LMFDB - Embedded newform 4650.2.d.bd.3349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4650,2,Mod(3349,4650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4650, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4650.3349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4650.d (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:	$37.1304369399$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9x^{2} + 16 $ x^4 + 9*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 930)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3349.3
Root			$-1.56155i$ of defining polynomial
Character	$\chi$	$=$	4650.3349
Dual form			4650.2.d.bd.3349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -1.56155i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -1.56155i q^{7} -1.00000i q^{8} -1.00000 q^{9} -1.56155 q^{11} -1.00000i q^{12} -2.00000i q^{13} +1.56155 q^{14} +1.00000 q^{16} +5.12311i q^{17} -1.00000i q^{18} -4.68466 q^{19} +1.56155 q^{21} -1.56155i q^{22} -5.56155i q^{23} +1.00000 q^{24} +2.00000 q^{26} -1.00000i q^{27} +1.56155i q^{28} +1.12311 q^{29} +1.00000 q^{31} +1.00000i q^{32} -1.56155i q^{33} -5.12311 q^{34} +1.00000 q^{36} +5.12311i q^{37} -4.68466i q^{38} +2.00000 q^{39} -1.12311 q^{41} +1.56155i q^{42} +7.80776i q^{43} +1.56155 q^{44} +5.56155 q^{46} -3.12311i q^{47} +1.00000i q^{48} +4.56155 q^{49} -5.12311 q^{51} +2.00000i q^{52} -11.5616i q^{53} +1.00000 q^{54} -1.56155 q^{56} -4.68466i q^{57} +1.12311i q^{58} +4.87689 q^{59} +6.00000 q^{61} +1.00000i q^{62} +1.56155i q^{63} -1.00000 q^{64} +1.56155 q^{66} +9.36932i q^{67} -5.12311i q^{68} +5.56155 q^{69} +4.68466 q^{71} +1.00000i q^{72} -9.80776i q^{73} -5.12311 q^{74} +4.68466 q^{76} +2.43845i q^{77} +2.00000i q^{78} +16.6847 q^{79} +1.00000 q^{81} -1.12311i q^{82} +2.24621i q^{83} -1.56155 q^{84} -7.80776 q^{86} +1.12311i q^{87} +1.56155i q^{88} +1.31534 q^{89} -3.12311 q^{91} +5.56155i q^{92} +1.00000i q^{93} +3.12311 q^{94} -1.00000 q^{96} -6.00000i q^{97} +4.56155i q^{98} +1.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 2 q^{11} - 2 q^{14} + 4 q^{16} + 6 q^{19} - 2 q^{21} + 4 q^{24} + 8 q^{26} - 12 q^{29} + 4 q^{31} - 4 q^{34} + 4 q^{36} + 8 q^{39} + 12 q^{41} - 2 q^{44} + 14 q^{46} + 10 q^{49} - 4 q^{51} + 4 q^{54} + 2 q^{56} + 36 q^{59} + 24 q^{61} - 4 q^{64} - 2 q^{66} + 14 q^{69} - 6 q^{71} - 4 q^{74} - 6 q^{76} + 42 q^{79} + 4 q^{81} + 2 q^{84} + 10 q^{86} + 30 q^{89} + 4 q^{91} - 4 q^{94} - 4 q^{96} - 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 2 * q^11 - 2 * q^14 + 4 * q^16 + 6 * q^19 - 2 * q^21 + 4 * q^24 + 8 * q^26 - 12 * q^29 + 4 * q^31 - 4 * q^34 + 4 * q^36 + 8 * q^39 + 12 * q^41 - 2 * q^44 + 14 * q^46 + 10 * q^49 - 4 * q^51 + 4 * q^54 + 2 * q^56 + 36 * q^59 + 24 * q^61 - 4 * q^64 - 2 * q^66 + 14 * q^69 - 6 * q^71 - 4 * q^74 - 6 * q^76 + 42 * q^79 + 4 * q^81 + 2 * q^84 + 10 * q^86 + 30 * q^89 + 4 * q^91 - 4 * q^94 - 4 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4650\mathbb{Z}\right)^\times$.

$n$	$1801$	$2977$	$3101$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	− 1.56155i	− 0.590211i	−0.955465	−	0.295106i	$-0.904645\pi$
$7$	− 1.56155i	− 0.590211i	0.955465	−	0.295106i	$-0.0953549\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−1.56155	−0.470826	−0.235413	−	0.971895i	$-0.575644\pi$
$11$	−1.56155	−0.470826	−0.235413	+	0.971895i	$0.575644\pi$
$12$	− 1.00000i	− 0.288675i
$13$	− 2.00000i	− 0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$	− 2.00000i	− 0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	1.56155	0.417343
$15$	0	0
$16$	1.00000	0.250000
$17$	5.12311i	1.24254i	0.783598	+	0.621268i	$0.213382\pi$
$17$	5.12311i	1.24254i	−0.783598	+	0.621268i	$0.786618\pi$
$18$	− 1.00000i	− 0.235702i
$19$	−4.68466	−1.07473	−0.537367	−	0.843348i	$-0.680581\pi$
$19$	−4.68466	−1.07473	−0.537367	+	0.843348i	$0.680581\pi$
$20$	0	0
$21$	1.56155	0.340759
$22$	− 1.56155i	− 0.332924i
$23$	− 5.56155i	− 1.15966i	−0.814736	−	0.579832i	$-0.803118\pi$
$23$	− 5.56155i	− 1.15966i	0.814736	−	0.579832i	$-0.196882\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	2.00000	0.392232
$27$	− 1.00000i	− 0.192450i
$28$	1.56155i	0.295106i
$29$	1.12311	0.208555	0.104278	−	0.994548i	$-0.466747\pi$
$29$	1.12311	0.208555	0.104278	+	0.994548i	$0.466747\pi$
$30$	0	0
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000i	0.176777i
$33$	− 1.56155i	− 0.271831i
$34$	−5.12311	−0.878605
$35$	0	0
$36$	1.00000	0.166667
$37$	5.12311i	0.842233i	0.907006	+	0.421117i	$0.138362\pi$
$37$	5.12311i	0.842233i	−0.907006	+	0.421117i	$0.861638\pi$
$38$	− 4.68466i	− 0.759952i
$39$	2.00000	0.320256
$40$	0	0
$41$	−1.12311	−0.175400	−0.0876998	−	0.996147i	$-0.527952\pi$
$41$	−1.12311	−0.175400	−0.0876998	+	0.996147i	$0.527952\pi$
$42$	1.56155i	0.240953i
$43$	7.80776i	1.19067i	0.803477	+	0.595336i	$0.202981\pi$
$43$	7.80776i	1.19067i	−0.803477	+	0.595336i	$0.797019\pi$
$44$	1.56155	0.235413
$45$	0	0
$46$	5.56155	0.820006
$47$	− 3.12311i	− 0.455552i	−0.973714	−	0.227776i	$-0.926855\pi$
$47$	− 3.12311i	− 0.455552i	0.973714	−	0.227776i	$-0.0731454\pi$
$48$	1.00000i	0.144338i
$49$	4.56155	0.651650
$50$	0	0
$51$	−5.12311	−0.717378
$52$	2.00000i	0.277350i
$53$	− 11.5616i	− 1.58810i	−0.607852	−	0.794051i	$-0.707968\pi$
$53$	− 11.5616i	− 1.58810i	0.607852	−	0.794051i	$-0.292032\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−1.56155	−0.208671
$57$	− 4.68466i	− 0.620498i
$58$	1.12311i	0.147471i
$59$	4.87689	0.634918	0.317459	−	0.948272i	$-0.397170\pi$
$59$	4.87689	0.634918	0.317459	+	0.948272i	$0.397170\pi$
$60$	0	0
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	1.00000i	0.127000i
$63$	1.56155i	0.196737i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	1.56155	0.192214
$67$	9.36932i	1.14464i	0.820029	+	0.572322i	$0.193957\pi$
$67$	9.36932i	1.14464i	−0.820029	+	0.572322i	$0.806043\pi$
$68$	− 5.12311i	− 0.621268i
$69$	5.56155	0.669532
$70$	0	0
$71$	4.68466	0.555967	0.277983	−	0.960586i	$-0.410334\pi$
$71$	4.68466	0.555967	0.277983	+	0.960586i	$0.410334\pi$
$72$	1.00000i	0.117851i
$73$	− 9.80776i	− 1.14791i	−0.818886	−	0.573956i	$-0.805408\pi$
$73$	− 9.80776i	− 1.14791i	0.818886	−	0.573956i	$-0.194592\pi$
$74$	−5.12311	−0.595549
$75$	0	0
$76$	4.68466	0.537367
$77$	2.43845i	0.277887i
$78$	2.00000i	0.226455i
$79$	16.6847	1.87717	0.938585	−	0.345047i	$-0.112137\pi$
$79$	16.6847	1.87717	0.938585	+	0.345047i	$0.112137\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 1.12311i	− 0.124026i
$83$	2.24621i	0.246554i	0.992372	+	0.123277i	$0.0393403\pi$
$83$	2.24621i	0.246554i	−0.992372	+	0.123277i	$0.960660\pi$
$84$	−1.56155	−0.170379
$85$	0	0
$86$	−7.80776	−0.841933
$87$	1.12311i	0.120410i
$88$	1.56155i	0.166462i
$89$	1.31534	0.139426	0.0697130	−	0.997567i	$-0.477792\pi$
$89$	1.31534	0.139426	0.0697130	+	0.997567i	$0.477792\pi$
$90$	0	0
$91$	−3.12311	−0.327390
$92$	5.56155i	0.579832i
$93$	1.00000i	0.103695i
$94$	3.12311	0.322124
$95$	0	0
$96$	−1.00000	−0.102062
$97$	− 6.00000i	− 0.609208i	−0.952479	−	0.304604i	$-0.901476\pi$
$97$	− 6.00000i	− 0.609208i	0.952479	−	0.304604i	$-0.0985241\pi$
$98$	4.56155i	0.460786i
$99$	1.56155	0.156942
$100$	0	0
$101$	3.56155	0.354388	0.177194	−	0.984176i	$-0.443298\pi$
$101$	3.56155	0.354388	0.177194	+	0.984176i	$0.443298\pi$
$102$	− 5.12311i	− 0.507263i
$103$	18.2462i	1.79785i	0.438100	+	0.898926i	$0.355652\pi$
$103$	18.2462i	1.79785i	−0.438100	+	0.898926i	$0.644348\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	11.5616	1.12296
$107$	1.56155i	0.150961i	0.997147	+	0.0754805i	$0.0240491\pi$
$107$	1.56155i	0.150961i	−0.997147	+	0.0754805i	$0.975951\pi$
$108$	1.00000i	0.0962250i
$109$	19.3693	1.85524	0.927622	−	0.373520i	$-0.121849\pi$
$109$	19.3693	1.85524	0.927622	+	0.373520i	$0.121849\pi$
$110$	0	0
$111$	−5.12311	−0.486264
$112$	− 1.56155i	− 0.147553i
$113$	− 10.6847i	− 1.00513i	−0.864540	−	0.502564i	$-0.832390\pi$
$113$	− 10.6847i	− 1.00513i	0.864540	−	0.502564i	$-0.167610\pi$
$114$	4.68466	0.438758
$115$	0	0
$116$	−1.12311	−0.104278
$117$	2.00000i	0.184900i
$118$	4.87689i	0.448955i
$119$	8.00000	0.733359
$120$	0	0
$121$	−8.56155	−0.778323
$122$	6.00000i	0.543214i
$123$	− 1.12311i	− 0.101267i
$124$	−1.00000	−0.0898027
$125$	0	0
$126$	−1.56155	−0.139114
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−7.80776	−0.687435
$130$	0	0
$131$	9.36932	0.818601	0.409301	−	0.912400i	$-0.365773\pi$
$131$	9.36932	0.818601	0.409301	+	0.912400i	$0.365773\pi$
$132$	1.56155i	0.135916i
$133$	7.31534i	0.634321i
$134$	−9.36932	−0.809386
$135$	0	0
$136$	5.12311	0.439303
$137$	3.75379i	0.320708i	0.987060	+	0.160354i	$0.0512635\pi$
$137$	3.75379i	0.320708i	−0.987060	+	0.160354i	$0.948736\pi$
$138$	5.56155i	0.473431i
$139$	8.87689	0.752928	0.376464	−	0.926431i	$-0.377140\pi$
$139$	8.87689	0.752928	0.376464	+	0.926431i	$0.377140\pi$
$140$	0	0
$141$	3.12311	0.263013
$142$	4.68466i	0.393128i
$143$	3.12311i	0.261167i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	9.80776	0.811696
$147$	4.56155i	0.376231i
$148$	− 5.12311i	− 0.421117i
$149$	20.0540	1.64289	0.821443	−	0.570291i	$-0.193170\pi$
$149$	20.0540	1.64289	0.821443	+	0.570291i	$0.193170\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	4.68466i	0.379976i
$153$	− 5.12311i	− 0.414179i
$154$	−2.43845	−0.196496
$155$	0	0
$156$	−2.00000	−0.160128
$157$	− 20.0540i	− 1.60048i	−0.599679	−	0.800241i	$-0.704705\pi$
$157$	− 20.0540i	− 1.60048i	0.599679	−	0.800241i	$-0.295295\pi$
$158$	16.6847i	1.32736i
$159$	11.5616	0.916891
$160$	0	0
$161$	−8.68466	−0.684447
$162$	1.00000i	0.0785674i
$163$	− 9.36932i	− 0.733862i	−0.930248	−	0.366931i	$-0.880409\pi$
$163$	− 9.36932i	− 0.733862i	0.930248	−	0.366931i	$-0.119591\pi$
$164$	1.12311	0.0876998
$165$	0	0
$166$	−2.24621	−0.174340
$167$	− 2.43845i	− 0.188693i	−0.995539	−	0.0943464i	$-0.969924\pi$
$167$	− 2.43845i	− 0.188693i	0.995539	−	0.0943464i	$-0.0300761\pi$
$168$	− 1.56155i	− 0.120476i
$169$	9.00000	0.692308
$170$	0	0
$171$	4.68466	0.358245
$172$	− 7.80776i	− 0.595336i
$173$	8.24621i	0.626948i	0.949597	+	0.313474i	$0.101493\pi$
$173$	8.24621i	0.626948i	−0.949597	+	0.313474i	$0.898507\pi$
$174$	−1.12311	−0.0851424
$175$	0	0
$176$	−1.56155	−0.117706
$177$	4.87689i	0.366570i
$178$	1.31534i	0.0985890i
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	24.0540	1.78792	0.893959	−	0.448149i	$-0.147917\pi$
$181$	24.0540	1.78792	0.893959	+	0.448149i	$0.147917\pi$
$182$	− 3.12311i	− 0.231500i
$183$	6.00000i	0.443533i
$184$	−5.56155	−0.410003
$185$	0	0
$186$	−1.00000	−0.0733236
$187$	− 8.00000i	− 0.585018i
$188$	3.12311i	0.227776i
$189$	−1.56155	−0.113586
$190$	0	0
$191$	2.24621	0.162530	0.0812651	−	0.996693i	$-0.474104\pi$
$191$	2.24621	0.162530	0.0812651	+	0.996693i	$0.474104\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	18.4924i	1.33111i	0.746347	+	0.665557i	$0.231806\pi$
$193$	18.4924i	1.33111i	−0.746347	+	0.665557i	$0.768194\pi$
$194$	6.00000	0.430775
$195$	0	0
$196$	−4.56155	−0.325825
$197$	6.00000i	0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$	6.00000i	0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$	1.56155i	0.110975i
$199$	−3.80776	−0.269925	−0.134963	−	0.990851i	$-0.543091\pi$
$199$	−3.80776	−0.269925	−0.134963	+	0.990851i	$0.543091\pi$
$200$	0	0
$201$	−9.36932	−0.660861
$202$	3.56155i	0.250590i
$203$	− 1.75379i	− 0.123092i
$204$	5.12311	0.358689
$205$	0	0
$206$	−18.2462	−1.27127
$207$	5.56155i	0.386555i
$208$	− 2.00000i	− 0.138675i
$209$	7.31534	0.506013
$210$	0	0
$211$	−11.3153	−0.778980	−0.389490	−	0.921031i	$-0.627349\pi$
$211$	−11.3153	−0.778980	−0.389490	+	0.921031i	$0.627349\pi$
$212$	11.5616i	0.794051i
$213$	4.68466i	0.320988i
$214$	−1.56155	−0.106746
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	− 1.56155i	− 0.106005i
$218$	19.3693i	1.31186i
$219$	9.80776	0.662747
$220$	0	0
$221$	10.2462	0.689235
$222$	− 5.12311i	− 0.343840i
$223$	12.8769i	0.862301i	0.902280	+	0.431150i	$0.141892\pi$
$223$	12.8769i	0.862301i	−0.902280	+	0.431150i	$0.858108\pi$
$224$	1.56155	0.104336
$225$	0	0
$226$	10.6847	0.710733
$227$	− 4.68466i	− 0.310932i	−0.987841	−	0.155466i	$-0.950312\pi$
$227$	− 4.68466i	− 0.310932i	0.987841	−	0.155466i	$-0.0496879\pi$
$228$	4.68466i	0.310249i
$229$	12.4384	0.821956	0.410978	−	0.911645i	$-0.365187\pi$
$229$	12.4384	0.821956	0.410978	+	0.911645i	$0.365187\pi$
$230$	0	0
$231$	−2.43845	−0.160438
$232$	− 1.12311i	− 0.0737355i
$233$	− 20.0540i	− 1.31378i	−0.753987	−	0.656890i	$-0.771872\pi$
$233$	− 20.0540i	− 1.31378i	0.753987	−	0.656890i	$-0.228128\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	−4.87689	−0.317459
$237$	16.6847i	1.08379i
$238$	8.00000i	0.518563i
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	0	0
$241$	−4.24621	−0.273523	−0.136761	−	0.990604i	$-0.543669\pi$
$241$	−4.24621	−0.273523	−0.136761	+	0.990604i	$0.543669\pi$
$242$	− 8.56155i	− 0.550357i
$243$	1.00000i	0.0641500i
$244$	−6.00000	−0.384111
$245$	0	0
$246$	1.12311	0.0716066
$247$	9.36932i	0.596155i
$248$	− 1.00000i	− 0.0635001i
$249$	−2.24621	−0.142348
$250$	0	0
$251$	−16.4924	−1.04099	−0.520496	−	0.853864i	$-0.674253\pi$
$251$	−16.4924	−1.04099	−0.520496	+	0.853864i	$0.674253\pi$
$252$	− 1.56155i	− 0.0983686i
$253$	8.68466i	0.546000i
$254$	0	0
$255$	0	0
$256$	1.00000	0.0625000
$257$	10.6847i	0.666491i	0.942840	+	0.333245i	$0.108144\pi$
$257$	10.6847i	0.666491i	−0.942840	+	0.333245i	$0.891856\pi$
$258$	− 7.80776i	− 0.486090i
$259$	8.00000	0.497096
$260$	0	0
$261$	−1.12311	−0.0695185
$262$	9.36932i	0.578838i
$263$	− 12.4924i	− 0.770316i	−0.922851	−	0.385158i	$-0.874147\pi$
$263$	− 12.4924i	− 0.770316i	0.922851	−	0.385158i	$-0.125853\pi$
$264$	−1.56155	−0.0961069
$265$	0	0
$266$	−7.31534	−0.448532
$267$	1.31534i	0.0804976i
$268$	− 9.36932i	− 0.572322i
$269$	−16.2462	−0.990549	−0.495274	−	0.868737i	$-0.664933\pi$
$269$	−16.2462	−0.990549	−0.495274	+	0.868737i	$0.664933\pi$
$270$	0	0
$271$	−10.0540	−0.610736	−0.305368	−	0.952234i	$-0.598779\pi$
$271$	−10.0540	−0.610736	−0.305368	+	0.952234i	$0.598779\pi$
$272$	5.12311i	0.310634i
$273$	− 3.12311i	− 0.189019i
$274$	−3.75379	−0.226775
$275$	0	0
$276$	−5.56155	−0.334766
$277$	19.3693i	1.16379i	0.813264	+	0.581895i	$0.197688\pi$
$277$	19.3693i	1.16379i	−0.813264	+	0.581895i	$0.802312\pi$
$278$	8.87689i	0.532401i
$279$	−1.00000	−0.0598684
$280$	0	0
$281$	13.1231	0.782859	0.391429	−	0.920208i	$-0.371981\pi$
$281$	13.1231	0.782859	0.391429	+	0.920208i	$0.371981\pi$
$282$	3.12311i	0.185978i
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	−4.68466	−0.277983
$285$	0	0
$286$	−3.12311	−0.184673
$287$	1.75379i	0.103523i
$288$	− 1.00000i	− 0.0589256i
$289$	−9.24621	−0.543895
$290$	0	0
$291$	6.00000	0.351726
$292$	9.80776i	0.573956i
$293$	6.49242i	0.379291i	0.981853	+	0.189646i	$0.0607339\pi$
$293$	6.49242i	0.379291i	−0.981853	+	0.189646i	$0.939266\pi$
$294$	−4.56155	−0.266035
$295$	0	0
$296$	5.12311	0.297774
$297$	1.56155i	0.0906105i
$298$	20.0540i	1.16170i
$299$	−11.1231	−0.643266
$300$	0	0
$301$	12.1922	0.702749
$302$	0	0
$303$	3.56155i	0.204606i
$304$	−4.68466	−0.268684
$305$	0	0
$306$	5.12311	0.292868
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	− 2.43845i	− 0.138943i
$309$	−18.2462	−1.03799
$310$	0	0
$311$	−18.2462	−1.03465	−0.517324	−	0.855790i	$-0.673072\pi$
$311$	−18.2462	−1.03465	−0.517324	+	0.855790i	$0.673072\pi$
$312$	− 2.00000i	− 0.113228i
$313$	10.0000i	0.565233i	0.959233	+	0.282617i	$0.0912024\pi$
$313$	10.0000i	0.565233i	−0.959233	+	0.282617i	$0.908798\pi$
$314$	20.0540	1.13171
$315$	0	0
$316$	−16.6847	−0.938585
$317$	25.1231i	1.41105i	0.708683	+	0.705527i	$0.249290\pi$
$317$	25.1231i	1.41105i	−0.708683	+	0.705527i	$0.750710\pi$
$318$	11.5616i	0.648340i
$319$	−1.75379	−0.0981933
$320$	0	0
$321$	−1.56155	−0.0871574
$322$	− 8.68466i	− 0.483977i
$323$	− 24.0000i	− 1.33540i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	9.36932	0.518918
$327$	19.3693i	1.07113i
$328$	1.12311i	0.0620131i
$329$	−4.87689	−0.268872
$330$	0	0
$331$	10.2462	0.563183	0.281591	−	0.959534i	$-0.409138\pi$
$331$	10.2462	0.563183	0.281591	+	0.959534i	$0.409138\pi$
$332$	− 2.24621i	− 0.123277i
$333$	− 5.12311i	− 0.280744i
$334$	2.43845	0.133426
$335$	0	0
$336$	1.56155	0.0851897
$337$	− 10.0000i	− 0.544735i	−0.962193	−	0.272367i	$-0.912193\pi$
$337$	− 10.0000i	− 0.544735i	0.962193	−	0.272367i	$-0.0878066\pi$
$338$	9.00000i	0.489535i
$339$	10.6847	0.580311
$340$	0	0
$341$	−1.56155	−0.0845628
$342$	4.68466i	0.253317i
$343$	− 18.0540i	− 0.974823i
$344$	7.80776	0.420966
$345$	0	0
$346$	−8.24621	−0.443319
$347$	− 2.24621i	− 0.120583i	−0.998181	−	0.0602915i	$-0.980797\pi$
$347$	− 2.24621i	− 0.120583i	0.998181	−	0.0602915i	$-0.0192030\pi$
$348$	− 1.12311i	− 0.0602048i
$349$	19.3693	1.03682	0.518408	−	0.855133i	$-0.326525\pi$
$349$	19.3693	1.03682	0.518408	+	0.855133i	$0.326525\pi$
$350$	0	0
$351$	−2.00000	−0.106752
$352$	− 1.56155i	− 0.0832310i
$353$	− 16.2462i	− 0.864699i	−0.901706	−	0.432349i	$-0.857685\pi$
$353$	− 16.2462i	− 0.864699i	0.901706	−	0.432349i	$-0.142315\pi$
$354$	−4.87689	−0.259204
$355$	0	0
$356$	−1.31534	−0.0697130
$357$	8.00000i	0.423405i
$358$	12.0000i	0.634220i
$359$	19.3153	1.01942	0.509712	−	0.860345i	$-0.329752\pi$
$359$	19.3153	1.01942	0.509712	+	0.860345i	$0.329752\pi$
$360$	0	0
$361$	2.94602	0.155054
$362$	24.0540i	1.26425i
$363$	− 8.56155i	− 0.449365i
$364$	3.12311	0.163695
$365$	0	0
$366$	−6.00000	−0.313625
$367$	− 9.36932i	− 0.489074i	−0.969640	−	0.244537i	$-0.921364\pi$
$367$	− 9.36932i	− 0.489074i	0.969640	−	0.244537i	$-0.0786360\pi$
$368$	− 5.56155i	− 0.289916i
$369$	1.12311	0.0584665
$370$	0	0
$371$	−18.0540	−0.937316
$372$	− 1.00000i	− 0.0518476i
$373$	− 6.68466i	− 0.346118i	−0.984911	−	0.173059i	$-0.944635\pi$
$373$	− 6.68466i	− 0.346118i	0.984911	−	0.173059i	$-0.0553652\pi$
$374$	8.00000	0.413670
$375$	0	0
$376$	−3.12311	−0.161062
$377$	− 2.24621i	− 0.115686i
$378$	− 1.56155i	− 0.0803176i
$379$	−30.0540	−1.54377	−0.771885	−	0.635763i	$-0.780686\pi$
$379$	−30.0540	−1.54377	−0.771885	+	0.635763i	$0.780686\pi$
$380$	0	0
$381$	0	0
$382$	2.24621i	0.114926i
$383$	− 6.24621i	− 0.319166i	−0.987184	−	0.159583i	$-0.948985\pi$
$383$	− 6.24621i	− 0.319166i	0.987184	−	0.159583i	$-0.0510150\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−18.4924	−0.941240
$387$	− 7.80776i	− 0.396891i
$388$	6.00000i	0.304604i
$389$	−24.2462	−1.22933	−0.614666	−	0.788788i	$-0.710709\pi$
$389$	−24.2462	−1.22933	−0.614666	+	0.788788i	$0.710709\pi$
$390$	0	0
$391$	28.4924	1.44092
$392$	− 4.56155i	− 0.230393i
$393$	9.36932i	0.472620i
$394$	−6.00000	−0.302276
$395$	0	0
$396$	−1.56155	−0.0784710
$397$	− 28.0540i	− 1.40799i	−0.710206	−	0.703994i	$-0.751398\pi$
$397$	− 28.0540i	− 1.40799i	0.710206	−	0.703994i	$-0.248602\pi$
$398$	− 3.80776i	− 0.190866i
$399$	−7.31534	−0.366225
$400$	0	0
$401$	−1.31534	−0.0656850	−0.0328425	−	0.999461i	$-0.510456\pi$
$401$	−1.31534	−0.0656850	−0.0328425	+	0.999461i	$0.510456\pi$
$402$	− 9.36932i	− 0.467299i
$403$	− 2.00000i	− 0.0996271i
$404$	−3.56155	−0.177194
$405$	0	0
$406$	1.75379	0.0870391
$407$	− 8.00000i	− 0.396545i
$408$	5.12311i	0.253632i
$409$	12.6307	0.624547	0.312274	−	0.949992i	$-0.398909\pi$
$409$	12.6307	0.624547	0.312274	+	0.949992i	$0.398909\pi$
$410$	0	0
$411$	−3.75379	−0.185161
$412$	− 18.2462i	− 0.898926i
$413$	− 7.61553i	− 0.374736i
$414$	−5.56155	−0.273335
$415$	0	0
$416$	2.00000	0.0980581
$417$	8.87689i	0.434703i
$418$	7.31534i	0.357805i
$419$	−22.2462	−1.08680	−0.543399	−	0.839474i	$-0.682863\pi$
$419$	−22.2462	−1.08680	−0.543399	+	0.839474i	$0.682863\pi$
$420$	0	0
$421$	18.4924	0.901266	0.450633	−	0.892709i	$-0.351198\pi$
$421$	18.4924	0.901266	0.450633	+	0.892709i	$0.351198\pi$
$422$	− 11.3153i	− 0.550822i
$423$	3.12311i	0.151851i
$424$	−11.5616	−0.561479
$425$	0	0
$426$	−4.68466	−0.226972
$427$	− 9.36932i	− 0.453413i
$428$	− 1.56155i	− 0.0754805i
$429$	−3.12311	−0.150785
$430$	0	0
$431$	−13.7538	−0.662497	−0.331248	−	0.943544i	$-0.607470\pi$
$431$	−13.7538	−0.662497	−0.331248	+	0.943544i	$0.607470\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	18.3002i	0.879451i	0.898132	+	0.439725i	$0.144924\pi$
$433$	18.3002i	0.879451i	−0.898132	+	0.439725i	$0.855076\pi$
$434$	1.56155	0.0749569
$435$	0	0
$436$	−19.3693	−0.927622
$437$	26.0540i	1.24633i
$438$	9.80776i	0.468633i
$439$	31.6155	1.50893	0.754463	−	0.656342i	$-0.227897\pi$
$439$	31.6155	1.50893	0.754463	+	0.656342i	$0.227897\pi$
$440$	0	0
$441$	−4.56155	−0.217217
$442$	10.2462i	0.487363i
$443$	14.0540i	0.667725i	0.942622	+	0.333862i	$0.108352\pi$
$443$	14.0540i	0.667725i	−0.942622	+	0.333862i	$0.891648\pi$
$444$	5.12311	0.243132
$445$	0	0
$446$	−12.8769	−0.609739
$447$	20.0540i	0.948520i
$448$	1.56155i	0.0737764i
$449$	22.4924	1.06148	0.530742	−	0.847534i	$-0.321913\pi$
$449$	22.4924	1.06148	0.530742	+	0.847534i	$0.321913\pi$
$450$	0	0
$451$	1.75379	0.0825827
$452$	10.6847i	0.502564i
$453$	0	0
$454$	4.68466	0.219862
$455$	0	0
$456$	−4.68466	−0.219379
$457$	24.7386i	1.15722i	0.815603	+	0.578612i	$0.196406\pi$
$457$	24.7386i	1.15722i	−0.815603	+	0.578612i	$0.803594\pi$
$458$	12.4384i	0.581210i
$459$	5.12311	0.239126
$460$	0	0
$461$	−15.3693	−0.715820	−0.357910	−	0.933756i	$-0.616511\pi$
$461$	−15.3693	−0.715820	−0.357910	+	0.933756i	$0.616511\pi$
$462$	− 2.43845i	− 0.113447i
$463$	18.7386i	0.870858i	0.900223	+	0.435429i	$0.143403\pi$
$463$	18.7386i	0.870858i	−0.900223	+	0.435429i	$0.856597\pi$
$464$	1.12311	0.0521389
$465$	0	0
$466$	20.0540	0.928982
$467$	− 26.2462i	− 1.21453i	−0.794499	−	0.607265i	$-0.792267\pi$
$467$	− 26.2462i	− 1.21453i	0.794499	−	0.607265i	$-0.207733\pi$
$468$	− 2.00000i	− 0.0924500i
$469$	14.6307	0.675582
$470$	0	0
$471$	20.0540	0.924038
$472$	− 4.87689i	− 0.224477i
$473$	− 12.1922i	− 0.560600i
$474$	−16.6847	−0.766352
$475$	0	0
$476$	−8.00000	−0.366679
$477$	11.5616i	0.529367i
$478$	− 24.0000i	− 1.09773i
$479$	−6.43845	−0.294180	−0.147090	−	0.989123i	$-0.546991\pi$
$479$	−6.43845	−0.294180	−0.147090	+	0.989123i	$0.546991\pi$
$480$	0	0
$481$	10.2462	0.467187
$482$	− 4.24621i	− 0.193410i
$483$	− 8.68466i	− 0.395166i
$484$	8.56155	0.389161
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	24.0000i	1.08754i	0.839233	+	0.543772i	$0.183004\pi$
$487$	24.0000i	1.08754i	−0.839233	+	0.543772i	$0.816996\pi$
$488$	− 6.00000i	− 0.271607i
$489$	9.36932	0.423695
$490$	0	0
$491$	2.93087	0.132268	0.0661341	−	0.997811i	$-0.478933\pi$
$491$	2.93087	0.132268	0.0661341	+	0.997811i	$0.478933\pi$
$492$	1.12311i	0.0506335i
$493$	5.75379i	0.259138i
$494$	−9.36932	−0.421545
$495$	0	0
$496$	1.00000	0.0449013
$497$	− 7.31534i	− 0.328138i
$498$	− 2.24621i	− 0.100655i
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	0	0
$501$	2.43845	0.108942
$502$	− 16.4924i	− 0.736093i
$503$	− 9.75379i	− 0.434900i	−0.976071	−	0.217450i	$-0.930226\pi$
$503$	− 9.75379i	− 0.434900i	0.976071	−	0.217450i	$-0.0697739\pi$
$504$	1.56155	0.0695571
$505$	0	0
$506$	−8.68466	−0.386080
$507$	9.00000i	0.399704i
$508$	0	0
$509$	21.6155	0.958091	0.479046	−	0.877790i	$-0.340983\pi$
$509$	21.6155	0.958091	0.479046	+	0.877790i	$0.340983\pi$
$510$	0	0
$511$	−15.3153	−0.677511
$512$	1.00000i	0.0441942i
$513$	4.68466i	0.206833i
$514$	−10.6847	−0.471280
$515$	0	0
$516$	7.80776	0.343718
$517$	4.87689i	0.214486i
$518$	8.00000i	0.351500i
$519$	−8.24621	−0.361968
$520$	0	0
$521$	−15.7538	−0.690186	−0.345093	−	0.938568i	$-0.612153\pi$
$521$	−15.7538	−0.690186	−0.345093	+	0.938568i	$0.612153\pi$
$522$	− 1.12311i	− 0.0491570i
$523$	− 39.4233i	− 1.72386i	−0.507027	−	0.861930i	$-0.669256\pi$
$523$	− 39.4233i	− 1.72386i	0.507027	−	0.861930i	$-0.330744\pi$
$524$	−9.36932	−0.409301
$525$	0	0
$526$	12.4924	0.544696
$527$	5.12311i	0.223166i
$528$	− 1.56155i	− 0.0679579i
$529$	−7.93087	−0.344820
$530$	0	0
$531$	−4.87689	−0.211639
$532$	− 7.31534i	− 0.317160i
$533$	2.24621i	0.0972942i
$534$	−1.31534	−0.0569204
$535$	0	0
$536$	9.36932	0.404693
$537$	12.0000i	0.517838i
$538$	− 16.2462i	− 0.700424i
$539$	−7.12311	−0.306814
$540$	0	0
$541$	36.2462	1.55835	0.779173	−	0.626809i	$-0.215639\pi$
$541$	36.2462	1.55835	0.779173	+	0.626809i	$0.215639\pi$
$542$	− 10.0540i	− 0.431855i
$543$	24.0540i	1.03225i
$544$	−5.12311	−0.219651
$545$	0	0
$546$	3.12311	0.133657
$547$	35.1231i	1.50176i	0.660441	+	0.750878i	$0.270369\pi$
$547$	35.1231i	1.50176i	−0.660441	+	0.750878i	$0.729631\pi$
$548$	− 3.75379i	− 0.160354i
$549$	−6.00000	−0.256074
$550$	0	0
$551$	−5.26137	−0.224142
$552$	− 5.56155i	− 0.236715i
$553$	− 26.0540i	− 1.10793i
$554$	−19.3693	−0.822923
$555$	0	0
$556$	−8.87689	−0.376464
$557$	− 6.19224i	− 0.262373i	−0.991358	−	0.131187i	$-0.958121\pi$
$557$	− 6.19224i	− 0.262373i	0.991358	−	0.131187i	$-0.0418787\pi$
$558$	− 1.00000i	− 0.0423334i
$559$	15.6155	0.660466
$560$	0	0
$561$	8.00000	0.337760
$562$	13.1231i	0.553565i
$563$	16.4924i	0.695073i	0.937667	+	0.347536i	$0.112982\pi$
$563$	16.4924i	0.695073i	−0.937667	+	0.347536i	$0.887018\pi$
$564$	−3.12311	−0.131506
$565$	0	0
$566$	0	0
$567$	− 1.56155i	− 0.0655791i
$568$	− 4.68466i	− 0.196564i
$569$	−10.1922	−0.427281	−0.213640	−	0.976912i	$-0.568532\pi$
$569$	−10.1922	−0.427281	−0.213640	+	0.976912i	$0.568532\pi$
$570$	0	0
$571$	32.8769	1.37586	0.687928	−	0.725779i	$-0.258521\pi$
$571$	32.8769	1.37586	0.687928	+	0.725779i	$0.258521\pi$
$572$	− 3.12311i	− 0.130584i
$573$	2.24621i	0.0938368i
$574$	−1.75379	−0.0732017
$575$	0	0
$576$	1.00000	0.0416667
$577$	6.87689i	0.286289i	0.989702	+	0.143144i	$0.0457213\pi$
$577$	6.87689i	0.286289i	−0.989702	+	0.143144i	$0.954279\pi$
$578$	− 9.24621i	− 0.384592i
$579$	−18.4924	−0.768519
$580$	0	0
$581$	3.50758	0.145519
$582$	6.00000i	0.248708i
$583$	18.0540i	0.747719i
$584$	−9.80776	−0.405848
$585$	0	0
$586$	−6.49242	−0.268200
$587$	32.4924i	1.34111i	0.741862	+	0.670553i	$0.233943\pi$
$587$	32.4924i	1.34111i	−0.741862	+	0.670553i	$0.766057\pi$
$588$	− 4.56155i	− 0.188115i
$589$	−4.68466	−0.193028
$590$	0	0
$591$	−6.00000	−0.246807
$592$	5.12311i	0.210558i
$593$	30.0000i	1.23195i	0.787765	+	0.615976i	$0.211238\pi$
$593$	30.0000i	1.23195i	−0.787765	+	0.615976i	$0.788762\pi$
$594$	−1.56155	−0.0640713
$595$	0	0
$596$	−20.0540	−0.821443
$597$	− 3.80776i	− 0.155841i
$598$	− 11.1231i	− 0.454858i
$599$	23.4233	0.957050	0.478525	−	0.878074i	$-0.341172\pi$
$599$	23.4233	0.957050	0.478525	+	0.878074i	$0.341172\pi$
$600$	0	0
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	12.1922i	0.496918i
$603$	− 9.36932i	− 0.381548i
$604$	0	0
$605$	0	0
$606$	−3.56155	−0.144678
$607$	− 30.0540i	− 1.21985i	−0.792458	−	0.609927i	$-0.791199\pi$
$607$	− 30.0540i	− 1.21985i	0.792458	−	0.609927i	$-0.208801\pi$
$608$	− 4.68466i	− 0.189988i
$609$	1.75379	0.0710671
$610$	0	0
$611$	−6.24621	−0.252695
$612$	5.12311i	0.207089i
$613$	− 2.00000i	− 0.0807792i	−0.999184	−	0.0403896i	$-0.987140\pi$
$613$	− 2.00000i	− 0.0807792i	0.999184	−	0.0403896i	$-0.0128599\pi$
$614$	0	0
$615$	0	0
$616$	2.43845	0.0982478
$617$	− 19.5616i	− 0.787518i	−0.919214	−	0.393759i	$-0.871174\pi$
$617$	− 19.5616i	− 0.787518i	0.919214	−	0.393759i	$-0.128826\pi$
$618$	− 18.2462i	− 0.733970i
$619$	13.3693	0.537358	0.268679	−	0.963230i	$-0.413413\pi$
$619$	13.3693	0.537358	0.268679	+	0.963230i	$0.413413\pi$
$620$	0	0
$621$	−5.56155	−0.223177
$622$	− 18.2462i	− 0.731606i
$623$	− 2.05398i	− 0.0822908i
$624$	2.00000	0.0800641
$625$	0	0
$626$	−10.0000	−0.399680
$627$	7.31534i	0.292147i
$628$	20.0540i	0.800241i
$629$	−26.2462	−1.04650
$630$	0	0
$631$	−24.3002	−0.967375	−0.483688	−	0.875241i	$-0.660703\pi$
$631$	−24.3002	−0.967375	−0.483688	+	0.875241i	$0.660703\pi$
$632$	− 16.6847i	− 0.663680i
$633$	− 11.3153i	− 0.449744i
$634$	−25.1231	−0.997766
$635$	0	0
$636$	−11.5616	−0.458445
$637$	− 9.12311i	− 0.361471i
$638$	− 1.75379i	− 0.0694332i
$639$	−4.68466	−0.185322
$640$	0	0
$641$	−38.4924	−1.52036	−0.760180	−	0.649713i	$-0.774889\pi$
$641$	−38.4924	−1.52036	−0.760180	+	0.649713i	$0.774889\pi$
$642$	− 1.56155i	− 0.0616296i
$643$	− 30.0540i	− 1.18521i	−0.805492	−	0.592607i	$-0.798099\pi$
$643$	− 30.0540i	− 1.18521i	0.805492	−	0.592607i	$-0.201901\pi$
$644$	8.68466	0.342223
$645$	0	0
$646$	24.0000	0.944267
$647$	− 17.0691i	− 0.671057i	−0.942030	−	0.335528i	$-0.891085\pi$
$647$	− 17.0691i	− 0.671057i	0.942030	−	0.335528i	$-0.108915\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	−7.61553	−0.298936
$650$	0	0
$651$	1.56155	0.0612021
$652$	9.36932i	0.366931i
$653$	− 23.7538i	− 0.929558i	−0.885427	−	0.464779i	$-0.846134\pi$
$653$	− 23.7538i	− 0.929558i	0.885427	−	0.464779i	$-0.153866\pi$
$654$	−19.3693	−0.757400
$655$	0	0
$656$	−1.12311	−0.0438499
$657$	9.80776i	0.382637i
$658$	− 4.87689i	− 0.190121i
$659$	−18.7386	−0.729954	−0.364977	−	0.931017i	$-0.618923\pi$
$659$	−18.7386	−0.729954	−0.364977	+	0.931017i	$0.618923\pi$
$660$	0	0
$661$	−6.49242	−0.252526	−0.126263	−	0.991997i	$-0.540298\pi$
$661$	−6.49242	−0.252526	−0.126263	+	0.991997i	$0.540298\pi$
$662$	10.2462i	0.398230i
$663$	10.2462i	0.397930i
$664$	2.24621	0.0871699
$665$	0	0
$666$	5.12311	0.198516
$667$	− 6.24621i	− 0.241854i
$668$	2.43845i	0.0943464i
$669$	−12.8769	−0.497849
$670$	0	0
$671$	−9.36932	−0.361698
$672$	1.56155i	0.0602382i
$673$	− 28.2462i	− 1.08881i	−0.838822	−	0.544406i	$-0.816755\pi$
$673$	− 28.2462i	− 1.08881i	0.838822	−	0.544406i	$-0.183245\pi$
$674$	10.0000	0.385186
$675$	0	0
$676$	−9.00000	−0.346154
$677$	− 29.4233i	− 1.13083i	−0.824807	−	0.565414i	$-0.808716\pi$
$677$	− 29.4233i	− 1.13083i	0.824807	−	0.565414i	$-0.191284\pi$
$678$	10.6847i	0.410342i
$679$	−9.36932	−0.359561
$680$	0	0
$681$	4.68466	0.179517
$682$	− 1.56155i	− 0.0597949i
$683$	− 19.3153i	− 0.739081i	−0.929215	−	0.369541i	$-0.879515\pi$
$683$	− 19.3153i	− 0.739081i	0.929215	−	0.369541i	$-0.120485\pi$
$684$	−4.68466	−0.179122
$685$	0	0
$686$	18.0540	0.689304
$687$	12.4384i	0.474556i
$688$	7.80776i	0.297668i
$689$	−23.1231	−0.880920
$690$	0	0
$691$	−22.0540	−0.838973	−0.419486	−	0.907762i	$-0.637790\pi$
$691$	−22.0540	−0.838973	−0.419486	+	0.907762i	$0.637790\pi$
$692$	− 8.24621i	− 0.313474i
$693$	− 2.43845i	− 0.0926289i
$694$	2.24621	0.0852650
$695$	0	0
$696$	1.12311	0.0425712
$697$	− 5.75379i	− 0.217940i
$698$	19.3693i	0.733139i
$699$	20.0540	0.758511
$700$	0	0
$701$	25.8078	0.974746	0.487373	−	0.873194i	$-0.337955\pi$
$701$	25.8078	0.974746	0.487373	+	0.873194i	$0.337955\pi$
$702$	− 2.00000i	− 0.0754851i
$703$	− 24.0000i	− 0.905177i
$704$	1.56155	0.0588532
$705$	0	0
$706$	16.2462	0.611434
$707$	− 5.56155i	− 0.209164i
$708$	− 4.87689i	− 0.183285i
$709$	20.0540	0.753143	0.376571	−	0.926388i	$-0.377103\pi$
$709$	20.0540	0.753143	0.376571	+	0.926388i	$0.377103\pi$
$710$	0	0
$711$	−16.6847	−0.625724
$712$	− 1.31534i	− 0.0492945i
$713$	− 5.56155i	− 0.208282i
$714$	−8.00000	−0.299392
$715$	0	0
$716$	−12.0000	−0.448461
$717$	− 24.0000i	− 0.896296i
$718$	19.3153i	0.720842i
$719$	43.1231	1.60822	0.804110	−	0.594480i	$-0.202642\pi$
$719$	43.1231	1.60822	0.804110	+	0.594480i	$0.202642\pi$
$720$	0	0
$721$	28.4924	1.06111
$722$	2.94602i	0.109640i
$723$	− 4.24621i	− 0.157918i
$724$	−24.0540	−0.893959
$725$	0	0
$726$	8.56155	0.317749
$727$	− 14.0540i	− 0.521233i	−0.965442	−	0.260617i	$-0.916074\pi$
$727$	− 14.0540i	− 0.521233i	0.965442	−	0.260617i	$-0.0839258\pi$
$728$	3.12311i	0.115750i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−40.0000	−1.47945
$732$	− 6.00000i	− 0.221766i
$733$	− 26.4924i	− 0.978520i	−0.872138	−	0.489260i	$-0.837267\pi$
$733$	− 26.4924i	− 0.978520i	0.872138	−	0.489260i	$-0.162733\pi$
$734$	9.36932	0.345828
$735$	0	0
$736$	5.56155	0.205002
$737$	− 14.6307i	− 0.538928i
$738$	1.12311i	0.0413421i
$739$	12.9848	0.477655	0.238828	−	0.971062i	$-0.423237\pi$
$739$	12.9848	0.477655	0.238828	+	0.971062i	$0.423237\pi$
$740$	0	0
$741$	−9.36932	−0.344190
$742$	− 18.0540i	− 0.662782i
$743$	− 11.4233i	− 0.419080i	−0.977800	−	0.209540i	$-0.932803\pi$
$743$	− 11.4233i	− 0.419080i	0.977800	−	0.209540i	$-0.0671966\pi$
$744$	1.00000	0.0366618
$745$	0	0
$746$	6.68466	0.244743
$747$	− 2.24621i	− 0.0821846i
$748$	8.00000i	0.292509i
$749$	2.43845	0.0890989
$750$	0	0
$751$	36.8769	1.34566	0.672828	−	0.739798i	$-0.265079\pi$
$751$	36.8769	1.34566	0.672828	+	0.739798i	$0.265079\pi$
$752$	− 3.12311i	− 0.113888i
$753$	− 16.4924i	− 0.601017i
$754$	2.24621	0.0818022
$755$	0	0
$756$	1.56155	0.0567931
$757$	10.0000i	0.363456i	0.983349	+	0.181728i	$0.0581691\pi$
$757$	10.0000i	0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$758$	− 30.0540i	− 1.09161i
$759$	−8.68466	−0.315233
$760$	0	0
$761$	41.4233	1.50159	0.750797	−	0.660533i	$-0.229670\pi$
$761$	41.4233	1.50159	0.750797	+	0.660533i	$0.229670\pi$
$762$	0	0
$763$	− 30.2462i	− 1.09499i
$764$	−2.24621	−0.0812651
$765$	0	0
$766$	6.24621	0.225685
$767$	− 9.75379i	− 0.352189i
$768$	1.00000i	0.0360844i
$769$	16.4384	0.592786	0.296393	−	0.955066i	$-0.404216\pi$
$769$	16.4384	0.592786	0.296393	+	0.955066i	$0.404216\pi$
$770$	0	0
$771$	−10.6847	−0.384799
$772$	− 18.4924i	− 0.665557i
$773$	15.5616i	0.559710i	0.960042	+	0.279855i	$0.0902864\pi$
$773$	15.5616i	0.559710i	−0.960042	+	0.279855i	$0.909714\pi$
$774$	7.80776	0.280644
$775$	0	0
$776$	−6.00000	−0.215387
$777$	8.00000i	0.286998i
$778$	− 24.2462i	− 0.869269i
$779$	5.26137	0.188508
$780$	0	0
$781$	−7.31534	−0.261764
$782$	28.4924i	1.01889i
$783$	− 1.12311i	− 0.0401365i
$784$	4.56155	0.162913
$785$	0	0
$786$	−9.36932	−0.334192
$787$	10.9309i	0.389643i	0.980839	+	0.194822i	$0.0624128\pi$
$787$	10.9309i	0.389643i	−0.980839	+	0.194822i	$0.937587\pi$
$788$	− 6.00000i	− 0.213741i
$789$	12.4924	0.444742
$790$	0	0
$791$	−16.6847	−0.593238
$792$	− 1.56155i	− 0.0554874i
$793$	− 12.0000i	− 0.426132i
$794$	28.0540	0.995598
$795$	0	0
$796$	3.80776	0.134963
$797$	38.9848i	1.38091i	0.723373	+	0.690457i	$0.242591\pi$
$797$	38.9848i	1.38091i	−0.723373	+	0.690457i	$0.757409\pi$
$798$	− 7.31534i	− 0.258960i
$799$	16.0000	0.566039
$800$	0	0
$801$	−1.31534	−0.0464753
$802$	− 1.31534i	− 0.0464463i
$803$	15.3153i	0.540467i
$804$	9.36932	0.330430
$805$	0	0
$806$	2.00000	0.0704470
$807$	− 16.2462i	− 0.571894i
$808$	− 3.56155i	− 0.125295i
$809$	25.3153	0.890040	0.445020	−	0.895521i	$-0.353197\pi$
$809$	25.3153	0.890040	0.445020	+	0.895521i	$0.353197\pi$
$810$	0	0
$811$	53.6695	1.88459	0.942296	−	0.334782i	$-0.108663\pi$
$811$	53.6695	1.88459	0.942296	+	0.334782i	$0.108663\pi$
$812$	1.75379i	0.0615459i
$813$	− 10.0540i	− 0.352608i
$814$	8.00000	0.280400
$815$	0	0
$816$	−5.12311	−0.179345
$817$	− 36.5767i	− 1.27966i
$818$	12.6307i	0.441621i
$819$	3.12311	0.109130
$820$	0	0
$821$	−21.6155	−0.754387	−0.377194	−	0.926134i	$-0.623111\pi$
$821$	−21.6155	−0.754387	−0.377194	+	0.926134i	$0.623111\pi$
$822$	− 3.75379i	− 0.130928i
$823$	− 15.6155i	− 0.544323i	−0.962252	−	0.272162i	$-0.912261\pi$
$823$	− 15.6155i	− 0.544323i	0.962252	−	0.272162i	$-0.0877385\pi$
$824$	18.2462	0.635637
$825$	0	0
$826$	7.61553	0.264978
$827$	18.2462i	0.634483i	0.948345	+	0.317241i	$0.102757\pi$
$827$	18.2462i	0.634483i	−0.948345	+	0.317241i	$0.897243\pi$
$828$	− 5.56155i	− 0.193277i
$829$	37.4233	1.29976	0.649882	−	0.760035i	$-0.274818\pi$
$829$	37.4233	1.29976	0.649882	+	0.760035i	$0.274818\pi$
$830$	0	0
$831$	−19.3693	−0.671914
$832$	2.00000i	0.0693375i
$833$	23.3693i	0.809699i
$834$	−8.87689	−0.307382
$835$	0	0
$836$	−7.31534	−0.253006
$837$	− 1.00000i	− 0.0345651i
$838$	− 22.2462i	− 0.768483i
$839$	−34.9309	−1.20595	−0.602974	−	0.797761i	$-0.706018\pi$
$839$	−34.9309	−1.20595	−0.602974	+	0.797761i	$0.706018\pi$
$840$	0	0
$841$	−27.7386	−0.956505
$842$	18.4924i	0.637291i
$843$	13.1231i	0.451984i
$844$	11.3153	0.389490
$845$	0	0
$846$	−3.12311	−0.107375
$847$	13.3693i	0.459375i
$848$	− 11.5616i	− 0.397025i
$849$	0	0
$850$	0	0
$851$	28.4924	0.976708
$852$	− 4.68466i	− 0.160494i
$853$	38.7926i	1.32823i	0.747629	+	0.664117i	$0.231192\pi$
$853$	38.7926i	1.32823i	−0.747629	+	0.664117i	$0.768808\pi$
$854$	9.36932	0.320611
$855$	0	0
$856$	1.56155	0.0533728
$857$	− 53.2311i	− 1.81834i	−0.416427	−	0.909169i	$-0.636718\pi$
$857$	− 53.2311i	− 1.81834i	0.416427	−	0.909169i	$-0.363282\pi$
$858$	− 3.12311i	− 0.106621i
$859$	22.7386	0.775832	0.387916	−	0.921695i	$-0.373195\pi$
$859$	22.7386	0.775832	0.387916	+	0.921695i	$0.373195\pi$
$860$	0	0
$861$	−1.75379	−0.0597690
$862$	− 13.7538i	− 0.468456i
$863$	30.5464i	1.03981i	0.854224	+	0.519906i	$0.174033\pi$
$863$	30.5464i	1.03981i	−0.854224	+	0.519906i	$0.825967\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−18.3002	−0.621866
$867$	− 9.24621i	− 0.314018i
$868$	1.56155i	0.0530026i
$869$	−26.0540	−0.883821
$870$	0	0
$871$	18.7386	0.634934
$872$	− 19.3693i	− 0.655928i
$873$	6.00000i	0.203069i
$874$	−26.0540	−0.881289
$875$	0	0
$876$	−9.80776	−0.331374
$877$	− 50.0000i	− 1.68838i	−0.536044	−	0.844190i	$-0.680082\pi$
$877$	− 50.0000i	− 1.68838i	0.536044	−	0.844190i	$-0.319918\pi$
$878$	31.6155i	1.06697i
$879$	−6.49242	−0.218984
$880$	0	0
$881$	42.4924	1.43161	0.715803	−	0.698302i	$-0.246061\pi$
$881$	42.4924	1.43161	0.715803	+	0.698302i	$0.246061\pi$
$882$	− 4.56155i	− 0.153595i
$883$	31.4233i	1.05748i	0.848784	+	0.528739i	$0.177335\pi$
$883$	31.4233i	1.05748i	−0.848784	+	0.528739i	$0.822665\pi$
$884$	−10.2462	−0.344617
$885$	0	0
$886$	−14.0540	−0.472153
$887$	− 57.3693i	− 1.92627i	−0.269013	−	0.963137i	$-0.586697\pi$
$887$	− 57.3693i	− 1.92627i	0.269013	−	0.963137i	$-0.413303\pi$
$888$	5.12311i	0.171920i
$889$	0	0
$890$	0	0
$891$	−1.56155	−0.0523140
$892$	− 12.8769i	− 0.431150i
$893$	14.6307i	0.489597i
$894$	−20.0540	−0.670705
$895$	0	0
$896$	−1.56155	−0.0521678
$897$	− 11.1231i	− 0.371390i
$898$	22.4924i	0.750582i
$899$	1.12311	0.0374577
$900$	0	0
$901$	59.2311	1.97327
$902$	1.75379i	0.0583948i
$903$	12.1922i	0.405732i
$904$	−10.6847	−0.355366
$905$	0	0
$906$	0	0
$907$	24.0000i	0.796907i	0.917189	+	0.398453i	$0.130453\pi$
$907$	24.0000i	0.796907i	−0.917189	+	0.398453i	$0.869547\pi$
$908$	4.68466i	0.155466i
$909$	−3.56155	−0.118129
$910$	0	0
$911$	−44.4924	−1.47410	−0.737050	−	0.675838i	$-0.763782\pi$
$911$	−44.4924	−1.47410	−0.737050	+	0.675838i	$0.763782\pi$
$912$	− 4.68466i	− 0.155125i
$913$	− 3.50758i	− 0.116084i
$914$	−24.7386	−0.818281
$915$	0	0
$916$	−12.4384	−0.410978
$917$	− 14.6307i	− 0.483148i
$918$	5.12311i	0.169088i
$919$	−39.6155	−1.30680	−0.653398	−	0.757015i	$-0.726657\pi$
$919$	−39.6155	−1.30680	−0.653398	+	0.757015i	$0.726657\pi$
$920$	0	0
$921$	0	0
$922$	− 15.3693i	− 0.506161i
$923$	− 9.36932i	− 0.308395i
$924$	2.43845	0.0802190
$925$	0	0
$926$	−18.7386	−0.615790
$927$	− 18.2462i	− 0.599284i
$928$	1.12311i	0.0368677i
$929$	−11.5616	−0.379322	−0.189661	−	0.981850i	$-0.560739\pi$
$929$	−11.5616	−0.379322	−0.189661	+	0.981850i	$0.560739\pi$
$930$	0	0
$931$	−21.3693	−0.700351
$932$	20.0540i	0.656890i
$933$	− 18.2462i	− 0.597354i
$934$	26.2462	0.858802
$935$	0	0
$936$	2.00000	0.0653720
$937$	16.6307i	0.543301i	0.962396	+	0.271650i	$0.0875694\pi$
$937$	16.6307i	0.543301i	−0.962396	+	0.271650i	$0.912431\pi$
$938$	14.6307i	0.477709i
$939$	−10.0000	−0.326338
$940$	0	0
$941$	27.3693	0.892214	0.446107	−	0.894980i	$-0.352810\pi$
$941$	27.3693	0.892214	0.446107	+	0.894980i	$0.352810\pi$
$942$	20.0540i	0.653394i
$943$	6.24621i	0.203405i
$944$	4.87689	0.158729
$945$	0	0
$946$	12.1922	0.396404
$947$	− 0.876894i	− 0.0284952i	−0.999898	−	0.0142476i	$-0.995465\pi$
$947$	− 0.876894i	− 0.0284952i	0.999898	−	0.0142476i	$-0.00453531\pi$
$948$	− 16.6847i	− 0.541893i
$949$	−19.6155	−0.636747
$950$	0	0
$951$	−25.1231	−0.814673
$952$	− 8.00000i	− 0.259281i
$953$	58.1080i	1.88230i	0.337988	+	0.941151i	$0.390254\pi$
$953$	58.1080i	1.88230i	−0.337988	+	0.941151i	$0.609746\pi$
$954$	−11.5616	−0.374319
$955$	0	0
$956$	24.0000	0.776215
$957$	− 1.75379i	− 0.0566919i
$958$	− 6.43845i	− 0.208017i
$959$	5.86174	0.189285
$960$	0	0
$961$	1.00000	0.0322581
$962$	10.2462i	0.330351i
$963$	− 1.56155i	− 0.0503203i
$964$	4.24621	0.136761
$965$	0	0
$966$	8.68466	0.279424
$967$	− 25.7538i	− 0.828186i	−0.910235	−	0.414093i	$-0.864099\pi$
$967$	− 25.7538i	− 0.828186i	0.910235	−	0.414093i	$-0.135901\pi$
$968$	8.56155i	0.275179i
$969$	24.0000	0.770991
$970$	0	0
$971$	−28.8769	−0.926704	−0.463352	−	0.886174i	$-0.653353\pi$
$971$	−28.8769	−0.926704	−0.463352	+	0.886174i	$0.653353\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	− 13.8617i	− 0.444387i
$974$	−24.0000	−0.769010
$975$	0	0
$976$	6.00000	0.192055
$977$	− 22.9848i	− 0.735350i	−0.929954	−	0.367675i	$-0.880154\pi$
$977$	− 22.9848i	− 0.735350i	0.929954	−	0.367675i	$-0.119846\pi$
$978$	9.36932i	0.299598i
$979$	−2.05398	−0.0656453
$980$	0	0
$981$	−19.3693	−0.618415
$982$	2.93087i	0.0935278i
$983$	24.9848i	0.796893i	0.917192	+	0.398446i	$0.130451\pi$
$983$	24.9848i	0.796893i	−0.917192	+	0.398446i	$0.869549\pi$
$984$	−1.12311	−0.0358033
$985$	0	0
$986$	−5.75379	−0.183238
$987$	− 4.87689i	− 0.155233i
$988$	− 9.36932i	− 0.298078i
$989$	43.4233	1.38078
$990$	0	0
$991$	23.3153	0.740636	0.370318	−	0.928905i	$-0.379249\pi$
$991$	23.3153	0.740636	0.370318	+	0.928905i	$0.379249\pi$
$992$	1.00000i	0.0317500i
$993$	10.2462i	0.325154i
$994$	7.31534	0.232029
$995$	0	0
$996$	2.24621	0.0711739
$997$	− 62.4924i	− 1.97915i	−0.144002	−	0.989577i	$-0.545997\pi$
$997$	− 62.4924i	− 1.97915i	0.144002	−	0.989577i	$-0.454003\pi$
$998$	− 20.0000i	− 0.633089i
$999$	5.12311	0.162088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4650.2.d.bd.3349.3		4
5.2	odd	4		4650.2.a.ce.1.2		2
5.3	odd	4		930.2.a.p.1.1	✓	2
5.4	even	2	inner	4650.2.d.bd.3349.2		4
15.8	even	4		2790.2.a.be.1.1		2
20.3	even	4		7440.2.a.bl.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.a.p.1.1	✓	2	5.3	odd	4
2790.2.a.be.1.1		2	15.8	even	4
4650.2.a.ce.1.2		2	5.2	odd	4
4650.2.d.bd.3349.2		4	5.4	even	2	inner
4650.2.d.bd.3349.3		4	1.1	even	1	trivial
7440.2.a.bl.1.2		2	20.3	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:	\( N \)	\(=\)	\( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4650.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -1.56155i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -1.56155i q^{7} -1.00000i q^{8} -1.00000 q^{9} -1.56155 q^{11} -1.00000i q^{12} -2.00000i q^{13} +1.56155 q^{14} +1.00000 q^{16} +5.12311i q^{17} -1.00000i q^{18} -4.68466 q^{19} +1.56155 q^{21} -1.56155i q^{22} -5.56155i q^{23} +1.00000 q^{24} +2.00000 q^{26} -1.00000i q^{27} +1.56155i q^{28} +1.12311 q^{29} +1.00000 q^{31} +1.00000i q^{32} -1.56155i q^{33} -5.12311 q^{34} +1.00000 q^{36} +5.12311i q^{37} -4.68466i q^{38} +2.00000 q^{39} -1.12311 q^{41} +1.56155i q^{42} +7.80776i q^{43} +1.56155 q^{44} +5.56155 q^{46} -3.12311i q^{47} +1.00000i q^{48} +4.56155 q^{49} -5.12311 q^{51} +2.00000i q^{52} -11.5616i q^{53} +1.00000 q^{54} -1.56155 q^{56} -4.68466i q^{57} +1.12311i q^{58} +4.87689 q^{59} +6.00000 q^{61} +1.00000i q^{62} +1.56155i q^{63} -1.00000 q^{64} +1.56155 q^{66} +9.36932i q^{67} -5.12311i q^{68} +5.56155 q^{69} +4.68466 q^{71} +1.00000i q^{72} -9.80776i q^{73} -5.12311 q^{74} +4.68466 q^{76} +2.43845i q^{77} +2.00000i q^{78} +16.6847 q^{79} +1.00000 q^{81} -1.12311i q^{82} +2.24621i q^{83} -1.56155 q^{84} -7.80776 q^{86} +1.12311i q^{87} +1.56155i q^{88} +1.31534 q^{89} -3.12311 q^{91} +5.56155i q^{92} +1.00000i q^{93} +3.12311 q^{94} -1.00000 q^{96} -6.00000i q^{97} +4.56155i q^{98} +1.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 2 q^{11} - 2 q^{14} + 4 q^{16} + 6 q^{19} - 2 q^{21} + 4 q^{24} + 8 q^{26} - 12 q^{29} + 4 q^{31} - 4 q^{34} + 4 q^{36} + 8 q^{39} + 12 q^{41} - 2 q^{44} + 14 q^{46} + 10 q^{49} - 4 q^{51} + 4 q^{54} + 2 q^{56} + 36 q^{59} + 24 q^{61} - 4 q^{64} - 2 q^{66} + 14 q^{69} - 6 q^{71} - 4 q^{74} - 6 q^{76} + 42 q^{79} + 4 q^{81} + 2 q^{84} + 10 q^{86} + 30 q^{89} + 4 q^{91} - 4 q^{94} - 4 q^{96} - 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 2 * q^11 - 2 * q^14 + 4 * q^16 + 6 * q^19 - 2 * q^21 + 4 * q^24 + 8 * q^26 - 12 * q^29 + 4 * q^31 - 4 * q^34 + 4 * q^36 + 8 * q^39 + 12 * q^41 - 2 * q^44 + 14 * q^46 + 10 * q^49 - 4 * q^51 + 4 * q^54 + 2 * q^56 + 36 * q^59 + 24 * q^61 - 4 * q^64 - 2 * q^66 + 14 * q^69 - 6 * q^71 - 4 * q^74 - 6 * q^76 + 42 * q^79 + 4 * q^81 + 2 * q^84 + 10 * q^86 + 30 * q^89 + 4 * q^91 - 4 * q^94 - 4 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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