LMFDB - Embedded newform 547.4.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,4,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	547.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.2740447731$
Analytic rank:	$0$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.26364 q^{2} -3.16796 q^{3} +19.7059 q^{4} +21.3074 q^{5} +16.6750 q^{6} -14.9641 q^{7} -61.6156 q^{8} -16.9640 q^{9} +O(q^{10})$	\(q-5.26364 q^{2} -3.16796 q^{3} +19.7059 q^{4} +21.3074 q^{5} +16.6750 q^{6} -14.9641 q^{7} -61.6156 q^{8} -16.9640 q^{9} -112.154 q^{10} -54.3265 q^{11} -62.4275 q^{12} -13.9286 q^{13} +78.7657 q^{14} -67.5009 q^{15} +166.675 q^{16} +67.6229 q^{17} +89.2925 q^{18} -101.959 q^{19} +419.881 q^{20} +47.4057 q^{21} +285.955 q^{22} -186.453 q^{23} +195.196 q^{24} +329.004 q^{25} +73.3152 q^{26} +139.276 q^{27} -294.881 q^{28} -148.869 q^{29} +355.300 q^{30} +309.051 q^{31} -384.392 q^{32} +172.104 q^{33} -355.942 q^{34} -318.846 q^{35} -334.291 q^{36} -99.4171 q^{37} +536.674 q^{38} +44.1253 q^{39} -1312.87 q^{40} +131.193 q^{41} -249.527 q^{42} -182.722 q^{43} -1070.55 q^{44} -361.459 q^{45} +981.421 q^{46} +459.707 q^{47} -528.020 q^{48} -119.076 q^{49} -1731.76 q^{50} -214.227 q^{51} -274.476 q^{52} +652.130 q^{53} -733.100 q^{54} -1157.55 q^{55} +922.022 q^{56} +323.001 q^{57} +783.594 q^{58} +130.875 q^{59} -1330.17 q^{60} +499.149 q^{61} -1626.73 q^{62} +253.851 q^{63} +689.903 q^{64} -296.782 q^{65} -905.895 q^{66} +277.653 q^{67} +1332.57 q^{68} +590.676 q^{69} +1678.29 q^{70} -422.194 q^{71} +1045.25 q^{72} +230.601 q^{73} +523.296 q^{74} -1042.27 q^{75} -2009.19 q^{76} +812.948 q^{77} -232.260 q^{78} -574.659 q^{79} +3551.41 q^{80} +16.8066 q^{81} -690.553 q^{82} +772.912 q^{83} +934.172 q^{84} +1440.86 q^{85} +961.781 q^{86} +471.612 q^{87} +3347.36 q^{88} +74.4513 q^{89} +1902.59 q^{90} +208.429 q^{91} -3674.22 q^{92} -979.061 q^{93} -2419.73 q^{94} -2172.47 q^{95} +1217.74 q^{96} +224.774 q^{97} +626.770 q^{98} +921.596 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9}+O(q^{10}) $ 71 * q + 14 * q^2 + 31 * q^3 + 294 * q^4 + 159 * q^5 + 60 * q^6 + 66 * q^7 + 168 * q^8 + 738 * q^9	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9} + 120 q^{10} + 139 q^{11} + 309 q^{12} + 343 q^{13} + 239 q^{14} + 194 q^{15} + 1346 q^{16} + 842 q^{17} + 423 q^{18} + 157 q^{19} + 1292 q^{20} + 434 q^{21} + 436 q^{22} + 1004 q^{23} + 935 q^{24} + 2206 q^{25} + 812 q^{26} + 1282 q^{27} + 584 q^{28} + 1459 q^{29} + 146 q^{30} + 582 q^{31} + 1428 q^{32} + 1080 q^{33} + 393 q^{34} + 1006 q^{35} + 2996 q^{36} + 1477 q^{37} + 1873 q^{38} + 626 q^{39} + 1272 q^{40} + 1112 q^{41} + 1812 q^{42} + 833 q^{43} + 1392 q^{44} + 3841 q^{45} + 782 q^{46} + 2484 q^{47} + 2034 q^{48} + 4727 q^{49} + 1248 q^{50} + 932 q^{51} + 2118 q^{52} + 5077 q^{53} + 1537 q^{54} + 1736 q^{55} + 2281 q^{56} + 1426 q^{57} + 992 q^{58} + 2977 q^{59} + 1418 q^{60} + 3363 q^{61} + 3438 q^{62} + 3194 q^{63} + 6138 q^{64} + 4640 q^{65} + 288 q^{66} + 955 q^{67} + 8553 q^{68} + 4440 q^{69} + 2203 q^{70} + 2458 q^{71} + 4495 q^{72} + 3724 q^{73} + 2099 q^{74} + 4491 q^{75} + 2260 q^{76} + 9774 q^{77} + 1057 q^{78} + 1638 q^{79} + 8221 q^{80} + 10151 q^{81} + 1018 q^{82} + 6121 q^{83} + 4847 q^{84} + 3836 q^{85} + 2305 q^{86} + 3894 q^{87} + 5815 q^{88} + 8110 q^{89} + 4951 q^{90} + 2312 q^{91} + 13138 q^{92} + 9250 q^{93} - 813 q^{94} + 4858 q^{95} + 6882 q^{96} + 4486 q^{97} + 4216 q^{98} + 4969 q^{99}+O(q^{100}) \) 71 * q + 14 * q^2 + 31 * q^3 + 294 * q^4 + 159 * q^5 + 60 * q^6 + 66 * q^7 + 168 * q^8 + 738 * q^9 + 120 * q^10 + 139 * q^11 + 309 * q^12 + 343 * q^13 + 239 * q^14 + 194 * q^15 + 1346 * q^16 + 842 * q^17 + 423 * q^18 + 157 * q^19 + 1292 * q^20 + 434 * q^21 + 436 * q^22 + 1004 * q^23 + 935 * q^24 + 2206 * q^25 + 812 * q^26 + 1282 * q^27 + 584 * q^28 + 1459 * q^29 + 146 * q^30 + 582 * q^31 + 1428 * q^32 + 1080 * q^33 + 393 * q^34 + 1006 * q^35 + 2996 * q^36 + 1477 * q^37 + 1873 * q^38 + 626 * q^39 + 1272 * q^40 + 1112 * q^41 + 1812 * q^42 + 833 * q^43 + 1392 * q^44 + 3841 * q^45 + 782 * q^46 + 2484 * q^47 + 2034 * q^48 + 4727 * q^49 + 1248 * q^50 + 932 * q^51 + 2118 * q^52 + 5077 * q^53 + 1537 * q^54 + 1736 * q^55 + 2281 * q^56 + 1426 * q^57 + 992 * q^58 + 2977 * q^59 + 1418 * q^60 + 3363 * q^61 + 3438 * q^62 + 3194 * q^63 + 6138 * q^64 + 4640 * q^65 + 288 * q^66 + 955 * q^67 + 8553 * q^68 + 4440 * q^69 + 2203 * q^70 + 2458 * q^71 + 4495 * q^72 + 3724 * q^73 + 2099 * q^74 + 4491 * q^75 + 2260 * q^76 + 9774 * q^77 + 1057 * q^78 + 1638 * q^79 + 8221 * q^80 + 10151 * q^81 + 1018 * q^82 + 6121 * q^83 + 4847 * q^84 + 3836 * q^85 + 2305 * q^86 + 3894 * q^87 + 5815 * q^88 + 8110 * q^89 + 4951 * q^90 + 2312 * q^91 + 13138 * q^92 + 9250 * q^93 - 813 * q^94 + 4858 * q^95 + 6882 * q^96 + 4486 * q^97 + 4216 * q^98 + 4969 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−5.26364	−1.86098	−0.930489	−	0.366321i	$-0.880617\pi$
$2$	−5.26364	−1.86098	−0.930489	+	0.366321i	$0.880617\pi$
$3$	−3.16796	−0.609674	−0.304837	−	0.952404i	$-0.598602\pi$
$3$	−3.16796	−0.609674	−0.304837	+	0.952404i	$0.598602\pi$
$4$	19.7059	2.46324
$5$	21.3074	1.90579	0.952894	−	0.303303i	$-0.0980893\pi$
$5$	21.3074	1.90579	0.952894	+	0.303303i	$0.0980893\pi$
$6$	16.6750	1.13459
$7$	−14.9641	−0.807986	−0.403993	−	0.914762i	$-0.632378\pi$
$7$	−14.9641	−0.807986	−0.403993	+	0.914762i	$0.632378\pi$
$8$	−61.6156	−2.72305
$9$	−16.9640	−0.628297
$10$	−112.154	−3.54663
$11$	−54.3265	−1.48910	−0.744548	−	0.667569i	$-0.767335\pi$
$11$	−54.3265	−1.48910	−0.744548	+	0.667569i	$0.767335\pi$
$12$	−62.4275	−1.50177
$13$	−13.9286	−0.297162	−0.148581	−	0.988900i	$-0.547471\pi$
$13$	−13.9286	−0.297162	−0.148581	+	0.988900i	$0.547471\pi$
$14$	78.7657	1.50364
$15$	−67.5009	−1.16191
$16$	166.675	2.60430
$17$	67.6229	0.964762	0.482381	−	0.875962i	$-0.339772\pi$
$17$	67.6229	0.964762	0.482381	+	0.875962i	$0.339772\pi$
$18$	89.2925	1.16925
$19$	−101.959	−1.23110	−0.615551	−	0.788097i	$-0.711067\pi$
$19$	−101.959	−1.23110	−0.615551	+	0.788097i	$0.711067\pi$
$20$	419.881	4.69441
$21$	47.4057	0.492608
$22$	285.955	2.77117
$23$	−186.453	−1.69035	−0.845177	−	0.534486i	$-0.820505\pi$
$23$	−186.453	−1.69035	−0.845177	+	0.534486i	$0.820505\pi$
$24$	195.196	1.66017
$25$	329.004	2.63203
$26$	73.3152	0.553012
$27$	139.276	0.992731
$28$	−294.881	−1.99026
$29$	−148.869	−0.953253	−0.476627	−	0.879106i	$-0.658141\pi$
$29$	−148.869	−0.953253	−0.476627	+	0.879106i	$0.658141\pi$
$30$	355.300	2.16229
$31$	309.051	1.79055	0.895277	−	0.445511i	$-0.146978\pi$
$31$	309.051	1.79055	0.895277	+	0.445511i	$0.146978\pi$
$32$	−384.392	−2.12349
$33$	172.104	0.907864
$34$	−355.942	−1.79540
$35$	−318.846	−1.53985
$36$	−334.291	−1.54764
$37$	−99.4171	−0.441732	−0.220866	−	0.975304i	$-0.570888\pi$
$37$	−99.4171	−0.441732	−0.220866	+	0.975304i	$0.570888\pi$
$38$	536.674	2.29105
$39$	44.1253	0.181172
$40$	−1312.87	−5.18956
$41$	131.193	0.499730	0.249865	−	0.968281i	$-0.419614\pi$
$41$	131.193	0.499730	0.249865	+	0.968281i	$0.419614\pi$
$42$	−249.527	−0.916733
$43$	−182.722	−0.648019	−0.324009	−	0.946054i	$-0.605031\pi$
$43$	−182.722	−0.648019	−0.324009	+	0.946054i	$0.605031\pi$
$44$	−1070.55	−3.66800
$45$	−361.459	−1.19740
$46$	981.421	3.14571
$47$	459.707	1.42671	0.713353	−	0.700805i	$-0.247176\pi$
$47$	459.707	1.42671	0.713353	+	0.700805i	$0.247176\pi$
$48$	−528.020	−1.58777
$49$	−119.076	−0.347159
$50$	−1731.76	−4.89815
$51$	−214.227	−0.588191
$52$	−274.476	−0.731980
$53$	652.130	1.69013	0.845065	−	0.534663i	$-0.179562\pi$
$53$	652.130	1.69013	0.845065	+	0.534663i	$0.179562\pi$
$54$	−733.100	−1.84745
$55$	−1157.55	−2.83790
$56$	922.022	2.20019
$57$	323.001	0.750572
$58$	783.594	1.77398
$59$	130.875	0.288788	0.144394	−	0.989520i	$-0.453877\pi$
$59$	130.875	0.288788	0.144394	+	0.989520i	$0.453877\pi$
$60$	−1330.17	−2.86206
$61$	499.149	1.04770	0.523848	−	0.851812i	$-0.324496\pi$
$61$	499.149	1.04770	0.523848	+	0.851812i	$0.324496\pi$
$62$	−1626.73	−3.33218
$63$	253.851	0.507655
$64$	689.903	1.34747
$65$	−296.782	−0.566328
$66$	−905.895	−1.68951
$67$	277.653	0.506279	0.253140	−	0.967430i	$-0.418537\pi$
$67$	277.653	0.506279	0.253140	+	0.967430i	$0.418537\pi$
$68$	1332.57	2.37644
$69$	590.676	1.03057
$70$	1678.29	2.86563
$71$	−422.194	−0.705707	−0.352854	−	0.935679i	$-0.614789\pi$
$71$	−422.194	−0.705707	−0.352854	+	0.935679i	$0.614789\pi$
$72$	1045.25	1.71088
$73$	230.601	0.369724	0.184862	−	0.982764i	$-0.440816\pi$
$73$	230.601	0.369724	0.184862	+	0.982764i	$0.440816\pi$
$74$	523.296	0.822053
$75$	−1042.27	−1.60468
$76$	−2009.19	−3.03250
$77$	812.948	1.20317
$78$	−232.260	−0.337157
$79$	−574.659	−0.818407	−0.409203	−	0.912443i	$-0.634193\pi$
$79$	−574.659	−0.818407	−0.409203	+	0.912443i	$0.634193\pi$
$80$	3551.41	4.96324
$81$	16.8066	0.0230543
$82$	−690.553	−0.929986
$83$	772.912	1.02215	0.511073	−	0.859537i	$-0.329248\pi$
$83$	772.912	1.02215	0.511073	+	0.859537i	$0.329248\pi$
$84$	934.172	1.21341
$85$	1440.86	1.83863
$86$	961.781	1.20595
$87$	471.612	0.581174
$88$	3347.36	4.05488
$89$	74.4513	0.0886721	0.0443360	−	0.999017i	$-0.485883\pi$
$89$	74.4513	0.0886721	0.0443360	+	0.999017i	$0.485883\pi$
$90$	1902.59	2.22834
$91$	208.429	0.240103
$92$	−3674.22	−4.16374
$93$	−979.061	−1.09165
$94$	−2419.73	−2.65507
$95$	−2172.47	−2.34622
$96$	1217.74	1.29464
$97$	224.774	0.235282	0.117641	−	0.993056i	$-0.462467\pi$
$97$	224.774	0.235282	0.117641	+	0.993056i	$0.462467\pi$
$98$	626.770	0.646055
$99$	921.596	0.935595
$100$	6483.31	6.48331
$101$	1192.65	1.17499	0.587493	−	0.809230i	$-0.300115\pi$
$101$	1192.65	1.17499	0.587493	+	0.809230i	$0.300115\pi$
$102$	1127.61	1.09461
$103$	79.5356	0.0760862	0.0380431	−	0.999276i	$-0.487888\pi$
$103$	79.5356	0.0760862	0.0380431	+	0.999276i	$0.487888\pi$
$104$	858.220	0.809187
$105$	1010.09	0.938807
$106$	−3432.58	−3.14529
$107$	1101.54	0.995235	0.497617	−	0.867397i	$-0.334208\pi$
$107$	1101.54	0.995235	0.497617	+	0.867397i	$0.334208\pi$
$108$	2744.56	2.44533
$109$	−1608.43	−1.41339	−0.706694	−	0.707520i	$-0.749814\pi$
$109$	−1608.43	−1.41339	−0.706694	+	0.707520i	$0.749814\pi$
$110$	6092.95	5.28127
$111$	314.950	0.269313
$112$	−2494.14	−2.10424
$113$	−1355.31	−1.12829	−0.564144	−	0.825677i	$-0.690794\pi$
$113$	−1355.31	−1.12829	−0.564144	+	0.825677i	$0.690794\pi$
$114$	−1700.16	−1.39680
$115$	−3972.82	−3.22146
$116$	−2933.60	−2.34809
$117$	236.285	0.186706
$118$	−688.879	−0.537427
$119$	−1011.92	−0.779514
$120$	4159.11	3.16394
$121$	1620.37	1.21741
$122$	−2627.34	−1.94974
$123$	−415.615	−0.304672
$124$	6090.12	4.41056
$125$	4346.78	3.11030
$126$	−1336.18	−0.944735
$127$	−518.393	−0.362205	−0.181102	−	0.983464i	$-0.557967\pi$
$127$	−518.393	−0.362205	−0.181102	+	0.983464i	$0.557967\pi$
$128$	−556.260	−0.384116
$129$	578.855	0.395080
$130$	1562.15	1.05392
$131$	−2740.76	−1.82795	−0.913976	−	0.405769i	$-0.867004\pi$
$131$	−2740.76	−1.82795	−0.913976	+	0.405769i	$0.867004\pi$
$132$	3391.47	2.23628
$133$	1525.72	0.994713
$134$	−1461.46	−0.942174
$135$	2967.61	1.89194
$136$	−4166.62	−2.62709
$137$	2826.41	1.76260	0.881300	−	0.472557i	$-0.156669\pi$
$137$	2826.41	1.76260	0.881300	+	0.472557i	$0.156669\pi$
$138$	−3109.10	−1.91786
$139$	402.456	0.245582	0.122791	−	0.992433i	$-0.460816\pi$
$139$	402.456	0.245582	0.122791	+	0.992433i	$0.460816\pi$
$140$	−6283.14	−3.79302
$141$	−1456.33	−0.869826
$142$	2222.28	1.31331
$143$	756.694	0.442503
$144$	−2827.48	−1.63627
$145$	−3172.01	−1.81670
$146$	−1213.80	−0.688048
$147$	377.227	0.211654
$148$	−1959.10	−1.08809
$149$	1611.54	0.886057	0.443028	−	0.896508i	$-0.353904\pi$
$149$	1611.54	0.886057	0.443028	+	0.896508i	$0.353904\pi$
$150$	5486.14	2.98628
$151$	841.330	0.453420	0.226710	−	0.973962i	$-0.427203\pi$
$151$	841.330	0.453420	0.226710	+	0.973962i	$0.427203\pi$
$152$	6282.25	3.35235
$153$	−1147.16	−0.606157
$154$	−4279.06	−2.23907
$155$	6585.06	3.41242
$156$	869.529	0.446270
$157$	277.488	0.141057	0.0705284	−	0.997510i	$-0.477531\pi$
$157$	277.488	0.141057	0.0705284	+	0.997510i	$0.477531\pi$
$158$	3024.79	1.52304
$159$	−2065.92	−1.03043
$160$	−8190.39	−4.04692
$161$	2790.10	1.36578
$162$	−88.4639	−0.0429036
$163$	−38.9987	−0.0187399	−0.00936997	−	0.999956i	$-0.502983\pi$
$163$	−38.9987	−0.0187399	−0.00936997	+	0.999956i	$0.502983\pi$
$164$	2585.28	1.23095
$165$	3667.09	1.73020
$166$	−4068.33	−1.90219
$167$	1351.79	0.626374	0.313187	−	0.949692i	$-0.398603\pi$
$167$	1351.79	0.626374	0.313187	+	0.949692i	$0.398603\pi$
$168$	−2920.93	−1.34140
$169$	−2002.99	−0.911695
$170$	−7584.19	−3.42165
$171$	1729.63	0.773498
$172$	−3600.69	−1.59622
$173$	2452.10	1.07763	0.538814	−	0.842425i	$-0.318873\pi$
$173$	2452.10	1.07763	0.538814	+	0.842425i	$0.318873\pi$
$174$	−2482.40	−1.08155
$175$	−4923.25	−2.12664
$176$	−9054.87	−3.87805
$177$	−414.607	−0.176067
$178$	−391.884	−0.165017
$179$	1948.77	0.813731	0.406866	−	0.913488i	$-0.366622\pi$
$179$	1948.77	0.813731	0.406866	+	0.913488i	$0.366622\pi$
$180$	−7122.86	−2.94948
$181$	−1243.78	−0.510770	−0.255385	−	0.966839i	$-0.582202\pi$
$181$	−1243.78	−0.510770	−0.255385	+	0.966839i	$0.582202\pi$
$182$	−1097.10	−0.446825
$183$	−1581.28	−0.638753
$184$	11488.4	4.60292
$185$	−2118.32	−0.841847
$186$	5153.42	2.03154
$187$	−3673.71	−1.43662
$188$	9058.94	3.51432
$189$	−2084.15	−0.802113
$190$	11435.1	4.36626
$191$	3289.92	1.24634	0.623168	−	0.782088i	$-0.285845\pi$
$191$	3289.92	1.24634	0.623168	+	0.782088i	$0.285845\pi$
$192$	−2185.59	−0.821516
$193$	−907.383	−0.338419	−0.169210	−	0.985580i	$-0.554121\pi$
$193$	−907.383	−0.338419	−0.169210	+	0.985580i	$0.554121\pi$
$194$	−1183.13	−0.437855
$195$	940.195	0.345276
$196$	−2346.49	−0.855134
$197$	2937.93	1.06253	0.531266	−	0.847205i	$-0.321716\pi$
$197$	2937.93	1.06253	0.531266	+	0.847205i	$0.321716\pi$
$198$	−4850.95	−1.74112
$199$	2194.73	0.781812	0.390906	−	0.920431i	$-0.372162\pi$
$199$	2194.73	0.781812	0.390906	+	0.920431i	$0.372162\pi$
$200$	−20271.8	−7.16715
$201$	−879.594	−0.308665
$202$	−6277.70	−2.18662
$203$	2227.70	0.770215
$204$	−4221.53	−1.44885
$205$	2795.38	0.952379
$206$	−418.647	−0.141595
$207$	3162.99	1.06204
$208$	−2321.55	−0.773898
$209$	5539.06	1.83323
$210$	−5316.75	−1.74710
$211$	−1112.80	−0.363073	−0.181536	−	0.983384i	$-0.558107\pi$
$211$	−1112.80	−0.363073	−0.181536	+	0.983384i	$0.558107\pi$
$212$	12850.8	4.16319
$213$	1337.49	0.430252
$214$	−5798.12	−1.85211
$215$	−3893.32	−1.23499
$216$	−8581.59	−2.70326
$217$	−4624.67	−1.44674
$218$	8466.17	2.63028
$219$	−730.537	−0.225411
$220$	−22810.7	−6.99043
$221$	−941.893	−0.286690
$222$	−1657.78	−0.501185
$223$	4739.28	1.42316	0.711582	−	0.702603i	$-0.247979\pi$
$223$	4739.28	1.42316	0.711582	+	0.702603i	$0.247979\pi$
$224$	5752.09	1.71575
$225$	−5581.23	−1.65370
$226$	7133.84	2.09972
$227$	3330.17	0.973707	0.486853	−	0.873484i	$-0.338145\pi$
$227$	3330.17	0.973707	0.486853	+	0.873484i	$0.338145\pi$
$228$	6365.03	1.84884
$229$	−2845.79	−0.821202	−0.410601	−	0.911815i	$-0.634681\pi$
$229$	−2845.79	−0.821202	−0.410601	+	0.911815i	$0.634681\pi$
$230$	20911.5	5.99506
$231$	−2575.39	−0.733541
$232$	9172.67	2.59576
$233$	−1444.21	−0.406065	−0.203033	−	0.979172i	$-0.565080\pi$
$233$	−1444.21	−0.406065	−0.203033	+	0.979172i	$0.565080\pi$
$234$	−1243.72	−0.347456
$235$	9795.15	2.71900
$236$	2579.01	0.711353
$237$	1820.50	0.498962
$238$	5326.36	1.45066
$239$	−5517.94	−1.49341	−0.746707	−	0.665153i	$-0.768366\pi$
$239$	−5517.94	−1.49341	−0.746707	+	0.665153i	$0.768366\pi$
$240$	−11250.7	−3.02596
$241$	−4393.59	−1.17434	−0.587170	−	0.809464i	$-0.699758\pi$
$241$	−4393.59	−1.17434	−0.587170	+	0.809464i	$0.699758\pi$
$242$	−8529.05	−2.26557
$243$	−3813.70	−1.00679
$244$	9836.17	2.58072
$245$	−2537.19	−0.661611
$246$	2187.65	0.566989
$247$	1420.14	0.365837
$248$	−19042.3	−4.87577
$249$	−2448.56	−0.623176
$250$	−22879.9	−5.78821
$251$	5593.52	1.40661	0.703306	−	0.710887i	$-0.251706\pi$
$251$	5593.52	1.40661	0.703306	+	0.710887i	$0.251706\pi$
$252$	5002.37	1.25047
$253$	10129.3	2.51710
$254$	2728.64	0.674054
$255$	−4564.60	−1.12097
$256$	−2591.27	−0.632635
$257$	−879.380	−0.213441	−0.106720	−	0.994289i	$-0.534035\pi$
$257$	−879.380	−0.213441	−0.106720	+	0.994289i	$0.534035\pi$
$258$	−3046.89	−0.735236
$259$	1487.69	0.356913
$260$	−5848.36	−1.39500
$261$	2525.42	0.598926
$262$	14426.4	3.40178
$263$	−2844.92	−0.667016	−0.333508	−	0.942747i	$-0.608232\pi$
$263$	−2844.92	−0.667016	−0.333508	+	0.942747i	$0.608232\pi$
$264$	−10604.3	−2.47216
$265$	13895.2	3.22103
$266$	−8030.85	−1.85114
$267$	−235.859	−0.0540611
$268$	5471.40	1.24709
$269$	−657.896	−0.149118	−0.0745588	−	0.997217i	$-0.523755\pi$
$269$	−657.896	−0.149118	−0.0745588	+	0.997217i	$0.523755\pi$
$270$	−15620.4	−3.52085
$271$	−2790.39	−0.625477	−0.312739	−	0.949839i	$-0.601246\pi$
$271$	−2790.39	−0.625477	−0.312739	+	0.949839i	$0.601246\pi$
$272$	11271.0	2.51253
$273$	−660.296	−0.146384
$274$	−14877.2	−3.28016
$275$	−17873.6	−3.91935
$276$	11639.8	2.53853
$277$	5613.65	1.21766	0.608829	−	0.793301i	$-0.291639\pi$
$277$	5613.65	1.21766	0.608829	+	0.793301i	$0.291639\pi$
$278$	−2118.38	−0.457022
$279$	−5242.74	−1.12500
$280$	19645.9	4.19309
$281$	4430.49	0.940572	0.470286	−	0.882514i	$-0.344151\pi$
$281$	4430.49	0.940572	0.470286	+	0.882514i	$0.344151\pi$
$282$	7665.62	1.61873
$283$	1263.70	0.265439	0.132719	−	0.991154i	$-0.457629\pi$
$283$	1263.70	0.265439	0.132719	+	0.991154i	$0.457629\pi$
$284$	−8319.71	−1.73832
$285$	6882.31	1.43043
$286$	−3982.96	−0.823488
$287$	−1963.19	−0.403775
$288$	6520.84	1.33418
$289$	−340.150	−0.0692346
$290$	16696.3	3.38084
$291$	−712.076	−0.143445
$292$	4544.21	0.910718
$293$	−1897.13	−0.378265	−0.189133	−	0.981952i	$-0.560568\pi$
$293$	−1897.13	−0.378265	−0.189133	+	0.981952i	$0.560568\pi$
$294$	−1985.58	−0.393883
$295$	2788.60	0.550368
$296$	6125.64	1.20286
$297$	−7566.40	−1.47827
$298$	−8482.56	−1.64893
$299$	2597.03	0.502309
$300$	−20538.9	−3.95271
$301$	2734.27	0.523590
$302$	−4428.46	−0.843805
$303$	−3778.28	−0.716358
$304$	−16994.0	−3.20616
$305$	10635.5	1.99669
$306$	6038.21	1.12804
$307$	−7015.05	−1.30414	−0.652068	−	0.758160i	$-0.726098\pi$
$307$	−7015.05	−1.30414	−0.652068	+	0.758160i	$0.726098\pi$
$308$	16019.9	2.96369
$309$	−251.966	−0.0463878
$310$	−34661.4	−6.35043
$311$	10053.5	1.83305	0.916526	−	0.399976i	$-0.130982\pi$
$311$	10053.5	1.83305	0.916526	+	0.399976i	$0.130982\pi$
$312$	−2718.81	−0.493340
$313$	6354.86	1.14760	0.573799	−	0.818996i	$-0.305469\pi$
$313$	6354.86	1.14760	0.573799	+	0.818996i	$0.305469\pi$
$314$	−1460.60	−0.262504
$315$	5408.90	0.967483
$316$	−11324.2	−2.01593
$317$	5397.48	0.956318	0.478159	−	0.878273i	$-0.341304\pi$
$317$	5397.48	0.956318	0.478159	+	0.878273i	$0.341304\pi$
$318$	10874.3	1.91761
$319$	8087.55	1.41949
$320$	14700.0	2.56799
$321$	−3489.64	−0.606769
$322$	−14686.1	−2.54169
$323$	−6894.74	−1.18772
$324$	331.189	0.0567882
$325$	−4582.57	−0.782139
$326$	205.275	0.0348746
$327$	5095.43	0.861706
$328$	−8083.54	−1.36079
$329$	−6879.11	−1.15276
$330$	−19302.2	−3.21986
$331$	−9539.76	−1.58415	−0.792074	−	0.610425i	$-0.790998\pi$
$331$	−9539.76	−1.58415	−0.792074	+	0.610425i	$0.790998\pi$
$332$	15230.9	2.51779
$333$	1686.51	0.277539
$334$	−7115.32	−1.16567
$335$	5916.05	0.964861
$336$	7901.35	1.28290
$337$	1626.65	0.262936	0.131468	−	0.991320i	$-0.458031\pi$
$337$	1626.65	0.262936	0.131468	+	0.991320i	$0.458031\pi$
$338$	10543.0	1.69664
$339$	4293.56	0.687888
$340$	28393.5	4.52899
$341$	−16789.6	−2.66631
$342$	−9104.15	−1.43946
$343$	6914.55	1.08849
$344$	11258.5	1.76459
$345$	12585.7	1.96404
$346$	−12907.0	−2.00544
$347$	1053.97	0.163054	0.0815272	−	0.996671i	$-0.474020\pi$
$347$	1053.97	0.163054	0.0815272	+	0.996671i	$0.474020\pi$
$348$	9293.54	1.43157
$349$	7737.80	1.18680	0.593402	−	0.804906i	$-0.297784\pi$
$349$	7737.80	1.18680	0.593402	+	0.804906i	$0.297784\pi$
$350$	25914.2	3.95763
$351$	−1939.93	−0.295002
$352$	20882.7	3.16208
$353$	−11473.6	−1.72996	−0.864980	−	0.501806i	$-0.832669\pi$
$353$	−11473.6	−1.72996	−0.864980	+	0.501806i	$0.832669\pi$
$354$	2182.34	0.327656
$355$	−8995.84	−1.34493
$356$	1467.13	0.218420
$357$	3205.71	0.475250
$358$	−10257.6	−1.51434
$359$	−4853.77	−0.713571	−0.356785	−	0.934186i	$-0.616127\pi$
$359$	−4853.77	−0.713571	−0.356785	+	0.934186i	$0.616127\pi$
$360$	22271.5	3.26058
$361$	3536.59	0.515612
$362$	6546.81	0.950532
$363$	−5133.27	−0.742223
$364$	4107.29	0.591429
$365$	4913.51	0.704616
$366$	8323.31	1.18871
$367$	−2937.23	−0.417772	−0.208886	−	0.977940i	$-0.566984\pi$
$367$	−2937.23	−0.417772	−0.208886	+	0.977940i	$0.566984\pi$
$368$	−31077.1	−4.40218
$369$	−2225.56	−0.313979
$370$	11150.1	1.56666
$371$	−9758.54	−1.36560
$372$	−19293.3	−2.68900
$373$	−698.289	−0.0969330	−0.0484665	−	0.998825i	$-0.515433\pi$
$373$	−698.289	−0.0969330	−0.0484665	+	0.998825i	$0.515433\pi$
$374$	19337.1	2.67352
$375$	−13770.4	−1.89627
$376$	−28325.1	−3.88499
$377$	2073.54	0.283270
$378$	10970.2	1.49271
$379$	11670.9	1.58177	0.790887	−	0.611962i	$-0.209619\pi$
$379$	11670.9	1.58177	0.790887	+	0.611962i	$0.209619\pi$
$380$	−42810.5	−5.77930
$381$	1642.25	0.220827
$382$	−17316.9	−2.31940
$383$	8120.43	1.08338	0.541690	−	0.840578i	$-0.317785\pi$
$383$	8120.43	1.08338	0.541690	+	0.840578i	$0.317785\pi$
$384$	1762.21	0.234186
$385$	17321.8	2.29299
$386$	4776.14	0.629790
$387$	3099.70	0.407148
$388$	4429.38	0.579555
$389$	−1712.18	−0.223164	−0.111582	−	0.993755i	$-0.535592\pi$
$389$	−1712.18	−0.223164	−0.111582	+	0.993755i	$0.535592\pi$
$390$	−4948.84	−0.642550
$391$	−12608.5	−1.63079
$392$	7336.91	0.945331
$393$	8682.63	1.11446
$394$	−15464.2	−1.97735
$395$	−12244.5	−1.55971
$396$	18160.9	2.30459
$397$	−1391.15	−0.175869	−0.0879343	−	0.996126i	$-0.528027\pi$
$397$	−1391.15	−0.175869	−0.0879343	+	0.996126i	$0.528027\pi$
$398$	−11552.3	−1.45493
$399$	−4833.43	−0.606451
$400$	54836.7	6.85459
$401$	4232.27	0.527056	0.263528	−	0.964652i	$-0.415114\pi$
$401$	4232.27	0.527056	0.263528	+	0.964652i	$0.415114\pi$
$402$	4629.86	0.574419
$403$	−4304.65	−0.532084
$404$	23502.3	2.89427
$405$	358.104	0.0439367
$406$	−11725.8	−1.43335
$407$	5400.99	0.657781
$408$	13199.7	1.60167
$409$	2326.02	0.281208	0.140604	−	0.990066i	$-0.455095\pi$
$409$	2326.02	0.281208	0.140604	+	0.990066i	$0.455095\pi$
$410$	−14713.9	−1.77236
$411$	−8953.95	−1.07461
$412$	1567.32	0.187418
$413$	−1958.43	−0.233336
$414$	−16648.9	−1.97644
$415$	16468.7	1.94799
$416$	5354.06	0.631020
$417$	−1274.97	−0.149725
$418$	−29155.6	−3.41160
$419$	7001.97	0.816393	0.408196	−	0.912894i	$-0.366158\pi$
$419$	7001.97	0.816393	0.408196	+	0.912894i	$0.366158\pi$
$420$	19904.7	2.31250
$421$	−13585.9	−1.57277	−0.786386	−	0.617735i	$-0.788050\pi$
$421$	−13585.9	−1.57277	−0.786386	+	0.617735i	$0.788050\pi$
$422$	5857.38	0.675670
$423$	−7798.48	−0.896395
$424$	−40181.4	−4.60231
$425$	22248.2	2.53928
$426$	−7040.09	−0.800689
$427$	−7469.32	−0.846524
$428$	21706.9	2.45150
$429$	−2397.18	−0.269783
$430$	20493.0	2.29828
$431$	−15390.3	−1.72001	−0.860006	−	0.510284i	$-0.829540\pi$
$431$	−15390.3	−1.72001	−0.860006	+	0.510284i	$0.829540\pi$
$432$	23213.9	2.58537
$433$	7913.52	0.878290	0.439145	−	0.898416i	$-0.355281\pi$
$433$	7913.52	0.878290	0.439145	+	0.898416i	$0.355281\pi$
$434$	24342.6	2.69235
$435$	10048.8	1.10759
$436$	−31695.5	−3.48151
$437$	19010.5	2.08100
$438$	3845.28	0.419485
$439$	14156.7	1.53910	0.769548	−	0.638589i	$-0.220482\pi$
$439$	14156.7	1.53910	0.769548	+	0.638589i	$0.220482\pi$
$440$	71323.4	7.72775
$441$	2020.00	0.218119
$442$	4957.79	0.533524
$443$	−4248.78	−0.455679	−0.227839	−	0.973699i	$-0.573166\pi$
$443$	−4248.78	−0.455679	−0.227839	+	0.973699i	$0.573166\pi$
$444$	6206.36	0.663381
$445$	1586.36	0.168990
$446$	−24945.8	−2.64847
$447$	−5105.29	−0.540206
$448$	−10323.8	−1.08873
$449$	−571.359	−0.0600537	−0.0300269	−	0.999549i	$-0.509559\pi$
$449$	−571.359	−0.0600537	−0.0300269	+	0.999549i	$0.509559\pi$
$450$	29377.6	3.07749
$451$	−7127.26	−0.744146
$452$	−26707.5	−2.77924
$453$	−2665.30	−0.276439
$454$	−17528.8	−1.81205
$455$	4441.08	0.457585
$456$	−19901.9	−2.04384
$457$	16300.3	1.66848	0.834242	−	0.551399i	$-0.185906\pi$
$457$	16300.3	1.66848	0.834242	+	0.551399i	$0.185906\pi$
$458$	14979.2	1.52824
$459$	9418.26	0.957749
$460$	−78288.0	−7.93521
$461$	−15116.1	−1.52717	−0.763585	−	0.645707i	$-0.776563\pi$
$461$	−15116.1	−1.52717	−0.763585	+	0.645707i	$0.776563\pi$
$462$	13555.9	1.36510
$463$	7849.83	0.787932	0.393966	−	0.919125i	$-0.371103\pi$
$463$	7849.83	0.787932	0.393966	+	0.919125i	$0.371103\pi$
$464$	−24812.8	−2.48255
$465$	−20861.2	−2.08046
$466$	7601.79	0.755678
$467$	10536.6	1.04406	0.522031	−	0.852927i	$-0.325175\pi$
$467$	10536.6	1.04406	0.522031	+	0.852927i	$0.325175\pi$
$468$	4656.22	0.459901
$469$	−4154.83	−0.409066
$470$	−51558.1	−5.06000
$471$	−879.070	−0.0859988
$472$	−8063.94	−0.786383
$473$	9926.64	0.964962
$474$	−9582.43	−0.928556
$475$	−33544.8	−3.24030
$476$	−19940.7	−1.92013
$477$	−11062.7	−1.06190
$478$	29044.4	2.77921
$479$	−7985.08	−0.761686	−0.380843	−	0.924640i	$-0.624366\pi$
$479$	−7985.08	−0.761686	−0.380843	+	0.924640i	$0.624366\pi$
$480$	25946.8	2.46730
$481$	1384.74	0.131266
$482$	23126.3	2.18542
$483$	−8838.94	−0.832682
$484$	31930.9	2.99877
$485$	4789.35	0.448398
$486$	20074.0	1.87361
$487$	−14026.4	−1.30513	−0.652565	−	0.757733i	$-0.726307\pi$
$487$	−14026.4	−1.30513	−0.652565	+	0.757733i	$0.726307\pi$
$488$	−30755.3	−2.85293
$489$	123.546	0.0114253
$490$	13354.8	1.23124
$491$	9293.28	0.854175	0.427087	−	0.904210i	$-0.359540\pi$
$491$	9293.28	0.854175	0.427087	+	0.904210i	$0.359540\pi$
$492$	−8190.06	−0.750480
$493$	−10067.0	−0.919662
$494$	−7475.13	−0.680814
$495$	19636.8	1.78305
$496$	51511.0	4.66313
$497$	6317.76	0.570202
$498$	12888.3	1.15972
$499$	9875.28	0.885928	0.442964	−	0.896539i	$-0.353927\pi$
$499$	9875.28	0.885928	0.442964	+	0.896539i	$0.353927\pi$
$500$	85657.2	7.66142
$501$	−4282.41	−0.381884
$502$	−29442.3	−2.61767
$503$	18696.6	1.65733	0.828667	−	0.559742i	$-0.189100\pi$
$503$	18696.6	1.65733	0.828667	+	0.559742i	$0.189100\pi$
$504$	−15641.2	−1.38237
$505$	25412.3	2.23927
$506$	−53317.2	−4.68427
$507$	6345.41	0.555837
$508$	−10215.4	−0.892196
$509$	2105.00	0.183305	0.0916527	−	0.995791i	$-0.470785\pi$
$509$	2105.00	0.183305	0.0916527	+	0.995791i	$0.470785\pi$
$510$	24026.4	2.08609
$511$	−3450.75	−0.298732
$512$	18089.6	1.56144
$513$	−14200.4	−1.22215
$514$	4628.74	0.397208
$515$	1694.69	0.145004
$516$	11406.9	0.973176
$517$	−24974.3	−2.12450
$518$	−7830.65	−0.664207
$519$	−7768.16	−0.657002
$520$	18286.4	1.54214
$521$	19007.4	1.59833	0.799164	−	0.601113i	$-0.205276\pi$
$521$	19007.4	1.59833	0.799164	+	0.601113i	$0.205276\pi$
$522$	−13292.9	−1.11459
$523$	−1654.39	−0.138320	−0.0691601	−	0.997606i	$-0.522032\pi$
$523$	−1654.39	−0.138320	−0.0691601	+	0.997606i	$0.522032\pi$
$524$	−54009.2	−4.50268
$525$	15596.7	1.29656
$526$	14974.6	1.24130
$527$	20898.9	1.72746
$528$	28685.5	2.36435
$529$	22597.7	1.85730
$530$	−73139.1	−5.99427
$531$	−2220.17	−0.181445
$532$	30065.7	2.45021
$533$	−1827.34	−0.148501
$534$	1241.47	0.100607
$535$	23471.0	1.89671
$536$	−17107.7	−1.37862
$537$	−6173.63	−0.496111
$538$	3462.93	0.277504
$539$	6468.96	0.516953
$540$	58479.4	4.66028
$541$	17640.4	1.40189	0.700944	−	0.713216i	$-0.252762\pi$
$541$	17640.4	1.40189	0.700944	+	0.713216i	$0.252762\pi$
$542$	14687.6	1.16400
$543$	3940.25	0.311404
$544$	−25993.7	−2.04866
$545$	−34271.3	−2.69362
$546$	3475.56	0.272418
$547$	−547.000	−0.0427569
$547$	−547.000	−0.0427569
$548$	55696.9	4.34170
$549$	−8467.57	−0.658264
$550$	94080.3	7.29382
$551$	15178.5	1.17355
$552$	−36394.8	−2.80628
$553$	8599.25	0.661261
$554$	−29548.2	−2.26603
$555$	6710.75	0.513253
$556$	7930.76	0.604926
$557$	−2620.70	−0.199359	−0.0996793	−	0.995020i	$-0.531782\pi$
$557$	−2620.70	−0.199359	−0.0996793	+	0.995020i	$0.531782\pi$
$558$	27595.9	2.09360
$559$	2545.06	0.192566
$560$	−53143.6	−4.01023
$561$	11638.2	0.875873
$562$	−23320.5	−1.75038
$563$	157.189	0.0117668	0.00588340	−	0.999983i	$-0.498127\pi$
$563$	157.189	0.0117668	0.00588340	+	0.999983i	$0.498127\pi$
$564$	−28698.4	−2.14259
$565$	−28878.0	−2.15028
$566$	−6651.66	−0.493976
$567$	−251.496	−0.0186276
$568$	26013.7	1.92168
$569$	−1747.60	−0.128758	−0.0643788	−	0.997926i	$-0.520507\pi$
$569$	−1747.60	−0.128758	−0.0643788	+	0.997926i	$0.520507\pi$
$570$	−36226.0	−2.66200
$571$	5447.25	0.399230	0.199615	−	0.979874i	$-0.436031\pi$
$571$	5447.25	0.399230	0.199615	+	0.979874i	$0.436031\pi$
$572$	14911.3	1.08999
$573$	−10422.3	−0.759859
$574$	10333.5	0.751415
$575$	−61343.8	−4.44906
$576$	−11703.5	−0.846609
$577$	−8860.83	−0.639309	−0.319654	−	0.947534i	$-0.603567\pi$
$577$	−8860.83	−0.639309	−0.319654	+	0.947534i	$0.603567\pi$
$578$	1790.43	0.128844
$579$	2874.56	0.206325
$580$	−62507.3	−4.47496
$581$	−11565.9	−0.825880
$582$	3748.11	0.266949
$583$	−35427.9	−2.51677
$584$	−14208.6	−1.00678
$585$	5034.62	0.355822
$586$	9985.82	0.703943
$587$	13112.3	0.921980	0.460990	−	0.887405i	$-0.347494\pi$
$587$	13112.3	0.921980	0.460990	+	0.887405i	$0.347494\pi$
$588$	7433.59	0.521354
$589$	−31510.4	−2.20435
$590$	−14678.2	−1.02422
$591$	−9307.25	−0.647799
$592$	−16570.4	−1.15040
$593$	−12787.1	−0.885503	−0.442751	−	0.896644i	$-0.645998\pi$
$593$	−12787.1	−0.885503	−0.442751	+	0.896644i	$0.645998\pi$
$594$	39826.8	2.75103
$595$	−21561.3	−1.48559
$596$	31756.8	2.18257
$597$	−6952.83	−0.476651
$598$	−13669.8	−0.934785
$599$	−15529.0	−1.05926	−0.529630	−	0.848229i	$-0.677669\pi$
$599$	−15529.0	−1.05926	−0.529630	+	0.848229i	$0.677669\pi$
$600$	64220.2	4.36963
$601$	−2299.74	−0.156087	−0.0780437	−	0.996950i	$-0.524867\pi$
$601$	−2299.74	−0.156087	−0.0780437	+	0.996950i	$0.524867\pi$
$602$	−14392.2	−0.974389
$603$	−4710.11	−0.318094
$604$	16579.2	1.11688
$605$	34525.8	2.32012
$606$	19887.5	1.33313
$607$	−21192.1	−1.41707	−0.708534	−	0.705677i	$-0.750643\pi$
$607$	−21192.1	−1.41707	−0.708534	+	0.705677i	$0.750643\pi$
$608$	39192.2	2.61423
$609$	−7057.26	−0.469580
$610$	−55981.7	−3.71579
$611$	−6403.09	−0.423963
$612$	−22605.7	−1.49311
$613$	−23057.4	−1.51922	−0.759609	−	0.650380i	$-0.774610\pi$
$613$	−23057.4	−1.51922	−0.759609	+	0.650380i	$0.774610\pi$
$614$	36924.7	2.42697
$615$	−8855.65	−0.580641
$616$	−50090.3	−3.27629
$617$	−19993.6	−1.30456	−0.652279	−	0.757979i	$-0.726187\pi$
$617$	−19993.6	−1.30456	−0.652279	+	0.757979i	$0.726187\pi$
$618$	1326.26	0.0863267
$619$	−5069.40	−0.329170	−0.164585	−	0.986363i	$-0.552629\pi$
$619$	−5069.40	−0.329170	−0.164585	+	0.986363i	$0.552629\pi$
$620$	129764.	8.40559
$621$	−25968.5	−1.67807
$622$	−52917.7	−3.41127
$623$	−1114.10	−0.0716458
$624$	7354.59	0.471826
$625$	51493.0	3.29555
$626$	−33449.7	−2.13565
$627$	−17547.5	−1.11767
$628$	5468.14	0.347456
$629$	−6722.87	−0.426166
$630$	−28470.5	−1.80046
$631$	5251.64	0.331323	0.165661	−	0.986183i	$-0.447024\pi$
$631$	5251.64	0.331323	0.165661	+	0.986183i	$0.447024\pi$
$632$	35407.9	2.22856
$633$	3525.31	0.221356
$634$	−28410.4	−1.77969
$635$	−11045.6	−0.690285
$636$	−40710.8	−2.53819
$637$	1658.56	0.103162
$638$	−42569.9	−2.64163
$639$	7162.11	0.443394
$640$	−11852.4	−0.732044
$641$	−11475.9	−0.707133	−0.353566	−	0.935409i	$-0.615031\pi$
$641$	−11475.9	−0.707133	−0.353566	+	0.935409i	$0.615031\pi$
$642$	18368.2	1.12918
$643$	−10675.2	−0.654727	−0.327364	−	0.944898i	$-0.606160\pi$
$643$	−10675.2	−0.654727	−0.327364	+	0.944898i	$0.606160\pi$
$644$	54981.5	3.36424
$645$	12333.9	0.752940
$646$	36291.4	2.21032
$647$	−3546.61	−0.215505	−0.107752	−	0.994178i	$-0.534365\pi$
$647$	−3546.61	−0.215505	−0.107752	+	0.994178i	$0.534365\pi$
$648$	−1035.55	−0.0627781
$649$	−7109.98	−0.430033
$650$	24121.0	1.45554
$651$	14650.8	0.882041
$652$	−768.503	−0.0461609
$653$	−16015.2	−0.959761	−0.479880	−	0.877334i	$-0.659320\pi$
$653$	−16015.2	−0.959761	−0.479880	+	0.877334i	$0.659320\pi$
$654$	−26820.5	−1.60362
$655$	−58398.4	−3.48369
$656$	21866.6	1.30144
$657$	−3911.93	−0.232297
$658$	36209.1	2.14526
$659$	−1369.55	−0.0809560	−0.0404780	−	0.999180i	$-0.512888\pi$
$659$	−1369.55	−0.0809560	−0.0404780	+	0.999180i	$0.512888\pi$
$660$	72263.3	4.26188
$661$	−12465.2	−0.733494	−0.366747	−	0.930321i	$-0.619529\pi$
$661$	−12465.2	−0.733494	−0.366747	+	0.930321i	$0.619529\pi$
$662$	50213.9	2.94806
$663$	2983.88	0.174788
$664$	−47623.4	−2.78336
$665$	32509.1	1.89571
$666$	−8877.20	−0.516493
$667$	27757.1	1.61134
$668$	26638.2	1.54291
$669$	−15013.8	−0.867666
$670$	−31140.0	−1.79558
$671$	−27117.0	−1.56012
$672$	−18222.4	−1.04605
$673$	−19688.8	−1.12771	−0.563854	−	0.825875i	$-0.690682\pi$
$673$	−19688.8	−1.12771	−0.563854	+	0.825875i	$0.690682\pi$
$674$	−8562.12	−0.489318
$675$	45822.4	2.61290
$676$	−39470.8	−2.24572
$677$	−8692.50	−0.493471	−0.246735	−	0.969083i	$-0.579358\pi$
$677$	−8692.50	−0.493471	−0.246735	+	0.969083i	$0.579358\pi$
$678$	−22599.7	−1.28014
$679$	−3363.55	−0.190105
$680$	−88779.7	−5.00669
$681$	−10549.9	−0.593644
$682$	88374.7	4.96194
$683$	23117.8	1.29514	0.647569	−	0.762007i	$-0.275786\pi$
$683$	23117.8	1.29514	0.647569	+	0.762007i	$0.275786\pi$
$684$	34083.9	1.90531
$685$	60223.3	3.35914
$686$	−36395.7	−2.02565
$687$	9015.36	0.500666
$688$	−30455.2	−1.68763
$689$	−9083.27	−0.502242
$690$	−66246.8	−3.65503
$691$	−13617.4	−0.749683	−0.374841	−	0.927089i	$-0.622303\pi$
$691$	−13617.4	−0.749683	−0.374841	+	0.927089i	$0.622303\pi$
$692$	48320.8	2.65445
$693$	−13790.9	−0.755948
$694$	−5547.70	−0.303441
$695$	8575.28	0.468027
$696$	−29058.7	−1.58257
$697$	8871.65	0.482120
$698$	−40729.0	−2.20862
$699$	4575.19	0.247568
$700$	−97017.0	−5.23842
$701$	10585.7	0.570354	0.285177	−	0.958475i	$-0.407948\pi$
$701$	10585.7	0.570354	0.285177	+	0.958475i	$0.407948\pi$
$702$	10211.1	0.548992
$703$	10136.4	0.543817
$704$	−37480.0	−2.00651
$705$	−31030.7	−1.65771
$706$	60392.7	3.21942
$707$	−17847.0	−0.949371
$708$	−8170.20	−0.433693
$709$	−2014.69	−0.106718	−0.0533592	−	0.998575i	$-0.516993\pi$
$709$	−2014.69	−0.106718	−0.0533592	+	0.998575i	$0.516993\pi$
$710$	47350.9	2.50288
$711$	9748.52	0.514203
$712$	−4587.36	−0.241459
$713$	−57623.4	−3.02667
$714$	−16873.7	−0.884429
$715$	16123.1	0.843317
$716$	38402.3	2.00441
$717$	17480.6	0.910496
$718$	25548.5	1.32794
$719$	17925.5	0.929775	0.464888	−	0.885370i	$-0.346095\pi$
$719$	17925.5	0.929775	0.464888	+	0.885370i	$0.346095\pi$
$720$	−60246.1	−3.11839
$721$	−1190.18	−0.0614766
$722$	−18615.3	−0.959543
$723$	13918.7	0.715965
$724$	−24509.8	−1.25815
$725$	−48978.6	−2.50899
$726$	27019.7	1.38126
$727$	−33118.4	−1.68954	−0.844770	−	0.535130i	$-0.820263\pi$
$727$	−33118.4	−1.68954	−0.844770	+	0.535130i	$0.820263\pi$
$728$	−12842.5	−0.653811
$729$	11627.9	0.590758
$730$	−25862.9	−1.31127
$731$	−12356.2	−0.625184
$732$	−31160.6	−1.57340
$733$	−2856.99	−0.143963	−0.0719817	−	0.997406i	$-0.522932\pi$
$733$	−2856.99	−0.143963	−0.0719817	+	0.997406i	$0.522932\pi$
$734$	15460.5	0.777464
$735$	8037.70	0.403368
$736$	71671.1	3.58945
$737$	−15083.9	−0.753898
$738$	11714.6	0.584307
$739$	32084.2	1.59707	0.798537	−	0.601946i	$-0.205608\pi$
$739$	32084.2	1.59707	0.798537	+	0.601946i	$0.205608\pi$
$740$	−41743.3	−2.07367
$741$	−4498.96	−0.223041
$742$	51365.4	2.54135
$743$	17804.0	0.879090	0.439545	−	0.898220i	$-0.355140\pi$
$743$	17804.0	0.879090	0.439545	+	0.898220i	$0.355140\pi$
$744$	60325.4	2.97263
$745$	34337.7	1.68864
$746$	3675.54	0.180390
$747$	−13111.7	−0.642211
$748$	−72393.8	−3.53874
$749$	−16483.6	−0.804136
$750$	72482.6	3.52892
$751$	20349.7	0.988778	0.494389	−	0.869241i	$-0.335392\pi$
$751$	20349.7	0.988778	0.494389	+	0.869241i	$0.335392\pi$
$752$	76621.7	3.71557
$753$	−17720.0	−0.857576
$754$	−10914.4	−0.527160
$755$	17926.5	0.864124
$756$	−41070.0	−1.97579
$757$	13939.1	0.669252	0.334626	−	0.942351i	$-0.391390\pi$
$757$	13939.1	0.669252	0.334626	+	0.942351i	$0.391390\pi$
$758$	−61431.3	−2.94365
$759$	−32089.4	−1.53461
$760$	133858.	6.38888
$761$	30149.8	1.43618	0.718088	−	0.695952i	$-0.245018\pi$
$761$	30149.8	1.43618	0.718088	+	0.695952i	$0.245018\pi$
$762$	−8644.21	−0.410954
$763$	24068.6	1.14200
$764$	64830.8	3.07002
$765$	−24442.9	−1.15521
$766$	−42743.0	−2.01615
$767$	−1822.91	−0.0858167
$768$	8209.06	0.385702
$769$	27818.0	1.30448	0.652238	−	0.758014i	$-0.273830\pi$
$769$	27818.0	1.30448	0.652238	+	0.758014i	$0.273830\pi$
$770$	−91175.6	−4.26719
$771$	2785.84	0.130129
$772$	−17880.8	−0.833606
$773$	−26606.1	−1.23798	−0.618988	−	0.785401i	$-0.712457\pi$
$773$	−26606.1	−1.23798	−0.618988	+	0.785401i	$0.712457\pi$
$774$	−16315.7	−0.757694
$775$	101679.	4.71279
$776$	−13849.6	−0.640685
$777$	−4712.94	−0.217601
$778$	9012.28	0.415303
$779$	−13376.3	−0.615218
$780$	18527.4	0.850495
$781$	22936.3	1.05087
$782$	66366.5	3.03486
$783$	−20734.0	−0.946324
$784$	−19846.9	−0.904105
$785$	5912.53	0.268825
$786$	−45702.2	−2.07398
$787$	−23830.6	−1.07937	−0.539687	−	0.841865i	$-0.681458\pi$
$787$	−23830.6	−1.07937	−0.539687	+	0.841865i	$0.681458\pi$
$788$	57894.5	2.61727
$789$	9012.59	0.406662
$790$	64450.4	2.90259
$791$	20281.0	0.911640
$792$	−56784.7	−2.54767
$793$	−6952.45	−0.311335
$794$	7322.51	0.327288
$795$	−44019.4	−1.96378
$796$	43249.2	1.92579
$797$	−4062.40	−0.180549	−0.0902745	−	0.995917i	$-0.528774\pi$
$797$	−4062.40	−0.180549	−0.0902745	+	0.995917i	$0.528774\pi$
$798$	25441.4	1.12859
$799$	31086.7	1.37643
$800$	−126467.	−5.58909
$801$	−1262.99	−0.0557124
$802$	−22277.1	−0.980839
$803$	−12527.8	−0.550555
$804$	−17333.2	−0.760316
$805$	59449.7	2.60289
$806$	22658.1	0.990197
$807$	2084.19	0.0909131
$808$	−73486.1	−3.19954
$809$	28583.7	1.24221	0.621105	−	0.783727i	$-0.286684\pi$
$809$	28583.7	1.24221	0.621105	+	0.783727i	$0.286684\pi$
$810$	−1884.93	−0.0817651
$811$	11604.8	0.502464	0.251232	−	0.967927i	$-0.419164\pi$
$811$	11604.8	0.502464	0.251232	+	0.967927i	$0.419164\pi$
$812$	43898.7	1.89722
$813$	8839.86	0.381338
$814$	−28428.8	−1.22412
$815$	−830.959	−0.0357144
$816$	−35706.2	−1.53182
$817$	18630.1	0.797777
$818$	−12243.3	−0.523323
$819$	−3535.80	−0.150856
$820$	55085.4	2.34594
$821$	24302.6	1.03309	0.516544	−	0.856261i	$-0.327218\pi$
$821$	24302.6	1.03309	0.516544	+	0.856261i	$0.327218\pi$
$822$	47130.3	1.99983
$823$	−23886.5	−1.01170	−0.505852	−	0.862620i	$-0.668822\pi$
$823$	−23886.5	−1.01170	−0.505852	+	0.862620i	$0.668822\pi$
$824$	−4900.63	−0.207187
$825$	56623.0	2.38953
$826$	10308.5	0.434234
$827$	−16553.3	−0.696029	−0.348014	−	0.937489i	$-0.613144\pi$
$827$	−16553.3	−0.696029	−0.348014	+	0.937489i	$0.613144\pi$
$828$	62329.6	2.61607
$829$	−34076.2	−1.42764	−0.713821	−	0.700328i	$-0.753037\pi$
$829$	−34076.2	−1.42764	−0.713821	+	0.700328i	$0.753037\pi$
$830$	−86685.4	−3.62517
$831$	−17783.8	−0.742375
$832$	−9609.40	−0.400416
$833$	−8052.23	−0.334926
$834$	6710.96	0.278635
$835$	28803.0	1.19374
$836$	109152.	4.51568
$837$	43043.4	1.77754
$838$	−36855.8	−1.51929
$839$	−37139.2	−1.52823	−0.764117	−	0.645077i	$-0.776825\pi$
$839$	−37139.2	−1.52823	−0.764117	+	0.645077i	$0.776825\pi$
$840$	−62237.3	−2.55642
$841$	−2226.93	−0.0913087
$842$	71511.4	2.92689
$843$	−14035.6	−0.573443
$844$	−21928.7	−0.894334
$845$	−42678.5	−1.73750
$846$	41048.4	1.66817
$847$	−24247.4	−0.983649
$848$	108694.	4.40160
$849$	−4003.35	−0.161831
$850$	−117106.	−4.72555
$851$	18536.6	0.746683
$852$	26356.5	1.05981
$853$	26258.0	1.05399	0.526996	−	0.849867i	$-0.323318\pi$
$853$	26258.0	1.05399	0.526996	+	0.849867i	$0.323318\pi$
$854$	39315.8	1.57536
$855$	36853.9	1.47412
$856$	−67872.2	−2.71007
$857$	31523.3	1.25649	0.628247	−	0.778014i	$-0.283773\pi$
$857$	31523.3	1.25649	0.628247	+	0.778014i	$0.283773\pi$
$858$	12617.9	0.502059
$859$	39551.0	1.57097	0.785485	−	0.618881i	$-0.212414\pi$
$859$	39551.0	1.57097	0.785485	+	0.618881i	$0.212414\pi$
$860$	−76721.3	−3.04206
$861$	6219.30	0.246171
$862$	81009.0	3.20090
$863$	20989.8	0.827928	0.413964	−	0.910293i	$-0.364144\pi$
$863$	20989.8	0.827928	0.413964	+	0.910293i	$0.364144\pi$
$864$	−53536.8	−2.10805
$865$	52247.8	2.05373
$866$	−41653.9	−1.63448
$867$	1077.58	0.0422106
$868$	−91133.2	−3.56367
$869$	31219.2	1.21869
$870$	−52893.3	−2.06121
$871$	−3867.32	−0.150447
$872$	99104.1	3.84872
$873$	−3813.07	−0.147827
$874$	−100064.	−3.87269
$875$	−65045.7	−2.51308
$876$	−14395.9	−0.555241
$877$	471.846	0.0181677	0.00908387	−	0.999959i	$-0.497108\pi$
$877$	471.846	0.0181677	0.00908387	+	0.999959i	$0.497108\pi$
$878$	−74515.8	−2.86422
$879$	6010.04	0.230619
$880$	−192936.	−7.39074
$881$	−2994.03	−0.114496	−0.0572482	−	0.998360i	$-0.518233\pi$
$881$	−2994.03	−0.114496	−0.0572482	+	0.998360i	$0.518233\pi$
$882$	−10632.5	−0.405914
$883$	21637.1	0.824627	0.412314	−	0.911042i	$-0.364721\pi$
$883$	21637.1	0.824627	0.412314	+	0.911042i	$0.364721\pi$
$884$	−18560.8	−0.706186
$885$	−8834.18	−0.335546
$886$	22364.1	0.848008
$887$	1190.51	0.0450659	0.0225330	−	0.999746i	$-0.492827\pi$
$887$	1190.51	0.0450659	0.0225330	+	0.999746i	$0.492827\pi$
$888$	−19405.8	−0.733352
$889$	7757.30	0.292656
$890$	−8350.03	−0.314487
$891$	−913.044	−0.0343301
$892$	93391.7	3.50559
$893$	−46871.2	−1.75642
$894$	26872.4	1.00531
$895$	41523.2	1.55080
$896$	8323.93	0.310360
$897$	−8227.30	−0.306245
$898$	3007.43	0.111759
$899$	−46008.2	−1.70685
$900$	−109983.	−4.07345
$901$	44098.9	1.63057
$902$	37515.3	1.38484
$903$	−8662.05	−0.319219
$904$	83508.0	3.07238
$905$	−26501.7	−0.973420
$906$	14029.2	0.514446
$907$	48401.2	1.77192	0.885962	−	0.463758i	$-0.153499\pi$
$907$	48401.2	1.77192	0.885962	+	0.463758i	$0.153499\pi$
$908$	65624.1	2.39847
$909$	−20232.2	−0.738240
$910$	−23376.2	−0.851555
$911$	23389.9	0.850650	0.425325	−	0.905041i	$-0.360160\pi$
$911$	23389.9	0.850650	0.425325	+	0.905041i	$0.360160\pi$
$912$	53836.3	1.95471
$913$	−41989.6	−1.52207
$914$	−85799.0	−3.10501
$915$	−33693.0	−1.21733
$916$	−56078.9	−2.02282
$917$	41013.1	1.47696
$918$	−49574.3	−1.78235
$919$	−3235.92	−0.116152	−0.0580758	−	0.998312i	$-0.518497\pi$
$919$	−3235.92	−0.116152	−0.0580758	+	0.998312i	$0.518497\pi$
$920$	244788.	8.77219
$921$	22223.4	0.795099
$922$	79565.5	2.84203
$923$	5880.58	0.209709
$924$	−50750.3	−1.80689
$925$	−32708.6	−1.16265
$926$	−41318.7	−1.46632
$927$	−1349.24	−0.0478047
$928$	57224.2	2.02422
$929$	−38730.1	−1.36781	−0.683904	−	0.729572i	$-0.739719\pi$
$929$	−38730.1	−1.36781	−0.683904	+	0.729572i	$0.739719\pi$
$930$	109806.	3.87169
$931$	12140.8	0.427388
$932$	−28459.4	−1.00023
$933$	−31848.9	−1.11756
$934$	−55461.0	−1.94298
$935$	−78277.2	−2.73790
$936$	−14558.9	−0.508410
$937$	−5303.70	−0.184914	−0.0924570	−	0.995717i	$-0.529472\pi$
$937$	−5303.70	−0.184914	−0.0924570	+	0.995717i	$0.529472\pi$
$938$	21869.5	0.761263
$939$	−20132.0	−0.699661
$940$	193022.	6.69754
$941$	−19165.4	−0.663948	−0.331974	−	0.943289i	$-0.607715\pi$
$941$	−19165.4	−0.663948	−0.331974	+	0.943289i	$0.607715\pi$
$942$	4627.11	0.160042
$943$	−24461.4	−0.844720
$944$	21813.6	0.752089
$945$	−44407.7	−1.52866
$946$	−52250.2	−1.79577
$947$	25732.2	0.882982	0.441491	−	0.897266i	$-0.354450\pi$
$947$	25732.2	0.882982	0.441491	+	0.897266i	$0.354450\pi$
$948$	35874.5	1.22906
$949$	−3211.96	−0.109868
$950$	176568.	6.03012
$951$	−17099.0	−0.583043
$952$	62349.8	2.12266
$953$	11090.1	0.376959	0.188480	−	0.982077i	$-0.439644\pi$
$953$	11090.1	0.376959	0.188480	+	0.982077i	$0.439644\pi$
$954$	58230.3	1.97618
$955$	70099.5	2.37525
$956$	−108736.	−3.67863
$957$	−25621.1	−0.865424
$958$	42030.6	1.41748
$959$	−42294.7	−1.42416
$960$	−46569.1	−1.56564
$961$	65721.3	2.20608
$962$	−7288.79	−0.244283
$963$	−18686.6	−0.625303
$964$	−86579.6	−2.89268
$965$	−19333.9	−0.644955
$966$	46525.0	1.54960
$967$	−35936.2	−1.19507	−0.597534	−	0.801843i	$-0.703853\pi$
$967$	−35936.2	−1.19507	−0.597534	+	0.801843i	$0.703853\pi$
$968$	−99840.1	−3.31506
$969$	21842.3	0.724123
$970$	−25209.4	−0.834458
$971$	−38335.7	−1.26699	−0.633496	−	0.773746i	$-0.718381\pi$
$971$	−38335.7	−1.26699	−0.633496	+	0.773746i	$0.718381\pi$
$972$	−75152.4	−2.47995
$973$	−6022.40	−0.198427
$974$	73830.0	2.42882
$975$	14517.4	0.476850
$976$	83195.6	2.72851
$977$	22548.9	0.738385	0.369192	−	0.929353i	$-0.379634\pi$
$977$	22548.9	0.738385	0.369192	+	0.929353i	$0.379634\pi$
$978$	−650.303	−0.0212622
$979$	−4044.68	−0.132041
$980$	−49997.5	−1.62971
$981$	27285.4	0.888027
$982$	−48916.4	−1.58960
$983$	27614.3	0.895990	0.447995	−	0.894036i	$-0.352138\pi$
$983$	27614.3	0.895990	0.447995	+	0.894036i	$0.352138\pi$
$984$	25608.3	0.829638
$985$	62599.5	2.02496
$986$	52988.9	1.71147
$987$	21792.8	0.702807
$988$	27985.2	0.901142
$989$	34069.0	1.09538
$990$	−103361.	−3.31821
$991$	−20666.5	−0.662455	−0.331227	−	0.943551i	$-0.607463\pi$
$991$	−20666.5	−0.662455	−0.331227	+	0.943551i	$0.607463\pi$
$992$	−118797.	−3.80222
$993$	30221.6	0.965814
$994$	−33254.4	−1.06113
$995$	46764.0	1.48997
$996$	−48251.0	−1.53503
$997$	−19594.1	−0.622417	−0.311209	−	0.950342i	$-0.600734\pi$
$997$	−19594.1	−0.622417	−0.311209	+	0.950342i	$0.600734\pi$
$998$	−51979.9	−1.64869
$999$	−13846.5	−0.438521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.b.1.2	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.b.1.2	✓	71	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-5.26364 q^{2} -3.16796 q^{3} +19.7059 q^{4} +21.3074 q^{5} +16.6750 q^{6} -14.9641 q^{7} -61.6156 q^{8} -16.9640 q^{9} +O(q^{10})\)	\(q-5.26364 q^{2} -3.16796 q^{3} +19.7059 q^{4} +21.3074 q^{5} +16.6750 q^{6} -14.9641 q^{7} -61.6156 q^{8} -16.9640 q^{9} -112.154 q^{10} -54.3265 q^{11} -62.4275 q^{12} -13.9286 q^{13} +78.7657 q^{14} -67.5009 q^{15} +166.675 q^{16} +67.6229 q^{17} +89.2925 q^{18} -101.959 q^{19} +419.881 q^{20} +47.4057 q^{21} +285.955 q^{22} -186.453 q^{23} +195.196 q^{24} +329.004 q^{25} +73.3152 q^{26} +139.276 q^{27} -294.881 q^{28} -148.869 q^{29} +355.300 q^{30} +309.051 q^{31} -384.392 q^{32} +172.104 q^{33} -355.942 q^{34} -318.846 q^{35} -334.291 q^{36} -99.4171 q^{37} +536.674 q^{38} +44.1253 q^{39} -1312.87 q^{40} +131.193 q^{41} -249.527 q^{42} -182.722 q^{43} -1070.55 q^{44} -361.459 q^{45} +981.421 q^{46} +459.707 q^{47} -528.020 q^{48} -119.076 q^{49} -1731.76 q^{50} -214.227 q^{51} -274.476 q^{52} +652.130 q^{53} -733.100 q^{54} -1157.55 q^{55} +922.022 q^{56} +323.001 q^{57} +783.594 q^{58} +130.875 q^{59} -1330.17 q^{60} +499.149 q^{61} -1626.73 q^{62} +253.851 q^{63} +689.903 q^{64} -296.782 q^{65} -905.895 q^{66} +277.653 q^{67} +1332.57 q^{68} +590.676 q^{69} +1678.29 q^{70} -422.194 q^{71} +1045.25 q^{72} +230.601 q^{73} +523.296 q^{74} -1042.27 q^{75} -2009.19 q^{76} +812.948 q^{77} -232.260 q^{78} -574.659 q^{79} +3551.41 q^{80} +16.8066 q^{81} -690.553 q^{82} +772.912 q^{83} +934.172 q^{84} +1440.86 q^{85} +961.781 q^{86} +471.612 q^{87} +3347.36 q^{88} +74.4513 q^{89} +1902.59 q^{90} +208.429 q^{91} -3674.22 q^{92} -979.061 q^{93} -2419.73 q^{94} -2172.47 q^{95} +1217.74 q^{96} +224.774 q^{97} +626.770 q^{98} +921.596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9}+O(q^{10}) \) 71 * q + 14 * q^2 + 31 * q^3 + 294 * q^4 + 159 * q^5 + 60 * q^6 + 66 * q^7 + 168 * q^8 + 738 * q^9	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9} + 120 q^{10} + 139 q^{11} + 309 q^{12} + 343 q^{13} + 239 q^{14} + 194 q^{15} + 1346 q^{16} + 842 q^{17} + 423 q^{18} + 157 q^{19} + 1292 q^{20} + 434 q^{21} + 436 q^{22} + 1004 q^{23} + 935 q^{24} + 2206 q^{25} + 812 q^{26} + 1282 q^{27} + 584 q^{28} + 1459 q^{29} + 146 q^{30} + 582 q^{31} + 1428 q^{32} + 1080 q^{33} + 393 q^{34} + 1006 q^{35} + 2996 q^{36} + 1477 q^{37} + 1873 q^{38} + 626 q^{39} + 1272 q^{40} + 1112 q^{41} + 1812 q^{42} + 833 q^{43} + 1392 q^{44} + 3841 q^{45} + 782 q^{46} + 2484 q^{47} + 2034 q^{48} + 4727 q^{49} + 1248 q^{50} + 932 q^{51} + 2118 q^{52} + 5077 q^{53} + 1537 q^{54} + 1736 q^{55} + 2281 q^{56} + 1426 q^{57} + 992 q^{58} + 2977 q^{59} + 1418 q^{60} + 3363 q^{61} + 3438 q^{62} + 3194 q^{63} + 6138 q^{64} + 4640 q^{65} + 288 q^{66} + 955 q^{67} + 8553 q^{68} + 4440 q^{69} + 2203 q^{70} + 2458 q^{71} + 4495 q^{72} + 3724 q^{73} + 2099 q^{74} + 4491 q^{75} + 2260 q^{76} + 9774 q^{77} + 1057 q^{78} + 1638 q^{79} + 8221 q^{80} + 10151 q^{81} + 1018 q^{82} + 6121 q^{83} + 4847 q^{84} + 3836 q^{85} + 2305 q^{86} + 3894 q^{87} + 5815 q^{88} + 8110 q^{89} + 4951 q^{90} + 2312 q^{91} + 13138 q^{92} + 9250 q^{93} - 813 q^{94} + 4858 q^{95} + 6882 q^{96} + 4486 q^{97} + 4216 q^{98} + 4969 q^{99}+O(q^{100}) \) 71 * q + 14 * q^2 + 31 * q^3 + 294 * q^4 + 159 * q^5 + 60 * q^6 + 66 * q^7 + 168 * q^8 + 738 * q^9 + 120 * q^10 + 139 * q^11 + 309 * q^12 + 343 * q^13 + 239 * q^14 + 194 * q^15 + 1346 * q^16 + 842 * q^17 + 423 * q^18 + 157 * q^19 + 1292 * q^20 + 434 * q^21 + 436 * q^22 + 1004 * q^23 + 935 * q^24 + 2206 * q^25 + 812 * q^26 + 1282 * q^27 + 584 * q^28 + 1459 * q^29 + 146 * q^30 + 582 * q^31 + 1428 * q^32 + 1080 * q^33 + 393 * q^34 + 1006 * q^35 + 2996 * q^36 + 1477 * q^37 + 1873 * q^38 + 626 * q^39 + 1272 * q^40 + 1112 * q^41 + 1812 * q^42 + 833 * q^43 + 1392 * q^44 + 3841 * q^45 + 782 * q^46 + 2484 * q^47 + 2034 * q^48 + 4727 * q^49 + 1248 * q^50 + 932 * q^51 + 2118 * q^52 + 5077 * q^53 + 1537 * q^54 + 1736 * q^55 + 2281 * q^56 + 1426 * q^57 + 992 * q^58 + 2977 * q^59 + 1418 * q^60 + 3363 * q^61 + 3438 * q^62 + 3194 * q^63 + 6138 * q^64 + 4640 * q^65 + 288 * q^66 + 955 * q^67 + 8553 * q^68 + 4440 * q^69 + 2203 * q^70 + 2458 * q^71 + 4495 * q^72 + 3724 * q^73 + 2099 * q^74 + 4491 * q^75 + 2260 * q^76 + 9774 * q^77 + 1057 * q^78 + 1638 * q^79 + 8221 * q^80 + 10151 * q^81 + 1018 * q^82 + 6121 * q^83 + 4847 * q^84 + 3836 * q^85 + 2305 * q^86 + 3894 * q^87 + 5815 * q^88 + 8110 * q^89 + 4951 * q^90 + 2312 * q^91 + 13138 * q^92 + 9250 * q^93 - 813 * q^94 + 4858 * q^95 + 6882 * q^96 + 4486 * q^97 + 4216 * q^98 + 4969 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more