LMFDB - Embedded newform 9065.2.a.bc.1.7

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:	$0$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	\(q-2.01175 q^{2} +2.93465 q^{3} +2.04715 q^{4} -1.00000 q^{5} -5.90379 q^{6} -0.0948516 q^{8} +5.61216 q^{9} +2.01175 q^{10} -6.42740 q^{11} +6.00766 q^{12} +1.56383 q^{13} -2.93465 q^{15} -3.90348 q^{16} +6.42248 q^{17} -11.2903 q^{18} +8.25786 q^{19} -2.04715 q^{20} +12.9303 q^{22} -4.74009 q^{23} -0.278356 q^{24} +1.00000 q^{25} -3.14604 q^{26} +7.66577 q^{27} +4.27563 q^{29} +5.90379 q^{30} +5.78128 q^{31} +8.04254 q^{32} -18.8621 q^{33} -12.9204 q^{34} +11.4889 q^{36} +1.00000 q^{37} -16.6128 q^{38} +4.58929 q^{39} +0.0948516 q^{40} -6.72419 q^{41} +3.24018 q^{43} -13.1578 q^{44} -5.61216 q^{45} +9.53589 q^{46} -4.06467 q^{47} -11.4553 q^{48} -2.01175 q^{50} +18.8477 q^{51} +3.20139 q^{52} +8.37228 q^{53} -15.4216 q^{54} +6.42740 q^{55} +24.2339 q^{57} -8.60151 q^{58} +9.12809 q^{59} -6.00766 q^{60} -4.90749 q^{61} -11.6305 q^{62} -8.37264 q^{64} -1.56383 q^{65} +37.9460 q^{66} +12.8008 q^{67} +13.1478 q^{68} -13.9105 q^{69} -3.76509 q^{71} -0.532322 q^{72} -12.3423 q^{73} -2.01175 q^{74} +2.93465 q^{75} +16.9051 q^{76} -9.23252 q^{78} -8.26105 q^{79} +3.90348 q^{80} +5.65987 q^{81} +13.5274 q^{82} -8.13625 q^{83} -6.42248 q^{85} -6.51843 q^{86} +12.5475 q^{87} +0.609649 q^{88} -6.14981 q^{89} +11.2903 q^{90} -9.70367 q^{92} +16.9660 q^{93} +8.17710 q^{94} -8.25786 q^{95} +23.6020 q^{96} -2.23767 q^{97} -36.0716 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.01175	−1.42252	−0.711262	−	0.702927i	$-0.751876\pi$
$2$	−2.01175	−1.42252	−0.711262	+	0.702927i	$0.751876\pi$
$3$	2.93465	1.69432	0.847160	−	0.531338i	$-0.178311\pi$
$3$	2.93465	1.69432	0.847160	+	0.531338i	$0.178311\pi$
$4$	2.04715	1.02357
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.90379	−2.41021
$7$	0	0
$7$	0	0
$8$	−0.0948516	−0.0335351
$9$	5.61216	1.87072
$10$	2.01175	0.636172
$11$	−6.42740	−1.93793	−0.968966	−	0.247192i	$-0.920492\pi$
$11$	−6.42740	−1.93793	−0.968966	+	0.247192i	$0.920492\pi$
$12$	6.00766	1.73426
$13$	1.56383	0.433728	0.216864	−	0.976202i	$-0.430417\pi$
$13$	1.56383	0.433728	0.216864	+	0.976202i	$0.430417\pi$
$14$	0	0
$15$	−2.93465	−0.757723
$16$	−3.90348	−0.975870
$17$	6.42248	1.55768	0.778840	−	0.627223i	$-0.215808\pi$
$17$	6.42248	1.55768	0.778840	+	0.627223i	$0.215808\pi$
$18$	−11.2903	−2.66114
$19$	8.25786	1.89448	0.947242	−	0.320519i	$-0.103857\pi$
$19$	8.25786	1.89448	0.947242	+	0.320519i	$0.103857\pi$
$20$	−2.04715	−0.457756
$21$	0	0
$22$	12.9303	2.75676
$23$	−4.74009	−0.988377	−0.494188	−	0.869355i	$-0.664535\pi$
$23$	−4.74009	−0.988377	−0.494188	+	0.869355i	$0.664535\pi$
$24$	−0.278356	−0.0568192
$25$	1.00000	0.200000
$26$	−3.14604	−0.616989
$27$	7.66577	1.47528
$28$	0	0
$29$	4.27563	0.793964	0.396982	−	0.917826i	$-0.370058\pi$
$29$	4.27563	0.793964	0.396982	+	0.917826i	$0.370058\pi$
$30$	5.90379	1.07788
$31$	5.78128	1.03835	0.519174	−	0.854668i	$-0.326240\pi$
$31$	5.78128	1.03835	0.519174	+	0.854668i	$0.326240\pi$
$32$	8.04254	1.42173
$33$	−18.8621	−3.28348
$34$	−12.9204	−2.21584
$35$	0	0
$36$	11.4889	1.91482
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−16.6128	−2.69495
$39$	4.58929	0.734875
$40$	0.0948516	0.0149974
$41$	−6.72419	−1.05014	−0.525071	−	0.851059i	$-0.675961\pi$
$41$	−6.72419	−1.05014	−0.525071	+	0.851059i	$0.675961\pi$
$42$	0	0
$43$	3.24018	0.494122	0.247061	−	0.969000i	$-0.420535\pi$
$43$	3.24018	0.494122	0.247061	+	0.969000i	$0.420535\pi$
$44$	−13.1578	−1.98362
$45$	−5.61216	−0.836612
$46$	9.53589	1.40599
$47$	−4.06467	−0.592893	−0.296446	−	0.955050i	$-0.595802\pi$
$47$	−4.06467	−0.592893	−0.296446	+	0.955050i	$0.595802\pi$
$48$	−11.4553	−1.65344
$49$	0	0
$50$	−2.01175	−0.284505
$51$	18.8477	2.63921
$52$	3.20139	0.443953
$53$	8.37228	1.15002	0.575011	−	0.818146i	$-0.304998\pi$
$53$	8.37228	1.15002	0.575011	+	0.818146i	$0.304998\pi$
$54$	−15.4216	−2.09862
$55$	6.42740	0.866670
$56$	0	0
$57$	24.2339	3.20986
$58$	−8.60151	−1.12943
$59$	9.12809	1.18838	0.594188	−	0.804326i	$-0.297473\pi$
$59$	9.12809	1.18838	0.594188	+	0.804326i	$0.297473\pi$
$60$	−6.00766	−0.775586
$61$	−4.90749	−0.628339	−0.314170	−	0.949367i	$-0.601726\pi$
$61$	−4.90749	−0.628339	−0.314170	+	0.949367i	$0.601726\pi$
$62$	−11.6305	−1.47708
$63$	0	0
$64$	−8.37264	−1.04658
$65$	−1.56383	−0.193969
$66$	37.9460	4.67083
$67$	12.8008	1.56387	0.781933	−	0.623363i	$-0.214234\pi$
$67$	12.8008	1.56387	0.781933	+	0.623363i	$0.214234\pi$
$68$	13.1478	1.59440
$69$	−13.9105	−1.67463
$70$	0	0
$71$	−3.76509	−0.446834	−0.223417	−	0.974723i	$-0.571721\pi$
$71$	−3.76509	−0.446834	−0.223417	+	0.974723i	$0.571721\pi$
$72$	−0.532322	−0.0627348
$73$	−12.3423	−1.44455	−0.722276	−	0.691605i	$-0.756904\pi$
$73$	−12.3423	−1.44455	−0.722276	+	0.691605i	$0.756904\pi$
$74$	−2.01175	−0.233861
$75$	2.93465	0.338864
$76$	16.9051	1.93915
$77$	0	0
$78$	−9.23252	−1.04538
$79$	−8.26105	−0.929441	−0.464720	−	0.885457i	$-0.653845\pi$
$79$	−8.26105	−0.929441	−0.464720	+	0.885457i	$0.653845\pi$
$80$	3.90348	0.436422
$81$	5.65987	0.628874
$82$	13.5274	1.49385
$83$	−8.13625	−0.893069	−0.446534	−	0.894766i	$-0.647342\pi$
$83$	−8.13625	−0.893069	−0.446534	+	0.894766i	$0.647342\pi$
$84$	0	0
$85$	−6.42248	−0.696616
$86$	−6.51843	−0.702901
$87$	12.5475	1.34523
$88$	0.609649	0.0649888
$89$	−6.14981	−0.651879	−0.325940	−	0.945391i	$-0.605681\pi$
$89$	−6.14981	−0.651879	−0.325940	+	0.945391i	$0.605681\pi$
$90$	11.2903	1.19010
$91$	0	0
$92$	−9.70367	−1.01168
$93$	16.9660	1.75929
$94$	8.17710	0.843404
$95$	−8.25786	−0.847239
$96$	23.6020	2.40887
$97$	−2.23767	−0.227201	−0.113600	−	0.993527i	$-0.536238\pi$
$97$	−2.23767	−0.227201	−0.113600	+	0.993527i	$0.536238\pi$
$98$	0	0
$99$	−36.0716	−3.62533
$100$	2.04715	0.204715
$101$	−0.289835	−0.0288396	−0.0144198	−	0.999896i	$-0.504590\pi$
$101$	−0.289835	−0.0288396	−0.0144198	+	0.999896i	$0.504590\pi$
$102$	−37.9169	−3.75434
$103$	1.66793	0.164346	0.0821729	−	0.996618i	$-0.473814\pi$
$103$	1.66793	0.164346	0.0821729	+	0.996618i	$0.473814\pi$
$104$	−0.148332	−0.0145451
$105$	0	0
$106$	−16.8430	−1.63593
$107$	3.56513	0.344654	0.172327	−	0.985040i	$-0.444871\pi$
$107$	3.56513	0.344654	0.172327	+	0.985040i	$0.444871\pi$
$108$	15.6930	1.51006
$109$	12.5860	1.20552	0.602759	−	0.797923i	$-0.294068\pi$
$109$	12.5860	1.20552	0.602759	+	0.797923i	$0.294068\pi$
$110$	−12.9303	−1.23286
$111$	2.93465	0.278545
$112$	0	0
$113$	−2.71289	−0.255208	−0.127604	−	0.991825i	$-0.540729\pi$
$113$	−2.71289	−0.255208	−0.127604	+	0.991825i	$0.540729\pi$
$114$	−48.7527	−4.56611
$115$	4.74009	0.442016
$116$	8.75285	0.812681
$117$	8.77646	0.811384
$118$	−18.3635	−1.69049
$119$	0	0
$120$	0.278356	0.0254103
$121$	30.3114	2.75558
$122$	9.87265	0.893828
$123$	−19.7331	−1.77928
$124$	11.8351	1.06283
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−3.13941	−0.278578	−0.139289	−	0.990252i	$-0.544482\pi$
$127$	−3.13941	−0.278578	−0.139289	+	0.990252i	$0.544482\pi$
$128$	0.758602	0.0670516
$129$	9.50878	0.837201
$130$	3.14604	0.275926
$131$	−16.0759	−1.40456	−0.702281	−	0.711900i	$-0.747835\pi$
$131$	−16.0759	−1.40456	−0.702281	+	0.711900i	$0.747835\pi$
$132$	−38.6136	−3.36088
$133$	0	0
$134$	−25.7520	−2.22464
$135$	−7.66577	−0.659765
$136$	−0.609182	−0.0522369
$137$	−6.90058	−0.589556	−0.294778	−	0.955566i	$-0.595246\pi$
$137$	−6.90058	−0.589556	−0.294778	+	0.955566i	$0.595246\pi$
$138$	27.9845	2.38220
$139$	13.5523	1.14949	0.574747	−	0.818331i	$-0.305100\pi$
$139$	13.5523	1.14949	0.574747	+	0.818331i	$0.305100\pi$
$140$	0	0
$141$	−11.9284	−1.00455
$142$	7.57443	0.635632
$143$	−10.0514	−0.840536
$144$	−21.9070	−1.82558
$145$	−4.27563	−0.355072
$146$	24.8296	2.05491
$147$	0	0
$148$	2.04715	0.168275
$149$	9.90556	0.811495	0.405747	−	0.913985i	$-0.367011\pi$
$149$	9.90556	0.811495	0.405747	+	0.913985i	$0.367011\pi$
$150$	−5.90379	−0.482042
$151$	4.63753	0.377397	0.188699	−	0.982035i	$-0.439573\pi$
$151$	4.63753	0.377397	0.188699	+	0.982035i	$0.439573\pi$
$152$	−0.783271	−0.0635317
$153$	36.0440	2.91398
$154$	0	0
$155$	−5.78128	−0.464364
$156$	9.39496	0.752199
$157$	−10.7674	−0.859329	−0.429665	−	0.902989i	$-0.641368\pi$
$157$	−10.7674	−0.859329	−0.429665	+	0.902989i	$0.641368\pi$
$158$	16.6192	1.32215
$159$	24.5697	1.94850
$160$	−8.04254	−0.635818
$161$	0	0
$162$	−11.3863	−0.894589
$163$	7.56859	0.592818	0.296409	−	0.955061i	$-0.404211\pi$
$163$	7.56859	0.592818	0.296409	+	0.955061i	$0.404211\pi$
$164$	−13.7654	−1.07490
$165$	18.8621	1.46842
$166$	16.3681	1.27041
$167$	−25.0686	−1.93987	−0.969933	−	0.243371i	$-0.921747\pi$
$167$	−25.0686	−1.93987	−0.969933	+	0.243371i	$0.921747\pi$
$168$	0	0
$169$	−10.5544	−0.811880
$170$	12.9204	0.990952
$171$	46.3445	3.54405
$172$	6.63312	0.505771
$173$	10.6891	0.812679	0.406340	−	0.913722i	$-0.366805\pi$
$173$	10.6891	0.812679	0.406340	+	0.913722i	$0.366805\pi$
$174$	−25.2424	−1.91362
$175$	0	0
$176$	25.0892	1.89117
$177$	26.7877	2.01349
$178$	12.3719	0.927314
$179$	11.8676	0.887027	0.443513	−	0.896268i	$-0.353732\pi$
$179$	11.8676	0.887027	0.443513	+	0.896268i	$0.353732\pi$
$180$	−11.4889	−0.856334
$181$	12.4641	0.926452	0.463226	−	0.886240i	$-0.346692\pi$
$181$	12.4641	0.926452	0.463226	+	0.886240i	$0.346692\pi$
$182$	0	0
$183$	−14.4017	−1.06461
$184$	0.449605	0.0331453
$185$	−1.00000	−0.0735215
$186$	−34.1314	−2.50264
$187$	−41.2798	−3.01868
$188$	−8.32098	−0.606870
$189$	0	0
$190$	16.6128	1.20522
$191$	14.3266	1.03663	0.518317	−	0.855188i	$-0.326559\pi$
$191$	14.3266	1.03663	0.518317	+	0.855188i	$0.326559\pi$
$192$	−24.5708	−1.77324
$193$	−2.69030	−0.193652	−0.0968259	−	0.995301i	$-0.530869\pi$
$193$	−2.69030	−0.193652	−0.0968259	+	0.995301i	$0.530869\pi$
$194$	4.50163	0.323198
$195$	−4.58929	−0.328646
$196$	0	0
$197$	9.87464	0.703539	0.351769	−	0.936087i	$-0.385580\pi$
$197$	9.87464	0.703539	0.351769	+	0.936087i	$0.385580\pi$
$198$	72.5671	5.15712
$199$	24.4248	1.73143	0.865713	−	0.500541i	$-0.166865\pi$
$199$	24.4248	1.73143	0.865713	+	0.500541i	$0.166865\pi$
$200$	−0.0948516	−0.00670702
$201$	37.5658	2.64969
$202$	0.583076	0.0410251
$203$	0	0
$204$	38.5841	2.70143
$205$	6.72419	0.469637
$206$	−3.35546	−0.233786
$207$	−26.6021	−1.84898
$208$	−6.10438	−0.423262
$209$	−53.0766	−3.67138
$210$	0	0
$211$	−20.5880	−1.41734	−0.708668	−	0.705542i	$-0.750704\pi$
$211$	−20.5880	−1.41734	−0.708668	+	0.705542i	$0.750704\pi$
$212$	17.1393	1.17713
$213$	−11.0492	−0.757080
$214$	−7.17216	−0.490279
$215$	−3.24018	−0.220978
$216$	−0.727111	−0.0494736
$217$	0	0
$218$	−25.3199	−1.71488
$219$	−36.2202	−2.44753
$220$	13.1578	0.887101
$221$	10.0437	0.675610
$222$	−5.90379	−0.396236
$223$	4.33966	0.290605	0.145303	−	0.989387i	$-0.453584\pi$
$223$	4.33966	0.290605	0.145303	+	0.989387i	$0.453584\pi$
$224$	0	0
$225$	5.61216	0.374144
$226$	5.45767	0.363039
$227$	1.51458	0.100526	0.0502631	−	0.998736i	$-0.483994\pi$
$227$	1.51458	0.100526	0.0502631	+	0.998736i	$0.483994\pi$
$228$	49.6105	3.28553
$229$	24.9060	1.64583	0.822916	−	0.568162i	$-0.192345\pi$
$229$	24.9060	1.64583	0.822916	+	0.568162i	$0.192345\pi$
$230$	−9.53589	−0.628778
$231$	0	0
$232$	−0.405550	−0.0266257
$233$	−1.66186	−0.108872	−0.0544361	−	0.998517i	$-0.517336\pi$
$233$	−1.66186	−0.108872	−0.0544361	+	0.998517i	$0.517336\pi$
$234$	−17.6561	−1.15421
$235$	4.06467	0.265150
$236$	18.6866	1.21639
$237$	−24.2433	−1.57477
$238$	0	0
$239$	21.3246	1.37938	0.689688	−	0.724107i	$-0.257748\pi$
$239$	21.3246	1.37938	0.689688	+	0.724107i	$0.257748\pi$
$240$	11.4553	0.739439
$241$	2.86268	0.184401	0.0922007	−	0.995740i	$-0.470610\pi$
$241$	2.86268	0.184401	0.0922007	+	0.995740i	$0.470610\pi$
$242$	−60.9791	−3.91988
$243$	−6.38760	−0.409764
$244$	−10.0464	−0.643152
$245$	0	0
$246$	39.6982	2.53106
$247$	12.9139	0.821691
$248$	−0.548363	−0.0348211
$249$	−23.8770	−1.51314
$250$	2.01175	0.127234
$251$	−3.59322	−0.226802	−0.113401	−	0.993549i	$-0.536174\pi$
$251$	−3.59322	−0.226802	−0.113401	+	0.993549i	$0.536174\pi$
$252$	0	0
$253$	30.4664	1.91541
$254$	6.31572	0.396284
$255$	−18.8477	−1.18029
$256$	15.2192	0.951197
$257$	6.27930	0.391692	0.195846	−	0.980635i	$-0.437255\pi$
$257$	6.27930	0.391692	0.195846	+	0.980635i	$0.437255\pi$
$258$	−19.1293	−1.19094
$259$	0	0
$260$	−3.20139	−0.198542
$261$	23.9955	1.48528
$262$	32.3408	1.99802
$263$	8.21428	0.506514	0.253257	−	0.967399i	$-0.418498\pi$
$263$	8.21428	0.506514	0.253257	+	0.967399i	$0.418498\pi$
$264$	1.78910	0.110112
$265$	−8.37228	−0.514305
$266$	0	0
$267$	−18.0475	−1.10449
$268$	26.2051	1.60073
$269$	16.3316	0.995755	0.497877	−	0.867247i	$-0.334113\pi$
$269$	16.3316	0.995755	0.497877	+	0.867247i	$0.334113\pi$
$270$	15.4216	0.938531
$271$	3.07096	0.186548	0.0932739	−	0.995640i	$-0.470267\pi$
$271$	3.07096	0.186548	0.0932739	+	0.995640i	$0.470267\pi$
$272$	−25.0700	−1.52009
$273$	0	0
$274$	13.8823	0.838657
$275$	−6.42740	−0.387587
$276$	−28.4769	−1.71411
$277$	20.3242	1.22116	0.610581	−	0.791954i	$-0.290936\pi$
$277$	20.3242	1.22116	0.610581	+	0.791954i	$0.290936\pi$
$278$	−27.2639	−1.63518
$279$	32.4455	1.94246
$280$	0	0
$281$	−21.8771	−1.30508	−0.652538	−	0.757756i	$-0.726296\pi$
$281$	−21.8771	−1.30508	−0.652538	+	0.757756i	$0.726296\pi$
$282$	23.9969	1.42900
$283$	−25.3898	−1.50927	−0.754633	−	0.656147i	$-0.772185\pi$
$283$	−25.3898	−1.50927	−0.754633	+	0.656147i	$0.772185\pi$
$284$	−7.70770	−0.457368
$285$	−24.2339	−1.43549
$286$	20.2208	1.19568
$287$	0	0
$288$	45.1360	2.65967
$289$	24.2482	1.42637
$290$	8.60151	0.505098
$291$	−6.56677	−0.384951
$292$	−25.2664	−1.47861
$293$	27.4406	1.60310	0.801550	−	0.597928i	$-0.204009\pi$
$293$	27.4406	1.60310	0.801550	+	0.597928i	$0.204009\pi$
$294$	0	0
$295$	−9.12809	−0.531458
$296$	−0.0948516	−0.00551314
$297$	−49.2710	−2.85899
$298$	−19.9275	−1.15437
$299$	−7.41269	−0.428687
$300$	6.00766	0.346853
$301$	0	0
$302$	−9.32957	−0.536856
$303$	−0.850563	−0.0488636
$304$	−32.2344	−1.84877
$305$	4.90749	0.281002
$306$	−72.5116	−4.14521
$307$	19.7184	1.12539	0.562696	−	0.826664i	$-0.309764\pi$
$307$	19.7184	1.12539	0.562696	+	0.826664i	$0.309764\pi$
$308$	0	0
$309$	4.89478	0.278454
$310$	11.6305	0.660568
$311$	22.7298	1.28889	0.644445	−	0.764651i	$-0.277088\pi$
$311$	22.7298	1.28889	0.644445	+	0.764651i	$0.277088\pi$
$312$	−0.435301	−0.0246441
$313$	−16.2641	−0.919301	−0.459650	−	0.888100i	$-0.652025\pi$
$313$	−16.2641	−0.919301	−0.459650	+	0.888100i	$0.652025\pi$
$314$	21.6613	1.22242
$315$	0	0
$316$	−16.9116	−0.951352
$317$	−28.3073	−1.58989	−0.794947	−	0.606679i	$-0.792501\pi$
$317$	−28.3073	−1.58989	−0.794947	+	0.606679i	$0.792501\pi$
$318$	−49.4282	−2.77179
$319$	−27.4812	−1.53865
$320$	8.37264	0.468045
$321$	10.4624	0.583954
$322$	0	0
$323$	53.0360	2.95100
$324$	11.5866	0.643700
$325$	1.56383	0.0867457
$326$	−15.2261	−0.843297
$327$	36.9354	2.04253
$328$	0.637800	0.0352166
$329$	0	0
$330$	−37.9460	−2.08886
$331$	2.68702	0.147692	0.0738460	−	0.997270i	$-0.476473\pi$
$331$	2.68702	0.147692	0.0738460	+	0.997270i	$0.476473\pi$
$332$	−16.6561	−0.914122
$333$	5.61216	0.307545
$334$	50.4318	2.75951
$335$	−12.8008	−0.699382
$336$	0	0
$337$	7.33690	0.399667	0.199833	−	0.979830i	$-0.435960\pi$
$337$	7.33690	0.399667	0.199833	+	0.979830i	$0.435960\pi$
$338$	21.2329	1.15492
$339$	−7.96139	−0.432403
$340$	−13.1478	−0.713038
$341$	−37.1586	−2.01225
$342$	−93.2336	−5.04150
$343$	0	0
$344$	−0.307336	−0.0165704
$345$	13.9105	0.748916
$346$	−21.5039	−1.15606
$347$	22.2481	1.19434	0.597170	−	0.802115i	$-0.296292\pi$
$347$	22.2481	1.19434	0.597170	+	0.802115i	$0.296292\pi$
$348$	25.6865	1.37694
$349$	26.0185	1.39274	0.696369	−	0.717684i	$-0.254798\pi$
$349$	26.0185	1.39274	0.696369	+	0.717684i	$0.254798\pi$
$350$	0	0
$351$	11.9880	0.639870
$352$	−51.6926	−2.75522
$353$	33.0688	1.76007	0.880037	−	0.474905i	$-0.157517\pi$
$353$	33.0688	1.76007	0.880037	+	0.474905i	$0.157517\pi$
$354$	−53.8903	−2.86424
$355$	3.76509	0.199830
$356$	−12.5896	−0.667247
$357$	0	0
$358$	−23.8747	−1.26182
$359$	11.1500	0.588476	0.294238	−	0.955732i	$-0.404934\pi$
$359$	11.1500	0.588476	0.294238	+	0.955732i	$0.404934\pi$
$360$	0.532322	0.0280558
$361$	49.1923	2.58907
$362$	−25.0748	−1.31790
$363$	88.9534	4.66884
$364$	0	0
$365$	12.3423	0.646024
$366$	28.9728	1.51443
$367$	34.7949	1.81628	0.908141	−	0.418665i	$-0.137502\pi$
$367$	34.7949	1.81628	0.908141	+	0.418665i	$0.137502\pi$
$368$	18.5028	0.964527
$369$	−37.7372	−1.96452
$370$	2.01175	0.104586
$371$	0	0
$372$	34.7320	1.80077
$373$	−18.0042	−0.932224	−0.466112	−	0.884726i	$-0.654346\pi$
$373$	−18.0042	−0.932224	−0.466112	+	0.884726i	$0.654346\pi$
$374$	83.0448	4.29414
$375$	−2.93465	−0.151545
$376$	0.385540	0.0198827
$377$	6.68635	0.344365
$378$	0	0
$379$	12.8719	0.661183	0.330592	−	0.943774i	$-0.392752\pi$
$379$	12.8719	0.661183	0.330592	+	0.943774i	$0.392752\pi$
$380$	−16.9051	−0.867212
$381$	−9.21308	−0.472000
$382$	−28.8215	−1.47464
$383$	−14.1145	−0.721219	−0.360609	−	0.932717i	$-0.617431\pi$
$383$	−14.1145	−0.721219	−0.360609	+	0.932717i	$0.617431\pi$
$384$	2.22623	0.113607
$385$	0	0
$386$	5.41221	0.275474
$387$	18.1844	0.924365
$388$	−4.58084	−0.232557
$389$	12.0554	0.611235	0.305618	−	0.952154i	$-0.401137\pi$
$389$	12.0554	0.611235	0.305618	+	0.952154i	$0.401137\pi$
$390$	9.23252	0.467507
$391$	−30.4431	−1.53957
$392$	0	0
$393$	−47.1773	−2.37978
$394$	−19.8653	−1.00080
$395$	8.26105	0.415659
$396$	−73.8439	−3.71080
$397$	8.27549	0.415335	0.207668	−	0.978199i	$-0.433413\pi$
$397$	8.27549	0.415335	0.207668	+	0.978199i	$0.433413\pi$
$398$	−49.1366	−2.46299
$399$	0	0
$400$	−3.90348	−0.195174
$401$	−4.03248	−0.201373	−0.100686	−	0.994918i	$-0.532104\pi$
$401$	−4.03248	−0.201373	−0.100686	+	0.994918i	$0.532104\pi$
$402$	−75.5731	−3.76925
$403$	9.04094	0.450361
$404$	−0.593335	−0.0295195
$405$	−5.65987	−0.281241
$406$	0	0
$407$	−6.42740	−0.318594
$408$	−1.78774	−0.0885061
$409$	−10.2150	−0.505101	−0.252550	−	0.967584i	$-0.581269\pi$
$409$	−10.2150	−0.505101	−0.252550	+	0.967584i	$0.581269\pi$
$410$	−13.5274	−0.668071
$411$	−20.2508	−0.998897
$412$	3.41449	0.168220
$413$	0	0
$414$	53.5169	2.63021
$415$	8.13625	0.399393
$416$	12.5772	0.616646
$417$	39.7713	1.94761
$418$	106.777	5.22263
$419$	−23.2222	−1.13448	−0.567240	−	0.823553i	$-0.691989\pi$
$419$	−23.2222	−1.13448	−0.567240	+	0.823553i	$0.691989\pi$
$420$	0	0
$421$	−14.1906	−0.691606	−0.345803	−	0.938307i	$-0.612393\pi$
$421$	−14.1906	−0.691606	−0.345803	+	0.938307i	$0.612393\pi$
$422$	41.4180	2.01620
$423$	−22.8116	−1.10914
$424$	−0.794124	−0.0385661
$425$	6.42248	0.311536
$426$	22.2283	1.07696
$427$	0	0
$428$	7.29835	0.352779
$429$	−29.4972	−1.42414
$430$	6.51843	0.314347
$431$	−6.09547	−0.293609	−0.146804	−	0.989166i	$-0.546899\pi$
$431$	−6.09547	−0.293609	−0.146804	+	0.989166i	$0.546899\pi$
$432$	−29.9232	−1.43968
$433$	38.7673	1.86304	0.931520	−	0.363691i	$-0.118484\pi$
$433$	38.7673	1.86304	0.931520	+	0.363691i	$0.118484\pi$
$434$	0	0
$435$	−12.5475	−0.601605
$436$	25.7654	1.23394
$437$	−39.1430	−1.87246
$438$	72.8661	3.48168
$439$	26.9185	1.28475	0.642375	−	0.766390i	$-0.277949\pi$
$439$	26.9185	1.28475	0.642375	+	0.766390i	$0.277949\pi$
$440$	−0.609649	−0.0290639
$441$	0	0
$442$	−20.2054	−0.961071
$443$	25.4368	1.20854	0.604270	−	0.796780i	$-0.293465\pi$
$443$	25.4368	1.20854	0.604270	+	0.796780i	$0.293465\pi$
$444$	6.00766	0.285111
$445$	6.14981	0.291529
$446$	−8.73033	−0.413393
$447$	29.0693	1.37493
$448$	0	0
$449$	−0.175865	−0.00829959	−0.00414980	−	0.999991i	$-0.501321\pi$
$449$	−0.175865	−0.00829959	−0.00414980	+	0.999991i	$0.501321\pi$
$450$	−11.2903	−0.532229
$451$	43.2190	2.03510
$452$	−5.55370	−0.261224
$453$	13.6095	0.639431
$454$	−3.04696	−0.143001
$455$	0	0
$456$	−2.29863	−0.107643
$457$	−35.1594	−1.64469	−0.822344	−	0.568990i	$-0.807334\pi$
$457$	−35.1594	−1.64469	−0.822344	+	0.568990i	$0.807334\pi$
$458$	−50.1047	−2.34124
$459$	49.2333	2.29801
$460$	9.70367	0.452436
$461$	28.2627	1.31633	0.658163	−	0.752876i	$-0.271334\pi$
$461$	28.2627	1.31633	0.658163	+	0.752876i	$0.271334\pi$
$462$	0	0
$463$	27.8108	1.29248	0.646240	−	0.763135i	$-0.276341\pi$
$463$	27.8108	1.29248	0.646240	+	0.763135i	$0.276341\pi$
$464$	−16.6898	−0.774806
$465$	−16.9660	−0.786781
$466$	3.34325	0.154873
$467$	37.3591	1.72877	0.864386	−	0.502829i	$-0.167708\pi$
$467$	37.3591	1.72877	0.864386	+	0.502829i	$0.167708\pi$
$468$	17.9667	0.830512
$469$	0	0
$470$	−8.17710	−0.377182
$471$	−31.5984	−1.45598
$472$	−0.865814	−0.0398523
$473$	−20.8259	−0.957576
$474$	48.7715	2.24015
$475$	8.25786	0.378897
$476$	0	0
$477$	46.9866	2.15137
$478$	−42.8999	−1.96219
$479$	−34.9838	−1.59845	−0.799226	−	0.601031i	$-0.794757\pi$
$479$	−34.9838	−1.59845	−0.799226	+	0.601031i	$0.794757\pi$
$480$	−23.6020	−1.07728
$481$	1.56383	0.0713045
$482$	−5.75901	−0.262316
$483$	0	0
$484$	62.0520	2.82055
$485$	2.23767	0.101607
$486$	12.8503	0.582900
$487$	10.6963	0.484695	0.242347	−	0.970190i	$-0.422083\pi$
$487$	10.6963	0.484695	0.242347	+	0.970190i	$0.422083\pi$
$488$	0.465483	0.0210714
$489$	22.2111	1.00442
$490$	0	0
$491$	6.26832	0.282885	0.141443	−	0.989946i	$-0.454826\pi$
$491$	6.26832	0.282885	0.141443	+	0.989946i	$0.454826\pi$
$492$	−40.3966	−1.82122
$493$	27.4601	1.23674
$494$	−25.9796	−1.16888
$495$	36.0716	1.62130
$496$	−22.5671	−1.01329
$497$	0	0
$498$	48.0347	2.15248
$499$	−2.18333	−0.0977393	−0.0488697	−	0.998805i	$-0.515562\pi$
$499$	−2.18333	−0.0977393	−0.0488697	+	0.998805i	$0.515562\pi$
$500$	−2.04715	−0.0915513
$501$	−73.5675	−3.28675
$502$	7.22867	0.322631
$503$	9.88222	0.440626	0.220313	−	0.975429i	$-0.429292\pi$
$503$	9.88222	0.440626	0.220313	+	0.975429i	$0.429292\pi$
$504$	0	0
$505$	0.289835	0.0128975
$506$	−61.2909	−2.72471
$507$	−30.9736	−1.37558
$508$	−6.42685	−0.285145
$509$	−26.0927	−1.15654	−0.578269	−	0.815846i	$-0.696272\pi$
$509$	−26.0927	−1.15654	−0.578269	+	0.815846i	$0.696272\pi$
$510$	37.9169	1.67899
$511$	0	0
$512$	−32.1344	−1.42015
$513$	63.3029	2.79489
$514$	−12.6324	−0.557191
$515$	−1.66793	−0.0734976
$516$	19.4659	0.856938
$517$	26.1252	1.14899
$518$	0	0
$519$	31.3688	1.37694
$520$	0.148332	0.00650478
$521$	−16.6498	−0.729440	−0.364720	−	0.931117i	$-0.618835\pi$
$521$	−16.6498	−0.729440	−0.364720	+	0.931117i	$0.618835\pi$
$522$	−48.2730	−2.11285
$523$	−13.6835	−0.598339	−0.299170	−	0.954200i	$-0.596710\pi$
$523$	−13.6835	−0.598339	−0.299170	+	0.954200i	$0.596710\pi$
$524$	−32.9099	−1.43767
$525$	0	0
$526$	−16.5251	−0.720529
$527$	37.1301	1.61741
$528$	73.6280	3.20425
$529$	−0.531556	−0.0231111
$530$	16.8430	0.731611
$531$	51.2283	2.22312
$532$	0	0
$533$	−10.5155	−0.455476
$534$	36.3072	1.57117
$535$	−3.56513	−0.154134
$536$	−1.21418	−0.0524444
$537$	34.8273	1.50291
$538$	−32.8551	−1.41648
$539$	0	0
$540$	−15.6930	−0.675318
$541$	−39.7309	−1.70816	−0.854081	−	0.520139i	$-0.825880\pi$
$541$	−39.7309	−1.70816	−0.854081	+	0.520139i	$0.825880\pi$
$542$	−6.17802	−0.265369
$543$	36.5779	1.56971
$544$	51.6530	2.21461
$545$	−12.5860	−0.539124
$546$	0	0
$547$	8.11088	0.346796	0.173398	−	0.984852i	$-0.444525\pi$
$547$	8.11088	0.346796	0.173398	+	0.984852i	$0.444525\pi$
$548$	−14.1265	−0.603454
$549$	−27.5416	−1.17545
$550$	12.9303	0.551351
$551$	35.3076	1.50415
$552$	1.31943	0.0561588
$553$	0	0
$554$	−40.8872	−1.73713
$555$	−2.93465	−0.124569
$556$	27.7436	1.17659
$557$	33.7732	1.43102	0.715509	−	0.698604i	$-0.246195\pi$
$557$	33.7732	1.43102	0.715509	+	0.698604i	$0.246195\pi$
$558$	−65.2723	−2.76320
$559$	5.06709	0.214315
$560$	0	0
$561$	−121.142	−5.11461
$562$	44.0112	1.85650
$563$	15.1641	0.639093	0.319546	−	0.947571i	$-0.396470\pi$
$563$	15.1641	0.639093	0.319546	+	0.947571i	$0.396470\pi$
$564$	−24.4191	−1.02823
$565$	2.71289	0.114132
$566$	51.0780	2.14697
$567$	0	0
$568$	0.357125	0.0149846
$569$	35.2915	1.47950	0.739748	−	0.672884i	$-0.234945\pi$
$569$	35.2915	1.47950	0.739748	+	0.672884i	$0.234945\pi$
$570$	48.7527	2.04202
$571$	23.2351	0.972360	0.486180	−	0.873859i	$-0.338390\pi$
$571$	23.2351	0.972360	0.486180	+	0.873859i	$0.338390\pi$
$572$	−20.5766	−0.860352
$573$	42.0435	1.75639
$574$	0	0
$575$	−4.74009	−0.197675
$576$	−46.9886	−1.95786
$577$	−29.2985	−1.21971	−0.609856	−	0.792512i	$-0.708773\pi$
$577$	−29.2985	−1.21971	−0.609856	+	0.792512i	$0.708773\pi$
$578$	−48.7814	−2.02904
$579$	−7.89507	−0.328108
$580$	−8.75285	−0.363442
$581$	0	0
$582$	13.2107	0.547602
$583$	−53.8120	−2.22866
$584$	1.17068	0.0484432
$585$	−8.77646	−0.362862
$586$	−55.2038	−2.28045
$587$	−32.4500	−1.33935	−0.669677	−	0.742652i	$-0.733568\pi$
$587$	−32.4500	−1.33935	−0.669677	+	0.742652i	$0.733568\pi$
$588$	0	0
$589$	47.7410	1.96713
$590$	18.3635	0.756012
$591$	28.9786	1.19202
$592$	−3.90348	−0.160432
$593$	−10.7567	−0.441724	−0.220862	−	0.975305i	$-0.570887\pi$
$593$	−10.7567	−0.441724	−0.220862	+	0.975305i	$0.570887\pi$
$594$	99.1210	4.06698
$595$	0	0
$596$	20.2781	0.830625
$597$	71.6781	2.93359
$598$	14.9125	0.609818
$599$	−39.9189	−1.63104	−0.815521	−	0.578728i	$-0.803549\pi$
$599$	−39.9189	−1.63104	−0.815521	+	0.578728i	$0.803549\pi$
$600$	−0.278356	−0.0113638
$601$	−25.1479	−1.02580	−0.512901	−	0.858448i	$-0.671429\pi$
$601$	−25.1479	−1.02580	−0.512901	+	0.858448i	$0.671429\pi$
$602$	0	0
$603$	71.8401	2.92556
$604$	9.49372	0.386294
$605$	−30.3114	−1.23233
$606$	1.71112	0.0695096
$607$	3.99083	0.161983	0.0809913	−	0.996715i	$-0.474191\pi$
$607$	3.99083	0.161983	0.0809913	+	0.996715i	$0.474191\pi$
$608$	66.4142	2.69345
$609$	0	0
$610$	−9.87265	−0.399732
$611$	−6.35645	−0.257154
$612$	73.7874	2.98268
$613$	−14.4977	−0.585557	−0.292778	−	0.956180i	$-0.594580\pi$
$613$	−14.4977	−0.585557	−0.292778	+	0.956180i	$0.594580\pi$
$614$	−39.6686	−1.60090
$615$	19.7331	0.795716
$616$	0	0
$617$	−34.9942	−1.40882	−0.704408	−	0.709796i	$-0.748787\pi$
$617$	−34.9942	−1.40882	−0.704408	+	0.709796i	$0.748787\pi$
$618$	−9.84708	−0.396108
$619$	−30.3236	−1.21881	−0.609403	−	0.792860i	$-0.708591\pi$
$619$	−30.3236	−1.21881	−0.609403	+	0.792860i	$0.708591\pi$
$620$	−11.8351	−0.475311
$621$	−36.3365	−1.45813
$622$	−45.7268	−1.83348
$623$	0	0
$624$	−17.9142	−0.717142
$625$	1.00000	0.0400000
$626$	32.7193	1.30773
$627$	−155.761	−6.22050
$628$	−22.0424	−0.879587
$629$	6.42248	0.256081
$630$	0	0
$631$	−39.0682	−1.55528	−0.777640	−	0.628710i	$-0.783583\pi$
$631$	−39.0682	−1.55528	−0.777640	+	0.628710i	$0.783583\pi$
$632$	0.783574	0.0311689
$633$	−60.4186	−2.40142
$634$	56.9472	2.26166
$635$	3.13941	0.124584
$636$	50.2978	1.99444
$637$	0	0
$638$	55.2853	2.18877
$639$	−21.1303	−0.835902
$640$	−0.758602	−0.0299864
$641$	−31.6127	−1.24863	−0.624313	−	0.781175i	$-0.714621\pi$
$641$	−31.6127	−1.24863	−0.624313	+	0.781175i	$0.714621\pi$
$642$	−21.0478	−0.830689
$643$	−39.2552	−1.54807	−0.774037	−	0.633140i	$-0.781766\pi$
$643$	−39.2552	−1.54807	−0.774037	+	0.633140i	$0.781766\pi$
$644$	0	0
$645$	−9.50878	−0.374408
$646$	−106.695	−4.19787
$647$	26.4858	1.04126	0.520632	−	0.853781i	$-0.325696\pi$
$647$	26.4858	1.04126	0.520632	+	0.853781i	$0.325696\pi$
$648$	−0.536848	−0.0210894
$649$	−58.6699	−2.30299
$650$	−3.14604	−0.123398
$651$	0	0
$652$	15.4940	0.606793
$653$	25.4808	0.997139	0.498570	−	0.866850i	$-0.333859\pi$
$653$	25.4808	0.997139	0.498570	+	0.866850i	$0.333859\pi$
$654$	−74.3050	−2.90555
$655$	16.0759	0.628139
$656$	26.2477	1.02480
$657$	−69.2668	−2.70235
$658$	0	0
$659$	9.28315	0.361620	0.180810	−	0.983518i	$-0.442128\pi$
$659$	9.28315	0.361620	0.180810	+	0.983518i	$0.442128\pi$
$660$	38.6136	1.50303
$661$	−35.7283	−1.38967	−0.694834	−	0.719170i	$-0.744522\pi$
$661$	−35.7283	−1.38967	−0.694834	+	0.719170i	$0.744522\pi$
$662$	−5.40562	−0.210095
$663$	29.4746	1.14470
$664$	0.771736	0.0299492
$665$	0	0
$666$	−11.2903	−0.437489
$667$	−20.2669	−0.784736
$668$	−51.3192	−1.98560
$669$	12.7354	0.492378
$670$	25.7520	0.994888
$671$	31.5424	1.21768
$672$	0	0
$673$	44.0035	1.69621	0.848105	−	0.529828i	$-0.177744\pi$
$673$	44.0035	1.69621	0.848105	+	0.529828i	$0.177744\pi$
$674$	−14.7600	−0.568535
$675$	7.66577	0.295056
$676$	−21.6065	−0.831019
$677$	−15.3869	−0.591365	−0.295683	−	0.955286i	$-0.595547\pi$
$677$	−15.3869	−0.591365	−0.295683	+	0.955286i	$0.595547\pi$
$678$	16.0163	0.615104
$679$	0	0
$680$	0.609182	0.0233611
$681$	4.44476	0.170324
$682$	74.7539	2.86247
$683$	0.507034	0.0194011	0.00970055	−	0.999953i	$-0.496912\pi$
$683$	0.507034	0.0194011	0.00970055	+	0.999953i	$0.496912\pi$
$684$	94.8740	3.62760
$685$	6.90058	0.263657
$686$	0	0
$687$	73.0903	2.78857
$688$	−12.6480	−0.482199
$689$	13.0928	0.498797
$690$	−27.9845	−1.06535
$691$	21.6468	0.823482	0.411741	−	0.911301i	$-0.364921\pi$
$691$	21.6468	0.823482	0.411741	+	0.911301i	$0.364921\pi$
$692$	21.8822	0.831838
$693$	0	0
$694$	−44.7577	−1.69898
$695$	−13.5523	−0.514069
$696$	−1.19015	−0.0451124
$697$	−43.1859	−1.63578
$698$	−52.3427	−1.98120
$699$	−4.87698	−0.184464
$700$	0	0
$701$	−16.4723	−0.622151	−0.311075	−	0.950385i	$-0.600689\pi$
$701$	−16.4723	−0.622151	−0.311075	+	0.950385i	$0.600689\pi$
$702$	−24.1168	−0.910231
$703$	8.25786	0.311451
$704$	53.8143	2.02820
$705$	11.9284	0.449248
$706$	−66.5262	−2.50375
$707$	0	0
$708$	54.8385	2.06096
$709$	−43.2714	−1.62509	−0.812547	−	0.582896i	$-0.801919\pi$
$709$	−43.2714	−1.62509	−0.812547	+	0.582896i	$0.801919\pi$
$710$	−7.57443	−0.284263
$711$	−46.3624	−1.73872
$712$	0.583320	0.0218608
$713$	−27.4038	−1.02628
$714$	0	0
$715$	10.0514	0.375899
$716$	24.2948	0.907938
$717$	62.5803	2.33710
$718$	−22.4311	−0.837121
$719$	13.0640	0.487203	0.243602	−	0.969875i	$-0.421671\pi$
$719$	13.0640	0.487203	0.243602	+	0.969875i	$0.421671\pi$
$720$	21.9070	0.816424
$721$	0	0
$722$	−98.9628	−3.68301
$723$	8.40096	0.312435
$724$	25.5160	0.948293
$725$	4.27563	0.158793
$726$	−178.952	−6.64154
$727$	19.8197	0.735071	0.367536	−	0.930009i	$-0.380202\pi$
$727$	19.8197	0.735071	0.367536	+	0.930009i	$0.380202\pi$
$728$	0	0
$729$	−35.7250	−1.32315
$730$	−24.8296	−0.918984
$731$	20.8100	0.769684
$732$	−29.4825	−1.08971
$733$	8.21599	0.303465	0.151732	−	0.988422i	$-0.451515\pi$
$733$	8.21599	0.303465	0.151732	+	0.988422i	$0.451515\pi$
$734$	−69.9988	−2.58370
$735$	0	0
$736$	−38.1223	−1.40521
$737$	−82.2758	−3.03067
$738$	75.9179	2.79458
$739$	−11.6985	−0.430337	−0.215168	−	0.976577i	$-0.569030\pi$
$739$	−11.6985	−0.430337	−0.215168	+	0.976577i	$0.569030\pi$
$740$	−2.04715	−0.0752547
$741$	37.8977	1.39221
$742$	0	0
$743$	3.80003	0.139410	0.0697049	−	0.997568i	$-0.477794\pi$
$743$	3.80003	0.139410	0.0697049	+	0.997568i	$0.477794\pi$
$744$	−1.60925	−0.0589981
$745$	−9.90556	−0.362911
$746$	36.2201	1.32611
$747$	−45.6619	−1.67068
$748$	−84.5059	−3.08984
$749$	0	0
$750$	5.90379	0.215576
$751$	−7.81264	−0.285087	−0.142544	−	0.989789i	$-0.545528\pi$
$751$	−7.81264	−0.285087	−0.142544	+	0.989789i	$0.545528\pi$
$752$	15.8663	0.578586
$753$	−10.5448	−0.384275
$754$	−13.4513	−0.489867
$755$	−4.63753	−0.168777
$756$	0	0
$757$	33.3188	1.21099	0.605495	−	0.795849i	$-0.292975\pi$
$757$	33.3188	1.21099	0.605495	+	0.795849i	$0.292975\pi$
$758$	−25.8950	−0.940549
$759$	89.4083	3.24531
$760$	0.783271	0.0284122
$761$	−2.78495	−0.100954	−0.0504771	−	0.998725i	$-0.516074\pi$
$761$	−2.78495	−0.100954	−0.0504771	+	0.998725i	$0.516074\pi$
$762$	18.5344	0.671432
$763$	0	0
$764$	29.3286	1.06107
$765$	−36.0440	−1.30317
$766$	28.3949	1.02595
$767$	14.2748	0.515432
$768$	44.6629	1.61163
$769$	19.0285	0.686184	0.343092	−	0.939302i	$-0.388526\pi$
$769$	19.0285	0.686184	0.343092	+	0.939302i	$0.388526\pi$
$770$	0	0
$771$	18.4275	0.663651
$772$	−5.50744	−0.198217
$773$	3.51173	0.126308	0.0631541	−	0.998004i	$-0.479884\pi$
$773$	3.51173	0.126308	0.0631541	+	0.998004i	$0.479884\pi$
$774$	−36.5825	−1.31493
$775$	5.78128	0.207670
$776$	0.212246	0.00761920
$777$	0	0
$778$	−24.2526	−0.869497
$779$	−55.5274	−1.98948
$780$	−9.39496	−0.336394
$781$	24.1997	0.865935
$782$	61.2440	2.19008
$783$	32.7760	1.17132
$784$	0	0
$785$	10.7674	0.384304
$786$	94.9090	3.38529
$787$	11.1812	0.398568	0.199284	−	0.979942i	$-0.436138\pi$
$787$	11.1812	0.398568	0.199284	+	0.979942i	$0.436138\pi$
$788$	20.2148	0.720124
$789$	24.1060	0.858197
$790$	−16.6192	−0.591284
$791$	0	0
$792$	3.42145	0.121576
$793$	−7.67447	−0.272529
$794$	−16.6482	−0.590824
$795$	−24.5697	−0.871397
$796$	50.0011	1.77224
$797$	−36.8760	−1.30621	−0.653107	−	0.757266i	$-0.726535\pi$
$797$	−36.8760	−1.30621	−0.653107	+	0.757266i	$0.726535\pi$
$798$	0	0
$799$	−26.1052	−0.923537
$800$	8.04254	0.284347
$801$	−34.5138	−1.21948
$802$	8.11236	0.286457
$803$	79.3286	2.79945
$804$	76.9028	2.71215
$805$	0	0
$806$	−18.1881	−0.640650
$807$	47.9275	1.68713
$808$	0.0274913	0.000967140 0
$809$	34.0851	1.19837	0.599185	−	0.800611i	$-0.295491\pi$
$809$	34.0851	1.19837	0.599185	+	0.800611i	$0.295491\pi$
$810$	11.3863	0.400072
$811$	5.90622	0.207395	0.103698	−	0.994609i	$-0.466933\pi$
$811$	5.90622	0.207395	0.103698	+	0.994609i	$0.466933\pi$
$812$	0	0
$813$	9.01220	0.316072
$814$	12.9303	0.453208
$815$	−7.56859	−0.265116
$816$	−73.5717	−2.57552
$817$	26.7569	0.936107
$818$	20.5501	0.718518
$819$	0	0
$820$	13.7654	0.480709
$821$	−43.8664	−1.53095	−0.765474	−	0.643467i	$-0.777495\pi$
$821$	−43.8664	−1.53095	−0.765474	+	0.643467i	$0.777495\pi$
$822$	40.7395	1.42095
$823$	−53.4406	−1.86282	−0.931412	−	0.363968i	$-0.881422\pi$
$823$	−53.4406	−1.86282	−0.931412	+	0.363968i	$0.881422\pi$
$824$	−0.158205	−0.00551135
$825$	−18.8621	−0.656696
$826$	0	0
$827$	−7.66937	−0.266690	−0.133345	−	0.991070i	$-0.542572\pi$
$827$	−7.66937	−0.266690	−0.133345	+	0.991070i	$0.542572\pi$
$828$	−54.4585	−1.89257
$829$	5.27338	0.183152	0.0915761	−	0.995798i	$-0.470810\pi$
$829$	5.27338	0.183152	0.0915761	+	0.995798i	$0.470810\pi$
$830$	−16.3681	−0.568145
$831$	59.6443	2.06904
$832$	−13.0934	−0.453931
$833$	0	0
$834$	−80.0101	−2.77052
$835$	25.0686	0.867535
$836$	−108.656	−3.75793
$837$	44.3180	1.53185
$838$	46.7174	1.61382
$839$	−47.9270	−1.65462	−0.827312	−	0.561743i	$-0.810131\pi$
$839$	−47.9270	−1.65462	−0.827312	+	0.561743i	$0.810131\pi$
$840$	0	0
$841$	−10.7190	−0.369621
$842$	28.5479	0.983826
$843$	−64.2015	−2.21122
$844$	−42.1467	−1.45075
$845$	10.5544	0.363084
$846$	45.8912	1.57777
$847$	0	0
$848$	−32.6810	−1.12227
$849$	−74.5101	−2.55718
$850$	−12.9204	−0.443167
$851$	−4.74009	−0.162488
$852$	−22.6194	−0.774928
$853$	0.0680494	0.00232997	0.00116498	−	0.999999i	$-0.499629\pi$
$853$	0.0680494	0.00232997	0.00116498	+	0.999999i	$0.499629\pi$
$854$	0	0
$855$	−46.3445	−1.58495
$856$	−0.338158	−0.0115580
$857$	−28.4492	−0.971805	−0.485903	−	0.874013i	$-0.661509\pi$
$857$	−28.4492	−0.971805	−0.485903	+	0.874013i	$0.661509\pi$
$858$	59.3411	2.02587
$859$	−24.3584	−0.831097	−0.415549	−	0.909571i	$-0.636410\pi$
$859$	−24.3584	−0.831097	−0.415549	+	0.909571i	$0.636410\pi$
$860$	−6.63312	−0.226188
$861$	0	0
$862$	12.2626	0.417665
$863$	−1.38694	−0.0472121	−0.0236061	−	0.999721i	$-0.507515\pi$
$863$	−1.38694	−0.0472121	−0.0236061	+	0.999721i	$0.507515\pi$
$864$	61.6523	2.09745
$865$	−10.6891	−0.363441
$866$	−77.9903	−2.65022
$867$	71.1600	2.41672
$868$	0	0
$869$	53.0971	1.80119
$870$	25.2424	0.855797
$871$	20.0183	0.678293
$872$	−1.19380	−0.0404272
$873$	−12.5581	−0.425029
$874$	78.7461	2.66363
$875$	0	0
$876$	−74.1481	−2.50523
$877$	23.2131	0.783850	0.391925	−	0.919997i	$-0.371809\pi$
$877$	23.2131	0.783850	0.391925	+	0.919997i	$0.371809\pi$
$878$	−54.1534	−1.82759
$879$	80.5286	2.71616
$880$	−25.0892	−0.845757
$881$	−44.9553	−1.51458	−0.757291	−	0.653077i	$-0.773478\pi$
$881$	−44.9553	−1.51458	−0.757291	+	0.653077i	$0.773478\pi$
$882$	0	0
$883$	10.6613	0.358781	0.179390	−	0.983778i	$-0.442587\pi$
$883$	10.6613	0.358781	0.179390	+	0.983778i	$0.442587\pi$
$884$	20.5609	0.691537
$885$	−26.7877	−0.900460
$886$	−51.1726	−1.71918
$887$	28.4408	0.954949	0.477474	−	0.878646i	$-0.341552\pi$
$887$	28.4408	0.954949	0.477474	+	0.878646i	$0.341552\pi$
$888$	−0.278356	−0.00934102
$889$	0	0
$890$	−12.3719	−0.414707
$891$	−36.3782	−1.21872
$892$	8.88393	0.297456
$893$	−33.5655	−1.12323
$894$	−58.4803	−1.95587
$895$	−11.8676	−0.396690
$896$	0	0
$897$	−21.7536	−0.726333
$898$	0.353797	0.0118064
$899$	24.7186	0.824411
$900$	11.4889	0.382964
$901$	53.7708	1.79136
$902$	−86.9459	−2.89498
$903$	0	0
$904$	0.257322	0.00855841
$905$	−12.4641	−0.414322
$906$	−27.3790	−0.909607
$907$	60.0347	1.99342	0.996710	−	0.0810444i	$-0.0258256\pi$
$907$	60.0347	1.99342	0.996710	+	0.0810444i	$0.0258256\pi$
$908$	3.10057	0.102896
$909$	−1.62660	−0.0539509
$910$	0	0
$911$	31.5719	1.04602	0.523011	−	0.852326i	$-0.324809\pi$
$911$	31.5719	1.04602	0.523011	+	0.852326i	$0.324809\pi$
$912$	−94.5966	−3.13241
$913$	52.2949	1.73071
$914$	70.7321	2.33961
$915$	14.4017	0.476107
$916$	50.9862	1.68463
$917$	0	0
$918$	−99.0452	−3.26898
$919$	−2.55976	−0.0844388	−0.0422194	−	0.999108i	$-0.513443\pi$
$919$	−2.55976	−0.0844388	−0.0422194	+	0.999108i	$0.513443\pi$
$920$	−0.449605	−0.0148230
$921$	57.8667	1.90677
$922$	−56.8576	−1.87250
$923$	−5.88796	−0.193805
$924$	0	0
$925$	1.00000	0.0328798
$926$	−55.9485	−1.83858
$927$	9.36067	0.307445
$928$	34.3869	1.12881
$929$	−26.2692	−0.861863	−0.430932	−	0.902385i	$-0.641815\pi$
$929$	−26.2692	−0.861863	−0.430932	+	0.902385i	$0.641815\pi$
$930$	34.1314	1.11921
$931$	0	0
$932$	−3.40208	−0.111439
$933$	66.7040	2.18379
$934$	−75.1572	−2.45922
$935$	41.2798	1.34999
$936$	−0.832461	−0.0272099
$937$	−35.7424	−1.16765	−0.583827	−	0.811878i	$-0.698445\pi$
$937$	−35.7424	−1.16765	−0.583827	+	0.811878i	$0.698445\pi$
$938$	0	0
$939$	−47.7294	−1.55759
$940$	8.32098	0.271400
$941$	52.2926	1.70469	0.852344	−	0.522981i	$-0.175180\pi$
$941$	52.2926	1.70469	0.852344	+	0.522981i	$0.175180\pi$
$942$	63.5682	2.07116
$943$	31.8732	1.03794
$944$	−35.6313	−1.15970
$945$	0	0
$946$	41.8966	1.36217
$947$	38.2613	1.24333	0.621663	−	0.783285i	$-0.286457\pi$
$947$	38.2613	1.24333	0.621663	+	0.783285i	$0.286457\pi$
$948$	−49.6296	−1.61189
$949$	−19.3012	−0.626543
$950$	−16.6128	−0.538990
$951$	−83.0719	−2.69379
$952$	0	0
$953$	−32.4798	−1.05212	−0.526061	−	0.850447i	$-0.676332\pi$
$953$	−32.4798	−1.05212	−0.526061	+	0.850447i	$0.676332\pi$
$954$	−94.5254	−3.06037
$955$	−14.3266	−0.463597
$956$	43.6547	1.41189
$957$	−80.6475	−2.60696
$958$	70.3788	2.27384
$959$	0	0
$960$	24.5708	0.793018
$961$	2.42320	0.0781677
$962$	−3.14604	−0.101432
$963$	20.0081	0.644751
$964$	5.86033	0.188749
$965$	2.69030	0.0866037
$966$	0	0
$967$	−28.4115	−0.913653	−0.456827	−	0.889556i	$-0.651014\pi$
$967$	−28.4115	−0.913653	−0.456827	+	0.889556i	$0.651014\pi$
$968$	−2.87509	−0.0924088
$969$	155.642	4.99994
$970$	−4.50163	−0.144539
$971$	−1.56730	−0.0502969	−0.0251485	−	0.999684i	$-0.508006\pi$
$971$	−1.56730	−0.0502969	−0.0251485	+	0.999684i	$0.508006\pi$
$972$	−13.0764	−0.419424
$973$	0	0
$974$	−21.5183	−0.689490
$975$	4.58929	0.146975
$976$	19.1563	0.613177
$977$	−5.86619	−0.187676	−0.0938380	−	0.995587i	$-0.529914\pi$
$977$	−5.86619	−0.187676	−0.0938380	+	0.995587i	$0.529914\pi$
$978$	−44.6833	−1.42882
$979$	39.5273	1.26330
$980$	0	0
$981$	70.6346	2.25519
$982$	−12.6103	−0.402411
$983$	13.9774	0.445809	0.222905	−	0.974840i	$-0.428446\pi$
$983$	13.9774	0.445809	0.222905	+	0.974840i	$0.428446\pi$
$984$	1.87172	0.0596682
$985$	−9.87464	−0.314632
$986$	−55.2430	−1.75929
$987$	0	0
$988$	26.4367	0.841062
$989$	−15.3587	−0.488379
$990$	−72.5671	−2.30633
$991$	7.18943	0.228380	0.114190	−	0.993459i	$-0.463573\pi$
$991$	7.18943	0.228380	0.114190	+	0.993459i	$0.463573\pi$
$992$	46.4962	1.47625
$993$	7.88546	0.250237
$994$	0	0
$995$	−24.4248	−0.774317
$996$	−48.8798	−1.54882
$997$	20.2860	0.642464	0.321232	−	0.947000i	$-0.395903\pi$
$997$	20.2860	0.642464	0.321232	+	0.947000i	$0.395903\pi$
$998$	4.39232	0.139037
$999$	7.66577	0.242534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9065.2.a.bc.1.7	yes	34
7.6	odd	2		9065.2.a.bb.1.7	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9065.2.a.bb.1.7	✓	34	7.6	odd	2
9065.2.a.bc.1.7	yes	34	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:	\( N \)	\(=\)	\( 9065 = 5 \cdot 7^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9065.a (trivial)

\(f(q)\)	\(=\)	\(q-2.01175 q^{2} +2.93465 q^{3} +2.04715 q^{4} -1.00000 q^{5} -5.90379 q^{6} -0.0948516 q^{8} +5.61216 q^{9} +2.01175 q^{10} -6.42740 q^{11} +6.00766 q^{12} +1.56383 q^{13} -2.93465 q^{15} -3.90348 q^{16} +6.42248 q^{17} -11.2903 q^{18} +8.25786 q^{19} -2.04715 q^{20} +12.9303 q^{22} -4.74009 q^{23} -0.278356 q^{24} +1.00000 q^{25} -3.14604 q^{26} +7.66577 q^{27} +4.27563 q^{29} +5.90379 q^{30} +5.78128 q^{31} +8.04254 q^{32} -18.8621 q^{33} -12.9204 q^{34} +11.4889 q^{36} +1.00000 q^{37} -16.6128 q^{38} +4.58929 q^{39} +0.0948516 q^{40} -6.72419 q^{41} +3.24018 q^{43} -13.1578 q^{44} -5.61216 q^{45} +9.53589 q^{46} -4.06467 q^{47} -11.4553 q^{48} -2.01175 q^{50} +18.8477 q^{51} +3.20139 q^{52} +8.37228 q^{53} -15.4216 q^{54} +6.42740 q^{55} +24.2339 q^{57} -8.60151 q^{58} +9.12809 q^{59} -6.00766 q^{60} -4.90749 q^{61} -11.6305 q^{62} -8.37264 q^{64} -1.56383 q^{65} +37.9460 q^{66} +12.8008 q^{67} +13.1478 q^{68} -13.9105 q^{69} -3.76509 q^{71} -0.532322 q^{72} -12.3423 q^{73} -2.01175 q^{74} +2.93465 q^{75} +16.9051 q^{76} -9.23252 q^{78} -8.26105 q^{79} +3.90348 q^{80} +5.65987 q^{81} +13.5274 q^{82} -8.13625 q^{83} -6.42248 q^{85} -6.51843 q^{86} +12.5475 q^{87} +0.609649 q^{88} -6.14981 q^{89} +11.2903 q^{90} -9.70367 q^{92} +16.9660 q^{93} +8.17710 q^{94} -8.25786 q^{95} +23.6020 q^{96} -2.23767 q^{97} -36.0716 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 2 q^{2} + 10 q^{3} + 30 q^{4} - 34 q^{5} + 8 q^{6} - 6 q^{8} + 28 q^{9} + 2 q^{10} - 30 q^{11} + 20 q^{12} + 18 q^{13} - 10 q^{15} + 18 q^{16} + 10 q^{17} + 40 q^{19} - 30 q^{20} - 4 q^{22} - 16 q^{23}+ \cdots - 100 q^{99}+O(q^{100}) \) 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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