LMFDB - Embedded newform 1445.2.a.s.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1445,2,Mod(1,1445)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1445.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1445, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,3,3,21,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 18 x^{10} + 55 x^{9} + 114 x^{8} - 354 x^{7} - 309 x^{6} + 936 x^{5} + 396 x^{4} + \cdots + 9 $ x^12 - 3x^11 - 18x^10 + 55x^9 + 114x^8 - 354x^7 - 309x^6 + 936x^5 + 396x^4 - 899x^3 - 297x^2 + 153*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.27524$ of defining polynomial
Character	$\chi$	$=$	1445.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.27524 q^{2} -1.70271 q^{3} +3.17670 q^{4} +1.00000 q^{5} -3.87408 q^{6} -2.70724 q^{7} +2.67727 q^{8} -0.100765 q^{9} +2.27524 q^{10} +2.17632 q^{11} -5.40901 q^{12} +5.37970 q^{13} -6.15962 q^{14} -1.70271 q^{15} -0.261974 q^{16} -0.229265 q^{18} +8.53588 q^{19} +3.17670 q^{20} +4.60966 q^{21} +4.95164 q^{22} +5.32570 q^{23} -4.55863 q^{24} +1.00000 q^{25} +12.2401 q^{26} +5.27972 q^{27} -8.60011 q^{28} -1.31247 q^{29} -3.87408 q^{30} -0.757667 q^{31} -5.95060 q^{32} -3.70565 q^{33} -2.70724 q^{35} -0.320102 q^{36} +8.20380 q^{37} +19.4212 q^{38} -9.16010 q^{39} +2.67727 q^{40} -0.0130696 q^{41} +10.4881 q^{42} -0.330596 q^{43} +6.91352 q^{44} -0.100765 q^{45} +12.1172 q^{46} +11.3395 q^{47} +0.446067 q^{48} +0.329174 q^{49} +2.27524 q^{50} +17.0897 q^{52} -8.04151 q^{53} +12.0126 q^{54} +2.17632 q^{55} -7.24803 q^{56} -14.5342 q^{57} -2.98619 q^{58} -13.1546 q^{59} -5.40901 q^{60} -7.20639 q^{61} -1.72387 q^{62} +0.272797 q^{63} -13.0151 q^{64} +5.37970 q^{65} -8.43123 q^{66} +2.67143 q^{67} -9.06814 q^{69} -6.15962 q^{70} +1.87106 q^{71} -0.269777 q^{72} -11.9780 q^{73} +18.6656 q^{74} -1.70271 q^{75} +27.1160 q^{76} -5.89183 q^{77} -20.8414 q^{78} +17.0477 q^{79} -0.261974 q^{80} -8.68755 q^{81} -0.0297365 q^{82} -3.35585 q^{83} +14.6435 q^{84} -0.752183 q^{86} +2.23477 q^{87} +5.82660 q^{88} -10.8909 q^{89} -0.229265 q^{90} -14.5642 q^{91} +16.9182 q^{92} +1.29009 q^{93} +25.8001 q^{94} +8.53588 q^{95} +10.1322 q^{96} +10.9119 q^{97} +0.748948 q^{98} -0.219298 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 3 q^{3} + 21 q^{4} + 12 q^{5} - 9 q^{6} + 6 q^{7} + 12 q^{8} + 21 q^{9} + 3 q^{10} - 6 q^{11} + 6 q^{12} + 9 q^{13} - 18 q^{14} + 3 q^{15} + 39 q^{16} - 9 q^{18} + 27 q^{19} + 21 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 12 * q + 3 * q^2 + 3 * q^3 + 21 * q^4 + 12 * q^5 - 9 * q^6 + 6 * q^7 + 12 * q^8 + 21 * q^9 + 3 * q^10 - 6 * q^11 + 6 * q^12 + 9 * q^13 - 18 * q^14 + 3 * q^15 + 39 * q^16 - 9 * q^18 + 27 * q^19 + 21 * q^20 + 6 * q^21 + 15 * q^22 + 18 * q^23 - 36 * q^24 + 12 * q^25 + 6 * q^26 + 12 * q^27 + 39 * q^28 - 9 * q^30 - 6 * q^31 + 12 * q^32 + 6 * q^35 + 48 * q^36 + 21 * q^37 - 3 * q^38 - 9 * q^39 + 12 * q^40 - 15 * q^41 + 30 * q^42 + 45 * q^43 - 42 * q^44 + 21 * q^45 - 15 * q^46 + 3 * q^47 - 63 * q^48 + 12 * q^49 + 3 * q^50 + 51 * q^52 - 12 * q^53 - 27 * q^54 - 6 * q^55 + 3 * q^56 + 6 * q^57 - 51 * q^58 + 36 * q^59 + 6 * q^60 + 3 * q^61 + 36 * q^62 + 72 * q^63 + 42 * q^64 + 9 * q^65 - 39 * q^66 + 78 * q^67 - 66 * q^69 - 18 * q^70 - 30 * q^71 - 12 * q^72 - 33 * q^73 + 9 * q^74 + 3 * q^75 + 27 * q^76 - 39 * q^77 - 24 * q^78 - 3 * q^79 + 39 * q^80 + 12 * q^81 - 51 * q^82 + 27 * q^83 + 27 * q^84 + 18 * q^86 + 24 * q^87 + 36 * q^88 + 6 * q^89 - 9 * q^90 - 24 * q^91 - 3 * q^92 - 12 * q^93 + 21 * q^94 + 27 * q^95 - 39 * q^96 - 6 * q^97 - 42 * q^98 - 6 * q^99

Coefficient data

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

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

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

$2$	2.27524	1.60884	0.804418	−	0.594064i	$-0.202478\pi$
$2$	2.27524	1.60884	0.804418	+	0.594064i	$0.202478\pi$
$3$	−1.70271	−0.983062	−0.491531	−	0.870860i	$-0.663563\pi$
$3$	−1.70271	−0.983062	−0.491531	+	0.870860i	$0.663563\pi$
$4$	3.17670	1.58835
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.87408	−1.58159
$7$	−2.70724	−1.02324	−0.511621	−	0.859211i	$-0.670955\pi$
$7$	−2.70724	−1.02324	−0.511621	+	0.859211i	$0.670955\pi$
$8$	2.67727	0.946559
$9$	−0.100765	−0.0335885
$10$	2.27524	0.719493
$11$	2.17632	0.656185	0.328093	−	0.944646i	$-0.393594\pi$
$11$	2.17632	0.656185	0.328093	+	0.944646i	$0.393594\pi$
$12$	−5.40901	−1.56145
$13$	5.37970	1.49206	0.746031	−	0.665912i	$-0.231957\pi$
$13$	5.37970	1.49206	0.746031	+	0.665912i	$0.231957\pi$
$14$	−6.15962	−1.64623
$15$	−1.70271	−0.439639
$16$	−0.261974	−0.0654935
$17$	0	0
$17$	0	0
$18$	−0.229265	−0.0540384
$19$	8.53588	1.95827	0.979133	−	0.203220i	$-0.0651406\pi$
$19$	8.53588	1.95827	0.979133	+	0.203220i	$0.0651406\pi$
$20$	3.17670	0.710332
$21$	4.60966	1.00591
$22$	4.95164	1.05569
$23$	5.32570	1.11049	0.555243	−	0.831688i	$-0.312625\pi$
$23$	5.32570	1.11049	0.555243	+	0.831688i	$0.312625\pi$
$24$	−4.55863	−0.930526
$25$	1.00000	0.200000
$26$	12.2401	2.40048
$27$	5.27972	1.01608
$28$	−8.60011	−1.62527
$29$	−1.31247	−0.243720	−0.121860	−	0.992547i	$-0.538886\pi$
$29$	−1.31247	−0.243720	−0.121860	+	0.992547i	$0.538886\pi$
$30$	−3.87408	−0.707306
$31$	−0.757667	−0.136081	−0.0680405	−	0.997683i	$-0.521675\pi$
$31$	−0.757667	−0.136081	−0.0680405	+	0.997683i	$0.521675\pi$
$32$	−5.95060	−1.05193
$33$	−3.70565	−0.645071
$34$	0	0
$35$	−2.70724	−0.457608
$36$	−0.320102	−0.0533503
$37$	8.20380	1.34870	0.674348	−	0.738414i	$-0.264425\pi$
$37$	8.20380	1.34870	0.674348	+	0.738414i	$0.264425\pi$
$38$	19.4212	3.15053
$39$	−9.16010	−1.46679
$40$	2.67727	0.423314
$41$	−0.0130696	−0.00204113	−0.00102057	−	0.999999i	$-0.500325\pi$
$41$	−0.0130696	−0.00204113	−0.00102057	+	0.999999i	$0.500325\pi$
$42$	10.4881	1.61834
$43$	−0.330596	−0.0504154	−0.0252077	−	0.999682i	$-0.508025\pi$
$43$	−0.330596	−0.0504154	−0.0252077	+	0.999682i	$0.508025\pi$
$44$	6.91352	1.04225
$45$	−0.100765	−0.0150212
$46$	12.1172	1.78659
$47$	11.3395	1.65404	0.827019	−	0.562175i	$-0.190035\pi$
$47$	11.3395	1.65404	0.827019	+	0.562175i	$0.190035\pi$
$48$	0.446067	0.0643842
$49$	0.329174	0.0470248
$50$	2.27524	0.321767
$51$	0	0
$52$	17.0897	2.36992
$53$	−8.04151	−1.10459	−0.552293	−	0.833650i	$-0.686247\pi$
$53$	−8.04151	−1.10459	−0.552293	+	0.833650i	$0.686247\pi$
$54$	12.0126	1.63471
$55$	2.17632	0.293455
$56$	−7.24803	−0.968559
$57$	−14.5342	−1.92510
$58$	−2.98619	−0.392106
$59$	−13.1546	−1.71259	−0.856293	−	0.516490i	$-0.827238\pi$
$59$	−13.1546	−1.71259	−0.856293	+	0.516490i	$0.827238\pi$
$60$	−5.40901	−0.698300
$61$	−7.20639	−0.922684	−0.461342	−	0.887222i	$-0.652632\pi$
$61$	−7.20639	−0.922684	−0.461342	+	0.887222i	$0.652632\pi$
$62$	−1.72387	−0.218932
$63$	0.272797	0.0343692
$64$	−13.0151	−1.62688
$65$	5.37970	0.667270
$66$	−8.43123	−1.03781
$67$	2.67143	0.326367	0.163184	−	0.986596i	$-0.447824\pi$
$67$	2.67143	0.326367	0.163184	+	0.986596i	$0.447824\pi$
$68$	0	0
$69$	−9.06814	−1.09168
$70$	−6.15962	−0.736216
$71$	1.87106	0.222054	0.111027	−	0.993817i	$-0.464586\pi$
$71$	1.87106	0.222054	0.111027	+	0.993817i	$0.464586\pi$
$72$	−0.269777	−0.0317935
$73$	−11.9780	−1.40192	−0.700962	−	0.713199i	$-0.747246\pi$
$73$	−11.9780	−1.40192	−0.700962	+	0.713199i	$0.747246\pi$
$74$	18.6656	2.16983
$75$	−1.70271	−0.196612
$76$	27.1160	3.11041
$77$	−5.89183	−0.671437
$78$	−20.8414	−2.35982
$79$	17.0477	1.91802	0.959009	−	0.283375i	$-0.0914541\pi$
$79$	17.0477	1.91802	0.959009	+	0.283375i	$0.0914541\pi$
$80$	−0.261974	−0.0292896
$81$	−8.68755	−0.965283
$82$	−0.0297365	−0.00328385
$83$	−3.35585	−0.368352	−0.184176	−	0.982893i	$-0.558962\pi$
$83$	−3.35585	−0.368352	−0.184176	+	0.982893i	$0.558962\pi$
$84$	14.6435	1.59774
$85$	0	0
$86$	−0.752183	−0.0811100
$87$	2.23477	0.239592
$88$	5.82660	0.621118
$89$	−10.8909	−1.15444	−0.577218	−	0.816590i	$-0.695862\pi$
$89$	−10.8909	−1.15444	−0.577218	+	0.816590i	$0.695862\pi$
$90$	−0.229265	−0.0241667
$91$	−14.5642	−1.52674
$92$	16.9182	1.76384
$93$	1.29009	0.133776
$94$	25.8001	2.66107
$95$	8.53588	0.875763
$96$	10.1322	1.03411
$97$	10.9119	1.10793	0.553965	−	0.832540i	$-0.313114\pi$
$97$	10.9119	1.10793	0.553965	+	0.832540i	$0.313114\pi$
$98$	0.748948	0.0756552
$99$	−0.219298	−0.0220403
$100$	3.17670	0.317670
$101$	−3.95599	−0.393636	−0.196818	−	0.980440i	$-0.563061\pi$
$101$	−3.95599	−0.393636	−0.196818	+	0.980440i	$0.563061\pi$
$102$	0	0
$103$	7.16779	0.706263	0.353132	−	0.935574i	$-0.385117\pi$
$103$	7.16779	0.706263	0.353132	+	0.935574i	$0.385117\pi$
$104$	14.4029	1.41232
$105$	4.60966	0.449857
$106$	−18.2963	−1.77710
$107$	3.70041	0.357732	0.178866	−	0.983873i	$-0.442757\pi$
$107$	3.70041	0.357732	0.178866	+	0.983873i	$0.442757\pi$
$108$	16.7721	1.61389
$109$	2.73869	0.262319	0.131160	−	0.991361i	$-0.458130\pi$
$109$	2.73869	0.262319	0.131160	+	0.991361i	$0.458130\pi$
$110$	4.95164	0.472121
$111$	−13.9687	−1.32585
$112$	0.709227	0.0670157
$113$	1.51487	0.142507	0.0712536	−	0.997458i	$-0.477300\pi$
$113$	1.51487	0.142507	0.0712536	+	0.997458i	$0.477300\pi$
$114$	−33.0687	−3.09716
$115$	5.32570	0.496624
$116$	−4.16934	−0.387114
$117$	−0.542088	−0.0501161
$118$	−29.9299	−2.75527
$119$	0	0
$120$	−4.55863	−0.416144
$121$	−6.26363	−0.569421
$122$	−16.3963	−1.48445
$123$	0.0222538	0.00200656
$124$	−2.40688	−0.216144
$125$	1.00000	0.0894427
$126$	0.620677	0.0552943
$127$	4.15113	0.368353	0.184176	−	0.982893i	$-0.441038\pi$
$127$	4.15113	0.368353	0.184176	+	0.982893i	$0.441038\pi$
$128$	−17.7112	−1.56546
$129$	0.562910	0.0495614
$130$	12.2401	1.07353
$131$	−12.3436	−1.07847	−0.539234	−	0.842156i	$-0.681286\pi$
$131$	−12.3436	−1.07847	−0.539234	+	0.842156i	$0.681286\pi$
$132$	−11.7717	−1.02460
$133$	−23.1087	−2.00378
$134$	6.07814	0.525071
$135$	5.27972	0.454406
$136$	0	0
$137$	13.1700	1.12519	0.562594	−	0.826733i	$-0.309803\pi$
$137$	13.1700	1.12519	0.562594	+	0.826733i	$0.309803\pi$
$138$	−20.6322	−1.75633
$139$	0.706325	0.0599097	0.0299548	−	0.999551i	$-0.490464\pi$
$139$	0.706325	0.0599097	0.0299548	+	0.999551i	$0.490464\pi$
$140$	−8.60011	−0.726842
$141$	−19.3079	−1.62602
$142$	4.25710	0.357248
$143$	11.7080	0.979069
$144$	0.0263979	0.00219983
$145$	−1.31247	−0.108995
$146$	−27.2529	−2.25546
$147$	−0.560489	−0.0462283
$148$	26.0610	2.14220
$149$	7.41327	0.607319	0.303659	−	0.952781i	$-0.401792\pi$
$149$	7.41327	0.607319	0.303659	+	0.952781i	$0.401792\pi$
$150$	−3.87408	−0.316317
$151$	−2.19280	−0.178448	−0.0892238	−	0.996012i	$-0.528439\pi$
$151$	−2.19280	−0.178448	−0.0892238	+	0.996012i	$0.528439\pi$
$152$	22.8529	1.85361
$153$	0	0
$154$	−13.4053	−1.08023
$155$	−0.757667	−0.0608573
$156$	−29.0989	−2.32978
$157$	5.33731	0.425963	0.212982	−	0.977056i	$-0.431683\pi$
$157$	5.33731	0.425963	0.212982	+	0.977056i	$0.431683\pi$
$158$	38.7876	3.08578
$159$	13.6924	1.08588
$160$	−5.95060	−0.470436
$161$	−14.4180	−1.13630
$162$	−19.7662	−1.55298
$163$	−7.78483	−0.609755	−0.304878	−	0.952392i	$-0.598616\pi$
$163$	−7.78483	−0.609755	−0.304878	+	0.952392i	$0.598616\pi$
$164$	−0.0415183	−0.00324204
$165$	−3.70565	−0.288485
$166$	−7.63534	−0.592617
$167$	−4.42165	−0.342157	−0.171079	−	0.985257i	$-0.554725\pi$
$167$	−4.42165	−0.342157	−0.171079	+	0.985257i	$0.554725\pi$
$168$	12.3413	0.952154
$169$	15.9412	1.22625
$170$	0	0
$171$	−0.860123	−0.0657752
$172$	−1.05020	−0.0800773
$173$	−14.6188	−1.11145	−0.555724	−	0.831367i	$-0.687559\pi$
$173$	−14.6188	−1.11145	−0.555724	+	0.831367i	$0.687559\pi$
$174$	5.08463	0.385465
$175$	−2.70724	−0.204648
$176$	−0.570139	−0.0429759
$177$	22.3986	1.68358
$178$	−24.7794	−1.85730
$179$	−5.42912	−0.405791	−0.202896	−	0.979200i	$-0.565035\pi$
$179$	−5.42912	−0.405791	−0.202896	+	0.979200i	$0.565035\pi$
$180$	−0.320102	−0.0238590
$181$	−18.3483	−1.36382	−0.681909	−	0.731437i	$-0.738850\pi$
$181$	−18.3483	−1.36382	−0.681909	+	0.731437i	$0.738850\pi$
$182$	−33.1369	−2.45627
$183$	12.2704	0.907056
$184$	14.2583	1.05114
$185$	8.20380	0.603155
$186$	2.93526	0.215224
$187$	0	0
$188$	36.0222	2.62719
$189$	−14.2935	−1.03970
$190$	19.4212	1.40896
$191$	4.91654	0.355748	0.177874	−	0.984053i	$-0.443078\pi$
$191$	4.91654	0.355748	0.177874	+	0.984053i	$0.443078\pi$
$192$	22.1609	1.59933
$193$	−17.5487	−1.26318	−0.631591	−	0.775302i	$-0.717598\pi$
$193$	−17.5487	−1.26318	−0.631591	+	0.775302i	$0.717598\pi$
$194$	24.8270	1.78248
$195$	−9.16010	−0.655968
$196$	1.04569	0.0746919
$197$	21.7620	1.55048	0.775239	−	0.631668i	$-0.217629\pi$
$197$	21.7620	1.55048	0.775239	+	0.631668i	$0.217629\pi$
$198$	−0.498955	−0.0354592
$199$	0.241280	0.0171039	0.00855196	−	0.999963i	$-0.497278\pi$
$199$	0.241280	0.0171039	0.00855196	+	0.999963i	$0.497278\pi$
$200$	2.67727	0.189312
$201$	−4.54869	−0.320840
$202$	−9.00082	−0.633295
$203$	3.55319	0.249385
$204$	0	0
$205$	−0.0130696	−0.000912823 0
$206$	16.3084	1.13626
$207$	−0.536647	−0.0372995
$208$	−1.40934	−0.0977203
$209$	18.5768	1.28499
$210$	10.4881	0.723746
$211$	9.41485	0.648145	0.324072	−	0.946032i	$-0.394948\pi$
$211$	9.41485	0.648145	0.324072	+	0.946032i	$0.394948\pi$
$212$	−25.5455	−1.75447
$213$	−3.18588	−0.218293
$214$	8.41931	0.575532
$215$	−0.330596	−0.0225464
$216$	14.1352	0.961781
$217$	2.05119	0.139244
$218$	6.23118	0.422029
$219$	20.3952	1.37818
$220$	6.91352	0.466109
$221$	0	0
$222$	−31.7821	−2.13308
$223$	−14.8338	−0.993345	−0.496672	−	0.867938i	$-0.665445\pi$
$223$	−14.8338	−0.993345	−0.496672	+	0.867938i	$0.665445\pi$
$224$	16.1097	1.07638
$225$	−0.100765	−0.00671770
$226$	3.44669	0.229271
$227$	9.83158	0.652545	0.326272	−	0.945276i	$-0.394207\pi$
$227$	9.83158	0.652545	0.326272	+	0.945276i	$0.394207\pi$
$228$	−46.1707	−3.05773
$229$	−12.4315	−0.821500	−0.410750	−	0.911748i	$-0.634733\pi$
$229$	−12.4315	−0.821500	−0.410750	+	0.911748i	$0.634733\pi$
$230$	12.1172	0.798986
$231$	10.0321	0.660064
$232$	−3.51385	−0.230696
$233$	12.5812	0.824224	0.412112	−	0.911133i	$-0.364791\pi$
$233$	12.5812	0.824224	0.412112	+	0.911133i	$0.364791\pi$
$234$	−1.23338	−0.0806285
$235$	11.3395	0.739708
$236$	−41.7883	−2.72019
$237$	−29.0274	−1.88553
$238$	0	0
$239$	−15.7966	−1.02179	−0.510897	−	0.859642i	$-0.670687\pi$
$239$	−15.7966	−1.02179	−0.510897	+	0.859642i	$0.670687\pi$
$240$	0.446067	0.0287935
$241$	−8.45284	−0.544496	−0.272248	−	0.962227i	$-0.587767\pi$
$241$	−8.45284	−0.544496	−0.272248	+	0.962227i	$0.587767\pi$
$242$	−14.2512	−0.916104
$243$	−1.04674	−0.0671482
$244$	−22.8926	−1.46555
$245$	0.329174	0.0210301
$246$	0.0506328	0.00322823
$247$	45.9205	2.92185
$248$	−2.02848	−0.128809
$249$	5.71404	0.362113
$250$	2.27524	0.143899
$251$	14.7900	0.933540	0.466770	−	0.884379i	$-0.345418\pi$
$251$	14.7900	0.933540	0.466770	+	0.884379i	$0.345418\pi$
$252$	0.866594	0.0545903
$253$	11.5904	0.728684
$254$	9.44480	0.592619
$255$	0	0
$256$	−14.2669	−0.891684
$257$	13.8681	0.865070	0.432535	−	0.901617i	$-0.357619\pi$
$257$	13.8681	0.865070	0.432535	+	0.901617i	$0.357619\pi$
$258$	1.28075	0.0797362
$259$	−22.2097	−1.38004
$260$	17.0897	1.05986
$261$	0.132252	0.00818620
$262$	−28.0847	−1.73508
$263$	0.382638	0.0235945	0.0117972	−	0.999930i	$-0.496245\pi$
$263$	0.382638	0.0235945	0.0117972	+	0.999930i	$0.496245\pi$
$264$	−9.92104	−0.610598
$265$	−8.04151	−0.493986
$266$	−52.5778	−3.22375
$267$	18.5441	1.13488
$268$	8.48634	0.518386
$269$	−21.8946	−1.33494	−0.667468	−	0.744638i	$-0.732622\pi$
$269$	−21.8946	−1.33494	−0.667468	+	0.744638i	$0.732622\pi$
$270$	12.0126	0.731064
$271$	16.9450	1.02933	0.514667	−	0.857390i	$-0.327916\pi$
$271$	16.9450	1.02933	0.514667	+	0.857390i	$0.327916\pi$
$272$	0	0
$273$	24.7986	1.50088
$274$	29.9648	1.81024
$275$	2.17632	0.131237
$276$	−28.8068	−1.73396
$277$	−24.4581	−1.46954	−0.734771	−	0.678315i	$-0.762710\pi$
$277$	−24.4581	−1.46954	−0.734771	+	0.678315i	$0.762710\pi$
$278$	1.60706	0.0963848
$279$	0.0763467	0.00457076
$280$	−7.24803	−0.433153
$281$	−13.2014	−0.787529	−0.393765	−	0.919211i	$-0.628827\pi$
$281$	−13.2014	−0.787529	−0.393765	+	0.919211i	$0.628827\pi$
$282$	−43.9301	−2.61600
$283$	13.7732	0.818730	0.409365	−	0.912371i	$-0.365750\pi$
$283$	13.7732	0.818730	0.409365	+	0.912371i	$0.365750\pi$
$284$	5.94379	0.352699
$285$	−14.5342	−0.860930
$286$	26.6384	1.57516
$287$	0.0353827	0.00208857
$288$	0.599615	0.0353326
$289$	0	0
$290$	−2.98619	−0.175355
$291$	−18.5798	−1.08916
$292$	−38.0507	−2.22675
$293$	21.1370	1.23483	0.617417	−	0.786636i	$-0.288179\pi$
$293$	21.1370	1.23483	0.617417	+	0.786636i	$0.288179\pi$
$294$	−1.27524	−0.0743737
$295$	−13.1546	−0.765892
$296$	21.9638	1.27662
$297$	11.4904	0.666738
$298$	16.8669	0.977076
$299$	28.6507	1.65691
$300$	−5.40901	−0.312289
$301$	0.895003	0.0515871
$302$	−4.98914	−0.287093
$303$	6.73592	0.386969
$304$	−2.23618	−0.128254
$305$	−7.20639	−0.412637
$306$	0	0
$307$	−23.2068	−1.32448	−0.662242	−	0.749290i	$-0.730395\pi$
$307$	−23.2068	−1.32448	−0.662242	+	0.749290i	$0.730395\pi$
$308$	−18.7166	−1.06648
$309$	−12.2047	−0.694301
$310$	−1.72387	−0.0979094
$311$	−19.0929	−1.08266	−0.541330	−	0.840810i	$-0.682079\pi$
$311$	−19.0929	−1.08266	−0.541330	+	0.840810i	$0.682079\pi$
$312$	−24.5241	−1.38840
$313$	−31.9061	−1.80344	−0.901720	−	0.432320i	$-0.857695\pi$
$313$	−31.9061	−1.80344	−0.901720	+	0.432320i	$0.857695\pi$
$314$	12.1436	0.685305
$315$	0.272797	0.0153704
$316$	54.1555	3.04649
$317$	−7.35179	−0.412917	−0.206459	−	0.978455i	$-0.566194\pi$
$317$	−7.35179	−0.412917	−0.206459	+	0.978455i	$0.566194\pi$
$318$	31.1534	1.74700
$319$	−2.85637	−0.159926
$320$	−13.0151	−0.727564
$321$	−6.30074	−0.351673
$322$	−32.8043	−1.82811
$323$	0	0
$324$	−27.5977	−1.53321
$325$	5.37970	0.298412
$326$	−17.7123	−0.980995
$327$	−4.66321	−0.257876
$328$	−0.0349910	−0.00193205
$329$	−30.6988	−1.69248
$330$	−8.43123	−0.464124
$331$	16.3546	0.898930	0.449465	−	0.893298i	$-0.351615\pi$
$331$	16.3546	0.898930	0.449465	+	0.893298i	$0.351615\pi$
$332$	−10.6605	−0.585072
$333$	−0.826660	−0.0453007
$334$	−10.0603	−0.550475
$335$	2.67143	0.145956
$336$	−1.20761	−0.0658806
$337$	2.73232	0.148839	0.0744196	−	0.997227i	$-0.476290\pi$
$337$	2.73232	0.148839	0.0744196	+	0.997227i	$0.476290\pi$
$338$	36.2700	1.97283
$339$	−2.57939	−0.140093
$340$	0	0
$341$	−1.64893	−0.0892944
$342$	−1.95698	−0.105821
$343$	18.0596	0.975125
$344$	−0.885095	−0.0477211
$345$	−9.06814	−0.488212
$346$	−33.2613	−1.78814
$347$	−18.9609	−1.01788	−0.508938	−	0.860803i	$-0.669962\pi$
$347$	−18.9609	−1.01788	−0.508938	+	0.860803i	$0.669962\pi$
$348$	7.09919	0.380557
$349$	−32.3382	−1.73102	−0.865511	−	0.500890i	$-0.833006\pi$
$349$	−32.3382	−1.73102	−0.865511	+	0.500890i	$0.833006\pi$
$350$	−6.15962	−0.329246
$351$	28.4033	1.51606
$352$	−12.9504	−0.690259
$353$	−13.0916	−0.696796	−0.348398	−	0.937347i	$-0.613274\pi$
$353$	−13.0916	−0.696796	−0.348398	+	0.937347i	$0.613274\pi$
$354$	50.9620	2.70860
$355$	1.87106	0.0993054
$356$	−34.5972	−1.83365
$357$	0	0
$358$	−12.3525	−0.652851
$359$	8.64264	0.456141	0.228071	−	0.973645i	$-0.426758\pi$
$359$	8.64264	0.456141	0.228071	+	0.973645i	$0.426758\pi$
$360$	−0.269777	−0.0142185
$361$	53.8613	2.83481
$362$	−41.7467	−2.19416
$363$	10.6652	0.559776
$364$	−46.2660	−2.42500
$365$	−11.9780	−0.626960
$366$	27.9181	1.45930
$367$	−6.61035	−0.345057	−0.172529	−	0.985005i	$-0.555194\pi$
$367$	−6.61035	−0.345057	−0.172529	+	0.985005i	$0.555194\pi$
$368$	−1.39519	−0.0727295
$369$	0.00131697	6.85586e−5 0
$370$	18.6656	0.970377
$371$	21.7703	1.13026
$372$	4.09823	0.212483
$373$	−7.14349	−0.369876	−0.184938	−	0.982750i	$-0.559208\pi$
$373$	−7.14349	−0.369876	−0.184938	+	0.982750i	$0.559208\pi$
$374$	0	0
$375$	−1.70271	−0.0879278
$376$	30.3589	1.56564
$377$	−7.06073	−0.363646
$378$	−32.5211	−1.67270
$379$	7.19225	0.369441	0.184720	−	0.982791i	$-0.440862\pi$
$379$	7.19225	0.369441	0.184720	+	0.982791i	$0.440862\pi$
$380$	27.1160	1.39102
$381$	−7.06818	−0.362114
$382$	11.1863	0.572340
$383$	−12.2903	−0.628006	−0.314003	−	0.949422i	$-0.601670\pi$
$383$	−12.2903	−0.628006	−0.314003	+	0.949422i	$0.601670\pi$
$384$	30.1570	1.53895
$385$	−5.89183	−0.300276
$386$	−39.9274	−2.03225
$387$	0.0333126	0.00169338
$388$	34.6637	1.75978
$389$	10.6413	0.539536	0.269768	−	0.962925i	$-0.413053\pi$
$389$	10.6413	0.539536	0.269768	+	0.962925i	$0.413053\pi$
$390$	−20.8414	−1.05534
$391$	0	0
$392$	0.881288	0.0445117
$393$	21.0177	1.06020
$394$	49.5137	2.49446
$395$	17.0477	0.857764
$396$	−0.696644	−0.0350077
$397$	24.0554	1.20731	0.603654	−	0.797247i	$-0.293711\pi$
$397$	24.0554	1.20731	0.603654	+	0.797247i	$0.293711\pi$
$398$	0.548970	0.0275174
$399$	39.3476	1.96984
$400$	−0.261974	−0.0130987
$401$	−22.9193	−1.14453	−0.572267	−	0.820067i	$-0.693936\pi$
$401$	−22.9193	−1.14453	−0.572267	+	0.820067i	$0.693936\pi$
$402$	−10.3493	−0.516178
$403$	−4.07603	−0.203041
$404$	−12.5670	−0.625232
$405$	−8.68755	−0.431688
$406$	8.08435	0.401220
$407$	17.8541	0.884995
$408$	0	0
$409$	−7.50913	−0.371303	−0.185651	−	0.982616i	$-0.559439\pi$
$409$	−7.50913	−0.371303	−0.185651	+	0.982616i	$0.559439\pi$
$410$	−0.0297365	−0.00146858
$411$	−22.4247	−1.10613
$412$	22.7699	1.12179
$413$	35.6128	1.75239
$414$	−1.22100	−0.0600088
$415$	−3.35585	−0.164732
$416$	−32.0124	−1.56954
$417$	−1.20267	−0.0588949
$418$	42.2667	2.06733
$419$	−13.3993	−0.654598	−0.327299	−	0.944921i	$-0.606138\pi$
$419$	−13.3993	−0.654598	−0.327299	+	0.944921i	$0.606138\pi$
$420$	14.6435	0.714531
$421$	−20.5078	−0.999491	−0.499745	−	0.866172i	$-0.666573\pi$
$421$	−20.5078	−0.999491	−0.499745	+	0.866172i	$0.666573\pi$
$422$	21.4210	1.04276
$423$	−1.14263	−0.0555566
$424$	−21.5293	−1.04556
$425$	0	0
$426$	−7.24862	−0.351197
$427$	19.5095	0.944130
$428$	11.7551	0.568204
$429$	−19.9353	−0.962486
$430$	−0.752183	−0.0362735
$431$	−8.98646	−0.432863	−0.216431	−	0.976298i	$-0.569442\pi$
$431$	−8.98646	−0.432863	−0.216431	+	0.976298i	$0.569442\pi$
$432$	−1.38315	−0.0665467
$433$	26.3738	1.26744	0.633721	−	0.773562i	$-0.281527\pi$
$433$	26.3738	1.26744	0.633721	+	0.773562i	$0.281527\pi$
$434$	4.66694	0.224020
$435$	2.23477	0.107149
$436$	8.70001	0.416655
$437$	45.4596	2.17463
$438$	46.4039	2.21726
$439$	29.3558	1.40108	0.700538	−	0.713615i	$-0.252943\pi$
$439$	29.3558	1.40108	0.700538	+	0.713615i	$0.252943\pi$
$440$	5.82660	0.277772
$441$	−0.0331693	−0.00157949
$442$	0	0
$443$	−23.4483	−1.11406	−0.557030	−	0.830492i	$-0.688059\pi$
$443$	−23.4483	−1.11406	−0.557030	+	0.830492i	$0.688059\pi$
$444$	−44.3744	−2.10592
$445$	−10.8909	−0.516279
$446$	−33.7504	−1.59813
$447$	−12.6227	−0.597032
$448$	35.2350	1.66470
$449$	11.8222	0.557926	0.278963	−	0.960302i	$-0.410009\pi$
$449$	11.8222	0.557926	0.278963	+	0.960302i	$0.410009\pi$
$450$	−0.229265	−0.0108077
$451$	−0.0284437	−0.00133936
$452$	4.81230	0.226351
$453$	3.73371	0.175425
$454$	22.3692	1.04984
$455$	−14.5642	−0.682779
$456$	−38.9119	−1.82222
$457$	−3.31478	−0.155059	−0.0775293	−	0.996990i	$-0.524703\pi$
$457$	−3.31478	−0.155059	−0.0775293	+	0.996990i	$0.524703\pi$
$458$	−28.2847	−1.32166
$459$	0	0
$460$	16.9182	0.788813
$461$	36.2559	1.68860	0.844302	−	0.535868i	$-0.180016\pi$
$461$	36.2559	1.68860	0.844302	+	0.535868i	$0.180016\pi$
$462$	22.8254	1.06193
$463$	10.9581	0.509268	0.254634	−	0.967038i	$-0.418045\pi$
$463$	10.9581	0.509268	0.254634	+	0.967038i	$0.418045\pi$
$464$	0.343834	0.0159621
$465$	1.29009	0.0598265
$466$	28.6253	1.32604
$467$	−34.3919	−1.59147	−0.795734	−	0.605647i	$-0.792914\pi$
$467$	−34.3919	−1.59147	−0.795734	+	0.605647i	$0.792914\pi$
$468$	−1.72205	−0.0796019
$469$	−7.23222	−0.333953
$470$	25.8001	1.19007
$471$	−9.08791	−0.418749
$472$	−35.2185	−1.62106
$473$	−0.719482	−0.0330818
$474$	−66.0442	−3.03351
$475$	8.53588	0.391653
$476$	0	0
$477$	0.810307	0.0371014
$478$	−35.9409	−1.64390
$479$	−27.5154	−1.25721	−0.628606	−	0.777724i	$-0.716374\pi$
$479$	−27.5154	−1.25721	−0.628606	+	0.777724i	$0.716374\pi$
$480$	10.1322	0.462468
$481$	44.1340	2.01234
$482$	−19.2322	−0.876004
$483$	24.5497	1.11705
$484$	−19.8977	−0.904440
$485$	10.9119	0.495482
$486$	−2.38158	−0.108030
$487$	−10.6229	−0.481368	−0.240684	−	0.970604i	$-0.577372\pi$
$487$	−10.6229	−0.481368	−0.240684	+	0.970604i	$0.577372\pi$
$488$	−19.2935	−0.873375
$489$	13.2553	0.599427
$490$	0.748948	0.0338340
$491$	36.2103	1.63415	0.817074	−	0.576533i	$-0.195595\pi$
$491$	36.2103	1.63415	0.817074	+	0.576533i	$0.195595\pi$
$492$	0.0706938	0.00318712
$493$	0	0
$494$	104.480	4.70078
$495$	−0.219298	−0.00985671
$496$	0.198489	0.00891242
$497$	−5.06541	−0.227215
$498$	13.0008	0.582580
$499$	20.8740	0.934447	0.467224	−	0.884139i	$-0.345254\pi$
$499$	20.8740	0.934447	0.467224	+	0.884139i	$0.345254\pi$
$500$	3.17670	0.142066
$501$	7.52880	0.336362
$502$	33.6509	1.50191
$503$	−7.63988	−0.340645	−0.170323	−	0.985388i	$-0.554481\pi$
$503$	−7.63988	−0.340645	−0.170323	+	0.985388i	$0.554481\pi$
$504$	0.730351	0.0325324
$505$	−3.95599	−0.176039
$506$	26.3710	1.17233
$507$	−27.1433	−1.20548
$508$	13.1869	0.585074
$509$	−20.9805	−0.929945	−0.464972	−	0.885325i	$-0.653936\pi$
$509$	−20.9805	−0.929945	−0.464972	+	0.885325i	$0.653936\pi$
$510$	0	0
$511$	32.4275	1.43451
$512$	2.96165	0.130888
$513$	45.0671	1.98976
$514$	31.5533	1.39175
$515$	7.16779	0.315851
$516$	1.78820	0.0787209
$517$	24.6784	1.08536
$518$	−50.5323	−2.22026
$519$	24.8917	1.09262
$520$	14.4029	0.631610
$521$	6.11774	0.268023	0.134012	−	0.990980i	$-0.457214\pi$
$521$	6.11774	0.268023	0.134012	+	0.990980i	$0.457214\pi$
$522$	0.300905	0.0131703
$523$	−5.40916	−0.236526	−0.118263	−	0.992982i	$-0.537733\pi$
$523$	−5.40916	−0.236526	−0.118263	+	0.992982i	$0.537733\pi$
$524$	−39.2120	−1.71298
$525$	4.60966	0.201182
$526$	0.870591	0.0379596
$527$	0	0
$528$	0.970784	0.0422480
$529$	5.36307	0.233177
$530$	−18.2963	−0.794742
$531$	1.32553	0.0575232
$532$	−73.4095	−3.18271
$533$	−0.0703107	−0.00304550
$534$	42.1923	1.82584
$535$	3.70041	0.159983
$536$	7.15215	0.308926
$537$	9.24423	0.398918
$538$	−49.8154	−2.14769
$539$	0.716388	0.0308570
$540$	16.7721	0.721755
$541$	20.4944	0.881124	0.440562	−	0.897722i	$-0.354779\pi$
$541$	20.4944	0.881124	0.440562	+	0.897722i	$0.354779\pi$
$542$	38.5538	1.65603
$543$	31.2419	1.34072
$544$	0	0
$545$	2.73869	0.117313
$546$	56.4227	2.41467
$547$	−10.1545	−0.434175	−0.217088	−	0.976152i	$-0.569656\pi$
$547$	−10.1545	−0.434175	−0.217088	+	0.976152i	$0.569656\pi$
$548$	41.8371	1.78719
$549$	0.726156	0.0309916
$550$	4.95164	0.211139
$551$	−11.2031	−0.477270
$552$	−24.2779	−1.03334
$553$	−46.1523	−1.96260
$554$	−55.6479	−2.36425
$555$	−13.9687	−0.592939
$556$	2.24378	0.0951575
$557$	30.1117	1.27587	0.637937	−	0.770088i	$-0.279788\pi$
$557$	30.1117	1.27587	0.637937	+	0.770088i	$0.279788\pi$
$558$	0.173707	0.00735360
$559$	−1.77851	−0.0752228
$560$	0.709227	0.0299703
$561$	0	0
$562$	−30.0363	−1.26700
$563$	12.8482	0.541486	0.270743	−	0.962652i	$-0.412731\pi$
$563$	12.8482	0.541486	0.270743	+	0.962652i	$0.412731\pi$
$564$	−61.3355	−2.58269
$565$	1.51487	0.0637312
$566$	31.3372	1.31720
$567$	23.5193	0.987719
$568$	5.00933	0.210187
$569$	19.6602	0.824196	0.412098	−	0.911139i	$-0.364796\pi$
$569$	19.6602	0.824196	0.412098	+	0.911139i	$0.364796\pi$
$570$	−33.0687	−1.38509
$571$	20.2253	0.846403	0.423202	−	0.906036i	$-0.360906\pi$
$571$	20.2253	0.846403	0.423202	+	0.906036i	$0.360906\pi$
$572$	37.1927	1.55510
$573$	−8.37146	−0.349723
$574$	0.0805040	0.00336017
$575$	5.32570	0.222097
$576$	1.31147	0.0546446
$577$	34.5597	1.43874	0.719369	−	0.694628i	$-0.244431\pi$
$577$	34.5597	1.43874	0.719369	+	0.694628i	$0.244431\pi$
$578$	0	0
$579$	29.8804	1.24179
$580$	−4.16934	−0.173122
$581$	9.08509	0.376913
$582$	−42.2734	−1.75229
$583$	−17.5009	−0.724814
$584$	−32.0685	−1.32700
$585$	−0.542088	−0.0224126
$586$	48.0916	1.98665
$587$	23.7081	0.978540	0.489270	−	0.872132i	$-0.337263\pi$
$587$	23.7081	0.978540	0.489270	+	0.872132i	$0.337263\pi$
$588$	−1.78050	−0.0734268
$589$	−6.46736	−0.266483
$590$	−29.9299	−1.23219
$591$	−37.0545	−1.52422
$592$	−2.14918	−0.0883308
$593$	−11.5371	−0.473770	−0.236885	−	0.971538i	$-0.576127\pi$
$593$	−11.5371	−0.473770	−0.236885	+	0.971538i	$0.576127\pi$
$594$	26.1433	1.07267
$595$	0	0
$596$	23.5497	0.964635
$597$	−0.410831	−0.0168142
$598$	65.1871	2.66570
$599$	−9.83844	−0.401988	−0.200994	−	0.979593i	$-0.564417\pi$
$599$	−9.83844	−0.401988	−0.200994	+	0.979593i	$0.564417\pi$
$600$	−4.55863	−0.186105
$601$	−10.1246	−0.412991	−0.206496	−	0.978448i	$-0.566206\pi$
$601$	−10.1246	−0.412991	−0.206496	+	0.978448i	$0.566206\pi$
$602$	2.03634	0.0829952
$603$	−0.269188	−0.0109622
$604$	−6.96587	−0.283437
$605$	−6.26363	−0.254653
$606$	15.3258	0.622569
$607$	0.707519	0.0287173	0.0143587	−	0.999897i	$-0.495429\pi$
$607$	0.707519	0.0287173	0.0143587	+	0.999897i	$0.495429\pi$
$608$	−50.7936	−2.05995
$609$	−6.05007	−0.245161
$610$	−16.3963	−0.663865
$611$	61.0032	2.46792
$612$	0	0
$613$	−28.1775	−1.13808	−0.569039	−	0.822310i	$-0.692685\pi$
$613$	−28.1775	−1.13808	−0.569039	+	0.822310i	$0.692685\pi$
$614$	−52.8010	−2.13088
$615$	0.0222538	0.000897362 0
$616$	−15.7740	−0.635554
$617$	39.8676	1.60501	0.802505	−	0.596645i	$-0.203500\pi$
$617$	39.8676	1.60501	0.802505	+	0.596645i	$0.203500\pi$
$618$	−27.7686	−1.11702
$619$	−37.4591	−1.50561	−0.752804	−	0.658244i	$-0.771299\pi$
$619$	−37.4591	−1.50561	−0.752804	+	0.658244i	$0.771299\pi$
$620$	−2.40688	−0.0966627
$621$	28.1182	1.12834
$622$	−43.4409	−1.74182
$623$	29.4844	1.18127
$624$	2.39971	0.0960651
$625$	1.00000	0.0400000
$626$	−72.5940	−2.90144
$627$	−31.6310	−1.26322
$628$	16.9550	0.676579
$629$	0	0
$630$	0.620677	0.0247284
$631$	−10.5005	−0.418020	−0.209010	−	0.977913i	$-0.567024\pi$
$631$	−10.5005	−0.418020	−0.209010	+	0.977913i	$0.567024\pi$
$632$	45.6414	1.81552
$633$	−16.0308	−0.637167
$634$	−16.7271	−0.664316
$635$	4.15113	0.164732
$636$	43.4966	1.72475
$637$	1.77086	0.0701639
$638$	−6.49891	−0.257294
$639$	−0.188538	−0.00745845
$640$	−17.7112	−0.700095
$641$	−44.9746	−1.77639	−0.888195	−	0.459466i	$-0.848041\pi$
$641$	−44.9746	−1.77639	−0.888195	+	0.459466i	$0.848041\pi$
$642$	−14.3357	−0.565784
$643$	−3.17835	−0.125342	−0.0626710	−	0.998034i	$-0.519962\pi$
$643$	−3.17835	−0.125342	−0.0626710	+	0.998034i	$0.519962\pi$
$644$	−45.8016	−1.80484
$645$	0.562910	0.0221645
$646$	0	0
$647$	3.28494	0.129144	0.0645721	−	0.997913i	$-0.479432\pi$
$647$	3.28494	0.129144	0.0645721	+	0.997913i	$0.479432\pi$
$648$	−23.2589	−0.913697
$649$	−28.6287	−1.12377
$650$	12.2401	0.480096
$651$	−3.49259	−0.136885
$652$	−24.7301	−0.968505
$653$	33.9120	1.32708	0.663540	−	0.748140i	$-0.269053\pi$
$653$	33.9120	1.32708	0.663540	+	0.748140i	$0.269053\pi$
$654$	−10.6099	−0.414880
$655$	−12.3436	−0.482305
$656$	0.00342390	0.000133681 0
$657$	1.20697	0.0470885
$658$	−69.8471	−2.72292
$659$	27.5756	1.07419	0.537097	−	0.843521i	$-0.319521\pi$
$659$	27.5756	1.07419	0.537097	+	0.843521i	$0.319521\pi$
$660$	−11.7717	−0.458215
$661$	−19.4561	−0.756756	−0.378378	−	0.925651i	$-0.623518\pi$
$661$	−19.4561	−0.756756	−0.378378	+	0.925651i	$0.623518\pi$
$662$	37.2106	1.44623
$663$	0	0
$664$	−8.98451	−0.348667
$665$	−23.1087	−0.896118
$666$	−1.88085	−0.0728813
$667$	−6.98985	−0.270648
$668$	−14.0463	−0.543466
$669$	25.2577	0.976520
$670$	6.07814	0.234819
$671$	−15.6834	−0.605452
$672$	−27.4302	−1.05814
$673$	2.96580	0.114323	0.0571616	−	0.998365i	$-0.481795\pi$
$673$	2.96580	0.114323	0.0571616	+	0.998365i	$0.481795\pi$
$674$	6.21668	0.239458
$675$	5.27972	0.203216
$676$	50.6404	1.94771
$677$	−4.50634	−0.173193	−0.0865964	−	0.996243i	$-0.527599\pi$
$677$	−4.50634	−0.173193	−0.0865964	+	0.996243i	$0.527599\pi$
$678$	−5.86873	−0.225387
$679$	−29.5411	−1.13368
$680$	0	0
$681$	−16.7404	−0.641492
$682$	−3.75170	−0.143660
$683$	−48.5495	−1.85769	−0.928847	−	0.370464i	$-0.879199\pi$
$683$	−48.5495	−1.85769	−0.928847	+	0.370464i	$0.879199\pi$
$684$	−2.73235	−0.104474
$685$	13.1700	0.503199
$686$	41.0898	1.56881
$687$	21.1674	0.807585
$688$	0.0866074	0.00330188
$689$	−43.2609	−1.64811
$690$	−20.6322	−0.785453
$691$	1.63196	0.0620827	0.0310413	−	0.999518i	$-0.490118\pi$
$691$	1.63196	0.0620827	0.0310413	+	0.999518i	$0.490118\pi$
$692$	−46.4396	−1.76537
$693$	0.593693	0.0225525
$694$	−43.1406	−1.63759
$695$	0.706325	0.0267924
$696$	5.98309	0.226788
$697$	0	0
$698$	−73.5769	−2.78493
$699$	−21.4222	−0.810264
$700$	−8.60011	−0.325053
$701$	−40.4449	−1.52758	−0.763792	−	0.645463i	$-0.776664\pi$
$701$	−40.4449	−1.52758	−0.763792	+	0.645463i	$0.776664\pi$
$702$	64.6242	2.43908
$703$	70.0267	2.64111
$704$	−28.3250	−1.06754
$705$	−19.3079	−0.727179
$706$	−29.7865	−1.12103
$707$	10.7098	0.402785
$708$	71.1535	2.67411
$709$	47.3049	1.77657	0.888286	−	0.459291i	$-0.151897\pi$
$709$	47.3049	1.77657	0.888286	+	0.459291i	$0.151897\pi$
$710$	4.25710	0.159766
$711$	−1.71782	−0.0644234
$712$	−29.1580	−1.09274
$713$	−4.03511	−0.151116
$714$	0	0
$715$	11.7080	0.437853
$716$	−17.2467	−0.644539
$717$	26.8970	1.00449
$718$	19.6640	0.733856
$719$	−8.17117	−0.304733	−0.152367	−	0.988324i	$-0.548689\pi$
$719$	−8.17117	−0.304733	−0.152367	+	0.988324i	$0.548689\pi$
$720$	0.0263979	0.000983793 0
$721$	−19.4050	−0.722679
$722$	122.547	4.56074
$723$	14.3928	0.535273
$724$	−58.2871	−2.16622
$725$	−1.31247	−0.0487441
$726$	24.2658	0.900587
$727$	−18.8237	−0.698133	−0.349067	−	0.937098i	$-0.613501\pi$
$727$	−18.8237	−0.698133	−0.349067	+	0.937098i	$0.613501\pi$
$728$	−38.9923	−1.44515
$729$	27.8449	1.03129
$730$	−27.2529	−1.00867
$731$	0	0
$732$	38.9795	1.44072
$733$	25.9444	0.958278	0.479139	−	0.877739i	$-0.340949\pi$
$733$	25.9444	0.958278	0.479139	+	0.877739i	$0.340949\pi$
$734$	−15.0401	−0.555140
$735$	−0.560489	−0.0206739
$736$	−31.6911	−1.16815
$737$	5.81389	0.214158
$738$	0.00299641	0.000110299 0
$739$	18.9248	0.696162	0.348081	−	0.937465i	$-0.386833\pi$
$739$	18.9248	0.696162	0.348081	+	0.937465i	$0.386833\pi$
$740$	26.0610	0.958022
$741$	−78.1895	−2.87236
$742$	49.5327	1.81840
$743$	0.0747338	0.00274172	0.00137086	−	0.999999i	$-0.499564\pi$
$743$	0.0747338	0.00274172	0.00137086	+	0.999999i	$0.499564\pi$
$744$	3.45392	0.126627
$745$	7.41327	0.271601
$746$	−16.2531	−0.595069
$747$	0.338153	0.0123724
$748$	0	0
$749$	−10.0179	−0.366047
$750$	−3.87408	−0.141461
$751$	31.3032	1.14227	0.571135	−	0.820856i	$-0.306503\pi$
$751$	31.3032	1.14227	0.571135	+	0.820856i	$0.306503\pi$
$752$	−2.97066	−0.108329
$753$	−25.1832	−0.917728
$754$	−16.0648	−0.585046
$755$	−2.19280	−0.0798042
$756$	−45.4061	−1.65140
$757$	−10.9290	−0.397223	−0.198612	−	0.980078i	$-0.563643\pi$
$757$	−10.9290	−0.397223	−0.198612	+	0.980078i	$0.563643\pi$
$758$	16.3641	0.594369
$759$	−19.7352	−0.716342
$760$	22.8529	0.828961
$761$	−34.7125	−1.25833	−0.629164	−	0.777272i	$-0.716603\pi$
$761$	−34.7125	−1.25833	−0.629164	+	0.777272i	$0.716603\pi$
$762$	−16.0818	−0.582582
$763$	−7.41431	−0.268416
$764$	15.6184	0.565053
$765$	0	0
$766$	−27.9634	−1.01036
$767$	−70.7680	−2.55528
$768$	24.2925	0.876581
$769$	28.5727	1.03036	0.515178	−	0.857083i	$-0.327726\pi$
$769$	28.5727	1.03036	0.515178	+	0.857083i	$0.327726\pi$
$770$	−13.4053	−0.483094
$771$	−23.6135	−0.850418
$772$	−55.7469	−2.00638
$773$	31.3773	1.12856	0.564281	−	0.825583i	$-0.309153\pi$
$773$	31.3773	1.12856	0.564281	+	0.825583i	$0.309153\pi$
$774$	0.0757941	0.00272436
$775$	−0.757667	−0.0272162
$776$	29.2140	1.04872
$777$	37.8167	1.35667
$778$	24.2115	0.868025
$779$	−0.111561	−0.00399708
$780$	−29.0989	−1.04191
$781$	4.07202	0.145708
$782$	0	0
$783$	−6.92950	−0.247640
$784$	−0.0862349	−0.00307982
$785$	5.33731	0.190497
$786$	47.8201	1.70569
$787$	19.5079	0.695380	0.347690	−	0.937610i	$-0.386966\pi$
$787$	19.5079	0.695380	0.347690	+	0.937610i	$0.386966\pi$
$788$	69.1314	2.46270
$789$	−0.651523	−0.0231948
$790$	38.7876	1.38000
$791$	−4.10113	−0.145819
$792$	−0.587121	−0.0208624
$793$	−38.7683	−1.37670
$794$	54.7318	1.94236
$795$	13.6924	0.485619
$796$	0.766476	0.0271670
$797$	−16.1734	−0.572892	−0.286446	−	0.958096i	$-0.592474\pi$
$797$	−16.1734	−0.572892	−0.286446	+	0.958096i	$0.592474\pi$
$798$	89.5250	3.16915
$799$	0	0
$800$	−5.95060	−0.210385
$801$	1.09743	0.0387757
$802$	−52.1468	−1.84137
$803$	−26.0681	−0.919922
$804$	−14.4498	−0.509606
$805$	−14.4180	−0.508167
$806$	−9.27392	−0.326660
$807$	37.2802	1.31233
$808$	−10.5913	−0.372600
$809$	−37.5852	−1.32143	−0.660713	−	0.750639i	$-0.729746\pi$
$809$	−37.5852	−1.32143	−0.660713	+	0.750639i	$0.729746\pi$
$810$	−19.7662	−0.694515
$811$	−34.8967	−1.22539	−0.612695	−	0.790320i	$-0.709915\pi$
$811$	−34.8967	−1.22539	−0.612695	+	0.790320i	$0.709915\pi$
$812$	11.2874	0.396111
$813$	−28.8524	−1.01190
$814$	40.6223	1.42381
$815$	−7.78483	−0.272691
$816$	0	0
$817$	−2.82193	−0.0987267
$818$	−17.0850	−0.597365
$819$	1.46757	0.0512809
$820$	−0.0415183	−0.00144988
$821$	−30.8990	−1.07838	−0.539191	−	0.842184i	$-0.681270\pi$
$821$	−30.8990	−1.07838	−0.539191	+	0.842184i	$0.681270\pi$
$822$	−51.0215	−1.77958
$823$	−42.4684	−1.48035	−0.740177	−	0.672412i	$-0.765258\pi$
$823$	−42.4684	−1.48035	−0.740177	+	0.672412i	$0.765258\pi$
$824$	19.1901	0.668520
$825$	−3.70565	−0.129014
$826$	81.0275	2.81931
$827$	−20.4596	−0.711449	−0.355724	−	0.934591i	$-0.615766\pi$
$827$	−20.4596	−0.711449	−0.355724	+	0.934591i	$0.615766\pi$
$828$	−1.70477	−0.0592447
$829$	−38.1368	−1.32455	−0.662273	−	0.749263i	$-0.730408\pi$
$829$	−38.1368	−1.32455	−0.662273	+	0.749263i	$0.730408\pi$
$830$	−7.63534	−0.265027
$831$	41.6451	1.44465
$832$	−70.0172	−2.42741
$833$	0	0
$834$	−2.73636	−0.0947522
$835$	−4.42165	−0.153017
$836$	59.0130	2.04101
$837$	−4.00027	−0.138270
$838$	−30.4866	−1.05314
$839$	−37.7486	−1.30323	−0.651613	−	0.758552i	$-0.725907\pi$
$839$	−37.7486	−1.30323	−0.651613	+	0.758552i	$0.725907\pi$
$840$	12.3413	0.425816
$841$	−27.2774	−0.940600
$842$	−46.6602	−1.60802
$843$	22.4782	0.774190
$844$	29.9082	1.02948
$845$	15.9412	0.548394
$846$	−2.59976	−0.0893814
$847$	16.9572	0.582655
$848$	2.10667	0.0723432
$849$	−23.4518	−0.804863
$850$	0	0
$851$	43.6910	1.49771
$852$	−10.1206	−0.346725
$853$	19.5859	0.670608	0.335304	−	0.942110i	$-0.391161\pi$
$853$	19.5859	0.670608	0.335304	+	0.942110i	$0.391161\pi$
$854$	44.3887	1.51895
$855$	−0.860123	−0.0294156
$856$	9.90701	0.338615
$857$	14.2754	0.487639	0.243820	−	0.969821i	$-0.421599\pi$
$857$	14.2754	0.487639	0.243820	+	0.969821i	$0.421599\pi$
$858$	−45.3575	−1.54848
$859$	50.2428	1.71426	0.857130	−	0.515099i	$-0.172245\pi$
$859$	50.2428	1.71426	0.857130	+	0.515099i	$0.172245\pi$
$860$	−1.05020	−0.0358116
$861$	−0.0602466	−0.00205320
$862$	−20.4463	−0.696405
$863$	13.1930	0.449095	0.224548	−	0.974463i	$-0.427910\pi$
$863$	13.1930	0.449095	0.224548	+	0.974463i	$0.427910\pi$
$864$	−31.4175	−1.06884
$865$	−14.6188	−0.497055
$866$	60.0065	2.03910
$867$	0	0
$868$	6.51602	0.221168
$869$	37.1013	1.25858
$870$	5.08463	0.172385
$871$	14.3715	0.486960
$872$	7.33223	0.248301
$873$	−1.09954	−0.0372137
$874$	103.431	3.49861
$875$	−2.70724	−0.0915216
$876$	64.7894	2.18903
$877$	−6.22918	−0.210345	−0.105172	−	0.994454i	$-0.533539\pi$
$877$	−6.22918	−0.210345	−0.105172	+	0.994454i	$0.533539\pi$
$878$	66.7914	2.25410
$879$	−35.9902	−1.21392
$880$	−0.570139	−0.0192194
$881$	30.3408	1.02221	0.511104	−	0.859519i	$-0.329237\pi$
$881$	30.3408	1.02221	0.511104	+	0.859519i	$0.329237\pi$
$882$	−0.0754681	−0.00254114
$883$	27.0762	0.911185	0.455593	−	0.890188i	$-0.349427\pi$
$883$	27.0762	0.911185	0.455593	+	0.890188i	$0.349427\pi$
$884$	0	0
$885$	22.3986	0.752920
$886$	−53.3504	−1.79234
$887$	28.1506	0.945205	0.472603	−	0.881276i	$-0.343315\pi$
$887$	28.1506	0.945205	0.472603	+	0.881276i	$0.343315\pi$
$888$	−37.3981	−1.25500
$889$	−11.2381	−0.376914
$890$	−24.7794	−0.830608
$891$	−18.9069	−0.633405
$892$	−47.1225	−1.57778
$893$	96.7927	3.23905
$894$	−28.7196	−0.960526
$895$	−5.42912	−0.181475
$896$	47.9484	1.60185
$897$	−48.7839	−1.62885
$898$	26.8984	0.897611
$899$	0.994419	0.0331657
$900$	−0.320102	−0.0106701
$901$	0	0
$902$	−0.0647162	−0.00215481
$903$	−1.52393	−0.0507134
$904$	4.05573	0.134891
$905$	−18.3483	−0.609918
$906$	8.49507	0.282230
$907$	37.7225	1.25256	0.626278	−	0.779600i	$-0.284577\pi$
$907$	37.7225	1.25256	0.626278	+	0.779600i	$0.284577\pi$
$908$	31.2320	1.03647
$909$	0.398628	0.0132216
$910$	−33.1369	−1.09848
$911$	−17.9517	−0.594765	−0.297383	−	0.954758i	$-0.596114\pi$
$911$	−17.9517	−0.594765	−0.297383	+	0.954758i	$0.596114\pi$
$912$	3.80757	0.126081
$913$	−7.30340	−0.241707
$914$	−7.54190	−0.249464
$915$	12.2704	0.405648
$916$	−39.4913	−1.30483
$917$	33.4172	1.10353
$918$	0	0
$919$	−25.0436	−0.826112	−0.413056	−	0.910706i	$-0.635539\pi$
$919$	−25.0436	−0.826112	−0.413056	+	0.910706i	$0.635539\pi$
$920$	14.2583	0.470084
$921$	39.5146	1.30205
$922$	82.4906	2.71668
$923$	10.0657	0.331318
$924$	31.8690	1.04841
$925$	8.20380	0.269739
$926$	24.9324	0.819328
$927$	−0.722266	−0.0237223
$928$	7.81001	0.256376
$929$	−21.1573	−0.694148	−0.347074	−	0.937838i	$-0.612825\pi$
$929$	−21.1573	−0.694148	−0.347074	+	0.937838i	$0.612825\pi$
$930$	2.93526	0.0962510
$931$	2.80979	0.0920871
$932$	39.9668	1.30916
$933$	32.5098	1.06432
$934$	−78.2497	−2.56041
$935$	0	0
$936$	−1.45132	−0.0474378
$937$	−6.56252	−0.214388	−0.107194	−	0.994238i	$-0.534187\pi$
$937$	−6.56252	−0.214388	−0.107194	+	0.994238i	$0.534187\pi$
$938$	−16.4550	−0.537275
$939$	54.3270	1.77289
$940$	36.0222	1.17492
$941$	−18.5109	−0.603439	−0.301719	−	0.953397i	$-0.597561\pi$
$941$	−18.5109	−0.603439	−0.301719	+	0.953397i	$0.597561\pi$
$942$	−20.6771	−0.673698
$943$	−0.0696049	−0.00226665
$944$	3.44617	0.112163
$945$	−14.2935	−0.464967
$946$	−1.63699	−0.0532232
$947$	−30.7922	−1.00061	−0.500307	−	0.865848i	$-0.666779\pi$
$947$	−30.7922	−1.00061	−0.500307	+	0.865848i	$0.666779\pi$
$948$	−92.2113	−2.99488
$949$	−64.4383	−2.09176
$950$	19.4212	0.630106
$951$	12.5180	0.405924
$952$	0	0
$953$	−12.7261	−0.412240	−0.206120	−	0.978527i	$-0.566084\pi$
$953$	−12.7261	−0.412240	−0.206120	+	0.978527i	$0.566084\pi$
$954$	1.84364	0.0596900
$955$	4.91654	0.159095
$956$	−50.1809	−1.62297
$957$	4.86358	0.157217
$958$	−62.6041	−2.02265
$959$	−35.6544	−1.15134
$960$	22.1609	0.715241
$961$	−30.4259	−0.981482
$962$	100.415	3.23752
$963$	−0.372874	−0.0120157
$964$	−26.8522	−0.864850
$965$	−17.5487	−0.564912
$966$	55.8563	1.79715
$967$	6.17919	0.198709	0.0993547	−	0.995052i	$-0.468322\pi$
$967$	6.17919	0.198709	0.0993547	+	0.995052i	$0.468322\pi$
$968$	−16.7694	−0.538990
$969$	0	0
$970$	24.8270	0.797148
$971$	8.79368	0.282202	0.141101	−	0.989995i	$-0.454936\pi$
$971$	8.79368	0.282202	0.141101	+	0.989995i	$0.454936\pi$
$972$	−3.32517	−0.106655
$973$	−1.91219	−0.0613021
$974$	−24.1695	−0.774442
$975$	−9.16010	−0.293358
$976$	1.88789	0.0604298
$977$	−14.5316	−0.464906	−0.232453	−	0.972608i	$-0.574675\pi$
$977$	−14.5316	−0.464906	−0.232453	+	0.972608i	$0.574675\pi$
$978$	30.1590	0.964380
$979$	−23.7021	−0.757524
$980$	1.04569	0.0334032
$981$	−0.275966	−0.00881091
$982$	82.3870	2.62907
$983$	22.7184	0.724603	0.362302	−	0.932061i	$-0.381991\pi$
$983$	22.7184	0.724603	0.362302	+	0.932061i	$0.381991\pi$
$984$	0.0595796	0.00189933
$985$	21.7620	0.693395
$986$	0	0
$987$	52.2713	1.66381
$988$	145.876	4.64093
$989$	−1.76065	−0.0559855
$990$	−0.498955	−0.0158578
$991$	3.88859	0.123525	0.0617626	−	0.998091i	$-0.480328\pi$
$991$	3.88859	0.123525	0.0617626	+	0.998091i	$0.480328\pi$
$992$	4.50857	0.143147
$993$	−27.8472	−0.883705
$994$	−11.5250	−0.365551
$995$	0.241280	0.00764910
$996$	18.1518	0.575162
$997$	−31.1914	−0.987842	−0.493921	−	0.869507i	$-0.664437\pi$
$997$	−31.1914	−0.987842	−0.493921	+	0.869507i	$0.664437\pi$
$998$	47.4932	1.50337
$999$	43.3137	1.37039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.a.s.1.10	yes	12
5.4	even	2		7225.2.a.bn.1.3		12
17.4	even	4		1445.2.d.i.866.6		24
17.13	even	4		1445.2.d.i.866.5		24
17.16	even	2		1445.2.a.r.1.10	✓	12
85.84	even	2		7225.2.a.bo.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1445.2.a.r.1.10	✓	12	17.16	even	2
1445.2.a.s.1.10	yes	12	1.1	even	1	trivial
1445.2.d.i.866.5		24	17.13	even	4
1445.2.d.i.866.6		24	17.4	even	4
7225.2.a.bn.1.3		12	5.4	even	2
7225.2.a.bo.1.3		12	85.84	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.a (trivial)

\(f(q)\)	\(=\)	\(q+2.27524 q^{2} -1.70271 q^{3} +3.17670 q^{4} +1.00000 q^{5} -3.87408 q^{6} -2.70724 q^{7} +2.67727 q^{8} -0.100765 q^{9} +2.27524 q^{10} +2.17632 q^{11} -5.40901 q^{12} +5.37970 q^{13} -6.15962 q^{14} -1.70271 q^{15} -0.261974 q^{16} -0.229265 q^{18} +8.53588 q^{19} +3.17670 q^{20} +4.60966 q^{21} +4.95164 q^{22} +5.32570 q^{23} -4.55863 q^{24} +1.00000 q^{25} +12.2401 q^{26} +5.27972 q^{27} -8.60011 q^{28} -1.31247 q^{29} -3.87408 q^{30} -0.757667 q^{31} -5.95060 q^{32} -3.70565 q^{33} -2.70724 q^{35} -0.320102 q^{36} +8.20380 q^{37} +19.4212 q^{38} -9.16010 q^{39} +2.67727 q^{40} -0.0130696 q^{41} +10.4881 q^{42} -0.330596 q^{43} +6.91352 q^{44} -0.100765 q^{45} +12.1172 q^{46} +11.3395 q^{47} +0.446067 q^{48} +0.329174 q^{49} +2.27524 q^{50} +17.0897 q^{52} -8.04151 q^{53} +12.0126 q^{54} +2.17632 q^{55} -7.24803 q^{56} -14.5342 q^{57} -2.98619 q^{58} -13.1546 q^{59} -5.40901 q^{60} -7.20639 q^{61} -1.72387 q^{62} +0.272797 q^{63} -13.0151 q^{64} +5.37970 q^{65} -8.43123 q^{66} +2.67143 q^{67} -9.06814 q^{69} -6.15962 q^{70} +1.87106 q^{71} -0.269777 q^{72} -11.9780 q^{73} +18.6656 q^{74} -1.70271 q^{75} +27.1160 q^{76} -5.89183 q^{77} -20.8414 q^{78} +17.0477 q^{79} -0.261974 q^{80} -8.68755 q^{81} -0.0297365 q^{82} -3.35585 q^{83} +14.6435 q^{84} -0.752183 q^{86} +2.23477 q^{87} +5.82660 q^{88} -10.8909 q^{89} -0.229265 q^{90} -14.5642 q^{91} +16.9182 q^{92} +1.29009 q^{93} +25.8001 q^{94} +8.53588 q^{95} +10.1322 q^{96} +10.9119 q^{97} +0.748948 q^{98} -0.219298 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{3} + 21 q^{4} + 12 q^{5} - 9 q^{6} + 6 q^{7} + 12 q^{8} + 21 q^{9} + 3 q^{10} - 6 q^{11} + 6 q^{12} + 9 q^{13} - 18 q^{14} + 3 q^{15} + 39 q^{16} - 9 q^{18} + 27 q^{19} + 21 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 + 21 * q^4 + 12 * q^5 - 9 * q^6 + 6 * q^7 + 12 * q^8 + 21 * q^9 + 3 * q^10 - 6 * q^11 + 6 * q^12 + 9 * q^13 - 18 * q^14 + 3 * q^15 + 39 * q^16 - 9 * q^18 + 27 * q^19 + 21 * q^20 + 6 * q^21 + 15 * q^22 + 18 * q^23 - 36 * q^24 + 12 * q^25 + 6 * q^26 + 12 * q^27 + 39 * q^28 - 9 * q^30 - 6 * q^31 + 12 * q^32 + 6 * q^35 + 48 * q^36 + 21 * q^37 - 3 * q^38 - 9 * q^39 + 12 * q^40 - 15 * q^41 + 30 * q^42 + 45 * q^43 - 42 * q^44 + 21 * q^45 - 15 * q^46 + 3 * q^47 - 63 * q^48 + 12 * q^49 + 3 * q^50 + 51 * q^52 - 12 * q^53 - 27 * q^54 - 6 * q^55 + 3 * q^56 + 6 * q^57 - 51 * q^58 + 36 * q^59 + 6 * q^60 + 3 * q^61 + 36 * q^62 + 72 * q^63 + 42 * q^64 + 9 * q^65 - 39 * q^66 + 78 * q^67 - 66 * q^69 - 18 * q^70 - 30 * q^71 - 12 * q^72 - 33 * q^73 + 9 * q^74 + 3 * q^75 + 27 * q^76 - 39 * q^77 - 24 * q^78 - 3 * q^79 + 39 * q^80 + 12 * q^81 - 51 * q^82 + 27 * q^83 + 27 * q^84 + 18 * q^86 + 24 * q^87 + 36 * q^88 + 6 * q^89 - 9 * q^90 - 24 * q^91 - 3 * q^92 - 12 * q^93 + 21 * q^94 + 27 * q^95 - 39 * q^96 - 6 * q^97 - 42 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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