LMFDB - Embedded newform 7381.2.a.v.1.16

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			1.16
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.49906 q^{2} +1.05312 q^{3} +0.247194 q^{4} -0.565778 q^{5} -1.57870 q^{6} +4.58937 q^{7} +2.62757 q^{8} -1.89094 q^{9} +O(q^{10})$	\(q-1.49906 q^{2} +1.05312 q^{3} +0.247194 q^{4} -0.565778 q^{5} -1.57870 q^{6} +4.58937 q^{7} +2.62757 q^{8} -1.89094 q^{9} +0.848138 q^{10} +0.260326 q^{12} -2.43801 q^{13} -6.87976 q^{14} -0.595832 q^{15} -4.43328 q^{16} +1.31478 q^{17} +2.83464 q^{18} +6.64521 q^{19} -0.139857 q^{20} +4.83316 q^{21} +7.72864 q^{23} +2.76715 q^{24} -4.67990 q^{25} +3.65473 q^{26} -5.15075 q^{27} +1.13447 q^{28} -1.45835 q^{29} +0.893191 q^{30} +10.2893 q^{31} +1.39064 q^{32} -1.97094 q^{34} -2.59656 q^{35} -0.467429 q^{36} -5.69200 q^{37} -9.96160 q^{38} -2.56752 q^{39} -1.48662 q^{40} -5.83224 q^{41} -7.24522 q^{42} +4.33725 q^{43} +1.06985 q^{45} -11.5857 q^{46} -0.120545 q^{47} -4.66878 q^{48} +14.0623 q^{49} +7.01547 q^{50} +1.38462 q^{51} -0.602662 q^{52} +2.59970 q^{53} +7.72130 q^{54} +12.0589 q^{56} +6.99821 q^{57} +2.18616 q^{58} +11.7050 q^{59} -0.147286 q^{60} +1.00000 q^{61} -15.4244 q^{62} -8.67821 q^{63} +6.78191 q^{64} +1.37937 q^{65} -11.5628 q^{67} +0.325006 q^{68} +8.13919 q^{69} +3.89242 q^{70} +10.4610 q^{71} -4.96857 q^{72} -14.5312 q^{73} +8.53267 q^{74} -4.92849 q^{75} +1.64266 q^{76} +3.84887 q^{78} -2.95602 q^{79} +2.50825 q^{80} +0.248453 q^{81} +8.74290 q^{82} -5.19868 q^{83} +1.19473 q^{84} -0.743873 q^{85} -6.50182 q^{86} -1.53582 q^{87} -3.39788 q^{89} -1.60377 q^{90} -11.1889 q^{91} +1.91048 q^{92} +10.8359 q^{93} +0.180704 q^{94} -3.75971 q^{95} +1.46451 q^{96} +12.4535 q^{97} -21.0803 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.49906	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$2$	−1.49906	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$3$	1.05312	0.608019	0.304010	−	0.952669i	$-0.401674\pi$
$3$	1.05312	0.608019	0.304010	+	0.952669i	$0.401674\pi$
$4$	0.247194	0.123597
$5$	−0.565778	−0.253024	−0.126512	−	0.991965i	$-0.540378\pi$
$5$	−0.565778	−0.253024	−0.126512	+	0.991965i	$0.540378\pi$
$6$	−1.57870	−0.644500
$7$	4.58937	1.73462	0.867310	−	0.497769i	$-0.165847\pi$
$7$	4.58937	1.73462	0.867310	+	0.497769i	$0.165847\pi$
$8$	2.62757	0.928986
$9$	−1.89094	−0.630312
$10$	0.848138	0.268205
$11$	0	0
$11$	0	0
$12$	0.260326	0.0751495
$13$	−2.43801	−0.676182	−0.338091	−	0.941114i	$-0.609781\pi$
$13$	−2.43801	−0.676182	−0.338091	+	0.941114i	$0.609781\pi$
$14$	−6.87976	−1.83869
$15$	−0.595832	−0.153843
$16$	−4.43328	−1.10832
$17$	1.31478	0.318881	0.159440	−	0.987208i	$-0.449031\pi$
$17$	1.31478	0.318881	0.159440	+	0.987208i	$0.449031\pi$
$18$	2.83464	0.668130
$19$	6.64521	1.52452	0.762258	−	0.647273i	$-0.224091\pi$
$19$	6.64521	1.52452	0.762258	+	0.647273i	$0.224091\pi$
$20$	−0.139857	−0.0312730
$21$	4.83316	1.05468
$22$	0	0
$23$	7.72864	1.61153	0.805766	−	0.592234i	$-0.201754\pi$
$23$	7.72864	1.61153	0.805766	+	0.592234i	$0.201754\pi$
$24$	2.76715	0.564841
$25$	−4.67990	−0.935979
$26$	3.65473	0.716752
$27$	−5.15075	−0.991262
$28$	1.13447	0.214394
$29$	−1.45835	−0.270809	−0.135404	−	0.990790i	$-0.543233\pi$
$29$	−1.45835	−0.270809	−0.135404	+	0.990790i	$0.543233\pi$
$30$	0.893191	0.163074
$31$	10.2893	1.84802	0.924010	−	0.382367i	$-0.124891\pi$
$31$	10.2893	1.84802	0.924010	+	0.382367i	$0.124891\pi$
$32$	1.39064	0.245833
$33$	0	0
$34$	−1.97094	−0.338013
$35$	−2.59656	−0.438900
$36$	−0.467429	−0.0779048
$37$	−5.69200	−0.935758	−0.467879	−	0.883792i	$-0.654982\pi$
$37$	−5.69200	−0.935758	−0.467879	+	0.883792i	$0.654982\pi$
$38$	−9.96160	−1.61598
$39$	−2.56752	−0.411132
$40$	−1.48662	−0.235055
$41$	−5.83224	−0.910842	−0.455421	−	0.890276i	$-0.650511\pi$
$41$	−5.83224	−0.910842	−0.455421	+	0.890276i	$0.650511\pi$
$42$	−7.24522	−1.11796
$43$	4.33725	0.661424	0.330712	−	0.943732i	$-0.392711\pi$
$43$	4.33725	0.661424	0.330712	+	0.943732i	$0.392711\pi$
$44$	0	0
$45$	1.06985	0.159484
$46$	−11.5857	−1.70822
$47$	−0.120545	−0.0175833	−0.00879163	−	0.999961i	$-0.502798\pi$
$47$	−0.120545	−0.0175833	−0.00879163	+	0.999961i	$0.502798\pi$
$48$	−4.66878	−0.673881
$49$	14.0623	2.00890
$50$	7.01547	0.992137
$51$	1.38462	0.193886
$52$	−0.602662	−0.0835741
$53$	2.59970	0.357097	0.178548	−	0.983931i	$-0.442860\pi$
$53$	2.59970	0.357097	0.178548	+	0.983931i	$0.442860\pi$
$54$	7.72130	1.05074
$55$	0	0
$56$	12.0589	1.61144
$57$	6.99821	0.926935
$58$	2.18616	0.287057
$59$	11.7050	1.52386	0.761929	−	0.647661i	$-0.224253\pi$
$59$	11.7050	1.52386	0.761929	+	0.647661i	$0.224253\pi$
$60$	−0.147286	−0.0190146
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−15.4244	−1.95890
$63$	−8.67821	−1.09335
$64$	6.78191	0.847738
$65$	1.37937	0.171090
$66$	0	0
$67$	−11.5628	−1.41262	−0.706309	−	0.707904i	$-0.749641\pi$
$67$	−11.5628	−1.41262	−0.706309	+	0.707904i	$0.749641\pi$
$68$	0.325006	0.0394128
$69$	8.13919	0.979843
$70$	3.89242	0.465233
$71$	10.4610	1.24149	0.620746	−	0.784012i	$-0.286830\pi$
$71$	10.4610	1.24149	0.620746	+	0.784012i	$0.286830\pi$
$72$	−4.96857	−0.585551
$73$	−14.5312	−1.70075	−0.850377	−	0.526174i	$-0.823626\pi$
$73$	−14.5312	−1.70075	−0.850377	+	0.526174i	$0.823626\pi$
$74$	8.53267	0.991903
$75$	−4.92849	−0.569094
$76$	1.64266	0.188426
$77$	0	0
$78$	3.84887	0.435799
$79$	−2.95602	−0.332578	−0.166289	−	0.986077i	$-0.553178\pi$
$79$	−2.95602	−0.332578	−0.166289	+	0.986077i	$0.553178\pi$
$80$	2.50825	0.280431
$81$	0.248453	0.0276059
$82$	8.74290	0.965492
$83$	−5.19868	−0.570629	−0.285315	−	0.958434i	$-0.592098\pi$
$83$	−5.19868	−0.570629	−0.285315	+	0.958434i	$0.592098\pi$
$84$	1.19473	0.130356
$85$	−0.743873	−0.0806843
$86$	−6.50182	−0.701109
$87$	−1.53582	−0.164657
$88$	0	0
$89$	−3.39788	−0.360174	−0.180087	−	0.983651i	$-0.557638\pi$
$89$	−3.39788	−0.360174	−0.180087	+	0.983651i	$0.557638\pi$
$90$	−1.60377	−0.169053
$91$	−11.1889	−1.17292
$92$	1.91048	0.199181
$93$	10.8359	1.12363
$94$	0.180704	0.0186382
$95$	−3.75971	−0.385738
$96$	1.46451	0.149471
$97$	12.4535	1.26446	0.632231	−	0.774780i	$-0.282139\pi$
$97$	12.4535	1.26446	0.632231	+	0.774780i	$0.282139\pi$
$98$	−21.0803	−2.12943
$99$	0	0
$100$	−1.15684	−0.115684
$101$	13.2086	1.31430	0.657151	−	0.753759i	$-0.271761\pi$
$101$	13.2086	1.31430	0.657151	+	0.753759i	$0.271761\pi$
$102$	−2.07564	−0.205519
$103$	9.57801	0.943749	0.471875	−	0.881666i	$-0.343577\pi$
$103$	9.57801	0.943749	0.471875	+	0.881666i	$0.343577\pi$
$104$	−6.40603	−0.628163
$105$	−2.73450	−0.266859
$106$	−3.89712	−0.378522
$107$	9.88245	0.955373	0.477686	−	0.878530i	$-0.341476\pi$
$107$	9.88245	0.955373	0.477686	+	0.878530i	$0.341476\pi$
$108$	−1.27324	−0.122517
$109$	0.489544	0.0468898	0.0234449	−	0.999725i	$-0.492537\pi$
$109$	0.489544	0.0468898	0.0234449	+	0.999725i	$0.492537\pi$
$110$	0	0
$111$	−5.99436	−0.568959
$112$	−20.3460	−1.92251
$113$	−17.1458	−1.61294	−0.806471	−	0.591274i	$-0.798625\pi$
$113$	−17.1458	−1.61294	−0.806471	+	0.591274i	$0.798625\pi$
$114$	−10.4908	−0.982550
$115$	−4.37269	−0.407756
$116$	−0.360496	−0.0334712
$117$	4.61012	0.426206
$118$	−17.5465	−1.61529
$119$	6.03401	0.553137
$120$	−1.56559	−0.142918
$121$	0	0
$122$	−1.49906	−0.135719
$123$	−6.14205	−0.553810
$124$	2.54347	0.228410
$125$	5.47667	0.489848
$126$	13.0092	1.15895
$127$	−1.11274	−0.0987396	−0.0493698	−	0.998781i	$-0.515721\pi$
$127$	−1.11274	−0.0987396	−0.0493698	+	0.998781i	$0.515721\pi$
$128$	−12.9478	−1.14443
$129$	4.56765	0.402159
$130$	−2.06777	−0.181355
$131$	13.1469	1.14865	0.574325	−	0.818628i	$-0.305265\pi$
$131$	13.1469	1.14865	0.574325	+	0.818628i	$0.305265\pi$
$132$	0	0
$133$	30.4973	2.64445
$134$	17.3333	1.49737
$135$	2.91418	0.250813
$136$	3.45467	0.296236
$137$	1.05715	0.0903185	0.0451593	−	0.998980i	$-0.485620\pi$
$137$	1.05715	0.0903185	0.0451593	+	0.998980i	$0.485620\pi$
$138$	−12.2012	−1.03863
$139$	−15.3513	−1.30208	−0.651040	−	0.759044i	$-0.725667\pi$
$139$	−15.3513	−1.30208	−0.651040	+	0.759044i	$0.725667\pi$
$140$	−0.641856	−0.0542468
$141$	−0.126948	−0.0106910
$142$	−15.6817	−1.31598
$143$	0	0
$144$	8.38306	0.698588
$145$	0.825102	0.0685210
$146$	21.7833	1.80280
$147$	14.8093	1.22145
$148$	−1.40703	−0.115657
$149$	9.87155	0.808709	0.404354	−	0.914602i	$-0.367496\pi$
$149$	9.87155	0.808709	0.404354	+	0.914602i	$0.367496\pi$
$150$	7.38813	0.603238
$151$	10.2030	0.830308	0.415154	−	0.909751i	$-0.363728\pi$
$151$	10.2030	0.830308	0.415154	+	0.909751i	$0.363728\pi$
$152$	17.4607	1.41625
$153$	−2.48616	−0.200994
$154$	0	0
$155$	−5.82148	−0.467593
$156$	−0.634675	−0.0508147
$157$	13.8578	1.10597	0.552985	−	0.833191i	$-0.313489\pi$
$157$	13.8578	1.10597	0.552985	+	0.833191i	$0.313489\pi$
$158$	4.43126	0.352532
$159$	2.73780	0.217122
$160$	−0.786794	−0.0622015
$161$	35.4696	2.79540
$162$	−0.372447	−0.0292622
$163$	−23.0050	−1.80189	−0.900945	−	0.433933i	$-0.857126\pi$
$163$	−23.0050	−1.80189	−0.900945	+	0.433933i	$0.857126\pi$
$164$	−1.44170	−0.112578
$165$	0	0
$166$	7.79316	0.604866
$167$	2.08651	0.161459	0.0807296	−	0.996736i	$-0.474275\pi$
$167$	2.08651	0.161459	0.0807296	+	0.996736i	$0.474275\pi$
$168$	12.6995	0.979785
$169$	−7.05612	−0.542779
$170$	1.11511	0.0855253
$171$	−12.5657	−0.960921
$172$	1.07214	0.0817502
$173$	−3.52582	−0.268063	−0.134032	−	0.990977i	$-0.542792\pi$
$173$	−3.52582	−0.268063	−0.134032	+	0.990977i	$0.542792\pi$
$174$	2.30229	0.174536
$175$	−21.4778	−1.62357
$176$	0	0
$177$	12.3267	0.926535
$178$	5.09364	0.381784
$179$	7.02129	0.524796	0.262398	−	0.964960i	$-0.415487\pi$
$179$	7.02129	0.524796	0.262398	+	0.964960i	$0.415487\pi$
$180$	0.264461	0.0197118
$181$	17.1408	1.27406	0.637031	−	0.770838i	$-0.280162\pi$
$181$	17.1408	1.27406	0.637031	+	0.770838i	$0.280162\pi$
$182$	16.7729	1.24329
$183$	1.05312	0.0778489
$184$	20.3075	1.49709
$185$	3.22041	0.236769
$186$	−16.2437	−1.19105
$187$	0	0
$188$	−0.0297980	−0.00217324
$189$	−23.6387	−1.71946
$190$	5.63605	0.408882
$191$	6.06445	0.438808	0.219404	−	0.975634i	$-0.429589\pi$
$191$	6.06445	0.438808	0.219404	+	0.975634i	$0.429589\pi$
$192$	7.14217	0.515441
$193$	−9.61140	−0.691844	−0.345922	−	0.938263i	$-0.612434\pi$
$193$	−9.61140	−0.691844	−0.345922	+	0.938263i	$0.612434\pi$
$194$	−18.6686	−1.34033
$195$	1.45264	0.104026
$196$	3.47613	0.248295
$197$	−9.09903	−0.648279	−0.324139	−	0.946009i	$-0.605075\pi$
$197$	−9.09903	−0.648279	−0.324139	+	0.946009i	$0.605075\pi$
$198$	0	0
$199$	3.07610	0.218059	0.109029	−	0.994039i	$-0.465226\pi$
$199$	3.07610	0.218059	0.109029	+	0.994039i	$0.465226\pi$
$200$	−12.2967	−0.869511
$201$	−12.1770	−0.858899
$202$	−19.8005	−1.39316
$203$	−6.69291	−0.469750
$204$	0.342270	0.0239637
$205$	3.29975	0.230465
$206$	−14.3581	−1.00037
$207$	−14.6144	−1.01577
$208$	10.8084	0.749426
$209$	0	0
$210$	4.09919	0.282871
$211$	−8.73937	−0.601643	−0.300822	−	0.953680i	$-0.597261\pi$
$211$	−8.73937	−0.601643	−0.300822	+	0.953680i	$0.597261\pi$
$212$	0.642632	0.0441362
$213$	11.0167	0.754851
$214$	−14.8144	−1.01269
$215$	−2.45392	−0.167356
$216$	−13.5339	−0.920868
$217$	47.2216	3.20561
$218$	−0.733858	−0.0497031
$219$	−15.3032	−1.03409
$220$	0	0
$221$	−3.20544	−0.215621
$222$	8.98593	0.603096
$223$	6.92086	0.463455	0.231727	−	0.972781i	$-0.425562\pi$
$223$	6.92086	0.463455	0.231727	+	0.972781i	$0.425562\pi$
$224$	6.38217	0.426426
$225$	8.84939	0.589959
$226$	25.7027	1.70972
$227$	16.4771	1.09363	0.546813	−	0.837255i	$-0.315841\pi$
$227$	16.4771	1.09363	0.546813	+	0.837255i	$0.315841\pi$
$228$	1.72992	0.114567
$229$	9.29216	0.614043	0.307022	−	0.951703i	$-0.400668\pi$
$229$	9.29216	0.614043	0.307022	+	0.951703i	$0.400668\pi$
$230$	6.55495	0.432221
$231$	0	0
$232$	−3.83191	−0.251578
$233$	3.39230	0.222237	0.111119	−	0.993807i	$-0.464557\pi$
$233$	3.39230	0.222237	0.111119	+	0.993807i	$0.464557\pi$
$234$	−6.91086	−0.451777
$235$	0.0682015	0.00444898
$236$	2.89340	0.188345
$237$	−3.11304	−0.202214
$238$	−9.04537	−0.586324
$239$	6.35926	0.411346	0.205673	−	0.978621i	$-0.434062\pi$
$239$	6.35926	0.411346	0.205673	+	0.978621i	$0.434062\pi$
$240$	2.64149	0.170508
$241$	6.92469	0.446058	0.223029	−	0.974812i	$-0.428405\pi$
$241$	6.92469	0.446058	0.223029	+	0.974812i	$0.428405\pi$
$242$	0	0
$243$	15.7139	1.00805
$244$	0.247194	0.0158250
$245$	−7.95615	−0.508300
$246$	9.20733	0.587038
$247$	−16.2011	−1.03085
$248$	27.0360	1.71679
$249$	−5.47484	−0.346954
$250$	−8.20988	−0.519239
$251$	−13.0117	−0.821290	−0.410645	−	0.911795i	$-0.634696\pi$
$251$	−13.0117	−0.821290	−0.410645	+	0.911795i	$0.634696\pi$
$252$	−2.14520	−0.135135
$253$	0	0
$254$	1.66807	0.104664
$255$	−0.783388	−0.0490576
$256$	5.84577	0.365361
$257$	−27.9931	−1.74616	−0.873080	−	0.487576i	$-0.837881\pi$
$257$	−27.9931	−1.74616	−0.873080	+	0.487576i	$0.837881\pi$
$258$	−6.84720	−0.426288
$259$	−26.1227	−1.62318
$260$	0.340973	0.0211462
$261$	2.75765	0.170694
$262$	−19.7080	−1.21757
$263$	−18.7719	−1.15753	−0.578763	−	0.815496i	$-0.696464\pi$
$263$	−18.7719	−1.15753	−0.578763	+	0.815496i	$0.696464\pi$
$264$	0	0
$265$	−1.47086	−0.0903539
$266$	−45.7175	−2.80312
$267$	−3.57837	−0.218993
$268$	−2.85825	−0.174596
$269$	26.3763	1.60819	0.804096	−	0.594499i	$-0.202650\pi$
$269$	26.3763	1.60819	0.804096	+	0.594499i	$0.202650\pi$
$270$	−4.36854	−0.265861
$271$	−19.1825	−1.16526	−0.582628	−	0.812739i	$-0.697976\pi$
$271$	−19.1825	−1.16526	−0.582628	+	0.812739i	$0.697976\pi$
$272$	−5.82879	−0.353422
$273$	−11.7833	−0.713157
$274$	−1.58474	−0.0957375
$275$	0	0
$276$	2.01196	0.121106
$277$	−25.2060	−1.51448	−0.757241	−	0.653135i	$-0.773453\pi$
$277$	−25.2060	−1.51448	−0.757241	+	0.653135i	$0.773453\pi$
$278$	23.0126	1.38020
$279$	−19.4565	−1.16483
$280$	−6.82265	−0.407731
$281$	−11.6346	−0.694062	−0.347031	−	0.937854i	$-0.612810\pi$
$281$	−11.6346	−0.694062	−0.347031	+	0.937854i	$0.612810\pi$
$282$	0.190303	0.0113324
$283$	22.3566	1.32896	0.664481	−	0.747305i	$-0.268653\pi$
$283$	22.3566	1.32896	0.664481	+	0.747305i	$0.268653\pi$
$284$	2.58590	0.153445
$285$	−3.95943	−0.234537
$286$	0	0
$287$	−26.7663	−1.57996
$288$	−2.62961	−0.154952
$289$	−15.2714	−0.898315
$290$	−1.23688	−0.0726322
$291$	13.1150	0.768818
$292$	−3.59204	−0.210208
$293$	1.57985	0.0922960	0.0461480	−	0.998935i	$-0.485305\pi$
$293$	1.57985	0.0922960	0.0461480	+	0.998935i	$0.485305\pi$
$294$	−22.2001	−1.29474
$295$	−6.62242	−0.385572
$296$	−14.9561	−0.869306
$297$	0	0
$298$	−14.7981	−0.857230
$299$	−18.8425	−1.08969
$300$	−1.21830	−0.0703384
$301$	19.9052	1.14732
$302$	−15.2950	−0.880126
$303$	13.9102	0.799122
$304$	−29.4601	−1.68965
$305$	−0.565778	−0.0323963
$306$	3.72692	0.213054
$307$	−12.8928	−0.735830	−0.367915	−	0.929859i	$-0.619928\pi$
$307$	−12.8928	−0.735830	−0.367915	+	0.929859i	$0.619928\pi$
$308$	0	0
$309$	10.0868	0.573818
$310$	8.72678	0.495648
$311$	3.81376	0.216258	0.108129	−	0.994137i	$-0.465514\pi$
$311$	3.81376	0.216258	0.108129	+	0.994137i	$0.465514\pi$
$312$	−6.74632	−0.381935
$313$	3.36392	0.190140	0.0950701	−	0.995471i	$-0.469692\pi$
$313$	3.36392	0.190140	0.0950701	+	0.995471i	$0.469692\pi$
$314$	−20.7737	−1.17233
$315$	4.90994	0.276644
$316$	−0.730711	−0.0411057
$317$	−4.53217	−0.254552	−0.127276	−	0.991867i	$-0.540623\pi$
$317$	−4.53217	−0.254552	−0.127276	+	0.991867i	$0.540623\pi$
$318$	−4.10414	−0.230149
$319$	0	0
$320$	−3.83705	−0.214498
$321$	10.4074	0.580885
$322$	−53.1712	−2.96312
$323$	8.73698	0.486139
$324$	0.0614162	0.00341201
$325$	11.4096	0.632892
$326$	34.4860	1.91000
$327$	0.515549	0.0285099
$328$	−15.3246	−0.846159
$329$	−0.553224	−0.0305002
$330$	0	0
$331$	−1.00035	−0.0549841	−0.0274920	−	0.999622i	$-0.508752\pi$
$331$	−1.00035	−0.0549841	−0.0274920	+	0.999622i	$0.508752\pi$
$332$	−1.28508	−0.0705282
$333$	10.7632	0.589820
$334$	−3.12782	−0.171147
$335$	6.54196	0.357426
$336$	−21.4268	−1.16893
$337$	24.4714	1.33304	0.666521	−	0.745486i	$-0.267783\pi$
$337$	24.4714	1.33304	0.666521	+	0.745486i	$0.267783\pi$
$338$	10.5776	0.575345
$339$	−18.0566	−0.980700
$340$	−0.183881	−0.00997236
$341$	0	0
$342$	18.8368	1.01858
$343$	32.4116	1.75006
$344$	11.3964	0.614454
$345$	−4.60497	−0.247923
$346$	5.28543	0.284147
$347$	−1.47537	−0.0792020	−0.0396010	−	0.999216i	$-0.512609\pi$
$347$	−1.47537	−0.0792020	−0.0396010	+	0.999216i	$0.512609\pi$
$348$	−0.379646	−0.0203511
$349$	−33.6651	−1.80205	−0.901027	−	0.433763i	$-0.857185\pi$
$349$	−33.6651	−1.80205	−0.901027	+	0.433763i	$0.857185\pi$
$350$	32.1966	1.72098
$351$	12.5576	0.670273
$352$	0	0
$353$	20.8007	1.10711	0.553555	−	0.832812i	$-0.313271\pi$
$353$	20.8007	1.10711	0.553555	+	0.832812i	$0.313271\pi$
$354$	−18.4786	−0.982126
$355$	−5.91860	−0.314127
$356$	−0.839936	−0.0445165
$357$	6.35454	0.336318
$358$	−10.5254	−0.556283
$359$	8.80481	0.464700	0.232350	−	0.972632i	$-0.425359\pi$
$359$	8.80481	0.464700	0.232350	+	0.972632i	$0.425359\pi$
$360$	2.81111	0.148158
$361$	25.1588	1.32415
$362$	−25.6951	−1.35050
$363$	0	0
$364$	−2.76584	−0.144969
$365$	8.22146	0.430331
$366$	−1.57870	−0.0825198
$367$	8.59463	0.448636	0.224318	−	0.974516i	$-0.427985\pi$
$367$	8.59463	0.448636	0.224318	+	0.974516i	$0.427985\pi$
$368$	−34.2633	−1.78610
$369$	11.0284	0.574115
$370$	−4.82760	−0.250975
$371$	11.9310	0.619427
$372$	2.67858	0.138878
$373$	−13.3654	−0.692034	−0.346017	−	0.938228i	$-0.612466\pi$
$373$	−13.3654	−0.692034	−0.346017	+	0.938228i	$0.612466\pi$
$374$	0	0
$375$	5.76760	0.297837
$376$	−0.316740	−0.0163346
$377$	3.55547	0.183116
$378$	35.4359	1.82263
$379$	6.12401	0.314569	0.157285	−	0.987553i	$-0.449726\pi$
$379$	6.12401	0.314569	0.157285	+	0.987553i	$0.449726\pi$
$380$	−0.929380	−0.0476762
$381$	−1.17185	−0.0600356
$382$	−9.09100	−0.465136
$383$	−19.5309	−0.997981	−0.498990	−	0.866608i	$-0.666296\pi$
$383$	−19.5309	−0.997981	−0.498990	+	0.866608i	$0.666296\pi$
$384$	−13.6356	−0.695838
$385$	0	0
$386$	14.4081	0.733353
$387$	−8.20147	−0.416904
$388$	3.07844	0.156284
$389$	17.8718	0.906134	0.453067	−	0.891476i	$-0.350330\pi$
$389$	17.8718	0.906134	0.453067	+	0.891476i	$0.350330\pi$
$390$	−2.17761	−0.110267
$391$	10.1615	0.513887
$392$	36.9497	1.86624
$393$	13.8453	0.698401
$394$	13.6400	0.687175
$395$	1.67245	0.0841501
$396$	0	0
$397$	−6.49365	−0.325907	−0.162953	−	0.986634i	$-0.552102\pi$
$397$	−6.49365	−0.325907	−0.162953	+	0.986634i	$0.552102\pi$
$398$	−4.61127	−0.231142
$399$	32.1174	1.60788
$400$	20.7473	1.03737
$401$	22.0701	1.10213	0.551065	−	0.834463i	$-0.314222\pi$
$401$	22.0701	1.10213	0.551065	+	0.834463i	$0.314222\pi$
$402$	18.2541	0.910432
$403$	−25.0855	−1.24960
$404$	3.26509	0.162444
$405$	−0.140569	−0.00698494
$406$	10.0331	0.497935
$407$	0	0
$408$	3.63819	0.180117
$409$	−18.9438	−0.936712	−0.468356	−	0.883540i	$-0.655153\pi$
$409$	−18.9438	−0.936712	−0.468356	+	0.883540i	$0.655153\pi$
$410$	−4.94654	−0.244292
$411$	1.11331	0.0549154
$412$	2.36763	0.116645
$413$	53.7185	2.64331
$414$	21.9079	1.07671
$415$	2.94130	0.144383
$416$	−3.39039	−0.166228
$417$	−16.1668	−0.791690
$418$	0	0
$419$	23.0722	1.12715	0.563575	−	0.826065i	$-0.309426\pi$
$419$	23.0722	1.12715	0.563575	+	0.826065i	$0.309426\pi$
$420$	−0.675952	−0.0329831
$421$	34.9820	1.70492	0.852459	−	0.522795i	$-0.175111\pi$
$421$	34.9820	1.70492	0.852459	+	0.522795i	$0.175111\pi$
$422$	13.1009	0.637741
$423$	0.227942	0.0110829
$424$	6.83090	0.331738
$425$	−6.15303	−0.298466
$426$	−16.5147	−0.800141
$427$	4.58937	0.222095
$428$	2.44289	0.118081
$429$	0	0
$430$	3.67858	0.177397
$431$	−7.06013	−0.340075	−0.170037	−	0.985438i	$-0.554389\pi$
$431$	−7.06013	−0.340075	−0.170037	+	0.985438i	$0.554389\pi$
$432$	22.8347	1.09864
$433$	4.31024	0.207137	0.103568	−	0.994622i	$-0.466974\pi$
$433$	4.31024	0.207137	0.103568	+	0.994622i	$0.466974\pi$
$434$	−70.7882	−3.39794
$435$	0.868932	0.0416621
$436$	0.121012	0.00579545
$437$	51.3584	2.45681
$438$	22.9404	1.09614
$439$	31.8976	1.52239	0.761195	−	0.648523i	$-0.224613\pi$
$439$	31.8976	1.52239	0.761195	+	0.648523i	$0.224613\pi$
$440$	0	0
$441$	−26.5910	−1.26624
$442$	4.80516	0.228558
$443$	36.3218	1.72570	0.862850	−	0.505461i	$-0.168678\pi$
$443$	36.3218	1.72570	0.862850	+	0.505461i	$0.168678\pi$
$444$	−1.48177	−0.0703218
$445$	1.92244	0.0911326
$446$	−10.3748	−0.491261
$447$	10.3959	0.491711
$448$	31.1247	1.47050
$449$	−3.61741	−0.170716	−0.0853580	−	0.996350i	$-0.527203\pi$
$449$	−3.61741	−0.170716	−0.0853580	+	0.996350i	$0.527203\pi$
$450$	−13.2658	−0.625356
$451$	0	0
$452$	−4.23835	−0.199355
$453$	10.7450	0.504844
$454$	−24.7003	−1.15924
$455$	6.33044	0.296776
$456$	18.3883	0.861110
$457$	31.0643	1.45313	0.726563	−	0.687100i	$-0.241117\pi$
$457$	31.0643	1.45313	0.726563	+	0.687100i	$0.241117\pi$
$458$	−13.9295	−0.650885
$459$	−6.77209	−0.316094
$460$	−1.08091	−0.0503975
$461$	40.4663	1.88470	0.942352	−	0.334622i	$-0.108609\pi$
$461$	40.4663	1.88470	0.942352	+	0.334622i	$0.108609\pi$
$462$	0	0
$463$	28.3192	1.31610	0.658052	−	0.752973i	$-0.271381\pi$
$463$	28.3192	1.31610	0.658052	+	0.752973i	$0.271381\pi$
$464$	6.46528	0.300143
$465$	−6.13072	−0.284306
$466$	−5.08528	−0.235571
$467$	16.6168	0.768933	0.384466	−	0.923139i	$-0.374385\pi$
$467$	16.6168	0.768933	0.384466	+	0.923139i	$0.374385\pi$
$468$	1.13960	0.0526778
$469$	−53.0659	−2.45035
$470$	−0.102239	−0.00471591
$471$	14.5939	0.672451
$472$	30.7556	1.41564
$473$	0	0
$474$	4.66665	0.214347
$475$	−31.0989	−1.42691
$476$	1.49157	0.0683661
$477$	−4.91588	−0.225083
$478$	−9.53293	−0.436026
$479$	−8.73853	−0.399274	−0.199637	−	0.979870i	$-0.563976\pi$
$479$	−8.73853	−0.399274	−0.199637	+	0.979870i	$0.563976\pi$
$480$	−0.828589	−0.0378197
$481$	13.8771	0.632743
$482$	−10.3806	−0.472821
$483$	37.3538	1.69965
$484$	0	0
$485$	−7.04592	−0.319939
$486$	−23.5561	−1.06853
$487$	−20.9955	−0.951396	−0.475698	−	0.879609i	$-0.657804\pi$
$487$	−20.9955	−0.951396	−0.475698	+	0.879609i	$0.657804\pi$
$488$	2.62757	0.118944
$489$	−24.2270	−1.09558
$490$	11.9268	0.538797
$491$	−6.30833	−0.284691	−0.142346	−	0.989817i	$-0.545464\pi$
$491$	−6.30833	−0.284691	−0.142346	+	0.989817i	$0.545464\pi$
$492$	−1.51828	−0.0684493
$493$	−1.91741	−0.0863557
$494$	24.2865	1.09270
$495$	0	0
$496$	−45.6156	−2.04820
$497$	48.0094	2.15351
$498$	8.20713	0.367770
$499$	−25.1091	−1.12404	−0.562019	−	0.827124i	$-0.689975\pi$
$499$	−25.1091	−1.12404	−0.562019	+	0.827124i	$0.689975\pi$
$500$	1.35380	0.0605439
$501$	2.19735	0.0981704
$502$	19.5053	0.870566
$503$	4.74874	0.211736	0.105868	−	0.994380i	$-0.466238\pi$
$503$	4.74874	0.211736	0.105868	+	0.994380i	$0.466238\pi$
$504$	−22.8026	−1.01571
$505$	−7.47312	−0.332550
$506$	0	0
$507$	−7.43095	−0.330020
$508$	−0.275063	−0.0122039
$509$	21.9927	0.974811	0.487405	−	0.873176i	$-0.337943\pi$
$509$	21.9927	0.974811	0.487405	+	0.873176i	$0.337943\pi$
$510$	1.17435	0.0520010
$511$	−66.6893	−2.95016
$512$	17.1324	0.757153
$513$	−34.2278	−1.51119
$514$	41.9634	1.85093
$515$	−5.41903	−0.238791
$516$	1.12910	0.0497057
$517$	0	0
$518$	39.1596	1.72057
$519$	−3.71311	−0.162988
$520$	3.62439	0.158940
$521$	−23.1269	−1.01321	−0.506604	−	0.862179i	$-0.669100\pi$
$521$	−23.1269	−1.01321	−0.506604	+	0.862179i	$0.669100\pi$
$522$	−4.13389	−0.180936
$523$	−29.0632	−1.27084	−0.635422	−	0.772165i	$-0.719174\pi$
$523$	−29.0632	−1.27084	−0.635422	+	0.772165i	$0.719174\pi$
$524$	3.24984	0.141970
$525$	−22.6187	−0.987160
$526$	28.1403	1.22698
$527$	13.5282	0.589298
$528$	0	0
$529$	36.7319	1.59704
$530$	2.20491	0.0957750
$531$	−22.1334	−0.960506
$532$	7.53877	0.326847
$533$	14.2190	0.615895
$534$	5.36421	0.232132
$535$	−5.59127	−0.241732
$536$	−30.3820	−1.31230
$537$	7.39426	0.319086
$538$	−39.5398	−1.70468
$539$	0	0
$540$	0.720369	0.0309997
$541$	1.92561	0.0827884	0.0413942	−	0.999143i	$-0.486820\pi$
$541$	1.92561	0.0827884	0.0413942	+	0.999143i	$0.486820\pi$
$542$	28.7559	1.23517
$543$	18.0513	0.774655
$544$	1.82839	0.0783914
$545$	−0.276973	−0.0118642
$546$	17.6639	0.755945
$547$	−40.7750	−1.74341	−0.871706	−	0.490029i	$-0.836986\pi$
$547$	−40.7750	−1.74341	−0.871706	+	0.490029i	$0.836986\pi$
$548$	0.261322	0.0111631
$549$	−1.89094	−0.0807032
$550$	0	0
$551$	−9.69104	−0.412852
$552$	21.3863	0.910261
$553$	−13.5663	−0.576896
$554$	37.7854	1.60535
$555$	3.39148	0.143960
$556$	−3.79475	−0.160933
$557$	33.8833	1.43568	0.717840	−	0.696208i	$-0.245131\pi$
$557$	33.8833	1.43568	0.717840	+	0.696208i	$0.245131\pi$
$558$	29.1665	1.23472
$559$	−10.5742	−0.447243
$560$	11.5113	0.486442
$561$	0	0
$562$	17.4410	0.735705
$563$	7.99199	0.336822	0.168411	−	0.985717i	$-0.446136\pi$
$563$	7.99199	0.336822	0.168411	+	0.985717i	$0.446136\pi$
$564$	−0.0313809	−0.00132137
$565$	9.70072	0.408112
$566$	−33.5140	−1.40870
$567$	1.14024	0.0478857
$568$	27.4870	1.15333
$569$	−16.3790	−0.686642	−0.343321	−	0.939218i	$-0.611552\pi$
$569$	−16.3790	−0.686642	−0.343321	+	0.939218i	$0.611552\pi$
$570$	5.93544	0.248608
$571$	−3.44758	−0.144277	−0.0721383	−	0.997395i	$-0.522982\pi$
$571$	−3.44758	−0.144277	−0.0721383	+	0.997395i	$0.522982\pi$
$572$	0	0
$573$	6.38659	0.266804
$574$	40.1244	1.67476
$575$	−36.1692	−1.50836
$576$	−12.8242	−0.534340
$577$	−7.86758	−0.327532	−0.163766	−	0.986499i	$-0.552364\pi$
$577$	−7.86758	−0.327532	−0.163766	+	0.986499i	$0.552364\pi$
$578$	22.8927	0.952213
$579$	−10.1220	−0.420654
$580$	0.203961	0.00846901
$581$	−23.8587	−0.989824
$582$	−19.6603	−0.814946
$583$	0	0
$584$	−38.1818	−1.57998
$585$	−2.60830	−0.107840
$586$	−2.36830	−0.0978337
$587$	37.2672	1.53818	0.769092	−	0.639138i	$-0.220709\pi$
$587$	37.2672	1.53818	0.769092	+	0.639138i	$0.220709\pi$
$588$	3.66078	0.150968
$589$	68.3749	2.81734
$590$	9.92743	0.408706
$591$	−9.58237	−0.394166
$592$	25.2342	1.03712
$593$	27.5278	1.13043	0.565216	−	0.824943i	$-0.308793\pi$
$593$	27.5278	1.13043	0.565216	+	0.824943i	$0.308793\pi$
$594$	0	0
$595$	−3.41391	−0.139957
$596$	2.44019	0.0999542
$597$	3.23950	0.132584
$598$	28.2461	1.15507
$599$	34.2836	1.40079	0.700394	−	0.713756i	$-0.253008\pi$
$599$	34.2836	1.40079	0.700394	+	0.713756i	$0.253008\pi$
$600$	−12.9500	−0.528680
$601$	−7.60115	−0.310057	−0.155029	−	0.987910i	$-0.549547\pi$
$601$	−7.60115	−0.310057	−0.155029	+	0.987910i	$0.549547\pi$
$602$	−29.8392	−1.21616
$603$	21.8645	0.890390
$604$	2.52212	0.102624
$605$	0	0
$606$	−20.8523	−0.847068
$607$	37.1733	1.50882	0.754409	−	0.656404i	$-0.227923\pi$
$607$	37.1733	1.50882	0.754409	+	0.656404i	$0.227923\pi$
$608$	9.24110	0.374776
$609$	−7.04844	−0.285617
$610$	0.848138	0.0343401
$611$	0.293889	0.0118895
$612$	−0.614566	−0.0248423
$613$	30.1396	1.21733	0.608663	−	0.793429i	$-0.291706\pi$
$613$	30.1396	1.21733	0.608663	+	0.793429i	$0.291706\pi$
$614$	19.3271	0.779979
$615$	3.47504	0.140127
$616$	0	0
$617$	−43.1987	−1.73911	−0.869556	−	0.493834i	$-0.835595\pi$
$617$	−43.1987	−1.73911	−0.869556	+	0.493834i	$0.835595\pi$
$618$	−15.1208	−0.608246
$619$	−10.7197	−0.430863	−0.215431	−	0.976519i	$-0.569116\pi$
$619$	−10.7197	−0.430863	−0.215431	+	0.976519i	$0.569116\pi$
$620$	−1.43904	−0.0577932
$621$	−39.8083	−1.59745
$622$	−5.71707	−0.229234
$623$	−15.5941	−0.624765
$624$	11.3825	0.455666
$625$	20.3009	0.812036
$626$	−5.04274	−0.201548
$627$	0	0
$628$	3.42556	0.136695
$629$	−7.48372	−0.298395
$630$	−7.36032	−0.293242
$631$	−1.27659	−0.0508202	−0.0254101	−	0.999677i	$-0.508089\pi$
$631$	−1.27659	−0.0508202	−0.0254101	+	0.999677i	$0.508089\pi$
$632$	−7.76714	−0.308960
$633$	−9.20361	−0.365811
$634$	6.79402	0.269825
$635$	0.629563	0.0249834
$636$	0.676769	0.0268357
$637$	−34.2840	−1.35838
$638$	0	0
$639$	−19.7811	−0.782527
$640$	7.32558	0.289569
$641$	−49.0876	−1.93885	−0.969423	−	0.245397i	$-0.921082\pi$
$641$	−49.0876	−1.93885	−0.969423	+	0.245397i	$0.921082\pi$
$642$	−15.6014	−0.615738
$643$	−1.89090	−0.0745700	−0.0372850	−	0.999305i	$-0.511871\pi$
$643$	−1.89090	−0.0745700	−0.0372850	+	0.999305i	$0.511871\pi$
$644$	8.76788	0.345503
$645$	−2.58427	−0.101756
$646$	−13.0973	−0.515306
$647$	−10.6833	−0.420002	−0.210001	−	0.977701i	$-0.567347\pi$
$647$	−10.6833	−0.420002	−0.210001	+	0.977701i	$0.567347\pi$
$648$	0.652827	0.0256455
$649$	0	0
$650$	−17.1038	−0.670864
$651$	49.7301	1.94907
$652$	−5.68671	−0.222709
$653$	12.7695	0.499709	0.249854	−	0.968283i	$-0.419617\pi$
$653$	12.7695	0.499709	0.249854	+	0.968283i	$0.419617\pi$
$654$	−0.772841	−0.0302205
$655$	−7.43822	−0.290635
$656$	25.8560	1.00951
$657$	27.4777	1.07201
$658$	0.829319	0.0323302
$659$	10.3579	0.403488	0.201744	−	0.979438i	$-0.435339\pi$
$659$	10.3579	0.403488	0.201744	+	0.979438i	$0.435339\pi$
$660$	0	0
$661$	16.2526	0.632154	0.316077	−	0.948733i	$-0.397634\pi$
$661$	16.2526	0.632154	0.316077	+	0.948733i	$0.397634\pi$
$662$	1.49959	0.0582831
$663$	−3.37572	−0.131102
$664$	−13.6599	−0.530106
$665$	−17.2547	−0.669109
$666$	−16.1347	−0.625208
$667$	−11.2711	−0.436417
$668$	0.515774	0.0199559
$669$	7.28850	0.281790
$670$	−9.80682	−0.378871
$671$	0	0
$672$	6.72119	0.259276
$673$	19.2321	0.741343	0.370672	−	0.928764i	$-0.379128\pi$
$673$	19.2321	0.741343	0.370672	+	0.928764i	$0.379128\pi$
$674$	−36.6842	−1.41302
$675$	24.1050	0.927800
$676$	−1.74423	−0.0670859
$677$	−27.4429	−1.05472	−0.527358	−	0.849643i	$-0.676817\pi$
$677$	−27.4429	−1.05472	−0.527358	+	0.849643i	$0.676817\pi$
$678$	27.0680	1.03954
$679$	57.1538	2.19336
$680$	−1.95458	−0.0749546
$681$	17.3524	0.664945
$682$	0	0
$683$	−21.5019	−0.822746	−0.411373	−	0.911467i	$-0.634951\pi$
$683$	−21.5019	−0.822746	−0.411373	+	0.911467i	$0.634951\pi$
$684$	−3.10616	−0.118767
$685$	−0.598113	−0.0228527
$686$	−48.5871	−1.85506
$687$	9.78577	0.373350
$688$	−19.2283	−0.733070
$689$	−6.33810	−0.241462
$690$	6.90315	0.262799
$691$	43.2383	1.64486	0.822432	−	0.568863i	$-0.192617\pi$
$691$	43.2383	1.64486	0.822432	+	0.568863i	$0.192617\pi$
$692$	−0.871563	−0.0331319
$693$	0	0
$694$	2.21167	0.0839540
$695$	8.68542	0.329457
$696$	−4.03547	−0.152964
$697$	−7.66810	−0.290450
$698$	50.4662	1.91017
$699$	3.57251	0.135125
$700$	−5.30919	−0.200668
$701$	−4.33716	−0.163812	−0.0819061	−	0.996640i	$-0.526101\pi$
$701$	−4.33716	−0.163812	−0.0819061	+	0.996640i	$0.526101\pi$
$702$	−18.8246	−0.710488
$703$	−37.8245	−1.42658
$704$	0	0
$705$	0.0718244	0.00270507
$706$	−31.1816	−1.17354
$707$	60.6191	2.27981
$708$	3.04710	0.114517
$709$	−9.30534	−0.349470	−0.174735	−	0.984616i	$-0.555907\pi$
$709$	−9.30534	−0.349470	−0.174735	+	0.984616i	$0.555907\pi$
$710$	8.87236	0.332974
$711$	5.58964	0.209628
$712$	−8.92815	−0.334597
$713$	79.5226	2.97815
$714$	−9.52586	−0.356496
$715$	0	0
$716$	1.73562	0.0648633
$717$	6.69706	0.250106
$718$	−13.1990	−0.492581
$719$	25.6894	0.958053	0.479027	−	0.877800i	$-0.340990\pi$
$719$	25.6894	0.958053	0.479027	+	0.877800i	$0.340990\pi$
$720$	−4.74295	−0.176759
$721$	43.9570	1.63705
$722$	−37.7147	−1.40360
$723$	7.29253	0.271212
$724$	4.23710	0.157471
$725$	6.82493	0.253471
$726$	0	0
$727$	30.3831	1.12685	0.563423	−	0.826169i	$-0.309484\pi$
$727$	30.3831	1.12685	0.563423	+	0.826169i	$0.309484\pi$
$728$	−29.3997	−1.08962
$729$	15.8033	0.585306
$730$	−12.3245	−0.456150
$731$	5.70252	0.210915
$732$	0.260326	0.00962191
$733$	30.0035	1.10820	0.554102	−	0.832449i	$-0.313062\pi$
$733$	30.0035	1.10820	0.554102	+	0.832449i	$0.313062\pi$
$734$	−12.8839	−0.475554
$735$	−8.37879	−0.309056
$736$	10.7478	0.396168
$737$	0	0
$738$	−16.5323	−0.608561
$739$	25.4974	0.937936	0.468968	−	0.883215i	$-0.344626\pi$
$739$	25.4974	0.937936	0.468968	+	0.883215i	$0.344626\pi$
$740$	0.796066	0.0292640
$741$	−17.0617	−0.626777
$742$	−17.8853	−0.656592
$743$	21.2212	0.778529	0.389265	−	0.921126i	$-0.372729\pi$
$743$	21.2212	0.778529	0.389265	+	0.921126i	$0.372729\pi$
$744$	28.4721	1.04384
$745$	−5.58511	−0.204622
$746$	20.0356	0.733555
$747$	9.83038	0.359675
$748$	0	0
$749$	45.3542	1.65721
$750$	−8.64600	−0.315707
$751$	−24.7310	−0.902449	−0.451224	−	0.892411i	$-0.649013\pi$
$751$	−24.7310	−0.902449	−0.451224	+	0.892411i	$0.649013\pi$
$752$	0.534409	0.0194879
$753$	−13.7029	−0.499360
$754$	−5.32988	−0.194103
$755$	−5.77263	−0.210088
$756$	−5.84335	−0.212521
$757$	−30.2823	−1.10063	−0.550315	−	0.834957i	$-0.685492\pi$
$757$	−30.2823	−1.10063	−0.550315	+	0.834957i	$0.685492\pi$
$758$	−9.18028	−0.333443
$759$	0	0
$760$	−9.87891	−0.358346
$761$	−0.150603	−0.00545935	−0.00272967	−	0.999996i	$-0.500869\pi$
$761$	−0.150603	−0.00545935	−0.00272967	+	0.999996i	$0.500869\pi$
$762$	1.75668	0.0636376
$763$	2.24670	0.0813359
$764$	1.49910	0.0542354
$765$	1.40662	0.0508563
$766$	29.2780	1.05786
$767$	−28.5368	−1.03040
$768$	6.15630	0.222146
$769$	−8.63234	−0.311290	−0.155645	−	0.987813i	$-0.549746\pi$
$769$	−8.63234	−0.311290	−0.155645	+	0.987813i	$0.549746\pi$
$770$	0	0
$771$	−29.4801	−1.06170
$772$	−2.37588	−0.0855099
$773$	35.1632	1.26473	0.632366	−	0.774670i	$-0.282084\pi$
$773$	35.1632	1.26473	0.632366	+	0.774670i	$0.282084\pi$
$774$	12.2945	0.441918
$775$	−48.1531	−1.72971
$776$	32.7224	1.17467
$777$	−27.5103	−0.986928
$778$	−26.7909	−0.960501
$779$	−38.7564	−1.38859
$780$	0.359085	0.0128573
$781$	0	0
$782$	−15.2327	−0.544719
$783$	7.51159	0.268442
$784$	−62.3423	−2.22651
$785$	−7.84041	−0.279836
$786$	−20.7549	−0.740304
$787$	−30.9720	−1.10403	−0.552016	−	0.833834i	$-0.686141\pi$
$787$	−30.9720	−1.10403	−0.552016	+	0.833834i	$0.686141\pi$
$788$	−2.24923	−0.0801254
$789$	−19.7691	−0.703798
$790$	−2.50711	−0.0891990
$791$	−78.6885	−2.79784
$792$	0	0
$793$	−2.43801	−0.0865762
$794$	9.73439	0.345461
$795$	−1.54899	−0.0549369
$796$	0.760394	0.0269515
$797$	28.6813	1.01594	0.507972	−	0.861373i	$-0.330395\pi$
$797$	28.6813	1.01594	0.507972	+	0.861373i	$0.330395\pi$
$798$	−48.1460	−1.70435
$799$	−0.158490	−0.00560696
$800$	−6.50805	−0.230094
$801$	6.42517	0.227022
$802$	−33.0845	−1.16826
$803$	0	0
$804$	−3.01009	−0.106158
$805$	−20.0679	−0.707301
$806$	37.6048	1.32457
$807$	27.7775	0.977813
$808$	34.7064	1.22097
$809$	−5.13682	−0.180601	−0.0903004	−	0.995915i	$-0.528783\pi$
$809$	−5.13682	−0.180601	−0.0903004	+	0.995915i	$0.528783\pi$
$810$	0.210722	0.00740403
$811$	−5.19035	−0.182258	−0.0911288	−	0.995839i	$-0.529048\pi$
$811$	−5.19035	−0.182258	−0.0911288	+	0.995839i	$0.529048\pi$
$812$	−1.65445	−0.0580598
$813$	−20.2015	−0.708498
$814$	0	0
$815$	13.0157	0.455921
$816$	−6.13842	−0.214888
$817$	28.8219	1.00835
$818$	28.3980	0.992913
$819$	21.1575	0.739304
$820$	0.815680	0.0284848
$821$	19.7648	0.689797	0.344899	−	0.938640i	$-0.387913\pi$
$821$	19.7648	0.689797	0.344899	+	0.938640i	$0.387913\pi$
$822$	−1.66892	−0.0582103
$823$	−51.9575	−1.81113	−0.905563	−	0.424213i	$-0.860551\pi$
$823$	−51.9575	−1.81113	−0.905563	+	0.424213i	$0.860551\pi$
$824$	25.1669	0.876730
$825$	0	0
$826$	−80.5274	−2.80191
$827$	30.2376	1.05146	0.525732	−	0.850650i	$-0.323791\pi$
$827$	30.2376	1.05146	0.525732	+	0.850650i	$0.323791\pi$
$828$	−3.61259	−0.125546
$829$	−32.6118	−1.13266	−0.566328	−	0.824180i	$-0.691636\pi$
$829$	−32.6118	−1.13266	−0.566328	+	0.824180i	$0.691636\pi$
$830$	−4.40920	−0.153045
$831$	−26.5450	−0.920835
$832$	−16.5343	−0.573225
$833$	18.4888	0.640600
$834$	24.2350	0.839190
$835$	−1.18050	−0.0408530
$836$	0	0
$837$	−52.9978	−1.83187
$838$	−34.5867	−1.19478
$839$	43.1983	1.49137	0.745686	−	0.666298i	$-0.232122\pi$
$839$	43.1983	1.49137	0.745686	+	0.666298i	$0.232122\pi$
$840$	−7.18508	−0.247909
$841$	−26.8732	−0.926663
$842$	−52.4402	−1.80721
$843$	−12.2526	−0.422003
$844$	−2.16032	−0.0743614
$845$	3.99220	0.137336
$846$	−0.341700	−0.0117479
$847$	0	0
$848$	−11.5252	−0.395778
$849$	23.5442	0.808035
$850$	9.22378	0.316373
$851$	−43.9914	−1.50801
$852$	2.72326	0.0932974
$853$	13.1873	0.451525	0.225763	−	0.974182i	$-0.427513\pi$
$853$	13.1873	0.451525	0.225763	+	0.974182i	$0.427513\pi$
$854$	−6.87976	−0.235421
$855$	7.10938	0.243136
$856$	25.9668	0.887528
$857$	−34.7524	−1.18712	−0.593560	−	0.804790i	$-0.702278\pi$
$857$	−34.7524	−1.18712	−0.593560	+	0.804790i	$0.702278\pi$
$858$	0	0
$859$	37.4706	1.27848	0.639241	−	0.769007i	$-0.279249\pi$
$859$	37.4706	1.27848	0.639241	+	0.769007i	$0.279249\pi$
$860$	−0.606595	−0.0206847
$861$	−28.1881	−0.960649
$862$	10.5836	0.360479
$863$	48.9613	1.66666	0.833331	−	0.552774i	$-0.186431\pi$
$863$	48.9613	1.66666	0.833331	+	0.552774i	$0.186431\pi$
$864$	−7.16284	−0.243685
$865$	1.99483	0.0678263
$866$	−6.46133	−0.219565
$867$	−16.0826	−0.546193
$868$	11.6729	0.396205
$869$	0	0
$870$	−1.30259	−0.0441618
$871$	28.1901	0.955186
$872$	1.28631	0.0435599
$873$	−23.5488	−0.797006
$874$	−76.9896	−2.60421
$875$	25.1345	0.849700
$876$	−3.78285	−0.127811
$877$	−9.19075	−0.310350	−0.155175	−	0.987887i	$-0.549594\pi$
$877$	−9.19075	−0.310350	−0.155175	+	0.987887i	$0.549594\pi$
$878$	−47.8166	−1.61373
$879$	1.66378	0.0561178
$880$	0	0
$881$	40.1939	1.35417	0.677084	−	0.735906i	$-0.263244\pi$
$881$	40.1939	1.35417	0.677084	+	0.735906i	$0.263244\pi$
$882$	39.8616	1.34221
$883$	13.3632	0.449709	0.224854	−	0.974392i	$-0.427809\pi$
$883$	13.3632	0.449709	0.224854	+	0.974392i	$0.427809\pi$
$884$	−0.792367	−0.0266502
$885$	−6.97420	−0.234435
$886$	−54.4487	−1.82924
$887$	9.92601	0.333283	0.166641	−	0.986018i	$-0.446708\pi$
$887$	9.92601	0.333283	0.166641	+	0.986018i	$0.446708\pi$
$888$	−15.7506	−0.528555
$889$	−5.10677	−0.171276
$890$	−2.88187	−0.0966004
$891$	0	0
$892$	1.71080	0.0572817
$893$	−0.801045	−0.0268060
$894$	−15.5842	−0.521213
$895$	−3.97249	−0.132786
$896$	−59.4222	−1.98516
$897$	−19.8434	−0.662552
$898$	5.42273	0.180959
$899$	−15.0055	−0.500460
$900$	2.18752	0.0729173
$901$	3.41804	0.113871
$902$	0	0
$903$	20.9626	0.697593
$904$	−45.0518	−1.49840
$905$	−9.69786	−0.322368
$906$	−16.1074	−0.535134
$907$	49.8629	1.65567	0.827836	−	0.560970i	$-0.189572\pi$
$907$	49.8629	1.65567	0.827836	+	0.560970i	$0.189572\pi$
$908$	4.07305	0.135169
$909$	−24.9766	−0.828421
$910$	−9.48974	−0.314582
$911$	−13.2662	−0.439529	−0.219765	−	0.975553i	$-0.570529\pi$
$911$	−13.2662	−0.439529	−0.219765	+	0.975553i	$0.570529\pi$
$912$	−31.0250	−1.02734
$913$	0	0
$914$	−46.5674	−1.54031
$915$	−0.595832	−0.0196976
$916$	2.29697	0.0758940
$917$	60.3360	1.99247
$918$	10.1518	0.335059
$919$	−36.2339	−1.19524	−0.597622	−	0.801778i	$-0.703888\pi$
$919$	−36.2339	−1.19524	−0.597622	+	0.801778i	$0.703888\pi$
$920$	−11.4896	−0.378799
$921$	−13.5777	−0.447399
$922$	−60.6616	−1.99778
$923$	−25.5040	−0.839473
$924$	0	0
$925$	26.6379	0.875850
$926$	−42.4523	−1.39507
$927$	−18.1114	−0.594857
$928$	−2.02804	−0.0665737
$929$	−22.0863	−0.724628	−0.362314	−	0.932056i	$-0.618013\pi$
$929$	−22.0863	−0.724628	−0.362314	+	0.932056i	$0.618013\pi$
$930$	9.19035	0.301364
$931$	93.4471	3.06260
$932$	0.838559	0.0274679
$933$	4.01635	0.131489
$934$	−24.9096	−0.815068
$935$	0	0
$936$	12.1134	0.395939
$937$	0.170010	0.00555399	0.00277700	−	0.999996i	$-0.499116\pi$
$937$	0.170010	0.00555399	0.00277700	+	0.999996i	$0.499116\pi$
$938$	79.5492	2.59737
$939$	3.54262	0.115609
$940$	0.0168590	0.000549881 0
$941$	39.6386	1.29218	0.646091	−	0.763260i	$-0.276403\pi$
$941$	39.6386	1.29218	0.646091	+	0.763260i	$0.276403\pi$
$942$	−21.8772	−0.712797
$943$	−45.0752	−1.46785
$944$	−51.8915	−1.68892
$945$	13.3742	0.435064
$946$	0	0
$947$	20.8732	0.678288	0.339144	−	0.940735i	$-0.389863\pi$
$947$	20.8732	0.678288	0.339144	+	0.940735i	$0.389863\pi$
$948$	−0.769527	−0.0249931
$949$	35.4273	1.15002
$950$	46.6192	1.51253
$951$	−4.77293	−0.154773
$952$	15.8548	0.513856
$953$	28.1434	0.911653	0.455827	−	0.890069i	$-0.349344\pi$
$953$	28.1434	0.911653	0.455827	+	0.890069i	$0.349344\pi$
$954$	7.36922	0.238587
$955$	−3.43113	−0.111029
$956$	1.57197	0.0508412
$957$	0	0
$958$	13.0996	0.423230
$959$	4.85166	0.156668
$960$	−4.04088	−0.130419
$961$	74.8706	2.41518
$962$	−20.8027	−0.670706
$963$	−18.6871	−0.602183
$964$	1.71174	0.0551316
$965$	5.43792	0.175053
$966$	−55.9957	−1.80163
$967$	−41.0392	−1.31973	−0.659865	−	0.751384i	$-0.729387\pi$
$967$	−41.0392	−1.31973	−0.659865	+	0.751384i	$0.729387\pi$
$968$	0	0
$969$	9.20110	0.295582
$970$	10.5623	0.339135
$971$	37.8931	1.21605	0.608024	−	0.793919i	$-0.291962\pi$
$971$	37.8931	1.21605	0.608024	+	0.793919i	$0.291962\pi$
$972$	3.88439	0.124592
$973$	−70.4527	−2.25861
$974$	31.4736	1.00848
$975$	12.0157	0.384811
$976$	−4.43328	−0.141906
$977$	−60.7768	−1.94442	−0.972211	−	0.234107i	$-0.924783\pi$
$977$	−60.7768	−1.94442	−0.972211	+	0.234107i	$0.924783\pi$
$978$	36.3179	1.16132
$979$	0	0
$980$	−1.96672	−0.0628244
$981$	−0.925696	−0.0295552
$982$	9.45660	0.301772
$983$	35.0537	1.11804	0.559020	−	0.829154i	$-0.311178\pi$
$983$	35.0537	1.11804	0.559020	+	0.829154i	$0.311178\pi$
$984$	−16.1387	−0.514481
$985$	5.14803	0.164030
$986$	2.87432	0.0915369
$987$	−0.582612	−0.0185447
$988$	−4.00481	−0.127410
$989$	33.5210	1.06591
$990$	0	0
$991$	11.1528	0.354280	0.177140	−	0.984186i	$-0.443316\pi$
$991$	11.1528	0.354280	0.177140	+	0.984186i	$0.443316\pi$
$992$	14.3088	0.454304
$993$	−1.05349	−0.0334314
$994$	−71.9691	−2.28272
$995$	−1.74039	−0.0551740
$996$	−1.35335	−0.0428825
$997$	−25.5926	−0.810526	−0.405263	−	0.914200i	$-0.632820\pi$
$997$	−25.5926	−0.810526	−0.405263	+	0.914200i	$0.632820\pi$
$998$	37.6402	1.19148
$999$	29.3180	0.927581

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.v.1.16		64
11.5	even	5		671.2.j.c.245.25	✓	128
11.9	even	5		671.2.j.c.367.25	yes	128
11.10	odd	2		7381.2.a.u.1.49		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.c.245.25	✓	128	11.5	even	5
671.2.j.c.367.25	yes	128	11.9	even	5
7381.2.a.u.1.49		64	11.10	odd	2
7381.2.a.v.1.16		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)

\(f(q)\)	\(=\)	\(q-1.49906 q^{2} +1.05312 q^{3} +0.247194 q^{4} -0.565778 q^{5} -1.57870 q^{6} +4.58937 q^{7} +2.62757 q^{8} -1.89094 q^{9} +O(q^{10})\)	\(q-1.49906 q^{2} +1.05312 q^{3} +0.247194 q^{4} -0.565778 q^{5} -1.57870 q^{6} +4.58937 q^{7} +2.62757 q^{8} -1.89094 q^{9} +0.848138 q^{10} +0.260326 q^{12} -2.43801 q^{13} -6.87976 q^{14} -0.595832 q^{15} -4.43328 q^{16} +1.31478 q^{17} +2.83464 q^{18} +6.64521 q^{19} -0.139857 q^{20} +4.83316 q^{21} +7.72864 q^{23} +2.76715 q^{24} -4.67990 q^{25} +3.65473 q^{26} -5.15075 q^{27} +1.13447 q^{28} -1.45835 q^{29} +0.893191 q^{30} +10.2893 q^{31} +1.39064 q^{32} -1.97094 q^{34} -2.59656 q^{35} -0.467429 q^{36} -5.69200 q^{37} -9.96160 q^{38} -2.56752 q^{39} -1.48662 q^{40} -5.83224 q^{41} -7.24522 q^{42} +4.33725 q^{43} +1.06985 q^{45} -11.5857 q^{46} -0.120545 q^{47} -4.66878 q^{48} +14.0623 q^{49} +7.01547 q^{50} +1.38462 q^{51} -0.602662 q^{52} +2.59970 q^{53} +7.72130 q^{54} +12.0589 q^{56} +6.99821 q^{57} +2.18616 q^{58} +11.7050 q^{59} -0.147286 q^{60} +1.00000 q^{61} -15.4244 q^{62} -8.67821 q^{63} +6.78191 q^{64} +1.37937 q^{65} -11.5628 q^{67} +0.325006 q^{68} +8.13919 q^{69} +3.89242 q^{70} +10.4610 q^{71} -4.96857 q^{72} -14.5312 q^{73} +8.53267 q^{74} -4.92849 q^{75} +1.64266 q^{76} +3.84887 q^{78} -2.95602 q^{79} +2.50825 q^{80} +0.248453 q^{81} +8.74290 q^{82} -5.19868 q^{83} +1.19473 q^{84} -0.743873 q^{85} -6.50182 q^{86} -1.53582 q^{87} -3.39788 q^{89} -1.60377 q^{90} -11.1889 q^{91} +1.91048 q^{92} +10.8359 q^{93} +0.180704 q^{94} -3.75971 q^{95} +1.46451 q^{96} +12.4535 q^{97} -21.0803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) \) 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

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Representations

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Database

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