LMFDB - Embedded newform 1805.2.a.w.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 29x^{14} + 339x^{12} - 2038x^{10} + 6639x^{8} - 11261x^{6} + 8701x^{4} - 2592x^{2} + 256 $ x^16 - 29x^14 + 339x^12 - 2038x^10 + 6639x^8 - 11261x^6 + 8701x^4 - 2592*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.486735$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.486735 q^{2} -0.821147 q^{3} -1.76309 q^{4} +1.00000 q^{5} +0.399681 q^{6} +3.94354 q^{7} +1.83163 q^{8} -2.32572 q^{9} +O(q^{10})$	\(q-0.486735 q^{2} -0.821147 q^{3} -1.76309 q^{4} +1.00000 q^{5} +0.399681 q^{6} +3.94354 q^{7} +1.83163 q^{8} -2.32572 q^{9} -0.486735 q^{10} +4.13411 q^{11} +1.44776 q^{12} -0.310860 q^{13} -1.91946 q^{14} -0.821147 q^{15} +2.63466 q^{16} +1.37102 q^{17} +1.13201 q^{18} -1.76309 q^{20} -3.23823 q^{21} -2.01221 q^{22} +0.331809 q^{23} -1.50404 q^{24} +1.00000 q^{25} +0.151307 q^{26} +4.37320 q^{27} -6.95281 q^{28} +7.26503 q^{29} +0.399681 q^{30} -6.55547 q^{31} -4.94564 q^{32} -3.39471 q^{33} -0.667322 q^{34} +3.94354 q^{35} +4.10045 q^{36} -9.27902 q^{37} +0.255262 q^{39} +1.83163 q^{40} +9.25000 q^{41} +1.57616 q^{42} -6.49792 q^{43} -7.28880 q^{44} -2.32572 q^{45} -0.161503 q^{46} +4.19090 q^{47} -2.16345 q^{48} +8.55151 q^{49} -0.486735 q^{50} -1.12581 q^{51} +0.548075 q^{52} -10.5136 q^{53} -2.12859 q^{54} +4.13411 q^{55} +7.22310 q^{56} -3.53614 q^{58} -7.23383 q^{59} +1.44776 q^{60} +15.0639 q^{61} +3.19078 q^{62} -9.17156 q^{63} -2.86211 q^{64} -0.310860 q^{65} +1.65232 q^{66} +11.5497 q^{67} -2.41723 q^{68} -0.272464 q^{69} -1.91946 q^{70} -4.54326 q^{71} -4.25985 q^{72} +8.86098 q^{73} +4.51642 q^{74} -0.821147 q^{75} +16.3030 q^{77} -0.124245 q^{78} -7.42705 q^{79} +2.63466 q^{80} +3.38611 q^{81} -4.50230 q^{82} +1.50176 q^{83} +5.70928 q^{84} +1.37102 q^{85} +3.16277 q^{86} -5.96566 q^{87} +7.57214 q^{88} -4.72287 q^{89} +1.13201 q^{90} -1.22589 q^{91} -0.585008 q^{92} +5.38301 q^{93} -2.03986 q^{94} +4.06110 q^{96} +12.4271 q^{97} -4.16232 q^{98} -9.61476 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9}+O(q^{10}) $ 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9	$ 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9} + 12 q^{11} + 42 q^{16} + 22 q^{17} + 26 q^{20} + 42 q^{23} - 14 q^{24} + 16 q^{25} - 26 q^{26} + 46 q^{28} - 2 q^{30} + 22 q^{35} - 8 q^{36} - 38 q^{39} + 74 q^{42} + 88 q^{43} - 48 q^{44} + 18 q^{45} + 32 q^{47} + 30 q^{49} - 22 q^{54} + 12 q^{55} - 2 q^{58} + 20 q^{61} + 6 q^{62} - 6 q^{63} + 24 q^{64} - 24 q^{66} + 84 q^{68} + 44 q^{73} - 122 q^{74} + 4 q^{77} + 42 q^{80} - 36 q^{81} - 50 q^{82} + 56 q^{83} + 22 q^{85} + 34 q^{87} + 6 q^{92} - 58 q^{93} - 96 q^{96} + 6 q^{99}+O(q^{100}) $ 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9 + 12 * q^11 + 42 * q^16 + 22 * q^17 + 26 * q^20 + 42 * q^23 - 14 * q^24 + 16 * q^25 - 26 * q^26 + 46 * q^28 - 2 * q^30 + 22 * q^35 - 8 * q^36 - 38 * q^39 + 74 * q^42 + 88 * q^43 - 48 * q^44 + 18 * q^45 + 32 * q^47 + 30 * q^49 - 22 * q^54 + 12 * q^55 - 2 * q^58 + 20 * q^61 + 6 * q^62 - 6 * q^63 + 24 * q^64 - 24 * q^66 + 84 * q^68 + 44 * q^73 - 122 * q^74 + 4 * q^77 + 42 * q^80 - 36 * q^81 - 50 * q^82 + 56 * q^83 + 22 * q^85 + 34 * q^87 + 6 * q^92 - 58 * q^93 - 96 * q^96 + 6 * 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 $

$2$	−0.486735	−0.344174	−0.172087	−	0.985082i	$-0.555051\pi$
$2$	−0.486735	−0.344174	−0.172087	+	0.985082i	$0.555051\pi$
$3$	−0.821147	−0.474090	−0.237045	−	0.971499i	$-0.576179\pi$
$3$	−0.821147	−0.474090	−0.237045	+	0.971499i	$0.576179\pi$
$4$	−1.76309	−0.881545
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.399681	0.163169
$7$	3.94354	1.49052	0.745259	−	0.666775i	$-0.232326\pi$
$7$	3.94354	1.49052	0.745259	+	0.666775i	$0.232326\pi$
$8$	1.83163	0.647578
$9$	−2.32572	−0.775239
$10$	−0.486735	−0.153919
$11$	4.13411	1.24648	0.623240	−	0.782031i	$-0.285816\pi$
$11$	4.13411	1.24648	0.623240	+	0.782031i	$0.285816\pi$
$12$	1.44776	0.417931
$13$	−0.310860	−0.0862172	−0.0431086	−	0.999070i	$-0.513726\pi$
$13$	−0.310860	−0.0862172	−0.0431086	+	0.999070i	$0.513726\pi$
$14$	−1.91946	−0.512997
$15$	−0.821147	−0.212019
$16$	2.63466	0.658665
$17$	1.37102	0.332521	0.166260	−	0.986082i	$-0.446831\pi$
$17$	1.37102	0.332521	0.166260	+	0.986082i	$0.446831\pi$
$18$	1.13201	0.266817
$19$	0	0
$19$	0	0
$20$	−1.76309	−0.394239
$21$	−3.23823	−0.706639
$22$	−2.01221	−0.429006
$23$	0.331809	0.0691869	0.0345935	−	0.999401i	$-0.488986\pi$
$23$	0.331809	0.0691869	0.0345935	+	0.999401i	$0.488986\pi$
$24$	−1.50404	−0.307010
$25$	1.00000	0.200000
$26$	0.151307	0.0296737
$27$	4.37320	0.841622
$28$	−6.95281	−1.31396
$29$	7.26503	1.34908	0.674541	−	0.738237i	$-0.264342\pi$
$29$	7.26503	1.34908	0.674541	+	0.738237i	$0.264342\pi$
$30$	0.399681	0.0729715
$31$	−6.55547	−1.17740	−0.588699	−	0.808353i	$-0.700360\pi$
$31$	−6.55547	−1.17740	−0.588699	+	0.808353i	$0.700360\pi$
$32$	−4.94564	−0.874273
$33$	−3.39471	−0.590943
$34$	−0.667322	−0.114445
$35$	3.94354	0.666580
$36$	4.10045	0.683408
$37$	−9.27902	−1.52546	−0.762731	−	0.646716i	$-0.776142\pi$
$37$	−9.27902	−1.52546	−0.762731	+	0.646716i	$0.776142\pi$
$38$	0	0
$39$	0.255262	0.0408747
$40$	1.83163	0.289606
$41$	9.25000	1.44461	0.722304	−	0.691576i	$-0.243083\pi$
$41$	9.25000	1.44461	0.722304	+	0.691576i	$0.243083\pi$
$42$	1.57616	0.243207
$43$	−6.49792	−0.990924	−0.495462	−	0.868630i	$-0.665001\pi$
$43$	−6.49792	−0.990924	−0.495462	+	0.868630i	$0.665001\pi$
$44$	−7.28880	−1.09883
$45$	−2.32572	−0.346697
$46$	−0.161503	−0.0238123
$47$	4.19090	0.611305	0.305653	−	0.952143i	$-0.401125\pi$
$47$	4.19090	0.611305	0.305653	+	0.952143i	$0.401125\pi$
$48$	−2.16345	−0.312266
$49$	8.55151	1.22164
$50$	−0.486735	−0.0688347
$51$	−1.12581	−0.157645
$52$	0.548075	0.0760043
$53$	−10.5136	−1.44416	−0.722079	−	0.691811i	$-0.756813\pi$
$53$	−10.5136	−1.44416	−0.722079	+	0.691811i	$0.756813\pi$
$54$	−2.12859	−0.289664
$55$	4.13411	0.557443
$56$	7.22310	0.965227
$57$	0	0
$58$	−3.53614	−0.464318
$59$	−7.23383	−0.941765	−0.470882	−	0.882196i	$-0.656064\pi$
$59$	−7.23383	−0.941765	−0.470882	+	0.882196i	$0.656064\pi$
$60$	1.44776	0.186904
$61$	15.0639	1.92873	0.964367	−	0.264570i	$-0.0852299\pi$
$61$	15.0639	1.92873	0.964367	+	0.264570i	$0.0852299\pi$
$62$	3.19078	0.405229
$63$	−9.17156	−1.15551
$64$	−2.86211	−0.357764
$65$	−0.310860	−0.0385575
$66$	1.65232	0.203387
$67$	11.5497	1.41101	0.705507	−	0.708703i	$-0.250719\pi$
$67$	11.5497	1.41101	0.705507	+	0.708703i	$0.250719\pi$
$68$	−2.41723	−0.293132
$69$	−0.272464	−0.0328008
$70$	−1.91946	−0.229419
$71$	−4.54326	−0.539185	−0.269593	−	0.962974i	$-0.586889\pi$
$71$	−4.54326	−0.539185	−0.269593	+	0.962974i	$0.586889\pi$
$72$	−4.25985	−0.502028
$73$	8.86098	1.03710	0.518550	−	0.855047i	$-0.326472\pi$
$73$	8.86098	1.03710	0.518550	+	0.855047i	$0.326472\pi$
$74$	4.51642	0.525024
$75$	−0.821147	−0.0948179
$76$	0	0
$77$	16.3030	1.85790
$78$	−0.124245	−0.0140680
$79$	−7.42705	−0.835608	−0.417804	−	0.908537i	$-0.637200\pi$
$79$	−7.42705	−0.835608	−0.417804	+	0.908537i	$0.637200\pi$
$80$	2.63466	0.294564
$81$	3.38611	0.376234
$82$	−4.50230	−0.497196
$83$	1.50176	0.164839	0.0824197	−	0.996598i	$-0.473735\pi$
$83$	1.50176	0.164839	0.0824197	+	0.996598i	$0.473735\pi$
$84$	5.70928	0.622934
$85$	1.37102	0.148708
$86$	3.16277	0.341050
$87$	−5.96566	−0.639586
$88$	7.57214	0.807193
$89$	−4.72287	−0.500623	−0.250312	−	0.968165i	$-0.580533\pi$
$89$	−4.72287	−0.500623	−0.250312	+	0.968165i	$0.580533\pi$
$90$	1.13201	0.119324
$91$	−1.22589	−0.128508
$92$	−0.585008	−0.0609913
$93$	5.38301	0.558192
$94$	−2.03986	−0.210395
$95$	0	0
$96$	4.06110	0.414484
$97$	12.4271	1.26178	0.630889	−	0.775873i	$-0.282690\pi$
$97$	12.4271	1.26178	0.630889	+	0.775873i	$0.282690\pi$
$98$	−4.16232	−0.420458
$99$	−9.61476	−0.966320
$100$	−1.76309	−0.176309
$101$	1.09236	0.108694	0.0543468	−	0.998522i	$-0.482692\pi$
$101$	1.09236	0.108694	0.0543468	+	0.998522i	$0.482692\pi$
$102$	0.547970	0.0542571
$103$	16.0202	1.57852	0.789259	−	0.614061i	$-0.210465\pi$
$103$	16.0202	1.57852	0.789259	+	0.614061i	$0.210465\pi$
$104$	−0.569380	−0.0558323
$105$	−3.23823	−0.316019
$106$	5.11735	0.497041
$107$	19.5136	1.88645	0.943225	−	0.332156i	$-0.107776\pi$
$107$	19.5136	1.88645	0.943225	+	0.332156i	$0.107776\pi$
$108$	−7.71034	−0.741928
$109$	−4.50836	−0.431823	−0.215911	−	0.976413i	$-0.569272\pi$
$109$	−4.50836	−0.431823	−0.215911	+	0.976413i	$0.569272\pi$
$110$	−2.01221	−0.191857
$111$	7.61944	0.723205
$112$	10.3899	0.981752
$113$	5.14621	0.484114	0.242057	−	0.970262i	$-0.422178\pi$
$113$	5.14621	0.484114	0.242057	+	0.970262i	$0.422178\pi$
$114$	0	0
$115$	0.331809	0.0309413
$116$	−12.8089	−1.18928
$117$	0.722973	0.0668389
$118$	3.52096	0.324131
$119$	5.40666	0.495628
$120$	−1.50404	−0.137299
$121$	6.09084	0.553712
$122$	−7.33212	−0.663819
$123$	−7.59562	−0.684874
$124$	11.5579	1.03793
$125$	1.00000	0.0894427
$126$	4.46412	0.397695
$127$	−4.78671	−0.424752	−0.212376	−	0.977188i	$-0.568120\pi$
$127$	−4.78671	−0.424752	−0.212376	+	0.977188i	$0.568120\pi$
$128$	11.2844	0.997406
$129$	5.33575	0.469787
$130$	0.151307	0.0132705
$131$	−7.78512	−0.680190	−0.340095	−	0.940391i	$-0.610459\pi$
$131$	−7.78512	−0.680190	−0.340095	+	0.940391i	$0.610459\pi$
$132$	5.98518	0.520943
$133$	0	0
$134$	−5.62162	−0.485634
$135$	4.37320	0.376385
$136$	2.51119	0.215333
$137$	13.4437	1.14857	0.574287	−	0.818654i	$-0.305279\pi$
$137$	13.4437	1.14857	0.574287	+	0.818654i	$0.305279\pi$
$138$	0.132618	0.0112892
$139$	16.3441	1.38628	0.693142	−	0.720801i	$-0.256226\pi$
$139$	16.3441	1.38628	0.693142	+	0.720801i	$0.256226\pi$
$140$	−6.95281	−0.587620
$141$	−3.44134	−0.289814
$142$	2.21136	0.185573
$143$	−1.28513	−0.107468
$144$	−6.12748	−0.510623
$145$	7.26503	0.603328
$146$	−4.31295	−0.356942
$147$	−7.02205	−0.579169
$148$	16.3597	1.34476
$149$	17.4190	1.42702	0.713509	−	0.700646i	$-0.247105\pi$
$149$	17.4190	1.42702	0.713509	+	0.700646i	$0.247105\pi$
$150$	0.399681	0.0326338
$151$	−12.8121	−1.04263	−0.521317	−	0.853363i	$-0.674559\pi$
$151$	−12.8121	−1.04263	−0.521317	+	0.853363i	$0.674559\pi$
$152$	0	0
$153$	−3.18860	−0.257783
$154$	−7.93525	−0.639440
$155$	−6.55547	−0.526548
$156$	−0.450050	−0.0360328
$157$	−5.31193	−0.423938	−0.211969	−	0.977276i	$-0.567988\pi$
$157$	−5.31193	−0.423938	−0.211969	+	0.977276i	$0.567988\pi$
$158$	3.61501	0.287594
$159$	8.63324	0.684660
$160$	−4.94564	−0.390987
$161$	1.30850	0.103124
$162$	−1.64814	−0.129490
$163$	19.1184	1.49747	0.748736	−	0.662869i	$-0.230661\pi$
$163$	19.1184	1.49747	0.748736	+	0.662869i	$0.230661\pi$
$164$	−16.3086	−1.27349
$165$	−3.39471	−0.264278
$166$	−0.730958	−0.0567333
$167$	−1.73086	−0.133938	−0.0669688	−	0.997755i	$-0.521333\pi$
$167$	−1.73086	−0.133938	−0.0669688	+	0.997755i	$0.521333\pi$
$168$	−5.93123	−0.457604
$169$	−12.9034	−0.992567
$170$	−0.667322	−0.0511813
$171$	0	0
$172$	11.4564	0.873543
$173$	4.93419	0.375139	0.187570	−	0.982251i	$-0.439939\pi$
$173$	4.93419	0.375139	0.187570	+	0.982251i	$0.439939\pi$
$174$	2.90370	0.220129
$175$	3.94354	0.298104
$176$	10.8920	0.821013
$177$	5.94004	0.446481
$178$	2.29879	0.172301
$179$	23.3238	1.74330	0.871652	−	0.490125i	$-0.163049\pi$
$179$	23.3238	1.74330	0.871652	+	0.490125i	$0.163049\pi$
$180$	4.10045	0.305629
$181$	7.80668	0.580266	0.290133	−	0.956986i	$-0.406300\pi$
$181$	7.80668	0.580266	0.290133	+	0.956986i	$0.406300\pi$
$182$	0.596684	0.0442291
$183$	−12.3697	−0.914392
$184$	0.607750	0.0448039
$185$	−9.27902	−0.682207
$186$	−2.62010	−0.192115
$187$	5.66793	0.414480
$188$	−7.38893	−0.538893
$189$	17.2459	1.25445
$190$	0	0
$191$	−16.3524	−1.18322	−0.591608	−	0.806226i	$-0.701507\pi$
$191$	−16.3524	−1.18322	−0.591608	+	0.806226i	$0.701507\pi$
$192$	2.35021	0.169612
$193$	−9.18817	−0.661379	−0.330690	−	0.943740i	$-0.607281\pi$
$193$	−9.18817	−0.661379	−0.330690	+	0.943740i	$0.607281\pi$
$194$	−6.04869	−0.434271
$195$	0.255262	0.0182797
$196$	−15.0771	−1.07693
$197$	−20.1352	−1.43457	−0.717287	−	0.696777i	$-0.754617\pi$
$197$	−20.1352	−1.43457	−0.717287	+	0.696777i	$0.754617\pi$
$198$	4.67984	0.332582
$199$	−8.35943	−0.592584	−0.296292	−	0.955097i	$-0.595750\pi$
$199$	−8.35943	−0.592584	−0.296292	+	0.955097i	$0.595750\pi$
$200$	1.83163	0.129516
$201$	−9.48397	−0.668947
$202$	−0.531689	−0.0374095
$203$	28.6499	2.01083
$204$	1.98490	0.138971
$205$	9.25000	0.646048
$206$	−7.79759	−0.543284
$207$	−0.771693	−0.0536364
$208$	−0.819012	−0.0567883
$209$	0	0
$210$	1.57616	0.108765
$211$	4.13102	0.284391	0.142195	−	0.989839i	$-0.454584\pi$
$211$	4.13102	0.284391	0.142195	+	0.989839i	$0.454584\pi$
$212$	18.5365	1.27309
$213$	3.73068	0.255622
$214$	−9.49794	−0.649266
$215$	−6.49792	−0.443154
$216$	8.01007	0.545016
$217$	−25.8518	−1.75493
$218$	2.19438	0.148622
$219$	−7.27617	−0.491678
$220$	−7.28880	−0.491411
$221$	−0.426195	−0.0286690
$222$	−3.70865	−0.248908
$223$	13.7796	0.922747	0.461374	−	0.887206i	$-0.347357\pi$
$223$	13.7796	0.922747	0.461374	+	0.887206i	$0.347357\pi$
$224$	−19.5033	−1.30312
$225$	−2.32572	−0.155048
$226$	−2.50484	−0.166619
$227$	1.84527	0.122475	0.0612373	−	0.998123i	$-0.480495\pi$
$227$	1.84527	0.122475	0.0612373	+	0.998123i	$0.480495\pi$
$228$	0	0
$229$	−13.5517	−0.895519	−0.447760	−	0.894154i	$-0.647778\pi$
$229$	−13.5517	−0.895519	−0.447760	+	0.894154i	$0.647778\pi$
$230$	−0.161503	−0.0106492
$231$	−13.3872	−0.880812
$232$	13.3068	0.873636
$233$	−5.80230	−0.380121	−0.190061	−	0.981772i	$-0.560868\pi$
$233$	−5.80230	−0.380121	−0.190061	+	0.981772i	$0.560868\pi$
$234$	−0.351896	−0.0230042
$235$	4.19090	0.273384
$236$	12.7539	0.830208
$237$	6.09870	0.396153
$238$	−2.63161	−0.170582
$239$	15.8664	1.02631	0.513157	−	0.858295i	$-0.328476\pi$
$239$	15.8664	1.02631	0.513157	+	0.858295i	$0.328476\pi$
$240$	−2.16345	−0.139650
$241$	23.5134	1.51463	0.757317	−	0.653048i	$-0.226510\pi$
$241$	23.5134	1.51463	0.757317	+	0.653048i	$0.226510\pi$
$242$	−2.96462	−0.190573
$243$	−15.9001	−1.01999
$244$	−26.5590	−1.70026
$245$	8.55151	0.546336
$246$	3.69705	0.235715
$247$	0	0
$248$	−12.0072	−0.762457
$249$	−1.23316	−0.0781486
$250$	−0.486735	−0.0307838
$251$	−23.3098	−1.47130	−0.735652	−	0.677360i	$-0.763124\pi$
$251$	−23.3098	−1.47130	−0.735652	+	0.677360i	$0.763124\pi$
$252$	16.1703	1.01863
$253$	1.37173	0.0862401
$254$	2.32986	0.146188
$255$	−1.12581	−0.0705008
$256$	0.231723	0.0144827
$257$	−18.7257	−1.16808	−0.584038	−	0.811727i	$-0.698528\pi$
$257$	−18.7257	−1.16808	−0.584038	+	0.811727i	$0.698528\pi$
$258$	−2.59710	−0.161688
$259$	−36.5922	−2.27373
$260$	0.548075	0.0339901
$261$	−16.8964	−1.04586
$262$	3.78929	0.234103
$263$	−10.3004	−0.635151	−0.317575	−	0.948233i	$-0.602869\pi$
$263$	−10.3004	−0.635151	−0.317575	+	0.948233i	$0.602869\pi$
$264$	−6.21784	−0.382682
$265$	−10.5136	−0.645847
$266$	0	0
$267$	3.87817	0.237340
$268$	−20.3631	−1.24387
$269$	−7.11280	−0.433675	−0.216838	−	0.976208i	$-0.569574\pi$
$269$	−7.11280	−0.433675	−0.216838	+	0.976208i	$0.569574\pi$
$270$	−2.12859	−0.129542
$271$	−12.5497	−0.762341	−0.381170	−	0.924505i	$-0.624479\pi$
$271$	−12.5497	−0.762341	−0.381170	+	0.924505i	$0.624479\pi$
$272$	3.61217	0.219020
$273$	1.00664	0.0609244
$274$	−6.54353	−0.395309
$275$	4.13411	0.249296
$276$	0.480378	0.0289154
$277$	−6.11653	−0.367507	−0.183753	−	0.982972i	$-0.558825\pi$
$277$	−6.11653	−0.367507	−0.183753	+	0.982972i	$0.558825\pi$
$278$	−7.95523	−0.477123
$279$	15.2462	0.912764
$280$	7.22310	0.431662
$281$	12.9154	0.770468	0.385234	−	0.922819i	$-0.374121\pi$
$281$	12.9154	0.770468	0.385234	+	0.922819i	$0.374121\pi$
$282$	1.67502	0.0997462
$283$	−4.84266	−0.287866	−0.143933	−	0.989587i	$-0.545975\pi$
$283$	−4.84266	−0.287866	−0.143933	+	0.989587i	$0.545975\pi$
$284$	8.01017	0.475316
$285$	0	0
$286$	0.625518	0.0369876
$287$	36.4778	2.15321
$288$	11.5021	0.677771
$289$	−15.1203	−0.889430
$290$	−3.53614	−0.207650
$291$	−10.2045	−0.598196
$292$	−15.6227	−0.914250
$293$	−11.9856	−0.700205	−0.350102	−	0.936711i	$-0.613853\pi$
$293$	−11.9856	−0.700205	−0.350102	+	0.936711i	$0.613853\pi$
$294$	3.41788	0.199335
$295$	−7.23383	−0.421170
$296$	−16.9957	−0.987855
$297$	18.0793	1.04907
$298$	−8.47842	−0.491142
$299$	−0.103146	−0.00596510
$300$	1.44776	0.0835862
$301$	−25.6248	−1.47699
$302$	6.23610	0.358847
$303$	−0.896987	−0.0515305
$304$	0	0
$305$	15.0639	0.862556
$306$	1.55200	0.0887221
$307$	7.14551	0.407816	0.203908	−	0.978990i	$-0.434636\pi$
$307$	7.14551	0.407816	0.203908	+	0.978990i	$0.434636\pi$
$308$	−28.7437	−1.63782
$309$	−13.1549	−0.748359
$310$	3.19078	0.181224
$311$	−0.488483	−0.0276993	−0.0138497	−	0.999904i	$-0.504409\pi$
$311$	−0.488483	−0.0276993	−0.0138497	+	0.999904i	$0.504409\pi$
$312$	0.467545	0.0264695
$313$	−8.53756	−0.482571	−0.241286	−	0.970454i	$-0.577569\pi$
$313$	−8.53756	−0.482571	−0.241286	+	0.970454i	$0.577569\pi$
$314$	2.58550	0.145908
$315$	−9.17156	−0.516759
$316$	13.0946	0.736626
$317$	−7.49294	−0.420845	−0.210423	−	0.977610i	$-0.567484\pi$
$317$	−7.49294	−0.420845	−0.210423	+	0.977610i	$0.567484\pi$
$318$	−4.20210	−0.235642
$319$	30.0344	1.68160
$320$	−2.86211	−0.159997
$321$	−16.0235	−0.894346
$322$	−0.636893	−0.0354927
$323$	0	0
$324$	−5.97001	−0.331667
$325$	−0.310860	−0.0172434
$326$	−9.30561	−0.515390
$327$	3.70203	0.204723
$328$	16.9426	0.935496
$329$	16.5270	0.911162
$330$	1.65232	0.0909575
$331$	2.71687	0.149333	0.0746664	−	0.997209i	$-0.476211\pi$
$331$	2.71687	0.149333	0.0746664	+	0.997209i	$0.476211\pi$
$332$	−2.64773	−0.145313
$333$	21.5804	1.18260
$334$	0.842468	0.0460978
$335$	11.5497	0.631025
$336$	−8.53163	−0.465439
$337$	32.4773	1.76915	0.884575	−	0.466398i	$-0.154448\pi$
$337$	32.4773	1.76915	0.884575	+	0.466398i	$0.154448\pi$
$338$	6.28052	0.341615
$339$	−4.22579	−0.229514
$340$	−2.41723	−0.131092
$341$	−27.1010	−1.46760
$342$	0	0
$343$	6.11844	0.330365
$344$	−11.9018	−0.641700
$345$	−0.272464	−0.0146690
$346$	−2.40164	−0.129113
$347$	9.48154	0.508996	0.254498	−	0.967073i	$-0.418090\pi$
$347$	9.48154	0.508996	0.254498	+	0.967073i	$0.418090\pi$
$348$	10.5180	0.563823
$349$	1.86682	0.0999286	0.0499643	−	0.998751i	$-0.484089\pi$
$349$	1.86682	0.0999286	0.0499643	+	0.998751i	$0.484089\pi$
$350$	−1.91946	−0.102599
$351$	−1.35945	−0.0725623
$352$	−20.4458	−1.08976
$353$	0.705567	0.0375536	0.0187768	−	0.999824i	$-0.494023\pi$
$353$	0.705567	0.0375536	0.0187768	+	0.999824i	$0.494023\pi$
$354$	−2.89123	−0.153667
$355$	−4.54326	−0.241131
$356$	8.32684	0.441322
$357$	−4.43967	−0.234972
$358$	−11.3525	−0.599999
$359$	−18.1880	−0.959926	−0.479963	−	0.877289i	$-0.659350\pi$
$359$	−18.1880	−0.959926	−0.479963	+	0.877289i	$0.659350\pi$
$360$	−4.25985	−0.224514
$361$	0	0
$362$	−3.79978	−0.199712
$363$	−5.00147	−0.262509
$364$	2.16135	0.113286
$365$	8.86098	0.463805
$366$	6.02075	0.314710
$367$	31.0512	1.62086	0.810430	−	0.585835i	$-0.199233\pi$
$367$	31.0512	1.62086	0.810430	+	0.585835i	$0.199233\pi$
$368$	0.874204	0.0455710
$369$	−21.5129	−1.11992
$370$	4.51642	0.234798
$371$	−41.4609	−2.15254
$372$	−9.49072	−0.492071
$373$	−6.83254	−0.353775	−0.176888	−	0.984231i	$-0.556603\pi$
$373$	−6.83254	−0.353775	−0.176888	+	0.984231i	$0.556603\pi$
$374$	−2.75878	−0.142653
$375$	−0.821147	−0.0424039
$376$	7.67616	0.395868
$377$	−2.25841	−0.116314
$378$	−8.39418	−0.431750
$379$	13.6532	0.701318	0.350659	−	0.936503i	$-0.385958\pi$
$379$	13.6532	0.701318	0.350659	+	0.936503i	$0.385958\pi$
$380$	0	0
$381$	3.93059	0.201370
$382$	7.95927	0.407232
$383$	15.1563	0.774452	0.387226	−	0.921985i	$-0.373433\pi$
$383$	15.1563	0.774452	0.387226	+	0.921985i	$0.373433\pi$
$384$	−9.26612	−0.472860
$385$	16.3030	0.830879
$386$	4.47220	0.227629
$387$	15.1123	0.768203
$388$	−21.9100	−1.11231
$389$	−29.3419	−1.48769	−0.743846	−	0.668351i	$-0.767000\pi$
$389$	−29.3419	−1.48769	−0.743846	+	0.668351i	$0.767000\pi$
$390$	−0.124245	−0.00629139
$391$	0.454916	0.0230061
$392$	15.6632	0.791110
$393$	6.39274	0.322471
$394$	9.80051	0.493743
$395$	−7.42705	−0.373695
$396$	16.9517	0.851854
$397$	32.0863	1.61037	0.805183	−	0.593027i	$-0.202067\pi$
$397$	32.0863	1.61037	0.805183	+	0.593027i	$0.202067\pi$
$398$	4.06883	0.203952
$399$	0	0
$400$	2.63466	0.131733
$401$	14.1485	0.706543	0.353271	−	0.935521i	$-0.385069\pi$
$401$	14.1485	0.706543	0.353271	+	0.935521i	$0.385069\pi$
$402$	4.61618	0.230234
$403$	2.03784	0.101512
$404$	−1.92592	−0.0958183
$405$	3.38611	0.168257
$406$	−13.9449	−0.692075
$407$	−38.3605	−1.90146
$408$	−2.06206	−0.102087
$409$	−17.7264	−0.876516	−0.438258	−	0.898849i	$-0.644404\pi$
$409$	−17.7264	−0.876516	−0.438258	+	0.898849i	$0.644404\pi$
$410$	−4.50230	−0.222353
$411$	−11.0393	−0.544527
$412$	−28.2450	−1.39153
$413$	−28.5269	−1.40372
$414$	0.375610	0.0184602
$415$	1.50176	0.0737184
$416$	1.53740	0.0753774
$417$	−13.4209	−0.657223
$418$	0	0
$419$	−15.4517	−0.754866	−0.377433	−	0.926037i	$-0.623193\pi$
$419$	−15.4517	−0.754866	−0.377433	+	0.926037i	$0.623193\pi$
$420$	5.70928	0.278585
$421$	0.0444305	0.00216541	0.00108271	−	0.999999i	$-0.499655\pi$
$421$	0.0444305	0.00216541	0.00108271	+	0.999999i	$0.499655\pi$
$422$	−2.01071	−0.0978798
$423$	−9.74684	−0.473908
$424$	−19.2570	−0.935205
$425$	1.37102	0.0665041
$426$	−1.81585	−0.0879784
$427$	59.4050	2.87481
$428$	−34.4042	−1.66299
$429$	1.05528	0.0509495
$430$	3.16277	0.152522
$431$	9.23296	0.444736	0.222368	−	0.974963i	$-0.428621\pi$
$431$	9.23296	0.444736	0.222368	+	0.974963i	$0.428621\pi$
$432$	11.5219	0.554347
$433$	27.7471	1.33344	0.666719	−	0.745309i	$-0.267698\pi$
$433$	27.7471	1.33344	0.666719	+	0.745309i	$0.267698\pi$
$434$	12.5830	0.604001
$435$	−5.96566	−0.286032
$436$	7.94864	0.380671
$437$	0	0
$438$	3.54157	0.169223
$439$	−16.1422	−0.770427	−0.385214	−	0.922827i	$-0.625872\pi$
$439$	−16.1422	−0.770427	−0.385214	+	0.922827i	$0.625872\pi$
$440$	7.57214	0.360988
$441$	−19.8884	−0.947066
$442$	0.207444	0.00986711
$443$	6.83505	0.324743	0.162372	−	0.986730i	$-0.448086\pi$
$443$	6.83505	0.324743	0.162372	+	0.986730i	$0.448086\pi$
$444$	−13.4338	−0.637538
$445$	−4.72287	−0.223886
$446$	−6.70699	−0.317585
$447$	−14.3035	−0.676534
$448$	−11.2868	−0.533253
$449$	14.2282	0.671470	0.335735	−	0.941957i	$-0.391015\pi$
$449$	14.2282	0.671470	0.335735	+	0.941957i	$0.391015\pi$
$450$	1.13201	0.0533634
$451$	38.2405	1.80067
$452$	−9.07322	−0.426768
$453$	10.5206	0.494302
$454$	−0.898155	−0.0421525
$455$	−1.22589	−0.0574706
$456$	0	0
$457$	18.9125	0.884688	0.442344	−	0.896845i	$-0.354147\pi$
$457$	18.9125	0.884688	0.442344	+	0.896845i	$0.354147\pi$
$458$	6.59607	0.308214
$459$	5.99573	0.279857
$460$	−0.585008	−0.0272762
$461$	−18.9918	−0.884538	−0.442269	−	0.896882i	$-0.645826\pi$
$461$	−18.9918	−0.884538	−0.442269	+	0.896882i	$0.645826\pi$
$462$	6.51601	0.303152
$463$	14.2655	0.662976	0.331488	−	0.943459i	$-0.392449\pi$
$463$	14.2655	0.662976	0.331488	+	0.943459i	$0.392449\pi$
$464$	19.1409	0.888594
$465$	5.38301	0.249631
$466$	2.82418	0.130828
$467$	−31.0728	−1.43788	−0.718938	−	0.695074i	$-0.755372\pi$
$467$	−31.0728	−1.43788	−0.718938	+	0.695074i	$0.755372\pi$
$468$	−1.27467	−0.0589215
$469$	45.5465	2.10314
$470$	−2.03986	−0.0940916
$471$	4.36188	0.200985
$472$	−13.2497	−0.609866
$473$	−26.8631	−1.23517
$474$	−2.96845	−0.136346
$475$	0	0
$476$	−9.53243	−0.436918
$477$	24.4517	1.11957
$478$	−7.72274	−0.353230
$479$	−9.30229	−0.425032	−0.212516	−	0.977158i	$-0.568166\pi$
$479$	−9.30229	−0.425032	−0.212516	+	0.977158i	$0.568166\pi$
$480$	4.06110	0.185363
$481$	2.88448	0.131521
$482$	−11.4448	−0.521297
$483$	−1.07447	−0.0488902
$484$	−10.7387	−0.488122
$485$	12.4271	0.564284
$486$	7.73913	0.351054
$487$	4.99376	0.226289	0.113144	−	0.993579i	$-0.463908\pi$
$487$	4.99376	0.226289	0.113144	+	0.993579i	$0.463908\pi$
$488$	27.5914	1.24901
$489$	−15.6991	−0.709936
$490$	−4.16232	−0.188034
$491$	5.74419	0.259232	0.129616	−	0.991564i	$-0.458626\pi$
$491$	5.74419	0.259232	0.129616	+	0.991564i	$0.458626\pi$
$492$	13.3917	0.603747
$493$	9.96048	0.448598
$494$	0	0
$495$	−9.61476	−0.432151
$496$	−17.2714	−0.775511
$497$	−17.9165	−0.803666
$498$	0.600224	0.0268967
$499$	0.895797	0.0401014	0.0200507	−	0.999799i	$-0.493617\pi$
$499$	0.895797	0.0401014	0.0200507	+	0.999799i	$0.493617\pi$
$500$	−1.76309	−0.0788477
$501$	1.42129	0.0634984
$502$	11.3457	0.506384
$503$	37.6903	1.68053	0.840264	−	0.542178i	$-0.182400\pi$
$503$	37.6903	1.68053	0.840264	+	0.542178i	$0.182400\pi$
$504$	−16.7989	−0.748281
$505$	1.09236	0.0486093
$506$	−0.667670	−0.0296816
$507$	10.5956	0.470566
$508$	8.43939	0.374438
$509$	−24.1589	−1.07082	−0.535412	−	0.844591i	$-0.679844\pi$
$509$	−24.1589	−1.07082	−0.535412	+	0.844591i	$0.679844\pi$
$510$	0.547970	0.0242645
$511$	34.9436	1.54582
$512$	−22.6815	−1.00239
$513$	0	0
$514$	9.11444	0.402021
$515$	16.0202	0.705934
$516$	−9.40740	−0.414138
$517$	17.3256	0.761980
$518$	17.8107	0.782557
$519$	−4.05170	−0.177850
$520$	−0.569380	−0.0249690
$521$	−43.0504	−1.88607	−0.943036	−	0.332690i	$-0.892044\pi$
$521$	−43.0504	−1.88607	−0.943036	+	0.332690i	$0.892044\pi$
$522$	8.22407	0.359958
$523$	39.2765	1.71744	0.858720	−	0.512444i	$-0.171260\pi$
$523$	39.2765	1.71744	0.858720	+	0.512444i	$0.171260\pi$
$524$	13.7259	0.599617
$525$	−3.23823	−0.141328
$526$	5.01357	0.218602
$527$	−8.98767	−0.391509
$528$	−8.94391	−0.389234
$529$	−22.8899	−0.995213
$530$	5.11735	0.222283
$531$	16.8239	0.730093
$532$	0	0
$533$	−2.87546	−0.124550
$534$	−1.88764	−0.0816863
$535$	19.5136	0.843646
$536$	21.1547	0.913742
$537$	−19.1523	−0.826482
$538$	3.46205	0.149260
$539$	35.3528	1.52275
$540$	−7.71034	−0.331800
$541$	7.69634	0.330891	0.165446	−	0.986219i	$-0.447094\pi$
$541$	7.69634	0.330891	0.165446	+	0.986219i	$0.447094\pi$
$542$	6.10838	0.262378
$543$	−6.41043	−0.275098
$544$	−6.78055	−0.290714
$545$	−4.50836	−0.193117
$546$	−0.489965	−0.0209686
$547$	−3.85134	−0.164672	−0.0823358	−	0.996605i	$-0.526238\pi$
$547$	−3.85134	−0.164672	−0.0823358	+	0.996605i	$0.526238\pi$
$548$	−23.7025	−1.01252
$549$	−35.0343	−1.49523
$550$	−2.01221	−0.0858011
$551$	0	0
$552$	−0.499052	−0.0212411
$553$	−29.2889	−1.24549
$554$	2.97713	0.126486
$555$	7.61944	0.323427
$556$	−28.8160	−1.22207
$557$	−33.2316	−1.40807	−0.704033	−	0.710167i	$-0.748619\pi$
$557$	−33.2316	−1.40807	−0.704033	+	0.710167i	$0.748619\pi$
$558$	−7.42084	−0.314149
$559$	2.01995	0.0854346
$560$	10.3899	0.439053
$561$	−4.65421	−0.196501
$562$	−6.28637	−0.265175
$563$	−25.3059	−1.06652	−0.533259	−	0.845952i	$-0.679033\pi$
$563$	−25.3059	−1.06652	−0.533259	+	0.845952i	$0.679033\pi$
$564$	6.06740	0.255484
$565$	5.14621	0.216502
$566$	2.35709	0.0990760
$567$	13.3533	0.560784
$568$	−8.32155	−0.349165
$569$	−1.02278	−0.0428773	−0.0214387	−	0.999770i	$-0.506825\pi$
$569$	−1.02278	−0.0428773	−0.0214387	+	0.999770i	$0.506825\pi$
$570$	0	0
$571$	−13.1612	−0.550780	−0.275390	−	0.961333i	$-0.588807\pi$
$571$	−13.1612	−0.550780	−0.275390	+	0.961333i	$0.588807\pi$
$572$	2.26580	0.0947378
$573$	13.4277	0.560951
$574$	−17.7550	−0.741079
$575$	0.331809	0.0138374
$576$	6.65645	0.277352
$577$	−19.7049	−0.820324	−0.410162	−	0.912013i	$-0.634528\pi$
$577$	−19.7049	−0.820324	−0.410162	+	0.912013i	$0.634528\pi$
$578$	7.35958	0.306118
$579$	7.54484	0.313553
$580$	−12.8089	−0.531860
$581$	5.92224	0.245696
$582$	4.96686	0.205883
$583$	−43.4645	−1.80011
$584$	16.2300	0.671603
$585$	0.722973	0.0298913
$586$	5.83380	0.240992
$587$	−32.4022	−1.33738	−0.668691	−	0.743540i	$-0.733145\pi$
$587$	−32.4022	−1.33738	−0.668691	+	0.743540i	$0.733145\pi$
$588$	12.3805	0.510563
$589$	0	0
$590$	3.52096	0.144956
$591$	16.5340	0.680117
$592$	−24.4471	−1.00477
$593$	−37.6128	−1.54457	−0.772286	−	0.635275i	$-0.780887\pi$
$593$	−37.6128	−1.54457	−0.772286	+	0.635275i	$0.780887\pi$
$594$	−8.79981	−0.361061
$595$	5.40666	0.221652
$596$	−30.7112	−1.25798
$597$	6.86432	0.280938
$598$	0.0502049	0.00205303
$599$	46.7320	1.90942	0.954709	−	0.297541i	$-0.0961665\pi$
$599$	46.7320	1.90942	0.954709	+	0.297541i	$0.0961665\pi$
$600$	−1.50404	−0.0614020
$601$	−31.4346	−1.28224	−0.641122	−	0.767439i	$-0.721531\pi$
$601$	−31.4346	−1.28224	−0.641122	+	0.767439i	$0.721531\pi$
$602$	12.4725	0.508341
$603$	−26.8612	−1.09387
$604$	22.5889	0.919129
$605$	6.09084	0.247628
$606$	0.436595	0.0177355
$607$	−33.7764	−1.37094	−0.685471	−	0.728100i	$-0.740404\pi$
$607$	−33.7764	−1.37094	−0.685471	+	0.728100i	$0.740404\pi$
$608$	0	0
$609$	−23.5258	−0.953314
$610$	−7.33212	−0.296869
$611$	−1.30278	−0.0527050
$612$	5.62178	0.227247
$613$	−20.5371	−0.829486	−0.414743	−	0.909939i	$-0.636129\pi$
$613$	−20.5371	−0.829486	−0.414743	+	0.909939i	$0.636129\pi$
$614$	−3.47797	−0.140359
$615$	−7.59562	−0.306285
$616$	29.8610	1.20314
$617$	−25.4123	−1.02306	−0.511531	−	0.859265i	$-0.670922\pi$
$617$	−25.4123	−1.02306	−0.511531	+	0.859265i	$0.670922\pi$
$618$	6.40297	0.257565
$619$	8.94872	0.359680	0.179840	−	0.983696i	$-0.442442\pi$
$619$	8.94872	0.359680	0.179840	+	0.983696i	$0.442442\pi$
$620$	11.5579	0.464176
$621$	1.45107	0.0582293
$622$	0.237762	0.00953337
$623$	−18.6248	−0.746188
$624$	0.672529	0.0269227
$625$	1.00000	0.0400000
$626$	4.15553	0.166088
$627$	0	0
$628$	9.36541	0.373721
$629$	−12.7217	−0.507247
$630$	4.46412	0.177855
$631$	13.4931	0.537154	0.268577	−	0.963258i	$-0.413447\pi$
$631$	13.4931	0.537154	0.268577	+	0.963258i	$0.413447\pi$
$632$	−13.6036	−0.541122
$633$	−3.39217	−0.134827
$634$	3.64708	0.144844
$635$	−4.78671	−0.189955
$636$	−15.2212	−0.603559
$637$	−2.65833	−0.105327
$638$	−14.6188	−0.578764
$639$	10.5663	0.417998
$640$	11.2844	0.446053
$641$	−15.8937	−0.627764	−0.313882	−	0.949462i	$-0.601630\pi$
$641$	−15.8937	−0.627764	−0.313882	+	0.949462i	$0.601630\pi$
$642$	7.79921	0.307810
$643$	21.4325	0.845217	0.422608	−	0.906312i	$-0.361115\pi$
$643$	21.4325	0.845217	0.422608	+	0.906312i	$0.361115\pi$
$644$	−2.30700	−0.0909087
$645$	5.33575	0.210095
$646$	0	0
$647$	20.4894	0.805523	0.402761	−	0.915305i	$-0.368050\pi$
$647$	20.4894	0.805523	0.402761	+	0.915305i	$0.368050\pi$
$648$	6.20209	0.243641
$649$	−29.9054	−1.17389
$650$	0.151307	0.00593473
$651$	21.2281	0.831995
$652$	−33.7075	−1.32009
$653$	25.4306	0.995174	0.497587	−	0.867414i	$-0.334219\pi$
$653$	25.4306	0.995174	0.497587	+	0.867414i	$0.334219\pi$
$654$	−1.80191	−0.0704601
$655$	−7.78512	−0.304190
$656$	24.3706	0.951513
$657$	−20.6081	−0.804000
$658$	−8.04426	−0.313598
$659$	−6.31345	−0.245937	−0.122969	−	0.992411i	$-0.539241\pi$
$659$	−6.31345	−0.245937	−0.122969	+	0.992411i	$0.539241\pi$
$660$	5.98518	0.232973
$661$	−19.3656	−0.753234	−0.376617	−	0.926369i	$-0.622913\pi$
$661$	−19.3656	−0.753234	−0.376617	+	0.926369i	$0.622913\pi$
$662$	−1.32240	−0.0513964
$663$	0.349969	0.0135917
$664$	2.75066	0.106746
$665$	0	0
$666$	−10.5039	−0.407019
$667$	2.41060	0.0933388
$668$	3.05165	0.118072
$669$	−11.3150	−0.437465
$670$	−5.62162	−0.217182
$671$	62.2757	2.40413
$672$	16.0151	0.617796
$673$	13.0894	0.504560	0.252280	−	0.967654i	$-0.418820\pi$
$673$	13.0894	0.504560	0.252280	+	0.967654i	$0.418820\pi$
$674$	−15.8078	−0.608895
$675$	4.37320	0.168324
$676$	22.7498	0.874992
$677$	31.2154	1.19970	0.599852	−	0.800111i	$-0.295226\pi$
$677$	31.2154	1.19970	0.599852	+	0.800111i	$0.295226\pi$
$678$	2.05684	0.0789925
$679$	49.0066	1.88070
$680$	2.51119	0.0962998
$681$	−1.51524	−0.0580639
$682$	13.1910	0.505110
$683$	−17.8089	−0.681440	−0.340720	−	0.940165i	$-0.610671\pi$
$683$	−17.8089	−0.681440	−0.340720	+	0.940165i	$0.610671\pi$
$684$	0	0
$685$	13.4437	0.513658
$686$	−2.97806	−0.113703
$687$	11.1279	0.424556
$688$	−17.1198	−0.652687
$689$	3.26827	0.124511
$690$	0.132618	0.00504867
$691$	3.67194	0.139687	0.0698437	−	0.997558i	$-0.477750\pi$
$691$	3.67194	0.139687	0.0698437	+	0.997558i	$0.477750\pi$
$692$	−8.69941	−0.330702
$693$	−37.9162	−1.44032
$694$	−4.61500	−0.175183
$695$	16.3441	0.619965
$696$	−10.9269	−0.414182
$697$	12.6819	0.480362
$698$	−0.908647	−0.0343928
$699$	4.76454	0.180212
$700$	−6.95281	−0.262792
$701$	−22.4443	−0.847711	−0.423855	−	0.905730i	$-0.639324\pi$
$701$	−22.4443	−0.847711	−0.423855	+	0.905730i	$0.639324\pi$
$702$	0.661694	0.0249740
$703$	0	0
$704$	−11.8323	−0.445945
$705$	−3.44134	−0.129609
$706$	−0.343424	−0.0129249
$707$	4.30776	0.162010
$708$	−10.4728	−0.393593
$709$	−14.1832	−0.532662	−0.266331	−	0.963882i	$-0.585811\pi$
$709$	−14.1832	−0.532662	−0.266331	+	0.963882i	$0.585811\pi$
$710$	2.21136	0.0829909
$711$	17.2732	0.647796
$712$	−8.65054	−0.324193
$713$	−2.17516	−0.0814605
$714$	2.16094	0.0808712
$715$	−1.28513	−0.0480611
$716$	−41.1220	−1.53680
$717$	−13.0287	−0.486565
$718$	8.85273	0.330381
$719$	−9.58542	−0.357476	−0.178738	−	0.983897i	$-0.557201\pi$
$719$	−9.58542	−0.357476	−0.178738	+	0.983897i	$0.557201\pi$
$720$	−6.12748	−0.228358
$721$	63.1763	2.35281
$722$	0	0
$723$	−19.3080	−0.718072
$724$	−13.7639	−0.511530
$725$	7.26503	0.269816
$726$	2.43439	0.0903488
$727$	37.2501	1.38153	0.690766	−	0.723079i	$-0.257274\pi$
$727$	37.2501	1.38153	0.690766	+	0.723079i	$0.257274\pi$
$728$	−2.24537	−0.0832191
$729$	2.89799	0.107333
$730$	−4.31295	−0.159629
$731$	−8.90876	−0.329502
$732$	21.8088	0.806078
$733$	36.5477	1.34992	0.674960	−	0.737855i	$-0.264161\pi$
$733$	36.5477	1.34992	0.674960	+	0.737855i	$0.264161\pi$
$734$	−15.1137	−0.557858
$735$	−7.02205	−0.259012
$736$	−1.64101	−0.0604883
$737$	47.7475	1.75880
$738$	10.4711	0.385446
$739$	26.3205	0.968214	0.484107	−	0.875009i	$-0.339145\pi$
$739$	26.3205	0.968214	0.484107	+	0.875009i	$0.339145\pi$
$740$	16.3597	0.601396
$741$	0	0
$742$	20.1805	0.740849
$743$	−17.6872	−0.648879	−0.324440	−	0.945906i	$-0.605176\pi$
$743$	−17.6872	−0.648879	−0.324440	+	0.945906i	$0.605176\pi$
$744$	9.85966	0.361473
$745$	17.4190	0.638182
$746$	3.32564	0.121760
$747$	−3.49266	−0.127790
$748$	−9.99307	−0.365383
$749$	76.9526	2.81179
$750$	0.399681	0.0145943
$751$	−36.3676	−1.32707	−0.663536	−	0.748144i	$-0.730945\pi$
$751$	−36.3676	−1.32707	−0.663536	+	0.748144i	$0.730945\pi$
$752$	11.0416	0.402646
$753$	19.1408	0.697530
$754$	1.09925	0.0400322
$755$	−12.8121	−0.466280
$756$	−30.4060	−1.10586
$757$	6.58459	0.239321	0.119661	−	0.992815i	$-0.461819\pi$
$757$	6.58459	0.239321	0.119661	+	0.992815i	$0.461819\pi$
$758$	−6.64549	−0.241375
$759$	−1.12639	−0.0408855
$760$	0	0
$761$	−2.25625	−0.0817889	−0.0408944	−	0.999163i	$-0.513021\pi$
$761$	−2.25625	−0.0817889	−0.0408944	+	0.999163i	$0.513021\pi$
$762$	−1.91316	−0.0693064
$763$	−17.7789	−0.643639
$764$	28.8307	1.04306
$765$	−3.18860	−0.115284
$766$	−7.37711	−0.266546
$767$	2.24871	0.0811963
$768$	−0.190279	−0.00686610
$769$	−11.9087	−0.429438	−0.214719	−	0.976676i	$-0.568884\pi$
$769$	−11.9087	−0.429438	−0.214719	+	0.976676i	$0.568884\pi$
$770$	−7.93525	−0.285966
$771$	15.3765	0.553772
$772$	16.1996	0.583035
$773$	−25.8796	−0.930825	−0.465413	−	0.885094i	$-0.654094\pi$
$773$	−25.8796	−0.930825	−0.465413	+	0.885094i	$0.654094\pi$
$774$	−7.35570	−0.264395
$775$	−6.55547	−0.235479
$776$	22.7618	0.817099
$777$	30.0476	1.07795
$778$	14.2817	0.512024
$779$	0	0
$780$	−0.450050	−0.0161144
$781$	−18.7823	−0.672084
$782$	−0.221423	−0.00791808
$783$	31.7714	1.13542
$784$	22.5303	0.804655
$785$	−5.31193	−0.189591
$786$	−3.11157	−0.110986
$787$	−1.04436	−0.0372276	−0.0186138	−	0.999827i	$-0.505925\pi$
$787$	−1.04436	−0.0372276	−0.0186138	+	0.999827i	$0.505925\pi$
$788$	35.5002	1.26464
$789$	8.45816	0.301118
$790$	3.61501	0.128616
$791$	20.2943	0.721581
$792$	−17.6107	−0.625767
$793$	−4.68277	−0.166290
$794$	−15.6175	−0.554245
$795$	8.63324	0.306189
$796$	14.7384	0.522389
$797$	34.2326	1.21258	0.606291	−	0.795243i	$-0.292657\pi$
$797$	34.2326	1.21258	0.606291	+	0.795243i	$0.292657\pi$
$798$	0	0
$799$	5.74579	0.203272
$800$	−4.94564	−0.174855
$801$	10.9841	0.388103
$802$	−6.88658	−0.243173
$803$	36.6323	1.29272
$804$	16.7211	0.589707
$805$	1.30850	0.0461186
$806$	−0.991886	−0.0349377
$807$	5.84066	0.205601
$808$	2.00079	0.0703876
$809$	−10.3027	−0.362225	−0.181113	−	0.983462i	$-0.557970\pi$
$809$	−10.3027	−0.362225	−0.181113	+	0.983462i	$0.557970\pi$
$810$	−1.64814	−0.0579097
$811$	−1.70121	−0.0597377	−0.0298689	−	0.999554i	$-0.509509\pi$
$811$	−1.70121	−0.0597377	−0.0298689	+	0.999554i	$0.509509\pi$
$812$	−50.5124	−1.77264
$813$	10.3052	0.361418
$814$	18.6714	0.654431
$815$	19.1184	0.669690
$816$	−2.96612	−0.103835
$817$	0	0
$818$	8.62808	0.301674
$819$	2.85107	0.0996246
$820$	−16.3086	−0.569520
$821$	−16.1378	−0.563213	−0.281606	−	0.959530i	$-0.590867\pi$
$821$	−16.1378	−0.563213	−0.281606	+	0.959530i	$0.590867\pi$
$822$	5.37320	0.187412
$823$	3.56271	0.124188	0.0620941	−	0.998070i	$-0.480222\pi$
$823$	3.56271	0.124188	0.0620941	+	0.998070i	$0.480222\pi$
$824$	29.3430	1.02221
$825$	−3.39471	−0.118189
$826$	13.8850	0.483123
$827$	0.677140	0.0235465	0.0117732	−	0.999931i	$-0.496252\pi$
$827$	0.677140	0.0235465	0.0117732	+	0.999931i	$0.496252\pi$
$828$	1.36056	0.0472829
$829$	−18.7206	−0.650192	−0.325096	−	0.945681i	$-0.605397\pi$
$829$	−18.7206	−0.650192	−0.325096	+	0.945681i	$0.605397\pi$
$830$	−0.730958	−0.0253719
$831$	5.02257	0.174231
$832$	0.889716	0.0308454
$833$	11.7243	0.406222
$834$	6.53241	0.226199
$835$	−1.73086	−0.0598987
$836$	0	0
$837$	−28.6684	−0.990924
$838$	7.52089	0.259805
$839$	18.2401	0.629717	0.314859	−	0.949139i	$-0.398043\pi$
$839$	18.2401	0.629717	0.314859	+	0.949139i	$0.398043\pi$
$840$	−5.93123	−0.204647
$841$	23.7807	0.820022
$842$	−0.0216259	−0.000745277 0
$843$	−10.6054	−0.365271
$844$	−7.28335	−0.250703
$845$	−12.9034	−0.443889
$846$	4.74413	0.163107
$847$	24.0195	0.825318
$848$	−27.6998	−0.951217
$849$	3.97654	0.136475
$850$	−0.667322	−0.0228890
$851$	−3.07886	−0.105542
$852$	−6.57753	−0.225342
$853$	58.1335	1.99045	0.995226	−	0.0975965i	$-0.0311155\pi$
$853$	58.1335	1.99045	0.995226	+	0.0975965i	$0.0311155\pi$
$854$	−28.9145	−0.989434
$855$	0	0
$856$	35.7416	1.22162
$857$	−23.9656	−0.818651	−0.409325	−	0.912388i	$-0.634236\pi$
$857$	−23.9656	−0.818651	−0.409325	+	0.912388i	$0.634236\pi$
$858$	−0.513642	−0.0175355
$859$	36.2800	1.23786	0.618928	−	0.785448i	$-0.287567\pi$
$859$	36.2800	1.23786	0.618928	+	0.785448i	$0.287567\pi$
$860$	11.4564	0.390660
$861$	−29.9536	−1.02082
$862$	−4.49401	−0.153066
$863$	47.5594	1.61894	0.809471	−	0.587160i	$-0.199754\pi$
$863$	47.5594	1.61894	0.809471	+	0.587160i	$0.199754\pi$
$864$	−21.6282	−0.735808
$865$	4.93419	0.167767
$866$	−13.5055	−0.458934
$867$	12.4160	0.421670
$868$	45.5790	1.54705
$869$	−30.7042	−1.04157
$870$	2.90370	0.0984445
$871$	−3.59033	−0.121654
$872$	−8.25763	−0.279639
$873$	−28.9018	−0.978179
$874$	0	0
$875$	3.94354	0.133316
$876$	12.8285	0.433436
$877$	−32.5474	−1.09905	−0.549524	−	0.835478i	$-0.685191\pi$
$877$	−32.5474	−1.09905	−0.549524	+	0.835478i	$0.685191\pi$
$878$	7.85700	0.265161
$879$	9.84192	0.331960
$880$	10.8920	0.367168
$881$	4.45990	0.150258	0.0751289	−	0.997174i	$-0.476063\pi$
$881$	4.45990	0.150258	0.0751289	+	0.997174i	$0.476063\pi$
$882$	9.68037	0.325955
$883$	−13.0697	−0.439832	−0.219916	−	0.975519i	$-0.570578\pi$
$883$	−13.0697	−0.439832	−0.219916	+	0.975519i	$0.570578\pi$
$884$	0.751420	0.0252730
$885$	5.94004	0.199672
$886$	−3.32686	−0.111768
$887$	−39.1678	−1.31513	−0.657564	−	0.753399i	$-0.728413\pi$
$887$	−39.1678	−1.31513	−0.657564	+	0.753399i	$0.728413\pi$
$888$	13.9560	0.468332
$889$	−18.8766	−0.633100
$890$	2.29879	0.0770555
$891$	13.9985	0.468969
$892$	−24.2946	−0.813443
$893$	0	0
$894$	6.96203	0.232845
$895$	23.3238	0.779629
$896$	44.5003	1.48665
$897$	0.0846982	0.00282799
$898$	−6.92536	−0.231102
$899$	−47.6257	−1.58841
$900$	4.10045	0.136682
$901$	−14.4144	−0.480212
$902$	−18.6130	−0.619745
$903$	21.0417	0.700225
$904$	9.42593	0.313502
$905$	7.80668	0.259503
$906$	−5.12076	−0.170126
$907$	−17.5529	−0.582834	−0.291417	−	0.956596i	$-0.594127\pi$
$907$	−17.5529	−0.582834	−0.291417	+	0.956596i	$0.594127\pi$
$908$	−3.25337	−0.107967
$909$	−2.54052	−0.0842636
$910$	0.596684	0.0197799
$911$	−26.2186	−0.868662	−0.434331	−	0.900753i	$-0.643015\pi$
$911$	−26.2186	−0.868662	−0.434331	+	0.900753i	$0.643015\pi$
$912$	0	0
$913$	6.20843	0.205469
$914$	−9.20537	−0.304486
$915$	−12.3697	−0.408929
$916$	23.8928	0.789440
$917$	−30.7010	−1.01383
$918$	−2.91833	−0.0963193
$919$	−10.3985	−0.343015	−0.171508	−	0.985183i	$-0.554864\pi$
$919$	−10.3985	−0.343015	−0.171508	+	0.985183i	$0.554864\pi$
$920$	0.607750	0.0200369
$921$	−5.86752	−0.193341
$922$	9.24399	0.304435
$923$	1.41232	0.0464870
$924$	23.6028	0.776475
$925$	−9.27902	−0.305092
$926$	−6.94354	−0.228179
$927$	−37.2585	−1.22373
$928$	−35.9302	−1.17947
$929$	−13.2358	−0.434252	−0.217126	−	0.976144i	$-0.569668\pi$
$929$	−13.2358	−0.434252	−0.217126	+	0.976144i	$0.569668\pi$
$930$	−2.62010	−0.0859164
$931$	0	0
$932$	10.2300	0.335094
$933$	0.401116	0.0131320
$934$	15.1242	0.494879
$935$	5.66793	0.185361
$936$	1.32422	0.0432834
$937$	−4.05374	−0.132430	−0.0662149	−	0.997805i	$-0.521092\pi$
$937$	−4.05374	−0.132430	−0.0662149	+	0.997805i	$0.521092\pi$
$938$	−22.1691	−0.723846
$939$	7.01059	0.228782
$940$	−7.38893	−0.241000
$941$	60.2851	1.96524	0.982618	−	0.185637i	$-0.0594349\pi$
$941$	60.2851	1.96524	0.982618	+	0.185637i	$0.0594349\pi$
$942$	−2.12308	−0.0691737
$943$	3.06923	0.0999479
$944$	−19.0587	−0.620308
$945$	17.2459	0.561009
$946$	13.0752	0.425112
$947$	17.9068	0.581892	0.290946	−	0.956739i	$-0.406030\pi$
$947$	17.9068	0.581892	0.290946	+	0.956739i	$0.406030\pi$
$948$	−10.7526	−0.349227
$949$	−2.75453	−0.0894158
$950$	0	0
$951$	6.15281	0.199518
$952$	9.90299	0.320958
$953$	−47.0458	−1.52396	−0.761981	−	0.647600i	$-0.775773\pi$
$953$	−47.0458	−1.52396	−0.761981	+	0.647600i	$0.775773\pi$
$954$	−11.9015	−0.385326
$955$	−16.3524	−0.529151
$956$	−27.9739	−0.904741
$957$	−24.6627	−0.797231
$958$	4.52775	0.146285
$959$	53.0158	1.71197
$960$	2.35021	0.0758528
$961$	11.9742	0.386265
$962$	−1.40398	−0.0452660
$963$	−45.3831	−1.46245
$964$	−41.4563	−1.33522
$965$	−9.18817	−0.295778
$966$	0.522983	0.0168267
$967$	−5.61537	−0.180578	−0.0902891	−	0.995916i	$-0.528779\pi$
$967$	−5.61537	−0.180578	−0.0902891	+	0.995916i	$0.528779\pi$
$968$	11.1561	0.358572
$969$	0	0
$970$	−6.04869	−0.194212
$971$	35.8060	1.14907	0.574535	−	0.818480i	$-0.305183\pi$
$971$	35.8060	1.14907	0.574535	+	0.818480i	$0.305183\pi$
$972$	28.0333	0.899168
$973$	64.4535	2.06628
$974$	−2.43064	−0.0778826
$975$	0.255262	0.00817493
$976$	39.6882	1.27039
$977$	−15.5873	−0.498681	−0.249340	−	0.968416i	$-0.580214\pi$
$977$	−15.5873	−0.498681	−0.249340	+	0.968416i	$0.580214\pi$
$978$	7.64128	0.244341
$979$	−19.5249	−0.624017
$980$	−15.0771	−0.481619
$981$	10.4852	0.334766
$982$	−2.79590	−0.0892207
$983$	33.4370	1.06647	0.533237	−	0.845966i	$-0.320976\pi$
$983$	33.4370	1.06647	0.533237	+	0.845966i	$0.320976\pi$
$984$	−13.9123	−0.443509
$985$	−20.1352	−0.641561
$986$	−4.84812	−0.154395
$987$	−13.5711	−0.431972
$988$	0	0
$989$	−2.15607	−0.0685589
$990$	4.67984	0.148735
$991$	−23.7375	−0.754046	−0.377023	−	0.926204i	$-0.623052\pi$
$991$	−23.7375	−0.754046	−0.377023	+	0.926204i	$0.623052\pi$
$992$	32.4210	1.02937
$993$	−2.23095	−0.0707972
$994$	8.72059	0.276600
$995$	−8.35943	−0.265012
$996$	2.17418	0.0688915
$997$	24.2371	0.767596	0.383798	−	0.923417i	$-0.374616\pi$
$997$	24.2371	0.767596	0.383798	+	0.923417i	$0.374616\pi$
$998$	−0.436016	−0.0138018
$999$	−40.5790	−1.28386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.w.1.8	✓	16
5.4	even	2		9025.2.a.cm.1.9		16
19.18	odd	2	inner	1805.2.a.w.1.9	yes	16
95.94	odd	2		9025.2.a.cm.1.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.w.1.8	✓	16	1.1	even	1	trivial
1805.2.a.w.1.9	yes	16	19.18	odd	2	inner
9025.2.a.cm.1.8		16	95.94	odd	2
9025.2.a.cm.1.9		16	5.4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-0.486735 q^{2} -0.821147 q^{3} -1.76309 q^{4} +1.00000 q^{5} +0.399681 q^{6} +3.94354 q^{7} +1.83163 q^{8} -2.32572 q^{9} +O(q^{10})\)	\(q-0.486735 q^{2} -0.821147 q^{3} -1.76309 q^{4} +1.00000 q^{5} +0.399681 q^{6} +3.94354 q^{7} +1.83163 q^{8} -2.32572 q^{9} -0.486735 q^{10} +4.13411 q^{11} +1.44776 q^{12} -0.310860 q^{13} -1.91946 q^{14} -0.821147 q^{15} +2.63466 q^{16} +1.37102 q^{17} +1.13201 q^{18} -1.76309 q^{20} -3.23823 q^{21} -2.01221 q^{22} +0.331809 q^{23} -1.50404 q^{24} +1.00000 q^{25} +0.151307 q^{26} +4.37320 q^{27} -6.95281 q^{28} +7.26503 q^{29} +0.399681 q^{30} -6.55547 q^{31} -4.94564 q^{32} -3.39471 q^{33} -0.667322 q^{34} +3.94354 q^{35} +4.10045 q^{36} -9.27902 q^{37} +0.255262 q^{39} +1.83163 q^{40} +9.25000 q^{41} +1.57616 q^{42} -6.49792 q^{43} -7.28880 q^{44} -2.32572 q^{45} -0.161503 q^{46} +4.19090 q^{47} -2.16345 q^{48} +8.55151 q^{49} -0.486735 q^{50} -1.12581 q^{51} +0.548075 q^{52} -10.5136 q^{53} -2.12859 q^{54} +4.13411 q^{55} +7.22310 q^{56} -3.53614 q^{58} -7.23383 q^{59} +1.44776 q^{60} +15.0639 q^{61} +3.19078 q^{62} -9.17156 q^{63} -2.86211 q^{64} -0.310860 q^{65} +1.65232 q^{66} +11.5497 q^{67} -2.41723 q^{68} -0.272464 q^{69} -1.91946 q^{70} -4.54326 q^{71} -4.25985 q^{72} +8.86098 q^{73} +4.51642 q^{74} -0.821147 q^{75} +16.3030 q^{77} -0.124245 q^{78} -7.42705 q^{79} +2.63466 q^{80} +3.38611 q^{81} -4.50230 q^{82} +1.50176 q^{83} +5.70928 q^{84} +1.37102 q^{85} +3.16277 q^{86} -5.96566 q^{87} +7.57214 q^{88} -4.72287 q^{89} +1.13201 q^{90} -1.22589 q^{91} -0.585008 q^{92} +5.38301 q^{93} -2.03986 q^{94} +4.06110 q^{96} +12.4271 q^{97} -4.16232 q^{98} -9.61476 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9}+O(q^{10}) \) 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9	\( 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9} + 12 q^{11} + 42 q^{16} + 22 q^{17} + 26 q^{20} + 42 q^{23} - 14 q^{24} + 16 q^{25} - 26 q^{26} + 46 q^{28} - 2 q^{30} + 22 q^{35} - 8 q^{36} - 38 q^{39} + 74 q^{42} + 88 q^{43} - 48 q^{44} + 18 q^{45} + 32 q^{47} + 30 q^{49} - 22 q^{54} + 12 q^{55} - 2 q^{58} + 20 q^{61} + 6 q^{62} - 6 q^{63} + 24 q^{64} - 24 q^{66} + 84 q^{68} + 44 q^{73} - 122 q^{74} + 4 q^{77} + 42 q^{80} - 36 q^{81} - 50 q^{82} + 56 q^{83} + 22 q^{85} + 34 q^{87} + 6 q^{92} - 58 q^{93} - 96 q^{96} + 6 q^{99}+O(q^{100}) \) 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9 + 12 * q^11 + 42 * q^16 + 22 * q^17 + 26 * q^20 + 42 * q^23 - 14 * q^24 + 16 * q^25 - 26 * q^26 + 46 * q^28 - 2 * q^30 + 22 * q^35 - 8 * q^36 - 38 * q^39 + 74 * q^42 + 88 * q^43 - 48 * q^44 + 18 * q^45 + 32 * q^47 + 30 * q^49 - 22 * q^54 + 12 * q^55 - 2 * q^58 + 20 * q^61 + 6 * q^62 - 6 * q^63 + 24 * q^64 - 24 * q^66 + 84 * q^68 + 44 * q^73 - 122 * q^74 + 4 * q^77 + 42 * q^80 - 36 * q^81 - 50 * q^82 + 56 * q^83 + 22 * q^85 + 34 * q^87 + 6 * q^92 - 58 * q^93 - 96 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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