LMFDB - Embedded newform 1573.4.a.o.1.30

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			1.30
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)

$f(q)$	$=$	$q+4.13806 q^{2} -5.83637 q^{3} +9.12355 q^{4} -0.336615 q^{5} -24.1513 q^{6} +10.5216 q^{7} +4.64934 q^{8} +7.06321 q^{9} +O(q^{10})$	\(q+4.13806 q^{2} -5.83637 q^{3} +9.12355 q^{4} -0.336615 q^{5} -24.1513 q^{6} +10.5216 q^{7} +4.64934 q^{8} +7.06321 q^{9} -1.39293 q^{10} -53.2484 q^{12} +13.0000 q^{13} +43.5390 q^{14} +1.96461 q^{15} -53.7492 q^{16} +28.0969 q^{17} +29.2280 q^{18} -2.19171 q^{19} -3.07113 q^{20} -61.4080 q^{21} +188.847 q^{23} -27.1353 q^{24} -124.887 q^{25} +53.7948 q^{26} +116.358 q^{27} +95.9944 q^{28} -69.4368 q^{29} +8.12968 q^{30} -152.087 q^{31} -259.612 q^{32} +116.267 q^{34} -3.54173 q^{35} +64.4416 q^{36} -146.365 q^{37} -9.06945 q^{38} -75.8728 q^{39} -1.56504 q^{40} +110.103 q^{41} -254.110 q^{42} +264.319 q^{43} -2.37758 q^{45} +781.462 q^{46} -81.5760 q^{47} +313.700 q^{48} -232.296 q^{49} -516.789 q^{50} -163.984 q^{51} +118.606 q^{52} -374.848 q^{53} +481.499 q^{54} +48.9185 q^{56} +12.7917 q^{57} -287.334 q^{58} +275.262 q^{59} +17.9242 q^{60} -650.669 q^{61} -629.347 q^{62} +74.3163 q^{63} -644.298 q^{64} -4.37600 q^{65} +719.222 q^{67} +256.343 q^{68} -1102.18 q^{69} -14.6559 q^{70} +56.1728 q^{71} +32.8393 q^{72} -490.171 q^{73} -605.665 q^{74} +728.885 q^{75} -19.9962 q^{76} -313.966 q^{78} -426.777 q^{79} +18.0928 q^{80} -869.818 q^{81} +455.613 q^{82} -1035.26 q^{83} -560.259 q^{84} -9.45784 q^{85} +1093.77 q^{86} +405.259 q^{87} -412.378 q^{89} -9.83859 q^{90} +136.781 q^{91} +1722.96 q^{92} +887.638 q^{93} -337.567 q^{94} +0.737765 q^{95} +1515.19 q^{96} -910.059 q^{97} -961.255 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.13806	1.46303	0.731513	−	0.681828i	$-0.238815\pi$
$2$	4.13806	1.46303	0.731513	+	0.681828i	$0.238815\pi$
$3$	−5.83637	−1.12321	−0.561605	−	0.827406i	$-0.689816\pi$
$3$	−5.83637	−1.12321	−0.561605	+	0.827406i	$0.689816\pi$
$4$	9.12355	1.14044
$5$	−0.336615	−0.0301078	−0.0150539	−	0.999887i	$-0.504792\pi$
$5$	−0.336615	−0.0301078	−0.0150539	+	0.999887i	$0.504792\pi$
$6$	−24.1513	−1.64328
$7$	10.5216	0.568113	0.284057	−	0.958808i	$-0.408320\pi$
$7$	10.5216	0.568113	0.284057	+	0.958808i	$0.408320\pi$
$8$	4.64934	0.205474
$9$	7.06321	0.261600
$10$	−1.39293	−0.0440485
$11$	0	0
$11$	0	0
$12$	−53.2484	−1.28096
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	43.5390	0.831164
$15$	1.96461	0.0338174
$16$	−53.7492	−0.839831
$17$	28.0969	0.400853	0.200426	−	0.979709i	$-0.435767\pi$
$17$	28.0969	0.400853	0.200426	+	0.979709i	$0.435767\pi$
$18$	29.2280	0.382728
$19$	−2.19171	−0.0264639	−0.0132319	−	0.999912i	$-0.504212\pi$
$19$	−2.19171	−0.0264639	−0.0132319	+	0.999912i	$0.504212\pi$
$20$	−3.07113	−0.0343363
$21$	−61.4080	−0.638110
$22$	0	0
$23$	188.847	1.71206	0.856030	−	0.516926i	$-0.172924\pi$
$23$	188.847	1.71206	0.856030	+	0.516926i	$0.172924\pi$
$24$	−27.1353	−0.230790
$25$	−124.887	−0.999094
$26$	53.7948	0.405770
$27$	116.358	0.829378
$28$	95.9944	0.647901
$29$	−69.4368	−0.444624	−0.222312	−	0.974976i	$-0.571360\pi$
$29$	−69.4368	−0.444624	−0.222312	+	0.974976i	$0.571360\pi$
$30$	8.12968	0.0494757
$31$	−152.087	−0.881151	−0.440576	−	0.897715i	$-0.645226\pi$
$31$	−152.087	−0.881151	−0.440576	+	0.897715i	$0.645226\pi$
$32$	−259.612	−1.43417
$33$	0	0
$34$	116.267	0.586458
$35$	−3.54173	−0.0171046
$36$	64.4416	0.298341
$37$	−146.365	−0.650329	−0.325165	−	0.945657i	$-0.605420\pi$
$37$	−146.365	−0.650329	−0.325165	+	0.945657i	$0.605420\pi$
$38$	−9.06945	−0.0387173
$39$	−75.8728	−0.311522
$40$	−1.56504	−0.00618636
$41$	110.103	0.419395	0.209698	−	0.977766i	$-0.432752\pi$
$41$	110.103	0.419395	0.209698	+	0.977766i	$0.432752\pi$
$42$	−254.110	−0.933572
$43$	264.319	0.937403	0.468701	−	0.883357i	$-0.344722\pi$
$43$	264.319	0.937403	0.468701	+	0.883357i	$0.344722\pi$
$44$	0	0
$45$	−2.37758	−0.00787621
$46$	781.462	2.50479
$47$	−81.5760	−0.253172	−0.126586	−	0.991956i	$-0.540402\pi$
$47$	−81.5760	−0.253172	−0.126586	+	0.991956i	$0.540402\pi$
$48$	313.700	0.943306
$49$	−232.296	−0.677247
$50$	−516.789	−1.46170
$51$	−163.984	−0.450242
$52$	118.606	0.316302
$53$	−374.848	−0.971497	−0.485748	−	0.874099i	$-0.661453\pi$
$53$	−374.848	−0.971497	−0.485748	+	0.874099i	$0.661453\pi$
$54$	481.499	1.21340
$55$	0	0
$56$	48.9185	0.116732
$57$	12.7917	0.0297245
$58$	−287.334	−0.650496
$59$	275.262	0.607391	0.303696	−	0.952769i	$-0.401779\pi$
$59$	275.262	0.607391	0.303696	+	0.952769i	$0.401779\pi$
$60$	17.9242	0.0385668
$61$	−650.669	−1.36573	−0.682866	−	0.730544i	$-0.739267\pi$
$61$	−650.669	−1.36573	−0.682866	+	0.730544i	$0.739267\pi$
$62$	−629.347	−1.28915
$63$	74.3163	0.148619
$64$	−644.298	−1.25839
$65$	−4.37600	−0.00835040
$66$	0	0
$67$	719.222	1.31145	0.655723	−	0.755001i	$-0.272364\pi$
$67$	719.222	1.31145	0.655723	+	0.755001i	$0.272364\pi$
$68$	256.343	0.457150
$69$	−1102.18	−1.92300
$70$	−14.6559	−0.0250245
$71$	56.1728	0.0938942	0.0469471	−	0.998897i	$-0.485051\pi$
$71$	56.1728	0.0938942	0.0469471	+	0.998897i	$0.485051\pi$
$72$	32.8393	0.0537520
$73$	−490.171	−0.785893	−0.392947	−	0.919561i	$-0.628544\pi$
$73$	−490.171	−0.785893	−0.392947	+	0.919561i	$0.628544\pi$
$74$	−605.665	−0.951448
$75$	728.885	1.12219
$76$	−19.9962	−0.0301806
$77$	0	0
$78$	−313.966	−0.455765
$79$	−426.777	−0.607800	−0.303900	−	0.952704i	$-0.598289\pi$
$79$	−426.777	−0.607800	−0.303900	+	0.952704i	$0.598289\pi$
$80$	18.0928	0.0252855
$81$	−869.818	−1.19317
$82$	455.613	0.613586
$83$	−1035.26	−1.36910	−0.684548	−	0.728968i	$-0.740000\pi$
$83$	−1035.26	−1.36910	−0.684548	+	0.728968i	$0.740000\pi$
$84$	−560.259	−0.727729
$85$	−9.45784	−0.0120688
$86$	1093.77	1.37144
$87$	405.259	0.499406
$88$	0	0
$89$	−412.378	−0.491145	−0.245573	−	0.969378i	$-0.578976\pi$
$89$	−412.378	−0.491145	−0.245573	+	0.969378i	$0.578976\pi$
$90$	−9.83859	−0.0115231
$91$	136.781	0.157566
$92$	1722.96	1.95251
$93$	887.638	0.989718
$94$	−337.567	−0.370397
$95$	0.737765	0.000796769 0
$96$	1515.19	1.61087
$97$	−910.059	−0.952603	−0.476301	−	0.879282i	$-0.658023\pi$
$97$	−910.059	−0.952603	−0.476301	+	0.879282i	$0.658023\pi$
$98$	−961.255	−0.990830
$99$	0	0
$100$	−1139.41	−1.13941
$101$	−222.850	−0.219548	−0.109774	−	0.993957i	$-0.535013\pi$
$101$	−222.850	−0.219548	−0.109774	+	0.993957i	$0.535013\pi$
$102$	−678.575	−0.658715
$103$	−826.416	−0.790575	−0.395287	−	0.918557i	$-0.629355\pi$
$103$	−826.416	−0.790575	−0.395287	+	0.918557i	$0.629355\pi$
$104$	60.4414	0.0569882
$105$	20.6709	0.0192121
$106$	−1551.14	−1.42132
$107$	597.229	0.539592	0.269796	−	0.962918i	$-0.413044\pi$
$107$	597.229	0.539592	0.269796	+	0.962918i	$0.413044\pi$
$108$	1061.60	0.945859
$109$	−1795.31	−1.57761	−0.788803	−	0.614646i	$-0.789299\pi$
$109$	−1795.31	−1.57761	−0.788803	+	0.614646i	$0.789299\pi$
$110$	0	0
$111$	854.237	0.730456
$112$	−565.528	−0.477119
$113$	1431.72	1.19191	0.595953	−	0.803019i	$-0.296775\pi$
$113$	1431.72	1.19191	0.595953	+	0.803019i	$0.296775\pi$
$114$	52.9327	0.0434877
$115$	−63.5689	−0.0515463
$116$	−633.511	−0.507069
$117$	91.8217	0.0725549
$118$	1139.05	0.888629
$119$	295.624	0.227730
$120$	9.13414	0.00694858
$121$	0	0
$122$	−2692.51	−1.99810
$123$	−642.602	−0.471069
$124$	−1387.58	−1.00490
$125$	84.1157	0.0601883
$126$	307.525	0.217433
$127$	−572.886	−0.400279	−0.200139	−	0.979767i	$-0.564139\pi$
$127$	−572.886	−0.400279	−0.200139	+	0.979767i	$0.564139\pi$
$128$	−589.246	−0.406895
$129$	−1542.66	−1.05290
$130$	−18.1082	−0.0122168
$131$	−1261.34	−0.841247	−0.420624	−	0.907235i	$-0.638189\pi$
$131$	−1261.34	−0.841247	−0.420624	+	0.907235i	$0.638189\pi$
$132$	0	0
$133$	−23.0604	−0.0150345
$134$	2976.18	1.91868
$135$	−39.1680	−0.0249707
$136$	130.632	0.0823647
$137$	985.061	0.614302	0.307151	−	0.951661i	$-0.400624\pi$
$137$	985.061	0.614302	0.307151	+	0.951661i	$0.400624\pi$
$138$	−4560.90	−2.81340
$139$	−2896.65	−1.76756	−0.883781	−	0.467901i	$-0.845010\pi$
$139$	−2896.65	−1.76756	−0.883781	+	0.467901i	$0.845010\pi$
$140$	−32.3132	−0.0195069
$141$	476.108	0.284365
$142$	232.447	0.137370
$143$	0	0
$144$	−379.642	−0.219700
$145$	23.3735	0.0133866
$146$	−2028.36	−1.14978
$147$	1355.76	0.760691
$148$	−1335.36	−0.741664
$149$	−1495.81	−0.822427	−0.411213	−	0.911539i	$-0.634895\pi$
$149$	−1495.81	−0.822427	−0.411213	+	0.911539i	$0.634895\pi$
$150$	3016.17	1.64180
$151$	−662.527	−0.357057	−0.178529	−	0.983935i	$-0.557134\pi$
$151$	−662.527	−0.357057	−0.178529	+	0.983935i	$0.557134\pi$
$152$	−10.1900	−0.00543763
$153$	198.454	0.104863
$154$	0	0
$155$	51.1949	0.0265295
$156$	−692.230	−0.355274
$157$	1381.62	0.702326	0.351163	−	0.936314i	$-0.385786\pi$
$157$	1381.62	0.702326	0.351163	+	0.936314i	$0.385786\pi$
$158$	−1766.03	−0.889227
$159$	2187.75	1.09119
$160$	87.3894	0.0431796
$161$	1986.98	0.972644
$162$	−3599.36	−1.74563
$163$	−3964.08	−1.90485	−0.952425	−	0.304773i	$-0.901419\pi$
$163$	−3964.08	−1.90485	−0.952425	+	0.304773i	$0.901419\pi$
$164$	1004.53	0.478297
$165$	0	0
$166$	−4283.98	−2.00302
$167$	844.564	0.391343	0.195672	−	0.980669i	$-0.437311\pi$
$167$	844.564	0.391343	0.195672	+	0.980669i	$0.437311\pi$
$168$	−285.506	−0.131115
$169$	169.000	0.0769231
$170$	−39.1371	−0.0176569
$171$	−15.4805	−0.00692296
$172$	2411.53	1.06906
$173$	−1299.16	−0.570944	−0.285472	−	0.958387i	$-0.592150\pi$
$173$	−1299.16	−0.570944	−0.285472	+	0.958387i	$0.592150\pi$
$174$	1676.99	0.730644
$175$	−1314.01	−0.567598
$176$	0	0
$177$	−1606.53	−0.682228
$178$	−1706.44	−0.718558
$179$	−432.192	−0.180467	−0.0902333	−	0.995921i	$-0.528761\pi$
$179$	−432.192	−0.180467	−0.0902333	+	0.995921i	$0.528761\pi$
$180$	−21.6920	−0.00898238
$181$	3442.43	1.41367	0.706835	−	0.707379i	$-0.250123\pi$
$181$	3442.43	1.41367	0.706835	+	0.707379i	$0.250123\pi$
$182$	566.008	0.230523
$183$	3797.54	1.53400
$184$	878.015	0.351783
$185$	49.2685	0.0195800
$186$	3673.10	1.44798
$187$	0	0
$188$	−744.263	−0.288729
$189$	1224.28	0.471180
$190$	3.05292	0.00116569
$191$	−2718.36	−1.02981	−0.514904	−	0.857248i	$-0.672173\pi$
$191$	−2718.36	−1.02981	−0.514904	+	0.857248i	$0.672173\pi$
$192$	3760.36	1.41344
$193$	−2467.65	−0.920339	−0.460169	−	0.887831i	$-0.652211\pi$
$193$	−2467.65	−0.920339	−0.460169	+	0.887831i	$0.652211\pi$
$194$	−3765.88	−1.39368
$195$	25.5399	0.00937925
$196$	−2119.36	−0.772363
$197$	15.9911	0.00578333	0.00289167	−	0.999996i	$-0.499080\pi$
$197$	15.9911	0.00578333	0.00289167	+	0.999996i	$0.499080\pi$
$198$	0	0
$199$	3284.37	1.16997	0.584983	−	0.811046i	$-0.301101\pi$
$199$	3284.37	1.16997	0.584983	+	0.811046i	$0.301101\pi$
$200$	−580.641	−0.205287
$201$	−4197.64	−1.47303
$202$	−922.166	−0.321205
$203$	−730.587	−0.252597
$204$	−1496.12	−0.513476
$205$	−37.0624	−0.0126271
$206$	−3419.76	−1.15663
$207$	1333.87	0.447876
$208$	−698.739	−0.232927
$209$	0	0
$210$	85.5373	0.0281078
$211$	−5924.51	−1.93299	−0.966494	−	0.256690i	$-0.917368\pi$
$211$	−5924.51	−1.93299	−0.966494	+	0.256690i	$0.917368\pi$
$212$	−3419.95	−1.10794
$213$	−327.845	−0.105463
$214$	2471.37	0.789437
$215$	−88.9739	−0.0282231
$216$	540.990	0.170415
$217$	−1600.20	−0.500594
$218$	−7429.09	−2.30808
$219$	2860.82	0.882723
$220$	0	0
$221$	365.259	0.111177
$222$	3534.89	1.06868
$223$	−3679.19	−1.10483	−0.552414	−	0.833570i	$-0.686293\pi$
$223$	−3679.19	−1.10483	−0.552414	+	0.833570i	$0.686293\pi$
$224$	−2731.54	−0.814770
$225$	−882.101	−0.261363
$226$	5924.57	1.74379
$227$	5465.97	1.59819	0.799095	−	0.601205i	$-0.205313\pi$
$227$	5465.97	1.59819	0.799095	+	0.601205i	$0.205313\pi$
$228$	116.705	0.0338991
$229$	473.265	0.136569	0.0682843	−	0.997666i	$-0.478247\pi$
$229$	473.265	0.136569	0.0682843	+	0.997666i	$0.478247\pi$
$230$	−263.052	−0.0754136
$231$	0	0
$232$	−322.835	−0.0913585
$233$	1787.20	0.502503	0.251251	−	0.967922i	$-0.419158\pi$
$233$	1787.20	0.502503	0.251251	+	0.967922i	$0.419158\pi$
$234$	379.964	0.106150
$235$	27.4597	0.00762245
$236$	2511.37	0.692696
$237$	2490.83	0.682687
$238$	1223.31	0.333174
$239$	−1878.66	−0.508454	−0.254227	−	0.967145i	$-0.581821\pi$
$239$	−1878.66	−0.508454	−0.254227	+	0.967145i	$0.581821\pi$
$240$	−105.596	−0.0284009
$241$	−154.777	−0.0413697	−0.0206848	−	0.999786i	$-0.506585\pi$
$241$	−154.777	−0.0413697	−0.0206848	+	0.999786i	$0.506585\pi$
$242$	0	0
$243$	1934.90	0.510798
$244$	−5936.41	−1.55754
$245$	78.1943	0.0203904
$246$	−2659.13	−0.689186
$247$	−28.4923	−0.00733976
$248$	−707.106	−0.181053
$249$	6042.18	1.53778
$250$	348.076	0.0880570
$251$	−3485.56	−0.876520	−0.438260	−	0.898848i	$-0.644405\pi$
$251$	−3485.56	−0.876520	−0.438260	+	0.898848i	$0.644405\pi$
$252$	678.029	0.169491
$253$	0	0
$254$	−2370.64	−0.585618
$255$	55.1994	0.0135558
$256$	2716.04	0.663097
$257$	2315.83	0.562091	0.281045	−	0.959695i	$-0.409319\pi$
$257$	2315.83	0.562091	0.281045	+	0.959695i	$0.409319\pi$
$258$	−6383.64	−1.54042
$259$	−1539.99	−0.369461
$260$	−39.9247	−0.00952316
$261$	−490.447	−0.116314
$262$	−5219.48	−1.23077
$263$	2350.87	0.551182	0.275591	−	0.961275i	$-0.411126\pi$
$263$	2350.87	0.551182	0.275591	+	0.961275i	$0.411126\pi$
$264$	0	0
$265$	126.180	0.0292496
$266$	−95.4252	−0.0219958
$267$	2406.79	0.551659
$268$	6561.86	1.49563
$269$	−5513.56	−1.24969	−0.624847	−	0.780747i	$-0.714839\pi$
$269$	−5513.56	−1.24969	−0.624847	+	0.780747i	$0.714839\pi$
$270$	−162.080	−0.0365328
$271$	8194.47	1.83682	0.918411	−	0.395628i	$-0.129473\pi$
$271$	8194.47	1.83682	0.918411	+	0.395628i	$0.129473\pi$
$272$	−1510.18	−0.336648
$273$	−798.304	−0.176980
$274$	4076.24	0.898740
$275$	0	0
$276$	−10055.8	−2.19308
$277$	8074.92	1.75153	0.875767	−	0.482735i	$-0.160356\pi$
$277$	8074.92	1.75153	0.875767	+	0.482735i	$0.160356\pi$
$278$	−11986.5	−2.58599
$279$	−1074.22	−0.230509
$280$	−16.4667	−0.00351455
$281$	−1654.20	−0.351178	−0.175589	−	0.984464i	$-0.556183\pi$
$281$	−1654.20	−0.351178	−0.175589	+	0.984464i	$0.556183\pi$
$282$	1970.16	0.416034
$283$	4447.09	0.934107	0.467054	−	0.884229i	$-0.345315\pi$
$283$	4447.09	0.934107	0.467054	+	0.884229i	$0.345315\pi$
$284$	512.496	0.107081
$285$	−4.30587	−0.000894939 0
$286$	0	0
$287$	1158.46	0.238264
$288$	−1833.70	−0.375179
$289$	−4123.57	−0.839317
$290$	96.7210	0.0195850
$291$	5311.44	1.06997
$292$	−4472.10	−0.896267
$293$	3946.77	0.786939	0.393469	−	0.919338i	$-0.371275\pi$
$293$	3946.77	0.786939	0.393469	+	0.919338i	$0.371275\pi$
$294$	5610.24	1.11291
$295$	−92.6575	−0.0182872
$296$	−680.498	−0.133626
$297$	0	0
$298$	−6189.76	−1.20323
$299$	2455.01	0.474840
$300$	6650.02	1.27980
$301$	2781.06	0.532551
$302$	−2741.58	−0.522384
$303$	1300.63	0.246599
$304$	117.803	0.0222252
$305$	219.025	0.0411191
$306$	821.216	0.153418
$307$	210.114	0.0390614	0.0195307	−	0.999809i	$-0.493783\pi$
$307$	210.114	0.0390614	0.0195307	+	0.999809i	$0.493783\pi$
$308$	0	0
$309$	4823.27	0.887981
$310$	211.848	0.0388134
$311$	713.133	0.130026	0.0650130	−	0.997884i	$-0.479291\pi$
$311$	713.133	0.130026	0.0650130	+	0.997884i	$0.479291\pi$
$312$	−352.758	−0.0640097
$313$	−4885.82	−0.882310	−0.441155	−	0.897431i	$-0.645431\pi$
$313$	−4885.82	−0.882310	−0.441155	+	0.897431i	$0.645431\pi$
$314$	5717.22	1.02752
$315$	−25.0160	−0.00447458
$316$	−3893.73	−0.693162
$317$	886.514	0.157071	0.0785356	−	0.996911i	$-0.474976\pi$
$317$	886.514	0.157071	0.0785356	+	0.996911i	$0.474976\pi$
$318$	9053.05	1.59645
$319$	0	0
$320$	216.880	0.0378875
$321$	−3485.65	−0.606075
$322$	8222.23	1.42300
$323$	−61.5804	−0.0106081
$324$	−7935.83	−1.36074
$325$	−1623.53	−0.277099
$326$	−16403.6	−2.78684
$327$	10478.1	1.77198
$328$	511.907	0.0861747
$329$	−858.311	−0.143830
$330$	0	0
$331$	−342.392	−0.0568567	−0.0284283	−	0.999596i	$-0.509050\pi$
$331$	−342.392	−0.0568567	−0.0284283	+	0.999596i	$0.509050\pi$
$332$	−9445.28	−1.56138
$333$	−1033.80	−0.170126
$334$	3494.86	0.572545
$335$	−242.101	−0.0394848
$336$	3300.63	0.535905
$337$	617.300	0.0997818	0.0498909	−	0.998755i	$-0.484113\pi$
$337$	617.300	0.0997818	0.0498909	+	0.998755i	$0.484113\pi$
$338$	699.332	0.112540
$339$	−8356.08	−1.33876
$340$	−86.2891	−0.0137638
$341$	0	0
$342$	−64.0594	−0.0101285
$343$	−6053.03	−0.952866
$344$	1228.91	0.192612
$345$	371.011	0.0578973
$346$	−5376.00	−0.835305
$347$	5538.97	0.856908	0.428454	−	0.903563i	$-0.359058\pi$
$347$	5538.97	0.856908	0.428454	+	0.903563i	$0.359058\pi$
$348$	3697.40	0.569545
$349$	−293.248	−0.0449776	−0.0224888	−	0.999747i	$-0.507159\pi$
$349$	−293.248	−0.0449776	−0.0224888	+	0.999747i	$0.507159\pi$
$350$	−5437.45	−0.830411
$351$	1512.66	0.230028
$352$	0	0
$353$	−5778.04	−0.871201	−0.435601	−	0.900140i	$-0.643464\pi$
$353$	−5778.04	−0.871201	−0.435601	+	0.900140i	$0.643464\pi$
$354$	−6647.93	−0.998117
$355$	−18.9086	−0.00282695
$356$	−3762.35	−0.560124
$357$	−1725.37	−0.255788
$358$	−1788.44	−0.264027
$359$	−13359.6	−1.96404	−0.982021	−	0.188773i	$-0.939549\pi$
$359$	−13359.6	−1.96404	−0.982021	+	0.188773i	$0.939549\pi$
$360$	−11.0542	−0.00161835
$361$	−6854.20	−0.999300
$362$	14245.0	2.06823
$363$	0	0
$364$	1247.93	0.179696
$365$	164.999	0.0236615
$366$	15714.5	2.24429
$367$	2279.44	0.324213	0.162106	−	0.986773i	$-0.448171\pi$
$367$	2279.44	0.324213	0.162106	+	0.986773i	$0.448171\pi$
$368$	−10150.4	−1.43784
$369$	777.681	0.109714
$370$	203.876	0.0286460
$371$	−3944.00	−0.551920
$372$	8098.41	1.12872
$373$	11372.1	1.57861	0.789306	−	0.614000i	$-0.210440\pi$
$373$	11372.1	1.57861	0.789306	+	0.614000i	$0.210440\pi$
$374$	0	0
$375$	−490.930	−0.0676041
$376$	−379.275	−0.0520202
$377$	−902.679	−0.123317
$378$	5066.14	0.689349
$379$	1072.44	0.145349	0.0726747	−	0.997356i	$-0.476847\pi$
$379$	1072.44	0.145349	0.0726747	+	0.997356i	$0.476847\pi$
$380$	6.73104	0.000908671 0
$381$	3343.57	0.449597
$382$	−11248.7	−1.50664
$383$	−5543.00	−0.739515	−0.369757	−	0.929128i	$-0.620559\pi$
$383$	−5543.00	−0.739515	−0.369757	+	0.929128i	$0.620559\pi$
$384$	3439.06	0.457028
$385$	0	0
$386$	−10211.3	−1.34648
$387$	1866.94	0.245225
$388$	−8302.97	−1.08639
$389$	10131.2	1.32050	0.660249	−	0.751047i	$-0.270451\pi$
$389$	10131.2	1.32050	0.660249	+	0.751047i	$0.270451\pi$
$390$	105.686	0.0137221
$391$	5306.02	0.686284
$392$	−1080.02	−0.139157
$393$	7361.62	0.944897
$394$	66.1720	0.00846116
$395$	143.660	0.0182995
$396$	0	0
$397$	12387.8	1.56606	0.783032	−	0.621981i	$-0.213672\pi$
$397$	12387.8	1.56606	0.783032	+	0.621981i	$0.213672\pi$
$398$	13590.9	1.71169
$399$	134.589	0.0168869
$400$	6712.56	0.839070
$401$	3034.78	0.377929	0.188965	−	0.981984i	$-0.439487\pi$
$401$	3034.78	0.377929	0.188965	+	0.981984i	$0.439487\pi$
$402$	−17370.1	−2.15508
$403$	−1977.14	−0.244387
$404$	−2033.18	−0.250383
$405$	292.794	0.0359236
$406$	−3023.21	−0.369556
$407$	0	0
$408$	−762.416	−0.0925128
$409$	−12005.6	−1.45144	−0.725721	−	0.687989i	$-0.758494\pi$
$409$	−12005.6	−1.45144	−0.725721	+	0.687989i	$0.758494\pi$
$410$	−153.366	−0.0184737
$411$	−5749.18	−0.689990
$412$	−7539.85	−0.901607
$413$	2896.20	0.345067
$414$	5519.63	0.655253
$415$	348.485	0.0412204
$416$	−3374.96	−0.397767
$417$	16905.9	1.98534
$418$	0	0
$419$	−15218.6	−1.77441	−0.887203	−	0.461379i	$-0.847355\pi$
$419$	−15218.6	−1.77441	−0.887203	+	0.461379i	$0.847355\pi$
$420$	188.592	0.0219103
$421$	−7440.66	−0.861367	−0.430683	−	0.902503i	$-0.641727\pi$
$421$	−7440.66	−0.861367	−0.430683	+	0.902503i	$0.641727\pi$
$422$	−24516.0	−2.82801
$423$	−576.189	−0.0662299
$424$	−1742.79	−0.199617
$425$	−3508.93	−0.400489
$426$	−1356.64	−0.154295
$427$	−6846.08	−0.775890
$428$	5448.85	0.615374
$429$	0	0
$430$	−368.179	−0.0412911
$431$	7037.22	0.786475	0.393238	−	0.919437i	$-0.371355\pi$
$431$	7037.22	0.786475	0.393238	+	0.919437i	$0.371355\pi$
$432$	−6254.17	−0.696537
$433$	16281.1	1.80697	0.903487	−	0.428616i	$-0.140999\pi$
$433$	16281.1	1.80697	0.903487	+	0.428616i	$0.140999\pi$
$434$	−6621.74	−0.732381
$435$	−136.416	−0.0150360
$436$	−16379.6	−1.79917
$437$	−413.899	−0.0453078
$438$	11838.3	1.29145
$439$	6378.80	0.693493	0.346747	−	0.937959i	$-0.387286\pi$
$439$	6378.80	0.693493	0.346747	+	0.937959i	$0.387286\pi$
$440$	0	0
$441$	−1640.75	−0.177168
$442$	1511.47	0.162654
$443$	10614.9	1.13844	0.569220	−	0.822185i	$-0.307245\pi$
$443$	10614.9	1.13844	0.569220	+	0.822185i	$0.307245\pi$
$444$	7793.68	0.833045
$445$	138.813	0.0147873
$446$	−15224.7	−1.61639
$447$	8730.10	0.923758
$448$	−6779.04	−0.714910
$449$	12281.0	1.29082	0.645408	−	0.763838i	$-0.276687\pi$
$449$	12281.0	1.29082	0.645408	+	0.763838i	$0.276687\pi$
$450$	−3650.19	−0.382381
$451$	0	0
$452$	13062.4	1.35930
$453$	3866.75	0.401050
$454$	22618.5	2.33819
$455$	−46.0425	−0.00474397
$456$	59.4728	0.00610760
$457$	8862.40	0.907146	0.453573	−	0.891219i	$-0.350149\pi$
$457$	8862.40	0.907146	0.453573	+	0.891219i	$0.350149\pi$
$458$	1958.40	0.199803
$459$	3269.31	0.332458
$460$	−579.974	−0.0587857
$461$	−18437.5	−1.86274	−0.931369	−	0.364078i	$-0.881384\pi$
$461$	−18437.5	−1.86274	−0.931369	+	0.364078i	$0.881384\pi$
$462$	0	0
$463$	17916.3	1.79837	0.899183	−	0.437573i	$-0.144162\pi$
$463$	17916.3	1.79837	0.899183	+	0.437573i	$0.144162\pi$
$464$	3732.17	0.373409
$465$	−298.792	−0.0297982
$466$	7395.53	0.735174
$467$	10236.5	1.01432	0.507159	−	0.861852i	$-0.330696\pi$
$467$	10236.5	1.01432	0.507159	+	0.861852i	$0.330696\pi$
$468$	837.741	0.0827448
$469$	7567.37	0.745050
$470$	113.630	0.0111518
$471$	−8063.64	−0.788859
$472$	1279.79	0.124803
$473$	0	0
$474$	10307.2	0.998789
$475$	273.716	0.0264399
$476$	2697.14	0.259713
$477$	−2647.63	−0.254144
$478$	−7774.01	−0.743881
$479$	17897.1	1.70718	0.853592	−	0.520943i	$-0.174419\pi$
$479$	17897.1	1.70718	0.853592	+	0.520943i	$0.174419\pi$
$480$	−510.037	−0.0484998
$481$	−1902.74	−0.180369
$482$	−640.478	−0.0605249
$483$	−11596.7	−1.09248
$484$	0	0
$485$	306.340	0.0286808
$486$	8006.73	0.747310
$487$	−9661.97	−0.899026	−0.449513	−	0.893274i	$-0.648402\pi$
$487$	−9661.97	−0.899026	−0.449513	+	0.893274i	$0.648402\pi$
$488$	−3025.18	−0.280622
$489$	23135.8	2.13955
$490$	323.573	0.0298317
$491$	12274.0	1.12815	0.564073	−	0.825725i	$-0.309234\pi$
$491$	12274.0	1.12815	0.564073	+	0.825725i	$0.309234\pi$
$492$	−5862.82	−0.537228
$493$	−1950.96	−0.178229
$494$	−117.903	−0.0107383
$495$	0	0
$496$	8174.57	0.740018
$497$	591.028	0.0533425
$498$	25002.9	2.24981
$499$	−18643.2	−1.67251	−0.836257	−	0.548338i	$-0.815261\pi$
$499$	−18643.2	−1.67251	−0.836257	+	0.548338i	$0.815261\pi$
$500$	767.434	0.0686414
$501$	−4929.19	−0.439561
$502$	−14423.5	−1.28237
$503$	9118.59	0.808306	0.404153	−	0.914691i	$-0.367566\pi$
$503$	9118.59	0.808306	0.404153	+	0.914691i	$0.367566\pi$
$504$	345.522	0.0305372
$505$	75.0147	0.00661012
$506$	0	0
$507$	−986.346	−0.0864008
$508$	−5226.75	−0.456496
$509$	842.592	0.0733737	0.0366869	−	0.999327i	$-0.488320\pi$
$509$	842.592	0.0733737	0.0366869	+	0.999327i	$0.488320\pi$
$510$	228.419	0.0198325
$511$	−5157.39	−0.446476
$512$	15953.1	1.37702
$513$	−255.025	−0.0219486
$514$	9583.03	0.822353
$515$	278.184	0.0238025
$516$	−14074.6	−1.20077
$517$	0	0
$518$	−6372.57	−0.540530
$519$	7582.37	0.641290
$520$	−20.3455	−0.00171579
$521$	7482.73	0.629222	0.314611	−	0.949221i	$-0.398126\pi$
$521$	7482.73	0.629222	0.314611	+	0.949221i	$0.398126\pi$
$522$	−2029.50	−0.170170
$523$	10686.4	0.893470	0.446735	−	0.894666i	$-0.352587\pi$
$523$	10686.4	0.893470	0.446735	+	0.894666i	$0.352587\pi$
$524$	−11507.9	−0.959395
$525$	7669.04	0.637532
$526$	9728.05	0.806394
$527$	−4273.18	−0.353212
$528$	0	0
$529$	23496.3	1.93115
$530$	522.139	0.0427929
$531$	1944.23	0.158894
$532$	−210.392	−0.0171460
$533$	1431.34	0.116319
$534$	9959.44	0.807092
$535$	−201.036	−0.0162459
$536$	3343.91	0.269468
$537$	2522.43	0.202702
$538$	−22815.4	−1.82833
$539$	0	0
$540$	−357.352	−0.0284777
$541$	11303.9	0.898320	0.449160	−	0.893451i	$-0.351723\pi$
$541$	11303.9	0.898320	0.449160	+	0.893451i	$0.351723\pi$
$542$	33909.2	2.68732
$543$	−20091.3	−1.58785
$544$	−7294.29	−0.574890
$545$	604.327	0.0474982
$546$	−3303.43	−0.258926
$547$	−10465.8	−0.818068	−0.409034	−	0.912519i	$-0.634134\pi$
$547$	−10465.8	−0.818068	−0.409034	+	0.912519i	$0.634134\pi$
$548$	8987.26	0.700578
$549$	−4595.81	−0.357276
$550$	0	0
$551$	152.186	0.0117665
$552$	−5124.42	−0.395127
$553$	−4490.38	−0.345299
$554$	33414.5	2.56254
$555$	−287.549	−0.0219924
$556$	−26427.8	−2.01581
$557$	12247.4	0.931670	0.465835	−	0.884872i	$-0.345754\pi$
$557$	12247.4	0.931670	0.465835	+	0.884872i	$0.345754\pi$
$558$	−4445.21	−0.337241
$559$	3436.15	0.259989
$560$	190.365	0.0143650
$561$	0	0
$562$	−6845.17	−0.513783
$563$	15409.6	1.15353	0.576764	−	0.816911i	$-0.304315\pi$
$563$	15409.6	1.15353	0.576764	+	0.816911i	$0.304315\pi$
$564$	4343.80	0.324303
$565$	−481.940	−0.0358856
$566$	18402.4	1.36662
$567$	−9151.88	−0.677853
$568$	261.167	0.0192928
$569$	−18061.8	−1.33074	−0.665370	−	0.746513i	$-0.731726\pi$
$569$	−18061.8	−1.33074	−0.665370	+	0.746513i	$0.731726\pi$
$570$	−17.8179	−0.00130932
$571$	−16817.7	−1.23257	−0.616286	−	0.787522i	$-0.711363\pi$
$571$	−16817.7	−1.23257	−0.616286	+	0.787522i	$0.711363\pi$
$572$	0	0
$573$	15865.3	1.15669
$574$	4793.78	0.348586
$575$	−23584.5	−1.71051
$576$	−4550.81	−0.329196
$577$	18766.8	1.35402	0.677012	−	0.735972i	$-0.263274\pi$
$577$	18766.8	1.35402	0.677012	+	0.735972i	$0.263274\pi$
$578$	−17063.6	−1.22794
$579$	14402.1	1.03373
$580$	213.249	0.0152667
$581$	−10892.6	−0.777801
$582$	21979.1	1.56540
$583$	0	0
$584$	−2278.97	−0.161480
$585$	−30.9086	−0.00218447
$586$	16332.0	1.15131
$587$	11948.8	0.840170	0.420085	−	0.907485i	$-0.362000\pi$
$587$	11948.8	0.840170	0.420085	+	0.907485i	$0.362000\pi$
$588$	12369.4	0.867526
$589$	333.332	0.0233187
$590$	−383.422	−0.0267547
$591$	−93.3298	−0.00649589
$592$	7866.97	0.546167
$593$	5989.96	0.414803	0.207401	−	0.978256i	$-0.433499\pi$
$593$	5989.96	0.414803	0.207401	+	0.978256i	$0.433499\pi$
$594$	0	0
$595$	−99.5116	−0.00685644
$596$	−13647.1	−0.937932
$597$	−19168.8	−1.31412
$598$	10159.0	0.694703
$599$	−21058.4	−1.43643	−0.718217	−	0.695819i	$-0.755042\pi$
$599$	−21058.4	−1.43643	−0.718217	+	0.695819i	$0.755042\pi$
$600$	3388.83	0.230581
$601$	26344.7	1.78806	0.894029	−	0.448010i	$-0.147867\pi$
$601$	26344.7	1.78806	0.894029	+	0.448010i	$0.147867\pi$
$602$	11508.2	0.779135
$603$	5080.01	0.343075
$604$	−6044.60	−0.407204
$605$	0	0
$606$	5382.10	0.360781
$607$	3254.00	0.217588	0.108794	−	0.994064i	$-0.465301\pi$
$607$	3254.00	0.217588	0.108794	+	0.994064i	$0.465301\pi$
$608$	568.996	0.0379537
$609$	4263.97	0.283719
$610$	906.339	0.0601584
$611$	−1060.49	−0.0702173
$612$	1810.61	0.119591
$613$	1915.21	0.126190	0.0630951	−	0.998008i	$-0.479903\pi$
$613$	1915.21	0.126190	0.0630951	+	0.998008i	$0.479903\pi$
$614$	869.465	0.0571478
$615$	216.310	0.0141828
$616$	0	0
$617$	−27013.9	−1.76263	−0.881313	−	0.472532i	$-0.843340\pi$
$617$	−27013.9	−1.76263	−0.881313	+	0.472532i	$0.843340\pi$
$618$	19959.0	1.29914
$619$	−16190.1	−1.05127	−0.525635	−	0.850710i	$-0.676172\pi$
$619$	−16190.1	−1.05127	−0.525635	+	0.850710i	$0.676172\pi$
$620$	467.080	0.0302554
$621$	21974.0	1.41994
$622$	2950.99	0.190231
$623$	−4338.87	−0.279026
$624$	4078.10	0.261626
$625$	15582.5	0.997281
$626$	−20217.8	−1.29084
$627$	0	0
$628$	12605.3	0.800964
$629$	−4112.39	−0.260686
$630$	−103.518	−0.00654642
$631$	4698.94	0.296453	0.148226	−	0.988953i	$-0.452644\pi$
$631$	4698.94	0.296453	0.148226	+	0.988953i	$0.452644\pi$
$632$	−1984.23	−0.124887
$633$	34577.7	2.17115
$634$	3668.45	0.229799
$635$	192.842	0.0120515
$636$	19960.1	1.24445
$637$	−3019.85	−0.187835
$638$	0	0
$639$	396.761	0.0245628
$640$	198.349	0.0122507
$641$	−7489.36	−0.461485	−0.230742	−	0.973015i	$-0.574115\pi$
$641$	−7489.36	−0.461485	−0.230742	+	0.973015i	$0.574115\pi$
$642$	−14423.8	−0.886703
$643$	−10425.1	−0.639388	−0.319694	−	0.947521i	$-0.603580\pi$
$643$	−10425.1	−0.639388	−0.319694	+	0.947521i	$0.603580\pi$
$644$	18128.3	1.10925
$645$	519.285	0.0317005
$646$	−254.823	−0.0155200
$647$	−4411.40	−0.268053	−0.134026	−	0.990978i	$-0.542791\pi$
$647$	−4411.40	−0.268053	−0.134026	+	0.990978i	$0.542791\pi$
$648$	−4044.08	−0.245164
$649$	0	0
$650$	−6718.25	−0.405403
$651$	9339.37	0.562272
$652$	−36166.5	−2.17238
$653$	−30057.6	−1.80130	−0.900648	−	0.434550i	$-0.856907\pi$
$653$	−30057.6	−1.80130	−0.900648	+	0.434550i	$0.856907\pi$
$654$	43358.9	2.59246
$655$	424.585	0.0253281
$656$	−5917.95	−0.352221
$657$	−3462.18	−0.205590
$658$	−3551.74	−0.210428
$659$	−14263.1	−0.843115	−0.421557	−	0.906802i	$-0.638516\pi$
$659$	−14263.1	−0.843115	−0.421557	+	0.906802i	$0.638516\pi$
$660$	0	0
$661$	−21861.5	−1.28640	−0.643202	−	0.765697i	$-0.722394\pi$
$661$	−21861.5	−1.28640	−0.643202	+	0.765697i	$0.722394\pi$
$662$	−1416.84	−0.0831827
$663$	−2131.79	−0.124875
$664$	−4813.29	−0.281313
$665$	7.76247	0.000452655 0
$666$	−4277.94	−0.248899
$667$	−13113.0	−0.761223
$668$	7705.43	0.446305
$669$	21473.1	1.24095
$670$	−1001.83	−0.0577672
$671$	0	0
$672$	15942.3	0.915157
$673$	−19706.7	−1.12873	−0.564367	−	0.825524i	$-0.690880\pi$
$673$	−19706.7	−1.12873	−0.564367	+	0.825524i	$0.690880\pi$
$674$	2554.43	0.145983
$675$	−14531.6	−0.828626
$676$	1541.88	0.0877265
$677$	−9069.96	−0.514899	−0.257450	−	0.966292i	$-0.582882\pi$
$677$	−9069.96	−0.514899	−0.257450	+	0.966292i	$0.582882\pi$
$678$	−34578.0	−1.95864
$679$	−9575.28	−0.541186
$680$	−43.9727	−0.00247982
$681$	−31901.4	−1.79510
$682$	0	0
$683$	−17430.8	−0.976532	−0.488266	−	0.872695i	$-0.662370\pi$
$683$	−17430.8	−0.976532	−0.488266	+	0.872695i	$0.662370\pi$
$684$	−141.238	−0.00789525
$685$	−331.586	−0.0184953
$686$	−25047.8	−1.39407
$687$	−2762.15	−0.153395
$688$	−14206.9	−0.787260
$689$	−4873.02	−0.269445
$690$	1535.27	0.0847053
$691$	35087.6	1.93169	0.965843	−	0.259127i	$-0.0834349\pi$
$691$	35087.6	1.93169	0.965843	+	0.259127i	$0.0834349\pi$
$692$	−11853.0	−0.651129
$693$	0	0
$694$	22920.6	1.25368
$695$	975.058	0.0532174
$696$	1884.19	0.102615
$697$	3093.55	0.168116
$698$	−1213.48	−0.0658035
$699$	−10430.7	−0.564416
$700$	−11988.4	−0.647314
$701$	759.577	0.0409256	0.0204628	−	0.999791i	$-0.493486\pi$
$701$	759.577	0.0409256	0.0204628	+	0.999791i	$0.493486\pi$
$702$	6259.48	0.336537
$703$	320.789	0.0172102
$704$	0	0
$705$	−160.265	−0.00856161
$706$	−23909.9	−1.27459
$707$	−2344.74	−0.124728
$708$	−14657.3	−0.778043
$709$	−13699.5	−0.725663	−0.362832	−	0.931855i	$-0.618190\pi$
$709$	−13699.5	−0.725663	−0.362832	+	0.931855i	$0.618190\pi$
$710$	−78.2451	−0.00413590
$711$	−3014.42	−0.159001
$712$	−1917.28	−0.100917
$713$	−28721.3	−1.50858
$714$	−7139.70	−0.374225
$715$	0	0
$716$	−3943.13	−0.205812
$717$	10964.6	0.571100
$718$	−55282.7	−2.87344
$719$	−27416.3	−1.42205	−0.711026	−	0.703166i	$-0.751769\pi$
$719$	−27416.3	−1.42205	−0.711026	+	0.703166i	$0.751769\pi$
$720$	127.793	0.00661468
$721$	−8695.22	−0.449136
$722$	−28363.1	−1.46200
$723$	903.338	0.0464668
$724$	31407.2	1.61221
$725$	8671.74	0.444221
$726$	0	0
$727$	24658.4	1.25795	0.628976	−	0.777425i	$-0.283474\pi$
$727$	24658.4	1.25795	0.628976	+	0.777425i	$0.283474\pi$
$728$	635.941	0.0323757
$729$	12192.3	0.619433
$730$	682.776	0.0346174
$731$	7426.55	0.375760
$732$	34647.1	1.74944
$733$	−16196.8	−0.816158	−0.408079	−	0.912947i	$-0.633801\pi$
$733$	−16196.8	−0.816158	−0.408079	+	0.912947i	$0.633801\pi$
$734$	9432.48	0.474331
$735$	−456.371	−0.0229027
$736$	−49027.1	−2.45538
$737$	0	0
$738$	3218.09	0.160514
$739$	−20812.4	−1.03599	−0.517995	−	0.855384i	$-0.673322\pi$
$739$	−20812.4	−1.03599	−0.517995	+	0.855384i	$0.673322\pi$
$740$	449.504	0.0223299
$741$	166.292	0.00824409
$742$	−16320.5	−0.807473
$743$	13858.4	0.684276	0.342138	−	0.939650i	$-0.388849\pi$
$743$	13858.4	0.684276	0.342138	+	0.939650i	$0.388849\pi$
$744$	4126.93	0.203361
$745$	503.513	0.0247614
$746$	47058.2	2.30955
$747$	−7312.28	−0.358156
$748$	0	0
$749$	6283.81	0.306549
$750$	−2031.50	−0.0989065
$751$	2747.07	0.133478	0.0667391	−	0.997770i	$-0.478740\pi$
$751$	2747.07	0.133478	0.0667391	+	0.997770i	$0.478740\pi$
$752$	4384.64	0.212622
$753$	20343.0	0.984516
$754$	−3735.34	−0.180415
$755$	223.017	0.0107502
$756$	11169.8	0.537355
$757$	−12709.5	−0.610215	−0.305108	−	0.952318i	$-0.598692\pi$
$757$	−12709.5	−0.610215	−0.305108	+	0.952318i	$0.598692\pi$
$758$	4437.81	0.212650
$759$	0	0
$760$	3.43012	0.000163715 0
$761$	−30056.2	−1.43172	−0.715858	−	0.698246i	$-0.753964\pi$
$761$	−30056.2	−1.43172	−0.715858	+	0.698246i	$0.753964\pi$
$762$	13835.9	0.657772
$763$	−18889.5	−0.896259
$764$	−24801.1	−1.17444
$765$	−66.8027	−0.00315720
$766$	−22937.3	−1.08193
$767$	3578.41	0.168460
$768$	−15851.8	−0.744797
$769$	−713.793	−0.0334721	−0.0167360	−	0.999860i	$-0.505327\pi$
$769$	−713.793	−0.0334721	−0.0167360	+	0.999860i	$0.505327\pi$
$770$	0	0
$771$	−13516.0	−0.631346
$772$	−22513.7	−1.04960
$773$	9215.29	0.428785	0.214393	−	0.976748i	$-0.431223\pi$
$773$	9215.29	0.428785	0.214393	+	0.976748i	$0.431223\pi$
$774$	7725.52	0.358770
$775$	18993.7	0.880353
$776$	−4231.17	−0.195735
$777$	8987.95	0.414982
$778$	41923.7	1.93192
$779$	−241.315	−0.0110988
$780$	233.015	0.0106965
$781$	0	0
$782$	21956.6	1.00405
$783$	−8079.56	−0.368761
$784$	12485.7	0.568773
$785$	−465.074	−0.0211455
$786$	30462.8	1.38241
$787$	−5427.81	−0.245846	−0.122923	−	0.992416i	$-0.539227\pi$
$787$	−5427.81	−0.245846	−0.122923	+	0.992416i	$0.539227\pi$
$788$	145.895	0.00659557
$789$	−13720.6	−0.619093
$790$	594.473	0.0267727
$791$	15064.0	0.677137
$792$	0	0
$793$	−8458.70	−0.378786
$794$	51261.6	2.29119
$795$	−736.430	−0.0328534
$796$	29965.2	1.33428
$797$	−35195.6	−1.56423	−0.782115	−	0.623135i	$-0.785859\pi$
$797$	−35195.6	−1.56423	−0.782115	+	0.623135i	$0.785859\pi$
$798$	556.936	0.0247059
$799$	−2292.03	−0.101485
$800$	32422.1	1.43287
$801$	−2912.71	−0.128484
$802$	12558.1	0.552920
$803$	0	0
$804$	−38297.4	−1.67991
$805$	−668.846	−0.0292842
$806$	−8181.51	−0.357545
$807$	32179.2	1.40367
$808$	−1036.10	−0.0451114
$809$	19596.5	0.851641	0.425820	−	0.904808i	$-0.359986\pi$
$809$	19596.5	0.851641	0.425820	+	0.904808i	$0.359986\pi$
$810$	1211.60	0.0525571
$811$	14653.4	0.634464	0.317232	−	0.948348i	$-0.397247\pi$
$811$	14653.4	0.634464	0.317232	+	0.948348i	$0.397247\pi$
$812$	−6665.55	−0.288073
$813$	−47826.0	−2.06314
$814$	0	0
$815$	1334.37	0.0573508
$816$	8814.00	0.378127
$817$	−579.312	−0.0248073
$818$	−49680.0	−2.12350
$819$	966.112	0.0412194
$820$	−338.141	−0.0144005
$821$	−39240.5	−1.66809	−0.834045	−	0.551697i	$-0.813981\pi$
$821$	−39240.5	−1.66809	−0.834045	+	0.551697i	$0.813981\pi$
$822$	−23790.5	−1.00947
$823$	−8048.39	−0.340886	−0.170443	−	0.985368i	$-0.554520\pi$
$823$	−8048.39	−0.340886	−0.170443	+	0.985368i	$0.554520\pi$
$824$	−3842.29	−0.162442
$825$	0	0
$826$	11984.7	0.504842
$827$	10946.3	0.460267	0.230134	−	0.973159i	$-0.426084\pi$
$827$	10946.3	0.460267	0.230134	+	0.973159i	$0.426084\pi$
$828$	12169.6	0.510777
$829$	11298.8	0.473368	0.236684	−	0.971587i	$-0.423939\pi$
$829$	11298.8	0.473368	0.236684	+	0.971587i	$0.423939\pi$
$830$	1442.05	0.0603065
$831$	−47128.2	−1.96734
$832$	−8375.87	−0.349016
$833$	−6526.79	−0.271476
$834$	69957.9	2.90461
$835$	−284.293	−0.0117825
$836$	0	0
$837$	−17696.6	−0.730807
$838$	−62975.4	−2.59600
$839$	−8376.05	−0.344664	−0.172332	−	0.985039i	$-0.555130\pi$
$839$	−8376.05	−0.344664	−0.172332	+	0.985039i	$0.555130\pi$
$840$	96.1058	0.00394758
$841$	−19567.5	−0.802309
$842$	−30789.9	−1.26020
$843$	9654.51	0.394447
$844$	−54052.6	−2.20446
$845$	−56.8880	−0.00231598
$846$	−2384.30	−0.0968960
$847$	0	0
$848$	20147.8	0.815893
$849$	−25954.9	−1.04920
$850$	−14520.2	−0.585926
$851$	−27640.5	−1.11340
$852$	−2991.12	−0.120275
$853$	7058.14	0.283313	0.141657	−	0.989916i	$-0.454757\pi$
$853$	7058.14	0.283313	0.141657	+	0.989916i	$0.454757\pi$
$854$	−28329.5	−1.13515
$855$	5.21099	0.000208435 0
$856$	2776.72	0.110872
$857$	35123.3	1.39999	0.699993	−	0.714149i	$-0.253186\pi$
$857$	35123.3	1.39999	0.699993	+	0.714149i	$0.253186\pi$
$858$	0	0
$859$	23407.7	0.929757	0.464879	−	0.885374i	$-0.346098\pi$
$859$	23407.7	0.929757	0.464879	+	0.885374i	$0.346098\pi$
$860$	−811.758	−0.0321869
$861$	−6761.21	−0.267621
$862$	29120.4	1.15063
$863$	−21591.6	−0.851666	−0.425833	−	0.904802i	$-0.640019\pi$
$863$	−21591.6	−0.851666	−0.425833	+	0.904802i	$0.640019\pi$
$864$	−30208.1	−1.18947
$865$	437.317	0.0171898
$866$	67372.2	2.64365
$867$	24066.7	0.942729
$868$	−14599.5	−0.570899
$869$	0	0
$870$	−564.499	−0.0219981
$871$	9349.88	0.363730
$872$	−8346.99	−0.324157
$873$	−6427.94	−0.249201
$874$	−1712.74	−0.0662864
$875$	885.032	0.0341938
$876$	26100.8	1.00670
$877$	−29887.9	−1.15079	−0.575395	−	0.817876i	$-0.695152\pi$
$877$	−29887.9	−1.15079	−0.575395	+	0.817876i	$0.695152\pi$
$878$	26395.9	1.01460
$879$	−23034.8	−0.883897
$880$	0	0
$881$	−5394.79	−0.206305	−0.103153	−	0.994666i	$-0.532893\pi$
$881$	−5394.79	−0.206305	−0.103153	+	0.994666i	$0.532893\pi$
$882$	−6789.54	−0.259202
$883$	−32909.8	−1.25425	−0.627126	−	0.778918i	$-0.715769\pi$
$883$	−32909.8	−1.25425	−0.627126	+	0.778918i	$0.715769\pi$
$884$	3332.46	0.126791
$885$	540.783	0.0205404
$886$	43925.1	1.66557
$887$	30492.2	1.15426	0.577129	−	0.816653i	$-0.304173\pi$
$887$	30492.2	1.15426	0.577129	+	0.816653i	$0.304173\pi$
$888$	3971.64	0.150090
$889$	−6027.68	−0.227404
$890$	574.415	0.0216342
$891$	0	0
$892$	−33567.3	−1.25999
$893$	178.791	0.00669992
$894$	36125.7	1.35148
$895$	145.482	0.00543345
$896$	−6199.81	−0.231162
$897$	−14328.4	−0.533345
$898$	50819.6	1.88850
$899$	10560.5	0.391781
$900$	−8047.90	−0.298070
$901$	−10532.1	−0.389427
$902$	0	0
$903$	−16231.3	−0.598166
$904$	6656.57	0.244905
$905$	−1158.78	−0.0425624
$906$	16000.9	0.586747
$907$	−46753.6	−1.71161	−0.855803	−	0.517302i	$-0.826937\pi$
$907$	−46753.6	−1.71161	−0.855803	+	0.517302i	$0.826937\pi$
$908$	49869.0	1.82265
$909$	−1574.04	−0.0574339
$910$	−190.527	−0.00694055
$911$	−23649.7	−0.860097	−0.430048	−	0.902806i	$-0.641504\pi$
$911$	−23649.7	−0.860097	−0.430048	+	0.902806i	$0.641504\pi$
$912$	−687.541	−0.0249636
$913$	0	0
$914$	36673.2	1.32718
$915$	−1278.31	−0.0461854
$916$	4317.86	0.155749
$917$	−13271.3	−0.477924
$918$	13528.6	0.486395
$919$	43205.0	1.55082	0.775408	−	0.631460i	$-0.217544\pi$
$919$	43205.0	1.55082	0.775408	+	0.631460i	$0.217544\pi$
$920$	−295.553	−0.0105914
$921$	−1226.30	−0.0438741
$922$	−76295.7	−2.72523
$923$	730.247	0.0260416
$924$	0	0
$925$	18279.0	0.649740
$926$	74138.9	2.63106
$927$	−5837.15	−0.206815
$928$	18026.6	0.637666
$929$	33359.2	1.17813	0.589063	−	0.808087i	$-0.299497\pi$
$929$	33359.2	1.17813	0.589063	+	0.808087i	$0.299497\pi$
$930$	−1236.42	−0.0435955
$931$	509.126	0.0179226
$932$	16305.6	0.573076
$933$	−4162.11	−0.146046
$934$	42359.1	1.48397
$935$	0	0
$936$	426.910	0.0149081
$937$	−33664.5	−1.17371	−0.586857	−	0.809690i	$-0.699635\pi$
$937$	−33664.5	−1.17371	−0.586857	+	0.809690i	$0.699635\pi$
$938$	31314.2	1.09003
$939$	28515.5	0.991019
$940$	250.530	0.00869298
$941$	−14518.6	−0.502967	−0.251484	−	0.967862i	$-0.580918\pi$
$941$	−14518.6	−0.502967	−0.251484	+	0.967862i	$0.580918\pi$
$942$	−33367.8	−1.15412
$943$	20792.7	0.718030
$944$	−14795.1	−0.510106
$945$	−412.111	−0.0141862
$946$	0	0
$947$	−23005.0	−0.789399	−0.394699	−	0.918810i	$-0.629151\pi$
$947$	−23005.0	−0.789399	−0.394699	+	0.918810i	$0.629151\pi$
$948$	22725.2	0.778567
$949$	−6372.23	−0.217968
$950$	1132.65	0.0386823
$951$	−5174.02	−0.176424
$952$	1374.46	0.0467925
$953$	29611.7	1.00652	0.503261	−	0.864134i	$-0.332133\pi$
$953$	29611.7	1.00652	0.503261	+	0.864134i	$0.332133\pi$
$954$	−10956.1	−0.371819
$955$	915.041	0.0310053
$956$	−17140.1	−0.579863
$957$	0	0
$958$	74059.4	2.49765
$959$	10364.4	0.348993
$960$	−1265.79	−0.0425556
$961$	−6660.45	−0.223572
$962$	−7873.65	−0.263884
$963$	4218.36	0.141157
$964$	−1412.12	−0.0471798
$965$	830.649	0.0277094
$966$	−47988.0	−1.59833
$967$	−28107.3	−0.934715	−0.467358	−	0.884068i	$-0.654794\pi$
$967$	−28107.3	−0.934715	−0.467358	+	0.884068i	$0.654794\pi$
$968$	0	0
$969$	359.406	0.0119151
$970$	1267.65	0.0419607
$971$	30406.6	1.00494	0.502469	−	0.864595i	$-0.332425\pi$
$971$	30406.6	1.00494	0.502469	+	0.864595i	$0.332425\pi$
$972$	17653.2	0.582536
$973$	−30477.5	−1.00417
$974$	−39981.8	−1.31530
$975$	9475.50	0.311240
$976$	34972.9	1.14698
$977$	7980.69	0.261336	0.130668	−	0.991426i	$-0.458288\pi$
$977$	7980.69	0.261336	0.130668	+	0.991426i	$0.458288\pi$
$978$	95737.5	3.13021
$979$	0	0
$980$	713.410	0.0232541
$981$	−12680.6	−0.412702
$982$	50790.8	1.65051
$983$	−59904.4	−1.94370	−0.971848	−	0.235608i	$-0.924292\pi$
$983$	−59904.4	−1.94370	−0.971848	+	0.235608i	$0.924292\pi$
$984$	−2987.68	−0.0967923
$985$	−5.38284	−0.000174123 0
$986$	−8073.19	−0.260753
$987$	5009.42	0.161552
$988$	−259.951	−0.00837059
$989$	49916.0	1.60489
$990$	0	0
$991$	−33814.2	−1.08390	−0.541949	−	0.840411i	$-0.682314\pi$
$991$	−33814.2	−1.08390	−0.541949	+	0.840411i	$0.682314\pi$
$992$	39483.7	1.26372
$993$	1998.32	0.0638619
$994$	2445.71	0.0780415
$995$	−1105.57	−0.0352251
$996$	55126.1	1.75375
$997$	29343.1	0.932102	0.466051	−	0.884758i	$-0.345676\pi$
$997$	29343.1	0.932102	0.466051	+	0.884758i	$0.345676\pi$
$998$	−77146.7	−2.44693
$999$	−17030.8	−0.539369

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.o.1.30		34
11.3	even	5		143.4.h.a.53.15	yes	68
11.4	even	5		143.4.h.a.27.15	✓	68
11.10	odd	2		1573.4.a.p.1.5		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.27.15	✓	68	11.4	even	5
143.4.h.a.53.15	yes	68	11.3	even	5
1573.4.a.o.1.30		34	1.1	even	1	trivial
1573.4.a.p.1.5		34	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)

\(f(q)\)	\(=\)	\(q+4.13806 q^{2} -5.83637 q^{3} +9.12355 q^{4} -0.336615 q^{5} -24.1513 q^{6} +10.5216 q^{7} +4.64934 q^{8} +7.06321 q^{9} +O(q^{10})\)	\(q+4.13806 q^{2} -5.83637 q^{3} +9.12355 q^{4} -0.336615 q^{5} -24.1513 q^{6} +10.5216 q^{7} +4.64934 q^{8} +7.06321 q^{9} -1.39293 q^{10} -53.2484 q^{12} +13.0000 q^{13} +43.5390 q^{14} +1.96461 q^{15} -53.7492 q^{16} +28.0969 q^{17} +29.2280 q^{18} -2.19171 q^{19} -3.07113 q^{20} -61.4080 q^{21} +188.847 q^{23} -27.1353 q^{24} -124.887 q^{25} +53.7948 q^{26} +116.358 q^{27} +95.9944 q^{28} -69.4368 q^{29} +8.12968 q^{30} -152.087 q^{31} -259.612 q^{32} +116.267 q^{34} -3.54173 q^{35} +64.4416 q^{36} -146.365 q^{37} -9.06945 q^{38} -75.8728 q^{39} -1.56504 q^{40} +110.103 q^{41} -254.110 q^{42} +264.319 q^{43} -2.37758 q^{45} +781.462 q^{46} -81.5760 q^{47} +313.700 q^{48} -232.296 q^{49} -516.789 q^{50} -163.984 q^{51} +118.606 q^{52} -374.848 q^{53} +481.499 q^{54} +48.9185 q^{56} +12.7917 q^{57} -287.334 q^{58} +275.262 q^{59} +17.9242 q^{60} -650.669 q^{61} -629.347 q^{62} +74.3163 q^{63} -644.298 q^{64} -4.37600 q^{65} +719.222 q^{67} +256.343 q^{68} -1102.18 q^{69} -14.6559 q^{70} +56.1728 q^{71} +32.8393 q^{72} -490.171 q^{73} -605.665 q^{74} +728.885 q^{75} -19.9962 q^{76} -313.966 q^{78} -426.777 q^{79} +18.0928 q^{80} -869.818 q^{81} +455.613 q^{82} -1035.26 q^{83} -560.259 q^{84} -9.45784 q^{85} +1093.77 q^{86} +405.259 q^{87} -412.378 q^{89} -9.83859 q^{90} +136.781 q^{91} +1722.96 q^{92} +887.638 q^{93} -337.567 q^{94} +0.737765 q^{95} +1515.19 q^{96} -910.059 q^{97} -961.255 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} + 36 q^{6} - 36 q^{7} - 57 q^{8} + 265 q^{9}+O(q^{10}) \) 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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