LMFDB - Embedded newform 7595.2.a.bf.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7595,2,Mod(1,7595)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7595, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7595.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7595 = 5 \cdot 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7595.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:	$60.6463803352$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 1085)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	7595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0843633 q^{2} -1.56695 q^{3} -1.99288 q^{4} +1.00000 q^{5} +0.132193 q^{6} +0.336853 q^{8} -0.544660 q^{9} +O(q^{10})$	\(q-0.0843633 q^{2} -1.56695 q^{3} -1.99288 q^{4} +1.00000 q^{5} +0.132193 q^{6} +0.336853 q^{8} -0.544660 q^{9} -0.0843633 q^{10} -0.417803 q^{11} +3.12275 q^{12} +5.82334 q^{13} -1.56695 q^{15} +3.95735 q^{16} -0.976364 q^{17} +0.0459493 q^{18} -2.75790 q^{19} -1.99288 q^{20} +0.0352472 q^{22} -5.32755 q^{23} -0.527832 q^{24} +1.00000 q^{25} -0.491276 q^{26} +5.55431 q^{27} -6.82472 q^{29} +0.132193 q^{30} -1.00000 q^{31} -1.00756 q^{32} +0.654678 q^{33} +0.0823692 q^{34} +1.08544 q^{36} +6.67113 q^{37} +0.232666 q^{38} -9.12489 q^{39} +0.336853 q^{40} +2.30190 q^{41} -4.56460 q^{43} +0.832633 q^{44} -0.544660 q^{45} +0.449450 q^{46} +6.42985 q^{47} -6.20098 q^{48} -0.0843633 q^{50} +1.52992 q^{51} -11.6052 q^{52} -3.30192 q^{53} -0.468580 q^{54} -0.417803 q^{55} +4.32150 q^{57} +0.575755 q^{58} -12.6488 q^{59} +3.12275 q^{60} -8.68329 q^{61} +0.0843633 q^{62} -7.82969 q^{64} +5.82334 q^{65} -0.0552307 q^{66} +4.23851 q^{67} +1.94578 q^{68} +8.34802 q^{69} +13.1823 q^{71} -0.183470 q^{72} -4.64044 q^{73} -0.562798 q^{74} -1.56695 q^{75} +5.49618 q^{76} +0.769806 q^{78} +14.5570 q^{79} +3.95735 q^{80} -7.06936 q^{81} -0.194196 q^{82} +15.6328 q^{83} -0.976364 q^{85} +0.385085 q^{86} +10.6940 q^{87} -0.140738 q^{88} -7.30423 q^{89} +0.0459493 q^{90} +10.6172 q^{92} +1.56695 q^{93} -0.542443 q^{94} -2.75790 q^{95} +1.57880 q^{96} +3.45312 q^{97} +0.227561 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * q^99

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 $

$2$	−0.0843633	−0.0596538	−0.0298269	−	0.999555i	$-0.509496\pi$
$2$	−0.0843633	−0.0596538	−0.0298269	+	0.999555i	$0.509496\pi$
$3$	−1.56695	−0.904680	−0.452340	−	0.891845i	$-0.649411\pi$
$3$	−1.56695	−0.904680	−0.452340	+	0.891845i	$0.649411\pi$
$4$	−1.99288	−0.996441
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.132193	0.0539677
$7$	0	0
$7$	0	0
$8$	0.336853	0.119095
$9$	−0.544660	−0.181553
$10$	−0.0843633	−0.0266780
$11$	−0.417803	−0.125972	−0.0629862	−	0.998014i	$-0.520062\pi$
$11$	−0.417803	−0.125972	−0.0629862	+	0.998014i	$0.520062\pi$
$12$	3.12275	0.901461
$13$	5.82334	1.61510	0.807552	−	0.589797i	$-0.200792\pi$
$13$	5.82334	1.61510	0.807552	+	0.589797i	$0.200792\pi$
$14$	0	0
$15$	−1.56695	−0.404585
$16$	3.95735	0.989337
$17$	−0.976364	−0.236803	−0.118401	−	0.992966i	$-0.537777\pi$
$17$	−0.976364	−0.236803	−0.118401	+	0.992966i	$0.537777\pi$
$18$	0.0459493	0.0108304
$19$	−2.75790	−0.632707	−0.316353	−	0.948641i	$-0.602459\pi$
$19$	−2.75790	−0.632707	−0.316353	+	0.948641i	$0.602459\pi$
$20$	−1.99288	−0.445622
$21$	0	0
$22$	0.0352472	0.00751474
$23$	−5.32755	−1.11087	−0.555436	−	0.831559i	$-0.687449\pi$
$23$	−5.32755	−1.11087	−0.555436	+	0.831559i	$0.687449\pi$
$24$	−0.527832	−0.107743
$25$	1.00000	0.200000
$26$	−0.491276	−0.0963471
$27$	5.55431	1.06893
$28$	0	0
$29$	−6.82472	−1.26732	−0.633659	−	0.773612i	$-0.718448\pi$
$29$	−6.82472	−1.26732	−0.633659	+	0.773612i	$0.718448\pi$
$30$	0.132193	0.0241351
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00756	−0.178113
$33$	0.654678	0.113965
$34$	0.0823692	0.0141262
$35$	0	0
$36$	1.08544	0.180907
$37$	6.67113	1.09673	0.548364	−	0.836240i	$-0.315251\pi$
$37$	6.67113	1.09673	0.548364	+	0.836240i	$0.315251\pi$
$38$	0.232666	0.0377434
$39$	−9.12489	−1.46115
$40$	0.336853	0.0532611
$41$	2.30190	0.359496	0.179748	−	0.983713i	$-0.442472\pi$
$41$	2.30190	0.359496	0.179748	+	0.983713i	$0.442472\pi$
$42$	0	0
$43$	−4.56460	−0.696095	−0.348048	−	0.937477i	$-0.613155\pi$
$43$	−4.56460	−0.696095	−0.348048	+	0.937477i	$0.613155\pi$
$44$	0.832633	0.125524
$45$	−0.544660	−0.0811932
$46$	0.449450	0.0662677
$47$	6.42985	0.937890	0.468945	−	0.883227i	$-0.344634\pi$
$47$	6.42985	0.937890	0.468945	+	0.883227i	$0.344634\pi$
$48$	−6.20098	−0.895034
$49$	0	0
$50$	−0.0843633	−0.0119308
$51$	1.52992	0.214231
$52$	−11.6052	−1.60936
$53$	−3.30192	−0.453554	−0.226777	−	0.973947i	$-0.572819\pi$
$53$	−3.30192	−0.453554	−0.226777	+	0.973947i	$0.572819\pi$
$54$	−0.468580	−0.0637657
$55$	−0.417803	−0.0563366
$56$	0	0
$57$	4.32150	0.572397
$58$	0.575755	0.0756004
$59$	−12.6488	−1.64674	−0.823368	−	0.567508i	$-0.807908\pi$
$59$	−12.6488	−1.64674	−0.823368	+	0.567508i	$0.807908\pi$
$60$	3.12275	0.403146
$61$	−8.68329	−1.11178	−0.555890	−	0.831256i	$-0.687623\pi$
$61$	−8.68329	−1.11178	−0.555890	+	0.831256i	$0.687623\pi$
$62$	0.0843633	0.0107141
$63$	0	0
$64$	−7.82969	−0.978712
$65$	5.82334	0.722296
$66$	−0.0552307	−0.00679843
$67$	4.23851	0.517817	0.258908	−	0.965902i	$-0.416637\pi$
$67$	4.23851	0.517817	0.258908	+	0.965902i	$0.416637\pi$
$68$	1.94578	0.235960
$69$	8.34802	1.00498
$70$	0	0
$71$	13.1823	1.56446	0.782228	−	0.622993i	$-0.214083\pi$
$71$	13.1823	1.56446	0.782228	+	0.622993i	$0.214083\pi$
$72$	−0.183470	−0.0216222
$73$	−4.64044	−0.543123	−0.271561	−	0.962421i	$-0.587540\pi$
$73$	−4.64044	−0.543123	−0.271561	+	0.962421i	$0.587540\pi$
$74$	−0.562798	−0.0654240
$75$	−1.56695	−0.180936
$76$	5.49618	0.630455
$77$	0	0
$78$	0.769806	0.0871633
$79$	14.5570	1.63780	0.818898	−	0.573940i	$-0.194586\pi$
$79$	14.5570	1.63780	0.818898	+	0.573940i	$0.194586\pi$
$80$	3.95735	0.442445
$81$	−7.06936	−0.785485
$82$	−0.194196	−0.0214453
$83$	15.6328	1.71592	0.857960	−	0.513716i	$-0.171732\pi$
$83$	15.6328	1.71592	0.857960	+	0.513716i	$0.171732\pi$
$84$	0	0
$85$	−0.976364	−0.105902
$86$	0.385085	0.0415247
$87$	10.6940	1.14652
$88$	−0.140738	−0.0150027
$89$	−7.30423	−0.774247	−0.387123	−	0.922028i	$-0.626531\pi$
$89$	−7.30423	−0.774247	−0.387123	+	0.922028i	$0.626531\pi$
$90$	0.0459493	0.00484348
$91$	0	0
$92$	10.6172	1.10692
$93$	1.56695	0.162485
$94$	−0.542443	−0.0559488
$95$	−2.75790	−0.282955
$96$	1.57880	0.161135
$97$	3.45312	0.350611	0.175305	−	0.984514i	$-0.443909\pi$
$97$	3.45312	0.350611	0.175305	+	0.984514i	$0.443909\pi$
$98$	0	0
$99$	0.227561	0.0228707
$100$	−1.99288	−0.199288
$101$	5.15019	0.512463	0.256231	−	0.966615i	$-0.417519\pi$
$101$	5.15019	0.512463	0.256231	+	0.966615i	$0.417519\pi$
$102$	−0.129069	−0.0127797
$103$	8.70759	0.857984	0.428992	−	0.903308i	$-0.358869\pi$
$103$	8.70759	0.857984	0.428992	+	0.903308i	$0.358869\pi$
$104$	1.96161	0.192351
$105$	0	0
$106$	0.278561	0.0270562
$107$	9.67221	0.935048	0.467524	−	0.883980i	$-0.345146\pi$
$107$	9.67221	0.935048	0.467524	+	0.883980i	$0.345146\pi$
$108$	−11.0691	−1.06512
$109$	−6.61075	−0.633195	−0.316598	−	0.948560i	$-0.602540\pi$
$109$	−6.61075	−0.633195	−0.316598	+	0.948560i	$0.602540\pi$
$110$	0.0352472	0.00336069
$111$	−10.4533	−0.992188
$112$	0	0
$113$	−1.07901	−0.101505	−0.0507525	−	0.998711i	$-0.516162\pi$
$113$	−1.07901	−0.101505	−0.0507525	+	0.998711i	$0.516162\pi$
$114$	−0.364576	−0.0341457
$115$	−5.32755	−0.496797
$116$	13.6009	1.26281
$117$	−3.17174	−0.293228
$118$	1.06710	0.0982341
$119$	0	0
$120$	−0.527832	−0.0481842
$121$	−10.8254	−0.984131
$122$	0.732550	0.0663220
$123$	−3.60696	−0.325229
$124$	1.99288	0.178966
$125$	1.00000	0.0894427
$126$	0	0
$127$	−2.69724	−0.239341	−0.119671	−	0.992814i	$-0.538184\pi$
$127$	−2.69724	−0.239341	−0.119671	+	0.992814i	$0.538184\pi$
$128$	2.67566	0.236497
$129$	7.15251	0.629744
$130$	−0.491276	−0.0430877
$131$	8.07156	0.705216	0.352608	−	0.935771i	$-0.385295\pi$
$131$	8.07156	0.705216	0.352608	+	0.935771i	$0.385295\pi$
$132$	−1.30470	−0.113559
$133$	0	0
$134$	−0.357575	−0.0308897
$135$	5.55431	0.478039
$136$	−0.328891	−0.0282021
$137$	−19.8108	−1.69255	−0.846277	−	0.532743i	$-0.821161\pi$
$137$	−19.8108	−1.69255	−0.846277	+	0.532743i	$0.821161\pi$
$138$	−0.704266	−0.0599511
$139$	−12.9035	−1.09446	−0.547231	−	0.836982i	$-0.684318\pi$
$139$	−12.9035	−1.09446	−0.547231	+	0.836982i	$0.684318\pi$
$140$	0	0
$141$	−10.0753	−0.848491
$142$	−1.11210	−0.0933257
$143$	−2.43301	−0.203458
$144$	−2.15541	−0.179618
$145$	−6.82472	−0.566762
$146$	0.391483	0.0323994
$147$	0	0
$148$	−13.2948	−1.09282
$149$	15.9687	1.30820	0.654102	−	0.756406i	$-0.273047\pi$
$149$	15.9687	1.30820	0.654102	+	0.756406i	$0.273047\pi$
$150$	0.132193	0.0107935
$151$	19.5816	1.59353	0.796766	−	0.604288i	$-0.206542\pi$
$151$	19.5816	1.59353	0.796766	+	0.604288i	$0.206542\pi$
$152$	−0.929007	−0.0753524
$153$	0.531786	0.0429924
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	18.1848	1.45595
$157$	−14.0979	−1.12514	−0.562569	−	0.826750i	$-0.690187\pi$
$157$	−14.0979	−1.12514	−0.562569	+	0.826750i	$0.690187\pi$
$158$	−1.22808	−0.0977008
$159$	5.17396	0.410322
$160$	−1.00756	−0.0796546
$161$	0	0
$162$	0.596395	0.0468572
$163$	−11.7852	−0.923084	−0.461542	−	0.887118i	$-0.652704\pi$
$163$	−11.7852	−0.923084	−0.461542	+	0.887118i	$0.652704\pi$
$164$	−4.58741	−0.358217
$165$	0.654678	0.0509666
$166$	−1.31883	−0.102361
$167$	12.1219	0.938021	0.469010	−	0.883193i	$-0.344611\pi$
$167$	12.1219	0.938021	0.469010	+	0.883193i	$0.344611\pi$
$168$	0	0
$169$	20.9113	1.60856
$170$	0.0823692	0.00631743
$171$	1.50212	0.114870
$172$	9.09672	0.693618
$173$	12.8633	0.977977	0.488988	−	0.872290i	$-0.337366\pi$
$173$	12.8633	0.977977	0.488988	+	0.872290i	$0.337366\pi$
$174$	−0.902181	−0.0683942
$175$	0	0
$176$	−1.65339	−0.124629
$177$	19.8201	1.48977
$178$	0.616208	0.0461868
$179$	3.77080	0.281843	0.140921	−	0.990021i	$-0.454994\pi$
$179$	3.77080	0.281843	0.140921	+	0.990021i	$0.454994\pi$
$180$	1.08544	0.0809042
$181$	−22.5985	−1.67974	−0.839868	−	0.542791i	$-0.817367\pi$
$181$	−22.5985	−1.67974	−0.839868	+	0.542791i	$0.817367\pi$
$182$	0	0
$183$	13.6063	1.00581
$184$	−1.79460	−0.132300
$185$	6.67113	0.490471
$186$	−0.132193	−0.00969288
$187$	0.407928	0.0298306
$188$	−12.8139	−0.934553
$189$	0	0
$190$	0.232666	0.0168794
$191$	−14.1765	−1.02578	−0.512888	−	0.858456i	$-0.671424\pi$
$191$	−14.1765	−1.02578	−0.512888	+	0.858456i	$0.671424\pi$
$192$	12.2688	0.885421
$193$	17.5843	1.26575	0.632873	−	0.774256i	$-0.281876\pi$
$193$	17.5843	1.26575	0.632873	+	0.774256i	$0.281876\pi$
$194$	−0.291316	−0.0209153
$195$	−9.12489	−0.653447
$196$	0	0
$197$	22.7485	1.62076	0.810382	−	0.585902i	$-0.199260\pi$
$197$	22.7485	1.62076	0.810382	+	0.585902i	$0.199260\pi$
$198$	−0.0191978	−0.00136433
$199$	−12.0318	−0.852910	−0.426455	−	0.904509i	$-0.640238\pi$
$199$	−12.0318	−0.852910	−0.426455	+	0.904509i	$0.640238\pi$
$200$	0.336853	0.0238191
$201$	−6.64154	−0.468458
$202$	−0.434487	−0.0305704
$203$	0	0
$204$	−3.04894	−0.213469
$205$	2.30190	0.160771
$206$	−0.734600	−0.0511820
$207$	2.90171	0.201683
$208$	23.0450	1.59788
$209$	1.15226	0.0797036
$210$	0	0
$211$	−4.21574	−0.290223	−0.145112	−	0.989415i	$-0.546354\pi$
$211$	−4.21574	−0.290223	−0.145112	+	0.989415i	$0.546354\pi$
$212$	6.58035	0.451940
$213$	−20.6561	−1.41533
$214$	−0.815979	−0.0557792
$215$	−4.56460	−0.311303
$216$	1.87099	0.127304
$217$	0	0
$218$	0.557705	0.0377725
$219$	7.27135	0.491353
$220$	0.832633	0.0561361
$221$	−5.68569	−0.382461
$222$	0.881878	0.0591878
$223$	−26.2601	−1.75851	−0.879253	−	0.476355i	$-0.841958\pi$
$223$	−26.2601	−1.75851	−0.879253	+	0.476355i	$0.841958\pi$
$224$	0	0
$225$	−0.544660	−0.0363107
$226$	0.0910291	0.00605517
$227$	−6.66186	−0.442163	−0.221082	−	0.975255i	$-0.570959\pi$
$227$	−6.66186	−0.442163	−0.221082	+	0.975255i	$0.570959\pi$
$228$	−8.61225	−0.570360
$229$	−15.9972	−1.05713	−0.528564	−	0.848894i	$-0.677269\pi$
$229$	−15.9972	−1.05713	−0.528564	+	0.848894i	$0.677269\pi$
$230$	0.449450	0.0296358
$231$	0	0
$232$	−2.29892	−0.150932
$233$	−5.54622	−0.363345	−0.181673	−	0.983359i	$-0.558151\pi$
$233$	−5.54622	−0.363345	−0.181673	+	0.983359i	$0.558151\pi$
$234$	0.267578	0.0174921
$235$	6.42985	0.419437
$236$	25.2076	1.64088
$237$	−22.8102	−1.48168
$238$	0	0
$239$	26.6301	1.72255	0.861277	−	0.508135i	$-0.169665\pi$
$239$	26.6301	1.72255	0.861277	+	0.508135i	$0.169665\pi$
$240$	−6.20098	−0.400271
$241$	−19.7572	−1.27267	−0.636336	−	0.771412i	$-0.719551\pi$
$241$	−19.7572	−1.27267	−0.636336	+	0.771412i	$0.719551\pi$
$242$	0.913269	0.0587072
$243$	−5.58558	−0.358315
$244$	17.3048	1.10782
$245$	0	0
$246$	0.304295	0.0194012
$247$	−16.0602	−1.02189
$248$	−0.336853	−0.0213902
$249$	−24.4958	−1.55236
$250$	−0.0843633	−0.00533560
$251$	7.27291	0.459062	0.229531	−	0.973301i	$-0.426281\pi$
$251$	7.27291	0.459062	0.229531	+	0.973301i	$0.426281\pi$
$252$	0	0
$253$	2.22587	0.139939
$254$	0.227548	0.0142776
$255$	1.52992	0.0958070
$256$	15.4337	0.964604
$257$	−17.6927	−1.10364	−0.551819	−	0.833964i	$-0.686066\pi$
$257$	−17.6927	−1.10364	−0.551819	+	0.833964i	$0.686066\pi$
$258$	−0.603409	−0.0375666
$259$	0	0
$260$	−11.6052	−0.719726
$261$	3.71715	0.230086
$262$	−0.680943	−0.0420688
$263$	4.09605	0.252573	0.126286	−	0.991994i	$-0.459694\pi$
$263$	4.09605	0.252573	0.126286	+	0.991994i	$0.459694\pi$
$264$	0.220530	0.0135727
$265$	−3.30192	−0.202836
$266$	0	0
$267$	11.4454	0.700446
$268$	−8.44686	−0.515974
$269$	2.57492	0.156996	0.0784980	−	0.996914i	$-0.474988\pi$
$269$	2.57492	0.156996	0.0784980	+	0.996914i	$0.474988\pi$
$270$	−0.468580	−0.0285169
$271$	15.2916	0.928897	0.464449	−	0.885600i	$-0.346252\pi$
$271$	15.2916	0.928897	0.464449	+	0.885600i	$0.346252\pi$
$272$	−3.86381	−0.234278
$273$	0	0
$274$	1.67131	0.100967
$275$	−0.417803	−0.0251945
$276$	−16.6366	−1.00141
$277$	−22.5290	−1.35363	−0.676817	−	0.736151i	$-0.736641\pi$
$277$	−22.5290	−1.35363	−0.676817	+	0.736151i	$0.736641\pi$
$278$	1.08858	0.0652888
$279$	0.544660	0.0326080
$280$	0	0
$281$	−14.4022	−0.859161	−0.429580	−	0.903029i	$-0.641339\pi$
$281$	−14.4022	−0.859161	−0.429580	+	0.903029i	$0.641339\pi$
$282$	0.849983	0.0506157
$283$	27.3538	1.62602	0.813008	−	0.582252i	$-0.197828\pi$
$283$	27.3538	1.62602	0.813008	+	0.582252i	$0.197828\pi$
$284$	−26.2708	−1.55889
$285$	4.32150	0.255984
$286$	0.205257	0.0121371
$287$	0	0
$288$	0.548778	0.0323370
$289$	−16.0467	−0.943924
$290$	0.575755	0.0338095
$291$	−5.41087	−0.317191
$292$	9.24786	0.541190
$293$	−27.6195	−1.61355	−0.806775	−	0.590859i	$-0.798789\pi$
$293$	−27.6195	−1.61355	−0.806775	+	0.590859i	$0.798789\pi$
$294$	0	0
$295$	−12.6488	−0.736443
$296$	2.24719	0.130615
$297$	−2.32061	−0.134655
$298$	−1.34717	−0.0780394
$299$	−31.0241	−1.79417
$300$	3.12275	0.180292
$301$	0	0
$302$	−1.65197	−0.0950603
$303$	−8.07010	−0.463615
$304$	−10.9140	−0.625960
$305$	−8.68329	−0.497204
$306$	−0.0448632	−0.00256466
$307$	−7.07453	−0.403765	−0.201882	−	0.979410i	$-0.564706\pi$
$307$	−7.07453	−0.403765	−0.201882	+	0.979410i	$0.564706\pi$
$308$	0	0
$309$	−13.6444	−0.776201
$310$	0.0843633	0.00479151
$311$	−25.0300	−1.41932	−0.709661	−	0.704544i	$-0.751152\pi$
$311$	−25.0300	−1.41932	−0.709661	+	0.704544i	$0.751152\pi$
$312$	−3.07374	−0.174016
$313$	−15.3963	−0.870248	−0.435124	−	0.900371i	$-0.643295\pi$
$313$	−15.3963	−0.870248	−0.435124	+	0.900371i	$0.643295\pi$
$314$	1.18935	0.0671188
$315$	0	0
$316$	−29.0105	−1.63197
$317$	10.2661	0.576603	0.288302	−	0.957540i	$-0.406909\pi$
$317$	10.2661	0.576603	0.288302	+	0.957540i	$0.406909\pi$
$318$	−0.436492	−0.0244773
$319$	2.85139	0.159647
$320$	−7.82969	−0.437693
$321$	−15.1559	−0.845919
$322$	0	0
$323$	2.69272	0.149827
$324$	14.0884	0.782690
$325$	5.82334	0.323021
$326$	0.994234	0.0550655
$327$	10.3587	0.572839
$328$	0.775400	0.0428143
$329$	0	0
$330$	−0.0552307	−0.00304035
$331$	−2.95096	−0.162200	−0.0810998	−	0.996706i	$-0.525843\pi$
$331$	−2.95096	−0.162200	−0.0810998	+	0.996706i	$0.525843\pi$
$332$	−31.1543	−1.70981
$333$	−3.63350	−0.199115
$334$	−1.02264	−0.0559565
$335$	4.23851	0.231575
$336$	0	0
$337$	−15.6930	−0.854854	−0.427427	−	0.904050i	$-0.640580\pi$
$337$	−15.6930	−0.854854	−0.427427	+	0.904050i	$0.640580\pi$
$338$	−1.76414	−0.0959567
$339$	1.69076	0.0918297
$340$	1.94578	0.105525
$341$	0.417803	0.0226253
$342$	−0.126724	−0.00685244
$343$	0	0
$344$	−1.53760	−0.0829017
$345$	8.34802	0.449442
$346$	−1.08519	−0.0583401
$347$	24.2500	1.30181	0.650904	−	0.759160i	$-0.274390\pi$
$347$	24.2500	1.30181	0.650904	+	0.759160i	$0.274390\pi$
$348$	−21.3119	−1.14244
$349$	−7.46015	−0.399333	−0.199666	−	0.979864i	$-0.563986\pi$
$349$	−7.46015	−0.399333	−0.199666	+	0.979864i	$0.563986\pi$
$350$	0	0
$351$	32.3446	1.72643
$352$	0.420962	0.0224373
$353$	3.71832	0.197906	0.0989531	−	0.995092i	$-0.468451\pi$
$353$	3.71832	0.197906	0.0989531	+	0.995092i	$0.468451\pi$
$354$	−1.67209	−0.0888705
$355$	13.1823	0.699646
$356$	14.5565	0.771491
$357$	0	0
$358$	−0.318117	−0.0168130
$359$	20.2058	1.06642	0.533211	−	0.845983i	$-0.320985\pi$
$359$	20.2058	1.06642	0.533211	+	0.845983i	$0.320985\pi$
$360$	−0.183470	−0.00966973
$361$	−11.3940	−0.599682
$362$	1.90649	0.100203
$363$	16.9629	0.890324
$364$	0	0
$365$	−4.64044	−0.242892
$366$	−1.14787	−0.0600002
$367$	7.88907	0.411806	0.205903	−	0.978572i	$-0.433987\pi$
$367$	7.88907	0.411806	0.205903	+	0.978572i	$0.433987\pi$
$368$	−21.0830	−1.09903
$369$	−1.25375	−0.0652677
$370$	−0.562798	−0.0292585
$371$	0	0
$372$	−3.12275	−0.161907
$373$	−13.0991	−0.678246	−0.339123	−	0.940742i	$-0.610130\pi$
$373$	−13.0991	−0.678246	−0.339123	+	0.940742i	$0.610130\pi$
$374$	−0.0344141	−0.00177951
$375$	−1.56695	−0.0809171
$376$	2.16591	0.111698
$377$	−39.7426	−2.04685
$378$	0	0
$379$	−27.3243	−1.40355	−0.701777	−	0.712397i	$-0.747610\pi$
$379$	−27.3243	−1.40355	−0.701777	+	0.712397i	$0.747610\pi$
$380$	5.49618	0.281948
$381$	4.22644	0.216527
$382$	1.19598	0.0611914
$383$	−15.4111	−0.787471	−0.393736	−	0.919224i	$-0.628817\pi$
$383$	−15.4111	−0.787471	−0.393736	+	0.919224i	$0.628817\pi$
$384$	−4.19263	−0.213954
$385$	0	0
$386$	−1.48347	−0.0755066
$387$	2.48616	0.126378
$388$	−6.88166	−0.349363
$389$	9.45290	0.479281	0.239641	−	0.970862i	$-0.422970\pi$
$389$	9.45290	0.479281	0.239641	+	0.970862i	$0.422970\pi$
$390$	0.769806	0.0389806
$391$	5.20163	0.263058
$392$	0	0
$393$	−12.6478	−0.637995
$394$	−1.91914	−0.0966848
$395$	14.5570	0.732444
$396$	−0.453502	−0.0227893
$397$	−26.0496	−1.30739	−0.653697	−	0.756757i	$-0.726783\pi$
$397$	−26.0496	−1.30739	−0.653697	+	0.756757i	$0.726783\pi$
$398$	1.01504	0.0508794
$399$	0	0
$400$	3.95735	0.197867
$401$	0.392311	0.0195911	0.00979554	−	0.999952i	$-0.496882\pi$
$401$	0.392311	0.0195911	0.00979554	+	0.999952i	$0.496882\pi$
$402$	0.560302	0.0279453
$403$	−5.82334	−0.290081
$404$	−10.2637	−0.510639
$405$	−7.06936	−0.351280
$406$	0	0
$407$	−2.78722	−0.138157
$408$	0.515356	0.0255139
$409$	9.37777	0.463701	0.231850	−	0.972751i	$-0.425522\pi$
$409$	9.37777	0.463701	0.231850	+	0.972751i	$0.425522\pi$
$410$	−0.194196	−0.00959063
$411$	31.0427	1.53122
$412$	−17.3532	−0.854931
$413$	0	0
$414$	−0.244797	−0.0120311
$415$	15.6328	0.767383
$416$	−5.86736	−0.287671
$417$	20.2192	0.990138
$418$	−0.0972085	−0.00475462
$419$	16.2136	0.792085	0.396042	−	0.918232i	$-0.370383\pi$
$419$	16.2136	0.792085	0.396042	+	0.918232i	$0.370383\pi$
$420$	0	0
$421$	−12.0580	−0.587670	−0.293835	−	0.955856i	$-0.594932\pi$
$421$	−12.0580	−0.587670	−0.293835	+	0.955856i	$0.594932\pi$
$422$	0.355653	0.0173129
$423$	−3.50209	−0.170277
$424$	−1.11226	−0.0540162
$425$	−0.976364	−0.0473606
$426$	1.74261	0.0844300
$427$	0	0
$428$	−19.2756	−0.931720
$429$	3.81241	0.184065
$430$	0.385085	0.0185704
$431$	17.7010	0.852627	0.426314	−	0.904575i	$-0.359812\pi$
$431$	17.7010	0.852627	0.426314	+	0.904575i	$0.359812\pi$
$432$	21.9804	1.05753
$433$	−16.5428	−0.794996	−0.397498	−	0.917603i	$-0.630121\pi$
$433$	−16.5428	−0.794996	−0.397498	+	0.917603i	$0.630121\pi$
$434$	0	0
$435$	10.6940	0.512738
$436$	13.1745	0.630942
$437$	14.6929	0.702856
$438$	−0.613435	−0.0293111
$439$	8.78548	0.419308	0.209654	−	0.977776i	$-0.432766\pi$
$439$	8.78548	0.419308	0.209654	+	0.977776i	$0.432766\pi$
$440$	−0.140738	−0.00670943
$441$	0	0
$442$	0.479664	0.0228153
$443$	−10.0349	−0.476774	−0.238387	−	0.971170i	$-0.576619\pi$
$443$	−10.0349	−0.476774	−0.238387	+	0.971170i	$0.576619\pi$
$444$	20.8323	0.988657
$445$	−7.30423	−0.346254
$446$	2.21539	0.104902
$447$	−25.0221	−1.18351
$448$	0	0
$449$	−31.9409	−1.50738	−0.753692	−	0.657228i	$-0.771729\pi$
$449$	−31.9409	−1.50738	−0.753692	+	0.657228i	$0.771729\pi$
$450$	0.0459493	0.00216607
$451$	−0.961740	−0.0452866
$452$	2.15035	0.101144
$453$	−30.6835	−1.44164
$454$	0.562016	0.0263767
$455$	0	0
$456$	1.45571	0.0681699
$457$	9.30313	0.435182	0.217591	−	0.976040i	$-0.430180\pi$
$457$	9.30313	0.435182	0.217591	+	0.976040i	$0.430180\pi$
$458$	1.34958	0.0630617
$459$	−5.42303	−0.253125
$460$	10.6172	0.495029
$461$	14.6939	0.684364	0.342182	−	0.939634i	$-0.388834\pi$
$461$	14.6939	0.684364	0.342182	+	0.939634i	$0.388834\pi$
$462$	0	0
$463$	−32.5119	−1.51096	−0.755478	−	0.655174i	$-0.772595\pi$
$463$	−32.5119	−1.51096	−0.755478	+	0.655174i	$0.772595\pi$
$464$	−27.0078	−1.25380
$465$	1.56695	0.0726657
$466$	0.467897	0.0216749
$467$	−40.2199	−1.86116	−0.930578	−	0.366093i	$-0.880695\pi$
$467$	−40.2199	−1.86116	−0.930578	+	0.366093i	$0.880695\pi$
$468$	6.32091	0.292184
$469$	0	0
$470$	−0.542443	−0.0250210
$471$	22.0908	1.01789
$472$	−4.26079	−0.196119
$473$	1.90710	0.0876888
$474$	1.92434	0.0883880
$475$	−2.75790	−0.126541
$476$	0	0
$477$	1.79843	0.0823443
$478$	−2.24660	−0.102757
$479$	−31.2589	−1.42825	−0.714127	−	0.700016i	$-0.753176\pi$
$479$	−31.2589	−1.42825	−0.714127	+	0.700016i	$0.753176\pi$
$480$	1.57880	0.0720620
$481$	38.8482	1.77133
$482$	1.66678	0.0759198
$483$	0	0
$484$	21.5738	0.980629
$485$	3.45312	0.156798
$486$	0.471218	0.0213749
$487$	28.8012	1.30511	0.652553	−	0.757743i	$-0.273698\pi$
$487$	28.8012	1.30511	0.652553	+	0.757743i	$0.273698\pi$
$488$	−2.92499	−0.132408
$489$	18.4668	0.835096
$490$	0	0
$491$	−33.6929	−1.52054	−0.760270	−	0.649607i	$-0.774934\pi$
$491$	−33.6929	−1.52054	−0.760270	+	0.649607i	$0.774934\pi$
$492$	7.18825	0.324072
$493$	6.66341	0.300105
$494$	1.35489	0.0609594
$495$	0.227561	0.0102281
$496$	−3.95735	−0.177690
$497$	0	0
$498$	2.06655	0.0926042
$499$	−0.496525	−0.0222275	−0.0111138	−	0.999938i	$-0.503538\pi$
$499$	−0.496525	−0.0222275	−0.0111138	+	0.999938i	$0.503538\pi$
$500$	−1.99288	−0.0891244
$501$	−18.9944	−0.848609
$502$	−0.613567	−0.0273848
$503$	−15.4223	−0.687648	−0.343824	−	0.939034i	$-0.611722\pi$
$503$	−15.4223	−0.687648	−0.343824	+	0.939034i	$0.611722\pi$
$504$	0	0
$505$	5.15019	0.229180
$506$	−0.187782	−0.00834791
$507$	−32.7669	−1.45523
$508$	5.37528	0.238489
$509$	−19.6817	−0.872376	−0.436188	−	0.899856i	$-0.643672\pi$
$509$	−19.6817	−0.872376	−0.436188	+	0.899856i	$0.643672\pi$
$510$	−0.129069	−0.00571526
$511$	0	0
$512$	−6.65335	−0.294039
$513$	−15.3183	−0.676318
$514$	1.49261	0.0658363
$515$	8.70759	0.383702
$516$	−14.2541	−0.627503
$517$	−2.68641	−0.118148
$518$	0	0
$519$	−20.1561	−0.884756
$520$	1.96161	0.0860221
$521$	3.69024	0.161672	0.0808362	−	0.996727i	$-0.474241\pi$
$521$	3.69024	0.161672	0.0808362	+	0.996727i	$0.474241\pi$
$522$	−0.313591	−0.0137255
$523$	−26.5095	−1.15918	−0.579590	−	0.814908i	$-0.696787\pi$
$523$	−26.5095	−1.15918	−0.579590	+	0.814908i	$0.696787\pi$
$524$	−16.0857	−0.702706
$525$	0	0
$526$	−0.345556	−0.0150669
$527$	0.976364	0.0425311
$528$	2.59079	0.112750
$529$	5.38281	0.234035
$530$	0.278561	0.0120999
$531$	6.88931	0.298971
$532$	0	0
$533$	13.4047	0.580623
$534$	−0.965569	−0.0417843
$535$	9.67221	0.418166
$536$	1.42775	0.0616696
$537$	−5.90866	−0.254978
$538$	−0.217229	−0.00936541
$539$	0	0
$540$	−11.0691	−0.476338
$541$	4.38813	0.188660	0.0943302	−	0.995541i	$-0.469929\pi$
$541$	4.38813	0.188660	0.0943302	+	0.995541i	$0.469929\pi$
$542$	−1.29005	−0.0554123
$543$	35.4108	1.51962
$544$	0.983745	0.0421777
$545$	−6.61075	−0.283174
$546$	0	0
$547$	21.4740	0.918161	0.459081	−	0.888395i	$-0.348179\pi$
$547$	21.4740	0.918161	0.459081	+	0.888395i	$0.348179\pi$
$548$	39.4807	1.68653
$549$	4.72944	0.201848
$550$	0.0352472	0.00150295
$551$	18.8219	0.801841
$552$	2.81205	0.119689
$553$	0	0
$554$	1.90062	0.0807495
$555$	−10.4533	−0.443720
$556$	25.7152	1.09057
$557$	2.82706	0.119787	0.0598933	−	0.998205i	$-0.480924\pi$
$557$	2.82706	0.119787	0.0598933	+	0.998205i	$0.480924\pi$
$558$	−0.0459493	−0.00194519
$559$	−26.5812	−1.12427
$560$	0	0
$561$	−0.639203	−0.0269872
$562$	1.21501	0.0512522
$563$	17.8029	0.750305	0.375152	−	0.926963i	$-0.377590\pi$
$563$	17.8029	0.750305	0.375152	+	0.926963i	$0.377590\pi$
$564$	20.0788	0.845472
$565$	−1.07901	−0.0453945
$566$	−2.30766	−0.0969981
$567$	0	0
$568$	4.44050	0.186319
$569$	−16.5704	−0.694667	−0.347333	−	0.937742i	$-0.612913\pi$
$569$	−16.5704	−0.694667	−0.347333	+	0.937742i	$0.612913\pi$
$570$	−0.364576	−0.0152704
$571$	−5.93416	−0.248337	−0.124169	−	0.992261i	$-0.539626\pi$
$571$	−5.93416	−0.248337	−0.124169	+	0.992261i	$0.539626\pi$
$572$	4.84870	0.202734
$573$	22.2139	0.927999
$574$	0	0
$575$	−5.32755	−0.222174
$576$	4.26452	0.177688
$577$	−1.88648	−0.0785352	−0.0392676	−	0.999229i	$-0.512502\pi$
$577$	−1.88648	−0.0785352	−0.0392676	+	0.999229i	$0.512502\pi$
$578$	1.35375	0.0563087
$579$	−27.5538	−1.14509
$580$	13.6009	0.564745
$581$	0	0
$582$	0.456479	0.0189217
$583$	1.37955	0.0571353
$584$	−1.56315	−0.0646834
$585$	−3.17174	−0.131135
$586$	2.33007	0.0962545
$587$	−7.67946	−0.316965	−0.158483	−	0.987362i	$-0.550660\pi$
$587$	−7.67946	−0.316965	−0.158483	+	0.987362i	$0.550660\pi$
$588$	0	0
$589$	2.75790	0.113637
$590$	1.06710	0.0439316
$591$	−35.6458	−1.46627
$592$	26.4000	1.08503
$593$	3.15261	0.129462	0.0647310	−	0.997903i	$-0.479381\pi$
$593$	3.15261	0.129462	0.0647310	+	0.997903i	$0.479381\pi$
$594$	0.195774	0.00803271
$595$	0	0
$596$	−31.8237	−1.30355
$597$	18.8532	0.771611
$598$	2.61730	0.107029
$599$	−35.3011	−1.44236	−0.721181	−	0.692746i	$-0.756401\pi$
$599$	−35.3011	−1.44236	−0.721181	+	0.692746i	$0.756401\pi$
$600$	−0.527832	−0.0215487
$601$	24.8008	1.01164	0.505822	−	0.862638i	$-0.331189\pi$
$601$	24.8008	1.01164	0.505822	+	0.862638i	$0.331189\pi$
$602$	0	0
$603$	−2.30855	−0.0940114
$604$	−39.0239	−1.58786
$605$	−10.8254	−0.440117
$606$	0.680820	0.0276564
$607$	−30.7431	−1.24782	−0.623911	−	0.781495i	$-0.714457\pi$
$607$	−30.7431	−1.24782	−0.623911	+	0.781495i	$0.714457\pi$
$608$	2.77875	0.112693
$609$	0	0
$610$	0.732550	0.0296601
$611$	37.4432	1.51479
$612$	−1.05979	−0.0428394
$613$	20.1621	0.814340	0.407170	−	0.913352i	$-0.366516\pi$
$613$	20.1621	0.814340	0.407170	+	0.913352i	$0.366516\pi$
$614$	0.596830	0.0240861
$615$	−3.60696	−0.145447
$616$	0	0
$617$	−37.5463	−1.51156	−0.755778	−	0.654828i	$-0.772741\pi$
$617$	−37.5463	−1.51156	−0.755778	+	0.654828i	$0.772741\pi$
$618$	1.15108	0.0463034
$619$	−36.2669	−1.45769	−0.728844	−	0.684679i	$-0.759942\pi$
$619$	−36.2669	−1.45769	−0.728844	+	0.684679i	$0.759942\pi$
$620$	1.99288	0.0800361
$621$	−29.5909	−1.18744
$622$	2.11161	0.0846679
$623$	0	0
$624$	−36.1104	−1.44557
$625$	1.00000	0.0400000
$626$	1.29888	0.0519136
$627$	−1.80554	−0.0721063
$628$	28.0955	1.12113
$629$	−6.51345	−0.259708
$630$	0	0
$631$	42.5907	1.69551	0.847755	−	0.530388i	$-0.177954\pi$
$631$	42.5907	1.69551	0.847755	+	0.530388i	$0.177954\pi$
$632$	4.90358	0.195054
$633$	6.60586	0.262559
$634$	−0.866084	−0.0343966
$635$	−2.69724	−0.107037
$636$	−10.3111	−0.408861
$637$	0	0
$638$	−0.240552	−0.00952356
$639$	−7.17989	−0.284032
$640$	2.67566	0.105765
$641$	20.4366	0.807195	0.403598	−	0.914937i	$-0.367760\pi$
$641$	20.4366	0.807195	0.403598	+	0.914937i	$0.367760\pi$
$642$	1.27860	0.0504623
$643$	−4.53002	−0.178647	−0.0893233	−	0.996003i	$-0.528470\pi$
$643$	−4.53002	−0.178647	−0.0893233	+	0.996003i	$0.528470\pi$
$644$	0	0
$645$	7.15251	0.281630
$646$	−0.227166	−0.00893774
$647$	1.05812	0.0415989	0.0207994	−	0.999784i	$-0.493379\pi$
$647$	1.05812	0.0415989	0.0207994	+	0.999784i	$0.493379\pi$
$648$	−2.38133	−0.0935476
$649$	5.28472	0.207443
$650$	−0.491276	−0.0192694
$651$	0	0
$652$	23.4864	0.919799
$653$	−11.0406	−0.432052	−0.216026	−	0.976388i	$-0.569310\pi$
$653$	−11.0406	−0.432052	−0.216026	+	0.976388i	$0.569310\pi$
$654$	−0.873897	−0.0341721
$655$	8.07156	0.315382
$656$	9.10941	0.355663
$657$	2.52747	0.0986058
$658$	0	0
$659$	37.2927	1.45272	0.726358	−	0.687316i	$-0.241211\pi$
$659$	37.2927	1.45272	0.726358	+	0.687316i	$0.241211\pi$
$660$	−1.30470	−0.0507852
$661$	23.1690	0.901171	0.450586	−	0.892733i	$-0.351215\pi$
$661$	23.1690	0.901171	0.450586	+	0.892733i	$0.351215\pi$
$662$	0.248953	0.00967582
$663$	8.90921	0.346005
$664$	5.26594	0.204358
$665$	0	0
$666$	0.306534	0.0118779
$667$	36.3590	1.40783
$668$	−24.1575	−0.934683
$669$	41.1483	1.59089
$670$	−0.357575	−0.0138143
$671$	3.62791	0.140054
$672$	0	0
$673$	−36.5932	−1.41056	−0.705282	−	0.708926i	$-0.749180\pi$
$673$	−36.5932	−1.41056	−0.705282	+	0.708926i	$0.749180\pi$
$674$	1.32392	0.0509953
$675$	5.55431	0.213786
$676$	−41.6737	−1.60283
$677$	16.3685	0.629093	0.314547	−	0.949242i	$-0.398148\pi$
$677$	16.3685	0.629093	0.314547	+	0.949242i	$0.398148\pi$
$678$	−0.142638	−0.00547799
$679$	0	0
$680$	−0.328891	−0.0126124
$681$	10.4388	0.400016
$682$	−0.0352472	−0.00134969
$683$	−17.9921	−0.688449	−0.344225	−	0.938887i	$-0.611858\pi$
$683$	−17.9921	−0.688449	−0.344225	+	0.938887i	$0.611858\pi$
$684$	−2.99355	−0.114461
$685$	−19.8108	−0.756934
$686$	0	0
$687$	25.0669	0.956362
$688$	−18.0637	−0.688673
$689$	−19.2282	−0.732537
$690$	−0.704266	−0.0268110
$691$	−30.1221	−1.14590	−0.572950	−	0.819590i	$-0.694201\pi$
$691$	−30.1221	−1.14590	−0.572950	+	0.819590i	$0.694201\pi$
$692$	−25.6350	−0.974496
$693$	0	0
$694$	−2.04581	−0.0776579
$695$	−12.9035	−0.489458
$696$	3.60230	0.136545
$697$	−2.24749	−0.0851297
$698$	0.629363	0.0238217
$699$	8.69067	0.328711
$700$	0	0
$701$	28.3296	1.07000	0.534998	−	0.844853i	$-0.320312\pi$
$701$	28.3296	1.07000	0.534998	+	0.844853i	$0.320312\pi$
$702$	−2.72870	−0.102988
$703$	−18.3983	−0.693907
$704$	3.27127	0.123291
$705$	−10.0753	−0.379457
$706$	−0.313690	−0.0118059
$707$	0	0
$708$	−39.4991	−1.48447
$709$	−14.6256	−0.549277	−0.274639	−	0.961548i	$-0.588558\pi$
$709$	−14.6256	−0.549277	−0.274639	+	0.961548i	$0.588558\pi$
$710$	−1.11210	−0.0417365
$711$	−7.92864	−0.297347
$712$	−2.46045	−0.0922092
$713$	5.32755	0.199518
$714$	0	0
$715$	−2.43301	−0.0909894
$716$	−7.51476	−0.280840
$717$	−41.7280	−1.55836
$718$	−1.70463	−0.0636161
$719$	−22.6426	−0.844426	−0.422213	−	0.906497i	$-0.638747\pi$
$719$	−22.6426	−0.844426	−0.422213	+	0.906497i	$0.638747\pi$
$720$	−2.15541	−0.0803274
$721$	0	0
$722$	0.961232	0.0357733
$723$	30.9586	1.15136
$724$	45.0362	1.67376
$725$	−6.82472	−0.253464
$726$	−1.43105	−0.0531112
$727$	48.5828	1.80184	0.900919	−	0.433988i	$-0.142894\pi$
$727$	48.5828	1.80184	0.900919	+	0.433988i	$0.142894\pi$
$728$	0	0
$729$	29.9604	1.10965
$730$	0.391483	0.0144894
$731$	4.45671	0.164837
$732$	−27.1158	−1.00223
$733$	−31.1516	−1.15061	−0.575306	−	0.817938i	$-0.695117\pi$
$733$	−31.1516	−1.15061	−0.575306	+	0.817938i	$0.695117\pi$
$734$	−0.665547	−0.0245658
$735$	0	0
$736$	5.36783	0.197861
$737$	−1.77086	−0.0652306
$738$	0.105771	0.00389347
$739$	18.1289	0.666883	0.333441	−	0.942771i	$-0.391790\pi$
$739$	18.1289	0.666883	0.333441	+	0.942771i	$0.391790\pi$
$740$	−13.2948	−0.488726
$741$	25.1656	0.924481
$742$	0	0
$743$	−7.49404	−0.274930	−0.137465	−	0.990507i	$-0.543895\pi$
$743$	−7.49404	−0.274930	−0.137465	+	0.990507i	$0.543895\pi$
$744$	0.527832	0.0193513
$745$	15.9687	0.585047
$746$	1.10508	0.0404600
$747$	−8.51455	−0.311531
$748$	−0.812952	−0.0297245
$749$	0	0
$750$	0.132193	0.00482701
$751$	28.1338	1.02662	0.513309	−	0.858204i	$-0.328420\pi$
$751$	28.1338	1.02662	0.513309	+	0.858204i	$0.328420\pi$
$752$	25.4452	0.927890
$753$	−11.3963	−0.415305
$754$	3.35282	0.122102
$755$	19.5816	0.712649
$756$	0	0
$757$	−13.4716	−0.489632	−0.244816	−	0.969570i	$-0.578728\pi$
$757$	−13.4716	−0.489632	−0.244816	+	0.969570i	$0.578728\pi$
$758$	2.30516	0.0837274
$759$	−3.48783	−0.126600
$760$	−0.929007	−0.0336986
$761$	3.88821	0.140948	0.0704738	−	0.997514i	$-0.477549\pi$
$761$	3.88821	0.140948	0.0704738	+	0.997514i	$0.477549\pi$
$762$	−0.356556	−0.0129167
$763$	0	0
$764$	28.2521	1.02212
$765$	0.531786	0.0192268
$766$	1.30013	0.0469757
$767$	−73.6583	−2.65965
$768$	−24.1838	−0.872658
$769$	34.8381	1.25629	0.628147	−	0.778094i	$-0.283814\pi$
$769$	34.8381	1.25629	0.628147	+	0.778094i	$0.283814\pi$
$770$	0	0
$771$	27.7236	0.998440
$772$	−35.0434	−1.26124
$773$	40.9213	1.47184	0.735918	−	0.677071i	$-0.236751\pi$
$773$	40.9213	1.47184	0.735918	+	0.677071i	$0.236751\pi$
$774$	−0.209740	−0.00753896
$775$	−1.00000	−0.0359211
$776$	1.16319	0.0417561
$777$	0	0
$778$	−0.797478	−0.0285910
$779$	−6.34841	−0.227455
$780$	18.1848	0.651122
$781$	−5.50762	−0.197078
$782$	−0.438826	−0.0156924
$783$	−37.9066	−1.35467
$784$	0	0
$785$	−14.0979	−0.503177
$786$	1.06701	0.0380588
$787$	−47.1709	−1.68146	−0.840731	−	0.541452i	$-0.817875\pi$
$787$	−47.1709	−1.68146	−0.840731	+	0.541452i	$0.817875\pi$
$788$	−45.3351	−1.61500
$789$	−6.41831	−0.228498
$790$	−1.22808	−0.0436931
$791$	0	0
$792$	0.0766545	0.00272380
$793$	−50.5657	−1.79564
$794$	2.19763	0.0779910
$795$	5.17396	0.183501
$796$	23.9779	0.849875
$797$	17.8587	0.632588	0.316294	−	0.948661i	$-0.397561\pi$
$797$	17.8587	0.632588	0.316294	+	0.948661i	$0.397561\pi$
$798$	0	0
$799$	−6.27787	−0.222095
$800$	−1.00756	−0.0356226
$801$	3.97832	0.140567
$802$	−0.0330966	−0.00116868
$803$	1.93879	0.0684185
$804$	13.2358	0.466791
$805$	0	0
$806$	0.491276	0.0173044
$807$	−4.03478	−0.142031
$808$	1.73485	0.0610320
$809$	−43.6655	−1.53520	−0.767599	−	0.640930i	$-0.778549\pi$
$809$	−43.6655	−1.53520	−0.767599	+	0.640930i	$0.778549\pi$
$810$	0.596395	0.0209552
$811$	0.387111	0.0135933	0.00679665	−	0.999977i	$-0.497837\pi$
$811$	0.387111	0.0135933	0.00679665	+	0.999977i	$0.497837\pi$
$812$	0	0
$813$	−23.9612	−0.840355
$814$	0.235139	0.00824162
$815$	−11.7852	−0.412816
$816$	6.05441	0.211947
$817$	12.5887	0.440424
$818$	−0.791139	−0.0276615
$819$	0	0
$820$	−4.58741	−0.160199
$821$	−18.0266	−0.629134	−0.314567	−	0.949235i	$-0.601859\pi$
$821$	−18.0266	−0.629134	−0.314567	+	0.949235i	$0.601859\pi$
$822$	−2.61886	−0.0913432
$823$	−20.8871	−0.728078	−0.364039	−	0.931384i	$-0.618602\pi$
$823$	−20.8871	−0.728078	−0.364039	+	0.931384i	$0.618602\pi$
$824$	2.93317	0.102182
$825$	0.654678	0.0227930
$826$	0	0
$827$	−21.7298	−0.755618	−0.377809	−	0.925884i	$-0.623322\pi$
$827$	−21.7298	−0.755618	−0.377809	+	0.925884i	$0.623322\pi$
$828$	−5.78276	−0.200965
$829$	2.09893	0.0728988	0.0364494	−	0.999335i	$-0.488395\pi$
$829$	2.09893	0.0728988	0.0364494	+	0.999335i	$0.488395\pi$
$830$	−1.31883	−0.0457773
$831$	35.3018	1.22461
$832$	−45.5949	−1.58072
$833$	0	0
$834$	−1.70576	−0.0590655
$835$	12.1219	0.419496
$836$	−2.29632	−0.0794199
$837$	−5.55431	−0.191985
$838$	−1.36783	−0.0472509
$839$	−24.6440	−0.850804	−0.425402	−	0.905004i	$-0.639867\pi$
$839$	−24.6440	−0.850804	−0.425402	+	0.905004i	$0.639867\pi$
$840$	0	0
$841$	17.5768	0.606095
$842$	1.01725	0.0350567
$843$	22.5675	0.777266
$844$	8.40147	0.289190
$845$	20.9113	0.719369
$846$	0.295447	0.0101577
$847$	0	0
$848$	−13.0669	−0.448718
$849$	−42.8622	−1.47103
$850$	0.0823692	0.00282524
$851$	−35.5408	−1.21832
$852$	41.1652	1.41030
$853$	−17.3343	−0.593516	−0.296758	−	0.954953i	$-0.595905\pi$
$853$	−17.3343	−0.593516	−0.296758	+	0.954953i	$0.595905\pi$
$854$	0	0
$855$	1.50212	0.0513715
$856$	3.25811	0.111360
$857$	−22.4285	−0.766142	−0.383071	−	0.923719i	$-0.625134\pi$
$857$	−22.4285	−0.766142	−0.383071	+	0.923719i	$0.625134\pi$
$858$	−0.321627	−0.0109802
$859$	41.5321	1.41706	0.708529	−	0.705682i	$-0.249359\pi$
$859$	41.5321	1.41706	0.708529	+	0.705682i	$0.249359\pi$
$860$	9.09672	0.310195
$861$	0	0
$862$	−1.49331	−0.0508625
$863$	−27.0560	−0.920996	−0.460498	−	0.887661i	$-0.652329\pi$
$863$	−27.0560	−0.920996	−0.460498	+	0.887661i	$0.652329\pi$
$864$	−5.59630	−0.190390
$865$	12.8633	0.437364
$866$	1.39560	0.0474245
$867$	25.1444	0.853950
$868$	0	0
$869$	−6.08198	−0.206317
$870$	−0.902181	−0.0305868
$871$	24.6823	0.836327
$872$	−2.22685	−0.0754106
$873$	−1.88078	−0.0636546
$874$	−1.23954	−0.0419280
$875$	0	0
$876$	−14.4910	−0.489604
$877$	10.3296	0.348804	0.174402	−	0.984675i	$-0.444201\pi$
$877$	10.3296	0.348804	0.174402	+	0.984675i	$0.444201\pi$
$878$	−0.741172	−0.0250133
$879$	43.2785	1.45975
$880$	−1.65339	−0.0557358
$881$	−22.2743	−0.750439	−0.375219	−	0.926936i	$-0.622433\pi$
$881$	−22.2743	−0.750439	−0.375219	+	0.926936i	$0.622433\pi$
$882$	0	0
$883$	−54.5504	−1.83577	−0.917883	−	0.396851i	$-0.870103\pi$
$883$	−54.5504	−1.83577	−0.917883	+	0.396851i	$0.870103\pi$
$884$	11.3309	0.381100
$885$	19.8201	0.666245
$886$	0.846579	0.0284414
$887$	−38.6856	−1.29894	−0.649468	−	0.760389i	$-0.725009\pi$
$887$	−38.6856	−1.29894	−0.649468	+	0.760389i	$0.725009\pi$
$888$	−3.52124	−0.118165
$889$	0	0
$890$	0.616208	0.0206554
$891$	2.95360	0.0989494
$892$	52.3333	1.75225
$893$	−17.7329	−0.593409
$894$	2.11095	0.0706007
$895$	3.77080	0.126044
$896$	0	0
$897$	48.6133	1.62315
$898$	2.69464	0.0899212
$899$	6.82472	0.227617
$900$	1.08544	0.0361815
$901$	3.22388	0.107403
$902$	0.0811355	0.00270152
$903$	0	0
$904$	−0.363469	−0.0120888
$905$	−22.5985	−0.751200
$906$	2.58856	0.0859992
$907$	5.93151	0.196953	0.0984763	−	0.995139i	$-0.468603\pi$
$907$	5.93151	0.196953	0.0984763	+	0.995139i	$0.468603\pi$
$908$	13.2763	0.440590
$909$	−2.80510	−0.0930394
$910$	0	0
$911$	−7.33048	−0.242869	−0.121435	−	0.992599i	$-0.538750\pi$
$911$	−7.33048	−0.242869	−0.121435	+	0.992599i	$0.538750\pi$
$912$	17.1017	0.566294
$913$	−6.53142	−0.216159
$914$	−0.784843	−0.0259603
$915$	13.6063	0.449810
$916$	31.8806	1.05337
$917$	0	0
$918$	0.457504	0.0150999
$919$	−18.8095	−0.620467	−0.310234	−	0.950660i	$-0.600407\pi$
$919$	−18.8095	−0.620467	−0.310234	+	0.950660i	$0.600407\pi$
$920$	−1.79460	−0.0591662
$921$	11.0855	0.365278
$922$	−1.23963	−0.0408249
$923$	76.7652	2.52676
$924$	0	0
$925$	6.67113	0.219345
$926$	2.74281	0.0901343
$927$	−4.74268	−0.155770
$928$	6.87631	0.225726
$929$	−22.0589	−0.723728	−0.361864	−	0.932231i	$-0.617860\pi$
$929$	−22.0589	−0.723728	−0.361864	+	0.932231i	$0.617860\pi$
$930$	−0.132193	−0.00433479
$931$	0	0
$932$	11.0530	0.362052
$933$	39.2208	1.28403
$934$	3.39308	0.111025
$935$	0.407928	0.0133407
$936$	−1.06841	−0.0349220
$937$	−2.51705	−0.0822286	−0.0411143	−	0.999154i	$-0.513091\pi$
$937$	−2.51705	−0.0822286	−0.0411143	+	0.999154i	$0.513091\pi$
$938$	0	0
$939$	24.1252	0.787296
$940$	−12.8139	−0.417945
$941$	−20.4311	−0.666035	−0.333018	−	0.942921i	$-0.608067\pi$
$941$	−20.4311	−0.666035	−0.333018	+	0.942921i	$0.608067\pi$
$942$	−1.86365	−0.0607210
$943$	−12.2635	−0.399354
$944$	−50.0558	−1.62918
$945$	0	0
$946$	−0.160890	−0.00523097
$947$	−51.2849	−1.66653	−0.833267	−	0.552870i	$-0.813533\pi$
$947$	−51.2849	−1.66653	−0.833267	+	0.552870i	$0.813533\pi$
$948$	45.4580	1.47641
$949$	−27.0229	−0.877199
$950$	0.232666	0.00754868
$951$	−16.0865	−0.521642
$952$	0	0
$953$	34.3256	1.11192	0.555958	−	0.831210i	$-0.312352\pi$
$953$	34.3256	1.11192	0.555958	+	0.831210i	$0.312352\pi$
$954$	−0.151721	−0.00491215
$955$	−14.1765	−0.458741
$956$	−53.0706	−1.71643
$957$	−4.46799	−0.144430
$958$	2.63710	0.0852009
$959$	0	0
$960$	12.2688	0.395972
$961$	1.00000	0.0322581
$962$	−3.27736	−0.105666
$963$	−5.26807	−0.169761
$964$	39.3738	1.26814
$965$	17.5843	0.566059
$966$	0	0
$967$	12.7111	0.408761	0.204381	−	0.978892i	$-0.434482\pi$
$967$	12.7111	0.408761	0.204381	+	0.978892i	$0.434482\pi$
$968$	−3.64658	−0.117205
$969$	−4.21936	−0.135545
$970$	−0.291316	−0.00935360
$971$	55.8634	1.79274	0.896371	−	0.443304i	$-0.146194\pi$
$971$	55.8634	1.79274	0.896371	+	0.443304i	$0.146194\pi$
$972$	11.1314	0.357040
$973$	0	0
$974$	−2.42976	−0.0778546
$975$	−9.12489	−0.292230
$976$	−34.3628	−1.09993
$977$	23.9736	0.766985	0.383492	−	0.923544i	$-0.374721\pi$
$977$	23.9736	0.766985	0.383492	+	0.923544i	$0.374721\pi$
$978$	−1.55792	−0.0498167
$979$	3.05173	0.0975337
$980$	0	0
$981$	3.60061	0.114959
$982$	2.84245	0.0907061
$983$	−8.93690	−0.285043	−0.142521	−	0.989792i	$-0.545521\pi$
$983$	−8.93690	−0.285043	−0.142521	+	0.989792i	$0.545521\pi$
$984$	−1.21501	−0.0387333
$985$	22.7485	0.724828
$986$	−0.562147	−0.0179024
$987$	0	0
$988$	32.0061	1.01825
$989$	24.3182	0.773272
$990$	−0.0191978	−0.000610145 0
$991$	7.07937	0.224884	0.112442	−	0.993658i	$-0.464133\pi$
$991$	7.07937	0.224884	0.112442	+	0.993658i	$0.464133\pi$
$992$	1.00756	0.0319901
$993$	4.62402	0.146739
$994$	0	0
$995$	−12.0318	−0.381433
$996$	48.8173	1.54684
$997$	−25.8069	−0.817314	−0.408657	−	0.912688i	$-0.634003\pi$
$997$	−25.8069	−0.817314	−0.408657	+	0.912688i	$0.634003\pi$
$998$	0.0418885	0.00132596
$999$	37.0536	1.17232

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.bf.1.12		21
7.3	odd	6		1085.2.j.d.156.10	✓	42
7.5	odd	6		1085.2.j.d.466.10	yes	42
7.6	odd	2		7595.2.a.bg.1.12		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1085.2.j.d.156.10	✓	42	7.3	odd	6
1085.2.j.d.466.10	yes	42	7.5	odd	6
7595.2.a.bf.1.12		21	1.1	even	1	trivial
7595.2.a.bg.1.12		21	7.6	odd	2

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:	\( N \)	\(=\)	\( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7595.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0843633 q^{2} -1.56695 q^{3} -1.99288 q^{4} +1.00000 q^{5} +0.132193 q^{6} +0.336853 q^{8} -0.544660 q^{9} +O(q^{10})\)	\(q-0.0843633 q^{2} -1.56695 q^{3} -1.99288 q^{4} +1.00000 q^{5} +0.132193 q^{6} +0.336853 q^{8} -0.544660 q^{9} -0.0843633 q^{10} -0.417803 q^{11} +3.12275 q^{12} +5.82334 q^{13} -1.56695 q^{15} +3.95735 q^{16} -0.976364 q^{17} +0.0459493 q^{18} -2.75790 q^{19} -1.99288 q^{20} +0.0352472 q^{22} -5.32755 q^{23} -0.527832 q^{24} +1.00000 q^{25} -0.491276 q^{26} +5.55431 q^{27} -6.82472 q^{29} +0.132193 q^{30} -1.00000 q^{31} -1.00756 q^{32} +0.654678 q^{33} +0.0823692 q^{34} +1.08544 q^{36} +6.67113 q^{37} +0.232666 q^{38} -9.12489 q^{39} +0.336853 q^{40} +2.30190 q^{41} -4.56460 q^{43} +0.832633 q^{44} -0.544660 q^{45} +0.449450 q^{46} +6.42985 q^{47} -6.20098 q^{48} -0.0843633 q^{50} +1.52992 q^{51} -11.6052 q^{52} -3.30192 q^{53} -0.468580 q^{54} -0.417803 q^{55} +4.32150 q^{57} +0.575755 q^{58} -12.6488 q^{59} +3.12275 q^{60} -8.68329 q^{61} +0.0843633 q^{62} -7.82969 q^{64} +5.82334 q^{65} -0.0552307 q^{66} +4.23851 q^{67} +1.94578 q^{68} +8.34802 q^{69} +13.1823 q^{71} -0.183470 q^{72} -4.64044 q^{73} -0.562798 q^{74} -1.56695 q^{75} +5.49618 q^{76} +0.769806 q^{78} +14.5570 q^{79} +3.95735 q^{80} -7.06936 q^{81} -0.194196 q^{82} +15.6328 q^{83} -0.976364 q^{85} +0.385085 q^{86} +10.6940 q^{87} -0.140738 q^{88} -7.30423 q^{89} +0.0459493 q^{90} +10.6172 q^{92} +1.56695 q^{93} -0.542443 q^{94} -2.75790 q^{95} +1.57880 q^{96} +3.45312 q^{97} +0.227561 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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