LMFDB - Embedded newform 1849.2.a.q.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 27 x^{18} + 300 x^{16} - 1775 x^{14} + 6037 x^{12} - 11859 x^{10} + 12809 x^{8} - 6823 x^{6} + \cdots + 1 $ x^20 - 27x^18 + 300x^16 - 1775x^14 + 6037x^12 - 11859x^10 + 12809x^8 - 6823x^6 + 1500x^4 - 75*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.200809$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.200809 q^{2} +2.02007 q^{3} -1.95968 q^{4} +1.96610 q^{5} -0.405649 q^{6} -2.70408 q^{7} +0.795139 q^{8} +1.08069 q^{9} +O(q^{10})$	\(q-0.200809 q^{2} +2.02007 q^{3} -1.95968 q^{4} +1.96610 q^{5} -0.405649 q^{6} -2.70408 q^{7} +0.795139 q^{8} +1.08069 q^{9} -0.394811 q^{10} -4.18709 q^{11} -3.95869 q^{12} +1.98194 q^{13} +0.543004 q^{14} +3.97167 q^{15} +3.75968 q^{16} +3.68593 q^{17} -0.217013 q^{18} -6.87049 q^{19} -3.85292 q^{20} -5.46245 q^{21} +0.840805 q^{22} -7.32184 q^{23} +1.60624 q^{24} -1.13445 q^{25} -0.397991 q^{26} -3.87714 q^{27} +5.29913 q^{28} +1.13262 q^{29} -0.797546 q^{30} +8.28096 q^{31} -2.34525 q^{32} -8.45822 q^{33} -0.740168 q^{34} -5.31650 q^{35} -2.11781 q^{36} -3.58706 q^{37} +1.37966 q^{38} +4.00366 q^{39} +1.56332 q^{40} -7.37661 q^{41} +1.09691 q^{42} +8.20533 q^{44} +2.12475 q^{45} +1.47029 q^{46} +6.62472 q^{47} +7.59483 q^{48} +0.312065 q^{49} +0.227807 q^{50} +7.44585 q^{51} -3.88396 q^{52} -4.56449 q^{53} +0.778564 q^{54} -8.23223 q^{55} -2.15012 q^{56} -13.8789 q^{57} -0.227440 q^{58} -10.4600 q^{59} -7.78318 q^{60} -9.53277 q^{61} -1.66289 q^{62} -2.92229 q^{63} -7.04841 q^{64} +3.89669 q^{65} +1.69849 q^{66} -4.05207 q^{67} -7.22323 q^{68} -14.7907 q^{69} +1.06760 q^{70} +5.94128 q^{71} +0.859302 q^{72} +3.82961 q^{73} +0.720315 q^{74} -2.29167 q^{75} +13.4639 q^{76} +11.3222 q^{77} -0.803972 q^{78} -8.12179 q^{79} +7.39191 q^{80} -11.0742 q^{81} +1.48129 q^{82} -5.00889 q^{83} +10.7046 q^{84} +7.24691 q^{85} +2.28797 q^{87} -3.32931 q^{88} -1.50233 q^{89} -0.426670 q^{90} -5.35933 q^{91} +14.3484 q^{92} +16.7281 q^{93} -1.33030 q^{94} -13.5081 q^{95} -4.73759 q^{96} +3.54914 q^{97} -0.0626654 q^{98} -4.52496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9}+O(q^{10}) $ 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9	$ 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9} + 12 q^{10} - 20 q^{11} + 6 q^{13} - 34 q^{14} - 34 q^{15} + 14 q^{16} - 8 q^{17} + 12 q^{21} - 46 q^{23} + 2 q^{24} + 20 q^{25} - 38 q^{31} - 76 q^{35} - 46 q^{36} - 68 q^{38} - 64 q^{40} - 56 q^{41} - 58 q^{44} - 24 q^{47} - 20 q^{49} - 20 q^{52} - 42 q^{53} + 66 q^{54} - 46 q^{56} + 2 q^{57} + 12 q^{58} - 90 q^{59} + 18 q^{60} - 28 q^{64} + 76 q^{66} - 62 q^{67} - 54 q^{68} + 24 q^{74} - 36 q^{78} - 10 q^{79} - 48 q^{81} - 68 q^{83} + 70 q^{84} - 12 q^{87} + 58 q^{90} - 8 q^{92} - 42 q^{95} - 22 q^{96} - 44 q^{97} - 38 q^{99}+O(q^{100}) $ 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9 + 12 * q^10 - 20 * q^11 + 6 * q^13 - 34 * q^14 - 34 * q^15 + 14 * q^16 - 8 * q^17 + 12 * q^21 - 46 * q^23 + 2 * q^24 + 20 * q^25 - 38 * q^31 - 76 * q^35 - 46 * q^36 - 68 * q^38 - 64 * q^40 - 56 * q^41 - 58 * q^44 - 24 * q^47 - 20 * q^49 - 20 * q^52 - 42 * q^53 + 66 * q^54 - 46 * q^56 + 2 * q^57 + 12 * q^58 - 90 * q^59 + 18 * q^60 - 28 * q^64 + 76 * q^66 - 62 * q^67 - 54 * q^68 + 24 * q^74 - 36 * q^78 - 10 * q^79 - 48 * q^81 - 68 * q^83 + 70 * q^84 - 12 * q^87 + 58 * q^90 - 8 * q^92 - 42 * q^95 - 22 * q^96 - 44 * q^97 - 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.200809	−0.141993	−0.0709967	−	0.997477i	$-0.522618\pi$
$2$	−0.200809	−0.141993	−0.0709967	+	0.997477i	$0.522618\pi$
$3$	2.02007	1.16629	0.583145	−	0.812368i	$-0.301822\pi$
$3$	2.02007	1.16629	0.583145	+	0.812368i	$0.301822\pi$
$4$	−1.95968	−0.979838
$5$	1.96610	0.879267	0.439633	−	0.898177i	$-0.355108\pi$
$5$	1.96610	0.879267	0.439633	+	0.898177i	$0.355108\pi$
$6$	−0.405649	−0.165605
$7$	−2.70408	−1.02205	−0.511024	−	0.859567i	$-0.670734\pi$
$7$	−2.70408	−1.02205	−0.511024	+	0.859567i	$0.670734\pi$
$8$	0.795139	0.281124
$9$	1.08069	0.360232
$10$	−0.394811	−0.124850
$11$	−4.18709	−1.26245	−0.631227	−	0.775598i	$-0.717448\pi$
$11$	−4.18709	−1.26245	−0.631227	+	0.775598i	$0.717448\pi$
$12$	−3.95869	−1.14277
$13$	1.98194	0.549691	0.274846	−	0.961488i	$-0.411373\pi$
$13$	1.98194	0.549691	0.274846	+	0.961488i	$0.411373\pi$
$14$	0.543004	0.145124
$15$	3.97167	1.02548
$16$	3.75968	0.939920
$17$	3.68593	0.893969	0.446985	−	0.894542i	$-0.352498\pi$
$17$	3.68593	0.893969	0.446985	+	0.894542i	$0.352498\pi$
$18$	−0.217013	−0.0511505
$19$	−6.87049	−1.57620	−0.788100	−	0.615547i	$-0.788935\pi$
$19$	−6.87049	−1.57620	−0.788100	+	0.615547i	$0.788935\pi$
$20$	−3.85292	−0.861539
$21$	−5.46245	−1.19200
$22$	0.840805	0.179260
$23$	−7.32184	−1.52671	−0.763355	−	0.645979i	$-0.776449\pi$
$23$	−7.32184	−1.52671	−0.763355	+	0.645979i	$0.776449\pi$
$24$	1.60624	0.327872
$25$	−1.13445	−0.226890
$26$	−0.397991	−0.0780525
$27$	−3.87714	−0.746155
$28$	5.29913	1.00144
$29$	1.13262	0.210322	0.105161	−	0.994455i	$-0.466464\pi$
$29$	1.13262	0.210322	0.105161	+	0.994455i	$0.466464\pi$
$30$	−0.797546	−0.145611
$31$	8.28096	1.48730	0.743652	−	0.668567i	$-0.233092\pi$
$31$	8.28096	1.48730	0.743652	+	0.668567i	$0.233092\pi$
$32$	−2.34525	−0.414586
$33$	−8.45822	−1.47239
$34$	−0.740168	−0.126938
$35$	−5.31650	−0.898652
$36$	−2.11781	−0.352969
$37$	−3.58706	−0.589710	−0.294855	−	0.955542i	$-0.595271\pi$
$37$	−3.58706	−0.589710	−0.294855	+	0.955542i	$0.595271\pi$
$38$	1.37966	0.223810
$39$	4.00366	0.641099
$40$	1.56332	0.247183
$41$	−7.37661	−1.15203	−0.576016	−	0.817438i	$-0.695394\pi$
$41$	−7.37661	−1.15203	−0.576016	+	0.817438i	$0.695394\pi$
$42$	1.09691	0.169257
$43$	0	0
$43$	0	0
$44$	8.20533	1.23700
$45$	2.12475	0.316740
$46$	1.47029	0.216783
$47$	6.62472	0.966315	0.483158	−	0.875533i	$-0.339490\pi$
$47$	6.62472	0.966315	0.483158	+	0.875533i	$0.339490\pi$
$48$	7.59483	1.09622
$49$	0.312065	0.0445807
$50$	0.227807	0.0322168
$51$	7.44585	1.04263
$52$	−3.88396	−0.538608
$53$	−4.56449	−0.626982	−0.313491	−	0.949591i	$-0.601498\pi$
$53$	−4.56449	−0.626982	−0.313491	+	0.949591i	$0.601498\pi$
$54$	0.778564	0.105949
$55$	−8.23223	−1.11003
$56$	−2.15012	−0.287322
$57$	−13.8789	−1.83831
$58$	−0.227440	−0.0298643
$59$	−10.4600	−1.36177	−0.680885	−	0.732390i	$-0.738405\pi$
$59$	−10.4600	−1.36177	−0.680885	+	0.732390i	$0.738405\pi$
$60$	−7.78318	−1.00480
$61$	−9.53277	−1.22055	−0.610273	−	0.792191i	$-0.708940\pi$
$61$	−9.53277	−1.22055	−0.610273	+	0.792191i	$0.708940\pi$
$62$	−1.66289	−0.211187
$63$	−2.92229	−0.368174
$64$	−7.04841	−0.881052
$65$	3.89669	0.483325
$66$	1.69849	0.209069
$67$	−4.05207	−0.495040	−0.247520	−	0.968883i	$-0.579616\pi$
$67$	−4.05207	−0.495040	−0.247520	+	0.968883i	$0.579616\pi$
$68$	−7.22323	−0.875945
$69$	−14.7907	−1.78059
$70$	1.06760	0.127603
$71$	5.94128	0.705101	0.352550	−	0.935793i	$-0.385315\pi$
$71$	5.94128	0.705101	0.352550	+	0.935793i	$0.385315\pi$
$72$	0.859302	0.101270
$73$	3.82961	0.448222	0.224111	−	0.974564i	$-0.428052\pi$
$73$	3.82961	0.448222	0.224111	+	0.974564i	$0.428052\pi$
$74$	0.720315	0.0837349
$75$	−2.29167	−0.264619
$76$	13.4639	1.54442
$77$	11.3222	1.29029
$78$	−0.803972	−0.0910319
$79$	−8.12179	−0.913773	−0.456886	−	0.889525i	$-0.651035\pi$
$79$	−8.12179	−0.913773	−0.456886	+	0.889525i	$0.651035\pi$
$80$	7.39191	0.826441
$81$	−11.0742	−1.23046
$82$	1.48129	0.163581
$83$	−5.00889	−0.549797	−0.274898	−	0.961473i	$-0.588644\pi$
$83$	−5.00889	−0.549797	−0.274898	+	0.961473i	$0.588644\pi$
$84$	10.7046	1.16797
$85$	7.24691	0.786038
$86$	0	0
$87$	2.28797	0.245296
$88$	−3.32931	−0.354906
$89$	−1.50233	−0.159247	−0.0796235	−	0.996825i	$-0.525372\pi$
$89$	−1.50233	−0.159247	−0.0796235	+	0.996825i	$0.525372\pi$
$90$	−0.426670	−0.0449750
$91$	−5.35933	−0.561810
$92$	14.3484	1.49593
$93$	16.7281	1.73463
$94$	−1.33030	−0.137210
$95$	−13.5081	−1.38590
$96$	−4.73759	−0.483528
$97$	3.54914	0.360361	0.180180	−	0.983634i	$-0.442332\pi$
$97$	3.54914	0.360361	0.180180	+	0.983634i	$0.442332\pi$
$98$	−0.0626654	−0.00633017
$99$	−4.52496	−0.454776
$100$	2.22315	0.222315
$101$	12.5088	1.24467	0.622335	−	0.782751i	$-0.286184\pi$
$101$	12.5088	1.24467	0.622335	+	0.782751i	$0.286184\pi$
$102$	−1.49519	−0.148046
$103$	−7.88480	−0.776912	−0.388456	−	0.921467i	$-0.626991\pi$
$103$	−7.88480	−0.776912	−0.388456	+	0.921467i	$0.626991\pi$
$104$	1.57592	0.154531
$105$	−10.7397	−1.04809
$106$	0.916592	0.0890272
$107$	4.62033	0.446664	0.223332	−	0.974742i	$-0.428307\pi$
$107$	4.62033	0.446664	0.223332	+	0.974742i	$0.428307\pi$
$108$	7.59793	0.731111
$109$	8.41098	0.805625	0.402813	−	0.915282i	$-0.368033\pi$
$109$	8.41098	0.805625	0.402813	+	0.915282i	$0.368033\pi$
$110$	1.65311	0.157618
$111$	−7.24613	−0.687772
$112$	−10.1665	−0.960643
$113$	21.1956	1.99391	0.996955	−	0.0779750i	$-0.0248454\pi$
$113$	21.1956	1.99391	0.996955	+	0.0779750i	$0.0248454\pi$
$114$	2.78701	0.261027
$115$	−14.3955	−1.34239
$116$	−2.21956	−0.206081
$117$	2.14187	0.198016
$118$	2.10045	0.193362
$119$	−9.96706	−0.913679
$120$	3.15803	0.288287
$121$	6.53169	0.593790
$122$	1.91427	0.173309
$123$	−14.9013	−1.34360
$124$	−16.2280	−1.45732
$125$	−12.0609	−1.07876
$126$	0.586822	0.0522783
$127$	−17.3458	−1.53919	−0.769596	−	0.638531i	$-0.779542\pi$
$127$	−17.3458	−1.53919	−0.769596	+	0.638531i	$0.779542\pi$
$128$	6.10589	0.539690
$129$	0	0
$130$	−0.782491	−0.0686290
$131$	10.9622	0.957773	0.478887	−	0.877877i	$-0.341040\pi$
$131$	10.9622	0.957773	0.478887	+	0.877877i	$0.341040\pi$
$132$	16.5754	1.44270
$133$	18.5784	1.61095
$134$	0.813693	0.0702923
$135$	−7.62284	−0.656070
$136$	2.93083	0.251316
$137$	4.17652	0.356824	0.178412	−	0.983956i	$-0.442904\pi$
$137$	4.17652	0.356824	0.178412	+	0.983956i	$0.442904\pi$
$138$	2.97010	0.252831
$139$	1.08410	0.0919520	0.0459760	−	0.998943i	$-0.485360\pi$
$139$	1.08410	0.0919520	0.0459760	+	0.998943i	$0.485360\pi$
$140$	10.4186	0.880534
$141$	13.3824	1.12700
$142$	−1.19306	−0.100120
$143$	−8.29855	−0.693960
$144$	4.06307	0.338589
$145$	2.22684	0.184929
$146$	−0.769021	−0.0636446
$147$	0.630394	0.0519940
$148$	7.02948	0.577820
$149$	0.534290	0.0437707	0.0218854	−	0.999760i	$-0.493033\pi$
$149$	0.534290	0.0437707	0.0218854	+	0.999760i	$0.493033\pi$
$150$	0.460188	0.0375742
$151$	9.08456	0.739291	0.369646	−	0.929173i	$-0.379479\pi$
$151$	9.08456	0.739291	0.369646	+	0.929173i	$0.379479\pi$
$152$	−5.46300	−0.443107
$153$	3.98337	0.322036
$154$	−2.27361	−0.183212
$155$	16.2812	1.30774
$156$	−7.84588	−0.628173
$157$	8.78890	0.701430	0.350715	−	0.936482i	$-0.385939\pi$
$157$	8.78890	0.701430	0.350715	+	0.936482i	$0.385939\pi$
$158$	1.63093	0.129750
$159$	−9.22061	−0.731242
$160$	−4.61101	−0.364532
$161$	19.7989	1.56037
$162$	2.22380	0.174718
$163$	−5.87323	−0.460027	−0.230013	−	0.973187i	$-0.573877\pi$
$163$	−5.87323	−0.460027	−0.230013	+	0.973187i	$0.573877\pi$
$164$	14.4558	1.12881
$165$	−16.6297	−1.29462
$166$	1.00583	0.0780675
$167$	−3.35443	−0.259574	−0.129787	−	0.991542i	$-0.541429\pi$
$167$	−3.35443	−0.259574	−0.129787	+	0.991542i	$0.541429\pi$
$168$	−4.34340	−0.335101
$169$	−9.07191	−0.697840
$170$	−1.45524	−0.111612
$171$	−7.42491	−0.567797
$172$	0	0
$173$	−5.18034	−0.393854	−0.196927	−	0.980418i	$-0.563096\pi$
$173$	−5.18034	−0.393854	−0.196927	+	0.980418i	$0.563096\pi$
$174$	−0.459445	−0.0348305
$175$	3.06764	0.231892
$176$	−15.7421	−1.18661
$177$	−21.1299	−1.58822
$178$	0.301682	0.0226120
$179$	−12.0797	−0.902876	−0.451438	−	0.892302i	$-0.649089\pi$
$179$	−12.0797	−0.902876	−0.451438	+	0.892302i	$0.649089\pi$
$180$	−4.16383	−0.310354
$181$	5.57308	0.414244	0.207122	−	0.978315i	$-0.433590\pi$
$181$	5.57308	0.414244	0.207122	+	0.978315i	$0.433590\pi$
$182$	1.07620	0.0797734
$183$	−19.2569	−1.42351
$184$	−5.82188	−0.429195
$185$	−7.05253	−0.518512
$186$	−3.35916	−0.246306
$187$	−15.4333	−1.12860
$188$	−12.9823	−0.946832
$189$	10.4841	0.762606
$190$	2.71254	0.196789
$191$	−5.76570	−0.417191	−0.208596	−	0.978002i	$-0.566889\pi$
$191$	−5.76570	−0.417191	−0.208596	+	0.978002i	$0.566889\pi$
$192$	−14.2383	−1.02756
$193$	−17.1993	−1.23804	−0.619018	−	0.785377i	$-0.712469\pi$
$193$	−17.1993	−1.23804	−0.619018	+	0.785377i	$0.712469\pi$
$194$	−0.712700	−0.0511689
$195$	7.87160	0.563697
$196$	−0.611546	−0.0436819
$197$	10.6238	0.756915	0.378458	−	0.925619i	$-0.376455\pi$
$197$	10.6238	0.756915	0.378458	+	0.925619i	$0.376455\pi$
$198$	0.908653	0.0645752
$199$	−1.94432	−0.137829	−0.0689146	−	0.997623i	$-0.521954\pi$
$199$	−1.94432	−0.137829	−0.0689146	+	0.997623i	$0.521954\pi$
$200$	−0.902044	−0.0637841
$201$	−8.18548	−0.577359
$202$	−2.51188	−0.176735
$203$	−3.06269	−0.214959
$204$	−14.5914	−1.02161
$205$	−14.5032	−1.01294
$206$	1.58334	0.110316
$207$	−7.91268	−0.549969
$208$	7.45146	0.516666
$209$	28.7674	1.98988
$210$	2.15663	0.148822
$211$	6.80054	0.468169	0.234084	−	0.972216i	$-0.424791\pi$
$211$	6.80054	0.468169	0.234084	+	0.972216i	$0.424791\pi$
$212$	8.94493	0.614340
$213$	12.0018	0.822352
$214$	−0.927804	−0.0634234
$215$	0	0
$216$	−3.08286	−0.209762
$217$	−22.3924	−1.52010
$218$	−1.68900	−0.114393
$219$	7.73610	0.522757
$220$	16.1325	1.08765
$221$	7.30529	0.491407
$222$	1.45509	0.0976591
$223$	2.66301	0.178328	0.0891640	−	0.996017i	$-0.471580\pi$
$223$	2.66301	0.178328	0.0891640	+	0.996017i	$0.471580\pi$
$224$	6.34176	0.423727
$225$	−1.22599	−0.0817328
$226$	−4.25626	−0.283122
$227$	−14.1441	−0.938775	−0.469388	−	0.882992i	$-0.655525\pi$
$227$	−14.1441	−0.938775	−0.469388	+	0.882992i	$0.655525\pi$
$228$	27.1981	1.80124
$229$	18.2842	1.20825	0.604126	−	0.796889i	$-0.293522\pi$
$229$	18.2842	1.20825	0.604126	+	0.796889i	$0.293522\pi$
$230$	2.89074	0.190610
$231$	22.8717	1.50485
$232$	0.900589	0.0591265
$233$	−12.1765	−0.797706	−0.398853	−	0.917015i	$-0.630592\pi$
$233$	−12.1765	−0.797706	−0.398853	+	0.917015i	$0.630592\pi$
$234$	−0.430107	−0.0281170
$235$	13.0249	0.849649
$236$	20.4981	1.33431
$237$	−16.4066	−1.06572
$238$	2.00148	0.129736
$239$	8.92289	0.577174	0.288587	−	0.957454i	$-0.406815\pi$
$239$	8.92289	0.577174	0.288587	+	0.957454i	$0.406815\pi$
$240$	14.9322	0.963869
$241$	8.99535	0.579442	0.289721	−	0.957111i	$-0.406438\pi$
$241$	8.99535	0.579442	0.289721	+	0.957111i	$0.406438\pi$
$242$	−1.31162	−0.0843143
$243$	−10.7392	−0.688923
$244$	18.6811	1.19594
$245$	0.613551	0.0391983
$246$	2.99231	0.190783
$247$	−13.6169	−0.866423
$248$	6.58451	0.418117
$249$	−10.1183	−0.641222
$250$	2.42195	0.153177
$251$	15.9213	1.00494	0.502472	−	0.864593i	$-0.332424\pi$
$251$	15.9213	1.00494	0.502472	+	0.864593i	$0.332424\pi$
$252$	5.72674	0.360751
$253$	30.6572	1.92740
$254$	3.48319	0.218555
$255$	14.6393	0.916748
$256$	12.8707	0.804419
$257$	−22.7299	−1.41785	−0.708927	−	0.705282i	$-0.750820\pi$
$257$	−22.7299	−1.41785	−0.708927	+	0.705282i	$0.750820\pi$
$258$	0	0
$259$	9.69972	0.602711
$260$	−7.63626	−0.473580
$261$	1.22401	0.0757646
$262$	−2.20131	−0.135998
$263$	17.6787	1.09011	0.545057	−	0.838399i	$-0.316508\pi$
$263$	17.6787	1.09011	0.545057	+	0.838399i	$0.316508\pi$
$264$	−6.72546	−0.413923
$265$	−8.97426	−0.551284
$266$	−3.73071	−0.228744
$267$	−3.03482	−0.185728
$268$	7.94075	0.485058
$269$	6.25327	0.381268	0.190634	−	0.981661i	$-0.438946\pi$
$269$	6.25327	0.381268	0.190634	+	0.981661i	$0.438946\pi$
$270$	1.53074	0.0931576
$271$	−2.75249	−0.167202	−0.0836010	−	0.996499i	$-0.526642\pi$
$271$	−2.75249	−0.167202	−0.0836010	+	0.996499i	$0.526642\pi$
$272$	13.8579	0.840260
$273$	−10.8262	−0.655234
$274$	−0.838683	−0.0506667
$275$	4.75003	0.286438
$276$	28.9849	1.74469
$277$	31.5010	1.89271	0.946355	−	0.323128i	$-0.104735\pi$
$277$	31.5010	1.89271	0.946355	+	0.323128i	$0.104735\pi$
$278$	−0.217697	−0.0130566
$279$	8.94919	0.535774
$280$	−4.22735	−0.252633
$281$	−28.7207	−1.71333	−0.856666	−	0.515872i	$-0.827468\pi$
$281$	−28.7207	−1.71333	−0.856666	+	0.515872i	$0.827468\pi$
$282$	−2.68731	−0.160027
$283$	1.64248	0.0976351	0.0488175	−	0.998808i	$-0.484455\pi$
$283$	1.64248	0.0976351	0.0488175	+	0.998808i	$0.484455\pi$
$284$	−11.6430	−0.690884
$285$	−27.2873	−1.61636
$286$	1.66642	0.0985377
$287$	19.9470	1.17743
$288$	−2.53450	−0.149347
$289$	−3.41392	−0.200819
$290$	−0.447170	−0.0262587
$291$	7.16953	0.420285
$292$	−7.50480	−0.439185
$293$	−9.50663	−0.555383	−0.277691	−	0.960670i	$-0.589569\pi$
$293$	−9.50663	−0.555383	−0.277691	+	0.960670i	$0.589569\pi$
$294$	−0.126589	−0.00738281
$295$	−20.5653	−1.19736
$296$	−2.85221	−0.165782
$297$	16.2339	0.941987
$298$	−0.107290	−0.00621516
$299$	−14.5115	−0.839219
$300$	4.49093	0.259284
$301$	0	0
$302$	−1.82426	−0.104974
$303$	25.2687	1.45165
$304$	−25.8309	−1.48150
$305$	−18.7424	−1.07319
$306$	−0.799896	−0.0457270
$307$	−31.5148	−1.79865	−0.899323	−	0.437284i	$-0.855940\pi$
$307$	−31.5148	−1.79865	−0.899323	+	0.437284i	$0.855940\pi$
$308$	−22.1879	−1.26427
$309$	−15.9279	−0.906105
$310$	−3.26941	−0.185690
$311$	6.63344	0.376148	0.188074	−	0.982155i	$-0.439776\pi$
$311$	6.63344	0.376148	0.188074	+	0.982155i	$0.439776\pi$
$312$	3.18347	0.180228
$313$	12.6012	0.712262	0.356131	−	0.934436i	$-0.384096\pi$
$313$	12.6012	0.712262	0.356131	+	0.934436i	$0.384096\pi$
$314$	−1.76489	−0.0995985
$315$	−5.74551	−0.323723
$316$	15.9161	0.895349
$317$	5.60978	0.315076	0.157538	−	0.987513i	$-0.449644\pi$
$317$	5.60978	0.315076	0.157538	+	0.987513i	$0.449644\pi$
$318$	1.85158	0.103832
$319$	−4.74237	−0.265522
$320$	−13.8579	−0.774680
$321$	9.33340	0.520940
$322$	−3.97579	−0.221562
$323$	−25.3242	−1.40907
$324$	21.7018	1.20566
$325$	−2.24841	−0.124719
$326$	1.17940	0.0653208
$327$	16.9908	0.939593
$328$	−5.86543	−0.323864
$329$	−17.9138	−0.987620
$330$	3.33940	0.183828
$331$	26.4135	1.45182	0.725909	−	0.687791i	$-0.241419\pi$
$331$	26.4135	1.45182	0.725909	+	0.687791i	$0.241419\pi$
$332$	9.81580	0.538712
$333$	−3.87652	−0.212432
$334$	0.673600	0.0368578
$335$	−7.96678	−0.435272
$336$	−20.5370	−1.12039
$337$	4.24232	0.231094	0.115547	−	0.993302i	$-0.463138\pi$
$337$	4.24232	0.231094	0.115547	+	0.993302i	$0.463138\pi$
$338$	1.82172	0.0990886
$339$	42.8166	2.32548
$340$	−14.2016	−0.770190
$341$	−34.6731	−1.87765
$342$	1.49099	0.0806234
$343$	18.0847	0.976484
$344$	0	0
$345$	−29.0799	−1.56561
$346$	1.04026	0.0559247
$347$	−28.3537	−1.52211	−0.761054	−	0.648688i	$-0.775318\pi$
$347$	−28.3537	−1.52211	−0.761054	+	0.648688i	$0.775318\pi$
$348$	−4.48368	−0.240351
$349$	−19.9393	−1.06733	−0.533663	−	0.845697i	$-0.679185\pi$
$349$	−19.9393	−1.06733	−0.533663	+	0.845697i	$0.679185\pi$
$350$	−0.616010	−0.0329271
$351$	−7.68425	−0.410155
$352$	9.81978	0.523396
$353$	33.1133	1.76244	0.881221	−	0.472704i	$-0.156722\pi$
$353$	33.1133	1.76244	0.881221	+	0.472704i	$0.156722\pi$
$354$	4.24307	0.225517
$355$	11.6812	0.619972
$356$	2.94409	0.156036
$357$	−20.1342	−1.06561
$358$	2.42570	0.128202
$359$	−33.6427	−1.77559	−0.887797	−	0.460235i	$-0.847765\pi$
$359$	−33.6427	−1.77559	−0.887797	+	0.460235i	$0.847765\pi$
$360$	1.68947	0.0890431
$361$	28.2037	1.48441
$362$	−1.11912	−0.0588199
$363$	13.1945	0.692531
$364$	10.5025	0.550483
$365$	7.52941	0.394107
$366$	3.86696	0.202129
$367$	−14.9253	−0.779092	−0.389546	−	0.921007i	$-0.627368\pi$
$367$	−14.9253	−0.779092	−0.389546	+	0.921007i	$0.627368\pi$
$368$	−27.5278	−1.43499
$369$	−7.97186	−0.414999
$370$	1.41621	0.0736253
$371$	12.3428	0.640805
$372$	−32.7817	−1.69965
$373$	−5.06377	−0.262192	−0.131096	−	0.991370i	$-0.541850\pi$
$373$	−5.06377	−0.262192	−0.131096	+	0.991370i	$0.541850\pi$
$374$	3.09915	0.160253
$375$	−24.3640	−1.25815
$376$	5.26757	0.271654
$377$	2.24478	0.115612
$378$	−2.10530	−0.108285
$379$	−12.0533	−0.619136	−0.309568	−	0.950877i	$-0.600185\pi$
$379$	−12.0533	−0.619136	−0.309568	+	0.950877i	$0.600185\pi$
$380$	26.4715	1.35796
$381$	−35.0398	−1.79514
$382$	1.15780	0.0592384
$383$	7.03009	0.359221	0.179610	−	0.983738i	$-0.442516\pi$
$383$	7.03009	0.359221	0.179610	+	0.983738i	$0.442516\pi$
$384$	12.3344	0.629435
$385$	22.2606	1.13451
$386$	3.45378	0.175793
$387$	0	0
$388$	−6.95517	−0.353095
$389$	15.7298	0.797534	0.398767	−	0.917052i	$-0.369438\pi$
$389$	15.7298	0.797534	0.398767	+	0.917052i	$0.369438\pi$
$390$	−1.58069	−0.0800413
$391$	−26.9878	−1.36483
$392$	0.248135	0.0125327
$393$	22.1445	1.11704
$394$	−2.13336	−0.107477
$395$	−15.9683	−0.803450
$396$	8.86746	0.445607
$397$	−6.95008	−0.348814	−0.174407	−	0.984674i	$-0.555801\pi$
$397$	−6.95008	−0.348814	−0.174407	+	0.984674i	$0.555801\pi$
$398$	0.390437	0.0195708
$399$	37.5297	1.87883
$400$	−4.26516	−0.213258
$401$	31.6810	1.58207	0.791036	−	0.611770i	$-0.209542\pi$
$401$	31.6810	1.58207	0.791036	+	0.611770i	$0.209542\pi$
$402$	1.64372	0.0819812
$403$	16.4124	0.817558
$404$	−24.5132	−1.21958
$405$	−21.7730	−1.08191
$406$	0.615017	0.0305228
$407$	15.0193	0.744481
$408$	5.92048	0.293108
$409$	29.2596	1.44679	0.723396	−	0.690433i	$-0.242580\pi$
$409$	29.2596	1.44679	0.723396	+	0.690433i	$0.242580\pi$
$410$	2.91236	0.143831
$411$	8.43688	0.416161
$412$	15.4516	0.761248
$413$	28.2846	1.39179
$414$	1.58894	0.0780920
$415$	−9.84798	−0.483418
$416$	−4.64815	−0.227895
$417$	2.18996	0.107243
$418$	−5.77674	−0.282550
$419$	13.8182	0.675062	0.337531	−	0.941314i	$-0.390408\pi$
$419$	13.8182	0.675062	0.337531	+	0.941314i	$0.390408\pi$
$420$	21.0464	1.02696
$421$	12.0246	0.586043	0.293021	−	0.956106i	$-0.405339\pi$
$421$	12.0246	0.586043	0.293021	+	0.956106i	$0.405339\pi$
$422$	−1.36561	−0.0664769
$423$	7.15931	0.348097
$424$	−3.62941	−0.176260
$425$	−4.18150	−0.202832
$426$	−2.41008	−0.116769
$427$	25.7774	1.24746
$428$	−9.05435	−0.437658
$429$	−16.7637	−0.809358
$430$	0	0
$431$	21.8068	1.05039	0.525197	−	0.850981i	$-0.323992\pi$
$431$	21.8068	1.05039	0.525197	+	0.850981i	$0.323992\pi$
$432$	−14.5768	−0.701326
$433$	−14.1746	−0.681189	−0.340594	−	0.940210i	$-0.610628\pi$
$433$	−14.1746	−0.681189	−0.340594	+	0.940210i	$0.610628\pi$
$434$	4.49660	0.215844
$435$	4.49838	0.215681
$436$	−16.4828	−0.789382
$437$	50.3047	2.40640
$438$	−1.55348	−0.0742281
$439$	−24.0711	−1.14885	−0.574425	−	0.818557i	$-0.694774\pi$
$439$	−24.0711	−1.14885	−0.574425	+	0.818557i	$0.694774\pi$
$440$	−6.54577	−0.312057
$441$	0.337247	0.0160594
$442$	−1.46697	−0.0697766
$443$	2.60907	0.123960	0.0619802	−	0.998077i	$-0.480258\pi$
$443$	2.60907	0.123960	0.0619802	+	0.998077i	$0.480258\pi$
$444$	14.2001	0.673905
$445$	−2.95374	−0.140021
$446$	−0.534755	−0.0253214
$447$	1.07930	0.0510494
$448$	19.0595	0.900476
$449$	2.99761	0.141466	0.0707330	−	0.997495i	$-0.477466\pi$
$449$	2.99761	0.141466	0.0707330	+	0.997495i	$0.477466\pi$
$450$	0.246190	0.0116055
$451$	30.8865	1.45439
$452$	−41.5364	−1.95371
$453$	18.3515	0.862228
$454$	2.84026	0.133300
$455$	−10.5370	−0.493981
$456$	−11.0356	−0.516792
$457$	−6.34150	−0.296643	−0.148322	−	0.988939i	$-0.547387\pi$
$457$	−6.34150	−0.296643	−0.148322	+	0.988939i	$0.547387\pi$
$458$	−3.67163	−0.171564
$459$	−14.2909	−0.667040
$460$	28.2105	1.31532
$461$	−17.2440	−0.803135	−0.401568	−	0.915829i	$-0.631535\pi$
$461$	−17.2440	−0.803135	−0.401568	+	0.915829i	$0.631535\pi$
$462$	−4.59285	−0.213679
$463$	27.6201	1.28361	0.641807	−	0.766866i	$-0.278185\pi$
$463$	27.6201	1.28361	0.641807	+	0.766866i	$0.278185\pi$
$464$	4.25828	0.197686
$465$	32.8892	1.52520
$466$	2.44514	0.113269
$467$	25.7874	1.19330	0.596649	−	0.802502i	$-0.296498\pi$
$467$	25.7874	1.19330	0.596649	+	0.802502i	$0.296498\pi$
$468$	−4.19738	−0.194024
$469$	10.9571	0.505954
$470$	−2.61551	−0.120645
$471$	17.7542	0.818071
$472$	−8.31711	−0.382826
$473$	0	0
$474$	3.29459	0.151326
$475$	7.79422	0.357623
$476$	19.5322	0.895257
$477$	−4.93283	−0.225859
$478$	−1.79180	−0.0819549
$479$	−9.48218	−0.433252	−0.216626	−	0.976255i	$-0.569505\pi$
$479$	−9.48218	−0.433252	−0.216626	+	0.976255i	$0.569505\pi$
$480$	−9.31457	−0.425150
$481$	−7.10935	−0.324158
$482$	−1.80635	−0.0822769
$483$	39.9952	1.81984
$484$	−12.8000	−0.581818
$485$	6.97797	0.316853
$486$	2.15654	0.0978226
$487$	−17.4549	−0.790956	−0.395478	−	0.918475i	$-0.629421\pi$
$487$	−17.4549	−0.790956	−0.395478	+	0.918475i	$0.629421\pi$
$488$	−7.57987	−0.343125
$489$	−11.8644	−0.536525
$490$	−0.123207	−0.00556591
$491$	35.8752	1.61903	0.809514	−	0.587101i	$-0.199731\pi$
$491$	35.8752	1.61903	0.809514	+	0.587101i	$0.199731\pi$
$492$	29.2017	1.31651
$493$	4.17475	0.188021
$494$	2.73440	0.123026
$495$	−8.89653	−0.399869
$496$	31.1338	1.39795
$497$	−16.0657	−0.720646
$498$	2.03185	0.0910494
$499$	13.4872	0.603768	0.301884	−	0.953345i	$-0.402384\pi$
$499$	13.4872	0.603768	0.301884	+	0.953345i	$0.402384\pi$
$500$	23.6355	1.05701
$501$	−6.77620	−0.302738
$502$	−3.19714	−0.142695
$503$	−31.2917	−1.39523	−0.697615	−	0.716473i	$-0.745755\pi$
$503$	−31.2917	−1.39523	−0.697615	+	0.716473i	$0.745755\pi$
$504$	−2.32362	−0.103502
$505$	24.5935	1.09440
$506$	−6.15624	−0.273678
$507$	−18.3259	−0.813883
$508$	33.9922	1.50816
$509$	16.6833	0.739475	0.369738	−	0.929136i	$-0.379448\pi$
$509$	16.6833	0.739475	0.369738	+	0.929136i	$0.379448\pi$
$510$	−2.93970	−0.130172
$511$	−10.3556	−0.458104
$512$	−14.7963	−0.653912
$513$	26.6378	1.17609
$514$	4.56437	0.201326
$515$	−15.5023	−0.683113
$516$	0	0
$517$	−27.7383	−1.21993
$518$	−1.94779	−0.0855810
$519$	−10.4647	−0.459348
$520$	3.09841	0.135874
$521$	−26.5588	−1.16356	−0.581781	−	0.813345i	$-0.697644\pi$
$521$	−26.5588	−1.16356	−0.581781	+	0.813345i	$0.697644\pi$
$522$	−0.245793	−0.0107581
$523$	−1.24579	−0.0544746	−0.0272373	−	0.999629i	$-0.508671\pi$
$523$	−1.24579	−0.0544746	−0.0272373	+	0.999629i	$0.508671\pi$
$524$	−21.4824	−0.938463
$525$	6.19686	0.270453
$526$	−3.55004	−0.154789
$527$	30.5230	1.32960
$528$	−31.8002	−1.38393
$529$	30.6094	1.33084
$530$	1.80211	0.0782787
$531$	−11.3040	−0.490553
$532$	−36.4076	−1.57847
$533$	−14.6200	−0.633262
$534$	0.609420	0.0263722
$535$	9.08403	0.392737
$536$	−3.22196	−0.139167
$537$	−24.4018	−1.05302
$538$	−1.25571	−0.0541376
$539$	−1.30664	−0.0562811
$540$	14.9383	0.642842
$541$	0.759133	0.0326377	0.0163188	−	0.999867i	$-0.494805\pi$
$541$	0.759133	0.0326377	0.0163188	+	0.999867i	$0.494805\pi$
$542$	0.552725	0.0237416
$543$	11.2580	0.483128
$544$	−8.64445	−0.370628
$545$	16.5368	0.708360
$546$	2.17401	0.0930389
$547$	−17.2048	−0.735624	−0.367812	−	0.929900i	$-0.619893\pi$
$547$	−17.2048	−0.735624	−0.367812	+	0.929900i	$0.619893\pi$
$548$	−8.18463	−0.349630
$549$	−10.3020	−0.439679
$550$	−0.953849	−0.0406723
$551$	−7.78165	−0.331509
$552$	−11.7606	−0.500565
$553$	21.9620	0.933919
$554$	−6.32568	−0.268752
$555$	−14.2466	−0.604736
$556$	−2.12448	−0.0900981
$557$	−13.4205	−0.568643	−0.284322	−	0.958729i	$-0.591768\pi$
$557$	−13.4205	−0.568643	−0.284322	+	0.958729i	$0.591768\pi$
$558$	−1.79708	−0.0760764
$559$	0	0
$560$	−19.9883	−0.844661
$561$	−31.1764	−1.31627
$562$	5.76737	0.243282
$563$	12.2402	0.515864	0.257932	−	0.966163i	$-0.416959\pi$
$563$	12.2402	0.515864	0.257932	+	0.966163i	$0.416959\pi$
$564$	−26.2252	−1.10428
$565$	41.6726	1.75318
$566$	−0.329824	−0.0138635
$567$	29.9455	1.25759
$568$	4.72414	0.198221
$569$	−7.52792	−0.315587	−0.157793	−	0.987472i	$-0.550438\pi$
$569$	−7.52792	−0.315587	−0.157793	+	0.987472i	$0.550438\pi$
$570$	5.47954	0.229513
$571$	42.2887	1.76973	0.884864	−	0.465850i	$-0.154251\pi$
$571$	42.2887	1.76973	0.884864	+	0.465850i	$0.154251\pi$
$572$	16.2625	0.679968
$573$	−11.6471	−0.486566
$574$	−4.00553	−0.167188
$575$	8.30625	0.346395
$576$	−7.61718	−0.317383
$577$	10.1240	0.421468	0.210734	−	0.977543i	$-0.432415\pi$
$577$	10.1240	0.421468	0.210734	+	0.977543i	$0.432415\pi$
$578$	0.685545	0.0285149
$579$	−34.7439	−1.44391
$580$	−4.36389	−0.181201
$581$	13.5444	0.561918
$582$	−1.43971	−0.0596777
$583$	19.1119	0.791535
$584$	3.04507	0.126006
$585$	4.21114	0.174109
$586$	1.90902	0.0788607
$587$	36.1826	1.49342	0.746709	−	0.665151i	$-0.231633\pi$
$587$	36.1826	1.49342	0.746709	+	0.665151i	$0.231633\pi$
$588$	−1.23537	−0.0509457
$589$	−56.8943	−2.34429
$590$	4.12970	0.170017
$591$	21.4609	0.882782
$592$	−13.4862	−0.554280
$593$	−2.52543	−0.103707	−0.0518535	−	0.998655i	$-0.516513\pi$
$593$	−2.52543	−0.103707	−0.0518535	+	0.998655i	$0.516513\pi$
$594$	−3.25991	−0.133756
$595$	−19.5962	−0.803368
$596$	−1.04704	−0.0428882
$597$	−3.92767	−0.160749
$598$	2.91403	0.119164
$599$	−39.7298	−1.62331	−0.811657	−	0.584135i	$-0.801434\pi$
$599$	−39.7298	−1.62331	−0.811657	+	0.584135i	$0.801434\pi$
$600$	−1.82219	−0.0743908
$601$	32.2219	1.31436	0.657179	−	0.753734i	$-0.271750\pi$
$601$	32.2219	1.31436	0.657179	+	0.753734i	$0.271750\pi$
$602$	0	0
$603$	−4.37905	−0.178329
$604$	−17.8028	−0.724385
$605$	12.8420	0.522100
$606$	−5.07417	−0.206124
$607$	1.25328	0.0508689	0.0254345	−	0.999676i	$-0.491903\pi$
$607$	1.25328	0.0508689	0.0254345	+	0.999676i	$0.491903\pi$
$608$	16.1131	0.653471
$609$	−6.18687	−0.250704
$610$	3.76364	0.152385
$611$	13.1298	0.531175
$612$	−7.80611	−0.315543
$613$	0.340579	0.0137558	0.00687792	−	0.999976i	$-0.497811\pi$
$613$	0.340579	0.0137558	0.00687792	+	0.999976i	$0.497811\pi$
$614$	6.32846	0.255396
$615$	−29.2974	−1.18139
$616$	9.00274	0.362731
$617$	−27.8018	−1.11926	−0.559630	−	0.828743i	$-0.689057\pi$
$617$	−27.8018	−1.11926	−0.559630	+	0.828743i	$0.689057\pi$
$618$	3.19846	0.128661
$619$	6.93655	0.278803	0.139402	−	0.990236i	$-0.455482\pi$
$619$	6.93655	0.278803	0.139402	+	0.990236i	$0.455482\pi$
$620$	−31.9059	−1.28137
$621$	28.3878	1.13916
$622$	−1.33205	−0.0534105
$623$	4.06243	0.162758
$624$	15.0525	0.602582
$625$	−18.0408	−0.721631
$626$	−2.53044	−0.101137
$627$	58.1122	2.32078
$628$	−17.2234	−0.687288
$629$	−13.2217	−0.527183
$630$	1.15375	0.0459665
$631$	−28.9157	−1.15112	−0.575558	−	0.817761i	$-0.695215\pi$
$631$	−28.9157	−1.15112	−0.575558	+	0.817761i	$0.695215\pi$
$632$	−6.45795	−0.256883
$633$	13.7376	0.546020
$634$	−1.12649	−0.0447388
$635$	−34.1036	−1.35336
$636$	18.0694	0.716499
$637$	0.618494	0.0245056
$638$	0.952311	0.0377023
$639$	6.42072	0.254000
$640$	12.0048	0.474532
$641$	−37.0467	−1.46326	−0.731628	−	0.681704i	$-0.761239\pi$
$641$	−37.0467	−1.46326	−0.731628	+	0.681704i	$0.761239\pi$
$642$	−1.87423	−0.0739700
$643$	−20.6941	−0.816095	−0.408047	−	0.912961i	$-0.633790\pi$
$643$	−20.6941	−0.816095	−0.408047	+	0.912961i	$0.633790\pi$
$644$	−38.7994	−1.52891
$645$	0	0
$646$	5.08532	0.200079
$647$	−12.6369	−0.496808	−0.248404	−	0.968656i	$-0.579906\pi$
$647$	−12.6369	−0.496808	−0.248404	+	0.968656i	$0.579906\pi$
$648$	−8.80551	−0.345913
$649$	43.7967	1.71917
$650$	0.451501	0.0177093
$651$	−45.2343	−1.77287
$652$	11.5096	0.450752
$653$	−27.3740	−1.07123	−0.535613	−	0.844463i	$-0.679920\pi$
$653$	−27.3740	−1.07123	−0.535613	+	0.844463i	$0.679920\pi$
$654$	−3.41190	−0.133416
$655$	21.5528	0.842138
$656$	−27.7337	−1.08282
$657$	4.13864	0.161464
$658$	3.59725	0.140236
$659$	−36.6854	−1.42906	−0.714531	−	0.699604i	$-0.753360\pi$
$659$	−36.6854	−1.42906	−0.714531	+	0.699604i	$0.753360\pi$
$660$	32.5888	1.26852
$661$	7.87494	0.306300	0.153150	−	0.988203i	$-0.451058\pi$
$661$	7.87494	0.306300	0.153150	+	0.988203i	$0.451058\pi$
$662$	−5.30407	−0.206149
$663$	14.7572	0.573123
$664$	−3.98276	−0.154561
$665$	36.5270	1.41646
$666$	0.778441	0.0301640
$667$	−8.29285	−0.321101
$668$	6.57360	0.254340
$669$	5.37947	0.207982
$670$	1.59980	0.0618057
$671$	39.9145	1.54088
$672$	12.8108	0.494188
$673$	−10.5116	−0.405191	−0.202596	−	0.979262i	$-0.564938\pi$
$673$	−10.5116	−0.405191	−0.202596	+	0.979262i	$0.564938\pi$
$674$	−0.851896	−0.0328138
$675$	4.39841	0.169295
$676$	17.7780	0.683770
$677$	−29.0244	−1.11550	−0.557750	−	0.830009i	$-0.688335\pi$
$677$	−29.0244	−1.11550	−0.557750	+	0.830009i	$0.688335\pi$
$678$	−8.59795	−0.330202
$679$	−9.59718	−0.368306
$680$	5.76230	0.220974
$681$	−28.5721	−1.09488
$682$	6.96267	0.266614
$683$	−40.4065	−1.54611	−0.773056	−	0.634338i	$-0.781273\pi$
$683$	−40.4065	−1.54611	−0.773056	+	0.634338i	$0.781273\pi$
$684$	14.5504	0.556349
$685$	8.21146	0.313744
$686$	−3.63158	−0.138654
$687$	36.9354	1.40917
$688$	0	0
$689$	−9.04655	−0.344646
$690$	5.83951	0.222306
$691$	31.4341	1.19581	0.597904	−	0.801567i	$-0.296000\pi$
$691$	31.4341	1.19581	0.597904	+	0.801567i	$0.296000\pi$
$692$	10.1518	0.385913
$693$	12.2359	0.464802
$694$	5.69369	0.216129
$695$	2.13145	0.0808504
$696$	1.81925	0.0689587
$697$	−27.1897	−1.02988
$698$	4.00399	0.151553
$699$	−24.5973	−0.930356
$700$	−6.01158	−0.227217
$701$	−12.6220	−0.476727	−0.238364	−	0.971176i	$-0.576611\pi$
$701$	−12.6220	−0.476727	−0.238364	+	0.971176i	$0.576611\pi$
$702$	1.54307	0.0582393
$703$	24.6449	0.929500
$704$	29.5123	1.11229
$705$	26.3112	0.990937
$706$	−6.64945	−0.250255
$707$	−33.8248	−1.27211
$708$	41.4077	1.55620
$709$	11.9299	0.448038	0.224019	−	0.974585i	$-0.428082\pi$
$709$	11.9299	0.448038	0.224019	+	0.974585i	$0.428082\pi$
$710$	−2.34568	−0.0880319
$711$	−8.77718	−0.329170
$712$	−1.19456	−0.0447681
$713$	−60.6319	−2.27068
$714$	4.04313	0.151310
$715$	−16.3158	−0.610176
$716$	23.6722	0.884672
$717$	18.0249	0.673152
$718$	6.75576	0.252123
$719$	−1.14548	−0.0427193	−0.0213597	−	0.999772i	$-0.506800\pi$
$719$	−1.14548	−0.0427193	−0.0213597	+	0.999772i	$0.506800\pi$
$720$	7.98840	0.297710
$721$	21.3211	0.794041
$722$	−5.66356	−0.210776
$723$	18.1713	0.675797
$724$	−10.9214	−0.405892
$725$	−1.28490	−0.0477199
$726$	−2.64957	−0.0983349
$727$	31.7716	1.17834	0.589172	−	0.808008i	$-0.299454\pi$
$727$	31.7716	1.17834	0.589172	+	0.808008i	$0.299454\pi$
$728$	−4.26141	−0.157938
$729$	11.5285	0.426981
$730$	−1.51197	−0.0559606
$731$	0	0
$732$	37.7372	1.39481
$733$	46.1935	1.70619	0.853097	−	0.521752i	$-0.174721\pi$
$733$	46.1935	1.70619	0.853097	+	0.521752i	$0.174721\pi$
$734$	2.99713	0.110626
$735$	1.23942	0.0457166
$736$	17.1716	0.632953
$737$	16.9664	0.624965
$738$	1.60082	0.0589271
$739$	27.7884	1.02221	0.511107	−	0.859517i	$-0.329236\pi$
$739$	27.7884	1.02221	0.511107	+	0.859517i	$0.329236\pi$
$740$	13.8207	0.508058
$741$	−27.5071	−1.01050
$742$	−2.47854	−0.0909901
$743$	−48.5239	−1.78017	−0.890085	−	0.455794i	$-0.849355\pi$
$743$	−48.5239	−1.78017	−0.890085	+	0.455794i	$0.849355\pi$
$744$	13.3012	0.487645
$745$	1.05047	0.0384862
$746$	1.01685	0.0372295
$747$	−5.41308	−0.198054
$748$	30.2443	1.10584
$749$	−12.4938	−0.456512
$750$	4.89251	0.178649
$751$	−44.3102	−1.61690	−0.808452	−	0.588563i	$-0.799694\pi$
$751$	−44.3102	−1.61690	−0.808452	+	0.588563i	$0.799694\pi$
$752$	24.9068	0.908259
$753$	32.1622	1.17206
$754$	−0.450772	−0.0164162
$755$	17.8612	0.650034
$756$	−20.5454	−0.747230
$757$	−50.2456	−1.82621	−0.913104	−	0.407727i	$-0.866322\pi$
$757$	−50.2456	−1.82621	−0.913104	+	0.407727i	$0.866322\pi$
$758$	2.42041	0.0879133
$759$	61.9297	2.24791
$760$	−10.7408	−0.389610
$761$	52.5381	1.90451	0.952253	−	0.305311i	$-0.0987604\pi$
$761$	52.5381	1.90451	0.952253	+	0.305311i	$0.0987604\pi$
$762$	7.03631	0.254899
$763$	−22.7440	−0.823387
$764$	11.2989	0.408780
$765$	7.83170	0.283156
$766$	−1.41171	−0.0510070
$767$	−20.7310	−0.748553
$768$	25.9998	0.938186
$769$	28.2409	1.01839	0.509197	−	0.860650i	$-0.329942\pi$
$769$	28.2409	1.01839	0.509197	+	0.860650i	$0.329942\pi$
$770$	−4.47014	−0.161093
$771$	−45.9161	−1.65363
$772$	33.7051	1.21307
$773$	−17.3475	−0.623948	−0.311974	−	0.950091i	$-0.600990\pi$
$773$	−17.3475	−0.623948	−0.311974	+	0.950091i	$0.600990\pi$
$774$	0	0
$775$	−9.39432	−0.337454
$776$	2.82206	0.101306
$777$	19.5941	0.702936
$778$	−3.15869	−0.113245
$779$	50.6810	1.81583
$780$	−15.4258	−0.552332
$781$	−24.8767	−0.890157
$782$	5.41939	0.193797
$783$	−4.39132	−0.156933
$784$	1.17326	0.0419023
$785$	17.2799	0.616745
$786$	−4.44681	−0.158612
$787$	−10.7984	−0.384923	−0.192461	−	0.981305i	$-0.561647\pi$
$787$	−10.7984	−0.384923	−0.192461	+	0.981305i	$0.561647\pi$
$788$	−20.8192	−0.741654
$789$	35.7122	1.27139
$790$	3.20657	0.114085
$791$	−57.3146	−2.03787
$792$	−3.59797	−0.127848
$793$	−18.8934	−0.670923
$794$	1.39564	0.0495294
$795$	−18.1287	−0.642957
$796$	3.81024	0.135050
$797$	−21.9150	−0.776269	−0.388134	−	0.921603i	$-0.626880\pi$
$797$	−21.9150	−0.776269	−0.388134	+	0.921603i	$0.626880\pi$
$798$	−7.53630	−0.266782
$799$	24.4183	0.863856
$800$	2.66057	0.0940654
$801$	−1.62356	−0.0573658
$802$	−6.36182	−0.224644
$803$	−16.0349	−0.565860
$804$	16.0409	0.565719
$805$	38.9266	1.37198
$806$	−3.29575	−0.116088
$807$	12.6321	0.444670
$808$	9.94621	0.349907
$809$	−37.7543	−1.32737	−0.663684	−	0.748013i	$-0.731008\pi$
$809$	−37.7543	−1.32737	−0.663684	+	0.748013i	$0.731008\pi$
$810$	4.37221	0.153624
$811$	−24.6605	−0.865948	−0.432974	−	0.901406i	$-0.642536\pi$
$811$	−24.6605	−0.865948	−0.432974	+	0.901406i	$0.642536\pi$
$812$	6.00189	0.210625
$813$	−5.56023	−0.195006
$814$	−3.01602	−0.105711
$815$	−11.5474	−0.404486
$816$	27.9940	0.979986
$817$	0	0
$818$	−5.87558	−0.205435
$819$	−5.79180	−0.202382
$820$	28.4215	0.992521
$821$	−53.7703	−1.87660	−0.938298	−	0.345828i	$-0.887598\pi$
$821$	−53.7703	−1.87660	−0.938298	+	0.345828i	$0.887598\pi$
$822$	−1.69420	−0.0590921
$823$	6.54667	0.228202	0.114101	−	0.993469i	$-0.463601\pi$
$823$	6.54667	0.228202	0.114101	+	0.993469i	$0.463601\pi$
$824$	−6.26951	−0.218409
$825$	9.59541	0.334069
$826$	−5.67980	−0.197625
$827$	−55.2953	−1.92281	−0.961403	−	0.275145i	$-0.911274\pi$
$827$	−55.2953	−1.92281	−0.961403	+	0.275145i	$0.911274\pi$
$828$	15.5063	0.538881
$829$	−29.6398	−1.02943	−0.514717	−	0.857360i	$-0.672103\pi$
$829$	−29.6398	−1.02943	−0.514717	+	0.857360i	$0.672103\pi$
$830$	1.97756	0.0686422
$831$	63.6343	2.20745
$832$	−13.9695	−0.484306
$833$	1.15025	0.0398538
$834$	−0.439763	−0.0152278
$835$	−6.59515	−0.228235
$836$	−56.3747	−1.94976
$837$	−32.1064	−1.10976
$838$	−2.77481	−0.0958543
$839$	5.99060	0.206819	0.103409	−	0.994639i	$-0.467025\pi$
$839$	5.99060	0.206819	0.103409	+	0.994639i	$0.467025\pi$
$840$	−8.53956	−0.294643
$841$	−27.7172	−0.955765
$842$	−2.41465	−0.0832142
$843$	−58.0179	−1.99824
$844$	−13.3269	−0.458729
$845$	−17.8363	−0.613587
$846$	−1.43765	−0.0494275
$847$	−17.6622	−0.606881
$848$	−17.1610	−0.589313
$849$	3.31792	0.113871
$850$	0.839682	0.0288009
$851$	26.2639	0.900316
$852$	−23.5197	−0.805771
$853$	21.0511	0.720777	0.360388	−	0.932802i	$-0.382644\pi$
$853$	21.0511	0.720777	0.360388	+	0.932802i	$0.382644\pi$
$854$	−5.17633	−0.177130
$855$	−14.5981	−0.499245
$856$	3.67380	0.125568
$857$	11.6663	0.398514	0.199257	−	0.979947i	$-0.436147\pi$
$857$	11.6663	0.398514	0.199257	+	0.979947i	$0.436147\pi$
$858$	3.36630	0.114924
$859$	21.0453	0.718056	0.359028	−	0.933327i	$-0.383108\pi$
$859$	21.0453	0.718056	0.359028	+	0.933327i	$0.383108\pi$
$860$	0	0
$861$	40.2943	1.37323
$862$	−4.37899	−0.149149
$863$	−40.4005	−1.37525	−0.687625	−	0.726066i	$-0.741347\pi$
$863$	−40.4005	−1.37525	−0.687625	+	0.726066i	$0.741347\pi$
$864$	9.09287	0.309346
$865$	−10.1851	−0.346303
$866$	2.84639	0.0967243
$867$	−6.89636	−0.234213
$868$	43.8818	1.48945
$869$	34.0066	1.15360
$870$	−0.903316	−0.0306253
$871$	−8.03096	−0.272119
$872$	6.68789	0.226481
$873$	3.83554	0.129813
$874$	−10.1016	−0.341693
$875$	32.6138	1.10255
$876$	−15.1602	−0.512217
$877$	16.8767	0.569886	0.284943	−	0.958545i	$-0.408025\pi$
$877$	16.8767	0.569886	0.284943	+	0.958545i	$0.408025\pi$
$878$	4.83369	0.163129
$879$	−19.2041	−0.647737
$880$	−30.9506	−1.04334
$881$	−36.6979	−1.23638	−0.618192	−	0.786027i	$-0.712135\pi$
$881$	−36.6979	−1.23638	−0.618192	+	0.786027i	$0.712135\pi$
$882$	−0.0677222	−0.00228033
$883$	43.1682	1.45272	0.726362	−	0.687312i	$-0.241210\pi$
$883$	43.1682	1.45272	0.726362	+	0.687312i	$0.241210\pi$
$884$	−14.3160	−0.481499
$885$	−41.5434	−1.39647
$886$	−0.523924	−0.0176016
$887$	−12.2054	−0.409817	−0.204909	−	0.978781i	$-0.565690\pi$
$887$	−12.2054	−0.409817	−0.204909	+	0.978781i	$0.565690\pi$
$888$	−5.76168	−0.193349
$889$	46.9045	1.57313
$890$	0.593137	0.0198820
$891$	46.3686	1.55341
$892$	−5.21863	−0.174733
$893$	−45.5151	−1.52311
$894$	−0.216734	−0.00724867
$895$	−23.7498	−0.793869
$896$	−16.5108	−0.551589
$897$	−29.3142	−0.978772
$898$	−0.601947	−0.0200872
$899$	9.37917	0.312813
$900$	2.40255	0.0800849
$901$	−16.8244	−0.560502
$902$	−6.20229	−0.206514
$903$	0	0
$904$	16.8534	0.560536
$905$	10.9572	0.364231
$906$	−3.68514	−0.122431
$907$	19.0217	0.631605	0.315803	−	0.948825i	$-0.397726\pi$
$907$	19.0217	0.631605	0.315803	+	0.948825i	$0.397726\pi$
$908$	27.7178	0.919848
$909$	13.5182	0.448370
$910$	2.11592	0.0701421
$911$	−10.3763	−0.343781	−0.171891	−	0.985116i	$-0.554988\pi$
$911$	−10.3763	−0.343781	−0.171891	+	0.985116i	$0.554988\pi$
$912$	−52.1802	−1.72786
$913$	20.9726	0.694093
$914$	1.27343	0.0421214
$915$	−37.8610	−1.25165
$916$	−35.8311	−1.18389
$917$	−29.6427	−0.978890
$918$	2.86973	0.0947153
$919$	−21.5920	−0.712253	−0.356126	−	0.934438i	$-0.615903\pi$
$919$	−21.5920	−0.712253	−0.356126	+	0.934438i	$0.615903\pi$
$920$	−11.4464	−0.377377
$921$	−63.6623	−2.09774
$922$	3.46276	0.114040
$923$	11.7753	0.387588
$924$	−44.8212	−1.47451
$925$	4.06934	0.133799
$926$	−5.54636	−0.182265
$927$	−8.52106	−0.279868
$928$	−2.65628	−0.0871966
$929$	−36.5143	−1.19799	−0.598997	−	0.800751i	$-0.704434\pi$
$929$	−36.5143	−1.19799	−0.598997	+	0.800751i	$0.704434\pi$
$930$	−6.60445	−0.216568
$931$	−2.14404	−0.0702681
$932$	23.8619	0.781623
$933$	13.4000	0.438698
$934$	−5.17834	−0.169441
$935$	−30.3434	−0.992337
$936$	1.70309	0.0556671
$937$	22.8163	0.745376	0.372688	−	0.927957i	$-0.378436\pi$
$937$	22.8163	0.745376	0.372688	+	0.927957i	$0.378436\pi$
$938$	−2.20029	−0.0718421
$939$	25.4554	0.830704
$940$	−25.5245	−0.832518
$941$	−20.9812	−0.683968	−0.341984	−	0.939706i	$-0.611099\pi$
$941$	−20.9812	−0.683968	−0.341984	+	0.939706i	$0.611099\pi$
$942$	−3.56521	−0.116161
$943$	54.0104	1.75882
$944$	−39.3261	−1.27995
$945$	20.6128	0.670534
$946$	0	0
$947$	36.1863	1.17590	0.587948	−	0.808899i	$-0.299936\pi$
$947$	36.1863	1.17590	0.587948	+	0.808899i	$0.299936\pi$
$948$	32.1516	1.04424
$949$	7.59006	0.246384
$950$	−1.56515	−0.0507802
$951$	11.3322	0.367470
$952$	−7.92520	−0.256857
$953$	−21.7737	−0.705319	−0.352659	−	0.935752i	$-0.614723\pi$
$953$	−21.7737	−0.705319	−0.352659	+	0.935752i	$0.614723\pi$
$954$	0.990556	0.0320704
$955$	−11.3359	−0.366822
$956$	−17.4860	−0.565537
$957$	−9.57994	−0.309675
$958$	1.90411	0.0615189
$959$	−11.2937	−0.364691
$960$	−27.9939	−0.903501
$961$	37.5743	1.21207
$962$	1.42762	0.0460283
$963$	4.99317	0.160903
$964$	−17.6280	−0.567759
$965$	−33.8157	−1.08856
$966$	−8.03139	−0.258406
$967$	−33.3406	−1.07216	−0.536081	−	0.844166i	$-0.680096\pi$
$967$	−33.3406	−1.07216	−0.536081	+	0.844166i	$0.680096\pi$
$968$	5.19360	0.166929
$969$	−51.1567	−1.64339
$970$	−1.40124	−0.0449911
$971$	−7.11804	−0.228429	−0.114214	−	0.993456i	$-0.536435\pi$
$971$	−7.11804	−0.228429	−0.114214	+	0.993456i	$0.536435\pi$
$972$	21.0454	0.675033
$973$	−2.93149	−0.0939793
$974$	3.50510	0.112311
$975$	−4.54195	−0.145459
$976$	−35.8402	−1.14722
$977$	20.7469	0.663751	0.331876	−	0.943323i	$-0.392319\pi$
$977$	20.7469	0.663751	0.331876	+	0.943323i	$0.392319\pi$
$978$	2.38247	0.0761830
$979$	6.29040	0.201042
$980$	−1.20236	−0.0384080
$981$	9.08970	0.290212
$982$	−7.20407	−0.229891
$983$	4.89381	0.156088	0.0780441	−	0.996950i	$-0.475133\pi$
$983$	4.89381	0.156088	0.0780441	+	0.996950i	$0.475133\pi$
$984$	−11.8486	−0.377719
$985$	20.8875	0.665531
$986$	−0.838328	−0.0266978
$987$	−36.1872	−1.15185
$988$	26.6847	0.848954
$989$	0	0
$990$	1.78650	0.0567788
$991$	25.2922	0.803434	0.401717	−	0.915764i	$-0.368414\pi$
$991$	25.2922	0.803434	0.401717	+	0.915764i	$0.368414\pi$
$992$	−19.4210	−0.616616
$993$	53.3572	1.69324
$994$	3.22614	0.102327
$995$	−3.82273	−0.121189
$996$	19.8286	0.628294
$997$	−49.5367	−1.56884	−0.784422	−	0.620227i	$-0.787040\pi$
$997$	−49.5367	−1.56884	−0.784422	+	0.620227i	$0.787040\pi$
$998$	−2.70834	−0.0857311
$999$	13.9075	0.440015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.q.1.9	✓	20
43.42	odd	2	inner	1849.2.a.q.1.12	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.q.1.9	✓	20	1.1	even	1	trivial
1849.2.a.q.1.12	yes	20	43.42	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-0.200809 q^{2} +2.02007 q^{3} -1.95968 q^{4} +1.96610 q^{5} -0.405649 q^{6} -2.70408 q^{7} +0.795139 q^{8} +1.08069 q^{9} +O(q^{10})\)	\(q-0.200809 q^{2} +2.02007 q^{3} -1.95968 q^{4} +1.96610 q^{5} -0.405649 q^{6} -2.70408 q^{7} +0.795139 q^{8} +1.08069 q^{9} -0.394811 q^{10} -4.18709 q^{11} -3.95869 q^{12} +1.98194 q^{13} +0.543004 q^{14} +3.97167 q^{15} +3.75968 q^{16} +3.68593 q^{17} -0.217013 q^{18} -6.87049 q^{19} -3.85292 q^{20} -5.46245 q^{21} +0.840805 q^{22} -7.32184 q^{23} +1.60624 q^{24} -1.13445 q^{25} -0.397991 q^{26} -3.87714 q^{27} +5.29913 q^{28} +1.13262 q^{29} -0.797546 q^{30} +8.28096 q^{31} -2.34525 q^{32} -8.45822 q^{33} -0.740168 q^{34} -5.31650 q^{35} -2.11781 q^{36} -3.58706 q^{37} +1.37966 q^{38} +4.00366 q^{39} +1.56332 q^{40} -7.37661 q^{41} +1.09691 q^{42} +8.20533 q^{44} +2.12475 q^{45} +1.47029 q^{46} +6.62472 q^{47} +7.59483 q^{48} +0.312065 q^{49} +0.227807 q^{50} +7.44585 q^{51} -3.88396 q^{52} -4.56449 q^{53} +0.778564 q^{54} -8.23223 q^{55} -2.15012 q^{56} -13.8789 q^{57} -0.227440 q^{58} -10.4600 q^{59} -7.78318 q^{60} -9.53277 q^{61} -1.66289 q^{62} -2.92229 q^{63} -7.04841 q^{64} +3.89669 q^{65} +1.69849 q^{66} -4.05207 q^{67} -7.22323 q^{68} -14.7907 q^{69} +1.06760 q^{70} +5.94128 q^{71} +0.859302 q^{72} +3.82961 q^{73} +0.720315 q^{74} -2.29167 q^{75} +13.4639 q^{76} +11.3222 q^{77} -0.803972 q^{78} -8.12179 q^{79} +7.39191 q^{80} -11.0742 q^{81} +1.48129 q^{82} -5.00889 q^{83} +10.7046 q^{84} +7.24691 q^{85} +2.28797 q^{87} -3.32931 q^{88} -1.50233 q^{89} -0.426670 q^{90} -5.35933 q^{91} +14.3484 q^{92} +16.7281 q^{93} -1.33030 q^{94} -13.5081 q^{95} -4.73759 q^{96} +3.54914 q^{97} -0.0626654 q^{98} -4.52496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9}+O(q^{10}) \) 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9	\( 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9} + 12 q^{10} - 20 q^{11} + 6 q^{13} - 34 q^{14} - 34 q^{15} + 14 q^{16} - 8 q^{17} + 12 q^{21} - 46 q^{23} + 2 q^{24} + 20 q^{25} - 38 q^{31} - 76 q^{35} - 46 q^{36} - 68 q^{38} - 64 q^{40} - 56 q^{41} - 58 q^{44} - 24 q^{47} - 20 q^{49} - 20 q^{52} - 42 q^{53} + 66 q^{54} - 46 q^{56} + 2 q^{57} + 12 q^{58} - 90 q^{59} + 18 q^{60} - 28 q^{64} + 76 q^{66} - 62 q^{67} - 54 q^{68} + 24 q^{74} - 36 q^{78} - 10 q^{79} - 48 q^{81} - 68 q^{83} + 70 q^{84} - 12 q^{87} + 58 q^{90} - 8 q^{92} - 42 q^{95} - 22 q^{96} - 44 q^{97} - 38 q^{99}+O(q^{100}) \) 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9 + 12 * q^10 - 20 * q^11 + 6 * q^13 - 34 * q^14 - 34 * q^15 + 14 * q^16 - 8 * q^17 + 12 * q^21 - 46 * q^23 + 2 * q^24 + 20 * q^25 - 38 * q^31 - 76 * q^35 - 46 * q^36 - 68 * q^38 - 64 * q^40 - 56 * q^41 - 58 * q^44 - 24 * q^47 - 20 * q^49 - 20 * q^52 - 42 * q^53 + 66 * q^54 - 46 * q^56 + 2 * q^57 + 12 * q^58 - 90 * q^59 + 18 * q^60 - 28 * q^64 + 76 * q^66 - 62 * q^67 - 54 * q^68 + 24 * q^74 - 36 * q^78 - 10 * q^79 - 48 * q^81 - 68 * q^83 + 70 * q^84 - 12 * q^87 + 58 * q^90 - 8 * q^92 - 42 * q^95 - 22 * q^96 - 44 * q^97 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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