LMFDB - Embedded newform 1573.4.a.h.1.4

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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 6 x^{14} - 69 x^{13} + 418 x^{12} + 1806 x^{11} - 10742 x^{10} - 24098 x^{9} + 129758 x^{8} + \cdots + 47232 $ x^15 - 6x^14 - 69x^13 + 418x^12 + 1806x^11 - 10742x^10 - 24098x^9 + 129758x^8 + 183825x^7 - 750764x^6 - 813769x^5 + 1744424x^4 + 1731312x^3 - 516000x^2 - 352704x + 47232
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.43729$ of defining polynomial
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)

$f(q)$	$=$	$q-3.43729 q^{2} -6.00304 q^{3} +3.81493 q^{4} -4.47666 q^{5} +20.6342 q^{6} -28.7105 q^{7} +14.3853 q^{8} +9.03648 q^{9} +O(q^{10})$	\(q-3.43729 q^{2} -6.00304 q^{3} +3.81493 q^{4} -4.47666 q^{5} +20.6342 q^{6} -28.7105 q^{7} +14.3853 q^{8} +9.03648 q^{9} +15.3875 q^{10} -22.9012 q^{12} -13.0000 q^{13} +98.6863 q^{14} +26.8736 q^{15} -79.9657 q^{16} +34.3594 q^{17} -31.0610 q^{18} -99.0004 q^{19} -17.0781 q^{20} +172.350 q^{21} -65.2301 q^{23} -86.3554 q^{24} -104.960 q^{25} +44.6847 q^{26} +107.836 q^{27} -109.529 q^{28} -137.917 q^{29} -92.3721 q^{30} -71.7443 q^{31} +159.783 q^{32} -118.103 q^{34} +128.527 q^{35} +34.4735 q^{36} -124.211 q^{37} +340.293 q^{38} +78.0395 q^{39} -64.3980 q^{40} +221.175 q^{41} -592.418 q^{42} +55.0994 q^{43} -40.4532 q^{45} +224.214 q^{46} +198.120 q^{47} +480.038 q^{48} +481.294 q^{49} +360.776 q^{50} -206.261 q^{51} -49.5941 q^{52} +105.462 q^{53} -370.662 q^{54} -413.009 q^{56} +594.304 q^{57} +474.060 q^{58} +99.3451 q^{59} +102.521 q^{60} -87.8561 q^{61} +246.606 q^{62} -259.442 q^{63} +90.5067 q^{64} +58.1965 q^{65} -975.642 q^{67} +131.079 q^{68} +391.579 q^{69} -441.785 q^{70} +1083.53 q^{71} +129.992 q^{72} -948.252 q^{73} +426.949 q^{74} +630.076 q^{75} -377.680 q^{76} -268.244 q^{78} +734.380 q^{79} +357.979 q^{80} -891.327 q^{81} -760.241 q^{82} +307.255 q^{83} +657.505 q^{84} -153.815 q^{85} -189.392 q^{86} +827.922 q^{87} +1252.31 q^{89} +139.049 q^{90} +373.237 q^{91} -248.848 q^{92} +430.684 q^{93} -680.997 q^{94} +443.191 q^{95} -959.183 q^{96} +1739.81 q^{97} -1654.35 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9}+O(q^{10}) $ 15 * q - 6 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 + 25 * q^6 - 28 * q^7 - 108 * q^8 + 133 * q^9	\( 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9} + 16 q^{10} - 3 q^{12} - 195 q^{13} + 60 q^{14} + 202 q^{15} + 282 q^{16} - 136 q^{17} - 351 q^{18} - 136 q^{19} - 62 q^{20} - 625 q^{21} - 176 q^{23} + 227 q^{24} + 479 q^{25} + 78 q^{26} - 13 q^{27} + 86 q^{28} - 344 q^{29} - 542 q^{30} + 275 q^{31} + 170 q^{32} - 1505 q^{34} - 655 q^{35} + 623 q^{36} + 346 q^{37} - 848 q^{38} - 26 q^{39} - 256 q^{40} - 38 q^{41} + 575 q^{42} - 534 q^{43} - 633 q^{45} + 375 q^{46} + 276 q^{47} - 723 q^{48} + 773 q^{49} - 1684 q^{50} - 1111 q^{51} - 702 q^{52} + 706 q^{53} + 178 q^{54} - 2056 q^{56} - 1320 q^{57} - 983 q^{58} - 174 q^{59} + 2004 q^{60} - 1078 q^{61} - 1365 q^{62} + 2055 q^{63} + 1338 q^{64} + 26 q^{65} - 260 q^{67} - 559 q^{68} + 154 q^{69} - 1161 q^{70} + 2910 q^{71} - 6171 q^{72} - 1000 q^{73} - 688 q^{74} - 553 q^{75} - 178 q^{76} - 325 q^{78} + 386 q^{79} + 1702 q^{80} - 2805 q^{81} + 3380 q^{82} - 4318 q^{83} - 6681 q^{84} + 1391 q^{85} + 4139 q^{86} - 3144 q^{87} - 810 q^{89} + 3789 q^{90} + 364 q^{91} - 4857 q^{92} + 394 q^{93} + 116 q^{94} - 5204 q^{95} + 893 q^{96} - 1860 q^{97} - 8 q^{98}+O(q^{100}) \) 15 * q - 6 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 + 25 * q^6 - 28 * q^7 - 108 * q^8 + 133 * q^9 + 16 * q^10 - 3 * q^12 - 195 * q^13 + 60 * q^14 + 202 * q^15 + 282 * q^16 - 136 * q^17 - 351 * q^18 - 136 * q^19 - 62 * q^20 - 625 * q^21 - 176 * q^23 + 227 * q^24 + 479 * q^25 + 78 * q^26 - 13 * q^27 + 86 * q^28 - 344 * q^29 - 542 * q^30 + 275 * q^31 + 170 * q^32 - 1505 * q^34 - 655 * q^35 + 623 * q^36 + 346 * q^37 - 848 * q^38 - 26 * q^39 - 256 * q^40 - 38 * q^41 + 575 * q^42 - 534 * q^43 - 633 * q^45 + 375 * q^46 + 276 * q^47 - 723 * q^48 + 773 * q^49 - 1684 * q^50 - 1111 * q^51 - 702 * q^52 + 706 * q^53 + 178 * q^54 - 2056 * q^56 - 1320 * q^57 - 983 * q^58 - 174 * q^59 + 2004 * q^60 - 1078 * q^61 - 1365 * q^62 + 2055 * q^63 + 1338 * q^64 + 26 * q^65 - 260 * q^67 - 559 * q^68 + 154 * q^69 - 1161 * q^70 + 2910 * q^71 - 6171 * q^72 - 1000 * q^73 - 688 * q^74 - 553 * q^75 - 178 * q^76 - 325 * q^78 + 386 * q^79 + 1702 * q^80 - 2805 * q^81 + 3380 * q^82 - 4318 * q^83 - 6681 * q^84 + 1391 * q^85 + 4139 * q^86 - 3144 * q^87 - 810 * q^89 + 3789 * q^90 + 364 * q^91 - 4857 * q^92 + 394 * q^93 + 116 * q^94 - 5204 * q^95 + 893 * q^96 - 1860 * q^97 - 8 * 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 $

$2$	−3.43729	−1.21526	−0.607632	−	0.794219i	$-0.707880\pi$
$2$	−3.43729	−1.21526	−0.607632	+	0.794219i	$0.707880\pi$
$3$	−6.00304	−1.15529	−0.577643	−	0.816290i	$-0.696027\pi$
$3$	−6.00304	−1.15529	−0.577643	+	0.816290i	$0.696027\pi$
$4$	3.81493	0.476866
$5$	−4.47666	−0.400404	−0.200202	−	0.979755i	$-0.564160\pi$
$5$	−4.47666	−0.400404	−0.200202	+	0.979755i	$0.564160\pi$
$6$	20.6342	1.40398
$7$	−28.7105	−1.55022	−0.775111	−	0.631825i	$-0.782306\pi$
$7$	−28.7105	−1.55022	−0.775111	+	0.631825i	$0.782306\pi$
$8$	14.3853	0.635746
$9$	9.03648	0.334684
$10$	15.3875	0.486597
$11$	0	0
$11$	0	0
$12$	−22.9012	−0.550917
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	98.6863	1.88393
$15$	26.8736	0.462581
$16$	−79.9657	−1.24946
$17$	34.3594	0.490199	0.245100	−	0.969498i	$-0.421179\pi$
$17$	34.3594	0.490199	0.245100	+	0.969498i	$0.421179\pi$
$18$	−31.0610	−0.406730
$19$	−99.0004	−1.19538	−0.597691	−	0.801727i	$-0.703915\pi$
$19$	−99.0004	−1.19538	−0.597691	+	0.801727i	$0.703915\pi$
$20$	−17.0781	−0.190939
$21$	172.350	1.79095
$22$	0	0
$23$	−65.2301	−0.591366	−0.295683	−	0.955286i	$-0.595547\pi$
$23$	−65.2301	−0.591366	−0.295683	+	0.955286i	$0.595547\pi$
$24$	−86.3554	−0.734468
$25$	−104.960	−0.839676
$26$	44.6847	0.337054
$27$	107.836	0.768629
$28$	−109.529	−0.739249
$29$	−137.917	−0.883123	−0.441561	−	0.897231i	$-0.645575\pi$
$29$	−137.917	−0.883123	−0.441561	+	0.897231i	$0.645575\pi$
$30$	−92.3721	−0.562158
$31$	−71.7443	−0.415666	−0.207833	−	0.978164i	$-0.566641\pi$
$31$	−71.7443	−0.415666	−0.207833	+	0.978164i	$0.566641\pi$
$32$	159.783	0.882684
$33$	0	0
$34$	−118.103	−0.595722
$35$	128.527	0.620716
$36$	34.4735	0.159600
$37$	−124.211	−0.551897	−0.275948	−	0.961172i	$-0.588992\pi$
$37$	−124.211	−0.551897	−0.275948	+	0.961172i	$0.588992\pi$
$38$	340.293	1.45270
$39$	78.0395	0.320419
$40$	−64.3980	−0.254555
$41$	221.175	0.842481	0.421240	−	0.906949i	$-0.361595\pi$
$41$	221.175	0.842481	0.421240	+	0.906949i	$0.361595\pi$
$42$	−592.418	−2.17648
$43$	55.0994	0.195409	0.0977044	−	0.995215i	$-0.468850\pi$
$43$	55.0994	0.195409	0.0977044	+	0.995215i	$0.468850\pi$
$44$	0	0
$45$	−40.4532	−0.134009
$46$	224.214	0.718665
$47$	198.120	0.614869	0.307435	−	0.951569i	$-0.400530\pi$
$47$	198.120	0.614869	0.307435	+	0.951569i	$0.400530\pi$
$48$	480.038	1.44349
$49$	481.294	1.40319
$50$	360.776	1.02043
$51$	−206.261	−0.566320
$52$	−49.5941	−0.132259
$53$	105.462	0.273327	0.136663	−	0.990618i	$-0.456362\pi$
$53$	105.462	0.273327	0.136663	+	0.990618i	$0.456362\pi$
$54$	−370.662	−0.934087
$55$	0	0
$56$	−413.009	−0.985547
$57$	594.304	1.38101
$58$	474.060	1.07323
$59$	99.3451	0.219214	0.109607	−	0.993975i	$-0.465041\pi$
$59$	99.3451	0.219214	0.109607	+	0.993975i	$0.465041\pi$
$60$	102.521	0.220589
$61$	−87.8561	−0.184407	−0.0922035	−	0.995740i	$-0.529391\pi$
$61$	−87.8561	−0.184407	−0.0922035	+	0.995740i	$0.529391\pi$
$62$	246.606	0.505144
$63$	−259.442	−0.518835
$64$	90.5067	0.176771
$65$	58.1965	0.111052
$66$	0	0
$67$	−975.642	−1.77901	−0.889505	−	0.456926i	$-0.848950\pi$
$67$	−975.642	−1.77901	−0.889505	+	0.456926i	$0.848950\pi$
$68$	131.079	0.233760
$69$	391.579	0.683196
$70$	−441.785	−0.754334
$71$	1083.53	1.81114	0.905569	−	0.424199i	$-0.139444\pi$
$71$	1083.53	1.81114	0.905569	+	0.424199i	$0.139444\pi$
$72$	129.992	0.212774
$73$	−948.252	−1.52034	−0.760168	−	0.649727i	$-0.774883\pi$
$73$	−948.252	−1.52034	−0.760168	+	0.649727i	$0.774883\pi$
$74$	426.949	0.670700
$75$	630.076	0.970066
$76$	−377.680	−0.570037
$77$	0	0
$78$	−268.244	−0.389393
$79$	734.380	1.04588	0.522938	−	0.852371i	$-0.324836\pi$
$79$	734.380	1.04588	0.522938	+	0.852371i	$0.324836\pi$
$80$	357.979	0.500291
$81$	−891.327	−1.22267
$82$	−760.241	−1.02384
$83$	307.255	0.406333	0.203167	−	0.979144i	$-0.434877\pi$
$83$	307.255	0.406333	0.203167	+	0.979144i	$0.434877\pi$
$84$	657.505	0.854044
$85$	−153.815	−0.196278
$86$	−189.392	−0.237473
$87$	827.922	1.02026
$88$	0	0
$89$	1252.31	1.49151	0.745755	−	0.666221i	$-0.232089\pi$
$89$	1252.31	1.49151	0.745755	+	0.666221i	$0.232089\pi$
$90$	139.049	0.162856
$91$	373.237	0.429954
$92$	−248.848	−0.282002
$93$	430.684	0.480213
$94$	−680.997	−0.747228
$95$	443.191	0.478636
$96$	−959.183	−1.01975
$97$	1739.81	1.82115	0.910574	−	0.413345i	$-0.135640\pi$
$97$	1739.81	1.82115	0.910574	+	0.413345i	$0.135640\pi$
$98$	−1654.35	−1.70525
$99$	0	0
$100$	−400.413	−0.400413
$101$	197.274	0.194351	0.0971757	−	0.995267i	$-0.469019\pi$
$101$	197.274	0.194351	0.0971757	+	0.995267i	$0.469019\pi$
$102$	708.978	0.688228
$103$	574.909	0.549975	0.274988	−	0.961448i	$-0.411326\pi$
$103$	574.909	0.549975	0.274988	+	0.961448i	$0.411326\pi$
$104$	−187.009	−0.176324
$105$	−771.554	−0.717104
$106$	−362.503	−0.332164
$107$	352.038	0.318063	0.159032	−	0.987273i	$-0.449163\pi$
$107$	352.038	0.318063	0.159032	+	0.987273i	$0.449163\pi$
$108$	411.386	0.366533
$109$	−1409.17	−1.23829	−0.619146	−	0.785276i	$-0.712521\pi$
$109$	−1409.17	−1.23829	−0.619146	+	0.785276i	$0.712521\pi$
$110$	0	0
$111$	745.644	0.637598
$112$	2295.86	1.93695
$113$	1748.22	1.45538	0.727692	−	0.685904i	$-0.240593\pi$
$113$	1748.22	1.45538	0.727692	+	0.685904i	$0.240593\pi$
$114$	−2042.79	−1.67829
$115$	292.013	0.236785
$116$	−526.144	−0.421131
$117$	−117.474	−0.0928248
$118$	−341.477	−0.266403
$119$	−986.478	−0.759918
$120$	386.584	0.294084
$121$	0	0
$122$	301.987	0.224103
$123$	−1327.72	−0.973306
$124$	−273.699	−0.198217
$125$	1029.45	0.736615
$126$	891.777	0.630522
$127$	−182.821	−0.127738	−0.0638690	−	0.997958i	$-0.520344\pi$
$127$	−182.821	−0.127738	−0.0638690	+	0.997958i	$0.520344\pi$
$128$	−1589.36	−1.09751
$129$	−330.764	−0.225753
$130$	−200.038	−0.134958
$131$	−636.214	−0.424322	−0.212161	−	0.977235i	$-0.568050\pi$
$131$	−636.214	−0.424322	−0.212161	+	0.977235i	$0.568050\pi$
$132$	0	0
$133$	2842.36	1.85311
$134$	3353.56	2.16197
$135$	−482.744	−0.307763
$136$	494.270	0.311642
$137$	2802.48	1.74768	0.873839	−	0.486216i	$-0.161623\pi$
$137$	2802.48	1.74768	0.873839	+	0.486216i	$0.161623\pi$
$138$	−1345.97	−0.830264
$139$	−813.175	−0.496206	−0.248103	−	0.968734i	$-0.579807\pi$
$139$	−813.175	−0.496206	−0.248103	+	0.968734i	$0.579807\pi$
$140$	490.322	0.295999
$141$	−1189.33	−0.710349
$142$	−3724.39	−2.20101
$143$	0	0
$144$	−722.609	−0.418176
$145$	617.407	0.353606
$146$	3259.41	1.84761
$147$	−2889.23	−1.62109
$148$	−473.857	−0.263181
$149$	3040.24	1.67159	0.835793	−	0.549045i	$-0.185008\pi$
$149$	3040.24	1.67159	0.835793	+	0.549045i	$0.185008\pi$
$150$	−2165.75	−1.17889
$151$	1017.54	0.548387	0.274193	−	0.961675i	$-0.411589\pi$
$151$	1017.54	0.548387	0.274193	+	0.961675i	$0.411589\pi$
$152$	−1424.15	−0.759959
$153$	310.488	0.164062
$154$	0	0
$155$	321.175	0.166435
$156$	297.715	0.152797
$157$	−65.0888	−0.0330870	−0.0165435	−	0.999863i	$-0.505266\pi$
$157$	−65.0888	−0.0330870	−0.0165435	+	0.999863i	$0.505266\pi$
$158$	−2524.27	−1.27101
$159$	−633.093	−0.315771
$160$	−715.293	−0.353431
$161$	1872.79	0.916749
$162$	3063.75	1.48587
$163$	54.5344	0.0262053	0.0131027	−	0.999914i	$-0.495829\pi$
$163$	54.5344	0.0262053	0.0131027	+	0.999914i	$0.495829\pi$
$164$	843.766	0.401751
$165$	0	0
$166$	−1056.12	−0.493802
$167$	−2286.27	−1.05938	−0.529690	−	0.848191i	$-0.677692\pi$
$167$	−2286.27	−1.05938	−0.529690	+	0.848191i	$0.677692\pi$
$168$	2479.31	1.13859
$169$	169.000	0.0769231
$170$	528.708	0.238530
$171$	−894.616	−0.400076
$172$	210.200	0.0931839
$173$	−2140.26	−0.940582	−0.470291	−	0.882511i	$-0.655851\pi$
$173$	−2140.26	−0.940582	−0.470291	+	0.882511i	$0.655851\pi$
$174$	−2845.80	−1.23988
$175$	3013.44	1.30169
$176$	0	0
$177$	−596.372	−0.253255
$178$	−4304.54	−1.81258
$179$	1966.28	0.821041	0.410521	−	0.911851i	$-0.365347\pi$
$179$	1966.28	0.821041	0.410521	+	0.911851i	$0.365347\pi$
$180$	−154.326	−0.0639044
$181$	2877.71	1.18176	0.590879	−	0.806760i	$-0.298781\pi$
$181$	2877.71	1.18176	0.590879	+	0.806760i	$0.298781\pi$
$182$	−1282.92	−0.522508
$183$	527.404	0.213043
$184$	−938.353	−0.375958
$185$	556.051	0.220982
$186$	−1480.38	−0.583586
$187$	0	0
$188$	755.816	0.293210
$189$	−3096.02	−1.19155
$190$	−1523.37	−0.581669
$191$	3289.20	1.24607	0.623033	−	0.782196i	$-0.285900\pi$
$191$	3289.20	1.24607	0.623033	+	0.782196i	$0.285900\pi$
$192$	−543.315	−0.204221
$193$	−1911.10	−0.712766	−0.356383	−	0.934340i	$-0.615990\pi$
$193$	−1911.10	−0.712766	−0.356383	+	0.934340i	$0.615990\pi$
$194$	−5980.24	−2.21318
$195$	−349.356	−0.128297
$196$	1836.10	0.669134
$197$	3166.19	1.14508	0.572542	−	0.819875i	$-0.305957\pi$
$197$	3166.19	1.14508	0.572542	+	0.819875i	$0.305957\pi$
$198$	0	0
$199$	−3814.45	−1.35879	−0.679395	−	0.733773i	$-0.737757\pi$
$199$	−3814.45	−1.35879	−0.679395	+	0.733773i	$0.737757\pi$
$200$	−1509.87	−0.533820
$201$	5856.82	2.05526
$202$	−678.087	−0.236188
$203$	3959.67	1.36904
$204$	−786.872	−0.270059
$205$	−990.124	−0.337333
$206$	−1976.13	−0.668365
$207$	−589.450	−0.197921
$208$	1039.55	0.346539
$209$	0	0
$210$	2652.05	0.871471
$211$	−2858.69	−0.932702	−0.466351	−	0.884600i	$-0.654432\pi$
$211$	−2858.69	−0.932702	−0.466351	+	0.884600i	$0.654432\pi$
$212$	402.330	0.130340
$213$	−6504.45	−2.09238
$214$	−1210.05	−0.386531
$215$	−246.661	−0.0782426
$216$	1551.25	0.488653
$217$	2059.82	0.644375
$218$	4843.71	1.50485
$219$	5692.39	1.75642
$220$	0	0
$221$	−446.673	−0.135957
$222$	−2562.99	−0.774850
$223$	−3146.08	−0.944740	−0.472370	−	0.881400i	$-0.656601\pi$
$223$	−3146.08	−0.944740	−0.472370	+	0.881400i	$0.656601\pi$
$224$	−4587.45	−1.36836
$225$	−948.465	−0.281027
$226$	−6009.12	−1.76868
$227$	−2662.12	−0.778375	−0.389188	−	0.921159i	$-0.627244\pi$
$227$	−2662.12	−0.778375	−0.389188	+	0.921159i	$0.627244\pi$
$228$	2267.23	0.658556
$229$	3450.25	0.995627	0.497814	−	0.867284i	$-0.334136\pi$
$229$	3450.25	0.995627	0.497814	+	0.867284i	$0.334136\pi$
$230$	−1003.73	−0.287757
$231$	0	0
$232$	−1983.98	−0.561441
$233$	−2106.20	−0.592198	−0.296099	−	0.955157i	$-0.595686\pi$
$233$	−2106.20	−0.592198	−0.296099	+	0.955157i	$0.595686\pi$
$234$	403.793	0.112807
$235$	−886.918	−0.246196
$236$	378.994	0.104536
$237$	−4408.51	−1.20829
$238$	3390.81	0.923501
$239$	−5734.05	−1.55190	−0.775951	−	0.630793i	$-0.782730\pi$
$239$	−5734.05	−1.55190	−0.775951	+	0.630793i	$0.782730\pi$
$240$	−2148.96	−0.577979
$241$	4502.12	1.20335	0.601675	−	0.798741i	$-0.294500\pi$
$241$	4502.12	1.20335	0.601675	+	0.798741i	$0.294500\pi$
$242$	0	0
$243$	2439.11	0.643904
$244$	−335.165	−0.0879374
$245$	−2154.59	−0.561844
$246$	4563.76	1.18282
$247$	1287.01	0.331539
$248$	−1032.06	−0.264258
$249$	−1844.47	−0.469431
$250$	−3538.51	−0.895181
$251$	−3568.48	−0.897372	−0.448686	−	0.893690i	$-0.648108\pi$
$251$	−3568.48	−0.897372	−0.448686	+	0.893690i	$0.648108\pi$
$252$	−989.754	−0.247415
$253$	0	0
$254$	628.408	0.155235
$255$	923.360	0.226757
$256$	4739.03	1.15699
$257$	−5722.45	−1.38894	−0.694468	−	0.719524i	$-0.744360\pi$
$257$	−5722.45	−1.38894	−0.694468	+	0.719524i	$0.744360\pi$
$258$	1136.93	0.274349
$259$	3566.17	0.855563
$260$	222.016	0.0529571
$261$	−1246.28	−0.295567
$262$	2186.85	0.515664
$263$	617.733	0.144833	0.0724165	−	0.997374i	$-0.476929\pi$
$263$	617.733	0.144833	0.0724165	+	0.997374i	$0.476929\pi$
$264$	0	0
$265$	−472.118	−0.109441
$266$	−9769.99	−2.25202
$267$	−7517.65	−1.72312
$268$	−3722.01	−0.848349
$269$	−4982.05	−1.12922	−0.564612	−	0.825357i	$-0.690974\pi$
$269$	−4982.05	−1.12922	−0.564612	+	0.825357i	$0.690974\pi$
$270$	1659.33	0.374013
$271$	−2261.89	−0.507011	−0.253505	−	0.967334i	$-0.581584\pi$
$271$	−2261.89	−0.507011	−0.253505	+	0.967334i	$0.581584\pi$
$272$	−2747.58	−0.612487
$273$	−2240.56	−0.496720
$274$	−9632.91	−2.12389
$275$	0	0
$276$	1493.85	0.325793
$277$	−2584.81	−0.560671	−0.280336	−	0.959902i	$-0.590446\pi$
$277$	−2584.81	−0.560671	−0.280336	+	0.959902i	$0.590446\pi$
$278$	2795.11	0.603021
$279$	−648.316	−0.139117
$280$	1848.90	0.394617
$281$	1313.07	0.278758	0.139379	−	0.990239i	$-0.455489\pi$
$281$	1313.07	0.278758	0.139379	+	0.990239i	$0.455489\pi$
$282$	4088.05	0.863262
$283$	3696.34	0.776413	0.388206	−	0.921572i	$-0.373095\pi$
$283$	3696.34	0.776413	0.388206	+	0.921572i	$0.373095\pi$
$284$	4133.57	0.863671
$285$	−2660.49	−0.552962
$286$	0	0
$287$	−6350.05	−1.30603
$288$	1443.87	0.295421
$289$	−3732.43	−0.759705
$290$	−2122.21	−0.429725
$291$	−10444.2	−2.10395
$292$	−3617.51	−0.724997
$293$	−4682.18	−0.933571	−0.466785	−	0.884371i	$-0.654588\pi$
$293$	−4682.18	−0.933571	−0.466785	+	0.884371i	$0.654588\pi$
$294$	9931.11	1.97005
$295$	−444.734	−0.0877743
$296$	−1786.81	−0.350866
$297$	0	0
$298$	−10450.2	−2.03142
$299$	847.991	0.164015
$300$	2403.70	0.462592
$301$	−1581.93	−0.302927
$302$	−3497.58	−0.666435
$303$	−1184.24	−0.224531
$304$	7916.64	1.49359
$305$	393.302	0.0738373
$306$	−1067.24	−0.199379
$307$	−5304.39	−0.986115	−0.493058	−	0.869997i	$-0.664121\pi$
$307$	−5304.39	−0.986115	−0.493058	+	0.869997i	$0.664121\pi$
$308$	0	0
$309$	−3451.20	−0.635378
$310$	−1103.97	−0.202262
$311$	4937.27	0.900215	0.450107	−	0.892974i	$-0.351386\pi$
$311$	4937.27	0.900215	0.450107	+	0.892974i	$0.351386\pi$
$312$	1122.62	0.203705
$313$	5167.06	0.933098	0.466549	−	0.884495i	$-0.345497\pi$
$313$	5167.06	0.933098	0.466549	+	0.884495i	$0.345497\pi$
$314$	223.729	0.0402094
$315$	1161.43	0.207744
$316$	2801.61	0.498743
$317$	10736.7	1.90230	0.951152	−	0.308722i	$-0.0999014\pi$
$317$	10736.7	1.90230	0.951152	+	0.308722i	$0.0999014\pi$
$318$	2176.12	0.383745
$319$	0	0
$320$	−405.168	−0.0707799
$321$	−2113.30	−0.367454
$322$	−6437.31	−1.11409
$323$	−3401.60	−0.585975
$324$	−3400.35	−0.583050
$325$	1364.47	0.232884
$326$	−187.450	−0.0318464
$327$	8459.29	1.43058
$328$	3181.66	0.535603
$329$	−5688.14	−0.953184
$330$	0	0
$331$	4559.92	0.757208	0.378604	−	0.925559i	$-0.376404\pi$
$331$	4559.92	0.757208	0.378604	+	0.925559i	$0.376404\pi$
$332$	1172.16	0.193767
$333$	−1122.43	−0.184711
$334$	7858.55	1.28743
$335$	4367.61	0.712323
$336$	−13782.1	−2.23773
$337$	7420.22	1.19942	0.599711	−	0.800217i	$-0.295282\pi$
$337$	7420.22	1.19942	0.599711	+	0.800217i	$0.295282\pi$
$338$	−580.901	−0.0934818
$339$	−10494.6	−1.68138
$340$	−586.795	−0.0935983
$341$	0	0
$342$	3075.05	0.486198
$343$	−3970.51	−0.625035
$344$	792.620	0.124230
$345$	−1752.96	−0.273555
$346$	7356.67	1.14306
$347$	−7620.71	−1.17897	−0.589483	−	0.807781i	$-0.700669\pi$
$347$	−7620.71	−1.17897	−0.589483	+	0.807781i	$0.700669\pi$
$348$	3158.46	0.486527
$349$	9140.85	1.40200	0.701001	−	0.713161i	$-0.252737\pi$
$349$	9140.85	1.40200	0.701001	+	0.713161i	$0.252737\pi$
$350$	−10358.1	−1.58189
$351$	−1401.86	−0.213179
$352$	0	0
$353$	−11042.8	−1.66501	−0.832507	−	0.554015i	$-0.813095\pi$
$353$	−11042.8	−1.66501	−0.832507	+	0.554015i	$0.813095\pi$
$354$	2049.90	0.307771
$355$	−4850.57	−0.725188
$356$	4777.47	0.711251
$357$	5921.86	0.877922
$358$	−6758.65	−0.997782
$359$	−1017.88	−0.149643	−0.0748214	−	0.997197i	$-0.523839\pi$
$359$	−1017.88	−0.149643	−0.0748214	+	0.997197i	$0.523839\pi$
$360$	−581.931	−0.0851957
$361$	2942.09	0.428938
$362$	−9891.50	−1.43615
$363$	0	0
$364$	1423.87	0.205031
$365$	4245.00	0.608749
$366$	−1812.84	−0.258903
$367$	−11521.2	−1.63870	−0.819350	−	0.573293i	$-0.805666\pi$
$367$	−11521.2	−1.63870	−0.819350	+	0.573293i	$0.805666\pi$
$368$	5216.17	0.738891
$369$	1998.64	0.281965
$370$	−1911.30	−0.268551
$371$	−3027.87	−0.423718
$372$	1643.03	0.228997
$373$	1574.76	0.218601	0.109301	−	0.994009i	$-0.465139\pi$
$373$	1574.76	0.218601	0.109301	+	0.994009i	$0.465139\pi$
$374$	0	0
$375$	−6179.83	−0.851000
$376$	2850.02	0.390900
$377$	1792.92	0.244934
$378$	10641.9	1.44804
$379$	−11138.9	−1.50968	−0.754839	−	0.655910i	$-0.772285\pi$
$379$	−11138.9	−1.50968	−0.754839	+	0.655910i	$0.772285\pi$
$380$	1690.74	0.228245
$381$	1097.48	0.147574
$382$	−11305.9	−1.51430
$383$	3751.32	0.500479	0.250240	−	0.968184i	$-0.419491\pi$
$383$	3751.32	0.500479	0.250240	+	0.968184i	$0.419491\pi$
$384$	9540.99	1.26793
$385$	0	0
$386$	6568.99	0.866199
$387$	497.905	0.0654003
$388$	6637.27	0.868444
$389$	8097.34	1.05540	0.527701	−	0.849430i	$-0.323054\pi$
$389$	8097.34	1.05540	0.527701	+	0.849430i	$0.323054\pi$
$390$	1200.84	0.155915
$391$	−2241.27	−0.289887
$392$	6923.55	0.892072
$393$	3819.22	0.490214
$394$	−10883.1	−1.39158
$395$	−3287.57	−0.418773
$396$	0	0
$397$	−6781.37	−0.857297	−0.428649	−	0.903471i	$-0.641010\pi$
$397$	−6781.37	−0.857297	−0.428649	+	0.903471i	$0.641010\pi$
$398$	13111.3	1.65129
$399$	−17062.8	−2.14087
$400$	8393.17	1.04915
$401$	−11839.9	−1.47446	−0.737230	−	0.675642i	$-0.763867\pi$
$401$	−11839.9	−1.47446	−0.737230	+	0.675642i	$0.763867\pi$
$402$	−20131.5	−2.49769
$403$	932.676	0.115285
$404$	752.587	0.0926797
$405$	3990.17	0.489563
$406$	−13610.5	−1.66374
$407$	0	0
$408$	−2967.12	−0.360035
$409$	−11353.6	−1.37262	−0.686310	−	0.727309i	$-0.740771\pi$
$409$	−11353.6	−1.37262	−0.686310	+	0.727309i	$0.740771\pi$
$410$	3403.34	0.409949
$411$	−16823.4	−2.01907
$412$	2193.24	0.262265
$413$	−2852.25	−0.339831
$414$	2026.11	0.240526
$415$	−1375.48	−0.162698
$416$	−2077.18	−0.244812
$417$	4881.52	0.573259
$418$	0	0
$419$	4443.36	0.518073	0.259036	−	0.965868i	$-0.416595\pi$
$419$	4443.36	0.518073	0.259036	+	0.965868i	$0.416595\pi$
$420$	−2943.42	−0.341963
$421$	3850.51	0.445754	0.222877	−	0.974847i	$-0.428455\pi$
$421$	3850.51	0.445754	0.222877	+	0.974847i	$0.428455\pi$
$422$	9826.12	1.13348
$423$	1790.31	0.205787
$424$	1517.10	0.173766
$425$	−3606.35	−0.411609
$426$	22357.6	2.54280
$427$	2522.40	0.285872
$428$	1343.00	0.151674
$429$	0	0
$430$	847.845	0.0950854
$431$	−3538.60	−0.395472	−0.197736	−	0.980255i	$-0.563359\pi$
$431$	−3538.60	−0.395472	−0.197736	+	0.980255i	$0.563359\pi$
$432$	−8623.16	−0.960375
$433$	−541.488	−0.0600976	−0.0300488	−	0.999548i	$-0.509566\pi$
$433$	−541.488	−0.0600976	−0.0300488	+	0.999548i	$0.509566\pi$
$434$	−7080.18	−0.783086
$435$	−3706.32	−0.408516
$436$	−5375.88	−0.590500
$437$	6457.81	0.706908
$438$	−19566.4	−2.13452
$439$	15849.4	1.72312	0.861561	−	0.507653i	$-0.169487\pi$
$439$	15849.4	1.72312	0.861561	+	0.507653i	$0.169487\pi$
$440$	0	0
$441$	4349.21	0.469626
$442$	1535.34	0.165223
$443$	−5637.24	−0.604590	−0.302295	−	0.953214i	$-0.597753\pi$
$443$	−5637.24	−0.604590	−0.302295	+	0.953214i	$0.597753\pi$
$444$	2844.58	0.304049
$445$	−5606.15	−0.597207
$446$	10814.0	1.14811
$447$	−18250.7	−1.93116
$448$	−2598.50	−0.274034
$449$	15477.5	1.62679	0.813393	−	0.581715i	$-0.197618\pi$
$449$	15477.5	1.62679	0.813393	+	0.581715i	$0.197618\pi$
$450$	3260.14	0.341521
$451$	0	0
$452$	6669.33	0.694024
$453$	−6108.35	−0.633543
$454$	9150.47	0.945931
$455$	−1670.85	−0.172156
$456$	8549.22	0.877969
$457$	18979.7	1.94274	0.971372	−	0.237564i	$-0.0763491\pi$
$457$	18979.7	1.94274	0.971372	+	0.237564i	$0.0763491\pi$
$458$	−11859.5	−1.20995
$459$	3705.17	0.376782
$460$	1114.01	0.112915
$461$	1983.70	0.200413	0.100206	−	0.994967i	$-0.468050\pi$
$461$	1983.70	0.200413	0.100206	+	0.994967i	$0.468050\pi$
$462$	0	0
$463$	−5593.59	−0.561461	−0.280730	−	0.959787i	$-0.590577\pi$
$463$	−5593.59	−0.561461	−0.280730	+	0.959787i	$0.590577\pi$
$464$	11028.6	1.10343
$465$	−1928.02	−0.192279
$466$	7239.63	0.719676
$467$	3104.32	0.307603	0.153802	−	0.988102i	$-0.450848\pi$
$467$	3104.32	0.307603	0.153802	+	0.988102i	$0.450848\pi$
$468$	−448.156	−0.0442650
$469$	28011.2	2.75786
$470$	3048.59	0.299193
$471$	390.731	0.0382249
$472$	1429.11	0.139364
$473$	0	0
$474$	15153.3	1.46839
$475$	10391.0	1.00373
$476$	−3763.34	−0.362379
$477$	953.006	0.0914783
$478$	19709.6	1.88597
$479$	4510.25	0.430226	0.215113	−	0.976589i	$-0.430988\pi$
$479$	4510.25	0.430226	0.215113	+	0.976589i	$0.430988\pi$
$480$	4293.93	0.408313
$481$	1614.74	0.153069
$482$	−15475.1	−1.46239
$483$	−11242.4	−1.05911
$484$	0	0
$485$	−7788.55	−0.729196
$486$	−8383.91	−0.782514
$487$	−5948.91	−0.553534	−0.276767	−	0.960937i	$-0.589263\pi$
$487$	−5948.91	−0.553534	−0.276767	+	0.960937i	$0.589263\pi$
$488$	−1263.83	−0.117236
$489$	−327.372	−0.0302746
$490$	7405.94	0.682788
$491$	−9383.39	−0.862457	−0.431228	−	0.902243i	$-0.641920\pi$
$491$	−9383.39	−0.862457	−0.431228	+	0.902243i	$0.641920\pi$
$492$	−5065.16	−0.464137
$493$	−4738.75	−0.432906
$494$	−4423.81	−0.402908
$495$	0	0
$496$	5737.09	0.519360
$497$	−31108.6	−2.80767
$498$	6339.96	0.570482
$499$	20200.7	1.81224	0.906120	−	0.423021i	$-0.139030\pi$
$499$	20200.7	1.81224	0.906120	+	0.423021i	$0.139030\pi$
$500$	3927.28	0.351267
$501$	13724.5	1.22389
$502$	12265.9	1.09054
$503$	−13833.5	−1.22626	−0.613128	−	0.789983i	$-0.710089\pi$
$503$	−13833.5	−1.22626	−0.613128	+	0.789983i	$0.710089\pi$
$504$	−3732.15	−0.329847
$505$	−883.128	−0.0778192
$506$	0	0
$507$	−1014.51	−0.0888681
$508$	−697.449	−0.0609140
$509$	−3954.04	−0.344322	−0.172161	−	0.985069i	$-0.555075\pi$
$509$	−3954.04	−0.344322	−0.172161	+	0.985069i	$0.555075\pi$
$510$	−3173.85	−0.275570
$511$	27224.8	2.35686
$512$	−3574.52	−0.308541
$513$	−10675.8	−0.918806
$514$	19669.7	1.68792
$515$	−2573.67	−0.220212
$516$	−1261.84	−0.107654
$517$	0	0
$518$	−12257.9	−1.03973
$519$	12848.0	1.08664
$520$	837.174	0.0706009
$521$	11709.7	0.984667	0.492334	−	0.870407i	$-0.336144\pi$
$521$	11709.7	0.984667	0.492334	+	0.870407i	$0.336144\pi$
$522$	4283.84	0.359192
$523$	−10231.2	−0.855408	−0.427704	−	0.903919i	$-0.640677\pi$
$523$	−10231.2	−0.855408	−0.427704	+	0.903919i	$0.640677\pi$
$524$	−2427.11	−0.202345
$525$	−18089.8	−1.50382
$526$	−2123.33	−0.176010
$527$	−2465.09	−0.203759
$528$	0	0
$529$	−7912.04	−0.650287
$530$	1622.80	0.133000
$531$	897.730	0.0733675
$532$	10843.4	0.883685
$533$	−2875.27	−0.233662
$534$	25840.3	2.09404
$535$	−1575.95	−0.127354
$536$	−14034.9	−1.13100
$537$	−11803.6	−0.948537
$538$	17124.7	1.37230
$539$	0	0
$540$	−1841.63	−0.146762
$541$	20820.0	1.65457	0.827284	−	0.561784i	$-0.189885\pi$
$541$	20820.0	1.65457	0.827284	+	0.561784i	$0.189885\pi$
$542$	7774.76	0.616152
$543$	−17275.0	−1.36527
$544$	5490.05	0.432691
$545$	6308.36	0.495818
$546$	7701.43	0.603646
$547$	2503.44	0.195684	0.0978422	−	0.995202i	$-0.468806\pi$
$547$	2503.44	0.195684	0.0978422	+	0.995202i	$0.468806\pi$
$548$	10691.3	0.833408
$549$	−793.910	−0.0617181
$550$	0	0
$551$	13653.9	1.05567
$552$	5632.97	0.434339
$553$	−21084.4	−1.62134
$554$	8884.72	0.681364
$555$	−3337.99	−0.255297
$556$	−3102.20	−0.236624
$557$	16574.8	1.26086	0.630429	−	0.776247i	$-0.282879\pi$
$557$	16574.8	1.26086	0.630429	+	0.776247i	$0.282879\pi$
$558$	2228.45	0.169064
$559$	−716.292	−0.0541967
$560$	−10277.8	−0.775563
$561$	0	0
$562$	−4513.38	−0.338764
$563$	−92.2880	−0.00690848	−0.00345424	−	0.999994i	$-0.501100\pi$
$563$	−92.2880	−0.00690848	−0.00345424	+	0.999994i	$0.501100\pi$
$564$	−4537.19	−0.338742
$565$	−7826.17	−0.582742
$566$	−12705.4	−0.943546
$567$	25590.5	1.89541
$568$	15586.8	1.15142
$569$	6433.41	0.473994	0.236997	−	0.971510i	$-0.423837\pi$
$569$	6433.41	0.473994	0.236997	+	0.971510i	$0.423837\pi$
$570$	9144.88	0.671994
$571$	21605.3	1.58346	0.791730	−	0.610871i	$-0.209181\pi$
$571$	21605.3	1.58346	0.791730	+	0.610871i	$0.209181\pi$
$572$	0	0
$573$	−19745.2	−1.43956
$574$	21826.9	1.58717
$575$	6846.52	0.496556
$576$	817.862	0.0591625
$577$	−6901.75	−0.497961	−0.248981	−	0.968508i	$-0.580096\pi$
$577$	−6901.75	−0.497961	−0.248981	+	0.968508i	$0.580096\pi$
$578$	12829.4	0.923242
$579$	11472.4	0.823449
$580$	2355.37	0.168623
$581$	−8821.46	−0.629907
$582$	35899.6	2.55685
$583$	0	0
$584$	−13640.9	−0.966546
$585$	525.892	0.0371674
$586$	16094.0	1.13453
$587$	843.264	0.0592934	0.0296467	−	0.999560i	$-0.490562\pi$
$587$	843.264	0.0592934	0.0296467	+	0.999560i	$0.490562\pi$
$588$	−11022.2	−0.773041
$589$	7102.72	0.496880
$590$	1528.68	0.106669
$591$	−19006.7	−1.32290
$592$	9932.63	0.689576
$593$	−2549.24	−0.176534	−0.0882669	−	0.996097i	$-0.528133\pi$
$593$	−2549.24	−0.176534	−0.0882669	+	0.996097i	$0.528133\pi$
$594$	0	0
$595$	4416.12	0.304275
$596$	11598.3	0.797123
$597$	22898.3	1.56979
$598$	−2914.79	−0.199322
$599$	−2139.34	−0.145929	−0.0729643	−	0.997335i	$-0.523246\pi$
$599$	−2139.34	−0.145929	−0.0729643	+	0.997335i	$0.523246\pi$
$600$	9063.82	0.616715
$601$	6010.33	0.407931	0.203966	−	0.978978i	$-0.434617\pi$
$601$	6010.33	0.407931	0.203966	+	0.978978i	$0.434617\pi$
$602$	5437.56	0.368137
$603$	−8816.37	−0.595407
$604$	3881.85	0.261507
$605$	0	0
$606$	4070.58	0.272865
$607$	13936.5	0.931905	0.465952	−	0.884810i	$-0.345712\pi$
$607$	13936.5	0.931905	0.465952	+	0.884810i	$0.345712\pi$
$608$	−15818.6	−1.05514
$609$	−23770.1	−1.58163
$610$	−1351.89	−0.0897319
$611$	−2575.57	−0.170534
$612$	1184.49	0.0782357
$613$	−28896.4	−1.90394	−0.951969	−	0.306196i	$-0.900944\pi$
$613$	−28896.4	−1.90394	−0.951969	+	0.306196i	$0.900944\pi$
$614$	18232.7	1.19839
$615$	5943.75	0.389716
$616$	0	0
$617$	12635.6	0.824455	0.412227	−	0.911081i	$-0.364751\pi$
$617$	12635.6	0.824455	0.412227	+	0.911081i	$0.364751\pi$
$618$	11862.8	0.772152
$619$	6763.28	0.439159	0.219579	−	0.975595i	$-0.429531\pi$
$619$	6763.28	0.439159	0.219579	+	0.975595i	$0.429531\pi$
$620$	1225.26	0.0793671
$621$	−7034.13	−0.454541
$622$	−16970.8	−1.09400
$623$	−35954.4	−2.31217
$624$	−6240.49	−0.400352
$625$	8511.45	0.544733
$626$	−17760.7	−1.13396
$627$	0	0
$628$	−248.309	−0.0157781
$629$	−4267.82	−0.270539
$630$	−3992.18	−0.252464
$631$	−5430.03	−0.342577	−0.171289	−	0.985221i	$-0.554793\pi$
$631$	−5430.03	−0.342577	−0.171289	+	0.985221i	$0.554793\pi$
$632$	10564.3	0.664911
$633$	17160.8	1.07754
$634$	−36904.9	−2.31180
$635$	818.427	0.0511469
$636$	−2415.21	−0.150580
$637$	−6256.83	−0.389175
$638$	0	0
$639$	9791.26	0.606160
$640$	7115.02	0.439447
$641$	17648.8	1.08750	0.543748	−	0.839249i	$-0.317005\pi$
$641$	17648.8	1.08750	0.543748	+	0.839249i	$0.317005\pi$
$642$	7264.00	0.446554
$643$	−23999.8	−1.47194	−0.735971	−	0.677013i	$-0.763274\pi$
$643$	−23999.8	−1.47194	−0.735971	+	0.677013i	$0.763274\pi$
$644$	7144.56	0.437167
$645$	1480.72	0.0903925
$646$	11692.3	0.712115
$647$	−23641.4	−1.43654	−0.718268	−	0.695767i	$-0.755065\pi$
$647$	−23641.4	−1.43654	−0.718268	+	0.695767i	$0.755065\pi$
$648$	−12822.0	−0.777307
$649$	0	0
$650$	−4690.09	−0.283016
$651$	−12365.2	−0.744437
$652$	208.045	0.0124964
$653$	−23080.4	−1.38316	−0.691580	−	0.722299i	$-0.743085\pi$
$653$	−23080.4	−1.38316	−0.691580	+	0.722299i	$0.743085\pi$
$654$	−29077.0	−1.73853
$655$	2848.11	0.169901
$656$	−17686.4	−1.05265
$657$	−8568.86	−0.508833
$658$	19551.8	1.15837
$659$	−8042.59	−0.475409	−0.237705	−	0.971337i	$-0.576395\pi$
$659$	−8042.59	−0.475409	−0.237705	+	0.971337i	$0.576395\pi$
$660$	0	0
$661$	4545.84	0.267493	0.133746	−	0.991016i	$-0.457299\pi$
$661$	4545.84	0.267493	0.133746	+	0.991016i	$0.457299\pi$
$662$	−15673.8	−0.920208
$663$	2681.39	0.157069
$664$	4419.95	0.258325
$665$	−12724.3	−0.741993
$666$	3858.12	0.224473
$667$	8996.34	0.522248
$668$	−8721.95	−0.505183
$669$	18886.0	1.09144
$670$	−15012.7	−0.865661
$671$	0	0
$672$	27538.6	1.58084
$673$	−33036.3	−1.89221	−0.946105	−	0.323861i	$-0.895019\pi$
$673$	−33036.3	−1.89221	−0.946105	+	0.323861i	$0.895019\pi$
$674$	−25505.4	−1.45761
$675$	−11318.4	−0.645400
$676$	644.723	0.0366820
$677$	−22796.3	−1.29414	−0.647070	−	0.762431i	$-0.724006\pi$
$677$	−22796.3	−1.29414	−0.647070	+	0.762431i	$0.724006\pi$
$678$	36073.0	2.04333
$679$	−49951.0	−2.82319
$680$	−2212.68	−0.124783
$681$	15980.8	0.899245
$682$	0	0
$683$	35515.6	1.98970	0.994852	−	0.101336i	$-0.0323117\pi$
$683$	35515.6	1.98970	0.994852	+	0.101336i	$0.0323117\pi$
$684$	−3412.90	−0.190783
$685$	−12545.7	−0.699778
$686$	13647.8	0.759583
$687$	−20712.0	−1.15023
$688$	−4406.07	−0.244156
$689$	−1371.01	−0.0758073
$690$	6025.44	0.332441
$691$	28925.9	1.59246	0.796232	−	0.604992i	$-0.206824\pi$
$691$	28925.9	1.59246	0.796232	+	0.604992i	$0.206824\pi$
$692$	−8164.93	−0.448532
$693$	0	0
$694$	26194.6	1.43275
$695$	3640.30	0.198683
$696$	11909.9	0.648625
$697$	7599.44	0.412983
$698$	−31419.7	−1.70380
$699$	12643.6	0.684157
$700$	11496.1	0.620730
$701$	−5353.68	−0.288453	−0.144227	−	0.989545i	$-0.546069\pi$
$701$	−5353.68	−0.288453	−0.144227	+	0.989545i	$0.546069\pi$
$702$	4818.61	0.259069
$703$	12297.0	0.659728
$704$	0	0
$705$	5324.20	0.284427
$706$	37957.3	2.02343
$707$	−5663.84	−0.301288
$708$	−2275.12	−0.120769
$709$	−7354.36	−0.389561	−0.194780	−	0.980847i	$-0.562399\pi$
$709$	−7354.36	−0.389561	−0.194780	+	0.980847i	$0.562399\pi$
$710$	16672.8	0.881294
$711$	6636.21	0.350038
$712$	18014.8	0.948221
$713$	4679.89	0.245811
$714$	−20355.1	−1.06691
$715$	0	0
$716$	7501.21	0.391527
$717$	34421.7	1.79289
$718$	3498.75	0.181856
$719$	31589.8	1.63853	0.819264	−	0.573416i	$-0.194382\pi$
$719$	31589.8	1.63853	0.819264	+	0.573416i	$0.194382\pi$
$720$	3234.87	0.167440
$721$	−16505.9	−0.852584
$722$	−10112.8	−0.521273
$723$	−27026.4	−1.39021
$724$	10978.3	0.563541
$725$	14475.7	0.741537
$726$	0	0
$727$	19891.0	1.01474	0.507370	−	0.861728i	$-0.330618\pi$
$727$	19891.0	1.01474	0.507370	+	0.861728i	$0.330618\pi$
$728$	5369.12	0.273342
$729$	9423.78	0.478777
$730$	−14591.3	−0.739791
$731$	1893.18	0.0957893
$732$	2012.01	0.101593
$733$	−32196.7	−1.62239	−0.811196	−	0.584774i	$-0.801183\pi$
$733$	−32196.7	−1.62239	−0.811196	+	0.584774i	$0.801183\pi$
$734$	39601.7	1.99145
$735$	12934.1	0.649090
$736$	−10422.6	−0.521989
$737$	0	0
$738$	−6869.90	−0.342662
$739$	−17370.2	−0.864645	−0.432322	−	0.901719i	$-0.642306\pi$
$739$	−17370.2	−0.864645	−0.432322	+	0.901719i	$0.642306\pi$
$740$	2121.29	0.105379
$741$	−7725.95	−0.383023
$742$	10407.7	0.514929
$743$	10683.9	0.527531	0.263765	−	0.964587i	$-0.415036\pi$
$743$	10683.9	0.527531	0.263765	+	0.964587i	$0.415036\pi$
$744$	6195.51	0.305293
$745$	−13610.1	−0.669310
$746$	−5412.91	−0.265658
$747$	2776.51	0.135993
$748$	0	0
$749$	−10107.2	−0.493069
$750$	21241.8	1.03419
$751$	564.722	0.0274394	0.0137197	−	0.999906i	$-0.495633\pi$
$751$	564.722	0.0274394	0.0137197	+	0.999906i	$0.495633\pi$
$752$	−15842.9	−0.768257
$753$	21421.7	1.03672
$754$	−6162.78	−0.297660
$755$	−4555.19	−0.219577
$756$	−11811.1	−0.568208
$757$	35979.1	1.72746	0.863728	−	0.503959i	$-0.168124\pi$
$757$	35979.1	1.72746	0.863728	+	0.503959i	$0.168124\pi$
$758$	38287.6	1.83466
$759$	0	0
$760$	6375.43	0.304291
$761$	24297.9	1.15742	0.578712	−	0.815532i	$-0.303556\pi$
$761$	24297.9	1.15742	0.578712	+	0.815532i	$0.303556\pi$
$762$	−3772.36	−0.179341
$763$	40458.0	1.91963
$764$	12548.1	0.594207
$765$	−1389.95	−0.0656912
$766$	−12894.4	−0.608214
$767$	−1291.49	−0.0607990
$768$	−28448.6	−1.33665
$769$	20196.8	0.947094	0.473547	−	0.880768i	$-0.342973\pi$
$769$	20196.8	0.947094	0.473547	+	0.880768i	$0.342973\pi$
$770$	0	0
$771$	34352.1	1.60462
$772$	−7290.71	−0.339894
$773$	33730.5	1.56947	0.784736	−	0.619830i	$-0.212799\pi$
$773$	33730.5	1.56947	0.784736	+	0.619830i	$0.212799\pi$
$774$	−1711.44	−0.0794786
$775$	7530.25	0.349025
$776$	25027.7	1.15779
$777$	−21407.8	−0.988419
$778$	−27832.9	−1.28259
$779$	−21896.4	−1.00709
$780$	−1332.77	−0.0611805
$781$	0	0
$782$	7703.88	0.352289
$783$	−14872.4	−0.678794
$784$	−38487.1	−1.75324
$785$	291.380	0.0132482
$786$	−13127.7	−0.595739
$787$	−19747.0	−0.894414	−0.447207	−	0.894431i	$-0.647581\pi$
$787$	−19747.0	−0.894414	−0.447207	+	0.894431i	$0.647581\pi$
$788$	12078.8	0.546052
$789$	−3708.28	−0.167323
$790$	11300.3	0.508920
$791$	−50192.2	−2.25617
$792$	0	0
$793$	1142.13	0.0511453
$794$	23309.5	1.04184
$795$	2834.14	0.126436
$796$	−14551.9	−0.647961
$797$	−1302.77	−0.0579003	−0.0289502	−	0.999581i	$-0.509216\pi$
$797$	−1302.77	−0.0579003	−0.0289502	+	0.999581i	$0.509216\pi$
$798$	58649.6	2.60172
$799$	6807.31	0.301408
$800$	−16770.7	−0.741169
$801$	11316.5	0.499185
$802$	40697.3	1.79186
$803$	0	0
$804$	22343.3	0.980086
$805$	−8383.84	−0.367070
$806$	−3205.87	−0.140102
$807$	29907.5	1.30458
$808$	2837.84	0.123558
$809$	−31410.6	−1.36507	−0.682533	−	0.730855i	$-0.739122\pi$
$809$	−31410.6	−1.36507	−0.682533	+	0.730855i	$0.739122\pi$
$810$	−13715.3	−0.594948
$811$	−27836.5	−1.20527	−0.602633	−	0.798018i	$-0.705882\pi$
$811$	−27836.5	−1.20527	−0.602633	+	0.798018i	$0.705882\pi$
$812$	15105.9	0.652847
$813$	13578.2	0.585742
$814$	0	0
$815$	−244.132	−0.0104927
$816$	16493.8	0.707597
$817$	−5454.87	−0.233588
$818$	39025.7	1.66810
$819$	3372.75	0.143899
$820$	−3777.25	−0.160863
$821$	690.277	0.0293433	0.0146716	−	0.999892i	$-0.495330\pi$
$821$	690.277	0.0293433	0.0146716	+	0.999892i	$0.495330\pi$
$822$	57826.8	2.45370
$823$	−7759.50	−0.328650	−0.164325	−	0.986406i	$-0.552545\pi$
$823$	−7759.50	−0.328650	−0.164325	+	0.986406i	$0.552545\pi$
$824$	8270.22	0.349644
$825$	0	0
$826$	9803.99	0.412984
$827$	11768.1	0.494823	0.247411	−	0.968911i	$-0.420420\pi$
$827$	11768.1	0.494823	0.247411	+	0.968911i	$0.420420\pi$
$828$	−2248.71	−0.0943818
$829$	31348.5	1.31336	0.656682	−	0.754167i	$-0.271959\pi$
$829$	31348.5	1.31336	0.656682	+	0.754167i	$0.271959\pi$
$830$	4727.91	0.197721
$831$	15516.7	0.647735
$832$	−1176.59	−0.0490274
$833$	16537.0	0.687843
$834$	−16779.2	−0.696661
$835$	10234.8	0.424181
$836$	0	0
$837$	−7736.60	−0.319493
$838$	−15273.1	−0.629595
$839$	−30704.9	−1.26347	−0.631735	−	0.775184i	$-0.717657\pi$
$839$	−30704.9	−1.26347	−0.631735	+	0.775184i	$0.717657\pi$
$840$	−11099.0	−0.455896
$841$	−5367.89	−0.220095
$842$	−13235.3	−0.541708
$843$	−7882.38	−0.322045
$844$	−10905.7	−0.444774
$845$	−756.555	−0.0308003
$846$	−6153.81	−0.250086
$847$	0	0
$848$	−8433.35	−0.341512
$849$	−22189.3	−0.896978
$850$	12396.1	0.500213
$851$	8102.30	0.326373
$852$	−24814.0	−0.997786
$853$	4519.79	0.181424	0.0907119	−	0.995877i	$-0.471086\pi$
$853$	4519.79	0.181424	0.0907119	+	0.995877i	$0.471086\pi$
$854$	−8670.19	−0.347410
$855$	4004.89	0.160192
$856$	5064.16	0.202207
$857$	370.847	0.0147817	0.00739083	−	0.999973i	$-0.497647\pi$
$857$	370.847	0.0147817	0.00739083	+	0.999973i	$0.497647\pi$
$858$	0	0
$859$	−3818.79	−0.151683	−0.0758413	−	0.997120i	$-0.524164\pi$
$859$	−3818.79	−0.151683	−0.0758413	+	0.997120i	$0.524164\pi$
$860$	−940.995	−0.0373112
$861$	38119.6	1.50884
$862$	12163.2	0.480603
$863$	−38414.1	−1.51522	−0.757609	−	0.652709i	$-0.773632\pi$
$863$	−38414.1	−1.51522	−0.757609	+	0.652709i	$0.773632\pi$
$864$	17230.3	0.678457
$865$	9581.20	0.376613
$866$	1861.25	0.0730345
$867$	22405.9	0.877676
$868$	7858.06	0.307281
$869$	0	0
$870$	12739.7	0.496455
$871$	12683.3	0.493408
$872$	−20271.3	−0.787239
$873$	15721.8	0.609510
$874$	−22197.3	−0.859080
$875$	−29556.1	−1.14192
$876$	21716.1	0.837578
$877$	4493.02	0.172997	0.0864986	−	0.996252i	$-0.472432\pi$
$877$	4493.02	0.172997	0.0864986	+	0.996252i	$0.472432\pi$
$878$	−54478.9	−2.09405
$879$	28107.3	1.07854
$880$	0	0
$881$	1383.85	0.0529206	0.0264603	−	0.999650i	$-0.491576\pi$
$881$	1383.85	0.0529206	0.0264603	+	0.999650i	$0.491576\pi$
$882$	−14949.5	−0.570720
$883$	−38116.6	−1.45269	−0.726345	−	0.687330i	$-0.758783\pi$
$883$	−38116.6	−1.45269	−0.726345	+	0.687330i	$0.758783\pi$
$884$	−1704.03	−0.0648332
$885$	2669.75	0.101404
$886$	19376.8	0.734736
$887$	24351.8	0.921817	0.460909	−	0.887448i	$-0.347524\pi$
$887$	24351.8	0.921817	0.460909	+	0.887448i	$0.347524\pi$
$888$	10726.3	0.405350
$889$	5248.89	0.198022
$890$	19269.9	0.725764
$891$	0	0
$892$	−12002.1	−0.450514
$893$	−19614.0	−0.735003
$894$	62732.8	2.34687
$895$	−8802.35	−0.328749
$896$	45631.4	1.70138
$897$	−5090.52	−0.189485
$898$	−53200.5	−1.97697
$899$	9894.76	0.367084
$900$	−3618.33	−0.134012
$901$	3623.62	0.133985
$902$	0	0
$903$	9496.41	0.349967
$904$	25148.6	0.925254
$905$	−12882.5	−0.473181
$906$	20996.1	0.769922
$907$	35367.0	1.29475	0.647376	−	0.762171i	$-0.275866\pi$
$907$	35367.0	1.29475	0.647376	+	0.762171i	$0.275866\pi$
$908$	−10155.8	−0.371181
$909$	1782.66	0.0650464
$910$	5743.20	0.209215
$911$	46697.9	1.69832	0.849161	−	0.528134i	$-0.177108\pi$
$911$	46697.9	1.69832	0.849161	+	0.528134i	$0.177108\pi$
$912$	−47523.9	−1.72552
$913$	0	0
$914$	−65238.7	−2.36095
$915$	−2361.01	−0.0853032
$916$	13162.4	0.474781
$917$	18266.0	0.657794
$918$	−12735.7	−0.457889
$919$	2787.52	0.100056	0.0500281	−	0.998748i	$-0.484069\pi$
$919$	2787.52	0.100056	0.0500281	+	0.998748i	$0.484069\pi$
$920$	4200.68	0.150535
$921$	31842.4	1.13924
$922$	−6818.55	−0.243554
$923$	−14085.8	−0.502319
$924$	0	0
$925$	13037.1	0.463415
$926$	19226.8	0.682323
$927$	5195.15	0.184068
$928$	−22036.8	−0.779518
$929$	12864.9	0.454342	0.227171	−	0.973855i	$-0.427052\pi$
$929$	12864.9	0.454342	0.227171	+	0.973855i	$0.427052\pi$
$930$	6627.17	0.233670
$931$	−47648.4	−1.67735
$932$	−8035.02	−0.282399
$933$	−29638.6	−1.04000
$934$	−10670.4	−0.373819
$935$	0	0
$936$	−1689.90	−0.0590129
$937$	−31938.4	−1.11353	−0.556767	−	0.830669i	$-0.687958\pi$
$937$	−31938.4	−1.11353	−0.556767	+	0.830669i	$0.687958\pi$
$938$	−96282.5	−3.35153
$939$	−31018.1	−1.07799
$940$	−3383.53	−0.117403
$941$	49087.1	1.70052	0.850262	−	0.526359i	$-0.176443\pi$
$941$	49087.1	1.70052	0.850262	+	0.526359i	$0.176443\pi$
$942$	−1343.05	−0.0464533
$943$	−14427.3	−0.498214
$944$	−7944.20	−0.273900
$945$	13859.8	0.477101
$946$	0	0
$947$	−16056.6	−0.550972	−0.275486	−	0.961305i	$-0.588839\pi$
$947$	−16056.6	−0.550972	−0.275486	+	0.961305i	$0.588839\pi$
$948$	−16818.2	−0.576190
$949$	12327.3	0.421665
$950$	−35717.0	−1.21980
$951$	−64452.5	−2.19770
$952$	−14190.8	−0.483115
$953$	−17156.5	−0.583163	−0.291582	−	0.956546i	$-0.594181\pi$
$953$	−17156.5	−0.583163	−0.291582	+	0.956546i	$0.594181\pi$
$954$	−3275.75	−0.111170
$955$	−14724.6	−0.498930
$956$	−21875.0	−0.740050
$957$	0	0
$958$	−15503.0	−0.522838
$959$	−80460.6	−2.70929
$960$	2432.24	0.0817709
$961$	−24643.8	−0.827222
$962$	−5550.34	−0.186019
$963$	3181.18	0.106451
$964$	17175.3	0.573837
$965$	8555.34	0.285395
$966$	38643.4	1.28709
$967$	12945.9	0.430518	0.215259	−	0.976557i	$-0.430940\pi$
$967$	12945.9	0.430518	0.215259	+	0.976557i	$0.430940\pi$
$968$	0	0
$969$	20419.9	0.676969
$970$	26771.5	0.886166
$971$	−44741.7	−1.47871	−0.739357	−	0.673314i	$-0.764870\pi$
$971$	−44741.7	−1.47871	−0.739357	+	0.673314i	$0.764870\pi$
$972$	9305.02	0.307056
$973$	23346.7	0.769229
$974$	20448.1	0.672690
$975$	−8190.99	−0.269048
$976$	7025.48	0.230410
$977$	−1240.04	−0.0406062	−0.0203031	−	0.999794i	$-0.506463\pi$
$977$	−1240.04	−0.0406062	−0.0203031	+	0.999794i	$0.506463\pi$
$978$	1125.27	0.0367916
$979$	0	0
$980$	−8219.61	−0.267924
$981$	−12733.9	−0.414437
$982$	32253.4	1.04811
$983$	−28939.6	−0.938994	−0.469497	−	0.882934i	$-0.655565\pi$
$983$	−28939.6	−0.938994	−0.469497	+	0.882934i	$0.655565\pi$
$984$	−19099.6	−0.618775
$985$	−14173.9	−0.458497
$986$	16288.4	0.526095
$987$	34146.2	1.10120
$988$	4909.84	0.158100
$989$	−3594.14	−0.115558
$990$	0	0
$991$	−19350.6	−0.620273	−0.310137	−	0.950692i	$-0.600375\pi$
$991$	−19350.6	−0.620273	−0.310137	+	0.950692i	$0.600375\pi$
$992$	−11463.5	−0.366902
$993$	−27373.4	−0.874792
$994$	106929.	3.41206
$995$	17076.0	0.544065
$996$	−7036.51	−0.223856
$997$	10122.7	0.321552	0.160776	−	0.986991i	$-0.448600\pi$
$997$	10122.7	0.321552	0.160776	+	0.986991i	$0.448600\pi$
$998$	−69435.6	−2.20235
$999$	−13394.4	−0.424204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.h.1.4	✓	15
11.10	odd	2		1573.4.a.k.1.12	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1573.4.a.h.1.4	✓	15	1.1	even	1	trivial
1573.4.a.k.1.12	yes	15	11.10	odd	2

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)

\(f(q)\)	\(=\)	\(q-3.43729 q^{2} -6.00304 q^{3} +3.81493 q^{4} -4.47666 q^{5} +20.6342 q^{6} -28.7105 q^{7} +14.3853 q^{8} +9.03648 q^{9} +O(q^{10})\)	\(q-3.43729 q^{2} -6.00304 q^{3} +3.81493 q^{4} -4.47666 q^{5} +20.6342 q^{6} -28.7105 q^{7} +14.3853 q^{8} +9.03648 q^{9} +15.3875 q^{10} -22.9012 q^{12} -13.0000 q^{13} +98.6863 q^{14} +26.8736 q^{15} -79.9657 q^{16} +34.3594 q^{17} -31.0610 q^{18} -99.0004 q^{19} -17.0781 q^{20} +172.350 q^{21} -65.2301 q^{23} -86.3554 q^{24} -104.960 q^{25} +44.6847 q^{26} +107.836 q^{27} -109.529 q^{28} -137.917 q^{29} -92.3721 q^{30} -71.7443 q^{31} +159.783 q^{32} -118.103 q^{34} +128.527 q^{35} +34.4735 q^{36} -124.211 q^{37} +340.293 q^{38} +78.0395 q^{39} -64.3980 q^{40} +221.175 q^{41} -592.418 q^{42} +55.0994 q^{43} -40.4532 q^{45} +224.214 q^{46} +198.120 q^{47} +480.038 q^{48} +481.294 q^{49} +360.776 q^{50} -206.261 q^{51} -49.5941 q^{52} +105.462 q^{53} -370.662 q^{54} -413.009 q^{56} +594.304 q^{57} +474.060 q^{58} +99.3451 q^{59} +102.521 q^{60} -87.8561 q^{61} +246.606 q^{62} -259.442 q^{63} +90.5067 q^{64} +58.1965 q^{65} -975.642 q^{67} +131.079 q^{68} +391.579 q^{69} -441.785 q^{70} +1083.53 q^{71} +129.992 q^{72} -948.252 q^{73} +426.949 q^{74} +630.076 q^{75} -377.680 q^{76} -268.244 q^{78} +734.380 q^{79} +357.979 q^{80} -891.327 q^{81} -760.241 q^{82} +307.255 q^{83} +657.505 q^{84} -153.815 q^{85} -189.392 q^{86} +827.922 q^{87} +1252.31 q^{89} +139.049 q^{90} +373.237 q^{91} -248.848 q^{92} +430.684 q^{93} -680.997 q^{94} +443.191 q^{95} -959.183 q^{96} +1739.81 q^{97} -1654.35 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9}+O(q^{10}) \) 15 * q - 6 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 + 25 * q^6 - 28 * q^7 - 108 * q^8 + 133 * q^9	\( 15 q - 6 q^{2} + 2 q^{3} + 54 q^{4} - 2 q^{5} + 25 q^{6} - 28 q^{7} - 108 q^{8} + 133 q^{9} + 16 q^{10} - 3 q^{12} - 195 q^{13} + 60 q^{14} + 202 q^{15} + 282 q^{16} - 136 q^{17} - 351 q^{18} - 136 q^{19} - 62 q^{20} - 625 q^{21} - 176 q^{23} + 227 q^{24} + 479 q^{25} + 78 q^{26} - 13 q^{27} + 86 q^{28} - 344 q^{29} - 542 q^{30} + 275 q^{31} + 170 q^{32} - 1505 q^{34} - 655 q^{35} + 623 q^{36} + 346 q^{37} - 848 q^{38} - 26 q^{39} - 256 q^{40} - 38 q^{41} + 575 q^{42} - 534 q^{43} - 633 q^{45} + 375 q^{46} + 276 q^{47} - 723 q^{48} + 773 q^{49} - 1684 q^{50} - 1111 q^{51} - 702 q^{52} + 706 q^{53} + 178 q^{54} - 2056 q^{56} - 1320 q^{57} - 983 q^{58} - 174 q^{59} + 2004 q^{60} - 1078 q^{61} - 1365 q^{62} + 2055 q^{63} + 1338 q^{64} + 26 q^{65} - 260 q^{67} - 559 q^{68} + 154 q^{69} - 1161 q^{70} + 2910 q^{71} - 6171 q^{72} - 1000 q^{73} - 688 q^{74} - 553 q^{75} - 178 q^{76} - 325 q^{78} + 386 q^{79} + 1702 q^{80} - 2805 q^{81} + 3380 q^{82} - 4318 q^{83} - 6681 q^{84} + 1391 q^{85} + 4139 q^{86} - 3144 q^{87} - 810 q^{89} + 3789 q^{90} + 364 q^{91} - 4857 q^{92} + 394 q^{93} + 116 q^{94} - 5204 q^{95} + 893 q^{96} - 1860 q^{97} - 8 q^{98}+O(q^{100}) \) 15 * q - 6 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 + 25 * q^6 - 28 * q^7 - 108 * q^8 + 133 * q^9 + 16 * q^10 - 3 * q^12 - 195 * q^13 + 60 * q^14 + 202 * q^15 + 282 * q^16 - 136 * q^17 - 351 * q^18 - 136 * q^19 - 62 * q^20 - 625 * q^21 - 176 * q^23 + 227 * q^24 + 479 * q^25 + 78 * q^26 - 13 * q^27 + 86 * q^28 - 344 * q^29 - 542 * q^30 + 275 * q^31 + 170 * q^32 - 1505 * q^34 - 655 * q^35 + 623 * q^36 + 346 * q^37 - 848 * q^38 - 26 * q^39 - 256 * q^40 - 38 * q^41 + 575 * q^42 - 534 * q^43 - 633 * q^45 + 375 * q^46 + 276 * q^47 - 723 * q^48 + 773 * q^49 - 1684 * q^50 - 1111 * q^51 - 702 * q^52 + 706 * q^53 + 178 * q^54 - 2056 * q^56 - 1320 * q^57 - 983 * q^58 - 174 * q^59 + 2004 * q^60 - 1078 * q^61 - 1365 * q^62 + 2055 * q^63 + 1338 * q^64 + 26 * q^65 - 260 * q^67 - 559 * q^68 + 154 * q^69 - 1161 * q^70 + 2910 * q^71 - 6171 * q^72 - 1000 * q^73 - 688 * q^74 - 553 * q^75 - 178 * q^76 - 325 * q^78 + 386 * q^79 + 1702 * q^80 - 2805 * q^81 + 3380 * q^82 - 4318 * q^83 - 6681 * q^84 + 1391 * q^85 + 4139 * q^86 - 3144 * q^87 - 810 * q^89 + 3789 * q^90 + 364 * q^91 - 4857 * q^92 + 394 * q^93 + 116 * q^94 - 5204 * q^95 + 893 * q^96 - 1860 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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