LMFDB - Embedded newform 8017.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, 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("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$1$
Dimension:	$327$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79413 q^{2} -2.90420 q^{3} +5.80714 q^{4} -2.69949 q^{5} +8.11470 q^{6} -0.505392 q^{7} -10.6376 q^{8} +5.43438 q^{9} +O(q^{10})$	\(q-2.79413 q^{2} -2.90420 q^{3} +5.80714 q^{4} -2.69949 q^{5} +8.11470 q^{6} -0.505392 q^{7} -10.6376 q^{8} +5.43438 q^{9} +7.54271 q^{10} -3.41934 q^{11} -16.8651 q^{12} +4.64120 q^{13} +1.41213 q^{14} +7.83985 q^{15} +18.1086 q^{16} -6.09188 q^{17} -15.1843 q^{18} -1.15499 q^{19} -15.6763 q^{20} +1.46776 q^{21} +9.55406 q^{22} -3.05017 q^{23} +30.8938 q^{24} +2.28723 q^{25} -12.9681 q^{26} -7.06991 q^{27} -2.93488 q^{28} +3.32396 q^{29} -21.9055 q^{30} +2.96212 q^{31} -29.3225 q^{32} +9.93044 q^{33} +17.0215 q^{34} +1.36430 q^{35} +31.5582 q^{36} +0.409289 q^{37} +3.22718 q^{38} -13.4790 q^{39} +28.7161 q^{40} +5.78269 q^{41} -4.10111 q^{42} -10.0028 q^{43} -19.8566 q^{44} -14.6700 q^{45} +8.52257 q^{46} +6.50235 q^{47} -52.5910 q^{48} -6.74458 q^{49} -6.39080 q^{50} +17.6920 q^{51} +26.9521 q^{52} -5.49281 q^{53} +19.7542 q^{54} +9.23046 q^{55} +5.37618 q^{56} +3.35432 q^{57} -9.28757 q^{58} +3.03031 q^{59} +45.5271 q^{60} +7.01459 q^{61} -8.27654 q^{62} -2.74649 q^{63} +45.7135 q^{64} -12.5289 q^{65} -27.7469 q^{66} -14.4467 q^{67} -35.3764 q^{68} +8.85831 q^{69} -3.81202 q^{70} -14.8218 q^{71} -57.8089 q^{72} +15.6715 q^{73} -1.14360 q^{74} -6.64256 q^{75} -6.70718 q^{76} +1.72811 q^{77} +37.6620 q^{78} -0.834082 q^{79} -48.8839 q^{80} +4.22931 q^{81} -16.1576 q^{82} +5.43656 q^{83} +8.52349 q^{84} +16.4450 q^{85} +27.9490 q^{86} -9.65345 q^{87} +36.3737 q^{88} -2.66743 q^{89} +40.9899 q^{90} -2.34563 q^{91} -17.7128 q^{92} -8.60259 q^{93} -18.1684 q^{94} +3.11788 q^{95} +85.1583 q^{96} -13.8903 q^{97} +18.8452 q^{98} -18.5820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) $ 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * 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 $

$2$	−2.79413	−1.97575	−0.987873	−	0.155265i	$-0.950377\pi$
$2$	−2.79413	−1.97575	−0.987873	+	0.155265i	$0.950377\pi$
$3$	−2.90420	−1.67674	−0.838370	−	0.545101i	$-0.816491\pi$
$3$	−2.90420	−1.67674	−0.838370	+	0.545101i	$0.816491\pi$
$4$	5.80714	2.90357
$5$	−2.69949	−1.20725	−0.603624	−	0.797270i	$-0.706277\pi$
$5$	−2.69949	−1.20725	−0.603624	+	0.797270i	$0.706277\pi$
$6$	8.11470	3.31281
$7$	−0.505392	−0.191020	−0.0955102	−	0.995428i	$-0.530448\pi$
$7$	−0.505392	−0.191020	−0.0955102	+	0.995428i	$0.530448\pi$
$8$	−10.6376	−3.76097
$9$	5.43438	1.81146
$10$	7.54271	2.38521
$11$	−3.41934	−1.03097	−0.515485	−	0.856899i	$-0.672388\pi$
$11$	−3.41934	−1.03097	−0.515485	+	0.856899i	$0.672388\pi$
$12$	−16.8651	−4.86853
$13$	4.64120	1.28724	0.643619	−	0.765346i	$-0.277432\pi$
$13$	4.64120	1.28724	0.643619	+	0.765346i	$0.277432\pi$
$14$	1.41213	0.377408
$15$	7.83985	2.02424
$16$	18.1086	4.52715
$17$	−6.09188	−1.47750	−0.738749	−	0.673980i	$-0.764583\pi$
$17$	−6.09188	−1.47750	−0.738749	+	0.673980i	$0.764583\pi$
$18$	−15.1843	−3.57898
$19$	−1.15499	−0.264973	−0.132486	−	0.991185i	$-0.542296\pi$
$19$	−1.15499	−0.264973	−0.132486	+	0.991185i	$0.542296\pi$
$20$	−15.6763	−3.50533
$21$	1.46776	0.320291
$22$	9.55406	2.03693
$23$	−3.05017	−0.636005	−0.318003	−	0.948090i	$-0.603012\pi$
$23$	−3.05017	−0.636005	−0.318003	+	0.948090i	$0.603012\pi$
$24$	30.8938	6.30617
$25$	2.28723	0.457445
$26$	−12.9681	−2.54326
$27$	−7.06991	−1.36061
$28$	−2.93488	−0.554641
$29$	3.32396	0.617244	0.308622	−	0.951185i	$-0.400132\pi$
$29$	3.32396	0.617244	0.308622	+	0.951185i	$0.400132\pi$
$30$	−21.9055	−3.99938
$31$	2.96212	0.532012	0.266006	−	0.963971i	$-0.414296\pi$
$31$	2.96212	0.532012	0.266006	+	0.963971i	$0.414296\pi$
$32$	−29.3225	−5.18353
$33$	9.93044	1.72867
$34$	17.0215	2.91916
$35$	1.36430	0.230609
$36$	31.5582	5.25970
$37$	0.409289	0.0672867	0.0336433	−	0.999434i	$-0.489289\pi$
$37$	0.409289	0.0672867	0.0336433	+	0.999434i	$0.489289\pi$
$38$	3.22718	0.523519
$39$	−13.4790	−2.15836
$40$	28.7161	4.54042
$41$	5.78269	0.903105	0.451552	−	0.892245i	$-0.350870\pi$
$41$	5.78269	0.903105	0.451552	+	0.892245i	$0.350870\pi$
$42$	−4.10111	−0.632814
$43$	−10.0028	−1.52541	−0.762703	−	0.646749i	$-0.776128\pi$
$43$	−10.0028	−1.52541	−0.762703	+	0.646749i	$0.776128\pi$
$44$	−19.8566	−2.99349
$45$	−14.6700	−2.18688
$46$	8.52257	1.25658
$47$	6.50235	0.948466	0.474233	−	0.880399i	$-0.342725\pi$
$47$	6.50235	0.948466	0.474233	+	0.880399i	$0.342725\pi$
$48$	−52.5910	−7.59086
$49$	−6.74458	−0.963511
$50$	−6.39080	−0.903796
$51$	17.6920	2.47738
$52$	26.9521	3.73759
$53$	−5.49281	−0.754496	−0.377248	−	0.926112i	$-0.623129\pi$
$53$	−5.49281	−0.754496	−0.377248	+	0.926112i	$0.623129\pi$
$54$	19.7542	2.68821
$55$	9.23046	1.24463
$56$	5.37618	0.718422
$57$	3.35432	0.444290
$58$	−9.28757	−1.21952
$59$	3.03031	0.394513	0.197256	−	0.980352i	$-0.436797\pi$
$59$	3.03031	0.394513	0.197256	+	0.980352i	$0.436797\pi$
$60$	45.5271	5.87752
$61$	7.01459	0.898126	0.449063	−	0.893500i	$-0.351758\pi$
$61$	7.01459	0.898126	0.449063	+	0.893500i	$0.351758\pi$
$62$	−8.27654	−1.05112
$63$	−2.74649	−0.346025
$64$	45.7135	5.71418
$65$	−12.5289	−1.55401
$66$	−27.7469	−3.41541
$67$	−14.4467	−1.76494	−0.882470	−	0.470369i	$-0.844121\pi$
$67$	−14.4467	−1.76494	−0.882470	+	0.470369i	$0.844121\pi$
$68$	−35.3764	−4.29002
$69$	8.85831	1.06642
$70$	−3.81202	−0.455624
$71$	−14.8218	−1.75902	−0.879510	−	0.475880i	$-0.842130\pi$
$71$	−14.8218	−1.75902	−0.879510	+	0.475880i	$0.842130\pi$
$72$	−57.8089	−6.81284
$73$	15.6715	1.83421	0.917107	−	0.398640i	$-0.130518\pi$
$73$	15.6715	1.83421	0.917107	+	0.398640i	$0.130518\pi$
$74$	−1.14360	−0.132941
$75$	−6.64256	−0.767017
$76$	−6.70718	−0.769367
$77$	1.72811	0.196936
$78$	37.6620	4.26438
$79$	−0.834082	−0.0938416	−0.0469208	−	0.998899i	$-0.514941\pi$
$79$	−0.834082	−0.0938416	−0.0469208	+	0.998899i	$0.514941\pi$
$80$	−48.8839	−5.46539
$81$	4.22931	0.469923
$82$	−16.1576	−1.78431
$83$	5.43656	0.596740	0.298370	−	0.954450i	$-0.403557\pi$
$83$	5.43656	0.596740	0.298370	+	0.954450i	$0.403557\pi$
$84$	8.52349	0.929989
$85$	16.4450	1.78371
$86$	27.9490	3.01381
$87$	−9.65345	−1.03496
$88$	36.3737	3.87745
$89$	−2.66743	−0.282747	−0.141374	−	0.989956i	$-0.545152\pi$
$89$	−2.66743	−0.282747	−0.141374	+	0.989956i	$0.545152\pi$
$90$	40.9899	4.32071
$91$	−2.34563	−0.245889
$92$	−17.7128	−1.84669
$93$	−8.60259	−0.892047
$94$	−18.1684	−1.87393
$95$	3.11788	0.319887
$96$	85.1583	8.69143
$97$	−13.8903	−1.41034	−0.705172	−	0.709036i	$-0.749130\pi$
$97$	−13.8903	−1.41034	−0.705172	+	0.709036i	$0.749130\pi$
$98$	18.8452	1.90365
$99$	−18.5820	−1.86756
$100$	13.2822	1.32822
$101$	−0.807119	−0.0803113	−0.0401556	−	0.999193i	$-0.512785\pi$
$101$	−0.807119	−0.0803113	−0.0401556	+	0.999193i	$0.512785\pi$
$102$	−49.4338	−4.89468
$103$	−3.28560	−0.323740	−0.161870	−	0.986812i	$-0.551753\pi$
$103$	−3.28560	−0.323740	−0.161870	+	0.986812i	$0.551753\pi$
$104$	−49.3714	−4.84127
$105$	−3.96220	−0.386671
$106$	15.3476	1.49069
$107$	2.46067	0.237882	0.118941	−	0.992901i	$-0.462050\pi$
$107$	2.46067	0.237882	0.118941	+	0.992901i	$0.462050\pi$
$108$	−41.0560	−3.95061
$109$	−1.27912	−0.122517	−0.0612587	−	0.998122i	$-0.519511\pi$
$109$	−1.27912	−0.122517	−0.0612587	+	0.998122i	$0.519511\pi$
$110$	−25.7911	−2.45908
$111$	−1.18866	−0.112822
$112$	−9.15195	−0.864778
$113$	18.1463	1.70706	0.853532	−	0.521040i	$-0.174456\pi$
$113$	18.1463	1.70706	0.853532	+	0.521040i	$0.174456\pi$
$114$	−9.37239	−0.877805
$115$	8.23390	0.767815
$116$	19.3027	1.79221
$117$	25.2220	2.33178
$118$	−8.46707	−0.779457
$119$	3.07879	0.282232
$120$	−83.3974	−7.61311
$121$	0.691875	0.0628977
$122$	−19.5997	−1.77447
$123$	−16.7941	−1.51427
$124$	17.2014	1.54474
$125$	7.32309	0.654997
$126$	7.67404	0.683658
$127$	5.66240	0.502456	0.251228	−	0.967928i	$-0.419166\pi$
$127$	5.66240	0.502456	0.251228	+	0.967928i	$0.419166\pi$
$128$	−69.0843	−6.10624
$129$	29.0500	2.55771
$130$	35.0072	3.07034
$131$	14.9964	1.31025	0.655123	−	0.755523i	$-0.272617\pi$
$131$	14.9964	1.31025	0.655123	+	0.755523i	$0.272617\pi$
$132$	57.6675	5.01931
$133$	0.583722	0.0506152
$134$	40.3658	3.48707
$135$	19.0851	1.64259
$136$	64.8032	5.55683
$137$	−9.51504	−0.812925	−0.406462	−	0.913668i	$-0.633238\pi$
$137$	−9.51504	−0.812925	−0.406462	+	0.913668i	$0.633238\pi$
$138$	−24.7512	−2.10697
$139$	−4.43565	−0.376227	−0.188114	−	0.982147i	$-0.560237\pi$
$139$	−4.43565	−0.376227	−0.188114	+	0.982147i	$0.560237\pi$
$140$	7.92268	0.669589
$141$	−18.8841	−1.59033
$142$	41.4139	3.47538
$143$	−15.8698	−1.32710
$144$	98.4090	8.20075
$145$	−8.97299	−0.745166
$146$	−43.7883	−3.62394
$147$	19.5876	1.61556
$148$	2.37680	0.195372
$149$	12.1745	0.997370	0.498685	−	0.866783i	$-0.333816\pi$
$149$	12.1745	0.997370	0.498685	+	0.866783i	$0.333816\pi$
$150$	18.5602	1.51543
$151$	−2.53166	−0.206023	−0.103012	−	0.994680i	$-0.532848\pi$
$151$	−2.53166	−0.206023	−0.103012	+	0.994680i	$0.532848\pi$
$152$	12.2863	0.996555
$153$	−33.1056	−2.67643
$154$	−4.82855	−0.389096
$155$	−7.99620	−0.642270
$156$	−78.2743	−6.26696
$157$	−4.76459	−0.380256	−0.190128	−	0.981759i	$-0.560890\pi$
$157$	−4.76459	−0.380256	−0.190128	+	0.981759i	$0.560890\pi$
$158$	2.33053	0.185407
$159$	15.9522	1.26509
$160$	79.1556	6.25780
$161$	1.54153	0.121490
$162$	−11.8172	−0.928449
$163$	2.01813	0.158072	0.0790361	−	0.996872i	$-0.474816\pi$
$163$	2.01813	0.158072	0.0790361	+	0.996872i	$0.474816\pi$
$164$	33.5809	2.62223
$165$	−26.8071	−2.08693
$166$	−15.1904	−1.17901
$167$	−17.2887	−1.33784	−0.668920	−	0.743334i	$-0.733243\pi$
$167$	−17.2887	−1.33784	−0.668920	+	0.743334i	$0.733243\pi$
$168$	−15.6135	−1.20461
$169$	8.54077	0.656982
$170$	−45.9493	−3.52415
$171$	−6.27664	−0.479987
$172$	−58.0874	−4.42912
$173$	−19.0669	−1.44963	−0.724813	−	0.688945i	$-0.758074\pi$
$173$	−19.0669	−1.44963	−0.724813	+	0.688945i	$0.758074\pi$
$174$	26.9730	2.04482
$175$	−1.15595	−0.0873814
$176$	−61.9195	−4.66736
$177$	−8.80062	−0.661495
$178$	7.45314	0.558637
$179$	13.4838	1.00783	0.503913	−	0.863755i	$-0.331893\pi$
$179$	13.4838	1.00783	0.503913	+	0.863755i	$0.331893\pi$
$180$	−85.1909	−6.34975
$181$	−10.2980	−0.765448	−0.382724	−	0.923863i	$-0.625014\pi$
$181$	−10.2980	−0.765448	−0.382724	+	0.923863i	$0.625014\pi$
$182$	6.55398	0.485813
$183$	−20.3718	−1.50592
$184$	32.4466	2.39200
$185$	−1.10487	−0.0812316
$186$	24.0367	1.76246
$187$	20.8302	1.52326
$188$	37.7601	2.75394
$189$	3.57308	0.259903
$190$	−8.71174	−0.632016
$191$	−10.7056	−0.774632	−0.387316	−	0.921947i	$-0.626598\pi$
$191$	−10.7056	−0.774632	−0.387316	+	0.921947i	$0.626598\pi$
$192$	−132.761	−9.58120
$193$	5.13086	0.369327	0.184664	−	0.982802i	$-0.440880\pi$
$193$	5.13086	0.369327	0.184664	+	0.982802i	$0.440880\pi$
$194$	38.8112	2.78648
$195$	36.3863	2.60568
$196$	−39.1667	−2.79762
$197$	21.5914	1.53832	0.769162	−	0.639054i	$-0.220674\pi$
$197$	21.5914	1.53832	0.769162	+	0.639054i	$0.220674\pi$
$198$	51.9204	3.68982
$199$	−15.6277	−1.10782	−0.553908	−	0.832578i	$-0.686864\pi$
$199$	−15.6277	−1.10782	−0.553908	+	0.832578i	$0.686864\pi$
$200$	−24.3307	−1.72044
$201$	41.9560	2.95935
$202$	2.25519	0.158675
$203$	−1.67990	−0.117906
$204$	102.740	7.19325
$205$	−15.6103	−1.09027
$206$	9.18039	0.639628
$207$	−16.5758	−1.15210
$208$	84.0457	5.82752
$209$	3.94930	0.273179
$210$	11.0709	0.763963
$211$	21.4075	1.47375	0.736877	−	0.676027i	$-0.236300\pi$
$211$	21.4075	1.47375	0.736877	+	0.676027i	$0.236300\pi$
$212$	−31.8975	−2.19073
$213$	43.0454	2.94942
$214$	−6.87542	−0.469994
$215$	27.0023	1.84154
$216$	75.2071	5.11720
$217$	−1.49703	−0.101625
$218$	3.57402	0.242063
$219$	−45.5133	−3.07550
$220$	53.6026	3.61388
$221$	−28.2737	−1.90189
$222$	3.32126	0.222908
$223$	−17.6899	−1.18460	−0.592301	−	0.805716i	$-0.701781\pi$
$223$	−17.6899	−1.18460	−0.592301	+	0.805716i	$0.701781\pi$
$224$	14.8193	0.990159
$225$	12.4296	0.828643
$226$	−50.7032	−3.37273
$227$	−17.4771	−1.16000	−0.579999	−	0.814617i	$-0.696947\pi$
$227$	−17.4771	−1.16000	−0.579999	+	0.814617i	$0.696947\pi$
$228$	19.4790	1.29003
$229$	13.2288	0.874186	0.437093	−	0.899416i	$-0.356008\pi$
$229$	13.2288	0.874186	0.437093	+	0.899416i	$0.356008\pi$
$230$	−23.0066	−1.51701
$231$	−5.01877	−0.330211
$232$	−35.3591	−2.32144
$233$	19.6922	1.29008	0.645040	−	0.764149i	$-0.276841\pi$
$233$	19.6922	1.29008	0.645040	+	0.764149i	$0.276841\pi$
$234$	−70.4736	−4.60700
$235$	−17.5530	−1.14503
$236$	17.5974	1.14550
$237$	2.42234	0.157348
$238$	−8.60253	−0.557619
$239$	8.29447	0.536525	0.268262	−	0.963346i	$-0.413551\pi$
$239$	8.29447	0.536525	0.268262	+	0.963346i	$0.413551\pi$
$240$	141.969	9.16404
$241$	−18.4530	−1.18867	−0.594333	−	0.804219i	$-0.702584\pi$
$241$	−18.4530	−1.18867	−0.594333	+	0.804219i	$0.702584\pi$
$242$	−1.93318	−0.124270
$243$	8.92698	0.572666
$244$	40.7347	2.60777
$245$	18.2069	1.16320
$246$	46.9248	2.99182
$247$	−5.36054	−0.341083
$248$	−31.5099	−2.00088
$249$	−15.7889	−1.00058
$250$	−20.4616	−1.29411
$251$	−0.0967279	−0.00610541	−0.00305271	−	0.999995i	$-0.500972\pi$
$251$	−0.0967279	−0.00610541	−0.00305271	+	0.999995i	$0.500972\pi$
$252$	−15.9493	−1.00471
$253$	10.4296	0.655702
$254$	−15.8214	−0.992726
$255$	−47.7594	−2.99081
$256$	101.603	6.35020
$257$	23.2674	1.45138	0.725689	−	0.688023i	$-0.241521\pi$
$257$	23.2674	1.45138	0.725689	+	0.688023i	$0.241521\pi$
$258$	−81.1694	−5.05339
$259$	−0.206851	−0.0128531
$260$	−72.7569	−4.51219
$261$	18.0637	1.11811
$262$	−41.9020	−2.58871
$263$	27.7261	1.70967	0.854834	−	0.518902i	$-0.173659\pi$
$263$	27.7261	1.70967	0.854834	+	0.518902i	$0.173659\pi$
$264$	−105.636	−6.50147
$265$	14.8278	0.910863
$266$	−1.63099	−0.100003
$267$	7.74675	0.474094
$268$	−83.8938	−5.12463
$269$	24.1395	1.47181	0.735906	−	0.677084i	$-0.236756\pi$
$269$	24.1395	1.47181	0.735906	+	0.677084i	$0.236756\pi$
$270$	−53.3263	−3.24533
$271$	27.5409	1.67299	0.836495	−	0.547974i	$-0.184601\pi$
$271$	27.5409	1.67299	0.836495	+	0.547974i	$0.184601\pi$
$272$	−110.316	−6.68886
$273$	6.81217	0.412291
$274$	26.5862	1.60613
$275$	−7.82080	−0.471612
$276$	51.4415	3.09641
$277$	−3.17348	−0.190676	−0.0953379	−	0.995445i	$-0.530393\pi$
$277$	−3.17348	−0.190676	−0.0953379	+	0.995445i	$0.530393\pi$
$278$	12.3938	0.743329
$279$	16.0973	0.963718
$280$	−14.5129	−0.867313
$281$	11.0265	0.657787	0.328893	−	0.944367i	$-0.393324\pi$
$281$	11.0265	0.657787	0.328893	+	0.944367i	$0.393324\pi$
$282$	52.7646	3.14209
$283$	0.275658	0.0163862	0.00819310	−	0.999966i	$-0.497392\pi$
$283$	0.275658	0.0163862	0.00819310	+	0.999966i	$0.497392\pi$
$284$	−86.0721	−5.10744
$285$	−9.05494	−0.536368
$286$	44.3423	2.62202
$287$	−2.92253	−0.172511
$288$	−159.349	−9.38975
$289$	20.1111	1.18300
$290$	25.0717	1.47226
$291$	40.3402	2.36478
$292$	91.0068	5.32577
$293$	16.9806	0.992015	0.496008	−	0.868318i	$-0.334799\pi$
$293$	16.9806	0.992015	0.496008	+	0.868318i	$0.334799\pi$
$294$	−54.7302	−3.19193
$295$	−8.18028	−0.476274
$296$	−4.35386	−0.253063
$297$	24.1744	1.40274
$298$	−34.0170	−1.97055
$299$	−14.1565	−0.818690
$300$	−38.5743	−2.22709
$301$	5.05532	0.291384
$302$	7.07378	0.407050
$303$	2.34403	0.134661
$304$	−20.9152	−1.19957
$305$	−18.9358	−1.08426
$306$	92.5012	5.28794
$307$	12.4772	0.712113	0.356057	−	0.934464i	$-0.384121\pi$
$307$	12.4772	0.712113	0.356057	+	0.934464i	$0.384121\pi$
$308$	10.0354	0.571818
$309$	9.54205	0.542828
$310$	22.3424	1.26896
$311$	19.6139	1.11220	0.556102	−	0.831114i	$-0.312296\pi$
$311$	19.6139	1.11220	0.556102	+	0.831114i	$0.312296\pi$
$312$	143.384	8.11755
$313$	−30.8933	−1.74619	−0.873096	−	0.487548i	$-0.837891\pi$
$313$	−30.8933	−1.74619	−0.873096	+	0.487548i	$0.837891\pi$
$314$	13.3129	0.751288
$315$	7.41412	0.417738
$316$	−4.84363	−0.272476
$317$	−2.14508	−0.120480	−0.0602399	−	0.998184i	$-0.519187\pi$
$317$	−2.14508	−0.120480	−0.0602399	+	0.998184i	$0.519187\pi$
$318$	−44.5725	−2.49950
$319$	−11.3658	−0.636360
$320$	−123.403	−6.89843
$321$	−7.14627	−0.398866
$322$	−4.30724	−0.240033
$323$	7.03606	0.391497
$324$	24.5602	1.36446
$325$	10.6155	0.588841
$326$	−5.63892	−0.312311
$327$	3.71482	0.205430
$328$	−61.5142	−3.39655
$329$	−3.28624	−0.181176
$330$	74.9024	4.12324
$331$	35.6911	1.96176	0.980880	−	0.194614i	$-0.0623455\pi$
$331$	35.6911	1.96176	0.980880	+	0.194614i	$0.0623455\pi$
$332$	31.5709	1.73268
$333$	2.22423	0.121887
$334$	48.3068	2.64323
$335$	38.9985	2.13072
$336$	26.5791	1.45001
$337$	−0.438029	−0.0238609	−0.0119305	−	0.999929i	$-0.503798\pi$
$337$	−0.438029	−0.0238609	−0.0119305	+	0.999929i	$0.503798\pi$
$338$	−23.8640	−1.29803
$339$	−52.7006	−2.86230
$340$	95.4982	5.17912
$341$	−10.1285	−0.548488
$342$	17.5377	0.948332
$343$	6.94640	0.375071
$344$	106.406	5.73701
$345$	−23.9129	−1.28743
$346$	53.2752	2.86409
$347$	16.8836	0.906359	0.453180	−	0.891419i	$-0.350290\pi$
$347$	16.8836	0.906359	0.453180	+	0.891419i	$0.350290\pi$
$348$	−56.0590	−3.00508
$349$	29.7423	1.59207	0.796034	−	0.605252i	$-0.206928\pi$
$349$	29.7423	1.59207	0.796034	+	0.605252i	$0.206928\pi$
$350$	3.22986	0.172643
$351$	−32.8129	−1.75142
$352$	100.263	5.34406
$353$	28.5084	1.51735	0.758675	−	0.651470i	$-0.225847\pi$
$353$	28.5084	1.51735	0.758675	+	0.651470i	$0.225847\pi$
$354$	24.5900	1.30695
$355$	40.0112	2.12357
$356$	−15.4902	−0.820977
$357$	−8.94142	−0.473230
$358$	−37.6754	−1.99121
$359$	−15.5553	−0.820975	−0.410487	−	0.911866i	$-0.634641\pi$
$359$	−15.5553	−0.820975	−0.410487	+	0.911866i	$0.634641\pi$
$360$	156.054	8.22479
$361$	−17.6660	−0.929790
$362$	28.7740	1.51233
$363$	−2.00934	−0.105463
$364$	−13.6214	−0.713955
$365$	−42.3051	−2.21435
$366$	56.9213	2.97532
$367$	8.58615	0.448194	0.224097	−	0.974567i	$-0.428057\pi$
$367$	8.58615	0.448194	0.224097	+	0.974567i	$0.428057\pi$
$368$	−55.2344	−2.87929
$369$	31.4253	1.63594
$370$	3.08714	0.160493
$371$	2.77602	0.144124
$372$	−49.9564	−2.59012
$373$	30.5438	1.58150	0.790749	−	0.612140i	$-0.209691\pi$
$373$	30.5438	1.58150	0.790749	+	0.612140i	$0.209691\pi$
$374$	−58.2022	−3.00957
$375$	−21.2677	−1.09826
$376$	−69.1696	−3.56715
$377$	15.4272	0.794541
$378$	−9.98363	−0.513503
$379$	−9.20847	−0.473007	−0.236504	−	0.971631i	$-0.576002\pi$
$379$	−9.20847	−0.473007	−0.236504	+	0.971631i	$0.576002\pi$
$380$	18.1060	0.928816
$381$	−16.4447	−0.842489
$382$	29.9129	1.53048
$383$	24.4026	1.24692	0.623458	−	0.781857i	$-0.285727\pi$
$383$	24.4026	1.24692	0.623458	+	0.781857i	$0.285727\pi$
$384$	200.634	10.2386
$385$	−4.66500	−0.237750
$386$	−14.3363	−0.729696
$387$	−54.3587	−2.76321
$388$	−80.6628	−4.09504
$389$	−27.9058	−1.41488	−0.707439	−	0.706774i	$-0.750150\pi$
$389$	−27.9058	−1.41488	−0.707439	+	0.706774i	$0.750150\pi$
$390$	−101.668	−5.14816
$391$	18.5813	0.939697
$392$	71.7464	3.62374
$393$	−43.5527	−2.19694
$394$	−60.3291	−3.03934
$395$	2.25159	0.113290
$396$	−107.908	−5.42259
$397$	0.657070	0.0329774	0.0164887	−	0.999864i	$-0.494751\pi$
$397$	0.657070	0.0329774	0.0164887	+	0.999864i	$0.494751\pi$
$398$	43.6657	2.18876
$399$	−1.69525	−0.0848685
$400$	41.4185	2.07092
$401$	−2.24586	−0.112153	−0.0560765	−	0.998426i	$-0.517859\pi$
$401$	−2.24586	−0.112153	−0.0560765	+	0.998426i	$0.517859\pi$
$402$	−117.230	−5.84691
$403$	13.7478	0.684827
$404$	−4.68705	−0.233190
$405$	−11.4170	−0.567314
$406$	4.69387	0.232953
$407$	−1.39950	−0.0693705
$408$	−188.202	−9.31736
$409$	−7.26840	−0.359399	−0.179700	−	0.983722i	$-0.557513\pi$
$409$	−7.26840	−0.359399	−0.179700	+	0.983722i	$0.557513\pi$
$410$	43.6172	2.15410
$411$	27.6336	1.36306
$412$	−19.0800	−0.940002
$413$	−1.53149	−0.0753599
$414$	46.3149	2.27625
$415$	−14.6759	−0.720413
$416$	−136.092	−6.67244
$417$	12.8820	0.630835
$418$	−11.0348	−0.539732
$419$	−20.7909	−1.01570	−0.507852	−	0.861444i	$-0.669560\pi$
$419$	−20.7909	−1.01570	−0.507852	+	0.861444i	$0.669560\pi$
$420$	−23.0090	−1.12273
$421$	17.2395	0.840202	0.420101	−	0.907477i	$-0.361995\pi$
$421$	17.2395	0.840202	0.420101	+	0.907477i	$0.361995\pi$
$422$	−59.8153	−2.91176
$423$	35.3362	1.71811
$424$	58.4305	2.83764
$425$	−13.9335	−0.675875
$426$	−120.274	−5.82731
$427$	−3.54512	−0.171560
$428$	14.2895	0.690707
$429$	46.0892	2.22521
$430$	−75.4479	−3.63842
$431$	18.3814	0.885400	0.442700	−	0.896670i	$-0.354021\pi$
$431$	18.3814	0.885400	0.442700	+	0.896670i	$0.354021\pi$
$432$	−128.026	−6.15967
$433$	10.2536	0.492757	0.246379	−	0.969174i	$-0.420759\pi$
$433$	10.2536	0.492757	0.246379	+	0.969174i	$0.420759\pi$
$434$	4.18290	0.200785
$435$	26.0594	1.24945
$436$	−7.42803	−0.355738
$437$	3.52292	0.168524
$438$	127.170	6.07641
$439$	−14.6253	−0.698030	−0.349015	−	0.937117i	$-0.613484\pi$
$439$	−14.6253	−0.698030	−0.349015	+	0.937117i	$0.613484\pi$
$440$	−98.1902	−4.68104
$441$	−36.6526	−1.74536
$442$	79.0002	3.75766
$443$	−38.1025	−1.81030	−0.905151	−	0.425090i	$-0.860243\pi$
$443$	−38.1025	−1.81030	−0.905151	+	0.425090i	$0.860243\pi$
$444$	−6.90269	−0.327587
$445$	7.20070	0.341346
$446$	49.4278	2.34047
$447$	−35.3570	−1.67233
$448$	−23.1032	−1.09153
$449$	16.8144	0.793520	0.396760	−	0.917922i	$-0.370135\pi$
$449$	16.8144	0.793520	0.396760	+	0.917922i	$0.370135\pi$
$450$	−34.7300	−1.63719
$451$	−19.7730	−0.931073
$452$	105.378	4.95658
$453$	7.35244	0.345448
$454$	48.8333	2.29186
$455$	6.33199	0.296848
$456$	−35.6820	−1.67096
$457$	10.6024	0.495960	0.247980	−	0.968765i	$-0.420233\pi$
$457$	10.6024	0.495960	0.247980	+	0.968765i	$0.420233\pi$
$458$	−36.9631	−1.72717
$459$	43.0691	2.01029
$460$	47.8154	2.22941
$461$	20.6256	0.960629	0.480315	−	0.877096i	$-0.340522\pi$
$461$	20.6256	0.960629	0.480315	+	0.877096i	$0.340522\pi$
$462$	14.0231	0.652412
$463$	4.36696	0.202950	0.101475	−	0.994838i	$-0.467644\pi$
$463$	4.36696	0.202950	0.101475	+	0.994838i	$0.467644\pi$
$464$	60.1923	2.79436
$465$	23.2226	1.07692
$466$	−55.0225	−2.54887
$467$	−39.0813	−1.80847	−0.904233	−	0.427039i	$-0.859557\pi$
$467$	−39.0813	−1.80847	−0.904233	+	0.427039i	$0.859557\pi$
$468$	146.468	6.77048
$469$	7.30123	0.337139
$470$	49.0453	2.26229
$471$	13.8373	0.637590
$472$	−32.2353	−1.48375
$473$	34.2028	1.57265
$474$	−6.76833	−0.310880
$475$	−2.64172	−0.121211
$476$	17.8790	0.819481
$477$	−29.8500	−1.36674
$478$	−23.1758	−1.06004
$479$	−17.4729	−0.798357	−0.399179	−	0.916873i	$-0.630705\pi$
$479$	−17.4729	−0.798357	−0.399179	+	0.916873i	$0.630705\pi$
$480$	−229.884	−10.4927
$481$	1.89959	0.0866139
$482$	51.5601	2.34850
$483$	−4.47692	−0.203707
$484$	4.01781	0.182628
$485$	37.4966	1.70263
$486$	−24.9431	−1.13144
$487$	25.4863	1.15489	0.577447	−	0.816428i	$-0.304049\pi$
$487$	25.4863	1.15489	0.577447	+	0.816428i	$0.304049\pi$
$488$	−74.6187	−3.37783
$489$	−5.86106	−0.265046
$490$	−50.8724	−2.29818
$491$	9.83848	0.444004	0.222002	−	0.975046i	$-0.428741\pi$
$491$	9.83848	0.444004	0.222002	+	0.975046i	$0.428741\pi$
$492$	−97.5257	−4.39680
$493$	−20.2492	−0.911978
$494$	14.9780	0.673893
$495$	50.1618	2.25460
$496$	53.6399	2.40850
$497$	7.49081	0.336009
$498$	44.1161	1.97689
$499$	12.7416	0.570390	0.285195	−	0.958469i	$-0.407942\pi$
$499$	12.7416	0.570390	0.285195	+	0.958469i	$0.407942\pi$
$500$	42.5262	1.90183
$501$	50.2099	2.24321
$502$	0.270270	0.0120627
$503$	22.0398	0.982706	0.491353	−	0.870961i	$-0.336503\pi$
$503$	22.0398	0.982706	0.491353	+	0.870961i	$0.336503\pi$
$504$	29.2162	1.30139
$505$	2.17881	0.0969556
$506$	−29.1416	−1.29550
$507$	−24.8041	−1.10159
$508$	32.8823	1.45892
$509$	23.1511	1.02615	0.513077	−	0.858343i	$-0.328506\pi$
$509$	23.1511	1.02615	0.513077	+	0.858343i	$0.328506\pi$
$510$	133.446	5.90908
$511$	−7.92027	−0.350372
$512$	−145.724	−6.44014
$513$	8.16567	0.360523
$514$	−65.0119	−2.86755
$515$	8.86944	0.390834
$516$	168.697	7.42649
$517$	−22.2337	−0.977839
$518$	0.577969	0.0253945
$519$	55.3740	2.43065
$520$	133.277	5.84460
$521$	17.5317	0.768079	0.384040	−	0.923317i	$-0.374533\pi$
$521$	17.5317	0.768079	0.384040	+	0.923317i	$0.374533\pi$
$522$	−50.4722	−2.20911
$523$	33.8689	1.48098	0.740492	−	0.672065i	$-0.234592\pi$
$523$	33.8689	1.48098	0.740492	+	0.672065i	$0.234592\pi$
$524$	87.0865	3.80439
$525$	3.35710	0.146516
$526$	−77.4704	−3.37787
$527$	−18.0449	−0.786048
$528$	179.826	7.82594
$529$	−13.6964	−0.595497
$530$	−41.4307	−1.79963
$531$	16.4678	0.714643
$532$	3.38976	0.146965
$533$	26.8387	1.16251
$534$	−21.6454	−0.936689
$535$	−6.64254	−0.287182
$536$	153.678	6.63789
$537$	−39.1596	−1.68986
$538$	−67.4489	−2.90793
$539$	23.0620	0.993351
$540$	110.830	4.76937
$541$	−1.32513	−0.0569717	−0.0284859	−	0.999594i	$-0.509069\pi$
$541$	−1.32513	−0.0569717	−0.0284859	+	0.999594i	$0.509069\pi$
$542$	−76.9527	−3.30540
$543$	29.9076	1.28346
$544$	178.629	7.65866
$545$	3.45296	0.147909
$546$	−19.0341	−0.814583
$547$	−21.2058	−0.906693	−0.453347	−	0.891334i	$-0.649770\pi$
$547$	−21.2058	−0.906693	−0.453347	+	0.891334i	$0.649770\pi$
$548$	−55.2552	−2.36038
$549$	38.1199	1.62692
$550$	21.8523	0.931786
$551$	−3.83914	−0.163553
$552$	−94.2315	−4.01076
$553$	0.421539	0.0179256
$554$	8.86710	0.376727
$555$	3.20876	0.136204
$556$	−25.7585	−1.09240
$557$	19.9214	0.844095	0.422047	−	0.906574i	$-0.361312\pi$
$557$	19.9214	0.844095	0.422047	+	0.906574i	$0.361312\pi$
$558$	−44.9778	−1.90406
$559$	−46.4248	−1.96356
$560$	24.7056	1.04400
$561$	−60.4951	−2.55410
$562$	−30.8095	−1.29962
$563$	0.796044	0.0335493	0.0167746	−	0.999859i	$-0.494660\pi$
$563$	0.796044	0.0335493	0.0167746	+	0.999859i	$0.494660\pi$
$564$	−109.663	−4.61764
$565$	−48.9858	−2.06085
$566$	−0.770224	−0.0323749
$567$	−2.13746	−0.0897649
$568$	157.669	6.61563
$569$	6.49046	0.272094	0.136047	−	0.990702i	$-0.456560\pi$
$569$	6.49046	0.272094	0.136047	+	0.990702i	$0.456560\pi$
$570$	25.3006	1.05973
$571$	18.9486	0.792975	0.396488	−	0.918040i	$-0.370229\pi$
$571$	18.9486	0.792975	0.396488	+	0.918040i	$0.370229\pi$
$572$	−92.1584	−3.85334
$573$	31.0913	1.29886
$574$	8.16591	0.340839
$575$	−6.97644	−0.290938
$576$	248.424	10.3510
$577$	11.8834	0.494712	0.247356	−	0.968925i	$-0.420438\pi$
$577$	11.8834	0.494712	0.247356	+	0.968925i	$0.420438\pi$
$578$	−56.1928	−2.33731
$579$	−14.9010	−0.619266
$580$	−52.1074	−2.16364
$581$	−2.74760	−0.113989
$582$	−112.715	−4.67221
$583$	18.7818	0.777862
$584$	−166.708	−6.89843
$585$	−68.0866	−2.81503
$586$	−47.4458	−1.95997
$587$	2.11458	0.0872782	0.0436391	−	0.999047i	$-0.486105\pi$
$587$	2.11458	0.0872782	0.0436391	+	0.999047i	$0.486105\pi$
$588$	113.748	4.69089
$589$	−3.42122	−0.140969
$590$	22.8567	0.940997
$591$	−62.7057	−2.57937
$592$	7.41165	0.304617
$593$	−48.4818	−1.99091	−0.995454	−	0.0952447i	$-0.969637\pi$
$593$	−48.4818	−1.99091	−0.995454	+	0.0952447i	$0.969637\pi$
$594$	−67.5464	−2.77146
$595$	−8.31115	−0.340724
$596$	70.6988	2.89593
$597$	45.3859	1.85752
$598$	39.5550	1.61752
$599$	12.8096	0.523388	0.261694	−	0.965151i	$-0.415719\pi$
$599$	12.8096	0.523388	0.261694	+	0.965151i	$0.415719\pi$
$600$	70.6612	2.88473
$601$	−11.2659	−0.459544	−0.229772	−	0.973244i	$-0.573798\pi$
$601$	−11.2659	−0.459544	−0.229772	+	0.973244i	$0.573798\pi$
$602$	−14.1252	−0.575700
$603$	−78.5085	−3.19711
$604$	−14.7017	−0.598204
$605$	−1.86771	−0.0759330
$606$	−6.54953	−0.266056
$607$	−39.9623	−1.62202	−0.811009	−	0.585034i	$-0.801081\pi$
$607$	−39.9623	−1.62202	−0.811009	+	0.585034i	$0.801081\pi$
$608$	33.8671	1.37349
$609$	4.87878	0.197698
$610$	52.9090	2.14222
$611$	30.1787	1.22090
$612$	−192.249	−7.77120
$613$	−42.3893	−1.71209	−0.856044	−	0.516903i	$-0.827085\pi$
$613$	−42.3893	−1.71209	−0.856044	+	0.516903i	$0.827085\pi$
$614$	−34.8629	−1.40695
$615$	45.3354	1.82810
$616$	−18.3830	−0.740671
$617$	0.262837	0.0105814	0.00529070	−	0.999986i	$-0.498316\pi$
$617$	0.262837	0.0105814	0.00529070	+	0.999986i	$0.498316\pi$
$618$	−26.6617	−1.07249
$619$	−15.5339	−0.624362	−0.312181	−	0.950023i	$-0.601060\pi$
$619$	−15.5339	−0.624362	−0.312181	+	0.950023i	$0.601060\pi$
$620$	−46.4351	−1.86488
$621$	21.5645	0.865352
$622$	−54.8038	−2.19743
$623$	1.34810	0.0540105
$624$	−244.086	−9.77124
$625$	−31.2047	−1.24819
$626$	86.3198	3.45003
$627$	−11.4695	−0.458050
$628$	−27.6686	−1.10410
$629$	−2.49334	−0.0994160
$630$	−20.7160	−0.825344
$631$	1.24595	0.0496003	0.0248002	−	0.999692i	$-0.492105\pi$
$631$	1.24595	0.0496003	0.0248002	+	0.999692i	$0.492105\pi$
$632$	8.87266	0.352935
$633$	−62.1717	−2.47110
$634$	5.99363	0.238038
$635$	−15.2856	−0.606589
$636$	92.6368	3.67329
$637$	−31.3030	−1.24027
$638$	31.7574	1.25729
$639$	−80.5471	−3.18639
$640$	186.492	7.37174
$641$	−30.8768	−1.21956	−0.609780	−	0.792571i	$-0.708742\pi$
$641$	−30.8768	−1.21956	−0.609780	+	0.792571i	$0.708742\pi$
$642$	19.9676	0.788058
$643$	35.0840	1.38358	0.691789	−	0.722100i	$-0.256823\pi$
$643$	35.0840	1.38358	0.691789	+	0.722100i	$0.256823\pi$
$644$	8.95191	0.352755
$645$	−78.4201	−3.08779
$646$	−19.6596	−0.773498
$647$	−32.6891	−1.28514	−0.642571	−	0.766226i	$-0.722132\pi$
$647$	−32.6891	−1.28514	−0.642571	+	0.766226i	$0.722132\pi$
$648$	−44.9899	−1.76737
$649$	−10.3617	−0.406730
$650$	−29.6610	−1.16340
$651$	4.34768	0.170399
$652$	11.7196	0.458974
$653$	3.76716	0.147420	0.0737101	−	0.997280i	$-0.476516\pi$
$653$	3.76716	0.147420	0.0737101	+	0.997280i	$0.476516\pi$
$654$	−10.3797	−0.405877
$655$	−40.4827	−1.58179
$656$	104.717	4.08849
$657$	85.1650	3.32260
$658$	9.18217	0.357958
$659$	−10.0738	−0.392418	−0.196209	−	0.980562i	$-0.562863\pi$
$659$	−10.0738	−0.392418	−0.196209	+	0.980562i	$0.562863\pi$
$660$	−155.673	−6.05955
$661$	18.4796	0.718772	0.359386	−	0.933189i	$-0.382986\pi$
$661$	18.4796	0.718772	0.359386	+	0.933189i	$0.382986\pi$
$662$	−99.7254	−3.87594
$663$	82.1124	3.18898
$664$	−57.8321	−2.24432
$665$	−1.57575	−0.0611050
$666$	−6.21478	−0.240818
$667$	−10.1387	−0.392571
$668$	−100.398	−3.88452
$669$	51.3750	1.98627
$670$	−108.967	−4.20976
$671$	−23.9853	−0.925941
$672$	−43.0383	−1.66024
$673$	−15.4179	−0.594315	−0.297158	−	0.954828i	$-0.596039\pi$
$673$	−15.4179	−0.594315	−0.297158	+	0.954828i	$0.596039\pi$
$674$	1.22391	0.0471431
$675$	−16.1705	−0.622403
$676$	49.5974	1.90759
$677$	24.1910	0.929737	0.464868	−	0.885380i	$-0.346102\pi$
$677$	24.1910	0.929737	0.464868	+	0.885380i	$0.346102\pi$
$678$	147.252	5.65519
$679$	7.02004	0.269404
$680$	−174.935	−6.70847
$681$	50.7571	1.94501
$682$	28.3003	1.08367
$683$	−40.9909	−1.56847	−0.784236	−	0.620463i	$-0.786945\pi$
$683$	−40.9909	−1.56847	−0.784236	+	0.620463i	$0.786945\pi$
$684$	−36.4494	−1.39368
$685$	25.6857	0.981401
$686$	−19.4091	−0.741044
$687$	−38.4192	−1.46578
$688$	−181.136	−6.90575
$689$	−25.4932	−0.971215
$690$	66.8157	2.54363
$691$	−35.4279	−1.34774	−0.673871	−	0.738849i	$-0.735370\pi$
$691$	−35.4279	−1.34774	−0.673871	+	0.738849i	$0.735370\pi$
$692$	−110.724	−4.20909
$693$	9.39118	0.356742
$694$	−47.1749	−1.79074
$695$	11.9740	0.454199
$696$	102.690	3.89245
$697$	−35.2275	−1.33434
$698$	−83.1037	−3.14552
$699$	−57.1901	−2.16313
$700$	−6.71275	−0.253718
$701$	22.1772	0.837622	0.418811	−	0.908073i	$-0.362447\pi$
$701$	22.1772	0.837622	0.418811	+	0.908073i	$0.362447\pi$
$702$	91.6834	3.46037
$703$	−0.472724	−0.0178291
$704$	−156.310	−5.89115
$705$	50.9775	1.91992
$706$	−79.6561	−2.99790
$707$	0.407911	0.0153411
$708$	−51.1065	−1.92070
$709$	24.4806	0.919388	0.459694	−	0.888077i	$-0.347959\pi$
$709$	24.4806	0.919388	0.459694	+	0.888077i	$0.347959\pi$
$710$	−111.796	−4.19564
$711$	−4.53272	−0.169990
$712$	28.3752	1.06340
$713$	−9.03498	−0.338363
$714$	24.9835	0.934983
$715$	42.8404	1.60214
$716$	78.3022	2.92629
$717$	−24.0888	−0.899613
$718$	43.4633	1.62204
$719$	−30.0502	−1.12068	−0.560341	−	0.828262i	$-0.689330\pi$
$719$	−30.0502	−1.12068	−0.560341	+	0.828262i	$0.689330\pi$
$720$	−265.654	−9.90033
$721$	1.66052	0.0618409
$722$	49.3610	1.83703
$723$	53.5913	1.99308
$724$	−59.8022	−2.22253
$725$	7.60266	0.282356
$726$	5.61435	0.208368
$727$	10.5787	0.392342	0.196171	−	0.980570i	$-0.437149\pi$
$727$	10.5787	0.392342	0.196171	+	0.980570i	$0.437149\pi$
$728$	24.9519	0.924780
$729$	−38.6137	−1.43014
$730$	118.206	4.37499
$731$	60.9356	2.25379
$732$	−118.302	−4.37256
$733$	49.6908	1.83537	0.917686	−	0.397306i	$-0.130055\pi$
$733$	49.6908	1.83537	0.917686	+	0.397306i	$0.130055\pi$
$734$	−23.9908	−0.885517
$735$	−52.8765	−1.95038
$736$	89.4386	3.29675
$737$	49.3980	1.81960
$738$	−87.8063	−3.23220
$739$	−19.2308	−0.707418	−0.353709	−	0.935356i	$-0.615080\pi$
$739$	−19.2308	−0.707418	−0.353709	+	0.935356i	$0.615080\pi$
$740$	−6.41613	−0.235862
$741$	15.5681	0.571907
$742$	−7.75656	−0.284752
$743$	−33.6281	−1.23370	−0.616849	−	0.787082i	$-0.711591\pi$
$743$	−33.6281	−1.23370	−0.616849	+	0.787082i	$0.711591\pi$
$744$	91.5112	3.35496
$745$	−32.8648	−1.20407
$746$	−85.3433	−3.12464
$747$	29.5443	1.08097
$748$	120.964	4.42288
$749$	−1.24360	−0.0454403
$750$	59.4247	2.16988
$751$	10.0994	0.368532	0.184266	−	0.982876i	$-0.441009\pi$
$751$	10.0994	0.368532	0.184266	+	0.982876i	$0.441009\pi$
$752$	117.749	4.29385
$753$	0.280917	0.0102372
$754$	−43.1055	−1.56981
$755$	6.83418	0.248721
$756$	20.7494	0.754647
$757$	−13.7078	−0.498217	−0.249109	−	0.968476i	$-0.580138\pi$
$757$	−13.7078	−0.498217	−0.249109	+	0.968476i	$0.580138\pi$
$758$	25.7296	0.934542
$759$	−30.2896	−1.09944
$760$	−33.1668	−1.20309
$761$	−14.5756	−0.528363	−0.264182	−	0.964473i	$-0.585102\pi$
$761$	−14.5756	−0.528363	−0.264182	+	0.964473i	$0.585102\pi$
$762$	45.9486	1.66454
$763$	0.646457	0.0234033
$764$	−62.1691	−2.24920
$765$	89.3681	3.23111
$766$	−68.1840	−2.46359
$767$	14.0643	0.507832
$768$	−295.076	−10.6476
$769$	−12.5261	−0.451704	−0.225852	−	0.974162i	$-0.572517\pi$
$769$	−12.5261	−0.451704	−0.225852	+	0.974162i	$0.572517\pi$
$770$	13.0346	0.469734
$771$	−67.5731	−2.43358
$772$	29.7956	1.07237
$773$	−5.71809	−0.205666	−0.102833	−	0.994699i	$-0.532791\pi$
$773$	−5.71809	−0.205666	−0.102833	+	0.994699i	$0.532791\pi$
$774$	151.885	5.45940
$775$	6.77504	0.243367
$776$	147.760	5.30427
$777$	0.600738	0.0215513
$778$	77.9722	2.79544
$779$	−6.67895	−0.239298
$780$	211.301	7.56577
$781$	50.6807	1.81350
$782$	−51.9185	−1.85660
$783$	−23.5001	−0.839826
$784$	−122.135	−4.36196
$785$	12.8619	0.459063
$786$	121.692	4.34060
$787$	16.6144	0.592240	0.296120	−	0.955151i	$-0.404307\pi$
$787$	16.6144	0.592240	0.296120	+	0.955151i	$0.404307\pi$
$788$	125.384	4.46663
$789$	−80.5223	−2.86667
$790$	−6.29124	−0.223832
$791$	−9.17102	−0.326084
$792$	197.668	7.02383
$793$	32.5561	1.15610
$794$	−1.83594	−0.0651550
$795$	−43.0628	−1.52728
$796$	−90.7520	−3.21662
$797$	−30.8315	−1.09211	−0.546054	−	0.837750i	$-0.683871\pi$
$797$	−30.8315	−1.09211	−0.546054	+	0.837750i	$0.683871\pi$
$798$	4.73673	0.167679
$799$	−39.6116	−1.40136
$800$	−67.0671	−2.37118
$801$	−14.4958	−0.512185
$802$	6.27522	0.221586
$803$	−53.5863	−1.89102
$804$	243.644	8.59267
$805$	−4.16135	−0.146668
$806$	−38.4131	−1.35304
$807$	−70.1060	−2.46785
$808$	8.58583	0.302049
$809$	6.79300	0.238829	0.119415	−	0.992844i	$-0.461898\pi$
$809$	6.79300	0.238829	0.119415	+	0.992844i	$0.461898\pi$
$810$	31.9004	1.12087
$811$	−46.5319	−1.63396	−0.816979	−	0.576668i	$-0.804353\pi$
$811$	−46.5319	−1.63396	−0.816979	+	0.576668i	$0.804353\pi$
$812$	−9.75545	−0.342349
$813$	−79.9843	−2.80517
$814$	3.91037	0.137058
$815$	−5.44792	−0.190832
$816$	320.378	11.2155
$817$	11.5531	0.404191
$818$	20.3088	0.710081
$819$	−12.7470	−0.445417
$820$	−90.6512	−3.16568
$821$	30.6335	1.06912	0.534559	−	0.845131i	$-0.320478\pi$
$821$	30.6335	1.06912	0.534559	+	0.845131i	$0.320478\pi$
$822$	−77.2117	−2.69307
$823$	10.7595	0.375052	0.187526	−	0.982260i	$-0.439953\pi$
$823$	10.7595	0.375052	0.187526	+	0.982260i	$0.439953\pi$
$824$	34.9510	1.21758
$825$	22.7132	0.790771
$826$	4.27919	0.148892
$827$	−49.6296	−1.72579	−0.862895	−	0.505383i	$-0.831351\pi$
$827$	−49.6296	−1.72579	−0.862895	+	0.505383i	$0.831351\pi$
$828$	−96.2580	−3.34520
$829$	7.89761	0.274295	0.137148	−	0.990551i	$-0.456207\pi$
$829$	7.89761	0.274295	0.137148	+	0.990551i	$0.456207\pi$
$830$	41.0064	1.42335
$831$	9.21642	0.319714
$832$	212.166	7.35552
$833$	41.0872	1.42359
$834$	−35.9940	−1.24637
$835$	46.6706	1.61510
$836$	22.9341	0.793194
$837$	−20.9419	−0.723859
$838$	58.0925	2.00677
$839$	43.2821	1.49426	0.747132	−	0.664676i	$-0.231430\pi$
$839$	43.2821	1.49426	0.747132	+	0.664676i	$0.231430\pi$
$840$	42.1484	1.45426
$841$	−17.9513	−0.619009
$842$	−48.1694	−1.66003
$843$	−32.0232	−1.10294
$844$	124.316	4.27915
$845$	−23.0557	−0.793140
$846$	−98.7339	−3.39454
$847$	−0.349668	−0.0120147
$848$	−99.4672	−3.41572
$849$	−0.800567	−0.0274754
$850$	38.9320	1.33536
$851$	−1.24840	−0.0427947
$852$	249.971	8.56385
$853$	−45.0737	−1.54329	−0.771647	−	0.636052i	$-0.780567\pi$
$853$	−45.0737	−1.54329	−0.771647	+	0.636052i	$0.780567\pi$
$854$	9.90551	0.338960
$855$	16.9437	0.579463
$856$	−26.1757	−0.894667
$857$	−26.5520	−0.906999	−0.453499	−	0.891257i	$-0.649825\pi$
$857$	−26.5520	−0.906999	−0.453499	+	0.891257i	$0.649825\pi$
$858$	−128.779	−4.39644
$859$	−35.8962	−1.22476	−0.612381	−	0.790563i	$-0.709788\pi$
$859$	−35.8962	−1.22476	−0.612381	+	0.790563i	$0.709788\pi$
$860$	156.806	5.34705
$861$	8.48760	0.289257
$862$	−51.3599	−1.74932
$863$	−7.77308	−0.264599	−0.132299	−	0.991210i	$-0.542236\pi$
$863$	−7.77308	−0.264599	−0.132299	+	0.991210i	$0.542236\pi$
$864$	207.307	7.05274
$865$	51.4707	1.75006
$866$	−28.6499	−0.973563
$867$	−58.4065	−1.98359
$868$	−8.69348	−0.295076
$869$	2.85201	0.0967478
$870$	−72.8131	−2.46860
$871$	−67.0498	−2.27190
$872$	13.6068	0.460784
$873$	−75.4850	−2.55478
$874$	−9.84348	−0.332961
$875$	−3.70103	−0.125118
$876$	−264.302	−8.92994
$877$	−15.6788	−0.529434	−0.264717	−	0.964326i	$-0.585279\pi$
$877$	−15.6788	−0.529434	−0.264717	+	0.964326i	$0.585279\pi$
$878$	40.8651	1.37913
$879$	−49.3150	−1.66335
$880$	167.151	5.63465
$881$	11.7028	0.394276	0.197138	−	0.980376i	$-0.436835\pi$
$881$	11.7028	0.394276	0.197138	+	0.980376i	$0.436835\pi$
$882$	102.412	3.44839
$883$	−40.9533	−1.37819	−0.689093	−	0.724673i	$-0.741991\pi$
$883$	−40.9533	−1.37819	−0.689093	+	0.724673i	$0.741991\pi$
$884$	−164.189	−5.52228
$885$	23.7572	0.798588
$886$	106.463	3.57670
$887$	−31.9713	−1.07349	−0.536745	−	0.843744i	$-0.680346\pi$
$887$	−31.9713	−1.07349	−0.536745	+	0.843744i	$0.680346\pi$
$888$	12.6445	0.424321
$889$	−2.86173	−0.0959794
$890$	−20.1197	−0.674412
$891$	−14.4614	−0.484477
$892$	−102.728	−3.43958
$893$	−7.51015	−0.251317
$894$	98.7920	3.30410
$895$	−36.3993	−1.21669
$896$	34.9146	1.16642
$897$	41.1132	1.37273
$898$	−46.9815	−1.56779
$899$	9.84598	0.328382
$900$	72.1807	2.40602
$901$	33.4616	1.11477
$902$	55.2482	1.83956
$903$	−14.6816	−0.488575
$904$	−193.034	−6.42022
$905$	27.7994	0.924084
$906$	−20.5437	−0.682517
$907$	44.2080	1.46790	0.733951	−	0.679202i	$-0.237674\pi$
$907$	44.2080	1.46790	0.733951	+	0.679202i	$0.237674\pi$
$908$	−101.492	−3.36813
$909$	−4.38619	−0.145481
$910$	−17.6924	−0.586497
$911$	−27.0535	−0.896323	−0.448162	−	0.893953i	$-0.647921\pi$
$911$	−27.0535	−0.896323	−0.448162	+	0.893953i	$0.647921\pi$
$912$	60.7420	2.01137
$913$	−18.5894	−0.615221
$914$	−29.6245	−0.979891
$915$	54.9933	1.81802
$916$	76.8218	2.53826
$917$	−7.57909	−0.250283
$918$	−120.340	−3.97183
$919$	−25.6230	−0.845226	−0.422613	−	0.906310i	$-0.638887\pi$
$919$	−25.6230	−0.845226	−0.422613	+	0.906310i	$0.638887\pi$
$920$	−87.5892	−2.88773
$921$	−36.2364	−1.19403
$922$	−57.6305	−1.89796
$923$	−68.7909	−2.26428
$924$	−29.1447	−0.958790
$925$	0.936136	0.0307800
$926$	−12.2018	−0.400978
$927$	−17.8552	−0.586442
$928$	−97.4668	−3.19950
$929$	22.3661	0.733809	0.366904	−	0.930259i	$-0.380418\pi$
$929$	22.3661	0.733809	0.366904	+	0.930259i	$0.380418\pi$
$930$	−64.8868	−2.12772
$931$	7.78991	0.255304
$932$	114.355	3.74584
$933$	−56.9628	−1.86488
$934$	109.198	3.57307
$935$	−56.2309	−1.83895
$936$	−268.303	−8.76975
$937$	9.81410	0.320613	0.160306	−	0.987067i	$-0.448752\pi$
$937$	9.81410	0.320613	0.160306	+	0.987067i	$0.448752\pi$
$938$	−20.4005	−0.666101
$939$	89.7203	2.92791
$940$	−101.933	−3.32468
$941$	−23.2652	−0.758425	−0.379213	−	0.925310i	$-0.623805\pi$
$941$	−23.2652	−0.758425	−0.379213	+	0.925310i	$0.623805\pi$
$942$	−38.6632	−1.25972
$943$	−17.6382	−0.574379
$944$	54.8747	1.78602
$945$	−9.64548	−0.313767
$946$	−95.5670	−3.10715
$947$	8.88307	0.288661	0.144331	−	0.989530i	$-0.453897\pi$
$947$	8.88307	0.288661	0.144331	+	0.989530i	$0.453897\pi$
$948$	14.0669	0.456871
$949$	72.7348	2.36107
$950$	7.38130	0.239481
$951$	6.22975	0.202013
$952$	−32.7510	−1.06147
$953$	−13.8788	−0.449580	−0.224790	−	0.974407i	$-0.572170\pi$
$953$	−13.8788	−0.449580	−0.224790	+	0.974407i	$0.572170\pi$
$954$	83.4047	2.70033
$955$	28.8997	0.935172
$956$	48.1672	1.55784
$957$	33.0084	1.06701
$958$	48.8215	1.57735
$959$	4.80883	0.155285
$960$	358.387	11.5669
$961$	−22.2258	−0.716963
$962$	−5.30770	−0.171127
$963$	13.3722	0.430913
$964$	−107.159	−3.45137
$965$	−13.8507	−0.445869
$966$	12.5091	0.402473
$967$	22.5168	0.724093	0.362046	−	0.932160i	$-0.382078\pi$
$967$	22.5168	0.724093	0.362046	+	0.932160i	$0.382078\pi$
$968$	−7.35991	−0.236556
$969$	−20.4341	−0.656439
$970$	−104.770	−3.36397
$971$	−38.0599	−1.22140	−0.610700	−	0.791862i	$-0.709112\pi$
$971$	−38.0599	−1.22140	−0.610700	+	0.791862i	$0.709112\pi$
$972$	51.8402	1.66278
$973$	2.24174	0.0718670
$974$	−71.2120	−2.28178
$975$	−30.8295	−0.987334
$976$	127.024	4.06595
$977$	34.7990	1.11332	0.556659	−	0.830741i	$-0.312083\pi$
$977$	34.7990	1.11332	0.556659	+	0.830741i	$0.312083\pi$
$978$	16.3765	0.523664
$979$	9.12085	0.291504
$980$	105.730	3.37742
$981$	−6.95121	−0.221935
$982$	−27.4900	−0.877240
$983$	50.4900	1.61038	0.805190	−	0.593017i	$-0.202063\pi$
$983$	50.4900	1.61038	0.805190	+	0.593017i	$0.202063\pi$
$984$	178.649	5.69514
$985$	−58.2857	−1.85714
$986$	56.5788	1.80184
$987$	9.54389	0.303785
$988$	−31.1294	−0.990358
$989$	30.5102	0.970166
$990$	−140.158	−4.45452
$991$	23.4255	0.744135	0.372068	−	0.928206i	$-0.378649\pi$
$991$	23.4255	0.744135	0.372068	+	0.928206i	$0.378649\pi$
$992$	−86.8567	−2.75770
$993$	−103.654	−3.28936
$994$	−20.9303	−0.663868
$995$	42.1867	1.33741
$996$	−91.6881	−2.90525
$997$	−16.7534	−0.530586	−0.265293	−	0.964168i	$-0.585469\pi$
$997$	−16.7534	−0.530586	−0.265293	+	0.964168i	$0.585469\pi$
$998$	−35.6015	−1.12695
$999$	−2.89364	−0.0915506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.a.1.2	✓	327

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.a.1.2	✓	327	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79413 q^{2} -2.90420 q^{3} +5.80714 q^{4} -2.69949 q^{5} +8.11470 q^{6} -0.505392 q^{7} -10.6376 q^{8} +5.43438 q^{9} +O(q^{10})\)	\(q-2.79413 q^{2} -2.90420 q^{3} +5.80714 q^{4} -2.69949 q^{5} +8.11470 q^{6} -0.505392 q^{7} -10.6376 q^{8} +5.43438 q^{9} +7.54271 q^{10} -3.41934 q^{11} -16.8651 q^{12} +4.64120 q^{13} +1.41213 q^{14} +7.83985 q^{15} +18.1086 q^{16} -6.09188 q^{17} -15.1843 q^{18} -1.15499 q^{19} -15.6763 q^{20} +1.46776 q^{21} +9.55406 q^{22} -3.05017 q^{23} +30.8938 q^{24} +2.28723 q^{25} -12.9681 q^{26} -7.06991 q^{27} -2.93488 q^{28} +3.32396 q^{29} -21.9055 q^{30} +2.96212 q^{31} -29.3225 q^{32} +9.93044 q^{33} +17.0215 q^{34} +1.36430 q^{35} +31.5582 q^{36} +0.409289 q^{37} +3.22718 q^{38} -13.4790 q^{39} +28.7161 q^{40} +5.78269 q^{41} -4.10111 q^{42} -10.0028 q^{43} -19.8566 q^{44} -14.6700 q^{45} +8.52257 q^{46} +6.50235 q^{47} -52.5910 q^{48} -6.74458 q^{49} -6.39080 q^{50} +17.6920 q^{51} +26.9521 q^{52} -5.49281 q^{53} +19.7542 q^{54} +9.23046 q^{55} +5.37618 q^{56} +3.35432 q^{57} -9.28757 q^{58} +3.03031 q^{59} +45.5271 q^{60} +7.01459 q^{61} -8.27654 q^{62} -2.74649 q^{63} +45.7135 q^{64} -12.5289 q^{65} -27.7469 q^{66} -14.4467 q^{67} -35.3764 q^{68} +8.85831 q^{69} -3.81202 q^{70} -14.8218 q^{71} -57.8089 q^{72} +15.6715 q^{73} -1.14360 q^{74} -6.64256 q^{75} -6.70718 q^{76} +1.72811 q^{77} +37.6620 q^{78} -0.834082 q^{79} -48.8839 q^{80} +4.22931 q^{81} -16.1576 q^{82} +5.43656 q^{83} +8.52349 q^{84} +16.4450 q^{85} +27.9490 q^{86} -9.65345 q^{87} +36.3737 q^{88} -2.66743 q^{89} +40.9899 q^{90} -2.34563 q^{91} -17.7128 q^{92} -8.60259 q^{93} -18.1684 q^{94} +3.11788 q^{95} +85.1583 q^{96} -13.8903 q^{97} +18.8452 q^{98} -18.5820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more