LMFDB - Embedded newform 1404.2.cj.a.1097.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1404,2,Mod(125,1404)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1404, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 10, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1404.125"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1404 = 2^{2} \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1404.cj (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.2109964438$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 468)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1097.9
Character	$\chi$	$=$	1404.1097
Dual form			1404.2.cj.a.1061.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.575123 - 0.154104i) q^{5} +(-0.0243233 + 0.0907757i) q^{7} +(0.433424 + 0.116136i) q^{11} +(2.66720 + 2.42612i) q^{13} +5.51273 q^{17} +(-4.88963 + 4.88963i) q^{19} +(4.18646 - 7.25117i) q^{23} +(-4.02311 + 2.32274i) q^{25} +(-5.25947 + 3.03656i) q^{29} +(-0.449819 - 1.67875i) q^{31} +0.0559555i q^{35} +(6.26928 + 6.26928i) q^{37} +(5.68000 - 1.52195i) q^{41} +(3.22894 - 1.86423i) q^{43} +(12.2249 + 3.27565i) q^{47} +(6.05453 + 3.49558i) q^{49} -0.788507i q^{53} +0.267169 q^{55} +(-1.89515 - 7.07279i) q^{59} +(-0.455275 - 0.788559i) q^{61} +(1.90784 + 0.984291i) q^{65} +(2.57215 + 9.59938i) q^{67} +(0.624421 + 0.624421i) q^{71} +(-3.61085 - 3.61085i) q^{73} +(-0.0210846 + 0.0365196i) q^{77} +(-4.09126 - 7.08627i) q^{79} +(-2.62073 + 9.78070i) q^{83} +(3.17050 - 0.849533i) q^{85} +(-4.46678 + 4.46678i) q^{89} +(-0.285108 + 0.183106i) q^{91} +(-2.05863 + 3.56565i) q^{95} +(15.1985 + 4.07242i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{7} + 12 q^{11} + 4 q^{19} - 4 q^{31} - 4 q^{37} - 24 q^{41} - 66 q^{47} + 78 q^{65} - 14 q^{67} + 28 q^{73} - 24 q^{79} + 78 q^{83} + 36 q^{85} - 8 q^{91} + 26 q^{97}+O(q^{100}) $ 56 * q - 2 * q^7 + 12 * q^11 + 4 * q^19 - 4 * q^31 - 4 * q^37 - 24 * q^41 - 66 * q^47 + 78 * q^65 - 14 * q^67 + 28 * q^73 - 24 * q^79 + 78 * q^83 + 36 * q^85 - 8 * q^91 + 26 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1404\mathbb{Z}\right)^\times$.

$n$	$677$	$703$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.575123	−	0.154104i	0.257203	−	0.0689173i	−0.127913	−	0.991785i	$-0.540828\pi$
$5$	0.575123	−	0.154104i	0.257203	−	0.0689173i	0.385116	+	0.922868i	$0.374161\pi$
$6$		0			0
$7$	−0.0243233	+	0.0907757i	−0.00919334	+	0.0343100i	−0.970370	−	0.241623i	$-0.922320\pi$
$7$	−0.0243233	+	0.0907757i	−0.00919334	+	0.0343100i	0.961177	+	0.275933i	$0.0889869\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.433424	+	0.116136i	0.130682	+	0.0350162i	0.323567	−	0.946205i	$-0.395118\pi$
$11$	0.433424	+	0.116136i	0.130682	+	0.0350162i	−0.192885	+	0.981221i	$0.561784\pi$
$12$		0			0
$13$	2.66720	+	2.42612i	0.739748	+	0.672884i
$13$	2.66720	+	2.42612i	0.739748	+	0.672884i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.51273			1.33703			0.668517	−	0.743697i	$-0.266929\pi$
$17$	5.51273			1.33703			0.668517	+	0.743697i	$0.266929\pi$
$18$		0			0
$19$	−4.88963	+	4.88963i	−1.12176	+	1.12176i	−0.130282	+	0.991477i	$0.541588\pi$
$19$	−4.88963	+	4.88963i	−1.12176	+	1.12176i	−0.991477	+	0.130282i	$0.958412\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.18646	−	7.25117i	0.872938	−	1.51197i	0.0139952	−	0.999902i	$-0.495545\pi$
$23$	4.18646	−	7.25117i	0.872938	−	1.51197i	0.858943	−	0.512071i	$-0.171122\pi$
$24$		0			0
$25$	−4.02311	+	2.32274i	−0.804622	+	0.464549i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.25947	+	3.03656i	−0.976660	+	0.563875i	−0.901260	−	0.433279i	$-0.857357\pi$
$29$	−5.25947	+	3.03656i	−0.976660	+	0.563875i	−0.0753996	+	0.997153i	$0.524023\pi$
$30$		0			0
$31$	−0.449819	−	1.67875i	−0.0807899	−	0.301512i	0.913694	−	0.406403i	$-0.133217\pi$
$31$	−0.449819	−	1.67875i	−0.0807899	−	0.301512i	−0.994484	+	0.104891i	$0.966551\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			0.0559555i			0.00945821i
$36$		0			0
$37$	6.26928	+	6.26928i	1.03066	+	1.03066i	0.999515	+	0.0311493i	$0.00991673\pi$
$37$	6.26928	+	6.26928i	1.03066	+	1.03066i	0.0311493	+	0.999515i	$0.490083\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.68000	−	1.52195i	0.887067	−	0.237689i	0.213613	−	0.976918i	$-0.431477\pi$
$41$	5.68000	−	1.52195i	0.887067	−	0.237689i	0.673454	+	0.739229i	$0.264810\pi$
$42$		0			0
$43$	3.22894	−	1.86423i	0.492409	−	0.284292i	−0.233164	−	0.972437i	$-0.574908\pi$
$43$	3.22894	−	1.86423i	0.492409	−	0.284292i	0.725573	+	0.688145i	$0.241575\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	12.2249	+	3.27565i	1.78318	+	0.477803i	0.991158	−	0.132684i	$-0.0423594\pi$
$47$	12.2249	+	3.27565i	1.78318	+	0.477803i	0.792027	+	0.610487i	$0.209026\pi$
$48$		0			0
$49$	6.05453	+	3.49558i	0.864933	+	0.499369i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	0.788507i		−	0.108310i	−0.998533	−	0.0541549i	$-0.982754\pi$
$53$		−	0.788507i		−	0.108310i	0.998533	−	0.0541549i	$-0.0172465\pi$
$54$		0			0
$55$	0.267169			0.0360251
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.89515	−	7.07279i	−0.246727	−	0.920799i	−0.972507	−	0.232872i	$-0.925188\pi$
$59$	−1.89515	−	7.07279i	−0.246727	−	0.920799i	0.725780	−	0.687927i	$-0.241479\pi$
$60$		0			0
$61$	−0.455275	−	0.788559i	−0.0582919	−	0.100965i	0.835407	−	0.549632i	$-0.185232\pi$
$61$	−0.455275	−	0.788559i	−0.0582919	−	0.100965i	−0.893699	+	0.448667i	$0.851899\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.90784	+	0.984291i	0.236639	+	0.122086i
$66$		0			0
$67$	2.57215	+	9.59938i	0.314238	+	1.17275i	0.924697	+	0.380703i	$0.124318\pi$
$67$	2.57215	+	9.59938i	0.314238	+	1.17275i	−0.610460	+	0.792047i	$0.709015\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.624421	+	0.624421i	0.0741051	+	0.0741051i	0.743188	−	0.669083i	$-0.233313\pi$
$71$	0.624421	+	0.624421i	0.0741051	+	0.0741051i	−0.669083	+	0.743188i	$0.733313\pi$
$72$		0			0
$73$	−3.61085	−	3.61085i	−0.422618	−	0.422618i	0.463486	−	0.886104i	$-0.346598\pi$
$73$	−3.61085	−	3.61085i	−0.422618	−	0.422618i	−0.886104	+	0.463486i	$0.846598\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.0210846	+	0.0365196i	−0.00240281	+	0.00416179i
$78$		0			0
$79$	−4.09126	−	7.08627i	−0.460303	−	0.797268i	0.538673	−	0.842515i	$-0.318926\pi$
$79$	−4.09126	−	7.08627i	−0.460303	−	0.797268i	−0.998976	+	0.0452472i	$0.985592\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.62073	+	9.78070i	−0.287662	+	1.07357i	0.659209	+	0.751960i	$0.270891\pi$
$83$	−2.62073	+	9.78070i	−0.287662	+	1.07357i	−0.946872	+	0.321611i	$0.895776\pi$
$84$		0			0
$85$	3.17050	−	0.849533i	0.343889	−	0.0921448i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.46678	+	4.46678i	−0.473478	+	0.473478i	−0.903038	−	0.429560i	$-0.858669\pi$
$89$	−4.46678	+	4.46678i	−0.473478	+	0.473478i	0.429560	+	0.903038i	$0.358669\pi$
$90$		0			0
$91$	−0.285108	+	0.183106i	−0.0298874	+	0.0191947i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.05863	+	3.56565i	−0.211211	+	0.365828i
$96$		0			0
$97$	15.1985	+	4.07242i	1.54317	+	0.413491i	0.927289	−	0.374347i	$-0.122133\pi$
$97$	15.1985	+	4.07242i	1.54317	+	0.413491i	0.615882	+	0.787838i	$0.288800\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.40675	+	4.16862i	0.239481	+	0.414793i	0.960565	−	0.278054i	$-0.0896894\pi$
$101$	2.40675	+	4.16862i	0.239481	+	0.414793i	−0.721084	+	0.692847i	$0.756356\pi$
$102$		0			0
$103$	5.26666	+	3.04071i	0.518940	+	0.299610i	0.736501	−	0.676437i	$-0.236477\pi$
$103$	5.26666	+	3.04071i	0.518940	+	0.299610i	−0.217561	+	0.976047i	$0.569810\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	6.16867i		−	0.596348i	−0.954512	−	0.298174i	$-0.903622\pi$
$107$		−	6.16867i		−	0.596348i	0.954512	−	0.298174i	$-0.0963775\pi$
$108$		0			0
$109$	3.28996	−	3.28996i	0.315121	−	0.315121i	−0.531769	−	0.846890i	$-0.678472\pi$
$109$	3.28996	−	3.28996i	0.315121	−	0.315121i	0.846890	+	0.531769i	$0.178472\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.843186	−	0.486814i	−0.0793203	−	0.0457956i	0.459815	−	0.888015i	$-0.347916\pi$
$113$	−0.843186	−	0.486814i	−0.0793203	−	0.0457956i	−0.539136	+	0.842219i	$0.681249\pi$
$114$		0			0
$115$	1.29030	−	4.81547i	0.120321	−	0.449045i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.134088	+	0.500422i	−0.0122918	+	0.0458736i
$120$		0			0
$121$	−9.35191	−	5.39933i	−0.850174	−	0.490848i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.06094	+	4.06094i	−0.363221	+	0.363221i
$126$		0			0
$127$			5.76365i			0.511441i	0.966751	+	0.255721i	$0.0823127\pi$
$127$			5.76365i			0.511441i	−0.966751	+	0.255721i	$0.917687\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.554624	−	0.320212i	−0.0484577	−	0.0279771i	0.475575	−	0.879675i	$-0.342240\pi$
$131$	−0.554624	−	0.320212i	−0.0484577	−	0.0279771i	−0.524033	+	0.851698i	$0.675573\pi$
$132$		0			0
$133$	−0.324928	−	0.562792i	−0.0281748	−	0.0488003i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.84124	+	1.83310i	0.584486	+	0.156613i	0.538932	−	0.842349i	$-0.318828\pi$
$137$	6.84124	+	1.83310i	0.584486	+	0.156613i	0.0455542	+	0.998962i	$0.485495\pi$
$138$		0			0
$139$	7.31643	−	12.6724i	0.620571	−	1.07486i	−0.368808	−	0.929506i	$-0.620234\pi$
$139$	7.31643	−	12.6724i	0.620571	−	1.07486i	0.989379	−	0.145355i	$-0.0464326\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.874269	+	1.36129i	0.0731101	+	0.113837i
$144$		0			0
$145$	−2.55690	+	2.55690i	−0.212339	+	0.212339i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	18.2742	−	4.89656i	1.49708	−	0.401142i	0.584961	−	0.811061i	$-0.301110\pi$
$149$	18.2742	−	4.89656i	1.49708	−	0.401142i	0.912122	+	0.409919i	$0.134443\pi$
$150$		0			0
$151$	−1.77157	+	6.61159i	−0.144168	+	0.538043i	0.855623	+	0.517600i	$0.173174\pi$
$151$	−1.77157	+	6.61159i	−0.144168	+	0.538043i	−0.999791	+	0.0204434i	$0.993492\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.517403	−	0.896168i	−0.0415588	−	0.0719820i
$156$		0			0
$157$	−5.25770	+	9.10660i	−0.419610	+	0.726786i	−0.995900	−	0.0904592i	$-0.971167\pi$
$157$	−5.25770	+	9.10660i	−0.419610	+	0.726786i	0.576290	+	0.817245i	$0.304500\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.556402	+	0.556402i	0.0438506	+	0.0438506i
$162$		0			0
$163$	−7.35881	−	7.35881i	−0.576387	−	0.576387i	0.357519	−	0.933906i	$-0.383623\pi$
$163$	−7.35881	−	7.35881i	−0.576387	−	0.576387i	−0.933906	+	0.357519i	$0.883623\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.81045	−	21.6849i	−0.449626	−	1.67803i	−0.703425	−	0.710770i	$-0.748347\pi$
$167$	−5.81045	−	21.6849i	−0.449626	−	1.67803i	0.253799	−	0.967257i	$-0.418320\pi$
$168$		0			0
$169$	1.22790	+	12.9419i	0.0944541	+	0.995529i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.21662	+	14.2316i	0.624698	+	1.08201i	0.988599	+	0.150571i	$0.0481113\pi$
$173$	8.21662	+	14.2316i	0.624698	+	1.08201i	−0.363901	+	0.931438i	$0.618555\pi$
$174$		0			0
$175$	−0.112993	−	0.421697i	−0.00854150	−	0.0318773i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−17.4503			−1.30430			−0.652149	−	0.758090i	$-0.726133\pi$
$179$	−17.4503			−1.30430			−0.652149	+	0.758090i	$0.726133\pi$
$180$		0			0
$181$			13.2331i			0.983608i	0.870706	+	0.491804i	$0.163662\pi$
$181$			13.2331i			0.983608i	−0.870706	+	0.491804i	$0.836338\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.57173	+	2.63949i	0.336120	+	0.194059i
$186$		0			0
$187$	2.38935	+	0.640224i	0.174727	+	0.0468178i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.2787	+	6.51178i	−0.816100	+	0.471176i	−0.849070	−	0.528281i	$-0.822837\pi$
$191$	−11.2787	+	6.51178i	−0.816100	+	0.471176i	0.0329696	+	0.999456i	$0.489504\pi$
$192$		0			0
$193$	−2.47786	+	0.663942i	−0.178361	+	0.0477916i	−0.346894	−	0.937904i	$-0.612764\pi$
$193$	−2.47786	+	0.663942i	−0.178361	+	0.0477916i	0.168533	+	0.985696i	$0.446097\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.0351	−	14.0351i	−0.999960	−	0.999960i	4.02191e−5	−	1.00000i	$-0.499987\pi$
$197$	−14.0351	−	14.0351i	−0.999960	−	0.999960i	−1.00000		4.02191e-5i	$0.999987\pi$
$198$		0			0
$199$		−	17.2254i		−	1.22108i	−0.791986	−	0.610539i	$-0.790953\pi$
$199$		−	17.2254i		−	1.22108i	0.791986	−	0.610539i	$-0.209047\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.147718	−	0.551291i	−0.0103678	−	0.0386931i
$204$		0			0
$205$	3.03216	−	1.75062i	0.211775	−	0.122269i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.68715	+	1.55142i	−0.185874	+	0.107314i
$210$		0			0
$211$	10.2869	−	17.8175i	0.708181	−	1.22660i	−0.257351	−	0.966318i	$-0.582850\pi$
$211$	10.2869	−	17.8175i	0.708181	−	1.22660i	0.965531	−	0.260287i	$-0.0838171\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.56975	−	1.56975i	0.107056	−	0.107056i
$216$		0			0
$217$	0.163331			0.0110876
$218$		0			0
$219$		0			0
$220$		0			0
$221$	14.7036	+	13.3745i	0.989068	+	0.899669i
$222$		0			0
$223$	−27.5422	−	7.37990i	−1.84436	−	0.494195i	−0.845172	−	0.534494i	$-0.820502\pi$
$223$	−27.5422	−	7.37990i	−1.84436	−	0.494195i	−0.999188	+	0.0402997i	$0.987169\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.20639	−	15.6985i	0.279188	−	1.04194i	−0.673794	−	0.738919i	$-0.735337\pi$
$227$	4.20639	−	15.6985i	0.279188	−	1.04194i	0.952982	−	0.303026i	$-0.0979968\pi$
$228$		0			0
$229$	−17.2030	+	4.60954i	−1.13681	+	0.304607i	−0.777667	−	0.628677i	$-0.783597\pi$
$229$	−17.2030	+	4.60954i	−1.13681	+	0.304607i	−0.359141	+	0.933283i	$0.616930\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−17.9589			−1.17653			−0.588263	−	0.808669i	$-0.700188\pi$
$233$	−17.9589			−1.17653			−0.588263	+	0.808669i	$0.700188\pi$
$234$		0			0
$235$	7.53562			0.491569
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.64515	+	2.04851i	−0.494523	+	0.132507i	−0.497457	−	0.867489i	$-0.665733\pi$
$239$	−7.64515	+	2.04851i	−0.494523	+	0.132507i	0.00293378	+	0.999996i	$0.499066\pi$
$240$		0			0
$241$	3.04324	−	11.3575i	0.196032	−	0.731603i	−0.795965	−	0.605343i	$-0.793036\pi$
$241$	3.04324	−	11.3575i	0.196032	−	0.731603i	0.991997	−	0.126260i	$-0.0402973\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.02078	+	1.07737i	0.256878	+	0.0688304i
$246$		0			0
$247$	−24.9045	+	1.17880i	−1.58463	+	0.0750052i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.78689			−0.428385			−0.214192	−	0.976792i	$-0.568712\pi$
$251$	−6.78689			−0.428385			−0.214192	+	0.976792i	$0.568712\pi$
$252$		0			0
$253$	2.65663	−	2.65663i	0.167021	−	0.167021i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.74724	−	13.4186i	0.483259	−	0.837030i	−0.516556	−	0.856253i	$-0.672786\pi$
$257$	7.74724	−	13.4186i	0.483259	−	0.837030i	0.999815	+	0.0192238i	$0.00611950\pi$
$258$		0			0
$259$	−0.721588	+	0.416609i	−0.0448373	+	0.0258868i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−18.8929	+	10.9078i	−1.16499	+	0.672606i	−0.952494	−	0.304556i	$-0.901492\pi$
$263$	−18.8929	+	10.9078i	−1.16499	+	0.672606i	−0.212494	+	0.977162i	$0.568159\pi$
$264$		0			0
$265$	−0.121512	−	0.453489i	−0.00746442	−	0.0278576i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	1.62378i		−	0.0990035i	−0.998774	−	0.0495017i	$-0.984237\pi$
$269$		−	1.62378i		−	0.0990035i	0.998774	−	0.0495017i	$-0.0157633\pi$
$270$		0			0
$271$	3.57292	+	3.57292i	0.217039	+	0.217039i	0.807250	−	0.590210i	$-0.200955\pi$
$271$	3.57292	+	3.57292i	0.217039	+	0.217039i	−0.590210	+	0.807250i	$0.700955\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.01346	+	0.539506i	−0.121416	+	0.0325334i
$276$		0			0
$277$	−9.52727	+	5.50057i	−0.572438	+	0.330497i	−0.758123	−	0.652112i	$-0.773883\pi$
$277$	−9.52727	+	5.50057i	−0.572438	+	0.330497i	0.185684	+	0.982609i	$0.440550\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.43668	−	2.52855i	−0.562945	−	0.150841i	−0.0338861	−	0.999426i	$-0.510788\pi$
$281$	−9.43668	−	2.52855i	−0.562945	−	0.150841i	−0.529059	+	0.848585i	$0.677455\pi$
$282$		0			0
$283$	3.28632	+	1.89736i	0.195351	+	0.112786i	0.594485	−	0.804106i	$-0.297356\pi$
$283$	3.28632	+	1.89736i	0.195351	+	0.112786i	−0.399134	+	0.916893i	$0.630689\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			0.552625i			0.0326204i
$288$		0			0
$289$	13.3902			0.787659
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.24954	−	12.1275i	−0.189840	−	0.708494i	−0.993542	−	0.113462i	$-0.963806\pi$
$293$	−3.24954	−	12.1275i	−0.189840	−	0.708494i	0.803702	−	0.595032i	$-0.202861\pi$
$294$		0			0
$295$	−2.17989	−	3.77568i	−0.126918	−	0.219829i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	28.7583	−	9.18346i	1.66314	−	0.531093i
$300$		0			0
$301$	0.0906884	+	0.338454i	0.00522719	+	0.0195081i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.383359	−	0.383359i	−0.0219511	−	0.0219511i
$306$		0			0
$307$	−3.99494	−	3.99494i	−0.228003	−	0.228003i	0.583855	−	0.811858i	$-0.301544\pi$
$307$	−3.99494	−	3.99494i	−0.228003	−	0.228003i	−0.811858	+	0.583855i	$0.801544\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.11900	+	15.7946i	−0.517091	+	0.895628i	0.482712	+	0.875779i	$0.339652\pi$
$311$	−9.11900	+	15.7946i	−0.517091	+	0.895628i	−0.999803	+	0.0198485i	$0.993682\pi$
$312$		0			0
$313$	2.02810	+	3.51277i	0.114635	+	0.198553i	0.917634	−	0.397427i	$-0.130097\pi$
$313$	2.02810	+	3.51277i	0.114635	+	0.198553i	−0.802999	+	0.595980i	$0.796764\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.36127	−	8.81239i	0.132622	−	0.494953i	−0.867374	−	0.497657i	$-0.834194\pi$
$317$	2.36127	−	8.81239i	0.132622	−	0.494953i	0.999996	+	0.00270356i	$0.000860570\pi$
$318$		0			0
$319$	−2.63223	+	0.705305i	−0.147377	+	0.0394895i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−26.9552	+	26.9552i	−1.49983	+	1.49983i
$324$		0			0
$325$	−16.3657	−	3.56532i	−0.907804	−	0.197768i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.594699	+	1.03005i	−0.0327868	+	0.0567885i
$330$		0			0
$331$	10.2991	+	2.75963i	0.566088	+	0.151683i	0.530502	−	0.847684i	$-0.322003\pi$
$331$	10.2991	+	2.75963i	0.566088	+	0.151683i	0.0355863	+	0.999367i	$0.488670\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.95860	+	5.12445i	0.161646	+	0.279979i
$336$		0			0
$337$	−28.8295	−	16.6447i	−1.57044	−	0.906694i	−0.996115	−	0.0880675i	$-0.971931\pi$
$337$	−28.8295	−	16.6447i	−1.57044	−	0.906694i	−0.574326	−	0.818627i	$-0.694736\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	0.779850i		−	0.0422312i
$342$		0			0
$343$	−0.929747	+	0.929747i	−0.0502016	+	0.0502016i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−26.5898	−	15.3516i	−1.42742	−	0.824119i	−0.430500	−	0.902591i	$-0.641663\pi$
$347$	−26.5898	−	15.3516i	−1.42742	−	0.824119i	−0.996916	+	0.0784717i	$0.974996\pi$
$348$		0			0
$349$	−5.67610	+	21.1835i	−0.303835	+	1.13393i	0.630109	+	0.776506i	$0.283010\pi$
$349$	−5.67610	+	21.1835i	−0.303835	+	1.13393i	−0.933944	+	0.357420i	$0.883657\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.56350	−	28.2274i	0.402565	−	1.50239i	−0.405939	−	0.913900i	$-0.633056\pi$
$353$	7.56350	−	28.2274i	0.402565	−	1.50239i	0.808504	−	0.588491i	$-0.200278\pi$
$354$		0			0
$355$	0.455345	+	0.262893i	0.0241672	+	0.0139529i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.20779	−	9.20779i	0.485969	−	0.485969i	−0.421063	−	0.907031i	$-0.638343\pi$
$359$	9.20779	−	9.20779i	0.485969	−	0.485969i	0.907031	+	0.421063i	$0.138343\pi$
$360$		0			0
$361$		−	28.8171i		−	1.51669i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.63313	−	1.52024i	−0.137824	−	0.0795729i
$366$		0			0
$367$	−1.31371	−	2.27542i	−0.0685752	−	0.118776i	0.829699	−	0.558211i	$-0.188512\pi$
$367$	−1.31371	−	2.27542i	−0.0685752	−	0.118776i	−0.898274	+	0.439435i	$0.855179\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.0715773	+	0.0191791i	0.00371611	+	0.000995728i
$372$		0			0
$373$	7.30630	−	12.6549i	0.378306	−	0.655245i	−0.612510	−	0.790463i	$-0.709840\pi$
$373$	7.30630	−	12.6549i	0.378306	−	0.655245i	0.990816	+	0.135218i	$0.0431734\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−21.3951	−	4.66100i	−1.10190	−	0.240054i
$378$		0			0
$379$	−0.202557	+	0.202557i	−0.0104047	+	0.0104047i	−0.712290	−	0.701885i	$-0.752342\pi$
$379$	−0.202557	+	0.202557i	−0.0104047	+	0.0104047i	0.701885	+	0.712290i	$0.252342\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	11.9165	−	3.19302i	0.608904	−	0.163155i	0.0588257	−	0.998268i	$-0.481264\pi$
$383$	11.9165	−	3.19302i	0.608904	−	0.163155i	0.550079	+	0.835113i	$0.314598\pi$
$384$		0			0
$385$	−0.00649843	+	0.0242525i	−0.000331191	+	0.00123602i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	10.0814	+	17.4615i	0.511148	+	0.885335i	0.999917	+	0.0129213i	$0.00411310\pi$
$389$	10.0814	+	17.4615i	0.511148	+	0.885335i	−0.488768	+	0.872414i	$0.662554\pi$
$390$		0			0
$391$	23.0789	−	39.9737i	1.16715	−	2.02156i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.44500	−	3.44500i	−0.173337	−	0.173337i
$396$		0			0
$397$	−10.1506	−	10.1506i	−0.509444	−	0.509444i	0.404912	−	0.914356i	$-0.367302\pi$
$397$	−10.1506	−	10.1506i	−0.509444	−	0.509444i	−0.914356	+	0.404912i	$0.867302\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.14839	+	34.1423i	0.456849	+	1.70498i	0.682595	+	0.730797i	$0.260851\pi$
$401$	9.14839	+	34.1423i	0.456849	+	1.70498i	−0.225746	+	0.974186i	$0.572482\pi$
$402$		0			0
$403$	2.87308	−	5.56887i	0.143118	−	0.277405i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.98917	+	3.44534i	0.0985995	+	0.170779i
$408$		0			0
$409$	8.36144	+	31.2053i	0.413447	+	1.54300i	0.787927	+	0.615769i	$0.211155\pi$
$409$	8.36144	+	31.2053i	0.413447	+	1.54300i	−0.374480	+	0.927235i	$0.622179\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.688134			0.0338609
$414$		0			0
$415$			6.02897i			0.295951i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−24.2744	−	14.0148i	−1.18588	−	0.684668i	−0.228512	−	0.973541i	$-0.573386\pi$
$419$	−24.2744	−	14.0148i	−1.18588	−	0.684668i	−0.957367	+	0.288873i	$0.906719\pi$
$420$		0			0
$421$	4.94935	+	1.32618i	0.241217	+	0.0646338i	0.377402	−	0.926050i	$-0.376818\pi$
$421$	4.94935	+	1.32618i	0.241217	+	0.0646338i	−0.136185	+	0.990683i	$0.543484\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−22.1783	+	12.8047i	−1.07581	+	0.621117i
$426$		0			0
$427$	0.0826558	−	0.0221475i	0.00399999	−	0.00107179i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.88442	+	7.88442i	0.379779	+	0.379779i	0.871022	−	0.491243i	$-0.163457\pi$
$431$	7.88442	+	7.88442i	0.379779	+	0.379779i	−0.491243	+	0.871022i	$0.663457\pi$
$432$		0			0
$433$		−	21.4637i		−	1.03148i	−0.856746	−	0.515739i	$-0.827517\pi$
$433$		−	21.4637i		−	1.03148i	0.856746	−	0.515739i	$-0.172483\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	14.9853	+	55.9259i	0.716843	+	2.67530i
$438$		0			0
$439$	8.91004	−	5.14422i	0.425253	−	0.245520i	−0.272069	−	0.962278i	$-0.587708\pi$
$439$	8.91004	−	5.14422i	0.425253	−	0.245520i	0.697322	+	0.716758i	$0.254375\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−33.9414	+	19.5961i	−1.61260	+	0.931037i	−0.623840	+	0.781552i	$0.714428\pi$
$443$	−33.9414	+	19.5961i	−1.61260	+	0.931037i	−0.988764	+	0.149486i	$0.952238\pi$
$444$		0			0
$445$	−1.88060	+	3.25730i	−0.0891491	+	0.154411i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.87941	+	1.87941i	−0.0886947	+	0.0886947i	−0.750062	−	0.661367i	$-0.769976\pi$
$449$	−1.87941	+	1.87941i	−0.0886947	+	0.0886947i	0.661367	+	0.750062i	$0.269976\pi$
$450$		0			0
$451$	2.63860			0.124247
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.135755	+	0.149245i	−0.00636428	+	0.00699669i
$456$		0			0
$457$	38.0595	+	10.1980i	1.78035	+	0.477042i	0.990647	−	0.136451i	$-0.0435698\pi$
$457$	38.0595	+	10.1980i	1.78035	+	0.477042i	0.789700	+	0.613494i	$0.210236\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.08960	+	4.06644i	−0.0507477	+	0.189393i	−0.986647	−	0.162876i	$-0.947923\pi$
$461$	−1.08960	+	4.06644i	−0.0507477	+	0.189393i	0.935899	+	0.352269i	$0.114590\pi$
$462$		0			0
$463$	−23.2968	+	6.24235i	−1.08269	+	0.290107i	−0.755698	−	0.654920i	$-0.772702\pi$
$463$	−23.2968	+	6.24235i	−1.08269	+	0.290107i	−0.326994	+	0.945026i	$0.606036\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−24.1608			−1.11803			−0.559013	−	0.829159i	$-0.688820\pi$
$467$	−24.1608			−1.11803			−0.559013	+	0.829159i	$0.688820\pi$
$468$		0			0
$469$	−0.933953			−0.0431260
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.61600	−	0.433007i	0.0743039	−	0.0199097i
$474$		0			0
$475$	8.31417	−	31.0289i	0.381480	−	1.42370i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	9.32218	+	2.49787i	0.425941	+	0.114131i	0.465420	−	0.885090i	$-0.345903\pi$
$479$	9.32218	+	2.49787i	0.425941	+	0.114131i	−0.0394790	+	0.999220i	$0.512570\pi$
$480$		0			0
$481$	1.51141	+	31.9315i	0.0689142	+	1.45595i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9.36857			0.425405
$486$		0			0
$487$	15.4742	−	15.4742i	0.701205	−	0.701205i	−0.263464	−	0.964669i	$-0.584865\pi$
$487$	15.4742	−	15.4742i	0.701205	−	0.701205i	0.964669	+	0.263464i	$0.0848651\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.89886	−	11.9492i	0.311341	−	0.539258i	−0.667312	−	0.744778i	$-0.732555\pi$
$491$	6.89886	−	11.9492i	0.311341	−	0.539258i	0.978653	+	0.205520i	$0.0658885\pi$
$492$		0			0
$493$	−28.9941	+	16.7397i	−1.30583	+	0.753919i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.0718702	+	0.0414943i	−0.00322382	+	0.00186127i
$498$		0			0
$499$	0.170077	+	0.634735i	0.00761368	+	0.0284146i	0.969628	−	0.244584i	$-0.0786513\pi$
$499$	0.170077	+	0.634735i	0.00761368	+	0.0284146i	−0.962014	+	0.272998i	$0.911985\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	20.4283i		−	0.910852i	−0.890274	−	0.455426i	$-0.849487\pi$
$503$		−	20.4283i		−	0.910852i	0.890274	−	0.455426i	$-0.150513\pi$
$504$		0			0
$505$	2.02658	+	2.02658i	0.0901817	+	0.0901817i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.0161032	−	0.00431483i	0.000713760	−	0.000191252i	−0.258462	−	0.966021i	$-0.583216\pi$
$509$	0.0161032	−	0.00431483i	0.000713760	−	0.000191252i	0.259176	+	0.965830i	$0.416549\pi$
$510$		0			0
$511$	0.415605	−	0.239950i	0.0183853	−	0.0106147i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.49756	+	0.937170i	0.154121	+	0.0412966i
$516$		0			0
$517$	4.91814	+	2.83949i	0.216300	+	0.124881i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	31.5428i		−	1.38191i	−0.722896	−	0.690957i	$-0.757189\pi$
$521$		−	31.5428i		−	1.38191i	0.722896	−	0.690957i	$-0.242811\pi$
$522$		0			0
$523$	2.86422			0.125243			0.0626217	−	0.998037i	$-0.480054\pi$
$523$	2.86422			0.125243			0.0626217	+	0.998037i	$0.480054\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.47973	−	9.25449i	−0.108019	−	0.403132i
$528$		0			0
$529$	−23.5530	−	40.7949i	−1.02404	−	1.77369i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	18.8421	+	9.72101i	0.816143	+	0.421064i
$534$		0			0
$535$	−0.950615	−	3.54774i	−0.0410987	−	0.153382i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.21822	+	2.21822i	0.0955453	+	0.0955453i
$540$		0			0
$541$	24.0790	+	24.0790i	1.03524	+	1.03524i	0.999356	+	0.0358828i	$0.0114243\pi$
$541$	24.0790	+	24.0790i	1.03524	+	1.03524i	0.0358828	+	0.999356i	$0.488576\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.38514	−	2.39913i	0.0593327	−	0.102767i
$546$		0			0
$547$	3.28072	+	5.68237i	0.140273	+	0.242960i	0.927599	−	0.373576i	$-0.121869\pi$
$547$	3.28072	+	5.68237i	0.140273	+	0.242960i	−0.787326	+	0.616537i	$0.788535\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	10.8692	−	40.5646i	0.463045	−	1.72811i
$552$		0			0
$553$	0.742774	−	0.199026i	0.0315860	−	0.00846343i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	31.2392	−	31.2392i	1.32365	−	1.32365i	0.412846	−	0.910801i	$-0.364535\pi$
$557$	31.2392	−	31.2392i	1.32365	−	1.32365i	0.910801	−	0.412846i	$-0.135465\pi$
$558$		0			0
$559$	13.1351	+	2.86152i	0.555554	+	0.121029i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.67778	−	4.63804i	0.112855	−	0.195470i	−0.804065	−	0.594541i	$-0.797334\pi$
$563$	2.67778	−	4.63804i	0.112855	−	0.195470i	0.916920	+	0.399071i	$0.130667\pi$
$564$		0			0
$565$	−0.559956	−	0.150040i	−0.0235575	−	0.00631222i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.91658	−	11.9799i	−0.289958	−	0.502222i	0.683841	−	0.729631i	$-0.260308\pi$
$569$	−6.91658	−	11.9799i	−0.289958	−	0.502222i	−0.973799	+	0.227408i	$0.926975\pi$
$570$		0			0
$571$	0.279180	+	0.161184i	0.0116833	+	0.00674536i	0.505830	−	0.862633i	$-0.331186\pi$
$571$	0.279180	+	0.161184i	0.0116833	+	0.00674536i	−0.494147	+	0.869378i	$0.664520\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			38.8963i			1.62209i
$576$		0			0
$577$	−14.4319	+	14.4319i	−0.600807	+	0.600807i	−0.940527	−	0.339720i	$-0.889668\pi$
$577$	−14.4319	+	14.4319i	−0.600807	+	0.600807i	0.339720	+	0.940527i	$0.389668\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.824105	−	0.475797i	−0.0341896	−	0.0197394i
$582$		0			0
$583$	0.0915738	−	0.341758i	0.00379260	−	0.0141542i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−5.97237	+	22.2892i	−0.246506	+	0.919973i	0.726115	+	0.687574i	$0.241324\pi$
$587$	−5.97237	+	22.2892i	−0.246506	+	0.919973i	−0.972621	+	0.232399i	$0.925343\pi$
$588$		0			0
$589$	10.4079	+	6.00901i	0.428851	+	0.247597i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.94470	−	1.94470i	0.0798591	−	0.0798591i	−0.666049	−	0.745908i	$-0.732016\pi$
$593$	1.94470	−	1.94470i	0.0798591	−	0.0798591i	0.745908	+	0.666049i	$0.232016\pi$
$594$		0			0
$595$			0.308468i			0.0126460i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−11.1324	−	6.42730i	−0.454858	−	0.262613i	0.255022	−	0.966935i	$-0.417917\pi$
$599$	−11.1324	−	6.42730i	−0.454858	−	0.262613i	−0.709880	+	0.704323i	$0.751251\pi$
$600$		0			0
$601$	−7.22889	−	12.5208i	−0.294873	−	0.510734i	0.680083	−	0.733135i	$-0.261944\pi$
$601$	−7.22889	−	12.5208i	−0.294873	−	0.510734i	−0.974955	+	0.222401i	$0.928611\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.21056	−	1.66411i	−0.252495	−	0.0676559i
$606$		0			0
$607$	2.33525	−	4.04478i	0.0947850	−	0.164172i	−0.814734	−	0.579835i	$-0.803117\pi$
$607$	2.33525	−	4.04478i	0.0947850	−	0.164172i	0.909519	+	0.415663i	$0.136450\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	24.6591	+	38.3959i	0.997601	+	1.55333i
$612$		0			0
$613$	−32.2764	+	32.2764i	−1.30363	+	1.30363i	−0.377709	+	0.925924i	$0.623288\pi$
$613$	−32.2764	+	32.2764i	−1.30363	+	1.30363i	−0.925924	+	0.377709i	$0.876712\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	29.1612	−	7.81372i	1.17399	−	0.314569i	0.381448	−	0.924390i	$-0.375426\pi$
$617$	29.1612	−	7.81372i	1.17399	−	0.314569i	0.792538	+	0.609822i	$0.208759\pi$
$618$		0			0
$619$	−7.87339	+	29.3839i	−0.316458	+	1.18104i	0.606166	+	0.795338i	$0.292707\pi$
$619$	−7.87339	+	29.3839i	−0.316458	+	1.18104i	−0.922624	+	0.385700i	$0.873960\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.296829	−	0.514122i	−0.0118922	−	0.0205979i
$624$		0			0
$625$	9.90398	−	17.1542i	0.396159	−	0.686168i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	34.5609	+	34.5609i	1.37803	+	1.37803i
$630$		0			0
$631$	18.0342	+	18.0342i	0.717931	+	0.717931i	0.968181	−	0.250251i	$-0.0805130\pi$
$631$	18.0342	+	18.0342i	0.717931	+	0.717931i	−0.250251	+	0.968181i	$0.580513\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.888201	+	3.31481i	0.0352472	+	0.131544i
$636$		0			0
$637$	7.66794	+	24.0124i	0.303815	+	0.951407i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−18.9014	−	32.7382i	−0.746562	−	1.29308i	−0.949461	−	0.313884i	$-0.898370\pi$
$641$	−18.9014	−	32.7382i	−0.746562	−	1.29308i	0.202900	−	0.979200i	$-0.434963\pi$
$642$		0			0
$643$	10.0245	+	37.4118i	0.395326	+	1.47538i	0.821224	+	0.570606i	$0.193292\pi$
$643$	10.0245	+	37.4118i	0.395326	+	1.47538i	−0.425898	+	0.904771i	$0.640042\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	37.4085			1.47068			0.735339	−	0.677699i	$-0.237023\pi$
$647$	37.4085			1.47068			0.735339	+	0.677699i	$0.237023\pi$
$648$		0			0
$649$		−	3.28561i		−	0.128972i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−22.3962	−	12.9304i	−0.876431	−	0.506008i	−0.00695093	−	0.999976i	$-0.502213\pi$
$653$	−22.3962	−	12.9304i	−0.876431	−	0.506008i	−0.869480	+	0.493968i	$0.835546\pi$
$654$		0			0
$655$	−0.368323	−	0.0986919i	−0.0143916	−	0.00385621i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	21.5416	−	12.4370i	0.839140	−	0.484478i	−0.0178318	−	0.999841i	$-0.505676\pi$
$659$	21.5416	−	12.4370i	0.839140	−	0.484478i	0.856972	+	0.515363i	$0.172343\pi$
$660$		0			0
$661$	−2.13017	+	0.570777i	−0.0828540	+	0.0222007i	−0.300008	−	0.953937i	$-0.596989\pi$
$661$	−2.13017	+	0.570777i	−0.0828540	+	0.0222007i	0.217154	+	0.976137i	$0.430323\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.273602	−	0.273602i	−0.0106098	−	0.0106098i
$666$		0			0
$667$			50.8498i			1.96891i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.105747	−	0.394654i	−0.00408232	−	0.0152354i
$672$		0			0
$673$	19.8145	−	11.4399i	0.763795	−	0.440977i	−0.0668619	−	0.997762i	$-0.521299\pi$
$673$	19.8145	−	11.4399i	0.763795	−	0.440977i	0.830656	+	0.556785i	$0.187965\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.77596	+	5.06680i	−0.337287	+	0.194733i	−0.659072	−	0.752080i	$-0.729051\pi$
$677$	−8.77596	+	5.06680i	−0.337287	+	0.194733i	0.321784	+	0.946813i	$0.395717\pi$
$678$		0			0
$679$	−0.739353	+	1.28060i	−0.0283738	+	0.0491448i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	17.0297	−	17.0297i	0.651622	−	0.651622i	−0.301761	−	0.953384i	$-0.597575\pi$
$683$	17.0297	−	17.0297i	0.651622	−	0.651622i	0.953384	+	0.301761i	$0.0975745\pi$
$684$		0			0
$685$	4.21704			0.161125
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.91301	−	2.10311i	0.0728799	−	0.0801220i
$690$		0			0
$691$	−22.1164	−	5.92606i	−0.841346	−	0.225438i	−0.187689	−	0.982229i	$-0.560100\pi$
$691$	−22.1164	−	5.92606i	−0.841346	−	0.225438i	−0.653657	+	0.756791i	$0.726766\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.25498	−	8.41570i	0.0855362	−	0.319226i
$696$		0			0
$697$	31.3123	−	8.39011i	1.18604	−	0.317798i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	37.0143			1.39801			0.699005	−	0.715116i	$-0.253626\pi$
$701$	37.0143			1.39801			0.699005	+	0.715116i	$0.253626\pi$
$702$		0			0
$703$	−61.3090			−2.31231
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.436950	+	0.117080i	−0.0164332	+	0.00440326i
$708$		0			0
$709$	−2.55799	+	9.54653i	−0.0960672	+	0.358528i	−0.997179	−	0.0750590i	$-0.976085\pi$
$709$	−2.55799	+	9.54653i	−0.0960672	+	0.358528i	0.901112	+	0.433587i	$0.142752\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−14.0560	−	3.76630i	−0.526403	−	0.141049i
$714$		0			0
$715$	0.712593	+	0.648184i	0.0266495	+	0.0242407i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.8636			0.591613			0.295807	−	0.955248i	$-0.404412\pi$
$719$	15.8636			0.591613			0.295807	+	0.955248i	$0.404412\pi$
$720$		0			0
$721$	−0.404125	+	0.404125i	−0.0150504	+	0.0150504i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	14.1063	−	24.4328i	0.523894	−	0.907411i
$726$		0			0
$727$	−28.3237	+	16.3527i	−1.05047	+	0.606489i	−0.922781	−	0.385325i	$-0.874089\pi$
$727$	−28.3237	+	16.3527i	−1.05047	+	0.606489i	−0.127689	+	0.991814i	$0.540756\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	17.8003	−	10.2770i	0.658367	−	0.380109i
$732$		0			0
$733$	−2.45680	−	9.16892i	−0.0907442	−	0.338662i	0.905596	−	0.424142i	$-0.139424\pi$
$733$	−2.45680	−	9.16892i	−0.0907442	−	0.338662i	−0.996340	+	0.0854802i	$0.972758\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			4.45932i			0.164261i
$738$		0			0
$739$	−15.9355	−	15.9355i	−0.586198	−	0.586198i	0.350402	−	0.936599i	$-0.386045\pi$
$739$	−15.9355	−	15.9355i	−0.586198	−	0.586198i	−0.936599	+	0.350402i	$0.886045\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−29.4945	+	7.90302i	−1.08205	+	0.289934i	−0.755434	−	0.655224i	$-0.772574\pi$
$743$	−29.4945	+	7.90302i	−1.08205	+	0.289934i	−0.326613	+	0.945158i	$0.605907\pi$
$744$		0			0
$745$	9.75535	−	5.63226i	0.357408	−	0.206350i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.559965	+	0.150042i	0.0204607	+	0.00548242i
$750$		0			0
$751$	27.5324	+	15.8958i	1.00467	+	0.580048i	0.909627	−	0.415425i	$-0.136367\pi$
$751$	27.5324	+	15.8958i	1.00467	+	0.580048i	0.0950448	+	0.995473i	$0.469701\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			4.07548i			0.148322i
$756$		0			0
$757$	9.24174			0.335897			0.167948	−	0.985796i	$-0.446286\pi$
$757$	9.24174			0.335897			0.167948	+	0.985796i	$0.446286\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−8.57104	−	31.9876i	−0.310700	−	1.15955i	−0.927927	−	0.372763i	$-0.878411\pi$
$761$	−8.57104	−	31.9876i	−0.310700	−	1.15955i	0.617227	−	0.786785i	$-0.288256\pi$
$762$		0			0
$763$	0.218626	+	0.378671i	0.00791478	+	0.0137088i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.1047	−	23.4624i	0.437075	−	0.847179i
$768$		0			0
$769$	−2.63678	−	9.84061i	−0.0950849	−	0.354862i	0.901947	−	0.431846i	$-0.142138\pi$
$769$	−2.63678	−	9.84061i	−0.0950849	−	0.354862i	−0.997032	+	0.0769842i	$0.975471\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	12.1060	+	12.1060i	0.435421	+	0.435421i	0.890468	−	0.455046i	$-0.150377\pi$
$773$	12.1060	+	12.1060i	0.435421	+	0.435421i	−0.455046	+	0.890468i	$0.650377\pi$
$774$		0			0
$775$	5.70897	+	5.70897i	0.205072	+	0.205072i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−20.3313	+	35.2149i	−0.728446	+	1.26171i
$780$		0			0
$781$	0.198121	+	0.343156i	0.00708934	+	0.0122791i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.62046	+	6.04765i	−0.0578368	+	0.215850i
$786$		0			0
$787$	28.9697	−	7.76240i	1.03266	−	0.276700i	0.297590	−	0.954694i	$-0.403817\pi$
$787$	28.9697	−	7.76240i	1.03266	−	0.276700i	0.735067	+	0.677994i	$0.237151\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.0646999	−	0.0646999i	0.00230047	−	0.00230047i
$792$		0			0
$793$	0.698829	−	3.20779i	0.0248161	−	0.113912i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.1855	+	24.5700i	−0.502476	+	0.870314i	0.497520	+	0.867453i	$0.334244\pi$
$797$	−14.1855	+	24.5700i	−0.502476	+	0.870314i	−0.999996	+	0.00286136i	$0.999089\pi$
$798$		0			0
$799$	67.3926	+	18.0578i	2.38418	+	0.638839i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.14568	−	1.98438i	−0.0404302	−	0.0700271i
$804$		0			0
$805$	0.405743	+	0.234256i	0.0143006	+	0.00825644i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	41.8676i		−	1.47199i	−0.676989	−	0.735993i	$-0.736715\pi$
$809$		−	41.8676i		−	1.47199i	0.676989	−	0.735993i	$-0.263285\pi$
$810$		0			0
$811$	24.9544	−	24.9544i	0.876267	−	0.876267i	−0.116879	−	0.993146i	$-0.537289\pi$
$811$	24.9544	−	24.9544i	0.876267	−	0.876267i	0.993146	+	0.116879i	$0.0372890\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.36625	−	3.09820i	−0.187971	−	0.108525i
$816$		0			0
$817$	−6.67294	+	24.9037i	−0.233457	+	0.871272i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.93204	+	18.4066i	−0.172129	+	0.642396i	0.824893	+	0.565288i	$0.191235\pi$
$821$	−4.93204	+	18.4066i	−0.172129	+	0.642396i	−0.997023	+	0.0771075i	$0.975432\pi$
$822$		0			0
$823$	8.28351	+	4.78249i	0.288745	+	0.166707i	0.637376	−	0.770553i	$-0.280020\pi$
$823$	8.28351	+	4.78249i	0.288745	+	0.166707i	−0.348631	+	0.937260i	$0.613353\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.8587	−	13.8587i	0.481915	−	0.481915i	−0.423828	−	0.905743i	$-0.639314\pi$
$827$	13.8587	−	13.8587i	0.481915	−	0.481915i	0.905743	+	0.423828i	$0.139314\pi$
$828$		0			0
$829$			45.6637i			1.58597i	0.609244	+	0.792983i	$0.291473\pi$
$829$			45.6637i			1.58597i	−0.609244	+	0.792983i	$0.708527\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	33.3770	+	19.2702i	1.15644	+	0.667673i
$834$		0			0
$835$	−6.68345	−	11.5761i	−0.231290	−	0.400606i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−13.6275	−	3.65147i	−0.470472	−	0.126063i	0.0157905	−	0.999875i	$-0.494974\pi$
$839$	−13.6275	−	3.65147i	−0.470472	−	0.126063i	−0.486263	+	0.873813i	$0.661640\pi$
$840$		0			0
$841$	3.94137	−	6.82665i	0.135909	−	0.235402i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.70059	+	7.25395i	0.0929031	+	0.249544i
$846$		0			0
$847$	0.717597	−	0.717597i	0.0246569	−	0.0246569i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	71.7058	−	19.2135i	2.45804	−	0.658631i
$852$		0			0
$853$	9.76933	−	36.4596i	0.334495	−	1.24835i	−0.569920	−	0.821700i	$-0.693026\pi$
$853$	9.76933	−	36.4596i	0.334495	−	1.24835i	0.904415	−	0.426653i	$-0.140308\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.38094	+	7.58800i	0.149650	+	0.259201i	0.931098	−	0.364769i	$-0.118852\pi$
$857$	4.38094	+	7.58800i	0.149650	+	0.259201i	−0.781448	+	0.623970i	$0.785519\pi$
$858$		0			0
$859$	−17.2450	+	29.8692i	−0.588391	+	1.01912i	0.406052	+	0.913850i	$0.366905\pi$
$859$	−17.2450	+	29.8692i	−0.588391	+	1.01912i	−0.994443	+	0.105274i	$0.966428\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	27.1745	+	27.1745i	0.925029	+	0.925029i	0.997379	−	0.0723499i	$-0.0230498\pi$
$863$	27.1745	+	27.1745i	0.925029	+	0.925029i	−0.0723499	+	0.997379i	$0.523050\pi$
$864$		0			0
$865$	6.91872	+	6.91872i	0.235243	+	0.235243i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.950282	−	3.54650i	−0.0322361	−	0.120307i
$870$		0			0
$871$	−16.4288	+	31.8438i	−0.556669	+	1.07899i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.269859	−	0.467410i	−0.00912291	−	0.0158013i
$876$		0			0
$877$	1.12631	+	4.20346i	0.0380329	+	0.141941i	0.982332	−	0.187149i	$-0.0599248\pi$
$877$	1.12631	+	4.20346i	0.0380329	+	0.141941i	−0.944299	+	0.329090i	$0.893258\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−17.7491			−0.597983			−0.298992	−	0.954256i	$-0.596650\pi$
$881$	−17.7491			−0.597983			−0.298992	+	0.954256i	$0.596650\pi$
$882$		0			0
$883$			13.6618i			0.459757i	0.973219	+	0.229879i	$0.0738329\pi$
$883$			13.6618i			0.459757i	−0.973219	+	0.229879i	$0.926167\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	27.8424	+	16.0748i	0.934858	+	0.539740i	0.888345	−	0.459177i	$-0.151856\pi$
$887$	27.8424	+	16.0748i	0.934858	+	0.539740i	0.0465133	+	0.998918i	$0.485189\pi$
$888$		0			0
$889$	−0.523200	−	0.140191i	−0.0175476	−	0.00470185i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−75.7920	+	43.7586i	−2.53628	+	1.46432i
$894$		0			0
$895$	−10.0361	+	2.68916i	−0.335470	+	0.0898888i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	7.46343	+	7.46343i	0.248919	+	0.248919i
$900$		0			0
$901$		−	4.34683i		−	0.144814i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.03927	+	7.61066i	0.0677877	+	0.252987i
$906$		0			0
$907$	22.2907	−	12.8695i	0.740149	−	0.427325i	−0.0819746	−	0.996634i	$-0.526123\pi$
$907$	22.2907	−	12.8695i	0.740149	−	0.427325i	0.822123	+	0.569309i	$0.192789\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	11.7787	−	6.80041i	0.390244	−	0.225308i	−0.292022	−	0.956412i	$-0.594328\pi$
$911$	11.7787	−	6.80041i	0.390244	−	0.225308i	0.682266	+	0.731104i	$0.260995\pi$
$912$		0			0
$913$	−2.27177	+	3.93483i	−0.0751847	+	0.130224i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.0425578	−	0.0425578i	0.00140538	−	0.00140538i
$918$		0			0
$919$	3.46854			0.114417			0.0572083	−	0.998362i	$-0.481780\pi$
$919$	3.46854			0.114417			0.0572083	+	0.998362i	$0.481780\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.150536	+	3.18037i	0.00495496	+	0.104683i
$924$		0			0
$925$	−39.7839	−	10.6601i	−1.30809	−	0.350501i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	7.03879	−	26.2691i	0.230935	−	0.861862i	−0.749004	−	0.662565i	$-0.769468\pi$
$929$	7.03879	−	26.2691i	0.230935	−	0.861862i	0.979939	−	0.199296i	$-0.0638657\pi$
$930$		0			0
$931$	−46.6966	+	12.5123i	−1.53042	+	0.410074i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.47283			0.0481668
$936$		0			0
$937$	40.3459			1.31804			0.659022	−	0.752124i	$-0.270970\pi$
$937$	40.3459			1.31804			0.659022	+	0.752124i	$0.270970\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−49.4561	+	13.2517i	−1.61222	+	0.431994i	−0.948704	−	0.316165i	$-0.897605\pi$
$941$	−49.4561	+	13.2517i	−1.61222	+	0.431994i	−0.663520	+	0.748159i	$0.730938\pi$
$942$		0			0
$943$	12.7432	−	47.5583i	0.414976	−	1.54871i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.4567	+	6.28521i	0.762241	+	0.204242i	0.618941	−	0.785438i	$-0.287562\pi$
$947$	23.4567	+	6.28521i	0.762241	+	0.204242i	0.143300	+	0.989679i	$0.454229\pi$
$948$		0			0
$949$	−0.870508	−	18.3912i	−0.0282579	−	0.597003i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	35.8048			1.15983			0.579915	−	0.814677i	$-0.303086\pi$
$953$	35.8048			1.15983			0.579915	+	0.814677i	$0.303086\pi$
$954$		0			0
$955$	−5.48317	+	5.48317i	−0.177431	+	0.177431i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.332803	+	0.576431i	−0.0107468	+	0.0186139i
$960$		0			0
$961$	24.2309	−	13.9897i	0.781643	−	0.451282i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.32276	+	0.763697i	−0.0425812	+	0.0245843i
$966$		0			0
$967$	14.8327	+	55.3566i	0.476989	+	1.78015i	0.613703	+	0.789537i	$0.289679\pi$
$967$	14.8327	+	55.3566i	0.476989	+	1.78015i	−0.136714	+	0.990611i	$0.543654\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	33.6934i		−	1.08127i	−0.841257	−	0.540636i	$-0.818184\pi$
$971$		−	33.6934i		−	1.08127i	0.841257	−	0.540636i	$-0.181816\pi$
$972$		0			0
$973$	0.972389	+	0.972389i	0.0311734	+	0.0311734i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−48.6894	+	13.0463i	−1.55771	+	0.417387i	−0.931938	−	0.362618i	$-0.881883\pi$
$977$	−48.6894	+	13.0463i	−1.55771	+	0.417387i	−0.625773	+	0.780006i	$0.715216\pi$
$978$		0			0
$979$	−2.45476	+	1.41726i	−0.0784546	+	0.0452958i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−8.37401	−	2.24381i	−0.267090	−	0.0715664i	0.122789	−	0.992433i	$-0.460816\pi$
$983$	−8.37401	−	2.24381i	−0.267090	−	0.0715664i	−0.389878	+	0.920866i	$0.627483\pi$
$984$		0			0
$985$	−10.2348	−	5.90905i	−0.326107	−	0.188278i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	31.2181i		−	0.992679i
$990$		0			0
$991$	−41.3299			−1.31289			−0.656443	−	0.754376i	$-0.727940\pi$
$991$	−41.3299			−1.31289			−0.656443	+	0.754376i	$0.727940\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.65450	−	9.90675i	−0.0841535	−	0.314065i
$996$		0			0
$997$	−21.3446	−	36.9700i	−0.675991	−	1.17085i	−0.976178	−	0.216970i	$-0.930383\pi$
$997$	−21.3446	−	36.9700i	−0.675991	−	1.17085i	0.300187	−	0.953880i	$-0.402951\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1404.2.cj.a.1097.9		56
3.2	odd	2		468.2.cg.a.5.1	✓	56
9.2	odd	6	inner	1404.2.cj.a.629.9		56
9.7	even	3		468.2.cg.a.317.1	yes	56
13.8	odd	4	inner	1404.2.cj.a.125.9		56
39.8	even	4		468.2.cg.a.437.1	yes	56
117.34	odd	12		468.2.cg.a.281.1	yes	56
117.47	even	12	inner	1404.2.cj.a.1061.9		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.cg.a.5.1	✓	56	3.2	odd	2
468.2.cg.a.281.1	yes	56	117.34	odd	12
468.2.cg.a.317.1	yes	56	9.7	even	3
468.2.cg.a.437.1	yes	56	39.8	even	4
1404.2.cj.a.125.9		56	13.8	odd	4	inner
1404.2.cj.a.629.9		56	9.2	odd	6	inner
1404.2.cj.a.1061.9		56	117.47	even	12	inner
1404.2.cj.a.1097.9		56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1404 = 2^{2} \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1404.cj (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.575123 - 0.154104i) q^{5} +(-0.0243233 + 0.0907757i) q^{7} +(0.433424 + 0.116136i) q^{11} +(2.66720 + 2.42612i) q^{13} +5.51273 q^{17} +(-4.88963 + 4.88963i) q^{19} +(4.18646 - 7.25117i) q^{23} +(-4.02311 + 2.32274i) q^{25} +(-5.25947 + 3.03656i) q^{29} +(-0.449819 - 1.67875i) q^{31} +0.0559555i q^{35} +(6.26928 + 6.26928i) q^{37} +(5.68000 - 1.52195i) q^{41} +(3.22894 - 1.86423i) q^{43} +(12.2249 + 3.27565i) q^{47} +(6.05453 + 3.49558i) q^{49} -0.788507i q^{53} +0.267169 q^{55} +(-1.89515 - 7.07279i) q^{59} +(-0.455275 - 0.788559i) q^{61} +(1.90784 + 0.984291i) q^{65} +(2.57215 + 9.59938i) q^{67} +(0.624421 + 0.624421i) q^{71} +(-3.61085 - 3.61085i) q^{73} +(-0.0210846 + 0.0365196i) q^{77} +(-4.09126 - 7.08627i) q^{79} +(-2.62073 + 9.78070i) q^{83} +(3.17050 - 0.849533i) q^{85} +(-4.46678 + 4.46678i) q^{89} +(-0.285108 + 0.183106i) q^{91} +(-2.05863 + 3.56565i) q^{95} +(15.1985 + 4.07242i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{7} + 12 q^{11} + 4 q^{19} - 4 q^{31} - 4 q^{37} - 24 q^{41} - 66 q^{47} + 78 q^{65} - 14 q^{67} + 28 q^{73} - 24 q^{79} + 78 q^{83} + 36 q^{85} - 8 q^{91} + 26 q^{97}+O(q^{100}) \) 56 * q - 2 * q^7 + 12 * q^11 + 4 * q^19 - 4 * q^31 - 4 * q^37 - 24 * q^41 - 66 * q^47 + 78 * q^65 - 14 * q^67 + 28 * q^73 - 24 * q^79 + 78 * q^83 + 36 * q^85 - 8 * q^91 + 26 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more