LMFDB - Embedded newform 1681.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1681,2,Mod(1,1681)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1681, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1681.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1681 = 41^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1681.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:	$13.4228525798$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 41)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1681.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41490 q^{2} -2.36665 q^{3} +3.83176 q^{4} +2.87275 q^{5} +5.71522 q^{6} -2.09872 q^{7} -4.42352 q^{8} +2.60102 q^{9} +O(q^{10})$	\(q-2.41490 q^{2} -2.36665 q^{3} +3.83176 q^{4} +2.87275 q^{5} +5.71522 q^{6} -2.09872 q^{7} -4.42352 q^{8} +2.60102 q^{9} -6.93742 q^{10} +0.389367 q^{11} -9.06842 q^{12} -3.45802 q^{13} +5.06819 q^{14} -6.79879 q^{15} +3.01885 q^{16} -5.11396 q^{17} -6.28121 q^{18} +6.44330 q^{19} +11.0077 q^{20} +4.96692 q^{21} -0.940284 q^{22} -1.32893 q^{23} +10.4689 q^{24} +3.25271 q^{25} +8.35079 q^{26} +0.944245 q^{27} -8.04177 q^{28} -0.597109 q^{29} +16.4184 q^{30} -1.23180 q^{31} +1.55681 q^{32} -0.921494 q^{33} +12.3497 q^{34} -6.02909 q^{35} +9.96648 q^{36} +2.57023 q^{37} -15.5599 q^{38} +8.18392 q^{39} -12.7077 q^{40} -11.9946 q^{42} +9.91211 q^{43} +1.49196 q^{44} +7.47209 q^{45} +3.20924 q^{46} -2.21328 q^{47} -7.14455 q^{48} -2.59539 q^{49} -7.85497 q^{50} +12.1029 q^{51} -13.2503 q^{52} -5.40798 q^{53} -2.28026 q^{54} +1.11856 q^{55} +9.28370 q^{56} -15.2490 q^{57} +1.44196 q^{58} +6.60776 q^{59} -26.0513 q^{60} -6.39309 q^{61} +2.97467 q^{62} -5.45880 q^{63} -9.79723 q^{64} -9.93404 q^{65} +2.22532 q^{66} -5.58862 q^{67} -19.5955 q^{68} +3.14511 q^{69} +14.5597 q^{70} +7.00260 q^{71} -11.5057 q^{72} -14.4984 q^{73} -6.20686 q^{74} -7.69801 q^{75} +24.6892 q^{76} -0.817170 q^{77} -19.7634 q^{78} -5.98405 q^{79} +8.67240 q^{80} -10.0378 q^{81} +15.4232 q^{83} +19.0320 q^{84} -14.6911 q^{85} -23.9368 q^{86} +1.41315 q^{87} -1.72237 q^{88} +0.334607 q^{89} -18.0444 q^{90} +7.25741 q^{91} -5.09214 q^{92} +2.91523 q^{93} +5.34487 q^{94} +18.5100 q^{95} -3.68441 q^{96} +14.4212 q^{97} +6.26763 q^{98} +1.01275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 + 20 * q^4 + 12 * q^5 + 24 * q^8 + 24 * q^9	$ 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 20 q^{16} + 20 q^{18} + 40 q^{20} + 56 q^{21} + 48 q^{23} + 8 q^{25} + 32 q^{31} + 36 q^{32} + 24 q^{33} + 108 q^{36} + 60 q^{39} + 44 q^{40} - 40 q^{42} + 36 q^{43} - 36 q^{45} + 36 q^{46} + 32 q^{49} - 60 q^{50} + 36 q^{51} - 60 q^{57} + 116 q^{59} + 40 q^{61} + 48 q^{62} + 60 q^{64} + 16 q^{66} + 4 q^{72} + 16 q^{73} + 24 q^{74} - 16 q^{77} - 60 q^{78} + 84 q^{80} - 28 q^{81} + 80 q^{83} - 24 q^{84} - 24 q^{86} + 76 q^{87} + 56 q^{90} + 40 q^{91} - 40 q^{92} + 36 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 20 * q^4 + 12 * q^5 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 20 * q^16 + 20 * q^18 + 40 * q^20 + 56 * q^21 + 48 * q^23 + 8 * q^25 + 32 * q^31 + 36 * q^32 + 24 * q^33 + 108 * q^36 + 60 * q^39 + 44 * q^40 - 40 * q^42 + 36 * q^43 - 36 * q^45 + 36 * q^46 + 32 * q^49 - 60 * q^50 + 36 * q^51 - 60 * q^57 + 116 * q^59 + 40 * q^61 + 48 * q^62 + 60 * q^64 + 16 * q^66 + 4 * q^72 + 16 * q^73 + 24 * q^74 - 16 * q^77 - 60 * q^78 + 84 * q^80 - 28 * q^81 + 80 * q^83 - 24 * q^84 - 24 * q^86 + 76 * q^87 + 56 * q^90 + 40 * q^91 - 40 * q^92 + 36 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.41490	−1.70759	−0.853797	−	0.520606i	$-0.825706\pi$
$2$	−2.41490	−1.70759	−0.853797	+	0.520606i	$0.825706\pi$
$3$	−2.36665	−1.36638	−0.683192	−	0.730239i	$-0.739409\pi$
$3$	−2.36665	−1.36638	−0.683192	+	0.730239i	$0.739409\pi$
$4$	3.83176	1.91588
$5$	2.87275	1.28473	0.642367	−	0.766397i	$-0.277953\pi$
$5$	2.87275	1.28473	0.642367	+	0.766397i	$0.277953\pi$
$6$	5.71522	2.33323
$7$	−2.09872	−0.793240	−0.396620	−	0.917983i	$-0.629817\pi$
$7$	−2.09872	−0.793240	−0.396620	+	0.917983i	$0.629817\pi$
$8$	−4.42352	−1.56395
$9$	2.60102	0.867007
$10$	−6.93742	−2.19380
$11$	0.389367	0.117399	0.0586993	−	0.998276i	$-0.481305\pi$
$11$	0.389367	0.117399	0.0586993	+	0.998276i	$0.481305\pi$
$12$	−9.06842	−2.61783
$13$	−3.45802	−0.959083	−0.479542	−	0.877519i	$-0.659197\pi$
$13$	−3.45802	−0.959083	−0.479542	+	0.877519i	$0.659197\pi$
$14$	5.06819	1.35453
$15$	−6.79879	−1.75544
$16$	3.01885	0.754712
$17$	−5.11396	−1.24032	−0.620159	−	0.784476i	$-0.712932\pi$
$17$	−5.11396	−1.24032	−0.620159	+	0.784476i	$0.712932\pi$
$18$	−6.28121	−1.48050
$19$	6.44330	1.47819	0.739097	−	0.673599i	$-0.235252\pi$
$19$	6.44330	1.47819	0.739097	+	0.673599i	$0.235252\pi$
$20$	11.0077	2.46139
$21$	4.96692	1.08387
$22$	−0.940284	−0.200469
$23$	−1.32893	−0.277101	−0.138551	−	0.990355i	$-0.544244\pi$
$23$	−1.32893	−0.277101	−0.138551	+	0.990355i	$0.544244\pi$
$24$	10.4689	2.13696
$25$	3.25271	0.650541
$26$	8.35079	1.63772
$27$	0.944245	0.181720
$28$	−8.04177	−1.51975
$29$	−0.597109	−0.110880	−0.0554402	−	0.998462i	$-0.517656\pi$
$29$	−0.597109	−0.110880	−0.0554402	+	0.998462i	$0.517656\pi$
$30$	16.4184	2.99758
$31$	−1.23180	−0.221238	−0.110619	−	0.993863i	$-0.535283\pi$
$31$	−1.23180	−0.221238	−0.110619	+	0.993863i	$0.535283\pi$
$32$	1.55681	0.275207
$33$	−0.921494	−0.160412
$34$	12.3497	2.11796
$35$	−6.02909	−1.01910
$36$	9.96648	1.66108
$37$	2.57023	0.422544	0.211272	−	0.977427i	$-0.432239\pi$
$37$	2.57023	0.422544	0.211272	+	0.977427i	$0.432239\pi$
$38$	−15.5599	−2.52416
$39$	8.18392	1.31048
$40$	−12.7077	−2.00926
$41$	0	0
$41$	0	0
$42$	−11.9946	−1.85081
$43$	9.91211	1.51158	0.755791	−	0.654813i	$-0.227253\pi$
$43$	9.91211	1.51158	0.755791	+	0.654813i	$0.227253\pi$
$44$	1.49196	0.224921
$45$	7.47209	1.11387
$46$	3.20924	0.473176
$47$	−2.21328	−0.322841	−0.161420	−	0.986886i	$-0.551607\pi$
$47$	−2.21328	−0.322841	−0.161420	+	0.986886i	$0.551607\pi$
$48$	−7.14455	−1.03123
$49$	−2.59539	−0.370771
$50$	−7.85497	−1.11086
$51$	12.1029	1.69475
$52$	−13.2503	−1.83749
$53$	−5.40798	−0.742844	−0.371422	−	0.928464i	$-0.621130\pi$
$53$	−5.40798	−0.742844	−0.371422	+	0.928464i	$0.621130\pi$
$54$	−2.28026	−0.310304
$55$	1.11856	0.150826
$56$	9.28370	1.24059
$57$	−15.2490	−2.01978
$58$	1.44196	0.189339
$59$	6.60776	0.860257	0.430128	−	0.902768i	$-0.358468\pi$
$59$	6.60776	0.860257	0.430128	+	0.902768i	$0.358468\pi$
$60$	−26.0513	−3.36321
$61$	−6.39309	−0.818552	−0.409276	−	0.912411i	$-0.634219\pi$
$61$	−6.39309	−0.818552	−0.409276	+	0.912411i	$0.634219\pi$
$62$	2.97467	0.377784
$63$	−5.45880	−0.687744
$64$	−9.79723	−1.22465
$65$	−9.93404	−1.23217
$66$	2.22532	0.273918
$67$	−5.58862	−0.682758	−0.341379	−	0.939926i	$-0.610894\pi$
$67$	−5.58862	−0.682758	−0.341379	+	0.939926i	$0.610894\pi$
$68$	−19.5955	−2.37630
$69$	3.14511	0.378627
$70$	14.5597	1.74021
$71$	7.00260	0.831056	0.415528	−	0.909580i	$-0.363597\pi$
$71$	7.00260	0.831056	0.415528	+	0.909580i	$0.363597\pi$
$72$	−11.5057	−1.35595
$73$	−14.4984	−1.69692	−0.848458	−	0.529263i	$-0.822468\pi$
$73$	−14.4984	−1.69692	−0.848458	+	0.529263i	$0.822468\pi$
$74$	−6.20686	−0.721533
$75$	−7.69801	−0.888889
$76$	24.6892	2.83204
$77$	−0.817170	−0.0931252
$78$	−19.7634	−2.23776
$79$	−5.98405	−0.673258	−0.336629	−	0.941637i	$-0.609287\pi$
$79$	−5.98405	−0.673258	−0.336629	+	0.941637i	$0.609287\pi$
$80$	8.67240	0.969604
$81$	−10.0378	−1.11531
$82$	0	0
$83$	15.4232	1.69292	0.846458	−	0.532456i	$-0.178731\pi$
$83$	15.4232	1.69292	0.846458	+	0.532456i	$0.178731\pi$
$84$	19.0320	2.07656
$85$	−14.6911	−1.59348
$86$	−23.9368	−2.58117
$87$	1.41315	0.151505
$88$	−1.72237	−0.183605
$89$	0.334607	0.0354682	0.0177341	−	0.999843i	$-0.494355\pi$
$89$	0.334607	0.0354682	0.0177341	+	0.999843i	$0.494355\pi$
$90$	−18.0444	−1.90204
$91$	7.25741	0.760783
$92$	−5.09214	−0.530892
$93$	2.91523	0.302296
$94$	5.34487	0.551281
$95$	18.5100	1.89909
$96$	−3.68441	−0.376039
$97$	14.4212	1.46425	0.732123	−	0.681172i	$-0.238530\pi$
$97$	14.4212	1.46425	0.732123	+	0.681172i	$0.238530\pi$
$98$	6.26763	0.633126
$99$	1.01275	0.101785
$100$	12.4636	1.24636
$101$	11.4755	1.14185	0.570925	−	0.821002i	$-0.306585\pi$
$101$	11.4755	1.14185	0.570925	+	0.821002i	$0.306585\pi$
$102$	−29.2274	−2.89395
$103$	−13.0776	−1.28858	−0.644288	−	0.764783i	$-0.722846\pi$
$103$	−13.0776	−1.28858	−0.644288	+	0.764783i	$0.722846\pi$
$104$	15.2966	1.49996
$105$	14.2687	1.39249
$106$	13.0598	1.26848
$107$	6.89690	0.666749	0.333374	−	0.942794i	$-0.391813\pi$
$107$	6.89690	0.666749	0.333374	+	0.942794i	$0.391813\pi$
$108$	3.61812	0.348154
$109$	8.19557	0.784993	0.392497	−	0.919753i	$-0.371611\pi$
$109$	8.19557	0.784993	0.392497	+	0.919753i	$0.371611\pi$
$110$	−2.70120	−0.257550
$111$	−6.08283	−0.577357
$112$	−6.33570	−0.598668
$113$	−3.61403	−0.339980	−0.169990	−	0.985446i	$-0.554374\pi$
$113$	−3.61403	−0.339980	−0.169990	+	0.985446i	$0.554374\pi$
$114$	36.8249	3.44897
$115$	−3.81769	−0.356001
$116$	−2.28798	−0.212433
$117$	−8.99439	−0.831531
$118$	−15.9571	−1.46897
$119$	10.7327	0.983869
$120$	30.0746	2.74542
$121$	−10.8484	−0.986218
$122$	15.4387	1.39775
$123$	0	0
$124$	−4.71995	−0.423864
$125$	−5.01954	−0.448962
$126$	13.1825	1.17439
$127$	10.2323	0.907973	0.453986	−	0.891009i	$-0.350001\pi$
$127$	10.2323	0.907973	0.453986	+	0.891009i	$0.350001\pi$
$128$	20.5458	1.81601
$129$	−23.4585	−2.06540
$130$	23.9898	2.10404
$131$	10.3810	0.906995	0.453498	−	0.891257i	$-0.350176\pi$
$131$	10.3810	0.906995	0.453498	+	0.891257i	$0.350176\pi$
$132$	−3.53094	−0.307329
$133$	−13.5227	−1.17256
$134$	13.4960	1.16587
$135$	2.71258	0.233462
$136$	22.6217	1.93979
$137$	3.83854	0.327949	0.163974	−	0.986465i	$-0.447569\pi$
$137$	3.83854	0.327949	0.163974	+	0.986465i	$0.447569\pi$
$138$	−7.59513	−0.646541
$139$	6.78433	0.575440	0.287720	−	0.957715i	$-0.407103\pi$
$139$	6.78433	0.575440	0.287720	+	0.957715i	$0.407103\pi$
$140$	−23.1020	−1.95248
$141$	5.23806	0.441125
$142$	−16.9106	−1.41911
$143$	−1.34644	−0.112595
$144$	7.85208	0.654340
$145$	−1.71535	−0.142452
$146$	35.0123	2.89764
$147$	6.14238	0.506615
$148$	9.84851	0.809542
$149$	12.7571	1.04510	0.522552	−	0.852607i	$-0.324980\pi$
$149$	12.7571	1.04510	0.522552	+	0.852607i	$0.324980\pi$
$150$	18.5899	1.51786
$151$	2.68721	0.218682	0.109341	−	0.994004i	$-0.465126\pi$
$151$	2.68721	0.218682	0.109341	+	0.994004i	$0.465126\pi$
$152$	−28.5020	−2.31182
$153$	−13.3015	−1.07536
$154$	1.97339	0.159020
$155$	−3.53865	−0.284231
$156$	31.3588	2.51071
$157$	−10.3860	−0.828890	−0.414445	−	0.910074i	$-0.636024\pi$
$157$	−10.3860	−0.828890	−0.414445	+	0.910074i	$0.636024\pi$
$158$	14.4509	1.14965
$159$	12.7988	1.01501
$160$	4.47232	0.353568
$161$	2.78905	0.219808
$162$	24.2402	1.90449
$163$	−3.48663	−0.273094	−0.136547	−	0.990634i	$-0.543601\pi$
$163$	−3.48663	−0.273094	−0.136547	+	0.990634i	$0.543601\pi$
$164$	0	0
$165$	−2.64723	−0.206086
$166$	−37.2455	−2.89081
$167$	19.5513	1.51292	0.756461	−	0.654039i	$-0.226927\pi$
$167$	19.5513	1.51292	0.756461	+	0.654039i	$0.226927\pi$
$168$	−21.9712	−1.69512
$169$	−1.04208	−0.0801596
$170$	35.4777	2.72101
$171$	16.7592	1.28160
$172$	37.9808	2.89601
$173$	12.0871	0.918962	0.459481	−	0.888187i	$-0.348035\pi$
$173$	12.0871	0.918962	0.459481	+	0.888187i	$0.348035\pi$
$174$	−3.41261	−0.258710
$175$	−6.82650	−0.516035
$176$	1.17544	0.0886021
$177$	−15.6382	−1.17544
$178$	−0.808042	−0.0605653
$179$	1.99358	0.149007	0.0745036	−	0.997221i	$-0.476263\pi$
$179$	1.99358	0.149007	0.0745036	+	0.997221i	$0.476263\pi$
$180$	28.6312	2.13405
$181$	16.2346	1.20671	0.603355	−	0.797473i	$-0.293830\pi$
$181$	16.2346	1.20671	0.603355	+	0.797473i	$0.293830\pi$
$182$	−17.5259	−1.29911
$183$	15.1302	1.11846
$184$	5.87854	0.433372
$185$	7.38364	0.542856
$186$	−7.04001	−0.516198
$187$	−1.99121	−0.145611
$188$	−8.48077	−0.618524
$189$	−1.98170	−0.144148
$190$	−44.6999	−3.24287
$191$	−5.53192	−0.400276	−0.200138	−	0.979768i	$-0.564139\pi$
$191$	−5.53192	−0.400276	−0.200138	+	0.979768i	$0.564139\pi$
$192$	23.1866	1.67335
$193$	8.41305	0.605585	0.302792	−	0.953057i	$-0.402081\pi$
$193$	8.41305	0.605585	0.302792	+	0.953057i	$0.402081\pi$
$194$	−34.8257	−2.50034
$195$	23.5104	1.68361
$196$	−9.94492	−0.710352
$197$	26.2154	1.86777	0.933886	−	0.357571i	$-0.116395\pi$
$197$	26.2154	1.86777	0.933886	+	0.357571i	$0.116395\pi$
$198$	−2.44570	−0.173808
$199$	−11.2998	−0.801023	−0.400511	−	0.916292i	$-0.631167\pi$
$199$	−11.2998	−0.801023	−0.400511	+	0.916292i	$0.631167\pi$
$200$	−14.3884	−1.01741
$201$	13.2263	0.932910
$202$	−27.7121	−1.94982
$203$	1.25316	0.0879548
$204$	46.3755	3.24694
$205$	0	0
$206$	31.5812	2.20036
$207$	−3.45657	−0.240248
$208$	−10.4392	−0.723831
$209$	2.50881	0.173538
$210$	−34.4576	−2.37780
$211$	−5.31857	−0.366145	−0.183073	−	0.983099i	$-0.558604\pi$
$211$	−5.31857	−0.366145	−0.183073	+	0.983099i	$0.558604\pi$
$212$	−20.7221	−1.42320
$213$	−16.5727	−1.13554
$214$	−16.6554	−1.13854
$215$	28.4750	1.94198
$216$	−4.17688	−0.284201
$217$	2.58519	0.175494
$218$	−19.7915	−1.34045
$219$	34.3127	2.31864
$220$	4.28603	0.288964
$221$	17.6842	1.18957
$222$	14.6895	0.985892
$223$	7.01229	0.469577	0.234789	−	0.972046i	$-0.424560\pi$
$223$	7.01229	0.469577	0.234789	+	0.972046i	$0.424560\pi$
$224$	−3.26729	−0.218305
$225$	8.46035	0.564024
$226$	8.72754	0.580548
$227$	−20.2759	−1.34576	−0.672879	−	0.739752i	$-0.734943\pi$
$227$	−20.2759	−1.34576	−0.672879	+	0.739752i	$0.734943\pi$
$228$	−58.4305	−3.86966
$229$	0.336384	0.0222289	0.0111144	−	0.999938i	$-0.496462\pi$
$229$	0.336384	0.0222289	0.0111144	+	0.999938i	$0.496462\pi$
$230$	9.21934	0.607906
$231$	1.93395	0.127245
$232$	2.64132	0.173411
$233$	12.9614	0.849131	0.424565	−	0.905397i	$-0.360427\pi$
$233$	12.9614	0.849131	0.424565	+	0.905397i	$0.360427\pi$
$234$	21.7206	1.41992
$235$	−6.35822	−0.414764
$236$	25.3193	1.64815
$237$	14.1621	0.919930
$238$	−25.9185	−1.68005
$239$	11.8711	0.767876	0.383938	−	0.923359i	$-0.374568\pi$
$239$	11.8711	0.767876	0.383938	+	0.923359i	$0.374568\pi$
$240$	−20.5245	−1.32485
$241$	27.2093	1.75271	0.876353	−	0.481670i	$-0.159970\pi$
$241$	27.2093	1.75271	0.876353	+	0.481670i	$0.159970\pi$
$242$	26.1978	1.68406
$243$	20.9231	1.34222
$244$	−24.4968	−1.56825
$245$	−7.45593	−0.476342
$246$	0	0
$247$	−22.2811	−1.41771
$248$	5.44888	0.346004
$249$	−36.5013	−2.31317
$250$	12.1217	0.766644
$251$	1.35501	0.0855272	0.0427636	−	0.999085i	$-0.486384\pi$
$251$	1.35501	0.0855272	0.0427636	+	0.999085i	$0.486384\pi$
$252$	−20.9168	−1.31763
$253$	−0.517442	−0.0325313
$254$	−24.7101	−1.55045
$255$	34.7687	2.17730
$256$	−30.0215	−1.87635
$257$	−5.28333	−0.329565	−0.164783	−	0.986330i	$-0.552692\pi$
$257$	−5.28333	−0.329565	−0.164783	+	0.986330i	$0.552692\pi$
$258$	56.6499	3.52687
$259$	−5.39419	−0.335178
$260$	−38.0648	−2.36068
$261$	−1.55309	−0.0961341
$262$	−25.0692	−1.54878
$263$	2.35996	0.145521	0.0727606	−	0.997349i	$-0.476819\pi$
$263$	2.35996	0.145521	0.0727606	+	0.997349i	$0.476819\pi$
$264$	4.07625	0.250876
$265$	−15.5358	−0.954356
$266$	32.6559	2.00226
$267$	−0.791896	−0.0484632
$268$	−21.4142	−1.30808
$269$	16.8975	1.03026	0.515130	−	0.857112i	$-0.327744\pi$
$269$	16.8975	1.03026	0.515130	+	0.857112i	$0.327744\pi$
$270$	−6.55062	−0.398658
$271$	−21.1674	−1.28583	−0.642915	−	0.765938i	$-0.722275\pi$
$271$	−21.1674	−1.28583	−0.642915	+	0.765938i	$0.722275\pi$
$272$	−15.4383	−0.936082
$273$	−17.1757	−1.03952
$274$	−9.26971	−0.560004
$275$	1.26650	0.0763726
$276$	12.0513	0.725403
$277$	−11.4007	−0.685003	−0.342502	−	0.939517i	$-0.611274\pi$
$277$	−11.4007	−0.685003	−0.342502	+	0.939517i	$0.611274\pi$
$278$	−16.3835	−0.982618
$279$	−3.20393	−0.191814
$280$	26.6698	1.59382
$281$	−27.0457	−1.61341	−0.806707	−	0.590952i	$-0.798752\pi$
$281$	−27.0457	−1.61341	−0.806707	+	0.590952i	$0.798752\pi$
$282$	−12.6494	−0.753262
$283$	11.2199	0.666954	0.333477	−	0.942758i	$-0.391778\pi$
$283$	11.2199	0.666954	0.333477	+	0.942758i	$0.391778\pi$
$284$	26.8323	1.59220
$285$	−43.8067	−2.59488
$286$	3.25152	0.192267
$287$	0	0
$288$	4.04928	0.238606
$289$	9.15258	0.538387
$290$	4.14240	0.243250
$291$	−34.1298	−2.00072
$292$	−55.5545	−3.25108
$293$	21.6782	1.26645	0.633227	−	0.773966i	$-0.281730\pi$
$293$	21.6782	1.26645	0.633227	+	0.773966i	$0.281730\pi$
$294$	−14.8333	−0.865093
$295$	18.9825	1.10520
$296$	−11.3695	−0.660837
$297$	0.367658	0.0213337
$298$	−30.8072	−1.78461
$299$	4.59547	0.265763
$300$	−29.4969	−1.70300
$301$	−20.8027	−1.19905
$302$	−6.48934	−0.373420
$303$	−27.1584	−1.56021
$304$	19.4513	1.11561
$305$	−18.3658	−1.05162
$306$	32.1219	1.83628
$307$	17.3042	0.987603	0.493802	−	0.869575i	$-0.335607\pi$
$307$	17.3042	0.987603	0.493802	+	0.869575i	$0.335607\pi$
$308$	−3.13120	−0.178417
$309$	30.9501	1.76069
$310$	8.54550	0.485352
$311$	−12.0905	−0.685589	−0.342794	−	0.939410i	$-0.611373\pi$
$311$	−12.0905	−0.685589	−0.342794	+	0.939410i	$0.611373\pi$
$312$	−36.2017	−2.04952
$313$	21.6787	1.22535	0.612677	−	0.790333i	$-0.290093\pi$
$313$	21.6787	1.22535	0.612677	+	0.790333i	$0.290093\pi$
$314$	25.0811	1.41541
$315$	−15.6818	−0.883568
$316$	−22.9294	−1.28988
$317$	19.7828	1.11111	0.555556	−	0.831479i	$-0.312506\pi$
$317$	19.7828	1.11111	0.555556	+	0.831479i	$0.312506\pi$
$318$	−30.9078	−1.73323
$319$	−0.232495	−0.0130172
$320$	−28.1450	−1.57335
$321$	−16.3225	−0.911035
$322$	−6.73527	−0.375342
$323$	−32.9508	−1.83343
$324$	−38.4622	−2.13679
$325$	−11.2479	−0.623923
$326$	8.41988	0.466334
$327$	−19.3960	−1.07260
$328$	0	0
$329$	4.64505	0.256090
$330$	6.39279	0.351912
$331$	28.8432	1.58537	0.792683	−	0.609634i	$-0.208683\pi$
$331$	28.8432	1.58537	0.792683	+	0.609634i	$0.208683\pi$
$332$	59.0979	3.24342
$333$	6.68523	0.366348
$334$	−47.2144	−2.58346
$335$	−16.0547	−0.877163
$336$	14.9944	0.818010
$337$	−23.4367	−1.27668	−0.638340	−	0.769754i	$-0.720379\pi$
$337$	−23.4367	−1.27668	−0.638340	+	0.769754i	$0.720379\pi$
$338$	2.51651	0.136880
$339$	8.55315	0.464543
$340$	−56.2929	−3.05291
$341$	−0.479622	−0.0259730
$342$	−40.4717	−2.18846
$343$	20.1380	1.08735
$344$	−43.8464	−2.36404
$345$	9.03512	0.486434
$346$	−29.1891	−1.56922
$347$	−13.4314	−0.721033	−0.360517	−	0.932753i	$-0.617400\pi$
$347$	−13.4314	−0.721033	−0.360517	+	0.932753i	$0.617400\pi$
$348$	5.41484	0.290266
$349$	−11.1370	−0.596148	−0.298074	−	0.954543i	$-0.596344\pi$
$349$	−11.1370	−0.596148	−0.298074	+	0.954543i	$0.596344\pi$
$350$	16.4853	0.881179
$351$	−3.26522	−0.174285
$352$	0.606169	0.0323089
$353$	14.0454	0.747559	0.373780	−	0.927518i	$-0.378062\pi$
$353$	14.0454	0.747559	0.373780	+	0.927518i	$0.378062\pi$
$354$	37.7648	2.00718
$355$	20.1167	1.06769
$356$	1.28213	0.0679528
$357$	−25.4006	−1.34434
$358$	−4.81430	−0.254444
$359$	28.7060	1.51505	0.757523	−	0.652809i	$-0.226409\pi$
$359$	28.7060	1.51505	0.757523	+	0.652809i	$0.226409\pi$
$360$	−33.0529	−1.74204
$361$	22.5161	1.18506
$362$	−39.2050	−2.06057
$363$	25.6743	1.34755
$364$	27.8086	1.45757
$365$	−41.6505	−2.18008
$366$	−36.5380	−1.90987
$367$	22.2165	1.15969	0.579847	−	0.814725i	$-0.303112\pi$
$367$	22.2165	1.15969	0.579847	+	0.814725i	$0.303112\pi$
$368$	−4.01184	−0.209131
$369$	0	0
$370$	−17.8308	−0.926978
$371$	11.3498	0.589253
$372$	11.1705	0.579162
$373$	17.3111	0.896334	0.448167	−	0.893950i	$-0.352077\pi$
$373$	17.3111	0.896334	0.448167	+	0.893950i	$0.352077\pi$
$374$	4.80857	0.248645
$375$	11.8795	0.613454
$376$	9.79050	0.504906
$377$	2.06482	0.106344
$378$	4.78562	0.246146
$379$	2.64416	0.135822	0.0679108	−	0.997691i	$-0.478367\pi$
$379$	2.64416	0.135822	0.0679108	+	0.997691i	$0.478367\pi$
$380$	70.9258	3.63842
$381$	−24.2163	−1.24064
$382$	13.3591	0.683509
$383$	28.9777	1.48069	0.740345	−	0.672228i	$-0.234662\pi$
$383$	28.9777	1.48069	0.740345	+	0.672228i	$0.234662\pi$
$384$	−48.6246	−2.48136
$385$	−2.34753	−0.119641
$386$	−20.3167	−1.03409
$387$	25.7816	1.31055
$388$	55.2584	2.80532
$389$	−21.2155	−1.07567	−0.537834	−	0.843051i	$-0.680757\pi$
$389$	−21.2155	−1.07567	−0.537834	+	0.843051i	$0.680757\pi$
$390$	−56.7753	−2.87493
$391$	6.79609	0.343693
$392$	11.4808	0.579866
$393$	−24.5683	−1.23930
$394$	−63.3077	−3.18940
$395$	−17.1907	−0.864958
$396$	3.88062	0.195008
$397$	4.54885	0.228300	0.114150	−	0.993464i	$-0.463586\pi$
$397$	4.54885	0.228300	0.114150	+	0.993464i	$0.463586\pi$
$398$	27.2880	1.36782
$399$	32.0033	1.60217
$400$	9.81942	0.490971
$401$	−7.53484	−0.376272	−0.188136	−	0.982143i	$-0.560245\pi$
$401$	−7.53484	−0.376272	−0.188136	+	0.982143i	$0.560245\pi$
$402$	−31.9402	−1.59303
$403$	4.25959	0.212185
$404$	43.9712	2.18765
$405$	−28.8360	−1.43287
$406$	−3.02627	−0.150191
$407$	1.00076	0.0496060
$408$	−53.5375	−2.65050
$409$	−1.03548	−0.0512013	−0.0256007	−	0.999672i	$-0.508150\pi$
$409$	−1.03548	−0.0512013	−0.0256007	+	0.999672i	$0.508150\pi$
$410$	0	0
$411$	−9.08448	−0.448104
$412$	−50.1103	−2.46875
$413$	−13.8678	−0.682390
$414$	8.34729	0.410247
$415$	44.3070	2.17495
$416$	−5.38347	−0.263946
$417$	−16.0561	−0.786272
$418$	−6.05853	−0.296332
$419$	−5.57406	−0.272310	−0.136155	−	0.990688i	$-0.543475\pi$
$419$	−5.57406	−0.272310	−0.136155	+	0.990688i	$0.543475\pi$
$420$	54.6743	2.66783
$421$	31.2342	1.52226	0.761131	−	0.648598i	$-0.224644\pi$
$421$	31.2342	1.52226	0.761131	+	0.648598i	$0.224644\pi$
$422$	12.8438	0.625227
$423$	−5.75680	−0.279905
$424$	23.9223	1.16177
$425$	−16.6342	−0.806878
$426$	40.0214	1.93905
$427$	13.4173	0.649308
$428$	26.4273	1.27741
$429$	3.18655	0.153848
$430$	−68.7644	−3.31611
$431$	14.9535	0.720285	0.360142	−	0.932897i	$-0.382728\pi$
$431$	14.9535	0.720285	0.360142	+	0.932897i	$0.382728\pi$
$432$	2.85053	0.137146
$433$	−17.5464	−0.843226	−0.421613	−	0.906776i	$-0.638536\pi$
$433$	−17.5464	−0.843226	−0.421613	+	0.906776i	$0.638536\pi$
$434$	−6.24300	−0.299673
$435$	4.05962	0.194644
$436$	31.4034	1.50395
$437$	−8.56270	−0.409609
$438$	−82.8619	−3.95929
$439$	6.83255	0.326100	0.163050	−	0.986618i	$-0.447867\pi$
$439$	6.83255	0.326100	0.163050	+	0.986618i	$0.447867\pi$
$440$	−4.94795	−0.235884
$441$	−6.75067	−0.321461
$442$	−42.7056	−2.03130
$443$	−8.45301	−0.401615	−0.200807	−	0.979631i	$-0.564357\pi$
$443$	−8.45301	−0.401615	−0.200807	+	0.979631i	$0.564357\pi$
$444$	−23.3079	−1.10615
$445$	0.961242	0.0455672
$446$	−16.9340	−0.801848
$447$	−30.1916	−1.42801
$448$	20.5616	0.971444
$449$	−3.12209	−0.147340	−0.0736702	−	0.997283i	$-0.523471\pi$
$449$	−3.12209	−0.147340	−0.0736702	+	0.997283i	$0.523471\pi$
$450$	−20.4309	−0.963123
$451$	0	0
$452$	−13.8481	−0.651360
$453$	−6.35967	−0.298803
$454$	48.9643	2.29801
$455$	20.8487	0.977403
$456$	67.4543	3.15884
$457$	11.0859	0.518578	0.259289	−	0.965800i	$-0.416512\pi$
$457$	11.0859	0.518578	0.259289	+	0.965800i	$0.416512\pi$
$458$	−0.812335	−0.0379579
$459$	−4.82883	−0.225391
$460$	−14.6284	−0.682055
$461$	17.9020	0.833781	0.416891	−	0.908957i	$-0.363120\pi$
$461$	17.9020	0.833781	0.416891	+	0.908957i	$0.363120\pi$
$462$	−4.67031	−0.217283
$463$	−16.4196	−0.763083	−0.381542	−	0.924352i	$-0.624607\pi$
$463$	−16.4196	−0.763083	−0.381542	+	0.924352i	$0.624607\pi$
$464$	−1.80258	−0.0836828
$465$	8.37474	0.388369
$466$	−31.3006	−1.44997
$467$	−12.5230	−0.579495	−0.289747	−	0.957103i	$-0.593571\pi$
$467$	−12.5230	−0.579495	−0.289747	+	0.957103i	$0.593571\pi$
$468$	−34.4643	−1.59311
$469$	11.7289	0.541591
$470$	15.3545	0.708249
$471$	24.5799	1.13258
$472$	−29.2295	−1.34540
$473$	3.85945	0.177458
$474$	−34.2002	−1.57087
$475$	20.9582	0.961626
$476$	41.1253	1.88497
$477$	−14.0663	−0.644050
$478$	−28.6675	−1.31122
$479$	−7.01682	−0.320607	−0.160303	−	0.987068i	$-0.551247\pi$
$479$	−7.01682	−0.320607	−0.160303	+	0.987068i	$0.551247\pi$
$480$	−10.5844	−0.483110
$481$	−8.88792	−0.405254
$482$	−65.7078	−2.99291
$483$	−6.60069	−0.300342
$484$	−41.5684	−1.88947
$485$	41.4284	1.88117
$486$	−50.5272	−2.29196
$487$	29.7613	1.34861	0.674307	−	0.738451i	$-0.264443\pi$
$487$	29.7613	1.34861	0.674307	+	0.738451i	$0.264443\pi$
$488$	28.2799	1.28017
$489$	8.25163	0.373152
$490$	18.0053	0.813398
$491$	31.3635	1.41542	0.707708	−	0.706505i	$-0.249729\pi$
$491$	31.3635	1.41542	0.707708	+	0.706505i	$0.249729\pi$
$492$	0	0
$493$	3.05359	0.137527
$494$	53.8067	2.42088
$495$	2.90938	0.130767
$496$	−3.71861	−0.166971
$497$	−14.6965	−0.659227
$498$	88.1470	3.94996
$499$	26.8329	1.20120	0.600602	−	0.799548i	$-0.294928\pi$
$499$	26.8329	1.20120	0.600602	+	0.799548i	$0.294928\pi$
$500$	−19.2337	−0.860156
$501$	−46.2710	−2.06723
$502$	−3.27221	−0.146046
$503$	24.0160	1.07082	0.535410	−	0.844592i	$-0.320157\pi$
$503$	24.0160	1.07082	0.535410	+	0.844592i	$0.320157\pi$
$504$	24.1471	1.07560
$505$	32.9661	1.46697
$506$	1.24957	0.0555502
$507$	2.46623	0.109529
$508$	39.2078	1.73957
$509$	14.7929	0.655685	0.327842	−	0.944732i	$-0.393679\pi$
$509$	14.7929	0.655685	0.327842	+	0.944732i	$0.393679\pi$
$510$	−83.9632	−3.71795
$511$	30.4281	1.34606
$512$	31.4076	1.38803
$513$	6.08405	0.268618
$514$	12.7587	0.562764
$515$	−37.5688	−1.65548
$516$	−89.8871	−3.95706
$517$	−0.861780	−0.0379010
$518$	13.0264	0.572349
$519$	−28.6058	−1.25566
$520$	43.9434	1.92705
$521$	16.2119	0.710258	0.355129	−	0.934817i	$-0.384437\pi$
$521$	16.2119	0.710258	0.355129	+	0.934817i	$0.384437\pi$
$522$	3.75057	0.164158
$523$	2.83915	0.124147	0.0620737	−	0.998072i	$-0.480229\pi$
$523$	2.83915	0.124147	0.0620737	+	0.998072i	$0.480229\pi$
$524$	39.7776	1.73769
$525$	16.1559	0.705102
$526$	−5.69907	−0.248491
$527$	6.29937	0.274405
$528$	−2.78185	−0.121065
$529$	−21.2339	−0.923215
$530$	37.5174	1.62965
$531$	17.1869	0.745849
$532$	−51.8155	−2.24649
$533$	0	0
$534$	1.91235	0.0827555
$535$	19.8131	0.856595
$536$	24.7213	1.06780
$537$	−4.71810	−0.203601
$538$	−40.8058	−1.75927
$539$	−1.01056	−0.0435280
$540$	10.3940	0.447285
$541$	25.8376	1.11084	0.555422	−	0.831569i	$-0.312557\pi$
$541$	25.8376	1.11084	0.555422	+	0.831569i	$0.312557\pi$
$542$	51.1173	2.19567
$543$	−38.4216	−1.64883
$544$	−7.96145	−0.341344
$545$	23.5438	1.00851
$546$	41.4777	1.77508
$547$	−43.8915	−1.87667	−0.938333	−	0.345732i	$-0.887631\pi$
$547$	−43.8915	−1.87667	−0.938333	+	0.345732i	$0.887631\pi$
$548$	14.7084	0.628310
$549$	−16.6286	−0.709690
$550$	−3.05847	−0.130413
$551$	−3.84736	−0.163903
$552$	−13.9124	−0.592153
$553$	12.5588	0.534055
$554$	27.5317	1.16971
$555$	−17.4745	−0.741750
$556$	25.9959	1.10247
$557$	36.5501	1.54868	0.774338	−	0.632773i	$-0.218083\pi$
$557$	36.5501	1.54868	0.774338	+	0.632773i	$0.218083\pi$
$558$	7.73719	0.327541
$559$	−34.2763	−1.44973
$560$	−18.2009	−0.769128
$561$	4.71249	0.198961
$562$	65.3128	2.75506
$563$	−10.8853	−0.458761	−0.229381	−	0.973337i	$-0.573670\pi$
$563$	−10.8853	−0.458761	−0.229381	+	0.973337i	$0.573670\pi$
$564$	20.0710	0.845141
$565$	−10.3822	−0.436784
$566$	−27.0950	−1.13889
$567$	21.0664	0.884705
$568$	−30.9761	−1.29973
$569$	10.8755	0.455924	0.227962	−	0.973670i	$-0.426794\pi$
$569$	10.8755	0.455924	0.227962	+	0.973670i	$0.426794\pi$
$570$	105.789	4.43101
$571$	4.87400	0.203970	0.101985	−	0.994786i	$-0.467481\pi$
$571$	4.87400	0.203970	0.101985	+	0.994786i	$0.467481\pi$
$572$	−5.15923	−0.215718
$573$	13.0921	0.546931
$574$	0	0
$575$	−4.32262	−0.180266
$576$	−25.4828	−1.06178
$577$	−39.0422	−1.62535	−0.812675	−	0.582717i	$-0.801989\pi$
$577$	−39.0422	−1.62535	−0.812675	+	0.582717i	$0.801989\pi$
$578$	−22.1026	−0.919347
$579$	−19.9107	−0.827462
$580$	−6.57279	−0.272920
$581$	−32.3689	−1.34289
$582$	82.4201	3.41642
$583$	−2.10569	−0.0872088
$584$	64.1341	2.65389
$585$	−25.8386	−1.06830
$586$	−52.3508	−2.16259
$587$	5.64320	0.232920	0.116460	−	0.993195i	$-0.462845\pi$
$587$	5.64320	0.232920	0.116460	+	0.993195i	$0.462845\pi$
$588$	23.5361	0.970613
$589$	−7.93685	−0.327032
$590$	−45.8408	−1.88724
$591$	−62.0427	−2.55209
$592$	7.75914	0.318899
$593$	−4.51305	−0.185329	−0.0926645	−	0.995697i	$-0.529538\pi$
$593$	−4.51305	−0.185329	−0.0926645	+	0.995697i	$0.529538\pi$
$594$	−0.887858	−0.0364293
$595$	30.8325	1.26401
$596$	48.8822	2.00229
$597$	26.7427	1.09450
$598$	−11.0976	−0.453815
$599$	−30.3568	−1.24035	−0.620173	−	0.784465i	$-0.712938\pi$
$599$	−30.3568	−1.24035	−0.620173	+	0.784465i	$0.712938\pi$
$600$	34.0523	1.39018
$601$	−14.9766	−0.610907	−0.305454	−	0.952207i	$-0.598808\pi$
$601$	−14.9766	−0.610907	−0.305454	+	0.952207i	$0.598808\pi$
$602$	50.2365	2.04749
$603$	−14.5361	−0.591956
$604$	10.2967	0.418968
$605$	−31.1647	−1.26703
$606$	65.5848	2.66420
$607$	−19.2713	−0.782198	−0.391099	−	0.920349i	$-0.627905\pi$
$607$	−19.2713	−0.782198	−0.391099	+	0.920349i	$0.627905\pi$
$608$	10.0310	0.406810
$609$	−2.96579	−0.120180
$610$	44.3516	1.79574
$611$	7.65359	0.309631
$612$	−50.9682	−2.06027
$613$	−12.1975	−0.492654	−0.246327	−	0.969187i	$-0.579224\pi$
$613$	−12.1975	−0.492654	−0.246327	+	0.969187i	$0.579224\pi$
$614$	−41.7880	−1.68643
$615$	0	0
$616$	3.61477	0.145643
$617$	−21.4454	−0.863359	−0.431680	−	0.902027i	$-0.642079\pi$
$617$	−21.4454	−0.863359	−0.431680	+	0.902027i	$0.642079\pi$
$618$	−74.7415	−3.00654
$619$	−45.6384	−1.83436	−0.917181	−	0.398472i	$-0.869541\pi$
$619$	−45.6384	−1.83436	−0.917181	+	0.398472i	$0.869541\pi$
$620$	−13.5593	−0.544553
$621$	−1.25484	−0.0503548
$622$	29.1974	1.17071
$623$	−0.702244	−0.0281348
$624$	24.7060	0.989032
$625$	−30.6834	−1.22734
$626$	−52.3520	−2.09241
$627$	−5.93747	−0.237120
$628$	−39.7965	−1.58805
$629$	−13.1441	−0.524088
$630$	37.8700	1.50878
$631$	27.0288	1.07600	0.538000	−	0.842945i	$-0.319180\pi$
$631$	27.0288	1.07600	0.538000	+	0.842945i	$0.319180\pi$
$632$	26.4705	1.05294
$633$	12.5872	0.500295
$634$	−47.7735	−1.89733
$635$	29.3950	1.16650
$636$	49.0419	1.94464
$637$	8.97494	0.355600
$638$	0.561452	0.0222281
$639$	18.2139	0.720531
$640$	59.0229	2.33308
$641$	−14.0481	−0.554868	−0.277434	−	0.960745i	$-0.589484\pi$
$641$	−14.0481	−0.554868	−0.277434	+	0.960745i	$0.589484\pi$
$642$	39.4174	1.55568
$643$	20.5043	0.808609	0.404304	−	0.914625i	$-0.367514\pi$
$643$	20.5043	0.808609	0.404304	+	0.914625i	$0.367514\pi$
$644$	10.6869	0.421125
$645$	−67.3903	−2.65349
$646$	79.5729	3.13076
$647$	15.8806	0.624333	0.312166	−	0.950027i	$-0.398945\pi$
$647$	15.8806	0.624333	0.312166	+	0.950027i	$0.398945\pi$
$648$	44.4022	1.74428
$649$	2.57284	0.100993
$650$	27.1627	1.06541
$651$	−6.11824	−0.239793
$652$	−13.3599	−0.523215
$653$	−32.5131	−1.27233	−0.636167	−	0.771551i	$-0.719481\pi$
$653$	−32.5131	−1.27233	−0.636167	+	0.771551i	$0.719481\pi$
$654$	46.8395	1.83157
$655$	29.8222	1.16525
$656$	0	0
$657$	−37.7108	−1.47124
$658$	−11.2174	−0.437298
$659$	2.07526	0.0808405	0.0404203	−	0.999183i	$-0.487130\pi$
$659$	2.07526	0.0808405	0.0404203	+	0.999183i	$0.487130\pi$
$660$	−10.1435	−0.394836
$661$	31.0164	1.20640	0.603199	−	0.797591i	$-0.293892\pi$
$661$	31.0164	1.20640	0.603199	+	0.797591i	$0.293892\pi$
$662$	−69.6536	−2.70716
$663$	−41.8522	−1.62541
$664$	−68.2247	−2.64763
$665$	−38.8472	−1.50643
$666$	−16.1442	−0.625574
$667$	0.793517	0.0307251
$668$	74.9157	2.89858
$669$	−16.5956	−0.641623
$670$	38.7706	1.49784
$671$	−2.48926	−0.0960968
$672$	7.73253	0.298289
$673$	1.95414	0.0753266	0.0376633	−	0.999290i	$-0.488009\pi$
$673$	1.95414	0.0753266	0.0376633	+	0.999290i	$0.488009\pi$
$674$	56.5974	2.18005
$675$	3.07135	0.118216
$676$	−3.99298	−0.153576
$677$	17.9870	0.691296	0.345648	−	0.938364i	$-0.387659\pi$
$677$	17.9870	0.691296	0.345648	+	0.938364i	$0.387659\pi$
$678$	−20.6550	−0.793251
$679$	−30.2659	−1.16150
$680$	64.9865	2.49212
$681$	47.9859	1.83882
$682$	1.15824	0.0443513
$683$	15.9541	0.610468	0.305234	−	0.952277i	$-0.401265\pi$
$683$	15.9541	0.610468	0.305234	+	0.952277i	$0.401265\pi$
$684$	64.2170	2.45540
$685$	11.0272	0.421327
$686$	−48.6313	−1.85675
$687$	−0.796103	−0.0303732
$688$	29.9231	1.14081
$689$	18.7009	0.712449
$690$	−21.8189	−0.830633
$691$	−43.9724	−1.67279	−0.836394	−	0.548129i	$-0.815340\pi$
$691$	−43.9724	−1.67279	−0.836394	+	0.548129i	$0.815340\pi$
$692$	46.3147	1.76062
$693$	−2.12548	−0.0807402
$694$	32.4354	1.23123
$695$	19.4897	0.739287
$696$	−6.25108	−0.236947
$697$	0	0
$698$	26.8947	1.01798
$699$	−30.6751	−1.16024
$700$	−26.1575	−0.988661
$701$	−3.41997	−0.129170	−0.0645852	−	0.997912i	$-0.520572\pi$
$701$	−3.41997	−0.129170	−0.0645852	+	0.997912i	$0.520572\pi$
$702$	7.88519	0.297607
$703$	16.5608	0.624602
$704$	−3.81472	−0.143773
$705$	15.0477	0.566728
$706$	−33.9182	−1.27653
$707$	−24.0837	−0.905761
$708$	−59.9219	−2.25200
$709$	−4.59862	−0.172705	−0.0863525	−	0.996265i	$-0.527521\pi$
$709$	−4.59862	−0.172705	−0.0863525	+	0.996265i	$0.527521\pi$
$710$	−48.5800	−1.82317
$711$	−15.5646	−0.583720
$712$	−1.48014	−0.0554705
$713$	1.63697	0.0613052
$714$	61.3400	2.29559
$715$	−3.86799	−0.144655
$716$	7.63892	0.285480
$717$	−28.0947	−1.04921
$718$	−69.3222	−2.58708
$719$	−9.88832	−0.368772	−0.184386	−	0.982854i	$-0.559030\pi$
$719$	−9.88832	−0.368772	−0.184386	+	0.982854i	$0.559030\pi$
$720$	22.5571	0.840653
$721$	27.4462	1.02215
$722$	−54.3742	−2.02360
$723$	−64.3948	−2.39487
$724$	62.2071	2.31191
$725$	−1.94222	−0.0721323
$726$	−62.0010	−2.30107
$727$	11.1815	0.414697	0.207349	−	0.978267i	$-0.433517\pi$
$727$	11.1815	0.414697	0.207349	+	0.978267i	$0.433517\pi$
$728$	−32.1032	−1.18983
$729$	−19.4043	−0.718678
$730$	100.582	3.72270
$731$	−50.6901	−1.87484
$732$	57.9752	2.14283
$733$	−29.7454	−1.09867	−0.549336	−	0.835602i	$-0.685119\pi$
$733$	−29.7454	−1.09867	−0.549336	+	0.835602i	$0.685119\pi$
$734$	−53.6508	−1.98029
$735$	17.6455	0.650866
$736$	−2.06889	−0.0762602
$737$	−2.17602	−0.0801549
$738$	0	0
$739$	17.1524	0.630961	0.315481	−	0.948932i	$-0.397834\pi$
$739$	17.1524	0.630961	0.315481	+	0.948932i	$0.397834\pi$
$740$	28.2923	1.04005
$741$	52.7315	1.93714
$742$	−27.4087	−1.00621
$743$	−48.5468	−1.78101	−0.890504	−	0.454975i	$-0.849648\pi$
$743$	−48.5468	−1.78101	−0.890504	+	0.454975i	$0.849648\pi$
$744$	−12.8956	−0.472775
$745$	36.6480	1.34268
$746$	−41.8046	−1.53057
$747$	40.1160	1.46777
$748$	−7.62982	−0.278974
$749$	−14.4746	−0.528892
$750$	−28.6878	−1.04753
$751$	12.2325	0.446369	0.223185	−	0.974776i	$-0.428355\pi$
$751$	12.2325	0.446369	0.223185	+	0.974776i	$0.428355\pi$
$752$	−6.68157	−0.243652
$753$	−3.20682	−0.116863
$754$	−4.98634	−0.181592
$755$	7.71968	0.280948
$756$	−7.59340	−0.276169
$757$	−37.1871	−1.35159	−0.675795	−	0.737090i	$-0.736199\pi$
$757$	−37.1871	−1.35159	−0.675795	+	0.737090i	$0.736199\pi$
$758$	−6.38540	−0.231928
$759$	1.22460	0.0444502
$760$	−81.8793	−2.97007
$761$	9.30474	0.337296	0.168648	−	0.985676i	$-0.446060\pi$
$761$	9.30474	0.337296	0.168648	+	0.985676i	$0.446060\pi$
$762$	58.4801	2.11851
$763$	−17.2002	−0.622688
$764$	−21.1970	−0.766880
$765$	−38.2119	−1.38156
$766$	−69.9782	−2.52842
$767$	−22.8498	−0.825058
$768$	71.0504	2.56381
$769$	−39.6374	−1.42936	−0.714680	−	0.699451i	$-0.753428\pi$
$769$	−39.6374	−1.42936	−0.714680	+	0.699451i	$0.753428\pi$
$770$	5.66905	0.204299
$771$	12.5038	0.450313
$772$	32.2368	1.16023
$773$	40.7933	1.46723	0.733616	−	0.679564i	$-0.237831\pi$
$773$	40.7933	1.46723	0.733616	+	0.679564i	$0.237831\pi$
$774$	−62.2600	−2.23789
$775$	−4.00668	−0.143924
$776$	−63.7922	−2.29001
$777$	12.7661	0.457983
$778$	51.2334	1.83681
$779$	0	0
$780$	90.0861	3.22560
$781$	2.72658	0.0975648
$782$	−16.4119	−0.586889
$783$	−0.563818	−0.0201492
$784$	−7.83510	−0.279825
$785$	−29.8363	−1.06490
$786$	59.3300	2.11623
$787$	−3.68197	−0.131248	−0.0656240	−	0.997844i	$-0.520904\pi$
$787$	−3.68197	−0.131248	−0.0656240	+	0.997844i	$0.520904\pi$
$788$	100.451	3.57842
$789$	−5.58519	−0.198838
$790$	41.5139	1.47700
$791$	7.58483	0.269685
$792$	−4.47992	−0.159187
$793$	22.1075	0.785059
$794$	−10.9850	−0.389844
$795$	36.7678	1.30402
$796$	−43.2981	−1.53466
$797$	43.0903	1.52634	0.763168	−	0.646200i	$-0.223643\pi$
$797$	43.0903	1.52634	0.763168	+	0.646200i	$0.223643\pi$
$798$	−77.2850	−2.73586
$799$	11.3186	0.400425
$800$	5.06383	0.179034
$801$	0.870318	0.0307512
$802$	18.1959	0.642520
$803$	−5.64522	−0.199215
$804$	50.6799	1.78734
$805$	8.01224	0.282394
$806$	−10.2865	−0.362326
$807$	−39.9904	−1.40773
$808$	−50.7619	−1.78580
$809$	18.9832	0.667412	0.333706	−	0.942677i	$-0.391701\pi$
$809$	18.9832	0.667412	0.333706	+	0.942677i	$0.391701\pi$
$810$	69.6361	2.44676
$811$	8.79807	0.308942	0.154471	−	0.987997i	$-0.450633\pi$
$811$	8.79807	0.308942	0.154471	+	0.987997i	$0.450633\pi$
$812$	4.80181	0.168511
$813$	50.0958	1.75694
$814$	−2.41675	−0.0847069
$815$	−10.0162	−0.350853
$816$	36.5369	1.27905
$817$	63.8667	2.23441
$818$	2.50059	0.0874311
$819$	18.8767	0.659604
$820$	0	0
$821$	−54.2917	−1.89479	−0.947397	−	0.320060i	$-0.896297\pi$
$821$	−54.2917	−1.89479	−0.947397	+	0.320060i	$0.896297\pi$
$822$	21.9381	0.765181
$823$	3.81368	0.132937	0.0664683	−	0.997789i	$-0.478827\pi$
$823$	3.81368	0.132937	0.0664683	+	0.997789i	$0.478827\pi$
$824$	57.8490	2.01527
$825$	−2.99735	−0.104354
$826$	33.4894	1.16525
$827$	−30.2236	−1.05098	−0.525489	−	0.850800i	$-0.676118\pi$
$827$	−30.2236	−1.05098	−0.525489	+	0.850800i	$0.676118\pi$
$828$	−13.2448	−0.460287
$829$	42.4307	1.47368	0.736840	−	0.676067i	$-0.236317\pi$
$829$	42.4307	1.47368	0.736840	+	0.676067i	$0.236317\pi$
$830$	−106.997	−3.71393
$831$	26.9815	0.935978
$832$	33.8791	1.17454
$833$	13.2727	0.459873
$834$	38.7740	1.34263
$835$	56.1659	1.94370
$836$	9.61315	0.332478
$837$	−1.16312	−0.0402033
$838$	13.4608	0.464996
$839$	−10.5099	−0.362844	−0.181422	−	0.983405i	$-0.558070\pi$
$839$	−10.5099	−0.362844	−0.181422	+	0.983405i	$0.558070\pi$
$840$	−63.1179	−2.17778
$841$	−28.6435	−0.987706
$842$	−75.4276	−2.59941
$843$	64.0077	2.20454
$844$	−20.3794	−0.701490
$845$	−2.99362	−0.102984
$846$	13.9021	0.477964
$847$	22.7677	0.782307
$848$	−16.3259	−0.560633
$849$	−26.5536	−0.911316
$850$	40.1700	1.37782
$851$	−3.41566	−0.117087
$852$	−63.5025	−2.17556
$853$	−42.6889	−1.46164	−0.730820	−	0.682570i	$-0.760862\pi$
$853$	−42.6889	−1.46164	−0.730820	+	0.682570i	$0.760862\pi$
$854$	−32.4014	−1.10875
$855$	48.1449	1.64652
$856$	−30.5086	−1.04276
$857$	0.629598	0.0215066	0.0107533	−	0.999942i	$-0.496577\pi$
$857$	0.629598	0.0215066	0.0107533	+	0.999942i	$0.496577\pi$
$858$	−7.69521	−0.262710
$859$	−6.97945	−0.238136	−0.119068	−	0.992886i	$-0.537991\pi$
$859$	−6.97945	−0.238136	−0.119068	+	0.992886i	$0.537991\pi$
$860$	109.109	3.72060
$861$	0	0
$862$	−36.1113	−1.22995
$863$	35.5204	1.20913	0.604565	−	0.796556i	$-0.293347\pi$
$863$	35.5204	1.20913	0.604565	+	0.796556i	$0.293347\pi$
$864$	1.47001	0.0500106
$865$	34.7231	1.18062
$866$	42.3728	1.43989
$867$	−21.6609	−0.735644
$868$	9.90584	0.336226
$869$	−2.32999	−0.0790396
$870$	−9.80360	−0.332373
$871$	19.3256	0.654822
$872$	−36.2532	−1.22769
$873$	37.5097	1.26951
$874$	20.6781	0.699446
$875$	10.5346	0.356134
$876$	131.478	4.44223
$877$	17.8965	0.604322	0.302161	−	0.953257i	$-0.402292\pi$
$877$	17.8965	0.604322	0.302161	+	0.953257i	$0.402292\pi$
$878$	−16.5000	−0.556846
$879$	−51.3047	−1.73046
$880$	3.37675	0.113830
$881$	−21.2645	−0.716418	−0.358209	−	0.933641i	$-0.616612\pi$
$881$	−21.2645	−0.716418	−0.358209	+	0.933641i	$0.616612\pi$
$882$	16.3022	0.548924
$883$	40.3488	1.35785	0.678923	−	0.734210i	$-0.262447\pi$
$883$	40.3488	1.35785	0.678923	+	0.734210i	$0.262447\pi$
$884$	67.7615	2.27907
$885$	−44.9248	−1.51013
$886$	20.4132	0.685795
$887$	25.3043	0.849635	0.424817	−	0.905279i	$-0.360338\pi$
$887$	25.3043	0.849635	0.424817	+	0.905279i	$0.360338\pi$
$888$	26.9075	0.902957
$889$	−21.4748	−0.720240
$890$	−2.32131	−0.0778103
$891$	−3.90837	−0.130935
$892$	26.8694	0.899653
$893$	−14.2609	−0.477221
$894$	72.9098	2.43847
$895$	5.72706	0.191435
$896$	−43.1197	−1.44053
$897$	−10.8759	−0.363134
$898$	7.53953	0.251597
$899$	0.735519	0.0245309
$900$	32.4180	1.08060
$901$	27.6562	0.921362
$902$	0	0
$903$	49.2326	1.63836
$904$	15.9867	0.531711
$905$	46.6380	1.55030
$906$	15.3580	0.510235
$907$	−39.5775	−1.31415	−0.657075	−	0.753825i	$-0.728207\pi$
$907$	−39.5775	−1.31415	−0.657075	+	0.753825i	$0.728207\pi$
$908$	−77.6923	−2.57831
$909$	29.8479	0.989992
$910$	−50.3477	−1.66901
$911$	−34.8374	−1.15422	−0.577108	−	0.816668i	$-0.695819\pi$
$911$	−34.8374	−1.15422	−0.577108	+	0.816668i	$0.695819\pi$
$912$	−46.0345	−1.52435
$913$	6.00528	0.198746
$914$	−26.7715	−0.885521
$915$	43.4653	1.43692
$916$	1.28894	0.0425879
$917$	−21.7868	−0.719465
$918$	11.6612	0.384876
$919$	23.7053	0.781966	0.390983	−	0.920398i	$-0.372135\pi$
$919$	23.7053	0.781966	0.390983	+	0.920398i	$0.372135\pi$
$920$	16.8876	0.556768
$921$	−40.9530	−1.34945
$922$	−43.2317	−1.42376
$923$	−24.2152	−0.797052
$924$	7.41044	0.243786
$925$	8.36021	0.274882
$926$	39.6517	1.30304
$927$	−34.0151	−1.11720
$928$	−0.929584	−0.0305151
$929$	19.1108	0.627004	0.313502	−	0.949587i	$-0.398498\pi$
$929$	19.1108	0.627004	0.313502	+	0.949587i	$0.398498\pi$
$930$	−20.2242	−0.663177
$931$	−16.7229	−0.548071
$932$	49.6650	1.62683
$933$	28.6139	0.936778
$934$	30.2418	0.989542
$935$	−5.72025	−0.187072
$936$	39.7868	1.30047
$937$	28.5056	0.931237	0.465619	−	0.884985i	$-0.345832\pi$
$937$	28.5056	0.931237	0.465619	+	0.884985i	$0.345832\pi$
$938$	−28.3242	−0.924818
$939$	−51.3059	−1.67431
$940$	−24.3631	−0.794638
$941$	−6.63985	−0.216453	−0.108227	−	0.994126i	$-0.534517\pi$
$941$	−6.63985	−0.216453	−0.108227	+	0.994126i	$0.534517\pi$
$942$	−59.3581	−1.93399
$943$	0	0
$944$	19.9478	0.649246
$945$	−5.69294	−0.185191
$946$	−9.32019	−0.303026
$947$	−30.6099	−0.994688	−0.497344	−	0.867553i	$-0.665691\pi$
$947$	−30.6099	−0.994688	−0.497344	+	0.867553i	$0.665691\pi$
$948$	54.2659	1.76247
$949$	50.1360	1.62748
$950$	−50.6119	−1.64207
$951$	−46.8189	−1.51821
$952$	−47.4765	−1.53872
$953$	25.7759	0.834962	0.417481	−	0.908686i	$-0.362913\pi$
$953$	25.7759	0.834962	0.417481	+	0.908686i	$0.362913\pi$
$954$	33.9687	1.09978
$955$	−15.8918	−0.514248
$956$	45.4871	1.47116
$957$	0.550233	0.0177865
$958$	16.9449	0.547466
$959$	−8.05601	−0.260142
$960$	66.6093	2.14981
$961$	−29.4827	−0.951054
$962$	21.4635	0.692010
$963$	17.9390	0.578076
$964$	104.259	3.35797
$965$	24.1686	0.778015
$966$	15.9400	0.512862
$967$	23.9682	0.770764	0.385382	−	0.922757i	$-0.374070\pi$
$967$	23.9682	0.770764	0.385382	+	0.922757i	$0.374070\pi$
$968$	47.9880	1.54239
$969$	77.9829	2.50517
$970$	−100.046	−3.21227
$971$	11.3754	0.365053	0.182526	−	0.983201i	$-0.441573\pi$
$971$	11.3754	0.365053	0.182526	+	0.983201i	$0.441573\pi$
$972$	80.1722	2.57152
$973$	−14.2384	−0.456462
$974$	−71.8707	−2.30289
$975$	26.6199	0.852519
$976$	−19.2998	−0.617771
$977$	−35.1575	−1.12479	−0.562395	−	0.826869i	$-0.690120\pi$
$977$	−35.1575	−1.12479	−0.562395	+	0.826869i	$0.690120\pi$
$978$	−19.9269	−0.637192
$979$	0.130285	0.00416392
$980$	−28.5693	−0.912613
$981$	21.3168	0.680594
$982$	−75.7398	−2.41696
$983$	−58.6885	−1.87187	−0.935937	−	0.352169i	$-0.885444\pi$
$983$	−58.6885	−1.87187	−0.935937	+	0.352169i	$0.885444\pi$
$984$	0	0
$985$	75.3104	2.39959
$986$	−7.37413	−0.234840
$987$	−10.9932	−0.349918
$988$	−85.3757	−2.71616
$989$	−13.1725	−0.418861
$990$	−7.02588	−0.223297
$991$	−53.3298	−1.69408	−0.847038	−	0.531532i	$-0.821617\pi$
$991$	−53.3298	−1.69408	−0.847038	+	0.531532i	$0.821617\pi$
$992$	−1.91767	−0.0608862
$993$	−68.2617	−2.16622
$994$	35.4905	1.12569
$995$	−32.4616	−1.02910
$996$	−139.864	−4.43176
$997$	−45.0797	−1.42769	−0.713844	−	0.700304i	$-0.753048\pi$
$997$	−45.0797	−1.42769	−0.713844	+	0.700304i	$0.753048\pi$
$998$	−64.7988	−2.05117
$999$	2.42693	0.0767846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1681.2.a.m.1.1		24
41.11	odd	40		41.2.g.a.39.1	yes	24
41.15	odd	40		41.2.g.a.20.1	✓	24
41.40	even	2	inner	1681.2.a.m.1.2		24
123.11	even	40		369.2.u.a.244.3		24
123.56	even	40		369.2.u.a.307.3		24
164.11	even	40		656.2.bs.d.449.3		24
164.15	even	40		656.2.bs.d.225.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.20.1	✓	24	41.15	odd	40
41.2.g.a.39.1	yes	24	41.11	odd	40
369.2.u.a.244.3		24	123.11	even	40
369.2.u.a.307.3		24	123.56	even	40
656.2.bs.d.225.3		24	164.15	even	40
656.2.bs.d.449.3		24	164.11	even	40
1681.2.a.m.1.1		24	1.1	even	1	trivial
1681.2.a.m.1.2		24	41.40	even	2	inner

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:	\( N \)	\(=\)	\( 1681 = 41^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1681.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41490 q^{2} -2.36665 q^{3} +3.83176 q^{4} +2.87275 q^{5} +5.71522 q^{6} -2.09872 q^{7} -4.42352 q^{8} +2.60102 q^{9} +O(q^{10})\)	\(q-2.41490 q^{2} -2.36665 q^{3} +3.83176 q^{4} +2.87275 q^{5} +5.71522 q^{6} -2.09872 q^{7} -4.42352 q^{8} +2.60102 q^{9} -6.93742 q^{10} +0.389367 q^{11} -9.06842 q^{12} -3.45802 q^{13} +5.06819 q^{14} -6.79879 q^{15} +3.01885 q^{16} -5.11396 q^{17} -6.28121 q^{18} +6.44330 q^{19} +11.0077 q^{20} +4.96692 q^{21} -0.940284 q^{22} -1.32893 q^{23} +10.4689 q^{24} +3.25271 q^{25} +8.35079 q^{26} +0.944245 q^{27} -8.04177 q^{28} -0.597109 q^{29} +16.4184 q^{30} -1.23180 q^{31} +1.55681 q^{32} -0.921494 q^{33} +12.3497 q^{34} -6.02909 q^{35} +9.96648 q^{36} +2.57023 q^{37} -15.5599 q^{38} +8.18392 q^{39} -12.7077 q^{40} -11.9946 q^{42} +9.91211 q^{43} +1.49196 q^{44} +7.47209 q^{45} +3.20924 q^{46} -2.21328 q^{47} -7.14455 q^{48} -2.59539 q^{49} -7.85497 q^{50} +12.1029 q^{51} -13.2503 q^{52} -5.40798 q^{53} -2.28026 q^{54} +1.11856 q^{55} +9.28370 q^{56} -15.2490 q^{57} +1.44196 q^{58} +6.60776 q^{59} -26.0513 q^{60} -6.39309 q^{61} +2.97467 q^{62} -5.45880 q^{63} -9.79723 q^{64} -9.93404 q^{65} +2.22532 q^{66} -5.58862 q^{67} -19.5955 q^{68} +3.14511 q^{69} +14.5597 q^{70} +7.00260 q^{71} -11.5057 q^{72} -14.4984 q^{73} -6.20686 q^{74} -7.69801 q^{75} +24.6892 q^{76} -0.817170 q^{77} -19.7634 q^{78} -5.98405 q^{79} +8.67240 q^{80} -10.0378 q^{81} +15.4232 q^{83} +19.0320 q^{84} -14.6911 q^{85} -23.9368 q^{86} +1.41315 q^{87} -1.72237 q^{88} +0.334607 q^{89} -18.0444 q^{90} +7.25741 q^{91} -5.09214 q^{92} +2.91523 q^{93} +5.34487 q^{94} +18.5100 q^{95} -3.68441 q^{96} +14.4212 q^{97} +6.26763 q^{98} +1.01275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 + 20 * q^4 + 12 * q^5 + 24 * q^8 + 24 * q^9	\( 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 20 q^{16} + 20 q^{18} + 40 q^{20} + 56 q^{21} + 48 q^{23} + 8 q^{25} + 32 q^{31} + 36 q^{32} + 24 q^{33} + 108 q^{36} + 60 q^{39} + 44 q^{40} - 40 q^{42} + 36 q^{43} - 36 q^{45} + 36 q^{46} + 32 q^{49} - 60 q^{50} + 36 q^{51} - 60 q^{57} + 116 q^{59} + 40 q^{61} + 48 q^{62} + 60 q^{64} + 16 q^{66} + 4 q^{72} + 16 q^{73} + 24 q^{74} - 16 q^{77} - 60 q^{78} + 84 q^{80} - 28 q^{81} + 80 q^{83} - 24 q^{84} - 24 q^{86} + 76 q^{87} + 56 q^{90} + 40 q^{91} - 40 q^{92} + 36 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 20 * q^4 + 12 * q^5 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 20 * q^16 + 20 * q^18 + 40 * q^20 + 56 * q^21 + 48 * q^23 + 8 * q^25 + 32 * q^31 + 36 * q^32 + 24 * q^33 + 108 * q^36 + 60 * q^39 + 44 * q^40 - 40 * q^42 + 36 * q^43 - 36 * q^45 + 36 * q^46 + 32 * q^49 - 60 * q^50 + 36 * q^51 - 60 * q^57 + 116 * q^59 + 40 * q^61 + 48 * q^62 + 60 * q^64 + 16 * q^66 + 4 * q^72 + 16 * q^73 + 24 * q^74 - 16 * q^77 - 60 * q^78 + 84 * q^80 - 28 * q^81 + 80 * q^83 - 24 * q^84 - 24 * q^86 + 76 * q^87 + 56 * q^90 + 40 * q^91 - 40 * q^92 + 36 * q^98

Introduction

L-functions

Modular forms

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Database

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