LMFDB - Embedded newform 3900.2.by.j.3649.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3900,2,Mod(1849,3900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("3900.1849");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3900.by (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:	$31.1416567883$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} + 192x^{8} - 952x^{6} + 3520x^{4} - 2304x^{2} + 1296 $ x^12 - 16x^10 + 192x^8 - 952x^6 + 3520x^4 - 2304*x^2 + 1296
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 780)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3649.1
Root			$-0.708892 - 0.409279i$ of defining polynomial
Character	$\chi$	$=$	3900.3649
Dual form			3900.2.by.j.1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{3} +(-3.04097 + 1.75570i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(-0.866025 - 0.500000i) q^{3} +(-3.04097 + 1.75570i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-0.818558 + 1.41778i) q^{11} +(0.157133 + 3.60213i) q^{13} +(-5.32478 + 3.07426i) q^{17} +(2.84642 + 4.93015i) q^{19} +3.51140 q^{21} -1.00000i q^{27} +(-0.409279 + 0.708892i) q^{29} -0.329963 q^{31} +(1.41778 - 0.818558i) q^{33} +(-4.66415 - 2.69285i) q^{37} +(1.66498 - 3.19810i) q^{39} +(1.92068 - 3.32672i) q^{41} +(7.65685 - 4.42068i) q^{43} -2.87429i q^{47} +(2.66498 - 4.61588i) q^{49} +6.14852 q^{51} +9.02281i q^{53} -5.69285i q^{57} +(-5.73924 - 9.94066i) q^{59} +(0.835019 + 1.44629i) q^{61} +(-3.04097 - 1.75570i) q^{63} +(-6.55333 - 3.78357i) q^{67} +(-3.40928 - 5.90504i) q^{71} +1.87429i q^{73} -5.74858i q^{77} +13.7157 q^{79} +(-0.500000 + 0.866025i) q^{81} +9.27423i q^{83} +(0.708892 - 0.409279i) q^{87} +(3.28357 - 5.68731i) q^{89} +(-6.80210 - 10.6781i) q^{91} +(0.285756 + 0.164981i) q^{93} +(-14.0530 + 8.11353i) q^{97} -1.63712 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^9	$ 12 q + 6 q^{9} + 16 q^{19} - 4 q^{21} + 52 q^{31} - 8 q^{39} - 28 q^{41} + 4 q^{49} + 8 q^{51} - 8 q^{59} + 38 q^{61} - 36 q^{71} + 36 q^{79} - 6 q^{81} + 8 q^{89} - 34 q^{91}+O(q^{100}) $ 12 * q + 6 * q^9 + 16 * q^19 - 4 * q^21 + 52 * q^31 - 8 * q^39 - 28 * q^41 + 4 * q^49 + 8 * q^51 - 8 * q^59 + 38 * q^61 - 36 * q^71 + 36 * q^79 - 6 * q^81 + 8 * q^89 - 34 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3900\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1951$	$3277$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$-1$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.04097	+	1.75570i	−1.14938	+	0.663593i	−0.948735	−	0.316072i	$-0.897636\pi$
$7$	−3.04097	+	1.75570i	−1.14938	+	0.663593i	−0.200642	+	0.979665i	$0.564303\pi$
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−0.818558	+	1.41778i	−0.246805	+	0.427478i	−0.962637	−	0.270794i	$-0.912714\pi$
$11$	−0.818558	+	1.41778i	−0.246805	+	0.427478i	0.715833	+	0.698272i	$0.246047\pi$
$12$		0			0
$13$	0.157133	+	3.60213i	0.0435809	+	0.999050i
$13$	0.157133	+	3.60213i	0.0435809	+	0.999050i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.32478	+	3.07426i	−1.29145	+	0.745618i	−0.978911	−	0.204288i	$-0.934512\pi$
$17$	−5.32478	+	3.07426i	−1.29145	+	0.745618i	−0.312537	+	0.949906i	$0.601179\pi$
$18$		0			0
$19$	2.84642	+	4.93015i	0.653014	+	1.13105i	0.982388	+	0.186854i	$0.0598292\pi$
$19$	2.84642	+	4.93015i	0.653014	+	1.13105i	−0.329373	+	0.944200i	$0.606837\pi$
$20$		0			0
$21$	3.51140			0.766251
$22$		0			0
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−0.409279	+	0.708892i	−0.0760012	+	0.131638i	−0.901521	−	0.432735i	$-0.857549\pi$
$29$	−0.409279	+	0.708892i	−0.0760012	+	0.131638i	0.825520	+	0.564373i	$0.190882\pi$
$30$		0			0
$31$	−0.329963			−0.0592631			−0.0296315	−	0.999561i	$-0.509433\pi$
$31$	−0.329963			−0.0592631			−0.0296315	+	0.999561i	$0.509433\pi$
$32$		0			0
$33$	1.41778	−	0.818558i	0.246805	−	0.142493i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.66415	−	2.69285i	−0.766781	−	0.442701i	0.0649441	−	0.997889i	$-0.479313\pi$
$37$	−4.66415	−	2.69285i	−0.766781	−	0.442701i	−0.831725	+	0.555188i	$0.812646\pi$
$38$		0			0
$39$	1.66498	−	3.19810i	0.266610	−	0.512106i
$40$		0			0
$41$	1.92068	−	3.32672i	0.299960	−	0.519547i	−0.676166	−	0.736749i	$-0.736360\pi$
$41$	1.92068	−	3.32672i	0.299960	−	0.519547i	0.976127	+	0.217203i	$0.0696932\pi$
$42$		0			0
$43$	7.65685	−	4.42068i	1.16766	−	0.674148i	0.214531	−	0.976717i	$-0.431178\pi$
$43$	7.65685	−	4.42068i	1.16766	−	0.674148i	0.953127	+	0.302569i	$0.0978443\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	2.87429i		−	0.419258i	−0.977781	−	0.209629i	$-0.932774\pi$
$47$		−	2.87429i		−	0.419258i	0.977781	−	0.209629i	$-0.0672256\pi$
$48$		0			0
$49$	2.66498	−	4.61588i	0.380712	−	0.659412i
$50$		0			0
$51$	6.14852			0.860965
$52$		0			0
$53$			9.02281i			1.23938i	0.784847	+	0.619689i	$0.212741\pi$
$53$			9.02281i			1.23938i	−0.784847	+	0.619689i	$0.787259\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	5.69285i		−	0.754036i
$58$		0			0
$59$	−5.73924	−	9.94066i	−0.747186	−	1.29416i	−0.949167	−	0.314774i	$-0.898071\pi$
$59$	−5.73924	−	9.94066i	−0.747186	−	1.29416i	0.201981	−	0.979389i	$-0.435262\pi$
$60$		0			0
$61$	0.835019	+	1.44629i	0.106913	+	0.185179i	0.914518	−	0.404545i	$-0.132570\pi$
$61$	0.835019	+	1.44629i	0.106913	+	0.185179i	−0.807605	+	0.589724i	$0.799237\pi$
$62$		0			0
$63$	−3.04097	−	1.75570i	−0.383126	−	0.221198i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.55333	−	3.78357i	−0.800617	−	0.462236i	0.0430700	−	0.999072i	$-0.486286\pi$
$67$	−6.55333	−	3.78357i	−0.800617	−	0.462236i	−0.843687	+	0.536836i	$0.819619\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.40928	−	5.90504i	−0.404607	−	0.700800i	0.589669	−	0.807645i	$-0.299258\pi$
$71$	−3.40928	−	5.90504i	−0.404607	−	0.700800i	−0.994276	+	0.106845i	$0.965925\pi$
$72$		0			0
$73$			1.87429i			0.219369i	0.993966	+	0.109684i	$0.0349840\pi$
$73$			1.87429i			0.219369i	−0.993966	+	0.109684i	$0.965016\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	5.74858i		−	0.655111i
$78$		0			0
$79$	13.7157			1.54313			0.771566	−	0.636149i	$-0.219474\pi$
$79$	13.7157			1.54313			0.771566	+	0.636149i	$0.219474\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			9.27423i			1.01798i	0.860773	+	0.508990i	$0.169981\pi$
$83$			9.27423i			1.01798i	−0.860773	+	0.508990i	$0.830019\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.708892	−	0.409279i	0.0760012	−	0.0438793i
$88$		0			0
$89$	3.28357	−	5.68731i	0.348057	−	0.602853i	−0.637847	−	0.770163i	$-0.720175\pi$
$89$	3.28357	−	5.68731i	0.348057	−	0.602853i	0.985904	+	0.167310i	$0.0535081\pi$
$90$		0			0
$91$	−6.80210	−	10.6781i	−0.713054	−	1.11936i
$92$		0			0
$93$	0.285756	+	0.164981i	0.0296315	+	0.0171078i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−14.0530	+	8.11353i	−1.42687	+	0.823804i	−0.996873	−	0.0790256i	$-0.974819\pi$
$97$	−14.0530	+	8.11353i	−1.42687	+	0.823804i	−0.429998	+	0.902830i	$0.641486\pi$
$98$		0			0
$99$	−1.63712			−0.164536
$100$		0			0
$101$	−3.69285	+	6.39620i	−0.367452	+	0.636445i	−0.989166	−	0.146799i	$-0.953103\pi$
$101$	−3.69285	+	6.39620i	−0.367452	+	0.636445i	0.621714	+	0.783244i	$0.286436\pi$
$102$		0			0
$103$		−	16.5899i		−	1.63466i	−0.576173	−	0.817328i	$-0.695454\pi$
$103$		−	16.5899i		−	1.63466i	0.576173	−	0.817328i	$-0.304546\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.74256	−	3.89282i	−0.651828	−	0.376333i	0.137328	−	0.990526i	$-0.456148\pi$
$107$	−6.74256	−	3.89282i	−0.651828	−	0.376333i	−0.789156	+	0.614193i	$0.789482\pi$
$108$		0			0
$109$	2.38569			0.228508			0.114254	−	0.993452i	$-0.463552\pi$
$109$	2.38569			0.228508			0.114254	+	0.993452i	$0.463552\pi$
$110$		0			0
$111$	2.69285	+	4.66415i	0.255594	+	0.442701i
$112$		0			0
$113$	−10.1746	+	5.87429i	−0.957143	+	0.552607i	−0.895292	−	0.445479i	$-0.853033\pi$
$113$	−10.1746	+	5.87429i	−0.957143	+	0.552607i	−0.0618502	+	0.998085i	$0.519700\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.04097	+	1.93714i	−0.281137	+	0.179089i
$118$		0			0
$119$	10.7950	−	18.6974i	0.989573	−	1.71399i
$120$		0			0
$121$	4.15993	+	7.20520i	0.378175	+	0.655018i
$122$		0			0
$123$	−3.32672	+	1.92068i	−0.299960	+	0.173182i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−1.93745	−	1.11859i	−0.171921	−	0.0992585i	0.411570	−	0.911378i	$-0.364980\pi$
$127$	−1.93745	−	1.11859i	−0.171921	−	0.0992585i	−0.583491	+	0.812119i	$0.698314\pi$
$128$		0			0
$129$	−8.84137			−0.778439
$130$		0			0
$131$	−20.5013			−1.79121			−0.895603	−	0.444854i	$-0.853256\pi$
$131$	−20.5013			−1.79121			−0.895603	+	0.444854i	$0.853256\pi$
$132$		0			0
$133$	−17.3118	−	9.99494i	−1.50112	−	0.866672i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	19.7527	−	11.4042i	1.68759	−	0.974329i	0.731228	−	0.682133i	$-0.238948\pi$
$137$	19.7527	−	11.4042i	1.68759	−	0.974329i	0.956359	−	0.292195i	$-0.0943857\pi$
$138$		0			0
$139$	−6.64852	−	11.5156i	−0.563920	−	0.976738i	−0.997149	−	0.0754545i	$-0.975959\pi$
$139$	−6.64852	−	11.5156i	−0.563920	−	0.976738i	0.433229	−	0.901284i	$-0.357374\pi$
$140$		0			0
$141$	−1.43714	+	2.48921i	−0.121029	+	0.209629i
$142$		0			0
$143$	−5.23566	−	2.72577i	−0.437828	−	0.227940i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.61588	+	2.66498i	−0.380712	+	0.219804i
$148$		0			0
$149$	4.48860	+	7.77448i	0.367720	+	0.636910i	0.989209	−	0.146513i	$-0.0468051\pi$
$149$	4.48860	+	7.77448i	0.367720	+	0.636910i	−0.621489	+	0.783423i	$0.713472\pi$
$150$		0			0
$151$	12.2413			0.996184			0.498092	−	0.867124i	$-0.334034\pi$
$151$	12.2413			0.996184			0.498092	+	0.867124i	$0.334034\pi$
$152$		0			0
$153$	−5.32478	−	3.07426i	−0.430483	−	0.248539i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			4.84137i			0.386383i	0.981161	+	0.193192i	$0.0618839\pi$
$157$			4.84137i			0.386383i	−0.981161	+	0.193192i	$0.938116\pi$
$158$		0			0
$159$	4.51140	−	7.81398i	0.357778	−	0.619689i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.205397	−	0.118586i	0.0160880	−	0.00928839i	−0.491934	−	0.870632i	$-0.663710\pi$
$163$	0.205397	−	0.118586i	0.0160880	−	0.00928839i	0.508022	+	0.861344i	$0.330377\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.16054	+	0.670037i	0.0898052	+	0.0518490i	0.544230	−	0.838936i	$-0.316822\pi$
$167$	1.16054	+	0.670037i	0.0898052	+	0.0518490i	−0.454425	+	0.890785i	$0.650155\pi$
$168$		0			0
$169$	−12.9506	+	1.13203i	−0.996201	+	0.0870791i
$170$		0			0
$171$	−2.84642	+	4.93015i	−0.217671	+	0.377018i
$172$		0			0
$173$	−0.128623	+	0.0742604i	−0.00977901	+	0.00564591i	−0.504882	−	0.863189i	$-0.668464\pi$
$173$	−0.128623	+	0.0742604i	−0.00977901	+	0.00564591i	0.495103	+	0.868835i	$0.335130\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			11.4785i			0.862776i
$178$		0			0
$179$	6.97641	−	12.0835i	0.521442	−	0.903163i	−0.478247	−	0.878225i	$-0.658728\pi$
$179$	6.97641	−	12.0835i	0.521442	−	0.903163i	0.999689	−	0.0249383i	$-0.00793892\pi$
$180$		0			0
$181$	−6.05573			−0.450119			−0.225059	−	0.974345i	$-0.572258\pi$
$181$	−6.05573			−0.450119			−0.225059	+	0.974345i	$0.572258\pi$
$182$		0			0
$183$		−	1.67004i		−	0.123453i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	10.0658i		−	0.736087i
$188$		0			0
$189$	1.75570	+	3.04097i	0.127709	+	0.221198i
$190$		0			0
$191$	5.04640	+	8.74061i	0.365144	+	0.632449i	0.988799	−	0.149251i	$-0.0476863\pi$
$191$	5.04640	+	8.74061i	0.365144	+	0.632449i	−0.623655	+	0.781700i	$0.714353\pi$
$192$		0			0
$193$	7.82632	+	4.51853i	0.563351	+	0.325251i	0.754489	−	0.656312i	$-0.227885\pi$
$193$	7.82632	+	4.51853i	0.563351	+	0.325251i	−0.191138	+	0.981563i	$0.561218\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.61783	−	1.51140i	−0.186513	−	0.107683i	0.403836	−	0.914831i	$-0.367677\pi$
$197$	−2.61783	−	1.51140i	−0.186513	−	0.107683i	−0.590349	+	0.807148i	$0.701010\pi$
$198$		0			0
$199$	−3.52281	−	6.10168i	−0.249725	−	0.432537i	0.713724	−	0.700427i	$-0.247007\pi$
$199$	−3.52281	−	6.10168i	−0.249725	−	0.432537i	−0.963450	+	0.267890i	$0.913674\pi$
$200$		0			0
$201$	3.78357	+	6.55333i	0.266872	+	0.462236i
$202$		0			0
$203$		−	2.87429i		−	0.201736i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.31985			−0.644668
$210$		0			0
$211$	−3.98860	+	6.90845i	−0.274586	+	0.475597i	−0.970031	−	0.242983i	$-0.921874\pi$
$211$	−3.98860	+	6.90845i	−0.274586	+	0.475597i	0.695444	+	0.718580i	$0.255208\pi$
$212$		0			0
$213$			6.81856i			0.467200i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.00341	−	0.579316i	0.0681156	−	0.0393266i
$218$		0			0
$219$	0.937144	−	1.62318i	0.0633263	−	0.109684i
$220$		0			0
$221$	−11.9106	−	18.6974i	−0.801192	−	1.25773i
$222$		0			0
$223$	−22.8134	−	13.1713i	−1.52770	−	0.882018i	−0.999458	−	0.0329232i	$-0.989518\pi$
$223$	−22.8134	−	13.1713i	−1.52770	−	0.882018i	−0.528241	−	0.849094i	$-0.677148\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.5032	−	6.64140i	0.763496	−	0.440805i	−0.0670532	−	0.997749i	$-0.521360\pi$
$227$	11.5032	−	6.64140i	0.763496	−	0.440805i	0.830550	+	0.556944i	$0.188026\pi$
$228$		0			0
$229$	6.35277			0.419803			0.209901	−	0.977723i	$-0.432686\pi$
$229$	6.35277			0.419803			0.209901	+	0.977723i	$0.432686\pi$
$230$		0			0
$231$	−2.87429	+	4.97841i	−0.189114	+	0.327556i
$232$		0			0
$233$		−	6.25142i		−	0.409544i	−0.978810	−	0.204772i	$-0.934355\pi$
$233$		−	6.25142i		−	0.409544i	0.978810	−	0.204772i	$-0.0656453\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−11.8781	−	6.85783i	−0.771566	−	0.445464i
$238$		0			0
$239$	−22.4085			−1.44949			−0.724743	−	0.689020i	$-0.758041\pi$
$239$	−22.4085			−1.44949			−0.724743	+	0.689020i	$0.758041\pi$
$240$		0			0
$241$	5.23212	+	9.06229i	0.337030	+	0.583754i	0.983873	−	0.178870i	$-0.0572442\pi$
$241$	5.23212	+	9.06229i	0.337030	+	0.583754i	−0.646842	+	0.762624i	$0.723911\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−17.3118	+	11.0279i	−1.10152	+	0.701686i
$248$		0			0
$249$	4.63712	−	8.03172i	0.293865	−	0.508990i
$250$		0			0
$251$	−5.05573	−	8.75678i	−0.319115	−	0.552723i	0.661189	−	0.750220i	$-0.270052\pi$
$251$	−5.05573	−	8.75678i	−0.319115	−	0.552723i	−0.980304	+	0.197496i	$0.936719\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−24.7311	−	14.2785i	−1.54268	−	0.890669i	−0.998668	−	0.0515942i	$-0.983570\pi$
$257$	−24.7311	−	14.2785i	−1.54268	−	0.890669i	−0.544016	−	0.839075i	$-0.683097\pi$
$258$		0			0
$259$	18.9113			1.17509
$260$		0			0
$261$	−0.818558			−0.0506675
$262$		0			0
$263$	−16.6994	−	9.64140i	−1.02973	−	0.594514i	−0.112821	−	0.993615i	$-0.535989\pi$
$263$	−16.6994	−	9.64140i	−1.02973	−	0.594514i	−0.916907	+	0.399101i	$0.869322\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.68731	+	3.28357i	−0.348057	+	0.200951i
$268$		0			0
$269$	−4.77216	−	8.26563i	−0.290964	−	0.503964i	0.683074	−	0.730349i	$-0.260643\pi$
$269$	−4.77216	−	8.26563i	−0.290964	−	0.503964i	−0.974038	+	0.226385i	$0.927309\pi$
$270$		0			0
$271$	12.3971	−	21.4724i	0.753070	−	1.30436i	−0.193258	−	0.981148i	$-0.561905\pi$
$271$	12.3971	−	21.4724i	0.753070	−	1.30436i	0.946328	−	0.323208i	$-0.104761\pi$
$272$		0			0
$273$	0.551759	+	12.6485i	0.0333940	+	0.765523i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−22.5167	+	13.0000i	−1.35290	+	0.781094i	−0.988654	−	0.150210i	$-0.952005\pi$
$277$	−22.5167	+	13.0000i	−1.35290	+	0.781094i	−0.364241	+	0.931305i	$0.618672\pi$
$278$		0			0
$279$	−0.164981	−	0.285756i	−0.00987718	−	0.0171078i
$280$		0			0
$281$	−3.58994			−0.214158			−0.107079	−	0.994251i	$-0.534150\pi$
$281$	−3.58994			−0.214158			−0.107079	+	0.994251i	$0.534150\pi$
$282$		0			0
$283$	23.2365	+	13.4156i	1.38127	+	0.797476i	0.992310	−	0.123779i	$-0.0395012\pi$
$283$	23.2365	+	13.4156i	1.38127	+	0.797476i	0.388960	+	0.921255i	$0.372835\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			13.4886i			0.796207i
$288$		0			0
$289$	10.4022	−	18.0171i	0.611891	−	1.05983i
$290$		0			0
$291$	16.2271			0.951247
$292$		0			0
$293$	27.6062	−	15.9384i	1.61277	−	0.931133i	0.624046	−	0.781388i	$-0.285488\pi$
$293$	27.6062	−	15.9384i	1.61277	−	0.931133i	0.988725	−	0.149746i	$-0.0478455\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.41778	+	0.818558i	0.0822682	+	0.0474976i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−15.5228	+	26.8863i	−0.894720	+	1.54970i
$302$		0			0
$303$	6.39620	−	3.69285i	0.367452	−	0.212148i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	6.90721i		−	0.394215i	−0.980382	−	0.197108i	$-0.936845\pi$
$307$		−	6.90721i		−	0.394215i	0.980382	−	0.197108i	$-0.0631548\pi$
$308$		0			0
$309$	−8.29497	+	14.3673i	−0.471884	+	0.817328i
$310$		0			0
$311$	26.4557			1.50016			0.750082	−	0.661345i	$-0.230014\pi$
$311$	26.4557			1.50016			0.750082	+	0.661345i	$0.230014\pi$
$312$		0			0
$313$			33.1840i			1.87567i	0.347079	+	0.937836i	$0.387174\pi$
$313$			33.1840i			1.87567i	−0.347079	+	0.937836i	$0.612826\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	27.0228i		−	1.51775i	−0.651235	−	0.758876i	$-0.725749\pi$
$317$		−	27.0228i		−	1.51775i	0.651235	−	0.758876i	$-0.274251\pi$
$318$		0			0
$319$	−0.670037	−	1.16054i	−0.0375149	−	0.0649777i
$320$		0			0
$321$	3.89282	+	6.74256i	0.217276	+	0.376333i
$322$		0			0
$323$	−30.3131	−	17.5013i	−1.68667	−	0.973798i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.06607	−	1.19285i	−0.114254	−	0.0659646i
$328$		0			0
$329$	5.04640	+	8.74061i	0.278217	+	0.481886i
$330$		0			0
$331$	9.37429	+	16.2367i	0.515257	+	0.892452i	0.999843	+	0.0177084i	$0.00563705\pi$
$331$	9.37429	+	16.2367i	0.515257	+	0.892452i	−0.484586	+	0.874744i	$0.661030\pi$
$332$		0			0
$333$		−	5.38569i		−	0.295134i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			26.1156i			1.42261i	0.702885	+	0.711304i	$0.251895\pi$
$337$			26.1156i			1.42261i	−0.702885	+	0.711304i	$0.748105\pi$
$338$		0			0
$339$	11.7486			0.638095
$340$		0			0
$341$	0.270094	−	0.467816i	0.0146264	−	0.0253337i
$342$		0			0
$343$		−	5.86418i		−	0.316636i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.81398	+	4.51140i	−0.419477	+	0.242185i	−0.694853	−	0.719151i	$-0.744531\pi$
$347$	−7.81398	+	4.51140i	−0.419477	+	0.242185i	0.275377	+	0.961336i	$0.411197\pi$
$348$		0			0
$349$	−2.89075	+	5.00692i	−0.154738	+	0.268015i	−0.932964	−	0.359970i	$-0.882787\pi$
$349$	−2.89075	+	5.00692i	−0.154738	+	0.268015i	0.778225	+	0.627985i	$0.216120\pi$
$350$		0			0
$351$	3.60213	−	0.157133i	0.192267	−	0.00838716i
$352$		0			0
$353$	−19.3668	−	11.1814i	−1.03079	−	0.595128i	−0.113581	−	0.993529i	$-0.536232\pi$
$353$	−19.3668	−	11.1814i	−1.03079	−	0.595128i	−0.917211	+	0.398401i	$0.869565\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−18.6974	+	10.7950i	−0.989573	+	0.571331i
$358$		0			0
$359$	−17.1814			−0.906802			−0.453401	−	0.891307i	$-0.649789\pi$
$359$	−17.1814			−0.906802			−0.453401	+	0.891307i	$0.649789\pi$
$360$		0			0
$361$	−6.70425	+	11.6121i	−0.352855	+	0.611163i
$362$		0			0
$363$		−	8.31985i		−	0.436679i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−9.42841	−	5.44349i	−0.492159	−	0.284148i	0.233311	−	0.972402i	$-0.425044\pi$
$367$	−9.42841	−	5.44349i	−0.492159	−	0.284148i	−0.725470	+	0.688254i	$0.758377\pi$
$368$		0			0
$369$	3.84137			0.199974
$370$		0			0
$371$	−15.8414	−	27.4381i	−0.822443	−	1.42451i
$372$		0			0
$373$	−14.2225	+	8.21138i	−0.736414	+	0.425169i	−0.820764	−	0.571267i	$-0.806452\pi$
$373$	−14.2225	+	8.21138i	−0.736414	+	0.425169i	0.0843499	+	0.996436i	$0.473119\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.61783	−	1.36288i	−0.134825	−	0.0701921i
$378$		0			0
$379$	−10.9506	+	18.9670i	−0.562495	+	0.974271i	0.434782	+	0.900536i	$0.356825\pi$
$379$	−10.9506	+	18.9670i	−0.562495	+	0.974271i	−0.997278	+	0.0737352i	$0.976508\pi$
$380$		0			0
$381$	1.11859	+	1.93745i	0.0573069	+	0.0992585i
$382$		0			0
$383$	15.4993	−	8.94855i	0.791979	−	0.457249i	−0.0486796	−	0.998814i	$-0.515501\pi$
$383$	15.4993	−	8.94855i	0.791979	−	0.457249i	0.840659	+	0.541565i	$0.182168\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.65685	+	4.42068i	0.389219	+	0.224716i
$388$		0			0
$389$	17.4972			0.887141			0.443570	−	0.896239i	$-0.353712\pi$
$389$	17.4972			0.887141			0.443570	+	0.896239i	$0.353712\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	17.7546	+	10.2506i	0.895603	+	0.517077i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	19.9989	−	11.5464i	1.00372	−	0.579497i	0.0943719	−	0.995537i	$-0.469916\pi$
$397$	19.9989	−	11.5464i	1.00372	−	0.579497i	0.909346	+	0.416040i	$0.136582\pi$
$398$		0			0
$399$	9.99494	+	17.3118i	0.500373	+	0.866672i
$400$		0			0
$401$	8.20425	−	14.2102i	0.409701	−	0.709623i	−0.585155	−	0.810921i	$-0.698966\pi$
$401$	8.20425	−	14.2102i	0.409701	−	0.709623i	0.994856	+	0.101299i	$0.0322998\pi$
$402$		0			0
$403$	−0.0518481	−	1.18857i	−0.00258274	−	0.0592067i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.63575	−	4.40850i	0.378490	−	0.218521i
$408$		0			0
$409$	−6.85783	−	11.8781i	−0.339098	−	0.587335i	0.645165	−	0.764043i	$-0.276788\pi$
$409$	−6.85783	−	11.8781i	−0.339098	−	0.587335i	−0.984263	+	0.176708i	$0.943455\pi$
$410$		0			0
$411$	−22.8084			−1.12506
$412$		0			0
$413$	34.9057	+	20.1528i	1.71760	+	0.991654i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			13.2970i			0.651159i
$418$		0			0
$419$	−10.8178	+	18.7369i	−0.528483	+	0.915360i	0.470965	+	0.882152i	$0.343906\pi$
$419$	−10.8178	+	18.7369i	−0.528483	+	0.915360i	−0.999448	+	0.0332080i	$0.989428\pi$
$420$		0			0
$421$	6.26412			0.305295			0.152647	−	0.988281i	$-0.451220\pi$
$421$	6.26412			0.305295			0.152647	+	0.988281i	$0.451220\pi$
$422$		0			0
$423$	2.48921	−	1.43714i	0.121029	−	0.0698763i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−5.07853	−	2.93209i	−0.245767	−	0.141894i
$428$		0			0
$429$	3.17133	+	4.97841i	0.153113	+	0.240360i
$430$		0			0
$431$	−0.795749	+	1.37828i	−0.0383299	+	0.0663893i	−0.884554	−	0.466438i	$-0.845537\pi$
$431$	−0.795749	+	1.37828i	−0.0383299	+	0.0663893i	0.846224	+	0.532827i	$0.178870\pi$
$432$		0			0
$433$	25.7183	−	14.8485i	1.23594	−	0.713573i	0.267682	−	0.963507i	$-0.413742\pi$
$433$	25.7183	−	14.8485i	1.23594	−	0.713573i	0.968263	+	0.249934i	$0.0804090\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−16.5507	+	28.6666i	−0.789921	+	1.36818i	0.136094	+	0.990696i	$0.456545\pi$
$439$	−16.5507	+	28.6666i	−0.789921	+	1.36818i	−0.926015	+	0.377487i	$0.876788\pi$
$440$		0			0
$441$	5.32996			0.253808
$442$		0			0
$443$		−	39.1713i		−	1.86109i	−0.366183	−	0.930543i	$-0.619335\pi$
$443$		−	39.1713i		−	1.86109i	0.366183	−	0.930543i	$-0.380665\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	8.97719i		−	0.424607i
$448$		0			0
$449$	−20.2271	−	35.0343i	−0.954574	−	1.65337i	−0.735340	−	0.677698i	$-0.762978\pi$
$449$	−20.2271	−	35.0343i	−0.954574	−	1.65337i	−0.219234	−	0.975672i	$-0.570356\pi$
$450$		0			0
$451$	3.14438	+	5.44623i	0.148063	+	0.256453i
$452$		0			0
$453$	−10.6013	−	6.12066i	−0.498092	−	0.287573i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.66074	+	2.11353i	0.171242	+	0.0988668i	0.583171	−	0.812349i	$-0.301812\pi$
$457$	3.66074	+	2.11353i	0.171242	+	0.0988668i	−0.411929	+	0.911216i	$0.635145\pi$
$458$		0			0
$459$	3.07426	+	5.32478i	0.143494	+	0.248539i
$460$		0			0
$461$	−15.1807	−	26.2937i	−0.707034	−	1.22462i	−0.965952	−	0.258720i	$-0.916699\pi$
$461$	−15.1807	−	26.2937i	−0.707034	−	1.22462i	0.258918	−	0.965899i	$-0.416634\pi$
$462$		0			0
$463$			21.9300i			1.01917i	0.860419	+	0.509587i	$0.170202\pi$
$463$			21.9300i			1.01917i	−0.860419	+	0.509587i	$0.829798\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	39.4684i		−	1.82638i	−0.407536	−	0.913189i	$-0.633612\pi$
$467$		−	39.4684i		−	1.82638i	0.407536	−	0.913189i	$-0.366388\pi$
$468$		0			0
$469$	26.5713			1.22695
$470$		0			0
$471$	2.42068	−	4.19275i	0.111539	−	0.193192i
$472$		0			0
$473$			14.4743i			0.665531i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.81398	+	4.51140i	−0.357778	+	0.206563i
$478$		0			0
$479$	−13.9435	+	24.1508i	−0.637094	+	1.10348i	0.348973	+	0.937133i	$0.386531\pi$
$479$	−13.9435	+	24.1508i	−0.637094	+	1.10348i	−0.986067	+	0.166347i	$0.946803\pi$
$480$		0			0
$481$	8.96708	−	17.2240i	0.408864	−	0.785346i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$	31.9574	−	18.4506i	1.44813	−	0.836077i	0.449758	−	0.893150i	$-0.351510\pi$
$487$	31.9574	−	18.4506i	1.44813	−	0.836077i	0.998370	+	0.0570729i	$0.0181768\pi$
$488$		0			0
$489$	−0.237172			−0.0107253
$490$		0			0
$491$	4.66926	−	8.08740i	0.210721	−	0.364979i	−0.741220	−	0.671263i	$-0.765752\pi$
$491$	4.66926	−	8.08740i	0.210721	−	0.364979i	0.951940	+	0.306284i	$0.0990856\pi$
$492$		0			0
$493$		−	5.03292i		−	0.226671i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.7350	+	11.9714i	0.930092	+	0.536989i
$498$		0			0
$499$	−28.6498			−1.28254			−0.641271	−	0.767315i	$-0.721593\pi$
$499$	−28.6498			−1.28254			−0.641271	+	0.767315i	$0.721593\pi$
$500$		0			0
$501$	−0.670037	−	1.16054i	−0.0299351	−	0.0518490i
$502$		0			0
$503$	−14.4279	+	8.32996i	−0.643309	+	0.371415i	−0.785888	−	0.618369i	$-0.787794\pi$
$503$	−14.4279	+	8.32996i	−0.643309	+	0.371415i	0.142579	+	0.989783i	$0.454461\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	11.7816	+	5.49494i	0.523238	+	0.244039i
$508$		0			0
$509$	6.39994	−	11.0850i	0.283673	−	0.491335i	−0.688614	−	0.725128i	$-0.741780\pi$
$509$	6.39994	−	11.0850i	0.283673	−	0.491335i	0.972286	+	0.233793i	$0.0751138\pi$
$510$		0			0
$511$	−3.29069	−	5.69965i	−0.145572	−	0.252138i
$512$		0			0
$513$	4.93015	−	2.84642i	0.217671	−	0.125673i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	4.07512	+	2.35277i	0.179224	+	0.103475i
$518$		0			0
$519$	0.148521			0.00651934
$520$		0			0
$521$	−35.2727			−1.54532			−0.772662	−	0.634818i	$-0.781075\pi$
$521$	−35.2727			−1.54532			−0.772662	+	0.634818i	$0.781075\pi$
$522$		0			0
$523$	12.5176	+	7.22706i	0.547358	+	0.316017i	0.748056	−	0.663636i	$-0.230988\pi$
$523$	12.5176	+	7.22706i	0.547358	+	0.316017i	−0.200698	+	0.979653i	$0.564321\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.75698	−	1.01439i	0.0765351	−	0.0441876i
$528$		0			0
$529$	−11.5000	−	19.9186i	−0.500000	−	0.866025i
$530$		0			0
$531$	5.73924	−	9.94066i	0.249062	−	0.431388i
$532$		0			0
$533$	12.2851	+	6.39581i	0.532126	+	0.277033i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−12.0835	+	6.97641i	−0.521442	+	0.301054i
$538$		0			0
$539$	4.36288	+	7.55674i	0.187923	+	0.325492i
$540$		0			0
$541$	−0.748577			−0.0321838			−0.0160919	−	0.999871i	$-0.505122\pi$
$541$	−0.748577			−0.0321838			−0.0160919	+	0.999871i	$0.505122\pi$
$542$		0			0
$543$	5.24442	+	3.02787i	0.225059	+	0.129938i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	1.50129i		−	0.0641906i	−0.999485	−	0.0320953i	$-0.989782\pi$
$547$		−	1.50129i		−	0.0641906i	0.999485	−	0.0320953i	$-0.0102180\pi$
$548$		0			0
$549$	−0.835019	+	1.44629i	−0.0356377	+	0.0617264i
$550$		0			0
$551$	−4.65993			−0.198519
$552$		0			0
$553$	−41.7088	+	24.0806i	−1.77364	+	1.02401i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	37.3554	+	21.5671i	1.58280	+	0.913829i	0.994449	+	0.105222i	$0.0335553\pi$
$557$	37.3554	+	21.5671i	1.58280	+	0.913829i	0.588349	+	0.808607i	$0.299778\pi$
$558$		0			0
$559$	17.1270	+	26.8863i	0.724395	+	1.13717i
$560$		0			0
$561$	−5.03292	+	8.71728i	−0.212490	+	0.368044i
$562$		0			0
$563$	−18.4240	+	10.6371i	−0.776480	+	0.448301i	−0.835181	−	0.549975i	$-0.814637\pi$
$563$	−18.4240	+	10.6371i	−0.776480	+	0.448301i	0.0587013	+	0.998276i	$0.481304\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	3.51140i		−	0.147465i
$568$		0			0
$569$	9.45490	−	16.3764i	0.396370	−	0.686533i	−0.596905	−	0.802312i	$-0.703603\pi$
$569$	9.45490	−	16.3764i	0.396370	−	0.686533i	0.993275	+	0.115779i	$0.0369364\pi$
$570$		0			0
$571$	40.9842			1.71514			0.857568	−	0.514371i	$-0.171975\pi$
$571$	40.9842			1.71514			0.857568	+	0.514371i	$0.171975\pi$
$572$		0			0
$573$		−	10.0928i		−	0.421632i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	38.8911i		−	1.61906i	−0.587079	−	0.809529i	$-0.699722\pi$
$577$		−	38.8911i		−	1.61906i	0.587079	−	0.809529i	$-0.300278\pi$
$578$		0			0
$579$	−4.51853	−	7.82632i	−0.187784	−	0.325251i
$580$		0			0
$581$	−16.2828	−	28.2026i	−0.675524	−	1.17004i
$582$		0			0
$583$	−12.7924	−	7.38569i	−0.529807	−	0.305884i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.346361	−	0.199972i	−0.0142959	−	0.00825372i	0.492835	−	0.870123i	$-0.335961\pi$
$587$	−0.346361	−	0.199972i	−0.0142959	−	0.00825372i	−0.507131	+	0.861869i	$0.669294\pi$
$588$		0			0
$589$	−0.939214	−	1.62677i	−0.0386996	−	0.0670297i
$590$		0			0
$591$	1.51140	+	2.61783i	0.0621709	+	0.107683i
$592$		0			0
$593$			37.7740i			1.55119i	0.631230	+	0.775596i	$0.282550\pi$
$593$			37.7740i			1.55119i	−0.631230	+	0.775596i	$0.717450\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			7.04562i			0.288358i
$598$		0			0
$599$	4.04717			0.165363			0.0826815	−	0.996576i	$-0.473652\pi$
$599$	4.04717			0.165363			0.0826815	+	0.996576i	$0.473652\pi$
$600$		0			0
$601$	−16.9250	+	29.3149i	−0.690384	+	1.19578i	0.281329	+	0.959611i	$0.409225\pi$
$601$	−16.9250	+	29.3149i	−0.690384	+	1.19578i	−0.971712	+	0.236168i	$0.924108\pi$
$602$		0			0
$603$		−	7.56714i		−	0.308158i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−15.7974	+	9.12066i	−0.641198	+	0.370196i	−0.785076	−	0.619399i	$-0.787376\pi$
$607$	−15.7974	+	9.12066i	−0.641198	+	0.370196i	0.143878	+	0.989595i	$0.454043\pi$
$608$		0			0
$609$	−1.43714	+	2.48921i	−0.0582360	+	0.100868i
$610$		0			0
$611$	10.3535	−	0.451647i	0.418860	−	0.0182717i
$612$		0			0
$613$	8.44610	+	4.87636i	0.341135	+	0.196954i	0.660774	−	0.750585i	$-0.270228\pi$
$613$	8.44610	+	4.87636i	0.341135	+	0.196954i	−0.319639	+	0.947539i	$0.603562\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	14.2102	−	8.20425i	0.572080	−	0.330291i	−0.185899	−	0.982569i	$-0.559520\pi$
$617$	14.2102	−	8.20425i	0.572080	−	0.330291i	0.757980	+	0.652278i	$0.226187\pi$
$618$		0			0
$619$	−45.4541			−1.82696			−0.913478	−	0.406889i	$-0.866614\pi$
$619$	−45.4541			−1.82696			−0.913478	+	0.406889i	$0.866614\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			23.0599i			0.923874i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	8.07123	+	4.65993i	0.322334	+	0.186099i
$628$		0			0
$629$	33.1140			1.32034
$630$		0			0
$631$	8.39204	+	14.5354i	0.334082	+	0.578647i	0.983308	−	0.181949i	$-0.0582404\pi$
$631$	8.39204	+	14.5354i	0.334082	+	0.578647i	−0.649226	+	0.760595i	$0.724907\pi$
$632$		0			0
$633$	6.90845	−	3.98860i	0.274586	−	0.158532i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	17.0457	+	8.87429i	0.675377	+	0.351612i
$638$		0			0
$639$	3.40928	−	5.90504i	0.134869	−	0.233600i
$640$		0			0
$641$	−19.6371	−	34.0125i	−0.775619	−	1.34341i	−0.934446	−	0.356106i	$-0.884104\pi$
$641$	−19.6371	−	34.0125i	−0.775619	−	1.34341i	0.158826	−	0.987307i	$-0.449229\pi$
$642$		0			0
$643$	11.5477	−	6.66705i	0.455396	−	0.262923i	−0.254711	−	0.967017i	$-0.581980\pi$
$643$	11.5477	−	6.66705i	0.455396	−	0.262923i	0.710106	+	0.704095i	$0.248647\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	26.0993	+	15.0684i	1.02607	+	0.592401i	0.915856	−	0.401507i	$-0.131513\pi$
$647$	26.0993	+	15.0684i	1.02607	+	0.592401i	0.110213	+	0.993908i	$0.464847\pi$
$648$		0			0
$649$	18.7916			0.737635
$650$		0			0
$651$	−1.15863			−0.0454104
$652$		0			0
$653$	29.9273	+	17.2785i	1.17114	+	0.676160i	0.953949	−	0.299968i	$-0.0969760\pi$
$653$	29.9273	+	17.2785i	1.17114	+	0.676160i	0.217195	+	0.976128i	$0.430309\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.62318	+	0.937144i	−0.0633263	+	0.0365615i
$658$		0			0
$659$	−2.20425	−	3.81788i	−0.0858654	−	0.148723i	0.819894	−	0.572515i	$-0.194032\pi$
$659$	−2.20425	−	3.81788i	−0.0858654	−	0.148723i	−0.905760	+	0.423792i	$0.860699\pi$
$660$		0			0
$661$	−0.885693	+	1.53407i	−0.0344495	+	0.0596682i	−0.882736	−	0.469869i	$-0.844301\pi$
$661$	−0.885693	+	1.53407i	−0.0344495	+	0.0596682i	0.848287	+	0.529537i	$0.177634\pi$
$662$		0			0
$663$	0.966138	+	22.1477i	0.0375217	+	0.860147i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	13.1713	+	22.8134i	0.509233	+	0.882018i
$670$		0			0
$671$	−2.73404			−0.105547
$672$		0			0
$673$	−3.54829	−	2.04861i	−0.136776	−	0.0789679i	0.430050	−	0.902805i	$-0.358496\pi$
$673$	−3.54829	−	2.04861i	−0.136776	−	0.0789679i	−0.566827	+	0.823837i	$0.691829\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			36.8828i			1.41752i	0.705448	+	0.708761i	$0.250746\pi$
$677$			36.8828i			1.41752i	−0.705448	+	0.708761i	$0.749254\pi$
$678$		0			0
$679$	28.4899	−	49.3459i	1.09334	−	1.89372i
$680$		0			0
$681$	−13.2828			−0.508998
$682$		0			0
$683$	9.10314	−	5.25570i	0.348322	−	0.201104i	−0.315624	−	0.948884i	$-0.602214\pi$
$683$	9.10314	−	5.25570i	0.348322	−	0.201104i	0.663946	+	0.747781i	$0.268880\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−5.50166	−	3.17639i	−0.209901	−	0.121187i
$688$		0			0
$689$	−32.5013	+	1.41778i	−1.23820	+	0.0540133i
$690$		0			0
$691$	12.8806	−	22.3099i	0.490003	−	0.848709i	−0.509931	−	0.860215i	$-0.670329\pi$
$691$	12.8806	−	22.3099i	0.490003	−	0.848709i	0.999934	+	0.0115059i	$0.00366251\pi$
$692$		0			0
$693$	4.97841	−	2.87429i	0.189114	−	0.109185i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			23.6187i			0.894623i
$698$		0			0
$699$	−3.12571	+	5.41389i	−0.118225	+	0.204772i
$700$		0			0
$701$	14.9772			0.565681			0.282840	−	0.959167i	$-0.408723\pi$
$701$	14.9772			0.565681			0.282840	+	0.959167i	$0.408723\pi$
$702$		0			0
$703$		−	30.6599i		−	1.15636i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	25.9342i		−	0.975354i
$708$		0			0
$709$	19.2055	+	33.2650i	0.721279	+	1.24929i	0.960487	+	0.278324i	$0.0897789\pi$
$709$	19.2055	+	33.2650i	0.721279	+	1.24929i	−0.239208	+	0.970968i	$0.576888\pi$
$710$		0			0
$711$	6.85783	+	11.8781i	0.257189	+	0.445464i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	19.4063	+	11.2043i	0.724743	+	0.418430i
$718$		0			0
$719$	15.4777	+	26.8082i	0.577221	+	0.999776i	0.995796	+	0.0915941i	$0.0291962\pi$
$719$	15.4777	+	26.8082i	0.577221	+	0.999776i	−0.418575	+	0.908182i	$0.637470\pi$
$720$		0			0
$721$	29.1270	+	50.4495i	1.08475	+	1.87884i
$722$		0			0
$723$		−	10.4642i		−	0.389169i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			33.2043i			1.23148i	0.787950	+	0.615739i	$0.211142\pi$
$727$			33.2043i			1.23148i	−0.787950	+	0.615739i	$0.788858\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−27.1807	+	47.0783i	−1.00531	+	1.74125i
$732$		0			0
$733$		−	22.3012i		−	0.823713i	−0.911249	−	0.411856i	$-0.864881\pi$
$733$		−	22.3012i		−	0.823713i	0.911249	−	0.411856i	$-0.135119\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.7286	−	6.19414i	0.395192	−	0.228164i
$738$		0			0
$739$	12.9199	−	22.3779i	0.475266	−	0.823186i	−0.524332	−	0.851514i	$-0.675685\pi$
$739$	12.9199	−	22.3779i	0.475266	−	0.823186i	0.999599	+	0.0283281i	$0.00901833\pi$
$740$		0			0
$741$	20.5063	−	0.894536i	0.753320	−	0.0328616i
$742$		0			0
$743$	−19.4954	−	11.2557i	−0.715219	−	0.412932i	0.0977717	−	0.995209i	$-0.468829\pi$
$743$	−19.4954	−	11.2557i	−0.715219	−	0.412932i	−0.812990	+	0.582277i	$0.802162\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−8.03172	+	4.63712i	−0.293865	+	0.169663i
$748$		0			0
$749$	27.3385			0.998928
$750$		0			0
$751$	−11.3021	+	19.5758i	−0.412419	+	0.714331i	−0.995154	−	0.0983314i	$-0.968649\pi$
$751$	−11.3021	+	19.5758i	−0.412419	+	0.714331i	0.582734	+	0.812663i	$0.301983\pi$
$752$		0			0
$753$			10.1115i			0.368482i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	33.6078	+	19.4034i	1.22149	+	0.705230i	0.965236	−	0.261378i	$-0.0841769\pi$
$757$	33.6078	+	19.4034i	1.22149	+	0.705230i	0.256258	+	0.966608i	$0.417510\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.6457	−	25.3671i	−0.530905	−	0.919555i	−0.999350	−	0.0360619i	$-0.988519\pi$
$761$	−14.6457	−	25.3671i	−0.530905	−	0.919555i	0.468444	−	0.883493i	$-0.344815\pi$
$762$		0			0
$763$	−7.25481	+	4.18857i	−0.262642	+	0.151636i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	34.9057	−	22.2355i	1.26037	−	0.802877i
$768$		0			0
$769$	−21.7435	+	37.6609i	−0.784091	+	1.35809i	0.145449	+	0.989366i	$0.453537\pi$
$769$	−21.7435	+	37.6609i	−0.784091	+	1.35809i	−0.929540	+	0.368720i	$0.879796\pi$
$770$		0			0
$771$	14.2785	+	24.7311i	0.514228	+	0.890669i
$772$		0			0
$773$	20.6064	−	11.8971i	0.741160	−	0.427909i	−0.0813310	−	0.996687i	$-0.525917\pi$
$773$	20.6064	−	11.8971i	0.741160	−	0.427909i	0.822491	+	0.568778i	$0.192584\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−16.3777	−	9.45567i	−0.587547	−	0.339220i
$778$		0			0
$779$	21.8683			0.783514
$780$		0			0
$781$	11.1628			0.399435
$782$		0			0
$783$	0.708892	+	0.409279i	0.0253337	+	0.0146264i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	17.5654	−	10.1414i	0.626139	−	0.361502i	−0.153116	−	0.988208i	$-0.548931\pi$
$787$	17.5654	−	10.1414i	0.626139	−	0.361502i	0.779255	+	0.626707i	$0.215598\pi$
$788$		0			0
$789$	9.64140	+	16.6994i	0.343243	+	0.594514i
$790$		0			0
$791$	20.6270	−	35.7270i	0.733412	−	1.27031i
$792$		0			0
$793$	−5.07853	+	3.23510i	−0.180344	+	0.114882i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.03192	+	0.595777i	−0.0365523	+	0.0211035i	−0.518165	−	0.855281i	$-0.673385\pi$
$797$	−1.03192	+	0.595777i	−0.0365523	+	0.0211035i	0.481612	+	0.876384i	$0.340051\pi$
$798$		0			0
$799$	8.83631	+	15.3049i	0.312606	+	0.541450i
$800$		0			0
$801$	6.56714			0.232038
$802$		0			0
$803$	−2.65734	−	1.53421i	−0.0937754	−	0.0541412i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			9.54433i			0.335976i
$808$		0			0
$809$	−11.4785	+	19.8813i	−0.403562	+	0.698990i	−0.994153	−	0.107981i	$-0.965561\pi$
$809$	−11.4785	+	19.8813i	−0.403562	+	0.698990i	0.590591	+	0.806971i	$0.298895\pi$
$810$		0			0
$811$	15.7055			0.551496			0.275748	−	0.961230i	$-0.411074\pi$
$811$	15.7055			0.551496			0.275748	+	0.961230i	$0.411074\pi$
$812$		0			0
$813$	−21.4724	+	12.3971i	−0.753070	+	0.434785i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	43.5893	+	25.1663i	1.52500	+	0.880456i
$818$		0			0
$819$	5.84642	−	11.2298i	0.204291	−	0.392402i
$820$		0			0
$821$	−26.6270	+	46.1193i	−0.929289	+	1.60958i	−0.144775	+	0.989465i	$0.546246\pi$
$821$	−26.6270	+	46.1193i	−0.929289	+	1.60958i	−0.784514	+	0.620111i	$0.787088\pi$
$822$		0			0
$823$	16.8850	−	9.74858i	0.588575	−	0.339814i	−0.175959	−	0.984398i	$-0.556303\pi$
$823$	16.8850	−	9.74858i	0.588575	−	0.339814i	0.764534	+	0.644584i	$0.222969\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	18.4912i		−	0.643001i	−0.946909	−	0.321501i	$-0.895813\pi$
$827$		−	18.4912i		−	0.643001i	0.946909	−	0.321501i	$-0.104187\pi$
$828$		0			0
$829$	−9.01646	+	15.6170i	−0.313155	+	0.542400i	−0.979044	−	0.203651i	$-0.934719\pi$
$829$	−9.01646	+	15.6170i	−0.313155	+	0.542400i	0.665889	+	0.746051i	$0.268052\pi$
$830$		0			0
$831$	26.0000			0.901930
$832$		0			0
$833$			32.7714i			1.13546i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			0.329963i			0.0114052i
$838$		0			0
$839$	−11.0785	−	19.1886i	−0.382474	−	0.662464i	0.608942	−	0.793215i	$-0.291594\pi$
$839$	−11.0785	−	19.1886i	−0.382474	−	0.662464i	−0.991415	+	0.130751i	$0.958261\pi$
$840$		0			0
$841$	14.1650	+	24.5345i	0.488448	+	0.846016i
$842$		0			0
$843$	3.10898	+	1.79497i	0.107079	+	0.0618221i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−25.3004	−	14.6072i	−0.869331	−	0.501909i
$848$		0			0
$849$	−13.4156	−	23.2365i	−0.460423	−	0.797476i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		−	14.5798i		−	0.499204i	−0.968349	−	0.249602i	$-0.919700\pi$
$853$		−	14.5798i		−	0.499204i	0.968349	−	0.249602i	$-0.0802998\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			30.9857i			1.05845i	0.848481	+	0.529227i	$0.177518\pi$
$857$			30.9857i			1.05845i	−0.848481	+	0.529227i	$0.822482\pi$
$858$		0			0
$859$	−5.67004			−0.193459			−0.0967296	−	0.995311i	$-0.530838\pi$
$859$	−5.67004			−0.193459			−0.0967296	+	0.995311i	$0.530838\pi$
$860$		0			0
$861$	6.74430	−	11.6815i	0.229845	−	0.398103i
$862$		0			0
$863$			7.63712i			0.259970i	0.991516	+	0.129985i	$0.0414930\pi$
$863$			7.63712i			0.259970i	−0.991516	+	0.129985i	$0.958507\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−18.0171	+	10.4022i	−0.611891	+	0.353276i
$868$		0			0
$869$	−11.2271	+	19.4458i	−0.380852	+	0.659655i
$870$		0			0
$871$	12.5991	−	24.2004i	0.426906	−	0.820001i
$872$		0			0
$873$	−14.0530	−	8.11353i	−0.475624	−	0.274601i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.42477	+	1.39994i	−0.0818788	+	0.0472727i	−0.540380	−	0.841421i	$-0.681720\pi$
$877$	−2.42477	+	1.39994i	−0.0818788	+	0.0472727i	0.458502	+	0.888694i	$0.348386\pi$
$878$		0			0
$879$	−31.8769			−1.07518
$880$		0			0
$881$	−28.8084	+	49.8977i	−0.970581	+	1.68110i	−0.276774	+	0.960935i	$0.589265\pi$
$881$	−28.8084	+	49.8977i	−0.970581	+	1.68110i	−0.693807	+	0.720161i	$0.744068\pi$
$882$		0			0
$883$			13.7983i			0.464351i	0.972674	+	0.232175i	$0.0745844\pi$
$883$			13.7983i			0.464351i	−0.972674	+	0.232175i	$0.925416\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.5844	+	15.3485i	0.892616	+	0.515352i	0.874797	−	0.484489i	$-0.160995\pi$
$887$	26.5844	+	15.3485i	0.892616	+	0.515352i	0.0178186	+	0.999841i	$0.494328\pi$
$888$		0			0
$889$	7.85562			0.263469
$890$		0			0
$891$	−0.818558	−	1.41778i	−0.0274227	−	0.0474976i
$892$		0			0
$893$	14.1707	−	8.18144i	0.474203	−	0.273782i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.135047	−	0.233908i	0.00450406	−	0.00780127i
$900$		0			0
$901$	−27.7385	−	48.0444i	−0.924102	−	1.60059i
$902$		0			0
$903$	26.8863	−	15.5228i	0.894720	−	0.516567i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−28.3968	−	16.3949i	−0.942900	−	0.544383i	−0.0520315	−	0.998645i	$-0.516570\pi$
$907$	−28.3968	−	16.3949i	−0.942900	−	0.544383i	−0.890868	+	0.454262i	$0.849903\pi$
$908$		0			0
$909$	−7.38569			−0.244968
$910$		0			0
$911$	25.7284			0.852418			0.426209	−	0.904625i	$-0.359849\pi$
$911$	25.7284			0.852418			0.426209	+	0.904625i	$0.359849\pi$
$912$		0			0
$913$	−13.1489	−	7.59150i	−0.435164	−	0.251242i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	62.3437	−	35.9942i	2.05877	−	1.18863i
$918$		0			0
$919$	6.53927	+	11.3263i	0.215711	+	0.373622i	0.953492	−	0.301418i	$-0.0974599\pi$
$919$	6.53927	+	11.3263i	0.215711	+	0.373622i	−0.737782	+	0.675040i	$0.764127\pi$
$920$		0			0
$921$	−3.45360	+	5.98182i	−0.113800	+	0.197108i
$922$		0			0
$923$	20.7350	−	13.2085i	0.682501	−	0.434764i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	14.3673	−	8.29497i	0.471884	−	0.272443i
$928$		0			0
$929$	−3.44142	−	5.96072i	−0.112909	−	0.195565i	0.804033	−	0.594585i	$-0.202684\pi$
$929$	−3.44142	−	5.96072i	−0.112909	−	0.195565i	−0.916942	+	0.399020i	$0.869350\pi$
$930$		0			0
$931$	30.3427			0.994441
$932$		0			0
$933$	−22.9113	−	13.2278i	−0.750082	−	0.433060i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			10.0912i			0.329666i	0.986321	+	0.164833i	$0.0527086\pi$
$937$			10.0912i			0.329666i	−0.986321	+	0.164833i	$0.947291\pi$
$938$		0			0
$939$	16.5920	−	28.7382i	0.541460	−	0.937836i
$940$		0			0
$941$	−52.6869			−1.71754			−0.858771	−	0.512359i	$-0.828772\pi$
$941$	−52.6869			−1.71754			−0.858771	+	0.512359i	$0.828772\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	39.8841	+	23.0271i	1.29606	+	0.748280i	0.979721	−	0.200367i	$-0.0642134\pi$
$947$	39.8841	+	23.0271i	1.29606	+	0.748280i	0.316338	+	0.948647i	$0.397547\pi$
$948$		0			0
$949$	−6.75142	+	0.294513i	−0.219160	+	0.00956030i
$950$		0			0
$951$	−13.5114	+	23.4024i	−0.438137	+	0.758876i
$952$		0			0
$953$	−28.1631	+	16.2600i	−0.912293	+	0.526712i	−0.881168	−	0.472803i	$-0.843242\pi$
$953$	−28.1631	+	16.2600i	−0.912293	+	0.526712i	−0.0311246	+	0.999516i	$0.509909\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			1.34007i			0.0433185i
$958$		0			0
$959$	−40.0448	+	69.3597i	−1.29312	+	2.23974i
$960$		0			0
$961$	−30.8911			−0.996488
$962$		0			0
$963$		−	7.78564i		−	0.250889i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	4.93157i		−	0.158589i	−0.996851	−	0.0792943i	$-0.974733\pi$
$967$		−	4.93157i		−	0.158589i	0.996851	−	0.0792943i	$-0.0252667\pi$
$968$		0			0
$969$	17.5013	+	30.3131i	0.562223	+	0.973798i
$970$		0			0
$971$	−12.9899	−	22.4991i	−0.416865	−	0.722032i	0.578757	−	0.815500i	$-0.303538\pi$
$971$	−12.9899	−	22.4991i	−0.416865	−	0.722032i	−0.995622	+	0.0934681i	$0.970205\pi$
$972$		0			0
$973$	40.4358	+	23.3456i	1.29631	+	0.748427i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−9.41000	−	5.43286i	−0.301053	−	0.173813i	0.341863	−	0.939750i	$-0.388942\pi$
$977$	−9.41000	−	5.43286i	−0.301053	−	0.173813i	−0.642916	+	0.765937i	$0.722275\pi$
$978$		0			0
$979$	5.37558	+	9.31078i	0.171804	+	0.297574i
$980$		0			0
$981$	1.19285	+	2.06607i	0.0380847	+	0.0659646i
$982$		0			0
$983$		−	1.04303i		−	0.0332676i	−0.999862	−	0.0166338i	$-0.994705\pi$
$983$		−	1.04303i		−	0.0332676i	0.999862	−	0.0166338i	$-0.00529495\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	10.0928i		−	0.321257i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	2.52916	−	4.38063i	0.0803414	−	0.139155i	−0.823055	−	0.567961i	$-0.807732\pi$
$991$	2.52916	−	4.38063i	0.0803414	−	0.139155i	0.903397	+	0.428806i	$0.141066\pi$
$992$		0			0
$993$		−	18.7486i		−	0.594968i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	19.2009	−	11.0857i	0.608100	−	0.351087i	−0.164122	−	0.986440i	$-0.552479\pi$
$997$	19.2009	−	11.0857i	0.608100	−	0.351087i	0.772221	+	0.635354i	$0.219146\pi$
$998$		0			0
$999$	−2.69285	+	4.66415i	−0.0851979	+	0.147567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3900.2.by.j.3649.1		12
5.2	odd	4		780.2.q.e.61.1	✓	6
5.3	odd	4		3900.2.q.n.2401.3		6
5.4	even	2	inner	3900.2.by.j.3649.6		12
13.3	even	3	inner	3900.2.by.j.1849.6		12
15.2	even	4		2340.2.q.h.1621.1		6
65.3	odd	12		3900.2.q.n.601.3		6
65.29	even	6	inner	3900.2.by.j.1849.1		12
65.42	odd	12		780.2.q.e.601.1	yes	6
195.107	even	12		2340.2.q.h.2161.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.q.e.61.1	✓	6	5.2	odd	4
780.2.q.e.601.1	yes	6	65.42	odd	12
2340.2.q.h.1621.1		6	15.2	even	4
2340.2.q.h.2161.1		6	195.107	even	12
3900.2.q.n.601.3		6	65.3	odd	12
3900.2.q.n.2401.3		6	5.3	odd	4
3900.2.by.j.1849.1		12	65.29	even	6	inner
3900.2.by.j.1849.6		12	13.3	even	3	inner
3900.2.by.j.3649.1		12	1.1	even	1	trivial
3900.2.by.j.3649.6		12	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:	\( N \)	\(=\)	\( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3900.by (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-3.04097 + 1.75570i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-3.04097 + 1.75570i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-0.818558 + 1.41778i) q^{11} +(0.157133 + 3.60213i) q^{13} +(-5.32478 + 3.07426i) q^{17} +(2.84642 + 4.93015i) q^{19} +3.51140 q^{21} -1.00000i q^{27} +(-0.409279 + 0.708892i) q^{29} -0.329963 q^{31} +(1.41778 - 0.818558i) q^{33} +(-4.66415 - 2.69285i) q^{37} +(1.66498 - 3.19810i) q^{39} +(1.92068 - 3.32672i) q^{41} +(7.65685 - 4.42068i) q^{43} -2.87429i q^{47} +(2.66498 - 4.61588i) q^{49} +6.14852 q^{51} +9.02281i q^{53} -5.69285i q^{57} +(-5.73924 - 9.94066i) q^{59} +(0.835019 + 1.44629i) q^{61} +(-3.04097 - 1.75570i) q^{63} +(-6.55333 - 3.78357i) q^{67} +(-3.40928 - 5.90504i) q^{71} +1.87429i q^{73} -5.74858i q^{77} +13.7157 q^{79} +(-0.500000 + 0.866025i) q^{81} +9.27423i q^{83} +(0.708892 - 0.409279i) q^{87} +(3.28357 - 5.68731i) q^{89} +(-6.80210 - 10.6781i) q^{91} +(0.285756 + 0.164981i) q^{93} +(-14.0530 + 8.11353i) q^{97} -1.63712 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^9	\( 12 q + 6 q^{9} + 16 q^{19} - 4 q^{21} + 52 q^{31} - 8 q^{39} - 28 q^{41} + 4 q^{49} + 8 q^{51} - 8 q^{59} + 38 q^{61} - 36 q^{71} + 36 q^{79} - 6 q^{81} + 8 q^{89} - 34 q^{91}+O(q^{100}) \) 12 * q + 6 * q^9 + 16 * q^19 - 4 * q^21 + 52 * q^31 - 8 * q^39 - 28 * q^41 + 4 * q^49 + 8 * q^51 - 8 * q^59 + 38 * q^61 - 36 * q^71 + 36 * q^79 - 6 * q^81 + 8 * q^89 - 34 * q^91

Introduction

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Modular forms

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Database

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