LMFDB - Embedded newform 3179.2.a.bi.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3179,2,Mod(1,3179)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3179, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3179.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3179 = 11 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3179.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:	$25.3844428026$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 187)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	3179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.07580 q^{2} -1.79573 q^{3} +2.30896 q^{4} -1.45571 q^{5} +3.72759 q^{6} +4.42094 q^{7} -0.641346 q^{8} +0.224658 q^{9} +O(q^{10})$	\(q-2.07580 q^{2} -1.79573 q^{3} +2.30896 q^{4} -1.45571 q^{5} +3.72759 q^{6} +4.42094 q^{7} -0.641346 q^{8} +0.224658 q^{9} +3.02177 q^{10} -1.00000 q^{11} -4.14628 q^{12} +4.55252 q^{13} -9.17701 q^{14} +2.61406 q^{15} -3.28662 q^{16} -0.466345 q^{18} +5.89664 q^{19} -3.36118 q^{20} -7.93883 q^{21} +2.07580 q^{22} +7.73668 q^{23} +1.15169 q^{24} -2.88091 q^{25} -9.45013 q^{26} +4.98377 q^{27} +10.2078 q^{28} +2.58552 q^{29} -5.42629 q^{30} +4.50234 q^{31} +8.10506 q^{32} +1.79573 q^{33} -6.43561 q^{35} +0.518726 q^{36} +7.95713 q^{37} -12.2403 q^{38} -8.17510 q^{39} +0.933613 q^{40} -1.62048 q^{41} +16.4795 q^{42} +0.0727574 q^{43} -2.30896 q^{44} -0.327036 q^{45} -16.0598 q^{46} +9.01560 q^{47} +5.90189 q^{48} +12.5447 q^{49} +5.98021 q^{50} +10.5116 q^{52} -3.05201 q^{53} -10.3453 q^{54} +1.45571 q^{55} -2.83535 q^{56} -10.5888 q^{57} -5.36704 q^{58} -4.30140 q^{59} +6.03578 q^{60} +5.40254 q^{61} -9.34597 q^{62} +0.993198 q^{63} -10.2513 q^{64} -6.62714 q^{65} -3.72759 q^{66} +5.15253 q^{67} -13.8930 q^{69} +13.3591 q^{70} +5.74256 q^{71} -0.144083 q^{72} +2.32415 q^{73} -16.5174 q^{74} +5.17335 q^{75} +13.6151 q^{76} -4.42094 q^{77} +16.9699 q^{78} -3.04799 q^{79} +4.78436 q^{80} -9.62350 q^{81} +3.36380 q^{82} -0.578275 q^{83} -18.3305 q^{84} -0.151030 q^{86} -4.64291 q^{87} +0.641346 q^{88} -14.9787 q^{89} +0.678863 q^{90} +20.1264 q^{91} +17.8637 q^{92} -8.08500 q^{93} -18.7146 q^{94} -8.58379 q^{95} -14.5545 q^{96} -14.7024 q^{97} -26.0404 q^{98} -0.224658 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9}+O(q^{10}) $ 28 * q + 8 * q^3 + 24 * q^4 + 16 * q^5 + 16 * q^6 + 12 * q^7 + 20 * q^9	$ 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9} + 24 q^{10} - 28 q^{11} + 24 q^{12} + 16 q^{14} - 16 q^{15} + 16 q^{16} + 32 q^{20} + 8 q^{23} - 8 q^{24} + 20 q^{25} - 24 q^{26} + 32 q^{27} + 32 q^{28} + 36 q^{29} + 40 q^{30} + 56 q^{31} + 40 q^{32} - 8 q^{33} + 16 q^{35} + 40 q^{36} + 64 q^{37} - 8 q^{38} + 32 q^{39} + 72 q^{40} + 28 q^{41} + 24 q^{42} + 16 q^{43} - 24 q^{44} + 24 q^{45} - 36 q^{47} + 56 q^{48} + 16 q^{49} + 56 q^{50} - 20 q^{53} + 64 q^{54} - 16 q^{55} + 48 q^{56} + 32 q^{57} - 16 q^{58} - 28 q^{59} + 8 q^{60} + 104 q^{61} - 8 q^{62} + 28 q^{63} + 32 q^{65} - 16 q^{66} - 12 q^{67} - 32 q^{69} + 40 q^{71} + 40 q^{72} + 76 q^{73} + 24 q^{74} - 16 q^{75} - 16 q^{76} - 12 q^{77} - 24 q^{78} + 24 q^{79} + 8 q^{80} + 12 q^{81} + 56 q^{82} + 32 q^{83} - 40 q^{84} - 16 q^{86} - 8 q^{87} - 52 q^{89} + 16 q^{90} + 80 q^{91} - 56 q^{92} + 24 q^{97} - 24 q^{98} - 20 q^{99}+O(q^{100}) $ 28 * q + 8 * q^3 + 24 * q^4 + 16 * q^5 + 16 * q^6 + 12 * q^7 + 20 * q^9 + 24 * q^10 - 28 * q^11 + 24 * q^12 + 16 * q^14 - 16 * q^15 + 16 * q^16 + 32 * q^20 + 8 * q^23 - 8 * q^24 + 20 * q^25 - 24 * q^26 + 32 * q^27 + 32 * q^28 + 36 * q^29 + 40 * q^30 + 56 * q^31 + 40 * q^32 - 8 * q^33 + 16 * q^35 + 40 * q^36 + 64 * q^37 - 8 * q^38 + 32 * q^39 + 72 * q^40 + 28 * q^41 + 24 * q^42 + 16 * q^43 - 24 * q^44 + 24 * q^45 - 36 * q^47 + 56 * q^48 + 16 * q^49 + 56 * q^50 - 20 * q^53 + 64 * q^54 - 16 * q^55 + 48 * q^56 + 32 * q^57 - 16 * q^58 - 28 * q^59 + 8 * q^60 + 104 * q^61 - 8 * q^62 + 28 * q^63 + 32 * q^65 - 16 * q^66 - 12 * q^67 - 32 * q^69 + 40 * q^71 + 40 * q^72 + 76 * q^73 + 24 * q^74 - 16 * q^75 - 16 * q^76 - 12 * q^77 - 24 * q^78 + 24 * q^79 + 8 * q^80 + 12 * q^81 + 56 * q^82 + 32 * q^83 - 40 * q^84 - 16 * q^86 - 8 * q^87 - 52 * q^89 + 16 * q^90 + 80 * q^91 - 56 * q^92 + 24 * q^97 - 24 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.07580	−1.46782	−0.733908	−	0.679249i	$-0.762305\pi$
$2$	−2.07580	−1.46782	−0.733908	+	0.679249i	$0.762305\pi$
$3$	−1.79573	−1.03677	−0.518384	−	0.855148i	$-0.673466\pi$
$3$	−1.79573	−1.03677	−0.518384	+	0.855148i	$0.673466\pi$
$4$	2.30896	1.15448
$5$	−1.45571	−0.651013	−0.325506	−	0.945540i	$-0.605535\pi$
$5$	−1.45571	−0.651013	−0.325506	+	0.945540i	$0.605535\pi$
$6$	3.72759	1.52178
$7$	4.42094	1.67096	0.835480	−	0.549522i	$-0.185190\pi$
$7$	4.42094	1.67096	0.835480	+	0.549522i	$0.185190\pi$
$8$	−0.641346	−0.226750
$9$	0.224658	0.0748858
$10$	3.02177	0.955567
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.14628	−1.19693
$13$	4.55252	1.26264	0.631320	−	0.775522i	$-0.282513\pi$
$13$	4.55252	1.26264	0.631320	+	0.775522i	$0.282513\pi$
$14$	−9.17701	−2.45266
$15$	2.61406	0.674949
$16$	−3.28662	−0.821654
$17$	0	0
$17$	0	0
$18$	−0.466345	−0.109919
$19$	5.89664	1.35278	0.676391	−	0.736543i	$-0.263543\pi$
$19$	5.89664	1.35278	0.676391	+	0.736543i	$0.263543\pi$
$20$	−3.36118	−0.751582
$21$	−7.93883	−1.73240
$22$	2.07580	0.442563
$23$	7.73668	1.61321	0.806605	−	0.591091i	$-0.201303\pi$
$23$	7.73668	1.61321	0.806605	+	0.591091i	$0.201303\pi$
$24$	1.15169	0.235087
$25$	−2.88091	−0.576182
$26$	−9.45013	−1.85332
$27$	4.98377	0.959128
$28$	10.2078	1.92909
$29$	2.58552	0.480120	0.240060	−	0.970758i	$-0.422833\pi$
$29$	2.58552	0.480120	0.240060	+	0.970758i	$0.422833\pi$
$30$	−5.42629	−0.990700
$31$	4.50234	0.808644	0.404322	−	0.914617i	$-0.367508\pi$
$31$	4.50234	0.808644	0.404322	+	0.914617i	$0.367508\pi$
$32$	8.10506	1.43279
$33$	1.79573	0.312597
$34$	0	0
$35$	−6.43561	−1.08782
$36$	0.518726	0.0864543
$37$	7.95713	1.30814	0.654072	−	0.756432i	$-0.273059\pi$
$37$	7.95713	1.30814	0.654072	+	0.756432i	$0.273059\pi$
$38$	−12.2403	−1.98563
$39$	−8.17510	−1.30906
$40$	0.933613	0.147617
$41$	−1.62048	−0.253077	−0.126538	−	0.991962i	$-0.540387\pi$
$41$	−1.62048	−0.253077	−0.126538	+	0.991962i	$0.540387\pi$
$42$	16.4795	2.54284
$43$	0.0727574	0.0110954	0.00554770	−	0.999985i	$-0.498234\pi$
$43$	0.0727574	0.0110954	0.00554770	+	0.999985i	$0.498234\pi$
$44$	−2.30896	−0.348089
$45$	−0.327036	−0.0487516
$46$	−16.0598	−2.36789
$47$	9.01560	1.31506	0.657530	−	0.753428i	$-0.271601\pi$
$47$	9.01560	1.31506	0.657530	+	0.753428i	$0.271601\pi$
$48$	5.90189	0.851864
$49$	12.5447	1.79210
$50$	5.98021	0.845729
$51$	0	0
$52$	10.5116	1.45769
$53$	−3.05201	−0.419226	−0.209613	−	0.977784i	$-0.567220\pi$
$53$	−3.05201	−0.419226	−0.209613	+	0.977784i	$0.567220\pi$
$54$	−10.3453	−1.40782
$55$	1.45571	0.196288
$56$	−2.83535	−0.378890
$57$	−10.5888	−1.40252
$58$	−5.36704	−0.704727
$59$	−4.30140	−0.559995	−0.279997	−	0.960001i	$-0.590334\pi$
$59$	−4.30140	−0.559995	−0.279997	+	0.960001i	$0.590334\pi$
$60$	6.03578	0.779216
$61$	5.40254	0.691724	0.345862	−	0.938285i	$-0.387587\pi$
$61$	5.40254	0.691724	0.345862	+	0.938285i	$0.387587\pi$
$62$	−9.34597	−1.18694
$63$	0.993198	0.125131
$64$	−10.2513	−1.28141
$65$	−6.62714	−0.821995
$66$	−3.72759	−0.458835
$67$	5.15253	0.629482	0.314741	−	0.949178i	$-0.398082\pi$
$67$	5.15253	0.629482	0.314741	+	0.949178i	$0.398082\pi$
$68$	0	0
$69$	−13.8930	−1.67252
$70$	13.3591	1.59671
$71$	5.74256	0.681517	0.340758	−	0.940151i	$-0.389316\pi$
$71$	5.74256	0.681517	0.340758	+	0.940151i	$0.389316\pi$
$72$	−0.144083	−0.0169804
$73$	2.32415	0.272021	0.136011	−	0.990707i	$-0.456572\pi$
$73$	2.32415	0.272021	0.136011	+	0.990707i	$0.456572\pi$
$74$	−16.5174	−1.92011
$75$	5.17335	0.597367
$76$	13.6151	1.56176
$77$	−4.42094	−0.503813
$78$	16.9699	1.92146
$79$	−3.04799	−0.342926	−0.171463	−	0.985191i	$-0.554849\pi$
$79$	−3.04799	−0.342926	−0.171463	+	0.985191i	$0.554849\pi$
$80$	4.78436	0.534908
$81$	−9.62350	−1.06928
$82$	3.36380	0.371470
$83$	−0.578275	−0.0634740	−0.0317370	−	0.999496i	$-0.510104\pi$
$83$	−0.578275	−0.0634740	−0.0317370	+	0.999496i	$0.510104\pi$
$84$	−18.3305	−2.00002
$85$	0	0
$86$	−0.151030	−0.0162860
$87$	−4.64291	−0.497772
$88$	0.641346	0.0683677
$89$	−14.9787	−1.58774	−0.793868	−	0.608091i	$-0.791936\pi$
$89$	−14.9787	−1.58774	−0.793868	+	0.608091i	$0.791936\pi$
$90$	0.678863	0.0715584
$91$	20.1264	2.10982
$92$	17.8637	1.86242
$93$	−8.08500	−0.838375
$94$	−18.7146	−1.93026
$95$	−8.58379	−0.880678
$96$	−14.5545	−1.48547
$97$	−14.7024	−1.49280	−0.746401	−	0.665496i	$-0.768220\pi$
$97$	−14.7024	−1.49280	−0.746401	+	0.665496i	$0.768220\pi$
$98$	−26.0404	−2.63048
$99$	−0.224658	−0.0225789
$100$	−6.65192	−0.665192
$101$	−15.4026	−1.53261	−0.766307	−	0.642475i	$-0.777908\pi$
$101$	−15.4026	−1.53261	−0.766307	+	0.642475i	$0.777908\pi$
$102$	0	0
$103$	7.93416	0.781776	0.390888	−	0.920438i	$-0.372168\pi$
$103$	7.93416	0.781776	0.390888	+	0.920438i	$0.372168\pi$
$104$	−2.91974	−0.286304
$105$	11.5566	1.12781
$106$	6.33538	0.615346
$107$	3.05607	0.295441	0.147721	−	0.989029i	$-0.452806\pi$
$107$	3.05607	0.295441	0.147721	+	0.989029i	$0.452806\pi$
$108$	11.5073	1.10730
$109$	−0.0635604	−0.00608799	−0.00304399	−	0.999995i	$-0.500969\pi$
$109$	−0.0635604	−0.00608799	−0.00304399	+	0.999995i	$0.500969\pi$
$110$	−3.02177	−0.288114
$111$	−14.2889	−1.35624
$112$	−14.5299	−1.37295
$113$	−9.12645	−0.858544	−0.429272	−	0.903175i	$-0.641230\pi$
$113$	−9.12645	−0.858544	−0.429272	+	0.903175i	$0.641230\pi$
$114$	21.9802	2.05864
$115$	−11.2624	−1.05022
$116$	5.96988	0.554289
$117$	1.02276	0.0945539
$118$	8.92886	0.821969
$119$	0	0
$120$	−1.67652	−0.153045
$121$	1.00000	0.0909091
$122$	−11.2146	−1.01532
$123$	2.90995	0.262382
$124$	10.3957	0.933564
$125$	11.4723	1.02611
$126$	−2.06168	−0.183669
$127$	−7.91348	−0.702207	−0.351104	−	0.936337i	$-0.614194\pi$
$127$	−7.91348	−0.702207	−0.351104	+	0.936337i	$0.614194\pi$
$128$	5.06954	0.448089
$129$	−0.130653	−0.0115033
$130$	13.7566	1.20654
$131$	0.878858	0.0767862	0.0383931	−	0.999263i	$-0.487776\pi$
$131$	0.878858	0.0767862	0.0383931	+	0.999263i	$0.487776\pi$
$132$	4.14628	0.360887
$133$	26.0687	2.26044
$134$	−10.6957	−0.923963
$135$	−7.25493	−0.624405
$136$	0	0
$137$	10.4844	0.895745	0.447873	−	0.894097i	$-0.352182\pi$
$137$	10.4844	0.895745	0.447873	+	0.894097i	$0.352182\pi$
$138$	28.8392	2.45495
$139$	−5.23601	−0.444113	−0.222056	−	0.975034i	$-0.571277\pi$
$139$	−5.23601	−0.444113	−0.222056	+	0.975034i	$0.571277\pi$
$140$	−14.8596	−1.25586
$141$	−16.1896	−1.36341
$142$	−11.9204	−1.00034
$143$	−4.55252	−0.380700
$144$	−0.738363	−0.0615303
$145$	−3.76377	−0.312564
$146$	−4.82448	−0.399277
$147$	−22.5270	−1.85799
$148$	18.3727	1.51023
$149$	−13.5177	−1.10741	−0.553707	−	0.832712i	$-0.686787\pi$
$149$	−13.5177	−1.10741	−0.553707	+	0.832712i	$0.686787\pi$
$150$	−10.7389	−0.876824
$151$	−4.11155	−0.334593	−0.167297	−	0.985907i	$-0.553504\pi$
$151$	−4.11155	−0.334593	−0.167297	+	0.985907i	$0.553504\pi$
$152$	−3.78178	−0.306743
$153$	0	0
$154$	9.17701	0.739505
$155$	−6.55409	−0.526437
$156$	−18.8760	−1.51129
$157$	−15.8060	−1.26146	−0.630730	−	0.776002i	$-0.717244\pi$
$157$	−15.8060	−1.26146	−0.630730	+	0.776002i	$0.717244\pi$
$158$	6.32704	0.503352
$159$	5.48060	0.434640
$160$	−11.7986	−0.932762
$161$	34.2034	2.69561
$162$	19.9765	1.56950
$163$	15.1434	1.18613	0.593063	−	0.805156i	$-0.297919\pi$
$163$	15.1434	1.18613	0.593063	+	0.805156i	$0.297919\pi$
$164$	−3.74163	−0.292172
$165$	−2.61406	−0.203505
$166$	1.20039	0.0931681
$167$	−21.8616	−1.69170	−0.845852	−	0.533417i	$-0.820908\pi$
$167$	−21.8616	−1.69170	−0.845852	+	0.533417i	$0.820908\pi$
$168$	5.09154	0.392821
$169$	7.72539	0.594261
$170$	0	0
$171$	1.32472	0.101304
$172$	0.167994	0.0128094
$173$	12.5613	0.955020	0.477510	−	0.878626i	$-0.341539\pi$
$173$	12.5613	0.955020	0.477510	+	0.878626i	$0.341539\pi$
$174$	9.63778	0.730638
$175$	−12.7363	−0.962777
$176$	3.28662	0.247738
$177$	7.72417	0.580584
$178$	31.0928	2.33050
$179$	−7.36905	−0.550789	−0.275394	−	0.961331i	$-0.588808\pi$
$179$	−7.36905	−0.550789	−0.275394	+	0.961331i	$0.588808\pi$
$180$	−0.755114	−0.0562829
$181$	26.3185	1.95624	0.978118	−	0.208051i	$-0.0667119\pi$
$181$	26.3185	1.95624	0.978118	+	0.208051i	$0.0667119\pi$
$182$	−41.7785	−3.09683
$183$	−9.70151	−0.717156
$184$	−4.96189	−0.365795
$185$	−11.5833	−0.851619
$186$	16.7829	1.23058
$187$	0	0
$188$	20.8167	1.51821
$189$	22.0330	1.60266
$190$	17.8183	1.29267
$191$	17.9257	1.29706	0.648530	−	0.761189i	$-0.275384\pi$
$191$	17.9257	1.29706	0.648530	+	0.761189i	$0.275384\pi$
$192$	18.4086	1.32853
$193$	12.6599	0.911279	0.455639	−	0.890164i	$-0.349411\pi$
$193$	12.6599	0.911279	0.455639	+	0.890164i	$0.349411\pi$
$194$	30.5193	2.19116
$195$	11.9006	0.852218
$196$	28.9653	2.06895
$197$	−11.1828	−0.796739	−0.398370	−	0.917225i	$-0.630424\pi$
$197$	−11.1828	−0.796739	−0.398370	+	0.917225i	$0.630424\pi$
$198$	0.466345	0.0331417
$199$	24.2680	1.72031	0.860157	−	0.510029i	$-0.170365\pi$
$199$	24.2680	1.72031	0.860157	+	0.510029i	$0.170365\pi$
$200$	1.84766	0.130649
$201$	−9.25258	−0.652626
$202$	31.9727	2.24959
$203$	11.4305	0.802261
$204$	0	0
$205$	2.35895	0.164756
$206$	−16.4698	−1.14750
$207$	1.73810	0.120807
$208$	−14.9624	−1.03745
$209$	−5.89664	−0.407879
$210$	−23.9893	−1.65542
$211$	−8.43849	−0.580929	−0.290465	−	0.956886i	$-0.593810\pi$
$211$	−8.43849	−0.580929	−0.290465	+	0.956886i	$0.593810\pi$
$212$	−7.04698	−0.483989
$213$	−10.3121	−0.706574
$214$	−6.34380	−0.433653
$215$	−0.105914	−0.00722325
$216$	−3.19632	−0.217482
$217$	19.9046	1.35121
$218$	0.131939	0.00893604
$219$	−4.17355	−0.282023
$220$	3.36118	0.226611
$221$	0	0
$222$	29.6609	1.99071
$223$	−23.6069	−1.58084	−0.790419	−	0.612567i	$-0.790137\pi$
$223$	−23.6069	−1.58084	−0.790419	+	0.612567i	$0.790137\pi$
$224$	35.8320	2.39413
$225$	−0.647218	−0.0431479
$226$	18.9447	1.26018
$227$	8.67471	0.575761	0.287880	−	0.957666i	$-0.407049\pi$
$227$	8.67471	0.575761	0.287880	+	0.957666i	$0.407049\pi$
$228$	−24.4491	−1.61918
$229$	−13.1374	−0.868147	−0.434074	−	0.900877i	$-0.642924\pi$
$229$	−13.1374	−0.868147	−0.434074	+	0.900877i	$0.642924\pi$
$230$	23.3784	1.54153
$231$	7.93883	0.522337
$232$	−1.65821	−0.108867
$233$	−10.5351	−0.690175	−0.345087	−	0.938571i	$-0.612151\pi$
$233$	−10.5351	−0.690175	−0.345087	+	0.938571i	$0.612151\pi$
$234$	−2.12304	−0.138788
$235$	−13.1241	−0.856121
$236$	−9.93177	−0.646503
$237$	5.47338	0.355534
$238$	0	0
$239$	21.2215	1.37271	0.686353	−	0.727269i	$-0.259211\pi$
$239$	21.2215	1.37271	0.686353	+	0.727269i	$0.259211\pi$
$240$	−8.59143	−0.554574
$241$	17.2239	1.10949	0.554745	−	0.832021i	$-0.312816\pi$
$241$	17.2239	1.10949	0.554745	+	0.832021i	$0.312816\pi$
$242$	−2.07580	−0.133438
$243$	2.32992	0.149464
$244$	12.4743	0.798582
$245$	−18.2615	−1.16668
$246$	−6.04049	−0.385128
$247$	26.8445	1.70808
$248$	−2.88755	−0.183360
$249$	1.03843	0.0658077
$250$	−23.8143	−1.50615
$251$	5.13459	0.324092	0.162046	−	0.986783i	$-0.448191\pi$
$251$	5.13459	0.324092	0.162046	+	0.986783i	$0.448191\pi$
$252$	2.29326	0.144462
$253$	−7.73668	−0.486401
$254$	16.4268	1.03071
$255$	0	0
$256$	9.97920	0.623700
$257$	−13.4588	−0.839538	−0.419769	−	0.907631i	$-0.637889\pi$
$257$	−13.4588	−0.839538	−0.419769	+	0.907631i	$0.637889\pi$
$258$	0.271210	0.0168848
$259$	35.1780	2.18586
$260$	−15.3018	−0.948978
$261$	0.580858	0.0359542
$262$	−1.82434	−0.112708
$263$	−21.6160	−1.33290	−0.666451	−	0.745549i	$-0.732187\pi$
$263$	−21.6160	−1.33290	−0.666451	+	0.745549i	$0.732187\pi$
$264$	−1.15169	−0.0708814
$265$	4.44284	0.272922
$266$	−54.1135	−3.31791
$267$	26.8977	1.64611
$268$	11.8970	0.726725
$269$	−7.66346	−0.467249	−0.233625	−	0.972327i	$-0.575059\pi$
$269$	−7.66346	−0.467249	−0.233625	+	0.972327i	$0.575059\pi$
$270$	15.0598	0.916510
$271$	5.88038	0.357207	0.178604	−	0.983921i	$-0.442842\pi$
$271$	5.88038	0.357207	0.178604	+	0.983921i	$0.442842\pi$
$272$	0	0
$273$	−36.1417	−2.18739
$274$	−21.7636	−1.31479
$275$	2.88091	0.173725
$276$	−32.0784	−1.93090
$277$	9.60768	0.577270	0.288635	−	0.957439i	$-0.406799\pi$
$277$	9.60768	0.577270	0.288635	+	0.957439i	$0.406799\pi$
$278$	10.8689	0.651875
$279$	1.01148	0.0605560
$280$	4.12745	0.246662
$281$	−8.33720	−0.497356	−0.248678	−	0.968586i	$-0.579996\pi$
$281$	−8.33720	−0.497356	−0.248678	+	0.968586i	$0.579996\pi$
$282$	33.6064	2.00123
$283$	1.12989	0.0671648	0.0335824	−	0.999436i	$-0.489308\pi$
$283$	1.12989	0.0671648	0.0335824	+	0.999436i	$0.489308\pi$
$284$	13.2594	0.786798
$285$	15.4142	0.913058
$286$	9.45013	0.558798
$287$	−7.16406	−0.422881
$288$	1.82086	0.107295
$289$	0	0
$290$	7.81285	0.458786
$291$	26.4016	1.54769
$292$	5.36638	0.314043
$293$	19.5254	1.14068	0.570342	−	0.821407i	$-0.306811\pi$
$293$	19.5254	1.14068	0.570342	+	0.821407i	$0.306811\pi$
$294$	46.7616	2.72719
$295$	6.26159	0.364564
$296$	−5.10327	−0.296622
$297$	−4.98377	−0.289188
$298$	28.0601	1.62548
$299$	35.2214	2.03690
$300$	11.9451	0.689649
$301$	0.321656	0.0185400
$302$	8.53477	0.491121
$303$	27.6589	1.58896
$304$	−19.3800	−1.11152
$305$	−7.86452	−0.450321
$306$	0	0
$307$	1.14761	0.0654977	0.0327488	−	0.999464i	$-0.489574\pi$
$307$	1.14761	0.0654977	0.0327488	+	0.999464i	$0.489574\pi$
$308$	−10.2078	−0.581643
$309$	−14.2476	−0.810519
$310$	13.6050	0.772713
$311$	−6.16221	−0.349427	−0.174713	−	0.984619i	$-0.555900\pi$
$311$	−6.16221	−0.349427	−0.174713	+	0.984619i	$0.555900\pi$
$312$	5.24307	0.296830
$313$	−9.58571	−0.541817	−0.270908	−	0.962605i	$-0.587324\pi$
$313$	−9.58571	−0.541817	−0.270908	+	0.962605i	$0.587324\pi$
$314$	32.8103	1.85159
$315$	−1.44581	−0.0814620
$316$	−7.03770	−0.395902
$317$	16.3418	0.917845	0.458922	−	0.888476i	$-0.348236\pi$
$317$	16.3418	0.917845	0.458922	+	0.888476i	$0.348236\pi$
$318$	−11.3766	−0.637971
$319$	−2.58552	−0.144762
$320$	14.9229	0.834215
$321$	−5.48788	−0.306304
$322$	−70.9996	−3.95665
$323$	0	0
$324$	−22.2203	−1.23446
$325$	−13.1154	−0.727511
$326$	−31.4348	−1.74101
$327$	0.114138	0.00631182
$328$	1.03929	0.0573851
$329$	39.8574	2.19741
$330$	5.42629	0.298707
$331$	−10.7708	−0.592017	−0.296009	−	0.955185i	$-0.595656\pi$
$331$	−10.7708	−0.592017	−0.296009	+	0.955185i	$0.595656\pi$
$332$	−1.33522	−0.0732795
$333$	1.78763	0.0979615
$334$	45.3805	2.48311
$335$	−7.50059	−0.409801
$336$	26.0919	1.42343
$337$	16.1694	0.880802	0.440401	−	0.897801i	$-0.354836\pi$
$337$	16.1694	0.880802	0.440401	+	0.897801i	$0.354836\pi$
$338$	−16.0364	−0.872265
$339$	16.3887	0.890110
$340$	0	0
$341$	−4.50234	−0.243815
$342$	−2.74987	−0.148696
$343$	24.5129	1.32357
$344$	−0.0466626	−0.00251588
$345$	20.2242	1.08883
$346$	−26.0748	−1.40179
$347$	22.0119	1.18166	0.590831	−	0.806796i	$-0.298800\pi$
$347$	22.0119	1.18166	0.590831	+	0.806796i	$0.298800\pi$
$348$	−10.7203	−0.574669
$349$	−15.9214	−0.852254	−0.426127	−	0.904663i	$-0.640122\pi$
$349$	−15.9214	−0.852254	−0.426127	+	0.904663i	$0.640122\pi$
$350$	26.4382	1.41318
$351$	22.6887	1.21103
$352$	−8.10506	−0.432001
$353$	7.49958	0.399162	0.199581	−	0.979881i	$-0.436042\pi$
$353$	7.49958	0.399162	0.199581	+	0.979881i	$0.436042\pi$
$354$	−16.0339	−0.852190
$355$	−8.35950	−0.443676
$356$	−34.5852	−1.83301
$357$	0	0
$358$	15.2967	0.808456
$359$	34.0584	1.79753	0.898767	−	0.438428i	$-0.144464\pi$
$359$	34.0584	1.79753	0.898767	+	0.438428i	$0.144464\pi$
$360$	0.209743	0.0110544
$361$	15.7703	0.830018
$362$	−54.6320	−2.87139
$363$	−1.79573	−0.0942515
$364$	46.4711	2.43575
$365$	−3.38329	−0.177089
$366$	20.1384	1.05265
$367$	−35.7310	−1.86515	−0.932573	−	0.360982i	$-0.882442\pi$
$367$	−35.7310	−1.86515	−0.932573	+	0.360982i	$0.882442\pi$
$368$	−25.4275	−1.32550
$369$	−0.364053	−0.0189519
$370$	24.0446	1.25002
$371$	−13.4928	−0.700510
$372$	−18.6680	−0.967888
$373$	10.1168	0.523827	0.261914	−	0.965091i	$-0.415646\pi$
$373$	10.1168	0.523827	0.261914	+	0.965091i	$0.415646\pi$
$374$	0	0
$375$	−20.6012	−1.06384
$376$	−5.78211	−0.298190
$377$	11.7706	0.606219
$378$	−45.7361	−2.35241
$379$	22.4618	1.15379	0.576893	−	0.816820i	$-0.304265\pi$
$379$	22.4618	1.15379	0.576893	+	0.816820i	$0.304265\pi$
$380$	−19.8196	−1.01673
$381$	14.2105	0.728025
$382$	−37.2103	−1.90384
$383$	6.81602	0.348283	0.174141	−	0.984721i	$-0.444285\pi$
$383$	6.81602	0.348283	0.174141	+	0.984721i	$0.444285\pi$
$384$	−9.10355	−0.464563
$385$	6.43561	0.327989
$386$	−26.2794	−1.33759
$387$	0.0163455	0.000830888 0
$388$	−33.9473	−1.72341
$389$	14.3802	0.729105	0.364552	−	0.931183i	$-0.381222\pi$
$389$	14.3802	0.729105	0.364552	+	0.931183i	$0.381222\pi$
$390$	−24.7033	−1.25090
$391$	0	0
$392$	−8.04551	−0.406360
$393$	−1.57819	−0.0796094
$394$	23.2132	1.16947
$395$	4.43699	0.223249
$396$	−0.518726	−0.0260670
$397$	2.02787	0.101776	0.0508879	−	0.998704i	$-0.483795\pi$
$397$	2.02787	0.101776	0.0508879	+	0.998704i	$0.483795\pi$
$398$	−50.3757	−2.52510
$399$	−46.8124	−2.34355
$400$	9.46845	0.473423
$401$	−4.98005	−0.248692	−0.124346	−	0.992239i	$-0.539683\pi$
$401$	−4.98005	−0.248692	−0.124346	+	0.992239i	$0.539683\pi$
$402$	19.2065	0.957935
$403$	20.4970	1.02103
$404$	−35.5640	−1.76937
$405$	14.0090	0.696114
$406$	−23.7274	−1.17757
$407$	−7.95713	−0.394420
$408$	0	0
$409$	−17.8258	−0.881431	−0.440715	−	0.897647i	$-0.645275\pi$
$409$	−17.8258	−0.881431	−0.440715	+	0.897647i	$0.645275\pi$
$410$	−4.89672	−0.241832
$411$	−18.8272	−0.928679
$412$	18.3197	0.902545
$413$	−19.0162	−0.935728
$414$	−3.60796	−0.177322
$415$	0.841801	0.0413224
$416$	36.8984	1.80909
$417$	9.40248	0.460441
$418$	12.2403	0.598691
$419$	20.7159	1.01204	0.506020	−	0.862522i	$-0.331116\pi$
$419$	20.7159	1.01204	0.506020	+	0.862522i	$0.331116\pi$
$420$	26.6838	1.30204
$421$	−27.8289	−1.35630	−0.678149	−	0.734925i	$-0.737218\pi$
$421$	−27.8289	−1.35630	−0.678149	+	0.734925i	$0.737218\pi$
$422$	17.5166	0.852697
$423$	2.02542	0.0984794
$424$	1.95739	0.0950595
$425$	0	0
$426$	21.4059	1.03712
$427$	23.8843	1.15584
$428$	7.05634	0.341081
$429$	8.17510	0.394698
$430$	0.219856	0.0106024
$431$	−12.3382	−0.594309	−0.297155	−	0.954829i	$-0.596038\pi$
$431$	−12.3382	−0.594309	−0.297155	+	0.954829i	$0.596038\pi$
$432$	−16.3798	−0.788072
$433$	−25.2731	−1.21455	−0.607274	−	0.794493i	$-0.707737\pi$
$433$	−25.2731	−1.21455	−0.607274	+	0.794493i	$0.707737\pi$
$434$	−41.3180	−1.98333
$435$	6.75873	0.324056
$436$	−0.146759	−0.00702847
$437$	45.6204	2.18232
$438$	8.66348	0.413957
$439$	−14.3632	−0.685518	−0.342759	−	0.939423i	$-0.611361\pi$
$439$	−14.3632	−0.685518	−0.342759	+	0.939423i	$0.611361\pi$
$440$	−0.933613	−0.0445082
$441$	2.81827	0.134203
$442$	0	0
$443$	1.17108	0.0556399	0.0278199	−	0.999613i	$-0.491143\pi$
$443$	1.17108	0.0556399	0.0278199	+	0.999613i	$0.491143\pi$
$444$	−32.9925	−1.56575
$445$	21.8046	1.03364
$446$	49.0034	2.32038
$447$	24.2742	1.14813
$448$	−45.3204	−2.14119
$449$	−0.613987	−0.0289759	−0.0144879	−	0.999895i	$-0.504612\pi$
$449$	−0.613987	−0.0289759	−0.0144879	+	0.999895i	$0.504612\pi$
$450$	1.34350	0.0633331
$451$	1.62048	0.0763055
$452$	−21.0726	−0.991173
$453$	7.38325	0.346895
$454$	−18.0070	−0.845110
$455$	−29.2982	−1.37352
$456$	6.79107	0.318021
$457$	1.41144	0.0660243	0.0330122	−	0.999455i	$-0.489490\pi$
$457$	1.41144	0.0660243	0.0330122	+	0.999455i	$0.489490\pi$
$458$	27.2708	1.27428
$459$	0	0
$460$	−26.0044	−1.21246
$461$	5.17482	0.241015	0.120508	−	0.992712i	$-0.461548\pi$
$461$	5.17482	0.241015	0.120508	+	0.992712i	$0.461548\pi$
$462$	−16.4795	−0.766694
$463$	−39.3668	−1.82953	−0.914764	−	0.403988i	$-0.867624\pi$
$463$	−39.3668	−1.82953	−0.914764	+	0.403988i	$0.867624\pi$
$464$	−8.49763	−0.394493
$465$	11.7694	0.545793
$466$	21.8687	1.01305
$467$	20.8759	0.966021	0.483011	−	0.875614i	$-0.339543\pi$
$467$	20.8759	0.966021	0.483011	+	0.875614i	$0.339543\pi$
$468$	2.36151	0.109161
$469$	22.7791	1.05184
$470$	27.2430	1.25663
$471$	28.3834	1.30784
$472$	2.75868	0.126979
$473$	−0.0727574	−0.00334539
$474$	−11.3617	−0.521859
$475$	−16.9877	−0.779449
$476$	0	0
$477$	−0.685657	−0.0313941
$478$	−44.0517	−2.01488
$479$	−17.9823	−0.821635	−0.410817	−	0.911718i	$-0.634757\pi$
$479$	−17.9823	−0.821635	−0.410817	+	0.911718i	$0.634757\pi$
$480$	21.1872	0.967057
$481$	36.2250	1.65172
$482$	−35.7534	−1.62852
$483$	−61.4202	−2.79472
$484$	2.30896	0.104953
$485$	21.4024	0.971834
$486$	−4.83645	−0.219386
$487$	2.02618	0.0918150	0.0459075	−	0.998946i	$-0.485382\pi$
$487$	2.02618	0.0918150	0.0459075	+	0.998946i	$0.485382\pi$
$488$	−3.46489	−0.156848
$489$	−27.1936	−1.22974
$490$	37.9072	1.71247
$491$	7.85789	0.354622	0.177311	−	0.984155i	$-0.443260\pi$
$491$	7.85789	0.354622	0.177311	+	0.984155i	$0.443260\pi$
$492$	6.71897	0.302915
$493$	0	0
$494$	−55.7240	−2.50714
$495$	0.327036	0.0146992
$496$	−14.7975	−0.664426
$497$	25.3875	1.13879
$498$	−2.15557	−0.0965936
$499$	−20.5002	−0.917716	−0.458858	−	0.888510i	$-0.651741\pi$
$499$	−20.5002	−0.917716	−0.458858	+	0.888510i	$0.651741\pi$
$500$	26.4891	1.18463
$501$	39.2577	1.75390
$502$	−10.6584	−0.475708
$503$	−12.8207	−0.571647	−0.285824	−	0.958282i	$-0.592267\pi$
$503$	−12.8207	−0.571647	−0.285824	+	0.958282i	$0.592267\pi$
$504$	−0.636983	−0.0283735
$505$	22.4217	0.997751
$506$	16.0598	0.713947
$507$	−13.8727	−0.616110
$508$	−18.2719	−0.810685
$509$	30.3891	1.34697	0.673487	−	0.739199i	$-0.264796\pi$
$509$	30.3891	1.34697	0.673487	+	0.739199i	$0.264796\pi$
$510$	0	0
$511$	10.2749	0.454536
$512$	−30.8540	−1.36357
$513$	29.3875	1.29749
$514$	27.9379	1.23229
$515$	−11.5498	−0.508946
$516$	−0.301673	−0.0132804
$517$	−9.01560	−0.396505
$518$	−73.0227	−3.20843
$519$	−22.5568	−0.990133
$520$	4.25029	0.186387
$521$	−12.9110	−0.565640	−0.282820	−	0.959173i	$-0.591270\pi$
$521$	−12.9110	−0.565640	−0.282820	+	0.959173i	$0.591270\pi$
$522$	−1.20575	−0.0527741
$523$	36.2972	1.58717	0.793583	−	0.608462i	$-0.208213\pi$
$523$	36.2972	1.58717	0.793583	+	0.608462i	$0.208213\pi$
$524$	2.02925	0.0886482
$525$	22.8711	0.998175
$526$	44.8707	1.95645
$527$	0	0
$528$	−5.90189	−0.256847
$529$	36.8562	1.60244
$530$	−9.22247	−0.400598
$531$	−0.966342	−0.0419357
$532$	60.1916	2.60964
$533$	−7.37727	−0.319545
$534$	−55.8343	−2.41619
$535$	−4.44874	−0.192336
$536$	−3.30455	−0.142735
$537$	13.2328	0.571039
$538$	15.9078	0.685835
$539$	−12.5447	−0.540340
$540$	−16.7514	−0.720863
$541$	28.0297	1.20509	0.602546	−	0.798084i	$-0.294153\pi$
$541$	28.0297	1.20509	0.602546	+	0.798084i	$0.294153\pi$
$542$	−12.2065	−0.524314
$543$	−47.2609	−2.02816
$544$	0	0
$545$	0.0925255	0.00396336
$546$	75.0230	3.21069
$547$	−26.7578	−1.14408	−0.572041	−	0.820225i	$-0.693848\pi$
$547$	−26.7578	−1.14408	−0.572041	+	0.820225i	$0.693848\pi$
$548$	24.2081	1.03412
$549$	1.21372	0.0518003
$550$	−5.98021	−0.254997
$551$	15.2459	0.649497
$552$	8.91022	0.379244
$553$	−13.4750	−0.573015
$554$	−19.9437	−0.847325
$555$	20.8005	0.882930
$556$	−12.0898	−0.512720
$557$	−31.7874	−1.34687	−0.673437	−	0.739244i	$-0.735183\pi$
$557$	−31.7874	−1.34687	−0.673437	+	0.739244i	$0.735183\pi$
$558$	−2.09964	−0.0888850
$559$	0.331229	0.0140095
$560$	21.1514	0.893809
$561$	0	0
$562$	17.3064	0.730026
$563$	19.0455	0.802673	0.401337	−	0.915931i	$-0.368546\pi$
$563$	19.0455	0.802673	0.401337	+	0.915931i	$0.368546\pi$
$564$	−37.3812	−1.57403
$565$	13.2854	0.558923
$566$	−2.34543	−0.0985856
$567$	−42.5449	−1.78672
$568$	−3.68297	−0.154534
$569$	12.7428	0.534204	0.267102	−	0.963668i	$-0.413934\pi$
$569$	12.7428	0.534204	0.267102	+	0.963668i	$0.413934\pi$
$570$	−31.9968	−1.34020
$571$	40.9364	1.71313	0.856567	−	0.516036i	$-0.172593\pi$
$571$	40.9364	1.71313	0.856567	+	0.516036i	$0.172593\pi$
$572$	−10.5116	−0.439512
$573$	−32.1898	−1.34475
$574$	14.8712	0.620711
$575$	−22.2887	−0.929503
$576$	−2.30303	−0.0959596
$577$	12.1640	0.506394	0.253197	−	0.967415i	$-0.418518\pi$
$577$	12.1640	0.506394	0.253197	+	0.967415i	$0.418518\pi$
$578$	0	0
$579$	−22.7338	−0.944784
$580$	−8.69041	−0.360850
$581$	−2.55652	−0.106062
$582$	−54.8045	−2.27172
$583$	3.05201	0.126401
$584$	−1.49058	−0.0616808
$585$	−1.48884	−0.0615558
$586$	−40.5308	−1.67431
$587$	−5.58155	−0.230375	−0.115188	−	0.993344i	$-0.536747\pi$
$587$	−5.58155	−0.230375	−0.115188	+	0.993344i	$0.536747\pi$
$588$	−52.0140	−2.14502
$589$	26.5487	1.09392
$590$	−12.9978	−0.535112
$591$	20.0813	0.826033
$592$	−26.1520	−1.07484
$593$	5.89718	0.242168	0.121084	−	0.992642i	$-0.461363\pi$
$593$	5.89718	0.242168	0.121084	+	0.992642i	$0.461363\pi$
$594$	10.3453	0.424474
$595$	0	0
$596$	−31.2119	−1.27849
$597$	−43.5789	−1.78357
$598$	−73.1126	−2.98980
$599$	−32.2431	−1.31742	−0.658709	−	0.752398i	$-0.728897\pi$
$599$	−32.2431	−1.31742	−0.658709	+	0.752398i	$0.728897\pi$
$600$	−3.31790	−0.135453
$601$	−28.7995	−1.17475	−0.587377	−	0.809313i	$-0.699840\pi$
$601$	−28.7995	−1.17475	−0.587377	+	0.809313i	$0.699840\pi$
$602$	−0.667695	−0.0272132
$603$	1.15756	0.0471393
$604$	−9.49341	−0.386282
$605$	−1.45571	−0.0591830
$606$	−57.4145	−2.33230
$607$	16.2177	0.658255	0.329128	−	0.944285i	$-0.393245\pi$
$607$	16.2177	0.658255	0.329128	+	0.944285i	$0.393245\pi$
$608$	47.7926	1.93825
$609$	−20.5260	−0.831757
$610$	16.3252	0.660988
$611$	41.0436	1.66045
$612$	0	0
$613$	−29.6064	−1.19579	−0.597896	−	0.801574i	$-0.703996\pi$
$613$	−29.6064	−1.19579	−0.597896	+	0.801574i	$0.703996\pi$
$614$	−2.38222	−0.0961385
$615$	−4.23604	−0.170814
$616$	2.83535	0.114240
$617$	−8.32281	−0.335064	−0.167532	−	0.985867i	$-0.553580\pi$
$617$	−8.32281	−0.335064	−0.167532	+	0.985867i	$0.553580\pi$
$618$	29.5753	1.18969
$619$	28.8170	1.15825	0.579127	−	0.815238i	$-0.303394\pi$
$619$	28.8170	1.15825	0.579127	+	0.815238i	$0.303394\pi$
$620$	−15.1332	−0.607762
$621$	38.5579	1.54727
$622$	12.7915	0.512894
$623$	−66.2198	−2.65304
$624$	26.8684	1.07560
$625$	−2.29579	−0.0918317
$626$	19.8981	0.795286
$627$	10.5888	0.422875
$628$	−36.4956	−1.45633
$629$	0	0
$630$	3.00121	0.119571
$631$	−3.84555	−0.153089	−0.0765444	−	0.997066i	$-0.524389\pi$
$631$	−3.84555	−0.153089	−0.0765444	+	0.997066i	$0.524389\pi$
$632$	1.95482	0.0777585
$633$	15.1533	0.602289
$634$	−33.9223	−1.34723
$635$	11.5197	0.457146
$636$	12.6545	0.501783
$637$	57.1101	2.26278
$638$	5.36704	0.212483
$639$	1.29011	0.0510359
$640$	−7.37978	−0.291711
$641$	38.4928	1.52038	0.760188	−	0.649703i	$-0.225107\pi$
$641$	38.4928	1.52038	0.760188	+	0.649703i	$0.225107\pi$
$642$	11.3918	0.449597
$643$	−32.1197	−1.26668	−0.633339	−	0.773874i	$-0.718316\pi$
$643$	−32.1197	−1.26668	−0.633339	+	0.773874i	$0.718316\pi$
$644$	78.9744	3.11203
$645$	0.190193	0.00748883
$646$	0	0
$647$	26.6638	1.04826	0.524131	−	0.851638i	$-0.324390\pi$
$647$	26.6638	1.04826	0.524131	+	0.851638i	$0.324390\pi$
$648$	6.17199	0.242459
$649$	4.30140	0.168845
$650$	27.2250	1.06785
$651$	−35.7433	−1.40089
$652$	34.9656	1.36936
$653$	16.7461	0.655327	0.327664	−	0.944794i	$-0.393739\pi$
$653$	16.7461	0.655327	0.327664	+	0.944794i	$0.393739\pi$
$654$	−0.236927	−0.00926459
$655$	−1.27936	−0.0499888
$656$	5.32590	0.207942
$657$	0.522138	0.0203705
$658$	−82.7362	−3.22539
$659$	13.2523	0.516235	0.258117	−	0.966114i	$-0.416898\pi$
$659$	13.2523	0.516235	0.258117	+	0.966114i	$0.416898\pi$
$660$	−6.03578	−0.234942
$661$	19.0065	0.739267	0.369633	−	0.929178i	$-0.379483\pi$
$661$	19.0065	0.739267	0.369633	+	0.929178i	$0.379483\pi$
$662$	22.3581	0.868972
$663$	0	0
$664$	0.370874	0.0143927
$665$	−37.9484	−1.47158
$666$	−3.71077	−0.143789
$667$	20.0034	0.774534
$668$	−50.4777	−1.95304
$669$	42.3918	1.63896
$670$	15.5698	0.601512
$671$	−5.40254	−0.208563
$672$	−64.3447	−2.48215
$673$	−26.1313	−1.00729	−0.503644	−	0.863911i	$-0.668008\pi$
$673$	−26.1313	−1.00729	−0.503644	+	0.863911i	$0.668008\pi$
$674$	−33.5645	−1.29285
$675$	−14.3578	−0.552632
$676$	17.8376	0.686063
$677$	33.5441	1.28920	0.644602	−	0.764518i	$-0.277023\pi$
$677$	33.5441	1.28920	0.644602	+	0.764518i	$0.277023\pi$
$678$	−34.0197	−1.30652
$679$	−64.9985	−2.49441
$680$	0	0
$681$	−15.5775	−0.596930
$682$	9.34597	0.357876
$683$	−8.55518	−0.327355	−0.163677	−	0.986514i	$-0.552336\pi$
$683$	−8.55518	−0.327355	−0.163677	+	0.986514i	$0.552336\pi$
$684$	3.05874	0.116954
$685$	−15.2623	−0.583142
$686$	−50.8840	−1.94276
$687$	23.5914	0.900066
$688$	−0.239126	−0.00911658
$689$	−13.8943	−0.529332
$690$	−41.9814	−1.59821
$691$	−45.6023	−1.73479	−0.867397	−	0.497617i	$-0.834209\pi$
$691$	−45.6023	−1.73479	−0.867397	+	0.497617i	$0.834209\pi$
$692$	29.0036	1.10255
$693$	−0.993198	−0.0377285
$694$	−45.6924	−1.73446
$695$	7.62211	0.289123
$696$	2.97771	0.112870
$697$	0	0
$698$	33.0497	1.25095
$699$	18.9182	0.715550
$700$	−29.4077	−1.11151
$701$	−28.4991	−1.07640	−0.538198	−	0.842818i	$-0.680895\pi$
$701$	−28.4991	−1.07640	−0.538198	+	0.842818i	$0.680895\pi$
$702$	−47.0973	−1.77757
$703$	46.9203	1.76963
$704$	10.2513	0.386360
$705$	23.5674	0.887598
$706$	−15.5677	−0.585896
$707$	−68.0939	−2.56093
$708$	17.8348	0.670273
$709$	52.7677	1.98173	0.990866	−	0.134848i	$-0.0430546\pi$
$709$	52.7677	1.98173	0.990866	+	0.134848i	$0.0430546\pi$
$710$	17.3527	0.651234
$711$	−0.684755	−0.0256803
$712$	9.60650	0.360019
$713$	34.8331	1.30451
$714$	0	0
$715$	6.62714	0.247841
$716$	−17.0149	−0.635875
$717$	−38.1082	−1.42318
$718$	−70.6985	−2.63845
$719$	−2.89916	−0.108120	−0.0540602	−	0.998538i	$-0.517216\pi$
$719$	−2.89916	−0.108120	−0.0540602	+	0.998538i	$0.517216\pi$
$720$	1.07484	0.0400570
$721$	35.0764	1.30632
$722$	−32.7361	−1.21831
$723$	−30.9295	−1.15028
$724$	60.7684	2.25844
$725$	−7.44867	−0.276637
$726$	3.72759	0.138344
$727$	19.5502	0.725077	0.362539	−	0.931969i	$-0.381910\pi$
$727$	19.5502	0.725077	0.362539	+	0.931969i	$0.381910\pi$
$728$	−12.9080	−0.478402
$729$	24.6866	0.914318
$730$	7.02304	0.259934
$731$	0	0
$732$	−22.4004	−0.827944
$733$	−26.8974	−0.993477	−0.496739	−	0.867900i	$-0.665469\pi$
$733$	−26.8974	−0.993477	−0.496739	+	0.867900i	$0.665469\pi$
$734$	74.1707	2.73769
$735$	32.7927	1.20958
$736$	62.7063	2.31138
$737$	−5.15253	−0.189796
$738$	0.755703	0.0278178
$739$	−49.8350	−1.83321	−0.916605	−	0.399795i	$-0.869081\pi$
$739$	−49.8350	−1.83321	−0.916605	+	0.399795i	$0.869081\pi$
$740$	−26.7453	−0.983178
$741$	−48.2056	−1.77088
$742$	28.0083	1.02822
$743$	−28.3560	−1.04028	−0.520140	−	0.854081i	$-0.674120\pi$
$743$	−28.3560	−1.04028	−0.520140	+	0.854081i	$0.674120\pi$
$744$	5.18528	0.190101
$745$	19.6778	0.720940
$746$	−21.0005	−0.768881
$747$	−0.129914	−0.00475330
$748$	0	0
$749$	13.5107	0.493670
$750$	42.7641	1.56152
$751$	29.4486	1.07460	0.537298	−	0.843392i	$-0.319445\pi$
$751$	29.4486	1.07460	0.537298	+	0.843392i	$0.319445\pi$
$752$	−29.6308	−1.08052
$753$	−9.22035	−0.336008
$754$	−24.4335	−0.889817
$755$	5.98522	0.217824
$756$	50.8733	1.85024
$757$	8.36060	0.303871	0.151936	−	0.988390i	$-0.451449\pi$
$757$	8.36060	0.303871	0.151936	+	0.988390i	$0.451449\pi$
$758$	−46.6263	−1.69354
$759$	13.8930	0.504284
$760$	5.50518	0.199694
$761$	−29.4351	−1.06702	−0.533511	−	0.845793i	$-0.679128\pi$
$761$	−29.4351	−1.06702	−0.533511	+	0.845793i	$0.679128\pi$
$762$	−29.4982	−1.06861
$763$	−0.280997	−0.0101728
$764$	41.3898	1.49743
$765$	0	0
$766$	−14.1487	−0.511214
$767$	−19.5822	−0.707072
$768$	−17.9200	−0.646632
$769$	43.3733	1.56408	0.782041	−	0.623227i	$-0.214179\pi$
$769$	43.3733	1.56408	0.782041	+	0.623227i	$0.214179\pi$
$770$	−13.3591	−0.481427
$771$	24.1685	0.870406
$772$	29.2312	1.05205
$773$	−14.2842	−0.513768	−0.256884	−	0.966442i	$-0.582696\pi$
$773$	−14.2842	−0.513768	−0.256884	+	0.966442i	$0.582696\pi$
$774$	−0.0339301	−0.00121959
$775$	−12.9708	−0.465926
$776$	9.42932	0.338493
$777$	−63.1703	−2.26622
$778$	−29.8505	−1.07019
$779$	−9.55539	−0.342357
$780$	27.4780	0.983869
$781$	−5.74256	−0.205485
$782$	0	0
$783$	12.8857	0.460496
$784$	−41.2297	−1.47249
$785$	23.0090	0.821226
$786$	3.27602	0.116852
$787$	−46.6013	−1.66116	−0.830579	−	0.556901i	$-0.811990\pi$
$787$	−46.6013	−1.66116	−0.830579	+	0.556901i	$0.811990\pi$
$788$	−25.8206	−0.919821
$789$	38.8166	1.38191
$790$	−9.21033	−0.327689
$791$	−40.3475	−1.43459
$792$	0.144083	0.00511977
$793$	24.5951	0.873399
$794$	−4.20945	−0.149388
$795$	−7.97816	−0.282956
$796$	56.0340	1.98607
$797$	32.7278	1.15928	0.579640	−	0.814873i	$-0.303193\pi$
$797$	32.7278	1.15928	0.579640	+	0.814873i	$0.303193\pi$
$798$	97.1734	3.43990
$799$	0	0
$800$	−23.3500	−0.825546
$801$	−3.36507	−0.118899
$802$	10.3376	0.365033
$803$	−2.32415	−0.0820175
$804$	−21.3638	−0.753445
$805$	−49.7902	−1.75487
$806$	−42.5477	−1.49868
$807$	13.7615	0.484429
$808$	9.87838	0.347520
$809$	−29.4905	−1.03683	−0.518416	−	0.855128i	$-0.673478\pi$
$809$	−29.4905	−1.03683	−0.518416	+	0.855128i	$0.673478\pi$
$810$	−29.0800	−1.02177
$811$	−4.98228	−0.174952	−0.0874758	−	0.996167i	$-0.527880\pi$
$811$	−4.98228	−0.174952	−0.0874758	+	0.996167i	$0.527880\pi$
$812$	26.3925	0.926195
$813$	−10.5596	−0.370341
$814$	16.5174	0.578936
$815$	−22.0444	−0.772183
$816$	0	0
$817$	0.429024	0.0150097
$818$	37.0029	1.29378
$819$	4.52155	0.157996
$820$	5.44673	0.190208
$821$	−31.3835	−1.09529	−0.547645	−	0.836711i	$-0.684476\pi$
$821$	−31.3835	−1.09529	−0.547645	+	0.836711i	$0.684476\pi$
$822$	39.0816	1.36313
$823$	−43.1842	−1.50530	−0.752652	−	0.658418i	$-0.771226\pi$
$823$	−43.1842	−1.50530	−0.752652	+	0.658418i	$0.771226\pi$
$824$	−5.08854	−0.177268
$825$	−5.17335	−0.180113
$826$	39.4740	1.37348
$827$	−5.74725	−0.199851	−0.0999257	−	0.994995i	$-0.531861\pi$
$827$	−5.74725	−0.199851	−0.0999257	+	0.994995i	$0.531861\pi$
$828$	4.01322	0.139469
$829$	36.3488	1.26245	0.631223	−	0.775601i	$-0.282553\pi$
$829$	36.3488	1.26245	0.631223	+	0.775601i	$0.282553\pi$
$830$	−1.74741	−0.0606536
$831$	−17.2528	−0.598494
$832$	−46.6692	−1.61796
$833$	0	0
$834$	−19.5177	−0.675843
$835$	31.8242	1.10132
$836$	−13.6151	−0.470889
$837$	22.4386	0.775593
$838$	−43.0022	−1.48549
$839$	3.94122	0.136066	0.0680329	−	0.997683i	$-0.478328\pi$
$839$	3.94122	0.136066	0.0680329	+	0.997683i	$0.478328\pi$
$840$	−7.41179	−0.255731
$841$	−22.3151	−0.769485
$842$	57.7673	1.99079
$843$	14.9714	0.515642
$844$	−19.4842	−0.670672
$845$	−11.2459	−0.386872
$846$	−4.20438	−0.144549
$847$	4.42094	0.151905
$848$	10.0308	0.344459
$849$	−2.02898	−0.0696343
$850$	0	0
$851$	61.5618	2.11031
$852$	−23.8103	−0.815726
$853$	−0.409151	−0.0140091	−0.00700453	−	0.999975i	$-0.502230\pi$
$853$	−0.409151	−0.0140091	−0.00700453	+	0.999975i	$0.502230\pi$
$854$	−49.5791	−1.69656
$855$	−1.92841	−0.0659503
$856$	−1.96000	−0.0669913
$857$	7.92641	0.270761	0.135380	−	0.990794i	$-0.456774\pi$
$857$	7.92641	0.270761	0.135380	+	0.990794i	$0.456774\pi$
$858$	−16.9699	−0.579343
$859$	6.13230	0.209231	0.104616	−	0.994513i	$-0.466639\pi$
$859$	6.13230	0.209231	0.104616	+	0.994513i	$0.466639\pi$
$860$	−0.244551	−0.00833911
$861$	12.8647	0.438429
$862$	25.6116	0.872336
$863$	−15.9944	−0.544456	−0.272228	−	0.962233i	$-0.587761\pi$
$863$	−15.9944	−0.544456	−0.272228	+	0.962233i	$0.587761\pi$
$864$	40.3938	1.37423
$865$	−18.2856	−0.621730
$866$	52.4620	1.78273
$867$	0	0
$868$	45.9589	1.55995
$869$	3.04799	0.103396
$870$	−14.0298	−0.475655
$871$	23.4570	0.794810
$872$	0.0407642	0.00138045
$873$	−3.30300	−0.111790
$874$	−94.6990	−3.20324
$875$	50.7184	1.71460
$876$	−9.63658	−0.325590
$877$	−49.9968	−1.68827	−0.844137	−	0.536128i	$-0.819886\pi$
$877$	−49.9968	−1.68827	−0.844137	+	0.536128i	$0.819886\pi$
$878$	29.8152	1.00621
$879$	−35.0623	−1.18262
$880$	−4.78436	−0.161281
$881$	−23.2157	−0.782158	−0.391079	−	0.920357i	$-0.627898\pi$
$881$	−23.2157	−0.782158	−0.391079	+	0.920357i	$0.627898\pi$
$882$	−5.85017	−0.196986
$883$	−11.8906	−0.400151	−0.200075	−	0.979781i	$-0.564119\pi$
$883$	−11.8906	−0.400151	−0.200075	+	0.979781i	$0.564119\pi$
$884$	0	0
$885$	−11.2441	−0.377968
$886$	−2.43094	−0.0816690
$887$	−34.0523	−1.14336	−0.571682	−	0.820475i	$-0.693709\pi$
$887$	−34.0523	−1.14336	−0.571682	+	0.820475i	$0.693709\pi$
$888$	9.16411	0.307527
$889$	−34.9850	−1.17336
$890$	−45.2620	−1.51719
$891$	9.62350	0.322399
$892$	−54.5075	−1.82505
$893$	53.1617	1.77899
$894$	−50.3884	−1.68524
$895$	10.7272	0.358570
$896$	22.4122	0.748738
$897$	−63.2482	−2.11179
$898$	1.27452	0.0425312
$899$	11.6409	0.388246
$900$	−1.49440	−0.0498134
$901$	0	0
$902$	−3.36380	−0.112002
$903$	−0.577609	−0.0192216
$904$	5.85321	0.194675
$905$	−38.3120	−1.27353
$906$	−15.3262	−0.509178
$907$	23.6953	0.786788	0.393394	−	0.919370i	$-0.371301\pi$
$907$	23.6953	0.786788	0.393394	+	0.919370i	$0.371301\pi$
$908$	20.0296	0.664705
$909$	−3.46030	−0.114771
$910$	60.8173	2.01607
$911$	−40.0388	−1.32655	−0.663273	−	0.748378i	$-0.730833\pi$
$911$	−40.0388	−1.32655	−0.663273	+	0.748378i	$0.730833\pi$
$912$	34.8013	1.15239
$913$	0.578275	0.0191381
$914$	−2.92987	−0.0969115
$915$	14.1226	0.466878
$916$	−30.3339	−1.00226
$917$	3.88538	0.128307
$918$	0	0
$919$	−48.4123	−1.59697	−0.798487	−	0.602012i	$-0.794366\pi$
$919$	−48.4123	−1.59697	−0.798487	+	0.602012i	$0.794366\pi$
$920$	7.22306	0.238137
$921$	−2.06080	−0.0679058
$922$	−10.7419	−0.353766
$923$	26.1431	0.860510
$924$	18.3305	0.603028
$925$	−22.9238	−0.753729
$926$	81.7177	2.68541
$927$	1.78247	0.0585439
$928$	20.9558	0.687909
$929$	−39.0329	−1.28063	−0.640314	−	0.768113i	$-0.721196\pi$
$929$	−39.0329	−1.28063	−0.640314	+	0.768113i	$0.721196\pi$
$930$	−24.4310	−0.801123
$931$	73.9717	2.42433
$932$	−24.3251	−0.796794
$933$	11.0657	0.362274
$934$	−43.3343	−1.41794
$935$	0	0
$936$	−0.655941	−0.0214401
$937$	2.62259	0.0856761	0.0428381	−	0.999082i	$-0.486360\pi$
$937$	2.62259	0.0856761	0.0428381	+	0.999082i	$0.486360\pi$
$938$	−47.2849	−1.54391
$939$	17.2134	0.561737
$940$	−30.3030	−0.988375
$941$	25.3312	0.825772	0.412886	−	0.910783i	$-0.364521\pi$
$941$	25.3312	0.825772	0.412886	+	0.910783i	$0.364521\pi$
$942$	−58.9185	−1.91967
$943$	−12.5371	−0.408266
$944$	14.1371	0.460122
$945$	−32.0736	−1.04335
$946$	0.151030	0.00491041
$947$	5.09042	0.165416	0.0827082	−	0.996574i	$-0.473643\pi$
$947$	5.09042	0.165416	0.0827082	+	0.996574i	$0.473643\pi$
$948$	12.6378	0.410458
$949$	10.5807	0.343465
$950$	35.2631	1.14409
$951$	−29.3454	−0.951591
$952$	0	0
$953$	44.9010	1.45449	0.727244	−	0.686379i	$-0.240801\pi$
$953$	44.9010	1.45449	0.727244	+	0.686379i	$0.240801\pi$
$954$	1.42329	0.0460807
$955$	−26.0946	−0.844402
$956$	48.9997	1.58476
$957$	4.64291	0.150084
$958$	37.3278	1.20601
$959$	46.3510	1.49675
$960$	−26.7975	−0.864887
$961$	−10.7290	−0.346095
$962$	−75.1959	−2.42441
$963$	0.686568	0.0221244
$964$	39.7693	1.28088
$965$	−18.4291	−0.593254
$966$	127.496	4.10213
$967$	52.1702	1.67768	0.838840	−	0.544379i	$-0.183234\pi$
$967$	52.1702	1.67768	0.838840	+	0.544379i	$0.183234\pi$
$968$	−0.641346	−0.0206136
$969$	0	0
$970$	−44.4272	−1.42647
$971$	31.3127	1.00487	0.502437	−	0.864614i	$-0.332437\pi$
$971$	31.3127	1.00487	0.502437	+	0.864614i	$0.332437\pi$
$972$	5.37969	0.172554
$973$	−23.1481	−0.742094
$974$	−4.20595	−0.134767
$975$	23.5517	0.754259
$976$	−17.7561	−0.568358
$977$	33.1622	1.06095	0.530476	−	0.847700i	$-0.322013\pi$
$977$	33.1622	1.06095	0.530476	+	0.847700i	$0.322013\pi$
$978$	56.4485	1.80502
$979$	14.9787	0.478720
$980$	−42.1651	−1.34691
$981$	−0.0142793	−0.000455904 0
$982$	−16.3114	−0.520519
$983$	−13.0717	−0.416924	−0.208462	−	0.978030i	$-0.566846\pi$
$983$	−13.0717	−0.416924	−0.208462	+	0.978030i	$0.566846\pi$
$984$	−1.86629	−0.0594950
$985$	16.2789	0.518688
$986$	0	0
$987$	−71.5733	−2.27820
$988$	61.9830	1.97194
$989$	0.562901	0.0178992
$990$	−0.678863	−0.0215757
$991$	−1.41897	−0.0450751	−0.0225375	−	0.999746i	$-0.507175\pi$
$991$	−1.41897	−0.0450751	−0.0225375	+	0.999746i	$0.507175\pi$
$992$	36.4917	1.15861
$993$	19.3415	0.613784
$994$	−52.6995	−1.67153
$995$	−35.3272	−1.11995
$996$	2.39769	0.0759738
$997$	−38.5327	−1.22034	−0.610172	−	0.792269i	$-0.708899\pi$
$997$	−38.5327	−1.22034	−0.610172	+	0.792269i	$0.708899\pi$
$998$	42.5544	1.34704
$999$	39.6565	1.25468

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3179.2.a.bi.1.5		28
17.5	odd	16		187.2.h.a.144.13	yes	56
17.7	odd	16		187.2.h.a.100.13	✓	56
17.16	even	2		3179.2.a.bh.1.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.100.13	✓	56	17.7	odd	16
187.2.h.a.144.13	yes	56	17.5	odd	16
3179.2.a.bh.1.5		28	17.16	even	2
3179.2.a.bi.1.5		28	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:	\( N \)	\(=\)	\( 3179 = 11 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3179.a (trivial)

\(f(q)\)	\(=\)	\(q-2.07580 q^{2} -1.79573 q^{3} +2.30896 q^{4} -1.45571 q^{5} +3.72759 q^{6} +4.42094 q^{7} -0.641346 q^{8} +0.224658 q^{9} +O(q^{10})\)	\(q-2.07580 q^{2} -1.79573 q^{3} +2.30896 q^{4} -1.45571 q^{5} +3.72759 q^{6} +4.42094 q^{7} -0.641346 q^{8} +0.224658 q^{9} +3.02177 q^{10} -1.00000 q^{11} -4.14628 q^{12} +4.55252 q^{13} -9.17701 q^{14} +2.61406 q^{15} -3.28662 q^{16} -0.466345 q^{18} +5.89664 q^{19} -3.36118 q^{20} -7.93883 q^{21} +2.07580 q^{22} +7.73668 q^{23} +1.15169 q^{24} -2.88091 q^{25} -9.45013 q^{26} +4.98377 q^{27} +10.2078 q^{28} +2.58552 q^{29} -5.42629 q^{30} +4.50234 q^{31} +8.10506 q^{32} +1.79573 q^{33} -6.43561 q^{35} +0.518726 q^{36} +7.95713 q^{37} -12.2403 q^{38} -8.17510 q^{39} +0.933613 q^{40} -1.62048 q^{41} +16.4795 q^{42} +0.0727574 q^{43} -2.30896 q^{44} -0.327036 q^{45} -16.0598 q^{46} +9.01560 q^{47} +5.90189 q^{48} +12.5447 q^{49} +5.98021 q^{50} +10.5116 q^{52} -3.05201 q^{53} -10.3453 q^{54} +1.45571 q^{55} -2.83535 q^{56} -10.5888 q^{57} -5.36704 q^{58} -4.30140 q^{59} +6.03578 q^{60} +5.40254 q^{61} -9.34597 q^{62} +0.993198 q^{63} -10.2513 q^{64} -6.62714 q^{65} -3.72759 q^{66} +5.15253 q^{67} -13.8930 q^{69} +13.3591 q^{70} +5.74256 q^{71} -0.144083 q^{72} +2.32415 q^{73} -16.5174 q^{74} +5.17335 q^{75} +13.6151 q^{76} -4.42094 q^{77} +16.9699 q^{78} -3.04799 q^{79} +4.78436 q^{80} -9.62350 q^{81} +3.36380 q^{82} -0.578275 q^{83} -18.3305 q^{84} -0.151030 q^{86} -4.64291 q^{87} +0.641346 q^{88} -14.9787 q^{89} +0.678863 q^{90} +20.1264 q^{91} +17.8637 q^{92} -8.08500 q^{93} -18.7146 q^{94} -8.58379 q^{95} -14.5545 q^{96} -14.7024 q^{97} -26.0404 q^{98} -0.224658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9}+O(q^{10}) \) 28 * q + 8 * q^3 + 24 * q^4 + 16 * q^5 + 16 * q^6 + 12 * q^7 + 20 * q^9	\( 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9} + 24 q^{10} - 28 q^{11} + 24 q^{12} + 16 q^{14} - 16 q^{15} + 16 q^{16} + 32 q^{20} + 8 q^{23} - 8 q^{24} + 20 q^{25} - 24 q^{26} + 32 q^{27} + 32 q^{28} + 36 q^{29} + 40 q^{30} + 56 q^{31} + 40 q^{32} - 8 q^{33} + 16 q^{35} + 40 q^{36} + 64 q^{37} - 8 q^{38} + 32 q^{39} + 72 q^{40} + 28 q^{41} + 24 q^{42} + 16 q^{43} - 24 q^{44} + 24 q^{45} - 36 q^{47} + 56 q^{48} + 16 q^{49} + 56 q^{50} - 20 q^{53} + 64 q^{54} - 16 q^{55} + 48 q^{56} + 32 q^{57} - 16 q^{58} - 28 q^{59} + 8 q^{60} + 104 q^{61} - 8 q^{62} + 28 q^{63} + 32 q^{65} - 16 q^{66} - 12 q^{67} - 32 q^{69} + 40 q^{71} + 40 q^{72} + 76 q^{73} + 24 q^{74} - 16 q^{75} - 16 q^{76} - 12 q^{77} - 24 q^{78} + 24 q^{79} + 8 q^{80} + 12 q^{81} + 56 q^{82} + 32 q^{83} - 40 q^{84} - 16 q^{86} - 8 q^{87} - 52 q^{89} + 16 q^{90} + 80 q^{91} - 56 q^{92} + 24 q^{97} - 24 q^{98} - 20 q^{99}+O(q^{100}) \) 28 * q + 8 * q^3 + 24 * q^4 + 16 * q^5 + 16 * q^6 + 12 * q^7 + 20 * q^9 + 24 * q^10 - 28 * q^11 + 24 * q^12 + 16 * q^14 - 16 * q^15 + 16 * q^16 + 32 * q^20 + 8 * q^23 - 8 * q^24 + 20 * q^25 - 24 * q^26 + 32 * q^27 + 32 * q^28 + 36 * q^29 + 40 * q^30 + 56 * q^31 + 40 * q^32 - 8 * q^33 + 16 * q^35 + 40 * q^36 + 64 * q^37 - 8 * q^38 + 32 * q^39 + 72 * q^40 + 28 * q^41 + 24 * q^42 + 16 * q^43 - 24 * q^44 + 24 * q^45 - 36 * q^47 + 56 * q^48 + 16 * q^49 + 56 * q^50 - 20 * q^53 + 64 * q^54 - 16 * q^55 + 48 * q^56 + 32 * q^57 - 16 * q^58 - 28 * q^59 + 8 * q^60 + 104 * q^61 - 8 * q^62 + 28 * q^63 + 32 * q^65 - 16 * q^66 - 12 * q^67 - 32 * q^69 + 40 * q^71 + 40 * q^72 + 76 * q^73 + 24 * q^74 - 16 * q^75 - 16 * q^76 - 12 * q^77 - 24 * q^78 + 24 * q^79 + 8 * q^80 + 12 * q^81 + 56 * q^82 + 32 * q^83 - 40 * q^84 - 16 * q^86 - 8 * q^87 - 52 * q^89 + 16 * q^90 + 80 * q^91 - 56 * q^92 + 24 * q^97 - 24 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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