LMFDB - Embedded newform 1922.2.a.r.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1922,2,Mod(1,1922)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1922, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("1922.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1922 = 2 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1922.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,4,3,4,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$15.3472472685$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.4525.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 7x^{2} + 3x + 9 $ x^4 - x^3 - 7x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 62)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.06842$ of defining polynomial
Character	$\chi$	$=$	1922.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +3.06842 q^{3} +1.00000 q^{4} -3.34677 q^{5} +3.06842 q^{6} +2.51880 q^{7} +1.00000 q^{8} +6.41519 q^{9} -3.34677 q^{10} +1.72165 q^{11} +3.06842 q^{12} +2.33968 q^{13} +2.51880 q^{14} -10.2693 q^{15} +1.00000 q^{16} -0.790065 q^{17} +6.41519 q^{18} +0.403718 q^{19} -3.34677 q^{20} +7.72874 q^{21} +1.72165 q^{22} -5.06842 q^{23} +3.06842 q^{24} +6.20087 q^{25} +2.33968 q^{26} +10.4792 q^{27} +2.51880 q^{28} -5.20087 q^{29} -10.2693 q^{30} +1.00000 q^{32} +5.28273 q^{33} -0.790065 q^{34} -8.42985 q^{35} +6.41519 q^{36} +5.88930 q^{37} +0.403718 q^{38} +7.17912 q^{39} -3.34677 q^{40} +7.75758 q^{41} +7.72874 q^{42} +7.64688 q^{43} +1.72165 q^{44} -21.4702 q^{45} -5.06842 q^{46} -4.83944 q^{47} +3.06842 q^{48} -0.655638 q^{49} +6.20087 q^{50} -2.42425 q^{51} +2.33968 q^{52} -2.62950 q^{53} +10.4792 q^{54} -5.76196 q^{55} +2.51880 q^{56} +1.23878 q^{57} -5.20087 q^{58} -4.36581 q^{59} -10.2693 q^{60} +9.60897 q^{61} +16.1586 q^{63} +1.00000 q^{64} -7.83038 q^{65} +5.28273 q^{66} -8.86119 q^{67} -0.790065 q^{68} -15.5520 q^{69} -8.42985 q^{70} -11.8944 q^{71} +6.41519 q^{72} +7.84653 q^{73} +5.88930 q^{74} +19.0269 q^{75} +0.403718 q^{76} +4.33649 q^{77} +7.17912 q^{78} -2.09485 q^{79} -3.34677 q^{80} +12.9091 q^{81} +7.75758 q^{82} -12.2558 q^{83} +7.72874 q^{84} +2.64417 q^{85} +7.64688 q^{86} -15.9584 q^{87} +1.72165 q^{88} +14.6442 q^{89} -21.4702 q^{90} +5.89319 q^{91} -5.06842 q^{92} -4.83944 q^{94} -1.35115 q^{95} +3.06842 q^{96} -18.7837 q^{97} -0.655638 q^{98} +11.0447 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} - 2 q^{5} + 3 q^{6} - 4 q^{7} + 4 q^{8} + 5 q^{9} - 2 q^{10} + 9 q^{11} + 3 q^{12} + 7 q^{13} - 4 q^{14} - 7 q^{15} + 4 q^{16} + 4 q^{17} + 5 q^{18} - 7 q^{19} - 2 q^{20}+ \cdots + 7 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 - 2 * q^5 + 3 * q^6 - 4 * q^7 + 4 * q^8 + 5 * q^9 - 2 * q^10 + 9 * q^11 + 3 * q^12 + 7 * q^13 - 4 * q^14 - 7 * q^15 + 4 * q^16 + 4 * q^17 + 5 * q^18 - 7 * q^19 - 2 * q^20 + 24 * q^21 + 9 * q^22 - 11 * q^23 + 3 * q^24 + 7 * q^26 + 15 * q^27 - 4 * q^28 + 4 * q^29 - 7 * q^30 + 4 * q^32 + 16 * q^33 + 4 * q^34 - 9 * q^35 + 5 * q^36 + 26 * q^37 - 7 * q^38 + 17 * q^39 - 2 * q^40 + 2 * q^41 + 24 * q^42 + 4 * q^43 + 9 * q^44 - 27 * q^45 - 11 * q^46 - 10 * q^47 + 3 * q^48 + 30 * q^49 - 21 * q^51 + 7 * q^52 + 6 * q^53 + 15 * q^54 + 9 * q^55 - 4 * q^56 - 10 * q^57 + 4 * q^58 + q^59 - 7 * q^60 + 2 * q^61 + 33 * q^63 + 4 * q^64 + 10 * q^65 + 16 * q^66 - 13 * q^67 + 4 * q^68 - 23 * q^69 - 9 * q^70 + 5 * q^72 + 13 * q^73 + 26 * q^74 + 13 * q^75 - 7 * q^76 + 7 * q^77 + 17 * q^78 - 21 * q^79 - 2 * q^80 + 2 * q^82 + 14 * q^83 + 24 * q^84 - 10 * q^85 + 4 * q^86 - 10 * q^87 + 9 * q^88 + 38 * q^89 - 27 * q^90 + 9 * q^91 - 11 * q^92 - 10 * q^94 + 9 * q^95 + 3 * q^96 - 30 * q^97 + 30 * q^98 + 7 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	3.06842	1.77155	0.885776	−	0.464113i	$-0.153627\pi$
$3$	3.06842	1.77155	0.885776	+	0.464113i	$0.153627\pi$
$4$	1.00000	0.500000
$5$	−3.34677	−1.49672	−0.748361	−	0.663292i	$-0.769159\pi$
$5$	−3.34677	−1.49672	−0.748361	+	0.663292i	$0.769159\pi$
$6$	3.06842	1.25268
$7$	2.51880	0.952018	0.476009	−	0.879441i	$-0.342083\pi$
$7$	2.51880	0.952018	0.476009	+	0.879441i	$0.342083\pi$
$8$	1.00000	0.353553
$9$	6.41519	2.13840
$10$	−3.34677	−1.05834
$11$	1.72165	0.519096	0.259548	−	0.965730i	$-0.416426\pi$
$11$	1.72165	0.519096	0.259548	+	0.965730i	$0.416426\pi$
$12$	3.06842	0.885776
$13$	2.33968	0.648911	0.324455	−	0.945901i	$-0.394819\pi$
$13$	2.33968	0.648911	0.324455	+	0.945901i	$0.394819\pi$
$14$	2.51880	0.673178
$15$	−10.2693	−2.65152
$16$	1.00000	0.250000
$17$	−0.790065	−0.191619	−0.0958095	−	0.995400i	$-0.530544\pi$
$17$	−0.790065	−0.191619	−0.0958095	+	0.995400i	$0.530544\pi$
$18$	6.41519	1.51207
$19$	0.403718	0.0926193	0.0463096	−	0.998927i	$-0.485254\pi$
$19$	0.403718	0.0926193	0.0463096	+	0.998927i	$0.485254\pi$
$20$	−3.34677	−0.748361
$21$	7.72874	1.68655
$22$	1.72165	0.367056
$23$	−5.06842	−1.05684	−0.528419	−	0.848984i	$-0.677215\pi$
$23$	−5.06842	−1.05684	−0.528419	+	0.848984i	$0.677215\pi$
$24$	3.06842	0.626338
$25$	6.20087	1.24017
$26$	2.33968	0.458849
$27$	10.4792	2.01673
$28$	2.51880	0.476009
$29$	−5.20087	−0.965778	−0.482889	−	0.875682i	$-0.660412\pi$
$29$	−5.20087	−0.965778	−0.482889	+	0.875682i	$0.660412\pi$
$30$	−10.2693	−1.87491
$31$	0	0
$31$	0	0
$32$	1.00000	0.176777
$33$	5.28273	0.919606
$34$	−0.790065	−0.135495
$35$	−8.42985	−1.42490
$36$	6.41519	1.06920
$37$	5.88930	0.968195	0.484097	−	0.875014i	$-0.339148\pi$
$37$	5.88930	0.968195	0.484097	+	0.875014i	$0.339148\pi$
$38$	0.403718	0.0654917
$39$	7.17912	1.14958
$40$	−3.34677	−0.529171
$41$	7.75758	1.21153	0.605765	−	0.795644i	$-0.292867\pi$
$41$	7.75758	1.21153	0.605765	+	0.795644i	$0.292867\pi$
$42$	7.72874	1.19257
$43$	7.64688	1.16614	0.583069	−	0.812423i	$-0.301852\pi$
$43$	7.64688	1.16614	0.583069	+	0.812423i	$0.301852\pi$
$44$	1.72165	0.259548
$45$	−21.4702	−3.20058
$46$	−5.06842	−0.747297
$47$	−4.83944	−0.705905	−0.352952	−	0.935641i	$-0.614822\pi$
$47$	−4.83944	−0.705905	−0.352952	+	0.935641i	$0.614822\pi$
$48$	3.06842	0.442888
$49$	−0.655638	−0.0936625
$50$	6.20087	0.876936
$51$	−2.42425	−0.339463
$52$	2.33968	0.324455
$53$	−2.62950	−0.361190	−0.180595	−	0.983558i	$-0.557802\pi$
$53$	−2.62950	−0.361190	−0.180595	+	0.983558i	$0.557802\pi$
$54$	10.4792	1.42604
$55$	−5.76196	−0.776942
$56$	2.51880	0.336589
$57$	1.23878	0.164080
$58$	−5.20087	−0.682908
$59$	−4.36581	−0.568381	−0.284190	−	0.958768i	$-0.591725\pi$
$59$	−4.36581	−0.568381	−0.284190	+	0.958768i	$0.591725\pi$
$60$	−10.2693	−1.32576
$61$	9.60897	1.23030	0.615151	−	0.788409i	$-0.289095\pi$
$61$	9.60897	1.23030	0.615151	+	0.788409i	$0.289095\pi$
$62$	0	0
$63$	16.1586	2.03579
$64$	1.00000	0.125000
$65$	−7.83038	−0.971239
$66$	5.28273	0.650260
$67$	−8.86119	−1.08257	−0.541283	−	0.840840i	$-0.682061\pi$
$67$	−8.86119	−1.08257	−0.541283	+	0.840840i	$0.682061\pi$
$68$	−0.790065	−0.0958095
$69$	−15.5520	−1.87224
$70$	−8.42985	−1.00756
$71$	−11.8944	−1.41161	−0.705804	−	0.708408i	$-0.749414\pi$
$71$	−11.8944	−1.41161	−0.705804	+	0.708408i	$0.749414\pi$
$72$	6.41519	0.756037
$73$	7.84653	0.918367	0.459183	−	0.888342i	$-0.348142\pi$
$73$	7.84653	0.918367	0.459183	+	0.888342i	$0.348142\pi$
$74$	5.88930	0.684617
$75$	19.0269	2.19703
$76$	0.403718	0.0463096
$77$	4.33649	0.494189
$78$	7.17912	0.812875
$79$	−2.09485	−0.235689	−0.117845	−	0.993032i	$-0.537598\pi$
$79$	−2.09485	−0.235689	−0.117845	+	0.993032i	$0.537598\pi$
$80$	−3.34677	−0.374180
$81$	12.9091	1.43434
$82$	7.75758	0.856681
$83$	−12.2558	−1.34525	−0.672627	−	0.739982i	$-0.734834\pi$
$83$	−12.2558	−1.34525	−0.672627	+	0.739982i	$0.734834\pi$
$84$	7.72874	0.843274
$85$	2.64417	0.286800
$86$	7.64688	0.824584
$87$	−15.9584	−1.71093
$88$	1.72165	0.183528
$89$	14.6442	1.55228	0.776139	−	0.630561i	$-0.217175\pi$
$89$	14.6442	1.55228	0.776139	+	0.630561i	$0.217175\pi$
$90$	−21.4702	−2.26315
$91$	5.89319	0.617775
$92$	−5.06842	−0.528419
$93$	0	0
$94$	−4.83944	−0.499150
$95$	−1.35115	−0.138625
$96$	3.06842	0.313169
$97$	−18.7837	−1.90720	−0.953598	−	0.301081i	$-0.902652\pi$
$97$	−18.7837	−1.90720	−0.953598	+	0.301081i	$0.902652\pi$
$98$	−0.655638	−0.0662294
$99$	11.0447	1.11003
$100$	6.20087	0.620087
$101$	−9.45550	−0.940857	−0.470429	−	0.882438i	$-0.655901\pi$
$101$	−9.45550	−0.940857	−0.470429	+	0.882438i	$0.655901\pi$
$102$	−2.42425	−0.240037
$103$	−1.30719	−0.128802	−0.0644008	−	0.997924i	$-0.520514\pi$
$103$	−1.30719	−0.128802	−0.0644008	+	0.997924i	$0.520514\pi$
$104$	2.33968	0.229425
$105$	−25.8663	−2.52429
$106$	−2.62950	−0.255400
$107$	15.0122	1.45128	0.725642	−	0.688072i	$-0.241543\pi$
$107$	15.0122	1.45128	0.725642	+	0.688072i	$0.241543\pi$
$108$	10.4792	1.00836
$109$	7.06206	0.676423	0.338211	−	0.941070i	$-0.390178\pi$
$109$	7.06206	0.676423	0.338211	+	0.941070i	$0.390178\pi$
$110$	−5.76196	−0.549381
$111$	18.0708	1.71521
$112$	2.51880	0.238004
$113$	5.42985	0.510797	0.255399	−	0.966836i	$-0.417793\pi$
$113$	5.42985	0.510797	0.255399	+	0.966836i	$0.417793\pi$
$114$	1.23878	0.116022
$115$	16.9628	1.58179
$116$	−5.20087	−0.482889
$117$	15.0095	1.38763
$118$	−4.36581	−0.401906
$119$	−1.99002	−0.182425
$120$	−10.2693	−0.937454
$121$	−8.03593	−0.730539
$122$	9.60897	0.869955
$123$	23.8035	2.14629
$124$	0	0
$125$	−4.01904	−0.359474
$126$	16.1586	1.43952
$127$	4.17912	0.370837	0.185418	−	0.982660i	$-0.440636\pi$
$127$	4.17912	0.370837	0.185418	+	0.982660i	$0.440636\pi$
$128$	1.00000	0.0883883
$129$	23.4638	2.06587
$130$	−7.83038	−0.686769
$131$	6.92252	0.604823	0.302412	−	0.953177i	$-0.402208\pi$
$131$	6.92252	0.604823	0.302412	+	0.953177i	$0.402208\pi$
$132$	5.28273	0.459803
$133$	1.01689	0.0881752
$134$	−8.86119	−0.765490
$135$	−35.0716	−3.01848
$136$	−0.790065	−0.0677475
$137$	−3.55202	−0.303470	−0.151735	−	0.988421i	$-0.548486\pi$
$137$	−3.55202	−0.303470	−0.151735	+	0.988421i	$0.548486\pi$
$138$	−15.5520	−1.32388
$139$	−2.46775	−0.209312	−0.104656	−	0.994508i	$-0.533374\pi$
$139$	−2.46775	−0.209312	−0.104656	+	0.994508i	$0.533374\pi$
$140$	−8.42985	−0.712452
$141$	−14.8494	−1.25055
$142$	−11.8944	−0.998157
$143$	4.02811	0.336847
$144$	6.41519	0.534599
$145$	17.4061	1.44550
$146$	7.84653	0.649383
$147$	−2.01177	−0.165928
$148$	5.88930	0.484097
$149$	−14.2287	−1.16566	−0.582829	−	0.812595i	$-0.698054\pi$
$149$	−14.2287	−1.16566	−0.582829	+	0.812595i	$0.698054\pi$
$150$	19.0269	1.55354
$151$	−4.73583	−0.385396	−0.192698	−	0.981258i	$-0.561724\pi$
$151$	−4.73583	−0.385396	−0.192698	+	0.981258i	$0.561724\pi$
$152$	0.403718	0.0327459
$153$	−5.06842	−0.409757
$154$	4.33649	0.349444
$155$	0	0
$156$	7.17912	0.574790
$157$	−18.3682	−1.46594	−0.732972	−	0.680259i	$-0.761867\pi$
$157$	−18.3682	−1.46594	−0.732972	+	0.680259i	$0.761867\pi$
$158$	−2.09485	−0.166657
$159$	−8.06842	−0.639867
$160$	−3.34677	−0.264585
$161$	−12.7663	−1.00613
$162$	12.9091	1.01423
$163$	−12.6774	−0.992970	−0.496485	−	0.868045i	$-0.665376\pi$
$163$	−12.6774	−0.992970	−0.496485	+	0.868045i	$0.665376\pi$
$164$	7.75758	0.605765
$165$	−17.6801	−1.37639
$166$	−12.2558	−0.951238
$167$	23.0716	1.78533	0.892665	−	0.450720i	$-0.148833\pi$
$167$	23.0716	1.78533	0.892665	+	0.450720i	$0.148833\pi$
$168$	7.72874	0.596285
$169$	−7.52589	−0.578915
$170$	2.64417	0.202798
$171$	2.58993	0.198057
$172$	7.64688	0.583069
$173$	−20.2515	−1.53969	−0.769845	−	0.638231i	$-0.779667\pi$
$173$	−20.2515	−1.53969	−0.769845	+	0.638231i	$0.779667\pi$
$174$	−15.9584	−1.20981
$175$	15.6188	1.18067
$176$	1.72165	0.129774
$177$	−13.3961	−1.00692
$178$	14.6442	1.09763
$179$	−7.93596	−0.593162	−0.296581	−	0.955008i	$-0.595846\pi$
$179$	−7.93596	−0.593162	−0.296581	+	0.955008i	$0.595846\pi$
$180$	−21.4702	−1.60029
$181$	−24.2847	−1.80507	−0.902533	−	0.430620i	$-0.858295\pi$
$181$	−24.2847	−1.80507	−0.902533	+	0.430620i	$0.858295\pi$
$182$	5.89319	0.436833
$183$	29.4843	2.17955
$184$	−5.06842	−0.373649
$185$	−19.7101	−1.44912
$186$	0	0
$187$	−1.36021	−0.0994687
$188$	−4.83944	−0.352952
$189$	26.3951	1.91996
$190$	−1.35115	−0.0980228
$191$	11.3915	0.824257	0.412129	−	0.911126i	$-0.364785\pi$
$191$	11.3915	0.824257	0.412129	+	0.911126i	$0.364785\pi$
$192$	3.06842	0.221444
$193$	−10.1451	−0.730263	−0.365132	−	0.930956i	$-0.618976\pi$
$193$	−10.1451	−0.730263	−0.365132	+	0.930956i	$0.618976\pi$
$194$	−18.7837	−1.34859
$195$	−24.0269	−1.72060
$196$	−0.655638	−0.0468313
$197$	−2.34087	−0.166780	−0.0833900	−	0.996517i	$-0.526575\pi$
$197$	−2.34087	−0.166780	−0.0833900	+	0.996517i	$0.526575\pi$
$198$	11.0447	0.784912
$199$	−11.9110	−0.844352	−0.422176	−	0.906514i	$-0.638734\pi$
$199$	−11.9110	−0.844352	−0.422176	+	0.906514i	$0.638734\pi$
$200$	6.20087	0.438468
$201$	−27.1898	−1.91782
$202$	−9.45550	−0.665287
$203$	−13.1000	−0.919437
$204$	−2.42425	−0.169731
$205$	−25.9628	−1.81332
$206$	−1.30719	−0.0910765
$207$	−32.5149	−2.25994
$208$	2.33968	0.162228
$209$	0.695060	0.0480783
$210$	−25.8663	−1.78494
$211$	20.5097	1.41195	0.705974	−	0.708237i	$-0.250509\pi$
$211$	20.5097	1.41195	0.705974	+	0.708237i	$0.250509\pi$
$212$	−2.62950	−0.180595
$213$	−36.4970	−2.50074
$214$	15.0122	1.02621
$215$	−25.5923	−1.74538
$216$	10.4792	0.713021
$217$	0	0
$218$	7.06206	0.478303
$219$	24.0764	1.62693
$220$	−5.76196	−0.388471
$221$	−1.84850	−0.124344
$222$	18.0708	1.21283
$223$	−3.53346	−0.236618	−0.118309	−	0.992977i	$-0.537747\pi$
$223$	−3.53346	−0.236618	−0.118309	+	0.992977i	$0.537747\pi$
$224$	2.51880	0.168295
$225$	39.7798	2.65198
$226$	5.42985	0.361188
$227$	0.561086	0.0372406	0.0186203	−	0.999827i	$-0.494073\pi$
$227$	0.561086	0.0372406	0.0186203	+	0.999827i	$0.494073\pi$
$228$	1.23878	0.0820399
$229$	4.96919	0.328373	0.164187	−	0.986429i	$-0.447500\pi$
$229$	4.96919	0.328373	0.164187	+	0.986429i	$0.447500\pi$
$230$	16.9628	1.11850
$231$	13.3062	0.875481
$232$	−5.20087	−0.341454
$233$	−9.50049	−0.622398	−0.311199	−	0.950345i	$-0.600731\pi$
$233$	−9.50049	−0.622398	−0.311199	+	0.950345i	$0.600731\pi$
$234$	15.0095	0.981202
$235$	16.1965	1.05654
$236$	−4.36581	−0.284190
$237$	−6.42788	−0.417536
$238$	−1.99002	−0.128994
$239$	−12.3614	−0.799595	−0.399797	−	0.916604i	$-0.630919\pi$
$239$	−12.3614	−0.799595	−0.399797	+	0.916604i	$0.630919\pi$
$240$	−10.2693	−0.662880
$241$	19.9181	1.28304	0.641520	−	0.767106i	$-0.278304\pi$
$241$	19.9181	1.28304	0.641520	+	0.767106i	$0.278304\pi$
$242$	−8.03593	−0.516569
$243$	8.17277	0.524283
$244$	9.60897	0.615151
$245$	2.19427	0.140187
$246$	23.8035	1.51766
$247$	0.944572	0.0601017
$248$	0	0
$249$	−37.6061	−2.38319
$250$	−4.01904	−0.254187
$251$	−24.6158	−1.55373	−0.776867	−	0.629665i	$-0.783192\pi$
$251$	−24.6158	−1.55373	−0.776867	+	0.629665i	$0.783192\pi$
$252$	16.1586	1.01790
$253$	−8.72603	−0.548601
$254$	4.17912	0.262221
$255$	8.11341	0.508081
$256$	1.00000	0.0625000
$257$	20.5027	1.27892	0.639460	−	0.768824i	$-0.279158\pi$
$257$	20.5027	1.27892	0.639460	+	0.768824i	$0.279158\pi$
$258$	23.4638	1.46079
$259$	14.8340	0.921738
$260$	−7.83038	−0.485619
$261$	−33.3646	−2.06522
$262$	6.92252	0.427675
$263$	5.06994	0.312626	0.156313	−	0.987708i	$-0.450039\pi$
$263$	5.06994	0.312626	0.156313	+	0.987708i	$0.450039\pi$
$264$	5.28273	0.325130
$265$	8.80035	0.540601
$266$	1.01689	0.0623493
$267$	44.9344	2.74994
$268$	−8.86119	−0.541283
$269$	−5.29740	−0.322988	−0.161494	−	0.986874i	$-0.551631\pi$
$269$	−5.29740	−0.322988	−0.161494	+	0.986874i	$0.551631\pi$
$270$	−35.0716	−2.13439
$271$	−7.81423	−0.474680	−0.237340	−	0.971427i	$-0.576276\pi$
$271$	−7.81423	−0.474680	−0.237340	+	0.971427i	$0.576276\pi$
$272$	−0.790065	−0.0479047
$273$	18.0828	1.09442
$274$	−3.55202	−0.214586
$275$	10.6757	0.643770
$276$	−15.5520	−0.936122
$277$	−1.03033	−0.0619065	−0.0309532	−	0.999521i	$-0.509854\pi$
$277$	−1.03033	−0.0619065	−0.0309532	+	0.999521i	$0.509854\pi$
$278$	−2.46775	−0.148006
$279$	0	0
$280$	−8.42985	−0.503780
$281$	7.06252	0.421314	0.210657	−	0.977560i	$-0.432440\pi$
$281$	7.06252	0.421314	0.210657	+	0.977560i	$0.432440\pi$
$282$	−14.8494	−0.884270
$283$	21.6825	1.28889	0.644446	−	0.764650i	$-0.277088\pi$
$283$	21.6825	1.28889	0.644446	+	0.764650i	$0.277088\pi$
$284$	−11.8944	−0.705804
$285$	−4.14590	−0.245582
$286$	4.02811	0.238187
$287$	19.5398	1.15340
$288$	6.41519	0.378019
$289$	−16.3758	−0.963282
$290$	17.4061	1.02212
$291$	−57.6363	−3.37870
$292$	7.84653	0.459183
$293$	−8.98188	−0.524727	−0.262363	−	0.964969i	$-0.584502\pi$
$293$	−8.98188	−0.524727	−0.262363	+	0.964969i	$0.584502\pi$
$294$	−2.01177	−0.117329
$295$	14.6114	0.850707
$296$	5.88930	0.342308
$297$	18.0415	1.04688
$298$	−14.2287	−0.824245
$299$	−11.8585	−0.685794
$300$	19.0269	1.09852
$301$	19.2610	1.11018
$302$	−4.73583	−0.272516
$303$	−29.0134	−1.66678
$304$	0.403718	0.0231548
$305$	−32.1590	−1.84142
$306$	−5.06842	−0.289742
$307$	−14.5413	−0.829915	−0.414958	−	0.909841i	$-0.636204\pi$
$307$	−14.5413	−0.829915	−0.414958	+	0.909841i	$0.636204\pi$
$308$	4.33649	0.247094
$309$	−4.01102	−0.228179
$310$	0	0
$311$	−10.6398	−0.603327	−0.301663	−	0.953414i	$-0.597542\pi$
$311$	−10.6398	−0.603327	−0.301663	+	0.953414i	$0.597542\pi$
$312$	7.17912	0.406438
$313$	3.37758	0.190912	0.0954562	−	0.995434i	$-0.469569\pi$
$313$	3.37758	0.190912	0.0954562	+	0.995434i	$0.469569\pi$
$314$	−18.3682	−1.03658
$315$	−54.0791	−3.04701
$316$	−2.09485	−0.117845
$317$	6.53736	0.367175	0.183587	−	0.983003i	$-0.441229\pi$
$317$	6.53736	0.367175	0.183587	+	0.983003i	$0.441229\pi$
$318$	−8.06842	−0.452454
$319$	−8.95407	−0.501332
$320$	−3.34677	−0.187090
$321$	46.0637	2.57103
$322$	−12.7663	−0.711440
$323$	−0.318964	−0.0177476
$324$	12.9091	0.717171
$325$	14.5081	0.804763
$326$	−12.6774	−0.702136
$327$	21.6694	1.19832
$328$	7.75758	0.428341
$329$	−12.1896	−0.672034
$330$	−17.6801	−0.973257
$331$	28.0044	1.53926	0.769629	−	0.638491i	$-0.220441\pi$
$331$	28.0044	1.53926	0.769629	+	0.638491i	$0.220441\pi$
$332$	−12.2558	−0.672627
$333$	37.7810	2.07038
$334$	23.0716	1.26242
$335$	29.6564	1.62030
$336$	7.72874	0.421637
$337$	29.7109	1.61845	0.809227	−	0.587496i	$-0.199886\pi$
$337$	29.7109	1.61845	0.809227	+	0.587496i	$0.199886\pi$
$338$	−7.52589	−0.409354
$339$	16.6611	0.904904
$340$	2.64417	0.143400
$341$	0	0
$342$	2.58993	0.140047
$343$	−19.2830	−1.04119
$344$	7.64688	0.412292
$345$	52.0491	2.80223
$346$	−20.2515	−1.08873
$347$	−9.82039	−0.527186	−0.263593	−	0.964634i	$-0.584908\pi$
$347$	−9.82039	−0.527186	−0.263593	+	0.964634i	$0.584908\pi$
$348$	−15.9584	−0.855463
$349$	1.02613	0.0549277	0.0274638	−	0.999623i	$-0.491257\pi$
$349$	1.02613	0.0549277	0.0274638	+	0.999623i	$0.491257\pi$
$350$	15.6188	0.834858
$351$	24.5180	1.30868
$352$	1.72165	0.0917641
$353$	21.0122	1.11837	0.559183	−	0.829044i	$-0.311115\pi$
$353$	21.0122	1.11837	0.559183	+	0.829044i	$0.311115\pi$
$354$	−13.3961	−0.711997
$355$	39.8079	2.11278
$356$	14.6442	0.776139
$357$	−6.10621	−0.323175
$358$	−7.93596	−0.419429
$359$	−30.4196	−1.60548	−0.802742	−	0.596327i	$-0.796626\pi$
$359$	−30.4196	−1.60548	−0.802742	+	0.596327i	$0.796626\pi$
$360$	−21.4702	−1.13158
$361$	−18.8370	−0.991422
$362$	−24.2847	−1.27637
$363$	−24.6576	−1.29419
$364$	5.89319	0.308887
$365$	−26.2605	−1.37454
$366$	29.4843	1.54117
$367$	25.8054	1.34703	0.673516	−	0.739172i	$-0.264783\pi$
$367$	25.8054	1.34703	0.673516	+	0.739172i	$0.264783\pi$
$368$	−5.06842	−0.264210
$369$	49.7663	2.59073
$370$	−19.7101	−1.02468
$371$	−6.62320	−0.343859
$372$	0	0
$373$	12.4846	0.646430	0.323215	−	0.946326i	$-0.395236\pi$
$373$	12.4846	0.646430	0.323215	+	0.946326i	$0.395236\pi$
$374$	−1.36021	−0.0703350
$375$	−12.3321	−0.636827
$376$	−4.83944	−0.249575
$377$	−12.1684	−0.626704
$378$	26.3951	1.35762
$379$	1.88418	0.0967839	0.0483920	−	0.998828i	$-0.484590\pi$
$379$	1.88418	0.0967839	0.0483920	+	0.998828i	$0.484590\pi$
$380$	−1.35115	−0.0693126
$381$	12.8233	0.656957
$382$	11.3915	0.582838
$383$	13.0368	0.666152	0.333076	−	0.942900i	$-0.391913\pi$
$383$	13.0368	0.666152	0.333076	+	0.942900i	$0.391913\pi$
$384$	3.06842	0.156585
$385$	−14.5132	−0.739663
$386$	−10.1451	−0.516374
$387$	49.0561	2.49366
$388$	−18.7837	−0.953598
$389$	10.3218	0.523337	0.261669	−	0.965158i	$-0.415727\pi$
$389$	10.3218	0.523337	0.261669	+	0.965158i	$0.415727\pi$
$390$	−24.0269	−1.21665
$391$	4.00438	0.202510
$392$	−0.655638	−0.0331147
$393$	21.2412	1.07148
$394$	−2.34087	−0.117931
$395$	7.01099	0.352761
$396$	11.0447	0.555017
$397$	14.8604	0.745824	0.372912	−	0.927867i	$-0.378359\pi$
$397$	14.8604	0.745824	0.372912	+	0.927867i	$0.378359\pi$
$398$	−11.9110	−0.597047
$399$	3.12023	0.156207
$400$	6.20087	0.310044
$401$	12.2199	0.610234	0.305117	−	0.952315i	$-0.401305\pi$
$401$	12.2199	0.610234	0.305117	+	0.952315i	$0.401305\pi$
$402$	−27.1898	−1.35611
$403$	0	0
$404$	−9.45550	−0.470429
$405$	−43.2037	−2.14681
$406$	−13.1000	−0.650140
$407$	10.1393	0.502586
$408$	−2.42425	−0.120018
$409$	14.9660	0.740021	0.370010	−	0.929028i	$-0.379354\pi$
$409$	14.9660	0.740021	0.370010	+	0.929028i	$0.379354\pi$
$410$	−25.9628	−1.28221
$411$	−10.8991	−0.537613
$412$	−1.30719	−0.0644008
$413$	−10.9966	−0.541108
$414$	−32.5149	−1.59802
$415$	41.0175	2.01347
$416$	2.33968	0.114712
$417$	−7.57210	−0.370807
$418$	0.695060	0.0339965
$419$	15.2903	0.746978	0.373489	−	0.927635i	$-0.378161\pi$
$419$	15.2903	0.746978	0.373489	+	0.927635i	$0.378161\pi$
$420$	−25.8663	−1.26215
$421$	21.4454	1.04518	0.522592	−	0.852583i	$-0.324965\pi$
$421$	21.4454	1.04518	0.522592	+	0.852583i	$0.324965\pi$
$422$	20.5097	0.998398
$423$	−31.0459	−1.50950
$424$	−2.62950	−0.127700
$425$	−4.89909	−0.237641
$426$	−36.4970	−1.76829
$427$	24.2031	1.17127
$428$	15.0122	0.725642
$429$	12.3599	0.596742
$430$	−25.5923	−1.23417
$431$	8.95255	0.431229	0.215615	−	0.976479i	$-0.430825\pi$
$431$	8.95255	0.431229	0.215615	+	0.976479i	$0.430825\pi$
$432$	10.4792	0.504182
$433$	5.18109	0.248987	0.124494	−	0.992220i	$-0.460269\pi$
$433$	5.18109	0.248987	0.124494	+	0.992220i	$0.460269\pi$
$434$	0	0
$435$	53.4093	2.56078
$436$	7.06206	0.338211
$437$	−2.04621	−0.0978836
$438$	24.0764	1.15042
$439$	−2.26810	−0.108251	−0.0541253	−	0.998534i	$-0.517237\pi$
$439$	−2.26810	−0.108251	−0.0541253	+	0.998534i	$0.517237\pi$
$440$	−5.76196	−0.274691
$441$	−4.20604	−0.200288
$442$	−1.84850	−0.0879242
$443$	−22.1187	−1.05089	−0.525446	−	0.850827i	$-0.676101\pi$
$443$	−22.1187	−1.05089	−0.525446	+	0.850827i	$0.676101\pi$
$444$	18.0708	0.857603
$445$	−49.0107	−2.32333
$446$	−3.53346	−0.167314
$447$	−43.6595	−2.06503
$448$	2.51880	0.119002
$449$	−16.6105	−0.783896	−0.391948	−	0.919987i	$-0.628199\pi$
$449$	−16.6105	−0.783896	−0.391948	+	0.919987i	$0.628199\pi$
$450$	39.7798	1.87524
$451$	13.3558	0.628901
$452$	5.42985	0.255399
$453$	−14.5315	−0.682749
$454$	0.561086	0.0263331
$455$	−19.7232	−0.924636
$456$	1.23878	0.0580110
$457$	−36.3789	−1.70174	−0.850868	−	0.525380i	$-0.823923\pi$
$457$	−36.3789	−1.70174	−0.850868	+	0.525380i	$0.823923\pi$
$458$	4.96919	0.232195
$459$	−8.27927	−0.386443
$460$	16.9628	0.790896
$461$	3.49237	0.162656	0.0813279	−	0.996687i	$-0.474084\pi$
$461$	3.49237	0.162656	0.0813279	+	0.996687i	$0.474084\pi$
$462$	13.3062	0.619059
$463$	6.06601	0.281911	0.140956	−	0.990016i	$-0.454982\pi$
$463$	6.06601	0.281911	0.140956	+	0.990016i	$0.454982\pi$
$464$	−5.20087	−0.241444
$465$	0	0
$466$	−9.50049	−0.440102
$467$	3.06626	0.141890	0.0709448	−	0.997480i	$-0.477399\pi$
$467$	3.06626	0.141890	0.0709448	+	0.997480i	$0.477399\pi$
$468$	15.0095	0.693814
$469$	−22.3196	−1.03062
$470$	16.1965	0.747088
$471$	−56.3614	−2.59700
$472$	−4.36581	−0.200953
$473$	13.1652	0.605338
$474$	−6.42788	−0.295242
$475$	2.50340	0.114864
$476$	−1.99002	−0.0912123
$477$	−16.8688	−0.772368
$478$	−12.3614	−0.565399
$479$	5.25392	0.240058	0.120029	−	0.992770i	$-0.461701\pi$
$479$	5.25392	0.240058	0.120029	+	0.992770i	$0.461701\pi$
$480$	−10.2693	−0.468727
$481$	13.7791	0.628272
$482$	19.9181	0.907246
$483$	−39.1725	−1.78241
$484$	−8.03593	−0.365270
$485$	62.8648	2.85454
$486$	8.17277	0.370724
$487$	−6.79518	−0.307919	−0.153960	−	0.988077i	$-0.549203\pi$
$487$	−6.79518	−0.307919	−0.153960	+	0.988077i	$0.549203\pi$
$488$	9.60897	0.434978
$489$	−38.8995	−1.75910
$490$	2.19427	0.0991269
$491$	23.1009	1.04253	0.521264	−	0.853395i	$-0.325461\pi$
$491$	23.1009	1.04253	0.521264	+	0.853395i	$0.325461\pi$
$492$	23.8035	1.07314
$493$	4.10903	0.185061
$494$	0.944572	0.0424983
$495$	−36.9641	−1.66141
$496$	0	0
$497$	−29.9597	−1.34387
$498$	−37.6061	−1.68517
$499$	25.1701	1.12677	0.563383	−	0.826196i	$-0.309499\pi$
$499$	25.1701	1.12677	0.563383	+	0.826196i	$0.309499\pi$
$500$	−4.01904	−0.179737
$501$	70.7932	3.16281
$502$	−24.6158	−1.09866
$503$	−7.47046	−0.333091	−0.166546	−	0.986034i	$-0.553261\pi$
$503$	−7.47046	−0.333091	−0.166546	+	0.986034i	$0.553261\pi$
$504$	16.1586	0.719761
$505$	31.6454	1.40820
$506$	−8.72603	−0.387919
$507$	−23.0926	−1.02558
$508$	4.17912	0.185418
$509$	34.1956	1.51569	0.757846	−	0.652434i	$-0.226252\pi$
$509$	34.1956	1.51569	0.757846	+	0.652434i	$0.226252\pi$
$510$	8.11341	0.359268
$511$	19.7638	0.874301
$512$	1.00000	0.0441942
$513$	4.23065	0.186788
$514$	20.5027	0.904333
$515$	4.37488	0.192780
$516$	23.4638	1.03294
$517$	−8.33181	−0.366432
$518$	14.8340	0.651767
$519$	−62.1400	−2.72764
$520$	−7.83038	−0.343385
$521$	−6.22092	−0.272543	−0.136272	−	0.990671i	$-0.543512\pi$
$521$	−6.22092	−0.272543	−0.136272	+	0.990671i	$0.543512\pi$
$522$	−33.3646	−1.46033
$523$	−19.2360	−0.841132	−0.420566	−	0.907262i	$-0.638169\pi$
$523$	−19.2360	−0.841132	−0.420566	+	0.907262i	$0.638169\pi$
$524$	6.92252	0.302412
$525$	47.9249	2.09161
$526$	5.06994	0.221060
$527$	0	0
$528$	5.28273	0.229901
$529$	2.68886	0.116907
$530$	8.80035	0.382263
$531$	−28.0075	−1.21542
$532$	1.01689	0.0440876
$533$	18.1503	0.786175
$534$	44.9344	1.94450
$535$	−50.2424	−2.17217
$536$	−8.86119	−0.382745
$537$	−24.3509	−1.05082
$538$	−5.29740	−0.228387
$539$	−1.12878	−0.0486199
$540$	−35.0716	−1.50924
$541$	22.7752	0.979182	0.489591	−	0.871952i	$-0.337146\pi$
$541$	22.7752	0.979182	0.489591	+	0.871952i	$0.337146\pi$
$542$	−7.81423	−0.335650
$543$	−74.5156	−3.19777
$544$	−0.790065	−0.0338738
$545$	−23.6351	−1.01242
$546$	18.0828	0.773872
$547$	2.21283	0.0946137	0.0473068	−	0.998880i	$-0.484936\pi$
$547$	2.21283	0.0946137	0.0473068	+	0.998880i	$0.484936\pi$
$548$	−3.55202	−0.151735
$549$	61.6434	2.63087
$550$	10.6757	0.455214
$551$	−2.09969	−0.0894496
$552$	−15.5520	−0.661938
$553$	−5.27651	−0.224380
$554$	−1.03033	−0.0437745
$555$	−60.4789	−2.56719
$556$	−2.46775	−0.104656
$557$	30.0188	1.27194	0.635969	−	0.771715i	$-0.280601\pi$
$557$	30.0188	1.27194	0.635969	+	0.771715i	$0.280601\pi$
$558$	0	0
$559$	17.8913	0.756719
$560$	−8.42985	−0.356226
$561$	−4.17370	−0.176214
$562$	7.06252	0.297914
$563$	−4.60946	−0.194265	−0.0971327	−	0.995271i	$-0.530967\pi$
$563$	−4.60946	−0.194265	−0.0971327	+	0.995271i	$0.530967\pi$
$564$	−14.8494	−0.625273
$565$	−18.1725	−0.764521
$566$	21.6825	0.911384
$567$	32.5154	1.36552
$568$	−11.8944	−0.499078
$569$	15.5824	0.653246	0.326623	−	0.945155i	$-0.394089\pi$
$569$	15.5824	0.653246	0.326623	+	0.945155i	$0.394089\pi$
$570$	−4.14590	−0.173653
$571$	1.86661	0.0781151	0.0390575	−	0.999237i	$-0.487564\pi$
$571$	1.86661	0.0781151	0.0390575	+	0.999237i	$0.487564\pi$
$572$	4.02811	0.168424
$573$	34.9538	1.46021
$574$	19.5398	0.815575
$575$	−31.4286	−1.31066
$576$	6.41519	0.267300
$577$	−30.2432	−1.25904	−0.629520	−	0.776985i	$-0.716748\pi$
$577$	−30.2432	−1.25904	−0.629520	+	0.776985i	$0.716748\pi$
$578$	−16.3758	−0.681143
$579$	−31.1295	−1.29370
$580$	17.4061	0.722750
$581$	−30.8700	−1.28071
$582$	−57.6363	−2.38910
$583$	−4.52708	−0.187492
$584$	7.84653	0.324692
$585$	−50.2333	−2.07689
$586$	−8.98188	−0.371038
$587$	21.1815	0.874255	0.437128	−	0.899399i	$-0.355996\pi$
$587$	21.1815	0.874255	0.437128	+	0.899399i	$0.355996\pi$
$588$	−2.01177	−0.0829640
$589$	0	0
$590$	14.6114	0.601541
$591$	−7.18277	−0.295460
$592$	5.88930	0.242049
$593$	41.7520	1.71455	0.857274	−	0.514861i	$-0.172156\pi$
$593$	41.7520	1.71455	0.857274	+	0.514861i	$0.172156\pi$
$594$	18.0415	0.740253
$595$	6.66013	0.273039
$596$	−14.2287	−0.582829
$597$	−36.5481	−1.49581
$598$	−11.8585	−0.484929
$599$	−6.52924	−0.266777	−0.133389	−	0.991064i	$-0.542586\pi$
$599$	−6.52924	−0.266777	−0.133389	+	0.991064i	$0.542586\pi$
$600$	19.0269	0.776769
$601$	−5.23531	−0.213553	−0.106776	−	0.994283i	$-0.534053\pi$
$601$	−5.23531	−0.213553	−0.106776	+	0.994283i	$0.534053\pi$
$602$	19.2610	0.785018
$603$	−56.8462	−2.31496
$604$	−4.73583	−0.192698
$605$	26.8944	1.09341
$606$	−29.0134	−1.17859
$607$	20.2938	0.823698	0.411849	−	0.911252i	$-0.364883\pi$
$607$	20.2938	0.823698	0.411849	+	0.911252i	$0.364883\pi$
$608$	0.403718	0.0163729
$609$	−40.1962	−1.62883
$610$	−32.1590	−1.30208
$611$	−11.3227	−0.458069
$612$	−5.06842	−0.204879
$613$	−1.47725	−0.0596656	−0.0298328	−	0.999555i	$-0.509497\pi$
$613$	−1.47725	−0.0596656	−0.0298328	+	0.999555i	$0.509497\pi$
$614$	−14.5413	−0.586839
$615$	−79.6648	−3.21240
$616$	4.33649	0.174722
$617$	−20.6148	−0.829922	−0.414961	−	0.909839i	$-0.636205\pi$
$617$	−20.6148	−0.829922	−0.414961	+	0.909839i	$0.636205\pi$
$618$	−4.01102	−0.161347
$619$	−2.74094	−0.110168	−0.0550839	−	0.998482i	$-0.517543\pi$
$619$	−2.74094	−0.110168	−0.0550839	+	0.998482i	$0.517543\pi$
$620$	0	0
$621$	−53.1131	−2.13135
$622$	−10.6398	−0.426617
$623$	36.8858	1.47780
$624$	7.17912	0.287395
$625$	−17.5535	−0.702142
$626$	3.37758	0.134995
$627$	2.13274	0.0851732
$628$	−18.3682	−0.732972
$629$	−4.65293	−0.185524
$630$	−54.0791	−2.15456
$631$	−41.5150	−1.65269	−0.826344	−	0.563166i	$-0.809583\pi$
$631$	−41.5150	−1.65269	−0.826344	+	0.563166i	$0.809583\pi$
$632$	−2.09485	−0.0833287
$633$	62.9325	2.50134
$634$	6.53736	0.259632
$635$	−13.9866	−0.555040
$636$	−8.06842	−0.319934
$637$	−1.53398	−0.0607786
$638$	−8.95407	−0.354495
$639$	−76.3049	−3.01858
$640$	−3.34677	−0.132293
$641$	−9.81133	−0.387524	−0.193762	−	0.981049i	$-0.562069\pi$
$641$	−9.81133	−0.387524	−0.193762	+	0.981049i	$0.562069\pi$
$642$	46.0637	1.81799
$643$	37.9560	1.49684	0.748420	−	0.663225i	$-0.230813\pi$
$643$	37.9560	1.49684	0.748420	+	0.663225i	$0.230813\pi$
$644$	−12.7663	−0.503064
$645$	−78.5280	−3.09204
$646$	−0.318964	−0.0125495
$647$	−30.8832	−1.21414	−0.607072	−	0.794647i	$-0.707656\pi$
$647$	−30.8832	−1.21414	−0.607072	+	0.794647i	$0.707656\pi$
$648$	12.9091	0.507116
$649$	−7.51639	−0.295044
$650$	14.5081	0.569053
$651$	0	0
$652$	−12.6774	−0.496485
$653$	−3.86753	−0.151348	−0.0756740	−	0.997133i	$-0.524111\pi$
$653$	−3.86753	−0.151348	−0.0756740	+	0.997133i	$0.524111\pi$
$654$	21.6694	0.847339
$655$	−23.1681	−0.905252
$656$	7.75758	0.302883
$657$	50.3370	1.96383
$658$	−12.1896	−0.475200
$659$	29.8438	1.16255	0.581275	−	0.813707i	$-0.302554\pi$
$659$	29.8438	1.16255	0.581275	+	0.813707i	$0.302554\pi$
$660$	−17.6801	−0.688197
$661$	41.2333	1.60379	0.801895	−	0.597465i	$-0.203825\pi$
$661$	41.2333	1.60379	0.801895	+	0.597465i	$0.203825\pi$
$662$	28.0044	1.08842
$663$	−5.67197	−0.220281
$664$	−12.2558	−0.475619
$665$	−3.40328	−0.131974
$666$	37.7810	1.46398
$667$	26.3602	1.02067
$668$	23.0716	0.892665
$669$	−10.8421	−0.419182
$670$	29.6564	1.14573
$671$	16.5433	0.638646
$672$	7.72874	0.298142
$673$	−40.4650	−1.55981	−0.779905	−	0.625897i	$-0.784733\pi$
$673$	−40.4650	−1.55981	−0.779905	+	0.625897i	$0.784733\pi$
$674$	29.7109	1.14442
$675$	64.9803	2.50109
$676$	−7.52589	−0.289457
$677$	43.9447	1.68893	0.844466	−	0.535609i	$-0.179918\pi$
$677$	43.9447	1.68893	0.844466	+	0.535609i	$0.179918\pi$
$678$	16.6611	0.639864
$679$	−47.3124	−1.81568
$680$	2.64417	0.101399
$681$	1.72165	0.0659737
$682$	0	0
$683$	−4.87945	−0.186707	−0.0933535	−	0.995633i	$-0.529759\pi$
$683$	−4.87945	−0.186707	−0.0933535	+	0.995633i	$0.529759\pi$
$684$	2.58993	0.0990284
$685$	11.8878	0.454210
$686$	−19.2830	−0.736230
$687$	15.2475	0.581730
$688$	7.64688	0.291534
$689$	−6.15220	−0.234380
$690$	52.0491	1.98147
$691$	35.6502	1.35620	0.678099	−	0.734971i	$-0.262804\pi$
$691$	35.6502	1.35620	0.678099	+	0.734971i	$0.262804\pi$
$692$	−20.2515	−0.769845
$693$	27.8194	1.05677
$694$	−9.82039	−0.372777
$695$	8.25901	0.313282
$696$	−15.9584	−0.604903
$697$	−6.12899	−0.232152
$698$	1.02613	0.0388397
$699$	−29.1515	−1.10261
$700$	15.6188	0.590334
$701$	−20.3324	−0.767944	−0.383972	−	0.923345i	$-0.625444\pi$
$701$	−20.3324	−0.767944	−0.383972	+	0.923345i	$0.625444\pi$
$702$	24.5180	0.925374
$703$	2.37762	0.0896735
$704$	1.72165	0.0648870
$705$	49.6976	1.87172
$706$	21.0122	0.790805
$707$	−23.8165	−0.895713
$708$	−13.3961	−0.503458
$709$	−9.60069	−0.360562	−0.180281	−	0.983615i	$-0.557701\pi$
$709$	−9.60069	−0.360562	−0.180281	+	0.983615i	$0.557701\pi$
$710$	39.8079	1.49396
$711$	−13.4389	−0.503997
$712$	14.6442	0.548813
$713$	0	0
$714$	−6.10621	−0.228519
$715$	−13.4811	−0.504166
$716$	−7.93596	−0.296581
$717$	−37.9300	−1.41652
$718$	−30.4196	−1.13525
$719$	−36.7351	−1.36999	−0.684994	−	0.728549i	$-0.740195\pi$
$719$	−36.7351	−1.36999	−0.684994	+	0.728549i	$0.740195\pi$
$720$	−21.4702	−0.800146
$721$	−3.29256	−0.122621
$722$	−18.8370	−0.701041
$723$	61.1172	2.27297
$724$	−24.2847	−0.902533
$725$	−32.2499	−1.19773
$726$	−24.6576	−0.915129
$727$	16.6310	0.616811	0.308405	−	0.951255i	$-0.400205\pi$
$727$	16.6310	0.616811	0.308405	+	0.951255i	$0.400205\pi$
$728$	5.89319	0.218416
$729$	−13.6498	−0.505547
$730$	−26.2605	−0.971946
$731$	−6.04153	−0.223454
$732$	29.4843	1.08977
$733$	3.54478	0.130929	0.0654647	−	0.997855i	$-0.479147\pi$
$733$	3.54478	0.130929	0.0654647	+	0.997855i	$0.479147\pi$
$734$	25.8054	0.952496
$735$	6.73293	0.248348
$736$	−5.06842	−0.186824
$737$	−15.2558	−0.561956
$738$	49.7663	1.83192
$739$	9.42152	0.346576	0.173288	−	0.984871i	$-0.444561\pi$
$739$	9.42152	0.346576	0.173288	+	0.984871i	$0.444561\pi$
$740$	−19.7101	−0.724559
$741$	2.89834	0.106473
$742$	−6.62320	−0.243145
$743$	0.492369	0.0180633	0.00903163	−	0.999959i	$-0.497125\pi$
$743$	0.492369	0.0180633	0.00903163	+	0.999959i	$0.497125\pi$
$744$	0	0
$745$	47.6201	1.74467
$746$	12.4846	0.457095
$747$	−78.6236	−2.87669
$748$	−1.36021	−0.0497343
$749$	37.8128	1.38165
$750$	−12.3321	−0.450305
$751$	40.8985	1.49241	0.746204	−	0.665718i	$-0.231875\pi$
$751$	40.8985	1.49241	0.746204	+	0.665718i	$0.231875\pi$
$752$	−4.83944	−0.176476
$753$	−75.5314	−2.75252
$754$	−12.1684	−0.443146
$755$	15.8497	0.576830
$756$	26.3951	0.959980
$757$	−14.6050	−0.530829	−0.265414	−	0.964134i	$-0.585509\pi$
$757$	−14.6050	−0.530829	−0.265414	+	0.964134i	$0.585509\pi$
$758$	1.88418	0.0684366
$759$	−26.7751	−0.971875
$760$	−1.35115	−0.0490114
$761$	53.8460	1.95192	0.975958	−	0.217957i	$-0.0699392\pi$
$761$	53.8460	1.95192	0.975958	+	0.217957i	$0.0699392\pi$
$762$	12.8233	0.464539
$763$	17.7879	0.643967
$764$	11.3915	0.412129
$765$	16.9628	0.613292
$766$	13.0368	0.471041
$767$	−10.2146	−0.368828
$768$	3.06842	0.110722
$769$	41.8213	1.50811	0.754057	−	0.656809i	$-0.228094\pi$
$769$	41.8213	1.50811	0.754057	+	0.656809i	$0.228094\pi$
$770$	−14.5132	−0.523021
$771$	62.9107	2.26567
$772$	−10.1451	−0.365132
$773$	19.7207	0.709305	0.354652	−	0.934998i	$-0.384599\pi$
$773$	19.7207	0.709305	0.354652	+	0.934998i	$0.384599\pi$
$774$	49.0561	1.76329
$775$	0	0
$776$	−18.7837	−0.674296
$777$	45.5168	1.63291
$778$	10.3218	0.370055
$779$	3.13187	0.112211
$780$	−24.0269	−0.860300
$781$	−20.4780	−0.732760
$782$	4.00438	0.143196
$783$	−54.5011	−1.94771
$784$	−0.655638	−0.0234156
$785$	61.4742	2.19411
$786$	21.2412	0.757648
$787$	3.79037	0.135112	0.0675560	−	0.997715i	$-0.478480\pi$
$787$	3.79037	0.135112	0.0675560	+	0.997715i	$0.478480\pi$
$788$	−2.34087	−0.0833900
$789$	15.5567	0.553833
$790$	7.01099	0.249440
$791$	13.6767	0.486288
$792$	11.0447	0.392456
$793$	22.4819	0.798357
$794$	14.8604	0.527377
$795$	27.0031	0.957703
$796$	−11.9110	−0.422176
$797$	12.4130	0.439692	0.219846	−	0.975535i	$-0.429444\pi$
$797$	12.4130	0.439692	0.219846	+	0.975535i	$0.429444\pi$
$798$	3.12023	0.110455
$799$	3.82347	0.135265
$800$	6.20087	0.219234
$801$	93.9451	3.31939
$802$	12.2199	0.431500
$803$	13.5090	0.476721
$804$	−27.1898	−0.958912
$805$	42.7260	1.50589
$806$	0	0
$807$	−16.2546	−0.572190
$808$	−9.45550	−0.332643
$809$	−23.2060	−0.815878	−0.407939	−	0.913009i	$-0.633752\pi$
$809$	−23.2060	−0.815878	−0.407939	+	0.913009i	$0.633752\pi$
$810$	−43.2037	−1.51802
$811$	39.4836	1.38646	0.693228	−	0.720718i	$-0.256188\pi$
$811$	39.4836	1.38646	0.693228	+	0.720718i	$0.256188\pi$
$812$	−13.1000	−0.459719
$813$	−23.9773	−0.840921
$814$	10.1393	0.355382
$815$	42.4283	1.48620
$816$	−2.42425	−0.0848657
$817$	3.08718	0.108007
$818$	14.9660	0.523274
$819$	37.8059	1.32105
$820$	−25.9628	−0.906661
$821$	−17.9793	−0.627482	−0.313741	−	0.949509i	$-0.601582\pi$
$821$	−17.9793	−0.627482	−0.313741	+	0.949509i	$0.601582\pi$
$822$	−10.8991	−0.380150
$823$	3.71681	0.129560	0.0647800	−	0.997900i	$-0.479365\pi$
$823$	3.71681	0.129560	0.0647800	+	0.997900i	$0.479365\pi$
$824$	−1.30719	−0.0455382
$825$	32.7576	1.14047
$826$	−10.9966	−0.382621
$827$	38.8764	1.35186	0.675932	−	0.736964i	$-0.263741\pi$
$827$	38.8764	1.35186	0.675932	+	0.736964i	$0.263741\pi$
$828$	−32.5149	−1.12997
$829$	21.0176	0.729970	0.364985	−	0.931013i	$-0.381074\pi$
$829$	21.0176	0.729970	0.364985	+	0.931013i	$0.381074\pi$
$830$	41.0175	1.42374
$831$	−3.16148	−0.109671
$832$	2.33968	0.0811139
$833$	0.517997	0.0179475
$834$	−7.57210	−0.262200
$835$	−77.2152	−2.67214
$836$	0.695060	0.0240392
$837$	0	0
$838$	15.2903	0.528193
$839$	20.9531	0.723380	0.361690	−	0.932298i	$-0.382200\pi$
$839$	20.9531	0.723380	0.361690	+	0.932298i	$0.382200\pi$
$840$	−25.8663	−0.892472
$841$	−1.95093	−0.0672733
$842$	21.4454	0.739057
$843$	21.6708	0.746380
$844$	20.5097	0.705974
$845$	25.1874	0.866474
$846$	−31.0459	−1.06738
$847$	−20.2409	−0.695486
$848$	−2.62950	−0.0902975
$849$	66.5310	2.28334
$850$	−4.89909	−0.168038
$851$	−29.8494	−1.02322
$852$	−36.4970	−1.25037
$853$	53.2215	1.82227	0.911135	−	0.412107i	$-0.135207\pi$
$853$	53.2215	1.82227	0.911135	+	0.412107i	$0.135207\pi$
$854$	24.2031	0.828213
$855$	−8.66789	−0.296436
$856$	15.0122	0.513107
$857$	−14.1166	−0.482212	−0.241106	−	0.970499i	$-0.577510\pi$
$857$	−14.1166	−0.482212	−0.241106	+	0.970499i	$0.577510\pi$
$858$	12.3599	0.421961
$859$	−21.1882	−0.722931	−0.361465	−	0.932386i	$-0.617723\pi$
$859$	−21.1882	−0.722931	−0.361465	+	0.932386i	$0.617723\pi$
$860$	−25.5923	−0.872691
$861$	59.9563	2.04330
$862$	8.95255	0.304925
$863$	3.42261	0.116507	0.0582535	−	0.998302i	$-0.481447\pi$
$863$	3.42261	0.116507	0.0582535	+	0.998302i	$0.481447\pi$
$864$	10.4792	0.356510
$865$	67.7770	2.30449
$866$	5.18109	0.176061
$867$	−50.2478	−1.70650
$868$	0	0
$869$	−3.60659	−0.122345
$870$	53.4093	1.81074
$871$	−20.7324	−0.702489
$872$	7.06206	0.239152
$873$	−120.501	−4.07834
$874$	−2.04621	−0.0692141
$875$	−10.1232	−0.342226
$876$	24.0764	0.813467
$877$	−49.0825	−1.65740	−0.828700	−	0.559693i	$-0.810919\pi$
$877$	−49.0825	−1.65740	−0.828700	+	0.559693i	$0.810919\pi$
$878$	−2.26810	−0.0765447
$879$	−27.5601	−0.929581
$880$	−5.76196	−0.194236
$881$	26.4814	0.892180	0.446090	−	0.894988i	$-0.352816\pi$
$881$	26.4814	0.892180	0.446090	+	0.894988i	$0.352816\pi$
$882$	−4.20604	−0.141625
$883$	16.6772	0.561233	0.280616	−	0.959820i	$-0.409461\pi$
$883$	16.6772	0.561233	0.280616	+	0.959820i	$0.409461\pi$
$884$	−1.84850	−0.0621718
$885$	44.8338	1.50707
$886$	−22.1187	−0.743093
$887$	17.1609	0.576205	0.288103	−	0.957600i	$-0.406976\pi$
$887$	17.1609	0.576205	0.288103	+	0.957600i	$0.406976\pi$
$888$	18.0708	0.606417
$889$	10.5264	0.353043
$890$	−49.0107	−1.64284
$891$	22.2249	0.744561
$892$	−3.53346	−0.118309
$893$	−1.95377	−0.0653804
$894$	−43.6595	−1.46019
$895$	26.5598	0.887798
$896$	2.51880	0.0841473
$897$	−36.3868	−1.21492
$898$	−16.6105	−0.554298
$899$	0	0
$900$	39.7798	1.32599
$901$	2.07748	0.0692109
$902$	13.3558	0.444700
$903$	59.1007	1.96675
$904$	5.42985	0.180594
$905$	81.2753	2.70168
$906$	−14.5315	−0.482776
$907$	−37.5178	−1.24576	−0.622879	−	0.782318i	$-0.714037\pi$
$907$	−37.5178	−1.24576	−0.622879	+	0.782318i	$0.714037\pi$
$908$	0.561086	0.0186203
$909$	−60.6588	−2.01193
$910$	−19.7232	−0.653817
$911$	−26.0821	−0.864140	−0.432070	−	0.901840i	$-0.642217\pi$
$911$	−26.0821	−0.864140	−0.432070	+	0.901840i	$0.642217\pi$
$912$	1.23878	0.0410200
$913$	−21.1002	−0.698316
$914$	−36.3789	−1.20331
$915$	−98.6773	−3.26217
$916$	4.96919	0.164187
$917$	17.4365	0.575802
$918$	−8.27927	−0.273257
$919$	−50.7390	−1.67373	−0.836863	−	0.547413i	$-0.815613\pi$
$919$	−50.7390	−1.67373	−0.836863	+	0.547413i	$0.815613\pi$
$920$	16.9628	0.559248
$921$	−44.6187	−1.47024
$922$	3.49237	0.115015
$923$	−27.8291	−0.916007
$924$	13.3062	0.437741
$925$	36.5188	1.20073
$926$	6.06601	0.199341
$927$	−8.38589	−0.275429
$928$	−5.20087	−0.170727
$929$	−46.0097	−1.50953	−0.754764	−	0.655996i	$-0.772249\pi$
$929$	−46.0097	−1.50953	−0.754764	+	0.655996i	$0.772249\pi$
$930$	0	0
$931$	−0.264693	−0.00867495
$932$	−9.50049	−0.311199
$933$	−32.6473	−1.06882
$934$	3.06626	0.100331
$935$	4.55232	0.148877
$936$	15.0095	0.490601
$937$	35.9405	1.17413	0.587063	−	0.809542i	$-0.300284\pi$
$937$	35.9405	1.17413	0.587063	+	0.809542i	$0.300284\pi$
$938$	−22.3196	−0.728760
$939$	10.3638	0.338211
$940$	16.1965	0.528271
$941$	18.3159	0.597082	0.298541	−	0.954397i	$-0.403500\pi$
$941$	18.3159	0.597082	0.298541	+	0.954397i	$0.403500\pi$
$942$	−56.3614	−1.83635
$943$	−39.3186	−1.28039
$944$	−4.36581	−0.142095
$945$	−88.3383	−2.87365
$946$	13.1652	0.428038
$947$	−52.6611	−1.71125	−0.855627	−	0.517593i	$-0.826828\pi$
$947$	−52.6611	−1.71125	−0.855627	+	0.517593i	$0.826828\pi$
$948$	−6.42788	−0.208768
$949$	18.3584	0.595938
$950$	2.50340	0.0812212
$951$	20.0594	0.650469
$952$	−1.99002	−0.0644969
$953$	49.6076	1.60695	0.803474	−	0.595340i	$-0.202983\pi$
$953$	49.6076	1.60695	0.803474	+	0.595340i	$0.202983\pi$
$954$	−16.8688	−0.546146
$955$	−38.1246	−1.23368
$956$	−12.3614	−0.399797
$957$	−27.4748	−0.888135
$958$	5.25392	0.169747
$959$	−8.94684	−0.288909
$960$	−10.2693	−0.331440
$961$	0	0
$962$	13.7791	0.444255
$963$	96.3061	3.10342
$964$	19.9181	0.641520
$965$	33.9535	1.09300
$966$	−39.1725	−1.26035
$967$	56.5038	1.81704	0.908520	−	0.417841i	$-0.137213\pi$
$967$	56.5038	1.81704	0.908520	+	0.417841i	$0.137213\pi$
$968$	−8.03593	−0.258285
$969$	−0.978714	−0.0314408
$970$	62.8648	2.01847
$971$	−1.69640	−0.0544402	−0.0272201	−	0.999629i	$-0.508665\pi$
$971$	−1.69640	−0.0544402	−0.0272201	+	0.999629i	$0.508665\pi$
$972$	8.17277	0.262142
$973$	−6.21578	−0.199269
$974$	−6.79518	−0.217732
$975$	44.5168	1.42568
$976$	9.60897	0.307576
$977$	−20.4951	−0.655697	−0.327848	−	0.944730i	$-0.606323\pi$
$977$	−20.4951	−0.655697	−0.327848	+	0.944730i	$0.606323\pi$
$978$	−38.8995	−1.24387
$979$	25.2121	0.805782
$980$	2.19427	0.0700933
$981$	45.3045	1.44646
$982$	23.1009	0.737179
$983$	10.9679	0.349820	0.174910	−	0.984584i	$-0.444037\pi$
$983$	10.9679	0.349820	0.174910	+	0.984584i	$0.444037\pi$
$984$	23.8035	0.758828
$985$	7.83435	0.249623
$986$	4.10903	0.130858
$987$	−37.4027	−1.19054
$988$	0.944572	0.0300508
$989$	−38.7576	−1.23242
$990$	−36.9641	−1.17479
$991$	−32.5863	−1.03514	−0.517569	−	0.855642i	$-0.673163\pi$
$991$	−32.5863	−1.03514	−0.517569	+	0.855642i	$0.673163\pi$
$992$	0	0
$993$	85.9291	2.72688
$994$	−29.9597	−0.950263
$995$	39.8635	1.26376
$996$	−37.6061	−1.19159
$997$	−33.2453	−1.05289	−0.526445	−	0.850209i	$-0.676475\pi$
$997$	−33.2453	−1.05289	−0.526445	+	0.850209i	$0.676475\pi$
$998$	25.1701	0.796744
$999$	61.7153	1.95258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1922.2.a.r.1.4		4
31.4	even	5		62.2.d.a.47.1	yes	8
31.8	even	5		62.2.d.a.33.1	✓	8
31.30	odd	2		1922.2.a.n.1.1		4
93.8	odd	10		558.2.i.i.343.2		8
93.35	odd	10		558.2.i.i.109.2		8
124.35	odd	10		496.2.n.e.481.2		8
124.39	odd	10		496.2.n.e.33.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.d.a.33.1	✓	8	31.8	even	5
62.2.d.a.47.1	yes	8	31.4	even	5
496.2.n.e.33.2		8	124.39	odd	10
496.2.n.e.481.2		8	124.35	odd	10
558.2.i.i.109.2		8	93.35	odd	10
558.2.i.i.343.2		8	93.8	odd	10
1922.2.a.n.1.1		4	31.30	odd	2
1922.2.a.r.1.4		4	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:	\( N \)	\(=\)	\( 1922 = 2 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1922.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.06842 q^{3} +1.00000 q^{4} -3.34677 q^{5} +3.06842 q^{6} +2.51880 q^{7} +1.00000 q^{8} +6.41519 q^{9} -3.34677 q^{10} +1.72165 q^{11} +3.06842 q^{12} +2.33968 q^{13} +2.51880 q^{14} -10.2693 q^{15} +1.00000 q^{16} -0.790065 q^{17} +6.41519 q^{18} +0.403718 q^{19} -3.34677 q^{20} +7.72874 q^{21} +1.72165 q^{22} -5.06842 q^{23} +3.06842 q^{24} +6.20087 q^{25} +2.33968 q^{26} +10.4792 q^{27} +2.51880 q^{28} -5.20087 q^{29} -10.2693 q^{30} +1.00000 q^{32} +5.28273 q^{33} -0.790065 q^{34} -8.42985 q^{35} +6.41519 q^{36} +5.88930 q^{37} +0.403718 q^{38} +7.17912 q^{39} -3.34677 q^{40} +7.75758 q^{41} +7.72874 q^{42} +7.64688 q^{43} +1.72165 q^{44} -21.4702 q^{45} -5.06842 q^{46} -4.83944 q^{47} +3.06842 q^{48} -0.655638 q^{49} +6.20087 q^{50} -2.42425 q^{51} +2.33968 q^{52} -2.62950 q^{53} +10.4792 q^{54} -5.76196 q^{55} +2.51880 q^{56} +1.23878 q^{57} -5.20087 q^{58} -4.36581 q^{59} -10.2693 q^{60} +9.60897 q^{61} +16.1586 q^{63} +1.00000 q^{64} -7.83038 q^{65} +5.28273 q^{66} -8.86119 q^{67} -0.790065 q^{68} -15.5520 q^{69} -8.42985 q^{70} -11.8944 q^{71} +6.41519 q^{72} +7.84653 q^{73} +5.88930 q^{74} +19.0269 q^{75} +0.403718 q^{76} +4.33649 q^{77} +7.17912 q^{78} -2.09485 q^{79} -3.34677 q^{80} +12.9091 q^{81} +7.75758 q^{82} -12.2558 q^{83} +7.72874 q^{84} +2.64417 q^{85} +7.64688 q^{86} -15.9584 q^{87} +1.72165 q^{88} +14.6442 q^{89} -21.4702 q^{90} +5.89319 q^{91} -5.06842 q^{92} -4.83944 q^{94} -1.35115 q^{95} +3.06842 q^{96} -18.7837 q^{97} -0.655638 q^{98} +11.0447 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} - 2 q^{5} + 3 q^{6} - 4 q^{7} + 4 q^{8} + 5 q^{9} - 2 q^{10} + 9 q^{11} + 3 q^{12} + 7 q^{13} - 4 q^{14} - 7 q^{15} + 4 q^{16} + 4 q^{17} + 5 q^{18} - 7 q^{19} - 2 q^{20}+ \cdots + 7 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 - 2 * q^5 + 3 * q^6 - 4 * q^7 + 4 * q^8 + 5 * q^9 - 2 * q^10 + 9 * q^11 + 3 * q^12 + 7 * q^13 - 4 * q^14 - 7 * q^15 + 4 * q^16 + 4 * q^17 + 5 * q^18 - 7 * q^19 - 2 * q^20 + 24 * q^21 + 9 * q^22 - 11 * q^23 + 3 * q^24 + 7 * q^26 + 15 * q^27 - 4 * q^28 + 4 * q^29 - 7 * q^30 + 4 * q^32 + 16 * q^33 + 4 * q^34 - 9 * q^35 + 5 * q^36 + 26 * q^37 - 7 * q^38 + 17 * q^39 - 2 * q^40 + 2 * q^41 + 24 * q^42 + 4 * q^43 + 9 * q^44 - 27 * q^45 - 11 * q^46 - 10 * q^47 + 3 * q^48 + 30 * q^49 - 21 * q^51 + 7 * q^52 + 6 * q^53 + 15 * q^54 + 9 * q^55 - 4 * q^56 - 10 * q^57 + 4 * q^58 + q^59 - 7 * q^60 + 2 * q^61 + 33 * q^63 + 4 * q^64 + 10 * q^65 + 16 * q^66 - 13 * q^67 + 4 * q^68 - 23 * q^69 - 9 * q^70 + 5 * q^72 + 13 * q^73 + 26 * q^74 + 13 * q^75 - 7 * q^76 + 7 * q^77 + 17 * q^78 - 21 * q^79 - 2 * q^80 + 2 * q^82 + 14 * q^83 + 24 * q^84 - 10 * q^85 + 4 * q^86 - 10 * q^87 + 9 * q^88 + 38 * q^89 - 27 * q^90 + 9 * q^91 - 11 * q^92 - 10 * q^94 + 9 * q^95 + 3 * q^96 - 30 * q^97 + 30 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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