LMFDB - Embedded newform 950.2.bb.a.193.2

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			193.2
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.a.507.2

$q$-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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	0.0871557	+	0.996195i	0.0616284	+	0.704416i
$2$	0.0871557	+	0.996195i	0.0616284	+	0.704416i
$3$	1.01913	−	2.18554i	0.588397	−	1.26182i	−0.356452	−	0.934314i	$-0.616014\pi$
$3$	1.01913	−	2.18554i	0.588397	−	1.26182i	0.944849	−	0.327507i	$-0.106209\pi$
$4$	−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	0.444999	−	0.895531i	$-0.353204\pi$
$7$	1.01230	+	0.271245i	0.382614	+	0.102521i	−0.0623853	+	0.998052i	$0.519871\pi$
$8$	−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	−0.842086	−	0.539343i	$-0.818673\pi$
$11$	0.152704	−	0.264490i	0.0460419	−	0.0797469i	0.888128	+	0.459596i	$0.152006\pi$
$12$	−0.624135	+	2.32931i	−0.180172	+	0.672412i
$13$	2.92437	−	1.36365i	0.811073	−	0.378210i	0.0275876	−	0.999619i	$-0.491217\pi$
$13$	2.92437	−	1.36365i	0.811073	−	0.378210i	0.783486	+	0.621410i	$0.213440\pi$
$14$	−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	0.153309	−	0.988178i	$-0.451007\pi$
$17$	1.96212	−	0.171663i	0.475884	−	0.0416345i	0.322575	+	0.946544i	$0.395451\pi$
$18$	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	−0.876918	−	0.480640i	$-0.840405\pi$
$23$	−0.601114	+	0.858480i	−0.125341	+	0.179005i	0.751577	+	0.659645i	$0.229293\pi$
$24$	−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	−0.427088	−	0.904210i	$-0.640461\pi$
$29$	2.09602	−	1.75877i	0.389221	−	0.326595i	0.816310	+	0.577614i	$0.196016\pi$
$30$		0			0
$31$	3.31521	−	1.91404i	0.595429	−	0.343771i	−0.171812	−	0.985130i	$-0.554962\pi$
$31$	3.31521	−	1.91404i	0.595429	−	0.343771i	0.767241	+	0.641359i	$0.221629\pi$
$32$	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	0.636302	−	0.771440i	$-0.280463\pi$
$37$	−0.822014	−	0.822014i	−0.135138	−	0.135138i	−0.771440	+	0.636302i	$0.780463\pi$
$38$	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	−0.967590	−	0.252526i	$-0.918739\pi$
$41$	−2.48886	−	6.83807i	−0.388694	−	1.06793i	0.578896	−	0.815401i	$-0.303484\pi$
$42$	2.07020	+	1.44957i	0.319439	+	0.223674i
$43$	−5.48065	+	3.83759i	−0.835791	+	0.585227i	−0.911218	−	0.411924i	$-0.864857\pi$
$43$	−5.48065	+	3.83759i	−0.835791	+	0.585227i	0.0754269	+	0.997151i	$0.475968\pi$
$44$	−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	−0.991683	−	0.128702i	$-0.958919\pi$
$47$	0.0499299	−	0.570701i	0.00728302	−	0.0832453i	0.998966	+	0.0454570i	$0.0144744\pi$
$48$	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	0.994937	−	0.100499i	$-0.0320439\pi$
$53$	9.03307	+	6.32502i	1.24079	+	0.868809i	0.245850	+	0.969308i	$0.420933\pi$
$54$	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	0.938655	−	0.344859i	$-0.112073\pi$
$59$	5.85327	+	4.91147i	0.762030	+	0.639419i	−0.176624	+	0.984278i	$0.556518\pi$
$60$		0			0
$61$	−2.34864	−	13.3198i	−0.300713	−	1.70543i	−0.643030	−	0.765841i	$-0.722323\pi$
$61$	−2.34864	−	13.3198i	−0.300713	−	1.70543i	0.342317	−	0.939585i	$-0.388788\pi$
$62$	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	−0.263902	−	0.964549i	$-0.585010\pi$
$67$	−5.65843	−	0.495049i	−0.691287	−	0.0604798i	−0.427385	+	0.904070i	$0.640565\pi$
$68$	−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	0.0931277	−	0.995654i	$-0.470314\pi$
$71$	−1.34730	−	0.237565i	−0.159895	−	0.0281937i	−0.253022	+	0.967460i	$0.581425\pi$
$72$	−1.61474	+	2.30608i	−0.190299	+	0.271774i
$73$	13.4454	+	6.26968i	1.57366	+	0.733810i	0.996561	−	0.0828633i	$-0.0264065\pi$
$73$	13.4454	+	6.26968i	1.57366	+	0.733810i	0.577100	+	0.816673i	$0.304184\pi$
$74$	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	−0.208137	−	0.978100i	$-0.566740\pi$
$79$	2.32099	−	0.844770i	0.261131	−	0.0950441i	0.469268	+	0.883056i	$0.344518\pi$
$80$		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	0.775777	+	0.631007i	$0.217358\pi$
$83$	−1.92749	+	7.19347i	−0.211569	+	0.789586i	−0.987346	+	0.158579i	$0.949309\pi$
$84$	−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	−0.0996895	−	0.995019i	$-0.531785\pi$
$89$	−7.69475	−	2.80066i	−0.815642	−	0.296869i	−0.715952	+	0.698149i	$0.754007\pi$
$90$		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	−0.811301	−	0.584628i	$-0.801240\pi$
$97$	−1.12124	−	12.8159i	−0.113845	−	1.30126i	0.697456	−	0.716627i	$-0.254315\pi$
$98$	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	−0.0441839	−	0.999023i	$-0.514069\pi$
$101$	−7.23783	−	2.63435i	−0.720191	−	0.262128i	−0.676007	+	0.736895i	$0.736291\pi$
$102$	4.58784	+	1.22931i	0.454263	+	0.121720i
$103$	3.30798	+	12.3456i	0.325945	+	1.21644i	0.913358	+	0.407157i	$0.133480\pi$
$103$	3.30798	+	12.3456i	0.325945	+	1.21644i	−0.587413	+	0.809287i	$0.699854\pi$
$104$	−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	0.751400	+	0.659847i	$0.229379\pi$
$107$	−2.37143	+	8.85030i	−0.229255	+	0.855591i	−0.980655	+	0.195744i	$0.937288\pi$
$108$	−0.403871	+	0.188328i	−0.0388625	+	0.0181219i
$109$	−2.36986	+	13.4402i	−0.226992	+	1.28733i	0.631849	+	0.775091i	$0.282296\pi$
$109$	−2.36986	+	13.4402i	−0.226992	+	1.28733i	−0.858841	+	0.512242i	$0.828815\pi$
$110$		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	−0.721860	−	0.692039i	$-0.756713\pi$
$113$	−0.317004	+	0.317004i	−0.0298212	+	0.0298212i	0.692039	+	0.721860i	$0.256713\pi$
$114$	−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	0.652524	−	0.757768i	$-0.273710\pi$
$127$	−3.91493	−	8.39560i	−0.347394	−	0.744989i	−0.999918	+	0.0127789i	$0.995932\pi$
$128$	−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	0.922242	−	0.386612i	$-0.126355\pi$
$131$	8.03074	+	6.73859i	0.701649	+	0.588754i	−0.220593	+	0.975366i	$0.570799\pi$
$132$	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	0.952455	+	0.304681i	$0.0985498\pi$
$137$	18.3122	+	12.8224i	1.56452	+	1.09549i	0.612065	+	0.790808i	$0.290339\pi$
$138$	−2.07020	+	1.44957i	−0.176227	+	0.123396i
$139$	−4.46556	+	12.2690i	−0.378764	+	1.04065i	0.593105	+	0.805125i	$0.297902\pi$
$139$	−4.46556	+	12.2690i	−0.378764	+	1.04065i	−0.971869	+	0.235521i	$0.924320\pi$
$140$		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	0.934891	+	0.354934i	$0.115497\pi$
$149$	5.45475	+	14.9868i	0.446870	+	1.22777i	−0.488021	+	0.872832i	$0.662281\pi$
$150$		0			0
$151$			19.9589i			1.62423i	0.583495	+	0.812117i	$0.301685\pi$
$151$			19.9589i			1.62423i	−0.583495	+	0.812117i	$0.698315\pi$
$152$	−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	0.830440	−	0.557108i	$-0.188089\pi$
$157$	0.286976	+	0.409844i	0.0229032	+	0.0327091i	−0.807537	+	0.589817i	$0.799200\pi$
$158$	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	−0.564797	−	0.825230i	$-0.691046\pi$
$163$	−8.18771	+	2.19389i	−0.641311	+	0.171839i	−0.0765138	+	0.997069i	$0.524379\pi$
$164$	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	−0.955963	−	0.293486i	$-0.905185\pi$
$167$	−4.56458	+	6.51890i	−0.353218	+	0.504448i	0.602745	+	0.797934i	$0.294074\pi$
$168$	−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	0.318515	−	0.947918i	$-0.396816\pi$
$173$	10.4802	−	0.916898i	0.796795	−	0.0697105i	0.478280	+	0.878207i	$0.341260\pi$
$174$	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	0.142181	+	0.989841i	$0.454588\pi$
$179$	−10.5178	+	18.2173i	−0.786137	+	1.36163i	−0.928318	+	0.371788i	$0.878745\pi$
$180$		0			0
$181$	3.21213	+	3.82807i	0.238756	+	0.284538i	0.872095	−	0.489336i	$-0.162761\pi$
$181$	3.21213	+	3.82807i	0.238756	+	0.284538i	−0.633339	+	0.773874i	$0.718316\pi$
$182$	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	−0.682956	−	0.730459i	$-0.739306\pi$
$193$	4.38451	−	9.40261i	0.315604	−	0.676815i	0.998560	+	0.0536444i	$0.0170838\pi$
$194$	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	0.0830922	−	0.996542i	$-0.473520\pi$
$197$	−4.81731	−	1.29079i	−0.343219	−	0.0919652i	−0.426311	+	0.904577i	$0.640187\pi$
$198$	−0.222529	−	0.830488i	−0.0158144	−	0.0590202i
$199$	−17.2195	−	20.5214i	−1.22066	−	1.45472i	−0.850680	−	0.525684i	$-0.823809\pi$
$199$	−17.2195	−	20.5214i	−1.22066	−	1.45472i	−0.369979	−	0.929040i	$-0.620635\pi$
$200$		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	−0.778571	−	0.627557i	$-0.784055\pi$
$211$	−0.368241	+	0.438852i	−0.0253507	+	0.0302118i	0.753220	+	0.657769i	$0.228500\pi$
$212$	−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	0.763469	−	0.645845i	$-0.223495\pi$
$223$	−1.56124	−	2.22968i	−0.104548	−	0.149310i	−0.868017	+	0.496534i	$0.834606\pi$
$224$	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	0.994838	−	0.101477i	$-0.0323569\pi$
$227$	13.4598	+	13.4598i	0.893361	+	0.893361i	−0.101477	+	0.994838i	$0.532357\pi$
$228$	10.4570	−	1.06786i	0.692531	−	0.0707209i
$229$		−	9.44562i		−	0.624184i	−0.950052	−	0.312092i	$-0.898970\pi$
$229$		−	9.44562i		−	0.624184i	0.950052	−	0.312092i	$-0.101030\pi$
$230$		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	−0.996230	−	0.0867473i	$-0.972353\pi$
$233$	−19.1635	+	13.4185i	−1.25545	+	0.879072i	−0.259215	+	0.965820i	$0.583464\pi$
$234$	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	−0.145667	−	0.989334i	$-0.546533\pi$
$239$	−16.6235	−	9.59761i	−1.07529	−	0.620818i	−0.929621	+	0.368516i	$0.879866\pi$
$240$		0			0
$241$	2.36618	−	6.50103i	0.152419	−	0.418768i	−0.839858	−	0.542806i	$-0.817362\pi$
$241$	2.36618	−	6.50103i	0.152419	−	0.418768i	0.992278	+	0.124037i	$0.0395843\pi$
$242$	−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	0.995682	−	0.0928303i	$-0.0295914\pi$
$251$	0.448311	+	2.54250i	0.0282971	+	0.160481i	−0.967385	+	0.253311i	$0.918480\pi$
$252$	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	0.283088	−	0.959094i	$-0.408641\pi$
$257$	6.33764	+	0.554471i	0.395331	+	0.0345870i	0.112243	+	0.993681i	$0.464197\pi$
$258$	−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	0.902943	−	0.429761i	$-0.141402\pi$
$263$	18.7168	+	8.72779i	1.15413	+	0.538179i	0.251185	+	0.967939i	$0.419180\pi$
$264$	−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	0.346676	−	0.937985i	$-0.387310\pi$
$269$	19.9303	−	7.25402i	1.21517	−	0.442286i	0.868494	+	0.495700i	$0.165088\pi$
$270$		0			0
$271$	0.678701	−	3.84910i	0.0412281	−	0.233816i	−0.957230	−	0.289328i	$-0.906568\pi$
$271$	0.678701	−	3.84910i	0.0412281	−	0.233816i	0.998458	+	0.0555121i	$0.0176791\pi$
$272$	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	−0.995467	−	0.0951037i	$-0.969682\pi$
$277$	−3.01110	−	11.2376i	−0.180919	−	0.675200i	0.814548	−	0.580096i	$-0.196985\pi$
$278$	−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	−0.334134	−	0.942526i	$-0.608444\pi$
$281$	−5.46064	+	0.962858i	−0.325754	+	0.0574393i	0.00837959	+	0.999965i	$0.497333\pi$
$282$	0.583842	−	1.25205i	0.0347673	−	0.0745587i
$283$	−1.40549	−	16.0648i	−0.0835477	−	0.954955i	−0.916085	−	0.400985i	$-0.868668\pi$
$283$	−1.40549	−	16.0648i	−0.0835477	−	0.954955i	0.832537	−	0.553970i	$-0.186888\pi$
$284$	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	0.598054	+	0.801456i	$0.295941\pi$
$293$	8.23086	+	30.7180i	0.480852	+	1.79456i	−0.117203	+	0.993108i	$0.537393\pi$
$294$	−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	−0.998801	−	0.0489576i	$-0.984410\pi$
$307$	−29.4066	−	13.7125i	−1.67832	−	0.782614i	−0.679521	−	0.733656i	$-0.737812\pi$
$308$	−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	0.641397	−	0.767210i	$-0.278355\pi$
$311$	−6.06165	−	10.4991i	−0.343725	−	0.595349i	−0.985121	+	0.171861i	$0.945022\pi$
$312$	−7.51593	+	2.01389i	−0.425506	+	0.114014i
$313$	8.33172	+	0.728931i	0.470936	+	0.0412016i	0.320154	−	0.947365i	$-0.396265\pi$
$313$	8.33172	+	0.728931i	0.470936	+	0.0412016i	0.150782	+	0.988567i	$0.451821\pi$
$314$	−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	0.911052	−	0.412292i	$-0.135271\pi$
$317$	0.171020	+	0.366753i	0.00960542	+	0.0205989i	−0.901447	+	0.432890i	$0.857494\pi$
$318$	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	0.929963	−	0.367654i	$-0.119839\pi$
$331$	19.5861	+	11.3080i	1.07655	+	0.621545i	0.146584	+	0.989198i	$0.453172\pi$
$332$	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	−0.794762	−	0.606922i	$-0.792404\pi$
$337$	−9.11024	+	6.37906i	−0.496266	+	0.347489i	0.298495	+	0.954411i	$0.403515\pi$
$338$	−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	0.943342	−	0.331821i	$-0.107663\pi$
$347$	5.75400	+	8.21756i	0.308891	+	0.441142i	−0.634452	+	0.772963i	$0.718774\pi$
$348$	2.78851	+	5.97998i	0.149480	+	0.320561i
$349$	−12.5667	+	7.25537i	−0.672678	+	0.388371i	−0.797091	−	0.603860i	$-0.793629\pi$
$349$	−12.5667	+	7.25537i	−0.672678	+	0.388371i	0.124413	+	0.992231i	$0.460295\pi$
$350$		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	0.0146421	−	0.999893i	$-0.495339\pi$
$353$	9.90648	−	2.65443i	0.527269	−	0.141281i	0.512627	+	0.858611i	$0.328672\pi$
$354$	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	−0.272922	−	0.962036i	$-0.587990\pi$
$359$	13.6779	−	16.3007i	0.721891	−	0.860316i	0.994813	+	0.101720i	$0.0324346\pi$
$360$		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	0.256481	−	0.966549i	$-0.417437\pi$
$367$	22.2562	−	10.3782i	1.16176	−	0.541739i	0.905283	+	0.424810i	$0.139659\pi$
$368$	−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	−0.0623125	−	0.998057i	$-0.519848\pi$
$373$	−11.8835	−	3.18418i	−0.615305	−	0.164870i	−0.552993	+	0.833186i	$0.686514\pi$
$374$	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	−0.885062	−	0.465473i	$-0.845884\pi$
$383$	0.790991	−	1.69629i	0.0404178	−	0.0866762i	0.925480	+	0.378797i	$0.123662\pi$
$384$	−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	0.338113	−	0.941105i	$-0.390211\pi$
$389$	−12.7689	−	15.2173i	−0.647407	−	0.771550i	−0.985521	+	0.169555i	$0.945767\pi$
$390$		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	−0.369807	−	0.929108i	$-0.620576\pi$
$397$	−11.4101	+	0.998258i	−0.572658	+	0.0501011i	−0.202851	+	0.979210i	$0.565021\pi$
$398$	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	−0.937500	−	0.347984i	$-0.886866\pi$
$401$	−8.65095	+	10.3098i	−0.432008	+	0.514847i	0.505493	+	0.862831i	$0.331311\pi$
$402$	−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	0.0135122	−	0.999909i	$-0.495699\pi$
$409$	20.2354	−	16.9795i	1.00058	−	0.839583i	0.987064	+	0.160325i	$0.0512543\pi$
$410$		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	$0.158442\pi$
$419$			19.5466i			0.954916i	−0.878655	+	0.477458i	$0.841558\pi$
$420$		0			0
$421$	6.98246	+	19.1841i	0.340304	+	0.934978i	0.985306	+	0.170797i	$0.0546343\pi$
$421$	6.98246	+	19.1841i	0.340304	+	0.934978i	−0.645002	+	0.764181i	$0.723143\pi$
$422$	−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	−0.791699	−	0.610911i	$-0.790803\pi$
$431$	4.30706	−	11.8335i	0.207464	−	0.570002i	0.999163	+	0.0409095i	$0.0130255\pi$
$432$	0.365033	−	0.255599i	0.0175626	−	0.0122975i
$433$	20.9196	+	14.6480i	1.00533	+	0.703940i	0.955553	−	0.294821i	$-0.0952599\pi$
$433$	20.9196	+	14.6480i	1.00533	+	0.703940i	0.0497776	+	0.998760i	$0.484149\pi$
$434$	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	−0.00359221	−	0.999994i	$-0.501143\pi$
$439$	−20.7222	−	17.3880i	−0.989017	−	0.829884i	−0.985425	+	0.170109i	$0.945588\pi$
$440$		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	0.726842	−	0.686805i	$-0.240987\pi$
$443$	−5.60888	−	12.0283i	−0.266486	−	0.571481i	−0.993328	+	0.115324i	$0.963209\pi$
$444$	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	0.762810	−	0.646622i	$-0.223819\pi$
$449$	−3.78417	−	6.55438i	−0.178586	−	0.309320i	−0.941396	+	0.337302i	$0.890486\pi$
$450$		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	−0.641231	−	0.767348i	$-0.721576\pi$
$457$	2.69607	−	2.69607i	0.126117	−	0.126117i	0.767348	+	0.641231i	$0.221576\pi$
$458$	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	−0.264729	−	0.964323i	$-0.585283\pi$
$461$	6.73870	−	38.2171i	0.313853	−	1.77995i	0.578582	−	0.815624i	$-0.303606\pi$
$462$	0.699525	−	0.326194i	0.0325449	−	0.0151759i
$463$	7.84638	−	29.2831i	0.364652	−	1.36090i	−0.503240	−	0.864147i	$-0.667859\pi$
$463$	7.84638	−	29.2831i	0.364652	−	1.36090i	0.867892	−	0.496753i	$-0.165475\pi$
$464$	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	0.771138	+	0.636668i	$0.219688\pi$
$467$	9.11187	+	34.0060i	0.421647	+	1.57361i	−0.349491	+	0.936940i	$0.613645\pi$
$468$	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	−0.886129	−	0.463438i	$-0.846616\pi$
$479$	−34.1491	+	6.02141i	−1.56031	+	0.275125i	−0.674184	+	0.738564i	$0.735504\pi$
$480$		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	0.791736	+	0.610863i	$0.209177\pi$
$487$	−4.39947	+	16.4190i	−0.199359	+	0.744018i	−0.991095	+	0.133155i	$0.957489\pi$
$488$	−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	0.0464898	−	0.998919i	$-0.485197\pi$
$491$	16.0471	−	5.84067i	0.724196	−	0.263586i	0.677706	+	0.735333i	$0.262974\pi$
$492$	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	0.370621	−	0.928784i	$-0.379145\pi$
$499$	8.96275	+	1.58037i	0.401228	+	0.0707473i	0.0306068	+	0.999532i	$0.490256\pi$
$500$		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	0.964420	−	0.264375i	$-0.0851655\pi$
$503$	41.9012	+	3.66588i	1.86828	+	0.163453i	0.903860	+	0.427828i	$0.140721\pi$
$504$	−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	0.969183	+	0.246341i	$0.0792283\pi$
$509$	3.21951	+	18.2588i	0.142702	+	0.809306i	−0.826481	+	0.562965i	$0.809661\pi$
$510$		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	0.988855	+	0.148880i	$0.0475669\pi$
$521$	36.7995	+	21.2462i	1.61222	+	0.930814i	0.623362	+	0.781934i	$0.285766\pi$
$522$	0.671349	−	7.67355i	0.0293841	−	0.335862i
$523$	2.05251	−	23.4603i	0.0897501	−	1.02585i	−0.809123	−	0.587639i	$-0.800057\pi$
$523$	2.05251	−	23.4603i	0.0897501	−	1.02585i	0.898873	−	0.438209i	$-0.144387\pi$
$524$	−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	−0.442821	−	0.896610i	$-0.646022\pi$
$541$	8.44949	−	7.08997i	0.363272	−	0.304821i	0.806093	+	0.591788i	$0.201578\pi$
$542$	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	−0.279045	+	0.960278i	$0.590018\pi$
$547$	−25.3987	+	36.2732i	−1.08597	+	1.55093i	−0.806927	+	0.590651i	$0.798871\pi$
$548$	−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	0.526738	−	0.850028i	$-0.323415\pi$
$557$	35.7902	−	16.6892i	1.51648	−	0.707145i	0.989740	+	0.142883i	$0.0456372\pi$
$558$	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	0.0346836	−	0.999398i	$-0.488958\pi$
$563$	−10.3210	−	2.76551i	−0.434979	−	0.116552i	−0.469662	+	0.882846i	$0.655624\pi$
$564$	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	0.408308	−	0.912844i	$-0.366119\pi$
$577$	7.33814	+	1.96625i	0.305491	+	0.0818560i	−0.102817	+	0.994700i	$0.532786\pi$
$578$	−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	−0.571944	−	0.820293i	$-0.693811\pi$
$587$	−24.0526	+	2.10433i	−0.992757	+	0.0868549i	−0.420813	+	0.907148i	$0.638255\pi$
$588$	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	−0.681251	−	0.732050i	$-0.738564\pi$
$593$	5.83594	−	8.33458i	0.239653	−	0.342260i	0.920904	+	0.389790i	$0.127452\pi$
$594$	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	0.135669	−	0.990754i	$-0.456682\pi$
$599$	27.7768	−	23.3075i	1.13493	−	0.952320i	0.999261	+	0.0384346i	$0.0122371\pi$
$600$		0			0
$601$	−2.39141	+	1.38068i	−0.0975475	+	0.0563191i	−0.547980	−	0.836491i	$-0.684603\pi$
$601$	−2.39141	+	1.38068i	−0.0975475	+	0.0563191i	0.450433	+	0.892810i	$0.351270\pi$
$602$	−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	0.501546	−	0.865131i	$-0.332765\pi$
$607$	−8.95776	−	8.95776i	−0.363584	−	0.363584i	−0.865131	+	0.501546i	$0.832765\pi$
$608$	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	−0.974611	−	0.223903i	$-0.928120\pi$
$613$	−27.1740	+	19.0274i	−1.09755	+	0.768511i	−0.122937	+	0.992415i	$0.539231\pi$
$614$	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	−0.942845	−	0.333232i	$-0.891861\pi$
$617$	1.08154	−	12.3621i	0.0435411	−	0.497678i	0.986386	−	0.164446i	$-0.0525836\pi$
$618$	−2.68624	+	30.7039i	−0.108057	+	1.23509i
$619$	3.37305	+	1.94743i	0.135574	+	0.0782740i	0.566253	−	0.824231i	$-0.308392\pi$
$619$	3.37305	+	1.94743i	0.135574	+	0.0782740i	−0.430679	+	0.902505i	$0.641726\pi$
$620$		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	−0.999796	−	0.0202063i	$-0.993568\pi$
$631$	−1.68820	−	9.57424i	−0.0672060	−	0.381144i	0.932590	−	0.360938i	$-0.117543\pi$
$632$	−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	−0.0162449	−	0.999868i	$-0.505171\pi$
$641$	−9.45589	−	1.66733i	−0.373485	−	0.0658555i	−0.357240	+	0.934013i	$0.616282\pi$
$642$	−12.6733	+	18.0993i	−0.500173	+	0.714322i
$643$	13.4374	+	6.26598i	0.529921	+	0.247106i	0.669115	−	0.743159i	$-0.266673\pi$
$643$	13.4374	+	6.26598i	0.529921	+	0.247106i	−0.139194	+	0.990265i	$0.544451\pi$
$644$	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	−0.161223	+	0.986918i	$0.551544\pi$
$647$	−29.2043	+	29.2043i	−1.14814	+	1.14814i	−0.986918	+	0.161223i	$0.948456\pi$
$648$	−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	0.762790	+	0.646647i	$0.223829\pi$
$653$	−5.65070	+	21.0887i	−0.221129	+	0.825264i	−0.983919	+	0.178618i	$0.942838\pi$
$654$	−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	0.280931	−	0.959728i	$-0.409357\pi$
$659$	−3.10013	−	1.12836i	−0.120764	−	0.0439545i	−0.401695	+	0.915773i	$0.631579\pi$
$660$		0			0
$661$	−29.3410	+	5.17360i	−1.14123	+	0.201230i	−0.712144	−	0.702033i	$-0.752276\pi$
$661$	−29.3410	+	5.17360i	−1.14123	+	0.201230i	−0.429087	+	0.903263i	$0.641165\pi$
$662$	−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	−0.796060	−	0.605217i	$-0.793086\pi$
$673$	−10.6171	−	39.6237i	−0.409261	−	1.52738i	0.386800	−	0.922164i	$-0.373580\pi$
$674$	−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	−0.757035	−	0.653374i	$-0.773353\pi$
$677$	5.86119	−	21.8743i	0.225264	−	0.840696i	0.982299	−	0.187321i	$-0.0599806\pi$
$678$	−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	−0.997153	−	0.0754003i	$-0.975977\pi$
$683$	−24.0893	+	24.0893i	−0.921753	+	0.921753i	0.0754003	+	0.997153i	$0.475977\pi$
$684$	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	0.635653	−	0.771975i	$-0.280731\pi$
$691$	−9.21941	−	15.9685i	−0.350723	−	0.607470i	−0.986376	+	0.164505i	$0.947397\pi$
$692$	−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	0.554314	−	0.832308i	$-0.312981\pi$
$701$	−4.47700	−	3.75665i	−0.169094	−	0.141887i	−0.723408	+	0.690421i	$0.757425\pi$
$702$	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	−0.590225	−	0.807239i	$-0.700961\pi$
$709$	10.1395	−	27.8580i	0.380797	−	1.04623i	0.971022	−	0.238991i	$-0.0768168\pi$
$710$		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	−0.853428	−	0.521210i	$-0.825481\pi$
$719$	−14.3373	−	39.3915i	−0.534692	−	1.46905i	0.318736	−	0.947843i	$-0.396742\pi$
$720$		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	−0.997793	−	0.0663988i	$-0.978849\pi$
$727$	−19.3843	−	27.6836i	−0.718922	−	1.02673i	0.278871	−	0.960329i	$-0.410040\pi$
$728$	−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	0.269039	−	0.963129i	$-0.413294\pi$
$733$	26.6299	−	7.13547i	0.983599	−	0.263554i	0.714559	+	0.699575i	$0.246627\pi$
$734$	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	−0.764536	−	0.644581i	$-0.777032\pi$
$739$	0.0819052	−	0.0976108i	0.00301293	−	0.00359067i	0.767549	+	0.640991i	$0.221476\pi$
$740$		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	−0.548560	−	0.836111i	$-0.684824\pi$
$743$	−25.7206	+	2.25026i	−0.943597	+	0.0825540i	−0.395037	+	0.918665i	$0.629268\pi$
$744$	−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	0.331961	−	0.943293i	$-0.392290\pi$
$751$	−17.9402	−	21.3802i	−0.654646	−	0.780176i	−0.986607	+	0.163117i	$0.947845\pi$
$752$	−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	0.594012	+	0.804456i	$0.297543\pi$
$757$	−11.1172	+	23.8409i	−0.404061	+	0.866511i	−0.998073	+	0.0620549i	$0.980235\pi$
$758$	−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	0.695002	−	0.719008i	$-0.255403\pi$
$769$	−3.70950	−	4.42081i	−0.133768	−	0.159418i	−0.828770	+	0.559589i	$0.810959\pi$
$770$		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	−0.952126	−	0.305705i	$-0.901108\pi$
$773$	−36.9767	+	17.2425i	−1.32996	+	0.620170i	−0.377832	+	0.925874i	$0.623330\pi$
$774$	−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	−0.790447	−	0.612530i	$-0.790152\pi$
$787$	−32.7870	+	8.78524i	−1.16873	+	0.313160i	−0.378282	+	0.925690i	$0.623485\pi$
$788$	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	0.845852	−	0.533418i	$-0.179093\pi$
$797$	8.82038	+	8.82038i	0.312434	+	0.312434i	−0.533418	+	0.845852i	$0.679093\pi$
$798$	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	0.996787	−	0.0801005i	$-0.0255241\pi$
$809$	40.5542	+	23.4140i	1.42581	+	0.823192i	0.429024	+	0.903293i	$0.358857\pi$
$810$		0			0
$811$	0.441914	−	1.21415i	0.0155177	−	0.0426345i	−0.931692	−	0.363249i	$-0.881667\pi$
$811$	0.441914	−	1.21415i	0.0155177	−	0.0426345i	0.947210	+	0.320615i	$0.103890\pi$
$812$	−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	−0.784732	−	0.619835i	$-0.787199\pi$
$821$	−7.43036	−	42.1397i	−0.259321	−	1.47068i	0.525410	−	0.850849i	$-0.323912\pi$
$822$	30.9208	+	44.1595i	1.07849	+	1.54024i
$823$	−2.08691	−	4.47539i	−0.0727451	−	0.156002i	0.866572	−	0.499051i	$-0.166318\pi$
$823$	−2.08691	−	4.47539i	−0.0727451	−	0.156002i	−0.939318	+	0.343049i	$0.888540\pi$
$824$	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	0.407103	−	0.913382i	$-0.366539\pi$
$827$	18.6756	+	1.63390i	0.649413	+	0.0568163i	0.242311	+	0.970199i	$0.422095\pi$
$828$	−2.84984	+	0.763611i	−0.0990386	+	0.0265373i
$829$	−7.72076	−	13.3727i	−0.268153	−	0.464454i	0.700232	−	0.713915i	$-0.253080\pi$
$829$	−7.72076	−	13.3727i	−0.268153	−	0.464454i	−0.968385	+	0.249461i	$0.919747\pi$
$830$		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	−0.979940	−	0.199292i	$-0.936136\pi$
$839$	−46.4177	+	16.8946i	−1.60252	+	0.583268i	−0.622576	+	0.782560i	$0.713914\pi$
$840$		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	0.931148	+	0.364643i	$0.118809\pi$
$853$	2.26248	+	25.8602i	0.0774658	+	0.885438i	−0.853682	+	0.520795i	$0.825636\pi$
$854$	14.1746			0.485046
$855$		0			0
$856$	9.16250			0.313168
$857$	−3.52403	−	40.2799i	−0.120379	−	1.37594i	−0.780678	−	0.624933i	$-0.785126\pi$
$857$	−3.52403	−	40.2799i	−0.120379	−	1.37594i	0.660300	−	0.751002i	$-0.270429\pi$
$858$	1.00431	−	2.15374i	0.0342865	−	0.0735276i
$859$	8.58678	−	1.51408i	0.292977	−	0.0516598i	−0.0252278	−	0.999682i	$-0.508031\pi$
$859$	8.58678	−	1.51408i	0.292977	−	0.0516598i	0.318205	+	0.948022i	$0.396920\pi$
$860$		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	−0.993619	−	0.112793i	$-0.964020\pi$
$863$	−5.56739	−	20.7778i	−0.189516	−	0.707284i	0.804102	−	0.594491i	$-0.202646\pi$
$864$	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	0.647248	−	0.762279i	$-0.275920\pi$
$877$	14.1956	+	6.61953i	0.479352	+	0.223526i	−0.167896	+	0.985805i	$0.553697\pi$
$878$	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	0.935564	−	0.353158i	$-0.114892\pi$
$881$	4.80659	+	8.32526i	0.161938	+	0.280485i	−0.773626	+	0.633643i	$0.781559\pi$
$882$	−16.0483	+	4.30013i	−0.540375	+	0.144793i
$883$	−19.8684	−	1.73826i	−0.668625	−	0.0584971i	−0.252211	−	0.967672i	$-0.581158\pi$
$883$	−19.8684	−	1.73826i	−0.668625	−	0.0584971i	−0.416414	+	0.909175i	$0.636713\pi$
$884$	−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	0.964105	−	0.265520i	$-0.0855435\pi$
$887$	4.19906	+	9.00491i	0.140991	+	0.302355i	−0.823115	+	0.567875i	$0.807766\pi$
$888$	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	−0.290140	−	0.956984i	$-0.593702\pi$
$907$	15.3563	−	10.7526i	0.509898	−	0.357034i	0.800037	+	0.599950i	$0.204813\pi$
$908$	−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	$0.124711\pi$
$911$			23.0503i			0.763690i	−0.924226	+	0.381845i	$0.875289\pi$
$912$	−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	−0.160654	−	0.987011i	$-0.551360\pi$
$919$	18.6072	−	10.7429i	0.613795	−	0.354375i	0.774449	+	0.632636i	$0.218027\pi$
$920$		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	−0.901074	−	0.433665i	$-0.857220\pi$
$929$	−9.67809	+	11.5339i	−0.317528	+	0.378415i	0.583546	+	0.812080i	$0.301665\pi$
$930$		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	0.333517	−	0.942744i	$-0.391765\pi$
$937$	38.8778	−	18.1290i	1.27008	−	0.592248i	0.936564	+	0.350496i	$0.113987\pi$
$938$	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	0.232228	−	0.972661i	$-0.425398\pi$
$941$	−23.4971	−	28.0027i	−0.765982	−	0.912862i	−0.998210	+	0.0597991i	$0.980954\pi$
$942$	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	−0.529483	−	0.848320i	$-0.677614\pi$
$947$	14.1777	−	30.4041i	0.460713	−	0.988002i	0.990196	−	0.139682i	$-0.0446080\pi$
$948$	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	0.497071	+	0.867710i	$0.334409\pi$
$953$	−15.0385	+	32.2501i	−0.487144	+	1.04468i	−0.984215	+	0.176974i	$0.943369\pi$
$954$	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	−0.329849	−	0.944034i	$-0.606998\pi$
$967$	−15.2609	+	1.33516i	−0.490758	+	0.0429357i	−0.160908	+	0.986969i	$0.551442\pi$
$968$	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	−0.999293	−	0.0375929i	$-0.988031\pi$
$971$	−24.5780	+	29.2909i	−0.788746	+	0.939991i	0.210547	+	0.977584i	$0.432475\pi$
$972$	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	0.200409	−	0.979712i	$-0.435773\pi$
$977$	27.0006	−	7.23478i	0.863825	−	0.231461i	0.663416	+	0.748251i	$0.269106\pi$
$978$	−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	0.720443	−	0.693514i	$-0.243939\pi$
$983$	−5.56994	−	7.95470i	−0.177654	−	0.253716i	−0.898096	+	0.439799i	$0.855050\pi$
$984$	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	0.954735	−	0.297459i	$-0.0961390\pi$
$991$	1.01249	+	2.78179i	0.0321628	+	0.0883665i	−0.922572	+	0.385825i	$0.873917\pi$
$992$	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	−0.713240	−	0.700920i	$-0.752773\pi$
$997$	3.50100	−	40.0166i	0.110878	−	1.26734i	0.824118	−	0.566418i	$-0.191671\pi$
$998$	−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.193.2	yes	24
5.2	odd	4	inner	950.2.bb.a.307.1	yes	24
5.3	odd	4	inner	950.2.bb.a.307.2	yes	24
5.4	even	2	inner	950.2.bb.a.193.1	✓	24
19.13	odd	18	inner	950.2.bb.a.393.1	yes	24
95.13	even	36	inner	950.2.bb.a.507.1	yes	24
95.32	even	36	inner	950.2.bb.a.507.2	yes	24
95.89	odd	18	inner	950.2.bb.a.393.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.a.193.1	✓	24	5.4	even	2	inner
950.2.bb.a.193.2	yes	24	1.1	even	1	trivial
950.2.bb.a.307.1	yes	24	5.2	odd	4	inner
950.2.bb.a.307.2	yes	24	5.3	odd	4	inner
950.2.bb.a.393.1	yes	24	19.13	odd	18	inner
950.2.bb.a.393.2	yes	24	95.89	odd	18	inner
950.2.bb.a.507.1	yes	24	95.13	even	36	inner
950.2.bb.a.507.2	yes	24	95.32	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.0871557 + 0.996195i) q^{2} +(1.01913 - 2.18554i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(2.26604 + 0.824773i) q^{6} +(1.01230 + 0.271245i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(-1.80958 - 2.15657i) q^{9} +O(q^{10})\)	\(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

Related objects

Downloads

Learn more