LMFDB - Embedded newform 2150.2.b.o.1549.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2150,2,Mod(1549,2150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("2150.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2150 = 2 \cdot 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2150.b (of order $2$, degree $1$, 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:	$17.1678364346$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 430)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1549.3
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2150.1549
Dual form			2150.2.b.o.1549.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} +1.41421 q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} +1.41421 q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +0.585786 q^{11} +1.41421i q^{12} +1.82843i q^{13} -1.00000 q^{14} +1.00000 q^{16} +1.41421i q^{17} +1.00000i q^{18} +1.00000 q^{19} +1.41421 q^{21} +0.585786i q^{22} +5.07107i q^{23} -1.41421 q^{24} -1.82843 q^{26} -5.65685i q^{27} -1.00000i q^{28} -1.24264 q^{29} -0.414214 q^{31} +1.00000i q^{32} -0.828427i q^{33} -1.41421 q^{34} -1.00000 q^{36} +2.24264i q^{37} +1.00000i q^{38} +2.58579 q^{39} -1.82843 q^{41} +1.41421i q^{42} -1.00000i q^{43} -0.585786 q^{44} -5.07107 q^{46} +7.07107i q^{47} -1.41421i q^{48} +6.00000 q^{49} +2.00000 q^{51} -1.82843i q^{52} +5.65685i q^{53} +5.65685 q^{54} +1.00000 q^{56} -1.41421i q^{57} -1.24264i q^{58} +1.17157 q^{59} +0.0710678 q^{61} -0.414214i q^{62} +1.00000i q^{63} -1.00000 q^{64} +0.828427 q^{66} -1.24264i q^{67} -1.41421i q^{68} +7.17157 q^{69} +11.8995 q^{71} -1.00000i q^{72} +9.24264i q^{73} -2.24264 q^{74} -1.00000 q^{76} +0.585786i q^{77} +2.58579i q^{78} +8.41421 q^{79} -5.00000 q^{81} -1.82843i q^{82} -3.65685i q^{83} -1.41421 q^{84} +1.00000 q^{86} +1.75736i q^{87} -0.585786i q^{88} +9.07107 q^{89} -1.82843 q^{91} -5.07107i q^{92} +0.585786i q^{93} -7.07107 q^{94} +1.41421 q^{96} +13.5563i q^{97} +6.00000i q^{98} +0.585786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{9} + 8 q^{11} - 4 q^{14} + 4 q^{16} + 4 q^{19} + 4 q^{26} + 12 q^{29} + 4 q^{31} - 4 q^{36} + 16 q^{39} + 4 q^{41} - 8 q^{44} + 8 q^{46} + 24 q^{49} + 8 q^{51} + 4 q^{56} + 16 q^{59} - 28 q^{61} - 4 q^{64} - 8 q^{66} + 40 q^{69} + 8 q^{71} + 8 q^{74} - 4 q^{76} + 28 q^{79} - 20 q^{81} + 4 q^{86} + 8 q^{89} + 4 q^{91} + 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^9 + 8 * q^11 - 4 * q^14 + 4 * q^16 + 4 * q^19 + 4 * q^26 + 12 * q^29 + 4 * q^31 - 4 * q^36 + 16 * q^39 + 4 * q^41 - 8 * q^44 + 8 * q^46 + 24 * q^49 + 8 * q^51 + 4 * q^56 + 16 * q^59 - 28 * q^61 - 4 * q^64 - 8 * q^66 + 40 * q^69 + 8 * q^71 + 8 * q^74 - 4 * q^76 + 28 * q^79 - 20 * q^81 + 4 * q^86 + 8 * q^89 + 4 * q^91 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2150\mathbb{Z}\right)^\times$.

$n$	$1377$	$1551$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	− 1.41421i	− 0.816497i	−0.912871	−	0.408248i	$-0.866140\pi$
$3$	− 1.41421i	− 0.816497i	0.912871	−	0.408248i	$-0.133860\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.41421	0.577350
$7$	1.00000i	0.377964i	0.981981	+	0.188982i	$0.0605189\pi$
$7$	1.00000i	0.377964i	−0.981981	+	0.188982i	$0.939481\pi$
$8$	− 1.00000i	− 0.353553i
$9$	1.00000	0.333333
$10$	0	0
$11$	0.585786	0.176621	0.0883106	−	0.996093i	$-0.471853\pi$
$11$	0.585786	0.176621	0.0883106	+	0.996093i	$0.471853\pi$
$12$	1.41421i	0.408248i
$13$	1.82843i	0.507114i	0.967320	+	0.253557i	$0.0816006\pi$
$13$	1.82843i	0.507114i	−0.967320	+	0.253557i	$0.918399\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	1.41421i	0.342997i	0.985184	+	0.171499i	$0.0548609\pi$
$17$	1.41421i	0.342997i	−0.985184	+	0.171499i	$0.945139\pi$
$18$	1.00000i	0.235702i
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	0	0
$21$	1.41421	0.308607
$22$	0.585786i	0.124890i
$23$	5.07107i	1.05739i	0.848812	+	0.528695i	$0.177319\pi$
$23$	5.07107i	1.05739i	−0.848812	+	0.528695i	$0.822681\pi$
$24$	−1.41421	−0.288675
$25$	0	0
$26$	−1.82843	−0.358584
$27$	− 5.65685i	− 1.08866i
$28$	− 1.00000i	− 0.188982i
$29$	−1.24264	−0.230753	−0.115376	−	0.993322i	$-0.536807\pi$
$29$	−1.24264	−0.230753	−0.115376	+	0.993322i	$0.536807\pi$
$30$	0	0
$31$	−0.414214	−0.0743950	−0.0371975	−	0.999308i	$-0.511843\pi$
$31$	−0.414214	−0.0743950	−0.0371975	+	0.999308i	$0.511843\pi$
$32$	1.00000i	0.176777i
$33$	− 0.828427i	− 0.144211i
$34$	−1.41421	−0.242536
$35$	0	0
$36$	−1.00000	−0.166667
$37$	2.24264i	0.368688i	0.982862	+	0.184344i	$0.0590160\pi$
$37$	2.24264i	0.368688i	−0.982862	+	0.184344i	$0.940984\pi$
$38$	1.00000i	0.162221i
$39$	2.58579	0.414057
$40$	0	0
$41$	−1.82843	−0.285552	−0.142776	−	0.989755i	$-0.545603\pi$
$41$	−1.82843	−0.285552	−0.142776	+	0.989755i	$0.545603\pi$
$42$	1.41421i	0.218218i
$43$	− 1.00000i	− 0.152499i
$43$	− 1.00000i	− 0.152499i
$44$	−0.585786	−0.0883106
$45$	0	0
$46$	−5.07107	−0.747688
$47$	7.07107i	1.03142i	0.856763	+	0.515711i	$0.172472\pi$
$47$	7.07107i	1.03142i	−0.856763	+	0.515711i	$0.827528\pi$
$48$	− 1.41421i	− 0.204124i
$49$	6.00000	0.857143
$50$	0	0
$51$	2.00000	0.280056
$52$	− 1.82843i	− 0.253557i
$53$	5.65685i	0.777029i	0.921443	+	0.388514i	$0.127012\pi$
$53$	5.65685i	0.777029i	−0.921443	+	0.388514i	$0.872988\pi$
$54$	5.65685	0.769800
$55$	0	0
$56$	1.00000	0.133631
$57$	− 1.41421i	− 0.187317i
$58$	− 1.24264i	− 0.163167i
$59$	1.17157	0.152526	0.0762629	−	0.997088i	$-0.475701\pi$
$59$	1.17157	0.152526	0.0762629	+	0.997088i	$0.475701\pi$
$60$	0	0
$61$	0.0710678	0.00909930	0.00454965	−	0.999990i	$-0.498552\pi$
$61$	0.0710678	0.00909930	0.00454965	+	0.999990i	$0.498552\pi$
$62$	− 0.414214i	− 0.0526052i
$63$	1.00000i	0.125988i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	0.828427	0.101972
$67$	− 1.24264i	− 0.151813i	−0.997115	−	0.0759064i	$-0.975815\pi$
$67$	− 1.24264i	− 0.151813i	0.997115	−	0.0759064i	$-0.0241850\pi$
$68$	− 1.41421i	− 0.171499i
$69$	7.17157	0.863356
$70$	0	0
$71$	11.8995	1.41221	0.706105	−	0.708107i	$-0.250451\pi$
$71$	11.8995	1.41221	0.706105	+	0.708107i	$0.250451\pi$
$72$	− 1.00000i	− 0.117851i
$73$	9.24264i	1.08177i	0.841097	+	0.540885i	$0.181910\pi$
$73$	9.24264i	1.08177i	−0.841097	+	0.540885i	$0.818090\pi$
$74$	−2.24264	−0.260702
$75$	0	0
$76$	−1.00000	−0.114708
$77$	0.585786i	0.0667566i
$78$	2.58579i	0.292783i
$79$	8.41421	0.946673	0.473336	−	0.880882i	$-0.343049\pi$
$79$	8.41421	0.946673	0.473336	+	0.880882i	$0.343049\pi$
$80$	0	0
$81$	−5.00000	−0.555556
$82$	− 1.82843i	− 0.201916i
$83$	− 3.65685i	− 0.401392i	−0.979654	−	0.200696i	$-0.935680\pi$
$83$	− 3.65685i	− 0.401392i	0.979654	−	0.200696i	$-0.0643203\pi$
$84$	−1.41421	−0.154303
$85$	0	0
$86$	1.00000	0.107833
$87$	1.75736i	0.188409i
$88$	− 0.585786i	− 0.0624450i
$89$	9.07107	0.961531	0.480766	−	0.876849i	$-0.340359\pi$
$89$	9.07107	0.961531	0.480766	+	0.876849i	$0.340359\pi$
$90$	0	0
$91$	−1.82843	−0.191671
$92$	− 5.07107i	− 0.528695i
$93$	0.585786i	0.0607432i
$94$	−7.07107	−0.729325
$95$	0	0
$96$	1.41421	0.144338
$97$	13.5563i	1.37644i	0.725503	+	0.688219i	$0.241607\pi$
$97$	13.5563i	1.37644i	−0.725503	+	0.688219i	$0.758393\pi$
$98$	6.00000i	0.606092i
$99$	0.585786	0.0588738
$100$	0	0
$101$	1.41421	0.140720	0.0703598	−	0.997522i	$-0.477585\pi$
$101$	1.41421	0.140720	0.0703598	+	0.997522i	$0.477585\pi$
$102$	2.00000i	0.198030i
$103$	− 0.828427i	− 0.0816274i	−0.999167	−	0.0408137i	$-0.987005\pi$
$103$	− 0.828427i	− 0.0816274i	0.999167	−	0.0408137i	$-0.0129950\pi$
$104$	1.82843	0.179292
$105$	0	0
$106$	−5.65685	−0.549442
$107$	1.92893i	0.186477i	0.995644	+	0.0932385i	$0.0297219\pi$
$107$	1.92893i	0.186477i	−0.995644	+	0.0932385i	$0.970278\pi$
$108$	5.65685i	0.544331i
$109$	10.8284	1.03718	0.518588	−	0.855024i	$-0.326458\pi$
$109$	10.8284	1.03718	0.518588	+	0.855024i	$0.326458\pi$
$110$	0	0
$111$	3.17157	0.301032
$112$	1.00000i	0.0944911i
$113$	− 4.89949i	− 0.460906i	−0.973083	−	0.230453i	$-0.925979\pi$
$113$	− 4.89949i	− 0.460906i	0.973083	−	0.230453i	$-0.0740207\pi$
$114$	1.41421	0.132453
$115$	0	0
$116$	1.24264	0.115376
$117$	1.82843i	0.169038i
$118$	1.17157i	0.107852i
$119$	−1.41421	−0.129641
$120$	0	0
$121$	−10.6569	−0.968805
$122$	0.0710678i	0.00643418i
$123$	2.58579i	0.233153i
$124$	0.414214	0.0371975
$125$	0	0
$126$	−1.00000	−0.0890871
$127$	3.51472i	0.311881i	0.987766	+	0.155940i	$0.0498408\pi$
$127$	3.51472i	0.311881i	−0.987766	+	0.155940i	$0.950159\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−1.41421	−0.124515
$130$	0	0
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0.828427i	0.0721053i
$133$	1.00000i	0.0867110i
$134$	1.24264	0.107348
$135$	0	0
$136$	1.41421	0.121268
$137$	3.92893i	0.335671i	0.985815	+	0.167836i	$0.0536778\pi$
$137$	3.92893i	0.335671i	−0.985815	+	0.167836i	$0.946322\pi$
$138$	7.17157i	0.610485i
$139$	6.24264	0.529494	0.264747	−	0.964318i	$-0.414712\pi$
$139$	6.24264	0.529494	0.264747	+	0.964318i	$0.414712\pi$
$140$	0	0
$141$	10.0000	0.842152
$142$	11.8995i	0.998583i
$143$	1.07107i	0.0895672i
$144$	1.00000	0.0833333
$145$	0	0
$146$	−9.24264	−0.764926
$147$	− 8.48528i	− 0.699854i
$148$	− 2.24264i	− 0.184344i
$149$	10.5563	0.864810	0.432405	−	0.901680i	$-0.357665\pi$
$149$	10.5563	0.864810	0.432405	+	0.901680i	$0.357665\pi$
$150$	0	0
$151$	10.4853	0.853280	0.426640	−	0.904422i	$-0.359697\pi$
$151$	10.4853	0.853280	0.426640	+	0.904422i	$0.359697\pi$
$152$	− 1.00000i	− 0.0811107i
$153$	1.41421i	0.114332i
$154$	−0.585786	−0.0472040
$155$	0	0
$156$	−2.58579	−0.207029
$157$	10.2426i	0.817452i	0.912657	+	0.408726i	$0.134027\pi$
$157$	10.2426i	0.817452i	−0.912657	+	0.408726i	$0.865973\pi$
$158$	8.41421i	0.669399i
$159$	8.00000	0.634441
$160$	0	0
$161$	−5.07107	−0.399656
$162$	− 5.00000i	− 0.392837i
$163$	− 13.6569i	− 1.06969i	−0.844951	−	0.534844i	$-0.820370\pi$
$163$	− 13.6569i	− 1.06969i	0.844951	−	0.534844i	$-0.179630\pi$
$164$	1.82843	0.142776
$165$	0	0
$166$	3.65685	0.283827
$167$	13.5563i	1.04902i	0.851404	+	0.524511i	$0.175752\pi$
$167$	13.5563i	1.04902i	−0.851404	+	0.524511i	$0.824248\pi$
$168$	− 1.41421i	− 0.109109i
$169$	9.65685	0.742835
$170$	0	0
$171$	1.00000	0.0764719
$172$	1.00000i	0.0762493i
$173$	− 0.514719i	− 0.0391333i	−0.999809	−	0.0195667i	$-0.993771\pi$
$173$	− 0.514719i	− 0.0391333i	0.999809	−	0.0195667i	$-0.00622866\pi$
$174$	−1.75736	−0.133225
$175$	0	0
$176$	0.585786	0.0441553
$177$	− 1.65685i	− 0.124537i
$178$	9.07107i	0.679905i
$179$	−17.4853	−1.30691	−0.653456	−	0.756965i	$-0.726681\pi$
$179$	−17.4853	−1.30691	−0.653456	+	0.756965i	$0.726681\pi$
$180$	0	0
$181$	−15.0711	−1.12022	−0.560112	−	0.828417i	$-0.689242\pi$
$181$	−15.0711	−1.12022	−0.560112	+	0.828417i	$0.689242\pi$
$182$	− 1.82843i	− 0.135532i
$183$	− 0.100505i	− 0.00742955i
$184$	5.07107	0.373844
$185$	0	0
$186$	−0.585786	−0.0429519
$187$	0.828427i	0.0605806i
$188$	− 7.07107i	− 0.515711i
$189$	5.65685	0.411476
$190$	0	0
$191$	19.8995	1.43988	0.719938	−	0.694038i	$-0.244170\pi$
$191$	19.8995	1.43988	0.719938	+	0.694038i	$0.244170\pi$
$192$	1.41421i	0.102062i
$193$	− 6.82843i	− 0.491521i	−0.969331	−	0.245760i	$-0.920962\pi$
$193$	− 6.82843i	− 0.491521i	0.969331	−	0.245760i	$-0.0790377\pi$
$194$	−13.5563	−0.973289
$195$	0	0
$196$	−6.00000	−0.428571
$197$	25.1421i	1.79130i	0.444757	+	0.895651i	$0.353290\pi$
$197$	25.1421i	1.79130i	−0.444757	+	0.895651i	$0.646710\pi$
$198$	0.585786i	0.0416300i
$199$	0.100505	0.00712462	0.00356231	−	0.999994i	$-0.498866\pi$
$199$	0.100505	0.00712462	0.00356231	+	0.999994i	$0.498866\pi$
$200$	0	0
$201$	−1.75736	−0.123955
$202$	1.41421i	0.0995037i
$203$	− 1.24264i	− 0.0872163i
$204$	−2.00000	−0.140028
$205$	0	0
$206$	0.828427	0.0577193
$207$	5.07107i	0.352464i
$208$	1.82843i	0.126779i
$209$	0.585786	0.0405197
$210$	0	0
$211$	−1.65685	−0.114063	−0.0570313	−	0.998372i	$-0.518163\pi$
$211$	−1.65685	−0.114063	−0.0570313	+	0.998372i	$0.518163\pi$
$212$	− 5.65685i	− 0.388514i
$213$	− 16.8284i	− 1.15306i
$214$	−1.92893	−0.131859
$215$	0	0
$216$	−5.65685	−0.384900
$217$	− 0.414214i	− 0.0281186i
$218$	10.8284i	0.733394i
$219$	13.0711	0.883261
$220$	0	0
$221$	−2.58579	−0.173939
$222$	3.17157i	0.212862i
$223$	− 16.1421i	− 1.08096i	−0.841358	−	0.540479i	$-0.818243\pi$
$223$	− 16.1421i	− 1.08096i	0.841358	−	0.540479i	$-0.181757\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	4.89949	0.325910
$227$	9.17157i	0.608739i	0.952554	+	0.304369i	$0.0984457\pi$
$227$	9.17157i	0.608739i	−0.952554	+	0.304369i	$0.901554\pi$
$228$	1.41421i	0.0936586i
$229$	−0.828427	−0.0547440	−0.0273720	−	0.999625i	$-0.508714\pi$
$229$	−0.828427	−0.0547440	−0.0273720	+	0.999625i	$0.508714\pi$
$230$	0	0
$231$	0.828427	0.0545065
$232$	1.24264i	0.0815834i
$233$	− 8.48528i	− 0.555889i	−0.960597	−	0.277945i	$-0.910347\pi$
$233$	− 8.48528i	− 0.555889i	0.960597	−	0.277945i	$-0.0896532\pi$
$234$	−1.82843	−0.119528
$235$	0	0
$236$	−1.17157	−0.0762629
$237$	− 11.8995i	− 0.772955i
$238$	− 1.41421i	− 0.0916698i
$239$	−11.5858	−0.749422	−0.374711	−	0.927142i	$-0.622258\pi$
$239$	−11.5858	−0.749422	−0.374711	+	0.927142i	$0.622258\pi$
$240$	0	0
$241$	−21.4142	−1.37941	−0.689705	−	0.724090i	$-0.742260\pi$
$241$	−21.4142	−1.37941	−0.689705	+	0.724090i	$0.742260\pi$
$242$	− 10.6569i	− 0.685049i
$243$	− 9.89949i	− 0.635053i
$244$	−0.0710678	−0.00454965
$245$	0	0
$246$	−2.58579	−0.164864
$247$	1.82843i	0.116340i
$248$	0.414214i	0.0263026i
$249$	−5.17157	−0.327735
$250$	0	0
$251$	−10.9706	−0.692456	−0.346228	−	0.938150i	$-0.612538\pi$
$251$	−10.9706	−0.692456	−0.346228	+	0.938150i	$0.612538\pi$
$252$	− 1.00000i	− 0.0629941i
$253$	2.97056i	0.186758i
$254$	−3.51472	−0.220533
$255$	0	0
$256$	1.00000	0.0625000
$257$	8.89949i	0.555135i	0.960706	+	0.277568i	$0.0895283\pi$
$257$	8.89949i	0.555135i	−0.960706	+	0.277568i	$0.910472\pi$
$258$	− 1.41421i	− 0.0880451i
$259$	−2.24264	−0.139351
$260$	0	0
$261$	−1.24264	−0.0769175
$262$	6.00000i	0.370681i
$263$	− 17.4853i	− 1.07819i	−0.842245	−	0.539094i	$-0.818767\pi$
$263$	− 17.4853i	− 1.07819i	0.842245	−	0.539094i	$-0.181233\pi$
$264$	−0.828427	−0.0509862
$265$	0	0
$266$	−1.00000	−0.0613139
$267$	− 12.8284i	− 0.785087i
$268$	1.24264i	0.0759064i
$269$	−9.17157	−0.559201	−0.279600	−	0.960116i	$-0.590202\pi$
$269$	−9.17157	−0.559201	−0.279600	+	0.960116i	$0.590202\pi$
$270$	0	0
$271$	8.89949	0.540606	0.270303	−	0.962775i	$-0.412876\pi$
$271$	8.89949	0.540606	0.270303	+	0.962775i	$0.412876\pi$
$272$	1.41421i	0.0857493i
$273$	2.58579i	0.156499i
$274$	−3.92893	−0.237355
$275$	0	0
$276$	−7.17157	−0.431678
$277$	− 0.485281i	− 0.0291577i	−0.999894	−	0.0145789i	$-0.995359\pi$
$277$	− 0.485281i	− 0.0291577i	0.999894	−	0.0145789i	$-0.00464076\pi$
$278$	6.24264i	0.374409i
$279$	−0.414214	−0.0247983
$280$	0	0
$281$	−1.34315	−0.0801254	−0.0400627	−	0.999197i	$-0.512756\pi$
$281$	−1.34315	−0.0801254	−0.0400627	+	0.999197i	$0.512756\pi$
$282$	10.0000i	0.595491i
$283$	− 18.7574i	− 1.11501i	−0.830174	−	0.557505i	$-0.811759\pi$
$283$	− 18.7574i	− 1.11501i	0.830174	−	0.557505i	$-0.188241\pi$
$284$	−11.8995	−0.706105
$285$	0	0
$286$	−1.07107	−0.0633336
$287$	− 1.82843i	− 0.107929i
$288$	1.00000i	0.0589256i
$289$	15.0000	0.882353
$290$	0	0
$291$	19.1716	1.12386
$292$	− 9.24264i	− 0.540885i
$293$	− 10.9706i	− 0.640907i	−0.947264	−	0.320454i	$-0.896165\pi$
$293$	− 10.9706i	− 0.640907i	0.947264	−	0.320454i	$-0.103835\pi$
$294$	8.48528	0.494872
$295$	0	0
$296$	2.24264	0.130351
$297$	− 3.31371i	− 0.192281i
$298$	10.5563i	0.611513i
$299$	−9.27208	−0.536218
$300$	0	0
$301$	1.00000	0.0576390
$302$	10.4853i	0.603360i
$303$	− 2.00000i	− 0.114897i
$304$	1.00000	0.0573539
$305$	0	0
$306$	−1.41421	−0.0808452
$307$	− 5.92893i	− 0.338382i	−0.985583	−	0.169191i	$-0.945885\pi$
$307$	− 5.92893i	− 0.338382i	0.985583	−	0.169191i	$-0.0541155\pi$
$308$	− 0.585786i	− 0.0333783i
$309$	−1.17157	−0.0666485
$310$	0	0
$311$	−4.07107	−0.230849	−0.115425	−	0.993316i	$-0.536823\pi$
$311$	−4.07107	−0.230849	−0.115425	+	0.993316i	$0.536823\pi$
$312$	− 2.58579i	− 0.146391i
$313$	1.31371i	0.0742552i	0.999311	+	0.0371276i	$0.0118208\pi$
$313$	1.31371i	0.0742552i	−0.999311	+	0.0371276i	$0.988179\pi$
$314$	−10.2426	−0.578026
$315$	0	0
$316$	−8.41421	−0.473336
$317$	0.857864i	0.0481825i	0.999710	+	0.0240912i	$0.00766922\pi$
$317$	0.857864i	0.0481825i	−0.999710	+	0.0240912i	$0.992331\pi$
$318$	8.00000i	0.448618i
$319$	−0.727922	−0.0407558
$320$	0	0
$321$	2.72792	0.152258
$322$	− 5.07107i	− 0.282600i
$323$	1.41421i	0.0786889i
$324$	5.00000	0.277778
$325$	0	0
$326$	13.6569	0.756383
$327$	− 15.3137i	− 0.846850i
$328$	1.82843i	0.100958i
$329$	−7.07107	−0.389841
$330$	0	0
$331$	−25.3137	−1.39137	−0.695684	−	0.718348i	$-0.744898\pi$
$331$	−25.3137	−1.39137	−0.695684	+	0.718348i	$0.744898\pi$
$332$	3.65685i	0.200696i
$333$	2.24264i	0.122896i
$334$	−13.5563	−0.741770
$335$	0	0
$336$	1.41421	0.0771517
$337$	− 8.34315i	− 0.454480i	−0.973839	−	0.227240i	$-0.927030\pi$
$337$	− 8.34315i	− 0.454480i	0.973839	−	0.227240i	$-0.0729702\pi$
$338$	9.65685i	0.525264i
$339$	−6.92893	−0.376328
$340$	0	0
$341$	−0.242641	−0.0131397
$342$	1.00000i	0.0540738i
$343$	13.0000i	0.701934i
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	0.514719	0.0276714
$347$	− 22.2426i	− 1.19405i	−0.802224	−	0.597024i	$-0.796350\pi$
$347$	− 22.2426i	− 1.19405i	0.802224	−	0.597024i	$-0.203650\pi$
$348$	− 1.75736i	− 0.0942043i
$349$	−23.4558	−1.25556	−0.627781	−	0.778390i	$-0.716037\pi$
$349$	−23.4558	−1.25556	−0.627781	+	0.778390i	$0.716037\pi$
$350$	0	0
$351$	10.3431	0.552076
$352$	0.585786i	0.0312225i
$353$	32.3848i	1.72367i	0.507191	+	0.861834i	$0.330684\pi$
$353$	32.3848i	1.72367i	−0.507191	+	0.861834i	$0.669316\pi$
$354$	1.65685	0.0880608
$355$	0	0
$356$	−9.07107	−0.480766
$357$	2.00000i	0.105851i
$358$	− 17.4853i	− 0.924126i
$359$	−27.5269	−1.45281	−0.726407	−	0.687264i	$-0.758811\pi$
$359$	−27.5269	−1.45281	−0.726407	+	0.687264i	$0.758811\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	− 15.0711i	− 0.792118i
$363$	15.0711i	0.791026i
$364$	1.82843	0.0958356
$365$	0	0
$366$	0.100505	0.00525348
$367$	− 31.3137i	− 1.63456i	−0.576239	−	0.817281i	$-0.695480\pi$
$367$	− 31.3137i	− 1.63456i	0.576239	−	0.817281i	$-0.304520\pi$
$368$	5.07107i	0.264348i
$369$	−1.82843	−0.0951841
$370$	0	0
$371$	−5.65685	−0.293689
$372$	− 0.585786i	− 0.0303716i
$373$	− 14.7279i	− 0.762583i	−0.924455	−	0.381291i	$-0.875479\pi$
$373$	− 14.7279i	− 0.762583i	0.924455	−	0.381291i	$-0.124521\pi$
$374$	−0.828427	−0.0428369
$375$	0	0
$376$	7.07107	0.364662
$377$	− 2.27208i	− 0.117018i
$378$	5.65685i	0.290957i
$379$	−4.14214	−0.212767	−0.106384	−	0.994325i	$-0.533927\pi$
$379$	−4.14214	−0.212767	−0.106384	+	0.994325i	$0.533927\pi$
$380$	0	0
$381$	4.97056	0.254650
$382$	19.8995i	1.01815i
$383$	8.31371i	0.424811i	0.977182	+	0.212405i	$0.0681297\pi$
$383$	8.31371i	0.424811i	−0.977182	+	0.212405i	$0.931870\pi$
$384$	−1.41421	−0.0721688
$385$	0	0
$386$	6.82843	0.347558
$387$	− 1.00000i	− 0.0508329i
$388$	− 13.5563i	− 0.688219i
$389$	−20.8284	−1.05604	−0.528022	−	0.849231i	$-0.677066\pi$
$389$	−20.8284	−1.05604	−0.528022	+	0.849231i	$0.677066\pi$
$390$	0	0
$391$	−7.17157	−0.362682
$392$	− 6.00000i	− 0.303046i
$393$	− 8.48528i	− 0.428026i
$394$	−25.1421	−1.26664
$395$	0	0
$396$	−0.585786	−0.0294369
$397$	− 20.4853i	− 1.02813i	−0.857752	−	0.514063i	$-0.828140\pi$
$397$	− 20.4853i	− 1.02813i	0.857752	−	0.514063i	$-0.171860\pi$
$398$	0.100505i	0.00503786i
$399$	1.41421	0.0707992
$400$	0	0
$401$	−24.1127	−1.20413	−0.602065	−	0.798447i	$-0.705655\pi$
$401$	−24.1127	−1.20413	−0.602065	+	0.798447i	$0.705655\pi$
$402$	− 1.75736i	− 0.0876491i
$403$	− 0.757359i	− 0.0377268i
$404$	−1.41421	−0.0703598
$405$	0	0
$406$	1.24264	0.0616712
$407$	1.31371i	0.0651181i
$408$	− 2.00000i	− 0.0990148i
$409$	27.2132	1.34561	0.672803	−	0.739822i	$-0.265090\pi$
$409$	27.2132	1.34561	0.672803	+	0.739822i	$0.265090\pi$
$410$	0	0
$411$	5.55635	0.274074
$412$	0.828427i	0.0408137i
$413$	1.17157i	0.0576493i
$414$	−5.07107	−0.249229
$415$	0	0
$416$	−1.82843	−0.0896460
$417$	− 8.82843i	− 0.432330i
$418$	0.585786i	0.0286518i
$419$	12.7990	0.625272	0.312636	−	0.949873i	$-0.398788\pi$
$419$	12.7990	0.625272	0.312636	+	0.949873i	$0.398788\pi$
$420$	0	0
$421$	1.24264	0.0605626	0.0302813	−	0.999541i	$-0.490360\pi$
$421$	1.24264	0.0605626	0.0302813	+	0.999541i	$0.490360\pi$
$422$	− 1.65685i	− 0.0806544i
$423$	7.07107i	0.343807i
$424$	5.65685	0.274721
$425$	0	0
$426$	16.8284	0.815340
$427$	0.0710678i	0.00343921i
$428$	− 1.92893i	− 0.0932385i
$429$	1.51472	0.0731313
$430$	0	0
$431$	1.02944	0.0495862	0.0247931	−	0.999693i	$-0.492107\pi$
$431$	1.02944	0.0495862	0.0247931	+	0.999693i	$0.492107\pi$
$432$	− 5.65685i	− 0.272166i
$433$	36.0711i	1.73346i	0.498773	+	0.866732i	$0.333784\pi$
$433$	36.0711i	1.73346i	−0.498773	+	0.866732i	$0.666216\pi$
$434$	0.414214	0.0198829
$435$	0	0
$436$	−10.8284	−0.518588
$437$	5.07107i	0.242582i
$438$	13.0711i	0.624560i
$439$	15.3137	0.730883	0.365442	−	0.930834i	$-0.380918\pi$
$439$	15.3137	0.730883	0.365442	+	0.930834i	$0.380918\pi$
$440$	0	0
$441$	6.00000	0.285714
$442$	− 2.58579i	− 0.122993i
$443$	9.92893i	0.471738i	0.971785	+	0.235869i	$0.0757936\pi$
$443$	9.92893i	0.471738i	−0.971785	+	0.235869i	$0.924206\pi$
$444$	−3.17157	−0.150516
$445$	0	0
$446$	16.1421	0.764352
$447$	− 14.9289i	− 0.706114i
$448$	− 1.00000i	− 0.0472456i
$449$	−22.2426	−1.04970	−0.524848	−	0.851196i	$-0.675878\pi$
$449$	−22.2426	−1.04970	−0.524848	+	0.851196i	$0.675878\pi$
$450$	0	0
$451$	−1.07107	−0.0504346
$452$	4.89949i	0.230453i
$453$	− 14.8284i	− 0.696700i
$454$	−9.17157	−0.430443
$455$	0	0
$456$	−1.41421	−0.0662266
$457$	− 30.4853i	− 1.42604i	−0.701143	−	0.713021i	$-0.747327\pi$
$457$	− 30.4853i	− 1.42604i	0.701143	−	0.713021i	$-0.252673\pi$
$458$	− 0.828427i	− 0.0387099i
$459$	8.00000	0.373408
$460$	0	0
$461$	−15.0711	−0.701930	−0.350965	−	0.936389i	$-0.614146\pi$
$461$	−15.0711	−0.701930	−0.350965	+	0.936389i	$0.614146\pi$
$462$	0.828427i	0.0385419i
$463$	− 30.3137i	− 1.40880i	−0.709804	−	0.704399i	$-0.751217\pi$
$463$	− 30.3137i	− 1.40880i	0.709804	−	0.704399i	$-0.248783\pi$
$464$	−1.24264	−0.0576881
$465$	0	0
$466$	8.48528	0.393073
$467$	− 20.9289i	− 0.968475i	−0.874936	−	0.484238i	$-0.839097\pi$
$467$	− 20.9289i	− 0.968475i	0.874936	−	0.484238i	$-0.160903\pi$
$468$	− 1.82843i	− 0.0845191i
$469$	1.24264	0.0573798
$470$	0	0
$471$	14.4853	0.667447
$472$	− 1.17157i	− 0.0539260i
$473$	− 0.585786i	− 0.0269345i
$474$	11.8995	0.546562
$475$	0	0
$476$	1.41421	0.0648204
$477$	5.65685i	0.259010i
$478$	− 11.5858i	− 0.529922i
$479$	−9.17157	−0.419060	−0.209530	−	0.977802i	$-0.567193\pi$
$479$	−9.17157	−0.419060	−0.209530	+	0.977802i	$0.567193\pi$
$480$	0	0
$481$	−4.10051	−0.186967
$482$	− 21.4142i	− 0.975391i
$483$	7.17157i	0.326318i
$484$	10.6569	0.484402
$485$	0	0
$486$	9.89949	0.449050
$487$	− 33.2132i	− 1.50503i	−0.658573	−	0.752517i	$-0.728840\pi$
$487$	− 33.2132i	− 1.50503i	0.658573	−	0.752517i	$-0.271160\pi$
$488$	− 0.0710678i	− 0.00321709i
$489$	−19.3137	−0.873396
$490$	0	0
$491$	16.6274	0.750385	0.375192	−	0.926947i	$-0.377577\pi$
$491$	16.6274	0.750385	0.375192	+	0.926947i	$0.377577\pi$
$492$	− 2.58579i	− 0.116576i
$493$	− 1.75736i	− 0.0791475i
$494$	−1.82843	−0.0822648
$495$	0	0
$496$	−0.414214	−0.0185987
$497$	11.8995i	0.533765i
$498$	− 5.17157i	− 0.231744i
$499$	34.4558	1.54246	0.771228	−	0.636559i	$-0.219643\pi$
$499$	34.4558	1.54246	0.771228	+	0.636559i	$0.219643\pi$
$500$	0	0
$501$	19.1716	0.856523
$502$	− 10.9706i	− 0.489640i
$503$	31.6569i	1.41151i	0.708456	+	0.705755i	$0.249392\pi$
$503$	31.6569i	1.41151i	−0.708456	+	0.705755i	$0.750608\pi$
$504$	1.00000	0.0445435
$505$	0	0
$506$	−2.97056	−0.132058
$507$	− 13.6569i	− 0.606522i
$508$	− 3.51472i	− 0.155940i
$509$	20.4853	0.907994	0.453997	−	0.891003i	$-0.349998\pi$
$509$	20.4853	0.907994	0.453997	+	0.891003i	$0.349998\pi$
$510$	0	0
$511$	−9.24264	−0.408870
$512$	1.00000i	0.0441942i
$513$	− 5.65685i	− 0.249756i
$514$	−8.89949	−0.392540
$515$	0	0
$516$	1.41421	0.0622573
$517$	4.14214i	0.182171i
$518$	− 2.24264i	− 0.0985360i
$519$	−0.727922	−0.0319522
$520$	0	0
$521$	−11.0711	−0.485032	−0.242516	−	0.970147i	$-0.577973\pi$
$521$	−11.0711	−0.485032	−0.242516	+	0.970147i	$0.577973\pi$
$522$	− 1.24264i	− 0.0543889i
$523$	− 10.7279i	− 0.469099i	−0.972104	−	0.234550i	$-0.924638\pi$
$523$	− 10.7279i	− 0.469099i	0.972104	−	0.234550i	$-0.0753615\pi$
$524$	−6.00000	−0.262111
$525$	0	0
$526$	17.4853	0.762394
$527$	− 0.585786i	− 0.0255173i
$528$	− 0.828427i	− 0.0360527i
$529$	−2.71573	−0.118075
$530$	0	0
$531$	1.17157	0.0508419
$532$	− 1.00000i	− 0.0433555i
$533$	− 3.34315i	− 0.144808i
$534$	12.8284	0.555140
$535$	0	0
$536$	−1.24264	−0.0536739
$537$	24.7279i	1.06709i
$538$	− 9.17157i	− 0.395415i
$539$	3.51472	0.151390
$540$	0	0
$541$	7.85786	0.337836	0.168918	−	0.985630i	$-0.445973\pi$
$541$	7.85786	0.337836	0.168918	+	0.985630i	$0.445973\pi$
$542$	8.89949i	0.382266i
$543$	21.3137i	0.914659i
$544$	−1.41421	−0.0606339
$545$	0	0
$546$	−2.58579	−0.110661
$547$	− 12.0000i	− 0.513083i	−0.966533	−	0.256541i	$-0.917417\pi$
$547$	− 12.0000i	− 0.513083i	0.966533	−	0.256541i	$-0.0825830\pi$
$548$	− 3.92893i	− 0.167836i
$549$	0.0710678	0.00303310
$550$	0	0
$551$	−1.24264	−0.0529383
$552$	− 7.17157i	− 0.305242i
$553$	8.41421i	0.357809i
$554$	0.485281	0.0206176
$555$	0	0
$556$	−6.24264	−0.264747
$557$	41.8284i	1.77233i	0.463372	+	0.886164i	$0.346639\pi$
$557$	41.8284i	1.77233i	−0.463372	+	0.886164i	$0.653361\pi$
$558$	− 0.414214i	− 0.0175351i
$559$	1.82843	0.0773342
$560$	0	0
$561$	1.17157	0.0494638
$562$	− 1.34315i	− 0.0566572i
$563$	1.92893i	0.0812948i	0.999174	+	0.0406474i	$0.0129420\pi$
$563$	1.92893i	0.0812948i	−0.999174	+	0.0406474i	$0.987058\pi$
$564$	−10.0000	−0.421076
$565$	0	0
$566$	18.7574	0.788431
$567$	− 5.00000i	− 0.209980i
$568$	− 11.8995i	− 0.499292i
$569$	−22.7990	−0.955783	−0.477892	−	0.878419i	$-0.658599\pi$
$569$	−22.7990	−0.955783	−0.477892	+	0.878419i	$0.658599\pi$
$570$	0	0
$571$	33.0000	1.38101	0.690504	−	0.723329i	$-0.257389\pi$
$571$	33.0000	1.38101	0.690504	+	0.723329i	$0.257389\pi$
$572$	− 1.07107i	− 0.0447836i
$573$	− 28.1421i	− 1.17565i
$574$	1.82843	0.0763171
$575$	0	0
$576$	−1.00000	−0.0416667
$577$	− 5.58579i	− 0.232539i	−0.993218	−	0.116270i	$-0.962906\pi$
$577$	− 5.58579i	− 0.232539i	0.993218	−	0.116270i	$-0.0370937\pi$
$578$	15.0000i	0.623918i
$579$	−9.65685	−0.401325
$580$	0	0
$581$	3.65685	0.151712
$582$	19.1716i	0.794687i
$583$	3.31371i	0.137240i
$584$	9.24264	0.382463
$585$	0	0
$586$	10.9706	0.453190
$587$	− 27.5563i	− 1.13737i	−0.822555	−	0.568686i	$-0.807452\pi$
$587$	− 27.5563i	− 1.13737i	0.822555	−	0.568686i	$-0.192548\pi$
$588$	8.48528i	0.349927i
$589$	−0.414214	−0.0170674
$590$	0	0
$591$	35.5563	1.46259
$592$	2.24264i	0.0921720i
$593$	7.24264i	0.297420i	0.988881	+	0.148710i	$0.0475120\pi$
$593$	7.24264i	0.297420i	−0.988881	+	0.148710i	$0.952488\pi$
$594$	3.31371	0.135963
$595$	0	0
$596$	−10.5563	−0.432405
$597$	− 0.142136i	− 0.00581722i
$598$	− 9.27208i	− 0.379163i
$599$	−9.85786	−0.402781	−0.201391	−	0.979511i	$-0.564546\pi$
$599$	−9.85786	−0.402781	−0.201391	+	0.979511i	$0.564546\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	1.00000i	0.0407570i
$603$	− 1.24264i	− 0.0506042i
$604$	−10.4853	−0.426640
$605$	0	0
$606$	2.00000	0.0812444
$607$	6.00000i	0.243532i	0.992559	+	0.121766i	$0.0388558\pi$
$607$	6.00000i	0.243532i	−0.992559	+	0.121766i	$0.961144\pi$
$608$	1.00000i	0.0405554i
$609$	−1.75736	−0.0712118
$610$	0	0
$611$	−12.9289	−0.523049
$612$	− 1.41421i	− 0.0571662i
$613$	− 38.1716i	− 1.54174i	−0.636995	−	0.770868i	$-0.719823\pi$
$613$	− 38.1716i	− 1.54174i	0.636995	−	0.770868i	$-0.280177\pi$
$614$	5.92893	0.239272
$615$	0	0
$616$	0.585786	0.0236020
$617$	− 16.2843i	− 0.655580i	−0.944751	−	0.327790i	$-0.893696\pi$
$617$	− 16.2843i	− 0.655580i	0.944751	−	0.327790i	$-0.106304\pi$
$618$	− 1.17157i	− 0.0471276i
$619$	0.100505	0.00403964	0.00201982	−	0.999998i	$-0.499357\pi$
$619$	0.100505	0.00403964	0.00201982	+	0.999998i	$0.499357\pi$
$620$	0	0
$621$	28.6863	1.15114
$622$	− 4.07107i	− 0.163235i
$623$	9.07107i	0.363425i
$624$	2.58579	0.103514
$625$	0	0
$626$	−1.31371	−0.0525064
$627$	− 0.828427i	− 0.0330842i
$628$	− 10.2426i	− 0.408726i
$629$	−3.17157	−0.126459
$630$	0	0
$631$	−13.6985	−0.545328	−0.272664	−	0.962109i	$-0.587905\pi$
$631$	−13.6985	−0.545328	−0.272664	+	0.962109i	$0.587905\pi$
$632$	− 8.41421i	− 0.334699i
$633$	2.34315i	0.0931317i
$634$	−0.857864	−0.0340701
$635$	0	0
$636$	−8.00000	−0.317221
$637$	10.9706i	0.434670i
$638$	− 0.727922i	− 0.0288187i
$639$	11.8995	0.470737
$640$	0	0
$641$	42.7696	1.68930	0.844648	−	0.535322i	$-0.179810\pi$
$641$	42.7696	1.68930	0.844648	+	0.535322i	$0.179810\pi$
$642$	2.72792i	0.107662i
$643$	− 39.7279i	− 1.56672i	−0.621571	−	0.783358i	$-0.713505\pi$
$643$	− 39.7279i	− 1.56672i	0.621571	−	0.783358i	$-0.286495\pi$
$644$	5.07107	0.199828
$645$	0	0
$646$	−1.41421	−0.0556415
$647$	5.20101i	0.204473i	0.994760	+	0.102236i	$0.0325998\pi$
$647$	5.20101i	0.204473i	−0.994760	+	0.102236i	$0.967400\pi$
$648$	5.00000i	0.196419i
$649$	0.686292	0.0269393
$650$	0	0
$651$	−0.585786	−0.0229588
$652$	13.6569i	0.534844i
$653$	6.58579i	0.257722i	0.991663	+	0.128861i	$0.0411321\pi$
$653$	6.58579i	0.257722i	−0.991663	+	0.128861i	$0.958868\pi$
$654$	15.3137	0.598813
$655$	0	0
$656$	−1.82843	−0.0713881
$657$	9.24264i	0.360590i
$658$	− 7.07107i	− 0.275659i
$659$	−24.3848	−0.949896	−0.474948	−	0.880014i	$-0.657533\pi$
$659$	−24.3848	−0.949896	−0.474948	+	0.880014i	$0.657533\pi$
$660$	0	0
$661$	24.8701	0.967333	0.483667	−	0.875252i	$-0.339305\pi$
$661$	24.8701	0.967333	0.483667	+	0.875252i	$0.339305\pi$
$662$	− 25.3137i	− 0.983845i
$663$	3.65685i	0.142020i
$664$	−3.65685	−0.141913
$665$	0	0
$666$	−2.24264	−0.0869006
$667$	− 6.30152i	− 0.243996i
$668$	− 13.5563i	− 0.524511i
$669$	−22.8284	−0.882598
$670$	0	0
$671$	0.0416306	0.00160713
$672$	1.41421i	0.0545545i
$673$	− 20.4142i	− 0.786910i	−0.919344	−	0.393455i	$-0.871280\pi$
$673$	− 20.4142i	− 0.786910i	0.919344	−	0.393455i	$-0.128720\pi$
$674$	8.34315	0.321366
$675$	0	0
$676$	−9.65685	−0.371417
$677$	43.4558i	1.67014i	0.550141	+	0.835072i	$0.314574\pi$
$677$	43.4558i	1.67014i	−0.550141	+	0.835072i	$0.685426\pi$
$678$	− 6.92893i	− 0.266104i
$679$	−13.5563	−0.520245
$680$	0	0
$681$	12.9706	0.497033
$682$	− 0.242641i	− 0.00929119i
$683$	3.51472i	0.134487i	0.997737	+	0.0672435i	$0.0214204\pi$
$683$	3.51472i	0.134487i	−0.997737	+	0.0672435i	$0.978580\pi$
$684$	−1.00000	−0.0382360
$685$	0	0
$686$	−13.0000	−0.496342
$687$	1.17157i	0.0446983i
$688$	− 1.00000i	− 0.0381246i
$689$	−10.3431	−0.394042
$690$	0	0
$691$	18.4853	0.703213	0.351607	−	0.936148i	$-0.385635\pi$
$691$	18.4853	0.703213	0.351607	+	0.936148i	$0.385635\pi$
$692$	0.514719i	0.0195667i
$693$	0.585786i	0.0222522i
$694$	22.2426	0.844319
$695$	0	0
$696$	1.75736	0.0666125
$697$	− 2.58579i	− 0.0979436i
$698$	− 23.4558i	− 0.887817i
$699$	−12.0000	−0.453882
$700$	0	0
$701$	11.2721	0.425741	0.212870	−	0.977080i	$-0.431719\pi$
$701$	11.2721	0.425741	0.212870	+	0.977080i	$0.431719\pi$
$702$	10.3431i	0.390377i
$703$	2.24264i	0.0845828i
$704$	−0.585786	−0.0220777
$705$	0	0
$706$	−32.3848	−1.21882
$707$	1.41421i	0.0531870i
$708$	1.65685i	0.0622684i
$709$	7.21320	0.270898	0.135449	−	0.990784i	$-0.456752\pi$
$709$	7.21320	0.270898	0.135449	+	0.990784i	$0.456752\pi$
$710$	0	0
$711$	8.41421	0.315558
$712$	− 9.07107i	− 0.339953i
$713$	− 2.10051i	− 0.0786645i
$714$	−2.00000	−0.0748481
$715$	0	0
$716$	17.4853	0.653456
$717$	16.3848i	0.611901i
$718$	− 27.5269i	− 1.02730i
$719$	36.6274	1.36597	0.682986	−	0.730431i	$-0.260681\pi$
$719$	36.6274	1.36597	0.682986	+	0.730431i	$0.260681\pi$
$720$	0	0
$721$	0.828427	0.0308522
$722$	− 18.0000i	− 0.669891i
$723$	30.2843i	1.12628i
$724$	15.0711	0.560112
$725$	0	0
$726$	−15.0711	−0.559340
$727$	− 14.0000i	− 0.519231i	−0.965712	−	0.259616i	$-0.916404\pi$
$727$	− 14.0000i	− 0.519231i	0.965712	−	0.259616i	$-0.0835959\pi$
$728$	1.82843i	0.0677660i
$729$	−29.0000	−1.07407
$730$	0	0
$731$	1.41421	0.0523066
$732$	0.100505i	0.00371477i
$733$	− 27.7574i	− 1.02524i	−0.858615	−	0.512621i	$-0.828675\pi$
$733$	− 27.7574i	− 1.02524i	0.858615	−	0.512621i	$-0.171325\pi$
$734$	31.3137	1.15581
$735$	0	0
$736$	−5.07107	−0.186922
$737$	− 0.727922i	− 0.0268134i
$738$	− 1.82843i	− 0.0673053i
$739$	−8.02944	−0.295368	−0.147684	−	0.989035i	$-0.547182\pi$
$739$	−8.02944	−0.295368	−0.147684	+	0.989035i	$0.547182\pi$
$740$	0	0
$741$	2.58579	0.0949912
$742$	− 5.65685i	− 0.207670i
$743$	− 2.31371i	− 0.0848817i	−0.999099	−	0.0424409i	$-0.986487\pi$
$743$	− 2.31371i	− 0.0848817i	0.999099	−	0.0424409i	$-0.0135134\pi$
$744$	0.585786	0.0214760
$745$	0	0
$746$	14.7279	0.539228
$747$	− 3.65685i	− 0.133797i
$748$	− 0.828427i	− 0.0302903i
$749$	−1.92893	−0.0704816
$750$	0	0
$751$	−8.72792	−0.318486	−0.159243	−	0.987239i	$-0.550905\pi$
$751$	−8.72792	−0.318486	−0.159243	+	0.987239i	$0.550905\pi$
$752$	7.07107i	0.257855i
$753$	15.5147i	0.565388i
$754$	2.27208	0.0827442
$755$	0	0
$756$	−5.65685	−0.205738
$757$	36.4264i	1.32394i	0.749530	+	0.661970i	$0.230279\pi$
$757$	36.4264i	1.32394i	−0.749530	+	0.661970i	$0.769721\pi$
$758$	− 4.14214i	− 0.150449i
$759$	4.20101	0.152487
$760$	0	0
$761$	−44.8284	−1.62503	−0.812515	−	0.582941i	$-0.801902\pi$
$761$	−44.8284	−1.62503	−0.812515	+	0.582941i	$0.801902\pi$
$762$	4.97056i	0.180064i
$763$	10.8284i	0.392015i
$764$	−19.8995	−0.719938
$765$	0	0
$766$	−8.31371	−0.300386
$767$	2.14214i	0.0773480i
$768$	− 1.41421i	− 0.0510310i
$769$	−21.0000	−0.757279	−0.378640	−	0.925544i	$-0.623608\pi$
$769$	−21.0000	−0.757279	−0.378640	+	0.925544i	$0.623608\pi$
$770$	0	0
$771$	12.5858	0.453266
$772$	6.82843i	0.245760i
$773$	25.0711i	0.901744i	0.892589	+	0.450872i	$0.148887\pi$
$773$	25.0711i	0.901744i	−0.892589	+	0.450872i	$0.851113\pi$
$774$	1.00000	0.0359443
$775$	0	0
$776$	13.5563	0.486645
$777$	3.17157i	0.113780i
$778$	− 20.8284i	− 0.746735i
$779$	−1.82843	−0.0655102
$780$	0	0
$781$	6.97056	0.249426
$782$	− 7.17157i	− 0.256455i
$783$	7.02944i	0.251212i
$784$	6.00000	0.214286
$785$	0	0
$786$	8.48528	0.302660
$787$	31.2426i	1.11368i	0.830620	+	0.556840i	$0.187986\pi$
$787$	31.2426i	1.11368i	−0.830620	+	0.556840i	$0.812014\pi$
$788$	− 25.1421i	− 0.895651i
$789$	−24.7279	−0.880337
$790$	0	0
$791$	4.89949	0.174206
$792$	− 0.585786i	− 0.0208150i
$793$	0.129942i	0.00461439i
$794$	20.4853	0.726995
$795$	0	0
$796$	−0.100505	−0.00356231
$797$	− 42.9411i	− 1.52105i	−0.649307	−	0.760526i	$-0.724941\pi$
$797$	− 42.9411i	− 1.52105i	0.649307	−	0.760526i	$-0.275059\pi$
$798$	1.41421i	0.0500626i
$799$	−10.0000	−0.353775
$800$	0	0
$801$	9.07107	0.320510
$802$	− 24.1127i	− 0.851449i
$803$	5.41421i	0.191063i
$804$	1.75736	0.0619773
$805$	0	0
$806$	0.757359	0.0266768
$807$	12.9706i	0.456585i
$808$	− 1.41421i	− 0.0497519i
$809$	28.7990	1.01252	0.506259	−	0.862381i	$-0.331028\pi$
$809$	28.7990	1.01252	0.506259	+	0.862381i	$0.331028\pi$
$810$	0	0
$811$	−48.1127	−1.68947	−0.844733	−	0.535188i	$-0.820241\pi$
$811$	−48.1127	−1.68947	−0.844733	+	0.535188i	$0.820241\pi$
$812$	1.24264i	0.0436081i
$813$	− 12.5858i	− 0.441403i
$814$	−1.31371	−0.0460455
$815$	0	0
$816$	2.00000	0.0700140
$817$	− 1.00000i	− 0.0349856i
$818$	27.2132i	0.951487i
$819$	−1.82843	−0.0638904
$820$	0	0
$821$	−20.1421	−0.702965	−0.351483	−	0.936194i	$-0.614322\pi$
$821$	−20.1421	−0.702965	−0.351483	+	0.936194i	$0.614322\pi$
$822$	5.55635i	0.193800i
$823$	− 13.5147i	− 0.471093i	−0.971863	−	0.235547i	$-0.924312\pi$
$823$	− 13.5147i	− 0.471093i	0.971863	−	0.235547i	$-0.0756881\pi$
$824$	−0.828427	−0.0288596
$825$	0	0
$826$	−1.17157	−0.0407642
$827$	− 43.5269i	− 1.51358i	−0.653659	−	0.756790i	$-0.726767\pi$
$827$	− 43.5269i	− 1.51358i	0.653659	−	0.756790i	$-0.273233\pi$
$828$	− 5.07107i	− 0.176232i
$829$	−3.24264	−0.112622	−0.0563108	−	0.998413i	$-0.517934\pi$
$829$	−3.24264	−0.112622	−0.0563108	+	0.998413i	$0.517934\pi$
$830$	0	0
$831$	−0.686292	−0.0238072
$832$	− 1.82843i	− 0.0633893i
$833$	8.48528i	0.293998i
$834$	8.82843	0.305703
$835$	0	0
$836$	−0.585786	−0.0202598
$837$	2.34315i	0.0809910i
$838$	12.7990i	0.442134i
$839$	51.0122	1.76114	0.880568	−	0.473919i	$-0.157161\pi$
$839$	51.0122	1.76114	0.880568	+	0.473919i	$0.157161\pi$
$840$	0	0
$841$	−27.4558	−0.946753
$842$	1.24264i	0.0428242i
$843$	1.89949i	0.0654221i
$844$	1.65685	0.0570313
$845$	0	0
$846$	−7.07107	−0.243108
$847$	− 10.6569i	− 0.366174i
$848$	5.65685i	0.194257i
$849$	−26.5269	−0.910401
$850$	0	0
$851$	−11.3726	−0.389847
$852$	16.8284i	0.576532i
$853$	35.9411i	1.23060i	0.788293	+	0.615300i	$0.210965\pi$
$853$	35.9411i	1.23060i	−0.788293	+	0.615300i	$0.789035\pi$
$854$	−0.0710678	−0.00243189
$855$	0	0
$856$	1.92893	0.0659295
$857$	47.0711i	1.60792i	0.594685	+	0.803959i	$0.297277\pi$
$857$	47.0711i	1.60792i	−0.594685	+	0.803959i	$0.702723\pi$
$858$	1.51472i	0.0517116i
$859$	16.5147	0.563475	0.281737	−	0.959492i	$-0.409089\pi$
$859$	16.5147	0.563475	0.281737	+	0.959492i	$0.409089\pi$
$860$	0	0
$861$	−2.58579	−0.0881234
$862$	1.02944i	0.0350628i
$863$	40.8284i	1.38982i	0.719099	+	0.694908i	$0.244555\pi$
$863$	40.8284i	1.38982i	−0.719099	+	0.694908i	$0.755445\pi$
$864$	5.65685	0.192450
$865$	0	0
$866$	−36.0711	−1.22574
$867$	− 21.2132i	− 0.720438i
$868$	0.414214i	0.0140593i
$869$	4.92893	0.167203
$870$	0	0
$871$	2.27208	0.0769864
$872$	− 10.8284i	− 0.366697i
$873$	13.5563i	0.458813i
$874$	−5.07107	−0.171531
$875$	0	0
$876$	−13.0711	−0.441630
$877$	− 18.6274i	− 0.629003i	−0.949257	−	0.314502i	$-0.898163\pi$
$877$	− 18.6274i	− 0.629003i	0.949257	−	0.314502i	$-0.101837\pi$
$878$	15.3137i	0.516813i
$879$	−15.5147	−0.523298
$880$	0	0
$881$	−1.20101	−0.0404631	−0.0202315	−	0.999795i	$-0.506440\pi$
$881$	−1.20101	−0.0404631	−0.0202315	+	0.999795i	$0.506440\pi$
$882$	6.00000i	0.202031i
$883$	− 26.2132i	− 0.882145i	−0.897472	−	0.441072i	$-0.854598\pi$
$883$	− 26.2132i	− 0.882145i	0.897472	−	0.441072i	$-0.145402\pi$
$884$	2.58579	0.0869694
$885$	0	0
$886$	−9.92893	−0.333569
$887$	− 56.1127i	− 1.88408i	−0.335501	−	0.942040i	$-0.608905\pi$
$887$	− 56.1127i	− 1.88408i	0.335501	−	0.942040i	$-0.391095\pi$
$888$	− 3.17157i	− 0.106431i
$889$	−3.51472	−0.117880
$890$	0	0
$891$	−2.92893	−0.0981229
$892$	16.1421i	0.540479i
$893$	7.07107i	0.236624i
$894$	14.9289	0.499298
$895$	0	0
$896$	1.00000	0.0334077
$897$	13.1127i	0.437820i
$898$	− 22.2426i	− 0.742247i
$899$	0.514719	0.0171668
$900$	0	0
$901$	−8.00000	−0.266519
$902$	− 1.07107i	− 0.0356627i
$903$	− 1.41421i	− 0.0470621i
$904$	−4.89949	−0.162955
$905$	0	0
$906$	14.8284	0.492641
$907$	14.8995i	0.494730i	0.968922	+	0.247365i	$0.0795646\pi$
$907$	14.8995i	0.494730i	−0.968922	+	0.247365i	$0.920435\pi$
$908$	− 9.17157i	− 0.304369i
$909$	1.41421	0.0469065
$910$	0	0
$911$	−20.3848	−0.675378	−0.337689	−	0.941258i	$-0.609645\pi$
$911$	−20.3848	−0.675378	−0.337689	+	0.941258i	$0.609645\pi$
$912$	− 1.41421i	− 0.0468293i
$913$	− 2.14214i	− 0.0708943i
$914$	30.4853	1.00836
$915$	0	0
$916$	0.828427	0.0273720
$917$	6.00000i	0.198137i
$918$	8.00000i	0.264039i
$919$	34.8995	1.15123	0.575614	−	0.817722i	$-0.304763\pi$
$919$	34.8995	1.15123	0.575614	+	0.817722i	$0.304763\pi$
$920$	0	0
$921$	−8.38478	−0.276288
$922$	− 15.0711i	− 0.496339i
$923$	21.7574i	0.716152i
$924$	−0.828427	−0.0272533
$925$	0	0
$926$	30.3137	0.996170
$927$	− 0.828427i	− 0.0272091i
$928$	− 1.24264i	− 0.0407917i
$929$	13.7990	0.452730	0.226365	−	0.974043i	$-0.427316\pi$
$929$	13.7990	0.452730	0.226365	+	0.974043i	$0.427316\pi$
$930$	0	0
$931$	6.00000	0.196642
$932$	8.48528i	0.277945i
$933$	5.75736i	0.188487i
$934$	20.9289	0.684816
$935$	0	0
$936$	1.82843	0.0597640
$937$	− 34.4264i	− 1.12466i	−0.826912	−	0.562331i	$-0.809905\pi$
$937$	− 34.4264i	− 1.12466i	0.826912	−	0.562331i	$-0.190095\pi$
$938$	1.24264i	0.0405737i
$939$	1.85786	0.0606291
$940$	0	0
$941$	−53.0711	−1.73007	−0.865034	−	0.501714i	$-0.832703\pi$
$941$	−53.0711	−1.73007	−0.865034	+	0.501714i	$0.832703\pi$
$942$	14.4853i	0.471956i
$943$	− 9.27208i	− 0.301940i
$944$	1.17157	0.0381314
$945$	0	0
$946$	0.585786	0.0190456
$947$	59.1838i	1.92321i	0.274430	+	0.961607i	$0.411511\pi$
$947$	59.1838i	1.92321i	−0.274430	+	0.961607i	$0.588489\pi$
$948$	11.8995i	0.386478i
$949$	−16.8995	−0.548581
$950$	0	0
$951$	1.21320	0.0393408
$952$	1.41421i	0.0458349i
$953$	9.10051i	0.294794i	0.989077	+	0.147397i	$0.0470895\pi$
$953$	9.10051i	0.294794i	−0.989077	+	0.147397i	$0.952910\pi$
$954$	−5.65685	−0.183147
$955$	0	0
$956$	11.5858	0.374711
$957$	1.02944i	0.0332770i
$958$	− 9.17157i	− 0.296320i
$959$	−3.92893	−0.126872
$960$	0	0
$961$	−30.8284	−0.994465
$962$	− 4.10051i	− 0.132206i
$963$	1.92893i	0.0621590i
$964$	21.4142	0.689705
$965$	0	0
$966$	−7.17157	−0.230742
$967$	36.2426i	1.16548i	0.812657	+	0.582742i	$0.198020\pi$
$967$	36.2426i	1.16548i	−0.812657	+	0.582742i	$0.801980\pi$
$968$	10.6569i	0.342524i
$969$	2.00000	0.0642493
$970$	0	0
$971$	21.0711	0.676203	0.338101	−	0.941110i	$-0.390215\pi$
$971$	21.0711	0.676203	0.338101	+	0.941110i	$0.390215\pi$
$972$	9.89949i	0.317526i
$973$	6.24264i	0.200130i
$974$	33.2132	1.06422
$975$	0	0
$976$	0.0710678	0.00227483
$977$	− 17.0711i	− 0.546152i	−0.961992	−	0.273076i	$-0.911959\pi$
$977$	− 17.0711i	− 0.546152i	0.961992	−	0.273076i	$-0.0880410\pi$
$978$	− 19.3137i	− 0.617584i
$979$	5.31371	0.169827
$980$	0	0
$981$	10.8284	0.345725
$982$	16.6274i	0.530602i
$983$	27.3431i	0.872111i	0.899920	+	0.436055i	$0.143625\pi$
$983$	27.3431i	0.872111i	−0.899920	+	0.436055i	$0.856375\pi$
$984$	2.58579	0.0824319
$985$	0	0
$986$	1.75736	0.0559657
$987$	10.0000i	0.318304i
$988$	− 1.82843i	− 0.0581700i
$989$	5.07107	0.161251
$990$	0	0
$991$	41.2548	1.31050	0.655251	−	0.755411i	$-0.272563\pi$
$991$	41.2548	1.31050	0.655251	+	0.755411i	$0.272563\pi$
$992$	− 0.414214i	− 0.0131513i
$993$	35.7990i	1.13605i
$994$	−11.8995	−0.377429
$995$	0	0
$996$	5.17157	0.163868
$997$	37.1716i	1.17724i	0.808411	+	0.588618i	$0.200328\pi$
$997$	37.1716i	1.17724i	−0.808411	+	0.588618i	$0.799672\pi$
$998$	34.4558i	1.09068i
$999$	12.6863	0.401377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2150.2.b.o.1549.3		4
5.2	odd	4		2150.2.a.v.1.1		2
5.3	odd	4		430.2.a.g.1.2	✓	2
5.4	even	2	inner	2150.2.b.o.1549.2		4
15.8	even	4		3870.2.a.bc.1.2		2
20.3	even	4		3440.2.a.j.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.a.g.1.2	✓	2	5.3	odd	4
2150.2.a.v.1.1		2	5.2	odd	4
2150.2.b.o.1549.2		4	5.4	even	2	inner
2150.2.b.o.1549.3		4	1.1	even	1	trivial
3440.2.a.j.1.1		2	20.3	even	4
3870.2.a.bc.1.2		2	15.8	even	4

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:	\( N \)	\(=\)	\( 2150 = 2 \cdot 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} +1.41421 q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} +1.41421 q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +0.585786 q^{11} +1.41421i q^{12} +1.82843i q^{13} -1.00000 q^{14} +1.00000 q^{16} +1.41421i q^{17} +1.00000i q^{18} +1.00000 q^{19} +1.41421 q^{21} +0.585786i q^{22} +5.07107i q^{23} -1.41421 q^{24} -1.82843 q^{26} -5.65685i q^{27} -1.00000i q^{28} -1.24264 q^{29} -0.414214 q^{31} +1.00000i q^{32} -0.828427i q^{33} -1.41421 q^{34} -1.00000 q^{36} +2.24264i q^{37} +1.00000i q^{38} +2.58579 q^{39} -1.82843 q^{41} +1.41421i q^{42} -1.00000i q^{43} -0.585786 q^{44} -5.07107 q^{46} +7.07107i q^{47} -1.41421i q^{48} +6.00000 q^{49} +2.00000 q^{51} -1.82843i q^{52} +5.65685i q^{53} +5.65685 q^{54} +1.00000 q^{56} -1.41421i q^{57} -1.24264i q^{58} +1.17157 q^{59} +0.0710678 q^{61} -0.414214i q^{62} +1.00000i q^{63} -1.00000 q^{64} +0.828427 q^{66} -1.24264i q^{67} -1.41421i q^{68} +7.17157 q^{69} +11.8995 q^{71} -1.00000i q^{72} +9.24264i q^{73} -2.24264 q^{74} -1.00000 q^{76} +0.585786i q^{77} +2.58579i q^{78} +8.41421 q^{79} -5.00000 q^{81} -1.82843i q^{82} -3.65685i q^{83} -1.41421 q^{84} +1.00000 q^{86} +1.75736i q^{87} -0.585786i q^{88} +9.07107 q^{89} -1.82843 q^{91} -5.07107i q^{92} +0.585786i q^{93} -7.07107 q^{94} +1.41421 q^{96} +13.5563i q^{97} +6.00000i q^{98} +0.585786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{9} + 8 q^{11} - 4 q^{14} + 4 q^{16} + 4 q^{19} + 4 q^{26} + 12 q^{29} + 4 q^{31} - 4 q^{36} + 16 q^{39} + 4 q^{41} - 8 q^{44} + 8 q^{46} + 24 q^{49} + 8 q^{51} + 4 q^{56} + 16 q^{59} - 28 q^{61} - 4 q^{64} - 8 q^{66} + 40 q^{69} + 8 q^{71} + 8 q^{74} - 4 q^{76} + 28 q^{79} - 20 q^{81} + 4 q^{86} + 8 q^{89} + 4 q^{91} + 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^9 + 8 * q^11 - 4 * q^14 + 4 * q^16 + 4 * q^19 + 4 * q^26 + 12 * q^29 + 4 * q^31 - 4 * q^36 + 16 * q^39 + 4 * q^41 - 8 * q^44 + 8 * q^46 + 24 * q^49 + 8 * q^51 + 4 * q^56 + 16 * q^59 - 28 * q^61 - 4 * q^64 - 8 * q^66 + 40 * q^69 + 8 * q^71 + 8 * q^74 - 4 * q^76 + 28 * q^79 - 20 * q^81 + 4 * q^86 + 8 * q^89 + 4 * q^91 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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