LMFDB - Embedded newform 7225.2.a.bi.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7225,2,Mod(1,7225)] 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("7225.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7225, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7225 = 5^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7225.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,3,3,3,0,9,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$57.6919154604$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.1397493.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 3x^{4} + 10x^{3} + 3x^{2} - 6x + 1 $ x^6 - 3x^5 - 3x^4 + 10x^3 + 3x^2 - 6*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1445)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.05432$ of defining polynomial
Character	$\chi$	$=$	7225.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.40162 q^{2} +3.14741 q^{3} +3.76778 q^{4} +7.55888 q^{6} -2.45595 q^{7} +4.24555 q^{8} +6.90618 q^{9} +2.67294 q^{11} +11.8588 q^{12} +2.57085 q^{13} -5.89825 q^{14} +2.66063 q^{16} +16.5860 q^{18} -6.25456 q^{19} -7.72986 q^{21} +6.41940 q^{22} +3.11473 q^{23} +13.3625 q^{24} +6.17420 q^{26} +12.2943 q^{27} -9.25348 q^{28} -0.710678 q^{29} +3.99271 q^{31} -2.10127 q^{32} +8.41285 q^{33} +26.0210 q^{36} +3.63287 q^{37} -15.0211 q^{38} +8.09151 q^{39} +8.29741 q^{41} -18.5642 q^{42} +12.7653 q^{43} +10.0711 q^{44} +7.48040 q^{46} -2.78467 q^{47} +8.37409 q^{48} -0.968329 q^{49} +9.68640 q^{52} -0.165984 q^{53} +29.5263 q^{54} -10.4268 q^{56} -19.6857 q^{57} -1.70678 q^{58} -12.2972 q^{59} -0.680871 q^{61} +9.58898 q^{62} -16.9612 q^{63} -10.3677 q^{64} +20.2045 q^{66} +1.50354 q^{67} +9.80333 q^{69} -2.51376 q^{71} +29.3205 q^{72} -8.24985 q^{73} +8.72478 q^{74} -23.5658 q^{76} -6.56461 q^{77} +19.4327 q^{78} +4.47987 q^{79} +17.9768 q^{81} +19.9272 q^{82} -12.1257 q^{83} -29.1245 q^{84} +30.6575 q^{86} -2.23680 q^{87} +11.3481 q^{88} +1.16707 q^{89} -6.31386 q^{91} +11.7356 q^{92} +12.5667 q^{93} -6.68772 q^{94} -6.61356 q^{96} -3.12613 q^{97} -2.32556 q^{98} +18.4598 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 9 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 6 q^{11} + 6 q^{12} + 9 q^{13} - 18 q^{14} - 3 q^{16} + 15 q^{18} - 21 q^{19} - 12 q^{21} - 3 q^{22} + 18 q^{23} - 6 q^{26} + 12 q^{27}+ \cdots + 18 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 9 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9 + 6 * q^11 + 6 * q^12 + 9 * q^13 - 18 * q^14 - 3 * q^16 + 15 * q^18 - 21 * q^19 - 12 * q^21 - 3 * q^22 + 18 * q^23 - 6 * q^26 + 12 * q^27 - 15 * q^28 + 18 * q^29 - 6 * q^31 + 24 * q^33 + 18 * q^36 - 9 * q^37 - 15 * q^38 + 9 * q^39 + 3 * q^41 - 6 * q^42 + 39 * q^43 + 6 * q^44 + 27 * q^46 - 3 * q^47 + 21 * q^48 + 6 * q^49 - 3 * q^52 + 24 * q^53 + 33 * q^54 + 9 * q^56 - 12 * q^57 + 33 * q^58 - 12 * q^59 + 27 * q^61 - 12 * q^63 - 12 * q^64 + 21 * q^66 + 30 * q^67 - 18 * q^71 + 30 * q^72 - 9 * q^73 + 27 * q^74 - 45 * q^76 + 21 * q^77 + 36 * q^78 + 3 * q^79 + 6 * q^81 + 15 * q^82 + 21 * q^83 - 27 * q^84 + 36 * q^86 - 6 * q^87 + 12 * q^88 + 6 * q^89 + 36 * q^91 + 9 * q^92 + 30 * q^93 + 3 * q^94 + 27 * q^96 - 18 * q^97 - 42 * q^98 + 18 * 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 $

$2$	2.40162	1.69820	0.849101	−	0.528230i	$-0.177144\pi$
$2$	2.40162	1.69820	0.849101	+	0.528230i	$0.177144\pi$
$3$	3.14741	1.81716	0.908579	−	0.417714i	$-0.137169\pi$
$3$	3.14741	1.81716	0.908579	+	0.417714i	$0.137169\pi$
$4$	3.76778	1.88389
$5$	0	0
$5$	0	0
$6$	7.55888	3.08590
$7$	−2.45595	−0.928260	−0.464130	−	0.885767i	$-0.653633\pi$
$7$	−2.45595	−0.928260	−0.464130	+	0.885767i	$0.653633\pi$
$8$	4.24555	1.50103
$9$	6.90618	2.30206
$10$	0	0
$11$	2.67294	0.805923	0.402962	−	0.915217i	$-0.367981\pi$
$11$	2.67294	0.805923	0.402962	+	0.915217i	$0.367981\pi$
$12$	11.8588	3.42333
$13$	2.57085	0.713025	0.356512	−	0.934291i	$-0.383966\pi$
$13$	2.57085	0.713025	0.356512	+	0.934291i	$0.383966\pi$
$14$	−5.89825	−1.57637
$15$	0	0
$16$	2.66063	0.665158
$17$	0	0
$17$	0	0
$18$	16.5860	3.90936
$19$	−6.25456	−1.43490	−0.717448	−	0.696613i	$-0.754690\pi$
$19$	−6.25456	−1.43490	−0.717448	+	0.696613i	$0.754690\pi$
$20$	0	0
$21$	−7.72986	−1.68679
$22$	6.41940	1.36862
$23$	3.11473	0.649466	0.324733	−	0.945806i	$-0.394725\pi$
$23$	3.11473	0.649466	0.324733	+	0.945806i	$0.394725\pi$
$24$	13.3625	2.72760
$25$	0	0
$26$	6.17420	1.21086
$27$	12.2943	2.36605
$28$	−9.25348	−1.74874
$29$	−0.710678	−0.131970	−0.0659848	−	0.997821i	$-0.521019\pi$
$29$	−0.710678	−0.131970	−0.0659848	+	0.997821i	$0.521019\pi$
$30$	0	0
$31$	3.99271	0.717112	0.358556	−	0.933508i	$-0.383269\pi$
$31$	3.99271	0.717112	0.358556	+	0.933508i	$0.383269\pi$
$32$	−2.10127	−0.371456
$33$	8.41285	1.46449
$34$	0	0
$35$	0	0
$36$	26.0210	4.33683
$37$	3.63287	0.597240	0.298620	−	0.954372i	$-0.403474\pi$
$37$	3.63287	0.597240	0.298620	+	0.954372i	$0.403474\pi$
$38$	−15.0211	−2.43674
$39$	8.09151	1.29568
$40$	0	0
$41$	8.29741	1.29584	0.647919	−	0.761709i	$-0.275640\pi$
$41$	8.29741	1.29584	0.647919	+	0.761709i	$0.275640\pi$
$42$	−18.5642	−2.86452
$43$	12.7653	1.94669	0.973347	−	0.229338i	$-0.0736563\pi$
$43$	12.7653	1.94669	0.973347	+	0.229338i	$0.0736563\pi$
$44$	10.0711	1.51827
$45$	0	0
$46$	7.48040	1.10293
$47$	−2.78467	−0.406185	−0.203093	−	0.979160i	$-0.565099\pi$
$47$	−2.78467	−0.406185	−0.203093	+	0.979160i	$0.565099\pi$
$48$	8.37409	1.20870
$49$	−0.968329	−0.138333
$50$	0	0
$51$	0	0
$52$	9.68640	1.34326
$53$	−0.165984	−0.0227996	−0.0113998	−	0.999935i	$-0.503629\pi$
$53$	−0.165984	−0.0227996	−0.0113998	+	0.999935i	$0.503629\pi$
$54$	29.5263	4.01803
$55$	0	0
$56$	−10.4268	−1.39334
$57$	−19.6857	−2.60743
$58$	−1.70678	−0.224111
$59$	−12.2972	−1.60095	−0.800476	−	0.599364i	$-0.795420\pi$
$59$	−12.2972	−1.60095	−0.800476	+	0.599364i	$0.795420\pi$
$60$	0	0
$61$	−0.680871	−0.0871767	−0.0435883	−	0.999050i	$-0.513879\pi$
$61$	−0.680871	−0.0871767	−0.0435883	+	0.999050i	$0.513879\pi$
$62$	9.58898	1.21780
$63$	−16.9612	−2.13691
$64$	−10.3677	−1.29596
$65$	0	0
$66$	20.2045	2.48700
$67$	1.50354	0.183687	0.0918433	−	0.995773i	$-0.470724\pi$
$67$	1.50354	0.183687	0.0918433	+	0.995773i	$0.470724\pi$
$68$	0	0
$69$	9.80333	1.18018
$70$	0	0
$71$	−2.51376	−0.298328	−0.149164	−	0.988812i	$-0.547658\pi$
$71$	−2.51376	−0.298328	−0.149164	+	0.988812i	$0.547658\pi$
$72$	29.3205	3.45546
$73$	−8.24985	−0.965572	−0.482786	−	0.875738i	$-0.660375\pi$
$73$	−8.24985	−0.965572	−0.482786	+	0.875738i	$0.660375\pi$
$74$	8.72478	1.01423
$75$	0	0
$76$	−23.5658	−2.70319
$77$	−6.56461	−0.748107
$78$	19.4327	2.20032
$79$	4.47987	0.504025	0.252012	−	0.967724i	$-0.418908\pi$
$79$	4.47987	0.504025	0.252012	+	0.967724i	$0.418908\pi$
$80$	0	0
$81$	17.9768	1.99742
$82$	19.9272	2.20060
$83$	−12.1257	−1.33097	−0.665484	−	0.746412i	$-0.731775\pi$
$83$	−12.1257	−1.33097	−0.665484	+	0.746412i	$0.731775\pi$
$84$	−29.1245	−3.17774
$85$	0	0
$86$	30.6575	3.30588
$87$	−2.23680	−0.239810
$88$	11.3481	1.20971
$89$	1.16707	0.123709	0.0618546	−	0.998085i	$-0.480298\pi$
$89$	1.16707	0.123709	0.0618546	+	0.998085i	$0.480298\pi$
$90$	0	0
$91$	−6.31386	−0.661873
$92$	11.7356	1.22352
$93$	12.5667	1.30310
$94$	−6.68772	−0.689785
$95$	0	0
$96$	−6.61356	−0.674993
$97$	−3.12613	−0.317410	−0.158705	−	0.987326i	$-0.550732\pi$
$97$	−3.12613	−0.317410	−0.158705	+	0.987326i	$0.550732\pi$
$98$	−2.32556	−0.234917
$99$	18.4598	1.85528
$100$	0	0
$101$	0.963333	0.0958553	0.0479276	−	0.998851i	$-0.484738\pi$
$101$	0.963333	0.0958553	0.0479276	+	0.998851i	$0.484738\pi$
$102$	0	0
$103$	13.1842	1.29908	0.649539	−	0.760329i	$-0.274962\pi$
$103$	13.1842	1.29908	0.649539	+	0.760329i	$0.274962\pi$
$104$	10.9147	1.07027
$105$	0	0
$106$	−0.398630	−0.0387184
$107$	−1.20156	−0.116159	−0.0580797	−	0.998312i	$-0.518498\pi$
$107$	−1.20156	−0.116159	−0.0580797	+	0.998312i	$0.518498\pi$
$108$	46.3224	4.45738
$109$	−18.8394	−1.80449	−0.902243	−	0.431227i	$-0.858081\pi$
$109$	−18.8394	−1.80449	−0.902243	+	0.431227i	$0.858081\pi$
$110$	0	0
$111$	11.4341	1.08528
$112$	−6.53436	−0.617439
$113$	11.1118	1.04531	0.522656	−	0.852544i	$-0.324941\pi$
$113$	11.1118	1.04531	0.522656	+	0.852544i	$0.324941\pi$
$114$	−47.2775	−4.42794
$115$	0	0
$116$	−2.67768	−0.248617
$117$	17.7547	1.64143
$118$	−29.5331	−2.71874
$119$	0	0
$120$	0	0
$121$	−3.85537	−0.350488
$122$	−1.63520	−0.148044
$123$	26.1153	2.35474
$124$	15.0437	1.35096
$125$	0	0
$126$	−40.7344	−3.62891
$127$	−1.62949	−0.144594	−0.0722970	−	0.997383i	$-0.523033\pi$
$127$	−1.62949	−0.144594	−0.0722970	+	0.997383i	$0.523033\pi$
$128$	−20.6968	−1.82935
$129$	40.1777	3.53745
$130$	0	0
$131$	14.1257	1.23417	0.617083	−	0.786898i	$-0.288314\pi$
$131$	14.1257	1.23417	0.617083	+	0.786898i	$0.288314\pi$
$132$	31.6978	2.75894
$133$	15.3609	1.33196
$134$	3.61093	0.311937
$135$	0	0
$136$	0	0
$137$	−12.0396	−1.02861	−0.514305	−	0.857607i	$-0.671950\pi$
$137$	−12.0396	−1.02861	−0.514305	+	0.857607i	$0.671950\pi$
$138$	23.5439	2.00419
$139$	−12.7907	−1.08489	−0.542447	−	0.840090i	$-0.682502\pi$
$139$	−12.7907	−1.08489	−0.542447	+	0.840090i	$0.682502\pi$
$140$	0	0
$141$	−8.76448	−0.738103
$142$	−6.03709	−0.506622
$143$	6.87173	0.574643
$144$	18.3748	1.53123
$145$	0	0
$146$	−19.8130	−1.63974
$147$	−3.04773	−0.251372
$148$	13.6879	1.12514
$149$	5.52099	0.452297	0.226149	−	0.974093i	$-0.427386\pi$
$149$	5.52099	0.452297	0.226149	+	0.974093i	$0.427386\pi$
$150$	0	0
$151$	−20.1224	−1.63754	−0.818769	−	0.574123i	$-0.805343\pi$
$151$	−20.1224	−1.63754	−0.818769	+	0.574123i	$0.805343\pi$
$152$	−26.5540	−2.15382
$153$	0	0
$154$	−15.7657	−1.27044
$155$	0	0
$156$	30.4871	2.44092
$157$	−6.77751	−0.540904	−0.270452	−	0.962733i	$-0.587173\pi$
$157$	−6.77751	−0.540904	−0.270452	+	0.962733i	$0.587173\pi$
$158$	10.7589	0.855936
$159$	−0.522418	−0.0414305
$160$	0	0
$161$	−7.64961	−0.602874
$162$	43.1734	3.39202
$163$	−15.3503	−1.20233	−0.601165	−	0.799125i	$-0.705296\pi$
$163$	−15.3503	−1.20233	−0.601165	+	0.799125i	$0.705296\pi$
$164$	31.2629	2.44122
$165$	0	0
$166$	−29.1213	−2.26025
$167$	25.4830	1.97193	0.985965	−	0.166950i	$-0.0533918\pi$
$167$	25.4830	1.97193	0.985965	+	0.166950i	$0.0533918\pi$
$168$	−32.8175	−2.53193
$169$	−6.39074	−0.491596
$170$	0	0
$171$	−43.1951	−3.30321
$172$	48.0970	3.66736
$173$	−4.03225	−0.306566	−0.153283	−	0.988182i	$-0.548985\pi$
$173$	−4.03225	−0.306566	−0.153283	+	0.988182i	$0.548985\pi$
$174$	−5.37193	−0.407245
$175$	0	0
$176$	7.11172	0.536066
$177$	−38.7042	−2.90918
$178$	2.80286	0.210083
$179$	−21.2384	−1.58743	−0.793717	−	0.608287i	$-0.791857\pi$
$179$	−21.2384	−1.58743	−0.793717	+	0.608287i	$0.791857\pi$
$180$	0	0
$181$	−11.0451	−0.820973	−0.410486	−	0.911867i	$-0.634641\pi$
$181$	−11.0451	−0.820973	−0.410486	+	0.911867i	$0.634641\pi$
$182$	−15.1635	−1.12399
$183$	−2.14298	−0.158414
$184$	13.2237	0.974867
$185$	0	0
$186$	30.1804	2.21294
$187$	0	0
$188$	−10.4920	−0.765210
$189$	−30.1942	−2.19631
$190$	0	0
$191$	−11.9621	−0.865544	−0.432772	−	0.901503i	$-0.642464\pi$
$191$	−11.9621	−0.865544	−0.432772	+	0.901503i	$0.642464\pi$
$192$	−32.6314	−2.35497
$193$	−0.567470	−0.0408474	−0.0204237	−	0.999791i	$-0.506502\pi$
$193$	−0.567470	−0.0408474	−0.0204237	+	0.999791i	$0.506502\pi$
$194$	−7.50778	−0.539027
$195$	0	0
$196$	−3.64846	−0.260604
$197$	−8.93316	−0.636461	−0.318231	−	0.948013i	$-0.603089\pi$
$197$	−8.93316	−0.636461	−0.318231	+	0.948013i	$0.603089\pi$
$198$	44.3335	3.15065
$199$	16.6697	1.18168	0.590840	−	0.806789i	$-0.298796\pi$
$199$	16.6697	1.18168	0.590840	+	0.806789i	$0.298796\pi$
$200$	0	0
$201$	4.73225	0.333787
$202$	2.31356	0.162782
$203$	1.74539	0.122502
$204$	0	0
$205$	0	0
$206$	31.6634	2.20610
$207$	21.5109	1.49511
$208$	6.84007	0.474274
$209$	−16.7181	−1.15642
$210$	0	0
$211$	−19.6063	−1.34975	−0.674876	−	0.737931i	$-0.735803\pi$
$211$	−19.6063	−1.34975	−0.674876	+	0.737931i	$0.735803\pi$
$212$	−0.625391	−0.0429520
$213$	−7.91182	−0.542109
$214$	−2.88570	−0.197262
$215$	0	0
$216$	52.1962	3.55150
$217$	−9.80588	−0.665666
$218$	−45.2451	−3.06438
$219$	−25.9657	−1.75460
$220$	0	0
$221$	0	0
$222$	27.4604	1.84302
$223$	−17.7907	−1.19135	−0.595677	−	0.803224i	$-0.703116\pi$
$223$	−17.7907	−1.19135	−0.595677	+	0.803224i	$0.703116\pi$
$224$	5.16061	0.344808
$225$	0	0
$226$	26.6864	1.77515
$227$	−2.74184	−0.181982	−0.0909911	−	0.995852i	$-0.529003\pi$
$227$	−2.74184	−0.181982	−0.0909911	+	0.995852i	$0.529003\pi$
$228$	−74.1713	−4.91212
$229$	28.4081	1.87726	0.938630	−	0.344925i	$-0.112096\pi$
$229$	28.4081	1.87726	0.938630	+	0.344925i	$0.112096\pi$
$230$	0	0
$231$	−20.6615	−1.35943
$232$	−3.01722	−0.198090
$233$	14.7458	0.966032	0.483016	−	0.875611i	$-0.339541\pi$
$233$	14.7458	0.966032	0.483016	+	0.875611i	$0.339541\pi$
$234$	42.6401	2.78747
$235$	0	0
$236$	−46.3330	−3.01602
$237$	14.1000	0.915892
$238$	0	0
$239$	8.93034	0.577656	0.288828	−	0.957381i	$-0.406734\pi$
$239$	8.93034	0.577656	0.288828	+	0.957381i	$0.406734\pi$
$240$	0	0
$241$	25.4005	1.63619	0.818095	−	0.575083i	$-0.195030\pi$
$241$	25.4005	1.63619	0.818095	+	0.575083i	$0.195030\pi$
$242$	−9.25913	−0.595199
$243$	19.6972	1.26358
$244$	−2.56538	−0.164231
$245$	0	0
$246$	62.7192	3.99883
$247$	−16.0795	−1.02312
$248$	16.9512	1.07640
$249$	−38.1645	−2.41858
$250$	0	0
$251$	−0.459279	−0.0289894	−0.0144947	−	0.999895i	$-0.504614\pi$
$251$	−0.459279	−0.0289894	−0.0144947	+	0.999895i	$0.504614\pi$
$252$	−63.9062	−4.02571
$253$	8.32550	0.523420
$254$	−3.91342	−0.245550
$255$	0	0
$256$	−28.9704	−1.81065
$257$	−18.6397	−1.16271	−0.581357	−	0.813648i	$-0.697478\pi$
$257$	−18.6397	−1.16271	−0.581357	+	0.813648i	$0.697478\pi$
$258$	96.4916	6.00730
$259$	−8.92213	−0.554394
$260$	0	0
$261$	−4.90807	−0.303802
$262$	33.9245	2.09586
$263$	16.5539	1.02076	0.510379	−	0.859950i	$-0.329505\pi$
$263$	16.5539	1.02076	0.510379	+	0.859950i	$0.329505\pi$
$264$	35.7172	2.19824
$265$	0	0
$266$	36.8910	2.26193
$267$	3.67325	0.224799
$268$	5.66501	0.346046
$269$	7.70877	0.470012	0.235006	−	0.971994i	$-0.424489\pi$
$269$	7.70877	0.470012	0.235006	+	0.971994i	$0.424489\pi$
$270$	0	0
$271$	−21.0971	−1.28156	−0.640780	−	0.767725i	$-0.721389\pi$
$271$	−21.0971	−1.28156	−0.640780	+	0.767725i	$0.721389\pi$
$272$	0	0
$273$	−19.8723	−1.20273
$274$	−28.9145	−1.74679
$275$	0	0
$276$	36.9368	2.22334
$277$	−6.30787	−0.379003	−0.189501	−	0.981880i	$-0.560687\pi$
$277$	−6.30787	−0.379003	−0.189501	+	0.981880i	$0.560687\pi$
$278$	−30.7184	−1.84237
$279$	27.5744	1.65083
$280$	0	0
$281$	−23.6264	−1.40943	−0.704716	−	0.709490i	$-0.748925\pi$
$281$	−23.6264	−1.40943	−0.704716	+	0.709490i	$0.748925\pi$
$282$	−21.0490	−1.25345
$283$	19.3219	1.14857	0.574283	−	0.818657i	$-0.305281\pi$
$283$	19.3219	1.14857	0.574283	+	0.818657i	$0.305281\pi$
$284$	−9.47130	−0.562018
$285$	0	0
$286$	16.5033	0.975861
$287$	−20.3780	−1.20288
$288$	−14.5118	−0.855113
$289$	0	0
$290$	0	0
$291$	−9.83920	−0.576784
$292$	−31.0837	−1.81903
$293$	11.1159	0.649397	0.324698	−	0.945818i	$-0.394737\pi$
$293$	11.1159	0.649397	0.324698	+	0.945818i	$0.394737\pi$
$294$	−7.31949	−0.426881
$295$	0	0
$296$	15.4235	0.896474
$297$	32.8621	1.90685
$298$	13.2593	0.768093
$299$	8.00750	0.463086
$300$	0	0
$301$	−31.3509	−1.80704
$302$	−48.3264	−2.78087
$303$	3.03200	0.174184
$304$	−16.6411	−0.954431
$305$	0	0
$306$	0	0
$307$	8.08367	0.461359	0.230680	−	0.973030i	$-0.425905\pi$
$307$	8.08367	0.461359	0.230680	+	0.973030i	$0.425905\pi$
$308$	−24.7340	−1.40935
$309$	41.4960	2.36063
$310$	0	0
$311$	−13.5612	−0.768988	−0.384494	−	0.923128i	$-0.625624\pi$
$311$	−13.5612	−0.768988	−0.384494	+	0.923128i	$0.625624\pi$
$312$	34.3529	1.94485
$313$	9.12199	0.515605	0.257803	−	0.966198i	$-0.417002\pi$
$313$	9.12199	0.515605	0.257803	+	0.966198i	$0.417002\pi$
$314$	−16.2770	−0.918565
$315$	0	0
$316$	16.8792	0.949528
$317$	−33.7435	−1.89522	−0.947611	−	0.319426i	$-0.896510\pi$
$317$	−33.7435	−1.89522	−0.947611	+	0.319426i	$0.896510\pi$
$318$	−1.25465	−0.0703573
$319$	−1.89960	−0.106357
$320$	0	0
$321$	−3.78181	−0.211080
$322$	−18.3715	−1.02380
$323$	0	0
$324$	67.7326	3.76292
$325$	0	0
$326$	−36.8656	−2.04180
$327$	−59.2953	−3.27904
$328$	35.2271	1.94509
$329$	6.83899	0.377046
$330$	0	0
$331$	−21.2983	−1.17066	−0.585329	−	0.810796i	$-0.699035\pi$
$331$	−21.2983	−1.17066	−0.585329	+	0.810796i	$0.699035\pi$
$332$	−45.6870	−2.50740
$333$	25.0892	1.37488
$334$	61.2004	3.34874
$335$	0	0
$336$	−20.5663	−1.12198
$337$	22.4073	1.22061	0.610303	−	0.792168i	$-0.291048\pi$
$337$	22.4073	1.22061	0.610303	+	0.792168i	$0.291048\pi$
$338$	−15.3481	−0.834829
$339$	34.9734	1.89949
$340$	0	0
$341$	10.6723	0.577937
$342$	−103.738	−5.60953
$343$	19.5698	1.05667
$344$	54.1958	2.92204
$345$	0	0
$346$	−9.68393	−0.520611
$347$	18.0764	0.970393	0.485197	−	0.874405i	$-0.338748\pi$
$347$	18.0764	0.970393	0.485197	+	0.874405i	$0.338748\pi$
$348$	−8.42776	−0.451775
$349$	−9.00587	−0.482073	−0.241037	−	0.970516i	$-0.577487\pi$
$349$	−9.00587	−0.482073	−0.241037	+	0.970516i	$0.577487\pi$
$350$	0	0
$351$	31.6069	1.68705
$352$	−5.61658	−0.299365
$353$	27.4982	1.46358	0.731791	−	0.681530i	$-0.238685\pi$
$353$	27.4982	1.46358	0.731791	+	0.681530i	$0.238685\pi$
$354$	−92.9527	−4.94038
$355$	0	0
$356$	4.39727	0.233055
$357$	0	0
$358$	−51.0066	−2.69578
$359$	24.2551	1.28013	0.640066	−	0.768320i	$-0.278907\pi$
$359$	24.2551	1.28013	0.640066	+	0.768320i	$0.278907\pi$
$360$	0	0
$361$	20.1195	1.05892
$362$	−26.5261	−1.39418
$363$	−12.1344	−0.636891
$364$	−23.7893	−1.24690
$365$	0	0
$366$	−5.14663	−0.269019
$367$	25.1930	1.31506	0.657532	−	0.753427i	$-0.271601\pi$
$367$	25.1930	1.31506	0.657532	+	0.753427i	$0.271601\pi$
$368$	8.28715	0.431997
$369$	57.3034	2.98310
$370$	0	0
$371$	0.407647	0.0211640
$372$	47.3486	2.45491
$373$	12.3570	0.639823	0.319911	−	0.947447i	$-0.396347\pi$
$373$	12.3570	0.639823	0.319911	+	0.947447i	$0.396347\pi$
$374$	0	0
$375$	0	0
$376$	−11.8224	−0.609696
$377$	−1.82705	−0.0940976
$378$	−72.5151	−3.72977
$379$	−1.73645	−0.0891957	−0.0445978	−	0.999005i	$-0.514201\pi$
$379$	−1.73645	−0.0891957	−0.0445978	+	0.999005i	$0.514201\pi$
$380$	0	0
$381$	−5.12867	−0.262750
$382$	−28.7283	−1.46987
$383$	−17.5969	−0.899158	−0.449579	−	0.893241i	$-0.648426\pi$
$383$	−17.5969	−0.899158	−0.449579	+	0.893241i	$0.648426\pi$
$384$	−65.1412	−3.32422
$385$	0	0
$386$	−1.36285	−0.0693671
$387$	88.1596	4.48140
$388$	−11.7786	−0.597967
$389$	−11.0817	−0.561866	−0.280933	−	0.959727i	$-0.590644\pi$
$389$	−11.0817	−0.561866	−0.280933	+	0.959727i	$0.590644\pi$
$390$	0	0
$391$	0	0
$392$	−4.11109	−0.207641
$393$	44.4593	2.24267
$394$	−21.4541	−1.08084
$395$	0	0
$396$	69.5527	3.49515
$397$	8.03226	0.403128	0.201564	−	0.979475i	$-0.435398\pi$
$397$	8.03226	0.403128	0.201564	+	0.979475i	$0.435398\pi$
$398$	40.0342	2.00673
$399$	48.3469	2.42037
$400$	0	0
$401$	−10.9609	−0.547360	−0.273680	−	0.961821i	$-0.588241\pi$
$401$	−10.9609	−0.547360	−0.273680	+	0.961821i	$0.588241\pi$
$402$	11.3651	0.566838
$403$	10.2646	0.511319
$404$	3.62963	0.180581
$405$	0	0
$406$	4.19176	0.208034
$407$	9.71046	0.481330
$408$	0	0
$409$	8.43948	0.417306	0.208653	−	0.977990i	$-0.433092\pi$
$409$	8.43948	0.417306	0.208653	+	0.977990i	$0.433092\pi$
$410$	0	0
$411$	−37.8935	−1.86915
$412$	49.6752	2.44732
$413$	30.2011	1.48610
$414$	51.6610	2.53900
$415$	0	0
$416$	−5.40205	−0.264857
$417$	−40.2576	−1.97142
$418$	−40.1505	−1.96383
$419$	−14.4828	−0.707533	−0.353767	−	0.935334i	$-0.615099\pi$
$419$	−14.4828	−0.707533	−0.353767	+	0.935334i	$0.615099\pi$
$420$	0	0
$421$	1.51690	0.0739292	0.0369646	−	0.999317i	$-0.488231\pi$
$421$	1.51690	0.0739292	0.0369646	+	0.999317i	$0.488231\pi$
$422$	−47.0869	−2.29215
$423$	−19.2314	−0.935063
$424$	−0.704692	−0.0342229
$425$	0	0
$426$	−19.0012	−0.920611
$427$	1.67218	0.0809226
$428$	−4.52723	−0.218832
$429$	21.6282	1.04422
$430$	0	0
$431$	−19.7875	−0.953129	−0.476564	−	0.879140i	$-0.658118\pi$
$431$	−19.7875	−0.953129	−0.476564	+	0.879140i	$0.658118\pi$
$432$	32.7107	1.57379
$433$	−9.49722	−0.456407	−0.228204	−	0.973613i	$-0.573285\pi$
$433$	−9.49722	−0.456407	−0.228204	+	0.973613i	$0.573285\pi$
$434$	−23.5500	−1.13044
$435$	0	0
$436$	−70.9828	−3.39946
$437$	−19.4813	−0.931916
$438$	−62.3597	−2.97966
$439$	20.0395	0.956433	0.478217	−	0.878242i	$-0.341283\pi$
$439$	20.0395	0.956433	0.478217	+	0.878242i	$0.341283\pi$
$440$	0	0
$441$	−6.68745	−0.318450
$442$	0	0
$443$	13.1946	0.626894	0.313447	−	0.949606i	$-0.398516\pi$
$443$	13.1946	0.626894	0.313447	+	0.949606i	$0.398516\pi$
$444$	43.0813	2.04455
$445$	0	0
$446$	−42.7265	−2.02316
$447$	17.3768	0.821895
$448$	25.4626	1.20299
$449$	−16.1247	−0.760973	−0.380486	−	0.924786i	$-0.624243\pi$
$449$	−16.1247	−0.760973	−0.380486	+	0.924786i	$0.624243\pi$
$450$	0	0
$451$	22.1785	1.04435
$452$	41.8669	1.96925
$453$	−63.3334	−2.97566
$454$	−6.58486	−0.309043
$455$	0	0
$456$	−83.5764	−3.91382
$457$	8.78267	0.410836	0.205418	−	0.978674i	$-0.434145\pi$
$457$	8.78267	0.410836	0.205418	+	0.978674i	$0.434145\pi$
$458$	68.2255	3.18797
$459$	0	0
$460$	0	0
$461$	18.3746	0.855789	0.427895	−	0.903829i	$-0.359255\pi$
$461$	18.3746	0.855789	0.427895	+	0.903829i	$0.359255\pi$
$462$	−49.6211	−2.30858
$463$	29.1662	1.35547	0.677735	−	0.735306i	$-0.262962\pi$
$463$	29.1662	1.35547	0.677735	+	0.735306i	$0.262962\pi$
$464$	−1.89085	−0.0877806
$465$	0	0
$466$	35.4139	1.64052
$467$	8.21883	0.380322	0.190161	−	0.981753i	$-0.439099\pi$
$467$	8.21883	0.380322	0.190161	+	0.981753i	$0.439099\pi$
$468$	66.8960	3.09227
$469$	−3.69261	−0.170509
$470$	0	0
$471$	−21.3316	−0.982908
$472$	−52.2082	−2.40307
$473$	34.1210	1.56889
$474$	33.8628	1.55537
$475$	0	0
$476$	0	0
$477$	−1.14631	−0.0524861
$478$	21.4473	0.980977
$479$	−36.3883	−1.66262	−0.831312	−	0.555807i	$-0.812410\pi$
$479$	−36.3883	−1.66262	−0.831312	+	0.555807i	$0.812410\pi$
$480$	0	0
$481$	9.33955	0.425847
$482$	61.0024	2.77858
$483$	−24.0765	−1.09552
$484$	−14.5262	−0.660281
$485$	0	0
$486$	47.3052	2.14581
$487$	33.0821	1.49909	0.749547	−	0.661951i	$-0.230271\pi$
$487$	33.0821	1.49909	0.749547	+	0.661951i	$0.230271\pi$
$488$	−2.89067	−0.130855
$489$	−48.3137	−2.18482
$490$	0	0
$491$	12.1162	0.546797	0.273398	−	0.961901i	$-0.411852\pi$
$491$	12.1162	0.546797	0.273398	+	0.961901i	$0.411852\pi$
$492$	98.3970	4.43608
$493$	0	0
$494$	−38.6169	−1.73746
$495$	0	0
$496$	10.6231	0.476992
$497$	6.17365	0.276926
$498$	−91.6567	−4.10723
$499$	4.93983	0.221137	0.110568	−	0.993869i	$-0.464733\pi$
$499$	4.93983	0.221137	0.110568	+	0.993869i	$0.464733\pi$
$500$	0	0
$501$	80.2053	3.58331
$502$	−1.10301	−0.0492299
$503$	22.7414	1.01399	0.506995	−	0.861949i	$-0.330756\pi$
$503$	22.7414	1.01399	0.506995	+	0.861949i	$0.330756\pi$
$504$	−72.0096	−3.20756
$505$	0	0
$506$	19.9947	0.888873
$507$	−20.1143	−0.893306
$508$	−6.13957	−0.272399
$509$	−28.2780	−1.25340	−0.626701	−	0.779260i	$-0.715595\pi$
$509$	−28.2780	−1.25340	−0.626701	+	0.779260i	$0.715595\pi$
$510$	0	0
$511$	20.2612	0.896303
$512$	−28.1824	−1.24550
$513$	−76.8957	−3.39503
$514$	−44.7656	−1.97452
$515$	0	0
$516$	151.381	6.66417
$517$	−7.44326	−0.327354
$518$	−21.4276	−0.941474
$519$	−12.6911	−0.557079
$520$	0	0
$521$	15.0564	0.659632	0.329816	−	0.944045i	$-0.393013\pi$
$521$	15.0564	0.659632	0.329816	+	0.944045i	$0.393013\pi$
$522$	−11.7873	−0.515917
$523$	−15.3033	−0.669165	−0.334583	−	0.942366i	$-0.608595\pi$
$523$	−15.3033	−0.669165	−0.334583	+	0.942366i	$0.608595\pi$
$524$	53.2225	2.32504
$525$	0	0
$526$	39.7562	1.73345
$527$	0	0
$528$	22.3835	0.974116
$529$	−13.2984	−0.578193
$530$	0	0
$531$	−84.9263	−3.68549
$532$	57.8764	2.50926
$533$	21.3314	0.923965
$534$	8.82175	0.381755
$535$	0	0
$536$	6.38335	0.275719
$537$	−66.8460	−2.88462
$538$	18.5136	0.798176
$539$	−2.58829	−0.111486
$540$	0	0
$541$	5.89759	0.253557	0.126779	−	0.991931i	$-0.459536\pi$
$541$	5.89759	0.253557	0.126779	+	0.991931i	$0.459536\pi$
$542$	−50.6673	−2.17635
$543$	−34.7633	−1.49184
$544$	0	0
$545$	0	0
$546$	−47.7257	−2.04247
$547$	−13.6997	−0.585758	−0.292879	−	0.956149i	$-0.594613\pi$
$547$	−13.6997	−0.585758	−0.292879	+	0.956149i	$0.594613\pi$
$548$	−45.3625	−1.93779
$549$	−4.70222	−0.200686
$550$	0	0
$551$	4.44498	0.189363
$552$	41.6205	1.77149
$553$	−11.0023	−0.467866
$554$	−15.1491	−0.643624
$555$	0	0
$556$	−48.1926	−2.04382
$557$	−26.3831	−1.11789	−0.558943	−	0.829206i	$-0.688793\pi$
$557$	−26.3831	−1.11789	−0.558943	+	0.829206i	$0.688793\pi$
$558$	66.2232	2.80345
$559$	32.8177	1.38804
$560$	0	0
$561$	0	0
$562$	−56.7416	−2.39350
$563$	22.3909	0.943666	0.471833	−	0.881688i	$-0.343593\pi$
$563$	22.3909	0.943666	0.471833	+	0.881688i	$0.343593\pi$
$564$	−33.0227	−1.39051
$565$	0	0
$566$	46.4038	1.95050
$567$	−44.1500	−1.85412
$568$	−10.6723	−0.447799
$569$	1.33840	0.0561085	0.0280542	−	0.999606i	$-0.491069\pi$
$569$	1.33840	0.0561085	0.0280542	+	0.999606i	$0.491069\pi$
$570$	0	0
$571$	29.2226	1.22293	0.611464	−	0.791272i	$-0.290581\pi$
$571$	29.2226	1.22293	0.611464	+	0.791272i	$0.290581\pi$
$572$	25.8912	1.08257
$573$	−37.6495	−1.57283
$574$	−48.9402	−2.04273
$575$	0	0
$576$	−71.6013	−2.98339
$577$	−14.0956	−0.586809	−0.293405	−	0.955988i	$-0.594788\pi$
$577$	−14.0956	−0.586809	−0.293405	+	0.955988i	$0.594788\pi$
$578$	0	0
$579$	−1.78606	−0.0742261
$580$	0	0
$581$	29.7800	1.23548
$582$	−23.6300	−0.979497
$583$	−0.443665	−0.0183747
$584$	−35.0252	−1.44935
$585$	0	0
$586$	26.6961	1.10281
$587$	2.14440	0.0885089	0.0442545	−	0.999020i	$-0.485909\pi$
$587$	2.14440	0.0885089	0.0442545	+	0.999020i	$0.485909\pi$
$588$	−11.4832	−0.473558
$589$	−24.9727	−1.02898
$590$	0	0
$591$	−28.1163	−1.15655
$592$	9.66572	0.397259
$593$	−20.0106	−0.821736	−0.410868	−	0.911695i	$-0.634774\pi$
$593$	−20.0106	−0.821736	−0.410868	+	0.911695i	$0.634774\pi$
$594$	78.9223	3.23822
$595$	0	0
$596$	20.8019	0.852079
$597$	52.4662	2.14730
$598$	19.2310	0.786413
$599$	18.2512	0.745724	0.372862	−	0.927887i	$-0.378377\pi$
$599$	18.2512	0.745724	0.372862	+	0.927887i	$0.378377\pi$
$600$	0	0
$601$	−11.2285	−0.458020	−0.229010	−	0.973424i	$-0.573549\pi$
$601$	−11.2285	−0.458020	−0.229010	+	0.973424i	$0.573549\pi$
$602$	−75.2931	−3.06872
$603$	10.3837	0.422857
$604$	−75.8169	−3.08495
$605$	0	0
$606$	7.28172	0.295800
$607$	25.4461	1.03282	0.516412	−	0.856340i	$-0.327267\pi$
$607$	25.4461	1.03282	0.516412	+	0.856340i	$0.327267\pi$
$608$	13.1425	0.533000
$609$	5.49345	0.222606
$610$	0	0
$611$	−7.15895	−0.289620
$612$	0	0
$613$	38.4941	1.55476	0.777380	−	0.629031i	$-0.216548\pi$
$613$	38.4941	1.55476	0.777380	+	0.629031i	$0.216548\pi$
$614$	19.4139	0.783482
$615$	0	0
$616$	−27.8704	−1.12293
$617$	−23.0835	−0.929305	−0.464653	−	0.885493i	$-0.653821\pi$
$617$	−23.0835	−0.929305	−0.464653	+	0.885493i	$0.653821\pi$
$618$	99.6578	4.00882
$619$	7.27540	0.292423	0.146211	−	0.989253i	$-0.453292\pi$
$619$	7.27540	0.292423	0.146211	+	0.989253i	$0.453292\pi$
$620$	0	0
$621$	38.2936	1.53667
$622$	−32.5690	−1.30590
$623$	−2.86626	−0.114834
$624$	21.5285	0.861830
$625$	0	0
$626$	21.9076	0.875602
$627$	−52.6187	−2.10139
$628$	−25.5362	−1.01901
$629$	0	0
$630$	0	0
$631$	33.2465	1.32352	0.661761	−	0.749715i	$-0.269809\pi$
$631$	33.2465	1.32352	0.661761	+	0.749715i	$0.269809\pi$
$632$	19.0195	0.756555
$633$	−61.7090	−2.45271
$634$	−81.0390	−3.21847
$635$	0	0
$636$	−1.96836	−0.0780505
$637$	−2.48943	−0.0986347
$638$	−4.56213	−0.180616
$639$	−17.3605	−0.686769
$640$	0	0
$641$	−21.4007	−0.845276	−0.422638	−	0.906299i	$-0.638896\pi$
$641$	−21.4007	−0.845276	−0.422638	+	0.906299i	$0.638896\pi$
$642$	−9.08247	−0.358457
$643$	−12.3392	−0.486610	−0.243305	−	0.969950i	$-0.578232\pi$
$643$	−12.3392	−0.486610	−0.243305	+	0.969950i	$0.578232\pi$
$644$	−28.8221	−1.13575
$645$	0	0
$646$	0	0
$647$	2.48180	0.0975696	0.0487848	−	0.998809i	$-0.484465\pi$
$647$	2.48180	0.0975696	0.0487848	+	0.998809i	$0.484465\pi$
$648$	76.3212	2.99818
$649$	−32.8696	−1.29024
$650$	0	0
$651$	−30.8631	−1.20962
$652$	−57.8367	−2.26506
$653$	−24.2220	−0.947882	−0.473941	−	0.880557i	$-0.657169\pi$
$653$	−24.2220	−0.947882	−0.473941	+	0.880557i	$0.657169\pi$
$654$	−142.405	−5.56847
$655$	0	0
$656$	22.0763	0.861936
$657$	−56.9750	−2.22281
$658$	16.4247	0.640300
$659$	−0.298916	−0.0116441	−0.00582205	−	0.999983i	$-0.501853\pi$
$659$	−0.298916	−0.0116441	−0.00582205	+	0.999983i	$0.501853\pi$
$660$	0	0
$661$	45.7248	1.77849	0.889244	−	0.457434i	$-0.151231\pi$
$661$	45.7248	1.77849	0.889244	+	0.457434i	$0.151231\pi$
$662$	−51.1504	−1.98802
$663$	0	0
$664$	−51.4802	−1.99782
$665$	0	0
$666$	60.2549	2.33483
$667$	−2.21357	−0.0857099
$668$	96.0143	3.71491
$669$	−55.9946	−2.16488
$670$	0	0
$671$	−1.81993	−0.0702577
$672$	16.2425	0.626570
$673$	−24.6536	−0.950325	−0.475162	−	0.879898i	$-0.657611\pi$
$673$	−24.6536	−0.950325	−0.475162	+	0.879898i	$0.657611\pi$
$674$	53.8139	2.07284
$675$	0	0
$676$	−24.0789	−0.926113
$677$	34.2463	1.31619	0.658097	−	0.752933i	$-0.271362\pi$
$677$	34.2463	1.31619	0.658097	+	0.752933i	$0.271362\pi$
$678$	83.9929	3.22573
$679$	7.67760	0.294639
$680$	0	0
$681$	−8.62969	−0.330690
$682$	25.6308	0.981454
$683$	−46.3391	−1.77312	−0.886558	−	0.462618i	$-0.846910\pi$
$683$	−46.3391	−1.77312	−0.886558	+	0.462618i	$0.846910\pi$
$684$	−162.750	−6.22290
$685$	0	0
$686$	46.9992	1.79444
$687$	89.4119	3.41128
$688$	33.9638	1.29486
$689$	−0.426719	−0.0162567
$690$	0	0
$691$	−25.0441	−0.952724	−0.476362	−	0.879249i	$-0.658045\pi$
$691$	−25.0441	−0.952724	−0.476362	+	0.879249i	$0.658045\pi$
$692$	−15.1926	−0.577537
$693$	−45.3364	−1.72219
$694$	43.4127	1.64792
$695$	0	0
$696$	−9.49642	−0.359961
$697$	0	0
$698$	−21.6287	−0.818658
$699$	46.4112	1.75543
$700$	0	0
$701$	−45.8247	−1.73078	−0.865388	−	0.501102i	$-0.832928\pi$
$701$	−45.8247	−1.73078	−0.865388	+	0.501102i	$0.832928\pi$
$702$	75.9077	2.86495
$703$	−22.7220	−0.856977
$704$	−27.7123	−1.04445
$705$	0	0
$706$	66.0402	2.48546
$707$	−2.36589	−0.0889786
$708$	−145.829	−5.48059
$709$	−19.9724	−0.750078	−0.375039	−	0.927009i	$-0.622371\pi$
$709$	−19.9724	−0.750078	−0.375039	+	0.927009i	$0.622371\pi$
$710$	0	0
$711$	30.9388	1.16029
$712$	4.95486	0.185691
$713$	12.4362	0.465740
$714$	0	0
$715$	0	0
$716$	−80.0218	−2.99055
$717$	28.1074	1.04969
$718$	58.2514	2.17392
$719$	33.6934	1.25655	0.628277	−	0.777990i	$-0.283761\pi$
$719$	33.6934	1.25655	0.628277	+	0.777990i	$0.283761\pi$
$720$	0	0
$721$	−32.3797	−1.20588
$722$	48.3195	1.79827
$723$	79.9457	2.97321
$724$	−41.6154	−1.54662
$725$	0	0
$726$	−29.1423	−1.08157
$727$	6.28209	0.232990	0.116495	−	0.993191i	$-0.462834\pi$
$727$	6.28209	0.232990	0.116495	+	0.993191i	$0.462834\pi$
$728$	−26.8058	−0.993489
$729$	8.06486	0.298699
$730$	0	0
$731$	0	0
$732$	−8.07429	−0.298434
$733$	−10.1710	−0.375675	−0.187837	−	0.982200i	$-0.560148\pi$
$733$	−10.1710	−0.375675	−0.187837	+	0.982200i	$0.560148\pi$
$734$	60.5040	2.23324
$735$	0	0
$736$	−6.54489	−0.241248
$737$	4.01888	0.148037
$738$	137.621	5.06590
$739$	−14.2869	−0.525552	−0.262776	−	0.964857i	$-0.584638\pi$
$739$	−14.2869	−0.525552	−0.262776	+	0.964857i	$0.584638\pi$
$740$	0	0
$741$	−50.6088	−1.85916
$742$	0.979014	0.0359407
$743$	21.9933	0.806855	0.403428	−	0.915012i	$-0.367819\pi$
$743$	21.9933	0.806855	0.403428	+	0.915012i	$0.367819\pi$
$744$	53.3525	1.95600
$745$	0	0
$746$	29.6769	1.08655
$747$	−83.7422	−3.06397
$748$	0	0
$749$	2.95097	0.107826
$750$	0	0
$751$	11.9963	0.437751	0.218876	−	0.975753i	$-0.429761\pi$
$751$	11.9963	0.437751	0.218876	+	0.975753i	$0.429761\pi$
$752$	−7.40897	−0.270177
$753$	−1.44554	−0.0526784
$754$	−4.38787	−0.159797
$755$	0	0
$756$	−113.765	−4.13761
$757$	41.6081	1.51227	0.756135	−	0.654415i	$-0.227085\pi$
$757$	41.6081	1.51227	0.756135	+	0.654415i	$0.227085\pi$
$758$	−4.17031	−0.151472
$759$	26.2038	0.951136
$760$	0	0
$761$	50.6689	1.83675	0.918374	−	0.395715i	$-0.129503\pi$
$761$	50.6689	1.83675	0.918374	+	0.395715i	$0.129503\pi$
$762$	−12.3171	−0.446203
$763$	46.2685	1.67503
$764$	−45.0705	−1.63059
$765$	0	0
$766$	−42.2610	−1.52695
$767$	−31.6141	−1.14152
$768$	−91.1817	−3.29024
$769$	36.4245	1.31350	0.656750	−	0.754108i	$-0.271931\pi$
$769$	36.4245	1.31350	0.656750	+	0.754108i	$0.271931\pi$
$770$	0	0
$771$	−58.6668	−2.11283
$772$	−2.13810	−0.0769521
$773$	−40.5949	−1.46010	−0.730049	−	0.683395i	$-0.760503\pi$
$773$	−40.5949	−1.46010	−0.730049	+	0.683395i	$0.760503\pi$
$774$	211.726	7.61033
$775$	0	0
$776$	−13.2721	−0.476442
$777$	−28.0816	−1.00742
$778$	−26.6141	−0.954163
$779$	−51.8967	−1.85939
$780$	0	0
$781$	−6.71913	−0.240430
$782$	0	0
$783$	−8.73732	−0.312246
$784$	−2.57637	−0.0920131
$785$	0	0
$786$	106.774	3.80851
$787$	9.86307	0.351580	0.175790	−	0.984428i	$-0.443752\pi$
$787$	9.86307	0.351580	0.175790	+	0.984428i	$0.443752\pi$
$788$	−33.6582	−1.19902
$789$	52.1019	1.85488
$790$	0	0
$791$	−27.2900	−0.970321
$792$	78.3721	2.78483
$793$	−1.75042	−0.0621591
$794$	19.2904	0.684592
$795$	0	0
$796$	62.8076	2.22616
$797$	39.4185	1.39628	0.698138	−	0.715964i	$-0.254012\pi$
$797$	39.4185	1.39628	0.698138	+	0.715964i	$0.254012\pi$
$798$	116.111	4.11028
$799$	0	0
$800$	0	0
$801$	8.06000	0.284786
$802$	−26.3239	−0.929528
$803$	−22.0514	−0.778177
$804$	17.8301	0.628819
$805$	0	0
$806$	24.6518	0.868322
$807$	24.2627	0.854086
$808$	4.08988	0.143881
$809$	−9.42731	−0.331447	−0.165723	−	0.986172i	$-0.552996\pi$
$809$	−9.42731	−0.331447	−0.165723	+	0.986172i	$0.552996\pi$
$810$	0	0
$811$	22.2187	0.780203	0.390101	−	0.920772i	$-0.372440\pi$
$811$	22.2187	0.780203	0.390101	+	0.920772i	$0.372440\pi$
$812$	6.57624	0.230781
$813$	−66.4013	−2.32880
$814$	23.3208	0.817395
$815$	0	0
$816$	0	0
$817$	−79.8415	−2.79330
$818$	20.2684	0.708670
$819$	−43.6047	−1.52367
$820$	0	0
$821$	−14.1242	−0.492938	−0.246469	−	0.969151i	$-0.579270\pi$
$821$	−14.1242	−0.492938	−0.246469	+	0.969151i	$0.579270\pi$
$822$	−91.0058	−3.17419
$823$	−47.6084	−1.65953	−0.829763	−	0.558116i	$-0.811524\pi$
$823$	−47.6084	−1.65953	−0.829763	+	0.558116i	$0.811524\pi$
$824$	55.9741	1.94995
$825$	0	0
$826$	72.5317	2.52370
$827$	4.85003	0.168652	0.0843261	−	0.996438i	$-0.473126\pi$
$827$	4.85003	0.168652	0.0843261	+	0.996438i	$0.473126\pi$
$828$	81.0484	2.81663
$829$	19.9101	0.691508	0.345754	−	0.938325i	$-0.387623\pi$
$829$	19.9101	0.691508	0.345754	+	0.938325i	$0.387623\pi$
$830$	0	0
$831$	−19.8534	−0.688708
$832$	−26.6538	−0.924055
$833$	0	0
$834$	−96.6835	−3.34787
$835$	0	0
$836$	−62.9902	−2.17856
$837$	49.0877	1.69672
$838$	−34.7823	−1.20153
$839$	1.98935	0.0686799	0.0343400	−	0.999410i	$-0.489067\pi$
$839$	1.98935	0.0686799	0.0343400	+	0.999410i	$0.489067\pi$
$840$	0	0
$841$	−28.4949	−0.982584
$842$	3.64302	0.125547
$843$	−74.3618	−2.56116
$844$	−73.8722	−2.54279
$845$	0	0
$846$	−46.1866	−1.58793
$847$	9.46857	0.325344
$848$	−0.441621	−0.0151653
$849$	60.8138	2.08712
$850$	0	0
$851$	11.3154	0.387887
$852$	−29.8100	−1.02127
$853$	26.0104	0.890579	0.445289	−	0.895387i	$-0.353101\pi$
$853$	26.0104	0.890579	0.445289	+	0.895387i	$0.353101\pi$
$854$	4.01595	0.137423
$855$	0	0
$856$	−5.10129	−0.174359
$857$	−18.9964	−0.648904	−0.324452	−	0.945902i	$-0.605180\pi$
$857$	−18.9964	−0.648904	−0.324452	+	0.945902i	$0.605180\pi$
$858$	51.9426	1.77329
$859$	15.6479	0.533899	0.266950	−	0.963710i	$-0.413984\pi$
$859$	15.6479	0.533899	0.266950	+	0.963710i	$0.413984\pi$
$860$	0	0
$861$	−64.1379	−2.18581
$862$	−47.5220	−1.61861
$863$	44.1746	1.50372	0.751860	−	0.659322i	$-0.229157\pi$
$863$	44.1746	1.50372	0.751860	+	0.659322i	$0.229157\pi$
$864$	−25.8337	−0.878881
$865$	0	0
$866$	−22.8087	−0.775072
$867$	0	0
$868$	−36.9464	−1.25404
$869$	11.9744	0.406205
$870$	0	0
$871$	3.86537	0.130973
$872$	−79.9836	−2.70859
$873$	−21.5896	−0.730697
$874$	−46.7867	−1.58258
$875$	0	0
$876$	−97.8330	−3.30547
$877$	9.87744	0.333538	0.166769	−	0.985996i	$-0.446667\pi$
$877$	9.87744	0.333538	0.166769	+	0.985996i	$0.446667\pi$
$878$	48.1273	1.62422
$879$	34.9862	1.18006
$880$	0	0
$881$	−51.6330	−1.73956	−0.869780	−	0.493439i	$-0.835740\pi$
$881$	−51.6330	−1.73956	−0.869780	+	0.493439i	$0.835740\pi$
$882$	−16.0607	−0.540793
$883$	17.8503	0.600710	0.300355	−	0.953827i	$-0.402895\pi$
$883$	17.8503	0.600710	0.300355	+	0.953827i	$0.402895\pi$
$884$	0	0
$885$	0	0
$886$	31.6884	1.06459
$887$	−57.3894	−1.92695	−0.963474	−	0.267802i	$-0.913703\pi$
$887$	−57.3894	−1.92695	−0.963474	+	0.267802i	$0.913703\pi$
$888$	48.5441	1.62903
$889$	4.00194	0.134221
$890$	0	0
$891$	48.0509	1.60977
$892$	−67.0315	−2.24438
$893$	17.4169	0.582833
$894$	41.7325	1.39574
$895$	0	0
$896$	50.8302	1.69812
$897$	25.2029	0.841499
$898$	−38.7255	−1.29229
$899$	−2.83753	−0.0946370
$900$	0	0
$901$	0	0
$902$	53.2644	1.77351
$903$	−98.6742	−3.28367
$904$	47.1757	1.56904
$905$	0	0
$906$	−152.103	−5.05328
$907$	−7.21531	−0.239580	−0.119790	−	0.992799i	$-0.538222\pi$
$907$	−7.21531	−0.239580	−0.119790	+	0.992799i	$0.538222\pi$
$908$	−10.3307	−0.342835
$909$	6.65295	0.220665
$910$	0	0
$911$	47.1365	1.56170	0.780852	−	0.624717i	$-0.214786\pi$
$911$	47.1365	1.56170	0.780852	+	0.624717i	$0.214786\pi$
$912$	−52.3763	−1.73435
$913$	−32.4113	−1.07266
$914$	21.0927	0.697683
$915$	0	0
$916$	107.036	3.53656
$917$	−34.6919	−1.14563
$918$	0	0
$919$	−3.10828	−0.102533	−0.0512663	−	0.998685i	$-0.516326\pi$
$919$	−3.10828	−0.102533	−0.0512663	+	0.998685i	$0.516326\pi$
$920$	0	0
$921$	25.4426	0.838363
$922$	44.1288	1.45330
$923$	−6.46249	−0.212715
$924$	−77.8481	−2.56101
$925$	0	0
$926$	70.0463	2.30186
$927$	91.0524	2.99055
$928$	1.49333	0.0490209
$929$	18.2447	0.598588	0.299294	−	0.954161i	$-0.403249\pi$
$929$	18.2447	0.598588	0.299294	+	0.954161i	$0.403249\pi$
$930$	0	0
$931$	6.05647	0.198493
$932$	55.5592	1.81990
$933$	−42.6828	−1.39737
$934$	19.7385	0.645864
$935$	0	0
$936$	75.3786	2.46383
$937$	14.3214	0.467860	0.233930	−	0.972253i	$-0.424841\pi$
$937$	14.3214	0.467860	0.233930	+	0.972253i	$0.424841\pi$
$938$	−8.86825	−0.289559
$939$	28.7106	0.936936
$940$	0	0
$941$	29.4874	0.961261	0.480631	−	0.876923i	$-0.340408\pi$
$941$	29.4874	0.961261	0.480631	+	0.876923i	$0.340408\pi$
$942$	−51.2304	−1.66918
$943$	25.8442	0.841603
$944$	−32.7182	−1.06489
$945$	0	0
$946$	81.9457	2.66429
$947$	10.2467	0.332973	0.166486	−	0.986044i	$-0.446758\pi$
$947$	10.2467	0.332973	0.166486	+	0.986044i	$0.446758\pi$
$948$	53.1257	1.72544
$949$	−21.2091	−0.688477
$950$	0	0
$951$	−106.204	−3.44392
$952$	0	0
$953$	30.5425	0.989370	0.494685	−	0.869072i	$-0.335283\pi$
$953$	30.5425	0.989370	0.494685	+	0.869072i	$0.335283\pi$
$954$	−2.75301	−0.0891320
$955$	0	0
$956$	33.6476	1.08824
$957$	−5.97883	−0.193268
$958$	−87.3909	−2.82347
$959$	29.5686	0.954818
$960$	0	0
$961$	−15.0583	−0.485751
$962$	22.4301	0.723175
$963$	−8.29821	−0.267406
$964$	95.7036	3.08241
$965$	0	0
$966$	−57.8225	−1.86041
$967$	50.0287	1.60881	0.804407	−	0.594078i	$-0.202483\pi$
$967$	50.0287	1.60881	0.804407	+	0.594078i	$0.202483\pi$
$968$	−16.3681	−0.526092
$969$	0	0
$970$	0	0
$971$	0.00176375	5.66015e−5 0	2.83007e−5	−	1.00000i	$-0.499991\pi$
$971$	0.00176375	5.66015e−5 0	2.83007e−5		1.00000i	$0.499991\pi$
$972$	74.2148	2.38044
$973$	31.4133	1.00706
$974$	79.4507	2.54577
$975$	0	0
$976$	−1.81155	−0.0579862
$977$	15.5052	0.496055	0.248028	−	0.968753i	$-0.420218\pi$
$977$	15.5052	0.496055	0.248028	+	0.968753i	$0.420218\pi$
$978$	−116.031	−3.71027
$979$	3.11952	0.0997002
$980$	0	0
$981$	−130.108	−4.15404
$982$	29.0985	0.928571
$983$	16.7282	0.533547	0.266774	−	0.963759i	$-0.414042\pi$
$983$	16.7282	0.533547	0.266774	+	0.963759i	$0.414042\pi$
$984$	110.874	3.53453
$985$	0	0
$986$	0	0
$987$	21.5251	0.685151
$988$	−60.5842	−1.92744
$989$	39.7606	1.26431
$990$	0	0
$991$	2.57414	0.0817701	0.0408851	−	0.999164i	$-0.486982\pi$
$991$	2.57414	0.0817701	0.0408851	+	0.999164i	$0.486982\pi$
$992$	−8.38976	−0.266375
$993$	−67.0343	−2.12727
$994$	14.8268	0.470277
$995$	0	0
$996$	−143.796	−4.55634
$997$	16.8644	0.534101	0.267050	−	0.963683i	$-0.413951\pi$
$997$	16.8644	0.534101	0.267050	+	0.963683i	$0.413951\pi$
$998$	11.8636	0.375535
$999$	44.6637	1.41310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.bi.1.6		6
5.4	even	2		1445.2.a.l.1.1	✓	6
17.16	even	2		7225.2.a.bh.1.6		6
85.4	even	4		1445.2.d.h.866.12		12
85.64	even	4		1445.2.d.h.866.11		12
85.84	even	2		1445.2.a.m.1.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1445.2.a.l.1.1	✓	6	5.4	even	2
1445.2.a.m.1.1	yes	6	85.84	even	2
1445.2.d.h.866.11		12	85.64	even	4
1445.2.d.h.866.12		12	85.4	even	4
7225.2.a.bh.1.6		6	17.16	even	2
7225.2.a.bi.1.6		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7225 = 5^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7225.a (trivial)

\(f(q)\)	\(=\)	\(q+2.40162 q^{2} +3.14741 q^{3} +3.76778 q^{4} +7.55888 q^{6} -2.45595 q^{7} +4.24555 q^{8} +6.90618 q^{9} +2.67294 q^{11} +11.8588 q^{12} +2.57085 q^{13} -5.89825 q^{14} +2.66063 q^{16} +16.5860 q^{18} -6.25456 q^{19} -7.72986 q^{21} +6.41940 q^{22} +3.11473 q^{23} +13.3625 q^{24} +6.17420 q^{26} +12.2943 q^{27} -9.25348 q^{28} -0.710678 q^{29} +3.99271 q^{31} -2.10127 q^{32} +8.41285 q^{33} +26.0210 q^{36} +3.63287 q^{37} -15.0211 q^{38} +8.09151 q^{39} +8.29741 q^{41} -18.5642 q^{42} +12.7653 q^{43} +10.0711 q^{44} +7.48040 q^{46} -2.78467 q^{47} +8.37409 q^{48} -0.968329 q^{49} +9.68640 q^{52} -0.165984 q^{53} +29.5263 q^{54} -10.4268 q^{56} -19.6857 q^{57} -1.70678 q^{58} -12.2972 q^{59} -0.680871 q^{61} +9.58898 q^{62} -16.9612 q^{63} -10.3677 q^{64} +20.2045 q^{66} +1.50354 q^{67} +9.80333 q^{69} -2.51376 q^{71} +29.3205 q^{72} -8.24985 q^{73} +8.72478 q^{74} -23.5658 q^{76} -6.56461 q^{77} +19.4327 q^{78} +4.47987 q^{79} +17.9768 q^{81} +19.9272 q^{82} -12.1257 q^{83} -29.1245 q^{84} +30.6575 q^{86} -2.23680 q^{87} +11.3481 q^{88} +1.16707 q^{89} -6.31386 q^{91} +11.7356 q^{92} +12.5667 q^{93} -6.68772 q^{94} -6.61356 q^{96} -3.12613 q^{97} -2.32556 q^{98} +18.4598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 9 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 6 q^{11} + 6 q^{12} + 9 q^{13} - 18 q^{14} - 3 q^{16} + 15 q^{18} - 21 q^{19} - 12 q^{21} - 3 q^{22} + 18 q^{23} - 6 q^{26} + 12 q^{27}+ \cdots + 18 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 9 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9 + 6 * q^11 + 6 * q^12 + 9 * q^13 - 18 * q^14 - 3 * q^16 + 15 * q^18 - 21 * q^19 - 12 * q^21 - 3 * q^22 + 18 * q^23 - 6 * q^26 + 12 * q^27 - 15 * q^28 + 18 * q^29 - 6 * q^31 + 24 * q^33 + 18 * q^36 - 9 * q^37 - 15 * q^38 + 9 * q^39 + 3 * q^41 - 6 * q^42 + 39 * q^43 + 6 * q^44 + 27 * q^46 - 3 * q^47 + 21 * q^48 + 6 * q^49 - 3 * q^52 + 24 * q^53 + 33 * q^54 + 9 * q^56 - 12 * q^57 + 33 * q^58 - 12 * q^59 + 27 * q^61 - 12 * q^63 - 12 * q^64 + 21 * q^66 + 30 * q^67 - 18 * q^71 + 30 * q^72 - 9 * q^73 + 27 * q^74 - 45 * q^76 + 21 * q^77 + 36 * q^78 + 3 * q^79 + 6 * q^81 + 15 * q^82 + 21 * q^83 - 27 * q^84 + 36 * q^86 - 6 * q^87 + 12 * q^88 + 6 * q^89 + 36 * q^91 + 9 * q^92 + 30 * q^93 + 3 * q^94 + 27 * q^96 - 18 * q^97 - 42 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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