LMFDB - Embedded newform 4767.2.a.g.1.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [4767,2,Mod(1,4767)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4767, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4767.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 4767 = 3 \cdot 7 \cdot 227 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4767.a (trivial)

Newform invariants

comment:select newform

sage:traces = [35,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$38.0646866435$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4767.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.233639 q^{2} -1.00000 q^{3} -1.94541 q^{4} -1.48259 q^{5} +0.233639 q^{6} +1.00000 q^{7} +0.921803 q^{8} +1.00000 q^{9} +0.346390 q^{10} +5.41758 q^{11} +1.94541 q^{12} +4.94174 q^{13} -0.233639 q^{14} +1.48259 q^{15} +3.67546 q^{16} +6.13587 q^{17} -0.233639 q^{18} -5.83071 q^{19} +2.88424 q^{20} -1.00000 q^{21} -1.26576 q^{22} +7.09256 q^{23} -0.921803 q^{24} -2.80194 q^{25} -1.15458 q^{26} -1.00000 q^{27} -1.94541 q^{28} +9.88106 q^{29} -0.346390 q^{30} -3.28238 q^{31} -2.70234 q^{32} -5.41758 q^{33} -1.43358 q^{34} -1.48259 q^{35} -1.94541 q^{36} +8.66303 q^{37} +1.36228 q^{38} -4.94174 q^{39} -1.36665 q^{40} +8.49315 q^{41} +0.233639 q^{42} -0.270411 q^{43} -10.5394 q^{44} -1.48259 q^{45} -1.65710 q^{46} -8.27124 q^{47} -3.67546 q^{48} +1.00000 q^{49} +0.654643 q^{50} -6.13587 q^{51} -9.61372 q^{52} +10.3838 q^{53} +0.233639 q^{54} -8.03202 q^{55} +0.921803 q^{56} +5.83071 q^{57} -2.30860 q^{58} -11.5315 q^{59} -2.88424 q^{60} +5.96919 q^{61} +0.766893 q^{62} +1.00000 q^{63} -6.71954 q^{64} -7.32655 q^{65} +1.26576 q^{66} -2.51408 q^{67} -11.9368 q^{68} -7.09256 q^{69} +0.346390 q^{70} +2.71504 q^{71} +0.921803 q^{72} -3.97759 q^{73} -2.02402 q^{74} +2.80194 q^{75} +11.3431 q^{76} +5.41758 q^{77} +1.15458 q^{78} +6.44646 q^{79} -5.44918 q^{80} +1.00000 q^{81} -1.98433 q^{82} -0.577379 q^{83} +1.94541 q^{84} -9.09695 q^{85} +0.0631786 q^{86} -9.88106 q^{87} +4.99394 q^{88} -18.1493 q^{89} +0.346390 q^{90} +4.94174 q^{91} -13.7980 q^{92} +3.28238 q^{93} +1.93248 q^{94} +8.64453 q^{95} +2.70234 q^{96} -1.10284 q^{97} -0.233639 q^{98} +5.41758 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 7 q^{2} - 35 q^{3} + 45 q^{4} - 4 q^{5} - 7 q^{6} + 35 q^{7} + 21 q^{8} + 35 q^{9} + 11 q^{10} - 3 q^{11} - 45 q^{12} + 19 q^{13} + 7 q^{14} + 4 q^{15} + 65 q^{16} + 20 q^{17} + 7 q^{18} + 9 q^{19}+ \cdots - 3 q^{99}+O(q^{100}) $ 35 * q + 7 * q^2 - 35 * q^3 + 45 * q^4 - 4 * q^5 - 7 * q^6 + 35 * q^7 + 21 * q^8 + 35 * q^9 + 11 * q^10 - 3 * q^11 - 45 * q^12 + 19 * q^13 + 7 * q^14 + 4 * q^15 + 65 * q^16 + 20 * q^17 + 7 * q^18 + 9 * q^19 - 7 * q^20 - 35 * q^21 + 33 * q^22 + 17 * q^23 - 21 * q^24 + 67 * q^25 - 6 * q^26 - 35 * q^27 + 45 * q^28 + 17 * q^29 - 11 * q^30 + 5 * q^31 + 54 * q^32 + 3 * q^33 + 22 * q^34 - 4 * q^35 + 45 * q^36 + 35 * q^37 - 19 * q^38 - 19 * q^39 + 34 * q^40 + 18 * q^41 - 7 * q^42 + 33 * q^43 - 7 * q^44 - 4 * q^45 + 38 * q^46 - 13 * q^47 - 65 * q^48 + 35 * q^49 + 28 * q^50 - 20 * q^51 + 37 * q^52 + 36 * q^53 - 7 * q^54 + 21 * q^55 + 21 * q^56 - 9 * q^57 + 42 * q^58 - 54 * q^59 + 7 * q^60 + 35 * q^61 - 28 * q^62 + 35 * q^63 + 105 * q^64 + 27 * q^65 - 33 * q^66 + 37 * q^67 + 25 * q^68 - 17 * q^69 + 11 * q^70 + 44 * q^71 + 21 * q^72 + 59 * q^73 - 17 * q^74 - 67 * q^75 + 23 * q^76 - 3 * q^77 + 6 * q^78 + 77 * q^79 - 26 * q^80 + 35 * q^81 + 4 * q^82 - 41 * q^83 - 45 * q^84 + 39 * q^85 + 42 * q^86 - 17 * q^87 + 34 * q^88 - 9 * q^89 + 11 * q^90 + 19 * q^91 + 61 * q^92 - 5 * q^93 + 10 * q^94 + 25 * q^95 - 54 * q^96 + 79 * q^97 + 7 * q^98 - 3 * q^99

Coefficient data

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

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

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

$2$	−0.233639	−0.165208	−0.0826039	−	0.996582i	$-0.526324\pi$
$2$	−0.233639	−0.165208	−0.0826039	+	0.996582i	$0.526324\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.94541	−0.972706
$5$	−1.48259	−0.663033	−0.331516	−	0.943450i	$-0.607560\pi$
$5$	−1.48259	−0.663033	−0.331516	+	0.943450i	$0.607560\pi$
$6$	0.233639	0.0953828
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.921803	0.325906
$9$	1.00000	0.333333
$10$	0.346390	0.109538
$11$	5.41758	1.63346	0.816730	−	0.577020i	$-0.195784\pi$
$11$	5.41758	1.63346	0.816730	+	0.577020i	$0.195784\pi$
$12$	1.94541	0.561592
$13$	4.94174	1.37059	0.685296	−	0.728265i	$-0.259673\pi$
$13$	4.94174	1.37059	0.685296	+	0.728265i	$0.259673\pi$
$14$	−0.233639	−0.0624427
$15$	1.48259	0.382802
$16$	3.67546	0.918864
$17$	6.13587	1.48817	0.744083	−	0.668087i	$-0.232887\pi$
$17$	6.13587	1.48817	0.744083	+	0.668087i	$0.232887\pi$
$18$	−0.233639	−0.0550693
$19$	−5.83071	−1.33766	−0.668828	−	0.743417i	$-0.733204\pi$
$19$	−5.83071	−1.33766	−0.668828	+	0.743417i	$0.733204\pi$
$20$	2.88424	0.644936
$21$	−1.00000	−0.218218
$22$	−1.26576	−0.269860
$23$	7.09256	1.47890	0.739450	−	0.673211i	$-0.235086\pi$
$23$	7.09256	1.47890	0.739450	+	0.673211i	$0.235086\pi$
$24$	−0.921803	−0.188162
$25$	−2.80194	−0.560388
$26$	−1.15458	−0.226432
$27$	−1.00000	−0.192450
$28$	−1.94541	−0.367648
$29$	9.88106	1.83487	0.917433	−	0.397890i	$-0.130257\pi$
$29$	9.88106	1.83487	0.917433	+	0.397890i	$0.130257\pi$
$30$	−0.346390	−0.0632419
$31$	−3.28238	−0.589533	−0.294767	−	0.955569i	$-0.595242\pi$
$31$	−3.28238	−0.589533	−0.294767	+	0.955569i	$0.595242\pi$
$32$	−2.70234	−0.477710
$33$	−5.41758	−0.943079
$34$	−1.43358	−0.245857
$35$	−1.48259	−0.250603
$36$	−1.94541	−0.324235
$37$	8.66303	1.42419	0.712096	−	0.702082i	$-0.247746\pi$
$37$	8.66303	1.42419	0.712096	+	0.702082i	$0.247746\pi$
$38$	1.36228	0.220991
$39$	−4.94174	−0.791312
$40$	−1.36665	−0.216087
$41$	8.49315	1.32641	0.663203	−	0.748439i	$-0.269197\pi$
$41$	8.49315	1.32641	0.663203	+	0.748439i	$0.269197\pi$
$42$	0.233639	0.0360513
$43$	−0.270411	−0.0412373	−0.0206186	−	0.999787i	$-0.506564\pi$
$43$	−0.270411	−0.0412373	−0.0206186	+	0.999787i	$0.506564\pi$
$44$	−10.5394	−1.58888
$45$	−1.48259	−0.221011
$46$	−1.65710	−0.244326
$47$	−8.27124	−1.20648	−0.603242	−	0.797558i	$-0.706125\pi$
$47$	−8.27124	−1.20648	−0.603242	+	0.797558i	$0.706125\pi$
$48$	−3.67546	−0.530506
$49$	1.00000	0.142857
$50$	0.654643	0.0925804
$51$	−6.13587	−0.859193
$52$	−9.61372	−1.33318
$53$	10.3838	1.42633	0.713164	−	0.700997i	$-0.247262\pi$
$53$	10.3838	1.42633	0.713164	+	0.700997i	$0.247262\pi$
$54$	0.233639	0.0317943
$55$	−8.03202	−1.08304
$56$	0.921803	0.123181
$57$	5.83071	0.772296
$58$	−2.30860	−0.303134
$59$	−11.5315	−1.50128	−0.750639	−	0.660712i	$-0.770254\pi$
$59$	−11.5315	−1.50128	−0.750639	+	0.660712i	$0.770254\pi$
$60$	−2.88424	−0.372354
$61$	5.96919	0.764276	0.382138	−	0.924105i	$-0.375188\pi$
$61$	5.96919	0.764276	0.382138	+	0.924105i	$0.375188\pi$
$62$	0.766893	0.0973955
$63$	1.00000	0.125988
$64$	−6.71954	−0.839943
$65$	−7.32655	−0.908747
$66$	1.26576	0.155804
$67$	−2.51408	−0.307144	−0.153572	−	0.988137i	$-0.549078\pi$
$67$	−2.51408	−0.307144	−0.153572	+	0.988137i	$0.549078\pi$
$68$	−11.9368	−1.44755
$69$	−7.09256	−0.853844
$70$	0.346390	0.0414015
$71$	2.71504	0.322216	0.161108	−	0.986937i	$-0.448493\pi$
$71$	2.71504	0.322216	0.161108	+	0.986937i	$0.448493\pi$
$72$	0.921803	0.108635
$73$	−3.97759	−0.465542	−0.232771	−	0.972532i	$-0.574779\pi$
$73$	−3.97759	−0.465542	−0.232771	+	0.972532i	$0.574779\pi$
$74$	−2.02402	−0.235288
$75$	2.80194	0.323540
$76$	11.3431	1.30115
$77$	5.41758	0.617390
$78$	1.15458	0.130731
$79$	6.44646	0.725283	0.362642	−	0.931929i	$-0.381875\pi$
$79$	6.44646	0.725283	0.362642	+	0.931929i	$0.381875\pi$
$80$	−5.44918	−0.609237
$81$	1.00000	0.111111
$82$	−1.98433	−0.219133
$83$	−0.577379	−0.0633756	−0.0316878	−	0.999498i	$-0.510088\pi$
$83$	−0.577379	−0.0633756	−0.0316878	+	0.999498i	$0.510088\pi$
$84$	1.94541	0.212262
$85$	−9.09695	−0.986703
$86$	0.0631786	0.00681272
$87$	−9.88106	−1.05936
$88$	4.99394	0.532355
$89$	−18.1493	−1.92382	−0.961909	−	0.273371i	$-0.911861\pi$
$89$	−18.1493	−1.92382	−0.961909	+	0.273371i	$0.911861\pi$
$90$	0.346390	0.0365127
$91$	4.94174	0.518035
$92$	−13.7980	−1.43854
$93$	3.28238	0.340367
$94$	1.93248	0.199321
$95$	8.64453	0.886910
$96$	2.70234	0.275806
$97$	−1.10284	−0.111976	−0.0559881	−	0.998431i	$-0.517831\pi$
$97$	−1.10284	−0.111976	−0.0559881	+	0.998431i	$0.517831\pi$
$98$	−0.233639	−0.0236011
$99$	5.41758	0.544487
$100$	5.45093	0.545093
$101$	15.3358	1.52597	0.762985	−	0.646417i	$-0.223733\pi$
$101$	15.3358	1.52597	0.762985	+	0.646417i	$0.223733\pi$
$102$	1.43358	0.141945
$103$	−5.04823	−0.497417	−0.248709	−	0.968578i	$-0.580006\pi$
$103$	−5.04823	−0.497417	−0.248709	+	0.968578i	$0.580006\pi$
$104$	4.55531	0.446685
$105$	1.48259	0.144686
$106$	−2.42607	−0.235640
$107$	−20.3055	−1.96301	−0.981504	−	0.191442i	$-0.938684\pi$
$107$	−20.3055	−1.96301	−0.981504	+	0.191442i	$0.938684\pi$
$108$	1.94541	0.187197
$109$	−0.870389	−0.0833681	−0.0416841	−	0.999131i	$-0.513272\pi$
$109$	−0.870389	−0.0833681	−0.0416841	+	0.999131i	$0.513272\pi$
$110$	1.87659	0.178926
$111$	−8.66303	−0.822258
$112$	3.67546	0.347298
$113$	−11.6480	−1.09575	−0.547875	−	0.836560i	$-0.684563\pi$
$113$	−11.6480	−1.09575	−0.547875	+	0.836560i	$0.684563\pi$
$114$	−1.36228	−0.127589
$115$	−10.5153	−0.980559
$116$	−19.2227	−1.78479
$117$	4.94174	0.456864
$118$	2.69422	0.248023
$119$	6.13587	0.562474
$120$	1.36665	0.124758
$121$	18.3501	1.66819
$122$	−1.39464	−0.126264
$123$	−8.49315	−0.765801
$124$	6.38559	0.573443
$125$	11.5670	1.03459
$126$	−0.233639	−0.0208142
$127$	−1.38223	−0.122653	−0.0613265	−	0.998118i	$-0.519533\pi$
$127$	−1.38223	−0.122653	−0.0613265	+	0.998118i	$0.519533\pi$
$128$	6.97462	0.616475
$129$	0.270411	0.0238084
$130$	1.71177	0.150132
$131$	−14.8618	−1.29848	−0.649241	−	0.760583i	$-0.724913\pi$
$131$	−14.8618	−1.29848	−0.649241	+	0.760583i	$0.724913\pi$
$132$	10.5394	0.917339
$133$	−5.83071	−0.505587
$134$	0.587387	0.0507425
$135$	1.48259	0.127601
$136$	5.65606	0.485003
$137$	−19.5731	−1.67225	−0.836123	−	0.548543i	$-0.815183\pi$
$137$	−19.5731	−1.67225	−0.836123	+	0.548543i	$0.815183\pi$
$138$	1.65710	0.141062
$139$	14.4677	1.22714	0.613569	−	0.789641i	$-0.289733\pi$
$139$	14.4677	1.22714	0.613569	+	0.789641i	$0.289733\pi$
$140$	2.88424	0.243763
$141$	8.27124	0.696564
$142$	−0.634340	−0.0532327
$143$	26.7722	2.23881
$144$	3.67546	0.306288
$145$	−14.6495	−1.21658
$146$	0.929322	0.0769112
$147$	−1.00000	−0.0824786
$148$	−16.8532	−1.38532
$149$	4.53174	0.371254	0.185627	−	0.982620i	$-0.440568\pi$
$149$	4.53174	0.371254	0.185627	+	0.982620i	$0.440568\pi$
$150$	−0.654643	−0.0534513
$151$	9.47624	0.771165	0.385583	−	0.922673i	$-0.374000\pi$
$151$	9.47624	0.771165	0.385583	+	0.922673i	$0.374000\pi$
$152$	−5.37476	−0.435951
$153$	6.13587	0.496055
$154$	−1.26576	−0.101998
$155$	4.86641	0.390880
$156$	9.61372	0.769714
$157$	23.5581	1.88014	0.940071	−	0.340980i	$-0.110759\pi$
$157$	23.5581	1.88014	0.940071	+	0.340980i	$0.110759\pi$
$158$	−1.50615	−0.119822
$159$	−10.3838	−0.823491
$160$	4.00644	0.316737
$161$	7.09256	0.558972
$162$	−0.233639	−0.0183564
$163$	2.58640	0.202583	0.101291	−	0.994857i	$-0.467703\pi$
$163$	2.58640	0.202583	0.101291	+	0.994857i	$0.467703\pi$
$164$	−16.5227	−1.29020
$165$	8.03202	0.625292
$166$	0.134898	0.0104701
$167$	−5.18530	−0.401250	−0.200625	−	0.979668i	$-0.564297\pi$
$167$	−5.18530	−0.401250	−0.200625	+	0.979668i	$0.564297\pi$
$168$	−0.921803	−0.0711186
$169$	11.4208	0.878522
$170$	2.12540	0.163011
$171$	−5.83071	−0.445885
$172$	0.526061	0.0401118
$173$	18.1348	1.37876	0.689380	−	0.724400i	$-0.257883\pi$
$173$	18.1348	1.37876	0.689380	+	0.724400i	$0.257883\pi$
$174$	2.30860	0.175015
$175$	−2.80194	−0.211807
$176$	19.9121	1.50093
$177$	11.5315	0.866763
$178$	4.24038	0.317830
$179$	0.509410	0.0380751	0.0190376	−	0.999819i	$-0.493940\pi$
$179$	0.509410	0.0380751	0.0190376	+	0.999819i	$0.493940\pi$
$180$	2.88424	0.214979
$181$	−6.83038	−0.507698	−0.253849	−	0.967244i	$-0.581697\pi$
$181$	−6.83038	−0.507698	−0.253849	+	0.967244i	$0.581697\pi$
$182$	−1.15458	−0.0855834
$183$	−5.96919	−0.441255
$184$	6.53794	0.481983
$185$	−12.8437	−0.944286
$186$	−0.766893	−0.0562313
$187$	33.2415	2.43086
$188$	16.0910	1.17355
$189$	−1.00000	−0.0727393
$190$	−2.01970	−0.146524
$191$	11.7716	0.851762	0.425881	−	0.904779i	$-0.359964\pi$
$191$	11.7716	0.851762	0.425881	+	0.904779i	$0.359964\pi$
$192$	6.71954	0.484941
$193$	17.7698	1.27910	0.639549	−	0.768750i	$-0.279121\pi$
$193$	17.7698	1.27910	0.639549	+	0.768750i	$0.279121\pi$
$194$	0.257666	0.0184993
$195$	7.32655	0.524665
$196$	−1.94541	−0.138958
$197$	0.944056	0.0672612	0.0336306	−	0.999434i	$-0.489293\pi$
$197$	0.944056	0.0672612	0.0336306	+	0.999434i	$0.489293\pi$
$198$	−1.26576	−0.0899535
$199$	2.09676	0.148635	0.0743177	−	0.997235i	$-0.476322\pi$
$199$	2.09676	0.148635	0.0743177	+	0.997235i	$0.476322\pi$
$200$	−2.58284	−0.182634
$201$	2.51408	0.177329
$202$	−3.58304	−0.252102
$203$	9.88106	0.693514
$204$	11.9368	0.835743
$205$	−12.5918	−0.879451
$206$	1.17946	0.0821772
$207$	7.09256	0.492967
$208$	18.1631	1.25939
$209$	−31.5883	−2.18501
$210$	−0.346390	−0.0239032
$211$	−2.84088	−0.195574	−0.0977871	−	0.995207i	$-0.531176\pi$
$211$	−2.84088	−0.195574	−0.0977871	+	0.995207i	$0.531176\pi$
$212$	−20.2008	−1.38740
$213$	−2.71504	−0.186032
$214$	4.74416	0.324304
$215$	0.400907	0.0273417
$216$	−0.921803	−0.0627207
$217$	−3.28238	−0.222823
$218$	0.203357	0.0137731
$219$	3.97759	0.268781
$220$	15.6256	1.05348
$221$	30.3218	2.03967
$222$	2.02402	0.135843
$223$	17.7173	1.18644	0.593220	−	0.805041i	$-0.297857\pi$
$223$	17.7173	1.18644	0.593220	+	0.805041i	$0.297857\pi$
$224$	−2.70234	−0.180557
$225$	−2.80194	−0.186796
$226$	2.72143	0.181027
$227$	−1.00000	−0.0663723
$227$	−1.00000	−0.0663723
$228$	−11.3431	−0.751217
$229$	6.65562	0.439816	0.219908	−	0.975521i	$-0.429424\pi$
$229$	6.65562	0.439816	0.219908	+	0.975521i	$0.429424\pi$
$230$	2.45679	0.161996
$231$	−5.41758	−0.356450
$232$	9.10839	0.597995
$233$	2.80827	0.183976	0.0919880	−	0.995760i	$-0.470678\pi$
$233$	2.80827	0.183976	0.0919880	+	0.995760i	$0.470678\pi$
$234$	−1.15458	−0.0754775
$235$	12.2628	0.799938
$236$	22.4336	1.46030
$237$	−6.44646	−0.418743
$238$	−1.43358	−0.0929251
$239$	18.9776	1.22756	0.613778	−	0.789479i	$-0.289649\pi$
$239$	18.9776	1.22756	0.613778	+	0.789479i	$0.289649\pi$
$240$	5.44918	0.351743
$241$	−11.3574	−0.731594	−0.365797	−	0.930695i	$-0.619204\pi$
$241$	−11.3574	−0.731594	−0.365797	+	0.930695i	$0.619204\pi$
$242$	−4.28731	−0.275599
$243$	−1.00000	−0.0641500
$244$	−11.6125	−0.743416
$245$	−1.48259	−0.0947189
$246$	1.98433	0.126516
$247$	−28.8138	−1.83338
$248$	−3.02571	−0.192133
$249$	0.577379	0.0365899
$250$	−2.70251	−0.170922
$251$	−13.2019	−0.833298	−0.416649	−	0.909068i	$-0.636796\pi$
$251$	−13.2019	−0.833298	−0.416649	+	0.909068i	$0.636796\pi$
$252$	−1.94541	−0.122549
$253$	38.4245	2.41573
$254$	0.322943	0.0202632
$255$	9.09695	0.569673
$256$	11.8095	0.738096
$257$	8.71050	0.543346	0.271673	−	0.962390i	$-0.412423\pi$
$257$	8.71050	0.543346	0.271673	+	0.962390i	$0.412423\pi$
$258$	−0.0631786	−0.00393333
$259$	8.66303	0.538294
$260$	14.2532	0.883944
$261$	9.88106	0.611622
$262$	3.47230	0.214519
$263$	−17.5957	−1.08500	−0.542499	−	0.840056i	$-0.682522\pi$
$263$	−17.5957	−1.08500	−0.542499	+	0.840056i	$0.682522\pi$
$264$	−4.99394	−0.307356
$265$	−15.3949	−0.945702
$266$	1.36228	0.0835269
$267$	18.1493	1.11072
$268$	4.89092	0.298761
$269$	13.0821	0.797632	0.398816	−	0.917031i	$-0.369421\pi$
$269$	13.0821	0.797632	0.398816	+	0.917031i	$0.369421\pi$
$270$	−0.346390	−0.0210806
$271$	−13.4587	−0.817557	−0.408778	−	0.912634i	$-0.634045\pi$
$271$	−13.4587	−0.817557	−0.408778	+	0.912634i	$0.634045\pi$
$272$	22.5521	1.36742
$273$	−4.94174	−0.299088
$274$	4.57305	0.276268
$275$	−15.1797	−0.915372
$276$	13.7980	0.830539
$277$	−31.8391	−1.91302	−0.956512	−	0.291693i	$-0.905781\pi$
$277$	−31.8391	−1.91302	−0.956512	+	0.291693i	$0.905781\pi$
$278$	−3.38023	−0.202733
$279$	−3.28238	−0.196511
$280$	−1.36665	−0.0816731
$281$	17.1961	1.02583	0.512915	−	0.858439i	$-0.328565\pi$
$281$	17.1961	1.02583	0.512915	+	0.858439i	$0.328565\pi$
$282$	−1.93248	−0.115078
$283$	1.73316	0.103026	0.0515129	−	0.998672i	$-0.483596\pi$
$283$	1.73316	0.103026	0.0515129	+	0.998672i	$0.483596\pi$
$284$	−5.28188	−0.313422
$285$	−8.64453	−0.512058
$286$	−6.25504	−0.369869
$287$	8.49315	0.501335
$288$	−2.70234	−0.159237
$289$	20.6489	1.21464
$290$	3.42270	0.200988
$291$	1.10284	0.0646494
$292$	7.73806	0.452836
$293$	−2.53029	−0.147821	−0.0739107	−	0.997265i	$-0.523548\pi$
$293$	−2.53029	−0.147821	−0.0739107	+	0.997265i	$0.523548\pi$
$294$	0.233639	0.0136261
$295$	17.0965	0.995396
$296$	7.98560	0.464154
$297$	−5.41758	−0.314360
$298$	−1.05879	−0.0613341
$299$	35.0496	2.02697
$300$	−5.45093	−0.314709
$301$	−0.270411	−0.0155862
$302$	−2.21402	−0.127403
$303$	−15.3358	−0.881019
$304$	−21.4305	−1.22912
$305$	−8.84984	−0.506740
$306$	−1.43358	−0.0819522
$307$	−18.5168	−1.05681	−0.528405	−	0.848992i	$-0.677210\pi$
$307$	−18.5168	−1.05681	−0.528405	+	0.848992i	$0.677210\pi$
$308$	−10.5394	−0.600539
$309$	5.04823	0.287184
$310$	−1.13698	−0.0645764
$311$	16.9454	0.960887	0.480444	−	0.877026i	$-0.340476\pi$
$311$	16.9454	0.960887	0.480444	+	0.877026i	$0.340476\pi$
$312$	−4.55531	−0.257894
$313$	−26.1822	−1.47990	−0.739952	−	0.672659i	$-0.765152\pi$
$313$	−26.1822	−1.47990	−0.739952	+	0.672659i	$0.765152\pi$
$314$	−5.50409	−0.310614
$315$	−1.48259	−0.0835342
$316$	−12.5410	−0.705488
$317$	−16.8307	−0.945307	−0.472653	−	0.881248i	$-0.656704\pi$
$317$	−16.8307	−0.945307	−0.472653	+	0.881248i	$0.656704\pi$
$318$	2.42607	0.136047
$319$	53.5314	2.99718
$320$	9.96230	0.556909
$321$	20.3055	1.13334
$322$	−1.65710	−0.0923465
$323$	−35.7764	−1.99065
$324$	−1.94541	−0.108078
$325$	−13.8465	−0.768063
$326$	−0.604285	−0.0334682
$327$	0.870389	0.0481326
$328$	7.82901	0.432284
$329$	−8.27124	−0.456008
$330$	−1.87659	−0.103303
$331$	8.93670	0.491205	0.245603	−	0.969371i	$-0.421014\pi$
$331$	8.93670	0.491205	0.245603	+	0.969371i	$0.421014\pi$
$332$	1.12324	0.0616458
$333$	8.66303	0.474731
$334$	1.21149	0.0662897
$335$	3.72734	0.203646
$336$	−3.67546	−0.200513
$337$	14.6359	0.797271	0.398635	−	0.917109i	$-0.369484\pi$
$337$	14.6359	0.797271	0.398635	+	0.917109i	$0.369484\pi$
$338$	−2.66834	−0.145139
$339$	11.6480	0.632632
$340$	17.6973	0.959772
$341$	−17.7825	−0.962979
$342$	1.36228	0.0736638
$343$	1.00000	0.0539949
$344$	−0.249266	−0.0134395
$345$	10.5153	0.566126
$346$	−4.23699	−0.227782
$347$	−2.56661	−0.137783	−0.0688915	−	0.997624i	$-0.521946\pi$
$347$	−2.56661	−0.137783	−0.0688915	+	0.997624i	$0.521946\pi$
$348$	19.2227	1.03045
$349$	15.2130	0.814334	0.407167	−	0.913354i	$-0.366517\pi$
$349$	15.2130	0.814334	0.407167	+	0.913354i	$0.366517\pi$
$350$	0.654643	0.0349921
$351$	−4.94174	−0.263771
$352$	−14.6401	−0.780321
$353$	−33.2349	−1.76891	−0.884457	−	0.466621i	$-0.845471\pi$
$353$	−33.2349	−1.76891	−0.884457	+	0.466621i	$0.845471\pi$
$354$	−2.69422	−0.143196
$355$	−4.02529	−0.213640
$356$	35.3078	1.87131
$357$	−6.13587	−0.324744
$358$	−0.119018	−0.00629031
$359$	−7.40339	−0.390736	−0.195368	−	0.980730i	$-0.562590\pi$
$359$	−7.40339	−0.390736	−0.195368	+	0.980730i	$0.562590\pi$
$360$	−1.36665	−0.0720289
$361$	14.9972	0.789325
$362$	1.59584	0.0838757
$363$	−18.3501	−0.963132
$364$	−9.61372	−0.503896
$365$	5.89712	0.308670
$366$	1.39464	0.0728988
$367$	−12.5955	−0.657478	−0.328739	−	0.944421i	$-0.606624\pi$
$367$	−12.5955	−0.657478	−0.328739	+	0.944421i	$0.606624\pi$
$368$	26.0684	1.35891
$369$	8.49315	0.442135
$370$	3.00079	0.156003
$371$	10.3838	0.539101
$372$	−6.38559	−0.331077
$373$	−29.6137	−1.53334	−0.766669	−	0.642042i	$-0.778087\pi$
$373$	−29.6137	−1.53334	−0.766669	+	0.642042i	$0.778087\pi$
$374$	−7.76652	−0.401597
$375$	−11.5670	−0.597320
$376$	−7.62445	−0.393201
$377$	48.8296	2.51485
$378$	0.233639	0.0120171
$379$	−1.29867	−0.0667083	−0.0333541	−	0.999444i	$-0.510619\pi$
$379$	−1.29867	−0.0667083	−0.0333541	+	0.999444i	$0.510619\pi$
$380$	−16.8172	−0.862703
$381$	1.38223	0.0708138
$382$	−2.75030	−0.140718
$383$	24.7287	1.26358	0.631788	−	0.775141i	$-0.282321\pi$
$383$	24.7287	1.26358	0.631788	+	0.775141i	$0.282321\pi$
$384$	−6.97462	−0.355922
$385$	−8.03202	−0.409350
$386$	−4.15172	−0.211317
$387$	−0.270411	−0.0137458
$388$	2.14547	0.108920
$389$	8.56030	0.434024	0.217012	−	0.976169i	$-0.430369\pi$
$389$	8.56030	0.434024	0.217012	+	0.976169i	$0.430369\pi$
$390$	−1.71177	−0.0866788
$391$	43.5190	2.20085
$392$	0.921803	0.0465581
$393$	14.8618	0.749679
$394$	−0.220569	−0.0111121
$395$	−9.55743	−0.480887
$396$	−10.5394	−0.529626
$397$	−35.5166	−1.78252	−0.891262	−	0.453488i	$-0.850180\pi$
$397$	−35.5166	−1.78252	−0.891262	+	0.453488i	$0.850180\pi$
$398$	−0.489886	−0.0245557
$399$	5.83071	0.291901
$400$	−10.2984	−0.514920
$401$	3.56813	0.178184	0.0890920	−	0.996023i	$-0.471603\pi$
$401$	3.56813	0.178184	0.0890920	+	0.996023i	$0.471603\pi$
$402$	−0.587387	−0.0292962
$403$	−16.2207	−0.808009
$404$	−29.8345	−1.48432
$405$	−1.48259	−0.0736703
$406$	−2.30860	−0.114574
$407$	46.9326	2.32636
$408$	−5.65606	−0.280017
$409$	−0.474218	−0.0234486	−0.0117243	−	0.999931i	$-0.503732\pi$
$409$	−0.474218	−0.0234486	−0.0117243	+	0.999931i	$0.503732\pi$
$410$	2.94194	0.145292
$411$	19.5731	0.965471
$412$	9.82090	0.483841
$413$	−11.5315	−0.567430
$414$	−1.65710	−0.0814420
$415$	0.856014	0.0420201
$416$	−13.3542	−0.654745
$417$	−14.4677	−0.708488
$418$	7.38026	0.360981
$419$	−24.1420	−1.17941	−0.589706	−	0.807618i	$-0.700756\pi$
$419$	−24.1420	−1.17941	−0.589706	+	0.807618i	$0.700756\pi$
$420$	−2.88424	−0.140737
$421$	−28.2265	−1.37568	−0.687838	−	0.725864i	$-0.741440\pi$
$421$	−28.2265	−1.37568	−0.687838	+	0.725864i	$0.741440\pi$
$422$	0.663741	0.0323104
$423$	−8.27124	−0.402161
$424$	9.57183	0.464849
$425$	−17.1923	−0.833950
$426$	0.634340	0.0307339
$427$	5.96919	0.288869
$428$	39.5026	1.90943
$429$	−26.7722	−1.29258
$430$	−0.0936676	−0.00451705
$431$	−16.3896	−0.789457	−0.394729	−	0.918798i	$-0.629161\pi$
$431$	−16.3896	−0.789457	−0.394729	+	0.918798i	$0.629161\pi$
$432$	−3.67546	−0.176835
$433$	17.9432	0.862295	0.431147	−	0.902282i	$-0.358109\pi$
$433$	17.9432	0.862295	0.431147	+	0.902282i	$0.358109\pi$
$434$	0.766893	0.0368120
$435$	14.6495	0.702391
$436$	1.69327	0.0810927
$437$	−41.3546	−1.97826
$438$	−0.929322	−0.0444047
$439$	−13.7276	−0.655183	−0.327592	−	0.944819i	$-0.606237\pi$
$439$	−13.7276	−0.655183	−0.327592	+	0.944819i	$0.606237\pi$
$440$	−7.40394	−0.352969
$441$	1.00000	0.0476190
$442$	−7.08437	−0.336969
$443$	−25.6379	−1.21809	−0.609047	−	0.793134i	$-0.708448\pi$
$443$	−25.6379	−1.21809	−0.609047	+	0.793134i	$0.708448\pi$
$444$	16.8532	0.799816
$445$	26.9078	1.27555
$446$	−4.13946	−0.196009
$447$	−4.53174	−0.214344
$448$	−6.71954	−0.317468
$449$	4.52604	0.213597	0.106798	−	0.994281i	$-0.465940\pi$
$449$	4.52604	0.213597	0.106798	+	0.994281i	$0.465940\pi$
$450$	0.654643	0.0308601
$451$	46.0123	2.16663
$452$	22.6601	1.06584
$453$	−9.47624	−0.445232
$454$	0.233639	0.0109652
$455$	−7.32655	−0.343474
$456$	5.37476	0.251696
$457$	−0.544430	−0.0254673	−0.0127337	−	0.999919i	$-0.504053\pi$
$457$	−0.544430	−0.0254673	−0.0127337	+	0.999919i	$0.504053\pi$
$458$	−1.55501	−0.0726610
$459$	−6.13587	−0.286398
$460$	20.4566	0.953796
$461$	−27.2223	−1.26787	−0.633933	−	0.773388i	$-0.718561\pi$
$461$	−27.2223	−1.26787	−0.633933	+	0.773388i	$0.718561\pi$
$462$	1.26576	0.0588884
$463$	13.8501	0.643671	0.321835	−	0.946796i	$-0.395700\pi$
$463$	13.8501	0.643671	0.321835	+	0.946796i	$0.395700\pi$
$464$	36.3174	1.68599
$465$	−4.86641	−0.225674
$466$	−0.656122	−0.0303943
$467$	22.7412	1.05234	0.526168	−	0.850380i	$-0.323628\pi$
$467$	22.7412	1.05234	0.526168	+	0.850380i	$0.323628\pi$
$468$	−9.61372	−0.444394
$469$	−2.51408	−0.116089
$470$	−2.86507	−0.132156
$471$	−23.5581	−1.08550
$472$	−10.6298	−0.489276
$473$	−1.46497	−0.0673595
$474$	1.50615	0.0691795
$475$	16.3373	0.749606
$476$	−11.9368	−0.547122
$477$	10.3838	0.475442
$478$	−4.43390	−0.202802
$479$	18.2841	0.835424	0.417712	−	0.908579i	$-0.362832\pi$
$479$	18.2841	0.835424	0.417712	+	0.908579i	$0.362832\pi$
$480$	−4.00644	−0.182868
$481$	42.8104	1.95199
$482$	2.65353	0.120865
$483$	−7.09256	−0.322723
$484$	−35.6986	−1.62266
$485$	1.63505	0.0742438
$486$	0.233639	0.0105981
$487$	−2.61586	−0.118536	−0.0592680	−	0.998242i	$-0.518877\pi$
$487$	−2.61586	−0.118536	−0.0592680	+	0.998242i	$0.518877\pi$
$488$	5.50242	0.249083
$489$	−2.58640	−0.116961
$490$	0.346390	0.0156483
$491$	−30.3215	−1.36839	−0.684196	−	0.729299i	$-0.739847\pi$
$491$	−30.3215	−1.36839	−0.684196	+	0.729299i	$0.739847\pi$
$492$	16.5227	0.744900
$493$	60.6289	2.73059
$494$	6.73204	0.302889
$495$	−8.03202	−0.361013
$496$	−12.0642	−0.541701
$497$	2.71504	0.121786
$498$	−0.134898	−0.00604494
$499$	−24.2202	−1.08425	−0.542123	−	0.840299i	$-0.682379\pi$
$499$	−24.2202	−1.08425	−0.542123	+	0.840299i	$0.682379\pi$
$500$	−22.5027	−1.00635
$501$	5.18530	0.231662
$502$	3.08448	0.137667
$503$	13.6459	0.608439	0.304220	−	0.952602i	$-0.401604\pi$
$503$	13.6459	0.608439	0.304220	+	0.952602i	$0.401604\pi$
$504$	0.921803	0.0410604
$505$	−22.7366	−1.01177
$506$	−8.97746	−0.399097
$507$	−11.4208	−0.507215
$508$	2.68901	0.119305
$509$	−35.6435	−1.57987	−0.789935	−	0.613191i	$-0.789886\pi$
$509$	−35.6435	−1.57987	−0.789935	+	0.613191i	$0.789886\pi$
$510$	−2.12540	−0.0941144
$511$	−3.97759	−0.175958
$512$	−16.7084	−0.738414
$513$	5.83071	0.257432
$514$	−2.03511	−0.0897650
$515$	7.48444	0.329804
$516$	−0.526061	−0.0231585
$517$	−44.8101	−1.97074
$518$	−2.02402	−0.0889304
$519$	−18.1348	−0.796027
$520$	−6.75364	−0.296167
$521$	−5.66809	−0.248324	−0.124162	−	0.992262i	$-0.539624\pi$
$521$	−5.66809	−0.248324	−0.124162	+	0.992262i	$0.539624\pi$
$522$	−2.30860	−0.101045
$523$	16.3376	0.714393	0.357197	−	0.934029i	$-0.383733\pi$
$523$	16.3376	0.714393	0.357197	+	0.934029i	$0.383733\pi$
$524$	28.9124	1.26304
$525$	2.80194	0.122287
$526$	4.11105	0.179250
$527$	−20.1403	−0.877323
$528$	−19.9121	−0.866561
$529$	27.3044	1.18715
$530$	3.59685	0.156237
$531$	−11.5315	−0.500426
$532$	11.3431	0.491787
$533$	41.9709	1.81796
$534$	−4.24038	−0.183499
$535$	30.1047	1.30154
$536$	−2.31749	−0.100100
$537$	−0.509410	−0.0219827
$538$	−3.05650	−0.131775
$539$	5.41758	0.233352
$540$	−2.88424	−0.124118
$541$	5.22963	0.224839	0.112420	−	0.993661i	$-0.464140\pi$
$541$	5.22963	0.224839	0.112420	+	0.993661i	$0.464140\pi$
$542$	3.14448	0.135067
$543$	6.83038	0.293120
$544$	−16.5812	−0.710912
$545$	1.29043	0.0552758
$546$	1.15458	0.0494116
$547$	45.2012	1.93267	0.966333	−	0.257296i	$-0.0828315\pi$
$547$	45.2012	1.93267	0.966333	+	0.257296i	$0.0828315\pi$
$548$	38.0778	1.62660
$549$	5.96919	0.254759
$550$	3.54658	0.151227
$551$	−57.6136	−2.45442
$552$	−6.53794	−0.278273
$553$	6.44646	0.274131
$554$	7.43885	0.316046
$555$	12.8437	0.545184
$556$	−28.1457	−1.19364
$557$	−32.8668	−1.39261	−0.696305	−	0.717746i	$-0.745174\pi$
$557$	−32.8668	−1.39261	−0.696305	+	0.717746i	$0.745174\pi$
$558$	0.766893	0.0324652
$559$	−1.33630	−0.0565195
$560$	−5.44918	−0.230270
$561$	−33.2415	−1.40346
$562$	−4.01767	−0.169475
$563$	−20.3547	−0.857848	−0.428924	−	0.903340i	$-0.641107\pi$
$563$	−20.3547	−0.857848	−0.428924	+	0.903340i	$0.641107\pi$
$564$	−16.0910	−0.677552
$565$	17.2691	0.726518
$566$	−0.404934	−0.0170207
$567$	1.00000	0.0419961
$568$	2.50273	0.105012
$569$	−22.9719	−0.963032	−0.481516	−	0.876437i	$-0.659914\pi$
$569$	−22.9719	−0.963032	−0.481516	+	0.876437i	$0.659914\pi$
$570$	2.01970	0.0845959
$571$	38.4872	1.61064	0.805319	−	0.592842i	$-0.201994\pi$
$571$	38.4872	1.61064	0.805319	+	0.592842i	$0.201994\pi$
$572$	−52.0831	−2.17770
$573$	−11.7716	−0.491765
$574$	−1.98433	−0.0828244
$575$	−19.8729	−0.828758
$576$	−6.71954	−0.279981
$577$	−21.3650	−0.889437	−0.444718	−	0.895670i	$-0.646696\pi$
$577$	−21.3650	−0.889437	−0.444718	+	0.895670i	$0.646696\pi$
$578$	−4.82438	−0.200668
$579$	−17.7698	−0.738488
$580$	28.4994	1.18337
$581$	−0.577379	−0.0239537
$582$	−0.257666	−0.0106806
$583$	56.2551	2.32985
$584$	−3.66656	−0.151723
$585$	−7.32655	−0.302916
$586$	0.591176	0.0244213
$587$	40.5307	1.67288	0.836441	−	0.548057i	$-0.184632\pi$
$587$	40.5307	1.67288	0.836441	+	0.548057i	$0.184632\pi$
$588$	1.94541	0.0802275
$589$	19.1386	0.788593
$590$	−3.99441	−0.164447
$591$	−0.944056	−0.0388333
$592$	31.8406	1.30864
$593$	−29.1570	−1.19734	−0.598668	−	0.800998i	$-0.704303\pi$
$593$	−29.1570	−1.19734	−0.598668	+	0.800998i	$0.704303\pi$
$594$	1.26576	0.0519347
$595$	−9.09695	−0.372939
$596$	−8.81610	−0.361121
$597$	−2.09676	−0.0858147
$598$	−8.18895	−0.334871
$599$	23.4903	0.959786	0.479893	−	0.877327i	$-0.340676\pi$
$599$	23.4903	0.959786	0.479893	+	0.877327i	$0.340676\pi$
$600$	2.58284	0.105444
$601$	−15.9930	−0.652370	−0.326185	−	0.945306i	$-0.605763\pi$
$601$	−15.9930	−0.652370	−0.326185	+	0.945306i	$0.605763\pi$
$602$	0.0631786	0.00257497
$603$	−2.51408	−0.102381
$604$	−18.4352	−0.750117
$605$	−27.2056	−1.10607
$606$	3.58304	0.145551
$607$	28.6987	1.16484	0.582422	−	0.812887i	$-0.302105\pi$
$607$	28.6987	1.16484	0.582422	+	0.812887i	$0.302105\pi$
$608$	15.7565	0.639012
$609$	−9.88106	−0.400401
$610$	2.06767	0.0837174
$611$	−40.8743	−1.65360
$612$	−11.9368	−0.482516
$613$	31.2425	1.26187	0.630936	−	0.775835i	$-0.282671\pi$
$613$	31.2425	1.26187	0.630936	+	0.775835i	$0.282671\pi$
$614$	4.32625	0.174593
$615$	12.5918	0.507751
$616$	4.99394	0.201211
$617$	15.4258	0.621018	0.310509	−	0.950570i	$-0.399500\pi$
$617$	15.4258	0.621018	0.310509	+	0.950570i	$0.399500\pi$
$618$	−1.17946	−0.0474450
$619$	−18.6507	−0.749635	−0.374818	−	0.927099i	$-0.622295\pi$
$619$	−18.6507	−0.749635	−0.374818	+	0.927099i	$0.622295\pi$
$620$	−9.46718	−0.380211
$621$	−7.09256	−0.284615
$622$	−3.95911	−0.158746
$623$	−18.1493	−0.727135
$624$	−18.1631	−0.727108
$625$	−3.13944	−0.125578
$626$	6.11718	0.244492
$627$	31.5883	1.26152
$628$	−45.8302	−1.82883
$629$	53.1552	2.11944
$630$	0.346390	0.0138005
$631$	6.62472	0.263726	0.131863	−	0.991268i	$-0.457904\pi$
$631$	6.62472	0.263726	0.131863	+	0.991268i	$0.457904\pi$
$632$	5.94236	0.236375
$633$	2.84088	0.112915
$634$	3.93231	0.156172
$635$	2.04927	0.0813230
$636$	20.2008	0.801015
$637$	4.94174	0.195799
$638$	−12.5070	−0.495158
$639$	2.71504	0.107405
$640$	−10.3405	−0.408743
$641$	10.3172	0.407503	0.203751	−	0.979023i	$-0.434687\pi$
$641$	10.3172	0.407503	0.203751	+	0.979023i	$0.434687\pi$
$642$	−4.74416	−0.187237
$643$	17.2798	0.681450	0.340725	−	0.940163i	$-0.389327\pi$
$643$	17.2798	0.681450	0.340725	+	0.940163i	$0.389327\pi$
$644$	−13.7980	−0.543716
$645$	−0.400907	−0.0157857
$646$	8.35878	0.328872
$647$	0.730968	0.0287373	0.0143687	−	0.999897i	$-0.495426\pi$
$647$	0.730968	0.0287373	0.0143687	+	0.999897i	$0.495426\pi$
$648$	0.921803	0.0362118
$649$	−62.4730	−2.45228
$650$	3.23507	0.126890
$651$	3.28238	0.128647
$652$	−5.03162	−0.197053
$653$	2.81325	0.110091	0.0550454	−	0.998484i	$-0.482470\pi$
$653$	2.81325	0.110091	0.0550454	+	0.998484i	$0.482470\pi$
$654$	−0.203357	−0.00795188
$655$	22.0339	0.860936
$656$	31.2162	1.21879
$657$	−3.97759	−0.155181
$658$	1.93248	0.0753361
$659$	−4.62113	−0.180014	−0.0900069	−	0.995941i	$-0.528689\pi$
$659$	−4.62113	−0.180014	−0.0900069	+	0.995941i	$0.528689\pi$
$660$	−15.6256	−0.608226
$661$	−16.8602	−0.655785	−0.327893	−	0.944715i	$-0.606338\pi$
$661$	−16.8602	−0.655785	−0.327893	+	0.944715i	$0.606338\pi$
$662$	−2.08796	−0.0811510
$663$	−30.3218	−1.17760
$664$	−0.532229	−0.0206545
$665$	8.64453	0.335220
$666$	−2.02402	−0.0784293
$667$	70.0820	2.71359
$668$	10.0875	0.390299
$669$	−17.7173	−0.684991
$670$	−0.870852	−0.0336439
$671$	32.3385	1.24842
$672$	2.70234	0.104245
$673$	47.3561	1.82545	0.912723	−	0.408580i	$-0.133976\pi$
$673$	47.3561	1.82545	0.912723	+	0.408580i	$0.133976\pi$
$674$	−3.41953	−0.131715
$675$	2.80194	0.107847
$676$	−22.2181	−0.854544
$677$	4.74931	0.182531	0.0912654	−	0.995827i	$-0.470909\pi$
$677$	4.74931	0.182531	0.0912654	+	0.995827i	$0.470909\pi$
$678$	−2.72143	−0.104516
$679$	−1.10284	−0.0423230
$680$	−8.38559	−0.321573
$681$	1.00000	0.0383201
$682$	4.15470	0.159092
$683$	−48.0158	−1.83727	−0.918637	−	0.395102i	$-0.870709\pi$
$683$	−48.0158	−1.83727	−0.918637	+	0.395102i	$0.870709\pi$
$684$	11.3431	0.433716
$685$	29.0188	1.10875
$686$	−0.233639	−0.00892038
$687$	−6.65562	−0.253928
$688$	−0.993883	−0.0378915
$689$	51.3141	1.95491
$690$	−2.45679	−0.0935285
$691$	−9.24469	−0.351685	−0.175842	−	0.984418i	$-0.556265\pi$
$691$	−9.24469	−0.351685	−0.175842	+	0.984418i	$0.556265\pi$
$692$	−35.2796	−1.34113
$693$	5.41758	0.205797
$694$	0.599661	0.0227628
$695$	−21.4497	−0.813632
$696$	−9.10839	−0.345253
$697$	52.1128	1.97391
$698$	−3.55436	−0.134534
$699$	−2.80827	−0.106219
$700$	5.45093	0.206026
$701$	29.6555	1.12007	0.560035	−	0.828469i	$-0.310787\pi$
$701$	29.6555	1.12007	0.560035	+	0.828469i	$0.310787\pi$
$702$	1.15458	0.0435769
$703$	−50.5116	−1.90508
$704$	−36.4036	−1.37201
$705$	−12.2628	−0.461845
$706$	7.76497	0.292239
$707$	15.3358	0.576762
$708$	−22.4336	−0.843106
$709$	−47.9719	−1.80162	−0.900812	−	0.434210i	$-0.857027\pi$
$709$	−47.9719	−1.80162	−0.900812	+	0.434210i	$0.857027\pi$
$710$	0.940464	0.0352950
$711$	6.44646	0.241761
$712$	−16.7300	−0.626985
$713$	−23.2805	−0.871861
$714$	1.43358	0.0536503
$715$	−39.6922	−1.48440
$716$	−0.991014	−0.0370359
$717$	−18.9776	−0.708730
$718$	1.72972	0.0645527
$719$	−12.8217	−0.478170	−0.239085	−	0.970999i	$-0.576847\pi$
$719$	−12.8217	−0.478170	−0.239085	+	0.970999i	$0.576847\pi$
$720$	−5.44918	−0.203079
$721$	−5.04823	−0.188006
$722$	−3.50392	−0.130403
$723$	11.3574	0.422386
$724$	13.2879	0.493841
$725$	−27.6861	−1.02824
$726$	4.28731	0.159117
$727$	−26.0404	−0.965786	−0.482893	−	0.875679i	$-0.660414\pi$
$727$	−26.0404	−0.965786	−0.482893	+	0.875679i	$0.660414\pi$
$728$	4.55531	0.168831
$729$	1.00000	0.0370370
$730$	−1.37780	−0.0509946
$731$	−1.65921	−0.0613679
$732$	11.6125	0.429212
$733$	4.59002	0.169536	0.0847681	−	0.996401i	$-0.472985\pi$
$733$	4.59002	0.169536	0.0847681	+	0.996401i	$0.472985\pi$
$734$	2.94280	0.108621
$735$	1.48259	0.0546860
$736$	−19.1665	−0.706486
$737$	−13.6202	−0.501707
$738$	−1.98433	−0.0730442
$739$	−35.9474	−1.32235	−0.661174	−	0.750233i	$-0.729941\pi$
$739$	−35.9474	−1.32235	−0.661174	+	0.750233i	$0.729941\pi$
$740$	24.9863	0.918513
$741$	28.8138	1.05850
$742$	−2.42607	−0.0890637
$743$	−4.05673	−0.148827	−0.0744135	−	0.997227i	$-0.523708\pi$
$743$	−4.05673	−0.148827	−0.0744135	+	0.997227i	$0.523708\pi$
$744$	3.02571	0.110928
$745$	−6.71869	−0.246154
$746$	6.91892	0.253320
$747$	−0.577379	−0.0211252
$748$	−64.6685	−2.36451
$749$	−20.3055	−0.741947
$750$	2.70251	0.0986819
$751$	−18.6982	−0.682308	−0.341154	−	0.940007i	$-0.610818\pi$
$751$	−18.6982	−0.682308	−0.341154	+	0.940007i	$0.610818\pi$
$752$	−30.4006	−1.10859
$753$	13.2019	0.481105
$754$	−11.4085	−0.415473
$755$	−14.0493	−0.511308
$756$	1.94541	0.0707540
$757$	17.1096	0.621860	0.310930	−	0.950433i	$-0.399360\pi$
$757$	17.1096	0.621860	0.310930	+	0.950433i	$0.399360\pi$
$758$	0.303421	0.0110207
$759$	−38.4245	−1.39472
$760$	7.96855	0.289050
$761$	−7.90260	−0.286469	−0.143235	−	0.989689i	$-0.545750\pi$
$761$	−7.90260	−0.286469	−0.143235	+	0.989689i	$0.545750\pi$
$762$	−0.322943	−0.0116990
$763$	−0.870389	−0.0315102
$764$	−22.9006	−0.828514
$765$	−9.09695	−0.328901
$766$	−5.77759	−0.208753
$767$	−56.9858	−2.05764
$768$	−11.8095	−0.426140
$769$	−35.7692	−1.28987	−0.644935	−	0.764238i	$-0.723116\pi$
$769$	−35.7692	−1.28987	−0.644935	+	0.764238i	$0.723116\pi$
$770$	1.87659	0.0676278
$771$	−8.71050	−0.313701
$772$	−34.5696	−1.24419
$773$	47.7411	1.71713	0.858564	−	0.512706i	$-0.171357\pi$
$773$	47.7411	1.71713	0.858564	+	0.512706i	$0.171357\pi$
$774$	0.0631786	0.00227091
$775$	9.19703	0.330367
$776$	−1.01660	−0.0364937
$777$	−8.66303	−0.310784
$778$	−2.00002	−0.0717042
$779$	−49.5211	−1.77428
$780$	−14.2532	−0.510345
$781$	14.7090	0.526328
$782$	−10.1677	−0.363598
$783$	−9.88106	−0.353120
$784$	3.67546	0.131266
$785$	−34.9269	−1.24659
$786$	−3.47230	−0.123853
$787$	−1.76127	−0.0627826	−0.0313913	−	0.999507i	$-0.509994\pi$
$787$	−1.76127	−0.0627826	−0.0313913	+	0.999507i	$0.509994\pi$
$788$	−1.83658	−0.0654254
$789$	17.5957	0.626424
$790$	2.23299	0.0794462
$791$	−11.6480	−0.414155
$792$	4.99394	0.177452
$793$	29.4982	1.04751
$794$	8.29806	0.294487
$795$	15.3949	0.546001
$796$	−4.07907	−0.144579
$797$	45.9642	1.62813	0.814067	−	0.580771i	$-0.197249\pi$
$797$	45.9642	1.62813	0.814067	+	0.580771i	$0.197249\pi$
$798$	−1.36228	−0.0482242
$799$	−50.7512	−1.79545
$800$	7.57178	0.267703
$801$	−18.1493	−0.641273
$802$	−0.833655	−0.0294374
$803$	−21.5489	−0.760445
$804$	−4.89092	−0.172490
$805$	−10.5153	−0.370617
$806$	3.78978	0.133489
$807$	−13.0821	−0.460513
$808$	14.1366	0.497323
$809$	47.8622	1.68275	0.841373	−	0.540455i	$-0.181748\pi$
$809$	47.8622	1.68275	0.841373	+	0.540455i	$0.181748\pi$
$810$	0.346390	0.0121709
$811$	5.24320	0.184114	0.0920568	−	0.995754i	$-0.470656\pi$
$811$	5.24320	0.184114	0.0920568	+	0.995754i	$0.470656\pi$
$812$	−19.2227	−0.674586
$813$	13.4587	0.472017
$814$	−10.9653	−0.384333
$815$	−3.83456	−0.134319
$816$	−22.5521	−0.789482
$817$	1.57669	0.0551613
$818$	0.110796	0.00387389
$819$	4.94174	0.172678
$820$	24.4963	0.855447
$821$	33.0933	1.15496	0.577482	−	0.816403i	$-0.304035\pi$
$821$	33.0933	1.15496	0.577482	+	0.816403i	$0.304035\pi$
$822$	−4.57305	−0.159503
$823$	52.1987	1.81953	0.909765	−	0.415123i	$-0.136261\pi$
$823$	52.1987	1.81953	0.909765	+	0.415123i	$0.136261\pi$
$824$	−4.65347	−0.162111
$825$	15.1797	0.528490
$826$	2.69422	0.0937438
$827$	−15.6985	−0.545890	−0.272945	−	0.962030i	$-0.587998\pi$
$827$	−15.6985	−0.545890	−0.272945	+	0.962030i	$0.587998\pi$
$828$	−13.7980	−0.479512
$829$	−6.29080	−0.218489	−0.109244	−	0.994015i	$-0.534843\pi$
$829$	−6.29080	−0.218489	−0.109244	+	0.994015i	$0.534843\pi$
$830$	−0.199998	−0.00694204
$831$	31.8391	1.10448
$832$	−33.2062	−1.15122
$833$	6.13587	0.212595
$834$	3.38023	0.117048
$835$	7.68765	0.266042
$836$	61.4523	2.12537
$837$	3.28238	0.113456
$838$	5.64051	0.194848
$839$	36.5833	1.26300	0.631498	−	0.775378i	$-0.282441\pi$
$839$	36.5833	1.26300	0.631498	+	0.775378i	$0.282441\pi$
$840$	1.36665	0.0471540
$841$	68.6353	2.36674
$842$	6.59482	0.227272
$843$	−17.1961	−0.592264
$844$	5.52669	0.190236
$845$	−16.9323	−0.582488
$846$	1.93248	0.0664402
$847$	18.3501	0.630518
$848$	38.1653	1.31060
$849$	−1.73316	−0.0594819
$850$	4.01680	0.137775
$851$	61.4430	2.10624
$852$	5.28188	0.180954
$853$	27.0046	0.924619	0.462310	−	0.886719i	$-0.347021\pi$
$853$	27.0046	0.924619	0.462310	+	0.886719i	$0.347021\pi$
$854$	−1.39464	−0.0477235
$855$	8.64453	0.295637
$856$	−18.7177	−0.639757
$857$	9.69796	0.331276	0.165638	−	0.986187i	$-0.447032\pi$
$857$	9.69796	0.331276	0.165638	+	0.986187i	$0.447032\pi$
$858$	6.25504	0.213544
$859$	28.4438	0.970489	0.485244	−	0.874379i	$-0.338731\pi$
$859$	28.4438	0.970489	0.485244	+	0.874379i	$0.338731\pi$
$860$	−0.779930	−0.0265954
$861$	−8.49315	−0.289446
$862$	3.82924	0.130424
$863$	−4.94345	−0.168277	−0.0841385	−	0.996454i	$-0.526814\pi$
$863$	−4.94345	−0.168277	−0.0841385	+	0.996454i	$0.526814\pi$
$864$	2.70234	0.0919353
$865$	−26.8863	−0.914163
$866$	−4.19223	−0.142458
$867$	−20.6489	−0.701272
$868$	6.38559	0.216741
$869$	34.9242	1.18472
$870$	−3.42270	−0.116040
$871$	−12.4239	−0.420969
$872$	−0.802327	−0.0271702
$873$	−1.10284	−0.0373254
$874$	9.66206	0.326824
$875$	11.5670	0.391037
$876$	−7.73806	−0.261445
$877$	−46.4898	−1.56985	−0.784924	−	0.619592i	$-0.787298\pi$
$877$	−46.4898	−1.56985	−0.784924	+	0.619592i	$0.787298\pi$
$878$	3.20731	0.108241
$879$	2.53029	0.0853447
$880$	−29.5213	−0.995164
$881$	52.3911	1.76510	0.882550	−	0.470218i	$-0.155825\pi$
$881$	52.3911	1.76510	0.882550	+	0.470218i	$0.155825\pi$
$882$	−0.233639	−0.00786704
$883$	15.3437	0.516356	0.258178	−	0.966097i	$-0.416878\pi$
$883$	15.3437	0.516356	0.258178	+	0.966097i	$0.416878\pi$
$884$	−58.9885	−1.98400
$885$	−17.0965	−0.574692
$886$	5.99002	0.201239
$887$	−23.2348	−0.780148	−0.390074	−	0.920784i	$-0.627551\pi$
$887$	−23.2348	−0.780148	−0.390074	+	0.920784i	$0.627551\pi$
$888$	−7.98560	−0.267979
$889$	−1.38223	−0.0463585
$890$	−6.28672	−0.210731
$891$	5.41758	0.181496
$892$	−34.4675	−1.15406
$893$	48.2272	1.61386
$894$	1.05879	0.0354113
$895$	−0.755245	−0.0252450
$896$	6.97462	0.233006
$897$	−35.0496	−1.17027
$898$	−1.05746	−0.0352879
$899$	−32.4334	−1.08171
$900$	5.45093	0.181698
$901$	63.7137	2.12261
$902$	−10.7503	−0.357945
$903$	0.270411	0.00899871
$904$	−10.7371	−0.357112
$905$	10.1266	0.336620
$906$	2.21402	0.0735559
$907$	25.8865	0.859548	0.429774	−	0.902937i	$-0.358593\pi$
$907$	25.8865	0.859548	0.429774	+	0.902937i	$0.358593\pi$
$908$	1.94541	0.0645608
$909$	15.3358	0.508656
$910$	1.71177	0.0567446
$911$	−28.3766	−0.940158	−0.470079	−	0.882624i	$-0.655775\pi$
$911$	−28.3766	−0.940158	−0.470079	+	0.882624i	$0.655775\pi$
$912$	21.4305	0.709635
$913$	−3.12799	−0.103521
$914$	0.127200	0.00420740
$915$	8.84984	0.292567
$916$	−12.9479	−0.427812
$917$	−14.8618	−0.490780
$918$	1.43358	0.0473151
$919$	50.2900	1.65891	0.829456	−	0.558572i	$-0.188650\pi$
$919$	50.2900	1.65891	0.829456	+	0.558572i	$0.188650\pi$
$920$	−9.69306	−0.319571
$921$	18.5168	0.610150
$922$	6.36018	0.209461
$923$	13.4170	0.441627
$924$	10.5394	0.346722
$925$	−24.2733	−0.798100
$926$	−3.23593	−0.106339
$927$	−5.04823	−0.165806
$928$	−26.7019	−0.876534
$929$	−25.3164	−0.830603	−0.415302	−	0.909684i	$-0.636324\pi$
$929$	−25.3164	−0.830603	−0.415302	+	0.909684i	$0.636324\pi$
$930$	1.13698	0.0372832
$931$	−5.83071	−0.191094
$932$	−5.46325	−0.178955
$933$	−16.9454	−0.554768
$934$	−5.31323	−0.173854
$935$	−49.2834	−1.61174
$936$	4.55531	0.148895
$937$	45.4720	1.48551	0.742753	−	0.669565i	$-0.233520\pi$
$937$	45.4720	1.48551	0.742753	+	0.669565i	$0.233520\pi$
$938$	0.587387	0.0191789
$939$	26.1822	0.854424
$940$	−23.8562	−0.778105
$941$	34.9106	1.13805	0.569027	−	0.822319i	$-0.307320\pi$
$941$	34.9106	1.13805	0.569027	+	0.822319i	$0.307320\pi$
$942$	5.50409	0.179333
$943$	60.2381	1.96162
$944$	−42.3837	−1.37947
$945$	1.48259	0.0482285
$946$	0.342275	0.0111283
$947$	−2.68901	−0.0873809	−0.0436905	−	0.999045i	$-0.513912\pi$
$947$	−2.68901	−0.0873809	−0.0436905	+	0.999045i	$0.513912\pi$
$948$	12.5410	0.407314
$949$	−19.6562	−0.638068
$950$	−3.81703	−0.123841
$951$	16.8307	0.545773
$952$	5.65606	0.183314
$953$	−27.7630	−0.899333	−0.449666	−	0.893197i	$-0.648457\pi$
$953$	−27.7630	−0.899333	−0.449666	+	0.893197i	$0.648457\pi$
$954$	−2.42607	−0.0785468
$955$	−17.4524	−0.564746
$956$	−36.9192	−1.19405
$957$	−53.5314	−1.73042
$958$	−4.27189	−0.138019
$959$	−19.5731	−0.632049
$960$	−9.96230	−0.321532
$961$	−20.2260	−0.652451
$962$	−10.0022	−0.322483
$963$	−20.3055	−0.654336
$964$	22.0948	0.711626
$965$	−26.3453	−0.848084
$966$	1.65710	0.0533163
$967$	37.3245	1.20027	0.600137	−	0.799897i	$-0.295113\pi$
$967$	37.3245	1.20027	0.600137	+	0.799897i	$0.295113\pi$
$968$	16.9152	0.543675
$969$	35.7764	1.14931
$970$	−0.382012	−0.0122657
$971$	41.6220	1.33571	0.667857	−	0.744289i	$-0.267212\pi$
$971$	41.6220	1.33571	0.667857	+	0.744289i	$0.267212\pi$
$972$	1.94541	0.0623991
$973$	14.4677	0.463815
$974$	0.611167	0.0195831
$975$	13.8465	0.443441
$976$	21.9395	0.702266
$977$	12.6534	0.404819	0.202409	−	0.979301i	$-0.435123\pi$
$977$	12.6534	0.404819	0.202409	+	0.979301i	$0.435123\pi$
$978$	0.604285	0.0193229
$979$	−98.3250	−3.14248
$980$	2.88424	0.0921337
$981$	−0.870389	−0.0277894
$982$	7.08429	0.226069
$983$	−51.6448	−1.64721	−0.823606	−	0.567162i	$-0.808041\pi$
$983$	−51.6448	−1.64721	−0.823606	+	0.567162i	$0.808041\pi$
$984$	−7.82901	−0.249580
$985$	−1.39964	−0.0445964
$986$	−14.1653	−0.451114
$987$	8.27124	0.263276
$988$	56.0548	1.78334
$989$	−1.91790	−0.0609858
$990$	1.87659	0.0596421
$991$	−26.0789	−0.828424	−0.414212	−	0.910180i	$-0.635943\pi$
$991$	−26.0789	−0.828424	−0.414212	+	0.910180i	$0.635943\pi$
$992$	8.87010	0.281626
$993$	−8.93670	−0.283598
$994$	−0.634340	−0.0201201
$995$	−3.10863	−0.0985502
$996$	−1.12324	−0.0355912
$997$	−37.8472	−1.19863	−0.599316	−	0.800513i	$-0.704561\pi$
$997$	−37.8472	−1.19863	−0.599316	+	0.800513i	$0.704561\pi$
$998$	5.65879	0.179126
$999$	−8.66303	−0.274086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4767.2.a.g.1.15	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4767.2.a.g.1.15	✓	35	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 4767 = 3 \cdot 7 \cdot 227 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4767.a (trivial)

\(f(q)\)	\(=\)	\(q-0.233639 q^{2} -1.00000 q^{3} -1.94541 q^{4} -1.48259 q^{5} +0.233639 q^{6} +1.00000 q^{7} +0.921803 q^{8} +1.00000 q^{9} +0.346390 q^{10} +5.41758 q^{11} +1.94541 q^{12} +4.94174 q^{13} -0.233639 q^{14} +1.48259 q^{15} +3.67546 q^{16} +6.13587 q^{17} -0.233639 q^{18} -5.83071 q^{19} +2.88424 q^{20} -1.00000 q^{21} -1.26576 q^{22} +7.09256 q^{23} -0.921803 q^{24} -2.80194 q^{25} -1.15458 q^{26} -1.00000 q^{27} -1.94541 q^{28} +9.88106 q^{29} -0.346390 q^{30} -3.28238 q^{31} -2.70234 q^{32} -5.41758 q^{33} -1.43358 q^{34} -1.48259 q^{35} -1.94541 q^{36} +8.66303 q^{37} +1.36228 q^{38} -4.94174 q^{39} -1.36665 q^{40} +8.49315 q^{41} +0.233639 q^{42} -0.270411 q^{43} -10.5394 q^{44} -1.48259 q^{45} -1.65710 q^{46} -8.27124 q^{47} -3.67546 q^{48} +1.00000 q^{49} +0.654643 q^{50} -6.13587 q^{51} -9.61372 q^{52} +10.3838 q^{53} +0.233639 q^{54} -8.03202 q^{55} +0.921803 q^{56} +5.83071 q^{57} -2.30860 q^{58} -11.5315 q^{59} -2.88424 q^{60} +5.96919 q^{61} +0.766893 q^{62} +1.00000 q^{63} -6.71954 q^{64} -7.32655 q^{65} +1.26576 q^{66} -2.51408 q^{67} -11.9368 q^{68} -7.09256 q^{69} +0.346390 q^{70} +2.71504 q^{71} +0.921803 q^{72} -3.97759 q^{73} -2.02402 q^{74} +2.80194 q^{75} +11.3431 q^{76} +5.41758 q^{77} +1.15458 q^{78} +6.44646 q^{79} -5.44918 q^{80} +1.00000 q^{81} -1.98433 q^{82} -0.577379 q^{83} +1.94541 q^{84} -9.09695 q^{85} +0.0631786 q^{86} -9.88106 q^{87} +4.99394 q^{88} -18.1493 q^{89} +0.346390 q^{90} +4.94174 q^{91} -13.7980 q^{92} +3.28238 q^{93} +1.93248 q^{94} +8.64453 q^{95} +2.70234 q^{96} -1.10284 q^{97} -0.233639 q^{98} +5.41758 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 7 q^{2} - 35 q^{3} + 45 q^{4} - 4 q^{5} - 7 q^{6} + 35 q^{7} + 21 q^{8} + 35 q^{9} + 11 q^{10} - 3 q^{11} - 45 q^{12} + 19 q^{13} + 7 q^{14} + 4 q^{15} + 65 q^{16} + 20 q^{17} + 7 q^{18} + 9 q^{19}+ \cdots - 3 q^{99}+O(q^{100}) \) 35 * q + 7 * q^2 - 35 * q^3 + 45 * q^4 - 4 * q^5 - 7 * q^6 + 35 * q^7 + 21 * q^8 + 35 * q^9 + 11 * q^10 - 3 * q^11 - 45 * q^12 + 19 * q^13 + 7 * q^14 + 4 * q^15 + 65 * q^16 + 20 * q^17 + 7 * q^18 + 9 * q^19 - 7 * q^20 - 35 * q^21 + 33 * q^22 + 17 * q^23 - 21 * q^24 + 67 * q^25 - 6 * q^26 - 35 * q^27 + 45 * q^28 + 17 * q^29 - 11 * q^30 + 5 * q^31 + 54 * q^32 + 3 * q^33 + 22 * q^34 - 4 * q^35 + 45 * q^36 + 35 * q^37 - 19 * q^38 - 19 * q^39 + 34 * q^40 + 18 * q^41 - 7 * q^42 + 33 * q^43 - 7 * q^44 - 4 * q^45 + 38 * q^46 - 13 * q^47 - 65 * q^48 + 35 * q^49 + 28 * q^50 - 20 * q^51 + 37 * q^52 + 36 * q^53 - 7 * q^54 + 21 * q^55 + 21 * q^56 - 9 * q^57 + 42 * q^58 - 54 * q^59 + 7 * q^60 + 35 * q^61 - 28 * q^62 + 35 * q^63 + 105 * q^64 + 27 * q^65 - 33 * q^66 + 37 * q^67 + 25 * q^68 - 17 * q^69 + 11 * q^70 + 44 * q^71 + 21 * q^72 + 59 * q^73 - 17 * q^74 - 67 * q^75 + 23 * q^76 - 3 * q^77 + 6 * q^78 + 77 * q^79 - 26 * q^80 + 35 * q^81 + 4 * q^82 - 41 * q^83 - 45 * q^84 + 39 * q^85 + 42 * q^86 - 17 * q^87 + 34 * q^88 - 9 * q^89 + 11 * q^90 + 19 * q^91 + 61 * q^92 - 5 * q^93 + 10 * q^94 + 25 * q^95 - 54 * q^96 + 79 * q^97 + 7 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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