LMFDB - Embedded newform 626.4.a.d.1.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [626,4,Mod(1,626)] 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("626.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(626, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$N$	$=$	$626 = 2 \cdot 313$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	626.a (trivial)

Newform invariants

comment:select newform

sage:traces = [25] 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:	$36.9351956636$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	626.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +8.78232 q^{3} +4.00000 q^{4} +3.53466 q^{5} +17.5646 q^{6} -0.176992 q^{7} +8.00000 q^{8} +50.1291 q^{9} +7.06932 q^{10} +20.1570 q^{11} +35.1293 q^{12} +3.29635 q^{13} -0.353983 q^{14} +31.0425 q^{15} +16.0000 q^{16} +28.4220 q^{17} +100.258 q^{18} +12.8367 q^{19} +14.1386 q^{20} -1.55440 q^{21} +40.3139 q^{22} -58.5557 q^{23} +70.2585 q^{24} -112.506 q^{25} +6.59270 q^{26} +203.127 q^{27} -0.707967 q^{28} +283.840 q^{29} +62.0850 q^{30} -310.972 q^{31} +32.0000 q^{32} +177.025 q^{33} +56.8439 q^{34} -0.625605 q^{35} +200.516 q^{36} -332.783 q^{37} +25.6733 q^{38} +28.9496 q^{39} +28.2773 q^{40} +435.265 q^{41} -3.10879 q^{42} +364.732 q^{43} +80.6279 q^{44} +177.189 q^{45} -117.111 q^{46} -115.956 q^{47} +140.517 q^{48} -342.969 q^{49} -225.012 q^{50} +249.611 q^{51} +13.1854 q^{52} -241.315 q^{53} +406.254 q^{54} +71.2480 q^{55} -1.41593 q^{56} +112.736 q^{57} +567.680 q^{58} +34.6640 q^{59} +124.170 q^{60} +554.390 q^{61} -621.944 q^{62} -8.87244 q^{63} +64.0000 q^{64} +11.6515 q^{65} +354.050 q^{66} -340.425 q^{67} +113.688 q^{68} -514.255 q^{69} -1.25121 q^{70} +864.058 q^{71} +401.033 q^{72} +542.181 q^{73} -665.566 q^{74} -988.065 q^{75} +51.3466 q^{76} -3.56762 q^{77} +57.8992 q^{78} -726.133 q^{79} +56.5545 q^{80} +430.441 q^{81} +870.529 q^{82} -1325.90 q^{83} -6.21759 q^{84} +100.462 q^{85} +729.464 q^{86} +2492.77 q^{87} +161.256 q^{88} -523.778 q^{89} +354.378 q^{90} -0.583427 q^{91} -234.223 q^{92} -2731.05 q^{93} -231.913 q^{94} +45.3732 q^{95} +281.034 q^{96} +798.843 q^{97} -685.937 q^{98} +1010.45 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$25 q + 50 q^{2} + 16 q^{3} + 100 q^{4} + 40 q^{5} + 32 q^{6} + 51 q^{7} + 200 q^{8} + 351 q^{9} + 80 q^{10} + 178 q^{11} + 64 q^{12} + 142 q^{13} + 102 q^{14} + 151 q^{15} + 400 q^{16} + 339 q^{17} + 702 q^{18}+ \cdots + 2233 q^{99}+O(q^{100})$ 25 * q + 50 * q^2 + 16 * q^3 + 100 * q^4 + 40 * q^5 + 32 * q^6 + 51 * q^7 + 200 * q^8 + 351 * q^9 + 80 * q^10 + 178 * q^11 + 64 * q^12 + 142 * q^13 + 102 * q^14 + 151 * q^15 + 400 * q^16 + 339 * q^17 + 702 * q^18 + 305 * q^19 + 160 * q^20 + 326 * q^21 + 356 * q^22 + 128 * q^23 + 128 * q^24 + 1181 * q^25 + 284 * q^26 + 505 * q^27 + 204 * q^28 + 700 * q^29 + 302 * q^30 + 944 * q^31 + 800 * q^32 + 526 * q^33 + 678 * q^34 + 529 * q^35 + 1404 * q^36 + 1165 * q^37 + 610 * q^38 + 872 * q^39 + 320 * q^40 + 970 * q^41 + 652 * q^42 + 855 * q^43 + 712 * q^44 + 1749 * q^45 + 256 * q^46 + 894 * q^47 + 256 * q^48 + 3132 * q^49 + 2362 * q^50 + 1939 * q^51 + 568 * q^52 + 1756 * q^53 + 1010 * q^54 + 1518 * q^55 + 408 * q^56 + 1813 * q^57 + 1400 * q^58 + 1364 * q^59 + 604 * q^60 + 1972 * q^61 + 1888 * q^62 + 2199 * q^63 + 1600 * q^64 + 3344 * q^65 + 1052 * q^66 + 2383 * q^67 + 1356 * q^68 + 2516 * q^69 + 1058 * q^70 + 1487 * q^71 + 2808 * q^72 + 2284 * q^73 + 2330 * q^74 + 3715 * q^75 + 1220 * q^76 + 3746 * q^77 + 1744 * q^78 + 373 * q^79 + 640 * q^80 + 4521 * q^81 + 1940 * q^82 + 1012 * q^83 + 1304 * q^84 - 364 * q^85 + 1710 * q^86 - 5697 * q^87 + 1424 * q^88 - 654 * q^89 + 3498 * q^90 - 835 * q^91 + 512 * q^92 - 480 * q^93 + 1788 * q^94 - 2436 * q^95 + 512 * q^96 - 609 * q^97 + 6264 * q^98 + 2233 * q^99

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	8.78232	1.69016	0.845079	−	0.534642i	$-0.179553\pi$
$3$	8.78232	1.69016	0.845079	+	0.534642i	$0.179553\pi$
$4$	4.00000	0.500000
$5$	3.53466	0.316149	0.158075	−	0.987427i	$-0.449471\pi$
$5$	3.53466	0.316149	0.158075	+	0.987427i	$0.449471\pi$
$6$	17.5646	1.19512
$7$	−0.176992	−0.00955665	−0.00477833	−	0.999989i	$-0.501521\pi$
$7$	−0.176992	−0.00955665	−0.00477833	+	0.999989i	$0.501521\pi$
$8$	8.00000	0.353553
$9$	50.1291	1.85663
$10$	7.06932	0.223551
$11$	20.1570	0.552505	0.276253	−	0.961085i	$-0.410907\pi$
$11$	20.1570	0.552505	0.276253	+	0.961085i	$0.410907\pi$
$12$	35.1293	0.845079
$13$	3.29635	0.0703264	0.0351632	−	0.999382i	$-0.488805\pi$
$13$	3.29635	0.0703264	0.0351632	+	0.999382i	$0.488805\pi$
$14$	−0.353983	−0.00675758
$15$	31.0425	0.534342
$16$	16.0000	0.250000
$17$	28.4220	0.405490	0.202745	−	0.979232i	$-0.435014\pi$
$17$	28.4220	0.405490	0.202745	+	0.979232i	$0.435014\pi$
$18$	100.258	1.31284
$19$	12.8367	0.154996	0.0774982	−	0.996992i	$-0.475307\pi$
$19$	12.8367	0.154996	0.0774982	+	0.996992i	$0.475307\pi$
$20$	14.1386	0.158075
$21$	−1.55440	−0.0161523
$22$	40.3139	0.390680
$23$	−58.5557	−0.530857	−0.265428	−	0.964131i	$-0.585513\pi$
$23$	−58.5557	−0.530857	−0.265428	+	0.964131i	$0.585513\pi$
$24$	70.2585	0.597561
$25$	−112.506	−0.900050
$26$	6.59270	0.0497283
$27$	203.127	1.44785
$28$	−0.707967	−0.00477833
$29$	283.840	1.81751	0.908754	−	0.417332i	$-0.137035\pi$
$29$	283.840	1.81751	0.908754	+	0.417332i	$0.137035\pi$
$30$	62.0850	0.377837
$31$	−310.972	−1.80168	−0.900842	−	0.434147i	$-0.857050\pi$
$31$	−310.972	−1.80168	−0.900842	+	0.434147i	$0.857050\pi$
$32$	32.0000	0.176777
$33$	177.025	0.933821
$34$	56.8439	0.286725
$35$	−0.625605	−0.00302133
$36$	200.516	0.928317
$37$	−332.783	−1.47863	−0.739314	−	0.673361i	$-0.764850\pi$
$37$	−332.783	−1.47863	−0.739314	+	0.673361i	$0.764850\pi$
$38$	25.6733	0.109599
$39$	28.9496	0.118863
$40$	28.2773	0.111776
$41$	435.265	1.65797	0.828987	−	0.559268i	$-0.188918\pi$
$41$	435.265	1.65797	0.828987	+	0.559268i	$0.188918\pi$
$42$	−3.10879	−0.0114214
$43$	364.732	1.29351	0.646757	−	0.762696i	$-0.276125\pi$
$43$	364.732	1.29351	0.646757	+	0.762696i	$0.276125\pi$
$44$	80.6279	0.276253
$45$	177.189	0.586974
$46$	−117.111	−0.375373
$47$	−115.956	−0.359872	−0.179936	−	0.983678i	$-0.557589\pi$
$47$	−115.956	−0.359872	−0.179936	+	0.983678i	$0.557589\pi$
$48$	140.517	0.422539
$49$	−342.969	−0.999909
$50$	−225.012	−0.636431
$51$	249.611	0.685343
$52$	13.1854	0.0351632
$53$	−241.315	−0.625417	−0.312709	−	0.949849i	$-0.601236\pi$
$53$	−241.315	−0.625417	−0.312709	+	0.949849i	$0.601236\pi$
$54$	406.254	1.02378
$55$	71.2480	0.174674
$56$	−1.41593	−0.00337879
$57$	112.736	0.261968
$58$	567.680	1.28517
$59$	34.6640	0.0764893	0.0382446	−	0.999268i	$-0.487823\pi$
$59$	34.6640	0.0764893	0.0382446	+	0.999268i	$0.487823\pi$
$60$	124.170	0.267171
$61$	554.390	1.16364	0.581822	−	0.813316i	$-0.302340\pi$
$61$	554.390	1.16364	0.581822	+	0.813316i	$0.302340\pi$
$62$	−621.944	−1.27398
$63$	−8.87244	−0.0177432
$64$	64.0000	0.125000
$65$	11.6515	0.0222336
$66$	354.050	0.660311
$67$	−340.425	−0.620740	−0.310370	−	0.950616i	$-0.600453\pi$
$67$	−340.425	−0.620740	−0.310370	+	0.950616i	$0.600453\pi$
$68$	113.688	0.202745
$69$	−514.255	−0.897232
$70$	−1.25121	−0.00213640
$71$	864.058	1.44429	0.722146	−	0.691740i	$-0.243156\pi$
$71$	864.058	1.44429	0.722146	+	0.691740i	$0.243156\pi$
$72$	401.033	0.656419
$73$	542.181	0.869281	0.434641	−	0.900604i	$-0.356875\pi$
$73$	542.181	0.869281	0.434641	+	0.900604i	$0.356875\pi$
$74$	−665.566	−1.04555
$75$	−988.065	−1.52123
$76$	51.3466	0.0774982
$77$	−3.56762	−0.00528010
$78$	57.8992	0.0840486
$79$	−726.133	−1.03413	−0.517066	−	0.855946i	$-0.672976\pi$
$79$	−726.133	−1.03413	−0.517066	+	0.855946i	$0.672976\pi$
$80$	56.5545	0.0790374
$81$	430.441	0.590454
$82$	870.529	1.17236
$83$	−1325.90	−1.75345	−0.876724	−	0.480994i	$-0.840276\pi$
$83$	−1325.90	−1.75345	−0.876724	+	0.480994i	$0.840276\pi$
$84$	−6.21759	−0.00807613
$85$	100.462	0.128196
$86$	729.464	0.914652
$87$	2492.77	3.07187
$88$	161.256	0.195340
$89$	−523.778	−0.623824	−0.311912	−	0.950111i	$-0.600969\pi$
$89$	−523.778	−0.623824	−0.311912	+	0.950111i	$0.600969\pi$
$90$	354.378	0.415053
$91$	−0.583427	−0.000672085 0
$92$	−234.223	−0.265428
$93$	−2731.05	−3.04513
$94$	−231.913	−0.254468
$95$	45.3732	0.0490020
$96$	281.034	0.298781
$97$	798.843	0.836188	0.418094	−	0.908404i	$-0.362698\pi$
$97$	798.843	0.836188	0.418094	+	0.908404i	$0.362698\pi$
$98$	−685.937	−0.707042
$99$	1010.45	1.02580
$100$	−450.025	−0.450025
$101$	−428.573	−0.422224	−0.211112	−	0.977462i	$-0.567708\pi$
$101$	−428.573	−0.422224	−0.211112	+	0.977462i	$0.567708\pi$
$102$	499.221	0.484611
$103$	−1535.62	−1.46902	−0.734510	−	0.678598i	$-0.762588\pi$
$103$	−1535.62	−1.46902	−0.734510	+	0.678598i	$0.762588\pi$
$104$	26.3708	0.0248641
$105$	−5.49426	−0.00510653
$106$	−482.629	−0.442237
$107$	−713.930	−0.645030	−0.322515	−	0.946564i	$-0.604528\pi$
$107$	−713.930	−0.645030	−0.322515	+	0.946564i	$0.604528\pi$
$108$	812.508	0.723923
$109$	−147.822	−0.129897	−0.0649485	−	0.997889i	$-0.520688\pi$
$109$	−147.822	−0.129897	−0.0649485	+	0.997889i	$0.520688\pi$
$110$	142.496	0.123513
$111$	−2922.61	−2.49911
$112$	−2.83187	−0.00238916
$113$	157.158	0.130833	0.0654167	−	0.997858i	$-0.479162\pi$
$113$	157.158	0.130833	0.0654167	+	0.997858i	$0.479162\pi$
$114$	225.471	0.185240
$115$	−206.974	−0.167830
$116$	1135.36	0.908754
$117$	165.243	0.130570
$118$	69.3280	0.0540861
$119$	−5.03045	−0.00387513
$120$	248.340	0.188919
$121$	−924.697	−0.694738
$122$	1108.78	0.822821
$123$	3822.63	2.80224
$124$	−1243.89	−0.900842
$125$	−839.503	−0.600700
$126$	−17.7449	−0.0125463
$127$	−1423.37	−0.994519	−0.497260	−	0.867602i	$-0.665660\pi$
$127$	−1423.37	−0.994519	−0.497260	+	0.867602i	$0.665660\pi$
$128$	128.000	0.0883883
$129$	3203.19	2.18624
$130$	23.3029	0.0157216
$131$	606.153	0.404274	0.202137	−	0.979357i	$-0.435211\pi$
$131$	606.153	0.404274	0.202137	+	0.979357i	$0.435211\pi$
$132$	708.100	0.466910
$133$	−2.27198	−0.00148125
$134$	−680.850	−0.438929
$135$	717.985	0.457736
$136$	227.376	0.143363
$137$	2191.79	1.36684	0.683419	−	0.730026i	$-0.260492\pi$
$137$	2191.79	1.36684	0.683419	+	0.730026i	$0.260492\pi$
$138$	−1028.51	−0.634439
$139$	1219.32	0.744040	0.372020	−	0.928225i	$-0.378665\pi$
$139$	1219.32	0.744040	0.372020	+	0.928225i	$0.378665\pi$
$140$	−2.50242	−0.00151067
$141$	−1018.37	−0.608240
$142$	1728.12	1.02127
$143$	66.4444	0.0388557
$144$	802.066	0.464158
$145$	1003.28	0.574604
$146$	1084.36	0.614675
$147$	−3012.06	−1.69000
$148$	−1331.13	−0.739314
$149$	−365.843	−0.201148	−0.100574	−	0.994930i	$-0.532068\pi$
$149$	−365.843	−0.201148	−0.100574	+	0.994930i	$0.532068\pi$
$150$	−1976.13	−1.07567
$151$	989.792	0.533431	0.266716	−	0.963775i	$-0.414062\pi$
$151$	989.792	0.533431	0.266716	+	0.963775i	$0.414062\pi$
$152$	102.693	0.0547995
$153$	1424.77	0.752847
$154$	−7.13523	−0.00373359
$155$	−1099.18	−0.569601
$156$	115.798	0.0594313
$157$	531.569	0.270216	0.135108	−	0.990831i	$-0.456862\pi$
$157$	531.569	0.270216	0.135108	+	0.990831i	$0.456862\pi$
$158$	−1452.27	−0.731241
$159$	−2119.30	−1.05705
$160$	113.109	0.0558879
$161$	10.3639	0.00507322
$162$	860.882	0.417514
$163$	−3095.61	−1.48753	−0.743763	−	0.668443i	$-0.766961\pi$
$163$	−3095.61	−1.48753	−0.743763	+	0.668443i	$0.766961\pi$
$164$	1741.06	0.828987
$165$	625.723	0.295227
$166$	−2651.79	−1.23987
$167$	1708.29	0.791565	0.395782	−	0.918344i	$-0.370473\pi$
$167$	1708.29	0.791565	0.395782	+	0.918344i	$0.370473\pi$
$168$	−12.4352	−0.00571068
$169$	−2186.13	−0.995054
$170$	200.924	0.0906480
$171$	643.490	0.287771
$172$	1458.93	0.646757
$173$	−3042.23	−1.33698	−0.668488	−	0.743723i	$-0.733058\pi$
$173$	−3042.23	−1.33698	−0.668488	+	0.743723i	$0.733058\pi$
$174$	4985.54	2.17214
$175$	19.9127	0.00860146
$176$	322.512	0.138126
$177$	304.430	0.129279
$178$	−1047.56	−0.441110
$179$	3108.49	1.29799	0.648993	−	0.760795i	$-0.275191\pi$
$179$	3108.49	1.29799	0.648993	+	0.760795i	$0.275191\pi$
$180$	708.757	0.293487
$181$	−351.599	−0.144388	−0.0721938	−	0.997391i	$-0.523000\pi$
$181$	−351.599	−0.144388	−0.0721938	+	0.997391i	$0.523000\pi$
$182$	−1.16685	−0.000475236 0
$183$	4868.82	1.96674
$184$	−468.446	−0.187686
$185$	−1176.27	−0.467467
$186$	−5462.11	−2.15323
$187$	572.901	0.224035
$188$	−463.825	−0.179936
$189$	−35.9518	−0.0138366
$190$	90.7464	0.0346497
$191$	2800.58	1.06096	0.530479	−	0.847698i	$-0.322012\pi$
$191$	2800.58	1.06096	0.530479	+	0.847698i	$0.322012\pi$
$192$	562.068	0.211270
$193$	2072.49	0.772958	0.386479	−	0.922298i	$-0.373691\pi$
$193$	2072.49	0.772958	0.386479	+	0.922298i	$0.373691\pi$
$194$	1597.69	0.591274
$195$	102.327	0.0375784
$196$	−1371.87	−0.499954
$197$	−4754.59	−1.71954	−0.859772	−	0.510677i	$-0.829395\pi$
$197$	−4754.59	−1.71954	−0.859772	+	0.510677i	$0.829395\pi$
$198$	2020.90	0.725350
$199$	−3823.70	−1.36208	−0.681042	−	0.732244i	$-0.738473\pi$
$199$	−3823.70	−1.36208	−0.681042	+	0.732244i	$0.738473\pi$
$200$	−900.050	−0.318216
$201$	−2989.72	−1.04915
$202$	−857.146	−0.298557
$203$	−50.2373	−0.0173693
$204$	998.443	0.342671
$205$	1538.51	0.524167
$206$	−3071.24	−1.03875
$207$	−2935.34	−0.985607
$208$	52.7416	0.0175816
$209$	258.748	0.0856363
$210$	−10.9885	−0.00361086
$211$	6005.93	1.95955	0.979776	−	0.200099i	$-0.0641263\pi$
$211$	6005.93	1.95955	0.979776	+	0.200099i	$0.0641263\pi$
$212$	−965.259	−0.312709
$213$	7588.43	2.44108
$214$	−1427.86	−0.456105
$215$	1289.20	0.408944
$216$	1625.02	0.511891
$217$	55.0394	0.0172181
$218$	−295.644	−0.0918511
$219$	4761.61	1.46922
$220$	284.992	0.0873371
$221$	93.6887	0.0285167
$222$	−5845.21	−1.76714
$223$	4517.91	1.35669	0.678344	−	0.734745i	$-0.262698\pi$
$223$	4517.91	1.35669	0.678344	+	0.734745i	$0.262698\pi$
$224$	−5.66373	−0.00168939
$225$	−5639.83	−1.67106
$226$	314.316	0.0925132
$227$	414.053	0.121065	0.0605324	−	0.998166i	$-0.480720\pi$
$227$	414.053	0.121065	0.0605324	+	0.998166i	$0.480720\pi$
$228$	450.942	0.130984
$229$	5876.88	1.69587	0.847936	−	0.530098i	$-0.177845\pi$
$229$	5876.88	1.69587	0.847936	+	0.530098i	$0.177845\pi$
$230$	−413.949	−0.118674
$231$	−31.3319	−0.00892420
$232$	2270.72	0.642586
$233$	−4222.57	−1.18725	−0.593626	−	0.804741i	$-0.702304\pi$
$233$	−4222.57	−1.18725	−0.593626	+	0.804741i	$0.702304\pi$
$234$	330.486	0.0923272
$235$	−409.866	−0.113773
$236$	138.656	0.0382446
$237$	−6377.13	−1.74785
$238$	−10.0609	−0.00274013
$239$	−854.120	−0.231165	−0.115582	−	0.993298i	$-0.536873\pi$
$239$	−854.120	−0.231165	−0.115582	+	0.993298i	$0.536873\pi$
$240$	496.680	0.133586
$241$	−5747.13	−1.53612	−0.768060	−	0.640377i	$-0.778778\pi$
$241$	−5747.13	−1.53612	−0.768060	+	0.640377i	$0.778778\pi$
$242$	−1849.39	−0.491254
$243$	−1704.16	−0.449885
$244$	2217.56	0.581822
$245$	−1212.28	−0.316121
$246$	7645.26	1.98148
$247$	42.3141	0.0109003
$248$	−2487.77	−0.636991
$249$	−11644.5	−2.96360
$250$	−1679.01	−0.424759
$251$	4495.19	1.13041	0.565207	−	0.824949i	$-0.308796\pi$
$251$	4495.19	1.13041	0.565207	+	0.824949i	$0.308796\pi$
$252$	−35.4897	−0.00887160
$253$	−1180.31	−0.293301
$254$	−2846.75	−0.703231
$255$	882.288	0.216671
$256$	256.000	0.0625000
$257$	−3910.62	−0.949174	−0.474587	−	0.880209i	$-0.657403\pi$
$257$	−3910.62	−0.949174	−0.474587	+	0.880209i	$0.657403\pi$
$258$	6406.38	1.54591
$259$	58.8998	0.0141307
$260$	46.6059	0.0111168
$261$	14228.6	3.37445
$262$	1212.31	0.285865
$263$	−1210.34	−0.283774	−0.141887	−	0.989883i	$-0.545317\pi$
$263$	−1210.34	−0.283774	−0.141887	+	0.989883i	$0.545317\pi$
$264$	1416.20	0.330155
$265$	−852.965	−0.197725
$266$	−4.54396	−0.00104740
$267$	−4599.98	−1.05436
$268$	−1361.70	−0.310370
$269$	−6141.94	−1.39212	−0.696061	−	0.717983i	$-0.745066\pi$
$269$	−6141.94	−1.39212	−0.696061	+	0.717983i	$0.745066\pi$
$270$	1435.97	0.323668
$271$	−4173.58	−0.935523	−0.467762	−	0.883855i	$-0.654939\pi$
$271$	−4173.58	−0.935523	−0.467762	+	0.883855i	$0.654939\pi$
$272$	454.751	0.101373
$273$	−5.12384	−0.00113593
$274$	4383.57	0.966501
$275$	−2267.78	−0.497282
$276$	−2057.02	−0.448616
$277$	1572.01	0.340986	0.170493	−	0.985359i	$-0.445464\pi$
$277$	1572.01	0.340986	0.170493	+	0.985359i	$0.445464\pi$
$278$	2438.65	0.526116
$279$	−15588.7	−3.34507
$280$	−5.00484	−0.00106820
$281$	5722.87	1.21494	0.607469	−	0.794343i	$-0.292185\pi$
$281$	5722.87	1.21494	0.607469	+	0.794343i	$0.292185\pi$
$282$	−2036.73	−0.430091
$283$	−4909.48	−1.03123	−0.515616	−	0.856820i	$-0.672437\pi$
$283$	−4909.48	−1.03123	−0.515616	+	0.856820i	$0.672437\pi$
$284$	3456.23	0.722146
$285$	398.482	0.0828212
$286$	132.889	0.0274751
$287$	−77.0382	−0.0158447
$288$	1604.13	0.328210
$289$	−4105.19	−0.835578
$290$	2006.55	0.406306
$291$	7015.69	1.41329
$292$	2168.73	0.434641
$293$	−875.934	−0.174651	−0.0873253	−	0.996180i	$-0.527832\pi$
$293$	−875.934	−0.174651	−0.0873253	+	0.996180i	$0.527832\pi$
$294$	−6024.12	−1.19501
$295$	122.525	0.0241820
$296$	−2662.26	−0.522774
$297$	4094.43	0.799942
$298$	−731.687	−0.142233
$299$	−193.020	−0.0373333
$300$	−3952.26	−0.760613
$301$	−64.5545	−0.0123617
$302$	1979.58	0.377193
$303$	−3763.86	−0.713625
$304$	205.387	0.0387491
$305$	1959.58	0.367885
$306$	2849.53	0.532343
$307$	−5951.93	−1.10650	−0.553249	−	0.833016i	$-0.686612\pi$
$307$	−5951.93	−1.10650	−0.553249	+	0.833016i	$0.686612\pi$
$308$	−14.2705	−0.00264005
$309$	−13486.3	−2.48287
$310$	−2198.36	−0.402769
$311$	8300.62	1.51346	0.756729	−	0.653729i	$-0.226796\pi$
$311$	8300.62	1.51346	0.756729	+	0.653729i	$0.226796\pi$
$312$	231.597	0.0420243
$313$	313.000	0.0565233
$313$	313.000	0.0565233
$314$	1063.14	0.191071
$315$	−31.3610	−0.00560950
$316$	−2904.53	−0.517066
$317$	−6371.93	−1.12897	−0.564485	−	0.825443i	$-0.690925\pi$
$317$	−6371.93	−1.12897	−0.564485	+	0.825443i	$0.690925\pi$
$318$	−4238.60	−0.747450
$319$	5721.35	1.00418
$320$	226.218	0.0395187
$321$	−6269.96	−1.09020
$322$	20.7278	0.00358731
$323$	364.843	0.0628496
$324$	1721.76	0.295227
$325$	−370.860	−0.0632972
$326$	−6191.22	−1.05184
$327$	−1298.22	−0.219547
$328$	3482.12	0.586182
$329$	20.5233	0.00343917
$330$	1251.45	0.208757
$331$	−3338.15	−0.554325	−0.277162	−	0.960823i	$-0.589394\pi$
$331$	−3338.15	−0.554325	−0.277162	+	0.960823i	$0.589394\pi$
$332$	−5303.59	−0.876724
$333$	−16682.1	−2.74527
$334$	3416.58	0.559721
$335$	−1203.29	−0.196246
$336$	−24.8704	−0.00403806
$337$	1714.97	0.277212	0.138606	−	0.990348i	$-0.455738\pi$
$337$	1714.97	0.277212	0.138606	+	0.990348i	$0.455738\pi$
$338$	−4372.27	−0.703610
$339$	1380.21	0.221129
$340$	401.848	0.0640978
$341$	−6268.25	−0.995439
$342$	1286.98	0.203485
$343$	121.411	0.0191124
$344$	2917.86	0.457326
$345$	−1817.71	−0.283659
$346$	−6084.47	−0.945384
$347$	4011.19	0.620554	0.310277	−	0.950646i	$-0.399578\pi$
$347$	4011.19	0.620554	0.310277	+	0.950646i	$0.399578\pi$
$348$	9971.08	1.53594
$349$	7153.85	1.09724	0.548620	−	0.836072i	$-0.315153\pi$
$349$	7153.85	1.09724	0.548620	+	0.836072i	$0.315153\pi$
$350$	39.8253	0.00608215
$351$	669.578	0.101822
$352$	645.023	0.0976700
$353$	4597.36	0.693180	0.346590	−	0.938017i	$-0.387339\pi$
$353$	4597.36	0.693180	0.346590	+	0.938017i	$0.387339\pi$
$354$	608.860	0.0914140
$355$	3054.15	0.456612
$356$	−2095.11	−0.311912
$357$	−44.1790	−0.00654958
$358$	6216.98	0.917814
$359$	3810.93	0.560260	0.280130	−	0.959962i	$-0.409622\pi$
$359$	3810.93	0.560260	0.280130	+	0.959962i	$0.409622\pi$
$360$	1417.51	0.207526
$361$	−6694.22	−0.975976
$362$	−703.199	−0.102098
$363$	−8120.98	−1.17422
$364$	−2.33371	−0.000336042 0
$365$	1916.43	0.274823
$366$	9737.65	1.39070
$367$	−7392.17	−1.05141	−0.525706	−	0.850666i	$-0.676199\pi$
$367$	−7392.17	−1.05141	−0.525706	+	0.850666i	$0.676199\pi$
$368$	−936.891	−0.132714
$369$	21819.4	3.07825
$370$	−2352.55	−0.330549
$371$	42.7107	0.00597690
$372$	−10924.2	−1.52256
$373$	−44.3904	−0.00616206	−0.00308103	−	0.999995i	$-0.500981\pi$
$373$	−44.3904	−0.00616206	−0.00308103	+	0.999995i	$0.500981\pi$
$374$	1145.80	0.158417
$375$	−7372.78	−1.01528
$376$	−927.651	−0.127234
$377$	935.635	0.127819
$378$	−71.9036	−0.00978392
$379$	−3324.55	−0.450582	−0.225291	−	0.974292i	$-0.572333\pi$
$379$	−3324.55	−0.450582	−0.225291	+	0.974292i	$0.572333\pi$
$380$	181.493	0.0245010
$381$	−12500.5	−1.68089
$382$	5601.17	0.750211
$383$	−12320.0	−1.64366	−0.821831	−	0.569732i	$-0.807047\pi$
$383$	−12320.0	−1.64366	−0.821831	+	0.569732i	$0.807047\pi$
$384$	1124.14	0.149390
$385$	−12.6103	−0.00166930
$386$	4144.98	0.546564
$387$	18283.7	2.40158
$388$	3195.37	0.418094
$389$	7070.63	0.921581	0.460790	−	0.887509i	$-0.347566\pi$
$389$	7070.63	0.921581	0.460790	+	0.887509i	$0.347566\pi$
$390$	204.654	0.0265719
$391$	−1664.27	−0.215257
$392$	−2743.75	−0.353521
$393$	5323.43	0.683286
$394$	−9509.18	−1.21590
$395$	−2566.63	−0.326940
$396$	4041.80	0.512900
$397$	−1547.36	−0.195616	−0.0978081	−	0.995205i	$-0.531183\pi$
$397$	−1547.36	−0.195616	−0.0978081	+	0.995205i	$0.531183\pi$
$398$	−7647.40	−0.963139
$399$	−19.9533	−0.00250354
$400$	−1800.10	−0.225012
$401$	5579.36	0.694813	0.347406	−	0.937715i	$-0.387062\pi$
$401$	5579.36	0.694813	0.347406	+	0.937715i	$0.387062\pi$
$402$	−5979.44	−0.741859
$403$	−1025.07	−0.126706
$404$	−1714.29	−0.211112
$405$	1521.46	0.186672
$406$	−100.475	−0.0122819
$407$	−6707.90	−0.816949
$408$	1996.89	0.242305
$409$	7348.20	0.888374	0.444187	−	0.895934i	$-0.353493\pi$
$409$	7348.20	0.888374	0.444187	+	0.895934i	$0.353493\pi$
$410$	3077.02	0.370642
$411$	19249.0	2.31017
$412$	−6142.47	−0.734510
$413$	−6.13524	−0.000730982 0
$414$	−5870.69	−0.696929
$415$	−4686.59	−0.554351
$416$	105.483	0.0124321
$417$	10708.5	1.25755
$418$	517.496	0.0605540
$419$	−4543.26	−0.529720	−0.264860	−	0.964287i	$-0.585326\pi$
$419$	−4543.26	−0.529720	−0.264860	+	0.964287i	$0.585326\pi$
$420$	−21.9771	−0.00255326
$421$	−4120.99	−0.477066	−0.238533	−	0.971134i	$-0.576666\pi$
$421$	−4120.99	−0.477066	−0.238533	+	0.971134i	$0.576666\pi$
$422$	12011.9	1.38561
$423$	−5812.79	−0.668150
$424$	−1930.52	−0.221118
$425$	−3197.65	−0.364961
$426$	15176.9	1.72611
$427$	−98.1223	−0.0111205
$428$	−2855.72	−0.322515
$429$	583.536	0.0656722
$430$	2578.40	0.289167
$431$	4652.86	0.520001	0.260000	−	0.965608i	$-0.416277\pi$
$431$	4652.86	0.520001	0.260000	+	0.965608i	$0.416277\pi$
$432$	3250.03	0.361961
$433$	16821.2	1.86692	0.933458	−	0.358686i	$-0.116775\pi$
$433$	16821.2	1.86692	0.933458	+	0.358686i	$0.116775\pi$
$434$	110.079	0.0121750
$435$	8811.09	0.971172
$436$	−591.288	−0.0649485
$437$	−751.660	−0.0822809
$438$	9523.22	1.03890
$439$	15574.2	1.69320	0.846602	−	0.532226i	$-0.178644\pi$
$439$	15574.2	1.69320	0.846602	+	0.532226i	$0.178644\pi$
$440$	569.984	0.0617566
$441$	−17192.7	−1.85646
$442$	187.377	0.0201643
$443$	4632.53	0.496835	0.248418	−	0.968653i	$-0.420089\pi$
$443$	4632.53	0.496835	0.248418	+	0.968653i	$0.420089\pi$
$444$	−11690.4	−1.24956
$445$	−1851.38	−0.197222
$446$	9035.81	0.959323
$447$	−3212.95	−0.339972
$448$	−11.3275	−0.00119458
$449$	11818.5	1.24220	0.621100	−	0.783732i	$-0.286686\pi$
$449$	11818.5	1.24220	0.621100	+	0.783732i	$0.286686\pi$
$450$	−11279.7	−1.18162
$451$	8773.62	0.916039
$452$	628.632	0.0654167
$453$	8692.67	0.901583
$454$	828.107	0.0856057
$455$	−2.06221	−0.000212479 0
$456$	901.885	0.0926198
$457$	3839.70	0.393028	0.196514	−	0.980501i	$-0.437038\pi$
$457$	3839.70	0.393028	0.196514	+	0.980501i	$0.437038\pi$
$458$	11753.8	1.19916
$459$	5773.27	0.587087
$460$	−827.898	−0.0839151
$461$	14721.0	1.48725	0.743627	−	0.668595i	$-0.233104\pi$
$461$	14721.0	1.48725	0.743627	+	0.668595i	$0.233104\pi$
$462$	−62.6639	−0.00631036
$463$	7386.83	0.741458	0.370729	−	0.928741i	$-0.379108\pi$
$463$	7386.83	0.741458	0.370729	+	0.928741i	$0.379108\pi$
$464$	4541.44	0.454377
$465$	−9653.34	−0.962716
$466$	−8445.14	−0.839514
$467$	−154.573	−0.0153165	−0.00765823	−	0.999971i	$-0.502438\pi$
$467$	−154.573	−0.0153165	−0.00765823	+	0.999971i	$0.502438\pi$
$468$	660.972	0.0652852
$469$	60.2524	0.00593219
$470$	−819.732	−0.0804498
$471$	4668.41	0.456707
$472$	277.312	0.0270430
$473$	7351.89	0.714673
$474$	−12754.3	−1.23591
$475$	−1444.20	−0.139504
$476$	−20.1218	−0.00193757
$477$	−12096.9	−1.16117
$478$	−1708.24	−0.163458
$479$	−18362.1	−1.75154	−0.875769	−	0.482731i	$-0.839645\pi$
$479$	−18362.1	−1.75154	−0.875769	+	0.482731i	$0.839645\pi$
$480$	993.360	0.0944593
$481$	−1096.97	−0.103987
$482$	−11494.3	−1.08620
$483$	91.0188	0.00857454
$484$	−3698.79	−0.347369
$485$	2823.64	0.264360
$486$	−3408.32	−0.318117
$487$	6039.95	0.562005	0.281002	−	0.959707i	$-0.409333\pi$
$487$	6039.95	0.562005	0.281002	+	0.959707i	$0.409333\pi$
$488$	4435.12	0.411410
$489$	−27186.6	−2.51415
$490$	−2424.55	−0.223531
$491$	−8888.06	−0.816930	−0.408465	−	0.912774i	$-0.633936\pi$
$491$	−8888.06	−0.816930	−0.408465	+	0.912774i	$0.633936\pi$
$492$	15290.5	1.40112
$493$	8067.28	0.736982
$494$	84.6282	0.00770770
$495$	3571.60	0.324306
$496$	−4975.55	−0.450421
$497$	−152.931	−0.0138026
$498$	−23288.9	−2.09558
$499$	6991.58	0.627227	0.313613	−	0.949551i	$-0.398460\pi$
$499$	6991.58	0.627227	0.313613	+	0.949551i	$0.398460\pi$
$500$	−3358.01	−0.300350
$501$	15002.7	1.33787
$502$	8990.38	0.799323
$503$	1199.36	0.106316	0.0531581	−	0.998586i	$-0.483071\pi$
$503$	1199.36	0.106316	0.0531581	+	0.998586i	$0.483071\pi$
$504$	−70.9795	−0.00627317
$505$	−1514.86	−0.133486
$506$	−2360.61	−0.207395
$507$	−19199.3	−1.68180
$508$	−5693.49	−0.497260
$509$	−664.372	−0.0578542	−0.0289271	−	0.999582i	$-0.509209\pi$
$509$	−664.372	−0.0578542	−0.0289271	+	0.999582i	$0.509209\pi$
$510$	1764.58	0.153209
$511$	−95.9616	−0.00830742
$512$	512.000	0.0441942
$513$	2607.47	0.224411
$514$	−7821.24	−0.671168
$515$	−5427.89	−0.464430
$516$	12812.8	1.09312
$517$	−2337.33	−0.198831
$518$	117.800	0.00999193
$519$	−26717.9	−2.25970
$520$	93.2118	0.00786078
$521$	12493.3	1.05056	0.525279	−	0.850930i	$-0.323961\pi$
$521$	12493.3	1.05056	0.525279	+	0.850930i	$0.323961\pi$
$522$	28457.3	2.38609
$523$	11807.0	0.987161	0.493580	−	0.869700i	$-0.335688\pi$
$523$	11807.0	0.987161	0.493580	+	0.869700i	$0.335688\pi$
$524$	2424.61	0.202137
$525$	174.879	0.0145378
$526$	−2420.68	−0.200659
$527$	−8838.43	−0.730566
$528$	2832.40	0.233455
$529$	−8738.23	−0.718191
$530$	−1705.93	−0.139813
$531$	1737.68	0.142013
$532$	−9.08793	−0.000740624 0
$533$	1434.78	0.116599
$534$	−9199.96	−0.745546
$535$	−2523.50	−0.203926
$536$	−2723.40	−0.219465
$537$	27299.7	2.19380
$538$	−12283.9	−0.984378
$539$	−6913.21	−0.552455
$540$	2871.94	0.228868
$541$	10369.1	0.824030	0.412015	−	0.911177i	$-0.364825\pi$
$541$	10369.1	0.824030	0.412015	+	0.911177i	$0.364825\pi$
$542$	−8347.16	−0.661515
$543$	−3087.86	−0.244038
$544$	909.503	0.0716813
$545$	−522.500	−0.0410669
$546$	−10.2477	−0.000803224 0
$547$	3664.67	0.286454	0.143227	−	0.989690i	$-0.454252\pi$
$547$	3664.67	0.286454	0.143227	+	0.989690i	$0.454252\pi$
$548$	8767.14	0.683419
$549$	27791.0	2.16046
$550$	−4535.57	−0.351631
$551$	3643.55	0.281707
$552$	−4114.04	−0.317219
$553$	128.520	0.00988284
$554$	3144.03	0.241114
$555$	−10330.4	−0.790093
$556$	4877.29	0.372020
$557$	976.238	0.0742630	0.0371315	−	0.999310i	$-0.488178\pi$
$557$	976.238	0.0742630	0.0371315	+	0.999310i	$0.488178\pi$
$558$	−31177.5	−2.36532
$559$	1202.28	0.0909681
$560$	−10.0097	−0.000755333 0
$561$	5031.39	0.378655
$562$	11445.7	0.859091
$563$	−20213.8	−1.51316	−0.756580	−	0.653902i	$-0.773131\pi$
$563$	−20213.8	−1.51316	−0.756580	+	0.653902i	$0.773131\pi$
$564$	−4073.46	−0.304120
$565$	555.500	0.0413629
$566$	−9818.97	−0.729191
$567$	−76.1845	−0.00564277
$568$	6912.46	0.510634
$569$	18519.2	1.36444	0.682220	−	0.731147i	$-0.261015\pi$
$569$	18519.2	1.36444	0.682220	+	0.731147i	$0.261015\pi$
$570$	796.964	0.0585634
$571$	7702.18	0.564494	0.282247	−	0.959342i	$-0.408920\pi$
$571$	7702.18	0.564494	0.282247	+	0.959342i	$0.408920\pi$
$572$	265.778	0.0194278
$573$	24595.6	1.79319
$574$	−154.076	−0.0112039
$575$	6587.88	0.477798
$576$	3208.26	0.232079
$577$	17349.0	1.25173	0.625864	−	0.779932i	$-0.284746\pi$
$577$	17349.0	1.25173	0.625864	+	0.779932i	$0.284746\pi$
$578$	−8210.38	−0.590843
$579$	18201.2	1.30642
$580$	4013.11	0.287302
$581$	234.673	0.0167571
$582$	14031.4	0.999346
$583$	−4864.17	−0.345546
$584$	4337.45	0.307337
$585$	584.078	0.0412797
$586$	−1751.87	−0.123497
$587$	−6506.06	−0.457468	−0.228734	−	0.973489i	$-0.573459\pi$
$587$	−6506.06	−0.457468	−0.228734	+	0.973489i	$0.573459\pi$
$588$	−12048.2	−0.845002
$589$	−3991.84	−0.279255
$590$	245.051	0.0170993
$591$	−41756.3	−2.90630
$592$	−5324.53	−0.369657
$593$	10216.4	0.707480	0.353740	−	0.935344i	$-0.384910\pi$
$593$	10216.4	0.707480	0.353740	+	0.935344i	$0.384910\pi$
$594$	8188.85	0.565644
$595$	−17.7809	−0.00122512
$596$	−1463.37	−0.100574
$597$	−33580.9	−2.30214
$598$	−386.040	−0.0263986
$599$	17.1891	0.00117250	0.000586251	−	1.00000i	$-0.499813\pi$
$599$	17.1891	0.00117250	0.000586251		1.00000i	$0.499813\pi$
$600$	−7904.52	−0.537835
$601$	19593.9	1.32987	0.664936	−	0.746900i	$-0.268459\pi$
$601$	19593.9	1.32987	0.664936	+	0.746900i	$0.268459\pi$
$602$	−129.109	−0.00874102
$603$	−17065.2	−1.15249
$604$	3959.17	0.266716
$605$	−3268.49	−0.219641
$606$	−7527.73	−0.504609
$607$	−1597.01	−0.106789	−0.0533943	−	0.998574i	$-0.517004\pi$
$607$	−1597.01	−0.106789	−0.0533943	+	0.998574i	$0.517004\pi$
$608$	410.773	0.0273998
$609$	−441.200	−0.0293568
$610$	3919.15	0.260134
$611$	−382.233	−0.0253085
$612$	5699.07	0.376424
$613$	8745.11	0.576202	0.288101	−	0.957600i	$-0.406976\pi$
$613$	8745.11	0.576202	0.288101	+	0.957600i	$0.406976\pi$
$614$	−11903.9	−0.782412
$615$	13511.7	0.885926
$616$	−28.5409	−0.00186680
$617$	16922.4	1.10416	0.552082	−	0.833790i	$-0.313834\pi$
$617$	16922.4	1.10416	0.552082	+	0.833790i	$0.313834\pi$
$618$	−26972.6	−1.75566
$619$	12800.5	0.831170	0.415585	−	0.909554i	$-0.363577\pi$
$619$	12800.5	0.831170	0.415585	+	0.909554i	$0.363577\pi$
$620$	−4396.72	−0.284801
$621$	−11894.3	−0.768599
$622$	16601.2	1.07018
$623$	92.7043	0.00596167
$624$	463.194	0.0297157
$625$	11095.9	0.710139
$626$	626.000	0.0399680
$627$	2272.41	0.144739
$628$	2126.28	0.135108
$629$	−9458.35	−0.599569
$630$	−62.7221	−0.00396652
$631$	13438.3	0.847811	0.423906	−	0.905706i	$-0.360659\pi$
$631$	13438.3	0.847811	0.423906	+	0.905706i	$0.360659\pi$
$632$	−5809.07	−0.365621
$633$	52746.0	3.31195
$634$	−12743.9	−0.798302
$635$	−5031.14	−0.314417
$636$	−8477.21	−0.528527
$637$	−1130.54	−0.0703200
$638$	11442.7	0.710064
$639$	43314.4	2.68152
$640$	452.436	0.0279439
$641$	14203.9	0.875230	0.437615	−	0.899163i	$-0.355823\pi$
$641$	14203.9	0.875230	0.437615	+	0.899163i	$0.355823\pi$
$642$	−12539.9	−0.770889
$643$	17798.1	1.09158	0.545791	−	0.837922i	$-0.316229\pi$
$643$	17798.1	1.09158	0.545791	+	0.837922i	$0.316229\pi$
$644$	41.4555	0.00253661
$645$	11322.2	0.691179
$646$	729.686	0.0444413
$647$	3421.25	0.207888	0.103944	−	0.994583i	$-0.466854\pi$
$647$	3421.25	0.207888	0.103944	+	0.994583i	$0.466854\pi$
$648$	3443.53	0.208757
$649$	698.721	0.0422607
$650$	−741.720	−0.0447579
$651$	483.374	0.0291013
$652$	−12382.4	−0.743763
$653$	−669.568	−0.0401259	−0.0200630	−	0.999799i	$-0.506387\pi$
$653$	−669.568	−0.0401259	−0.0200630	+	0.999799i	$0.506387\pi$
$654$	−2596.44	−0.155243
$655$	2142.54	0.127811
$656$	6964.23	0.414493
$657$	27179.1	1.61394
$658$	41.0466	0.00243186
$659$	1274.29	0.0753251	0.0376626	−	0.999291i	$-0.488009\pi$
$659$	1274.29	0.0753251	0.0376626	+	0.999291i	$0.488009\pi$
$660$	2502.89	0.147613
$661$	−21318.5	−1.25445	−0.627226	−	0.778837i	$-0.715810\pi$
$661$	−21318.5	−1.25445	−0.627226	+	0.778837i	$0.715810\pi$
$662$	−6676.31	−0.391967
$663$	822.804	0.0481977
$664$	−10607.2	−0.619937
$665$	−8.03068	−0.000468295 0
$666$	−33364.2	−1.94120
$667$	−16620.4	−0.964837
$668$	6833.15	0.395782
$669$	39677.7	2.29302
$670$	−2406.57	−0.138767
$671$	11174.8	0.642919
$672$	−49.7407	−0.00285534
$673$	−9369.09	−0.536630	−0.268315	−	0.963331i	$-0.586467\pi$
$673$	−9369.09	−0.536630	−0.268315	+	0.963331i	$0.586467\pi$
$674$	3429.95	0.196019
$675$	−22853.1	−1.30313
$676$	−8744.54	−0.497527
$677$	−12067.6	−0.685075	−0.342537	−	0.939504i	$-0.611286\pi$
$677$	−12067.6	−0.685075	−0.342537	+	0.939504i	$0.611286\pi$
$678$	2760.42	0.156362
$679$	−141.389	−0.00799116
$680$	803.695	0.0453240
$681$	3636.35	0.204618
$682$	−12536.5	−0.703882
$683$	14525.5	0.813765	0.406882	−	0.913481i	$-0.366616\pi$
$683$	14525.5	0.813765	0.406882	+	0.913481i	$0.366616\pi$
$684$	2573.96	0.143886
$685$	7747.21	0.432125
$686$	242.822	0.0135145
$687$	51612.6	2.86629
$688$	5835.71	0.323378
$689$	−795.458	−0.0439834
$690$	−3635.43	−0.200577
$691$	−13291.4	−0.731734	−0.365867	−	0.930667i	$-0.619228\pi$
$691$	−13291.4	−0.731734	−0.365867	+	0.930667i	$0.619228\pi$
$692$	−12168.9	−0.668488
$693$	−178.841	−0.00980321
$694$	8022.39	0.438798
$695$	4309.89	0.235228
$696$	19942.2	1.08607
$697$	12371.1	0.672292
$698$	14307.7	0.775866
$699$	−37083.9	−2.00664
$700$	79.6507	0.00430073
$701$	5552.80	0.299182	0.149591	−	0.988748i	$-0.452204\pi$
$701$	5552.80	0.299182	0.149591	+	0.988748i	$0.452204\pi$
$702$	1339.16	0.0719988
$703$	−4271.82	−0.229182
$704$	1290.05	0.0690631
$705$	−3599.57	−0.192295
$706$	9194.72	0.490153
$707$	75.8539	0.00403505
$708$	1217.72	0.0646395
$709$	−30397.0	−1.61013	−0.805066	−	0.593185i	$-0.797870\pi$
$709$	−30397.0	−1.61013	−0.805066	+	0.593185i	$0.797870\pi$
$710$	6108.30	0.322874
$711$	−36400.4	−1.92000
$712$	−4190.22	−0.220555
$713$	18209.2	0.956436
$714$	−88.3580	−0.00463126
$715$	234.858	0.0122842
$716$	12434.0	0.648993
$717$	−7501.15	−0.390705
$718$	7621.86	0.396163
$719$	−6723.09	−0.348719	−0.174359	−	0.984682i	$-0.555785\pi$
$719$	−6723.09	−0.348719	−0.174359	+	0.984682i	$0.555785\pi$
$720$	2835.03	0.146743
$721$	271.792	0.0140389
$722$	−13388.4	−0.690119
$723$	−50473.1	−2.59629
$724$	−1406.40	−0.0721938
$725$	−31933.7	−1.63585
$726$	−16242.0	−0.830297
$727$	12755.1	0.650700	0.325350	−	0.945594i	$-0.394518\pi$
$727$	12755.1	0.650700	0.325350	+	0.945594i	$0.394518\pi$
$728$	−4.66741	−0.000237618 0
$729$	−26588.4	−1.35083
$730$	3832.85	0.194329
$731$	10366.4	0.524507
$732$	19475.3	0.983371
$733$	30266.8	1.52514	0.762571	−	0.646905i	$-0.223937\pi$
$733$	30266.8	1.52514	0.762571	+	0.646905i	$0.223937\pi$
$734$	−14784.3	−0.743460
$735$	−10646.6	−0.534294
$736$	−1873.78	−0.0938431
$737$	−6861.94	−0.342962
$738$	43638.9	2.17665
$739$	3324.57	0.165489	0.0827446	−	0.996571i	$-0.473631\pi$
$739$	3324.57	0.165489	0.0827446	+	0.996571i	$0.473631\pi$
$740$	−4705.10	−0.233734
$741$	371.616	0.0184233
$742$	85.4214	0.00422631
$743$	10466.9	0.516813	0.258406	−	0.966036i	$-0.416803\pi$
$743$	10466.9	0.516813	0.258406	+	0.966036i	$0.416803\pi$
$744$	−21848.4	−1.07662
$745$	−1293.13	−0.0635929
$746$	−88.7809	−0.00435724
$747$	−66466.0	−3.25551
$748$	2291.60	0.112018
$749$	126.360	0.00616433
$750$	−14745.6	−0.717909
$751$	−40781.6	−1.98154	−0.990772	−	0.135536i	$-0.956724\pi$
$751$	−40781.6	−1.98154	−0.990772	+	0.135536i	$0.956724\pi$
$752$	−1855.30	−0.0899679
$753$	39478.2	1.91058
$754$	1871.27	0.0903815
$755$	3498.58	0.168644
$756$	−143.807	−0.00691828
$757$	−10507.6	−0.504497	−0.252248	−	0.967663i	$-0.581170\pi$
$757$	−10507.6	−0.504497	−0.252248	+	0.967663i	$0.581170\pi$
$758$	−6649.09	−0.318609
$759$	−10365.8	−0.495725
$760$	362.986	0.0173248
$761$	14359.2	0.683998	0.341999	−	0.939700i	$-0.388896\pi$
$761$	14359.2	0.683998	0.341999	+	0.939700i	$0.388896\pi$
$762$	−25001.0	−1.18857
$763$	26.1633	0.00124138
$764$	11202.3	0.530479
$765$	5036.06	0.238012
$766$	−24640.0	−1.16224
$767$	114.265	0.00537922
$768$	2248.27	0.105635
$769$	25116.0	1.17777	0.588885	−	0.808217i	$-0.299567\pi$
$769$	25116.0	1.17777	0.588885	+	0.808217i	$0.299567\pi$
$770$	−25.2206	−0.00118037
$771$	−34344.3	−1.60425
$772$	8289.95	0.386479
$773$	20128.5	0.936574	0.468287	−	0.883576i	$-0.344871\pi$
$773$	20128.5	0.936574	0.468287	+	0.883576i	$0.344871\pi$
$774$	36567.4	1.69817
$775$	34986.3	1.62160
$776$	6390.74	0.295637
$777$	517.277	0.0238832
$778$	14141.3	0.651656
$779$	5587.34	0.256980
$780$	409.308	0.0187892
$781$	17416.8	0.797979
$782$	−3328.54	−0.152210
$783$	57655.6	2.63147
$784$	−5487.50	−0.249977
$785$	1878.92	0.0854285
$786$	10646.9	0.483156
$787$	17734.2	0.803250	0.401625	−	0.915804i	$-0.368446\pi$
$787$	17734.2	0.803250	0.401625	+	0.915804i	$0.368446\pi$
$788$	−19018.4	−0.859772
$789$	−10629.6	−0.479623
$790$	−5133.27	−0.231182
$791$	−27.8157	−0.00125033
$792$	8083.61	0.362675
$793$	1827.46	0.0818349
$794$	−3094.72	−0.138322
$795$	−7491.01	−0.334187
$796$	−15294.8	−0.681042
$797$	13278.5	0.590151	0.295075	−	0.955474i	$-0.404655\pi$
$797$	13278.5	0.590151	0.295075	+	0.955474i	$0.404655\pi$
$798$	−39.9065	−0.00177027
$799$	−3295.71	−0.145925
$800$	−3600.20	−0.159108
$801$	−26256.5	−1.15821
$802$	11158.7	0.491307
$803$	10928.7	0.480282
$804$	−11958.9	−0.524574
$805$	36.6328	0.00160389
$806$	−2050.14	−0.0895946
$807$	−53940.5	−2.35290
$808$	−3428.58	−0.149279
$809$	−36291.6	−1.57719	−0.788593	−	0.614915i	$-0.789190\pi$
$809$	−36291.6	−1.57719	−0.788593	+	0.614915i	$0.789190\pi$
$810$	3042.92	0.131997
$811$	28490.7	1.23359	0.616796	−	0.787123i	$-0.288430\pi$
$811$	28490.7	1.23359	0.616796	+	0.787123i	$0.288430\pi$
$812$	−200.949	−0.00868465
$813$	−36653.7	−1.58118
$814$	−13415.8	−0.577670
$815$	−10941.9	−0.470281
$816$	3993.77	0.171336
$817$	4681.94	0.200490
$818$	14696.4	0.628175
$819$	−29.2467	−0.00124782
$820$	6154.05	0.262084
$821$	−2394.63	−0.101794	−0.0508972	−	0.998704i	$-0.516208\pi$
$821$	−2394.63	−0.101794	−0.0508972	+	0.998704i	$0.516208\pi$
$822$	38497.9	1.63354
$823$	25442.2	1.07759	0.538797	−	0.842435i	$-0.318879\pi$
$823$	25442.2	1.07759	0.538797	+	0.842435i	$0.318879\pi$
$824$	−12284.9	−0.519377
$825$	−19916.4	−0.840485
$826$	−12.2705	−0.000516882 0
$827$	4016.77	0.168896	0.0844478	−	0.996428i	$-0.473087\pi$
$827$	4016.77	0.168896	0.0844478	+	0.996428i	$0.473087\pi$
$828$	−11741.4	−0.492803
$829$	−29079.4	−1.21830	−0.609149	−	0.793056i	$-0.708489\pi$
$829$	−29079.4	−1.21830	−0.609149	+	0.793056i	$0.708489\pi$
$830$	−9373.19	−0.391986
$831$	13805.9	0.576320
$832$	210.966	0.00879080
$833$	−9747.84	−0.405453
$834$	21417.0	0.889219
$835$	6038.22	0.250253
$836$	1034.99	0.0428181
$837$	−63166.8	−2.60856
$838$	−9086.52	−0.374569
$839$	−6888.96	−0.283472	−0.141736	−	0.989904i	$-0.545268\pi$
$839$	−6888.96	−0.283472	−0.141736	+	0.989904i	$0.545268\pi$
$840$	−43.9541	−0.00180543
$841$	56176.0	2.30333
$842$	−8241.98	−0.337336
$843$	50260.1	2.05344
$844$	24023.7	0.979776
$845$	−7727.24	−0.314586
$846$	−11625.6	−0.472453
$847$	163.664	0.00663937
$848$	−3861.04	−0.156354
$849$	−43116.7	−1.74294
$850$	−6395.29	−0.258067
$851$	19486.3	0.784939
$852$	30353.7	1.22054
$853$	24402.1	0.979500	0.489750	−	0.871863i	$-0.337088\pi$
$853$	24402.1	0.979500	0.489750	+	0.871863i	$0.337088\pi$
$854$	−196.245	−0.00786341
$855$	2274.52	0.0909788
$856$	−5711.44	−0.228052
$857$	28300.3	1.12803	0.564013	−	0.825766i	$-0.309257\pi$
$857$	28300.3	1.12803	0.564013	+	0.825766i	$0.309257\pi$
$858$	1167.07	0.0464373
$859$	−7891.20	−0.313439	−0.156720	−	0.987643i	$-0.550092\pi$
$859$	−7891.20	−0.313439	−0.156720	+	0.987643i	$0.550092\pi$
$860$	5156.81	0.204472
$861$	−676.574	−0.0267800
$862$	9305.72	0.367696
$863$	25708.7	1.01406	0.507030	−	0.861928i	$-0.330743\pi$
$863$	25708.7	1.01406	0.507030	+	0.861928i	$0.330743\pi$
$864$	6500.07	0.255945
$865$	−10753.3	−0.422684
$866$	33642.4	1.32011
$867$	−36053.1	−1.41226
$868$	220.158	0.00860903
$869$	−14636.6	−0.571363
$870$	17622.2	0.686722
$871$	−1122.16	−0.0436544
$872$	−1182.58	−0.0459255
$873$	40045.3	1.55249
$874$	−1503.32	−0.0581814
$875$	148.585	0.00574068
$876$	19046.4	0.734611
$877$	−8283.01	−0.318925	−0.159463	−	0.987204i	$-0.550976\pi$
$877$	−8283.01	−0.318925	−0.159463	+	0.987204i	$0.550976\pi$
$878$	31148.4	1.19728
$879$	−7692.73	−0.295187
$880$	1139.97	0.0436685
$881$	−39925.1	−1.52680	−0.763400	−	0.645926i	$-0.776472\pi$
$881$	−39925.1	−1.52680	−0.763400	+	0.645926i	$0.776472\pi$
$882$	−34385.4	−1.31272
$883$	−22313.1	−0.850390	−0.425195	−	0.905102i	$-0.639795\pi$
$883$	−22313.1	−0.850390	−0.425195	+	0.905102i	$0.639795\pi$
$884$	374.755	0.0142583
$885$	1076.06	0.0408715
$886$	9265.05	0.351316
$887$	−40975.2	−1.55108	−0.775542	−	0.631296i	$-0.782523\pi$
$887$	−40975.2	−1.55108	−0.775542	+	0.631296i	$0.782523\pi$
$888$	−23380.9	−0.883570
$889$	251.925	0.00950428
$890$	−3702.75	−0.139457
$891$	8676.39	0.326229
$892$	18071.6	0.678344
$893$	−1488.49	−0.0557788
$894$	−6425.91	−0.240397
$895$	10987.4	0.410357
$896$	−22.6549	−0.000844697 0
$897$	−1695.16	−0.0630991
$898$	23636.9	0.878368
$899$	−88266.2	−3.27457
$900$	−22559.3	−0.835531
$901$	−6858.64	−0.253601
$902$	17547.2	0.647737
$903$	−566.938	−0.0208932
$904$	1257.26	0.0462566
$905$	−1242.78	−0.0456481
$906$	17385.3	0.637516
$907$	−33914.3	−1.24157	−0.620787	−	0.783980i	$-0.713187\pi$
$907$	−33914.3	−1.24157	−0.620787	+	0.783980i	$0.713187\pi$
$908$	1656.21	0.0605324
$909$	−21484.0	−0.783915
$910$	−4.12443	−0.000150246 0
$911$	−30784.8	−1.11959	−0.559794	−	0.828632i	$-0.689120\pi$
$911$	−30784.8	−1.11959	−0.559794	+	0.828632i	$0.689120\pi$
$912$	1803.77	0.0654921
$913$	−26726.1	−0.968789
$914$	7679.40	0.277913
$915$	17209.6	0.621785
$916$	23507.5	0.847936
$917$	−107.284	−0.00386350
$918$	11546.5	0.415134
$919$	2368.60	0.0850195	0.0425098	−	0.999096i	$-0.486465\pi$
$919$	2368.60	0.0850195	0.0425098	+	0.999096i	$0.486465\pi$
$920$	−1655.80	−0.0593369
$921$	−52271.8	−1.87016
$922$	29441.9	1.05165
$923$	2848.24	0.101572
$924$	−125.328	−0.00446210
$925$	37440.2	1.33084
$926$	14773.7	0.524290
$927$	−76979.2	−2.72743
$928$	9082.87	0.321293
$929$	34049.6	1.20251	0.601255	−	0.799057i	$-0.294667\pi$
$929$	34049.6	1.20251	0.601255	+	0.799057i	$0.294667\pi$
$930$	−19306.7	−0.680743
$931$	−4402.57	−0.154982
$932$	−16890.3	−0.593626
$933$	72898.7	2.55798
$934$	−309.146	−0.0108304
$935$	2025.01	0.0708287
$936$	1321.94	0.0461636
$937$	−22028.5	−0.768024	−0.384012	−	0.923328i	$-0.625458\pi$
$937$	−22028.5	−0.768024	−0.384012	+	0.923328i	$0.625458\pi$
$938$	120.505	0.00419469
$939$	2748.87	0.0955334
$940$	−1639.46	−0.0568866
$941$	−45771.8	−1.58567	−0.792836	−	0.609435i	$-0.791396\pi$
$941$	−45771.8	−1.58567	−0.792836	+	0.609435i	$0.791396\pi$
$942$	9336.82	0.322941
$943$	−25487.2	−0.880147
$944$	554.624	0.0191223
$945$	−127.077	−0.00437442
$946$	14703.8	0.505350
$947$	−8684.95	−0.298018	−0.149009	−	0.988836i	$-0.547608\pi$
$947$	−8684.95	−0.298018	−0.149009	+	0.988836i	$0.547608\pi$
$948$	−25508.5	−0.873923
$949$	1787.22	0.0611334
$950$	−2888.41	−0.0986445
$951$	−55960.4	−1.90814
$952$	−40.2436	−0.00137007
$953$	−11521.5	−0.391623	−0.195811	−	0.980642i	$-0.562734\pi$
$953$	−11521.5	−0.391623	−0.195811	+	0.980642i	$0.562734\pi$
$954$	−24193.8	−0.821072
$955$	9899.10	0.335421
$956$	−3416.48	−0.115582
$957$	50246.7	1.69723
$958$	−36724.2	−1.23852
$959$	−387.928	−0.0130624
$960$	1986.72	0.0667928
$961$	66912.5	2.24606
$962$	−2193.94	−0.0735296
$963$	−35788.7	−1.19758
$964$	−22988.5	−0.768060
$965$	7325.53	0.244370
$966$	182.038	0.00606311
$967$	−59218.0	−1.96931	−0.984656	−	0.174509i	$-0.944166\pi$
$967$	−59218.0	−1.96931	−0.984656	+	0.174509i	$0.944166\pi$
$968$	−7397.57	−0.245627
$969$	3204.17	0.106226
$970$	5647.27	0.186931
$971$	−36473.2	−1.20544	−0.602719	−	0.797953i	$-0.705916\pi$
$971$	−36473.2	−1.20544	−0.602719	+	0.797953i	$0.705916\pi$
$972$	−6816.65	−0.224943
$973$	−215.810	−0.00711054
$974$	12079.9	0.397397
$975$	−3257.01	−0.106982
$976$	8870.23	0.290911
$977$	29502.6	0.966090	0.483045	−	0.875595i	$-0.339531\pi$
$977$	29502.6	0.966090	0.483045	+	0.875595i	$0.339531\pi$
$978$	−54373.2	−1.77778
$979$	−10557.8	−0.344666
$980$	−4849.11	−0.158060
$981$	−7410.18	−0.241171
$982$	−17776.1	−0.577657
$983$	−27771.3	−0.901086	−0.450543	−	0.892755i	$-0.648770\pi$
$983$	−27771.3	−0.901086	−0.450543	+	0.892755i	$0.648770\pi$
$984$	30581.1	0.990740
$985$	−16805.8	−0.543633
$986$	16134.6	0.521125
$987$	180.242	0.00581274
$988$	169.256	0.00545017
$989$	−21357.1	−0.686671
$990$	7143.20	0.229319
$991$	37911.2	1.21523	0.607613	−	0.794233i	$-0.292127\pi$
$991$	37911.2	1.21523	0.607613	+	0.794233i	$0.292127\pi$
$992$	−9951.10	−0.318496
$993$	−29316.7	−0.936896
$994$	−305.862	−0.00975991
$995$	−13515.5	−0.430622
$996$	−46577.8	−1.48180
$997$	−9857.16	−0.313119	−0.156559	−	0.987669i	$-0.550040\pi$
$997$	−9857.16	−0.313119	−0.156559	+	0.987669i	$0.550040\pi$
$998$	13983.2	0.443516
$999$	−67597.3	−2.14082

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	626.4.a.d.1.23	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
626.4.a.d.1.23	✓	25	1.1	even	1	trivial

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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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Newspace parameters

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$q$ -expansion

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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	626.4.a.d.1.23

Level	$626$
Weight	$4$
Character	626.1
Self dual	yes
Analytic conductor	$36.935$
Analytic rank	$0$
Dimension	$25$
CM	no
Inner twists	$1$