LMFDB - Embedded newform 4650.2.d.bh.3349.2

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:	$\Q(i, \sqrt{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 17x^{2} + 64 $ x^4 + 17*x^2 + 64
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			3349.2
Root			$2.37228i$ of defining polynomial
Character	$\chi$	$=$	4650.3349
Dual form			4650.2.d.bh.3349.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +2.37228i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +2.37228i q^{7} +1.00000i q^{8} -1.00000 q^{9} +6.37228 q^{11} -1.00000i q^{12} -2.00000i q^{13} +2.37228 q^{14} +1.00000 q^{16} -6.74456i q^{17} +1.00000i q^{18} +6.37228 q^{19} -2.37228 q^{21} -6.37228i q^{22} -2.37228i q^{23} -1.00000 q^{24} -2.00000 q^{26} -1.00000i q^{27} -2.37228i q^{28} -2.74456 q^{29} -1.00000 q^{31} -1.00000i q^{32} +6.37228i q^{33} -6.74456 q^{34} +1.00000 q^{36} -10.7446i q^{37} -6.37228i q^{38} +2.00000 q^{39} -10.7446 q^{41} +2.37228i q^{42} +6.37228i q^{43} -6.37228 q^{44} -2.37228 q^{46} -4.74456i q^{47} +1.00000i q^{48} +1.37228 q^{49} +6.74456 q^{51} +2.00000i q^{52} -4.37228i q^{53} -1.00000 q^{54} -2.37228 q^{56} +6.37228i q^{57} +2.74456i q^{58} +8.74456 q^{59} -11.4891 q^{61} +1.00000i q^{62} -2.37228i q^{63} -1.00000 q^{64} +6.37228 q^{66} +0.744563i q^{67} +6.74456i q^{68} +2.37228 q^{69} -2.37228 q^{71} -1.00000i q^{72} +9.11684i q^{73} -10.7446 q^{74} -6.37228 q^{76} +15.1168i q^{77} -2.00000i q^{78} +10.3723 q^{79} +1.00000 q^{81} +10.7446i q^{82} -12.0000i q^{83} +2.37228 q^{84} +6.37228 q^{86} -2.74456i q^{87} +6.37228i q^{88} -4.37228 q^{89} +4.74456 q^{91} +2.37228i q^{92} -1.00000i q^{93} -4.74456 q^{94} +1.00000 q^{96} -2.00000i q^{97} -1.37228i q^{98} -6.37228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 14 q^{11} - 2 q^{14} + 4 q^{16} + 14 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} - 20 q^{41} - 14 q^{44} + 2 q^{46} - 6 q^{49} + 4 q^{51} - 4 q^{54} + 2 q^{56} + 12 q^{59} - 4 q^{64} + 14 q^{66} - 2 q^{69} + 2 q^{71} - 20 q^{74} - 14 q^{76} + 30 q^{79} + 4 q^{81} - 2 q^{84} + 14 q^{86} - 6 q^{89} - 4 q^{91} + 4 q^{94} + 4 q^{96} - 14 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 14 * q^11 - 2 * q^14 + 4 * q^16 + 14 * 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 - 20 * q^41 - 14 * q^44 + 2 * q^46 - 6 * q^49 + 4 * q^51 - 4 * q^54 + 2 * q^56 + 12 * q^59 - 4 * q^64 + 14 * q^66 - 2 * q^69 + 2 * q^71 - 20 * q^74 - 14 * q^76 + 30 * q^79 + 4 * q^81 - 2 * q^84 + 14 * q^86 - 6 * q^89 - 4 * q^91 + 4 * q^94 + 4 * q^96 - 14 * 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
$7$	2.37228i	0.896638i	0.893874	+	0.448319i	$0.147977\pi$
$7$	2.37228i	0.896638i	−0.893874	+	0.448319i	$0.852023\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	6.37228	1.92132	0.960658	−	0.277736i	$-0.0895839\pi$
$11$	6.37228	1.92132	0.960658	+	0.277736i	$0.0895839\pi$
$12$	− 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	$-0.0894562\pi$
$14$	2.37228	0.634019
$15$	0	0
$16$	1.00000	0.250000
$17$	− 6.74456i	− 1.63580i	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	− 6.74456i	− 1.63580i	0.575363	−	0.817898i	$-0.304861\pi$
$18$	1.00000i	0.235702i
$19$	6.37228	1.46190	0.730951	−	0.682430i	$-0.239077\pi$
$19$	6.37228	1.46190	0.730951	+	0.682430i	$0.239077\pi$
$20$	0	0
$21$	−2.37228	−0.517674
$22$	− 6.37228i	− 1.35857i
$23$	− 2.37228i	− 0.494655i	−0.968932	−	0.247327i	$-0.920448\pi$
$23$	− 2.37228i	− 0.494655i	0.968932	−	0.247327i	$-0.0795523\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−2.00000	−0.392232
$27$	− 1.00000i	− 0.192450i
$28$	− 2.37228i	− 0.448319i
$29$	−2.74456	−0.509652	−0.254826	−	0.966987i	$-0.582018\pi$
$29$	−2.74456	−0.509652	−0.254826	+	0.966987i	$0.582018\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	− 1.00000i	− 0.176777i
$33$	6.37228i	1.10927i
$34$	−6.74456	−1.15668
$35$	0	0
$36$	1.00000	0.166667
$37$	− 10.7446i	− 1.76640i	−0.469001	−	0.883198i	$-0.655386\pi$
$37$	− 10.7446i	− 1.76640i	0.469001	−	0.883198i	$-0.344614\pi$
$38$	− 6.37228i	− 1.03372i
$39$	2.00000	0.320256
$40$	0	0
$41$	−10.7446	−1.67802	−0.839009	−	0.544117i	$-0.816865\pi$
$41$	−10.7446	−1.67802	−0.839009	+	0.544117i	$0.816865\pi$
$42$	2.37228i	0.366051i
$43$	6.37228i	0.971764i	0.874024	+	0.485882i	$0.161501\pi$
$43$	6.37228i	0.971764i	−0.874024	+	0.485882i	$0.838499\pi$
$44$	−6.37228	−0.960658
$45$	0	0
$46$	−2.37228	−0.349774
$47$	− 4.74456i	− 0.692066i	−0.938222	−	0.346033i	$-0.887529\pi$
$47$	− 4.74456i	− 0.692066i	0.938222	−	0.346033i	$-0.112471\pi$
$48$	1.00000i	0.144338i
$49$	1.37228	0.196040
$50$	0	0
$51$	6.74456	0.944428
$52$	2.00000i	0.277350i
$53$	− 4.37228i	− 0.600579i	−0.953848	−	0.300290i	$-0.902917\pi$
$53$	− 4.37228i	− 0.600579i	0.953848	−	0.300290i	$-0.0970833\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−2.37228	−0.317009
$57$	6.37228i	0.844029i
$58$	2.74456i	0.360379i
$59$	8.74456	1.13845	0.569223	−	0.822183i	$-0.307244\pi$
$59$	8.74456	1.13845	0.569223	+	0.822183i	$0.307244\pi$
$60$	0	0
$61$	−11.4891	−1.47103	−0.735516	−	0.677507i	$-0.763060\pi$
$61$	−11.4891	−1.47103	−0.735516	+	0.677507i	$0.763060\pi$
$62$	1.00000i	0.127000i
$63$	− 2.37228i	− 0.298879i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	6.37228	0.784374
$67$	0.744563i	0.0909628i	0.998965	+	0.0454814i	$0.0144822\pi$
$67$	0.744563i	0.0909628i	−0.998965	+	0.0454814i	$0.985518\pi$
$68$	6.74456i	0.817898i
$69$	2.37228	0.285589
$70$	0	0
$71$	−2.37228	−0.281538	−0.140769	−	0.990042i	$-0.544957\pi$
$71$	−2.37228	−0.281538	−0.140769	+	0.990042i	$0.544957\pi$
$72$	− 1.00000i	− 0.117851i
$73$	9.11684i	1.06705i	0.845786	+	0.533523i	$0.179132\pi$
$73$	9.11684i	1.06705i	−0.845786	+	0.533523i	$0.820868\pi$
$74$	−10.7446	−1.24903
$75$	0	0
$76$	−6.37228	−0.730951
$77$	15.1168i	1.72272i
$78$	− 2.00000i	− 0.226455i
$79$	10.3723	1.16697	0.583486	−	0.812123i	$-0.301688\pi$
$79$	10.3723	1.16697	0.583486	+	0.812123i	$0.301688\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	10.7446i	1.18654i
$83$	− 12.0000i	− 1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$	− 12.0000i	− 1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$	2.37228	0.258837
$85$	0	0
$86$	6.37228	0.687141
$87$	− 2.74456i	− 0.294248i
$88$	6.37228i	0.679287i
$89$	−4.37228	−0.463461	−0.231730	−	0.972780i	$-0.574439\pi$
$89$	−4.37228	−0.463461	−0.231730	+	0.972780i	$0.574439\pi$
$90$	0	0
$91$	4.74456	0.497365
$92$	2.37228i	0.247327i
$93$	− 1.00000i	− 0.103695i
$94$	−4.74456	−0.489364
$95$	0	0
$96$	1.00000	0.102062
$97$	− 2.00000i	− 0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$	− 2.00000i	− 0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$	− 1.37228i	− 0.138621i
$99$	−6.37228	−0.640438
$100$	0	0
$101$	−9.11684	−0.907160	−0.453580	−	0.891216i	$-0.649853\pi$
$101$	−9.11684	−0.907160	−0.453580	+	0.891216i	$0.649853\pi$
$102$	− 6.74456i	− 0.667811i
$103$	− 8.00000i	− 0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$	− 8.00000i	− 0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−4.37228	−0.424674
$107$	− 6.37228i	− 0.616032i	−0.951381	−	0.308016i	$-0.900335\pi$
$107$	− 6.37228i	− 0.616032i	0.951381	−	0.308016i	$-0.0996650\pi$
$108$	1.00000i	0.0962250i
$109$	6.74456	0.646012	0.323006	−	0.946397i	$-0.395307\pi$
$109$	6.74456	0.646012	0.323006	+	0.946397i	$0.395307\pi$
$110$	0	0
$111$	10.7446	1.01983
$112$	2.37228i	0.224160i
$113$	− 8.37228i	− 0.787598i	−0.919197	−	0.393799i	$-0.871161\pi$
$113$	− 8.37228i	− 0.787598i	0.919197	−	0.393799i	$-0.128839\pi$
$114$	6.37228	0.596819
$115$	0	0
$116$	2.74456	0.254826
$117$	2.00000i	0.184900i
$118$	− 8.74456i	− 0.805002i
$119$	16.0000	1.46672
$120$	0	0
$121$	29.6060	2.69145
$122$	11.4891i	1.04018i
$123$	− 10.7446i	− 0.968805i
$124$	1.00000	0.0898027
$125$	0	0
$126$	−2.37228	−0.211340
$127$	9.48913i	0.842024i	0.907055	+	0.421012i	$0.138325\pi$
$127$	9.48913i	0.842024i	−0.907055	+	0.421012i	$0.861675\pi$
$128$	1.00000i	0.0883883i
$129$	−6.37228	−0.561048
$130$	0	0
$131$	18.2337	1.59308	0.796542	−	0.604583i	$-0.206660\pi$
$131$	18.2337	1.59308	0.796542	+	0.604583i	$0.206660\pi$
$132$	− 6.37228i	− 0.554636i
$133$	15.1168i	1.31080i
$134$	0.744563	0.0643204
$135$	0	0
$136$	6.74456	0.578341
$137$	− 19.4891i	− 1.66507i	−0.553974	−	0.832534i	$-0.686889\pi$
$137$	− 19.4891i	− 1.66507i	0.553974	−	0.832534i	$-0.313111\pi$
$138$	− 2.37228i	− 0.201942i
$139$	−0.744563	−0.0631530	−0.0315765	−	0.999501i	$-0.510053\pi$
$139$	−0.744563	−0.0631530	−0.0315765	+	0.999501i	$0.510053\pi$
$140$	0	0
$141$	4.74456	0.399564
$142$	2.37228i	0.199077i
$143$	− 12.7446i	− 1.06575i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	9.11684	0.754515
$147$	1.37228i	0.113184i
$148$	10.7446i	0.883198i
$149$	−5.11684	−0.419188	−0.209594	−	0.977788i	$-0.567214\pi$
$149$	−5.11684	−0.419188	−0.209594	+	0.977788i	$0.567214\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	6.37228i	0.516860i
$153$	6.74456i	0.545266i
$154$	15.1168	1.21815
$155$	0	0
$156$	−2.00000	−0.160128
$157$	− 3.62772i	− 0.289523i	−0.989467	−	0.144762i	$-0.953758\pi$
$157$	− 3.62772i	− 0.289523i	0.989467	−	0.144762i	$-0.0462416\pi$
$158$	− 10.3723i	− 0.825174i
$159$	4.37228	0.346744
$160$	0	0
$161$	5.62772	0.443526
$162$	− 1.00000i	− 0.0785674i
$163$	− 10.2337i	− 0.801564i	−0.916173	−	0.400782i	$-0.868738\pi$
$163$	− 10.2337i	− 0.801564i	0.916173	−	0.400782i	$-0.131262\pi$
$164$	10.7446	0.839009
$165$	0	0
$166$	−12.0000	−0.931381
$167$	18.3723i	1.42169i	0.703349	+	0.710845i	$0.251687\pi$
$167$	18.3723i	1.42169i	−0.703349	+	0.710845i	$0.748313\pi$
$168$	− 2.37228i	− 0.183025i
$169$	9.00000	0.692308
$170$	0	0
$171$	−6.37228	−0.487301
$172$	− 6.37228i	− 0.485882i
$173$	− 18.0000i	− 1.36851i	−0.729241	−	0.684257i	$-0.760127\pi$
$173$	− 18.0000i	− 1.36851i	0.729241	−	0.684257i	$-0.239873\pi$
$174$	−2.74456	−0.208065
$175$	0	0
$176$	6.37228	0.480329
$177$	8.74456i	0.657282i
$178$	4.37228i	0.327716i
$179$	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
$181$	−13.8614	−1.03031	−0.515155	−	0.857097i	$-0.672266\pi$
$181$	−13.8614	−1.03031	−0.515155	+	0.857097i	$0.672266\pi$
$182$	− 4.74456i	− 0.351690i
$183$	− 11.4891i	− 0.849301i
$184$	2.37228	0.174887
$185$	0	0
$186$	−1.00000	−0.0733236
$187$	− 42.9783i	− 3.14288i
$188$	4.74456i	0.346033i
$189$	2.37228	0.172558
$190$	0	0
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	− 7.48913i	− 0.539079i	−0.962989	−	0.269540i	$-0.913129\pi$
$193$	− 7.48913i	− 0.539079i	0.962989	−	0.269540i	$-0.0868715\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	−1.37228	−0.0980201
$197$	3.48913i	0.248590i	0.992245	+	0.124295i	$0.0396669\pi$
$197$	3.48913i	0.248590i	−0.992245	+	0.124295i	$0.960333\pi$
$198$	6.37228i	0.452858i
$199$	18.3723	1.30238	0.651188	−	0.758916i	$-0.274271\pi$
$199$	18.3723	1.30238	0.651188	+	0.758916i	$0.274271\pi$
$200$	0	0
$201$	−0.744563	−0.0525174
$202$	9.11684i	0.641459i
$203$	− 6.51087i	− 0.456974i
$204$	−6.74456	−0.472214
$205$	0	0
$206$	−8.00000	−0.557386
$207$	2.37228i	0.164885i
$208$	− 2.00000i	− 0.138675i
$209$	40.6060	2.80877
$210$	0	0
$211$	−6.37228	−0.438686	−0.219343	−	0.975648i	$-0.570391\pi$
$211$	−6.37228	−0.438686	−0.219343	+	0.975648i	$0.570391\pi$
$212$	4.37228i	0.300290i
$213$	− 2.37228i	− 0.162546i
$214$	−6.37228	−0.435600
$215$	0	0
$216$	1.00000	0.0680414
$217$	− 2.37228i	− 0.161041i
$218$	− 6.74456i	− 0.456799i
$219$	−9.11684	−0.616059
$220$	0	0
$221$	−13.4891	−0.907377
$222$	− 10.7446i	− 0.721128i
$223$	20.7446i	1.38916i	0.719416	+	0.694579i	$0.244409\pi$
$223$	20.7446i	1.38916i	−0.719416	+	0.694579i	$0.755591\pi$
$224$	2.37228	0.158505
$225$	0	0
$226$	−8.37228	−0.556916
$227$	11.1168i	0.737851i	0.929459	+	0.368925i	$0.120274\pi$
$227$	11.1168i	0.737851i	−0.929459	+	0.368925i	$0.879726\pi$
$228$	− 6.37228i	− 0.422015i
$229$	−21.1168	−1.39544	−0.697720	−	0.716370i	$-0.745802\pi$
$229$	−21.1168	−1.39544	−0.697720	+	0.716370i	$0.745802\pi$
$230$	0	0
$231$	−15.1168	−0.994615
$232$	− 2.74456i	− 0.180189i
$233$	13.8614i	0.908091i	0.890979	+	0.454045i	$0.150020\pi$
$233$	13.8614i	0.908091i	−0.890979	+	0.454045i	$0.849980\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	−8.74456	−0.569223
$237$	10.3723i	0.673752i
$238$	− 16.0000i	− 1.03713i
$239$	6.51087	0.421153	0.210577	−	0.977577i	$-0.432466\pi$
$239$	6.51087	0.421153	0.210577	+	0.977577i	$0.432466\pi$
$240$	0	0
$241$	27.4891	1.77073	0.885365	−	0.464896i	$-0.153908\pi$
$241$	27.4891	1.77073	0.885365	+	0.464896i	$0.153908\pi$
$242$	− 29.6060i	− 1.90314i
$243$	1.00000i	0.0641500i
$244$	11.4891	0.735516
$245$	0	0
$246$	−10.7446	−0.685048
$247$	− 12.7446i	− 0.810917i
$248$	− 1.00000i	− 0.0635001i
$249$	12.0000	0.760469
$250$	0	0
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	2.37228i	0.149440i
$253$	− 15.1168i	− 0.950388i
$254$	9.48913	0.595401
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 7.62772i	− 0.475804i	−0.971289	−	0.237902i	$-0.923540\pi$
$257$	− 7.62772i	− 0.475804i	0.971289	−	0.237902i	$-0.0764597\pi$
$258$	6.37228i	0.396721i
$259$	25.4891	1.58382
$260$	0	0
$261$	2.74456	0.169884
$262$	− 18.2337i	− 1.12648i
$263$	26.9783i	1.66355i	0.555113	+	0.831775i	$0.312675\pi$
$263$	26.9783i	1.66355i	−0.555113	+	0.831775i	$0.687325\pi$
$264$	−6.37228	−0.392187
$265$	0	0
$266$	15.1168	0.926873
$267$	− 4.37228i	− 0.267579i
$268$	− 0.744563i	− 0.0454814i
$269$	2.00000	0.121942	0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000	0.121942	0.0609711	+	0.998140i	$0.480580\pi$
$270$	0	0
$271$	−31.1168	−1.89021	−0.945107	−	0.326762i	$-0.894043\pi$
$271$	−31.1168	−1.89021	−0.945107	+	0.326762i	$0.894043\pi$
$272$	− 6.74456i	− 0.408949i
$273$	4.74456i	0.287154i
$274$	−19.4891	−1.17738
$275$	0	0
$276$	−2.37228	−0.142795
$277$	− 26.7446i	− 1.60693i	−0.595355	−	0.803463i	$-0.702989\pi$
$277$	− 26.7446i	− 1.60693i	0.595355	−	0.803463i	$-0.297011\pi$
$278$	0.744563i	0.0446559i
$279$	1.00000	0.0598684
$280$	0	0
$281$	5.25544	0.313513	0.156757	−	0.987637i	$-0.449896\pi$
$281$	5.25544	0.313513	0.156757	+	0.987637i	$0.449896\pi$
$282$	− 4.74456i	− 0.282535i
$283$	12.0000i	0.713326i	0.934233	+	0.356663i	$0.116086\pi$
$283$	12.0000i	0.713326i	−0.934233	+	0.356663i	$0.883914\pi$
$284$	2.37228	0.140769
$285$	0	0
$286$	−12.7446	−0.753602
$287$	− 25.4891i	− 1.50458i
$288$	1.00000i	0.0589256i
$289$	−28.4891	−1.67583
$290$	0	0
$291$	2.00000	0.117242
$292$	− 9.11684i	− 0.533523i
$293$	15.4891i	0.904884i	0.891794	+	0.452442i	$0.149447\pi$
$293$	15.4891i	0.904884i	−0.891794	+	0.452442i	$0.850553\pi$
$294$	1.37228	0.0800331
$295$	0	0
$296$	10.7446	0.624515
$297$	− 6.37228i	− 0.369757i
$298$	5.11684i	0.296411i
$299$	−4.74456	−0.274385
$300$	0	0
$301$	−15.1168	−0.871320
$302$	8.00000i	0.460348i
$303$	− 9.11684i	− 0.523749i
$304$	6.37228	0.365475
$305$	0	0
$306$	6.74456	0.385561
$307$	14.9783i	0.854854i	0.904050	+	0.427427i	$0.140580\pi$
$307$	14.9783i	0.854854i	−0.904050	+	0.427427i	$0.859420\pi$
$308$	− 15.1168i	− 0.861362i
$309$	8.00000	0.455104
$310$	0	0
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	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	$0.908798\pi$
$314$	−3.62772	−0.204724
$315$	0	0
$316$	−10.3723	−0.583486
$317$	13.2554i	0.744500i	0.928133	+	0.372250i	$0.121414\pi$
$317$	13.2554i	0.744500i	−0.928133	+	0.372250i	$0.878586\pi$
$318$	− 4.37228i	− 0.245185i
$319$	−17.4891	−0.979203
$320$	0	0
$321$	6.37228	0.355666
$322$	− 5.62772i	− 0.313621i
$323$	− 42.9783i	− 2.39137i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−10.2337	−0.566792
$327$	6.74456i	0.372975i
$328$	− 10.7446i	− 0.593269i
$329$	11.2554	0.620532
$330$	0	0
$331$	21.4891	1.18115	0.590575	−	0.806983i	$-0.298901\pi$
$331$	21.4891	1.18115	0.590575	+	0.806983i	$0.298901\pi$
$332$	12.0000i	0.658586i
$333$	10.7446i	0.588798i
$334$	18.3723	1.00529
$335$	0	0
$336$	−2.37228	−0.129419
$337$	16.9783i	0.924864i	0.886655	+	0.462432i	$0.153023\pi$
$337$	16.9783i	0.924864i	−0.886655	+	0.462432i	$0.846977\pi$
$338$	− 9.00000i	− 0.489535i
$339$	8.37228	0.454720
$340$	0	0
$341$	−6.37228	−0.345078
$342$	6.37228i	0.344574i
$343$	19.8614i	1.07242i
$344$	−6.37228	−0.343570
$345$	0	0
$346$	−18.0000	−0.967686
$347$	32.4674i	1.74294i	0.490449	+	0.871470i	$0.336833\pi$
$347$	32.4674i	1.74294i	−0.490449	+	0.871470i	$0.663167\pi$
$348$	2.74456i	0.147124i
$349$	−18.7446	−1.00337	−0.501687	−	0.865049i	$-0.667287\pi$
$349$	−18.7446	−1.00337	−0.501687	+	0.865049i	$0.667287\pi$
$350$	0	0
$351$	−2.00000	−0.106752
$352$	− 6.37228i	− 0.339644i
$353$	− 7.48913i	− 0.398606i	−0.979938	−	0.199303i	$-0.936132\pi$
$353$	− 7.48913i	− 0.398606i	0.979938	−	0.199303i	$-0.0638678\pi$
$354$	8.74456	0.464768
$355$	0	0
$356$	4.37228	0.231730
$357$	16.0000i	0.846810i
$358$	− 12.0000i	− 0.634220i
$359$	2.37228	0.125204	0.0626021	−	0.998039i	$-0.480060\pi$
$359$	2.37228	0.125204	0.0626021	+	0.998039i	$0.480060\pi$
$360$	0	0
$361$	21.6060	1.13716
$362$	13.8614i	0.728539i
$363$	29.6060i	1.55391i
$364$	−4.74456	−0.248683
$365$	0	0
$366$	−11.4891	−0.600546
$367$	− 14.2337i	− 0.742992i	−0.928434	−	0.371496i	$-0.878845\pi$
$367$	− 14.2337i	− 0.742992i	0.928434	−	0.371496i	$-0.121155\pi$
$368$	− 2.37228i	− 0.123664i
$369$	10.7446	0.559340
$370$	0	0
$371$	10.3723	0.538502
$372$	1.00000i	0.0518476i
$373$	− 13.8614i	− 0.717716i	−0.933392	−	0.358858i	$-0.883166\pi$
$373$	− 13.8614i	− 0.717716i	0.933392	−	0.358858i	$-0.116834\pi$
$374$	−42.9783	−2.22235
$375$	0	0
$376$	4.74456	0.244682
$377$	5.48913i	0.282704i
$378$	− 2.37228i	− 0.122017i
$379$	0.138593	0.00711906	0.00355953	−	0.999994i	$-0.498867\pi$
$379$	0.138593	0.00711906	0.00355953	+	0.999994i	$0.498867\pi$
$380$	0	0
$381$	−9.48913	−0.486143
$382$	− 16.0000i	− 0.818631i
$383$	− 9.48913i	− 0.484872i	−0.970167	−	0.242436i	$-0.922054\pi$
$383$	− 9.48913i	− 0.484872i	0.970167	−	0.242436i	$-0.0779464\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−7.48913	−0.381186
$387$	− 6.37228i	− 0.323921i
$388$	2.00000i	0.101535i
$389$	28.9783	1.46926	0.734628	−	0.678470i	$-0.237357\pi$
$389$	28.9783	1.46926	0.734628	+	0.678470i	$0.237357\pi$
$390$	0	0
$391$	−16.0000	−0.809155
$392$	1.37228i	0.0693107i
$393$	18.2337i	0.919768i
$394$	3.48913	0.175780
$395$	0	0
$396$	6.37228	0.320219
$397$	− 38.6060i	− 1.93758i	−0.247887	−	0.968789i	$-0.579736\pi$
$397$	− 38.6060i	− 1.93758i	0.247887	−	0.968789i	$-0.420264\pi$
$398$	− 18.3723i	− 0.920919i
$399$	−15.1168	−0.756789
$400$	0	0
$401$	28.3723	1.41684	0.708422	−	0.705789i	$-0.249407\pi$
$401$	28.3723	1.41684	0.708422	+	0.705789i	$0.249407\pi$
$402$	0.744563i	0.0371354i
$403$	2.00000i	0.0996271i
$404$	9.11684	0.453580
$405$	0	0
$406$	−6.51087	−0.323129
$407$	− 68.4674i	− 3.39380i
$408$	6.74456i	0.333906i
$409$	−24.2337	−1.19828	−0.599139	−	0.800645i	$-0.704490\pi$
$409$	−24.2337	−1.19828	−0.599139	+	0.800645i	$0.704490\pi$
$410$	0	0
$411$	19.4891	0.961328
$412$	8.00000i	0.394132i
$413$	20.7446i	1.02077i
$414$	2.37228	0.116591
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	− 0.744563i	− 0.0364614i
$418$	− 40.6060i	− 1.98610i
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	−3.48913	−0.170050	−0.0850248	−	0.996379i	$-0.527097\pi$
$421$	−3.48913	−0.170050	−0.0850248	+	0.996379i	$0.527097\pi$
$422$	6.37228i	0.310198i
$423$	4.74456i	0.230689i
$424$	4.37228	0.212337
$425$	0	0
$426$	−2.37228	−0.114937
$427$	− 27.2554i	− 1.31898i
$428$	6.37228i	0.308016i
$429$	12.7446	0.615313
$430$	0	0
$431$	18.9783	0.914150	0.457075	−	0.889428i	$-0.348897\pi$
$431$	18.9783	0.914150	0.457075	+	0.889428i	$0.348897\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	18.8832i	0.907467i	0.891138	+	0.453733i	$0.149908\pi$
$433$	18.8832i	0.907467i	−0.891138	+	0.453733i	$0.850092\pi$
$434$	−2.37228	−0.113873
$435$	0	0
$436$	−6.74456	−0.323006
$437$	− 15.1168i	− 0.723137i
$438$	9.11684i	0.435620i
$439$	−3.25544	−0.155374	−0.0776868	−	0.996978i	$-0.524753\pi$
$439$	−3.25544	−0.155374	−0.0776868	+	0.996978i	$0.524753\pi$
$440$	0	0
$441$	−1.37228	−0.0653467
$442$	13.4891i	0.641612i
$443$	− 17.3505i	− 0.824349i	−0.911105	−	0.412174i	$-0.864769\pi$
$443$	− 17.3505i	− 0.824349i	0.911105	−	0.412174i	$-0.135231\pi$
$444$	−10.7446	−0.509914
$445$	0	0
$446$	20.7446	0.982284
$447$	− 5.11684i	− 0.242018i
$448$	− 2.37228i	− 0.112080i
$449$	−36.9783	−1.74511	−0.872556	−	0.488515i	$-0.837539\pi$
$449$	−36.9783	−1.74511	−0.872556	+	0.488515i	$0.837539\pi$
$450$	0	0
$451$	−68.4674	−3.22400
$452$	8.37228i	0.393799i
$453$	− 8.00000i	− 0.375873i
$454$	11.1168	0.521739
$455$	0	0
$456$	−6.37228	−0.298409
$457$	34.4674i	1.61232i	0.591700	+	0.806158i	$0.298457\pi$
$457$	34.4674i	1.61232i	−0.591700	+	0.806158i	$0.701543\pi$
$458$	21.1168i	0.986725i
$459$	−6.74456	−0.314809
$460$	0	0
$461$	37.7228	1.75693	0.878463	−	0.477810i	$-0.158569\pi$
$461$	37.7228	1.75693	0.878463	+	0.477810i	$0.158569\pi$
$462$	15.1168i	0.703299i
$463$	25.4891i	1.18458i	0.805725	+	0.592290i	$0.201776\pi$
$463$	25.4891i	1.18458i	−0.805725	+	0.592290i	$0.798224\pi$
$464$	−2.74456	−0.127413
$465$	0	0
$466$	13.8614	0.642117
$467$	− 29.4891i	− 1.36459i	−0.731075	−	0.682297i	$-0.760981\pi$
$467$	− 29.4891i	− 1.36459i	0.731075	−	0.682297i	$-0.239019\pi$
$468$	− 2.00000i	− 0.0924500i
$469$	−1.76631	−0.0815607
$470$	0	0
$471$	3.62772	0.167156
$472$	8.74456i	0.402501i
$473$	40.6060i	1.86706i
$474$	10.3723	0.476415
$475$	0	0
$476$	−16.0000	−0.733359
$477$	4.37228i	0.200193i
$478$	− 6.51087i	− 0.297800i
$479$	19.8614	0.907491	0.453745	−	0.891131i	$-0.350088\pi$
$479$	19.8614	0.907491	0.453745	+	0.891131i	$0.350088\pi$
$480$	0	0
$481$	−21.4891	−0.979820
$482$	− 27.4891i	− 1.25210i
$483$	5.62772i	0.256070i
$484$	−29.6060	−1.34573
$485$	0	0
$486$	1.00000	0.0453609
$487$	14.5109i	0.657550i	0.944408	+	0.328775i	$0.106636\pi$
$487$	14.5109i	0.657550i	−0.944408	+	0.328775i	$0.893364\pi$
$488$	− 11.4891i	− 0.520088i
$489$	10.2337	0.462783
$490$	0	0
$491$	−12.6060	−0.568899	−0.284450	−	0.958691i	$-0.591811\pi$
$491$	−12.6060	−0.568899	−0.284450	+	0.958691i	$0.591811\pi$
$492$	10.7446i	0.484402i
$493$	18.5109i	0.833688i
$494$	−12.7446	−0.573405
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	− 5.62772i	− 0.252438i
$498$	− 12.0000i	− 0.537733i
$499$	−10.5109	−0.470531	−0.235266	−	0.971931i	$-0.575596\pi$
$499$	−10.5109	−0.470531	−0.235266	+	0.971931i	$0.575596\pi$
$500$	0	0
$501$	−18.3723	−0.820813
$502$	4.00000i	0.178529i
$503$	− 17.4891i	− 0.779802i	−0.920857	−	0.389901i	$-0.872509\pi$
$503$	− 17.4891i	− 0.779802i	0.920857	−	0.389901i	$-0.127491\pi$
$504$	2.37228	0.105670
$505$	0	0
$506$	−15.1168	−0.672026
$507$	9.00000i	0.399704i
$508$	− 9.48913i	− 0.421012i
$509$	38.7446	1.71732	0.858661	−	0.512543i	$-0.171297\pi$
$509$	38.7446	1.71732	0.858661	+	0.512543i	$0.171297\pi$
$510$	0	0
$511$	−21.6277	−0.956754
$512$	− 1.00000i	− 0.0441942i
$513$	− 6.37228i	− 0.281343i
$514$	−7.62772	−0.336444
$515$	0	0
$516$	6.37228	0.280524
$517$	− 30.2337i	− 1.32968i
$518$	− 25.4891i	− 1.11993i
$519$	18.0000	0.790112
$520$	0	0
$521$	−8.97825	−0.393344	−0.196672	−	0.980469i	$-0.563013\pi$
$521$	−8.97825	−0.393344	−0.196672	+	0.980469i	$0.563013\pi$
$522$	− 2.74456i	− 0.120126i
$523$	15.8614i	0.693571i	0.937944	+	0.346785i	$0.112727\pi$
$523$	15.8614i	0.693571i	−0.937944	+	0.346785i	$0.887273\pi$
$524$	−18.2337	−0.796542
$525$	0	0
$526$	26.9783	1.17631
$527$	6.74456i	0.293798i
$528$	6.37228i	0.277318i
$529$	17.3723	0.755317
$530$	0	0
$531$	−8.74456	−0.379482
$532$	− 15.1168i	− 0.655398i
$533$	21.4891i	0.930797i
$534$	−4.37228	−0.189207
$535$	0	0
$536$	−0.744563	−0.0321602
$537$	12.0000i	0.517838i
$538$	− 2.00000i	− 0.0862261i
$539$	8.74456	0.376655
$540$	0	0
$541$	7.48913	0.321983	0.160991	−	0.986956i	$-0.448531\pi$
$541$	7.48913	0.321983	0.160991	+	0.986956i	$0.448531\pi$
$542$	31.1168i	1.33658i
$543$	− 13.8614i	− 0.594850i
$544$	−6.74456	−0.289171
$545$	0	0
$546$	4.74456	0.203049
$547$	− 8.74456i	− 0.373890i	−0.982370	−	0.186945i	$-0.940141\pi$
$547$	− 8.74456i	− 0.373890i	0.982370	−	0.186945i	$-0.0598587\pi$
$548$	19.4891i	0.832534i
$549$	11.4891	0.490344
$550$	0	0
$551$	−17.4891	−0.745062
$552$	2.37228i	0.100971i
$553$	24.6060i	1.04635i
$554$	−26.7446	−1.13627
$555$	0	0
$556$	0.744563	0.0315765
$557$	− 29.1168i	− 1.23372i	−0.787073	−	0.616860i	$-0.788404\pi$
$557$	− 29.1168i	− 1.23372i	0.787073	−	0.616860i	$-0.211596\pi$
$558$	− 1.00000i	− 0.0423334i
$559$	12.7446	0.539038
$560$	0	0
$561$	42.9783	1.81454
$562$	− 5.25544i	− 0.221687i
$563$	38.9783i	1.64274i	0.570398	+	0.821369i	$0.306789\pi$
$563$	38.9783i	1.64274i	−0.570398	+	0.821369i	$0.693211\pi$
$564$	−4.74456	−0.199782
$565$	0	0
$566$	12.0000	0.504398
$567$	2.37228i	0.0996265i
$568$	− 2.37228i	− 0.0995387i
$569$	−4.37228	−0.183296	−0.0916478	−	0.995791i	$-0.529213\pi$
$569$	−4.37228	−0.183296	−0.0916478	+	0.995791i	$0.529213\pi$
$570$	0	0
$571$	−15.2554	−0.638420	−0.319210	−	0.947684i	$-0.603418\pi$
$571$	−15.2554	−0.638420	−0.319210	+	0.947684i	$0.603418\pi$
$572$	12.7446i	0.532877i
$573$	16.0000i	0.668410i
$574$	−25.4891	−1.06390
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 32.2337i	− 1.34191i	−0.741500	−	0.670953i	$-0.765885\pi$
$577$	− 32.2337i	− 1.34191i	0.741500	−	0.670953i	$-0.234115\pi$
$578$	28.4891i	1.18499i
$579$	7.48913	0.311237
$580$	0	0
$581$	28.4674	1.18103
$582$	− 2.00000i	− 0.0829027i
$583$	− 27.8614i	− 1.15390i
$584$	−9.11684	−0.377258
$585$	0	0
$586$	15.4891	0.639850
$587$	− 12.0000i	− 0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$	− 12.0000i	− 0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$	− 1.37228i	− 0.0565919i
$589$	−6.37228	−0.262565
$590$	0	0
$591$	−3.48913	−0.143523
$592$	− 10.7446i	− 0.441599i
$593$	− 0.978251i	− 0.0401719i	−0.999798	−	0.0200860i	$-0.993606\pi$
$593$	− 0.978251i	− 0.0401719i	0.999798	−	0.0200860i	$-0.00639399\pi$
$594$	−6.37228	−0.261458
$595$	0	0
$596$	5.11684	0.209594
$597$	18.3723i	0.751927i
$598$	4.74456i	0.194020i
$599$	7.11684	0.290786	0.145393	−	0.989374i	$-0.453555\pi$
$599$	7.11684	0.290786	0.145393	+	0.989374i	$0.453555\pi$
$600$	0	0
$601$	35.4891	1.44763	0.723816	−	0.689993i	$-0.242387\pi$
$601$	35.4891	1.44763	0.723816	+	0.689993i	$0.242387\pi$
$602$	15.1168i	0.616117i
$603$	− 0.744563i	− 0.0303209i
$604$	8.00000	0.325515
$605$	0	0
$606$	−9.11684	−0.370346
$607$	10.3723i	0.420998i	0.977594	+	0.210499i	$0.0675089\pi$
$607$	10.3723i	0.420998i	−0.977594	+	0.210499i	$0.932491\pi$
$608$	− 6.37228i	− 0.258430i
$609$	6.51087	0.263834
$610$	0	0
$611$	−9.48913	−0.383889
$612$	− 6.74456i	− 0.272633i
$613$	12.5109i	0.505309i	0.967557	+	0.252655i	$0.0813037\pi$
$613$	12.5109i	0.505309i	−0.967557	+	0.252655i	$0.918696\pi$
$614$	14.9783	0.604473
$615$	0	0
$616$	−15.1168	−0.609075
$617$	− 25.1168i	− 1.01117i	−0.862778	−	0.505583i	$-0.831277\pi$
$617$	− 25.1168i	− 1.01117i	0.862778	−	0.505583i	$-0.168723\pi$
$618$	− 8.00000i	− 0.321807i
$619$	18.2337	0.732874	0.366437	−	0.930443i	$-0.380578\pi$
$619$	18.2337	0.732874	0.366437	+	0.930443i	$0.380578\pi$
$620$	0	0
$621$	−2.37228	−0.0951964
$622$	− 8.00000i	− 0.320771i
$623$	− 10.3723i	− 0.415557i
$624$	2.00000	0.0800641
$625$	0	0
$626$	10.0000	0.399680
$627$	40.6060i	1.62165i
$628$	3.62772i	0.144762i
$629$	−72.4674	−2.88946
$630$	0	0
$631$	5.35053	0.213001	0.106501	−	0.994313i	$-0.466035\pi$
$631$	5.35053	0.213001	0.106501	+	0.994313i	$0.466035\pi$
$632$	10.3723i	0.412587i
$633$	− 6.37228i	− 0.253275i
$634$	13.2554	0.526441
$635$	0	0
$636$	−4.37228	−0.173372
$637$	− 2.74456i	− 0.108744i
$638$	17.4891i	0.692401i
$639$	2.37228	0.0938460
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	− 6.37228i	− 0.251494i
$643$	38.0951i	1.50232i	0.660118	+	0.751162i	$0.270506\pi$
$643$	38.0951i	1.50232i	−0.660118	+	0.751162i	$0.729494\pi$
$644$	−5.62772	−0.221763
$645$	0	0
$646$	−42.9783	−1.69096
$647$	35.5842i	1.39896i	0.714652	+	0.699480i	$0.246585\pi$
$647$	35.5842i	1.39896i	−0.714652	+	0.699480i	$0.753415\pi$
$648$	1.00000i	0.0392837i
$649$	55.7228	2.18731
$650$	0	0
$651$	2.37228	0.0929770
$652$	10.2337i	0.400782i
$653$	− 4.97825i	− 0.194814i	−0.995245	−	0.0974070i	$-0.968945\pi$
$653$	− 4.97825i	− 0.194814i	0.995245	−	0.0974070i	$-0.0310549\pi$
$654$	6.74456	0.263733
$655$	0	0
$656$	−10.7446	−0.419505
$657$	− 9.11684i	− 0.355682i
$658$	− 11.2554i	− 0.438783i
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	40.9783	1.59387	0.796935	−	0.604066i	$-0.206454\pi$
$661$	40.9783	1.59387	0.796935	+	0.604066i	$0.206454\pi$
$662$	− 21.4891i	− 0.835199i
$663$	− 13.4891i	− 0.523874i
$664$	12.0000	0.465690
$665$	0	0
$666$	10.7446	0.416343
$667$	6.51087i	0.252102i
$668$	− 18.3723i	− 0.710845i
$669$	−20.7446	−0.802031
$670$	0	0
$671$	−73.2119	−2.82632
$672$	2.37228i	0.0915127i
$673$	− 23.4891i	− 0.905439i	−0.891653	−	0.452720i	$-0.850454\pi$
$673$	− 23.4891i	− 0.905439i	0.891653	−	0.452720i	$-0.149546\pi$
$674$	16.9783	0.653978
$675$	0	0
$676$	−9.00000	−0.346154
$677$	1.39403i	0.0535770i	0.999641	+	0.0267885i	$0.00852806\pi$
$677$	1.39403i	0.0535770i	−0.999641	+	0.0267885i	$0.991472\pi$
$678$	− 8.37228i	− 0.321536i
$679$	4.74456	0.182080
$680$	0	0
$681$	−11.1168	−0.425998
$682$	6.37228i	0.244007i
$683$	15.8614i	0.606920i	0.952844	+	0.303460i	$0.0981419\pi$
$683$	15.8614i	0.606920i	−0.952844	+	0.303460i	$0.901858\pi$
$684$	6.37228	0.243650
$685$	0	0
$686$	19.8614	0.758312
$687$	− 21.1168i	− 0.805658i
$688$	6.37228i	0.242941i
$689$	−8.74456	−0.333141
$690$	0	0
$691$	−47.8614	−1.82073	−0.910367	−	0.413802i	$-0.864201\pi$
$691$	−47.8614	−1.82073	−0.910367	+	0.413802i	$0.864201\pi$
$692$	18.0000i	0.684257i
$693$	− 15.1168i	− 0.574241i
$694$	32.4674	1.23244
$695$	0	0
$696$	2.74456	0.104032
$697$	72.4674i	2.74490i
$698$	18.7446i	0.709492i
$699$	−13.8614	−0.524287
$700$	0	0
$701$	5.39403	0.203730	0.101865	−	0.994798i	$-0.467519\pi$
$701$	5.39403	0.203730	0.101865	+	0.994798i	$0.467519\pi$
$702$	2.00000i	0.0754851i
$703$	− 68.4674i	− 2.58230i
$704$	−6.37228	−0.240164
$705$	0	0
$706$	−7.48913	−0.281857
$707$	− 21.6277i	− 0.813394i
$708$	− 8.74456i	− 0.328641i
$709$	−22.8832	−0.859395	−0.429697	−	0.902973i	$-0.641380\pi$
$709$	−22.8832	−0.859395	−0.429697	+	0.902973i	$0.641380\pi$
$710$	0	0
$711$	−10.3723	−0.388991
$712$	− 4.37228i	− 0.163858i
$713$	2.37228i	0.0888426i
$714$	16.0000	0.598785
$715$	0	0
$716$	−12.0000	−0.448461
$717$	6.51087i	0.243153i
$718$	− 2.37228i	− 0.0885328i
$719$	−27.2554	−1.01646	−0.508228	−	0.861222i	$-0.669699\pi$
$719$	−27.2554	−1.01646	−0.508228	+	0.861222i	$0.669699\pi$
$720$	0	0
$721$	18.9783	0.706787
$722$	− 21.6060i	− 0.804091i
$723$	27.4891i	1.02233i
$724$	13.8614	0.515155
$725$	0	0
$726$	29.6060	1.09878
$727$	− 13.6277i	− 0.505424i	−0.967542	−	0.252712i	$-0.918677\pi$
$727$	− 13.6277i	− 0.505424i	0.967542	−	0.252712i	$-0.0813225\pi$
$728$	4.74456i	0.175845i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	42.9783	1.58961
$732$	11.4891i	0.424650i
$733$	− 34.0000i	− 1.25582i	−0.778287	−	0.627909i	$-0.783911\pi$
$733$	− 34.0000i	− 1.25582i	0.778287	−	0.627909i	$-0.216089\pi$
$734$	−14.2337	−0.525375
$735$	0	0
$736$	−2.37228	−0.0874434
$737$	4.74456i	0.174768i
$738$	− 10.7446i	− 0.395513i
$739$	−22.9783	−0.845269	−0.422634	−	0.906300i	$-0.638895\pi$
$739$	−22.9783	−0.845269	−0.422634	+	0.906300i	$0.638895\pi$
$740$	0	0
$741$	12.7446	0.468183
$742$	− 10.3723i	− 0.380778i
$743$	− 29.6277i	− 1.08694i	−0.839430	−	0.543468i	$-0.817111\pi$
$743$	− 29.6277i	− 1.08694i	0.839430	−	0.543468i	$-0.182889\pi$
$744$	1.00000	0.0366618
$745$	0	0
$746$	−13.8614	−0.507502
$747$	12.0000i	0.439057i
$748$	42.9783i	1.57144i
$749$	15.1168	0.552357
$750$	0	0
$751$	−27.2554	−0.994565	−0.497283	−	0.867589i	$-0.665669\pi$
$751$	−27.2554	−0.994565	−0.497283	+	0.867589i	$0.665669\pi$
$752$	− 4.74456i	− 0.173016i
$753$	− 4.00000i	− 0.145768i
$754$	5.48913	0.199902
$755$	0	0
$756$	−2.37228	−0.0862790
$757$	26.0000i	0.944986i	0.881334	+	0.472493i	$0.156646\pi$
$757$	26.0000i	0.944986i	−0.881334	+	0.472493i	$0.843354\pi$
$758$	− 0.138593i	− 0.00503394i
$759$	15.1168	0.548707
$760$	0	0
$761$	−18.1386	−0.657523	−0.328762	−	0.944413i	$-0.606631\pi$
$761$	−18.1386	−0.657523	−0.328762	+	0.944413i	$0.606631\pi$
$762$	9.48913i	0.343755i
$763$	16.0000i	0.579239i
$764$	−16.0000	−0.578860
$765$	0	0
$766$	−9.48913	−0.342856
$767$	− 17.4891i	− 0.631496i
$768$	1.00000i	0.0360844i
$769$	3.62772	0.130819	0.0654094	−	0.997859i	$-0.479165\pi$
$769$	3.62772	0.130819	0.0654094	+	0.997859i	$0.479165\pi$
$770$	0	0
$771$	7.62772	0.274706
$772$	7.48913i	0.269540i
$773$	− 18.6060i	− 0.669210i	−0.942358	−	0.334605i	$-0.891397\pi$
$773$	− 18.6060i	− 0.669210i	0.942358	−	0.334605i	$-0.108603\pi$
$774$	−6.37228	−0.229047
$775$	0	0
$776$	2.00000	0.0717958
$777$	25.4891i	0.914417i
$778$	− 28.9783i	− 1.03892i
$779$	−68.4674	−2.45310
$780$	0	0
$781$	−15.1168	−0.540923
$782$	16.0000i	0.572159i
$783$	2.74456i	0.0980827i
$784$	1.37228	0.0490100
$785$	0	0
$786$	18.2337	0.650374
$787$	27.1168i	0.966611i	0.875452	+	0.483306i	$0.160564\pi$
$787$	27.1168i	0.966611i	−0.875452	+	0.483306i	$0.839436\pi$
$788$	− 3.48913i	− 0.124295i
$789$	−26.9783	−0.960451
$790$	0	0
$791$	19.8614	0.706190
$792$	− 6.37228i	− 0.226429i
$793$	22.9783i	0.815982i
$794$	−38.6060	−1.37007
$795$	0	0
$796$	−18.3723	−0.651188
$797$	43.4891i	1.54046i	0.637764	+	0.770232i	$0.279860\pi$
$797$	43.4891i	1.54046i	−0.637764	+	0.770232i	$0.720140\pi$
$798$	15.1168i	0.535130i
$799$	−32.0000	−1.13208
$800$	0	0
$801$	4.37228	0.154487
$802$	− 28.3723i	− 1.00186i
$803$	58.0951i	2.05013i
$804$	0.744563	0.0262587
$805$	0	0
$806$	2.00000	0.0704470
$807$	2.00000i	0.0704033i
$808$	− 9.11684i	− 0.320729i
$809$	30.6060	1.07605	0.538024	−	0.842929i	$-0.319171\pi$
$809$	30.6060	1.07605	0.538024	+	0.842929i	$0.319171\pi$
$810$	0	0
$811$	−46.3723	−1.62835	−0.814176	−	0.580619i	$-0.802811\pi$
$811$	−46.3723	−1.62835	−0.814176	+	0.580619i	$0.802811\pi$
$812$	6.51087i	0.228487i
$813$	− 31.1168i	− 1.09132i
$814$	−68.4674	−2.39978
$815$	0	0
$816$	6.74456	0.236107
$817$	40.6060i	1.42062i
$818$	24.2337i	0.847311i
$819$	−4.74456	−0.165788
$820$	0	0
$821$	26.7446	0.933392	0.466696	−	0.884418i	$-0.345444\pi$
$821$	26.7446	0.933392	0.466696	+	0.884418i	$0.345444\pi$
$822$	− 19.4891i	− 0.679761i
$823$	− 28.7446i	− 1.00197i	−0.865455	−	0.500986i	$-0.832971\pi$
$823$	− 28.7446i	− 1.00197i	0.865455	−	0.500986i	$-0.167029\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	20.7446	0.721796
$827$	− 5.48913i	− 0.190876i	−0.995435	−	0.0954378i	$-0.969575\pi$
$827$	− 5.48913i	− 0.190876i	0.995435	−	0.0954378i	$-0.0304251\pi$
$828$	− 2.37228i	− 0.0824425i
$829$	−32.0951	−1.11471	−0.557354	−	0.830275i	$-0.688184\pi$
$829$	−32.0951	−1.11471	−0.557354	+	0.830275i	$0.688184\pi$
$830$	0	0
$831$	26.7446	0.927759
$832$	2.00000i	0.0693375i
$833$	− 9.25544i	− 0.320682i
$834$	−0.744563	−0.0257821
$835$	0	0
$836$	−40.6060	−1.40439
$837$	1.00000i	0.0345651i
$838$	− 12.0000i	− 0.414533i
$839$	11.8614	0.409501	0.204751	−	0.978814i	$-0.434362\pi$
$839$	11.8614	0.409501	0.204751	+	0.978814i	$0.434362\pi$
$840$	0	0
$841$	−21.4674	−0.740254
$842$	3.48913i	0.120243i
$843$	5.25544i	0.181007i
$844$	6.37228	0.219343
$845$	0	0
$846$	4.74456	0.163121
$847$	70.2337i	2.41326i
$848$	− 4.37228i	− 0.150145i
$849$	−12.0000	−0.411839
$850$	0	0
$851$	−25.4891	−0.873756
$852$	2.37228i	0.0812730i
$853$	24.0951i	0.825000i	0.910958	+	0.412500i	$0.135344\pi$
$853$	24.0951i	0.825000i	−0.910958	+	0.412500i	$0.864656\pi$
$854$	−27.2554	−0.932662
$855$	0	0
$856$	6.37228	0.217800
$857$	15.4891i	0.529098i	0.964372	+	0.264549i	$0.0852232\pi$
$857$	15.4891i	0.529098i	−0.964372	+	0.264549i	$0.914777\pi$
$858$	− 12.7446i	− 0.435092i
$859$	−5.48913	−0.187287	−0.0936433	−	0.995606i	$-0.529851\pi$
$859$	−5.48913	−0.187287	−0.0936433	+	0.995606i	$0.529851\pi$
$860$	0	0
$861$	25.4891	0.868667
$862$	− 18.9783i	− 0.646402i
$863$	45.3505i	1.54375i	0.635774	+	0.771875i	$0.280681\pi$
$863$	45.3505i	1.54375i	−0.635774	+	0.771875i	$0.719319\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	18.8832	0.641676
$867$	− 28.4891i	− 0.967541i
$868$	2.37228i	0.0805205i
$869$	66.0951	2.24212
$870$	0	0
$871$	1.48913	0.0504571
$872$	6.74456i	0.228400i
$873$	2.00000i	0.0676897i
$874$	−15.1168	−0.511335
$875$	0	0
$876$	9.11684	0.308030
$877$	− 0.978251i	− 0.0330332i	−0.999864	−	0.0165166i	$-0.994742\pi$
$877$	− 0.978251i	− 0.0330332i	0.999864	−	0.0165166i	$-0.00525763\pi$
$878$	3.25544i	0.109866i
$879$	−15.4891	−0.522435
$880$	0	0
$881$	−48.9783	−1.65012	−0.825060	−	0.565046i	$-0.808859\pi$
$881$	−48.9783	−1.65012	−0.825060	+	0.565046i	$0.808859\pi$
$882$	1.37228i	0.0462071i
$883$	16.1386i	0.543107i	0.962423	+	0.271553i	$0.0875374\pi$
$883$	16.1386i	0.543107i	−0.962423	+	0.271553i	$0.912463\pi$
$884$	13.4891	0.453688
$885$	0	0
$886$	−17.3505	−0.582903
$887$	19.2554i	0.646534i	0.946308	+	0.323267i	$0.104781\pi$
$887$	19.2554i	0.646534i	−0.946308	+	0.323267i	$0.895219\pi$
$888$	10.7446i	0.360564i
$889$	−22.5109	−0.754991
$890$	0	0
$891$	6.37228	0.213479
$892$	− 20.7446i	− 0.694579i
$893$	− 30.2337i	− 1.01173i
$894$	−5.11684	−0.171133
$895$	0	0
$896$	−2.37228	−0.0792524
$897$	− 4.74456i	− 0.158416i
$898$	36.9783i	1.23398i
$899$	2.74456	0.0915363
$900$	0	0
$901$	−29.4891	−0.982425
$902$	68.4674i	2.27971i
$903$	− 15.1168i	− 0.503057i
$904$	8.37228	0.278458
$905$	0	0
$906$	−8.00000	−0.265782
$907$	− 5.48913i	− 0.182263i	−0.995839	−	0.0911317i	$-0.970952\pi$
$907$	− 5.48913i	− 0.182263i	0.995839	−	0.0911317i	$-0.0290484\pi$
$908$	− 11.1168i	− 0.368925i
$909$	9.11684	0.302387
$910$	0	0
$911$	−25.4891	−0.844492	−0.422246	−	0.906481i	$-0.638758\pi$
$911$	−25.4891	−0.844492	−0.422246	+	0.906481i	$0.638758\pi$
$912$	6.37228i	0.211007i
$913$	− 76.4674i	− 2.53070i
$914$	34.4674	1.14008
$915$	0	0
$916$	21.1168	0.697720
$917$	43.2554i	1.42842i
$918$	6.74456i	0.222604i
$919$	−22.2337	−0.733422	−0.366711	−	0.930335i	$-0.619516\pi$
$919$	−22.2337	−0.733422	−0.366711	+	0.930335i	$0.619516\pi$
$920$	0	0
$921$	−14.9783	−0.493550
$922$	− 37.7228i	− 1.24233i
$923$	4.74456i	0.156169i
$924$	15.1168	0.497308
$925$	0	0
$926$	25.4891	0.837625
$927$	8.00000i	0.262754i
$928$	2.74456i	0.0900947i
$929$	−1.11684	−0.0366425	−0.0183212	−	0.999832i	$-0.505832\pi$
$929$	−1.11684	−0.0366425	−0.0183212	+	0.999832i	$0.505832\pi$
$930$	0	0
$931$	8.74456	0.286591
$932$	− 13.8614i	− 0.454045i
$933$	8.00000i	0.261908i
$934$	−29.4891	−0.964914
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	42.7446i	1.39640i	0.715901	+	0.698202i	$0.246016\pi$
$937$	42.7446i	1.39640i	−0.715901	+	0.698202i	$0.753984\pi$
$938$	1.76631i	0.0576721i
$939$	−10.0000	−0.326338
$940$	0	0
$941$	37.7228	1.22973	0.614864	−	0.788633i	$-0.289211\pi$
$941$	37.7228	1.22973	0.614864	+	0.788633i	$0.289211\pi$
$942$	− 3.62772i	− 0.118197i
$943$	25.4891i	0.830040i
$944$	8.74456	0.284611
$945$	0	0
$946$	40.6060	1.32021
$947$	− 8.74456i	− 0.284160i	−0.989855	−	0.142080i	$-0.954621\pi$
$947$	− 8.74456i	− 0.284160i	0.989855	−	0.142080i	$-0.0453790\pi$
$948$	− 10.3723i	− 0.336876i
$949$	18.2337	0.591891
$950$	0	0
$951$	−13.2554	−0.429837
$952$	16.0000i	0.518563i
$953$	− 45.7228i	− 1.48111i	−0.671997	−	0.740554i	$-0.734563\pi$
$953$	− 45.7228i	− 1.48111i	0.671997	−	0.740554i	$-0.265437\pi$
$954$	4.37228	0.141558
$955$	0	0
$956$	−6.51087	−0.210577
$957$	− 17.4891i	− 0.565343i
$958$	− 19.8614i	− 0.641693i
$959$	46.2337	1.49296
$960$	0	0
$961$	1.00000	0.0322581
$962$	21.4891i	0.692837i
$963$	6.37228i	0.205344i
$964$	−27.4891	−0.885365
$965$	0	0
$966$	5.62772	0.181069
$967$	− 8.00000i	− 0.257263i	−0.991692	−	0.128631i	$-0.958942\pi$
$967$	− 8.00000i	− 0.257263i	0.991692	−	0.128631i	$-0.0410584\pi$
$968$	29.6060i	0.951572i
$969$	42.9783	1.38066
$970$	0	0
$971$	54.7011	1.75544	0.877720	−	0.479173i	$-0.159063\pi$
$971$	54.7011	1.75544	0.877720	+	0.479173i	$0.159063\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	− 1.76631i	− 0.0566254i
$974$	14.5109	0.464958
$975$	0	0
$976$	−11.4891	−0.367758
$977$	46.0000i	1.47167i	0.677161	+	0.735835i	$0.263210\pi$
$977$	46.0000i	1.47167i	−0.677161	+	0.735835i	$0.736790\pi$
$978$	− 10.2337i	− 0.327237i
$979$	−27.8614	−0.890454
$980$	0	0
$981$	−6.74456	−0.215337
$982$	12.6060i	0.402273i
$983$	42.9783i	1.37079i	0.728170	+	0.685397i	$0.240371\pi$
$983$	42.9783i	1.37079i	−0.728170	+	0.685397i	$0.759629\pi$
$984$	10.7446	0.342524
$985$	0	0
$986$	18.5109	0.589506
$987$	11.2554i	0.358265i
$988$	12.7446i	0.405459i
$989$	15.1168	0.480688
$990$	0	0
$991$	−7.39403	−0.234879	−0.117440	−	0.993080i	$-0.537469\pi$
$991$	−7.39403	−0.234879	−0.117440	+	0.993080i	$0.537469\pi$
$992$	1.00000i	0.0317500i
$993$	21.4891i	0.681937i
$994$	−5.62772	−0.178500
$995$	0	0
$996$	−12.0000	−0.380235
$997$	− 6.00000i	− 0.190022i	−0.995476	−	0.0950110i	$-0.969711\pi$
$997$	− 6.00000i	− 0.190022i	0.995476	−	0.0950110i	$-0.0302886\pi$
$998$	10.5109i	0.332716i
$999$	−10.7446	−0.339943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4650.2.d.bh.3349.2		4
5.2	odd	4		930.2.a.r.1.1	✓	2
5.3	odd	4		4650.2.a.by.1.2		2
5.4	even	2	inner	4650.2.d.bh.3349.3		4
15.2	even	4		2790.2.a.bd.1.1		2
20.7	even	4		7440.2.a.bg.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.a.r.1.1	✓	2	5.2	odd	4
2790.2.a.bd.1.1		2	15.2	even	4
4650.2.a.by.1.2		2	5.3	odd	4
4650.2.d.bh.3349.2		4	1.1	even	1	trivial
4650.2.d.bh.3349.3		4	5.4	even	2	inner
7440.2.a.bg.1.2		2	20.7	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +2.37228i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +2.37228i q^{7} +1.00000i q^{8} -1.00000 q^{9} +6.37228 q^{11} -1.00000i q^{12} -2.00000i q^{13} +2.37228 q^{14} +1.00000 q^{16} -6.74456i q^{17} +1.00000i q^{18} +6.37228 q^{19} -2.37228 q^{21} -6.37228i q^{22} -2.37228i q^{23} -1.00000 q^{24} -2.00000 q^{26} -1.00000i q^{27} -2.37228i q^{28} -2.74456 q^{29} -1.00000 q^{31} -1.00000i q^{32} +6.37228i q^{33} -6.74456 q^{34} +1.00000 q^{36} -10.7446i q^{37} -6.37228i q^{38} +2.00000 q^{39} -10.7446 q^{41} +2.37228i q^{42} +6.37228i q^{43} -6.37228 q^{44} -2.37228 q^{46} -4.74456i q^{47} +1.00000i q^{48} +1.37228 q^{49} +6.74456 q^{51} +2.00000i q^{52} -4.37228i q^{53} -1.00000 q^{54} -2.37228 q^{56} +6.37228i q^{57} +2.74456i q^{58} +8.74456 q^{59} -11.4891 q^{61} +1.00000i q^{62} -2.37228i q^{63} -1.00000 q^{64} +6.37228 q^{66} +0.744563i q^{67} +6.74456i q^{68} +2.37228 q^{69} -2.37228 q^{71} -1.00000i q^{72} +9.11684i q^{73} -10.7446 q^{74} -6.37228 q^{76} +15.1168i q^{77} -2.00000i q^{78} +10.3723 q^{79} +1.00000 q^{81} +10.7446i q^{82} -12.0000i q^{83} +2.37228 q^{84} +6.37228 q^{86} -2.74456i q^{87} +6.37228i q^{88} -4.37228 q^{89} +4.74456 q^{91} +2.37228i q^{92} -1.00000i q^{93} -4.74456 q^{94} +1.00000 q^{96} -2.00000i q^{97} -1.37228i q^{98} -6.37228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 14 q^{11} - 2 q^{14} + 4 q^{16} + 14 q^{19} + 2 q^{21} - 4 q^{24} - 8 q^{26} + 12 q^{29} - 4 q^{31} - 4 q^{34} + 4 q^{36} + 8 q^{39} - 20 q^{41} - 14 q^{44} + 2 q^{46} - 6 q^{49} + 4 q^{51} - 4 q^{54} + 2 q^{56} + 12 q^{59} - 4 q^{64} + 14 q^{66} - 2 q^{69} + 2 q^{71} - 20 q^{74} - 14 q^{76} + 30 q^{79} + 4 q^{81} - 2 q^{84} + 14 q^{86} - 6 q^{89} - 4 q^{91} + 4 q^{94} + 4 q^{96} - 14 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 14 * q^11 - 2 * q^14 + 4 * q^16 + 14 * 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 - 20 * q^41 - 14 * q^44 + 2 * q^46 - 6 * q^49 + 4 * q^51 - 4 * q^54 + 2 * q^56 + 12 * q^59 - 4 * q^64 + 14 * q^66 - 2 * q^69 + 2 * q^71 - 20 * q^74 - 14 * q^76 + 30 * q^79 + 4 * q^81 - 2 * q^84 + 14 * q^86 - 6 * q^89 - 4 * q^91 + 4 * q^94 + 4 * q^96 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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