LMFDB - Embedded newform 483.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("483.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.a (trivial)

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:	yes
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.15317.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 2 $ x^4 - 2x^3 - 4x^2 + 5*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.69353$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.69353 q^{2} -1.00000 q^{3} +0.868028 q^{4} +3.51256 q^{5} +1.69353 q^{6} -1.00000 q^{7} +1.91702 q^{8} +1.00000 q^{9} -5.94860 q^{10} -1.74252 q^{11} -0.868028 q^{12} +6.33805 q^{13} +1.69353 q^{14} -3.51256 q^{15} -4.98258 q^{16} -5.94860 q^{17} -1.69353 q^{18} +1.74252 q^{19} +3.04900 q^{20} +1.00000 q^{21} +2.95100 q^{22} +1.00000 q^{23} -1.91702 q^{24} +7.33805 q^{25} -10.7337 q^{26} -1.00000 q^{27} -0.868028 q^{28} -5.68466 q^{29} +5.94860 q^{30} +7.94860 q^{31} +4.60408 q^{32} +1.74252 q^{33} +10.0741 q^{34} -3.51256 q^{35} +0.868028 q^{36} +1.53644 q^{37} -2.95100 q^{38} -6.33805 q^{39} +6.73365 q^{40} +12.1547 q^{41} -1.69353 q^{42} +6.43605 q^{43} -1.51256 q^{44} +3.51256 q^{45} -1.69353 q^{46} +3.59313 q^{47} +4.98258 q^{48} +1.00000 q^{49} -12.4272 q^{50} +5.94860 q^{51} +5.50161 q^{52} +12.9397 q^{53} +1.69353 q^{54} -6.12071 q^{55} -1.91702 q^{56} -1.74252 q^{57} +9.62711 q^{58} -8.69353 q^{59} -3.04900 q^{60} +8.47618 q^{61} -13.4612 q^{62} -1.00000 q^{63} +2.16804 q^{64} +22.2628 q^{65} -2.95100 q^{66} -4.46971 q^{67} -5.16355 q^{68} -1.00000 q^{69} +5.94860 q^{70} -13.4612 q^{71} +1.91702 q^{72} +4.29761 q^{73} -2.60200 q^{74} -7.33805 q^{75} +1.51256 q^{76} +1.74252 q^{77} +10.7337 q^{78} -7.42071 q^{79} -17.5016 q^{80} +1.00000 q^{81} -20.5843 q^{82} -7.75262 q^{83} +0.868028 q^{84} -20.8948 q^{85} -10.8996 q^{86} +5.68466 q^{87} -3.34045 q^{88} +4.18503 q^{89} -5.94860 q^{90} -6.33805 q^{91} +0.868028 q^{92} -7.94860 q^{93} -6.08506 q^{94} +6.12071 q^{95} -4.60408 q^{96} +5.53644 q^{97} -1.69353 q^{98} -1.74252 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{3} + 4 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} + 4 q^{9} + 2 q^{10} + q^{11} - 4 q^{12} + 7 q^{13} - 2 q^{14} - 5 q^{15} + 8 q^{16} + 2 q^{17} + 2 q^{18} - q^{19} + 13 q^{20}+ \cdots + q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 + 4 * q^9 + 2 * q^10 + q^11 - 4 * q^12 + 7 * q^13 - 2 * q^14 - 5 * q^15 + 8 * q^16 + 2 * q^17 + 2 * q^18 - q^19 + 13 * q^20 + 4 * q^21 + 11 * q^22 + 4 * q^23 - 9 * q^24 + 11 * q^25 - 19 * q^26 - 4 * q^27 - 4 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 20 * q^32 - q^33 + 23 * q^34 - 5 * q^35 + 4 * q^36 + 16 * q^37 - 11 * q^38 - 7 * q^39 + 3 * q^40 + 5 * q^41 + 2 * q^42 + 9 * q^43 + 3 * q^44 + 5 * q^45 + 2 * q^46 - 21 * q^47 - 8 * q^48 + 4 * q^49 - 17 * q^50 - 2 * q^51 - 24 * q^52 + 10 * q^53 - 2 * q^54 + 17 * q^55 - 9 * q^56 + q^57 + q^58 - 26 * q^59 - 13 * q^60 + 2 * q^61 - 19 * q^62 - 4 * q^63 + 27 * q^64 + 26 * q^65 - 11 * q^66 + 5 * q^67 + 7 * q^68 - 4 * q^69 - 2 * q^70 - 19 * q^71 + 9 * q^72 + 10 * q^73 + 9 * q^74 - 11 * q^75 - 3 * q^76 - q^77 + 19 * q^78 - 6 * q^79 - 24 * q^80 + 4 * q^81 - 31 * q^82 - 2 * q^83 + 4 * q^84 - 7 * q^85 - 17 * q^86 - 2 * q^87 - 20 * q^88 - 17 * q^89 + 2 * q^90 - 7 * q^91 + 4 * q^92 - 6 * q^93 - 44 * q^94 - 17 * q^95 - 20 * q^96 + 32 * q^97 + 2 * q^98 + 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 $

$2$	−1.69353	−1.19750	−0.598752	−	0.800935i	$-0.704336\pi$
$2$	−1.69353	−1.19750	−0.598752	+	0.800935i	$0.704336\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.868028	0.434014
$5$	3.51256	1.57086	0.785432	−	0.618949i	$-0.212441\pi$
$5$	3.51256	1.57086	0.785432	+	0.618949i	$0.212441\pi$
$6$	1.69353	0.691379
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.91702	0.677770
$9$	1.00000	0.333333
$10$	−5.94860	−1.88111
$11$	−1.74252	−0.525390	−0.262695	−	0.964879i	$-0.584611\pi$
$11$	−1.74252	−0.525390	−0.262695	+	0.964879i	$0.584611\pi$
$12$	−0.868028	−0.250578
$13$	6.33805	1.75786	0.878930	−	0.476951i	$-0.158258\pi$
$13$	6.33805	1.75786	0.878930	+	0.476951i	$0.158258\pi$
$14$	1.69353	0.452614
$15$	−3.51256	−0.906938
$16$	−4.98258	−1.24565
$17$	−5.94860	−1.44275	−0.721374	−	0.692546i	$-0.756489\pi$
$17$	−5.94860	−1.44275	−0.721374	+	0.692546i	$0.756489\pi$
$18$	−1.69353	−0.399168
$19$	1.74252	0.399762	0.199881	−	0.979820i	$-0.435944\pi$
$19$	1.74252	0.399762	0.199881	+	0.979820i	$0.435944\pi$
$20$	3.04900	0.681776
$21$	1.00000	0.218218
$22$	2.95100	0.629156
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.91702	−0.391311
$25$	7.33805	1.46761
$26$	−10.7337	−2.10504
$27$	−1.00000	−0.192450
$28$	−0.868028	−0.164042
$29$	−5.68466	−1.05561	−0.527807	−	0.849364i	$-0.676986\pi$
$29$	−5.68466	−1.05561	−0.527807	+	0.849364i	$0.676986\pi$
$30$	5.94860	1.08606
$31$	7.94860	1.42761	0.713806	−	0.700344i	$-0.246970\pi$
$31$	7.94860	1.42761	0.713806	+	0.700344i	$0.246970\pi$
$32$	4.60408	0.813895
$33$	1.74252	0.303334
$34$	10.0741	1.72770
$35$	−3.51256	−0.593730
$36$	0.868028	0.144671
$37$	1.53644	0.252589	0.126295	−	0.991993i	$-0.459692\pi$
$37$	1.53644	0.252589	0.126295	+	0.991993i	$0.459692\pi$
$38$	−2.95100	−0.478716
$39$	−6.33805	−1.01490
$40$	6.73365	1.06468
$41$	12.1547	1.89824	0.949121	−	0.314910i	$-0.101974\pi$
$41$	12.1547	1.89824	0.949121	+	0.314910i	$0.101974\pi$
$42$	−1.69353	−0.261317
$43$	6.43605	0.981488	0.490744	−	0.871304i	$-0.336725\pi$
$43$	6.43605	0.981488	0.490744	+	0.871304i	$0.336725\pi$
$44$	−1.51256	−0.228026
$45$	3.51256	0.523621
$46$	−1.69353	−0.249697
$47$	3.59313	0.524112	0.262056	−	0.965053i	$-0.415599\pi$
$47$	3.59313	0.524112	0.262056	+	0.965053i	$0.415599\pi$
$48$	4.98258	0.719174
$49$	1.00000	0.142857
$50$	−12.4272	−1.75747
$51$	5.94860	0.832971
$52$	5.50161	0.762935
$53$	12.9397	1.77741	0.888705	−	0.458480i	$-0.151606\pi$
$53$	12.9397	1.77741	0.888705	+	0.458480i	$0.151606\pi$
$54$	1.69353	0.230460
$55$	−6.12071	−0.825316
$56$	−1.91702	−0.256173
$57$	−1.74252	−0.230803
$58$	9.62711	1.26410
$59$	−8.69353	−1.13180	−0.565900	−	0.824474i	$-0.691471\pi$
$59$	−8.69353	−1.13180	−0.565900	+	0.824474i	$0.691471\pi$
$60$	−3.04900	−0.393624
$61$	8.47618	1.08526	0.542632	−	0.839971i	$-0.317428\pi$
$61$	8.47618	1.08526	0.542632	+	0.839971i	$0.317428\pi$
$62$	−13.4612	−1.70957
$63$	−1.00000	−0.125988
$64$	2.16804	0.271005
$65$	22.2628	2.76136
$66$	−2.95100	−0.363243
$67$	−4.46971	−0.546062	−0.273031	−	0.962005i	$-0.588026\pi$
$67$	−4.46971	−0.546062	−0.273031	+	0.962005i	$0.588026\pi$
$68$	−5.16355	−0.626173
$69$	−1.00000	−0.120386
$70$	5.94860	0.710994
$71$	−13.4612	−1.59755	−0.798773	−	0.601633i	$-0.794517\pi$
$71$	−13.4612	−1.59755	−0.798773	+	0.601633i	$0.794517\pi$
$72$	1.91702	0.225923
$73$	4.29761	0.502997	0.251498	−	0.967858i	$-0.419077\pi$
$73$	4.29761	0.502997	0.251498	+	0.967858i	$0.419077\pi$
$74$	−2.60200	−0.302476
$75$	−7.33805	−0.847326
$76$	1.51256	0.173502
$77$	1.74252	0.198579
$78$	10.7337	1.21535
$79$	−7.42071	−0.834896	−0.417448	−	0.908701i	$-0.637075\pi$
$79$	−7.42071	−0.834896	−0.417448	+	0.908701i	$0.637075\pi$
$80$	−17.5016	−1.95674
$81$	1.00000	0.111111
$82$	−20.5843	−2.27315
$83$	−7.75262	−0.850960	−0.425480	−	0.904968i	$-0.639895\pi$
$83$	−7.75262	−0.850960	−0.425480	+	0.904968i	$0.639895\pi$
$84$	0.868028	0.0947096
$85$	−20.8948	−2.26636
$86$	−10.8996	−1.17533
$87$	5.68466	0.609459
$88$	−3.34045	−0.356094
$89$	4.18503	0.443613	0.221806	−	0.975091i	$-0.428805\pi$
$89$	4.18503	0.443613	0.221806	+	0.975091i	$0.428805\pi$
$90$	−5.94860	−0.627038
$91$	−6.33805	−0.664409
$92$	0.868028	0.0904981
$93$	−7.94860	−0.824232
$94$	−6.08506	−0.627626
$95$	6.12071	0.627971
$96$	−4.60408	−0.469902
$97$	5.53644	0.562140	0.281070	−	0.959687i	$-0.409311\pi$
$97$	5.53644	0.562140	0.281070	+	0.959687i	$0.409311\pi$
$98$	−1.69353	−0.171072
$99$	−1.74252	−0.175130
$100$	6.36963	0.636963
$101$	−15.9778	−1.58985	−0.794924	−	0.606709i	$-0.792490\pi$
$101$	−15.9778	−1.58985	−0.794924	+	0.606709i	$0.792490\pi$
$102$	−10.0741	−0.997485
$103$	8.96725	0.883569	0.441785	−	0.897121i	$-0.354346\pi$
$103$	8.96725	0.883569	0.441785	+	0.897121i	$0.354346\pi$
$104$	12.1502	1.19143
$105$	3.51256	0.342790
$106$	−21.9138	−2.12845
$107$	20.2353	1.95622	0.978108	−	0.208097i	$-0.0667269\pi$
$107$	20.2353	1.95622	0.978108	+	0.208097i	$0.0667269\pi$
$108$	−0.868028	−0.0835260
$109$	−3.31657	−0.317670	−0.158835	−	0.987305i	$-0.550774\pi$
$109$	−3.31657	−0.317670	−0.158835	+	0.987305i	$0.550774\pi$
$110$	10.3656	0.988318
$111$	−1.53644	−0.145832
$112$	4.98258	0.470810
$113$	16.1207	1.51651	0.758254	−	0.651959i	$-0.226053\pi$
$113$	16.1207	1.51651	0.758254	+	0.651959i	$0.226053\pi$
$114$	2.95100	0.276387
$115$	3.51256	0.327548
$116$	−4.93444	−0.458151
$117$	6.33805	0.585953
$118$	14.7227	1.35533
$119$	5.94860	0.545308
$120$	−6.73365	−0.614696
$121$	−7.96362	−0.723965
$122$	−14.3546	−1.29961
$123$	−12.1547	−1.09595
$124$	6.89961	0.619603
$125$	8.21255	0.734553
$126$	1.69353	0.150871
$127$	0.480977	0.0426798	0.0213399	−	0.999772i	$-0.493207\pi$
$127$	0.480977	0.0426798	0.0213399	+	0.999772i	$0.493207\pi$
$128$	−12.8798	−1.13842
$129$	−6.43605	−0.566662
$130$	−37.7026	−3.30673
$131$	−6.71741	−0.586903	−0.293451	−	0.955974i	$-0.594804\pi$
$131$	−6.71741	−0.586903	−0.293451	+	0.955974i	$0.594804\pi$
$132$	1.51256	0.131651
$133$	−1.74252	−0.151096
$134$	7.56957	0.653911
$135$	−3.51256	−0.302313
$136$	−11.4036	−0.977852
$137$	−2.96362	−0.253199	−0.126600	−	0.991954i	$-0.540406\pi$
$137$	−2.96362	−0.253199	−0.126600	+	0.991954i	$0.540406\pi$
$138$	1.69353	0.144162
$139$	−8.80161	−0.746543	−0.373272	−	0.927722i	$-0.621764\pi$
$139$	−8.80161	−0.746543	−0.373272	+	0.927722i	$0.621764\pi$
$140$	−3.04900	−0.257687
$141$	−3.59313	−0.302596
$142$	22.7968	1.91307
$143$	−11.0442	−0.923562
$144$	−4.98258	−0.415215
$145$	−19.9677	−1.65823
$146$	−7.27811	−0.602340
$147$	−1.00000	−0.0824786
$148$	1.33367	0.109627
$149$	−11.2441	−0.921155	−0.460577	−	0.887620i	$-0.652358\pi$
$149$	−11.2441	−0.921155	−0.460577	+	0.887620i	$0.652358\pi$
$150$	12.4272	1.01467
$151$	5.01502	0.408116	0.204058	−	0.978959i	$-0.434587\pi$
$151$	5.01502	0.408116	0.204058	+	0.978959i	$0.434587\pi$
$152$	3.34045	0.270947
$153$	−5.94860	−0.480916
$154$	−2.95100	−0.237799
$155$	27.9199	2.24258
$156$	−5.50161	−0.440481
$157$	14.8190	1.18269	0.591344	−	0.806420i	$-0.298598\pi$
$157$	14.8190	1.18269	0.591344	+	0.806420i	$0.298598\pi$
$158$	12.5672	0.999790
$159$	−12.9397	−1.02619
$160$	16.1721	1.27852
$161$	−1.00000	−0.0788110
$162$	−1.69353	−0.133056
$163$	2.11541	0.165692	0.0828458	−	0.996562i	$-0.473599\pi$
$163$	2.11541	0.165692	0.0828458	+	0.996562i	$0.473599\pi$
$164$	10.5506	0.823864
$165$	6.12071	0.476496
$166$	13.1293	1.01903
$167$	−14.4186	−1.11575	−0.557874	−	0.829926i	$-0.688383\pi$
$167$	−14.4186	−1.11575	−0.557874	+	0.829926i	$0.688383\pi$
$168$	1.91702	0.147902
$169$	27.1709	2.09007
$170$	35.3859	2.71397
$171$	1.74252	0.133254
$172$	5.58667	0.425979
$173$	−9.73969	−0.740495	−0.370247	−	0.928933i	$-0.620727\pi$
$173$	−9.73969	−0.740495	−0.370247	+	0.928933i	$0.620727\pi$
$174$	−9.62711	−0.729830
$175$	−7.33805	−0.554705
$176$	8.68226	0.654450
$177$	8.69353	0.653445
$178$	−7.08746	−0.531228
$179$	−0.376519	−0.0281423	−0.0140712	−	0.999901i	$-0.504479\pi$
$179$	−0.376519	−0.0281423	−0.0140712	+	0.999901i	$0.504479\pi$
$180$	3.04900	0.227259
$181$	−22.2580	−1.65442	−0.827211	−	0.561891i	$-0.810074\pi$
$181$	−22.2580	−1.65442	−0.827211	+	0.561891i	$0.810074\pi$
$182$	10.7337	0.795631
$183$	−8.47618	−0.626577
$184$	1.91702	0.141325
$185$	5.39683	0.396783
$186$	13.4612	0.987020
$187$	10.3656	0.758005
$188$	3.11894	0.227472
$189$	1.00000	0.0727393
$190$	−10.3656	−0.751997
$191$	2.98498	0.215986	0.107993	−	0.994152i	$-0.465558\pi$
$191$	2.98498	0.215986	0.107993	+	0.994152i	$0.465558\pi$
$192$	−2.16804	−0.156465
$193$	4.98498	0.358827	0.179413	−	0.983774i	$-0.442580\pi$
$193$	4.98498	0.358827	0.179413	+	0.983774i	$0.442580\pi$
$194$	−9.37610	−0.673165
$195$	−22.2628	−1.59427
$196$	0.868028	0.0620020
$197$	3.41573	0.243361	0.121681	−	0.992569i	$-0.461172\pi$
$197$	3.41573	0.243361	0.121681	+	0.992569i	$0.461172\pi$
$198$	2.95100	0.209719
$199$	−3.91462	−0.277500	−0.138750	−	0.990327i	$-0.544308\pi$
$199$	−3.91462	−0.277500	−0.138750	+	0.990327i	$0.544308\pi$
$200$	14.0672	0.994703
$201$	4.46971	0.315269
$202$	27.0588	1.90385
$203$	5.68466	0.398985
$204$	5.16355	0.361521
$205$	42.6940	2.98188
$206$	−15.1863	−1.05808
$207$	1.00000	0.0695048
$208$	−31.5799	−2.18967
$209$	−3.03638	−0.210031
$210$	−5.94860	−0.410493
$211$	−1.59430	−0.109756	−0.0548782	−	0.998493i	$-0.517477\pi$
$211$	−1.59430	−0.109756	−0.0548782	+	0.998493i	$0.517477\pi$
$212$	11.2320	0.771420
$213$	13.4612	0.922343
$214$	−34.2689	−2.34258
$215$	22.6070	1.54178
$216$	−1.91702	−0.130437
$217$	−7.94860	−0.539586
$218$	5.61670	0.380411
$219$	−4.29761	−0.290405
$220$	−5.31294	−0.358198
$221$	−37.7026	−2.53615
$222$	2.60200	0.174635
$223$	2.88667	0.193306	0.0966530	−	0.995318i	$-0.469186\pi$
$223$	2.88667	0.193306	0.0966530	+	0.995318i	$0.469186\pi$
$224$	−4.60408	−0.307623
$225$	7.33805	0.489204
$226$	−27.3008	−1.81602
$227$	2.14324	0.142252	0.0711259	−	0.997467i	$-0.477341\pi$
$227$	2.14324	0.142252	0.0711259	+	0.997467i	$0.477341\pi$
$228$	−1.51256	−0.100172
$229$	−14.1308	−0.933790	−0.466895	−	0.884313i	$-0.654627\pi$
$229$	−14.1308	−0.933790	−0.466895	+	0.884313i	$0.654627\pi$
$230$	−5.94860	−0.392239
$231$	−1.74252	−0.114649
$232$	−10.8976	−0.715464
$233$	−2.88187	−0.188798	−0.0943989	−	0.995534i	$-0.530093\pi$
$233$	−2.88187	−0.188798	−0.0943989	+	0.995534i	$0.530093\pi$
$234$	−10.7337	−0.701681
$235$	12.6211	0.823309
$236$	−7.54622	−0.491217
$237$	7.42071	0.482027
$238$	−10.0741	−0.653008
$239$	16.4956	1.06701	0.533505	−	0.845797i	$-0.320875\pi$
$239$	16.4956	1.06701	0.533505	+	0.845797i	$0.320875\pi$
$240$	17.5016	1.12972
$241$	−18.0017	−1.15959	−0.579795	−	0.814763i	$-0.696867\pi$
$241$	−18.0017	−1.15959	−0.579795	+	0.814763i	$0.696867\pi$
$242$	13.4866	0.866951
$243$	−1.00000	−0.0641500
$244$	7.35755	0.471019
$245$	3.51256	0.224409
$246$	20.5843	1.31240
$247$	11.0442	0.702725
$248$	15.2377	0.967592
$249$	7.75262	0.491302
$250$	−13.9082	−0.879629
$251$	11.4373	0.721915	0.360957	−	0.932582i	$-0.382450\pi$
$251$	11.4373	0.721915	0.360957	+	0.932582i	$0.382450\pi$
$252$	−0.868028	−0.0546806
$253$	−1.74252	−0.109551
$254$	−0.814547	−0.0511092
$255$	20.8948	1.30848
$256$	17.4762	1.09226
$257$	−30.4045	−1.89658	−0.948291	−	0.317402i	$-0.897190\pi$
$257$	−30.4045	−1.89658	−0.948291	+	0.317402i	$0.897190\pi$
$258$	10.8996	0.678580
$259$	−1.53644	−0.0954697
$260$	19.3247	1.19847
$261$	−5.68466	−0.351872
$262$	11.3761	0.702818
$263$	−18.2226	−1.12366	−0.561828	−	0.827254i	$-0.689902\pi$
$263$	−18.2226	−1.12366	−0.561828	+	0.827254i	$0.689902\pi$
$264$	3.34045	0.205591
$265$	45.4516	2.79207
$266$	2.95100	0.180938
$267$	−4.18503	−0.256120
$268$	−3.87983	−0.236998
$269$	7.65714	0.466864	0.233432	−	0.972373i	$-0.425004\pi$
$269$	7.65714	0.466864	0.233432	+	0.972373i	$0.425004\pi$
$270$	5.94860	0.362020
$271$	10.2628	0.623419	0.311710	−	0.950177i	$-0.399098\pi$
$271$	10.2628	0.623419	0.311710	+	0.950177i	$0.399098\pi$
$272$	29.6394	1.79715
$273$	6.33805	0.383596
$274$	5.01896	0.303207
$275$	−12.7867	−0.771068
$276$	−0.868028	−0.0522491
$277$	7.83319	0.470651	0.235326	−	0.971917i	$-0.424384\pi$
$277$	7.83319	0.470651	0.235326	+	0.971917i	$0.424384\pi$
$278$	14.9058	0.893988
$279$	7.94860	0.475870
$280$	−6.73365	−0.402413
$281$	−2.34420	−0.139843	−0.0699217	−	0.997552i	$-0.522275\pi$
$281$	−2.34420	−0.139843	−0.0699217	+	0.997552i	$0.522275\pi$
$282$	6.08506	0.362360
$283$	0.517476	0.0307607	0.0153804	−	0.999882i	$-0.495104\pi$
$283$	0.517476	0.0307607	0.0153804	+	0.999882i	$0.495104\pi$
$284$	−11.6847	−0.693357
$285$	−6.12071	−0.362559
$286$	18.7036	1.10597
$287$	−12.1547	−0.717468
$288$	4.60408	0.271298
$289$	18.3859	1.08152
$290$	33.8158	1.98573
$291$	−5.53644	−0.324552
$292$	3.73044	0.218308
$293$	−9.15314	−0.534732	−0.267366	−	0.963595i	$-0.586153\pi$
$293$	−9.15314	−0.534732	−0.267366	+	0.963595i	$0.586153\pi$
$294$	1.69353	0.0987684
$295$	−30.5365	−1.77790
$296$	2.94539	0.171197
$297$	1.74252	0.101111
$298$	19.0422	1.10309
$299$	6.33805	0.366539
$300$	−6.36963	−0.367751
$301$	−6.43605	−0.370968
$302$	−8.49306	−0.488720
$303$	15.9778	0.917900
$304$	−8.68226	−0.497962
$305$	29.7730	1.70480
$306$	10.0741	0.575899
$307$	−33.0492	−1.88622	−0.943108	−	0.332487i	$-0.892112\pi$
$307$	−33.0492	−1.88622	−0.943108	+	0.332487i	$0.892112\pi$
$308$	1.51256	0.0861859
$309$	−8.96725	−0.510129
$310$	−47.2831	−2.68550
$311$	−28.4591	−1.61377	−0.806883	−	0.590711i	$-0.798847\pi$
$311$	−28.4591	−1.61377	−0.806883	+	0.590711i	$0.798847\pi$
$312$	−12.1502	−0.687870
$313$	0.0903560	0.00510722	0.00255361	−	0.999997i	$-0.499187\pi$
$313$	0.0903560	0.00510722	0.00255361	+	0.999997i	$0.499187\pi$
$314$	−25.0964	−1.41627
$315$	−3.51256	−0.197910
$316$	−6.44138	−0.362356
$317$	−13.1029	−0.735930	−0.367965	−	0.929840i	$-0.619945\pi$
$317$	−13.1029	−0.735930	−0.367965	+	0.929840i	$0.619945\pi$
$318$	21.9138	1.22886
$319$	9.90564	0.554609
$320$	7.61535	0.425711
$321$	−20.2353	−1.12942
$322$	1.69353	0.0943765
$323$	−10.3656	−0.576756
$324$	0.868028	0.0482238
$325$	46.5090	2.57985
$326$	−3.58250	−0.198416
$327$	3.31657	0.183407
$328$	23.3008	1.28657
$329$	−3.59313	−0.198096
$330$	−10.3656	−0.570606
$331$	4.04013	0.222066	0.111033	−	0.993817i	$-0.464584\pi$
$331$	4.04013	0.222066	0.111033	+	0.993817i	$0.464584\pi$
$332$	−6.72949	−0.369329
$333$	1.53644	0.0841964
$334$	24.4183	1.33611
$335$	−15.7001	−0.857789
$336$	−4.98258	−0.271822
$337$	−2.24486	−0.122285	−0.0611427	−	0.998129i	$-0.519474\pi$
$337$	−2.24486	−0.122285	−0.0611427	+	0.998129i	$0.519474\pi$
$338$	−46.0147	−2.50287
$339$	−16.1207	−0.875557
$340$	−18.1373	−0.983631
$341$	−13.8506	−0.750053
$342$	−2.95100	−0.159572
$343$	−1.00000	−0.0539949
$344$	12.3381	0.665223
$345$	−3.51256	−0.189110
$346$	16.4944	0.886745
$347$	14.4458	0.775493	0.387746	−	0.921766i	$-0.373254\pi$
$347$	14.4458	0.775493	0.387746	+	0.921766i	$0.373254\pi$
$348$	4.93444	0.264514
$349$	−29.2438	−1.56539	−0.782693	−	0.622408i	$-0.786154\pi$
$349$	−29.2438	−1.56539	−0.782693	+	0.622408i	$0.786154\pi$
$350$	12.4272	0.664261
$351$	−6.33805	−0.338300
$352$	−8.02271	−0.427612
$353$	10.6595	0.567350	0.283675	−	0.958920i	$-0.408446\pi$
$353$	10.6595	0.567350	0.283675	+	0.958920i	$0.408446\pi$
$354$	−14.7227	−0.782503
$355$	−47.2831	−2.50953
$356$	3.63273	0.192534
$357$	−5.94860	−0.314833
$358$	0.637644	0.0337005
$359$	−5.44460	−0.287355	−0.143677	−	0.989625i	$-0.545893\pi$
$359$	−5.44460	−0.287355	−0.143677	+	0.989625i	$0.545893\pi$
$360$	6.73365	0.354895
$361$	−15.9636	−0.840190
$362$	37.6944	1.98118
$363$	7.96362	0.417982
$364$	−5.50161	−0.288363
$365$	15.0956	0.790139
$366$	14.3546	0.750328
$367$	11.4640	0.598416	0.299208	−	0.954188i	$-0.403278\pi$
$367$	11.4640	0.598416	0.299208	+	0.954188i	$0.403278\pi$
$368$	−4.98258	−0.259735
$369$	12.1547	0.632748
$370$	−9.13967	−0.475149
$371$	−12.9397	−0.671798
$372$	−6.89961	−0.357728
$373$	−27.9859	−1.44905	−0.724527	−	0.689246i	$-0.757942\pi$
$373$	−27.9859	−1.44905	−0.724527	+	0.689246i	$0.757942\pi$
$374$	−17.5544	−0.907714
$375$	−8.21255	−0.424094
$376$	6.88812	0.355228
$377$	−36.0297	−1.85562
$378$	−1.69353	−0.0871055
$379$	11.1604	0.573271	0.286636	−	0.958040i	$-0.407463\pi$
$379$	11.1604	0.573271	0.286636	+	0.958040i	$0.407463\pi$
$380$	5.31294	0.272548
$381$	−0.480977	−0.0246412
$382$	−5.05515	−0.258644
$383$	−17.2677	−0.882338	−0.441169	−	0.897424i	$-0.645436\pi$
$383$	−17.2677	−0.882338	−0.441169	+	0.897424i	$0.645436\pi$
$384$	12.8798	0.657269
$385$	6.12071	0.311940
$386$	−8.44220	−0.429696
$387$	6.43605	0.327163
$388$	4.80578	0.243977
$389$	27.8158	1.41032	0.705158	−	0.709050i	$-0.250876\pi$
$389$	27.8158	1.41032	0.705158	+	0.709050i	$0.250876\pi$
$390$	37.7026	1.90914
$391$	−5.94860	−0.300834
$392$	1.91702	0.0968243
$393$	6.71741	0.338848
$394$	−5.78463	−0.291426
$395$	−26.0657	−1.31151
$396$	−1.51256	−0.0760088
$397$	−36.4276	−1.82825	−0.914123	−	0.405436i	$-0.867120\pi$
$397$	−36.4276	−1.82825	−0.914123	+	0.405436i	$0.867120\pi$
$398$	6.62951	0.332307
$399$	1.74252	0.0872352
$400$	−36.5625	−1.82812
$401$	−1.41605	−0.0707142	−0.0353571	−	0.999375i	$-0.511257\pi$
$401$	−1.41605	−0.0707142	−0.0353571	+	0.999375i	$0.511257\pi$
$402$	−7.56957	−0.377536
$403$	50.3787	2.50954
$404$	−13.8692	−0.690016
$405$	3.51256	0.174540
$406$	−9.62711	−0.477786
$407$	−2.67728	−0.132708
$408$	11.4036	0.564563
$409$	−0.339704	−0.0167973	−0.00839863	−	0.999965i	$-0.502673\pi$
$409$	−0.339704	−0.0167973	−0.00839863	+	0.999965i	$0.502673\pi$
$410$	−72.3034	−3.57081
$411$	2.96362	0.146185
$412$	7.78382	0.383481
$413$	8.69353	0.427780
$414$	−1.69353	−0.0832322
$415$	−27.2315	−1.33674
$416$	29.1809	1.43071
$417$	8.80161	0.431017
$418$	5.14219	0.251513
$419$	36.7313	1.79444	0.897221	−	0.441582i	$-0.145582\pi$
$419$	36.7313	1.79444	0.897221	+	0.441582i	$0.145582\pi$
$420$	3.04900	0.148776
$421$	19.6701	0.958661	0.479330	−	0.877635i	$-0.340880\pi$
$421$	19.6701	0.958661	0.479330	+	0.877635i	$0.340880\pi$
$422$	2.69999	0.131434
$423$	3.59313	0.174704
$424$	24.8058	1.20468
$425$	−43.6512	−2.11739
$426$	−22.7968	−1.10451
$427$	−8.47618	−0.410191
$428$	17.5648	0.849025
$429$	11.0442	0.533219
$430$	−38.2855	−1.84629
$431$	−2.51827	−0.121301	−0.0606504	−	0.998159i	$-0.519317\pi$
$431$	−2.51827	−0.121301	−0.0606504	+	0.998159i	$0.519317\pi$
$432$	4.98258	0.239725
$433$	−27.8393	−1.33787	−0.668937	−	0.743319i	$-0.733250\pi$
$433$	−27.8393	−1.33787	−0.668937	+	0.743319i	$0.733250\pi$
$434$	13.4612	0.646156
$435$	19.9677	0.957377
$436$	−2.87888	−0.137873
$437$	1.74252	0.0833561
$438$	7.27811	0.347761
$439$	−28.7859	−1.37387	−0.686937	−	0.726717i	$-0.741045\pi$
$439$	−28.7859	−1.37387	−0.686937	+	0.726717i	$0.741045\pi$
$440$	−11.7335	−0.559374
$441$	1.00000	0.0476190
$442$	63.8503	3.03705
$443$	−12.3920	−0.588760	−0.294380	−	0.955688i	$-0.595113\pi$
$443$	−12.3920	−0.588760	−0.294380	+	0.955688i	$0.595113\pi$
$444$	−1.33367	−0.0632933
$445$	14.7002	0.696855
$446$	−4.88866	−0.231485
$447$	11.2441	0.531829
$448$	−2.16804	−0.102430
$449$	0.359419	0.0169620	0.00848101	−	0.999964i	$-0.497300\pi$
$449$	0.359419	0.0169620	0.00848101	+	0.999964i	$0.497300\pi$
$450$	−12.4272	−0.585823
$451$	−21.1798	−0.997318
$452$	13.9932	0.658186
$453$	−5.01502	−0.235626
$454$	−3.62963	−0.170347
$455$	−22.2628	−1.04369
$456$	−3.34045	−0.156431
$457$	−27.3677	−1.28021	−0.640103	−	0.768289i	$-0.721108\pi$
$457$	−27.3677	−1.28021	−0.640103	+	0.768289i	$0.721108\pi$
$458$	23.9309	1.11822
$459$	5.94860	0.277657
$460$	3.04900	0.142160
$461$	−7.43230	−0.346157	−0.173078	−	0.984908i	$-0.555371\pi$
$461$	−7.43230	−0.346157	−0.173078	+	0.984908i	$0.555371\pi$
$462$	2.95100	0.137293
$463$	6.45346	0.299918	0.149959	−	0.988692i	$-0.452086\pi$
$463$	6.45346	0.299918	0.149959	+	0.988692i	$0.452086\pi$
$464$	28.3243	1.31492
$465$	−27.9199	−1.29476
$466$	4.88053	0.226086
$467$	42.2953	1.95719	0.978596	−	0.205792i	$-0.0659770\pi$
$467$	42.2953	1.95719	0.978596	+	0.205792i	$0.0659770\pi$
$468$	5.50161	0.254312
$469$	4.46971	0.206392
$470$	−21.3741	−0.985915
$471$	−14.8190	−0.682825
$472$	−16.6657	−0.767101
$473$	−11.2149	−0.515664
$474$	−12.5672	−0.577229
$475$	12.7867	0.586695
$476$	5.16355	0.236671
$477$	12.9397	0.592470
$478$	−27.9357	−1.27775
$479$	−21.6417	−0.988834	−0.494417	−	0.869225i	$-0.664618\pi$
$479$	−21.6417	−0.988834	−0.494417	+	0.869225i	$0.664618\pi$
$480$	−16.1721	−0.738152
$481$	9.73804	0.444016
$482$	30.4863	1.38861
$483$	1.00000	0.0455016
$484$	−6.91264	−0.314211
$485$	19.4471	0.883045
$486$	1.69353	0.0768199
$487$	7.21180	0.326798	0.163399	−	0.986560i	$-0.447754\pi$
$487$	7.21180	0.326798	0.163399	+	0.986560i	$0.447754\pi$
$488$	16.2490	0.735559
$489$	−2.11541	−0.0956621
$490$	−5.94860	−0.268731
$491$	−7.42387	−0.335034	−0.167517	−	0.985869i	$-0.553575\pi$
$491$	−7.42387	−0.335034	−0.167517	+	0.985869i	$0.553575\pi$
$492$	−10.5506	−0.475658
$493$	33.8158	1.52299
$494$	−18.7036	−0.841516
$495$	−6.12071	−0.275105
$496$	−39.6046	−1.77830
$497$	13.4612	0.603816
$498$	−13.1293	−0.588336
$499$	−29.8147	−1.33469	−0.667344	−	0.744750i	$-0.732569\pi$
$499$	−29.8147	−1.33469	−0.667344	+	0.744750i	$0.732569\pi$
$500$	7.12872	0.318806
$501$	14.4186	0.644177
$502$	−19.3693	−0.864495
$503$	32.1036	1.43143	0.715715	−	0.698393i	$-0.246101\pi$
$503$	32.1036	1.43143	0.715715	+	0.698393i	$0.246101\pi$
$504$	−1.91702	−0.0853910
$505$	−56.1229	−2.49743
$506$	2.95100	0.131188
$507$	−27.1709	−1.20670
$508$	0.417501	0.0185236
$509$	19.4401	0.861668	0.430834	−	0.902431i	$-0.358219\pi$
$509$	19.4401	0.861668	0.430834	+	0.902431i	$0.358219\pi$
$510$	−35.3859	−1.56691
$511$	−4.29761	−0.190115
$512$	−3.83676	−0.169563
$513$	−1.74252	−0.0769342
$514$	51.4908	2.27116
$515$	31.4980	1.38797
$516$	−5.58667	−0.245939
$517$	−6.26111	−0.275363
$518$	2.60200	0.114325
$519$	9.73969	0.427525
$520$	42.6783	1.87157
$521$	−9.59843	−0.420515	−0.210257	−	0.977646i	$-0.567430\pi$
$521$	−9.59843	−0.420515	−0.210257	+	0.977646i	$0.567430\pi$
$522$	9.62711	0.421367
$523$	14.6384	0.640094	0.320047	−	0.947402i	$-0.396301\pi$
$523$	14.6384	0.640094	0.320047	+	0.947402i	$0.396301\pi$
$524$	−5.83090	−0.254724
$525$	7.33805	0.320259
$526$	30.8605	1.34558
$527$	−47.2831	−2.05968
$528$	−8.68226	−0.377847
$529$	1.00000	0.0434783
$530$	−76.9734	−3.34351
$531$	−8.69353	−0.377267
$532$	−1.51256	−0.0655776
$533$	77.0371	3.33685
$534$	7.08746	0.306704
$535$	71.0775	3.07295
$536$	−8.56854	−0.370105
$537$	0.376519	0.0162480
$538$	−12.9676	−0.559072
$539$	−1.74252	−0.0750557
$540$	−3.04900	−0.131208
$541$	5.49994	0.236461	0.118230	−	0.992986i	$-0.462278\pi$
$541$	5.49994	0.236461	0.118230	+	0.992986i	$0.462278\pi$
$542$	−17.3803	−0.746546
$543$	22.2580	0.955181
$544$	−27.3879	−1.17424
$545$	−11.6496	−0.499016
$546$	−10.7337	−0.459358
$547$	6.59357	0.281921	0.140960	−	0.990015i	$-0.454981\pi$
$547$	6.59357	0.281921	0.140960	+	0.990015i	$0.454981\pi$
$548$	−2.57250	−0.109892
$549$	8.47618	0.361754
$550$	21.6546	0.923356
$551$	−9.90564	−0.421994
$552$	−1.91702	−0.0815940
$553$	7.42071	0.315561
$554$	−13.2657	−0.563606
$555$	−5.39683	−0.229083
$556$	−7.64004	−0.324010
$557$	−5.45021	−0.230933	−0.115466	−	0.993311i	$-0.536836\pi$
$557$	−5.45021	−0.230933	−0.115466	+	0.993311i	$0.536836\pi$
$558$	−13.4612	−0.569856
$559$	40.7920	1.72532
$560$	17.5016	0.739578
$561$	−10.3656	−0.437635
$562$	3.96997	0.167463
$563$	−19.3154	−0.814047	−0.407024	−	0.913418i	$-0.633433\pi$
$563$	−19.3154	−0.814047	−0.407024	+	0.913418i	$0.633433\pi$
$564$	−3.11894	−0.131331
$565$	56.6249	2.38223
$566$	−0.876358	−0.0368361
$567$	−1.00000	−0.0419961
$568$	−25.8054	−1.08277
$569$	−20.2263	−0.847930	−0.423965	−	0.905679i	$-0.639362\pi$
$569$	−20.2263	−0.847930	−0.423965	+	0.905679i	$0.639362\pi$
$570$	10.3656	0.434166
$571$	34.6328	1.44934	0.724670	−	0.689096i	$-0.241992\pi$
$571$	34.6328	1.44934	0.724670	+	0.689096i	$0.241992\pi$
$572$	−9.58667	−0.400839
$573$	−2.98498	−0.124699
$574$	20.5843	0.859171
$575$	7.33805	0.306018
$576$	2.16804	0.0903348
$577$	−36.7645	−1.53053	−0.765263	−	0.643718i	$-0.777391\pi$
$577$	−36.7645	−1.53053	−0.765263	+	0.643718i	$0.777391\pi$
$578$	−31.1370	−1.29513
$579$	−4.98498	−0.207169
$580$	−17.3325	−0.719693
$581$	7.75262	0.321633
$582$	9.37610	0.388652
$583$	−22.5478	−0.933833
$584$	8.23862	0.340916
$585$	22.2628	0.920452
$586$	15.5011	0.640343
$587$	4.37818	0.180707	0.0903535	−	0.995910i	$-0.471200\pi$
$587$	4.37818	0.180707	0.0903535	+	0.995910i	$0.471200\pi$
$588$	−0.868028	−0.0357969
$589$	13.8506	0.570704
$590$	51.7143	2.12905
$591$	−3.41573	−0.140505
$592$	−7.65544	−0.314637
$593$	−23.5701	−0.967908	−0.483954	−	0.875093i	$-0.660800\pi$
$593$	−23.5701	−0.967908	−0.483954	+	0.875093i	$0.660800\pi$
$594$	−2.95100	−0.121081
$595$	20.8948	0.856604
$596$	−9.76021	−0.399794
$597$	3.91462	0.160215
$598$	−10.7337	−0.438932
$599$	−22.1721	−0.905928	−0.452964	−	0.891529i	$-0.649633\pi$
$599$	−22.1721	−0.905928	−0.452964	+	0.891529i	$0.649633\pi$
$600$	−14.0672	−0.574292
$601$	34.7190	1.41622	0.708109	−	0.706103i	$-0.249548\pi$
$601$	34.7190	1.41622	0.708109	+	0.706103i	$0.249548\pi$
$602$	10.8996	0.444235
$603$	−4.46971	−0.182021
$604$	4.35317	0.177128
$605$	−27.9727	−1.13725
$606$	−27.0588	−1.09919
$607$	−5.60938	−0.227678	−0.113839	−	0.993499i	$-0.536315\pi$
$607$	−5.60938	−0.227678	−0.113839	+	0.993499i	$0.536315\pi$
$608$	8.02271	0.325364
$609$	−5.68466	−0.230354
$610$	−50.4214	−2.04150
$611$	22.7735	0.921316
$612$	−5.16355	−0.208724
$613$	14.1194	0.570275	0.285138	−	0.958487i	$-0.407961\pi$
$613$	14.1194	0.570275	0.285138	+	0.958487i	$0.407961\pi$
$614$	55.9696	2.25875
$615$	−42.6940	−1.72159
$616$	3.34045	0.134591
$617$	37.0094	1.48994	0.744970	−	0.667098i	$-0.232464\pi$
$617$	37.0094	1.48994	0.744970	+	0.667098i	$0.232464\pi$
$618$	15.1863	0.610881
$619$	42.2855	1.69960	0.849799	−	0.527107i	$-0.176723\pi$
$619$	42.2855	1.69960	0.849799	+	0.527107i	$0.176723\pi$
$620$	24.2353	0.973311
$621$	−1.00000	−0.0401286
$622$	48.1962	1.93249
$623$	−4.18503	−0.167670
$624$	31.5799	1.26421
$625$	−7.84323	−0.313729
$626$	−0.153020	−0.00611592
$627$	3.03638	0.121261
$628$	12.8633	0.513303
$629$	−9.13967	−0.364422
$630$	5.94860	0.236998
$631$	31.1770	1.24114	0.620568	−	0.784153i	$-0.286902\pi$
$631$	31.1770	1.24114	0.620568	+	0.784153i	$0.286902\pi$
$632$	−14.2257	−0.565867
$633$	1.59430	0.0633678
$634$	22.1900	0.881278
$635$	1.68946	0.0670442
$636$	−11.2320	−0.445380
$637$	6.33805	0.251123
$638$	−16.7754	−0.664146
$639$	−13.4612	−0.532515
$640$	−45.2410	−1.78831
$641$	35.9135	1.41850	0.709248	−	0.704959i	$-0.249035\pi$
$641$	35.9135	1.41850	0.709248	+	0.704959i	$0.249035\pi$
$642$	34.2689	1.35249
$643$	−23.3808	−0.922047	−0.461024	−	0.887388i	$-0.652518\pi$
$643$	−23.3808	−0.922047	−0.461024	+	0.887388i	$0.652518\pi$
$644$	−0.868028	−0.0342051
$645$	−22.6070	−0.890149
$646$	17.5544	0.690667
$647$	−3.09559	−0.121700	−0.0608501	−	0.998147i	$-0.519381\pi$
$647$	−3.09559	−0.121700	−0.0608501	+	0.998147i	$0.519381\pi$
$648$	1.91702	0.0753078
$649$	15.1487	0.594637
$650$	−78.7641	−3.08938
$651$	7.94860	0.311530
$652$	1.83623	0.0719125
$653$	31.9927	1.25197	0.625985	−	0.779835i	$-0.284697\pi$
$653$	31.9927	1.25197	0.625985	+	0.779835i	$0.284697\pi$
$654$	−5.61670	−0.219630
$655$	−23.5953	−0.921944
$656$	−60.5617	−2.36454
$657$	4.29761	0.167666
$658$	6.08506	0.237220
$659$	−4.45396	−0.173502	−0.0867508	−	0.996230i	$-0.527648\pi$
$659$	−4.45396	−0.173502	−0.0867508	+	0.996230i	$0.527648\pi$
$660$	5.31294	0.206806
$661$	−18.8131	−0.731743	−0.365872	−	0.930665i	$-0.619229\pi$
$661$	−18.8131	−0.731743	−0.365872	+	0.930665i	$0.619229\pi$
$662$	−6.84206	−0.265924
$663$	37.7026	1.46425
$664$	−14.8620	−0.576756
$665$	−6.12071	−0.237351
$666$	−2.60200	−0.100825
$667$	−5.68466	−0.220111
$668$	−12.5158	−0.484250
$669$	−2.88667	−0.111605
$670$	26.5885	1.02720
$671$	−14.7699	−0.570186
$672$	4.60408	0.177606
$673$	−34.6850	−1.33701	−0.668505	−	0.743708i	$-0.733065\pi$
$673$	−34.6850	−1.33701	−0.668505	+	0.743708i	$0.733065\pi$
$674$	3.80173	0.146437
$675$	−7.33805	−0.282442
$676$	23.5851	0.907120
$677$	12.9841	0.499021	0.249510	−	0.968372i	$-0.419730\pi$
$677$	12.9841	0.499021	0.249510	+	0.968372i	$0.419730\pi$
$678$	27.3008	1.04848
$679$	−5.53644	−0.212469
$680$	−40.0558	−1.53607
$681$	−2.14324	−0.0821291
$682$	23.4564	0.898190
$683$	8.41814	0.322111	0.161055	−	0.986945i	$-0.448510\pi$
$683$	8.41814	0.322111	0.161055	+	0.986945i	$0.448510\pi$
$684$	1.51256	0.0578340
$685$	−10.4099	−0.397741
$686$	1.69353	0.0646591
$687$	14.1308	0.539124
$688$	−32.0681	−1.22259
$689$	82.0128	3.12444
$690$	5.94860	0.226459
$691$	37.8312	1.43917	0.719584	−	0.694406i	$-0.244333\pi$
$691$	37.8312	1.43917	0.719584	+	0.694406i	$0.244333\pi$
$692$	−8.45432	−0.321385
$693$	1.74252	0.0661929
$694$	−24.4644	−0.928655
$695$	−30.9162	−1.17272
$696$	10.8976	0.413073
$697$	−72.3034	−2.73869
$698$	49.5251	1.87455
$699$	2.88187	0.109002
$700$	−6.36963	−0.240750
$701$	7.93899	0.299851	0.149926	−	0.988697i	$-0.452097\pi$
$701$	7.93899	0.299851	0.149926	+	0.988697i	$0.452097\pi$
$702$	10.7337	0.405116
$703$	2.67728	0.100975
$704$	−3.77785	−0.142383
$705$	−12.6211	−0.475337
$706$	−18.0522	−0.679404
$707$	15.9778	0.600906
$708$	7.54622	0.283604
$709$	1.33730	0.0502235	0.0251117	−	0.999685i	$-0.492006\pi$
$709$	1.33730	0.0502235	0.0251117	+	0.999685i	$0.492006\pi$
$710$	80.0751	3.00516
$711$	−7.42071	−0.278299
$712$	8.02281	0.300668
$713$	7.94860	0.297678
$714$	10.0741	0.377014
$715$	−38.7934	−1.45079
$716$	−0.326829	−0.0122142
$717$	−16.4956	−0.616039
$718$	9.22056	0.344108
$719$	43.6532	1.62799	0.813994	−	0.580873i	$-0.197289\pi$
$719$	43.6532	1.62799	0.813994	+	0.580873i	$0.197289\pi$
$720$	−17.5016	−0.652246
$721$	−8.96725	−0.333958
$722$	27.0348	1.00613
$723$	18.0017	0.669489
$724$	−19.3205	−0.718042
$725$	−41.7143	−1.54923
$726$	−13.4866	−0.500534
$727$	13.1675	0.488356	0.244178	−	0.969730i	$-0.421482\pi$
$727$	13.1675	0.488356	0.244178	+	0.969730i	$0.421482\pi$
$728$	−12.1502	−0.450316
$729$	1.00000	0.0370370
$730$	−25.5648	−0.946194
$731$	−38.2855	−1.41604
$732$	−7.35755	−0.271943
$733$	−34.4447	−1.27224	−0.636121	−	0.771589i	$-0.719462\pi$
$733$	−34.4447	−1.27224	−0.636121	+	0.771589i	$0.719462\pi$
$734$	−19.4146	−0.716605
$735$	−3.51256	−0.129563
$736$	4.60408	0.169709
$737$	7.78856	0.286895
$738$	−20.5843	−0.757717
$739$	−7.05398	−0.259485	−0.129742	−	0.991548i	$-0.541415\pi$
$739$	−7.05398	−0.259485	−0.129742	+	0.991548i	$0.541415\pi$
$740$	4.68460	0.172209
$741$	−11.0442	−0.405719
$742$	21.9138	0.804480
$743$	−6.49211	−0.238172	−0.119086	−	0.992884i	$-0.537996\pi$
$743$	−6.49211	−0.238172	−0.119086	+	0.992884i	$0.537996\pi$
$744$	−15.2377	−0.558640
$745$	−39.4956	−1.44701
$746$	47.3948	1.73525
$747$	−7.75262	−0.283653
$748$	8.99760	0.328985
$749$	−20.2353	−0.739380
$750$	13.9082	0.507854
$751$	2.31669	0.0845372	0.0422686	−	0.999106i	$-0.486541\pi$
$751$	2.31669	0.0845372	0.0422686	+	0.999106i	$0.486541\pi$
$752$	−17.9031	−0.652858
$753$	−11.4373	−0.416798
$754$	61.0172	2.22211
$755$	17.6155	0.641095
$756$	0.868028	0.0315699
$757$	−10.8685	−0.395021	−0.197510	−	0.980301i	$-0.563286\pi$
$757$	−10.8685	−0.395021	−0.197510	+	0.980301i	$0.563286\pi$
$758$	−18.9004	−0.686494
$759$	1.74252	0.0632495
$760$	11.7335	0.425620
$761$	−14.1760	−0.513881	−0.256941	−	0.966427i	$-0.582715\pi$
$761$	−14.1760	−0.513881	−0.256941	+	0.966427i	$0.582715\pi$
$762$	0.814547	0.0295079
$763$	3.31657	0.120068
$764$	2.59105	0.0937408
$765$	−20.8948	−0.755453
$766$	29.2433	1.05660
$767$	−55.1000	−1.98955
$768$	−17.4762	−0.630617
$769$	11.0939	0.400058	0.200029	−	0.979790i	$-0.435896\pi$
$769$	11.0939	0.400058	0.200029	+	0.979790i	$0.435896\pi$
$770$	−10.3656	−0.373549
$771$	30.4045	1.09499
$772$	4.32710	0.155736
$773$	26.3956	0.949384	0.474692	−	0.880152i	$-0.342559\pi$
$773$	26.3956	0.949384	0.474692	+	0.880152i	$0.342559\pi$
$774$	−10.8996	−0.391778
$775$	58.3273	2.09518
$776$	10.6135	0.381002
$777$	1.53644	0.0551195
$778$	−47.1067	−1.68886
$779$	21.1798	0.758845
$780$	−19.3247	−0.691935
$781$	23.4564	0.839335
$782$	10.0741	0.360249
$783$	5.68466	0.203153
$784$	−4.98258	−0.177949
$785$	52.0527	1.85784
$786$	−11.3761	−0.405772
$787$	21.0254	0.749476	0.374738	−	0.927131i	$-0.377733\pi$
$787$	21.0254	0.749476	0.374738	+	0.927131i	$0.377733\pi$
$788$	2.96495	0.105622
$789$	18.2226	0.648743
$790$	44.1429	1.57053
$791$	−16.1207	−0.573186
$792$	−3.34045	−0.118698
$793$	53.7225	1.90774
$794$	61.6910	2.18933
$795$	−45.4516	−1.61200
$796$	−3.39800	−0.120439
$797$	−3.60323	−0.127633	−0.0638165	−	0.997962i	$-0.520327\pi$
$797$	−3.60323	−0.127633	−0.0638165	+	0.997962i	$0.520327\pi$
$798$	−2.95100	−0.104464
$799$	−21.3741	−0.756162
$800$	33.7850	1.19448
$801$	4.18503	0.147871
$802$	2.39812	0.0846805
$803$	−7.48867	−0.264270
$804$	3.87983	0.136831
$805$	−3.51256	−0.123801
$806$	−85.3176	−3.00518
$807$	−7.65714	−0.269544
$808$	−30.6298	−1.07755
$809$	−46.2734	−1.62689	−0.813443	−	0.581644i	$-0.802410\pi$
$809$	−46.2734	−1.62689	−0.813443	+	0.581644i	$0.802410\pi$
$810$	−5.94860	−0.209013
$811$	23.3657	0.820480	0.410240	−	0.911978i	$-0.365445\pi$
$811$	23.3657	0.820480	0.410240	+	0.911978i	$0.365445\pi$
$812$	4.93444	0.173165
$813$	−10.2628	−0.359931
$814$	4.53404	0.158918
$815$	7.43049	0.260279
$816$	−29.6394	−1.03759
$817$	11.2149	0.392361
$818$	0.575297	0.0201148
$819$	−6.33805	−0.221470
$820$	37.0596	1.29418
$821$	−29.6333	−1.03421	−0.517104	−	0.855923i	$-0.672990\pi$
$821$	−29.6333	−1.03421	−0.517104	+	0.855923i	$0.672990\pi$
$822$	−5.01896	−0.175056
$823$	3.93716	0.137241	0.0686203	−	0.997643i	$-0.478140\pi$
$823$	3.93716	0.137241	0.0686203	+	0.997643i	$0.478140\pi$
$824$	17.1904	0.598857
$825$	12.7867	0.445176
$826$	−14.7227	−0.512268
$827$	−21.6408	−0.752526	−0.376263	−	0.926513i	$-0.622791\pi$
$827$	−21.6408	−0.752526	−0.376263	+	0.926513i	$0.622791\pi$
$828$	0.868028	0.0301660
$829$	20.5616	0.714132	0.357066	−	0.934079i	$-0.383777\pi$
$829$	20.5616	0.714132	0.357066	+	0.934079i	$0.383777\pi$
$830$	46.1173	1.60075
$831$	−7.83319	−0.271730
$832$	13.7411	0.476388
$833$	−5.94860	−0.206107
$834$	−14.9058	−0.516144
$835$	−50.6463	−1.75269
$836$	−2.63566	−0.0911563
$837$	−7.94860	−0.274744
$838$	−62.2054	−2.14885
$839$	14.3203	0.494392	0.247196	−	0.968965i	$-0.420491\pi$
$839$	14.3203	0.494392	0.247196	+	0.968965i	$0.420491\pi$
$840$	6.73365	0.232333
$841$	3.31534	0.114322
$842$	−33.3118	−1.14800
$843$	2.34420	0.0807387
$844$	−1.38390	−0.0476358
$845$	95.4394	3.28322
$846$	−6.08506	−0.209209
$847$	7.96362	0.273633
$848$	−64.4733	−2.21402
$849$	−0.517476	−0.0177597
$850$	73.9244	2.53558
$851$	1.53644	0.0526685
$852$	11.6847	0.400310
$853$	6.04210	0.206877	0.103439	−	0.994636i	$-0.467015\pi$
$853$	6.04210	0.206877	0.103439	+	0.994636i	$0.467015\pi$
$854$	14.3546	0.491205
$855$	6.12071	0.209324
$856$	38.7915	1.32587
$857$	7.86521	0.268670	0.134335	−	0.990936i	$-0.457110\pi$
$857$	7.86521	0.268670	0.134335	+	0.990936i	$0.457110\pi$
$858$	−18.7036	−0.638531
$859$	−54.5758	−1.86210	−0.931051	−	0.364890i	$-0.881107\pi$
$859$	−54.5758	−1.86210	−0.931051	+	0.364890i	$0.881107\pi$
$860$	19.6235	0.669155
$861$	12.1547	0.414231
$862$	4.26476	0.145258
$863$	−41.3174	−1.40646	−0.703230	−	0.710962i	$-0.748260\pi$
$863$	−41.3174	−1.40646	−0.703230	+	0.710962i	$0.748260\pi$
$864$	−4.60408	−0.156634
$865$	−34.2112	−1.16322
$866$	47.1466	1.60211
$867$	−18.3859	−0.624417
$868$	−6.89961	−0.234188
$869$	12.9308	0.438646
$870$	−33.8158	−1.14646
$871$	−28.3293	−0.959900
$872$	−6.35795	−0.215307
$873$	5.53644	0.187380
$874$	−2.95100	−0.0998192
$875$	−8.21255	−0.277635
$876$	−3.73044	−0.126040
$877$	22.5939	0.762941	0.381471	−	0.924381i	$-0.375418\pi$
$877$	22.5939	0.762941	0.381471	+	0.924381i	$0.375418\pi$
$878$	48.7496	1.64522
$879$	9.15314	0.308728
$880$	30.4969	1.02805
$881$	−32.4203	−1.09227	−0.546134	−	0.837698i	$-0.683901\pi$
$881$	−32.4203	−1.09227	−0.546134	+	0.837698i	$0.683901\pi$
$882$	−1.69353	−0.0570240
$883$	46.9261	1.57919	0.789595	−	0.613628i	$-0.210291\pi$
$883$	46.9261	1.57919	0.789595	+	0.613628i	$0.210291\pi$
$884$	−32.7269	−1.10072
$885$	30.5365	1.02647
$886$	20.9861	0.705042
$887$	37.9121	1.27296	0.636482	−	0.771291i	$-0.280389\pi$
$887$	37.9121	1.27296	0.636482	+	0.771291i	$0.280389\pi$
$888$	−2.94539	−0.0988409
$889$	−0.480977	−0.0161315
$890$	−24.8951	−0.834486
$891$	−1.74252	−0.0583767
$892$	2.50571	0.0838975
$893$	6.26111	0.209520
$894$	−19.0422	−0.636867
$895$	−1.32254	−0.0442078
$896$	12.8798	0.430284
$897$	−6.33805	−0.211621
$898$	−0.608685	−0.0203121
$899$	−45.1851	−1.50701
$900$	6.36963	0.212321
$901$	−76.9734	−2.56435
$902$	35.8685	1.19429
$903$	6.43605	0.214178
$904$	30.9038	1.02784
$905$	−78.1824	−2.59887
$906$	8.49306	0.282163
$907$	−44.4382	−1.47555	−0.737773	−	0.675049i	$-0.764123\pi$
$907$	−44.4382	−1.47555	−0.737773	+	0.675049i	$0.764123\pi$
$908$	1.86039	0.0617393
$909$	−15.9778	−0.529950
$910$	37.7026	1.24983
$911$	−32.9725	−1.09243	−0.546215	−	0.837645i	$-0.683932\pi$
$911$	−32.9725	−1.09243	−0.546215	+	0.837645i	$0.683932\pi$
$912$	8.68226	0.287498
$913$	13.5091	0.447086
$914$	46.3478	1.53305
$915$	−29.7730	−0.984267
$916$	−12.2659	−0.405278
$917$	6.71741	0.221828
$918$	−10.0741	−0.332495
$919$	−41.8741	−1.38130	−0.690650	−	0.723189i	$-0.742676\pi$
$919$	−41.8741	−1.38130	−0.690650	+	0.723189i	$0.742676\pi$
$920$	6.73365	0.222002
$921$	33.0492	1.08901
$922$	12.5868	0.414524
$923$	−85.3176	−2.80826
$924$	−1.51256	−0.0497595
$925$	11.2745	0.370703
$926$	−10.9291	−0.359153
$927$	8.96725	0.294523
$928$	−26.1726	−0.859159
$929$	21.7717	0.714306	0.357153	−	0.934046i	$-0.383747\pi$
$929$	21.7717	0.714306	0.357153	+	0.934046i	$0.383747\pi$
$930$	47.2831	1.55047
$931$	1.74252	0.0571088
$932$	−2.50155	−0.0819409
$933$	28.4591	0.931708
$934$	−71.6281	−2.34374
$935$	36.4096	1.19072
$936$	12.1502	0.397142
$937$	51.2836	1.67536	0.837681	−	0.546160i	$-0.183911\pi$
$937$	51.2836	1.67536	0.837681	+	0.546160i	$0.183911\pi$
$938$	−7.56957	−0.247155
$939$	−0.0903560	−0.00294866
$940$	10.9554	0.357327
$941$	−50.8018	−1.65609	−0.828046	−	0.560661i	$-0.810547\pi$
$941$	−50.8018	−1.65609	−0.828046	+	0.560661i	$0.810547\pi$
$942$	25.0964	0.817685
$943$	12.1547	0.395811
$944$	43.3162	1.40982
$945$	3.51256	0.114263
$946$	18.9928	0.617509
$947$	40.5255	1.31690	0.658452	−	0.752623i	$-0.271212\pi$
$947$	40.5255	1.31690	0.658452	+	0.752623i	$0.271212\pi$
$948$	6.44138	0.209206
$949$	27.2385	0.884198
$950$	−21.6546	−0.702569
$951$	13.1029	0.424889
$952$	11.4036	0.369593
$953$	−6.05417	−0.196114	−0.0980570	−	0.995181i	$-0.531263\pi$
$953$	−6.05417	−0.196114	−0.0980570	+	0.995181i	$0.531263\pi$
$954$	−21.9138	−0.709484
$955$	10.4849	0.339284
$956$	14.3186	0.463097
$957$	−9.90564	−0.320204
$958$	36.6508	1.18413
$959$	2.96362	0.0957003
$960$	−7.61535	−0.245784
$961$	32.1803	1.03807
$962$	−16.4916	−0.531711
$963$	20.2353	0.652072
$964$	−15.6259	−0.503278
$965$	17.5100	0.563668
$966$	−1.69353	−0.0544883
$967$	40.4901	1.30207	0.651037	−	0.759046i	$-0.274334\pi$
$967$	40.4901	1.30207	0.651037	+	0.759046i	$0.274334\pi$
$968$	−15.2664	−0.490682
$969$	10.3656	0.332990
$970$	−32.9341	−1.05745
$971$	−17.9470	−0.575945	−0.287973	−	0.957639i	$-0.592981\pi$
$971$	−17.9470	−0.575945	−0.287973	+	0.957639i	$0.592981\pi$
$972$	−0.868028	−0.0278420
$973$	8.80161	0.282167
$974$	−12.2134	−0.391341
$975$	−46.5090	−1.48948
$976$	−42.2333	−1.35185
$977$	15.5013	0.495930	0.247965	−	0.968769i	$-0.420238\pi$
$977$	15.5013	0.495930	0.247965	+	0.968769i	$0.420238\pi$
$978$	3.58250	0.114556
$979$	−7.29251	−0.233070
$980$	3.04900	0.0973966
$981$	−3.31657	−0.105890
$982$	12.5725	0.401205
$983$	−24.1422	−0.770018	−0.385009	−	0.922913i	$-0.625802\pi$
$983$	−24.1422	−0.770018	−0.385009	+	0.922913i	$0.625802\pi$
$984$	−23.3008	−0.742803
$985$	11.9980	0.382287
$986$	−57.2679	−1.82378
$987$	3.59313	0.114371
$988$	9.58667	0.304992
$989$	6.43605	0.204654
$990$	10.3656	0.329439
$991$	−3.26567	−0.103737	−0.0518687	−	0.998654i	$-0.516518\pi$
$991$	−3.26567	−0.103737	−0.0518687	+	0.998654i	$0.516518\pi$
$992$	36.5960	1.16193
$993$	−4.04013	−0.128210
$994$	−22.7968	−0.723071
$995$	−13.7503	−0.435915
$996$	6.72949	0.213232
$997$	−16.6749	−0.528101	−0.264050	−	0.964509i	$-0.585058\pi$
$997$	−16.6749	−0.528101	−0.264050	+	0.964509i	$0.585058\pi$
$998$	50.4919	1.59829
$999$	−1.53644	−0.0486108

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.a.j.1.1	✓	4
3.2	odd	2		1449.2.a.o.1.4		4
4.3	odd	2		7728.2.a.ce.1.4		4
7.6	odd	2		3381.2.a.x.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.j.1.1	✓	4	1.1	even	1	trivial
1449.2.a.o.1.4		4	3.2	odd	2
3381.2.a.x.1.1		4	7.6	odd	2
7728.2.a.ce.1.4		4	4.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q-1.69353 q^{2} -1.00000 q^{3} +0.868028 q^{4} +3.51256 q^{5} +1.69353 q^{6} -1.00000 q^{7} +1.91702 q^{8} +1.00000 q^{9} -5.94860 q^{10} -1.74252 q^{11} -0.868028 q^{12} +6.33805 q^{13} +1.69353 q^{14} -3.51256 q^{15} -4.98258 q^{16} -5.94860 q^{17} -1.69353 q^{18} +1.74252 q^{19} +3.04900 q^{20} +1.00000 q^{21} +2.95100 q^{22} +1.00000 q^{23} -1.91702 q^{24} +7.33805 q^{25} -10.7337 q^{26} -1.00000 q^{27} -0.868028 q^{28} -5.68466 q^{29} +5.94860 q^{30} +7.94860 q^{31} +4.60408 q^{32} +1.74252 q^{33} +10.0741 q^{34} -3.51256 q^{35} +0.868028 q^{36} +1.53644 q^{37} -2.95100 q^{38} -6.33805 q^{39} +6.73365 q^{40} +12.1547 q^{41} -1.69353 q^{42} +6.43605 q^{43} -1.51256 q^{44} +3.51256 q^{45} -1.69353 q^{46} +3.59313 q^{47} +4.98258 q^{48} +1.00000 q^{49} -12.4272 q^{50} +5.94860 q^{51} +5.50161 q^{52} +12.9397 q^{53} +1.69353 q^{54} -6.12071 q^{55} -1.91702 q^{56} -1.74252 q^{57} +9.62711 q^{58} -8.69353 q^{59} -3.04900 q^{60} +8.47618 q^{61} -13.4612 q^{62} -1.00000 q^{63} +2.16804 q^{64} +22.2628 q^{65} -2.95100 q^{66} -4.46971 q^{67} -5.16355 q^{68} -1.00000 q^{69} +5.94860 q^{70} -13.4612 q^{71} +1.91702 q^{72} +4.29761 q^{73} -2.60200 q^{74} -7.33805 q^{75} +1.51256 q^{76} +1.74252 q^{77} +10.7337 q^{78} -7.42071 q^{79} -17.5016 q^{80} +1.00000 q^{81} -20.5843 q^{82} -7.75262 q^{83} +0.868028 q^{84} -20.8948 q^{85} -10.8996 q^{86} +5.68466 q^{87} -3.34045 q^{88} +4.18503 q^{89} -5.94860 q^{90} -6.33805 q^{91} +0.868028 q^{92} -7.94860 q^{93} -6.08506 q^{94} +6.12071 q^{95} -4.60408 q^{96} +5.53644 q^{97} -1.69353 q^{98} -1.74252 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{3} + 4 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} + 4 q^{9} + 2 q^{10} + q^{11} - 4 q^{12} + 7 q^{13} - 2 q^{14} - 5 q^{15} + 8 q^{16} + 2 q^{17} + 2 q^{18} - q^{19} + 13 q^{20}+ \cdots + q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 + 4 * q^9 + 2 * q^10 + q^11 - 4 * q^12 + 7 * q^13 - 2 * q^14 - 5 * q^15 + 8 * q^16 + 2 * q^17 + 2 * q^18 - q^19 + 13 * q^20 + 4 * q^21 + 11 * q^22 + 4 * q^23 - 9 * q^24 + 11 * q^25 - 19 * q^26 - 4 * q^27 - 4 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 20 * q^32 - q^33 + 23 * q^34 - 5 * q^35 + 4 * q^36 + 16 * q^37 - 11 * q^38 - 7 * q^39 + 3 * q^40 + 5 * q^41 + 2 * q^42 + 9 * q^43 + 3 * q^44 + 5 * q^45 + 2 * q^46 - 21 * q^47 - 8 * q^48 + 4 * q^49 - 17 * q^50 - 2 * q^51 - 24 * q^52 + 10 * q^53 - 2 * q^54 + 17 * q^55 - 9 * q^56 + q^57 + q^58 - 26 * q^59 - 13 * q^60 + 2 * q^61 - 19 * q^62 - 4 * q^63 + 27 * q^64 + 26 * q^65 - 11 * q^66 + 5 * q^67 + 7 * q^68 - 4 * q^69 - 2 * q^70 - 19 * q^71 + 9 * q^72 + 10 * q^73 + 9 * q^74 - 11 * q^75 - 3 * q^76 - q^77 + 19 * q^78 - 6 * q^79 - 24 * q^80 + 4 * q^81 - 31 * q^82 - 2 * q^83 + 4 * q^84 - 7 * q^85 - 17 * q^86 - 2 * q^87 - 20 * q^88 - 17 * q^89 + 2 * q^90 - 7 * q^91 + 4 * q^92 - 6 * q^93 - 44 * q^94 - 17 * q^95 - 20 * q^96 + 32 * q^97 + 2 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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