LMFDB - Embedded newform 1900.2.s.e.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(49,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1900.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.s (of order $6$, degree $2$, not 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:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.4
Character	$\chi$	$=$	1900.349
Dual form			1900.2.s.e.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36682 + 0.789132i) q^{3} +1.39989i q^{7} +(-0.254541 + 0.440878i) q^{9} +O(q^{10})$	\(q+(-1.36682 + 0.789132i) q^{3} +1.39989i q^{7} +(-0.254541 + 0.440878i) q^{9} -4.67848 q^{11} +(1.20624 + 0.696425i) q^{13} +(-3.76528 + 2.17388i) q^{17} +(0.608224 - 4.31626i) q^{19} +(-1.10470 - 1.91340i) q^{21} +(2.84373 + 1.64183i) q^{23} -5.53826i q^{27} +(1.19642 - 2.07227i) q^{29} -3.94001 q^{31} +(6.39463 - 3.69194i) q^{33} +11.3570i q^{37} -2.19828 q^{39} +(-5.99312 - 10.3804i) q^{41} +(6.37450 - 3.68032i) q^{43} +(-2.56504 - 1.48093i) q^{47} +5.04030 q^{49} +(3.43096 - 5.94260i) q^{51} +(6.60291 + 3.81219i) q^{53} +(2.57476 + 6.37950i) q^{57} +(-5.34285 - 9.25409i) q^{59} +(0.146691 - 0.254076i) q^{61} +(-0.617183 - 0.356331i) q^{63} +(-6.53018 - 3.77020i) q^{67} -5.18249 q^{69} +(-0.0920970 - 0.159517i) q^{71} +(1.59225 - 0.919287i) q^{73} -6.54938i q^{77} +(0.875405 + 1.51625i) q^{79} +(3.60679 + 6.24715i) q^{81} -2.49503i q^{83} +3.77655i q^{87} +(-1.02719 + 1.77915i) q^{89} +(-0.974921 + 1.68861i) q^{91} +(5.38527 - 3.10919i) q^{93} +(0.453081 - 0.261586i) q^{97} +(1.19087 - 2.06264i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^9	$ 24 q + 6 q^{9} + 4 q^{11} + 2 q^{21} - 2 q^{29} + 4 q^{31} - 72 q^{39} - 14 q^{41} - 16 q^{49} + 22 q^{51} - 10 q^{61} + 28 q^{69} + 16 q^{71} - 2 q^{79} + 4 q^{81} + 16 q^{89} + 6 q^{91} + 36 q^{99}+O(q^{100}) $ 24 * q + 6 * q^9 + 4 * q^11 + 2 * q^21 - 2 * q^29 + 4 * q^31 - 72 * q^39 - 14 * q^41 - 16 * q^49 + 22 * q^51 - 10 * q^61 + 28 * q^69 + 16 * q^71 - 2 * q^79 + 4 * q^81 + 16 * q^89 + 6 * q^91 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

$n$	$77$	$401$	$951$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$2$		0			0
$3$	−1.36682	+	0.789132i	−0.789132	+	0.455606i	−0.839657	−	0.543117i	$-0.817244\pi$
$3$	−1.36682	+	0.789132i	−0.789132	+	0.455606i	0.0505248	+	0.998723i	$0.483911\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			1.39989i			0.529110i	0.964371	+	0.264555i	$0.0852251\pi$
$7$			1.39989i			0.529110i	−0.964371	+	0.264555i	$0.914775\pi$
$8$		0			0
$9$	−0.254541	+	0.440878i	−0.0848470	+	0.146959i
$10$		0			0
$11$	−4.67848			−1.41061			−0.705307	−	0.708902i	$-0.749191\pi$
$11$	−4.67848			−1.41061			−0.705307	+	0.708902i	$0.749191\pi$
$12$		0			0
$13$	1.20624	+	0.696425i	0.334552	+	0.193153i	0.657860	−	0.753140i	$-0.271462\pi$
$13$	1.20624	+	0.696425i	0.334552	+	0.193153i	−0.323308	+	0.946294i	$0.604795\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.76528	+	2.17388i	−0.913214	+	0.527244i	−0.881464	−	0.472252i	$-0.843441\pi$
$17$	−3.76528	+	2.17388i	−0.913214	+	0.527244i	−0.0317500	+	0.999496i	$0.510108\pi$
$18$		0			0
$19$	0.608224	−	4.31626i	0.139536	−	0.990217i
$19$	0.608224	−	4.31626i	0.139536	−	0.990217i
$20$		0			0
$21$	−1.10470	−	1.91340i	−0.241066	−	0.417538i
$22$		0			0
$23$	2.84373	+	1.64183i	0.592960	+	0.342345i	0.766267	−	0.642522i	$-0.222112\pi$
$23$	2.84373	+	1.64183i	0.592960	+	0.342345i	−0.173307	+	0.984868i	$0.555445\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	5.53826i		−	1.06584i
$28$		0			0
$29$	1.19642	−	2.07227i	0.222170	−	0.384811i	−0.733296	−	0.679909i	$-0.762019\pi$
$29$	1.19642	−	2.07227i	0.222170	−	0.384811i	0.955467	+	0.295099i	$0.0953525\pi$
$30$		0			0
$31$	−3.94001			−0.707647			−0.353823	−	0.935312i	$-0.615119\pi$
$31$	−3.94001			−0.707647			−0.353823	+	0.935312i	$0.615119\pi$
$32$		0			0
$33$	6.39463	−	3.69194i	1.11316	−	0.642684i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			11.3570i			1.86707i	0.358483	+	0.933536i	$0.383294\pi$
$37$			11.3570i			1.86707i	−0.358483	+	0.933536i	$0.616706\pi$
$38$		0			0
$39$	−2.19828			−0.352007
$40$		0			0
$41$	−5.99312	−	10.3804i	−0.935968	−	1.62114i	−0.772898	−	0.634530i	$-0.781194\pi$
$41$	−5.99312	−	10.3804i	−0.935968	−	1.62114i	−0.163070	−	0.986614i	$-0.552140\pi$
$42$		0			0
$43$	6.37450	−	3.68032i	0.972102	−	0.561243i	0.0722255	−	0.997388i	$-0.476990\pi$
$43$	6.37450	−	3.68032i	0.972102	−	0.561243i	0.899876	+	0.436145i	$0.143657\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.56504	−	1.48093i	−0.374149	−	0.216015i	0.301120	−	0.953586i	$-0.402639\pi$
$47$	−2.56504	−	1.48093i	−0.374149	−	0.216015i	−0.675270	+	0.737571i	$0.735973\pi$
$48$		0			0
$49$	5.04030			0.720042
$50$		0			0
$51$	3.43096	−	5.94260i	0.480431	−	0.832131i
$52$		0			0
$53$	6.60291	+	3.81219i	0.906979	+	0.523645i	0.879458	−	0.475976i	$-0.157905\pi$
$53$	6.60291	+	3.81219i	0.906979	+	0.523645i	0.0275214	+	0.999621i	$0.491239\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.57476	+	6.37950i	0.341036	+	0.844985i
$58$		0			0
$59$	−5.34285	−	9.25409i	−0.695580	−	1.20478i	−0.969985	−	0.243166i	$-0.921814\pi$
$59$	−5.34285	−	9.25409i	−0.695580	−	1.20478i	0.274405	−	0.961614i	$-0.411519\pi$
$60$		0			0
$61$	0.146691	−	0.254076i	0.0187818	−	0.0325311i	−0.856482	−	0.516177i	$-0.827355\pi$
$61$	0.146691	−	0.254076i	0.0187818	−	0.0325311i	0.875264	+	0.483646i	$0.160688\pi$
$62$		0			0
$63$	−0.617183	−	0.356331i	−0.0777577	−	0.0448934i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.53018	−	3.77020i	−0.797789	−	0.460604i	0.0449086	−	0.998991i	$-0.485700\pi$
$67$	−6.53018	−	3.77020i	−0.797789	−	0.460604i	−0.842697	+	0.538388i	$0.819034\pi$
$68$		0			0
$69$	−5.18249			−0.623898
$70$		0			0
$71$	−0.0920970	−	0.159517i	−0.0109299	−	0.0189311i	0.860509	−	0.509436i	$-0.170146\pi$
$71$	−0.0920970	−	0.159517i	−0.0109299	−	0.0189311i	−0.871439	+	0.490505i	$0.836812\pi$
$72$		0			0
$73$	1.59225	−	0.919287i	0.186359	−	0.107594i	−0.403918	−	0.914795i	$-0.632352\pi$
$73$	1.59225	−	0.919287i	0.186359	−	0.107594i	0.590277	+	0.807201i	$0.299019\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	6.54938i		−	0.746371i
$78$		0			0
$79$	0.875405	+	1.51625i	0.0984907	+	0.170591i	0.911060	−	0.412273i	$-0.135265\pi$
$79$	0.875405	+	1.51625i	0.0984907	+	0.170591i	−0.812569	+	0.582864i	$0.801932\pi$
$80$		0			0
$81$	3.60679	+	6.24715i	0.400755	+	0.694128i
$82$		0			0
$83$		−	2.49503i		−	0.273866i	−0.990580	−	0.136933i	$-0.956276\pi$
$83$		−	2.49503i		−	0.273866i	0.990580	−	0.136933i	$-0.0437244\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			3.77655i			0.404888i
$88$		0			0
$89$	−1.02719	+	1.77915i	−0.108882	+	0.188590i	−0.915318	−	0.402733i	$-0.868060\pi$
$89$	−1.02719	+	1.77915i	−0.108882	+	0.188590i	0.806435	+	0.591322i	$0.201394\pi$
$90$		0			0
$91$	−0.974921	+	1.68861i	−0.102199	+	0.177015i
$92$		0			0
$93$	5.38527	−	3.10919i	0.558427	−	0.322408i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.453081	−	0.261586i	0.0460034	−	0.0265601i	−0.476822	−	0.879000i	$-0.658211\pi$
$97$	0.453081	−	0.261586i	0.0460034	−	0.0265601i	0.522825	+	0.852440i	$0.324878\pi$
$98$		0			0
$99$	1.19087	−	2.06264i	0.119686	−	0.207303i
$100$		0			0
$101$	1.61367	−	2.79497i	0.160567	−	0.278110i	−0.774505	−	0.632567i	$-0.782001\pi$
$101$	1.61367	−	2.79497i	0.160567	−	0.278110i	0.935072	+	0.354458i	$0.115335\pi$
$102$		0			0
$103$		−	13.4295i		−	1.32325i	−0.749835	−	0.661624i	$-0.769867\pi$
$103$		−	13.4295i		−	1.32325i	0.749835	−	0.661624i	$-0.230133\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	14.8197i		−	1.43268i	−0.697752	−	0.716339i	$-0.745816\pi$
$107$		−	14.8197i		−	1.43268i	0.697752	−	0.716339i	$-0.254184\pi$
$108$		0			0
$109$	0.591723	+	1.02489i	0.0566768	+	0.0981671i	0.892972	−	0.450113i	$-0.148616\pi$
$109$	0.591723	+	1.02489i	0.0566768	+	0.0981671i	−0.836295	+	0.548280i	$0.815283\pi$
$110$		0			0
$111$	−8.96214	−	15.5229i	−0.850649	−	1.47337i
$112$		0			0
$113$		−	5.57115i		−	0.524090i	−0.965056	−	0.262045i	$-0.915603\pi$
$113$		−	5.57115i		−	0.524090i	0.965056	−	0.262045i	$-0.0843968\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.614077	+	0.354537i	−0.0567714	+	0.0327770i
$118$		0			0
$119$	−3.04321	−	5.27099i	−0.278970	−	0.483191i
$120$		0			0
$121$	10.8882			0.989834
$122$		0			0
$123$	16.3830	+	9.45873i	1.47721	+	0.852865i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.91161	−	1.68102i	−0.258363	−	0.149166i	0.365224	−	0.930920i	$-0.380992\pi$
$127$	−2.91161	−	1.68102i	−0.258363	−	0.149166i	−0.623588	+	0.781753i	$0.714326\pi$
$128$		0			0
$129$	−5.80851	+	10.0606i	−0.511411	+	0.885790i
$130$		0			0
$131$	3.73438	+	6.46814i	0.326275	+	0.565124i	0.981769	−	0.190075i	$-0.0608733\pi$
$131$	3.73438	+	6.46814i	0.326275	+	0.565124i	−0.655495	+	0.755200i	$0.727540\pi$
$132$		0			0
$133$	6.04230	+	0.851450i	0.523934	+	0.0738300i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.17247	+	2.40898i	0.356478	+	0.205813i	0.667535	−	0.744579i	$-0.267350\pi$
$137$	4.17247	+	2.40898i	0.356478	+	0.205813i	−0.311057	+	0.950391i	$0.600683\pi$
$138$		0			0
$139$	10.7854	−	18.6809i	0.914807	−	1.58449i	0.107624	−	0.994192i	$-0.465676\pi$
$139$	10.7854	−	18.6809i	0.914807	−	1.58449i	0.807183	−	0.590301i	$-0.200991\pi$
$140$		0			0
$141$	4.67458			0.393671
$142$		0			0
$143$	−5.64338	−	3.25821i	−0.471923	−	0.272465i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−6.88916	+	3.97746i	−0.568208	+	0.328055i
$148$		0			0
$149$	−11.6341	−	20.1508i	−0.953102	−	1.65082i	−0.738652	−	0.674087i	$-0.764537\pi$
$149$	−11.6341	−	20.1508i	−0.953102	−	1.65082i	−0.214450	−	0.976735i	$-0.568796\pi$
$150$		0			0
$151$	10.2567			0.834682			0.417341	−	0.908750i	$-0.362962\pi$
$151$	10.2567			0.834682			0.417341	+	0.908750i	$0.362962\pi$
$152$		0			0
$153$		−	2.21337i		−	0.178940i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−19.4669	+	11.2392i	−1.55363	+	0.896988i	−0.555786	+	0.831325i	$0.687583\pi$
$157$	−19.4669	+	11.2392i	−1.55363	+	0.896988i	−0.997842	+	0.0656625i	$0.979084\pi$
$158$		0			0
$159$	−12.0333			−0.954302
$160$		0			0
$161$	−2.29839	+	3.98093i	−0.181138	+	0.313741i
$162$		0			0
$163$		−	7.27491i		−	0.569815i	−0.958555	−	0.284907i	$-0.908037\pi$
$163$		−	7.27491i		−	0.569815i	0.958555	−	0.284907i	$-0.0919629\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.92075	−	3.41834i	−0.458161	−	0.264519i	0.253110	−	0.967438i	$-0.418547\pi$
$167$	−5.92075	−	3.41834i	−0.458161	−	0.264519i	−0.711271	+	0.702918i	$0.751880\pi$
$168$		0			0
$169$	−5.52999	−	9.57822i	−0.425383	−	0.736786i
$170$		0			0
$171$	1.74812	+	1.36682i	0.133682	+	0.104523i
$172$		0			0
$173$	6.21780	−	3.58985i	0.472731	−	0.272931i	−0.244651	−	0.969611i	$-0.578674\pi$
$173$	6.21780	−	3.58985i	0.472731	−	0.272931i	0.717382	+	0.696680i	$0.245340\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	14.6054	+	8.43243i	1.09781	+	0.633820i
$178$		0			0
$179$	3.47867			0.260008			0.130004	−	0.991513i	$-0.458501\pi$
$179$	3.47867			0.260008			0.130004	+	0.991513i	$0.458501\pi$
$180$		0			0
$181$	9.22373	−	15.9760i	0.685594	−	1.18748i	−0.287655	−	0.957734i	$-0.592876\pi$
$181$	9.22373	−	15.9760i	0.685594	−	1.18748i	0.973250	−	0.229750i	$-0.0737909\pi$
$182$		0			0
$183$			0.463034i			0.0342284i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	17.6158	−	10.1705i	1.28819	−	0.743739i
$188$		0			0
$189$	7.75298			0.563946
$190$		0			0
$191$	−25.1007			−1.81622			−0.908112	−	0.418727i	$-0.862477\pi$
$191$	−25.1007			−1.81622			−0.908112	+	0.418727i	$0.862477\pi$
$192$		0			0
$193$	9.80083	−	5.65851i	0.705479	−	0.407309i	−0.103906	−	0.994587i	$-0.533134\pi$
$193$	9.80083	−	5.65851i	0.705479	−	0.407309i	0.809385	+	0.587279i	$0.199801\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	10.1926i		−	0.726195i	−0.931751	−	0.363098i	$-0.881719\pi$
$197$		−	10.1926i		−	0.726195i	0.931751	−	0.363098i	$-0.118281\pi$
$198$		0			0
$199$	−10.2142	+	17.6916i	−0.724068	+	1.25412i	0.235289	+	0.971926i	$0.424396\pi$
$199$	−10.2142	+	17.6916i	−0.724068	+	1.25412i	−0.959357	+	0.282197i	$0.908937\pi$
$200$		0			0
$201$	11.9008			0.839414
$202$		0			0
$203$	2.90096	+	1.67487i	0.203607	+	0.117553i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.44769	+	0.835827i	−0.100622	+	0.0580940i
$208$		0			0
$209$	−2.84556	+	20.1935i	−0.196832	+	1.39681i
$210$		0			0
$211$	−0.0585254	−	0.101369i	−0.00402905	−	0.00697853i	0.864004	−	0.503485i	$-0.167949\pi$
$211$	−0.0585254	−	0.101369i	−0.00402905	−	0.00697853i	−0.868033	+	0.496507i	$0.834616\pi$
$212$		0			0
$213$	0.251759	+	0.145353i	0.0172503	+	0.00995945i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	5.51560i		−	0.374423i
$218$		0			0
$219$	−1.45088	+	2.51299i	−0.0980412	+	0.169812i
$220$		0			0
$221$	−6.05578			−0.407356
$222$		0			0
$223$	−11.7930	+	6.80869i	−0.789718	+	0.455944i	−0.839863	−	0.542798i	$-0.817365\pi$
$223$	−11.7930	+	6.80869i	−0.789718	+	0.455944i	0.0501456	+	0.998742i	$0.484031\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			5.84713i			0.388088i	0.980993	+	0.194044i	$0.0621604\pi$
$227$			5.84713i			0.388088i	−0.980993	+	0.194044i	$0.937840\pi$
$228$		0			0
$229$	23.9558			1.58305			0.791523	−	0.611140i	$-0.209289\pi$
$229$	23.9558			1.58305			0.791523	+	0.611140i	$0.209289\pi$
$230$		0			0
$231$	5.16832	+	8.95180i	0.340051	+	0.588985i
$232$		0			0
$233$	−17.0582	+	9.84858i	−1.11752	+	0.645202i	−0.940767	−	0.339053i	$-0.889893\pi$
$233$	−17.0582	+	9.84858i	−1.11752	+	0.645202i	−0.176755	+	0.984255i	$0.556560\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−2.39304	−	1.38162i	−0.155444	−	0.0897459i
$238$		0			0
$239$	18.6424			1.20587			0.602937	−	0.797789i	$-0.293997\pi$
$239$	18.6424			1.20587			0.602937	+	0.797789i	$0.293997\pi$
$240$		0			0
$241$	−3.57780	+	6.19693i	−0.230466	+	0.399179i	−0.957945	−	0.286951i	$-0.907358\pi$
$241$	−3.57780	+	6.19693i	−0.230466	+	0.399179i	0.727479	+	0.686130i	$0.240692\pi$
$242$		0			0
$243$	4.52916	+	2.61491i	0.290546	+	0.167747i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.73961	−	4.78287i	0.237946	−	0.304327i
$248$		0			0
$249$	1.96891	+	3.41025i	0.124775	+	0.216116i
$250$		0			0
$251$	−3.67103	+	6.35840i	−0.231713	+	0.401339i	−0.958312	−	0.285723i	$-0.907766\pi$
$251$	−3.67103	+	6.35840i	−0.231713	+	0.401339i	0.726599	+	0.687062i	$0.241100\pi$
$252$		0			0
$253$	−13.3044	−	7.68127i	−0.836438	−	0.482917i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.91565	−	4.57010i	−0.493764	−	0.285075i	0.232370	−	0.972627i	$-0.425352\pi$
$257$	−7.91565	−	4.57010i	−0.493764	−	0.285075i	−0.726135	+	0.687552i	$0.758685\pi$
$258$		0			0
$259$	−15.8985			−0.987887
$260$		0			0
$261$	0.609078	+	1.05495i	0.0377010	+	0.0653001i
$262$		0			0
$263$	−20.6505	+	11.9226i	−1.27336	+	0.735177i	−0.975619	−	0.219469i	$-0.929568\pi$
$263$	−20.6505	+	11.9226i	−1.27336	+	0.735177i	−0.297744	+	0.954646i	$0.596234\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	3.24236i		−	0.198429i
$268$		0			0
$269$	7.56760	+	13.1075i	0.461405	+	0.799176i	0.999031	−	0.0440068i	$-0.0140123\pi$
$269$	7.56760	+	13.1075i	0.461405	+	0.799176i	−0.537627	+	0.843183i	$0.680679\pi$
$270$		0			0
$271$	−0.744750	−	1.28994i	−0.0452403	−	0.0783586i	0.842519	−	0.538667i	$-0.181072\pi$
$271$	−0.744750	−	1.28994i	−0.0452403	−	0.0783586i	−0.887759	+	0.460309i	$0.847739\pi$
$272$		0			0
$273$		−	3.07737i		−	0.186251i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			13.8346i			0.831241i	0.909538	+	0.415621i	$0.136436\pi$
$277$			13.8346i			0.831241i	−0.909538	+	0.415621i	$0.863564\pi$
$278$		0			0
$279$	1.00289	−	1.73706i	0.0600417	−	0.103995i
$280$		0			0
$281$	−0.437342	+	0.757498i	−0.0260896	+	0.0451885i	−0.878775	−	0.477236i	$-0.841639\pi$
$281$	−0.437342	+	0.757498i	−0.0260896	+	0.0451885i	0.852686	+	0.522424i	$0.174972\pi$
$282$		0			0
$283$	−11.3099	+	6.52975i	−0.672301	+	0.388153i	−0.796948	−	0.604048i	$-0.793554\pi$
$283$	−11.3099	+	6.52975i	−0.672301	+	0.388153i	0.124647	+	0.992201i	$0.460220\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	14.5314	−	8.38974i	0.857764	−	0.495230i
$288$		0			0
$289$	0.951541	−	1.64812i	0.0559730	−	0.0969481i
$290$		0			0
$291$	−0.412852	+	0.715081i	−0.0242018	+	0.0419188i
$292$		0			0
$293$			13.4807i			0.787548i	0.919207	+	0.393774i	$0.128831\pi$
$293$			13.4807i			0.787548i	−0.919207	+	0.393774i	$0.871169\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			25.9106i			1.50349i
$298$		0			0
$299$	2.28682	+	3.96089i	0.132250	+	0.229064i
$300$		0			0
$301$	5.15206	+	8.92362i	0.296960	+	0.514349i
$302$		0			0
$303$			5.09361i			0.292620i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	20.7403	−	11.9744i	1.18371	−	0.683418i	0.226843	−	0.973931i	$-0.427159\pi$
$307$	20.7403	−	11.9744i	1.18371	−	0.683418i	0.956871	+	0.290514i	$0.0938261\pi$
$308$		0			0
$309$	10.5977	+	18.3557i	0.602880	+	1.04422i
$310$		0			0
$311$	−20.8129			−1.18019			−0.590095	−	0.807334i	$-0.700910\pi$
$311$	−20.8129			−1.18019			−0.590095	+	0.807334i	$0.700910\pi$
$312$		0			0
$313$	−9.26130	−	5.34701i	−0.523479	−	0.302231i	0.214878	−	0.976641i	$-0.431065\pi$
$313$	−9.26130	−	5.34701i	−0.523479	−	0.302231i	−0.738357	+	0.674410i	$0.764398\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	25.3905	+	14.6592i	1.42607	+	0.823343i	0.996808	−	0.0798355i	$-0.0254395\pi$
$317$	25.3905	+	14.6592i	1.42607	+	0.823343i	0.429264	+	0.903179i	$0.358773\pi$
$318$		0			0
$319$	−5.59745	+	9.69507i	−0.313397	+	0.542819i
$320$		0			0
$321$	11.6947	+	20.2559i	0.652736	+	1.13057i
$322$		0			0
$323$	7.09291	+	17.5741i	0.394660	+	0.977849i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.61755	−	0.933895i	−0.0894509	−	0.0516445i
$328$		0			0
$329$	2.07314	−	3.59078i	0.114296	−	0.197966i
$330$		0			0
$331$	−29.8654			−1.64155			−0.820777	−	0.571249i	$-0.806459\pi$
$331$	−29.8654			−1.64155			−0.820777	+	0.571249i	$0.806459\pi$
$332$		0			0
$333$	−5.00703	−	2.89081i	−0.274384	−	0.158416i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−17.0837	+	9.86326i	−0.930607	+	0.537286i	−0.887003	−	0.461763i	$-0.847217\pi$
$337$	−17.0837	+	9.86326i	−0.930607	+	0.537286i	−0.0436035	+	0.999049i	$0.513884\pi$
$338$		0			0
$339$	4.39637	+	7.61474i	0.238778	+	0.413576i
$340$		0			0
$341$	18.4333			0.998217
$342$		0			0
$343$			16.8551i			0.910092i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.4562	+	8.92364i	−0.829732	+	0.479046i	−0.853761	−	0.520665i	$-0.825684\pi$
$347$	−15.4562	+	8.92364i	−0.829732	+	0.479046i	0.0240287	+	0.999711i	$0.492351\pi$
$348$		0			0
$349$	16.4218			0.879040			0.439520	−	0.898233i	$-0.355149\pi$
$349$	16.4218			0.879040			0.439520	+	0.898233i	$0.355149\pi$
$350$		0			0
$351$	3.85698	−	6.68049i	0.205870	−	0.356578i
$352$		0			0
$353$		−	18.9506i		−	1.00864i	−0.863517	−	0.504319i	$-0.831743\pi$
$353$		−	18.9506i		−	1.00864i	0.863517	−	0.504319i	$-0.168257\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	8.31902	+	4.80299i	0.440289	+	0.254201i
$358$		0			0
$359$	−13.9335	−	24.1335i	−0.735380	−	1.27371i	−0.954557	−	0.298030i	$-0.903671\pi$
$359$	−13.9335	−	24.1335i	−0.735380	−	1.27371i	0.219177	−	0.975685i	$-0.429663\pi$
$360$		0			0
$361$	−18.2601	−	5.25050i	−0.961059	−	0.276342i
$362$		0			0
$363$	−14.8821	+	8.59221i	−0.781110	+	0.450974i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−22.9090	−	13.2265i	−1.19584	−	0.690418i	−0.236214	−	0.971701i	$-0.575907\pi$
$367$	−22.9090	−	13.2265i	−1.19584	−	0.690418i	−0.959625	+	0.281283i	$0.909240\pi$
$368$		0			0
$369$	6.10198			0.317656
$370$		0			0
$371$	−5.33667	+	9.24338i	−0.277066	+	0.479892i
$372$		0			0
$373$			29.3566i			1.52003i	0.649908	+	0.760013i	$0.274807\pi$
$373$			29.3566i			1.52003i	−0.649908	+	0.760013i	$0.725193\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.88636	−	1.66644i	0.148655	−	0.0858260i
$378$		0			0
$379$	−7.49172			−0.384824			−0.192412	−	0.981314i	$-0.561631\pi$
$379$	−7.49172			−0.384824			−0.192412	+	0.981314i	$0.561631\pi$
$380$		0			0
$381$	5.30618			0.271844
$382$		0			0
$383$	−5.96207	+	3.44220i	−0.304648	+	0.175888i	−0.644529	−	0.764580i	$-0.722946\pi$
$383$	−5.96207	+	3.44220i	−0.304648	+	0.175888i	0.339881	+	0.940468i	$0.389613\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			3.74717i			0.190479i
$388$		0			0
$389$	−10.1533	+	17.5861i	−0.514794	+	0.891650i	0.485058	+	0.874482i	$0.338798\pi$
$389$	−10.1533	+	17.5861i	−0.514794	+	0.891650i	−0.999853	+	0.0171681i	$0.994535\pi$
$390$		0			0
$391$	−14.2766			−0.721999
$392$		0			0
$393$	−10.2084	−	5.89384i	−0.514948	−	0.297305i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.48303	+	4.89768i	−0.425751	+	0.245808i	−0.697535	−	0.716551i	$-0.745720\pi$
$397$	−8.48303	+	4.89768i	−0.425751	+	0.245808i	0.271784	+	0.962358i	$0.412386\pi$
$398$		0			0
$399$	−8.93063	+	3.60440i	−0.447091	+	0.180446i
$400$		0			0
$401$	1.78057	+	3.08404i	0.0889174	+	0.154009i	0.907054	−	0.421015i	$-0.138326\pi$
$401$	1.78057	+	3.08404i	0.0889174	+	0.154009i	−0.818136	+	0.575024i	$0.804993\pi$
$402$		0			0
$403$	−4.75261	−	2.74392i	−0.236744	−	0.136684i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	53.1333i		−	2.63372i
$408$		0			0
$409$	10.9468	−	18.9604i	0.541285	−	0.937533i	−0.457546	−	0.889186i	$-0.651271\pi$
$409$	10.9468	−	18.9604i	0.541285	−	0.937533i	0.998831	−	0.0483469i	$-0.0153953\pi$
$410$		0			0
$411$	−7.60400			−0.375078
$412$		0			0
$413$	12.9547	−	7.47943i	0.637462	−	0.368039i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			34.0445i			1.66717i
$418$		0			0
$419$	−25.6000			−1.25064			−0.625322	−	0.780367i	$-0.715032\pi$
$419$	−25.6000			−1.25064			−0.625322	+	0.780367i	$0.715032\pi$
$420$		0			0
$421$	5.61245	+	9.72105i	0.273534	+	0.473775i	0.969764	−	0.244044i	$-0.0784740\pi$
$421$	5.61245	+	9.72105i	0.273534	+	0.473775i	−0.696230	+	0.717819i	$0.745141\pi$
$422$		0			0
$423$	1.30582	−	0.753913i	0.0634909	−	0.0366565i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.355680	+	0.205352i	0.0172125	+	0.00993766i
$428$		0			0
$429$	10.2846			0.496547
$430$		0			0
$431$	13.4540	−	23.3030i	0.648057	−	1.12247i	−0.335529	−	0.942030i	$-0.608915\pi$
$431$	13.4540	−	23.3030i	0.648057	−	1.12247i	0.983586	−	0.180438i	$-0.0577515\pi$
$432$		0			0
$433$	−26.8758	−	15.5168i	−1.29157	−	0.745688i	−0.312637	−	0.949873i	$-0.601212\pi$
$433$	−26.8758	−	15.5168i	−1.29157	−	0.745688i	−0.978932	+	0.204185i	$0.934546\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.81619	−	11.2757i	0.421736	−	0.539389i
$438$		0			0
$439$	11.4195	+	19.7791i	0.545022	+	0.944005i	0.998606	+	0.0527915i	$0.0168119\pi$
$439$	11.4195	+	19.7791i	0.545022	+	0.944005i	−0.453584	+	0.891214i	$0.649855\pi$
$440$		0			0
$441$	−1.28296	+	2.22216i	−0.0610934	+	0.105817i
$442$		0			0
$443$	−22.1538	−	12.7905i	−1.05256	−	0.607696i	−0.129196	−	0.991619i	$-0.541240\pi$
$443$	−22.1538	−	12.7905i	−1.05256	−	0.607696i	−0.923365	+	0.383923i	$0.874573\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	31.8034	+	18.3617i	1.50425	+	0.868478i
$448$		0			0
$449$	29.7102			1.40211			0.701055	−	0.713107i	$-0.252713\pi$
$449$	29.7102			1.40211			0.701055	+	0.713107i	$0.252713\pi$
$450$		0			0
$451$	28.0387	+	48.5644i	1.32029	+	2.28681i
$452$		0			0
$453$	−14.0191	+	8.09393i	−0.658674	+	0.380286i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	13.9693i		−	0.653458i	−0.945118	−	0.326729i	$-0.894054\pi$
$457$		−	13.9693i		−	0.653458i	0.945118	−	0.326729i	$-0.105946\pi$
$458$		0			0
$459$	12.0395	+	20.8531i	0.561957	+	0.973338i
$460$		0			0
$461$	10.7999	+	18.7060i	0.503001	+	0.871224i	0.999994	+	0.00346920i	$0.00110428\pi$
$461$	10.7999	+	18.7060i	0.503001	+	0.871224i	−0.496993	+	0.867755i	$0.665562\pi$
$462$		0			0
$463$			14.4002i			0.669233i	0.942354	+	0.334617i	$0.108607\pi$
$463$			14.4002i			0.669233i	−0.942354	+	0.334617i	$0.891393\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	34.9770i		−	1.61854i	−0.587435	−	0.809271i	$-0.699862\pi$
$467$		−	34.9770i		−	1.61854i	0.587435	−	0.809271i	$-0.300138\pi$
$468$		0			0
$469$	5.27789	−	9.14157i	0.243710	−	0.422118i
$470$		0			0
$471$	17.7385	−	30.7239i	0.817345	−	1.41568i
$472$		0			0
$473$	−29.8230	+	17.2183i	−1.37126	+	0.791698i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−3.36142	+	1.94072i	−0.153909	+	0.0888594i
$478$		0			0
$479$	−9.14007	+	15.8311i	−0.417620	+	0.723340i	−0.995700	−	0.0926410i	$-0.970469\pi$
$479$	−9.14007	+	15.8311i	−0.417620	+	0.723340i	0.578079	+	0.815981i	$0.303802\pi$
$480$		0			0
$481$	−7.90927	+	13.6993i	−0.360632	+	0.624632i
$482$		0			0
$483$		−	7.25493i		−	0.330111i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			19.3488i			0.876780i	0.898785	+	0.438390i	$0.144451\pi$
$487$			19.3488i			0.876780i	−0.898785	+	0.438390i	$0.855549\pi$
$488$		0			0
$489$	5.74086	+	9.94347i	0.259611	+	0.449659i
$490$		0			0
$491$	6.23725	+	10.8032i	0.281483	+	0.487543i	0.971750	−	0.236012i	$-0.0758404\pi$
$491$	6.23725	+	10.8032i	0.281483	+	0.487543i	−0.690267	+	0.723554i	$0.742507\pi$
$492$		0			0
$493$			10.4036i			0.468552i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.223306	−	0.128926i	0.0100167	−	0.00578312i
$498$		0			0
$499$	6.58105	+	11.3987i	0.294608	+	0.510276i	0.974894	−	0.222671i	$-0.0714776\pi$
$499$	6.58105	+	11.3987i	0.294608	+	0.510276i	−0.680286	+	0.732947i	$0.738144\pi$
$500$		0			0
$501$	10.7901			0.482066
$502$		0			0
$503$	17.1067	+	9.87656i	0.762750	+	0.440374i	0.830282	−	0.557343i	$-0.188179\pi$
$503$	17.1067	+	9.87656i	0.762750	+	0.440374i	−0.0675323	+	0.997717i	$0.521513\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	15.1170	+	8.72778i	0.671368	+	0.387614i
$508$		0			0
$509$	5.63237	−	9.75556i	0.249651	−	0.432407i	−0.713778	−	0.700372i	$-0.753018\pi$
$509$	5.63237	−	9.75556i	0.249651	−	0.432407i	0.963429	+	0.267964i	$0.0863509\pi$
$510$		0			0
$511$	1.28690	+	2.22898i	0.0569293	+	0.0986044i
$512$		0			0
$513$	−23.9045	−	3.36850i	−1.05541	−	0.148723i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	12.0005	+	6.92848i	0.527781	+	0.304714i
$518$		0			0
$519$	−5.66573	+	9.81333i	−0.248698	+	0.430758i
$520$		0			0
$521$	−13.2410			−0.580098			−0.290049	−	0.957012i	$-0.593672\pi$
$521$	−13.2410			−0.580098			−0.290049	+	0.957012i	$0.593672\pi$
$522$		0			0
$523$	−4.75453	−	2.74503i	−0.207901	−	0.120032i	0.392434	−	0.919780i	$-0.371633\pi$
$523$	−4.75453	−	2.74503i	−0.207901	−	0.120032i	−0.600336	+	0.799748i	$0.704966\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.8352	−	8.56512i	0.646233	−	0.373103i
$528$		0			0
$529$	−6.10878	−	10.5807i	−0.265599	−	0.460031i
$530$		0			0
$531$	5.43990			0.236072
$532$		0			0
$533$		−	16.6950i		−	0.723142i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−4.75470	+	2.74513i	−0.205181	+	0.118461i
$538$		0			0
$539$	−23.5809			−1.01570
$540$		0			0
$541$	−0.888663	+	1.53921i	−0.0382066	+	0.0661758i	−0.884496	−	0.466547i	$-0.845498\pi$
$541$	−0.888663	+	1.53921i	−0.0382066	+	0.0661758i	0.846290	+	0.532723i	$0.178831\pi$
$542$		0			0
$543$			29.1150i			1.24944i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	33.9427	+	19.5968i	1.45128	+	0.837899i	0.998554	−	0.0537486i	$-0.0171170\pi$
$547$	33.9427	+	19.5968i	1.45128	+	0.837899i	0.452730	+	0.891648i	$0.350450\pi$
$548$		0			0
$549$	0.0746777	+	0.129346i	0.00318717	+	0.00552033i
$550$		0			0
$551$	−8.21675	−	6.42448i	−0.350045	−	0.273692i
$552$		0			0
$553$	−2.12258	+	1.22547i	−0.0902615	+	0.0521125i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−38.7443	−	22.3691i	−1.64165	−	0.947807i	−0.980247	−	0.197777i	$-0.936628\pi$
$557$	−38.7443	−	22.3691i	−1.64165	−	0.947807i	−0.661403	−	0.750031i	$-0.730039\pi$
$558$		0			0
$559$	10.2523			0.433624
$560$		0			0
$561$	−16.0517	+	27.8023i	−0.677703	+	1.17382i
$562$		0			0
$563$		−	16.3322i		−	0.688318i	−0.938911	−	0.344159i	$-0.888164\pi$
$563$		−	16.3322i		−	0.688318i	0.938911	−	0.344159i	$-0.111836\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−8.74535	+	5.04913i	−0.367270	+	0.212044i
$568$		0			0
$569$	−27.0171			−1.13261			−0.566307	−	0.824194i	$-0.691628\pi$
$569$	−27.0171			−1.13261			−0.566307	+	0.824194i	$0.691628\pi$
$570$		0			0
$571$	34.0260			1.42395			0.711973	−	0.702207i	$-0.247802\pi$
$571$	34.0260			1.42395			0.711973	+	0.702207i	$0.247802\pi$
$572$		0			0
$573$	34.3081	−	19.8078i	1.43324	−	0.827482i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	7.96551i		−	0.331608i	−0.986159	−	0.165804i	$-0.946978\pi$
$577$		−	7.96551i		−	0.331608i	0.986159	−	0.165804i	$-0.0530220\pi$
$578$		0			0
$579$	−8.93063	+	15.4683i	−0.371144	+	0.642841i
$580$		0			0
$581$	3.49278			0.144905
$582$		0			0
$583$	−30.8916	−	17.8353i	−1.27940	−	0.738661i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.8395	−	11.4543i	0.818864	−	0.472771i	−0.0311607	−	0.999514i	$-0.509920\pi$
$587$	19.8395	−	11.4543i	0.818864	−	0.472771i	0.850025	+	0.526743i	$0.176587\pi$
$588$		0			0
$589$	−2.39641	+	17.0061i	−0.0987423	+	0.700724i
$590$		0			0
$591$	8.04334	+	13.9315i	0.330859	+	0.573064i
$592$		0			0
$593$	2.62852	+	1.51758i	0.107940	+	0.0623194i	0.552998	−	0.833182i	$-0.313484\pi$
$593$	2.62852	+	1.51758i	0.107940	+	0.0623194i	−0.445058	+	0.895502i	$0.646817\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	32.2415i		−	1.31956i
$598$		0			0
$599$	−0.0457108	+	0.0791734i	−0.00186769	+	0.00323494i	−0.866958	−	0.498382i	$-0.833928\pi$
$599$	−0.0457108	+	0.0791734i	−0.00186769	+	0.00323494i	0.865090	+	0.501617i	$0.167261\pi$
$600$		0			0
$601$	27.2190			1.11029			0.555144	−	0.831754i	$-0.312663\pi$
$601$	27.2190			1.11029			0.555144	+	0.831754i	$0.312663\pi$
$602$		0			0
$603$	3.32440	−	1.91934i	0.135380	−	0.0781617i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			22.9612i			0.931965i	0.884794	+	0.465983i	$0.154299\pi$
$607$			22.9612i			0.931965i	−0.884794	+	0.465983i	$0.845701\pi$
$608$		0			0
$609$	−5.28677			−0.214231
$610$		0			0
$611$	−2.06271	−	3.57271i	−0.0834482	−	0.144536i
$612$		0			0
$613$	20.2825	−	11.7101i	0.819202	−	0.472967i	−0.0309391	−	0.999521i	$-0.509850\pi$
$613$	20.2825	−	11.7101i	0.819202	−	0.472967i	0.850141	+	0.526555i	$0.176516\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−23.3773	−	13.4969i	−0.941136	−	0.543365i	−0.0508196	−	0.998708i	$-0.516183\pi$
$617$	−23.3773	−	13.4969i	−0.941136	−	0.543365i	−0.890316	+	0.455343i	$0.849517\pi$
$618$		0			0
$619$	8.52401			0.342609			0.171304	−	0.985218i	$-0.445202\pi$
$619$	8.52401			0.342609			0.171304	+	0.985218i	$0.445202\pi$
$620$		0			0
$621$	9.09288	−	15.7493i	0.364885	−	0.631999i
$622$		0			0
$623$	−2.49062	−	1.43796i	−0.0997847	−	0.0576107i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−12.0460	−	29.8464i	−0.481070	−	1.19195i
$628$		0			0
$629$	−24.6887	−	42.7621i	−0.984403	−	1.70504i
$630$		0			0
$631$	−0.243045	+	0.420966i	−0.00967547	+	0.0167584i	−0.870823	−	0.491597i	$-0.836413\pi$
$631$	−0.243045	+	0.420966i	−0.00967547	+	0.0167584i	0.861147	+	0.508356i	$0.169747\pi$
$632$		0			0
$633$	0.159987	+	0.0923685i	0.00635891	+	0.00367132i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	6.07982	+	3.51019i	0.240891	+	0.139079i
$638$		0			0
$639$	0.0937698			0.00370948
$640$		0			0
$641$	−4.40147	−	7.62356i	−0.173847	−	0.301113i	0.765914	−	0.642943i	$-0.222287\pi$
$641$	−4.40147	−	7.62356i	−0.173847	−	0.301113i	−0.939762	+	0.341830i	$0.888953\pi$
$642$		0			0
$643$	24.3336	−	14.0490i	0.959623	−	0.554039i	0.0635663	−	0.997978i	$-0.479753\pi$
$643$	24.3336	−	14.0490i	0.959623	−	0.554039i	0.896057	+	0.443939i	$0.146419\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	22.9675i		−	0.902946i	−0.892285	−	0.451473i	$-0.850899\pi$
$647$		−	22.9675i		−	0.902946i	0.892285	−	0.451473i	$-0.149101\pi$
$648$		0			0
$649$	24.9964	+	43.2951i	0.981195	+	1.69948i
$650$		0			0
$651$	4.35254	+	7.53881i	0.170589	+	0.295469i
$652$		0			0
$653$			47.8297i			1.87172i	0.352372	+	0.935860i	$0.385375\pi$
$653$			47.8297i			1.87172i	−0.352372	+	0.935860i	$0.614625\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			0.935985i			0.0365162i
$658$		0			0
$659$	−2.61520	+	4.52966i	−0.101874	+	0.176451i	−0.912457	−	0.409173i	$-0.865817\pi$
$659$	−2.61520	+	4.52966i	−0.101874	+	0.176451i	0.810583	+	0.585624i	$0.199150\pi$
$660$		0			0
$661$	15.6767	−	27.1529i	0.609754	−	1.05613i	−0.381527	−	0.924358i	$-0.624602\pi$
$661$	15.6767	−	27.1529i	0.609754	−	1.05613i	0.991281	−	0.131767i	$-0.0420652\pi$
$662$		0			0
$663$	8.27715	−	4.77881i	0.321458	−	0.185594i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	6.80463	−	3.92865i	0.263476	−	0.152118i
$668$		0			0
$669$	10.7459	−	18.6125i	0.415461	−	0.719600i
$670$		0			0
$671$	−0.686290	+	1.18869i	−0.0264939	+	0.0458888i
$672$		0			0
$673$		−	28.6781i		−	1.10546i	−0.833361	−	0.552729i	$-0.813586\pi$
$673$		−	28.6781i		−	1.10546i	0.833361	−	0.552729i	$-0.186414\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	17.1600i		−	0.659513i	−0.944066	−	0.329757i	$-0.893033\pi$
$677$		−	17.1600i		−	0.659513i	0.944066	−	0.329757i	$-0.106967\pi$
$678$		0			0
$679$	0.366193	+	0.634265i	0.0140532	+	0.0243409i
$680$		0			0
$681$	−4.61416	−	7.99195i	−0.176815	−	0.306252i
$682$		0			0
$683$		−	0.150796i		−	0.00577004i	−0.999996	−	0.00288502i	$-0.999082\pi$
$683$		−	0.150796i		−	0.00577004i	0.999996	−	0.00288502i	$-0.000918332\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−32.7432	+	18.9043i	−1.24923	+	0.721244i
$688$		0			0
$689$	5.30981	+	9.19686i	0.202288	+	0.350372i
$690$		0			0
$691$	−33.0669			−1.25792			−0.628962	−	0.777436i	$-0.716520\pi$
$691$	−33.0669			−1.25792			−0.628962	+	0.777436i	$0.716520\pi$
$692$		0			0
$693$	2.88748	+	1.66709i	0.109686	+	0.0633273i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	45.1315	+	26.0567i	1.70948	+	0.986968i
$698$		0			0
$699$	15.5437	−	26.9224i	0.587915	−	1.01830i
$700$		0			0
$701$	−19.7648	−	34.2336i	−0.746505	−	1.29298i	−0.949488	−	0.313802i	$-0.898397\pi$
$701$	−19.7648	−	34.2336i	−0.746505	−	1.29298i	0.202984	−	0.979182i	$-0.434936\pi$
$702$		0			0
$703$	49.0195	+	6.90758i	1.84881	+	0.260524i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.91266	+	2.25897i	0.147151	+	0.0849575i
$708$		0			0
$709$	19.2276	−	33.3032i	0.722108	−	1.25073i	−0.238045	−	0.971254i	$-0.576507\pi$
$709$	19.2276	−	33.3032i	0.722108	−	1.25073i	0.960153	−	0.279474i	$-0.0901601\pi$
$710$		0			0
$711$	−0.891306			−0.0334266
$712$		0			0
$713$	−11.2043	−	6.46883i	−0.419606	−	0.242260i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−25.4807	+	14.7113i	−0.951593	+	0.549403i
$718$		0			0
$719$	−13.7416	−	23.8011i	−0.512475	−	0.887633i	−0.999895	−	0.0144653i	$-0.995395\pi$
$719$	−13.7416	−	23.8011i	−0.512475	−	0.887633i	0.487420	−	0.873167i	$-0.337938\pi$
$720$		0			0
$721$	18.7999			0.700145
$722$		0			0
$723$		−	11.2934i		−	0.420007i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−42.6727	+	24.6371i	−1.58264	+	0.913739i	−0.588171	+	0.808737i	$0.700152\pi$
$727$	−42.6727	+	24.6371i	−1.58264	+	0.913739i	−0.994472	+	0.105003i	$0.966515\pi$
$728$		0			0
$729$	−29.8948			−1.10722
$730$		0			0
$731$	−16.0012	+	27.7148i	−0.591825	+	1.02507i
$732$		0			0
$733$		−	39.6606i		−	1.46490i	−0.680821	−	0.732449i	$-0.738377\pi$
$733$		−	39.6606i		−	1.46490i	0.680821	−	0.732449i	$-0.261623\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	30.5513	+	17.6388i	1.12537	+	0.649734i
$738$		0			0
$739$	−16.9817	−	29.4131i	−0.624680	−	1.08198i	−0.988603	−	0.150549i	$-0.951896\pi$
$739$	−16.9817	−	29.4131i	−0.624680	−	1.08198i	0.363922	−	0.931429i	$-0.381437\pi$
$740$		0			0
$741$	−1.33705	+	9.48836i	−0.0491177	+	0.348563i
$742$		0			0
$743$	2.45347	−	1.41651i	0.0900091	−	0.0519668i	−0.454320	−	0.890839i	$-0.650118\pi$
$743$	2.45347	−	1.41651i	0.0900091	−	0.0519668i	0.544329	+	0.838872i	$0.316784\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.10001	+	0.635088i	0.0402471	+	0.0232367i
$748$		0			0
$749$	20.7461			0.758045
$750$		0			0
$751$	16.9289	−	29.3217i	0.617743	−	1.06996i	−0.372153	−	0.928171i	$-0.621380\pi$
$751$	16.9289	−	29.3217i	0.617743	−	1.06996i	0.989897	−	0.141792i	$-0.0452863\pi$
$752$		0			0
$753$		−	11.5877i		−	0.422279i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−19.4722	+	11.2423i	−0.707729	+	0.408608i	−0.810220	−	0.586126i	$-0.800652\pi$
$757$	−19.4722	+	11.2423i	−0.707729	+	0.408608i	0.102490	+	0.994734i	$0.467319\pi$
$758$		0			0
$759$	24.2462			0.880080
$760$		0			0
$761$	−27.7383			−1.00551			−0.502755	−	0.864429i	$-0.667680\pi$
$761$	−27.7383			−1.00551			−0.502755	+	0.864429i	$0.667680\pi$
$762$		0			0
$763$	−1.43474	+	0.828350i	−0.0519412	+	0.0299883i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	14.8836i		−	0.537415i
$768$		0			0
$769$	−25.2036	+	43.6539i	−0.908865	+	1.57420i	−0.0932225	+	0.995645i	$0.529717\pi$
$769$	−25.2036	+	43.6539i	−0.908865	+	1.57420i	−0.815643	+	0.578556i	$0.803617\pi$
$770$		0			0
$771$	14.4257			0.519527
$772$		0			0
$773$	33.8717	+	19.5558i	1.21828	+	0.703374i	0.964550	−	0.263901i	$-0.0850093\pi$
$773$	33.8717	+	19.5558i	1.21828	+	0.703374i	0.253730	+	0.967275i	$0.418343\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	21.7304	−	12.5461i	0.779574	−	0.450087i
$778$		0			0
$779$	−48.4496	+	19.5542i	−1.73589	+	0.700603i
$780$		0			0
$781$	0.430874	+	0.746295i	0.0154179	+	0.0267046i
$782$		0			0
$783$	−11.4768	−	6.62611i	−0.410146	−	0.236798i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			10.6415i			0.379328i	0.981849	+	0.189664i	$0.0607399\pi$
$787$			10.6415i			0.379328i	−0.981849	+	0.189664i	$0.939260\pi$
$788$		0			0
$789$	18.8170	−	32.5919i	0.669901	−	1.16030i
$790$		0			0
$791$	7.79902			0.277301
$792$		0			0
$793$	0.353890	−	0.204318i	0.0125670	−	0.00725555i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	16.1004i		−	0.570304i	−0.958482	−	0.285152i	$-0.907956\pi$
$797$		−	16.1004i		−	0.570304i	0.958482	−	0.285152i	$-0.0920441\pi$
$798$		0			0
$799$	12.8774			0.455571
$800$		0			0
$801$	−0.522926	−	0.905734i	−0.0184767	−	0.0320025i
$802$		0			0
$803$	−7.44932	+	4.30086i	−0.262881	+	0.151774i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−20.6870	−	11.9437i	−0.728218	−	0.420437i
$808$		0			0
$809$	−21.1658			−0.744151			−0.372075	−	0.928202i	$-0.621354\pi$
$809$	−21.1658			−0.744151			−0.372075	+	0.928202i	$0.621354\pi$
$810$		0			0
$811$	20.6707	−	35.8028i	0.725848	−	1.25721i	−0.232776	−	0.972530i	$-0.574781\pi$
$811$	20.6707	−	35.8028i	0.725848	−	1.25721i	0.958624	−	0.284675i	$-0.0918857\pi$
$812$		0			0
$813$	2.03587	+	1.17541i	0.0714012	+	0.0412235i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−12.0081	−	29.7524i	−0.420109	−	1.04091i
$818$		0			0
$819$	−0.496315	−	0.859642i	−0.0173426	−	0.0300383i
$820$		0			0
$821$	2.98387	−	5.16822i	0.104138	−	0.180372i	−0.809248	−	0.587467i	$-0.800125\pi$
$821$	2.98387	−	5.16822i	0.104138	−	0.180372i	0.913386	+	0.407095i	$0.133458\pi$
$822$		0			0
$823$	26.8239	+	15.4868i	0.935022	+	0.539835i	0.888396	−	0.459077i	$-0.151820\pi$
$823$	26.8239	+	15.4868i	0.935022	+	0.539835i	0.0466254	+	0.998912i	$0.485153\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	22.6140	+	13.0562i	0.786367	+	0.454009i	0.838682	−	0.544622i	$-0.183327\pi$
$827$	22.6140	+	13.0562i	0.786367	+	0.454009i	−0.0523152	+	0.998631i	$0.516660\pi$
$828$		0			0
$829$	−2.68227			−0.0931591			−0.0465795	−	0.998915i	$-0.514832\pi$
$829$	−2.68227			−0.0931591			−0.0465795	+	0.998915i	$0.514832\pi$
$830$		0			0
$831$	−10.9173	−	18.9094i	−0.378718	−	0.655959i
$832$		0			0
$833$	−18.9781	+	10.9570i	−0.657553	+	0.379638i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			21.8208i			0.754237i
$838$		0			0
$839$	5.25063	+	9.09436i	0.181272	+	0.313972i	0.942314	−	0.334730i	$-0.108645\pi$
$839$	5.25063	+	9.09436i	0.181272	+	0.313972i	−0.761042	+	0.648703i	$0.775312\pi$
$840$		0			0
$841$	11.6371	+	20.1561i	0.401281	+	0.695038i
$842$		0			0
$843$		−	1.38048i		−	0.0475463i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			15.2423i			0.523731i
$848$		0			0
$849$	10.3057	−	17.8499i	0.353690	−	0.612608i
$850$		0			0
$851$	−18.6462	+	32.2962i	−0.639184	+	1.10710i
$852$		0			0
$853$	−34.3826	+	19.8508i	−1.17724	+	0.679678i	−0.955374	−	0.295400i	$-0.904547\pi$
$853$	−34.3826	+	19.8508i	−1.17724	+	0.679678i	−0.221863	+	0.975078i	$0.571214\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−15.6573	+	9.03975i	−0.534843	+	0.308792i	−0.742986	−	0.669306i	$-0.766591\pi$
$857$	−15.6573	+	9.03975i	−0.534843	+	0.308792i	0.208143	+	0.978098i	$0.433258\pi$
$858$		0			0
$859$	13.4851	−	23.3569i	0.460105	−	0.796926i	−0.538860	−	0.842395i	$-0.681145\pi$
$859$	13.4851	−	23.3569i	0.460105	−	0.796926i	0.998966	+	0.0454693i	$0.0144783\pi$
$860$		0			0
$861$	−13.2412	+	22.9345i	−0.451260	+	0.781605i
$862$		0			0
$863$			18.3734i			0.625438i	0.949846	+	0.312719i	$0.101240\pi$
$863$			18.3734i			0.625438i	−0.949846	+	0.312719i	$0.898760\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			3.00357i			0.102006i
$868$		0			0
$869$	−4.09556	−	7.09373i	−0.138933	−	0.240638i
$870$		0			0
$871$	−5.25132	−	9.09556i	−0.177934	−	0.308191i
$872$		0			0
$873$			0.266338i			0.00901416i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−40.9832	+	23.6617i	−1.38391	+	0.798998i	−0.992619	−	0.121271i	$-0.961303\pi$
$877$	−40.9832	+	23.6617i	−1.38391	+	0.798998i	−0.391286	+	0.920269i	$0.627970\pi$
$878$		0			0
$879$	−10.6380	−	18.4256i	−0.358811	−	0.621480i
$880$		0			0
$881$	−15.8395			−0.533646			−0.266823	−	0.963745i	$-0.585974\pi$
$881$	−15.8395			−0.533646			−0.266823	+	0.963745i	$0.585974\pi$
$882$		0			0
$883$	36.9695	+	21.3443i	1.24412	+	0.718294i	0.969931	−	0.243381i	$-0.0782566\pi$
$883$	36.9695	+	21.3443i	1.24412	+	0.718294i	0.274191	+	0.961675i	$0.411590\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	20.7006	+	11.9515i	0.695059	+	0.401293i	0.805505	−	0.592589i	$-0.201894\pi$
$887$	20.7006	+	11.9515i	0.695059	+	0.401293i	−0.110445	+	0.993882i	$0.535228\pi$
$888$		0			0
$889$	2.35325	−	4.07594i	0.0789254	−	0.136703i
$890$		0			0
$891$	−16.8743	−	29.2272i	−0.565311	−	0.979147i
$892$		0			0
$893$	−7.95217	+	10.1706i	−0.266109	+	0.340347i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−6.25134	−	3.60921i	−0.208726	−	0.120508i
$898$		0			0
$899$	−4.71393	+	8.16476i	−0.157218	+	0.272310i
$900$		0			0
$901$	−33.1490			−1.10435
$902$		0			0
$903$	−14.0838	−	8.13131i	−0.468681	−	0.270593i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−31.6336	+	18.2637i	−1.05038	+	0.606435i	−0.922755	−	0.385387i	$-0.874068\pi$
$907$	−31.6336	+	18.2637i	−1.05038	+	0.606435i	−0.127622	+	0.991823i	$0.540734\pi$
$908$		0			0
$909$	0.821493	+	1.42287i	0.0272472	+	0.0471935i
$910$		0			0
$911$	−25.1950			−0.834749			−0.417374	−	0.908735i	$-0.637050\pi$
$911$	−25.1950			−0.834749			−0.417374	+	0.908735i	$0.637050\pi$
$912$		0			0
$913$			11.6730i			0.386319i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−9.05472	+	5.22774i	−0.299013	+	0.172635i
$918$		0			0
$919$	−8.16199			−0.269239			−0.134620	−	0.990897i	$-0.542981\pi$
$919$	−8.16199			−0.269239			−0.134620	+	0.990897i	$0.542981\pi$
$920$		0			0
$921$	−18.8988	+	32.7338i	−0.622738	+	1.07861i
$922$		0			0
$923$		−	0.256554i		−	0.00844459i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	5.92078	+	3.41836i	0.194464	+	0.112274i
$928$		0			0
$929$	−6.01835	−	10.4241i	−0.197456	−	0.342003i	0.750247	−	0.661158i	$-0.229935\pi$
$929$	−6.01835	−	10.4241i	−0.197456	−	0.342003i	−0.947703	+	0.319154i	$0.896601\pi$
$930$		0			0
$931$	3.06563	−	21.7552i	0.100472	−	0.712998i
$932$		0			0
$933$	28.4474	−	16.4241i	0.931326	−	0.537701i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	30.4135	+	17.5593i	0.993567	+	0.573636i	0.906339	−	0.422552i	$-0.138866\pi$
$937$	30.4135	+	17.5593i	0.993567	+	0.573636i	0.0872286	+	0.996188i	$0.472199\pi$
$938$		0			0
$939$	16.8780			0.550793
$940$		0			0
$941$	29.8189	−	51.6478i	0.972067	−	1.68367i	0.282775	−	0.959186i	$-0.408745\pi$
$941$	29.8189	−	51.6478i	0.972067	−	1.68367i	0.689292	−	0.724483i	$-0.257922\pi$
$942$		0			0
$943$		−	39.3588i		−	1.28170i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	8.79590	−	5.07831i	0.285828	−	0.165023i	−0.350231	−	0.936663i	$-0.613897\pi$
$947$	8.79590	−	5.07831i	0.285828	−	0.165023i	0.636059	+	0.771640i	$0.280563\pi$
$948$		0			0
$949$	2.56086			0.0831289
$950$		0			0
$951$	−46.2722			−1.50048
$952$		0			0
$953$	43.0199	−	24.8376i	1.39355	−	0.804568i	0.399846	−	0.916583i	$-0.369064\pi$
$953$	43.0199	−	24.8376i	1.39355	−	0.804568i	0.993707	+	0.112015i	$0.0357304\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	17.6685i		−	0.571142i
$958$		0			0
$959$	−3.37231	+	5.84102i	−0.108898	+	0.188616i
$960$		0			0
$961$	−15.4763			−0.499236
$962$		0			0
$963$	6.53370	+	3.77223i	0.210545	+	0.121558i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−31.1319	+	17.9740i	−1.00113	+	0.578005i	−0.908584	−	0.417703i	$-0.862835\pi$
$967$	−31.1319	+	17.9740i	−1.00113	+	0.578005i	−0.0925508	+	0.995708i	$0.529502\pi$
$968$		0			0
$969$	−23.5630	−	18.4233i	−0.756952	−	0.591843i
$970$		0			0
$971$	−19.8394	−	34.3628i	−0.636676	−	1.10276i	−0.986157	−	0.165812i	$-0.946975\pi$
$971$	−19.8394	−	34.3628i	−0.636676	−	1.10276i	0.349481	−	0.936943i	$-0.386358\pi$
$972$		0			0
$973$	26.1513	+	15.0984i	0.838372	+	0.484034i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	34.3337i		−	1.09843i	−0.835681	−	0.549216i	$-0.814926\pi$
$977$		−	34.3337i		−	1.09843i	0.835681	−	0.549216i	$-0.185074\pi$
$978$		0			0
$979$	4.80570	−	8.32372i	0.153591	−	0.266027i
$980$		0			0
$981$	−0.602471			−0.0192354
$982$		0			0
$983$	5.25253	−	3.03255i	0.167530	−	0.0967234i	−0.413891	−	0.910327i	$-0.635830\pi$
$983$	5.25253	−	3.03255i	0.167530	−	0.0967234i	0.581421	+	0.813603i	$0.302497\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			6.54392i			0.208295i
$988$		0			0
$989$	24.1698			0.768556
$990$		0			0
$991$	13.7694	+	23.8493i	0.437400	+	0.757599i	0.997488	−	0.0708340i	$-0.0225661\pi$
$991$	13.7694	+	23.8493i	0.437400	+	0.757599i	−0.560088	+	0.828433i	$0.689233\pi$
$992$		0			0
$993$	40.8206	−	23.5678i	1.29540	−	0.747901i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−3.73748	−	2.15784i	−0.118367	−	0.0683394i	0.439647	−	0.898170i	$-0.355103\pi$
$997$	−3.73748	−	2.15784i	−0.118367	−	0.0683394i	−0.558015	+	0.829831i	$0.688437\pi$
$998$		0			0
$999$	62.8978			1.99000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.s.e.349.4		24
5.2	odd	4		1900.2.i.e.501.5	yes	12
5.3	odd	4		1900.2.i.f.501.2	yes	12
5.4	even	2	inner	1900.2.s.e.349.9		24
19.11	even	3	inner	1900.2.s.e.49.9		24
95.49	even	6	inner	1900.2.s.e.49.4		24
95.68	odd	12		1900.2.i.f.201.2	yes	12
95.87	odd	12		1900.2.i.e.201.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.2.i.e.201.5	✓	12	95.87	odd	12
1900.2.i.e.501.5	yes	12	5.2	odd	4
1900.2.i.f.201.2	yes	12	95.68	odd	12
1900.2.i.f.501.2	yes	12	5.3	odd	4
1900.2.s.e.49.4		24	95.49	even	6	inner
1900.2.s.e.49.9		24	19.11	even	3	inner
1900.2.s.e.349.4		24	1.1	even	1	trivial
1900.2.s.e.349.9		24	5.4	even	2	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:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36682 + 0.789132i) q^{3} +1.39989i q^{7} +(-0.254541 + 0.440878i) q^{9} +O(q^{10})\)	\(q+(-1.36682 + 0.789132i) q^{3} +1.39989i q^{7} +(-0.254541 + 0.440878i) q^{9} -4.67848 q^{11} +(1.20624 + 0.696425i) q^{13} +(-3.76528 + 2.17388i) q^{17} +(0.608224 - 4.31626i) q^{19} +(-1.10470 - 1.91340i) q^{21} +(2.84373 + 1.64183i) q^{23} -5.53826i q^{27} +(1.19642 - 2.07227i) q^{29} -3.94001 q^{31} +(6.39463 - 3.69194i) q^{33} +11.3570i q^{37} -2.19828 q^{39} +(-5.99312 - 10.3804i) q^{41} +(6.37450 - 3.68032i) q^{43} +(-2.56504 - 1.48093i) q^{47} +5.04030 q^{49} +(3.43096 - 5.94260i) q^{51} +(6.60291 + 3.81219i) q^{53} +(2.57476 + 6.37950i) q^{57} +(-5.34285 - 9.25409i) q^{59} +(0.146691 - 0.254076i) q^{61} +(-0.617183 - 0.356331i) q^{63} +(-6.53018 - 3.77020i) q^{67} -5.18249 q^{69} +(-0.0920970 - 0.159517i) q^{71} +(1.59225 - 0.919287i) q^{73} -6.54938i q^{77} +(0.875405 + 1.51625i) q^{79} +(3.60679 + 6.24715i) q^{81} -2.49503i q^{83} +3.77655i q^{87} +(-1.02719 + 1.77915i) q^{89} +(-0.974921 + 1.68861i) q^{91} +(5.38527 - 3.10919i) q^{93} +(0.453081 - 0.261586i) q^{97} +(1.19087 - 2.06264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^9	\( 24 q + 6 q^{9} + 4 q^{11} + 2 q^{21} - 2 q^{29} + 4 q^{31} - 72 q^{39} - 14 q^{41} - 16 q^{49} + 22 q^{51} - 10 q^{61} + 28 q^{69} + 16 q^{71} - 2 q^{79} + 4 q^{81} + 16 q^{89} + 6 q^{91} + 36 q^{99}+O(q^{100}) \) 24 * q + 6 * q^9 + 4 * q^11 + 2 * q^21 - 2 * q^29 + 4 * q^31 - 72 * q^39 - 14 * q^41 - 16 * q^49 + 22 * q^51 - 10 * q^61 + 28 * q^69 + 16 * q^71 - 2 * q^79 + 4 * q^81 + 16 * q^89 + 6 * q^91 + 36 * q^99

Introduction

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