LMFDB - Embedded newform 2550.2.d.a.2449.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2550,2,Mod(2449,2550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2550, 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("2550.2449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2550.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:	$20.3618525154$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2449.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	2550.2449
Dual form			2550.2.d.a.2449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -5.00000 q^{11} +1.00000i q^{12} -2.00000i q^{13} -3.00000 q^{14} +1.00000 q^{16} -1.00000i q^{17} +1.00000i q^{18} -1.00000 q^{19} -3.00000 q^{21} +5.00000i q^{22} +6.00000i q^{23} +1.00000 q^{24} -2.00000 q^{26} +1.00000i q^{27} +3.00000i q^{28} -10.0000 q^{29} +5.00000 q^{31} -1.00000i q^{32} +5.00000i q^{33} -1.00000 q^{34} +1.00000 q^{36} +3.00000i q^{37} +1.00000i q^{38} -2.00000 q^{39} +6.00000 q^{41} +3.00000i q^{42} -1.00000i q^{43} +5.00000 q^{44} +6.00000 q^{46} -3.00000i q^{47} -1.00000i q^{48} -2.00000 q^{49} -1.00000 q^{51} +2.00000i q^{52} -1.00000i q^{53} +1.00000 q^{54} +3.00000 q^{56} +1.00000i q^{57} +10.0000i q^{58} -8.00000 q^{59} -2.00000 q^{61} -5.00000i q^{62} +3.00000i q^{63} -1.00000 q^{64} +5.00000 q^{66} +11.0000i q^{67} +1.00000i q^{68} +6.00000 q^{69} +6.00000 q^{71} -1.00000i q^{72} -12.0000i q^{73} +3.00000 q^{74} +1.00000 q^{76} +15.0000i q^{77} +2.00000i q^{78} -5.00000 q^{79} +1.00000 q^{81} -6.00000i q^{82} +18.0000i q^{83} +3.00000 q^{84} -1.00000 q^{86} +10.0000i q^{87} -5.00000i q^{88} -12.0000 q^{89} -6.00000 q^{91} -6.00000i q^{92} -5.00000i q^{93} -3.00000 q^{94} -1.00000 q^{96} +14.0000i q^{97} +2.00000i q^{98} +5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9} - 10 q^{11} - 6 q^{14} + 2 q^{16} - 2 q^{19} - 6 q^{21} + 2 q^{24} - 4 q^{26} - 20 q^{29} + 10 q^{31} - 2 q^{34} + 2 q^{36} - 4 q^{39} + 12 q^{41} + 10 q^{44} + 12 q^{46} - 4 q^{49} - 2 q^{51} + 2 q^{54} + 6 q^{56} - 16 q^{59} - 4 q^{61} - 2 q^{64} + 10 q^{66} + 12 q^{69} + 12 q^{71} + 6 q^{74} + 2 q^{76} - 10 q^{79} + 2 q^{81} + 6 q^{84} - 2 q^{86} - 24 q^{89} - 12 q^{91} - 6 q^{94} - 2 q^{96} + 10 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9 - 10 * q^11 - 6 * q^14 + 2 * q^16 - 2 * q^19 - 6 * q^21 + 2 * q^24 - 4 * q^26 - 20 * q^29 + 10 * q^31 - 2 * q^34 + 2 * q^36 - 4 * q^39 + 12 * q^41 + 10 * q^44 + 12 * q^46 - 4 * q^49 - 2 * q^51 + 2 * q^54 + 6 * q^56 - 16 * q^59 - 4 * q^61 - 2 * q^64 + 10 * q^66 + 12 * q^69 + 12 * q^71 + 6 * q^74 + 2 * q^76 - 10 * q^79 + 2 * q^81 + 6 * q^84 - 2 * q^86 - 24 * q^89 - 12 * q^91 - 6 * q^94 - 2 * q^96 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2550\mathbb{Z}\right)^\times$.

$n$	$751$	$851$	$1327$
$\chi(n)$	$1$	$1$	$-1$

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
$7$	− 3.00000i	− 1.13389i	−0.823754	−	0.566947i	$-0.808125\pi$
$7$	− 3.00000i	− 1.13389i	0.823754	−	0.566947i	$-0.191875\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	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	$-0.0894562\pi$
$14$	−3.00000	−0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	− 1.00000i	− 0.242536i
$17$	− 1.00000i	− 0.242536i
$18$	1.00000i	0.235702i
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	0	0
$21$	−3.00000	−0.654654
$22$	5.00000i	1.06600i
$23$	6.00000i	1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$	6.00000i	1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−2.00000	−0.392232
$27$	1.00000i	0.192450i
$28$	3.00000i	0.566947i
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	− 1.00000i	− 0.176777i
$33$	5.00000i	0.870388i
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	3.00000i	0.493197i	0.969118	+	0.246598i	$0.0793129\pi$
$37$	3.00000i	0.493197i	−0.969118	+	0.246598i	$0.920687\pi$
$38$	1.00000i	0.162221i
$39$	−2.00000	−0.320256
$40$	0	0
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	3.00000i	0.462910i
$43$	− 1.00000i	− 0.152499i	−0.997089	−	0.0762493i	$-0.975706\pi$
$43$	− 1.00000i	− 0.152499i	0.997089	−	0.0762493i	$-0.0242945\pi$
$44$	5.00000	0.753778
$45$	0	0
$46$	6.00000	0.884652
$47$	− 3.00000i	− 0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$	− 3.00000i	− 0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$	− 1.00000i	− 0.144338i
$49$	−2.00000	−0.285714
$50$	0	0
$51$	−1.00000	−0.140028
$52$	2.00000i	0.277350i
$53$	− 1.00000i	− 0.137361i	−0.997639	−	0.0686803i	$-0.978121\pi$
$53$	− 1.00000i	− 0.137361i	0.997639	−	0.0686803i	$-0.0218788\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	3.00000	0.400892
$57$	1.00000i	0.132453i
$58$	10.0000i	1.31306i
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	− 5.00000i	− 0.635001i
$63$	3.00000i	0.377964i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	5.00000	0.615457
$67$	11.0000i	1.34386i	0.740613	+	0.671932i	$0.234535\pi$
$67$	11.0000i	1.34386i	−0.740613	+	0.671932i	$0.765465\pi$
$68$	1.00000i	0.121268i
$69$	6.00000	0.722315
$70$	0	0
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	− 1.00000i	− 0.117851i
$73$	− 12.0000i	− 1.40449i	−0.711934	−	0.702247i	$-0.752180\pi$
$73$	− 12.0000i	− 1.40449i	0.711934	−	0.702247i	$-0.247820\pi$
$74$	3.00000	0.348743
$75$	0	0
$76$	1.00000	0.114708
$77$	15.0000i	1.70941i
$78$	2.00000i	0.226455i
$79$	−5.00000	−0.562544	−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000	−0.562544	−0.281272	+	0.959628i	$0.590756\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 6.00000i	− 0.662589i
$83$	18.0000i	1.97576i	0.155230	+	0.987878i	$0.450388\pi$
$83$	18.0000i	1.97576i	−0.155230	+	0.987878i	$0.549612\pi$
$84$	3.00000	0.327327
$85$	0	0
$86$	−1.00000	−0.107833
$87$	10.0000i	1.07211i
$88$	− 5.00000i	− 0.533002i
$89$	−12.0000	−1.27200	−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000	−1.27200	−0.635999	+	0.771690i	$0.719412\pi$
$90$	0	0
$91$	−6.00000	−0.628971
$92$	− 6.00000i	− 0.625543i
$93$	− 5.00000i	− 0.518476i
$94$	−3.00000	−0.309426
$95$	0	0
$96$	−1.00000	−0.102062
$97$	14.0000i	1.42148i	0.703452	+	0.710742i	$0.251641\pi$
$97$	14.0000i	1.42148i	−0.703452	+	0.710742i	$0.748359\pi$
$98$	2.00000i	0.202031i
$99$	5.00000	0.502519
$100$	0	0
$101$	11.0000	1.09454	0.547270	−	0.836956i	$-0.315667\pi$
$101$	11.0000	1.09454	0.547270	+	0.836956i	$0.315667\pi$
$102$	1.00000i	0.0990148i
$103$	4.00000i	0.394132i	0.980390	+	0.197066i	$0.0631413\pi$
$103$	4.00000i	0.394132i	−0.980390	+	0.197066i	$0.936859\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−1.00000	−0.0971286
$107$	5.00000i	0.483368i	0.970355	+	0.241684i	$0.0776998\pi$
$107$	5.00000i	0.483368i	−0.970355	+	0.241684i	$0.922300\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	−5.00000	−0.478913	−0.239457	−	0.970907i	$-0.576969\pi$
$109$	−5.00000	−0.478913	−0.239457	+	0.970907i	$0.576969\pi$
$110$	0	0
$111$	3.00000	0.284747
$112$	− 3.00000i	− 0.283473i
$113$	1.00000i	0.0940721i	0.998893	+	0.0470360i	$0.0149776\pi$
$113$	1.00000i	0.0940721i	−0.998893	+	0.0470360i	$0.985022\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	10.0000	0.928477
$117$	2.00000i	0.184900i
$118$	8.00000i	0.736460i
$119$	−3.00000	−0.275010
$120$	0	0
$121$	14.0000	1.27273
$122$	2.00000i	0.181071i
$123$	− 6.00000i	− 0.541002i
$124$	−5.00000	−0.449013
$125$	0	0
$126$	3.00000	0.267261
$127$	− 12.0000i	− 1.06483i	−0.846484	−	0.532414i	$-0.821285\pi$
$127$	− 12.0000i	− 1.06483i	0.846484	−	0.532414i	$-0.178715\pi$
$128$	1.00000i	0.0883883i
$129$	−1.00000	−0.0880451
$130$	0	0
$131$	−20.0000	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$132$	− 5.00000i	− 0.435194i
$133$	3.00000i	0.260133i
$134$	11.0000	0.950255
$135$	0	0
$136$	1.00000	0.0857493
$137$	− 16.0000i	− 1.36697i	−0.729964	−	0.683486i	$-0.760463\pi$
$137$	− 16.0000i	− 1.36697i	0.729964	−	0.683486i	$-0.239537\pi$
$138$	− 6.00000i	− 0.510754i
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	0	0
$141$	−3.00000	−0.252646
$142$	− 6.00000i	− 0.503509i
$143$	10.0000i	0.836242i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−12.0000	−0.993127
$147$	2.00000i	0.164957i
$148$	− 3.00000i	− 0.246598i
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	− 1.00000i	− 0.0811107i
$153$	1.00000i	0.0808452i
$154$	15.0000	1.20873
$155$	0	0
$156$	2.00000	0.160128
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	5.00000i	0.397779i
$159$	−1.00000	−0.0793052
$160$	0	0
$161$	18.0000	1.41860
$162$	− 1.00000i	− 0.0785674i
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	18.0000	1.39707
$167$	18.0000i	1.39288i	0.717614	+	0.696441i	$0.245234\pi$
$167$	18.0000i	1.39288i	−0.717614	+	0.696441i	$0.754766\pi$
$168$	− 3.00000i	− 0.231455i
$169$	9.00000	0.692308
$170$	0	0
$171$	1.00000	0.0764719
$172$	1.00000i	0.0762493i
$173$	20.0000i	1.52057i	0.649589	+	0.760286i	$0.274941\pi$
$173$	20.0000i	1.52057i	−0.649589	+	0.760286i	$0.725059\pi$
$174$	10.0000	0.758098
$175$	0	0
$176$	−5.00000	−0.376889
$177$	8.00000i	0.601317i
$178$	12.0000i	0.899438i
$179$	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
$181$	−17.0000	−1.26360	−0.631800	−	0.775131i	$-0.717684\pi$
$181$	−17.0000	−1.26360	−0.631800	+	0.775131i	$0.717684\pi$
$182$	6.00000i	0.444750i
$183$	2.00000i	0.147844i
$184$	−6.00000	−0.442326
$185$	0	0
$186$	−5.00000	−0.366618
$187$	5.00000i	0.365636i
$188$	3.00000i	0.218797i
$189$	3.00000	0.218218
$190$	0	0
$191$	3.00000	0.217072	0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000	0.217072	0.108536	+	0.994092i	$0.465384\pi$
$192$	1.00000i	0.0721688i
$193$	− 24.0000i	− 1.72756i	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	− 24.0000i	− 1.72756i	0.503871	−	0.863779i	$-0.331909\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	2.00000	0.142857
$197$	− 12.0000i	− 0.854965i	−0.904024	−	0.427482i	$-0.859401\pi$
$197$	− 12.0000i	− 0.854965i	0.904024	−	0.427482i	$-0.140599\pi$
$198$	− 5.00000i	− 0.355335i
$199$	−17.0000	−1.20510	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−17.0000	−1.20510	−0.602549	+	0.798082i	$0.705848\pi$
$200$	0	0
$201$	11.0000	0.775880
$202$	− 11.0000i	− 0.773957i
$203$	30.0000i	2.10559i
$204$	1.00000	0.0700140
$205$	0	0
$206$	4.00000	0.278693
$207$	− 6.00000i	− 0.417029i
$208$	− 2.00000i	− 0.138675i
$209$	5.00000	0.345857
$210$	0	0
$211$	18.0000	1.23917	0.619586	−	0.784929i	$-0.287301\pi$
$211$	18.0000	1.23917	0.619586	+	0.784929i	$0.287301\pi$
$212$	1.00000i	0.0686803i
$213$	− 6.00000i	− 0.411113i
$214$	5.00000	0.341793
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	− 15.0000i	− 1.01827i
$218$	5.00000i	0.338643i
$219$	−12.0000	−0.810885
$220$	0	0
$221$	−2.00000	−0.134535
$222$	− 3.00000i	− 0.201347i
$223$	18.0000i	1.20537i	0.797980	+	0.602685i	$0.205902\pi$
$223$	18.0000i	1.20537i	−0.797980	+	0.602685i	$0.794098\pi$
$224$	−3.00000	−0.200446
$225$	0	0
$226$	1.00000	0.0665190
$227$	27.0000i	1.79205i	0.444001	+	0.896026i	$0.353559\pi$
$227$	27.0000i	1.79205i	−0.444001	+	0.896026i	$0.646441\pi$
$228$	− 1.00000i	− 0.0662266i
$229$	−24.0000	−1.58596	−0.792982	−	0.609245i	$-0.791473\pi$
$229$	−24.0000	−1.58596	−0.792982	+	0.609245i	$0.791473\pi$
$230$	0	0
$231$	15.0000	0.986928
$232$	− 10.0000i	− 0.656532i
$233$	− 10.0000i	− 0.655122i	−0.944830	−	0.327561i	$-0.893773\pi$
$233$	− 10.0000i	− 0.655122i	0.944830	−	0.327561i	$-0.106227\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	8.00000	0.520756
$237$	5.00000i	0.324785i
$238$	3.00000i	0.194461i
$239$	−13.0000	−0.840900	−0.420450	−	0.907316i	$-0.638128\pi$
$239$	−13.0000	−0.840900	−0.420450	+	0.907316i	$0.638128\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	− 14.0000i	− 0.899954i
$243$	− 1.00000i	− 0.0641500i
$244$	2.00000	0.128037
$245$	0	0
$246$	−6.00000	−0.382546
$247$	2.00000i	0.127257i
$248$	5.00000i	0.317500i
$249$	18.0000	1.14070
$250$	0	0
$251$	−18.0000	−1.13615	−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000	−1.13615	−0.568075	+	0.822977i	$0.692312\pi$
$252$	− 3.00000i	− 0.188982i
$253$	− 30.0000i	− 1.88608i
$254$	−12.0000	−0.752947
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 2.00000i	− 0.124757i	−0.998053	−	0.0623783i	$-0.980131\pi$
$257$	− 2.00000i	− 0.124757i	0.998053	−	0.0623783i	$-0.0198685\pi$
$258$	1.00000i	0.0622573i
$259$	9.00000	0.559233
$260$	0	0
$261$	10.0000	0.618984
$262$	20.0000i	1.23560i
$263$	3.00000i	0.184988i	0.995713	+	0.0924940i	$0.0294839\pi$
$263$	3.00000i	0.184988i	−0.995713	+	0.0924940i	$0.970516\pi$
$264$	−5.00000	−0.307729
$265$	0	0
$266$	3.00000	0.183942
$267$	12.0000i	0.734388i
$268$	− 11.0000i	− 0.671932i
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	0	0
$271$	14.0000	0.850439	0.425220	−	0.905090i	$-0.360197\pi$
$271$	14.0000	0.850439	0.425220	+	0.905090i	$0.360197\pi$
$272$	− 1.00000i	− 0.0606339i
$273$	6.00000i	0.363137i
$274$	−16.0000	−0.966595
$275$	0	0
$276$	−6.00000	−0.361158
$277$	31.0000i	1.86261i	0.364241	+	0.931305i	$0.381328\pi$
$277$	31.0000i	1.86261i	−0.364241	+	0.931305i	$0.618672\pi$
$278$	8.00000i	0.479808i
$279$	−5.00000	−0.299342
$280$	0	0
$281$	−30.0000	−1.78965	−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000	−1.78965	−0.894825	+	0.446417i	$0.852700\pi$
$282$	3.00000i	0.178647i
$283$	− 14.0000i	− 0.832214i	−0.909316	−	0.416107i	$-0.863394\pi$
$283$	− 14.0000i	− 0.832214i	0.909316	−	0.416107i	$-0.136606\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	10.0000	0.591312
$287$	− 18.0000i	− 1.06251i
$288$	1.00000i	0.0589256i
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	14.0000	0.820695
$292$	12.0000i	0.702247i
$293$	− 18.0000i	− 1.05157i	−0.850617	−	0.525786i	$-0.823771\pi$
$293$	− 18.0000i	− 1.05157i	0.850617	−	0.525786i	$-0.176229\pi$
$294$	2.00000	0.116642
$295$	0	0
$296$	−3.00000	−0.174371
$297$	− 5.00000i	− 0.290129i
$298$	− 6.00000i	− 0.347571i
$299$	12.0000	0.693978
$300$	0	0
$301$	−3.00000	−0.172917
$302$	− 8.00000i	− 0.460348i
$303$	− 11.0000i	− 0.631933i
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	1.00000	0.0571662
$307$	− 20.0000i	− 1.14146i	−0.821138	−	0.570730i	$-0.806660\pi$
$307$	− 20.0000i	− 1.14146i	0.821138	−	0.570730i	$-0.193340\pi$
$308$	− 15.0000i	− 0.854704i
$309$	4.00000	0.227552
$310$	0	0
$311$	−2.00000	−0.113410	−0.0567048	−	0.998391i	$-0.518059\pi$
$311$	−2.00000	−0.113410	−0.0567048	+	0.998391i	$0.518059\pi$
$312$	− 2.00000i	− 0.113228i
$313$	− 34.0000i	− 1.92179i	−0.276907	−	0.960897i	$-0.589309\pi$
$313$	− 34.0000i	− 1.92179i	0.276907	−	0.960897i	$-0.410691\pi$
$314$	0	0
$315$	0	0
$316$	5.00000	0.281272
$317$	12.0000i	0.673987i	0.941507	+	0.336994i	$0.109410\pi$
$317$	12.0000i	0.673987i	−0.941507	+	0.336994i	$0.890590\pi$
$318$	1.00000i	0.0560772i
$319$	50.0000	2.79946
$320$	0	0
$321$	5.00000	0.279073
$322$	− 18.0000i	− 1.00310i
$323$	1.00000i	0.0556415i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	0	0
$327$	5.00000i	0.276501i
$328$	6.00000i	0.331295i
$329$	−9.00000	−0.496186
$330$	0	0
$331$	−25.0000	−1.37412	−0.687062	−	0.726599i	$-0.741100\pi$
$331$	−25.0000	−1.37412	−0.687062	+	0.726599i	$0.741100\pi$
$332$	− 18.0000i	− 0.987878i
$333$	− 3.00000i	− 0.164399i
$334$	18.0000	0.984916
$335$	0	0
$336$	−3.00000	−0.163663
$337$	− 12.0000i	− 0.653682i	−0.945079	−	0.326841i	$-0.894016\pi$
$337$	− 12.0000i	− 0.653682i	0.945079	−	0.326841i	$-0.105984\pi$
$338$	− 9.00000i	− 0.489535i
$339$	1.00000	0.0543125
$340$	0	0
$341$	−25.0000	−1.35383
$342$	− 1.00000i	− 0.0540738i
$343$	− 15.0000i	− 0.809924i
$344$	1.00000	0.0539164
$345$	0	0
$346$	20.0000	1.07521
$347$	23.0000i	1.23470i	0.786687	+	0.617352i	$0.211795\pi$
$347$	23.0000i	1.23470i	−0.786687	+	0.617352i	$0.788205\pi$
$348$	− 10.0000i	− 0.536056i
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	2.00000	0.106752
$352$	5.00000i	0.266501i
$353$	− 2.00000i	− 0.106449i	−0.998583	−	0.0532246i	$-0.983050\pi$
$353$	− 2.00000i	− 0.106449i	0.998583	−	0.0532246i	$-0.0169499\pi$
$354$	8.00000	0.425195
$355$	0	0
$356$	12.0000	0.635999
$357$	3.00000i	0.158777i
$358$	− 12.0000i	− 0.634220i
$359$	−15.0000	−0.791670	−0.395835	−	0.918322i	$-0.629545\pi$
$359$	−15.0000	−0.791670	−0.395835	+	0.918322i	$0.629545\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	17.0000i	0.893500i
$363$	− 14.0000i	− 0.734809i
$364$	6.00000	0.314485
$365$	0	0
$366$	2.00000	0.104542
$367$	− 5.00000i	− 0.260998i	−0.991448	−	0.130499i	$-0.958342\pi$
$367$	− 5.00000i	− 0.260998i	0.991448	−	0.130499i	$-0.0416579\pi$
$368$	6.00000i	0.312772i
$369$	−6.00000	−0.312348
$370$	0	0
$371$	−3.00000	−0.155752
$372$	5.00000i	0.259238i
$373$	− 18.0000i	− 0.932005i	−0.884783	−	0.466002i	$-0.845694\pi$
$373$	− 18.0000i	− 0.932005i	0.884783	−	0.466002i	$-0.154306\pi$
$374$	5.00000	0.258544
$375$	0	0
$376$	3.00000	0.154713
$377$	20.0000i	1.03005i
$378$	− 3.00000i	− 0.154303i
$379$	8.00000	0.410932	0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000	0.410932	0.205466	+	0.978664i	$0.434129\pi$
$380$	0	0
$381$	−12.0000	−0.614779
$382$	− 3.00000i	− 0.153493i
$383$	− 8.00000i	− 0.408781i	−0.978889	−	0.204390i	$-0.934479\pi$
$383$	− 8.00000i	− 0.408781i	0.978889	−	0.204390i	$-0.0655212\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−24.0000	−1.22157
$387$	1.00000i	0.0508329i
$388$	− 14.0000i	− 0.710742i
$389$	5.00000	0.253510	0.126755	−	0.991934i	$-0.459544\pi$
$389$	5.00000	0.253510	0.126755	+	0.991934i	$0.459544\pi$
$390$	0	0
$391$	6.00000	0.303433
$392$	− 2.00000i	− 0.101015i
$393$	20.0000i	1.00887i
$394$	−12.0000	−0.604551
$395$	0	0
$396$	−5.00000	−0.251259
$397$	− 21.0000i	− 1.05396i	−0.849878	−	0.526980i	$-0.823324\pi$
$397$	− 21.0000i	− 1.05396i	0.849878	−	0.526980i	$-0.176676\pi$
$398$	17.0000i	0.852133i
$399$	3.00000	0.150188
$400$	0	0
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	− 11.0000i	− 0.548630i
$403$	− 10.0000i	− 0.498135i
$404$	−11.0000	−0.547270
$405$	0	0
$406$	30.0000	1.48888
$407$	− 15.0000i	− 0.743522i
$408$	− 1.00000i	− 0.0495074i
$409$	2.00000	0.0988936	0.0494468	−	0.998777i	$-0.484254\pi$
$409$	2.00000	0.0988936	0.0494468	+	0.998777i	$0.484254\pi$
$410$	0	0
$411$	−16.0000	−0.789222
$412$	− 4.00000i	− 0.197066i
$413$	24.0000i	1.18096i
$414$	−6.00000	−0.294884
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	8.00000i	0.391762i
$418$	− 5.00000i	− 0.244558i
$419$	−24.0000	−1.17248	−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000	−1.17248	−0.586238	+	0.810139i	$0.699392\pi$
$420$	0	0
$421$	18.0000	0.877266	0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000	0.877266	0.438633	+	0.898666i	$0.355463\pi$
$422$	− 18.0000i	− 0.876226i
$423$	3.00000i	0.145865i
$424$	1.00000	0.0485643
$425$	0	0
$426$	−6.00000	−0.290701
$427$	6.00000i	0.290360i
$428$	− 5.00000i	− 0.241684i
$429$	10.0000	0.482805
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	1.00000i	0.0481125i
$433$	21.0000i	1.00920i	0.863355	+	0.504598i	$0.168359\pi$
$433$	21.0000i	1.00920i	−0.863355	+	0.504598i	$0.831641\pi$
$434$	−15.0000	−0.720023
$435$	0	0
$436$	5.00000	0.239457
$437$	− 6.00000i	− 0.287019i
$438$	12.0000i	0.573382i
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	2.00000i	0.0951303i
$443$	− 24.0000i	− 1.14027i	−0.821549	−	0.570137i	$-0.806890\pi$
$443$	− 24.0000i	− 1.14027i	0.821549	−	0.570137i	$-0.193110\pi$
$444$	−3.00000	−0.142374
$445$	0	0
$446$	18.0000	0.852325
$447$	− 6.00000i	− 0.283790i
$448$	3.00000i	0.141737i
$449$	−21.0000	−0.991051	−0.495526	−	0.868593i	$-0.665025\pi$
$449$	−21.0000	−0.991051	−0.495526	+	0.868593i	$0.665025\pi$
$450$	0	0
$451$	−30.0000	−1.41264
$452$	− 1.00000i	− 0.0470360i
$453$	− 8.00000i	− 0.375873i
$454$	27.0000	1.26717
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	25.0000i	1.16945i	0.811231	+	0.584725i	$0.198798\pi$
$457$	25.0000i	1.16945i	−0.811231	+	0.584725i	$0.801202\pi$
$458$	24.0000i	1.12145i
$459$	1.00000	0.0466760
$460$	0	0
$461$	−15.0000	−0.698620	−0.349310	−	0.937007i	$-0.613584\pi$
$461$	−15.0000	−0.698620	−0.349310	+	0.937007i	$0.613584\pi$
$462$	− 15.0000i	− 0.697863i
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	−10.0000	−0.464238
$465$	0	0
$466$	−10.0000	−0.463241
$467$	− 18.0000i	− 0.832941i	−0.909149	−	0.416470i	$-0.863267\pi$
$467$	− 18.0000i	− 0.832941i	0.909149	−	0.416470i	$-0.136733\pi$
$468$	− 2.00000i	− 0.0924500i
$469$	33.0000	1.52380
$470$	0	0
$471$	0	0
$472$	− 8.00000i	− 0.368230i
$473$	5.00000i	0.229900i
$474$	5.00000	0.229658
$475$	0	0
$476$	3.00000	0.137505
$477$	1.00000i	0.0457869i
$478$	13.0000i	0.594606i
$479$	−26.0000	−1.18797	−0.593985	−	0.804476i	$-0.702446\pi$
$479$	−26.0000	−1.18797	−0.593985	+	0.804476i	$0.702446\pi$
$480$	0	0
$481$	6.00000	0.273576
$482$	0	0
$483$	− 18.0000i	− 0.819028i
$484$	−14.0000	−0.636364
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	40.0000i	1.81257i	0.422664	+	0.906287i	$0.361095\pi$
$487$	40.0000i	1.81257i	−0.422664	+	0.906287i	$0.638905\pi$
$488$	− 2.00000i	− 0.0905357i
$489$	0	0
$490$	0	0
$491$	4.00000	0.180517	0.0902587	−	0.995918i	$-0.471231\pi$
$491$	4.00000	0.180517	0.0902587	+	0.995918i	$0.471231\pi$
$492$	6.00000i	0.270501i
$493$	10.0000i	0.450377i
$494$	2.00000	0.0899843
$495$	0	0
$496$	5.00000	0.224507
$497$	− 18.0000i	− 0.807410i
$498$	− 18.0000i	− 0.806599i
$499$	−22.0000	−0.984855	−0.492428	−	0.870353i	$-0.663890\pi$
$499$	−22.0000	−0.984855	−0.492428	+	0.870353i	$0.663890\pi$
$500$	0	0
$501$	18.0000	0.804181
$502$	18.0000i	0.803379i
$503$	6.00000i	0.267527i	0.991013	+	0.133763i	$0.0427062\pi$
$503$	6.00000i	0.267527i	−0.991013	+	0.133763i	$0.957294\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	−30.0000	−1.33366
$507$	− 9.00000i	− 0.399704i
$508$	12.0000i	0.532414i
$509$	−9.00000	−0.398918	−0.199459	−	0.979906i	$-0.563918\pi$
$509$	−9.00000	−0.398918	−0.199459	+	0.979906i	$0.563918\pi$
$510$	0	0
$511$	−36.0000	−1.59255
$512$	− 1.00000i	− 0.0441942i
$513$	− 1.00000i	− 0.0441511i
$514$	−2.00000	−0.0882162
$515$	0	0
$516$	1.00000	0.0440225
$517$	15.0000i	0.659699i
$518$	− 9.00000i	− 0.395437i
$519$	20.0000	0.877903
$520$	0	0
$521$	−39.0000	−1.70862	−0.854311	−	0.519763i	$-0.826020\pi$
$521$	−39.0000	−1.70862	−0.854311	+	0.519763i	$0.826020\pi$
$522$	− 10.0000i	− 0.437688i
$523$	20.0000i	0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$	20.0000i	0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	20.0000	0.873704
$525$	0	0
$526$	3.00000	0.130806
$527$	− 5.00000i	− 0.217803i
$528$	5.00000i	0.217597i
$529$	−13.0000	−0.565217
$530$	0	0
$531$	8.00000	0.347170
$532$	− 3.00000i	− 0.130066i
$533$	− 12.0000i	− 0.519778i
$534$	12.0000	0.519291
$535$	0	0
$536$	−11.0000	−0.475128
$537$	− 12.0000i	− 0.517838i
$538$	− 6.00000i	− 0.258678i
$539$	10.0000	0.430730
$540$	0	0
$541$	−41.0000	−1.76273	−0.881364	−	0.472438i	$-0.843374\pi$
$541$	−41.0000	−1.76273	−0.881364	+	0.472438i	$0.843374\pi$
$542$	− 14.0000i	− 0.601351i
$543$	17.0000i	0.729540i
$544$	−1.00000	−0.0428746
$545$	0	0
$546$	6.00000	0.256776
$547$	− 22.0000i	− 0.940652i	−0.882493	−	0.470326i	$-0.844136\pi$
$547$	− 22.0000i	− 0.940652i	0.882493	−	0.470326i	$-0.155864\pi$
$548$	16.0000i	0.683486i
$549$	2.00000	0.0853579
$550$	0	0
$551$	10.0000	0.426014
$552$	6.00000i	0.255377i
$553$	15.0000i	0.637865i
$554$	31.0000	1.31706
$555$	0	0
$556$	8.00000	0.339276
$557$	− 17.0000i	− 0.720313i	−0.932892	−	0.360157i	$-0.882723\pi$
$557$	− 17.0000i	− 0.720313i	0.932892	−	0.360157i	$-0.117277\pi$
$558$	5.00000i	0.211667i
$559$	−2.00000	−0.0845910
$560$	0	0
$561$	5.00000	0.211100
$562$	30.0000i	1.26547i
$563$	− 8.00000i	− 0.337160i	−0.985688	−	0.168580i	$-0.946082\pi$
$563$	− 8.00000i	− 0.337160i	0.985688	−	0.168580i	$-0.0539181\pi$
$564$	3.00000	0.126323
$565$	0	0
$566$	−14.0000	−0.588464
$567$	− 3.00000i	− 0.125988i
$568$	6.00000i	0.251754i
$569$	36.0000	1.50920	0.754599	−	0.656186i	$-0.227831\pi$
$569$	36.0000	1.50920	0.754599	+	0.656186i	$0.227831\pi$
$570$	0	0
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	− 10.0000i	− 0.418121i
$573$	− 3.00000i	− 0.125327i
$574$	−18.0000	−0.751305
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 33.0000i	− 1.37381i	−0.726748	−	0.686904i	$-0.758969\pi$
$577$	− 33.0000i	− 1.37381i	0.726748	−	0.686904i	$-0.241031\pi$
$578$	1.00000i	0.0415945i
$579$	−24.0000	−0.997406
$580$	0	0
$581$	54.0000	2.24030
$582$	− 14.0000i	− 0.580319i
$583$	5.00000i	0.207079i
$584$	12.0000	0.496564
$585$	0	0
$586$	−18.0000	−0.743573
$587$	18.0000i	0.742940i	0.928445	+	0.371470i	$0.121146\pi$
$587$	18.0000i	0.742940i	−0.928445	+	0.371470i	$0.878854\pi$
$588$	− 2.00000i	− 0.0824786i
$589$	−5.00000	−0.206021
$590$	0	0
$591$	−12.0000	−0.493614
$592$	3.00000i	0.123299i
$593$	12.0000i	0.492781i	0.969171	+	0.246390i	$0.0792446\pi$
$593$	12.0000i	0.492781i	−0.969171	+	0.246390i	$0.920755\pi$
$594$	−5.00000	−0.205152
$595$	0	0
$596$	−6.00000	−0.245770
$597$	17.0000i	0.695764i
$598$	− 12.0000i	− 0.490716i
$599$	−35.0000	−1.43006	−0.715031	−	0.699093i	$-0.753587\pi$
$599$	−35.0000	−1.43006	−0.715031	+	0.699093i	$0.753587\pi$
$600$	0	0
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	3.00000i	0.122271i
$603$	− 11.0000i	− 0.447955i
$604$	−8.00000	−0.325515
$605$	0	0
$606$	−11.0000	−0.446844
$607$	− 20.0000i	− 0.811775i	−0.913923	−	0.405887i	$-0.866962\pi$
$607$	− 20.0000i	− 0.811775i	0.913923	−	0.405887i	$-0.133038\pi$
$608$	1.00000i	0.0405554i
$609$	30.0000	1.21566
$610$	0	0
$611$	−6.00000	−0.242734
$612$	− 1.00000i	− 0.0404226i
$613$	− 26.0000i	− 1.05013i	−0.851062	−	0.525065i	$-0.824041\pi$
$613$	− 26.0000i	− 1.05013i	0.851062	−	0.525065i	$-0.175959\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	−15.0000	−0.604367
$617$	13.0000i	0.523360i	0.965155	+	0.261680i	$0.0842766\pi$
$617$	13.0000i	0.523360i	−0.965155	+	0.261680i	$0.915723\pi$
$618$	− 4.00000i	− 0.160904i
$619$	8.00000	0.321547	0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000	0.321547	0.160774	+	0.986991i	$0.448601\pi$
$620$	0	0
$621$	−6.00000	−0.240772
$622$	2.00000i	0.0801927i
$623$	36.0000i	1.44231i
$624$	−2.00000	−0.0800641
$625$	0	0
$626$	−34.0000	−1.35891
$627$	− 5.00000i	− 0.199681i
$628$	0	0
$629$	3.00000	0.119618
$630$	0	0
$631$	−14.0000	−0.557331	−0.278666	−	0.960388i	$-0.589892\pi$
$631$	−14.0000	−0.557331	−0.278666	+	0.960388i	$0.589892\pi$
$632$	− 5.00000i	− 0.198889i
$633$	− 18.0000i	− 0.715436i
$634$	12.0000	0.476581
$635$	0	0
$636$	1.00000	0.0396526
$637$	4.00000i	0.158486i
$638$	− 50.0000i	− 1.97952i
$639$	−6.00000	−0.237356
$640$	0	0
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	− 5.00000i	− 0.197334i
$643$	34.0000i	1.34083i	0.741987	+	0.670415i	$0.233884\pi$
$643$	34.0000i	1.34083i	−0.741987	+	0.670415i	$0.766116\pi$
$644$	−18.0000	−0.709299
$645$	0	0
$646$	1.00000	0.0393445
$647$	− 24.0000i	− 0.943537i	−0.881722	−	0.471769i	$-0.843616\pi$
$647$	− 24.0000i	− 0.943537i	0.881722	−	0.471769i	$-0.156384\pi$
$648$	1.00000i	0.0392837i
$649$	40.0000	1.57014
$650$	0	0
$651$	−15.0000	−0.587896
$652$	0	0
$653$	− 16.0000i	− 0.626128i	−0.949732	−	0.313064i	$-0.898644\pi$
$653$	− 16.0000i	− 0.626128i	0.949732	−	0.313064i	$-0.101356\pi$
$654$	5.00000	0.195515
$655$	0	0
$656$	6.00000	0.234261
$657$	12.0000i	0.468165i
$658$	9.00000i	0.350857i
$659$	−16.0000	−0.623272	−0.311636	−	0.950202i	$-0.600877\pi$
$659$	−16.0000	−0.623272	−0.311636	+	0.950202i	$0.600877\pi$
$660$	0	0
$661$	8.00000	0.311164	0.155582	−	0.987823i	$-0.450275\pi$
$661$	8.00000	0.311164	0.155582	+	0.987823i	$0.450275\pi$
$662$	25.0000i	0.971653i
$663$	2.00000i	0.0776736i
$664$	−18.0000	−0.698535
$665$	0	0
$666$	−3.00000	−0.116248
$667$	− 60.0000i	− 2.32321i
$668$	− 18.0000i	− 0.696441i
$669$	18.0000	0.695920
$670$	0	0
$671$	10.0000	0.386046
$672$	3.00000i	0.115728i
$673$	14.0000i	0.539660i	0.962908	+	0.269830i	$0.0869676\pi$
$673$	14.0000i	0.539660i	−0.962908	+	0.269830i	$0.913032\pi$
$674$	−12.0000	−0.462223
$675$	0	0
$676$	−9.00000	−0.346154
$677$	− 12.0000i	− 0.461197i	−0.973049	−	0.230599i	$-0.925932\pi$
$677$	− 12.0000i	− 0.461197i	0.973049	−	0.230599i	$-0.0740685\pi$
$678$	− 1.00000i	− 0.0384048i
$679$	42.0000	1.61181
$680$	0	0
$681$	27.0000	1.03464
$682$	25.0000i	0.957299i
$683$	− 8.00000i	− 0.306111i	−0.988218	−	0.153056i	$-0.951089\pi$
$683$	− 8.00000i	− 0.306111i	0.988218	−	0.153056i	$-0.0489114\pi$
$684$	−1.00000	−0.0382360
$685$	0	0
$686$	−15.0000	−0.572703
$687$	24.0000i	0.915657i
$688$	− 1.00000i	− 0.0381246i
$689$	−2.00000	−0.0761939
$690$	0	0
$691$	−48.0000	−1.82601	−0.913003	−	0.407953i	$-0.866243\pi$
$691$	−48.0000	−1.82601	−0.913003	+	0.407953i	$0.866243\pi$
$692$	− 20.0000i	− 0.760286i
$693$	− 15.0000i	− 0.569803i
$694$	23.0000	0.873068
$695$	0	0
$696$	−10.0000	−0.379049
$697$	− 6.00000i	− 0.227266i
$698$	− 14.0000i	− 0.529908i
$699$	−10.0000	−0.378235
$700$	0	0
$701$	18.0000	0.679851	0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000	0.679851	0.339925	+	0.940452i	$0.389598\pi$
$702$	− 2.00000i	− 0.0754851i
$703$	− 3.00000i	− 0.113147i
$704$	5.00000	0.188445
$705$	0	0
$706$	−2.00000	−0.0752710
$707$	− 33.0000i	− 1.24109i
$708$	− 8.00000i	− 0.300658i
$709$	−25.0000	−0.938895	−0.469447	−	0.882960i	$-0.655547\pi$
$709$	−25.0000	−0.938895	−0.469447	+	0.882960i	$0.655547\pi$
$710$	0	0
$711$	5.00000	0.187515
$712$	− 12.0000i	− 0.449719i
$713$	30.0000i	1.12351i
$714$	3.00000	0.112272
$715$	0	0
$716$	−12.0000	−0.448461
$717$	13.0000i	0.485494i
$718$	15.0000i	0.559795i
$719$	−6.00000	−0.223762	−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000	−0.223762	−0.111881	+	0.993722i	$0.535688\pi$
$720$	0	0
$721$	12.0000	0.446903
$722$	18.0000i	0.669891i
$723$	0	0
$724$	17.0000	0.631800
$725$	0	0
$726$	−14.0000	−0.519589
$727$	− 2.00000i	− 0.0741759i	−0.999312	−	0.0370879i	$-0.988192\pi$
$727$	− 2.00000i	− 0.0741759i	0.999312	−	0.0370879i	$-0.0118082\pi$
$728$	− 6.00000i	− 0.222375i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−1.00000	−0.0369863
$732$	− 2.00000i	− 0.0739221i
$733$	− 16.0000i	− 0.590973i	−0.955347	−	0.295487i	$-0.904518\pi$
$733$	− 16.0000i	− 0.590973i	0.955347	−	0.295487i	$-0.0954818\pi$
$734$	−5.00000	−0.184553
$735$	0	0
$736$	6.00000	0.221163
$737$	− 55.0000i	− 2.02595i
$738$	6.00000i	0.220863i
$739$	19.0000	0.698926	0.349463	−	0.936950i	$-0.386364\pi$
$739$	19.0000	0.698926	0.349463	+	0.936950i	$0.386364\pi$
$740$	0	0
$741$	2.00000	0.0734718
$742$	3.00000i	0.110133i
$743$	18.0000i	0.660356i	0.943919	+	0.330178i	$0.107109\pi$
$743$	18.0000i	0.660356i	−0.943919	+	0.330178i	$0.892891\pi$
$744$	5.00000	0.183309
$745$	0	0
$746$	−18.0000	−0.659027
$747$	− 18.0000i	− 0.658586i
$748$	− 5.00000i	− 0.182818i
$749$	15.0000	0.548088
$750$	0	0
$751$	−48.0000	−1.75154	−0.875772	−	0.482724i	$-0.839647\pi$
$751$	−48.0000	−1.75154	−0.875772	+	0.482724i	$0.839647\pi$
$752$	− 3.00000i	− 0.109399i
$753$	18.0000i	0.655956i
$754$	20.0000	0.728357
$755$	0	0
$756$	−3.00000	−0.109109
$757$	− 14.0000i	− 0.508839i	−0.967094	−	0.254419i	$-0.918116\pi$
$757$	− 14.0000i	− 0.508839i	0.967094	−	0.254419i	$-0.0818843\pi$
$758$	− 8.00000i	− 0.290573i
$759$	−30.0000	−1.08893
$760$	0	0
$761$	36.0000	1.30500	0.652499	−	0.757789i	$-0.273720\pi$
$761$	36.0000	1.30500	0.652499	+	0.757789i	$0.273720\pi$
$762$	12.0000i	0.434714i
$763$	15.0000i	0.543036i
$764$	−3.00000	−0.108536
$765$	0	0
$766$	−8.00000	−0.289052
$767$	16.0000i	0.577727i
$768$	− 1.00000i	− 0.0360844i
$769$	37.0000	1.33425	0.667127	−	0.744944i	$-0.267524\pi$
$769$	37.0000	1.33425	0.667127	+	0.744944i	$0.267524\pi$
$770$	0	0
$771$	−2.00000	−0.0720282
$772$	24.0000i	0.863779i
$773$	− 34.0000i	− 1.22290i	−0.791285	−	0.611448i	$-0.790588\pi$
$773$	− 34.0000i	− 1.22290i	0.791285	−	0.611448i	$-0.209412\pi$
$774$	1.00000	0.0359443
$775$	0	0
$776$	−14.0000	−0.502571
$777$	− 9.00000i	− 0.322873i
$778$	− 5.00000i	− 0.179259i
$779$	−6.00000	−0.214972
$780$	0	0
$781$	−30.0000	−1.07348
$782$	− 6.00000i	− 0.214560i
$783$	− 10.0000i	− 0.357371i
$784$	−2.00000	−0.0714286
$785$	0	0
$786$	20.0000	0.713376
$787$	− 18.0000i	− 0.641631i	−0.947142	−	0.320815i	$-0.896043\pi$
$787$	− 18.0000i	− 0.641631i	0.947142	−	0.320815i	$-0.103957\pi$
$788$	12.0000i	0.427482i
$789$	3.00000	0.106803
$790$	0	0
$791$	3.00000	0.106668
$792$	5.00000i	0.177667i
$793$	4.00000i	0.142044i
$794$	−21.0000	−0.745262
$795$	0	0
$796$	17.0000	0.602549
$797$	11.0000i	0.389640i	0.980839	+	0.194820i	$0.0624123\pi$
$797$	11.0000i	0.389640i	−0.980839	+	0.194820i	$0.937588\pi$
$798$	− 3.00000i	− 0.106199i
$799$	−3.00000	−0.106132
$800$	0	0
$801$	12.0000	0.423999
$802$	18.0000i	0.635602i
$803$	60.0000i	2.11735i
$804$	−11.0000	−0.387940
$805$	0	0
$806$	−10.0000	−0.352235
$807$	− 6.00000i	− 0.211210i
$808$	11.0000i	0.386979i
$809$	39.0000	1.37117	0.685583	−	0.727994i	$-0.259547\pi$
$809$	39.0000	1.37117	0.685583	+	0.727994i	$0.259547\pi$
$810$	0	0
$811$	56.0000	1.96643	0.983213	−	0.182462i	$-0.0584065\pi$
$811$	56.0000	1.96643	0.983213	+	0.182462i	$0.0584065\pi$
$812$	− 30.0000i	− 1.05279i
$813$	− 14.0000i	− 0.491001i
$814$	−15.0000	−0.525750
$815$	0	0
$816$	−1.00000	−0.0350070
$817$	1.00000i	0.0349856i
$818$	− 2.00000i	− 0.0699284i
$819$	6.00000	0.209657
$820$	0	0
$821$	54.0000	1.88461	0.942306	−	0.334751i	$-0.108652\pi$
$821$	54.0000	1.88461	0.942306	+	0.334751i	$0.108652\pi$
$822$	16.0000i	0.558064i
$823$	4.00000i	0.139431i	0.997567	+	0.0697156i	$0.0222092\pi$
$823$	4.00000i	0.139431i	−0.997567	+	0.0697156i	$0.977791\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	24.0000	0.835067
$827$	53.0000i	1.84299i	0.388390	+	0.921495i	$0.373032\pi$
$827$	53.0000i	1.84299i	−0.388390	+	0.921495i	$0.626968\pi$
$828$	6.00000i	0.208514i
$829$	30.0000	1.04194	0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000	1.04194	0.520972	+	0.853574i	$0.325570\pi$
$830$	0	0
$831$	31.0000	1.07538
$832$	2.00000i	0.0693375i
$833$	2.00000i	0.0692959i
$834$	8.00000	0.277017
$835$	0	0
$836$	−5.00000	−0.172929
$837$	5.00000i	0.172825i
$838$	24.0000i	0.829066i
$839$	8.00000	0.276191	0.138095	−	0.990419i	$-0.455902\pi$
$839$	8.00000	0.276191	0.138095	+	0.990419i	$0.455902\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	− 18.0000i	− 0.620321i
$843$	30.0000i	1.03325i
$844$	−18.0000	−0.619586
$845$	0	0
$846$	3.00000	0.103142
$847$	− 42.0000i	− 1.44314i
$848$	− 1.00000i	− 0.0343401i
$849$	−14.0000	−0.480479
$850$	0	0
$851$	−18.0000	−0.617032
$852$	6.00000i	0.205557i
$853$	− 37.0000i	− 1.26686i	−0.773802	−	0.633428i	$-0.781647\pi$
$853$	− 37.0000i	− 1.26686i	0.773802	−	0.633428i	$-0.218353\pi$
$854$	6.00000	0.205316
$855$	0	0
$856$	−5.00000	−0.170896
$857$	21.0000i	0.717346i	0.933463	+	0.358673i	$0.116771\pi$
$857$	21.0000i	0.717346i	−0.933463	+	0.358673i	$0.883229\pi$
$858$	− 10.0000i	− 0.341394i
$859$	23.0000	0.784750	0.392375	−	0.919805i	$-0.371654\pi$
$859$	23.0000	0.784750	0.392375	+	0.919805i	$0.371654\pi$
$860$	0	0
$861$	−18.0000	−0.613438
$862$	0	0
$863$	− 33.0000i	− 1.12333i	−0.827364	−	0.561667i	$-0.810160\pi$
$863$	− 33.0000i	− 1.12333i	0.827364	−	0.561667i	$-0.189840\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	21.0000	0.713609
$867$	1.00000i	0.0339618i
$868$	15.0000i	0.509133i
$869$	25.0000	0.848067
$870$	0	0
$871$	22.0000	0.745442
$872$	− 5.00000i	− 0.169321i
$873$	− 14.0000i	− 0.473828i
$874$	−6.00000	−0.202953
$875$	0	0
$876$	12.0000	0.405442
$877$	− 14.0000i	− 0.472746i	−0.971662	−	0.236373i	$-0.924041\pi$
$877$	− 14.0000i	− 0.472746i	0.971662	−	0.236373i	$-0.0759588\pi$
$878$	16.0000i	0.539974i
$879$	−18.0000	−0.607125
$880$	0	0
$881$	−9.00000	−0.303218	−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000	−0.303218	−0.151609	+	0.988441i	$0.548445\pi$
$882$	− 2.00000i	− 0.0673435i
$883$	− 20.0000i	− 0.673054i	−0.941674	−	0.336527i	$-0.890748\pi$
$883$	− 20.0000i	− 0.673054i	0.941674	−	0.336527i	$-0.109252\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	−24.0000	−0.806296
$887$	− 48.0000i	− 1.61168i	−0.592132	−	0.805841i	$-0.701714\pi$
$887$	− 48.0000i	− 1.61168i	0.592132	−	0.805841i	$-0.298286\pi$
$888$	3.00000i	0.100673i
$889$	−36.0000	−1.20740
$890$	0	0
$891$	−5.00000	−0.167506
$892$	− 18.0000i	− 0.602685i
$893$	3.00000i	0.100391i
$894$	−6.00000	−0.200670
$895$	0	0
$896$	3.00000	0.100223
$897$	− 12.0000i	− 0.400668i
$898$	21.0000i	0.700779i
$899$	−50.0000	−1.66759
$900$	0	0
$901$	−1.00000	−0.0333148
$902$	30.0000i	0.998891i
$903$	3.00000i	0.0998337i
$904$	−1.00000	−0.0332595
$905$	0	0
$906$	−8.00000	−0.265782
$907$	30.0000i	0.996134i	0.867139	+	0.498067i	$0.165957\pi$
$907$	30.0000i	0.996134i	−0.867139	+	0.498067i	$0.834043\pi$
$908$	− 27.0000i	− 0.896026i
$909$	−11.0000	−0.364847
$910$	0	0
$911$	56.0000	1.85536	0.927681	−	0.373373i	$-0.121799\pi$
$911$	56.0000	1.85536	0.927681	+	0.373373i	$0.121799\pi$
$912$	1.00000i	0.0331133i
$913$	− 90.0000i	− 2.97857i
$914$	25.0000	0.826927
$915$	0	0
$916$	24.0000	0.792982
$917$	60.0000i	1.98137i
$918$	− 1.00000i	− 0.0330049i
$919$	−44.0000	−1.45143	−0.725713	−	0.687998i	$-0.758490\pi$
$919$	−44.0000	−1.45143	−0.725713	+	0.687998i	$0.758490\pi$
$920$	0	0
$921$	−20.0000	−0.659022
$922$	15.0000i	0.493999i
$923$	− 12.0000i	− 0.394985i
$924$	−15.0000	−0.493464
$925$	0	0
$926$	0	0
$927$	− 4.00000i	− 0.131377i
$928$	10.0000i	0.328266i
$929$	−27.0000	−0.885841	−0.442921	−	0.896561i	$-0.646058\pi$
$929$	−27.0000	−0.885841	−0.442921	+	0.896561i	$0.646058\pi$
$930$	0	0
$931$	2.00000	0.0655474
$932$	10.0000i	0.327561i
$933$	2.00000i	0.0654771i
$934$	−18.0000	−0.588978
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	− 10.0000i	− 0.326686i	−0.986569	−	0.163343i	$-0.947772\pi$
$937$	− 10.0000i	− 0.326686i	0.986569	−	0.163343i	$-0.0522277\pi$
$938$	− 33.0000i	− 1.07749i
$939$	−34.0000	−1.10955
$940$	0	0
$941$	22.0000	0.717180	0.358590	−	0.933495i	$-0.383258\pi$
$941$	22.0000	0.717180	0.358590	+	0.933495i	$0.383258\pi$
$942$	0	0
$943$	36.0000i	1.17232i
$944$	−8.00000	−0.260378
$945$	0	0
$946$	5.00000	0.162564
$947$	− 61.0000i	− 1.98223i	−0.132994	−	0.991117i	$-0.542459\pi$
$947$	− 61.0000i	− 1.98223i	0.132994	−	0.991117i	$-0.457541\pi$
$948$	− 5.00000i	− 0.162392i
$949$	−24.0000	−0.779073
$950$	0	0
$951$	12.0000	0.389127
$952$	− 3.00000i	− 0.0972306i
$953$	− 14.0000i	− 0.453504i	−0.973952	−	0.226752i	$-0.927189\pi$
$953$	− 14.0000i	− 0.453504i	0.973952	−	0.226752i	$-0.0728108\pi$
$954$	1.00000	0.0323762
$955$	0	0
$956$	13.0000	0.420450
$957$	− 50.0000i	− 1.61627i
$958$	26.0000i	0.840022i
$959$	−48.0000	−1.55000
$960$	0	0
$961$	−6.00000	−0.193548
$962$	− 6.00000i	− 0.193448i
$963$	− 5.00000i	− 0.161123i
$964$	0	0
$965$	0	0
$966$	−18.0000	−0.579141
$967$	36.0000i	1.15768i	0.815440	+	0.578841i	$0.196495\pi$
$967$	36.0000i	1.15768i	−0.815440	+	0.578841i	$0.803505\pi$
$968$	14.0000i	0.449977i
$969$	1.00000	0.0321246
$970$	0	0
$971$	−38.0000	−1.21948	−0.609739	−	0.792602i	$-0.708726\pi$
$971$	−38.0000	−1.21948	−0.609739	+	0.792602i	$0.708726\pi$
$972$	1.00000i	0.0320750i
$973$	24.0000i	0.769405i
$974$	40.0000	1.28168
$975$	0	0
$976$	−2.00000	−0.0640184
$977$	10.0000i	0.319928i	0.987123	+	0.159964i	$0.0511379\pi$
$977$	10.0000i	0.319928i	−0.987123	+	0.159964i	$0.948862\pi$
$978$	0	0
$979$	60.0000	1.91761
$980$	0	0
$981$	5.00000	0.159638
$982$	− 4.00000i	− 0.127645i
$983$	− 6.00000i	− 0.191370i	−0.995412	−	0.0956851i	$-0.969496\pi$
$983$	− 6.00000i	− 0.191370i	0.995412	−	0.0956851i	$-0.0305042\pi$
$984$	6.00000	0.191273
$985$	0	0
$986$	10.0000	0.318465
$987$	9.00000i	0.286473i
$988$	− 2.00000i	− 0.0636285i
$989$	6.00000	0.190789
$990$	0	0
$991$	52.0000	1.65183	0.825917	−	0.563791i	$-0.190658\pi$
$991$	52.0000	1.65183	0.825917	+	0.563791i	$0.190658\pi$
$992$	− 5.00000i	− 0.158750i
$993$	25.0000i	0.793351i
$994$	−18.0000	−0.570925
$995$	0	0
$996$	−18.0000	−0.570352
$997$	43.0000i	1.36182i	0.732365	+	0.680912i	$0.238416\pi$
$997$	43.0000i	1.36182i	−0.732365	+	0.680912i	$0.761584\pi$
$998$	22.0000i	0.696398i
$999$	−3.00000	−0.0949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2550.2.d.a.2449.1		2
5.2	odd	4		2550.2.a.z.1.1	yes	1
5.3	odd	4		2550.2.a.h.1.1	✓	1
5.4	even	2	inner	2550.2.d.a.2449.2		2
15.2	even	4		7650.2.a.be.1.1		1
15.8	even	4		7650.2.a.bl.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2550.2.a.h.1.1	✓	1	5.3	odd	4
2550.2.a.z.1.1	yes	1	5.2	odd	4
2550.2.d.a.2449.1		2	1.1	even	1	trivial
2550.2.d.a.2449.2		2	5.4	even	2	inner
7650.2.a.be.1.1		1	15.2	even	4
7650.2.a.bl.1.1		1	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2550.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -5.00000 q^{11} +1.00000i q^{12} -2.00000i q^{13} -3.00000 q^{14} +1.00000 q^{16} -1.00000i q^{17} +1.00000i q^{18} -1.00000 q^{19} -3.00000 q^{21} +5.00000i q^{22} +6.00000i q^{23} +1.00000 q^{24} -2.00000 q^{26} +1.00000i q^{27} +3.00000i q^{28} -10.0000 q^{29} +5.00000 q^{31} -1.00000i q^{32} +5.00000i q^{33} -1.00000 q^{34} +1.00000 q^{36} +3.00000i q^{37} +1.00000i q^{38} -2.00000 q^{39} +6.00000 q^{41} +3.00000i q^{42} -1.00000i q^{43} +5.00000 q^{44} +6.00000 q^{46} -3.00000i q^{47} -1.00000i q^{48} -2.00000 q^{49} -1.00000 q^{51} +2.00000i q^{52} -1.00000i q^{53} +1.00000 q^{54} +3.00000 q^{56} +1.00000i q^{57} +10.0000i q^{58} -8.00000 q^{59} -2.00000 q^{61} -5.00000i q^{62} +3.00000i q^{63} -1.00000 q^{64} +5.00000 q^{66} +11.0000i q^{67} +1.00000i q^{68} +6.00000 q^{69} +6.00000 q^{71} -1.00000i q^{72} -12.0000i q^{73} +3.00000 q^{74} +1.00000 q^{76} +15.0000i q^{77} +2.00000i q^{78} -5.00000 q^{79} +1.00000 q^{81} -6.00000i q^{82} +18.0000i q^{83} +3.00000 q^{84} -1.00000 q^{86} +10.0000i q^{87} -5.00000i q^{88} -12.0000 q^{89} -6.00000 q^{91} -6.00000i q^{92} -5.00000i q^{93} -3.00000 q^{94} -1.00000 q^{96} +14.0000i q^{97} +2.00000i q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9} - 10 q^{11} - 6 q^{14} + 2 q^{16} - 2 q^{19} - 6 q^{21} + 2 q^{24} - 4 q^{26} - 20 q^{29} + 10 q^{31} - 2 q^{34} + 2 q^{36} - 4 q^{39} + 12 q^{41} + 10 q^{44} + 12 q^{46} - 4 q^{49} - 2 q^{51} + 2 q^{54} + 6 q^{56} - 16 q^{59} - 4 q^{61} - 2 q^{64} + 10 q^{66} + 12 q^{69} + 12 q^{71} + 6 q^{74} + 2 q^{76} - 10 q^{79} + 2 q^{81} + 6 q^{84} - 2 q^{86} - 24 q^{89} - 12 q^{91} - 6 q^{94} - 2 q^{96} + 10 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9 - 10 * q^11 - 6 * q^14 + 2 * q^16 - 2 * q^19 - 6 * q^21 + 2 * q^24 - 4 * q^26 - 20 * q^29 + 10 * q^31 - 2 * q^34 + 2 * q^36 - 4 * q^39 + 12 * q^41 + 10 * q^44 + 12 * q^46 - 4 * q^49 - 2 * q^51 + 2 * q^54 + 6 * q^56 - 16 * q^59 - 4 * q^61 - 2 * q^64 + 10 * q^66 + 12 * q^69 + 12 * q^71 + 6 * q^74 + 2 * q^76 - 10 * q^79 + 2 * q^81 + 6 * q^84 - 2 * q^86 - 24 * q^89 - 12 * q^91 - 6 * q^94 - 2 * q^96 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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