LMFDB - Embedded newform 1183.2.a.q.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1183,2,Mod(1,1183)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1183.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1183, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,-3,8,15,4,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	yes
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} + \cdots + 29 $ x^12 - 3x^11 - 15x^10 + 46x^9 + 80x^8 - 246x^7 - 199x^6 + 562x^5 + 262x^4 - 542x^3 - 157x^2 + 183*x + 29
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.842530$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.842530 q^{2} +0.161973 q^{3} -1.29014 q^{4} +3.72786 q^{5} -0.136467 q^{6} -1.00000 q^{7} +2.77204 q^{8} -2.97376 q^{9} -3.14083 q^{10} -3.51379 q^{11} -0.208968 q^{12} +0.842530 q^{14} +0.603811 q^{15} +0.244755 q^{16} +7.43189 q^{17} +2.50549 q^{18} +2.67482 q^{19} -4.80947 q^{20} -0.161973 q^{21} +2.96048 q^{22} -2.49854 q^{23} +0.448995 q^{24} +8.89694 q^{25} -0.967586 q^{27} +1.29014 q^{28} +7.30473 q^{29} -0.508729 q^{30} -2.54405 q^{31} -5.75030 q^{32} -0.569138 q^{33} -6.26159 q^{34} -3.72786 q^{35} +3.83658 q^{36} +2.17903 q^{37} -2.25362 q^{38} +10.3338 q^{40} +8.40738 q^{41} +0.136467 q^{42} +11.8923 q^{43} +4.53329 q^{44} -11.0858 q^{45} +2.10510 q^{46} -9.40740 q^{47} +0.0396435 q^{48} +1.00000 q^{49} -7.49594 q^{50} +1.20376 q^{51} -5.84583 q^{53} +0.815220 q^{54} -13.0989 q^{55} -2.77204 q^{56} +0.433247 q^{57} -6.15445 q^{58} -4.25410 q^{59} -0.779003 q^{60} +5.07200 q^{61} +2.14344 q^{62} +2.97376 q^{63} +4.35529 q^{64} +0.479516 q^{66} +1.29175 q^{67} -9.58820 q^{68} -0.404695 q^{69} +3.14083 q^{70} -1.30601 q^{71} -8.24341 q^{72} +4.31232 q^{73} -1.83590 q^{74} +1.44106 q^{75} -3.45090 q^{76} +3.51379 q^{77} +14.2264 q^{79} +0.912411 q^{80} +8.76457 q^{81} -7.08347 q^{82} +9.81167 q^{83} +0.208968 q^{84} +27.7051 q^{85} -10.0196 q^{86} +1.18316 q^{87} -9.74039 q^{88} +4.77241 q^{89} +9.34010 q^{90} +3.22347 q^{92} -0.412067 q^{93} +7.92602 q^{94} +9.97135 q^{95} -0.931391 q^{96} +5.92836 q^{97} -0.842530 q^{98} +10.4492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 8 q^{3} + 15 q^{4} + 4 q^{5} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 26 q^{9} - 6 q^{10} - 12 q^{11} + 13 q^{12} + 3 q^{14} - 11 q^{15} + 13 q^{16} + 31 q^{17} + 29 q^{18} + 3 q^{19} + 18 q^{20}+ \cdots - 37 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 + 8 * q^3 + 15 * q^4 + 4 * q^5 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 26 * q^9 - 6 * q^10 - 12 * q^11 + 13 * q^12 + 3 * q^14 - 11 * q^15 + 13 * q^16 + 31 * q^17 + 29 * q^18 + 3 * q^19 + 18 * q^20 - 8 * q^21 - 4 * q^22 + 18 * q^23 + 6 * q^24 + 32 * q^25 + 32 * q^27 - 15 * q^28 + 15 * q^29 - 10 * q^30 + 21 * q^31 + 3 * q^32 + 29 * q^33 - 3 * q^34 - 4 * q^35 + 49 * q^36 - 5 * q^37 + 45 * q^38 - 20 * q^40 + 16 * q^41 + 2 * q^42 - 22 * q^43 - 35 * q^44 - 5 * q^45 - 2 * q^46 + 4 * q^47 + 11 * q^48 + 12 * q^49 - 13 * q^50 + 18 * q^51 + 53 * q^53 + 5 * q^54 - 26 * q^55 + 12 * q^56 + 8 * q^57 - 32 * q^58 + 26 * q^59 - 38 * q^60 + 22 * q^61 + 19 * q^62 - 26 * q^63 + 2 * q^64 - 34 * q^66 - 12 * q^67 + 34 * q^68 + 3 * q^69 + 6 * q^70 - 21 * q^71 + 4 * q^72 + 15 * q^73 - 40 * q^74 + 15 * q^75 - 43 * q^76 + 12 * q^77 + 2 * q^79 - 13 * q^80 + 36 * q^81 - 32 * q^82 + 9 * q^83 - 13 * q^84 + 39 * q^85 - 44 * q^86 + 27 * q^87 - 48 * q^88 + 22 * q^89 - 26 * q^90 + 52 * q^92 + 53 * q^93 - 44 * q^94 + 29 * q^95 + 114 * q^96 - 9 * q^97 - 3 * q^98 - 37 * q^99

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 $

$2$	−0.842530	−0.595759	−0.297879	−	0.954604i	$-0.596279\pi$
$2$	−0.842530	−0.595759	−0.297879	+	0.954604i	$0.596279\pi$
$3$	0.161973	0.0935149	0.0467574	−	0.998906i	$-0.485111\pi$
$3$	0.161973	0.0935149	0.0467574	+	0.998906i	$0.485111\pi$
$4$	−1.29014	−0.645071
$5$	3.72786	1.66715	0.833575	−	0.552406i	$-0.186290\pi$
$5$	3.72786	1.66715	0.833575	+	0.552406i	$0.186290\pi$
$6$	−0.136467	−0.0557123
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.77204	0.980066
$9$	−2.97376	−0.991255
$10$	−3.14083	−0.993219
$11$	−3.51379	−1.05945	−0.529724	−	0.848170i	$-0.677705\pi$
$11$	−3.51379	−1.05945	−0.529724	+	0.848170i	$0.677705\pi$
$12$	−0.208968	−0.0603238
$13$	0	0
$13$	0	0
$14$	0.842530	0.225176
$15$	0.603811	0.155903
$16$	0.244755	0.0611887
$17$	7.43189	1.80250	0.901249	−	0.433301i	$-0.142651\pi$
$17$	7.43189	1.80250	0.901249	+	0.433301i	$0.142651\pi$
$18$	2.50549	0.590549
$19$	2.67482	0.613646	0.306823	−	0.951767i	$-0.400734\pi$
$19$	2.67482	0.613646	0.306823	+	0.951767i	$0.400734\pi$
$20$	−4.80947	−1.07543
$21$	−0.161973	−0.0353453
$22$	2.96048	0.631176
$23$	−2.49854	−0.520982	−0.260491	−	0.965476i	$-0.583884\pi$
$23$	−2.49854	−0.520982	−0.260491	+	0.965476i	$0.583884\pi$
$24$	0.448995	0.0916507
$25$	8.89694	1.77939
$26$	0	0
$27$	−0.967586	−0.186212
$28$	1.29014	0.243814
$29$	7.30473	1.35645	0.678227	−	0.734853i	$-0.262749\pi$
$29$	7.30473	1.35645	0.678227	+	0.734853i	$0.262749\pi$
$30$	−0.508729	−0.0928808
$31$	−2.54405	−0.456925	−0.228463	−	0.973553i	$-0.573370\pi$
$31$	−2.54405	−0.456925	−0.228463	+	0.973553i	$0.573370\pi$
$32$	−5.75030	−1.01652
$33$	−0.569138	−0.0990742
$34$	−6.26159	−1.07385
$35$	−3.72786	−0.630123
$36$	3.83658	0.639430
$37$	2.17903	0.358230	0.179115	−	0.983828i	$-0.442677\pi$
$37$	2.17903	0.358230	0.179115	+	0.983828i	$0.442677\pi$
$38$	−2.25362	−0.365585
$39$	0	0
$40$	10.3338	1.63392
$41$	8.40738	1.31301	0.656506	−	0.754321i	$-0.272034\pi$
$41$	8.40738	1.31301	0.656506	+	0.754321i	$0.272034\pi$
$42$	0.136467	0.0210573
$43$	11.8923	1.81356	0.906780	−	0.421603i	$-0.138533\pi$
$43$	11.8923	1.81356	0.906780	+	0.421603i	$0.138533\pi$
$44$	4.53329	0.683420
$45$	−11.0858	−1.65257
$46$	2.10510	0.310379
$47$	−9.40740	−1.37221	−0.686105	−	0.727502i	$-0.740681\pi$
$47$	−9.40740	−1.37221	−0.686105	+	0.727502i	$0.740681\pi$
$48$	0.0396435	0.00572205
$49$	1.00000	0.142857
$50$	−7.49594	−1.06009
$51$	1.20376	0.168560
$52$	0	0
$53$	−5.84583	−0.802986	−0.401493	−	0.915862i	$-0.631509\pi$
$53$	−5.84583	−0.802986	−0.401493	+	0.915862i	$0.631509\pi$
$54$	0.815220	0.110937
$55$	−13.0989	−1.76626
$56$	−2.77204	−0.370430
$57$	0.433247	0.0573850
$58$	−6.15445	−0.808119
$59$	−4.25410	−0.553836	−0.276918	−	0.960893i	$-0.589313\pi$
$59$	−4.25410	−0.553836	−0.276918	+	0.960893i	$0.589313\pi$
$60$	−0.779003	−0.100569
$61$	5.07200	0.649403	0.324701	−	0.945817i	$-0.394736\pi$
$61$	5.07200	0.649403	0.324701	+	0.945817i	$0.394736\pi$
$62$	2.14344	0.272217
$63$	2.97376	0.374659
$64$	4.35529	0.544412
$65$	0	0
$66$	0.479516	0.0590243
$67$	1.29175	0.157812	0.0789060	−	0.996882i	$-0.474857\pi$
$67$	1.29175	0.157812	0.0789060	+	0.996882i	$0.474857\pi$
$68$	−9.58820	−1.16274
$69$	−0.404695	−0.0487195
$70$	3.14083	0.375402
$71$	−1.30601	−0.154995	−0.0774975	−	0.996993i	$-0.524693\pi$
$71$	−1.30601	−0.154995	−0.0774975	+	0.996993i	$0.524693\pi$
$72$	−8.24341	−0.971495
$73$	4.31232	0.504719	0.252359	−	0.967634i	$-0.418793\pi$
$73$	4.31232	0.504719	0.252359	+	0.967634i	$0.418793\pi$
$74$	−1.83590	−0.213419
$75$	1.44106	0.166399
$76$	−3.45090	−0.395845
$77$	3.51379	0.400434
$78$	0	0
$79$	14.2264	1.60060	0.800299	−	0.599601i	$-0.204674\pi$
$79$	14.2264	1.60060	0.800299	+	0.599601i	$0.204674\pi$
$80$	0.912411	0.102011
$81$	8.76457	0.973841
$82$	−7.08347	−0.782238
$83$	9.81167	1.07697	0.538485	−	0.842635i	$-0.318997\pi$
$83$	9.81167	1.07697	0.538485	+	0.842635i	$0.318997\pi$
$84$	0.208968	0.0228002
$85$	27.7051	3.00504
$86$	−10.0196	−1.08044
$87$	1.18316	0.126849
$88$	−9.74039	−1.03833
$89$	4.77241	0.505874	0.252937	−	0.967483i	$-0.418603\pi$
$89$	4.77241	0.505874	0.252937	+	0.967483i	$0.418603\pi$
$90$	9.34010	0.984533
$91$	0	0
$92$	3.22347	0.336070
$93$	−0.412067	−0.0427293
$94$	7.92602	0.817506
$95$	9.97135	1.02304
$96$	−0.931391	−0.0950597
$97$	5.92836	0.601934	0.300967	−	0.953635i	$-0.402691\pi$
$97$	5.92836	0.601934	0.300967	+	0.953635i	$0.402691\pi$
$98$	−0.842530	−0.0851084
$99$	10.4492	1.05018
$100$	−11.4783	−1.14783
$101$	−3.18992	−0.317409	−0.158705	−	0.987326i	$-0.550732\pi$
$101$	−3.18992	−0.317409	−0.158705	+	0.987326i	$0.550732\pi$
$102$	−1.01421	−0.100421
$103$	−9.80005	−0.965627	−0.482814	−	0.875723i	$-0.660385\pi$
$103$	−9.80005	−0.965627	−0.482814	+	0.875723i	$0.660385\pi$
$104$	0	0
$105$	−0.603811	−0.0589259
$106$	4.92529	0.478386
$107$	9.03013	0.872975	0.436488	−	0.899710i	$-0.356222\pi$
$107$	9.03013	0.872975	0.436488	+	0.899710i	$0.356222\pi$
$108$	1.24832	0.120120
$109$	−2.85038	−0.273017	−0.136508	−	0.990639i	$-0.543588\pi$
$109$	−2.85038	−0.273017	−0.136508	+	0.990639i	$0.543588\pi$
$110$	11.0362	1.05226
$111$	0.352943	0.0334998
$112$	−0.244755	−0.0231271
$113$	11.5351	1.08513	0.542566	−	0.840013i	$-0.317453\pi$
$113$	11.5351	1.08513	0.542566	+	0.840013i	$0.317453\pi$
$114$	−0.365024	−0.0341876
$115$	−9.31421	−0.868554
$116$	−9.42414	−0.875009
$117$	0	0
$118$	3.58421	0.329953
$119$	−7.43189	−0.681281
$120$	1.67379	0.152796
$121$	1.34673	0.122430
$122$	−4.27331	−0.386887
$123$	1.36176	0.122786
$124$	3.28219	0.294749
$125$	14.5273	1.29936
$126$	−2.50549	−0.223206
$127$	0.885393	0.0785659	0.0392830	−	0.999228i	$-0.487493\pi$
$127$	0.885393	0.0785659	0.0392830	+	0.999228i	$0.487493\pi$
$128$	7.83114	0.692181
$129$	1.92623	0.169595
$130$	0	0
$131$	13.3660	1.16779	0.583896	−	0.811829i	$-0.301528\pi$
$131$	13.3660	1.16779	0.583896	+	0.811829i	$0.301528\pi$
$132$	0.734269	0.0639099
$133$	−2.67482	−0.231936
$134$	−1.08834	−0.0940179
$135$	−3.60703	−0.310443
$136$	20.6015	1.76657
$137$	−18.2881	−1.56246	−0.781230	−	0.624243i	$-0.785408\pi$
$137$	−18.2881	−1.56246	−0.781230	+	0.624243i	$0.785408\pi$
$138$	0.340968	0.0290251
$139$	3.21091	0.272346	0.136173	−	0.990685i	$-0.456520\pi$
$139$	3.21091	0.272346	0.136173	+	0.990685i	$0.456520\pi$
$140$	4.80947	0.406475
$141$	−1.52374	−0.128322
$142$	1.10035	0.0923397
$143$	0	0
$144$	−0.727843	−0.0606536
$145$	27.2310	2.26141
$146$	−3.63326	−0.300691
$147$	0.161973	0.0133593
$148$	−2.81126	−0.231084
$149$	0.508593	0.0416656	0.0208328	−	0.999783i	$-0.493368\pi$
$149$	0.508593	0.0416656	0.0208328	+	0.999783i	$0.493368\pi$
$150$	−1.21414	−0.0991339
$151$	15.4491	1.25723	0.628614	−	0.777718i	$-0.283623\pi$
$151$	15.4491	1.25723	0.628614	+	0.777718i	$0.283623\pi$
$152$	7.41472	0.601413
$153$	−22.1007	−1.78674
$154$	−2.96048	−0.238562
$155$	−9.48387	−0.761763
$156$	0	0
$157$	−8.63873	−0.689446	−0.344723	−	0.938705i	$-0.612027\pi$
$157$	−8.63873	−0.689446	−0.344723	+	0.938705i	$0.612027\pi$
$158$	−11.9862	−0.953570
$159$	−0.946864	−0.0750912
$160$	−21.4363	−1.69469
$161$	2.49854	0.196913
$162$	−7.38442	−0.580175
$163$	−4.33684	−0.339688	−0.169844	−	0.985471i	$-0.554326\pi$
$163$	−4.33684	−0.339688	−0.169844	+	0.985471i	$0.554326\pi$
$164$	−10.8467	−0.846986
$165$	−2.12167	−0.165172
$166$	−8.26663	−0.641615
$167$	−11.0384	−0.854173	−0.427087	−	0.904211i	$-0.640460\pi$
$167$	−11.0384	−0.854173	−0.427087	+	0.904211i	$0.640460\pi$
$168$	−0.448995	−0.0346407
$169$	0	0
$170$	−23.3423	−1.79028
$171$	−7.95428	−0.608279
$172$	−15.3428	−1.16988
$173$	−10.3380	−0.785987	−0.392994	−	0.919541i	$-0.628561\pi$
$173$	−10.3380	−0.785987	−0.392994	+	0.919541i	$0.628561\pi$
$174$	−0.996852	−0.0755712
$175$	−8.89694	−0.672546
$176$	−0.860017	−0.0648262
$177$	−0.689047	−0.0517920
$178$	−4.02090	−0.301379
$179$	18.0134	1.34639	0.673194	−	0.739466i	$-0.264922\pi$
$179$	18.0134	1.34639	0.673194	+	0.739466i	$0.264922\pi$
$180$	14.3022	1.06603
$181$	−21.3187	−1.58460	−0.792302	−	0.610129i	$-0.791118\pi$
$181$	−21.3187	−1.58460	−0.792302	+	0.610129i	$0.791118\pi$
$182$	0	0
$183$	0.821524	0.0607288
$184$	−6.92606	−0.510596
$185$	8.12311	0.597223
$186$	0.347178	0.0254564
$187$	−26.1141	−1.90965
$188$	12.1369	0.885174
$189$	0.967586	0.0703815
$190$	−8.40117	−0.609485
$191$	5.90224	0.427071	0.213535	−	0.976935i	$-0.431502\pi$
$191$	5.90224	0.427071	0.213535	+	0.976935i	$0.431502\pi$
$192$	0.705438	0.0509106
$193$	3.24842	0.233827	0.116913	−	0.993142i	$-0.462700\pi$
$193$	3.24842	0.233827	0.116913	+	0.993142i	$0.462700\pi$
$194$	−4.99483	−0.358608
$195$	0	0
$196$	−1.29014	−0.0921531
$197$	−8.99244	−0.640685	−0.320342	−	0.947302i	$-0.603798\pi$
$197$	−8.99244	−0.640685	−0.320342	+	0.947302i	$0.603798\pi$
$198$	−8.80376	−0.625656
$199$	5.58657	0.396021	0.198011	−	0.980200i	$-0.436552\pi$
$199$	5.58657	0.396021	0.198011	+	0.980200i	$0.436552\pi$
$200$	24.6627	1.74392
$201$	0.209228	0.0147578
$202$	2.68761	0.189099
$203$	−7.30473	−0.512691
$204$	−1.55303	−0.108734
$205$	31.3415	2.18899
$206$	8.25684	0.575281
$207$	7.43007	0.516426
$208$	0	0
$209$	−9.39876	−0.650126
$210$	0.508729	0.0351056
$211$	−19.2145	−1.32278	−0.661391	−	0.750041i	$-0.730034\pi$
$211$	−19.2145	−1.32278	−0.661391	+	0.750041i	$0.730034\pi$
$212$	7.54195	0.517984
$213$	−0.211538	−0.0144943
$214$	−7.60815	−0.520083
$215$	44.3329	3.02348
$216$	−2.68219	−0.182500
$217$	2.54405	0.172701
$218$	2.40153	0.162652
$219$	0.698478	0.0471987
$220$	16.8995	1.13936
$221$	0	0
$222$	−0.297365	−0.0199578
$223$	−13.3068	−0.891089	−0.445545	−	0.895260i	$-0.646990\pi$
$223$	−13.3068	−0.891089	−0.445545	+	0.895260i	$0.646990\pi$
$224$	5.75030	0.384208
$225$	−26.4574	−1.76383
$226$	−9.71868	−0.646477
$227$	−13.3532	−0.886286	−0.443143	−	0.896451i	$-0.646137\pi$
$227$	−13.3532	−0.886286	−0.443143	+	0.896451i	$0.646137\pi$
$228$	−0.558951	−0.0370174
$229$	10.5744	0.698773	0.349387	−	0.936979i	$-0.386390\pi$
$229$	10.5744	0.698773	0.349387	+	0.936979i	$0.386390\pi$
$230$	7.84750	0.517449
$231$	0.569138	0.0374465
$232$	20.2490	1.32941
$233$	5.25696	0.344395	0.172197	−	0.985062i	$-0.444913\pi$
$233$	5.25696	0.344395	0.172197	+	0.985062i	$0.444913\pi$
$234$	0	0
$235$	−35.0695	−2.28768
$236$	5.48840	0.357264
$237$	2.30429	0.149680
$238$	6.26159	0.405879
$239$	−20.0403	−1.29630	−0.648149	−	0.761513i	$-0.724457\pi$
$239$	−20.0403	−1.29630	−0.648149	+	0.761513i	$0.724457\pi$
$240$	0.147786	0.00953952
$241$	−23.3489	−1.50403	−0.752017	−	0.659144i	$-0.770919\pi$
$241$	−23.3489	−1.50403	−0.752017	+	0.659144i	$0.770919\pi$
$242$	−1.13466	−0.0729390
$243$	4.32238	0.277281
$244$	−6.54360	−0.418911
$245$	3.72786	0.238164
$246$	−1.14733	−0.0731509
$247$	0	0
$248$	−7.05223	−0.447817
$249$	1.58922	0.100713
$250$	−12.2397	−0.774104
$251$	14.4261	0.910570	0.455285	−	0.890346i	$-0.349537\pi$
$251$	14.4261	0.910570	0.455285	+	0.890346i	$0.349537\pi$
$252$	−3.83658	−0.241682
$253$	8.77935	0.551953
$254$	−0.745970	−0.0468063
$255$	4.48746	0.281016
$256$	−15.3086	−0.956785
$257$	13.0464	0.813810	0.406905	−	0.913471i	$-0.366608\pi$
$257$	13.0464	0.813810	0.406905	+	0.913471i	$0.366608\pi$
$258$	−1.62291	−0.101038
$259$	−2.17903	−0.135398
$260$	0	0
$261$	−21.7225	−1.34459
$262$	−11.2612	−0.695722
$263$	16.7189	1.03093	0.515464	−	0.856911i	$-0.327619\pi$
$263$	16.7189	1.03093	0.515464	+	0.856911i	$0.327619\pi$
$264$	−1.57768	−0.0970992
$265$	−21.7924	−1.33870
$266$	2.25362	0.138178
$267$	0.772999	0.0473068
$268$	−1.66654	−0.101800
$269$	6.17733	0.376639	0.188319	−	0.982108i	$-0.439696\pi$
$269$	6.17733	0.376639	0.188319	+	0.982108i	$0.439696\pi$
$270$	3.03903	0.184949
$271$	−30.1026	−1.82860	−0.914301	−	0.405036i	$-0.867259\pi$
$271$	−30.1026	−1.82860	−0.914301	+	0.405036i	$0.867259\pi$
$272$	1.81899	0.110292
$273$	0	0
$274$	15.4083	0.930850
$275$	−31.2620	−1.88517
$276$	0.522114	0.0314276
$277$	−6.01177	−0.361212	−0.180606	−	0.983556i	$-0.557806\pi$
$277$	−6.01177	−0.361212	−0.180606	+	0.983556i	$0.557806\pi$
$278$	−2.70529	−0.162252
$279$	7.56541	0.452929
$280$	−10.3338	−0.617562
$281$	−26.4812	−1.57974	−0.789868	−	0.613277i	$-0.789851\pi$
$281$	−26.4812	−1.57974	−0.789868	+	0.613277i	$0.789851\pi$
$282$	1.28380	0.0764490
$283$	−0.200682	−0.0119293	−0.00596465	−	0.999982i	$-0.501899\pi$
$283$	−0.200682	−0.0119293	−0.00596465	+	0.999982i	$0.501899\pi$
$284$	1.68494	0.0999829
$285$	1.61509	0.0956694
$286$	0	0
$287$	−8.40738	−0.496272
$288$	17.1000	1.00763
$289$	38.2330	2.24900
$290$	−22.9429	−1.34726
$291$	0.960232	0.0562898
$292$	−5.56351	−0.325580
$293$	1.96008	0.114509	0.0572544	−	0.998360i	$-0.481765\pi$
$293$	1.96008	0.114509	0.0572544	+	0.998360i	$0.481765\pi$
$294$	−0.136467	−0.00795890
$295$	−15.8587	−0.923328
$296$	6.04036	0.351089
$297$	3.39990	0.197282
$298$	−0.428505	−0.0248226
$299$	0	0
$300$	−1.85917	−0.107339
$301$	−11.8923	−0.685462
$302$	−13.0163	−0.749004
$303$	−0.516680	−0.0296825
$304$	0.654674	0.0375482
$305$	18.9077	1.08265
$306$	18.6205	1.06446
$307$	25.1368	1.43463	0.717317	−	0.696747i	$-0.245370\pi$
$307$	25.1368	1.43463	0.717317	+	0.696747i	$0.245370\pi$
$308$	−4.53329	−0.258308
$309$	−1.58734	−0.0903005
$310$	7.99045	0.453827
$311$	−29.5322	−1.67462	−0.837308	−	0.546731i	$-0.815872\pi$
$311$	−29.5322	−1.67462	−0.837308	+	0.546731i	$0.815872\pi$
$312$	0	0
$313$	6.68905	0.378087	0.189044	−	0.981969i	$-0.439461\pi$
$313$	6.68905	0.378087	0.189044	+	0.981969i	$0.439461\pi$
$314$	7.27839	0.410743
$315$	11.0858	0.624613
$316$	−18.3541	−1.03250
$317$	20.6867	1.16188	0.580941	−	0.813946i	$-0.302685\pi$
$317$	20.6867	1.16188	0.580941	+	0.813946i	$0.302685\pi$
$318$	0.797761	0.0447362
$319$	−25.6673	−1.43709
$320$	16.2359	0.907616
$321$	1.46263	0.0816362
$322$	−2.10510	−0.117312
$323$	19.8790	1.10610
$324$	−11.3076	−0.628197
$325$	0	0
$326$	3.65392	0.202372
$327$	−0.461683	−0.0255311
$328$	23.3056	1.28684
$329$	9.40740	0.518647
$330$	1.78757	0.0984024
$331$	−35.4014	−1.94584	−0.972918	−	0.231149i	$-0.925752\pi$
$331$	−35.4014	−1.94584	−0.972918	+	0.231149i	$0.925752\pi$
$332$	−12.6585	−0.694723
$333$	−6.47992	−0.355097
$334$	9.30014	0.508881
$335$	4.81545	0.263096
$336$	−0.0396435	−0.00216273
$337$	−6.69897	−0.364916	−0.182458	−	0.983214i	$-0.558405\pi$
$337$	−6.69897	−0.364916	−0.182458	+	0.983214i	$0.558405\pi$
$338$	0	0
$339$	1.86837	0.101476
$340$	−35.7435	−1.93846
$341$	8.93927	0.484089
$342$	6.70172	0.362388
$343$	−1.00000	−0.0539949
$344$	32.9660	1.77741
$345$	−1.50865	−0.0812228
$346$	8.71012	0.468259
$347$	−7.38059	−0.396211	−0.198105	−	0.980181i	$-0.563479\pi$
$347$	−7.38059	−0.396211	−0.198105	+	0.980181i	$0.563479\pi$
$348$	−1.52645	−0.0818264
$349$	15.2129	0.814326	0.407163	−	0.913355i	$-0.366518\pi$
$349$	15.2129	0.814326	0.407163	+	0.913355i	$0.366518\pi$
$350$	7.49594	0.400675
$351$	0	0
$352$	20.2054	1.07695
$353$	−12.5476	−0.667843	−0.333921	−	0.942601i	$-0.608372\pi$
$353$	−12.5476	−0.667843	−0.333921	+	0.942601i	$0.608372\pi$
$354$	0.580543	0.0308555
$355$	−4.86863	−0.258400
$356$	−6.15709	−0.326325
$357$	−1.20376	−0.0637099
$358$	−15.1769	−0.802123
$359$	17.8460	0.941877	0.470939	−	0.882166i	$-0.343915\pi$
$359$	17.8460	0.941877	0.470939	+	0.882166i	$0.343915\pi$
$360$	−30.7303	−1.61963
$361$	−11.8453	−0.623439
$362$	17.9616	0.944042
$363$	0.218134	0.0114491
$364$	0	0
$365$	16.0757	0.841442
$366$	−0.692159	−0.0361797
$367$	−30.9271	−1.61438	−0.807190	−	0.590291i	$-0.799013\pi$
$367$	−30.9271	−1.61438	−0.807190	+	0.590291i	$0.799013\pi$
$368$	−0.611529	−0.0318782
$369$	−25.0016	−1.30153
$370$	−6.84397	−0.355801
$371$	5.84583	0.303500
$372$	0.531625	0.0275635
$373$	−28.6520	−1.48354	−0.741772	−	0.670652i	$-0.766014\pi$
$373$	−28.6520	−1.48354	−0.741772	+	0.670652i	$0.766014\pi$
$374$	22.0019	1.13769
$375$	2.35302	0.121509
$376$	−26.0777	−1.34486
$377$	0	0
$378$	−0.815220	−0.0419304
$379$	4.61700	0.237159	0.118580	−	0.992945i	$-0.462166\pi$
$379$	4.61700	0.237159	0.118580	+	0.992945i	$0.462166\pi$
$380$	−12.8645	−0.659933
$381$	0.143409	0.00734708
$382$	−4.97281	−0.254431
$383$	27.7969	1.42036	0.710178	−	0.704022i	$-0.248614\pi$
$383$	27.7969	1.42036	0.710178	+	0.704022i	$0.248614\pi$
$384$	1.26843	0.0647293
$385$	13.0989	0.667583
$386$	−2.73689	−0.139304
$387$	−35.3649	−1.79770
$388$	−7.64844	−0.388291
$389$	16.8702	0.855352	0.427676	−	0.903932i	$-0.359332\pi$
$389$	16.8702	0.855352	0.427676	+	0.903932i	$0.359332\pi$
$390$	0	0
$391$	−18.5689	−0.939069
$392$	2.77204	0.140009
$393$	2.16492	0.109206
$394$	7.57640	0.381694
$395$	53.0341	2.66844
$396$	−13.4810	−0.677443
$397$	24.2776	1.21846	0.609228	−	0.792995i	$-0.291479\pi$
$397$	24.2776	1.21846	0.609228	+	0.792995i	$0.291479\pi$
$398$	−4.70685	−0.235933
$399$	−0.433247	−0.0216895
$400$	2.17757	0.108878
$401$	−24.0304	−1.20002	−0.600010	−	0.799992i	$-0.704837\pi$
$401$	−24.0304	−1.20002	−0.600010	+	0.799992i	$0.704837\pi$
$402$	−0.176281	−0.00879207
$403$	0	0
$404$	4.11546	0.204752
$405$	32.6731	1.62354
$406$	6.15445	0.305440
$407$	−7.65665	−0.379526
$408$	3.33688	0.165200
$409$	−2.04813	−0.101274	−0.0506368	−	0.998717i	$-0.516125\pi$
$409$	−2.04813	−0.101274	−0.0506368	+	0.998717i	$0.516125\pi$
$410$	−26.4062	−1.30411
$411$	−2.96218	−0.146113
$412$	12.6435	0.622899
$413$	4.25410	0.209331
$414$	−6.26006	−0.307665
$415$	36.5765	1.79547
$416$	0	0
$417$	0.520079	0.0254684
$418$	7.91874	0.387318
$419$	−25.9332	−1.26692	−0.633461	−	0.773775i	$-0.718366\pi$
$419$	−25.9332	−1.26692	−0.633461	+	0.773775i	$0.718366\pi$
$420$	0.779003	0.0380114
$421$	22.5137	1.09725	0.548626	−	0.836068i	$-0.315151\pi$
$421$	22.5137	1.09725	0.548626	+	0.836068i	$0.315151\pi$
$422$	16.1888	0.788059
$423$	27.9754	1.36021
$424$	−16.2049	−0.786979
$425$	66.1211	3.20735
$426$	0.178227	0.00863514
$427$	−5.07200	−0.245451
$428$	−11.6502	−0.563131
$429$	0	0
$430$	−37.3518	−1.80126
$431$	−2.78073	−0.133943	−0.0669716	−	0.997755i	$-0.521334\pi$
$431$	−2.78073	−0.133943	−0.0669716	+	0.997755i	$0.521334\pi$
$432$	−0.236821	−0.0113941
$433$	25.5607	1.22837	0.614186	−	0.789162i	$-0.289485\pi$
$433$	25.5607	1.22837	0.614186	+	0.789162i	$0.289485\pi$
$434$	−2.14344	−0.102888
$435$	4.41067	0.211476
$436$	3.67740	0.176115
$437$	−6.68314	−0.319698
$438$	−0.588488	−0.0281191
$439$	−31.6821	−1.51210	−0.756052	−	0.654512i	$-0.772874\pi$
$439$	−31.6821	−1.51210	−0.756052	+	0.654512i	$0.772874\pi$
$440$	−36.3108	−1.73105
$441$	−2.97376	−0.141608
$442$	0	0
$443$	−17.1943	−0.816928	−0.408464	−	0.912774i	$-0.633935\pi$
$443$	−17.1943	−0.816928	−0.408464	+	0.912774i	$0.633935\pi$
$444$	−0.455346	−0.0216098
$445$	17.7909	0.843368
$446$	11.2114	0.530874
$447$	0.0823781	0.00389635
$448$	−4.35529	−0.205768
$449$	−14.3503	−0.677230	−0.338615	−	0.940925i	$-0.609958\pi$
$449$	−14.3503	−0.677230	−0.338615	+	0.940925i	$0.609958\pi$
$450$	22.2912	1.05082
$451$	−29.5418	−1.39107
$452$	−14.8819	−0.699988
$453$	2.50232	0.117569
$454$	11.2505	0.528013
$455$	0	0
$456$	1.20098	0.0562411
$457$	−15.0888	−0.705822	−0.352911	−	0.935657i	$-0.614808\pi$
$457$	−15.0888	−0.705822	−0.352911	+	0.935657i	$0.614808\pi$
$458$	−8.90921	−0.416300
$459$	−7.19100	−0.335647
$460$	12.0167	0.560280
$461$	−15.8856	−0.739868	−0.369934	−	0.929058i	$-0.620620\pi$
$461$	−15.8856	−0.739868	−0.369934	+	0.929058i	$0.620620\pi$
$462$	−0.479516	−0.0223091
$463$	−7.03356	−0.326877	−0.163439	−	0.986553i	$-0.552259\pi$
$463$	−7.03356	−0.326877	−0.163439	+	0.986553i	$0.552259\pi$
$464$	1.78787	0.0829996
$465$	−1.53613	−0.0712362
$466$	−4.42915	−0.205176
$467$	−0.621410	−0.0287554	−0.0143777	−	0.999897i	$-0.504577\pi$
$467$	−0.621410	−0.0287554	−0.0143777	+	0.999897i	$0.504577\pi$
$468$	0	0
$469$	−1.29175	−0.0596473
$470$	29.5471	1.36291
$471$	−1.39924	−0.0644734
$472$	−11.7926	−0.542796
$473$	−41.7871	−1.92137
$474$	−1.94143	−0.0891730
$475$	23.7977	1.09191
$476$	9.58820	0.439475
$477$	17.3841	0.795964
$478$	16.8846	0.772281
$479$	24.6401	1.12584	0.562919	−	0.826512i	$-0.309678\pi$
$479$	24.6401	1.12584	0.562919	+	0.826512i	$0.309678\pi$
$480$	−3.47210	−0.158479
$481$	0	0
$482$	19.6721	0.896041
$483$	0.404695	0.0184143
$484$	−1.73748	−0.0789764
$485$	22.1001	1.00351
$486$	−3.64173	−0.165192
$487$	−20.8751	−0.945941	−0.472971	−	0.881078i	$-0.656818\pi$
$487$	−20.8751	−0.945941	−0.472971	+	0.881078i	$0.656818\pi$
$488$	14.0598	0.636457
$489$	−0.702449	−0.0317659
$490$	−3.14083	−0.141888
$491$	−2.48344	−0.112076	−0.0560380	−	0.998429i	$-0.517847\pi$
$491$	−2.48344	−0.112076	−0.0560380	+	0.998429i	$0.517847\pi$
$492$	−1.75687	−0.0792058
$493$	54.2879	2.44501
$494$	0	0
$495$	38.9531	1.75081
$496$	−0.622668	−0.0279586
$497$	1.30601	0.0585826
$498$	−1.33897	−0.0600005
$499$	−0.427604	−0.0191422	−0.00957109	−	0.999954i	$-0.503047\pi$
$499$	−0.427604	−0.0191422	−0.00957109	+	0.999954i	$0.503047\pi$
$500$	−18.7422	−0.838178
$501$	−1.78791	−0.0798779
$502$	−12.1545	−0.542480
$503$	36.2684	1.61713	0.808565	−	0.588407i	$-0.200245\pi$
$503$	36.2684	1.61713	0.808565	+	0.588407i	$0.200245\pi$
$504$	8.24341	0.367191
$505$	−11.8916	−0.529169
$506$	−7.39687	−0.328831
$507$	0	0
$508$	−1.14228	−0.0506806
$509$	16.9910	0.753113	0.376557	−	0.926394i	$-0.377108\pi$
$509$	16.9910	0.753113	0.376557	+	0.926394i	$0.377108\pi$
$510$	−3.78082	−0.167418
$511$	−4.31232	−0.190766
$512$	−2.76435	−0.122168
$513$	−2.58812	−0.114268
$514$	−10.9920	−0.484834
$515$	−36.5332	−1.60985
$516$	−2.48511	−0.109401
$517$	33.0556	1.45379
$518$	1.83590	0.0806647
$519$	−1.67448	−0.0735015
$520$	0	0
$521$	16.3640	0.716920	0.358460	−	0.933545i	$-0.383302\pi$
$521$	16.3640	0.716920	0.358460	+	0.933545i	$0.383302\pi$
$522$	18.3019	0.801052
$523$	−12.5863	−0.550359	−0.275180	−	0.961393i	$-0.588737\pi$
$523$	−12.5863	−0.550359	−0.275180	+	0.961393i	$0.588737\pi$
$524$	−17.2440	−0.753309
$525$	−1.44106	−0.0628930
$526$	−14.0861	−0.614185
$527$	−18.9071	−0.823607
$528$	−0.139299	−0.00606222
$529$	−16.7573	−0.728578
$530$	18.3608	0.797541
$531$	12.6507	0.548993
$532$	3.45090	0.149615
$533$	0	0
$534$	−0.651275	−0.0281834
$535$	33.6631	1.45538
$536$	3.58078	0.154666
$537$	2.91768	0.125907
$538$	−5.20459	−0.224386
$539$	−3.51379	−0.151350
$540$	4.65358	0.200258
$541$	−44.7256	−1.92290	−0.961452	−	0.274974i	$-0.911331\pi$
$541$	−44.7256	−1.92290	−0.961452	+	0.274974i	$0.911331\pi$
$542$	25.3623	1.08941
$543$	−3.45304	−0.148184
$544$	−42.7356	−1.83228
$545$	−10.6258	−0.455160
$546$	0	0
$547$	23.5754	1.00801	0.504006	−	0.863700i	$-0.331859\pi$
$547$	23.5754	1.00801	0.504006	+	0.863700i	$0.331859\pi$
$548$	23.5943	1.00790
$549$	−15.0829	−0.643724
$550$	26.3392	1.12311
$551$	19.5388	0.832382
$552$	−1.12183	−0.0477484
$553$	−14.2264	−0.604969
$554$	5.06510	0.215195
$555$	1.31572	0.0558492
$556$	−4.14253	−0.175682
$557$	−19.5362	−0.827774	−0.413887	−	0.910328i	$-0.635829\pi$
$557$	−19.5362	−0.827774	−0.413887	+	0.910328i	$0.635829\pi$
$558$	−6.37409	−0.269837
$559$	0	0
$560$	−0.912411	−0.0385564
$561$	−4.22977	−0.178581
$562$	22.3112	0.941142
$563$	26.1631	1.10264	0.551322	−	0.834293i	$-0.314124\pi$
$563$	26.1631	1.10264	0.551322	+	0.834293i	$0.314124\pi$
$564$	1.96584	0.0827769
$565$	43.0013	1.80908
$566$	0.169081	0.00710698
$567$	−8.76457	−0.368077
$568$	−3.62032	−0.151905
$569$	−13.5349	−0.567412	−0.283706	−	0.958911i	$-0.591564\pi$
$569$	−13.5349	−0.567412	−0.283706	+	0.958911i	$0.591564\pi$
$570$	−1.36076	−0.0569959
$571$	−8.45496	−0.353829	−0.176914	−	0.984226i	$-0.556612\pi$
$571$	−8.45496	−0.353829	−0.176914	+	0.984226i	$0.556612\pi$
$572$	0	0
$573$	0.956001	0.0399375
$574$	7.08347	0.295658
$575$	−22.2294	−0.927029
$576$	−12.9516	−0.539651
$577$	−16.9054	−0.703780	−0.351890	−	0.936041i	$-0.614461\pi$
$577$	−16.9054	−0.703780	−0.351890	+	0.936041i	$0.614461\pi$
$578$	−32.2125	−1.33986
$579$	0.526155	0.0218663
$580$	−35.1319	−1.45877
$581$	−9.81167	−0.407057
$582$	−0.809025	−0.0335351
$583$	20.5410	0.850722
$584$	11.9539	0.494658
$585$	0	0
$586$	−1.65142	−0.0682197
$587$	−10.2055	−0.421227	−0.210613	−	0.977569i	$-0.567546\pi$
$587$	−10.2055	−0.421227	−0.210613	+	0.977569i	$0.567546\pi$
$588$	−0.208968	−0.00861768
$589$	−6.80488	−0.280390
$590$	13.3614	0.550081
$591$	−1.45653	−0.0599136
$592$	0.533327	0.0219196
$593$	3.79490	0.155838	0.0779190	−	0.996960i	$-0.475172\pi$
$593$	3.79490	0.155838	0.0779190	+	0.996960i	$0.475172\pi$
$594$	−2.86451	−0.117532
$595$	−27.7051	−1.13580
$596$	−0.656158	−0.0268773
$597$	0.904871	0.0370339
$598$	0	0
$599$	14.8629	0.607281	0.303640	−	0.952787i	$-0.401798\pi$
$599$	14.8629	0.607281	0.303640	+	0.952787i	$0.401798\pi$
$600$	3.99468	0.163082
$601$	6.70162	0.273365	0.136682	−	0.990615i	$-0.456356\pi$
$601$	6.70162	0.273365	0.136682	+	0.990615i	$0.456356\pi$
$602$	10.0196	0.408370
$603$	−3.84135	−0.156432
$604$	−19.9315	−0.811001
$605$	5.02044	0.204110
$606$	0.435319	0.0176836
$607$	0.0721187	0.00292721	0.00146360	−	0.999999i	$-0.499534\pi$
$607$	0.0721187	0.00292721	0.00146360	+	0.999999i	$0.499534\pi$
$608$	−15.3810	−0.623783
$609$	−1.18316	−0.0479443
$610$	−15.9303	−0.644999
$611$	0	0
$612$	28.5131	1.15257
$613$	3.55353	0.143526	0.0717628	−	0.997422i	$-0.477138\pi$
$613$	3.55353	0.143526	0.0717628	+	0.997422i	$0.477138\pi$
$614$	−21.1785	−0.854695
$615$	5.07647	0.204703
$616$	9.74039	0.392451
$617$	33.1215	1.33342	0.666711	−	0.745316i	$-0.267701\pi$
$617$	33.1215	1.33342	0.666711	+	0.745316i	$0.267701\pi$
$618$	1.33738	0.0537973
$619$	3.55028	0.142698	0.0713489	−	0.997451i	$-0.477270\pi$
$619$	3.55028	0.142698	0.0713489	+	0.997451i	$0.477270\pi$
$620$	12.2355	0.491391
$621$	2.41755	0.0970130
$622$	24.8817	0.997667
$623$	−4.77241	−0.191202
$624$	0	0
$625$	9.67087	0.386835
$626$	−5.63572	−0.225249
$627$	−1.52234	−0.0607964
$628$	11.1452	0.444742
$629$	16.1943	0.645709
$630$	−9.34010	−0.372119
$631$	27.9899	1.11426	0.557131	−	0.830425i	$-0.311902\pi$
$631$	27.9899	1.11426	0.557131	+	0.830425i	$0.311902\pi$
$632$	39.4363	1.56869
$633$	−3.11222	−0.123700
$634$	−17.4292	−0.692201
$635$	3.30062	0.130981
$636$	1.22159	0.0484392
$637$	0	0
$638$	21.6255	0.856160
$639$	3.88377	0.153640
$640$	29.1934	1.15397
$641$	9.33085	0.368547	0.184273	−	0.982875i	$-0.441007\pi$
$641$	9.33085	0.368547	0.184273	+	0.982875i	$0.441007\pi$
$642$	−1.23231	−0.0486355
$643$	−7.22132	−0.284781	−0.142390	−	0.989811i	$-0.545479\pi$
$643$	−7.22132	−0.284781	−0.142390	+	0.989811i	$0.545479\pi$
$644$	−3.22347	−0.127023
$645$	7.18071	0.282740
$646$	−16.7486	−0.658966
$647$	−7.65676	−0.301018	−0.150509	−	0.988609i	$-0.548091\pi$
$647$	−7.65676	−0.301018	−0.150509	+	0.988609i	$0.548091\pi$
$648$	24.2958	0.954429
$649$	14.9480	0.586761
$650$	0	0
$651$	0.412067	0.0161502
$652$	5.59515	0.219123
$653$	−11.6265	−0.454979	−0.227490	−	0.973780i	$-0.573052\pi$
$653$	−11.6265	−0.454979	−0.227490	+	0.973780i	$0.573052\pi$
$654$	0.388982	0.0152104
$655$	49.8265	1.94688
$656$	2.05774	0.0803414
$657$	−12.8238	−0.500305
$658$	−7.92602	−0.308988
$659$	42.8815	1.67043	0.835213	−	0.549927i	$-0.185344\pi$
$659$	42.8815	1.67043	0.835213	+	0.549927i	$0.185344\pi$
$660$	2.73725	0.106547
$661$	−41.0681	−1.59736	−0.798682	−	0.601753i	$-0.794469\pi$
$661$	−41.0681	−1.59736	−0.798682	+	0.601753i	$0.794469\pi$
$662$	29.8267	1.15925
$663$	0	0
$664$	27.1984	1.05550
$665$	−9.97135	−0.386672
$666$	5.45952	0.211552
$667$	−18.2512	−0.706687
$668$	14.2410	0.551003
$669$	−2.15534	−0.0833301
$670$	−4.05716	−0.156742
$671$	−17.8219	−0.688009
$672$	0.931391	0.0359292
$673$	−33.2669	−1.28234	−0.641172	−	0.767397i	$-0.721551\pi$
$673$	−33.2669	−1.28234	−0.641172	+	0.767397i	$0.721551\pi$
$674$	5.64408	0.217402
$675$	−8.60856	−0.331343
$676$	0	0
$677$	36.6928	1.41022	0.705110	−	0.709098i	$-0.250898\pi$
$677$	36.6928	1.41022	0.705110	+	0.709098i	$0.250898\pi$
$678$	−1.57416	−0.0604552
$679$	−5.92836	−0.227510
$680$	76.7997	2.94513
$681$	−2.16286	−0.0828810
$682$	−7.53160	−0.288400
$683$	19.0493	0.728903	0.364451	−	0.931222i	$-0.381257\pi$
$683$	19.0493	0.728903	0.364451	+	0.931222i	$0.381257\pi$
$684$	10.2622	0.392384
$685$	−68.1756	−2.60486
$686$	0.842530	0.0321680
$687$	1.71276	0.0653457
$688$	2.91070	0.110969
$689$	0	0
$690$	1.27108	0.0483892
$691$	30.5436	1.16193	0.580967	−	0.813927i	$-0.302674\pi$
$691$	30.5436	1.16193	0.580967	+	0.813927i	$0.302674\pi$
$692$	13.3376	0.507018
$693$	−10.4492	−0.396932
$694$	6.21837	0.236046
$695$	11.9698	0.454041
$696$	3.27979	0.124320
$697$	62.4827	2.36670
$698$	−12.8173	−0.485142
$699$	0.851483	0.0322060
$700$	11.4783	0.433840
$701$	8.37561	0.316343	0.158171	−	0.987412i	$-0.449440\pi$
$701$	8.37561	0.316343	0.158171	+	0.987412i	$0.449440\pi$
$702$	0	0
$703$	5.82850	0.219826
$704$	−15.3036	−0.576776
$705$	−5.68029	−0.213932
$706$	10.5718	0.397873
$707$	3.18992	0.119969
$708$	0.888969	0.0334095
$709$	8.96509	0.336691	0.168345	−	0.985728i	$-0.446158\pi$
$709$	8.96509	0.336691	0.168345	+	0.985728i	$0.446158\pi$
$710$	4.10197	0.153944
$711$	−42.3061	−1.58660
$712$	13.2293	0.495790
$713$	6.35642	0.238050
$714$	1.01421	0.0379557
$715$	0	0
$716$	−23.2399	−0.868517
$717$	−3.24598	−0.121223
$718$	−15.0358	−0.561132
$719$	−14.3101	−0.533678	−0.266839	−	0.963741i	$-0.585979\pi$
$719$	−14.3101	−0.533678	−0.266839	+	0.963741i	$0.585979\pi$
$720$	−2.71330	−0.101119
$721$	9.80005	0.364973
$722$	9.98006	0.371419
$723$	−3.78188	−0.140650
$724$	27.5041	1.02218
$725$	64.9897	2.41366
$726$	−0.183784	−0.00682088
$727$	−19.0723	−0.707354	−0.353677	−	0.935368i	$-0.615069\pi$
$727$	−19.0723	−0.707354	−0.353677	+	0.935368i	$0.615069\pi$
$728$	0	0
$729$	−25.5936	−0.947911
$730$	−13.5443	−0.501297
$731$	88.3824	3.26894
$732$	−1.05988	−0.0391744
$733$	26.7063	0.986418	0.493209	−	0.869911i	$-0.335824\pi$
$733$	26.7063	0.986418	0.493209	+	0.869911i	$0.335824\pi$
$734$	26.0570	0.961782
$735$	0.603811	0.0222719
$736$	14.3674	0.529588
$737$	−4.53893	−0.167194
$738$	21.0646	0.775397
$739$	27.5346	1.01288	0.506438	−	0.862276i	$-0.330962\pi$
$739$	27.5346	1.01288	0.506438	+	0.862276i	$0.330962\pi$
$740$	−10.4800	−0.385251
$741$	0	0
$742$	−4.92529	−0.180813
$743$	−28.8668	−1.05902	−0.529510	−	0.848304i	$-0.677624\pi$
$743$	−28.8668	−1.05902	−0.529510	+	0.848304i	$0.677624\pi$
$744$	−1.14227	−0.0418775
$745$	1.89596	0.0694628
$746$	24.1402	0.883835
$747$	−29.1776	−1.06755
$748$	33.6910	1.23186
$749$	−9.03013	−0.329954
$750$	−1.98249	−0.0723902
$751$	6.62174	0.241631	0.120815	−	0.992675i	$-0.461449\pi$
$751$	6.62174	0.241631	0.120815	+	0.992675i	$0.461449\pi$
$752$	−2.30250	−0.0839637
$753$	2.33664	0.0851519
$754$	0	0
$755$	57.5920	2.09599
$756$	−1.24832	−0.0454011
$757$	35.9013	1.30485	0.652427	−	0.757852i	$-0.273751\pi$
$757$	35.9013	1.30485	0.652427	+	0.757852i	$0.273751\pi$
$758$	−3.88996	−0.141290
$759$	1.42201	0.0516158
$760$	27.6410	1.00265
$761$	−27.2881	−0.989191	−0.494596	−	0.869123i	$-0.664684\pi$
$761$	−27.2881	−0.989191	−0.494596	+	0.869123i	$0.664684\pi$
$762$	−0.120827	−0.00437709
$763$	2.85038	0.103191
$764$	−7.61473	−0.275491
$765$	−82.3883	−2.97876
$766$	−23.4197	−0.846190
$767$	0	0
$768$	−2.47957	−0.0894736
$769$	20.3268	0.733003	0.366501	−	0.930418i	$-0.380556\pi$
$769$	20.3268	0.733003	0.366501	+	0.930418i	$0.380556\pi$
$770$	−11.0362	−0.397718
$771$	2.11315	0.0761033
$772$	−4.19093	−0.150835
$773$	−4.74178	−0.170550	−0.0852750	−	0.996357i	$-0.527177\pi$
$773$	−4.74178	−0.170550	−0.0852750	+	0.996357i	$0.527177\pi$
$774$	29.7960	1.07100
$775$	−22.6343	−0.813047
$776$	16.4337	0.589935
$777$	−0.352943	−0.0126617
$778$	−14.2136	−0.509584
$779$	22.4882	0.805724
$780$	0	0
$781$	4.58905	0.164209
$782$	15.6448	0.559459
$783$	−7.06795	−0.252588
$784$	0.244755	0.00874124
$785$	−32.2040	−1.14941
$786$	−1.82401	−0.0650604
$787$	−31.6106	−1.12679	−0.563397	−	0.826186i	$-0.690506\pi$
$787$	−31.6106	−1.12679	−0.563397	+	0.826186i	$0.690506\pi$
$788$	11.6015	0.413287
$789$	2.70799	0.0964072
$790$	−44.6829	−1.58974
$791$	−11.5351	−0.410141
$792$	28.9656	1.02925
$793$	0	0
$794$	−20.4546	−0.725906
$795$	−3.52978	−0.125188
$796$	−7.20747	−0.255462
$797$	−47.1670	−1.67074	−0.835370	−	0.549688i	$-0.814747\pi$
$797$	−47.1670	−1.67074	−0.835370	+	0.549688i	$0.814747\pi$
$798$	0.365024	0.0129217
$799$	−69.9148	−2.47341
$800$	−51.1601	−1.80878
$801$	−14.1920	−0.501450
$802$	20.2463	0.714923
$803$	−15.1526	−0.534724
$804$	−0.269933	−0.00951982
$805$	9.31421	0.328283
$806$	0	0
$807$	1.00056	0.0352213
$808$	−8.84261	−0.311082
$809$	−11.6238	−0.408672	−0.204336	−	0.978901i	$-0.565504\pi$
$809$	−11.6238	−0.408672	−0.204336	+	0.978901i	$0.565504\pi$
$810$	−27.5281	−0.967238
$811$	9.29601	0.326427	0.163214	−	0.986591i	$-0.447814\pi$
$811$	9.29601	0.326427	0.163214	+	0.986591i	$0.447814\pi$
$812$	9.42414	0.330722
$813$	−4.87579	−0.171001
$814$	6.45096	0.226106
$815$	−16.1671	−0.566310
$816$	0.294626	0.0103140
$817$	31.8098	1.11288
$818$	1.72561	0.0603347
$819$	0	0
$820$	−40.4350	−1.41205
$821$	44.2153	1.54312	0.771562	−	0.636154i	$-0.219476\pi$
$821$	44.2153	1.54312	0.771562	+	0.636154i	$0.219476\pi$
$822$	2.49572	0.0870483
$823$	20.1303	0.701700	0.350850	−	0.936432i	$-0.385893\pi$
$823$	20.1303	0.701700	0.350850	+	0.936432i	$0.385893\pi$
$824$	−27.1662	−0.946378
$825$	−5.06359	−0.176291
$826$	−3.58421	−0.124710
$827$	13.4329	0.467109	0.233554	−	0.972344i	$-0.424964\pi$
$827$	13.4329	0.467109	0.233554	+	0.972344i	$0.424964\pi$
$828$	−9.58585	−0.333131
$829$	−4.62491	−0.160630	−0.0803148	−	0.996770i	$-0.525593\pi$
$829$	−4.62491	−0.160630	−0.0803148	+	0.996770i	$0.525593\pi$
$830$	−30.8168	−1.06967
$831$	−0.973741	−0.0337787
$832$	0	0
$833$	7.43189	0.257500
$834$	−0.438182	−0.0151730
$835$	−41.1494	−1.42403
$836$	12.1257	0.419378
$837$	2.46159	0.0850849
$838$	21.8495	0.754780
$839$	−44.5747	−1.53889	−0.769446	−	0.638712i	$-0.779467\pi$
$839$	−44.5747	−1.53889	−0.769446	+	0.638712i	$0.779467\pi$
$840$	−1.67379	−0.0577513
$841$	24.3590	0.839966
$842$	−18.9685	−0.653698
$843$	−4.28923	−0.147729
$844$	24.7895	0.853289
$845$	0	0
$846$	−23.5701	−0.810357
$847$	−1.34673	−0.0462743
$848$	−1.43079	−0.0491337
$849$	−0.0325050	−0.00111557
$850$	−55.7090	−1.91080
$851$	−5.44439	−0.186631
$852$	0.272914	0.00934989
$853$	−4.58159	−0.156870	−0.0784352	−	0.996919i	$-0.524992\pi$
$853$	−4.58159	−0.156870	−0.0784352	+	0.996919i	$0.524992\pi$
$854$	4.27331	0.146230
$855$	−29.6525	−1.01409
$856$	25.0319	0.855573
$857$	15.4008	0.526080	0.263040	−	0.964785i	$-0.415275\pi$
$857$	15.4008	0.526080	0.263040	+	0.964785i	$0.415275\pi$
$858$	0	0
$859$	−52.8596	−1.80355	−0.901774	−	0.432208i	$-0.857735\pi$
$859$	−52.8596	−1.80355	−0.901774	+	0.432208i	$0.857735\pi$
$860$	−57.1958	−1.95036
$861$	−1.36176	−0.0464088
$862$	2.34285	0.0797979
$863$	33.2346	1.13132	0.565659	−	0.824639i	$-0.308622\pi$
$863$	33.2346	1.13132	0.565659	+	0.824639i	$0.308622\pi$
$864$	5.56391	0.189288
$865$	−38.5388	−1.31036
$866$	−21.5357	−0.731813
$867$	6.19270	0.210315
$868$	−3.28219	−0.111405
$869$	−49.9887	−1.69575
$870$	−3.71613	−0.125988
$871$	0	0
$872$	−7.90138	−0.267574
$873$	−17.6296	−0.596670
$874$	5.63075	0.190463
$875$	−14.5273	−0.491111
$876$	−0.901136	−0.0304466
$877$	24.1314	0.814858	0.407429	−	0.913237i	$-0.366425\pi$
$877$	24.1314	0.814858	0.407429	+	0.913237i	$0.366425\pi$
$878$	26.6931	0.900849
$879$	0.317478	0.0107083
$880$	−3.20602	−0.108075
$881$	59.0833	1.99057	0.995284	−	0.0970036i	$-0.0309258\pi$
$881$	59.0833	1.99057	0.995284	+	0.0970036i	$0.0309258\pi$
$882$	2.50549	0.0843641
$883$	−8.09950	−0.272570	−0.136285	−	0.990670i	$-0.543516\pi$
$883$	−8.09950	−0.272570	−0.136285	+	0.990670i	$0.543516\pi$
$884$	0	0
$885$	−2.56867	−0.0863449
$886$	14.4868	0.486692
$887$	−34.8540	−1.17028	−0.585142	−	0.810931i	$-0.698961\pi$
$887$	−34.8540	−1.17028	−0.585142	+	0.810931i	$0.698961\pi$
$888$	0.978373	0.0328320
$889$	−0.885393	−0.0296951
$890$	−14.9893	−0.502444
$891$	−30.7969	−1.03173
$892$	17.1677	0.574816
$893$	−25.1631	−0.842051
$894$	−0.0694061	−0.00232129
$895$	67.1516	2.24463
$896$	−7.83114	−0.261620
$897$	0	0
$898$	12.0905	0.403466
$899$	−18.5836	−0.619798
$900$	34.1338	1.13779
$901$	−43.4456	−1.44738
$902$	24.8898	0.828741
$903$	−1.92623	−0.0641009
$904$	31.9758	1.06350
$905$	−79.4730	−2.64177
$906$	−2.10828	−0.0700430
$907$	10.2919	0.341738	0.170869	−	0.985294i	$-0.445343\pi$
$907$	10.2919	0.341738	0.170869	+	0.985294i	$0.445343\pi$
$908$	17.2276	0.571718
$909$	9.48609	0.314634
$910$	0	0
$911$	−54.2867	−1.79860	−0.899299	−	0.437334i	$-0.855923\pi$
$911$	−54.2867	−1.79860	−0.899299	+	0.437334i	$0.855923\pi$
$912$	0.106039	0.00351131
$913$	−34.4762	−1.14099
$914$	12.7127	0.420500
$915$	3.06253	0.101244
$916$	−13.6424	−0.450759
$917$	−13.3660	−0.441384
$918$	6.05863	0.199965
$919$	43.4286	1.43258	0.716289	−	0.697803i	$-0.245839\pi$
$919$	43.4286	1.43258	0.716289	+	0.697803i	$0.245839\pi$
$920$	−25.8194	−0.851240
$921$	4.07147	0.134160
$922$	13.3841	0.440783
$923$	0	0
$924$	−0.734269	−0.0241557
$925$	19.3867	0.637430
$926$	5.92599	0.194740
$927$	29.1430	0.957183
$928$	−42.0044	−1.37886
$929$	−30.8380	−1.01176	−0.505881	−	0.862603i	$-0.668832\pi$
$929$	−30.8380	−1.01176	−0.505881	+	0.862603i	$0.668832\pi$
$930$	1.29423	0.0424396
$931$	2.67482	0.0876637
$932$	−6.78223	−0.222159
$933$	−4.78340	−0.156602
$934$	0.523556	0.0171313
$935$	−97.3498	−3.18368
$936$	0	0
$937$	22.4073	0.732013	0.366007	−	0.930612i	$-0.380725\pi$
$937$	22.4073	0.732013	0.366007	+	0.930612i	$0.380725\pi$
$938$	1.08834	0.0355354
$939$	1.08344	0.0353568
$940$	45.2446	1.47572
$941$	−12.2484	−0.399287	−0.199644	−	0.979869i	$-0.563978\pi$
$941$	−12.2484	−0.399287	−0.199644	+	0.979869i	$0.563978\pi$
$942$	1.17890	0.0384106
$943$	−21.0062	−0.684055
$944$	−1.04121	−0.0338885
$945$	3.60703	0.117337
$946$	35.2069	1.14468
$947$	53.1071	1.72575	0.862875	−	0.505418i	$-0.168662\pi$
$947$	53.1071	1.72575	0.862875	+	0.505418i	$0.168662\pi$
$948$	−2.97286	−0.0965541
$949$	0	0
$950$	−20.0503	−0.650517
$951$	3.35068	0.108653
$952$	−20.6015	−0.667700
$953$	−9.63675	−0.312165	−0.156082	−	0.987744i	$-0.549887\pi$
$953$	−9.63675	−0.312165	−0.156082	+	0.987744i	$0.549887\pi$
$954$	−14.6466	−0.474203
$955$	22.0027	0.711991
$956$	25.8548	0.836205
$957$	−4.15740	−0.134390
$958$	−20.7601	−0.670727
$959$	18.2881	0.590555
$960$	2.62977	0.0848756
$961$	−24.5278	−0.791219
$962$	0	0
$963$	−26.8535	−0.865341
$964$	30.1234	0.970209
$965$	12.1097	0.389824
$966$	−0.340968	−0.0109705
$967$	−12.8720	−0.413937	−0.206968	−	0.978348i	$-0.566360\pi$
$967$	−12.8720	−0.413937	−0.206968	+	0.978348i	$0.566360\pi$
$968$	3.73321	0.119990
$969$	3.21985	0.103436
$970$	−18.6200	−0.597853
$971$	−58.2615	−1.86970	−0.934850	−	0.355042i	$-0.884467\pi$
$971$	−58.2615	−1.86970	−0.934850	+	0.355042i	$0.884467\pi$
$972$	−5.57649	−0.178866
$973$	−3.21091	−0.102937
$974$	17.5879	0.563553
$975$	0	0
$976$	1.24139	0.0397361
$977$	−29.7552	−0.951954	−0.475977	−	0.879458i	$-0.657906\pi$
$977$	−29.7552	−0.951954	−0.475977	+	0.879458i	$0.657906\pi$
$978$	0.591835	0.0189248
$979$	−16.7692	−0.535948
$980$	−4.80947	−0.153633
$981$	8.47636	0.270629
$982$	2.09237	0.0667703
$983$	−11.6376	−0.371181	−0.185591	−	0.982627i	$-0.559420\pi$
$983$	−11.6376	−0.371181	−0.185591	+	0.982627i	$0.559420\pi$
$984$	3.77487	0.120338
$985$	−33.5226	−1.06812
$986$	−45.7392	−1.45663
$987$	1.52374	0.0485012
$988$	0	0
$989$	−29.7134	−0.944832
$990$	−32.8192	−1.04306
$991$	3.02153	0.0959820	0.0479910	−	0.998848i	$-0.484718\pi$
$991$	3.02153	0.0959820	0.0479910	+	0.998848i	$0.484718\pi$
$992$	14.6291	0.464473
$993$	−5.73405	−0.181965
$994$	−1.10035	−0.0349011
$995$	20.8259	0.660227
$996$	−2.05032	−0.0649670
$997$	20.0738	0.635742	0.317871	−	0.948134i	$-0.397032\pi$
$997$	20.0738	0.635742	0.317871	+	0.948134i	$0.397032\pi$
$998$	0.360269	0.0114041
$999$	−2.10840	−0.0667067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.q.1.6	✓	12
7.6	odd	2		8281.2.a.cn.1.6		12
13.5	odd	4		1183.2.c.j.337.14		24
13.8	odd	4		1183.2.c.j.337.11		24
13.12	even	2		1183.2.a.r.1.7	yes	12
91.90	odd	2		8281.2.a.cq.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.6	✓	12	1.1	even	1	trivial
1183.2.a.r.1.7	yes	12	13.12	even	2
1183.2.c.j.337.11		24	13.8	odd	4
1183.2.c.j.337.14		24	13.5	odd	4
8281.2.a.cn.1.6		12	7.6	odd	2
8281.2.a.cq.1.7		12	91.90	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q-0.842530 q^{2} +0.161973 q^{3} -1.29014 q^{4} +3.72786 q^{5} -0.136467 q^{6} -1.00000 q^{7} +2.77204 q^{8} -2.97376 q^{9} -3.14083 q^{10} -3.51379 q^{11} -0.208968 q^{12} +0.842530 q^{14} +0.603811 q^{15} +0.244755 q^{16} +7.43189 q^{17} +2.50549 q^{18} +2.67482 q^{19} -4.80947 q^{20} -0.161973 q^{21} +2.96048 q^{22} -2.49854 q^{23} +0.448995 q^{24} +8.89694 q^{25} -0.967586 q^{27} +1.29014 q^{28} +7.30473 q^{29} -0.508729 q^{30} -2.54405 q^{31} -5.75030 q^{32} -0.569138 q^{33} -6.26159 q^{34} -3.72786 q^{35} +3.83658 q^{36} +2.17903 q^{37} -2.25362 q^{38} +10.3338 q^{40} +8.40738 q^{41} +0.136467 q^{42} +11.8923 q^{43} +4.53329 q^{44} -11.0858 q^{45} +2.10510 q^{46} -9.40740 q^{47} +0.0396435 q^{48} +1.00000 q^{49} -7.49594 q^{50} +1.20376 q^{51} -5.84583 q^{53} +0.815220 q^{54} -13.0989 q^{55} -2.77204 q^{56} +0.433247 q^{57} -6.15445 q^{58} -4.25410 q^{59} -0.779003 q^{60} +5.07200 q^{61} +2.14344 q^{62} +2.97376 q^{63} +4.35529 q^{64} +0.479516 q^{66} +1.29175 q^{67} -9.58820 q^{68} -0.404695 q^{69} +3.14083 q^{70} -1.30601 q^{71} -8.24341 q^{72} +4.31232 q^{73} -1.83590 q^{74} +1.44106 q^{75} -3.45090 q^{76} +3.51379 q^{77} +14.2264 q^{79} +0.912411 q^{80} +8.76457 q^{81} -7.08347 q^{82} +9.81167 q^{83} +0.208968 q^{84} +27.7051 q^{85} -10.0196 q^{86} +1.18316 q^{87} -9.74039 q^{88} +4.77241 q^{89} +9.34010 q^{90} +3.22347 q^{92} -0.412067 q^{93} +7.92602 q^{94} +9.97135 q^{95} -0.931391 q^{96} +5.92836 q^{97} -0.842530 q^{98} +10.4492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 8 q^{3} + 15 q^{4} + 4 q^{5} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 26 q^{9} - 6 q^{10} - 12 q^{11} + 13 q^{12} + 3 q^{14} - 11 q^{15} + 13 q^{16} + 31 q^{17} + 29 q^{18} + 3 q^{19} + 18 q^{20}+ \cdots - 37 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 8 * q^3 + 15 * q^4 + 4 * q^5 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 26 * q^9 - 6 * q^10 - 12 * q^11 + 13 * q^12 + 3 * q^14 - 11 * q^15 + 13 * q^16 + 31 * q^17 + 29 * q^18 + 3 * q^19 + 18 * q^20 - 8 * q^21 - 4 * q^22 + 18 * q^23 + 6 * q^24 + 32 * q^25 + 32 * q^27 - 15 * q^28 + 15 * q^29 - 10 * q^30 + 21 * q^31 + 3 * q^32 + 29 * q^33 - 3 * q^34 - 4 * q^35 + 49 * q^36 - 5 * q^37 + 45 * q^38 - 20 * q^40 + 16 * q^41 + 2 * q^42 - 22 * q^43 - 35 * q^44 - 5 * q^45 - 2 * q^46 + 4 * q^47 + 11 * q^48 + 12 * q^49 - 13 * q^50 + 18 * q^51 + 53 * q^53 + 5 * q^54 - 26 * q^55 + 12 * q^56 + 8 * q^57 - 32 * q^58 + 26 * q^59 - 38 * q^60 + 22 * q^61 + 19 * q^62 - 26 * q^63 + 2 * q^64 - 34 * q^66 - 12 * q^67 + 34 * q^68 + 3 * q^69 + 6 * q^70 - 21 * q^71 + 4 * q^72 + 15 * q^73 - 40 * q^74 + 15 * q^75 - 43 * q^76 + 12 * q^77 + 2 * q^79 - 13 * q^80 + 36 * q^81 - 32 * q^82 + 9 * q^83 - 13 * q^84 + 39 * q^85 - 44 * q^86 + 27 * q^87 - 48 * q^88 + 22 * q^89 - 26 * q^90 + 52 * q^92 + 53 * q^93 - 44 * q^94 + 29 * q^95 + 114 * q^96 - 9 * q^97 - 3 * q^98 - 37 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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