LMFDB - Embedded newform 4235.2.a.bf.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.270017.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 7x^{2} + 7x - 3 $ x^5 - 2x^4 - 5x^3 + 7x^2 + 7x - 3
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			1.4
Root			$2.51766$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.82093 q^{2} +2.51766 q^{3} +1.31579 q^{4} +1.00000 q^{5} +4.58448 q^{6} +1.00000 q^{7} -1.24589 q^{8} +3.33859 q^{9} +O(q^{10})$	\(q+1.82093 q^{2} +2.51766 q^{3} +1.31579 q^{4} +1.00000 q^{5} +4.58448 q^{6} +1.00000 q^{7} -1.24589 q^{8} +3.33859 q^{9} +1.82093 q^{10} +3.31272 q^{12} -0.370102 q^{13} +1.82093 q^{14} +2.51766 q^{15} -4.90027 q^{16} +6.87440 q^{17} +6.07934 q^{18} +1.02587 q^{19} +1.31579 q^{20} +2.51766 q^{21} +0.406799 q^{23} -3.13673 q^{24} +1.00000 q^{25} -0.673930 q^{26} +0.852446 q^{27} +1.31579 q^{28} +1.24897 q^{29} +4.58448 q^{30} -1.54609 q^{31} -6.43128 q^{32} +12.5178 q^{34} +1.00000 q^{35} +4.39289 q^{36} +2.42665 q^{37} +1.86804 q^{38} -0.931788 q^{39} -1.24589 q^{40} +5.77859 q^{41} +4.58448 q^{42} +11.7565 q^{43} +3.33859 q^{45} +0.740754 q^{46} +3.42441 q^{47} -12.3372 q^{48} +1.00000 q^{49} +1.82093 q^{50} +17.3074 q^{51} -0.486978 q^{52} +4.97582 q^{53} +1.55225 q^{54} -1.24589 q^{56} +2.58279 q^{57} +2.27429 q^{58} -12.4282 q^{59} +3.31272 q^{60} +6.16007 q^{61} -2.81533 q^{62} +3.33859 q^{63} -1.91038 q^{64} -0.370102 q^{65} +0.157829 q^{67} +9.04530 q^{68} +1.02418 q^{69} +1.82093 q^{70} -7.93614 q^{71} -4.15952 q^{72} +10.7315 q^{73} +4.41877 q^{74} +2.51766 q^{75} +1.34984 q^{76} -1.69672 q^{78} -9.20216 q^{79} -4.90027 q^{80} -7.86960 q^{81} +10.5224 q^{82} -16.9752 q^{83} +3.31272 q^{84} +6.87440 q^{85} +21.4078 q^{86} +3.14448 q^{87} -6.41877 q^{89} +6.07934 q^{90} -0.370102 q^{91} +0.535264 q^{92} -3.89252 q^{93} +6.23562 q^{94} +1.02587 q^{95} -16.1918 q^{96} -11.6107 q^{97} +1.82093 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} - q^{6} + 5 q^{7} - q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 - q^6 + 5 * q^7 - q^9	$ 5 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} - q^{6} + 5 q^{7} - q^{9} + 2 q^{10} - 3 q^{12} + 8 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} + 6 q^{17} + 11 q^{18} + 7 q^{19} + 4 q^{20} + 2 q^{21} + 3 q^{23} - 6 q^{24} + 5 q^{25} - 15 q^{26} + 5 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 12 q^{31} - 3 q^{32} - 12 q^{34} + 5 q^{35} - 3 q^{36} - 2 q^{37} + 21 q^{38} + 14 q^{39} + 5 q^{41} - q^{42} + 4 q^{43} - q^{45} + 2 q^{46} - 12 q^{48} + 5 q^{49} + 2 q^{50} + 14 q^{51} + 2 q^{52} + 8 q^{53} + 22 q^{54} + 4 q^{57} + 6 q^{58} - 16 q^{59} - 3 q^{60} + 24 q^{61} + 9 q^{62} - q^{63} - 38 q^{64} + 8 q^{65} - 9 q^{67} + 19 q^{68} + 22 q^{69} + 2 q^{70} - 10 q^{71} + 4 q^{72} + 11 q^{73} - q^{74} + 2 q^{75} + 11 q^{76} - 5 q^{78} + 9 q^{79} + 2 q^{80} - 19 q^{81} + 44 q^{82} + 10 q^{83} - 3 q^{84} + 6 q^{85} + 15 q^{86} - 2 q^{87} - 9 q^{89} + 11 q^{90} + 8 q^{91} - 26 q^{92} - q^{93} + 34 q^{94} + 7 q^{95} - 18 q^{96} + 11 q^{97} + 2 q^{98}+O(q^{100}) $ 5 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 - q^6 + 5 * q^7 - q^9 + 2 * q^10 - 3 * q^12 + 8 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 + 6 * q^17 + 11 * q^18 + 7 * q^19 + 4 * q^20 + 2 * q^21 + 3 * q^23 - 6 * q^24 + 5 * q^25 - 15 * q^26 + 5 * q^27 + 4 * q^28 + 17 * q^29 - q^30 + 12 * q^31 - 3 * q^32 - 12 * q^34 + 5 * q^35 - 3 * q^36 - 2 * q^37 + 21 * q^38 + 14 * q^39 + 5 * q^41 - q^42 + 4 * q^43 - q^45 + 2 * q^46 - 12 * q^48 + 5 * q^49 + 2 * q^50 + 14 * q^51 + 2 * q^52 + 8 * q^53 + 22 * q^54 + 4 * q^57 + 6 * q^58 - 16 * q^59 - 3 * q^60 + 24 * q^61 + 9 * q^62 - q^63 - 38 * q^64 + 8 * q^65 - 9 * q^67 + 19 * q^68 + 22 * q^69 + 2 * q^70 - 10 * q^71 + 4 * q^72 + 11 * q^73 - q^74 + 2 * q^75 + 11 * q^76 - 5 * q^78 + 9 * q^79 + 2 * q^80 - 19 * q^81 + 44 * q^82 + 10 * q^83 - 3 * q^84 + 6 * q^85 + 15 * q^86 - 2 * q^87 - 9 * q^89 + 11 * q^90 + 8 * q^91 - 26 * q^92 - q^93 + 34 * q^94 + 7 * q^95 - 18 * q^96 + 11 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	1.82093	1.28759	0.643797	−	0.765197i	$-0.277358\pi$
$2$	1.82093	1.28759	0.643797	+	0.765197i	$0.277358\pi$
$3$	2.51766	1.45357	0.726784	−	0.686866i	$-0.241014\pi$
$3$	2.51766	1.45357	0.726784	+	0.686866i	$0.241014\pi$
$4$	1.31579	0.657897
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.58448	1.87161
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.24589	−0.440489
$9$	3.33859	1.11286
$10$	1.82093	0.575829
$11$	0	0
$11$	0	0
$12$	3.31272	0.956299
$13$	−0.370102	−0.102648	−0.0513238	−	0.998682i	$-0.516344\pi$
$13$	−0.370102	−0.102648	−0.0513238	+	0.998682i	$0.516344\pi$
$14$	1.82093	0.486665
$15$	2.51766	0.650056
$16$	−4.90027	−1.22507
$17$	6.87440	1.66729	0.833644	−	0.552302i	$-0.186251\pi$
$17$	6.87440	1.66729	0.833644	+	0.552302i	$0.186251\pi$
$18$	6.07934	1.43291
$19$	1.02587	0.235351	0.117675	−	0.993052i	$-0.462456\pi$
$19$	1.02587	0.235351	0.117675	+	0.993052i	$0.462456\pi$
$20$	1.31579	0.294221
$21$	2.51766	0.549397
$22$	0	0
$23$	0.406799	0.0848235	0.0424118	−	0.999100i	$-0.486496\pi$
$23$	0.406799	0.0848235	0.0424118	+	0.999100i	$0.486496\pi$
$24$	−3.13673	−0.640282
$25$	1.00000	0.200000
$26$	−0.673930	−0.132169
$27$	0.852446	0.164053
$28$	1.31579	0.248662
$29$	1.24897	0.231928	0.115964	−	0.993253i	$-0.463004\pi$
$29$	1.24897	0.231928	0.115964	+	0.993253i	$0.463004\pi$
$30$	4.58448	0.837008
$31$	−1.54609	−0.277686	−0.138843	−	0.990314i	$-0.544338\pi$
$31$	−1.54609	−0.277686	−0.138843	+	0.990314i	$0.544338\pi$
$32$	−6.43128	−1.13690
$33$	0	0
$34$	12.5178	2.14679
$35$	1.00000	0.169031
$36$	4.39289	0.732149
$37$	2.42665	0.398939	0.199469	−	0.979904i	$-0.436078\pi$
$37$	2.42665	0.398939	0.199469	+	0.979904i	$0.436078\pi$
$38$	1.86804	0.303036
$39$	−0.931788	−0.149205
$40$	−1.24589	−0.196993
$41$	5.77859	0.902464	0.451232	−	0.892407i	$-0.350985\pi$
$41$	5.77859	0.902464	0.451232	+	0.892407i	$0.350985\pi$
$42$	4.58448	0.707401
$43$	11.7565	1.79285	0.896426	−	0.443193i	$-0.146155\pi$
$43$	11.7565	1.79285	0.896426	+	0.443193i	$0.146155\pi$
$44$	0	0
$45$	3.33859	0.497687
$46$	0.740754	0.109218
$47$	3.42441	0.499501	0.249751	−	0.968310i	$-0.419651\pi$
$47$	3.42441	0.499501	0.249751	+	0.968310i	$0.419651\pi$
$48$	−12.3372	−1.78072
$49$	1.00000	0.142857
$50$	1.82093	0.257519
$51$	17.3074	2.42352
$52$	−0.486978	−0.0675316
$53$	4.97582	0.683481	0.341741	−	0.939794i	$-0.388984\pi$
$53$	4.97582	0.683481	0.341741	+	0.939794i	$0.388984\pi$
$54$	1.55225	0.211234
$55$	0	0
$56$	−1.24589	−0.166489
$57$	2.58279	0.342099
$58$	2.27429	0.298629
$59$	−12.4282	−1.61801	−0.809007	−	0.587799i	$-0.799995\pi$
$59$	−12.4282	−1.61801	−0.809007	+	0.587799i	$0.799995\pi$
$60$	3.31272	0.427670
$61$	6.16007	0.788716	0.394358	−	0.918957i	$-0.370967\pi$
$61$	6.16007	0.788716	0.394358	+	0.918957i	$0.370967\pi$
$62$	−2.81533	−0.357547
$63$	3.33859	0.420622
$64$	−1.91038	−0.238798
$65$	−0.370102	−0.0459054
$66$	0	0
$67$	0.157829	0.0192819	0.00964097	−	0.999954i	$-0.496931\pi$
$67$	0.157829	0.0192819	0.00964097	+	0.999954i	$0.496931\pi$
$68$	9.04530	1.09690
$69$	1.02418	0.123297
$70$	1.82093	0.217643
$71$	−7.93614	−0.941846	−0.470923	−	0.882174i	$-0.656079\pi$
$71$	−7.93614	−0.941846	−0.470923	+	0.882174i	$0.656079\pi$
$72$	−4.15952	−0.490204
$73$	10.7315	1.25602	0.628012	−	0.778203i	$-0.283869\pi$
$73$	10.7315	1.25602	0.628012	+	0.778203i	$0.283869\pi$
$74$	4.41877	0.513671
$75$	2.51766	0.290714
$76$	1.34984	0.154837
$77$	0	0
$78$	−1.69672	−0.192116
$79$	−9.20216	−1.03532	−0.517662	−	0.855585i	$-0.673198\pi$
$79$	−9.20216	−1.03532	−0.517662	+	0.855585i	$0.673198\pi$
$80$	−4.90027	−0.547867
$81$	−7.86960	−0.874400
$82$	10.5224	1.16201
$83$	−16.9752	−1.86326	−0.931632	−	0.363402i	$-0.881615\pi$
$83$	−16.9752	−1.86326	−0.931632	+	0.363402i	$0.881615\pi$
$84$	3.31272	0.361447
$85$	6.87440	0.745634
$86$	21.4078	2.30846
$87$	3.14448	0.337123
$88$	0	0
$89$	−6.41877	−0.680388	−0.340194	−	0.940355i	$-0.610493\pi$
$89$	−6.41877	−0.680388	−0.340194	+	0.940355i	$0.610493\pi$
$90$	6.07934	0.640819
$91$	−0.370102	−0.0387972
$92$	0.535264	0.0558052
$93$	−3.89252	−0.403636
$94$	6.23562	0.643155
$95$	1.02587	0.105252
$96$	−16.1918	−1.65256
$97$	−11.6107	−1.17888	−0.589442	−	0.807811i	$-0.700652\pi$
$97$	−11.6107	−1.17888	−0.589442	+	0.807811i	$0.700652\pi$
$98$	1.82093	0.183942
$99$	0	0
$100$	1.31579	0.131579
$101$	−5.08654	−0.506130	−0.253065	−	0.967449i	$-0.581439\pi$
$101$	−5.08654	−0.506130	−0.253065	+	0.967449i	$0.581439\pi$
$102$	31.5156	3.12051
$103$	−11.8950	−1.17204	−0.586022	−	0.810295i	$-0.699307\pi$
$103$	−11.8950	−1.17204	−0.586022	+	0.810295i	$0.699307\pi$
$104$	0.461107	0.0452152
$105$	2.51766	0.245698
$106$	9.06063	0.880046
$107$	8.27024	0.799514	0.399757	−	0.916621i	$-0.369094\pi$
$107$	8.27024	0.799514	0.399757	+	0.916621i	$0.369094\pi$
$108$	1.12164	0.107930
$109$	−17.1878	−1.64629	−0.823146	−	0.567829i	$-0.807783\pi$
$109$	−17.1878	−1.64629	−0.823146	+	0.567829i	$0.807783\pi$
$110$	0	0
$111$	6.10947	0.579885
$112$	−4.90027	−0.463032
$113$	−6.65901	−0.626427	−0.313214	−	0.949683i	$-0.601406\pi$
$113$	−6.65901	−0.626427	−0.313214	+	0.949683i	$0.601406\pi$
$114$	4.70308	0.440484
$115$	0.406799	0.0379342
$116$	1.64339	0.152585
$117$	−1.23562	−0.114233
$118$	−22.6309	−2.08335
$119$	6.87440	0.630175
$120$	−3.13673	−0.286343
$121$	0	0
$122$	11.2171	1.01555
$123$	14.5485	1.31179
$124$	−2.03434	−0.182689
$125$	1.00000	0.0894427
$126$	6.07934	0.541591
$127$	0.602337	0.0534488	0.0267244	−	0.999643i	$-0.491492\pi$
$127$	0.602337	0.0534488	0.0267244	+	0.999643i	$0.491492\pi$
$128$	9.38389	0.829426
$129$	29.5989	2.60603
$130$	−0.673930	−0.0591076
$131$	−14.4575	−1.26315	−0.631577	−	0.775313i	$-0.717592\pi$
$131$	−14.4575	−1.26315	−0.631577	+	0.775313i	$0.717592\pi$
$132$	0	0
$133$	1.02587	0.0889543
$134$	0.287397	0.0248273
$135$	0.852446	0.0733669
$136$	−8.56476	−0.734422
$137$	5.01729	0.428656	0.214328	−	0.976762i	$-0.431244\pi$
$137$	5.01729	0.428656	0.214328	+	0.976762i	$0.431244\pi$
$138$	1.86496	0.158756
$139$	−22.6709	−1.92292	−0.961459	−	0.274949i	$-0.911339\pi$
$139$	−22.6709	−1.92292	−0.961459	+	0.274949i	$0.911339\pi$
$140$	1.31579	0.111205
$141$	8.62148	0.726060
$142$	−14.4512	−1.21271
$143$	0	0
$144$	−16.3600	−1.36333
$145$	1.24897	0.103721
$146$	19.5413	1.61725
$147$	2.51766	0.207653
$148$	3.19297	0.262461
$149$	16.6429	1.36344	0.681720	−	0.731613i	$-0.261232\pi$
$149$	16.6429	1.36344	0.681720	+	0.731613i	$0.261232\pi$
$150$	4.58448	0.374321
$151$	14.3597	1.16857	0.584287	−	0.811547i	$-0.301374\pi$
$151$	14.3597	1.16857	0.584287	+	0.811547i	$0.301374\pi$
$152$	−1.27812	−0.103670
$153$	22.9508	1.85546
$154$	0	0
$155$	−1.54609	−0.124185
$156$	−1.22604	−0.0981619
$157$	16.6654	1.33004	0.665021	−	0.746825i	$-0.268423\pi$
$157$	16.6654	1.33004	0.665021	+	0.746825i	$0.268423\pi$
$158$	−16.7565	−1.33308
$159$	12.5274	0.993487
$160$	−6.43128	−0.508438
$161$	0.406799	0.0320603
$162$	−14.3300	−1.12587
$163$	−13.7517	−1.07712	−0.538559	−	0.842588i	$-0.681031\pi$
$163$	−13.7517	−1.07712	−0.538559	+	0.842588i	$0.681031\pi$
$164$	7.60344	0.593729
$165$	0	0
$166$	−30.9106	−2.39913
$167$	11.2085	0.867340	0.433670	−	0.901072i	$-0.357218\pi$
$167$	11.2085	0.867340	0.433670	+	0.901072i	$0.357218\pi$
$168$	−3.13673	−0.242004
$169$	−12.8630	−0.989463
$170$	12.5178	0.960073
$171$	3.42496	0.261913
$172$	15.4692	1.17951
$173$	13.8410	1.05231	0.526154	−	0.850389i	$-0.323634\pi$
$173$	13.8410	1.05231	0.526154	+	0.850389i	$0.323634\pi$
$174$	5.72588	0.434078
$175$	1.00000	0.0755929
$176$	0	0
$177$	−31.2899	−2.35190
$178$	−11.6881	−0.876063
$179$	11.2474	0.840674	0.420337	−	0.907368i	$-0.361912\pi$
$179$	11.2474	0.840674	0.420337	+	0.907368i	$0.361912\pi$
$180$	4.39289	0.327427
$181$	−2.69501	−0.200319	−0.100159	−	0.994971i	$-0.531935\pi$
$181$	−2.69501	−0.200319	−0.100159	+	0.994971i	$0.531935\pi$
$182$	−0.673930	−0.0499550
$183$	15.5089	1.14645
$184$	−0.506828	−0.0373639
$185$	2.42665	0.178411
$186$	−7.08802	−0.519719
$187$	0	0
$188$	4.50582	0.328621
$189$	0.852446	0.0620064
$190$	1.86804	0.135522
$191$	−26.0632	−1.88587	−0.942934	−	0.332980i	$-0.891946\pi$
$191$	−26.0632	−1.88587	−0.942934	+	0.332980i	$0.891946\pi$
$192$	−4.80968	−0.347109
$193$	−8.40356	−0.604902	−0.302451	−	0.953165i	$-0.597805\pi$
$193$	−8.40356	−0.604902	−0.302451	+	0.953165i	$0.597805\pi$
$194$	−21.1422	−1.51792
$195$	−0.931788	−0.0667267
$196$	1.31579	0.0939853
$197$	−4.27568	−0.304629	−0.152315	−	0.988332i	$-0.548673\pi$
$197$	−4.27568	−0.304629	−0.152315	+	0.988332i	$0.548673\pi$
$198$	0	0
$199$	11.8295	0.838571	0.419285	−	0.907854i	$-0.362281\pi$
$199$	11.8295	0.838571	0.419285	+	0.907854i	$0.362281\pi$
$200$	−1.24589	−0.0880979
$201$	0.397360	0.0280276
$202$	−9.26224	−0.651689
$203$	1.24897	0.0876605
$204$	22.7729	1.59443
$205$	5.77859	0.403594
$206$	−21.6599	−1.50912
$207$	1.35814	0.0943969
$208$	1.81360	0.125750
$209$	0	0
$210$	4.58448	0.316359
$211$	5.55618	0.382503	0.191252	−	0.981541i	$-0.438745\pi$
$211$	5.55618	0.382503	0.191252	+	0.981541i	$0.438745\pi$
$212$	6.54716	0.449660
$213$	−19.9805	−1.36904
$214$	15.0595	1.02945
$215$	11.7565	0.801788
$216$	−1.06206	−0.0722638
$217$	−1.54609	−0.104956
$218$	−31.2978	−2.11976
$219$	27.0182	1.82572
$220$	0	0
$221$	−2.54423	−0.171143
$222$	11.1249	0.746656
$223$	−2.23856	−0.149905	−0.0749525	−	0.997187i	$-0.523881\pi$
$223$	−2.23856	−0.149905	−0.0749525	+	0.997187i	$0.523881\pi$
$224$	−6.43128	−0.429708
$225$	3.33859	0.222572
$226$	−12.1256	−0.806584
$227$	−14.0233	−0.930761	−0.465380	−	0.885111i	$-0.654082\pi$
$227$	−14.0233	−0.930761	−0.465380	+	0.885111i	$0.654082\pi$
$228$	3.39842	0.225066
$229$	−9.70360	−0.641232	−0.320616	−	0.947209i	$-0.603890\pi$
$229$	−9.70360	−0.641232	−0.320616	+	0.947209i	$0.603890\pi$
$230$	0.740754	0.0488439
$231$	0	0
$232$	−1.55608	−0.102162
$233$	−26.8273	−1.75752	−0.878758	−	0.477268i	$-0.841627\pi$
$233$	−26.8273	−1.75752	−0.878758	+	0.477268i	$0.841627\pi$
$234$	−2.24997	−0.147085
$235$	3.42441	0.223384
$236$	−16.3530	−1.06449
$237$	−23.1679	−1.50492
$238$	12.5178	0.811410
$239$	14.6823	0.949719	0.474860	−	0.880062i	$-0.342499\pi$
$239$	14.6823	0.949719	0.474860	+	0.880062i	$0.342499\pi$
$240$	−12.3372	−0.796363
$241$	−7.89210	−0.508375	−0.254188	−	0.967155i	$-0.581808\pi$
$241$	−7.89210	−0.508375	−0.254188	+	0.967155i	$0.581808\pi$
$242$	0	0
$243$	−22.3703	−1.43505
$244$	8.10539	0.518894
$245$	1.00000	0.0638877
$246$	26.4918	1.68906
$247$	−0.379676	−0.0241582
$248$	1.92626	0.122318
$249$	−42.7376	−2.70838
$250$	1.82093	0.115166
$251$	−20.7502	−1.30974	−0.654871	−	0.755741i	$-0.727277\pi$
$251$	−20.7502	−1.30974	−0.654871	+	0.755741i	$0.727277\pi$
$252$	4.39289	0.276726
$253$	0	0
$254$	1.09682	0.0688203
$255$	17.3074	1.08383
$256$	20.9082	1.30676
$257$	27.6237	1.72312	0.861560	−	0.507656i	$-0.169488\pi$
$257$	27.6237	1.72312	0.861560	+	0.507656i	$0.169488\pi$
$258$	53.8975	3.35551
$259$	2.42665	0.150785
$260$	−0.486978	−0.0302011
$261$	4.16980	0.258104
$262$	−26.3260	−1.62643
$263$	−17.4225	−1.07432	−0.537158	−	0.843482i	$-0.680502\pi$
$263$	−17.4225	−1.07432	−0.537158	+	0.843482i	$0.680502\pi$
$264$	0	0
$265$	4.97582	0.305662
$266$	1.86804	0.114537
$267$	−16.1602	−0.988991
$268$	0.207671	0.0126855
$269$	23.4206	1.42798	0.713990	−	0.700156i	$-0.246886\pi$
$269$	23.4206	1.42798	0.713990	+	0.700156i	$0.246886\pi$
$270$	1.55225	0.0944668
$271$	−21.8788	−1.32904	−0.664522	−	0.747268i	$-0.731365\pi$
$271$	−21.8788	−1.32904	−0.664522	+	0.747268i	$0.731365\pi$
$272$	−33.6865	−2.04254
$273$	−0.931788	−0.0563944
$274$	9.13614	0.551934
$275$	0	0
$276$	1.34761	0.0811167
$277$	−4.86485	−0.292300	−0.146150	−	0.989262i	$-0.546688\pi$
$277$	−4.86485	−0.292300	−0.146150	+	0.989262i	$0.546688\pi$
$278$	−41.2821	−2.47594
$279$	−5.16176	−0.309027
$280$	−1.24589	−0.0744563
$281$	25.6017	1.52727	0.763634	−	0.645650i	$-0.223413\pi$
$281$	25.6017	1.52727	0.763634	+	0.645650i	$0.223413\pi$
$282$	15.6991	0.934870
$283$	3.38229	0.201057	0.100528	−	0.994934i	$-0.467947\pi$
$283$	3.38229	0.201057	0.100528	+	0.994934i	$0.467947\pi$
$284$	−10.4423	−0.619638
$285$	2.58279	0.152991
$286$	0	0
$287$	5.77859	0.341099
$288$	−21.4714	−1.26521
$289$	30.2574	1.77985
$290$	2.27429	0.133551
$291$	−29.2316	−1.71359
$292$	14.1204	0.826335
$293$	−17.5554	−1.02560	−0.512798	−	0.858509i	$-0.671391\pi$
$293$	−17.5554	−1.02560	−0.512798	+	0.858509i	$0.671391\pi$
$294$	4.58448	0.267372
$295$	−12.4282	−0.723598
$296$	−3.02334	−0.175728
$297$	0	0
$298$	30.3056	1.75556
$299$	−0.150557	−0.00870694
$300$	3.31272	0.191260
$301$	11.7565	0.677634
$302$	26.1480	1.50465
$303$	−12.8062	−0.735694
$304$	−5.02705	−0.288321
$305$	6.16007	0.352725
$306$	41.7918	2.38908
$307$	1.81975	0.103859	0.0519294	−	0.998651i	$-0.483463\pi$
$307$	1.81975	0.103859	0.0519294	+	0.998651i	$0.483463\pi$
$308$	0	0
$309$	−29.9474	−1.70365
$310$	−2.81533	−0.159900
$311$	−6.22044	−0.352729	−0.176364	−	0.984325i	$-0.556434\pi$
$311$	−6.22044	−0.352729	−0.176364	+	0.984325i	$0.556434\pi$
$312$	1.16091	0.0657234
$313$	−30.2880	−1.71198	−0.855989	−	0.516993i	$-0.827051\pi$
$313$	−30.2880	−1.71198	−0.855989	+	0.516993i	$0.827051\pi$
$314$	30.3465	1.71255
$315$	3.33859	0.188108
$316$	−12.1082	−0.681137
$317$	21.5345	1.20950	0.604748	−	0.796417i	$-0.293274\pi$
$317$	21.5345	1.20950	0.604748	+	0.796417i	$0.293274\pi$
$318$	22.8115	1.27921
$319$	0	0
$320$	−1.91038	−0.106794
$321$	20.8216	1.16215
$322$	0.740754	0.0412806
$323$	7.05225	0.392398
$324$	−10.3548	−0.575265
$325$	−0.370102	−0.0205295
$326$	−25.0410	−1.38689
$327$	−43.2730	−2.39300
$328$	−7.19950	−0.397526
$329$	3.42441	0.188794
$330$	0	0
$331$	−2.25828	−0.124126	−0.0620631	−	0.998072i	$-0.519768\pi$
$331$	−2.25828	−0.124126	−0.0620631	+	0.998072i	$0.519768\pi$
$332$	−22.3358	−1.22584
$333$	8.10158	0.443964
$334$	20.4099	1.11678
$335$	0.157829	0.00862314
$336$	−12.3372	−0.673049
$337$	16.9158	0.921461	0.460731	−	0.887540i	$-0.347587\pi$
$337$	16.9158	0.921461	0.460731	+	0.887540i	$0.347587\pi$
$338$	−23.4227	−1.27403
$339$	−16.7651	−0.910555
$340$	9.04530	0.490550
$341$	0	0
$342$	6.23662	0.337238
$343$	1.00000	0.0539949
$344$	−14.6474	−0.789732
$345$	1.02418	0.0551400
$346$	25.2034	1.35494
$347$	−2.93614	−0.157620	−0.0788100	−	0.996890i	$-0.525112\pi$
$347$	−2.93614	−0.157620	−0.0788100	+	0.996890i	$0.525112\pi$
$348$	4.13748	0.221792
$349$	8.86356	0.474455	0.237228	−	0.971454i	$-0.423761\pi$
$349$	8.86356	0.474455	0.237228	+	0.971454i	$0.423761\pi$
$350$	1.82093	0.0973329
$351$	−0.315492	−0.0168397
$352$	0	0
$353$	27.2160	1.44856	0.724279	−	0.689507i	$-0.242173\pi$
$353$	27.2160	1.44856	0.724279	+	0.689507i	$0.242173\pi$
$354$	−56.9769	−3.02829
$355$	−7.93614	−0.421206
$356$	−8.44578	−0.447625
$357$	17.3074	0.916003
$358$	20.4808	1.08245
$359$	16.6504	0.878777	0.439388	−	0.898297i	$-0.355195\pi$
$359$	16.6504	0.878777	0.439388	+	0.898297i	$0.355195\pi$
$360$	−4.15952	−0.219226
$361$	−17.9476	−0.944610
$362$	−4.90743	−0.257929
$363$	0	0
$364$	−0.486978	−0.0255246
$365$	10.7315	0.561711
$366$	28.2407	1.47617
$367$	28.3043	1.47747	0.738736	−	0.673995i	$-0.235423\pi$
$367$	28.3043	1.47747	0.738736	+	0.673995i	$0.235423\pi$
$368$	−1.99343	−0.103915
$369$	19.2923	1.00432
$370$	4.41877	0.229721
$371$	4.97582	0.258332
$372$	−5.12176	−0.265551
$373$	32.6253	1.68927	0.844636	−	0.535340i	$-0.179817\pi$
$373$	32.6253	1.68927	0.844636	+	0.535340i	$0.179817\pi$
$374$	0	0
$375$	2.51766	0.130011
$376$	−4.26644	−0.220025
$377$	−0.462246	−0.0238069
$378$	1.55225	0.0798390
$379$	−21.4683	−1.10275	−0.551376	−	0.834257i	$-0.685897\pi$
$379$	−21.4683	−1.10275	−0.551376	+	0.834257i	$0.685897\pi$
$380$	1.34984	0.0692451
$381$	1.51648	0.0776915
$382$	−47.4593	−2.42823
$383$	12.4616	0.636756	0.318378	−	0.947964i	$-0.396862\pi$
$383$	12.4616	0.636756	0.318378	+	0.947964i	$0.396862\pi$
$384$	23.6254	1.20563
$385$	0	0
$386$	−15.3023	−0.778868
$387$	39.2502	1.99520
$388$	−15.2772	−0.775584
$389$	10.6063	0.537759	0.268880	−	0.963174i	$-0.413347\pi$
$389$	10.6063	0.537759	0.268880	+	0.963174i	$0.413347\pi$
$390$	−1.69672	−0.0859169
$391$	2.79650	0.141425
$392$	−1.24589	−0.0629271
$393$	−36.3989	−1.83608
$394$	−7.78572	−0.392239
$395$	−9.20216	−0.463011
$396$	0	0
$397$	−29.4013	−1.47561	−0.737805	−	0.675014i	$-0.764137\pi$
$397$	−29.4013	−1.47561	−0.737805	+	0.675014i	$0.764137\pi$
$398$	21.5407	1.07974
$399$	2.58279	0.129301
$400$	−4.90027	−0.245014
$401$	−23.2802	−1.16256	−0.581278	−	0.813705i	$-0.697447\pi$
$401$	−23.2802	−1.16256	−0.581278	+	0.813705i	$0.697447\pi$
$402$	0.723566	0.0360882
$403$	0.572211	0.0285038
$404$	−6.69284	−0.332981
$405$	−7.86960	−0.391043
$406$	2.27429	0.112871
$407$	0	0
$408$	−21.5631	−1.06753
$409$	13.5985	0.672402	0.336201	−	0.941790i	$-0.390858\pi$
$409$	13.5985	0.672402	0.336201	+	0.941790i	$0.390858\pi$
$410$	10.5224	0.519665
$411$	12.6318	0.623080
$412$	−15.6513	−0.771085
$413$	−12.4282	−0.611552
$414$	2.47307	0.121545
$415$	−16.9752	−0.833277
$416$	2.38023	0.116700
$417$	−57.0774	−2.79509
$418$	0	0
$419$	26.0492	1.27259	0.636293	−	0.771448i	$-0.280467\pi$
$419$	26.0492	1.27259	0.636293	+	0.771448i	$0.280467\pi$
$420$	3.31272	0.161644
$421$	−18.6965	−0.911210	−0.455605	−	0.890182i	$-0.650577\pi$
$421$	−18.6965	−0.911210	−0.455605	+	0.890182i	$0.650577\pi$
$422$	10.1174	0.492509
$423$	11.4327	0.555876
$424$	−6.19933	−0.301066
$425$	6.87440	0.333458
$426$	−36.3831	−1.76276
$427$	6.16007	0.298107
$428$	10.8819	0.525998
$429$	0	0
$430$	21.4078	1.03238
$431$	−32.6779	−1.57404	−0.787020	−	0.616928i	$-0.788377\pi$
$431$	−32.6779	−1.57404	−0.787020	+	0.616928i	$0.788377\pi$
$432$	−4.17722	−0.200977
$433$	1.09583	0.0526622	0.0263311	−	0.999653i	$-0.491618\pi$
$433$	1.09583	0.0526622	0.0263311	+	0.999653i	$0.491618\pi$
$434$	−2.81533	−0.135140
$435$	3.14448	0.150766
$436$	−22.6156	−1.08309
$437$	0.417324	0.0199633
$438$	49.1983	2.35078
$439$	36.6273	1.74813	0.874064	−	0.485812i	$-0.161476\pi$
$439$	36.6273	1.74813	0.874064	+	0.485812i	$0.161476\pi$
$440$	0	0
$441$	3.33859	0.158980
$442$	−4.63287	−0.220363
$443$	−10.5347	−0.500518	−0.250259	−	0.968179i	$-0.580516\pi$
$443$	−10.5347	−0.500518	−0.250259	+	0.968179i	$0.580516\pi$
$444$	8.03880	0.381505
$445$	−6.41877	−0.304279
$446$	−4.07626	−0.193017
$447$	41.9011	1.98185
$448$	−1.91038	−0.0902571
$449$	−11.0065	−0.519430	−0.259715	−	0.965685i	$-0.583629\pi$
$449$	−11.0065	−0.519430	−0.259715	+	0.965685i	$0.583629\pi$
$450$	6.07934	0.286583
$451$	0	0
$452$	−8.76189	−0.412125
$453$	36.1527	1.69860
$454$	−25.5355	−1.19844
$455$	−0.370102	−0.0173506
$456$	−3.21788	−0.150691
$457$	18.5180	0.866238	0.433119	−	0.901337i	$-0.357413\pi$
$457$	18.5180	0.866238	0.433119	+	0.901337i	$0.357413\pi$
$458$	−17.6696	−0.825646
$459$	5.86006	0.273524
$460$	0.535264	0.0249568
$461$	−33.6330	−1.56645	−0.783223	−	0.621740i	$-0.786426\pi$
$461$	−33.6330	−1.56645	−0.783223	+	0.621740i	$0.786426\pi$
$462$	0	0
$463$	27.1149	1.26013	0.630067	−	0.776541i	$-0.283027\pi$
$463$	27.1149	1.26013	0.630067	+	0.776541i	$0.283027\pi$
$464$	−6.12030	−0.284128
$465$	−3.89252	−0.180512
$466$	−48.8507	−2.26297
$467$	7.81113	0.361456	0.180728	−	0.983533i	$-0.442155\pi$
$467$	7.81113	0.361456	0.180728	+	0.983533i	$0.442155\pi$
$468$	−1.62582	−0.0751534
$469$	0.157829	0.00728789
$470$	6.23562	0.287628
$471$	41.9577	1.93331
$472$	15.4842	0.712718
$473$	0	0
$474$	−42.1871	−1.93772
$475$	1.02587	0.0470702
$476$	9.04530	0.414591
$477$	16.6122	0.760621
$478$	26.7355	1.22285
$479$	−8.79284	−0.401755	−0.200877	−	0.979616i	$-0.564379\pi$
$479$	−8.79284	−0.401755	−0.200877	+	0.979616i	$0.564379\pi$
$480$	−16.1918	−0.739049
$481$	−0.898107	−0.0409501
$482$	−14.3710	−0.654581
$483$	1.02418	0.0466018
$484$	0	0
$485$	−11.6107	−0.527213
$486$	−40.7347	−1.84777
$487$	−1.54119	−0.0698382	−0.0349191	−	0.999390i	$-0.511117\pi$
$487$	−1.54119	−0.0698382	−0.0349191	+	0.999390i	$0.511117\pi$
$488$	−7.67478	−0.347421
$489$	−34.6221	−1.56567
$490$	1.82093	0.0822613
$491$	−10.1281	−0.457076	−0.228538	−	0.973535i	$-0.573395\pi$
$491$	−10.1281	−0.457076	−0.228538	+	0.973535i	$0.573395\pi$
$492$	19.1428	0.863026
$493$	8.58592	0.386691
$494$	−0.691365	−0.0311060
$495$	0	0
$496$	7.57627	0.340185
$497$	−7.93614	−0.355984
$498$	−77.8222	−3.48730
$499$	−20.5372	−0.919370	−0.459685	−	0.888082i	$-0.652038\pi$
$499$	−20.5372	−0.919370	−0.459685	+	0.888082i	$0.652038\pi$
$500$	1.31579	0.0588441
$501$	28.2192	1.26074
$502$	−37.7847	−1.68641
$503$	18.8903	0.842278	0.421139	−	0.906996i	$-0.361630\pi$
$503$	18.8903	0.842278	0.421139	+	0.906996i	$0.361630\pi$
$504$	−4.15952	−0.185280
$505$	−5.08654	−0.226348
$506$	0	0
$507$	−32.3847	−1.43825
$508$	0.792552	0.0351638
$509$	14.3928	0.637950	0.318975	−	0.947763i	$-0.396661\pi$
$509$	14.3928	0.637950	0.318975	+	0.947763i	$0.396661\pi$
$510$	31.5156	1.39553
$511$	10.7315	0.474733
$512$	19.3046	0.853152
$513$	0.874500	0.0386101
$514$	50.3009	2.21868
$515$	−11.8950	−0.524154
$516$	38.9460	1.71450
$517$	0	0
$518$	4.41877	0.194149
$519$	34.8467	1.52960
$520$	0.461107	0.0202209
$521$	−18.5694	−0.813542	−0.406771	−	0.913530i	$-0.633345\pi$
$521$	−18.5694	−0.813542	−0.406771	+	0.913530i	$0.633345\pi$
$522$	7.59292	0.332333
$523$	−14.8266	−0.648320	−0.324160	−	0.946002i	$-0.605082\pi$
$523$	−14.8266	−0.648320	−0.324160	+	0.946002i	$0.605082\pi$
$524$	−19.0230	−0.831025
$525$	2.51766	0.109879
$526$	−31.7251	−1.38328
$527$	−10.6285	−0.462983
$528$	0	0
$529$	−22.8345	−0.992805
$530$	9.06063	0.393569
$531$	−41.4926	−1.80063
$532$	1.34984	0.0585228
$533$	−2.13867	−0.0926359
$534$	−29.4267	−1.27342
$535$	8.27024	0.357554
$536$	−0.196638	−0.00849349
$537$	28.3172	1.22198
$538$	42.6473	1.83866
$539$	0	0
$540$	1.12164	0.0482679
$541$	39.3238	1.69066	0.845331	−	0.534243i	$-0.179403\pi$
$541$	39.3238	1.69066	0.845331	+	0.534243i	$0.179403\pi$
$542$	−39.8399	−1.71127
$543$	−6.78511	−0.291177
$544$	−44.2112	−1.89554
$545$	−17.1878	−0.736244
$546$	−1.69672	−0.0726130
$547$	28.3917	1.21394	0.606970	−	0.794725i	$-0.292385\pi$
$547$	28.3917	1.21394	0.606970	+	0.794725i	$0.292385\pi$
$548$	6.60172	0.282011
$549$	20.5659	0.877733
$550$	0	0
$551$	1.28128	0.0545844
$552$	−1.27602	−0.0543110
$553$	−9.20216	−0.391316
$554$	−8.85855	−0.376364
$555$	6.10947	0.259332
$556$	−29.8302	−1.26508
$557$	17.6836	0.749280	0.374640	−	0.927170i	$-0.377766\pi$
$557$	17.6836	0.749280	0.374640	+	0.927170i	$0.377766\pi$
$558$	−9.39922	−0.397901
$559$	−4.35110	−0.184032
$560$	−4.90027	−0.207074
$561$	0	0
$562$	46.6189	1.96650
$563$	35.2852	1.48709	0.743546	−	0.668684i	$-0.233142\pi$
$563$	35.2852	1.48709	0.743546	+	0.668684i	$0.233142\pi$
$564$	11.3441	0.477673
$565$	−6.65901	−0.280147
$566$	6.15893	0.258879
$567$	−7.86960	−0.330492
$568$	9.88757	0.414873
$569$	8.27188	0.346775	0.173388	−	0.984854i	$-0.444529\pi$
$569$	8.27188	0.346775	0.173388	+	0.984854i	$0.444529\pi$
$570$	4.70308	0.196991
$571$	−26.5884	−1.11269	−0.556344	−	0.830952i	$-0.687796\pi$
$571$	−26.5884	−1.11269	−0.556344	+	0.830952i	$0.687796\pi$
$572$	0	0
$573$	−65.6182	−2.74124
$574$	10.5224	0.439197
$575$	0.406799	0.0169647
$576$	−6.37798	−0.265749
$577$	14.7052	0.612187	0.306093	−	0.952002i	$-0.400978\pi$
$577$	14.7052	0.612187	0.306093	+	0.952002i	$0.400978\pi$
$578$	55.0967	2.29172
$579$	−21.1573	−0.879266
$580$	1.64339	0.0682380
$581$	−16.9752	−0.704248
$582$	−53.2288	−2.20640
$583$	0	0
$584$	−13.3703	−0.553266
$585$	−1.23562	−0.0510864
$586$	−31.9671	−1.32055
$587$	−9.93218	−0.409945	−0.204973	−	0.978768i	$-0.565711\pi$
$587$	−9.93218	−0.409945	−0.204973	+	0.978768i	$0.565711\pi$
$588$	3.31272	0.136614
$589$	−1.58609	−0.0653537
$590$	−22.6309	−0.931700
$591$	−10.7647	−0.442800
$592$	−11.8913	−0.488727
$593$	−40.2510	−1.65291	−0.826455	−	0.563003i	$-0.809646\pi$
$593$	−40.2510	−1.65291	−0.826455	+	0.563003i	$0.809646\pi$
$594$	0	0
$595$	6.87440	0.281823
$596$	21.8986	0.897003
$597$	29.7826	1.21892
$598$	−0.274154	−0.0112110
$599$	−22.7566	−0.929811	−0.464905	−	0.885360i	$-0.653912\pi$
$599$	−22.7566	−0.929811	−0.464905	+	0.885360i	$0.653912\pi$
$600$	−3.13673	−0.128056
$601$	33.0247	1.34710	0.673552	−	0.739140i	$-0.264768\pi$
$601$	33.0247	1.34710	0.673552	+	0.739140i	$0.264768\pi$
$602$	21.4078	0.872518
$603$	0.526927	0.0214581
$604$	18.8944	0.768801
$605$	0	0
$606$	−23.3191	−0.947275
$607$	44.7058	1.81455	0.907275	−	0.420537i	$-0.138158\pi$
$607$	44.7058	1.81455	0.907275	+	0.420537i	$0.138158\pi$
$608$	−6.59767	−0.267571
$609$	3.14448	0.127421
$610$	11.2171	0.454166
$611$	−1.26738	−0.0512727
$612$	30.1985	1.22070
$613$	6.84889	0.276624	0.138312	−	0.990389i	$-0.455832\pi$
$613$	6.84889	0.276624	0.138312	+	0.990389i	$0.455832\pi$
$614$	3.31365	0.133728
$615$	14.5485	0.586652
$616$	0	0
$617$	40.0203	1.61116	0.805579	−	0.592489i	$-0.201855\pi$
$617$	40.0203	1.61116	0.805579	+	0.592489i	$0.201855\pi$
$618$	−54.5322	−2.19361
$619$	11.8232	0.475214	0.237607	−	0.971361i	$-0.423637\pi$
$619$	11.8232	0.475214	0.237607	+	0.971361i	$0.423637\pi$
$620$	−2.03434	−0.0817010
$621$	0.346775	0.0139156
$622$	−11.3270	−0.454171
$623$	−6.41877	−0.257162
$624$	4.56602	0.182787
$625$	1.00000	0.0400000
$626$	−55.1524	−2.20433
$627$	0	0
$628$	21.9282	0.875031
$629$	16.6818	0.665146
$630$	6.07934	0.242207
$631$	−11.0005	−0.437923	−0.218961	−	0.975734i	$-0.570267\pi$
$631$	−11.0005	−0.437923	−0.218961	+	0.975734i	$0.570267\pi$
$632$	11.4649	0.456049
$633$	13.9885	0.555995
$634$	39.2128	1.55734
$635$	0.602337	0.0239030
$636$	16.4835	0.653612
$637$	−0.370102	−0.0146640
$638$	0	0
$639$	−26.4955	−1.04815
$640$	9.38389	0.370931
$641$	12.9776	0.512586	0.256293	−	0.966599i	$-0.417499\pi$
$641$	12.9776	0.512586	0.256293	+	0.966599i	$0.417499\pi$
$642$	37.9147	1.49638
$643$	31.3497	1.23631	0.618157	−	0.786055i	$-0.287880\pi$
$643$	31.3497	1.23631	0.618157	+	0.786055i	$0.287880\pi$
$644$	0.535264	0.0210924
$645$	29.5989	1.16545
$646$	12.8417	0.505249
$647$	−12.3077	−0.483864	−0.241932	−	0.970293i	$-0.577781\pi$
$647$	−12.3077	−0.483864	−0.241932	+	0.970293i	$0.577781\pi$
$648$	9.80467	0.385164
$649$	0	0
$650$	−0.673930	−0.0264337
$651$	−3.89252	−0.152560
$652$	−18.0944	−0.708633
$653$	5.94653	0.232706	0.116353	−	0.993208i	$-0.462880\pi$
$653$	5.94653	0.232706	0.116353	+	0.993208i	$0.462880\pi$
$654$	−78.7971	−3.08121
$655$	−14.4575	−0.564900
$656$	−28.3167	−1.10558
$657$	35.8280	1.39778
$658$	6.23562	0.243090
$659$	−5.59201	−0.217834	−0.108917	−	0.994051i	$-0.534738\pi$
$659$	−5.59201	−0.217834	−0.108917	+	0.994051i	$0.534738\pi$
$660$	0	0
$661$	9.28440	0.361121	0.180561	−	0.983564i	$-0.442209\pi$
$661$	9.28440	0.361121	0.180561	+	0.983564i	$0.442209\pi$
$662$	−4.11217	−0.159824
$663$	−6.40549	−0.248768
$664$	21.1492	0.820748
$665$	1.02587	0.0397816
$666$	14.7524	0.571645
$667$	0.508080	0.0196729
$668$	14.7481	0.570621
$669$	−5.63592	−0.217897
$670$	0.287397	0.0111031
$671$	0	0
$672$	−16.1918	−0.624610
$673$	−30.7976	−1.18716	−0.593580	−	0.804775i	$-0.702286\pi$
$673$	−30.7976	−1.18716	−0.593580	+	0.804775i	$0.702286\pi$
$674$	30.8025	1.18647
$675$	0.852446	0.0328107
$676$	−16.9251	−0.650965
$677$	22.1494	0.851269	0.425634	−	0.904895i	$-0.360051\pi$
$677$	22.1494	0.851269	0.425634	+	0.904895i	$0.360051\pi$
$678$	−30.5281	−1.17243
$679$	−11.6107	−0.445576
$680$	−8.56476	−0.328444
$681$	−35.3059	−1.35292
$682$	0	0
$683$	20.4772	0.783537	0.391769	−	0.920064i	$-0.371863\pi$
$683$	20.4772	0.783537	0.391769	+	0.920064i	$0.371863\pi$
$684$	4.50654	0.172312
$685$	5.01729	0.191701
$686$	1.82093	0.0695235
$687$	−24.4303	−0.932074
$688$	−57.6102	−2.19637
$689$	−1.84156	−0.0701578
$690$	1.86496	0.0709980
$691$	−13.1712	−0.501056	−0.250528	−	0.968109i	$-0.580604\pi$
$691$	−13.1712	−0.501056	−0.250528	+	0.968109i	$0.580604\pi$
$692$	18.2118	0.692310
$693$	0	0
$694$	−5.34650	−0.202951
$695$	−22.6709	−0.859955
$696$	−3.91768	−0.148499
$697$	39.7244	1.50467
$698$	16.1399	0.610906
$699$	−67.5419	−2.55467
$700$	1.31579	0.0497324
$701$	7.29383	0.275484	0.137742	−	0.990468i	$-0.456015\pi$
$701$	7.29383	0.275484	0.137742	+	0.990468i	$0.456015\pi$
$702$	−0.574489	−0.0216827
$703$	2.48943	0.0938906
$704$	0	0
$705$	8.62148	0.324704
$706$	49.5584	1.86516
$707$	−5.08654	−0.191299
$708$	−41.1711	−1.54731
$709$	−46.8560	−1.75971	−0.879857	−	0.475238i	$-0.842362\pi$
$709$	−46.8560	−1.75971	−0.879857	+	0.475238i	$0.842362\pi$
$710$	−14.4512	−0.542343
$711$	−30.7222	−1.15217
$712$	7.99709	0.299704
$713$	−0.628949	−0.0235543
$714$	31.5156	1.17944
$715$	0	0
$716$	14.7993	0.553077
$717$	36.9650	1.38048
$718$	30.3193	1.13151
$719$	0.734847	0.0274052	0.0137026	−	0.999906i	$-0.495638\pi$
$719$	0.734847	0.0274052	0.0137026	+	0.999906i	$0.495638\pi$
$720$	−16.3600	−0.609701
$721$	−11.8950	−0.442991
$722$	−32.6813	−1.21627
$723$	−19.8696	−0.738958
$724$	−3.54608	−0.131789
$725$	1.24897	0.0463856
$726$	0	0
$727$	−9.67827	−0.358947	−0.179474	−	0.983763i	$-0.557439\pi$
$727$	−9.67827	−0.358947	−0.179474	+	0.983763i	$0.557439\pi$
$728$	0.461107	0.0170897
$729$	−32.7118	−1.21155
$730$	19.5413	0.723256
$731$	80.8190	2.98920
$732$	20.4066	0.754248
$733$	−22.3039	−0.823813	−0.411906	−	0.911226i	$-0.635137\pi$
$733$	−22.3039	−0.823813	−0.411906	+	0.911226i	$0.635137\pi$
$734$	51.5402	1.90238
$735$	2.51766	0.0928651
$736$	−2.61624	−0.0964360
$737$	0	0
$738$	35.1300	1.29315
$739$	−0.342616	−0.0126033	−0.00630166	−	0.999980i	$-0.502006\pi$
$739$	−0.342616	−0.0126033	−0.00630166	+	0.999980i	$0.502006\pi$
$740$	3.19297	0.117376
$741$	−0.955894	−0.0351157
$742$	9.06063	0.332626
$743$	−21.5479	−0.790516	−0.395258	−	0.918570i	$-0.629345\pi$
$743$	−21.5479	−0.790516	−0.395258	+	0.918570i	$0.629345\pi$
$744$	4.84967	0.177797
$745$	16.6429	0.609749
$746$	59.4084	2.17510
$747$	−56.6730	−2.07356
$748$	0	0
$749$	8.27024	0.302188
$750$	4.58448	0.167402
$751$	−45.3703	−1.65558	−0.827792	−	0.561035i	$-0.810403\pi$
$751$	−45.3703	−1.65558	−0.827792	+	0.561035i	$0.810403\pi$
$752$	−16.7805	−0.611923
$753$	−52.2419	−1.90380
$754$	−0.841718	−0.0306536
$755$	14.3597	0.522602
$756$	1.12164	0.0407938
$757$	7.26640	0.264102	0.132051	−	0.991243i	$-0.457844\pi$
$757$	7.26640	0.264102	0.132051	+	0.991243i	$0.457844\pi$
$758$	−39.0923	−1.41990
$759$	0	0
$760$	−1.27812	−0.0463624
$761$	−5.55891	−0.201510	−0.100755	−	0.994911i	$-0.532126\pi$
$761$	−5.55891	−0.201510	−0.100755	+	0.994911i	$0.532126\pi$
$762$	2.76140	0.100035
$763$	−17.1878	−0.622240
$764$	−34.2938	−1.24071
$765$	22.9508	0.829788
$766$	22.6917	0.819883
$767$	4.59970	0.166085
$768$	52.6396	1.89947
$769$	11.0042	0.396823	0.198411	−	0.980119i	$-0.436422\pi$
$769$	11.0042	0.396823	0.198411	+	0.980119i	$0.436422\pi$
$770$	0	0
$771$	69.5470	2.50467
$772$	−11.0574	−0.397963
$773$	−0.443309	−0.0159447	−0.00797235	−	0.999968i	$-0.502538\pi$
$773$	−0.443309	−0.0159447	−0.00797235	+	0.999968i	$0.502538\pi$
$774$	71.4719	2.56900
$775$	−1.54609	−0.0555372
$776$	14.4656	0.519286
$777$	6.10947	0.219176
$778$	19.3133	0.692415
$779$	5.92809	0.212396
$780$	−1.22604	−0.0438993
$781$	0	0
$782$	5.09224	0.182098
$783$	1.06468	0.0380486
$784$	−4.90027	−0.175010
$785$	16.6654	0.594813
$786$	−66.2799	−2.36413
$787$	1.87990	0.0670111	0.0335055	−	0.999439i	$-0.489333\pi$
$787$	1.87990	0.0670111	0.0335055	+	0.999439i	$0.489333\pi$
$788$	−5.62591	−0.200415
$789$	−43.8638	−1.56159
$790$	−16.7565	−0.596170
$791$	−6.65901	−0.236767
$792$	0	0
$793$	−2.27985	−0.0809599
$794$	−53.5378	−1.89998
$795$	12.5274	0.444301
$796$	15.5652	0.551693
$797$	−19.7467	−0.699462	−0.349731	−	0.936850i	$-0.613727\pi$
$797$	−19.7467	−0.699462	−0.349731	+	0.936850i	$0.613727\pi$
$798$	4.70308	0.166487
$799$	23.5408	0.832812
$800$	−6.43128	−0.227380
$801$	−21.4296	−0.757178
$802$	−42.3916	−1.49690
$803$	0	0
$804$	0.522844	0.0184393
$805$	0.406799	0.0143378
$806$	1.04196	0.0367014
$807$	58.9650	2.07567
$808$	6.33728	0.222945
$809$	−7.59904	−0.267168	−0.133584	−	0.991037i	$-0.542649\pi$
$809$	−7.59904	−0.267168	−0.133584	+	0.991037i	$0.542649\pi$
$810$	−14.3300	−0.503505
$811$	36.9954	1.29908	0.649542	−	0.760325i	$-0.274961\pi$
$811$	36.9954	1.29908	0.649542	+	0.760325i	$0.274961\pi$
$812$	1.64339	0.0576716
$813$	−55.0834	−1.93186
$814$	0	0
$815$	−13.7517	−0.481702
$816$	−84.8109	−2.96897
$817$	12.0607	0.421949
$818$	24.7619	0.865781
$819$	−1.23562	−0.0431759
$820$	7.60344	0.265524
$821$	−13.3556	−0.466113	−0.233057	−	0.972463i	$-0.574873\pi$
$821$	−13.3556	−0.466113	−0.233057	+	0.972463i	$0.574873\pi$
$822$	23.0016	0.802274
$823$	45.0011	1.56864	0.784319	−	0.620358i	$-0.213013\pi$
$823$	45.0011	1.56864	0.784319	+	0.620358i	$0.213013\pi$
$824$	14.8198	0.516273
$825$	0	0
$826$	−22.6309	−0.787430
$827$	−32.9622	−1.14621	−0.573103	−	0.819483i	$-0.694261\pi$
$827$	−32.9622	−1.14621	−0.573103	+	0.819483i	$0.694261\pi$
$828$	1.78703	0.0621035
$829$	−42.7651	−1.48529	−0.742647	−	0.669683i	$-0.766430\pi$
$829$	−42.7651	−1.48529	−0.742647	+	0.669683i	$0.766430\pi$
$830$	−30.9106	−1.07292
$831$	−12.2480	−0.424879
$832$	0.707035	0.0245120
$833$	6.87440	0.238184
$834$	−103.934	−3.59894
$835$	11.2085	0.387886
$836$	0	0
$837$	−1.31796	−0.0455554
$838$	47.4338	1.63857
$839$	−45.0302	−1.55462	−0.777308	−	0.629120i	$-0.783415\pi$
$839$	−45.0302	−1.55462	−0.777308	+	0.629120i	$0.783415\pi$
$840$	−3.13673	−0.108227
$841$	−27.4401	−0.946209
$842$	−34.0450	−1.17327
$843$	64.4562	2.21999
$844$	7.31079	0.251648
$845$	−12.8630	−0.442502
$846$	20.8182	0.715743
$847$	0	0
$848$	−24.3829	−0.837311
$849$	8.51545	0.292250
$850$	12.5178	0.429358
$851$	0.987160	0.0338394
$852$	−26.2902	−0.900686
$853$	−8.10157	−0.277392	−0.138696	−	0.990335i	$-0.544291\pi$
$853$	−8.10157	−0.277392	−0.138696	+	0.990335i	$0.544291\pi$
$854$	11.2171	0.383840
$855$	3.42496	0.117131
$856$	−10.3038	−0.352178
$857$	3.44930	0.117826	0.0589130	−	0.998263i	$-0.481237\pi$
$857$	3.44930	0.117826	0.0589130	+	0.998263i	$0.481237\pi$
$858$	0	0
$859$	51.6881	1.76357	0.881787	−	0.471648i	$-0.156341\pi$
$859$	51.6881	1.76357	0.881787	+	0.471648i	$0.156341\pi$
$860$	15.4692	0.527494
$861$	14.5485	0.495812
$862$	−59.5042	−2.02672
$863$	42.2012	1.43654	0.718272	−	0.695762i	$-0.244933\pi$
$863$	42.2012	1.43654	0.718272	+	0.695762i	$0.244933\pi$
$864$	−5.48232	−0.186512
$865$	13.8410	0.470606
$866$	1.99543	0.0678075
$867$	76.1777	2.58713
$868$	−2.03434	−0.0690499
$869$	0	0
$870$	5.72588	0.194125
$871$	−0.0584129	−0.00197925
$872$	21.4141	0.725174
$873$	−38.7632	−1.31193
$874$	0.759918	0.0257046
$875$	1.00000	0.0338062
$876$	35.5504	1.20114
$877$	−11.3455	−0.383109	−0.191554	−	0.981482i	$-0.561353\pi$
$877$	−11.3455	−0.383109	−0.191554	+	0.981482i	$0.561353\pi$
$878$	66.6959	2.25088
$879$	−44.1984	−1.49077
$880$	0	0
$881$	−3.41882	−0.115183	−0.0575915	−	0.998340i	$-0.518342\pi$
$881$	−3.41882	−0.115183	−0.0575915	+	0.998340i	$0.518342\pi$
$882$	6.07934	0.204702
$883$	−11.3628	−0.382389	−0.191194	−	0.981552i	$-0.561236\pi$
$883$	−11.3628	−0.382389	−0.191194	+	0.981552i	$0.561236\pi$
$884$	−3.34768	−0.112595
$885$	−31.2899	−1.05180
$886$	−19.1829	−0.644463
$887$	−24.8294	−0.833691	−0.416846	−	0.908977i	$-0.636864\pi$
$887$	−24.8294	−0.833691	−0.416846	+	0.908977i	$0.636864\pi$
$888$	−7.61174	−0.255433
$889$	0.602337	0.0202017
$890$	−11.6881	−0.391787
$891$	0	0
$892$	−2.94548	−0.0986221
$893$	3.51300	0.117558
$894$	76.2991	2.55182
$895$	11.2474	0.375961
$896$	9.38389	0.313494
$897$	−0.379051	−0.0126561
$898$	−20.0421	−0.668814
$899$	−1.93102	−0.0644032
$900$	4.39289	0.146430
$901$	34.2058	1.13956
$902$	0	0
$903$	29.5989	0.984988
$904$	8.29641	0.275935
$905$	−2.69501	−0.0895852
$906$	65.8316	2.18711
$907$	3.83164	0.127228	0.0636138	−	0.997975i	$-0.479737\pi$
$907$	3.83164	0.127228	0.0636138	+	0.997975i	$0.479737\pi$
$908$	−18.4518	−0.612345
$909$	−16.9819	−0.563253
$910$	−0.673930	−0.0223406
$911$	−23.7213	−0.785922	−0.392961	−	0.919555i	$-0.628549\pi$
$911$	−23.7213	−0.785922	−0.392961	+	0.919555i	$0.628549\pi$
$912$	−12.6564	−0.419094
$913$	0	0
$914$	33.7201	1.11536
$915$	15.5089	0.512710
$916$	−12.7679	−0.421865
$917$	−14.4575	−0.477427
$918$	10.6708	0.352188
$919$	−3.79855	−0.125303	−0.0626514	−	0.998035i	$-0.519956\pi$
$919$	−3.79855	−0.125303	−0.0626514	+	0.998035i	$0.519956\pi$
$920$	−0.506828	−0.0167096
$921$	4.58151	0.150966
$922$	−61.2435	−2.01695
$923$	2.93718	0.0966783
$924$	0	0
$925$	2.42665	0.0797878
$926$	49.3743	1.62254
$927$	−39.7123	−1.30432
$928$	−8.03248	−0.263679
$929$	−38.5516	−1.26484	−0.632418	−	0.774627i	$-0.717938\pi$
$929$	−38.5516	−1.26484	−0.632418	+	0.774627i	$0.717938\pi$
$930$	−7.08802	−0.232425
$931$	1.02587	0.0336216
$932$	−35.2992	−1.15626
$933$	−15.6609	−0.512716
$934$	14.2235	0.465408
$935$	0	0
$936$	1.53944	0.0503183
$937$	−11.7001	−0.382224	−0.191112	−	0.981568i	$-0.561209\pi$
$937$	−11.7001	−0.382224	−0.191112	+	0.981568i	$0.561209\pi$
$938$	0.287397	0.00938383
$939$	−76.2547	−2.48848
$940$	4.50582	0.146964
$941$	11.8230	0.385418	0.192709	−	0.981256i	$-0.438273\pi$
$941$	11.8230	0.385418	0.192709	+	0.981256i	$0.438273\pi$
$942$	76.4021	2.48931
$943$	2.35073	0.0765502
$944$	60.9016	1.98218
$945$	0.852446	0.0277301
$946$	0	0
$947$	56.5153	1.83650	0.918250	−	0.396001i	$-0.129602\pi$
$947$	56.5153	1.83650	0.918250	+	0.396001i	$0.129602\pi$
$948$	−30.4842	−0.990079
$949$	−3.97174	−0.128928
$950$	1.86804	0.0606073
$951$	54.2163	1.75809
$952$	−8.56476	−0.277586
$953$	−50.4611	−1.63460	−0.817298	−	0.576215i	$-0.804529\pi$
$953$	−50.4611	−1.63460	−0.817298	+	0.576215i	$0.804529\pi$
$954$	30.2497	0.979370
$955$	−26.0632	−0.843386
$956$	19.3189	0.624818
$957$	0	0
$958$	−16.0112	−0.517297
$959$	5.01729	0.162017
$960$	−4.80968	−0.155232
$961$	−28.6096	−0.922890
$962$	−1.63539	−0.0527271
$963$	27.6109	0.889749
$964$	−10.3844	−0.334459
$965$	−8.40356	−0.270520
$966$	1.86496	0.0600042
$967$	39.5803	1.27282	0.636408	−	0.771353i	$-0.280419\pi$
$967$	39.5803	1.27282	0.636408	+	0.771353i	$0.280419\pi$
$968$	0	0
$969$	17.7551	0.570377
$970$	−21.1422	−0.678836
$971$	22.1455	0.710683	0.355341	−	0.934737i	$-0.384365\pi$
$971$	22.1455	0.710683	0.355341	+	0.934737i	$0.384365\pi$
$972$	−29.4347	−0.944118
$973$	−22.6709	−0.726794
$974$	−2.80641	−0.0899232
$975$	−0.931788	−0.0298411
$976$	−30.1860	−0.966231
$977$	18.0584	0.577741	0.288870	−	0.957368i	$-0.406720\pi$
$977$	18.0584	0.577741	0.288870	+	0.957368i	$0.406720\pi$
$978$	−63.0445	−2.01594
$979$	0	0
$980$	1.31579	0.0420315
$981$	−57.3830	−1.83210
$982$	−18.4426	−0.588529
$983$	−49.1867	−1.56881	−0.784406	−	0.620248i	$-0.787032\pi$
$983$	−49.1867	−1.56881	−0.784406	+	0.620248i	$0.787032\pi$
$984$	−18.1259	−0.577831
$985$	−4.27568	−0.136234
$986$	15.6344	0.497900
$987$	8.62148	0.274425
$988$	−0.499576	−0.0158936
$989$	4.78254	0.152076
$990$	0	0
$991$	−34.2381	−1.08761	−0.543805	−	0.839212i	$-0.683017\pi$
$991$	−34.2381	−1.08761	−0.543805	+	0.839212i	$0.683017\pi$
$992$	9.94335	0.315702
$993$	−5.68557	−0.180426
$994$	−14.4512	−0.458363
$995$	11.8295	0.375020
$996$	−56.2339	−1.78184
$997$	−12.5706	−0.398116	−0.199058	−	0.979988i	$-0.563788\pi$
$997$	−12.5706	−0.398116	−0.199058	+	0.979988i	$0.563788\pi$
$998$	−37.3968	−1.18378
$999$	2.06859	0.0654473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bf.1.4	yes	5
11.10	odd	2		4235.2.a.z.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.z.1.2	✓	5	11.10	odd	2
4235.2.a.bf.1.4	yes	5	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+1.82093 q^{2} +2.51766 q^{3} +1.31579 q^{4} +1.00000 q^{5} +4.58448 q^{6} +1.00000 q^{7} -1.24589 q^{8} +3.33859 q^{9} +O(q^{10})\)	\(q+1.82093 q^{2} +2.51766 q^{3} +1.31579 q^{4} +1.00000 q^{5} +4.58448 q^{6} +1.00000 q^{7} -1.24589 q^{8} +3.33859 q^{9} +1.82093 q^{10} +3.31272 q^{12} -0.370102 q^{13} +1.82093 q^{14} +2.51766 q^{15} -4.90027 q^{16} +6.87440 q^{17} +6.07934 q^{18} +1.02587 q^{19} +1.31579 q^{20} +2.51766 q^{21} +0.406799 q^{23} -3.13673 q^{24} +1.00000 q^{25} -0.673930 q^{26} +0.852446 q^{27} +1.31579 q^{28} +1.24897 q^{29} +4.58448 q^{30} -1.54609 q^{31} -6.43128 q^{32} +12.5178 q^{34} +1.00000 q^{35} +4.39289 q^{36} +2.42665 q^{37} +1.86804 q^{38} -0.931788 q^{39} -1.24589 q^{40} +5.77859 q^{41} +4.58448 q^{42} +11.7565 q^{43} +3.33859 q^{45} +0.740754 q^{46} +3.42441 q^{47} -12.3372 q^{48} +1.00000 q^{49} +1.82093 q^{50} +17.3074 q^{51} -0.486978 q^{52} +4.97582 q^{53} +1.55225 q^{54} -1.24589 q^{56} +2.58279 q^{57} +2.27429 q^{58} -12.4282 q^{59} +3.31272 q^{60} +6.16007 q^{61} -2.81533 q^{62} +3.33859 q^{63} -1.91038 q^{64} -0.370102 q^{65} +0.157829 q^{67} +9.04530 q^{68} +1.02418 q^{69} +1.82093 q^{70} -7.93614 q^{71} -4.15952 q^{72} +10.7315 q^{73} +4.41877 q^{74} +2.51766 q^{75} +1.34984 q^{76} -1.69672 q^{78} -9.20216 q^{79} -4.90027 q^{80} -7.86960 q^{81} +10.5224 q^{82} -16.9752 q^{83} +3.31272 q^{84} +6.87440 q^{85} +21.4078 q^{86} +3.14448 q^{87} -6.41877 q^{89} +6.07934 q^{90} -0.370102 q^{91} +0.535264 q^{92} -3.89252 q^{93} +6.23562 q^{94} +1.02587 q^{95} -16.1918 q^{96} -11.6107 q^{97} +1.82093 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} - q^{6} + 5 q^{7} - q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 - q^6 + 5 * q^7 - q^9	\( 5 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} - q^{6} + 5 q^{7} - q^{9} + 2 q^{10} - 3 q^{12} + 8 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} + 6 q^{17} + 11 q^{18} + 7 q^{19} + 4 q^{20} + 2 q^{21} + 3 q^{23} - 6 q^{24} + 5 q^{25} - 15 q^{26} + 5 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 12 q^{31} - 3 q^{32} - 12 q^{34} + 5 q^{35} - 3 q^{36} - 2 q^{37} + 21 q^{38} + 14 q^{39} + 5 q^{41} - q^{42} + 4 q^{43} - q^{45} + 2 q^{46} - 12 q^{48} + 5 q^{49} + 2 q^{50} + 14 q^{51} + 2 q^{52} + 8 q^{53} + 22 q^{54} + 4 q^{57} + 6 q^{58} - 16 q^{59} - 3 q^{60} + 24 q^{61} + 9 q^{62} - q^{63} - 38 q^{64} + 8 q^{65} - 9 q^{67} + 19 q^{68} + 22 q^{69} + 2 q^{70} - 10 q^{71} + 4 q^{72} + 11 q^{73} - q^{74} + 2 q^{75} + 11 q^{76} - 5 q^{78} + 9 q^{79} + 2 q^{80} - 19 q^{81} + 44 q^{82} + 10 q^{83} - 3 q^{84} + 6 q^{85} + 15 q^{86} - 2 q^{87} - 9 q^{89} + 11 q^{90} + 8 q^{91} - 26 q^{92} - q^{93} + 34 q^{94} + 7 q^{95} - 18 q^{96} + 11 q^{97} + 2 q^{98}+O(q^{100}) \) 5 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 - q^6 + 5 * q^7 - q^9 + 2 * q^10 - 3 * q^12 + 8 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 + 6 * q^17 + 11 * q^18 + 7 * q^19 + 4 * q^20 + 2 * q^21 + 3 * q^23 - 6 * q^24 + 5 * q^25 - 15 * q^26 + 5 * q^27 + 4 * q^28 + 17 * q^29 - q^30 + 12 * q^31 - 3 * q^32 - 12 * q^34 + 5 * q^35 - 3 * q^36 - 2 * q^37 + 21 * q^38 + 14 * q^39 + 5 * q^41 - q^42 + 4 * q^43 - q^45 + 2 * q^46 - 12 * q^48 + 5 * q^49 + 2 * q^50 + 14 * q^51 + 2 * q^52 + 8 * q^53 + 22 * q^54 + 4 * q^57 + 6 * q^58 - 16 * q^59 - 3 * q^60 + 24 * q^61 + 9 * q^62 - q^63 - 38 * q^64 + 8 * q^65 - 9 * q^67 + 19 * q^68 + 22 * q^69 + 2 * q^70 - 10 * q^71 + 4 * q^72 + 11 * q^73 - q^74 + 2 * q^75 + 11 * q^76 - 5 * q^78 + 9 * q^79 + 2 * q^80 - 19 * q^81 + 44 * q^82 + 10 * q^83 - 3 * q^84 + 6 * q^85 + 15 * q^86 - 2 * q^87 - 9 * q^89 + 11 * q^90 + 8 * q^91 - 26 * q^92 - q^93 + 34 * q^94 + 7 * q^95 - 18 * q^96 + 11 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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