LMFDB - Embedded newform 6025.2.a.j.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.05446 q^{2} -2.79403 q^{3} -0.888118 q^{4} +2.94619 q^{6} +1.63707 q^{7} +3.04540 q^{8} +4.80663 q^{9} +O(q^{10})$	\(q-1.05446 q^{2} -2.79403 q^{3} -0.888118 q^{4} +2.94619 q^{6} +1.63707 q^{7} +3.04540 q^{8} +4.80663 q^{9} +3.48187 q^{11} +2.48143 q^{12} -1.54127 q^{13} -1.72622 q^{14} -1.43501 q^{16} -5.66858 q^{17} -5.06839 q^{18} +8.06291 q^{19} -4.57402 q^{21} -3.67149 q^{22} +9.08730 q^{23} -8.50895 q^{24} +1.62521 q^{26} -5.04778 q^{27} -1.45391 q^{28} -5.83770 q^{29} -0.515390 q^{31} -4.57764 q^{32} -9.72848 q^{33} +5.97728 q^{34} -4.26885 q^{36} -8.17318 q^{37} -8.50200 q^{38} +4.30637 q^{39} -2.50706 q^{41} +4.82311 q^{42} +2.34062 q^{43} -3.09232 q^{44} -9.58218 q^{46} -7.36336 q^{47} +4.00947 q^{48} -4.32002 q^{49} +15.8382 q^{51} +1.36883 q^{52} +6.12837 q^{53} +5.32267 q^{54} +4.98552 q^{56} -22.5281 q^{57} +6.15561 q^{58} +1.35442 q^{59} -11.6587 q^{61} +0.543457 q^{62} +7.86876 q^{63} +7.69695 q^{64} +10.2583 q^{66} -1.12494 q^{67} +5.03437 q^{68} -25.3902 q^{69} -6.10631 q^{71} +14.6381 q^{72} -5.57776 q^{73} +8.61827 q^{74} -7.16082 q^{76} +5.70006 q^{77} -4.54089 q^{78} -9.29499 q^{79} -0.316215 q^{81} +2.64359 q^{82} +4.55159 q^{83} +4.06227 q^{84} -2.46809 q^{86} +16.3107 q^{87} +10.6037 q^{88} -2.59790 q^{89} -2.52316 q^{91} -8.07060 q^{92} +1.44002 q^{93} +7.76435 q^{94} +12.7901 q^{96} +12.3273 q^{97} +4.55528 q^{98} +16.7361 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) $ 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9	$ 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) $ 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9 + 2 * q^11 - 20 * q^12 - 14 * q^13 - 5 * q^14 + 38 * q^16 - 7 * q^17 - 9 * q^18 + 30 * q^19 + q^21 - q^22 - 43 * q^23 - 6 * q^24 - 22 * q^26 - 42 * q^27 - 32 * q^28 - 4 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 + 7 * q^34 + 15 * q^36 - 16 * q^37 - 14 * q^38 - 21 * q^39 - q^41 + 25 * q^42 - 35 * q^43 - 52 * q^44 - 27 * q^46 - 50 * q^47 - 26 * q^48 + 46 * q^49 - 7 * q^51 - 3 * q^52 - 4 * q^53 - 31 * q^54 - 51 * q^56 - 2 * q^58 + 6 * q^59 + 19 * q^61 - 28 * q^63 + 49 * q^64 - 27 * q^66 - 65 * q^67 + 25 * q^68 + 2 * q^69 - 34 * q^71 + 10 * q^72 - 8 * q^73 - 42 * q^74 + 71 * q^76 - q^77 + 59 * q^78 - 12 * q^79 + 29 * q^81 - 11 * q^82 - 41 * q^83 - 10 * q^84 - 13 * q^86 - 40 * q^87 + 52 * q^88 - 24 * q^89 + 46 * q^91 - 85 * q^92 + 30 * q^93 + 14 * q^94 - 30 * q^96 - 9 * q^97 + 64 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.05446	−0.745614	−0.372807	−	0.927909i	$-0.621605\pi$
$2$	−1.05446	−0.745614	−0.372807	+	0.927909i	$0.621605\pi$
$3$	−2.79403	−1.61314	−0.806568	−	0.591141i	$-0.798678\pi$
$3$	−2.79403	−1.61314	−0.806568	+	0.591141i	$0.798678\pi$
$4$	−0.888118	−0.444059
$5$	0	0
$5$	0	0
$6$	2.94619	1.20278
$7$	1.63707	0.618752	0.309376	−	0.950940i	$-0.399880\pi$
$7$	1.63707	0.618752	0.309376	+	0.950940i	$0.399880\pi$
$8$	3.04540	1.07671
$9$	4.80663	1.60221
$10$	0	0
$11$	3.48187	1.04982	0.524912	−	0.851156i	$-0.324098\pi$
$11$	3.48187	1.04982	0.524912	+	0.851156i	$0.324098\pi$
$12$	2.48143	0.716328
$13$	−1.54127	−0.427472	−0.213736	−	0.976891i	$-0.568563\pi$
$13$	−1.54127	−0.427472	−0.213736	+	0.976891i	$0.568563\pi$
$14$	−1.72622	−0.461351
$15$	0	0
$16$	−1.43501	−0.358752
$17$	−5.66858	−1.37483	−0.687416	−	0.726264i	$-0.741255\pi$
$17$	−5.66858	−1.37483	−0.687416	+	0.726264i	$0.741255\pi$
$18$	−5.06839	−1.19463
$19$	8.06291	1.84976	0.924879	−	0.380260i	$-0.124166\pi$
$19$	8.06291	1.84976	0.924879	+	0.380260i	$0.124166\pi$
$20$	0	0
$21$	−4.57402	−0.998132
$22$	−3.67149	−0.782765
$23$	9.08730	1.89483	0.947417	−	0.320002i	$-0.103684\pi$
$23$	9.08730	1.89483	0.947417	+	0.320002i	$0.103684\pi$
$24$	−8.50895	−1.73688
$25$	0	0
$26$	1.62521	0.318729
$27$	−5.04778	−0.971446
$28$	−1.45391	−0.274763
$29$	−5.83770	−1.08403	−0.542017	−	0.840367i	$-0.682339\pi$
$29$	−5.83770	−1.08403	−0.542017	+	0.840367i	$0.682339\pi$
$30$	0	0
$31$	−0.515390	−0.0925668	−0.0462834	−	0.998928i	$-0.514738\pi$
$31$	−0.515390	−0.0925668	−0.0462834	+	0.998928i	$0.514738\pi$
$32$	−4.57764	−0.809220
$33$	−9.72848	−1.69351
$34$	5.97728	1.02509
$35$	0	0
$36$	−4.26885	−0.711476
$37$	−8.17318	−1.34366	−0.671831	−	0.740704i	$-0.734492\pi$
$37$	−8.17318	−1.34366	−0.671831	+	0.740704i	$0.734492\pi$
$38$	−8.50200	−1.37921
$39$	4.30637	0.689571
$40$	0	0
$41$	−2.50706	−0.391537	−0.195768	−	0.980650i	$-0.562720\pi$
$41$	−2.50706	−0.391537	−0.195768	+	0.980650i	$0.562720\pi$
$42$	4.82311	0.744222
$43$	2.34062	0.356942	0.178471	−	0.983945i	$-0.442885\pi$
$43$	2.34062	0.356942	0.178471	+	0.983945i	$0.442885\pi$
$44$	−3.09232	−0.466184
$45$	0	0
$46$	−9.58218	−1.41282
$47$	−7.36336	−1.07406	−0.537028	−	0.843564i	$-0.680453\pi$
$47$	−7.36336	−1.07406	−0.537028	+	0.843564i	$0.680453\pi$
$48$	4.00947	0.578717
$49$	−4.32002	−0.617145
$50$	0	0
$51$	15.8382	2.21779
$52$	1.36883	0.189823
$53$	6.12837	0.841796	0.420898	−	0.907108i	$-0.361715\pi$
$53$	6.12837	0.841796	0.420898	+	0.907108i	$0.361715\pi$
$54$	5.32267	0.724324
$55$	0	0
$56$	4.98552	0.666218
$57$	−22.5281	−2.98391
$58$	6.15561	0.808272
$59$	1.35442	0.176330	0.0881652	−	0.996106i	$-0.471900\pi$
$59$	1.35442	0.176330	0.0881652	+	0.996106i	$0.471900\pi$
$60$	0	0
$61$	−11.6587	−1.49274	−0.746370	−	0.665531i	$-0.768205\pi$
$61$	−11.6587	−1.49274	−0.746370	+	0.665531i	$0.768205\pi$
$62$	0.543457	0.0690191
$63$	7.86876	0.991371
$64$	7.69695	0.962119
$65$	0	0
$66$	10.2583	1.26271
$67$	−1.12494	−0.137433	−0.0687164	−	0.997636i	$-0.521890\pi$
$67$	−1.12494	−0.137433	−0.0687164	+	0.997636i	$0.521890\pi$
$68$	5.03437	0.610506
$69$	−25.3902	−3.05663
$70$	0	0
$71$	−6.10631	−0.724686	−0.362343	−	0.932045i	$-0.618023\pi$
$71$	−6.10631	−0.724686	−0.362343	+	0.932045i	$0.618023\pi$
$72$	14.6381	1.72512
$73$	−5.57776	−0.652828	−0.326414	−	0.945227i	$-0.605840\pi$
$73$	−5.57776	−0.652828	−0.326414	+	0.945227i	$0.605840\pi$
$74$	8.61827	1.00185
$75$	0	0
$76$	−7.16082	−0.821402
$77$	5.70006	0.649582
$78$	−4.54089	−0.514154
$79$	−9.29499	−1.04577	−0.522884	−	0.852404i	$-0.675144\pi$
$79$	−9.29499	−1.04577	−0.522884	+	0.852404i	$0.675144\pi$
$80$	0	0
$81$	−0.316215	−0.0351350
$82$	2.64359	0.291936
$83$	4.55159	0.499601	0.249801	−	0.968297i	$-0.419635\pi$
$83$	4.55159	0.499601	0.249801	+	0.968297i	$0.419635\pi$
$84$	4.06227	0.443230
$85$	0	0
$86$	−2.46809	−0.266141
$87$	16.3107	1.74869
$88$	10.6037	1.13036
$89$	−2.59790	−0.275376	−0.137688	−	0.990476i	$-0.543967\pi$
$89$	−2.59790	−0.275376	−0.137688	+	0.990476i	$0.543967\pi$
$90$	0	0
$91$	−2.52316	−0.264499
$92$	−8.07060	−0.841418
$93$	1.44002	0.149323
$94$	7.76435	0.800832
$95$	0	0
$96$	12.7901	1.30538
$97$	12.3273	1.25165	0.625824	−	0.779965i	$-0.284763\pi$
$97$	12.3273	1.25165	0.625824	+	0.779965i	$0.284763\pi$
$98$	4.55528	0.460153
$99$	16.7361	1.68204
$100$	0	0
$101$	5.94499	0.591549	0.295774	−	0.955258i	$-0.404422\pi$
$101$	5.94499	0.591549	0.295774	+	0.955258i	$0.404422\pi$
$102$	−16.7007	−1.65362
$103$	14.0762	1.38697	0.693487	−	0.720469i	$-0.256074\pi$
$103$	14.0762	1.38697	0.693487	+	0.720469i	$0.256074\pi$
$104$	−4.69379	−0.460264
$105$	0	0
$106$	−6.46211	−0.627655
$107$	−15.7771	−1.52523	−0.762613	−	0.646855i	$-0.776084\pi$
$107$	−15.7771	−1.52523	−0.762613	+	0.646855i	$0.776084\pi$
$108$	4.48302	0.431379
$109$	5.72700	0.548547	0.274274	−	0.961652i	$-0.411563\pi$
$109$	5.72700	0.548547	0.274274	+	0.961652i	$0.411563\pi$
$110$	0	0
$111$	22.8361	2.16751
$112$	−2.34920	−0.221979
$113$	8.94457	0.841435	0.420717	−	0.907192i	$-0.361778\pi$
$113$	8.94457	0.841435	0.420717	+	0.907192i	$0.361778\pi$
$114$	23.7549	2.22485
$115$	0	0
$116$	5.18457	0.481375
$117$	−7.40832	−0.684900
$118$	−1.42818	−0.131475
$119$	−9.27983	−0.850680
$120$	0	0
$121$	1.12345	0.102132
$122$	12.2936	1.11301
$123$	7.00481	0.631602
$124$	0.457727	0.0411051
$125$	0	0
$126$	−8.29728	−0.739180
$127$	12.8828	1.14316	0.571580	−	0.820547i	$-0.306331\pi$
$127$	12.8828	1.14316	0.571580	+	0.820547i	$0.306331\pi$
$128$	1.03917	0.0918506
$129$	−6.53978	−0.575796
$130$	0	0
$131$	−8.85544	−0.773703	−0.386852	−	0.922142i	$-0.626437\pi$
$131$	−8.85544	−0.773703	−0.386852	+	0.922142i	$0.626437\pi$
$132$	8.64004	0.752019
$133$	13.1995	1.14454
$134$	1.18620	0.102472
$135$	0	0
$136$	−17.2631	−1.48030
$137$	−9.38215	−0.801571	−0.400785	−	0.916172i	$-0.631263\pi$
$137$	−9.38215	−0.801571	−0.400785	+	0.916172i	$0.631263\pi$
$138$	26.7729	2.27906
$139$	−2.58528	−0.219281	−0.109640	−	0.993971i	$-0.534970\pi$
$139$	−2.58528	−0.219281	−0.109640	+	0.993971i	$0.534970\pi$
$140$	0	0
$141$	20.5735	1.73260
$142$	6.43885	0.540336
$143$	−5.36652	−0.448771
$144$	−6.89756	−0.574796
$145$	0	0
$146$	5.88152	0.486758
$147$	12.0703	0.995540
$148$	7.25875	0.596665
$149$	−12.3891	−1.01495	−0.507476	−	0.861666i	$-0.669421\pi$
$149$	−12.3891	−1.01495	−0.507476	+	0.861666i	$0.669421\pi$
$150$	0	0
$151$	19.3470	1.57444	0.787219	−	0.616673i	$-0.211520\pi$
$151$	19.3470	1.57444	0.787219	+	0.616673i	$0.211520\pi$
$152$	24.5548	1.99166
$153$	−27.2467	−2.20277
$154$	−6.01047	−0.484337
$155$	0	0
$156$	−3.82456	−0.306210
$157$	6.87800	0.548925	0.274462	−	0.961598i	$-0.411500\pi$
$157$	6.87800	0.548925	0.274462	+	0.961598i	$0.411500\pi$
$158$	9.80117	0.779740
$159$	−17.1229	−1.35793
$160$	0	0
$161$	14.8765	1.17243
$162$	0.333435	0.0261972
$163$	−21.9432	−1.71872	−0.859361	−	0.511369i	$-0.829138\pi$
$163$	−21.9432	−1.71872	−0.859361	+	0.511369i	$0.829138\pi$
$164$	2.22656	0.173865
$165$	0	0
$166$	−4.79946	−0.372510
$167$	−4.56559	−0.353296	−0.176648	−	0.984274i	$-0.556525\pi$
$167$	−4.56559	−0.353296	−0.176648	+	0.984274i	$0.556525\pi$
$168$	−13.9297	−1.07470
$169$	−10.6245	−0.817268
$170$	0	0
$171$	38.7554	2.96370
$172$	−2.07875	−0.158503
$173$	5.76678	0.438440	0.219220	−	0.975675i	$-0.429649\pi$
$173$	5.76678	0.438440	0.219220	+	0.975675i	$0.429649\pi$
$174$	−17.1990	−1.30385
$175$	0	0
$176$	−4.99652	−0.376627
$177$	−3.78430	−0.284445
$178$	2.73937	0.205325
$179$	9.76703	0.730022	0.365011	−	0.931003i	$-0.381065\pi$
$179$	9.76703	0.730022	0.365011	+	0.931003i	$0.381065\pi$
$180$	0	0
$181$	−13.2947	−0.988187	−0.494093	−	0.869409i	$-0.664500\pi$
$181$	−13.2947	−0.988187	−0.494093	+	0.869409i	$0.664500\pi$
$182$	2.66057	0.197215
$183$	32.5747	2.40799
$184$	27.6745	2.04019
$185$	0	0
$186$	−1.51844	−0.111337
$187$	−19.7373	−1.44333
$188$	6.53953	0.476944
$189$	−8.26354	−0.601084
$190$	0	0
$191$	−7.08002	−0.512292	−0.256146	−	0.966638i	$-0.582453\pi$
$191$	−7.08002	−0.512292	−0.256146	+	0.966638i	$0.582453\pi$
$192$	−21.5055	−1.55203
$193$	−6.95584	−0.500693	−0.250346	−	0.968156i	$-0.580544\pi$
$193$	−6.95584	−0.500693	−0.250346	+	0.968156i	$0.580544\pi$
$194$	−12.9986	−0.933246
$195$	0	0
$196$	3.83669	0.274049
$197$	0.690805	0.0492178	0.0246089	−	0.999697i	$-0.492166\pi$
$197$	0.690805	0.0492178	0.0246089	+	0.999697i	$0.492166\pi$
$198$	−17.6475	−1.25415
$199$	22.4460	1.59116	0.795579	−	0.605850i	$-0.207167\pi$
$199$	22.4460	1.59116	0.795579	+	0.605850i	$0.207167\pi$
$200$	0	0
$201$	3.14311	0.221698
$202$	−6.26874	−0.441067
$203$	−9.55670	−0.670749
$204$	−14.0662	−0.984830
$205$	0	0
$206$	−14.8428	−1.03415
$207$	43.6793	3.03592
$208$	2.21174	0.153357
$209$	28.0741	1.94192
$210$	0	0
$211$	−17.6232	−1.21323	−0.606614	−	0.794996i	$-0.707473\pi$
$211$	−17.6232	−1.21323	−0.606614	+	0.794996i	$0.707473\pi$
$212$	−5.44271	−0.373807
$213$	17.0612	1.16902
$214$	16.6363	1.13723
$215$	0	0
$216$	−15.3725	−1.04597
$217$	−0.843727	−0.0572759
$218$	−6.03889	−0.409005
$219$	15.5845	1.05310
$220$	0	0
$221$	8.73682	0.587702
$222$	−24.0798	−1.61613
$223$	−19.7302	−1.32123	−0.660615	−	0.750725i	$-0.729704\pi$
$223$	−19.7302	−1.32123	−0.660615	+	0.750725i	$0.729704\pi$
$224$	−7.49390	−0.500707
$225$	0	0
$226$	−9.43168	−0.627386
$227$	26.9603	1.78942	0.894708	−	0.446652i	$-0.147384\pi$
$227$	26.9603	1.78942	0.894708	+	0.446652i	$0.147384\pi$
$228$	20.0076	1.32503
$229$	22.0051	1.45414	0.727069	−	0.686565i	$-0.240882\pi$
$229$	22.0051	1.45414	0.727069	+	0.686565i	$0.240882\pi$
$230$	0	0
$231$	−15.9262	−1.04786
$232$	−17.7781	−1.16719
$233$	−22.4590	−1.47134	−0.735669	−	0.677341i	$-0.763132\pi$
$233$	−22.4590	−1.47134	−0.735669	+	0.677341i	$0.763132\pi$
$234$	7.81177	0.510671
$235$	0	0
$236$	−1.20288	−0.0783011
$237$	25.9705	1.68697
$238$	9.78519	0.634280
$239$	−8.19022	−0.529781	−0.264891	−	0.964278i	$-0.585336\pi$
$239$	−8.19022	−0.529781	−0.264891	+	0.964278i	$0.585336\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−1.18463	−0.0761512
$243$	16.0269	1.02812
$244$	10.3543	0.662865
$245$	0	0
$246$	−7.38628	−0.470932
$247$	−12.4271	−0.790720
$248$	−1.56957	−0.0996677
$249$	−12.7173	−0.805925
$250$	0	0
$251$	26.4262	1.66801	0.834003	−	0.551761i	$-0.186044\pi$
$251$	26.4262	1.66801	0.834003	+	0.551761i	$0.186044\pi$
$252$	−6.98839	−0.440227
$253$	31.6409	1.98924
$254$	−13.5843	−0.852356
$255$	0	0
$256$	−16.4897	−1.03060
$257$	7.70531	0.480644	0.240322	−	0.970693i	$-0.422747\pi$
$257$	7.70531	0.480644	0.240322	+	0.970693i	$0.422747\pi$
$258$	6.89593	0.429322
$259$	−13.3800	−0.831394
$260$	0	0
$261$	−28.0597	−1.73685
$262$	9.33769	0.576884
$263$	2.81855	0.173800	0.0868998	−	0.996217i	$-0.472304\pi$
$263$	2.81855	0.173800	0.0868998	+	0.996217i	$0.472304\pi$
$264$	−29.6271	−1.82342
$265$	0	0
$266$	−13.9183	−0.853388
$267$	7.25861	0.444220
$268$	0.999076	0.0610283
$269$	−14.8449	−0.905110	−0.452555	−	0.891737i	$-0.649487\pi$
$269$	−14.8449	−0.905110	−0.452555	+	0.891737i	$0.649487\pi$
$270$	0	0
$271$	24.6495	1.49735	0.748675	−	0.662938i	$-0.230691\pi$
$271$	24.6495	1.49735	0.748675	+	0.662938i	$0.230691\pi$
$272$	8.13446	0.493224
$273$	7.04981	0.426674
$274$	9.89308	0.597663
$275$	0	0
$276$	22.5495	1.35732
$277$	−9.81233	−0.589566	−0.294783	−	0.955564i	$-0.595247\pi$
$277$	−9.81233	−0.589566	−0.294783	+	0.955564i	$0.595247\pi$
$278$	2.72607	0.163499
$279$	−2.47729	−0.148311
$280$	0	0
$281$	−20.3307	−1.21283	−0.606414	−	0.795149i	$-0.707393\pi$
$281$	−20.3307	−1.21283	−0.606414	+	0.795149i	$0.707393\pi$
$282$	−21.6939	−1.29185
$283$	−1.04410	−0.0620654	−0.0310327	−	0.999518i	$-0.509880\pi$
$283$	−1.04410	−0.0620654	−0.0310327	+	0.999518i	$0.509880\pi$
$284$	5.42313	0.321803
$285$	0	0
$286$	5.65877	0.334610
$287$	−4.10422	−0.242264
$288$	−22.0030	−1.29654
$289$	15.1328	0.890162
$290$	0	0
$291$	−34.4429	−2.01908
$292$	4.95371	0.289894
$293$	−11.4411	−0.668396	−0.334198	−	0.942503i	$-0.608465\pi$
$293$	−11.4411	−0.668396	−0.334198	+	0.942503i	$0.608465\pi$
$294$	−12.7276	−0.742289
$295$	0	0
$296$	−24.8906	−1.44674
$297$	−17.5757	−1.01985
$298$	13.0638	0.756763
$299$	−14.0060	−0.809989
$300$	0	0
$301$	3.83175	0.220859
$302$	−20.4006	−1.17392
$303$	−16.6105	−0.954249
$304$	−11.5704	−0.663606
$305$	0	0
$306$	28.7305	1.64242
$307$	13.5057	0.770810	0.385405	−	0.922747i	$-0.374062\pi$
$307$	13.5057	0.770810	0.385405	+	0.922747i	$0.374062\pi$
$308$	−5.06232	−0.288453
$309$	−39.3295	−2.23738
$310$	0	0
$311$	13.9235	0.789529	0.394765	−	0.918782i	$-0.370826\pi$
$311$	13.9235	0.789529	0.394765	+	0.918782i	$0.370826\pi$
$312$	13.1146	0.742469
$313$	−3.11900	−0.176296	−0.0881482	−	0.996107i	$-0.528095\pi$
$313$	−3.11900	−0.176296	−0.0881482	+	0.996107i	$0.528095\pi$
$314$	−7.25257	−0.409286
$315$	0	0
$316$	8.25505	0.464383
$317$	−27.7341	−1.55770	−0.778852	−	0.627208i	$-0.784198\pi$
$317$	−27.7341	−1.55770	−0.778852	+	0.627208i	$0.784198\pi$
$318$	18.0553	1.01249
$319$	−20.3262	−1.13805
$320$	0	0
$321$	44.0817	2.46040
$322$	−15.6867	−0.874183
$323$	−45.7052	−2.54311
$324$	0.280836	0.0156020
$325$	0	0
$326$	23.1382	1.28150
$327$	−16.0014	−0.884882
$328$	−7.63500	−0.421572
$329$	−12.0543	−0.664575
$330$	0	0
$331$	−22.3339	−1.22758	−0.613790	−	0.789469i	$-0.710356\pi$
$331$	−22.3339	−1.22758	−0.613790	+	0.789469i	$0.710356\pi$
$332$	−4.04235	−0.221853
$333$	−39.2854	−2.15283
$334$	4.81423	0.263423
$335$	0	0
$336$	6.56376	0.358082
$337$	−4.07474	−0.221965	−0.110983	−	0.993822i	$-0.535400\pi$
$337$	−4.07474	−0.221965	−0.110983	+	0.993822i	$0.535400\pi$
$338$	11.2031	0.609367
$339$	−24.9914	−1.35735
$340$	0	0
$341$	−1.79452	−0.0971789
$342$	−40.8660	−2.20978
$343$	−18.5316	−1.00061
$344$	7.12813	0.384323
$345$	0	0
$346$	−6.08082	−0.326907
$347$	−11.5031	−0.617517	−0.308758	−	0.951140i	$-0.599913\pi$
$347$	−11.5031	−0.617517	−0.308758	+	0.951140i	$0.599913\pi$
$348$	−14.4859	−0.776524
$349$	−36.4019	−1.94855	−0.974275	−	0.225364i	$-0.927643\pi$
$349$	−36.4019	−1.94855	−0.974275	+	0.225364i	$0.927643\pi$
$350$	0	0
$351$	7.78000	0.415266
$352$	−15.9388	−0.849540
$353$	8.31570	0.442600	0.221300	−	0.975206i	$-0.428970\pi$
$353$	8.31570	0.442600	0.221300	+	0.975206i	$0.428970\pi$
$354$	3.99038	0.212086
$355$	0	0
$356$	2.30724	0.122283
$357$	25.9282	1.37226
$358$	−10.2989	−0.544315
$359$	−6.85192	−0.361631	−0.180815	−	0.983517i	$-0.557874\pi$
$359$	−6.85192	−0.361631	−0.180815	+	0.983517i	$0.557874\pi$
$360$	0	0
$361$	46.0106	2.42161
$362$	14.0187	0.736806
$363$	−3.13897	−0.164753
$364$	2.24087	0.117453
$365$	0	0
$366$	−34.3487	−1.79544
$367$	−23.7426	−1.23935	−0.619677	−	0.784857i	$-0.712737\pi$
$367$	−23.7426	−1.23935	−0.619677	+	0.784857i	$0.712737\pi$
$368$	−13.0404	−0.679776
$369$	−12.0505	−0.627324
$370$	0	0
$371$	10.0325	0.520863
$372$	−1.27891	−0.0663082
$373$	−6.28408	−0.325377	−0.162689	−	0.986677i	$-0.552017\pi$
$373$	−6.28408	−0.325377	−0.162689	+	0.986677i	$0.552017\pi$
$374$	20.8121	1.07617
$375$	0	0
$376$	−22.4244	−1.15645
$377$	8.99749	0.463394
$378$	8.71356	0.448177
$379$	−32.3509	−1.66175	−0.830877	−	0.556457i	$-0.812161\pi$
$379$	−32.3509	−1.66175	−0.830877	+	0.556457i	$0.812161\pi$
$380$	0	0
$381$	−35.9949	−1.84407
$382$	7.46559	0.381973
$383$	21.9938	1.12383	0.561914	−	0.827195i	$-0.310065\pi$
$383$	21.9938	1.12383	0.561914	+	0.827195i	$0.310065\pi$
$384$	−2.90348	−0.148168
$385$	0	0
$386$	7.33464	0.373324
$387$	11.2505	0.571895
$388$	−10.9481	−0.555805
$389$	16.2176	0.822264	0.411132	−	0.911576i	$-0.365134\pi$
$389$	16.2176	0.822264	0.411132	+	0.911576i	$0.365134\pi$
$390$	0	0
$391$	−51.5121	−2.60508
$392$	−13.1562	−0.664487
$393$	24.7424	1.24809
$394$	−0.728425	−0.0366975
$395$	0	0
$396$	−14.8636	−0.746925
$397$	−17.7440	−0.890547	−0.445273	−	0.895395i	$-0.646894\pi$
$397$	−17.7440	−0.890547	−0.445273	+	0.895395i	$0.646894\pi$
$398$	−23.6684	−1.18639
$399$	−36.8799	−1.84630
$400$	0	0
$401$	−13.6586	−0.682079	−0.341039	−	0.940049i	$-0.610779\pi$
$401$	−13.6586	−0.682079	−0.341039	+	0.940049i	$0.610779\pi$
$402$	−3.31428	−0.165301
$403$	0.794357	0.0395697
$404$	−5.27985	−0.262683
$405$	0	0
$406$	10.0771	0.500120
$407$	−28.4580	−1.41061
$408$	48.2336	2.38792
$409$	4.73162	0.233963	0.116982	−	0.993134i	$-0.462678\pi$
$409$	4.73162	0.233963	0.116982	+	0.993134i	$0.462678\pi$
$410$	0	0
$411$	26.2140	1.29304
$412$	−12.5014	−0.615898
$413$	2.21727	0.109105
$414$	−46.0580	−2.26363
$415$	0	0
$416$	7.05539	0.345919
$417$	7.22337	0.353730
$418$	−29.6029	−1.44793
$419$	−17.9594	−0.877373	−0.438686	−	0.898640i	$-0.644556\pi$
$419$	−17.9594	−0.877373	−0.438686	+	0.898640i	$0.644556\pi$
$420$	0	0
$421$	25.1465	1.22557	0.612783	−	0.790251i	$-0.290050\pi$
$421$	25.1465	1.22557	0.612783	+	0.790251i	$0.290050\pi$
$422$	18.5829	0.904600
$423$	−35.3929	−1.72086
$424$	18.6633	0.906371
$425$	0	0
$426$	−17.9904	−0.871636
$427$	−19.0860	−0.923637
$428$	14.0119	0.677291
$429$	14.9942	0.723929
$430$	0	0
$431$	1.28313	0.0618060	0.0309030	−	0.999522i	$-0.490162\pi$
$431$	1.28313	0.0618060	0.0309030	+	0.999522i	$0.490162\pi$
$432$	7.24361	0.348508
$433$	27.0984	1.30226	0.651132	−	0.758965i	$-0.274294\pi$
$433$	27.0984	1.30226	0.651132	+	0.758965i	$0.274294\pi$
$434$	0.889675	0.0427058
$435$	0	0
$436$	−5.08626	−0.243587
$437$	73.2701	3.50499
$438$	−16.4332	−0.785207
$439$	−11.1696	−0.533097	−0.266549	−	0.963822i	$-0.585883\pi$
$439$	−11.1696	−0.533097	−0.266549	+	0.963822i	$0.585883\pi$
$440$	0	0
$441$	−20.7647	−0.988796
$442$	−9.21261	−0.438199
$443$	−15.0784	−0.716395	−0.358198	−	0.933646i	$-0.616609\pi$
$443$	−15.0784	−0.716395	−0.358198	+	0.933646i	$0.616609\pi$
$444$	−20.2812	−0.962503
$445$	0	0
$446$	20.8046	0.985128
$447$	34.6155	1.63726
$448$	12.6004	0.595313
$449$	−30.3624	−1.43289	−0.716446	−	0.697643i	$-0.754232\pi$
$449$	−30.3624	−1.43289	−0.716446	+	0.697643i	$0.754232\pi$
$450$	0	0
$451$	−8.72927	−0.411045
$452$	−7.94384	−0.373647
$453$	−54.0563	−2.53978
$454$	−28.4285	−1.33421
$455$	0	0
$456$	−68.6069	−3.21281
$457$	−36.8679	−1.72461	−0.862305	−	0.506390i	$-0.830980\pi$
$457$	−36.8679	−1.72461	−0.862305	+	0.506390i	$0.830980\pi$
$458$	−23.2034	−1.08423
$459$	28.6137	1.33557
$460$	0	0
$461$	9.47241	0.441174	0.220587	−	0.975367i	$-0.429203\pi$
$461$	9.47241	0.441174	0.220587	+	0.975367i	$0.429203\pi$
$462$	16.7935	0.781302
$463$	−26.8175	−1.24631	−0.623156	−	0.782097i	$-0.714150\pi$
$463$	−26.8175	−1.24631	−0.623156	+	0.782097i	$0.714150\pi$
$464$	8.37716	0.388900
$465$	0	0
$466$	23.6821	1.09705
$467$	9.85314	0.455949	0.227975	−	0.973667i	$-0.426790\pi$
$467$	9.85314	0.455949	0.227975	+	0.973667i	$0.426790\pi$
$468$	6.57947	0.304136
$469$	−1.84159	−0.0850369
$470$	0	0
$471$	−19.2174	−0.885490
$472$	4.12475	0.189857
$473$	8.14976	0.374726
$474$	−27.3848	−1.25783
$475$	0	0
$476$	8.24158	0.377752
$477$	29.4568	1.34873
$478$	8.63624	0.395012
$479$	−11.9289	−0.545043	−0.272522	−	0.962150i	$-0.587858\pi$
$479$	−11.9289	−0.545043	−0.272522	+	0.962150i	$0.587858\pi$
$480$	0	0
$481$	12.5971	0.574378
$482$	1.05446	0.0480292
$483$	−41.5655	−1.89129
$484$	−0.997759	−0.0453527
$485$	0	0
$486$	−16.8996	−0.766583
$487$	10.8850	0.493246	0.246623	−	0.969112i	$-0.420679\pi$
$487$	10.8850	0.493246	0.246623	+	0.969112i	$0.420679\pi$
$488$	−35.5053	−1.60725
$489$	61.3100	2.77253
$490$	0	0
$491$	31.9444	1.44163	0.720815	−	0.693128i	$-0.243768\pi$
$491$	31.9444	1.44163	0.720815	+	0.693128i	$0.243768\pi$
$492$	−6.22110	−0.280469
$493$	33.0915	1.49036
$494$	13.1039	0.589573
$495$	0	0
$496$	0.739590	0.0332086
$497$	−9.99643	−0.448401
$498$	13.4098	0.600910
$499$	−30.8274	−1.38003	−0.690013	−	0.723797i	$-0.742395\pi$
$499$	−30.8274	−1.38003	−0.690013	+	0.723797i	$0.742395\pi$
$500$	0	0
$501$	12.7564	0.569915
$502$	−27.8653	−1.24369
$503$	5.52996	0.246569	0.123284	−	0.992371i	$-0.460657\pi$
$503$	5.52996	0.246569	0.123284	+	0.992371i	$0.460657\pi$
$504$	23.9635	1.06742
$505$	0	0
$506$	−33.3640	−1.48321
$507$	29.6852	1.31836
$508$	−11.4414	−0.507630
$509$	9.57644	0.424468	0.212234	−	0.977219i	$-0.431926\pi$
$509$	9.57644	0.424468	0.212234	+	0.977219i	$0.431926\pi$
$510$	0	0
$511$	−9.13116	−0.403939
$512$	15.3093	0.676583
$513$	−40.6998	−1.79694
$514$	−8.12492	−0.358375
$515$	0	0
$516$	5.80810	0.255687
$517$	−25.6383	−1.12757
$518$	14.1087	0.619900
$519$	−16.1126	−0.707263
$520$	0	0
$521$	−35.5269	−1.55646	−0.778230	−	0.627979i	$-0.783882\pi$
$521$	−35.5269	−1.55646	−0.778230	+	0.627979i	$0.783882\pi$
$522$	29.5877	1.29502
$523$	30.2099	1.32099	0.660493	−	0.750832i	$-0.270347\pi$
$523$	30.2099	1.32099	0.660493	+	0.750832i	$0.270347\pi$
$524$	7.86467	0.343570
$525$	0	0
$526$	−2.97205	−0.129587
$527$	2.92153	0.127264
$528$	13.9605	0.607551
$529$	59.5791	2.59040
$530$	0	0
$531$	6.51019	0.282518
$532$	−11.7227	−0.508245
$533$	3.86406	0.167371
$534$	−7.65390	−0.331217
$535$	0	0
$536$	−3.42588	−0.147975
$537$	−27.2894	−1.17763
$538$	15.6533	0.674863
$539$	−15.0418	−0.647895
$540$	0	0
$541$	−4.21274	−0.181120	−0.0905600	−	0.995891i	$-0.528866\pi$
$541$	−4.21274	−0.181120	−0.0905600	+	0.995891i	$0.528866\pi$
$542$	−25.9918	−1.11645
$543$	37.1458	1.59408
$544$	25.9487	1.11254
$545$	0	0
$546$	−7.43373	−0.318134
$547$	25.6016	1.09464	0.547322	−	0.836922i	$-0.315647\pi$
$547$	25.6016	1.09464	0.547322	+	0.836922i	$0.315647\pi$
$548$	8.33246	0.355945
$549$	−56.0389	−2.39168
$550$	0	0
$551$	−47.0689	−2.00520
$552$	−77.3234	−3.29110
$553$	−15.2165	−0.647071
$554$	10.3467	0.439589
$555$	0	0
$556$	2.29604	0.0973737
$557$	−8.44569	−0.357855	−0.178928	−	0.983862i	$-0.557263\pi$
$557$	−8.44569	−0.357855	−0.178928	+	0.983862i	$0.557263\pi$
$558$	2.61220	0.110583
$559$	−3.60754	−0.152583
$560$	0	0
$561$	55.1466	2.32829
$562$	21.4379	0.904302
$563$	4.02353	0.169572	0.0847858	−	0.996399i	$-0.472979\pi$
$563$	4.02353	0.169572	0.0847858	+	0.996399i	$0.472979\pi$
$564$	−18.2717	−0.769376
$565$	0	0
$566$	1.10096	0.0462769
$567$	−0.517664	−0.0217399
$568$	−18.5962	−0.780278
$569$	21.4219	0.898054	0.449027	−	0.893518i	$-0.351771\pi$
$569$	21.4219	0.898054	0.449027	+	0.893518i	$0.351771\pi$
$570$	0	0
$571$	31.0188	1.29810	0.649048	−	0.760747i	$-0.275167\pi$
$571$	31.0188	1.29810	0.649048	+	0.760747i	$0.275167\pi$
$572$	4.76610	0.199281
$573$	19.7818	0.826398
$574$	4.32773	0.180636
$575$	0	0
$576$	36.9964	1.54152
$577$	−9.10433	−0.379018	−0.189509	−	0.981879i	$-0.560690\pi$
$577$	−9.10433	−0.379018	−0.189509	+	0.981879i	$0.560690\pi$
$578$	−15.9569	−0.663718
$579$	19.4349	0.807685
$580$	0	0
$581$	7.45124	0.309130
$582$	36.3186	1.50545
$583$	21.3382	0.883738
$584$	−16.9865	−0.702907
$585$	0	0
$586$	12.0642	0.498366
$587$	23.2720	0.960540	0.480270	−	0.877121i	$-0.340539\pi$
$587$	23.2720	0.960540	0.480270	+	0.877121i	$0.340539\pi$
$588$	−10.7198	−0.442078
$589$	−4.15555	−0.171226
$590$	0	0
$591$	−1.93013	−0.0793951
$592$	11.7286	0.482042
$593$	−5.45489	−0.224005	−0.112003	−	0.993708i	$-0.535727\pi$
$593$	−5.45489	−0.224005	−0.112003	+	0.993708i	$0.535727\pi$
$594$	18.5329	0.760413
$595$	0	0
$596$	11.0030	0.450699
$597$	−62.7150	−2.56675
$598$	14.7688	0.603939
$599$	35.7616	1.46118	0.730590	−	0.682817i	$-0.239245\pi$
$599$	35.7616	1.46118	0.730590	+	0.682817i	$0.239245\pi$
$600$	0	0
$601$	15.8192	0.645277	0.322639	−	0.946522i	$-0.395430\pi$
$601$	15.8192	0.645277	0.322639	+	0.946522i	$0.395430\pi$
$602$	−4.04042	−0.164675
$603$	−5.40715	−0.220196
$604$	−17.1824	−0.699144
$605$	0	0
$606$	17.5151	0.711502
$607$	−38.5787	−1.56586	−0.782931	−	0.622109i	$-0.786276\pi$
$607$	−38.5787	−1.56586	−0.782931	+	0.622109i	$0.786276\pi$
$608$	−36.9091	−1.49686
$609$	26.7017	1.08201
$610$	0	0
$611$	11.3489	0.459129
$612$	24.1983	0.978159
$613$	−11.8347	−0.477999	−0.239000	−	0.971020i	$-0.576820\pi$
$613$	−11.8347	−0.477999	−0.239000	+	0.971020i	$0.576820\pi$
$614$	−14.2412	−0.574727
$615$	0	0
$616$	17.3589	0.699412
$617$	−39.6717	−1.59712	−0.798562	−	0.601913i	$-0.794405\pi$
$617$	−39.6717	−1.59712	−0.798562	+	0.601913i	$0.794405\pi$
$618$	41.4713	1.66822
$619$	8.91772	0.358433	0.179217	−	0.983810i	$-0.442644\pi$
$619$	8.91772	0.358433	0.179217	+	0.983810i	$0.442644\pi$
$620$	0	0
$621$	−45.8707	−1.84073
$622$	−14.6817	−0.588684
$623$	−4.25292	−0.170390
$624$	−6.17968	−0.247385
$625$	0	0
$626$	3.28886	0.131449
$627$	−78.4399	−3.13259
$628$	−6.10848	−0.243755
$629$	46.3303	1.84731
$630$	0	0
$631$	4.50997	0.179539	0.0897696	−	0.995963i	$-0.471387\pi$
$631$	4.50997	0.179539	0.0897696	+	0.995963i	$0.471387\pi$
$632$	−28.3069	−1.12599
$633$	49.2397	1.95710
$634$	29.2445	1.16145
$635$	0	0
$636$	15.2071	0.603002
$637$	6.65833	0.263812
$638$	21.4331	0.848544
$639$	−29.3508	−1.16110
$640$	0	0
$641$	8.51496	0.336321	0.168160	−	0.985760i	$-0.446217\pi$
$641$	8.51496	0.336321	0.168160	+	0.985760i	$0.446217\pi$
$642$	−46.4823	−1.83451
$643$	−37.8001	−1.49069	−0.745345	−	0.666679i	$-0.767715\pi$
$643$	−37.8001	−1.49069	−0.745345	+	0.666679i	$0.767715\pi$
$644$	−13.2121	−0.520630
$645$	0	0
$646$	48.1943	1.89618
$647$	−16.2259	−0.637906	−0.318953	−	0.947771i	$-0.603331\pi$
$647$	−16.2259	−0.637906	−0.318953	+	0.947771i	$0.603331\pi$
$648$	−0.963001	−0.0378302
$649$	4.71592	0.185116
$650$	0	0
$651$	2.35740	0.0923939
$652$	19.4881	0.763214
$653$	41.0192	1.60520	0.802602	−	0.596515i	$-0.203448\pi$
$653$	41.0192	1.60520	0.802602	+	0.596515i	$0.203448\pi$
$654$	16.8729	0.659781
$655$	0	0
$656$	3.59765	0.140465
$657$	−26.8102	−1.04597
$658$	12.7107	0.495517
$659$	10.6147	0.413490	0.206745	−	0.978395i	$-0.433713\pi$
$659$	10.6147	0.413490	0.206745	+	0.978395i	$0.433713\pi$
$660$	0	0
$661$	28.9677	1.12671	0.563356	−	0.826214i	$-0.309510\pi$
$661$	28.9677	1.12671	0.563356	+	0.826214i	$0.309510\pi$
$662$	23.5501	0.915302
$663$	−24.4110	−0.948044
$664$	13.8614	0.537927
$665$	0	0
$666$	41.4248	1.60518
$667$	−53.0490	−2.05406
$668$	4.05479	0.156884
$669$	55.1268	2.13132
$670$	0	0
$671$	−40.5941	−1.56712
$672$	20.9382	0.807709
$673$	46.5073	1.79272	0.896362	−	0.443323i	$-0.146201\pi$
$673$	46.5073	1.79272	0.896362	+	0.443323i	$0.146201\pi$
$674$	4.29665	0.165501
$675$	0	0
$676$	9.43579	0.362915
$677$	29.8062	1.14555	0.572773	−	0.819714i	$-0.305868\pi$
$677$	29.8062	1.14555	0.572773	+	0.819714i	$0.305868\pi$
$678$	26.3524	1.01206
$679$	20.1806	0.774460
$680$	0	0
$681$	−75.3279	−2.88657
$682$	1.89225	0.0724580
$683$	−35.8028	−1.36996	−0.684978	−	0.728564i	$-0.740188\pi$
$683$	−35.8028	−1.36996	−0.684978	+	0.728564i	$0.740188\pi$
$684$	−34.4194	−1.31606
$685$	0	0
$686$	19.5408	0.746071
$687$	−61.4830	−2.34572
$688$	−3.35882	−0.128054
$689$	−9.44549	−0.359844
$690$	0	0
$691$	32.5225	1.23721	0.618607	−	0.785700i	$-0.287697\pi$
$691$	32.5225	1.23721	0.618607	+	0.785700i	$0.287697\pi$
$692$	−5.12158	−0.194693
$693$	27.3980	1.04077
$694$	12.1295	0.460430
$695$	0	0
$696$	49.6727	1.88284
$697$	14.2115	0.538297
$698$	38.3843	1.45287
$699$	62.7512	2.37347
$700$	0	0
$701$	−14.1055	−0.532757	−0.266379	−	0.963868i	$-0.585827\pi$
$701$	−14.1055	−0.532757	−0.266379	+	0.963868i	$0.585827\pi$
$702$	−8.20369	−0.309628
$703$	−65.8996	−2.48545
$704$	26.7998	1.01006
$705$	0	0
$706$	−8.76856	−0.330009
$707$	9.73233	0.366022
$708$	3.36090	0.126310
$709$	19.9520	0.749315	0.374657	−	0.927163i	$-0.377760\pi$
$709$	19.9520	0.749315	0.374657	+	0.927163i	$0.377760\pi$
$710$	0	0
$711$	−44.6775	−1.67554
$712$	−7.91163	−0.296501
$713$	−4.68351	−0.175399
$714$	−27.3402	−1.02318
$715$	0	0
$716$	−8.67428	−0.324173
$717$	22.8837	0.854609
$718$	7.22507	0.269637
$719$	−47.2522	−1.76221	−0.881105	−	0.472921i	$-0.843200\pi$
$719$	−47.2522	−1.76221	−0.881105	+	0.472921i	$0.843200\pi$
$720$	0	0
$721$	23.0437	0.858193
$722$	−48.5162	−1.80559
$723$	2.79403	0.103911
$724$	11.8073	0.438813
$725$	0	0
$726$	3.30991	0.122842
$727$	42.3566	1.57092	0.785460	−	0.618912i	$-0.212426\pi$
$727$	42.3566	1.57092	0.785460	+	0.618912i	$0.212426\pi$
$728$	−7.68404	−0.284790
$729$	−43.8309	−1.62337
$730$	0	0
$731$	−13.2680	−0.490735
$732$	−28.9302	−1.06929
$733$	26.4674	0.977597	0.488799	−	0.872397i	$-0.337435\pi$
$733$	26.4674	0.977597	0.488799	+	0.872397i	$0.337435\pi$
$734$	25.0356	0.924081
$735$	0	0
$736$	−41.5984	−1.53334
$737$	−3.91689	−0.144280
$738$	12.7067	0.467742
$739$	−25.6941	−0.945171	−0.472586	−	0.881285i	$-0.656679\pi$
$739$	−25.6941	−0.945171	−0.472586	+	0.881285i	$0.656679\pi$
$740$	0	0
$741$	34.7219	1.27554
$742$	−10.5789	−0.388363
$743$	−17.9250	−0.657605	−0.328803	−	0.944399i	$-0.606645\pi$
$743$	−17.9250	−0.657605	−0.328803	+	0.944399i	$0.606645\pi$
$744$	4.38543	0.160778
$745$	0	0
$746$	6.62630	0.242606
$747$	21.8778	0.800466
$748$	17.5290	0.640925
$749$	−25.8281	−0.943738
$750$	0	0
$751$	41.8868	1.52847	0.764236	−	0.644936i	$-0.223116\pi$
$751$	41.8868	1.52847	0.764236	+	0.644936i	$0.223116\pi$
$752$	10.5665	0.385320
$753$	−73.8356	−2.69072
$754$	−9.48748	−0.345514
$755$	0	0
$756$	7.33900	0.266917
$757$	2.42982	0.0883133	0.0441566	−	0.999025i	$-0.485940\pi$
$757$	2.42982	0.0883133	0.0441566	+	0.999025i	$0.485940\pi$
$758$	34.1127	1.23903
$759$	−88.4056	−3.20892
$760$	0	0
$761$	−39.7501	−1.44094	−0.720470	−	0.693486i	$-0.756074\pi$
$761$	−39.7501	−1.44094	−0.720470	+	0.693486i	$0.756074\pi$
$762$	37.9551	1.37497
$763$	9.37548	0.339415
$764$	6.28790	0.227488
$765$	0	0
$766$	−23.1915	−0.837943
$767$	−2.08753	−0.0753763
$768$	46.0727	1.66250
$769$	23.8206	0.858993	0.429497	−	0.903069i	$-0.358691\pi$
$769$	23.8206	0.858993	0.429497	+	0.903069i	$0.358691\pi$
$770$	0	0
$771$	−21.5289	−0.775344
$772$	6.17761	0.222337
$773$	−23.2106	−0.834829	−0.417414	−	0.908716i	$-0.637064\pi$
$773$	−23.2106	−0.834829	−0.417414	+	0.908716i	$0.637064\pi$
$774$	−11.8632	−0.426413
$775$	0	0
$776$	37.5415	1.34766
$777$	37.3842	1.34115
$778$	−17.1008	−0.613092
$779$	−20.2142	−0.724249
$780$	0	0
$781$	−21.2614	−0.760793
$782$	54.3173	1.94238
$783$	29.4674	1.05308
$784$	6.19927	0.221402
$785$	0	0
$786$	−26.0898	−0.930593
$787$	−28.9293	−1.03122	−0.515609	−	0.856824i	$-0.672434\pi$
$787$	−28.9293	−1.03122	−0.515609	+	0.856824i	$0.672434\pi$
$788$	−0.613517	−0.0218556
$789$	−7.87514	−0.280362
$790$	0	0
$791$	14.6429	0.520640
$792$	50.9680	1.81107
$793$	17.9692	0.638105
$794$	18.7103	0.664005
$795$	0	0
$796$	−19.9347	−0.706568
$797$	−14.6683	−0.519578	−0.259789	−	0.965665i	$-0.583653\pi$
$797$	−14.6683	−0.519578	−0.259789	+	0.965665i	$0.583653\pi$
$798$	38.8883	1.37663
$799$	41.7398	1.47665
$800$	0	0
$801$	−12.4871	−0.441211
$802$	14.4024	0.508568
$803$	−19.4211	−0.685355
$804$	−2.79145	−0.0984469
$805$	0	0
$806$	−0.837616	−0.0295038
$807$	41.4772	1.46007
$808$	18.1049	0.636927
$809$	5.88041	0.206744	0.103372	−	0.994643i	$-0.467037\pi$
$809$	5.88041	0.206744	0.103372	+	0.994643i	$0.467037\pi$
$810$	0	0
$811$	54.6211	1.91801	0.959004	−	0.283393i	$-0.0914600\pi$
$811$	54.6211	1.91801	0.959004	+	0.283393i	$0.0914600\pi$
$812$	8.48748	0.297852
$813$	−68.8715	−2.41543
$814$	30.0078	1.05177
$815$	0	0
$816$	−22.7280	−0.795638
$817$	18.8722	0.660256
$818$	−4.98929	−0.174447
$819$	−12.1279	−0.423783
$820$	0	0
$821$	−39.3076	−1.37185	−0.685923	−	0.727674i	$-0.740601\pi$
$821$	−39.3076	−1.37185	−0.685923	+	0.727674i	$0.740601\pi$
$822$	−27.6416	−0.964112
$823$	−43.0976	−1.50229	−0.751145	−	0.660138i	$-0.770498\pi$
$823$	−43.0976	−1.50229	−0.751145	+	0.660138i	$0.770498\pi$
$824$	42.8678	1.49337
$825$	0	0
$826$	−2.33802	−0.0813502
$827$	28.9347	1.00616	0.503079	−	0.864241i	$-0.332201\pi$
$827$	28.9347	1.00616	0.503079	+	0.864241i	$0.332201\pi$
$828$	−38.7924	−1.34813
$829$	37.3545	1.29737	0.648687	−	0.761055i	$-0.275318\pi$
$829$	37.3545	1.29737	0.648687	+	0.761055i	$0.275318\pi$
$830$	0	0
$831$	27.4160	0.951050
$832$	−11.8631	−0.411279
$833$	24.4883	0.848471
$834$	−7.61674	−0.263746
$835$	0	0
$836$	−24.9331	−0.862328
$837$	2.60158	0.0899236
$838$	18.9374	0.654182
$839$	21.6809	0.748507	0.374254	−	0.927326i	$-0.377899\pi$
$839$	21.6809	0.748507	0.374254	+	0.927326i	$0.377899\pi$
$840$	0	0
$841$	5.07877	0.175130
$842$	−26.5159	−0.913800
$843$	56.8047	1.95646
$844$	15.6514	0.538745
$845$	0	0
$846$	37.3203	1.28310
$847$	1.83917	0.0631945
$848$	−8.79427	−0.301996
$849$	2.91726	0.100120
$850$	0	0
$851$	−74.2722	−2.54602
$852$	−15.1524	−0.519113
$853$	32.7846	1.12252	0.561262	−	0.827638i	$-0.310316\pi$
$853$	32.7846	1.12252	0.561262	+	0.827638i	$0.310316\pi$
$854$	20.1254	0.688677
$855$	0	0
$856$	−48.0475	−1.64223
$857$	10.2792	0.351131	0.175566	−	0.984468i	$-0.443825\pi$
$857$	10.2792	0.351131	0.175566	+	0.984468i	$0.443825\pi$
$858$	−15.8108	−0.539772
$859$	28.3672	0.967875	0.483938	−	0.875102i	$-0.339206\pi$
$859$	28.3672	0.967875	0.483938	+	0.875102i	$0.339206\pi$
$860$	0	0
$861$	11.4673	0.390806
$862$	−1.35300	−0.0460835
$863$	−40.9311	−1.39331	−0.696656	−	0.717405i	$-0.745330\pi$
$863$	−40.9311	−1.39331	−0.696656	+	0.717405i	$0.745330\pi$
$864$	23.1069	0.786113
$865$	0	0
$866$	−28.5741	−0.970987
$867$	−42.2814	−1.43595
$868$	0.749329	0.0254339
$869$	−32.3640	−1.09787
$870$	0	0
$871$	1.73383	0.0587487
$872$	17.4410	0.590627
$873$	59.2527	2.00540
$874$	−77.2603	−2.61337
$875$	0	0
$876$	−13.8408	−0.467639
$877$	−17.1968	−0.580695	−0.290348	−	0.956921i	$-0.593771\pi$
$877$	−17.1968	−0.580695	−0.290348	+	0.956921i	$0.593771\pi$
$878$	11.7779	0.397485
$879$	31.9668	1.07821
$880$	0	0
$881$	−46.3133	−1.56034	−0.780168	−	0.625571i	$-0.784866\pi$
$881$	−46.3133	−1.56034	−0.780168	+	0.625571i	$0.784866\pi$
$882$	21.8955	0.737261
$883$	−22.7174	−0.764501	−0.382251	−	0.924059i	$-0.624851\pi$
$883$	−22.7174	−0.764501	−0.382251	+	0.924059i	$0.624851\pi$
$884$	−7.75933	−0.260975
$885$	0	0
$886$	15.8995	0.534155
$887$	−26.3777	−0.885677	−0.442838	−	0.896602i	$-0.646028\pi$
$887$	−26.3777	−0.885677	−0.442838	+	0.896602i	$0.646028\pi$
$888$	69.5452	2.33378
$889$	21.0899	0.707333
$890$	0	0
$891$	−1.10102	−0.0368856
$892$	17.5227	0.586704
$893$	−59.3701	−1.98674
$894$	−36.5006	−1.22076
$895$	0	0
$896$	1.70119	0.0568328
$897$	39.1333	1.30662
$898$	32.0159	1.06838
$899$	3.00869	0.100346
$900$	0	0
$901$	−34.7391	−1.15733
$902$	9.20465	0.306481
$903$	−10.7061	−0.356275
$904$	27.2398	0.905982
$905$	0	0
$906$	57.0001	1.89370
$907$	28.2859	0.939218	0.469609	−	0.882875i	$-0.344395\pi$
$907$	28.2859	0.939218	0.469609	+	0.882875i	$0.344395\pi$
$908$	−23.9439	−0.794606
$909$	28.5753	0.947785
$910$	0	0
$911$	−16.8558	−0.558458	−0.279229	−	0.960224i	$-0.590079\pi$
$911$	−16.8558	−0.558458	−0.279229	+	0.960224i	$0.590079\pi$
$912$	32.3280	1.07049
$913$	15.8481	0.524494
$914$	38.8757	1.28589
$915$	0	0
$916$	−19.5431	−0.645723
$917$	−14.4969	−0.478731
$918$	−30.1720	−0.995823
$919$	−1.29982	−0.0428770	−0.0214385	−	0.999770i	$-0.506825\pi$
$919$	−1.29982	−0.0428770	−0.0214385	+	0.999770i	$0.506825\pi$
$920$	0	0
$921$	−37.7354	−1.24342
$922$	−9.98826	−0.328946
$923$	9.41150	0.309783
$924$	14.1443	0.465313
$925$	0	0
$926$	28.2779	0.929269
$927$	67.6593	2.22222
$928$	26.7229	0.877222
$929$	−39.6792	−1.30183	−0.650916	−	0.759150i	$-0.725615\pi$
$929$	−39.6792	−1.30183	−0.650916	+	0.759150i	$0.725615\pi$
$930$	0	0
$931$	−34.8319	−1.14157
$932$	19.9462	0.653361
$933$	−38.9027	−1.27362
$934$	−10.3897	−0.339962
$935$	0	0
$936$	−22.5613	−0.737439
$937$	−20.9516	−0.684460	−0.342230	−	0.939616i	$-0.611182\pi$
$937$	−20.9516	−0.684460	−0.342230	+	0.939616i	$0.611182\pi$
$938$	1.94188	0.0634047
$939$	8.71460	0.284390
$940$	0	0
$941$	−53.5965	−1.74720	−0.873598	−	0.486648i	$-0.838219\pi$
$941$	−53.5965	−1.74720	−0.873598	+	0.486648i	$0.838219\pi$
$942$	20.2639	0.660234
$943$	−22.7824	−0.741897
$944$	−1.94361	−0.0632590
$945$	0	0
$946$	−8.59358	−0.279401
$947$	29.3031	0.952222	0.476111	−	0.879385i	$-0.342046\pi$
$947$	29.3031	0.952222	0.476111	+	0.879385i	$0.342046\pi$
$948$	−23.0649	−0.749113
$949$	8.59685	0.279066
$950$	0	0
$951$	77.4901	2.51279
$952$	−28.2608	−0.915937
$953$	5.54779	0.179711	0.0898553	−	0.995955i	$-0.471360\pi$
$953$	5.54779	0.179711	0.0898553	+	0.995955i	$0.471360\pi$
$954$	−31.0609	−1.00564
$955$	0	0
$956$	7.27388	0.235254
$957$	56.7920	1.83582
$958$	12.5785	0.406392
$959$	−15.3592	−0.495974
$960$	0	0
$961$	−30.7344	−0.991431
$962$	−13.2831	−0.428265
$963$	−75.8345	−2.44373
$964$	0.888118	0.0286044
$965$	0	0
$966$	43.8290	1.41018
$967$	−37.2637	−1.19832	−0.599160	−	0.800629i	$-0.704499\pi$
$967$	−37.2637	−1.19832	−0.599160	+	0.800629i	$0.704499\pi$
$968$	3.42136	0.109967
$969$	127.702	4.10238
$970$	0	0
$971$	−43.1081	−1.38341	−0.691703	−	0.722183i	$-0.743139\pi$
$971$	−43.1081	−1.38341	−0.691703	+	0.722183i	$0.743139\pi$
$972$	−14.2337	−0.456547
$973$	−4.23228	−0.135681
$974$	−11.4778	−0.367771
$975$	0	0
$976$	16.7303	0.535524
$977$	−41.1995	−1.31809	−0.659045	−	0.752104i	$-0.729039\pi$
$977$	−41.1995	−1.31809	−0.659045	+	0.752104i	$0.729039\pi$
$978$	−64.6488	−2.06724
$979$	−9.04555	−0.289097
$980$	0	0
$981$	27.5276	0.878888
$982$	−33.6840	−1.07490
$983$	−13.6061	−0.433967	−0.216984	−	0.976175i	$-0.569622\pi$
$983$	−13.6061	−0.433967	−0.216984	+	0.976175i	$0.569622\pi$
$984$	21.3324	0.680053
$985$	0	0
$986$	−34.8936	−1.11124
$987$	33.6801	1.07205
$988$	11.0368	0.351127
$989$	21.2700	0.676345
$990$	0	0
$991$	47.5600	1.51079	0.755396	−	0.655268i	$-0.227444\pi$
$991$	47.5600	1.51079	0.755396	+	0.655268i	$0.227444\pi$
$992$	2.35927	0.0749069
$993$	62.4016	1.98025
$994$	10.5408	0.334334
$995$	0	0
$996$	11.2945	0.357878
$997$	61.0129	1.93230	0.966149	−	0.257986i	$-0.0830589\pi$
$997$	61.0129	1.93230	0.966149	+	0.257986i	$0.0830589\pi$
$998$	32.5062	1.02897
$999$	41.2564	1.30529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.j.1.10		25
5.4	even	2		1205.2.a.e.1.16	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.16	✓	25	5.4	even	2
6025.2.a.j.1.10		25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.05446 q^{2} -2.79403 q^{3} -0.888118 q^{4} +2.94619 q^{6} +1.63707 q^{7} +3.04540 q^{8} +4.80663 q^{9} +O(q^{10})\)	\(q-1.05446 q^{2} -2.79403 q^{3} -0.888118 q^{4} +2.94619 q^{6} +1.63707 q^{7} +3.04540 q^{8} +4.80663 q^{9} +3.48187 q^{11} +2.48143 q^{12} -1.54127 q^{13} -1.72622 q^{14} -1.43501 q^{16} -5.66858 q^{17} -5.06839 q^{18} +8.06291 q^{19} -4.57402 q^{21} -3.67149 q^{22} +9.08730 q^{23} -8.50895 q^{24} +1.62521 q^{26} -5.04778 q^{27} -1.45391 q^{28} -5.83770 q^{29} -0.515390 q^{31} -4.57764 q^{32} -9.72848 q^{33} +5.97728 q^{34} -4.26885 q^{36} -8.17318 q^{37} -8.50200 q^{38} +4.30637 q^{39} -2.50706 q^{41} +4.82311 q^{42} +2.34062 q^{43} -3.09232 q^{44} -9.58218 q^{46} -7.36336 q^{47} +4.00947 q^{48} -4.32002 q^{49} +15.8382 q^{51} +1.36883 q^{52} +6.12837 q^{53} +5.32267 q^{54} +4.98552 q^{56} -22.5281 q^{57} +6.15561 q^{58} +1.35442 q^{59} -11.6587 q^{61} +0.543457 q^{62} +7.86876 q^{63} +7.69695 q^{64} +10.2583 q^{66} -1.12494 q^{67} +5.03437 q^{68} -25.3902 q^{69} -6.10631 q^{71} +14.6381 q^{72} -5.57776 q^{73} +8.61827 q^{74} -7.16082 q^{76} +5.70006 q^{77} -4.54089 q^{78} -9.29499 q^{79} -0.316215 q^{81} +2.64359 q^{82} +4.55159 q^{83} +4.06227 q^{84} -2.46809 q^{86} +16.3107 q^{87} +10.6037 q^{88} -2.59790 q^{89} -2.52316 q^{91} -8.07060 q^{92} +1.44002 q^{93} +7.76435 q^{94} +12.7901 q^{96} +12.3273 q^{97} +4.55528 q^{98} +16.7361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) \) 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9 + 2 * q^11 - 20 * q^12 - 14 * q^13 - 5 * q^14 + 38 * q^16 - 7 * q^17 - 9 * q^18 + 30 * q^19 + q^21 - q^22 - 43 * q^23 - 6 * q^24 - 22 * q^26 - 42 * q^27 - 32 * q^28 - 4 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 + 7 * q^34 + 15 * q^36 - 16 * q^37 - 14 * q^38 - 21 * q^39 - q^41 + 25 * q^42 - 35 * q^43 - 52 * q^44 - 27 * q^46 - 50 * q^47 - 26 * q^48 + 46 * q^49 - 7 * q^51 - 3 * q^52 - 4 * q^53 - 31 * q^54 - 51 * q^56 - 2 * q^58 + 6 * q^59 + 19 * q^61 - 28 * q^63 + 49 * q^64 - 27 * q^66 - 65 * q^67 + 25 * q^68 + 2 * q^69 - 34 * q^71 + 10 * q^72 - 8 * q^73 - 42 * q^74 + 71 * q^76 - q^77 + 59 * q^78 - 12 * q^79 + 29 * q^81 - 11 * q^82 - 41 * q^83 - 10 * q^84 - 13 * q^86 - 40 * q^87 + 52 * q^88 - 24 * q^89 + 46 * q^91 - 85 * q^92 + 30 * q^93 + 14 * q^94 - 30 * q^96 - 9 * q^97 + 64 * q^98 + 2 * q^99

Introduction

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