198i	−1.38858	+	0.101221i
$58$	1.93476	−	1.93476i	0.254046	−	0.254046i
$59$	5.85327	−	4.91147i	0.762030	−	0.639419i	−0.176624	−	0.984278i	$-0.556518\pi$
$59$	5.85327	−	4.91147i	0.762030	−	0.639419i	0.938655	+	0.344859i	$0.112073\pi$
$60$		0			0
$61$	−2.34864	+	13.3198i	−0.300713	+	1.70543i	0.342317	+	0.939585i	$0.388788\pi$
$61$	−2.34864	+	13.3198i	−0.300713	+	1.70543i	−0.643030	+	0.765841i	$0.722323\pi$
$62$	2.19569	−	3.13577i	0.278853	−	0.398244i
$63$	−1.24688	+	2.67394i	−0.157092	+	0.336885i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$		0			0
$66$	0.564178	+	0.473401i	0.0694455	+	0.0582717i
$67$	−5.65843	+	0.495049i	−0.691287	+	0.0604798i	−0.427385	−	0.904070i	$-0.640565\pi$
$67$	−5.65843	+	0.495049i	−0.691287	+	0.0604798i	−0.263902	+	0.964549i	$0.585010\pi$
$68$	−1.90250	−	0.509774i	−0.230712	−	0.0618192i
$69$	1.26363	−	2.18866i	0.152123	−	0.263484i
$70$		0			0
$71$	−1.34730	+	0.237565i	−0.159895	+	0.0281937i	−0.253022	−	0.967460i	$-0.581425\pi$
$71$	−1.34730	+	0.237565i	−0.159895	+	0.0281937i	0.0931277	+	0.995654i	$0.470314\pi$
$72$	−1.61474	−	2.30608i	−0.190299	−	0.271774i
$73$	13.4454	−	6.26968i	1.57366	−	0.733810i	0.577100	−	0.816673i	$-0.304184\pi$
$73$	13.4454	−	6.26968i	1.57366	−	0.733810i	0.996561	+	0.0828633i	$0.0264065\pi$
$74$	0.747243	+	0.890530i	0.0868652	+	0.103522i
$75$		0			0
$76$	2.23396	−	3.74292i	0.256252	−	0.429342i
$77$	0.226324	+	0.226324i	0.0257920	+	0.0257920i
$78$	7.75145	+	0.678164i	0.877679	+	0.0767870i
$79$	2.32099	+	0.844770i	0.261131	+	0.0950441i	0.469268	−	0.883056i	$-0.344518\pi$
$79$	2.32099	+	0.844770i	0.261131	+	0.0950441i	−0.208137	+	0.978100i	$0.566740\pi$
$80$		0			0
$81$	1.65317	+	9.37560i	0.183686	+	1.04173i
$82$	6.59514	+	3.07536i	0.728311	+	0.339617i
$83$	−1.92749	−	7.19347i	−0.211569	−	0.789586i	−0.987346	−	0.158579i	$-0.949309\pi$
$83$	−1.92749	−	7.19347i	−0.211569	−	0.789586i	0.775777	−	0.631007i	$-0.217358\pi$
$84$	−1.26363	−	2.18866i	−0.137873	−	0.238803i
$85$		0			0
$86$	−4.30066	+	5.12533i	−0.463752	+	0.552678i
$87$	−1.70774	+	6.37335i	−0.183088	+	0.683295i
$88$	−0.295001	+	0.0790452i	−0.0314472	+	0.00842625i
$89$	−7.69475	+	2.80066i	−0.815642	+	0.296869i	−0.715952	−	0.698149i	$-0.754007\pi$
$89$	−7.69475	+	2.80066i	−0.815642	+	0.296869i	−0.0996895	+	0.995019i	$0.531785\pi$
$90$		0			0
$91$	3.33022	+	0.587208i	0.349102	+	0.0615561i
$92$	0.442908	+	0.949820i	0.0461764	+	0.0990256i
$93$	−0.804560	+	9.19617i	−0.0834290	+	0.953598i
$94$	0.572881			0.0590882
$95$		0			0
$96$	2.41147			0.246120
$97$	−1.12124	+	12.8159i	−0.113845	+	1.30126i	0.697456	+	0.716627i	$0.254315\pi$
$97$	−1.12124	+	12.8159i	−0.113845	+	1.30126i	−0.811301	+	0.584628i	$0.801240\pi$
$98$	2.49416	+	5.34873i	0.251948	+	0.540304i
$99$	−0.846723	−	0.149300i	−0.0850988	−	0.0150052i
$100$		0			0
$101$	−7.23783	+	2.63435i	−0.720191	+	0.262128i	−0.676007	−	0.736895i	$-0.736291\pi$
$101$	−7.23783	+	2.63435i	−0.720191	+	0.262128i	−0.0441839	+	0.999023i	$0.514069\pi$
$102$	4.58784	−	1.22931i	0.454263	−	0.121720i
$103$	3.30798	−	12.3456i	0.325945	−	1.21644i	−0.587413	−	0.809287i	$-0.699854\pi$
$103$	3.30798	−	12.3456i	0.325945	−	1.21644i	0.913358	−	0.407157i	$-0.133480\pi$
$104$	−2.07407	+	2.47178i	−0.203379	+	0.242378i
$105$		0			0
$106$	−5.51367	−	9.54996i	−0.535535	−	0.927574i
$107$	−2.37143	−	8.85030i	−0.229255	−	0.855591i	−0.980655	−	0.195744i	$-0.937288\pi$
$107$	−2.37143	−	8.85030i	−0.229255	−	0.855591i	0.751400	−	0.659847i	$-0.229379\pi$
$108$	−0.403871	−	0.188328i	−0.0388625	−	0.0181219i
$109$	−2.36986	−	13.4402i	−0.226992	−	1.28733i	−0.858841	−	0.512242i	$-0.828815\pi$
$109$	−2.36986	−	13.4402i	−0.226992	−	1.28733i	0.631849	−	0.775091i	$-0.282296\pi$
$110$		0			0
$111$	−2.63429	−	0.958801i	−0.250035	−	0.0910054i
$112$	1.04402	+	0.0913401i	0.0986509	+	0.00863083i
$113$	−0.317004	−	0.317004i	−0.0298212	−	0.0298212i	0.692039	−	0.721860i	$-0.256713\pi$
$113$	−0.317004	−	0.317004i	−0.0298212	−	0.0298212i	−0.721860	+	0.692039i	$0.756713\pi$
$114$	−0.152412	+	10.5103i	−0.0142747	+	0.984377i
$115$		0			0
$116$	−1.75877	−	2.09602i	−0.163298	−	0.194611i
$117$	−8.23270	+	3.83897i	−0.761113	+	0.354913i
$118$	−4.38264	−	6.25906i	−0.403455	−	0.576193i
$119$	2.03282	−	0.358441i	0.186348	−	0.0328582i
$120$		0			0
$121$	5.45336	−	9.44550i	0.495760	−	0.858682i
$122$	13.0644	+	3.50060i	1.18280	+	0.316929i
$123$	−17.4813	+	1.52942i	−1.57624	+	0.137903i
$124$	−2.93247	−	2.46064i	−0.263344	−	0.220972i
$125$		0			0
$126$	2.55509	+	1.47518i	0.227626	+	0.131420i
$127$	−3.91493	+	8.39560i	−0.347394	+	0.744989i	−0.999918	−	0.0127789i	$-0.995932\pi$
$127$	−3.91493	+	8.39560i	−0.347394	+	0.744989i	0.652524	+	0.757768i	$0.273710\pi$
$128$	−0.573576	+	0.819152i	−0.0506975	+	0.0724035i
$129$	2.80169	−	15.8892i	0.246675	−	1.39896i
$130$		0			0
$131$	8.03074	−	6.73859i	0.701649	−	0.588754i	−0.220593	−	0.975366i	$-0.570799\pi$
$131$	8.03074	−	6.73859i	0.701649	−	0.588754i	0.922242	+	0.386612i	$0.126355\pi$
$132$	0.520771	−	0.520771i	0.0453273	−	0.0453273i
$133$	−0.464086	+	4.54454i	−0.0402413	+	0.394061i
$134$			5.68004i			0.490681i
$135$		0			0
$136$	−0.673648	+	1.85083i	−0.0577649	+	0.158708i
$137$	18.3122	−	12.8224i	1.56452	−	1.09549i	0.612065	−	0.790808i	$-0.290339\pi$
$137$	18.3122	−	12.8224i	1.56452	−	1.09549i	0.952455	−	0.304681i	$-0.0985498\pi$
$138$	−2.07020	−	1.44957i	−0.176227	−	0.123396i
$139$	−4.46556	−	12.2690i	−0.378764	−	1.04065i	−0.971869	−	0.235521i	$-0.924320\pi$
$139$	−4.46556	−	12.2690i	−0.378764	−	1.04065i	0.593105	−	0.805125i	$-0.297902\pi$
$140$		0			0
$141$	−1.19640	+	0.690744i	−0.100755	+	0.0581711i
$142$	0.119236	+	1.36287i	0.0100061	+	0.114370i
$143$	0.0858878	+	0.981702i	0.00718230	+	0.0820941i
$144$	−2.43804	+	1.40760i	−0.203170	+	0.117300i
$145$		0			0
$146$	−5.07398	−	13.9406i	−0.419925	−	1.15374i
$147$	−11.6580	−	8.16299i	−0.961532	−	0.673272i
$148$	0.952267	−	0.666785i	0.0782759	−	0.0548094i
$149$	5.45475	−	14.9868i	0.446870	−	1.22777i	−0.488021	−	0.872832i	$-0.662281\pi$
$149$	5.45475	−	14.9868i	0.446870	−	1.22777i	0.934891	−	0.354934i	$-0.115497\pi$
$150$		0			0
$151$		−	19.9589i		−	1.62423i	−0.583495	−	0.812117i	$-0.698315\pi$
$151$		−	19.9589i		−	1.62423i	0.583495	−	0.812117i	$-0.301685\pi$
$152$	−3.53397	−	2.55167i	−0.286643	−	0.206968i
$153$	−3.92082	+	3.92082i	−0.316979	+	0.316979i
$154$	0.245188	−	0.205737i	0.0197578	−	0.0165788i
$155$		0			0
$156$	1.35117	−	7.66285i	0.108180	−	0.613519i
$157$	0.286976	−	0.409844i	0.0229032	−	0.0327091i	−0.807537	−	0.589817i	$-0.799200\pi$
$157$	0.286976	−	0.409844i	0.0229032	−	0.0327091i	0.830440	+	0.557108i	$0.188089\pi$
$158$	1.04384	−	2.23853i	0.0830437	−	0.178088i
$159$	23.0295	+	13.2961i	1.82636	+	1.05445i
$160$		0			0
$161$	−0.841367	−	0.705990i	−0.0663090	−	0.0556398i
$162$	9.48400	−	0.829743i	0.745134	−	0.0651907i
$163$	−8.18771	−	2.19389i	−0.641311	−	0.171839i	−0.0765138	−	0.997069i	$-0.524379\pi$
$163$	−8.18771	−	2.19389i	−0.641311	−	0.171839i	−0.564797	+	0.825230i	$0.691046\pi$
$164$	3.63846	−	6.30200i	0.284116	−	0.492104i
$165$		0			0
$166$	−7.33409	+	1.29320i	−0.569236	+	0.100372i
$167$	−4.56458	−	6.51890i	−0.353218	−	0.504448i	0.602745	−	0.797934i	$-0.294074\pi$
$167$	−4.56458	−	6.51890i	−0.353218	−	0.504448i	−0.955963	+	0.293486i	$0.905185\pi$
$168$	−2.29047	+	1.06806i	−0.176713	+	0.0824028i
$169$	−1.66387	−	1.98293i	−0.127990	−	0.152533i
$170$		0			0
$171$	−5.98087	−	10.7150i	−0.457368	−	0.819398i
$172$	4.73100	+	4.73100i	0.360735	+	0.360735i
$173$	10.4802	+	0.916898i	0.796795	+	0.0697105i	0.478280	−	0.878207i	$-0.341260\pi$
$173$	10.4802	+	0.916898i	0.796795	+	0.0697105i	0.318515	+	0.947918i	$0.396816\pi$
$174$	6.20026	+	2.25671i	0.470041	+	0.171081i
$175$		0			0
$176$	0.0530334	+	0.300767i	0.00399754	+	0.0226712i
$177$	16.6995	+	7.78709i	1.25521	+	0.585314i
$178$	2.11936	+	7.90956i	0.158853	+	0.592847i
$179$	−10.5178	−	18.2173i	−0.786137	−	1.36163i	−0.928318	−	0.371788i	$-0.878745\pi$
$179$	−10.5178	−	18.2173i	−0.786137	−	1.36163i	0.142181	−	0.989841i	$-0.454588\pi$
$180$		0			0
$181$	3.21213	−	3.82807i	0.238756	−	0.284538i	−0.633339	−	0.773874i	$-0.718316\pi$
$181$	3.21213	−	3.82807i	0.238756	−	0.284538i	0.872095	+	0.489336i	$0.162761\pi$
$182$	0.875222	−	3.26637i	0.0648757	−	0.242120i
$183$	−31.5045	+	8.44161i	−2.32888	+	0.624022i
$184$	0.984808	−	0.358441i	0.0726010	−	0.0264246i
$185$		0			0
$186$	9.09105	+	1.60300i	0.666588	+	0.117537i
$187$	0.254220	+	0.545176i	0.0185904	+	0.0398672i
$188$	0.0499299	−	0.570701i	0.00364151	−	0.0416227i
$189$	0.467017			0.0339705
$190$		0			0
$191$	−11.7638			−0.851200			−0.425600	−	0.904911i	$-0.639937\pi$
$191$	−11.7638			−0.851200			−0.425600	+	0.904911i	$0.639937\pi$
$192$	0.210174	−	2.40230i	0.0151680	−	0.173371i
$193$	4.38451	+	9.40261i	0.315604	+	0.676815i	0.998560	−	0.0536444i	$-0.0170838\pi$
$193$	4.38451	+	9.40261i	0.315604	+	0.676815i	−0.682956	+	0.730459i	$0.739306\pi$
$194$	12.6694	+	2.23396i	0.909609	+	0.160389i
$195$		0			0
$196$	5.54576	−	2.01849i	0.396126	−	0.144178i
$197$	−4.81731	+	1.29079i	−0.343219	+	0.0919652i	−0.426311	−	0.904577i	$-0.640187\pi$
$197$	−4.81731	+	1.29079i	−0.343219	+	0.0919652i	0.0830922	+	0.996542i	$0.473520\pi$
$198$	−0.222529	+	0.830488i	−0.0158144	+	0.0590202i
$199$	−17.2195	+	20.5214i	−1.22066	+	1.45472i	−0.369979	+	0.929040i	$0.620635\pi$
$199$	−17.2195	+	20.5214i	−1.22066	+	1.45472i	−0.850680	+	0.525684i	$0.823809\pi$
$200$		0			0
$201$	−6.84864	−	11.8622i	−0.483066	−	0.836695i
$202$	1.99351	+	7.43988i	0.140263	+	0.523468i
$203$	2.59886	+	1.21187i	0.182404	+	0.0850565i
$204$	−0.824773	−	4.67752i	−0.0577456	−	0.327492i
$205$		0			0
$206$	−12.0103	−	4.37138i	−0.836795	−	0.304568i
$207$	2.93914	+	0.257141i	0.204284	+	0.0178726i
$208$	2.28161	+	2.28161i	0.158201	+	0.158201i
$209$	−1.31423	+	0.212134i	−0.0909071	+	0.0146736i
$210$		0			0
$211$	−0.368241	−	0.438852i	−0.0253507	−	0.0302118i	0.753220	−	0.657769i	$-0.228500\pi$
$211$	−0.368241	−	0.438852i	−0.0253507	−	0.0302118i	−0.778571	+	0.627557i	$0.784055\pi$
$212$	−9.99417	+	4.66036i	−0.686402	+	0.320075i
$213$	−1.89228	−	2.70246i	−0.129657	−	0.185169i
$214$	−9.02330	+	1.59105i	−0.616820	+	0.108762i
$215$		0			0
$216$	−0.222811	+	0.385920i	−0.0151604	+	0.0262586i
$217$	3.87516	+	1.03835i	0.263063	+	0.0704875i
$218$	−13.5956	+	1.18946i	−0.920808	+	0.0805602i
$219$	27.4052	+	22.9957i	1.85187	+	1.55391i
$220$		0			0
$221$	5.50387	+	3.17766i	0.370230	+	0.213753i
$222$	−1.18475	+	2.54070i	−0.0795149	+	0.170520i
$223$	−1.56124	+	2.22968i	−0.104548	+	0.149310i	−0.868017	−	0.496534i	$-0.834606\pi$
$223$	−1.56124	+	2.22968i	−0.104548	+	0.149310i	0.763469	+	0.645845i	$0.223495\pi$
$224$	0.181985	−	1.03209i	0.0121594	−	0.0689593i
$225$		0			0
$226$	−0.343426	+	0.288169i	−0.0228444	+	0.0191687i
$227$	13.4598	−	13.4598i	0.893361	−	0.893361i	−0.101477	−	0.994838i	$-0.532357\pi$
$227$	13.4598	−	13.4598i	0.893361	−	0.893361i	0.994838	+	0.101477i	$0.0323569\pi$
$228$	10.4570	+	1.06786i	0.692531	+	0.0707209i
$229$			9.44562i			0.624184i	0.950052	+	0.312092i	$0.101030\pi$
$229$			9.44562i			0.624184i	−0.950052	+	0.312092i	$0.898970\pi$
$230$		0			0
$231$	−0.263985	+	0.725293i	−0.0173689	+	0.0477208i
$232$	−2.24133	+	1.56940i	−0.147151	+	0.103036i
$233$	−19.1635	−	13.4185i	−1.25545	−	0.879072i	−0.259215	−	0.965820i	$-0.583464\pi$
$233$	−19.1635	−	13.4185i	−1.25545	−	0.879072i	−0.996230	+	0.0867473i	$0.972353\pi$
$234$	3.10684	+	8.53596i	0.203100	+	0.558013i
$235$		0			0
$236$	−6.61721	+	3.82045i	−0.430744	+	0.248690i
$237$	0.519117	+	5.93354i	0.0337203	+	0.385425i
$238$	−0.179905	−	2.05632i	−0.0116615	−	0.133292i
$239$	−16.6235	+	9.59761i	−1.07529	+	0.620818i	−0.929621	−	0.368516i	$-0.879866\pi$
$239$	−16.6235	+	9.59761i	−1.07529	+	0.620818i	−0.145667	+	0.989334i	$0.546533\pi$
$240$		0			0
$241$	2.36618	+	6.50103i	0.152419	+	0.418768i	0.992278	−	0.124037i	$-0.0395843\pi$
$241$	2.36618	+	6.50103i	0.152419	+	0.418768i	−0.839858	+	0.542806i	$0.817362\pi$
$242$	−8.93427	−	6.25584i	−0.574316	−	0.402141i
$243$	−17.7108	+	12.4012i	−1.13615	+	0.795541i
$244$	4.62592	−	12.7096i	0.296144	−	0.813649i
$245$		0			0
$246$			17.5481i			1.11883i
$247$	−10.0885	+	9.80005i	−0.641913	+	0.623562i
$248$	−2.70686	+	2.70686i	−0.171886	+	0.171886i
$249$	13.7572	−	11.5437i	0.871830	−	0.731552i
$250$		0			0
$251$	0.448311	−	2.54250i	0.0282971	−	0.160481i	−0.967385	−	0.253311i	$-0.918480\pi$
$251$	0.448311	−	2.54250i	0.0282971	−	0.160481i	0.995682	+	0.0928303i	$0.0295914\pi$
$252$	1.69226	−	2.41680i	0.106602	−	0.152244i
$253$	0.135267	−	0.290082i	0.00850419	−	0.0182373i
$254$	8.02244	+	4.63176i	0.503373	+	0.290622i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	6.33764	−	0.554471i	0.395331	−	0.0345870i	0.112243	−	0.993681i	$-0.464197\pi$
$257$	6.33764	−	0.554471i	0.395331	−	0.0345870i	0.283088	+	0.959094i	$0.408641\pi$
$258$	−15.5845	−	4.17586i	−0.970251	−	0.259978i
$259$	−0.609158	+	1.05509i	−0.0378512	+	0.0655603i
$260$		0			0
$261$	−7.58584	+	1.33759i	−0.469552	+	0.0827946i
$262$	−6.01303	−	8.58749i	−0.371486	−	0.530537i
$263$	18.7168	−	8.72779i	1.15413	−	0.538179i	0.251185	−	0.967939i	$-0.419180\pi$
$263$	18.7168	−	8.72779i	1.15413	−	0.538179i	0.902943	+	0.429761i	$0.141402\pi$
$264$	−0.473401	−	0.564178i	−0.0291358	−	0.0347227i
$265$		0			0
$266$	4.48680	+	0.858402i	0.275103	+	0.0526320i
$267$	−13.9629	−	13.9629i	−0.854517	−	0.854517i
$268$	5.65843	+	0.495049i	0.345644	+	0.0302399i
$269$	19.9303	+	7.25402i	1.21517	+	0.442286i	0.868494	−	0.495700i	$-0.165088\pi$
$269$	19.9303	+	7.25402i	1.21517	+	0.442286i	0.346676	+	0.937985i	$0.387310\pi$
$270$		0			0
$271$	0.678701	+	3.84910i	0.0412281	+	0.233816i	0.998458	−	0.0555121i	$-0.0176791\pi$
$271$	0.678701	+	3.84910i	0.0412281	+	0.233816i	−0.957230	+	0.289328i	$0.906568\pi$
$272$	1.78508	+	0.832395i	0.108236	+	0.0504714i
$273$	2.11057	+	7.87677i	0.127738	+	0.476724i
$274$	−11.1776	−	19.3601i	−0.675261	−	1.16959i
$275$		0			0
$276$	−1.62449	+	1.93599i	−0.0977825	+	0.116533i
$277$	−3.01110	+	11.2376i	−0.180919	+	0.675200i	0.814548	+	0.580096i	$0.196985\pi$
$277$	−3.01110	+	11.2376i	−0.180919	+	0.675200i	−0.995467	+	0.0951037i	$0.969682\pi$
$278$	−12.6115	+	3.37925i	−0.756390	+	0.202674i
$279$	−10.1269	+	3.68589i	−0.606281	+	0.220668i
$280$		0			0
$281$	−5.46064	−	0.962858i	−0.325754	−	0.0574393i	0.00837959	−	0.999965i	$-0.497333\pi$
$281$	−5.46064	−	0.962858i	−0.325754	−	0.0574393i	−0.334134	+	0.942526i	$0.608444\pi$
$282$	0.583842	+	1.25205i	0.0347673	+	0.0745587i
$283$	−1.40549	+	16.0648i	−0.0835477	+	0.954955i	0.832537	+	0.553970i	$0.186888\pi$
$283$	−1.40549	+	16.0648i	−0.0835477	+	0.954955i	−0.916085	+	0.400985i	$0.868668\pi$
$284$	1.36808			0.0811806
$285$		0			0
$286$	0.985452			0.0582710
$287$	−0.664676	+	7.59728i	−0.0392346	+	0.448453i
$288$	1.18976	+	2.55144i	0.0701072	+	0.150345i
$289$	−12.9213	−	2.27837i	−0.760075	−	0.134022i
$290$		0			0
$291$	−29.1523	+	10.6106i	−1.70894	+	0.622002i
$292$	−14.3298	+	3.83966i	−0.838589	+	0.224699i
$293$	8.23086	−	30.7180i	0.480852	−	1.79456i	−0.117203	−	0.993108i	$-0.537393\pi$
$293$	8.23086	−	30.7180i	0.480852	−	1.79456i	0.598054	−	0.801456i	$-0.295941\pi$
$294$	−9.14798	+	10.9021i	−0.533521	+	0.635826i
$295$		0			0
$296$	−0.581252	−	1.00676i	−0.0337846	−	0.0585166i
$297$	0.0352243	+	0.131459i	0.00204392	+	0.00762802i
$298$	−14.4544	−	6.74018i	−0.837318	−	0.390448i
$299$	−0.587208	−	3.33022i	−0.0339591	−	0.192592i
$300$		0			0
$301$	−6.58899	−	2.39820i	−0.379783	−	0.138230i
$302$	−19.8830	−	1.73953i	−1.14414	−	0.100099i
$303$	−13.1338	−	13.1338i	−0.754516	−	0.754516i
$304$	−2.84997	+	3.29813i	−0.163457	+	0.189161i
$305$		0			0
$306$	3.56418	+	4.24762i	0.203750	+	0.242820i
$307$	−29.4066	+	13.7125i	−1.67832	+	0.782614i	−0.679521	+	0.733656i	$0.737812\pi$
$307$	−29.4066	+	13.7125i	−1.67832	+	0.782614i	−0.998801	+	0.0489576i	$0.984410\pi$
$308$	−0.183585	−	0.262186i	−0.0104607	−	0.0149394i
$309$	30.3530	−	5.35204i	1.72672	−	0.304467i
$310$		0			0
$311$	−6.06165	+	10.4991i	−0.343725	+	0.595349i	−0.985121	−	0.171861i	$-0.945022\pi$
$311$	−6.06165	+	10.4991i	−0.343725	+	0.595349i	0.641397	+	0.767210i	$0.278355\pi$
$312$	−7.51593	−	2.01389i	−0.425506	−	0.114014i
$313$	8.33172	−	0.728931i	0.470936	−	0.0412016i	0.150782	−	0.988567i	$-0.451821\pi$
$313$	8.33172	−	0.728931i	0.470936	−	0.0412016i	0.320154	+	0.947365i	$0.396265\pi$
$314$	−0.383273	−	0.321604i	−0.0216293	−	0.0181492i
$315$		0			0
$316$	−2.13903	−	1.23497i	−0.120330	−	0.0694726i
$317$	0.171020	−	0.366753i	0.00960542	−	0.0205989i	−0.901447	−	0.432890i	$-0.857494\pi$
$317$	0.171020	−	0.366753i	0.00960542	−	0.0205989i	0.911052	+	0.412292i	$0.135271\pi$
$318$	15.2526	−	21.7830i	0.855325	−	1.22153i
$319$	−0.145108	+	0.822948i	−0.00812449	+	0.0460763i
$320$		0			0
$321$	16.9259	−	14.2025i	0.944709	−	0.792705i
$322$	−0.776634	+	0.776634i	−0.0432801	+	0.0432801i
$323$	−3.74077	+	7.72755i	−0.208142	+	0.429972i
$324$		−	9.52023i		−	0.528902i
$325$		0			0
$326$	−2.89915	+	7.96534i	−0.160569	+	0.441160i
$327$	26.9588	−	18.8767i	1.49082	−	1.04389i
$328$	−5.96091	−	4.17387i	−0.329136	−	0.230464i
$329$	0.205344	+	0.564178i	0.0113210	+	0.0311041i
$330$		0			0
$331$	19.5861	−	11.3080i	1.07655	−	0.621545i	0.146584	−	0.989198i	$-0.453172\pi$
$331$	19.5861	−	11.3080i	1.07655	−	0.621545i	0.929963	+	0.367654i	$0.119839\pi$
$332$	0.649069	+	7.41889i	0.0356223	+	0.407165i
$333$	−0.285234	−	3.26024i	−0.0156307	−	0.178660i
$334$	−6.89193	+	3.97906i	−0.377109	+	0.217724i
$335$		0			0
$336$	0.864370	+	2.37484i	0.0471553	+	0.129558i
$337$	−9.11024	−	6.37906i	−0.496266	−	0.347489i	0.298495	−	0.954411i	$-0.403515\pi$
$337$	−9.11024	−	6.37906i	−0.496266	−	0.347489i	−0.794762	+	0.606922i	$0.792404\pi$
$338$	−2.12040	+	1.48472i	−0.115334	+	0.0807580i
$339$	0.369754	−	1.01589i	0.0200823	−	0.0551757i
$340$		0			0
$341$			1.16912i			0.0633115i
$342$	−11.1955	+	5.02423i	−0.605384	+	0.271679i
$343$	−9.56085	+	9.56085i	−0.516238	+	0.516238i
$344$	5.12533	−	4.30066i	0.276339	−	0.231876i
$345$		0			0
$346$	1.82682	−	10.3604i	0.0982104	−	0.556979i
$347$	5.75400	−	8.21756i	0.308891	−	0.441142i	−0.634452	−	0.772963i	$-0.718774\pi$
$347$	5.75400	−	8.21756i	0.308891	−	0.441142i	0.943342	+	0.331821i	$0.107663\pi$
$348$	2.78851	−	5.97998i	0.149480	−	0.320561i
$349$	−12.5667	−	7.25537i	−0.672678	−	0.388371i	0.124413	−	0.992231i	$-0.460295\pi$
$349$	−12.5667	−	7.25537i	−0.672678	−	0.388371i	−0.797091	+	0.603860i	$0.793629\pi$
$350$		0			0
$351$	1.10148	+	0.924252i	0.0587927	+	0.0493329i
$352$	0.304245	−	0.0266180i	0.0162163	−	0.00141874i
$353$	9.90648	+	2.65443i	0.527269	+	0.141281i	0.512627	−	0.858611i	$-0.328672\pi$
$353$	9.90648	+	2.65443i	0.527269	+	0.141281i	0.0146421	+	0.999893i	$0.495339\pi$
$354$	9.21291	−	15.9572i	0.489661	−	0.848117i
$355$		0			0
$356$	8.06418	−	1.42193i	0.427401	−	0.0753623i
$357$	2.85510	+	4.07750i	0.151108	+	0.215804i
$358$	−19.0647	+	8.89002i	−1.00760	+	0.469852i
$359$	13.6779	+	16.3007i	0.721891	+	0.860316i	0.994813	−	0.101720i	$-0.0324346\pi$
$359$	13.6779	+	16.3007i	0.721891	+	0.860316i	−0.272922	+	0.962036i	$0.587990\pi$
$360$		0			0
$361$	−14.1946	−	12.6299i	−0.747084	−	0.664730i
$362$	−3.53355	−	3.53355i	−0.185719	−	0.185719i
$363$	26.2012	+	2.29231i	1.37521	+	0.120315i
$364$	−3.17766	−	1.15657i	−0.166555	−	0.0606210i
$365$		0			0
$366$	5.66369	+	32.1204i	0.296046	+	1.67896i
$367$	22.2562	+	10.3782i	1.16176	+	0.541739i	0.905283	−	0.424810i	$-0.139659\pi$
$367$	22.2562	+	10.3782i	1.16176	+	0.541739i	0.256481	+	0.966549i	$0.417437\pi$
$368$	−0.271245	−	1.01230i	−0.0141396	−	0.0527698i
$369$	−10.2430	−	17.7414i	−0.533231	−	0.923583i
$370$		0			0
$371$	7.42855	−	8.85300i	0.385671	−	0.459625i
$372$	2.38924	−	8.91675i	0.123876	−	0.462312i
$373$	−11.8835	+	3.18418i	−0.615305	+	0.164870i	−0.552993	−	0.833186i	$-0.686514\pi$
$373$	−11.8835	+	3.18418i	−0.615305	+	0.164870i	−0.0623125	+	0.998057i	$0.519848\pi$
$374$	0.565258	−	0.205737i	0.0292288	−	0.0106384i
$375$		0			0
$376$	−0.564178	−	0.0994798i	−0.0290952	−	0.00513028i
$377$	3.73118	+	8.00154i	0.192165	+	0.412100i
$378$	0.0407032	−	0.465240i	0.00209355	−	0.0239294i
$379$	−23.8642			−1.22582			−0.612911	−	0.790152i	$-0.710002\pi$
$379$	−23.8642			−1.22582			−0.612911	+	0.790152i	$0.710002\pi$
$380$		0			0
$381$	−22.3387			−1.14445
$382$	−1.02528	+	11.7191i	−0.0524581	+	0.599599i
$383$	0.790991	+	1.69629i	0.0404178	+	0.0866762i	0.925480	−	0.378797i	$-0.123662\pi$
$383$	0.790991	+	1.69629i	0.0404178	+	0.0866762i	−0.885062	+	0.465473i	$0.845884\pi$
$384$	−2.37484	−	0.418748i	−0.121190	−	0.0213691i
$385$		0			0
$386$	9.74897	−	3.54834i	0.496210	−	0.180605i
$387$	18.1937	−	4.87500i	0.924839	−	0.247810i
$388$	3.32966	−	12.4265i	0.169038	−	0.630859i
$389$	−12.7689	+	15.2173i	−0.647407	+	0.771550i	−0.985521	−	0.169555i	$-0.945767\pi$
$389$	−12.7689	+	15.2173i	−0.647407	+	0.771550i	0.338113	+	0.941105i	$0.390211\pi$
$390$		0			0
$391$	−1.03209	−	1.78763i	−0.0521950	−	0.0904044i
$392$	−1.52747	−	5.70058i	−0.0771487	−	0.287923i
$393$	22.9119	+	10.6840i	1.15575	+	0.538935i
$394$	0.866025	+	4.91147i	0.0436297	+	0.247436i
$395$		0			0
$396$	0.807934	+	0.294064i	0.0406002	+	0.0147773i
$397$	−11.4101	−	0.998258i	−0.572658	−	0.0501011i	−0.202851	−	0.979210i	$-0.565021\pi$
$397$	−11.4101	−	0.998258i	−0.572658	−	0.0501011i	−0.369807	+	0.929108i	$0.620576\pi$
$398$	18.9425	+	18.9425i	0.949504	+	0.949504i
$399$	−10.4052	+	3.61721i	−0.520913	+	0.181087i
$400$		0			0
$401$	−8.65095	−	10.3098i	−0.432008	−	0.514847i	0.505493	−	0.862831i	$-0.331311\pi$
$401$	−8.65095	−	10.3098i	−0.432008	−	0.514847i	−0.937500	+	0.347984i	$0.886866\pi$
$402$	−12.4140	+	5.78872i	−0.619152	+	0.288715i
$403$	7.08480	+	10.1181i	0.352919	+	0.504020i
$404$	7.58532	−	1.33750i	0.377384	−	0.0665429i
$405$		0			0
$406$	1.43376	−	2.48335i	0.0711565	−	0.123247i
$407$	−0.342940	−	0.0918904i	−0.0169989	−	0.00455484i
$408$	−4.73160	+	0.413962i	−0.234249	+	0.0204942i
$409$	20.2354	+	16.9795i	1.00058	+	0.839583i	0.987064	−	0.160325i	$-0.0512543\pi$
$409$	20.2354	+	16.9795i	1.00058	+	0.839583i	0.0135122	+	0.999909i	$0.495699\pi$
$410$		0			0
$411$	46.6864	+	26.9544i	2.30287	+	1.32956i
$412$	−5.40151	+	11.5836i	−0.266113	+	0.570682i
$413$	4.59305	−	6.55956i	0.226009	−	0.322775i
$414$	0.512326	−	2.90554i	0.0251794	−	0.142800i
$415$		0			0
$416$	2.47178	−	2.07407i	0.121189	−	0.101690i
$417$	22.2634	−	22.2634i	1.09025	−	1.09025i
$418$	0.0967838	+	1.32772i	0.00473385	+	0.0649407i
$419$		−	19.5466i		−	0.954916i	−0.878655	−	0.477458i	$-0.841558\pi$
$419$		−	19.5466i		−	0.954916i	0.878655	−	0.477458i	$-0.158442\pi$
$420$		0			0
$421$	6.98246	−	19.1841i	0.340304	−	0.934978i	−0.645002	−	0.764181i	$-0.723143\pi$
$421$	6.98246	−	19.1841i	0.340304	−	0.934978i	0.985306	−	0.170797i	$-0.0546343\pi$
$422$	−0.469277	+	0.328591i	−0.0228440	+	0.0159956i
$423$	−1.32111	−	0.925052i	−0.0642346	−	0.0449776i
$424$	3.77157	+	10.3623i	0.183164	+	0.503238i
$425$		0			0
$426$	−2.85710	+	1.64955i	−0.138427	+	0.0799207i
$427$	1.23540	+	14.1207i	0.0597852	+	0.683349i
$428$	0.798565	+	9.12764i	0.0386001	+	0.441201i
$429$	−2.05802	+	1.18820i	−0.0993619	+	0.0573666i
$430$		0			0
$431$	4.30706	+	11.8335i	0.207464	+	0.570002i	0.999163	−	0.0409095i	$-0.0130255\pi$
$431$	4.30706	+	11.8335i	0.207464	+	0.570002i	−0.791699	+	0.610911i	$0.790803\pi$
$432$	0.365033	+	0.255599i	0.0175626	+	0.0122975i
$433$	20.9196	−	14.6480i	1.00533	−	0.703940i	0.0497776	−	0.998760i	$-0.484149\pi$
$433$	20.9196	−	14.6480i	1.00533	−	0.703940i	0.955553	+	0.294821i	$0.0952599\pi$
$434$	1.37214	−	3.76991i	0.0658647	−	0.180962i
$435$		0			0
$436$			13.6475i			0.653596i
$437$	4.42919	−	1.11823i	0.211877	−	0.0534920i
$438$	25.2967	−	25.2967i	1.20872	−	1.20872i
$439$	−20.7222	+	17.3880i	−0.989017	+	0.829884i	−0.985425	−	0.170109i	$-0.945588\pi$
$439$	−20.7222	+	17.3880i	−0.989017	+	0.829884i	−0.00359221	+	0.999994i	$0.501143\pi$
$440$		0			0
$441$	2.88507	−	16.3620i	0.137384	−	0.779144i
$442$	3.64526	−	5.20598i	0.173387	−	0.247623i
$443$	−5.60888	+	12.0283i	−0.266486	+	0.571481i	−0.993328	−	0.115324i	$-0.963209\pi$
$443$	−5.60888	+	12.0283i	−0.266486	+	0.571481i	0.726842	+	0.686805i	$0.240987\pi$
$444$	2.42777	+	1.40167i	0.115217	+	0.0665205i
$445$		0			0
$446$	2.08512	+	1.74963i	0.0987334	+	0.0828472i
$447$	38.3133	−	3.35198i	1.81216	−	0.158543i
$448$	−1.01230	−	0.271245i	−0.0478267	−	0.0128151i
$449$	−3.78417	+	6.55438i	−0.178586	+	0.309320i	−0.941396	−	0.337302i	$-0.890486\pi$
$449$	−3.78417	+	6.55438i	−0.178586	+	0.309320i	0.762810	+	0.646622i	$0.223819\pi$
$450$		0			0
$451$	−2.18866	+	0.385920i	−0.103060	+	0.0181723i
$452$	0.257140	+	0.367235i	0.0120949	+	0.0172733i
$453$	43.6210	−	20.3408i	2.04949	−	0.955694i
$454$	−12.2355	−	14.5817i	−0.574241	−	0.684354i
$455$		0			0
$456$	1.97519	−	10.3241i	0.0924965	−	0.483472i
$457$	2.69607	+	2.69607i	0.126117	+	0.126117i	0.767348	−	0.641231i	$-0.221576\pi$
$457$	2.69607	+	2.69607i	0.126117	+	0.126117i	−0.641231	+	0.767348i	$0.721576\pi$
$458$	9.40968	+	0.823240i	0.439685	+	0.0384675i
$459$	0.824773	+	0.300193i	0.0384971	+	0.0140118i
$460$		0			0
$461$	6.73870	+	38.2171i	0.313853	+	1.77995i	0.578582	+	0.815624i	$0.303606\pi$
$461$	6.73870	+	38.2171i	0.313853	+	1.77995i	−0.264729	+	0.964323i	$0.585283\pi$
$462$	0.699525	+	0.326194i	0.0325449	+	0.0151759i
$463$	7.84638	+	29.2831i	0.364652	+	1.36090i	0.867892	+	0.496753i	$0.165475\pi$
$463$	7.84638	+	29.2831i	0.364652	+	1.36090i	−0.503240	+	0.864147i	$0.667859\pi$
$464$	1.36808	+	2.36959i	0.0635115	+	0.110005i
$465$		0			0
$466$	−15.0376	+	17.9211i	−0.696604	+	0.830180i
$467$	9.11187	−	34.0060i	0.421647	−	1.57361i	−0.349491	−	0.936940i	$-0.613645\pi$
$467$	9.11187	−	34.0060i	0.421647	−	1.57361i	0.771138	−	0.636668i	$-0.219688\pi$
$468$	8.77426	−	2.35105i	0.405590	−	0.108678i
$469$	−5.59375	+	2.03596i	−0.258295	+	0.0940119i
$470$		0			0
$471$	1.18820	+	0.209511i	0.0547492	+	0.00965376i
$472$	3.22918	+	6.92500i	0.148635	+	0.318749i
$473$	0.178091	−	2.03559i	0.00818865	−	0.0935967i
$474$	5.95620			0.273577
$475$		0			0
$476$	−2.06418			−0.0946114
$477$	−2.70568	+	30.9261i	−0.123885	+	1.41601i
$478$	8.11225	+	17.3968i	0.371046	+	0.795710i
$479$	−34.1491	−	6.02141i	−1.56031	−	0.275125i	−0.674184	−	0.738564i	$-0.735504\pi$
$479$	−34.1491	−	6.02141i	−1.56031	−	0.275125i	−0.886129	+	0.463438i	$0.846616\pi$
$480$		0			0
$481$	−3.52481	+	1.28293i	−0.160718	+	0.0584965i
$482$	6.68252	−	1.79058i	0.304380	−	0.0815585i
$483$	0.685504	−	2.55834i	0.0311915	−	0.116408i
$484$	−7.01071	+	8.35504i	−0.318669	+	0.379774i
$485$		0			0
$486$	10.8105	+	18.7243i	0.490372	+	0.849350i
$487$	−4.39947	−	16.4190i	−0.199359	−	0.744018i	−0.991095	−	0.133155i	$-0.957489\pi$
$487$	−4.39947	−	16.4190i	−0.199359	−	0.744018i	0.791736	−	0.610863i	$-0.209177\pi$
$488$	−12.2581	−	5.71603i	−0.554897	−	0.258753i
$489$	−3.54954	−	20.1304i	−0.160516	−	0.910329i
$490$		0			0
$491$	16.0471	+	5.84067i	0.724196	+	0.263586i	0.677706	−	0.735333i	$-0.262974\pi$
$491$	16.0471	+	5.84067i	0.724196	+	0.263586i	0.0464898	+	0.998919i	$0.485197\pi$
$492$	17.4813	+	1.52942i	0.788120	+	0.0689516i
$493$	3.81073	+	3.81073i	0.171627	+	0.171627i
$494$	8.88349	+	10.9042i	0.399687	+	0.490603i
$495$		0			0
$496$	2.46064	+	2.93247i	0.110486	+	0.131672i
$497$	−1.29943	+	0.605934i	−0.0582874	+	0.0271799i
$498$	−10.3007	−	14.7110i	−0.461588	−	0.659215i
$499$	8.96275	−	1.58037i	0.401228	−	0.0707473i	0.0306068	−	0.999532i	$-0.490256\pi$
$499$	8.96275	−	1.58037i	0.401228	−	0.0707473i	0.370621	+	0.928784i	$0.379145\pi$
$500$		0			0
$501$	9.59539	−	16.6197i	0.428690	−	0.742514i
$502$	−2.49375	−	0.668198i	−0.111301	−	0.0298231i
$503$	41.9012	−	3.66588i	1.86828	−	0.163453i	0.903860	−	0.427828i	$-0.140721\pi$
$503$	41.9012	−	3.66588i	1.86828	−	0.163453i	0.964420	+	0.264375i	$0.0851655\pi$
$504$	−2.26011	−	1.89646i	−0.100673	−	0.0844750i
$505$		0			0
$506$	−0.277189	−	0.160035i	−0.0123225	−	0.00711442i
$507$	2.63805	−	5.65732i	0.117160	−	0.251250i
$508$	5.31334	−	7.58823i	0.235741	−	0.336673i
$509$	3.21951	−	18.2588i	0.142702	−	0.809306i	−0.826481	−	0.562965i	$-0.809661\pi$
$509$	3.21951	−	18.2588i	0.142702	−	0.809306i	0.969183	−	0.246341i	$-0.0792283\pi$
$510$		0			0
$511$	11.9101	−	9.99379i	0.526873	−	0.442099i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.13708	+	1.57482i	−0.0502034	+	0.0695299i
$514$		−	6.36184i		−	0.280609i
$515$		0			0
$516$	−5.51826	+	15.1613i	−0.242928	+	0.667438i
$517$	−0.143321	+	0.100354i	−0.00630323	+	0.00441357i
$518$	0.997986	+	0.698797i	0.0438490	+	0.0307034i
$519$	8.67680	+	23.8393i	0.380869	+	1.04643i
$520$		0			0
$521$	36.7995	−	21.2462i	1.61222	−	0.930814i	0.623362	−	0.781934i	$-0.285766\pi$
$521$	36.7995	−	21.2462i	1.61222	−	0.930814i	0.988855	−	0.148880i	$-0.0475669\pi$
$522$	0.671349	+	7.67355i	0.0293841	+	0.335862i
$523$	2.05251	+	23.4603i	0.0897501	+	1.02585i	0.898873	+	0.438209i	$0.144387\pi$
$523$	2.05251	+	23.4603i	0.0897501	+	1.02585i	−0.809123	+	0.587639i	$0.800057\pi$
$524$	−9.07888	+	5.24170i	−0.396613	+	0.228985i
$525$		0			0
$526$	−7.06330	−	19.4063i	−0.307975	−	0.846153i
$527$	6.17627	+	4.32467i	0.269042	+	0.188386i
$528$	−0.603291	+	0.422429i	−0.0262549	+	0.0183838i
$529$	7.49081	−	20.5808i	0.325688	−	0.894819i
$530$		0			0
$531$			21.5107i			0.933485i
$532$	1.24619	−	4.39491i	0.0540290	−	0.190543i
$533$	−16.6031	+	16.6031i	−0.719160	+	0.719160i
$534$	−15.1267	+	12.6928i	−0.654598	+	0.549273i
$535$		0			0
$536$	0.986329	−	5.59375i	0.0426029	−	0.241613i
$537$	29.0957	−	41.5529i	1.25557	−	1.79314i
$538$	8.96346	−	19.2222i	0.386442	−	0.828728i
$539$	−1.56094	−	0.901207i	−0.0672343	−	0.0388177i
$540$		0			0
$541$	8.44949	+	7.08997i	0.363272	+	0.304821i	0.806093	−	0.591788i	$-0.201578\pi$
$541$	8.44949	+	7.08997i	0.363272	+	0.304821i	−0.442821	+	0.896610i	$0.646022\pi$
$542$	3.89361	−	0.340647i	0.167245	−	0.0146320i
$543$	11.6400	+	3.11893i	0.499520	+	0.133846i
$544$	0.984808	−	1.70574i	0.0422233	−	0.0731329i
$545$		0			0
$546$	8.03074	−	1.41604i	0.343684	−	0.0606008i
$547$	−25.3987	−	36.2732i	−1.08597	−	1.55093i	−0.806927	−	0.590651i	$-0.798871\pi$
$547$	−25.3987	−	36.2732i	−1.08597	−	1.55093i	−0.279045	−	0.960278i	$-0.590018\pi$
$548$	−20.2606	+	9.44768i	−0.865490	+	0.403585i
$549$	−24.4751	−	29.1683i	−1.04457	−	1.24487i
$550$		0			0
$551$	−10.4142	+	5.81293i	−0.443658	+	0.247639i
$552$	1.78704	+	1.78704i	0.0760613	+	0.0760613i
$553$	2.57868	+	0.225605i	0.109656	+	0.00959370i
$554$	10.9324	+	3.97906i	0.464472	+	0.169054i
$555$		0			0
$556$	2.26723	+	12.8581i	0.0961518	+	0.545304i
$557$	35.7902	+	16.6892i	1.51648	+	0.707145i	0.989740	−	0.142883i	$-0.0456372\pi$
$557$	35.7902	+	16.6892i	1.51648	+	0.707145i	0.526738	+	0.850028i	$0.323415\pi$
$558$	2.78925	+	10.4096i	0.118078	+	0.440674i
$559$	−10.7943	−	18.6962i	−0.456549	−	0.790767i
$560$		0			0
$561$	−0.932419	+	1.11121i	−0.0393667	+	0.0469155i
$562$	−1.43512	+	5.35594i	−0.0605369	+	0.225927i
$563$	−10.3210	+	2.76551i	−0.434979	+	0.116552i	−0.469662	−	0.882846i	$-0.655624\pi$
$563$	−10.3210	+	2.76551i	−0.434979	+	0.116552i	0.0346836	+	0.999398i	$0.488958\pi$
$564$	1.29817	−	0.472497i	0.0546630	−	0.0198957i
$565$		0			0
$566$	15.8812	+	2.80028i	0.667536	+	0.117705i
$567$	4.21659	+	9.04251i	0.177080	+	0.379750i
$568$	0.119236	−	1.36287i	0.00500303	−	0.0571849i
$569$	30.8012			1.29125			0.645626	−	0.763654i	$-0.276597\pi$
$569$	30.8012			1.29125			0.645626	+	0.763654i	$0.276597\pi$
$570$		0			0
$571$	19.0310			0.796421			0.398211	−	0.917294i	$-0.369631\pi$
$571$	19.0310			0.796421			0.398211	+	0.917294i	$0.369631\pi$
$572$	0.0858878	−	0.981702i	0.00359115	−	0.0410470i
$573$	−11.9889	−	25.7103i	−0.500843	−	1.07406i
$574$	7.51044	+	1.32429i	0.313480	+	0.0552749i
$575$		0			0
$576$	2.64543	−	0.962858i	0.110226	−	0.0401191i
$577$	7.33814	−	1.96625i	0.305491	−	0.0818560i	−0.102817	−	0.994700i	$-0.532786\pi$
$577$	7.33814	−	1.96625i	0.305491	−	0.0818560i	0.408308	+	0.912844i	$0.366119\pi$
$578$	−3.39586	+	12.6735i	−0.141249	+	0.527150i
$579$	−16.0814	+	19.1650i	−0.668319	+	0.796471i
$580$		0			0
$581$	−3.90239	−	6.75914i	−0.161898	−	0.280416i
$582$	8.02940	+	29.9661i	0.332829	+	1.24214i
$583$	3.05229	+	1.42331i	0.126413	+	0.0589473i
$584$	2.57613	+	14.6099i	0.106601	+	0.604564i
$585$		0			0
$586$	−29.8837	−	10.8768i	−1.23449	−	0.449316i
$587$	−24.0526	−	2.10433i	−0.992757	−	0.0868549i	−0.420813	−	0.907148i	$-0.638255\pi$
$587$	−24.0526	−	2.10433i	−0.992757	−	0.0868549i	−0.571944	+	0.820293i	$0.693811\pi$
$588$	10.0634	+	10.0634i	0.415006	+	0.415006i
$589$	−12.9365	+	10.5392i	−0.533040	+	0.434260i
$590$		0			0
$591$	−7.73055	−	9.21291i	−0.317992	−	0.378969i
$592$	−1.05359	+	0.491295i	−0.0433021	+	0.0201921i
$593$	5.83594	+	8.33458i	0.239653	+	0.342260i	0.920904	−	0.389790i	$-0.127452\pi$
$593$	5.83594	+	8.33458i	0.239653	+	0.342260i	−0.681251	+	0.732050i	$0.738564\pi$
$594$	0.134029	−	0.0236329i	0.00549927	−	0.000969669i
$595$		0			0
$596$	−7.97431	+	13.8119i	−0.326640	+	0.565758i
$597$	−62.3993	−	16.7198i	−2.55383	−	0.684297i
$598$	−3.36873	+	0.294726i	−0.137758	+	0.0120522i
$599$	27.7768	+	23.3075i	1.13493	+	0.952320i	0.999261	−	0.0384346i	$-0.0122371\pi$
$599$	27.7768	+	23.3075i	1.13493	+	0.952320i	0.135669	+	0.990754i	$0.456682\pi$
$600$		0			0
$601$	−2.39141	−	1.38068i	−0.0975475	−	0.0563191i	0.450433	−	0.892810i	$-0.351270\pi$
$601$	−2.39141	−	1.38068i	−0.0975475	−	0.0563191i	−0.547980	+	0.836491i	$0.684603\pi$
$602$	−2.96334	+	6.35490i	−0.120777	+	0.259007i
$603$	9.17178	−	13.0987i	0.373504	−	0.533418i
$604$	−3.46583	+	19.6557i	−0.141023	+	0.799779i
$605$		0			0
$606$	−14.2285	+	11.9391i	−0.577993	+	0.484994i
$607$	−8.95776	+	8.95776i	−0.363584	+	0.363584i	−0.865131	−	0.501546i	$-0.832765\pi$
$607$	−8.95776	+	8.95776i	−0.363584	+	0.363584i	0.501546	+	0.865131i	$0.332765\pi$
$608$	3.03719	+	3.12657i	0.123174	+	0.126799i
$609$			6.91496i			0.280208i
$610$		0			0
$611$	−0.632226	+	1.73703i	−0.0255771	+	0.0702726i
$612$	4.54210	−	3.18041i	0.183603	−	0.128560i
$613$	−27.1740	−	19.0274i	−1.09755	−	0.768511i	−0.122937	−	0.992415i	$-0.539231\pi$
$613$	−27.1740	−	19.0274i	−1.09755	−	0.768511i	−0.974611	+	0.223903i	$0.928120\pi$
$614$	11.0974	+	30.4898i	0.447854	+	1.23047i
$615$		0			0
$616$	−0.277189	+	0.160035i	−0.0111683	+	0.00644799i
$617$	1.08154	+	12.3621i	0.0435411	+	0.497678i	0.986386	+	0.164446i	$0.0525836\pi$
$617$	1.08154	+	12.3621i	0.0435411	+	0.497678i	−0.942845	+	0.333232i	$0.891861\pi$
$618$	−2.68624	−	30.7039i	−0.108057	−	1.23509i
$619$	3.37305	−	1.94743i	0.135574	−	0.0782740i	−0.430679	−	0.902505i	$-0.641726\pi$
$619$	3.37305	−	1.94743i	0.135574	−	0.0782740i	0.566253	+	0.824231i	$0.308392\pi$
$620$		0			0
$621$	−0.159729	−	0.438852i	−0.00640971	−	0.0176105i
$622$	9.93083	+	6.95364i	0.398190	+	0.278816i
$623$	−7.02973	+	4.92227i	−0.281640	+	0.197207i
$624$	−2.66128	+	7.31180i	−0.106536	+	0.292706i
$625$		0			0
$626$		−	8.36354i		−	0.334274i
$627$	−1.80300	−	2.65610i	−0.0720049	−	0.106075i
$628$	−0.353785	+	0.353785i	−0.0141175	+	0.0141175i
$629$	−1.75400	+	1.47178i	−0.0699366	+	0.0586838i
$630$		0			0
$631$	−1.68820	+	9.57424i	−0.0672060	+	0.381144i	0.932590	+	0.360938i	$0.117543\pi$
$631$	−1.68820	+	9.57424i	−0.0672060	+	0.381144i	−0.999796	+	0.0202063i	$0.993568\pi$
$632$	−1.41670	+	2.02326i	−0.0563533	+	0.0804809i
$633$	0.583842	−	1.25205i	0.0232056	−	0.0497647i
$634$	−0.350452	−	0.202333i	−0.0139182	−	0.00803569i
$635$		0			0
$636$	−20.3708	−	17.0931i	−0.807753	−	0.677786i
$637$	−18.9704	+	1.65969i	−0.751633	+	0.0657594i
$638$	0.807170	+	0.216280i	0.0319562	+	0.00856263i
$639$	1.92572	−	3.33544i	0.0761801	−	0.131948i
$640$		0			0
$641$	−9.45589	+	1.66733i	−0.373485	+	0.0658555i	−0.357240	−	0.934013i	$-0.616282\pi$
$641$	−9.45589	+	1.66733i	−0.373485	+	0.0658555i	−0.0162449	+	0.999868i	$0.505171\pi$
$642$	−12.6733	−	18.0993i	−0.500173	−	0.714322i
$643$	13.4374	−	6.26598i	0.529921	−	0.247106i	−0.139194	−	0.990265i	$-0.544451\pi$
$643$	13.4374	−	6.26598i	0.529921	−	0.247106i	0.669115	+	0.743159i	$0.266673\pi$
$644$	0.705990	+	0.841367i	0.0278199	+	0.0331545i
$645$		0			0
$646$	7.37211	+	4.40003i	0.290052	+	0.173117i
$647$	−29.2043	−	29.2043i	−1.14814	−	1.14814i	−0.986918	−	0.161223i	$-0.948456\pi$
$647$	−29.2043	−	29.2043i	−1.14814	−	1.14814i	−0.161223	−	0.986918i	$-0.551544\pi$
$648$	−9.48400	−	0.829743i	−0.372567	−	0.0325954i
$649$	2.19285	+	0.798133i	0.0860770	+	0.0313295i
$650$		0			0
$651$	1.67996	+	9.52752i	0.0658428	+	0.373413i
$652$	7.68236	+	3.58234i	0.300864	+	0.140295i
$653$	−5.65070	−	21.0887i	−0.221129	−	0.825264i	−0.983919	−	0.178618i	$-0.942838\pi$
$653$	−5.65070	−	21.0887i	−0.221129	−	0.825264i	0.762790	−	0.646647i	$-0.223829\pi$
$654$	−16.4553	−	28.5014i	−0.643453	−	1.11449i
$655$		0			0
$656$	−4.67752	+	5.57445i	−0.182626	+	0.217646i
$657$	−10.8094	+	40.3414i	−0.421717	+	1.57387i
$658$	0.579928	−	0.155391i	0.0226079	−	0.00605778i
$659$	−3.10013	+	1.12836i	−0.120764	+	0.0439545i	−0.401695	−	0.915773i	$-0.631579\pi$
$659$	−3.10013	+	1.12836i	−0.120764	+	0.0439545i	0.280931	+	0.959728i	$0.409357\pi$
$660$		0			0
$661$	−29.3410	−	5.17360i	−1.14123	−	0.201230i	−0.429087	−	0.903263i	$-0.641165\pi$
$661$	−29.3410	−	5.17360i	−1.14123	−	0.201230i	−0.712144	+	0.702033i	$0.752276\pi$
$662$	−9.55795	−	20.4971i	−0.371480	−	0.796642i
$663$	−1.33572	+	15.2674i	−0.0518752	+	0.592936i
$664$	7.44723			0.289009
$665$		0			0
$666$	−3.27269			−0.126814
$667$	0.249921	−	2.85661i	0.00967699	−	0.110609i
$668$	3.36324	+	7.21250i	0.130128	+	0.279060i
$669$	−6.46415	−	1.13980i	−0.249919	−	0.0440674i
$670$		0			0
$671$	−3.88161	+	1.41279i	−0.149848	+	0.0545401i
$672$	2.44114	−	0.654100i	0.0941689	−	0.0252325i
$673$	−10.6171	+	39.6237i	−0.409261	+	1.52738i	0.386800	+	0.922164i	$0.373580\pi$
$673$	−10.6171	+	39.6237i	−0.409261	+	1.52738i	−0.796060	+	0.605217i	$0.793086\pi$
$674$	−7.14879	+	8.51960i	−0.275361	+	0.328163i
$675$		0			0
$676$	1.29426	+	2.24173i	0.0497793	+	0.0862204i
$677$	5.86119	+	21.8743i	0.225264	+	0.840696i	0.982299	+	0.187321i	$0.0599806\pi$
$677$	5.86119	+	21.8743i	0.225264	+	0.840696i	−0.757035	+	0.653374i	$0.773353\pi$
$678$	−0.979800	−	0.456888i	−0.0376290	−	0.0175467i
$679$	2.34121	+	13.2777i	0.0898474	+	0.509550i
$680$		0			0
$681$	43.1343	+	15.6996i	1.65291	+	0.601611i
$682$	1.16467	+	0.101896i	0.0445976	+	0.00390178i
$683$	−24.0893	−	24.0893i	−0.921753	−	0.921753i	0.0754003	−	0.997153i	$-0.475977\pi$
$683$	−24.0893	−	24.0893i	−0.921753	−	0.921753i	−0.997153	+	0.0754003i	$0.975977\pi$
$684$	4.02936	+	11.5908i	0.154066	+	0.443185i
$685$		0			0
$686$	8.69119	+	10.3578i	0.331831	+	0.395461i
$687$	−20.6438	+	9.62635i	−0.787609	+	0.367268i
$688$	−3.83759	−	5.48065i	−0.146307	−	0.208948i
$689$	35.0412	−	6.17870i	1.33496	−	0.235390i
$690$		0			0
$691$	−9.21941	+	15.9685i	−0.350723	+	0.607470i	−0.986376	−	0.164505i	$-0.947397\pi$
$691$	−9.21941	+	15.9685i	−0.350723	+	0.607470i	0.635653	+	0.771975i	$0.280731\pi$
$692$	−10.1618	−	2.72284i	−0.386292	−	0.103507i
$693$	−0.897635	+	0.0785329i	−0.0340983	+	0.00298322i
$694$	−7.68480	−	6.44831i	−0.291711	−	0.244775i
$695$		0			0
$696$	−5.71419	−	3.29909i	−0.216596	−	0.125052i
$697$	−6.05728	+	12.9899i	−0.229436	+	0.492027i
$698$	−8.32302	+	11.8865i	−0.315031	+	0.449911i
$699$	9.79635	−	55.5578i	0.370532	−	2.10139i
$700$		0			0
$701$	−4.47700	+	3.75665i	−0.169094	+	0.141887i	−0.723408	−	0.690421i	$-0.757425\pi$
$701$	−4.47700	+	3.75665i	−0.169094	+	0.141887i	0.554314	+	0.832308i	$0.312981\pi$
$702$	1.01674	−	1.01674i	0.0383742	−	0.0383742i
$703$	−2.07469	−	4.62304i	−0.0782485	−	0.174361i
$704$		−	0.305407i		−	0.0115105i
$705$		0			0
$706$	3.50774	−	9.63744i	0.132016	−	0.362710i
$707$	−6.61230	+	4.62998i	−0.248681	+	0.174128i
$708$	−15.0936	−	10.5686i	−0.567250	−	0.397193i
$709$	10.1395	+	27.8580i	0.380797	+	1.04623i	0.971022	+	0.238991i	$0.0768168\pi$
$709$	10.1395	+	27.8580i	0.380797	+	1.04623i	−0.590225	+	0.807239i	$0.700961\pi$
$710$		0			0
$711$	−6.02182	+	3.47670i	−0.225836	+	0.130386i
$712$	−0.713682	−	8.15742i	−0.0267464	−	0.305712i
$713$	−0.349657	−	3.99659i	−0.0130947	−	0.149674i
$714$	4.31082	−	2.48886i	0.161329	−	0.0931431i
$715$		0			0
$716$	7.19459	+	19.7670i	0.268875	+	0.738727i
$717$	−37.9175	−	26.5502i	−1.41606	−	0.991534i
$718$	17.4307	−	12.2051i	0.650509	−	0.455492i
$719$	−14.3373	+	39.3915i	−0.534692	+	1.46905i	0.318736	+	0.947843i	$0.396742\pi$
$719$	−14.3373	+	39.3915i	−0.534692	+	1.46905i	−0.853428	+	0.521210i	$0.825481\pi$
$720$		0			0
$721$		−	13.3947i		−	0.498844i
$722$	−13.8189	+	13.0398i	−0.514288	+	0.485292i
$723$	−11.7968	+	11.7968i	−0.438727	+	0.438727i
$724$	−3.82807	+	3.21213i	−0.142269	+	0.119378i
$725$		0			0
$726$	4.56717	−	25.9017i	0.169504	−	0.961303i
$727$	−19.3843	+	27.6836i	−0.718922	+	1.02673i	0.278871	+	0.960329i	$0.410040\pi$
$727$	−19.3843	+	27.6836i	−0.718922	+	1.02673i	−0.997793	+	0.0663988i	$0.978849\pi$
$728$	−1.42912	+	3.06477i	−0.0529669	+	0.113588i
$729$	−20.4188	−	11.7888i	−0.756252	−	0.436622i
$730$		0			0
$731$	−10.0949	−	8.47065i	−0.373374	−	0.313298i
$732$	32.4918	−	2.84266i	1.20093	−	0.105068i
$733$	26.6299	+	7.13547i	0.983599	+	0.263554i	0.714559	−	0.699575i	$-0.246627\pi$
$733$	26.6299	+	7.13547i	0.983599	+	0.263554i	0.269039	+	0.963129i	$0.413294\pi$
$734$	12.2785	−	21.2670i	0.453208	−	0.784978i
$735$		0			0
$736$	−1.03209	+	0.181985i	−0.0380433	+	0.00670806i
$737$	−0.994999	−	1.42101i	−0.0366512	−	0.0523434i
$738$	−18.5667	+	8.65778i	−0.683449	+	0.318697i
$739$	0.0819052	+	0.0976108i	0.00301293	+	0.00359067i	0.767549	−	0.640991i	$-0.221476\pi$
$739$	0.0819052	+	0.0976108i	0.00301293	+	0.00359067i	−0.764536	+	0.644581i	$0.777032\pi$
$740$		0			0
$741$	−31.6999	−	12.0612i	−1.16452	−	0.443078i
$742$	−8.17187	−	8.17187i	−0.299999	−	0.299999i
$743$	−25.7206	−	2.25026i	−0.943597	−	0.0825540i	−0.395037	−	0.918665i	$-0.629268\pi$
$743$	−25.7206	−	2.25026i	−0.943597	−	0.0825540i	−0.548560	+	0.836111i	$0.684824\pi$
$744$	−8.67458	−	3.15729i	−0.318026	−	0.115752i
$745$		0			0
$746$	2.13634	+	12.1158i	0.0782171	+	0.443591i
$747$	19.0012	+	8.86041i	0.695218	+	0.324185i
$748$	−0.155689	−	0.581038i	−0.00569254	−	0.0212449i
$749$	−4.80120	−	8.31592i	−0.175432	−	0.303857i
$750$		0			0
$751$	−17.9402	+	21.3802i	−0.654646	+	0.780176i	−0.986607	−	0.163117i	$-0.947845\pi$
$751$	−17.9402	+	21.3802i	−0.654646	+	0.780176i	0.331961	+	0.943293i	$0.392290\pi$
$752$	−0.148273	+	0.553361i	−0.00540694	+	0.0201790i
$753$	6.01361	−	1.61134i	0.219148	−	0.0587206i
$754$	8.29628	−	3.01960i	0.302133	−	0.109967i
$755$		0			0
$756$	−0.459922	−	0.0810966i	−0.0167272	−	0.00294946i
$757$	−11.1172	−	23.8409i	−0.404061	−	0.866511i	−0.998073	−	0.0620549i	$-0.980235\pi$
$757$	−11.1172	−	23.8409i	−0.404061	−	0.866511i	0.594012	−	0.804456i	$-0.297543\pi$
$758$	−2.07990	+	23.7734i	−0.0755454	+	0.863488i
$759$	0.771841			0.0280160
$760$		0			0
$761$	23.4620			0.850498			0.425249	−	0.905076i	$-0.360186\pi$
$761$	23.4620			0.850498			0.425249	+	0.905076i	$0.360186\pi$
$762$	−1.94695	+	22.2537i	−0.0705305	+	0.806168i
$763$	−6.04459	−	12.9627i	−0.218829	−	0.469280i
$764$	11.5851	+	2.04277i	0.419134	+	0.0739047i
$765$		0			0
$766$	1.75877	−	0.640140i	0.0635470	−	0.0231292i
$767$	23.8147	−	6.38112i	0.859897	−	0.230409i
$768$	−0.624135	+	2.32931i	−0.0225215	+	0.0840516i
$769$	−3.70950	+	4.42081i	−0.133768	+	0.159418i	−0.828770	−	0.559589i	$-0.810959\pi$
$769$	−3.70950	+	4.42081i	−0.133768	+	0.159418i	0.695002	+	0.719008i	$0.255403\pi$
$770$		0			0
$771$	7.67071	+	13.2861i	0.276254	+	0.478486i
$772$	−2.68515	−	10.0211i	−0.0966408	−	0.360668i
$773$	−36.9767	−	17.2425i	−1.32996	−	0.620170i	−0.377832	−	0.925874i	$-0.623330\pi$
$773$	−36.9767	−	17.2425i	−1.32996	−	0.620170i	−0.952126	+	0.305705i	$0.901108\pi$
$774$	−3.27076	−	18.5494i	−0.117565	−	0.666744i
$775$		0			0
$776$	−12.0890	−	4.40003i	−0.433970	−	0.157952i
$777$	−2.92676	−	0.256058i	−0.104997	−	0.00918604i
$778$	14.0466	+	14.0466i	0.503594	+	0.503594i
$779$	−24.0003	−	20.7390i	−0.859899	−	0.743052i
$780$		0			0
$781$	−0.268571	−	0.320070i	−0.00961021	−	0.0114530i
$782$	−1.87078	+	0.872359i	−0.0668990	+	0.0311955i
$783$	0.699359	+	0.998788i	0.0249930	+	0.0356938i
$784$	−5.81201	+	1.02481i	−0.207572	+	0.0366005i
$785$		0			0
$786$	12.6402	−	21.8935i	0.450862	−	0.780915i
$787$	−32.7870	−	8.78524i	−1.16873	−	0.313160i	−0.378282	−	0.925690i	$-0.623485\pi$
$787$	−32.7870	−	8.78524i	−1.16873	−	0.313160i	−0.790447	+	0.612530i	$0.790152\pi$
$788$	4.96826	−	0.434667i	0.176987	−	0.0154844i
$789$	38.1498	+	32.0115i	1.35817	+	1.13964i
$790$		0			0
$791$	−0.406889	−	0.234917i	−0.0144673	−	0.00835269i
$792$	0.363361	−	0.779230i	0.0129115	−	0.0276887i
$793$	−25.0319	+	35.7493i	−0.888909	+	1.26949i
$794$	−1.98892	+	11.2797i	−0.0705841	+	0.400302i
$795$		0			0
$796$	20.5214	−	17.2195i	0.727362	−	0.610329i
$797$	8.82038	−	8.82038i	0.312434	−	0.312434i	−0.533418	−	0.845852i	$-0.679093\pi$
$797$	8.82038	−	8.82038i	0.312434	−	0.312434i	0.845852	+	0.533418i	$0.179093\pi$
$798$	2.69657	+	10.6809i	0.0954576	+	0.378099i
$799$			1.12836i			0.0399183i
$800$		0			0
$801$	7.88444	−	21.6623i	0.278583	−	0.765400i
$802$	−11.0245	+	7.71947i	−0.389290	+	0.272584i
$803$	3.71143	+	2.59877i	0.130973	+	0.0917085i
$804$	4.68475	+	12.8712i	0.165218	+	0.453933i
$805$		0			0
$806$	10.6971	−	6.17598i	0.376790	−	0.217540i
$807$	4.45765	+	50.9512i	0.156917	+	1.79357i
$808$	−0.671303	−	7.67302i	−0.0236163	−	0.269936i
$809$	40.5542	−	23.4140i	1.42581	−	0.823192i	0.429024	−	0.903293i	$-0.358857\pi$
$809$	40.5542	−	23.4140i	1.42581	−	0.823192i	0.996787	+	0.0801005i	$0.0255241\pi$
$810$		0			0
$811$	0.441914	+	1.21415i	0.0155177	+	0.0426345i	0.947210	−	0.320615i	$-0.103890\pi$
$811$	0.441914	+	1.21415i	0.0155177	+	0.0426345i	−0.931692	+	0.363249i	$0.881667\pi$
$812$	−2.34894	−	1.64475i	−0.0824316	−	0.0577192i
$813$	−7.72067	+	5.40607i	−0.270776	+	0.189599i
$814$	−0.121430	+	0.333626i	−0.00425611	+	0.0116936i
$815$		0			0
$816$			4.74968i			0.166272i
$817$	24.1296	−	16.3795i	0.844189	−	0.573047i
$818$	18.6785	−	18.6785i	0.653080	−	0.653080i
$819$	−7.29266	+	6.11927i	−0.254826	+	0.213825i
$820$		0			0
$821$	−7.43036	+	42.1397i	−0.259321	+	1.47068i	0.525410	+	0.850849i	$0.323912\pi$
$821$	−7.43036	+	42.1397i	−0.259321	+	1.47068i	−0.784732	+	0.619835i	$0.787199\pi$
$822$	30.9208	−	44.1595i	1.07849	−	1.54024i
$823$	−2.08691	+	4.47539i	−0.0727451	+	0.156002i	−0.939318	−	0.343049i	$-0.888540\pi$
$823$	−2.08691	+	4.47539i	−0.0727451	+	0.156002i	0.866572	+	0.499051i	$0.166318\pi$
$824$	11.0687	+	6.39053i	0.385597	+	0.222625i
$825$		0			0
$826$	−6.13429	−	5.14728i	−0.213439	−	0.179097i
$827$	18.6756	−	1.63390i	0.649413	−	0.0568163i	0.242311	−	0.970199i	$-0.422095\pi$
$827$	18.6756	−	1.63390i	0.649413	−	0.0568163i	0.407103	+	0.913382i	$0.366539\pi$
$828$	−2.84984	−	0.763611i	−0.0990386	−	0.0265373i
$829$	−7.72076	+	13.3727i	−0.268153	+	0.464454i	−0.968385	−	0.249461i	$-0.919747\pi$
$829$	−7.72076	+	13.3727i	−0.268153	+	0.464454i	0.700232	+	0.713915i	$0.253080\pi$
$830$		0			0
$831$	−27.6288	+	4.87171i	−0.958433	+	0.168998i
$832$	−1.85075	−	2.64314i	−0.0641632	−	0.0916345i
$833$	−10.5349	+	4.91253i	−0.365014	+	0.170209i
$834$	−20.2383	−	24.1191i	−0.700796	−	0.835176i
$835$		0			0
$836$	1.33110	+	0.0193026i	0.0460370	+	0.000667594i
$837$	1.20624	+	1.20624i	0.0416936	+	0.0416936i
$838$	−19.4723	−	1.70360i	−0.672658	−	0.0588499i
$839$	−46.4177	−	16.8946i	−1.60252	−	0.583268i	−0.622576	−	0.782560i	$-0.713914\pi$
$839$	−46.4177	−	16.8946i	−1.60252	−	0.583268i	−0.979940	+	0.199292i	$0.936136\pi$
$840$		0			0
$841$	−3.73577	−	21.1866i	−0.128820	−	0.730572i
$842$	−18.5026	−	8.62790i	−0.637641	−	0.297337i
$843$	−3.46075	−	12.9157i	−0.119195	−	0.444841i
$844$	0.286441	+	0.496130i	0.00985969	+	0.0170775i
$845$		0			0
$846$	−1.03667	+	1.23546i	−0.0356416	+	0.0424760i
$847$	2.95840	−	11.0409i	0.101652	−	0.379369i
$848$	10.6516	−	2.85409i	0.365777	−	0.0980097i
$849$	−36.5427	+	13.3004i	−1.25414	+	0.456470i
$850$		0			0
$851$	1.19981	+	0.211558i	0.0411289	+	0.00725213i
$852$	1.39426	+	2.98999i	0.0477664	+	0.102435i
$853$	2.26248	−	25.8602i	0.0774658	−	0.885438i	−0.853682	−	0.520795i	$-0.825636\pi$
$853$	2.26248	−	25.8602i	0.0774658	−	0.885438i	0.931148	−	0.364643i	$-0.118809\pi$
$854$	14.1746			0.485046
$855$		0			0
$856$	9.16250			0.313168
$857$	−3.52403	+	40.2799i	−0.120379	+	1.37594i	0.660300	+	0.751002i	$0.270429\pi$
$857$	−3.52403	+	40.2799i	−0.120379	+	1.37594i	−0.780678	+	0.624933i	$0.785126\pi$
$858$	1.00431	+	2.15374i	0.0342865	+	0.0735276i
$859$	8.58678	+	1.51408i	0.292977	+	0.0516598i	0.318205	−	0.948022i	$-0.396920\pi$
$859$	8.58678	+	1.51408i	0.292977	+	0.0516598i	−0.0252278	+	0.999682i	$0.508031\pi$
$860$		0			0
$861$	−17.2815	+	6.28996i	−0.588953	+	0.214361i
$862$	12.1639	−	3.25931i	0.414304	−	0.111012i
$863$	−5.56739	+	20.7778i	−0.189516	+	0.707284i	0.804102	+	0.594491i	$0.202646\pi$
$863$	−5.56739	+	20.7778i	−0.189516	+	0.707284i	−0.993619	+	0.112793i	$0.964020\pi$
$864$	0.286441	−	0.341367i	0.00974491	−	0.0116135i
$865$		0			0
$866$	−12.7690	−	22.1166i	−0.433910	−	0.751553i
$867$	−8.18904	−	30.5619i	−0.278114	−	1.03794i
$868$	−3.63598	−	1.69549i	−0.123413	−	0.0575485i
$869$	0.130990	+	0.742878i	0.00444351	+	0.0252004i
$870$		0			0
$871$	−17.2224	−	6.26844i	−0.583559	−	0.212398i
$872$	13.5956	+	1.18946i	0.460404	+	0.0402801i
$873$	−25.6094	−	25.6094i	−0.866747	−	0.866747i
$874$	−0.727940	−	4.50980i	−0.0246230	−	0.152546i
$875$		0			0
$876$	−22.9957	−	27.4052i	−0.776953	−	0.925937i
$877$	14.1956	−	6.61953i	0.479352	−	0.223526i	−0.167896	−	0.985805i	$-0.553697\pi$
$877$	14.1956	−	6.61953i	0.479352	−	0.223526i	0.647248	+	0.762279i	$0.275920\pi$
$878$	15.5158	+	22.1588i	0.523632	+	0.747824i
$879$	75.5236	−	13.3169i	2.54735	−	0.449166i
$880$		0			0
$881$	4.80659	−	8.32526i	0.161938	−	0.280485i	−0.773626	−	0.633643i	$-0.781559\pi$
$881$	4.80659	−	8.32526i	0.161938	−	0.280485i	0.935564	+	0.353158i	$0.114892\pi$
$882$	−16.0483	−	4.30013i	−0.540375	−	0.144793i
$883$	−19.8684	+	1.73826i	−0.668625	+	0.0584971i	−0.416414	−	0.909175i	$-0.636713\pi$
$883$	−19.8684	+	1.73826i	−0.668625	+	0.0584971i	−0.252211	+	0.967672i	$0.581158\pi$
$884$	−4.86846	−	4.08512i	−0.163744	−	0.137398i
$885$		0			0
$886$	11.4937	+	6.63587i	0.386137	+	0.222936i
$887$	4.19906	−	9.00491i	0.140991	−	0.302355i	−0.823115	−	0.567875i	$-0.807766\pi$
$887$	4.19906	−	9.00491i	0.140991	−	0.302355i	0.964105	+	0.265520i	$0.0855435\pi$
$888$	1.60793	−	2.29637i	0.0539587	−	0.0770611i
$889$	−1.68582	+	9.56077i	−0.0565407	+	0.320658i
$890$		0			0
$891$	−2.22731	+	1.86894i	−0.0746177	+	0.0626117i
$892$	1.92470	−	1.92470i	0.0644437	−	0.0644437i
$893$	−2.40242	−	0.681211i	−0.0803939	−	0.0227959i
$894$		−	38.4597i		−	1.28628i
$895$		0			0
$896$	−0.358441	+	0.984808i	−0.0119747	+	0.0329001i
$897$	6.67988	−	4.67730i	0.223035	−	0.156171i
$898$	6.19962	+	4.34102i	0.206884	+	0.144862i
$899$	3.58239	+	9.84255i	0.119480	+	0.328267i
$900$		0			0
$901$	18.8097	−	10.8598i	0.626643	−	0.361793i
$902$	0.193697	+	2.21397i	0.00644941	+	0.0737171i
$903$	−1.47371	−	16.8446i	−0.0490420	−	0.560552i
$904$	0.388249	−	0.224155i	0.0129130	−	0.00745530i
$905$		0			0
$906$	−16.4616	−	45.2278i	−0.546899	−	1.50259i
$907$	15.3563	+	10.7526i	0.509898	+	0.357034i	0.800037	−	0.599950i	$-0.204813\pi$
$907$	15.3563	+	10.7526i	0.509898	+	0.357034i	−0.290140	+	0.956984i	$0.593702\pi$
$908$	−15.5926	+	10.9181i	−0.517459	+	0.362329i
$909$	7.41625	−	20.3760i	0.245982	−	0.675829i
$910$		0			0
$911$		−	23.0503i		−	0.763690i	−0.924226	−	0.381845i	$-0.875289\pi$
$911$		−	23.0503i		−	0.763690i	0.924226	−	0.381845i	$-0.124711\pi$
$912$	−10.1127	−	2.86748i	−0.334865	−	0.0949516i
$913$	1.60827	−	1.60827i	0.0532260	−	0.0532260i
$914$	2.92079	−	2.45084i	0.0966113	−	0.0810665i
$915$		0			0
$916$	1.64022	−	9.30212i	0.0541942	−	0.307351i
$917$	6.30172	−	8.99978i	0.208101	−	0.297199i
$918$	0.370934	−	0.795471i	0.0122426	−	0.0262544i
$919$	18.6072	+	10.7429i	0.613795	+	0.354375i	0.774449	−	0.632636i	$-0.218027\pi$
$919$	18.6072	+	10.7429i	0.613795	+	0.354375i	−0.160654	+	0.987011i	$0.551360\pi$
$920$		0			0
$921$	−59.9384	−	50.2943i	−1.97504	−	1.65725i
$922$	38.6590	−	3.38222i	1.27317	−	0.111388i
$923$	−4.26394	−	1.14252i	−0.140349	−	0.0376065i
$924$	0.385920	−	0.668434i	0.0126958	−	0.0219899i
$925$		0			0
$926$	29.8555	−	5.26433i	0.981113	−	0.172997i
$927$	20.6380	+	29.4742i	0.677842	+	0.968059i
$928$	2.47980	−	1.15635i	0.0814036	−	0.0379591i
$929$	−9.67809	−	11.5339i	−0.317528	−	0.378415i	0.583546	−	0.812080i	$-0.301665\pi$
$929$	−9.67809	−	11.5339i	−0.317528	−	0.378415i	−0.901074	+	0.433665i	$0.857220\pi$
$930$		0			0
$931$	−4.09926	−	25.3961i	−0.134348	−	0.832323i
$932$	16.5423	+	16.5423i	0.541862	+	0.541862i
$933$	−29.1238	−	2.54800i	−0.953470	−	0.0834178i
$934$	−33.0824	−	12.0410i	−1.08249	−	0.393994i
$935$		0			0
$936$	−1.57738	−	8.94578i	−0.0515583	−	0.292402i
$937$	38.8778	+	18.1290i	1.27008	+	0.592248i	0.936564	−	0.350496i	$-0.113987\pi$
$937$	38.8778	+	18.1290i	1.27008	+	0.592248i	0.333517	+	0.942744i	$0.391765\pi$
$938$	1.54068	+	5.74991i	0.0503051	+	0.187741i
$939$	10.0842	+	17.4664i	0.329087	+	0.569995i
$940$		0			0
$941$	−23.4971	+	28.0027i	−0.765982	+	0.912862i	−0.998210	−	0.0597991i	$-0.980954\pi$
$941$	−23.4971	+	28.0027i	−0.765982	+	0.912862i	0.232228	+	0.972661i	$0.425398\pi$
$942$	0.312272	−	1.16541i	0.0101744	−	0.0379713i
$943$	7.36644	−	1.97383i	0.239884	−	0.0642768i
$944$	7.18009	−	2.61334i	0.233692	−	0.0850570i
$945$		0			0
$946$	−2.01233	−	0.354827i	−0.0654264	−	0.0115364i
$947$	14.1777	+	30.4041i	0.460713	+	0.988002i	0.990196	+	0.139682i	$0.0446080\pi$
$947$	14.1777	+	30.4041i	0.460713	+	0.988002i	−0.529483	+	0.848320i	$0.677614\pi$
$948$	0.519117	−	5.93354i	0.0168601	−	0.192712i
$949$	47.8689			1.55389
$950$		0			0
$951$	0.975844			0.0316439
$952$	−0.179905	+	2.05632i	−0.00583075	+	0.0666458i
$953$	−15.0385	−	32.2501i	−0.487144	−	1.04468i	−0.984215	−	0.176974i	$-0.943369\pi$
$953$	−15.0385	−	32.2501i	−0.487144	−	1.04468i	0.497071	−	0.867710i	$-0.334409\pi$
$954$	30.5726	+	5.39078i	0.989825	+	0.174533i
$955$		0			0
$956$	18.0376	−	6.56515i	0.583378	−	0.212332i
$957$	−1.94647	+	0.521555i	−0.0629204	+	0.0168595i
$958$	−8.97479	+	33.4944i	−0.289962	+	1.08215i
$959$	15.0595	−	17.9472i	0.486296	−	0.579545i
$960$		0			0
$961$	−8.17293	−	14.1559i	−0.263643	−	0.456643i
$962$	0.970838	+	3.62322i	0.0313011	+	0.116817i
$963$	23.3776	+	10.9012i	0.753333	+	0.351285i
$964$	−1.20134	−	6.81315i	−0.0386926	−	0.219437i
$965$		0			0
$966$	−2.48886	−	0.905869i	−0.0800776	−	0.0291459i
$967$	−15.2609	−	1.33516i	−0.490758	−	0.0429357i	−0.160908	−	0.986969i	$-0.551442\pi$
$967$	−15.2609	−	1.33516i	−0.490758	−	0.0429357i	−0.329849	+	0.944034i	$0.606998\pi$
$968$	7.71222	+	7.71222i	0.247880	+	0.247880i
$969$	−20.7012	−	0.300193i	−0.665018	−	0.00964358i
$970$		0			0
$971$	−24.5780	−	29.2909i	−0.788746	−	0.939991i	0.210547	−	0.977584i	$-0.432475\pi$
$971$	−24.5780	−	29.2909i	−0.788746	−	0.939991i	−0.999293	+	0.0375929i	$0.988031\pi$
$972$	19.5952	−	9.13740i	0.628517	−	0.293082i
$973$	−7.84841	−	11.2087i	−0.251608	−	0.359334i
$974$	−16.7400	+	2.95171i	−0.536384	+	0.0945790i
$975$		0			0
$976$	−6.76264	+	11.7132i	−0.216467	+	0.374932i
$977$	27.0006	+	7.23478i	0.863825	+	0.231461i	0.663416	−	0.748251i	$-0.269106\pi$
$977$	27.0006	+	7.23478i	0.863825	+	0.231461i	0.200409	+	0.979712i	$0.435773\pi$
$978$	−20.3632	+	1.78155i	−0.651143	+	0.0569676i
$979$	−1.91576	−	1.60752i	−0.0612281	−	0.0513765i
$980$		0			0
$981$	33.2732	+	19.2103i	1.06233	+	0.613337i
$982$	7.21704	−	15.4770i	0.230305	−	0.493891i
$983$	−5.56994	+	7.95470i	−0.177654	+	0.253716i	−0.898096	−	0.439799i	$-0.855050\pi$
$983$	−5.56994	+	7.95470i	−0.177654	+	0.253716i	0.720443	+	0.693514i	$0.243939\pi$
$984$	3.04720	−	17.2815i	0.0971412	−	0.550915i
$985$		0			0
$986$	4.12836	−	3.46410i	0.131474	−	0.110319i
$987$	−1.02376	+	1.02376i	−0.0325866	+	0.0325866i
$988$	11.6370	−	7.89932i	0.370221	−	0.251311i
$989$			7.01186i			0.222964i
$990$		0			0
$991$	1.01249	−	2.78179i	0.0321628	−	0.0883665i	−0.922572	−	0.385825i	$-0.873917\pi$
$991$	1.01249	−	2.78179i	0.0321628	−	0.0883665i	0.954735	+	0.297459i	$0.0961390\pi$
$992$	3.13577	−	2.19569i	0.0995609	−	0.0697133i
$993$	44.6749	+	31.2817i	1.41771	+	0.992695i
$994$	0.490376	+	1.34730i	0.0155538	+	0.0427336i
$995$		0			0
$996$	−15.5528	+	8.97940i	−0.492809	+	0.284523i
$997$	3.50100	+	40.0166i	0.110878	+	1.26734i	0.824118	+	0.566418i	$0.191671\pi$
$997$	3.50100	+	40.0166i	0.110878	+	1.26734i	−0.713240	+	0.700920i	$0.752773\pi$
$998$	−0.793206	−	9.06638i	−0.0251085	−	0.286991i
$999$	−0.448634	+	0.259019i	−0.0141941	+	0.00819499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.a.507.2	yes	24
5.2	odd	4	inner	950.2.bb.a.393.2	yes	24
5.3	odd	4	inner	950.2.bb.a.393.1	yes	24
5.4	even	2	inner	950.2.bb.a.507.1	yes	24
19.3	odd	18	inner	950.2.bb.a.307.1	yes	24
95.3	even	36	inner	950.2.bb.a.193.2	yes	24
95.22	even	36	inner	950.2.bb.a.193.1	✓	24
95.79	odd	18	inner	950.2.bb.a.307.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.a.193.1	✓	24	95.22	even	36	inner
950.2.bb.a.193.2	yes	24	95.3	even	36	inner
950.2.bb.a.307.1	yes	24	19.3	odd	18	inner
950.2.bb.a.307.2	yes	24	95.79	odd	18	inner
950.2.bb.a.393.1	yes	24	5.3	odd	4	inner
950.2.bb.a.393.2	yes	24	5.2	odd	4	inner
950.2.bb.a.507.1	yes	24	5.4	even	2	inner
950.2.bb.a.507.2	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.0871557 - 0.996195i) q^{2} +(1.01913 + 2.18554i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(2.26604 - 0.824773i) q^{6} +(1.01230 - 0.271245i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.80958 + 2.15657i) q^{9} +O(q^{10})\)	\(q+(0.0871557 - 0.996195i) q^{2} +(1.01913 + 2.18554i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(2.26604 - 0.824773i) q^{6} +(1.01230 - 0.271245i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.80958 + 2.15657i) q^{9} +(0.152704 + 0.264490i) q^{11} +(-0.624135 - 2.32931i) q^{12} +(2.92437 + 1.36365i) q^{13} +(-0.181985 - 1.03209i) q^{14} +(0.939693 + 0.342020i) q^{16} +(1.96212 + 0.171663i) q^{17} +(1.99065 + 1.99065i) q^{18} +(-1.55007 + 4.07398i) q^{19} +(1.62449 + 1.93599i) q^{21} +(0.276793 - 0.129071i) q^{22} +(-0.601114 - 0.858480i) q^{23} +(-2.37484 + 0.418748i) q^{24} +(1.61334 - 2.79439i) q^{26} +(0.430438 + 0.115336i) q^{27} +(-1.04402 + 0.0913401i) q^{28} +(2.09602 + 1.75877i) q^{29} +(3.31521 + 1.91404i) q^{31} +(0.422618 - 0.906308i) q^{32} +(-0.422429 + 0.603291i) q^{33} +(0.342020 - 1.93969i) q^{34} +(2.15657 - 1.80958i) q^{36} +(-0.822014 + 0.822014i) q^{37} +(3.92338 + 1.89924i) q^{38} +7.78106i q^{39} +(-2.48886 + 6.83807i) q^{41} +(2.07020 - 1.44957i) q^{42} +(-5.48065 - 3.83759i) q^{43} +(-0.104455 - 0.286989i) q^{44} +(-0.907604 + 0.524005i) q^{46} +(0.0499299 + 0.570701i) q^{47} +(0.210174 + 2.40230i) q^{48} +(-5.11100 + 2.95084i) q^{49} +(1.62449 + 4.46324i) q^{51} +(-2.64314 - 1.85075i) q^{52} +(9.03307 - 6.32502i) q^{53} +(0.152412 - 0.418748i) q^{54} +1.04801i q^{56} +(-10.4836 + 0.764198i) q^{57} +(1.93476 - 1.93476i) q^{58} +(5.85327 - 4.91147i) q^{59} +(-2.34864 + 13.3198i) q^{61} +(2.19569 - 3.13577i) q^{62} +(-1.24688 + 2.67394i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(0.564178 + 0.473401i) q^{66} +(-5.65843 + 0.495049i) q^{67} +(-1.90250 - 0.509774i) q^{68} +(1.26363 - 2.18866i) q^{69} +(-1.34730 + 0.237565i) q^{71} +(-1.61474 - 2.30608i) q^{72} +(13.4454 - 6.26968i) q^{73} +(0.747243 + 0.890530i) q^{74} +(2.23396 - 3.74292i) q^{76} +(0.226324 + 0.226324i) q^{77} +(7.75145 + 0.678164i) q^{78} +(2.32099 + 0.844770i) q^{79} +(1.65317 + 9.37560i) q^{81} +(6.59514 + 3.07536i) q^{82} +(-1.92749 - 7.19347i) q^{83} +(-1.26363 - 2.18866i) q^{84} +(-4.30066 + 5.12533i) q^{86} +(-1.70774 + 6.37335i) q^{87} +(-0.295001 + 0.0790452i) q^{88} +(-7.69475 + 2.80066i) q^{89} +(3.33022 + 0.587208i) q^{91} +(0.442908 + 0.949820i) q^{92} +(-0.804560 + 9.19617i) q^{93} +0.572881 q^{94} +2.41147 q^{96} +(-1.12124 + 12.8159i) q^{97} +(2.49416 + 5.34873i) q^{98} +(-0.846723 - 0.149300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 36 q^{6}+O(q^{10}) \) 24 * q + 36 * q^6	\( 24 q + 36 q^{6} + 12 q^{11} - 12 q^{21} + 12 q^{26} + 108 q^{31} - 36 q^{36} - 84 q^{41} - 36 q^{46} - 12 q^{51} - 12 q^{61} - 60 q^{66} - 24 q^{71} + 72 q^{76} - 216 q^{81} + 12 q^{86} - 12 q^{91} - 24 q^{96}+O(q^{100}) \) 24 * q + 36 * q^6 + 12 * q^11 - 12 * q^21 + 12 * q^26 + 108 * q^31 - 36 * q^36 - 84 * q^41 - 36 * q^46 - 12 * q^51 - 12 * q^61 - 60 * q^66 - 24 * q^71 + 72 * q^76 - 216 * q^81 + 12 * q^86 - 12 * q^91 - 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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