LMFDB - Embedded newform 9065.2.a.bb.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9065,2,Mod(1,9065)] 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("9065.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9065, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 9065 = 5 \cdot 7^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9065.a (trivial)

Newform invariants

comment:select newform

sage:traces = [34,-2,-10,30,34,-8,0,-6,28,-2,-30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	yes
Analytic conductor:	$72.3843894323$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	9065.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.87679 q^{2} -0.533259 q^{3} +1.52234 q^{4} +1.00000 q^{5} +1.00082 q^{6} +0.896460 q^{8} -2.71564 q^{9} -1.87679 q^{10} -3.86585 q^{11} -0.811803 q^{12} +0.244815 q^{13} -0.533259 q^{15} -4.72716 q^{16} -1.24830 q^{17} +5.09668 q^{18} -2.17945 q^{19} +1.52234 q^{20} +7.25539 q^{22} -7.42384 q^{23} -0.478045 q^{24} +1.00000 q^{25} -0.459466 q^{26} +3.04791 q^{27} +4.67882 q^{29} +1.00082 q^{30} +7.54603 q^{31} +7.07896 q^{32} +2.06150 q^{33} +2.34279 q^{34} -4.13413 q^{36} +1.00000 q^{37} +4.09038 q^{38} -0.130550 q^{39} +0.896460 q^{40} -3.99358 q^{41} -5.19343 q^{43} -5.88516 q^{44} -2.71564 q^{45} +13.9330 q^{46} +6.18990 q^{47} +2.52080 q^{48} -1.87679 q^{50} +0.665665 q^{51} +0.372692 q^{52} -0.604044 q^{53} -5.72029 q^{54} -3.86585 q^{55} +1.16221 q^{57} -8.78117 q^{58} +12.9598 q^{59} -0.811803 q^{60} +2.75156 q^{61} -14.1623 q^{62} -3.83142 q^{64} +0.244815 q^{65} -3.86900 q^{66} +2.66108 q^{67} -1.90034 q^{68} +3.95883 q^{69} +13.7239 q^{71} -2.43446 q^{72} -1.63933 q^{73} -1.87679 q^{74} -0.533259 q^{75} -3.31788 q^{76} +0.245014 q^{78} +6.53589 q^{79} -4.72716 q^{80} +6.52158 q^{81} +7.49511 q^{82} +16.6413 q^{83} -1.24830 q^{85} +9.74699 q^{86} -2.49502 q^{87} -3.46558 q^{88} +17.3355 q^{89} +5.09668 q^{90} -11.3016 q^{92} -4.02398 q^{93} -11.6171 q^{94} -2.17945 q^{95} -3.77492 q^{96} +11.8774 q^{97} +10.4982 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 2 q^{2} - 10 q^{3} + 30 q^{4} + 34 q^{5} - 8 q^{6} - 6 q^{8} + 28 q^{9} - 2 q^{10} - 30 q^{11} - 20 q^{12} - 18 q^{13} - 10 q^{15} + 18 q^{16} - 10 q^{17} - 40 q^{19} + 30 q^{20} - 4 q^{22} - 16 q^{23}+ \cdots - 100 q^{99}+O(q^{100}) $ 34 * q - 2 * q^2 - 10 * q^3 + 30 * q^4 + 34 * q^5 - 8 * q^6 - 6 * q^8 + 28 * q^9 - 2 * q^10 - 30 * q^11 - 20 * q^12 - 18 * q^13 - 10 * q^15 + 18 * q^16 - 10 * q^17 - 40 * q^19 + 30 * q^20 - 4 * q^22 - 16 * q^23 - 24 * q^24 + 34 * q^25 - 12 * q^26 - 34 * q^27 - 22 * q^29 - 8 * q^30 - 52 * q^31 + 6 * q^32 - 10 * q^33 - 36 * q^34 + 14 * q^36 + 34 * q^37 - 16 * q^38 - 2 * q^39 - 6 * q^40 - 16 * q^41 - 56 * q^44 + 28 * q^45 - 28 * q^46 - 38 * q^47 - 18 * q^48 - 2 * q^50 - 2 * q^51 - 52 * q^52 + 4 * q^53 - 32 * q^54 - 30 * q^55 - 12 * q^57 - 8 * q^58 - 16 * q^59 - 20 * q^60 - 60 * q^61 + 14 * q^62 - 38 * q^64 - 18 * q^65 - 14 * q^66 + 12 * q^67 - 36 * q^68 - 8 * q^69 - 44 * q^71 - 6 * q^72 - 48 * q^73 - 2 * q^74 - 10 * q^75 - 50 * q^76 + 8 * q^78 - 26 * q^79 + 18 * q^80 - 10 * q^81 - 60 * q^82 - 28 * q^83 - 10 * q^85 - 28 * q^86 - 86 * q^87 + 42 * q^88 + 4 * q^89 - 22 * q^92 + 48 * q^93 - 40 * q^94 - 40 * q^95 - 86 * q^96 - 18 * q^97 - 100 * 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 $

$2$	−1.87679	−1.32709	−0.663546	−	0.748136i	$-0.730949\pi$
$2$	−1.87679	−1.32709	−0.663546	+	0.748136i	$0.730949\pi$
$3$	−0.533259	−0.307877	−0.153939	−	0.988080i	$-0.549196\pi$
$3$	−0.533259	−0.307877	−0.153939	+	0.988080i	$0.549196\pi$
$4$	1.52234	0.761172
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00082	0.408581
$7$	0	0
$7$	0	0
$8$	0.896460	0.316947
$9$	−2.71564	−0.905212
$10$	−1.87679	−0.593493
$11$	−3.86585	−1.16560	−0.582799	−	0.812616i	$-0.698043\pi$
$11$	−3.86585	−1.16560	−0.582799	+	0.812616i	$0.698043\pi$
$12$	−0.811803	−0.234347
$13$	0.244815	0.0678994	0.0339497	−	0.999424i	$-0.489191\pi$
$13$	0.244815	0.0678994	0.0339497	+	0.999424i	$0.489191\pi$
$14$	0	0
$15$	−0.533259	−0.137687
$16$	−4.72716	−1.18179
$17$	−1.24830	−0.302756	−0.151378	−	0.988476i	$-0.548371\pi$
$17$	−1.24830	−0.302756	−0.151378	+	0.988476i	$0.548371\pi$
$18$	5.09668	1.20130
$19$	−2.17945	−0.500001	−0.250001	−	0.968246i	$-0.580431\pi$
$19$	−2.17945	−0.500001	−0.250001	+	0.968246i	$0.580431\pi$
$20$	1.52234	0.340406
$21$	0	0
$22$	7.25539	1.54686
$23$	−7.42384	−1.54798	−0.773988	−	0.633200i	$-0.781741\pi$
$23$	−7.42384	−1.54798	−0.773988	+	0.633200i	$0.781741\pi$
$24$	−0.478045	−0.0975806
$25$	1.00000	0.200000
$26$	−0.459466	−0.0901087
$27$	3.04791	0.586571
$28$	0	0
$29$	4.67882	0.868835	0.434418	−	0.900712i	$-0.356954\pi$
$29$	4.67882	0.868835	0.434418	+	0.900712i	$0.356954\pi$
$30$	1.00082	0.182723
$31$	7.54603	1.35531	0.677653	−	0.735382i	$-0.262997\pi$
$31$	7.54603	1.35531	0.677653	+	0.735382i	$0.262997\pi$
$32$	7.07896	1.25140
$33$	2.06150	0.358861
$34$	2.34279	0.401785
$35$	0	0
$36$	−4.13413	−0.689022
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	4.09038	0.663547
$39$	−0.130550	−0.0209047
$40$	0.896460	0.141743
$41$	−3.99358	−0.623692	−0.311846	−	0.950133i	$-0.600947\pi$
$41$	−3.99358	−0.623692	−0.311846	+	0.950133i	$0.600947\pi$
$42$	0	0
$43$	−5.19343	−0.791991	−0.395996	−	0.918252i	$-0.629600\pi$
$43$	−5.19343	−0.791991	−0.395996	+	0.918252i	$0.629600\pi$
$44$	−5.88516	−0.887221
$45$	−2.71564	−0.404823
$46$	13.9330	2.05431
$47$	6.18990	0.902890	0.451445	−	0.892299i	$-0.350909\pi$
$47$	6.18990	0.902890	0.451445	+	0.892299i	$0.350909\pi$
$48$	2.52080	0.363846
$49$	0	0
$50$	−1.87679	−0.265418
$51$	0.665665	0.0932117
$52$	0.372692	0.0516831
$53$	−0.604044	−0.0829719	−0.0414859	−	0.999139i	$-0.513209\pi$
$53$	−0.604044	−0.0829719	−0.0414859	+	0.999139i	$0.513209\pi$
$54$	−5.72029	−0.778433
$55$	−3.86585	−0.521271
$56$	0	0
$57$	1.16221	0.153939
$58$	−8.78117	−1.15302
$59$	12.9598	1.68722	0.843610	−	0.536957i	$-0.180426\pi$
$59$	12.9598	1.68722	0.843610	+	0.536957i	$0.180426\pi$
$60$	−0.811803	−0.104803
$61$	2.75156	0.352301	0.176151	−	0.984363i	$-0.443635\pi$
$61$	2.75156	0.352301	0.176151	+	0.984363i	$0.443635\pi$
$62$	−14.1623	−1.79862
$63$	0	0
$64$	−3.83142	−0.478928
$65$	0.244815	0.0303655
$66$	−3.86900	−0.476241
$67$	2.66108	0.325103	0.162551	−	0.986700i	$-0.448028\pi$
$67$	2.66108	0.325103	0.162551	+	0.986700i	$0.448028\pi$
$68$	−1.90034	−0.230450
$69$	3.95883	0.476587
$70$	0	0
$71$	13.7239	1.62873	0.814363	−	0.580356i	$-0.197087\pi$
$71$	13.7239	1.62873	0.814363	+	0.580356i	$0.197087\pi$
$72$	−2.43446	−0.286904
$73$	−1.63933	−0.191868	−0.0959342	−	0.995388i	$-0.530584\pi$
$73$	−1.63933	−0.191868	−0.0959342	+	0.995388i	$0.530584\pi$
$74$	−1.87679	−0.218173
$75$	−0.533259	−0.0615754
$76$	−3.31788	−0.380587
$77$	0	0
$78$	0.245014	0.0277424
$79$	6.53589	0.735345	0.367673	−	0.929955i	$-0.380155\pi$
$79$	6.53589	0.735345	0.367673	+	0.929955i	$0.380155\pi$
$80$	−4.72716	−0.528512
$81$	6.52158	0.724620
$82$	7.49511	0.827696
$83$	16.6413	1.82661	0.913307	−	0.407271i	$-0.133520\pi$
$83$	16.6413	1.82661	0.913307	+	0.407271i	$0.133520\pi$
$84$	0	0
$85$	−1.24830	−0.135397
$86$	9.74699	1.05104
$87$	−2.49502	−0.267494
$88$	−3.46558	−0.369432
$89$	17.3355	1.83756	0.918781	−	0.394768i	$-0.129175\pi$
$89$	17.3355	1.83756	0.918781	+	0.394768i	$0.129175\pi$
$90$	5.09668	0.537237
$91$	0	0
$92$	−11.3016	−1.17828
$93$	−4.02398	−0.417268
$94$	−11.6171	−1.19822
$95$	−2.17945	−0.223607
$96$	−3.77492	−0.385276
$97$	11.8774	1.20597	0.602985	−	0.797752i	$-0.293978\pi$
$97$	11.8774	1.20597	0.602985	+	0.797752i	$0.293978\pi$
$98$	0	0
$99$	10.4982	1.05511
$100$	1.52234	0.152234
$101$	−5.28351	−0.525729	−0.262865	−	0.964833i	$-0.584667\pi$
$101$	−5.28351	−0.525729	−0.262865	+	0.964833i	$0.584667\pi$
$102$	−1.24931	−0.123701
$103$	−10.3574	−1.02055	−0.510273	−	0.860013i	$-0.670456\pi$
$103$	−10.3574	−1.02055	−0.510273	+	0.860013i	$0.670456\pi$
$104$	0.219467	0.0215205
$105$	0	0
$106$	1.13366	0.110111
$107$	−16.7801	−1.62220	−0.811098	−	0.584911i	$-0.801129\pi$
$107$	−16.7801	−1.62220	−0.811098	+	0.584911i	$0.801129\pi$
$108$	4.63997	0.446481
$109$	−15.9025	−1.52318	−0.761590	−	0.648060i	$-0.775581\pi$
$109$	−15.9025	−1.52318	−0.761590	+	0.648060i	$0.775581\pi$
$110$	7.25539	0.691775
$111$	−0.533259	−0.0506147
$112$	0	0
$113$	7.08456	0.666460	0.333230	−	0.942846i	$-0.391862\pi$
$113$	7.08456	0.666460	0.333230	+	0.942846i	$0.391862\pi$
$114$	−2.18123	−0.204291
$115$	−7.42384	−0.692276
$116$	7.12277	0.661333
$117$	−0.664828	−0.0614633
$118$	−24.3228	−2.23909
$119$	0	0
$120$	−0.478045	−0.0436394
$121$	3.94481	0.358619
$122$	−5.16411	−0.467536
$123$	2.12961	0.192020
$124$	11.4876	1.03162
$125$	1.00000	0.0894427
$126$	0	0
$127$	−1.07660	−0.0955332	−0.0477666	−	0.998859i	$-0.515210\pi$
$127$	−1.07660	−0.0955332	−0.0477666	+	0.998859i	$0.515210\pi$
$128$	−6.96715	−0.615815
$129$	2.76944	0.243836
$130$	−0.459466	−0.0402979
$131$	−12.9206	−1.12887	−0.564437	−	0.825476i	$-0.690907\pi$
$131$	−12.9206	−1.12887	−0.564437	+	0.825476i	$0.690907\pi$
$132$	3.13831	0.273155
$133$	0	0
$134$	−4.99429	−0.431441
$135$	3.04791	0.262323
$136$	−1.11905	−0.0959576
$137$	8.39661	0.717371	0.358685	−	0.933459i	$-0.383225\pi$
$137$	8.39661	0.717371	0.358685	+	0.933459i	$0.383225\pi$
$138$	−7.42989	−0.632474
$139$	−15.7892	−1.33923	−0.669613	−	0.742710i	$-0.733540\pi$
$139$	−15.7892	−1.33923	−0.669613	+	0.742710i	$0.733540\pi$
$140$	0	0
$141$	−3.30082	−0.277979
$142$	−25.7569	−2.16147
$143$	−0.946418	−0.0791434
$144$	12.8372	1.06977
$145$	4.67882	0.388555
$146$	3.07667	0.254627
$147$	0	0
$148$	1.52234	0.125136
$149$	−20.9644	−1.71747	−0.858735	−	0.512419i	$-0.828749\pi$
$149$	−20.9644	−1.71747	−0.858735	+	0.512419i	$0.828749\pi$
$150$	1.00082	0.0817162
$151$	−19.0276	−1.54845	−0.774223	−	0.632913i	$-0.781859\pi$
$151$	−19.0276	−1.54845	−0.774223	+	0.632913i	$0.781859\pi$
$152$	−1.95379	−0.158474
$153$	3.38992	0.274059
$154$	0	0
$155$	7.54603	0.606111
$156$	−0.198742	−0.0159121
$157$	13.8988	1.10924	0.554621	−	0.832103i	$-0.312863\pi$
$157$	13.8988	1.10924	0.554621	+	0.832103i	$0.312863\pi$
$158$	−12.2665	−0.975871
$159$	0.322112	0.0255451
$160$	7.07896	0.559641
$161$	0	0
$162$	−12.2396	−0.961637
$163$	23.0080	1.80212	0.901062	−	0.433689i	$-0.142789\pi$
$163$	23.0080	1.80212	0.901062	+	0.433689i	$0.142789\pi$
$164$	−6.07960	−0.474737
$165$	2.06150	0.160487
$166$	−31.2321	−2.42408
$167$	−23.2231	−1.79706	−0.898529	−	0.438914i	$-0.855363\pi$
$167$	−23.2231	−1.79706	−0.898529	+	0.438914i	$0.855363\pi$
$168$	0	0
$169$	−12.9401	−0.995390
$170$	2.34279	0.179684
$171$	5.91860	0.452607
$172$	−7.90619	−0.602842
$173$	10.2740	0.781121	0.390561	−	0.920577i	$-0.372281\pi$
$173$	10.2740	0.781121	0.390561	+	0.920577i	$0.372281\pi$
$174$	4.68263	0.354990
$175$	0	0
$176$	18.2745	1.37749
$177$	−6.91091	−0.519456
$178$	−32.5352	−2.43861
$179$	16.8184	1.25707	0.628534	−	0.777782i	$-0.283655\pi$
$179$	16.8184	1.25707	0.628534	+	0.777782i	$0.283655\pi$
$180$	−4.13413	−0.308140
$181$	−1.61092	−0.119738	−0.0598692	−	0.998206i	$-0.519068\pi$
$181$	−1.61092	−0.119738	−0.0598692	+	0.998206i	$0.519068\pi$
$182$	0	0
$183$	−1.46729	−0.108466
$184$	−6.65517	−0.490626
$185$	1.00000	0.0735215
$186$	7.55218	0.553752
$187$	4.82573	0.352892
$188$	9.42316	0.687254
$189$	0	0
$190$	4.09038	0.296747
$191$	−20.3164	−1.47004	−0.735020	−	0.678045i	$-0.762827\pi$
$191$	−20.3164	−1.47004	−0.735020	+	0.678045i	$0.762827\pi$
$192$	2.04314	0.147451
$193$	8.30172	0.597571	0.298785	−	0.954320i	$-0.403419\pi$
$193$	8.30172	0.597571	0.298785	+	0.954320i	$0.403419\pi$
$194$	−22.2914	−1.60043
$195$	−0.130550	−0.00934886
$196$	0	0
$197$	−26.1453	−1.86277	−0.931386	−	0.364033i	$-0.881400\pi$
$197$	−26.1453	−1.86277	−0.931386	+	0.364033i	$0.881400\pi$
$198$	−19.7030	−1.40023
$199$	−24.8167	−1.75921	−0.879605	−	0.475705i	$-0.842193\pi$
$199$	−24.8167	−1.75921	−0.879605	+	0.475705i	$0.842193\pi$
$200$	0.896460	0.0633893
$201$	−1.41904	−0.100092
$202$	9.91605	0.697691
$203$	0	0
$204$	1.01337	0.0709502
$205$	−3.99358	−0.278924
$206$	19.4387	1.35436
$207$	20.1604	1.40125
$208$	−1.15728	−0.0802428
$209$	8.42545	0.582800
$210$	0	0
$211$	21.1821	1.45823	0.729117	−	0.684389i	$-0.239931\pi$
$211$	21.1821	1.45823	0.729117	+	0.684389i	$0.239931\pi$
$212$	−0.919563	−0.0631559
$213$	−7.31838	−0.501447
$214$	31.4928	2.15280
$215$	−5.19343	−0.354189
$216$	2.73233	0.185912
$217$	0	0
$218$	29.8456	2.02140
$219$	0.874184	0.0590719
$220$	−5.88516	−0.396777
$221$	−0.305601	−0.0205570
$222$	1.00082	0.0671703
$223$	6.10618	0.408900	0.204450	−	0.978877i	$-0.434459\pi$
$223$	6.10618	0.408900	0.204450	+	0.978877i	$0.434459\pi$
$224$	0	0
$225$	−2.71564	−0.181042
$226$	−13.2962	−0.884453
$227$	−24.0979	−1.59943	−0.799717	−	0.600377i	$-0.795017\pi$
$227$	−24.0979	−1.59943	−0.799717	+	0.600377i	$0.795017\pi$
$228$	1.76929	0.117174
$229$	−0.640475	−0.0423237	−0.0211619	−	0.999776i	$-0.506737\pi$
$229$	−0.640475	−0.0423237	−0.0211619	+	0.999776i	$0.506737\pi$
$230$	13.9330	0.918714
$231$	0	0
$232$	4.19438	0.275374
$233$	9.41242	0.616628	0.308314	−	0.951285i	$-0.400235\pi$
$233$	9.41242	0.616628	0.308314	+	0.951285i	$0.400235\pi$
$234$	1.24774	0.0815675
$235$	6.18990	0.403784
$236$	19.7292	1.28426
$237$	−3.48532	−0.226396
$238$	0	0
$239$	14.5459	0.940893	0.470446	−	0.882429i	$-0.344093\pi$
$239$	14.5459	0.940893	0.470446	+	0.882429i	$0.344093\pi$
$240$	2.52080	0.162717
$241$	−24.0548	−1.54951	−0.774754	−	0.632262i	$-0.782127\pi$
$241$	−24.0548	−1.54951	−0.774754	+	0.632262i	$0.782127\pi$
$242$	−7.40358	−0.475920
$243$	−12.6214	−0.809665
$244$	4.18882	0.268162
$245$	0	0
$246$	−3.99683	−0.254829
$247$	−0.533563	−0.0339498
$248$	6.76471	0.429560
$249$	−8.87409	−0.562373
$250$	−1.87679	−0.118699
$251$	22.5495	1.42331	0.711657	−	0.702527i	$-0.247945\pi$
$251$	22.5495	1.42331	0.711657	+	0.702527i	$0.247945\pi$
$252$	0	0
$253$	28.6994	1.80432
$254$	2.02056	0.126781
$255$	0.665665	0.0416856
$256$	20.7387	1.29617
$257$	6.23453	0.388899	0.194450	−	0.980912i	$-0.437708\pi$
$257$	6.23453	0.388899	0.194450	+	0.980912i	$0.437708\pi$
$258$	−5.19767	−0.323593
$259$	0	0
$260$	0.372692	0.0231134
$261$	−12.7060	−0.786480
$262$	24.2492	1.49812
$263$	11.3477	0.699730	0.349865	−	0.936800i	$-0.386228\pi$
$263$	11.3477	0.699730	0.349865	+	0.936800i	$0.386228\pi$
$264$	1.84805	0.113740
$265$	−0.604044	−0.0371061
$266$	0	0
$267$	−9.24432	−0.565743
$268$	4.05108	0.247459
$269$	19.2527	1.17386	0.586928	−	0.809639i	$-0.300337\pi$
$269$	19.2527	1.17386	0.586928	+	0.809639i	$0.300337\pi$
$270$	−5.72029	−0.348126
$271$	−20.0884	−1.22028	−0.610141	−	0.792293i	$-0.708887\pi$
$271$	−20.0884	−1.22028	−0.610141	+	0.792293i	$0.708887\pi$
$272$	5.90089	0.357794
$273$	0	0
$274$	−15.7587	−0.952016
$275$	−3.86585	−0.233120
$276$	6.02669	0.362764
$277$	−10.2497	−0.615847	−0.307924	−	0.951411i	$-0.599634\pi$
$277$	−10.2497	−0.615847	−0.307924	+	0.951411i	$0.599634\pi$
$278$	29.6331	1.77728
$279$	−20.4923	−1.22684
$280$	0	0
$281$	−28.7390	−1.71442	−0.857212	−	0.514965i	$-0.827805\pi$
$281$	−28.7390	−1.71442	−0.857212	+	0.514965i	$0.827805\pi$
$282$	6.19494	0.368904
$283$	17.3531	1.03153	0.515767	−	0.856729i	$-0.327507\pi$
$283$	17.3531	1.03153	0.515767	+	0.856729i	$0.327507\pi$
$284$	20.8925	1.23974
$285$	1.16221	0.0688436
$286$	1.77623	0.105031
$287$	0	0
$288$	−19.2239	−1.13278
$289$	−15.4418	−0.908339
$290$	−8.78117	−0.515648
$291$	−6.33374	−0.371291
$292$	−2.49562	−0.146045
$293$	9.17111	0.535782	0.267891	−	0.963449i	$-0.413673\pi$
$293$	9.17111	0.535782	0.267891	+	0.963449i	$0.413673\pi$
$294$	0	0
$295$	12.9598	0.754547
$296$	0.896460	0.0521057
$297$	−11.7828	−0.683706
$298$	39.3458	2.27924
$299$	−1.81747	−0.105107
$300$	−0.811803	−0.0468695
$301$	0	0
$302$	35.7109	2.05493
$303$	2.81748	0.161860
$304$	10.3026	0.590896
$305$	2.75156	0.157554
$306$	−6.36217	−0.363701
$307$	−1.26615	−0.0722628	−0.0361314	−	0.999347i	$-0.511503\pi$
$307$	−1.26615	−0.0722628	−0.0361314	+	0.999347i	$0.511503\pi$
$308$	0	0
$309$	5.52318	0.314203
$310$	−14.1623	−0.804365
$311$	−8.66525	−0.491361	−0.245681	−	0.969351i	$-0.579011\pi$
$311$	−8.66525	−0.491361	−0.245681	+	0.969351i	$0.579011\pi$
$312$	−0.117033	−0.00662567
$313$	−5.15611	−0.291441	−0.145720	−	0.989326i	$-0.546550\pi$
$313$	−5.15611	−0.291441	−0.145720	+	0.989326i	$0.546550\pi$
$314$	−26.0851	−1.47207
$315$	0	0
$316$	9.94988	0.559724
$317$	2.36495	0.132829	0.0664144	−	0.997792i	$-0.478844\pi$
$317$	2.36495	0.132829	0.0664144	+	0.997792i	$0.478844\pi$
$318$	−0.604537	−0.0339007
$319$	−18.0876	−1.01271
$320$	−3.83142	−0.214183
$321$	8.94814	0.499437
$322$	0	0
$323$	2.72060	0.151379
$324$	9.92809	0.551560
$325$	0.244815	0.0135799
$326$	−43.1812	−2.39158
$327$	8.48012	0.468952
$328$	−3.58008	−0.197677
$329$	0	0
$330$	−3.86900	−0.212982
$331$	−28.0554	−1.54207	−0.771033	−	0.636795i	$-0.780260\pi$
$331$	−28.0554	−1.54207	−0.771033	+	0.636795i	$0.780260\pi$
$332$	25.3337	1.39037
$333$	−2.71564	−0.148816
$334$	43.5849	2.38486
$335$	2.66108	0.145390
$336$	0	0
$337$	24.5201	1.33570	0.667848	−	0.744297i	$-0.267215\pi$
$337$	24.5201	1.33570	0.667848	+	0.744297i	$0.267215\pi$
$338$	24.2858	1.32097
$339$	−3.77791	−0.205188
$340$	−1.90034	−0.103060
$341$	−29.1718	−1.57974
$342$	−11.1080	−0.600651
$343$	0	0
$344$	−4.65571	−0.251019
$345$	3.95883	0.213136
$346$	−19.2822	−1.03662
$347$	−8.88300	−0.476865	−0.238432	−	0.971159i	$-0.576634\pi$
$347$	−8.88300	−0.476865	−0.238432	+	0.971159i	$0.576634\pi$
$348$	−3.79828	−0.203609
$349$	−6.04267	−0.323457	−0.161728	−	0.986835i	$-0.551707\pi$
$349$	−6.04267	−0.323457	−0.161728	+	0.986835i	$0.551707\pi$
$350$	0	0
$351$	0.746174	0.0398278
$352$	−27.3662	−1.45862
$353$	3.88386	0.206717	0.103358	−	0.994644i	$-0.467041\pi$
$353$	3.88386	0.206717	0.103358	+	0.994644i	$0.467041\pi$
$354$	12.9703	0.689366
$355$	13.7239	0.728388
$356$	26.3906	1.39870
$357$	0	0
$358$	−31.5647	−1.66824
$359$	5.90397	0.311600	0.155800	−	0.987789i	$-0.450205\pi$
$359$	5.90397	0.311600	0.155800	+	0.987789i	$0.450205\pi$
$360$	−2.43446	−0.128307
$361$	−14.2500	−0.749999
$362$	3.02335	0.158904
$363$	−2.10360	−0.110410
$364$	0	0
$365$	−1.63933	−0.0858062
$366$	2.75381	0.143944
$367$	−7.21623	−0.376684	−0.188342	−	0.982103i	$-0.560311\pi$
$367$	−7.21623	−0.376684	−0.188342	+	0.982103i	$0.560311\pi$
$368$	35.0936	1.82938
$369$	10.8451	0.564573
$370$	−1.87679	−0.0975697
$371$	0	0
$372$	−6.12589	−0.317613
$373$	28.0026	1.44992	0.724959	−	0.688792i	$-0.241859\pi$
$373$	28.0026	1.44992	0.724959	+	0.688792i	$0.241859\pi$
$374$	−9.05688	−0.468320
$375$	−0.533259	−0.0275374
$376$	5.54900	0.286168
$377$	1.14544	0.0589934
$378$	0	0
$379$	−17.2925	−0.888257	−0.444128	−	0.895963i	$-0.646487\pi$
$379$	−17.2925	−0.888257	−0.444128	+	0.895963i	$0.646487\pi$
$380$	−3.31788	−0.170204
$381$	0.574109	0.0294125
$382$	38.1296	1.95088
$383$	−20.7717	−1.06139	−0.530693	−	0.847564i	$-0.678068\pi$
$383$	−20.7717	−1.06139	−0.530693	+	0.847564i	$0.678068\pi$
$384$	3.71529	0.189595
$385$	0	0
$386$	−15.5806	−0.793031
$387$	14.1035	0.716920
$388$	18.0815	0.917951
$389$	19.2839	0.977732	0.488866	−	0.872359i	$-0.337411\pi$
$389$	19.2839	0.977732	0.488866	+	0.872359i	$0.337411\pi$
$390$	0.245014	0.0124068
$391$	9.26715	0.468660
$392$	0	0
$393$	6.89000	0.347555
$394$	49.0692	2.47207
$395$	6.53589	0.328856
$396$	15.9819	0.803122
$397$	−25.9073	−1.30025	−0.650124	−	0.759828i	$-0.725283\pi$
$397$	−25.9073	−1.30025	−0.650124	+	0.759828i	$0.725283\pi$
$398$	46.5758	2.33463
$399$	0	0
$400$	−4.72716	−0.236358
$401$	−0.699373	−0.0349250	−0.0174625	−	0.999848i	$-0.505559\pi$
$401$	−0.699373	−0.0349250	−0.0174625	+	0.999848i	$0.505559\pi$
$402$	2.66325	0.132831
$403$	1.84738	0.0920245
$404$	−8.04333	−0.400170
$405$	6.52158	0.324060
$406$	0	0
$407$	−3.86585	−0.191623
$408$	0.596742	0.0295431
$409$	−20.1330	−0.995511	−0.497756	−	0.867317i	$-0.665842\pi$
$409$	−20.1330	−0.995511	−0.497756	+	0.867317i	$0.665842\pi$
$410$	7.49511	0.370157
$411$	−4.47756	−0.220862
$412$	−15.7675	−0.776811
$413$	0	0
$414$	−37.8369	−1.85958
$415$	16.6413	0.816887
$416$	1.73304	0.0849691
$417$	8.41975	0.412317
$418$	−15.8128	−0.773429
$419$	−29.8685	−1.45917	−0.729586	−	0.683889i	$-0.760287\pi$
$419$	−29.8685	−1.45917	−0.729586	+	0.683889i	$0.760287\pi$
$420$	0	0
$421$	13.7813	0.671658	0.335829	−	0.941923i	$-0.390984\pi$
$421$	13.7813	0.671658	0.335829	+	0.941923i	$0.390984\pi$
$422$	−39.7543	−1.93521
$423$	−16.8095	−0.817306
$424$	−0.541502	−0.0262976
$425$	−1.24830	−0.0605513
$426$	13.7351	0.665466
$427$	0	0
$428$	−25.5451	−1.23477
$429$	0.504686	0.0243664
$430$	9.74699	0.470042
$431$	−19.4538	−0.937056	−0.468528	−	0.883449i	$-0.655216\pi$
$431$	−19.4538	−0.937056	−0.468528	+	0.883449i	$0.655216\pi$
$432$	−14.4080	−0.693203
$433$	16.5776	0.796670	0.398335	−	0.917240i	$-0.369588\pi$
$433$	16.5776	0.796670	0.398335	+	0.917240i	$0.369588\pi$
$434$	0	0
$435$	−2.49502	−0.119627
$436$	−24.2090	−1.15940
$437$	16.1799	0.773990
$438$	−1.64066	−0.0783938
$439$	10.2514	0.489272	0.244636	−	0.969615i	$-0.421332\pi$
$439$	10.2514	0.489272	0.244636	+	0.969615i	$0.421332\pi$
$440$	−3.46558	−0.165215
$441$	0	0
$442$	0.573550	0.0272810
$443$	14.3125	0.680007	0.340004	−	0.940424i	$-0.389572\pi$
$443$	14.3125	0.680007	0.340004	+	0.940424i	$0.389572\pi$
$444$	−0.811803	−0.0385265
$445$	17.3355	0.821783
$446$	−11.4600	−0.542648
$447$	11.1795	0.528770
$448$	0	0
$449$	−9.18148	−0.433301	−0.216650	−	0.976249i	$-0.569513\pi$
$449$	−9.18148	−0.433301	−0.216650	+	0.976249i	$0.569513\pi$
$450$	5.09668	0.240260
$451$	15.4386	0.726974
$452$	10.7851	0.507290
$453$	10.1466	0.476731
$454$	45.2267	2.12260
$455$	0	0
$456$	1.04188	0.0487904
$457$	15.7676	0.737578	0.368789	−	0.929513i	$-0.379773\pi$
$457$	15.7676	0.737578	0.368789	+	0.929513i	$0.379773\pi$
$458$	1.20204	0.0561675
$459$	−3.80470	−0.177588
$460$	−11.3016	−0.526941
$461$	27.5353	1.28245	0.641224	−	0.767354i	$-0.278427\pi$
$461$	27.5353	1.28245	0.641224	+	0.767354i	$0.278427\pi$
$462$	0	0
$463$	−1.89929	−0.0882676	−0.0441338	−	0.999026i	$-0.514053\pi$
$463$	−1.89929	−0.0882676	−0.0441338	+	0.999026i	$0.514053\pi$
$464$	−22.1175	−1.02678
$465$	−4.02398	−0.186608
$466$	−17.6651	−0.818322
$467$	9.28954	0.429868	0.214934	−	0.976629i	$-0.431046\pi$
$467$	9.28954	0.429868	0.214934	+	0.976629i	$0.431046\pi$
$468$	−1.01210	−0.0467842
$469$	0	0
$470$	−11.6171	−0.535859
$471$	−7.41164	−0.341510
$472$	11.6179	0.534758
$473$	20.0770	0.923143
$474$	6.54122	0.300448
$475$	−2.17945	−0.100000
$476$	0	0
$477$	1.64036	0.0751071
$478$	−27.2995	−1.24865
$479$	−6.82328	−0.311764	−0.155882	−	0.987776i	$-0.549822\pi$
$479$	−6.82328	−0.311764	−0.155882	+	0.987776i	$0.549822\pi$
$480$	−3.77492	−0.172301
$481$	0.244815	0.0111626
$482$	45.1459	2.05634
$483$	0	0
$484$	6.00535	0.272971
$485$	11.8774	0.539326
$486$	23.6878	1.07450
$487$	−1.21429	−0.0550248	−0.0275124	−	0.999621i	$-0.508759\pi$
$487$	−1.21429	−0.0550248	−0.0275124	+	0.999621i	$0.508759\pi$
$488$	2.46667	0.111661
$489$	−12.2692	−0.554833
$490$	0	0
$491$	−11.8312	−0.533937	−0.266968	−	0.963705i	$-0.586022\pi$
$491$	−11.8312	−0.533937	−0.266968	+	0.963705i	$0.586022\pi$
$492$	3.24200	0.146161
$493$	−5.84055	−0.263045
$494$	1.00139	0.0450545
$495$	10.4982	0.471861
$496$	−35.6712	−1.60169
$497$	0	0
$498$	16.6548	0.746320
$499$	34.5352	1.54601	0.773005	−	0.634400i	$-0.218753\pi$
$499$	34.5352	1.54601	0.773005	+	0.634400i	$0.218753\pi$
$500$	1.52234	0.0680813
$501$	12.3839	0.553273
$502$	−42.3208	−1.88887
$503$	14.5521	0.648847	0.324423	−	0.945912i	$-0.394830\pi$
$503$	14.5521	0.648847	0.324423	+	0.945912i	$0.394830\pi$
$504$	0	0
$505$	−5.28351	−0.235113
$506$	−53.8629	−2.39450
$507$	6.90040	0.306458
$508$	−1.63896	−0.0727172
$509$	−1.80602	−0.0800502	−0.0400251	−	0.999199i	$-0.512744\pi$
$509$	−1.80602	−0.0800502	−0.0400251	+	0.999199i	$0.512744\pi$
$510$	−1.24931	−0.0553206
$511$	0	0
$512$	−24.9880	−1.10432
$513$	−6.64279	−0.293286
$514$	−11.7009	−0.516105
$515$	−10.3574	−0.456402
$516$	4.21605	0.185601
$517$	−23.9292	−1.05241
$518$	0	0
$519$	−5.47873	−0.240489
$520$	0.219467	0.00962425
$521$	17.8979	0.784120	0.392060	−	0.919940i	$-0.371763\pi$
$521$	17.8979	0.784120	0.392060	+	0.919940i	$0.371763\pi$
$522$	23.8464	1.04373
$523$	−25.0233	−1.09419	−0.547095	−	0.837070i	$-0.684267\pi$
$523$	−25.0233	−1.09419	−0.547095	+	0.837070i	$0.684267\pi$
$524$	−19.6695	−0.859268
$525$	0	0
$526$	−21.2973	−0.928605
$527$	−9.41968	−0.410328
$528$	−9.74503	−0.424098
$529$	32.1133	1.39623
$530$	1.13366	0.0492433
$531$	−35.1940	−1.52729
$532$	0	0
$533$	−0.977687	−0.0423483
$534$	17.3497	0.750793
$535$	−16.7801	−0.725468
$536$	2.38555	0.103040
$537$	−8.96857	−0.387023
$538$	−36.1333	−1.55782
$539$	0	0
$540$	4.63997	0.199673
$541$	−15.4620	−0.664762	−0.332381	−	0.943145i	$-0.607852\pi$
$541$	−15.4620	−0.664762	−0.332381	+	0.943145i	$0.607852\pi$
$542$	37.7017	1.61943
$543$	0.859035	0.0368647
$544$	−8.83664	−0.378868
$545$	−15.9025	−0.681186
$546$	0	0
$547$	−14.7053	−0.628754	−0.314377	−	0.949298i	$-0.601796\pi$
$547$	−14.7053	−0.628754	−0.314377	+	0.949298i	$0.601796\pi$
$548$	12.7825	0.546042
$549$	−7.47224	−0.318907
$550$	7.25539	0.309371
$551$	−10.1973	−0.434419
$552$	3.54893	0.151052
$553$	0	0
$554$	19.2366	0.817286
$555$	−0.533259	−0.0226356
$556$	−24.0367	−1.01938
$557$	−16.7581	−0.710065	−0.355032	−	0.934854i	$-0.615530\pi$
$557$	−16.7581	−0.710065	−0.355032	+	0.934854i	$0.615530\pi$
$558$	38.4597	1.62813
$559$	−1.27143	−0.0537757
$560$	0	0
$561$	−2.57336	−0.108647
$562$	53.9370	2.27520
$563$	−32.0362	−1.35016	−0.675082	−	0.737743i	$-0.735892\pi$
$563$	−32.0362	−1.35016	−0.675082	+	0.737743i	$0.735892\pi$
$564$	−5.02498	−0.211590
$565$	7.08456	0.298050
$566$	−32.5681	−1.36894
$567$	0	0
$568$	12.3029	0.516219
$569$	−34.5435	−1.44814	−0.724069	−	0.689727i	$-0.757730\pi$
$569$	−34.5435	−1.44814	−0.724069	+	0.689727i	$0.757730\pi$
$570$	−2.18123	−0.0913617
$571$	4.48844	0.187835	0.0939176	−	0.995580i	$-0.470061\pi$
$571$	4.48844	0.187835	0.0939176	+	0.995580i	$0.470061\pi$
$572$	−1.44077	−0.0602418
$573$	10.8339	0.452592
$574$	0	0
$575$	−7.42384	−0.309595
$576$	10.4047	0.433531
$577$	−1.05452	−0.0439004	−0.0219502	−	0.999759i	$-0.506988\pi$
$577$	−1.05452	−0.0439004	−0.0219502	+	0.999759i	$0.506988\pi$
$578$	28.9809	1.20545
$579$	−4.42696	−0.183978
$580$	7.12277	0.295757
$581$	0	0
$582$	11.8871	0.492737
$583$	2.33515	0.0967118
$584$	−1.46959	−0.0608121
$585$	−0.664828	−0.0274872
$586$	−17.2123	−0.711032
$587$	7.39205	0.305103	0.152551	−	0.988296i	$-0.451251\pi$
$587$	7.39205	0.305103	0.152551	+	0.988296i	$0.451251\pi$
$588$	0	0
$589$	−16.4462	−0.677655
$590$	−24.3228	−1.00135
$591$	13.9422	0.573505
$592$	−4.72716	−0.194285
$593$	−4.08662	−0.167817	−0.0839087	−	0.996473i	$-0.526740\pi$
$593$	−4.08662	−0.167817	−0.0839087	+	0.996473i	$0.526740\pi$
$594$	22.1138	0.907341
$595$	0	0
$596$	−31.9150	−1.30729
$597$	13.2337	0.541620
$598$	3.41100	0.139486
$599$	9.62010	0.393067	0.196533	−	0.980497i	$-0.437032\pi$
$599$	9.62010	0.393067	0.196533	+	0.980497i	$0.437032\pi$
$600$	−0.478045	−0.0195161
$601$	34.3533	1.40130	0.700651	−	0.713505i	$-0.252893\pi$
$601$	34.3533	1.40130	0.700651	+	0.713505i	$0.252893\pi$
$602$	0	0
$603$	−7.22652	−0.294287
$604$	−28.9666	−1.17863
$605$	3.94481	0.160379
$606$	−5.28782	−0.214803
$607$	−28.3868	−1.15219	−0.576093	−	0.817384i	$-0.695423\pi$
$607$	−28.3868	−1.15219	−0.576093	+	0.817384i	$0.695423\pi$
$608$	−15.4283	−0.625699
$609$	0	0
$610$	−5.16411	−0.209089
$611$	1.51538	0.0613057
$612$	5.16062	0.208606
$613$	34.1357	1.37873	0.689365	−	0.724414i	$-0.257890\pi$
$613$	34.1357	1.37873	0.689365	+	0.724414i	$0.257890\pi$
$614$	2.37629	0.0958993
$615$	2.12961	0.0858742
$616$	0	0
$617$	4.44523	0.178958	0.0894791	−	0.995989i	$-0.471480\pi$
$617$	4.44523	0.178958	0.0894791	+	0.995989i	$0.471480\pi$
$618$	−10.3659	−0.416976
$619$	0.0400506	0.00160977	0.000804885	−	1.00000i	$-0.499744\pi$
$619$	0.0400506	0.00160977	0.000804885		1.00000i	$0.499744\pi$
$620$	11.4876	0.461355
$621$	−22.6272	−0.907998
$622$	16.2629	0.652081
$623$	0	0
$624$	0.617129	0.0247049
$625$	1.00000	0.0400000
$626$	9.67695	0.386769
$627$	−4.49294	−0.179431
$628$	21.1587	0.844324
$629$	−1.24830	−0.0497728
$630$	0	0
$631$	−36.5673	−1.45572	−0.727861	−	0.685725i	$-0.759485\pi$
$631$	−36.5673	−1.45572	−0.727861	+	0.685725i	$0.759485\pi$
$632$	5.85917	0.233065
$633$	−11.2955	−0.448957
$634$	−4.43851	−0.176276
$635$	−1.07660	−0.0427238
$636$	0.490365	0.0194442
$637$	0	0
$638$	33.9467	1.34396
$639$	−37.2691	−1.47434
$640$	−6.96715	−0.275401
$641$	13.4844	0.532603	0.266301	−	0.963890i	$-0.414198\pi$
$641$	13.4844	0.532603	0.266301	+	0.963890i	$0.414198\pi$
$642$	−16.7938	−0.662798
$643$	−31.3194	−1.23512	−0.617559	−	0.786525i	$-0.711878\pi$
$643$	−31.3194	−1.23512	−0.617559	+	0.786525i	$0.711878\pi$
$644$	0	0
$645$	2.76944	0.109047
$646$	−5.10601	−0.200893
$647$	−16.5322	−0.649948	−0.324974	−	0.945723i	$-0.605356\pi$
$647$	−16.5322	−0.649948	−0.324974	+	0.945723i	$0.605356\pi$
$648$	5.84634	0.229666
$649$	−50.1006	−1.96662
$650$	−0.459466	−0.0180217
$651$	0	0
$652$	35.0261	1.37173
$653$	27.1984	1.06436	0.532178	−	0.846632i	$-0.321374\pi$
$653$	27.1984	1.06436	0.532178	+	0.846632i	$0.321374\pi$
$654$	−15.9154	−0.622342
$655$	−12.9206	−0.504848
$656$	18.8783	0.737073
$657$	4.45181	0.173682
$658$	0	0
$659$	11.8757	0.462613	0.231307	−	0.972881i	$-0.425700\pi$
$659$	11.8757	0.462613	0.231307	+	0.972881i	$0.425700\pi$
$660$	3.13831	0.122159
$661$	21.4364	0.833779	0.416889	−	0.908957i	$-0.363120\pi$
$661$	21.4364	0.833779	0.416889	+	0.908957i	$0.363120\pi$
$662$	52.6542	2.04646
$663$	0.162965	0.00632902
$664$	14.9182	0.578939
$665$	0	0
$666$	5.09668	0.197492
$667$	−34.7348	−1.34494
$668$	−35.3536	−1.36787
$669$	−3.25617	−0.125891
$670$	−4.99429	−0.192946
$671$	−10.6371	−0.410642
$672$	0	0
$673$	18.1117	0.698154	0.349077	−	0.937094i	$-0.386495\pi$
$673$	18.1117	0.698154	0.349077	+	0.937094i	$0.386495\pi$
$674$	−46.0192	−1.77259
$675$	3.04791	0.117314
$676$	−19.6992	−0.757663
$677$	47.3236	1.81879	0.909397	−	0.415928i	$-0.136543\pi$
$677$	47.3236	1.81879	0.909397	+	0.415928i	$0.136543\pi$
$678$	7.09034	0.272303
$679$	0	0
$680$	−1.11905	−0.0429135
$681$	12.8504	0.492429
$682$	54.7494	2.09646
$683$	−10.9586	−0.419320	−0.209660	−	0.977774i	$-0.567236\pi$
$683$	−10.9586	−0.419320	−0.209660	+	0.977774i	$0.567236\pi$
$684$	9.01015	0.344512
$685$	8.39661	0.320818
$686$	0	0
$687$	0.341539	0.0130305
$688$	24.5502	0.935967
$689$	−0.147879	−0.00563374
$690$	−7.42989	−0.282851
$691$	−30.9159	−1.17610	−0.588048	−	0.808826i	$-0.700104\pi$
$691$	−30.9159	−1.17610	−0.588048	+	0.808826i	$0.700104\pi$
$692$	15.6406	0.594568
$693$	0	0
$694$	16.6715	0.632843
$695$	−15.7892	−0.598920
$696$	−2.23669	−0.0847814
$697$	4.98517	0.188827
$698$	11.3408	0.429257
$699$	−5.01925	−0.189846
$700$	0	0
$701$	3.34563	0.126363	0.0631813	−	0.998002i	$-0.479875\pi$
$701$	3.34563	0.126363	0.0631813	+	0.998002i	$0.479875\pi$
$702$	−1.40041	−0.0528552
$703$	−2.17945	−0.0821997
$704$	14.8117	0.558237
$705$	−3.30082	−0.124316
$706$	−7.28919	−0.274332
$707$	0	0
$708$	−10.5208	−0.395395
$709$	40.1187	1.50669	0.753345	−	0.657625i	$-0.228439\pi$
$709$	40.1187	1.50669	0.753345	+	0.657625i	$0.228439\pi$
$710$	−25.7569	−0.966638
$711$	−17.7491	−0.665643
$712$	15.5406	0.582409
$713$	−56.0205	−2.09798
$714$	0	0
$715$	−0.946418	−0.0353940
$716$	25.6034	0.956845
$717$	−7.75670	−0.289679
$718$	−11.0805	−0.413521
$719$	29.5210	1.10095	0.550474	−	0.834853i	$-0.314447\pi$
$719$	29.5210	1.10095	0.550474	+	0.834853i	$0.314447\pi$
$720$	12.8372	0.478415
$721$	0	0
$722$	26.7442	0.995317
$723$	12.8275	0.477058
$724$	−2.45237	−0.0911416
$725$	4.67882	0.173767
$726$	3.94802	0.146525
$727$	−45.6492	−1.69303	−0.846517	−	0.532362i	$-0.821305\pi$
$727$	−45.6492	−1.69303	−0.846517	+	0.532362i	$0.821305\pi$
$728$	0	0
$729$	−12.8343	−0.475343
$730$	3.07667	0.113873
$731$	6.48294	0.239780
$732$	−2.23373	−0.0825609
$733$	−30.4462	−1.12456	−0.562278	−	0.826948i	$-0.690075\pi$
$733$	−30.4462	−1.12456	−0.562278	+	0.826948i	$0.690075\pi$
$734$	13.5434	0.499894
$735$	0	0
$736$	−52.5531	−1.93713
$737$	−10.2873	−0.378939
$738$	−20.3540	−0.749241
$739$	−30.2838	−1.11401	−0.557004	−	0.830510i	$-0.688049\pi$
$739$	−30.2838	−1.11401	−0.557004	+	0.830510i	$0.688049\pi$
$740$	1.52234	0.0559625
$741$	0.284527	0.0104524
$742$	0	0
$743$	−0.667473	−0.0244872	−0.0122436	−	0.999925i	$-0.503897\pi$
$743$	−0.667473	−0.0244872	−0.0122436	+	0.999925i	$0.503897\pi$
$744$	−3.60734	−0.132252
$745$	−20.9644	−0.768076
$746$	−52.5550	−1.92417
$747$	−45.1916	−1.65347
$748$	7.34642	0.268612
$749$	0	0
$750$	1.00082	0.0365446
$751$	38.8715	1.41844	0.709221	−	0.704986i	$-0.249047\pi$
$751$	38.8715	1.41844	0.709221	+	0.704986i	$0.249047\pi$
$752$	−29.2606	−1.06703
$753$	−12.0247	−0.438206
$754$	−2.14976	−0.0782896
$755$	−19.0276	−0.692486
$756$	0	0
$757$	−11.1884	−0.406648	−0.203324	−	0.979112i	$-0.565174\pi$
$757$	−11.1884	−0.406648	−0.203324	+	0.979112i	$0.565174\pi$
$758$	32.4544	1.17880
$759$	−15.3042	−0.555508
$760$	−1.95379	−0.0708716
$761$	15.0610	0.545960	0.272980	−	0.962020i	$-0.411991\pi$
$761$	15.0610	0.545960	0.272980	+	0.962020i	$0.411991\pi$
$762$	−1.07748	−0.0390331
$763$	0	0
$764$	−30.9285	−1.11895
$765$	3.38992	0.122563
$766$	38.9842	1.40856
$767$	3.17275	0.114561
$768$	−11.0591	−0.399061
$769$	12.2704	0.442482	0.221241	−	0.975219i	$-0.428989\pi$
$769$	12.2704	0.442482	0.221241	+	0.975219i	$0.428989\pi$
$770$	0	0
$771$	−3.32462	−0.119733
$772$	12.6381	0.454854
$773$	−21.7077	−0.780771	−0.390386	−	0.920651i	$-0.627658\pi$
$773$	−21.7077	−0.780771	−0.390386	+	0.920651i	$0.627658\pi$
$774$	−26.4693	−0.951418
$775$	7.54603	0.271061
$776$	10.6476	0.382228
$777$	0	0
$778$	−36.1918	−1.29754
$779$	8.70382	0.311847
$780$	−0.198742	−0.00711609
$781$	−53.0545	−1.89844
$782$	−17.3925	−0.621954
$783$	14.2606	0.509633
$784$	0	0
$785$	13.8988	0.496068
$786$	−12.9311	−0.461237
$787$	−47.7956	−1.70373	−0.851865	−	0.523761i	$-0.824529\pi$
$787$	−47.7956	−1.70373	−0.851865	+	0.523761i	$0.824529\pi$
$788$	−39.8021	−1.41789
$789$	−6.05126	−0.215431
$790$	−12.2665	−0.436423
$791$	0	0
$792$	9.41126	0.334414
$793$	0.673623	0.0239211
$794$	48.6225	1.72555
$795$	0.322112	0.0114241
$796$	−37.7796	−1.33906
$797$	−25.5451	−0.904854	−0.452427	−	0.891801i	$-0.649442\pi$
$797$	−25.5451	−0.904854	−0.452427	+	0.891801i	$0.649442\pi$
$798$	0	0
$799$	−7.72683	−0.273356
$800$	7.07896	0.250279
$801$	−47.0770	−1.66338
$802$	1.31258	0.0463487
$803$	6.33739	0.223642
$804$	−2.16027	−0.0761870
$805$	0	0
$806$	−3.46714	−0.122125
$807$	−10.2667	−0.361404
$808$	−4.73646	−0.166628
$809$	−17.0113	−0.598085	−0.299043	−	0.954240i	$-0.596667\pi$
$809$	−17.0113	−0.598085	−0.299043	+	0.954240i	$0.596667\pi$
$810$	−12.2396	−0.430057
$811$	−36.2850	−1.27414	−0.637070	−	0.770806i	$-0.719854\pi$
$811$	−36.2850	−1.27414	−0.637070	+	0.770806i	$0.719854\pi$
$812$	0	0
$813$	10.7123	0.375697
$814$	7.25539	0.254301
$815$	23.0080	0.805935
$816$	−3.14670	−0.110157
$817$	11.3189	0.395996
$818$	37.7854	1.32113
$819$	0	0
$820$	−6.07960	−0.212309
$821$	−25.2476	−0.881149	−0.440574	−	0.897716i	$-0.645225\pi$
$821$	−25.2476	−0.881149	−0.440574	+	0.897716i	$0.645225\pi$
$822$	8.40345	0.293104
$823$	12.0472	0.419938	0.209969	−	0.977708i	$-0.432664\pi$
$823$	12.0472	0.419938	0.209969	+	0.977708i	$0.432664\pi$
$824$	−9.28501	−0.323459
$825$	2.06150	0.0717722
$826$	0	0
$827$	10.8886	0.378632	0.189316	−	0.981916i	$-0.439373\pi$
$827$	10.8886	0.378632	0.189316	+	0.981916i	$0.439373\pi$
$828$	30.6911	1.06659
$829$	−48.1413	−1.67202	−0.836008	−	0.548717i	$-0.815117\pi$
$829$	−48.1413	−1.67202	−0.836008	+	0.548717i	$0.815117\pi$
$830$	−31.2321	−1.08408
$831$	5.46577	0.189605
$832$	−0.937989	−0.0325189
$833$	0	0
$834$	−15.8021	−0.547182
$835$	−23.2231	−0.803669
$836$	12.8264	0.443611
$837$	22.9996	0.794983
$838$	56.0570	1.93646
$839$	−41.0815	−1.41829	−0.709145	−	0.705063i	$-0.750919\pi$
$839$	−41.0815	−1.41829	−0.709145	+	0.705063i	$0.750919\pi$
$840$	0	0
$841$	−7.10864	−0.245126
$842$	−25.8646	−0.891352
$843$	15.3253	0.527832
$844$	32.2464	1.10997
$845$	−12.9401	−0.445152
$846$	31.5479	1.08464
$847$	0	0
$848$	2.85541	0.0980553
$849$	−9.25368	−0.317586
$850$	2.34279	0.0803571
$851$	−7.42384	−0.254486
$852$	−11.1411	−0.381688
$853$	−29.6529	−1.01529	−0.507647	−	0.861565i	$-0.669485\pi$
$853$	−29.6529	−1.01529	−0.507647	+	0.861565i	$0.669485\pi$
$854$	0	0
$855$	5.91860	0.202412
$856$	−15.0427	−0.514149
$857$	−12.4426	−0.425031	−0.212516	−	0.977158i	$-0.568166\pi$
$857$	−12.4426	−0.425031	−0.212516	+	0.977158i	$0.568166\pi$
$858$	−0.947189	−0.0323365
$859$	21.5978	0.736907	0.368454	−	0.929646i	$-0.379887\pi$
$859$	21.5978	0.736907	0.368454	+	0.929646i	$0.379887\pi$
$860$	−7.90619	−0.269599
$861$	0	0
$862$	36.5107	1.24356
$863$	43.9039	1.49451	0.747253	−	0.664540i	$-0.231372\pi$
$863$	43.9039	1.49451	0.747253	+	0.664540i	$0.231372\pi$
$864$	21.5761	0.734033
$865$	10.2740	0.349328
$866$	−31.1127	−1.05725
$867$	8.23445	0.279657
$868$	0	0
$869$	−25.2668	−0.857117
$870$	4.68263	0.158756
$871$	0.651472	0.0220743
$872$	−14.2559	−0.482766
$873$	−32.2548	−1.09166
$874$	−30.3663	−1.02716
$875$	0	0
$876$	1.33081	0.0449639
$877$	2.68720	0.0907402	0.0453701	−	0.998970i	$-0.485553\pi$
$877$	2.68720	0.0907402	0.0453701	+	0.998970i	$0.485553\pi$
$878$	−19.2397	−0.649308
$879$	−4.89058	−0.164955
$880$	18.2745	0.616033
$881$	−20.4965	−0.690544	−0.345272	−	0.938503i	$-0.612213\pi$
$881$	−20.4965	−0.690544	−0.345272	+	0.938503i	$0.612213\pi$
$882$	0	0
$883$	−18.1919	−0.612208	−0.306104	−	0.951998i	$-0.599025\pi$
$883$	−18.1919	−0.612208	−0.306104	+	0.951998i	$0.599025\pi$
$884$	−0.465231	−0.0156474
$885$	−6.91091	−0.232308
$886$	−26.8616	−0.902432
$887$	26.8636	0.901991	0.450996	−	0.892526i	$-0.351069\pi$
$887$	26.8636	0.901991	0.450996	+	0.892526i	$0.351069\pi$
$888$	−0.478045	−0.0160421
$889$	0	0
$890$	−32.5352	−1.09058
$891$	−25.2115	−0.844616
$892$	9.29571	0.311243
$893$	−13.4906	−0.451446
$894$	−20.9815	−0.701726
$895$	16.8184	0.562178
$896$	0	0
$897$	0.969179	0.0323600
$898$	17.2317	0.575030
$899$	35.3065	1.17754
$900$	−4.13413	−0.137804
$901$	0.754026	0.0251203
$902$	−28.9750	−0.964761
$903$	0	0
$904$	6.35103	0.211232
$905$	−1.61092	−0.0535487
$906$	−19.0431	−0.632666
$907$	−56.8744	−1.88848	−0.944241	−	0.329254i	$-0.893203\pi$
$907$	−56.8744	−1.88848	−0.944241	+	0.329254i	$0.893203\pi$
$908$	−36.6853	−1.21744
$909$	14.3481	0.475896
$910$	0	0
$911$	52.2530	1.73122	0.865610	−	0.500719i	$-0.166931\pi$
$911$	52.2530	1.73122	0.865610	+	0.500719i	$0.166931\pi$
$912$	−5.49396	−0.181923
$913$	−64.3326	−2.12910
$914$	−29.5925	−0.978833
$915$	−1.46729	−0.0485073
$916$	−0.975023	−0.0322157
$917$	0	0
$918$	7.14062	0.235676
$919$	−44.6187	−1.47184	−0.735918	−	0.677071i	$-0.763249\pi$
$919$	−44.6187	−1.47184	−0.735918	+	0.677071i	$0.763249\pi$
$920$	−6.65517	−0.219415
$921$	0.675183	0.0222480
$922$	−51.6781	−1.70193
$923$	3.35981	0.110590
$924$	0	0
$925$	1.00000	0.0328798
$926$	3.56457	0.117139
$927$	28.1269	0.923810
$928$	33.1212	1.08726
$929$	−19.4893	−0.639423	−0.319712	−	0.947515i	$-0.603586\pi$
$929$	−19.4893	−0.639423	−0.319712	+	0.947515i	$0.603586\pi$
$930$	7.55218	0.247646
$931$	0	0
$932$	14.3289	0.469360
$933$	4.62082	0.151279
$934$	−17.4345	−0.570475
$935$	4.82573	0.157818
$936$	−0.595992	−0.0194806
$937$	−33.7457	−1.10242	−0.551211	−	0.834366i	$-0.685834\pi$
$937$	−33.7457	−1.10242	−0.551211	+	0.834366i	$0.685834\pi$
$938$	0	0
$939$	2.74954	0.0897279
$940$	9.42316	0.307349
$941$	30.4020	0.991076	0.495538	−	0.868586i	$-0.334971\pi$
$941$	30.4020	0.991076	0.495538	+	0.868586i	$0.334971\pi$
$942$	13.9101	0.453215
$943$	29.6477	0.965461
$944$	−61.2629	−1.99394
$945$	0	0
$946$	−37.6804	−1.22510
$947$	52.2095	1.69658	0.848290	−	0.529532i	$-0.177632\pi$
$947$	52.2095	1.69658	0.848290	+	0.529532i	$0.177632\pi$
$948$	−5.30586	−0.172326
$949$	−0.401331	−0.0130278
$950$	4.09038	0.132709
$951$	−1.26113	−0.0408949
$952$	0	0
$953$	16.9434	0.548852	0.274426	−	0.961608i	$-0.411512\pi$
$953$	16.9434	0.548852	0.274426	+	0.961608i	$0.411512\pi$
$954$	−3.07862	−0.0996740
$955$	−20.3164	−0.657422
$956$	22.1438	0.716181
$957$	9.64538	0.311791
$958$	12.8059	0.413739
$959$	0	0
$960$	2.04314	0.0659420
$961$	25.9425	0.836855
$962$	−0.459466	−0.0148138
$963$	45.5687	1.46843
$964$	−36.6198	−1.17944
$965$	8.30172	0.267242
$966$	0	0
$967$	−17.0591	−0.548582	−0.274291	−	0.961647i	$-0.588443\pi$
$967$	−17.0591	−0.548582	−0.274291	+	0.961647i	$0.588443\pi$
$968$	3.53636	0.113663
$969$	−1.45079	−0.0466060
$970$	−22.2914	−0.715735
$971$	−53.4351	−1.71481	−0.857407	−	0.514639i	$-0.827926\pi$
$971$	−53.4351	−1.71481	−0.857407	+	0.514639i	$0.827926\pi$
$972$	−19.2142	−0.616294
$973$	0	0
$974$	2.27897	0.0730229
$975$	−0.130550	−0.00418094
$976$	−13.0071	−0.416346
$977$	−3.29025	−0.105264	−0.0526322	−	0.998614i	$-0.516761\pi$
$977$	−3.29025	−0.105264	−0.0526322	+	0.998614i	$0.516761\pi$
$978$	23.0267	0.736314
$979$	−67.0166	−2.14186
$980$	0	0
$981$	43.1853	1.37880
$982$	22.2048	0.708583
$983$	−14.7664	−0.470974	−0.235487	−	0.971878i	$-0.575668\pi$
$983$	−14.7664	−0.470974	−0.235487	+	0.971878i	$0.575668\pi$
$984$	1.90911	0.0608602
$985$	−26.1453	−0.833057
$986$	10.9615	0.349085
$987$	0	0
$988$	−0.812266	−0.0258416
$989$	38.5552	1.22598
$990$	−19.7030	−0.626203
$991$	−39.1638	−1.24408	−0.622040	−	0.782986i	$-0.713696\pi$
$991$	−39.1638	−1.24408	−0.622040	+	0.782986i	$0.713696\pi$
$992$	53.4180	1.69602
$993$	14.9608	0.474767
$994$	0	0
$995$	−24.8167	−0.786742
$996$	−13.5094	−0.428062
$997$	41.8882	1.32661	0.663307	−	0.748348i	$-0.269152\pi$
$997$	41.8882	1.32661	0.663307	+	0.748348i	$0.269152\pi$
$998$	−64.8154	−2.05170
$999$	3.04791	0.0964317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9065.2.a.bb.1.8	✓	34
7.6	odd	2		9065.2.a.bc.1.8	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9065.2.a.bb.1.8	✓	34	1.1	even	1	trivial
9065.2.a.bc.1.8	yes	34	7.6	odd	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:	\( N \)	\(=\)	\( 9065 = 5 \cdot 7^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9065.a (trivial)

\(f(q)\)	\(=\)	\(q-1.87679 q^{2} -0.533259 q^{3} +1.52234 q^{4} +1.00000 q^{5} +1.00082 q^{6} +0.896460 q^{8} -2.71564 q^{9} -1.87679 q^{10} -3.86585 q^{11} -0.811803 q^{12} +0.244815 q^{13} -0.533259 q^{15} -4.72716 q^{16} -1.24830 q^{17} +5.09668 q^{18} -2.17945 q^{19} +1.52234 q^{20} +7.25539 q^{22} -7.42384 q^{23} -0.478045 q^{24} +1.00000 q^{25} -0.459466 q^{26} +3.04791 q^{27} +4.67882 q^{29} +1.00082 q^{30} +7.54603 q^{31} +7.07896 q^{32} +2.06150 q^{33} +2.34279 q^{34} -4.13413 q^{36} +1.00000 q^{37} +4.09038 q^{38} -0.130550 q^{39} +0.896460 q^{40} -3.99358 q^{41} -5.19343 q^{43} -5.88516 q^{44} -2.71564 q^{45} +13.9330 q^{46} +6.18990 q^{47} +2.52080 q^{48} -1.87679 q^{50} +0.665665 q^{51} +0.372692 q^{52} -0.604044 q^{53} -5.72029 q^{54} -3.86585 q^{55} +1.16221 q^{57} -8.78117 q^{58} +12.9598 q^{59} -0.811803 q^{60} +2.75156 q^{61} -14.1623 q^{62} -3.83142 q^{64} +0.244815 q^{65} -3.86900 q^{66} +2.66108 q^{67} -1.90034 q^{68} +3.95883 q^{69} +13.7239 q^{71} -2.43446 q^{72} -1.63933 q^{73} -1.87679 q^{74} -0.533259 q^{75} -3.31788 q^{76} +0.245014 q^{78} +6.53589 q^{79} -4.72716 q^{80} +6.52158 q^{81} +7.49511 q^{82} +16.6413 q^{83} -1.24830 q^{85} +9.74699 q^{86} -2.49502 q^{87} -3.46558 q^{88} +17.3355 q^{89} +5.09668 q^{90} -11.3016 q^{92} -4.02398 q^{93} -11.6171 q^{94} -2.17945 q^{95} -3.77492 q^{96} +11.8774 q^{97} +10.4982 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 2 q^{2} - 10 q^{3} + 30 q^{4} + 34 q^{5} - 8 q^{6} - 6 q^{8} + 28 q^{9} - 2 q^{10} - 30 q^{11} - 20 q^{12} - 18 q^{13} - 10 q^{15} + 18 q^{16} - 10 q^{17} - 40 q^{19} + 30 q^{20} - 4 q^{22} - 16 q^{23}+ \cdots - 100 q^{99}+O(q^{100}) \) 34 * q - 2 * q^2 - 10 * q^3 + 30 * q^4 + 34 * q^5 - 8 * q^6 - 6 * q^8 + 28 * q^9 - 2 * q^10 - 30 * q^11 - 20 * q^12 - 18 * q^13 - 10 * q^15 + 18 * q^16 - 10 * q^17 - 40 * q^19 + 30 * q^20 - 4 * q^22 - 16 * q^23 - 24 * q^24 + 34 * q^25 - 12 * q^26 - 34 * q^27 - 22 * q^29 - 8 * q^30 - 52 * q^31 + 6 * q^32 - 10 * q^33 - 36 * q^34 + 14 * q^36 + 34 * q^37 - 16 * q^38 - 2 * q^39 - 6 * q^40 - 16 * q^41 - 56 * q^44 + 28 * q^45 - 28 * q^46 - 38 * q^47 - 18 * q^48 - 2 * q^50 - 2 * q^51 - 52 * q^52 + 4 * q^53 - 32 * q^54 - 30 * q^55 - 12 * q^57 - 8 * q^58 - 16 * q^59 - 20 * q^60 - 60 * q^61 + 14 * q^62 - 38 * q^64 - 18 * q^65 - 14 * q^66 + 12 * q^67 - 36 * q^68 - 8 * q^69 - 44 * q^71 - 6 * q^72 - 48 * q^73 - 2 * q^74 - 10 * q^75 - 50 * q^76 + 8 * q^78 - 26 * q^79 + 18 * q^80 - 10 * q^81 - 60 * q^82 - 28 * q^83 - 10 * q^85 - 28 * q^86 - 86 * q^87 + 42 * q^88 + 4 * q^89 - 22 * q^92 + 48 * q^93 - 40 * q^94 - 40 * q^95 - 86 * q^96 - 18 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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