LMFDB - Embedded newform 7935.2.a.bs.1.5

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:	$16$
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			1.5
Root			$1.30963$ 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)

$f(q)$	$=$	$q-1.30963 q^{2} -1.00000 q^{3} -0.284864 q^{4} +1.00000 q^{5} +1.30963 q^{6} +3.58187 q^{7} +2.99233 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.30963 q^{2} -1.00000 q^{3} -0.284864 q^{4} +1.00000 q^{5} +1.30963 q^{6} +3.58187 q^{7} +2.99233 q^{8} +1.00000 q^{9} -1.30963 q^{10} -2.84353 q^{11} +0.284864 q^{12} +5.52986 q^{13} -4.69094 q^{14} -1.00000 q^{15} -3.34912 q^{16} -1.00586 q^{17} -1.30963 q^{18} +4.45884 q^{19} -0.284864 q^{20} -3.58187 q^{21} +3.72398 q^{22} -2.99233 q^{24} +1.00000 q^{25} -7.24207 q^{26} -1.00000 q^{27} -1.02035 q^{28} -6.25694 q^{29} +1.30963 q^{30} +5.43934 q^{31} -1.59854 q^{32} +2.84353 q^{33} +1.31731 q^{34} +3.58187 q^{35} -0.284864 q^{36} +6.60734 q^{37} -5.83944 q^{38} -5.52986 q^{39} +2.99233 q^{40} -11.0073 q^{41} +4.69094 q^{42} -4.85255 q^{43} +0.810021 q^{44} +1.00000 q^{45} +11.0414 q^{47} +3.34912 q^{48} +5.82982 q^{49} -1.30963 q^{50} +1.00586 q^{51} -1.57526 q^{52} +7.03860 q^{53} +1.30963 q^{54} -2.84353 q^{55} +10.7182 q^{56} -4.45884 q^{57} +8.19429 q^{58} +1.07003 q^{59} +0.284864 q^{60} +4.78135 q^{61} -7.12353 q^{62} +3.58187 q^{63} +8.79175 q^{64} +5.52986 q^{65} -3.72398 q^{66} +9.82621 q^{67} +0.286534 q^{68} -4.69094 q^{70} -2.41453 q^{71} +2.99233 q^{72} +13.4671 q^{73} -8.65319 q^{74} -1.00000 q^{75} -1.27017 q^{76} -10.1852 q^{77} +7.24207 q^{78} -7.52516 q^{79} -3.34912 q^{80} +1.00000 q^{81} +14.4156 q^{82} +9.32690 q^{83} +1.02035 q^{84} -1.00586 q^{85} +6.35505 q^{86} +6.25694 q^{87} -8.50879 q^{88} -13.6887 q^{89} -1.30963 q^{90} +19.8072 q^{91} -5.43934 q^{93} -14.4601 q^{94} +4.45884 q^{95} +1.59854 q^{96} +10.5380 q^{97} -7.63492 q^{98} -2.84353 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.30963	−0.926050	−0.463025	−	0.886345i	$-0.653236\pi$
$2$	−1.30963	−0.926050	−0.463025	+	0.886345i	$0.653236\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.284864	−0.142432
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.30963	0.534655
$7$	3.58187	1.35382	0.676911	−	0.736065i	$-0.263318\pi$
$7$	3.58187	1.35382	0.676911	+	0.736065i	$0.263318\pi$
$8$	2.99233	1.05795
$9$	1.00000	0.333333
$10$	−1.30963	−0.414142
$11$	−2.84353	−0.857357	−0.428679	−	0.903457i	$-0.641021\pi$
$11$	−2.84353	−0.857357	−0.428679	+	0.903457i	$0.641021\pi$
$12$	0.284864	0.0822333
$13$	5.52986	1.53371	0.766853	−	0.641823i	$-0.221822\pi$
$13$	5.52986	1.53371	0.766853	+	0.641823i	$0.221822\pi$
$14$	−4.69094	−1.25371
$15$	−1.00000	−0.258199
$16$	−3.34912	−0.837281
$17$	−1.00586	−0.243957	−0.121979	−	0.992533i	$-0.538924\pi$
$17$	−1.00586	−0.243957	−0.121979	+	0.992533i	$0.538924\pi$
$18$	−1.30963	−0.308683
$19$	4.45884	1.02293	0.511464	−	0.859305i	$-0.329103\pi$
$19$	4.45884	1.02293	0.511464	+	0.859305i	$0.329103\pi$
$20$	−0.284864	−0.0636976
$21$	−3.58187	−0.781629
$22$	3.72398	0.793955
$23$	0	0
$23$	0	0
$24$	−2.99233	−0.610807
$25$	1.00000	0.200000
$26$	−7.24207	−1.42029
$27$	−1.00000	−0.192450
$28$	−1.02035	−0.192828
$29$	−6.25694	−1.16189	−0.580943	−	0.813945i	$-0.697316\pi$
$29$	−6.25694	−1.16189	−0.580943	+	0.813945i	$0.697316\pi$
$30$	1.30963	0.239105
$31$	5.43934	0.976934	0.488467	−	0.872582i	$-0.337556\pi$
$31$	5.43934	0.976934	0.488467	+	0.872582i	$0.337556\pi$
$32$	−1.59854	−0.282585
$33$	2.84353	0.494995
$34$	1.31731	0.225917
$35$	3.58187	0.605447
$36$	−0.284864	−0.0474774
$37$	6.60734	1.08624	0.543120	−	0.839655i	$-0.317243\pi$
$37$	6.60734	1.08624	0.543120	+	0.839655i	$0.317243\pi$
$38$	−5.83944	−0.947283
$39$	−5.52986	−0.885485
$40$	2.99233	0.473129
$41$	−11.0073	−1.71906	−0.859529	−	0.511087i	$-0.829243\pi$
$41$	−11.0073	−1.71906	−0.859529	+	0.511087i	$0.829243\pi$
$42$	4.69094	0.723827
$43$	−4.85255	−0.740007	−0.370003	−	0.929030i	$-0.620643\pi$
$43$	−4.85255	−0.740007	−0.370003	+	0.929030i	$0.620643\pi$
$44$	0.810021	0.122115
$45$	1.00000	0.149071
$46$	0	0
$47$	11.0414	1.61055	0.805276	−	0.592901i	$-0.202017\pi$
$47$	11.0414	1.61055	0.805276	+	0.592901i	$0.202017\pi$
$48$	3.34912	0.483404
$49$	5.82982	0.832832
$50$	−1.30963	−0.185210
$51$	1.00586	0.140849
$52$	−1.57526	−0.218449
$53$	7.03860	0.966826	0.483413	−	0.875392i	$-0.339397\pi$
$53$	7.03860	0.966826	0.483413	+	0.875392i	$0.339397\pi$
$54$	1.30963	0.178218
$55$	−2.84353	−0.383422
$56$	10.7182	1.43227
$57$	−4.45884	−0.590588
$58$	8.19429	1.07596
$59$	1.07003	0.139307	0.0696533	−	0.997571i	$-0.477811\pi$
$59$	1.07003	0.139307	0.0696533	+	0.997571i	$0.477811\pi$
$60$	0.284864	0.0367758
$61$	4.78135	0.612189	0.306094	−	0.952001i	$-0.400978\pi$
$61$	4.78135	0.612189	0.306094	+	0.952001i	$0.400978\pi$
$62$	−7.12353	−0.904690
$63$	3.58187	0.451274
$64$	8.79175	1.09897
$65$	5.52986	0.685894
$66$	−3.72398	−0.458390
$67$	9.82621	1.20046	0.600231	−	0.799827i	$-0.295075\pi$
$67$	9.82621	1.20046	0.600231	+	0.799827i	$0.295075\pi$
$68$	0.286534	0.0347474
$69$	0	0
$70$	−4.69094	−0.560674
$71$	−2.41453	−0.286551	−0.143276	−	0.989683i	$-0.545764\pi$
$71$	−2.41453	−0.286551	−0.143276	+	0.989683i	$0.545764\pi$
$72$	2.99233	0.352650
$73$	13.4671	1.57620	0.788101	−	0.615546i	$-0.211064\pi$
$73$	13.4671	1.57620	0.788101	+	0.615546i	$0.211064\pi$
$74$	−8.65319	−1.00591
$75$	−1.00000	−0.115470
$76$	−1.27017	−0.145698
$77$	−10.1852	−1.16071
$78$	7.24207	0.820003
$79$	−7.52516	−0.846646	−0.423323	−	0.905979i	$-0.639136\pi$
$79$	−7.52516	−0.846646	−0.423323	+	0.905979i	$0.639136\pi$
$80$	−3.34912	−0.374443
$81$	1.00000	0.111111
$82$	14.4156	1.59193
$83$	9.32690	1.02376	0.511880	−	0.859057i	$-0.328949\pi$
$83$	9.32690	1.02376	0.511880	+	0.859057i	$0.328949\pi$
$84$	1.02035	0.111329
$85$	−1.00586	−0.109101
$86$	6.35505	0.685283
$87$	6.25694	0.670815
$88$	−8.50879	−0.907040
$89$	−13.6887	−1.45100	−0.725502	−	0.688220i	$-0.758392\pi$
$89$	−13.6887	−1.45100	−0.725502	+	0.688220i	$0.758392\pi$
$90$	−1.30963	−0.138047
$91$	19.8072	2.07636
$92$	0	0
$93$	−5.43934	−0.564033
$94$	−14.4601	−1.49145
$95$	4.45884	0.457468
$96$	1.59854	0.163151
$97$	10.5380	1.06997	0.534985	−	0.844861i	$-0.320317\pi$
$97$	10.5380	1.06997	0.534985	+	0.844861i	$0.320317\pi$
$98$	−7.63492	−0.771243
$99$	−2.84353	−0.285786
$100$	−0.284864	−0.0284864
$101$	13.2464	1.31806	0.659032	−	0.752115i	$-0.270966\pi$
$101$	13.2464	1.31806	0.659032	+	0.752115i	$0.270966\pi$
$102$	−1.31731	−0.130433
$103$	1.78878	0.176254	0.0881268	−	0.996109i	$-0.471912\pi$
$103$	1.78878	0.176254	0.0881268	+	0.996109i	$0.471912\pi$
$104$	16.5472	1.62258
$105$	−3.58187	−0.349555
$106$	−9.21798	−0.895329
$107$	−5.59816	−0.541195	−0.270597	−	0.962693i	$-0.587221\pi$
$107$	−5.59816	−0.541195	−0.270597	+	0.962693i	$0.587221\pi$
$108$	0.284864	0.0274111
$109$	−16.5712	−1.58724	−0.793619	−	0.608415i	$-0.791806\pi$
$109$	−16.5712	−1.58724	−0.793619	+	0.608415i	$0.791806\pi$
$110$	3.72398	0.355068
$111$	−6.60734	−0.627141
$112$	−11.9961	−1.13353
$113$	2.92366	0.275035	0.137517	−	0.990499i	$-0.456088\pi$
$113$	2.92366	0.275035	0.137517	+	0.990499i	$0.456088\pi$
$114$	5.83944	0.546914
$115$	0	0
$116$	1.78238	0.165490
$117$	5.52986	0.511235
$118$	−1.40135	−0.129005
$119$	−3.60287	−0.330274
$120$	−2.99233	−0.273161
$121$	−2.91432	−0.264939
$122$	−6.26180	−0.566917
$123$	11.0073	0.992499
$124$	−1.54947	−0.139147
$125$	1.00000	0.0894427
$126$	−4.69094	−0.417902
$127$	−17.2725	−1.53269	−0.766343	−	0.642432i	$-0.777926\pi$
$127$	−17.2725	−1.53269	−0.766343	+	0.642432i	$0.777926\pi$
$128$	−8.31687	−0.735114
$129$	4.85255	0.427243
$130$	−7.24207	−0.635172
$131$	2.06112	0.180081	0.0900406	−	0.995938i	$-0.471300\pi$
$131$	2.06112	0.180081	0.0900406	+	0.995938i	$0.471300\pi$
$132$	−0.810021	−0.0705033
$133$	15.9710	1.38486
$134$	−12.8687	−1.11169
$135$	−1.00000	−0.0860663
$136$	−3.00987	−0.258094
$137$	15.6872	1.34025	0.670123	−	0.742250i	$-0.266242\pi$
$137$	15.6872	1.34025	0.670123	+	0.742250i	$0.266242\pi$
$138$	0	0
$139$	19.8270	1.68170	0.840852	−	0.541266i	$-0.182055\pi$
$139$	19.8270	1.68170	0.840852	+	0.541266i	$0.182055\pi$
$140$	−1.02035	−0.0862352
$141$	−11.0414	−0.929852
$142$	3.16214	0.265361
$143$	−15.7243	−1.31493
$144$	−3.34912	−0.279094
$145$	−6.25694	−0.519611
$146$	−17.6369	−1.45964
$147$	−5.82982	−0.480836
$148$	−1.88220	−0.154716
$149$	−10.0316	−0.821817	−0.410908	−	0.911677i	$-0.634788\pi$
$149$	−10.0316	−0.821817	−0.410908	+	0.911677i	$0.634788\pi$
$150$	1.30963	0.106931
$151$	7.65000	0.622548	0.311274	−	0.950320i	$-0.399244\pi$
$151$	7.65000	0.622548	0.311274	+	0.950320i	$0.399244\pi$
$152$	13.3423	1.08221
$153$	−1.00586	−0.0813191
$154$	13.3388	1.07487
$155$	5.43934	0.436898
$156$	1.57526	0.126122
$157$	−12.2306	−0.976105	−0.488053	−	0.872814i	$-0.662293\pi$
$157$	−12.2306	−0.976105	−0.488053	+	0.872814i	$0.662293\pi$
$158$	9.85518	0.784036
$159$	−7.03860	−0.558197
$160$	−1.59854	−0.126376
$161$	0	0
$162$	−1.30963	−0.102894
$163$	−2.52743	−0.197964	−0.0989818	−	0.995089i	$-0.531559\pi$
$163$	−2.52743	−0.197964	−0.0989818	+	0.995089i	$0.531559\pi$
$164$	3.13560	0.244849
$165$	2.84353	0.221369
$166$	−12.2148	−0.948053
$167$	−8.71737	−0.674570	−0.337285	−	0.941403i	$-0.609509\pi$
$167$	−8.71737	−0.674570	−0.337285	+	0.941403i	$0.609509\pi$
$168$	−10.7182	−0.826923
$169$	17.5793	1.35225
$170$	1.31731	0.101033
$171$	4.45884	0.340976
$172$	1.38232	0.105401
$173$	5.30482	0.403318	0.201659	−	0.979456i	$-0.435367\pi$
$173$	5.30482	0.403318	0.201659	+	0.979456i	$0.435367\pi$
$174$	−8.19429	−0.621208
$175$	3.58187	0.270764
$176$	9.52334	0.717849
$177$	−1.07003	−0.0804287
$178$	17.9272	1.34370
$179$	7.62288	0.569761	0.284881	−	0.958563i	$-0.408046\pi$
$179$	7.62288	0.569761	0.284881	+	0.958563i	$0.408046\pi$
$180$	−0.284864	−0.0212325
$181$	−18.4592	−1.37206	−0.686032	−	0.727571i	$-0.740649\pi$
$181$	−18.4592	−1.37206	−0.686032	+	0.727571i	$0.740649\pi$
$182$	−25.9402	−1.92282
$183$	−4.78135	−0.353447
$184$	0	0
$185$	6.60734	0.485781
$186$	7.12353	0.522323
$187$	2.86020	0.209159
$188$	−3.14530	−0.229394
$189$	−3.58187	−0.260543
$190$	−5.83944	−0.423638
$191$	3.39775	0.245853	0.122926	−	0.992416i	$-0.460772\pi$
$191$	3.39775	0.245853	0.122926	+	0.992416i	$0.460772\pi$
$192$	−8.79175	−0.634490
$193$	−8.73721	−0.628918	−0.314459	−	0.949271i	$-0.601823\pi$
$193$	−8.73721	−0.628918	−0.314459	+	0.949271i	$0.601823\pi$
$194$	−13.8009	−0.990846
$195$	−5.52986	−0.396001
$196$	−1.66071	−0.118622
$197$	20.1145	1.43310	0.716549	−	0.697537i	$-0.245721\pi$
$197$	20.1145	1.43310	0.716549	+	0.697537i	$0.245721\pi$
$198$	3.72398	0.264652
$199$	12.2670	0.869586	0.434793	−	0.900530i	$-0.356821\pi$
$199$	12.2670	0.869586	0.434793	+	0.900530i	$0.356821\pi$
$200$	2.99233	0.211590
$201$	−9.82621	−0.693087
$202$	−17.3479	−1.22059
$203$	−22.4116	−1.57298
$204$	−0.286534	−0.0200614
$205$	−11.0073	−0.768786
$206$	−2.34264	−0.163220
$207$	0	0
$208$	−18.5202	−1.28414
$209$	−12.6789	−0.877015
$210$	4.69094	0.323705
$211$	0.0842979	0.00580330	0.00290165	−	0.999996i	$-0.499076\pi$
$211$	0.0842979	0.00580330	0.00290165	+	0.999996i	$0.499076\pi$
$212$	−2.00505	−0.137707
$213$	2.41453	0.165441
$214$	7.33153	0.501173
$215$	−4.85255	−0.330941
$216$	−2.99233	−0.203602
$217$	19.4830	1.32259
$218$	21.7022	1.46986
$219$	−13.4671	−0.910021
$220$	0.810021	0.0546116
$221$	−5.56227	−0.374159
$222$	8.65319	0.580764
$223$	−27.1542	−1.81838	−0.909191	−	0.416379i	$-0.863299\pi$
$223$	−27.1542	−1.81838	−0.909191	+	0.416379i	$0.863299\pi$
$224$	−5.72578	−0.382570
$225$	1.00000	0.0666667
$226$	−3.82891	−0.254696
$227$	−2.24068	−0.148719	−0.0743596	−	0.997231i	$-0.523691\pi$
$227$	−2.24068	−0.148719	−0.0743596	+	0.997231i	$0.523691\pi$
$228$	1.27017	0.0841188
$229$	27.1049	1.79115	0.895573	−	0.444916i	$-0.146766\pi$
$229$	27.1049	1.79115	0.895573	+	0.444916i	$0.146766\pi$
$230$	0	0
$231$	10.1852	0.670135
$232$	−18.7228	−1.22922
$233$	20.1616	1.32083	0.660416	−	0.750900i	$-0.270380\pi$
$233$	20.1616	1.32083	0.660416	+	0.750900i	$0.270380\pi$
$234$	−7.24207	−0.473429
$235$	11.0414	0.720260
$236$	−0.304815	−0.0198418
$237$	7.52516	0.488811
$238$	4.71843	0.305851
$239$	17.4223	1.12695	0.563477	−	0.826132i	$-0.309463\pi$
$239$	17.4223	1.12695	0.563477	+	0.826132i	$0.309463\pi$
$240$	3.34912	0.216185
$241$	−8.16811	−0.526154	−0.263077	−	0.964775i	$-0.584737\pi$
$241$	−8.16811	−0.526154	−0.263077	+	0.964775i	$0.584737\pi$
$242$	3.81669	0.245346
$243$	−1.00000	−0.0641500
$244$	−1.36204	−0.0871954
$245$	5.82982	0.372454
$246$	−14.4156	−0.919103
$247$	24.6568	1.56887
$248$	16.2763	1.03355
$249$	−9.32690	−0.591068
$250$	−1.30963	−0.0828284
$251$	−30.4031	−1.91902	−0.959512	−	0.281668i	$-0.909112\pi$
$251$	−30.4031	−1.91902	−0.959512	+	0.281668i	$0.909112\pi$
$252$	−1.02035	−0.0642759
$253$	0	0
$254$	22.6206	1.41934
$255$	1.00586	0.0629895
$256$	−6.69146	−0.418217
$257$	−5.84314	−0.364485	−0.182243	−	0.983254i	$-0.558336\pi$
$257$	−5.84314	−0.364485	−0.182243	+	0.983254i	$0.558336\pi$
$258$	−6.35505	−0.395648
$259$	23.6667	1.47058
$260$	−1.57526	−0.0976934
$261$	−6.25694	−0.387295
$262$	−2.69931	−0.166764
$263$	14.4716	0.892355	0.446177	−	0.894945i	$-0.352785\pi$
$263$	14.4716	0.892355	0.446177	+	0.894945i	$0.352785\pi$
$264$	8.50879	0.523680
$265$	7.03860	0.432378
$266$	−20.9161	−1.28245
$267$	13.6887	0.837738
$268$	−2.79914	−0.170984
$269$	−27.3315	−1.66643	−0.833214	−	0.552950i	$-0.813502\pi$
$269$	−27.3315	−1.66643	−0.833214	+	0.552950i	$0.813502\pi$
$270$	1.30963	0.0797017
$271$	−0.546929	−0.0332236	−0.0166118	−	0.999862i	$-0.505288\pi$
$271$	−0.546929	−0.0332236	−0.0166118	+	0.999862i	$0.505288\pi$
$272$	3.36875	0.204261
$273$	−19.8072	−1.19879
$274$	−20.5444	−1.24113
$275$	−2.84353	−0.171471
$276$	0	0
$277$	−26.7137	−1.60507	−0.802536	−	0.596604i	$-0.796516\pi$
$277$	−26.7137	−1.60507	−0.802536	+	0.596604i	$0.796516\pi$
$278$	−25.9661	−1.55734
$279$	5.43934	0.325645
$280$	10.7182	0.640532
$281$	−3.59100	−0.214221	−0.107111	−	0.994247i	$-0.534160\pi$
$281$	−3.59100	−0.214221	−0.107111	+	0.994247i	$0.534160\pi$
$282$	14.4601	0.861089
$283$	−3.54121	−0.210503	−0.105251	−	0.994446i	$-0.533565\pi$
$283$	−3.54121	−0.210503	−0.105251	+	0.994446i	$0.533565\pi$
$284$	0.687813	0.0408142
$285$	−4.45884	−0.264119
$286$	20.5931	1.21769
$287$	−39.4269	−2.32730
$288$	−1.59854	−0.0941951
$289$	−15.9882	−0.940485
$290$	8.19429	0.481185
$291$	−10.5380	−0.617748
$292$	−3.83629	−0.224502
$293$	27.3644	1.59865	0.799323	−	0.600901i	$-0.205192\pi$
$293$	27.3644	1.59865	0.799323	+	0.600901i	$0.205192\pi$
$294$	7.63492	0.445278
$295$	1.07003	0.0622998
$296$	19.7714	1.14919
$297$	2.84353	0.164998
$298$	13.1376	0.761043
$299$	0	0
$300$	0.284864	0.0164467
$301$	−17.3812	−1.00184
$302$	−10.0187	−0.576511
$303$	−13.2464	−0.760984
$304$	−14.9332	−0.856478
$305$	4.78135	0.273779
$306$	1.31731	0.0753055
$307$	−24.1539	−1.37853	−0.689267	−	0.724508i	$-0.742067\pi$
$307$	−24.1539	−1.37853	−0.689267	+	0.724508i	$0.742067\pi$
$308$	2.90139	0.165322
$309$	−1.78878	−0.101760
$310$	−7.12353	−0.404589
$311$	−13.7867	−0.781770	−0.390885	−	0.920440i	$-0.627831\pi$
$311$	−13.7867	−0.781770	−0.390885	+	0.920440i	$0.627831\pi$
$312$	−16.5472	−0.936798
$313$	−19.2227	−1.08653	−0.543265	−	0.839561i	$-0.682812\pi$
$313$	−19.2227	−1.08653	−0.543265	+	0.839561i	$0.682812\pi$
$314$	16.0175	0.903922
$315$	3.58187	0.201816
$316$	2.14365	0.120590
$317$	2.42592	0.136253	0.0681266	−	0.997677i	$-0.478298\pi$
$317$	2.42592	0.136253	0.0681266	+	0.997677i	$0.478298\pi$
$318$	9.21798	0.516918
$319$	17.7918	0.996151
$320$	8.79175	0.491474
$321$	5.59816	0.312459
$322$	0	0
$323$	−4.48498	−0.249551
$324$	−0.284864	−0.0158258
$325$	5.52986	0.306741
$326$	3.31000	0.183324
$327$	16.5712	0.916392
$328$	−32.9376	−1.81868
$329$	39.5488	2.18040
$330$	−3.72398	−0.204998
$331$	0.777959	0.0427605	0.0213802	−	0.999771i	$-0.493194\pi$
$331$	0.777959	0.0427605	0.0213802	+	0.999771i	$0.493194\pi$
$332$	−2.65690	−0.145816
$333$	6.60734	0.362080
$334$	11.4165	0.624685
$335$	9.82621	0.536863
$336$	11.9961	0.654443
$337$	11.5684	0.630171	0.315085	−	0.949063i	$-0.397967\pi$
$337$	11.5684	0.630171	0.315085	+	0.949063i	$0.397967\pi$
$338$	−23.0224	−1.25225
$339$	−2.92366	−0.158791
$340$	0.286534	0.0155395
$341$	−15.4669	−0.837582
$342$	−5.83944	−0.315761
$343$	−4.19143	−0.226316
$344$	−14.5204	−0.782889
$345$	0	0
$346$	−6.94736	−0.373492
$347$	−11.2721	−0.605116	−0.302558	−	0.953131i	$-0.597841\pi$
$347$	−11.2721	−0.605116	−0.302558	+	0.953131i	$0.597841\pi$
$348$	−1.78238	−0.0955456
$349$	24.9939	1.33790	0.668948	−	0.743310i	$-0.266745\pi$
$349$	24.9939	1.33790	0.668948	+	0.743310i	$0.266745\pi$
$350$	−4.69094	−0.250741
$351$	−5.52986	−0.295162
$352$	4.54551	0.242277
$353$	23.1561	1.23248	0.616238	−	0.787560i	$-0.288656\pi$
$353$	23.1561	1.23248	0.616238	+	0.787560i	$0.288656\pi$
$354$	1.40135	0.0744810
$355$	−2.41453	−0.128150
$356$	3.89944	0.206670
$357$	3.60287	0.190684
$358$	−9.98317	−0.527627
$359$	4.36676	0.230469	0.115234	−	0.993338i	$-0.463238\pi$
$359$	4.36676	0.230469	0.115234	+	0.993338i	$0.463238\pi$
$360$	2.99233	0.157710
$361$	0.881274	0.0463828
$362$	24.1748	1.27060
$363$	2.91432	0.152962
$364$	−5.64238	−0.295741
$365$	13.4671	0.704899
$366$	6.26180	0.327310
$367$	−4.41929	−0.230685	−0.115342	−	0.993326i	$-0.536797\pi$
$367$	−4.41929	−0.230685	−0.115342	+	0.993326i	$0.536797\pi$
$368$	0	0
$369$	−11.0073	−0.573019
$370$	−8.65319	−0.449858
$371$	25.2114	1.30891
$372$	1.54947	0.0803365
$373$	5.24713	0.271686	0.135843	−	0.990730i	$-0.456626\pi$
$373$	5.24713	0.271686	0.135843	+	0.990730i	$0.456626\pi$
$374$	−3.74581	−0.193691
$375$	−1.00000	−0.0516398
$376$	33.0395	1.70388
$377$	−34.6000	−1.78199
$378$	4.69094	0.241276
$379$	22.0543	1.13285	0.566427	−	0.824112i	$-0.308325\pi$
$379$	22.0543	1.13285	0.566427	+	0.824112i	$0.308325\pi$
$380$	−1.27017	−0.0651581
$381$	17.2725	0.884897
$382$	−4.44980	−0.227672
$383$	−27.5132	−1.40586	−0.702928	−	0.711261i	$-0.748125\pi$
$383$	−27.5132	−1.40586	−0.702928	+	0.711261i	$0.748125\pi$
$384$	8.31687	0.424418
$385$	−10.1852	−0.519085
$386$	11.4425	0.582409
$387$	−4.85255	−0.246669
$388$	−3.00190	−0.152398
$389$	24.8945	1.26220	0.631100	−	0.775701i	$-0.282604\pi$
$389$	24.8945	1.26220	0.631100	+	0.775701i	$0.282604\pi$
$390$	7.24207	0.366717
$391$	0	0
$392$	17.4448	0.881093
$393$	−2.06112	−0.103970
$394$	−26.3426	−1.32712
$395$	−7.52516	−0.378632
$396$	0.810021	0.0407051
$397$	−24.6666	−1.23798	−0.618992	−	0.785398i	$-0.712459\pi$
$397$	−24.6666	−1.23798	−0.618992	+	0.785398i	$0.712459\pi$
$398$	−16.0653	−0.805280
$399$	−15.9710	−0.799551
$400$	−3.34912	−0.167456
$401$	−21.9125	−1.09426	−0.547129	−	0.837048i	$-0.684279\pi$
$401$	−21.9125	−1.09426	−0.547129	+	0.837048i	$0.684279\pi$
$402$	12.8687	0.641833
$403$	30.0788	1.49833
$404$	−3.77342	−0.187735
$405$	1.00000	0.0496904
$406$	29.3509	1.45666
$407$	−18.7882	−0.931296
$408$	3.00987	0.149011
$409$	6.45736	0.319296	0.159648	−	0.987174i	$-0.448964\pi$
$409$	6.45736	0.319296	0.159648	+	0.987174i	$0.448964\pi$
$410$	14.4156	0.711934
$411$	−15.6872	−0.773791
$412$	−0.509560	−0.0251042
$413$	3.83273	0.188596
$414$	0	0
$415$	9.32690	0.457840
$416$	−8.83972	−0.433403
$417$	−19.8270	−0.970932
$418$	16.6046	0.812160
$419$	−21.0229	−1.02704	−0.513518	−	0.858079i	$-0.671658\pi$
$419$	−21.0229	−1.02704	−0.513518	+	0.858079i	$0.671658\pi$
$420$	1.02035	0.0497879
$421$	20.2357	0.986226	0.493113	−	0.869965i	$-0.335859\pi$
$421$	20.2357	0.986226	0.493113	+	0.869965i	$0.335859\pi$
$422$	−0.110399	−0.00537415
$423$	11.0414	0.536850
$424$	21.0618	1.02285
$425$	−1.00586	−0.0487915
$426$	−3.16214	−0.153206
$427$	17.1262	0.828794
$428$	1.59472	0.0770835
$429$	15.7243	0.759177
$430$	6.35505	0.306468
$431$	−14.9835	−0.721731	−0.360865	−	0.932618i	$-0.617519\pi$
$431$	−14.9835	−0.721731	−0.360865	+	0.932618i	$0.617519\pi$
$432$	3.34912	0.161135
$433$	40.6923	1.95554	0.977772	−	0.209669i	$-0.0672387\pi$
$433$	40.6923	1.95554	0.977772	+	0.209669i	$0.0672387\pi$
$434$	−25.5156	−1.22479
$435$	6.25694	0.299997
$436$	4.72056	0.226074
$437$	0	0
$438$	17.6369	0.842724
$439$	−3.41106	−0.162801	−0.0814004	−	0.996681i	$-0.525939\pi$
$439$	−3.41106	−0.162801	−0.0814004	+	0.996681i	$0.525939\pi$
$440$	−8.50879	−0.405641
$441$	5.82982	0.277611
$442$	7.28452	0.346489
$443$	−0.553506	−0.0262979	−0.0131489	−	0.999914i	$-0.504186\pi$
$443$	−0.553506	−0.0262979	−0.0131489	+	0.999914i	$0.504186\pi$
$444$	1.88220	0.0893251
$445$	−13.6887	−0.648909
$446$	35.5620	1.68391
$447$	10.0316	0.474476
$448$	31.4909	1.48781
$449$	15.5645	0.734532	0.367266	−	0.930116i	$-0.380294\pi$
$449$	15.5645	0.734532	0.367266	+	0.930116i	$0.380294\pi$
$450$	−1.30963	−0.0617366
$451$	31.2997	1.47385
$452$	−0.832846	−0.0391738
$453$	−7.65000	−0.359429
$454$	2.93447	0.137721
$455$	19.8072	0.928578
$456$	−13.3423	−0.624812
$457$	34.1352	1.59678	0.798388	−	0.602144i	$-0.205687\pi$
$457$	34.1352	1.59678	0.798388	+	0.602144i	$0.205687\pi$
$458$	−35.4975	−1.65869
$459$	1.00586	0.0469496
$460$	0	0
$461$	−16.4338	−0.765399	−0.382700	−	0.923873i	$-0.625006\pi$
$461$	−16.4338	−0.765399	−0.382700	+	0.923873i	$0.625006\pi$
$462$	−13.3388	−0.620578
$463$	−37.5706	−1.74605	−0.873026	−	0.487674i	$-0.837845\pi$
$463$	−37.5706	−1.74605	−0.873026	+	0.487674i	$0.837845\pi$
$464$	20.9553	0.972824
$465$	−5.43934	−0.252243
$466$	−26.4043	−1.22316
$467$	−21.3013	−0.985705	−0.492853	−	0.870113i	$-0.664046\pi$
$467$	−21.3013	−0.985705	−0.492853	+	0.870113i	$0.664046\pi$
$468$	−1.57526	−0.0728164
$469$	35.1962	1.62521
$470$	−14.4601	−0.666997
$471$	12.2306	0.563555
$472$	3.20190	0.147379
$473$	13.7984	0.634450
$474$	−9.85518	−0.452664
$475$	4.45884	0.204586
$476$	1.02633	0.0470417
$477$	7.03860	0.322275
$478$	−22.8168	−1.04362
$479$	19.0745	0.871538	0.435769	−	0.900058i	$-0.356476\pi$
$479$	19.0745	0.871538	0.435769	+	0.900058i	$0.356476\pi$
$480$	1.59854	0.0729632
$481$	36.5376	1.66597
$482$	10.6972	0.487245
$483$	0	0
$484$	0.830187	0.0377358
$485$	10.5380	0.478506
$486$	1.30963	0.0594061
$487$	37.1788	1.68473	0.842366	−	0.538905i	$-0.181162\pi$
$487$	37.1788	1.68473	0.842366	+	0.538905i	$0.181162\pi$
$488$	14.3074	0.647664
$489$	2.52743	0.114294
$490$	−7.63492	−0.344910
$491$	−17.3183	−0.781562	−0.390781	−	0.920484i	$-0.627795\pi$
$491$	−17.3183	−0.781562	−0.390781	+	0.920484i	$0.627795\pi$
$492$	−3.13560	−0.141364
$493$	6.29362	0.283450
$494$	−32.2913	−1.45285
$495$	−2.84353	−0.127807
$496$	−18.2170	−0.817968
$497$	−8.64853	−0.387939
$498$	12.2148	0.547359
$499$	7.32351	0.327846	0.163923	−	0.986473i	$-0.447585\pi$
$499$	7.32351	0.327846	0.163923	+	0.986473i	$0.447585\pi$
$500$	−0.284864	−0.0127395
$501$	8.71737	0.389463
$502$	39.8168	1.77711
$503$	−17.8434	−0.795599	−0.397799	−	0.917472i	$-0.630226\pi$
$503$	−17.8434	−0.795599	−0.397799	+	0.917472i	$0.630226\pi$
$504$	10.7182	0.477424
$505$	13.2464	0.589456
$506$	0	0
$507$	−17.5793	−0.780724
$508$	4.92032	0.218304
$509$	34.9729	1.55015	0.775073	−	0.631872i	$-0.217713\pi$
$509$	34.9729	1.55015	0.775073	+	0.631872i	$0.217713\pi$
$510$	−1.31731	−0.0583314
$511$	48.2374	2.13390
$512$	25.3971	1.12240
$513$	−4.45884	−0.196863
$514$	7.65237	0.337531
$515$	1.78878	0.0788230
$516$	−1.38232	−0.0608532
$517$	−31.3965	−1.38082
$518$	−30.9946	−1.36183
$519$	−5.30482	−0.232856
$520$	16.5472	0.725641
$521$	18.6941	0.819004	0.409502	−	0.912309i	$-0.365702\pi$
$521$	18.6941	0.819004	0.409502	+	0.912309i	$0.365702\pi$
$522$	8.19429	0.358654
$523$	−22.9852	−1.00507	−0.502535	−	0.864557i	$-0.667599\pi$
$523$	−22.9852	−1.00507	−0.502535	+	0.864557i	$0.667599\pi$
$524$	−0.587141	−0.0256494
$525$	−3.58187	−0.156326
$526$	−18.9524	−0.826365
$527$	−5.47122	−0.238330
$528$	−9.52334	−0.414450
$529$	0	0
$530$	−9.21798	−0.400403
$531$	1.07003	0.0464355
$532$	−4.54957	−0.197249
$533$	−60.8690	−2.63653
$534$	−17.9272	−0.775787
$535$	−5.59816	−0.242030
$536$	29.4033	1.27003
$537$	−7.62288	−0.328952
$538$	35.7942	1.54320
$539$	−16.5773	−0.714034
$540$	0.284864	0.0122586
$541$	−4.49368	−0.193198	−0.0965992	−	0.995323i	$-0.530796\pi$
$541$	−4.49368	−0.193198	−0.0965992	+	0.995323i	$0.530796\pi$
$542$	0.716275	0.0307667
$543$	18.4592	0.792162
$544$	1.60791	0.0689387
$545$	−16.5712	−0.709834
$546$	25.9402	1.11014
$547$	37.6267	1.60880	0.804400	−	0.594088i	$-0.202487\pi$
$547$	37.6267	1.60880	0.804400	+	0.594088i	$0.202487\pi$
$548$	−4.46872	−0.190894
$549$	4.78135	0.204063
$550$	3.72398	0.158791
$551$	−27.8987	−1.18853
$552$	0	0
$553$	−26.9542	−1.14621
$554$	34.9851	1.48638
$555$	−6.60734	−0.280466
$556$	−5.64800	−0.239529
$557$	26.3953	1.11841	0.559203	−	0.829031i	$-0.311107\pi$
$557$	26.3953	1.11841	0.559203	+	0.829031i	$0.311107\pi$
$558$	−7.12353	−0.301563
$559$	−26.8339	−1.13495
$560$	−11.9961	−0.506929
$561$	−2.86020	−0.120758
$562$	4.70289	0.198379
$563$	8.54582	0.360163	0.180082	−	0.983652i	$-0.442364\pi$
$563$	8.54582	0.360163	0.180082	+	0.983652i	$0.442364\pi$
$564$	3.14530	0.132441
$565$	2.92366	0.122999
$566$	4.63768	0.194936
$567$	3.58187	0.150425
$568$	−7.22506	−0.303157
$569$	−1.65392	−0.0693360	−0.0346680	−	0.999399i	$-0.511037\pi$
$569$	−1.65392	−0.0693360	−0.0346680	+	0.999399i	$0.511037\pi$
$570$	5.83944	0.244587
$571$	−2.46478	−0.103148	−0.0515739	−	0.998669i	$-0.516424\pi$
$571$	−2.46478	−0.103148	−0.0515739	+	0.998669i	$0.516424\pi$
$572$	4.47930	0.187289
$573$	−3.39775	−0.141943
$574$	51.6347	2.15519
$575$	0	0
$576$	8.79175	0.366323
$577$	−0.371851	−0.0154804	−0.00774019	−	0.999970i	$-0.502464\pi$
$577$	−0.371851	−0.0154804	−0.00774019	+	0.999970i	$0.502464\pi$
$578$	20.9387	0.870936
$579$	8.73721	0.363106
$580$	1.78238	0.0740093
$581$	33.4078	1.38599
$582$	13.8009	0.572065
$583$	−20.0145	−0.828915
$584$	40.2980	1.66754
$585$	5.52986	0.228631
$586$	−35.8373	−1.48043
$587$	−2.74162	−0.113159	−0.0565793	−	0.998398i	$-0.518019\pi$
$587$	−2.74162	−0.113159	−0.0565793	+	0.998398i	$0.518019\pi$
$588$	1.66071	0.0684865
$589$	24.2532	0.999334
$590$	−1.40135	−0.0576927
$591$	−20.1145	−0.827399
$592$	−22.1288	−0.909488
$593$	−37.0009	−1.51945	−0.759723	−	0.650247i	$-0.774665\pi$
$593$	−37.0009	−1.51945	−0.759723	+	0.650247i	$0.774665\pi$
$594$	−3.72398	−0.152797
$595$	−3.60287	−0.147703
$596$	2.85763	0.117053
$597$	−12.2670	−0.502056
$598$	0	0
$599$	27.5694	1.12646	0.563228	−	0.826301i	$-0.309559\pi$
$599$	27.5694	1.12646	0.563228	+	0.826301i	$0.309559\pi$
$600$	−2.99233	−0.122161
$601$	22.1755	0.904556	0.452278	−	0.891877i	$-0.350611\pi$
$601$	22.1755	0.904556	0.452278	+	0.891877i	$0.350611\pi$
$602$	22.7630	0.927751
$603$	9.82621	0.400154
$604$	−2.17921	−0.0886710
$605$	−2.91432	−0.118484
$606$	17.3479	0.704709
$607$	42.7617	1.73564	0.867822	−	0.496875i	$-0.165519\pi$
$607$	42.7617	1.73564	0.867822	+	0.496875i	$0.165519\pi$
$608$	−7.12765	−0.289065
$609$	22.4116	0.908163
$610$	−6.26180	−0.253533
$611$	61.0572	2.47011
$612$	0.286534	0.0115825
$613$	8.50885	0.343669	0.171835	−	0.985126i	$-0.445031\pi$
$613$	8.50885	0.343669	0.171835	+	0.985126i	$0.445031\pi$
$614$	31.6327	1.27659
$615$	11.0073	0.443859
$616$	−30.4774	−1.22797
$617$	−6.42899	−0.258821	−0.129411	−	0.991591i	$-0.541309\pi$
$617$	−6.42899	−0.258821	−0.129411	+	0.991591i	$0.541309\pi$
$618$	2.34264	0.0942349
$619$	34.8539	1.40090	0.700448	−	0.713703i	$-0.252984\pi$
$619$	34.8539	1.40090	0.700448	+	0.713703i	$0.252984\pi$
$620$	−1.54947	−0.0622284
$621$	0	0
$622$	18.0555	0.723958
$623$	−49.0314	−1.96440
$624$	18.5202	0.741400
$625$	1.00000	0.0400000
$626$	25.1746	1.00618
$627$	12.6789	0.506345
$628$	3.48405	0.139029
$629$	−6.64607	−0.264996
$630$	−4.69094	−0.186891
$631$	−6.77350	−0.269649	−0.134824	−	0.990870i	$-0.543047\pi$
$631$	−6.77350	−0.269649	−0.134824	+	0.990870i	$0.543047\pi$
$632$	−22.5178	−0.895708
$633$	−0.0842979	−0.00335054
$634$	−3.17706	−0.126177
$635$	−17.2725	−0.685438
$636$	2.00505	0.0795053
$637$	32.2381	1.27732
$638$	−23.3007	−0.922485
$639$	−2.41453	−0.0955172
$640$	−8.31687	−0.328753
$641$	14.5299	0.573896	0.286948	−	0.957946i	$-0.407359\pi$
$641$	14.5299	0.573896	0.286948	+	0.957946i	$0.407359\pi$
$642$	−7.33153	−0.289352
$643$	8.52226	0.336085	0.168043	−	0.985780i	$-0.446255\pi$
$643$	8.52226	0.336085	0.168043	+	0.985780i	$0.446255\pi$
$644$	0	0
$645$	4.85255	0.191069
$646$	5.87367	0.231096
$647$	37.0807	1.45779	0.728896	−	0.684625i	$-0.240034\pi$
$647$	37.0807	1.45779	0.728896	+	0.684625i	$0.240034\pi$
$648$	2.99233	0.117550
$649$	−3.04268	−0.119436
$650$	−7.24207	−0.284058
$651$	−19.4830	−0.763600
$652$	0.719975	0.0281964
$653$	11.4996	0.450014	0.225007	−	0.974357i	$-0.427759\pi$
$653$	11.4996	0.450014	0.225007	+	0.974357i	$0.427759\pi$
$654$	−21.7022	−0.848625
$655$	2.06112	0.0805348
$656$	36.8650	1.43933
$657$	13.4671	0.525401
$658$	−51.7944	−2.01916
$659$	−9.12986	−0.355649	−0.177824	−	0.984062i	$-0.556906\pi$
$659$	−9.12986	−0.355649	−0.177824	+	0.984062i	$0.556906\pi$
$660$	−0.810021	−0.0315300
$661$	−15.8329	−0.615829	−0.307914	−	0.951414i	$-0.599631\pi$
$661$	−15.8329	−0.615829	−0.307914	+	0.951414i	$0.599631\pi$
$662$	−1.01884	−0.0395983
$663$	5.56227	0.216021
$664$	27.9092	1.08309
$665$	15.9710	0.619329
$666$	−8.65319	−0.335304
$667$	0	0
$668$	2.48327	0.0960805
$669$	27.1542	1.04984
$670$	−12.8687	−0.497162
$671$	−13.5959	−0.524864
$672$	5.72578	0.220877
$673$	−0.0646526	−0.00249217	−0.00124609	−	0.999999i	$-0.500397\pi$
$673$	−0.0646526	−0.00249217	−0.00124609	+	0.999999i	$0.500397\pi$
$674$	−15.1503	−0.583569
$675$	−1.00000	−0.0384900
$676$	−5.00772	−0.192604
$677$	8.65113	0.332490	0.166245	−	0.986084i	$-0.446836\pi$
$677$	8.65113	0.332490	0.166245	+	0.986084i	$0.446836\pi$
$678$	3.82891	0.147049
$679$	37.7458	1.44855
$680$	−3.00987	−0.115423
$681$	2.24068	0.0858631
$682$	20.2560	0.775642
$683$	19.5066	0.746398	0.373199	−	0.927751i	$-0.378261\pi$
$683$	19.5066	0.746398	0.373199	+	0.927751i	$0.378261\pi$
$684$	−1.27017	−0.0485660
$685$	15.6872	0.599376
$686$	5.48924	0.209580
$687$	−27.1049	−1.03412
$688$	16.2518	0.619594
$689$	38.9224	1.48283
$690$	0	0
$691$	−42.8313	−1.62938	−0.814690	−	0.579897i	$-0.803093\pi$
$691$	−42.8313	−1.62938	−0.814690	+	0.579897i	$0.803093\pi$
$692$	−1.51115	−0.0574455
$693$	−10.1852	−0.386903
$694$	14.7623	0.560367
$695$	19.8270	0.752080
$696$	18.7228	0.709688
$697$	11.0719	0.419377
$698$	−32.7329	−1.23896
$699$	−20.1616	−0.762583
$700$	−1.02035	−0.0385655
$701$	37.7750	1.42674	0.713371	−	0.700786i	$-0.247167\pi$
$701$	37.7750	1.42674	0.713371	+	0.700786i	$0.247167\pi$
$702$	7.24207	0.273334
$703$	29.4611	1.11115
$704$	−24.9996	−0.942209
$705$	−11.0414	−0.415843
$706$	−30.3260	−1.14133
$707$	47.4468	1.78442
$708$	0.304815	0.0114556
$709$	52.5806	1.97470	0.987352	−	0.158543i	$-0.0506798\pi$
$709$	52.5806	1.97470	0.987352	+	0.158543i	$0.0506798\pi$
$710$	3.16214	0.118673
$711$	−7.52516	−0.282215
$712$	−40.9613	−1.53509
$713$	0	0
$714$	−4.71843	−0.176583
$715$	−15.7243	−0.588056
$716$	−2.17149	−0.0811523
$717$	−17.4223	−0.650647
$718$	−5.71885	−0.213426
$719$	45.6240	1.70149	0.850744	−	0.525580i	$-0.176152\pi$
$719$	45.6240	1.70149	0.850744	+	0.525580i	$0.176152\pi$
$720$	−3.34912	−0.124814
$721$	6.40718	0.238616
$722$	−1.15414	−0.0429528
$723$	8.16811	0.303775
$724$	5.25838	0.195426
$725$	−6.25694	−0.232377
$726$	−3.81669	−0.141651
$727$	38.9327	1.44394	0.721968	−	0.691927i	$-0.243238\pi$
$727$	38.9327	1.44394	0.721968	+	0.691927i	$0.243238\pi$
$728$	59.2698	2.19669
$729$	1.00000	0.0370370
$730$	−17.6369	−0.652772
$731$	4.88099	0.180530
$732$	1.36204	0.0503423
$733$	14.9272	0.551350	0.275675	−	0.961251i	$-0.411099\pi$
$733$	14.9272	0.551350	0.275675	+	0.961251i	$0.411099\pi$
$734$	5.78764	0.213626
$735$	−5.82982	−0.215036
$736$	0	0
$737$	−27.9411	−1.02922
$738$	14.4156	0.530644
$739$	10.8235	0.398147	0.199074	−	0.979985i	$-0.436207\pi$
$739$	10.8235	0.398147	0.199074	+	0.979985i	$0.436207\pi$
$740$	−1.88220	−0.0691909
$741$	−24.6568	−0.905788
$742$	−33.0176	−1.21212
$743$	32.3340	1.18622	0.593110	−	0.805121i	$-0.297900\pi$
$743$	32.3340	1.18622	0.593110	+	0.805121i	$0.297900\pi$
$744$	−16.2763	−0.596718
$745$	−10.0316	−0.367528
$746$	−6.87181	−0.251595
$747$	9.32690	0.341253
$748$	−0.814769	−0.0297909
$749$	−20.0519	−0.732681
$750$	1.30963	0.0478210
$751$	−8.27117	−0.301819	−0.150910	−	0.988548i	$-0.548220\pi$
$751$	−8.27117	−0.301819	−0.150910	+	0.988548i	$0.548220\pi$
$752$	−36.9790	−1.34848
$753$	30.4031	1.10795
$754$	45.3132	1.65021
$755$	7.65000	0.278412
$756$	1.02035	0.0371097
$757$	−3.24336	−0.117882	−0.0589410	−	0.998261i	$-0.518772\pi$
$757$	−3.24336	−0.117882	−0.0589410	+	0.998261i	$0.518772\pi$
$758$	−28.8830	−1.04908
$759$	0	0
$760$	13.3423	0.483977
$761$	5.52453	0.200264	0.100132	−	0.994974i	$-0.468073\pi$
$761$	5.52453	0.200264	0.100132	+	0.994974i	$0.468073\pi$
$762$	−22.6206	−0.819458
$763$	−59.3561	−2.14884
$764$	−0.967898	−0.0350173
$765$	−1.00586	−0.0363670
$766$	36.0321	1.30189
$767$	5.91714	0.213655
$768$	6.69146	0.241457
$769$	16.2134	0.584671	0.292336	−	0.956316i	$-0.405568\pi$
$769$	16.2134	0.584671	0.292336	+	0.956316i	$0.405568\pi$
$770$	13.3388	0.480698
$771$	5.84314	0.210436
$772$	2.48892	0.0895782
$773$	−31.7240	−1.14103	−0.570516	−	0.821287i	$-0.693257\pi$
$773$	−31.7240	−1.14103	−0.570516	+	0.821287i	$0.693257\pi$
$774$	6.35505	0.228428
$775$	5.43934	0.195387
$776$	31.5332	1.13197
$777$	−23.6667	−0.849037
$778$	−32.6026	−1.16886
$779$	−49.0800	−1.75847
$780$	1.57526	0.0564033
$781$	6.86578	0.245677
$782$	0	0
$783$	6.25694	0.223605
$784$	−19.5248	−0.697314
$785$	−12.2306	−0.436528
$786$	2.69931	0.0962813
$787$	36.8430	1.31331	0.656655	−	0.754191i	$-0.271971\pi$
$787$	36.8430	1.31331	0.656655	+	0.754191i	$0.271971\pi$
$788$	−5.72990	−0.204119
$789$	−14.4716	−0.515201
$790$	9.85518	0.350632
$791$	10.4722	0.372348
$792$	−8.50879	−0.302347
$793$	26.4401	0.938917
$794$	32.3042	1.14643
$795$	−7.03860	−0.249633
$796$	−3.49444	−0.123857
$797$	42.4016	1.50194	0.750971	−	0.660336i	$-0.229586\pi$
$797$	42.4016	1.50194	0.750971	+	0.660336i	$0.229586\pi$
$798$	20.9161	0.740423
$799$	−11.1061	−0.392906
$800$	−1.59854	−0.0565171
$801$	−13.6887	−0.483668
$802$	28.6973	1.01334
$803$	−38.2941	−1.35137
$804$	2.79914	0.0987179
$805$	0	0
$806$	−39.3921	−1.38753
$807$	27.3315	0.962113
$808$	39.6375	1.39444
$809$	−36.8403	−1.29523	−0.647617	−	0.761966i	$-0.724234\pi$
$809$	−36.8403	−1.29523	−0.647617	+	0.761966i	$0.724234\pi$
$810$	−1.30963	−0.0460158
$811$	−38.2770	−1.34409	−0.672044	−	0.740511i	$-0.734584\pi$
$811$	−38.2770	−1.34409	−0.672044	+	0.740511i	$0.734584\pi$
$812$	6.38426	0.224044
$813$	0.546929	0.0191816
$814$	24.6056	0.862426
$815$	−2.52743	−0.0885320
$816$	−3.36875	−0.117930
$817$	−21.6368	−0.756974
$818$	−8.45676	−0.295684
$819$	19.8072	0.692121
$820$	3.13560	0.109500
$821$	10.5180	0.367082	0.183541	−	0.983012i	$-0.441244\pi$
$821$	10.5180	0.367082	0.183541	+	0.983012i	$0.441244\pi$
$822$	20.5444	0.716569
$823$	−28.5022	−0.993525	−0.496762	−	0.867887i	$-0.665478\pi$
$823$	−28.5022	−0.993525	−0.496762	+	0.867887i	$0.665478\pi$
$824$	5.35262	0.186467
$825$	2.84353	0.0989991
$826$	−5.01946	−0.174650
$827$	−47.9439	−1.66717	−0.833587	−	0.552388i	$-0.813717\pi$
$827$	−47.9439	−1.66717	−0.833587	+	0.552388i	$0.813717\pi$
$828$	0	0
$829$	−35.7827	−1.24278	−0.621391	−	0.783500i	$-0.713432\pi$
$829$	−35.7827	−1.24278	−0.621391	+	0.783500i	$0.713432\pi$
$830$	−12.2148	−0.423982
$831$	26.7137	0.926689
$832$	48.6171	1.68549
$833$	−5.86399	−0.203175
$834$	25.9661	0.899131
$835$	−8.71737	−0.301677
$836$	3.61176	0.124915
$837$	−5.43934	−0.188011
$838$	27.5323	0.951087
$839$	12.8079	0.442178	0.221089	−	0.975254i	$-0.429039\pi$
$839$	12.8079	0.442178	0.221089	+	0.975254i	$0.429039\pi$
$840$	−10.7182	−0.369811
$841$	10.1493	0.349977
$842$	−26.5013	−0.913294
$843$	3.59100	0.123681
$844$	−0.0240135	−0.000826577 0
$845$	17.5793	0.604746
$846$	−14.4601	−0.497150
$847$	−10.4387	−0.358679
$848$	−23.5731	−0.809505
$849$	3.54121	0.121534
$850$	1.31731	0.0451833
$851$	0	0
$852$	−0.687813	−0.0235641
$853$	32.0003	1.09567	0.547835	−	0.836586i	$-0.315452\pi$
$853$	32.0003	1.09567	0.547835	+	0.836586i	$0.315452\pi$
$854$	−22.4290	−0.767504
$855$	4.45884	0.152489
$856$	−16.7515	−0.572556
$857$	−41.1042	−1.40409	−0.702046	−	0.712132i	$-0.747730\pi$
$857$	−41.1042	−1.40409	−0.702046	+	0.712132i	$0.747730\pi$
$858$	−20.5931	−0.703036
$859$	15.2784	0.521292	0.260646	−	0.965434i	$-0.416065\pi$
$859$	15.2784	0.521292	0.260646	+	0.965434i	$0.416065\pi$
$860$	1.38232	0.0471367
$861$	39.4269	1.34367
$862$	19.6229	0.668358
$863$	−11.5654	−0.393690	−0.196845	−	0.980435i	$-0.563070\pi$
$863$	−11.5654	−0.393690	−0.196845	+	0.980435i	$0.563070\pi$
$864$	1.59854	0.0543836
$865$	5.30482	0.180369
$866$	−53.2919	−1.81093
$867$	15.9882	0.542989
$868$	−5.55002	−0.188380
$869$	21.3980	0.725878
$870$	−8.19429	−0.277813
$871$	54.3375	1.84116
$872$	−49.5867	−1.67922
$873$	10.5380	0.356657
$874$	0	0
$875$	3.58187	0.121089
$876$	3.83629	0.129616
$877$	−29.5809	−0.998875	−0.499437	−	0.866350i	$-0.666460\pi$
$877$	−29.5809	−0.998875	−0.499437	+	0.866350i	$0.666460\pi$
$878$	4.46723	0.150762
$879$	−27.3644	−0.922979
$880$	9.52334	0.321032
$881$	50.6536	1.70656	0.853281	−	0.521452i	$-0.174609\pi$
$881$	50.6536	1.70656	0.853281	+	0.521452i	$0.174609\pi$
$882$	−7.63492	−0.257081
$883$	−25.6030	−0.861609	−0.430804	−	0.902445i	$-0.641770\pi$
$883$	−25.6030	−0.861609	−0.430804	+	0.902445i	$0.641770\pi$
$884$	1.58449	0.0532923
$885$	−1.07003	−0.0359688
$886$	0.724890	0.0243531
$887$	−55.4461	−1.86170	−0.930849	−	0.365404i	$-0.880931\pi$
$887$	−55.4461	−1.86170	−0.930849	+	0.365404i	$0.880931\pi$
$888$	−19.7714	−0.663483
$889$	−61.8679	−2.07498
$890$	17.9272	0.600922
$891$	−2.84353	−0.0952619
$892$	7.73528	0.258996
$893$	49.2318	1.64748
$894$	−13.1376	−0.439388
$895$	7.62288	0.254805
$896$	−29.7900	−0.995213
$897$	0	0
$898$	−20.3837	−0.680213
$899$	−34.0336	−1.13509
$900$	−0.284864	−0.00949548
$901$	−7.07986	−0.235864
$902$	−40.9911	−1.36486
$903$	17.3812	0.578411
$904$	8.74855	0.290972
$905$	−18.4592	−0.613606
$906$	10.0187	0.332849
$907$	−34.3658	−1.14110	−0.570549	−	0.821264i	$-0.693270\pi$
$907$	−34.3658	−1.14110	−0.570549	+	0.821264i	$0.693270\pi$
$908$	0.638290	0.0211824
$909$	13.2464	0.439355
$910$	−25.9402	−0.859909
$911$	2.37469	0.0786769	0.0393384	−	0.999226i	$-0.487475\pi$
$911$	2.37469	0.0786769	0.0393384	+	0.999226i	$0.487475\pi$
$912$	14.9332	0.494488
$913$	−26.5213	−0.877728
$914$	−44.7045	−1.47869
$915$	−4.78135	−0.158066
$916$	−7.72123	−0.255117
$917$	7.38269	0.243798
$918$	−1.31731	−0.0434777
$919$	2.60116	0.0858042	0.0429021	−	0.999079i	$-0.486340\pi$
$919$	2.60116	0.0858042	0.0429021	+	0.999079i	$0.486340\pi$
$920$	0	0
$921$	24.1539	0.795897
$922$	21.5222	0.708797
$923$	−13.3520	−0.439486
$924$	−2.90139	−0.0954489
$925$	6.60734	0.217248
$926$	49.2036	1.61693
$927$	1.78878	0.0587512
$928$	10.0020	0.328332
$929$	−23.7743	−0.780008	−0.390004	−	0.920813i	$-0.627526\pi$
$929$	−23.7743	−0.780008	−0.390004	+	0.920813i	$0.627526\pi$
$930$	7.12353	0.233590
$931$	25.9943	0.851927
$932$	−5.74333	−0.188129
$933$	13.7867	0.451355
$934$	27.8968	0.912812
$935$	2.86020	0.0935385
$936$	16.5472	0.540861
$937$	−7.03434	−0.229802	−0.114901	−	0.993377i	$-0.536655\pi$
$937$	−7.03434	−0.229802	−0.114901	+	0.993377i	$0.536655\pi$
$938$	−46.0941	−1.50503
$939$	19.2227	0.627309
$940$	−3.14530	−0.102588
$941$	−45.9333	−1.49738	−0.748691	−	0.662919i	$-0.769317\pi$
$941$	−45.9333	−1.49738	−0.748691	+	0.662919i	$0.769317\pi$
$942$	−16.0175	−0.521879
$943$	0	0
$944$	−3.58368	−0.116639
$945$	−3.58187	−0.116518
$946$	−18.0708	−0.587532
$947$	−39.2614	−1.27582	−0.637911	−	0.770110i	$-0.720201\pi$
$947$	−39.2614	−1.27582	−0.637911	+	0.770110i	$0.720201\pi$
$948$	−2.14365	−0.0696225
$949$	74.4710	2.41743
$950$	−5.83944	−0.189457
$951$	−2.42592	−0.0786658
$952$	−10.7810	−0.349414
$953$	45.4024	1.47073	0.735364	−	0.677673i	$-0.237011\pi$
$953$	45.4024	1.47073	0.735364	+	0.677673i	$0.237011\pi$
$954$	−9.21798	−0.298443
$955$	3.39775	0.109949
$956$	−4.96299	−0.160515
$957$	−17.7918	−0.575128
$958$	−24.9806	−0.807088
$959$	56.1895	1.81445
$960$	−8.79175	−0.283753
$961$	−1.41358	−0.0455993
$962$	−47.8509	−1.54277
$963$	−5.59816	−0.180398
$964$	2.32680	0.0749413
$965$	−8.73721	−0.281261
$966$	0	0
$967$	−10.4642	−0.336506	−0.168253	−	0.985744i	$-0.553813\pi$
$967$	−10.4642	−0.336506	−0.168253	+	0.985744i	$0.553813\pi$
$968$	−8.72062	−0.280291
$969$	4.48498	0.144078
$970$	−13.8009	−0.443120
$971$	−27.3303	−0.877071	−0.438536	−	0.898714i	$-0.644503\pi$
$971$	−27.3303	−0.877071	−0.438536	+	0.898714i	$0.644503\pi$
$972$	0.284864	0.00913703
$973$	71.0178	2.27673
$974$	−48.6906	−1.56015
$975$	−5.52986	−0.177097
$976$	−16.0133	−0.512574
$977$	−7.59574	−0.243009	−0.121505	−	0.992591i	$-0.538772\pi$
$977$	−7.59574	−0.243009	−0.121505	+	0.992591i	$0.538772\pi$
$978$	−3.31000	−0.105842
$979$	38.9244	1.24403
$980$	−1.66071	−0.0530494
$981$	−16.5712	−0.529079
$982$	22.6806	0.723766
$983$	1.98264	0.0632363	0.0316181	−	0.999500i	$-0.489934\pi$
$983$	1.98264	0.0632363	0.0316181	+	0.999500i	$0.489934\pi$
$984$	32.9376	1.05001
$985$	20.1145	0.640901
$986$	−8.24232	−0.262489
$987$	−39.5488	−1.25885
$988$	−7.02383	−0.223458
$989$	0	0
$990$	3.72398	0.118356
$991$	16.7194	0.531108	0.265554	−	0.964096i	$-0.414445\pi$
$991$	16.7194	0.531108	0.265554	+	0.964096i	$0.414445\pi$
$992$	−8.69502	−0.276067
$993$	−0.777959	−0.0246878
$994$	11.3264	0.359251
$995$	12.2670	0.388891
$996$	2.65690	0.0841872
$997$	−40.0833	−1.26945	−0.634725	−	0.772738i	$-0.718887\pi$
$997$	−40.0833	−1.26945	−0.634725	+	0.772738i	$0.718887\pi$
$998$	−9.59111	−0.303601
$999$	−6.60734	−0.209047

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bs.1.5	yes	16
23.22	odd	2		7935.2.a.br.1.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.br.1.5	✓	16	23.22	odd	2
7935.2.a.bs.1.5	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.30963 q^{2} -1.00000 q^{3} -0.284864 q^{4} +1.00000 q^{5} +1.30963 q^{6} +3.58187 q^{7} +2.99233 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.30963 q^{2} -1.00000 q^{3} -0.284864 q^{4} +1.00000 q^{5} +1.30963 q^{6} +3.58187 q^{7} +2.99233 q^{8} +1.00000 q^{9} -1.30963 q^{10} -2.84353 q^{11} +0.284864 q^{12} +5.52986 q^{13} -4.69094 q^{14} -1.00000 q^{15} -3.34912 q^{16} -1.00586 q^{17} -1.30963 q^{18} +4.45884 q^{19} -0.284864 q^{20} -3.58187 q^{21} +3.72398 q^{22} -2.99233 q^{24} +1.00000 q^{25} -7.24207 q^{26} -1.00000 q^{27} -1.02035 q^{28} -6.25694 q^{29} +1.30963 q^{30} +5.43934 q^{31} -1.59854 q^{32} +2.84353 q^{33} +1.31731 q^{34} +3.58187 q^{35} -0.284864 q^{36} +6.60734 q^{37} -5.83944 q^{38} -5.52986 q^{39} +2.99233 q^{40} -11.0073 q^{41} +4.69094 q^{42} -4.85255 q^{43} +0.810021 q^{44} +1.00000 q^{45} +11.0414 q^{47} +3.34912 q^{48} +5.82982 q^{49} -1.30963 q^{50} +1.00586 q^{51} -1.57526 q^{52} +7.03860 q^{53} +1.30963 q^{54} -2.84353 q^{55} +10.7182 q^{56} -4.45884 q^{57} +8.19429 q^{58} +1.07003 q^{59} +0.284864 q^{60} +4.78135 q^{61} -7.12353 q^{62} +3.58187 q^{63} +8.79175 q^{64} +5.52986 q^{65} -3.72398 q^{66} +9.82621 q^{67} +0.286534 q^{68} -4.69094 q^{70} -2.41453 q^{71} +2.99233 q^{72} +13.4671 q^{73} -8.65319 q^{74} -1.00000 q^{75} -1.27017 q^{76} -10.1852 q^{77} +7.24207 q^{78} -7.52516 q^{79} -3.34912 q^{80} +1.00000 q^{81} +14.4156 q^{82} +9.32690 q^{83} +1.02035 q^{84} -1.00586 q^{85} +6.35505 q^{86} +6.25694 q^{87} -8.50879 q^{88} -13.6887 q^{89} -1.30963 q^{90} +19.8072 q^{91} -5.43934 q^{93} -14.4601 q^{94} +4.45884 q^{95} +1.59854 q^{96} +10.5380 q^{97} -7.63492 q^{98} -2.84353 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} + 16 q^{4} + 16 q^{5} + 12 q^{7} + 16 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

Properties

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