LMFDB - Embedded newform 1859.4.a.j.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1859,4,Mod(1,1859)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1859, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1859.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$N$	$=$	$1859 = 11 \cdot 13^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1859.a (trivial)

Newform invariants

comment:select newform

sage:traces = [18,-2,0,76,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{18} - 2 x^{17} - 108 x^{16} + 212 x^{15} + 4721 x^{14} - 8963 x^{13} - 107626 x^{12} + 194656 x^{11} + \cdots + 9847296$ x^18 - 2x^17 - 108x^16 + 212x^15 + 4721x^14 - 8963x^13 - 107626x^12 + 194656x^11 + 1375700x^10 - 2336289x^9 - 9875440x^8 + 15599166x^7 + 37652624x^6 - 55787484x^5 - 64147728x^4 + 92949968x^3 + 22620800x^2 - 43697856*x + 9847296
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$2^{5}\cdot 3^{2}$
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.370518$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-0.370518 q^{2} -0.548979 q^{3} -7.86272 q^{4} +11.6192 q^{5} +0.203406 q^{6} -19.9902 q^{7} +5.87742 q^{8} -26.6986 q^{9} -4.30511 q^{10} -11.0000 q^{11} +4.31646 q^{12} +7.40673 q^{14} -6.37868 q^{15} +60.7240 q^{16} +6.29819 q^{17} +9.89231 q^{18} +71.8312 q^{19} -91.3583 q^{20} +10.9742 q^{21} +4.07569 q^{22} -37.7543 q^{23} -3.22658 q^{24} +10.0053 q^{25} +29.4794 q^{27} +157.177 q^{28} +113.264 q^{29} +2.36341 q^{30} +253.495 q^{31} -69.5187 q^{32} +6.03876 q^{33} -2.33359 q^{34} -232.270 q^{35} +209.924 q^{36} +100.341 q^{37} -26.6147 q^{38} +68.2908 q^{40} +25.1578 q^{41} -4.06613 q^{42} -297.870 q^{43} +86.4899 q^{44} -310.216 q^{45} +13.9886 q^{46} +409.760 q^{47} -33.3362 q^{48} +56.6087 q^{49} -3.70715 q^{50} -3.45757 q^{51} +385.030 q^{53} -10.9226 q^{54} -127.811 q^{55} -117.491 q^{56} -39.4338 q^{57} -41.9662 q^{58} +416.523 q^{59} +50.1538 q^{60} -460.113 q^{61} -93.9243 q^{62} +533.711 q^{63} -460.034 q^{64} -2.23747 q^{66} +241.736 q^{67} -49.5209 q^{68} +20.7263 q^{69} +86.0601 q^{70} -554.420 q^{71} -156.919 q^{72} -402.299 q^{73} -37.1781 q^{74} -5.49270 q^{75} -564.788 q^{76} +219.892 q^{77} -490.363 q^{79} +705.564 q^{80} +704.679 q^{81} -9.32143 q^{82} -294.088 q^{83} -86.2870 q^{84} +73.1798 q^{85} +110.366 q^{86} -62.1794 q^{87} -64.6516 q^{88} -396.547 q^{89} +114.941 q^{90} +296.852 q^{92} -139.163 q^{93} -151.823 q^{94} +834.620 q^{95} +38.1643 q^{96} -852.333 q^{97} -20.9745 q^{98} +293.685 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$18 q - 2 q^{2} + 76 q^{4} - 20 q^{5} - 49 q^{6} - 28 q^{7} + 12 q^{8} + 180 q^{9} + 56 q^{10} - 198 q^{11} + 54 q^{12} + 4 q^{14} - 60 q^{15} + 364 q^{16} - 138 q^{17} - 298 q^{18} - 24 q^{19} - 160 q^{20}+ \cdots - 1980 q^{99}+O(q^{100})$ 18 * q - 2 * q^2 + 76 * q^4 - 20 * q^5 - 49 * q^6 - 28 * q^7 + 12 * q^8 + 180 * q^9 + 56 * q^10 - 198 * q^11 + 54 * q^12 + 4 * q^14 - 60 * q^15 + 364 * q^16 - 138 * q^17 - 298 * q^18 - 24 * q^19 - 160 * q^20 - 352 * q^21 + 22 * q^22 + 236 * q^23 - 124 * q^24 + 586 * q^25 - 6 * q^27 - 691 * q^28 - 286 * q^29 - 356 * q^30 - 642 * q^31 + 379 * q^32 - 2068 * q^34 + 34 * q^35 + 215 * q^36 - 530 * q^37 + 25 * q^38 - 108 * q^40 - 608 * q^41 + 563 * q^42 - 460 * q^43 - 836 * q^44 - 452 * q^45 + 580 * q^46 - 986 * q^47 + 837 * q^48 + 1082 * q^49 + 2578 * q^50 + 170 * q^51 + 1216 * q^53 - 1539 * q^54 + 220 * q^55 + 1137 * q^56 - 1282 * q^57 - 90 * q^58 - 1366 * q^59 - 5104 * q^60 - 922 * q^61 - 1398 * q^62 + 3236 * q^63 + 1296 * q^64 + 539 * q^66 - 1118 * q^67 - 2274 * q^68 + 1644 * q^69 - 416 * q^70 - 1118 * q^71 - 3295 * q^72 - 2444 * q^73 - 2018 * q^74 - 410 * q^75 + 1326 * q^76 + 308 * q^77 + 180 * q^79 - 5446 * q^80 + 426 * q^81 - 974 * q^82 + 696 * q^83 - 1061 * q^84 - 4580 * q^85 - 4652 * q^86 - 1240 * q^87 - 132 * q^88 + 3664 * q^89 + 248 * q^90 + 227 * q^92 - 3696 * q^93 - 244 * q^94 - 476 * q^95 + 5426 * q^96 - 2660 * q^97 - 6003 * q^98 - 1980 * 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

)

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

$2$	−0.370518	−0.130998	−0.0654989	−	0.997853i	$-0.520864\pi$
$2$	−0.370518	−0.130998	−0.0654989	+	0.997853i	$0.520864\pi$
$3$	−0.548979	−0.105651	−0.0528255	−	0.998604i	$-0.516823\pi$
$3$	−0.548979	−0.105651	−0.0528255	+	0.998604i	$0.516823\pi$
$4$	−7.86272	−0.982840
$5$	11.6192	1.03925	0.519625	−	0.854394i	$-0.326071\pi$
$5$	11.6192	1.03925	0.519625	+	0.854394i	$0.326071\pi$
$6$	0.203406	0.0138400
$7$	−19.9902	−1.07937	−0.539685	−	0.841867i	$-0.681457\pi$
$7$	−19.9902	−1.07937	−0.539685	+	0.841867i	$0.681457\pi$
$8$	5.87742	0.259748
$9$	−26.6986	−0.988838
$10$	−4.30511	−0.136140
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	4.31646	0.103838
$13$	0	0
$13$	0	0
$14$	7.40673	0.141395
$15$	−6.37868	−0.109798
$16$	60.7240	0.948813
$17$	6.29819	0.0898550	0.0449275	−	0.998990i	$-0.485694\pi$
$17$	6.29819	0.0898550	0.0449275	+	0.998990i	$0.485694\pi$
$18$	9.89231	0.129536
$19$	71.8312	0.867327	0.433663	−	0.901075i	$-0.357221\pi$
$19$	71.8312	0.867327	0.433663	+	0.901075i	$0.357221\pi$
$20$	−91.3583	−1.02142
$21$	10.9742	0.114037
$22$	4.07569	0.0394973
$23$	−37.7543	−0.342275	−0.171137	−	0.985247i	$-0.554744\pi$
$23$	−37.7543	−0.342275	−0.171137	+	0.985247i	$0.554744\pi$
$24$	−3.22658	−0.0274426
$25$	10.0053	0.0800425
$26$	0	0
$27$	29.4794	0.210123
$28$	157.177	1.06085
$29$	113.264	0.725261	0.362630	−	0.931933i	$-0.381879\pi$
$29$	113.264	0.725261	0.362630	+	0.931933i	$0.381879\pi$
$30$	2.36341	0.0143833
$31$	253.495	1.46868	0.734339	−	0.678783i	$-0.237492\pi$
$31$	253.495	1.46868	0.734339	+	0.678783i	$0.237492\pi$
$32$	−69.5187	−0.384040
$33$	6.03876	0.0318550
$34$	−2.33359	−0.0117708
$35$	−232.270	−1.12174
$36$	209.924	0.971869
$37$	100.341	0.445837	0.222919	−	0.974837i	$-0.428442\pi$
$37$	100.341	0.445837	0.222919	+	0.974837i	$0.428442\pi$
$38$	−26.6147	−0.113618
$39$	0	0
$40$	68.2908	0.269943
$41$	25.1578	0.0958292	0.0479146	−	0.998851i	$-0.484742\pi$
$41$	25.1578	0.0958292	0.0479146	+	0.998851i	$0.484742\pi$
$42$	−4.06613	−0.0149385
$43$	−297.870	−1.05639	−0.528195	−	0.849123i	$-0.677131\pi$
$43$	−297.870	−1.05639	−0.528195	+	0.849123i	$0.677131\pi$
$44$	86.4899	0.296337
$45$	−310.216	−1.02765
$46$	13.9886	0.0448373
$47$	409.760	1.27169	0.635847	−	0.771815i	$-0.280651\pi$
$47$	409.760	1.27169	0.635847	+	0.771815i	$0.280651\pi$
$48$	−33.3362	−0.100243
$49$	56.6087	0.165040
$50$	−3.70715	−0.0104854
$51$	−3.45757	−0.00949327
$52$	0	0
$53$	385.030	0.997884	0.498942	−	0.866635i	$-0.333722\pi$
$53$	385.030	0.997884	0.498942	+	0.866635i	$0.333722\pi$
$54$	−10.9226	−0.0275256
$55$	−127.811	−0.313346
$56$	−117.491	−0.280364
$57$	−39.4338	−0.0916339
$58$	−41.9662	−0.0950075
$59$	416.523	0.919097	0.459549	−	0.888153i	$-0.348011\pi$
$59$	416.523	0.919097	0.459549	+	0.888153i	$0.348011\pi$
$60$	50.1538	0.107914
$61$	−460.113	−0.965761	−0.482881	−	0.875686i	$-0.660410\pi$
$61$	−460.113	−0.965761	−0.482881	+	0.875686i	$0.660410\pi$
$62$	−93.9243	−0.192393
$63$	533.711	1.06732
$64$	−460.034	−0.898505
$65$	0	0
$66$	−2.23747	−0.00417293
$67$	241.736	0.440788	0.220394	−	0.975411i	$-0.429266\pi$
$67$	241.736	0.440788	0.220394	+	0.975411i	$0.429266\pi$
$68$	−49.5209	−0.0883131
$69$	20.7263	0.0361617
$70$	86.0601	0.146945
$71$	−554.420	−0.926727	−0.463363	−	0.886168i	$-0.653358\pi$
$71$	−554.420	−0.926727	−0.463363	+	0.886168i	$0.653358\pi$
$72$	−156.919	−0.256848
$73$	−402.299	−0.645008	−0.322504	−	0.946568i	$-0.604525\pi$
$73$	−402.299	−0.645008	−0.322504	+	0.946568i	$0.604525\pi$
$74$	−37.1781	−0.0584037
$75$	−5.49270	−0.00845657
$76$	−564.788	−0.852443
$77$	219.892	0.325442
$78$	0	0
$79$	−490.363	−0.698357	−0.349178	−	0.937056i	$-0.613539\pi$
$79$	−490.363	−0.698357	−0.349178	+	0.937056i	$0.613539\pi$
$80$	705.564	0.986055
$81$	704.679	0.966638
$82$	−9.32143	−0.0125534
$83$	−294.088	−0.388920	−0.194460	−	0.980910i	$-0.562295\pi$
$83$	−294.088	−0.388920	−0.194460	+	0.980910i	$0.562295\pi$
$84$	−86.2870	−0.112080
$85$	73.1798	0.0933819
$86$	110.366	0.138385
$87$	−62.1794	−0.0766245
$88$	−64.6516	−0.0783168
$89$	−396.547	−0.472291	−0.236146	−	0.971718i	$-0.575884\pi$
$89$	−396.547	−0.472291	−0.236146	+	0.971718i	$0.575884\pi$
$90$	114.941	0.134620
$91$	0	0
$92$	296.852	0.336401
$93$	−139.163	−0.155167
$94$	−151.823	−0.166589
$95$	834.620	0.901370
$96$	38.1643	0.0405742
$97$	−852.333	−0.892179	−0.446089	−	0.894988i	$-0.647184\pi$
$97$	−852.333	−0.892179	−0.446089	+	0.894988i	$0.647184\pi$
$98$	−20.9745	−0.0216199
$99$	293.685	0.298146
$100$	−78.6690	−0.0786690
$101$	414.163	0.408028	0.204014	−	0.978968i	$-0.434601\pi$
$101$	414.163	0.408028	0.204014	+	0.978968i	$0.434601\pi$
$102$	1.28109	0.00124360
$103$	−1094.16	−1.04671	−0.523353	−	0.852116i	$-0.675319\pi$
$103$	−1094.16	−1.04671	−0.523353	+	0.852116i	$0.675319\pi$
$104$	0	0
$105$	127.511	0.118513
$106$	−142.660	−0.130721
$107$	−1001.90	−0.905207	−0.452603	−	0.891712i	$-0.649505\pi$
$107$	−1001.90	−0.905207	−0.452603	+	0.891712i	$0.649505\pi$
$108$	−231.788	−0.206517
$109$	1310.76	1.15182	0.575909	−	0.817514i	$-0.304648\pi$
$109$	1310.76	1.15182	0.575909	+	0.817514i	$0.304648\pi$
$110$	47.3562	0.0410476
$111$	−55.0851	−0.0471031
$112$	−1213.89	−1.02412
$113$	1059.52	0.882045	0.441023	−	0.897496i	$-0.354616\pi$
$113$	1059.52	0.882045	0.441023	+	0.897496i	$0.354616\pi$
$114$	14.6109	0.0120038
$115$	−438.674	−0.355710
$116$	−890.561	−0.712815
$117$	0	0
$118$	−154.329	−0.120400
$119$	−125.902	−0.0969869
$120$	−37.4902	−0.0285197
$121$	121.000	0.0909091
$122$	170.480	0.126513
$123$	−13.8111	−0.0101244
$124$	−1993.16	−1.44347
$125$	−1336.14	−0.956067
$126$	−197.749	−0.139817
$127$	−288.170	−0.201346	−0.100673	−	0.994920i	$-0.532100\pi$
$127$	−288.170	−0.201346	−0.100673	+	0.994920i	$0.532100\pi$
$128$	726.600	0.501742
$129$	163.524	0.111609
$130$	0	0
$131$	−777.678	−0.518672	−0.259336	−	0.965787i	$-0.583504\pi$
$131$	−777.678	−0.518672	−0.259336	+	0.965787i	$0.583504\pi$
$132$	−47.4811	−0.0313083
$133$	−1435.92	−0.936167
$134$	−89.5676	−0.0577423
$135$	342.526	0.218370
$136$	37.0171	0.0233396
$137$	−1489.37	−0.928802	−0.464401	−	0.885625i	$-0.653730\pi$
$137$	−1489.37	−0.928802	−0.464401	+	0.885625i	$0.653730\pi$
$138$	−7.67947	−0.00473710
$139$	2056.72	1.25503	0.627514	−	0.778605i	$-0.284072\pi$
$139$	2056.72	1.25503	0.627514	+	0.778605i	$0.284072\pi$
$140$	1826.27	1.10249
$141$	−224.949	−0.134356
$142$	205.423	0.121399
$143$	0	0
$144$	−1621.25	−0.938222
$145$	1316.03	0.753728
$146$	149.059	0.0844946
$147$	−31.0769	−0.0174366
$148$	−788.953	−0.438186
$149$	−799.199	−0.439416	−0.219708	−	0.975566i	$-0.570510\pi$
$149$	−799.199	−0.439416	−0.219708	+	0.975566i	$0.570510\pi$
$150$	2.03514	0.00110779
$151$	−2561.75	−1.38061	−0.690306	−	0.723517i	$-0.742524\pi$
$151$	−2561.75	−1.38061	−0.690306	+	0.723517i	$0.742524\pi$
$152$	422.182	0.225286
$153$	−168.153	−0.0888521
$154$	−81.4740	−0.0426322
$155$	2945.40	1.52632
$156$	0	0
$157$	895.890	0.455413	0.227706	−	0.973730i	$-0.426877\pi$
$157$	895.890	0.455413	0.227706	+	0.973730i	$0.426877\pi$
$158$	181.688	0.0914832
$159$	−211.373	−0.105427
$160$	−807.750	−0.399114
$161$	754.717	0.369441
$162$	−261.096	−0.126627
$163$	841.453	0.404342	0.202171	−	0.979350i	$-0.435200\pi$
$163$	841.453	0.404342	0.202171	+	0.979350i	$0.435200\pi$
$164$	−197.809	−0.0941847
$165$	70.1655	0.0331053
$166$	108.965	0.0509476
$167$	4256.21	1.97219	0.986095	−	0.166184i	$-0.0531445\pi$
$167$	4256.21	1.97219	0.986095	+	0.166184i	$0.0531445\pi$
$168$	64.4999	0.0296207
$169$	0	0
$170$	−27.1144	−0.0122328
$171$	−1917.79	−0.857646
$172$	2342.07	1.03826
$173$	2668.41	1.17269	0.586346	−	0.810061i	$-0.300566\pi$
$173$	2668.41	1.17269	0.586346	+	0.810061i	$0.300566\pi$
$174$	23.0386	0.0100376
$175$	−200.008	−0.0863955
$176$	−667.965	−0.286078
$177$	−228.662	−0.0971035
$178$	146.928	0.0618691
$179$	−4420.16	−1.84569	−0.922845	−	0.385173i	$-0.874142\pi$
$179$	−4420.16	−1.84569	−0.922845	+	0.385173i	$0.874142\pi$
$180$	2439.14	1.01002
$181$	354.730	0.145673	0.0728367	−	0.997344i	$-0.476795\pi$
$181$	354.730	0.145673	0.0728367	+	0.997344i	$0.476795\pi$
$182$	0	0
$183$	252.592	0.102034
$184$	−221.898	−0.0889051
$185$	1165.88	0.463337
$186$	51.5624	0.0203266
$187$	−69.2801	−0.0270923
$188$	−3221.82	−1.24987
$189$	−589.299	−0.226800
$190$	−309.241	−0.118078
$191$	798.518	0.302507	0.151253	−	0.988495i	$-0.451669\pi$
$191$	798.518	0.302507	0.151253	+	0.988495i	$0.451669\pi$
$192$	252.549	0.0949279
$193$	2394.76	0.893155	0.446578	−	0.894745i	$-0.352643\pi$
$193$	2394.76	0.893155	0.446578	+	0.894745i	$0.352643\pi$
$194$	315.805	0.116873
$195$	0	0
$196$	−445.098	−0.162208
$197$	−4331.69	−1.56660	−0.783299	−	0.621645i	$-0.786465\pi$
$197$	−4331.69	−1.56660	−0.783299	+	0.621645i	$0.786465\pi$
$198$	−108.815	−0.0390564
$199$	4850.75	1.72794	0.863971	−	0.503541i	$-0.167970\pi$
$199$	4850.75	1.72794	0.863971	+	0.503541i	$0.167970\pi$
$200$	58.8054	0.0207909
$201$	−132.708	−0.0465697
$202$	−153.455	−0.0534507
$203$	−2264.17	−0.782825
$204$	27.1859	0.00933036
$205$	292.313	0.0995905
$206$	405.406	0.137116
$207$	1007.99	0.338454
$208$	0	0
$209$	−790.143	−0.261509
$210$	−47.2451	−0.0155249
$211$	2211.57	0.721569	0.360784	−	0.932649i	$-0.382509\pi$
$211$	2211.57	0.721569	0.360784	+	0.932649i	$0.382509\pi$
$212$	−3027.38	−0.980760
$213$	304.365	0.0979096
$214$	371.221	0.118580
$215$	−3461.00	−1.09785
$216$	173.263	0.0545789
$217$	−5067.41	−1.58525
$218$	−485.660	−0.150886
$219$	220.854	0.0681457
$220$	1004.94	0.307969
$221$	0	0
$222$	20.4100	0.00617040
$223$	−2734.21	−0.821059	−0.410530	−	0.911847i	$-0.634656\pi$
$223$	−2734.21	−0.821059	−0.410530	+	0.911847i	$0.634656\pi$
$224$	1389.69	0.414521
$225$	−267.128	−0.0791491
$226$	−392.570	−0.115546
$227$	−2762.57	−0.807745	−0.403873	−	0.914815i	$-0.632336\pi$
$227$	−2762.57	−0.807745	−0.403873	+	0.914815i	$0.632336\pi$
$228$	310.057	0.0900614
$229$	−6302.02	−1.81855	−0.909277	−	0.416191i	$-0.863365\pi$
$229$	−6302.02	−1.81855	−0.909277	+	0.416191i	$0.863365\pi$
$230$	162.537	0.0465972
$231$	−120.716	−0.0343833
$232$	665.699	0.188385
$233$	506.850	0.142510	0.0712551	−	0.997458i	$-0.477300\pi$
$233$	506.850	0.142510	0.0712551	+	0.997458i	$0.477300\pi$
$234$	0	0
$235$	4761.07	1.32161
$236$	−3275.01	−0.903325
$237$	269.199	0.0737821
$238$	46.6490	0.0127051
$239$	−570.486	−0.154400	−0.0772001	−	0.997016i	$-0.524598\pi$
$239$	−570.486	−0.154400	−0.0772001	+	0.997016i	$0.524598\pi$
$240$	−387.339	−0.104178
$241$	−5154.44	−1.37770	−0.688852	−	0.724902i	$-0.741885\pi$
$241$	−5154.44	−1.37770	−0.688852	+	0.724902i	$0.741885\pi$
$242$	−44.8326	−0.0119089
$243$	−1182.80	−0.312249
$244$	3617.74	0.949188
$245$	657.746	0.171518
$246$	5.11726	0.00132628
$247$	0	0
$248$	1489.89	0.381485
$249$	161.448	0.0410897
$250$	495.065	0.125243
$251$	−6819.28	−1.71486	−0.857429	−	0.514602i	$-0.827940\pi$
$251$	−6819.28	−1.71486	−0.857429	+	0.514602i	$0.827940\pi$
$252$	−4196.42	−1.04901
$253$	415.298	0.103200
$254$	106.772	0.0263759
$255$	−40.1741	−0.00986589
$256$	3411.06	0.832778
$257$	−5607.15	−1.36095	−0.680476	−	0.732771i	$-0.738227\pi$
$257$	−5607.15	−1.36095	−0.680476	+	0.732771i	$0.738227\pi$
$258$	−60.5886	−0.0146205
$259$	−2005.84	−0.481223
$260$	0	0
$261$	−3023.99	−0.717165
$262$	288.144	0.0679449
$263$	−3781.28	−0.886555	−0.443278	−	0.896384i	$-0.646184\pi$
$263$	−3781.28	−0.886555	−0.443278	+	0.896384i	$0.646184\pi$
$264$	35.4923	0.00827425
$265$	4473.73	1.03705
$266$	532.034	0.122636
$267$	217.696	0.0498980
$268$	−1900.71	−0.433224
$269$	−4827.98	−1.09430	−0.547151	−	0.837034i	$-0.684288\pi$
$269$	−4827.98	−1.09430	−0.547151	+	0.837034i	$0.684288\pi$
$270$	−126.912	−0.0286060
$271$	−5864.01	−1.31444	−0.657220	−	0.753699i	$-0.728268\pi$
$271$	−5864.01	−1.31444	−0.657220	+	0.753699i	$0.728268\pi$
$272$	382.452	0.0852557
$273$	0	0
$274$	551.840	0.121671
$275$	−110.058	−0.0241337
$276$	−162.965	−0.0355411
$277$	5378.70	1.16670	0.583348	−	0.812222i	$-0.301742\pi$
$277$	5378.70	1.16670	0.583348	+	0.812222i	$0.301742\pi$
$278$	−762.053	−0.164406
$279$	−6767.96	−1.45228
$280$	−1365.15	−0.291368
$281$	−7785.08	−1.65274	−0.826368	−	0.563131i	$-0.809597\pi$
$281$	−7785.08	−1.65274	−0.826368	+	0.563131i	$0.809597\pi$
$282$	83.3477	0.0176003
$283$	5481.62	1.15141	0.575704	−	0.817658i	$-0.304728\pi$
$283$	5481.62	1.15141	0.575704	+	0.817658i	$0.304728\pi$
$284$	4359.25	0.910824
$285$	−458.188	−0.0952306
$286$	0	0
$287$	−502.911	−0.103435
$288$	1856.05	0.379753
$289$	−4873.33	−0.991926
$290$	−487.613	−0.0987367
$291$	467.913	0.0942595
$292$	3163.17	0.633939
$293$	−6656.08	−1.32714	−0.663571	−	0.748114i	$-0.730960\pi$
$293$	−6656.08	−1.32714	−0.663571	+	0.748114i	$0.730960\pi$
$294$	11.5146	0.00228416
$295$	4839.66	0.955173
$296$	589.746	0.115805
$297$	−324.273	−0.0633544
$298$	296.117	0.0575625
$299$	0	0
$300$	43.1876	0.00831145
$301$	5954.49	1.14024
$302$	949.175	0.180857
$303$	−227.367	−0.0431085
$304$	4361.88	0.822931
$305$	−5346.14	−1.00367
$306$	62.3037	0.0116394
$307$	−6778.67	−1.26019	−0.630096	−	0.776517i	$-0.716985\pi$
$307$	−6778.67	−1.26019	−0.630096	+	0.776517i	$0.716985\pi$
$308$	−1728.95	−0.319858
$309$	600.670	0.110586
$310$	−1091.32	−0.199945
$311$	1691.71	0.308451	0.154226	−	0.988036i	$-0.450712\pi$
$311$	1691.71	0.308451	0.154226	+	0.988036i	$0.450712\pi$
$312$	0	0
$313$	4230.92	0.764043	0.382022	−	0.924153i	$-0.375228\pi$
$313$	4230.92	0.764043	0.382022	+	0.924153i	$0.375228\pi$
$314$	−331.943	−0.0596581
$315$	6201.29	1.10922
$316$	3855.59	0.686373
$317$	−867.246	−0.153657	−0.0768287	−	0.997044i	$-0.524479\pi$
$317$	−867.246	−0.153657	−0.0768287	+	0.997044i	$0.524479\pi$
$318$	78.3174	0.0138108
$319$	−1245.90	−0.218674
$320$	−5345.22	−0.933772
$321$	550.020	0.0956360
$322$	−279.636	−0.0483960
$323$	452.407	0.0779337
$324$	−5540.69	−0.950050
$325$	0	0
$326$	−311.773	−0.0529679
$327$	−719.580	−0.121691
$328$	147.863	0.0248914
$329$	−8191.18	−1.37263
$330$	−25.9976	−0.00433672
$331$	−3642.56	−0.604874	−0.302437	−	0.953169i	$-0.597800\pi$
$331$	−3642.56	−0.604874	−0.302437	+	0.953169i	$0.597800\pi$
$332$	2312.33	0.382246
$333$	−2678.97	−0.440861
$334$	−1577.00	−0.258352
$335$	2808.78	0.458090
$336$	666.398	0.108199
$337$	−8388.11	−1.35587	−0.677937	−	0.735120i	$-0.737126\pi$
$337$	−8388.11	−1.35587	−0.677937	+	0.735120i	$0.737126\pi$
$338$	0	0
$339$	−581.653	−0.0931889
$340$	−575.392	−0.0917795
$341$	−2788.44	−0.442823
$342$	710.577	0.112350
$343$	5725.02	0.901231
$344$	−1750.71	−0.274395
$345$	240.823	0.0375811
$346$	−988.695	−0.153620
$347$	−7895.82	−1.22153	−0.610763	−	0.791813i	$-0.709137\pi$
$347$	−7895.82	−1.22153	−0.610763	+	0.791813i	$0.709137\pi$
$348$	488.899	0.0753096
$349$	3785.89	0.580670	0.290335	−	0.956925i	$-0.406233\pi$
$349$	3785.89	0.580670	0.290335	+	0.956925i	$0.406233\pi$
$350$	74.1066	0.0113176
$351$	0	0
$352$	764.705	0.115792
$353$	11750.9	1.77177	0.885886	−	0.463902i	$-0.153551\pi$
$353$	11750.9	1.77177	0.885886	+	0.463902i	$0.153551\pi$
$354$	84.7235	0.0127203
$355$	−6441.91	−0.963102
$356$	3117.94	0.464187
$357$	69.1176	0.0102468
$358$	1637.75	0.241781
$359$	12559.3	1.84639	0.923195	−	0.384332i	$-0.125568\pi$
$359$	12559.3	1.84639	0.923195	+	0.384332i	$0.125568\pi$
$360$	−1823.27	−0.266930
$361$	−1699.28	−0.247744
$362$	−131.434	−0.0190829
$363$	−66.4264	−0.00960463
$364$	0	0
$365$	−4674.39	−0.670325
$366$	−93.5899	−0.0133662
$367$	−2343.63	−0.333342	−0.166671	−	0.986013i	$-0.553302\pi$
$367$	−2343.63	−0.333342	−0.166671	+	0.986013i	$0.553302\pi$
$368$	−2292.60	−0.324755
$369$	−671.680	−0.0947595
$370$	−431.980	−0.0606961
$371$	−7696.82	−1.07709
$372$	1094.20	0.152504
$373$	6730.50	0.934296	0.467148	−	0.884179i	$-0.345282\pi$
$373$	6730.50	0.934296	0.467148	+	0.884179i	$0.345282\pi$
$374$	25.6695	0.00354903
$375$	733.514	0.101009
$376$	2408.33	0.330319
$377$	0	0
$378$	218.346	0.0297103
$379$	−11278.4	−1.52858	−0.764288	−	0.644875i	$-0.776910\pi$
$379$	−11278.4	−1.52858	−0.764288	+	0.644875i	$0.776910\pi$
$380$	−6562.38	−0.885902
$381$	158.199	0.0212724
$382$	−295.865	−0.0396277
$383$	−5394.67	−0.719726	−0.359863	−	0.933005i	$-0.617177\pi$
$383$	−5394.67	−0.719726	−0.359863	+	0.933005i	$0.617177\pi$
$384$	−398.888	−0.0530095
$385$	2554.97	0.338216
$386$	−887.303	−0.117001
$387$	7952.72	1.04460
$388$	6701.65	0.876868
$389$	−8909.94	−1.16132	−0.580658	−	0.814148i	$-0.697205\pi$
$389$	−8909.94	−1.16132	−0.580658	+	0.814148i	$0.697205\pi$
$390$	0	0
$391$	−237.784	−0.0307551
$392$	332.713	0.0428687
$393$	426.929	0.0547982
$394$	1604.97	0.205221
$395$	−5697.62	−0.725768
$396$	−2309.16	−0.293030
$397$	7513.36	0.949835	0.474918	−	0.880030i	$-0.342478\pi$
$397$	7513.36	0.949835	0.474918	+	0.880030i	$0.342478\pi$
$398$	−1797.29	−0.226357
$399$	788.290	0.0989069
$400$	607.563	0.0759454
$401$	−4025.54	−0.501311	−0.250656	−	0.968076i	$-0.580646\pi$
$401$	−4025.54	−0.501311	−0.250656	+	0.968076i	$0.580646\pi$
$402$	49.1707	0.00610053
$403$	0	0
$404$	−3256.45	−0.401026
$405$	8187.79	1.00458
$406$	838.914	0.102548
$407$	−1103.75	−0.134425
$408$	−20.3216	−0.00246585
$409$	−13707.7	−1.65722	−0.828609	−	0.559828i	$-0.810867\pi$
$409$	−13707.7	−1.65722	−0.828609	+	0.559828i	$0.810867\pi$
$410$	−108.307	−0.0130461
$411$	817.635	0.0981288
$412$	8603.07	1.02874
$413$	−8326.39	−0.992046
$414$	−373.478	−0.0443368
$415$	−3417.06	−0.404185
$416$	0	0
$417$	−1129.10	−0.132595
$418$	292.762	0.0342571
$419$	−6830.53	−0.796404	−0.398202	−	0.917298i	$-0.630366\pi$
$419$	−6830.53	−0.796404	−0.398202	+	0.917298i	$0.630366\pi$
$420$	−1002.58	−0.116479
$421$	13958.9	1.61595	0.807974	−	0.589218i	$-0.200564\pi$
$421$	13958.9	1.61595	0.807974	+	0.589218i	$0.200564\pi$
$422$	−819.427	−0.0945239
$423$	−10940.0	−1.25750
$424$	2262.98	0.259198
$425$	63.0154	0.00719222
$426$	−112.773	−0.0128259
$427$	9197.76	1.04241
$428$	7877.64	0.889673
$429$	0	0
$430$	1282.36	0.143816
$431$	−2206.57	−0.246604	−0.123302	−	0.992369i	$-0.539348\pi$
$431$	−2206.57	−0.246604	−0.123302	+	0.992369i	$0.539348\pi$
$432$	1790.11	0.199367
$433$	7897.72	0.876536	0.438268	−	0.898844i	$-0.355592\pi$
$433$	7897.72	0.876536	0.438268	+	0.898844i	$0.355592\pi$
$434$	1877.57	0.207664
$435$	−722.473	−0.0796321
$436$	−10306.1	−1.13205
$437$	−2711.94	−0.296864
$438$	−81.8302	−0.00892694
$439$	−2111.17	−0.229523	−0.114762	−	0.993393i	$-0.536610\pi$
$439$	−2111.17	−0.229523	−0.114762	+	0.993393i	$0.536610\pi$
$440$	−751.198	−0.0813909
$441$	−1511.37	−0.163198
$442$	0	0
$443$	−4984.00	−0.534530	−0.267265	−	0.963623i	$-0.586120\pi$
$443$	−4984.00	−0.534530	−0.267265	+	0.963623i	$0.586120\pi$
$444$	433.119	0.0462948
$445$	−4607.55	−0.490829
$446$	1013.07	0.107557
$447$	438.743	0.0464247
$448$	9196.19	0.969819
$449$	11621.5	1.22150	0.610751	−	0.791823i	$-0.290868\pi$
$449$	11621.5	1.22150	0.610751	+	0.791823i	$0.290868\pi$
$450$	98.9757	0.0103684
$451$	−276.736	−0.0288936
$452$	−8330.69	−0.866909
$453$	1406.35	0.145863
$454$	1023.58	0.105813
$455$	0	0
$456$	−231.769	−0.0238017
$457$	−17200.8	−1.76066	−0.880329	−	0.474364i	$-0.842678\pi$
$457$	−17200.8	−1.76066	−0.880329	+	0.474364i	$0.842678\pi$
$458$	2335.01	0.238227
$459$	185.667	0.0188806
$460$	3449.17	0.349605
$461$	−2531.30	−0.255736	−0.127868	−	0.991791i	$-0.540813\pi$
$461$	−2531.30	−0.255736	−0.127868	+	0.991791i	$0.540813\pi$
$462$	44.7275	0.00450414
$463$	16502.1	1.65641	0.828203	−	0.560428i	$-0.189363\pi$
$463$	16502.1	1.65641	0.828203	+	0.560428i	$0.189363\pi$
$464$	6877.84	0.688137
$465$	−1616.96	−0.161258
$466$	−187.797	−0.0186685
$467$	12689.4	1.25737	0.628686	−	0.777659i	$-0.283593\pi$
$467$	12689.4	1.25737	0.628686	+	0.777659i	$0.283593\pi$
$468$	0	0
$469$	−4832.36	−0.475774
$470$	−1764.06	−0.173128
$471$	−491.824	−0.0481148
$472$	2448.08	0.238733
$473$	3276.57	0.318513
$474$	−99.7430	−0.00966529
$475$	718.694	0.0694230
$476$	989.933	0.0953225
$477$	−10279.8	−0.986746
$478$	211.375	0.0202261
$479$	861.353	0.0821633	0.0410817	−	0.999156i	$-0.486920\pi$
$479$	861.353	0.0821633	0.0410817	+	0.999156i	$0.486920\pi$
$480$	443.437	0.0421668
$481$	0	0
$482$	1909.81	0.180476
$483$	−414.324	−0.0390318
$484$	−951.389	−0.0893491
$485$	−9903.41	−0.927197
$486$	438.247	0.0409039
$487$	−10759.2	−1.00112	−0.500560	−	0.865702i	$-0.666873\pi$
$487$	−10759.2	−1.00112	−0.500560	+	0.865702i	$0.666873\pi$
$488$	−2704.28	−0.250854
$489$	−461.940	−0.0427191
$490$	−243.707	−0.0224685
$491$	17282.5	1.58849	0.794245	−	0.607598i	$-0.207867\pi$
$491$	17282.5	1.58849	0.794245	+	0.607598i	$0.207867\pi$
$492$	108.593	0.00995070
$493$	713.357	0.0651683
$494$	0	0
$495$	3412.38	0.309848
$496$	15393.2	1.39350
$497$	11083.0	1.00028
$498$	−59.8193	−0.00538266
$499$	265.837	0.0238487	0.0119244	−	0.999929i	$-0.496204\pi$
$499$	265.837	0.0238487	0.0119244	+	0.999929i	$0.496204\pi$
$500$	10505.7	0.939660
$501$	−2336.57	−0.208364
$502$	2526.67	0.224643
$503$	11660.0	1.03358	0.516792	−	0.856111i	$-0.327126\pi$
$503$	11660.0	1.03358	0.516792	+	0.856111i	$0.327126\pi$
$504$	3136.84	0.277234
$505$	4812.24	0.424043
$506$	−153.875	−0.0135189
$507$	0	0
$508$	2265.80	0.197891
$509$	19777.1	1.72221	0.861105	−	0.508427i	$-0.169773\pi$
$509$	19777.1	1.72221	0.861105	+	0.508427i	$0.169773\pi$
$510$	14.8852	0.00129241
$511$	8042.05	0.696202
$512$	−7076.66	−0.610834
$513$	2117.54	0.182245
$514$	2077.55	0.178282
$515$	−12713.2	−1.08779
$516$	−1285.74	−0.109693
$517$	−4507.36	−0.383430
$518$	743.199	0.0630392
$519$	−1464.90	−0.123896
$520$	0	0
$521$	10244.5	0.861458	0.430729	−	0.902481i	$-0.358256\pi$
$521$	10244.5	0.861458	0.430729	+	0.902481i	$0.358256\pi$
$522$	1120.44	0.0939470
$523$	535.008	0.0447309	0.0223654	−	0.999750i	$-0.492880\pi$
$523$	535.008	0.0447309	0.0223654	+	0.999750i	$0.492880\pi$
$524$	6114.66	0.509772
$525$	109.800	0.00912777
$526$	1401.03	0.116137
$527$	1596.56	0.131968
$528$	366.698	0.0302244
$529$	−10741.6	−0.882848
$530$	−1657.59	−0.135852
$531$	−11120.6	−0.908838
$532$	11290.2	0.920102
$533$	0	0
$534$	−80.6602	−0.00653653
$535$	−11641.2	−0.940737
$536$	1420.79	0.114494
$537$	2426.57	0.194999
$538$	1788.85	0.143351
$539$	−622.695	−0.0497614
$540$	−2693.19	−0.214623
$541$	−6941.17	−0.551616	−0.275808	−	0.961213i	$-0.588945\pi$
$541$	−6941.17	−0.551616	−0.275808	+	0.961213i	$0.588945\pi$
$542$	2172.72	0.172189
$543$	−194.739	−0.0153905
$544$	−437.842	−0.0345079
$545$	15230.0	1.19703
$546$	0	0
$547$	9812.69	0.767020	0.383510	−	0.923537i	$-0.374715\pi$
$547$	9812.69	0.767020	0.383510	+	0.923537i	$0.374715\pi$
$548$	11710.5	0.912863
$549$	12284.4	0.954981
$550$	40.7786	0.00316146
$551$	8135.88	0.629038
$552$	121.817	0.00939291
$553$	9802.47	0.753785
$554$	−1992.90	−0.152835
$555$	−640.044	−0.0489520
$556$	−16171.4	−1.23349
$557$	−20923.0	−1.59163	−0.795813	−	0.605542i	$-0.792956\pi$
$557$	−20923.0	−1.59163	−0.795813	+	0.605542i	$0.792956\pi$
$558$	2507.65	0.190246
$559$	0	0
$560$	−14104.4	−1.06432
$561$	38.0333	0.00286233
$562$	2884.51	0.216505
$563$	−18951.1	−1.41864	−0.709319	−	0.704887i	$-0.750998\pi$
$563$	−18951.1	−1.41864	−0.709319	+	0.704887i	$0.750998\pi$
$564$	1768.71	0.132050
$565$	12310.7	0.916666
$566$	−2031.04	−0.150832
$567$	−14086.7	−1.04336
$568$	−3258.56	−0.240715
$569$	−24060.2	−1.77268	−0.886342	−	0.463031i	$-0.846762\pi$
$569$	−24060.2	−1.77268	−0.886342	+	0.463031i	$0.846762\pi$
$570$	169.767	0.0124750
$571$	5557.77	0.407330	0.203665	−	0.979041i	$-0.434715\pi$
$571$	5557.77	0.407330	0.203665	+	0.979041i	$0.434715\pi$
$572$	0	0
$573$	−438.369	−0.0319601
$574$	186.337	0.0135498
$575$	−377.744	−0.0273965
$576$	12282.3	0.888476
$577$	−24437.9	−1.76319	−0.881597	−	0.472003i	$-0.843531\pi$
$577$	−24437.9	−1.76319	−0.881597	+	0.472003i	$0.843531\pi$
$578$	1805.66	0.129940
$579$	−1314.67	−0.0943627
$580$	−10347.6	−0.740793
$581$	5878.88	0.419788
$582$	−173.370	−0.0123478
$583$	−4235.32	−0.300873
$584$	−2364.48	−0.167539
$585$	0	0
$586$	2466.20	0.173853
$587$	−5503.17	−0.386951	−0.193476	−	0.981105i	$-0.561976\pi$
$587$	−5503.17	−0.386951	−0.193476	+	0.981105i	$0.561976\pi$
$588$	244.349	0.0171374
$589$	18208.8	1.27382
$590$	−1793.18	−0.125125
$591$	2378.00	0.165513
$592$	6093.12	0.423016
$593$	−2330.82	−0.161409	−0.0807043	−	0.996738i	$-0.525717\pi$
$593$	−2330.82	−0.161409	−0.0807043	+	0.996738i	$0.525717\pi$
$594$	120.149	0.00829928
$595$	−1462.88	−0.100794
$596$	6283.87	0.431875
$597$	−2662.96	−0.182559
$598$	0	0
$599$	3514.35	0.239720	0.119860	−	0.992791i	$-0.461755\pi$
$599$	3514.35	0.239720	0.119860	+	0.992791i	$0.461755\pi$
$600$	−32.2829	−0.00219657
$601$	5198.76	0.352849	0.176424	−	0.984314i	$-0.443547\pi$
$601$	5198.76	0.352849	0.176424	+	0.984314i	$0.443547\pi$
$602$	−2206.24	−0.149368
$603$	−6454.03	−0.435868
$604$	20142.3	1.35692
$605$	1405.92	0.0944774
$606$	84.2434	0.00564712
$607$	20939.8	1.40019	0.700097	−	0.714047i	$-0.253140\pi$
$607$	20939.8	1.40019	0.700097	+	0.714047i	$0.253140\pi$
$608$	−4993.61	−0.333088
$609$	1242.98	0.0827062
$610$	1980.84	0.131478
$611$	0	0
$612$	1322.14	0.0873273
$613$	−20854.6	−1.37408	−0.687038	−	0.726622i	$-0.741089\pi$
$613$	−20854.6	−1.37408	−0.687038	+	0.726622i	$0.741089\pi$
$614$	2511.62	0.165082
$615$	−160.474	−0.0105218
$616$	1292.40	0.0845329
$617$	−16354.9	−1.06714	−0.533569	−	0.845757i	$-0.679150\pi$
$617$	−16354.9	−1.06714	−0.533569	+	0.845757i	$0.679150\pi$
$618$	−222.559	−0.0144865
$619$	23288.7	1.51220	0.756099	−	0.654457i	$-0.227103\pi$
$619$	23288.7	1.51220	0.756099	+	0.654457i	$0.227103\pi$
$620$	−23158.8	−1.50013
$621$	−1112.97	−0.0719197
$622$	−626.810	−0.0404064
$623$	7927.06	0.509777
$624$	0	0
$625$	−16775.6	−1.07364
$626$	−1567.63	−0.100088
$627$	433.772	0.0276287
$628$	−7044.13	−0.447598
$629$	631.967	0.0400607
$630$	−2297.69	−0.145305
$631$	25716.8	1.62246	0.811229	−	0.584728i	$-0.198799\pi$
$631$	25716.8	1.62246	0.811229	+	0.584728i	$0.198799\pi$
$632$	−2882.07	−0.181396
$633$	−1214.11	−0.0762344
$634$	321.330	0.0201288
$635$	−3348.30	−0.209249
$636$	1661.97	0.103618
$637$	0	0
$638$	461.629	0.0286458
$639$	14802.3	0.916382
$640$	8442.50	0.521436
$641$	10221.0	0.629806	0.314903	−	0.949124i	$-0.398028\pi$
$641$	10221.0	0.629806	0.314903	+	0.949124i	$0.398028\pi$
$642$	−203.792	−0.0125281
$643$	9836.84	0.603308	0.301654	−	0.953417i	$-0.402461\pi$
$643$	9836.84	0.603308	0.301654	+	0.953417i	$0.402461\pi$
$644$	−5934.13	−0.363102
$645$	1900.02	0.115989
$646$	−167.625	−0.0102091
$647$	27544.5	1.67370	0.836851	−	0.547431i	$-0.184394\pi$
$647$	27544.5	1.67370	0.836851	+	0.547431i	$0.184394\pi$
$648$	4141.69	0.251082
$649$	−4581.76	−0.277118
$650$	0	0
$651$	2781.90	0.167483
$652$	−6616.11	−0.397403
$653$	−27098.7	−1.62397	−0.811986	−	0.583677i	$-0.801614\pi$
$653$	−27098.7	−1.62397	−0.811986	+	0.583677i	$0.801614\pi$
$654$	266.617	0.0159412
$655$	−9035.98	−0.539031
$656$	1527.69	0.0909240
$657$	10740.8	0.637808
$658$	3034.98	0.179811
$659$	24699.6	1.46003	0.730014	−	0.683432i	$-0.239513\pi$
$659$	24699.6	1.46003	0.730014	+	0.683432i	$0.239513\pi$
$660$	−551.691	−0.0325372
$661$	−5548.01	−0.326464	−0.163232	−	0.986588i	$-0.552192\pi$
$661$	−5548.01	−0.326464	−0.163232	+	0.986588i	$0.552192\pi$
$662$	1349.63	0.0792372
$663$	0	0
$664$	−1728.48	−0.101021
$665$	−16684.2	−0.972912
$666$	992.605	0.0577518
$667$	−4276.20	−0.248238
$668$	−33465.4	−1.93835
$669$	1501.02	0.0867457
$670$	−1040.70	−0.0600087
$671$	5061.24	0.291188
$672$	−762.912	−0.0437946
$673$	26941.8	1.54314	0.771569	−	0.636146i	$-0.219472\pi$
$673$	26941.8	1.54314	0.771569	+	0.636146i	$0.219472\pi$
$674$	3107.94	0.177617
$675$	294.951	0.0168187
$676$	0	0
$677$	2357.13	0.133814	0.0669069	−	0.997759i	$-0.478687\pi$
$677$	2357.13	0.133814	0.0669069	+	0.997759i	$0.478687\pi$
$678$	215.513	0.0122075
$679$	17038.3	0.962991
$680$	430.108	0.0242557
$681$	1516.59	0.0853391
$682$	1033.17	0.0580088
$683$	7349.73	0.411756	0.205878	−	0.978578i	$-0.433995\pi$
$683$	7349.73	0.411756	0.205878	+	0.978578i	$0.433995\pi$
$684$	15079.1	0.842928
$685$	−17305.3	−0.965258
$686$	−2121.22	−0.118059
$687$	3459.67	0.192132
$688$	−18087.9	−1.00232
$689$	0	0
$690$	−89.2291	−0.00492304
$691$	−7901.25	−0.434990	−0.217495	−	0.976061i	$-0.569789\pi$
$691$	−7901.25	−0.434990	−0.217495	+	0.976061i	$0.569789\pi$
$692$	−20981.0	−1.15257
$693$	−5870.82	−0.321810
$694$	2925.54	0.160017
$695$	23897.4	1.30429
$696$	−365.454	−0.0199030
$697$	158.449	0.00861073
$698$	−1402.74	−0.0760665
$699$	−278.250	−0.0150563
$700$	1572.61	0.0849129
$701$	−22650.1	−1.22037	−0.610187	−	0.792258i	$-0.708906\pi$
$701$	−22650.1	−1.22037	−0.610187	+	0.792258i	$0.708906\pi$
$702$	0	0
$703$	7207.62	0.386686
$704$	5060.38	0.270909
$705$	−2613.73	−0.139629
$706$	−4353.91	−0.232098
$707$	−8279.22	−0.440413
$708$	1797.91	0.0954372
$709$	−1520.18	−0.0805243	−0.0402621	−	0.999189i	$-0.512819\pi$
$709$	−1520.18	−0.0805243	−0.0402621	+	0.999189i	$0.512819\pi$
$710$	2386.84	0.126164
$711$	13092.0	0.690562
$712$	−2330.67	−0.122677
$713$	−9570.52	−0.502691
$714$	−25.6093	−0.00134230
$715$	0	0
$716$	34754.5	1.81402
$717$	313.184	0.0163125
$718$	−4653.44	−0.241873
$719$	−7000.07	−0.363085	−0.181543	−	0.983383i	$-0.558109\pi$
$719$	−7000.07	−0.363085	−0.181543	+	0.983383i	$0.558109\pi$
$720$	−18837.6	−0.975049
$721$	21872.5	1.12978
$722$	629.612	0.0324539
$723$	2829.68	0.145556
$724$	−2789.14	−0.143174
$725$	1133.24	0.0580517
$726$	24.6122	0.00125819
$727$	−31551.4	−1.60960	−0.804798	−	0.593549i	$-0.797726\pi$
$727$	−31551.4	−1.60960	−0.804798	+	0.593549i	$0.797726\pi$
$728$	0	0
$729$	−18377.0	−0.933649
$730$	1731.94	0.0878111
$731$	−1876.04	−0.0949219
$732$	−1986.06	−0.100283
$733$	16460.8	0.829458	0.414729	−	0.909945i	$-0.363876\pi$
$733$	16460.8	0.829458	0.414729	+	0.909945i	$0.363876\pi$
$734$	868.357	0.0436671
$735$	−361.089	−0.0181210
$736$	2624.63	0.131447
$737$	−2659.10	−0.132903
$738$	248.869	0.0124133
$739$	−9719.80	−0.483828	−0.241914	−	0.970298i	$-0.577775\pi$
$739$	−9719.80	−0.483828	−0.241914	+	0.970298i	$0.577775\pi$
$740$	−9166.99	−0.455386
$741$	0	0
$742$	2851.81	0.141096
$743$	−16063.9	−0.793174	−0.396587	−	0.917997i	$-0.629805\pi$
$743$	−16063.9	−0.793174	−0.396587	+	0.917997i	$0.629805\pi$
$744$	−817.920	−0.0403043
$745$	−9286.03	−0.456663
$746$	−2493.77	−0.122391
$747$	7851.74	0.384578
$748$	544.730	0.0266274
$749$	20028.2	0.977053
$750$	−271.780	−0.0132320
$751$	26001.5	1.26339	0.631695	−	0.775217i	$-0.282359\pi$
$751$	26001.5	1.26339	0.631695	+	0.775217i	$0.282359\pi$
$752$	24882.3	1.20660
$753$	3743.64	0.181176
$754$	0	0
$755$	−29765.5	−1.43480
$756$	4633.49	0.222908
$757$	9051.63	0.434593	0.217297	−	0.976106i	$-0.430276\pi$
$757$	9051.63	0.434593	0.217297	+	0.976106i	$0.430276\pi$
$758$	4178.83	0.200240
$759$	−227.990	−0.0109032
$760$	4905.41	0.234129
$761$	9914.92	0.472294	0.236147	−	0.971717i	$-0.424115\pi$
$761$	9914.92	0.472294	0.236147	+	0.971717i	$0.424115\pi$
$762$	−58.6156	−0.00278664
$763$	−26202.4	−1.24324
$764$	−6278.52	−0.297315
$765$	−1953.80	−0.0923396
$766$	1998.82	0.0942825
$767$	0	0
$768$	−1872.60	−0.0879838
$769$	−33616.0	−1.57636	−0.788181	−	0.615443i	$-0.788977\pi$
$769$	−33616.0	−1.57636	−0.788181	+	0.615443i	$0.788977\pi$
$770$	−946.661	−0.0443056
$771$	3078.21	0.143786
$772$	−18829.4	−0.877828
$773$	5047.85	0.234875	0.117438	−	0.993080i	$-0.462532\pi$
$773$	5047.85	0.234875	0.117438	+	0.993080i	$0.462532\pi$
$774$	−2946.62	−0.136840
$775$	2536.29	0.117557
$776$	−5009.52	−0.231741
$777$	1101.16	0.0508417
$778$	3301.29	0.152130
$779$	1807.12	0.0831152
$780$	0	0
$781$	6098.62	0.279419
$782$	88.1032	0.00402885
$783$	3338.95	0.152394
$784$	3437.51	0.156592
$785$	10409.5	0.473288
$786$	−158.185	−0.00717845
$787$	14751.4	0.668144	0.334072	−	0.942548i	$-0.391577\pi$
$787$	14751.4	0.668144	0.334072	+	0.942548i	$0.391577\pi$
$788$	34058.8	1.53971
$789$	2075.84	0.0936654
$790$	2111.07	0.0950740
$791$	−21180.0	−0.952053
$792$	1726.11	0.0774427
$793$	0	0
$794$	−2783.83	−0.124426
$795$	−2455.98	−0.109566
$796$	−38140.1	−1.69829
$797$	−13011.7	−0.578293	−0.289146	−	0.957285i	$-0.593371\pi$
$797$	−13011.7	−0.578293	−0.289146	+	0.957285i	$0.593371\pi$
$798$	−292.075	−0.0129566
$799$	2580.74	0.114268
$800$	−695.556	−0.0307395
$801$	10587.3	0.467019
$802$	1491.53	0.0656707
$803$	4425.29	0.194477
$804$	1043.45	0.0457705
$805$	8769.19	0.383942
$806$	0	0
$807$	2650.46	0.115614
$808$	2434.21	0.105984
$809$	−29356.1	−1.27578	−0.637891	−	0.770127i	$-0.720193\pi$
$809$	−29356.1	−1.27578	−0.637891	+	0.770127i	$0.720193\pi$
$810$	−3033.72	−0.131598
$811$	26529.9	1.14869	0.574347	−	0.818612i	$-0.305256\pi$
$811$	26529.9	1.14869	0.574347	+	0.818612i	$0.305256\pi$
$812$	17802.5	0.769391
$813$	3219.22	0.138872
$814$	408.960	0.0176094
$815$	9776.99	0.420212
$816$	−209.958	−0.00900734
$817$	−21396.4	−0.916235
$818$	5078.94	0.217092
$819$	0	0
$820$	−2298.38	−0.0978815
$821$	36143.0	1.53642	0.768210	−	0.640198i	$-0.221148\pi$
$821$	36143.0	1.53642	0.768210	+	0.640198i	$0.221148\pi$
$822$	−302.948	−0.0128547
$823$	−17671.9	−0.748484	−0.374242	−	0.927331i	$-0.622097\pi$
$823$	−17671.9	−0.748484	−0.374242	+	0.927331i	$0.622097\pi$
$824$	−6430.83	−0.271879
$825$	60.4197	0.00254975
$826$	3085.08	0.129956
$827$	3830.34	0.161057	0.0805284	−	0.996752i	$-0.474339\pi$
$827$	3830.34	0.161057	0.0805284	+	0.996752i	$0.474339\pi$
$828$	−7925.53	−0.332646
$829$	−27299.5	−1.14373	−0.571863	−	0.820349i	$-0.693779\pi$
$829$	−27299.5	−1.14373	−0.571863	+	0.820349i	$0.693779\pi$
$830$	1266.08	0.0529473
$831$	−2952.79	−0.123263
$832$	0	0
$833$	356.532	0.0148297
$834$	418.350	0.0173697
$835$	49453.7	2.04960
$836$	6212.67	0.257021
$837$	7472.87	0.308602
$838$	2530.83	0.104327
$839$	−10105.9	−0.415845	−0.207922	−	0.978145i	$-0.566670\pi$
$839$	−10105.9	−0.415845	−0.207922	+	0.978145i	$0.566670\pi$
$840$	749.436	0.0307833
$841$	−11560.3	−0.473997
$842$	−5172.01	−0.211686
$843$	4273.84	0.174613
$844$	−17389.0	−0.709186
$845$	0	0
$846$	4053.47	0.164730
$847$	−2418.82	−0.0981246
$848$	23380.5	0.946806
$849$	−3009.29	−0.121647
$850$	−23.3483	−0.000942165 0
$851$	−3788.31	−0.152599
$852$	−2393.13	−0.0962294
$853$	1436.66	0.0576672	0.0288336	−	0.999584i	$-0.490821\pi$
$853$	1436.66	0.0576672	0.0288336	+	0.999584i	$0.490821\pi$
$854$	−3407.93	−0.136554
$855$	−22283.2	−0.891309
$856$	−5888.57	−0.235125
$857$	−17076.2	−0.680645	−0.340323	−	0.940309i	$-0.610536\pi$
$857$	−17076.2	−0.680645	−0.340323	+	0.940309i	$0.610536\pi$
$858$	0	0
$859$	−1750.31	−0.0695226	−0.0347613	−	0.999396i	$-0.511067\pi$
$859$	−1750.31	−0.0695226	−0.0347613	+	0.999396i	$0.511067\pi$
$860$	27212.9	1.07901
$861$	276.087	0.0109280
$862$	817.571	0.0323046
$863$	43005.0	1.69630	0.848151	−	0.529755i	$-0.177716\pi$
$863$	43005.0	1.69630	0.848151	+	0.529755i	$0.177716\pi$
$864$	−2049.37	−0.0806955
$865$	31004.8	1.21872
$866$	−2926.24	−0.114824
$867$	2675.36	0.104798
$868$	39843.6	1.55804
$869$	5394.00	0.210562
$870$	267.689	0.0104316
$871$	0	0
$872$	7703.89	0.299182
$873$	22756.1	0.882220
$874$	1004.82	0.0388886
$875$	26709.8	1.03195
$876$	−1736.51	−0.0669763
$877$	14133.5	0.544191	0.272095	−	0.962270i	$-0.412283\pi$
$877$	14133.5	0.544191	0.272095	+	0.962270i	$0.412283\pi$
$878$	782.226	0.0300670
$879$	3654.05	0.140214
$880$	−7761.20	−0.297307
$881$	−22316.1	−0.853405	−0.426703	−	0.904392i	$-0.640325\pi$
$881$	−22316.1	−0.853405	−0.426703	+	0.904392i	$0.640325\pi$
$882$	559.991	0.0213785
$883$	14579.8	0.555660	0.277830	−	0.960630i	$-0.410385\pi$
$883$	14579.8	0.555660	0.277830	+	0.960630i	$0.410385\pi$
$884$	0	0
$885$	−2656.87	−0.100915
$886$	1846.66	0.0700222
$887$	−18320.9	−0.693524	−0.346762	−	0.937953i	$-0.612719\pi$
$887$	−18320.9	−0.693524	−0.346762	+	0.937953i	$0.612719\pi$
$888$	−323.758	−0.0122349
$889$	5760.58	0.217327
$890$	1707.18	0.0642975
$891$	−7751.47	−0.291452
$892$	21498.3	0.806969
$893$	29433.5	1.10297
$894$	−162.562	−0.00608153
$895$	−51358.6	−1.91813
$896$	−14524.9	−0.541566
$897$	0	0
$898$	−4305.98	−0.160014
$899$	28711.8	1.06517
$900$	2100.35	0.0777908
$901$	2424.99	0.0896649
$902$	102.536	0.00378499
$903$	−3268.88	−0.120467
$904$	6227.23	0.229109
$905$	4121.68	0.151391
$906$	−521.077	−0.0191077
$907$	34884.3	1.27708	0.638541	−	0.769588i	$-0.279538\pi$
$907$	34884.3	1.27708	0.638541	+	0.769588i	$0.279538\pi$
$908$	21721.3	0.793884
$909$	−11057.6	−0.403473
$910$	0	0
$911$	−2978.83	−0.108335	−0.0541674	−	0.998532i	$-0.517250\pi$
$911$	−2978.83	−0.108335	−0.0541674	+	0.998532i	$0.517250\pi$
$912$	−2394.58	−0.0869435
$913$	3234.96	0.117264
$914$	6373.21	0.230642
$915$	2934.91	0.106039
$916$	49551.0	1.78735
$917$	15546.0	0.559839
$918$	−68.7929	−0.00247331
$919$	−37880.6	−1.35970	−0.679850	−	0.733351i	$-0.737955\pi$
$919$	−37880.6	−1.35970	−0.679850	+	0.733351i	$0.737955\pi$
$920$	−2578.27	−0.0923947
$921$	3721.34	0.133141
$922$	937.892	0.0335009
$923$	0	0
$924$	949.157	0.0337933
$925$	1003.94	0.0356859
$926$	−6114.31	−0.216986
$927$	29212.6	1.03502
$928$	−7873.95	−0.278529
$929$	−9454.47	−0.333898	−0.166949	−	0.985966i	$-0.553391\pi$
$929$	−9454.47	−0.333898	−0.166949	+	0.985966i	$0.553391\pi$
$930$	599.113	0.0211244
$931$	4066.27	0.143144
$932$	−3985.22	−0.140065
$933$	−928.715	−0.0325882
$934$	−4701.63	−0.164713
$935$	−804.978	−0.0281557
$936$	0	0
$937$	−5608.48	−0.195540	−0.0977701	−	0.995209i	$-0.531171\pi$
$937$	−5608.48	−0.195540	−0.0977701	+	0.995209i	$0.531171\pi$
$938$	1790.48	0.0623253
$939$	−2322.68	−0.0807219
$940$	−37434.9	−1.29893
$941$	−44502.3	−1.54169	−0.770847	−	0.637020i	$-0.780167\pi$
$941$	−44502.3	−1.54169	−0.770847	+	0.637020i	$0.780167\pi$
$942$	182.230	0.00630293
$943$	−949.818	−0.0327999
$944$	25293.0	0.872051
$945$	−6847.17	−0.235702
$946$	−1214.03	−0.0417246
$947$	−44740.3	−1.53523	−0.767615	−	0.640911i	$-0.778557\pi$
$947$	−44740.3	−1.53523	−0.767615	+	0.640911i	$0.778557\pi$
$948$	−2116.64	−0.0725159
$949$	0	0
$950$	−266.289	−0.00909426
$951$	476.099	0.0162340
$952$	−739.980	−0.0251921
$953$	−10505.5	−0.357090	−0.178545	−	0.983932i	$-0.557139\pi$
$953$	−10505.5	−0.357090	−0.178545	+	0.983932i	$0.557139\pi$
$954$	3808.83	0.129262
$955$	9278.13	0.314380
$956$	4485.57	0.151751
$957$	683.973	0.0231032
$958$	−319.147	−0.0107632
$959$	29772.9	1.00252
$960$	2934.41	0.0986539
$961$	34468.5	1.15701
$962$	0	0
$963$	26749.3	0.895103
$964$	40527.9	1.35406
$965$	27825.2	0.928212
$966$	153.514	0.00511308
$967$	−41413.0	−1.37720	−0.688600	−	0.725141i	$-0.741775\pi$
$967$	−41413.0	−1.37720	−0.688600	+	0.725141i	$0.741775\pi$
$968$	711.167	0.0236134
$969$	−248.362	−0.00823377
$970$	3669.39	0.121461
$971$	11424.5	0.377579	0.188789	−	0.982018i	$-0.439544\pi$
$971$	11424.5	0.377579	0.188789	+	0.982018i	$0.439544\pi$
$972$	9300.00	0.306891
$973$	−41114.3	−1.35464
$974$	3986.47	0.131145
$975$	0	0
$976$	−27939.9	−0.916327
$977$	−56529.6	−1.85112	−0.925559	−	0.378603i	$-0.876405\pi$
$977$	−56529.6	−1.85112	−0.925559	+	0.378603i	$0.876405\pi$
$978$	171.157	0.00559611
$979$	4362.02	0.142401
$980$	−5171.67	−0.168575
$981$	−34995.5	−1.13896
$982$	−6403.47	−0.208089
$983$	31465.5	1.02095	0.510474	−	0.859893i	$-0.329470\pi$
$983$	31465.5	1.02095	0.510474	+	0.859893i	$0.329470\pi$
$984$	−81.1737	−0.00262980
$985$	−50330.6	−1.62809
$986$	−264.311	−0.00853691
$987$	4496.78	0.145019
$988$	0	0
$989$	11245.9	0.361576
$990$	−1264.35	−0.0405894
$991$	−18338.5	−0.587832	−0.293916	−	0.955831i	$-0.594959\pi$
$991$	−18338.5	−0.587832	−0.293916	+	0.955831i	$0.594959\pi$
$992$	−17622.6	−0.564031
$993$	1999.69	0.0639055
$994$	−4106.44	−0.131035
$995$	56361.7	1.79577
$996$	−1269.42	−0.0403846
$997$	28193.3	0.895577	0.447789	−	0.894140i	$-0.352212\pi$
$997$	28193.3	0.895577	0.447789	+	0.894140i	$0.352212\pi$
$998$	−98.4975	−0.00312413
$999$	2957.99	0.0936805

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.j.1.10		18
13.5	odd	4		143.4.b.a.12.19	yes	36
13.8	odd	4		143.4.b.a.12.18	✓	36
13.12	even	2		1859.4.a.k.1.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.18	✓	36	13.8	odd	4
143.4.b.a.12.19	yes	36	13.5	odd	4
1859.4.a.j.1.10		18	1.1	even	1	trivial
1859.4.a.k.1.9		18	13.12	even	2

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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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1859.4.a.j.1.10

Level	$1859$
Weight	$4$
Character	1859.1
Self dual	yes
Analytic conductor	$109.685$
Analytic rank	$1$
Dimension	$18$
CM	no
Inner twists	$1$