LMFDB - Embedded newform 1150.2.b.f.599.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(599,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, 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("1150.599");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.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:	$9.18279623245$
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 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.2
Root			$1.30278i$ of defining polynomial
Character	$\chi$	$=$	1150.599
Dual form			1150.2.b.f.599.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +0.302776i q^{3} -1.00000 q^{4} +0.302776 q^{6} +3.30278i q^{7} +1.00000i q^{8} +2.90833 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +0.302776i q^{3} -1.00000 q^{4} +0.302776 q^{6} +3.30278i q^{7} +1.00000i q^{8} +2.90833 q^{9} -1.69722 q^{11} -0.302776i q^{12} -3.30278i q^{13} +3.30278 q^{14} +1.00000 q^{16} +6.90833i q^{17} -2.90833i q^{18} -5.90833 q^{19} -1.00000 q^{21} +1.69722i q^{22} +1.00000i q^{23} -0.302776 q^{24} -3.30278 q^{26} +1.78890i q^{27} -3.30278i q^{28} +2.60555 q^{29} -7.90833 q^{31} -1.00000i q^{32} -0.513878i q^{33} +6.90833 q^{34} -2.90833 q^{36} +8.00000i q^{37} +5.90833i q^{38} +1.00000 q^{39} +0.908327 q^{41} +1.00000i q^{42} +9.21110i q^{43} +1.69722 q^{44} +1.00000 q^{46} -2.60555i q^{47} +0.302776i q^{48} -3.90833 q^{49} -2.09167 q^{51} +3.30278i q^{52} +11.2111i q^{53} +1.78890 q^{54} -3.30278 q^{56} -1.78890i q^{57} -2.60555i q^{58} +3.39445 q^{59} +11.5139 q^{61} +7.90833i q^{62} +9.60555i q^{63} -1.00000 q^{64} -0.513878 q^{66} -4.00000i q^{67} -6.90833i q^{68} -0.302776 q^{69} -16.3028 q^{71} +2.90833i q^{72} +5.81665i q^{73} +8.00000 q^{74} +5.90833 q^{76} -5.60555i q^{77} -1.00000i q^{78} +14.4222 q^{79} +8.18335 q^{81} -0.908327i q^{82} -11.2111i q^{83} +1.00000 q^{84} +9.21110 q^{86} +0.788897i q^{87} -1.69722i q^{88} +10.9083 q^{91} -1.00000i q^{92} -2.39445i q^{93} -2.60555 q^{94} +0.302776 q^{96} +6.30278i q^{97} +3.90833i q^{98} -4.93608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 6 q^{6} - 10 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 6 * q^6 - 10 * q^9	$ 4 q - 4 q^{4} - 6 q^{6} - 10 q^{9} - 14 q^{11} + 6 q^{14} + 4 q^{16} - 2 q^{19} - 4 q^{21} + 6 q^{24} - 6 q^{26} - 4 q^{29} - 10 q^{31} + 6 q^{34} + 10 q^{36} + 4 q^{39} - 18 q^{41} + 14 q^{44} + 4 q^{46} + 6 q^{49} - 30 q^{51} + 36 q^{54} - 6 q^{56} + 28 q^{59} + 10 q^{61} - 4 q^{64} + 34 q^{66} + 6 q^{69} - 58 q^{71} + 32 q^{74} + 2 q^{76} + 76 q^{81} + 4 q^{84} + 8 q^{86} + 22 q^{91} + 4 q^{94} - 6 q^{96} + 74 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 6 * q^6 - 10 * q^9 - 14 * q^11 + 6 * q^14 + 4 * q^16 - 2 * q^19 - 4 * q^21 + 6 * q^24 - 6 * q^26 - 4 * q^29 - 10 * q^31 + 6 * q^34 + 10 * q^36 + 4 * q^39 - 18 * q^41 + 14 * q^44 + 4 * q^46 + 6 * q^49 - 30 * q^51 + 36 * q^54 - 6 * q^56 + 28 * q^59 + 10 * q^61 - 4 * q^64 + 34 * q^66 + 6 * q^69 - 58 * q^71 + 32 * q^74 + 2 * q^76 + 76 * q^81 + 4 * q^84 + 8 * q^86 + 22 * q^91 + 4 * q^94 - 6 * q^96 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$1$	$-1$

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
$3$	0.302776i	0.174808i	0.996173	+	0.0874038i	$0.0278570\pi$
$3$	0.302776i	0.174808i	−0.996173	+	0.0874038i	$0.972143\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0.302776	0.123608
$7$	3.30278i	1.24833i	0.781292	+	0.624166i	$0.214561\pi$
$7$	3.30278i	1.24833i	−0.781292	+	0.624166i	$0.785439\pi$
$8$	1.00000i	0.353553i
$9$	2.90833	0.969442
$10$	0	0
$11$	−1.69722	−0.511732	−0.255866	−	0.966712i	$-0.582361\pi$
$11$	−1.69722	−0.511732	−0.255866	+	0.966712i	$0.582361\pi$
$12$	− 0.302776i	− 0.0874038i
$13$	− 3.30278i	− 0.916025i	−0.888946	−	0.458013i	$-0.848561\pi$
$13$	− 3.30278i	− 0.916025i	0.888946	−	0.458013i	$-0.151439\pi$
$14$	3.30278	0.882704
$15$	0	0
$16$	1.00000	0.250000
$17$	6.90833i	1.67552i	0.546042	+	0.837758i	$0.316134\pi$
$17$	6.90833i	1.67552i	−0.546042	+	0.837758i	$0.683866\pi$
$18$	− 2.90833i	− 0.685499i
$19$	−5.90833	−1.35546	−0.677732	−	0.735309i	$-0.737037\pi$
$19$	−5.90833	−1.35546	−0.677732	+	0.735309i	$0.737037\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	1.69722i	0.361849i
$23$	1.00000i	0.208514i
$23$	1.00000i	0.208514i
$24$	−0.302776	−0.0618038
$25$	0	0
$26$	−3.30278	−0.647728
$27$	1.78890i	0.344273i
$28$	− 3.30278i	− 0.624166i
$29$	2.60555	0.483839	0.241919	−	0.970296i	$-0.422223\pi$
$29$	2.60555	0.483839	0.241919	+	0.970296i	$0.422223\pi$
$30$	0	0
$31$	−7.90833	−1.42038	−0.710189	−	0.704011i	$-0.751390\pi$
$31$	−7.90833	−1.42038	−0.710189	+	0.704011i	$0.751390\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 0.513878i	− 0.0894547i
$34$	6.90833	1.18477
$35$	0	0
$36$	−2.90833	−0.484721
$37$	8.00000i	1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$	8.00000i	1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$	5.90833i	0.958457i
$39$	1.00000	0.160128
$40$	0	0
$41$	0.908327	0.141857	0.0709284	−	0.997481i	$-0.477404\pi$
$41$	0.908327	0.141857	0.0709284	+	0.997481i	$0.477404\pi$
$42$	1.00000i	0.154303i
$43$	9.21110i	1.40468i	0.711842	+	0.702340i	$0.247861\pi$
$43$	9.21110i	1.40468i	−0.711842	+	0.702340i	$0.752139\pi$
$44$	1.69722	0.255866
$45$	0	0
$46$	1.00000	0.147442
$47$	− 2.60555i	− 0.380059i	−0.981778	−	0.190029i	$-0.939142\pi$
$47$	− 2.60555i	− 0.380059i	0.981778	−	0.190029i	$-0.0608583\pi$
$48$	0.302776i	0.0437019i
$49$	−3.90833	−0.558332
$50$	0	0
$51$	−2.09167	−0.292893
$52$	3.30278i	0.458013i
$53$	11.2111i	1.53996i	0.638066	+	0.769982i	$0.279735\pi$
$53$	11.2111i	1.53996i	−0.638066	+	0.769982i	$0.720265\pi$
$54$	1.78890	0.243438
$55$	0	0
$56$	−3.30278	−0.441352
$57$	− 1.78890i	− 0.236945i
$58$	− 2.60555i	− 0.342126i
$59$	3.39445	0.441920	0.220960	−	0.975283i	$-0.429081\pi$
$59$	3.39445	0.441920	0.220960	+	0.975283i	$0.429081\pi$
$60$	0	0
$61$	11.5139	1.47420	0.737101	−	0.675783i	$-0.236194\pi$
$61$	11.5139	1.47420	0.737101	+	0.675783i	$0.236194\pi$
$62$	7.90833i	1.00436i
$63$	9.60555i	1.21019i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−0.513878	−0.0632540
$67$	− 4.00000i	− 0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$	− 4.00000i	− 0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$	− 6.90833i	− 0.837758i
$69$	−0.302776	−0.0364499
$70$	0	0
$71$	−16.3028	−1.93478	−0.967392	−	0.253285i	$-0.918489\pi$
$71$	−16.3028	−1.93478	−0.967392	+	0.253285i	$0.918489\pi$
$72$	2.90833i	0.342750i
$73$	5.81665i	0.680788i	0.940283	+	0.340394i	$0.110560\pi$
$73$	5.81665i	0.680788i	−0.940283	+	0.340394i	$0.889440\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	5.90833	0.677732
$77$	− 5.60555i	− 0.638812i
$78$	− 1.00000i	− 0.113228i
$79$	14.4222	1.62262	0.811312	−	0.584613i	$-0.198754\pi$
$79$	14.4222	1.62262	0.811312	+	0.584613i	$0.198754\pi$
$80$	0	0
$81$	8.18335	0.909261
$82$	− 0.908327i	− 0.100308i
$83$	− 11.2111i	− 1.23058i	−0.788301	−	0.615289i	$-0.789039\pi$
$83$	− 11.2111i	− 1.23058i	0.788301	−	0.615289i	$-0.210961\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	9.21110	0.993259
$87$	0.788897i	0.0845787i
$88$	− 1.69722i	− 0.180925i
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	10.9083	1.14350
$92$	− 1.00000i	− 0.104257i
$93$	− 2.39445i	− 0.248293i
$94$	−2.60555	−0.268742
$95$	0	0
$96$	0.302776	0.0309019
$97$	6.30278i	0.639950i	0.947426	+	0.319975i	$0.103675\pi$
$97$	6.30278i	0.639950i	−0.947426	+	0.319975i	$0.896325\pi$
$98$	3.90833i	0.394801i
$99$	−4.93608	−0.496095
$100$	0	0
$101$	2.60555	0.259262	0.129631	−	0.991562i	$-0.458621\pi$
$101$	2.60555	0.259262	0.129631	+	0.991562i	$0.458621\pi$
$102$	2.09167i	0.207106i
$103$	− 8.11943i	− 0.800031i	−0.916508	−	0.400016i	$-0.869005\pi$
$103$	− 8.11943i	− 0.800031i	0.916508	−	0.400016i	$-0.130995\pi$
$104$	3.30278	0.323864
$105$	0	0
$106$	11.2111	1.08892
$107$	− 2.60555i	− 0.251888i	−0.992037	−	0.125944i	$-0.959804\pi$
$107$	− 2.60555i	− 0.251888i	0.992037	−	0.125944i	$-0.0401960\pi$
$108$	− 1.78890i	− 0.172137i
$109$	−1.48612	−0.142345	−0.0711723	−	0.997464i	$-0.522674\pi$
$109$	−1.48612	−0.142345	−0.0711723	+	0.997464i	$0.522674\pi$
$110$	0	0
$111$	−2.42221	−0.229906
$112$	3.30278i	0.312083i
$113$	16.4222i	1.54487i	0.635093	+	0.772436i	$0.280962\pi$
$113$	16.4222i	1.54487i	−0.635093	+	0.772436i	$0.719038\pi$
$114$	−1.78890	−0.167546
$115$	0	0
$116$	−2.60555	−0.241919
$117$	− 9.60555i	− 0.888034i
$118$	− 3.39445i	− 0.312484i
$119$	−22.8167	−2.09160
$120$	0	0
$121$	−8.11943	−0.738130
$122$	− 11.5139i	− 1.04242i
$123$	0.275019i	0.0247977i
$124$	7.90833	0.710189
$125$	0	0
$126$	9.60555	0.855731
$127$	9.81665i	0.871087i	0.900168	+	0.435544i	$0.143444\pi$
$127$	9.81665i	0.871087i	−0.900168	+	0.435544i	$0.856556\pi$
$128$	1.00000i	0.0883883i
$129$	−2.78890	−0.245549
$130$	0	0
$131$	−11.2111	−0.979519	−0.489759	−	0.871858i	$-0.662915\pi$
$131$	−11.2111	−0.979519	−0.489759	+	0.871858i	$0.662915\pi$
$132$	0.513878i	0.0447274i
$133$	− 19.5139i	− 1.69207i
$134$	−4.00000	−0.345547
$135$	0	0
$136$	−6.90833	−0.592384
$137$	3.90833i	0.333911i	0.985964	+	0.166955i	$0.0533936\pi$
$137$	3.90833i	0.333911i	−0.985964	+	0.166955i	$0.946606\pi$
$138$	0.302776i	0.0257740i
$139$	12.6056	1.06919	0.534594	−	0.845109i	$-0.320464\pi$
$139$	12.6056	1.06919	0.534594	+	0.845109i	$0.320464\pi$
$140$	0	0
$141$	0.788897	0.0664372
$142$	16.3028i	1.36810i
$143$	5.60555i	0.468760i
$144$	2.90833	0.242361
$145$	0	0
$146$	5.81665	0.481390
$147$	− 1.18335i	− 0.0976007i
$148$	− 8.00000i	− 0.657596i
$149$	−13.3028	−1.08981	−0.544903	−	0.838499i	$-0.683433\pi$
$149$	−13.3028	−1.08981	−0.544903	+	0.838499i	$0.683433\pi$
$150$	0	0
$151$	8.90833	0.724949	0.362475	−	0.931994i	$-0.381932\pi$
$151$	8.90833	0.724949	0.362475	+	0.931994i	$0.381932\pi$
$152$	− 5.90833i	− 0.479229i
$153$	20.0917i	1.62432i
$154$	−5.60555	−0.451708
$155$	0	0
$156$	−1.00000	−0.0800641
$157$	− 18.6056i	− 1.48488i	−0.669910	−	0.742442i	$-0.733667\pi$
$157$	− 18.6056i	− 1.48488i	0.669910	−	0.742442i	$-0.266333\pi$
$158$	− 14.4222i	− 1.14737i
$159$	−3.39445	−0.269197
$160$	0	0
$161$	−3.30278	−0.260295
$162$	− 8.18335i	− 0.642944i
$163$	− 9.30278i	− 0.728650i	−0.931272	−	0.364325i	$-0.881300\pi$
$163$	− 9.30278i	− 0.728650i	0.931272	−	0.364325i	$-0.118700\pi$
$164$	−0.908327	−0.0709284
$165$	0	0
$166$	−11.2111	−0.870150
$167$	6.78890i	0.525341i	0.964886	+	0.262670i	$0.0846032\pi$
$167$	6.78890i	0.525341i	−0.964886	+	0.262670i	$0.915397\pi$
$168$	− 1.00000i	− 0.0771517i
$169$	2.09167	0.160898
$170$	0	0
$171$	−17.1833	−1.31404
$172$	− 9.21110i	− 0.702340i
$173$	− 19.6972i	− 1.49755i	−0.662823	−	0.748776i	$-0.730642\pi$
$173$	− 19.6972i	− 1.49755i	0.662823	−	0.748776i	$-0.269358\pi$
$174$	0.788897	0.0598062
$175$	0	0
$176$	−1.69722	−0.127933
$177$	1.02776i	0.0772509i
$178$	0	0
$179$	−9.39445	−0.702174	−0.351087	−	0.936343i	$-0.614188\pi$
$179$	−9.39445	−0.702174	−0.351087	+	0.936343i	$0.614188\pi$
$180$	0	0
$181$	17.1194	1.27248	0.636239	−	0.771492i	$-0.280489\pi$
$181$	17.1194	1.27248	0.636239	+	0.771492i	$0.280489\pi$
$182$	− 10.9083i	− 0.808579i
$183$	3.48612i	0.257702i
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	−2.39445	−0.175569
$187$	− 11.7250i	− 0.857416i
$188$	2.60555i	0.190029i
$189$	−5.90833	−0.429768
$190$	0	0
$191$	−8.60555	−0.622676	−0.311338	−	0.950299i	$-0.600777\pi$
$191$	−8.60555	−0.622676	−0.311338	+	0.950299i	$0.600777\pi$
$192$	− 0.302776i	− 0.0218509i
$193$	17.8167i	1.28247i	0.767344	+	0.641235i	$0.221578\pi$
$193$	17.8167i	1.28247i	−0.767344	+	0.641235i	$0.778422\pi$
$194$	6.30278	0.452513
$195$	0	0
$196$	3.90833	0.279166
$197$	4.30278i	0.306560i	0.988183	+	0.153280i	$0.0489837\pi$
$197$	4.30278i	0.306560i	−0.988183	+	0.153280i	$0.951016\pi$
$198$	4.93608i	0.350792i
$199$	20.4222	1.44769	0.723846	−	0.689962i	$-0.242373\pi$
$199$	20.4222	1.44769	0.723846	+	0.689962i	$0.242373\pi$
$200$	0	0
$201$	1.21110	0.0854246
$202$	− 2.60555i	− 0.183326i
$203$	8.60555i	0.603991i
$204$	2.09167	0.146446
$205$	0	0
$206$	−8.11943	−0.565707
$207$	2.90833i	0.202143i
$208$	− 3.30278i	− 0.229006i
$209$	10.0278	0.693634
$210$	0	0
$211$	7.21110	0.496433	0.248216	−	0.968705i	$-0.420156\pi$
$211$	7.21110	0.496433	0.248216	+	0.968705i	$0.420156\pi$
$212$	− 11.2111i	− 0.769982i
$213$	− 4.93608i	− 0.338215i
$214$	−2.60555	−0.178112
$215$	0	0
$216$	−1.78890	−0.121719
$217$	− 26.1194i	− 1.77310i
$218$	1.48612i	0.100653i
$219$	−1.76114	−0.119007
$220$	0	0
$221$	22.8167	1.53481
$222$	2.42221i	0.162568i
$223$	4.00000i	0.267860i	0.990991	+	0.133930i	$0.0427597\pi$
$223$	4.00000i	0.267860i	−0.990991	+	0.133930i	$0.957240\pi$
$224$	3.30278	0.220676
$225$	0	0
$226$	16.4222	1.09239
$227$	− 14.6056i	− 0.969404i	−0.874679	−	0.484702i	$-0.838928\pi$
$227$	− 14.6056i	− 0.969404i	0.874679	−	0.484702i	$-0.161072\pi$
$228$	1.78890i	0.118473i
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	0	0
$231$	1.69722	0.111669
$232$	2.60555i	0.171063i
$233$	− 25.8167i	− 1.69131i	−0.533734	−	0.845653i	$-0.679212\pi$
$233$	− 25.8167i	− 1.69131i	0.533734	−	0.845653i	$-0.320788\pi$
$234$	−9.60555	−0.627935
$235$	0	0
$236$	−3.39445	−0.220960
$237$	4.36669i	0.283647i
$238$	22.8167i	1.47898i
$239$	−5.21110	−0.337078	−0.168539	−	0.985695i	$-0.553905\pi$
$239$	−5.21110	−0.337078	−0.168539	+	0.985695i	$0.553905\pi$
$240$	0	0
$241$	−14.4222	−0.929016	−0.464508	−	0.885569i	$-0.653769\pi$
$241$	−14.4222	−0.929016	−0.464508	+	0.885569i	$0.653769\pi$
$242$	8.11943i	0.521937i
$243$	7.84441i	0.503219i
$244$	−11.5139	−0.737101
$245$	0	0
$246$	0.275019	0.0175346
$247$	19.5139i	1.24164i
$248$	− 7.90833i	− 0.502179i
$249$	3.39445	0.215114
$250$	0	0
$251$	12.5139	0.789869	0.394934	−	0.918709i	$-0.370767\pi$
$251$	12.5139	0.789869	0.394934	+	0.918709i	$0.370767\pi$
$252$	− 9.60555i	− 0.605093i
$253$	− 1.69722i	− 0.106704i
$254$	9.81665	0.615952
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 1.81665i	− 0.113320i	−0.998394	−	0.0566599i	$-0.981955\pi$
$257$	− 1.81665i	− 0.113320i	0.998394	−	0.0566599i	$-0.0180451\pi$
$258$	2.78890i	0.173629i
$259$	−26.4222	−1.64180
$260$	0	0
$261$	7.57779	0.469054
$262$	11.2111i	0.692624i
$263$	− 3.51388i	− 0.216675i	−0.994114	−	0.108338i	$-0.965447\pi$
$263$	− 3.51388i	− 0.216675i	0.994114	−	0.108338i	$-0.0345527\pi$
$264$	0.513878	0.0316270
$265$	0	0
$266$	−19.5139	−1.19647
$267$	0	0
$268$	4.00000i	0.244339i
$269$	−4.18335	−0.255063	−0.127532	−	0.991835i	$-0.540705\pi$
$269$	−4.18335	−0.255063	−0.127532	+	0.991835i	$0.540705\pi$
$270$	0	0
$271$	−2.69722	−0.163845	−0.0819224	−	0.996639i	$-0.526106\pi$
$271$	−2.69722	−0.163845	−0.0819224	+	0.996639i	$0.526106\pi$
$272$	6.90833i	0.418879i
$273$	3.30278i	0.199893i
$274$	3.90833	0.236111
$275$	0	0
$276$	0.302776	0.0182250
$277$	− 27.2111i	− 1.63496i	−0.575959	−	0.817478i	$-0.695371\pi$
$277$	− 27.2111i	− 1.63496i	0.575959	−	0.817478i	$-0.304629\pi$
$278$	− 12.6056i	− 0.756031i
$279$	−23.0000	−1.37697
$280$	0	0
$281$	−26.6056	−1.58715	−0.793577	−	0.608470i	$-0.791784\pi$
$281$	−26.6056	−1.58715	−0.793577	+	0.608470i	$0.791784\pi$
$282$	− 0.788897i	− 0.0469782i
$283$	− 2.00000i	− 0.118888i	−0.998232	−	0.0594438i	$-0.981067\pi$
$283$	− 2.00000i	− 0.118888i	0.998232	−	0.0594438i	$-0.0189327\pi$
$284$	16.3028	0.967392
$285$	0	0
$286$	5.60555	0.331463
$287$	3.00000i	0.177084i
$288$	− 2.90833i	− 0.171375i
$289$	−30.7250	−1.80735
$290$	0	0
$291$	−1.90833	−0.111868
$292$	− 5.81665i	− 0.340394i
$293$	− 23.2111i	− 1.35601i	−0.735059	−	0.678004i	$-0.762845\pi$
$293$	− 23.2111i	− 1.35601i	0.735059	−	0.678004i	$-0.237155\pi$
$294$	−1.18335	−0.0690142
$295$	0	0
$296$	−8.00000	−0.464991
$297$	− 3.03616i	− 0.176176i
$298$	13.3028i	0.770609i
$299$	3.30278	0.191004
$300$	0	0
$301$	−30.4222	−1.75351
$302$	− 8.90833i	− 0.512617i
$303$	0.788897i	0.0453210i
$304$	−5.90833	−0.338866
$305$	0	0
$306$	20.0917	1.14856
$307$	− 11.6972i	− 0.667596i	−0.942645	−	0.333798i	$-0.891670\pi$
$307$	− 11.6972i	− 0.667596i	0.942645	−	0.333798i	$-0.108330\pi$
$308$	5.60555i	0.319406i
$309$	2.45837	0.139852
$310$	0	0
$311$	22.4222	1.27145	0.635723	−	0.771917i	$-0.280702\pi$
$311$	22.4222	1.27145	0.635723	+	0.771917i	$0.280702\pi$
$312$	1.00000i	0.0566139i
$313$	− 19.7250i	− 1.11492i	−0.830203	−	0.557461i	$-0.811776\pi$
$313$	− 19.7250i	− 1.11492i	0.830203	−	0.557461i	$-0.188224\pi$
$314$	−18.6056	−1.04997
$315$	0	0
$316$	−14.4222	−0.811312
$317$	17.7250i	0.995534i	0.867311	+	0.497767i	$0.165847\pi$
$317$	17.7250i	0.995534i	−0.867311	+	0.497767i	$0.834153\pi$
$318$	3.39445i	0.190351i
$319$	−4.42221	−0.247596
$320$	0	0
$321$	0.788897	0.0440320
$322$	3.30278i	0.184056i
$323$	− 40.8167i	− 2.27110i
$324$	−8.18335	−0.454630
$325$	0	0
$326$	−9.30278	−0.515233
$327$	− 0.449961i	− 0.0248829i
$328$	0.908327i	0.0501540i
$329$	8.60555	0.474439
$330$	0	0
$331$	16.6056	0.912724	0.456362	−	0.889794i	$-0.349152\pi$
$331$	16.6056	0.912724	0.456362	+	0.889794i	$0.349152\pi$
$332$	11.2111i	0.615289i
$333$	23.2666i	1.27500i
$334$	6.78890	0.371472
$335$	0	0
$336$	−1.00000	−0.0545545
$337$	− 22.5139i	− 1.22641i	−0.789924	−	0.613205i	$-0.789880\pi$
$337$	− 22.5139i	− 1.22641i	0.789924	−	0.613205i	$-0.210120\pi$
$338$	− 2.09167i	− 0.113772i
$339$	−4.97224	−0.270055
$340$	0	0
$341$	13.4222	0.726853
$342$	17.1833i	0.929169i
$343$	10.2111i	0.551348i
$344$	−9.21110	−0.496629
$345$	0	0
$346$	−19.6972	−1.05893
$347$	28.5416i	1.53220i	0.642724	+	0.766098i	$0.277804\pi$
$347$	28.5416i	1.53220i	−0.642724	+	0.766098i	$0.722196\pi$
$348$	− 0.788897i	− 0.0422893i
$349$	27.2111	1.45658	0.728288	−	0.685271i	$-0.240316\pi$
$349$	27.2111	1.45658	0.728288	+	0.685271i	$0.240316\pi$
$350$	0	0
$351$	5.90833	0.315363
$352$	1.69722i	0.0904624i
$353$	10.4222i	0.554718i	0.960766	+	0.277359i	$0.0894591\pi$
$353$	10.4222i	0.554718i	−0.960766	+	0.277359i	$0.910541\pi$
$354$	1.02776	0.0546246
$355$	0	0
$356$	0	0
$357$	− 6.90833i	− 0.365627i
$358$	9.39445i	0.496512i
$359$	−11.2111	−0.591699	−0.295850	−	0.955235i	$-0.595603\pi$
$359$	−11.2111	−0.591699	−0.295850	+	0.955235i	$0.595603\pi$
$360$	0	0
$361$	15.9083	0.837280
$362$	− 17.1194i	− 0.899777i
$363$	− 2.45837i	− 0.129031i
$364$	−10.9083	−0.571752
$365$	0	0
$366$	3.48612	0.182223
$367$	14.7889i	0.771974i	0.922504	+	0.385987i	$0.126139\pi$
$367$	14.7889i	0.771974i	−0.922504	+	0.385987i	$0.873861\pi$
$368$	1.00000i	0.0521286i
$369$	2.64171	0.137522
$370$	0	0
$371$	−37.0278	−1.92239
$372$	2.39445i	0.124146i
$373$	− 4.60555i	− 0.238466i	−0.992866	−	0.119233i	$-0.961956\pi$
$373$	− 4.60555i	− 0.238466i	0.992866	−	0.119233i	$-0.0380436\pi$
$374$	−11.7250	−0.606284
$375$	0	0
$376$	2.60555	0.134371
$377$	− 8.60555i	− 0.443208i
$378$	5.90833i	0.303892i
$379$	−14.9083	−0.765789	−0.382895	−	0.923792i	$-0.625073\pi$
$379$	−14.9083	−0.765789	−0.382895	+	0.923792i	$0.625073\pi$
$380$	0	0
$381$	−2.97224	−0.152273
$382$	8.60555i	0.440298i
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	−0.302776	−0.0154510
$385$	0	0
$386$	17.8167	0.906844
$387$	26.7889i	1.36176i
$388$	− 6.30278i	− 0.319975i
$389$	25.9361	1.31501	0.657506	−	0.753449i	$-0.271612\pi$
$389$	25.9361	1.31501	0.657506	+	0.753449i	$0.271612\pi$
$390$	0	0
$391$	−6.90833	−0.349369
$392$	− 3.90833i	− 0.197400i
$393$	− 3.39445i	− 0.171227i
$394$	4.30278	0.216771
$395$	0	0
$396$	4.93608	0.248048
$397$	10.7250i	0.538271i	0.963102	+	0.269136i	$0.0867380\pi$
$397$	10.7250i	0.538271i	−0.963102	+	0.269136i	$0.913262\pi$
$398$	− 20.4222i	− 1.02367i
$399$	5.90833	0.295786
$400$	0	0
$401$	−8.60555	−0.429741	−0.214870	−	0.976643i	$-0.568933\pi$
$401$	−8.60555	−0.429741	−0.214870	+	0.976643i	$0.568933\pi$
$402$	− 1.21110i	− 0.0604043i
$403$	26.1194i	1.30110i
$404$	−2.60555	−0.129631
$405$	0	0
$406$	8.60555	0.427086
$407$	− 13.5778i	− 0.673026i
$408$	− 2.09167i	− 0.103553i
$409$	25.9083	1.28108	0.640542	−	0.767923i	$-0.278710\pi$
$409$	25.9083	1.28108	0.640542	+	0.767923i	$0.278710\pi$
$410$	0	0
$411$	−1.18335	−0.0583702
$412$	8.11943i	0.400016i
$413$	11.2111i	0.551662i
$414$	2.90833	0.142936
$415$	0	0
$416$	−3.30278	−0.161932
$417$	3.81665i	0.186902i
$418$	− 10.0278i	− 0.490474i
$419$	−3.63331	−0.177499	−0.0887493	−	0.996054i	$-0.528287\pi$
$419$	−3.63331	−0.177499	−0.0887493	+	0.996054i	$0.528287\pi$
$420$	0	0
$421$	30.6972	1.49609	0.748046	−	0.663647i	$-0.230992\pi$
$421$	30.6972	1.49609	0.748046	+	0.663647i	$0.230992\pi$
$422$	− 7.21110i	− 0.351031i
$423$	− 7.57779i	− 0.368445i
$424$	−11.2111	−0.544459
$425$	0	0
$426$	−4.93608	−0.239154
$427$	38.0278i	1.84029i
$428$	2.60555i	0.125944i
$429$	−1.69722	−0.0819428
$430$	0	0
$431$	−30.2389	−1.45655	−0.728277	−	0.685283i	$-0.759679\pi$
$431$	−30.2389	−1.45655	−0.728277	+	0.685283i	$0.759679\pi$
$432$	1.78890i	0.0860684i
$433$	24.0917i	1.15777i	0.815409	+	0.578886i	$0.196512\pi$
$433$	24.0917i	1.15777i	−0.815409	+	0.578886i	$0.803488\pi$
$434$	−26.1194	−1.25377
$435$	0	0
$436$	1.48612	0.0711723
$437$	− 5.90833i	− 0.282634i
$438$	1.76114i	0.0841506i
$439$	14.6972	0.701460	0.350730	−	0.936477i	$-0.385933\pi$
$439$	14.6972	0.701460	0.350730	+	0.936477i	$0.385933\pi$
$440$	0	0
$441$	−11.3667	−0.541271
$442$	− 22.8167i	− 1.08528i
$443$	− 17.4861i	− 0.830791i	−0.909641	−	0.415395i	$-0.863643\pi$
$443$	− 17.4861i	− 0.830791i	0.909641	−	0.415395i	$-0.136357\pi$
$444$	2.42221	0.114953
$445$	0	0
$446$	4.00000	0.189405
$447$	− 4.02776i	− 0.190506i
$448$	− 3.30278i	− 0.156041i
$449$	2.09167	0.0987122	0.0493561	−	0.998781i	$-0.484283\pi$
$449$	2.09167	0.0987122	0.0493561	+	0.998781i	$0.484283\pi$
$450$	0	0
$451$	−1.54163	−0.0725927
$452$	− 16.4222i	− 0.772436i
$453$	2.69722i	0.126727i
$454$	−14.6056	−0.685472
$455$	0	0
$456$	1.78890	0.0837728
$457$	− 32.4222i	− 1.51665i	−0.651879	−	0.758323i	$-0.726019\pi$
$457$	− 32.4222i	− 1.51665i	0.651879	−	0.758323i	$-0.273981\pi$
$458$	2.00000i	0.0934539i
$459$	−12.3583	−0.576836
$460$	0	0
$461$	10.1833	0.474286	0.237143	−	0.971475i	$-0.423789\pi$
$461$	10.1833	0.474286	0.237143	+	0.971475i	$0.423789\pi$
$462$	− 1.69722i	− 0.0789620i
$463$	− 17.6333i	− 0.819489i	−0.912200	−	0.409745i	$-0.865618\pi$
$463$	− 17.6333i	− 0.819489i	0.912200	−	0.409745i	$-0.134382\pi$
$464$	2.60555	0.120960
$465$	0	0
$466$	−25.8167	−1.19593
$467$	− 1.81665i	− 0.0840647i	−0.999116	−	0.0420324i	$-0.986617\pi$
$467$	− 1.81665i	− 0.0840647i	0.999116	−	0.0420324i	$-0.0133833\pi$
$468$	9.60555i	0.444017i
$469$	13.2111	0.610032
$470$	0	0
$471$	5.63331	0.259569
$472$	3.39445i	0.156242i
$473$	− 15.6333i	− 0.718820i
$474$	4.36669	0.200569
$475$	0	0
$476$	22.8167	1.04580
$477$	32.6056i	1.49291i
$478$	5.21110i	0.238350i
$479$	30.0000	1.37073	0.685367	−	0.728197i	$-0.259642\pi$
$479$	30.0000	1.37073	0.685367	+	0.728197i	$0.259642\pi$
$480$	0	0
$481$	26.4222	1.20475
$482$	14.4222i	0.656913i
$483$	− 1.00000i	− 0.0455016i
$484$	8.11943	0.369065
$485$	0	0
$486$	7.84441	0.355830
$487$	9.81665i	0.444835i	0.974952	+	0.222418i	$0.0713948\pi$
$487$	9.81665i	0.444835i	−0.974952	+	0.222418i	$0.928605\pi$
$488$	11.5139i	0.521209i
$489$	2.81665	0.127373
$490$	0	0
$491$	−4.18335	−0.188792	−0.0943959	−	0.995535i	$-0.530092\pi$
$491$	−4.18335	−0.188792	−0.0943959	+	0.995535i	$0.530092\pi$
$492$	− 0.275019i	− 0.0123988i
$493$	18.0000i	0.810679i
$494$	19.5139	0.877971
$495$	0	0
$496$	−7.90833	−0.355094
$497$	− 53.8444i	− 2.41525i
$498$	− 3.39445i	− 0.152109i
$499$	31.6333	1.41610	0.708051	−	0.706162i	$-0.249575\pi$
$499$	31.6333	1.41610	0.708051	+	0.706162i	$0.249575\pi$
$500$	0	0
$501$	−2.05551	−0.0918335
$502$	− 12.5139i	− 0.558522i
$503$	− 29.7250i	− 1.32537i	−0.748898	−	0.662686i	$-0.769417\pi$
$503$	− 29.7250i	− 1.32537i	0.748898	−	0.662686i	$-0.230583\pi$
$504$	−9.60555	−0.427865
$505$	0	0
$506$	−1.69722	−0.0754508
$507$	0.633308i	0.0281262i
$508$	− 9.81665i	− 0.435544i
$509$	35.4500	1.57129	0.785646	−	0.618676i	$-0.212331\pi$
$509$	35.4500	1.57129	0.785646	+	0.618676i	$0.212331\pi$
$510$	0	0
$511$	−19.2111	−0.849849
$512$	− 1.00000i	− 0.0441942i
$513$	− 10.5694i	− 0.466650i
$514$	−1.81665	−0.0801292
$515$	0	0
$516$	2.78890	0.122774
$517$	4.42221i	0.194488i
$518$	26.4222i	1.16093i
$519$	5.96384	0.261784
$520$	0	0
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	− 7.57779i	− 0.331671i
$523$	20.4222i	0.893001i	0.894783	+	0.446500i	$0.147330\pi$
$523$	20.4222i	0.893001i	−0.894783	+	0.446500i	$0.852670\pi$
$524$	11.2111	0.489759
$525$	0	0
$526$	−3.51388	−0.153212
$527$	− 54.6333i	− 2.37986i
$528$	− 0.513878i	− 0.0223637i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	9.87217	0.428416
$532$	19.5139i	0.846034i
$533$	− 3.00000i	− 0.129944i
$534$	0	0
$535$	0	0
$536$	4.00000	0.172774
$537$	− 2.84441i	− 0.122745i
$538$	4.18335i	0.180357i
$539$	6.63331	0.285717
$540$	0	0
$541$	28.8444	1.24012	0.620059	−	0.784555i	$-0.287109\pi$
$541$	28.8444	1.24012	0.620059	+	0.784555i	$0.287109\pi$
$542$	2.69722i	0.115856i
$543$	5.18335i	0.222439i
$544$	6.90833	0.296192
$545$	0	0
$546$	3.30278	0.141346
$547$	− 10.5139i	− 0.449541i	−0.974412	−	0.224770i	$-0.927837\pi$
$547$	− 10.5139i	− 0.449541i	0.974412	−	0.224770i	$-0.0721632\pi$
$548$	− 3.90833i	− 0.166955i
$549$	33.4861	1.42915
$550$	0	0
$551$	−15.3944	−0.655826
$552$	− 0.302776i	− 0.0128870i
$553$	47.6333i	2.02557i
$554$	−27.2111	−1.15609
$555$	0	0
$556$	−12.6056	−0.534594
$557$	22.4222i	0.950059i	0.879970	+	0.475030i	$0.157563\pi$
$557$	22.4222i	0.950059i	−0.879970	+	0.475030i	$0.842437\pi$
$558$	23.0000i	0.973668i
$559$	30.4222	1.28672
$560$	0	0
$561$	3.55004	0.149883
$562$	26.6056i	1.12229i
$563$	3.63331i	0.153126i	0.997065	+	0.0765628i	$0.0243946\pi$
$563$	3.63331i	0.153126i	−0.997065	+	0.0765628i	$0.975605\pi$
$564$	−0.788897	−0.0332186
$565$	0	0
$566$	−2.00000	−0.0840663
$567$	27.0278i	1.13506i
$568$	− 16.3028i	− 0.684049i
$569$	−28.4222	−1.19152	−0.595760	−	0.803162i	$-0.703149\pi$
$569$	−28.4222	−1.19152	−0.595760	+	0.803162i	$0.703149\pi$
$570$	0	0
$571$	−16.1194	−0.674577	−0.337289	−	0.941401i	$-0.609510\pi$
$571$	−16.1194	−0.674577	−0.337289	+	0.941401i	$0.609510\pi$
$572$	− 5.60555i	− 0.234380i
$573$	− 2.60555i	− 0.108848i
$574$	3.00000	0.125218
$575$	0	0
$576$	−2.90833	−0.121180
$577$	2.00000i	0.0832611i	0.999133	+	0.0416305i	$0.0132552\pi$
$577$	2.00000i	0.0832611i	−0.999133	+	0.0416305i	$0.986745\pi$
$578$	30.7250i	1.27799i
$579$	−5.39445	−0.224186
$580$	0	0
$581$	37.0278	1.53617
$582$	1.90833i	0.0791027i
$583$	− 19.0278i	− 0.788049i
$584$	−5.81665	−0.240695
$585$	0	0
$586$	−23.2111	−0.958842
$587$	16.5416i	0.682746i	0.939928	+	0.341373i	$0.110892\pi$
$587$	16.5416i	0.682746i	−0.939928	+	0.341373i	$0.889108\pi$
$588$	1.18335i	0.0488004i
$589$	46.7250	1.92527
$590$	0	0
$591$	−1.30278	−0.0535890
$592$	8.00000i	0.328798i
$593$	1.81665i	0.0746010i	0.999304	+	0.0373005i	$0.0118759\pi$
$593$	1.81665i	0.0746010i	−0.999304	+	0.0373005i	$0.988124\pi$
$594$	−3.03616	−0.124575
$595$	0	0
$596$	13.3028	0.544903
$597$	6.18335i	0.253068i
$598$	− 3.30278i	− 0.135061i
$599$	35.3305	1.44357	0.721783	−	0.692119i	$-0.243323\pi$
$599$	35.3305	1.44357	0.721783	+	0.692119i	$0.243323\pi$
$600$	0	0
$601$	42.9361	1.75140	0.875700	−	0.482856i	$-0.160401\pi$
$601$	42.9361	1.75140	0.875700	+	0.482856i	$0.160401\pi$
$602$	30.4222i	1.23992i
$603$	− 11.6333i	− 0.473745i
$604$	−8.90833	−0.362475
$605$	0	0
$606$	0.788897	0.0320468
$607$	46.0555i	1.86934i	0.355522	+	0.934668i	$0.384303\pi$
$607$	46.0555i	1.86934i	−0.355522	+	0.934668i	$0.615697\pi$
$608$	5.90833i	0.239614i
$609$	−2.60555	−0.105582
$610$	0	0
$611$	−8.60555	−0.348143
$612$	− 20.0917i	− 0.812158i
$613$	− 3.57779i	− 0.144506i	−0.997386	−	0.0722529i	$-0.976981\pi$
$613$	− 3.57779i	− 0.144506i	0.997386	−	0.0722529i	$-0.0230189\pi$
$614$	−11.6972	−0.472062
$615$	0	0
$616$	5.60555	0.225854
$617$	18.9083i	0.761221i	0.924736	+	0.380610i	$0.124286\pi$
$617$	18.9083i	0.761221i	−0.924736	+	0.380610i	$0.875714\pi$
$618$	− 2.45837i	− 0.0988900i
$619$	12.3305	0.495606	0.247803	−	0.968810i	$-0.420291\pi$
$619$	12.3305	0.495606	0.247803	+	0.968810i	$0.420291\pi$
$620$	0	0
$621$	−1.78890	−0.0717860
$622$	− 22.4222i	− 0.899049i
$623$	0	0
$624$	1.00000	0.0400320
$625$	0	0
$626$	−19.7250	−0.788369
$627$	3.03616i	0.121253i
$628$	18.6056i	0.742442i
$629$	−55.2666	−2.20362
$630$	0	0
$631$	23.3944	0.931318	0.465659	−	0.884964i	$-0.345817\pi$
$631$	23.3944	0.931318	0.465659	+	0.884964i	$0.345817\pi$
$632$	14.4222i	0.573685i
$633$	2.18335i	0.0867802i
$634$	17.7250	0.703949
$635$	0	0
$636$	3.39445	0.134599
$637$	12.9083i	0.511447i
$638$	4.42221i	0.175077i
$639$	−47.4138	−1.87566
$640$	0	0
$641$	−36.0000	−1.42191	−0.710957	−	0.703235i	$-0.751738\pi$
$641$	−36.0000	−1.42191	−0.710957	+	0.703235i	$0.751738\pi$
$642$	− 0.788897i	− 0.0311353i
$643$	34.2389i	1.35025i	0.737704	+	0.675124i	$0.235910\pi$
$643$	34.2389i	1.35025i	−0.737704	+	0.675124i	$0.764090\pi$
$644$	3.30278	0.130148
$645$	0	0
$646$	−40.8167	−1.60591
$647$	26.8444i	1.05536i	0.849442	+	0.527681i	$0.176938\pi$
$647$	26.8444i	1.05536i	−0.849442	+	0.527681i	$0.823062\pi$
$648$	8.18335i	0.321472i
$649$	−5.76114	−0.226145
$650$	0	0
$651$	7.90833	0.309952
$652$	9.30278i	0.364325i
$653$	− 41.7250i	− 1.63282i	−0.577469	−	0.816412i	$-0.695960\pi$
$653$	− 41.7250i	− 1.63282i	0.577469	−	0.816412i	$-0.304040\pi$
$654$	−0.449961	−0.0175949
$655$	0	0
$656$	0.908327	0.0354642
$657$	16.9167i	0.659985i
$658$	− 8.60555i	− 0.335479i
$659$	−15.6333	−0.608987	−0.304494	−	0.952514i	$-0.598487\pi$
$659$	−15.6333	−0.608987	−0.304494	+	0.952514i	$0.598487\pi$
$660$	0	0
$661$	−34.9083	−1.35778	−0.678888	−	0.734242i	$-0.737538\pi$
$661$	−34.9083	−1.35778	−0.678888	+	0.734242i	$0.737538\pi$
$662$	− 16.6056i	− 0.645393i
$663$	6.90833i	0.268297i
$664$	11.2111	0.435075
$665$	0	0
$666$	23.2666	0.901563
$667$	2.60555i	0.100887i
$668$	− 6.78890i	− 0.262670i
$669$	−1.21110	−0.0468239
$670$	0	0
$671$	−19.5416	−0.754396
$672$	1.00000i	0.0385758i
$673$	37.6333i	1.45066i	0.688403	+	0.725329i	$0.258312\pi$
$673$	37.6333i	1.45066i	−0.688403	+	0.725329i	$0.741688\pi$
$674$	−22.5139	−0.867202
$675$	0	0
$676$	−2.09167	−0.0804490
$677$	16.4222i	0.631157i	0.948900	+	0.315578i	$0.102198\pi$
$677$	16.4222i	0.631157i	−0.948900	+	0.315578i	$0.897802\pi$
$678$	4.97224i	0.190958i
$679$	−20.8167	−0.798870
$680$	0	0
$681$	4.42221	0.169459
$682$	− 13.4222i	− 0.513963i
$683$	0.275019i	0.0105233i	0.999986	+	0.00526166i	$0.00167485\pi$
$683$	0.275019i	0.0105233i	−0.999986	+	0.00526166i	$0.998325\pi$
$684$	17.1833	0.657022
$685$	0	0
$686$	10.2111	0.389862
$687$	− 0.605551i	− 0.0231032i
$688$	9.21110i	0.351170i
$689$	37.0278	1.41065
$690$	0	0
$691$	51.8167	1.97120	0.985599	−	0.169098i	$-0.0540855\pi$
$691$	51.8167	1.97120	0.985599	+	0.169098i	$0.0540855\pi$
$692$	19.6972i	0.748776i
$693$	− 16.3028i	− 0.619291i
$694$	28.5416	1.08343
$695$	0	0
$696$	−0.788897	−0.0299031
$697$	6.27502i	0.237683i
$698$	− 27.2111i	− 1.02996i
$699$	7.81665	0.295653
$700$	0	0
$701$	32.0917	1.21209	0.606043	−	0.795432i	$-0.292756\pi$
$701$	32.0917	1.21209	0.606043	+	0.795432i	$0.292756\pi$
$702$	− 5.90833i	− 0.222995i
$703$	− 47.2666i	− 1.78269i
$704$	1.69722	0.0639665
$705$	0	0
$706$	10.4222	0.392245
$707$	8.60555i	0.323645i
$708$	− 1.02776i	− 0.0386254i
$709$	15.8806	0.596407	0.298204	−	0.954502i	$-0.403613\pi$
$709$	15.8806	0.596407	0.298204	+	0.954502i	$0.403613\pi$
$710$	0	0
$711$	41.9445	1.57304
$712$	0	0
$713$	− 7.90833i	− 0.296169i
$714$	−6.90833	−0.258538
$715$	0	0
$716$	9.39445	0.351087
$717$	− 1.57779i	− 0.0589238i
$718$	11.2111i	0.418395i
$719$	−10.6972	−0.398939	−0.199470	−	0.979904i	$-0.563922\pi$
$719$	−10.6972	−0.398939	−0.199470	+	0.979904i	$0.563922\pi$
$720$	0	0
$721$	26.8167	0.998704
$722$	− 15.9083i	− 0.592047i
$723$	− 4.36669i	− 0.162399i
$724$	−17.1194	−0.636239
$725$	0	0
$726$	−2.45837	−0.0912385
$727$	2.90833i	0.107864i	0.998545	+	0.0539319i	$0.0171754\pi$
$727$	2.90833i	0.107864i	−0.998545	+	0.0539319i	$0.982825\pi$
$728$	10.9083i	0.404289i
$729$	22.1749	0.821294
$730$	0	0
$731$	−63.6333	−2.35356
$732$	− 3.48612i	− 0.128851i
$733$	− 29.6333i	− 1.09453i	−0.836959	−	0.547266i	$-0.815669\pi$
$733$	− 29.6333i	− 1.09453i	0.836959	−	0.547266i	$-0.184331\pi$
$734$	14.7889	0.545868
$735$	0	0
$736$	1.00000	0.0368605
$737$	6.78890i	0.250072i
$738$	− 2.64171i	− 0.0972427i
$739$	−35.6333	−1.31079	−0.655396	−	0.755285i	$-0.727498\pi$
$739$	−35.6333	−1.31079	−0.655396	+	0.755285i	$0.727498\pi$
$740$	0	0
$741$	−5.90833	−0.217048
$742$	37.0278i	1.35933i
$743$	32.3305i	1.18609i	0.805169	+	0.593046i	$0.202075\pi$
$743$	32.3305i	1.18609i	−0.805169	+	0.593046i	$0.797925\pi$
$744$	2.39445	0.0877847
$745$	0	0
$746$	−4.60555	−0.168621
$747$	− 32.6056i	− 1.19297i
$748$	11.7250i	0.428708i
$749$	8.60555	0.314440
$750$	0	0
$751$	21.8167	0.796101	0.398051	−	0.917364i	$-0.369687\pi$
$751$	21.8167	0.796101	0.398051	+	0.917364i	$0.369687\pi$
$752$	− 2.60555i	− 0.0950147i
$753$	3.78890i	0.138075i
$754$	−8.60555	−0.313396
$755$	0	0
$756$	5.90833	0.214884
$757$	13.2111i	0.480166i	0.970752	+	0.240083i	$0.0771746\pi$
$757$	13.2111i	0.480166i	−0.970752	+	0.240083i	$0.922825\pi$
$758$	14.9083i	0.541495i
$759$	0.513878	0.0186526
$760$	0	0
$761$	−49.5416	−1.79588	−0.897941	−	0.440115i	$-0.854938\pi$
$761$	−49.5416	−1.79588	−0.897941	+	0.440115i	$0.854938\pi$
$762$	2.97224i	0.107673i
$763$	− 4.90833i	− 0.177693i
$764$	8.60555	0.311338
$765$	0	0
$766$	0	0
$767$	− 11.2111i	− 0.404809i
$768$	0.302776i	0.0109255i
$769$	−45.2666	−1.63236	−0.816178	−	0.577801i	$-0.803911\pi$
$769$	−45.2666	−1.63236	−0.816178	+	0.577801i	$0.803911\pi$
$770$	0	0
$771$	0.550039	0.0198092
$772$	− 17.8167i	− 0.641235i
$773$	− 12.0000i	− 0.431610i	−0.976436	−	0.215805i	$-0.930762\pi$
$773$	− 12.0000i	− 0.431610i	0.976436	−	0.215805i	$-0.0692376\pi$
$774$	26.7889	0.962907
$775$	0	0
$776$	−6.30278	−0.226256
$777$	− 8.00000i	− 0.286998i
$778$	− 25.9361i	− 0.929854i
$779$	−5.36669	−0.192282
$780$	0	0
$781$	27.6695	0.990091
$782$	6.90833i	0.247041i
$783$	4.66106i	0.166573i
$784$	−3.90833	−0.139583
$785$	0	0
$786$	−3.39445	−0.121076
$787$	37.4500i	1.33495i	0.744634	+	0.667473i	$0.232624\pi$
$787$	37.4500i	1.33495i	−0.744634	+	0.667473i	$0.767376\pi$
$788$	− 4.30278i	− 0.153280i
$789$	1.06392	0.0378764
$790$	0	0
$791$	−54.2389	−1.92851
$792$	− 4.93608i	− 0.175396i
$793$	− 38.0278i	− 1.35041i
$794$	10.7250	0.380615
$795$	0	0
$796$	−20.4222	−0.723846
$797$	1.81665i	0.0643492i	0.999482	+	0.0321746i	$0.0102433\pi$
$797$	1.81665i	0.0643492i	−0.999482	+	0.0321746i	$0.989757\pi$
$798$	− 5.90833i	− 0.209153i
$799$	18.0000	0.636794
$800$	0	0
$801$	0	0
$802$	8.60555i	0.303873i
$803$	− 9.87217i	− 0.348381i
$804$	−1.21110	−0.0427123
$805$	0	0
$806$	26.1194	0.920018
$807$	− 1.26662i	− 0.0445870i
$808$	2.60555i	0.0916630i
$809$	−50.7250	−1.78340	−0.891698	−	0.452631i	$-0.850485\pi$
$809$	−50.7250	−1.78340	−0.891698	+	0.452631i	$0.850485\pi$
$810$	0	0
$811$	−41.0278	−1.44068	−0.720340	−	0.693621i	$-0.756014\pi$
$811$	−41.0278	−1.44068	−0.720340	+	0.693621i	$0.756014\pi$
$812$	− 8.60555i	− 0.301996i
$813$	− 0.816654i	− 0.0286413i
$814$	−13.5778	−0.475901
$815$	0	0
$816$	−2.09167	−0.0732232
$817$	− 54.4222i	− 1.90399i
$818$	− 25.9083i	− 0.905863i
$819$	31.7250	1.10856
$820$	0	0
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	1.18335i	0.0412739i
$823$	15.2111i	0.530226i	0.964217	+	0.265113i	$0.0854092\pi$
$823$	15.2111i	0.530226i	−0.964217	+	0.265113i	$0.914591\pi$
$824$	8.11943	0.282854
$825$	0	0
$826$	11.2111	0.390084
$827$	− 29.4500i	− 1.02408i	−0.858963	−	0.512038i	$-0.828891\pi$
$827$	− 29.4500i	− 1.02408i	0.858963	−	0.512038i	$-0.171109\pi$
$828$	− 2.90833i	− 0.101071i
$829$	−31.2111	−1.08401	−0.542003	−	0.840376i	$-0.682334\pi$
$829$	−31.2111	−1.08401	−0.542003	+	0.840376i	$0.682334\pi$
$830$	0	0
$831$	8.23886	0.285803
$832$	3.30278i	0.114503i
$833$	− 27.0000i	− 0.935495i
$834$	3.81665	0.132160
$835$	0	0
$836$	−10.0278	−0.346817
$837$	− 14.1472i	− 0.488998i
$838$	3.63331i	0.125511i
$839$	43.8167	1.51272	0.756359	−	0.654156i	$-0.226976\pi$
$839$	43.8167	1.51272	0.756359	+	0.654156i	$0.226976\pi$
$840$	0	0
$841$	−22.2111	−0.765900
$842$	− 30.6972i	− 1.05790i
$843$	− 8.05551i	− 0.277447i
$844$	−7.21110	−0.248216
$845$	0	0
$846$	−7.57779	−0.260530
$847$	− 26.8167i	− 0.921431i
$848$	11.2111i	0.384991i
$849$	0.605551	0.0207825
$850$	0	0
$851$	−8.00000	−0.274236
$852$	4.93608i	0.169107i
$853$	21.7250i	0.743849i	0.928263	+	0.371925i	$0.121302\pi$
$853$	21.7250i	0.743849i	−0.928263	+	0.371925i	$0.878698\pi$
$854$	38.0278	1.30128
$855$	0	0
$856$	2.60555	0.0890559
$857$	9.63331i	0.329068i	0.986371	+	0.164534i	$0.0526119\pi$
$857$	9.63331i	0.329068i	−0.986371	+	0.164534i	$0.947388\pi$
$858$	1.69722i	0.0579423i
$859$	35.8167	1.22205	0.611024	−	0.791612i	$-0.290758\pi$
$859$	35.8167	1.22205	0.611024	+	0.791612i	$0.290758\pi$
$860$	0	0
$861$	−0.908327	−0.0309557
$862$	30.2389i	1.02994i
$863$	41.4500i	1.41097i	0.708723	+	0.705487i	$0.249271\pi$
$863$	41.4500i	1.41097i	−0.708723	+	0.705487i	$0.750729\pi$
$864$	1.78890	0.0608595
$865$	0	0
$866$	24.0917	0.818668
$867$	− 9.30278i	− 0.315939i
$868$	26.1194i	0.886551i
$869$	−24.4777	−0.830350
$870$	0	0
$871$	−13.2111	−0.447641
$872$	− 1.48612i	− 0.0503264i
$873$	18.3305i	0.620395i
$874$	−5.90833	−0.199852
$875$	0	0
$876$	1.76114	0.0595034
$877$	− 48.1749i	− 1.62675i	−0.581738	−	0.813376i	$-0.697627\pi$
$877$	− 48.1749i	− 1.62675i	0.581738	−	0.813376i	$-0.302373\pi$
$878$	− 14.6972i	− 0.496007i
$879$	7.02776	0.237040
$880$	0	0
$881$	55.2666	1.86198	0.930990	−	0.365045i	$-0.118946\pi$
$881$	55.2666	1.86198	0.930990	+	0.365045i	$0.118946\pi$
$882$	11.3667i	0.382736i
$883$	− 8.27502i	− 0.278477i	−0.990259	−	0.139238i	$-0.955535\pi$
$883$	− 8.27502i	− 0.278477i	0.990259	−	0.139238i	$-0.0444654\pi$
$884$	−22.8167	−0.767407
$885$	0	0
$886$	−17.4861	−0.587458
$887$	27.6333i	0.927836i	0.885878	+	0.463918i	$0.153557\pi$
$887$	27.6333i	0.927836i	−0.885878	+	0.463918i	$0.846443\pi$
$888$	− 2.42221i	− 0.0812839i
$889$	−32.4222	−1.08741
$890$	0	0
$891$	−13.8890	−0.465298
$892$	− 4.00000i	− 0.133930i
$893$	15.3944i	0.515156i
$894$	−4.02776	−0.134708
$895$	0	0
$896$	−3.30278	−0.110338
$897$	1.00000i	0.0333890i
$898$	− 2.09167i	− 0.0698000i
$899$	−20.6056	−0.687234
$900$	0	0
$901$	−77.4500	−2.58023
$902$	1.54163i	0.0513308i
$903$	− 9.21110i	− 0.306526i
$904$	−16.4222	−0.546194
$905$	0	0
$906$	2.69722	0.0896093
$907$	48.6611i	1.61576i	0.589344	+	0.807882i	$0.299386\pi$
$907$	48.6611i	1.61576i	−0.589344	+	0.807882i	$0.700614\pi$
$908$	14.6056i	0.484702i
$909$	7.57779	0.251340
$910$	0	0
$911$	−4.18335	−0.138600	−0.0693002	−	0.997596i	$-0.522077\pi$
$911$	−4.18335	−0.138600	−0.0693002	+	0.997596i	$0.522077\pi$
$912$	− 1.78890i	− 0.0592363i
$913$	19.0278i	0.629727i
$914$	−32.4222	−1.07243
$915$	0	0
$916$	2.00000	0.0660819
$917$	− 37.0278i	− 1.22276i
$918$	12.3583i	0.407884i
$919$	−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
$921$	3.54163	0.116701
$922$	− 10.1833i	− 0.335371i
$923$	53.8444i	1.77231i
$924$	−1.69722	−0.0558346
$925$	0	0
$926$	−17.6333	−0.579466
$927$	− 23.6140i	− 0.775584i
$928$	− 2.60555i	− 0.0855314i
$929$	14.3667	0.471356	0.235678	−	0.971831i	$-0.424269\pi$
$929$	14.3667	0.471356	0.235678	+	0.971831i	$0.424269\pi$
$930$	0	0
$931$	23.0917	0.756799
$932$	25.8167i	0.845653i
$933$	6.78890i	0.222259i
$934$	−1.81665	−0.0594427
$935$	0	0
$936$	9.60555	0.313967
$937$	37.9638i	1.24022i	0.784513	+	0.620112i	$0.212913\pi$
$937$	37.9638i	1.24022i	−0.784513	+	0.620112i	$0.787087\pi$
$938$	− 13.2111i	− 0.431358i
$939$	5.97224	0.194897
$940$	0	0
$941$	25.9361	0.845492	0.422746	−	0.906248i	$-0.361066\pi$
$941$	25.9361	0.845492	0.422746	+	0.906248i	$0.361066\pi$
$942$	− 5.63331i	− 0.183543i
$943$	0.908327i	0.0295792i
$944$	3.39445	0.110480
$945$	0	0
$946$	−15.6333	−0.508283
$947$	− 4.93608i	− 0.160401i	−0.996779	−	0.0802006i	$-0.974444\pi$
$947$	− 4.93608i	− 0.160401i	0.996779	−	0.0802006i	$-0.0255561\pi$
$948$	− 4.36669i	− 0.141824i
$949$	19.2111	0.623619
$950$	0	0
$951$	−5.36669	−0.174027
$952$	− 22.8167i	− 0.739492i
$953$	41.3305i	1.33883i	0.742890	+	0.669414i	$0.233455\pi$
$953$	41.3305i	1.33883i	−0.742890	+	0.669414i	$0.766545\pi$
$954$	32.6056	1.05564
$955$	0	0
$956$	5.21110	0.168539
$957$	− 1.33894i	− 0.0432817i
$958$	− 30.0000i	− 0.969256i
$959$	−12.9083	−0.416832
$960$	0	0
$961$	31.5416	1.01747
$962$	− 26.4222i	− 0.851886i
$963$	− 7.57779i	− 0.244191i
$964$	14.4222	0.464508
$965$	0	0
$966$	−1.00000	−0.0321745
$967$	− 12.6056i	− 0.405367i	−0.979244	−	0.202684i	$-0.935034\pi$
$967$	− 12.6056i	− 0.405367i	0.979244	−	0.202684i	$-0.0649663\pi$
$968$	− 8.11943i	− 0.260968i
$969$	12.3583	0.397005
$970$	0	0
$971$	−17.0917	−0.548498	−0.274249	−	0.961659i	$-0.588429\pi$
$971$	−17.0917	−0.548498	−0.274249	+	0.961659i	$0.588429\pi$
$972$	− 7.84441i	− 0.251610i
$973$	41.6333i	1.33470i
$974$	9.81665	0.314546
$975$	0	0
$976$	11.5139	0.368550
$977$	6.51388i	0.208397i	0.994556	+	0.104199i	$0.0332278\pi$
$977$	6.51388i	0.208397i	−0.994556	+	0.104199i	$0.966772\pi$
$978$	− 2.81665i	− 0.0900667i
$979$	0	0
$980$	0	0
$981$	−4.32213	−0.137995
$982$	4.18335i	0.133496i
$983$	− 34.5416i	− 1.10171i	−0.834602	−	0.550854i	$-0.814302\pi$
$983$	− 34.5416i	− 1.10171i	0.834602	−	0.550854i	$-0.185698\pi$
$984$	−0.275019	−0.00876729
$985$	0	0
$986$	18.0000	0.573237
$987$	2.60555i	0.0829356i
$988$	− 19.5139i	− 0.620819i
$989$	−9.21110	−0.292896
$990$	0	0
$991$	−15.3305	−0.486990	−0.243495	−	0.969902i	$-0.578294\pi$
$991$	−15.3305	−0.486990	−0.243495	+	0.969902i	$0.578294\pi$
$992$	7.90833i	0.251090i
$993$	5.02776i	0.159551i
$994$	−53.8444	−1.70784
$995$	0	0
$996$	−3.39445	−0.107557
$997$	− 16.7889i	− 0.531710i	−0.964013	−	0.265855i	$-0.914346\pi$
$997$	− 16.7889i	− 0.531710i	0.964013	−	0.265855i	$-0.0856542\pi$
$998$	− 31.6333i	− 1.00133i
$999$	−14.3112	−0.452786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.b.f.599.2		4
5.2	odd	4		1150.2.a.m.1.2		2
5.3	odd	4		230.2.a.b.1.1	✓	2
5.4	even	2	inner	1150.2.b.f.599.3		4
15.8	even	4		2070.2.a.w.1.2		2
20.3	even	4		1840.2.a.j.1.2		2
20.7	even	4		9200.2.a.ca.1.1		2
40.3	even	4		7360.2.a.bu.1.1		2
40.13	odd	4		7360.2.a.bc.1.2		2
115.68	even	4		5290.2.a.j.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.b.1.1	✓	2	5.3	odd	4
1150.2.a.m.1.2		2	5.2	odd	4
1150.2.b.f.599.2		4	1.1	even	1	trivial
1150.2.b.f.599.3		4	5.4	even	2	inner
1840.2.a.j.1.2		2	20.3	even	4
2070.2.a.w.1.2		2	15.8	even	4
5290.2.a.j.1.1		2	115.68	even	4
7360.2.a.bc.1.2		2	40.13	odd	4
7360.2.a.bu.1.1		2	40.3	even	4
9200.2.a.ca.1.1		2	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +0.302776i q^{3} -1.00000 q^{4} +0.302776 q^{6} +3.30278i q^{7} +1.00000i q^{8} +2.90833 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +0.302776i q^{3} -1.00000 q^{4} +0.302776 q^{6} +3.30278i q^{7} +1.00000i q^{8} +2.90833 q^{9} -1.69722 q^{11} -0.302776i q^{12} -3.30278i q^{13} +3.30278 q^{14} +1.00000 q^{16} +6.90833i q^{17} -2.90833i q^{18} -5.90833 q^{19} -1.00000 q^{21} +1.69722i q^{22} +1.00000i q^{23} -0.302776 q^{24} -3.30278 q^{26} +1.78890i q^{27} -3.30278i q^{28} +2.60555 q^{29} -7.90833 q^{31} -1.00000i q^{32} -0.513878i q^{33} +6.90833 q^{34} -2.90833 q^{36} +8.00000i q^{37} +5.90833i q^{38} +1.00000 q^{39} +0.908327 q^{41} +1.00000i q^{42} +9.21110i q^{43} +1.69722 q^{44} +1.00000 q^{46} -2.60555i q^{47} +0.302776i q^{48} -3.90833 q^{49} -2.09167 q^{51} +3.30278i q^{52} +11.2111i q^{53} +1.78890 q^{54} -3.30278 q^{56} -1.78890i q^{57} -2.60555i q^{58} +3.39445 q^{59} +11.5139 q^{61} +7.90833i q^{62} +9.60555i q^{63} -1.00000 q^{64} -0.513878 q^{66} -4.00000i q^{67} -6.90833i q^{68} -0.302776 q^{69} -16.3028 q^{71} +2.90833i q^{72} +5.81665i q^{73} +8.00000 q^{74} +5.90833 q^{76} -5.60555i q^{77} -1.00000i q^{78} +14.4222 q^{79} +8.18335 q^{81} -0.908327i q^{82} -11.2111i q^{83} +1.00000 q^{84} +9.21110 q^{86} +0.788897i q^{87} -1.69722i q^{88} +10.9083 q^{91} -1.00000i q^{92} -2.39445i q^{93} -2.60555 q^{94} +0.302776 q^{96} +6.30278i q^{97} +3.90833i q^{98} -4.93608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 6 q^{6} - 10 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 6 * q^6 - 10 * q^9	\( 4 q - 4 q^{4} - 6 q^{6} - 10 q^{9} - 14 q^{11} + 6 q^{14} + 4 q^{16} - 2 q^{19} - 4 q^{21} + 6 q^{24} - 6 q^{26} - 4 q^{29} - 10 q^{31} + 6 q^{34} + 10 q^{36} + 4 q^{39} - 18 q^{41} + 14 q^{44} + 4 q^{46} + 6 q^{49} - 30 q^{51} + 36 q^{54} - 6 q^{56} + 28 q^{59} + 10 q^{61} - 4 q^{64} + 34 q^{66} + 6 q^{69} - 58 q^{71} + 32 q^{74} + 2 q^{76} + 76 q^{81} + 4 q^{84} + 8 q^{86} + 22 q^{91} + 4 q^{94} - 6 q^{96} + 74 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 6 * q^6 - 10 * q^9 - 14 * q^11 + 6 * q^14 + 4 * q^16 - 2 * q^19 - 4 * q^21 + 6 * q^24 - 6 * q^26 - 4 * q^29 - 10 * q^31 + 6 * q^34 + 10 * q^36 + 4 * q^39 - 18 * q^41 + 14 * q^44 + 4 * q^46 + 6 * q^49 - 30 * q^51 + 36 * q^54 - 6 * q^56 + 28 * q^59 + 10 * q^61 - 4 * q^64 + 34 * q^66 + 6 * q^69 - 58 * q^71 + 32 * q^74 + 2 * q^76 + 76 * q^81 + 4 * q^84 + 8 * q^86 + 22 * q^91 + 4 * q^94 - 6 * q^96 + 74 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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