LMFDB - Embedded newform 7381.2.a.j.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:	$21$
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)

$f(q)$	$=$	$q-0.942064 q^{2} +2.26946 q^{3} -1.11252 q^{4} +4.16220 q^{5} -2.13797 q^{6} +0.914635 q^{7} +2.93219 q^{8} +2.15044 q^{9} +O(q^{10})$	\(q-0.942064 q^{2} +2.26946 q^{3} -1.11252 q^{4} +4.16220 q^{5} -2.13797 q^{6} +0.914635 q^{7} +2.93219 q^{8} +2.15044 q^{9} -3.92106 q^{10} -2.52481 q^{12} -6.85514 q^{13} -0.861645 q^{14} +9.44594 q^{15} -0.537277 q^{16} +7.07723 q^{17} -2.02585 q^{18} +0.758442 q^{19} -4.63051 q^{20} +2.07573 q^{21} +0.119595 q^{23} +6.65448 q^{24} +12.3239 q^{25} +6.45798 q^{26} -1.92804 q^{27} -1.01755 q^{28} +6.47853 q^{29} -8.89868 q^{30} +8.12191 q^{31} -5.35823 q^{32} -6.66720 q^{34} +3.80690 q^{35} -2.39240 q^{36} -3.59142 q^{37} -0.714500 q^{38} -15.5575 q^{39} +12.2044 q^{40} +3.48107 q^{41} -1.95547 q^{42} +5.70063 q^{43} +8.95057 q^{45} -0.112666 q^{46} -3.93114 q^{47} -1.21933 q^{48} -6.16344 q^{49} -11.6099 q^{50} +16.0615 q^{51} +7.62645 q^{52} +7.61747 q^{53} +1.81633 q^{54} +2.68188 q^{56} +1.72125 q^{57} -6.10319 q^{58} -8.02724 q^{59} -10.5088 q^{60} -1.00000 q^{61} -7.65135 q^{62} +1.96687 q^{63} +6.12235 q^{64} -28.5325 q^{65} -9.13346 q^{67} -7.87353 q^{68} +0.271415 q^{69} -3.58634 q^{70} +12.7273 q^{71} +6.30550 q^{72} -10.0229 q^{73} +3.38335 q^{74} +27.9686 q^{75} -0.843778 q^{76} +14.6561 q^{78} -6.32794 q^{79} -2.23625 q^{80} -10.8269 q^{81} -3.27939 q^{82} +16.9673 q^{83} -2.30928 q^{84} +29.4569 q^{85} -5.37035 q^{86} +14.7028 q^{87} -0.929850 q^{89} -8.43201 q^{90} -6.26995 q^{91} -0.133051 q^{92} +18.4323 q^{93} +3.70338 q^{94} +3.15679 q^{95} -12.1603 q^{96} +15.9555 q^{97} +5.80636 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} - 5 q^{6} - 5 q^{7} + 6 q^{8} + 40 q^{9}+O(q^{10}) $ 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 - 5 * q^6 - 5 * q^7 + 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} - 5 q^{6} - 5 q^{7} + 6 q^{8} + 40 q^{9} - q^{10} + 6 q^{12} - 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} - q^{17} + 5 q^{18} - 15 q^{19} - 2 q^{20} - 16 q^{21} + 11 q^{23} + 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} + 16 q^{28} + 9 q^{29} - 16 q^{30} + 22 q^{31} - 3 q^{32} + 33 q^{34} + 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} + 28 q^{39} + 16 q^{40} - 7 q^{41} - 55 q^{42} - 16 q^{43} + 44 q^{45} + 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} + 33 q^{50} + 19 q^{51} - 60 q^{52} + 9 q^{53} - 13 q^{54} + 44 q^{56} - 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} - 21 q^{61} + 23 q^{62} - 24 q^{63} + 66 q^{64} - 25 q^{65} + 38 q^{67} + 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} + 75 q^{72} - 20 q^{73} + 12 q^{74} - 10 q^{75} - 59 q^{76} - 14 q^{78} - q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} + 19 q^{83} + 14 q^{84} - 38 q^{85} - 3 q^{86} - 4 q^{87} + 37 q^{89} + 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} + 64 q^{94} + 43 q^{95} + 38 q^{96} + 68 q^{97} + 2 q^{98}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 - 5 * q^6 - 5 * q^7 + 6 * q^8 + 40 * q^9 - q^10 + 6 * q^12 - 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 - q^17 + 5 * q^18 - 15 * q^19 - 2 * q^20 - 16 * q^21 + 11 * q^23 + 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 + 16 * q^28 + 9 * q^29 - 16 * q^30 + 22 * q^31 - 3 * q^32 + 33 * q^34 + 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 + 28 * q^39 + 16 * q^40 - 7 * q^41 - 55 * q^42 - 16 * q^43 + 44 * q^45 + 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 + 33 * q^50 + 19 * q^51 - 60 * q^52 + 9 * q^53 - 13 * q^54 + 44 * q^56 - 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 - 21 * q^61 + 23 * q^62 - 24 * q^63 + 66 * q^64 - 25 * q^65 + 38 * q^67 + 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 + 75 * q^72 - 20 * q^73 + 12 * q^74 - 10 * q^75 - 59 * q^76 - 14 * q^78 - q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 + 19 * q^83 + 14 * q^84 - 38 * q^85 - 3 * q^86 - 4 * q^87 + 37 * q^89 + 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 + 64 * q^94 + 43 * q^95 + 38 * q^96 + 68 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.942064	−0.666140	−0.333070	−	0.942902i	$-0.608084\pi$
$2$	−0.942064	−0.666140	−0.333070	+	0.942902i	$0.608084\pi$
$3$	2.26946	1.31027	0.655136	−	0.755511i	$-0.272611\pi$
$3$	2.26946	1.31027	0.655136	+	0.755511i	$0.272611\pi$
$4$	−1.11252	−0.556258
$5$	4.16220	1.86139	0.930696	−	0.365792i	$-0.119202\pi$
$5$	4.16220	1.86139	0.930696	+	0.365792i	$0.119202\pi$
$6$	−2.13797	−0.872824
$7$	0.914635	0.345700	0.172850	−	0.984948i	$-0.444702\pi$
$7$	0.914635	0.345700	0.172850	+	0.984948i	$0.444702\pi$
$8$	2.93219	1.03669
$9$	2.15044	0.716814
$10$	−3.92106	−1.23995
$11$	0	0
$11$	0	0
$12$	−2.52481	−0.728849
$13$	−6.85514	−1.90127	−0.950637	−	0.310306i	$-0.899569\pi$
$13$	−6.85514	−1.90127	−0.950637	+	0.310306i	$0.899569\pi$
$14$	−0.861645	−0.230284
$15$	9.44594	2.43893
$16$	−0.537277	−0.134319
$17$	7.07723	1.71648	0.858241	−	0.513248i	$-0.171558\pi$
$17$	7.07723	1.71648	0.858241	+	0.513248i	$0.171558\pi$
$18$	−2.02585	−0.477498
$19$	0.758442	0.173998	0.0869992	−	0.996208i	$-0.472272\pi$
$19$	0.758442	0.173998	0.0869992	+	0.996208i	$0.472272\pi$
$20$	−4.63051	−1.03541
$21$	2.07573	0.452961
$22$	0	0
$23$	0.119595	0.0249372	0.0124686	−	0.999922i	$-0.496031\pi$
$23$	0.119595	0.0249372	0.0124686	+	0.999922i	$0.496031\pi$
$24$	6.65448	1.35834
$25$	12.3239	2.46478
$26$	6.45798	1.26651
$27$	−1.92804	−0.371051
$28$	−1.01755	−0.192298
$29$	6.47853	1.20303	0.601517	−	0.798860i	$-0.294563\pi$
$29$	6.47853	1.20303	0.601517	+	0.798860i	$0.294563\pi$
$30$	−8.89868	−1.62467
$31$	8.12191	1.45874	0.729369	−	0.684121i	$-0.239814\pi$
$31$	8.12191	1.45874	0.729369	+	0.684121i	$0.239814\pi$
$32$	−5.35823	−0.947210
$33$	0	0
$34$	−6.66720	−1.14342
$35$	3.80690	0.643483
$36$	−2.39240	−0.398733
$37$	−3.59142	−0.590426	−0.295213	−	0.955431i	$-0.595391\pi$
$37$	−3.59142	−0.590426	−0.295213	+	0.955431i	$0.595391\pi$
$38$	−0.714500	−0.115907
$39$	−15.5575	−2.49119
$40$	12.2044	1.92968
$41$	3.48107	0.543651	0.271826	−	0.962346i	$-0.412373\pi$
$41$	3.48107	0.543651	0.271826	+	0.962346i	$0.412373\pi$
$42$	−1.95547	−0.301735
$43$	5.70063	0.869338	0.434669	−	0.900590i	$-0.356865\pi$
$43$	5.70063	0.869338	0.434669	+	0.900590i	$0.356865\pi$
$44$	0	0
$45$	8.95057	1.33427
$46$	−0.112666	−0.0166117
$47$	−3.93114	−0.573415	−0.286708	−	0.958018i	$-0.592561\pi$
$47$	−3.93114	−0.573415	−0.286708	+	0.958018i	$0.592561\pi$
$48$	−1.21933	−0.175995
$49$	−6.16344	−0.880492
$50$	−11.6099	−1.64189
$51$	16.0615	2.24906
$52$	7.62645	1.05760
$53$	7.61747	1.04634	0.523170	−	0.852228i	$-0.324749\pi$
$53$	7.61747	1.04634	0.523170	+	0.852228i	$0.324749\pi$
$54$	1.81633	0.247172
$55$	0	0
$56$	2.68188	0.358382
$57$	1.72125	0.227985
$58$	−6.10319	−0.801388
$59$	−8.02724	−1.04506	−0.522529	−	0.852621i	$-0.675011\pi$
$59$	−8.02724	−1.04506	−0.522529	+	0.852621i	$0.675011\pi$
$60$	−10.5088	−1.35668
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−7.65135	−0.971723
$63$	1.96687	0.247802
$64$	6.12235	0.765293
$65$	−28.5325	−3.53902
$66$	0	0
$67$	−9.13346	−1.11583	−0.557915	−	0.829898i	$-0.688399\pi$
$67$	−9.13346	−1.11583	−0.557915	+	0.829898i	$0.688399\pi$
$68$	−7.87353	−0.954806
$69$	0.271415	0.0326745
$70$	−3.58634	−0.428650
$71$	12.7273	1.51046	0.755229	−	0.655461i	$-0.227526\pi$
$71$	12.7273	1.51046	0.755229	+	0.655461i	$0.227526\pi$
$72$	6.30550	0.743110
$73$	−10.0229	−1.17309	−0.586545	−	0.809917i	$-0.699512\pi$
$73$	−10.0229	−1.17309	−0.586545	+	0.809917i	$0.699512\pi$
$74$	3.38335	0.393306
$75$	27.9686	3.22954
$76$	−0.843778	−0.0967880
$77$	0	0
$78$	14.6561	1.65948
$79$	−6.32794	−0.711949	−0.355975	−	0.934496i	$-0.615851\pi$
$79$	−6.32794	−0.711949	−0.355975	+	0.934496i	$0.615851\pi$
$80$	−2.23625	−0.250021
$81$	−10.8269	−1.20299
$82$	−3.27939	−0.362148
$83$	16.9673	1.86240	0.931202	−	0.364504i	$-0.118762\pi$
$83$	16.9673	1.86240	0.931202	+	0.364504i	$0.118762\pi$
$84$	−2.30928	−0.251963
$85$	29.4569	3.19505
$86$	−5.37035	−0.579100
$87$	14.7028	1.57630
$88$	0	0
$89$	−0.929850	−0.0985639	−0.0492820	−	0.998785i	$-0.515693\pi$
$89$	−0.929850	−0.0985639	−0.0492820	+	0.998785i	$0.515693\pi$
$90$	−8.43201	−0.888812
$91$	−6.26995	−0.657270
$92$	−0.133051	−0.0138715
$93$	18.4323	1.91134
$94$	3.70338	0.381975
$95$	3.15679	0.323879
$96$	−12.1603	−1.24110
$97$	15.9555	1.62003	0.810016	−	0.586408i	$-0.199458\pi$
$97$	15.9555	1.62003	0.810016	+	0.586408i	$0.199458\pi$
$98$	5.80636	0.586530
$99$	0	0
$100$	−13.7106	−1.37106
$101$	−3.89969	−0.388034	−0.194017	−	0.980998i	$-0.562152\pi$
$101$	−3.89969	−0.388034	−0.194017	+	0.980998i	$0.562152\pi$
$102$	−15.1309	−1.49819
$103$	−8.88441	−0.875407	−0.437703	−	0.899119i	$-0.644208\pi$
$103$	−8.88441	−0.875407	−0.437703	+	0.899119i	$0.644208\pi$
$104$	−20.1006	−1.97102
$105$	8.63959	0.843138
$106$	−7.17615	−0.697009
$107$	−1.43091	−0.138331	−0.0691657	−	0.997605i	$-0.522034\pi$
$107$	−1.43091	−0.138331	−0.0691657	+	0.997605i	$0.522034\pi$
$108$	2.14497	0.206400
$109$	−5.58225	−0.534682	−0.267341	−	0.963602i	$-0.586145\pi$
$109$	−5.58225	−0.534682	−0.267341	+	0.963602i	$0.586145\pi$
$110$	0	0
$111$	−8.15058	−0.773619
$112$	−0.491412	−0.0464341
$113$	−0.911691	−0.0857646	−0.0428823	−	0.999080i	$-0.513654\pi$
$113$	−0.911691	−0.0857646	−0.0428823	+	0.999080i	$0.513654\pi$
$114$	−1.62153	−0.151870
$115$	0.497777	0.0464179
$116$	−7.20747	−0.669197
$117$	−14.7416	−1.36286
$118$	7.56218	0.696155
$119$	6.47309	0.593387
$120$	27.6973	2.52840
$121$	0	0
$122$	0.942064	0.0852904
$123$	7.90014	0.712332
$124$	−9.03575	−0.811434
$125$	30.4836	2.72654
$126$	−1.85292	−0.165071
$127$	−2.04484	−0.181450	−0.0907250	−	0.995876i	$-0.528918\pi$
$127$	−2.04484	−0.181450	−0.0907250	+	0.995876i	$0.528918\pi$
$128$	4.94882	0.437418
$129$	12.9373	1.13907
$130$	26.8794	2.35748
$131$	−2.29123	−0.200185	−0.100093	−	0.994978i	$-0.531914\pi$
$131$	−2.29123	−0.200185	−0.100093	+	0.994978i	$0.531914\pi$
$132$	0	0
$133$	0.693698	0.0601512
$134$	8.60431	0.743299
$135$	−8.02488	−0.690672
$136$	20.7518	1.77945
$137$	−14.0851	−1.20337	−0.601686	−	0.798733i	$-0.705504\pi$
$137$	−14.0851	−1.20337	−0.601686	+	0.798733i	$0.705504\pi$
$138$	−0.255690	−0.0217658
$139$	10.8222	0.917926	0.458963	−	0.888455i	$-0.348221\pi$
$139$	10.8222	0.917926	0.458963	+	0.888455i	$0.348221\pi$
$140$	−4.23523	−0.357942
$141$	−8.92155	−0.751330
$142$	−11.9900	−1.00618
$143$	0	0
$144$	−1.15538	−0.0962819
$145$	26.9650	2.23932
$146$	9.44219	0.781441
$147$	−13.9877	−1.15368
$148$	3.99551	0.328429
$149$	7.68545	0.629617	0.314808	−	0.949155i	$-0.398060\pi$
$149$	7.68545	0.629617	0.314808	+	0.949155i	$0.398060\pi$
$150$	−26.3482	−2.15132
$151$	14.2789	1.16200	0.580998	−	0.813905i	$-0.302662\pi$
$151$	14.2789	1.16200	0.580998	+	0.813905i	$0.302662\pi$
$152$	2.22389	0.180382
$153$	15.2192	1.23040
$154$	0	0
$155$	33.8050	2.71528
$156$	17.3079	1.38574
$157$	13.5063	1.07792	0.538961	−	0.842331i	$-0.318817\pi$
$157$	13.5063	1.07792	0.538961	+	0.842331i	$0.318817\pi$
$158$	5.96133	0.474258
$159$	17.2875	1.37099
$160$	−22.3020	−1.76313
$161$	0.109385	0.00862078
$162$	10.1997	0.801361
$163$	−10.8779	−0.852024	−0.426012	−	0.904718i	$-0.640082\pi$
$163$	−10.8779	−0.852024	−0.426012	+	0.904718i	$0.640082\pi$
$164$	−3.87274	−0.302410
$165$	0	0
$166$	−15.9843	−1.24062
$167$	2.20692	0.170777	0.0853884	−	0.996348i	$-0.472787\pi$
$167$	2.20692	0.170777	0.0853884	+	0.996348i	$0.472787\pi$
$168$	6.08642	0.469578
$169$	33.9929	2.61484
$170$	−27.7502	−2.12835
$171$	1.63098	0.124725
$172$	−6.34204	−0.483576
$173$	−4.28336	−0.325658	−0.162829	−	0.986654i	$-0.552062\pi$
$173$	−4.28336	−0.325658	−0.162829	+	0.986654i	$0.552062\pi$
$174$	−13.8509	−1.05004
$175$	11.2719	0.852075
$176$	0	0
$177$	−18.2175	−1.36931
$178$	0.875978	0.0656573
$179$	−7.64364	−0.571312	−0.285656	−	0.958332i	$-0.592212\pi$
$179$	−7.64364	−0.571312	−0.285656	+	0.958332i	$0.592212\pi$
$180$	−9.95765	−0.742200
$181$	11.9672	0.889515	0.444757	−	0.895651i	$-0.353290\pi$
$181$	11.9672	0.889515	0.444757	+	0.895651i	$0.353290\pi$
$182$	5.90670	0.437833
$183$	−2.26946	−0.167763
$184$	0.350674	0.0258520
$185$	−14.9482	−1.09901
$186$	−17.3644	−1.27322
$187$	0	0
$188$	4.37345	0.318967
$189$	−1.76345	−0.128272
$190$	−2.97389	−0.215749
$191$	−0.835454	−0.0604513	−0.0302257	−	0.999543i	$-0.509623\pi$
$191$	−0.835454	−0.0604513	−0.0302257	+	0.999543i	$0.509623\pi$
$192$	13.8944	1.00274
$193$	10.7787	0.775869	0.387934	−	0.921687i	$-0.373189\pi$
$193$	10.7787	0.775869	0.387934	+	0.921687i	$0.373189\pi$
$194$	−15.0311	−1.07917
$195$	−64.7532	−4.63708
$196$	6.85693	0.489780
$197$	−9.31428	−0.663615	−0.331808	−	0.943347i	$-0.607658\pi$
$197$	−9.31428	−0.663615	−0.331808	+	0.943347i	$0.607658\pi$
$198$	0	0
$199$	18.7278	1.32758	0.663788	−	0.747921i	$-0.268948\pi$
$199$	18.7278	1.32758	0.663788	+	0.747921i	$0.268948\pi$
$200$	36.1361	2.55520
$201$	−20.7280	−1.46204
$202$	3.67376	0.258485
$203$	5.92550	0.415888
$204$	−17.8687	−1.25106
$205$	14.4889	1.01195
$206$	8.36968	0.583143
$207$	0.257181	0.0178753
$208$	3.68311	0.255378
$209$	0	0
$210$	−8.13905	−0.561648
$211$	21.8515	1.50432	0.752159	−	0.658982i	$-0.229013\pi$
$211$	21.8515	1.50432	0.752159	+	0.658982i	$0.229013\pi$
$212$	−8.47456	−0.582035
$213$	28.8842	1.97911
$214$	1.34801	0.0921481
$215$	23.7272	1.61818
$216$	−5.65337	−0.384663
$217$	7.42858	0.504285
$218$	5.25883	0.356173
$219$	−22.7465	−1.53707
$220$	0	0
$221$	−48.5154	−3.26350
$222$	7.67837	0.515338
$223$	5.38796	0.360805	0.180402	−	0.983593i	$-0.442260\pi$
$223$	5.38796	0.360805	0.180402	+	0.983593i	$0.442260\pi$
$224$	−4.90082	−0.327450
$225$	26.5019	1.76679
$226$	0.858871	0.0571312
$227$	−6.06937	−0.402838	−0.201419	−	0.979505i	$-0.564555\pi$
$227$	−6.06937	−0.402838	−0.201419	+	0.979505i	$0.564555\pi$
$228$	−1.91492	−0.126819
$229$	3.78348	0.250019	0.125010	−	0.992156i	$-0.460104\pi$
$229$	3.78348	0.250019	0.125010	+	0.992156i	$0.460104\pi$
$230$	−0.468937	−0.0309208
$231$	0	0
$232$	18.9963	1.24717
$233$	−17.0813	−1.11903	−0.559515	−	0.828820i	$-0.689013\pi$
$233$	−17.0813	−1.11903	−0.559515	+	0.828820i	$0.689013\pi$
$234$	13.8875	0.907855
$235$	−16.3622	−1.06735
$236$	8.93044	0.581322
$237$	−14.3610	−0.932847
$238$	−6.09806	−0.395279
$239$	−5.52756	−0.357548	−0.178774	−	0.983890i	$-0.557213\pi$
$239$	−5.52756	−0.357548	−0.178774	+	0.983890i	$0.557213\pi$
$240$	−5.07509	−0.327595
$241$	−18.4791	−1.19034	−0.595172	−	0.803598i	$-0.702916\pi$
$241$	−18.4791	−1.19034	−0.595172	+	0.803598i	$0.702916\pi$
$242$	0	0
$243$	−18.7871	−1.20520
$244$	1.11252	0.0712215
$245$	−25.6535	−1.63894
$246$	−7.44244	−0.474512
$247$	−5.19922	−0.330819
$248$	23.8150	1.51225
$249$	38.5066	2.44026
$250$	−28.7175	−1.81626
$251$	14.0522	0.886966	0.443483	−	0.896283i	$-0.353743\pi$
$251$	14.0522	0.886966	0.443483	+	0.896283i	$0.353743\pi$
$252$	−2.18817	−0.137842
$253$	0	0
$254$	1.92637	0.120871
$255$	66.8511	4.18638
$256$	−16.9068	−1.05667
$257$	−18.0106	−1.12347	−0.561734	−	0.827318i	$-0.689866\pi$
$257$	−18.0106	−1.12347	−0.561734	+	0.827318i	$0.689866\pi$
$258$	−12.1878	−0.758779
$259$	−3.28484	−0.204110
$260$	31.7428	1.96861
$261$	13.9317	0.862351
$262$	2.15848	0.133351
$263$	−8.90385	−0.549035	−0.274517	−	0.961582i	$-0.588518\pi$
$263$	−8.90385	−0.549035	−0.274517	+	0.961582i	$0.588518\pi$
$264$	0	0
$265$	31.7055	1.94765
$266$	−0.653507	−0.0400691
$267$	−2.11026	−0.129146
$268$	10.1611	0.620689
$269$	22.2434	1.35620	0.678102	−	0.734968i	$-0.262803\pi$
$269$	22.2434	1.35620	0.678102	+	0.734968i	$0.262803\pi$
$270$	7.55995	0.460084
$271$	15.7517	0.956850	0.478425	−	0.878128i	$-0.341208\pi$
$271$	15.7517	0.956850	0.478425	+	0.878128i	$0.341208\pi$
$272$	−3.80243	−0.230556
$273$	−14.2294	−0.861202
$274$	13.2691	0.801614
$275$	0	0
$276$	−0.301953	−0.0181755
$277$	8.81685	0.529753	0.264876	−	0.964282i	$-0.414669\pi$
$277$	8.81685	0.529753	0.264876	+	0.964282i	$0.414669\pi$
$278$	−10.1952	−0.611467
$279$	17.4657	1.04564
$280$	11.1625	0.667089
$281$	−5.42753	−0.323779	−0.161890	−	0.986809i	$-0.551759\pi$
$281$	−5.42753	−0.323779	−0.161890	+	0.986809i	$0.551759\pi$
$282$	8.40467	0.500491
$283$	−25.2993	−1.50389	−0.751943	−	0.659228i	$-0.770883\pi$
$283$	−25.2993	−1.50389	−0.751943	+	0.659228i	$0.770883\pi$
$284$	−14.1594	−0.840204
$285$	7.16420	0.424370
$286$	0	0
$287$	3.18391	0.187940
$288$	−11.5226	−0.678973
$289$	33.0872	1.94631
$290$	−25.4027	−1.49170
$291$	36.2103	2.12268
$292$	11.1506	0.652540
$293$	−30.7679	−1.79748	−0.898739	−	0.438485i	$-0.855515\pi$
$293$	−30.7679	−1.79748	−0.898739	+	0.438485i	$0.855515\pi$
$294$	13.1773	0.768515
$295$	−33.4110	−1.94526
$296$	−10.5307	−0.612086
$297$	0	0
$298$	−7.24018	−0.419413
$299$	−0.819837	−0.0474124
$300$	−31.1155	−1.79646
$301$	5.21400	0.300530
$302$	−13.4516	−0.774052
$303$	−8.85019	−0.508430
$304$	−0.407493	−0.0233713
$305$	−4.16220	−0.238327
$306$	−14.3374	−0.819617
$307$	−5.68781	−0.324620	−0.162310	−	0.986740i	$-0.551895\pi$
$307$	−5.68781	−0.324620	−0.162310	+	0.986740i	$0.551895\pi$
$308$	0	0
$309$	−20.1628	−1.14702
$310$	−31.8465	−1.80876
$311$	4.03491	0.228799	0.114399	−	0.993435i	$-0.463506\pi$
$311$	4.03491	0.228799	0.114399	+	0.993435i	$0.463506\pi$
$312$	−45.6174	−2.58258
$313$	21.9128	1.23859	0.619294	−	0.785159i	$-0.287419\pi$
$313$	21.9128	1.23859	0.619294	+	0.785159i	$0.287419\pi$
$314$	−12.7238	−0.718046
$315$	8.18651	0.461258
$316$	7.03994	0.396027
$317$	−25.9100	−1.45525	−0.727625	−	0.685975i	$-0.759376\pi$
$317$	−25.9100	−1.45525	−0.727625	+	0.685975i	$0.759376\pi$
$318$	−16.2860	−0.913272
$319$	0	0
$320$	25.4824	1.42451
$321$	−3.24740	−0.181252
$322$	−0.103048	−0.00574264
$323$	5.36767	0.298665
$324$	12.0451	0.669174
$325$	−84.4822	−4.68623
$326$	10.2477	0.567567
$327$	−12.6687	−0.700579
$328$	10.2071	0.563595
$329$	−3.59556	−0.198230
$330$	0	0
$331$	−4.18807	−0.230197	−0.115099	−	0.993354i	$-0.536718\pi$
$331$	−4.18807	−0.230197	−0.115099	+	0.993354i	$0.536718\pi$
$332$	−18.8764	−1.03598
$333$	−7.72314	−0.423225
$334$	−2.07906	−0.113761
$335$	−38.0153	−2.07700
$336$	−1.11524	−0.0608413
$337$	−31.1255	−1.69551	−0.847757	−	0.530385i	$-0.822047\pi$
$337$	−31.1255	−1.69551	−0.847757	+	0.530385i	$0.822047\pi$
$338$	−32.0235	−1.74185
$339$	−2.06904	−0.112375
$340$	−32.7712	−1.77727
$341$	0	0
$342$	−1.53649	−0.0830839
$343$	−12.0398	−0.650085
$344$	16.7153	0.901229
$345$	1.12968	0.0608201
$346$	4.03520	0.216934
$347$	−15.5977	−0.837326	−0.418663	−	0.908142i	$-0.637501\pi$
$347$	−15.5977	−0.837326	−0.418663	+	0.908142i	$0.637501\pi$
$348$	−16.3571	−0.876830
$349$	6.70862	0.359104	0.179552	−	0.983748i	$-0.442535\pi$
$349$	6.70862	0.359104	0.179552	+	0.983748i	$0.442535\pi$
$350$	−10.6188	−0.567601
$351$	13.2170	0.705469
$352$	0	0
$353$	−1.11688	−0.0594453	−0.0297227	−	0.999558i	$-0.509462\pi$
$353$	−1.11688	−0.0594453	−0.0297227	+	0.999558i	$0.509462\pi$
$354$	17.1620	0.912152
$355$	52.9738	2.81156
$356$	1.03447	0.0548270
$357$	14.6904	0.777499
$358$	7.20079	0.380574
$359$	−27.4685	−1.44973	−0.724866	−	0.688890i	$-0.758098\pi$
$359$	−27.4685	−1.44973	−0.724866	+	0.688890i	$0.758098\pi$
$360$	26.2448	1.38322
$361$	−18.4248	−0.969725
$362$	−11.2739	−0.592541
$363$	0	0
$364$	6.97542	0.365611
$365$	−41.7172	−2.18358
$366$	2.13797	0.111754
$367$	37.7724	1.97170	0.985852	−	0.167620i	$-0.0536082\pi$
$367$	37.7724	1.97170	0.985852	+	0.167620i	$0.0536082\pi$
$368$	−0.0642554	−0.00334954
$369$	7.48583	0.389697
$370$	14.0822	0.732097
$371$	6.96721	0.361720
$372$	−20.5063	−1.06320
$373$	11.1892	0.579353	0.289676	−	0.957125i	$-0.406452\pi$
$373$	11.1892	0.579353	0.289676	+	0.957125i	$0.406452\pi$
$374$	0	0
$375$	69.1813	3.57251
$376$	−11.5268	−0.594451
$377$	−44.4112	−2.28730
$378$	1.66128	0.0854472
$379$	22.3776	1.14946	0.574730	−	0.818343i	$-0.305107\pi$
$379$	22.3776	1.14946	0.574730	+	0.818343i	$0.305107\pi$
$380$	−3.51198	−0.180161
$381$	−4.64067	−0.237749
$382$	0.787051	0.0402690
$383$	18.5532	0.948022	0.474011	−	0.880519i	$-0.342806\pi$
$383$	18.5532	0.948022	0.474011	+	0.880519i	$0.342806\pi$
$384$	11.2311	0.573136
$385$	0	0
$386$	−10.1542	−0.516837
$387$	12.2589	0.623153
$388$	−17.7507	−0.901156
$389$	−18.3647	−0.931126	−0.465563	−	0.885015i	$-0.654148\pi$
$389$	−18.3647	−0.931126	−0.465563	+	0.885015i	$0.654148\pi$
$390$	61.0017	3.08894
$391$	0.846399	0.0428042
$392$	−18.0724	−0.912793
$393$	−5.19984	−0.262297
$394$	8.77465	0.442060
$395$	−26.3382	−1.32522
$396$	0	0
$397$	−1.08826	−0.0546182	−0.0273091	−	0.999627i	$-0.508694\pi$
$397$	−1.08826	−0.0546182	−0.0273091	+	0.999627i	$0.508694\pi$
$398$	−17.6427	−0.884351
$399$	1.57432	0.0788145
$400$	−6.62136	−0.331068
$401$	−6.73481	−0.336320	−0.168160	−	0.985760i	$-0.553783\pi$
$401$	−6.73481	−0.336320	−0.168160	+	0.985760i	$0.553783\pi$
$402$	19.5271	0.973924
$403$	−55.6768	−2.77346
$404$	4.33847	0.215847
$405$	−45.0638	−2.23924
$406$	−5.58220	−0.277040
$407$	0	0
$408$	47.0953	2.33156
$409$	30.6490	1.51550	0.757748	−	0.652547i	$-0.226300\pi$
$409$	30.6490	1.51550	0.757748	+	0.652547i	$0.226300\pi$
$410$	−13.6495	−0.674099
$411$	−31.9656	−1.57675
$412$	9.88405	0.486952
$413$	−7.34200	−0.361276
$414$	−0.242281	−0.0119075
$415$	70.6213	3.46666
$416$	36.7314	1.80090
$417$	24.5605	1.20273
$418$	0	0
$419$	−17.2551	−0.842966	−0.421483	−	0.906836i	$-0.638490\pi$
$419$	−17.2551	−0.842966	−0.421483	+	0.906836i	$0.638490\pi$
$420$	−9.61168	−0.469002
$421$	−5.65725	−0.275717	−0.137859	−	0.990452i	$-0.544022\pi$
$421$	−5.65725	−0.275717	−0.137859	+	0.990452i	$0.544022\pi$
$422$	−20.5855	−1.00209
$423$	−8.45368	−0.411032
$424$	22.3359	1.08473
$425$	87.2192	4.23075
$426$	−27.2107	−1.31836
$427$	−0.914635	−0.0442623
$428$	1.59191	0.0769480
$429$	0	0
$430$	−22.3525	−1.07793
$431$	11.6170	0.559571	0.279786	−	0.960062i	$-0.409737\pi$
$431$	11.6170	0.559571	0.279786	+	0.960062i	$0.409737\pi$
$432$	1.03589	0.0498393
$433$	2.70697	0.130089	0.0650444	−	0.997882i	$-0.479281\pi$
$433$	2.70697	0.130089	0.0650444	+	0.997882i	$0.479281\pi$
$434$	−6.99820	−0.335924
$435$	61.1959	2.93412
$436$	6.21034	0.297421
$437$	0.0907055	0.00433903
$438$	21.4287	1.02390
$439$	−11.8107	−0.563694	−0.281847	−	0.959459i	$-0.590947\pi$
$439$	−11.8107	−0.563694	−0.281847	+	0.959459i	$0.590947\pi$
$440$	0	0
$441$	−13.2541	−0.631149
$442$	45.7046	2.17395
$443$	1.36325	0.0647702	0.0323851	−	0.999475i	$-0.489690\pi$
$443$	1.36325	0.0647702	0.0323851	+	0.999475i	$0.489690\pi$
$444$	9.06765	0.430332
$445$	−3.87022	−0.183466
$446$	−5.07581	−0.240346
$447$	17.4418	0.824969
$448$	5.59971	0.264562
$449$	22.8380	1.07779	0.538895	−	0.842373i	$-0.318842\pi$
$449$	22.8380	1.07779	0.538895	+	0.842373i	$0.318842\pi$
$450$	−24.9664	−1.17693
$451$	0	0
$452$	1.01427	0.0477073
$453$	32.4053	1.52253
$454$	5.71774	0.268347
$455$	−26.0968	−1.22344
$456$	5.04703	0.236349
$457$	−3.92443	−0.183577	−0.0917886	−	0.995779i	$-0.529258\pi$
$457$	−3.92443	−0.183577	−0.0917886	+	0.995779i	$0.529258\pi$
$458$	−3.56428	−0.166548
$459$	−13.6452	−0.636902
$460$	−0.553784	−0.0258203
$461$	18.0655	0.841396	0.420698	−	0.907201i	$-0.361785\pi$
$461$	18.0655	0.841396	0.420698	+	0.907201i	$0.361785\pi$
$462$	0	0
$463$	−26.8804	−1.24924	−0.624618	−	0.780930i	$-0.714745\pi$
$463$	−26.8804	−1.24924	−0.624618	+	0.780930i	$0.714745\pi$
$464$	−3.48077	−0.161591
$465$	76.7191	3.55776
$466$	16.0916	0.745431
$467$	28.9914	1.34156	0.670781	−	0.741655i	$-0.265959\pi$
$467$	28.9914	1.34156	0.670781	+	0.741655i	$0.265959\pi$
$468$	16.4002	0.758101
$469$	−8.35379	−0.385742
$470$	15.4142	0.711005
$471$	30.6520	1.41237
$472$	−23.5374	−1.08340
$473$	0	0
$474$	13.5290	0.621407
$475$	9.34697	0.428869
$476$	−7.20141	−0.330076
$477$	16.3809	0.750031
$478$	5.20731	0.238177
$479$	12.0538	0.550752	0.275376	−	0.961337i	$-0.411198\pi$
$479$	12.0538	0.550752	0.275376	+	0.961337i	$0.411198\pi$
$480$	−50.6135	−2.31018
$481$	24.6197	1.12256
$482$	17.4085	0.792935
$483$	0.248246	0.0112956
$484$	0	0
$485$	66.4099	3.01552
$486$	17.6987	0.802829
$487$	2.40506	0.108984	0.0544918	−	0.998514i	$-0.482646\pi$
$487$	2.40506	0.108984	0.0544918	+	0.998514i	$0.482646\pi$
$488$	−2.93219	−0.132734
$489$	−24.6870	−1.11638
$490$	24.1672	1.09176
$491$	3.18966	0.143947	0.0719737	−	0.997407i	$-0.477070\pi$
$491$	3.18966	0.143947	0.0719737	+	0.997407i	$0.477070\pi$
$492$	−8.78903	−0.396240
$493$	45.8501	2.06498
$494$	4.89800	0.220371
$495$	0	0
$496$	−4.36371	−0.195936
$497$	11.6409	0.522165
$498$	−36.2757	−1.62555
$499$	−31.1467	−1.39432	−0.697160	−	0.716916i	$-0.745553\pi$
$499$	−31.1467	−1.39432	−0.697160	+	0.716916i	$0.745553\pi$
$500$	−33.9135	−1.51666
$501$	5.00852	0.223764
$502$	−13.2381	−0.590844
$503$	0.912851	0.0407020	0.0203510	−	0.999793i	$-0.493522\pi$
$503$	0.912851	0.0407020	0.0203510	+	0.999793i	$0.493522\pi$
$504$	5.76723	0.256893
$505$	−16.2313	−0.722284
$506$	0	0
$507$	77.1455	3.42615
$508$	2.27491	0.100933
$509$	15.5630	0.689820	0.344910	−	0.938636i	$-0.387910\pi$
$509$	15.5630	0.689820	0.344910	+	0.938636i	$0.387910\pi$
$510$	−62.9780	−2.78871
$511$	−9.16728	−0.405537
$512$	6.02965	0.266475
$513$	−1.46230	−0.0645623
$514$	16.9671	0.748387
$515$	−36.9787	−1.62948
$516$	−14.3930	−0.633616
$517$	0	0
$518$	3.09453	0.135966
$519$	−9.72092	−0.426701
$520$	−83.6626	−3.66885
$521$	20.7782	0.910309	0.455155	−	0.890412i	$-0.349584\pi$
$521$	20.7782	0.910309	0.455155	+	0.890412i	$0.349584\pi$
$522$	−13.1246	−0.574446
$523$	23.9406	1.04685	0.523426	−	0.852071i	$-0.324654\pi$
$523$	23.9406	1.04685	0.523426	+	0.852071i	$0.324654\pi$
$524$	2.54903	0.111355
$525$	25.5811	1.11645
$526$	8.38799	0.365734
$527$	57.4806	2.50390
$528$	0	0
$529$	−22.9857	−0.999378
$530$	−29.8686	−1.29741
$531$	−17.2621	−0.749112
$532$	−0.771750	−0.0334596
$533$	−23.8632	−1.03363
$534$	1.98800	0.0860290
$535$	−5.95574	−0.257489
$536$	−26.7810	−1.15676
$537$	−17.3469	−0.748575
$538$	−20.9547	−0.903421
$539$	0	0
$540$	8.92781	0.384192
$541$	−32.2705	−1.38742	−0.693709	−	0.720256i	$-0.744025\pi$
$541$	−32.2705	−1.38742	−0.693709	+	0.720256i	$0.744025\pi$
$542$	−14.8391	−0.637396
$543$	27.1591	1.16551
$544$	−37.9214	−1.62587
$545$	−23.2344	−0.995254
$546$	13.4050	0.573681
$547$	−5.16940	−0.221028	−0.110514	−	0.993875i	$-0.535250\pi$
$547$	−5.16940	−0.221028	−0.110514	+	0.993875i	$0.535250\pi$
$548$	15.6699	0.669385
$549$	−2.15044	−0.0917786
$550$	0	0
$551$	4.91359	0.209326
$552$	0.795840	0.0338732
$553$	−5.78776	−0.246121
$554$	−8.30603	−0.352889
$555$	−33.9243	−1.44001
$556$	−12.0399	−0.510604
$557$	−28.5616	−1.21019	−0.605096	−	0.796153i	$-0.706865\pi$
$557$	−28.5616	−1.21019	−0.605096	+	0.796153i	$0.706865\pi$
$558$	−16.4538	−0.696544
$559$	−39.0786	−1.65285
$560$	−2.04536	−0.0864321
$561$	0	0
$562$	5.11308	0.215682
$563$	41.5103	1.74945	0.874724	−	0.484621i	$-0.161042\pi$
$563$	41.5103	1.74945	0.874724	+	0.484621i	$0.161042\pi$
$564$	9.92537	0.417933
$565$	−3.79464	−0.159642
$566$	23.8335	1.00180
$567$	−9.90269	−0.415874
$568$	37.3190	1.56587
$569$	13.2623	0.555985	0.277992	−	0.960583i	$-0.410331\pi$
$569$	13.2623	0.555985	0.277992	+	0.960583i	$0.410331\pi$
$570$	−6.74913	−0.282690
$571$	1.52594	0.0638588	0.0319294	−	0.999490i	$-0.489835\pi$
$571$	1.52594	0.0638588	0.0319294	+	0.999490i	$0.489835\pi$
$572$	0	0
$573$	−1.89603	−0.0792077
$574$	−2.99944	−0.125194
$575$	1.47387	0.0614648
$576$	13.1657	0.548573
$577$	−13.1176	−0.546091	−0.273046	−	0.962001i	$-0.588031\pi$
$577$	−13.1176	−0.546091	−0.273046	+	0.962001i	$0.588031\pi$
$578$	−31.1703	−1.29651
$579$	24.4618	1.01660
$580$	−29.9989	−1.24564
$581$	15.5189	0.643832
$582$	−34.1124	−1.41400
$583$	0	0
$584$	−29.3890	−1.21612
$585$	−61.3574	−2.53682
$586$	28.9853	1.19737
$587$	−12.6007	−0.520088	−0.260044	−	0.965597i	$-0.583737\pi$
$587$	−12.6007	−0.520088	−0.260044	+	0.965597i	$0.583737\pi$
$588$	15.5615	0.641746
$589$	6.15999	0.253818
$590$	31.4753	1.29582
$591$	−21.1384	−0.869517
$592$	1.92959	0.0793055
$593$	15.0972	0.619967	0.309984	−	0.950742i	$-0.399676\pi$
$593$	15.0972	0.619967	0.309984	+	0.950742i	$0.399676\pi$
$594$	0	0
$595$	26.9423	1.10453
$596$	−8.55018	−0.350229
$597$	42.5019	1.73949
$598$	0.772339	0.0315833
$599$	−37.1076	−1.51618	−0.758089	−	0.652151i	$-0.773867\pi$
$599$	−37.1076	−1.51618	−0.758089	+	0.652151i	$0.773867\pi$
$600$	82.0093	3.34801
$601$	−0.977214	−0.0398614	−0.0199307	−	0.999801i	$-0.506345\pi$
$601$	−0.977214	−0.0398614	−0.0199307	+	0.999801i	$0.506345\pi$
$602$	−4.91192	−0.200195
$603$	−19.6410	−0.799843
$604$	−15.8854	−0.646370
$605$	0	0
$606$	8.33745	0.338686
$607$	12.9781	0.526763	0.263382	−	0.964692i	$-0.415162\pi$
$607$	12.9781	0.526763	0.263382	+	0.964692i	$0.415162\pi$
$608$	−4.06390	−0.164813
$609$	13.4477	0.544927
$610$	3.92106	0.158759
$611$	26.9485	1.09022
$612$	−16.9316	−0.684418
$613$	−31.6608	−1.27877	−0.639383	−	0.768888i	$-0.720810\pi$
$613$	−31.6608	−1.27877	−0.639383	+	0.768888i	$0.720810\pi$
$614$	5.35828	0.216243
$615$	32.8820	1.32593
$616$	0	0
$617$	2.15571	0.0867857	0.0433928	−	0.999058i	$-0.486183\pi$
$617$	2.15571	0.0867857	0.0433928	+	0.999058i	$0.486183\pi$
$618$	18.9946	0.764077
$619$	−3.90531	−0.156968	−0.0784839	−	0.996915i	$-0.525008\pi$
$619$	−3.90531	−0.156968	−0.0784839	+	0.996915i	$0.525008\pi$
$620$	−37.6086	−1.51040
$621$	−0.230583	−0.00925297
$622$	−3.80114	−0.152412
$623$	−0.850474	−0.0340735
$624$	8.35866	0.334614
$625$	65.2594	2.61037
$626$	−20.6433	−0.825072
$627$	0	0
$628$	−15.0260	−0.599602
$629$	−25.4173	−1.01345
$630$	−7.71221	−0.307262
$631$	−28.4071	−1.13087	−0.565434	−	0.824793i	$-0.691291\pi$
$631$	−28.4071	−1.13087	−0.565434	+	0.824793i	$0.691291\pi$
$632$	−18.5547	−0.738067
$633$	49.5910	1.97107
$634$	24.4089	0.969400
$635$	−8.51103	−0.337750
$636$	−19.2327	−0.762625
$637$	42.2513	1.67406
$638$	0	0
$639$	27.3694	1.08272
$640$	20.5980	0.814206
$641$	27.3714	1.08111	0.540553	−	0.841310i	$-0.318215\pi$
$641$	27.3714	1.08111	0.540553	+	0.841310i	$0.318215\pi$
$642$	3.05925	0.120739
$643$	45.1938	1.78227	0.891135	−	0.453738i	$-0.149910\pi$
$643$	45.1938	1.78227	0.891135	+	0.453738i	$0.149910\pi$
$644$	−0.121693	−0.00479538
$645$	53.8478	2.12025
$646$	−5.05669	−0.198953
$647$	−28.4332	−1.11783	−0.558913	−	0.829226i	$-0.688781\pi$
$647$	−28.4332	−1.11783	−0.558913	+	0.829226i	$0.688781\pi$
$648$	−31.7466	−1.24712
$649$	0	0
$650$	79.5876	3.12168
$651$	16.8589	0.660751
$652$	12.1018	0.473945
$653$	−26.0993	−1.02134	−0.510672	−	0.859776i	$-0.670603\pi$
$653$	−26.0993	−1.02134	−0.510672	+	0.859776i	$0.670603\pi$
$654$	11.9347	0.466684
$655$	−9.53654	−0.372624
$656$	−1.87030	−0.0730228
$657$	−21.5536	−0.840887
$658$	3.38724	0.132049
$659$	14.9194	0.581178	0.290589	−	0.956848i	$-0.406149\pi$
$659$	14.9194	0.581178	0.290589	+	0.956848i	$0.406149\pi$
$660$	0	0
$661$	8.03694	0.312601	0.156300	−	0.987710i	$-0.450043\pi$
$661$	8.03694	0.312601	0.156300	+	0.987710i	$0.450043\pi$
$662$	3.94543	0.153343
$663$	−110.104	−4.27607
$664$	49.7513	1.93073
$665$	2.88731	0.111965
$666$	7.27569	0.281927
$667$	0.774797	0.0300003
$668$	−2.45524	−0.0949959
$669$	12.2278	0.472753
$670$	35.8129	1.38357
$671$	0	0
$672$	−11.1222	−0.429049
$673$	−4.23492	−0.163244	−0.0816220	−	0.996663i	$-0.526010\pi$
$673$	−4.23492	−0.163244	−0.0816220	+	0.996663i	$0.526010\pi$
$674$	29.3222	1.12945
$675$	−23.7610	−0.914560
$676$	−37.8177	−1.45453
$677$	−9.81344	−0.377161	−0.188580	−	0.982058i	$-0.560389\pi$
$677$	−9.81344	−0.377161	−0.188580	+	0.982058i	$0.560389\pi$
$678$	1.94917	0.0748575
$679$	14.5934	0.560045
$680$	86.3731	3.31226
$681$	−13.7742	−0.527828
$682$	0	0
$683$	13.0230	0.498312	0.249156	−	0.968463i	$-0.419847\pi$
$683$	13.0230	0.498312	0.249156	+	0.968463i	$0.419847\pi$
$684$	−1.81450	−0.0693790
$685$	−58.6251	−2.23995
$686$	11.3422	0.433048
$687$	8.58645	0.327594
$688$	−3.06281	−0.116769
$689$	−52.2188	−1.98938
$690$	−1.06423	−0.0405147
$691$	−15.1399	−0.575950	−0.287975	−	0.957638i	$-0.592982\pi$
$691$	−15.1399	−0.575950	−0.287975	+	0.957638i	$0.592982\pi$
$692$	4.76531	0.181150
$693$	0	0
$694$	14.6940	0.557776
$695$	45.0441	1.70862
$696$	43.1113	1.63413
$697$	24.6363	0.933168
$698$	−6.31995	−0.239214
$699$	−38.7652	−1.46624
$700$	−12.5402	−0.473973
$701$	−21.3905	−0.807909	−0.403954	−	0.914779i	$-0.632365\pi$
$701$	−21.3905	−0.807909	−0.403954	+	0.914779i	$0.632365\pi$
$702$	−12.4512	−0.469941
$703$	−2.72388	−0.102733
$704$	0	0
$705$	−37.1333	−1.39852
$706$	1.05217	0.0395989
$707$	−3.56680	−0.134143
$708$	20.2673	0.761690
$709$	−15.7681	−0.592182	−0.296091	−	0.955160i	$-0.595683\pi$
$709$	−15.7681	−0.592182	−0.296091	+	0.955160i	$0.595683\pi$
$710$	−49.9047	−1.87289
$711$	−13.6079	−0.510335
$712$	−2.72650	−0.102180
$713$	0.971336	0.0363768
$714$	−13.8393	−0.517923
$715$	0	0
$716$	8.50367	0.317797
$717$	−12.5446	−0.468485
$718$	25.8771	0.965723
$719$	−25.7622	−0.960767	−0.480383	−	0.877059i	$-0.659502\pi$
$719$	−25.7622	−0.960767	−0.480383	+	0.877059i	$0.659502\pi$
$720$	−4.80893	−0.179218
$721$	−8.12600	−0.302628
$722$	17.3573	0.645972
$723$	−41.9376	−1.55967
$724$	−13.3137	−0.494800
$725$	79.8409	2.96522
$726$	0	0
$727$	5.90292	0.218927	0.109464	−	0.993991i	$-0.465087\pi$
$727$	5.90292	0.218927	0.109464	+	0.993991i	$0.465087\pi$
$728$	−18.3847	−0.681382
$729$	−10.1559	−0.376143
$730$	39.3003	1.45457
$731$	40.3447	1.49220
$732$	2.52481	0.0933196
$733$	19.2956	0.712700	0.356350	−	0.934353i	$-0.384021\pi$
$733$	19.2956	0.712700	0.356350	+	0.934353i	$0.384021\pi$
$734$	−35.5840	−1.31343
$735$	−58.2195	−2.14746
$736$	−0.640815	−0.0236208
$737$	0	0
$738$	−7.05213	−0.259593
$739$	−29.4469	−1.08322	−0.541612	−	0.840629i	$-0.682186\pi$
$739$	−29.4469	−1.08322	−0.541612	+	0.840629i	$0.682186\pi$
$740$	16.6301	0.611336
$741$	−11.7994	−0.433463
$742$	−6.56356	−0.240956
$743$	−20.4062	−0.748630	−0.374315	−	0.927302i	$-0.622122\pi$
$743$	−20.4062	−0.748630	−0.374315	+	0.927302i	$0.622122\pi$
$744$	54.0471	1.98146
$745$	31.9884	1.17196
$746$	−10.5409	−0.385930
$747$	36.4872	1.33500
$748$	0	0
$749$	−1.30876	−0.0478212
$750$	−65.1732	−2.37979
$751$	−52.1463	−1.90284	−0.951422	−	0.307890i	$-0.900377\pi$
$751$	−52.1463	−1.90284	−0.951422	+	0.307890i	$0.900377\pi$
$752$	2.11211	0.0770207
$753$	31.8909	1.16217
$754$	41.8382	1.52366
$755$	59.4315	2.16293
$756$	1.96187	0.0713524
$757$	−16.2427	−0.590350	−0.295175	−	0.955443i	$-0.595378\pi$
$757$	−16.2427	−0.590350	−0.295175	+	0.955443i	$0.595378\pi$
$758$	−21.0811	−0.765701
$759$	0	0
$760$	9.25629	0.335761
$761$	4.13096	0.149747	0.0748737	−	0.997193i	$-0.476145\pi$
$761$	4.13096	0.149747	0.0748737	+	0.997193i	$0.476145\pi$
$762$	4.37181	0.158374
$763$	−5.10572	−0.184839
$764$	0.929456	0.0336265
$765$	63.3453	2.29025
$766$	−17.4783	−0.631515
$767$	55.0279	1.98694
$768$	−38.3693	−1.38453
$769$	−39.8109	−1.43562	−0.717809	−	0.696240i	$-0.754855\pi$
$769$	−39.8109	−1.43562	−0.717809	+	0.696240i	$0.754855\pi$
$770$	0	0
$771$	−40.8742	−1.47205
$772$	−11.9915	−0.431583
$773$	−44.1442	−1.58776	−0.793879	−	0.608076i	$-0.791941\pi$
$773$	−44.1442	−1.58776	−0.793879	+	0.608076i	$0.791941\pi$
$774$	−11.5486	−0.415107
$775$	100.094	3.59547
$776$	46.7844	1.67946
$777$	−7.45481	−0.267440
$778$	17.3007	0.620260
$779$	2.64019	0.0945945
$780$	72.0390	2.57941
$781$	0	0
$782$	−0.797361	−0.0285136
$783$	−12.4909	−0.446387
$784$	3.31147	0.118267
$785$	56.2160	2.00644
$786$	4.89858	0.174727
$787$	−6.00401	−0.214020	−0.107010	−	0.994258i	$-0.534128\pi$
$787$	−6.00401	−0.214020	−0.107010	+	0.994258i	$0.534128\pi$
$788$	10.3623	0.369141
$789$	−20.2069	−0.719385
$790$	24.8122	0.882780
$791$	−0.833864	−0.0296488
$792$	0	0
$793$	6.85514	0.243433
$794$	1.02521	0.0363834
$795$	71.9542	2.55195
$796$	−20.8349	−0.738474
$797$	−29.5364	−1.04623	−0.523116	−	0.852261i	$-0.675231\pi$
$797$	−29.5364	−1.04623	−0.523116	+	0.852261i	$0.675231\pi$
$798$	−1.48311	−0.0525014
$799$	−27.8216	−0.984257
$800$	−66.0344	−2.33467
$801$	−1.99959	−0.0706520
$802$	6.34462	0.224036
$803$	0	0
$804$	23.0602	0.813272
$805$	0.455284	0.0160467
$806$	52.4511	1.84751
$807$	50.4805	1.77700
$808$	−11.4346	−0.402269
$809$	28.0765	0.987119	0.493559	−	0.869712i	$-0.335696\pi$
$809$	28.0765	0.987119	0.493559	+	0.869712i	$0.335696\pi$
$810$	42.4530	1.49165
$811$	25.8877	0.909039	0.454520	−	0.890737i	$-0.349811\pi$
$811$	25.8877	0.909039	0.454520	+	0.890737i	$0.349811\pi$
$812$	−6.59221	−0.231341
$813$	35.7479	1.25373
$814$	0	0
$815$	−45.2761	−1.58595
$816$	−8.62946	−0.302092
$817$	4.32359	0.151263
$818$	−28.8733	−1.00953
$819$	−13.4832	−0.471140
$820$	−16.1191	−0.562905
$821$	29.0400	1.01350	0.506752	−	0.862092i	$-0.330846\pi$
$821$	29.0400	1.01350	0.506752	+	0.862092i	$0.330846\pi$
$822$	30.1136	1.05033
$823$	−44.3381	−1.54553	−0.772764	−	0.634694i	$-0.781126\pi$
$823$	−44.3381	−1.54553	−0.772764	+	0.634694i	$0.781126\pi$
$824$	−26.0508	−0.907521
$825$	0	0
$826$	6.91663	0.240660
$827$	36.0307	1.25291	0.626455	−	0.779457i	$-0.284505\pi$
$827$	36.0307	1.25291	0.626455	+	0.779457i	$0.284505\pi$
$828$	−0.286118	−0.00994329
$829$	7.27308	0.252604	0.126302	−	0.991992i	$-0.459689\pi$
$829$	7.27308	0.252604	0.126302	+	0.991992i	$0.459689\pi$
$830$	−66.5298	−2.30928
$831$	20.0095	0.694121
$832$	−41.9695	−1.45503
$833$	−43.6201	−1.51135
$834$	−23.1376	−0.801188
$835$	9.18565	0.317883
$836$	0	0
$837$	−15.6593	−0.541266
$838$	16.2554	0.561533
$839$	−33.4149	−1.15361	−0.576806	−	0.816881i	$-0.695701\pi$
$839$	−33.4149	−1.15361	−0.576806	+	0.816881i	$0.695701\pi$
$840$	25.3329	0.874069
$841$	12.9714	0.447290
$842$	5.32949	0.183666
$843$	−12.3176	−0.424239
$844$	−24.3101	−0.836788
$845$	141.485	4.86725
$846$	7.96391	0.273805
$847$	0	0
$848$	−4.09269	−0.140544
$849$	−57.4157	−1.97050
$850$	−82.1661	−2.81827
$851$	−0.429514	−0.0147236
$852$	−32.1341	−1.10090
$853$	−10.4507	−0.357824	−0.178912	−	0.983865i	$-0.557258\pi$
$853$	−10.4507	−0.357824	−0.178912	+	0.983865i	$0.557258\pi$
$854$	0.861645	0.0294849
$855$	6.78849	0.232161
$856$	−4.19570	−0.143406
$857$	4.06247	0.138771	0.0693857	−	0.997590i	$-0.477896\pi$
$857$	4.06247	0.138771	0.0693857	+	0.997590i	$0.477896\pi$
$858$	0	0
$859$	−33.1960	−1.13263	−0.566317	−	0.824187i	$-0.691632\pi$
$859$	−33.1960	−1.13263	−0.566317	+	0.824187i	$0.691632\pi$
$860$	−26.3968	−0.900125
$861$	7.22575	0.246253
$862$	−10.9440	−0.372753
$863$	−38.9594	−1.32619	−0.663097	−	0.748533i	$-0.730758\pi$
$863$	−38.9594	−1.32619	−0.663097	+	0.748533i	$0.730758\pi$
$864$	10.3309	0.351463
$865$	−17.8282	−0.606178
$866$	−2.55014	−0.0866574
$867$	75.0901	2.55019
$868$	−8.26442	−0.280513
$869$	0	0
$870$	−57.6504	−1.95453
$871$	62.6112	2.12150
$872$	−16.3682	−0.554297
$873$	34.3113	1.16126
$874$	−0.0854504	−0.00289040
$875$	27.8814	0.942563
$876$	25.3058	0.855005
$877$	45.7454	1.54471	0.772356	−	0.635190i	$-0.219078\pi$
$877$	45.7454	1.54471	0.772356	+	0.635190i	$0.219078\pi$
$878$	11.1264	0.375499
$879$	−69.8264	−2.35518
$880$	0	0
$881$	32.9922	1.11154	0.555768	−	0.831337i	$-0.312424\pi$
$881$	32.9922	1.11154	0.555768	+	0.831337i	$0.312424\pi$
$882$	12.4862	0.420433
$883$	33.9586	1.14280	0.571399	−	0.820672i	$-0.306401\pi$
$883$	33.9586	1.14280	0.571399	+	0.820672i	$0.306401\pi$
$884$	53.9742	1.81535
$885$	−75.8249	−2.54883
$886$	−1.28427	−0.0431460
$887$	−4.70806	−0.158081	−0.0790406	−	0.996871i	$-0.525186\pi$
$887$	−4.70806	−0.158081	−0.0790406	+	0.996871i	$0.525186\pi$
$888$	−23.8990	−0.801999
$889$	−1.87028	−0.0627272
$890$	3.64600	0.122214
$891$	0	0
$892$	−5.99420	−0.200701
$893$	−2.98154	−0.0997734
$894$	−16.4313	−0.549545
$895$	−31.8144	−1.06344
$896$	4.52636	0.151215
$897$	−1.86059	−0.0621232
$898$	−21.5148	−0.717959
$899$	52.6180	1.75491
$900$	−29.4837	−0.982792
$901$	53.9106	1.79602
$902$	0	0
$903$	11.8329	0.393776
$904$	−2.67325	−0.0889109
$905$	49.8099	1.65574
$906$	−30.5278	−1.01422
$907$	−9.21665	−0.306034	−0.153017	−	0.988224i	$-0.548899\pi$
$907$	−9.21665	−0.306034	−0.153017	+	0.988224i	$0.548899\pi$
$908$	6.75227	0.224082
$909$	−8.38606	−0.278148
$910$	24.5849	0.814980
$911$	34.1955	1.13295	0.566474	−	0.824080i	$-0.308307\pi$
$911$	34.1955	1.13295	0.566474	+	0.824080i	$0.308307\pi$
$912$	−0.924789	−0.0306228
$913$	0	0
$914$	3.69707	0.122288
$915$	−9.44594	−0.312273
$916$	−4.20918	−0.139075
$917$	−2.09564	−0.0692040
$918$	12.8546	0.424266
$919$	−51.2959	−1.69210	−0.846048	−	0.533107i	$-0.821024\pi$
$919$	−51.2959	−1.69210	−0.846048	+	0.533107i	$0.821024\pi$
$920$	1.45957	0.0481208
$921$	−12.9082	−0.425341
$922$	−17.0189	−0.560487
$923$	−87.2477	−2.87179
$924$	0	0
$925$	−44.2604	−1.45527
$926$	25.3230	0.832166
$927$	−19.1054	−0.627504
$928$	−34.7135	−1.13953
$929$	−11.3176	−0.371317	−0.185658	−	0.982614i	$-0.559442\pi$
$929$	−11.3176	−0.371317	−0.185658	+	0.982614i	$0.559442\pi$
$930$	−72.2742	−2.36997
$931$	−4.67461	−0.153204
$932$	19.0032	0.622470
$933$	9.15706	0.299789
$934$	−27.3117	−0.893668
$935$	0	0
$936$	−43.2251	−1.41286
$937$	7.92226	0.258809	0.129404	−	0.991592i	$-0.458693\pi$
$937$	7.92226	0.258809	0.129404	+	0.991592i	$0.458693\pi$
$938$	7.86980	0.256958
$939$	49.7303	1.62289
$940$	18.2032	0.593723
$941$	19.8214	0.646161	0.323080	−	0.946372i	$-0.395282\pi$
$941$	19.8214	0.646161	0.323080	+	0.946372i	$0.395282\pi$
$942$	−28.8762	−0.940836
$943$	0.416317	0.0135571
$944$	4.31285	0.140371
$945$	−7.33984	−0.238765
$946$	0	0
$947$	−3.76239	−0.122261	−0.0611306	−	0.998130i	$-0.519471\pi$
$947$	−3.76239	−0.122261	−0.0611306	+	0.998130i	$0.519471\pi$
$948$	15.9768	0.518904
$949$	68.7082	2.23036
$950$	−8.80544	−0.285686
$951$	−58.8017	−1.90678
$952$	18.9803	0.615155
$953$	22.2293	0.720077	0.360039	−	0.932937i	$-0.382764\pi$
$953$	22.2293	0.720077	0.360039	+	0.932937i	$0.382764\pi$
$954$	−15.4319	−0.499626
$955$	−3.47733	−0.112524
$956$	6.14950	0.198889
$957$	0	0
$958$	−11.3554	−0.366878
$959$	−12.8827	−0.416005
$960$	57.8313	1.86650
$961$	34.9654	1.12791
$962$	−23.1933	−0.747782
$963$	−3.07709	−0.0991579
$964$	20.5583	0.662138
$965$	44.8632	1.44420
$966$	−0.233863	−0.00752443
$967$	−6.82929	−0.219615	−0.109808	−	0.993953i	$-0.535023\pi$
$967$	−6.82929	−0.219615	−0.109808	+	0.993953i	$0.535023\pi$
$968$	0	0
$969$	12.1817	0.391333
$970$	−62.5623	−2.00875
$971$	−35.6329	−1.14351	−0.571757	−	0.820423i	$-0.693738\pi$
$971$	−35.6329	−1.14351	−0.571757	+	0.820423i	$0.693738\pi$
$972$	20.9010	0.670400
$973$	9.89835	0.317327
$974$	−2.26572	−0.0725984
$975$	−191.729	−6.14024
$976$	0.537277	0.0171978
$977$	−46.8490	−1.49883	−0.749417	−	0.662099i	$-0.769666\pi$
$977$	−46.8490	−1.49883	−0.749417	+	0.662099i	$0.769666\pi$
$978$	23.2567	0.743667
$979$	0	0
$980$	28.5399	0.911674
$981$	−12.0043	−0.383268
$982$	−3.00487	−0.0958891
$983$	−20.4677	−0.652818	−0.326409	−	0.945229i	$-0.605839\pi$
$983$	−20.4677	−0.652818	−0.326409	+	0.945229i	$0.605839\pi$
$984$	23.1647	0.738464
$985$	−38.7679	−1.23525
$986$	−43.1937	−1.37557
$987$	−8.15997	−0.259735
$988$	5.78422	0.184020
$989$	0.681764	0.0216788
$990$	0	0
$991$	56.8308	1.80529	0.902646	−	0.430384i	$-0.141622\pi$
$991$	56.8308	1.80529	0.902646	+	0.430384i	$0.141622\pi$
$992$	−43.5190	−1.38173
$993$	−9.50465	−0.301621
$994$	−10.9665	−0.347835
$995$	77.9487	2.47114
$996$	−42.8392	−1.35741
$997$	9.65434	0.305756	0.152878	−	0.988245i	$-0.451146\pi$
$997$	9.65434	0.305756	0.152878	+	0.988245i	$0.451146\pi$
$998$	29.3422	0.928812
$999$	6.92439	0.219078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.j.1.8		21
11.10	odd	2		671.2.a.d.1.14	✓	21
33.32	even	2		6039.2.a.l.1.8		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.14	✓	21	11.10	odd	2
6039.2.a.l.1.8		21	33.32	even	2
7381.2.a.j.1.8		21	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)

\(f(q)\)	\(=\)	\(q-0.942064 q^{2} +2.26946 q^{3} -1.11252 q^{4} +4.16220 q^{5} -2.13797 q^{6} +0.914635 q^{7} +2.93219 q^{8} +2.15044 q^{9} +O(q^{10})\)	\(q-0.942064 q^{2} +2.26946 q^{3} -1.11252 q^{4} +4.16220 q^{5} -2.13797 q^{6} +0.914635 q^{7} +2.93219 q^{8} +2.15044 q^{9} -3.92106 q^{10} -2.52481 q^{12} -6.85514 q^{13} -0.861645 q^{14} +9.44594 q^{15} -0.537277 q^{16} +7.07723 q^{17} -2.02585 q^{18} +0.758442 q^{19} -4.63051 q^{20} +2.07573 q^{21} +0.119595 q^{23} +6.65448 q^{24} +12.3239 q^{25} +6.45798 q^{26} -1.92804 q^{27} -1.01755 q^{28} +6.47853 q^{29} -8.89868 q^{30} +8.12191 q^{31} -5.35823 q^{32} -6.66720 q^{34} +3.80690 q^{35} -2.39240 q^{36} -3.59142 q^{37} -0.714500 q^{38} -15.5575 q^{39} +12.2044 q^{40} +3.48107 q^{41} -1.95547 q^{42} +5.70063 q^{43} +8.95057 q^{45} -0.112666 q^{46} -3.93114 q^{47} -1.21933 q^{48} -6.16344 q^{49} -11.6099 q^{50} +16.0615 q^{51} +7.62645 q^{52} +7.61747 q^{53} +1.81633 q^{54} +2.68188 q^{56} +1.72125 q^{57} -6.10319 q^{58} -8.02724 q^{59} -10.5088 q^{60} -1.00000 q^{61} -7.65135 q^{62} +1.96687 q^{63} +6.12235 q^{64} -28.5325 q^{65} -9.13346 q^{67} -7.87353 q^{68} +0.271415 q^{69} -3.58634 q^{70} +12.7273 q^{71} +6.30550 q^{72} -10.0229 q^{73} +3.38335 q^{74} +27.9686 q^{75} -0.843778 q^{76} +14.6561 q^{78} -6.32794 q^{79} -2.23625 q^{80} -10.8269 q^{81} -3.27939 q^{82} +16.9673 q^{83} -2.30928 q^{84} +29.4569 q^{85} -5.37035 q^{86} +14.7028 q^{87} -0.929850 q^{89} -8.43201 q^{90} -6.26995 q^{91} -0.133051 q^{92} +18.4323 q^{93} +3.70338 q^{94} +3.15679 q^{95} -12.1603 q^{96} +15.9555 q^{97} +5.80636 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} - 5 q^{6} - 5 q^{7} + 6 q^{8} + 40 q^{9}+O(q^{10}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 - 5 * q^6 - 5 * q^7 + 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} - 5 q^{6} - 5 q^{7} + 6 q^{8} + 40 q^{9} - q^{10} + 6 q^{12} - 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} - q^{17} + 5 q^{18} - 15 q^{19} - 2 q^{20} - 16 q^{21} + 11 q^{23} + 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} + 16 q^{28} + 9 q^{29} - 16 q^{30} + 22 q^{31} - 3 q^{32} + 33 q^{34} + 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} + 28 q^{39} + 16 q^{40} - 7 q^{41} - 55 q^{42} - 16 q^{43} + 44 q^{45} + 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} + 33 q^{50} + 19 q^{51} - 60 q^{52} + 9 q^{53} - 13 q^{54} + 44 q^{56} - 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} - 21 q^{61} + 23 q^{62} - 24 q^{63} + 66 q^{64} - 25 q^{65} + 38 q^{67} + 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} + 75 q^{72} - 20 q^{73} + 12 q^{74} - 10 q^{75} - 59 q^{76} - 14 q^{78} - q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} + 19 q^{83} + 14 q^{84} - 38 q^{85} - 3 q^{86} - 4 q^{87} + 37 q^{89} + 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} + 64 q^{94} + 43 q^{95} + 38 q^{96} + 68 q^{97} + 2 q^{98}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 - 5 * q^6 - 5 * q^7 + 6 * q^8 + 40 * q^9 - q^10 + 6 * q^12 - 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 - q^17 + 5 * q^18 - 15 * q^19 - 2 * q^20 - 16 * q^21 + 11 * q^23 + 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 + 16 * q^28 + 9 * q^29 - 16 * q^30 + 22 * q^31 - 3 * q^32 + 33 * q^34 + 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 + 28 * q^39 + 16 * q^40 - 7 * q^41 - 55 * q^42 - 16 * q^43 + 44 * q^45 + 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 + 33 * q^50 + 19 * q^51 - 60 * q^52 + 9 * q^53 - 13 * q^54 + 44 * q^56 - 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 - 21 * q^61 + 23 * q^62 - 24 * q^63 + 66 * q^64 - 25 * q^65 + 38 * q^67 + 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 + 75 * q^72 - 20 * q^73 + 12 * q^74 - 10 * q^75 - 59 * q^76 - 14 * q^78 - q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 + 19 * q^83 + 14 * q^84 - 38 * q^85 - 3 * q^86 - 4 * q^87 + 37 * q^89 + 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 + 64 * q^94 + 43 * q^95 + 38 * q^96 + 68 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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