LMFDB - Embedded newform 4925.2.a.p.1.30

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [4925,2,Mod(1,4925)] 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("4925.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4925, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 4925 = 5^{2} \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4925.a (trivial)

Newform invariants

comment:select newform

sage:traces = [37,-2,-1] 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:	$39.3263229955$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.30
Character	$\chi$	$=$	4925.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.87761 q^{2} -1.07939 q^{3} +1.52542 q^{4} -2.02668 q^{6} +3.38183 q^{7} -0.891075 q^{8} -1.83491 q^{9} -3.24153 q^{11} -1.64653 q^{12} +3.82785 q^{13} +6.34976 q^{14} -4.72393 q^{16} +5.13529 q^{17} -3.44525 q^{18} +0.661045 q^{19} -3.65032 q^{21} -6.08634 q^{22} -2.86378 q^{23} +0.961820 q^{24} +7.18722 q^{26} +5.21877 q^{27} +5.15872 q^{28} +2.90516 q^{29} +1.13789 q^{31} -7.08756 q^{32} +3.49889 q^{33} +9.64207 q^{34} -2.79901 q^{36} +6.20771 q^{37} +1.24118 q^{38} -4.13176 q^{39} -7.52150 q^{41} -6.85388 q^{42} +7.75992 q^{43} -4.94470 q^{44} -5.37706 q^{46} +1.58619 q^{47} +5.09898 q^{48} +4.43678 q^{49} -5.54299 q^{51} +5.83909 q^{52} -2.16411 q^{53} +9.79881 q^{54} -3.01347 q^{56} -0.713527 q^{57} +5.45476 q^{58} -9.54872 q^{59} -0.171187 q^{61} +2.13652 q^{62} -6.20536 q^{63} -3.85980 q^{64} +6.56955 q^{66} +4.57097 q^{67} +7.83348 q^{68} +3.09114 q^{69} +8.39750 q^{71} +1.63504 q^{72} +12.6997 q^{73} +11.6557 q^{74} +1.00837 q^{76} -10.9623 q^{77} -7.75783 q^{78} +13.8668 q^{79} -0.128364 q^{81} -14.1225 q^{82} +0.00439733 q^{83} -5.56828 q^{84} +14.5701 q^{86} -3.13581 q^{87} +2.88845 q^{88} +4.78416 q^{89} +12.9452 q^{91} -4.36847 q^{92} -1.22824 q^{93} +2.97824 q^{94} +7.65025 q^{96} -2.91549 q^{97} +8.33055 q^{98} +5.94793 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 2 q^{2} - q^{3} + 50 q^{4} + 8 q^{6} + 4 q^{7} + 50 q^{9} + 17 q^{11} + 2 q^{12} + 3 q^{13} + 14 q^{14} + 72 q^{16} + 10 q^{17} + 4 q^{18} + 54 q^{19} + 15 q^{21} + 11 q^{22} - 4 q^{23} + 28 q^{24}+ \cdots + 40 q^{99}+O(q^{100}) $ 37 * q - 2 * q^2 - q^3 + 50 * q^4 + 8 * q^6 + 4 * q^7 + 50 * q^9 + 17 * q^11 + 2 * q^12 + 3 * q^13 + 14 * q^14 + 72 * q^16 + 10 * q^17 + 4 * q^18 + 54 * q^19 + 15 * q^21 + 11 * q^22 - 4 * q^23 + 28 * q^24 + 19 * q^26 + 2 * q^27 - 3 * q^28 - 4 * q^29 + 58 * q^31 - 22 * q^32 + 7 * q^33 + 63 * q^34 + 66 * q^36 - 7 * q^37 - 12 * q^38 + 23 * q^39 + 17 * q^41 + 17 * q^42 - 11 * q^43 + 34 * q^44 + 41 * q^46 + 19 * q^47 - 10 * q^48 + 81 * q^49 + 39 * q^51 - 31 * q^52 + 14 * q^53 + 5 * q^54 + 21 * q^56 - 24 * q^57 + 15 * q^58 + 56 * q^59 + 40 * q^61 - 4 * q^62 - 5 * q^63 + 78 * q^64 + 22 * q^66 - 2 * q^67 + 3 * q^68 + 24 * q^69 + 31 * q^71 - 85 * q^72 - 4 * q^73 - 32 * q^74 + 137 * q^76 - 16 * q^77 + 113 * q^78 + 17 * q^79 + 85 * q^81 - 52 * q^82 + 18 * q^83 - 32 * q^84 + 35 * q^86 - 39 * q^87 + 63 * q^88 + 23 * q^89 + 152 * q^91 - 75 * q^92 - 8 * q^93 + 32 * q^94 + 72 * q^96 - 34 * q^97 + 40 * q^98 + 40 * 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 $

$2$	1.87761	1.32767	0.663836	−	0.747879i	$-0.268927\pi$
$2$	1.87761	1.32767	0.663836	+	0.747879i	$0.268927\pi$
$3$	−1.07939	−0.623188	−0.311594	−	0.950215i	$-0.600863\pi$
$3$	−1.07939	−0.623188	−0.311594	+	0.950215i	$0.600863\pi$
$4$	1.52542	0.762710
$5$	0	0
$5$	0	0
$6$	−2.02668	−0.827388
$7$	3.38183	1.27821	0.639106	−	0.769119i	$-0.279304\pi$
$7$	3.38183	1.27821	0.639106	+	0.769119i	$0.279304\pi$
$8$	−0.891075	−0.315043
$9$	−1.83491	−0.611637
$10$	0	0
$11$	−3.24153	−0.977360	−0.488680	−	0.872463i	$-0.662521\pi$
$11$	−3.24153	−0.977360	−0.488680	+	0.872463i	$0.662521\pi$
$12$	−1.64653	−0.475312
$13$	3.82785	1.06166	0.530828	−	0.847480i	$-0.321881\pi$
$13$	3.82785	1.06166	0.530828	+	0.847480i	$0.321881\pi$
$14$	6.34976	1.69705
$15$	0	0
$16$	−4.72393	−1.18098
$17$	5.13529	1.24549	0.622745	−	0.782425i	$-0.286017\pi$
$17$	5.13529	1.24549	0.622745	+	0.782425i	$0.286017\pi$
$18$	−3.44525	−0.812053
$19$	0.661045	0.151654	0.0758271	−	0.997121i	$-0.475840\pi$
$19$	0.661045	0.151654	0.0758271	+	0.997121i	$0.475840\pi$
$20$	0	0
$21$	−3.65032	−0.796566
$22$	−6.08634	−1.29761
$23$	−2.86378	−0.597139	−0.298570	−	0.954388i	$-0.596509\pi$
$23$	−2.86378	−0.597139	−0.298570	+	0.954388i	$0.596509\pi$
$24$	0.961820	0.196331
$25$	0	0
$26$	7.18722	1.40953
$27$	5.21877	1.00435
$28$	5.15872	0.974906
$29$	2.90516	0.539475	0.269737	−	0.962934i	$-0.413063\pi$
$29$	2.90516	0.539475	0.269737	+	0.962934i	$0.413063\pi$
$30$	0	0
$31$	1.13789	0.204372	0.102186	−	0.994765i	$-0.467416\pi$
$31$	1.13789	0.204372	0.102186	+	0.994765i	$0.467416\pi$
$32$	−7.08756	−1.25291
$33$	3.49889	0.609078
$34$	9.64207	1.65360
$35$	0	0
$36$	−2.79901	−0.466502
$37$	6.20771	1.02054	0.510271	−	0.860014i	$-0.329545\pi$
$37$	6.20771	1.02054	0.510271	+	0.860014i	$0.329545\pi$
$38$	1.24118	0.201347
$39$	−4.13176	−0.661611
$40$	0	0
$41$	−7.52150	−1.17466	−0.587331	−	0.809347i	$-0.699821\pi$
$41$	−7.52150	−1.17466	−0.587331	+	0.809347i	$0.699821\pi$
$42$	−6.85388	−1.05758
$43$	7.75992	1.18338	0.591689	−	0.806167i	$-0.298461\pi$
$43$	7.75992	1.18338	0.591689	+	0.806167i	$0.298461\pi$
$44$	−4.94470	−0.745442
$45$	0	0
$46$	−5.37706	−0.792804
$47$	1.58619	0.231369	0.115684	−	0.993286i	$-0.463094\pi$
$47$	1.58619	0.231369	0.115684	+	0.993286i	$0.463094\pi$
$48$	5.09898	0.735974
$49$	4.43678	0.633826
$50$	0	0
$51$	−5.54299	−0.776174
$52$	5.83909	0.809736
$53$	−2.16411	−0.297263	−0.148632	−	0.988893i	$-0.547487\pi$
$53$	−2.16411	−0.297263	−0.148632	+	0.988893i	$0.547487\pi$
$54$	9.79881	1.33345
$55$	0	0
$56$	−3.01347	−0.402691
$57$	−0.713527	−0.0945090
$58$	5.45476	0.716245
$59$	−9.54872	−1.24314	−0.621569	−	0.783360i	$-0.713504\pi$
$59$	−9.54872	−1.24314	−0.621569	+	0.783360i	$0.713504\pi$
$60$	0	0
$61$	−0.171187	−0.0219183	−0.0109592	−	0.999940i	$-0.503488\pi$
$61$	−0.171187	−0.0219183	−0.0109592	+	0.999940i	$0.503488\pi$
$62$	2.13652	0.271339
$63$	−6.20536	−0.781802
$64$	−3.85980	−0.482475
$65$	0	0
$66$	6.56955	0.808656
$67$	4.57097	0.558433	0.279217	−	0.960228i	$-0.409925\pi$
$67$	4.57097	0.558433	0.279217	+	0.960228i	$0.409925\pi$
$68$	7.83348	0.949949
$69$	3.09114	0.372130
$70$	0	0
$71$	8.39750	0.996600	0.498300	−	0.867005i	$-0.333958\pi$
$71$	8.39750	0.996600	0.498300	+	0.867005i	$0.333958\pi$
$72$	1.63504	0.192692
$73$	12.6997	1.48639	0.743193	−	0.669077i	$-0.233311\pi$
$73$	12.6997	1.48639	0.743193	+	0.669077i	$0.233311\pi$
$74$	11.6557	1.35494
$75$	0	0
$76$	1.00837	0.115668
$77$	−10.9623	−1.24927
$78$	−7.75783	−0.878401
$79$	13.8668	1.56014	0.780068	−	0.625694i	$-0.215184\pi$
$79$	13.8668	1.56014	0.780068	+	0.625694i	$0.215184\pi$
$80$	0	0
$81$	−0.128364	−0.0142626
$82$	−14.1225	−1.55956
$83$	0.00439733	0.000482670 0	0.000241335	−	1.00000i	$-0.499923\pi$
$83$	0.00439733	0.000482670 0	0.000241335		1.00000i	$0.499923\pi$
$84$	−5.56828	−0.607549
$85$	0	0
$86$	14.5701	1.57114
$87$	−3.13581	−0.336194
$88$	2.88845	0.307910
$89$	4.78416	0.507120	0.253560	−	0.967320i	$-0.418398\pi$
$89$	4.78416	0.507120	0.253560	+	0.967320i	$0.418398\pi$
$90$	0	0
$91$	12.9452	1.35702
$92$	−4.36847	−0.455444
$93$	−1.22824	−0.127362
$94$	2.97824	0.307182
$95$	0	0
$96$	7.65025	0.780801
$97$	−2.91549	−0.296024	−0.148012	−	0.988986i	$-0.547287\pi$
$97$	−2.91549	−0.296024	−0.148012	+	0.988986i	$0.547287\pi$
$98$	8.33055	0.841512
$99$	5.94793	0.597790
$100$	0	0
$101$	3.19634	0.318048	0.159024	−	0.987275i	$-0.449165\pi$
$101$	3.19634	0.318048	0.159024	+	0.987275i	$0.449165\pi$
$102$	−10.4076	−1.03050
$103$	13.5063	1.33082	0.665408	−	0.746480i	$-0.268258\pi$
$103$	13.5063	1.33082	0.665408	+	0.746480i	$0.268258\pi$
$104$	−3.41091	−0.334467
$105$	0	0
$106$	−4.06335	−0.394667
$107$	15.6753	1.51539	0.757695	−	0.652609i	$-0.226326\pi$
$107$	15.6753	1.51539	0.757695	+	0.652609i	$0.226326\pi$
$108$	7.96082	0.766030
$109$	15.9707	1.52971	0.764856	−	0.644201i	$-0.222810\pi$
$109$	15.9707	1.52971	0.764856	+	0.644201i	$0.222810\pi$
$110$	0	0
$111$	−6.70056	−0.635989
$112$	−15.9755	−1.50955
$113$	−0.482758	−0.0454140	−0.0227070	−	0.999742i	$-0.507228\pi$
$113$	−0.482758	−0.0454140	−0.0227070	+	0.999742i	$0.507228\pi$
$114$	−1.33973	−0.125477
$115$	0	0
$116$	4.43159	0.411463
$117$	−7.02378	−0.649348
$118$	−17.9288	−1.65048
$119$	17.3667	1.59200
$120$	0	0
$121$	−0.492451	−0.0447683
$122$	−0.321423	−0.0291003
$123$	8.11866	0.732035
$124$	1.73577	0.155877
$125$	0	0
$126$	−11.6513	−1.03798
$127$	9.26276	0.821937	0.410969	−	0.911650i	$-0.365191\pi$
$127$	9.26276	0.821937	0.410969	+	0.911650i	$0.365191\pi$
$128$	6.92791	0.612346
$129$	−8.37600	−0.737466
$130$	0	0
$131$	−8.34419	−0.729035	−0.364518	−	0.931196i	$-0.618766\pi$
$131$	−8.34419	−0.729035	−0.364518	+	0.931196i	$0.618766\pi$
$132$	5.33728	0.464550
$133$	2.23554	0.193846
$134$	8.58251	0.741416
$135$	0	0
$136$	−4.57593	−0.392383
$137$	−12.9183	−1.10368	−0.551841	−	0.833949i	$-0.686074\pi$
$137$	−12.9183	−1.10368	−0.551841	+	0.833949i	$0.686074\pi$
$138$	5.80396	0.494066
$139$	2.45797	0.208482	0.104241	−	0.994552i	$-0.466759\pi$
$139$	2.45797	0.208482	0.104241	+	0.994552i	$0.466759\pi$
$140$	0	0
$141$	−1.71212	−0.144186
$142$	15.7672	1.32316
$143$	−12.4081	−1.03762
$144$	8.66800	0.722333
$145$	0	0
$146$	23.8451	1.97343
$147$	−4.78903	−0.394993
$148$	9.46937	0.778378
$149$	−3.41151	−0.279482	−0.139741	−	0.990188i	$-0.544627\pi$
$149$	−3.41151	−0.279482	−0.139741	+	0.990188i	$0.544627\pi$
$150$	0	0
$151$	5.96173	0.485159	0.242579	−	0.970132i	$-0.422007\pi$
$151$	5.96173	0.485159	0.242579	+	0.970132i	$0.422007\pi$
$152$	−0.589041	−0.0477775
$153$	−9.42280	−0.761789
$154$	−20.5830	−1.65862
$155$	0	0
$156$	−6.30267	−0.504617
$157$	−4.91932	−0.392604	−0.196302	−	0.980543i	$-0.562893\pi$
$157$	−4.91932	−0.392604	−0.196302	+	0.980543i	$0.562893\pi$
$158$	26.0364	2.07135
$159$	2.33592	0.185251
$160$	0	0
$161$	−9.68482	−0.763270
$162$	−0.241017	−0.0189361
$163$	−14.4796	−1.13413	−0.567064	−	0.823674i	$-0.691921\pi$
$163$	−14.4796	−1.13413	−0.567064	+	0.823674i	$0.691921\pi$
$164$	−11.4735	−0.895927
$165$	0	0
$166$	0.00825648	0.000640827 0
$167$	−16.8204	−1.30160	−0.650801	−	0.759248i	$-0.725567\pi$
$167$	−16.8204	−1.30160	−0.650801	+	0.759248i	$0.725567\pi$
$168$	3.25271	0.250952
$169$	1.65247	0.127113
$170$	0	0
$171$	−1.21296	−0.0927573
$172$	11.8371	0.902574
$173$	−16.7320	−1.27211	−0.636056	−	0.771643i	$-0.719435\pi$
$173$	−16.7320	−1.27211	−0.636056	+	0.771643i	$0.719435\pi$
$174$	−5.88782	−0.446355
$175$	0	0
$176$	15.3128	1.15425
$177$	10.3068	0.774708
$178$	8.98279	0.673289
$179$	11.9464	0.892913	0.446457	−	0.894805i	$-0.352686\pi$
$179$	11.9464	0.892913	0.446457	+	0.894805i	$0.352686\pi$
$180$	0	0
$181$	1.69330	0.125862	0.0629310	−	0.998018i	$-0.479955\pi$
$181$	1.69330	0.125862	0.0629310	+	0.998018i	$0.479955\pi$
$182$	24.3060	1.80168
$183$	0.184778	0.0136592
$184$	2.55184	0.188124
$185$	0	0
$186$	−2.30615	−0.169095
$187$	−16.6462	−1.21729
$188$	2.41960	0.176467
$189$	17.6490	1.28378
$190$	0	0
$191$	8.83632	0.639374	0.319687	−	0.947523i	$-0.396422\pi$
$191$	8.83632	0.639374	0.319687	+	0.947523i	$0.396422\pi$
$192$	4.16624	0.300673
$193$	−15.8170	−1.13853	−0.569267	−	0.822153i	$-0.692773\pi$
$193$	−15.8170	−1.13853	−0.569267	+	0.822153i	$0.692773\pi$
$194$	−5.47416	−0.393022
$195$	0	0
$196$	6.76796	0.483426
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	11.1679	0.793668
$199$	−2.85476	−0.202368	−0.101184	−	0.994868i	$-0.532263\pi$
$199$	−2.85476	−0.202368	−0.101184	+	0.994868i	$0.532263\pi$
$200$	0	0
$201$	−4.93387	−0.348009
$202$	6.00148	0.422263
$203$	9.82476	0.689563
$204$	−8.45540	−0.591996
$205$	0	0
$206$	25.3596	1.76688
$207$	5.25478	0.365232
$208$	−18.0825	−1.25380
$209$	−2.14280	−0.148221
$210$	0	0
$211$	−11.5849	−0.797541	−0.398770	−	0.917051i	$-0.630563\pi$
$211$	−11.5849	−0.797541	−0.398770	+	0.917051i	$0.630563\pi$
$212$	−3.30117	−0.226726
$213$	−9.06420	−0.621069
$214$	29.4321	2.01194
$215$	0	0
$216$	−4.65031	−0.316414
$217$	3.84817	0.261231
$218$	29.9867	2.03095
$219$	−13.7079	−0.926297
$220$	0	0
$221$	19.6571	1.32228
$222$	−12.5810	−0.844384
$223$	12.5950	0.843421	0.421711	−	0.906730i	$-0.361430\pi$
$223$	12.5950	0.843421	0.421711	+	0.906730i	$0.361430\pi$
$224$	−23.9689	−1.60149
$225$	0	0
$226$	−0.906431	−0.0602949
$227$	17.2527	1.14510	0.572552	−	0.819869i	$-0.305954\pi$
$227$	17.2527	1.14510	0.572552	+	0.819869i	$0.305954\pi$
$228$	−1.08843	−0.0720830
$229$	7.90696	0.522506	0.261253	−	0.965270i	$-0.415864\pi$
$229$	7.90696	0.522506	0.261253	+	0.965270i	$0.415864\pi$
$230$	0	0
$231$	11.8327	0.778531
$232$	−2.58872	−0.169957
$233$	14.4144	0.944320	0.472160	−	0.881513i	$-0.343474\pi$
$233$	14.4144	0.944320	0.472160	+	0.881513i	$0.343474\pi$
$234$	−13.1879	−0.862121
$235$	0	0
$236$	−14.5658	−0.948153
$237$	−14.9677	−0.972258
$238$	32.6079	2.11365
$239$	−17.2175	−1.11371	−0.556853	−	0.830611i	$-0.687991\pi$
$239$	−17.2175	−1.11371	−0.556853	+	0.830611i	$0.687991\pi$
$240$	0	0
$241$	2.64086	0.170113	0.0850563	−	0.996376i	$-0.472893\pi$
$241$	2.64086	0.170113	0.0850563	+	0.996376i	$0.472893\pi$
$242$	−0.924632	−0.0594376
$243$	−15.5177	−0.995464
$244$	−0.261133	−0.0167173
$245$	0	0
$246$	15.2437	0.971901
$247$	2.53038	0.161004
$248$	−1.01395	−0.0643859
$249$	−0.00474645	−0.000300794 0
$250$	0	0
$251$	23.7274	1.49766	0.748829	−	0.662764i	$-0.230617\pi$
$251$	23.7274	1.49766	0.748829	+	0.662764i	$0.230617\pi$
$252$	−9.46579	−0.596289
$253$	9.28304	0.583620
$254$	17.3919	1.09126
$255$	0	0
$256$	20.7275	1.29547
$257$	14.9704	0.933829	0.466914	−	0.884303i	$-0.345366\pi$
$257$	14.9704	0.933829	0.466914	+	0.884303i	$0.345366\pi$
$258$	−15.7269	−0.979112
$259$	20.9934	1.30447
$260$	0	0
$261$	−5.33071	−0.329963
$262$	−15.6671	−0.967919
$263$	32.1018	1.97948	0.989740	−	0.142879i	$-0.0456359\pi$
$263$	32.1018	1.97948	0.989740	+	0.142879i	$0.0456359\pi$
$264$	−3.11777	−0.191886
$265$	0	0
$266$	4.19748	0.257364
$267$	−5.16399	−0.316031
$268$	6.97266	0.425923
$269$	0.0650614	0.00396687	0.00198343	−	0.999998i	$-0.499369\pi$
$269$	0.0650614	0.00396687	0.00198343	+	0.999998i	$0.499369\pi$
$270$	0	0
$271$	10.7212	0.651265	0.325633	−	0.945496i	$-0.394423\pi$
$271$	10.7212	0.651265	0.325633	+	0.945496i	$0.394423\pi$
$272$	−24.2588	−1.47090
$273$	−13.9729	−0.845679
$274$	−24.2555	−1.46533
$275$	0	0
$276$	4.71529	0.283827
$277$	1.37697	0.0827342	0.0413671	−	0.999144i	$-0.486829\pi$
$277$	1.37697	0.0827342	0.0413671	+	0.999144i	$0.486829\pi$
$278$	4.61511	0.276796
$279$	−2.08794	−0.125002
$280$	0	0
$281$	−10.7783	−0.642978	−0.321489	−	0.946913i	$-0.604183\pi$
$281$	−10.7783	−0.642978	−0.321489	+	0.946913i	$0.604183\pi$
$282$	−3.21469	−0.191432
$283$	13.6668	0.812406	0.406203	−	0.913783i	$-0.366853\pi$
$283$	13.6668	0.812406	0.406203	+	0.913783i	$0.366853\pi$
$284$	12.8097	0.760117
$285$	0	0
$286$	−23.2976	−1.37762
$287$	−25.4365	−1.50147
$288$	13.0050	0.766329
$289$	9.37120	0.551247
$290$	0	0
$291$	3.14696	0.184478
$292$	19.3724	1.13368
$293$	−10.0597	−0.587692	−0.293846	−	0.955853i	$-0.594935\pi$
$293$	−10.0597	−0.587692	−0.293846	+	0.955853i	$0.594935\pi$
$294$	−8.99193	−0.524420
$295$	0	0
$296$	−5.53154	−0.321514
$297$	−16.9168	−0.981613
$298$	−6.40548	−0.371060
$299$	−10.9621	−0.633956
$300$	0	0
$301$	26.2428	1.51261
$302$	11.1938	0.644131
$303$	−3.45011	−0.198203
$304$	−3.12273	−0.179101
$305$	0	0
$306$	−17.6924	−1.01140
$307$	−8.52103	−0.486321	−0.243160	−	0.969986i	$-0.578184\pi$
$307$	−8.52103	−0.486321	−0.243160	+	0.969986i	$0.578184\pi$
$308$	−16.7222	−0.952833
$309$	−14.5786	−0.829348
$310$	0	0
$311$	−2.25219	−0.127710	−0.0638551	−	0.997959i	$-0.520340\pi$
$311$	−2.25219	−0.127710	−0.0638551	+	0.997959i	$0.520340\pi$
$312$	3.68171	0.208436
$313$	−6.49383	−0.367053	−0.183526	−	0.983015i	$-0.558751\pi$
$313$	−6.49383	−0.367053	−0.183526	+	0.983015i	$0.558751\pi$
$314$	−9.23656	−0.521249
$315$	0	0
$316$	21.1527	1.18993
$317$	23.1258	1.29887	0.649437	−	0.760415i	$-0.275004\pi$
$317$	23.1258	1.29887	0.649437	+	0.760415i	$0.275004\pi$
$318$	4.38595	0.245952
$319$	−9.41718	−0.527261
$320$	0	0
$321$	−16.9198	−0.944372
$322$	−18.1843	−1.01337
$323$	3.39466	0.188884
$324$	−0.195809	−0.0108783
$325$	0	0
$326$	−27.1870	−1.50575
$327$	−17.2386	−0.953297
$328$	6.70223	0.370069
$329$	5.36421	0.295739
$330$	0	0
$331$	24.3046	1.33590	0.667950	−	0.744206i	$-0.267172\pi$
$331$	24.3046	1.33590	0.667950	+	0.744206i	$0.267172\pi$
$332$	0.00670778	0.000368137 0
$333$	−11.3906	−0.624201
$334$	−31.5822	−1.72810
$335$	0	0
$336$	17.2439	0.940731
$337$	−31.2328	−1.70136	−0.850679	−	0.525685i	$-0.823809\pi$
$337$	−31.2328	−1.70136	−0.850679	+	0.525685i	$0.823809\pi$
$338$	3.10270	0.168764
$339$	0.521085	0.0283015
$340$	0	0
$341$	−3.68853	−0.199745
$342$	−2.27746	−0.123151
$343$	−8.66837	−0.468048
$344$	−6.91468	−0.372814
$345$	0	0
$346$	−31.4162	−1.68895
$347$	0.873880	0.0469123	0.0234562	−	0.999725i	$-0.492533\pi$
$347$	0.873880	0.0469123	0.0234562	+	0.999725i	$0.492533\pi$
$348$	−4.78343	−0.256419
$349$	13.3600	0.715146	0.357573	−	0.933885i	$-0.383604\pi$
$349$	13.3600	0.715146	0.357573	+	0.933885i	$0.383604\pi$
$350$	0	0
$351$	19.9767	1.06628
$352$	22.9746	1.22455
$353$	36.3355	1.93394	0.966971	−	0.254887i	$-0.0820383\pi$
$353$	36.3355	1.93394	0.966971	+	0.254887i	$0.0820383\pi$
$354$	19.3522	1.02856
$355$	0	0
$356$	7.29786	0.386786
$357$	−18.7455	−0.992115
$358$	22.4306	1.18550
$359$	−24.1300	−1.27354	−0.636768	−	0.771056i	$-0.719729\pi$
$359$	−24.1300	−1.27354	−0.636768	+	0.771056i	$0.719729\pi$
$360$	0	0
$361$	−18.5630	−0.977001
$362$	3.17936	0.167103
$363$	0.531548	0.0278991
$364$	19.7468	1.03501
$365$	0	0
$366$	0.346942	0.0181349
$367$	−3.26641	−0.170505	−0.0852526	−	0.996359i	$-0.527170\pi$
$367$	−3.26641	−0.170505	−0.0852526	+	0.996359i	$0.527170\pi$
$368$	13.5283	0.705211
$369$	13.8013	0.718467
$370$	0	0
$371$	−7.31865	−0.379965
$372$	−1.87358	−0.0971404
$373$	−6.70363	−0.347101	−0.173551	−	0.984825i	$-0.555524\pi$
$373$	−6.70363	−0.347101	−0.173551	+	0.984825i	$0.555524\pi$
$374$	−31.2551	−1.61616
$375$	0	0
$376$	−1.41341	−0.0728911
$377$	11.1205	0.572736
$378$	33.1379	1.70443
$379$	−20.7421	−1.06545	−0.532726	−	0.846288i	$-0.678832\pi$
$379$	−20.7421	−1.06545	−0.532726	+	0.846288i	$0.678832\pi$
$380$	0	0
$381$	−9.99815	−0.512221
$382$	16.5912	0.848878
$383$	−35.4063	−1.80918	−0.904589	−	0.426285i	$-0.859822\pi$
$383$	−35.4063	−1.80918	−0.904589	+	0.426285i	$0.859822\pi$
$384$	−7.47793	−0.381607
$385$	0	0
$386$	−29.6982	−1.51160
$387$	−14.2388	−0.723798
$388$	−4.44736	−0.225780
$389$	1.49212	0.0756533	0.0378266	−	0.999284i	$-0.487957\pi$
$389$	1.49212	0.0756533	0.0378266	+	0.999284i	$0.487957\pi$
$390$	0	0
$391$	−14.7063	−0.743731
$392$	−3.95351	−0.199682
$393$	9.00666	0.454326
$394$	−1.87761	−0.0945926
$395$	0	0
$396$	9.07310	0.455940
$397$	2.66709	0.133857	0.0669287	−	0.997758i	$-0.478680\pi$
$397$	2.66709	0.133857	0.0669287	+	0.997758i	$0.478680\pi$
$398$	−5.36012	−0.268679
$399$	−2.41303	−0.120802
$400$	0	0
$401$	13.7107	0.684682	0.342341	−	0.939576i	$-0.388780\pi$
$401$	13.7107	0.684682	0.342341	+	0.939576i	$0.388780\pi$
$402$	−9.26389	−0.462041
$403$	4.35570	0.216973
$404$	4.87576	0.242578
$405$	0	0
$406$	18.4471	0.915513
$407$	−20.1225	−0.997436
$408$	4.93922	0.244528
$409$	20.5160	1.01445	0.507226	−	0.861813i	$-0.330671\pi$
$409$	20.5160	1.01445	0.507226	+	0.861813i	$0.330671\pi$
$410$	0	0
$411$	13.9439	0.687801
$412$	20.6028	1.01503
$413$	−32.2921	−1.58899
$414$	9.86643	0.484909
$415$	0	0
$416$	−27.1301	−1.33016
$417$	−2.65311	−0.129923
$418$	−4.02334	−0.196788
$419$	−11.0354	−0.539115	−0.269558	−	0.962984i	$-0.586877\pi$
$419$	−11.0354	−0.539115	−0.269558	+	0.962984i	$0.586877\pi$
$420$	0	0
$421$	−20.6835	−1.00805	−0.504026	−	0.863689i	$-0.668148\pi$
$421$	−20.6835	−1.00805	−0.504026	+	0.863689i	$0.668148\pi$
$422$	−21.7520	−1.05887
$423$	−2.91051	−0.141514
$424$	1.92838	0.0936505
$425$	0	0
$426$	−17.0190	−0.824575
$427$	−0.578927	−0.0280162
$428$	23.9114	1.15580
$429$	13.3932	0.646632
$430$	0	0
$431$	−19.5509	−0.941736	−0.470868	−	0.882204i	$-0.656059\pi$
$431$	−19.5509	−0.941736	−0.470868	+	0.882204i	$0.656059\pi$
$432$	−24.6531	−1.18612
$433$	−26.8252	−1.28914	−0.644569	−	0.764546i	$-0.722963\pi$
$433$	−26.8252	−1.28914	−0.644569	+	0.764546i	$0.722963\pi$
$434$	7.22536	0.346828
$435$	0	0
$436$	24.3620	1.16673
$437$	−1.89309	−0.0905586
$438$	−25.7382	−1.22982
$439$	−12.2338	−0.583888	−0.291944	−	0.956435i	$-0.594302\pi$
$439$	−12.2338	−0.583888	−0.291944	+	0.956435i	$0.594302\pi$
$440$	0	0
$441$	−8.14110	−0.387672
$442$	36.9085	1.75556
$443$	−6.58035	−0.312642	−0.156321	−	0.987706i	$-0.549963\pi$
$443$	−6.58035	−0.312642	−0.156321	+	0.987706i	$0.549963\pi$
$444$	−10.2212	−0.485075
$445$	0	0
$446$	23.6484	1.11979
$447$	3.68236	0.174169
$448$	−13.0532	−0.616706
$449$	31.7215	1.49703	0.748515	−	0.663118i	$-0.230767\pi$
$449$	31.7215	1.49703	0.748515	+	0.663118i	$0.230767\pi$
$450$	0	0
$451$	24.3812	1.14807
$452$	−0.736409	−0.0346378
$453$	−6.43505	−0.302345
$454$	32.3939	1.52032
$455$	0	0
$456$	0.635806	0.0297744
$457$	38.6356	1.80730	0.903650	−	0.428273i	$-0.140878\pi$
$457$	38.6356	1.80730	0.903650	+	0.428273i	$0.140878\pi$
$458$	14.8462	0.693717
$459$	26.7999	1.25091
$460$	0	0
$461$	−13.3465	−0.621607	−0.310803	−	0.950474i	$-0.600598\pi$
$461$	−13.3465	−0.621607	−0.310803	+	0.950474i	$0.600598\pi$
$462$	22.2171	1.03363
$463$	−10.0013	−0.464798	−0.232399	−	0.972621i	$-0.574658\pi$
$463$	−10.0013	−0.464798	−0.232399	+	0.972621i	$0.574658\pi$
$464$	−13.7238	−0.637110
$465$	0	0
$466$	27.0647	1.25375
$467$	−13.8635	−0.641525	−0.320762	−	0.947160i	$-0.603939\pi$
$467$	−13.8635	−0.641525	−0.320762	+	0.947160i	$0.603939\pi$
$468$	−10.7142	−0.495265
$469$	15.4583	0.713796
$470$	0	0
$471$	5.30988	0.244666
$472$	8.50862	0.391641
$473$	−25.1541	−1.15659
$474$	−28.1035	−1.29084
$475$	0	0
$476$	26.4915	1.21424
$477$	3.97095	0.181817
$478$	−32.3277	−1.47864
$479$	4.44341	0.203025	0.101512	−	0.994834i	$-0.467632\pi$
$479$	4.44341	0.203025	0.101512	+	0.994834i	$0.467632\pi$
$480$	0	0
$481$	23.7622	1.08346
$482$	4.95850	0.225854
$483$	10.4537	0.475661
$484$	−0.751196	−0.0341453
$485$	0	0
$486$	−29.1363	−1.32165
$487$	15.6140	0.707540	0.353770	−	0.935332i	$-0.384900\pi$
$487$	15.6140	0.707540	0.353770	+	0.935332i	$0.384900\pi$
$488$	0.152541	0.00690520
$489$	15.6291	0.706774
$490$	0	0
$491$	−8.75542	−0.395126	−0.197563	−	0.980290i	$-0.563303\pi$
$491$	−8.75542	−0.395126	−0.197563	+	0.980290i	$0.563303\pi$
$492$	12.3844	0.558330
$493$	14.9188	0.671911
$494$	4.75108	0.213761
$495$	0	0
$496$	−5.37534	−0.241360
$497$	28.3989	1.27387
$498$	−0.00891198	−0.000399355 0
$499$	−0.343982	−0.0153988	−0.00769938	−	0.999970i	$-0.502451\pi$
$499$	−0.343982	−0.0153988	−0.00769938	+	0.999970i	$0.502451\pi$
$500$	0	0
$501$	18.1558	0.811142
$502$	44.5507	1.98840
$503$	−16.1053	−0.718099	−0.359050	−	0.933318i	$-0.616899\pi$
$503$	−16.1053	−0.718099	−0.359050	+	0.933318i	$0.616899\pi$
$504$	5.52944	0.246301
$505$	0	0
$506$	17.4299	0.774855
$507$	−1.78367	−0.0792154
$508$	14.1296	0.626900
$509$	−16.5658	−0.734266	−0.367133	−	0.930168i	$-0.619661\pi$
$509$	−16.5658	−0.734266	−0.367133	+	0.930168i	$0.619661\pi$
$510$	0	0
$511$	42.9482	1.89992
$512$	25.0624	1.10761
$513$	3.44984	0.152314
$514$	28.1086	1.23982
$515$	0	0
$516$	−12.7769	−0.562473
$517$	−5.14167	−0.226131
$518$	39.4175	1.73191
$519$	18.0604	0.792764
$520$	0	0
$521$	−33.4712	−1.46640	−0.733199	−	0.680014i	$-0.761974\pi$
$521$	−33.4712	−1.46640	−0.733199	+	0.680014i	$0.761974\pi$
$522$	−10.0090	−0.438082
$523$	−14.6120	−0.638939	−0.319470	−	0.947597i	$-0.603505\pi$
$523$	−14.6120	−0.638939	−0.319470	+	0.947597i	$0.603505\pi$
$524$	−12.7284	−0.556043
$525$	0	0
$526$	60.2746	2.62810
$527$	5.84342	0.254543
$528$	−16.5285	−0.719311
$529$	−14.7988	−0.643425
$530$	0	0
$531$	17.5211	0.760349
$532$	3.41014	0.147848
$533$	−28.7912	−1.24709
$534$	−9.69596	−0.419585
$535$	0	0
$536$	−4.07308	−0.175930
$537$	−12.8948	−0.556453
$538$	0.122160	0.00526669
$539$	−14.3820	−0.619476
$540$	0	0
$541$	−1.62796	−0.0699914	−0.0349957	−	0.999387i	$-0.511142\pi$
$541$	−1.62796	−0.0699914	−0.0349957	+	0.999387i	$0.511142\pi$
$542$	20.1302	0.864666
$543$	−1.82773	−0.0784356
$544$	−36.3967	−1.56049
$545$	0	0
$546$	−26.2357	−1.12278
$547$	−2.39466	−0.102388	−0.0511942	−	0.998689i	$-0.516303\pi$
$547$	−2.39466	−0.102388	−0.0511942	+	0.998689i	$0.516303\pi$
$548$	−19.7058	−0.841790
$549$	0.314114	0.0134060
$550$	0	0
$551$	1.92044	0.0818135
$552$	−2.75444	−0.117237
$553$	46.8952	1.99419
$554$	2.58542	0.109844
$555$	0	0
$556$	3.74943	0.159011
$557$	−7.45022	−0.315676	−0.157838	−	0.987465i	$-0.550452\pi$
$557$	−7.45022	−0.315676	−0.157838	+	0.987465i	$0.550452\pi$
$558$	−3.92033	−0.165961
$559$	29.7039	1.25634
$560$	0	0
$561$	17.9678	0.758601
$562$	−20.2374	−0.853664
$563$	−21.4000	−0.901902	−0.450951	−	0.892549i	$-0.648915\pi$
$563$	−21.4000	−0.901902	−0.450951	+	0.892549i	$0.648915\pi$
$564$	−2.61170	−0.109972
$565$	0	0
$566$	25.6609	1.07861
$567$	−0.434104	−0.0182307
$568$	−7.48281	−0.313972
$569$	−44.5683	−1.86840	−0.934200	−	0.356751i	$-0.883885\pi$
$569$	−44.5683	−1.86840	−0.934200	+	0.356751i	$0.883885\pi$
$570$	0	0
$571$	33.6876	1.40978	0.704890	−	0.709316i	$-0.250996\pi$
$571$	33.6876	1.40978	0.704890	+	0.709316i	$0.250996\pi$
$572$	−18.9276	−0.791403
$573$	−9.53786	−0.398450
$574$	−47.7598	−1.99345
$575$	0	0
$576$	7.08239	0.295100
$577$	−39.3738	−1.63915	−0.819576	−	0.572970i	$-0.805791\pi$
$577$	−39.3738	−1.63915	−0.819576	+	0.572970i	$0.805791\pi$
$578$	17.5955	0.731875
$579$	17.0728	0.709520
$580$	0	0
$581$	0.0148710	0.000616955 0
$582$	5.90877	0.244926
$583$	7.01503	0.290533
$584$	−11.3164	−0.468275
$585$	0	0
$586$	−18.8881	−0.780261
$587$	5.64677	0.233067	0.116534	−	0.993187i	$-0.462822\pi$
$587$	5.64677	0.233067	0.116534	+	0.993187i	$0.462822\pi$
$588$	−7.30528	−0.301265
$589$	0.752200	0.0309938
$590$	0	0
$591$	1.07939	0.0444003
$592$	−29.3248	−1.20524
$593$	−25.8164	−1.06015	−0.530076	−	0.847950i	$-0.677837\pi$
$593$	−25.8164	−1.06015	−0.530076	+	0.847950i	$0.677837\pi$
$594$	−31.7632	−1.30326
$595$	0	0
$596$	−5.20398	−0.213163
$597$	3.08141	0.126114
$598$	−20.5826	−0.841685
$599$	−1.55557	−0.0635590	−0.0317795	−	0.999495i	$-0.510117\pi$
$599$	−1.55557	−0.0635590	−0.0317795	+	0.999495i	$0.510117\pi$
$600$	0	0
$601$	15.9922	0.652335	0.326168	−	0.945312i	$-0.394243\pi$
$601$	15.9922	0.652335	0.326168	+	0.945312i	$0.394243\pi$
$602$	49.2737	2.00824
$603$	−8.38733	−0.341559
$604$	9.09415	0.370036
$605$	0	0
$606$	−6.47795	−0.263149
$607$	−19.5144	−0.792065	−0.396032	−	0.918237i	$-0.629613\pi$
$607$	−19.5144	−0.792065	−0.396032	+	0.918237i	$0.629613\pi$
$608$	−4.68519	−0.190010
$609$	−10.6048	−0.429727
$610$	0	0
$611$	6.07169	0.245634
$612$	−14.3737	−0.581024
$613$	−35.3269	−1.42684	−0.713421	−	0.700736i	$-0.752855\pi$
$613$	−35.3269	−1.42684	−0.713421	+	0.700736i	$0.752855\pi$
$614$	−15.9992	−0.645674
$615$	0	0
$616$	9.76825	0.393574
$617$	−23.7473	−0.956031	−0.478015	−	0.878351i	$-0.658644\pi$
$617$	−23.7473	−0.956031	−0.478015	+	0.878351i	$0.658644\pi$
$618$	−27.3729	−1.10110
$619$	−7.18722	−0.288879	−0.144439	−	0.989514i	$-0.546138\pi$
$619$	−7.18722	−0.288879	−0.144439	+	0.989514i	$0.546138\pi$
$620$	0	0
$621$	−14.9454	−0.599738
$622$	−4.22874	−0.169557
$623$	16.1792	0.648207
$624$	19.5181	0.781351
$625$	0	0
$626$	−12.1929	−0.487325
$627$	2.31292	0.0923692
$628$	−7.50403	−0.299443
$629$	31.8784	1.27108
$630$	0	0
$631$	30.1042	1.19843	0.599214	−	0.800589i	$-0.295480\pi$
$631$	30.1042	1.19843	0.599214	+	0.800589i	$0.295480\pi$
$632$	−12.3564	−0.491510
$633$	12.5047	0.497018
$634$	43.4213	1.72448
$635$	0	0
$636$	3.56326	0.141293
$637$	16.9834	0.672905
$638$	−17.6818	−0.700029
$639$	−15.4087	−0.609558
$640$	0	0
$641$	−24.1244	−0.952858	−0.476429	−	0.879213i	$-0.658069\pi$
$641$	−24.1244	−0.952858	−0.476429	+	0.879213i	$0.658069\pi$
$642$	−31.7688	−1.25382
$643$	−43.1500	−1.70167	−0.850835	−	0.525434i	$-0.823903\pi$
$643$	−43.1500	−1.70167	−0.850835	+	0.525434i	$0.823903\pi$
$644$	−14.7734	−0.582154
$645$	0	0
$646$	6.37384	0.250776
$647$	28.2853	1.11201	0.556005	−	0.831179i	$-0.312333\pi$
$647$	28.2853	1.11201	0.556005	+	0.831179i	$0.312333\pi$
$648$	0.114382	0.00449334
$649$	30.9525	1.21499
$650$	0	0
$651$	−4.15368	−0.162796
$652$	−22.0874	−0.865011
$653$	−28.6564	−1.12141	−0.560706	−	0.828015i	$-0.689470\pi$
$653$	−28.6564	−1.12141	−0.560706	+	0.828015i	$0.689470\pi$
$654$	−32.3674	−1.26567
$655$	0	0
$656$	35.5311	1.38726
$657$	−23.3028	−0.909129
$658$	10.0719	0.392643
$659$	−11.7629	−0.458219	−0.229109	−	0.973401i	$-0.573581\pi$
$659$	−11.7629	−0.458219	−0.229109	+	0.973401i	$0.573581\pi$
$660$	0	0
$661$	−11.0164	−0.428488	−0.214244	−	0.976780i	$-0.568729\pi$
$661$	−11.0164	−0.428488	−0.214244	+	0.976780i	$0.568729\pi$
$662$	45.6345	1.77364
$663$	−21.2178	−0.824030
$664$	−0.00391835	−0.000152062 0
$665$	0	0
$666$	−21.3871	−0.828734
$667$	−8.31973	−0.322141
$668$	−25.6582	−0.992745
$669$	−13.5949	−0.525610
$670$	0	0
$671$	0.554910	0.0214221
$672$	25.8719	0.998029
$673$	−43.5107	−1.67721	−0.838607	−	0.544737i	$-0.816629\pi$
$673$	−43.5107	−1.67721	−0.838607	+	0.544737i	$0.816629\pi$
$674$	−58.6430	−2.25884
$675$	0	0
$676$	2.52071	0.0969505
$677$	47.8060	1.83733	0.918667	−	0.395033i	$-0.129267\pi$
$677$	47.8060	1.83733	0.918667	+	0.395033i	$0.129267\pi$
$678$	0.978395	0.0375750
$679$	−9.85971	−0.378381
$680$	0	0
$681$	−18.6225	−0.713614
$682$	−6.92561	−0.265195
$683$	−35.2424	−1.34851	−0.674256	−	0.738498i	$-0.735535\pi$
$683$	−35.2424	−1.34851	−0.674256	+	0.738498i	$0.735535\pi$
$684$	−1.85027	−0.0707470
$685$	0	0
$686$	−16.2758	−0.621414
$687$	−8.53471	−0.325620
$688$	−36.6574	−1.39755
$689$	−8.28389	−0.315591
$690$	0	0
$691$	−45.7758	−1.74139	−0.870696	−	0.491821i	$-0.836332\pi$
$691$	−45.7758	−1.74139	−0.870696	+	0.491821i	$0.836332\pi$
$692$	−25.5234	−0.970252
$693$	20.1149	0.764102
$694$	1.64081	0.0622841
$695$	0	0
$696$	2.79424	0.105915
$697$	−38.6251	−1.46303
$698$	25.0849	0.949479
$699$	−15.5588	−0.588489
$700$	0	0
$701$	−38.7609	−1.46398	−0.731989	−	0.681317i	$-0.761408\pi$
$701$	−38.7609	−1.46398	−0.731989	+	0.681317i	$0.761408\pi$
$702$	37.5084	1.41566
$703$	4.10358	0.154769
$704$	12.5117	0.471552
$705$	0	0
$706$	68.2238	2.56764
$707$	10.8095	0.406532
$708$	15.7222	0.590877
$709$	12.7446	0.478632	0.239316	−	0.970942i	$-0.423077\pi$
$709$	12.7446	0.478632	0.239316	+	0.970942i	$0.423077\pi$
$710$	0	0
$711$	−25.4444	−0.954238
$712$	−4.26305	−0.159764
$713$	−3.25868	−0.122038
$714$	−35.1967	−1.31720
$715$	0	0
$716$	18.2232	0.681034
$717$	18.5844	0.694048
$718$	−45.3068	−1.69084
$719$	43.4210	1.61933	0.809666	−	0.586892i	$-0.199649\pi$
$719$	43.4210	1.61933	0.809666	+	0.586892i	$0.199649\pi$
$720$	0	0
$721$	45.6760	1.70106
$722$	−34.8541	−1.29714
$723$	−2.85052	−0.106012
$724$	2.58299	0.0959962
$725$	0	0
$726$	0.998041	0.0370408
$727$	10.9915	0.407653	0.203827	−	0.979007i	$-0.434662\pi$
$727$	10.9915	0.407653	0.203827	+	0.979007i	$0.434662\pi$
$728$	−11.5351	−0.427520
$729$	17.1348	0.634623
$730$	0	0
$731$	39.8495	1.47389
$732$	0.281865	0.0104180
$733$	5.52299	0.203996	0.101998	−	0.994785i	$-0.467476\pi$
$733$	5.52299	0.203996	0.101998	+	0.994785i	$0.467476\pi$
$734$	−6.13304	−0.226375
$735$	0	0
$736$	20.2972	0.748164
$737$	−14.8170	−0.545790
$738$	25.9135	0.953888
$739$	46.9877	1.72847	0.864234	−	0.503089i	$-0.167803\pi$
$739$	46.9877	1.72847	0.864234	+	0.503089i	$0.167803\pi$
$740$	0	0
$741$	−2.73128	−0.100336
$742$	−13.7416	−0.504469
$743$	43.1459	1.58287	0.791435	−	0.611253i	$-0.209334\pi$
$743$	43.1459	1.58287	0.791435	+	0.611253i	$0.209334\pi$
$744$	1.09445	0.0401245
$745$	0	0
$746$	−12.5868	−0.460836
$747$	−0.00806872	−0.000295219 0
$748$	−25.3925	−0.928441
$749$	53.0113	1.93699
$750$	0	0
$751$	−27.6783	−1.01000	−0.504998	−	0.863121i	$-0.668507\pi$
$751$	−27.6783	−1.01000	−0.504998	+	0.863121i	$0.668507\pi$
$752$	−7.49303	−0.273243
$753$	−25.6111	−0.933322
$754$	20.8800	0.760405
$755$	0	0
$756$	26.9221	0.979149
$757$	38.6375	1.40430	0.702152	−	0.712028i	$-0.252223\pi$
$757$	38.6375	1.40430	0.702152	+	0.712028i	$0.252223\pi$
$758$	−38.9456	−1.41457
$759$	−10.0200	−0.363704
$760$	0	0
$761$	−17.7386	−0.643024	−0.321512	−	0.946906i	$-0.604191\pi$
$761$	−17.7386	−0.643024	−0.321512	+	0.946906i	$0.604191\pi$
$762$	−18.7726	−0.680061
$763$	54.0101	1.95530
$764$	13.4791	0.487657
$765$	0	0
$766$	−66.4793	−2.40199
$767$	−36.5511	−1.31978
$768$	−22.3731	−0.807321
$769$	3.23542	0.116672	0.0583361	−	0.998297i	$-0.481421\pi$
$769$	3.23542	0.116672	0.0583361	+	0.998297i	$0.481421\pi$
$770$	0	0
$771$	−16.1590	−0.581950
$772$	−24.1276	−0.868371
$773$	12.5145	0.450117	0.225058	−	0.974345i	$-0.427743\pi$
$773$	12.5145	0.450117	0.225058	+	0.974345i	$0.427743\pi$
$774$	−26.7349	−0.960965
$775$	0	0
$776$	2.59792	0.0932601
$777$	−22.6602	−0.812929
$778$	2.80161	0.100443
$779$	−4.97205	−0.178142
$780$	0	0
$781$	−27.2208	−0.974037
$782$	−27.6128	−0.987430
$783$	15.1614	0.541823
$784$	−20.9591	−0.748538
$785$	0	0
$786$	16.9110	0.603195
$787$	−33.1968	−1.18334	−0.591669	−	0.806181i	$-0.701531\pi$
$787$	−33.1968	−1.18334	−0.591669	+	0.806181i	$0.701531\pi$
$788$	−1.52542	−0.0543409
$789$	−34.6504	−1.23359
$790$	0	0
$791$	−1.63261	−0.0580488
$792$	−5.30005	−0.188329
$793$	−0.655281	−0.0232697
$794$	5.00776	0.177719
$795$	0	0
$796$	−4.35471	−0.154349
$797$	−12.2248	−0.433023	−0.216512	−	0.976280i	$-0.569468\pi$
$797$	−12.2248	−0.433023	−0.216512	+	0.976280i	$0.569468\pi$
$798$	−4.53073	−0.160386
$799$	8.14552	0.288168
$800$	0	0
$801$	−8.77851	−0.310173
$802$	25.7434	0.909032
$803$	−41.1665	−1.45273
$804$	−7.52623	−0.265430
$805$	0	0
$806$	8.17830	0.288068
$807$	−0.0702268	−0.00247210
$808$	−2.84818	−0.100199
$809$	−30.9174	−1.08700	−0.543499	−	0.839410i	$-0.682901\pi$
$809$	−30.9174	−1.08700	−0.543499	+	0.839410i	$0.682901\pi$
$810$	0	0
$811$	−23.8343	−0.836935	−0.418468	−	0.908232i	$-0.637433\pi$
$811$	−23.8343	−0.836935	−0.418468	+	0.908232i	$0.637433\pi$
$812$	14.9869	0.525937
$813$	−11.5724	−0.405860
$814$	−37.7822	−1.32427
$815$	0	0
$816$	26.1847	0.916649
$817$	5.12966	0.179464
$818$	38.5211	1.34686
$819$	−23.7532	−0.830005
$820$	0	0
$821$	−17.5483	−0.612440	−0.306220	−	0.951961i	$-0.599064\pi$
$821$	−17.5483	−0.612440	−0.306220	+	0.951961i	$0.599064\pi$
$822$	26.1812	0.913173
$823$	31.1736	1.08664	0.543322	−	0.839524i	$-0.317166\pi$
$823$	31.1736	1.08664	0.543322	+	0.839524i	$0.317166\pi$
$824$	−12.0351	−0.419264
$825$	0	0
$826$	−60.6321	−2.10966
$827$	28.3113	0.984479	0.492239	−	0.870460i	$-0.336178\pi$
$827$	28.3113	0.984479	0.492239	+	0.870460i	$0.336178\pi$
$828$	8.01575	0.278567
$829$	27.5353	0.956339	0.478170	−	0.878268i	$-0.341300\pi$
$829$	27.5353	0.956339	0.478170	+	0.878268i	$0.341300\pi$
$830$	0	0
$831$	−1.48629	−0.0515590
$832$	−14.7748	−0.512223
$833$	22.7842	0.789425
$834$	−4.98151	−0.172496
$835$	0	0
$836$	−3.26867	−0.113049
$837$	5.93841	0.205261
$838$	−20.7202	−0.715767
$839$	12.1407	0.419144	0.209572	−	0.977793i	$-0.432793\pi$
$839$	12.1407	0.419144	0.209572	+	0.977793i	$0.432793\pi$
$840$	0	0
$841$	−20.5600	−0.708967
$842$	−38.8355	−1.33836
$843$	11.6340	0.400696
$844$	−17.6719	−0.608293
$845$	0	0
$846$	−5.46480	−0.187884
$847$	−1.66539	−0.0572234
$848$	10.2231	0.351063
$849$	−14.7518	−0.506281
$850$	0	0
$851$	−17.7775	−0.609405
$852$	−13.8267	−0.473696
$853$	38.4076	1.31505	0.657525	−	0.753432i	$-0.271603\pi$
$853$	38.4076	1.31505	0.657525	+	0.753432i	$0.271603\pi$
$854$	−1.08700	−0.0371963
$855$	0	0
$856$	−13.9679	−0.477412
$857$	45.7916	1.56421	0.782105	−	0.623146i	$-0.214146\pi$
$857$	45.7916	1.56421	0.782105	+	0.623146i	$0.214146\pi$
$858$	25.1473	0.858514
$859$	26.0195	0.887774	0.443887	−	0.896083i	$-0.353599\pi$
$859$	26.0195	0.887774	0.443887	+	0.896083i	$0.353599\pi$
$860$	0	0
$861$	27.4559	0.935695
$862$	−36.7091	−1.25032
$863$	−19.2150	−0.654085	−0.327042	−	0.945010i	$-0.606052\pi$
$863$	−19.2150	−0.654085	−0.327042	+	0.945010i	$0.606052\pi$
$864$	−36.9883	−1.25837
$865$	0	0
$866$	−50.3673	−1.71155
$867$	−10.1152	−0.343530
$868$	5.87008	0.199243
$869$	−44.9497	−1.52481
$870$	0	0
$871$	17.4970	0.592864
$872$	−14.2311	−0.481924
$873$	5.34967	0.181059
$874$	−3.55448	−0.120232
$875$	0	0
$876$	−20.9104	−0.706496
$877$	43.1360	1.45660	0.728300	−	0.685258i	$-0.240311\pi$
$877$	43.1360	1.45660	0.728300	+	0.685258i	$0.240311\pi$
$878$	−22.9703	−0.775211
$879$	10.8583	0.366242
$880$	0	0
$881$	−41.5736	−1.40065	−0.700325	−	0.713824i	$-0.746962\pi$
$881$	−41.5736	−1.40065	−0.700325	+	0.713824i	$0.746962\pi$
$882$	−15.2858	−0.514700
$883$	−25.0969	−0.844579	−0.422289	−	0.906461i	$-0.638773\pi$
$883$	−25.0969	−0.844579	−0.422289	+	0.906461i	$0.638773\pi$
$884$	29.9854	1.00852
$885$	0	0
$886$	−12.3553	−0.415086
$887$	−9.87871	−0.331695	−0.165847	−	0.986151i	$-0.553036\pi$
$887$	−9.87871	−0.331695	−0.165847	+	0.986151i	$0.553036\pi$
$888$	5.97070	0.200364
$889$	31.3251	1.05061
$890$	0	0
$891$	0.416095	0.0139397
$892$	19.2126	0.643286
$893$	1.04854	0.0350880
$894$	6.91403	0.231240
$895$	0	0
$896$	23.4290	0.782709
$897$	11.8324	0.395074
$898$	59.5606	1.98756
$899$	3.30577	0.110253
$900$	0	0
$901$	−11.1133	−0.370238
$902$	45.7784	1.52425
$903$	−28.3262	−0.942638
$904$	0.430174	0.0143074
$905$	0	0
$906$	−12.0825	−0.401415
$907$	0.517898	0.0171965	0.00859827	−	0.999963i	$-0.497263\pi$
$907$	0.517898	0.0171965	0.00859827	+	0.999963i	$0.497263\pi$
$908$	26.3177	0.873382
$909$	−5.86500	−0.194530
$910$	0	0
$911$	18.7618	0.621605	0.310803	−	0.950474i	$-0.399402\pi$
$911$	18.7618	0.621605	0.310803	+	0.950474i	$0.399402\pi$
$912$	3.37065	0.111614
$913$	−0.0142541	−0.000471742 0
$914$	72.5427	2.39950
$915$	0	0
$916$	12.0614	0.398521
$917$	−28.2186	−0.931862
$918$	50.3197	1.66080
$919$	51.3316	1.69327	0.846636	−	0.532172i	$-0.178624\pi$
$919$	51.3316	1.69327	0.846636	+	0.532172i	$0.178624\pi$
$920$	0	0
$921$	9.19754	0.303069
$922$	−25.0594	−0.825289
$923$	32.1444	1.05805
$924$	18.0498	0.593794
$925$	0	0
$926$	−18.7785	−0.617099
$927$	−24.7829	−0.813976
$928$	−20.5905	−0.675916
$929$	1.97472	0.0647886	0.0323943	−	0.999475i	$-0.489687\pi$
$929$	1.97472	0.0647886	0.0323943	+	0.999475i	$0.489687\pi$
$930$	0	0
$931$	2.93291	0.0961223
$932$	21.9881	0.720243
$933$	2.43100	0.0795874
$934$	−26.0302	−0.851734
$935$	0	0
$936$	6.25871	0.204572
$937$	−23.9078	−0.781032	−0.390516	−	0.920596i	$-0.627703\pi$
$937$	−23.9078	−0.781032	−0.390516	+	0.920596i	$0.627703\pi$
$938$	29.0246	0.947686
$939$	7.00939	0.228743
$940$	0	0
$941$	−4.61764	−0.150531	−0.0752654	−	0.997164i	$-0.523980\pi$
$941$	−4.61764	−0.150531	−0.0752654	+	0.997164i	$0.523980\pi$
$942$	9.96988	0.324836
$943$	21.5399	0.701436
$944$	45.1075	1.46812
$945$	0	0
$946$	−47.2295	−1.53556
$947$	47.1474	1.53208	0.766042	−	0.642790i	$-0.222223\pi$
$947$	47.1474	1.53208	0.766042	+	0.642790i	$0.222223\pi$
$948$	−22.8321	−0.741551
$949$	48.6125	1.57803
$950$	0	0
$951$	−24.9618	−0.809443
$952$	−15.4750	−0.501548
$953$	24.8068	0.803572	0.401786	−	0.915734i	$-0.368390\pi$
$953$	24.8068	0.803572	0.401786	+	0.915734i	$0.368390\pi$
$954$	7.45589	0.241393
$955$	0	0
$956$	−26.2639	−0.849436
$957$	10.1648	0.328582
$958$	8.34300	0.269550
$959$	−43.6874	−1.41074
$960$	0	0
$961$	−29.7052	−0.958232
$962$	44.6162	1.43848
$963$	−28.7628	−0.926869
$964$	4.02842	0.129747
$965$	0	0
$966$	19.6280	0.631521
$967$	−40.1719	−1.29184	−0.645921	−	0.763404i	$-0.723526\pi$
$967$	−40.1719	−1.29184	−0.645921	+	0.763404i	$0.723526\pi$
$968$	0.438811	0.0141039
$969$	−3.66417	−0.117710
$970$	0	0
$971$	44.8733	1.44005	0.720026	−	0.693947i	$-0.244130\pi$
$971$	44.8733	1.44005	0.720026	+	0.693947i	$0.244130\pi$
$972$	−23.6711	−0.759251
$973$	8.31243	0.266484
$974$	29.3171	0.939380
$975$	0	0
$976$	0.808678	0.0258851
$977$	6.17087	0.197424	0.0987119	−	0.995116i	$-0.468528\pi$
$977$	6.17087	0.197424	0.0987119	+	0.995116i	$0.468528\pi$
$978$	29.3454	0.938363
$979$	−15.5080	−0.495639
$980$	0	0
$981$	−29.3048	−0.935629
$982$	−16.4393	−0.524598
$983$	19.1761	0.611622	0.305811	−	0.952092i	$-0.401072\pi$
$983$	19.1761	0.611622	0.305811	+	0.952092i	$0.401072\pi$
$984$	−7.23433	−0.230622
$985$	0	0
$986$	28.0118	0.892076
$987$	−5.79009	−0.184301
$988$	3.85990	0.122800
$989$	−22.2227	−0.706641
$990$	0	0
$991$	−40.3959	−1.28322	−0.641609	−	0.767032i	$-0.721733\pi$
$991$	−40.3959	−1.28322	−0.641609	+	0.767032i	$0.721733\pi$
$992$	−8.06489	−0.256061
$993$	−26.2342	−0.832517
$994$	53.3221	1.69128
$995$	0	0
$996$	−0.00724033	−0.000229419 0
$997$	43.0493	1.36339	0.681693	−	0.731638i	$-0.261244\pi$
$997$	43.0493	1.36339	0.681693	+	0.731638i	$0.261244\pi$
$998$	−0.645864	−0.0204445
$999$	32.3966	1.02498

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4925.2.a.p.1.30	✓	37
5.4	even	2		4925.2.a.q.1.8	yes	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4925.2.a.p.1.30	✓	37	1.1	even	1	trivial
4925.2.a.q.1.8	yes	37	5.4	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:	\( N \)	\(=\)	\( 4925 = 5^{2} \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4925.a (trivial)

\(f(q)\)	\(=\)	\(q+1.87761 q^{2} -1.07939 q^{3} +1.52542 q^{4} -2.02668 q^{6} +3.38183 q^{7} -0.891075 q^{8} -1.83491 q^{9} -3.24153 q^{11} -1.64653 q^{12} +3.82785 q^{13} +6.34976 q^{14} -4.72393 q^{16} +5.13529 q^{17} -3.44525 q^{18} +0.661045 q^{19} -3.65032 q^{21} -6.08634 q^{22} -2.86378 q^{23} +0.961820 q^{24} +7.18722 q^{26} +5.21877 q^{27} +5.15872 q^{28} +2.90516 q^{29} +1.13789 q^{31} -7.08756 q^{32} +3.49889 q^{33} +9.64207 q^{34} -2.79901 q^{36} +6.20771 q^{37} +1.24118 q^{38} -4.13176 q^{39} -7.52150 q^{41} -6.85388 q^{42} +7.75992 q^{43} -4.94470 q^{44} -5.37706 q^{46} +1.58619 q^{47} +5.09898 q^{48} +4.43678 q^{49} -5.54299 q^{51} +5.83909 q^{52} -2.16411 q^{53} +9.79881 q^{54} -3.01347 q^{56} -0.713527 q^{57} +5.45476 q^{58} -9.54872 q^{59} -0.171187 q^{61} +2.13652 q^{62} -6.20536 q^{63} -3.85980 q^{64} +6.56955 q^{66} +4.57097 q^{67} +7.83348 q^{68} +3.09114 q^{69} +8.39750 q^{71} +1.63504 q^{72} +12.6997 q^{73} +11.6557 q^{74} +1.00837 q^{76} -10.9623 q^{77} -7.75783 q^{78} +13.8668 q^{79} -0.128364 q^{81} -14.1225 q^{82} +0.00439733 q^{83} -5.56828 q^{84} +14.5701 q^{86} -3.13581 q^{87} +2.88845 q^{88} +4.78416 q^{89} +12.9452 q^{91} -4.36847 q^{92} -1.22824 q^{93} +2.97824 q^{94} +7.65025 q^{96} -2.91549 q^{97} +8.33055 q^{98} +5.94793 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 2 q^{2} - q^{3} + 50 q^{4} + 8 q^{6} + 4 q^{7} + 50 q^{9} + 17 q^{11} + 2 q^{12} + 3 q^{13} + 14 q^{14} + 72 q^{16} + 10 q^{17} + 4 q^{18} + 54 q^{19} + 15 q^{21} + 11 q^{22} - 4 q^{23} + 28 q^{24}+ \cdots + 40 q^{99}+O(q^{100}) \) 37 * q - 2 * q^2 - q^3 + 50 * q^4 + 8 * q^6 + 4 * q^7 + 50 * q^9 + 17 * q^11 + 2 * q^12 + 3 * q^13 + 14 * q^14 + 72 * q^16 + 10 * q^17 + 4 * q^18 + 54 * q^19 + 15 * q^21 + 11 * q^22 - 4 * q^23 + 28 * q^24 + 19 * q^26 + 2 * q^27 - 3 * q^28 - 4 * q^29 + 58 * q^31 - 22 * q^32 + 7 * q^33 + 63 * q^34 + 66 * q^36 - 7 * q^37 - 12 * q^38 + 23 * q^39 + 17 * q^41 + 17 * q^42 - 11 * q^43 + 34 * q^44 + 41 * q^46 + 19 * q^47 - 10 * q^48 + 81 * q^49 + 39 * q^51 - 31 * q^52 + 14 * q^53 + 5 * q^54 + 21 * q^56 - 24 * q^57 + 15 * q^58 + 56 * q^59 + 40 * q^61 - 4 * q^62 - 5 * q^63 + 78 * q^64 + 22 * q^66 - 2 * q^67 + 3 * q^68 + 24 * q^69 + 31 * q^71 - 85 * q^72 - 4 * q^73 - 32 * q^74 + 137 * q^76 - 16 * q^77 + 113 * q^78 + 17 * q^79 + 85 * q^81 - 52 * q^82 + 18 * q^83 - 32 * q^84 + 35 * q^86 - 39 * q^87 + 63 * q^88 + 23 * q^89 + 152 * q^91 - 75 * q^92 - 8 * q^93 + 32 * q^94 + 72 * q^96 - 34 * q^97 + 40 * q^98 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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