LMFDB - Embedded newform 1450.2.b.g.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(349,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1450.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 9 $ x^4 + 7*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.3
Root			$-1.30278i$ of defining polynomial
Character	$\chi$	$=$	1450.349
Dual form			1450.2.b.g.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.30278i q^{3} -1.00000 q^{4} +1.30278 q^{6} -4.30278i q^{7} -1.00000i q^{8} +1.30278 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.30278i q^{3} -1.00000 q^{4} +1.30278 q^{6} -4.30278i q^{7} -1.00000i q^{8} +1.30278 q^{9} -4.60555 q^{11} +1.30278i q^{12} +2.69722i q^{13} +4.30278 q^{14} +1.00000 q^{16} -6.90833i q^{17} +1.30278i q^{18} -6.60555 q^{19} -5.60555 q^{21} -4.60555i q^{22} +5.30278i q^{23} -1.30278 q^{24} -2.69722 q^{26} -5.60555i q^{27} +4.30278i q^{28} -1.00000 q^{29} +2.90833 q^{31} +1.00000i q^{32} +6.00000i q^{33} +6.90833 q^{34} -1.30278 q^{36} +11.8167i q^{37} -6.60555i q^{38} +3.51388 q^{39} -1.39445 q^{41} -5.60555i q^{42} -0.302776i q^{43} +4.60555 q^{44} -5.30278 q^{46} -1.30278i q^{48} -11.5139 q^{49} -9.00000 q^{51} -2.69722i q^{52} +6.90833i q^{53} +5.60555 q^{54} -4.30278 q^{56} +8.60555i q^{57} -1.00000i q^{58} -9.90833 q^{59} -13.9083 q^{61} +2.90833i q^{62} -5.60555i q^{63} -1.00000 q^{64} -6.00000 q^{66} -5.21110i q^{67} +6.90833i q^{68} +6.90833 q^{69} -1.30278i q^{72} -15.5139i q^{73} -11.8167 q^{74} +6.60555 q^{76} +19.8167i q^{77} +3.51388i q^{78} -5.90833 q^{79} -3.39445 q^{81} -1.39445i q^{82} -1.39445i q^{83} +5.60555 q^{84} +0.302776 q^{86} +1.30278i q^{87} +4.60555i q^{88} +7.39445 q^{89} +11.6056 q^{91} -5.30278i q^{92} -3.78890i q^{93} +1.30278 q^{96} -11.9083i q^{97} -11.5139i q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9	$ 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9} - 4 q^{11} + 10 q^{14} + 4 q^{16} - 12 q^{19} - 8 q^{21} + 2 q^{24} - 18 q^{26} - 4 q^{29} - 10 q^{31} + 6 q^{34} + 2 q^{36} - 22 q^{39} - 20 q^{41} + 4 q^{44} - 14 q^{46} - 10 q^{49} - 36 q^{51} + 8 q^{54} - 10 q^{56} - 18 q^{59} - 34 q^{61} - 4 q^{64} - 24 q^{66} + 6 q^{69} - 4 q^{74} + 12 q^{76} - 2 q^{79} - 28 q^{81} + 8 q^{84} - 6 q^{86} + 44 q^{89} + 32 q^{91} - 2 q^{96} - 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9 - 4 * q^11 + 10 * q^14 + 4 * q^16 - 12 * q^19 - 8 * q^21 + 2 * q^24 - 18 * q^26 - 4 * q^29 - 10 * q^31 + 6 * q^34 + 2 * q^36 - 22 * q^39 - 20 * q^41 + 4 * q^44 - 14 * q^46 - 10 * q^49 - 36 * q^51 + 8 * q^54 - 10 * q^56 - 18 * q^59 - 34 * q^61 - 4 * q^64 - 24 * q^66 + 6 * q^69 - 4 * q^74 + 12 * q^76 - 2 * q^79 - 28 * q^81 + 8 * q^84 - 6 * q^86 + 44 * q^89 + 32 * q^91 - 2 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	− 1.30278i	− 0.752158i	−0.926588	−	0.376079i	$-0.877272\pi$
$3$	− 1.30278i	− 0.752158i	0.926588	−	0.376079i	$-0.122728\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.30278	0.531856
$7$	− 4.30278i	− 1.62630i	−0.582057	−	0.813148i	$-0.697752\pi$
$7$	− 4.30278i	− 1.62630i	0.582057	−	0.813148i	$-0.302248\pi$
$8$	− 1.00000i	− 0.353553i
$9$	1.30278	0.434259
$10$	0	0
$11$	−4.60555	−1.38863	−0.694313	−	0.719673i	$-0.744292\pi$
$11$	−4.60555	−1.38863	−0.694313	+	0.719673i	$0.744292\pi$
$12$	1.30278i	0.376079i
$13$	2.69722i	0.748075i	0.927413	+	0.374038i	$0.122027\pi$
$13$	2.69722i	0.748075i	−0.927413	+	0.374038i	$0.877973\pi$
$14$	4.30278	1.14997
$15$	0	0
$16$	1.00000	0.250000
$17$	− 6.90833i	− 1.67552i	−0.546042	−	0.837758i	$-0.683866\pi$
$17$	− 6.90833i	− 1.67552i	0.546042	−	0.837758i	$-0.316134\pi$
$18$	1.30278i	0.307067i
$19$	−6.60555	−1.51542	−0.757709	−	0.652593i	$-0.773681\pi$
$19$	−6.60555	−1.51542	−0.757709	+	0.652593i	$0.773681\pi$
$20$	0	0
$21$	−5.60555	−1.22323
$22$	− 4.60555i	− 0.981907i
$23$	5.30278i	1.10571i	0.833279	+	0.552853i	$0.186461\pi$
$23$	5.30278i	1.10571i	−0.833279	+	0.552853i	$0.813539\pi$
$24$	−1.30278	−0.265928
$25$	0	0
$26$	−2.69722	−0.528969
$27$	− 5.60555i	− 1.07879i
$28$	4.30278i	0.813148i
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	2.90833	0.522351	0.261175	−	0.965291i	$-0.415890\pi$
$31$	2.90833	0.522351	0.261175	+	0.965291i	$0.415890\pi$
$32$	1.00000i	0.176777i
$33$	6.00000i	1.04447i
$34$	6.90833	1.18477
$35$	0	0
$36$	−1.30278	−0.217129
$37$	11.8167i	1.94265i	0.237764	+	0.971323i	$0.423586\pi$
$37$	11.8167i	1.94265i	−0.237764	+	0.971323i	$0.576414\pi$
$38$	− 6.60555i	− 1.07156i
$39$	3.51388	0.562671
$40$	0	0
$41$	−1.39445	−0.217776	−0.108888	−	0.994054i	$-0.534729\pi$
$41$	−1.39445	−0.217776	−0.108888	+	0.994054i	$0.534729\pi$
$42$	− 5.60555i	− 0.864955i
$43$	− 0.302776i	− 0.0461729i	−0.999733	−	0.0230864i	$-0.992651\pi$
$43$	− 0.302776i	− 0.0461729i	0.999733	−	0.0230864i	$-0.00734929\pi$
$44$	4.60555	0.694313
$45$	0	0
$46$	−5.30278	−0.781852
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	− 1.30278i	− 0.188039i
$49$	−11.5139	−1.64484
$50$	0	0
$51$	−9.00000	−1.26025
$52$	− 2.69722i	− 0.374038i
$53$	6.90833i	0.948932i	0.880274	+	0.474466i	$0.157359\pi$
$53$	6.90833i	0.948932i	−0.880274	+	0.474466i	$0.842641\pi$
$54$	5.60555	0.762819
$55$	0	0
$56$	−4.30278	−0.574983
$57$	8.60555i	1.13983i
$58$	− 1.00000i	− 0.131306i
$59$	−9.90833	−1.28995	−0.644977	−	0.764202i	$-0.723133\pi$
$59$	−9.90833	−1.28995	−0.644977	+	0.764202i	$0.723133\pi$
$60$	0	0
$61$	−13.9083	−1.78078	−0.890389	−	0.455200i	$-0.849568\pi$
$61$	−13.9083	−1.78078	−0.890389	+	0.455200i	$0.849568\pi$
$62$	2.90833i	0.369358i
$63$	− 5.60555i	− 0.706233i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−6.00000	−0.738549
$67$	− 5.21110i	− 0.636638i	−0.947984	−	0.318319i	$-0.896882\pi$
$67$	− 5.21110i	− 0.636638i	0.947984	−	0.318319i	$-0.103118\pi$
$68$	6.90833i	0.837758i
$69$	6.90833	0.831665
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	− 1.30278i	− 0.153534i
$73$	− 15.5139i	− 1.81576i	−0.419228	−	0.907881i	$-0.637699\pi$
$73$	− 15.5139i	− 1.81576i	0.419228	−	0.907881i	$-0.362301\pi$
$74$	−11.8167	−1.37366
$75$	0	0
$76$	6.60555	0.757709
$77$	19.8167i	2.25832i
$78$	3.51388i	0.397868i
$79$	−5.90833	−0.664739	−0.332369	−	0.943149i	$-0.607848\pi$
$79$	−5.90833	−0.664739	−0.332369	+	0.943149i	$0.607848\pi$
$80$	0	0
$81$	−3.39445	−0.377161
$82$	− 1.39445i	− 0.153991i
$83$	− 1.39445i	− 0.153061i	−0.997067	−	0.0765303i	$-0.975616\pi$
$83$	− 1.39445i	− 0.153061i	0.997067	−	0.0765303i	$-0.0243842\pi$
$84$	5.60555	0.611616
$85$	0	0
$86$	0.302776	0.0326491
$87$	1.30278i	0.139672i
$88$	4.60555i	0.490953i
$89$	7.39445	0.783810	0.391905	−	0.920006i	$-0.371816\pi$
$89$	7.39445	0.783810	0.391905	+	0.920006i	$0.371816\pi$
$90$	0	0
$91$	11.6056	1.21659
$92$	− 5.30278i	− 0.552853i
$93$	− 3.78890i	− 0.392890i
$94$	0	0
$95$	0	0
$96$	1.30278	0.132964
$97$	− 11.9083i	− 1.20911i	−0.796564	−	0.604554i	$-0.793351\pi$
$97$	− 11.9083i	− 1.20911i	0.796564	−	0.604554i	$-0.206649\pi$
$98$	− 11.5139i	− 1.16308i
$99$	−6.00000	−0.603023
$100$	0	0
$101$	−2.09167	−0.208129	−0.104065	−	0.994571i	$-0.533185\pi$
$101$	−2.09167	−0.208129	−0.104065	+	0.994571i	$0.533185\pi$
$102$	− 9.00000i	− 0.891133i
$103$	− 10.4222i	− 1.02693i	−0.858110	−	0.513465i	$-0.828362\pi$
$103$	− 10.4222i	− 1.02693i	0.858110	−	0.513465i	$-0.171638\pi$
$104$	2.69722	0.264485
$105$	0	0
$106$	−6.90833	−0.670996
$107$	− 1.39445i	− 0.134806i	−0.997726	−	0.0674032i	$-0.978529\pi$
$107$	− 1.39445i	− 0.134806i	0.997726	−	0.0674032i	$-0.0214714\pi$
$108$	5.60555i	0.539394i
$109$	14.6056	1.39896	0.699479	−	0.714653i	$-0.253415\pi$
$109$	14.6056	1.39896	0.699479	+	0.714653i	$0.253415\pi$
$110$	0	0
$111$	15.3944	1.46118
$112$	− 4.30278i	− 0.406574i
$113$	6.69722i	0.630022i	0.949088	+	0.315011i	$0.102008\pi$
$113$	6.69722i	0.630022i	−0.949088	+	0.315011i	$0.897992\pi$
$114$	−8.60555	−0.805984
$115$	0	0
$116$	1.00000	0.0928477
$117$	3.51388i	0.324858i
$118$	− 9.90833i	− 0.912135i
$119$	−29.7250	−2.72488
$120$	0	0
$121$	10.2111	0.928282
$122$	− 13.9083i	− 1.25920i
$123$	1.81665i	0.163802i
$124$	−2.90833	−0.261175
$125$	0	0
$126$	5.60555	0.499382
$127$	− 20.0000i	− 1.77471i	−0.461084	−	0.887357i	$-0.652539\pi$
$127$	− 20.0000i	− 1.77471i	0.461084	−	0.887357i	$-0.347461\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−0.394449	−0.0347293
$130$	0	0
$131$	−21.6333	−1.89011	−0.945055	−	0.326910i	$-0.893993\pi$
$131$	−21.6333	−1.89011	−0.945055	+	0.326910i	$0.893993\pi$
$132$	− 6.00000i	− 0.522233i
$133$	28.4222i	2.46452i
$134$	5.21110	0.450171
$135$	0	0
$136$	−6.90833	−0.592384
$137$	8.09167i	0.691318i	0.938360	+	0.345659i	$0.112345\pi$
$137$	8.09167i	0.691318i	−0.938360	+	0.345659i	$0.887655\pi$
$138$	6.90833i	0.588076i
$139$	−10.3028	−0.873870	−0.436935	−	0.899493i	$-0.643936\pi$
$139$	−10.3028	−0.873870	−0.436935	+	0.899493i	$0.643936\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	− 12.4222i	− 1.03880i
$144$	1.30278	0.108565
$145$	0	0
$146$	15.5139	1.28394
$147$	15.0000i	1.23718i
$148$	− 11.8167i	− 0.971323i
$149$	1.81665	0.148826	0.0744130	−	0.997228i	$-0.476292\pi$
$149$	1.81665	0.148826	0.0744130	+	0.997228i	$0.476292\pi$
$150$	0	0
$151$	−2.60555	−0.212037	−0.106018	−	0.994364i	$-0.533810\pi$
$151$	−2.60555	−0.212037	−0.106018	+	0.994364i	$0.533810\pi$
$152$	6.60555i	0.535781i
$153$	− 9.00000i	− 0.727607i
$154$	−19.8167	−1.59687
$155$	0	0
$156$	−3.51388	−0.281335
$157$	− 20.4222i	− 1.62987i	−0.579553	−	0.814935i	$-0.696773\pi$
$157$	− 20.4222i	− 1.62987i	0.579553	−	0.814935i	$-0.303227\pi$
$158$	− 5.90833i	− 0.470041i
$159$	9.00000	0.713746
$160$	0	0
$161$	22.8167	1.79820
$162$	− 3.39445i	− 0.266693i
$163$	− 6.78890i	− 0.531747i	−0.964008	−	0.265874i	$-0.914340\pi$
$163$	− 6.78890i	− 0.531747i	0.964008	−	0.265874i	$-0.0856604\pi$
$164$	1.39445	0.108888
$165$	0	0
$166$	1.39445	0.108230
$167$	3.69722i	0.286100i	0.989715	+	0.143050i	$0.0456909\pi$
$167$	3.69722i	0.286100i	−0.989715	+	0.143050i	$0.954309\pi$
$168$	5.60555i	0.432478i
$169$	5.72498	0.440383
$170$	0	0
$171$	−8.60555	−0.658083
$172$	0.302776i	0.0230864i
$173$	8.09167i	0.615199i	0.951516	+	0.307599i	$0.0995256\pi$
$173$	8.09167i	0.615199i	−0.951516	+	0.307599i	$0.900474\pi$
$174$	−1.30278	−0.0987632
$175$	0	0
$176$	−4.60555	−0.347156
$177$	12.9083i	0.970249i
$178$	7.39445i	0.554237i
$179$	9.90833	0.740583	0.370292	−	0.928916i	$-0.379258\pi$
$179$	9.90833	0.740583	0.370292	+	0.928916i	$0.379258\pi$
$180$	0	0
$181$	−5.39445	−0.400966	−0.200483	−	0.979697i	$-0.564251\pi$
$181$	−5.39445	−0.400966	−0.200483	+	0.979697i	$0.564251\pi$
$182$	11.6056i	0.860261i
$183$	18.1194i	1.33943i
$184$	5.30278	0.390926
$185$	0	0
$186$	3.78890	0.277815
$187$	31.8167i	2.32666i
$188$	0	0
$189$	−24.1194	−1.75443
$190$	0	0
$191$	5.09167	0.368421	0.184210	−	0.982887i	$-0.441027\pi$
$191$	5.09167	0.368421	0.184210	+	0.982887i	$0.441027\pi$
$192$	1.30278i	0.0940197i
$193$	7.72498i	0.556056i	0.960573	+	0.278028i	$0.0896809\pi$
$193$	7.72498i	0.556056i	−0.960573	+	0.278028i	$0.910319\pi$
$194$	11.9083	0.854968
$195$	0	0
$196$	11.5139	0.822420
$197$	− 6.90833i	− 0.492198i	−0.969245	−	0.246099i	$-0.920851\pi$
$197$	− 6.90833i	− 0.492198i	0.969245	−	0.246099i	$-0.0791488\pi$
$198$	− 6.00000i	− 0.426401i
$199$	17.8167	1.26299	0.631495	−	0.775380i	$-0.282442\pi$
$199$	17.8167	1.26299	0.631495	+	0.775380i	$0.282442\pi$
$200$	0	0
$201$	−6.78890	−0.478852
$202$	− 2.09167i	− 0.147170i
$203$	4.30278i	0.301996i
$204$	9.00000	0.630126
$205$	0	0
$206$	10.4222	0.726149
$207$	6.90833i	0.480162i
$208$	2.69722i	0.187019i
$209$	30.4222	2.10435
$210$	0	0
$211$	6.18335	0.425679	0.212840	−	0.977087i	$-0.431729\pi$
$211$	6.18335	0.425679	0.212840	+	0.977087i	$0.431729\pi$
$212$	− 6.90833i	− 0.474466i
$213$	0	0
$214$	1.39445	0.0953226
$215$	0	0
$216$	−5.60555	−0.381409
$217$	− 12.5139i	− 0.849497i
$218$	14.6056i	0.989213i
$219$	−20.2111	−1.36574
$220$	0	0
$221$	18.6333	1.25341
$222$	15.3944i	1.03321i
$223$	10.5139i	0.704061i	0.935988	+	0.352031i	$0.114509\pi$
$223$	10.5139i	0.704061i	−0.935988	+	0.352031i	$0.885491\pi$
$224$	4.30278	0.287491
$225$	0	0
$226$	−6.69722	−0.445493
$227$	− 15.2111i	− 1.00960i	−0.863237	−	0.504798i	$-0.831567\pi$
$227$	− 15.2111i	− 1.00960i	0.863237	−	0.504798i	$-0.168433\pi$
$228$	− 8.60555i	− 0.569917i
$229$	4.90833	0.324351	0.162176	−	0.986762i	$-0.448149\pi$
$229$	4.90833	0.324351	0.162176	+	0.986762i	$0.448149\pi$
$230$	0	0
$231$	25.8167	1.69861
$232$	1.00000i	0.0656532i
$233$	8.78890i	0.575780i	0.957664	+	0.287890i	$0.0929537\pi$
$233$	8.78890i	0.575780i	−0.957664	+	0.287890i	$0.907046\pi$
$234$	−3.51388	−0.229709
$235$	0	0
$236$	9.90833	0.644977
$237$	7.69722i	0.499988i
$238$	− 29.7250i	− 1.92678i
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	0	0
$241$	−3.30278	−0.212750	−0.106375	−	0.994326i	$-0.533924\pi$
$241$	−3.30278	−0.212750	−0.106375	+	0.994326i	$0.533924\pi$
$242$	10.2111i	0.656395i
$243$	− 12.3944i	− 0.795104i
$244$	13.9083	0.890389
$245$	0	0
$246$	−1.81665	−0.115826
$247$	− 17.8167i	− 1.13365i
$248$	− 2.90833i	− 0.184679i
$249$	−1.81665	−0.115126
$250$	0	0
$251$	−1.39445	−0.0880168	−0.0440084	−	0.999031i	$-0.514013\pi$
$251$	−1.39445	−0.0880168	−0.0440084	+	0.999031i	$0.514013\pi$
$252$	5.60555i	0.353117i
$253$	− 24.4222i	− 1.53541i
$254$	20.0000	1.25491
$255$	0	0
$256$	1.00000	0.0625000
$257$	29.0278i	1.81070i	0.424664	+	0.905351i	$0.360392\pi$
$257$	29.0278i	1.81070i	−0.424664	+	0.905351i	$0.639608\pi$
$258$	− 0.394449i	− 0.0245573i
$259$	50.8444	3.15932
$260$	0	0
$261$	−1.30278	−0.0806398
$262$	− 21.6333i	− 1.33651i
$263$	− 9.21110i	− 0.567981i	−0.958827	−	0.283990i	$-0.908342\pi$
$263$	− 9.21110i	− 0.567981i	0.958827	−	0.283990i	$-0.0916584\pi$
$264$	6.00000	0.369274
$265$	0	0
$266$	−28.4222	−1.74268
$267$	− 9.63331i	− 0.589549i
$268$	5.21110i	0.318319i
$269$	−5.51388	−0.336187	−0.168094	−	0.985771i	$-0.553761\pi$
$269$	−5.51388	−0.336187	−0.168094	+	0.985771i	$0.553761\pi$
$270$	0	0
$271$	−1.21110	−0.0735692	−0.0367846	−	0.999323i	$-0.511712\pi$
$271$	−1.21110	−0.0735692	−0.0367846	+	0.999323i	$0.511712\pi$
$272$	− 6.90833i	− 0.418879i
$273$	− 15.1194i	− 0.915069i
$274$	−8.09167	−0.488836
$275$	0	0
$276$	−6.90833	−0.415832
$277$	− 14.0000i	− 0.841178i	−0.907251	−	0.420589i	$-0.861823\pi$
$277$	− 14.0000i	− 0.841178i	0.907251	−	0.420589i	$-0.138177\pi$
$278$	− 10.3028i	− 0.617919i
$279$	3.78890	0.226835
$280$	0	0
$281$	−10.1194	−0.603675	−0.301837	−	0.953359i	$-0.597600\pi$
$281$	−10.1194	−0.603675	−0.301837	+	0.953359i	$0.597600\pi$
$282$	0	0
$283$	− 21.0278i	− 1.24997i	−0.780637	−	0.624985i	$-0.785105\pi$
$283$	− 21.0278i	− 1.24997i	0.780637	−	0.624985i	$-0.214895\pi$
$284$	0	0
$285$	0	0
$286$	12.4222	0.734540
$287$	6.00000i	0.354169i
$288$	1.30278i	0.0767668i
$289$	−30.7250	−1.80735
$290$	0	0
$291$	−15.5139	−0.909440
$292$	15.5139i	0.907881i
$293$	4.18335i	0.244394i	0.992506	+	0.122197i	$0.0389939\pi$
$293$	4.18335i	0.244394i	−0.992506	+	0.122197i	$0.961006\pi$
$294$	−15.0000	−0.874818
$295$	0	0
$296$	11.8167	0.686829
$297$	25.8167i	1.49803i
$298$	1.81665i	0.105236i
$299$	−14.3028	−0.827151
$300$	0	0
$301$	−1.30278	−0.0750907
$302$	− 2.60555i	− 0.149933i
$303$	2.72498i	0.156546i
$304$	−6.60555	−0.378854
$305$	0	0
$306$	9.00000	0.514496
$307$	13.2111i	0.753997i	0.926214	+	0.376999i	$0.123044\pi$
$307$	13.2111i	0.753997i	−0.926214	+	0.376999i	$0.876956\pi$
$308$	− 19.8167i	− 1.12916i
$309$	−13.5778	−0.772414
$310$	0	0
$311$	14.0917	0.799065	0.399533	−	0.916719i	$-0.369172\pi$
$311$	14.0917	0.799065	0.399533	+	0.916719i	$0.369172\pi$
$312$	− 3.51388i	− 0.198934i
$313$	− 28.4222i	− 1.60652i	−0.595630	−	0.803259i	$-0.703097\pi$
$313$	− 28.4222i	− 1.60652i	0.595630	−	0.803259i	$-0.296903\pi$
$314$	20.4222	1.15249
$315$	0	0
$316$	5.90833	0.332369
$317$	− 11.0278i	− 0.619381i	−0.950837	−	0.309690i	$-0.899775\pi$
$317$	− 11.0278i	− 0.619381i	0.950837	−	0.309690i	$-0.100225\pi$
$318$	9.00000i	0.504695i
$319$	4.60555	0.257861
$320$	0	0
$321$	−1.81665	−0.101396
$322$	22.8167i	1.27152i
$323$	45.6333i	2.53911i
$324$	3.39445	0.188580
$325$	0	0
$326$	6.78890	0.376002
$327$	− 19.0278i	− 1.05224i
$328$	1.39445i	0.0769956i
$329$	0	0
$330$	0	0
$331$	15.3944	0.846155	0.423078	−	0.906093i	$-0.360950\pi$
$331$	15.3944	0.846155	0.423078	+	0.906093i	$0.360950\pi$
$332$	1.39445i	0.0765303i
$333$	15.3944i	0.843611i
$334$	−3.69722	−0.202303
$335$	0	0
$336$	−5.60555	−0.305808
$337$	1.69722i	0.0924537i	0.998931	+	0.0462269i	$0.0147197\pi$
$337$	1.69722i	0.0924537i	−0.998931	+	0.0462269i	$0.985280\pi$
$338$	5.72498i	0.311398i
$339$	8.72498	0.473876
$340$	0	0
$341$	−13.3944	−0.725350
$342$	− 8.60555i	− 0.465335i
$343$	19.4222i	1.04870i
$344$	−0.302776	−0.0163246
$345$	0	0
$346$	−8.09167	−0.435011
$347$	7.81665i	0.419620i	0.977742	+	0.209810i	$0.0672845\pi$
$347$	7.81665i	0.419620i	−0.977742	+	0.209810i	$0.932715\pi$
$348$	− 1.30278i	− 0.0698361i
$349$	−8.00000	−0.428230	−0.214115	−	0.976808i	$-0.568687\pi$
$349$	−8.00000	−0.428230	−0.214115	+	0.976808i	$0.568687\pi$
$350$	0	0
$351$	15.1194	0.807015
$352$	− 4.60555i	− 0.245477i
$353$	2.78890i	0.148438i	0.997242	+	0.0742190i	$0.0236464\pi$
$353$	2.78890i	0.148438i	−0.997242	+	0.0742190i	$0.976354\pi$
$354$	−12.9083	−0.686070
$355$	0	0
$356$	−7.39445	−0.391905
$357$	38.7250i	2.04954i
$358$	9.90833i	0.523671i
$359$	15.4861	0.817326	0.408663	−	0.912685i	$-0.365995\pi$
$359$	15.4861	0.817326	0.408663	+	0.912685i	$0.365995\pi$
$360$	0	0
$361$	24.6333	1.29649
$362$	− 5.39445i	− 0.283526i
$363$	− 13.3028i	− 0.698215i
$364$	−11.6056	−0.608296
$365$	0	0
$366$	−18.1194	−0.947118
$367$	17.3944i	0.907983i	0.891006	+	0.453991i	$0.150000\pi$
$367$	17.3944i	0.907983i	−0.891006	+	0.453991i	$0.850000\pi$
$368$	5.30278i	0.276426i
$369$	−1.81665	−0.0945712
$370$	0	0
$371$	29.7250	1.54324
$372$	3.78890i	0.196445i
$373$	− 21.0917i	− 1.09209i	−0.837757	−	0.546043i	$-0.816134\pi$
$373$	− 21.0917i	− 1.09209i	0.837757	−	0.546043i	$-0.183866\pi$
$374$	−31.8167	−1.64520
$375$	0	0
$376$	0	0
$377$	− 2.69722i	− 0.138914i
$378$	− 24.1194i	− 1.24057i
$379$	23.3944	1.20169	0.600846	−	0.799365i	$-0.294830\pi$
$379$	23.3944	1.20169	0.600846	+	0.799365i	$0.294830\pi$
$380$	0	0
$381$	−26.0555	−1.33486
$382$	5.09167i	0.260513i
$383$	8.30278i	0.424252i	0.977242	+	0.212126i	$0.0680387\pi$
$383$	8.30278i	0.424252i	−0.977242	+	0.212126i	$0.931961\pi$
$384$	−1.30278	−0.0664820
$385$	0	0
$386$	−7.72498	−0.393191
$387$	− 0.394449i	− 0.0200510i
$388$	11.9083i	0.604554i
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	0	0
$391$	36.6333	1.85263
$392$	11.5139i	0.581539i
$393$	28.1833i	1.42166i
$394$	6.90833	0.348036
$395$	0	0
$396$	6.00000	0.301511
$397$	− 1.09167i	− 0.0547895i	−0.999625	−	0.0273948i	$-0.991279\pi$
$397$	− 1.09167i	− 0.0547895i	0.999625	−	0.0273948i	$-0.00872111\pi$
$398$	17.8167i	0.893068i
$399$	37.0278	1.85371
$400$	0	0
$401$	24.6972	1.23332	0.616660	−	0.787229i	$-0.288485\pi$
$401$	24.6972	1.23332	0.616660	+	0.787229i	$0.288485\pi$
$402$	− 6.78890i	− 0.338599i
$403$	7.84441i	0.390758i
$404$	2.09167	0.104065
$405$	0	0
$406$	−4.30278	−0.213543
$407$	− 54.4222i	− 2.69761i
$408$	9.00000i	0.445566i
$409$	−5.21110	−0.257672	−0.128836	−	0.991666i	$-0.541124\pi$
$409$	−5.21110	−0.257672	−0.128836	+	0.991666i	$0.541124\pi$
$410$	0	0
$411$	10.5416	0.519980
$412$	10.4222i	0.513465i
$413$	42.6333i	2.09785i
$414$	−6.90833	−0.339526
$415$	0	0
$416$	−2.69722	−0.132242
$417$	13.4222i	0.657288i
$418$	30.4222i	1.48800i
$419$	−16.1194	−0.787486	−0.393743	−	0.919221i	$-0.628820\pi$
$419$	−16.1194	−0.787486	−0.393743	+	0.919221i	$0.628820\pi$
$420$	0	0
$421$	17.6333	0.859395	0.429697	−	0.902973i	$-0.358620\pi$
$421$	17.6333	0.859395	0.429697	+	0.902973i	$0.358620\pi$
$422$	6.18335i	0.301001i
$423$	0	0
$424$	6.90833	0.335498
$425$	0	0
$426$	0	0
$427$	59.8444i	2.89607i
$428$	1.39445i	0.0674032i
$429$	−16.1833	−0.781339
$430$	0	0
$431$	−38.2389	−1.84190	−0.920951	−	0.389680i	$-0.872586\pi$
$431$	−38.2389	−1.84190	−0.920951	+	0.389680i	$0.872586\pi$
$432$	− 5.60555i	− 0.269697i
$433$	− 0.788897i	− 0.0379120i	−0.999820	−	0.0189560i	$-0.993966\pi$
$433$	− 0.788897i	− 0.0379120i	0.999820	−	0.0189560i	$-0.00603424\pi$
$434$	12.5139	0.600685
$435$	0	0
$436$	−14.6056	−0.699479
$437$	− 35.0278i	− 1.67560i
$438$	− 20.2111i	− 0.965724i
$439$	−5.63331	−0.268863	−0.134432	−	0.990923i	$-0.542921\pi$
$439$	−5.63331	−0.268863	−0.134432	+	0.990923i	$0.542921\pi$
$440$	0	0
$441$	−15.0000	−0.714286
$442$	18.6333i	0.886296i
$443$	− 40.7527i	− 1.93622i	−0.250524	−	0.968110i	$-0.580603\pi$
$443$	− 40.7527i	− 1.93622i	0.250524	−	0.968110i	$-0.419397\pi$
$444$	−15.3944	−0.730588
$445$	0	0
$446$	−10.5139	−0.497847
$447$	− 2.36669i	− 0.111941i
$448$	4.30278i	0.203287i
$449$	22.6056	1.06682	0.533411	−	0.845856i	$-0.320910\pi$
$449$	22.6056	1.06682	0.533411	+	0.845856i	$0.320910\pi$
$450$	0	0
$451$	6.42221	0.302410
$452$	− 6.69722i	− 0.315011i
$453$	3.39445i	0.159485i
$454$	15.2111	0.713892
$455$	0	0
$456$	8.60555	0.402992
$457$	10.0000i	0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$	10.0000i	0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$	4.90833i	0.229351i
$459$	−38.7250	−1.80753
$460$	0	0
$461$	−28.5416	−1.32932	−0.664658	−	0.747148i	$-0.731423\pi$
$461$	−28.5416	−1.32932	−0.664658	+	0.747148i	$0.731423\pi$
$462$	25.8167i	1.20110i
$463$	− 16.8444i	− 0.782826i	−0.920215	−	0.391413i	$-0.871986\pi$
$463$	− 16.8444i	− 0.782826i	0.920215	−	0.391413i	$-0.128014\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	−8.78890	−0.407138
$467$	− 16.5416i	− 0.765456i	−0.923861	−	0.382728i	$-0.874985\pi$
$467$	− 16.5416i	− 0.765456i	0.923861	−	0.382728i	$-0.125015\pi$
$468$	− 3.51388i	− 0.162429i
$469$	−22.4222	−1.03536
$470$	0	0
$471$	−26.6056	−1.22592
$472$	9.90833i	0.456068i
$473$	1.39445i	0.0641168i
$474$	−7.69722	−0.353545
$475$	0	0
$476$	29.7250	1.36244
$477$	9.00000i	0.412082i
$478$	− 6.00000i	− 0.274434i
$479$	−20.7250	−0.946949	−0.473474	−	0.880808i	$-0.657000\pi$
$479$	−20.7250	−0.946949	−0.473474	+	0.880808i	$0.657000\pi$
$480$	0	0
$481$	−31.8722	−1.45325
$482$	− 3.30278i	− 0.150437i
$483$	− 29.7250i	− 1.35253i
$484$	−10.2111	−0.464141
$485$	0	0
$486$	12.3944	0.562224
$487$	12.9361i	0.586190i	0.956083	+	0.293095i	$0.0946852\pi$
$487$	12.9361i	0.586190i	−0.956083	+	0.293095i	$0.905315\pi$
$488$	13.9083i	0.629600i
$489$	−8.84441	−0.399958
$490$	0	0
$491$	39.6333	1.78863	0.894313	−	0.447442i	$-0.147665\pi$
$491$	39.6333	1.78863	0.894313	+	0.447442i	$0.147665\pi$
$492$	− 1.81665i	− 0.0819011i
$493$	6.90833i	0.311135i
$494$	17.8167	0.801609
$495$	0	0
$496$	2.90833	0.130588
$497$	0	0
$498$	− 1.81665i	− 0.0814062i
$499$	−13.7250	−0.614415	−0.307207	−	0.951643i	$-0.599394\pi$
$499$	−13.7250	−0.614415	−0.307207	+	0.951643i	$0.599394\pi$
$500$	0	0
$501$	4.81665	0.215192
$502$	− 1.39445i	− 0.0622373i
$503$	− 12.0000i	− 0.535054i	−0.963550	−	0.267527i	$-0.913794\pi$
$503$	− 12.0000i	− 0.535054i	0.963550	−	0.267527i	$-0.0862064\pi$
$504$	−5.60555	−0.249691
$505$	0	0
$506$	24.4222	1.08570
$507$	− 7.45837i	− 0.331238i
$508$	20.0000i	0.887357i
$509$	19.8167	0.878358	0.439179	−	0.898400i	$-0.355269\pi$
$509$	19.8167	0.878358	0.439179	+	0.898400i	$0.355269\pi$
$510$	0	0
$511$	−66.7527	−2.95297
$512$	1.00000i	0.0441942i
$513$	37.0278i	1.63482i
$514$	−29.0278	−1.28036
$515$	0	0
$516$	0.394449	0.0173646
$517$	0	0
$518$	50.8444i	2.23398i
$519$	10.5416	0.462726
$520$	0	0
$521$	8.30278	0.363751	0.181876	−	0.983322i	$-0.441783\pi$
$521$	8.30278	0.363751	0.181876	+	0.983322i	$0.441783\pi$
$522$	− 1.30278i	− 0.0570209i
$523$	− 35.8167i	− 1.56615i	−0.621925	−	0.783076i	$-0.713649\pi$
$523$	− 35.8167i	− 1.56615i	0.621925	−	0.783076i	$-0.286351\pi$
$524$	21.6333	0.945055
$525$	0	0
$526$	9.21110	0.401623
$527$	− 20.0917i	− 0.875207i
$528$	6.00000i	0.261116i
$529$	−5.11943	−0.222584
$530$	0	0
$531$	−12.9083	−0.560174
$532$	− 28.4222i	− 1.23226i
$533$	− 3.76114i	− 0.162913i
$534$	9.63331	0.416874
$535$	0	0
$536$	−5.21110	−0.225085
$537$	− 12.9083i	− 0.557035i
$538$	− 5.51388i	− 0.237720i
$539$	53.0278	2.28407
$540$	0	0
$541$	−26.1194	−1.12296	−0.561481	−	0.827490i	$-0.689768\pi$
$541$	−26.1194	−1.12296	−0.561481	+	0.827490i	$0.689768\pi$
$542$	− 1.21110i	− 0.0520213i
$543$	7.02776i	0.301590i
$544$	6.90833	0.296192
$545$	0	0
$546$	15.1194	0.647052
$547$	− 10.2389i	− 0.437782i	−0.975749	−	0.218891i	$-0.929756\pi$
$547$	− 10.2389i	− 0.437782i	0.975749	−	0.218891i	$-0.0702439\pi$
$548$	− 8.09167i	− 0.345659i
$549$	−18.1194	−0.773318
$550$	0	0
$551$	6.60555	0.281406
$552$	− 6.90833i	− 0.294038i
$553$	25.4222i	1.08106i
$554$	14.0000	0.594803
$555$	0	0
$556$	10.3028	0.436935
$557$	31.5416i	1.33646i	0.743954	+	0.668231i	$0.232948\pi$
$557$	31.5416i	1.33646i	−0.743954	+	0.668231i	$0.767052\pi$
$558$	3.78890i	0.160397i
$559$	0.816654	0.0345408
$560$	0	0
$561$	41.4500	1.75002
$562$	− 10.1194i	− 0.426862i
$563$	27.9083i	1.17620i	0.808790	+	0.588098i	$0.200123\pi$
$563$	27.9083i	1.17620i	−0.808790	+	0.588098i	$0.799877\pi$
$564$	0	0
$565$	0	0
$566$	21.0278	0.883863
$567$	14.6056i	0.613375i
$568$	0	0
$569$	3.63331	0.152316	0.0761581	−	0.997096i	$-0.475735\pi$
$569$	3.63331	0.152316	0.0761581	+	0.997096i	$0.475735\pi$
$570$	0	0
$571$	0.880571	0.0368507	0.0184254	−	0.999830i	$-0.494135\pi$
$571$	0.880571	0.0368507	0.0184254	+	0.999830i	$0.494135\pi$
$572$	12.4222i	0.519398i
$573$	− 6.63331i	− 0.277110i
$574$	−6.00000	−0.250435
$575$	0	0
$576$	−1.30278	−0.0542823
$577$	− 20.4861i	− 0.852848i	−0.904523	−	0.426424i	$-0.859773\pi$
$577$	− 20.4861i	− 0.852848i	0.904523	−	0.426424i	$-0.140227\pi$
$578$	− 30.7250i	− 1.27799i
$579$	10.0639	0.418242
$580$	0	0
$581$	−6.00000	−0.248922
$582$	− 15.5139i	− 0.643071i
$583$	− 31.8167i	− 1.31771i
$584$	−15.5139	−0.641969
$585$	0	0
$586$	−4.18335	−0.172812
$587$	15.2111i	0.627829i	0.949451	+	0.313915i	$0.101641\pi$
$587$	15.2111i	0.627829i	−0.949451	+	0.313915i	$0.898359\pi$
$588$	− 15.0000i	− 0.618590i
$589$	−19.2111	−0.791580
$590$	0	0
$591$	−9.00000	−0.370211
$592$	11.8167i	0.485661i
$593$	− 1.81665i	− 0.0746010i	−0.999304	−	0.0373005i	$-0.988124\pi$
$593$	− 1.81665i	− 0.0746010i	0.999304	−	0.0373005i	$-0.0118759\pi$
$594$	−25.8167	−1.05927
$595$	0	0
$596$	−1.81665	−0.0744130
$597$	− 23.2111i	− 0.949967i
$598$	− 14.3028i	− 0.584884i
$599$	−30.9083	−1.26288	−0.631440	−	0.775425i	$-0.717536\pi$
$599$	−30.9083	−1.26288	−0.631440	+	0.775425i	$0.717536\pi$
$600$	0	0
$601$	−44.6056	−1.81950	−0.909749	−	0.415158i	$-0.863726\pi$
$601$	−44.6056	−1.81950	−0.909749	+	0.415158i	$0.863726\pi$
$602$	− 1.30278i	− 0.0530972i
$603$	− 6.78890i	− 0.276465i
$604$	2.60555	0.106018
$605$	0	0
$606$	−2.72498	−0.110695
$607$	− 23.6333i	− 0.959246i	−0.877475	−	0.479623i	$-0.840773\pi$
$607$	− 23.6333i	− 0.959246i	0.877475	−	0.479623i	$-0.159227\pi$
$608$	− 6.60555i	− 0.267890i
$609$	5.60555	0.227148
$610$	0	0
$611$	0	0
$612$	9.00000i	0.363803i
$613$	− 2.66947i	− 0.107819i	−0.998546	−	0.0539094i	$-0.982832\pi$
$613$	− 2.66947i	− 0.107819i	0.998546	−	0.0539094i	$-0.0171682\pi$
$614$	−13.2111	−0.533157
$615$	0	0
$616$	19.8167	0.798436
$617$	6.90833i	0.278119i	0.990284	+	0.139059i	$0.0444079\pi$
$617$	6.90833i	0.278119i	−0.990284	+	0.139059i	$0.955592\pi$
$618$	− 13.5778i	− 0.546179i
$619$	−11.2111	−0.450612	−0.225306	−	0.974288i	$-0.572338\pi$
$619$	−11.2111	−0.450612	−0.225306	+	0.974288i	$0.572338\pi$
$620$	0	0
$621$	29.7250	1.19282
$622$	14.0917i	0.565025i
$623$	− 31.8167i	− 1.27471i
$624$	3.51388	0.140668
$625$	0	0
$626$	28.4222	1.13598
$627$	− 39.6333i	− 1.58280i
$628$	20.4222i	0.814935i
$629$	81.6333	3.25493
$630$	0	0
$631$	38.8444	1.54637	0.773186	−	0.634180i	$-0.218662\pi$
$631$	38.8444	1.54637	0.773186	+	0.634180i	$0.218662\pi$
$632$	5.90833i	0.235021i
$633$	− 8.05551i	− 0.320178i
$634$	11.0278	0.437968
$635$	0	0
$636$	−9.00000	−0.356873
$637$	− 31.0555i	− 1.23046i
$638$	4.60555i	0.182336i
$639$	0	0
$640$	0	0
$641$	−19.8167	−0.782711	−0.391355	−	0.920240i	$-0.627994\pi$
$641$	−19.8167	−0.782711	−0.391355	+	0.920240i	$0.627994\pi$
$642$	− 1.81665i	− 0.0716976i
$643$	− 11.3944i	− 0.449353i	−0.974433	−	0.224677i	$-0.927867\pi$
$643$	− 11.3944i	− 0.449353i	0.974433	−	0.224677i	$-0.0721326\pi$
$644$	−22.8167	−0.899102
$645$	0	0
$646$	−45.6333	−1.79542
$647$	15.6333i	0.614609i	0.951611	+	0.307304i	$0.0994270\pi$
$647$	15.6333i	0.614609i	−0.951611	+	0.307304i	$0.900573\pi$
$648$	3.39445i	0.133347i
$649$	45.6333	1.79126
$650$	0	0
$651$	−16.3028	−0.638956
$652$	6.78890i	0.265874i
$653$	− 10.1833i	− 0.398505i	−0.979948	−	0.199253i	$-0.936149\pi$
$653$	− 10.1833i	− 0.398505i	0.979948	−	0.199253i	$-0.0638514\pi$
$654$	19.0278	0.744044
$655$	0	0
$656$	−1.39445	−0.0544441
$657$	− 20.2111i	− 0.788510i
$658$	0	0
$659$	37.8167	1.47313	0.736564	−	0.676368i	$-0.236447\pi$
$659$	37.8167	1.47313	0.736564	+	0.676368i	$0.236447\pi$
$660$	0	0
$661$	9.81665	0.381824	0.190912	−	0.981607i	$-0.438856\pi$
$661$	9.81665	0.381824	0.190912	+	0.981607i	$0.438856\pi$
$662$	15.3944i	0.598322i
$663$	− 24.2750i	− 0.942764i
$664$	−1.39445	−0.0541151
$665$	0	0
$666$	−15.3944	−0.596523
$667$	− 5.30278i	− 0.205324i
$668$	− 3.69722i	− 0.143050i
$669$	13.6972	0.529565
$670$	0	0
$671$	64.0555	2.47284
$672$	− 5.60555i	− 0.216239i
$673$	− 15.4500i	− 0.595552i	−0.954636	−	0.297776i	$-0.903755\pi$
$673$	− 15.4500i	− 0.595552i	0.954636	−	0.297776i	$-0.0962449\pi$
$674$	−1.69722	−0.0653746
$675$	0	0
$676$	−5.72498	−0.220192
$677$	− 48.8444i	− 1.87724i	−0.344949	−	0.938622i	$-0.612104\pi$
$677$	− 48.8444i	− 1.87724i	0.344949	−	0.938622i	$-0.387896\pi$
$678$	8.72498i	0.335081i
$679$	−51.2389	−1.96637
$680$	0	0
$681$	−19.8167	−0.759376
$682$	− 13.3944i	− 0.512900i
$683$	− 23.4500i	− 0.897288i	−0.893711	−	0.448644i	$-0.851907\pi$
$683$	− 23.4500i	− 0.897288i	0.893711	−	0.448644i	$-0.148093\pi$
$684$	8.60555	0.329041
$685$	0	0
$686$	−19.4222	−0.741543
$687$	− 6.39445i	− 0.243963i
$688$	− 0.302776i	− 0.0115432i
$689$	−18.6333	−0.709872
$690$	0	0
$691$	−34.9083	−1.32798	−0.663988	−	0.747744i	$-0.731137\pi$
$691$	−34.9083	−1.32798	−0.663988	+	0.747744i	$0.731137\pi$
$692$	− 8.09167i	− 0.307599i
$693$	25.8167i	0.980694i
$694$	−7.81665	−0.296716
$695$	0	0
$696$	1.30278	0.0493816
$697$	9.63331i	0.364888i
$698$	− 8.00000i	− 0.302804i
$699$	11.4500	0.433077
$700$	0	0
$701$	−16.6056	−0.627183	−0.313592	−	0.949558i	$-0.601532\pi$
$701$	−16.6056	−0.627183	−0.313592	+	0.949558i	$0.601532\pi$
$702$	15.1194i	0.570646i
$703$	− 78.0555i	− 2.94392i
$704$	4.60555	0.173578
$705$	0	0
$706$	−2.78890	−0.104962
$707$	9.00000i	0.338480i
$708$	− 12.9083i	− 0.485125i
$709$	15.0278	0.564379	0.282190	−	0.959359i	$-0.408939\pi$
$709$	15.0278	0.564379	0.282190	+	0.959359i	$0.408939\pi$
$710$	0	0
$711$	−7.69722	−0.288668
$712$	− 7.39445i	− 0.277119i
$713$	15.4222i	0.577566i
$714$	−38.7250	−1.44925
$715$	0	0
$716$	−9.90833	−0.370292
$717$	7.81665i	0.291918i
$718$	15.4861i	0.577937i
$719$	14.2389	0.531020	0.265510	−	0.964108i	$-0.414460\pi$
$719$	14.2389	0.531020	0.265510	+	0.964108i	$0.414460\pi$
$720$	0	0
$721$	−44.8444	−1.67009
$722$	24.6333i	0.916757i
$723$	4.30278i	0.160022i
$724$	5.39445	0.200483
$725$	0	0
$726$	13.3028	0.493712
$727$	− 27.3944i	− 1.01600i	−0.861356	−	0.508002i	$-0.830384\pi$
$727$	− 27.3944i	− 1.01600i	0.861356	−	0.508002i	$-0.169616\pi$
$728$	− 11.6056i	− 0.430130i
$729$	−26.3305	−0.975205
$730$	0	0
$731$	−2.09167	−0.0773633
$732$	− 18.1194i	− 0.669713i
$733$	44.8444i	1.65637i	0.560458	+	0.828183i	$0.310625\pi$
$733$	44.8444i	1.65637i	−0.560458	+	0.828183i	$0.689375\pi$
$734$	−17.3944	−0.642041
$735$	0	0
$736$	−5.30278	−0.195463
$737$	24.0000i	0.884051i
$738$	− 1.81665i	− 0.0668720i
$739$	1.21110	0.0445511	0.0222756	−	0.999752i	$-0.492909\pi$
$739$	1.21110	0.0445511	0.0222756	+	0.999752i	$0.492909\pi$
$740$	0	0
$741$	−23.2111	−0.852681
$742$	29.7250i	1.09124i
$743$	26.7889i	0.982789i	0.870937	+	0.491395i	$0.163513\pi$
$743$	26.7889i	0.982789i	−0.870937	+	0.491395i	$0.836487\pi$
$744$	−3.78890	−0.138908
$745$	0	0
$746$	21.0917	0.772221
$747$	− 1.81665i	− 0.0664679i
$748$	− 31.8167i	− 1.16333i
$749$	−6.00000	−0.219235
$750$	0	0
$751$	−16.8444	−0.614661	−0.307331	−	0.951603i	$-0.599436\pi$
$751$	−16.8444	−0.614661	−0.307331	+	0.951603i	$0.599436\pi$
$752$	0	0
$753$	1.81665i	0.0662025i
$754$	2.69722	0.0982271
$755$	0	0
$756$	24.1194	0.877215
$757$	− 43.4500i	− 1.57922i	−0.613612	−	0.789608i	$-0.710284\pi$
$757$	− 43.4500i	− 1.57922i	0.613612	−	0.789608i	$-0.289716\pi$
$758$	23.3944i	0.849725i
$759$	−31.8167	−1.15487
$760$	0	0
$761$	−42.3583	−1.53549	−0.767743	−	0.640757i	$-0.778620\pi$
$761$	−42.3583	−1.53549	−0.767743	+	0.640757i	$0.778620\pi$
$762$	− 26.0555i	− 0.943892i
$763$	− 62.8444i	− 2.27512i
$764$	−5.09167	−0.184210
$765$	0	0
$766$	−8.30278	−0.299991
$767$	− 26.7250i	− 0.964983i
$768$	− 1.30278i	− 0.0470099i
$769$	−8.97224	−0.323547	−0.161774	−	0.986828i	$-0.551721\pi$
$769$	−8.97224	−0.323547	−0.161774	+	0.986828i	$0.551721\pi$
$770$	0	0
$771$	37.8167	1.36193
$772$	− 7.72498i	− 0.278028i
$773$	− 11.5778i	− 0.416424i	−0.978084	−	0.208212i	$-0.933236\pi$
$773$	− 11.5778i	− 0.416424i	0.978084	−	0.208212i	$-0.0667645\pi$
$774$	0.394449	0.0141782
$775$	0	0
$776$	−11.9083	−0.427484
$777$	− 66.2389i	− 2.37631i
$778$	18.0000i	0.645331i
$779$	9.21110	0.330022
$780$	0	0
$781$	0	0
$782$	36.6333i	1.31000i
$783$	5.60555i	0.200326i
$784$	−11.5139	−0.411210
$785$	0	0
$786$	−28.1833	−1.00527
$787$	9.02776i	0.321805i	0.986970	+	0.160902i	$0.0514404\pi$
$787$	9.02776i	0.321805i	−0.986970	+	0.160902i	$0.948560\pi$
$788$	6.90833i	0.246099i
$789$	−12.0000	−0.427211
$790$	0	0
$791$	28.8167	1.02460
$792$	6.00000i	0.213201i
$793$	− 37.5139i	− 1.33216i
$794$	1.09167	0.0387420
$795$	0	0
$796$	−17.8167	−0.631495
$797$	− 55.2666i	− 1.95764i	−0.204713	−	0.978822i	$-0.565626\pi$
$797$	− 55.2666i	− 1.95764i	0.204713	−	0.978822i	$-0.434374\pi$
$798$	37.0278i	1.31077i
$799$	0	0
$800$	0	0
$801$	9.63331	0.340376
$802$	24.6972i	0.872089i
$803$	71.4500i	2.52141i
$804$	6.78890	0.239426
$805$	0	0
$806$	−7.84441	−0.276308
$807$	7.18335i	0.252866i
$808$	2.09167i	0.0735848i
$809$	−46.0555	−1.61923	−0.809613	−	0.586964i	$-0.800323\pi$
$809$	−46.0555	−1.61923	−0.809613	+	0.586964i	$0.800323\pi$
$810$	0	0
$811$	−21.9361	−0.770280	−0.385140	−	0.922858i	$-0.625847\pi$
$811$	−21.9361	−0.770280	−0.385140	+	0.922858i	$0.625847\pi$
$812$	− 4.30278i	− 0.150998i
$813$	1.57779i	0.0553357i
$814$	54.4222	1.90750
$815$	0	0
$816$	−9.00000	−0.315063
$817$	2.00000i	0.0699711i
$818$	− 5.21110i	− 0.182202i
$819$	15.1194	0.528316
$820$	0	0
$821$	−3.76114	−0.131265	−0.0656324	−	0.997844i	$-0.520906\pi$
$821$	−3.76114	−0.131265	−0.0656324	+	0.997844i	$0.520906\pi$
$822$	10.5416i	0.367682i
$823$	5.63331i	0.196365i	0.995168	+	0.0981824i	$0.0313029\pi$
$823$	5.63331i	0.196365i	−0.995168	+	0.0981824i	$0.968697\pi$
$824$	−10.4222	−0.363075
$825$	0	0
$826$	−42.6333	−1.48340
$827$	34.1194i	1.18645i	0.805037	+	0.593224i	$0.202145\pi$
$827$	34.1194i	1.18645i	−0.805037	+	0.593224i	$0.797855\pi$
$828$	− 6.90833i	− 0.240081i
$829$	17.7527	0.616578	0.308289	−	0.951293i	$-0.400244\pi$
$829$	17.7527	0.616578	0.308289	+	0.951293i	$0.400244\pi$
$830$	0	0
$831$	−18.2389	−0.632699
$832$	− 2.69722i	− 0.0935094i
$833$	79.5416i	2.75595i
$834$	−13.4222	−0.464773
$835$	0	0
$836$	−30.4222	−1.05217
$837$	− 16.3028i	− 0.563506i
$838$	− 16.1194i	− 0.556836i
$839$	14.7889	0.510569	0.255285	−	0.966866i	$-0.417831\pi$
$839$	14.7889	0.510569	0.255285	+	0.966866i	$0.417831\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	17.6333i	0.607684i
$843$	13.1833i	0.454059i
$844$	−6.18335	−0.212840
$845$	0	0
$846$	0	0
$847$	− 43.9361i	− 1.50966i
$848$	6.90833i	0.237233i
$849$	−27.3944	−0.940175
$850$	0	0
$851$	−62.6611	−2.14799
$852$	0	0
$853$	22.2389i	0.761444i	0.924690	+	0.380722i	$0.124325\pi$
$853$	22.2389i	0.761444i	−0.924690	+	0.380722i	$0.875675\pi$
$854$	−59.8444	−2.04783
$855$	0	0
$856$	−1.39445	−0.0476613
$857$	− 20.2389i	− 0.691346i	−0.938355	−	0.345673i	$-0.887651\pi$
$857$	− 20.2389i	− 0.691346i	0.938355	−	0.345673i	$-0.112349\pi$
$858$	− 16.1833i	− 0.552490i
$859$	−21.3944	−0.729969	−0.364985	−	0.931014i	$-0.618926\pi$
$859$	−21.3944	−0.729969	−0.364985	+	0.931014i	$0.618926\pi$
$860$	0	0
$861$	7.81665	0.266391
$862$	− 38.2389i	− 1.30242i
$863$	15.9083i	0.541526i	0.962646	+	0.270763i	$0.0872759\pi$
$863$	15.9083i	0.541526i	−0.962646	+	0.270763i	$0.912724\pi$
$864$	5.60555	0.190705
$865$	0	0
$866$	0.788897	0.0268078
$867$	40.0278i	1.35941i
$868$	12.5139i	0.424749i
$869$	27.2111	0.923073
$870$	0	0
$871$	14.0555	0.476253
$872$	− 14.6056i	− 0.494606i
$873$	− 15.5139i	− 0.525065i
$874$	35.0278	1.18483
$875$	0	0
$876$	20.2111	0.682870
$877$	− 37.3028i	− 1.25963i	−0.776747	−	0.629813i	$-0.783132\pi$
$877$	− 37.3028i	− 1.25963i	0.776747	−	0.629813i	$-0.216868\pi$
$878$	− 5.63331i	− 0.190115i
$879$	5.44996	0.183823
$880$	0	0
$881$	5.02776	0.169389	0.0846947	−	0.996407i	$-0.473009\pi$
$881$	5.02776	0.169389	0.0846947	+	0.996407i	$0.473009\pi$
$882$	− 15.0000i	− 0.505076i
$883$	18.6056i	0.626127i	0.949732	+	0.313063i	$0.101355\pi$
$883$	18.6056i	0.626127i	−0.949732	+	0.313063i	$0.898645\pi$
$884$	−18.6333	−0.626706
$885$	0	0
$886$	40.7527	1.36911
$887$	− 8.36669i	− 0.280926i	−0.990086	−	0.140463i	$-0.955141\pi$
$887$	− 8.36669i	− 0.280926i	0.990086	−	0.140463i	$-0.0448591\pi$
$888$	− 15.3944i	− 0.516604i
$889$	−86.0555	−2.88621
$890$	0	0
$891$	15.6333	0.523736
$892$	− 10.5139i	− 0.352031i
$893$	0	0
$894$	2.36669	0.0791540
$895$	0	0
$896$	−4.30278	−0.143746
$897$	18.6333i	0.622148i
$898$	22.6056i	0.754357i
$899$	−2.90833	−0.0969981
$900$	0	0
$901$	47.7250	1.58995
$902$	6.42221i	0.213836i
$903$	1.69722i	0.0564801i
$904$	6.69722	0.222746
$905$	0	0
$906$	−3.39445	−0.112773
$907$	− 40.3028i	− 1.33823i	−0.743158	−	0.669116i	$-0.766673\pi$
$907$	− 40.3028i	− 1.33823i	0.743158	−	0.669116i	$-0.233327\pi$
$908$	15.2111i	0.504798i
$909$	−2.72498	−0.0903819
$910$	0	0
$911$	−10.7527	−0.356254	−0.178127	−	0.984007i	$-0.557004\pi$
$911$	−10.7527	−0.356254	−0.178127	+	0.984007i	$0.557004\pi$
$912$	8.60555i	0.284958i
$913$	6.42221i	0.212544i
$914$	−10.0000	−0.330771
$915$	0	0
$916$	−4.90833	−0.162176
$917$	93.0833i	3.07388i
$918$	− 38.7250i	− 1.27811i
$919$	7.63331	0.251800	0.125900	−	0.992043i	$-0.459818\pi$
$919$	7.63331	0.251800	0.125900	+	0.992043i	$0.459818\pi$
$920$	0	0
$921$	17.2111	0.567125
$922$	− 28.5416i	− 0.939969i
$923$	0	0
$924$	−25.8167	−0.849306
$925$	0	0
$926$	16.8444	0.553542
$927$	− 13.5778i	− 0.445953i
$928$	− 1.00000i	− 0.0328266i
$929$	20.3028	0.666112	0.333056	−	0.942907i	$-0.391920\pi$
$929$	20.3028	0.666112	0.333056	+	0.942907i	$0.391920\pi$
$930$	0	0
$931$	76.0555	2.49262
$932$	− 8.78890i	− 0.287890i
$933$	− 18.3583i	− 0.601023i
$934$	16.5416	0.541259
$935$	0	0
$936$	3.51388	0.114855
$937$	35.8167i	1.17008i	0.811005	+	0.585040i	$0.198921\pi$
$937$	35.8167i	1.17008i	−0.811005	+	0.585040i	$0.801079\pi$
$938$	− 22.4222i	− 0.732111i
$939$	−37.0278	−1.20836
$940$	0	0
$941$	51.6333	1.68320	0.841599	−	0.540103i	$-0.181615\pi$
$941$	51.6333	1.68320	0.841599	+	0.540103i	$0.181615\pi$
$942$	− 26.6056i	− 0.866856i
$943$	− 7.39445i	− 0.240796i
$944$	−9.90833	−0.322489
$945$	0	0
$946$	−1.39445	−0.0453374
$947$	18.1472i	0.589704i	0.955543	+	0.294852i	$0.0952704\pi$
$947$	18.1472i	0.589704i	−0.955543	+	0.294852i	$0.904730\pi$
$948$	− 7.69722i	− 0.249994i
$949$	41.8444	1.35833
$950$	0	0
$951$	−14.3667	−0.465872
$952$	29.7250i	0.963392i
$953$	0.422205i	0.0136766i	0.999977	+	0.00683828i	$0.00217671\pi$
$953$	0.422205i	0.0136766i	−0.999977	+	0.00683828i	$0.997823\pi$
$954$	−9.00000	−0.291386
$955$	0	0
$956$	6.00000	0.194054
$957$	− 6.00000i	− 0.193952i
$958$	− 20.7250i	− 0.669594i
$959$	34.8167	1.12429
$960$	0	0
$961$	−22.5416	−0.727150
$962$	− 31.8722i	− 1.02760i
$963$	− 1.81665i	− 0.0585409i
$964$	3.30278	0.106375
$965$	0	0
$966$	29.7250	0.956386
$967$	30.6611i	0.985993i	0.870031	+	0.492997i	$0.164099\pi$
$967$	30.6611i	0.985993i	−0.870031	+	0.492997i	$0.835901\pi$
$968$	− 10.2111i	− 0.328197i
$969$	59.4500	1.90981
$970$	0	0
$971$	−4.18335	−0.134250	−0.0671250	−	0.997745i	$-0.521383\pi$
$971$	−4.18335	−0.134250	−0.0671250	+	0.997745i	$0.521383\pi$
$972$	12.3944i	0.397552i
$973$	44.3305i	1.42117i
$974$	−12.9361	−0.414499
$975$	0	0
$976$	−13.9083	−0.445195
$977$	10.1833i	0.325794i	0.986643	+	0.162897i	$0.0520838\pi$
$977$	10.1833i	0.325794i	−0.986643	+	0.162897i	$0.947916\pi$
$978$	− 8.84441i	− 0.282813i
$979$	−34.0555	−1.08842
$980$	0	0
$981$	19.0278	0.607510
$982$	39.6333i	1.26475i
$983$	16.0555i	0.512091i	0.966665	+	0.256046i	$0.0824197\pi$
$983$	16.0555i	0.512091i	−0.966665	+	0.256046i	$0.917580\pi$
$984$	1.81665	0.0579128
$985$	0	0
$986$	−6.90833	−0.220006
$987$	0	0
$988$	17.8167i	0.566823i
$989$	1.60555	0.0510536
$990$	0	0
$991$	27.3944	0.870213	0.435107	−	0.900379i	$-0.356711\pi$
$991$	27.3944	0.870213	0.435107	+	0.900379i	$0.356711\pi$
$992$	2.90833i	0.0923395i
$993$	− 20.0555i	− 0.636442i
$994$	0	0
$995$	0	0
$996$	1.81665	0.0575629
$997$	18.6611i	0.591002i	0.955342	+	0.295501i	$0.0954865\pi$
$997$	18.6611i	0.591002i	−0.955342	+	0.295501i	$0.904513\pi$
$998$	− 13.7250i	− 0.434457i
$999$	66.2389	2.09570

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.b.g.349.3		4
5.2	odd	4		290.2.a.b.1.1	✓	2
5.3	odd	4		1450.2.a.m.1.2		2
5.4	even	2	inner	1450.2.b.g.349.2		4
15.2	even	4		2610.2.a.v.1.2		2
20.7	even	4		2320.2.a.i.1.2		2
40.27	even	4		9280.2.a.bc.1.1		2
40.37	odd	4		9280.2.a.z.1.2		2
145.57	odd	4		8410.2.a.r.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.b.1.1	✓	2	5.2	odd	4
1450.2.a.m.1.2		2	5.3	odd	4
1450.2.b.g.349.2		4	5.4	even	2	inner
1450.2.b.g.349.3		4	1.1	even	1	trivial
2320.2.a.i.1.2		2	20.7	even	4
2610.2.a.v.1.2		2	15.2	even	4
8410.2.a.r.1.2		2	145.57	odd	4
9280.2.a.z.1.2		2	40.37	odd	4
9280.2.a.bc.1.1		2	40.27	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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.30278i q^{3} -1.00000 q^{4} +1.30278 q^{6} -4.30278i q^{7} -1.00000i q^{8} +1.30278 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.30278i q^{3} -1.00000 q^{4} +1.30278 q^{6} -4.30278i q^{7} -1.00000i q^{8} +1.30278 q^{9} -4.60555 q^{11} +1.30278i q^{12} +2.69722i q^{13} +4.30278 q^{14} +1.00000 q^{16} -6.90833i q^{17} +1.30278i q^{18} -6.60555 q^{19} -5.60555 q^{21} -4.60555i q^{22} +5.30278i q^{23} -1.30278 q^{24} -2.69722 q^{26} -5.60555i q^{27} +4.30278i q^{28} -1.00000 q^{29} +2.90833 q^{31} +1.00000i q^{32} +6.00000i q^{33} +6.90833 q^{34} -1.30278 q^{36} +11.8167i q^{37} -6.60555i q^{38} +3.51388 q^{39} -1.39445 q^{41} -5.60555i q^{42} -0.302776i q^{43} +4.60555 q^{44} -5.30278 q^{46} -1.30278i q^{48} -11.5139 q^{49} -9.00000 q^{51} -2.69722i q^{52} +6.90833i q^{53} +5.60555 q^{54} -4.30278 q^{56} +8.60555i q^{57} -1.00000i q^{58} -9.90833 q^{59} -13.9083 q^{61} +2.90833i q^{62} -5.60555i q^{63} -1.00000 q^{64} -6.00000 q^{66} -5.21110i q^{67} +6.90833i q^{68} +6.90833 q^{69} -1.30278i q^{72} -15.5139i q^{73} -11.8167 q^{74} +6.60555 q^{76} +19.8167i q^{77} +3.51388i q^{78} -5.90833 q^{79} -3.39445 q^{81} -1.39445i q^{82} -1.39445i q^{83} +5.60555 q^{84} +0.302776 q^{86} +1.30278i q^{87} +4.60555i q^{88} +7.39445 q^{89} +11.6056 q^{91} -5.30278i q^{92} -3.78890i q^{93} +1.30278 q^{96} -11.9083i q^{97} -11.5139i q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9	\( 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9} - 4 q^{11} + 10 q^{14} + 4 q^{16} - 12 q^{19} - 8 q^{21} + 2 q^{24} - 18 q^{26} - 4 q^{29} - 10 q^{31} + 6 q^{34} + 2 q^{36} - 22 q^{39} - 20 q^{41} + 4 q^{44} - 14 q^{46} - 10 q^{49} - 36 q^{51} + 8 q^{54} - 10 q^{56} - 18 q^{59} - 34 q^{61} - 4 q^{64} - 24 q^{66} + 6 q^{69} - 4 q^{74} + 12 q^{76} - 2 q^{79} - 28 q^{81} + 8 q^{84} - 6 q^{86} + 44 q^{89} + 32 q^{91} - 2 q^{96} - 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9 - 4 * q^11 + 10 * q^14 + 4 * q^16 - 12 * q^19 - 8 * q^21 + 2 * q^24 - 18 * q^26 - 4 * q^29 - 10 * q^31 + 6 * q^34 + 2 * q^36 - 22 * q^39 - 20 * q^41 + 4 * q^44 - 14 * q^46 - 10 * q^49 - 36 * q^51 + 8 * q^54 - 10 * q^56 - 18 * q^59 - 34 * q^61 - 4 * q^64 - 24 * q^66 + 6 * q^69 - 4 * q^74 + 12 * q^76 - 2 * q^79 - 28 * q^81 + 8 * q^84 - 6 * q^86 + 44 * q^89 + 32 * q^91 - 2 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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