LMFDB - Embedded newform 197.4.a.b.1.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [197,4,Mod(1,197)] 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("197.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(197, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$N$	$=$	$197$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	197.a (trivial)

Newform invariants

comment:select newform

sage:traces = [27] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$11.6233762711$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
Character	$\chi$	$=$	197.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+5.09115 q^{2} -7.11573 q^{3} +17.9199 q^{4} +8.87787 q^{5} -36.2273 q^{6} -1.96838 q^{7} +50.5035 q^{8} +23.6336 q^{9} +45.1986 q^{10} +42.4210 q^{11} -127.513 q^{12} +41.5738 q^{13} -10.0213 q^{14} -63.1725 q^{15} +113.762 q^{16} +12.7473 q^{17} +120.322 q^{18} +52.0955 q^{19} +159.090 q^{20} +14.0064 q^{21} +215.972 q^{22} +43.8278 q^{23} -359.369 q^{24} -46.1834 q^{25} +211.659 q^{26} +23.9545 q^{27} -35.2730 q^{28} -233.629 q^{29} -321.621 q^{30} +15.4468 q^{31} +175.153 q^{32} -301.856 q^{33} +64.8985 q^{34} -17.4750 q^{35} +423.510 q^{36} -215.942 q^{37} +265.226 q^{38} -295.828 q^{39} +448.364 q^{40} +240.398 q^{41} +71.3089 q^{42} +72.1424 q^{43} +760.177 q^{44} +209.816 q^{45} +223.134 q^{46} +249.723 q^{47} -809.502 q^{48} -339.125 q^{49} -235.127 q^{50} -90.7063 q^{51} +744.996 q^{52} -656.998 q^{53} +121.956 q^{54} +376.608 q^{55} -99.4099 q^{56} -370.698 q^{57} -1189.44 q^{58} +282.407 q^{59} -1132.04 q^{60} -705.791 q^{61} +78.6422 q^{62} -46.5198 q^{63} -18.3653 q^{64} +369.087 q^{65} -1536.80 q^{66} -601.712 q^{67} +228.430 q^{68} -311.867 q^{69} -88.9679 q^{70} -839.471 q^{71} +1193.58 q^{72} +194.552 q^{73} -1099.40 q^{74} +328.629 q^{75} +933.544 q^{76} -83.5004 q^{77} -1506.10 q^{78} +450.776 q^{79} +1009.97 q^{80} -808.561 q^{81} +1223.90 q^{82} -156.891 q^{83} +250.993 q^{84} +113.169 q^{85} +367.288 q^{86} +1662.44 q^{87} +2142.41 q^{88} +315.273 q^{89} +1068.21 q^{90} -81.8329 q^{91} +785.389 q^{92} -109.915 q^{93} +1271.38 q^{94} +462.497 q^{95} -1246.34 q^{96} +1203.72 q^{97} -1726.54 q^{98} +1002.56 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$27 q + 4 q^{2} + 32 q^{3} + 128 q^{4} + 29 q^{5} + 36 q^{6} + 122 q^{7} + 27 q^{8} + 287 q^{9} + 127 q^{10} + 98 q^{11} + 256 q^{12} + 193 q^{13} + 113 q^{14} + 194 q^{15} + 672 q^{16} + 124 q^{17} + 61 q^{18}+ \cdots + 1940 q^{99}+O(q^{100})$ 27 * q + 4 * q^2 + 32 * q^3 + 128 * q^4 + 29 * q^5 + 36 * q^6 + 122 * q^7 + 27 * q^8 + 287 * q^9 + 127 * q^10 + 98 * q^11 + 256 * q^12 + 193 * q^13 + 113 * q^14 + 194 * q^15 + 672 * q^16 + 124 * q^17 + 61 * q^18 + 535 * q^19 + 279 * q^20 + 188 * q^21 + 165 * q^22 + 344 * q^23 + 165 * q^24 + 910 * q^25 - 44 * q^26 + 1382 * q^27 + 1038 * q^28 + 346 * q^29 + 115 * q^30 + 599 * q^31 + 100 * q^32 + 794 * q^33 + 886 * q^34 + 12 * q^35 + 1714 * q^36 + 1428 * q^37 + 1108 * q^38 + 568 * q^39 + 1206 * q^40 + 549 * q^41 + 355 * q^42 + 2091 * q^43 + 586 * q^44 + 1167 * q^45 + 469 * q^46 + 1270 * q^47 + 2258 * q^48 + 2165 * q^49 - 353 * q^50 - 128 * q^51 + 1000 * q^52 - 208 * q^53 - 2945 * q^54 + 810 * q^55 - 5592 * q^56 - 1006 * q^57 + 287 * q^58 + 603 * q^59 - 2211 * q^60 - 314 * q^61 - 1347 * q^62 + 2416 * q^63 + 5 * q^64 - 1958 * q^65 - 8706 * q^66 + 4372 * q^67 - 6709 * q^68 - 306 * q^69 - 4329 * q^70 - 871 * q^71 - 7589 * q^72 + 942 * q^73 - 5237 * q^74 - 1530 * q^75 - 2470 * q^76 - 1868 * q^77 - 10179 * q^78 - 197 * q^79 - 1882 * q^80 + 1083 * q^81 - 961 * q^82 - 799 * q^83 - 3140 * q^84 - 1444 * q^85 - 7066 * q^86 - 794 * q^87 - 2409 * q^88 - 572 * q^89 - 10939 * q^90 + 3872 * q^91 - 6154 * q^92 - 1506 * q^93 + 1231 * q^94 - 756 * q^95 - 10975 * q^96 + 6335 * q^97 - 5330 * q^98 + 1940 * 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

)

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

$2$	5.09115	1.79999	0.899997	−	0.435895i	$-0.143568\pi$
$2$	5.09115	1.79999	0.899997	+	0.435895i	$0.143568\pi$
$3$	−7.11573	−1.36942	−0.684711	−	0.728814i	$-0.740072\pi$
$3$	−7.11573	−1.36942	−0.684711	+	0.728814i	$0.740072\pi$
$4$	17.9199	2.23998
$5$	8.87787	0.794061	0.397030	−	0.917805i	$-0.370041\pi$
$5$	8.87787	0.794061	0.397030	+	0.917805i	$0.370041\pi$
$6$	−36.2273	−2.46495
$7$	−1.96838	−0.106282	−0.0531412	−	0.998587i	$-0.516923\pi$
$7$	−1.96838	−0.106282	−0.0531412	+	0.998587i	$0.516923\pi$
$8$	50.5035	2.23196
$9$	23.6336	0.875318
$10$	45.1986	1.42931
$11$	42.4210	1.16276	0.581382	−	0.813631i	$-0.302512\pi$
$11$	42.4210	1.16276	0.581382	+	0.813631i	$0.302512\pi$
$12$	−127.513	−3.06748
$13$	41.5738	0.886961	0.443481	−	0.896284i	$-0.353744\pi$
$13$	41.5738	0.886961	0.443481	+	0.896284i	$0.353744\pi$
$14$	−10.0213	−0.191308
$15$	−63.1725	−1.08740
$16$	113.762	1.77754
$17$	12.7473	0.181863	0.0909316	−	0.995857i	$-0.471016\pi$
$17$	12.7473	0.181863	0.0909316	+	0.995857i	$0.471016\pi$
$18$	120.322	1.57557
$19$	52.0955	0.629028	0.314514	−	0.949253i	$-0.398158\pi$
$19$	52.0955	0.629028	0.314514	+	0.949253i	$0.398158\pi$
$20$	159.090	1.77868
$21$	14.0064	0.145545
$22$	215.972	2.09297
$23$	43.8278	0.397336	0.198668	−	0.980067i	$-0.436338\pi$
$23$	43.8278	0.397336	0.198668	+	0.980067i	$0.436338\pi$
$24$	−359.369	−3.05650
$25$	−46.1834	−0.369467
$26$	211.659	1.59653
$27$	23.9545	0.170743
$28$	−35.2730	−0.238071
$29$	−233.629	−1.49600	−0.747998	−	0.663701i	$-0.768985\pi$
$29$	−233.629	−1.49600	−0.747998	+	0.663701i	$0.768985\pi$
$30$	−321.621	−1.95732
$31$	15.4468	0.0894946	0.0447473	−	0.998998i	$-0.485752\pi$
$31$	15.4468	0.0894946	0.0447473	+	0.998998i	$0.485752\pi$
$32$	175.153	0.967595
$33$	−301.856	−1.59231
$34$	64.8985	0.327353
$35$	−17.4750	−0.0843947
$36$	423.510	1.96070
$37$	−215.942	−0.959478	−0.479739	−	0.877411i	$-0.659269\pi$
$37$	−215.942	−0.959478	−0.479739	+	0.877411i	$0.659269\pi$
$38$	265.226	1.13225
$39$	−295.828	−1.21462
$40$	448.364	1.77231
$41$	240.398	0.915704	0.457852	−	0.889028i	$-0.348619\pi$
$41$	240.398	0.915704	0.457852	+	0.889028i	$0.348619\pi$
$42$	71.3089	0.261981
$43$	72.1424	0.255851	0.127926	−	0.991784i	$-0.459168\pi$
$43$	72.1424	0.255851	0.127926	+	0.991784i	$0.459168\pi$
$44$	760.177	2.60457
$45$	209.816	0.695056
$46$	223.134	0.715204
$47$	249.723	0.775017	0.387508	−	0.921866i	$-0.373336\pi$
$47$	249.723	0.775017	0.387508	+	0.921866i	$0.373336\pi$
$48$	−809.502	−2.43420
$49$	−339.125	−0.988704
$50$	−235.127	−0.665039
$51$	−90.7063	−0.249047
$52$	744.996	1.98678
$53$	−656.998	−1.70275	−0.851374	−	0.524559i	$-0.824230\pi$
$53$	−656.998	−1.70275	−0.851374	+	0.524559i	$0.824230\pi$
$54$	121.956	0.307336
$55$	376.608	0.923305
$56$	−99.4099	−0.237218
$57$	−370.698	−0.861405
$58$	−1189.44	−2.69279
$59$	282.407	0.623156	0.311578	−	0.950221i	$-0.399142\pi$
$59$	282.407	0.623156	0.311578	+	0.950221i	$0.399142\pi$
$60$	−1132.04	−2.43577
$61$	−705.791	−1.48143	−0.740715	−	0.671819i	$-0.765513\pi$
$61$	−705.791	−1.48143	−0.740715	+	0.671819i	$0.765513\pi$
$62$	78.6422	0.161090
$63$	−46.5198	−0.0930309
$64$	−18.3653	−0.0358698
$65$	369.087	0.704301
$66$	−1536.80	−2.86616
$67$	−601.712	−1.09718	−0.548588	−	0.836093i	$-0.684835\pi$
$67$	−601.712	−1.09718	−0.548588	+	0.836093i	$0.684835\pi$
$68$	228.430	0.407370
$69$	−311.867	−0.544121
$70$	−88.9679	−0.151910
$71$	−839.471	−1.40320	−0.701598	−	0.712573i	$-0.747530\pi$
$71$	−839.471	−1.40320	−0.701598	+	0.712573i	$0.747530\pi$
$72$	1193.58	1.95367
$73$	194.552	0.311927	0.155963	−	0.987763i	$-0.450152\pi$
$73$	194.552	0.311927	0.155963	+	0.987763i	$0.450152\pi$
$74$	−1099.40	−1.72706
$75$	328.629	0.505957
$76$	933.544	1.40901
$77$	−83.5004	−0.123581
$78$	−1506.10	−2.18632
$79$	450.776	0.641978	0.320989	−	0.947083i	$-0.395985\pi$
$79$	450.776	0.641978	0.320989	+	0.947083i	$0.395985\pi$
$80$	1009.97	1.41147
$81$	−808.561	−1.10914
$82$	1223.90	1.64826
$83$	−156.891	−0.207482	−0.103741	−	0.994604i	$-0.533081\pi$
$83$	−156.891	−0.207482	−0.103741	+	0.994604i	$0.533081\pi$
$84$	250.993	0.326019
$85$	113.169	0.144410
$86$	367.288	0.460531
$87$	1662.44	2.04865
$88$	2142.41	2.59524
$89$	315.273	0.375493	0.187746	−	0.982218i	$-0.439882\pi$
$89$	315.273	0.375493	0.187746	+	0.982218i	$0.439882\pi$
$90$	1068.21	1.25110
$91$	−81.8329	−0.0942683
$92$	785.389	0.890026
$93$	−109.915	−0.122556
$94$	1271.38	1.39503
$95$	462.497	0.499487
$96$	−1246.34	−1.32505
$97$	1203.72	1.25999	0.629997	−	0.776598i	$-0.283056\pi$
$97$	1203.72	1.25999	0.629997	+	0.776598i	$0.283056\pi$
$98$	−1726.54	−1.77966
$99$	1002.56	1.01779
$100$	−827.600	−0.827600
$101$	−765.123	−0.753788	−0.376894	−	0.926256i	$-0.623008\pi$
$101$	−765.123	−0.753788	−0.376894	+	0.926256i	$0.623008\pi$
$102$	−461.800	−0.448284
$103$	−1107.57	−1.05954	−0.529770	−	0.848142i	$-0.677722\pi$
$103$	−1107.57	−1.05954	−0.529770	+	0.848142i	$0.677722\pi$
$104$	2099.62	1.97966
$105$	124.347	0.115572
$106$	−3344.88	−3.06494
$107$	1518.06	1.37156	0.685779	−	0.727810i	$-0.259462\pi$
$107$	1518.06	1.37156	0.685779	+	0.727810i	$0.259462\pi$
$108$	429.261	0.382460
$109$	1225.87	1.07722	0.538610	−	0.842555i	$-0.318950\pi$
$109$	1225.87	1.07722	0.538610	+	0.842555i	$0.318950\pi$
$110$	1917.37	1.66194
$111$	1536.59	1.31393
$112$	−223.927	−0.188921
$113$	1620.59	1.34914	0.674568	−	0.738213i	$-0.264330\pi$
$113$	1620.59	1.34914	0.674568	+	0.738213i	$0.264330\pi$
$114$	−1887.28	−1.55052
$115$	389.098	0.315509
$116$	−4186.61	−3.35100
$117$	982.538	0.776373
$118$	1437.78	1.12168
$119$	−25.0915	−0.0193288
$120$	−3190.43	−2.42704
$121$	468.538	0.352019
$122$	−3593.29	−2.66657
$123$	−1710.61	−1.25399
$124$	276.805	0.200466
$125$	−1519.74	−1.08744
$126$	−236.839	−0.167455
$127$	134.430	0.0939268	0.0469634	−	0.998897i	$-0.485046\pi$
$127$	134.430	0.0939268	0.0469634	+	0.998897i	$0.485046\pi$
$128$	−1494.73	−1.03216
$129$	−513.346	−0.350369
$130$	1879.08	1.26774
$131$	1528.94	1.01973	0.509863	−	0.860256i	$-0.329696\pi$
$131$	1528.94	1.01973	0.509863	+	0.860256i	$0.329696\pi$
$132$	−5409.21	−3.56676
$133$	−102.544	−0.0668546
$134$	−3063.41	−1.97491
$135$	212.665	0.135580
$136$	643.783	0.405911
$137$	1604.07	1.00033	0.500165	−	0.865930i	$-0.333273\pi$
$137$	1604.07	1.00033	0.500165	+	0.865930i	$0.333273\pi$
$138$	−1587.76	−0.979416
$139$	−768.214	−0.468770	−0.234385	−	0.972144i	$-0.575308\pi$
$139$	−768.214	−0.468770	−0.234385	+	0.972144i	$0.575308\pi$
$140$	−313.149	−0.189043
$141$	−1776.96	−1.06133
$142$	−4273.88	−2.52574
$143$	1763.60	1.03133
$144$	2688.61	1.55591
$145$	−2074.13	−1.18791
$146$	990.496	0.561466
$147$	2413.12	1.35395
$148$	−3869.65	−2.14921
$149$	1587.53	0.872854	0.436427	−	0.899740i	$-0.356244\pi$
$149$	1587.53	0.872854	0.436427	+	0.899740i	$0.356244\pi$
$150$	1673.10	0.910720
$151$	2177.99	1.17379	0.586894	−	0.809664i	$-0.300351\pi$
$151$	2177.99	1.17379	0.586894	+	0.809664i	$0.300351\pi$
$152$	2631.01	1.40397
$153$	301.264	0.159188
$154$	−425.114	−0.222446
$155$	137.135	0.0710641
$156$	−5301.19	−2.72074
$157$	313.509	0.159368	0.0796839	−	0.996820i	$-0.474609\pi$
$157$	313.509	0.159368	0.0796839	+	0.996820i	$0.474609\pi$
$158$	2294.97	1.15556
$159$	4675.02	2.33178
$160$	1554.99	0.768329
$161$	−86.2697	−0.0422299
$162$	−4116.51	−1.99644
$163$	987.449	0.474497	0.237248	−	0.971449i	$-0.423754\pi$
$163$	987.449	0.474497	0.237248	+	0.971449i	$0.423754\pi$
$164$	4307.90	2.05116
$165$	−2679.84	−1.26439
$166$	−798.757	−0.373467
$167$	−3272.79	−1.51650	−0.758252	−	0.651962i	$-0.773946\pi$
$167$	−3272.79	−1.51650	−0.758252	+	0.651962i	$0.773946\pi$
$168$	707.374	0.324852
$169$	−468.620	−0.213300
$170$	576.160	0.259938
$171$	1231.20	0.550599
$172$	1292.78	0.573103
$173$	19.2438	0.00845711	0.00422856	−	0.999991i	$-0.498654\pi$
$173$	19.2438	0.00845711	0.00422856	+	0.999991i	$0.498654\pi$
$174$	8463.76	3.68756
$175$	90.9064	0.0392679
$176$	4825.91	2.06685
$177$	−2009.53	−0.853364
$178$	1605.10	0.675885
$179$	4285.49	1.78946	0.894728	−	0.446612i	$-0.147370\pi$
$179$	4285.49	1.78946	0.894728	+	0.446612i	$0.147370\pi$
$180$	3759.87	1.55691
$181$	−4484.90	−1.84177	−0.920885	−	0.389835i	$-0.872532\pi$
$181$	−4484.90	−1.84177	−0.920885	+	0.389835i	$0.872532\pi$
$182$	−416.624	−0.169683
$183$	5022.22	2.02870
$184$	2213.46	0.886839
$185$	−1917.11	−0.761884
$186$	−559.596	−0.220600
$187$	540.753	0.211464
$188$	4474.99	1.73602
$189$	−47.1515	−0.0181469
$190$	2354.65	0.899073
$191$	−4180.58	−1.58375	−0.791876	−	0.610683i	$-0.790895\pi$
$191$	−4180.58	−1.58375	−0.791876	+	0.610683i	$0.790895\pi$
$192$	130.683	0.0491209
$193$	−4134.36	−1.54196	−0.770978	−	0.636861i	$-0.780232\pi$
$193$	−4134.36	−1.54196	−0.770978	+	0.636861i	$0.780232\pi$
$194$	6128.33	2.26798
$195$	−2626.32	−0.964486
$196$	−6077.08	−2.21468
$197$	−197.000	−0.0712470
$197$	−197.000	−0.0712470
$198$	5104.18	1.83201
$199$	−3110.70	−1.10810	−0.554050	−	0.832483i	$-0.686918\pi$
$199$	−3110.70	−1.10810	−0.554050	+	0.832483i	$0.686918\pi$
$200$	−2332.42	−0.824636
$201$	4281.62	1.50250
$202$	−3895.36	−1.35681
$203$	459.871	0.158998
$204$	−1625.44	−0.557862
$205$	2134.22	0.727125
$206$	−5638.83	−1.90717
$207$	1035.81	0.347796
$208$	4729.53	1.57661
$209$	2209.94	0.731411
$210$	633.071	0.208029
$211$	−4073.35	−1.32901	−0.664505	−	0.747284i	$-0.731358\pi$
$211$	−4073.35	−1.32901	−0.664505	+	0.747284i	$0.731358\pi$
$212$	−11773.3	−3.81412
$213$	5973.45	1.92157
$214$	7728.69	2.46880
$215$	640.471	0.203162
$216$	1209.79	0.381091
$217$	−30.4052	−0.00951170
$218$	6241.09	1.93899
$219$	−1384.38	−0.427159
$220$	6748.76	2.06819
$221$	529.953	0.161306
$222$	7823.00	2.36507
$223$	966.544	0.290245	0.145122	−	0.989414i	$-0.453642\pi$
$223$	966.544	0.290245	0.145122	+	0.989414i	$0.453642\pi$
$224$	−344.768	−0.102838
$225$	−1091.48	−0.323401
$226$	8250.68	2.42844
$227$	1535.00	0.448817	0.224408	−	0.974495i	$-0.427955\pi$
$227$	1535.00	0.448817	0.224408	+	0.974495i	$0.427955\pi$
$228$	−6642.85	−1.92953
$229$	−1732.52	−0.499949	−0.249974	−	0.968252i	$-0.580422\pi$
$229$	−1732.52	−0.499949	−0.249974	+	0.968252i	$0.580422\pi$
$230$	1980.96	0.567915
$231$	594.166	0.169235
$232$	−11799.1	−3.33901
$233$	1099.95	0.309271	0.154636	−	0.987972i	$-0.450580\pi$
$233$	1099.95	0.309271	0.154636	+	0.987972i	$0.450580\pi$
$234$	5002.25	1.39747
$235$	2217.00	0.615410
$236$	5060.69	1.39586
$237$	−3207.60	−0.879139
$238$	−127.745	−0.0347918
$239$	−5081.87	−1.37539	−0.687696	−	0.725998i	$-0.741378\pi$
$239$	−5081.87	−1.37539	−0.687696	+	0.725998i	$0.741378\pi$
$240$	−7186.65	−1.93290
$241$	2518.15	0.673063	0.336531	−	0.941672i	$-0.390746\pi$
$241$	2518.15	0.673063	0.336531	+	0.941672i	$0.390746\pi$
$242$	2385.40	0.633633
$243$	5106.72	1.34813
$244$	−12647.7	−3.31838
$245$	−3010.71	−0.785091
$246$	−8708.97	−2.25717
$247$	2165.81	0.557923
$248$	780.119	0.199748
$249$	1116.39	0.284131
$250$	−7737.25	−1.95739
$251$	−7405.92	−1.86238	−0.931190	−	0.364533i	$-0.881229\pi$
$251$	−7405.92	−1.86238	−0.931190	+	0.364533i	$0.881229\pi$
$252$	−833.628	−0.208387
$253$	1859.22	0.462008
$254$	684.402	0.169068
$255$	−805.279	−0.197759
$256$	−7462.97	−1.82201
$257$	−2828.26	−0.686468	−0.343234	−	0.939250i	$-0.611522\pi$
$257$	−2828.26	−0.686468	−0.343234	+	0.939250i	$0.611522\pi$
$258$	−2613.52	−0.630662
$259$	425.056	0.101976
$260$	6613.98	1.57762
$261$	−5521.50	−1.30947
$262$	7784.07	1.83550
$263$	−837.347	−0.196323	−0.0981616	−	0.995170i	$-0.531296\pi$
$263$	−837.347	−0.196323	−0.0981616	+	0.995170i	$0.531296\pi$
$264$	−15244.8	−3.55398
$265$	−5832.74	−1.35209
$266$	−522.065	−0.120338
$267$	−2243.39	−0.514208
$268$	−10782.6	−2.45765
$269$	4497.30	1.01935	0.509675	−	0.860367i	$-0.329765\pi$
$269$	4497.30	1.01935	0.509675	+	0.860367i	$0.329765\pi$
$270$	1082.71	0.244043
$271$	5054.80	1.13305	0.566527	−	0.824044i	$-0.308287\pi$
$271$	5054.80	1.13305	0.566527	+	0.824044i	$0.308287\pi$
$272$	1450.16	0.323268
$273$	582.301	0.129093
$274$	8166.58	1.80059
$275$	−1959.14	−0.429603
$276$	−5588.61	−1.21882
$277$	802.454	0.174061	0.0870303	−	0.996206i	$-0.472262\pi$
$277$	802.454	0.174061	0.0870303	+	0.996206i	$0.472262\pi$
$278$	−3911.09	−0.843784
$279$	365.064	0.0783362
$280$	−882.549	−0.188366
$281$	317.255	0.0673518	0.0336759	−	0.999433i	$-0.489279\pi$
$281$	317.255	0.0673518	0.0336759	+	0.999433i	$0.489279\pi$
$282$	−9046.77	−1.91038
$283$	8877.78	1.86477	0.932384	−	0.361469i	$-0.117725\pi$
$283$	8877.78	1.86477	0.932384	+	0.361469i	$0.117725\pi$
$284$	−15043.2	−3.14313
$285$	−3291.01	−0.684008
$286$	8978.76	1.85638
$287$	−473.194	−0.0973232
$288$	4139.50	0.846953
$289$	−4750.51	−0.966926
$290$	−10559.7	−2.13824
$291$	−8565.36	−1.72546
$292$	3486.35	0.698710
$293$	−4476.58	−0.892576	−0.446288	−	0.894889i	$-0.647254\pi$
$293$	−4476.58	−0.892576	−0.446288	+	0.894889i	$0.647254\pi$
$294$	12285.6	2.43711
$295$	2507.17	0.494824
$296$	−10905.8	−2.14152
$297$	1016.17	0.198533
$298$	8082.35	1.57113
$299$	1822.09	0.352422
$300$	5888.98	1.13333
$301$	−142.003	−0.0271925
$302$	11088.5	2.11281
$303$	5444.41	1.03225
$304$	5926.51	1.11812
$305$	−6265.92	−1.17635
$306$	1533.78	0.286538
$307$	8536.52	1.58699	0.793493	−	0.608579i	$-0.208260\pi$
$307$	8536.52	1.58699	0.793493	+	0.608579i	$0.208260\pi$
$308$	−1496.32	−0.276820
$309$	7881.20	1.45096
$310$	698.175	0.127915
$311$	4646.49	0.847198	0.423599	−	0.905850i	$-0.360767\pi$
$311$	4646.49	0.847198	0.423599	+	0.905850i	$0.360767\pi$
$312$	−14940.3	−2.71099
$313$	−142.834	−0.0257938	−0.0128969	−	0.999917i	$-0.504105\pi$
$313$	−142.834	−0.0257938	−0.0128969	+	0.999917i	$0.504105\pi$
$314$	1596.12	0.286861
$315$	−412.997	−0.0738722
$316$	8077.84	1.43802
$317$	5928.47	1.05040	0.525199	−	0.850980i	$-0.323991\pi$
$317$	5928.47	1.05040	0.525199	+	0.850980i	$0.323991\pi$
$318$	23801.2	4.19719
$319$	−9910.78	−1.73949
$320$	−163.045	−0.0284828
$321$	−10802.1	−1.87824
$322$	−439.213	−0.0760135
$323$	664.077	0.114397
$324$	−14489.3	−2.48445
$325$	−1920.02	−0.327703
$326$	5027.25	0.854092
$327$	−8722.95	−1.47517
$328$	12140.9	2.04382
$329$	−491.548	−0.0823706
$330$	−13643.5	−2.27590
$331$	−4672.81	−0.775954	−0.387977	−	0.921669i	$-0.626826\pi$
$331$	−4672.81	−0.775954	−0.387977	+	0.921669i	$0.626826\pi$
$332$	−2811.47	−0.464757
$333$	−5103.49	−0.839848
$334$	−16662.3	−2.72970
$335$	−5341.92	−0.871225
$336$	1593.40	0.258712
$337$	11080.2	1.79103	0.895516	−	0.445029i	$-0.146807\pi$
$337$	11080.2	1.79103	0.895516	+	0.445029i	$0.146807\pi$
$338$	−2385.82	−0.383939
$339$	−11531.7	−1.84754
$340$	2027.97	0.323477
$341$	655.269	0.104061
$342$	6268.25	0.991076
$343$	1342.68	0.211364
$344$	3643.44	0.571050
$345$	−2768.72	−0.432066
$346$	97.9732	0.0152228
$347$	4385.47	0.678457	0.339229	−	0.940704i	$-0.389834\pi$
$347$	4385.47	0.678457	0.339229	+	0.940704i	$0.389834\pi$
$348$	29790.7	4.58894
$349$	9625.37	1.47632	0.738158	−	0.674628i	$-0.235696\pi$
$349$	9625.37	1.47632	0.738158	+	0.674628i	$0.235696\pi$
$350$	462.818	0.0706819
$351$	995.880	0.151442
$352$	7430.18	1.12508
$353$	−1358.83	−0.204882	−0.102441	−	0.994739i	$-0.532665\pi$
$353$	−1358.83	−0.204882	−0.102441	+	0.994739i	$0.532665\pi$
$354$	−10230.8	−1.53605
$355$	−7452.71	−1.11422
$356$	5649.64	0.841097
$357$	178.544	0.0264694
$358$	21818.1	3.22101
$359$	−9675.16	−1.42238	−0.711192	−	0.702998i	$-0.751844\pi$
$359$	−9675.16	−1.42238	−0.711192	+	0.702998i	$0.751844\pi$
$360$	10596.4	1.55134
$361$	−4145.06	−0.604324
$362$	−22833.3	−3.31518
$363$	−3333.99	−0.482063
$364$	−1466.43	−0.211159
$365$	1727.21	0.247689
$366$	25568.9	3.65166
$367$	5885.72	0.837145	0.418573	−	0.908183i	$-0.362531\pi$
$367$	5885.72	0.837145	0.418573	+	0.908183i	$0.362531\pi$
$368$	4985.96	0.706280
$369$	5681.47	0.801532
$370$	−9760.29	−1.37139
$371$	1293.22	0.180972
$372$	−1969.67	−0.274523
$373$	1559.60	0.216496	0.108248	−	0.994124i	$-0.465476\pi$
$373$	1559.60	0.216496	0.108248	+	0.994124i	$0.465476\pi$
$374$	2753.05	0.380634
$375$	10814.1	1.48917
$376$	12611.9	1.72981
$377$	−9712.86	−1.32689
$378$	−240.056	−0.0326644
$379$	5934.09	0.804258	0.402129	−	0.915583i	$-0.368270\pi$
$379$	5934.09	0.804258	0.402129	+	0.915583i	$0.368270\pi$
$380$	8287.88	1.11884
$381$	−956.565	−0.128625
$382$	−21284.0	−2.85074
$383$	−1391.38	−0.185630	−0.0928149	−	0.995683i	$-0.529586\pi$
$383$	−1391.38	−0.185630	−0.0928149	+	0.995683i	$0.529586\pi$
$384$	10636.1	1.41346
$385$	−741.306	−0.0981311
$386$	−21048.7	−2.77551
$387$	1704.98	0.223951
$388$	21570.5	2.82236
$389$	−3761.01	−0.490207	−0.245104	−	0.969497i	$-0.578822\pi$
$389$	−3761.01	−0.490207	−0.245104	+	0.969497i	$0.578822\pi$
$390$	−13371.0	−1.73607
$391$	558.687	0.0722609
$392$	−17127.0	−2.20675
$393$	−10879.5	−1.39644
$394$	−1002.96	−0.128244
$395$	4001.93	0.509770
$396$	17965.7	2.27983
$397$	9683.21	1.22415	0.612074	−	0.790801i	$-0.290336\pi$
$397$	9683.21	1.22415	0.612074	+	0.790801i	$0.290336\pi$
$398$	−15837.1	−1.99457
$399$	729.673	0.0915522
$400$	−5253.93	−0.656741
$401$	−12438.4	−1.54899	−0.774493	−	0.632582i	$-0.781995\pi$
$401$	−12438.4	−1.54899	−0.774493	+	0.632582i	$0.781995\pi$
$402$	21798.4	2.70449
$403$	642.183	0.0793782
$404$	−13710.9	−1.68847
$405$	−7178.30	−0.880722
$406$	2341.27	0.286196
$407$	−9160.48	−1.11565
$408$	−4580.99	−0.555864
$409$	−2117.72	−0.256026	−0.128013	−	0.991772i	$-0.540860\pi$
$409$	−2117.72	−0.256026	−0.128013	+	0.991772i	$0.540860\pi$
$410$	10865.7	1.30882
$411$	−11414.1	−1.36987
$412$	−19847.6	−2.37335
$413$	−555.883	−0.0662305
$414$	5273.46	0.626030
$415$	−1392.86	−0.164754
$416$	7281.79	0.858219
$417$	5466.40	0.641944
$418$	11251.2	1.31654
$419$	10082.6	1.17558	0.587789	−	0.809014i	$-0.299998\pi$
$419$	10082.6	1.17558	0.587789	+	0.809014i	$0.299998\pi$
$420$	2228.29	0.258879
$421$	11745.3	1.35970	0.679848	−	0.733353i	$-0.262046\pi$
$421$	11745.3	1.35970	0.679848	+	0.733353i	$0.262046\pi$
$422$	−20738.1	−2.39221
$423$	5901.84	0.678386
$424$	−33180.7	−3.80047
$425$	−588.714	−0.0671925
$426$	30411.7	3.45881
$427$	1389.26	0.157450
$428$	27203.5	3.07226
$429$	−12549.3	−1.41232
$430$	3260.74	0.365690
$431$	−9257.97	−1.03467	−0.517333	−	0.855784i	$-0.673075\pi$
$431$	−9257.97	−1.03467	−0.517333	+	0.855784i	$0.673075\pi$
$432$	2725.12	0.303501
$433$	5169.53	0.573745	0.286872	−	0.957969i	$-0.407384\pi$
$433$	5169.53	0.573745	0.286872	+	0.957969i	$0.407384\pi$
$434$	−154.797	−0.0171210
$435$	14759.0	1.62675
$436$	21967.4	2.41295
$437$	2283.23	0.249936
$438$	−7048.10	−0.768884
$439$	15346.1	1.66841	0.834204	−	0.551457i	$-0.185928\pi$
$439$	15346.1	1.66841	0.834204	+	0.551457i	$0.185928\pi$
$440$	19020.0	2.06078
$441$	−8014.75	−0.865430
$442$	2698.07	0.290349
$443$	−3378.59	−0.362351	−0.181176	−	0.983451i	$-0.557990\pi$
$443$	−3378.59	−0.362351	−0.181176	+	0.983451i	$0.557990\pi$
$444$	27535.4	2.94318
$445$	2798.95	0.298164
$446$	4920.83	0.522439
$447$	−11296.4	−1.19531
$448$	36.1499	0.00381233
$449$	−16118.8	−1.69420	−0.847098	−	0.531437i	$-0.821652\pi$
$449$	−16118.8	−1.69420	−0.847098	+	0.531437i	$0.821652\pi$
$450$	−5556.89	−0.582121
$451$	10197.9	1.06475
$452$	29040.8	3.02204
$453$	−15498.0	−1.60741
$454$	7814.91	0.807868
$455$	−726.502	−0.0748548
$456$	−18721.5	−1.92262
$457$	6957.36	0.712148	0.356074	−	0.934458i	$-0.384115\pi$
$457$	6957.36	0.712148	0.356074	+	0.934458i	$0.384115\pi$
$458$	−8820.54	−0.899906
$459$	305.355	0.0310518
$460$	6972.58	0.706735
$461$	7966.28	0.804830	0.402415	−	0.915457i	$-0.368171\pi$
$461$	7966.28	0.804830	0.402415	+	0.915457i	$0.368171\pi$
$462$	3024.99	0.304622
$463$	−12547.2	−1.25943	−0.629715	−	0.776826i	$-0.716828\pi$
$463$	−12547.2	−1.25943	−0.629715	+	0.776826i	$0.716828\pi$
$464$	−26578.2	−2.65919
$465$	−975.815	−0.0973168
$466$	5600.02	0.556687
$467$	−5847.24	−0.579396	−0.289698	−	0.957118i	$-0.593555\pi$
$467$	−5847.24	−0.579396	−0.289698	+	0.957118i	$0.593555\pi$
$468$	17606.9	1.73906
$469$	1184.40	0.116611
$470$	11287.1	1.10774
$471$	−2230.85	−0.218242
$472$	14262.5	1.39086
$473$	3060.35	0.297495
$474$	−16330.4	−1.58245
$475$	−2405.95	−0.232405
$476$	−449.636	−0.0432963
$477$	−15527.2	−1.49045
$478$	−25872.6	−2.47570
$479$	9687.36	0.924064	0.462032	−	0.886863i	$-0.347121\pi$
$479$	9687.36	0.924064	0.462032	+	0.886863i	$0.347121\pi$
$480$	−11064.9	−1.05217
$481$	−8977.54	−0.851020
$482$	12820.3	1.21151
$483$	613.872	0.0578305
$484$	8396.13	0.788517
$485$	10686.5	1.00051
$486$	25999.1	2.42663
$487$	13285.1	1.23615	0.618077	−	0.786118i	$-0.287912\pi$
$487$	13285.1	1.23615	0.618077	+	0.786118i	$0.287912\pi$
$488$	−35644.9	−3.30649
$489$	−7026.42	−0.649786
$490$	−15328.0	−1.41316
$491$	314.428	0.0289001	0.0144500	−	0.999896i	$-0.495400\pi$
$491$	314.428	0.0289001	0.0144500	+	0.999896i	$0.495400\pi$
$492$	−30653.8	−2.80891
$493$	−2978.14	−0.272067
$494$	11026.5	1.00426
$495$	8900.59	0.808185
$496$	1757.27	0.159080
$497$	1652.40	0.149135
$498$	5683.74	0.511435
$499$	4919.63	0.441349	0.220674	−	0.975348i	$-0.429174\pi$
$499$	4919.63	0.441349	0.220674	+	0.975348i	$0.429174\pi$
$500$	−27233.6	−2.43585
$501$	23288.3	2.07673
$502$	−37704.7	−3.35228
$503$	−10059.0	−0.891668	−0.445834	−	0.895116i	$-0.647093\pi$
$503$	−10059.0	−0.891668	−0.445834	+	0.895116i	$0.647093\pi$
$504$	−2349.41	−0.207641
$505$	−6792.66	−0.598554
$506$	9465.57	0.831613
$507$	3334.57	0.292098
$508$	2408.96	0.210394
$509$	17209.6	1.49863	0.749314	−	0.662215i	$-0.230383\pi$
$509$	17209.6	1.49863	0.749314	+	0.662215i	$0.230383\pi$
$510$	−4099.80	−0.355965
$511$	−382.952	−0.0331523
$512$	−26037.3	−2.24746
$513$	1247.92	0.107402
$514$	−14399.1	−1.23564
$515$	−9832.90	−0.841339
$516$	−9199.08	−0.784820
$517$	10593.5	0.901161
$518$	2164.03	0.183556
$519$	−136.934	−0.0115814
$520$	18640.2	1.57197
$521$	−10037.5	−0.844049	−0.422025	−	0.906584i	$-0.638680\pi$
$521$	−10037.5	−0.844049	−0.422025	+	0.906584i	$0.638680\pi$
$522$	−28110.8	−2.35704
$523$	−13924.3	−1.16418	−0.582091	−	0.813123i	$-0.697765\pi$
$523$	−13924.3	−1.16418	−0.582091	+	0.813123i	$0.697765\pi$
$524$	27398.4	2.28417
$525$	−646.865	−0.0537743
$526$	−4263.06	−0.353381
$527$	196.905	0.0162758
$528$	−34339.8	−2.83040
$529$	−10246.1	−0.842124
$530$	−29695.4	−2.43375
$531$	6674.28	0.545460
$532$	−1837.57	−0.149753
$533$	9994.26	0.812194
$534$	−11421.5	−0.925572
$535$	13477.2	1.08910
$536$	−30388.6	−2.44885
$537$	−30494.4	−2.45052
$538$	22896.5	1.83483
$539$	−14386.0	−1.14963
$540$	3810.93	0.303697
$541$	16622.4	1.32099	0.660493	−	0.750832i	$-0.270347\pi$
$541$	16622.4	1.32099	0.660493	+	0.750832i	$0.270347\pi$
$542$	25734.8	2.03949
$543$	31913.3	2.52216
$544$	2232.73	0.175970
$545$	10883.1	0.855378
$546$	2964.58	0.232367
$547$	8676.59	0.678216	0.339108	−	0.940747i	$-0.389875\pi$
$547$	8676.59	0.678216	0.339108	+	0.940747i	$0.389875\pi$
$548$	28744.7	2.24072
$549$	−16680.4	−1.29672
$550$	−9974.31	−0.773283
$551$	−12171.0	−0.941024
$552$	−15750.4	−1.21446
$553$	−887.297	−0.0682309
$554$	4085.42	0.313308
$555$	13641.6	1.04334
$556$	−13766.3	−1.05004
$557$	−16648.8	−1.26648	−0.633242	−	0.773954i	$-0.718276\pi$
$557$	−16648.8	−1.26648	−0.633242	+	0.773954i	$0.718276\pi$
$558$	1858.60	0.141005
$559$	2999.23	0.226930
$560$	−1988.00	−0.150015
$561$	−3847.85	−0.289583
$562$	1615.20	0.121233
$563$	1950.39	0.146002	0.0730012	−	0.997332i	$-0.476742\pi$
$563$	1950.39	0.146002	0.0730012	+	0.997332i	$0.476742\pi$
$564$	−31842.8	−2.37735
$565$	14387.4	1.07130
$566$	45198.2	3.35657
$567$	1591.55	0.117882
$568$	−42396.2	−3.13188
$569$	19007.7	1.40043	0.700214	−	0.713933i	$-0.253088\pi$
$569$	19007.7	1.40043	0.700214	+	0.713933i	$0.253088\pi$
$570$	−16755.0	−1.23121
$571$	5073.12	0.371810	0.185905	−	0.982568i	$-0.440478\pi$
$571$	5073.12	0.371810	0.185905	+	0.982568i	$0.440478\pi$
$572$	31603.5	2.31015
$573$	29747.9	2.16882
$574$	−2409.10	−0.175181
$575$	−2024.12	−0.146803
$576$	−434.039	−0.0313975
$577$	17129.7	1.23591	0.617954	−	0.786215i	$-0.287962\pi$
$577$	17129.7	1.23591	0.617954	+	0.786215i	$0.287962\pi$
$578$	−24185.6	−1.74046
$579$	29419.0	2.11159
$580$	−37168.1	−2.66090
$581$	308.821	0.0220517
$582$	−43607.6	−3.10583
$583$	−27870.5	−1.97989
$584$	9825.58	0.696208
$585$	8722.84	0.616487
$586$	−22791.0	−1.60663
$587$	−23396.1	−1.64508	−0.822538	−	0.568710i	$-0.807443\pi$
$587$	−23396.1	−1.64508	−0.822538	+	0.568710i	$0.807443\pi$
$588$	43242.8	3.03283
$589$	804.710	0.0562946
$590$	12764.4	0.890681
$591$	1401.80	0.0975673
$592$	−24566.1	−1.70551
$593$	−3895.43	−0.269757	−0.134879	−	0.990862i	$-0.543064\pi$
$593$	−3895.43	−0.269757	−0.134879	+	0.990862i	$0.543064\pi$
$594$	5173.50	0.357359
$595$	−222.759	−0.0153483
$596$	28448.3	1.95518
$597$	22134.9	1.51746
$598$	9276.54	0.634358
$599$	26717.5	1.82245	0.911224	−	0.411911i	$-0.135138\pi$
$599$	26717.5	1.82245	0.911224	+	0.411911i	$0.135138\pi$
$600$	16596.9	1.12928
$601$	−17492.0	−1.18721	−0.593605	−	0.804757i	$-0.702296\pi$
$601$	−17492.0	−1.18721	−0.593605	+	0.804757i	$0.702296\pi$
$602$	−722.962	−0.0489464
$603$	−14220.6	−0.960378
$604$	39029.2	2.62926
$605$	4159.62	0.279525
$606$	27718.3	1.85805
$607$	26049.0	1.74184	0.870919	−	0.491427i	$-0.163524\pi$
$607$	26049.0	1.74184	0.870919	+	0.491427i	$0.163524\pi$
$608$	9124.71	0.608644
$609$	−3272.32	−0.217736
$610$	−31900.8	−2.11742
$611$	10381.9	0.687410
$612$	5398.61	0.356578
$613$	5630.12	0.370960	0.185480	−	0.982648i	$-0.440616\pi$
$613$	5630.12	0.370960	0.185480	+	0.982648i	$0.440616\pi$
$614$	43460.7	2.85657
$615$	−15186.5	−0.995741
$616$	−4217.06	−0.275829
$617$	7143.71	0.466118	0.233059	−	0.972463i	$-0.425126\pi$
$617$	7143.71	0.466118	0.233059	+	0.972463i	$0.425126\pi$
$618$	40124.4	2.61172
$619$	−19910.8	−1.29286	−0.646432	−	0.762972i	$-0.723740\pi$
$619$	−19910.8	−1.29286	−0.646432	+	0.762972i	$0.723740\pi$
$620$	2457.44	0.159182
$621$	1049.87	0.0678422
$622$	23656.0	1.52495
$623$	−620.576	−0.0399082
$624$	−33654.0	−2.15904
$625$	−7719.17	−0.494027
$626$	−727.190	−0.0464287
$627$	−15725.3	−1.00161
$628$	5618.04	0.356981
$629$	−2752.68	−0.174494
$630$	−2102.63	−0.132970
$631$	−1718.49	−0.108419	−0.0542093	−	0.998530i	$-0.517264\pi$
$631$	−1718.49	−0.108419	−0.0542093	+	0.998530i	$0.517264\pi$
$632$	22765.8	1.43287
$633$	28984.9	1.81998
$634$	30182.8	1.89071
$635$	1193.45	0.0745836
$636$	83775.7	5.22315
$637$	−14098.7	−0.876942
$638$	−50457.3	−3.13107
$639$	−19839.7	−1.22824
$640$	−13270.0	−0.819598
$641$	0.0373128	2.29917e−6 0	1.14958e−6	−	1.00000i	$-0.500000\pi$
$641$	0.0373128	2.29917e−6 0	1.14958e−6		1.00000i	$0.500000\pi$
$642$	−54995.3	−3.38083
$643$	2056.28	0.126115	0.0630573	−	0.998010i	$-0.479915\pi$
$643$	2056.28	0.126115	0.0630573	+	0.998010i	$0.479915\pi$
$644$	−1545.94	−0.0945941
$645$	−4557.42	−0.278214
$646$	3380.92	0.205914
$647$	22266.9	1.35302	0.676508	−	0.736436i	$-0.263493\pi$
$647$	22266.9	1.35302	0.676508	+	0.736436i	$0.263493\pi$
$648$	−40835.1	−2.47555
$649$	11980.0	0.724584
$650$	−9775.12	−0.589864
$651$	216.355	0.0130255
$652$	17694.9	1.06286
$653$	−3198.27	−0.191666	−0.0958329	−	0.995397i	$-0.530551\pi$
$653$	−3198.27	−0.191666	−0.0958329	+	0.995397i	$0.530551\pi$
$654$	−44409.9	−2.65530
$655$	13573.7	0.809724
$656$	27348.2	1.62770
$657$	4597.97	0.273035
$658$	−2502.55	−0.148267
$659$	23280.2	1.37612	0.688062	−	0.725652i	$-0.258462\pi$
$659$	23280.2	1.37612	0.688062	+	0.725652i	$0.258462\pi$
$660$	−48022.3	−2.83222
$661$	−19938.3	−1.17324	−0.586620	−	0.809862i	$-0.699542\pi$
$661$	−19938.3	−1.17324	−0.586620	+	0.809862i	$0.699542\pi$
$662$	−23790.0	−1.39671
$663$	−3771.00	−0.220895
$664$	−7923.55	−0.463093
$665$	−910.369	−0.0530866
$666$	−25982.7	−1.51172
$667$	−10239.5	−0.594414
$668$	−58647.9	−3.39694
$669$	−6877.66	−0.397468
$670$	−27196.5	−1.56820
$671$	−29940.3	−1.72255
$672$	2453.28	0.140829
$673$	−4.15055	−0.000237730 0	−0.000118865	−	1.00000i	$-0.500038\pi$
$673$	−4.15055	−0.000237730 0	−0.000118865		1.00000i	$0.500038\pi$
$674$	56411.1	3.22385
$675$	−1106.30	−0.0630838
$676$	−8397.60	−0.477788
$677$	−30768.8	−1.74674	−0.873369	−	0.487060i	$-0.838069\pi$
$677$	−30768.8	−1.74674	−0.873369	+	0.487060i	$0.838069\pi$
$678$	−58709.6	−3.32556
$679$	−2369.38	−0.133915
$680$	5715.42	0.322318
$681$	−10922.6	−0.614620
$682$	3336.08	0.187309
$683$	27056.3	1.51578	0.757891	−	0.652381i	$-0.226230\pi$
$683$	27056.3	1.51578	0.757891	+	0.652381i	$0.226230\pi$
$684$	22063.0	1.23333
$685$	14240.7	0.794323
$686$	6835.79	0.380454
$687$	12328.2	0.684641
$688$	8207.09	0.454785
$689$	−27313.9	−1.51027
$690$	−14096.0	−0.777716
$691$	−903.177	−0.0497228	−0.0248614	−	0.999691i	$-0.507914\pi$
$691$	−903.177	−0.0497228	−0.0248614	+	0.999691i	$0.507914\pi$
$692$	344.846	0.0189438
$693$	−1973.41	−0.108173
$694$	22327.1	1.22122
$695$	−6820.10	−0.372232
$696$	83959.2	4.57251
$697$	3064.43	0.166533
$698$	49004.2	2.65736
$699$	−7826.95	−0.423523
$700$	1629.03	0.0879593
$701$	−22712.2	−1.22372	−0.611861	−	0.790965i	$-0.709579\pi$
$701$	−22712.2	−1.22372	−0.611861	+	0.790965i	$0.709579\pi$
$702$	5070.18	0.272595
$703$	−11249.6	−0.603539
$704$	−779.075	−0.0417081
$705$	−15775.6	−0.842757
$706$	−6918.02	−0.368786
$707$	1506.05	0.0801144
$708$	−36010.5	−1.91152
$709$	3067.71	0.162497	0.0812484	−	0.996694i	$-0.474109\pi$
$709$	3067.71	0.162497	0.0812484	+	0.996694i	$0.474109\pi$
$710$	−37942.9	−2.00559
$711$	10653.5	0.561935
$712$	15922.4	0.838085
$713$	677.001	0.0355595
$714$	908.996	0.0476447
$715$	15657.0	0.818936
$716$	76795.3	4.00835
$717$	36161.2	1.88349
$718$	−49257.7	−2.56028
$719$	−20342.8	−1.05516	−0.527579	−	0.849506i	$-0.676900\pi$
$719$	−20342.8	−1.05516	−0.527579	+	0.849506i	$0.676900\pi$
$720$	23869.1	1.23549
$721$	2180.12	0.112610
$722$	−21103.1	−1.08778
$723$	−17918.5	−0.921707
$724$	−80368.8	−4.12553
$725$	10789.8	0.552722
$726$	−16973.8	−0.867711
$727$	10426.1	0.531887	0.265944	−	0.963989i	$-0.414316\pi$
$727$	10426.1	0.531887	0.265944	+	0.963989i	$0.414316\pi$
$728$	−4132.85	−0.210403
$729$	−14506.9	−0.737028
$730$	8793.50	0.445838
$731$	919.621	0.0465300
$732$	89997.4	4.54426
$733$	−11589.4	−0.583988	−0.291994	−	0.956420i	$-0.594319\pi$
$733$	−11589.4	−0.583988	−0.291994	+	0.956420i	$0.594319\pi$
$734$	29965.1	1.50686
$735$	21423.4	1.07512
$736$	7676.60	0.384461
$737$	−25525.2	−1.27576
$738$	28925.2	1.44275
$739$	3636.68	0.181025	0.0905124	−	0.995895i	$-0.471150\pi$
$739$	3636.68	0.181025	0.0905124	+	0.995895i	$0.471150\pi$
$740$	−34354.3	−1.70661
$741$	−15411.3	−0.764033
$742$	6583.98	0.325749
$743$	12414.1	0.612961	0.306480	−	0.951877i	$-0.400849\pi$
$743$	12414.1	0.612961	0.306480	+	0.951877i	$0.400849\pi$
$744$	−5551.11	−0.273540
$745$	14093.9	0.693100
$746$	7940.16	0.389691
$747$	−3707.90	−0.181613
$748$	9690.21	0.473675
$749$	−2988.12	−0.145772
$750$	55056.2	2.68049
$751$	28651.5	1.39215	0.696077	−	0.717967i	$-0.254927\pi$
$751$	28651.5	1.39215	0.696077	+	0.717967i	$0.254927\pi$
$752$	28409.0	1.37762
$753$	52698.5	2.55039
$754$	−49449.7	−2.38840
$755$	19335.9	0.932059
$756$	−844.948	−0.0406488
$757$	−13011.9	−0.624734	−0.312367	−	0.949961i	$-0.601122\pi$
$757$	−13011.9	−0.624734	−0.312367	+	0.949961i	$0.601122\pi$
$758$	30211.4	1.44766
$759$	−13229.7	−0.632685
$760$	23357.7	1.11483
$761$	−8099.47	−0.385815	−0.192908	−	0.981217i	$-0.561792\pi$
$761$	−8099.47	−0.385815	−0.192908	+	0.981217i	$0.561792\pi$
$762$	−4870.02	−0.231525
$763$	−2412.97	−0.114489
$764$	−74915.4	−3.54757
$765$	2674.59	0.126405
$766$	−7083.73	−0.334133
$767$	11740.7	0.552715
$768$	53104.5	2.49511
$769$	26343.4	1.23533	0.617665	−	0.786442i	$-0.288079\pi$
$769$	26343.4	1.23533	0.617665	+	0.786442i	$0.288079\pi$
$770$	−3774.10	−0.176635
$771$	20125.2	0.940064
$772$	−74087.1	−3.45395
$773$	23352.2	1.08657	0.543286	−	0.839548i	$-0.317180\pi$
$773$	23352.2	1.08657	0.543286	+	0.839548i	$0.317180\pi$
$774$	8680.33	0.403111
$775$	−713.387	−0.0330653
$776$	60792.2	2.81226
$777$	−3024.58	−0.139648
$778$	−19147.9	−0.882371
$779$	12523.7	0.576004
$780$	−47063.3	−2.16043
$781$	−35611.2	−1.63158
$782$	2844.36	0.130069
$783$	−5596.48	−0.255430
$784$	−38579.7	−1.75746
$785$	2783.29	0.126548
$786$	−55389.3	−2.51358
$787$	20271.1	0.918151	0.459076	−	0.888397i	$-0.348181\pi$
$787$	20271.1	0.918151	0.459076	+	0.888397i	$0.348181\pi$
$788$	−3530.21	−0.159592
$789$	5958.33	0.268849
$790$	20374.4	0.917583
$791$	−3189.94	−0.143389
$792$	50632.7	2.27166
$793$	−29342.4	−1.31397
$794$	49298.7	2.20346
$795$	41504.2	1.85158
$796$	−55743.3	−2.48212
$797$	11220.7	0.498690	0.249345	−	0.968415i	$-0.419785\pi$
$797$	11220.7	0.498690	0.249345	+	0.968415i	$0.419785\pi$
$798$	3714.88	0.164793
$799$	3183.29	0.140947
$800$	−8089.18	−0.357495
$801$	7451.02	0.328675
$802$	−63325.8	−2.78817
$803$	8253.10	0.362697
$804$	76726.0	3.36557
$805$	−765.892	−0.0335331
$806$	3269.45	0.142880
$807$	−32001.6	−1.39592
$808$	−38641.4	−1.68243
$809$	−12295.3	−0.534339	−0.267169	−	0.963650i	$-0.586088\pi$
$809$	−12295.3	−0.534339	−0.267169	+	0.963650i	$0.586088\pi$
$810$	−36545.8	−1.58530
$811$	13327.2	0.577043	0.288522	−	0.957473i	$-0.406836\pi$
$811$	13327.2	0.577043	0.288522	+	0.957473i	$0.406836\pi$
$812$	8240.82	0.356153
$813$	−35968.6	−1.55163
$814$	−46637.4	−2.00816
$815$	8766.44	0.376779
$816$	−10319.0	−0.442691
$817$	3758.30	0.160938
$818$	−10781.7	−0.460846
$819$	−1934.00	−0.0825148
$820$	38245.0	1.62875
$821$	10149.0	0.431430	0.215715	−	0.976456i	$-0.430792\pi$
$821$	10149.0	0.431430	0.215715	+	0.976456i	$0.430792\pi$
$822$	−58111.2	−2.46577
$823$	−1678.06	−0.0710735	−0.0355367	−	0.999368i	$-0.511314\pi$
$823$	−1678.06	−0.0710735	−0.0355367	+	0.999368i	$0.511314\pi$
$824$	−55936.4	−2.36485
$825$	13940.7	0.588308
$826$	−2830.09	−0.119215
$827$	3829.52	0.161022	0.0805111	−	0.996754i	$-0.474345\pi$
$827$	3829.52	0.161022	0.0805111	+	0.996754i	$0.474345\pi$
$828$	18561.5	0.779056
$829$	−1190.54	−0.0498785	−0.0249393	−	0.999689i	$-0.507939\pi$
$829$	−1190.54	−0.0498785	−0.0249393	+	0.999689i	$0.507939\pi$
$830$	−7091.26	−0.296556
$831$	−5710.04	−0.238362
$832$	−763.517	−0.0318151
$833$	−4322.93	−0.179809
$834$	27830.3	1.15550
$835$	−29055.4	−1.20420
$836$	39601.8	1.63835
$837$	370.021	0.0152805
$838$	51332.1	2.11604
$839$	5759.00	0.236976	0.118488	−	0.992955i	$-0.462195\pi$
$839$	5759.00	0.236976	0.118488	+	0.992955i	$0.462195\pi$
$840$	6279.98	0.257952
$841$	30193.7	1.23801
$842$	59797.3	2.44745
$843$	−2257.50	−0.0922331
$844$	−72993.9	−2.97696
$845$	−4160.35	−0.169373
$846$	30047.2	1.22109
$847$	−922.259	−0.0374135
$848$	−74741.6	−3.02670
$849$	−63171.9	−2.55366
$850$	−2997.23	−0.120946
$851$	−9464.29	−0.381236
$852$	107043.	4.30427
$853$	20665.5	0.829510	0.414755	−	0.909933i	$-0.363867\pi$
$853$	20665.5	0.829510	0.414755	+	0.909933i	$0.363867\pi$
$854$	7072.95	0.283409
$855$	10930.5	0.437209
$856$	76667.5	3.06126
$857$	−46087.6	−1.83702	−0.918508	−	0.395402i	$-0.870605\pi$
$857$	−46087.6	−1.83702	−0.918508	+	0.395402i	$0.870605\pi$
$858$	−63890.4	−2.54217
$859$	13995.2	0.555892	0.277946	−	0.960597i	$-0.410346\pi$
$859$	13995.2	0.555892	0.277946	+	0.960597i	$0.410346\pi$
$860$	11477.1	0.455078
$861$	3367.12	0.133277
$862$	−47133.8	−1.86239
$863$	−39087.3	−1.54177	−0.770886	−	0.636974i	$-0.780186\pi$
$863$	−39087.3	−1.54177	−0.770886	+	0.636974i	$0.780186\pi$
$864$	4195.72	0.165210
$865$	170.844	0.00671546
$866$	26318.9	1.03274
$867$	33803.3	1.32413
$868$	−544.856	−0.0213060
$869$	19122.3	0.746469
$870$	75140.1	2.92815
$871$	−25015.4	−0.973153
$872$	61910.6	2.40431
$873$	28448.3	1.10290
$874$	11624.3	0.449883
$875$	2991.43	0.115576
$876$	−24807.9	−0.956829
$877$	15332.4	0.590351	0.295176	−	0.955443i	$-0.404622\pi$
$877$	15332.4	0.590351	0.295176	+	0.955443i	$0.404622\pi$
$878$	78129.5	3.00312
$879$	31854.1	1.22231
$880$	42843.8	1.64121
$881$	−3728.34	−0.142578	−0.0712889	−	0.997456i	$-0.522711\pi$
$881$	−3728.34	−0.142578	−0.0712889	+	0.997456i	$0.522711\pi$
$882$	−40804.3	−1.55777
$883$	4470.74	0.170388	0.0851939	−	0.996364i	$-0.472849\pi$
$883$	4470.74	0.170388	0.0851939	+	0.996364i	$0.472849\pi$
$884$	9496.69	0.361321
$885$	−17840.3	−0.677623
$886$	−17200.9	−0.652231
$887$	−8546.27	−0.323513	−0.161756	−	0.986831i	$-0.551716\pi$
$887$	−8546.27	−0.323513	−0.161756	+	0.986831i	$0.551716\pi$
$888$	77603.0	2.93264
$889$	−264.608	−0.00998276
$890$	14249.9	0.536694
$891$	−34299.9	−1.28966
$892$	17320.3	0.650143
$893$	13009.4	0.487507
$894$	−57511.8	−2.15155
$895$	38046.0	1.42094
$896$	2942.19	0.109700
$897$	−12965.5	−0.482615
$898$	−82063.4	−3.04954
$899$	−3608.83	−0.133884
$900$	−19559.1	−0.724413
$901$	−8374.95	−0.309667
$902$	51919.2	1.91654
$903$	1010.46	0.0372380
$904$	81845.5	3.01122
$905$	−39816.4	−1.46248
$906$	−78902.5	−2.89333
$907$	−4732.57	−0.173255	−0.0866275	−	0.996241i	$-0.527609\pi$
$907$	−4732.57	−0.173255	−0.0866275	+	0.996241i	$0.527609\pi$
$908$	27506.9	1.00534
$909$	−18082.6	−0.659804
$910$	−3698.73	−0.134738
$911$	14254.5	0.518411	0.259205	−	0.965822i	$-0.416539\pi$
$911$	14254.5	0.518411	0.259205	+	0.965822i	$0.416539\pi$
$912$	−42171.4	−1.53118
$913$	−6655.47	−0.241253
$914$	35421.0	1.28186
$915$	44586.6	1.61091
$916$	−31046.5	−1.11988
$917$	−3009.53	−0.108379
$918$	1554.61	0.0558930
$919$	−40020.2	−1.43650	−0.718251	−	0.695784i	$-0.755057\pi$
$919$	−40020.2	−1.43650	−0.718251	+	0.695784i	$0.755057\pi$
$920$	19650.8	0.704204
$921$	−60743.6	−2.17326
$922$	40557.6	1.44869
$923$	−34900.0	−1.24458
$924$	10647.4	0.379083
$925$	9972.95	0.354496
$926$	−63879.6	−2.26697
$927$	−26176.0	−0.927434
$928$	−40921.0	−1.44752
$929$	−25632.2	−0.905236	−0.452618	−	0.891705i	$-0.649510\pi$
$929$	−25632.2	−0.905236	−0.452618	+	0.891705i	$0.649510\pi$
$930$	−4968.02	−0.175170
$931$	−17666.9	−0.621923
$932$	19711.0	0.692762
$933$	−33063.2	−1.16017
$934$	−29769.2	−1.04291
$935$	4800.73	0.167915
$936$	49621.6	1.73283
$937$	21589.0	0.752701	0.376351	−	0.926477i	$-0.377179\pi$
$937$	21589.0	0.752701	0.376351	+	0.926477i	$0.377179\pi$
$938$	6029.94	0.209898
$939$	1016.37	0.0353226
$940$	39728.4	1.37851
$941$	1920.06	0.0665167	0.0332584	−	0.999447i	$-0.489412\pi$
$941$	1920.06	0.0665167	0.0332584	+	0.999447i	$0.489412\pi$
$942$	−11357.6	−0.392834
$943$	10536.1	0.363843
$944$	32127.2	1.10768
$945$	−418.605	−0.0144098
$946$	15580.7	0.535489
$947$	16682.3	0.572441	0.286221	−	0.958164i	$-0.407601\pi$
$947$	16682.3	0.572441	0.286221	+	0.958164i	$0.407601\pi$
$948$	−57479.7	−1.96926
$949$	8088.28	0.276667
$950$	−12249.1	−0.418328
$951$	−42185.4	−1.43844
$952$	−1267.21	−0.0431412
$953$	21054.5	0.715658	0.357829	−	0.933787i	$-0.383517\pi$
$953$	21054.5	0.715658	0.357829	+	0.933787i	$0.383517\pi$
$954$	−79051.5	−2.68279
$955$	−37114.7	−1.25759
$956$	−91066.4	−3.08085
$957$	70522.4	2.38210
$958$	49319.8	1.66331
$959$	−3157.42	−0.106317
$960$	1160.18	0.0390050
$961$	−29552.4	−0.991991
$962$	−45706.0	−1.53183
$963$	35877.3	1.20055
$964$	45124.8	1.50765
$965$	−36704.3	−1.22441
$966$	3125.32	0.104095
$967$	32902.7	1.09419	0.547093	−	0.837072i	$-0.315734\pi$
$967$	32902.7	1.09419	0.547093	+	0.837072i	$0.315734\pi$
$968$	23662.8	0.785693
$969$	−4725.39	−0.156658
$970$	54406.6	1.80092
$971$	−24276.1	−0.802325	−0.401163	−	0.916007i	$-0.631394\pi$
$971$	−24276.1	−0.802325	−0.401163	+	0.916007i	$0.631394\pi$
$972$	91511.8	3.01980
$973$	1512.13	0.0498220
$974$	67636.7	2.22507
$975$	13662.3	0.448764
$976$	−80292.4	−2.63330
$977$	−23144.0	−0.757872	−0.378936	−	0.925423i	$-0.623710\pi$
$977$	−23144.0	−0.757872	−0.378936	+	0.925423i	$0.623710\pi$
$978$	−35772.6	−1.16961
$979$	13374.2	0.436609
$980$	−53951.5	−1.75859
$981$	28971.7	0.942909
$982$	1600.80	0.0520200
$983$	21353.3	0.692844	0.346422	−	0.938079i	$-0.387397\pi$
$983$	21353.3	0.692844	0.346422	+	0.938079i	$0.387397\pi$
$984$	−86391.7	−2.79885
$985$	−1748.94	−0.0565745
$986$	−15162.2	−0.489719
$987$	3497.72	0.112800
$988$	38811.0	1.24974
$989$	3161.85	0.101659
$990$	45314.3	1.45473
$991$	6413.96	0.205597	0.102798	−	0.994702i	$-0.467220\pi$
$991$	6413.96	0.205597	0.102798	+	0.994702i	$0.467220\pi$
$992$	2705.56	0.0865945
$993$	33250.4	1.06261
$994$	8412.60	0.268442
$995$	−27616.4	−0.879899
$996$	20005.6	0.636448
$997$	27804.9	0.883240	0.441620	−	0.897202i	$-0.354404\pi$
$997$	27804.9	0.883240	0.441620	+	0.897202i	$0.354404\pi$
$998$	25046.6	0.794426
$999$	−5172.79	−0.163824

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.a.b.1.25	✓	27
3.2	odd	2		1773.4.a.d.1.3		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.a.b.1.25	✓	27	1.1	even	1	trivial
1773.4.a.d.1.3		27	3.2	odd	2

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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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Properties

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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	197.4.a.b.1.25

Level	$197$
Weight	$4$
Character	197.1
Self dual	yes
Analytic conductor	$11.623$
Analytic rank	$0$
Dimension	$27$
CM	no
Inner twists	$1$