LMFDB - Embedded newform 4205.2.a.e.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [4205,2,Mod(1,4205)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4205.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4205, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 4205 = 5 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4205.a (trivial)

Newform invariants

comment:select newform

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

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

Self dual:	yes
Analytic conductor:	$33.5770940499$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 145)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.17009$ of defining polynomial
Character	$\chi$	$=$	4205.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.53919 q^{2} -1.70928 q^{3} +0.369102 q^{4} -1.00000 q^{5} +2.63090 q^{6} +0.630898 q^{7} +2.51026 q^{8} -0.0783777 q^{9} +1.53919 q^{10} -0.290725 q^{11} -0.630898 q^{12} -0.921622 q^{13} -0.971071 q^{14} +1.70928 q^{15} -4.60197 q^{16} -4.97107 q^{17} +0.120638 q^{18} +6.04945 q^{19} -0.369102 q^{20} -1.07838 q^{21} +0.447480 q^{22} +2.29072 q^{23} -4.29072 q^{24} +1.00000 q^{25} +1.41855 q^{26} +5.26180 q^{27} +0.232866 q^{28} -2.63090 q^{30} -10.0494 q^{31} +2.06278 q^{32} +0.496928 q^{33} +7.65142 q^{34} -0.630898 q^{35} -0.0289294 q^{36} -1.55252 q^{37} -9.31124 q^{38} +1.57531 q^{39} -2.51026 q^{40} -0.340173 q^{41} +1.65983 q^{42} +5.70928 q^{43} -0.107307 q^{44} +0.0783777 q^{45} -3.52586 q^{46} +1.12783 q^{47} +7.86603 q^{48} -6.60197 q^{49} -1.53919 q^{50} +8.49693 q^{51} -0.340173 q^{52} -0.340173 q^{53} -8.09890 q^{54} +0.290725 q^{55} +1.58372 q^{56} -10.3402 q^{57} +9.75872 q^{59} +0.630898 q^{60} -3.07838 q^{61} +15.4680 q^{62} -0.0494483 q^{63} +6.02893 q^{64} +0.921622 q^{65} -0.764867 q^{66} -5.70928 q^{67} -1.83483 q^{68} -3.91548 q^{69} +0.971071 q^{70} +9.07838 q^{71} -0.196748 q^{72} +6.94441 q^{73} +2.38962 q^{74} -1.70928 q^{75} +2.23287 q^{76} -0.183417 q^{77} -2.42469 q^{78} -12.3896 q^{79} +4.60197 q^{80} -8.75872 q^{81} +0.523590 q^{82} +2.78765 q^{83} -0.398032 q^{84} +4.97107 q^{85} -8.78765 q^{86} -0.729794 q^{88} -4.73820 q^{89} -0.120638 q^{90} -0.581449 q^{91} +0.845512 q^{92} +17.1773 q^{93} -1.73594 q^{94} -6.04945 q^{95} -3.52586 q^{96} +15.8927 q^{97} +10.1617 q^{98} +0.0227863 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 2 q^{3} + 5 q^{4} - 3 q^{5} + 4 q^{6} - 2 q^{7} - 9 q^{8} + 3 q^{9} + 3 q^{10} - 8 q^{11} + 2 q^{12} - 6 q^{13} + 12 q^{14} - 2 q^{15} + 5 q^{16} + 13 q^{18} - 5 q^{20} + 2 q^{22} + 14 q^{23}+ \cdots - 20 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 2 * q^3 + 5 * q^4 - 3 * q^5 + 4 * q^6 - 2 * q^7 - 9 * q^8 + 3 * q^9 + 3 * q^10 - 8 * q^11 + 2 * q^12 - 6 * q^13 + 12 * q^14 - 2 * q^15 + 5 * q^16 + 13 * q^18 - 5 * q^20 + 2 * q^22 + 14 * q^23 - 20 * q^24 + 3 * q^25 - 10 * q^26 + 8 * q^27 - 22 * q^28 - 4 * q^30 - 12 * q^31 - 11 * q^32 - 16 * q^33 - 14 * q^34 + 2 * q^35 - 15 * q^36 - 4 * q^37 - 2 * q^38 - 16 * q^39 + 9 * q^40 + 10 * q^41 + 16 * q^42 + 10 * q^43 - 12 * q^44 - 3 * q^45 - 8 * q^46 - 18 * q^47 + 10 * q^48 - q^49 - 3 * q^50 + 8 * q^51 + 10 * q^52 + 10 * q^53 + 12 * q^54 + 8 * q^55 + 32 * q^56 - 20 * q^57 + 4 * q^59 - 2 * q^60 - 6 * q^61 + 14 * q^62 + 18 * q^63 + 33 * q^64 + 6 * q^65 - 12 * q^66 - 10 * q^67 + 36 * q^68 + 20 * q^69 - 12 * q^70 + 24 * q^71 + 3 * q^72 + 4 * q^73 - 22 * q^74 + 2 * q^75 - 16 * q^76 + 4 * q^77 - 28 * q^78 - 8 * q^79 - 5 * q^80 - q^81 - 14 * q^82 - 2 * q^83 - 20 * q^84 - 16 * q^86 + 38 * q^88 - 22 * q^89 - 13 * q^90 - 16 * q^91 + 22 * q^92 + 12 * q^93 - 8 * q^96 + 36 * q^97 - 23 * q^98 - 20 * 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 $

$2$	−1.53919	−1.08837	−0.544185	−	0.838965i	$-0.683161\pi$
$2$	−1.53919	−1.08837	−0.544185	+	0.838965i	$0.683161\pi$
$3$	−1.70928	−0.986851	−0.493425	−	0.869788i	$-0.664255\pi$
$3$	−1.70928	−0.986851	−0.493425	+	0.869788i	$0.664255\pi$
$4$	0.369102	0.184551
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.63090	1.07406
$7$	0.630898	0.238457	0.119228	−	0.992867i	$-0.461958\pi$
$7$	0.630898	0.238457	0.119228	+	0.992867i	$0.461958\pi$
$8$	2.51026	0.887511
$9$	−0.0783777	−0.0261259
$10$	1.53919	0.486734
$11$	−0.290725	−0.0876568	−0.0438284	−	0.999039i	$-0.513955\pi$
$11$	−0.290725	−0.0876568	−0.0438284	+	0.999039i	$0.513955\pi$
$12$	−0.630898	−0.182124
$13$	−0.921622	−0.255612	−0.127806	−	0.991799i	$-0.540793\pi$
$13$	−0.921622	−0.255612	−0.127806	+	0.991799i	$0.540793\pi$
$14$	−0.971071	−0.259530
$15$	1.70928	0.441333
$16$	−4.60197	−1.15049
$17$	−4.97107	−1.20566	−0.602831	−	0.797869i	$-0.705961\pi$
$17$	−4.97107	−1.20566	−0.602831	+	0.797869i	$0.705961\pi$
$18$	0.120638	0.0284347
$19$	6.04945	1.38784	0.693919	−	0.720053i	$-0.255882\pi$
$19$	6.04945	1.38784	0.693919	+	0.720053i	$0.255882\pi$
$20$	−0.369102	−0.0825338
$21$	−1.07838	−0.235321
$22$	0.447480	0.0954031
$23$	2.29072	0.477649	0.238825	−	0.971063i	$-0.423238\pi$
$23$	2.29072	0.477649	0.238825	+	0.971063i	$0.423238\pi$
$24$	−4.29072	−0.875840
$25$	1.00000	0.200000
$26$	1.41855	0.278201
$27$	5.26180	1.01263
$28$	0.232866	0.0440075
$29$	0	0
$29$	0	0
$30$	−2.63090	−0.480334
$31$	−10.0494	−1.80493	−0.902467	−	0.430759i	$-0.858246\pi$
$31$	−10.0494	−1.80493	−0.902467	+	0.430759i	$0.858246\pi$
$32$	2.06278	0.364651
$33$	0.496928	0.0865041
$34$	7.65142	1.31221
$35$	−0.630898	−0.106641
$36$	−0.0289294	−0.00482157
$37$	−1.55252	−0.255233	−0.127616	−	0.991824i	$-0.540733\pi$
$37$	−1.55252	−0.255233	−0.127616	+	0.991824i	$0.540733\pi$
$38$	−9.31124	−1.51048
$39$	1.57531	0.252251
$40$	−2.51026	−0.396907
$41$	−0.340173	−0.0531261	−0.0265630	−	0.999647i	$-0.508456\pi$
$41$	−0.340173	−0.0531261	−0.0265630	+	0.999647i	$0.508456\pi$
$42$	1.65983	0.256117
$43$	5.70928	0.870656	0.435328	−	0.900272i	$-0.356632\pi$
$43$	5.70928	0.870656	0.435328	+	0.900272i	$0.356632\pi$
$44$	−0.107307	−0.0161772
$45$	0.0783777	0.0116839
$46$	−3.52586	−0.519859
$47$	1.12783	0.164510	0.0822552	−	0.996611i	$-0.473788\pi$
$47$	1.12783	0.164510	0.0822552	+	0.996611i	$0.473788\pi$
$48$	7.86603	1.13536
$49$	−6.60197	−0.943138
$50$	−1.53919	−0.217674
$51$	8.49693	1.18981
$52$	−0.340173	−0.0471735
$53$	−0.340173	−0.0467264	−0.0233632	−	0.999727i	$-0.507437\pi$
$53$	−0.340173	−0.0467264	−0.0233632	+	0.999727i	$0.507437\pi$
$54$	−8.09890	−1.10212
$55$	0.290725	0.0392013
$56$	1.58372	0.211633
$57$	−10.3402	−1.36959
$58$	0	0
$59$	9.75872	1.27048	0.635239	−	0.772316i	$-0.280902\pi$
$59$	9.75872	1.27048	0.635239	+	0.772316i	$0.280902\pi$
$60$	0.630898	0.0814485
$61$	−3.07838	−0.394146	−0.197073	−	0.980389i	$-0.563144\pi$
$61$	−3.07838	−0.394146	−0.197073	+	0.980389i	$0.563144\pi$
$62$	15.4680	1.96444
$63$	−0.0494483	−0.00622990
$64$	6.02893	0.753616
$65$	0.921622	0.114313
$66$	−0.764867	−0.0941486
$67$	−5.70928	−0.697499	−0.348749	−	0.937216i	$-0.613394\pi$
$67$	−5.70928	−0.697499	−0.348749	+	0.937216i	$0.613394\pi$
$68$	−1.83483	−0.222506
$69$	−3.91548	−0.471368
$70$	0.971071	0.116065
$71$	9.07838	1.07741	0.538703	−	0.842496i	$-0.318915\pi$
$71$	9.07838	1.07741	0.538703	+	0.842496i	$0.318915\pi$
$72$	−0.196748	−0.0231870
$73$	6.94441	0.812782	0.406391	−	0.913699i	$-0.366787\pi$
$73$	6.94441	0.812782	0.406391	+	0.913699i	$0.366787\pi$
$74$	2.38962	0.277788
$75$	−1.70928	−0.197370
$76$	2.23287	0.256127
$77$	−0.183417	−0.0209024
$78$	−2.42469	−0.274543
$79$	−12.3896	−1.39394	−0.696971	−	0.717100i	$-0.745469\pi$
$79$	−12.3896	−1.39394	−0.696971	+	0.717100i	$0.745469\pi$
$80$	4.60197	0.514516
$81$	−8.75872	−0.973192
$82$	0.523590	0.0578209
$83$	2.78765	0.305985	0.152992	−	0.988227i	$-0.451109\pi$
$83$	2.78765	0.305985	0.152992	+	0.988227i	$0.451109\pi$
$84$	−0.398032	−0.0434288
$85$	4.97107	0.539188
$86$	−8.78765	−0.947597
$87$	0	0
$88$	−0.729794	−0.0777963
$89$	−4.73820	−0.502249	−0.251124	−	0.967955i	$-0.580800\pi$
$89$	−4.73820	−0.502249	−0.251124	+	0.967955i	$0.580800\pi$
$90$	−0.120638	−0.0127164
$91$	−0.581449	−0.0609524
$92$	0.845512	0.0881507
$93$	17.1773	1.78120
$94$	−1.73594	−0.179048
$95$	−6.04945	−0.620660
$96$	−3.52586	−0.359856
$97$	15.8927	1.61366	0.806829	−	0.590785i	$-0.201182\pi$
$97$	15.8927	1.61366	0.806829	+	0.590785i	$0.201182\pi$
$98$	10.1617	1.02648
$99$	0.0227863	0.00229011
$100$	0.369102	0.0369102
$101$	12.2557	1.21948	0.609741	−	0.792600i	$-0.291273\pi$
$101$	12.2557	1.21948	0.609741	+	0.792600i	$0.291273\pi$
$102$	−13.0784	−1.29495
$103$	−7.86603	−0.775063	−0.387532	−	0.921856i	$-0.626672\pi$
$103$	−7.86603	−0.775063	−0.387532	+	0.921856i	$0.626672\pi$
$104$	−2.31351	−0.226858
$105$	1.07838	0.105239
$106$	0.523590	0.0508556
$107$	12.7298	1.23064	0.615318	−	0.788279i	$-0.289028\pi$
$107$	12.7298	1.23064	0.615318	+	0.788279i	$0.289028\pi$
$108$	1.94214	0.186883
$109$	12.4391	1.19145	0.595723	−	0.803190i	$-0.296865\pi$
$109$	12.4391	1.19145	0.595723	+	0.803190i	$0.296865\pi$
$110$	−0.447480	−0.0426656
$111$	2.65368	0.251877
$112$	−2.90337	−0.274343
$113$	−12.5730	−1.18277	−0.591386	−	0.806389i	$-0.701419\pi$
$113$	−12.5730	−1.18277	−0.591386	+	0.806389i	$0.701419\pi$
$114$	15.9155	1.49062
$115$	−2.29072	−0.213611
$116$	0	0
$117$	0.0722347	0.00667810
$118$	−15.0205	−1.38275
$119$	−3.13624	−0.287498
$120$	4.29072	0.391688
$121$	−10.9155	−0.992316
$122$	4.73820	0.428977
$123$	0.581449	0.0524275
$124$	−3.70928	−0.333103
$125$	−1.00000	−0.0894427
$126$	0.0761103	0.00678045
$127$	20.9132	1.85575	0.927874	−	0.372895i	$-0.121635\pi$
$127$	20.9132	1.85575	0.927874	+	0.372895i	$0.121635\pi$
$128$	−13.4052	−1.18487
$129$	−9.75872	−0.859208
$130$	−1.41855	−0.124415
$131$	13.4680	1.17670	0.588352	−	0.808605i	$-0.299777\pi$
$131$	13.4680	1.17670	0.588352	+	0.808605i	$0.299777\pi$
$132$	0.183417	0.0159644
$133$	3.81658	0.330940
$134$	8.78765	0.759138
$135$	−5.26180	−0.452863
$136$	−12.4787	−1.07004
$137$	13.5525	1.15787	0.578935	−	0.815374i	$-0.303469\pi$
$137$	13.5525	1.15787	0.578935	+	0.815374i	$0.303469\pi$
$138$	6.02666	0.513024
$139$	−4.89496	−0.415185	−0.207593	−	0.978215i	$-0.566563\pi$
$139$	−4.89496	−0.415185	−0.207593	+	0.978215i	$0.566563\pi$
$140$	−0.232866	−0.0196808
$141$	−1.92777	−0.162347
$142$	−13.9733	−1.17262
$143$	0.267938	0.0224061
$144$	0.360692	0.0300577
$145$	0	0
$146$	−10.6888	−0.884608
$147$	11.2846	0.930737
$148$	−0.573039	−0.0471035
$149$	−12.5236	−1.02597	−0.512986	−	0.858397i	$-0.671461\pi$
$149$	−12.5236	−1.02597	−0.512986	+	0.858397i	$0.671461\pi$
$150$	2.63090	0.214812
$151$	7.60197	0.618639	0.309320	−	0.950958i	$-0.399899\pi$
$151$	7.60197	0.618639	0.309320	+	0.950958i	$0.399899\pi$
$152$	15.1857	1.23172
$153$	0.389621	0.0314990
$154$	0.282314	0.0227495
$155$	10.0494	0.807191
$156$	0.581449	0.0465532
$157$	24.8865	1.98616	0.993081	−	0.117428i	$-0.0374648\pi$
$157$	24.8865	1.98616	0.993081	+	0.117428i	$0.0374648\pi$
$158$	19.0700	1.51713
$159$	0.581449	0.0461119
$160$	−2.06278	−0.163077
$161$	1.44521	0.113899
$162$	13.4813	1.05919
$163$	−0.447480	−0.0350493	−0.0175247	−	0.999846i	$-0.505579\pi$
$163$	−0.447480	−0.0350493	−0.0175247	+	0.999846i	$0.505579\pi$
$164$	−0.125559	−0.00980448
$165$	−0.496928	−0.0386858
$166$	−4.29072	−0.333025
$167$	19.8660	1.53728	0.768640	−	0.639682i	$-0.220934\pi$
$167$	19.8660	1.53728	0.768640	+	0.639682i	$0.220934\pi$
$168$	−2.70701	−0.208850
$169$	−12.1506	−0.934662
$170$	−7.65142	−0.586837
$171$	−0.474142	−0.0362586
$172$	2.10731	0.160681
$173$	−25.4329	−1.93363	−0.966815	−	0.255478i	$-0.917767\pi$
$173$	−25.4329	−1.93363	−0.966815	+	0.255478i	$0.917767\pi$
$174$	0	0
$175$	0.630898	0.0476914
$176$	1.33791	0.100848
$177$	−16.6803	−1.25377
$178$	7.29299	0.546633
$179$	14.8371	1.10898	0.554489	−	0.832191i	$-0.312914\pi$
$179$	14.8371	1.10898	0.554489	+	0.832191i	$0.312914\pi$
$180$	0.0289294	0.00215627
$181$	−5.91548	−0.439694	−0.219847	−	0.975534i	$-0.570556\pi$
$181$	−5.91548	−0.439694	−0.219847	+	0.975534i	$0.570556\pi$
$182$	0.894960	0.0663389
$183$	5.26180	0.388963
$184$	5.75031	0.423919
$185$	1.55252	0.114144
$186$	−26.4391	−1.93861
$187$	1.44521	0.105684
$188$	0.416283	0.0303606
$189$	3.31965	0.241469
$190$	9.31124	0.675509
$191$	−7.02893	−0.508595	−0.254298	−	0.967126i	$-0.581844\pi$
$191$	−7.02893	−0.508595	−0.254298	+	0.967126i	$0.581844\pi$
$192$	−10.3051	−0.743707
$193$	−17.8660	−1.28603	−0.643013	−	0.765856i	$-0.722316\pi$
$193$	−17.8660	−1.28603	−0.643013	+	0.765856i	$0.722316\pi$
$194$	−24.4619	−1.75626
$195$	−1.57531	−0.112810
$196$	−2.43680	−0.174057
$197$	6.09890	0.434528	0.217264	−	0.976113i	$-0.430287\pi$
$197$	6.09890	0.434528	0.217264	+	0.976113i	$0.430287\pi$
$198$	−0.0350725	−0.00249249
$199$	−9.75872	−0.691778	−0.345889	−	0.938276i	$-0.612423\pi$
$199$	−9.75872	−0.691778	−0.345889	+	0.938276i	$0.612423\pi$
$200$	2.51026	0.177502
$201$	9.75872	0.688327
$202$	−18.8638	−1.32725
$203$	0	0
$204$	3.13624	0.219580
$205$	0.340173	0.0237587
$206$	12.1073	0.843556
$207$	−0.179542	−0.0124790
$208$	4.24128	0.294080
$209$	−1.75872	−0.121653
$210$	−1.65983	−0.114539
$211$	−9.86603	−0.679206	−0.339603	−	0.940569i	$-0.610293\pi$
$211$	−9.86603	−0.679206	−0.339603	+	0.940569i	$0.610293\pi$
$212$	−0.125559	−0.00862340
$213$	−15.5174	−1.06324
$214$	−19.5936	−1.33939
$215$	−5.70928	−0.389369
$216$	13.2085	0.898723
$217$	−6.34017	−0.430399
$218$	−19.1461	−1.29674
$219$	−11.8699	−0.802094
$220$	0.107307	0.00723465
$221$	4.58145	0.308182
$222$	−4.08452	−0.274135
$223$	10.9711	0.734677	0.367339	−	0.930087i	$-0.380269\pi$
$223$	10.9711	0.734677	0.367339	+	0.930087i	$0.380269\pi$
$224$	1.30140	0.0869536
$225$	−0.0783777	−0.00522518
$226$	19.3523	1.28729
$227$	−12.5464	−0.832732	−0.416366	−	0.909197i	$-0.636697\pi$
$227$	−12.5464	−0.832732	−0.416366	+	0.909197i	$0.636697\pi$
$228$	−3.81658	−0.252759
$229$	−23.3607	−1.54372	−0.771859	−	0.635794i	$-0.780673\pi$
$229$	−23.3607	−1.54372	−0.771859	+	0.635794i	$0.780673\pi$
$230$	3.52586	0.232488
$231$	0.313511	0.0206275
$232$	0	0
$233$	12.4703	0.816954	0.408477	−	0.912769i	$-0.366060\pi$
$233$	12.4703	0.816954	0.408477	+	0.912769i	$0.366060\pi$
$234$	−0.111183	−0.00726825
$235$	−1.12783	−0.0735713
$236$	3.60197	0.234468
$237$	21.1773	1.37561
$238$	4.82726	0.312905
$239$	13.7587	0.889978	0.444989	−	0.895536i	$-0.353208\pi$
$239$	13.7587	0.889978	0.444989	+	0.895536i	$0.353208\pi$
$240$	−7.86603	−0.507750
$241$	−14.6803	−0.945644	−0.472822	−	0.881158i	$-0.656765\pi$
$241$	−14.6803	−0.945644	−0.472822	+	0.881158i	$0.656765\pi$
$242$	16.8010	1.08001
$243$	−0.814315	−0.0522383
$244$	−1.13624	−0.0727401
$245$	6.60197	0.421784
$246$	−0.894960	−0.0570606
$247$	−5.57531	−0.354748
$248$	−25.2267	−1.60190
$249$	−4.76487	−0.301961
$250$	1.53919	0.0973469
$251$	−15.4413	−0.974649	−0.487324	−	0.873221i	$-0.662027\pi$
$251$	−15.4413	−0.974649	−0.487324	+	0.873221i	$0.662027\pi$
$252$	−0.0182515	−0.00114974
$253$	−0.665970	−0.0418692
$254$	−32.1894	−2.01974
$255$	−8.49693	−0.532098
$256$	8.57531	0.535957
$257$	−6.28231	−0.391880	−0.195940	−	0.980616i	$-0.562776\pi$
$257$	−6.28231	−0.391880	−0.195940	+	0.980616i	$0.562776\pi$
$258$	15.0205	0.935137
$259$	−0.979481	−0.0608620
$260$	0.340173	0.0210966
$261$	0	0
$262$	−20.7298	−1.28069
$263$	−10.0761	−0.621320	−0.310660	−	0.950521i	$-0.600550\pi$
$263$	−10.0761	−0.621320	−0.310660	+	0.950521i	$0.600550\pi$
$264$	1.24742	0.0767734
$265$	0.340173	0.0208967
$266$	−5.87444	−0.360185
$267$	8.09890	0.495644
$268$	−2.10731	−0.128724
$269$	−28.1711	−1.71762	−0.858812	−	0.512291i	$-0.828797\pi$
$269$	−28.1711	−1.71762	−0.858812	+	0.512291i	$0.828797\pi$
$270$	8.09890	0.492883
$271$	−28.8020	−1.74960	−0.874799	−	0.484485i	$-0.839007\pi$
$271$	−28.8020	−1.74960	−0.874799	+	0.484485i	$0.839007\pi$
$272$	22.8767	1.38710
$273$	0.993857	0.0601510
$274$	−20.8599	−1.26019
$275$	−0.290725	−0.0175314
$276$	−1.44521	−0.0869916
$277$	0.0266620	0.00160196	0.000800982	−	1.00000i	$-0.499745\pi$
$277$	0.0266620	0.00160196	0.000800982		1.00000i	$0.499745\pi$
$278$	7.53427	0.451875
$279$	0.787653	0.0471556
$280$	−1.58372	−0.0946452
$281$	−28.0722	−1.67465	−0.837325	−	0.546706i	$-0.815881\pi$
$281$	−28.0722	−1.67465	−0.837325	+	0.546706i	$0.815881\pi$
$282$	2.96719	0.176694
$283$	−20.8143	−1.23728	−0.618641	−	0.785674i	$-0.712317\pi$
$283$	−20.8143	−1.23728	−0.618641	+	0.785674i	$0.712317\pi$
$284$	3.35085	0.198836
$285$	10.3402	0.612499
$286$	−0.412408	−0.0243862
$287$	−0.214614	−0.0126683
$288$	−0.161676	−0.00952685
$289$	7.71154	0.453620
$290$	0	0
$291$	−27.1650	−1.59244
$292$	2.56320	0.150000
$293$	15.4101	0.900270	0.450135	−	0.892961i	$-0.351376\pi$
$293$	15.4101	0.900270	0.450135	+	0.892961i	$0.351376\pi$
$294$	−17.3691	−1.01299
$295$	−9.75872	−0.568175
$296$	−3.89723	−0.226522
$297$	−1.52973	−0.0887641
$298$	19.2762	1.11664
$299$	−2.11118	−0.122093
$300$	−0.630898	−0.0364249
$301$	3.60197	0.207614
$302$	−11.7009	−0.673309
$303$	−20.9483	−1.20345
$304$	−27.8394	−1.59670
$305$	3.07838	0.176267
$306$	−0.599701	−0.0342826
$307$	28.4307	1.62262	0.811312	−	0.584614i	$-0.198754\pi$
$307$	28.4307	1.62262	0.811312	+	0.584614i	$0.198754\pi$
$308$	−0.0676998	−0.00385756
$309$	13.4452	0.764871
$310$	−15.4680	−0.878523
$311$	19.6248	1.11282	0.556409	−	0.830909i	$-0.312179\pi$
$311$	19.6248	1.11282	0.556409	+	0.830909i	$0.312179\pi$
$312$	3.95443	0.223875
$313$	22.9093	1.29491	0.647456	−	0.762103i	$-0.275833\pi$
$313$	22.9093	1.29491	0.647456	+	0.762103i	$0.275833\pi$
$314$	−38.3051	−2.16168
$315$	0.0494483	0.00278610
$316$	−4.57304	−0.257254
$317$	−22.8599	−1.28394	−0.641970	−	0.766730i	$-0.721882\pi$
$317$	−22.8599	−1.28394	−0.641970	+	0.766730i	$0.721882\pi$
$318$	−0.894960	−0.0501869
$319$	0	0
$320$	−6.02893	−0.337027
$321$	−21.7587	−1.21445
$322$	−2.22446	−0.123964
$323$	−30.0722	−1.67326
$324$	−3.23287	−0.179604
$325$	−0.921622	−0.0511224
$326$	0.688756	0.0381467
$327$	−21.2618	−1.17578
$328$	−0.853922	−0.0471500
$329$	0.711543	0.0392286
$330$	0.764867	0.0421045
$331$	−24.0905	−1.32413	−0.662066	−	0.749445i	$-0.730320\pi$
$331$	−24.0905	−1.32413	−0.662066	+	0.749445i	$0.730320\pi$
$332$	1.02893	0.0564698
$333$	0.121683	0.00666819
$334$	−30.5776	−1.67313
$335$	5.70928	0.311931
$336$	4.96266	0.270735
$337$	−12.7877	−0.696588	−0.348294	−	0.937385i	$-0.613239\pi$
$337$	−12.7877	−0.696588	−0.348294	+	0.937385i	$0.613239\pi$
$338$	18.7021	1.01726
$339$	21.4908	1.16722
$340$	1.83483	0.0995078
$341$	2.92162	0.158215
$342$	0.729794	0.0394628
$343$	−8.58145	−0.463355
$344$	14.3318	0.772717
$345$	3.91548	0.210802
$346$	39.1461	2.10451
$347$	8.41628	0.451810	0.225905	−	0.974149i	$-0.427466\pi$
$347$	8.41628	0.451810	0.225905	+	0.974149i	$0.427466\pi$
$348$	0	0
$349$	22.1978	1.18822	0.594110	−	0.804384i	$-0.297504\pi$
$349$	22.1978	1.18822	0.594110	+	0.804384i	$0.297504\pi$
$350$	−0.971071	−0.0519059
$351$	−4.84939	−0.258841
$352$	−0.599701	−0.0319642
$353$	−6.18342	−0.329110	−0.164555	−	0.986368i	$-0.552619\pi$
$353$	−6.18342	−0.329110	−0.164555	+	0.986368i	$0.552619\pi$
$354$	25.6742	1.36457
$355$	−9.07838	−0.481830
$356$	−1.74888	−0.0926906
$357$	5.36069	0.283718
$358$	−22.8371	−1.20698
$359$	−5.05559	−0.266824	−0.133412	−	0.991061i	$-0.542593\pi$
$359$	−5.05559	−0.266824	−0.133412	+	0.991061i	$0.542593\pi$
$360$	0.196748	0.0103696
$361$	17.5958	0.926096
$362$	9.10504	0.478550
$363$	18.6576	0.979268
$364$	−0.214614	−0.0112488
$365$	−6.94441	−0.363487
$366$	−8.09890	−0.423336
$367$	−29.5402	−1.54199	−0.770994	−	0.636843i	$-0.780240\pi$
$367$	−29.5402	−1.54199	−0.770994	+	0.636843i	$0.780240\pi$
$368$	−10.5418	−0.549531
$369$	0.0266620	0.00138797
$370$	−2.38962	−0.124230
$371$	−0.214614	−0.0111422
$372$	6.34017	0.328723
$373$	14.4124	0.746246	0.373123	−	0.927782i	$-0.378287\pi$
$373$	14.4124	0.746246	0.373123	+	0.927782i	$0.378287\pi$
$374$	−2.22446	−0.115024
$375$	1.70928	0.0882666
$376$	2.83114	0.146005
$377$	0	0
$378$	−5.10957	−0.262808
$379$	−14.1340	−0.726013	−0.363007	−	0.931787i	$-0.618250\pi$
$379$	−14.1340	−0.726013	−0.363007	+	0.931787i	$0.618250\pi$
$380$	−2.23287	−0.114544
$381$	−35.7464	−1.83135
$382$	10.8188	0.553541
$383$	−15.7815	−0.806397	−0.403199	−	0.915112i	$-0.632102\pi$
$383$	−15.7815	−0.806397	−0.403199	+	0.915112i	$0.632102\pi$
$384$	22.9132	1.16928
$385$	0.183417	0.00934782
$386$	27.4992	1.39967
$387$	−0.447480	−0.0227467
$388$	5.86603	0.297803
$389$	13.8166	0.700529	0.350264	−	0.936651i	$-0.386092\pi$
$389$	13.8166	0.700529	0.350264	+	0.936651i	$0.386092\pi$
$390$	2.42469	0.122779
$391$	−11.3874	−0.575883
$392$	−16.5727	−0.837045
$393$	−23.0205	−1.16123
$394$	−9.38735	−0.472928
$395$	12.3896	0.623390
$396$	0.00841049	0.000422643 0
$397$	9.05172	0.454293	0.227146	−	0.973861i	$-0.427060\pi$
$397$	9.05172	0.454293	0.227146	+	0.973861i	$0.427060\pi$
$398$	15.0205	0.752911
$399$	−6.52359	−0.326588
$400$	−4.60197	−0.230098
$401$	19.7587	0.986704	0.493352	−	0.869830i	$-0.335772\pi$
$401$	19.7587	0.986704	0.493352	+	0.869830i	$0.335772\pi$
$402$	−15.0205	−0.749155
$403$	9.26180	0.461363
$404$	4.52359	0.225057
$405$	8.75872	0.435224
$406$	0	0
$407$	0.451356	0.0223729
$408$	21.3295	1.05597
$409$	1.71769	0.0849341	0.0424670	−	0.999098i	$-0.486478\pi$
$409$	1.71769	0.0849341	0.0424670	+	0.999098i	$0.486478\pi$
$410$	−0.523590	−0.0258583
$411$	−23.1650	−1.14264
$412$	−2.90337	−0.143039
$413$	6.15676	0.302954
$414$	0.276349	0.0135818
$415$	−2.78765	−0.136841
$416$	−1.90110	−0.0932093
$417$	8.36683	0.409726
$418$	2.70701	0.132404
$419$	−35.5318	−1.73584	−0.867922	−	0.496701i	$-0.834544\pi$
$419$	−35.5318	−1.73584	−0.867922	+	0.496701i	$0.834544\pi$
$420$	0.398032	0.0194220
$421$	12.0722	0.588365	0.294182	−	0.955749i	$-0.404953\pi$
$421$	12.0722	0.588365	0.294182	+	0.955749i	$0.404953\pi$
$422$	15.1857	0.739228
$423$	−0.0883965	−0.00429798
$424$	−0.853922	−0.0414701
$425$	−4.97107	−0.241132
$426$	23.8843	1.15720
$427$	−1.94214	−0.0939868
$428$	4.69860	0.227115
$429$	−0.457980	−0.0221115
$430$	8.78765	0.423778
$431$	19.8310	0.955224	0.477612	−	0.878571i	$-0.341503\pi$
$431$	19.8310	0.955224	0.477612	+	0.878571i	$0.341503\pi$
$432$	−24.2146	−1.16503
$433$	−14.8143	−0.711931	−0.355965	−	0.934499i	$-0.615848\pi$
$433$	−14.8143	−0.711931	−0.355965	+	0.934499i	$0.615848\pi$
$434$	9.75872	0.468434
$435$	0	0
$436$	4.59129	0.219883
$437$	13.8576	0.662900
$438$	18.2700	0.872976
$439$	−17.8576	−0.852298	−0.426149	−	0.904653i	$-0.640130\pi$
$439$	−17.8576	−0.852298	−0.426149	+	0.904653i	$0.640130\pi$
$440$	0.729794	0.0347916
$441$	0.517447	0.0246404
$442$	−7.05172	−0.335416
$443$	−33.5936	−1.59608	−0.798039	−	0.602606i	$-0.794129\pi$
$443$	−33.5936	−1.59608	−0.798039	+	0.602606i	$0.794129\pi$
$444$	0.979481	0.0464841
$445$	4.73820	0.224612
$446$	−16.8865	−0.799601
$447$	21.4063	1.01248
$448$	3.80364	0.179705
$449$	−7.07838	−0.334049	−0.167025	−	0.985953i	$-0.553416\pi$
$449$	−7.07838	−0.334049	−0.167025	+	0.985953i	$0.553416\pi$
$450$	0.120638	0.00568694
$451$	0.0988967	0.00465686
$452$	−4.64074	−0.218282
$453$	−12.9939	−0.610505
$454$	19.3112	0.906322
$455$	0.581449	0.0272588
$456$	−25.9565	−1.21553
$457$	−5.81658	−0.272088	−0.136044	−	0.990703i	$-0.543439\pi$
$457$	−5.81658	−0.272088	−0.136044	+	0.990703i	$0.543439\pi$
$458$	35.9565	1.68014
$459$	−26.1568	−1.22089
$460$	−0.845512	−0.0394222
$461$	32.3090	1.50478	0.752390	−	0.658718i	$-0.228901\pi$
$461$	32.3090	1.50478	0.752390	+	0.658718i	$0.228901\pi$
$462$	−0.482553	−0.0224504
$463$	1.44134	0.0669846	0.0334923	−	0.999439i	$-0.489337\pi$
$463$	1.44134	0.0669846	0.0334923	+	0.999439i	$0.489337\pi$
$464$	0	0
$465$	−17.1773	−0.796577
$466$	−19.1941	−0.889149
$467$	11.7503	0.543740	0.271870	−	0.962334i	$-0.412358\pi$
$467$	11.7503	0.543740	0.271870	+	0.962334i	$0.412358\pi$
$468$	0.0266620	0.00123245
$469$	−3.60197	−0.166323
$470$	1.73594	0.0800728
$471$	−42.5380	−1.96005
$472$	24.4969	1.12756
$473$	−1.65983	−0.0763189
$474$	−32.5958	−1.49718
$475$	6.04945	0.277568
$476$	−1.15759	−0.0530582
$477$	0.0266620	0.00122077
$478$	−21.1773	−0.968626
$479$	−17.1689	−0.784465	−0.392233	−	0.919866i	$-0.628297\pi$
$479$	−17.1689	−0.784465	−0.392233	+	0.919866i	$0.628297\pi$
$480$	3.52586	0.160933
$481$	1.43084	0.0652405
$482$	22.5958	1.02921
$483$	−2.47027	−0.112401
$484$	−4.02893	−0.183133
$485$	−15.8927	−0.721650
$486$	1.25338	0.0568547
$487$	−4.10277	−0.185914	−0.0929572	−	0.995670i	$-0.529632\pi$
$487$	−4.10277	−0.185914	−0.0929572	+	0.995670i	$0.529632\pi$
$488$	−7.72753	−0.349809
$489$	0.764867	0.0345885
$490$	−10.1617	−0.459058
$491$	−40.7708	−1.83996	−0.919981	−	0.391963i	$-0.871796\pi$
$491$	−40.7708	−1.83996	−0.919981	+	0.391963i	$0.871796\pi$
$492$	0.214614	0.00967556
$493$	0	0
$494$	8.58145	0.386098
$495$	−0.0227863	−0.00102417
$496$	46.2472	2.07656
$497$	5.72753	0.256915
$498$	7.33403	0.328646
$499$	−18.4703	−0.826843	−0.413421	−	0.910540i	$-0.635666\pi$
$499$	−18.4703	−0.826843	−0.413421	+	0.910540i	$0.635666\pi$
$500$	−0.369102	−0.0165068
$501$	−33.9565	−1.51707
$502$	23.7671	1.06078
$503$	21.4947	0.958400	0.479200	−	0.877706i	$-0.340927\pi$
$503$	21.4947	0.958400	0.479200	+	0.877706i	$0.340927\pi$
$504$	−0.124128	−0.00552911
$505$	−12.2557	−0.545369
$506$	1.02505	0.0455692
$507$	20.7687	0.922372
$508$	7.71912	0.342480
$509$	3.75872	0.166602	0.0833012	−	0.996524i	$-0.473454\pi$
$509$	3.75872	0.166602	0.0833012	+	0.996524i	$0.473454\pi$
$510$	13.0784	0.579120
$511$	4.38121	0.193813
$512$	13.6114	0.601546
$513$	31.8310	1.40537
$514$	9.66967	0.426511
$515$	7.86603	0.346619
$516$	−3.60197	−0.158568
$517$	−0.327887	−0.0144204
$518$	1.50761	0.0662404
$519$	43.4719	1.90820
$520$	2.31351	0.101454
$521$	12.8059	0.561037	0.280518	−	0.959849i	$-0.409494\pi$
$521$	12.8059	0.561037	0.280518	+	0.959849i	$0.409494\pi$
$522$	0	0
$523$	−21.1278	−0.923855	−0.461928	−	0.886918i	$-0.652842\pi$
$523$	−21.1278	−0.923855	−0.461928	+	0.886918i	$0.652842\pi$
$524$	4.97107	0.217162
$525$	−1.07838	−0.0470643
$526$	15.5090	0.676226
$527$	49.9565	2.17614
$528$	−2.28685	−0.0995223
$529$	−17.7526	−0.771851
$530$	−0.523590	−0.0227433
$531$	−0.764867	−0.0331924
$532$	1.40871	0.0610753
$533$	0.313511	0.0135797
$534$	−12.4657	−0.539445
$535$	−12.7298	−0.550357
$536$	−14.3318	−0.619038
$537$	−25.3607	−1.09439
$538$	43.3607	1.86941
$539$	1.91935	0.0826725
$540$	−1.94214	−0.0835764
$541$	−32.7382	−1.40753	−0.703763	−	0.710435i	$-0.748498\pi$
$541$	−32.7382	−1.40753	−0.703763	+	0.710435i	$0.748498\pi$
$542$	44.3318	1.90421
$543$	10.1112	0.433912
$544$	−10.2542	−0.439646
$545$	−12.4391	−0.532831
$546$	−1.52973	−0.0654666
$547$	−22.1073	−0.945240	−0.472620	−	0.881266i	$-0.656692\pi$
$547$	−22.1073	−0.945240	−0.472620	+	0.881266i	$0.656692\pi$
$548$	5.00227	0.213686
$549$	0.241276	0.0102974
$550$	0.447480	0.0190806
$551$	0	0
$552$	−9.82887	−0.418344
$553$	−7.81658	−0.332395
$554$	−0.0410378	−0.00174353
$555$	−2.65368	−0.112643
$556$	−1.80674	−0.0766229
$557$	−39.8720	−1.68943	−0.844715	−	0.535216i	$-0.820230\pi$
$557$	−39.8720	−1.68943	−0.844715	+	0.535216i	$0.820230\pi$
$558$	−1.21235	−0.0513227
$559$	−5.26180	−0.222550
$560$	2.90337	0.122690
$561$	−2.47027	−0.104295
$562$	43.2085	1.82264
$563$	−10.1217	−0.426578	−0.213289	−	0.976989i	$-0.568418\pi$
$563$	−10.1217	−0.426578	−0.213289	+	0.976989i	$0.568418\pi$
$564$	−0.711543	−0.0299614
$565$	12.5730	0.528952
$566$	32.0372	1.34662
$567$	−5.52586	−0.232064
$568$	22.7891	0.956209
$569$	24.4391	1.02454	0.512270	−	0.858825i	$-0.328805\pi$
$569$	24.4391	1.02454	0.512270	+	0.858825i	$0.328805\pi$
$570$	−15.9155	−0.666626
$571$	−28.2511	−1.18227	−0.591136	−	0.806572i	$-0.701320\pi$
$571$	−28.2511	−1.18227	−0.591136	+	0.806572i	$0.701320\pi$
$572$	0.0988967	0.00413508
$573$	12.0144	0.501908
$574$	0.330332	0.0137878
$575$	2.29072	0.0955298
$576$	−0.472534	−0.0196889
$577$	−46.1171	−1.91988	−0.959941	−	0.280202i	$-0.909598\pi$
$577$	−46.1171	−1.91988	−0.959941	+	0.280202i	$0.909598\pi$
$578$	−11.8695	−0.493707
$579$	30.5380	1.26911
$580$	0	0
$581$	1.75872	0.0729642
$582$	41.8120	1.73317
$583$	0.0988967	0.00409588
$584$	17.4323	0.721352
$585$	−0.0722347	−0.00298654
$586$	−23.7191	−0.979828
$587$	−0.715418	−0.0295285	−0.0147642	−	0.999891i	$-0.504700\pi$
$587$	−0.715418	−0.0295285	−0.0147642	+	0.999891i	$0.504700\pi$
$588$	4.16517	0.171769
$589$	−60.7936	−2.50496
$590$	15.0205	0.618385
$591$	−10.4247	−0.428815
$592$	7.14465	0.293643
$593$	15.5441	0.638320	0.319160	−	0.947701i	$-0.396599\pi$
$593$	15.5441	0.638320	0.319160	+	0.947701i	$0.396599\pi$
$594$	2.35455	0.0966083
$595$	3.13624	0.128573
$596$	−4.62249	−0.189344
$597$	16.6803	0.682681
$598$	3.24951	0.132882
$599$	9.59809	0.392167	0.196084	−	0.980587i	$-0.437178\pi$
$599$	9.59809	0.392167	0.196084	+	0.980587i	$0.437178\pi$
$600$	−4.29072	−0.175168
$601$	−6.81044	−0.277804	−0.138902	−	0.990306i	$-0.544357\pi$
$601$	−6.81044	−0.277804	−0.138902	+	0.990306i	$0.544357\pi$
$602$	−5.54411	−0.225961
$603$	0.447480	0.0182228
$604$	2.80590	0.114171
$605$	10.9155	0.443777
$606$	32.2434	1.30980
$607$	−31.6970	−1.28654	−0.643271	−	0.765639i	$-0.722423\pi$
$607$	−31.6970	−1.28654	−0.643271	+	0.765639i	$0.722423\pi$
$608$	12.4787	0.506077
$609$	0	0
$610$	−4.73820	−0.191844
$611$	−1.03943	−0.0420508
$612$	0.143810	0.00581318
$613$	1.20394	0.0486265	0.0243133	−	0.999704i	$-0.492260\pi$
$613$	1.20394	0.0486265	0.0243133	+	0.999704i	$0.492260\pi$
$614$	−43.7602	−1.76602
$615$	−0.581449	−0.0234463
$616$	−0.460425	−0.0185511
$617$	37.9337	1.52715	0.763577	−	0.645716i	$-0.223441\pi$
$617$	37.9337	1.52715	0.763577	+	0.645716i	$0.223441\pi$
$618$	−20.6947	−0.832464
$619$	4.60424	0.185060	0.0925299	−	0.995710i	$-0.470505\pi$
$619$	4.60424	0.185060	0.0925299	+	0.995710i	$0.470505\pi$
$620$	3.70928	0.148968
$621$	12.0533	0.483683
$622$	−30.2062	−1.21116
$623$	−2.98932	−0.119765
$624$	−7.24951	−0.290213
$625$	1.00000	0.0400000
$626$	−35.2618	−1.40934
$627$	3.00614	0.120054
$628$	9.18568	0.366549
$629$	7.71769	0.307724
$630$	−0.0761103	−0.00303231
$631$	−8.41241	−0.334893	−0.167446	−	0.985881i	$-0.553552\pi$
$631$	−8.41241	−0.334893	−0.167446	+	0.985881i	$0.553552\pi$
$632$	−31.1012	−1.23714
$633$	16.8638	0.670274
$634$	35.1857	1.39740
$635$	−20.9132	−0.829915
$636$	0.214614	0.00851001
$637$	6.08452	0.241077
$638$	0	0
$639$	−0.711543	−0.0281482
$640$	13.4052	0.529888
$641$	−32.5380	−1.28517	−0.642586	−	0.766213i	$-0.722139\pi$
$641$	−32.5380	−1.28517	−0.642586	+	0.766213i	$0.722139\pi$
$642$	33.4908	1.32178
$643$	−2.09293	−0.0825372	−0.0412686	−	0.999148i	$-0.513140\pi$
$643$	−2.09293	−0.0825372	−0.0412686	+	0.999148i	$0.513140\pi$
$644$	0.533431	0.0210201
$645$	9.75872	0.384249
$646$	46.2868	1.82113
$647$	45.1955	1.77682	0.888410	−	0.459051i	$-0.151811\pi$
$647$	45.1955	1.77682	0.888410	+	0.459051i	$0.151811\pi$
$648$	−21.9867	−0.863718
$649$	−2.83710	−0.111366
$650$	1.41855	0.0556401
$651$	10.8371	0.424739
$652$	−0.165166	−0.00646840
$653$	2.14834	0.0840712	0.0420356	−	0.999116i	$-0.486616\pi$
$653$	2.14834	0.0840712	0.0420356	+	0.999116i	$0.486616\pi$
$654$	32.7259	1.27968
$655$	−13.4680	−0.526238
$656$	1.56547	0.0611211
$657$	−0.544287	−0.0212347
$658$	−1.09520	−0.0426953
$659$	45.0843	1.75624	0.878118	−	0.478444i	$-0.158799\pi$
$659$	45.0843	1.75624	0.878118	+	0.478444i	$0.158799\pi$
$660$	−0.183417	−0.00713952
$661$	−36.3234	−1.41281	−0.706407	−	0.707806i	$-0.749685\pi$
$661$	−36.3234	−1.41281	−0.706407	+	0.707806i	$0.749685\pi$
$662$	37.0798	1.44115
$663$	−7.83096	−0.304129
$664$	6.99773	0.271565
$665$	−3.81658	−0.148001
$666$	−0.187293	−0.00725746
$667$	0	0
$668$	7.33260	0.283707
$669$	−18.7526	−0.725017
$670$	−8.78765	−0.339497
$671$	0.894960	0.0345496
$672$	−2.22446	−0.0858102
$673$	−17.4719	−0.673491	−0.336746	−	0.941596i	$-0.609326\pi$
$673$	−17.4719	−0.673491	−0.336746	+	0.941596i	$0.609326\pi$
$674$	19.6826	0.758146
$675$	5.26180	0.202527
$676$	−4.48482	−0.172493
$677$	40.0372	1.53875	0.769377	−	0.638796i	$-0.220567\pi$
$677$	40.0372	1.53875	0.769377	+	0.638796i	$0.220567\pi$
$678$	−33.0784	−1.27037
$679$	10.0267	0.384788
$680$	12.4787	0.478535
$681$	21.4452	0.821782
$682$	−4.49693	−0.172196
$683$	2.07611	0.0794402	0.0397201	−	0.999211i	$-0.487353\pi$
$683$	2.07611	0.0794402	0.0397201	+	0.999211i	$0.487353\pi$
$684$	−0.175007	−0.00669156
$685$	−13.5525	−0.517815
$686$	13.2085	0.504302
$687$	39.9299	1.52342
$688$	−26.2739	−1.00168
$689$	0.313511	0.0119438
$690$	−6.02666	−0.229431
$691$	26.7070	1.01598	0.507991	−	0.861362i	$-0.330388\pi$
$691$	26.7070	1.01598	0.507991	+	0.861362i	$0.330388\pi$
$692$	−9.38735	−0.356854
$693$	0.0143758	0.000546093 0
$694$	−12.9542	−0.491737
$695$	4.89496	0.185676
$696$	0	0
$697$	1.69102	0.0640521
$698$	−34.1666	−1.29322
$699$	−21.3151	−0.806212
$700$	0.232866	0.00880150
$701$	−21.9155	−0.827736	−0.413868	−	0.910337i	$-0.635823\pi$
$701$	−21.9155	−0.827736	−0.413868	+	0.910337i	$0.635823\pi$
$702$	7.46412	0.281715
$703$	−9.39189	−0.354222
$704$	−1.75276	−0.0660596
$705$	1.92777	0.0726038
$706$	9.51745	0.358194
$707$	7.73206	0.290794
$708$	−6.15676	−0.231385
$709$	−4.60811	−0.173061	−0.0865306	−	0.996249i	$-0.527578\pi$
$709$	−4.60811	−0.173061	−0.0865306	+	0.996249i	$0.527578\pi$
$710$	13.9733	0.524410
$711$	0.971071	0.0364180
$712$	−11.8941	−0.445751
$713$	−23.0205	−0.862125
$714$	−8.25112	−0.308790
$715$	−0.267938	−0.0100203
$716$	5.47641	0.204663
$717$	−23.5174	−0.878275
$718$	7.78151	0.290403
$719$	6.80590	0.253817	0.126909	−	0.991914i	$-0.459494\pi$
$719$	6.80590	0.253817	0.126909	+	0.991914i	$0.459494\pi$
$720$	−0.360692	−0.0134422
$721$	−4.96266	−0.184819
$722$	−27.0833	−1.00794
$723$	25.0928	0.933210
$724$	−2.18342	−0.0811461
$725$	0	0
$726$	−28.7175	−1.06581
$727$	26.9711	1.00030	0.500151	−	0.865938i	$-0.333278\pi$
$727$	26.9711	1.00030	0.500151	+	0.865938i	$0.333278\pi$
$728$	−1.45959	−0.0540960
$729$	27.6681	1.02474
$730$	10.6888	0.395609
$731$	−28.3812	−1.04972
$732$	1.94214	0.0717836
$733$	30.0638	1.11043	0.555216	−	0.831706i	$-0.312635\pi$
$733$	30.0638	1.11043	0.555216	+	0.831706i	$0.312635\pi$
$734$	45.4680	1.67825
$735$	−11.2846	−0.416238
$736$	4.72526	0.174175
$737$	1.65983	0.0611405
$738$	−0.0410378	−0.00151062
$739$	−51.1422	−1.88130	−0.940648	−	0.339383i	$-0.889782\pi$
$739$	−51.1422	−1.88130	−0.940648	+	0.339383i	$0.889782\pi$
$740$	0.573039	0.0210653
$741$	9.52973	0.350084
$742$	0.330332	0.0121269
$743$	−11.1857	−0.410363	−0.205181	−	0.978724i	$-0.565778\pi$
$743$	−11.1857	−0.410363	−0.205181	+	0.978724i	$0.565778\pi$
$744$	43.1194	1.58083
$745$	12.5236	0.458829
$746$	−22.1834	−0.812193
$747$	−0.218490	−0.00799413
$748$	0.533431	0.0195042
$749$	8.03120	0.293454
$750$	−2.63090	−0.0960668
$751$	18.3630	0.670074	0.335037	−	0.942205i	$-0.391251\pi$
$751$	18.3630	0.670074	0.335037	+	0.942205i	$0.391251\pi$
$752$	−5.19022	−0.189268
$753$	26.3935	0.961832
$754$	0	0
$755$	−7.60197	−0.276664
$756$	1.22529	0.0445634
$757$	−15.8927	−0.577630	−0.288815	−	0.957385i	$-0.593261\pi$
$757$	−15.8927	−0.577630	−0.288815	+	0.957385i	$0.593261\pi$
$758$	21.7548	0.790172
$759$	1.13833	0.0413186
$760$	−15.1857	−0.550843
$761$	13.8843	0.503305	0.251652	−	0.967818i	$-0.419026\pi$
$761$	13.8843	0.503305	0.251652	+	0.967818i	$0.419026\pi$
$762$	55.0205	1.99318
$763$	7.84778	0.284109
$764$	−2.59439	−0.0938619
$765$	−0.389621	−0.0140868
$766$	24.2907	0.877660
$767$	−8.99386	−0.324749
$768$	−14.6576	−0.528909
$769$	35.4063	1.27678	0.638391	−	0.769712i	$-0.279600\pi$
$769$	35.4063	1.27678	0.638391	+	0.769712i	$0.279600\pi$
$770$	−0.282314	−0.0101739
$771$	10.7382	0.386727
$772$	−6.59439	−0.237337
$773$	0.488518	0.0175708	0.00878539	−	0.999961i	$-0.497203\pi$
$773$	0.488518	0.0175708	0.00878539	+	0.999961i	$0.497203\pi$
$774$	0.688756	0.0247568
$775$	−10.0494	−0.360987
$776$	39.8948	1.43214
$777$	1.67420	0.0600617
$778$	−21.2663	−0.762435
$779$	−2.05786	−0.0737304
$780$	−0.581449	−0.0208192
$781$	−2.63931	−0.0944419
$782$	17.5273	0.626775
$783$	0	0
$784$	30.3820	1.08507
$785$	−24.8865	−0.888239
$786$	35.4329	1.26385
$787$	−1.99159	−0.0709925	−0.0354962	−	0.999370i	$-0.511301\pi$
$787$	−1.99159	−0.0709925	−0.0354962	+	0.999370i	$0.511301\pi$
$788$	2.25112	0.0801927
$789$	17.2228	0.613150
$790$	−19.0700	−0.678479
$791$	−7.93230	−0.282040
$792$	0.0571996	0.00203250
$793$	2.83710	0.100748
$794$	−13.9323	−0.494439
$795$	−0.581449	−0.0206219
$796$	−3.60197	−0.127668
$797$	17.2702	0.611742	0.305871	−	0.952073i	$-0.401052\pi$
$797$	17.2702	0.611742	0.305871	+	0.952073i	$0.401052\pi$
$798$	10.0410	0.355449
$799$	−5.60650	−0.198344
$800$	2.06278	0.0729303
$801$	0.371370	0.0131217
$802$	−30.4124	−1.07390
$803$	−2.01891	−0.0712458
$804$	3.60197	0.127032
$805$	−1.44521	−0.0509371
$806$	−14.2557	−0.502134
$807$	48.1522	1.69504
$808$	30.7649	1.08230
$809$	56.5068	1.98667	0.993336	−	0.115254i	$-0.0367680\pi$
$809$	56.5068	1.98667	0.993336	+	0.115254i	$0.0367680\pi$
$810$	−13.4813	−0.473686
$811$	−8.77924	−0.308281	−0.154140	−	0.988049i	$-0.549261\pi$
$811$	−8.77924	−0.308281	−0.154140	+	0.988049i	$0.549261\pi$
$812$	0	0
$813$	49.2306	1.72659
$814$	−0.694722	−0.0243500
$815$	0.447480	0.0156745
$816$	−39.1026	−1.36886
$817$	34.5380	1.20833
$818$	−2.64384	−0.0924398
$819$	0.0455727	0.00159244
$820$	0.125559	0.00438470
$821$	−28.1568	−0.982678	−0.491339	−	0.870969i	$-0.663492\pi$
$821$	−28.1568	−0.982678	−0.491339	+	0.870969i	$0.663492\pi$
$822$	35.6553	1.24362
$823$	−20.7442	−0.723096	−0.361548	−	0.932353i	$-0.617752\pi$
$823$	−20.7442	−0.723096	−0.361548	+	0.932353i	$0.617752\pi$
$824$	−19.7458	−0.687877
$825$	0.496928	0.0173008
$826$	−9.47641	−0.329726
$827$	9.12783	0.317406	0.158703	−	0.987326i	$-0.449269\pi$
$827$	9.12783	0.317406	0.158703	+	0.987326i	$0.449269\pi$
$828$	−0.0662693	−0.00230302
$829$	−31.8576	−1.10646	−0.553230	−	0.833028i	$-0.686605\pi$
$829$	−31.8576	−1.10646	−0.553230	+	0.833028i	$0.686605\pi$
$830$	4.29072	0.148933
$831$	−0.0455727	−0.00158090
$832$	−5.55640	−0.192633
$833$	32.8188	1.13711
$834$	−12.8781	−0.445933
$835$	−19.8660	−0.687492
$836$	−0.649149	−0.0224513
$837$	−52.8781	−1.82774
$838$	54.6902	1.88924
$839$	−27.4413	−0.947380	−0.473690	−	0.880692i	$-0.657078\pi$
$839$	−27.4413	−0.947380	−0.473690	+	0.880692i	$0.657078\pi$
$840$	2.70701	0.0934006
$841$	0	0
$842$	−18.5814	−0.640359
$843$	47.9832	1.65263
$844$	−3.64158	−0.125348
$845$	12.1506	0.417994
$846$	0.136059	0.00467780
$847$	−6.88655	−0.236625
$848$	1.56547	0.0537583
$849$	35.5774	1.22101
$850$	7.65142	0.262441
$851$	−3.55640	−0.121912
$852$	−5.72753	−0.196222
$853$	56.0515	1.91917	0.959584	−	0.281422i	$-0.0908061\pi$
$853$	56.0515	1.91917	0.959584	+	0.281422i	$0.0908061\pi$
$854$	2.98932	0.102292
$855$	0.474142	0.0162153
$856$	31.9551	1.09220
$857$	−6.08452	−0.207843	−0.103922	−	0.994585i	$-0.533139\pi$
$857$	−6.08452	−0.207843	−0.103922	+	0.994585i	$0.533139\pi$
$858$	0.704918	0.0240655
$859$	−35.5936	−1.21444	−0.607218	−	0.794535i	$-0.707715\pi$
$859$	−35.5936	−1.21444	−0.607218	+	0.794535i	$0.707715\pi$
$860$	−2.10731	−0.0718586
$861$	0.366835	0.0125017
$862$	−30.5236	−1.03964
$863$	−12.8287	−0.436694	−0.218347	−	0.975871i	$-0.570066\pi$
$863$	−12.8287	−0.436694	−0.218347	+	0.975871i	$0.570066\pi$
$864$	10.8539	0.369258
$865$	25.4329	0.864745
$866$	22.8020	0.774844
$867$	−13.1812	−0.447655
$868$	−2.34017	−0.0794306
$869$	3.60197	0.122188
$870$	0	0
$871$	5.26180	0.178289
$872$	31.2253	1.05742
$873$	−1.24563	−0.0421583
$874$	−21.3295	−0.721481
$875$	−0.630898	−0.0213282
$876$	−4.38121	−0.148027
$877$	−1.50307	−0.0507551	−0.0253776	−	0.999678i	$-0.508079\pi$
$877$	−1.50307	−0.0507551	−0.0253776	+	0.999678i	$0.508079\pi$
$878$	27.4863	0.927616
$879$	−26.3402	−0.888432
$880$	−1.33791	−0.0451008
$881$	−23.4908	−0.791425	−0.395712	−	0.918375i	$-0.629502\pi$
$881$	−23.4908	−0.791425	−0.395712	+	0.918375i	$0.629502\pi$
$882$	−0.796449	−0.0268178
$883$	−29.0433	−0.977385	−0.488693	−	0.872456i	$-0.662526\pi$
$883$	−29.0433	−0.977385	−0.488693	+	0.872456i	$0.662526\pi$
$884$	1.69102	0.0568753
$885$	16.6803	0.560704
$886$	51.7068	1.73712
$887$	19.0700	0.640307	0.320153	−	0.947366i	$-0.396266\pi$
$887$	19.0700	0.640307	0.320153	+	0.947366i	$0.396266\pi$
$888$	6.66144	0.223543
$889$	13.1941	0.442516
$890$	−7.29299	−0.244462
$891$	2.54638	0.0853068
$892$	4.04945	0.135586
$893$	6.82273	0.228314
$894$	−32.9483	−1.10196
$895$	−14.8371	−0.495950
$896$	−8.45732	−0.282539
$897$	3.60859	0.120487
$898$	10.8950	0.363570
$899$	0	0
$900$	−0.0289294	−0.000964314 0
$901$	1.69102	0.0563362
$902$	−0.152221	−0.00506839
$903$	−6.15676	−0.204884
$904$	−31.5616	−1.04972
$905$	5.91548	0.196637
$906$	20.0000	0.664455
$907$	−5.54023	−0.183960	−0.0919802	−	0.995761i	$-0.529320\pi$
$907$	−5.54023	−0.183960	−0.0919802	+	0.995761i	$0.529320\pi$
$908$	−4.63090	−0.153682
$909$	−0.960570	−0.0318601
$910$	−0.894960	−0.0296676
$911$	−53.2990	−1.76587	−0.882937	−	0.469492i	$-0.844437\pi$
$911$	−53.2990	−1.76587	−0.882937	+	0.469492i	$0.844437\pi$
$912$	47.5851	1.57570
$913$	−0.810439	−0.0268216
$914$	8.95282	0.296133
$915$	−5.26180	−0.173950
$916$	−8.62249	−0.284895
$917$	8.49693	0.280593
$918$	40.2602	1.32878
$919$	37.5897	1.23997	0.619985	−	0.784614i	$-0.287139\pi$
$919$	37.5897	1.23997	0.619985	+	0.784614i	$0.287139\pi$
$920$	−5.75031	−0.189582
$921$	−48.5958	−1.60129
$922$	−49.7296	−1.63776
$923$	−8.36683	−0.275398
$924$	0.115718	0.00380683
$925$	−1.55252	−0.0510465
$926$	−2.21849	−0.0729041
$927$	0.616522	0.0202492
$928$	0	0
$929$	37.3197	1.22442	0.612209	−	0.790696i	$-0.290281\pi$
$929$	37.3197	1.22442	0.612209	+	0.790696i	$0.290281\pi$
$930$	26.4391	0.866971
$931$	−39.9383	−1.30892
$932$	4.60281	0.150770
$933$	−33.5441	−1.09818
$934$	−18.0860	−0.591790
$935$	−1.44521	−0.0472635
$936$	0.181328	0.00592688
$937$	−22.8638	−0.746927	−0.373463	−	0.927645i	$-0.621830\pi$
$937$	−22.8638	−0.746927	−0.373463	+	0.927645i	$0.621830\pi$
$938$	5.54411	0.181022
$939$	−39.1584	−1.27788
$940$	−0.416283	−0.0135777
$941$	0.523590	0.0170686	0.00853428	−	0.999964i	$-0.497283\pi$
$941$	0.523590	0.0170686	0.00853428	+	0.999964i	$0.497283\pi$
$942$	65.4740	2.13326
$943$	−0.779243	−0.0253756
$944$	−44.9093	−1.46167
$945$	−3.31965	−0.107988
$946$	2.55479	0.0830633
$947$	10.0228	0.325697	0.162848	−	0.986651i	$-0.447932\pi$
$947$	10.0228	0.325697	0.162848	+	0.986651i	$0.447932\pi$
$948$	7.81658	0.253871
$949$	−6.40012	−0.207757
$950$	−9.31124	−0.302097
$951$	39.0738	1.26706
$952$	−7.87277	−0.255158
$953$	−8.15676	−0.264223	−0.132112	−	0.991235i	$-0.542176\pi$
$953$	−8.15676	−0.264223	−0.132112	+	0.991235i	$0.542176\pi$
$954$	−0.0410378	−0.00132865
$955$	7.02893	0.227451
$956$	5.07838	0.164246
$957$	0	0
$958$	26.4261	0.853789
$959$	8.55025	0.276102
$960$	10.3051	0.332596
$961$	69.9914	2.25779
$962$	−2.20233	−0.0710059
$963$	−0.997733	−0.0321515
$964$	−5.41855	−0.174520
$965$	17.8660	0.575128
$966$	3.80221	0.122334
$967$	−15.7671	−0.507037	−0.253518	−	0.967331i	$-0.581588\pi$
$967$	−15.7671	−0.507037	−0.253518	+	0.967331i	$0.581588\pi$
$968$	−27.4007	−0.880691
$969$	51.4017	1.65126
$970$	24.4619	0.785423
$971$	17.8804	0.573810	0.286905	−	0.957959i	$-0.407374\pi$
$971$	17.8804	0.573810	0.286905	+	0.957959i	$0.407374\pi$
$972$	−0.300566	−0.00964065
$973$	−3.08822	−0.0990037
$974$	6.31494	0.202344
$975$	1.57531	0.0504502
$976$	14.1666	0.453462
$977$	−55.1071	−1.76303	−0.881517	−	0.472153i	$-0.843477\pi$
$977$	−55.1071	−1.76303	−0.881517	+	0.472153i	$0.843477\pi$
$978$	−1.17727	−0.0376451
$979$	1.37751	0.0440255
$980$	2.43680	0.0778408
$981$	−0.974946	−0.0311276
$982$	62.7540	2.00256
$983$	1.29687	0.0413637	0.0206818	−	0.999786i	$-0.493416\pi$
$983$	1.29687	0.0413637	0.0206818	+	0.999786i	$0.493416\pi$
$984$	1.45959	0.0465300
$985$	−6.09890	−0.194327
$986$	0	0
$987$	−1.21622	−0.0387128
$988$	−2.05786	−0.0654692
$989$	13.0784	0.415868
$990$	0.0350725	0.00111468
$991$	−3.11942	−0.0990915	−0.0495458	−	0.998772i	$-0.515777\pi$
$991$	−3.11942	−0.0990915	−0.0495458	+	0.998772i	$0.515777\pi$
$992$	−20.7298	−0.658172
$993$	41.1773	1.30672
$994$	−8.81575	−0.279618
$995$	9.75872	0.309372
$996$	−1.75872	−0.0557273
$997$	−30.2472	−0.957940	−0.478970	−	0.877831i	$-0.658990\pi$
$997$	−30.2472	−0.957940	−0.478970	+	0.877831i	$0.658990\pi$
$998$	28.4292	0.899912
$999$	−8.16904	−0.258457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4205.2.a.e.1.2		3
29.28	even	2		145.2.a.d.1.2	✓	3
87.86	odd	2		1305.2.a.o.1.2		3
116.115	odd	2		2320.2.a.s.1.1		3
145.28	odd	4		725.2.b.d.349.2		6
145.57	odd	4		725.2.b.d.349.5		6
145.144	even	2		725.2.a.d.1.2		3
203.202	odd	2		7105.2.a.p.1.2		3
232.115	odd	2		9280.2.a.bm.1.3		3
232.173	even	2		9280.2.a.bu.1.1		3
435.434	odd	2		6525.2.a.bh.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.a.d.1.2	✓	3	29.28	even	2
725.2.a.d.1.2		3	145.144	even	2
725.2.b.d.349.2		6	145.28	odd	4
725.2.b.d.349.5		6	145.57	odd	4
1305.2.a.o.1.2		3	87.86	odd	2
2320.2.a.s.1.1		3	116.115	odd	2
4205.2.a.e.1.2		3	1.1	even	1	trivial
6525.2.a.bh.1.2		3	435.434	odd	2
7105.2.a.p.1.2		3	203.202	odd	2
9280.2.a.bm.1.3		3	232.115	odd	2
9280.2.a.bu.1.1		3	232.173	even	2

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:	\( N \)	\(=\)	\( 4205 = 5 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4205.a (trivial)

\(f(q)\)	\(=\)	\(q-1.53919 q^{2} -1.70928 q^{3} +0.369102 q^{4} -1.00000 q^{5} +2.63090 q^{6} +0.630898 q^{7} +2.51026 q^{8} -0.0783777 q^{9} +1.53919 q^{10} -0.290725 q^{11} -0.630898 q^{12} -0.921622 q^{13} -0.971071 q^{14} +1.70928 q^{15} -4.60197 q^{16} -4.97107 q^{17} +0.120638 q^{18} +6.04945 q^{19} -0.369102 q^{20} -1.07838 q^{21} +0.447480 q^{22} +2.29072 q^{23} -4.29072 q^{24} +1.00000 q^{25} +1.41855 q^{26} +5.26180 q^{27} +0.232866 q^{28} -2.63090 q^{30} -10.0494 q^{31} +2.06278 q^{32} +0.496928 q^{33} +7.65142 q^{34} -0.630898 q^{35} -0.0289294 q^{36} -1.55252 q^{37} -9.31124 q^{38} +1.57531 q^{39} -2.51026 q^{40} -0.340173 q^{41} +1.65983 q^{42} +5.70928 q^{43} -0.107307 q^{44} +0.0783777 q^{45} -3.52586 q^{46} +1.12783 q^{47} +7.86603 q^{48} -6.60197 q^{49} -1.53919 q^{50} +8.49693 q^{51} -0.340173 q^{52} -0.340173 q^{53} -8.09890 q^{54} +0.290725 q^{55} +1.58372 q^{56} -10.3402 q^{57} +9.75872 q^{59} +0.630898 q^{60} -3.07838 q^{61} +15.4680 q^{62} -0.0494483 q^{63} +6.02893 q^{64} +0.921622 q^{65} -0.764867 q^{66} -5.70928 q^{67} -1.83483 q^{68} -3.91548 q^{69} +0.971071 q^{70} +9.07838 q^{71} -0.196748 q^{72} +6.94441 q^{73} +2.38962 q^{74} -1.70928 q^{75} +2.23287 q^{76} -0.183417 q^{77} -2.42469 q^{78} -12.3896 q^{79} +4.60197 q^{80} -8.75872 q^{81} +0.523590 q^{82} +2.78765 q^{83} -0.398032 q^{84} +4.97107 q^{85} -8.78765 q^{86} -0.729794 q^{88} -4.73820 q^{89} -0.120638 q^{90} -0.581449 q^{91} +0.845512 q^{92} +17.1773 q^{93} -1.73594 q^{94} -6.04945 q^{95} -3.52586 q^{96} +15.8927 q^{97} +10.1617 q^{98} +0.0227863 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 2 q^{3} + 5 q^{4} - 3 q^{5} + 4 q^{6} - 2 q^{7} - 9 q^{8} + 3 q^{9} + 3 q^{10} - 8 q^{11} + 2 q^{12} - 6 q^{13} + 12 q^{14} - 2 q^{15} + 5 q^{16} + 13 q^{18} - 5 q^{20} + 2 q^{22} + 14 q^{23}+ \cdots - 20 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 2 * q^3 + 5 * q^4 - 3 * q^5 + 4 * q^6 - 2 * q^7 - 9 * q^8 + 3 * q^9 + 3 * q^10 - 8 * q^11 + 2 * q^12 - 6 * q^13 + 12 * q^14 - 2 * q^15 + 5 * q^16 + 13 * q^18 - 5 * q^20 + 2 * q^22 + 14 * q^23 - 20 * q^24 + 3 * q^25 - 10 * q^26 + 8 * q^27 - 22 * q^28 - 4 * q^30 - 12 * q^31 - 11 * q^32 - 16 * q^33 - 14 * q^34 + 2 * q^35 - 15 * q^36 - 4 * q^37 - 2 * q^38 - 16 * q^39 + 9 * q^40 + 10 * q^41 + 16 * q^42 + 10 * q^43 - 12 * q^44 - 3 * q^45 - 8 * q^46 - 18 * q^47 + 10 * q^48 - q^49 - 3 * q^50 + 8 * q^51 + 10 * q^52 + 10 * q^53 + 12 * q^54 + 8 * q^55 + 32 * q^56 - 20 * q^57 + 4 * q^59 - 2 * q^60 - 6 * q^61 + 14 * q^62 + 18 * q^63 + 33 * q^64 + 6 * q^65 - 12 * q^66 - 10 * q^67 + 36 * q^68 + 20 * q^69 - 12 * q^70 + 24 * q^71 + 3 * q^72 + 4 * q^73 - 22 * q^74 + 2 * q^75 - 16 * q^76 + 4 * q^77 - 28 * q^78 - 8 * q^79 - 5 * q^80 - q^81 - 14 * q^82 - 2 * q^83 - 20 * q^84 - 16 * q^86 + 38 * q^88 - 22 * q^89 - 13 * q^90 - 16 * q^91 + 22 * q^92 + 12 * q^93 - 8 * q^96 + 36 * q^97 - 23 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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