LMFDB - Embedded newform 7935.2.a.br.1.10

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:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 24 x^{14} + 228 x^{12} - 4 x^{11} - 1098 x^{10} + 56 x^{9} + 2836 x^{8} - 276 x^{7} - 3812 x^{6} + \cdots + 64 $ x^16 - 24x^14 + 228x^12 - 4x^11 - 1098x^10 + 56x^9 + 2836x^8 - 276x^7 - 3812x^6 + 552x^5 + 2414x^4 - 368x^3 - 656x^2 + 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.497130$ of defining polynomial
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)

$f(q)$	$=$	$q+0.497130 q^{2} -1.00000 q^{3} -1.75286 q^{4} -1.00000 q^{5} -0.497130 q^{6} -2.87397 q^{7} -1.86566 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.497130 q^{2} -1.00000 q^{3} -1.75286 q^{4} -1.00000 q^{5} -0.497130 q^{6} -2.87397 q^{7} -1.86566 q^{8} +1.00000 q^{9} -0.497130 q^{10} -2.59009 q^{11} +1.75286 q^{12} -6.61858 q^{13} -1.42874 q^{14} +1.00000 q^{15} +2.57825 q^{16} +0.503290 q^{17} +0.497130 q^{18} +5.19703 q^{19} +1.75286 q^{20} +2.87397 q^{21} -1.28761 q^{22} +1.86566 q^{24} +1.00000 q^{25} -3.29030 q^{26} -1.00000 q^{27} +5.03767 q^{28} -4.57425 q^{29} +0.497130 q^{30} +5.90553 q^{31} +5.01304 q^{32} +2.59009 q^{33} +0.250200 q^{34} +2.87397 q^{35} -1.75286 q^{36} +8.53682 q^{37} +2.58360 q^{38} +6.61858 q^{39} +1.86566 q^{40} +12.2116 q^{41} +1.42874 q^{42} -1.21043 q^{43} +4.54007 q^{44} -1.00000 q^{45} +6.34526 q^{47} -2.57825 q^{48} +1.25970 q^{49} +0.497130 q^{50} -0.503290 q^{51} +11.6015 q^{52} +5.05791 q^{53} -0.497130 q^{54} +2.59009 q^{55} +5.36185 q^{56} -5.19703 q^{57} -2.27400 q^{58} +4.58658 q^{59} -1.75286 q^{60} -0.573068 q^{61} +2.93582 q^{62} -2.87397 q^{63} -2.66436 q^{64} +6.61858 q^{65} +1.28761 q^{66} -11.6925 q^{67} -0.882198 q^{68} +1.42874 q^{70} -7.35740 q^{71} -1.86566 q^{72} -4.52924 q^{73} +4.24391 q^{74} -1.00000 q^{75} -9.10967 q^{76} +7.44383 q^{77} +3.29030 q^{78} -2.46505 q^{79} -2.57825 q^{80} +1.00000 q^{81} +6.07075 q^{82} +1.03482 q^{83} -5.03767 q^{84} -0.503290 q^{85} -0.601741 q^{86} +4.57425 q^{87} +4.83222 q^{88} -10.4358 q^{89} -0.497130 q^{90} +19.0216 q^{91} -5.90553 q^{93} +3.15442 q^{94} -5.19703 q^{95} -5.01304 q^{96} +7.39802 q^{97} +0.626235 q^{98} -2.59009 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} + 16 q^{4} - 16 q^{5} - 12 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^3 + 16 * q^4 - 16 * q^5 - 12 * q^7 + 16 * q^9	$ 16 q - 16 q^{3} + 16 q^{4} - 16 q^{5} - 12 q^{7} + 16 q^{9} + 8 q^{11} - 16 q^{12} - 8 q^{13} + 16 q^{15} + 16 q^{16} - 20 q^{17} - 16 q^{19} - 16 q^{20} + 12 q^{21} - 16 q^{22} + 16 q^{25} + 20 q^{26} - 16 q^{27} + 16 q^{28} + 40 q^{29} + 16 q^{31} - 20 q^{32} - 8 q^{33} - 16 q^{34} + 12 q^{35} + 16 q^{36} - 28 q^{37} - 56 q^{38} + 8 q^{39} + 12 q^{41} - 4 q^{43} + 48 q^{44} - 16 q^{45} - 20 q^{47} - 16 q^{48} + 20 q^{49} + 20 q^{51} - 36 q^{52} - 4 q^{53} - 8 q^{55} + 8 q^{56} + 16 q^{57} - 16 q^{58} + 20 q^{59} + 16 q^{60} - 32 q^{61} + 28 q^{62} - 12 q^{63} + 28 q^{64} + 8 q^{65} + 16 q^{66} - 4 q^{67} + 24 q^{68} + 24 q^{71} - 36 q^{73} + 100 q^{74} - 16 q^{75} - 88 q^{76} + 4 q^{77} - 20 q^{78} - 24 q^{79} - 16 q^{80} + 16 q^{81} - 20 q^{82} - 44 q^{83} - 16 q^{84} + 20 q^{85} - 52 q^{86} - 40 q^{87} - 48 q^{88} - 16 q^{89} - 24 q^{91} - 16 q^{93} - 20 q^{94} + 16 q^{95} + 20 q^{96} - 64 q^{97} + 4 q^{98} + 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^3 + 16 * q^4 - 16 * q^5 - 12 * q^7 + 16 * q^9 + 8 * q^11 - 16 * q^12 - 8 * q^13 + 16 * q^15 + 16 * q^16 - 20 * q^17 - 16 * q^19 - 16 * q^20 + 12 * q^21 - 16 * q^22 + 16 * q^25 + 20 * q^26 - 16 * q^27 + 16 * q^28 + 40 * q^29 + 16 * q^31 - 20 * q^32 - 8 * q^33 - 16 * q^34 + 12 * q^35 + 16 * q^36 - 28 * q^37 - 56 * q^38 + 8 * q^39 + 12 * q^41 - 4 * q^43 + 48 * q^44 - 16 * q^45 - 20 * q^47 - 16 * q^48 + 20 * q^49 + 20 * q^51 - 36 * q^52 - 4 * q^53 - 8 * q^55 + 8 * q^56 + 16 * q^57 - 16 * q^58 + 20 * q^59 + 16 * q^60 - 32 * q^61 + 28 * q^62 - 12 * q^63 + 28 * q^64 + 8 * q^65 + 16 * q^66 - 4 * q^67 + 24 * q^68 + 24 * q^71 - 36 * q^73 + 100 * q^74 - 16 * q^75 - 88 * q^76 + 4 * q^77 - 20 * q^78 - 24 * q^79 - 16 * q^80 + 16 * q^81 - 20 * q^82 - 44 * q^83 - 16 * q^84 + 20 * q^85 - 52 * q^86 - 40 * q^87 - 48 * q^88 - 16 * q^89 - 24 * q^91 - 16 * q^93 - 20 * q^94 + 16 * q^95 + 20 * q^96 - 64 * q^97 + 4 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.497130	0.351524	0.175762	−	0.984433i	$-0.443761\pi$
$2$	0.497130	0.351524	0.175762	+	0.984433i	$0.443761\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.75286	−0.876431
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.497130	−0.202952
$7$	−2.87397	−1.08626	−0.543129	−	0.839649i	$-0.682761\pi$
$7$	−2.87397	−1.08626	−0.543129	+	0.839649i	$0.682761\pi$
$8$	−1.86566	−0.659610
$9$	1.00000	0.333333
$10$	−0.497130	−0.157206
$11$	−2.59009	−0.780941	−0.390471	−	0.920615i	$-0.627688\pi$
$11$	−2.59009	−0.780941	−0.390471	+	0.920615i	$0.627688\pi$
$12$	1.75286	0.506008
$13$	−6.61858	−1.83566	−0.917832	−	0.396969i	$-0.870062\pi$
$13$	−6.61858	−1.83566	−0.917832	+	0.396969i	$0.870062\pi$
$14$	−1.42874	−0.381846
$15$	1.00000	0.258199
$16$	2.57825	0.644562
$17$	0.503290	0.122066	0.0610329	−	0.998136i	$-0.480561\pi$
$17$	0.503290	0.122066	0.0610329	+	0.998136i	$0.480561\pi$
$18$	0.497130	0.117175
$19$	5.19703	1.19228	0.596140	−	0.802881i	$-0.296700\pi$
$19$	5.19703	1.19228	0.596140	+	0.802881i	$0.296700\pi$
$20$	1.75286	0.391952
$21$	2.87397	0.627152
$22$	−1.28761	−0.274520
$23$	0	0
$23$	0	0
$24$	1.86566	0.380826
$25$	1.00000	0.200000
$26$	−3.29030	−0.645280
$27$	−1.00000	−0.192450
$28$	5.03767	0.952030
$29$	−4.57425	−0.849418	−0.424709	−	0.905330i	$-0.639624\pi$
$29$	−4.57425	−0.849418	−0.424709	+	0.905330i	$0.639624\pi$
$30$	0.497130	0.0907631
$31$	5.90553	1.06066	0.530332	−	0.847790i	$-0.322067\pi$
$31$	5.90553	1.06066	0.530332	+	0.847790i	$0.322067\pi$
$32$	5.01304	0.886189
$33$	2.59009	0.450877
$34$	0.250200	0.0429090
$35$	2.87397	0.485789
$36$	−1.75286	−0.292144
$37$	8.53682	1.40345	0.701723	−	0.712450i	$-0.252415\pi$
$37$	8.53682	1.40345	0.701723	+	0.712450i	$0.252415\pi$
$38$	2.58360	0.419115
$39$	6.61858	1.05982
$40$	1.86566	0.294987
$41$	12.2116	1.90713	0.953565	−	0.301187i	$-0.0973827\pi$
$41$	12.2116	1.90713	0.953565	+	0.301187i	$0.0973827\pi$
$42$	1.42874	0.220459
$43$	−1.21043	−0.184589	−0.0922944	−	0.995732i	$-0.529420\pi$
$43$	−1.21043	−0.184589	−0.0922944	+	0.995732i	$0.529420\pi$
$44$	4.54007	0.684441
$45$	−1.00000	−0.149071
$46$	0	0
$47$	6.34526	0.925552	0.462776	−	0.886475i	$-0.346853\pi$
$47$	6.34526	0.925552	0.462776	+	0.886475i	$0.346853\pi$
$48$	−2.57825	−0.372138
$49$	1.25970	0.179957
$50$	0.497130	0.0703048
$51$	−0.503290	−0.0704747
$52$	11.6015	1.60883
$53$	5.05791	0.694757	0.347379	−	0.937725i	$-0.387072\pi$
$53$	5.05791	0.694757	0.347379	+	0.937725i	$0.387072\pi$
$54$	−0.497130	−0.0676508
$55$	2.59009	0.349247
$56$	5.36185	0.716507
$57$	−5.19703	−0.688363
$58$	−2.27400	−0.298591
$59$	4.58658	0.597122	0.298561	−	0.954391i	$-0.403493\pi$
$59$	4.58658	0.597122	0.298561	+	0.954391i	$0.403493\pi$
$60$	−1.75286	−0.226293
$61$	−0.573068	−0.0733738	−0.0366869	−	0.999327i	$-0.511680\pi$
$61$	−0.573068	−0.0733738	−0.0366869	+	0.999327i	$0.511680\pi$
$62$	2.93582	0.372849
$63$	−2.87397	−0.362086
$64$	−2.66436	−0.333045
$65$	6.61858	0.820934
$66$	1.28761	0.158494
$67$	−11.6925	−1.42846	−0.714231	−	0.699910i	$-0.753224\pi$
$67$	−11.6925	−1.42846	−0.714231	+	0.699910i	$0.753224\pi$
$68$	−0.882198	−0.106982
$69$	0	0
$70$	1.42874	0.170767
$71$	−7.35740	−0.873163	−0.436582	−	0.899665i	$-0.643811\pi$
$71$	−7.35740	−0.873163	−0.436582	+	0.899665i	$0.643811\pi$
$72$	−1.86566	−0.219870
$73$	−4.52924	−0.530107	−0.265054	−	0.964234i	$-0.585390\pi$
$73$	−4.52924	−0.530107	−0.265054	+	0.964234i	$0.585390\pi$
$74$	4.24391	0.493345
$75$	−1.00000	−0.115470
$76$	−9.10967	−1.04495
$77$	7.44383	0.848304
$78$	3.29030	0.372553
$79$	−2.46505	−0.277340	−0.138670	−	0.990339i	$-0.544283\pi$
$79$	−2.46505	−0.277340	−0.138670	+	0.990339i	$0.544283\pi$
$80$	−2.57825	−0.288257
$81$	1.00000	0.111111
$82$	6.07075	0.670402
$83$	1.03482	0.113586	0.0567930	−	0.998386i	$-0.481912\pi$
$83$	1.03482	0.113586	0.0567930	+	0.998386i	$0.481912\pi$
$84$	−5.03767	−0.549655
$85$	−0.503290	−0.0545894
$86$	−0.601741	−0.0648874
$87$	4.57425	0.490412
$88$	4.83222	0.515117
$89$	−10.4358	−1.10619	−0.553097	−	0.833117i	$-0.686554\pi$
$89$	−10.4358	−1.10619	−0.553097	+	0.833117i	$0.686554\pi$
$90$	−0.497130	−0.0524021
$91$	19.0216	1.99401
$92$	0	0
$93$	−5.90553	−0.612375
$94$	3.15442	0.325354
$95$	−5.19703	−0.533204
$96$	−5.01304	−0.511642
$97$	7.39802	0.751155	0.375578	−	0.926791i	$-0.377444\pi$
$97$	7.39802	0.751155	0.375578	+	0.926791i	$0.377444\pi$
$98$	0.626235	0.0632593
$99$	−2.59009	−0.260314
$100$	−1.75286	−0.175286
$101$	2.99975	0.298486	0.149243	−	0.988801i	$-0.452316\pi$
$101$	2.99975	0.298486	0.149243	+	0.988801i	$0.452316\pi$
$102$	−0.250200	−0.0247735
$103$	7.48501	0.737520	0.368760	−	0.929525i	$-0.379782\pi$
$103$	7.48501	0.737520	0.368760	+	0.929525i	$0.379782\pi$
$104$	12.3480	1.21082
$105$	−2.87397	−0.280471
$106$	2.51444	0.244224
$107$	−14.6369	−1.41500	−0.707502	−	0.706711i	$-0.750178\pi$
$107$	−14.6369	−1.41500	−0.707502	+	0.706711i	$0.750178\pi$
$108$	1.75286	0.168669
$109$	−9.08906	−0.870574	−0.435287	−	0.900292i	$-0.643353\pi$
$109$	−9.08906	−0.870574	−0.435287	+	0.900292i	$0.643353\pi$
$110$	1.28761	0.122769
$111$	−8.53682	−0.810279
$112$	−7.40981	−0.700161
$113$	−17.0323	−1.60226	−0.801130	−	0.598490i	$-0.795768\pi$
$113$	−17.0323	−1.60226	−0.801130	+	0.598490i	$0.795768\pi$
$114$	−2.58360	−0.241976
$115$	0	0
$116$	8.01804	0.744456
$117$	−6.61858	−0.611888
$118$	2.28013	0.209903
$119$	−1.44644	−0.132595
$120$	−1.86566	−0.170311
$121$	−4.29144	−0.390131
$122$	−0.284889	−0.0257927
$123$	−12.2116	−1.10108
$124$	−10.3516	−0.929599
$125$	−1.00000	−0.0894427
$126$	−1.42874	−0.127282
$127$	−20.5805	−1.82623	−0.913113	−	0.407707i	$-0.866329\pi$
$127$	−20.5805	−1.82623	−0.913113	+	0.407707i	$0.866329\pi$
$128$	−11.3506	−1.00326
$129$	1.21043	0.106572
$130$	3.29030	0.288578
$131$	20.7015	1.80870	0.904351	−	0.426789i	$-0.140355\pi$
$131$	20.7015	1.80870	0.904351	+	0.426789i	$0.140355\pi$
$132$	−4.54007	−0.395162
$133$	−14.9361	−1.29512
$134$	−5.81268	−0.502139
$135$	1.00000	0.0860663
$136$	−0.938968	−0.0805158
$137$	9.34650	0.798526	0.399263	−	0.916837i	$-0.369266\pi$
$137$	9.34650	0.798526	0.399263	+	0.916837i	$0.369266\pi$
$138$	0	0
$139$	18.4545	1.56529	0.782646	−	0.622467i	$-0.213869\pi$
$139$	18.4545	1.56529	0.782646	+	0.622467i	$0.213869\pi$
$140$	−5.03767	−0.425761
$141$	−6.34526	−0.534368
$142$	−3.65759	−0.306938
$143$	17.1427	1.43355
$144$	2.57825	0.214854
$145$	4.57425	0.379871
$146$	−2.25162	−0.186345
$147$	−1.25970	−0.103898
$148$	−14.9639	−1.23002
$149$	19.6960	1.61356	0.806780	−	0.590851i	$-0.201208\pi$
$149$	19.6960	1.61356	0.806780	+	0.590851i	$0.201208\pi$
$150$	−0.497130	−0.0405905
$151$	13.0382	1.06103	0.530517	−	0.847674i	$-0.321998\pi$
$151$	13.0382	1.06103	0.530517	+	0.847674i	$0.321998\pi$
$152$	−9.69589	−0.786440
$153$	0.503290	0.0406886
$154$	3.70055	0.298199
$155$	−5.90553	−0.474343
$156$	−11.6015	−0.928860
$157$	9.84300	0.785557	0.392779	−	0.919633i	$-0.371514\pi$
$157$	9.84300	0.785557	0.392779	+	0.919633i	$0.371514\pi$
$158$	−1.22545	−0.0974916
$159$	−5.05791	−0.401118
$160$	−5.01304	−0.396316
$161$	0	0
$162$	0.497130	0.0390582
$163$	−3.98046	−0.311774	−0.155887	−	0.987775i	$-0.549824\pi$
$163$	−3.98046	−0.311774	−0.155887	+	0.987775i	$0.549824\pi$
$164$	−21.4052	−1.67147
$165$	−2.59009	−0.201638
$166$	0.514439	0.0399282
$167$	−4.11819	−0.318675	−0.159338	−	0.987224i	$-0.550936\pi$
$167$	−4.11819	−0.318675	−0.159338	+	0.987224i	$0.550936\pi$
$168$	−5.36185	−0.413676
$169$	30.8056	2.36966
$170$	−0.250200	−0.0191895
$171$	5.19703	0.397427
$172$	2.12172	0.161779
$173$	−4.30293	−0.327146	−0.163573	−	0.986531i	$-0.552302\pi$
$173$	−4.30293	−0.327146	−0.163573	+	0.986531i	$0.552302\pi$
$174$	2.27400	0.172391
$175$	−2.87397	−0.217252
$176$	−6.67789	−0.503365
$177$	−4.58658	−0.344749
$178$	−5.18796	−0.388854
$179$	−12.6046	−0.942108	−0.471054	−	0.882104i	$-0.656126\pi$
$179$	−12.6046	−0.942108	−0.471054	+	0.882104i	$0.656126\pi$
$180$	1.75286	0.130651
$181$	2.06236	0.153294	0.0766469	−	0.997058i	$-0.475579\pi$
$181$	2.06236	0.153294	0.0766469	+	0.997058i	$0.475579\pi$
$182$	9.45621	0.700941
$183$	0.573068	0.0423624
$184$	0	0
$185$	−8.53682	−0.627640
$186$	−2.93582	−0.215264
$187$	−1.30357	−0.0953261
$188$	−11.1224	−0.811182
$189$	2.87397	0.209051
$190$	−2.58360	−0.187434
$191$	−18.5827	−1.34460	−0.672298	−	0.740280i	$-0.734693\pi$
$191$	−18.5827	−1.34460	−0.672298	+	0.740280i	$0.734693\pi$
$192$	2.66436	0.192284
$193$	12.9570	0.932667	0.466334	−	0.884609i	$-0.345575\pi$
$193$	12.9570	0.932667	0.466334	+	0.884609i	$0.345575\pi$
$194$	3.67778	0.264049
$195$	−6.61858	−0.473966
$196$	−2.20808	−0.157720
$197$	22.6428	1.61323	0.806616	−	0.591076i	$-0.201297\pi$
$197$	22.6428	1.61323	0.806616	+	0.591076i	$0.201297\pi$
$198$	−1.28761	−0.0915065
$199$	21.7010	1.53834	0.769172	−	0.639042i	$-0.220669\pi$
$199$	21.7010	1.53834	0.769172	+	0.639042i	$0.220669\pi$
$200$	−1.86566	−0.131922
$201$	11.6925	0.824723
$202$	1.49127	0.104925
$203$	13.1463	0.922687
$204$	0.882198	0.0617662
$205$	−12.2116	−0.852895
$206$	3.72102	0.259256
$207$	0	0
$208$	−17.0643	−1.18320
$209$	−13.4608	−0.931100
$210$	−1.42874	−0.0985922
$211$	11.9776	0.824574	0.412287	−	0.911054i	$-0.364730\pi$
$211$	11.9776	0.824574	0.412287	+	0.911054i	$0.364730\pi$
$212$	−8.86582	−0.608907
$213$	7.35740	0.504121
$214$	−7.27645	−0.497408
$215$	1.21043	0.0825506
$216$	1.86566	0.126942
$217$	−16.9723	−1.15216
$218$	−4.51844	−0.306028
$219$	4.52924	0.306057
$220$	−4.54007	−0.306091
$221$	−3.33106	−0.224072
$222$	−4.24391	−0.284833
$223$	14.5627	0.975189	0.487595	−	0.873070i	$-0.337874\pi$
$223$	14.5627	0.975189	0.487595	+	0.873070i	$0.337874\pi$
$224$	−14.4073	−0.962631
$225$	1.00000	0.0666667
$226$	−8.46725	−0.563233
$227$	−3.89814	−0.258728	−0.129364	−	0.991597i	$-0.541294\pi$
$227$	−3.89814	−0.258728	−0.129364	+	0.991597i	$0.541294\pi$
$228$	9.10967	0.603303
$229$	0.850084	0.0561751	0.0280876	−	0.999605i	$-0.491058\pi$
$229$	0.850084	0.0561751	0.0280876	+	0.999605i	$0.491058\pi$
$230$	0	0
$231$	−7.44383	−0.489768
$232$	8.53400	0.560285
$233$	−26.8541	−1.75927	−0.879637	−	0.475646i	$-0.842214\pi$
$233$	−26.8541	−1.75927	−0.879637	+	0.475646i	$0.842214\pi$
$234$	−3.29030	−0.215093
$235$	−6.34526	−0.413919
$236$	−8.03965	−0.523336
$237$	2.46505	0.160122
$238$	−0.719069	−0.0466103
$239$	17.3701	1.12358	0.561788	−	0.827281i	$-0.310114\pi$
$239$	17.3701	1.12358	0.561788	+	0.827281i	$0.310114\pi$
$240$	2.57825	0.166425
$241$	−1.33337	−0.0858898	−0.0429449	−	0.999077i	$-0.513674\pi$
$241$	−1.33337	−0.0858898	−0.0429449	+	0.999077i	$0.513674\pi$
$242$	−2.13340	−0.137140
$243$	−1.00000	−0.0641500
$244$	1.00451	0.0643071
$245$	−1.25970	−0.0804793
$246$	−6.07075	−0.387057
$247$	−34.3970	−2.18863
$248$	−11.0177	−0.699625
$249$	−1.03482	−0.0655789
$250$	−0.497130	−0.0314413
$251$	−9.39767	−0.593176	−0.296588	−	0.955006i	$-0.595849\pi$
$251$	−9.39767	−0.593176	−0.296588	+	0.955006i	$0.595849\pi$
$252$	5.03767	0.317343
$253$	0	0
$254$	−10.2312	−0.641962
$255$	0.503290	0.0315172
$256$	−0.314014	−0.0196259
$257$	−7.48385	−0.466830	−0.233415	−	0.972377i	$-0.574990\pi$
$257$	−7.48385	−0.466830	−0.233415	+	0.972377i	$0.574990\pi$
$258$	0.601741	0.0374628
$259$	−24.5346	−1.52450
$260$	−11.6015	−0.719492
$261$	−4.57425	−0.283139
$262$	10.2914	0.635802
$263$	−23.6879	−1.46066	−0.730328	−	0.683096i	$-0.760633\pi$
$263$	−23.6879	−1.46066	−0.730328	+	0.683096i	$0.760633\pi$
$264$	−4.83222	−0.297403
$265$	−5.05791	−0.310705
$266$	−7.42518	−0.455267
$267$	10.4358	0.638662
$268$	20.4953	1.25195
$269$	−29.6221	−1.80609	−0.903045	−	0.429547i	$-0.858673\pi$
$269$	−29.6221	−1.80609	−0.903045	+	0.429547i	$0.858673\pi$
$270$	0.497130	0.0302544
$271$	3.69307	0.224338	0.112169	−	0.993689i	$-0.464220\pi$
$271$	3.69307	0.224338	0.112169	+	0.993689i	$0.464220\pi$
$272$	1.29761	0.0786789
$273$	−19.0216	−1.15124
$274$	4.64643	0.280701
$275$	−2.59009	−0.156188
$276$	0	0
$277$	−3.26430	−0.196133	−0.0980663	−	0.995180i	$-0.531266\pi$
$277$	−3.26430	−0.196133	−0.0980663	+	0.995180i	$0.531266\pi$
$278$	9.17430	0.550238
$279$	5.90553	0.353555
$280$	−5.36185	−0.320432
$281$	−20.5268	−1.22453	−0.612265	−	0.790653i	$-0.709741\pi$
$281$	−20.5268	−1.22453	−0.612265	+	0.790653i	$0.709741\pi$
$282$	−3.15442	−0.187843
$283$	−29.9308	−1.77920	−0.889601	−	0.456738i	$-0.849018\pi$
$283$	−29.9308	−1.77920	−0.889601	+	0.456738i	$0.849018\pi$
$284$	12.8965	0.765267
$285$	5.19703	0.307845
$286$	8.52216	0.503926
$287$	−35.0957	−2.07164
$288$	5.01304	0.295396
$289$	−16.7467	−0.985100
$290$	2.27400	0.133534
$291$	−7.39802	−0.433680
$292$	7.93913	0.464602
$293$	23.5660	1.37674	0.688371	−	0.725359i	$-0.258326\pi$
$293$	23.5660	1.37674	0.688371	+	0.725359i	$0.258326\pi$
$294$	−0.626235	−0.0365227
$295$	−4.58658	−0.267041
$296$	−15.9268	−0.925727
$297$	2.59009	0.150292
$298$	9.79148	0.567205
$299$	0	0
$300$	1.75286	0.101202
$301$	3.47874	0.200511
$302$	6.48168	0.372979
$303$	−2.99975	−0.172331
$304$	13.3992	0.768498
$305$	0.573068	0.0328138
$306$	0.250200	0.0143030
$307$	11.9053	0.679471	0.339736	−	0.940521i	$-0.389662\pi$
$307$	11.9053	0.679471	0.339736	+	0.940521i	$0.389662\pi$
$308$	−13.0480	−0.743480
$309$	−7.48501	−0.425807
$310$	−2.93582	−0.166743
$311$	5.28913	0.299919	0.149959	−	0.988692i	$-0.452086\pi$
$311$	5.28913	0.299919	0.149959	+	0.988692i	$0.452086\pi$
$312$	−12.3480	−0.699069
$313$	−26.7608	−1.51261	−0.756304	−	0.654221i	$-0.772997\pi$
$313$	−26.7608	−1.51261	−0.756304	+	0.654221i	$0.772997\pi$
$314$	4.89325	0.276142
$315$	2.87397	0.161930
$316$	4.32089	0.243069
$317$	21.3249	1.19773	0.598864	−	0.800851i	$-0.295619\pi$
$317$	21.3249	1.19773	0.598864	+	0.800851i	$0.295619\pi$
$318$	−2.51444	−0.141003
$319$	11.8477	0.663345
$320$	2.66436	0.148942
$321$	14.6369	0.816953
$322$	0	0
$323$	2.61561	0.145537
$324$	−1.75286	−0.0973812
$325$	−6.61858	−0.367133
$326$	−1.97881	−0.109596
$327$	9.08906	0.502626
$328$	−22.7827	−1.25796
$329$	−18.2361	−1.00539
$330$	−1.28761	−0.0708806
$331$	5.89341	0.323931	0.161966	−	0.986796i	$-0.448217\pi$
$331$	5.89341	0.323931	0.161966	+	0.986796i	$0.448217\pi$
$332$	−1.81389	−0.0995503
$333$	8.53682	0.467815
$334$	−2.04728	−0.112022
$335$	11.6925	0.638828
$336$	7.40981	0.404238
$337$	−5.31711	−0.289641	−0.144821	−	0.989458i	$-0.546261\pi$
$337$	−5.31711	−0.289641	−0.144821	+	0.989458i	$0.546261\pi$
$338$	15.3144	0.832993
$339$	17.0323	0.925066
$340$	0.882198	0.0478439
$341$	−15.2958	−0.828316
$342$	2.58360	0.139705
$343$	16.4974	0.890778
$344$	2.25825	0.121757
$345$	0	0
$346$	−2.13912	−0.115000
$347$	32.9230	1.76740	0.883699	−	0.468056i	$-0.155046\pi$
$347$	32.9230	1.76740	0.883699	+	0.468056i	$0.155046\pi$
$348$	−8.01804	−0.429812
$349$	6.94820	0.371929	0.185964	−	0.982556i	$-0.440459\pi$
$349$	6.94820	0.371929	0.185964	+	0.982556i	$0.440459\pi$
$350$	−1.42874	−0.0763692
$351$	6.61858	0.353274
$352$	−12.9842	−0.692062
$353$	18.3068	0.974372	0.487186	−	0.873298i	$-0.338023\pi$
$353$	18.3068	0.974372	0.487186	+	0.873298i	$0.338023\pi$
$354$	−2.28013	−0.121187
$355$	7.35740	0.390490
$356$	18.2925	0.969503
$357$	1.44644	0.0765537
$358$	−6.26610	−0.331174
$359$	−29.7389	−1.56956	−0.784779	−	0.619775i	$-0.787224\pi$
$359$	−29.7389	−1.56956	−0.784779	+	0.619775i	$0.787224\pi$
$360$	1.86566	0.0983289
$361$	8.00910	0.421531
$362$	1.02526	0.0538864
$363$	4.29144	0.225242
$364$	−33.3422	−1.74761
$365$	4.52924	0.237071
$366$	0.284889	0.0148914
$367$	0.721692	0.0376720	0.0188360	−	0.999823i	$-0.494004\pi$
$367$	0.721692	0.0376720	0.0188360	+	0.999823i	$0.494004\pi$
$368$	0	0
$369$	12.2116	0.635710
$370$	−4.24391	−0.220630
$371$	−14.5363	−0.754686
$372$	10.3516	0.536704
$373$	−15.4226	−0.798550	−0.399275	−	0.916831i	$-0.630738\pi$
$373$	−15.4226	−0.798550	−0.399275	+	0.916831i	$0.630738\pi$
$374$	−0.648041	−0.0335094
$375$	1.00000	0.0516398
$376$	−11.8381	−0.610504
$377$	30.2751	1.55925
$378$	1.42874	0.0734863
$379$	−28.2819	−1.45274	−0.726371	−	0.687303i	$-0.758794\pi$
$379$	−28.2819	−1.45274	−0.726371	+	0.687303i	$0.758794\pi$
$380$	9.10967	0.467316
$381$	20.5805	1.05437
$382$	−9.23802	−0.472658
$383$	−17.1584	−0.876753	−0.438377	−	0.898791i	$-0.644446\pi$
$383$	−17.1584	−0.876753	−0.438377	+	0.898791i	$0.644446\pi$
$384$	11.3506	0.579234
$385$	−7.44383	−0.379373
$386$	6.44133	0.327855
$387$	−1.21043	−0.0615296
$388$	−12.9677	−0.658336
$389$	26.2508	1.33097	0.665485	−	0.746411i	$-0.268225\pi$
$389$	26.2508	1.33097	0.665485	+	0.746411i	$0.268225\pi$
$390$	−3.29030	−0.166611
$391$	0	0
$392$	−2.35017	−0.118702
$393$	−20.7015	−1.04425
$394$	11.2564	0.567090
$395$	2.46505	0.124030
$396$	4.54007	0.228147
$397$	−17.5413	−0.880374	−0.440187	−	0.897906i	$-0.645088\pi$
$397$	−17.5413	−0.880374	−0.440187	+	0.897906i	$0.645088\pi$
$398$	10.7882	0.540765
$399$	14.9361	0.747740
$400$	2.57825	0.128912
$401$	−15.7526	−0.786649	−0.393325	−	0.919400i	$-0.628675\pi$
$401$	−15.7526	−0.786649	−0.393325	+	0.919400i	$0.628675\pi$
$402$	5.81268	0.289910
$403$	−39.0862	−1.94702
$404$	−5.25815	−0.261603
$405$	−1.00000	−0.0496904
$406$	6.53540	0.324347
$407$	−22.1111	−1.09601
$408$	0.938968	0.0464858
$409$	−0.734921	−0.0363395	−0.0181698	−	0.999835i	$-0.505784\pi$
$409$	−0.734921	−0.0363395	−0.0181698	+	0.999835i	$0.505784\pi$
$410$	−6.07075	−0.299813
$411$	−9.34650	−0.461029
$412$	−13.1202	−0.646385
$413$	−13.1817	−0.648629
$414$	0	0
$415$	−1.03482	−0.0507972
$416$	−33.1792	−1.62675
$417$	−18.4545	−0.903722
$418$	−6.69175	−0.327304
$419$	13.4427	0.656718	0.328359	−	0.944553i	$-0.393504\pi$
$419$	13.4427	0.656718	0.328359	+	0.944553i	$0.393504\pi$
$420$	5.03767	0.245813
$421$	8.33536	0.406240	0.203120	−	0.979154i	$-0.434892\pi$
$421$	8.33536	0.406240	0.203120	+	0.979154i	$0.434892\pi$
$422$	5.95444	0.289857
$423$	6.34526	0.308517
$424$	−9.43634	−0.458269
$425$	0.503290	0.0244131
$426$	3.65759	0.177211
$427$	1.64698	0.0797029
$428$	25.6565	1.24015
$429$	−17.1427	−0.827658
$430$	0.601741	0.0290185
$431$	39.4672	1.90107	0.950534	−	0.310620i	$-0.100537\pi$
$431$	39.4672	1.90107	0.950534	+	0.310620i	$0.100537\pi$
$432$	−2.57825	−0.124046
$433$	−18.6070	−0.894196	−0.447098	−	0.894485i	$-0.647543\pi$
$433$	−18.6070	−0.894196	−0.447098	+	0.894485i	$0.647543\pi$
$434$	−8.43744	−0.405010
$435$	−4.57425	−0.219319
$436$	15.9319	0.762998
$437$	0	0
$438$	2.25162	0.107587
$439$	−8.06653	−0.384995	−0.192497	−	0.981298i	$-0.561659\pi$
$439$	−8.06653	−0.384995	−0.192497	+	0.981298i	$0.561659\pi$
$440$	−4.83222	−0.230367
$441$	1.25970	0.0599857
$442$	−1.65597	−0.0787666
$443$	21.8243	1.03691	0.518453	−	0.855106i	$-0.326508\pi$
$443$	21.8243	1.03691	0.518453	+	0.855106i	$0.326508\pi$
$444$	14.9639	0.710154
$445$	10.4358	0.494705
$446$	7.23955	0.342802
$447$	−19.6960	−0.931590
$448$	7.65729	0.361773
$449$	30.5262	1.44062	0.720310	−	0.693653i	$-0.244000\pi$
$449$	30.5262	1.44062	0.720310	+	0.693653i	$0.244000\pi$
$450$	0.497130	0.0234349
$451$	−31.6291	−1.48936
$452$	29.8552	1.40427
$453$	−13.0382	−0.612588
$454$	−1.93788	−0.0909493
$455$	−19.0216	−0.891746
$456$	9.69589	0.454052
$457$	−13.4090	−0.627247	−0.313624	−	0.949547i	$-0.601543\pi$
$457$	−13.4090	−0.627247	−0.313624	+	0.949547i	$0.601543\pi$
$458$	0.422602	0.0197469
$459$	−0.503290	−0.0234916
$460$	0	0
$461$	−7.83140	−0.364745	−0.182372	−	0.983230i	$-0.558378\pi$
$461$	−7.83140	−0.364745	−0.182372	+	0.983230i	$0.558378\pi$
$462$	−3.70055	−0.172165
$463$	−8.95585	−0.416214	−0.208107	−	0.978106i	$-0.566730\pi$
$463$	−8.95585	−0.416214	−0.208107	+	0.978106i	$0.566730\pi$
$464$	−11.7936	−0.547502
$465$	5.90553	0.273862
$466$	−13.3500	−0.618427
$467$	−6.89568	−0.319094	−0.159547	−	0.987190i	$-0.551003\pi$
$467$	−6.89568	−0.319094	−0.159547	+	0.987190i	$0.551003\pi$
$468$	11.6015	0.536278
$469$	33.6038	1.55168
$470$	−3.15442	−0.145503
$471$	−9.84300	−0.453542
$472$	−8.55700	−0.393868
$473$	3.13512	0.144153
$474$	1.22545	0.0562868
$475$	5.19703	0.238456
$476$	2.53541	0.116210
$477$	5.05791	0.231586
$478$	8.63518	0.394964
$479$	7.74182	0.353733	0.176867	−	0.984235i	$-0.443404\pi$
$479$	7.74182	0.353733	0.176867	+	0.984235i	$0.443404\pi$
$480$	5.01304	0.228813
$481$	−56.5017	−2.57625
$482$	−0.662858	−0.0301923
$483$	0	0
$484$	7.52230	0.341923
$485$	−7.39802	−0.335927
$486$	−0.497130	−0.0225503
$487$	18.4742	0.837146	0.418573	−	0.908183i	$-0.362530\pi$
$487$	18.4742	0.837146	0.418573	+	0.908183i	$0.362530\pi$
$488$	1.06915	0.0483981
$489$	3.98046	0.180003
$490$	−0.626235	−0.0282904
$491$	13.1663	0.594186	0.297093	−	0.954849i	$-0.403983\pi$
$491$	13.1663	0.594186	0.297093	+	0.954849i	$0.403983\pi$
$492$	21.4052	0.965023
$493$	−2.30218	−0.103685
$494$	−17.0998	−0.769354
$495$	2.59009	0.116416
$496$	15.2259	0.683664
$497$	21.1450	0.948481
$498$	−0.514439	−0.0230526
$499$	41.3867	1.85272	0.926362	−	0.376634i	$-0.122918\pi$
$499$	41.3867	1.85272	0.926362	+	0.376634i	$0.122918\pi$
$500$	1.75286	0.0783904
$501$	4.11819	0.183987
$502$	−4.67186	−0.208515
$503$	−22.9462	−1.02312	−0.511561	−	0.859247i	$-0.670933\pi$
$503$	−22.9462	−1.02312	−0.511561	+	0.859247i	$0.670933\pi$
$504$	5.36185	0.238836
$505$	−2.99975	−0.133487
$506$	0	0
$507$	−30.8056	−1.36813
$508$	36.0748	1.60056
$509$	34.6674	1.53660	0.768302	−	0.640087i	$-0.221102\pi$
$509$	34.6674	1.53660	0.768302	+	0.640087i	$0.221102\pi$
$510$	0.250200	0.0110791
$511$	13.0169	0.575833
$512$	22.5451	0.996364
$513$	−5.19703	−0.229454
$514$	−3.72045	−0.164102
$515$	−7.48501	−0.329829
$516$	−2.12172	−0.0934034
$517$	−16.4348	−0.722801
$518$	−12.1969	−0.535900
$519$	4.30293	0.188878
$520$	−12.3480	−0.541497
$521$	−34.5245	−1.51254	−0.756272	−	0.654257i	$-0.772982\pi$
$521$	−34.5245	−1.51254	−0.756272	+	0.654257i	$0.772982\pi$
$522$	−2.27400	−0.0995302
$523$	16.6807	0.729395	0.364698	−	0.931126i	$-0.381172\pi$
$523$	16.6807	0.729395	0.364698	+	0.931126i	$0.381172\pi$
$524$	−36.2869	−1.58520
$525$	2.87397	0.125430
$526$	−11.7760	−0.513456
$527$	2.97219	0.129471
$528$	6.67789	0.290618
$529$	0	0
$530$	−2.51444	−0.109220
$531$	4.58658	0.199041
$532$	26.1809	1.13509
$533$	−80.8234	−3.50085
$534$	5.18796	0.224505
$535$	14.6369	0.632809
$536$	21.8142	0.942229
$537$	12.6046	0.543927
$538$	−14.7260	−0.634884
$539$	−3.26273	−0.140536
$540$	−1.75286	−0.0754312
$541$	2.20190	0.0946672	0.0473336	−	0.998879i	$-0.484928\pi$
$541$	2.20190	0.0946672	0.0473336	+	0.998879i	$0.484928\pi$
$542$	1.83594	0.0788603
$543$	−2.06236	−0.0885042
$544$	2.52301	0.108173
$545$	9.08906	0.389333
$546$	−9.45621	−0.404688
$547$	−6.26222	−0.267753	−0.133877	−	0.990998i	$-0.542743\pi$
$547$	−6.26222	−0.267753	−0.133877	+	0.990998i	$0.542743\pi$
$548$	−16.3831	−0.699853
$549$	−0.573068	−0.0244579
$550$	−1.28761	−0.0549039
$551$	−23.7725	−1.01274
$552$	0	0
$553$	7.08448	0.301263
$554$	−1.62278	−0.0689453
$555$	8.53682	0.362368
$556$	−32.3482	−1.37187
$557$	27.6813	1.17289	0.586446	−	0.809988i	$-0.300527\pi$
$557$	27.6813	1.17289	0.586446	+	0.809988i	$0.300527\pi$
$558$	2.93582	0.124283
$559$	8.01133	0.338843
$560$	7.40981	0.313121
$561$	1.30357	0.0550366
$562$	−10.2045	−0.430451
$563$	−12.1292	−0.511183	−0.255592	−	0.966785i	$-0.582270\pi$
$563$	−12.1292	−0.511183	−0.255592	+	0.966785i	$0.582270\pi$
$564$	11.1224	0.468336
$565$	17.0323	0.716553
$566$	−14.8795	−0.625432
$567$	−2.87397	−0.120695
$568$	13.7264	0.575948
$569$	−24.1665	−1.01311	−0.506556	−	0.862207i	$-0.669082\pi$
$569$	−24.1665	−1.01311	−0.506556	+	0.862207i	$0.669082\pi$
$570$	2.58360	0.108215
$571$	7.51587	0.314529	0.157265	−	0.987556i	$-0.449732\pi$
$571$	7.51587	0.314529	0.157265	+	0.987556i	$0.449732\pi$
$572$	−30.0488	−1.25640
$573$	18.5827	0.776303
$574$	−17.4471	−0.728230
$575$	0	0
$576$	−2.66436	−0.111015
$577$	−16.1382	−0.671844	−0.335922	−	0.941890i	$-0.609048\pi$
$577$	−16.1382	−0.671844	−0.335922	+	0.941890i	$0.609048\pi$
$578$	−8.32529	−0.346286
$579$	−12.9570	−0.538476
$580$	−8.01804	−0.332931
$581$	−2.97404	−0.123384
$582$	−3.67778	−0.152449
$583$	−13.1004	−0.542564
$584$	8.45002	0.349664
$585$	6.61858	0.273645
$586$	11.7154	0.483958
$587$	5.94862	0.245526	0.122763	−	0.992436i	$-0.460825\pi$
$587$	5.94862	0.245526	0.122763	+	0.992436i	$0.460825\pi$
$588$	2.20808	0.0910597
$589$	30.6912	1.26461
$590$	−2.28013	−0.0938714
$591$	−22.6428	−0.931400
$592$	22.0100	0.904607
$593$	20.9184	0.859018	0.429509	−	0.903063i	$-0.358687\pi$
$593$	20.9184	0.859018	0.429509	+	0.903063i	$0.358687\pi$
$594$	1.28761	0.0528313
$595$	1.44644	0.0592982
$596$	−34.5244	−1.41417
$597$	−21.7010	−0.888163
$598$	0	0
$599$	−19.1730	−0.783388	−0.391694	−	0.920096i	$-0.628111\pi$
$599$	−19.1730	−0.783388	−0.391694	+	0.920096i	$0.628111\pi$
$600$	1.86566	0.0761653
$601$	−32.4038	−1.32178	−0.660889	−	0.750483i	$-0.729821\pi$
$601$	−32.4038	−1.32178	−0.660889	+	0.750483i	$0.729821\pi$
$602$	1.72939	0.0704845
$603$	−11.6925	−0.476154
$604$	−22.8542	−0.929923
$605$	4.29144	0.174472
$606$	−1.49127	−0.0605785
$607$	−34.3804	−1.39546	−0.697728	−	0.716363i	$-0.745806\pi$
$607$	−34.3804	−1.39546	−0.697728	+	0.716363i	$0.745806\pi$
$608$	26.0529	1.05659
$609$	−13.1463	−0.532714
$610$	0.284889	0.0115348
$611$	−41.9966	−1.69900
$612$	−0.882198	−0.0356607
$613$	−21.7166	−0.877124	−0.438562	−	0.898701i	$-0.644512\pi$
$613$	−21.7166	−0.877124	−0.438562	+	0.898701i	$0.644512\pi$
$614$	5.91848	0.238850
$615$	12.2116	0.492419
$616$	−13.8877	−0.559550
$617$	26.1929	1.05448	0.527242	−	0.849715i	$-0.323226\pi$
$617$	26.1929	1.05448	0.527242	+	0.849715i	$0.323226\pi$
$618$	−3.72102	−0.149682
$619$	−32.4204	−1.30309	−0.651543	−	0.758612i	$-0.725878\pi$
$619$	−32.4204	−1.30309	−0.651543	+	0.758612i	$0.725878\pi$
$620$	10.3516	0.415729
$621$	0	0
$622$	2.62938	0.105429
$623$	29.9922	1.20161
$624$	17.0643	0.683120
$625$	1.00000	0.0400000
$626$	−13.3036	−0.531718
$627$	13.4608	0.537571
$628$	−17.2534	−0.688487
$629$	4.29650	0.171313
$630$	1.42874	0.0569222
$631$	−21.2671	−0.846628	−0.423314	−	0.905983i	$-0.639133\pi$
$631$	−21.2671	−0.846628	−0.423314	+	0.905983i	$0.639133\pi$
$632$	4.59894	0.182936
$633$	−11.9776	−0.476068
$634$	10.6013	0.421030
$635$	20.5805	0.816713
$636$	8.86582	0.351552
$637$	−8.33743	−0.330341
$638$	5.88986	0.233182
$639$	−7.35740	−0.291054
$640$	11.3506	0.448673
$641$	−27.7515	−1.09612	−0.548060	−	0.836439i	$-0.684633\pi$
$641$	−27.7515	−1.09612	−0.548060	+	0.836439i	$0.684633\pi$
$642$	7.27645	0.287178
$643$	−0.164158	−0.00647374	−0.00323687	−	0.999995i	$-0.501030\pi$
$643$	−0.164158	−0.00647374	−0.00323687	+	0.999995i	$0.501030\pi$
$644$	0	0
$645$	−1.21043	−0.0476606
$646$	1.30030	0.0511596
$647$	−10.2199	−0.401787	−0.200893	−	0.979613i	$-0.564384\pi$
$647$	−10.2199	−0.401787	−0.200893	+	0.979613i	$0.564384\pi$
$648$	−1.86566	−0.0732901
$649$	−11.8797	−0.466317
$650$	−3.29030	−0.129056
$651$	16.9723	0.665197
$652$	6.97720	0.273248
$653$	−37.7713	−1.47811	−0.739053	−	0.673647i	$-0.764727\pi$
$653$	−37.7713	−1.47811	−0.739053	+	0.673647i	$0.764727\pi$
$654$	4.51844	0.176685
$655$	−20.7015	−0.808876
$656$	31.4845	1.22926
$657$	−4.52924	−0.176702
$658$	−9.06571	−0.353418
$659$	38.4823	1.49906	0.749529	−	0.661972i	$-0.230280\pi$
$659$	38.4823	1.49906	0.749529	+	0.661972i	$0.230280\pi$
$660$	4.54007	0.176722
$661$	19.3574	0.752916	0.376458	−	0.926434i	$-0.377142\pi$
$661$	19.3574	0.752916	0.376458	+	0.926434i	$0.377142\pi$
$662$	2.92979	0.113870
$663$	3.33106	0.129368
$664$	−1.93062	−0.0749225
$665$	14.9361	0.579197
$666$	4.24391	0.164448
$667$	0	0
$668$	7.21862	0.279297
$669$	−14.5627	−0.563026
$670$	5.81268	0.224563
$671$	1.48430	0.0573006
$672$	14.4073	0.555775
$673$	43.8933	1.69196	0.845982	−	0.533212i	$-0.179015\pi$
$673$	43.8933	1.69196	0.845982	+	0.533212i	$0.179015\pi$
$674$	−2.64329	−0.101816
$675$	−1.00000	−0.0384900
$676$	−53.9980	−2.07685
$677$	21.0244	0.808035	0.404017	−	0.914751i	$-0.367614\pi$
$677$	21.0244	0.808035	0.404017	+	0.914751i	$0.367614\pi$
$678$	8.46725	0.325183
$679$	−21.2617	−0.815949
$680$	0.938968	0.0360078
$681$	3.89814	0.149377
$682$	−7.60402	−0.291173
$683$	−13.5615	−0.518916	−0.259458	−	0.965754i	$-0.583544\pi$
$683$	−13.5615	−0.518916	−0.259458	+	0.965754i	$0.583544\pi$
$684$	−9.10967	−0.348317
$685$	−9.34650	−0.357112
$686$	8.20138	0.313130
$687$	−0.850084	−0.0324327
$688$	−3.12079	−0.118979
$689$	−33.4762	−1.27534
$690$	0	0
$691$	−23.1516	−0.880727	−0.440363	−	0.897820i	$-0.645150\pi$
$691$	−23.1516	−0.880727	−0.440363	+	0.897820i	$0.645150\pi$
$692$	7.54244	0.286721
$693$	7.44383	0.282768
$694$	16.3670	0.621283
$695$	−18.4545	−0.700020
$696$	−8.53400	−0.323481
$697$	6.14597	0.232795
$698$	3.45416	0.130742
$699$	26.8541	1.01572
$700$	5.03767	0.190406
$701$	−25.5192	−0.963847	−0.481924	−	0.876213i	$-0.660062\pi$
$701$	−25.5192	−0.963847	−0.481924	+	0.876213i	$0.660062\pi$
$702$	3.29030	0.124184
$703$	44.3661	1.67330
$704$	6.90093	0.260089
$705$	6.34526	0.238976
$706$	9.10085	0.342515
$707$	−8.62119	−0.324233
$708$	8.03965	0.302148
$709$	−31.6327	−1.18799	−0.593996	−	0.804468i	$-0.702451\pi$
$709$	−31.6327	−1.18799	−0.593996	+	0.804468i	$0.702451\pi$
$710$	3.65759	0.137267
$711$	−2.46505	−0.0924466
$712$	19.4697	0.729657
$713$	0	0
$714$	0.719069	0.0269105
$715$	−17.1427	−0.641101
$716$	22.0940	0.825693
$717$	−17.3701	−0.648697
$718$	−14.7841	−0.551738
$719$	−6.42476	−0.239603	−0.119802	−	0.992798i	$-0.538226\pi$
$719$	−6.42476	−0.239603	−0.119802	+	0.992798i	$0.538226\pi$
$720$	−2.57825	−0.0960856
$721$	−21.5117	−0.801137
$722$	3.98156	0.148178
$723$	1.33337	0.0495885
$724$	−3.61502	−0.134351
$725$	−4.57425	−0.169884
$726$	2.13340	0.0791781
$727$	−47.5294	−1.76277	−0.881384	−	0.472401i	$-0.843387\pi$
$727$	−47.5294	−1.76277	−0.881384	+	0.472401i	$0.843387\pi$
$728$	−35.4878	−1.31527
$729$	1.00000	0.0370370
$730$	2.25162	0.0833362
$731$	−0.609197	−0.0225320
$732$	−1.00451	−0.0371277
$733$	6.96003	0.257075	0.128537	−	0.991705i	$-0.458972\pi$
$733$	6.96003	0.257075	0.128537	+	0.991705i	$0.458972\pi$
$734$	0.358775	0.0132426
$735$	1.25970	0.0464647
$736$	0	0
$737$	30.2845	1.11555
$738$	6.07075	0.223467
$739$	−40.7600	−1.49938	−0.749690	−	0.661790i	$-0.769797\pi$
$739$	−40.7600	−1.49938	−0.749690	+	0.661790i	$0.769797\pi$
$740$	14.9639	0.550083
$741$	34.3970	1.26360
$742$	−7.22642	−0.265290
$743$	−9.61685	−0.352808	−0.176404	−	0.984318i	$-0.556446\pi$
$743$	−9.61685	−0.352808	−0.176404	+	0.984318i	$0.556446\pi$
$744$	11.0177	0.403929
$745$	−19.6960	−0.721606
$746$	−7.66702	−0.280710
$747$	1.03482	0.0378620
$748$	2.28497	0.0835468
$749$	42.0660	1.53706
$750$	0.497130	0.0181526
$751$	17.8345	0.650790	0.325395	−	0.945578i	$-0.394503\pi$
$751$	17.8345	0.650790	0.325395	+	0.945578i	$0.394503\pi$
$752$	16.3597	0.596576
$753$	9.39767	0.342470
$754$	15.0506	0.548112
$755$	−13.0382	−0.474509
$756$	−5.03767	−0.183218
$757$	−31.4041	−1.14140	−0.570701	−	0.821158i	$-0.693329\pi$
$757$	−31.4041	−1.14140	−0.570701	+	0.821158i	$0.693329\pi$
$758$	−14.0598	−0.510674
$759$	0	0
$760$	9.69589	0.351707
$761$	−3.32458	−0.120516	−0.0602580	−	0.998183i	$-0.519192\pi$
$761$	−3.32458	−0.120516	−0.0602580	+	0.998183i	$0.519192\pi$
$762$	10.2312	0.370637
$763$	26.1217	0.945668
$764$	32.5729	1.17845
$765$	−0.503290	−0.0181965
$766$	−8.52995	−0.308200
$767$	−30.3567	−1.09612
$768$	0.314014	0.0113310
$769$	−22.7305	−0.819684	−0.409842	−	0.912157i	$-0.634416\pi$
$769$	−22.7305	−0.819684	−0.409842	+	0.912157i	$0.634416\pi$
$770$	−3.70055	−0.133359
$771$	7.48385	0.269524
$772$	−22.7119	−0.817419
$773$	6.23107	0.224116	0.112058	−	0.993702i	$-0.464256\pi$
$773$	6.23107	0.224116	0.112058	+	0.993702i	$0.464256\pi$
$774$	−0.601741	−0.0216291
$775$	5.90553	0.212133
$776$	−13.8022	−0.495470
$777$	24.5346	0.880173
$778$	13.0501	0.467868
$779$	63.4640	2.27383
$780$	11.6015	0.415399
$781$	19.0563	0.681889
$782$	0	0
$783$	4.57425	0.163471
$784$	3.24782	0.115994
$785$	−9.84300	−0.351312
$786$	−10.2914	−0.367081
$787$	26.7965	0.955193	0.477596	−	0.878579i	$-0.341508\pi$
$787$	26.7965	0.955193	0.477596	+	0.878579i	$0.341508\pi$
$788$	−39.6897	−1.41389
$789$	23.6879	0.843311
$790$	1.22545	0.0435995
$791$	48.9502	1.74047
$792$	4.83222	0.171706
$793$	3.79290	0.134690
$794$	−8.72032	−0.309473
$795$	5.05791	0.179386
$796$	−38.0389	−1.34825
$797$	27.7434	0.982722	0.491361	−	0.870956i	$-0.336500\pi$
$797$	27.7434	0.982722	0.491361	+	0.870956i	$0.336500\pi$
$798$	7.42518	0.262849
$799$	3.19351	0.112978
$800$	5.01304	0.177238
$801$	−10.4358	−0.368731
$802$	−7.83111	−0.276526
$803$	11.7311	0.413982
$804$	−20.4953	−0.722813
$805$	0	0
$806$	−19.4309	−0.684425
$807$	29.6221	1.04275
$808$	−5.59652	−0.196885
$809$	2.73014	0.0959867	0.0479934	−	0.998848i	$-0.484717\pi$
$809$	2.73014	0.0959867	0.0479934	+	0.998848i	$0.484717\pi$
$810$	−0.497130	−0.0174674
$811$	−28.8068	−1.01154	−0.505772	−	0.862667i	$-0.668792\pi$
$811$	−28.8068	−1.01154	−0.505772	+	0.862667i	$0.668792\pi$
$812$	−23.0436	−0.808671
$813$	−3.69307	−0.129522
$814$	−10.9921	−0.385273
$815$	3.98046	0.139429
$816$	−1.29761	−0.0454253
$817$	−6.29064	−0.220082
$818$	−0.365351	−0.0127742
$819$	19.0216	0.664668
$820$	21.4052	0.747503
$821$	−22.8484	−0.797416	−0.398708	−	0.917078i	$-0.630541\pi$
$821$	−22.8484	−0.797416	−0.398708	+	0.917078i	$0.630541\pi$
$822$	−4.64643	−0.162063
$823$	5.17230	0.180295	0.0901475	−	0.995928i	$-0.471266\pi$
$823$	5.17230	0.180295	0.0901475	+	0.995928i	$0.471266\pi$
$824$	−13.9645	−0.486476
$825$	2.59009	0.0901753
$826$	−6.55302	−0.228009
$827$	49.9154	1.73573	0.867865	−	0.496800i	$-0.165492\pi$
$827$	49.9154	1.73573	0.867865	+	0.496800i	$0.165492\pi$
$828$	0	0
$829$	54.3787	1.88865	0.944324	−	0.329016i	$-0.106717\pi$
$829$	54.3787	1.88865	0.944324	+	0.329016i	$0.106717\pi$
$830$	−0.514439	−0.0178564
$831$	3.26430	0.113237
$832$	17.6343	0.611359
$833$	0.633994	0.0219666
$834$	−9.17430	−0.317680
$835$	4.11819	0.142516
$836$	23.5949	0.816045
$837$	−5.90553	−0.204125
$838$	6.68276	0.230852
$839$	−16.5270	−0.570577	−0.285288	−	0.958442i	$-0.592089\pi$
$839$	−16.5270	−0.570577	−0.285288	+	0.958442i	$0.592089\pi$
$840$	5.36185	0.185001
$841$	−8.07620	−0.278490
$842$	4.14376	0.142803
$843$	20.5268	0.706982
$844$	−20.9951	−0.722682
$845$	−30.8056	−1.05975
$846$	3.15442	0.108451
$847$	12.3335	0.423783
$848$	13.0405	0.447814
$849$	29.9308	1.02722
$850$	0.250200	0.00858181
$851$	0	0
$852$	−12.8965	−0.441827
$853$	21.7533	0.744821	0.372410	−	0.928068i	$-0.378531\pi$
$853$	21.7533	0.744821	0.372410	+	0.928068i	$0.378531\pi$
$854$	0.818763	0.0280175
$855$	−5.19703	−0.177735
$856$	27.3075	0.933351
$857$	−12.9228	−0.441435	−0.220718	−	0.975338i	$-0.570840\pi$
$857$	−12.9228	−0.441435	−0.220718	+	0.975338i	$0.570840\pi$
$858$	−8.52216	−0.290942
$859$	24.4817	0.835304	0.417652	−	0.908607i	$-0.362853\pi$
$859$	24.4817	0.835304	0.417652	+	0.908607i	$0.362853\pi$
$860$	−2.12172	−0.0723499
$861$	35.0957	1.19606
$862$	19.6203	0.668271
$863$	−6.48000	−0.220582	−0.110291	−	0.993899i	$-0.535178\pi$
$863$	−6.48000	−0.220582	−0.110291	+	0.993899i	$0.535178\pi$
$864$	−5.01304	−0.170547
$865$	4.30293	0.146304
$866$	−9.25011	−0.314331
$867$	16.7467	0.568748
$868$	29.7501	1.00978
$869$	6.38469	0.216586
$870$	−2.27400	−0.0770958
$871$	77.3876	2.62218
$872$	16.9571	0.574240
$873$	7.39802	0.250385
$874$	0	0
$875$	2.87397	0.0971579
$876$	−7.93913	−0.268238
$877$	−12.0629	−0.407335	−0.203667	−	0.979040i	$-0.565286\pi$
$877$	−12.0629	−0.407335	−0.203667	+	0.979040i	$0.565286\pi$
$878$	−4.01012	−0.135335
$879$	−23.5660	−0.794862
$880$	6.67789	0.225112
$881$	−45.8370	−1.54429	−0.772144	−	0.635447i	$-0.780816\pi$
$881$	−45.8370	−1.54429	−0.772144	+	0.635447i	$0.780816\pi$
$882$	0.626235	0.0210864
$883$	−45.1630	−1.51986	−0.759928	−	0.650007i	$-0.774766\pi$
$883$	−45.1630	−1.51986	−0.759928	+	0.650007i	$0.774766\pi$
$884$	5.83890	0.196383
$885$	4.58658	0.154176
$886$	10.8495	0.364497
$887$	−0.145642	−0.00489019	−0.00244509	−	0.999997i	$-0.500778\pi$
$887$	−0.145642	−0.00489019	−0.00244509	+	0.999997i	$0.500778\pi$
$888$	15.9268	0.534469
$889$	59.1478	1.98375
$890$	5.18796	0.173901
$891$	−2.59009	−0.0867712
$892$	−25.5264	−0.854686
$893$	32.9765	1.10352
$894$	−9.79148	−0.327476
$895$	12.6046	0.421324
$896$	32.6213	1.08980
$897$	0	0
$898$	15.1755	0.506412
$899$	−27.0134	−0.900947
$900$	−1.75286	−0.0584287
$901$	2.54559	0.0848060
$902$	−15.7238	−0.523545
$903$	−3.47874	−0.115765
$904$	31.7764	1.05687
$905$	−2.06236	−0.0685550
$906$	−6.48168	−0.215340
$907$	5.09159	0.169063	0.0845317	−	0.996421i	$-0.473061\pi$
$907$	5.09159	0.169063	0.0845317	+	0.996421i	$0.473061\pi$
$908$	6.83290	0.226758
$909$	2.99975	0.0994955
$910$	−9.45621	−0.313470
$911$	52.3427	1.73419	0.867096	−	0.498141i	$-0.165984\pi$
$911$	52.3427	1.73419	0.867096	+	0.498141i	$0.165984\pi$
$912$	−13.3992	−0.443693
$913$	−2.68027	−0.0887040
$914$	−6.66603	−0.220493
$915$	−0.573068	−0.0189450
$916$	−1.49008	−0.0492336
$917$	−59.4956	−1.96472
$918$	−0.250200	−0.00825785
$919$	5.47100	0.180471	0.0902357	−	0.995920i	$-0.471238\pi$
$919$	5.47100	0.180471	0.0902357	+	0.995920i	$0.471238\pi$
$920$	0	0
$921$	−11.9053	−0.392293
$922$	−3.89322	−0.128216
$923$	48.6956	1.60283
$924$	13.0480	0.429248
$925$	8.53682	0.280689
$926$	−4.45222	−0.146309
$927$	7.48501	0.245840
$928$	−22.9309	−0.752745
$929$	41.7989	1.37138	0.685689	−	0.727894i	$-0.259501\pi$
$929$	41.7989	1.37138	0.685689	+	0.727894i	$0.259501\pi$
$930$	2.93582	0.0962692
$931$	6.54670	0.214559
$932$	47.0716	1.54188
$933$	−5.28913	−0.173158
$934$	−3.42805	−0.112169
$935$	1.30357	0.0426311
$936$	12.3480	0.403608
$937$	−46.0192	−1.50338	−0.751691	−	0.659516i	$-0.770761\pi$
$937$	−46.0192	−1.50338	−0.751691	+	0.659516i	$0.770761\pi$
$938$	16.7055	0.545453
$939$	26.7608	0.873304
$940$	11.1224	0.362772
$941$	0.703821	0.0229439	0.0114720	−	0.999934i	$-0.496348\pi$
$941$	0.703821	0.0229439	0.0114720	+	0.999934i	$0.496348\pi$
$942$	−4.89325	−0.159431
$943$	0	0
$944$	11.8253	0.384882
$945$	−2.87397	−0.0934902
$946$	1.55856	0.0506732
$947$	−9.35103	−0.303868	−0.151934	−	0.988391i	$-0.548550\pi$
$947$	−9.35103	−0.303868	−0.151934	+	0.988391i	$0.548550\pi$
$948$	−4.32089	−0.140336
$949$	29.9771	0.973099
$950$	2.58360	0.0838230
$951$	−21.3249	−0.691508
$952$	2.69856	0.0874610
$953$	3.82287	0.123835	0.0619175	−	0.998081i	$-0.480278\pi$
$953$	3.82287	0.123835	0.0619175	+	0.998081i	$0.480278\pi$
$954$	2.51444	0.0814080
$955$	18.5827	0.601322
$956$	−30.4473	−0.984736
$957$	−11.8477	−0.382982
$958$	3.84869	0.124346
$959$	−26.8616	−0.867405
$960$	−2.66436	−0.0859919
$961$	3.87526	0.125008
$962$	−28.0887	−0.905615
$963$	−14.6369	−0.471668
$964$	2.33721	0.0752765
$965$	−12.9570	−0.417102
$966$	0	0
$967$	−18.1797	−0.584620	−0.292310	−	0.956324i	$-0.594424\pi$
$967$	−18.1797	−0.584620	−0.292310	+	0.956324i	$0.594424\pi$
$968$	8.00637	0.257335
$969$	−2.61561	−0.0840255
$970$	−3.67778	−0.118086
$971$	2.48292	0.0796807	0.0398404	−	0.999206i	$-0.487315\pi$
$971$	2.48292	0.0796807	0.0398404	+	0.999206i	$0.487315\pi$
$972$	1.75286	0.0562231
$973$	−53.0378	−1.70031
$974$	9.18408	0.294277
$975$	6.61858	0.211964
$976$	−1.47751	−0.0472940
$977$	32.8511	1.05100	0.525499	−	0.850794i	$-0.323879\pi$
$977$	32.8511	1.05100	0.525499	+	0.850794i	$0.323879\pi$
$978$	1.97881	0.0632753
$979$	27.0297	0.863873
$980$	2.20808	0.0705345
$981$	−9.08906	−0.290191
$982$	6.54536	0.208871
$983$	−17.8166	−0.568261	−0.284131	−	0.958786i	$-0.591705\pi$
$983$	−17.8166	−0.568261	−0.284131	+	0.958786i	$0.591705\pi$
$984$	22.7827	0.726285
$985$	−22.6428	−0.721459
$986$	−1.14448	−0.0364477
$987$	18.2361	0.580461
$988$	60.2931	1.91818
$989$	0	0
$990$	1.28761	0.0409230
$991$	46.7911	1.48637	0.743184	−	0.669087i	$-0.233315\pi$
$991$	46.7911	1.48637	0.743184	+	0.669087i	$0.233315\pi$
$992$	29.6047	0.939949
$993$	−5.89341	−0.187022
$994$	10.5118	0.333414
$995$	−21.7010	−0.687968
$996$	1.81389	0.0574754
$997$	−15.3419	−0.485884	−0.242942	−	0.970041i	$-0.578112\pi$
$997$	−15.3419	−0.485884	−0.242942	+	0.970041i	$0.578112\pi$
$998$	20.5746	0.651277
$999$	−8.53682	−0.270093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.br.1.10	✓	16
23.22	odd	2		7935.2.a.bs.1.10	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.br.1.10	✓	16	1.1	even	1	trivial
7935.2.a.bs.1.10	yes	16	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)

\(f(q)\)	\(=\)	\(q+0.497130 q^{2} -1.00000 q^{3} -1.75286 q^{4} -1.00000 q^{5} -0.497130 q^{6} -2.87397 q^{7} -1.86566 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.497130 q^{2} -1.00000 q^{3} -1.75286 q^{4} -1.00000 q^{5} -0.497130 q^{6} -2.87397 q^{7} -1.86566 q^{8} +1.00000 q^{9} -0.497130 q^{10} -2.59009 q^{11} +1.75286 q^{12} -6.61858 q^{13} -1.42874 q^{14} +1.00000 q^{15} +2.57825 q^{16} +0.503290 q^{17} +0.497130 q^{18} +5.19703 q^{19} +1.75286 q^{20} +2.87397 q^{21} -1.28761 q^{22} +1.86566 q^{24} +1.00000 q^{25} -3.29030 q^{26} -1.00000 q^{27} +5.03767 q^{28} -4.57425 q^{29} +0.497130 q^{30} +5.90553 q^{31} +5.01304 q^{32} +2.59009 q^{33} +0.250200 q^{34} +2.87397 q^{35} -1.75286 q^{36} +8.53682 q^{37} +2.58360 q^{38} +6.61858 q^{39} +1.86566 q^{40} +12.2116 q^{41} +1.42874 q^{42} -1.21043 q^{43} +4.54007 q^{44} -1.00000 q^{45} +6.34526 q^{47} -2.57825 q^{48} +1.25970 q^{49} +0.497130 q^{50} -0.503290 q^{51} +11.6015 q^{52} +5.05791 q^{53} -0.497130 q^{54} +2.59009 q^{55} +5.36185 q^{56} -5.19703 q^{57} -2.27400 q^{58} +4.58658 q^{59} -1.75286 q^{60} -0.573068 q^{61} +2.93582 q^{62} -2.87397 q^{63} -2.66436 q^{64} +6.61858 q^{65} +1.28761 q^{66} -11.6925 q^{67} -0.882198 q^{68} +1.42874 q^{70} -7.35740 q^{71} -1.86566 q^{72} -4.52924 q^{73} +4.24391 q^{74} -1.00000 q^{75} -9.10967 q^{76} +7.44383 q^{77} +3.29030 q^{78} -2.46505 q^{79} -2.57825 q^{80} +1.00000 q^{81} +6.07075 q^{82} +1.03482 q^{83} -5.03767 q^{84} -0.503290 q^{85} -0.601741 q^{86} +4.57425 q^{87} +4.83222 q^{88} -10.4358 q^{89} -0.497130 q^{90} +19.0216 q^{91} -5.90553 q^{93} +3.15442 q^{94} -5.19703 q^{95} -5.01304 q^{96} +7.39802 q^{97} +0.626235 q^{98} -2.59009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} + 16 q^{4} - 16 q^{5} - 12 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^3 + 16 * q^4 - 16 * q^5 - 12 * q^7 + 16 * q^9	\( 16 q - 16 q^{3} + 16 q^{4} - 16 q^{5} - 12 q^{7} + 16 q^{9} + 8 q^{11} - 16 q^{12} - 8 q^{13} + 16 q^{15} + 16 q^{16} - 20 q^{17} - 16 q^{19} - 16 q^{20} + 12 q^{21} - 16 q^{22} + 16 q^{25} + 20 q^{26} - 16 q^{27} + 16 q^{28} + 40 q^{29} + 16 q^{31} - 20 q^{32} - 8 q^{33} - 16 q^{34} + 12 q^{35} + 16 q^{36} - 28 q^{37} - 56 q^{38} + 8 q^{39} + 12 q^{41} - 4 q^{43} + 48 q^{44} - 16 q^{45} - 20 q^{47} - 16 q^{48} + 20 q^{49} + 20 q^{51} - 36 q^{52} - 4 q^{53} - 8 q^{55} + 8 q^{56} + 16 q^{57} - 16 q^{58} + 20 q^{59} + 16 q^{60} - 32 q^{61} + 28 q^{62} - 12 q^{63} + 28 q^{64} + 8 q^{65} + 16 q^{66} - 4 q^{67} + 24 q^{68} + 24 q^{71} - 36 q^{73} + 100 q^{74} - 16 q^{75} - 88 q^{76} + 4 q^{77} - 20 q^{78} - 24 q^{79} - 16 q^{80} + 16 q^{81} - 20 q^{82} - 44 q^{83} - 16 q^{84} + 20 q^{85} - 52 q^{86} - 40 q^{87} - 48 q^{88} - 16 q^{89} - 24 q^{91} - 16 q^{93} - 20 q^{94} + 16 q^{95} + 20 q^{96} - 64 q^{97} + 4 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 + 16 * q^4 - 16 * q^5 - 12 * q^7 + 16 * q^9 + 8 * q^11 - 16 * q^12 - 8 * q^13 + 16 * q^15 + 16 * q^16 - 20 * q^17 - 16 * q^19 - 16 * q^20 + 12 * q^21 - 16 * q^22 + 16 * q^25 + 20 * q^26 - 16 * q^27 + 16 * q^28 + 40 * q^29 + 16 * q^31 - 20 * q^32 - 8 * q^33 - 16 * q^34 + 12 * q^35 + 16 * q^36 - 28 * q^37 - 56 * q^38 + 8 * q^39 + 12 * q^41 - 4 * q^43 + 48 * q^44 - 16 * q^45 - 20 * q^47 - 16 * q^48 + 20 * q^49 + 20 * q^51 - 36 * q^52 - 4 * q^53 - 8 * q^55 + 8 * q^56 + 16 * q^57 - 16 * q^58 + 20 * q^59 + 16 * q^60 - 32 * q^61 + 28 * q^62 - 12 * q^63 + 28 * q^64 + 8 * q^65 + 16 * q^66 - 4 * q^67 + 24 * q^68 + 24 * q^71 - 36 * q^73 + 100 * q^74 - 16 * q^75 - 88 * q^76 + 4 * q^77 - 20 * q^78 - 24 * q^79 - 16 * q^80 + 16 * q^81 - 20 * q^82 - 44 * q^83 - 16 * q^84 + 20 * q^85 - 52 * q^86 - 40 * q^87 - 48 * q^88 - 16 * q^89 - 24 * q^91 - 16 * q^93 - 20 * q^94 + 16 * q^95 + 20 * q^96 - 64 * q^97 + 4 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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