LMFDB - Embedded newform 7935.2.a.bt.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.54434 q^{2} -1.00000 q^{3} +4.47365 q^{4} -1.00000 q^{5} -2.54434 q^{6} -0.866803 q^{7} +6.29379 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.54434 q^{2} -1.00000 q^{3} +4.47365 q^{4} -1.00000 q^{5} -2.54434 q^{6} -0.866803 q^{7} +6.29379 q^{8} +1.00000 q^{9} -2.54434 q^{10} -6.32487 q^{11} -4.47365 q^{12} +5.34349 q^{13} -2.20544 q^{14} +1.00000 q^{15} +7.06623 q^{16} -3.99140 q^{17} +2.54434 q^{18} +3.64235 q^{19} -4.47365 q^{20} +0.866803 q^{21} -16.0926 q^{22} -6.29379 q^{24} +1.00000 q^{25} +13.5956 q^{26} -1.00000 q^{27} -3.87777 q^{28} +2.64583 q^{29} +2.54434 q^{30} -2.74860 q^{31} +5.39127 q^{32} +6.32487 q^{33} -10.1555 q^{34} +0.866803 q^{35} +4.47365 q^{36} +8.21282 q^{37} +9.26736 q^{38} -5.34349 q^{39} -6.29379 q^{40} +9.13059 q^{41} +2.20544 q^{42} +7.13440 q^{43} -28.2953 q^{44} -1.00000 q^{45} +3.77059 q^{47} -7.06623 q^{48} -6.24865 q^{49} +2.54434 q^{50} +3.99140 q^{51} +23.9049 q^{52} +5.07773 q^{53} -2.54434 q^{54} +6.32487 q^{55} -5.45548 q^{56} -3.64235 q^{57} +6.73187 q^{58} +2.78933 q^{59} +4.47365 q^{60} +10.3493 q^{61} -6.99336 q^{62} -0.866803 q^{63} -0.415241 q^{64} -5.34349 q^{65} +16.0926 q^{66} +8.41426 q^{67} -17.8561 q^{68} +2.20544 q^{70} +8.96239 q^{71} +6.29379 q^{72} -12.9611 q^{73} +20.8962 q^{74} -1.00000 q^{75} +16.2946 q^{76} +5.48242 q^{77} -13.5956 q^{78} +3.97067 q^{79} -7.06623 q^{80} +1.00000 q^{81} +23.2313 q^{82} +5.37512 q^{83} +3.87777 q^{84} +3.99140 q^{85} +18.1523 q^{86} -2.64583 q^{87} -39.8074 q^{88} +3.28242 q^{89} -2.54434 q^{90} -4.63175 q^{91} +2.74860 q^{93} +9.59364 q^{94} -3.64235 q^{95} -5.39127 q^{96} -9.99338 q^{97} -15.8987 q^{98} -6.32487 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + q^{2} - 25 q^{3} + 31 q^{4} - 25 q^{5} - q^{6} + 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + q^2 - 25 * q^3 + 31 * q^4 - 25 * q^5 - q^6 + 15 * q^7 + 3 * q^8 + 25 * q^9	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} - 25 q^{5} - q^{6} + 15 q^{7} + 3 q^{8} + 25 q^{9} - q^{10} - 15 q^{11} - 31 q^{12} + 24 q^{13} - 5 q^{14} + 25 q^{15} + 39 q^{16} + 6 q^{17} + q^{18} - 13 q^{19} - 31 q^{20} - 15 q^{21} + 21 q^{22} - 3 q^{24} + 25 q^{25} + 21 q^{26} - 25 q^{27} + 41 q^{28} + q^{29} + q^{30} + 18 q^{31} + 17 q^{32} + 15 q^{33} - 7 q^{34} - 15 q^{35} + 31 q^{36} + 8 q^{37} - 15 q^{38} - 24 q^{39} - 3 q^{40} + 36 q^{41} + 5 q^{42} + 36 q^{43} - 90 q^{44} - 25 q^{45} + 11 q^{47} - 39 q^{48} + 92 q^{49} + q^{50} - 6 q^{51} + 35 q^{52} - 6 q^{53} - q^{54} + 15 q^{55} - 15 q^{56} + 13 q^{57} + 42 q^{58} - 3 q^{59} + 31 q^{60} - 71 q^{61} - 7 q^{62} + 15 q^{63} + 47 q^{64} - 24 q^{65} - 21 q^{66} + 10 q^{67} + 23 q^{68} + 5 q^{70} - 18 q^{71} + 3 q^{72} + 83 q^{73} - 67 q^{74} - 25 q^{75} + 12 q^{76} + 27 q^{77} - 21 q^{78} - 33 q^{79} - 39 q^{80} + 25 q^{81} + 49 q^{82} + 2 q^{83} - 41 q^{84} - 6 q^{85} + 35 q^{86} - q^{87} + 33 q^{88} - 11 q^{89} - q^{90} - 28 q^{91} - 18 q^{93} + 80 q^{94} + 13 q^{95} - 17 q^{96} + 48 q^{97} + 4 q^{98} - 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 - 25 * q^5 - q^6 + 15 * q^7 + 3 * q^8 + 25 * q^9 - q^10 - 15 * q^11 - 31 * q^12 + 24 * q^13 - 5 * q^14 + 25 * q^15 + 39 * q^16 + 6 * q^17 + q^18 - 13 * q^19 - 31 * q^20 - 15 * q^21 + 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 + 41 * q^28 + q^29 + q^30 + 18 * q^31 + 17 * q^32 + 15 * q^33 - 7 * q^34 - 15 * q^35 + 31 * q^36 + 8 * q^37 - 15 * q^38 - 24 * q^39 - 3 * q^40 + 36 * q^41 + 5 * q^42 + 36 * q^43 - 90 * q^44 - 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 - 6 * q^51 + 35 * q^52 - 6 * q^53 - q^54 + 15 * q^55 - 15 * q^56 + 13 * q^57 + 42 * q^58 - 3 * q^59 + 31 * q^60 - 71 * q^61 - 7 * q^62 + 15 * q^63 + 47 * q^64 - 24 * q^65 - 21 * q^66 + 10 * q^67 + 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 - 67 * q^74 - 25 * q^75 + 12 * q^76 + 27 * q^77 - 21 * q^78 - 33 * q^79 - 39 * q^80 + 25 * q^81 + 49 * q^82 + 2 * q^83 - 41 * q^84 - 6 * q^85 + 35 * q^86 - q^87 + 33 * q^88 - 11 * q^89 - q^90 - 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 + 48 * q^97 + 4 * q^98 - 15 * 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 $

$2$	2.54434	1.79912	0.899559	−	0.436800i	$-0.143888\pi$
$2$	2.54434	1.79912	0.899559	+	0.436800i	$0.143888\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.47365	2.23682
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.54434	−1.03872
$7$	−0.866803	−0.327621	−0.163810	−	0.986492i	$-0.552379\pi$
$7$	−0.866803	−0.327621	−0.163810	+	0.986492i	$0.552379\pi$
$8$	6.29379	2.22519
$9$	1.00000	0.333333
$10$	−2.54434	−0.804590
$11$	−6.32487	−1.90702	−0.953511	−	0.301359i	$-0.902560\pi$
$11$	−6.32487	−1.90702	−0.953511	+	0.301359i	$0.902560\pi$
$12$	−4.47365	−1.29143
$13$	5.34349	1.48202	0.741008	−	0.671496i	$-0.234348\pi$
$13$	5.34349	1.48202	0.741008	+	0.671496i	$0.234348\pi$
$14$	−2.20544	−0.589428
$15$	1.00000	0.258199
$16$	7.06623	1.76656
$17$	−3.99140	−0.968056	−0.484028	−	0.875052i	$-0.660827\pi$
$17$	−3.99140	−0.968056	−0.484028	+	0.875052i	$0.660827\pi$
$18$	2.54434	0.599706
$19$	3.64235	0.835612	0.417806	−	0.908536i	$-0.362799\pi$
$19$	3.64235	0.835612	0.417806	+	0.908536i	$0.362799\pi$
$20$	−4.47365	−1.00034
$21$	0.866803	0.189152
$22$	−16.0926	−3.43096
$23$	0	0
$23$	0	0
$24$	−6.29379	−1.28471
$25$	1.00000	0.200000
$26$	13.5956	2.66632
$27$	−1.00000	−0.192450
$28$	−3.87777	−0.732830
$29$	2.64583	0.491317	0.245659	−	0.969356i	$-0.420996\pi$
$29$	2.64583	0.491317	0.245659	+	0.969356i	$0.420996\pi$
$30$	2.54434	0.464530
$31$	−2.74860	−0.493663	−0.246831	−	0.969058i	$-0.579389\pi$
$31$	−2.74860	−0.493663	−0.246831	+	0.969058i	$0.579389\pi$
$32$	5.39127	0.953051
$33$	6.32487	1.10102
$34$	−10.1555	−1.74165
$35$	0.866803	0.146516
$36$	4.47365	0.745608
$37$	8.21282	1.35018	0.675089	−	0.737736i	$-0.264105\pi$
$37$	8.21282	1.35018	0.675089	+	0.737736i	$0.264105\pi$
$38$	9.26736	1.50336
$39$	−5.34349	−0.855642
$40$	−6.29379	−0.995136
$41$	9.13059	1.42596	0.712979	−	0.701185i	$-0.247345\pi$
$41$	9.13059	1.42596	0.712979	+	0.701185i	$0.247345\pi$
$42$	2.20544	0.340307
$43$	7.13440	1.08799	0.543993	−	0.839090i	$-0.316912\pi$
$43$	7.13440	1.08799	0.543993	+	0.839090i	$0.316912\pi$
$44$	−28.2953	−4.26567
$45$	−1.00000	−0.149071
$46$	0	0
$47$	3.77059	0.549997	0.274998	−	0.961445i	$-0.411323\pi$
$47$	3.77059	0.549997	0.274998	+	0.961445i	$0.411323\pi$
$48$	−7.06623	−1.01992
$49$	−6.24865	−0.892665
$50$	2.54434	0.359823
$51$	3.99140	0.558908
$52$	23.9049	3.31501
$53$	5.07773	0.697479	0.348740	−	0.937220i	$-0.386610\pi$
$53$	5.07773	0.697479	0.348740	+	0.937220i	$0.386610\pi$
$54$	−2.54434	−0.346240
$55$	6.32487	0.852846
$56$	−5.45548	−0.729019
$57$	−3.64235	−0.482441
$58$	6.73187	0.883938
$59$	2.78933	0.363139	0.181570	−	0.983378i	$-0.441882\pi$
$59$	2.78933	0.363139	0.181570	+	0.983378i	$0.441882\pi$
$60$	4.47365	0.577545
$61$	10.3493	1.32509	0.662546	−	0.749021i	$-0.269476\pi$
$61$	10.3493	1.32509	0.662546	+	0.749021i	$0.269476\pi$
$62$	−6.99336	−0.888157
$63$	−0.866803	−0.109207
$64$	−0.415241	−0.0519051
$65$	−5.34349	−0.662778
$66$	16.0926	1.98086
$67$	8.41426	1.02796	0.513982	−	0.857801i	$-0.328170\pi$
$67$	8.41426	1.02796	0.513982	+	0.857801i	$0.328170\pi$
$68$	−17.8561	−2.16537
$69$	0	0
$70$	2.20544	0.263600
$71$	8.96239	1.06364	0.531820	−	0.846858i	$-0.321508\pi$
$71$	8.96239	1.06364	0.531820	+	0.846858i	$0.321508\pi$
$72$	6.29379	0.741730
$73$	−12.9611	−1.51698	−0.758488	−	0.651687i	$-0.774062\pi$
$73$	−12.9611	−1.51698	−0.758488	+	0.651687i	$0.774062\pi$
$74$	20.8962	2.42913
$75$	−1.00000	−0.115470
$76$	16.2946	1.86912
$77$	5.48242	0.624780
$78$	−13.5956	−1.53940
$79$	3.97067	0.446735	0.223368	−	0.974734i	$-0.428295\pi$
$79$	3.97067	0.446735	0.223368	+	0.974734i	$0.428295\pi$
$80$	−7.06623	−0.790028
$81$	1.00000	0.111111
$82$	23.2313	2.56547
$83$	5.37512	0.589996	0.294998	−	0.955498i	$-0.404681\pi$
$83$	5.37512	0.589996	0.294998	+	0.955498i	$0.404681\pi$
$84$	3.87777	0.423100
$85$	3.99140	0.432928
$86$	18.1523	1.95741
$87$	−2.64583	−0.283662
$88$	−39.8074	−4.24349
$89$	3.28242	0.347935	0.173968	−	0.984751i	$-0.444341\pi$
$89$	3.28242	0.347935	0.173968	+	0.984751i	$0.444341\pi$
$90$	−2.54434	−0.268197
$91$	−4.63175	−0.485539
$92$	0	0
$93$	2.74860	0.285016
$94$	9.59364	0.989509
$95$	−3.64235	−0.373697
$96$	−5.39127	−0.550244
$97$	−9.99338	−1.01467	−0.507337	−	0.861748i	$-0.669370\pi$
$97$	−9.99338	−1.01467	−0.507337	+	0.861748i	$0.669370\pi$
$98$	−15.8987	−1.60601
$99$	−6.32487	−0.635674
$100$	4.47365	0.447365
$101$	1.69757	0.168914	0.0844571	−	0.996427i	$-0.473084\pi$
$101$	1.69757	0.168914	0.0844571	+	0.996427i	$0.473084\pi$
$102$	10.1555	1.00554
$103$	6.78721	0.668763	0.334382	−	0.942438i	$-0.391473\pi$
$103$	6.78721	0.668763	0.334382	+	0.942438i	$0.391473\pi$
$104$	33.6308	3.29777
$105$	−0.866803	−0.0845913
$106$	12.9194	1.25485
$107$	11.0647	1.06967	0.534835	−	0.844957i	$-0.320374\pi$
$107$	11.0647	1.06967	0.534835	+	0.844957i	$0.320374\pi$
$108$	−4.47365	−0.430477
$109$	4.23169	0.405323	0.202661	−	0.979249i	$-0.435041\pi$
$109$	4.23169	0.405323	0.202661	+	0.979249i	$0.435041\pi$
$110$	16.0926	1.53437
$111$	−8.21282	−0.779526
$112$	−6.12503	−0.578761
$113$	−15.2874	−1.43812	−0.719060	−	0.694948i	$-0.755427\pi$
$113$	−15.2874	−1.43812	−0.719060	+	0.694948i	$0.755427\pi$
$114$	−9.26736	−0.867968
$115$	0	0
$116$	11.8365	1.09899
$117$	5.34349	0.494005
$118$	7.09698	0.653330
$119$	3.45976	0.317155
$120$	6.29379	0.574542
$121$	29.0040	2.63673
$122$	26.3321	2.38400
$123$	−9.13059	−0.823278
$124$	−12.2963	−1.10424
$125$	−1.00000	−0.0894427
$126$	−2.20544	−0.196476
$127$	−17.8469	−1.58365	−0.791826	−	0.610746i	$-0.790869\pi$
$127$	−17.8469	−1.58365	−0.791826	+	0.610746i	$0.790869\pi$
$128$	−11.8391	−1.04643
$129$	−7.13440	−0.628149
$130$	−13.5956	−1.19242
$131$	4.56597	0.398931	0.199466	−	0.979905i	$-0.436079\pi$
$131$	4.56597	0.398931	0.199466	+	0.979905i	$0.436079\pi$
$132$	28.2953	2.46279
$133$	−3.15720	−0.273764
$134$	21.4087	1.84943
$135$	1.00000	0.0860663
$136$	−25.1210	−2.15411
$137$	−1.97264	−0.168534	−0.0842669	−	0.996443i	$-0.526855\pi$
$137$	−1.97264	−0.168534	−0.0842669	+	0.996443i	$0.526855\pi$
$138$	0	0
$139$	1.91783	0.162668	0.0813339	−	0.996687i	$-0.474082\pi$
$139$	1.91783	0.162668	0.0813339	+	0.996687i	$0.474082\pi$
$140$	3.87777	0.327731
$141$	−3.77059	−0.317541
$142$	22.8033	1.91361
$143$	−33.7969	−2.82624
$144$	7.06623	0.588852
$145$	−2.64583	−0.219724
$146$	−32.9773	−2.72922
$147$	6.24865	0.515380
$148$	36.7412	3.02011
$149$	−6.85144	−0.561292	−0.280646	−	0.959811i	$-0.590549\pi$
$149$	−6.85144	−0.561292	−0.280646	+	0.959811i	$0.590549\pi$
$150$	−2.54434	−0.207744
$151$	5.38158	0.437946	0.218973	−	0.975731i	$-0.429729\pi$
$151$	5.38158	0.437946	0.218973	+	0.975731i	$0.429729\pi$
$152$	22.9242	1.85940
$153$	−3.99140	−0.322685
$154$	13.9491	1.12405
$155$	2.74860	0.220773
$156$	−23.9049	−1.91392
$157$	17.7539	1.41692	0.708459	−	0.705752i	$-0.249391\pi$
$157$	17.7539	1.41692	0.708459	+	0.705752i	$0.249391\pi$
$158$	10.1027	0.803729
$159$	−5.07773	−0.402690
$160$	−5.39127	−0.426217
$161$	0	0
$162$	2.54434	0.199902
$163$	10.4043	0.814926	0.407463	−	0.913222i	$-0.366414\pi$
$163$	10.4043	0.814926	0.407463	+	0.913222i	$0.366414\pi$
$164$	40.8470	3.18962
$165$	−6.32487	−0.492391
$166$	13.6761	1.06147
$167$	−23.5729	−1.82413	−0.912064	−	0.410048i	$-0.865512\pi$
$167$	−23.5729	−1.82413	−0.912064	+	0.410048i	$0.865512\pi$
$168$	5.45548	0.420899
$169$	15.5528	1.19637
$170$	10.1555	0.778888
$171$	3.64235	0.278537
$172$	31.9168	2.43363
$173$	9.28396	0.705847	0.352923	−	0.935652i	$-0.385188\pi$
$173$	9.28396	0.705847	0.352923	+	0.935652i	$0.385188\pi$
$174$	−6.73187	−0.510342
$175$	−0.866803	−0.0655242
$176$	−44.6930	−3.36886
$177$	−2.78933	−0.209659
$178$	8.35157	0.625977
$179$	−17.3974	−1.30035	−0.650173	−	0.759786i	$-0.725304\pi$
$179$	−17.3974	−1.30035	−0.650173	+	0.759786i	$0.725304\pi$
$180$	−4.47365	−0.333446
$181$	19.6433	1.46007	0.730037	−	0.683408i	$-0.239503\pi$
$181$	19.6433	1.46007	0.730037	+	0.683408i	$0.239503\pi$
$182$	−11.7847	−0.873542
$183$	−10.3493	−0.765042
$184$	0	0
$185$	−8.21282	−0.603818
$186$	6.99336	0.512778
$187$	25.2451	1.84610
$188$	16.8683	1.23025
$189$	0.866803	0.0630506
$190$	−9.26736	−0.672325
$191$	3.60648	0.260956	0.130478	−	0.991451i	$-0.458349\pi$
$191$	3.60648	0.260956	0.130478	+	0.991451i	$0.458349\pi$
$192$	0.415241	0.0299674
$193$	22.8310	1.64341	0.821706	−	0.569911i	$-0.193022\pi$
$193$	22.8310	1.64341	0.821706	+	0.569911i	$0.193022\pi$
$194$	−25.4265	−1.82552
$195$	5.34349	0.382655
$196$	−27.9543	−1.99673
$197$	1.33643	0.0952165	0.0476082	−	0.998866i	$-0.484840\pi$
$197$	1.33643	0.0952165	0.0476082	+	0.998866i	$0.484840\pi$
$198$	−16.0926	−1.14365
$199$	−8.93902	−0.633671	−0.316835	−	0.948481i	$-0.602620\pi$
$199$	−8.93902	−0.633671	−0.316835	+	0.948481i	$0.602620\pi$
$200$	6.29379	0.445038
$201$	−8.41426	−0.593496
$202$	4.31918	0.303896
$203$	−2.29341	−0.160966
$204$	17.8561	1.25018
$205$	−9.13059	−0.637708
$206$	17.2689	1.20318
$207$	0	0
$208$	37.7583	2.61806
$209$	−23.0374	−1.59353
$210$	−2.20544	−0.152190
$211$	−17.6342	−1.21399	−0.606995	−	0.794706i	$-0.707625\pi$
$211$	−17.6342	−1.21399	−0.606995	+	0.794706i	$0.707625\pi$
$212$	22.7160	1.56014
$213$	−8.96239	−0.614093
$214$	28.1524	1.92446
$215$	−7.13440	−0.486562
$216$	−6.29379	−0.428238
$217$	2.38249	0.161734
$218$	10.7668	0.729223
$219$	12.9611	0.875827
$220$	28.2953	1.90767
$221$	−21.3280	−1.43468
$222$	−20.8962	−1.40246
$223$	13.8725	0.928970	0.464485	−	0.885581i	$-0.346239\pi$
$223$	13.8725	0.928970	0.464485	+	0.885581i	$0.346239\pi$
$224$	−4.67317	−0.312239
$225$	1.00000	0.0666667
$226$	−38.8963	−2.58735
$227$	−27.1429	−1.80154	−0.900770	−	0.434296i	$-0.856997\pi$
$227$	−27.1429	−1.80154	−0.900770	+	0.434296i	$0.856997\pi$
$228$	−16.2946	−1.07914
$229$	7.54437	0.498546	0.249273	−	0.968433i	$-0.419808\pi$
$229$	7.54437	0.498546	0.249273	+	0.968433i	$0.419808\pi$
$230$	0	0
$231$	−5.48242	−0.360717
$232$	16.6523	1.09327
$233$	6.24358	0.409030	0.204515	−	0.978863i	$-0.434438\pi$
$233$	6.24358	0.409030	0.204515	+	0.978863i	$0.434438\pi$
$234$	13.5956	0.888774
$235$	−3.77059	−0.245966
$236$	12.4785	0.812279
$237$	−3.97067	−0.257923
$238$	8.80278	0.570600
$239$	11.8009	0.763335	0.381668	−	0.924300i	$-0.375350\pi$
$239$	11.8009	0.763335	0.381668	+	0.924300i	$0.375350\pi$
$240$	7.06623	0.456123
$241$	−22.2271	−1.43177	−0.715887	−	0.698217i	$-0.753977\pi$
$241$	−22.2271	−1.43177	−0.715887	+	0.698217i	$0.753977\pi$
$242$	73.7960	4.74379
$243$	−1.00000	−0.0641500
$244$	46.2991	2.96400
$245$	6.24865	0.399212
$246$	−23.2313	−1.48117
$247$	19.4628	1.23839
$248$	−17.2991	−1.09849
$249$	−5.37512	−0.340634
$250$	−2.54434	−0.160918
$251$	3.32796	0.210059	0.105030	−	0.994469i	$-0.466506\pi$
$251$	3.32796	0.210059	0.105030	+	0.994469i	$0.466506\pi$
$252$	−3.87777	−0.244277
$253$	0	0
$254$	−45.4084	−2.84918
$255$	−3.99140	−0.249951
$256$	−29.2921	−1.83075
$257$	23.7897	1.48396	0.741981	−	0.670421i	$-0.233886\pi$
$257$	23.7897	1.48396	0.741981	+	0.670421i	$0.233886\pi$
$258$	−18.1523	−1.13011
$259$	−7.11889	−0.442347
$260$	−23.9049	−1.48252
$261$	2.64583	0.163772
$262$	11.6174	0.717724
$263$	−23.8691	−1.47183	−0.735915	−	0.677074i	$-0.763247\pi$
$263$	−23.8691	−1.47183	−0.735915	+	0.677074i	$0.763247\pi$
$264$	39.8074	2.44998
$265$	−5.07773	−0.311922
$266$	−8.03298	−0.492533
$267$	−3.28242	−0.200881
$268$	37.6424	2.29938
$269$	−3.99387	−0.243511	−0.121755	−	0.992560i	$-0.538852\pi$
$269$	−3.99387	−0.243511	−0.121755	+	0.992560i	$0.538852\pi$
$270$	2.54434	0.154843
$271$	1.59932	0.0971518	0.0485759	−	0.998819i	$-0.484532\pi$
$271$	1.59932	0.0971518	0.0485759	+	0.998819i	$0.484532\pi$
$272$	−28.2041	−1.71013
$273$	4.63175	0.280326
$274$	−5.01906	−0.303212
$275$	−6.32487	−0.381404
$276$	0	0
$277$	2.32107	0.139459	0.0697297	−	0.997566i	$-0.477786\pi$
$277$	2.32107	0.139459	0.0697297	+	0.997566i	$0.477786\pi$
$278$	4.87959	0.292659
$279$	−2.74860	−0.164554
$280$	5.45548	0.326027
$281$	25.2750	1.50778	0.753891	−	0.657000i	$-0.228175\pi$
$281$	25.2750	1.50778	0.753891	+	0.657000i	$0.228175\pi$
$282$	−9.59364	−0.571293
$283$	1.66304	0.0988573	0.0494286	−	0.998778i	$-0.484260\pi$
$283$	1.66304	0.0988573	0.0494286	+	0.998778i	$0.484260\pi$
$284$	40.0946	2.37917
$285$	3.64235	0.215754
$286$	−85.9906	−5.08473
$287$	−7.91442	−0.467174
$288$	5.39127	0.317684
$289$	−1.06874	−0.0628669
$290$	−6.73187	−0.395309
$291$	9.99338	0.585822
$292$	−57.9832	−3.39321
$293$	−9.67926	−0.565468	−0.282734	−	0.959198i	$-0.591241\pi$
$293$	−9.67926	−0.565468	−0.282734	+	0.959198i	$0.591241\pi$
$294$	15.8987	0.927229
$295$	−2.78933	−0.162401
$296$	51.6897	3.00441
$297$	6.32487	0.367006
$298$	−17.4324	−1.00983
$299$	0	0
$300$	−4.47365	−0.258286
$301$	−6.18412	−0.356447
$302$	13.6925	0.787917
$303$	−1.69757	−0.0975226
$304$	25.7377	1.47616
$305$	−10.3493	−0.592599
$306$	−10.1555	−0.580549
$307$	0.0356551	0.00203494	0.00101747	−	0.999999i	$-0.499676\pi$
$307$	0.0356551	0.00203494	0.00101747	+	0.999999i	$0.499676\pi$
$308$	24.5264	1.39752
$309$	−6.78721	−0.386111
$310$	6.99336	0.397196
$311$	2.65831	0.150739	0.0753696	−	0.997156i	$-0.475986\pi$
$311$	2.65831	0.150739	0.0753696	+	0.997156i	$0.475986\pi$
$312$	−33.6308	−1.90397
$313$	8.22425	0.464862	0.232431	−	0.972613i	$-0.425332\pi$
$313$	8.22425	0.464862	0.232431	+	0.972613i	$0.425332\pi$
$314$	45.1720	2.54920
$315$	0.866803	0.0488388
$316$	17.7634	0.999268
$317$	−26.0724	−1.46437	−0.732185	−	0.681106i	$-0.761499\pi$
$317$	−26.0724	−1.46437	−0.732185	+	0.681106i	$0.761499\pi$
$318$	−12.9194	−0.724486
$319$	−16.7345	−0.936953
$320$	0.415241	0.0232127
$321$	−11.0647	−0.617574
$322$	0	0
$323$	−14.5381	−0.808920
$324$	4.47365	0.248536
$325$	5.34349	0.296403
$326$	26.4720	1.46615
$327$	−4.23169	−0.234013
$328$	57.4660	3.17303
$329$	−3.26836	−0.180190
$330$	−16.0926	−0.885869
$331$	17.1880	0.944735	0.472368	−	0.881402i	$-0.343399\pi$
$331$	17.1880	0.944735	0.472368	+	0.881402i	$0.343399\pi$
$332$	24.0464	1.31972
$333$	8.21282	0.450060
$334$	−59.9775	−3.28182
$335$	−8.41426	−0.459720
$336$	6.12503	0.334148
$337$	−5.48977	−0.299047	−0.149523	−	0.988758i	$-0.547774\pi$
$337$	−5.48977	−0.299047	−0.149523	+	0.988758i	$0.547774\pi$
$338$	39.5716	2.15241
$339$	15.2874	0.830299
$340$	17.8561	0.968383
$341$	17.3845	0.941425
$342$	9.26736	0.501122
$343$	11.4840	0.620076
$344$	44.9024	2.42098
$345$	0	0
$346$	23.6215	1.26990
$347$	−4.46935	−0.239927	−0.119964	−	0.992778i	$-0.538278\pi$
$347$	−4.46935	−0.239927	−0.119964	+	0.992778i	$0.538278\pi$
$348$	−11.8365	−0.634502
$349$	25.0212	1.33935	0.669676	−	0.742653i	$-0.266433\pi$
$349$	25.0212	1.33935	0.669676	+	0.742653i	$0.266433\pi$
$350$	−2.20544	−0.117886
$351$	−5.34349	−0.285214
$352$	−34.0991	−1.81749
$353$	27.2418	1.44993	0.724967	−	0.688784i	$-0.241855\pi$
$353$	27.2418	1.44993	0.724967	+	0.688784i	$0.241855\pi$
$354$	−7.09698	−0.377200
$355$	−8.96239	−0.475674
$356$	14.6844	0.778270
$357$	−3.45976	−0.183110
$358$	−44.2650	−2.33948
$359$	15.5386	0.820095	0.410048	−	0.912064i	$-0.365512\pi$
$359$	15.5386	0.820095	0.410048	+	0.912064i	$0.365512\pi$
$360$	−6.29379	−0.331712
$361$	−5.73329	−0.301752
$362$	49.9791	2.62684
$363$	−29.0040	−1.52232
$364$	−20.7208	−1.08607
$365$	12.9611	0.678413
$366$	−26.3321	−1.37640
$367$	−4.12175	−0.215153	−0.107577	−	0.994197i	$-0.534309\pi$
$367$	−4.12175	−0.215153	−0.107577	+	0.994197i	$0.534309\pi$
$368$	0	0
$369$	9.13059	0.475320
$370$	−20.8962	−1.08634
$371$	−4.40139	−0.228509
$372$	12.2963	0.637531
$373$	11.1179	0.575663	0.287832	−	0.957681i	$-0.407066\pi$
$373$	11.1179	0.575663	0.287832	+	0.957681i	$0.407066\pi$
$374$	64.2320	3.32136
$375$	1.00000	0.0516398
$376$	23.7313	1.22385
$377$	14.1379	0.728140
$378$	2.20544	0.113436
$379$	3.23937	0.166395	0.0831977	−	0.996533i	$-0.473487\pi$
$379$	3.23937	0.166395	0.0831977	+	0.996533i	$0.473487\pi$
$380$	−16.2946	−0.835895
$381$	17.8469	0.914322
$382$	9.17609	0.469490
$383$	−23.6057	−1.20620	−0.603098	−	0.797667i	$-0.706067\pi$
$383$	−23.6057	−1.20620	−0.603098	+	0.797667i	$0.706067\pi$
$384$	11.8391	0.604159
$385$	−5.48242	−0.279410
$386$	58.0898	2.95669
$387$	7.13440	0.362662
$388$	−44.7069	−2.26965
$389$	19.6734	0.997482	0.498741	−	0.866751i	$-0.333796\pi$
$389$	19.6734	0.997482	0.498741	+	0.866751i	$0.333796\pi$
$390$	13.5956	0.688441
$391$	0	0
$392$	−39.3277	−1.98635
$393$	−4.56597	−0.230323
$394$	3.40032	0.171306
$395$	−3.97067	−0.199786
$396$	−28.2953	−1.42189
$397$	36.5151	1.83264	0.916321	−	0.400444i	$-0.131144\pi$
$397$	36.5151	1.83264	0.916321	+	0.400444i	$0.131144\pi$
$398$	−22.7439	−1.14005
$399$	3.15720	0.158058
$400$	7.06623	0.353311
$401$	−37.1463	−1.85500	−0.927498	−	0.373829i	$-0.878045\pi$
$401$	−37.1463	−1.85500	−0.927498	+	0.373829i	$0.878045\pi$
$402$	−21.4087	−1.06777
$403$	−14.6871	−0.731616
$404$	7.59431	0.377831
$405$	−1.00000	−0.0496904
$406$	−5.83520	−0.289596
$407$	−51.9450	−2.57482
$408$	25.1210	1.24368
$409$	−21.6795	−1.07198	−0.535991	−	0.844224i	$-0.680062\pi$
$409$	−21.6795	−1.07198	−0.535991	+	0.844224i	$0.680062\pi$
$410$	−23.2313	−1.14731
$411$	1.97264	0.0973031
$412$	30.3636	1.49591
$413$	−2.41780	−0.118972
$414$	0	0
$415$	−5.37512	−0.263854
$416$	28.8082	1.41244
$417$	−1.91783	−0.0939163
$418$	−58.6149	−2.86695
$419$	18.0337	0.881003	0.440502	−	0.897752i	$-0.354801\pi$
$419$	18.0337	0.881003	0.440502	+	0.897752i	$0.354801\pi$
$420$	−3.87777	−0.189216
$421$	−9.65808	−0.470706	−0.235353	−	0.971910i	$-0.575625\pi$
$421$	−9.65808	−0.470706	−0.235353	+	0.971910i	$0.575625\pi$
$422$	−44.8674	−2.18411
$423$	3.77059	0.183332
$424$	31.9581	1.55202
$425$	−3.99140	−0.193611
$426$	−22.8033	−1.10482
$427$	−8.97080	−0.434128
$428$	49.4998	2.39266
$429$	33.7969	1.63173
$430$	−18.1523	−0.875382
$431$	−10.2355	−0.493029	−0.246514	−	0.969139i	$-0.579285\pi$
$431$	−10.2355	−0.493029	−0.246514	+	0.969139i	$0.579285\pi$
$432$	−7.06623	−0.339974
$433$	12.1014	0.581556	0.290778	−	0.956791i	$-0.406086\pi$
$433$	12.1014	0.581556	0.290778	+	0.956791i	$0.406086\pi$
$434$	6.06186	0.290979
$435$	2.64583	0.126858
$436$	18.9311	0.906635
$437$	0	0
$438$	32.9773	1.57572
$439$	8.59859	0.410388	0.205194	−	0.978721i	$-0.434217\pi$
$439$	8.59859	0.410388	0.205194	+	0.978721i	$0.434217\pi$
$440$	39.8074	1.89774
$441$	−6.24865	−0.297555
$442$	−54.2656	−2.58115
$443$	−12.4639	−0.592177	−0.296089	−	0.955160i	$-0.595682\pi$
$443$	−12.4639	−0.592177	−0.296089	+	0.955160i	$0.595682\pi$
$444$	−36.7412	−1.74366
$445$	−3.28242	−0.155601
$446$	35.2963	1.67133
$447$	6.85144	0.324062
$448$	0.359932	0.0170052
$449$	−21.6029	−1.01950	−0.509752	−	0.860321i	$-0.670263\pi$
$449$	−21.6029	−1.01950	−0.509752	+	0.860321i	$0.670263\pi$
$450$	2.54434	0.119941
$451$	−57.7498	−2.71933
$452$	−68.3905	−3.21682
$453$	−5.38158	−0.252849
$454$	−69.0608	−3.24118
$455$	4.63175	0.217140
$456$	−22.9242	−1.07352
$457$	0.818051	0.0382668	0.0191334	−	0.999817i	$-0.493909\pi$
$457$	0.818051	0.0382668	0.0191334	+	0.999817i	$0.493909\pi$
$458$	19.1954	0.896943
$459$	3.99140	0.186303
$460$	0	0
$461$	38.9346	1.81336	0.906682	−	0.421814i	$-0.138607\pi$
$461$	38.9346	1.81336	0.906682	+	0.421814i	$0.138607\pi$
$462$	−13.9491	−0.648972
$463$	−29.9177	−1.39039	−0.695196	−	0.718820i	$-0.744682\pi$
$463$	−29.9177	−1.39039	−0.695196	+	0.718820i	$0.744682\pi$
$464$	18.6960	0.867940
$465$	−2.74860	−0.127463
$466$	15.8858	0.735894
$467$	−37.7651	−1.74756	−0.873780	−	0.486321i	$-0.838339\pi$
$467$	−37.7651	−1.74756	−0.873780	+	0.486321i	$0.838339\pi$
$468$	23.9049	1.10500
$469$	−7.29350	−0.336783
$470$	−9.59364	−0.442522
$471$	−17.7539	−0.818058
$472$	17.5554	0.808054
$473$	−45.1242	−2.07481
$474$	−10.1027	−0.464033
$475$	3.64235	0.167122
$476$	15.4777	0.709421
$477$	5.07773	0.232493
$478$	30.0254	1.37333
$479$	12.9548	0.591921	0.295961	−	0.955200i	$-0.404360\pi$
$479$	12.9548	0.591921	0.295961	+	0.955200i	$0.404360\pi$
$480$	5.39127	0.246077
$481$	43.8851	2.00099
$482$	−56.5532	−2.57593
$483$	0	0
$484$	129.754	5.89790
$485$	9.99338	0.453776
$486$	−2.54434	−0.115413
$487$	8.57010	0.388348	0.194174	−	0.980967i	$-0.437797\pi$
$487$	8.57010	0.388348	0.194174	+	0.980967i	$0.437797\pi$
$488$	65.1363	2.94858
$489$	−10.4043	−0.470498
$490$	15.8987	0.718229
$491$	−13.8057	−0.623040	−0.311520	−	0.950240i	$-0.600838\pi$
$491$	−13.8057	−0.623040	−0.311520	+	0.950240i	$0.600838\pi$
$492$	−40.8470	−1.84153
$493$	−10.5605	−0.475623
$494$	49.5200	2.22801
$495$	6.32487	0.284282
$496$	−19.4222	−0.872083
$497$	−7.76862	−0.348470
$498$	−13.6761	−0.612841
$499$	−44.1579	−1.97678	−0.988389	−	0.151943i	$-0.951447\pi$
$499$	−44.1579	−1.97678	−0.988389	+	0.151943i	$0.951447\pi$
$500$	−4.47365	−0.200068
$501$	23.5729	1.05316
$502$	8.46746	0.377921
$503$	20.2121	0.901211	0.450606	−	0.892723i	$-0.351208\pi$
$503$	20.2121	0.901211	0.450606	+	0.892723i	$0.351208\pi$
$504$	−5.45548	−0.243006
$505$	−1.69757	−0.0755407
$506$	0	0
$507$	−15.5528	−0.690726
$508$	−79.8405	−3.54235
$509$	−30.4469	−1.34953	−0.674767	−	0.738031i	$-0.735756\pi$
$509$	−30.4469	−1.34953	−0.674767	+	0.738031i	$0.735756\pi$
$510$	−10.1555	−0.449691
$511$	11.2347	0.496993
$512$	−50.8507	−2.24731
$513$	−3.64235	−0.160814
$514$	60.5291	2.66982
$515$	−6.78721	−0.299080
$516$	−31.9168	−1.40506
$517$	−23.8485	−1.04886
$518$	−18.1129	−0.795834
$519$	−9.28396	−0.407521
$520$	−33.6308	−1.47481
$521$	6.15067	0.269466	0.134733	−	0.990882i	$-0.456982\pi$
$521$	6.15067	0.269466	0.134733	+	0.990882i	$0.456982\pi$
$522$	6.73187	0.294646
$523$	27.7615	1.21393	0.606964	−	0.794730i	$-0.292387\pi$
$523$	27.7615	1.21393	0.606964	+	0.794730i	$0.292387\pi$
$524$	20.4266	0.892338
$525$	0.866803	0.0378304
$526$	−60.7309	−2.64799
$527$	10.9707	0.477893
$528$	44.6930	1.94501
$529$	0	0
$530$	−12.9194	−0.561185
$531$	2.78933	0.121046
$532$	−14.1242	−0.612362
$533$	48.7892	2.11329
$534$	−8.35157	−0.361408
$535$	−11.0647	−0.478371
$536$	52.9576	2.28742
$537$	17.3974	0.750755
$538$	−10.1618	−0.438105
$539$	39.5219	1.70233
$540$	4.47365	0.192515
$541$	7.99666	0.343803	0.171902	−	0.985114i	$-0.445009\pi$
$541$	7.99666	0.343803	0.171902	+	0.985114i	$0.445009\pi$
$542$	4.06921	0.174787
$543$	−19.6433	−0.842974
$544$	−21.5187	−0.922607
$545$	−4.23169	−0.181266
$546$	11.7847	0.504340
$547$	−22.3831	−0.957031	−0.478515	−	0.878079i	$-0.658825\pi$
$547$	−22.3831	−0.957031	−0.478515	+	0.878079i	$0.658825\pi$
$548$	−8.82489	−0.376981
$549$	10.3493	0.441697
$550$	−16.0926	−0.686191
$551$	9.63702	0.410551
$552$	0	0
$553$	−3.44179	−0.146360
$554$	5.90557	0.250904
$555$	8.21282	0.348615
$556$	8.57968	0.363859
$557$	33.8489	1.43422	0.717111	−	0.696959i	$-0.245464\pi$
$557$	33.8489	1.43422	0.717111	+	0.696959i	$0.245464\pi$
$558$	−6.99336	−0.296052
$559$	38.1226	1.61241
$560$	6.12503	0.258830
$561$	−25.2451	−1.06585
$562$	64.3082	2.71268
$563$	−6.31640	−0.266205	−0.133102	−	0.991102i	$-0.542494\pi$
$563$	−6.31640	−0.266205	−0.133102	+	0.991102i	$0.542494\pi$
$564$	−16.8683	−0.710283
$565$	15.2874	0.643147
$566$	4.23132	0.177856
$567$	−0.866803	−0.0364023
$568$	56.4074	2.36680
$569$	−28.9972	−1.21563	−0.607813	−	0.794080i	$-0.707953\pi$
$569$	−28.9972	−1.21563	−0.607813	+	0.794080i	$0.707953\pi$
$570$	9.26736	0.388167
$571$	−35.6644	−1.49251	−0.746253	−	0.665662i	$-0.768149\pi$
$571$	−35.6644	−1.49251	−0.746253	+	0.665662i	$0.768149\pi$
$572$	−151.195	−6.32179
$573$	−3.60648	−0.150663
$574$	−20.1370	−0.840500
$575$	0	0
$576$	−0.415241	−0.0173017
$577$	−6.28810	−0.261777	−0.130888	−	0.991397i	$-0.541783\pi$
$577$	−6.28810	−0.261777	−0.130888	+	0.991397i	$0.541783\pi$
$578$	−2.71923	−0.113105
$579$	−22.8310	−0.948825
$580$	−11.8365	−0.491483
$581$	−4.65917	−0.193295
$582$	25.4265	1.05396
$583$	−32.1160	−1.33011
$584$	−81.5742	−3.37556
$585$	−5.34349	−0.220926
$586$	−24.6273	−1.01734
$587$	−30.2135	−1.24705	−0.623523	−	0.781805i	$-0.714299\pi$
$587$	−30.2135	−1.24705	−0.623523	+	0.781805i	$0.714299\pi$
$588$	27.9543	1.15281
$589$	−10.0114	−0.412511
$590$	−7.09698	−0.292178
$591$	−1.33643	−0.0549733
$592$	58.0336	2.38517
$593$	−19.6981	−0.808904	−0.404452	−	0.914559i	$-0.632538\pi$
$593$	−19.6981	−0.808904	−0.404452	+	0.914559i	$0.632538\pi$
$594$	16.0926	0.660288
$595$	−3.45976	−0.141836
$596$	−30.6509	−1.25551
$597$	8.93902	0.365850
$598$	0	0
$599$	−3.86727	−0.158012	−0.0790061	−	0.996874i	$-0.525175\pi$
$599$	−3.86727	−0.158012	−0.0790061	+	0.996874i	$0.525175\pi$
$600$	−6.29379	−0.256943
$601$	21.3554	0.871105	0.435553	−	0.900163i	$-0.356553\pi$
$601$	21.3554	0.871105	0.435553	+	0.900163i	$0.356553\pi$
$602$	−15.7345	−0.641290
$603$	8.41426	0.342655
$604$	24.0753	0.979609
$605$	−29.0040	−1.17918
$606$	−4.31918	−0.175455
$607$	−9.43144	−0.382810	−0.191405	−	0.981511i	$-0.561304\pi$
$607$	−9.43144	−0.382810	−0.191405	+	0.981511i	$0.561304\pi$
$608$	19.6369	0.796381
$609$	2.29341	0.0929336
$610$	−26.3321	−1.06616
$611$	20.1481	0.815104
$612$	−17.8561	−0.721790
$613$	31.0694	1.25488	0.627441	−	0.778664i	$-0.284102\pi$
$613$	31.0694	1.25488	0.627441	+	0.778664i	$0.284102\pi$
$614$	0.0907186	0.00366110
$615$	9.13059	0.368181
$616$	34.5052	1.39025
$617$	−6.90658	−0.278048	−0.139024	−	0.990289i	$-0.544397\pi$
$617$	−6.90658	−0.278048	−0.139024	+	0.990289i	$0.544397\pi$
$618$	−17.2689	−0.694658
$619$	−17.0075	−0.683588	−0.341794	−	0.939775i	$-0.611035\pi$
$619$	−17.0075	−0.683588	−0.341794	+	0.939775i	$0.611035\pi$
$620$	12.2963	0.493829
$621$	0	0
$622$	6.76364	0.271197
$623$	−2.84521	−0.113991
$624$	−37.7583	−1.51154
$625$	1.00000	0.0400000
$626$	20.9253	0.836342
$627$	23.0374	0.920025
$628$	79.4248	3.16939
$629$	−32.7806	−1.30705
$630$	2.20544	0.0878668
$631$	2.85115	0.113503	0.0567513	−	0.998388i	$-0.481926\pi$
$631$	2.85115	0.113503	0.0567513	+	0.998388i	$0.481926\pi$
$632$	24.9906	0.994071
$633$	17.6342	0.700897
$634$	−66.3368	−2.63457
$635$	17.8469	0.708231
$636$	−22.7160	−0.900746
$637$	−33.3896	−1.32294
$638$	−42.5782	−1.68569
$639$	8.96239	0.354547
$640$	11.8391	0.467980
$641$	−13.0862	−0.516874	−0.258437	−	0.966028i	$-0.583207\pi$
$641$	−13.0862	−0.516874	−0.258437	+	0.966028i	$0.583207\pi$
$642$	−28.1524	−1.11109
$643$	0.665047	0.0262269	0.0131134	−	0.999914i	$-0.495826\pi$
$643$	0.665047	0.0262269	0.0131134	+	0.999914i	$0.495826\pi$
$644$	0	0
$645$	7.13440	0.280917
$646$	−36.9897	−1.45534
$647$	23.1635	0.910651	0.455326	−	0.890325i	$-0.349523\pi$
$647$	23.1635	0.910651	0.455326	+	0.890325i	$0.349523\pi$
$648$	6.29379	0.247243
$649$	−17.6421	−0.692514
$650$	13.5956	0.533264
$651$	−2.38249	−0.0933772
$652$	46.5451	1.82285
$653$	43.8785	1.71710	0.858549	−	0.512732i	$-0.171366\pi$
$653$	43.8785	1.71710	0.858549	+	0.512732i	$0.171366\pi$
$654$	−10.7668	−0.421017
$655$	−4.56597	−0.178407
$656$	64.5188	2.51904
$657$	−12.9611	−0.505659
$658$	−8.31580	−0.324184
$659$	−28.5774	−1.11322	−0.556608	−	0.830775i	$-0.687898\pi$
$659$	−28.5774	−1.11322	−0.556608	+	0.830775i	$0.687898\pi$
$660$	−28.2953	−1.10139
$661$	−34.6930	−1.34940	−0.674700	−	0.738092i	$-0.735727\pi$
$661$	−34.6930	−1.34940	−0.674700	+	0.738092i	$0.735727\pi$
$662$	43.7319	1.69969
$663$	21.3280	0.828310
$664$	33.8299	1.31285
$665$	3.15720	0.122431
$666$	20.8962	0.809710
$667$	0	0
$668$	−105.457	−4.08025
$669$	−13.8725	−0.536341
$670$	−21.4087	−0.827090
$671$	−65.4580	−2.52698
$672$	4.67317	0.180271
$673$	10.7801	0.415543	0.207772	−	0.978177i	$-0.433379\pi$
$673$	10.7801	0.415543	0.207772	+	0.978177i	$0.433379\pi$
$674$	−13.9678	−0.538020
$675$	−1.00000	−0.0384900
$676$	69.5779	2.67607
$677$	11.2751	0.433338	0.216669	−	0.976245i	$-0.430481\pi$
$677$	11.2751	0.433338	0.216669	+	0.976245i	$0.430481\pi$
$678$	38.8963	1.49380
$679$	8.66229	0.332428
$680$	25.1210	0.963347
$681$	27.1429	1.04012
$682$	44.2321	1.69373
$683$	−30.2303	−1.15673	−0.578364	−	0.815779i	$-0.696309\pi$
$683$	−30.2303	−1.15673	−0.578364	+	0.815779i	$0.696309\pi$
$684$	16.2946	0.623039
$685$	1.97264	0.0753706
$686$	29.2191	1.11559
$687$	−7.54437	−0.287836
$688$	50.4133	1.92199
$689$	27.1328	1.03368
$690$	0	0
$691$	−12.2315	−0.465310	−0.232655	−	0.972559i	$-0.574741\pi$
$691$	−12.2315	−0.465310	−0.232655	+	0.972559i	$0.574741\pi$
$692$	41.5332	1.57885
$693$	5.48242	0.208260
$694$	−11.3715	−0.431657
$695$	−1.91783	−0.0727473
$696$	−16.6523	−0.631203
$697$	−36.4438	−1.38041
$698$	63.6623	2.40965
$699$	−6.24358	−0.236154
$700$	−3.87777	−0.146566
$701$	−27.5060	−1.03889	−0.519444	−	0.854504i	$-0.673861\pi$
$701$	−27.5060	−1.03889	−0.519444	+	0.854504i	$0.673861\pi$
$702$	−13.5956	−0.513134
$703$	29.9139	1.12823
$704$	2.62635	0.0989841
$705$	3.77059	0.142009
$706$	69.3122	2.60860
$707$	−1.47146	−0.0553398
$708$	−12.4785	−0.468969
$709$	38.6892	1.45300	0.726501	−	0.687165i	$-0.241145\pi$
$709$	38.6892	1.45300	0.726501	+	0.687165i	$0.241145\pi$
$710$	−22.8033	−0.855794
$711$	3.97067	0.148912
$712$	20.6588	0.774223
$713$	0	0
$714$	−8.80278	−0.329436
$715$	33.7969	1.26393
$716$	−77.8300	−2.90865
$717$	−11.8009	−0.440712
$718$	39.5354	1.47545
$719$	15.8215	0.590043	0.295021	−	0.955491i	$-0.404673\pi$
$719$	15.8215	0.590043	0.295021	+	0.955491i	$0.404673\pi$
$720$	−7.06623	−0.263343
$721$	−5.88317	−0.219101
$722$	−14.5874	−0.542888
$723$	22.2271	0.826635
$724$	87.8771	3.26593
$725$	2.64583	0.0982635
$726$	−73.7960	−2.73883
$727$	25.9988	0.964241	0.482120	−	0.876105i	$-0.339867\pi$
$727$	25.9988	0.964241	0.482120	+	0.876105i	$0.339867\pi$
$728$	−29.1513	−1.08042
$729$	1.00000	0.0370370
$730$	32.9773	1.22054
$731$	−28.4762	−1.05323
$732$	−46.2991	−1.71126
$733$	27.6722	1.02209	0.511047	−	0.859553i	$-0.329258\pi$
$733$	27.6722	1.02209	0.511047	+	0.859553i	$0.329258\pi$
$734$	−10.4871	−0.387086
$735$	−6.24865	−0.230485
$736$	0	0
$737$	−53.2191	−1.96035
$738$	23.2313	0.855156
$739$	43.2770	1.59197	0.795984	−	0.605317i	$-0.206954\pi$
$739$	43.2770	1.59197	0.795984	+	0.605317i	$0.206954\pi$
$740$	−36.7412	−1.35064
$741$	−19.4628	−0.714985
$742$	−11.1986	−0.411114
$743$	13.4755	0.494369	0.247185	−	0.968968i	$-0.420495\pi$
$743$	13.4755	0.494369	0.247185	+	0.968968i	$0.420495\pi$
$744$	17.2991	0.634216
$745$	6.85144	0.251017
$746$	28.2877	1.03569
$747$	5.37512	0.196665
$748$	112.938	4.12941
$749$	−9.59096	−0.350446
$750$	2.54434	0.0929060
$751$	−1.51514	−0.0552882	−0.0276441	−	0.999618i	$-0.508801\pi$
$751$	−1.51514	−0.0552882	−0.0276441	+	0.999618i	$0.508801\pi$
$752$	26.6438	0.971600
$753$	−3.32796	−0.121278
$754$	35.9716	1.31001
$755$	−5.38158	−0.195856
$756$	3.87777	0.141033
$757$	9.22852	0.335416	0.167708	−	0.985837i	$-0.446363\pi$
$757$	9.22852	0.335416	0.167708	+	0.985837i	$0.446363\pi$
$758$	8.24205	0.299365
$759$	0	0
$760$	−22.9242	−0.831548
$761$	27.5783	0.999713	0.499856	−	0.866108i	$-0.333386\pi$
$761$	27.5783	0.999713	0.499856	+	0.866108i	$0.333386\pi$
$762$	45.4084	1.64497
$763$	−3.66804	−0.132792
$764$	16.1341	0.583712
$765$	3.99140	0.144309
$766$	−60.0609	−2.17009
$767$	14.9047	0.538178
$768$	29.2921	1.05699
$769$	−20.2743	−0.731109	−0.365554	−	0.930790i	$-0.619121\pi$
$769$	−20.2743	−0.731109	−0.365554	+	0.930790i	$0.619121\pi$
$770$	−13.9491	−0.502691
$771$	−23.7897	−0.856766
$772$	102.138	3.67602
$773$	−3.68732	−0.132624	−0.0663119	−	0.997799i	$-0.521123\pi$
$773$	−3.68732	−0.132624	−0.0663119	+	0.997799i	$0.521123\pi$
$774$	18.1523	0.652471
$775$	−2.74860	−0.0987325
$776$	−62.8962	−2.25784
$777$	7.11889	0.255389
$778$	50.0558	1.79459
$779$	33.2568	1.19155
$780$	23.9049	0.855932
$781$	−56.6860	−2.02838
$782$	0	0
$783$	−2.64583	−0.0945541
$784$	−44.1544	−1.57694
$785$	−17.7539	−0.633665
$786$	−11.6174	−0.414378
$787$	−37.0159	−1.31947	−0.659737	−	0.751497i	$-0.729332\pi$
$787$	−37.0159	−1.31947	−0.659737	+	0.751497i	$0.729332\pi$
$788$	5.97870	0.212982
$789$	23.8691	0.849761
$790$	−10.1027	−0.359439
$791$	13.2512	0.471158
$792$	−39.8074	−1.41450
$793$	55.3013	1.96381
$794$	92.9068	3.29714
$795$	5.07773	0.180088
$796$	−39.9900	−1.41741
$797$	−5.58309	−0.197763	−0.0988815	−	0.995099i	$-0.531526\pi$
$797$	−5.58309	−0.197763	−0.0988815	+	0.995099i	$0.531526\pi$
$798$	8.03298	0.284364
$799$	−15.0499	−0.532428
$800$	5.39127	0.190610
$801$	3.28242	0.115978
$802$	−94.5126	−3.33735
$803$	81.9770	2.89291
$804$	−37.6424	−1.32755
$805$	0	0
$806$	−37.3689	−1.31626
$807$	3.99387	0.140591
$808$	10.6841	0.375866
$809$	−43.8578	−1.54196	−0.770980	−	0.636860i	$-0.780233\pi$
$809$	−43.8578	−1.54196	−0.770980	+	0.636860i	$0.780233\pi$
$810$	−2.54434	−0.0893989
$811$	−41.1974	−1.44664	−0.723318	−	0.690515i	$-0.757384\pi$
$811$	−41.1974	−1.44664	−0.723318	+	0.690515i	$0.757384\pi$
$812$	−10.2599	−0.360052
$813$	−1.59932	−0.0560906
$814$	−132.166	−4.63240
$815$	−10.4043	−0.364446
$816$	28.2041	0.987342
$817$	25.9860	0.909134
$818$	−55.1599	−1.92862
$819$	−4.63175	−0.161846
$820$	−40.8470	−1.42644
$821$	−27.0840	−0.945239	−0.472619	−	0.881267i	$-0.656691\pi$
$821$	−27.0840	−0.945239	−0.472619	+	0.881267i	$0.656691\pi$
$822$	5.01906	0.175060
$823$	39.3285	1.37091	0.685453	−	0.728117i	$-0.259604\pi$
$823$	39.3285	1.37091	0.685453	+	0.728117i	$0.259604\pi$
$824$	42.7173	1.48813
$825$	6.32487	0.220204
$826$	−6.15169	−0.214045
$827$	39.4189	1.37073	0.685365	−	0.728200i	$-0.259643\pi$
$827$	39.4189	1.37073	0.685365	+	0.728200i	$0.259643\pi$
$828$	0	0
$829$	23.0539	0.800694	0.400347	−	0.916364i	$-0.368890\pi$
$829$	23.0539	0.800694	0.400347	+	0.916364i	$0.368890\pi$
$830$	−13.6761	−0.474704
$831$	−2.32107	−0.0805169
$832$	−2.21883	−0.0769242
$833$	24.9409	0.864150
$834$	−4.87959	−0.168966
$835$	23.5729	0.815775
$836$	−103.061	−3.56445
$837$	2.74860	0.0950054
$838$	45.8838	1.58503
$839$	19.9294	0.688038	0.344019	−	0.938963i	$-0.388212\pi$
$839$	19.9294	0.688038	0.344019	+	0.938963i	$0.388212\pi$
$840$	−5.45548	−0.188232
$841$	−21.9996	−0.758607
$842$	−24.5734	−0.846855
$843$	−25.2750	−0.870518
$844$	−78.8893	−2.71548
$845$	−15.5528	−0.535034
$846$	9.59364	0.329836
$847$	−25.1408	−0.863847
$848$	35.8804	1.23214
$849$	−1.66304	−0.0570753
$850$	−10.1555	−0.348329
$851$	0	0
$852$	−40.0946	−1.37362
$853$	26.8795	0.920338	0.460169	−	0.887831i	$-0.347789\pi$
$853$	26.8795	0.920338	0.460169	+	0.887831i	$0.347789\pi$
$854$	−22.8247	−0.781047
$855$	−3.64235	−0.124566
$856$	69.6392	2.38022
$857$	19.8156	0.676890	0.338445	−	0.940986i	$-0.390099\pi$
$857$	19.8156	0.676890	0.338445	+	0.940986i	$0.390099\pi$
$858$	85.9906	2.93567
$859$	44.6864	1.52468	0.762340	−	0.647176i	$-0.224050\pi$
$859$	44.6864	1.52468	0.762340	+	0.647176i	$0.224050\pi$
$860$	−31.9168	−1.08835
$861$	7.91442	0.269723
$862$	−26.0427	−0.887016
$863$	−45.0451	−1.53335	−0.766677	−	0.642033i	$-0.778091\pi$
$863$	−45.0451	−1.53335	−0.766677	+	0.642033i	$0.778091\pi$
$864$	−5.39127	−0.183415
$865$	−9.28396	−0.315664
$866$	30.7900	1.04629
$867$	1.06874	0.0362962
$868$	10.6584	0.361771
$869$	−25.1140	−0.851934
$870$	6.73187	0.228232
$871$	44.9615	1.52346
$872$	26.6334	0.901920
$873$	−9.99338	−0.338225
$874$	0	0
$875$	0.866803	0.0293033
$876$	57.9832	1.95907
$877$	−11.9982	−0.405152	−0.202576	−	0.979267i	$-0.564931\pi$
$877$	−11.9982	−0.405152	−0.202576	+	0.979267i	$0.564931\pi$
$878$	21.8777	0.738337
$879$	9.67926	0.326473
$880$	44.6930	1.50660
$881$	21.3046	0.717772	0.358886	−	0.933381i	$-0.383157\pi$
$881$	21.3046	0.717772	0.358886	+	0.933381i	$0.383157\pi$
$882$	−15.8987	−0.535336
$883$	−52.5686	−1.76907	−0.884537	−	0.466469i	$-0.845526\pi$
$883$	−52.5686	−1.76907	−0.884537	+	0.466469i	$0.845526\pi$
$884$	−95.4139	−3.20912
$885$	2.78933	0.0937622
$886$	−31.7123	−1.06540
$887$	0.314962	0.0105754	0.00528769	−	0.999986i	$-0.498317\pi$
$887$	0.314962	0.0105754	0.00528769	+	0.999986i	$0.498317\pi$
$888$	−51.6897	−1.73459
$889$	15.4697	0.518837
$890$	−8.35157	−0.279945
$891$	−6.32487	−0.211891
$892$	62.0606	2.07794
$893$	13.7338	0.459584
$894$	17.4324	0.583026
$895$	17.3974	0.581533
$896$	10.2621	0.342834
$897$	0	0
$898$	−54.9651	−1.83421
$899$	−7.27231	−0.242545
$900$	4.47365	0.149122
$901$	−20.2672	−0.675199
$902$	−146.935	−4.89240
$903$	6.18412	0.205795
$904$	−96.2158	−3.20009
$905$	−19.6433	−0.652965
$906$	−13.6925	−0.454904
$907$	−14.9981	−0.498005	−0.249003	−	0.968503i	$-0.580103\pi$
$907$	−14.9981	−0.498005	−0.249003	+	0.968503i	$0.580103\pi$
$908$	−121.428	−4.02973
$909$	1.69757	0.0563047
$910$	11.7847	0.390660
$911$	−5.04107	−0.167018	−0.0835090	−	0.996507i	$-0.526613\pi$
$911$	−5.04107	−0.167018	−0.0835090	+	0.996507i	$0.526613\pi$
$912$	−25.7377	−0.852259
$913$	−33.9969	−1.12513
$914$	2.08140	0.0688465
$915$	10.3493	0.342137
$916$	33.7509	1.11516
$917$	−3.95780	−0.130698
$918$	10.1555	0.335180
$919$	−16.4249	−0.541808	−0.270904	−	0.962606i	$-0.587323\pi$
$919$	−16.4249	−0.541808	−0.270904	+	0.962606i	$0.587323\pi$
$920$	0	0
$921$	−0.0356551	−0.00117488
$922$	99.0627	3.26246
$923$	47.8904	1.57633
$924$	−24.5264	−0.806860
$925$	8.21282	0.270036
$926$	−76.1206	−2.50148
$927$	6.78721	0.222921
$928$	14.2644	0.468251
$929$	46.6336	1.53000	0.765000	−	0.644030i	$-0.222739\pi$
$929$	46.6336	1.53000	0.765000	+	0.644030i	$0.222739\pi$
$930$	−6.99336	−0.229321
$931$	−22.7598	−0.745922
$932$	27.9316	0.914929
$933$	−2.65831	−0.0870293
$934$	−96.0871	−3.14407
$935$	−25.2451	−0.825603
$936$	33.6308	1.09926
$937$	9.06351	0.296092	0.148046	−	0.988980i	$-0.452702\pi$
$937$	9.06351	0.296092	0.148046	+	0.988980i	$0.452702\pi$
$938$	−18.5571	−0.605912
$939$	−8.22425	−0.268388
$940$	−16.8683	−0.550183
$941$	−21.2233	−0.691858	−0.345929	−	0.938261i	$-0.612436\pi$
$941$	−21.2233	−0.691858	−0.345929	+	0.938261i	$0.612436\pi$
$942$	−45.1720	−1.47178
$943$	0	0
$944$	19.7100	0.641506
$945$	−0.866803	−0.0281971
$946$	−114.811	−3.73283
$947$	−35.9091	−1.16689	−0.583444	−	0.812153i	$-0.698295\pi$
$947$	−35.9091	−1.16689	−0.583444	+	0.812153i	$0.698295\pi$
$948$	−17.7634	−0.576928
$949$	−69.2572	−2.24818
$950$	9.26736	0.300673
$951$	26.0724	0.845454
$952$	21.7750	0.705731
$953$	−31.7483	−1.02843	−0.514214	−	0.857662i	$-0.671916\pi$
$953$	−31.7483	−1.02843	−0.514214	+	0.857662i	$0.671916\pi$
$954$	12.9194	0.418282
$955$	−3.60648	−0.116703
$956$	52.7930	1.70745
$957$	16.7345	0.540950
$958$	32.9614	1.06494
$959$	1.70989	0.0552152
$960$	−0.415241	−0.0134018
$961$	−23.4452	−0.756297
$962$	111.658	3.60001
$963$	11.0647	0.356557
$964$	−99.4362	−3.20262
$965$	−22.8310	−0.734956
$966$	0	0
$967$	−37.6883	−1.21197	−0.605987	−	0.795474i	$-0.707222\pi$
$967$	−37.6883	−1.21197	−0.605987	+	0.795474i	$0.707222\pi$
$968$	182.545	5.86723
$969$	14.5381	0.467030
$970$	25.4265	0.816396
$971$	−48.3021	−1.55009	−0.775045	−	0.631907i	$-0.782273\pi$
$971$	−48.3021	−1.55009	−0.775045	+	0.631907i	$0.782273\pi$
$972$	−4.47365	−0.143492
$973$	−1.66238	−0.0532934
$974$	21.8052	0.698684
$975$	−5.34349	−0.171128
$976$	73.1305	2.34085
$977$	32.7312	1.04717	0.523583	−	0.851975i	$-0.324595\pi$
$977$	32.7312	1.04717	0.523583	+	0.851975i	$0.324595\pi$
$978$	−26.4720	−0.846481
$979$	−20.7609	−0.663520
$980$	27.9543	0.892966
$981$	4.23169	0.135108
$982$	−35.1262	−1.12092
$983$	−0.876031	−0.0279411	−0.0139705	−	0.999902i	$-0.504447\pi$
$983$	−0.876031	−0.0279411	−0.0139705	+	0.999902i	$0.504447\pi$
$984$	−57.4660	−1.83195
$985$	−1.33643	−0.0425821
$986$	−26.8696	−0.855701
$987$	3.26836	0.104033
$988$	87.0699	2.77006
$989$	0	0
$990$	16.0926	0.511457
$991$	10.7895	0.342738	0.171369	−	0.985207i	$-0.445181\pi$
$991$	10.7895	0.342738	0.171369	+	0.985207i	$0.445181\pi$
$992$	−14.8184	−0.470486
$993$	−17.1880	−0.545443
$994$	−19.7660	−0.626939
$995$	8.93902	0.283386
$996$	−24.0464	−0.761938
$997$	−22.1987	−0.703041	−0.351520	−	0.936180i	$-0.614335\pi$
$997$	−22.1987	−0.703041	−0.351520	+	0.936180i	$0.614335\pi$
$998$	−112.353	−3.55646
$999$	−8.21282	−0.259842

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bt.1.23		25
23.7	odd	22		345.2.m.d.256.1	yes	50
23.10	odd	22		345.2.m.d.31.1	✓	50
23.22	odd	2		7935.2.a.bu.1.23		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.31.1	✓	50	23.10	odd	22
345.2.m.d.256.1	yes	50	23.7	odd	22
7935.2.a.bt.1.23		25	1.1	even	1	trivial
7935.2.a.bu.1.23		25	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+2.54434 q^{2} -1.00000 q^{3} +4.47365 q^{4} -1.00000 q^{5} -2.54434 q^{6} -0.866803 q^{7} +6.29379 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.54434 q^{2} -1.00000 q^{3} +4.47365 q^{4} -1.00000 q^{5} -2.54434 q^{6} -0.866803 q^{7} +6.29379 q^{8} +1.00000 q^{9} -2.54434 q^{10} -6.32487 q^{11} -4.47365 q^{12} +5.34349 q^{13} -2.20544 q^{14} +1.00000 q^{15} +7.06623 q^{16} -3.99140 q^{17} +2.54434 q^{18} +3.64235 q^{19} -4.47365 q^{20} +0.866803 q^{21} -16.0926 q^{22} -6.29379 q^{24} +1.00000 q^{25} +13.5956 q^{26} -1.00000 q^{27} -3.87777 q^{28} +2.64583 q^{29} +2.54434 q^{30} -2.74860 q^{31} +5.39127 q^{32} +6.32487 q^{33} -10.1555 q^{34} +0.866803 q^{35} +4.47365 q^{36} +8.21282 q^{37} +9.26736 q^{38} -5.34349 q^{39} -6.29379 q^{40} +9.13059 q^{41} +2.20544 q^{42} +7.13440 q^{43} -28.2953 q^{44} -1.00000 q^{45} +3.77059 q^{47} -7.06623 q^{48} -6.24865 q^{49} +2.54434 q^{50} +3.99140 q^{51} +23.9049 q^{52} +5.07773 q^{53} -2.54434 q^{54} +6.32487 q^{55} -5.45548 q^{56} -3.64235 q^{57} +6.73187 q^{58} +2.78933 q^{59} +4.47365 q^{60} +10.3493 q^{61} -6.99336 q^{62} -0.866803 q^{63} -0.415241 q^{64} -5.34349 q^{65} +16.0926 q^{66} +8.41426 q^{67} -17.8561 q^{68} +2.20544 q^{70} +8.96239 q^{71} +6.29379 q^{72} -12.9611 q^{73} +20.8962 q^{74} -1.00000 q^{75} +16.2946 q^{76} +5.48242 q^{77} -13.5956 q^{78} +3.97067 q^{79} -7.06623 q^{80} +1.00000 q^{81} +23.2313 q^{82} +5.37512 q^{83} +3.87777 q^{84} +3.99140 q^{85} +18.1523 q^{86} -2.64583 q^{87} -39.8074 q^{88} +3.28242 q^{89} -2.54434 q^{90} -4.63175 q^{91} +2.74860 q^{93} +9.59364 q^{94} -3.64235 q^{95} -5.39127 q^{96} -9.99338 q^{97} -15.8987 q^{98} -6.32487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} - 25 q^{5} - q^{6} + 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 - 25 * q^5 - q^6 + 15 * q^7 + 3 * q^8 + 25 * q^9	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} - 25 q^{5} - q^{6} + 15 q^{7} + 3 q^{8} + 25 q^{9} - q^{10} - 15 q^{11} - 31 q^{12} + 24 q^{13} - 5 q^{14} + 25 q^{15} + 39 q^{16} + 6 q^{17} + q^{18} - 13 q^{19} - 31 q^{20} - 15 q^{21} + 21 q^{22} - 3 q^{24} + 25 q^{25} + 21 q^{26} - 25 q^{27} + 41 q^{28} + q^{29} + q^{30} + 18 q^{31} + 17 q^{32} + 15 q^{33} - 7 q^{34} - 15 q^{35} + 31 q^{36} + 8 q^{37} - 15 q^{38} - 24 q^{39} - 3 q^{40} + 36 q^{41} + 5 q^{42} + 36 q^{43} - 90 q^{44} - 25 q^{45} + 11 q^{47} - 39 q^{48} + 92 q^{49} + q^{50} - 6 q^{51} + 35 q^{52} - 6 q^{53} - q^{54} + 15 q^{55} - 15 q^{56} + 13 q^{57} + 42 q^{58} - 3 q^{59} + 31 q^{60} - 71 q^{61} - 7 q^{62} + 15 q^{63} + 47 q^{64} - 24 q^{65} - 21 q^{66} + 10 q^{67} + 23 q^{68} + 5 q^{70} - 18 q^{71} + 3 q^{72} + 83 q^{73} - 67 q^{74} - 25 q^{75} + 12 q^{76} + 27 q^{77} - 21 q^{78} - 33 q^{79} - 39 q^{80} + 25 q^{81} + 49 q^{82} + 2 q^{83} - 41 q^{84} - 6 q^{85} + 35 q^{86} - q^{87} + 33 q^{88} - 11 q^{89} - q^{90} - 28 q^{91} - 18 q^{93} + 80 q^{94} + 13 q^{95} - 17 q^{96} + 48 q^{97} + 4 q^{98} - 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 - 25 * q^5 - q^6 + 15 * q^7 + 3 * q^8 + 25 * q^9 - q^10 - 15 * q^11 - 31 * q^12 + 24 * q^13 - 5 * q^14 + 25 * q^15 + 39 * q^16 + 6 * q^17 + q^18 - 13 * q^19 - 31 * q^20 - 15 * q^21 + 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 + 41 * q^28 + q^29 + q^30 + 18 * q^31 + 17 * q^32 + 15 * q^33 - 7 * q^34 - 15 * q^35 + 31 * q^36 + 8 * q^37 - 15 * q^38 - 24 * q^39 - 3 * q^40 + 36 * q^41 + 5 * q^42 + 36 * q^43 - 90 * q^44 - 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 - 6 * q^51 + 35 * q^52 - 6 * q^53 - q^54 + 15 * q^55 - 15 * q^56 + 13 * q^57 + 42 * q^58 - 3 * q^59 + 31 * q^60 - 71 * q^61 - 7 * q^62 + 15 * q^63 + 47 * q^64 - 24 * q^65 - 21 * q^66 + 10 * q^67 + 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 - 67 * q^74 - 25 * q^75 + 12 * q^76 + 27 * q^77 - 21 * q^78 - 33 * q^79 - 39 * q^80 + 25 * q^81 + 49 * q^82 + 2 * q^83 - 41 * q^84 - 6 * q^85 + 35 * q^86 - q^87 + 33 * q^88 - 11 * q^89 - q^90 - 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 + 48 * q^97 + 4 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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