LMFDB - Embedded newform 1573.4.a.p.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,4,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1573.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1573.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:	$92.8100044390$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0313827 q^{2} +5.72009 q^{3} -7.99902 q^{4} +7.55527 q^{5} -0.179512 q^{6} +6.19881 q^{7} +0.502093 q^{8} +5.71940 q^{9} +O(q^{10})$	\(q-0.0313827 q^{2} +5.72009 q^{3} -7.99902 q^{4} +7.55527 q^{5} -0.179512 q^{6} +6.19881 q^{7} +0.502093 q^{8} +5.71940 q^{9} -0.237105 q^{10} -45.7551 q^{12} -13.0000 q^{13} -0.194536 q^{14} +43.2168 q^{15} +63.9764 q^{16} -66.2549 q^{17} -0.179491 q^{18} +42.0610 q^{19} -60.4347 q^{20} +35.4577 q^{21} -43.6708 q^{23} +2.87202 q^{24} -67.9179 q^{25} +0.407976 q^{26} -121.727 q^{27} -49.5843 q^{28} +190.712 q^{29} -1.35626 q^{30} -50.9243 q^{31} -6.02450 q^{32} +2.07926 q^{34} +46.8337 q^{35} -45.7496 q^{36} -103.091 q^{37} -1.31999 q^{38} -74.3611 q^{39} +3.79345 q^{40} -492.894 q^{41} -1.11276 q^{42} +178.619 q^{43} +43.2116 q^{45} +1.37051 q^{46} +511.388 q^{47} +365.950 q^{48} -304.575 q^{49} +2.13145 q^{50} -378.984 q^{51} +103.987 q^{52} -150.116 q^{53} +3.82012 q^{54} +3.11238 q^{56} +240.592 q^{57} -5.98506 q^{58} -58.9874 q^{59} -345.692 q^{60} -659.264 q^{61} +1.59814 q^{62} +35.4535 q^{63} -511.622 q^{64} -98.2185 q^{65} +331.723 q^{67} +529.974 q^{68} -249.801 q^{69} -1.46977 q^{70} -1003.68 q^{71} +2.87167 q^{72} +875.491 q^{73} +3.23529 q^{74} -388.496 q^{75} -336.446 q^{76} +2.33366 q^{78} +618.282 q^{79} +483.359 q^{80} -850.712 q^{81} +15.4684 q^{82} -529.598 q^{83} -283.627 q^{84} -500.573 q^{85} -5.60555 q^{86} +1090.89 q^{87} -1194.17 q^{89} -1.35610 q^{90} -80.5845 q^{91} +349.323 q^{92} -291.291 q^{93} -16.0488 q^{94} +317.782 q^{95} -34.4607 q^{96} -578.614 q^{97} +9.55839 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9}+O(q^{10}) $ 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9} + 18 q^{10} - 262 q^{12} - 442 q^{13} - 231 q^{14} - 196 q^{15} + 225 q^{16} + 209 q^{17} + 190 q^{18} + 107 q^{19} - 211 q^{20} + 68 q^{21} - 632 q^{23} - 152 q^{24} + 296 q^{25} - 39 q^{26} - 920 q^{27} + 931 q^{28} + 32 q^{29} + 300 q^{30} - 290 q^{31} - 876 q^{32} - 602 q^{34} - 104 q^{35} - 611 q^{36} - 656 q^{37} - 1361 q^{38} + 377 q^{39} - 1159 q^{40} + 1121 q^{41} + 79 q^{42} - 349 q^{43} - 1024 q^{45} - 490 q^{46} - 1608 q^{47} - 1827 q^{48} + 808 q^{49} + 1322 q^{50} - 1414 q^{51} - 1261 q^{52} - 2608 q^{53} - 3131 q^{54} - 1675 q^{56} + 2150 q^{57} - 1673 q^{58} - 2011 q^{59} - 201 q^{60} + 236 q^{61} - 1396 q^{62} - 1206 q^{63} + 1331 q^{64} + 364 q^{65} - 3213 q^{67} + 1321 q^{68} - 162 q^{69} + 174 q^{70} - 3756 q^{71} + 5074 q^{72} - 823 q^{73} - 2550 q^{74} - 3063 q^{75} - 2004 q^{76} + 468 q^{78} + 2120 q^{79} - 5005 q^{80} + 710 q^{81} - 2534 q^{82} + 3843 q^{83} - 7191 q^{84} - 1582 q^{85} - 3542 q^{86} - 962 q^{87} - 3633 q^{89} + 995 q^{90} - 468 q^{91} - 2072 q^{92} - 508 q^{93} + 6309 q^{94} - 1916 q^{95} + 2150 q^{96} + 1195 q^{97} + 1487 q^{98}+O(q^{100}) \) 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9 + 18 * q^10 - 262 * q^12 - 442 * q^13 - 231 * q^14 - 196 * q^15 + 225 * q^16 + 209 * q^17 + 190 * q^18 + 107 * q^19 - 211 * q^20 + 68 * q^21 - 632 * q^23 - 152 * q^24 + 296 * q^25 - 39 * q^26 - 920 * q^27 + 931 * q^28 + 32 * q^29 + 300 * q^30 - 290 * q^31 - 876 * q^32 - 602 * q^34 - 104 * q^35 - 611 * q^36 - 656 * q^37 - 1361 * q^38 + 377 * q^39 - 1159 * q^40 + 1121 * q^41 + 79 * q^42 - 349 * q^43 - 1024 * q^45 - 490 * q^46 - 1608 * q^47 - 1827 * q^48 + 808 * q^49 + 1322 * q^50 - 1414 * q^51 - 1261 * q^52 - 2608 * q^53 - 3131 * q^54 - 1675 * q^56 + 2150 * q^57 - 1673 * q^58 - 2011 * q^59 - 201 * q^60 + 236 * q^61 - 1396 * q^62 - 1206 * q^63 + 1331 * q^64 + 364 * q^65 - 3213 * q^67 + 1321 * q^68 - 162 * q^69 + 174 * q^70 - 3756 * q^71 + 5074 * q^72 - 823 * q^73 - 2550 * q^74 - 3063 * q^75 - 2004 * q^76 + 468 * q^78 + 2120 * q^79 - 5005 * q^80 + 710 * q^81 - 2534 * q^82 + 3843 * q^83 - 7191 * q^84 - 1582 * q^85 - 3542 * q^86 - 962 * q^87 - 3633 * q^89 + 995 * q^90 - 468 * q^91 - 2072 * q^92 - 508 * q^93 + 6309 * q^94 - 1916 * q^95 + 2150 * q^96 + 1195 * q^97 + 1487 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.0313827	−0.0110955	−0.00554774	−	0.999985i	$-0.501766\pi$
$2$	−0.0313827	−0.0110955	−0.00554774	+	0.999985i	$0.501766\pi$
$3$	5.72009	1.10083	0.550416	−	0.834891i	$-0.314469\pi$
$3$	5.72009	1.10083	0.550416	+	0.834891i	$0.314469\pi$
$4$	−7.99902	−0.999877
$5$	7.55527	0.675764	0.337882	−	0.941188i	$-0.390290\pi$
$5$	7.55527	0.675764	0.337882	+	0.941188i	$0.390290\pi$
$6$	−0.179512	−0.0122142
$7$	6.19881	0.334704	0.167352	−	0.985897i	$-0.446478\pi$
$7$	6.19881	0.334704	0.167352	+	0.985897i	$0.446478\pi$
$8$	0.502093	0.0221896
$9$	5.71940	0.211830
$10$	−0.237105	−0.00749792
$11$	0	0
$11$	0	0
$12$	−45.7551	−1.10070
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−0.194536	−0.00371370
$15$	43.2168	0.743902
$16$	63.9764	0.999631
$17$	−66.2549	−0.945245	−0.472623	−	0.881265i	$-0.656693\pi$
$17$	−66.2549	−0.945245	−0.472623	+	0.881265i	$0.656693\pi$
$18$	−0.179491	−0.00235035
$19$	42.0610	0.507866	0.253933	−	0.967222i	$-0.418276\pi$
$19$	42.0610	0.507866	0.253933	+	0.967222i	$0.418276\pi$
$20$	−60.4347	−0.675681
$21$	35.4577	0.368453
$22$	0	0
$23$	−43.6708	−0.395912	−0.197956	−	0.980211i	$-0.563430\pi$
$23$	−43.6708	−0.395912	−0.197956	+	0.980211i	$0.563430\pi$
$24$	2.87202	0.0244270
$25$	−67.9179	−0.543343
$26$	0.407976	0.00307733
$27$	−121.727	−0.867643
$28$	−49.5843	−0.334663
$29$	190.712	1.22118	0.610591	−	0.791946i	$-0.290932\pi$
$29$	190.712	1.22118	0.610591	+	0.791946i	$0.290932\pi$
$30$	−1.35626	−0.00825395
$31$	−50.9243	−0.295041	−0.147521	−	0.989059i	$-0.547129\pi$
$31$	−50.9243	−0.295041	−0.147521	+	0.989059i	$0.547129\pi$
$32$	−6.02450	−0.0332810
$33$	0	0
$34$	2.07926	0.0104879
$35$	46.8337	0.226181
$36$	−45.7496	−0.211804
$37$	−103.091	−0.458057	−0.229028	−	0.973420i	$-0.573555\pi$
$37$	−103.091	−0.458057	−0.229028	+	0.973420i	$0.573555\pi$
$38$	−1.31999	−0.00563501
$39$	−74.3611	−0.305316
$40$	3.79345	0.0149949
$41$	−492.894	−1.87749	−0.938745	−	0.344612i	$-0.888010\pi$
$41$	−492.894	−1.87749	−0.938745	+	0.344612i	$0.888010\pi$
$42$	−1.11276	−0.00408816
$43$	178.619	0.633468	0.316734	−	0.948514i	$-0.397414\pi$
$43$	178.619	0.633468	0.316734	+	0.948514i	$0.397414\pi$
$44$	0	0
$45$	43.2116	0.143147
$46$	1.37051	0.00439283
$47$	511.388	1.58710	0.793549	−	0.608507i	$-0.208231\pi$
$47$	511.388	1.58710	0.793549	+	0.608507i	$0.208231\pi$
$48$	365.950	1.10042
$49$	−304.575	−0.887973
$50$	2.13145	0.00602865
$51$	−378.984	−1.04056
$52$	103.987	0.277316
$53$	−150.116	−0.389058	−0.194529	−	0.980897i	$-0.562318\pi$
$53$	−150.116	−0.389058	−0.194529	+	0.980897i	$0.562318\pi$
$54$	3.82012	0.00962691
$55$	0	0
$56$	3.11238	0.00742694
$57$	240.592	0.559074
$58$	−5.98506	−0.0135496
$59$	−58.9874	−0.130161	−0.0650806	−	0.997880i	$-0.520730\pi$
$59$	−58.9874	−0.130161	−0.0650806	+	0.997880i	$0.520730\pi$
$60$	−345.692	−0.743811
$61$	−659.264	−1.38377	−0.691887	−	0.722006i	$-0.743220\pi$
$61$	−659.264	−1.38377	−0.691887	+	0.722006i	$0.743220\pi$
$62$	1.59814	0.00327362
$63$	35.4535	0.0709003
$64$	−511.622	−0.999261
$65$	−98.2185	−0.187423
$66$	0	0
$67$	331.723	0.604872	0.302436	−	0.953170i	$-0.402200\pi$
$67$	331.723	0.604872	0.302436	+	0.953170i	$0.402200\pi$
$68$	529.974	0.945129
$69$	−249.801	−0.435833
$70$	−1.46977	−0.00250958
$71$	−1003.68	−1.67767	−0.838836	−	0.544385i	$-0.816763\pi$
$71$	−1003.68	−1.67767	−0.838836	+	0.544385i	$0.816763\pi$
$72$	2.87167	0.00470041
$73$	875.491	1.40368	0.701839	−	0.712336i	$-0.252363\pi$
$73$	875.491	1.40368	0.701839	+	0.712336i	$0.252363\pi$
$74$	3.23529	0.00508236
$75$	−388.496	−0.598129
$76$	−336.446	−0.507803
$77$	0	0
$78$	2.33366	0.00338762
$79$	618.282	0.880534	0.440267	−	0.897867i	$-0.354884\pi$
$79$	618.282	0.880534	0.440267	+	0.897867i	$0.354884\pi$
$80$	483.359	0.675514
$81$	−850.712	−1.16696
$82$	15.4684	0.0208316
$83$	−529.598	−0.700373	−0.350186	−	0.936680i	$-0.613882\pi$
$83$	−529.598	−0.700373	−0.350186	+	0.936680i	$0.613882\pi$
$84$	−283.627	−0.368407
$85$	−500.573	−0.638763
$86$	−5.60555	−0.00702862
$87$	1090.89	1.34432
$88$	0	0
$89$	−1194.17	−1.42227	−0.711135	−	0.703055i	$-0.751819\pi$
$89$	−1194.17	−1.42227	−0.711135	+	0.703055i	$0.751819\pi$
$90$	−1.35610	−0.00158828
$91$	−80.5845	−0.0928302
$92$	349.323	0.395864
$93$	−291.291	−0.324790
$94$	−16.0488	−0.0176096
$95$	317.782	0.343197
$96$	−34.4607	−0.0366367
$97$	−578.614	−0.605663	−0.302831	−	0.953044i	$-0.597932\pi$
$97$	−578.614	−0.605663	−0.302831	+	0.953044i	$0.597932\pi$
$98$	9.55839	0.00985248
$99$	0	0
$100$	543.276	0.543276
$101$	−437.293	−0.430815	−0.215408	−	0.976524i	$-0.569108\pi$
$101$	−437.293	−0.430815	−0.215408	+	0.976524i	$0.569108\pi$
$102$	11.8935	0.0115455
$103$	−376.586	−0.360253	−0.180127	−	0.983643i	$-0.557651\pi$
$103$	−376.586	−0.360253	−0.180127	+	0.983643i	$0.557651\pi$
$104$	−6.52721	−0.00615428
$105$	267.893	0.248987
$106$	4.71106	0.00431678
$107$	1365.46	1.23369	0.616843	−	0.787086i	$-0.288411\pi$
$107$	1365.46	1.23369	0.616843	+	0.787086i	$0.288411\pi$
$108$	973.695	0.867536
$109$	−46.7610	−0.0410907	−0.0205454	−	0.999789i	$-0.506540\pi$
$109$	−46.7610	−0.0410907	−0.0205454	+	0.999789i	$0.506540\pi$
$110$	0	0
$111$	−589.691	−0.504243
$112$	396.577	0.334580
$113$	−207.733	−0.172937	−0.0864687	−	0.996255i	$-0.527558\pi$
$113$	−207.733	−0.172937	−0.0864687	+	0.996255i	$0.527558\pi$
$114$	−7.55045	−0.00620320
$115$	−329.944	−0.267543
$116$	−1525.51	−1.22103
$117$	−74.3522	−0.0587510
$118$	1.85119	0.00144420
$119$	−410.701	−0.316377
$120$	21.6989	0.0165069
$121$	0	0
$122$	20.6895	0.0153536
$123$	−2819.40	−2.06680
$124$	407.344	0.295005
$125$	−1457.55	−1.04294
$126$	−1.11263	−0.000786672 0
$127$	1824.38	1.27471	0.637353	−	0.770572i	$-0.280029\pi$
$127$	1824.38	1.27471	0.637353	+	0.770572i	$0.280029\pi$
$128$	64.2521	0.0443682
$129$	1021.72	0.697341
$130$	3.08237	0.00207955
$131$	259.077	0.172791	0.0863957	−	0.996261i	$-0.472465\pi$
$131$	259.077	0.172791	0.0863957	+	0.996261i	$0.472465\pi$
$132$	0	0
$133$	260.728	0.169985
$134$	−10.4104	−0.00671135
$135$	−919.680	−0.586322
$136$	−33.2661	−0.0209746
$137$	−847.146	−0.528296	−0.264148	−	0.964482i	$-0.585091\pi$
$137$	−847.146	−0.528296	−0.264148	+	0.964482i	$0.585091\pi$
$138$	7.83943	0.00483577
$139$	−2132.26	−1.30112	−0.650560	−	0.759455i	$-0.725466\pi$
$139$	−2132.26	−1.30112	−0.650560	+	0.759455i	$0.725466\pi$
$140$	−374.623	−0.226153
$141$	2925.18	1.74713
$142$	31.4982	0.0186146
$143$	0	0
$144$	365.907	0.211752
$145$	1440.88	0.825231
$146$	−27.4753	−0.0155745
$147$	−1742.19	−0.977509
$148$	824.629	0.458000
$149$	−443.151	−0.243653	−0.121827	−	0.992551i	$-0.538875\pi$
$149$	−443.151	−0.243653	−0.121827	+	0.992551i	$0.538875\pi$
$150$	12.1921	0.00663653
$151$	−67.5144	−0.0363857	−0.0181929	−	0.999834i	$-0.505791\pi$
$151$	−67.5144	−0.0363857	−0.0181929	+	0.999834i	$0.505791\pi$
$152$	21.1185	0.0112693
$153$	−378.938	−0.200231
$154$	0	0
$155$	−384.747	−0.199378
$156$	594.816	0.305278
$157$	−316.921	−0.161102	−0.0805510	−	0.996750i	$-0.525668\pi$
$157$	−316.921	−0.161102	−0.0805510	+	0.996750i	$0.525668\pi$
$158$	−19.4034	−0.00976994
$159$	−858.679	−0.428287
$160$	−45.5167	−0.0224901
$161$	−270.707	−0.132513
$162$	26.6977	0.0129480
$163$	−136.449	−0.0655675	−0.0327837	−	0.999462i	$-0.510437\pi$
$163$	−136.449	−0.0655675	−0.0327837	+	0.999462i	$0.510437\pi$
$164$	3942.67	1.87726
$165$	0	0
$166$	16.6202	0.00777097
$167$	633.114	0.293364	0.146682	−	0.989184i	$-0.453141\pi$
$167$	633.114	0.293364	0.146682	+	0.989184i	$0.453141\pi$
$168$	17.8031	0.00817581
$169$	169.000	0.0769231
$170$	15.7094	0.00708737
$171$	240.564	0.107581
$172$	−1428.77	−0.633390
$173$	−1853.02	−0.814351	−0.407176	−	0.913350i	$-0.633486\pi$
$173$	−1853.02	−0.814351	−0.407176	+	0.913350i	$0.633486\pi$
$174$	−34.2351	−0.0149158
$175$	−421.010	−0.181859
$176$	0	0
$177$	−337.413	−0.143285
$178$	37.4764	0.0157808
$179$	−212.097	−0.0885635	−0.0442817	−	0.999019i	$-0.514100\pi$
$179$	−212.097	−0.0885635	−0.0442817	+	0.999019i	$0.514100\pi$
$180$	−345.651	−0.143129
$181$	−3824.96	−1.57076	−0.785379	−	0.619015i	$-0.787532\pi$
$181$	−3824.96	−1.57076	−0.785379	+	0.619015i	$0.787532\pi$
$182$	2.52896	0.00103000
$183$	−3771.05	−1.52330
$184$	−21.9268	−0.00878513
$185$	−778.883	−0.309538
$186$	9.14152	0.00360370
$187$	0	0
$188$	−4090.60	−1.58690
$189$	−754.561	−0.290403
$190$	−9.97287	−0.00380794
$191$	−3462.84	−1.31184	−0.655922	−	0.754828i	$-0.727720\pi$
$191$	−3462.84	−1.31184	−0.655922	+	0.754828i	$0.727720\pi$
$192$	−2926.52	−1.10002
$193$	1442.00	0.537811	0.268906	−	0.963167i	$-0.413338\pi$
$193$	1442.00	0.537811	0.268906	+	0.963167i	$0.413338\pi$
$194$	18.1585	0.00672012
$195$	−561.819	−0.206321
$196$	2436.30	0.887864
$197$	−2494.63	−0.902208	−0.451104	−	0.892471i	$-0.648970\pi$
$197$	−2494.63	−0.902208	−0.451104	+	0.892471i	$0.648970\pi$
$198$	0	0
$199$	−2605.97	−0.928304	−0.464152	−	0.885756i	$-0.653641\pi$
$199$	−2605.97	−0.928304	−0.464152	+	0.885756i	$0.653641\pi$
$200$	−34.1011	−0.0120566
$201$	1897.49	0.665862
$202$	13.7235	0.00478010
$203$	1182.19	0.408735
$204$	3031.50	1.04043
$205$	−3723.95	−1.26874
$206$	11.8183	0.00399718
$207$	−249.771	−0.0838660
$208$	−831.693	−0.277248
$209$	0	0
$210$	−8.40720	−0.00276263
$211$	5067.69	1.65343	0.826716	−	0.562619i	$-0.190206\pi$
$211$	5067.69	1.65343	0.826716	+	0.562619i	$0.190206\pi$
$212$	1200.78	0.389010
$213$	−5741.13	−1.84683
$214$	−42.8520	−0.0136883
$215$	1349.51	0.428075
$216$	−61.1182	−0.0192526
$217$	−315.670	−0.0987514
$218$	1.46749	0.000455921 0
$219$	5007.88	1.54521
$220$	0	0
$221$	861.313	0.262164
$222$	18.5061	0.00559482
$223$	−6453.64	−1.93797	−0.968986	−	0.247116i	$-0.920517\pi$
$223$	−6453.64	−1.93797	−0.968986	+	0.247116i	$0.920517\pi$
$224$	−37.3447	−0.0111393
$225$	−388.450	−0.115096
$226$	6.51925	0.00191882
$227$	−3262.82	−0.954014	−0.477007	−	0.878899i	$-0.658278\pi$
$227$	−3262.82	−0.954014	−0.477007	+	0.878899i	$0.658278\pi$
$228$	−1924.50	−0.559006
$229$	−3606.87	−1.04082	−0.520411	−	0.853916i	$-0.674221\pi$
$229$	−3606.87	−1.04082	−0.520411	+	0.853916i	$0.674221\pi$
$230$	10.3546	0.00296852
$231$	0	0
$232$	95.7550	0.0270975
$233$	1894.17	0.532579	0.266290	−	0.963893i	$-0.414202\pi$
$233$	1894.17	0.532579	0.266290	+	0.963893i	$0.414202\pi$
$234$	2.33338	0.000651870 0
$235$	3863.67	1.07250
$236$	471.841	0.130145
$237$	3536.63	0.969319
$238$	12.8889	0.00351036
$239$	−3462.62	−0.937146	−0.468573	−	0.883425i	$-0.655232\pi$
$239$	−3462.62	−0.937146	−0.468573	+	0.883425i	$0.655232\pi$
$240$	2764.85	0.743627
$241$	−424.521	−0.113468	−0.0567340	−	0.998389i	$-0.518069\pi$
$241$	−424.521	−0.113468	−0.0567340	+	0.998389i	$0.518069\pi$
$242$	0	0
$243$	−1579.52	−0.416981
$244$	5273.47	1.38360
$245$	−2301.15	−0.600060
$246$	88.4804	0.0229321
$247$	−546.793	−0.140857
$248$	−25.5687	−0.00654684
$249$	−3029.35	−0.770992
$250$	45.7418	0.0115719
$251$	7323.80	1.84173	0.920865	−	0.389881i	$-0.127484\pi$
$251$	7323.80	1.84173	0.920865	+	0.389881i	$0.127484\pi$
$252$	−283.593	−0.0708915
$253$	0	0
$254$	−57.2541	−0.0141435
$255$	−2863.32	−0.703170
$256$	4090.96	0.998769
$257$	6559.67	1.59214	0.796072	−	0.605202i	$-0.206908\pi$
$257$	6559.67	1.59214	0.796072	+	0.605202i	$0.206908\pi$
$258$	−32.0642	−0.00773733
$259$	−639.043	−0.153313
$260$	785.651	0.187400
$261$	1090.76	0.258683
$262$	−8.13055	−0.00191720
$263$	3689.18	0.864961	0.432481	−	0.901643i	$-0.357638\pi$
$263$	3689.18	0.864961	0.432481	+	0.901643i	$0.357638\pi$
$264$	0	0
$265$	−1134.17	−0.262911
$266$	−8.18235	−0.00188606
$267$	−6830.77	−1.56568
$268$	−2653.46	−0.604798
$269$	1518.38	0.344153	0.172077	−	0.985084i	$-0.444952\pi$
$269$	1518.38	0.344153	0.172077	+	0.985084i	$0.444952\pi$
$270$	28.8621	0.00650552
$271$	2781.70	0.623529	0.311765	−	0.950159i	$-0.399080\pi$
$271$	2781.70	0.623529	0.311765	+	0.950159i	$0.399080\pi$
$272$	−4238.75	−0.944896
$273$	−460.950	−0.102190
$274$	26.5858	0.00586170
$275$	0	0
$276$	1998.16	0.435779
$277$	−5169.42	−1.12130	−0.560651	−	0.828052i	$-0.689449\pi$
$277$	−5169.42	−1.12130	−0.560651	+	0.828052i	$0.689449\pi$
$278$	66.9161	0.0144365
$279$	−291.257	−0.0624985
$280$	23.5148	0.00501886
$281$	−2826.70	−0.600095	−0.300048	−	0.953924i	$-0.597003\pi$
$281$	−2826.70	−0.600095	−0.300048	+	0.953924i	$0.597003\pi$
$282$	−91.8003	−0.0193852
$283$	3270.78	0.687023	0.343512	−	0.939148i	$-0.388384\pi$
$283$	3270.78	0.687023	0.343512	+	0.939148i	$0.388384\pi$
$284$	8028.44	1.67746
$285$	1817.74	0.377802
$286$	0	0
$287$	−3055.35	−0.628404
$288$	−34.4565	−0.00704990
$289$	−523.293	−0.106512
$290$	−45.2187	−0.00915633
$291$	−3309.72	−0.666733
$292$	−7003.06	−1.40350
$293$	4.52450	0.000902130 0	0.000451065	−	1.00000i	$-0.499856\pi$
$293$	4.52450	0.000902130 0	0.000451065		1.00000i	$0.499856\pi$
$294$	54.6748	0.0108459
$295$	−445.666	−0.0879582
$296$	−51.7614	−0.0101641
$297$	0	0
$298$	13.9073	0.00270345
$299$	567.720	0.109806
$300$	3107.59	0.598055
$301$	1107.22	0.212024
$302$	2.11879	0.000403717 0
$303$	−2501.36	−0.474255
$304$	2690.91	0.507678
$305$	−4980.92	−0.935104
$306$	11.8921	0.00222166
$307$	7580.22	1.40920	0.704602	−	0.709602i	$-0.251125\pi$
$307$	7580.22	1.40920	0.704602	+	0.709602i	$0.251125\pi$
$308$	0	0
$309$	−2154.10	−0.396578
$310$	12.0744	0.00221219
$311$	8075.92	1.47249	0.736244	−	0.676716i	$-0.236598\pi$
$311$	8075.92	1.47249	0.736244	+	0.676716i	$0.236598\pi$
$312$	−37.3362	−0.00677483
$313$	−10519.6	−1.89969	−0.949846	−	0.312718i	$-0.898761\pi$
$313$	−10519.6	−1.89969	−0.949846	+	0.312718i	$0.898761\pi$
$314$	9.94584	0.00178750
$315$	267.861	0.0479119
$316$	−4945.65	−0.880425
$317$	−1235.33	−0.218873	−0.109437	−	0.993994i	$-0.534905\pi$
$317$	−1235.33	−0.218873	−0.109437	+	0.993994i	$0.534905\pi$
$318$	26.9477	0.00475205
$319$	0	0
$320$	−3865.44	−0.675265
$321$	7810.57	1.35808
$322$	8.49551	0.00147030
$323$	−2786.74	−0.480057
$324$	6804.86	1.16681
$325$	882.932	0.150696
$326$	4.28214	0.000727502 0
$327$	−267.477	−0.0452340
$328$	−247.479	−0.0416607
$329$	3169.99	0.531208
$330$	0	0
$331$	527.214	0.0875478	0.0437739	−	0.999041i	$-0.486062\pi$
$331$	527.214	0.0875478	0.0437739	+	0.999041i	$0.486062\pi$
$332$	4236.26	0.700287
$333$	−589.621	−0.0970301
$334$	−19.8689	−0.00325502
$335$	2506.26	0.408751
$336$	2268.46	0.368317
$337$	−6878.10	−1.11179	−0.555896	−	0.831252i	$-0.687625\pi$
$337$	−6878.10	−1.11179	−0.555896	+	0.831252i	$0.687625\pi$
$338$	−5.30368	−0.000853498 0
$339$	−1188.25	−0.190375
$340$	4004.09	0.638684
$341$	0	0
$342$	−7.54955	−0.00119366
$343$	−4014.19	−0.631912
$344$	89.6832	0.0140564
$345$	−1887.31	−0.294520
$346$	58.1530	0.00903561
$347$	−1290.04	−0.199576	−0.0997880	−	0.995009i	$-0.531816\pi$
$347$	−1290.04	−0.199576	−0.0997880	+	0.995009i	$0.531816\pi$
$348$	−8726.03	−1.34415
$349$	822.348	0.126130	0.0630649	−	0.998009i	$-0.479912\pi$
$349$	822.348	0.126130	0.0630649	+	0.998009i	$0.479912\pi$
$350$	13.2124	0.00201781
$351$	1582.45	0.240641
$352$	0	0
$353$	10872.5	1.63934	0.819670	−	0.572835i	$-0.194157\pi$
$353$	10872.5	1.63934	0.819670	+	0.572835i	$0.194157\pi$
$354$	10.5890	0.00158982
$355$	−7583.06	−1.13371
$356$	9552.20	1.42209
$357$	−2349.25	−0.348278
$358$	6.65618	0.000982654 0
$359$	−1152.94	−0.169498	−0.0847488	−	0.996402i	$-0.527009\pi$
$359$	−1152.94	−0.169498	−0.0847488	+	0.996402i	$0.527009\pi$
$360$	21.6963	0.00317637
$361$	−5089.88	−0.742072
$362$	120.038	0.0174283
$363$	0	0
$364$	644.596	0.0928188
$365$	6614.57	0.948555
$366$	118.346	0.0169017
$367$	451.843	0.0642670	0.0321335	−	0.999484i	$-0.489770\pi$
$367$	451.843	0.0642670	0.0321335	+	0.999484i	$0.489770\pi$
$368$	−2793.90	−0.395766
$369$	−2819.06	−0.397708
$370$	24.4435	0.00343447
$371$	−930.542	−0.130219
$372$	2330.04	0.324750
$373$	6142.83	0.852718	0.426359	−	0.904554i	$-0.359796\pi$
$373$	6142.83	0.852718	0.426359	+	0.904554i	$0.359796\pi$
$374$	0	0
$375$	−8337.30	−1.14810
$376$	256.764	0.0352170
$377$	−2479.25	−0.338695
$378$	23.6802	0.00322216
$379$	−14062.2	−1.90587	−0.952934	−	0.303176i	$-0.901953\pi$
$379$	−14062.2	−1.90587	−0.952934	+	0.303176i	$0.901953\pi$
$380$	−2541.94	−0.343155
$381$	10435.6	1.40324
$382$	108.673	0.0145555
$383$	−5218.69	−0.696247	−0.348124	−	0.937449i	$-0.613181\pi$
$383$	−5218.69	−0.696247	−0.348124	+	0.937449i	$0.613181\pi$
$384$	367.528	0.0488420
$385$	0	0
$386$	−45.2540	−0.00596727
$387$	1021.59	0.134187
$388$	4628.34	0.605588
$389$	−6257.13	−0.815550	−0.407775	−	0.913082i	$-0.633695\pi$
$389$	−6257.13	−0.815550	−0.407775	+	0.913082i	$0.633695\pi$
$390$	17.6314	0.00228923
$391$	2893.40	0.374234
$392$	−152.925	−0.0197038
$393$	1481.94	0.190214
$394$	78.2883	0.0100104
$395$	4671.29	0.595033
$396$	0	0
$397$	3163.59	0.399939	0.199970	−	0.979802i	$-0.435916\pi$
$397$	3163.59	0.399939	0.199970	+	0.979802i	$0.435916\pi$
$398$	81.7825	0.0103000
$399$	1491.39	0.187124
$400$	−4345.14	−0.543142
$401$	−9737.78	−1.21267	−0.606336	−	0.795209i	$-0.707361\pi$
$401$	−9737.78	−1.21267	−0.606336	+	0.795209i	$0.707361\pi$
$402$	−59.5483	−0.00738806
$403$	662.016	0.0818297
$404$	3497.92	0.430762
$405$	−6427.36	−0.788588
$406$	−37.1002	−0.00453510
$407$	0	0
$408$	−190.285	−0.0230895
$409$	−4997.53	−0.604186	−0.302093	−	0.953278i	$-0.597685\pi$
$409$	−4997.53	−0.604186	−0.302093	+	0.953278i	$0.597685\pi$
$410$	116.868	0.0140773
$411$	−4845.75	−0.581565
$412$	3012.31	0.360209
$413$	−365.652	−0.0435655
$414$	7.83849	0.000930533 0
$415$	−4001.26	−0.473287
$416$	78.3185	0.00923048
$417$	−12196.7	−1.43231
$418$	0	0
$419$	4510.79	0.525935	0.262967	−	0.964805i	$-0.415299\pi$
$419$	4510.79	0.525935	0.262967	+	0.964805i	$0.415299\pi$
$420$	−2142.88	−0.248956
$421$	12155.9	1.40722	0.703611	−	0.710586i	$-0.251570\pi$
$421$	12155.9	1.40722	0.703611	+	0.710586i	$0.251570\pi$
$422$	−159.038	−0.0183456
$423$	2924.83	0.336195
$424$	−75.3723	−0.00863303
$425$	4499.89	0.513592
$426$	180.172	0.0204915
$427$	−4086.65	−0.463154
$428$	−10922.4	−1.23353
$429$	0	0
$430$	−42.3514	−0.00474969
$431$	−3680.43	−0.411322	−0.205661	−	0.978623i	$-0.565934\pi$
$431$	−3680.43	−0.411322	−0.205661	+	0.978623i	$0.565934\pi$
$432$	−7787.64	−0.867322
$433$	−4219.32	−0.468286	−0.234143	−	0.972202i	$-0.575228\pi$
$433$	−4219.32	−0.468286	−0.234143	+	0.972202i	$0.575228\pi$
$434$	9.90658	0.00109569
$435$	8241.96	0.908440
$436$	374.042	0.0410857
$437$	−1836.83	−0.201070
$438$	−157.161	−0.0171449
$439$	−11701.6	−1.27218	−0.636088	−	0.771617i	$-0.719448\pi$
$439$	−11701.6	−1.27218	−0.636088	+	0.771617i	$0.719448\pi$
$440$	0	0
$441$	−1741.99	−0.188099
$442$	−27.0304	−0.00290883
$443$	2041.84	0.218986	0.109493	−	0.993988i	$-0.465077\pi$
$443$	2041.84	0.218986	0.109493	+	0.993988i	$0.465077\pi$
$444$	4716.95	0.504181
$445$	−9022.30	−0.961119
$446$	202.533	0.0215027
$447$	−2534.86	−0.268221
$448$	−3171.44	−0.334457
$449$	3842.98	0.403923	0.201961	−	0.979393i	$-0.435268\pi$
$449$	3842.98	0.403923	0.201961	+	0.979393i	$0.435268\pi$
$450$	12.1906	0.00127705
$451$	0	0
$452$	1661.66	0.172916
$453$	−386.189	−0.0400546
$454$	102.396	0.0105852
$455$	−608.837	−0.0627313
$456$	120.800	0.0124056
$457$	−10628.8	−1.08795	−0.543976	−	0.839101i	$-0.683082\pi$
$457$	−10628.8	−1.08795	−0.543976	+	0.839101i	$0.683082\pi$
$458$	113.193	0.0115484
$459$	8065.00	0.820135
$460$	2639.23	0.267510
$461$	−1510.32	−0.152587	−0.0762934	−	0.997085i	$-0.524309\pi$
$461$	−1510.32	−0.152587	−0.0762934	+	0.997085i	$0.524309\pi$
$462$	0	0
$463$	14709.0	1.47642	0.738212	−	0.674569i	$-0.235671\pi$
$463$	14709.0	1.47642	0.738212	+	0.674569i	$0.235671\pi$
$464$	12201.0	1.22073
$465$	−2200.79	−0.219482
$466$	−59.4442	−0.00590922
$467$	13266.5	1.31457	0.657283	−	0.753644i	$-0.271706\pi$
$467$	13266.5	1.31457	0.657283	+	0.753644i	$0.271706\pi$
$468$	594.745	0.0587438
$469$	2056.29	0.202453
$470$	−121.253	−0.0118999
$471$	−1812.81	−0.177346
$472$	−29.6172	−0.00288822
$473$	0	0
$474$	−110.989	−0.0107551
$475$	−2856.69	−0.275945
$476$	3285.20	0.316338
$477$	−858.576	−0.0824140
$478$	108.666	0.0103981
$479$	−5321.69	−0.507629	−0.253815	−	0.967253i	$-0.581685\pi$
$479$	−5321.69	−0.507629	−0.253815	+	0.967253i	$0.581685\pi$
$480$	−260.360	−0.0247578
$481$	1340.19	0.127042
$482$	13.3226	0.00125898
$483$	−1548.47	−0.145875
$484$	0	0
$485$	−4371.58	−0.409285
$486$	49.5698	0.00462661
$487$	12585.7	1.17107	0.585537	−	0.810646i	$-0.300884\pi$
$487$	12585.7	1.17107	0.585537	+	0.810646i	$0.300884\pi$
$488$	−331.012	−0.0307054
$489$	−780.500	−0.0721788
$490$	72.2162	0.00665795
$491$	7416.12	0.681639	0.340820	−	0.940129i	$-0.389295\pi$
$491$	7416.12	0.681639	0.340820	+	0.940129i	$0.389295\pi$
$492$	22552.4	2.06655
$493$	−12635.6	−1.15432
$494$	17.1598	0.00156287
$495$	0	0
$496$	−3257.95	−0.294932
$497$	−6221.61	−0.561523
$498$	95.0692	0.00855453
$499$	2689.53	0.241282	0.120641	−	0.992696i	$-0.461505\pi$
$499$	2689.53	0.241282	0.120641	+	0.992696i	$0.461505\pi$
$500$	11658.9	1.04281
$501$	3621.47	0.322945
$502$	−229.841	−0.0204349
$503$	14243.4	1.26259	0.631293	−	0.775545i	$-0.282525\pi$
$503$	14243.4	1.26259	0.631293	+	0.775545i	$0.282525\pi$
$504$	17.8009	0.00157325
$505$	−3303.87	−0.291129
$506$	0	0
$507$	966.695	0.0846793
$508$	−14593.3	−1.27455
$509$	4773.21	0.415656	0.207828	−	0.978165i	$-0.433361\pi$
$509$	4773.21	0.415656	0.207828	+	0.978165i	$0.433361\pi$
$510$	89.8590	0.00780200
$511$	5427.00	0.469816
$512$	−642.402	−0.0554501
$513$	−5119.95	−0.440646
$514$	−205.860	−0.0176656
$515$	−2845.21	−0.243446
$516$	−8172.71	−0.697255
$517$	0	0
$518$	20.0549	0.00170109
$519$	−10599.5	−0.896463
$520$	−49.3148	−0.00415884
$521$	12074.2	1.01532	0.507660	−	0.861557i	$-0.330511\pi$
$521$	12074.2	1.01532	0.507660	+	0.861557i	$0.330511\pi$
$522$	−34.2310	−0.00287021
$523$	−11877.7	−0.993071	−0.496535	−	0.868017i	$-0.665395\pi$
$523$	−11877.7	−0.993071	−0.496535	+	0.868017i	$0.665395\pi$
$524$	−2072.36	−0.172770
$525$	−2408.21	−0.200196
$526$	−115.777	−0.00959715
$527$	3373.98	0.278886
$528$	0	0
$529$	−10259.9	−0.843253
$530$	35.5933	0.00291712
$531$	−337.373	−0.0275720
$532$	−2085.57	−0.169964
$533$	6407.62	0.520722
$534$	214.368	0.0173720
$535$	10316.4	0.833680
$536$	166.556	0.0134219
$537$	−1213.21	−0.0974934
$538$	−47.6509	−0.00381854
$539$	0	0
$540$	7356.53	0.586249
$541$	−23257.4	−1.84827	−0.924135	−	0.382065i	$-0.875213\pi$
$541$	−23257.4	−1.84827	−0.924135	+	0.382065i	$0.875213\pi$
$542$	−87.2974	−0.00691835
$543$	−21879.1	−1.72914
$544$	399.152	0.0314587
$545$	−353.292	−0.0277676
$546$	14.4659	0.00113385
$547$	21153.9	1.65352	0.826759	−	0.562556i	$-0.190182\pi$
$547$	21153.9	1.65352	0.826759	+	0.562556i	$0.190182\pi$
$548$	6776.33	0.528231
$549$	−3770.60	−0.293124
$550$	0	0
$551$	8021.52	0.620197
$552$	−125.423	−0.00967095
$553$	3832.61	0.294718
$554$	162.231	0.0124414
$555$	−4455.28	−0.340750
$556$	17056.0	1.30096
$557$	15174.2	1.15431	0.577155	−	0.816635i	$-0.304163\pi$
$557$	15174.2	1.15431	0.577155	+	0.816635i	$0.304163\pi$
$558$	9.14043	0.000693450 0
$559$	−2322.04	−0.175692
$560$	2996.25	0.226097
$561$	0	0
$562$	88.7096	0.00665834
$563$	18178.3	1.36079	0.680395	−	0.732845i	$-0.261808\pi$
$563$	18178.3	1.36079	0.680395	+	0.732845i	$0.261808\pi$
$564$	−23398.6	−1.74691
$565$	−1569.48	−0.116865
$566$	−102.646	−0.00762285
$567$	−5273.40	−0.390586
$568$	−503.940	−0.0372268
$569$	−21592.3	−1.59085	−0.795427	−	0.606050i	$-0.792753\pi$
$569$	−21592.3	−1.59085	−0.795427	+	0.606050i	$0.792753\pi$
$570$	−57.0457	−0.00419190
$571$	11933.7	0.874625	0.437312	−	0.899310i	$-0.355930\pi$
$571$	11933.7	0.874625	0.437312	+	0.899310i	$0.355930\pi$
$572$	0	0
$573$	−19807.8	−1.44412
$574$	95.8854	0.00697244
$575$	2966.03	0.215116
$576$	−2926.17	−0.211673
$577$	19963.1	1.44034	0.720168	−	0.693800i	$-0.244065\pi$
$577$	19963.1	1.44034	0.720168	+	0.693800i	$0.244065\pi$
$578$	16.4224	0.00118180
$579$	8248.38	0.592039
$580$	−11525.6	−0.825129
$581$	−3282.88	−0.234418
$582$	103.868	0.00739772
$583$	0	0
$584$	439.578	0.0311470
$585$	−561.751	−0.0397018
$586$	−0.141991	−1.00096e−5 0
$587$	5518.03	0.387996	0.193998	−	0.981002i	$-0.437854\pi$
$587$	5518.03	0.387996	0.193998	+	0.981002i	$0.437854\pi$
$588$	13935.8	0.977388
$589$	−2141.92	−0.149841
$590$	13.9862	0.000975938 0
$591$	−14269.5	−0.993179
$592$	−6595.41	−0.457888
$593$	−9167.75	−0.634864	−0.317432	−	0.948281i	$-0.602821\pi$
$593$	−9167.75	−0.634864	−0.317432	+	0.948281i	$0.602821\pi$
$594$	0	0
$595$	−3102.96	−0.213796
$596$	3544.77	0.243623
$597$	−14906.4	−1.02191
$598$	−17.8166	−0.00121835
$599$	−7573.34	−0.516591	−0.258296	−	0.966066i	$-0.583161\pi$
$599$	−7573.34	−0.516591	−0.258296	+	0.966066i	$0.583161\pi$
$600$	−195.061	−0.0132722
$601$	23453.3	1.59181	0.795905	−	0.605421i	$-0.206995\pi$
$601$	23453.3	1.59181	0.795905	+	0.605421i	$0.206995\pi$
$602$	−34.7477	−0.00235251
$603$	1897.26	0.128130
$604$	540.049	0.0363813
$605$	0	0
$606$	78.4994	0.00526208
$607$	−653.670	−0.0437095	−0.0218547	−	0.999761i	$-0.506957\pi$
$607$	−653.670	−0.0437095	−0.0218547	+	0.999761i	$0.506957\pi$
$608$	−253.396	−0.0169023
$609$	6762.20	0.449948
$610$	156.315	0.0103754
$611$	−6648.04	−0.440182
$612$	3031.13	0.200206
$613$	29275.8	1.92893	0.964467	−	0.264203i	$-0.0851090\pi$
$613$	29275.8	1.92893	0.964467	+	0.264203i	$0.0851090\pi$
$614$	−237.888	−0.0156358
$615$	−21301.3	−1.39667
$616$	0	0
$617$	−13172.3	−0.859479	−0.429740	−	0.902953i	$-0.641395\pi$
$617$	−13172.3	−0.859479	−0.429740	+	0.902953i	$0.641395\pi$
$618$	67.6016	0.00440022
$619$	−22147.5	−1.43810	−0.719048	−	0.694960i	$-0.755422\pi$
$619$	−22147.5	−1.43810	−0.719048	+	0.694960i	$0.755422\pi$
$620$	3077.60	0.199354
$621$	5315.90	0.343510
$622$	−253.445	−0.0163379
$623$	−7402.44	−0.476039
$624$	−4757.36	−0.305203
$625$	−2522.43	−0.161435
$626$	330.134	0.0210780
$627$	0	0
$628$	2535.05	0.161082
$629$	6830.30	0.432976
$630$	−8.40620	−0.000531605 0
$631$	−13529.7	−0.853577	−0.426788	−	0.904352i	$-0.640355\pi$
$631$	−13529.7	−0.853577	−0.426788	+	0.904352i	$0.640355\pi$
$632$	310.435	0.0195387
$633$	28987.6	1.82015
$634$	38.7679	0.00242850
$635$	13783.7	0.861400
$636$	6868.58	0.428234
$637$	3959.47	0.246279
$638$	0	0
$639$	−5740.44	−0.355381
$640$	485.442	0.0299825
$641$	9922.06	0.611385	0.305692	−	0.952130i	$-0.401112\pi$
$641$	9922.06	0.611385	0.305692	+	0.952130i	$0.401112\pi$
$642$	−245.117	−0.0150685
$643$	22347.2	1.37059	0.685295	−	0.728265i	$-0.259673\pi$
$643$	22347.2	1.37059	0.685295	+	0.728265i	$0.259673\pi$
$644$	2165.39	0.132497
$645$	7719.33	0.471238
$646$	87.4557	0.00532647
$647$	2548.47	0.154854	0.0774270	−	0.996998i	$-0.475330\pi$
$647$	2548.47	0.154854	0.0774270	+	0.996998i	$0.475330\pi$
$648$	−427.137	−0.0258943
$649$	0	0
$650$	−27.7088	−0.00167205
$651$	−1805.66	−0.108709
$652$	1091.46	0.0655594
$653$	10393.5	0.622864	0.311432	−	0.950268i	$-0.399191\pi$
$653$	10393.5	0.622864	0.311432	+	0.950268i	$0.399191\pi$
$654$	8.39416	0.000501892 0
$655$	1957.40	0.116766
$656$	−31533.6	−1.87680
$657$	5007.29	0.297341
$658$	−99.4831	−0.00589400
$659$	−22219.3	−1.31342	−0.656708	−	0.754145i	$-0.728052\pi$
$659$	−22219.3	−1.31342	−0.656708	+	0.754145i	$0.728052\pi$
$660$	0	0
$661$	26192.2	1.54124	0.770620	−	0.637295i	$-0.219947\pi$
$661$	26192.2	1.54124	0.770620	+	0.637295i	$0.219947\pi$
$662$	−16.5454	−0.000971385 0
$663$	4926.79	0.288598
$664$	−265.907	−0.0155410
$665$	1969.87	0.114870
$666$	18.5039	0.00107659
$667$	−8328.53	−0.483481
$668$	−5064.29	−0.293328
$669$	−36915.4	−2.13338
$670$	−78.6533	−0.00453529
$671$	0	0
$672$	−213.615	−0.0122625
$673$	5882.21	0.336913	0.168456	−	0.985709i	$-0.446122\pi$
$673$	5882.21	0.336913	0.168456	+	0.985709i	$0.446122\pi$
$674$	215.854	0.0123359
$675$	8267.43	0.471428
$676$	−1351.83	−0.0769136
$677$	−23932.7	−1.35865	−0.679326	−	0.733837i	$-0.737728\pi$
$677$	−23932.7	−1.35865	−0.679326	+	0.733837i	$0.737728\pi$
$678$	37.2907	0.00211230
$679$	−3586.71	−0.202718
$680$	−251.334	−0.0141739
$681$	−18663.6	−1.05021
$682$	0	0
$683$	1873.49	0.104959	0.0524795	−	0.998622i	$-0.483288\pi$
$683$	1873.49	0.104959	0.0524795	+	0.998622i	$0.483288\pi$
$684$	−1924.27	−0.107568
$685$	−6400.42	−0.357004
$686$	125.976	0.00701137
$687$	−20631.6	−1.14577
$688$	11427.4	0.633234
$689$	1951.51	0.107905
$690$	59.2290	0.00326784
$691$	26193.1	1.44202	0.721008	−	0.692927i	$-0.243679\pi$
$691$	26193.1	1.44202	0.721008	+	0.692927i	$0.243679\pi$
$692$	14822.4	0.814251
$693$	0	0
$694$	40.4849	0.00221439
$695$	−16109.8	−0.879250
$696$	547.727	0.0298298
$697$	32656.6	1.77469
$698$	−25.8075	−0.00139947
$699$	10834.8	0.586280
$700$	3367.66	0.181837
$701$	−31366.4	−1.69000	−0.845001	−	0.534765i	$-0.820400\pi$
$701$	−31366.4	−1.69000	−0.845001	+	0.534765i	$0.820400\pi$
$702$	−49.6616	−0.00267002
$703$	−4336.12	−0.232631
$704$	0	0
$705$	22100.6	1.18065
$706$	−341.210	−0.0181893
$707$	−2710.70	−0.144196
$708$	2698.97	0.143268
$709$	8714.17	0.461590	0.230795	−	0.973002i	$-0.425867\pi$
$709$	8714.17	0.461590	0.230795	+	0.973002i	$0.425867\pi$
$710$	237.977	0.0125791
$711$	3536.20	0.186523
$712$	−599.586	−0.0315596
$713$	2223.90	0.116810
$714$	73.7258	0.00386431
$715$	0	0
$716$	1696.57	0.0885526
$717$	−19806.5	−1.03164
$718$	36.1823	0.00188066
$719$	20596.3	1.06830	0.534152	−	0.845388i	$-0.320631\pi$
$719$	20596.3	1.06830	0.534152	+	0.845388i	$0.320631\pi$
$720$	2764.52	0.143094
$721$	−2334.38	−0.120578
$722$	159.734	0.00823365
$723$	−2428.30	−0.124909
$724$	30595.9	1.57057
$725$	−12952.7	−0.663521
$726$	0	0
$727$	9744.45	0.497114	0.248557	−	0.968617i	$-0.420044\pi$
$727$	9744.45	0.497114	0.248557	+	0.968617i	$0.420044\pi$
$728$	−40.4609	−0.00205986
$729$	13934.2	0.707932
$730$	−207.583	−0.0105247
$731$	−11834.4	−0.598782
$732$	30164.7	1.52311
$733$	34576.5	1.74231	0.871153	−	0.491011i	$-0.163373\pi$
$733$	34576.5	1.74231	0.871153	+	0.491011i	$0.163373\pi$
$734$	−14.1801	−0.000713073 0
$735$	−13162.8	−0.660565
$736$	263.094	0.0131763
$737$	0	0
$738$	88.4698	0.00441276
$739$	25631.5	1.27587	0.637935	−	0.770090i	$-0.279789\pi$
$739$	25631.5	1.27587	0.637935	+	0.770090i	$0.279789\pi$
$740$	6230.29	0.309500
$741$	−3127.70	−0.155059
$742$	29.2030	0.00144484
$743$	−1602.22	−0.0791115	−0.0395558	−	0.999217i	$-0.512594\pi$
$743$	−1602.22	−0.0791115	−0.0395558	+	0.999217i	$0.512594\pi$
$744$	−146.255	−0.00720696
$745$	−3348.13	−0.164652
$746$	−192.779	−0.00946131
$747$	−3028.99	−0.148360
$748$	0	0
$749$	8464.24	0.412920
$750$	261.647	0.0127387
$751$	3439.62	0.167129	0.0835644	−	0.996502i	$-0.473370\pi$
$751$	3439.62	0.167129	0.0835644	+	0.996502i	$0.473370\pi$
$752$	32716.7	1.58651
$753$	41892.8	2.02743
$754$	77.8058	0.00375798
$755$	−510.090	−0.0245882
$756$	6035.75	0.290368
$757$	31587.0	1.51658	0.758290	−	0.651918i	$-0.226035\pi$
$757$	31587.0	1.51658	0.758290	+	0.651918i	$0.226035\pi$
$758$	441.309	0.0211465
$759$	0	0
$760$	159.556	0.00761541
$761$	23619.9	1.12512	0.562562	−	0.826755i	$-0.309816\pi$
$761$	23619.9	1.12512	0.562562	+	0.826755i	$0.309816\pi$
$762$	−327.498	−0.0155696
$763$	−289.862	−0.0137532
$764$	27699.3	1.31168
$765$	−2862.98	−0.135309
$766$	163.777	0.00772519
$767$	766.836	0.0361002
$768$	23400.6	1.09948
$769$	28980.4	1.35899	0.679493	−	0.733682i	$-0.262200\pi$
$769$	28980.4	1.35899	0.679493	+	0.733682i	$0.262200\pi$
$770$	0	0
$771$	37521.9	1.75268
$772$	−11534.6	−0.537745
$773$	20083.6	0.934483	0.467241	−	0.884130i	$-0.345248\pi$
$773$	20083.6	0.934483	0.467241	+	0.884130i	$0.345248\pi$
$774$	−32.0604	−0.00148887
$775$	3458.67	0.160308
$776$	−290.518	−0.0134394
$777$	−3655.38	−0.168772
$778$	196.366	0.00904892
$779$	−20731.6	−0.953513
$780$	4494.00	0.206296
$781$	0	0
$782$	−90.8028	−0.00415231
$783$	−23214.7	−1.05955
$784$	−19485.6	−0.887645
$785$	−2394.42	−0.108867
$786$	−46.5075	−0.00211052
$787$	11765.8	0.532915	0.266457	−	0.963847i	$-0.414147\pi$
$787$	11765.8	0.532915	0.266457	+	0.963847i	$0.414147\pi$
$788$	19954.6	0.902097
$789$	21102.5	0.952176
$790$	−146.598	−0.00660217
$791$	−1287.70	−0.0578828
$792$	0	0
$793$	8570.44	0.383790
$794$	−99.2820	−0.00443752
$795$	−6487.55	−0.289421
$796$	20845.2	0.928190
$797$	26511.8	1.17829	0.589145	−	0.808027i	$-0.299465\pi$
$797$	26511.8	1.17829	0.589145	+	0.808027i	$0.299465\pi$
$798$	−46.8038	−0.00207623
$799$	−33881.9	−1.50020
$800$	409.171	0.0180830
$801$	−6829.95	−0.301279
$802$	305.598	0.0134552
$803$	0	0
$804$	−15178.0	−0.665780
$805$	−2045.26	−0.0895478
$806$	−20.7759	−0.000907939 0
$807$	8685.26	0.378855
$808$	−219.562	−0.00955961
$809$	−9866.08	−0.428768	−0.214384	−	0.976749i	$-0.568774\pi$
$809$	−9866.08	−0.428768	−0.214384	+	0.976749i	$0.568774\pi$
$810$	201.708	0.00874976
$811$	−14201.5	−0.614899	−0.307449	−	0.951564i	$-0.599475\pi$
$811$	−14201.5	−0.614899	−0.307449	+	0.951564i	$0.599475\pi$
$812$	−9456.32	−0.408684
$813$	15911.6	0.686400
$814$	0	0
$815$	−1030.91	−0.0443082
$816$	−24246.0	−1.04017
$817$	7512.88	0.321716
$818$	156.836	0.00670373
$819$	−460.895	−0.0196642
$820$	29787.9	1.26858
$821$	35557.1	1.51151	0.755756	−	0.654854i	$-0.227270\pi$
$821$	35557.1	1.51151	0.755756	+	0.654854i	$0.227270\pi$
$822$	152.073	0.00645274
$823$	−29272.4	−1.23982	−0.619911	−	0.784672i	$-0.712831\pi$
$823$	−29272.4	−1.23982	−0.619911	+	0.784672i	$0.712831\pi$
$824$	−189.081	−0.00799387
$825$	0	0
$826$	11.4751	0.000483379 0
$827$	5419.17	0.227863	0.113932	−	0.993489i	$-0.463655\pi$
$827$	5419.17	0.227863	0.113932	+	0.993489i	$0.463655\pi$
$828$	1997.92	0.0838557
$829$	37958.6	1.59030	0.795149	−	0.606414i	$-0.207393\pi$
$829$	37958.6	1.59030	0.795149	+	0.606414i	$0.207393\pi$
$830$	125.570	0.00525134
$831$	−29569.6	−1.23436
$832$	6651.08	0.277145
$833$	20179.6	0.839352
$834$	382.766	0.0158922
$835$	4783.35	0.198245
$836$	0	0
$837$	6198.85	0.255990
$838$	−141.561	−0.00583549
$839$	12594.5	0.518250	0.259125	−	0.965844i	$-0.416566\pi$
$839$	12594.5	0.518250	0.259125	+	0.965844i	$0.416566\pi$
$840$	134.507	0.00552492
$841$	11982.0	0.491286
$842$	−381.484	−0.0156138
$843$	−16169.0	−0.660604
$844$	−40536.5	−1.65323
$845$	1276.84	0.0519818
$846$	−91.7893	−0.00373024
$847$	0	0
$848$	−9603.90	−0.388914
$849$	18709.1	0.756297
$850$	−141.219	−0.00569855
$851$	4502.07	0.181350
$852$	45923.4	1.84661
$853$	−37409.5	−1.50161	−0.750807	−	0.660522i	$-0.770335\pi$
$853$	−37409.5	−1.50161	−0.750807	+	0.660522i	$0.770335\pi$
$854$	128.250	0.00513892
$855$	1817.52	0.0726994
$856$	685.590	0.0273750
$857$	−39180.1	−1.56169	−0.780844	−	0.624726i	$-0.785211\pi$
$857$	−39180.1	−1.56169	−0.780844	+	0.624726i	$0.785211\pi$
$858$	0	0
$859$	−5109.67	−0.202956	−0.101478	−	0.994838i	$-0.532357\pi$
$859$	−5109.67	−0.202956	−0.101478	+	0.994838i	$0.532357\pi$
$860$	−10794.8	−0.428022
$861$	−17476.9	−0.691766
$862$	115.502	0.00456382
$863$	−18924.7	−0.746469	−0.373234	−	0.927737i	$-0.621751\pi$
$863$	−18924.7	−0.746469	−0.373234	+	0.927737i	$0.621751\pi$
$864$	733.343	0.0288760
$865$	−14000.1	−0.550309
$866$	132.414	0.00519585
$867$	−2993.28	−0.117252
$868$	2525.05	0.0987393
$869$	0	0
$870$	−258.655	−0.0100796
$871$	−4312.40	−0.167761
$872$	−23.4784	−0.000911786 0
$873$	−3309.32	−0.128297
$874$	57.6449	0.00223097
$875$	−9035.05	−0.349075
$876$	−40058.1	−1.54502
$877$	−3881.20	−0.149440	−0.0747199	−	0.997205i	$-0.523806\pi$
$877$	−3881.20	−0.149440	−0.0747199	+	0.997205i	$0.523806\pi$
$878$	367.227	0.0141154
$879$	25.8805	0.000993093 0
$880$	0	0
$881$	−50153.0	−1.91793	−0.958965	−	0.283525i	$-0.908496\pi$
$881$	−50153.0	−1.91793	−0.958965	+	0.283525i	$0.908496\pi$
$882$	54.6683	0.00208705
$883$	44361.0	1.69068	0.845338	−	0.534231i	$-0.179399\pi$
$883$	44361.0	1.69068	0.845338	+	0.534231i	$0.179399\pi$
$884$	−6889.66	−0.262132
$885$	−2549.25	−0.0968272
$886$	−64.0785	−0.00242975
$887$	51678.9	1.95627	0.978133	−	0.207979i	$-0.0666887\pi$
$887$	51678.9	1.95627	0.978133	+	0.207979i	$0.0666887\pi$
$888$	−296.080	−0.0111890
$889$	11309.0	0.426649
$890$	283.144	0.0106641
$891$	0	0
$892$	51622.8	1.93773
$893$	21509.5	0.806032
$894$	79.5510	0.00297604
$895$	−1602.45	−0.0598480
$896$	398.286	0.0148502
$897$	3247.41	0.120878
$898$	−120.603	−0.00448171
$899$	−9711.86	−0.360299
$900$	3107.22	0.115082
$901$	9945.94	0.367755
$902$	0	0
$903$	6333.41	0.233403
$904$	−104.302	−0.00383741
$905$	−28898.6	−1.06146
$906$	12.1197	0.000444425 0
$907$	5579.97	0.204278	0.102139	−	0.994770i	$-0.467431\pi$
$907$	5579.97	0.204278	0.102139	+	0.994770i	$0.467431\pi$
$908$	26099.4	0.953897
$909$	−2501.06	−0.0912595
$910$	19.1070	0.000696034 0
$911$	42343.8	1.53997	0.769984	−	0.638063i	$-0.220264\pi$
$911$	42343.8	1.53997	0.769984	+	0.638063i	$0.220264\pi$
$912$	15392.2	0.558868
$913$	0	0
$914$	333.561	0.0120713
$915$	−28491.3	−1.02939
$916$	28851.4	1.04069
$917$	1605.97	0.0578340
$918$	−253.102	−0.00909978
$919$	−1776.97	−0.0637834	−0.0318917	−	0.999491i	$-0.510153\pi$
$919$	−1776.97	−0.0637834	−0.0318917	+	0.999491i	$0.510153\pi$
$920$	−165.663	−0.00593667
$921$	43359.5	1.55130
$922$	47.3979	0.00169302
$923$	13047.8	0.465302
$924$	0	0
$925$	7001.74	0.248882
$926$	−461.608	−0.0163816
$927$	−2153.84	−0.0763123
$928$	−1148.94	−0.0406421
$929$	16362.3	0.577858	0.288929	−	0.957350i	$-0.406701\pi$
$929$	16362.3	0.577858	0.288929	+	0.957350i	$0.406701\pi$
$930$	69.0667	0.00243525
$931$	−12810.7	−0.450971
$932$	−15151.5	−0.532514
$933$	46195.0	1.62096
$934$	−416.340	−0.0145857
$935$	0	0
$936$	−37.3317	−0.00130366
$937$	1201.16	0.0418785	0.0209393	−	0.999781i	$-0.493334\pi$
$937$	1201.16	0.0418785	0.0209393	+	0.999781i	$0.493334\pi$
$938$	−64.5320	−0.00224631
$939$	−60173.1	−2.09124
$940$	−30905.6	−1.07237
$941$	−12598.7	−0.436457	−0.218229	−	0.975898i	$-0.570028\pi$
$941$	−12598.7	−0.436457	−0.218229	+	0.975898i	$0.570028\pi$
$942$	56.8911	0.00196774
$943$	21525.1	0.743321
$944$	−3773.80	−0.130113
$945$	−5700.91	−0.196244
$946$	0	0
$947$	16263.0	0.558054	0.279027	−	0.960283i	$-0.409988\pi$
$947$	16263.0	0.558054	0.279027	+	0.960283i	$0.409988\pi$
$948$	−28289.5	−0.969200
$949$	−11381.4	−0.389310
$950$	89.6508	0.00306174
$951$	−7066.17	−0.240942
$952$	−206.210	−0.00702028
$953$	7259.49	0.246755	0.123378	−	0.992360i	$-0.460627\pi$
$953$	7259.49	0.246755	0.123378	+	0.992360i	$0.460627\pi$
$954$	26.9445	0.000914423 0
$955$	−26162.7	−0.886498
$956$	27697.5	0.937031
$957$	0	0
$958$	167.009	0.00563239
$959$	−5251.29	−0.176823
$960$	−22110.7	−0.743353
$961$	−27197.7	−0.912951
$962$	−42.0587	−0.00140959
$963$	7809.64	0.261331
$964$	3395.75	0.113454
$965$	10894.7	0.363433
$966$	48.5951	0.00161855
$967$	−28671.3	−0.953472	−0.476736	−	0.879047i	$-0.658180\pi$
$967$	−28671.3	−0.953472	−0.476736	+	0.879047i	$0.658180\pi$
$968$	0	0
$969$	−15940.4	−0.528462
$970$	137.192	0.00454121
$971$	31065.0	1.02670	0.513349	−	0.858180i	$-0.328405\pi$
$971$	31065.0	1.02670	0.513349	+	0.858180i	$0.328405\pi$
$972$	12634.6	0.416930
$973$	−13217.5	−0.435490
$974$	−394.974	−0.0129936
$975$	5050.45	0.165891
$976$	−42177.3	−1.38326
$977$	−39138.8	−1.28164	−0.640820	−	0.767691i	$-0.721405\pi$
$977$	−39138.8	−1.28164	−0.640820	+	0.767691i	$0.721405\pi$
$978$	24.4942	0.000800858 0
$979$	0	0
$980$	18406.9	0.599986
$981$	−267.445	−0.00870424
$982$	−232.738	−0.00756311
$983$	2420.54	0.0785385	0.0392693	−	0.999229i	$-0.487497\pi$
$983$	2420.54	0.0785385	0.0392693	+	0.999229i	$0.487497\pi$
$984$	−1415.60	−0.0458614
$985$	−18847.6	−0.609680
$986$	396.539	0.0128077
$987$	18132.6	0.584770
$988$	4373.80	0.140839
$989$	−7800.42	−0.250798
$990$	0	0
$991$	25093.9	0.804375	0.402187	−	0.915557i	$-0.368250\pi$
$991$	25093.9	0.804375	0.402187	+	0.915557i	$0.368250\pi$
$992$	306.793	0.00981925
$993$	3015.71	0.0963754
$994$	195.251	0.00623037
$995$	−19688.8	−0.627314
$996$	24231.8	0.770897
$997$	−5895.45	−0.187273	−0.0936363	−	0.995606i	$-0.529849\pi$
$997$	−5895.45	−0.187273	−0.0936363	+	0.995606i	$0.529849\pi$
$998$	−84.4047	−0.00267714
$999$	12549.0	0.397430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.p.1.18		34
11.2	odd	10		143.4.h.a.92.9	yes	68
11.6	odd	10		143.4.h.a.14.9	✓	68
11.10	odd	2		1573.4.a.o.1.17		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.9	✓	68	11.6	odd	10
143.4.h.a.92.9	yes	68	11.2	odd	10
1573.4.a.o.1.17		34	11.10	odd	2
1573.4.a.p.1.18		34	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:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0313827 q^{2} +5.72009 q^{3} -7.99902 q^{4} +7.55527 q^{5} -0.179512 q^{6} +6.19881 q^{7} +0.502093 q^{8} +5.71940 q^{9} +O(q^{10})\)	\(q-0.0313827 q^{2} +5.72009 q^{3} -7.99902 q^{4} +7.55527 q^{5} -0.179512 q^{6} +6.19881 q^{7} +0.502093 q^{8} +5.71940 q^{9} -0.237105 q^{10} -45.7551 q^{12} -13.0000 q^{13} -0.194536 q^{14} +43.2168 q^{15} +63.9764 q^{16} -66.2549 q^{17} -0.179491 q^{18} +42.0610 q^{19} -60.4347 q^{20} +35.4577 q^{21} -43.6708 q^{23} +2.87202 q^{24} -67.9179 q^{25} +0.407976 q^{26} -121.727 q^{27} -49.5843 q^{28} +190.712 q^{29} -1.35626 q^{30} -50.9243 q^{31} -6.02450 q^{32} +2.07926 q^{34} +46.8337 q^{35} -45.7496 q^{36} -103.091 q^{37} -1.31999 q^{38} -74.3611 q^{39} +3.79345 q^{40} -492.894 q^{41} -1.11276 q^{42} +178.619 q^{43} +43.2116 q^{45} +1.37051 q^{46} +511.388 q^{47} +365.950 q^{48} -304.575 q^{49} +2.13145 q^{50} -378.984 q^{51} +103.987 q^{52} -150.116 q^{53} +3.82012 q^{54} +3.11238 q^{56} +240.592 q^{57} -5.98506 q^{58} -58.9874 q^{59} -345.692 q^{60} -659.264 q^{61} +1.59814 q^{62} +35.4535 q^{63} -511.622 q^{64} -98.2185 q^{65} +331.723 q^{67} +529.974 q^{68} -249.801 q^{69} -1.46977 q^{70} -1003.68 q^{71} +2.87167 q^{72} +875.491 q^{73} +3.23529 q^{74} -388.496 q^{75} -336.446 q^{76} +2.33366 q^{78} +618.282 q^{79} +483.359 q^{80} -850.712 q^{81} +15.4684 q^{82} -529.598 q^{83} -283.627 q^{84} -500.573 q^{85} -5.60555 q^{86} +1090.89 q^{87} -1194.17 q^{89} -1.35610 q^{90} -80.5845 q^{91} +349.323 q^{92} -291.291 q^{93} -16.0488 q^{94} +317.782 q^{95} -34.4607 q^{96} -578.614 q^{97} +9.55839 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9}+O(q^{10}) \) 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9} + 18 q^{10} - 262 q^{12} - 442 q^{13} - 231 q^{14} - 196 q^{15} + 225 q^{16} + 209 q^{17} + 190 q^{18} + 107 q^{19} - 211 q^{20} + 68 q^{21} - 632 q^{23} - 152 q^{24} + 296 q^{25} - 39 q^{26} - 920 q^{27} + 931 q^{28} + 32 q^{29} + 300 q^{30} - 290 q^{31} - 876 q^{32} - 602 q^{34} - 104 q^{35} - 611 q^{36} - 656 q^{37} - 1361 q^{38} + 377 q^{39} - 1159 q^{40} + 1121 q^{41} + 79 q^{42} - 349 q^{43} - 1024 q^{45} - 490 q^{46} - 1608 q^{47} - 1827 q^{48} + 808 q^{49} + 1322 q^{50} - 1414 q^{51} - 1261 q^{52} - 2608 q^{53} - 3131 q^{54} - 1675 q^{56} + 2150 q^{57} - 1673 q^{58} - 2011 q^{59} - 201 q^{60} + 236 q^{61} - 1396 q^{62} - 1206 q^{63} + 1331 q^{64} + 364 q^{65} - 3213 q^{67} + 1321 q^{68} - 162 q^{69} + 174 q^{70} - 3756 q^{71} + 5074 q^{72} - 823 q^{73} - 2550 q^{74} - 3063 q^{75} - 2004 q^{76} + 468 q^{78} + 2120 q^{79} - 5005 q^{80} + 710 q^{81} - 2534 q^{82} + 3843 q^{83} - 7191 q^{84} - 1582 q^{85} - 3542 q^{86} - 962 q^{87} - 3633 q^{89} + 995 q^{90} - 468 q^{91} - 2072 q^{92} - 508 q^{93} + 6309 q^{94} - 1916 q^{95} + 2150 q^{96} + 1195 q^{97} + 1487 q^{98}+O(q^{100}) \) 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9 + 18 * q^10 - 262 * q^12 - 442 * q^13 - 231 * q^14 - 196 * q^15 + 225 * q^16 + 209 * q^17 + 190 * q^18 + 107 * q^19 - 211 * q^20 + 68 * q^21 - 632 * q^23 - 152 * q^24 + 296 * q^25 - 39 * q^26 - 920 * q^27 + 931 * q^28 + 32 * q^29 + 300 * q^30 - 290 * q^31 - 876 * q^32 - 602 * q^34 - 104 * q^35 - 611 * q^36 - 656 * q^37 - 1361 * q^38 + 377 * q^39 - 1159 * q^40 + 1121 * q^41 + 79 * q^42 - 349 * q^43 - 1024 * q^45 - 490 * q^46 - 1608 * q^47 - 1827 * q^48 + 808 * q^49 + 1322 * q^50 - 1414 * q^51 - 1261 * q^52 - 2608 * q^53 - 3131 * q^54 - 1675 * q^56 + 2150 * q^57 - 1673 * q^58 - 2011 * q^59 - 201 * q^60 + 236 * q^61 - 1396 * q^62 - 1206 * q^63 + 1331 * q^64 + 364 * q^65 - 3213 * q^67 + 1321 * q^68 - 162 * q^69 + 174 * q^70 - 3756 * q^71 + 5074 * q^72 - 823 * q^73 - 2550 * q^74 - 3063 * q^75 - 2004 * q^76 + 468 * q^78 + 2120 * q^79 - 5005 * q^80 + 710 * q^81 - 2534 * q^82 + 3843 * q^83 - 7191 * q^84 - 1582 * q^85 - 3542 * q^86 - 962 * q^87 - 3633 * q^89 + 995 * q^90 - 468 * q^91 - 2072 * q^92 - 508 * q^93 + 6309 * q^94 - 1916 * q^95 + 2150 * q^96 + 1195 * q^97 + 1487 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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