LMFDB - Embedded newform 950.2.bb.a.307.2

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			307.2
Character	$\chi$	$=$	950.307
Dual form			950.2.bb.a.393.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 - 0.0871557i) q^{2} +(2.18554 + 1.01913i) q^{3} +(0.984808 - 0.173648i) q^{4} +(2.26604 + 0.824773i) q^{6} +(0.271245 - 1.01230i) q^{7} +(0.965926 - 0.258819i) q^{8} +(1.80958 + 2.15657i) q^{9} +O(q^{10})$	\(q+(0.996195 - 0.0871557i) q^{2} +(2.18554 + 1.01913i) q^{3} +(0.984808 - 0.173648i) q^{4} +(2.26604 + 0.824773i) q^{6} +(0.271245 - 1.01230i) q^{7} +(0.965926 - 0.258819i) q^{8} +(1.80958 + 2.15657i) q^{9} +(0.152704 - 0.264490i) q^{11} +(2.32931 + 0.624135i) q^{12} +(1.36365 + 2.92437i) q^{13} +(0.181985 - 1.03209i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-0.171663 - 1.96212i) q^{17} +(1.99065 + 1.99065i) q^{18} +(1.55007 + 4.07398i) q^{19} +(1.62449 - 1.93599i) q^{21} +(0.129071 - 0.276793i) q^{22} +(-0.858480 - 0.601114i) q^{23} +(2.37484 + 0.418748i) q^{24} +(1.61334 + 2.79439i) q^{26} +(-0.115336 - 0.430438i) q^{27} +(0.0913401 - 1.04402i) q^{28} +(-2.09602 + 1.75877i) q^{29} +(3.31521 - 1.91404i) q^{31} +(0.906308 - 0.422618i) q^{32} +(0.603291 - 0.422429i) q^{33} +(-0.342020 - 1.93969i) q^{34} +(2.15657 + 1.80958i) q^{36} +(-0.822014 + 0.822014i) q^{37} +(1.89924 + 3.92338i) q^{38} +7.78106i q^{39} +(-2.48886 - 6.83807i) q^{41} +(1.44957 - 2.07020i) q^{42} +(-3.83759 - 5.48065i) q^{43} +(0.104455 - 0.286989i) q^{44} +(-0.907604 - 0.524005i) q^{46} +(-0.570701 - 0.0499299i) q^{47} +(2.40230 + 0.210174i) q^{48} +(5.11100 + 2.95084i) q^{49} +(1.62449 - 4.46324i) q^{51} +(1.85075 + 2.64314i) q^{52} +(-6.32502 + 9.03307i) q^{53} +(-0.152412 - 0.418748i) q^{54} -1.04801i q^{56} +(-0.764198 + 10.4836i) q^{57} +(-1.93476 + 1.93476i) q^{58} +(-5.85327 - 4.91147i) q^{59} +(-2.34864 - 13.3198i) q^{61} +(3.13577 - 2.19569i) q^{62} +(2.67394 - 1.24688i) q^{63} +(0.866025 - 0.500000i) q^{64} +(0.564178 - 0.473401i) q^{66} +(-0.495049 + 5.65843i) q^{67} +(-0.509774 - 1.90250i) q^{68} +(-1.26363 - 2.18866i) q^{69} +(-1.34730 - 0.237565i) q^{71} +(2.30608 + 1.61474i) q^{72} +(-6.26968 + 13.4454i) q^{73} +(-0.747243 + 0.890530i) q^{74} +(2.23396 + 3.74292i) q^{76} +(-0.226324 - 0.226324i) q^{77} +(0.678164 + 7.75145i) q^{78} +(-2.32099 + 0.844770i) q^{79} +(1.65317 - 9.37560i) q^{81} +(-3.07536 - 6.59514i) q^{82} +(-7.19347 - 1.92749i) q^{83} +(1.26363 - 2.18866i) q^{84} +(-4.30066 - 5.12533i) q^{86} +(-6.37335 + 1.70774i) q^{87} +(0.0790452 - 0.295001i) q^{88} +(7.69475 + 2.80066i) q^{89} +(3.33022 - 0.587208i) q^{91} +(-0.949820 - 0.442908i) q^{92} +(9.19617 - 0.804560i) q^{93} -0.572881 q^{94} +2.41147 q^{96} +(-12.8159 + 1.12124i) q^{97} +(5.34873 + 2.49416i) 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.996195	−	0.0871557i	0.704416	−	0.0616284i
$2$	0.996195	−	0.0871557i	0.704416	−	0.0616284i
$3$	2.18554	+	1.01913i	1.26182	+	0.588397i	0.934314	−	0.356452i	$-0.116014\pi$
$3$	2.18554	+	1.01913i	1.26182	+	0.588397i	0.327507	+	0.944849i	$0.393791\pi$
$4$	0.984808	−	0.173648i	0.492404	−	0.0868241i
$5$		0			0
$5$		0			0
$6$	2.26604	+	0.824773i	0.925109	+	0.336712i
$7$	0.271245	−	1.01230i	0.102521	−	0.382614i	−0.895531	−	0.444999i	$-0.853204\pi$
$7$	0.271245	−	1.01230i	0.102521	−	0.382614i	0.998052	+	0.0623853i	$0.0198707\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$	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	$0.152006\pi$
$12$	2.32931	+	0.624135i	0.672412	+	0.180172i
$13$	1.36365	+	2.92437i	0.378210	+	0.811073i	0.999619	+	0.0275876i	$0.00878251\pi$
$13$	1.36365	+	2.92437i	0.378210	+	0.811073i	−0.621410	+	0.783486i	$0.713440\pi$
$14$	0.181985	−	1.03209i	0.0486376	−	0.275837i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	−0.171663	−	1.96212i	−0.0416345	−	0.475884i	−0.988178	−	0.153309i	$-0.951007\pi$
$17$	−0.171663	−	1.96212i	−0.0416345	−	0.475884i	0.946544	−	0.322575i	$-0.104549\pi$
$18$	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
$22$	0.129071	−	0.276793i	0.0275180	−	0.0590125i
$23$	−0.858480	−	0.601114i	−0.179005	−	0.125341i	0.480640	−	0.876918i	$-0.340405\pi$
$23$	−0.858480	−	0.601114i	−0.179005	−	0.125341i	−0.659645	+	0.751577i	$0.729293\pi$
$24$	2.37484	+	0.418748i	0.484762	+	0.0854766i
$25$		0			0
$26$	1.61334	+	2.79439i	0.316402	+	0.548025i
$27$	−0.115336	−	0.430438i	−0.0221963	−	0.0828379i
$28$	0.0913401	−	1.04402i	0.0172617	−	0.197302i
$29$	−2.09602	+	1.75877i	−0.389221	+	0.326595i	−0.816310	−	0.577614i	$-0.803984\pi$
$29$	−2.09602	+	1.75877i	−0.389221	+	0.326595i	0.427088	+	0.904210i	$0.359539\pi$
$30$		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	$0.221629\pi$
$32$	0.906308	−	0.422618i	0.160214	−	0.0747091i
$33$	0.603291	−	0.422429i	0.105019	−	0.0735354i
$34$	−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	$0.280463\pi$
$38$	1.89924	+	3.92338i	0.308097	+	0.636456i
$39$			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	$-0.303484\pi$
$42$	1.44957	−	2.07020i	0.223674	−	0.319439i
$43$	−3.83759	−	5.48065i	−0.585227	−	0.835791i	0.411924	−	0.911218i	$-0.364857\pi$
$43$	−3.83759	−	5.48065i	−0.585227	−	0.835791i	−0.997151	+	0.0754269i	$0.975968\pi$
$44$	0.104455	−	0.286989i	0.0157473	−	0.0432652i
$45$		0			0
$46$	−0.907604	−	0.524005i	−0.133819	−	0.0772604i
$47$	−0.570701	−	0.0499299i	−0.0832453	−	0.00728302i	0.0454570	−	0.998966i	$-0.485526\pi$
$47$	−0.570701	−	0.0499299i	−0.0832453	−	0.00728302i	−0.128702	+	0.991683i	$0.541081\pi$
$48$	2.40230	+	0.210174i	0.346742	+	0.0303360i
$49$	5.11100	+	2.95084i	0.730143	+	0.421548i
$50$		0			0
$51$	1.62449	−	4.46324i	0.227473	−	0.624978i
$52$	1.85075	+	2.64314i	0.256653	+	0.366538i
$53$	−6.32502	+	9.03307i	−0.868809	+	1.24079i	0.100499	+	0.994937i	$0.467956\pi$
$53$	−6.32502	+	9.03307i	−0.868809	+	1.24079i	−0.969308	+	0.245850i	$0.920933\pi$
$54$	−0.152412	−	0.418748i	−0.0207406	−	0.0569844i
$55$		0			0
$56$		−	1.04801i		−	0.140046i
$57$	−0.764198	+	10.4836i	−0.101221	+	1.38858i
$58$	−1.93476	+	1.93476i	−0.254046	+	0.254046i
$59$	−5.85327	−	4.91147i	−0.762030	−	0.639419i	0.176624	−	0.984278i	$-0.443482\pi$
$59$	−5.85327	−	4.91147i	−0.762030	−	0.639419i	−0.938655	+	0.344859i	$0.887927\pi$
$60$		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	$-0.388788\pi$
$62$	3.13577	−	2.19569i	0.398244	−	0.278853i
$63$	2.67394	−	1.24688i	0.336885	−	0.157092i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$		0			0
$66$	0.564178	−	0.473401i	0.0694455	−	0.0582717i
$67$	−0.495049	+	5.65843i	−0.0604798	+	0.691287i	0.904070	+	0.427385i	$0.140565\pi$
$67$	−0.495049	+	5.65843i	−0.0604798	+	0.691287i	−0.964549	+	0.263902i	$0.914990\pi$
$68$	−0.509774	−	1.90250i	−0.0618192	−	0.230712i
$69$	−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	$0.581425\pi$
$72$	2.30608	+	1.61474i	0.271774	+	0.190299i
$73$	−6.26968	+	13.4454i	−0.733810	+	1.57366i	0.0828633	+	0.996561i	$0.473594\pi$
$73$	−6.26968	+	13.4454i	−0.733810	+	1.57366i	−0.816673	+	0.577100i	$0.804184\pi$
$74$	−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
$78$	0.678164	+	7.75145i	0.0767870	+	0.877679i
$79$	−2.32099	+	0.844770i	−0.261131	+	0.0950441i	−0.469268	−	0.883056i	$-0.655482\pi$
$79$	−2.32099	+	0.844770i	−0.261131	+	0.0950441i	0.208137	+	0.978100i	$0.433260\pi$
$80$		0			0
$81$	1.65317	−	9.37560i	0.183686	−	1.04173i
$82$	−3.07536	−	6.59514i	−0.339617	−	0.728311i
$83$	−7.19347	−	1.92749i	−0.789586	−	0.211569i	−0.158579	−	0.987346i	$-0.550691\pi$
$83$	−7.19347	−	1.92749i	−0.789586	−	0.211569i	−0.631007	+	0.775777i	$0.717358\pi$
$84$	1.26363	−	2.18866i	0.137873	−	0.238803i
$85$		0			0
$86$	−4.30066	−	5.12533i	−0.463752	−	0.552678i
$87$	−6.37335	+	1.70774i	−0.683295	+	0.183088i
$88$	0.0790452	−	0.295001i	0.00842625	−	0.0314472i
$89$	7.69475	+	2.80066i	0.815642	+	0.296869i	0.715952	−	0.698149i	$-0.245993\pi$
$89$	7.69475	+	2.80066i	0.815642	+	0.296869i	0.0996895	+	0.995019i	$0.468215\pi$
$90$		0			0
$91$	3.33022	−	0.587208i	0.349102	−	0.0615561i
$92$	−0.949820	−	0.442908i	−0.0990256	−	0.0461764i
$93$	9.19617	−	0.804560i	0.953598	−	0.0834290i
$94$	−0.572881			−0.0590882
$95$		0			0
$96$	2.41147			0.246120
$97$	−12.8159	+	1.12124i	−1.30126	+	0.113845i	−0.716627	−	0.697456i	$-0.754315\pi$
$97$	−12.8159	+	1.12124i	−1.30126	+	0.113845i	−0.584628	+	0.811301i	$0.698760\pi$
$98$	5.34873	+	2.49416i	0.540304	+	0.251948i
$99$	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	$0.736291\pi$
$102$	1.22931	−	4.58784i	0.121720	−	0.454263i
$103$	−12.3456	+	3.30798i	−1.21644	+	0.325945i	−0.809287	−	0.587413i	$-0.800146\pi$
$103$	−12.3456	+	3.30798i	−1.21644	+	0.325945i	−0.407157	+	0.913358i	$0.633480\pi$
$104$	2.07407	+	2.47178i	0.203379	+	0.242378i
$105$		0			0
$106$	−5.51367	+	9.54996i	−0.535535	+	0.927574i
$107$	8.85030	+	2.37143i	0.855591	+	0.229255i	0.659847	−	0.751400i	$-0.270621\pi$
$107$	8.85030	+	2.37143i	0.855591	+	0.229255i	0.195744	+	0.980655i	$0.437288\pi$
$108$	−0.188328	−	0.403871i	−0.0181219	−	0.0388625i
$109$	2.36986	−	13.4402i	0.226992	−	1.28733i	−0.631849	−	0.775091i	$-0.717704\pi$
$109$	2.36986	−	13.4402i	0.226992	−	1.28733i	0.858841	−	0.512242i	$-0.171185\pi$
$110$		0			0
$111$	−2.63429	+	0.958801i	−0.250035	+	0.0910054i
$112$	−0.0913401	−	1.04402i	−0.00863083	−	0.0986509i
$113$	−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
$117$	−3.83897	+	8.23270i	−0.354913	+	0.761113i
$118$	−6.25906	−	4.38264i	−0.576193	−	0.403455i
$119$	−2.03282	−	0.358441i	−0.186348	−	0.0328582i
$120$		0			0
$121$	5.45336	+	9.44550i	0.495760	+	0.858682i
$122$	−3.50060	−	13.0644i	−0.316929	−	1.18280i
$123$	1.52942	−	17.4813i	0.137903	−	1.57624i
$124$	2.93247	−	2.46064i	0.263344	−	0.220972i
$125$		0			0
$126$	2.55509	−	1.47518i	0.227626	−	0.131420i
$127$	−8.39560	+	3.91493i	−0.744989	+	0.347394i	−0.757768	−	0.652524i	$-0.773710\pi$
$127$	−8.39560	+	3.91493i	−0.744989	+	0.347394i	0.0127789	+	0.999918i	$0.495932\pi$
$128$	0.819152	−	0.573576i	0.0724035	−	0.0506975i
$129$	−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
$133$	4.54454	−	0.464086i	0.394061	−	0.0402413i
$134$			5.68004i			0.490681i
$135$		0			0
$136$	−0.673648	−	1.85083i	−0.0577649	−	0.158708i
$137$	12.8224	−	18.3122i	1.09549	−	1.56452i	0.304681	−	0.952455i	$-0.401450\pi$
$137$	12.8224	−	18.3122i	1.09549	−	1.56452i	0.790808	−	0.612065i	$-0.209661\pi$
$138$	−1.44957	−	2.07020i	−0.123396	−	0.176227i
$139$	4.46556	−	12.2690i	0.378764	−	1.04065i	−0.593105	−	0.805125i	$-0.702098\pi$
$139$	4.46556	−	12.2690i	0.378764	−	1.04065i	0.971869	−	0.235521i	$-0.0756797\pi$
$140$		0			0
$141$	−1.19640	−	0.690744i	−0.100755	−	0.0581711i
$142$	−1.36287	−	0.119236i	−0.114370	−	0.0100061i
$143$	0.981702	+	0.0858878i	0.0820941	+	0.00718230i
$144$	2.43804	+	1.40760i	0.203170	+	0.117300i
$145$		0			0
$146$	−5.07398	+	13.9406i	−0.419925	+	1.15374i
$147$	8.16299	+	11.6580i	0.673272	+	0.961532i
$148$	−0.666785	+	0.952267i	−0.0548094	+	0.0782759i
$149$	−5.45475	−	14.9868i	−0.446870	−	1.22777i	−0.934891	−	0.354934i	$-0.884503\pi$
$149$	−5.45475	−	14.9868i	−0.446870	−	1.22777i	0.488021	−	0.872832i	$-0.337719\pi$
$150$		0			0
$151$			19.9589i			1.62423i	0.583495	+	0.812117i	$0.301685\pi$
$151$			19.9589i			1.62423i	−0.583495	+	0.812117i	$0.698315\pi$
$152$	2.55167	+	3.53397i	0.206968	+	0.286643i
$153$	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
$157$	0.409844	−	0.286976i	0.0327091	−	0.0229032i	−0.557108	−	0.830440i	$-0.688089\pi$
$157$	0.409844	−	0.286976i	0.0327091	−	0.0229032i	0.589817	+	0.807537i	$0.299200\pi$
$158$	−2.23853	+	1.04384i	−0.178088	+	0.0830437i
$159$	−23.0295	+	13.2961i	−1.82636	+	1.05445i
$160$		0			0
$161$	−0.841367	+	0.705990i	−0.0663090	+	0.0556398i
$162$	0.829743	−	9.48400i	0.0651907	−	0.745134i
$163$	−2.19389	−	8.18771i	−0.171839	−	0.641311i	−0.997069	−	0.0765138i	$-0.975621\pi$
$163$	−2.19389	−	8.18771i	−0.171839	−	0.641311i	0.825230	−	0.564797i	$-0.191046\pi$
$164$	−3.63846	−	6.30200i	−0.284116	−	0.492104i
$165$		0			0
$166$	−7.33409	−	1.29320i	−0.569236	−	0.100372i
$167$	6.51890	+	4.56458i	0.504448	+	0.353218i	0.797934	−	0.602745i	$-0.205926\pi$
$167$	6.51890	+	4.56458i	0.504448	+	0.353218i	−0.293486	+	0.955963i	$0.594815\pi$
$168$	1.06806	−	2.29047i	0.0824028	−	0.176713i
$169$	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
$173$	0.916898	+	10.4802i	0.0697105	+	0.796795i	0.947918	+	0.318515i	$0.103184\pi$
$173$	0.916898	+	10.4802i	0.0697105	+	0.796795i	−0.878207	+	0.478280i	$0.841260\pi$
$174$	−6.20026	+	2.25671i	−0.470041	+	0.171081i
$175$		0			0
$176$	0.0530334	−	0.300767i	0.00399754	−	0.0226712i
$177$	−7.78709	−	16.6995i	−0.585314	−	1.25521i
$178$	7.90956	+	2.11936i	0.592847	+	0.158853i
$179$	10.5178	−	18.2173i	0.786137	−	1.36163i	−0.142181	−	0.989841i	$-0.545412\pi$
$179$	10.5178	−	18.2173i	0.786137	−	1.36163i	0.928318	−	0.371788i	$-0.121255\pi$
$180$		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	$0.718316\pi$
$182$	3.26637	−	0.875222i	0.242120	−	0.0648757i
$183$	8.44161	−	31.5045i	0.624022	−	2.32888i
$184$	−0.984808	−	0.358441i	−0.0726010	−	0.0264246i
$185$		0			0
$186$	9.09105	−	1.60300i	0.666588	−	0.117537i
$187$	−0.545176	−	0.254220i	−0.0398672	−	0.0185904i
$188$	−0.570701	+	0.0499299i	−0.0416227	+	0.00364151i
$189$	−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	$0.639937\pi$
$192$	2.40230	−	0.210174i	0.173371	−	0.0151680i
$193$	9.40261	+	4.38451i	0.676815	+	0.315604i	0.730459	−	0.682956i	$-0.239306\pi$
$193$	9.40261	+	4.38451i	0.676815	+	0.315604i	−0.0536444	+	0.998560i	$0.517084\pi$
$194$	−12.6694	+	2.23396i	−0.909609	+	0.160389i
$195$		0			0
$196$	5.54576	+	2.01849i	0.396126	+	0.144178i
$197$	−1.29079	+	4.81731i	−0.0919652	+	0.343219i	−0.996542	−	0.0830922i	$-0.973520\pi$
$197$	−1.29079	+	4.81731i	−0.0919652	+	0.343219i	0.904577	+	0.426311i	$0.140187\pi$
$198$	0.830488	−	0.222529i	0.0590202	−	0.0158144i
$199$	17.2195	+	20.5214i	1.22066	+	1.45472i	0.850680	+	0.525684i	$0.176191\pi$
$199$	17.2195	+	20.5214i	1.22066	+	1.45472i	0.369979	+	0.929040i	$0.379365\pi$
$200$		0			0
$201$	−6.84864	+	11.8622i	−0.483066	+	0.836695i
$202$	−7.43988	−	1.99351i	−0.523468	−	0.140263i
$203$	1.21187	+	2.59886i	0.0850565	+	0.182404i
$204$	0.824773	−	4.67752i	0.0577456	−	0.327492i
$205$		0			0
$206$	−12.0103	+	4.37138i	−0.836795	+	0.304568i
$207$	−0.257141	−	2.93914i	−0.0178726	−	0.204284i
$208$	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	$0.228500\pi$
$212$	−4.66036	+	9.99417i	−0.320075	+	0.686402i
$213$	−2.70246	−	1.89228i	−0.185169	−	0.129657i
$214$	9.02330	+	1.59105i	0.616820	+	0.108762i
$215$		0			0
$216$	−0.222811	−	0.385920i	−0.0151604	−	0.0262586i
$217$	−1.03835	−	3.87516i	−0.0704875	−	0.263063i
$218$	1.18946	−	13.5956i	0.0805602	−	0.920808i
$219$	−27.4052	+	22.9957i	−1.85187	+	1.55391i
$220$		0			0
$221$	5.50387	−	3.17766i	0.370230	−	0.213753i
$222$	−2.54070	+	1.18475i	−0.170520	+	0.0795149i
$223$	2.22968	−	1.56124i	0.149310	−	0.104548i	−0.496534	−	0.868017i	$-0.665394\pi$
$223$	2.22968	−	1.56124i	0.149310	−	0.104548i	0.645845	+	0.763469i	$0.276505\pi$
$224$	−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	$0.0323569\pi$
$228$	1.06786	+	10.4570i	0.0707209	+	0.692531i
$229$			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
$232$	−1.56940	+	2.24133i	−0.103036	+	0.147151i
$233$	−13.4185	−	19.1635i	−0.879072	−	1.25545i	−0.965820	−	0.259215i	$-0.916536\pi$
$233$	−13.4185	−	19.1635i	−0.879072	−	1.25545i	0.0867473	−	0.996230i	$-0.472353\pi$
$234$	−3.10684	+	8.53596i	−0.203100	+	0.558013i
$235$		0			0
$236$	−6.61721	−	3.82045i	−0.430744	−	0.248690i
$237$	−5.93354	−	0.519117i	−0.385425	−	0.0337203i
$238$	−2.05632	−	0.179905i	−0.133292	−	0.0116615i
$239$	16.6235	+	9.59761i	1.07529	+	0.620818i	0.929621	−	0.368516i	$-0.120134\pi$
$239$	16.6235	+	9.59761i	1.07529	+	0.620818i	0.145667	+	0.989334i	$0.453467\pi$
$240$		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	$0.0395843\pi$
$242$	6.25584	+	8.93427i	0.402141	+	0.574316i
$243$	12.4012	−	17.7108i	0.795541	−	1.13615i
$244$	−4.62592	−	12.7096i	−0.296144	−	0.813649i
$245$		0			0
$246$		−	17.5481i		−	1.11883i
$247$	−9.80005	+	10.0885i	−0.623562	+	0.641913i
$248$	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	$0.918480\pi$
$252$	2.41680	−	1.69226i	0.152244	−	0.106602i
$253$	−0.290082	+	0.135267i	−0.0182373	+	0.00850419i
$254$	−8.02244	+	4.63176i	−0.503373	+	0.290622i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	0.554471	−	6.33764i	0.0345870	−	0.395331i	−0.959094	−	0.283088i	$-0.908641\pi$
$257$	0.554471	−	6.33764i	0.0345870	−	0.395331i	0.993681	−	0.112243i	$-0.0358034\pi$
$258$	−4.17586	−	15.5845i	−0.259978	−	0.970251i
$259$	0.609158	+	1.05509i	0.0378512	+	0.0655603i
$260$		0			0
$261$	−7.58584	−	1.33759i	−0.469552	−	0.0827946i
$262$	8.58749	+	6.01303i	0.530537	+	0.371486i
$263$	−8.72779	+	18.7168i	−0.538179	+	1.15413i	0.429761	+	0.902943i	$0.358598\pi$
$263$	−8.72779	+	18.7168i	−0.538179	+	1.15413i	−0.967939	+	0.251185i	$0.919180\pi$
$264$	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
$268$	0.495049	+	5.65843i	0.0302399	+	0.345644i
$269$	−19.9303	+	7.25402i	−1.21517	+	0.442286i	−0.868494	−	0.495700i	$-0.834912\pi$
$269$	−19.9303	+	7.25402i	−1.21517	+	0.442286i	−0.346676	+	0.937985i	$0.612690\pi$
$270$		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	$0.0176791\pi$
$272$	−0.832395	−	1.78508i	−0.0504714	−	0.108236i
$273$	7.87677	+	2.11057i	0.476724	+	0.127738i
$274$	11.1776	−	19.3601i	0.675261	−	1.16959i
$275$		0			0
$276$	−1.62449	−	1.93599i	−0.0977825	−	0.116533i
$277$	−11.2376	+	3.01110i	−0.675200	+	0.180919i	−0.580096	−	0.814548i	$-0.696985\pi$
$277$	−11.2376	+	3.01110i	−0.675200	+	0.180919i	−0.0951037	+	0.995467i	$0.530318\pi$
$278$	3.37925	−	12.6115i	0.202674	−	0.756390i
$279$	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	$0.497333\pi$
$282$	−1.25205	−	0.583842i	−0.0745587	−	0.0347673i
$283$	16.0648	−	1.40549i	0.954955	−	0.0835477i	0.400985	−	0.916085i	$-0.368668\pi$
$283$	16.0648	−	1.40549i	0.954955	−	0.0835477i	0.553970	+	0.832537i	$0.313112\pi$
$284$	−1.36808			−0.0811806
$285$		0			0
$286$	0.985452			0.0582710
$287$	−7.59728	+	0.664676i	−0.448453	+	0.0392346i
$288$	2.55144	+	1.18976i	0.150345	+	0.0701072i
$289$	12.9213	−	2.27837i	0.760075	−	0.134022i
$290$		0			0
$291$	−29.1523	−	10.6106i	−1.70894	−	0.622002i
$292$	−3.83966	+	14.3298i	−0.224699	+	0.838589i
$293$	−30.7180	+	8.23086i	−1.79456	+	0.480852i	−0.993108	−	0.117203i	$-0.962607\pi$
$293$	−30.7180	+	8.23086i	−1.79456	+	0.480852i	−0.801456	+	0.598054i	$0.795941\pi$
$294$	9.14798	+	10.9021i	0.533521	+	0.635826i
$295$		0			0
$296$	−0.581252	+	1.00676i	−0.0337846	+	0.0585166i
$297$	−0.131459	−	0.0352243i	−0.00762802	−	0.00204392i
$298$	−6.74018	−	14.4544i	−0.390448	−	0.837318i
$299$	0.587208	−	3.33022i	0.0339591	−	0.192592i
$300$		0			0
$301$	−6.58899	+	2.39820i	−0.379783	+	0.138230i
$302$	1.73953	+	19.8830i	0.100099	+	1.14414i
$303$	−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
$307$	−13.7125	+	29.4066i	−0.782614	+	1.67832i	−0.0489576	+	0.998801i	$0.515590\pi$
$307$	−13.7125	+	29.4066i	−0.782614	+	1.67832i	−0.733656	+	0.679521i	$0.762188\pi$
$308$	−0.262186	−	0.183585i	−0.0149394	−	0.0104607i
$309$	−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	$0.945022\pi$
$312$	2.01389	+	7.51593i	0.114014	+	0.425506i
$313$	−0.728931	+	8.33172i	−0.0412016	+	0.470936i	0.947365	+	0.320154i	$0.103735\pi$
$313$	−0.728931	+	8.33172i	−0.0412016	+	0.470936i	−0.988567	+	0.150782i	$0.951821\pi$
$314$	0.383273	−	0.321604i	0.0216293	−	0.0181492i
$315$		0			0
$316$	−2.13903	+	1.23497i	−0.120330	+	0.0694726i
$317$	0.366753	−	0.171020i	0.0205989	−	0.00960542i	−0.412292	−	0.911052i	$-0.635271\pi$
$317$	0.366753	−	0.171020i	0.0205989	−	0.00960542i	0.432890	+	0.901447i	$0.357494\pi$
$318$	−21.7830	+	15.2526i	−1.22153	+	0.855325i
$319$	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
$323$	7.72755	−	3.74077i	0.429972	−	0.208142i
$324$		−	9.52023i		−	0.528902i
$325$		0			0
$326$	−2.89915	−	7.96534i	−0.160569	−	0.441160i
$327$	18.8767	−	26.9588i	1.04389	−	1.49082i
$328$	−4.17387	−	5.96091i	−0.230464	−	0.329136i
$329$	−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	$0.453172\pi$
$332$	−7.41889	−	0.649069i	−0.407165	−	0.0356223i
$333$	−3.26024	−	0.285234i	−0.178660	−	0.0156307i
$334$	6.89193	+	3.97906i	0.377109	+	0.217724i
$335$		0			0
$336$	0.864370	−	2.37484i	0.0471553	−	0.129558i
$337$	6.37906	+	9.11024i	0.347489	+	0.496266i	0.954411	−	0.298495i	$-0.0964847\pi$
$337$	6.37906	+	9.11024i	0.347489	+	0.496266i	−0.606922	+	0.794762i	$0.707596\pi$
$338$	1.48472	−	2.12040i	0.0807580	−	0.115334i
$339$	−0.369754	−	1.01589i	−0.0200823	−	0.0551757i
$340$		0			0
$341$		−	1.16912i		−	0.0633115i
$342$	−5.02423	+	11.1955i	−0.271679	+	0.605384i
$343$	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
$347$	8.21756	−	5.75400i	0.441142	−	0.308891i	−0.331821	−	0.943342i	$-0.607663\pi$
$347$	8.21756	−	5.75400i	0.441142	−	0.308891i	0.772963	+	0.634452i	$0.218774\pi$
$348$	−5.97998	+	2.78851i	−0.320561	+	0.149480i
$349$	12.5667	−	7.25537i	0.672678	−	0.388371i	−0.124413	−	0.992231i	$-0.539705\pi$
$349$	12.5667	−	7.25537i	0.672678	−	0.388371i	0.797091	+	0.603860i	$0.206371\pi$
$350$		0			0
$351$	1.10148	−	0.924252i	0.0587927	−	0.0493329i
$352$	0.0266180	−	0.304245i	0.00141874	−	0.0162163i
$353$	2.65443	+	9.90648i	0.141281	+	0.527269i	0.999893	+	0.0146421i	$0.00466090\pi$
$353$	2.65443	+	9.90648i	0.141281	+	0.527269i	−0.858611	+	0.512627i	$0.828672\pi$
$354$	−9.21291	−	15.9572i	−0.489661	−	0.848117i
$355$		0			0
$356$	8.06418	+	1.42193i	0.427401	+	0.0753623i
$357$	−4.07750	−	2.85510i	−0.215804	−	0.151108i
$358$	8.89002	−	19.0647i	0.469852	−	1.00760i
$359$	−13.6779	+	16.3007i	−0.721891	+	0.860316i	−0.994813	−	0.101720i	$-0.967565\pi$
$359$	−13.6779	+	16.3007i	−0.721891	+	0.860316i	0.272922	+	0.962036i	$0.412010\pi$
$360$		0			0
$361$	−14.1946	+	12.6299i	−0.747084	+	0.664730i
$362$	3.53355	+	3.53355i	0.185719	+	0.185719i
$363$	2.29231	+	26.2012i	0.120315	+	1.37521i
$364$	3.17766	−	1.15657i	0.166555	−	0.0606210i
$365$		0			0
$366$	5.66369	−	32.1204i	0.296046	−	1.67896i
$367$	−10.3782	−	22.2562i	−0.541739	−	1.16176i	−0.966549	−	0.256481i	$-0.917437\pi$
$367$	−10.3782	−	22.2562i	−0.541739	−	1.16176i	0.424810	−	0.905283i	$-0.360341\pi$
$368$	−1.01230	−	0.271245i	−0.0527698	−	0.0141396i
$369$	10.2430	−	17.7414i	0.533231	−	0.923583i
$370$		0			0
$371$	7.42855	+	8.85300i	0.385671	+	0.459625i
$372$	8.91675	−	2.38924i	0.462312	−	0.123876i
$373$	3.18418	−	11.8835i	0.164870	−	0.615305i	−0.833186	−	0.552993i	$-0.813486\pi$
$373$	3.18418	−	11.8835i	0.164870	−	0.615305i	0.998057	−	0.0623125i	$-0.0198475\pi$
$374$	−0.565258	−	0.205737i	−0.0292288	−	0.0106384i
$375$		0			0
$376$	−0.564178	+	0.0994798i	−0.0290952	+	0.00513028i
$377$	−8.00154	−	3.73118i	−0.412100	−	0.192165i
$378$	−0.465240	+	0.0407032i	−0.0239294	+	0.00209355i
$379$	23.8642			1.22582			0.612911	−	0.790152i	$-0.289998\pi$
$379$	23.8642			1.22582			0.612911	+	0.790152i	$0.289998\pi$
$380$		0			0
$381$	−22.3387			−1.14445
$382$	−11.7191	+	1.02528i	−0.599599	+	0.0524581i
$383$	1.69629	+	0.790991i	0.0866762	+	0.0404178i	0.465473	−	0.885062i	$-0.345884\pi$
$383$	1.69629	+	0.790991i	0.0866762	+	0.0404178i	−0.378797	+	0.925480i	$0.623662\pi$
$384$	2.37484	−	0.418748i	0.121190	−	0.0213691i
$385$		0			0
$386$	9.74897	+	3.54834i	0.496210	+	0.180605i
$387$	4.87500	−	18.1937i	0.247810	−	0.924839i
$388$	−12.4265	+	3.32966i	−0.630859	+	0.169038i
$389$	12.7689	+	15.2173i	0.647407	+	0.771550i	0.985521	−	0.169555i	$-0.0542331\pi$
$389$	12.7689	+	15.2173i	0.647407	+	0.771550i	−0.338113	+	0.941105i	$0.609789\pi$
$390$		0			0
$391$	−1.03209	+	1.78763i	−0.0521950	+	0.0904044i
$392$	5.70058	+	1.52747i	0.287923	+	0.0771487i
$393$	10.6840	+	22.9119i	0.538935	+	1.15575i
$394$	−0.866025	+	4.91147i	−0.0436297	+	0.247436i
$395$		0			0
$396$	0.807934	−	0.294064i	0.0406002	−	0.0147773i
$397$	0.998258	+	11.4101i	0.0501011	+	0.572658i	0.979210	+	0.202851i	$0.0650207\pi$
$397$	0.998258	+	11.4101i	0.0501011	+	0.572658i	−0.929108	+	0.369807i	$0.879424\pi$
$398$	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	$0.331311\pi$
$402$	−5.78872	+	12.4140i	−0.288715	+	0.619152i
$403$	10.1181	+	7.08480i	0.504020	+	0.352919i
$404$	−7.58532	−	1.33750i	−0.377384	−	0.0665429i
$405$		0			0
$406$	1.43376	+	2.48335i	0.0711565	+	0.123247i
$407$	0.0918904	+	0.342940i	0.00455484	+	0.0169989i
$408$	0.413962	−	4.73160i	0.0204942	−	0.234249i
$409$	−20.2354	+	16.9795i	−1.00058	+	0.839583i	−0.987064	−	0.160325i	$-0.948746\pi$
$409$	−20.2354	+	16.9795i	−1.00058	+	0.839583i	−0.0135122	+	0.999909i	$0.504301\pi$
$410$		0			0
$411$	46.6864	−	26.9544i	2.30287	−	1.32956i
$412$	−11.5836	+	5.40151i	−0.570682	+	0.266113i
$413$	−6.55956	+	4.59305i	−0.322775	+	0.226009i
$414$	−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
$418$	1.32772	+	0.0967838i	0.0649407	+	0.00473385i
$419$		−	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	0.985306	+	0.170797i	$0.0546343\pi$
$421$	6.98246	+	19.1841i	0.340304	+	0.934978i	−0.645002	+	0.764181i	$0.723143\pi$
$422$	−0.328591	+	0.469277i	−0.0159956	+	0.0228440i
$423$	−0.925052	−	1.32111i	−0.0449776	−	0.0642346i
$424$	−3.77157	+	10.3623i	−0.183164	+	0.503238i
$425$		0			0
$426$	−2.85710	−	1.64955i	−0.138427	−	0.0799207i
$427$	−14.1207	−	1.23540i	−0.683349	−	0.0597852i
$428$	9.12764	+	0.798565i	0.441201	+	0.0386001i
$429$	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	$0.0130255\pi$
$432$	−0.255599	−	0.365033i	−0.0122975	−	0.0175626i
$433$	−14.6480	+	20.9196i	−0.703940	+	1.00533i	0.294821	+	0.955553i	$0.404740\pi$
$433$	−14.6480	+	20.9196i	−0.703940	+	1.00533i	−0.998760	+	0.0497776i	$0.984149\pi$
$434$	−1.37214	−	3.76991i	−0.0658647	−	0.180962i
$435$		0			0
$436$		−	13.6475i		−	0.653596i
$437$	1.11823	−	4.42919i	0.0534920	−	0.211877i
$438$	−25.2967	+	25.2967i	−1.20872	+	1.20872i
$439$	20.7222	+	17.3880i	0.989017	+	0.829884i	0.985425	−	0.170109i	$-0.0544121\pi$
$439$	20.7222	+	17.3880i	0.989017	+	0.829884i	0.00359221	+	0.999994i	$0.498857\pi$
$440$		0			0
$441$	2.88507	+	16.3620i	0.137384	+	0.779144i
$442$	5.20598	−	3.64526i	0.247623	−	0.173387i
$443$	12.0283	−	5.60888i	0.571481	−	0.266486i	−0.115324	−	0.993328i	$-0.536791\pi$
$443$	12.0283	−	5.60888i	0.571481	−	0.266486i	0.686805	+	0.726842i	$0.259013\pi$
$444$	−2.42777	+	1.40167i	−0.115217	+	0.0665205i
$445$		0			0
$446$	2.08512	−	1.74963i	0.0987334	−	0.0828472i
$447$	3.35198	−	38.3133i	0.158543	−	1.81216i
$448$	−0.271245	−	1.01230i	−0.0128151	−	0.0478267i
$449$	3.78417	+	6.55438i	0.178586	+	0.309320i	0.941396	−	0.337302i	$-0.109514\pi$
$449$	3.78417	+	6.55438i	0.178586	+	0.309320i	−0.762810	+	0.646622i	$0.776181\pi$
$450$		0			0
$451$	−2.18866	−	0.385920i	−0.103060	−	0.0181723i
$452$	−0.367235	−	0.257140i	−0.0172733	−	0.0120949i
$453$	−20.3408	+	43.6210i	−0.955694	+	2.04949i
$454$	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	$-0.278424\pi$
$457$	−2.69607	−	2.69607i	−0.126117	−	0.126117i	−0.767348	+	0.641231i	$0.778424\pi$
$458$	0.823240	+	9.40968i	0.0384675	+	0.439685i
$459$	−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	$-0.303606\pi$
$462$	−0.326194	−	0.699525i	−0.0151759	−	0.0325449i
$463$	29.2831	+	7.84638i	1.36090	+	0.364652i	0.864147	−	0.503240i	$-0.167859\pi$
$463$	29.2831	+	7.84638i	1.36090	+	0.364652i	0.496753	+	0.867892i	$0.334525\pi$
$464$	−1.36808	+	2.36959i	−0.0635115	+	0.110005i
$465$		0			0
$466$	−15.0376	−	17.9211i	−0.696604	−	0.830180i
$467$	34.0060	−	9.11187i	1.57361	−	0.421647i	0.636668	−	0.771138i	$-0.280312\pi$
$467$	34.0060	−	9.11187i	1.57361	−	0.421647i	0.936940	+	0.349491i	$0.113645\pi$
$468$	−2.35105	+	8.77426i	−0.108678	+	0.405590i
$469$	5.59375	+	2.03596i	0.258295	+	0.0940119i
$470$		0			0
$471$	1.18820	−	0.209511i	0.0547492	−	0.00965376i
$472$	−6.92500	−	3.22918i	−0.318749	−	0.148635i
$473$	−2.03559	+	0.178091i	−0.0935967	+	0.00818865i
$474$	−5.95620			−0.273577
$475$		0			0
$476$	−2.06418			−0.0946114
$477$	−30.9261	+	2.70568i	−1.41601	+	0.123885i
$478$	17.3968	+	8.11225i	0.795710	+	0.371046i
$479$	34.1491	−	6.02141i	1.56031	−	0.275125i	0.674184	−	0.738564i	$-0.264496\pi$
$479$	34.1491	−	6.02141i	1.56031	−	0.275125i	0.886129	+	0.463438i	$0.153384\pi$
$480$		0			0
$481$	−3.52481	−	1.28293i	−0.160718	−	0.0584965i
$482$	1.79058	−	6.68252i	0.0815585	−	0.304380i
$483$	−2.55834	+	0.685504i	−0.116408	+	0.0311915i
$484$	7.01071	+	8.35504i	0.318669	+	0.379774i
$485$		0			0
$486$	10.8105	−	18.7243i	0.490372	−	0.849350i
$487$	16.4190	+	4.39947i	0.744018	+	0.199359i	0.610863	−	0.791736i	$-0.290823\pi$
$487$	16.4190	+	4.39947i	0.744018	+	0.199359i	0.133155	+	0.991095i	$0.457489\pi$
$488$	−5.71603	−	12.2581i	−0.258753	−	0.554897i
$489$	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	$0.262974\pi$
$492$	−1.52942	−	17.4813i	−0.0689516	−	0.788120i
$493$	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
$497$	−0.605934	+	1.29943i	−0.0271799	+	0.0582874i
$498$	−14.7110	−	10.3007i	−0.659215	−	0.461588i
$499$	−8.96275	−	1.58037i	−0.401228	−	0.0707473i	−0.0306068	−	0.999532i	$-0.509744\pi$
$499$	−8.96275	−	1.58037i	−0.401228	−	0.0707473i	−0.370621	+	0.928784i	$0.620855\pi$
$500$		0			0
$501$	9.59539	+	16.6197i	0.428690	+	0.742514i
$502$	0.668198	+	2.49375i	0.0298231	+	0.111301i
$503$	−3.66588	+	41.9012i	−0.163453	+	1.86828i	0.264375	+	0.964420i	$0.414834\pi$
$503$	−3.66588	+	41.9012i	−0.163453	+	1.86828i	−0.427828	+	0.903860i	$0.640721\pi$
$504$	2.26011	−	1.89646i	0.100673	−	0.0844750i
$505$		0			0
$506$	−0.277189	+	0.160035i	−0.0123225	+	0.00711442i
$507$	5.65732	−	2.63805i	0.251250	−	0.117160i
$508$	−7.58823	+	5.31334i	−0.336673	+	0.235741i
$509$	−3.21951	−	18.2588i	−0.142702	−	0.809306i	−0.969183	−	0.246341i	$-0.920772\pi$
$509$	−3.21951	−	18.2588i	−0.142702	−	0.809306i	0.826481	−	0.562965i	$-0.190339\pi$
$510$		0			0
$511$	11.9101	+	9.99379i	0.526873	+	0.442099i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	1.57482	−	1.13708i	0.0695299	−	0.0502034i
$514$		−	6.36184i		−	0.280609i
$515$		0			0
$516$	−5.51826	−	15.1613i	−0.242928	−	0.667438i
$517$	−0.100354	+	0.143321i	−0.00441357	+	0.00630323i
$518$	0.698797	+	0.997986i	0.0307034	+	0.0438490i
$519$	−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	$0.285766\pi$
$522$	−7.67355	−	0.671349i	−0.335862	−	0.0293841i
$523$	23.4603	+	2.05251i	1.02585	+	0.0897501i	0.587639	−	0.809123i	$-0.300057\pi$
$523$	23.4603	+	2.05251i	1.02585	+	0.0897501i	0.438209	+	0.898873i	$0.355613\pi$
$524$	9.07888	+	5.24170i	0.396613	+	0.228985i
$525$		0			0
$526$	−7.06330	+	19.4063i	−0.307975	+	0.846153i
$527$	−4.32467	−	6.17627i	−0.188386	−	0.269042i
$528$	0.422429	−	0.603291i	0.0183838	−	0.0262549i
$529$	−7.49081	−	20.5808i	−0.325688	−	0.894819i
$530$		0			0
$531$		−	21.5107i		−	0.933485i
$532$	4.39491	−	1.24619i	0.190543	−	0.0540290i
$533$	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
$537$	41.5529	−	29.0957i	1.79314	−	1.25557i
$538$	−19.2222	+	8.96346i	−0.828728	+	0.386442i
$539$	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	$0.201578\pi$
$542$	0.340647	−	3.89361i	0.0146320	−	0.167245i
$543$	3.11893	+	11.6400i	0.133846	+	0.499520i
$544$	−0.984808	−	1.70574i	−0.0422233	−	0.0731329i
$545$		0			0
$546$	8.03074	+	1.41604i	0.343684	+	0.0606008i
$547$	36.2732	+	25.3987i	1.55093	+	1.08597i	0.960278	+	0.279045i	$0.0900177\pi$
$547$	36.2732	+	25.3987i	1.55093	+	1.08597i	0.590651	+	0.806927i	$0.298871\pi$
$548$	9.44768	−	20.2606i	0.403585	−	0.865490i
$549$	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
$553$	0.225605	+	2.57868i	0.00959370	+	0.109656i
$554$	−10.9324	+	3.97906i	−0.464472	+	0.169054i
$555$		0			0
$556$	2.26723	−	12.8581i	0.0961518	−	0.545304i
$557$	−16.6892	−	35.7902i	−0.707145	−	1.51648i	−0.850028	−	0.526738i	$-0.823415\pi$
$557$	−16.6892	−	35.7902i	−0.707145	−	1.51648i	0.142883	−	0.989740i	$-0.454363\pi$
$558$	10.4096	+	2.78925i	0.440674	+	0.118078i
$559$	10.7943	−	18.6962i	0.456549	−	0.790767i
$560$		0			0
$561$	−0.932419	−	1.11121i	−0.0393667	−	0.0469155i
$562$	−5.35594	+	1.43512i	−0.225927	+	0.0605369i
$563$	2.76551	−	10.3210i	0.116552	−	0.434979i	−0.882846	−	0.469662i	$-0.844376\pi$
$563$	2.76551	−	10.3210i	0.116552	−	0.434979i	0.999398	+	0.0346836i	$0.0110423\pi$
$564$	−1.29817	−	0.472497i	−0.0546630	−	0.0198957i
$565$		0			0
$566$	15.8812	−	2.80028i	0.667536	−	0.117705i
$567$	−9.04251	−	4.21659i	−0.379750	−	0.177080i
$568$	−1.36287	+	0.119236i	−0.0571849	+	0.00500303i
$569$	−30.8012			−1.29125			−0.645626	−	0.763654i	$-0.723403\pi$
$569$	−30.8012			−1.29125			−0.645626	+	0.763654i	$0.723403\pi$
$570$		0			0
$571$	19.0310			0.796421			0.398211	−	0.917294i	$-0.369631\pi$
$571$	19.0310			0.796421			0.398211	+	0.917294i	$0.369631\pi$
$572$	0.981702	−	0.0858878i	0.0410470	−	0.00359115i
$573$	−25.7103	−	11.9889i	−1.07406	−	0.500843i
$574$	−7.51044	+	1.32429i	−0.313480	+	0.0552749i
$575$		0			0
$576$	2.64543	+	0.962858i	0.110226	+	0.0401191i
$577$	1.96625	−	7.33814i	0.0818560	−	0.305491i	−0.912844	−	0.408308i	$-0.866119\pi$
$577$	1.96625	−	7.33814i	0.0818560	−	0.305491i	0.994700	+	0.102817i	$0.0327857\pi$
$578$	12.6735	−	3.39586i	0.527150	−	0.141249i
$579$	16.0814	+	19.1650i	0.668319	+	0.796471i
$580$		0			0
$581$	−3.90239	+	6.75914i	−0.161898	+	0.280416i
$582$	−29.9661	−	8.02940i	−1.24214	−	0.332829i
$583$	1.42331	+	3.05229i	0.0589473	+	0.126413i
$584$	−2.57613	+	14.6099i	−0.106601	+	0.604564i
$585$		0			0
$586$	−29.8837	+	10.8768i	−1.23449	+	0.449316i
$587$	2.10433	+	24.0526i	0.0868549	+	0.992757i	0.907148	+	0.420813i	$0.138255\pi$
$587$	2.10433	+	24.0526i	0.0868549	+	0.992757i	−0.820293	+	0.571944i	$0.806189\pi$
$588$	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
$592$	−0.491295	+	1.05359i	−0.0201921	+	0.0433021i
$593$	8.33458	+	5.83594i	0.342260	+	0.239653i	0.732050	−	0.681251i	$-0.238564\pi$
$593$	8.33458	+	5.83594i	0.342260	+	0.239653i	−0.389790	+	0.920904i	$0.627452\pi$
$594$	−0.134029	−	0.0236329i	−0.00549927	−	0.000969669i
$595$		0			0
$596$	−7.97431	−	13.8119i	−0.326640	−	0.565758i
$597$	16.7198	+	62.3993i	0.684297	+	2.55383i
$598$	0.294726	−	3.36873i	0.0120522	−	0.137758i
$599$	−27.7768	+	23.3075i	−1.13493	+	0.952320i	−0.999261	−	0.0384346i	$-0.987763\pi$
$599$	−27.7768	+	23.3075i	−1.13493	+	0.952320i	−0.135669	+	0.990754i	$0.543318\pi$
$600$		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	$0.351270\pi$
$602$	−6.35490	+	2.96334i	−0.259007	+	0.120777i
$603$	−13.0987	+	9.17178i	−0.533418	+	0.373504i
$604$	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	$0.332765\pi$
$608$	3.12657	+	3.03719i	0.126799	+	0.123174i
$609$			6.91496i			0.280208i
$610$		0			0
$611$	−0.632226	−	1.73703i	−0.0255771	−	0.0702726i
$612$	3.18041	−	4.54210i	0.128560	−	0.183603i
$613$	−19.0274	−	27.1740i	−0.768511	−	1.09755i	−0.992415	−	0.122937i	$-0.960769\pi$
$613$	−19.0274	−	27.1740i	−0.768511	−	1.09755i	0.223903	−	0.974611i	$-0.428120\pi$
$614$	−11.0974	+	30.4898i	−0.447854	+	1.23047i
$615$		0			0
$616$	−0.277189	−	0.160035i	−0.0111683	−	0.00644799i
$617$	−12.3621	−	1.08154i	−0.497678	−	0.0435411i	−0.164446	−	0.986386i	$-0.552584\pi$
$617$	−12.3621	−	1.08154i	−0.497678	−	0.0435411i	−0.333232	+	0.942845i	$0.608139\pi$
$618$	−30.7039	−	2.68624i	−1.23509	−	0.108057i
$619$	−3.37305	−	1.94743i	−0.135574	−	0.0782740i	0.430679	−	0.902505i	$-0.358274\pi$
$619$	−3.37305	−	1.94743i	−0.135574	−	0.0782740i	−0.566253	+	0.824231i	$0.691608\pi$
$620$		0			0
$621$	−0.159729	+	0.438852i	−0.00640971	+	0.0176105i
$622$	−6.95364	−	9.93083i	−0.278816	−	0.398190i
$623$	4.92227	−	7.02973i	0.197207	−	0.281640i
$624$	2.66128	+	7.31180i	0.106536	+	0.292706i
$625$		0			0
$626$			8.36354i			0.334274i
$627$	2.65610	+	1.80300i	0.106075	+	0.0720049i
$628$	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	$-0.117543\pi$
$632$	−2.02326	+	1.41670i	−0.0804809	+	0.0563533i
$633$	−1.25205	+	0.583842i	−0.0497647	+	0.0232056i
$634$	0.350452	−	0.202333i	0.0139182	−	0.00803569i
$635$		0			0
$636$	−20.3708	+	17.0931i	−0.807753	+	0.677786i
$637$	−1.65969	+	18.9704i	−0.0657594	+	0.751633i
$638$	0.216280	+	0.807170i	0.00856263	+	0.0319562i
$639$	−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	$0.616282\pi$
$642$	18.0993	+	12.6733i	0.714322	+	0.500173i
$643$	−6.26598	+	13.4374i	−0.247106	+	0.529921i	−0.990265	−	0.139194i	$-0.955549\pi$
$643$	−6.26598	+	13.4374i	−0.247106	+	0.529921i	0.743159	+	0.669115i	$0.233327\pi$
$644$	−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	$0.0515437\pi$
$647$	29.2043	+	29.2043i	1.14814	+	1.14814i	0.161223	+	0.986918i	$0.448456\pi$
$648$	−0.829743	−	9.48400i	−0.0325954	−	0.372567i
$649$	−2.19285	+	0.798133i	−0.0860770	+	0.0313295i
$650$		0			0
$651$	1.67996	−	9.52752i	0.0658428	−	0.373413i
$652$	−3.58234	−	7.68236i	−0.140295	−	0.300864i
$653$	−21.0887	−	5.65070i	−0.825264	−	0.221129i	−0.178618	−	0.983919i	$-0.557162\pi$
$653$	−21.0887	−	5.65070i	−0.825264	−	0.221129i	−0.646647	+	0.762790i	$0.723829\pi$
$654$	16.4553	−	28.5014i	0.643453	−	1.11449i
$655$		0			0
$656$	−4.67752	−	5.57445i	−0.182626	−	0.217646i
$657$	−40.3414	+	10.8094i	−1.57387	+	0.421717i
$658$	−0.155391	+	0.579928i	−0.00605778	+	0.0226079i
$659$	3.10013	+	1.12836i	0.120764	+	0.0439545i	0.401695	−	0.915773i	$-0.368421\pi$
$659$	3.10013	+	1.12836i	0.120764	+	0.0439545i	−0.280931	+	0.959728i	$0.590643\pi$
$660$		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	$0.641165\pi$
$662$	20.4971	+	9.55795i	0.796642	+	0.371480i
$663$	15.2674	−	1.33572i	0.592936	−	0.0518752i
$664$	−7.44723			−0.289009
$665$		0			0
$666$	−3.27269			−0.126814
$667$	2.85661	−	0.249921i	0.110609	−	0.00967699i
$668$	7.21250	+	3.36324i	0.279060	+	0.130128i
$669$	6.46415	−	1.13980i	0.249919	−	0.0440674i
$670$		0			0
$671$	−3.88161	−	1.41279i	−0.149848	−	0.0545401i
$672$	0.654100	−	2.44114i	0.0252325	−	0.0941689i
$673$	39.6237	−	10.6171i	1.52738	−	0.409261i	0.605217	−	0.796060i	$-0.293086\pi$
$673$	39.6237	−	10.6171i	1.52738	−	0.409261i	0.922164	+	0.386800i	$0.126420\pi$
$674$	7.14879	+	8.51960i	0.275361	+	0.328163i
$675$		0			0
$676$	1.29426	−	2.24173i	0.0497793	−	0.0862204i
$677$	−21.8743	−	5.86119i	−0.840696	−	0.225264i	−0.187321	−	0.982299i	$-0.559981\pi$
$677$	−21.8743	−	5.86119i	−0.840696	−	0.225264i	−0.653374	+	0.757035i	$0.726647\pi$
$678$	−0.456888	−	0.979800i	−0.0175467	−	0.0376290i
$679$	−2.34121	+	13.2777i	−0.0898474	+	0.509550i
$680$		0			0
$681$	43.1343	−	15.6996i	1.65291	−	0.601611i
$682$	−0.101896	−	1.16467i	−0.00390178	−	0.0445976i
$683$	−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
$687$	−9.62635	+	20.6438i	−0.367268	+	0.787609i
$688$	−5.48065	−	3.83759i	−0.208948	−	0.146307i
$689$	−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	$0.947397\pi$
$692$	2.72284	+	10.1618i	0.103507	+	0.386292i
$693$	0.0785329	−	0.897635i	0.00298322	−	0.0340983i
$694$	7.68480	−	6.44831i	0.291711	−	0.244775i
$695$		0			0
$696$	−5.71419	+	3.29909i	−0.216596	+	0.125052i
$697$	−12.9899	+	6.05728i	−0.492027	+	0.229436i
$698$	11.8865	−	8.32302i	0.449911	−	0.315031i
$699$	−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
$703$	−4.62304	−	2.07469i	−0.174361	−	0.0782485i
$704$		−	0.305407i		−	0.0115105i
$705$		0			0
$706$	3.50774	+	9.63744i	0.132016	+	0.362710i
$707$	−4.62998	+	6.61230i	−0.174128	+	0.248681i
$708$	−10.5686	−	15.0936i	−0.397193	−	0.567250i
$709$	−10.1395	+	27.8580i	−0.380797	+	1.04623i	0.590225	+	0.807239i	$0.299039\pi$
$709$	−10.1395	+	27.8580i	−0.380797	+	1.04623i	−0.971022	+	0.238991i	$0.923183\pi$
$710$		0			0
$711$	−6.02182	−	3.47670i	−0.225836	−	0.130386i
$712$	8.15742	+	0.713682i	0.305712	+	0.0267464i
$713$	−3.99659	−	0.349657i	−0.149674	−	0.0130947i
$714$	−4.31082	−	2.48886i	−0.161329	−	0.0931431i
$715$		0			0
$716$	7.19459	−	19.7670i	0.268875	−	0.738727i
$717$	26.5502	+	37.9175i	0.991534	+	1.41606i
$718$	−12.2051	+	17.4307i	−0.455492	+	0.650509i
$719$	14.3373	+	39.3915i	0.534692	+	1.46905i	0.853428	+	0.521210i	$0.174519\pi$
$719$	14.3373	+	39.3915i	0.534692	+	1.46905i	−0.318736	+	0.947843i	$0.603258\pi$
$720$		0			0
$721$			13.3947i			0.498844i
$722$	−13.0398	+	13.8189i	−0.485292	+	0.514288i
$723$	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
$727$	−27.6836	+	19.3843i	−1.02673	+	0.718922i	−0.960329	−	0.278871i	$-0.910040\pi$
$727$	−27.6836	+	19.3843i	−1.02673	+	0.718922i	−0.0663988	+	0.997793i	$0.521151\pi$
$728$	3.06477	−	1.42912i	0.113588	−	0.0529669i
$729$	20.4188	−	11.7888i	0.756252	−	0.436622i
$730$		0			0
$731$	−10.0949	+	8.47065i	−0.373374	+	0.313298i
$732$	2.84266	−	32.4918i	0.105068	−	1.20093i
$733$	7.13547	+	26.6299i	0.263554	+	0.983599i	0.963129	+	0.269039i	$0.0867061\pi$
$733$	7.13547	+	26.6299i	0.263554	+	0.983599i	−0.699575	+	0.714559i	$0.746627\pi$
$734$	−12.2785	−	21.2670i	−0.453208	−	0.784978i
$735$		0			0
$736$	−1.03209	−	0.181985i	−0.0380433	−	0.00670806i
$737$	1.42101	+	0.994999i	0.0523434	+	0.0366512i
$738$	8.65778	−	18.5667i	0.318697	−	0.683449i
$739$	−0.0819052	+	0.0976108i	−0.00301293	+	0.00359067i	−0.767549	−	0.640991i	$-0.778524\pi$
$739$	−0.0819052	+	0.0976108i	−0.00301293	+	0.00359067i	0.764536	+	0.644581i	$0.222968\pi$
$740$		0			0
$741$	−31.6999	+	12.0612i	−1.16452	+	0.443078i
$742$	8.17187	+	8.17187i	0.299999	+	0.299999i
$743$	−2.25026	−	25.7206i	−0.0825540	−	0.943597i	−0.918665	−	0.395037i	$-0.870732\pi$
$743$	−2.25026	−	25.7206i	−0.0825540	−	0.943597i	0.836111	−	0.548560i	$-0.184824\pi$
$744$	8.67458	−	3.15729i	0.318026	−	0.115752i
$745$		0			0
$746$	2.13634	−	12.1158i	0.0782171	−	0.443591i
$747$	−8.86041	−	19.0012i	−0.324185	−	0.695218i
$748$	−0.581038	−	0.155689i	−0.0212449	−	0.00569254i
$749$	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	$0.947845\pi$
$752$	−0.553361	+	0.148273i	−0.0201790	+	0.00540694i
$753$	−1.61134	+	6.01361i	−0.0587206	+	0.219148i
$754$	−8.29628	−	3.01960i	−0.302133	−	0.109967i
$755$		0			0
$756$	−0.459922	+	0.0810966i	−0.0167272	+	0.00294946i
$757$	23.8409	+	11.1172i	0.866511	+	0.404061i	0.804456	−	0.594012i	$-0.202457\pi$
$757$	23.8409	+	11.1172i	0.866511	+	0.404061i	0.0620549	+	0.998073i	$0.480235\pi$
$758$	23.7734	−	2.07990i	0.863488	−	0.0755454i
$759$	−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	$0.360186\pi$
$762$	−22.2537	+	1.94695i	−0.806168	+	0.0705305i
$763$	−12.9627	−	6.04459i	−0.469280	−	0.218829i
$764$	−11.5851	+	2.04277i	−0.419134	+	0.0739047i
$765$		0			0
$766$	1.75877	+	0.640140i	0.0635470	+	0.0231292i
$767$	6.38112	−	23.8147i	0.230409	−	0.859897i
$768$	2.32931	−	0.624135i	0.0840516	−	0.0225215i
$769$	3.70950	+	4.42081i	0.133768	+	0.159418i	0.828770	−	0.559589i	$-0.189041\pi$
$769$	3.70950	+	4.42081i	0.133768	+	0.159418i	−0.695002	+	0.719008i	$0.744597\pi$
$770$		0			0
$771$	7.67071	−	13.2861i	0.276254	−	0.478486i
$772$	10.0211	+	2.68515i	0.360668	+	0.0966408i
$773$	−17.2425	−	36.9767i	−0.620170	−	1.32996i	−0.925874	−	0.377832i	$-0.876670\pi$
$773$	−17.2425	−	36.9767i	−0.620170	−	1.32996i	0.305705	−	0.952126i	$-0.401108\pi$
$774$	3.27076	−	18.5494i	0.117565	−	0.666744i
$775$		0			0
$776$	−12.0890	+	4.40003i	−0.433970	+	0.157952i
$777$	0.256058	+	2.92676i	0.00918604	+	0.104997i
$778$	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
$782$	−0.872359	+	1.87078i	−0.0311955	+	0.0668990i
$783$	0.998788	+	0.699359i	0.0356938	+	0.0249930i
$784$	5.81201	+	1.02481i	0.207572	+	0.0366005i
$785$		0			0
$786$	12.6402	+	21.8935i	0.450862	+	0.780915i
$787$	8.78524	+	32.7870i	0.313160	+	1.16873i	0.925690	+	0.378282i	$0.123485\pi$
$787$	8.78524	+	32.7870i	0.313160	+	1.16873i	−0.612530	+	0.790447i	$0.709848\pi$
$788$	−0.434667	+	4.96826i	−0.0154844	+	0.176987i
$789$	−38.1498	+	32.0115i	−1.35817	+	1.13964i
$790$		0			0
$791$	−0.406889	+	0.234917i	−0.0144673	+	0.00835269i
$792$	0.779230	−	0.363361i	0.0276887	−	0.0129115i
$793$	35.7493	−	25.0319i	1.26949	−	0.888909i
$794$	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	$0.179093\pi$
$798$	10.6809	+	2.69657i	0.378099	+	0.0954576i
$799$			1.12836i			0.0399183i
$800$		0			0
$801$	7.88444	+	21.6623i	0.278583	+	0.765400i
$802$	−7.71947	+	11.0245i	−0.272584	+	0.389290i
$803$	2.59877	+	3.71143i	0.0917085	+	0.130973i
$804$	−4.68475	+	12.8712i	−0.165218	+	0.453933i
$805$		0			0
$806$	10.6971	+	6.17598i	0.376790	+	0.217540i
$807$	−50.9512	−	4.45765i	−1.79357	−	0.156917i
$808$	−7.67302	−	0.671303i	−0.269936	−	0.0236163i
$809$	−40.5542	−	23.4140i	−1.42581	−	0.823192i	−0.429024	−	0.903293i	$-0.641143\pi$
$809$	−40.5542	−	23.4140i	−1.42581	−	0.823192i	−0.996787	+	0.0801005i	$0.974476\pi$
$810$		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	$0.103890\pi$
$812$	1.64475	+	2.34894i	0.0577192	+	0.0824316i
$813$	5.40607	−	7.72067i	0.189599	−	0.270776i
$814$	0.121430	+	0.333626i	0.00425611	+	0.0116936i
$815$		0			0
$816$		−	4.74968i		−	0.166272i
$817$	16.3795	−	24.1296i	0.573047	−	0.844189i
$818$	−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	$-0.323912\pi$
$822$	44.1595	−	30.9208i	1.54024	−	1.07849i
$823$	4.47539	−	2.08691i	0.156002	−	0.0727451i	−0.343049	−	0.939318i	$-0.611460\pi$
$823$	4.47539	−	2.08691i	0.156002	−	0.0727451i	0.499051	+	0.866572i	$0.333682\pi$
$824$	−11.0687	+	6.39053i	−0.385597	+	0.222625i
$825$		0			0
$826$	−6.13429	+	5.14728i	−0.213439	+	0.179097i
$827$	1.63390	−	18.6756i	0.0568163	−	0.649413i	−0.913382	−	0.407103i	$-0.866539\pi$
$827$	1.63390	−	18.6756i	0.0568163	−	0.649413i	0.970199	−	0.242311i	$-0.0779053\pi$
$828$	−0.763611	−	2.84984i	−0.0265373	−	0.0990386i
$829$	7.72076	+	13.3727i	0.268153	+	0.464454i	0.968385	−	0.249461i	$-0.0802534\pi$
$829$	7.72076	+	13.3727i	0.268153	+	0.464454i	−0.700232	+	0.713915i	$0.746920\pi$
$830$		0			0
$831$	−27.6288	−	4.87171i	−0.958433	−	0.168998i
$832$	2.64314	+	1.85075i	0.0916345	+	0.0641632i
$833$	4.91253	−	10.5349i	0.170209	−	0.365014i
$834$	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
$838$	−1.70360	−	19.4723i	−0.0588499	−	0.672658i
$839$	46.4177	−	16.8946i	1.60252	−	0.583268i	0.622576	−	0.782560i	$-0.286086\pi$
$839$	46.4177	−	16.8946i	1.60252	−	0.583268i	0.979940	+	0.199292i	$0.0638641\pi$
$840$		0			0
$841$	−3.73577	+	21.1866i	−0.128820	+	0.730572i
$842$	8.62790	+	18.5026i	0.297337	+	0.637641i
$843$	−12.9157	−	3.46075i	−0.444841	−	0.119195i
$844$	−0.286441	+	0.496130i	−0.00985969	+	0.0170775i
$845$		0			0
$846$	−1.03667	−	1.23546i	−0.0356416	−	0.0424760i
$847$	11.0409	−	2.95840i	0.379369	−	0.101652i
$848$	−2.85409	+	10.6516i	−0.0980097	+	0.365777i
$849$	36.5427	+	13.3004i	1.25414	+	0.456470i
$850$		0			0
$851$	1.19981	−	0.211558i	0.0411289	−	0.00725213i
$852$	−2.98999	−	1.39426i	−0.102435	−	0.0477664i
$853$	−25.8602	+	2.26248i	−0.885438	+	0.0774658i	−0.520795	−	0.853682i	$-0.674364\pi$
$853$	−25.8602	+	2.26248i	−0.885438	+	0.0774658i	−0.364643	+	0.931148i	$0.618809\pi$
$854$	−14.1746			−0.485046
$855$		0			0
$856$	9.16250			0.313168
$857$	−40.2799	+	3.52403i	−1.37594	+	0.120379i	−0.751002	−	0.660300i	$-0.770429\pi$
$857$	−40.2799	+	3.52403i	−1.37594	+	0.120379i	−0.624933	+	0.780678i	$0.714874\pi$
$858$	2.15374	+	1.00431i	0.0735276	+	0.0342865i
$859$	−8.58678	+	1.51408i	−0.292977	+	0.0516598i	−0.318205	−	0.948022i	$-0.603080\pi$
$859$	−8.58678	+	1.51408i	−0.292977	+	0.0516598i	0.0252278	+	0.999682i	$0.491969\pi$
$860$		0			0
$861$	−17.2815	−	6.28996i	−0.588953	−	0.214361i
$862$	3.25931	−	12.1639i	0.111012	−	0.414304i
$863$	20.7778	−	5.56739i	0.707284	−	0.189516i	0.112793	−	0.993619i	$-0.464020\pi$
$863$	20.7778	−	5.56739i	0.707284	−	0.189516i	0.594491	+	0.804102i	$0.297354\pi$
$864$	−0.286441	−	0.341367i	−0.00974491	−	0.0116135i
$865$		0			0
$866$	−12.7690	+	22.1166i	−0.433910	+	0.751553i
$867$	30.5619	+	8.18904i	1.03794	+	0.278114i
$868$	−1.69549	−	3.63598i	−0.0575485	−	0.123413i
$869$	−0.130990	+	0.742878i	−0.00444351	+	0.0252004i
$870$		0			0
$871$	−17.2224	+	6.26844i	−0.583559	+	0.212398i
$872$	−1.18946	−	13.5956i	−0.0402801	−	0.460404i
$873$	−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
$877$	6.61953	−	14.1956i	0.223526	−	0.479352i	−0.762279	−	0.647248i	$-0.775920\pi$
$877$	6.61953	−	14.1956i	0.223526	−	0.479352i	0.985805	+	0.167896i	$0.0536974\pi$
$878$	22.1588	+	15.5158i	0.747824	+	0.523632i
$879$	−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	$0.781559\pi$
$882$	4.30013	+	16.0483i	0.144793	+	0.540375i
$883$	1.73826	−	19.8684i	0.0584971	−	0.668625i	−0.909175	−	0.416414i	$-0.863287\pi$
$883$	1.73826	−	19.8684i	0.0584971	−	0.668625i	0.967672	−	0.252211i	$-0.0811578\pi$
$884$	4.86846	−	4.08512i	0.163744	−	0.137398i
$885$		0			0
$886$	11.4937	−	6.63587i	0.386137	−	0.222936i
$887$	9.00491	−	4.19906i	0.302355	−	0.140991i	−0.265520	−	0.964105i	$-0.585543\pi$
$887$	9.00491	−	4.19906i	0.302355	−	0.140991i	0.567875	+	0.823115i	$0.307766\pi$
$888$	−2.29637	+	1.60793i	−0.0770611	+	0.0539587i
$889$	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
$893$	−0.681211	−	2.40242i	−0.0227959	−	0.0803939i
$894$		−	38.4597i		−	1.28628i
$895$		0			0
$896$	−0.358441	−	0.984808i	−0.0119747	−	0.0329001i
$897$	4.67730	−	6.67988i	0.156171	−	0.223035i
$898$	4.34102	+	6.19962i	0.144862	+	0.206884i
$899$	−3.58239	+	9.84255i	−0.119480	+	0.328267i
$900$		0			0
$901$	18.8097	+	10.8598i	0.626643	+	0.361793i
$902$	−2.21397	−	0.193697i	−0.0737171	−	0.00644941i
$903$	−16.8446	−	1.47371i	−0.560552	−	0.0490420i
$904$	−0.388249	−	0.224155i	−0.0129130	−	0.00745530i
$905$		0			0
$906$	−16.4616	+	45.2278i	−0.546899	+	1.50259i
$907$	−10.7526	−	15.3563i	−0.357034	−	0.509898i	0.599950	−	0.800037i	$-0.295187\pi$
$907$	−10.7526	−	15.3563i	−0.357034	−	0.509898i	−0.956984	+	0.290140i	$0.906298\pi$
$908$	10.9181	−	15.5926i	0.362329	−	0.517459i
$909$	−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	$0.875289\pi$
$912$	2.86748	+	10.1127i	0.0949516	+	0.334865i
$913$	−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
$917$	8.99978	−	6.30172i	0.297199	−	0.208101i
$918$	−0.795471	+	0.370934i	−0.0262544	+	0.0122426i
$919$	−18.6072	+	10.7429i	−0.613795	+	0.354375i	−0.774449	−	0.632636i	$-0.781973\pi$
$919$	−18.6072	+	10.7429i	−0.613795	+	0.354375i	0.160654	+	0.987011i	$0.448640\pi$
$920$		0			0
$921$	−59.9384	+	50.2943i	−1.97504	+	1.65725i
$922$	3.38222	−	38.6590i	0.111388	−	1.27317i
$923$	−1.14252	−	4.26394i	−0.0376065	−	0.140349i
$924$	−0.385920	−	0.668434i	−0.0126958	−	0.0219899i
$925$		0			0
$926$	29.8555	+	5.26433i	0.981113	+	0.172997i
$927$	−29.4742	−	20.6380i	−0.968059	−	0.677842i
$928$	−1.15635	+	2.47980i	−0.0379591	+	0.0814036i
$929$	9.67809	−	11.5339i	0.317528	−	0.378415i	−0.583546	−	0.812080i	$-0.698335\pi$
$929$	9.67809	−	11.5339i	0.317528	−	0.378415i	0.901074	+	0.433665i	$0.142780\pi$
$930$		0			0
$931$	−4.09926	+	25.3961i	−0.134348	+	0.832323i
$932$	−16.5423	−	16.5423i	−0.541862	−	0.541862i
$933$	−2.54800	−	29.1238i	−0.0834178	−	0.953470i
$934$	33.0824	−	12.0410i	1.08249	−	0.393994i
$935$		0			0
$936$	−1.57738	+	8.94578i	−0.0515583	+	0.292402i
$937$	−18.1290	−	38.8778i	−0.592248	−	1.27008i	−0.942744	−	0.333517i	$-0.891765\pi$
$937$	−18.1290	−	38.8778i	−0.592248	−	1.27008i	0.350496	−	0.936564i	$-0.386013\pi$
$938$	5.74991	+	1.54068i	0.187741	+	0.0503051i
$939$	−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	$0.980954\pi$
$942$	1.16541	−	0.312272i	0.0379713	−	0.0101744i
$943$	−1.97383	+	7.36644i	−0.0642768	+	0.239884i
$944$	−7.18009	−	2.61334i	−0.233692	−	0.0850570i
$945$		0			0
$946$	−2.01233	+	0.354827i	−0.0654264	+	0.0115364i
$947$	−30.4041	−	14.1777i	−0.988002	−	0.460713i	−0.139682	−	0.990196i	$-0.544608\pi$
$947$	−30.4041	−	14.1777i	−0.988002	−	0.460713i	−0.848320	+	0.529483i	$0.822386\pi$
$948$	−5.93354	+	0.519117i	−0.192712	+	0.0168601i
$949$	−47.8689			−1.55389
$950$		0			0
$951$	0.975844			0.0316439
$952$	−2.05632	+	0.179905i	−0.0666458	+	0.00583075i
$953$	−32.2501	−	15.0385i	−1.04468	−	0.487144i	−0.176974	−	0.984215i	$-0.556631\pi$
$953$	−32.2501	−	15.0385i	−1.04468	−	0.487144i	−0.867710	+	0.497071i	$0.834409\pi$
$954$	−30.5726	+	5.39078i	−0.989825	+	0.174533i
$955$		0			0
$956$	18.0376	+	6.56515i	0.583378	+	0.212332i
$957$	−0.521555	+	1.94647i	−0.0168595	+	0.0629204i
$958$	33.4944	−	8.97479i	1.08215	−	0.289962i
$959$	−15.0595	−	17.9472i	−0.486296	−	0.579545i
$960$		0			0
$961$	−8.17293	+	14.1559i	−0.263643	+	0.456643i
$962$	−3.62322	−	0.970838i	−0.116817	−	0.0313011i
$963$	10.9012	+	23.3776i	0.351285	+	0.753333i
$964$	1.20134	−	6.81315i	0.0386926	−	0.219437i
$965$		0			0
$966$	−2.48886	+	0.905869i	−0.0800776	+	0.0291459i
$967$	1.33516	+	15.2609i	0.0429357	+	0.490758i	0.986969	+	0.160908i	$0.0514424\pi$
$967$	1.33516	+	15.2609i	0.0429357	+	0.490758i	−0.944034	+	0.329849i	$0.893002\pi$
$968$	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	$0.432475\pi$
$972$	9.13740	−	19.5952i	0.293082	−	0.628517i
$973$	−11.2087	−	7.84841i	−0.359334	−	0.251608i
$974$	16.7400	+	2.95171i	0.536384	+	0.0945790i
$975$		0			0
$976$	−6.76264	−	11.7132i	−0.216467	−	0.374932i
$977$	−7.23478	−	27.0006i	−0.231461	−	0.863825i	−0.979712	−	0.200409i	$-0.935773\pi$
$977$	−7.23478	−	27.0006i	−0.231461	−	0.863825i	0.748251	−	0.663416i	$-0.230894\pi$
$978$	1.78155	−	20.3632i	0.0569676	−	0.651143i
$979$	1.91576	−	1.60752i	0.0612281	−	0.0513765i
$980$		0			0
$981$	33.2732	−	19.2103i	1.06233	−	0.613337i
$982$	15.4770	−	7.21704i	0.493891	−	0.230305i
$983$	7.95470	−	5.56994i	0.253716	−	0.177654i	−0.439799	−	0.898096i	$-0.644950\pi$
$983$	7.95470	−	5.56994i	0.253716	−	0.177654i	0.693514	+	0.720443i	$0.256061\pi$
$984$	−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
$988$	−7.89932	+	11.6370i	−0.251311	+	0.370221i
$989$			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	$0.873917\pi$
$992$	2.19569	−	3.13577i	0.0697133	−	0.0995609i
$993$	31.2817	+	44.6749i	0.992695	+	1.41771i
$994$	−0.490376	+	1.34730i	−0.0155538	+	0.0427336i
$995$		0			0
$996$	−15.5528	−	8.97940i	−0.492809	−	0.284523i
$997$	−40.0166	−	3.50100i	−1.26734	−	0.110878i	−0.566418	−	0.824118i	$-0.691671\pi$
$997$	−40.0166	−	3.50100i	−1.26734	−	0.110878i	−0.700920	+	0.713240i	$0.747227\pi$
$998$	−9.06638	−	0.793206i	−0.286991	−	0.0251085i
$999$	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.307.2	yes	24
5.2	odd	4	inner	950.2.bb.a.193.2	yes	24
5.3	odd	4	inner	950.2.bb.a.193.1	✓	24
5.4	even	2	inner	950.2.bb.a.307.1	yes	24
19.13	odd	18	inner	950.2.bb.a.507.1	yes	24
95.13	even	36	inner	950.2.bb.a.393.2	yes	24
95.32	even	36	inner	950.2.bb.a.393.1	yes	24
95.89	odd	18	inner	950.2.bb.a.507.2	yes	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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