LMFDB - Embedded newform 7381.2.a.r.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.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:	$58.9375817319$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.26825 q^{2} -3.01754 q^{3} -0.391539 q^{4} +0.665111 q^{5} +3.82700 q^{6} +3.10252 q^{7} +3.03307 q^{8} +6.10557 q^{9} +O(q^{10})$	\(q-1.26825 q^{2} -3.01754 q^{3} -0.391539 q^{4} +0.665111 q^{5} +3.82700 q^{6} +3.10252 q^{7} +3.03307 q^{8} +6.10557 q^{9} -0.843527 q^{10} +1.18149 q^{12} -1.63074 q^{13} -3.93477 q^{14} -2.00700 q^{15} -3.06362 q^{16} +3.60504 q^{17} -7.74340 q^{18} -2.80324 q^{19} -0.260417 q^{20} -9.36198 q^{21} +1.39741 q^{23} -9.15243 q^{24} -4.55763 q^{25} +2.06819 q^{26} -9.37120 q^{27} -1.21476 q^{28} +0.428354 q^{29} +2.54538 q^{30} -2.21833 q^{31} -2.18070 q^{32} -4.57210 q^{34} +2.06352 q^{35} -2.39057 q^{36} +9.90180 q^{37} +3.55521 q^{38} +4.92084 q^{39} +2.01733 q^{40} -7.15704 q^{41} +11.8733 q^{42} +5.79040 q^{43} +4.06088 q^{45} -1.77226 q^{46} -2.76336 q^{47} +9.24461 q^{48} +2.62562 q^{49} +5.78022 q^{50} -10.8784 q^{51} +0.638499 q^{52} +8.84065 q^{53} +11.8850 q^{54} +9.41016 q^{56} +8.45890 q^{57} -0.543260 q^{58} +1.45124 q^{59} +0.785819 q^{60} +1.00000 q^{61} +2.81340 q^{62} +18.9426 q^{63} +8.89292 q^{64} -1.08462 q^{65} +10.0607 q^{67} -1.41151 q^{68} -4.21674 q^{69} -2.61706 q^{70} +8.75417 q^{71} +18.5186 q^{72} -6.41738 q^{73} -12.5580 q^{74} +13.7528 q^{75} +1.09758 q^{76} -6.24086 q^{78} +15.9951 q^{79} -2.03765 q^{80} +9.96129 q^{81} +9.07692 q^{82} -8.39290 q^{83} +3.66558 q^{84} +2.39775 q^{85} -7.34368 q^{86} -1.29258 q^{87} +2.07471 q^{89} -5.15022 q^{90} -5.05941 q^{91} -0.547139 q^{92} +6.69390 q^{93} +3.50464 q^{94} -1.86446 q^{95} +6.58037 q^{96} +1.10826 q^{97} -3.32994 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 10 q^{2} - 2 q^{3} + 50 q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 30 q^{8} + 48 q^{9}+O(q^{10}) $ 50 * q + 10 * q^2 - 2 * q^3 + 50 * q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 30 * q^8 + 48 * q^9	\( 50 q + 10 q^{2} - 2 q^{3} + 50 q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 30 q^{8} + 48 q^{9} + 12 q^{10} - 14 q^{12} + 8 q^{13} - 2 q^{14} - 16 q^{15} + 42 q^{16} + 22 q^{17} + 32 q^{19} - 8 q^{20} + 24 q^{21} + 12 q^{23} - 8 q^{24} + 40 q^{25} + 10 q^{26} - 8 q^{27} + 72 q^{28} + 56 q^{29} + 24 q^{30} + 10 q^{31} + 70 q^{32} - 32 q^{34} + 70 q^{35} + 34 q^{36} - 8 q^{37} - 14 q^{38} + 96 q^{39} - 54 q^{40} + 56 q^{41} - 8 q^{42} + 44 q^{43} - 24 q^{45} - 4 q^{46} - 4 q^{47} - 28 q^{48} + 38 q^{49} + 120 q^{50} + 76 q^{51} + 24 q^{52} + 4 q^{53} + 48 q^{54} - 18 q^{56} + 8 q^{57} + 28 q^{58} + 12 q^{59} - 60 q^{60} + 50 q^{61} + 8 q^{62} + 30 q^{63} + 10 q^{64} + 64 q^{65} + 18 q^{67} - 22 q^{68} - 8 q^{69} + 34 q^{70} + 12 q^{71} + 104 q^{72} - 16 q^{73} + 84 q^{74} - 26 q^{75} + 64 q^{76} + 40 q^{78} + 78 q^{79} - 36 q^{80} + 34 q^{81} + 54 q^{82} + 68 q^{83} - 78 q^{84} - 4 q^{85} + 36 q^{86} + 48 q^{87} + 26 q^{89} - 20 q^{90} + 32 q^{92} + 22 q^{93} + 156 q^{94} + 100 q^{95} - 4 q^{96} - 14 q^{97} + 70 q^{98}+O(q^{100}) \) 50 * q + 10 * q^2 - 2 * q^3 + 50 * q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 30 * q^8 + 48 * q^9 + 12 * q^10 - 14 * q^12 + 8 * q^13 - 2 * q^14 - 16 * q^15 + 42 * q^16 + 22 * q^17 + 32 * q^19 - 8 * q^20 + 24 * q^21 + 12 * q^23 - 8 * q^24 + 40 * q^25 + 10 * q^26 - 8 * q^27 + 72 * q^28 + 56 * q^29 + 24 * q^30 + 10 * q^31 + 70 * q^32 - 32 * q^34 + 70 * q^35 + 34 * q^36 - 8 * q^37 - 14 * q^38 + 96 * q^39 - 54 * q^40 + 56 * q^41 - 8 * q^42 + 44 * q^43 - 24 * q^45 - 4 * q^46 - 4 * q^47 - 28 * q^48 + 38 * q^49 + 120 * q^50 + 76 * q^51 + 24 * q^52 + 4 * q^53 + 48 * q^54 - 18 * q^56 + 8 * q^57 + 28 * q^58 + 12 * q^59 - 60 * q^60 + 50 * q^61 + 8 * q^62 + 30 * q^63 + 10 * q^64 + 64 * q^65 + 18 * q^67 - 22 * q^68 - 8 * q^69 + 34 * q^70 + 12 * q^71 + 104 * q^72 - 16 * q^73 + 84 * q^74 - 26 * q^75 + 64 * q^76 + 40 * q^78 + 78 * q^79 - 36 * q^80 + 34 * q^81 + 54 * q^82 + 68 * q^83 - 78 * q^84 - 4 * q^85 + 36 * q^86 + 48 * q^87 + 26 * q^89 - 20 * q^90 + 32 * q^92 + 22 * q^93 + 156 * q^94 + 100 * q^95 - 4 * q^96 - 14 * q^97 + 70 * 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 $

$2$	−1.26825	−0.896789	−0.448395	−	0.893836i	$-0.648004\pi$
$2$	−1.26825	−0.896789	−0.448395	+	0.893836i	$0.648004\pi$
$3$	−3.01754	−1.74218	−0.871090	−	0.491124i	$-0.836586\pi$
$3$	−3.01754	−1.74218	−0.871090	+	0.491124i	$0.836586\pi$
$4$	−0.391539	−0.195769
$5$	0.665111	0.297447	0.148723	−	0.988879i	$-0.452484\pi$
$5$	0.665111	0.297447	0.148723	+	0.988879i	$0.452484\pi$
$6$	3.82700	1.56237
$7$	3.10252	1.17264	0.586321	−	0.810079i	$-0.300576\pi$
$7$	3.10252	1.17264	0.586321	+	0.810079i	$0.300576\pi$
$8$	3.03307	1.07235
$9$	6.10557	2.03519
$10$	−0.843527	−0.266747
$11$	0	0
$11$	0	0
$12$	1.18149	0.341066
$13$	−1.63074	−0.452287	−0.226143	−	0.974094i	$-0.572612\pi$
$13$	−1.63074	−0.452287	−0.226143	+	0.974094i	$0.572612\pi$
$14$	−3.93477	−1.05161
$15$	−2.00700	−0.518205
$16$	−3.06362	−0.765905
$17$	3.60504	0.874351	0.437175	−	0.899376i	$-0.355979\pi$
$17$	3.60504	0.874351	0.437175	+	0.899376i	$0.355979\pi$
$18$	−7.74340	−1.82514
$19$	−2.80324	−0.643107	−0.321554	−	0.946891i	$-0.604205\pi$
$19$	−2.80324	−0.643107	−0.321554	+	0.946891i	$0.604205\pi$
$20$	−0.260417	−0.0582309
$21$	−9.36198	−2.04295
$22$	0	0
$23$	1.39741	0.291379	0.145690	−	0.989330i	$-0.453460\pi$
$23$	1.39741	0.291379	0.145690	+	0.989330i	$0.453460\pi$
$24$	−9.15243	−1.86823
$25$	−4.55763	−0.911526
$26$	2.06819	0.405606
$27$	−9.37120	−1.80349
$28$	−1.21476	−0.229567
$29$	0.428354	0.0795433	0.0397716	−	0.999209i	$-0.487337\pi$
$29$	0.428354	0.0795433	0.0397716	+	0.999209i	$0.487337\pi$
$30$	2.54538	0.464721
$31$	−2.21833	−0.398423	−0.199212	−	0.979956i	$-0.563838\pi$
$31$	−2.21833	−0.398423	−0.199212	+	0.979956i	$0.563838\pi$
$32$	−2.18070	−0.385498
$33$	0	0
$34$	−4.57210	−0.784108
$35$	2.06352	0.348798
$36$	−2.39057	−0.398428
$37$	9.90180	1.62785	0.813923	−	0.580973i	$-0.197328\pi$
$37$	9.90180	1.62785	0.813923	+	0.580973i	$0.197328\pi$
$38$	3.55521	0.576732
$39$	4.92084	0.787965
$40$	2.01733	0.318968
$41$	−7.15704	−1.11774	−0.558871	−	0.829255i	$-0.688765\pi$
$41$	−7.15704	−1.11774	−0.558871	+	0.829255i	$0.688765\pi$
$42$	11.8733	1.83210
$43$	5.79040	0.883028	0.441514	−	0.897254i	$-0.354442\pi$
$43$	5.79040	0.883028	0.441514	+	0.897254i	$0.354442\pi$
$44$	0	0
$45$	4.06088	0.605360
$46$	−1.77226	−0.261306
$47$	−2.76336	−0.403078	−0.201539	−	0.979480i	$-0.564594\pi$
$47$	−2.76336	−0.403078	−0.201539	+	0.979480i	$0.564594\pi$
$48$	9.24461	1.33434
$49$	2.62562	0.375088
$50$	5.78022	0.817446
$51$	−10.8784	−1.52328
$52$	0.638499	0.0885439
$53$	8.84065	1.21436	0.607178	−	0.794566i	$-0.292301\pi$
$53$	8.84065	1.21436	0.607178	+	0.794566i	$0.292301\pi$
$54$	11.8850	1.61735
$55$	0	0
$56$	9.41016	1.25749
$57$	8.45890	1.12041
$58$	−0.543260	−0.0713335
$59$	1.45124	0.188935	0.0944674	−	0.995528i	$-0.469885\pi$
$59$	1.45124	0.188935	0.0944674	+	0.995528i	$0.469885\pi$
$60$	0.785819	0.101449
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	2.81340	0.357302
$63$	18.9426	2.38655
$64$	8.89292	1.11162
$65$	−1.08462	−0.134531
$66$	0	0
$67$	10.0607	1.22911	0.614553	−	0.788875i	$-0.289336\pi$
$67$	10.0607	1.22911	0.614553	+	0.788875i	$0.289336\pi$
$68$	−1.41151	−0.171171
$69$	−4.21674	−0.507635
$70$	−2.61706	−0.312798
$71$	8.75417	1.03893	0.519465	−	0.854492i	$-0.326131\pi$
$71$	8.75417	1.03893	0.519465	+	0.854492i	$0.326131\pi$
$72$	18.5186	2.18244
$73$	−6.41738	−0.751097	−0.375549	−	0.926803i	$-0.622546\pi$
$73$	−6.41738	−0.751097	−0.375549	+	0.926803i	$0.622546\pi$
$74$	−12.5580	−1.45983
$75$	13.7528	1.58804
$76$	1.09758	0.125901
$77$	0	0
$78$	−6.24086	−0.706638
$79$	15.9951	1.79959	0.899793	−	0.436318i	$-0.143718\pi$
$79$	15.9951	1.79959	0.899793	+	0.436318i	$0.143718\pi$
$80$	−2.03765	−0.227816
$81$	9.96129	1.10681
$82$	9.07692	1.00238
$83$	−8.39290	−0.921240	−0.460620	−	0.887597i	$-0.652373\pi$
$83$	−8.39290	−0.921240	−0.460620	+	0.887597i	$0.652373\pi$
$84$	3.66558	0.399948
$85$	2.39775	0.260073
$86$	−7.34368	−0.791889
$87$	−1.29258	−0.138579
$88$	0	0
$89$	2.07471	0.219918	0.109959	−	0.993936i	$-0.464928\pi$
$89$	2.07471	0.219918	0.109959	+	0.993936i	$0.464928\pi$
$90$	−5.15022	−0.542881
$91$	−5.05941	−0.530370
$92$	−0.547139	−0.0570432
$93$	6.69390	0.694125
$94$	3.50464	0.361476
$95$	−1.86446	−0.191290
$96$	6.58037	0.671606
$97$	1.10826	0.112527	0.0562633	−	0.998416i	$-0.482081\pi$
$97$	1.10826	0.112527	0.0562633	+	0.998416i	$0.482081\pi$
$98$	−3.32994	−0.336375
$99$	0	0
$100$	1.78449	0.178449
$101$	−1.74410	−0.173544	−0.0867720	−	0.996228i	$-0.527655\pi$
$101$	−1.74410	−0.173544	−0.0867720	+	0.996228i	$0.527655\pi$
$102$	13.7965	1.36606
$103$	−7.36934	−0.726122	−0.363061	−	0.931765i	$-0.618268\pi$
$103$	−7.36934	−0.726122	−0.363061	+	0.931765i	$0.618268\pi$
$104$	−4.94616	−0.485011
$105$	−6.22675	−0.607669
$106$	−11.2122	−1.08902
$107$	3.88925	0.375988	0.187994	−	0.982170i	$-0.439801\pi$
$107$	3.88925	0.375988	0.187994	+	0.982170i	$0.439801\pi$
$108$	3.66919	0.353068
$109$	−7.00024	−0.670501	−0.335251	−	0.942129i	$-0.608821\pi$
$109$	−7.00024	−0.670501	−0.335251	+	0.942129i	$0.608821\pi$
$110$	0	0
$111$	−29.8791	−2.83600
$112$	−9.50493	−0.898132
$113$	−13.4795	−1.26805	−0.634023	−	0.773314i	$-0.718598\pi$
$113$	−13.4795	−1.26805	−0.634023	+	0.773314i	$0.718598\pi$
$114$	−10.7280	−1.00477
$115$	0.929430	0.0866698
$116$	−0.167717	−0.0155721
$117$	−9.95662	−0.920489
$118$	−1.84053	−0.169435
$119$	11.1847	1.02530
$120$	−6.08738	−0.555699
$121$	0	0
$122$	−1.26825	−0.114822
$123$	21.5967	1.94731
$124$	0.868561	0.0779991
$125$	−6.35688	−0.568577
$126$	−24.0240	−2.14023
$127$	0.605006	0.0536856	0.0268428	−	0.999640i	$-0.491455\pi$
$127$	0.605006	0.0536856	0.0268428	+	0.999640i	$0.491455\pi$
$128$	−6.91705	−0.611386
$129$	−17.4728	−1.53839
$130$	1.37558	0.120646
$131$	−8.95046	−0.782006	−0.391003	−	0.920389i	$-0.627872\pi$
$131$	−8.95046	−0.782006	−0.391003	+	0.920389i	$0.627872\pi$
$132$	0	0
$133$	−8.69710	−0.754134
$134$	−12.7595	−1.10225
$135$	−6.23288	−0.536441
$136$	10.9343	0.937612
$137$	15.7411	1.34485	0.672427	−	0.740164i	$-0.265252\pi$
$137$	15.7411	1.34485	0.672427	+	0.740164i	$0.265252\pi$
$138$	5.34788	0.455242
$139$	12.4487	1.05589	0.527944	−	0.849279i	$-0.322963\pi$
$139$	12.4487	1.05589	0.527944	+	0.849279i	$0.322963\pi$
$140$	−0.807947	−0.0682840
$141$	8.33858	0.702235
$142$	−11.1025	−0.931700
$143$	0	0
$144$	−18.7051	−1.55876
$145$	0.284903	0.0236599
$146$	8.13885	0.673576
$147$	−7.92291	−0.653471
$148$	−3.87694	−0.318682
$149$	4.40399	0.360789	0.180395	−	0.983594i	$-0.442263\pi$
$149$	4.40399	0.360789	0.180395	+	0.983594i	$0.442263\pi$
$150$	−17.4421	−1.42414
$151$	9.00418	0.732749	0.366375	−	0.930467i	$-0.380599\pi$
$151$	9.00418	0.732749	0.366375	+	0.930467i	$0.380599\pi$
$152$	−8.50243	−0.689638
$153$	22.0108	1.77947
$154$	0	0
$155$	−1.47543	−0.118510
$156$	−1.92670	−0.154259
$157$	18.6870	1.49138	0.745691	−	0.666292i	$-0.232120\pi$
$157$	18.6870	1.49138	0.745691	+	0.666292i	$0.232120\pi$
$158$	−20.2858	−1.61385
$159$	−26.6770	−2.11563
$160$	−1.45041	−0.114665
$161$	4.33548	0.341684
$162$	−12.6334	−0.992575
$163$	18.5274	1.45118	0.725588	−	0.688129i	$-0.241568\pi$
$163$	18.5274	1.45118	0.725588	+	0.688129i	$0.241568\pi$
$164$	2.80226	0.218820
$165$	0	0
$166$	10.6443	0.826158
$167$	5.71763	0.442444	0.221222	−	0.975223i	$-0.428995\pi$
$167$	5.71763	0.442444	0.221222	+	0.975223i	$0.428995\pi$
$168$	−28.3956	−2.19077
$169$	−10.3407	−0.795437
$170$	−3.04095	−0.233230
$171$	−17.1154	−1.30885
$172$	−2.26717	−0.172870
$173$	−18.5760	−1.41231	−0.706155	−	0.708057i	$-0.749572\pi$
$173$	−18.5760	−1.41231	−0.706155	+	0.708057i	$0.749572\pi$
$174$	1.63931	0.124276
$175$	−14.1401	−1.06889
$176$	0	0
$177$	−4.37917	−0.329158
$178$	−2.63125	−0.197220
$179$	−8.42612	−0.629798	−0.314899	−	0.949125i	$-0.601971\pi$
$179$	−8.42612	−0.629798	−0.314899	+	0.949125i	$0.601971\pi$
$180$	−1.58999	−0.118511
$181$	−16.3518	−1.21542	−0.607708	−	0.794160i	$-0.707911\pi$
$181$	−16.3518	−1.21542	−0.607708	+	0.794160i	$0.707911\pi$
$182$	6.41660	0.475630
$183$	−3.01754	−0.223063
$184$	4.23844	0.312462
$185$	6.58579	0.484197
$186$	−8.48955	−0.622484
$187$	0	0
$188$	1.08196	0.0789104
$189$	−29.0743	−2.11484
$190$	2.36461	0.171547
$191$	−24.2369	−1.75372	−0.876859	−	0.480748i	$-0.840365\pi$
$191$	−24.2369	−1.75372	−0.876859	+	0.480748i	$0.840365\pi$
$192$	−26.8348	−1.93663
$193$	−16.3705	−1.17837	−0.589187	−	0.807997i	$-0.700552\pi$
$193$	−16.3705	−1.17837	−0.589187	+	0.807997i	$0.700552\pi$
$194$	−1.40555	−0.100913
$195$	3.27290	0.234377
$196$	−1.02803	−0.0734307
$197$	17.9526	1.27907	0.639533	−	0.768764i	$-0.279128\pi$
$197$	17.9526	1.27907	0.639533	+	0.768764i	$0.279128\pi$
$198$	0	0
$199$	−12.2419	−0.867802	−0.433901	−	0.900961i	$-0.642863\pi$
$199$	−12.2419	−0.867802	−0.433901	+	0.900961i	$0.642863\pi$
$200$	−13.8236	−0.977477
$201$	−30.3585	−2.14132
$202$	2.21195	0.155632
$203$	1.32897	0.0932757
$204$	4.25930	0.298211
$205$	−4.76022	−0.332468
$206$	9.34617	0.651179
$207$	8.53197	0.593013
$208$	4.99598	0.346409
$209$	0	0
$210$	7.89709	0.544951
$211$	17.4473	1.20112	0.600560	−	0.799580i	$-0.294944\pi$
$211$	17.4473	1.20112	0.600560	+	0.799580i	$0.294944\pi$
$212$	−3.46146	−0.237734
$213$	−26.4161	−1.81000
$214$	−4.93255	−0.337182
$215$	3.85126	0.262653
$216$	−28.4235	−1.93398
$217$	−6.88240	−0.467208
$218$	8.87806	0.601298
$219$	19.3647	1.30855
$220$	0	0
$221$	−5.87889	−0.395457
$222$	37.8942	2.54329
$223$	4.20828	0.281807	0.140904	−	0.990023i	$-0.454999\pi$
$223$	4.20828	0.281807	0.140904	+	0.990023i	$0.454999\pi$
$224$	−6.76567	−0.452051
$225$	−27.8269	−1.85513
$226$	17.0954	1.13717
$227$	22.6204	1.50137	0.750685	−	0.660661i	$-0.229724\pi$
$227$	22.6204	1.50137	0.750685	+	0.660661i	$0.229724\pi$
$228$	−3.31199	−0.219342
$229$	−14.6463	−0.967855	−0.483927	−	0.875108i	$-0.660790\pi$
$229$	−14.6463	−0.967855	−0.483927	+	0.875108i	$0.660790\pi$
$230$	−1.17875	−0.0777245
$231$	0	0
$232$	1.29923	0.0852985
$233$	9.05954	0.593510	0.296755	−	0.954954i	$-0.404095\pi$
$233$	9.05954	0.593510	0.296755	+	0.954954i	$0.404095\pi$
$234$	12.6275	0.825485
$235$	−1.83794	−0.119894
$236$	−0.568215	−0.0369877
$237$	−48.2658	−3.13520
$238$	−14.1850	−0.919478
$239$	−11.7297	−0.758729	−0.379365	−	0.925247i	$-0.623857\pi$
$239$	−11.7297	−0.758729	−0.379365	+	0.925247i	$0.623857\pi$
$240$	6.14869	0.396896
$241$	18.6628	1.20218	0.601088	−	0.799183i	$-0.294734\pi$
$241$	18.6628	1.20218	0.601088	+	0.799183i	$0.294734\pi$
$242$	0	0
$243$	−1.94503	−0.124774
$244$	−0.391539	−0.0250657
$245$	1.74632	0.111569
$246$	−27.3900	−1.74632
$247$	4.57136	0.290869
$248$	−6.72835	−0.427251
$249$	25.3259	1.60497
$250$	8.06212	0.509893
$251$	−17.3659	−1.09613	−0.548064	−	0.836436i	$-0.684635\pi$
$251$	−17.3659	−1.09613	−0.548064	+	0.836436i	$0.684635\pi$
$252$	−7.41678	−0.467213
$253$	0	0
$254$	−0.767299	−0.0481446
$255$	−7.23532	−0.453093
$256$	−9.01329	−0.563330
$257$	3.24107	0.202173	0.101086	−	0.994878i	$-0.467768\pi$
$257$	3.24107	0.202173	0.101086	+	0.994878i	$0.467768\pi$
$258$	22.1599	1.37961
$259$	30.7205	1.90888
$260$	0.424673	0.0263371
$261$	2.61534	0.161886
$262$	11.3514	0.701294
$263$	15.4762	0.954301	0.477150	−	0.878822i	$-0.341670\pi$
$263$	15.4762	0.954301	0.477150	+	0.878822i	$0.341670\pi$
$264$	0	0
$265$	5.88001	0.361206
$266$	11.0301	0.676299
$267$	−6.26051	−0.383137
$268$	−3.93914	−0.240621
$269$	21.6727	1.32141	0.660704	−	0.750647i	$-0.270258\pi$
$269$	21.6727	1.32141	0.660704	+	0.750647i	$0.270258\pi$
$270$	7.90486	0.481075
$271$	2.32415	0.141182	0.0705910	−	0.997505i	$-0.477511\pi$
$271$	2.32415	0.141182	0.0705910	+	0.997505i	$0.477511\pi$
$272$	−11.0445	−0.669669
$273$	15.2670	0.924000
$274$	−19.9637	−1.20605
$275$	0	0
$276$	1.65102	0.0993795
$277$	23.6581	1.42148	0.710739	−	0.703456i	$-0.248361\pi$
$277$	23.6581	1.42148	0.710739	+	0.703456i	$0.248361\pi$
$278$	−15.7881	−0.946908
$279$	−13.5442	−0.810868
$280$	6.25880	0.374035
$281$	28.4479	1.69706	0.848529	−	0.529149i	$-0.177489\pi$
$281$	28.4479	1.69706	0.848529	+	0.529149i	$0.177489\pi$
$282$	−10.5754	−0.629756
$283$	−2.64402	−0.157171	−0.0785854	−	0.996907i	$-0.525040\pi$
$283$	−2.64402	−0.157171	−0.0785854	+	0.996907i	$0.525040\pi$
$284$	−3.42760	−0.203391
$285$	5.62610	0.333262
$286$	0	0
$287$	−22.2048	−1.31071
$288$	−13.3144	−0.784561
$289$	−4.00369	−0.235511
$290$	−0.361328	−0.0212179
$291$	−3.34422	−0.196042
$292$	2.51265	0.147042
$293$	−11.8072	−0.689783	−0.344891	−	0.938643i	$-0.612084\pi$
$293$	−11.8072	−0.689783	−0.344891	+	0.938643i	$0.612084\pi$
$294$	10.0482	0.586025
$295$	0.965232	0.0561980
$296$	30.0329	1.74562
$297$	0	0
$298$	−5.58537	−0.323552
$299$	−2.27881	−0.131787
$300$	−5.38477	−0.310890
$301$	17.9648	1.03547
$302$	−11.4196	−0.657122
$303$	5.26289	0.302345
$304$	8.58806	0.492559
$305$	0.665111	0.0380841
$306$	−27.9153	−1.59581
$307$	−23.8419	−1.36073	−0.680365	−	0.732874i	$-0.738179\pi$
$307$	−23.8419	−1.36073	−0.680365	+	0.732874i	$0.738179\pi$
$308$	0	0
$309$	22.2373	1.26504
$310$	1.87122	0.106278
$311$	6.17237	0.350003	0.175002	−	0.984568i	$-0.444007\pi$
$311$	6.17237	0.350003	0.175002	+	0.984568i	$0.444007\pi$
$312$	14.9253	0.844976
$313$	−22.4467	−1.26876	−0.634382	−	0.773020i	$-0.718745\pi$
$313$	−22.4467	−1.26876	−0.634382	+	0.773020i	$0.718745\pi$
$314$	−23.6998	−1.33745
$315$	12.5990	0.709871
$316$	−6.26269	−0.352304
$317$	−15.3644	−0.862949	−0.431474	−	0.902125i	$-0.642006\pi$
$317$	−15.3644	−0.862949	−0.431474	+	0.902125i	$0.642006\pi$
$318$	33.8332	1.89727
$319$	0	0
$320$	5.91478	0.330646
$321$	−11.7360	−0.655039
$322$	−5.49848	−0.306418
$323$	−10.1058	−0.562301
$324$	−3.90023	−0.216680
$325$	7.43232	0.412271
$326$	−23.4974	−1.30140
$327$	21.1235	1.16813
$328$	−21.7078	−1.19861
$329$	−8.57339	−0.472666
$330$	0	0
$331$	10.9847	0.603776	0.301888	−	0.953343i	$-0.402383\pi$
$331$	10.9847	0.603776	0.301888	+	0.953343i	$0.402383\pi$
$332$	3.28614	0.180351
$333$	60.4561	3.31297
$334$	−7.25140	−0.396779
$335$	6.69146	0.365593
$336$	28.6816	1.56471
$337$	−33.1535	−1.80599	−0.902994	−	0.429653i	$-0.858636\pi$
$337$	−33.1535	−1.80599	−0.902994	+	0.429653i	$0.858636\pi$
$338$	13.1146	0.713339
$339$	40.6751	2.20917
$340$	−0.938812	−0.0509143
$341$	0	0
$342$	21.7066	1.17376
$343$	−13.5716	−0.732798
$344$	17.5627	0.946917
$345$	−2.80460	−0.150994
$346$	23.5591	1.26654
$347$	−23.4615	−1.25948	−0.629739	−	0.776807i	$-0.716838\pi$
$347$	−23.4615	−1.25948	−0.629739	+	0.776807i	$0.716838\pi$
$348$	0.506094	0.0271295
$349$	10.4558	0.559684	0.279842	−	0.960046i	$-0.409718\pi$
$349$	10.4558	0.559684	0.279842	+	0.960046i	$0.409718\pi$
$350$	17.9332	0.958571
$351$	15.2820	0.815694
$352$	0	0
$353$	−17.5618	−0.934722	−0.467361	−	0.884067i	$-0.654795\pi$
$353$	−17.5618	−0.934722	−0.467361	+	0.884067i	$0.654795\pi$
$354$	5.55389	0.295186
$355$	5.82249	0.309026
$356$	−0.812328	−0.0430533
$357$	−33.7503	−1.78626
$358$	10.6864	0.564796
$359$	23.0022	1.21401	0.607006	−	0.794697i	$-0.292370\pi$
$359$	23.0022	1.21401	0.607006	+	0.794697i	$0.292370\pi$
$360$	12.3169	0.649160
$361$	−11.1418	−0.586413
$362$	20.7381	1.08997
$363$	0	0
$364$	1.98095	0.103830
$365$	−4.26827	−0.223411
$366$	3.82700	0.200041
$367$	13.5936	0.709582	0.354791	−	0.934946i	$-0.384552\pi$
$367$	13.5936	0.709582	0.354791	+	0.934946i	$0.384552\pi$
$368$	−4.28112	−0.223169
$369$	−43.6978	−2.27482
$370$	−8.35244	−0.434222
$371$	27.4283	1.42400
$372$	−2.62092	−0.135888
$373$	−16.1511	−0.836272	−0.418136	−	0.908384i	$-0.637316\pi$
$373$	−16.1511	−0.836272	−0.418136	+	0.908384i	$0.637316\pi$
$374$	0	0
$375$	19.1822	0.990563
$376$	−8.38149	−0.432242
$377$	−0.698535	−0.0359764
$378$	36.8735	1.89657
$379$	−27.3409	−1.40441	−0.702205	−	0.711975i	$-0.747801\pi$
$379$	−27.3409	−1.40441	−0.702205	+	0.711975i	$0.747801\pi$
$380$	0.730010	0.0374487
$381$	−1.82563	−0.0935299
$382$	30.7384	1.57271
$383$	33.7261	1.72332	0.861661	−	0.507484i	$-0.169424\pi$
$383$	33.7261	1.72332	0.861661	+	0.507484i	$0.169424\pi$
$384$	20.8725	1.06515
$385$	0	0
$386$	20.7619	1.05675
$387$	35.3537	1.79713
$388$	−0.433926	−0.0220293
$389$	30.4134	1.54202	0.771010	−	0.636823i	$-0.219752\pi$
$389$	30.4134	1.54202	0.771010	+	0.636823i	$0.219752\pi$
$390$	−4.15086	−0.210187
$391$	5.03771	0.254768
$392$	7.96368	0.402227
$393$	27.0084	1.36239
$394$	−22.7683	−1.14705
$395$	10.6385	0.535280
$396$	0	0
$397$	−14.4936	−0.727414	−0.363707	−	0.931513i	$-0.618489\pi$
$397$	−14.4936	−0.727414	−0.363707	+	0.931513i	$0.618489\pi$
$398$	15.5257	0.778235
$399$	26.2439	1.31384
$400$	13.9628	0.698142
$401$	−9.20099	−0.459476	−0.229738	−	0.973253i	$-0.573787\pi$
$401$	−9.20099	−0.459476	−0.229738	+	0.973253i	$0.573787\pi$
$402$	38.5022	1.92032
$403$	3.61752	0.180202
$404$	0.682881	0.0339746
$405$	6.62536	0.329217
$406$	−1.68547	−0.0836487
$407$	0	0
$408$	−32.9949	−1.63349
$409$	−32.2926	−1.59677	−0.798383	−	0.602150i	$-0.794311\pi$
$409$	−32.2926	−1.59677	−0.798383	+	0.602150i	$0.794311\pi$
$410$	6.03716	0.298154
$411$	−47.4995	−2.34298
$412$	2.88538	0.142153
$413$	4.50248	0.221553
$414$	−10.8207	−0.531807
$415$	−5.58220	−0.274020
$416$	3.55617	0.174355
$417$	−37.5646	−1.83955
$418$	0	0
$419$	−16.7986	−0.820664	−0.410332	−	0.911936i	$-0.634587\pi$
$419$	−16.7986	−0.820664	−0.410332	+	0.911936i	$0.634587\pi$
$420$	2.43802	0.118963
$421$	29.8830	1.45641	0.728205	−	0.685360i	$-0.240355\pi$
$421$	29.8830	1.45641	0.728205	+	0.685360i	$0.240355\pi$
$422$	−22.1275	−1.07715
$423$	−16.8719	−0.820341
$424$	26.8143	1.30222
$425$	−16.4304	−0.796993
$426$	33.5023	1.62319
$427$	3.10252	0.150141
$428$	−1.52279	−0.0736070
$429$	0	0
$430$	−4.88436	−0.235545
$431$	28.0903	1.35306	0.676531	−	0.736414i	$-0.263482\pi$
$431$	28.0903	1.35306	0.676531	+	0.736414i	$0.263482\pi$
$432$	28.7098	1.38130
$433$	−31.6207	−1.51960	−0.759798	−	0.650160i	$-0.774702\pi$
$433$	−31.6207	−1.51960	−0.759798	+	0.650160i	$0.774702\pi$
$434$	8.72861	0.418987
$435$	−0.859706	−0.0412197
$436$	2.74087	0.131264
$437$	−3.91727	−0.187388
$438$	−24.5593	−1.17349
$439$	19.2893	0.920626	0.460313	−	0.887757i	$-0.347737\pi$
$439$	19.2893	0.920626	0.460313	+	0.887757i	$0.347737\pi$
$440$	0	0
$441$	16.0309	0.763375
$442$	7.45591	0.354642
$443$	−3.83992	−0.182440	−0.0912202	−	0.995831i	$-0.529077\pi$
$443$	−3.83992	−0.182440	−0.0912202	+	0.995831i	$0.529077\pi$
$444$	11.6988	0.555202
$445$	1.37991	0.0654139
$446$	−5.33715	−0.252721
$447$	−13.2892	−0.628560
$448$	27.5904	1.30353
$449$	8.15697	0.384951	0.192476	−	0.981302i	$-0.438348\pi$
$449$	8.15697	0.384951	0.192476	+	0.981302i	$0.438348\pi$
$450$	35.2915	1.66366
$451$	0	0
$452$	5.27776	0.248245
$453$	−27.1705	−1.27658
$454$	−28.6884	−1.34641
$455$	−3.36507	−0.157757
$456$	25.6564	1.20147
$457$	40.2568	1.88313	0.941566	−	0.336829i	$-0.109354\pi$
$457$	40.2568	1.88313	0.941566	+	0.336829i	$0.109354\pi$
$458$	18.5752	0.867961
$459$	−33.7835	−1.57688
$460$	−0.363908	−0.0169673
$461$	−1.42365	−0.0663062	−0.0331531	−	0.999450i	$-0.510555\pi$
$461$	−1.42365	−0.0663062	−0.0331531	+	0.999450i	$0.510555\pi$
$462$	0	0
$463$	24.7943	1.15229	0.576144	−	0.817348i	$-0.304557\pi$
$463$	24.7943	1.15229	0.576144	+	0.817348i	$0.304557\pi$
$464$	−1.31231	−0.0609226
$465$	4.45219	0.206465
$466$	−11.4898	−0.532254
$467$	0.0628383	0.00290781	0.00145391	−	0.999999i	$-0.499537\pi$
$467$	0.0628383	0.00290781	0.00145391	+	0.999999i	$0.499537\pi$
$468$	3.89840	0.180204
$469$	31.2134	1.44130
$470$	2.33097	0.107520
$471$	−56.3887	−2.59826
$472$	4.40170	0.202605
$473$	0	0
$474$	61.2132	2.81161
$475$	12.7761	0.586209
$476$	−4.37924	−0.200722
$477$	53.9772	2.47145
$478$	14.8762	0.680420
$479$	21.8692	0.999230	0.499615	−	0.866248i	$-0.333475\pi$
$479$	21.8692	0.999230	0.499615	+	0.866248i	$0.333475\pi$
$480$	4.37668	0.199767
$481$	−16.1473	−0.736253
$482$	−23.6691	−1.07810
$483$	−13.0825	−0.595274
$484$	0	0
$485$	0.737115	0.0334707
$486$	2.46679	0.111896
$487$	−16.1668	−0.732588	−0.366294	−	0.930499i	$-0.619374\pi$
$487$	−16.1668	−0.732588	−0.366294	+	0.930499i	$0.619374\pi$
$488$	3.03307	0.137301
$489$	−55.9072	−2.52821
$490$	−2.21478	−0.100053
$491$	31.0701	1.40217	0.701086	−	0.713077i	$-0.252699\pi$
$491$	31.0701	1.40217	0.701086	+	0.713077i	$0.252699\pi$
$492$	−8.45594	−0.381223
$493$	1.54423	0.0695487
$494$	−5.79764	−0.260848
$495$	0	0
$496$	6.79611	0.305154
$497$	27.1600	1.21829
$498$	−32.1196	−1.43932
$499$	1.65977	0.0743014	0.0371507	−	0.999310i	$-0.488172\pi$
$499$	1.65977	0.0743014	0.0371507	+	0.999310i	$0.488172\pi$
$500$	2.48897	0.111310
$501$	−17.2532	−0.770817
$502$	22.0244	0.982995
$503$	10.2060	0.455063	0.227531	−	0.973771i	$-0.426935\pi$
$503$	10.2060	0.455063	0.227531	+	0.973771i	$0.426935\pi$
$504$	57.4544	2.55922
$505$	−1.16002	−0.0516201
$506$	0	0
$507$	31.2035	1.38579
$508$	−0.236883	−0.0105100
$509$	32.2331	1.42871	0.714353	−	0.699785i	$-0.246721\pi$
$509$	32.2331	1.42871	0.714353	+	0.699785i	$0.246721\pi$
$510$	9.17620	0.406329
$511$	−19.9100	−0.880768
$512$	25.2652	1.11658
$513$	26.2697	1.15984
$514$	−4.11050	−0.181306
$515$	−4.90143	−0.215983
$516$	6.84127	0.301170
$517$	0	0
$518$	−38.9613	−1.71186
$519$	56.0540	2.46050
$520$	−3.28974	−0.144265
$521$	17.1753	0.752462	0.376231	−	0.926526i	$-0.377220\pi$
$521$	17.1753	0.752462	0.376231	+	0.926526i	$0.377220\pi$
$522$	−3.31691	−0.145177
$523$	8.18996	0.358122	0.179061	−	0.983838i	$-0.442694\pi$
$523$	8.18996	0.358122	0.179061	+	0.983838i	$0.442694\pi$
$524$	3.50445	0.153093
$525$	42.6684	1.86220
$526$	−19.6277	−0.855807
$527$	−7.99716	−0.348362
$528$	0	0
$529$	−21.0473	−0.915098
$530$	−7.45733	−0.323926
$531$	8.86062	0.384518
$532$	3.40525	0.147636
$533$	11.6713	0.505539
$534$	7.93991	0.343593
$535$	2.58678	0.111836
$536$	30.5147	1.31804
$537$	25.4262	1.09722
$538$	−27.4864	−1.18502
$539$	0	0
$540$	2.44042	0.105019
$541$	−3.58545	−0.154151	−0.0770754	−	0.997025i	$-0.524558\pi$
$541$	−3.58545	−0.154151	−0.0770754	+	0.997025i	$0.524558\pi$
$542$	−2.94761	−0.126611
$543$	49.3422	2.11747
$544$	−7.86153	−0.337060
$545$	−4.65593	−0.199438
$546$	−19.3624	−0.828633
$547$	−17.6474	−0.754549	−0.377275	−	0.926101i	$-0.623139\pi$
$547$	−17.6474	−0.754549	−0.377275	+	0.926101i	$0.623139\pi$
$548$	−6.16325	−0.263281
$549$	6.10557	0.260579
$550$	0	0
$551$	−1.20078	−0.0511549
$552$	−12.7897	−0.544364
$553$	49.6250	2.11027
$554$	−30.0044	−1.27477
$555$	−19.8729	−0.843558
$556$	−4.87416	−0.206710
$557$	24.6369	1.04390	0.521950	−	0.852976i	$-0.325205\pi$
$557$	24.6369	1.04390	0.521950	+	0.852976i	$0.325205\pi$
$558$	17.1774	0.727177
$559$	−9.44265	−0.399382
$560$	−6.32183	−0.267146
$561$	0	0
$562$	−36.0791	−1.52190
$563$	5.68951	0.239784	0.119892	−	0.992787i	$-0.461745\pi$
$563$	5.68951	0.239784	0.119892	+	0.992787i	$0.461745\pi$
$564$	−3.26488	−0.137476
$565$	−8.96537	−0.377176
$566$	3.35329	0.140949
$567$	30.9051	1.29789
$568$	26.5520	1.11410
$569$	−32.9764	−1.38244	−0.691220	−	0.722644i	$-0.742927\pi$
$569$	−32.9764	−1.38244	−0.691220	+	0.722644i	$0.742927\pi$
$570$	−7.13531	−0.298865
$571$	−2.68089	−0.112192	−0.0560958	−	0.998425i	$-0.517865\pi$
$571$	−2.68089	−0.112192	−0.0560958	+	0.998425i	$0.517865\pi$
$572$	0	0
$573$	73.1358	3.05529
$574$	28.1613	1.17543
$575$	−6.36886	−0.265600
$576$	54.2964	2.26235
$577$	−32.3457	−1.34657	−0.673284	−	0.739384i	$-0.735117\pi$
$577$	−32.3457	−1.34657	−0.673284	+	0.739384i	$0.735117\pi$
$578$	5.07768	0.211204
$579$	49.3987	2.05294
$580$	−0.111550	−0.00463188
$581$	−26.0391	−1.08028
$582$	4.24131	0.175808
$583$	0	0
$584$	−19.4644	−0.805441
$585$	−6.62225	−0.273796
$586$	14.9745	0.618590
$587$	−9.89737	−0.408508	−0.204254	−	0.978918i	$-0.565477\pi$
$587$	−9.89737	−0.408508	−0.204254	+	0.978918i	$0.565477\pi$
$588$	3.10213	0.127930
$589$	6.21850	0.256229
$590$	−1.22416	−0.0503978
$591$	−54.1726	−2.22836
$592$	−30.3353	−1.24677
$593$	30.1026	1.23617	0.618083	−	0.786113i	$-0.287910\pi$
$593$	30.1026	1.23617	0.618083	+	0.786113i	$0.287910\pi$
$594$	0	0
$595$	7.43906	0.304972
$596$	−1.72433	−0.0706315
$597$	36.9403	1.51187
$598$	2.89010	0.118185
$599$	38.7530	1.58341	0.791703	−	0.610907i	$-0.209195\pi$
$599$	38.7530	1.58341	0.791703	+	0.610907i	$0.209195\pi$
$600$	41.7134	1.70294
$601$	24.8790	1.01483	0.507417	−	0.861701i	$-0.330600\pi$
$601$	24.8790	1.01483	0.507417	+	0.861701i	$0.330600\pi$
$602$	−22.7839	−0.928602
$603$	61.4261	2.50147
$604$	−3.52548	−0.143450
$605$	0	0
$606$	−6.67466	−0.271140
$607$	−11.9877	−0.486567	−0.243283	−	0.969955i	$-0.578224\pi$
$607$	−11.9877	−0.486567	−0.243283	+	0.969955i	$0.578224\pi$
$608$	6.11304	0.247916
$609$	−4.01024	−0.162503
$610$	−0.843527	−0.0341534
$611$	4.50634	0.182307
$612$	−8.61809	−0.348366
$613$	−19.9359	−0.805205	−0.402603	−	0.915375i	$-0.631894\pi$
$613$	−19.9359	−0.805205	−0.402603	+	0.915375i	$0.631894\pi$
$614$	30.2375	1.22029
$615$	14.3642	0.579220
$616$	0	0
$617$	21.7075	0.873911	0.436956	−	0.899483i	$-0.356057\pi$
$617$	21.7075	0.873911	0.436956	+	0.899483i	$0.356057\pi$
$618$	−28.2025	−1.13447
$619$	41.3172	1.66068	0.830339	−	0.557258i	$-0.188147\pi$
$619$	41.3172	1.66068	0.830339	+	0.557258i	$0.188147\pi$
$620$	0.577690	0.0232006
$621$	−13.0954	−0.525499
$622$	−7.82812	−0.313879
$623$	6.43681	0.257885
$624$	−15.0756	−0.603506
$625$	18.5601	0.742404
$626$	28.4681	1.13781
$627$	0	0
$628$	−7.31667	−0.291967
$629$	35.6964	1.42331
$630$	−15.9786	−0.636604
$631$	−11.0153	−0.438511	−0.219255	−	0.975667i	$-0.570363\pi$
$631$	−11.0153	−0.438511	−0.219255	+	0.975667i	$0.570363\pi$
$632$	48.5142	1.92979
$633$	−52.6479	−2.09257
$634$	19.4859	0.773883
$635$	0.402396	0.0159686
$636$	10.4451	0.414175
$637$	−4.28170	−0.169647
$638$	0	0
$639$	53.4492	2.11442
$640$	−4.60060	−0.181855
$641$	32.1277	1.26897	0.634483	−	0.772937i	$-0.281213\pi$
$641$	32.1277	1.26897	0.634483	+	0.772937i	$0.281213\pi$
$642$	14.8842	0.587432
$643$	38.6253	1.52323	0.761617	−	0.648028i	$-0.224406\pi$
$643$	38.6253	1.52323	0.761617	+	0.648028i	$0.224406\pi$
$644$	−1.69751	−0.0668912
$645$	−11.6213	−0.457590
$646$	12.8167	0.504266
$647$	−37.3699	−1.46916	−0.734581	−	0.678520i	$-0.762621\pi$
$647$	−37.3699	−1.46916	−0.734581	+	0.678520i	$0.762621\pi$
$648$	30.2133	1.18689
$649$	0	0
$650$	−9.42605	−0.369720
$651$	20.7679	0.813960
$652$	−7.25419	−0.284096
$653$	−29.2167	−1.14334	−0.571669	−	0.820484i	$-0.693704\pi$
$653$	−29.2167	−1.14334	−0.571669	+	0.820484i	$0.693704\pi$
$654$	−26.7899	−1.04757
$655$	−5.95305	−0.232605
$656$	21.9264	0.856084
$657$	−39.1817	−1.52863
$658$	10.8732	0.423882
$659$	3.60156	0.140297	0.0701484	−	0.997537i	$-0.477653\pi$
$659$	3.60156	0.140297	0.0701484	+	0.997537i	$0.477653\pi$
$660$	0	0
$661$	−34.8298	−1.35472	−0.677361	−	0.735651i	$-0.736876\pi$
$661$	−34.8298	−1.35472	−0.677361	+	0.735651i	$0.736876\pi$
$662$	−13.9314	−0.541460
$663$	17.7398	0.688957
$664$	−25.4563	−0.987894
$665$	−5.78453	−0.224315
$666$	−76.6735	−2.97104
$667$	0.598584	0.0231773
$668$	−2.23868	−0.0866170
$669$	−12.6987	−0.490958
$670$	−8.48645	−0.327860
$671$	0	0
$672$	20.4157	0.787553
$673$	−43.0242	−1.65846	−0.829231	−	0.558906i	$-0.811221\pi$
$673$	−43.0242	−1.65846	−0.829231	+	0.558906i	$0.811221\pi$
$674$	42.0470	1.61959
$675$	42.7104	1.64393
$676$	4.04878	0.155722
$677$	−9.79062	−0.376284	−0.188142	−	0.982142i	$-0.560247\pi$
$677$	−9.79062	−0.376284	−0.188142	+	0.982142i	$0.560247\pi$
$678$	−51.5862	−1.98116
$679$	3.43839	0.131953
$680$	7.27255	0.278890
$681$	−68.2581	−2.61566
$682$	0	0
$683$	−11.4892	−0.439624	−0.219812	−	0.975542i	$-0.570544\pi$
$683$	−11.4892	−0.439624	−0.219812	+	0.975542i	$0.570544\pi$
$684$	6.70134	0.256232
$685$	10.4696	0.400022
$686$	17.2122	0.657165
$687$	44.1958	1.68618
$688$	−17.7396	−0.676315
$689$	−14.4168	−0.549237
$690$	3.55693	0.135410
$691$	−20.2087	−0.768774	−0.384387	−	0.923172i	$-0.625587\pi$
$691$	−20.2087	−0.768774	−0.384387	+	0.923172i	$0.625587\pi$
$692$	7.27324	0.276487
$693$	0	0
$694$	29.7550	1.12949
$695$	8.27978	0.314070
$696$	−3.92048	−0.148605
$697$	−25.8014	−0.977298
$698$	−13.2605	−0.501918
$699$	−27.3376	−1.03400
$700$	5.53641	0.209256
$701$	−39.2874	−1.48387	−0.741933	−	0.670474i	$-0.766091\pi$
$701$	−39.2874	−1.48387	−0.741933	+	0.670474i	$0.766091\pi$
$702$	−19.3814	−0.731505
$703$	−27.7571	−1.04688
$704$	0	0
$705$	5.54608	0.208877
$706$	22.2728	0.838248
$707$	−5.41109	−0.203505
$708$	1.71461	0.0644391
$709$	2.78628	0.104641	0.0523204	−	0.998630i	$-0.483338\pi$
$709$	2.78628	0.104641	0.0523204	+	0.998630i	$0.483338\pi$
$710$	−7.38438	−0.277131
$711$	97.6590	3.66250
$712$	6.29273	0.235830
$713$	−3.09991	−0.116092
$714$	42.8039	1.60190
$715$	0	0
$716$	3.29915	0.123295
$717$	35.3948	1.32184
$718$	−29.1726	−1.08871
$719$	−3.93659	−0.146810	−0.0734049	−	0.997302i	$-0.523387\pi$
$719$	−3.93659	−0.146810	−0.0734049	+	0.997302i	$0.523387\pi$
$720$	−12.4410	−0.463649
$721$	−22.8635	−0.851481
$722$	14.1307	0.525889
$723$	−56.3158	−2.09441
$724$	6.40235	0.237941
$725$	−1.95228	−0.0725057
$726$	0	0
$727$	−28.3390	−1.05103	−0.525517	−	0.850783i	$-0.676128\pi$
$727$	−28.3390	−1.05103	−0.525517	+	0.850783i	$0.676128\pi$
$728$	−15.3455	−0.568744
$729$	−24.0146	−0.889431
$730$	5.41323	0.200353
$731$	20.8746	0.772076
$732$	1.18149	0.0436690
$733$	23.1028	0.853320	0.426660	−	0.904412i	$-0.359690\pi$
$733$	23.1028	0.853320	0.426660	+	0.904412i	$0.359690\pi$
$734$	−17.2401	−0.636345
$735$	−5.26961	−0.194373
$736$	−3.04733	−0.112326
$737$	0	0
$738$	55.4198	2.04003
$739$	14.0850	0.518125	0.259063	−	0.965861i	$-0.416586\pi$
$739$	14.0850	0.518125	0.259063	+	0.965861i	$0.416586\pi$
$740$	−2.57859	−0.0947909
$741$	−13.7943	−0.506746
$742$	−34.7859	−1.27703
$743$	37.1528	1.36300	0.681502	−	0.731816i	$-0.261327\pi$
$743$	37.1528	1.36300	0.681502	+	0.731816i	$0.261327\pi$
$744$	20.3031	0.744347
$745$	2.92914	0.107316
$746$	20.4836	0.749960
$747$	−51.2434	−1.87490
$748$	0	0
$749$	12.0665	0.440899
$750$	−24.3278	−0.888326
$751$	25.0981	0.915841	0.457921	−	0.888993i	$-0.348594\pi$
$751$	25.0981	0.915841	0.457921	+	0.888993i	$0.348594\pi$
$752$	8.46590	0.308720
$753$	52.4025	1.90965
$754$	0.885917	0.0322632
$755$	5.98877	0.217954
$756$	11.3837	0.414022
$757$	25.9479	0.943093	0.471547	−	0.881841i	$-0.343696\pi$
$757$	25.9479	0.943093	0.471547	+	0.881841i	$0.343696\pi$
$758$	34.6752	1.25946
$759$	0	0
$760$	−5.65506	−0.205130
$761$	−10.3967	−0.376881	−0.188440	−	0.982085i	$-0.560343\pi$
$761$	−10.3967	−0.376881	−0.188440	+	0.982085i	$0.560343\pi$
$762$	2.31536	0.0838766
$763$	−21.7184	−0.786258
$764$	9.48967	0.343324
$765$	14.6396	0.529297
$766$	−42.7731	−1.54546
$767$	−2.36659	−0.0854527
$768$	27.1980	0.981423
$769$	16.0867	0.580101	0.290051	−	0.957011i	$-0.406328\pi$
$769$	16.0867	0.580101	0.290051	+	0.957011i	$0.406328\pi$
$770$	0	0
$771$	−9.78008	−0.352221
$772$	6.40969	0.230690
$773$	36.2302	1.30311	0.651555	−	0.758601i	$-0.274117\pi$
$773$	36.2302	1.30311	0.651555	+	0.758601i	$0.274117\pi$
$774$	−44.8374	−1.61165
$775$	10.1103	0.363173
$776$	3.36143	0.120668
$777$	−92.7004	−3.32561
$778$	−38.5718	−1.38287
$779$	20.0629	0.718828
$780$	−1.28147	−0.0458839
$781$	0	0
$782$	−6.38908	−0.228473
$783$	−4.01419	−0.143455
$784$	−8.04389	−0.287282
$785$	12.4289	0.443606
$786$	−34.2535	−1.22178
$787$	31.4524	1.12116	0.560578	−	0.828101i	$-0.310579\pi$
$787$	31.4524	1.12116	0.560578	+	0.828101i	$0.310579\pi$
$788$	−7.02912	−0.250402
$789$	−46.7000	−1.66256
$790$	−13.4923	−0.480034
$791$	−41.8205	−1.48696
$792$	0	0
$793$	−1.63074	−0.0579094
$794$	18.3816	0.652337
$795$	−17.7432	−0.629286
$796$	4.79316	0.169889
$797$	−18.0974	−0.641043	−0.320522	−	0.947241i	$-0.603858\pi$
$797$	−18.0974	−0.641043	−0.320522	+	0.947241i	$0.603858\pi$
$798$	−33.2838	−1.17823
$799$	−9.96204	−0.352432
$800$	9.93884	0.351391
$801$	12.6673	0.447576
$802$	11.6692	0.412053
$803$	0	0
$804$	11.8865	0.419206
$805$	2.88357	0.101633
$806$	−4.58793	−0.161603
$807$	−65.3983	−2.30213
$808$	−5.28997	−0.186100
$809$	38.9016	1.36771	0.683854	−	0.729618i	$-0.260302\pi$
$809$	38.9016	1.36771	0.683854	+	0.729618i	$0.260302\pi$
$810$	−8.40262	−0.295238
$811$	−1.40443	−0.0493163	−0.0246581	−	0.999696i	$-0.507850\pi$
$811$	−1.40443	−0.0493163	−0.0246581	+	0.999696i	$0.507850\pi$
$812$	−0.520345	−0.0182605
$813$	−7.01322	−0.245964
$814$	0	0
$815$	12.3228	0.431647
$816$	33.3272	1.16668
$817$	−16.2319	−0.567881
$818$	40.9551	1.43196
$819$	−30.8906	−1.07940
$820$	1.86381	0.0650871
$821$	25.8930	0.903672	0.451836	−	0.892101i	$-0.350769\pi$
$821$	25.8930	0.903672	0.451836	+	0.892101i	$0.350769\pi$
$822$	60.2413	2.10116
$823$	−14.4158	−0.502504	−0.251252	−	0.967922i	$-0.580842\pi$
$823$	−14.4158	−0.502504	−0.251252	+	0.967922i	$0.580842\pi$
$824$	−22.3517	−0.778659
$825$	0	0
$826$	−5.71028	−0.198686
$827$	−40.0199	−1.39163	−0.695814	−	0.718222i	$-0.744956\pi$
$827$	−40.0199	−1.39163	−0.695814	+	0.718222i	$0.744956\pi$
$828$	−3.34060	−0.116094
$829$	36.7816	1.27748	0.638738	−	0.769424i	$-0.279457\pi$
$829$	36.7816	1.27748	0.638738	+	0.769424i	$0.279457\pi$
$830$	7.07964	0.245738
$831$	−71.3894	−2.47647
$832$	−14.5021	−0.502769
$833$	9.46545	0.327958
$834$	47.6413	1.64968
$835$	3.80286	0.131603
$836$	0	0
$837$	20.7884	0.718552
$838$	21.3048	0.735962
$839$	−31.8168	−1.09844	−0.549219	−	0.835678i	$-0.685075\pi$
$839$	−31.8168	−1.09844	−0.549219	+	0.835678i	$0.685075\pi$
$840$	−18.8862	−0.651636
$841$	−28.8165	−0.993673
$842$	−37.8992	−1.30609
$843$	−85.8427	−2.95658
$844$	−6.83128	−0.235142
$845$	−6.87770	−0.236600
$846$	21.3978	0.735673
$847$	0	0
$848$	−27.0844	−0.930082
$849$	7.97846	0.273820
$850$	20.8379	0.714735
$851$	13.8368	0.474321
$852$	10.3429	0.354343
$853$	38.9963	1.33521	0.667604	−	0.744516i	$-0.267320\pi$
$853$	38.9963	1.33521	0.667604	+	0.744516i	$0.267320\pi$
$854$	−3.93477	−0.134645
$855$	−11.3836	−0.389312
$856$	11.7964	0.403192
$857$	−34.9476	−1.19379	−0.596894	−	0.802320i	$-0.703599\pi$
$857$	−34.9476	−1.19379	−0.596894	+	0.802320i	$0.703599\pi$
$858$	0	0
$859$	−16.2737	−0.555252	−0.277626	−	0.960689i	$-0.589548\pi$
$859$	−16.2737	−0.555252	−0.277626	+	0.960689i	$0.589548\pi$
$860$	−1.50792	−0.0514195
$861$	67.0041	2.28349
$862$	−35.6256	−1.21341
$863$	34.3784	1.17025	0.585126	−	0.810942i	$-0.301045\pi$
$863$	34.3784	1.17025	0.585126	+	0.810942i	$0.301045\pi$
$864$	20.4358	0.695241
$865$	−12.3551	−0.420087
$866$	40.1030	1.36276
$867$	12.0813	0.410302
$868$	2.69473	0.0914650
$869$	0	0
$870$	1.09032	0.0369654
$871$	−16.4064	−0.555908
$872$	−21.2322	−0.719014
$873$	6.76655	0.229013
$874$	4.96808	0.168048
$875$	−19.7223	−0.666737
$876$	−7.58204	−0.256173
$877$	34.6735	1.17084	0.585420	−	0.810730i	$-0.300930\pi$
$877$	34.6735	1.17084	0.585420	+	0.810730i	$0.300930\pi$
$878$	−24.4636	−0.825608
$879$	35.6287	1.20173
$880$	0	0
$881$	40.3362	1.35896	0.679480	−	0.733694i	$-0.262205\pi$
$881$	40.3362	1.35896	0.679480	+	0.733694i	$0.262205\pi$
$882$	−20.3312	−0.684587
$883$	14.5841	0.490793	0.245396	−	0.969423i	$-0.421082\pi$
$883$	14.5841	0.490793	0.245396	+	0.969423i	$0.421082\pi$
$884$	2.30181	0.0774184
$885$	−2.91263	−0.0979070
$886$	4.86999	0.163610
$887$	−4.29565	−0.144234	−0.0721169	−	0.997396i	$-0.522975\pi$
$887$	−4.29565	−0.144234	−0.0721169	+	0.997396i	$0.522975\pi$
$888$	−90.6255	−3.04119
$889$	1.87704	0.0629539
$890$	−1.75007	−0.0586625
$891$	0	0
$892$	−1.64770	−0.0551692
$893$	7.74637	0.259223
$894$	16.8541	0.563685
$895$	−5.60430	−0.187331
$896$	−21.4603	−0.716937
$897$	6.87641	0.229597
$898$	−10.3451	−0.345220
$899$	−0.950229	−0.0316919
$900$	10.8953	0.363177
$901$	31.8709	1.06177
$902$	0	0
$903$	−54.2096	−1.80398
$904$	−40.8844	−1.35979
$905$	−10.8757	−0.361522
$906$	34.4590	1.14482
$907$	10.4319	0.346386	0.173193	−	0.984888i	$-0.444591\pi$
$907$	10.4319	0.346386	0.173193	+	0.984888i	$0.444591\pi$
$908$	−8.85677	−0.293922
$909$	−10.6487	−0.353195
$910$	4.26775	0.141475
$911$	−42.0765	−1.39406	−0.697028	−	0.717044i	$-0.745495\pi$
$911$	−42.0765	−1.39406	−0.697028	+	0.717044i	$0.745495\pi$
$912$	−25.9148	−0.858126
$913$	0	0
$914$	−51.0557	−1.68877
$915$	−2.00700	−0.0663494
$916$	5.73459	0.189476
$917$	−27.7690	−0.917012
$918$	42.8460	1.41413
$919$	25.2181	0.831869	0.415935	−	0.909394i	$-0.363454\pi$
$919$	25.2181	0.831869	0.415935	+	0.909394i	$0.363454\pi$
$920$	2.81903	0.0929406
$921$	71.9440	2.37064
$922$	1.80555	0.0594627
$923$	−14.2758	−0.469894
$924$	0	0
$925$	−45.1287	−1.48382
$926$	−31.4454	−1.03336
$927$	−44.9940	−1.47780
$928$	−0.934113	−0.0306638
$929$	−3.36755	−0.110486	−0.0552429	−	0.998473i	$-0.517593\pi$
$929$	−3.36755	−0.110486	−0.0552429	+	0.998473i	$0.517593\pi$
$930$	−5.64649	−0.185156
$931$	−7.36023	−0.241222
$932$	−3.54716	−0.116191
$933$	−18.6254	−0.609768
$934$	−0.0796948	−0.00260769
$935$	0	0
$936$	−30.1991	−0.987090
$937$	9.64258	0.315009	0.157505	−	0.987518i	$-0.449655\pi$
$937$	9.64258	0.315009	0.157505	+	0.987518i	$0.449655\pi$
$938$	−39.5864	−1.29254
$939$	67.7340	2.21042
$940$	0.719626	0.0234716
$941$	−17.8398	−0.581560	−0.290780	−	0.956790i	$-0.593915\pi$
$941$	−17.8398	−0.581560	−0.290780	+	0.956790i	$0.593915\pi$
$942$	71.5151	2.33009
$943$	−10.0013	−0.325687
$944$	−4.44603	−0.144706
$945$	−19.3376	−0.629053
$946$	0	0
$947$	−14.6075	−0.474680	−0.237340	−	0.971427i	$-0.576276\pi$
$947$	−14.6075	−0.474680	−0.237340	+	0.971427i	$0.576276\pi$
$948$	18.8979	0.613776
$949$	10.4651	0.339711
$950$	−16.2033	−0.525706
$951$	46.3626	1.50341
$952$	33.9240	1.09948
$953$	−37.2704	−1.20731	−0.603653	−	0.797247i	$-0.706289\pi$
$953$	−37.2704	−1.20731	−0.603653	+	0.797247i	$0.706289\pi$
$954$	−68.4567	−2.21637
$955$	−16.1202	−0.521637
$956$	4.59262	0.148536
$957$	0	0
$958$	−27.7357	−0.896098
$959$	48.8371	1.57703
$960$	−17.8481	−0.576045
$961$	−26.0790	−0.841259
$962$	20.4788	0.660263
$963$	23.7461	0.765207
$964$	−7.30721	−0.235349
$965$	−10.8882	−0.350503
$966$	16.5919	0.533835
$967$	−2.58777	−0.0832172	−0.0416086	−	0.999134i	$-0.513248\pi$
$967$	−2.58777	−0.0832172	−0.0416086	+	0.999134i	$0.513248\pi$
$968$	0	0
$969$	30.4947	0.979630
$970$	−0.934847	−0.0300161
$971$	6.62957	0.212753	0.106376	−	0.994326i	$-0.466075\pi$
$971$	6.62957	0.212753	0.106376	+	0.994326i	$0.466075\pi$
$972$	0.761556	0.0244269
$973$	38.6224	1.23818
$974$	20.5036	0.656977
$975$	−22.4273	−0.718250
$976$	−3.06362	−0.0980641
$977$	−2.76206	−0.0883660	−0.0441830	−	0.999023i	$-0.514068\pi$
$977$	−2.76206	−0.0883660	−0.0441830	+	0.999023i	$0.514068\pi$
$978$	70.9043	2.26727
$979$	0	0
$980$	−0.683754	−0.0218417
$981$	−42.7405	−1.36460
$982$	−39.4046	−1.25745
$983$	34.1530	1.08931	0.544656	−	0.838660i	$-0.316660\pi$
$983$	34.1530	1.08931	0.544656	+	0.838660i	$0.316660\pi$
$984$	65.5043	2.08820
$985$	11.9404	0.380454
$986$	−1.95847	−0.0623705
$987$	25.8706	0.823470
$988$	−1.78987	−0.0569432
$989$	8.09154	0.257296
$990$	0	0
$991$	−38.4776	−1.22228	−0.611141	−	0.791522i	$-0.709289\pi$
$991$	−38.4776	−1.22228	−0.611141	+	0.791522i	$0.709289\pi$
$992$	4.83752	0.153591
$993$	−33.1470	−1.05189
$994$	−34.4457	−1.09255
$995$	−8.14219	−0.258125
$996$	−9.91609	−0.314203
$997$	45.9695	1.45587	0.727934	−	0.685648i	$-0.240481\pi$
$997$	45.9695	1.45587	0.727934	+	0.685648i	$0.240481\pi$
$998$	−2.10500	−0.0666327
$999$	−92.7917	−2.93580

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.r.1.14	yes	50
11.10	odd	2		7381.2.a.q.1.37	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7381.2.a.q.1.37	✓	50	11.10	odd	2
7381.2.a.r.1.14	yes	50	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:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.26825 q^{2} -3.01754 q^{3} -0.391539 q^{4} +0.665111 q^{5} +3.82700 q^{6} +3.10252 q^{7} +3.03307 q^{8} +6.10557 q^{9} +O(q^{10})\)	\(q-1.26825 q^{2} -3.01754 q^{3} -0.391539 q^{4} +0.665111 q^{5} +3.82700 q^{6} +3.10252 q^{7} +3.03307 q^{8} +6.10557 q^{9} -0.843527 q^{10} +1.18149 q^{12} -1.63074 q^{13} -3.93477 q^{14} -2.00700 q^{15} -3.06362 q^{16} +3.60504 q^{17} -7.74340 q^{18} -2.80324 q^{19} -0.260417 q^{20} -9.36198 q^{21} +1.39741 q^{23} -9.15243 q^{24} -4.55763 q^{25} +2.06819 q^{26} -9.37120 q^{27} -1.21476 q^{28} +0.428354 q^{29} +2.54538 q^{30} -2.21833 q^{31} -2.18070 q^{32} -4.57210 q^{34} +2.06352 q^{35} -2.39057 q^{36} +9.90180 q^{37} +3.55521 q^{38} +4.92084 q^{39} +2.01733 q^{40} -7.15704 q^{41} +11.8733 q^{42} +5.79040 q^{43} +4.06088 q^{45} -1.77226 q^{46} -2.76336 q^{47} +9.24461 q^{48} +2.62562 q^{49} +5.78022 q^{50} -10.8784 q^{51} +0.638499 q^{52} +8.84065 q^{53} +11.8850 q^{54} +9.41016 q^{56} +8.45890 q^{57} -0.543260 q^{58} +1.45124 q^{59} +0.785819 q^{60} +1.00000 q^{61} +2.81340 q^{62} +18.9426 q^{63} +8.89292 q^{64} -1.08462 q^{65} +10.0607 q^{67} -1.41151 q^{68} -4.21674 q^{69} -2.61706 q^{70} +8.75417 q^{71} +18.5186 q^{72} -6.41738 q^{73} -12.5580 q^{74} +13.7528 q^{75} +1.09758 q^{76} -6.24086 q^{78} +15.9951 q^{79} -2.03765 q^{80} +9.96129 q^{81} +9.07692 q^{82} -8.39290 q^{83} +3.66558 q^{84} +2.39775 q^{85} -7.34368 q^{86} -1.29258 q^{87} +2.07471 q^{89} -5.15022 q^{90} -5.05941 q^{91} -0.547139 q^{92} +6.69390 q^{93} +3.50464 q^{94} -1.86446 q^{95} +6.58037 q^{96} +1.10826 q^{97} -3.32994 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 10 q^{2} - 2 q^{3} + 50 q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 30 q^{8} + 48 q^{9}+O(q^{10}) \) 50 * q + 10 * q^2 - 2 * q^3 + 50 * q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 30 * q^8 + 48 * q^9	\( 50 q + 10 q^{2} - 2 q^{3} + 50 q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 30 q^{8} + 48 q^{9} + 12 q^{10} - 14 q^{12} + 8 q^{13} - 2 q^{14} - 16 q^{15} + 42 q^{16} + 22 q^{17} + 32 q^{19} - 8 q^{20} + 24 q^{21} + 12 q^{23} - 8 q^{24} + 40 q^{25} + 10 q^{26} - 8 q^{27} + 72 q^{28} + 56 q^{29} + 24 q^{30} + 10 q^{31} + 70 q^{32} - 32 q^{34} + 70 q^{35} + 34 q^{36} - 8 q^{37} - 14 q^{38} + 96 q^{39} - 54 q^{40} + 56 q^{41} - 8 q^{42} + 44 q^{43} - 24 q^{45} - 4 q^{46} - 4 q^{47} - 28 q^{48} + 38 q^{49} + 120 q^{50} + 76 q^{51} + 24 q^{52} + 4 q^{53} + 48 q^{54} - 18 q^{56} + 8 q^{57} + 28 q^{58} + 12 q^{59} - 60 q^{60} + 50 q^{61} + 8 q^{62} + 30 q^{63} + 10 q^{64} + 64 q^{65} + 18 q^{67} - 22 q^{68} - 8 q^{69} + 34 q^{70} + 12 q^{71} + 104 q^{72} - 16 q^{73} + 84 q^{74} - 26 q^{75} + 64 q^{76} + 40 q^{78} + 78 q^{79} - 36 q^{80} + 34 q^{81} + 54 q^{82} + 68 q^{83} - 78 q^{84} - 4 q^{85} + 36 q^{86} + 48 q^{87} + 26 q^{89} - 20 q^{90} + 32 q^{92} + 22 q^{93} + 156 q^{94} + 100 q^{95} - 4 q^{96} - 14 q^{97} + 70 q^{98}+O(q^{100}) \) 50 * q + 10 * q^2 - 2 * q^3 + 50 * q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 30 * q^8 + 48 * q^9 + 12 * q^10 - 14 * q^12 + 8 * q^13 - 2 * q^14 - 16 * q^15 + 42 * q^16 + 22 * q^17 + 32 * q^19 - 8 * q^20 + 24 * q^21 + 12 * q^23 - 8 * q^24 + 40 * q^25 + 10 * q^26 - 8 * q^27 + 72 * q^28 + 56 * q^29 + 24 * q^30 + 10 * q^31 + 70 * q^32 - 32 * q^34 + 70 * q^35 + 34 * q^36 - 8 * q^37 - 14 * q^38 + 96 * q^39 - 54 * q^40 + 56 * q^41 - 8 * q^42 + 44 * q^43 - 24 * q^45 - 4 * q^46 - 4 * q^47 - 28 * q^48 + 38 * q^49 + 120 * q^50 + 76 * q^51 + 24 * q^52 + 4 * q^53 + 48 * q^54 - 18 * q^56 + 8 * q^57 + 28 * q^58 + 12 * q^59 - 60 * q^60 + 50 * q^61 + 8 * q^62 + 30 * q^63 + 10 * q^64 + 64 * q^65 + 18 * q^67 - 22 * q^68 - 8 * q^69 + 34 * q^70 + 12 * q^71 + 104 * q^72 - 16 * q^73 + 84 * q^74 - 26 * q^75 + 64 * q^76 + 40 * q^78 + 78 * q^79 - 36 * q^80 + 34 * q^81 + 54 * q^82 + 68 * q^83 - 78 * q^84 - 4 * q^85 + 36 * q^86 + 48 * q^87 + 26 * q^89 - 20 * q^90 + 32 * q^92 + 22 * q^93 + 156 * q^94 + 100 * q^95 - 4 * q^96 - 14 * q^97 + 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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