LMFDB - Embedded newform 2583.2.a.r.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2583,2,Mod(1,2583)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2583, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2583.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2583 = 3^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2583.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$20.6253588421$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.633117.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 4x^{2} + 6x - 3 $ x^5 - x^4 - 6x^3 + 4x^2 + 6*x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.45719$ of defining polynomial
Character	$\chi$	$=$	2583.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.45719 q^{2} +4.03778 q^{4} +2.26685 q^{5} +1.00000 q^{7} +5.00722 q^{8} +O(q^{10})$	\(q+2.45719 q^{2} +4.03778 q^{4} +2.26685 q^{5} +1.00000 q^{7} +5.00722 q^{8} +5.57007 q^{10} +5.41988 q^{11} +3.23628 q^{13} +2.45719 q^{14} +4.22813 q^{16} -2.83206 q^{17} -4.32097 q^{19} +9.15303 q^{20} +13.3177 q^{22} -6.99907 q^{23} +0.138589 q^{25} +7.95216 q^{26} +4.03778 q^{28} -8.06741 q^{29} +9.18123 q^{31} +0.374872 q^{32} -6.95892 q^{34} +2.26685 q^{35} -0.0469023 q^{37} -10.6174 q^{38} +11.3506 q^{40} +1.00000 q^{41} -6.31281 q^{43} +21.8843 q^{44} -17.1980 q^{46} -5.26448 q^{47} +1.00000 q^{49} +0.340538 q^{50} +13.0674 q^{52} -6.43622 q^{53} +12.2860 q^{55} +5.00722 q^{56} -19.8232 q^{58} -2.45253 q^{59} +5.28319 q^{61} +22.5600 q^{62} -7.53512 q^{64} +7.33615 q^{65} -8.78423 q^{67} -11.4353 q^{68} +5.57007 q^{70} +12.1364 q^{71} +2.42993 q^{73} -0.115248 q^{74} -17.4471 q^{76} +5.41988 q^{77} +4.92882 q^{79} +9.58451 q^{80} +2.45719 q^{82} +1.63593 q^{83} -6.41985 q^{85} -15.5118 q^{86} +27.1385 q^{88} -1.68625 q^{89} +3.23628 q^{91} -28.2607 q^{92} -12.9358 q^{94} -9.79497 q^{95} +18.8278 q^{97} +2.45719 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 3 q^{4} + 5 q^{5} + 5 q^{7} + 3 q^{8}+O(q^{10}) $ 5 * q + q^2 + 3 * q^4 + 5 * q^5 + 5 * q^7 + 3 * q^8	$ 5 q + q^{2} + 3 q^{4} + 5 q^{5} + 5 q^{7} + 3 q^{8} - 2 q^{11} + 5 q^{13} + q^{14} - q^{16} - 13 q^{17} + 23 q^{20} + q^{22} - 2 q^{23} + 22 q^{25} + 3 q^{28} + 5 q^{29} + 17 q^{31} + 12 q^{32} - 8 q^{34} + 5 q^{35} - 7 q^{37} + 3 q^{38} + 7 q^{40} + 5 q^{41} + q^{43} + 47 q^{44} - 24 q^{46} - 9 q^{47} + 5 q^{49} - 2 q^{50} + 20 q^{52} - 5 q^{53} + 33 q^{55} + 3 q^{56} - 27 q^{58} - 7 q^{59} + 22 q^{61} + 28 q^{62} - 3 q^{64} + 31 q^{65} - 3 q^{67} - 17 q^{68} + 24 q^{71} + 40 q^{73} + 5 q^{74} - 19 q^{76} - 2 q^{77} - 42 q^{79} - 24 q^{80} + q^{82} + 12 q^{83} - 23 q^{85} - 16 q^{86} + 26 q^{88} - 8 q^{89} + 5 q^{91} - 12 q^{92} - 23 q^{94} + 17 q^{95} + 16 q^{97} + q^{98}+O(q^{100}) $ 5 * q + q^2 + 3 * q^4 + 5 * q^5 + 5 * q^7 + 3 * q^8 - 2 * q^11 + 5 * q^13 + q^14 - q^16 - 13 * q^17 + 23 * q^20 + q^22 - 2 * q^23 + 22 * q^25 + 3 * q^28 + 5 * q^29 + 17 * q^31 + 12 * q^32 - 8 * q^34 + 5 * q^35 - 7 * q^37 + 3 * q^38 + 7 * q^40 + 5 * q^41 + q^43 + 47 * q^44 - 24 * q^46 - 9 * q^47 + 5 * q^49 - 2 * q^50 + 20 * q^52 - 5 * q^53 + 33 * q^55 + 3 * q^56 - 27 * q^58 - 7 * q^59 + 22 * q^61 + 28 * q^62 - 3 * q^64 + 31 * q^65 - 3 * q^67 - 17 * q^68 + 24 * q^71 + 40 * q^73 + 5 * q^74 - 19 * q^76 - 2 * q^77 - 42 * q^79 - 24 * q^80 + q^82 + 12 * q^83 - 23 * q^85 - 16 * q^86 + 26 * q^88 - 8 * q^89 + 5 * q^91 - 12 * q^92 - 23 * q^94 + 17 * q^95 + 16 * q^97 + q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.45719	1.73750	0.868748	−	0.495255i	$-0.164925\pi$
$2$	2.45719	1.73750	0.868748	+	0.495255i	$0.164925\pi$
$3$	0	0
$3$	0	0
$4$	4.03778	2.01889
$5$	2.26685	1.01376	0.506882	−	0.862015i	$-0.330798\pi$
$5$	2.26685	1.01376	0.506882	+	0.862015i	$0.330798\pi$
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	5.00722	1.77032
$9$	0	0
$10$	5.57007	1.76141
$11$	5.41988	1.63415	0.817077	−	0.576528i	$-0.195593\pi$
$11$	5.41988	1.63415	0.817077	+	0.576528i	$0.195593\pi$
$12$	0	0
$13$	3.23628	0.897584	0.448792	−	0.893636i	$-0.351854\pi$
$13$	3.23628	0.897584	0.448792	+	0.893636i	$0.351854\pi$
$14$	2.45719	0.656712
$15$	0	0
$16$	4.22813	1.05703
$17$	−2.83206	−0.686876	−0.343438	−	0.939175i	$-0.611592\pi$
$17$	−2.83206	−0.686876	−0.343438	+	0.939175i	$0.611592\pi$
$18$	0	0
$19$	−4.32097	−0.991298	−0.495649	−	0.868523i	$-0.665070\pi$
$19$	−4.32097	−0.991298	−0.495649	+	0.868523i	$0.665070\pi$
$20$	9.15303	2.04668
$21$	0	0
$22$	13.3177	2.83934
$23$	−6.99907	−1.45941	−0.729703	−	0.683764i	$-0.760342\pi$
$23$	−6.99907	−1.45941	−0.729703	+	0.683764i	$0.760342\pi$
$24$	0	0
$25$	0.138589	0.0277177
$26$	7.95216	1.55955
$27$	0	0
$28$	4.03778	0.763069
$29$	−8.06741	−1.49808	−0.749040	−	0.662524i	$-0.769485\pi$
$29$	−8.06741	−1.49808	−0.749040	+	0.662524i	$0.769485\pi$
$30$	0	0
$31$	9.18123	1.64900	0.824498	−	0.565864i	$-0.191457\pi$
$31$	9.18123	1.64900	0.824498	+	0.565864i	$0.191457\pi$
$32$	0.374872	0.0662686
$33$	0	0
$34$	−6.95892	−1.19344
$35$	2.26685	0.383167
$36$	0	0
$37$	−0.0469023	−0.00771068	−0.00385534	−	0.999993i	$-0.501227\pi$
$37$	−0.0469023	−0.00771068	−0.00385534	+	0.999993i	$0.501227\pi$
$38$	−10.6174	−1.72238
$39$	0	0
$40$	11.3506	1.79469
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−6.31281	−0.962695	−0.481348	−	0.876530i	$-0.659852\pi$
$43$	−6.31281	−0.962695	−0.481348	+	0.876530i	$0.659852\pi$
$44$	21.8843	3.29918
$45$	0	0
$46$	−17.1980	−2.53571
$47$	−5.26448	−0.767903	−0.383952	−	0.923353i	$-0.625437\pi$
$47$	−5.26448	−0.767903	−0.383952	+	0.923353i	$0.625437\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0.340538	0.0481594
$51$	0	0
$52$	13.0674	1.81212
$53$	−6.43622	−0.884082	−0.442041	−	0.896995i	$-0.645745\pi$
$53$	−6.43622	−0.884082	−0.442041	+	0.896995i	$0.645745\pi$
$54$	0	0
$55$	12.2860	1.65665
$56$	5.00722	0.669118
$57$	0	0
$58$	−19.8232	−2.60291
$59$	−2.45253	−0.319292	−0.159646	−	0.987174i	$-0.551035\pi$
$59$	−2.45253	−0.319292	−0.159646	+	0.987174i	$0.551035\pi$
$60$	0	0
$61$	5.28319	0.676443	0.338221	−	0.941067i	$-0.390175\pi$
$61$	5.28319	0.676443	0.338221	+	0.941067i	$0.390175\pi$
$62$	22.5600	2.86513
$63$	0	0
$64$	−7.53512	−0.941891
$65$	7.33615	0.909938
$66$	0	0
$67$	−8.78423	−1.07316	−0.536582	−	0.843848i	$-0.680285\pi$
$67$	−8.78423	−1.07316	−0.536582	+	0.843848i	$0.680285\pi$
$68$	−11.4353	−1.38673
$69$	0	0
$70$	5.57007	0.665751
$71$	12.1364	1.44033	0.720165	−	0.693802i	$-0.244066\pi$
$71$	12.1364	1.44033	0.720165	+	0.693802i	$0.244066\pi$
$72$	0	0
$73$	2.42993	0.284402	0.142201	−	0.989838i	$-0.454582\pi$
$73$	2.42993	0.284402	0.142201	+	0.989838i	$0.454582\pi$
$74$	−0.115248	−0.0133973
$75$	0	0
$76$	−17.4471	−2.00132
$77$	5.41988	0.617652
$78$	0	0
$79$	4.92882	0.554536	0.277268	−	0.960793i	$-0.410571\pi$
$79$	4.92882	0.554536	0.277268	+	0.960793i	$0.410571\pi$
$80$	9.58451	1.07158
$81$	0	0
$82$	2.45719	0.271351
$83$	1.63593	0.179567	0.0897833	−	0.995961i	$-0.471383\pi$
$83$	1.63593	0.179567	0.0897833	+	0.995961i	$0.471383\pi$
$84$	0	0
$85$	−6.41985	−0.696330
$86$	−15.5118	−1.67268
$87$	0	0
$88$	27.1385	2.89298
$89$	−1.68625	−0.178742	−0.0893712	−	0.995998i	$-0.528486\pi$
$89$	−1.68625	−0.178742	−0.0893712	+	0.995998i	$0.528486\pi$
$90$	0	0
$91$	3.23628	0.339255
$92$	−28.2607	−2.94638
$93$	0	0
$94$	−12.9358	−1.33423
$95$	−9.79497	−1.00494
$96$	0	0
$97$	18.8278	1.91168	0.955838	−	0.293894i	$-0.0949512\pi$
$97$	18.8278	1.91168	0.955838	+	0.293894i	$0.0949512\pi$
$98$	2.45719	0.248214
$99$	0	0
$100$	0.559591	0.0559591
$101$	−7.44903	−0.741207	−0.370603	−	0.928791i	$-0.620849\pi$
$101$	−7.44903	−0.741207	−0.370603	+	0.928791i	$0.620849\pi$
$102$	0	0
$103$	3.68672	0.363264	0.181632	−	0.983367i	$-0.441862\pi$
$103$	3.68672	0.363264	0.181632	+	0.983367i	$0.441862\pi$
$104$	16.2048	1.58901
$105$	0	0
$106$	−15.8150	−1.53609
$107$	8.58781	0.830215	0.415108	−	0.909772i	$-0.363744\pi$
$107$	8.58781	0.830215	0.415108	+	0.909772i	$0.363744\pi$
$108$	0	0
$109$	−2.91912	−0.279601	−0.139800	−	0.990180i	$-0.544646\pi$
$109$	−2.91912	−0.279601	−0.139800	+	0.990180i	$0.544646\pi$
$110$	30.1891	2.87842
$111$	0	0
$112$	4.22813	0.399521
$113$	7.03990	0.662258	0.331129	−	0.943585i	$-0.392570\pi$
$113$	7.03990	0.662258	0.331129	+	0.943585i	$0.392570\pi$
$114$	0	0
$115$	−15.8658	−1.47949
$116$	−32.5745	−3.02446
$117$	0	0
$118$	−6.02633	−0.554768
$119$	−2.83206	−0.259615
$120$	0	0
$121$	18.3751	1.67046
$122$	12.9818	1.17532
$123$	0	0
$124$	37.0718	3.32915
$125$	−11.0201	−0.985665
$126$	0	0
$127$	19.1099	1.69573	0.847863	−	0.530216i	$-0.177889\pi$
$127$	19.1099	1.69573	0.847863	+	0.530216i	$0.177889\pi$
$128$	−19.2650	−1.70280
$129$	0	0
$130$	18.0263	1.58101
$131$	−9.99440	−0.873215	−0.436608	−	0.899652i	$-0.643820\pi$
$131$	−9.99440	−0.873215	−0.436608	+	0.899652i	$0.643820\pi$
$132$	0	0
$133$	−4.32097	−0.374676
$134$	−21.5845	−1.86462
$135$	0	0
$136$	−14.1808	−1.21599
$137$	−4.66385	−0.398459	−0.199230	−	0.979953i	$-0.563844\pi$
$137$	−4.66385	−0.398459	−0.199230	+	0.979953i	$0.563844\pi$
$138$	0	0
$139$	−10.3954	−0.881725	−0.440862	−	0.897575i	$-0.645327\pi$
$139$	−10.3954	−0.881725	−0.440862	+	0.897575i	$0.645327\pi$
$140$	9.15303	0.773572
$141$	0	0
$142$	29.8215	2.50257
$143$	17.5403	1.46679
$144$	0	0
$145$	−18.2876	−1.51870
$146$	5.97080	0.494147
$147$	0	0
$148$	−0.189381	−0.0155670
$149$	−6.23050	−0.510422	−0.255211	−	0.966885i	$-0.582145\pi$
$149$	−6.23050	−0.510422	−0.255211	+	0.966885i	$0.582145\pi$
$150$	0	0
$151$	−21.1548	−1.72156	−0.860778	−	0.508981i	$-0.830022\pi$
$151$	−21.1548	−1.72156	−0.860778	+	0.508981i	$0.830022\pi$
$152$	−21.6360	−1.75492
$153$	0	0
$154$	13.3177	1.07317
$155$	20.8124	1.67169
$156$	0	0
$157$	20.4912	1.63538	0.817688	−	0.575662i	$-0.195255\pi$
$157$	20.4912	1.63538	0.817688	+	0.575662i	$0.195255\pi$
$158$	12.1111	0.963504
$159$	0	0
$160$	0.849777	0.0671808
$161$	−6.99907	−0.551604
$162$	0	0
$163$	−1.63497	−0.128060	−0.0640302	−	0.997948i	$-0.520395\pi$
$163$	−1.63497	−0.128060	−0.0640302	+	0.997948i	$0.520395\pi$
$164$	4.03778	0.315298
$165$	0	0
$166$	4.01979	0.311996
$167$	19.8243	1.53405	0.767026	−	0.641616i	$-0.221736\pi$
$167$	19.8243	1.53405	0.767026	+	0.641616i	$0.221736\pi$
$168$	0	0
$169$	−2.52647	−0.194344
$170$	−15.7748	−1.20987
$171$	0	0
$172$	−25.4898	−1.94358
$173$	9.31394	0.708126	0.354063	−	0.935222i	$-0.384800\pi$
$173$	9.31394	0.708126	0.354063	+	0.935222i	$0.384800\pi$
$174$	0	0
$175$	0.138589	0.0104763
$176$	22.9159	1.72735
$177$	0	0
$178$	−4.14344	−0.310564
$179$	17.3459	1.29649	0.648245	−	0.761432i	$-0.275503\pi$
$179$	17.3459	1.29649	0.648245	+	0.761432i	$0.275503\pi$
$180$	0	0
$181$	10.1355	0.753364	0.376682	−	0.926343i	$-0.377065\pi$
$181$	10.1355	0.753364	0.376682	+	0.926343i	$0.377065\pi$
$182$	7.95216	0.589454
$183$	0	0
$184$	−35.0459	−2.58362
$185$	−0.106320	−0.00781681
$186$	0	0
$187$	−15.3494	−1.12246
$188$	−21.2568	−1.55031
$189$	0	0
$190$	−24.0681	−1.74608
$191$	−18.1959	−1.31661	−0.658306	−	0.752750i	$-0.728727\pi$
$191$	−18.1959	−1.31661	−0.658306	+	0.752750i	$0.728727\pi$
$192$	0	0
$193$	1.29950	0.0935398	0.0467699	−	0.998906i	$-0.485107\pi$
$193$	1.29950	0.0935398	0.0467699	+	0.998906i	$0.485107\pi$
$194$	46.2635	3.32153
$195$	0	0
$196$	4.03778	0.288413
$197$	−5.64679	−0.402317	−0.201159	−	0.979559i	$-0.564471\pi$
$197$	−5.64679	−0.402317	−0.201159	+	0.979559i	$0.564471\pi$
$198$	0	0
$199$	−11.5069	−0.815699	−0.407850	−	0.913049i	$-0.633721\pi$
$199$	−11.5069	−0.815699	−0.407850	+	0.913049i	$0.633721\pi$
$200$	0.693943	0.0490692
$201$	0	0
$202$	−18.3037	−1.28784
$203$	−8.06741	−0.566221
$204$	0	0
$205$	2.26685	0.158323
$206$	9.05898	0.631169
$207$	0	0
$208$	13.6834	0.948775
$209$	−23.4191	−1.61993
$210$	0	0
$211$	−9.92599	−0.683333	−0.341667	−	0.939821i	$-0.610991\pi$
$211$	−9.92599	−0.683333	−0.341667	+	0.939821i	$0.610991\pi$
$212$	−25.9880	−1.78487
$213$	0	0
$214$	21.1019	1.44250
$215$	−14.3102	−0.975946
$216$	0	0
$217$	9.18123	0.623262
$218$	−7.17282	−0.485805
$219$	0	0
$220$	49.6083	3.34459
$221$	−9.16536	−0.616529
$222$	0	0
$223$	−11.8232	−0.791738	−0.395869	−	0.918307i	$-0.629557\pi$
$223$	−11.8232	−0.791738	−0.395869	+	0.918307i	$0.629557\pi$
$224$	0.374872	0.0250472
$225$	0	0
$226$	17.2984	1.15067
$227$	−1.60275	−0.106378	−0.0531892	−	0.998584i	$-0.516939\pi$
$227$	−1.60275	−0.106378	−0.0531892	+	0.998584i	$0.516939\pi$
$228$	0	0
$229$	−9.93349	−0.656423	−0.328212	−	0.944604i	$-0.606446\pi$
$229$	−9.93349	−0.656423	−0.328212	+	0.944604i	$0.606446\pi$
$230$	−38.9853	−2.57061
$231$	0	0
$232$	−40.3953	−2.65208
$233$	7.91248	0.518364	0.259182	−	0.965829i	$-0.416547\pi$
$233$	7.91248	0.518364	0.259182	+	0.965829i	$0.416547\pi$
$234$	0	0
$235$	−11.9338	−0.778473
$236$	−9.90278	−0.644616
$237$	0	0
$238$	−6.95892	−0.451079
$239$	−27.1893	−1.75873	−0.879365	−	0.476148i	$-0.842033\pi$
$239$	−27.1893	−1.75873	−0.879365	+	0.476148i	$0.842033\pi$
$240$	0	0
$241$	19.4014	1.24975	0.624877	−	0.780723i	$-0.285149\pi$
$241$	19.4014	1.24975	0.624877	+	0.780723i	$0.285149\pi$
$242$	45.1510	2.90242
$243$	0	0
$244$	21.3324	1.36566
$245$	2.26685	0.144823
$246$	0	0
$247$	−13.9839	−0.889773
$248$	45.9724	2.91925
$249$	0	0
$250$	−27.0784	−1.71259
$251$	−27.4697	−1.73387	−0.866935	−	0.498421i	$-0.833913\pi$
$251$	−27.4697	−1.73387	−0.866935	+	0.498421i	$0.833913\pi$
$252$	0	0
$253$	−37.9341	−2.38489
$254$	46.9566	2.94632
$255$	0	0
$256$	−32.2675	−2.01672
$257$	−21.6328	−1.34942	−0.674710	−	0.738083i	$-0.735731\pi$
$257$	−21.6328	−1.34942	−0.674710	+	0.738083i	$0.735731\pi$
$258$	0	0
$259$	−0.0469023	−0.00291436
$260$	29.6218	1.83707
$261$	0	0
$262$	−24.5581	−1.51721
$263$	9.84482	0.607058	0.303529	−	0.952822i	$-0.401835\pi$
$263$	9.84482	0.607058	0.303529	+	0.952822i	$0.401835\pi$
$264$	0	0
$265$	−14.5899	−0.896251
$266$	−10.6174	−0.650997
$267$	0	0
$268$	−35.4688	−2.16660
$269$	26.0627	1.58907	0.794535	−	0.607219i	$-0.207715\pi$
$269$	26.0627	1.58907	0.794535	+	0.607219i	$0.207715\pi$
$270$	0	0
$271$	25.4506	1.54602	0.773008	−	0.634396i	$-0.218751\pi$
$271$	25.4506	1.54602	0.773008	+	0.634396i	$0.218751\pi$
$272$	−11.9743	−0.726050
$273$	0	0
$274$	−11.4600	−0.692321
$275$	0.751133	0.0452950
$276$	0	0
$277$	29.3678	1.76454	0.882270	−	0.470743i	$-0.156014\pi$
$277$	29.3678	1.76454	0.882270	+	0.470743i	$0.156014\pi$
$278$	−25.5434	−1.53199
$279$	0	0
$280$	11.3506	0.678328
$281$	−24.2120	−1.44437	−0.722184	−	0.691701i	$-0.756861\pi$
$281$	−24.2120	−1.44437	−0.722184	+	0.691701i	$0.756861\pi$
$282$	0	0
$283$	8.91251	0.529794	0.264897	−	0.964277i	$-0.414662\pi$
$283$	8.91251	0.529794	0.264897	+	0.964277i	$0.414662\pi$
$284$	49.0043	2.90787
$285$	0	0
$286$	43.0997	2.54854
$287$	1.00000	0.0590281
$288$	0	0
$289$	−8.97942	−0.528201
$290$	−44.9361	−2.63874
$291$	0	0
$292$	9.81153	0.574176
$293$	8.79238	0.513656	0.256828	−	0.966457i	$-0.417323\pi$
$293$	8.79238	0.513656	0.256828	+	0.966457i	$0.417323\pi$
$294$	0	0
$295$	−5.55950	−0.323687
$296$	−0.234850	−0.0136504
$297$	0	0
$298$	−15.3095	−0.886856
$299$	−22.6510	−1.30994
$300$	0	0
$301$	−6.31281	−0.363865
$302$	−51.9814	−2.99120
$303$	0	0
$304$	−18.2696	−1.04783
$305$	11.9762	0.685753
$306$	0	0
$307$	25.4509	1.45256	0.726281	−	0.687398i	$-0.241247\pi$
$307$	25.4509	1.45256	0.726281	+	0.687398i	$0.241247\pi$
$308$	21.8843	1.24697
$309$	0	0
$310$	51.1401	2.90456
$311$	8.20774	0.465418	0.232709	−	0.972546i	$-0.425241\pi$
$311$	8.20774	0.465418	0.232709	+	0.972546i	$0.425241\pi$
$312$	0	0
$313$	7.84025	0.443157	0.221578	−	0.975143i	$-0.428879\pi$
$313$	7.84025	0.443157	0.221578	+	0.975143i	$0.428879\pi$
$314$	50.3508	2.84146
$315$	0	0
$316$	19.9015	1.11955
$317$	−32.4359	−1.82178	−0.910891	−	0.412647i	$-0.864604\pi$
$317$	−32.4359	−1.82178	−0.910891	+	0.412647i	$0.864604\pi$
$318$	0	0
$319$	−43.7244	−2.44810
$320$	−17.0810	−0.954855
$321$	0	0
$322$	−17.1980	−0.958409
$323$	12.2373	0.680899
$324$	0	0
$325$	0.448512	0.0248790
$326$	−4.01742	−0.222504
$327$	0	0
$328$	5.00722	0.276478
$329$	−5.26448	−0.290240
$330$	0	0
$331$	13.8576	0.761685	0.380843	−	0.924640i	$-0.375634\pi$
$331$	13.8576	0.761685	0.380843	+	0.924640i	$0.375634\pi$
$332$	6.60553	0.362526
$333$	0	0
$334$	48.7121	2.66541
$335$	−19.9125	−1.08794
$336$	0	0
$337$	18.6080	1.01364	0.506822	−	0.862050i	$-0.330820\pi$
$337$	18.6080	1.01364	0.506822	+	0.862050i	$0.330820\pi$
$338$	−6.20802	−0.337672
$339$	0	0
$340$	−25.9220	−1.40582
$341$	49.7611	2.69472
$342$	0	0
$343$	1.00000	0.0539949
$344$	−31.6097	−1.70428
$345$	0	0
$346$	22.8861	1.23037
$347$	−23.3306	−1.25245	−0.626225	−	0.779642i	$-0.715401\pi$
$347$	−23.3306	−1.25245	−0.626225	+	0.779642i	$0.715401\pi$
$348$	0	0
$349$	−5.59571	−0.299531	−0.149766	−	0.988722i	$-0.547852\pi$
$349$	−5.59571	−0.299531	−0.149766	+	0.988722i	$0.547852\pi$
$350$	0.340538	0.0182025
$351$	0	0
$352$	2.03176	0.108293
$353$	19.4280	1.03405	0.517023	−	0.855971i	$-0.327040\pi$
$353$	19.4280	1.03405	0.517023	+	0.855971i	$0.327040\pi$
$354$	0	0
$355$	27.5114	1.46016
$356$	−6.80872	−0.360862
$357$	0	0
$358$	42.6221	2.25265
$359$	−14.3127	−0.755398	−0.377699	−	0.925929i	$-0.623285\pi$
$359$	−14.3127	−0.755398	−0.377699	+	0.925929i	$0.623285\pi$
$360$	0	0
$361$	−0.329226	−0.0173277
$362$	24.9048	1.30897
$363$	0	0
$364$	13.0674	0.684918
$365$	5.50827	0.288316
$366$	0	0
$367$	−21.2458	−1.10902	−0.554512	−	0.832176i	$-0.687095\pi$
$367$	−21.2458	−1.10902	−0.554512	+	0.832176i	$0.687095\pi$
$368$	−29.5929	−1.54264
$369$	0	0
$370$	−0.261249	−0.0135817
$371$	−6.43622	−0.334152
$372$	0	0
$373$	28.2272	1.46155	0.730774	−	0.682620i	$-0.239160\pi$
$373$	28.2272	1.46155	0.730774	+	0.682620i	$0.239160\pi$
$374$	−37.7165	−1.95027
$375$	0	0
$376$	−26.3604	−1.35943
$377$	−26.1084	−1.34465
$378$	0	0
$379$	−8.57635	−0.440538	−0.220269	−	0.975439i	$-0.570693\pi$
$379$	−8.57635	−0.440538	−0.220269	+	0.975439i	$0.570693\pi$
$380$	−39.5500	−2.02887
$381$	0	0
$382$	−44.7109	−2.28761
$383$	−2.63393	−0.134588	−0.0672938	−	0.997733i	$-0.521436\pi$
$383$	−2.63393	−0.134588	−0.0672938	+	0.997733i	$0.521436\pi$
$384$	0	0
$385$	12.2860	0.626154
$386$	3.19311	0.162525
$387$	0	0
$388$	76.0227	3.85947
$389$	13.2656	0.672595	0.336298	−	0.941756i	$-0.390825\pi$
$389$	13.2656	0.672595	0.336298	+	0.941756i	$0.390825\pi$
$390$	0	0
$391$	19.8218	1.00243
$392$	5.00722	0.252903
$393$	0	0
$394$	−13.8752	−0.699025
$395$	11.1729	0.562169
$396$	0	0
$397$	2.28602	0.114732	0.0573661	−	0.998353i	$-0.481730\pi$
$397$	2.28602	0.114732	0.0573661	+	0.998353i	$0.481730\pi$
$398$	−28.2745	−1.41727
$399$	0	0
$400$	0.585970	0.0292985
$401$	−2.79191	−0.139421	−0.0697107	−	0.997567i	$-0.522208\pi$
$401$	−2.79191	−0.139421	−0.0697107	+	0.997567i	$0.522208\pi$
$402$	0	0
$403$	29.7130	1.48011
$404$	−30.0776	−1.49642
$405$	0	0
$406$	−19.8232	−0.983807
$407$	−0.254204	−0.0126004
$408$	0	0
$409$	−10.8769	−0.537826	−0.268913	−	0.963164i	$-0.586664\pi$
$409$	−10.8769	−0.537826	−0.268913	+	0.963164i	$0.586664\pi$
$410$	5.57007	0.275086
$411$	0	0
$412$	14.8862	0.733390
$413$	−2.45253	−0.120681
$414$	0	0
$415$	3.70840	0.182038
$416$	1.21319	0.0594816
$417$	0	0
$418$	−57.5452	−2.81463
$419$	24.9047	1.21668	0.608338	−	0.793678i	$-0.291836\pi$
$419$	24.9047	1.21668	0.608338	+	0.793678i	$0.291836\pi$
$420$	0	0
$421$	−7.16405	−0.349155	−0.174577	−	0.984643i	$-0.555856\pi$
$421$	−7.16405	−0.349155	−0.174577	+	0.984643i	$0.555856\pi$
$422$	−24.3900	−1.18729
$423$	0	0
$424$	−32.2276	−1.56511
$425$	−0.392491	−0.0190386
$426$	0	0
$427$	5.28319	0.255671
$428$	34.6757	1.67611
$429$	0	0
$430$	−35.1628	−1.69570
$431$	14.6538	0.705850	0.352925	−	0.935652i	$-0.385187\pi$
$431$	14.6538	0.705850	0.352925	+	0.935652i	$0.385187\pi$
$432$	0	0
$433$	−29.4173	−1.41370	−0.706851	−	0.707362i	$-0.749885\pi$
$433$	−29.4173	−1.41370	−0.706851	+	0.707362i	$0.749885\pi$
$434$	22.5600	1.08292
$435$	0	0
$436$	−11.7868	−0.564483
$437$	30.2427	1.44671
$438$	0	0
$439$	26.5607	1.26767	0.633837	−	0.773466i	$-0.281479\pi$
$439$	26.5607	1.26767	0.633837	+	0.773466i	$0.281479\pi$
$440$	61.5188	2.93280
$441$	0	0
$442$	−22.5210	−1.07122
$443$	12.2373	0.581409	0.290705	−	0.956813i	$-0.406110\pi$
$443$	12.2373	0.581409	0.290705	+	0.956813i	$0.406110\pi$
$444$	0	0
$445$	−3.82247	−0.181203
$446$	−29.0518	−1.37564
$447$	0	0
$448$	−7.53512	−0.356001
$449$	23.4334	1.10589	0.552944	−	0.833218i	$-0.313504\pi$
$449$	23.4334	1.10589	0.552944	+	0.833218i	$0.313504\pi$
$450$	0	0
$451$	5.41988	0.255212
$452$	28.4256	1.33703
$453$	0	0
$454$	−3.93826	−0.184832
$455$	7.33615	0.343924
$456$	0	0
$457$	−8.25626	−0.386212	−0.193106	−	0.981178i	$-0.561856\pi$
$457$	−8.25626	−0.386212	−0.193106	+	0.981178i	$0.561856\pi$
$458$	−24.4085	−1.14053
$459$	0	0
$460$	−64.0627	−2.98694
$461$	8.79238	0.409502	0.204751	−	0.978814i	$-0.434362\pi$
$461$	8.79238	0.409502	0.204751	+	0.978814i	$0.434362\pi$
$462$	0	0
$463$	36.8884	1.71435	0.857175	−	0.515025i	$-0.172217\pi$
$463$	36.8884	1.71435	0.857175	+	0.515025i	$0.172217\pi$
$464$	−34.1100	−1.58352
$465$	0	0
$466$	19.4425	0.900655
$467$	21.8803	1.01250	0.506250	−	0.862387i	$-0.331031\pi$
$467$	21.8803	1.01250	0.506250	+	0.862387i	$0.331031\pi$
$468$	0	0
$469$	−8.78423	−0.405618
$470$	−29.3235	−1.35259
$471$	0	0
$472$	−12.2803	−0.565249
$473$	−34.2147	−1.57319
$474$	0	0
$475$	−0.598837	−0.0274765
$476$	−11.4353	−0.524134
$477$	0	0
$478$	−66.8093	−3.05579
$479$	−34.3678	−1.57030	−0.785152	−	0.619303i	$-0.787415\pi$
$479$	−34.3678	−1.57030	−0.785152	+	0.619303i	$0.787415\pi$
$480$	0	0
$481$	−0.151789	−0.00692098
$482$	47.6729	2.17144
$483$	0	0
$484$	74.1945	3.37248
$485$	42.6798	1.93799
$486$	0	0
$487$	15.9585	0.723146	0.361573	−	0.932344i	$-0.382240\pi$
$487$	15.9585	0.723146	0.361573	+	0.932344i	$0.382240\pi$
$488$	26.4541	1.19752
$489$	0	0
$490$	5.57007	0.251630
$491$	1.69863	0.0766581	0.0383290	−	0.999265i	$-0.487796\pi$
$491$	1.69863	0.0766581	0.0383290	+	0.999265i	$0.487796\pi$
$492$	0	0
$493$	22.8474	1.02900
$494$	−34.3611	−1.54598
$495$	0	0
$496$	38.8194	1.74304
$497$	12.1364	0.544394
$498$	0	0
$499$	−23.0520	−1.03195	−0.515975	−	0.856604i	$-0.672570\pi$
$499$	−23.0520	−1.03195	−0.515975	+	0.856604i	$0.672570\pi$
$500$	−44.4967	−1.98995
$501$	0	0
$502$	−67.4982	−3.01259
$503$	−34.6937	−1.54692	−0.773458	−	0.633848i	$-0.781474\pi$
$503$	−34.6937	−1.54692	−0.773458	+	0.633848i	$0.781474\pi$
$504$	0	0
$505$	−16.8858	−0.751409
$506$	−93.2112	−4.14374
$507$	0	0
$508$	77.1615	3.42349
$509$	7.41125	0.328498	0.164249	−	0.986419i	$-0.447480\pi$
$509$	7.41125	0.328498	0.164249	+	0.986419i	$0.447480\pi$
$510$	0	0
$511$	2.42993	0.107494
$512$	−40.7573	−1.80124
$513$	0	0
$514$	−53.1560	−2.34461
$515$	8.35723	0.368264
$516$	0	0
$517$	−28.5328	−1.25487
$518$	−0.115248	−0.00506370
$519$	0	0
$520$	36.7337	1.61088
$521$	24.2278	1.06144	0.530719	−	0.847548i	$-0.321922\pi$
$521$	24.2278	1.06144	0.530719	+	0.847548i	$0.321922\pi$
$522$	0	0
$523$	−43.3265	−1.89454	−0.947268	−	0.320442i	$-0.896169\pi$
$523$	−43.3265	−1.89454	−0.947268	+	0.320442i	$0.896169\pi$
$524$	−40.3552	−1.76293
$525$	0	0
$526$	24.1906	1.05476
$527$	−26.0018	−1.13266
$528$	0	0
$529$	25.9869	1.12987
$530$	−35.8502	−1.55723
$531$	0	0
$532$	−17.4471	−0.756429
$533$	3.23628	0.140179
$534$	0	0
$535$	19.4672	0.841643
$536$	−43.9846	−1.89984
$537$	0	0
$538$	64.0410	2.76100
$539$	5.41988	0.233451
$540$	0	0
$541$	−12.7180	−0.546788	−0.273394	−	0.961902i	$-0.588146\pi$
$541$	−12.7180	−0.546788	−0.273394	+	0.961902i	$0.588146\pi$
$542$	62.5370	2.68620
$543$	0	0
$544$	−1.06166	−0.0455183
$545$	−6.61718	−0.283449
$546$	0	0
$547$	−4.71489	−0.201594	−0.100797	−	0.994907i	$-0.532139\pi$
$547$	−4.71489	−0.201594	−0.100797	+	0.994907i	$0.532139\pi$
$548$	−18.8316	−0.804446
$549$	0	0
$550$	1.84568	0.0786999
$551$	34.8590	1.48504
$552$	0	0
$553$	4.92882	0.209595
$554$	72.1623	3.06588
$555$	0	0
$556$	−41.9743	−1.78011
$557$	11.0756	0.469288	0.234644	−	0.972081i	$-0.424608\pi$
$557$	11.0756	0.469288	0.234644	+	0.972081i	$0.424608\pi$
$558$	0	0
$559$	−20.4301	−0.864099
$560$	9.58451	0.405020
$561$	0	0
$562$	−59.4935	−2.50958
$563$	−24.9735	−1.05251	−0.526255	−	0.850327i	$-0.676404\pi$
$563$	−24.9735	−1.05251	−0.526255	+	0.850327i	$0.676404\pi$
$564$	0	0
$565$	15.9584	0.671374
$566$	21.8997	0.920515
$567$	0	0
$568$	60.7698	2.54985
$569$	−3.14116	−0.131684	−0.0658422	−	0.997830i	$-0.520973\pi$
$569$	−3.14116	−0.131684	−0.0658422	+	0.997830i	$0.520973\pi$
$570$	0	0
$571$	7.13418	0.298556	0.149278	−	0.988795i	$-0.452305\pi$
$571$	7.13418	0.298556	0.149278	+	0.988795i	$0.452305\pi$
$572$	70.8238	2.96129
$573$	0	0
$574$	2.45719	0.102561
$575$	−0.969990	−0.0404514
$576$	0	0
$577$	4.41995	0.184005	0.0920024	−	0.995759i	$-0.470673\pi$
$577$	4.41995	0.184005	0.0920024	+	0.995759i	$0.470673\pi$
$578$	−22.0642	−0.917748
$579$	0	0
$580$	−73.8413	−3.06609
$581$	1.63593	0.0678698
$582$	0	0
$583$	−34.8835	−1.44473
$584$	12.1672	0.503482
$585$	0	0
$586$	21.6046	0.892476
$587$	−29.7123	−1.22636	−0.613178	−	0.789944i	$-0.710109\pi$
$587$	−29.7123	−1.22636	−0.613178	+	0.789944i	$0.710109\pi$
$588$	0	0
$589$	−39.6718	−1.63465
$590$	−13.6608	−0.562404
$591$	0	0
$592$	−0.198309	−0.00815044
$593$	14.3020	0.587315	0.293657	−	0.955911i	$-0.405128\pi$
$593$	14.3020	0.587315	0.293657	+	0.955911i	$0.405128\pi$
$594$	0	0
$595$	−6.41985	−0.263188
$596$	−25.1574	−1.03049
$597$	0	0
$598$	−55.6577	−2.27601
$599$	−38.6159	−1.57780	−0.788902	−	0.614518i	$-0.789350\pi$
$599$	−38.6159	−1.57780	−0.788902	+	0.614518i	$0.789350\pi$
$600$	0	0
$601$	2.04839	0.0835557	0.0417779	−	0.999127i	$-0.486698\pi$
$601$	2.04839	0.0835557	0.0417779	+	0.999127i	$0.486698\pi$
$602$	−15.5118	−0.632213
$603$	0	0
$604$	−85.4186	−3.47563
$605$	41.6534	1.69345
$606$	0	0
$607$	5.79770	0.235321	0.117661	−	0.993054i	$-0.462460\pi$
$607$	5.79770	0.235321	0.117661	+	0.993054i	$0.462460\pi$
$608$	−1.61981	−0.0656920
$609$	0	0
$610$	29.4277	1.19149
$611$	−17.0373	−0.689257
$612$	0	0
$613$	45.3061	1.82989	0.914947	−	0.403573i	$-0.132232\pi$
$613$	45.3061	1.82989	0.914947	+	0.403573i	$0.132232\pi$
$614$	62.5378	2.52382
$615$	0	0
$616$	27.1385	1.09344
$617$	22.8349	0.919300	0.459650	−	0.888100i	$-0.347975\pi$
$617$	22.8349	0.919300	0.459650	+	0.888100i	$0.347975\pi$
$618$	0	0
$619$	15.2514	0.613007	0.306503	−	0.951870i	$-0.400841\pi$
$619$	15.2514	0.613007	0.306503	+	0.951870i	$0.400841\pi$
$620$	84.0360	3.37497
$621$	0	0
$622$	20.1680	0.808662
$623$	−1.68625	−0.0675583
$624$	0	0
$625$	−25.6737	−1.02695
$626$	19.2650	0.769983
$627$	0	0
$628$	82.7390	3.30165
$629$	0.132830	0.00529628
$630$	0	0
$631$	−40.2426	−1.60203	−0.801016	−	0.598643i	$-0.795707\pi$
$631$	−40.2426	−1.60203	−0.801016	+	0.598643i	$0.795707\pi$
$632$	24.6797	0.981706
$633$	0	0
$634$	−79.7012	−3.16534
$635$	43.3191	1.71907
$636$	0	0
$637$	3.23628	0.128226
$638$	−107.439	−4.25355
$639$	0	0
$640$	−43.6707	−1.72624
$641$	−8.41075	−0.332205	−0.166102	−	0.986109i	$-0.553118\pi$
$641$	−8.41075	−0.332205	−0.166102	+	0.986109i	$0.553118\pi$
$642$	0	0
$643$	−23.9146	−0.943101	−0.471550	−	0.881839i	$-0.656305\pi$
$643$	−23.9146	−0.943101	−0.471550	+	0.881839i	$0.656305\pi$
$644$	−28.2607	−1.11363
$645$	0	0
$646$	30.0693	1.18306
$647$	−10.9669	−0.431152	−0.215576	−	0.976487i	$-0.569163\pi$
$647$	−10.9669	−0.431152	−0.215576	+	0.976487i	$0.569163\pi$
$648$	0	0
$649$	−13.2924	−0.521772
$650$	1.10208	0.0432271
$651$	0	0
$652$	−6.60164	−0.258540
$653$	−29.3523	−1.14865	−0.574323	−	0.818629i	$-0.694735\pi$
$653$	−29.3523	−1.14865	−0.574323	+	0.818629i	$0.694735\pi$
$654$	0	0
$655$	−22.6558	−0.885234
$656$	4.22813	0.165081
$657$	0	0
$658$	−12.9358	−0.504291
$659$	12.7905	0.498245	0.249123	−	0.968472i	$-0.419858\pi$
$659$	12.7905	0.498245	0.249123	+	0.968472i	$0.419858\pi$
$660$	0	0
$661$	15.1159	0.587942	0.293971	−	0.955814i	$-0.405023\pi$
$661$	15.1159	0.587942	0.293971	+	0.955814i	$0.405023\pi$
$662$	34.0509	1.32342
$663$	0	0
$664$	8.19146	0.317890
$665$	−9.79497	−0.379833
$666$	0	0
$667$	56.4643	2.18631
$668$	80.0463	3.09708
$669$	0	0
$670$	−48.9288	−1.89028
$671$	28.6342	1.10541
$672$	0	0
$673$	10.3101	0.397425	0.198713	−	0.980058i	$-0.436324\pi$
$673$	10.3101	0.397425	0.198713	+	0.980058i	$0.436324\pi$
$674$	45.7235	1.76120
$675$	0	0
$676$	−10.2013	−0.392359
$677$	1.97105	0.0757535	0.0378768	−	0.999282i	$-0.487941\pi$
$677$	1.97105	0.0757535	0.0378768	+	0.999282i	$0.487941\pi$
$678$	0	0
$679$	18.8278	0.722546
$680$	−32.1456	−1.23273
$681$	0	0
$682$	122.273	4.68206
$683$	9.53970	0.365026	0.182513	−	0.983203i	$-0.441577\pi$
$683$	9.53970	0.365026	0.182513	+	0.983203i	$0.441577\pi$
$684$	0	0
$685$	−10.5722	−0.403944
$686$	2.45719	0.0938160
$687$	0	0
$688$	−26.6914	−1.01760
$689$	−20.8294	−0.793538
$690$	0	0
$691$	16.3915	0.623562	0.311781	−	0.950154i	$-0.399075\pi$
$691$	16.3915	0.623562	0.311781	+	0.950154i	$0.399075\pi$
$692$	37.6077	1.42963
$693$	0	0
$694$	−57.3276	−2.17613
$695$	−23.5647	−0.893861
$696$	0	0
$697$	−2.83206	−0.107272
$698$	−13.7497	−0.520434
$699$	0	0
$700$	0.559591	0.0211505
$701$	−12.1383	−0.458457	−0.229229	−	0.973373i	$-0.573620\pi$
$701$	−12.1383	−0.458457	−0.229229	+	0.973373i	$0.573620\pi$
$702$	0	0
$703$	0.202663	0.00764359
$704$	−40.8394	−1.53919
$705$	0	0
$706$	47.7382	1.79665
$707$	−7.44903	−0.280150
$708$	0	0
$709$	−29.6150	−1.11222	−0.556108	−	0.831110i	$-0.687706\pi$
$709$	−29.6150	−1.11222	−0.556108	+	0.831110i	$0.687706\pi$
$710$	67.6008	2.53701
$711$	0	0
$712$	−8.44344	−0.316431
$713$	−64.2600	−2.40656
$714$	0	0
$715$	39.7611	1.48698
$716$	70.0388	2.61747
$717$	0	0
$718$	−35.1691	−1.31250
$719$	−42.0273	−1.56735	−0.783676	−	0.621169i	$-0.786658\pi$
$719$	−42.0273	−1.56735	−0.783676	+	0.621169i	$0.786658\pi$
$720$	0	0
$721$	3.68672	0.137301
$722$	−0.808971	−0.0301068
$723$	0	0
$724$	40.9249	1.52096
$725$	−1.11805	−0.0415234
$726$	0	0
$727$	−41.0718	−1.52327	−0.761635	−	0.648007i	$-0.775603\pi$
$727$	−41.0718	−1.52327	−0.761635	+	0.648007i	$0.775603\pi$
$728$	16.2048	0.600589
$729$	0	0
$730$	13.5349	0.500948
$731$	17.8783	0.661252
$732$	0	0
$733$	9.51418	0.351414	0.175707	−	0.984442i	$-0.443779\pi$
$733$	9.51418	0.351414	0.175707	+	0.984442i	$0.443779\pi$
$734$	−52.2051	−1.92693
$735$	0	0
$736$	−2.62375	−0.0967128
$737$	−47.6094	−1.75372
$738$	0	0
$739$	−45.4606	−1.67230	−0.836148	−	0.548504i	$-0.815197\pi$
$739$	−45.4606	−1.67230	−0.836148	+	0.548504i	$0.815197\pi$
$740$	−0.429298	−0.0157813
$741$	0	0
$742$	−15.8150	−0.580587
$743$	51.1920	1.87805	0.939027	−	0.343845i	$-0.111729\pi$
$743$	51.1920	1.87805	0.939027	+	0.343845i	$0.111729\pi$
$744$	0	0
$745$	−14.1236	−0.517448
$746$	69.3595	2.53943
$747$	0	0
$748$	−61.9777	−2.26613
$749$	8.58781	0.313792
$750$	0	0
$751$	−32.2359	−1.17631	−0.588153	−	0.808750i	$-0.700145\pi$
$751$	−32.2359	−1.17631	−0.588153	+	0.808750i	$0.700145\pi$
$752$	−22.2589	−0.811698
$753$	0	0
$754$	−64.1534	−2.33633
$755$	−47.9547	−1.74525
$756$	0	0
$757$	−26.3465	−0.957581	−0.478790	−	0.877929i	$-0.658925\pi$
$757$	−26.3465	−0.957581	−0.478790	+	0.877929i	$0.658925\pi$
$758$	−21.0737	−0.765432
$759$	0	0
$760$	−49.0456	−1.77907
$761$	30.0811	1.09044	0.545219	−	0.838293i	$-0.316446\pi$
$761$	30.0811	1.09044	0.545219	+	0.838293i	$0.316446\pi$
$762$	0	0
$763$	−2.91912	−0.105679
$764$	−73.4713	−2.65810
$765$	0	0
$766$	−6.47207	−0.233845
$767$	−7.93707	−0.286591
$768$	0	0
$769$	−0.608700	−0.0219503	−0.0109751	−	0.999940i	$-0.503494\pi$
$769$	−0.608700	−0.0219503	−0.0109751	+	0.999940i	$0.503494\pi$
$770$	30.1891	1.08794
$771$	0	0
$772$	5.24708	0.188847
$773$	8.67944	0.312178	0.156089	−	0.987743i	$-0.450111\pi$
$773$	8.67944	0.312178	0.156089	+	0.987743i	$0.450111\pi$
$774$	0	0
$775$	1.27241	0.0457064
$776$	94.2751	3.38428
$777$	0	0
$778$	32.5962	1.16863
$779$	−4.32097	−0.154815
$780$	0	0
$781$	65.7780	2.35372
$782$	48.7059	1.74172
$783$	0	0
$784$	4.22813	0.151005
$785$	46.4504	1.65789
$786$	0	0
$787$	34.2640	1.22138	0.610689	−	0.791870i	$-0.290892\pi$
$787$	34.2640	1.22138	0.610689	+	0.791870i	$0.290892\pi$
$788$	−22.8005	−0.812235
$789$	0	0
$790$	27.4539	0.976766
$791$	7.03990	0.250310
$792$	0	0
$793$	17.0979	0.607164
$794$	5.61719	0.199347
$795$	0	0
$796$	−46.4622	−1.64681
$797$	−13.1568	−0.466036	−0.233018	−	0.972472i	$-0.574860\pi$
$797$	−13.1568	−0.466036	−0.233018	+	0.972472i	$0.574860\pi$
$798$	0	0
$799$	14.9093	0.527454
$800$	0.0519530	0.00183681
$801$	0	0
$802$	−6.86026	−0.242244
$803$	13.1699	0.464756
$804$	0	0
$805$	−15.8658	−0.559196
$806$	73.0106	2.57169
$807$	0	0
$808$	−37.2990	−1.31217
$809$	2.04798	0.0720033	0.0360017	−	0.999352i	$-0.488538\pi$
$809$	2.04798	0.0720033	0.0360017	+	0.999352i	$0.488538\pi$
$810$	0	0
$811$	5.48050	0.192446	0.0962232	−	0.995360i	$-0.469324\pi$
$811$	5.48050	0.192446	0.0962232	+	0.995360i	$0.469324\pi$
$812$	−32.5745	−1.14314
$813$	0	0
$814$	−0.624629	−0.0218932
$815$	−3.70622	−0.129823
$816$	0	0
$817$	27.2775	0.954318
$818$	−26.7265	−0.934471
$819$	0	0
$820$	9.15303	0.319638
$821$	1.55848	0.0543913	0.0271957	−	0.999630i	$-0.491342\pi$
$821$	1.55848	0.0543913	0.0271957	+	0.999630i	$0.491342\pi$
$822$	0	0
$823$	39.3703	1.37236	0.686182	−	0.727430i	$-0.259286\pi$
$823$	39.3703	1.37236	0.686182	+	0.727430i	$0.259286\pi$
$824$	18.4602	0.643093
$825$	0	0
$826$	−6.02633	−0.209683
$827$	26.3888	0.917628	0.458814	−	0.888532i	$-0.348274\pi$
$827$	26.3888	0.917628	0.458814	+	0.888532i	$0.348274\pi$
$828$	0	0
$829$	45.0610	1.56503	0.782517	−	0.622629i	$-0.213935\pi$
$829$	45.0610	1.56503	0.782517	+	0.622629i	$0.213935\pi$
$830$	9.11224	0.316291
$831$	0	0
$832$	−24.3858	−0.845425
$833$	−2.83206	−0.0981251
$834$	0	0
$835$	44.9387	1.55517
$836$	−94.5613	−3.27047
$837$	0	0
$838$	61.1957	2.11397
$839$	42.0761	1.45263	0.726314	−	0.687363i	$-0.241232\pi$
$839$	42.0761	1.45263	0.726314	+	0.687363i	$0.241232\pi$
$840$	0	0
$841$	36.0831	1.24425
$842$	−17.6034	−0.606655
$843$	0	0
$844$	−40.0790	−1.37958
$845$	−5.72712	−0.197019
$846$	0	0
$847$	18.3751	0.631375
$848$	−27.2131	−0.934503
$849$	0	0
$850$	−0.964426	−0.0330795
$851$	0.328272	0.0112530
$852$	0	0
$853$	−20.2803	−0.694384	−0.347192	−	0.937794i	$-0.612865\pi$
$853$	−20.2803	−0.694384	−0.347192	+	0.937794i	$0.612865\pi$
$854$	12.9818	0.444228
$855$	0	0
$856$	43.0011	1.46975
$857$	49.2604	1.68270	0.841351	−	0.540490i	$-0.181761\pi$
$857$	49.2604	1.68270	0.841351	+	0.540490i	$0.181761\pi$
$858$	0	0
$859$	−12.7326	−0.434430	−0.217215	−	0.976124i	$-0.569697\pi$
$859$	−12.7326	−0.434430	−0.217215	+	0.976124i	$0.569697\pi$
$860$	−57.7814	−1.97033
$861$	0	0
$862$	36.0072	1.22641
$863$	14.7535	0.502216	0.251108	−	0.967959i	$-0.419205\pi$
$863$	14.7535	0.502216	0.251108	+	0.967959i	$0.419205\pi$
$864$	0	0
$865$	21.1133	0.717872
$866$	−72.2838	−2.45630
$867$	0	0
$868$	37.0718	1.25830
$869$	26.7136	0.906197
$870$	0	0
$871$	−28.4282	−0.963254
$872$	−14.6167	−0.494982
$873$	0	0
$874$	74.3122	2.51365
$875$	−11.0201	−0.372546
$876$	0	0
$877$	−20.7432	−0.700450	−0.350225	−	0.936666i	$-0.613895\pi$
$877$	−20.7432	−0.700450	−0.350225	+	0.936666i	$0.613895\pi$
$878$	65.2648	2.20258
$879$	0	0
$880$	51.9469	1.75113
$881$	19.5041	0.657110	0.328555	−	0.944485i	$-0.393438\pi$
$881$	19.5041	0.657110	0.328555	+	0.944485i	$0.393438\pi$
$882$	0	0
$883$	27.7626	0.934286	0.467143	−	0.884182i	$-0.345283\pi$
$883$	27.7626	0.934286	0.467143	+	0.884182i	$0.345283\pi$
$884$	−37.0077	−1.24470
$885$	0	0
$886$	30.0693	1.01020
$887$	−35.3228	−1.18602	−0.593012	−	0.805194i	$-0.702061\pi$
$887$	−35.3228	−1.18602	−0.593012	+	0.805194i	$0.702061\pi$
$888$	0	0
$889$	19.1099	0.640924
$890$	−9.39254	−0.314839
$891$	0	0
$892$	−47.7394	−1.59843
$893$	22.7476	0.761221
$894$	0	0
$895$	39.3204	1.31434
$896$	−19.2650	−0.643598
$897$	0	0
$898$	57.5802	1.92148
$899$	−74.0687	−2.47033
$900$	0	0
$901$	18.2278	0.607255
$902$	13.3177	0.443430
$903$	0	0
$904$	35.2503	1.17241
$905$	22.9756	0.763734
$906$	0	0
$907$	10.5803	0.351312	0.175656	−	0.984452i	$-0.443795\pi$
$907$	10.5803	0.351312	0.175656	+	0.984452i	$0.443795\pi$
$908$	−6.47156	−0.214766
$909$	0	0
$910$	18.0263	0.597567
$911$	18.0853	0.599192	0.299596	−	0.954066i	$-0.403148\pi$
$911$	18.0853	0.599192	0.299596	+	0.954066i	$0.403148\pi$
$912$	0	0
$913$	8.86654	0.293440
$914$	−20.2872	−0.671041
$915$	0	0
$916$	−40.1093	−1.32525
$917$	−9.99440	−0.330044
$918$	0	0
$919$	9.90775	0.326826	0.163413	−	0.986558i	$-0.447750\pi$
$919$	9.90775	0.326826	0.163413	+	0.986558i	$0.447750\pi$
$920$	−79.4436	−2.61918
$921$	0	0
$922$	21.6046	0.711508
$923$	39.2770	1.29282
$924$	0	0
$925$	−0.00650012	−0.000213722 0
$926$	90.6419	2.97868
$927$	0	0
$928$	−3.02425	−0.0992757
$929$	15.2665	0.500878	0.250439	−	0.968132i	$-0.419425\pi$
$929$	15.2665	0.500878	0.250439	+	0.968132i	$0.419425\pi$
$930$	0	0
$931$	−4.32097	−0.141614
$932$	31.9489	1.04652
$933$	0	0
$934$	53.7641	1.75921
$935$	−34.7948	−1.13791
$936$	0	0
$937$	21.2126	0.692985	0.346492	−	0.938053i	$-0.387373\pi$
$937$	21.2126	0.692985	0.346492	+	0.938053i	$0.387373\pi$
$938$	−21.5845	−0.704759
$939$	0	0
$940$	−48.1859	−1.57165
$941$	34.1282	1.11255	0.556274	−	0.830999i	$-0.312230\pi$
$941$	34.1282	1.11255	0.556274	+	0.830999i	$0.312230\pi$
$942$	0	0
$943$	−6.99907	−0.227921
$944$	−10.3696	−0.337502
$945$	0	0
$946$	−84.0720	−2.73342
$947$	18.3584	0.596567	0.298284	−	0.954477i	$-0.403586\pi$
$947$	18.3584	0.596567	0.298284	+	0.954477i	$0.403586\pi$
$948$	0	0
$949$	7.86394	0.255274
$950$	−1.47146	−0.0477403
$951$	0	0
$952$	−14.1808	−0.459601
$953$	16.0790	0.520849	0.260424	−	0.965494i	$-0.416138\pi$
$953$	16.0790	0.520849	0.260424	+	0.965494i	$0.416138\pi$
$954$	0	0
$955$	−41.2474	−1.33473
$956$	−109.785	−3.55069
$957$	0	0
$958$	−84.4482	−2.72840
$959$	−4.66385	−0.150603
$960$	0	0
$961$	53.2949	1.71919
$962$	−0.372974	−0.0120252
$963$	0	0
$964$	78.3386	2.52312
$965$	2.94576	0.0948273
$966$	0	0
$967$	38.0340	1.22309	0.611546	−	0.791209i	$-0.290548\pi$
$967$	38.0340	1.22309	0.611546	+	0.791209i	$0.290548\pi$
$968$	92.0080	2.95725
$969$	0	0
$970$	104.872	3.36725
$971$	−60.7488	−1.94952	−0.974761	−	0.223250i	$-0.928333\pi$
$971$	−60.7488	−1.94952	−0.974761	+	0.223250i	$0.928333\pi$
$972$	0	0
$973$	−10.3954	−0.333261
$974$	39.2129	1.25646
$975$	0	0
$976$	22.3380	0.715021
$977$	4.23580	0.135515	0.0677576	−	0.997702i	$-0.478416\pi$
$977$	4.23580	0.135515	0.0677576	+	0.997702i	$0.478416\pi$
$978$	0	0
$979$	−9.13928	−0.292093
$980$	9.15303	0.292383
$981$	0	0
$982$	4.17386	0.133193
$983$	7.21490	0.230120	0.115060	−	0.993359i	$-0.463294\pi$
$983$	7.21490	0.230120	0.115060	+	0.993359i	$0.463294\pi$
$984$	0	0
$985$	−12.8004	−0.407855
$986$	56.1404	1.78788
$987$	0	0
$988$	−56.4639	−1.79636
$989$	44.1838	1.40496
$990$	0	0
$991$	−20.9196	−0.664533	−0.332267	−	0.943186i	$-0.607813\pi$
$991$	−20.9196	−0.664533	−0.332267	+	0.943186i	$0.607813\pi$
$992$	3.44178	0.109277
$993$	0	0
$994$	29.8215	0.945882
$995$	−26.0843	−0.826927
$996$	0	0
$997$	−18.4455	−0.584175	−0.292088	−	0.956392i	$-0.594350\pi$
$997$	−18.4455	−0.584175	−0.292088	+	0.956392i	$0.594350\pi$
$998$	−56.6432	−1.79301
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2583.2.a.r.1.5		5
3.2	odd	2		287.2.a.e.1.1	✓	5
12.11	even	2		4592.2.a.bb.1.5		5
15.14	odd	2		7175.2.a.n.1.5		5
21.20	even	2		2009.2.a.n.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.e.1.1	✓	5	3.2	odd	2
2009.2.a.n.1.1		5	21.20	even	2
2583.2.a.r.1.5		5	1.1	even	1	trivial
4592.2.a.bb.1.5		5	12.11	even	2
7175.2.a.n.1.5		5	15.14	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2583 = 3^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2583.a (trivial)

\(f(q)\)	\(=\)	\(q+2.45719 q^{2} +4.03778 q^{4} +2.26685 q^{5} +1.00000 q^{7} +5.00722 q^{8} +O(q^{10})\)	\(q+2.45719 q^{2} +4.03778 q^{4} +2.26685 q^{5} +1.00000 q^{7} +5.00722 q^{8} +5.57007 q^{10} +5.41988 q^{11} +3.23628 q^{13} +2.45719 q^{14} +4.22813 q^{16} -2.83206 q^{17} -4.32097 q^{19} +9.15303 q^{20} +13.3177 q^{22} -6.99907 q^{23} +0.138589 q^{25} +7.95216 q^{26} +4.03778 q^{28} -8.06741 q^{29} +9.18123 q^{31} +0.374872 q^{32} -6.95892 q^{34} +2.26685 q^{35} -0.0469023 q^{37} -10.6174 q^{38} +11.3506 q^{40} +1.00000 q^{41} -6.31281 q^{43} +21.8843 q^{44} -17.1980 q^{46} -5.26448 q^{47} +1.00000 q^{49} +0.340538 q^{50} +13.0674 q^{52} -6.43622 q^{53} +12.2860 q^{55} +5.00722 q^{56} -19.8232 q^{58} -2.45253 q^{59} +5.28319 q^{61} +22.5600 q^{62} -7.53512 q^{64} +7.33615 q^{65} -8.78423 q^{67} -11.4353 q^{68} +5.57007 q^{70} +12.1364 q^{71} +2.42993 q^{73} -0.115248 q^{74} -17.4471 q^{76} +5.41988 q^{77} +4.92882 q^{79} +9.58451 q^{80} +2.45719 q^{82} +1.63593 q^{83} -6.41985 q^{85} -15.5118 q^{86} +27.1385 q^{88} -1.68625 q^{89} +3.23628 q^{91} -28.2607 q^{92} -12.9358 q^{94} -9.79497 q^{95} +18.8278 q^{97} +2.45719 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 3 q^{4} + 5 q^{5} + 5 q^{7} + 3 q^{8}+O(q^{10}) \) 5 * q + q^2 + 3 * q^4 + 5 * q^5 + 5 * q^7 + 3 * q^8	\( 5 q + q^{2} + 3 q^{4} + 5 q^{5} + 5 q^{7} + 3 q^{8} - 2 q^{11} + 5 q^{13} + q^{14} - q^{16} - 13 q^{17} + 23 q^{20} + q^{22} - 2 q^{23} + 22 q^{25} + 3 q^{28} + 5 q^{29} + 17 q^{31} + 12 q^{32} - 8 q^{34} + 5 q^{35} - 7 q^{37} + 3 q^{38} + 7 q^{40} + 5 q^{41} + q^{43} + 47 q^{44} - 24 q^{46} - 9 q^{47} + 5 q^{49} - 2 q^{50} + 20 q^{52} - 5 q^{53} + 33 q^{55} + 3 q^{56} - 27 q^{58} - 7 q^{59} + 22 q^{61} + 28 q^{62} - 3 q^{64} + 31 q^{65} - 3 q^{67} - 17 q^{68} + 24 q^{71} + 40 q^{73} + 5 q^{74} - 19 q^{76} - 2 q^{77} - 42 q^{79} - 24 q^{80} + q^{82} + 12 q^{83} - 23 q^{85} - 16 q^{86} + 26 q^{88} - 8 q^{89} + 5 q^{91} - 12 q^{92} - 23 q^{94} + 17 q^{95} + 16 q^{97} + q^{98}+O(q^{100}) \) 5 * q + q^2 + 3 * q^4 + 5 * q^5 + 5 * q^7 + 3 * q^8 - 2 * q^11 + 5 * q^13 + q^14 - q^16 - 13 * q^17 + 23 * q^20 + q^22 - 2 * q^23 + 22 * q^25 + 3 * q^28 + 5 * q^29 + 17 * q^31 + 12 * q^32 - 8 * q^34 + 5 * q^35 - 7 * q^37 + 3 * q^38 + 7 * q^40 + 5 * q^41 + q^43 + 47 * q^44 - 24 * q^46 - 9 * q^47 + 5 * q^49 - 2 * q^50 + 20 * q^52 - 5 * q^53 + 33 * q^55 + 3 * q^56 - 27 * q^58 - 7 * q^59 + 22 * q^61 + 28 * q^62 - 3 * q^64 + 31 * q^65 - 3 * q^67 - 17 * q^68 + 24 * q^71 + 40 * q^73 + 5 * q^74 - 19 * q^76 - 2 * q^77 - 42 * q^79 - 24 * q^80 + q^82 + 12 * q^83 - 23 * q^85 - 16 * q^86 + 26 * q^88 - 8 * q^89 + 5 * q^91 - 12 * q^92 - 23 * q^94 + 17 * q^95 + 16 * q^97 + q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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