LMFDB - Embedded newform 7381.2.a.v.1.8

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:	$64$
Twist minimal:	no (minimal twist has level 671)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-2.30350 q^{2} +2.86548 q^{3} +3.30610 q^{4} +4.11838 q^{5} -6.60062 q^{6} +4.52556 q^{7} -3.00859 q^{8} +5.21098 q^{9} +O(q^{10})$	\(q-2.30350 q^{2} +2.86548 q^{3} +3.30610 q^{4} +4.11838 q^{5} -6.60062 q^{6} +4.52556 q^{7} -3.00859 q^{8} +5.21098 q^{9} -9.48668 q^{10} +9.47356 q^{12} -1.96052 q^{13} -10.4246 q^{14} +11.8011 q^{15} +0.318086 q^{16} -2.11303 q^{17} -12.0035 q^{18} -3.96158 q^{19} +13.6158 q^{20} +12.9679 q^{21} -1.66566 q^{23} -8.62106 q^{24} +11.9611 q^{25} +4.51605 q^{26} +6.33551 q^{27} +14.9620 q^{28} +6.61869 q^{29} -27.1839 q^{30} +2.08928 q^{31} +5.28447 q^{32} +4.86736 q^{34} +18.6380 q^{35} +17.2280 q^{36} +3.99243 q^{37} +9.12549 q^{38} -5.61783 q^{39} -12.3905 q^{40} +5.74572 q^{41} -29.8716 q^{42} -7.08111 q^{43} +21.4608 q^{45} +3.83685 q^{46} -7.77397 q^{47} +0.911470 q^{48} +13.4807 q^{49} -27.5523 q^{50} -6.05485 q^{51} -6.48167 q^{52} -9.16065 q^{53} -14.5938 q^{54} -13.6156 q^{56} -11.3518 q^{57} -15.2461 q^{58} +0.649946 q^{59} +39.0157 q^{60} +1.00000 q^{61} -4.81266 q^{62} +23.5826 q^{63} -12.8089 q^{64} -8.07417 q^{65} -8.85695 q^{67} -6.98589 q^{68} -4.77293 q^{69} -42.9326 q^{70} +12.6093 q^{71} -15.6777 q^{72} -0.780705 q^{73} -9.19654 q^{74} +34.2742 q^{75} -13.0974 q^{76} +12.9407 q^{78} +13.8774 q^{79} +1.31000 q^{80} +2.52135 q^{81} -13.2353 q^{82} -11.0248 q^{83} +42.8732 q^{84} -8.70227 q^{85} +16.3113 q^{86} +18.9657 q^{87} -9.40639 q^{89} -49.4349 q^{90} -8.87246 q^{91} -5.50685 q^{92} +5.98680 q^{93} +17.9073 q^{94} -16.3153 q^{95} +15.1426 q^{96} +1.27722 q^{97} -31.0528 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9} - 4 q^{10} + 41 q^{12} - q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} + 13 q^{17} + 38 q^{18} - q^{19} + 65 q^{20} + q^{21} + 52 q^{23} + 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} - q^{28} + 19 q^{29} - 19 q^{30} + 45 q^{31} - 24 q^{32} - 23 q^{34} + 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} - 6 q^{39} + 84 q^{40} - 12 q^{41} + 28 q^{42} + 5 q^{43} + 71 q^{45} - 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} + 14 q^{50} + 22 q^{51} - 24 q^{52} + 86 q^{53} - 114 q^{54} + 119 q^{56} - 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} + 64 q^{61} + 13 q^{62} - 28 q^{63} + 135 q^{64} - 30 q^{65} + 2 q^{67} + 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} + 48 q^{72} + 8 q^{73} - 27 q^{74} + 107 q^{75} - 82 q^{76} - 13 q^{78} - 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} + 14 q^{83} + 182 q^{84} - 52 q^{85} + 60 q^{86} - 8 q^{87} + 59 q^{89} - 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} + 21 q^{94} - 26 q^{95} - 86 q^{96} - 39 q^{97} - 57 q^{98}+O(q^{100}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9 - 4 * q^10 + 41 * q^12 - q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 + 13 * q^17 + 38 * q^18 - q^19 + 65 * q^20 + q^21 + 52 * q^23 + 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 - q^28 + 19 * q^29 - 19 * q^30 + 45 * q^31 - 24 * q^32 - 23 * q^34 + 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 - 6 * q^39 + 84 * q^40 - 12 * q^41 + 28 * q^42 + 5 * q^43 + 71 * q^45 - 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 + 14 * q^50 + 22 * q^51 - 24 * q^52 + 86 * q^53 - 114 * q^54 + 119 * q^56 - 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 + 64 * q^61 + 13 * q^62 - 28 * q^63 + 135 * q^64 - 30 * q^65 + 2 * q^67 + 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 + 48 * q^72 + 8 * q^73 - 27 * q^74 + 107 * q^75 - 82 * q^76 - 13 * q^78 - 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 + 14 * q^83 + 182 * q^84 - 52 * q^85 + 60 * q^86 - 8 * q^87 + 59 * q^89 - 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 + 21 * q^94 - 26 * q^95 - 86 * q^96 - 39 * q^97 - 57 * 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 $

$2$	−2.30350	−1.62882	−0.814409	−	0.580291i	$-0.802939\pi$
$2$	−2.30350	−1.62882	−0.814409	+	0.580291i	$0.802939\pi$
$3$	2.86548	1.65439	0.827193	−	0.561918i	$-0.189936\pi$
$3$	2.86548	1.65439	0.827193	+	0.561918i	$0.189936\pi$
$4$	3.30610	1.65305
$5$	4.11838	1.84180	0.920898	−	0.389803i	$-0.127457\pi$
$5$	4.11838	1.84180	0.920898	+	0.389803i	$0.127457\pi$
$6$	−6.60062	−2.69469
$7$	4.52556	1.71050	0.855251	−	0.518213i	$-0.173403\pi$
$7$	4.52556	1.71050	0.855251	+	0.518213i	$0.173403\pi$
$8$	−3.00859	−1.06370
$9$	5.21098	1.73699
$10$	−9.48668	−2.99995
$11$	0	0
$11$	0	0
$12$	9.47356	2.73478
$13$	−1.96052	−0.543750	−0.271875	−	0.962333i	$-0.587644\pi$
$13$	−1.96052	−0.543750	−0.271875	+	0.962333i	$0.587644\pi$
$14$	−10.4246	−2.78610
$15$	11.8011	3.04704
$16$	0.318086	0.0795215
$17$	−2.11303	−0.512486	−0.256243	−	0.966612i	$-0.582485\pi$
$17$	−2.11303	−0.512486	−0.256243	+	0.966612i	$0.582485\pi$
$18$	−12.0035	−2.82924
$19$	−3.96158	−0.908850	−0.454425	−	0.890785i	$-0.650155\pi$
$19$	−3.96158	−0.908850	−0.454425	+	0.890785i	$0.650155\pi$
$20$	13.6158	3.04458
$21$	12.9679	2.82983
$22$	0	0
$23$	−1.66566	−0.347315	−0.173658	−	0.984806i	$-0.555559\pi$
$23$	−1.66566	−0.347315	−0.173658	+	0.984806i	$0.555559\pi$
$24$	−8.62106	−1.75977
$25$	11.9611	2.39221
$26$	4.51605	0.885670
$27$	6.33551	1.21927
$28$	14.9620	2.82754
$29$	6.61869	1.22906	0.614530	−	0.788894i	$-0.289346\pi$
$29$	6.61869	1.22906	0.614530	+	0.788894i	$0.289346\pi$
$30$	−27.1839	−4.96308
$31$	2.08928	0.375247	0.187623	−	0.982241i	$-0.439922\pi$
$31$	2.08928	0.375247	0.187623	+	0.982241i	$0.439922\pi$
$32$	5.28447	0.934172
$33$	0	0
$34$	4.86736	0.834746
$35$	18.6380	3.15040
$36$	17.2280	2.87133
$37$	3.99243	0.656351	0.328175	−	0.944617i	$-0.393566\pi$
$37$	3.99243	0.656351	0.328175	+	0.944617i	$0.393566\pi$
$38$	9.12549	1.48035
$39$	−5.61783	−0.899573
$40$	−12.3905	−1.95911
$41$	5.74572	0.897331	0.448665	−	0.893700i	$-0.351899\pi$
$41$	5.74572	0.897331	0.448665	+	0.893700i	$0.351899\pi$
$42$	−29.8716	−4.60928
$43$	−7.08111	−1.07986	−0.539929	−	0.841710i	$-0.681549\pi$
$43$	−7.08111	−1.07986	−0.539929	+	0.841710i	$0.681549\pi$
$44$	0	0
$45$	21.4608	3.19919
$46$	3.83685	0.565713
$47$	−7.77397	−1.13395	−0.566975	−	0.823735i	$-0.691886\pi$
$47$	−7.77397	−1.13395	−0.566975	+	0.823735i	$0.691886\pi$
$48$	0.911470	0.131559
$49$	13.4807	1.92582
$50$	−27.5523	−3.89648
$51$	−6.05485	−0.847849
$52$	−6.48167	−0.898846
$53$	−9.16065	−1.25831	−0.629156	−	0.777279i	$-0.716599\pi$
$53$	−9.16065	−1.25831	−0.629156	+	0.777279i	$0.716599\pi$
$54$	−14.5938	−1.98597
$55$	0	0
$56$	−13.6156	−1.81946
$57$	−11.3518	−1.50359
$58$	−15.2461	−2.00191
$59$	0.649946	0.0846157	0.0423079	−	0.999105i	$-0.486529\pi$
$59$	0.649946	0.0846157	0.0423079	+	0.999105i	$0.486529\pi$
$60$	39.0157	5.03691
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−4.81266	−0.611209
$63$	23.5826	2.97113
$64$	−12.8089	−1.60112
$65$	−8.07417	−1.00148
$66$	0	0
$67$	−8.85695	−1.08205	−0.541024	−	0.841007i	$-0.681963\pi$
$67$	−8.85695	−1.08205	−0.541024	+	0.841007i	$0.681963\pi$
$68$	−6.98589	−0.847164
$69$	−4.77293	−0.574593
$70$	−42.9326	−5.13142
$71$	12.6093	1.49645	0.748223	−	0.663447i	$-0.230907\pi$
$71$	12.6093	1.49645	0.748223	+	0.663447i	$0.230907\pi$
$72$	−15.6777	−1.84763
$73$	−0.780705	−0.0913747	−0.0456873	−	0.998956i	$-0.514548\pi$
$73$	−0.780705	−0.0913747	−0.0456873	+	0.998956i	$0.514548\pi$
$74$	−9.19654	−1.06908
$75$	34.2742	3.95764
$76$	−13.0974	−1.50237
$77$	0	0
$78$	12.9407	1.46524
$79$	13.8774	1.56133	0.780666	−	0.624949i	$-0.214880\pi$
$79$	13.8774	1.56133	0.780666	+	0.624949i	$0.214880\pi$
$80$	1.31000	0.146462
$81$	2.52135	0.280150
$82$	−13.2353	−1.46159
$83$	−11.0248	−1.21013	−0.605066	−	0.796175i	$-0.706853\pi$
$83$	−11.0248	−1.21013	−0.605066	+	0.796175i	$0.706853\pi$
$84$	42.8732	4.67785
$85$	−8.70227	−0.943894
$86$	16.3113	1.75889
$87$	18.9657	2.03334
$88$	0	0
$89$	−9.40639	−0.997076	−0.498538	−	0.866868i	$-0.666130\pi$
$89$	−9.40639	−0.997076	−0.498538	+	0.866868i	$0.666130\pi$
$90$	−49.4349	−5.21089
$91$	−8.87246	−0.930086
$92$	−5.50685	−0.574129
$93$	5.98680	0.620803
$94$	17.9073	1.84700
$95$	−16.3153	−1.67392
$96$	15.1426	1.54548
$97$	1.27722	0.129682	0.0648411	−	0.997896i	$-0.479346\pi$
$97$	1.27722	0.129682	0.0648411	+	0.997896i	$0.479346\pi$
$98$	−31.0528	−3.13681
$99$	0	0
$100$	39.5445	3.95445
$101$	16.8586	1.67749	0.838747	−	0.544522i	$-0.183289\pi$
$101$	16.8586	1.67749	0.838747	+	0.544522i	$0.183289\pi$
$102$	13.9473	1.38099
$103$	12.0088	1.18326	0.591630	−	0.806210i	$-0.298485\pi$
$103$	12.0088	1.18326	0.591630	+	0.806210i	$0.298485\pi$
$104$	5.89840	0.578386
$105$	53.4068	5.21197
$106$	21.1015	2.04956
$107$	−8.27533	−0.800006	−0.400003	−	0.916514i	$-0.630991\pi$
$107$	−8.27533	−0.800006	−0.400003	+	0.916514i	$0.630991\pi$
$108$	20.9458	2.01551
$109$	−4.21162	−0.403400	−0.201700	−	0.979447i	$-0.564647\pi$
$109$	−4.21162	−0.403400	−0.201700	+	0.979447i	$0.564647\pi$
$110$	0	0
$111$	11.4402	1.08586
$112$	1.43952	0.136022
$113$	−6.90899	−0.649943	−0.324972	−	0.945724i	$-0.605355\pi$
$113$	−6.90899	−0.649943	−0.324972	+	0.945724i	$0.605355\pi$
$114$	26.1489	2.44907
$115$	−6.85984	−0.639684
$116$	21.8820	2.03169
$117$	−10.2162	−0.944490
$118$	−1.49715	−0.137824
$119$	−9.56266	−0.876608
$120$	−35.5048	−3.24113
$121$	0	0
$122$	−2.30350	−0.208549
$123$	16.4643	1.48453
$124$	6.90738	0.620301
$125$	28.6683	2.56417
$126$	−54.3225	−4.83943
$127$	−1.02183	−0.0906725	−0.0453362	−	0.998972i	$-0.514436\pi$
$127$	−1.02183	−0.0906725	−0.0453362	+	0.998972i	$0.514436\pi$
$128$	18.9364	1.67376
$129$	−20.2908	−1.78650
$130$	18.5988	1.63122
$131$	3.89351	0.340177	0.170089	−	0.985429i	$-0.445595\pi$
$131$	3.89351	0.340177	0.170089	+	0.985429i	$0.445595\pi$
$132$	0	0
$133$	−17.9284	−1.55459
$134$	20.4019	1.76246
$135$	26.0921	2.24565
$136$	6.35725	0.545130
$137$	7.77327	0.664115	0.332058	−	0.943259i	$-0.392257\pi$
$137$	7.77327	0.664115	0.332058	+	0.943259i	$0.392257\pi$
$138$	10.9944	0.935908
$139$	7.39533	0.627263	0.313632	−	0.949545i	$-0.398454\pi$
$139$	7.39533	0.627263	0.313632	+	0.949545i	$0.398454\pi$
$140$	61.6191	5.20776
$141$	−22.2762	−1.87599
$142$	−29.0454	−2.43744
$143$	0	0
$144$	1.65754	0.138128
$145$	27.2583	2.26368
$146$	1.79835	0.148833
$147$	38.6288	3.18605
$148$	13.1993	1.08498
$149$	13.2441	1.08500	0.542501	−	0.840055i	$-0.317477\pi$
$149$	13.2441	1.08500	0.542501	+	0.840055i	$0.317477\pi$
$150$	−78.9505	−6.44628
$151$	6.65480	0.541560	0.270780	−	0.962641i	$-0.412718\pi$
$151$	6.65480	0.541560	0.270780	+	0.962641i	$0.412718\pi$
$152$	11.9188	0.966741
$153$	−11.0110	−0.890183
$154$	0	0
$155$	8.60447	0.691128
$156$	−18.5731	−1.48704
$157$	−17.1849	−1.37150	−0.685751	−	0.727837i	$-0.740526\pi$
$157$	−17.1849	−1.37150	−0.685751	+	0.727837i	$0.740526\pi$
$158$	−31.9666	−2.54312
$159$	−26.2497	−2.08173
$160$	21.7635	1.72055
$161$	−7.53807	−0.594083
$162$	−5.80792	−0.456314
$163$	5.71050	0.447281	0.223640	−	0.974672i	$-0.428206\pi$
$163$	5.71050	0.447281	0.223640	+	0.974672i	$0.428206\pi$
$164$	18.9959	1.48333
$165$	0	0
$166$	25.3957	1.97109
$167$	−16.8481	−1.30374	−0.651871	−	0.758330i	$-0.726016\pi$
$167$	−16.8481	−1.30374	−0.651871	+	0.758330i	$0.726016\pi$
$168$	−39.0152	−3.01009
$169$	−9.15636	−0.704336
$170$	20.0457	1.53743
$171$	−20.6437	−1.57866
$172$	−23.4108	−1.78506
$173$	−12.0938	−0.919476	−0.459738	−	0.888055i	$-0.652057\pi$
$173$	−12.0938	−0.919476	−0.459738	+	0.888055i	$0.652057\pi$
$174$	−43.6875	−3.31194
$175$	54.1306	4.09189
$176$	0	0
$177$	1.86241	0.139987
$178$	21.6676	1.62406
$179$	16.4025	1.22598	0.612989	−	0.790091i	$-0.289967\pi$
$179$	16.4025	1.22598	0.612989	+	0.790091i	$0.289967\pi$
$180$	70.9515	5.28841
$181$	−17.4047	−1.29368	−0.646839	−	0.762626i	$-0.723910\pi$
$181$	−17.4047	−1.29368	−0.646839	+	0.762626i	$0.723910\pi$
$182$	20.4377	1.51494
$183$	2.86548	0.211822
$184$	5.01130	0.369438
$185$	16.4423	1.20886
$186$	−13.7906	−1.01117
$187$	0	0
$188$	−25.7015	−1.87447
$189$	28.6718	2.08556
$190$	37.5823	2.72650
$191$	18.7011	1.35316	0.676581	−	0.736368i	$-0.263461\pi$
$191$	18.7011	1.35316	0.676581	+	0.736368i	$0.263461\pi$
$192$	−36.7038	−2.64887
$193$	−8.59308	−0.618543	−0.309272	−	0.950974i	$-0.600085\pi$
$193$	−8.59308	−0.618543	−0.309272	+	0.950974i	$0.600085\pi$
$194$	−2.94207	−0.211229
$195$	−23.1364	−1.65683
$196$	44.5686	3.18347
$197$	9.19907	0.655407	0.327703	−	0.944781i	$-0.393725\pi$
$197$	9.19907	0.655407	0.327703	+	0.944781i	$0.393725\pi$
$198$	0	0
$199$	−7.13562	−0.505831	−0.252915	−	0.967488i	$-0.581389\pi$
$199$	−7.13562	−0.505831	−0.252915	+	0.967488i	$0.581389\pi$
$200$	−35.9860	−2.54459
$201$	−25.3794	−1.79013
$202$	−38.8337	−2.73233
$203$	29.9533	2.10231
$204$	−20.0179	−1.40154
$205$	23.6631	1.65270
$206$	−27.6622	−1.92732
$207$	−8.67974	−0.603284
$208$	−0.623614	−0.0432399
$209$	0	0
$210$	−123.022	−8.48936
$211$	0.756507	0.0520801	0.0260400	−	0.999661i	$-0.491710\pi$
$211$	0.756507	0.0520801	0.0260400	+	0.999661i	$0.491710\pi$
$212$	−30.2860	−2.08005
$213$	36.1316	2.47570
$214$	19.0622	1.30307
$215$	−29.1627	−1.98888
$216$	−19.0610	−1.29693
$217$	9.45519	0.641860
$218$	9.70146	0.657066
$219$	−2.23710	−0.151169
$220$	0	0
$221$	4.14264	0.278664
$222$	−26.3525	−1.76866
$223$	25.9628	1.73860	0.869298	−	0.494288i	$-0.164571\pi$
$223$	25.9628	1.73860	0.869298	+	0.494288i	$0.164571\pi$
$224$	23.9152	1.59790
$225$	62.3288	4.15526
$226$	15.9148	1.05864
$227$	−0.561554	−0.0372716	−0.0186358	−	0.999826i	$-0.505932\pi$
$227$	−0.561554	−0.0372716	−0.0186358	+	0.999826i	$0.505932\pi$
$228$	−37.5303	−2.48550
$229$	−18.8847	−1.24794	−0.623969	−	0.781449i	$-0.714481\pi$
$229$	−18.8847	−1.24794	−0.623969	+	0.781449i	$0.714481\pi$
$230$	15.8016	1.04193
$231$	0	0
$232$	−19.9129	−1.30735
$233$	0.855163	0.0560236	0.0280118	−	0.999608i	$-0.491082\pi$
$233$	0.855163	0.0560236	0.0280118	+	0.999608i	$0.491082\pi$
$234$	23.5330	1.53840
$235$	−32.0162	−2.08851
$236$	2.14878	0.139874
$237$	39.7655	2.58304
$238$	22.0276	1.42783
$239$	13.7766	0.891134	0.445567	−	0.895248i	$-0.353002\pi$
$239$	13.7766	0.891134	0.445567	+	0.895248i	$0.353002\pi$
$240$	3.75378	0.242305
$241$	−22.6556	−1.45937	−0.729686	−	0.683782i	$-0.760334\pi$
$241$	−22.6556	−1.45937	−0.729686	+	0.683782i	$0.760334\pi$
$242$	0	0
$243$	−11.7817	−0.755793
$244$	3.30610	0.211651
$245$	55.5188	3.54697
$246$	−37.9254	−2.41803
$247$	7.76676	0.494187
$248$	−6.28580	−0.399149
$249$	−31.5914	−2.00203
$250$	−66.0374	−4.17657
$251$	21.9568	1.38590	0.692951	−	0.720985i	$-0.256310\pi$
$251$	21.9568	1.38590	0.692951	+	0.720985i	$0.256310\pi$
$252$	77.9664	4.91142
$253$	0	0
$254$	2.35378	0.147689
$255$	−24.9362	−1.56156
$256$	−18.0021	−1.12513
$257$	−4.41990	−0.275706	−0.137853	−	0.990453i	$-0.544020\pi$
$257$	−4.41990	−0.275706	−0.137853	+	0.990453i	$0.544020\pi$
$258$	46.7397	2.90989
$259$	18.0680	1.12269
$260$	−26.6940	−1.65549
$261$	34.4898	2.13487
$262$	−8.96868	−0.554087
$263$	−11.5605	−0.712854	−0.356427	−	0.934323i	$-0.616005\pi$
$263$	−11.5605	−0.712854	−0.356427	+	0.934323i	$0.616005\pi$
$264$	0	0
$265$	−37.7270	−2.31755
$266$	41.2980	2.53214
$267$	−26.9538	−1.64955
$268$	−29.2819	−1.78868
$269$	−6.61732	−0.403465	−0.201733	−	0.979441i	$-0.564657\pi$
$269$	−6.61732	−0.403465	−0.201733	+	0.979441i	$0.564657\pi$
$270$	−60.1030	−3.65775
$271$	−8.02822	−0.487679	−0.243840	−	0.969816i	$-0.578407\pi$
$271$	−8.02822	−0.487679	−0.243840	+	0.969816i	$0.578407\pi$
$272$	−0.672126	−0.0407536
$273$	−25.4239	−1.53872
$274$	−17.9057	−1.08172
$275$	0	0
$276$	−15.7798	−0.949830
$277$	−15.9051	−0.955643	−0.477821	−	0.878457i	$-0.658573\pi$
$277$	−15.9051	−0.955643	−0.477821	+	0.878457i	$0.658573\pi$
$278$	−17.0351	−1.02170
$279$	10.8872	0.651800
$280$	−56.0741	−3.35107
$281$	−1.55120	−0.0925366	−0.0462683	−	0.998929i	$-0.514733\pi$
$281$	−1.55120	−0.0925366	−0.0462683	+	0.998929i	$0.514733\pi$
$282$	51.3131	3.05565
$283$	−2.45463	−0.145912	−0.0729562	−	0.997335i	$-0.523243\pi$
$283$	−2.45463	−0.145912	−0.0729562	+	0.997335i	$0.523243\pi$
$284$	41.6875	2.47370
$285$	−46.7512	−2.76930
$286$	0	0
$287$	26.0026	1.53489
$288$	27.5373	1.62265
$289$	−12.5351	−0.737359
$290$	−62.7894	−3.68712
$291$	3.65985	0.214544
$292$	−2.58109	−0.151047
$293$	33.2516	1.94258	0.971288	−	0.237906i	$-0.0764609\pi$
$293$	33.2516	1.94258	0.971288	+	0.237906i	$0.0764609\pi$
$294$	−88.9813	−5.18949
$295$	2.67672	0.155845
$296$	−12.0116	−0.698159
$297$	0	0
$298$	−30.5078	−1.76727
$299$	3.26557	0.188853
$300$	113.314	6.54218
$301$	−32.0460	−1.84710
$302$	−15.3293	−0.882103
$303$	48.3080	2.77522
$304$	−1.26012	−0.0722731
$305$	4.11838	0.235818
$306$	25.3637	1.44995
$307$	29.4127	1.67867	0.839336	−	0.543613i	$-0.182944\pi$
$307$	29.4127	1.67867	0.839336	+	0.543613i	$0.182944\pi$
$308$	0	0
$309$	34.4109	1.95757
$310$	−19.8204	−1.12572
$311$	13.6179	0.772201	0.386101	−	0.922457i	$-0.373822\pi$
$311$	13.6179	0.772201	0.386101	+	0.922457i	$0.373822\pi$
$312$	16.9018	0.956874
$313$	3.96185	0.223937	0.111968	−	0.993712i	$-0.464284\pi$
$313$	3.96185	0.223937	0.111968	+	0.993712i	$0.464284\pi$
$314$	39.5853	2.23393
$315$	97.1222	5.47222
$316$	45.8801	2.58096
$317$	−20.5977	−1.15688	−0.578442	−	0.815724i	$-0.696339\pi$
$317$	−20.5977	−1.15688	−0.578442	+	0.815724i	$0.696339\pi$
$318$	60.4660	3.39077
$319$	0	0
$320$	−52.7521	−2.94893
$321$	−23.7128	−1.32352
$322$	17.3639	0.967654
$323$	8.37095	0.465772
$324$	8.33583	0.463102
$325$	−23.4499	−1.30077
$326$	−13.1541	−0.728539
$327$	−12.0683	−0.667380
$328$	−17.2865	−0.954489
$329$	−35.1816	−1.93962
$330$	0	0
$331$	−5.54856	−0.304977	−0.152488	−	0.988305i	$-0.548729\pi$
$331$	−5.54856	−0.304977	−0.152488	+	0.988305i	$0.548729\pi$
$332$	−36.4492	−2.00041
$333$	20.8044	1.14008
$334$	38.8095	2.12356
$335$	−36.4763	−1.99291
$336$	4.12491	0.225033
$337$	−23.8506	−1.29923	−0.649613	−	0.760265i	$-0.725069\pi$
$337$	−23.8506	−1.29923	−0.649613	+	0.760265i	$0.725069\pi$
$338$	21.0917	1.14723
$339$	−19.7976	−1.07526
$340$	−28.7706	−1.56030
$341$	0	0
$342$	47.5527	2.57136
$343$	29.3290	1.58362
$344$	21.3042	1.14864
$345$	−19.6567	−1.05828
$346$	27.8581	1.49766
$347$	−29.4543	−1.58119	−0.790595	−	0.612339i	$-0.790229\pi$
$347$	−29.4543	−1.58119	−0.790595	+	0.612339i	$0.790229\pi$
$348$	62.7025	3.36121
$349$	−1.68558	−0.0902268	−0.0451134	−	0.998982i	$-0.514365\pi$
$349$	−1.68558	−0.0902268	−0.0451134	+	0.998982i	$0.514365\pi$
$350$	−124.690	−6.66494
$351$	−12.4209	−0.662978
$352$	0	0
$353$	26.9683	1.43538	0.717689	−	0.696364i	$-0.245200\pi$
$353$	26.9683	1.43538	0.717689	+	0.696364i	$0.245200\pi$
$354$	−4.29005	−0.228013
$355$	51.9298	2.75615
$356$	−31.0985	−1.64821
$357$	−27.4016	−1.45025
$358$	−37.7830	−1.99690
$359$	29.1947	1.54084	0.770418	−	0.637540i	$-0.220048\pi$
$359$	29.1947	1.54084	0.770418	+	0.637540i	$0.220048\pi$
$360$	−64.5668	−3.40297
$361$	−3.30586	−0.173992
$362$	40.0916	2.10717
$363$	0	0
$364$	−29.3332	−1.53748
$365$	−3.21524	−0.168293
$366$	−6.60062	−0.345020
$367$	3.46925	0.181093	0.0905467	−	0.995892i	$-0.471139\pi$
$367$	3.46925	0.181093	0.0905467	+	0.995892i	$0.471139\pi$
$368$	−0.529825	−0.0276190
$369$	29.9408	1.55866
$370$	−37.8749	−1.96902
$371$	−41.4571	−2.15235
$372$	19.7930	1.02622
$373$	2.16927	0.112321	0.0561604	−	0.998422i	$-0.482114\pi$
$373$	2.16927	0.112321	0.0561604	+	0.998422i	$0.482114\pi$
$374$	0	0
$375$	82.1485	4.24213
$376$	23.3887	1.20618
$377$	−12.9761	−0.668301
$378$	−66.0453	−3.39700
$379$	−22.1068	−1.13555	−0.567775	−	0.823184i	$-0.692196\pi$
$379$	−22.1068	−1.13555	−0.567775	+	0.823184i	$0.692196\pi$
$380$	−53.9400	−2.76706
$381$	−2.92803	−0.150007
$382$	−43.0779	−2.20406
$383$	−18.8987	−0.965677	−0.482838	−	0.875709i	$-0.660394\pi$
$383$	−18.8987	−0.965677	−0.482838	+	0.875709i	$0.660394\pi$
$384$	54.2619	2.76904
$385$	0	0
$386$	19.7941	1.00749
$387$	−36.8995	−1.87571
$388$	4.22262	0.214371
$389$	12.2584	0.621527	0.310763	−	0.950487i	$-0.399415\pi$
$389$	12.2584	0.621527	0.310763	+	0.950487i	$0.399415\pi$
$390$	53.2946	2.69867
$391$	3.51960	0.177994
$392$	−40.5580	−2.04849
$393$	11.1568	0.562785
$394$	−21.1900	−1.06754
$395$	57.1525	2.87565
$396$	0	0
$397$	3.14352	0.157769	0.0788844	−	0.996884i	$-0.474864\pi$
$397$	3.14352	0.157769	0.0788844	+	0.996884i	$0.474864\pi$
$398$	16.4369	0.823906
$399$	−51.3735	−2.57189
$400$	3.80465	0.190232
$401$	−33.8054	−1.68816	−0.844080	−	0.536217i	$-0.819853\pi$
$401$	−33.8054	−1.68816	−0.844080	+	0.536217i	$0.819853\pi$
$402$	58.4614	2.91579
$403$	−4.09608	−0.204040
$404$	55.7362	2.77298
$405$	10.3839	0.515979
$406$	−68.9973	−3.42428
$407$	0	0
$408$	18.2166	0.901855
$409$	−10.8131	−0.534675	−0.267338	−	0.963603i	$-0.586144\pi$
$409$	−10.8131	−0.534675	−0.267338	+	0.963603i	$0.586144\pi$
$410$	−54.5078	−2.69195
$411$	22.2742	1.09870
$412$	39.7022	1.95599
$413$	2.94137	0.144735
$414$	19.9938	0.982639
$415$	−45.4045	−2.22882
$416$	−10.3603	−0.507956
$417$	21.1912	1.03774
$418$	0	0
$419$	4.10855	0.200716	0.100358	−	0.994951i	$-0.468001\pi$
$419$	4.10855	0.200716	0.100358	+	0.994951i	$0.468001\pi$
$420$	176.568	8.61564
$421$	22.4982	1.09650	0.548248	−	0.836316i	$-0.315295\pi$
$421$	22.4982	1.09650	0.548248	+	0.836316i	$0.315295\pi$
$422$	−1.74261	−0.0848290
$423$	−40.5100	−1.96966
$424$	27.5607	1.33846
$425$	−25.2741	−1.22597
$426$	−83.2291	−4.03246
$427$	4.52556	0.219007
$428$	−27.3591	−1.32245
$429$	0	0
$430$	67.1762	3.23952
$431$	−24.2441	−1.16780	−0.583899	−	0.811826i	$-0.698474\pi$
$431$	−24.2441	−1.16780	−0.583899	+	0.811826i	$0.698474\pi$
$432$	2.01524	0.0969582
$433$	2.99850	0.144099	0.0720494	−	0.997401i	$-0.477046\pi$
$433$	2.99850	0.144099	0.0720494	+	0.997401i	$0.477046\pi$
$434$	−21.7800	−1.04547
$435$	78.1080	3.74499
$436$	−13.9240	−0.666840
$437$	6.59867	0.315657
$438$	5.15314	0.246227
$439$	1.99617	0.0952719	0.0476360	−	0.998865i	$-0.484831\pi$
$439$	1.99617	0.0952719	0.0476360	+	0.998865i	$0.484831\pi$
$440$	0	0
$441$	70.2478	3.34513
$442$	−9.54256	−0.453893
$443$	−15.0237	−0.713797	−0.356898	−	0.934143i	$-0.616166\pi$
$443$	−15.0237	−0.713797	−0.356898	+	0.934143i	$0.616166\pi$
$444$	37.8225	1.79498
$445$	−38.7391	−1.83641
$446$	−59.8052	−2.83186
$447$	37.9508	1.79501
$448$	−57.9677	−2.73872
$449$	−17.2687	−0.814962	−0.407481	−	0.913214i	$-0.633593\pi$
$449$	−17.2687	−0.814962	−0.407481	+	0.913214i	$0.633593\pi$
$450$	−143.574	−6.76816
$451$	0	0
$452$	−22.8418	−1.07439
$453$	19.0692	0.895950
$454$	1.29354	0.0607087
$455$	−36.5402	−1.71303
$456$	34.1530	1.59936
$457$	−6.48224	−0.303226	−0.151613	−	0.988440i	$-0.548447\pi$
$457$	−6.48224	−0.303226	−0.151613	+	0.988440i	$0.548447\pi$
$458$	43.5009	2.03267
$459$	−13.3871	−0.624858
$460$	−22.6793	−1.05743
$461$	−13.4808	−0.627864	−0.313932	−	0.949445i	$-0.601646\pi$
$461$	−13.4808	−0.627864	−0.313932	+	0.949445i	$0.601646\pi$
$462$	0	0
$463$	−28.5554	−1.32708	−0.663541	−	0.748140i	$-0.730947\pi$
$463$	−28.5554	−1.32708	−0.663541	+	0.748140i	$0.730947\pi$
$464$	2.10531	0.0977367
$465$	24.6559	1.14339
$466$	−1.96987	−0.0912522
$467$	−16.0498	−0.742697	−0.371349	−	0.928494i	$-0.621105\pi$
$467$	−16.0498	−0.742697	−0.371349	+	0.928494i	$0.621105\pi$
$468$	−33.7758	−1.56129
$469$	−40.0827	−1.85085
$470$	73.7492	3.40180
$471$	−49.2429	−2.26899
$472$	−1.95542	−0.0900056
$473$	0	0
$474$	−91.5996	−4.20731
$475$	−47.3848	−2.17416
$476$	−31.6151	−1.44908
$477$	−47.7359	−2.18568
$478$	−31.7344	−1.45150
$479$	29.9916	1.37035	0.685176	−	0.728378i	$-0.259725\pi$
$479$	29.9916	1.37035	0.685176	+	0.728378i	$0.259725\pi$
$480$	62.3628	2.84646
$481$	−7.82723	−0.356891
$482$	52.1870	2.37705
$483$	−21.6002	−0.982843
$484$	0	0
$485$	5.26008	0.238848
$486$	27.1390	1.23105
$487$	−14.3138	−0.648622	−0.324311	−	0.945951i	$-0.605132\pi$
$487$	−14.3138	−0.648622	−0.324311	+	0.945951i	$0.605132\pi$
$488$	−3.00859	−0.136193
$489$	16.3633	0.739975
$490$	−127.887	−5.77736
$491$	−15.3340	−0.692014	−0.346007	−	0.938232i	$-0.612463\pi$
$491$	−15.3340	−0.692014	−0.346007	+	0.938232i	$0.612463\pi$
$492$	54.4324	2.45400
$493$	−13.9855	−0.629875
$494$	−17.8907	−0.804941
$495$	0	0
$496$	0.664572	0.0298402
$497$	57.0641	2.55967
$498$	72.7708	3.26094
$499$	−2.36919	−0.106059	−0.0530297	−	0.998593i	$-0.516888\pi$
$499$	−2.36919	−0.106059	−0.0530297	+	0.998593i	$0.516888\pi$
$500$	94.7803	4.23870
$501$	−48.2778	−2.15689
$502$	−50.5774	−2.25738
$503$	−15.8376	−0.706164	−0.353082	−	0.935592i	$-0.614866\pi$
$503$	−15.8376	−0.706164	−0.353082	+	0.935592i	$0.614866\pi$
$504$	−70.9505	−3.16038
$505$	69.4301	3.08960
$506$	0	0
$507$	−26.2374	−1.16524
$508$	−3.37826	−0.149886
$509$	16.0272	0.710395	0.355197	−	0.934791i	$-0.384414\pi$
$509$	16.0272	0.710395	0.355197	+	0.934791i	$0.384414\pi$
$510$	57.4404	2.54351
$511$	−3.53313	−0.156297
$512$	3.59490	0.158874
$513$	−25.0987	−1.10813
$514$	10.1812	0.449075
$515$	49.4567	2.17932
$516$	−67.0833	−2.95318
$517$	0	0
$518$	−41.6195	−1.82866
$519$	−34.6546	−1.52117
$520$	24.2919	1.06527
$521$	3.10231	0.135915	0.0679573	−	0.997688i	$-0.478352\pi$
$521$	3.10231	0.135915	0.0679573	+	0.997688i	$0.478352\pi$
$522$	−79.4472	−3.47731
$523$	−25.3568	−1.10878	−0.554388	−	0.832259i	$-0.687048\pi$
$523$	−25.3568	−1.10878	−0.554388	+	0.832259i	$0.687048\pi$
$524$	12.8723	0.562330
$525$	155.110	6.76956
$526$	26.6297	1.16111
$527$	−4.41473	−0.192308
$528$	0	0
$529$	−20.2256	−0.879372
$530$	86.9041	3.77487
$531$	3.38685	0.146977
$532$	−59.2730	−2.56981
$533$	−11.2646	−0.487924
$534$	62.0881	2.68681
$535$	−34.0810	−1.47345
$536$	26.6469	1.15097
$537$	47.0009	2.02824
$538$	15.2430	0.657172
$539$	0	0
$540$	86.2629	3.71216
$541$	30.5672	1.31419	0.657094	−	0.753809i	$-0.271785\pi$
$541$	30.5672	1.31419	0.657094	+	0.753809i	$0.271785\pi$
$542$	18.4930	0.794341
$543$	−49.8727	−2.14024
$544$	−11.1663	−0.478749
$545$	−17.3451	−0.742981
$546$	58.5638	2.50630
$547$	7.83930	0.335184	0.167592	−	0.985856i	$-0.446401\pi$
$547$	7.83930	0.335184	0.167592	+	0.985856i	$0.446401\pi$
$548$	25.6992	1.09781
$549$	5.21098	0.222399
$550$	0	0
$551$	−26.2205	−1.11703
$552$	14.3598	0.611193
$553$	62.8031	2.67066
$554$	36.6373	1.55657
$555$	47.1152	1.99993
$556$	24.4497	1.03690
$557$	30.8135	1.30561	0.652804	−	0.757527i	$-0.273592\pi$
$557$	30.8135	1.30561	0.652804	+	0.757527i	$0.273592\pi$
$558$	−25.0787	−1.06166
$559$	13.8827	0.587174
$560$	5.92849	0.250524
$561$	0	0
$562$	3.57318	0.150725
$563$	−14.0490	−0.592093	−0.296046	−	0.955174i	$-0.595668\pi$
$563$	−14.0490	−0.592093	−0.296046	+	0.955174i	$0.595668\pi$
$564$	−73.6472	−3.10110
$565$	−28.4539	−1.19706
$566$	5.65422	0.237665
$567$	11.4105	0.479197
$568$	−37.9362	−1.59177
$569$	−2.50567	−0.105043	−0.0525217	−	0.998620i	$-0.516726\pi$
$569$	−2.50567	−0.105043	−0.0525217	+	0.998620i	$0.516726\pi$
$570$	107.691	4.51069
$571$	3.22155	0.134818	0.0674088	−	0.997725i	$-0.478527\pi$
$571$	3.22155	0.134818	0.0674088	+	0.997725i	$0.478527\pi$
$572$	0	0
$573$	53.5876	2.23865
$574$	−59.8970	−2.50005
$575$	−19.9231	−0.830852
$576$	−66.7471	−2.78113
$577$	−18.4684	−0.768849	−0.384424	−	0.923156i	$-0.625600\pi$
$577$	−18.4684	−0.768849	−0.384424	+	0.923156i	$0.625600\pi$
$578$	28.8746	1.20102
$579$	−24.6233	−1.02331
$580$	90.1185	3.74197
$581$	−49.8936	−2.06993
$582$	−8.43046	−0.349454
$583$	0	0
$584$	2.34882	0.0971950
$585$	−42.0743	−1.73956
$586$	−76.5948	−3.16410
$587$	14.9697	0.617866	0.308933	−	0.951084i	$-0.400028\pi$
$587$	14.9697	0.617866	0.308933	+	0.951084i	$0.400028\pi$
$588$	127.711	5.26669
$589$	−8.27688	−0.341043
$590$	−6.16583	−0.253843
$591$	26.3598	1.08430
$592$	1.26994	0.0521940
$593$	6.52704	0.268033	0.134017	−	0.990979i	$-0.457212\pi$
$593$	6.52704	0.268033	0.134017	+	0.990979i	$0.457212\pi$
$594$	0	0
$595$	−39.3827	−1.61453
$596$	43.7864	1.79356
$597$	−20.4470	−0.836839
$598$	−7.52223	−0.307607
$599$	−5.06539	−0.206966	−0.103483	−	0.994631i	$-0.532999\pi$
$599$	−5.06539	−0.206966	−0.103483	+	0.994631i	$0.532999\pi$
$600$	−103.117	−4.20974
$601$	29.2863	1.19461	0.597306	−	0.802013i	$-0.296238\pi$
$601$	29.2863	1.19461	0.597306	+	0.802013i	$0.296238\pi$
$602$	73.8179	3.00859
$603$	−46.1533	−1.87951
$604$	22.0014	0.895226
$605$	0	0
$606$	−111.277	−4.52033
$607$	4.01395	0.162921	0.0814607	−	0.996677i	$-0.474041\pi$
$607$	4.01395	0.162921	0.0814607	+	0.996677i	$0.474041\pi$
$608$	−20.9349	−0.849022
$609$	85.8306	3.47803
$610$	−9.48668	−0.384104
$611$	15.2410	0.616586
$612$	−36.4033	−1.47152
$613$	−5.84343	−0.236014	−0.118007	−	0.993013i	$-0.537651\pi$
$613$	−5.84343	−0.236014	−0.118007	+	0.993013i	$0.537651\pi$
$614$	−67.7521	−2.73425
$615$	67.8061	2.73420
$616$	0	0
$617$	−23.8970	−0.962056	−0.481028	−	0.876705i	$-0.659736\pi$
$617$	−23.8970	−0.962056	−0.481028	+	0.876705i	$0.659736\pi$
$618$	−79.2654	−3.18852
$619$	−14.9888	−0.602452	−0.301226	−	0.953553i	$-0.597396\pi$
$619$	−14.9888	−0.602452	−0.301226	+	0.953553i	$0.597396\pi$
$620$	28.4472	1.14247
$621$	−10.5528	−0.423471
$622$	−31.3688	−1.25778
$623$	−42.5692	−1.70550
$624$	−1.78695	−0.0715354
$625$	58.2618	2.33047
$626$	−9.12610	−0.364752
$627$	0	0
$628$	−56.8148	−2.26716
$629$	−8.43612	−0.336370
$630$	−223.721	−8.91325
$631$	10.2712	0.408889	0.204445	−	0.978878i	$-0.434461\pi$
$631$	10.2712	0.408889	0.204445	+	0.978878i	$0.434461\pi$
$632$	−41.7515	−1.66078
$633$	2.16776	0.0861606
$634$	47.4468	1.88435
$635$	−4.20827	−0.167000
$636$	−86.7839	−3.44121
$637$	−26.4292	−1.04716
$638$	0	0
$639$	65.7066	2.59931
$640$	77.9873	3.08272
$641$	−44.6556	−1.76379	−0.881896	−	0.471444i	$-0.843733\pi$
$641$	−44.6556	−1.76379	−0.881896	+	0.471444i	$0.843733\pi$
$642$	54.6224	2.15577
$643$	−7.99850	−0.315430	−0.157715	−	0.987485i	$-0.550413\pi$
$643$	−7.99850	−0.315430	−0.157715	+	0.987485i	$0.550413\pi$
$644$	−24.9216	−0.982049
$645$	−83.5652	−3.29038
$646$	−19.2825	−0.758658
$647$	31.8954	1.25394	0.626970	−	0.779044i	$-0.284295\pi$
$647$	31.8954	1.25394	0.626970	+	0.779044i	$0.284295\pi$
$648$	−7.58572	−0.297995
$649$	0	0
$650$	54.0168	2.11871
$651$	27.0937	1.06188
$652$	18.8795	0.739377
$653$	6.42158	0.251296	0.125648	−	0.992075i	$-0.459899\pi$
$653$	6.42158	0.251296	0.125648	+	0.992075i	$0.459899\pi$
$654$	27.7993	1.08704
$655$	16.0350	0.626537
$656$	1.82763	0.0713571
$657$	−4.06824	−0.158717
$658$	81.0407	3.15930
$659$	−37.2103	−1.44951	−0.724754	−	0.689007i	$-0.758047\pi$
$659$	−37.2103	−1.44951	−0.724754	+	0.689007i	$0.758047\pi$
$660$	0	0
$661$	31.2278	1.21462	0.607311	−	0.794464i	$-0.292248\pi$
$661$	31.2278	1.21462	0.607311	+	0.794464i	$0.292248\pi$
$662$	12.7811	0.496752
$663$	11.8707	0.461018
$664$	33.1692	1.28722
$665$	−73.8360	−2.86324
$666$	−47.9230	−1.85698
$667$	−11.0245	−0.426871
$668$	−55.7013	−2.15515
$669$	74.3958	2.87631
$670$	84.0230	3.24609
$671$	0	0
$672$	68.5286	2.64355
$673$	−37.4180	−1.44236	−0.721179	−	0.692749i	$-0.756399\pi$
$673$	−37.4180	−1.44236	−0.721179	+	0.692749i	$0.756399\pi$
$674$	54.9398	2.11620
$675$	75.7795	2.91675
$676$	−30.2718	−1.16430
$677$	12.0421	0.462816	0.231408	−	0.972857i	$-0.425667\pi$
$677$	12.0421	0.462816	0.231408	+	0.972857i	$0.425667\pi$
$678$	45.6037	1.75140
$679$	5.78015	0.221822
$680$	26.1816	1.00402
$681$	−1.60912	−0.0616617
$682$	0	0
$683$	23.0199	0.880832	0.440416	−	0.897794i	$-0.354831\pi$
$683$	23.0199	0.880832	0.440416	+	0.897794i	$0.354831\pi$
$684$	−68.2502	−2.60961
$685$	32.0133	1.22316
$686$	−67.5592	−2.57942
$687$	−54.1138	−2.06457
$688$	−2.25240	−0.0858720
$689$	17.9596	0.684208
$690$	45.2792	1.72375
$691$	−11.9212	−0.453505	−0.226752	−	0.973952i	$-0.572811\pi$
$691$	−11.9212	−0.453505	−0.226752	+	0.973952i	$0.572811\pi$
$692$	−39.9833	−1.51994
$693$	0	0
$694$	67.8479	2.57547
$695$	30.4568	1.15529
$696$	−57.0601	−2.16286
$697$	−12.1409	−0.459869
$698$	3.88272	0.146963
$699$	2.45045	0.0926846
$700$	178.961	6.76409
$701$	−16.0703	−0.606968	−0.303484	−	0.952836i	$-0.598150\pi$
$701$	−16.0703	−0.606968	−0.303484	+	0.952836i	$0.598150\pi$
$702$	28.6115	1.07987
$703$	−15.8163	−0.596524
$704$	0	0
$705$	−91.7417	−3.45519
$706$	−62.1214	−2.33797
$707$	76.2947	2.86936
$708$	6.15730	0.231405
$709$	29.7357	1.11675	0.558373	−	0.829590i	$-0.311426\pi$
$709$	29.7357	1.11675	0.558373	+	0.829590i	$0.311426\pi$
$710$	−119.620	−4.48926
$711$	72.3149	2.71202
$712$	28.3000	1.06059
$713$	−3.48005	−0.130329
$714$	63.1196	2.36219
$715$	0	0
$716$	54.2282	2.02660
$717$	39.4766	1.47428
$718$	−67.2498	−2.50974
$719$	−4.46745	−0.166608	−0.0833039	−	0.996524i	$-0.526547\pi$
$719$	−4.46745	−0.166608	−0.0833039	+	0.996524i	$0.526547\pi$
$720$	6.82638	0.254404
$721$	54.3465	2.02397
$722$	7.61503	0.283402
$723$	−64.9190	−2.41436
$724$	−57.5415	−2.13851
$725$	79.1665	2.94017
$726$	0	0
$727$	−16.0101	−0.593781	−0.296891	−	0.954911i	$-0.595950\pi$
$727$	−16.0101	−0.593781	−0.296891	+	0.954911i	$0.595950\pi$
$728$	26.6936	0.989331
$729$	−41.3241	−1.53052
$730$	7.40630	0.274119
$731$	14.9626	0.553412
$732$	9.47356	0.350153
$733$	−23.2758	−0.859710	−0.429855	−	0.902898i	$-0.641435\pi$
$733$	−23.2758	−0.859710	−0.429855	+	0.902898i	$0.641435\pi$
$734$	−7.99141	−0.294968
$735$	159.088	5.86805
$736$	−8.80216	−0.324452
$737$	0	0
$738$	−68.9686	−2.53877
$739$	−11.1063	−0.408550	−0.204275	−	0.978914i	$-0.565484\pi$
$739$	−11.1063	−0.408550	−0.204275	+	0.978914i	$0.565484\pi$
$740$	54.3600	1.99831
$741$	22.2555	0.817576
$742$	95.4963	3.50578
$743$	−17.7967	−0.652897	−0.326448	−	0.945215i	$-0.605852\pi$
$743$	−17.7967	−0.652897	−0.326448	+	0.945215i	$0.605852\pi$
$744$	−18.0118	−0.660346
$745$	54.5444	1.99835
$746$	−4.99692	−0.182950
$747$	−57.4501	−2.10199
$748$	0	0
$749$	−37.4505	−1.36841
$750$	−189.229	−6.90966
$751$	−5.27267	−0.192402	−0.0962011	−	0.995362i	$-0.530669\pi$
$751$	−5.27267	−0.192402	−0.0962011	+	0.995362i	$0.530669\pi$
$752$	−2.47279	−0.0901735
$753$	62.9168	2.29282
$754$	29.8903	1.08854
$755$	27.4070	0.997444
$756$	94.7917	3.44754
$757$	−7.30992	−0.265684	−0.132842	−	0.991137i	$-0.542410\pi$
$757$	−7.30992	−0.265684	−0.132842	+	0.991137i	$0.542410\pi$
$758$	50.9229	1.84960
$759$	0	0
$760$	49.0861	1.78054
$761$	−12.8998	−0.467618	−0.233809	−	0.972283i	$-0.575119\pi$
$761$	−12.8998	−0.467618	−0.233809	+	0.972283i	$0.575119\pi$
$762$	6.74470	0.244335
$763$	−19.0600	−0.690017
$764$	61.8276	2.23684
$765$	−45.3473	−1.63954
$766$	43.5330	1.57291
$767$	−1.27423	−0.0460098
$768$	−51.5846	−1.86140
$769$	−19.8026	−0.714099	−0.357050	−	0.934085i	$-0.616217\pi$
$769$	−19.8026	−0.714099	−0.357050	+	0.934085i	$0.616217\pi$
$770$	0	0
$771$	−12.6651	−0.456124
$772$	−28.4096	−1.02248
$773$	−2.45078	−0.0881485	−0.0440743	−	0.999028i	$-0.514034\pi$
$773$	−2.45078	−0.0881485	−0.0440743	+	0.999028i	$0.514034\pi$
$774$	84.9979	3.05519
$775$	24.9901	0.897670
$776$	−3.84264	−0.137943
$777$	51.7734	1.85736
$778$	−28.2372	−1.01235
$779$	−22.7622	−0.815539
$780$	−76.4911	−2.73882
$781$	0	0
$782$	−8.10739	−0.289920
$783$	41.9328	1.49855
$784$	4.28803	0.153144
$785$	−70.7738	−2.52603
$786$	−25.6996	−0.916674
$787$	−25.0711	−0.893690	−0.446845	−	0.894611i	$-0.647452\pi$
$787$	−25.0711	−0.893690	−0.446845	+	0.894611i	$0.647452\pi$
$788$	30.4130	1.08342
$789$	−33.1265	−1.17934
$790$	−131.651	−4.68392
$791$	−31.2671	−1.11173
$792$	0	0
$793$	−1.96052	−0.0696201
$794$	−7.24109	−0.256977
$795$	−108.106	−3.83413
$796$	−23.5911	−0.836163
$797$	1.48736	0.0526850	0.0263425	−	0.999653i	$-0.491614\pi$
$797$	1.48736	0.0526850	0.0263425	+	0.999653i	$0.491614\pi$
$798$	118.339	4.18914
$799$	16.4266	0.581133
$800$	63.2079	2.23474
$801$	−49.0165	−1.73191
$802$	77.8706	2.74971
$803$	0	0
$804$	−83.9068	−2.95916
$805$	−31.0447	−1.09418
$806$	9.43532	0.332345
$807$	−18.9618	−0.667487
$808$	−50.7206	−1.78435
$809$	−5.82625	−0.204840	−0.102420	−	0.994741i	$-0.532659\pi$
$809$	−5.82625	−0.204840	−0.102420	+	0.994741i	$0.532659\pi$
$810$	−23.9192	−0.840437
$811$	−17.5266	−0.615444	−0.307722	−	0.951476i	$-0.599567\pi$
$811$	−17.5266	−0.615444	−0.307722	+	0.951476i	$0.599567\pi$
$812$	99.0285	3.47522
$813$	−23.0047	−0.806810
$814$	0	0
$815$	23.5180	0.823800
$816$	−1.92596	−0.0674222
$817$	28.0524	0.981429
$818$	24.9080	0.870889
$819$	−46.2342	−1.61555
$820$	78.2324	2.73199
$821$	−37.9053	−1.32290	−0.661452	−	0.749987i	$-0.730060\pi$
$821$	−37.9053	−1.32290	−0.661452	+	0.749987i	$0.730060\pi$
$822$	−51.3084	−1.78959
$823$	−53.8346	−1.87655	−0.938277	−	0.345884i	$-0.887579\pi$
$823$	−53.8346	−1.87655	−0.938277	+	0.345884i	$0.887579\pi$
$824$	−36.1295	−1.25863
$825$	0	0
$826$	−6.77544	−0.235748
$827$	44.6221	1.55166	0.775831	−	0.630941i	$-0.217331\pi$
$827$	44.6221	1.55166	0.775831	+	0.630941i	$0.217331\pi$
$828$	−28.6961	−0.997257
$829$	−27.1495	−0.942943	−0.471471	−	0.881881i	$-0.656277\pi$
$829$	−27.1495	−0.942943	−0.471471	+	0.881881i	$0.656277\pi$
$830$	104.589	3.63034
$831$	−45.5756	−1.58100
$832$	25.1122	0.870608
$833$	−28.4852	−0.986955
$834$	−48.8138	−1.69028
$835$	−69.3867	−2.40123
$836$	0	0
$837$	13.2367	0.457527
$838$	−9.46402	−0.326929
$839$	26.3014	0.908025	0.454012	−	0.890995i	$-0.349992\pi$
$839$	26.3014	0.908025	0.454012	+	0.890995i	$0.349992\pi$
$840$	−160.679	−5.54396
$841$	14.8070	0.510587
$842$	−51.8246	−1.78599
$843$	−4.44492	−0.153091
$844$	2.50109	0.0860909
$845$	−37.7094	−1.29724
$846$	93.3146	3.20822
$847$	0	0
$848$	−2.91388	−0.100063
$849$	−7.03368	−0.241395
$850$	58.2188	1.99689
$851$	−6.65004	−0.227961
$852$	119.455	4.09245
$853$	−32.9902	−1.12956	−0.564782	−	0.825240i	$-0.691040\pi$
$853$	−32.9902	−1.12956	−0.564782	+	0.825240i	$0.691040\pi$
$854$	−10.4246	−0.356723
$855$	−85.0187	−2.90758
$856$	24.8971	0.850965
$857$	25.7137	0.878362	0.439181	−	0.898399i	$-0.355269\pi$
$857$	25.7137	0.878362	0.439181	+	0.898399i	$0.355269\pi$
$858$	0	0
$859$	−46.9250	−1.60106	−0.800531	−	0.599292i	$-0.795449\pi$
$859$	−46.9250	−1.60106	−0.800531	+	0.599292i	$0.795449\pi$
$860$	−96.4148	−3.28772
$861$	74.5100	2.53930
$862$	55.8462	1.90213
$863$	34.9606	1.19007	0.595037	−	0.803698i	$-0.297137\pi$
$863$	34.9606	1.19007	0.595037	+	0.803698i	$0.297137\pi$
$864$	33.4798	1.13901
$865$	−49.8069	−1.69349
$866$	−6.90704	−0.234711
$867$	−35.9191	−1.21988
$868$	31.2598	1.06103
$869$	0	0
$870$	−179.922	−6.09992
$871$	17.3642	0.588364
$872$	12.6711	0.429096
$873$	6.65557	0.225257
$874$	−15.2000	−0.514148
$875$	129.740	4.38602
$876$	−7.39606	−0.249890
$877$	37.7411	1.27443	0.637214	−	0.770687i	$-0.280087\pi$
$877$	37.7411	1.27443	0.637214	+	0.770687i	$0.280087\pi$
$878$	−4.59817	−0.155181
$879$	95.2817	3.21377
$880$	0	0
$881$	54.9594	1.85163	0.925814	−	0.377978i	$-0.123381\pi$
$881$	54.9594	1.85163	0.925814	+	0.377978i	$0.123381\pi$
$882$	−161.816	−5.44861
$883$	14.2942	0.481039	0.240519	−	0.970644i	$-0.422682\pi$
$883$	14.2942	0.481039	0.240519	+	0.970644i	$0.422682\pi$
$884$	13.6960	0.460646
$885$	7.67010	0.257828
$886$	34.6070	1.16265
$887$	−9.88879	−0.332033	−0.166016	−	0.986123i	$-0.553090\pi$
$887$	−9.88879	−0.332033	−0.166016	+	0.986123i	$0.553090\pi$
$888$	−34.4189	−1.15502
$889$	−4.62434	−0.155096
$890$	89.2354	2.99118
$891$	0	0
$892$	85.8355	2.87398
$893$	30.7972	1.03059
$894$	−87.4196	−2.92375
$895$	67.5516	2.25800
$896$	85.6979	2.86297
$897$	9.35742	0.312435
$898$	39.7785	1.32742
$899$	13.8283	0.461200
$900$	206.065	6.86884
$901$	19.3567	0.644867
$902$	0	0
$903$	−91.8272	−3.05582
$904$	20.7863	0.691343
$905$	−71.6790	−2.38269
$906$	−43.9259	−1.45934
$907$	47.8365	1.58839	0.794193	−	0.607665i	$-0.207894\pi$
$907$	47.8365	1.58839	0.794193	+	0.607665i	$0.207894\pi$
$908$	−1.85655	−0.0616118
$909$	87.8498	2.91379
$910$	84.1702	2.79021
$911$	−3.25500	−0.107843	−0.0539215	−	0.998545i	$-0.517172\pi$
$911$	−3.25500	−0.107843	−0.0539215	+	0.998545i	$0.517172\pi$
$912$	−3.61086	−0.119568
$913$	0	0
$914$	14.9318	0.493901
$915$	11.8011	0.390134
$916$	−62.4348	−2.06290
$917$	17.6203	0.581874
$918$	30.8372	1.01778
$919$	10.1858	0.335998	0.167999	−	0.985787i	$-0.446269\pi$
$919$	10.1858	0.335998	0.167999	+	0.985787i	$0.446269\pi$
$920$	20.6385	0.680430
$921$	84.2816	2.77717
$922$	31.0530	1.02268
$923$	−24.7207	−0.813693
$924$	0	0
$925$	47.7537	1.57013
$926$	65.7773	2.16158
$927$	62.5774	2.05531
$928$	34.9763	1.14815
$929$	−1.64448	−0.0539537	−0.0269769	−	0.999636i	$-0.508588\pi$
$929$	−1.64448	−0.0539537	−0.0269769	+	0.999636i	$0.508588\pi$
$930$	−56.7949	−1.86238
$931$	−53.4051	−1.75028
$932$	2.82725	0.0926097
$933$	39.0219	1.27752
$934$	36.9707	1.20972
$935$	0	0
$936$	30.7364	1.00465
$937$	−28.4157	−0.928301	−0.464151	−	0.885756i	$-0.653640\pi$
$937$	−28.4157	−0.928301	−0.464151	+	0.885756i	$0.653640\pi$
$938$	92.3303	3.01469
$939$	11.3526	0.370478
$940$	−105.849	−3.45240
$941$	−34.4934	−1.12445	−0.562227	−	0.826983i	$-0.690055\pi$
$941$	−34.4934	−1.12445	−0.562227	+	0.826983i	$0.690055\pi$
$942$	113.431	3.69578
$943$	−9.57044	−0.311657
$944$	0.206739	0.00672877
$945$	118.081	3.84118
$946$	0	0
$947$	24.7215	0.803342	0.401671	−	0.915784i	$-0.368430\pi$
$947$	24.7215	0.803342	0.401671	+	0.915784i	$0.368430\pi$
$948$	131.468	4.26990
$949$	1.53059	0.0496850
$950$	109.151	3.54131
$951$	−59.0224	−1.91393
$952$	28.7701	0.932446
$953$	42.7613	1.38518	0.692588	−	0.721334i	$-0.256471\pi$
$953$	42.7613	1.38518	0.692588	+	0.721334i	$0.256471\pi$
$954$	109.960	3.56007
$955$	77.0182	2.49225
$956$	45.5468	1.47309
$957$	0	0
$958$	−69.0856	−2.23205
$959$	35.1784	1.13597
$960$	−151.160	−4.87867
$961$	−26.6349	−0.859190
$962$	18.0300	0.581310
$963$	−43.1226	−1.38961
$964$	−74.9015	−2.41241
$965$	−35.3896	−1.13923
$966$	49.7560	1.60087
$967$	−37.6939	−1.21215	−0.606077	−	0.795406i	$-0.707258\pi$
$967$	−37.6939	−1.21215	−0.606077	+	0.795406i	$0.707258\pi$
$968$	0	0
$969$	23.9868	0.770567
$970$	−12.1166	−0.389040
$971$	47.1116	1.51188	0.755942	−	0.654639i	$-0.227179\pi$
$971$	47.1116	1.51188	0.755942	+	0.654639i	$0.227179\pi$
$972$	−38.9513	−1.24936
$973$	33.4680	1.07294
$974$	32.9719	1.05649
$975$	−67.1952	−2.15197
$976$	0.318086	0.0101817
$977$	2.41911	0.0773942	0.0386971	−	0.999251i	$-0.487679\pi$
$977$	2.41911	0.0773942	0.0386971	+	0.999251i	$0.487679\pi$
$978$	−37.6929	−1.20528
$979$	0	0
$980$	183.551	5.86331
$981$	−21.9467	−0.700703
$982$	35.3218	1.12716
$983$	33.1956	1.05877	0.529387	−	0.848380i	$-0.322422\pi$
$983$	33.1956	1.05877	0.529387	+	0.848380i	$0.322422\pi$
$984$	−49.5342	−1.57909
$985$	37.8853	1.20713
$986$	32.2155	1.02595
$987$	−100.812	−3.20889
$988$	25.6777	0.816916
$989$	11.7948	0.375051
$990$	0	0
$991$	−36.7374	−1.16700	−0.583501	−	0.812112i	$-0.698318\pi$
$991$	−36.7374	−1.16700	−0.583501	+	0.812112i	$0.698318\pi$
$992$	11.0408	0.350545
$993$	−15.8993	−0.504549
$994$	−131.447	−4.16924
$995$	−29.3872	−0.931637
$996$	−104.444	−3.30945
$997$	−11.8866	−0.376453	−0.188226	−	0.982126i	$-0.560274\pi$
$997$	−11.8866	−0.376453	−0.188226	+	0.982126i	$0.560274\pi$
$998$	5.45741	0.172751
$999$	25.2941	0.800269

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.v.1.8		64
11.3	even	5		671.2.j.c.306.4	✓	128
11.4	even	5		671.2.j.c.489.4	yes	128
11.10	odd	2		7381.2.a.u.1.57		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.c.306.4	✓	128	11.3	even	5
671.2.j.c.489.4	yes	128	11.4	even	5
7381.2.a.u.1.57		64	11.10	odd	2
7381.2.a.v.1.8		64	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)

\(f(q)\)	\(=\)	\(q-2.30350 q^{2} +2.86548 q^{3} +3.30610 q^{4} +4.11838 q^{5} -6.60062 q^{6} +4.52556 q^{7} -3.00859 q^{8} +5.21098 q^{9} +O(q^{10})\)	\(q-2.30350 q^{2} +2.86548 q^{3} +3.30610 q^{4} +4.11838 q^{5} -6.60062 q^{6} +4.52556 q^{7} -3.00859 q^{8} +5.21098 q^{9} -9.48668 q^{10} +9.47356 q^{12} -1.96052 q^{13} -10.4246 q^{14} +11.8011 q^{15} +0.318086 q^{16} -2.11303 q^{17} -12.0035 q^{18} -3.96158 q^{19} +13.6158 q^{20} +12.9679 q^{21} -1.66566 q^{23} -8.62106 q^{24} +11.9611 q^{25} +4.51605 q^{26} +6.33551 q^{27} +14.9620 q^{28} +6.61869 q^{29} -27.1839 q^{30} +2.08928 q^{31} +5.28447 q^{32} +4.86736 q^{34} +18.6380 q^{35} +17.2280 q^{36} +3.99243 q^{37} +9.12549 q^{38} -5.61783 q^{39} -12.3905 q^{40} +5.74572 q^{41} -29.8716 q^{42} -7.08111 q^{43} +21.4608 q^{45} +3.83685 q^{46} -7.77397 q^{47} +0.911470 q^{48} +13.4807 q^{49} -27.5523 q^{50} -6.05485 q^{51} -6.48167 q^{52} -9.16065 q^{53} -14.5938 q^{54} -13.6156 q^{56} -11.3518 q^{57} -15.2461 q^{58} +0.649946 q^{59} +39.0157 q^{60} +1.00000 q^{61} -4.81266 q^{62} +23.5826 q^{63} -12.8089 q^{64} -8.07417 q^{65} -8.85695 q^{67} -6.98589 q^{68} -4.77293 q^{69} -42.9326 q^{70} +12.6093 q^{71} -15.6777 q^{72} -0.780705 q^{73} -9.19654 q^{74} +34.2742 q^{75} -13.0974 q^{76} +12.9407 q^{78} +13.8774 q^{79} +1.31000 q^{80} +2.52135 q^{81} -13.2353 q^{82} -11.0248 q^{83} +42.8732 q^{84} -8.70227 q^{85} +16.3113 q^{86} +18.9657 q^{87} -9.40639 q^{89} -49.4349 q^{90} -8.87246 q^{91} -5.50685 q^{92} +5.98680 q^{93} +17.9073 q^{94} -16.3153 q^{95} +15.1426 q^{96} +1.27722 q^{97} -31.0528 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9} - 4 q^{10} + 41 q^{12} - q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} + 13 q^{17} + 38 q^{18} - q^{19} + 65 q^{20} + q^{21} + 52 q^{23} + 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} - q^{28} + 19 q^{29} - 19 q^{30} + 45 q^{31} - 24 q^{32} - 23 q^{34} + 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} - 6 q^{39} + 84 q^{40} - 12 q^{41} + 28 q^{42} + 5 q^{43} + 71 q^{45} - 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} + 14 q^{50} + 22 q^{51} - 24 q^{52} + 86 q^{53} - 114 q^{54} + 119 q^{56} - 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} + 64 q^{61} + 13 q^{62} - 28 q^{63} + 135 q^{64} - 30 q^{65} + 2 q^{67} + 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} + 48 q^{72} + 8 q^{73} - 27 q^{74} + 107 q^{75} - 82 q^{76} - 13 q^{78} - 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} + 14 q^{83} + 182 q^{84} - 52 q^{85} + 60 q^{86} - 8 q^{87} + 59 q^{89} - 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} + 21 q^{94} - 26 q^{95} - 86 q^{96} - 39 q^{97} - 57 q^{98}+O(q^{100}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9 - 4 * q^10 + 41 * q^12 - q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 + 13 * q^17 + 38 * q^18 - q^19 + 65 * q^20 + q^21 + 52 * q^23 + 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 - q^28 + 19 * q^29 - 19 * q^30 + 45 * q^31 - 24 * q^32 - 23 * q^34 + 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 - 6 * q^39 + 84 * q^40 - 12 * q^41 + 28 * q^42 + 5 * q^43 + 71 * q^45 - 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 + 14 * q^50 + 22 * q^51 - 24 * q^52 + 86 * q^53 - 114 * q^54 + 119 * q^56 - 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 + 64 * q^61 + 13 * q^62 - 28 * q^63 + 135 * q^64 - 30 * q^65 + 2 * q^67 + 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 + 48 * q^72 + 8 * q^73 - 27 * q^74 + 107 * q^75 - 82 * q^76 - 13 * q^78 - 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 + 14 * q^83 + 182 * q^84 - 52 * q^85 + 60 * q^86 - 8 * q^87 + 59 * q^89 - 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 + 21 * q^94 - 26 * q^95 - 86 * q^96 - 39 * q^97 - 57 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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