LMFDB - Embedded newform 637.4.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,4,Mod(1,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("637.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	637.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:	$37.5842166737$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 27x^{4} + 42x^{3} + 154x^{2} - 156x + 36 $ x^6 - 2x^5 - 27x^4 + 42x^3 + 154x^2 - 156*x + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.498984$ of defining polynomial
Character	$\chi$	$=$	637.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.498984 q^{2} +9.32638 q^{3} -7.75101 q^{4} -8.07429 q^{5} +4.65372 q^{6} -7.85951 q^{8} +59.9813 q^{9} +O(q^{10})$	\(q+0.498984 q^{2} +9.32638 q^{3} -7.75101 q^{4} -8.07429 q^{5} +4.65372 q^{6} -7.85951 q^{8} +59.9813 q^{9} -4.02894 q^{10} +4.80387 q^{11} -72.2889 q^{12} -13.0000 q^{13} -75.3039 q^{15} +58.0863 q^{16} -97.9331 q^{17} +29.9298 q^{18} -66.9456 q^{19} +62.5839 q^{20} +2.39705 q^{22} -172.737 q^{23} -73.3008 q^{24} -59.8058 q^{25} -6.48680 q^{26} +307.597 q^{27} +67.9405 q^{29} -37.5755 q^{30} -121.032 q^{31} +91.8603 q^{32} +44.8027 q^{33} -48.8671 q^{34} -464.916 q^{36} +390.408 q^{37} -33.4048 q^{38} -121.243 q^{39} +63.4600 q^{40} -69.1685 q^{41} +137.540 q^{43} -37.2348 q^{44} -484.307 q^{45} -86.1930 q^{46} -379.123 q^{47} +541.735 q^{48} -29.8422 q^{50} -913.361 q^{51} +100.763 q^{52} -194.280 q^{53} +153.486 q^{54} -38.7878 q^{55} -624.360 q^{57} +33.9013 q^{58} -265.062 q^{59} +583.682 q^{60} -598.526 q^{61} -60.3931 q^{62} -418.854 q^{64} +104.966 q^{65} +22.3558 q^{66} -736.018 q^{67} +759.081 q^{68} -1611.01 q^{69} +466.787 q^{71} -471.424 q^{72} +356.163 q^{73} +194.808 q^{74} -557.772 q^{75} +518.896 q^{76} -60.4983 q^{78} -1180.25 q^{79} -469.006 q^{80} +1249.27 q^{81} -34.5140 q^{82} -918.306 q^{83} +790.740 q^{85} +68.6302 q^{86} +633.639 q^{87} -37.7560 q^{88} -1210.55 q^{89} -241.662 q^{90} +1338.89 q^{92} -1128.79 q^{93} -189.177 q^{94} +540.538 q^{95} +856.724 q^{96} +1182.63 q^{97} +288.142 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 13 q^{3} + 10 q^{4} - 26 q^{5} - 3 q^{6} + 12 q^{8} + 111 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 - 13 * q^3 + 10 * q^4 - 26 * q^5 - 3 * q^6 + 12 * q^8 + 111 * q^9	\( 6 q + 2 q^{2} - 13 q^{3} + 10 q^{4} - 26 q^{5} - 3 q^{6} + 12 q^{8} + 111 q^{9} + 32 q^{10} + 11 q^{11} - 141 q^{12} - 78 q^{13} + 64 q^{15} - 54 q^{16} - 210 q^{17} + 65 q^{18} - 78 q^{19} - 38 q^{20} + 125 q^{22} - 75 q^{23} + 189 q^{24} + 90 q^{25} - 26 q^{26} - 31 q^{27} + 306 q^{29} - 864 q^{30} + 93 q^{31} + 108 q^{32} + 393 q^{33} + 706 q^{34} - 317 q^{36} - 611 q^{37} + 516 q^{38} + 169 q^{39} + 230 q^{40} - 131 q^{41} - 88 q^{43} - 1261 q^{44} - 566 q^{45} - 567 q^{46} - 587 q^{47} + 1279 q^{48} - 1140 q^{50} - 892 q^{51} - 130 q^{52} + 770 q^{53} - 645 q^{54} + 624 q^{55} - 1602 q^{57} - 824 q^{58} - 934 q^{59} + 888 q^{60} - 1629 q^{61} - 1207 q^{62} - 1622 q^{64} + 338 q^{65} - 2025 q^{66} + 263 q^{67} - 1986 q^{68} - 1425 q^{69} + 1032 q^{71} - 3129 q^{72} - 819 q^{73} + 1555 q^{74} - 2003 q^{75} + 1894 q^{76} + 39 q^{78} - 2169 q^{79} - 2074 q^{80} + 3222 q^{81} - 1225 q^{82} - 1580 q^{83} + 216 q^{85} - 1378 q^{86} - 2372 q^{87} + 861 q^{88} - 1244 q^{89} + 5648 q^{90} + 1369 q^{92} - 1685 q^{93} - 3439 q^{94} + 3052 q^{95} - 227 q^{96} + 1643 q^{97} - 2950 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 13 * q^3 + 10 * q^4 - 26 * q^5 - 3 * q^6 + 12 * q^8 + 111 * q^9 + 32 * q^10 + 11 * q^11 - 141 * q^12 - 78 * q^13 + 64 * q^15 - 54 * q^16 - 210 * q^17 + 65 * q^18 - 78 * q^19 - 38 * q^20 + 125 * q^22 - 75 * q^23 + 189 * q^24 + 90 * q^25 - 26 * q^26 - 31 * q^27 + 306 * q^29 - 864 * q^30 + 93 * q^31 + 108 * q^32 + 393 * q^33 + 706 * q^34 - 317 * q^36 - 611 * q^37 + 516 * q^38 + 169 * q^39 + 230 * q^40 - 131 * q^41 - 88 * q^43 - 1261 * q^44 - 566 * q^45 - 567 * q^46 - 587 * q^47 + 1279 * q^48 - 1140 * q^50 - 892 * q^51 - 130 * q^52 + 770 * q^53 - 645 * q^54 + 624 * q^55 - 1602 * q^57 - 824 * q^58 - 934 * q^59 + 888 * q^60 - 1629 * q^61 - 1207 * q^62 - 1622 * q^64 + 338 * q^65 - 2025 * q^66 + 263 * q^67 - 1986 * q^68 - 1425 * q^69 + 1032 * q^71 - 3129 * q^72 - 819 * q^73 + 1555 * q^74 - 2003 * q^75 + 1894 * q^76 + 39 * q^78 - 2169 * q^79 - 2074 * q^80 + 3222 * q^81 - 1225 * q^82 - 1580 * q^83 + 216 * q^85 - 1378 * q^86 - 2372 * q^87 + 861 * q^88 - 1244 * q^89 + 5648 * q^90 + 1369 * q^92 - 1685 * q^93 - 3439 * q^94 + 3052 * q^95 - 227 * q^96 + 1643 * q^97 - 2950 * 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 $

$2$	0.498984	0.176418	0.0882088	−	0.996102i	$-0.471886\pi$
$2$	0.498984	0.176418	0.0882088	+	0.996102i	$0.471886\pi$
$3$	9.32638	1.79486	0.897431	−	0.441154i	$-0.145431\pi$
$3$	9.32638	1.79486	0.897431	+	0.441154i	$0.145431\pi$
$4$	−7.75101	−0.968877
$5$	−8.07429	−0.722187	−0.361093	−	0.932530i	$-0.617596\pi$
$5$	−8.07429	−0.722187	−0.361093	+	0.932530i	$0.617596\pi$
$6$	4.65372	0.316645
$7$	0	0
$7$	0	0
$8$	−7.85951	−0.347345
$9$	59.9813	2.22153
$10$	−4.02894	−0.127406
$11$	4.80387	0.131675	0.0658373	−	0.997830i	$-0.479028\pi$
$11$	4.80387	0.131675	0.0658373	+	0.997830i	$0.479028\pi$
$12$	−72.2889	−1.73900
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	0	0
$15$	−75.3039	−1.29623
$16$	58.0863	0.907599
$17$	−97.9331	−1.39719	−0.698596	−	0.715516i	$-0.746192\pi$
$17$	−97.9331	−1.39719	−0.698596	+	0.715516i	$0.746192\pi$
$18$	29.9298	0.391917
$19$	−66.9456	−0.808335	−0.404168	−	0.914685i	$-0.632439\pi$
$19$	−66.9456	−0.808335	−0.404168	+	0.914685i	$0.632439\pi$
$20$	62.5839	0.699710
$21$	0	0
$22$	2.39705	0.0232297
$23$	−172.737	−1.56601	−0.783003	−	0.622018i	$-0.786313\pi$
$23$	−172.737	−1.56601	−0.783003	+	0.622018i	$0.786313\pi$
$24$	−73.3008	−0.623436
$25$	−59.8058	−0.478447
$26$	−6.48680	−0.0489294
$27$	307.597	2.19248
$28$	0	0
$29$	67.9405	0.435043	0.217521	−	0.976056i	$-0.430203\pi$
$29$	67.9405	0.435043	0.217521	+	0.976056i	$0.430203\pi$
$30$	−37.5755	−0.228677
$31$	−121.032	−0.701225	−0.350613	−	0.936521i	$-0.614027\pi$
$31$	−121.032	−0.701225	−0.350613	+	0.936521i	$0.614027\pi$
$32$	91.8603	0.507461
$33$	44.8027	0.236338
$34$	−48.8671	−0.246489
$35$	0	0
$36$	−464.916	−2.15239
$37$	390.408	1.73467	0.867334	−	0.497727i	$-0.165832\pi$
$37$	390.408	1.73467	0.867334	+	0.497727i	$0.165832\pi$
$38$	−33.4048	−0.142605
$39$	−121.243	−0.497805
$40$	63.4600	0.250848
$41$	−69.1685	−0.263471	−0.131735	−	0.991285i	$-0.542055\pi$
$41$	−69.1685	−0.263471	−0.131735	+	0.991285i	$0.542055\pi$
$42$	0	0
$43$	137.540	0.487782	0.243891	−	0.969803i	$-0.421576\pi$
$43$	137.540	0.487782	0.243891	+	0.969803i	$0.421576\pi$
$44$	−37.2348	−0.127576
$45$	−484.307	−1.60436
$46$	−86.1930	−0.276271
$47$	−379.123	−1.17661	−0.588307	−	0.808638i	$-0.700205\pi$
$47$	−379.123	−1.17661	−0.588307	+	0.808638i	$0.700205\pi$
$48$	541.735	1.62902
$49$	0	0
$50$	−29.8422	−0.0844064
$51$	−913.361	−2.50777
$52$	100.763	0.268718
$53$	−194.280	−0.503517	−0.251758	−	0.967790i	$-0.581009\pi$
$53$	−194.280	−0.503517	−0.251758	+	0.967790i	$0.581009\pi$
$54$	153.486	0.386792
$55$	−38.7878	−0.0950936
$56$	0	0
$57$	−624.360	−1.45085
$58$	33.9013	0.0767492
$59$	−265.062	−0.584884	−0.292442	−	0.956283i	$-0.594468\pi$
$59$	−265.062	−0.584884	−0.292442	+	0.956283i	$0.594468\pi$
$60$	583.682	1.25588
$61$	−598.526	−1.25629	−0.628143	−	0.778098i	$-0.716185\pi$
$61$	−598.526	−1.25629	−0.628143	+	0.778098i	$0.716185\pi$
$62$	−60.3931	−0.123709
$63$	0	0
$64$	−418.854	−0.818074
$65$	104.966	0.200298
$66$	22.3558	0.0416941
$67$	−736.018	−1.34207	−0.671037	−	0.741424i	$-0.734151\pi$
$67$	−736.018	−1.34207	−0.671037	+	0.741424i	$0.734151\pi$
$68$	759.081	1.35371
$69$	−1611.01	−2.81076
$70$	0	0
$71$	466.787	0.780245	0.390123	−	0.920763i	$-0.372433\pi$
$71$	466.787	0.780245	0.390123	+	0.920763i	$0.372433\pi$
$72$	−471.424	−0.771637
$73$	356.163	0.571037	0.285519	−	0.958373i	$-0.407834\pi$
$73$	356.163	0.571037	0.285519	+	0.958373i	$0.407834\pi$
$74$	194.808	0.306026
$75$	−557.772	−0.858746
$76$	518.896	0.783177
$77$	0	0
$78$	−60.4983	−0.0878216
$79$	−1180.25	−1.68086	−0.840430	−	0.541920i	$-0.817698\pi$
$79$	−1180.25	−1.68086	−0.840430	+	0.541920i	$0.817698\pi$
$80$	−469.006	−0.655456
$81$	1249.27	1.71367
$82$	−34.5140	−0.0464809
$83$	−918.306	−1.21442	−0.607212	−	0.794540i	$-0.707712\pi$
$83$	−918.306	−1.21442	−0.607212	+	0.794540i	$0.707712\pi$
$84$	0	0
$85$	790.740	1.00903
$86$	68.6302	0.0860533
$87$	633.639	0.780842
$88$	−37.7560	−0.0457364
$89$	−1210.55	−1.44178	−0.720890	−	0.693050i	$-0.756267\pi$
$89$	−1210.55	−1.44178	−0.720890	+	0.693050i	$0.756267\pi$
$90$	−241.662	−0.283037
$91$	0	0
$92$	1338.89	1.51727
$93$	−1128.79	−1.25860
$94$	−189.177	−0.207575
$95$	540.538	0.583769
$96$	856.724	0.910823
$97$	1182.63	1.23792	0.618959	−	0.785423i	$-0.287555\pi$
$97$	1182.63	1.23792	0.618959	+	0.785423i	$0.287555\pi$
$98$	0	0
$99$	288.142	0.292519
$100$	463.556	0.463556
$101$	1061.33	1.04561	0.522803	−	0.852454i	$-0.324886\pi$
$101$	1061.33	1.04561	0.522803	+	0.852454i	$0.324886\pi$
$102$	−455.753	−0.442414
$103$	747.833	0.715400	0.357700	−	0.933837i	$-0.383561\pi$
$103$	747.833	0.715400	0.357700	+	0.933837i	$0.383561\pi$
$104$	102.174	0.0963360
$105$	0	0
$106$	−96.9426	−0.0888293
$107$	−798.274	−0.721234	−0.360617	−	0.932714i	$-0.617434\pi$
$107$	−798.274	−0.721234	−0.360617	+	0.932714i	$0.617434\pi$
$108$	−2384.19	−2.12424
$109$	2131.27	1.87283	0.936415	−	0.350893i	$-0.114122\pi$
$109$	2131.27	1.87283	0.936415	+	0.350893i	$0.114122\pi$
$110$	−19.3545	−0.0167762
$111$	3641.09	3.11349
$112$	0	0
$113$	1611.51	1.34158	0.670788	−	0.741649i	$-0.265956\pi$
$113$	1611.51	1.34158	0.670788	+	0.741649i	$0.265956\pi$
$114$	−311.546	−0.255956
$115$	1394.73	1.13095
$116$	−526.608	−0.421503
$117$	−779.758	−0.616142
$118$	−132.262	−0.103184
$119$	0	0
$120$	591.852	0.450237
$121$	−1307.92	−0.982662
$122$	−298.655	−0.221631
$123$	−645.092	−0.472894
$124$	938.121	0.679401
$125$	1492.18	1.06771
$126$	0	0
$127$	−1490.49	−1.04141	−0.520707	−	0.853736i	$-0.674332\pi$
$127$	−1490.49	−1.04141	−0.520707	+	0.853736i	$0.674332\pi$
$128$	−943.884	−0.651784
$129$	1282.75	0.875501
$130$	52.3763	0.0353362
$131$	−2017.09	−1.34530	−0.672648	−	0.739962i	$-0.734843\pi$
$131$	−2017.09	−1.34530	−0.672648	+	0.739962i	$0.734843\pi$
$132$	−347.266	−0.228982
$133$	0	0
$134$	−367.262	−0.236765
$135$	−2483.62	−1.58338
$136$	769.706	0.485307
$137$	−1850.70	−1.15413	−0.577064	−	0.816699i	$-0.695802\pi$
$137$	−1850.70	−1.15413	−0.577064	+	0.816699i	$0.695802\pi$
$138$	−803.869	−0.495868
$139$	579.629	0.353694	0.176847	−	0.984238i	$-0.443410\pi$
$139$	579.629	0.353694	0.176847	+	0.984238i	$0.443410\pi$
$140$	0	0
$141$	−3535.85	−2.11186
$142$	232.919	0.137649
$143$	−62.4503	−0.0365200
$144$	3484.10	2.01626
$145$	−548.572	−0.314182
$146$	177.720	0.100741
$147$	0	0
$148$	−3026.06	−1.68068
$149$	3576.63	1.96650	0.983250	−	0.182260i	$-0.0583412\pi$
$149$	3576.63	1.96650	0.983250	+	0.182260i	$0.0583412\pi$
$150$	−278.319	−0.151498
$151$	1175.81	0.633681	0.316841	−	0.948479i	$-0.397378\pi$
$151$	1175.81	0.633681	0.316841	+	0.948479i	$0.397378\pi$
$152$	526.160	0.280771
$153$	−5874.16	−3.10391
$154$	0	0
$155$	977.247	0.506415
$156$	939.756	0.482312
$157$	−593.770	−0.301835	−0.150917	−	0.988546i	$-0.548223\pi$
$157$	−593.770	−0.301835	−0.150917	+	0.988546i	$0.548223\pi$
$158$	−588.924	−0.296533
$159$	−1811.93	−0.903744
$160$	−741.706	−0.366482
$161$	0	0
$162$	623.364	0.302322
$163$	2047.35	0.983807	0.491904	−	0.870650i	$-0.336301\pi$
$163$	2047.35	0.983807	0.491904	+	0.870650i	$0.336301\pi$
$164$	536.126	0.255271
$165$	−361.750	−0.170680
$166$	−458.221	−0.214246
$167$	1782.34	0.825877	0.412938	−	0.910759i	$-0.364502\pi$
$167$	1782.34	0.825877	0.412938	+	0.910759i	$0.364502\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	394.567	0.178011
$171$	−4015.49	−1.79574
$172$	−1066.07	−0.472600
$173$	2724.75	1.19745	0.598725	−	0.800955i	$-0.295674\pi$
$173$	2724.75	1.19745	0.598725	+	0.800955i	$0.295674\pi$
$174$	316.176	0.137754
$175$	0	0
$176$	279.039	0.119508
$177$	−2472.07	−1.04979
$178$	−604.047	−0.254355
$179$	1386.87	0.579102	0.289551	−	0.957163i	$-0.406494\pi$
$179$	1386.87	0.579102	0.289551	+	0.957163i	$0.406494\pi$
$180$	3753.87	1.55443
$181$	1048.63	0.430632	0.215316	−	0.976544i	$-0.430922\pi$
$181$	1048.63	0.430632	0.215316	+	0.976544i	$0.430922\pi$
$182$	0	0
$183$	−5582.08	−2.25486
$184$	1357.63	0.543944
$185$	−3152.27	−1.25275
$186$	−563.249	−0.222040
$187$	−470.458	−0.183975
$188$	2938.59	1.13999
$189$	0	0
$190$	269.720	0.102987
$191$	254.456	0.0963968	0.0481984	−	0.998838i	$-0.484652\pi$
$191$	254.456	0.0963968	0.0481984	+	0.998838i	$0.484652\pi$
$192$	−3906.39	−1.46833
$193$	−1301.28	−0.485329	−0.242664	−	0.970110i	$-0.578021\pi$
$193$	−1301.28	−0.485329	−0.242664	+	0.970110i	$0.578021\pi$
$194$	590.115	0.218391
$195$	978.951	0.359508
$196$	0	0
$197$	2810.41	1.01641	0.508207	−	0.861235i	$-0.330308\pi$
$197$	2810.41	1.01641	0.508207	+	0.861235i	$0.330308\pi$
$198$	143.779	0.0516055
$199$	−2581.61	−0.919624	−0.459812	−	0.888016i	$-0.652083\pi$
$199$	−2581.61	−0.919624	−0.459812	+	0.888016i	$0.652083\pi$
$200$	470.045	0.166186
$201$	−6864.38	−2.40884
$202$	529.587	0.184463
$203$	0	0
$204$	7079.48	2.42972
$205$	558.487	0.190275
$206$	373.157	0.126209
$207$	−10361.0	−3.47893
$208$	−755.122	−0.251723
$209$	−321.598	−0.106437
$210$	0	0
$211$	1358.19	0.443137	0.221569	−	0.975145i	$-0.428882\pi$
$211$	1358.19	0.443137	0.221569	+	0.975145i	$0.428882\pi$
$212$	1505.87	0.487846
$213$	4353.43	1.40043
$214$	−398.326	−0.127238
$215$	−1110.54	−0.352269
$216$	−2417.56	−0.761546
$217$	0	0
$218$	1063.47	0.330400
$219$	3321.71	1.02493
$220$	300.645	0.0921340
$221$	1273.13	0.387511
$222$	1816.85	0.549274
$223$	443.825	0.133277	0.0666384	−	0.997777i	$-0.478773\pi$
$223$	443.825	0.133277	0.0666384	+	0.997777i	$0.478773\pi$
$224$	0	0
$225$	−3587.23	−1.06288
$226$	804.119	0.236678
$227$	−3698.86	−1.08151	−0.540754	−	0.841181i	$-0.681861\pi$
$227$	−3698.86	−1.08151	−0.540754	+	0.841181i	$0.681861\pi$
$228$	4839.42	1.40570
$229$	5495.63	1.58586	0.792928	−	0.609315i	$-0.208555\pi$
$229$	5495.63	1.58586	0.792928	+	0.609315i	$0.208555\pi$
$230$	695.947	0.199519
$231$	0	0
$232$	−533.979	−0.151110
$233$	−307.332	−0.0864118	−0.0432059	−	0.999066i	$-0.513757\pi$
$233$	−307.332	−0.0864118	−0.0432059	+	0.999066i	$0.513757\pi$
$234$	−389.087	−0.108698
$235$	3061.15	0.849734
$236$	2054.50	0.566681
$237$	−11007.4	−3.01691
$238$	0	0
$239$	4292.30	1.16170	0.580849	−	0.814011i	$-0.302721\pi$
$239$	4292.30	1.16170	0.580849	+	0.814011i	$0.302721\pi$
$240$	−4374.13	−1.17645
$241$	2990.00	0.799181	0.399590	−	0.916694i	$-0.369152\pi$
$241$	2990.00	0.799181	0.399590	+	0.916694i	$0.369152\pi$
$242$	−652.633	−0.173359
$243$	3346.02	0.883322
$244$	4639.19	1.21719
$245$	0	0
$246$	−321.891	−0.0834268
$247$	870.293	0.224192
$248$	951.252	0.243567
$249$	−8564.47	−2.17972
$250$	744.573	0.188364
$251$	−1362.09	−0.342526	−0.171263	−	0.985225i	$-0.554785\pi$
$251$	−1362.09	−0.342526	−0.171263	+	0.985225i	$0.554785\pi$
$252$	0	0
$253$	−829.805	−0.206203
$254$	−743.731	−0.183724
$255$	7374.74	1.81108
$256$	2879.85	0.703088
$257$	−53.1148	−0.0128919	−0.00644593	−	0.999979i	$-0.502052\pi$
$257$	−53.1148	−0.0128919	−0.00644593	+	0.999979i	$0.502052\pi$
$258$	640.071	0.154454
$259$	0	0
$260$	−813.591	−0.194065
$261$	4075.16	0.966461
$262$	−1006.50	−0.237334
$263$	−4647.83	−1.08972	−0.544862	−	0.838526i	$-0.683418\pi$
$263$	−4647.83	−1.08972	−0.544862	+	0.838526i	$0.683418\pi$
$264$	−352.127	−0.0820906
$265$	1568.67	0.363633
$266$	0	0
$267$	−11290.1	−2.58780
$268$	5704.89	1.30030
$269$	3037.17	0.688400	0.344200	−	0.938896i	$-0.388150\pi$
$269$	3037.17	0.688400	0.344200	+	0.938896i	$0.388150\pi$
$270$	−1239.29	−0.279336
$271$	−3196.97	−0.716613	−0.358307	−	0.933604i	$-0.616646\pi$
$271$	−3196.97	−0.716613	−0.358307	+	0.933604i	$0.616646\pi$
$272$	−5688.58	−1.26809
$273$	0	0
$274$	−923.468	−0.203609
$275$	−287.299	−0.0629993
$276$	12487.0	2.72328
$277$	−6798.84	−1.47474	−0.737370	−	0.675489i	$-0.763933\pi$
$277$	−6798.84	−1.47474	−0.737370	+	0.675489i	$0.763933\pi$
$278$	289.226	0.0623979
$279$	−7259.66	−1.55779
$280$	0	0
$281$	−1119.40	−0.237644	−0.118822	−	0.992916i	$-0.537912\pi$
$281$	−1119.40	−0.237644	−0.118822	+	0.992916i	$0.537912\pi$
$282$	−1764.33	−0.372569
$283$	8480.95	1.78141	0.890707	−	0.454577i	$-0.150210\pi$
$283$	8480.95	1.78141	0.890707	+	0.454577i	$0.150210\pi$
$284$	−3618.07	−0.755961
$285$	5041.26	1.04778
$286$	−31.1617	−0.00644276
$287$	0	0
$288$	5509.90	1.12734
$289$	4677.89	0.952146
$290$	−273.729	−0.0554272
$291$	11029.7	2.22189
$292$	−2760.63	−0.553265
$293$	3538.23	0.705480	0.352740	−	0.935721i	$-0.385250\pi$
$293$	3538.23	0.705480	0.352740	+	0.935721i	$0.385250\pi$
$294$	0	0
$295$	2140.19	0.422396
$296$	−3068.42	−0.602527
$297$	1477.65	0.288694
$298$	1784.68	0.346925
$299$	2245.58	0.434332
$300$	4323.30	0.832019
$301$	0	0
$302$	586.710	0.111793
$303$	9898.36	1.87672
$304$	−3888.62	−0.733644
$305$	4832.67	0.907273
$306$	−2931.11	−0.547584
$307$	3579.95	0.665533	0.332766	−	0.943009i	$-0.392018\pi$
$307$	3579.95	0.665533	0.332766	+	0.943009i	$0.392018\pi$
$308$	0	0
$309$	6974.58	1.28404
$310$	487.631	0.0893406
$311$	−1863.22	−0.339723	−0.169861	−	0.985468i	$-0.554332\pi$
$311$	−1863.22	−0.339723	−0.169861	+	0.985468i	$0.554332\pi$
$312$	952.910	0.172910
$313$	−6847.42	−1.23655	−0.618273	−	0.785963i	$-0.712167\pi$
$313$	−6847.42	−1.23655	−0.618273	+	0.785963i	$0.712167\pi$
$314$	−296.282	−0.0532490
$315$	0	0
$316$	9148.10	1.62855
$317$	2279.20	0.403825	0.201913	−	0.979404i	$-0.435284\pi$
$317$	2279.20	0.403825	0.201913	+	0.979404i	$0.435284\pi$
$318$	−904.124	−0.159436
$319$	326.377	0.0572841
$320$	3381.95	0.590802
$321$	−7445.01	−1.29452
$322$	0	0
$323$	6556.19	1.12940
$324$	−9683.08	−1.66034
$325$	777.476	0.132697
$326$	1021.59	0.173561
$327$	19877.0	3.36147
$328$	543.630	0.0915152
$329$	0	0
$330$	−180.508	−0.0301109
$331$	−20.7440	−0.00344469	−0.00172235	−	0.999999i	$-0.500548\pi$
$331$	−20.7440	−0.00344469	−0.00172235	+	0.999999i	$0.500548\pi$
$332$	7117.81	1.17663
$333$	23417.2	3.85362
$334$	889.359	0.145699
$335$	5942.82	0.969227
$336$	0	0
$337$	1587.59	0.256622	0.128311	−	0.991734i	$-0.459044\pi$
$337$	1587.59	0.256622	0.128311	+	0.991734i	$0.459044\pi$
$338$	84.3284	0.0135706
$339$	15029.6	2.40795
$340$	−6129.04	−0.977629
$341$	−581.421	−0.0923335
$342$	−2003.67	−0.316801
$343$	0	0
$344$	−1080.99	−0.169428
$345$	13007.8	2.02990
$346$	1359.61	0.211251
$347$	−3132.88	−0.484673	−0.242337	−	0.970192i	$-0.577914\pi$
$347$	−3132.88	−0.484673	−0.242337	+	0.970192i	$0.577914\pi$
$348$	−4911.35	−0.756540
$349$	−6402.55	−0.982008	−0.491004	−	0.871157i	$-0.663370\pi$
$349$	−6402.55	−0.982008	−0.491004	+	0.871157i	$0.663370\pi$
$350$	0	0
$351$	−3998.76	−0.608085
$352$	441.284	0.0668197
$353$	−9857.49	−1.48629	−0.743146	−	0.669129i	$-0.766667\pi$
$353$	−9857.49	−1.48629	−0.743146	+	0.669129i	$0.766667\pi$
$354$	−1233.53	−0.185201
$355$	−3768.97	−0.563482
$356$	9383.02	1.39691
$357$	0	0
$358$	692.024	0.102164
$359$	−1859.11	−0.273314	−0.136657	−	0.990618i	$-0.543636\pi$
$359$	−1859.11	−0.273314	−0.136657	+	0.990618i	$0.543636\pi$
$360$	3806.41	0.557266
$361$	−2377.29	−0.346594
$362$	523.252	0.0759710
$363$	−12198.2	−1.76374
$364$	0	0
$365$	−2875.76	−0.412396
$366$	−2785.37	−0.397797
$367$	−2741.52	−0.389936	−0.194968	−	0.980810i	$-0.562460\pi$
$367$	−2741.52	−0.389936	−0.194968	+	0.980810i	$0.562460\pi$
$368$	−10033.7	−1.42131
$369$	−4148.82	−0.585309
$370$	−1572.93	−0.221008
$371$	0	0
$372$	8749.27	1.21943
$373$	−7976.12	−1.10721	−0.553603	−	0.832781i	$-0.686747\pi$
$373$	−7976.12	−1.10721	−0.553603	+	0.832781i	$0.686747\pi$
$374$	−234.751	−0.0324564
$375$	13916.6	1.91640
$376$	2979.72	0.408690
$377$	−883.227	−0.120659
$378$	0	0
$379$	−2104.33	−0.285203	−0.142602	−	0.989780i	$-0.545547\pi$
$379$	−2104.33	−0.285203	−0.142602	+	0.989780i	$0.545547\pi$
$380$	−4189.72	−0.565600
$381$	−13900.9	−1.86919
$382$	126.970	0.0170061
$383$	10516.0	1.40298	0.701489	−	0.712680i	$-0.252519\pi$
$383$	10516.0	1.40298	0.701489	+	0.712680i	$0.252519\pi$
$384$	−8803.02	−1.16986
$385$	0	0
$386$	−649.320	−0.0856205
$387$	8249.82	1.08362
$388$	−9166.60	−1.19939
$389$	−11758.2	−1.53255	−0.766276	−	0.642512i	$-0.777892\pi$
$389$	−11758.2	−1.53255	−0.766276	+	0.642512i	$0.777892\pi$
$390$	488.481	0.0634236
$391$	16916.7	2.18801
$392$	0	0
$393$	−18812.1	−2.41462
$394$	1402.35	0.179313
$395$	9529.65	1.21389
$396$	−2233.40	−0.283415
$397$	−7569.57	−0.956942	−0.478471	−	0.878103i	$-0.658809\pi$
$397$	−7569.57	−0.956942	−0.478471	+	0.878103i	$0.658809\pi$
$398$	−1288.18	−0.162238
$399$	0	0
$400$	−3473.90	−0.434238
$401$	−7149.74	−0.890376	−0.445188	−	0.895437i	$-0.646863\pi$
$401$	−7149.74	−0.890376	−0.445188	+	0.895437i	$0.646863\pi$
$402$	−3425.22	−0.424961
$403$	1573.42	0.194485
$404$	−8226.38	−1.01306
$405$	−10086.9	−1.23759
$406$	0	0
$407$	1875.47	0.228412
$408$	7178.57	0.871060
$409$	7661.05	0.926197	0.463099	−	0.886307i	$-0.346738\pi$
$409$	7661.05	0.926197	0.463099	+	0.886307i	$0.346738\pi$
$410$	278.676	0.0335679
$411$	−17260.3	−2.07150
$412$	−5796.47	−0.693135
$413$	0	0
$414$	−5169.97	−0.613745
$415$	7414.67	0.877041
$416$	−1194.18	−0.140744
$417$	5405.84	0.634833
$418$	−160.472	−0.0187774
$419$	1356.97	0.158215	0.0791077	−	0.996866i	$-0.474793\pi$
$419$	1356.97	0.158215	0.0791077	+	0.996866i	$0.474793\pi$
$420$	0	0
$421$	323.713	0.0374746	0.0187373	−	0.999824i	$-0.494035\pi$
$421$	323.713	0.0374746	0.0187373	+	0.999824i	$0.494035\pi$
$422$	677.718	0.0781772
$423$	−22740.3	−2.61388
$424$	1526.94	0.174894
$425$	5856.97	0.668482
$426$	2172.29	0.247061
$427$	0	0
$428$	6187.43	0.698787
$429$	−582.435	−0.0655483
$430$	−554.140	−0.0621465
$431$	−14302.5	−1.59844	−0.799219	−	0.601040i	$-0.794753\pi$
$431$	−14302.5	−1.59844	−0.799219	+	0.601040i	$0.794753\pi$
$432$	17867.2	1.98989
$433$	839.457	0.0931680	0.0465840	−	0.998914i	$-0.485166\pi$
$433$	839.457	0.0931680	0.0465840	+	0.998914i	$0.485166\pi$
$434$	0	0
$435$	−5116.19	−0.563914
$436$	−16519.5	−1.81454
$437$	11564.0	1.26586
$438$	1657.48	0.180816
$439$	−147.133	−0.0159961	−0.00799804	−	0.999968i	$-0.502546\pi$
$439$	−147.133	−0.0159961	−0.00799804	+	0.999968i	$0.502546\pi$
$440$	304.853	0.0330302
$441$	0	0
$442$	635.272	0.0683638
$443$	12368.3	1.32649	0.663245	−	0.748403i	$-0.269179\pi$
$443$	12368.3	1.32649	0.663245	+	0.748403i	$0.269179\pi$
$444$	−28222.2	−3.01659
$445$	9774.36	1.04123
$446$	221.462	0.0235124
$447$	33357.0	3.52960
$448$	0	0
$449$	−15350.0	−1.61339	−0.806696	−	0.590966i	$-0.798747\pi$
$449$	−15350.0	−1.61339	−0.806696	+	0.590966i	$0.798747\pi$
$450$	−1789.97	−0.187512
$451$	−332.276	−0.0346924
$452$	−12490.8	−1.29982
$453$	10966.0	1.13737
$454$	−1845.67	−0.190797
$455$	0	0
$456$	4907.16	0.503945
$457$	−12693.1	−1.29925	−0.649626	−	0.760254i	$-0.725074\pi$
$457$	−12693.1	−1.29925	−0.649626	+	0.760254i	$0.725074\pi$
$458$	2742.23	0.279773
$459$	−30123.9	−3.06332
$460$	−10810.6	−1.09575
$461$	−10497.5	−1.06055	−0.530277	−	0.847824i	$-0.677912\pi$
$461$	−10497.5	−1.06055	−0.530277	+	0.847824i	$0.677912\pi$
$462$	0	0
$463$	−7100.07	−0.712674	−0.356337	−	0.934357i	$-0.615975\pi$
$463$	−7100.07	−0.712674	−0.356337	+	0.934357i	$0.615975\pi$
$464$	3946.42	0.394844
$465$	9114.18	0.908946
$466$	−153.354	−0.0152446
$467$	−17727.0	−1.75655	−0.878275	−	0.478155i	$-0.841306\pi$
$467$	−17727.0	−1.75655	−0.878275	+	0.478155i	$0.841306\pi$
$468$	6043.91	0.596966
$469$	0	0
$470$	1527.47	0.149908
$471$	−5537.73	−0.541752
$472$	2083.26	0.203156
$473$	660.722	0.0642284
$474$	−5492.53	−0.532237
$475$	4003.74	0.386745
$476$	0	0
$477$	−11653.2	−1.11858
$478$	2141.79	0.204944
$479$	−7303.00	−0.696623	−0.348311	−	0.937379i	$-0.613245\pi$
$479$	−7303.00	−0.696623	−0.348311	+	0.937379i	$0.613245\pi$
$480$	−6917.44	−0.657784
$481$	−5075.30	−0.481110
$482$	1491.96	0.140990
$483$	0	0
$484$	10137.7	0.952078
$485$	−9548.92	−0.894008
$486$	1669.61	0.155834
$487$	−16002.9	−1.48904	−0.744519	−	0.667601i	$-0.767321\pi$
$487$	−16002.9	−1.48904	−0.744519	+	0.667601i	$0.767321\pi$
$488$	4704.12	0.436364
$489$	19094.3	1.76580
$490$	0	0
$491$	5992.16	0.550759	0.275379	−	0.961336i	$-0.411197\pi$
$491$	5992.16	0.550759	0.275379	+	0.961336i	$0.411197\pi$
$492$	5000.11	0.458176
$493$	−6653.63	−0.607838
$494$	434.262	0.0395514
$495$	−2326.55	−0.211253
$496$	−7030.30	−0.636431
$497$	0	0
$498$	−4273.54	−0.384542
$499$	19155.2	1.71844	0.859222	−	0.511603i	$-0.170948\pi$
$499$	19155.2	1.71844	0.859222	+	0.511603i	$0.170948\pi$
$500$	−11565.9	−1.03448
$501$	16622.8	1.48234
$502$	−679.660	−0.0604277
$503$	−1021.16	−0.0905195	−0.0452598	−	0.998975i	$-0.514412\pi$
$503$	−1021.16	−0.0905195	−0.0452598	+	0.998975i	$0.514412\pi$
$504$	0	0
$505$	−8569.48	−0.755122
$506$	−414.060	−0.0363779
$507$	1576.16	0.138066
$508$	11552.8	1.00900
$509$	11145.0	0.970516	0.485258	−	0.874371i	$-0.338726\pi$
$509$	11145.0	0.970516	0.485258	+	0.874371i	$0.338726\pi$
$510$	3679.88	0.319506
$511$	0	0
$512$	8988.07	0.775821
$513$	−20592.2	−1.77226
$514$	−26.5034	−0.00227435
$515$	−6038.22	−0.516652
$516$	−9942.59	−0.848253
$517$	−1821.26	−0.154930
$518$	0	0
$519$	25412.0	2.14926
$520$	−824.980	−0.0695726
$521$	−19706.0	−1.65707	−0.828536	−	0.559936i	$-0.810826\pi$
$521$	−19706.0	−1.65707	−0.828536	+	0.559936i	$0.810826\pi$
$522$	2033.44	0.170501
$523$	16486.8	1.37843	0.689214	−	0.724558i	$-0.257956\pi$
$523$	16486.8	1.37843	0.689214	+	0.724558i	$0.257956\pi$
$524$	15634.5	1.30343
$525$	0	0
$526$	−2319.19	−0.192246
$527$	11853.0	0.979747
$528$	2602.42	0.214500
$529$	17671.0	1.45237
$530$	782.743	0.0641513
$531$	−15898.8	−1.29934
$532$	0	0
$533$	899.190	0.0730737
$534$	−5633.57	−0.456533
$535$	6445.50	0.520866
$536$	5784.74	0.466162
$537$	12934.4	1.03941
$538$	1515.50	0.121446
$539$	0	0
$540$	19250.6	1.53410
$541$	−1272.78	−0.101148	−0.0505741	−	0.998720i	$-0.516105\pi$
$541$	−1272.78	−0.101148	−0.0505741	+	0.998720i	$0.516105\pi$
$542$	−1595.24	−0.126423
$543$	9779.96	0.772925
$544$	−8996.16	−0.709021
$545$	−17208.5	−1.35253
$546$	0	0
$547$	2605.36	0.203651	0.101826	−	0.994802i	$-0.467532\pi$
$547$	2605.36	0.203651	0.101826	+	0.994802i	$0.467532\pi$
$548$	14344.8	1.11821
$549$	−35900.4	−2.79088
$550$	−143.358	−0.0111142
$551$	−4548.32	−0.351660
$552$	12661.7	0.976304
$553$	0	0
$554$	−3392.52	−0.260170
$555$	−29399.2	−2.24852
$556$	−4492.72	−0.342686
$557$	10801.2	0.821655	0.410827	−	0.911713i	$-0.365240\pi$
$557$	10801.2	0.821655	0.410827	+	0.911713i	$0.365240\pi$
$558$	−3622.46	−0.274822
$559$	−1788.02	−0.135286
$560$	0	0
$561$	−4387.67	−0.330209
$562$	−558.565	−0.0419247
$563$	7411.77	0.554829	0.277415	−	0.960750i	$-0.410522\pi$
$563$	7411.77	0.554829	0.277415	+	0.960750i	$0.410522\pi$
$564$	27406.4	2.04613
$565$	−13011.8	−0.968869
$566$	4231.86	0.314273
$567$	0	0
$568$	−3668.72	−0.271014
$569$	−24987.2	−1.84098	−0.920491	−	0.390764i	$-0.872211\pi$
$569$	−24987.2	−1.84098	−0.920491	+	0.390764i	$0.872211\pi$
$570$	2515.51	0.184848
$571$	−12295.9	−0.901171	−0.450585	−	0.892733i	$-0.648785\pi$
$571$	−12295.9	−0.901171	−0.450585	+	0.892733i	$0.648785\pi$
$572$	484.053	0.0353833
$573$	2373.15	0.173019
$574$	0	0
$575$	10330.7	0.749250
$576$	−25123.4	−1.81738
$577$	14134.3	1.01979	0.509894	−	0.860237i	$-0.329685\pi$
$577$	14134.3	1.01979	0.509894	+	0.860237i	$0.329685\pi$
$578$	2334.20	0.167975
$579$	−12136.3	−0.871098
$580$	4251.99	0.304404
$581$	0	0
$582$	5503.64	0.391981
$583$	−933.295	−0.0663004
$584$	−2799.27	−0.198347
$585$	6295.99	0.444969
$586$	1765.52	0.124459
$587$	−25534.1	−1.79541	−0.897704	−	0.440598i	$-0.854766\pi$
$587$	−25534.1	−1.79541	−0.897704	+	0.440598i	$0.854766\pi$
$588$	0	0
$589$	8102.56	0.566825
$590$	1067.92	0.0745180
$591$	26211.0	1.82432
$592$	22677.4	1.57438
$593$	4780.98	0.331081	0.165541	−	0.986203i	$-0.447063\pi$
$593$	4780.98	0.331081	0.165541	+	0.986203i	$0.447063\pi$
$594$	737.326	0.0509307
$595$	0	0
$596$	−27722.5	−1.90530
$597$	−24077.0	−1.65060
$598$	1120.51	0.0766238
$599$	4930.66	0.336329	0.168165	−	0.985759i	$-0.446216\pi$
$599$	4930.66	0.336329	0.168165	+	0.985759i	$0.446216\pi$
$600$	4383.81	0.298281
$601$	12607.7	0.855708	0.427854	−	0.903848i	$-0.359270\pi$
$601$	12607.7	0.855708	0.427854	+	0.903848i	$0.359270\pi$
$602$	0	0
$603$	−44147.4	−2.98146
$604$	−9113.70	−0.613959
$605$	10560.5	0.709665
$606$	4939.12	0.331086
$607$	−4643.34	−0.310490	−0.155245	−	0.987876i	$-0.549617\pi$
$607$	−4643.34	−0.310490	−0.155245	+	0.987876i	$0.549617\pi$
$608$	−6149.64	−0.410199
$609$	0	0
$610$	2411.43	0.160059
$611$	4928.60	0.326334
$612$	45530.7	3.00730
$613$	−629.177	−0.0414555	−0.0207278	−	0.999785i	$-0.506598\pi$
$613$	−629.177	−0.0414555	−0.0207278	+	0.999785i	$0.506598\pi$
$614$	1786.34	0.117412
$615$	5208.66	0.341518
$616$	0	0
$617$	−8675.01	−0.566034	−0.283017	−	0.959115i	$-0.591335\pi$
$617$	−8675.01	−0.566034	−0.283017	+	0.959115i	$0.591335\pi$
$618$	3480.21	0.226528
$619$	274.795	0.0178432	0.00892161	−	0.999960i	$-0.497160\pi$
$619$	274.795	0.0178432	0.00892161	+	0.999960i	$0.497160\pi$
$620$	−7574.66	−0.490654
$621$	−53133.3	−3.43344
$622$	−929.720	−0.0599331
$623$	0	0
$624$	−7042.56	−0.451808
$625$	−4572.53	−0.292642
$626$	−3416.75	−0.218149
$627$	−2999.34	−0.191040
$628$	4602.32	0.292441
$629$	−38233.9	−2.42366
$630$	0	0
$631$	24973.8	1.57558	0.787791	−	0.615943i	$-0.211225\pi$
$631$	24973.8	1.57558	0.787791	+	0.615943i	$0.211225\pi$
$632$	9276.15	0.583838
$633$	12667.0	0.795371
$634$	1137.28	0.0712419
$635$	12034.6	0.752095
$636$	14044.3	0.875616
$637$	0	0
$638$	162.857	0.0101059
$639$	27998.5	1.73334
$640$	7621.19	0.470709
$641$	−5452.85	−0.335998	−0.167999	−	0.985787i	$-0.553731\pi$
$641$	−5452.85	−0.335998	−0.167999	+	0.985787i	$0.553731\pi$
$642$	−3714.94	−0.228375
$643$	6799.11	0.416999	0.208500	−	0.978022i	$-0.433142\pi$
$643$	6799.11	0.416999	0.208500	+	0.978022i	$0.433142\pi$
$644$	0	0
$645$	−10357.3	−0.632275
$646$	3271.44	0.199246
$647$	−10623.0	−0.645490	−0.322745	−	0.946486i	$-0.604606\pi$
$647$	−10623.0	−0.645490	−0.322745	+	0.946486i	$0.604606\pi$
$648$	−9818.62	−0.595234
$649$	−1273.32	−0.0770144
$650$	387.948	0.0234101
$651$	0	0
$652$	−15869.0	−0.953188
$653$	2364.18	0.141681	0.0708403	−	0.997488i	$-0.477432\pi$
$653$	2364.18	0.141681	0.0708403	+	0.997488i	$0.477432\pi$
$654$	9918.33	0.593023
$655$	16286.6	0.971555
$656$	−4017.74	−0.239126
$657$	21363.1	1.26858
$658$	0	0
$659$	8550.45	0.505430	0.252715	−	0.967541i	$-0.418677\pi$
$659$	8550.45	0.505430	0.252715	+	0.967541i	$0.418677\pi$
$660$	2803.93	0.165368
$661$	19801.2	1.16517	0.582585	−	0.812770i	$-0.302041\pi$
$661$	19801.2	1.16517	0.582585	+	0.812770i	$0.302041\pi$
$662$	−10.3509	−0.000607705 0
$663$	11873.7	0.695530
$664$	7217.44	0.421824
$665$	0	0
$666$	11684.8	0.679846
$667$	−11735.8	−0.681279
$668$	−13814.9	−0.800173
$669$	4139.28	0.239214
$670$	2965.38	0.170989
$671$	−2875.24	−0.165421
$672$	0	0
$673$	−16437.6	−0.941493	−0.470746	−	0.882269i	$-0.656015\pi$
$673$	−16437.6	−0.941493	−0.470746	+	0.882269i	$0.656015\pi$
$674$	792.184	0.0452727
$675$	−18396.1	−1.04899
$676$	−1309.92	−0.0745290
$677$	−16852.1	−0.956690	−0.478345	−	0.878172i	$-0.658763\pi$
$677$	−16852.1	−0.956690	−0.478345	+	0.878172i	$0.658763\pi$
$678$	7499.52	0.424804
$679$	0	0
$680$	−6214.83	−0.350482
$681$	−34497.0	−1.94116
$682$	−290.120	−0.0162893
$683$	−278.180	−0.0155846	−0.00779228	−	0.999970i	$-0.502480\pi$
$683$	−278.180	−0.0155846	−0.00779228	+	0.999970i	$0.502480\pi$
$684$	31124.1	1.73985
$685$	14943.1	0.833496
$686$	0	0
$687$	51254.3	2.84639
$688$	7989.18	0.442710
$689$	2525.64	0.139650
$690$	6490.67	0.358109
$691$	−9100.94	−0.501036	−0.250518	−	0.968112i	$-0.580601\pi$
$691$	−9100.94	−0.501036	−0.250518	+	0.968112i	$0.580601\pi$
$692$	−21119.6	−1.16018
$693$	0	0
$694$	−1563.26	−0.0855049
$695$	−4680.10	−0.255433
$696$	−4980.09	−0.271221
$697$	6773.89	0.368119
$698$	−3194.77	−0.173243
$699$	−2866.29	−0.155097
$700$	0	0
$701$	7889.90	0.425103	0.212552	−	0.977150i	$-0.431823\pi$
$701$	7889.90	0.425103	0.212552	+	0.977150i	$0.431823\pi$
$702$	−1995.32	−0.107277
$703$	−26136.1	−1.40219
$704$	−2012.12	−0.107720
$705$	28549.5	1.52516
$706$	−4918.73	−0.262208
$707$	0	0
$708$	19161.1	1.01711
$709$	−9333.87	−0.494416	−0.247208	−	0.968962i	$-0.579513\pi$
$709$	−9333.87	−0.494416	−0.247208	+	0.968962i	$0.579513\pi$
$710$	−1880.66	−0.0994082
$711$	−70792.7	−3.73409
$712$	9514.36	0.500794
$713$	20906.7	1.09812
$714$	0	0
$715$	504.242	0.0263742
$716$	−10749.6	−0.561078
$717$	40031.6	2.08509
$718$	−927.665	−0.0482175
$719$	8185.14	0.424554	0.212277	−	0.977210i	$-0.431912\pi$
$719$	8185.14	0.424554	0.212277	+	0.977210i	$0.431912\pi$
$720$	−28131.6	−1.45612
$721$	0	0
$722$	−1186.23	−0.0611453
$723$	27885.8	1.43442
$724$	−8127.98	−0.417229
$725$	−4063.24	−0.208145
$726$	−6086.70	−0.311155
$727$	−15981.2	−0.815280	−0.407640	−	0.913143i	$-0.633648\pi$
$727$	−15981.2	−0.815280	−0.407640	+	0.913143i	$0.633648\pi$
$728$	0	0
$729$	−2523.93	−0.128229
$730$	−1434.96	−0.0727538
$731$	−13469.7	−0.681525
$732$	43266.8	2.18468
$733$	12059.4	0.607673	0.303837	−	0.952724i	$-0.401732\pi$
$733$	12059.4	0.607673	0.303837	+	0.952724i	$0.401732\pi$
$734$	−1367.98	−0.0687915
$735$	0	0
$736$	−15867.7	−0.794687
$737$	−3535.73	−0.176717
$738$	−2070.20	−0.103259
$739$	3002.35	0.149449	0.0747247	−	0.997204i	$-0.476192\pi$
$739$	3002.35	0.149449	0.0747247	+	0.997204i	$0.476192\pi$
$740$	24433.3	1.21376
$741$	8116.68	0.402394
$742$	0	0
$743$	−6531.46	−0.322498	−0.161249	−	0.986914i	$-0.551552\pi$
$743$	−6531.46	−0.322498	−0.161249	+	0.986914i	$0.551552\pi$
$744$	8871.74	0.437169
$745$	−28878.7	−1.42018
$746$	−3979.96	−0.195331
$747$	−55081.3	−2.69788
$748$	3646.52	0.178249
$749$	0	0
$750$	6944.17	0.338087
$751$	−25272.8	−1.22798	−0.613992	−	0.789312i	$-0.710437\pi$
$751$	−25272.8	−1.22798	−0.613992	+	0.789312i	$0.710437\pi$
$752$	−22021.9	−1.06789
$753$	−12703.3	−0.614788
$754$	−440.716	−0.0212864
$755$	−9493.81	−0.457636
$756$	0	0
$757$	−12632.1	−0.606503	−0.303252	−	0.952910i	$-0.598072\pi$
$757$	−12632.1	−0.606503	−0.303252	+	0.952910i	$0.598072\pi$
$758$	−1050.03	−0.0503149
$759$	−7739.08	−0.370106
$760$	−4248.37	−0.202769
$761$	18070.6	0.860787	0.430393	−	0.902641i	$-0.358375\pi$
$761$	18070.6	0.860787	0.430393	+	0.902641i	$0.358375\pi$
$762$	−6936.32	−0.329759
$763$	0	0
$764$	−1972.29	−0.0933967
$765$	47429.7	2.24160
$766$	5247.30	0.247510
$767$	3445.81	0.162218
$768$	26858.6	1.26195
$769$	34150.4	1.60143	0.800713	−	0.599048i	$-0.204454\pi$
$769$	34150.4	1.60143	0.800713	+	0.599048i	$0.204454\pi$
$770$	0	0
$771$	−495.368	−0.0231391
$772$	10086.3	0.470224
$773$	18163.4	0.845136	0.422568	−	0.906331i	$-0.361129\pi$
$773$	18163.4	0.845136	0.422568	+	0.906331i	$0.361129\pi$
$774$	4116.53	0.191170
$775$	7238.42	0.335499
$776$	−9294.91	−0.429984
$777$	0	0
$778$	−5867.14	−0.270369
$779$	4630.53	0.212973
$780$	−7587.86	−0.348319
$781$	2242.38	0.102738
$782$	8441.15	0.386004
$783$	20898.3	0.953823
$784$	0	0
$785$	4794.28	0.217981
$786$	−9386.96	−0.425982
$787$	23585.3	1.06826	0.534132	−	0.845401i	$-0.320639\pi$
$787$	23585.3	1.06826	0.534132	+	0.845401i	$0.320639\pi$
$788$	−21783.5	−0.984780
$789$	−43347.4	−1.95590
$790$	4755.14	0.214152
$791$	0	0
$792$	−2264.66	−0.101605
$793$	7780.84	0.348431
$794$	−3777.10	−0.168821
$795$	14630.0	0.652671
$796$	20010.1	0.891002
$797$	−38225.3	−1.69888	−0.849442	−	0.527683i	$-0.823061\pi$
$797$	−38225.3	−1.69888	−0.849442	+	0.527683i	$0.823061\pi$
$798$	0	0
$799$	37128.7	1.64395
$800$	−5493.78	−0.242793
$801$	−72610.6	−3.20296
$802$	−3567.61	−0.157078
$803$	1710.96	0.0751911
$804$	53205.9	2.33387
$805$	0	0
$806$	785.110	0.0343106
$807$	28325.8	1.23558
$808$	−8341.53	−0.363185
$809$	−17461.5	−0.758857	−0.379428	−	0.925221i	$-0.623879\pi$
$809$	−17461.5	−0.758857	−0.379428	+	0.925221i	$0.623879\pi$
$810$	−5033.22	−0.218333
$811$	−30749.7	−1.33140	−0.665702	−	0.746218i	$-0.731868\pi$
$811$	−30749.7	−1.33140	−0.665702	+	0.746218i	$0.731868\pi$
$812$	0	0
$813$	−29816.2	−1.28622
$814$	935.829	0.0402958
$815$	−16530.9	−0.710492
$816$	−53053.8	−2.27605
$817$	−9207.68	−0.394291
$818$	3822.75	0.163398
$819$	0	0
$820$	−4328.84	−0.184353
$821$	18585.2	0.790048	0.395024	−	0.918671i	$-0.370736\pi$
$821$	18585.2	0.790048	0.395024	+	0.918671i	$0.370736\pi$
$822$	−8612.61	−0.365449
$823$	29029.7	1.22954	0.614771	−	0.788706i	$-0.289248\pi$
$823$	29029.7	1.22954	0.614771	+	0.788706i	$0.289248\pi$
$824$	−5877.60	−0.248490
$825$	−2679.46	−0.113075
$826$	0	0
$827$	−7044.88	−0.296221	−0.148110	−	0.988971i	$-0.547319\pi$
$827$	−7044.88	−0.296221	−0.148110	+	0.988971i	$0.547319\pi$
$828$	80308.2	3.37066
$829$	35805.2	1.50008	0.750041	−	0.661392i	$-0.230034\pi$
$829$	35805.2	1.50008	0.750041	+	0.661392i	$0.230034\pi$
$830$	3699.81	0.154725
$831$	−63408.6	−2.64696
$832$	5445.10	0.226893
$833$	0	0
$834$	2697.43	0.111996
$835$	−14391.1	−0.596437
$836$	2492.71	0.103125
$837$	−37229.0	−1.53742
$838$	677.107	0.0279120
$839$	−30093.5	−1.23831	−0.619157	−	0.785268i	$-0.712525\pi$
$839$	−30093.5	−1.23831	−0.619157	+	0.785268i	$0.712525\pi$
$840$	0	0
$841$	−19773.1	−0.810738
$842$	161.528	0.00661118
$843$	−10440.0	−0.426539
$844$	−10527.4	−0.429346
$845$	−1364.56	−0.0555528
$846$	−11347.1	−0.461135
$847$	0	0
$848$	−11285.0	−0.456992
$849$	79096.6	3.19739
$850$	2922.54	0.117932
$851$	−67437.9	−2.71650
$852$	−33743.5	−1.35685
$853$	−4239.40	−0.170169	−0.0850846	−	0.996374i	$-0.527116\pi$
$853$	−4239.40	−0.170169	−0.0850846	+	0.996374i	$0.527116\pi$
$854$	0	0
$855$	32422.2	1.29686
$856$	6274.04	0.250517
$857$	−10308.1	−0.410874	−0.205437	−	0.978670i	$-0.565862\pi$
$857$	−10308.1	−0.410874	−0.205437	+	0.978670i	$0.565862\pi$
$858$	−290.626	−0.0115639
$859$	27624.8	1.09726	0.548630	−	0.836065i	$-0.315150\pi$
$859$	27624.8	1.09726	0.548630	+	0.836065i	$0.315150\pi$
$860$	8607.78	0.341306
$861$	0	0
$862$	−7136.72	−0.281993
$863$	−32801.4	−1.29383	−0.646914	−	0.762563i	$-0.723941\pi$
$863$	−32801.4	−1.29383	−0.646914	+	0.762563i	$0.723941\pi$
$864$	28255.9	1.11260
$865$	−22000.4	−0.864782
$866$	418.876	0.0164365
$867$	43627.8	1.70897
$868$	0	0
$869$	−5669.74	−0.221327
$870$	−2552.90	−0.0994843
$871$	9568.23	0.372224
$872$	−16750.7	−0.650518
$873$	70935.9	2.75008
$874$	5770.24	0.223320
$875$	0	0
$876$	−25746.6	−0.993035
$877$	44756.4	1.72328	0.861640	−	0.507521i	$-0.169438\pi$
$877$	44756.4	1.72328	0.861640	+	0.507521i	$0.169438\pi$
$878$	−73.4172	−0.00282199
$879$	32998.9	1.26624
$880$	−2253.04	−0.0863069
$881$	−42815.8	−1.63734	−0.818672	−	0.574261i	$-0.805289\pi$
$881$	−42815.8	−1.63734	−0.818672	+	0.574261i	$0.805289\pi$
$882$	0	0
$883$	10991.5	0.418905	0.209453	−	0.977819i	$-0.432832\pi$
$883$	10991.5	0.418905	0.209453	+	0.977819i	$0.432832\pi$
$884$	−9868.05	−0.375451
$885$	19960.2	0.758142
$886$	6171.58	0.234016
$887$	−36724.8	−1.39019	−0.695095	−	0.718918i	$-0.744638\pi$
$887$	−36724.8	−1.39019	−0.695095	+	0.718918i	$0.744638\pi$
$888$	−28617.2	−1.08145
$889$	0	0
$890$	4877.25	0.183692
$891$	6001.31	0.225647
$892$	−3440.10	−0.129129
$893$	25380.6	0.951098
$894$	16644.6	0.622683
$895$	−11198.0	−0.418219
$896$	0	0
$897$	20943.1	0.779566
$898$	−7659.43	−0.284631
$899$	−8222.98	−0.305063
$900$	27804.7	1.02980
$901$	19026.4	0.703510
$902$	−165.801	−0.00612035
$903$	0	0
$904$	−12665.7	−0.465989
$905$	−8466.98	−0.310997
$906$	5471.88	0.200652
$907$	37726.2	1.38112	0.690560	−	0.723275i	$-0.257364\pi$
$907$	37726.2	1.38112	0.690560	+	0.723275i	$0.257364\pi$
$908$	28669.9	1.04785
$909$	63659.9	2.32285
$910$	0	0
$911$	9608.23	0.349435	0.174717	−	0.984619i	$-0.444099\pi$
$911$	9608.23	0.349435	0.174717	+	0.984619i	$0.444099\pi$
$912$	−36266.8	−1.31679
$913$	−4411.42	−0.159909
$914$	−6333.66	−0.229211
$915$	45071.4	1.62843
$916$	−42596.7	−1.53650
$917$	0	0
$918$	−15031.3	−0.540423
$919$	10118.9	0.363213	0.181607	−	0.983371i	$-0.441870\pi$
$919$	10118.9	0.363213	0.181607	+	0.983371i	$0.441870\pi$
$920$	−10961.9	−0.392829
$921$	33388.0	1.19454
$922$	−5238.07	−0.187101
$923$	−6068.23	−0.216401
$924$	0	0
$925$	−23348.7	−0.829946
$926$	−3542.82	−0.125728
$927$	44856.1	1.58928
$928$	6241.03	0.220767
$929$	−6093.72	−0.215208	−0.107604	−	0.994194i	$-0.534318\pi$
$929$	−6093.72	−0.215208	−0.107604	+	0.994194i	$0.534318\pi$
$930$	4547.83	0.160354
$931$	0	0
$932$	2382.13	0.0837224
$933$	−17377.1	−0.609755
$934$	−8845.51	−0.309887
$935$	3798.61	0.132864
$936$	6128.51	0.214014
$937$	−17073.8	−0.595279	−0.297640	−	0.954678i	$-0.596199\pi$
$937$	−17073.8	−0.595279	−0.297640	+	0.954678i	$0.596199\pi$
$938$	0	0
$939$	−63861.6	−2.21943
$940$	−23727.0	−0.823288
$941$	3711.15	0.128565	0.0642826	−	0.997932i	$-0.479524\pi$
$941$	3711.15	0.128565	0.0642826	+	0.997932i	$0.479524\pi$
$942$	−2763.24	−0.0955745
$943$	11947.9	0.412597
$944$	−15396.5	−0.530841
$945$	0	0
$946$	329.690	0.0113310
$947$	−52970.7	−1.81765	−0.908826	−	0.417176i	$-0.863020\pi$
$947$	−52970.7	−1.81765	−0.908826	+	0.417176i	$0.863020\pi$
$948$	85318.7	2.92302
$949$	−4630.12	−0.158377
$950$	1997.80	0.0682287
$951$	21256.7	0.724811
$952$	0	0
$953$	15908.1	0.540729	0.270365	−	0.962758i	$-0.412856\pi$
$953$	15908.1	0.540729	0.270365	+	0.962758i	$0.412856\pi$
$954$	−5814.75	−0.197337
$955$	−2054.55	−0.0696165
$956$	−33269.7	−1.12554
$957$	3043.92	0.102817
$958$	−3644.08	−0.122897
$959$	0	0
$960$	31541.3	1.06041
$961$	−15142.3	−0.508283
$962$	−2532.50	−0.0848763
$963$	−47881.6	−1.60224
$964$	−23175.5	−0.774308
$965$	10506.9	0.350498
$966$	0	0
$967$	5637.10	0.187463	0.0937316	−	0.995597i	$-0.470120\pi$
$967$	5637.10	0.187463	0.0937316	+	0.995597i	$0.470120\pi$
$968$	10279.6	0.341322
$969$	61145.5	2.02712
$970$	−4764.76	−0.157719
$971$	−9815.73	−0.324410	−0.162205	−	0.986757i	$-0.551861\pi$
$971$	−9815.73	−0.324410	−0.162205	+	0.986757i	$0.551861\pi$
$972$	−25935.0	−0.855830
$973$	0	0
$974$	−7985.21	−0.262693
$975$	7251.03	0.238173
$976$	−34766.2	−1.14020
$977$	53926.0	1.76586	0.882930	−	0.469505i	$-0.155568\pi$
$977$	53926.0	1.76586	0.882930	+	0.469505i	$0.155568\pi$
$978$	9527.77	0.311518
$979$	−5815.34	−0.189846
$980$	0	0
$981$	127836.	4.16055
$982$	2990.00	0.0971635
$983$	−12821.1	−0.416003	−0.208001	−	0.978129i	$-0.566696\pi$
$983$	−12821.1	−0.416003	−0.208001	+	0.978129i	$0.566696\pi$
$984$	5070.10	0.164257
$985$	−22692.1	−0.734040
$986$	−3320.06	−0.107233
$987$	0	0
$988$	−6745.65	−0.217214
$989$	−23758.2	−0.763869
$990$	−1160.91	−0.0372688
$991$	34575.3	1.10830	0.554148	−	0.832418i	$-0.313044\pi$
$991$	34575.3	1.10830	0.554148	+	0.832418i	$0.313044\pi$
$992$	−11118.0	−0.355845
$993$	−193.467	−0.00618275
$994$	0	0
$995$	20844.6	0.664140
$996$	66383.4	2.11188
$997$	14337.1	0.455427	0.227713	−	0.973728i	$-0.426875\pi$
$997$	14337.1	0.455427	0.227713	+	0.973728i	$0.426875\pi$
$998$	9558.13	0.303164
$999$	120088.	3.80322

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.4.a.f.1.4		6
7.6	odd	2		91.4.a.d.1.4	✓	6
21.20	even	2		819.4.a.l.1.3		6
28.27	even	2		1456.4.a.y.1.6		6
35.34	odd	2		2275.4.a.l.1.3		6
91.90	odd	2		1183.4.a.g.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.4.a.d.1.4	✓	6	7.6	odd	2
637.4.a.f.1.4		6	1.1	even	1	trivial
819.4.a.l.1.3		6	21.20	even	2
1183.4.a.g.1.3		6	91.90	odd	2
1456.4.a.y.1.6		6	28.27	even	2
2275.4.a.l.1.3		6	35.34	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	637.a (trivial)

\(f(q)\)	\(=\)	\(q+0.498984 q^{2} +9.32638 q^{3} -7.75101 q^{4} -8.07429 q^{5} +4.65372 q^{6} -7.85951 q^{8} +59.9813 q^{9} +O(q^{10})\)	\(q+0.498984 q^{2} +9.32638 q^{3} -7.75101 q^{4} -8.07429 q^{5} +4.65372 q^{6} -7.85951 q^{8} +59.9813 q^{9} -4.02894 q^{10} +4.80387 q^{11} -72.2889 q^{12} -13.0000 q^{13} -75.3039 q^{15} +58.0863 q^{16} -97.9331 q^{17} +29.9298 q^{18} -66.9456 q^{19} +62.5839 q^{20} +2.39705 q^{22} -172.737 q^{23} -73.3008 q^{24} -59.8058 q^{25} -6.48680 q^{26} +307.597 q^{27} +67.9405 q^{29} -37.5755 q^{30} -121.032 q^{31} +91.8603 q^{32} +44.8027 q^{33} -48.8671 q^{34} -464.916 q^{36} +390.408 q^{37} -33.4048 q^{38} -121.243 q^{39} +63.4600 q^{40} -69.1685 q^{41} +137.540 q^{43} -37.2348 q^{44} -484.307 q^{45} -86.1930 q^{46} -379.123 q^{47} +541.735 q^{48} -29.8422 q^{50} -913.361 q^{51} +100.763 q^{52} -194.280 q^{53} +153.486 q^{54} -38.7878 q^{55} -624.360 q^{57} +33.9013 q^{58} -265.062 q^{59} +583.682 q^{60} -598.526 q^{61} -60.3931 q^{62} -418.854 q^{64} +104.966 q^{65} +22.3558 q^{66} -736.018 q^{67} +759.081 q^{68} -1611.01 q^{69} +466.787 q^{71} -471.424 q^{72} +356.163 q^{73} +194.808 q^{74} -557.772 q^{75} +518.896 q^{76} -60.4983 q^{78} -1180.25 q^{79} -469.006 q^{80} +1249.27 q^{81} -34.5140 q^{82} -918.306 q^{83} +790.740 q^{85} +68.6302 q^{86} +633.639 q^{87} -37.7560 q^{88} -1210.55 q^{89} -241.662 q^{90} +1338.89 q^{92} -1128.79 q^{93} -189.177 q^{94} +540.538 q^{95} +856.724 q^{96} +1182.63 q^{97} +288.142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 13 q^{3} + 10 q^{4} - 26 q^{5} - 3 q^{6} + 12 q^{8} + 111 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 - 13 * q^3 + 10 * q^4 - 26 * q^5 - 3 * q^6 + 12 * q^8 + 111 * q^9	\( 6 q + 2 q^{2} - 13 q^{3} + 10 q^{4} - 26 q^{5} - 3 q^{6} + 12 q^{8} + 111 q^{9} + 32 q^{10} + 11 q^{11} - 141 q^{12} - 78 q^{13} + 64 q^{15} - 54 q^{16} - 210 q^{17} + 65 q^{18} - 78 q^{19} - 38 q^{20} + 125 q^{22} - 75 q^{23} + 189 q^{24} + 90 q^{25} - 26 q^{26} - 31 q^{27} + 306 q^{29} - 864 q^{30} + 93 q^{31} + 108 q^{32} + 393 q^{33} + 706 q^{34} - 317 q^{36} - 611 q^{37} + 516 q^{38} + 169 q^{39} + 230 q^{40} - 131 q^{41} - 88 q^{43} - 1261 q^{44} - 566 q^{45} - 567 q^{46} - 587 q^{47} + 1279 q^{48} - 1140 q^{50} - 892 q^{51} - 130 q^{52} + 770 q^{53} - 645 q^{54} + 624 q^{55} - 1602 q^{57} - 824 q^{58} - 934 q^{59} + 888 q^{60} - 1629 q^{61} - 1207 q^{62} - 1622 q^{64} + 338 q^{65} - 2025 q^{66} + 263 q^{67} - 1986 q^{68} - 1425 q^{69} + 1032 q^{71} - 3129 q^{72} - 819 q^{73} + 1555 q^{74} - 2003 q^{75} + 1894 q^{76} + 39 q^{78} - 2169 q^{79} - 2074 q^{80} + 3222 q^{81} - 1225 q^{82} - 1580 q^{83} + 216 q^{85} - 1378 q^{86} - 2372 q^{87} + 861 q^{88} - 1244 q^{89} + 5648 q^{90} + 1369 q^{92} - 1685 q^{93} - 3439 q^{94} + 3052 q^{95} - 227 q^{96} + 1643 q^{97} - 2950 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 13 * q^3 + 10 * q^4 - 26 * q^5 - 3 * q^6 + 12 * q^8 + 111 * q^9 + 32 * q^10 + 11 * q^11 - 141 * q^12 - 78 * q^13 + 64 * q^15 - 54 * q^16 - 210 * q^17 + 65 * q^18 - 78 * q^19 - 38 * q^20 + 125 * q^22 - 75 * q^23 + 189 * q^24 + 90 * q^25 - 26 * q^26 - 31 * q^27 + 306 * q^29 - 864 * q^30 + 93 * q^31 + 108 * q^32 + 393 * q^33 + 706 * q^34 - 317 * q^36 - 611 * q^37 + 516 * q^38 + 169 * q^39 + 230 * q^40 - 131 * q^41 - 88 * q^43 - 1261 * q^44 - 566 * q^45 - 567 * q^46 - 587 * q^47 + 1279 * q^48 - 1140 * q^50 - 892 * q^51 - 130 * q^52 + 770 * q^53 - 645 * q^54 + 624 * q^55 - 1602 * q^57 - 824 * q^58 - 934 * q^59 + 888 * q^60 - 1629 * q^61 - 1207 * q^62 - 1622 * q^64 + 338 * q^65 - 2025 * q^66 + 263 * q^67 - 1986 * q^68 - 1425 * q^69 + 1032 * q^71 - 3129 * q^72 - 819 * q^73 + 1555 * q^74 - 2003 * q^75 + 1894 * q^76 + 39 * q^78 - 2169 * q^79 - 2074 * q^80 + 3222 * q^81 - 1225 * q^82 - 1580 * q^83 + 216 * q^85 - 1378 * q^86 - 2372 * q^87 + 861 * q^88 - 1244 * q^89 + 5648 * q^90 + 1369 * q^92 - 1685 * q^93 - 3439 * q^94 + 3052 * q^95 - 227 * q^96 + 1643 * q^97 - 2950 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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