LMFDB - Embedded newform 242.4.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,4,Mod(1,242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(242, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("242.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	242.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:	$14.2784622214$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.978025.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 99x^{2} + 100x + 2420 $ x^4 - 2x^3 - 99x^2 + 100*x + 2420
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 11 $
Twist minimal:	no (minimal twist has level 22)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$8.19378$ of defining polynomial
Character	$\chi$	$=$	242.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -7.81182 q^{3} +4.00000 q^{4} +14.9181 q^{5} +15.6236 q^{6} +21.7679 q^{7} -8.00000 q^{8} +34.0245 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -7.81182 q^{3} +4.00000 q^{4} +14.9181 q^{5} +15.6236 q^{6} +21.7679 q^{7} -8.00000 q^{8} +34.0245 q^{9} -29.8363 q^{10} -31.2473 q^{12} -44.0286 q^{13} -43.5357 q^{14} -116.538 q^{15} +16.0000 q^{16} -24.9145 q^{17} -68.0489 q^{18} +21.9573 q^{19} +59.6725 q^{20} -170.046 q^{21} +177.749 q^{23} +62.4945 q^{24} +97.5508 q^{25} +88.0571 q^{26} -54.8738 q^{27} +87.0714 q^{28} -149.396 q^{29} +233.075 q^{30} +75.1436 q^{31} -32.0000 q^{32} +49.8290 q^{34} +324.736 q^{35} +136.098 q^{36} +222.336 q^{37} -43.9145 q^{38} +343.943 q^{39} -119.345 q^{40} -253.121 q^{41} +340.093 q^{42} +130.623 q^{43} +507.582 q^{45} -355.498 q^{46} +499.093 q^{47} -124.989 q^{48} +130.839 q^{49} -195.102 q^{50} +194.627 q^{51} -176.114 q^{52} +12.9421 q^{53} +109.748 q^{54} -174.143 q^{56} -171.526 q^{57} +298.793 q^{58} +35.5614 q^{59} -466.151 q^{60} +538.343 q^{61} -150.287 q^{62} +740.639 q^{63} +64.0000 q^{64} -656.824 q^{65} -519.621 q^{67} -99.6580 q^{68} -1388.54 q^{69} -649.472 q^{70} +78.4486 q^{71} -272.196 q^{72} +1144.07 q^{73} -444.673 q^{74} -762.049 q^{75} +87.8290 q^{76} -687.886 q^{78} +772.546 q^{79} +238.690 q^{80} -489.997 q^{81} +506.243 q^{82} +537.242 q^{83} -680.186 q^{84} -371.678 q^{85} -261.247 q^{86} +1167.06 q^{87} +667.089 q^{89} -1015.16 q^{90} -958.407 q^{91} +710.996 q^{92} -587.008 q^{93} -998.187 q^{94} +327.561 q^{95} +249.978 q^{96} -179.654 q^{97} -261.679 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 4 q^{3} + 16 q^{4} + 25 q^{5} - 8 q^{6} - 3 q^{7} - 32 q^{8} + 102 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 + 4 * q^3 + 16 * q^4 + 25 * q^5 - 8 * q^6 - 3 * q^7 - 32 * q^8 + 102 * q^9	\( 4 q - 8 q^{2} + 4 q^{3} + 16 q^{4} + 25 q^{5} - 8 q^{6} - 3 q^{7} - 32 q^{8} + 102 q^{9} - 50 q^{10} + 16 q^{12} + 41 q^{13} + 6 q^{14} + 68 q^{15} + 64 q^{16} - 52 q^{17} - 204 q^{18} - 16 q^{19} + 100 q^{20} - 25 q^{21} + 314 q^{23} - 32 q^{24} - 21 q^{25} - 82 q^{26} + 286 q^{27} - 12 q^{28} - 561 q^{29} - 136 q^{30} + 199 q^{31} - 128 q^{32} + 104 q^{34} + 714 q^{35} + 408 q^{36} + 357 q^{37} + 32 q^{38} + 1038 q^{39} - 200 q^{40} - 32 q^{41} + 50 q^{42} + 721 q^{43} + 1326 q^{45} - 628 q^{46} + 403 q^{47} + 64 q^{48} + 823 q^{49} + 42 q^{50} + 174 q^{51} + 164 q^{52} - 133 q^{53} - 572 q^{54} + 24 q^{56} + 1031 q^{57} + 1122 q^{58} + 1016 q^{59} + 272 q^{60} + 919 q^{61} - 398 q^{62} + 1367 q^{63} + 256 q^{64} - 69 q^{65} + 289 q^{67} - 208 q^{68} - 1620 q^{69} - 1428 q^{70} - 1205 q^{71} - 816 q^{72} + 1234 q^{73} - 714 q^{74} - 911 q^{75} - 64 q^{76} - 2076 q^{78} + 603 q^{79} + 400 q^{80} - 1400 q^{81} + 64 q^{82} - 1514 q^{83} - 100 q^{84} - 717 q^{85} - 1442 q^{86} + 1061 q^{87} - 1101 q^{89} - 2652 q^{90} - 2306 q^{91} + 1256 q^{92} - 2298 q^{93} - 806 q^{94} + 1766 q^{95} - 128 q^{96} + 2116 q^{97} - 1646 q^{98}+O(q^{100}) \) 4 * q - 8 * q^2 + 4 * q^3 + 16 * q^4 + 25 * q^5 - 8 * q^6 - 3 * q^7 - 32 * q^8 + 102 * q^9 - 50 * q^10 + 16 * q^12 + 41 * q^13 + 6 * q^14 + 68 * q^15 + 64 * q^16 - 52 * q^17 - 204 * q^18 - 16 * q^19 + 100 * q^20 - 25 * q^21 + 314 * q^23 - 32 * q^24 - 21 * q^25 - 82 * q^26 + 286 * q^27 - 12 * q^28 - 561 * q^29 - 136 * q^30 + 199 * q^31 - 128 * q^32 + 104 * q^34 + 714 * q^35 + 408 * q^36 + 357 * q^37 + 32 * q^38 + 1038 * q^39 - 200 * q^40 - 32 * q^41 + 50 * q^42 + 721 * q^43 + 1326 * q^45 - 628 * q^46 + 403 * q^47 + 64 * q^48 + 823 * q^49 + 42 * q^50 + 174 * q^51 + 164 * q^52 - 133 * q^53 - 572 * q^54 + 24 * q^56 + 1031 * q^57 + 1122 * q^58 + 1016 * q^59 + 272 * q^60 + 919 * q^61 - 398 * q^62 + 1367 * q^63 + 256 * q^64 - 69 * q^65 + 289 * q^67 - 208 * q^68 - 1620 * q^69 - 1428 * q^70 - 1205 * q^71 - 816 * q^72 + 1234 * q^73 - 714 * q^74 - 911 * q^75 - 64 * q^76 - 2076 * q^78 + 603 * q^79 + 400 * q^80 - 1400 * q^81 + 64 * q^82 - 1514 * q^83 - 100 * q^84 - 717 * q^85 - 1442 * q^86 + 1061 * q^87 - 1101 * q^89 - 2652 * q^90 - 2306 * q^91 + 1256 * q^92 - 2298 * q^93 - 806 * q^94 + 1766 * q^95 - 128 * q^96 + 2116 * q^97 - 1646 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−7.81182	−1.50338	−0.751692	−	0.659514i	$-0.770762\pi$
$3$	−7.81182	−1.50338	−0.751692	+	0.659514i	$0.770762\pi$
$4$	4.00000	0.500000
$5$	14.9181	1.33432	0.667159	−	0.744915i	$-0.267510\pi$
$5$	14.9181	1.33432	0.667159	+	0.744915i	$0.267510\pi$
$6$	15.6236	1.06305
$7$	21.7679	1.17535	0.587677	−	0.809096i	$-0.300043\pi$
$7$	21.7679	1.17535	0.587677	+	0.809096i	$0.300043\pi$
$8$	−8.00000	−0.353553
$9$	34.0245	1.26017
$10$	−29.8363	−0.943506
$11$	0	0
$11$	0	0
$12$	−31.2473	−0.751692
$13$	−44.0286	−0.939333	−0.469666	−	0.882844i	$-0.655626\pi$
$13$	−44.0286	−0.939333	−0.469666	+	0.882844i	$0.655626\pi$
$14$	−43.5357	−0.831101
$15$	−116.538	−2.00599
$16$	16.0000	0.250000
$17$	−24.9145	−0.355450	−0.177725	−	0.984080i	$-0.556874\pi$
$17$	−24.9145	−0.355450	−0.177725	+	0.984080i	$0.556874\pi$
$18$	−68.0489	−0.891071
$19$	21.9573	0.265123	0.132562	−	0.991175i	$-0.457680\pi$
$19$	21.9573	0.265123	0.132562	+	0.991175i	$0.457680\pi$
$20$	59.6725	0.667159
$21$	−170.046	−1.76701
$22$	0	0
$23$	177.749	1.61145	0.805723	−	0.592293i	$-0.201777\pi$
$23$	177.749	1.61145	0.805723	+	0.592293i	$0.201777\pi$
$24$	62.4945	0.531527
$25$	97.5508	0.780407
$26$	88.0571	0.664208
$27$	−54.8738	−0.391128
$28$	87.0714	0.587677
$29$	−149.396	−0.956628	−0.478314	−	0.878189i	$-0.658752\pi$
$29$	−149.396	−0.956628	−0.478314	+	0.878189i	$0.658752\pi$
$30$	233.075	1.41845
$31$	75.1436	0.435361	0.217681	−	0.976020i	$-0.430151\pi$
$31$	75.1436	0.435361	0.217681	+	0.976020i	$0.430151\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	49.8290	0.251341
$35$	324.736	1.56830
$36$	136.098	0.630083
$37$	222.336	0.987889	0.493944	−	0.869493i	$-0.335555\pi$
$37$	222.336	0.987889	0.493944	+	0.869493i	$0.335555\pi$
$38$	−43.9145	−0.187470
$39$	343.943	1.41218
$40$	−119.345	−0.471753
$41$	−253.121	−0.964168	−0.482084	−	0.876125i	$-0.660120\pi$
$41$	−253.121	−0.964168	−0.482084	+	0.876125i	$0.660120\pi$
$42$	340.093	1.24946
$43$	130.623	0.463253	0.231626	−	0.972805i	$-0.425595\pi$
$43$	130.623	0.463253	0.231626	+	0.972805i	$0.425595\pi$
$44$	0	0
$45$	507.582	1.68146
$46$	−355.498	−1.13946
$47$	499.093	1.54894	0.774471	−	0.632610i	$-0.218016\pi$
$47$	499.093	1.54894	0.774471	+	0.632610i	$0.218016\pi$
$48$	−124.989	−0.375846
$49$	130.839	0.381456
$50$	−195.102	−0.551831
$51$	194.627	0.534378
$52$	−176.114	−0.469666
$53$	12.9421	0.0335422	0.0167711	−	0.999859i	$-0.494661\pi$
$53$	12.9421	0.0335422	0.0167711	+	0.999859i	$0.494661\pi$
$54$	109.748	0.276569
$55$	0	0
$56$	−174.143	−0.415550
$57$	−171.526	−0.398582
$58$	298.793	0.676438
$59$	35.5614	0.0784694	0.0392347	−	0.999230i	$-0.487508\pi$
$59$	35.5614	0.0784694	0.0392347	+	0.999230i	$0.487508\pi$
$60$	−466.151	−1.00300
$61$	538.343	1.12996	0.564982	−	0.825103i	$-0.308883\pi$
$61$	538.343	1.12996	0.564982	+	0.825103i	$0.308883\pi$
$62$	−150.287	−0.307847
$63$	740.639	1.48114
$64$	64.0000	0.125000
$65$	−656.824	−1.25337
$66$	0	0
$67$	−519.621	−0.947491	−0.473745	−	0.880662i	$-0.657098\pi$
$67$	−519.621	−0.947491	−0.473745	+	0.880662i	$0.657098\pi$
$68$	−99.6580	−0.177725
$69$	−1388.54	−2.42262
$70$	−649.472	−1.10895
$71$	78.4486	0.131129	0.0655644	−	0.997848i	$-0.479115\pi$
$71$	78.4486	0.131129	0.0655644	+	0.997848i	$0.479115\pi$
$72$	−272.196	−0.445536
$73$	1144.07	1.83429	0.917145	−	0.398554i	$-0.130488\pi$
$73$	1144.07	1.83429	0.917145	+	0.398554i	$0.130488\pi$
$74$	−444.673	−0.698543
$75$	−762.049	−1.17325
$76$	87.8290	0.132562
$77$	0	0
$78$	−687.886	−0.998561
$79$	772.546	1.10023	0.550115	−	0.835089i	$-0.314584\pi$
$79$	772.546	1.10023	0.550115	+	0.835089i	$0.314584\pi$
$80$	238.690	0.333580
$81$	−489.997	−0.672149
$82$	506.243	0.681770
$83$	537.242	0.710481	0.355241	−	0.934775i	$-0.384399\pi$
$83$	537.242	0.710481	0.355241	+	0.934775i	$0.384399\pi$
$84$	−680.186	−0.883504
$85$	−371.678	−0.474284
$86$	−261.247	−0.327569
$87$	1167.06	1.43818
$88$	0	0
$89$	667.089	0.794509	0.397255	−	0.917708i	$-0.369963\pi$
$89$	667.089	0.794509	0.397255	+	0.917708i	$0.369963\pi$
$90$	−1015.16	−1.18897
$91$	−958.407	−1.10405
$92$	710.996	0.805723
$93$	−587.008	−0.654515
$94$	−998.187	−1.09527
$95$	327.561	0.353759
$96$	249.978	0.265763
$97$	−179.654	−0.188052	−0.0940262	−	0.995570i	$-0.529974\pi$
$97$	−179.654	−0.188052	−0.0940262	+	0.995570i	$0.529974\pi$
$98$	−261.679	−0.269730
$99$	0	0
$100$	390.203	0.390203
$101$	−410.736	−0.404651	−0.202325	−	0.979318i	$-0.564850\pi$
$101$	−410.736	−0.404651	−0.202325	+	0.979318i	$0.564850\pi$
$102$	−389.255	−0.377863
$103$	1367.66	1.30834	0.654172	−	0.756345i	$-0.273017\pi$
$103$	1367.66	1.30834	0.654172	+	0.756345i	$0.273017\pi$
$104$	352.228	0.332104
$105$	−2536.78	−2.35775
$106$	−25.8842	−0.0237179
$107$	−395.241	−0.357097	−0.178548	−	0.983931i	$-0.557140\pi$
$107$	−395.241	−0.357097	−0.178548	+	0.983931i	$0.557140\pi$
$108$	−219.495	−0.195564
$109$	505.826	0.444490	0.222245	−	0.974991i	$-0.428662\pi$
$109$	505.826	0.444490	0.222245	+	0.974991i	$0.428662\pi$
$110$	0	0
$111$	−1736.85	−1.48518
$112$	348.286	0.293838
$113$	1537.62	1.28007	0.640033	−	0.768347i	$-0.278921\pi$
$113$	1537.62	1.28007	0.640033	+	0.768347i	$0.278921\pi$
$114$	343.052	0.281840
$115$	2651.68	2.15018
$116$	−597.585	−0.478314
$117$	−1498.05	−1.18371
$118$	−71.1227	−0.0554862
$119$	−542.335	−0.417780
$120$	932.302	0.709226
$121$	0	0
$122$	−1076.69	−0.799005
$123$	1977.34	1.44952
$124$	300.574	0.217681
$125$	−409.491	−0.293008
$126$	−1481.28	−1.04732
$127$	−697.332	−0.487230	−0.243615	−	0.969872i	$-0.578333\pi$
$127$	−697.332	−0.487230	−0.243615	+	0.969872i	$0.578333\pi$
$128$	−128.000	−0.0883883
$129$	−1020.40	−0.696447
$130$	1313.65	0.886266
$131$	−259.910	−0.173347	−0.0866735	−	0.996237i	$-0.527624\pi$
$131$	−259.910	−0.173347	−0.0866735	+	0.996237i	$0.527624\pi$
$132$	0	0
$133$	477.962	0.311613
$134$	1039.24	0.669977
$135$	−818.615	−0.521890
$136$	199.316	0.125671
$137$	−2083.56	−1.29935	−0.649674	−	0.760213i	$-0.725094\pi$
$137$	−2083.56	−1.29935	−0.649674	+	0.760213i	$0.725094\pi$
$138$	2777.09	1.71305
$139$	173.429	0.105828	0.0529138	−	0.998599i	$-0.483149\pi$
$139$	173.429	0.105828	0.0529138	+	0.998599i	$0.483149\pi$
$140$	1298.94	0.784148
$141$	−3898.83	−2.32866
$142$	−156.897	−0.0927220
$143$	0	0
$144$	544.391	0.315041
$145$	−2228.71	−1.27645
$146$	−2288.14	−1.29704
$147$	−1022.09	−0.573475
$148$	889.346	0.493944
$149$	−449.055	−0.246899	−0.123450	−	0.992351i	$-0.539396\pi$
$149$	−449.055	−0.246899	−0.123450	+	0.992351i	$0.539396\pi$
$150$	1524.10	0.829614
$151$	28.5358	0.0153789	0.00768944	−	0.999970i	$-0.497552\pi$
$151$	28.5358	0.0153789	0.00768944	+	0.999970i	$0.497552\pi$
$152$	−175.658	−0.0937352
$153$	−847.702	−0.447926
$154$	0	0
$155$	1121.00	0.580910
$156$	1375.77	0.706089
$157$	1723.86	0.876300	0.438150	−	0.898902i	$-0.355634\pi$
$157$	1723.86	0.876300	0.438150	+	0.898902i	$0.355634\pi$
$158$	−1545.09	−0.777980
$159$	−101.101	−0.0504268
$160$	−477.380	−0.235876
$161$	3869.22	1.89402
$162$	979.993	0.475281
$163$	3318.22	1.59450	0.797249	−	0.603651i	$-0.206288\pi$
$163$	3318.22	1.59450	0.797249	+	0.603651i	$0.206288\pi$
$164$	−1012.49	−0.482084
$165$	0	0
$166$	−1074.48	−0.502386
$167$	−3015.60	−1.39733	−0.698665	−	0.715449i	$-0.746222\pi$
$167$	−3015.60	−1.39733	−0.698665	+	0.715449i	$0.746222\pi$
$168$	1360.37	0.624732
$169$	−258.486	−0.117654
$170$	743.356	0.335369
$171$	747.084	0.334099
$172$	522.493	0.231626
$173$	−2209.41	−0.970973	−0.485486	−	0.874244i	$-0.661357\pi$
$173$	−2209.41	−0.970973	−0.485486	+	0.874244i	$0.661357\pi$
$174$	−2334.11	−1.01695
$175$	2123.47	0.917254
$176$	0	0
$177$	−277.799	−0.117970
$178$	−1334.18	−0.561803
$179$	−2271.83	−0.948629	−0.474315	−	0.880355i	$-0.657304\pi$
$179$	−2271.83	−0.948629	−0.474315	+	0.880355i	$0.657304\pi$
$180$	2030.33	0.840731
$181$	−624.435	−0.256430	−0.128215	−	0.991746i	$-0.540925\pi$
$181$	−624.435	−0.256430	−0.128215	+	0.991746i	$0.540925\pi$
$182$	1916.81	0.780680
$183$	−4205.44	−1.69877
$184$	−1421.99	−0.569732
$185$	3316.85	1.31816
$186$	1174.02	0.462812
$187$	0	0
$188$	1996.37	0.774471
$189$	−1194.48	−0.459714
$190$	−655.123	−0.250145
$191$	−1344.20	−0.509229	−0.254615	−	0.967043i	$-0.581949\pi$
$191$	−1344.20	−0.509229	−0.254615	+	0.967043i	$0.581949\pi$
$192$	−499.956	−0.187923
$193$	4623.76	1.72449	0.862243	−	0.506496i	$-0.169059\pi$
$193$	4623.76	1.72449	0.862243	+	0.506496i	$0.169059\pi$
$194$	359.308	0.132973
$195$	5130.99	1.88430
$196$	523.358	0.190728
$197$	664.691	0.240392	0.120196	−	0.992750i	$-0.461648\pi$
$197$	664.691	0.240392	0.120196	+	0.992750i	$0.461648\pi$
$198$	0	0
$199$	−3042.82	−1.08392	−0.541959	−	0.840405i	$-0.682317\pi$
$199$	−3042.82	−1.08392	−0.541959	+	0.840405i	$0.682317\pi$
$200$	−780.407	−0.275915
$201$	4059.19	1.42444
$202$	821.471	0.286131
$203$	−3252.04	−1.12438
$204$	778.510	0.267189
$205$	−3776.10	−1.28651
$206$	−2735.32	−0.925139
$207$	6047.82	2.03069
$208$	−704.457	−0.234833
$209$	0	0
$210$	5073.55	1.66718
$211$	2591.61	0.845563	0.422781	−	0.906232i	$-0.361054\pi$
$211$	2591.61	0.845563	0.422781	+	0.906232i	$0.361054\pi$
$212$	51.7684	0.0167711
$213$	−612.826	−0.197137
$214$	790.481	0.252506
$215$	1948.66	0.618127
$216$	438.990	0.138285
$217$	1635.72	0.511703
$218$	−1011.65	−0.314302
$219$	−8937.26	−2.75764
$220$	0	0
$221$	1096.95	0.333886
$222$	3473.70	1.05018
$223$	2637.20	0.791929	0.395965	−	0.918266i	$-0.370410\pi$
$223$	2637.20	0.791929	0.395965	+	0.918266i	$0.370410\pi$
$224$	−696.571	−0.207775
$225$	3319.11	0.983441
$226$	−3075.25	−0.905143
$227$	250.670	0.0732932	0.0366466	−	0.999328i	$-0.488332\pi$
$227$	250.670	0.0732932	0.0366466	+	0.999328i	$0.488332\pi$
$228$	−686.104	−0.199291
$229$	1799.31	0.519222	0.259611	−	0.965713i	$-0.416406\pi$
$229$	1799.31	0.519222	0.259611	+	0.965713i	$0.416406\pi$
$230$	−5303.37	−1.52041
$231$	0	0
$232$	1195.17	0.338219
$233$	3180.48	0.894248	0.447124	−	0.894472i	$-0.352448\pi$
$233$	3180.48	0.894248	0.447124	+	0.894472i	$0.352448\pi$
$234$	2996.10	0.837012
$235$	7445.54	2.06678
$236$	142.245	0.0392347
$237$	−6034.98	−1.65407
$238$	1084.67	0.295415
$239$	5013.80	1.35697	0.678485	−	0.734614i	$-0.262637\pi$
$239$	5013.80	1.35697	0.678485	+	0.734614i	$0.262637\pi$
$240$	−1864.60	−0.501499
$241$	6074.13	1.62352	0.811761	−	0.583990i	$-0.198509\pi$
$241$	6074.13	1.62352	0.811761	+	0.583990i	$0.198509\pi$
$242$	0	0
$243$	5309.35	1.40163
$244$	2153.37	0.564982
$245$	1951.88	0.508984
$246$	−3954.67	−1.02496
$247$	−966.746	−0.249039
$248$	−601.149	−0.153923
$249$	−4196.83	−1.06813
$250$	818.981	0.207188
$251$	−5569.69	−1.40062	−0.700310	−	0.713838i	$-0.746955\pi$
$251$	−5569.69	−1.40062	−0.700310	+	0.713838i	$0.746955\pi$
$252$	2962.56	0.740570
$253$	0	0
$254$	1394.66	0.344524
$255$	2903.48	0.713031
$256$	256.000	0.0625000
$257$	−5907.05	−1.43374	−0.716871	−	0.697206i	$-0.754426\pi$
$257$	−5907.05	−1.43374	−0.716871	+	0.697206i	$0.754426\pi$
$258$	2040.81	0.492462
$259$	4839.79	1.16112
$260$	−2627.30	−0.626685
$261$	−5083.13	−1.20551
$262$	519.820	0.122575
$263$	−6853.74	−1.60692	−0.803459	−	0.595360i	$-0.797009\pi$
$263$	−6853.74	−1.60692	−0.803459	+	0.595360i	$0.797009\pi$
$264$	0	0
$265$	193.072	0.0447559
$266$	−955.924	−0.220344
$267$	−5211.18	−1.19445
$268$	−2078.49	−0.473745
$269$	1101.36	0.249633	0.124817	−	0.992180i	$-0.460166\pi$
$269$	1101.36	0.249633	0.124817	+	0.992180i	$0.460166\pi$
$270$	1637.23	0.369032
$271$	−2571.69	−0.576455	−0.288227	−	0.957562i	$-0.593066\pi$
$271$	−2571.69	−0.576455	−0.288227	+	0.957562i	$0.593066\pi$
$272$	−398.632	−0.0888626
$273$	7486.90	1.65981
$274$	4167.12	0.918777
$275$	0	0
$276$	−5554.17	−1.21131
$277$	−7340.10	−1.59214	−0.796072	−	0.605202i	$-0.793092\pi$
$277$	−7340.10	−1.59214	−0.796072	+	0.605202i	$0.793092\pi$
$278$	−346.857	−0.0748314
$279$	2556.72	0.548627
$280$	−2597.89	−0.554477
$281$	−7492.94	−1.59072	−0.795359	−	0.606139i	$-0.792718\pi$
$281$	−7492.94	−1.59072	−0.795359	+	0.606139i	$0.792718\pi$
$282$	7797.65	1.64661
$283$	−6494.10	−1.36408	−0.682039	−	0.731316i	$-0.738907\pi$
$283$	−6494.10	−1.36408	−0.682039	+	0.731316i	$0.738907\pi$
$284$	313.795	0.0655644
$285$	−2558.85	−0.531835
$286$	0	0
$287$	−5509.91	−1.13324
$288$	−1088.78	−0.222768
$289$	−4292.27	−0.873655
$290$	4457.43	0.902584
$291$	1403.42	0.282715
$292$	4576.28	0.917145
$293$	−2684.87	−0.535331	−0.267666	−	0.963512i	$-0.586252\pi$
$293$	−2684.87	−0.535331	−0.267666	+	0.963512i	$0.586252\pi$
$294$	2044.19	0.405508
$295$	530.509	0.104703
$296$	−1778.69	−0.349271
$297$	0	0
$298$	898.110	0.174584
$299$	−7826.03	−1.51368
$300$	−3048.20	−0.586626
$301$	2843.39	0.544486
$302$	−57.0716	−0.0108745
$303$	3208.59	0.608345
$304$	351.316	0.0662808
$305$	8031.08	1.50773
$306$	1695.40	0.316732
$307$	8331.66	1.54890	0.774451	−	0.632633i	$-0.218026\pi$
$307$	8331.66	1.54890	0.774451	+	0.632633i	$0.218026\pi$
$308$	0	0
$309$	−10683.9	−1.96695
$310$	−2242.01	−0.410766
$311$	−5020.35	−0.915363	−0.457682	−	0.889116i	$-0.651320\pi$
$311$	−5020.35	−0.915363	−0.457682	+	0.889116i	$0.651320\pi$
$312$	−2751.54	−0.499280
$313$	3022.08	0.545744	0.272872	−	0.962050i	$-0.412026\pi$
$313$	3022.08	0.545744	0.272872	+	0.962050i	$0.412026\pi$
$314$	−3447.72	−0.619637
$315$	11049.0	1.97631
$316$	3090.18	0.550115
$317$	−10540.1	−1.86749	−0.933744	−	0.357942i	$-0.883478\pi$
$317$	−10540.1	−1.86749	−0.933744	+	0.357942i	$0.883478\pi$
$318$	202.203	0.0356571
$319$	0	0
$320$	954.761	0.166790
$321$	3087.55	0.536854
$322$	−7738.43	−1.33927
$323$	−547.054	−0.0942381
$324$	−1959.99	−0.336074
$325$	−4295.02	−0.733061
$326$	−6636.44	−1.12748
$327$	−3951.42	−0.668239
$328$	2024.97	0.340885
$329$	10864.2	1.82055
$330$	0	0
$331$	309.871	0.0514563	0.0257281	−	0.999669i	$-0.491810\pi$
$331$	309.871	0.0514563	0.0257281	+	0.999669i	$0.491810\pi$
$332$	2148.97	0.355241
$333$	7564.88	1.24490
$334$	6031.20	0.988061
$335$	−7751.78	−1.26425
$336$	−2720.74	−0.441752
$337$	11164.7	1.80468	0.902340	−	0.431024i	$-0.141848\pi$
$337$	11164.7	1.80468	0.902340	+	0.431024i	$0.141848\pi$
$338$	516.972	0.0831941
$339$	−12011.6	−1.92443
$340$	−1486.71	−0.237142
$341$	0	0
$342$	−1494.17	−0.236244
$343$	−4618.28	−0.727008
$344$	−1044.99	−0.163785
$345$	−20714.5	−3.23255
$346$	4418.82	0.686581
$347$	2515.48	0.389159	0.194580	−	0.980887i	$-0.437666\pi$
$347$	2515.48	0.389159	0.194580	+	0.980887i	$0.437666\pi$
$348$	4668.23	0.719090
$349$	−11376.6	−1.74491	−0.872457	−	0.488692i	$-0.837474\pi$
$349$	−11376.6	−1.74491	−0.872457	+	0.488692i	$0.837474\pi$
$350$	−4246.94	−0.648596
$351$	2416.01	0.367400
$352$	0	0
$353$	6210.08	0.936343	0.468172	−	0.883638i	$-0.344913\pi$
$353$	6210.08	0.936343	0.468172	+	0.883638i	$0.344913\pi$
$354$	555.598	0.0834172
$355$	1170.31	0.174968
$356$	2668.36	0.397255
$357$	4236.62	0.628084
$358$	4543.66	0.670782
$359$	−2487.51	−0.365698	−0.182849	−	0.983141i	$-0.558532\pi$
$359$	−2487.51	−0.365698	−0.182849	+	0.983141i	$0.558532\pi$
$360$	−4060.65	−0.594487
$361$	−6376.88	−0.929710
$362$	1248.87	0.181324
$363$	0	0
$364$	−3833.63	−0.552024
$365$	17067.4	2.44753
$366$	8410.88	1.20121
$367$	6719.53	0.955739	0.477870	−	0.878431i	$-0.341409\pi$
$367$	6719.53	0.955739	0.477870	+	0.878431i	$0.341409\pi$
$368$	2843.98	0.402861
$369$	−8612.31	−1.21501
$370$	−6633.69	−0.932079
$371$	281.722	0.0394239
$372$	−2348.03	−0.327258
$373$	−8614.37	−1.19580	−0.597902	−	0.801569i	$-0.703999\pi$
$373$	−8614.37	−1.19580	−0.597902	+	0.801569i	$0.703999\pi$
$374$	0	0
$375$	3198.87	0.440503
$376$	−3992.75	−0.547634
$377$	6577.70	0.898592
$378$	2388.97	0.325067
$379$	−8009.10	−1.08549	−0.542744	−	0.839898i	$-0.682614\pi$
$379$	−8009.10	−1.08549	−0.542744	+	0.839898i	$0.682614\pi$
$380$	1310.25	0.176879
$381$	5447.43	0.732494
$382$	2688.40	0.360079
$383$	8011.95	1.06891	0.534454	−	0.845198i	$-0.320517\pi$
$383$	8011.95	1.06891	0.534454	+	0.845198i	$0.320517\pi$
$384$	999.912	0.132882
$385$	0	0
$386$	−9247.52	−1.21940
$387$	4444.39	0.583775
$388$	−718.615	−0.0940262
$389$	8029.60	1.04657	0.523287	−	0.852157i	$-0.324706\pi$
$389$	8029.60	1.04657	0.523287	+	0.852157i	$0.324706\pi$
$390$	−10262.0	−1.33240
$391$	−4428.53	−0.572789
$392$	−1046.72	−0.134865
$393$	2030.37	0.260607
$394$	−1329.38	−0.169983
$395$	11524.9	1.46806
$396$	0	0
$397$	4435.00	0.560670	0.280335	−	0.959902i	$-0.409554\pi$
$397$	4435.00	0.560670	0.280335	+	0.959902i	$0.409554\pi$
$398$	6085.64	0.766446
$399$	−3733.75	−0.468475
$400$	1560.81	0.195102
$401$	−3929.21	−0.489315	−0.244657	−	0.969610i	$-0.578675\pi$
$401$	−3929.21	−0.489315	−0.244657	+	0.969610i	$0.578675\pi$
$402$	−8118.37	−1.00723
$403$	−3308.46	−0.408949
$404$	−1642.94	−0.202325
$405$	−7309.84	−0.896861
$406$	6504.07	0.795054
$407$	0	0
$408$	−1557.02	−0.188931
$409$	−14564.2	−1.76077	−0.880384	−	0.474261i	$-0.842715\pi$
$409$	−14564.2	−1.76077	−0.880384	+	0.474261i	$0.842715\pi$
$410$	7552.20	0.909698
$411$	16276.4	1.95342
$412$	5470.64	0.654172
$413$	774.094	0.0922293
$414$	−12095.6	−1.43591
$415$	8014.65	0.948008
$416$	1408.91	0.166052
$417$	−1354.79	−0.159099
$418$	0	0
$419$	4028.77	0.469734	0.234867	−	0.972028i	$-0.424535\pi$
$419$	4028.77	0.469734	0.234867	+	0.972028i	$0.424535\pi$
$420$	−10147.1	−1.17888
$421$	−8527.60	−0.987197	−0.493599	−	0.869690i	$-0.664319\pi$
$421$	−8527.60	−0.987197	−0.493599	+	0.869690i	$0.664319\pi$
$422$	−5183.22	−0.597903
$423$	16981.4	1.95192
$424$	−103.537	−0.0118589
$425$	−2430.43	−0.277396
$426$	1225.65	0.139397
$427$	11718.6	1.32811
$428$	−1580.96	−0.178548
$429$	0	0
$430$	−3897.31	−0.437082
$431$	13415.2	1.49928	0.749639	−	0.661847i	$-0.230227\pi$
$431$	13415.2	1.49928	0.749639	+	0.661847i	$0.230227\pi$
$432$	−877.980	−0.0977821
$433$	4132.31	0.458628	0.229314	−	0.973352i	$-0.426352\pi$
$433$	4132.31	0.458628	0.229314	+	0.973352i	$0.426352\pi$
$434$	−3271.43	−0.361829
$435$	17410.3	1.91899
$436$	2023.30	0.222245
$437$	3902.88	0.427231
$438$	17874.5	1.94995
$439$	3358.46	0.365126	0.182563	−	0.983194i	$-0.441561\pi$
$439$	3358.46	0.365126	0.182563	+	0.983194i	$0.441561\pi$
$440$	0	0
$441$	4451.74	0.480698
$442$	−2193.90	−0.236093
$443$	−441.749	−0.0473773	−0.0236886	−	0.999719i	$-0.507541\pi$
$443$	−441.749	−0.0473773	−0.0236886	+	0.999719i	$0.507541\pi$
$444$	−6947.41	−0.742588
$445$	9951.73	1.06013
$446$	−5274.41	−0.559979
$447$	3507.93	0.371185
$448$	1393.14	0.146919
$449$	−408.478	−0.0429338	−0.0214669	−	0.999770i	$-0.506834\pi$
$449$	−408.478	−0.0429338	−0.0214669	+	0.999770i	$0.506834\pi$
$450$	−6638.23	−0.695398
$451$	0	0
$452$	6150.49	0.640033
$453$	−222.916	−0.0231204
$454$	−501.340	−0.0518261
$455$	−14297.6	−1.47315
$456$	1372.21	0.140920
$457$	1522.85	0.155877	0.0779384	−	0.996958i	$-0.475166\pi$
$457$	1522.85	0.155877	0.0779384	+	0.996958i	$0.475166\pi$
$458$	−3598.63	−0.367146
$459$	1367.15	0.139027
$460$	10606.7	1.07509
$461$	−13861.4	−1.40041	−0.700203	−	0.713944i	$-0.746907\pi$
$461$	−13861.4	−1.40041	−0.700203	+	0.713944i	$0.746907\pi$
$462$	0	0
$463$	−6502.26	−0.652669	−0.326334	−	0.945254i	$-0.605814\pi$
$463$	−6502.26	−0.652669	−0.326334	+	0.945254i	$0.605814\pi$
$464$	−2390.34	−0.239157
$465$	−8757.07	−0.873332
$466$	−6360.95	−0.632329
$467$	423.973	0.0420110	0.0210055	−	0.999779i	$-0.493313\pi$
$467$	423.973	0.0420110	0.0210055	+	0.999779i	$0.493313\pi$
$468$	−5992.19	−0.591857
$469$	−11311.0	−1.11364
$470$	−14891.1	−1.46144
$471$	−13466.5	−1.31742
$472$	−284.491	−0.0277431
$473$	0	0
$474$	12070.0	1.16960
$475$	2141.95	0.206904
$476$	−2169.34	−0.208890
$477$	440.348	0.0422687
$478$	−10027.6	−0.959523
$479$	4557.34	0.434718	0.217359	−	0.976092i	$-0.430256\pi$
$479$	4557.34	0.434718	0.217359	+	0.976092i	$0.430256\pi$
$480$	3729.21	0.354613
$481$	−9789.15	−0.927956
$482$	−12148.3	−1.14800
$483$	−30225.6	−2.84744
$484$	0	0
$485$	−2680.10	−0.250922
$486$	−10618.7	−0.991100
$487$	−6708.92	−0.624251	−0.312126	−	0.950041i	$-0.601041\pi$
$487$	−6708.92	−0.624251	−0.312126	+	0.950041i	$0.601041\pi$
$488$	−4306.75	−0.399503
$489$	−25921.3	−2.39714
$490$	−3903.76	−0.359906
$491$	14527.7	1.33528	0.667641	−	0.744483i	$-0.267304\pi$
$491$	14527.7	1.33528	0.667641	+	0.744483i	$0.267304\pi$
$492$	7909.35	0.724758
$493$	3722.13	0.340034
$494$	1933.49	0.176097
$495$	0	0
$496$	1202.30	0.108840
$497$	1707.66	0.154123
$498$	8393.67	0.755279
$499$	−9699.53	−0.870162	−0.435081	−	0.900391i	$-0.643280\pi$
$499$	−9699.53	−0.870162	−0.435081	+	0.900391i	$0.643280\pi$
$500$	−1637.96	−0.146504
$501$	23557.3	2.10072
$502$	11139.4	0.990388
$503$	15707.1	1.39234	0.696170	−	0.717877i	$-0.254886\pi$
$503$	15707.1	1.39234	0.696170	+	0.717877i	$0.254886\pi$
$504$	−5925.12	−0.523662
$505$	−6127.41	−0.539933
$506$	0	0
$507$	2019.25	0.176879
$508$	−2789.33	−0.243615
$509$	−1474.08	−0.128364	−0.0641822	−	0.997938i	$-0.520444\pi$
$509$	−1474.08	−0.128364	−0.0641822	+	0.997938i	$0.520444\pi$
$510$	−5806.96	−0.504189
$511$	24903.9	2.15594
$512$	−512.000	−0.0441942
$513$	−1204.88	−0.103697
$514$	11814.1	1.01381
$515$	20402.9	1.74575
$516$	−4081.62	−0.348223
$517$	0	0
$518$	−9679.57	−0.821035
$519$	17259.5	1.45975
$520$	5254.59	0.443133
$521$	−9272.84	−0.779752	−0.389876	−	0.920867i	$-0.627482\pi$
$521$	−9272.84	−0.779752	−0.389876	+	0.920867i	$0.627482\pi$
$522$	10166.3	0.852423
$523$	−4242.50	−0.354707	−0.177353	−	0.984147i	$-0.556754\pi$
$523$	−4242.50	−0.354707	−0.177353	+	0.984147i	$0.556754\pi$
$524$	−1039.64	−0.0866735
$525$	−16588.2	−1.37899
$526$	13707.5	1.13626
$527$	−1872.17	−0.154749
$528$	0	0
$529$	19427.7	1.59676
$530$	−386.144	−0.0316472
$531$	1209.96	0.0988844
$532$	1911.85	0.155807
$533$	11144.6	0.905675
$534$	10422.4	0.844606
$535$	−5896.25	−0.476481
$536$	4156.97	0.334988
$537$	17747.1	1.42615
$538$	−2202.73	−0.176517
$539$	0	0
$540$	−3274.46	−0.260945
$541$	−6520.25	−0.518166	−0.259083	−	0.965855i	$-0.583420\pi$
$541$	−6520.25	−0.518166	−0.259083	+	0.965855i	$0.583420\pi$
$542$	5143.39	0.407615
$543$	4877.97	0.385513
$544$	797.264	0.0628353
$545$	7545.98	0.593091
$546$	−14973.8	−1.17366
$547$	6370.78	0.497980	0.248990	−	0.968506i	$-0.419901\pi$
$547$	6370.78	0.497980	0.248990	+	0.968506i	$0.419901\pi$
$548$	−8334.24	−0.649674
$549$	18316.8	1.42394
$550$	0	0
$551$	−3280.33	−0.253624
$552$	11108.3	0.856526
$553$	16816.7	1.29316
$554$	14680.2	1.12582
$555$	−25910.6	−1.98170
$556$	693.715	0.0529138
$557$	6103.99	0.464335	0.232167	−	0.972676i	$-0.425418\pi$
$557$	6103.99	0.464335	0.232167	+	0.972676i	$0.425418\pi$
$558$	−5113.44	−0.387938
$559$	−5751.15	−0.435148
$560$	5195.77	0.392074
$561$	0	0
$562$	14985.9	1.12481
$563$	−13592.6	−1.01751	−0.508756	−	0.860911i	$-0.669894\pi$
$563$	−13592.6	−1.01751	−0.508756	+	0.860911i	$0.669894\pi$
$564$	−15595.3	−1.16433
$565$	22938.5	1.70802
$566$	12988.2	0.964549
$567$	−10666.2	−0.790013
$568$	−627.589	−0.0463610
$569$	17197.6	1.26706	0.633532	−	0.773717i	$-0.281605\pi$
$569$	17197.6	1.26706	0.633532	+	0.773717i	$0.281605\pi$
$570$	5117.70	0.376064
$571$	2475.65	0.181441	0.0907203	−	0.995876i	$-0.471083\pi$
$571$	2475.65	0.181441	0.0907203	+	0.995876i	$0.471083\pi$
$572$	0	0
$573$	10500.6	0.765567
$574$	11019.8	0.801321
$575$	17339.6	1.25758
$576$	2177.57	0.157521
$577$	−20339.7	−1.46751	−0.733755	−	0.679414i	$-0.762234\pi$
$577$	−20339.7	−1.46751	−0.733755	+	0.679414i	$0.762234\pi$
$578$	8584.54	0.617767
$579$	−36120.0	−2.59256
$580$	−8914.86	−0.638223
$581$	11694.6	0.835067
$582$	−2806.85	−0.199910
$583$	0	0
$584$	−9152.55	−0.648519
$585$	−22348.1	−1.57945
$586$	5369.75	0.378536
$587$	−14818.4	−1.04195	−0.520973	−	0.853573i	$-0.674431\pi$
$587$	−14818.4	−1.04195	−0.520973	+	0.853573i	$0.674431\pi$
$588$	−4088.37	−0.286738
$589$	1649.95	0.115424
$590$	−1061.02	−0.0740363
$591$	−5192.44	−0.361402
$592$	3557.38	0.246972
$593$	11123.2	0.770281	0.385140	−	0.922858i	$-0.374153\pi$
$593$	11123.2	0.770281	0.385140	+	0.922858i	$0.374153\pi$
$594$	0	0
$595$	−8090.63	−0.557451
$596$	−1796.22	−0.123450
$597$	23770.0	1.62955
$598$	15652.1	1.07034
$599$	8285.18	0.565147	0.282574	−	0.959246i	$-0.408812\pi$
$599$	8285.18	0.565147	0.282574	+	0.959246i	$0.408812\pi$
$600$	6096.39	0.414807
$601$	27318.3	1.85414	0.927069	−	0.374890i	$-0.122320\pi$
$601$	27318.3	1.85414	0.927069	+	0.374890i	$0.122320\pi$
$602$	−5686.78	−0.385009
$603$	−17679.8	−1.19399
$604$	114.143	0.00768944
$605$	0	0
$606$	−6417.18	−0.430165
$607$	16327.7	1.09180	0.545898	−	0.837851i	$-0.316188\pi$
$607$	16327.7	1.09180	0.545898	+	0.837851i	$0.316188\pi$
$608$	−702.632	−0.0468676
$609$	25404.3	1.69037
$610$	−16062.2	−1.06613
$611$	−21974.4	−1.45497
$612$	−3390.81	−0.223963
$613$	−21025.3	−1.38533	−0.692663	−	0.721262i	$-0.743563\pi$
$613$	−21025.3	−1.38533	−0.692663	+	0.721262i	$0.743563\pi$
$614$	−16663.3	−1.09524
$615$	29498.2	1.93412
$616$	0	0
$617$	871.824	0.0568854	0.0284427	−	0.999595i	$-0.490945\pi$
$617$	871.824	0.0568854	0.0284427	+	0.999595i	$0.490945\pi$
$618$	21367.8	1.39084
$619$	9397.52	0.610207	0.305104	−	0.952319i	$-0.401309\pi$
$619$	9397.52	0.610207	0.305104	+	0.952319i	$0.401309\pi$
$620$	4484.01	0.290455
$621$	−9753.76	−0.630282
$622$	10040.7	0.647260
$623$	14521.1	0.933829
$624$	5503.09	0.353045
$625$	−18302.7	−1.17137
$626$	−6044.15	−0.385899
$627$	0	0
$628$	6895.44	0.438150
$629$	−5539.40	−0.351145
$630$	−22097.9	−1.39746
$631$	−14535.9	−0.917062	−0.458531	−	0.888678i	$-0.651624\pi$
$631$	−14535.9	−0.917062	−0.458531	+	0.888678i	$0.651624\pi$
$632$	−6180.37	−0.388990
$633$	−20245.2	−1.27121
$634$	21080.3	1.32051
$635$	−10402.9	−0.650120
$636$	−404.405	−0.0252134
$637$	−5760.67	−0.358314
$638$	0	0
$639$	2669.17	0.165244
$640$	−1909.52	−0.117938
$641$	−11419.7	−0.703666	−0.351833	−	0.936063i	$-0.614441\pi$
$641$	−11419.7	−0.703666	−0.351833	+	0.936063i	$0.614441\pi$
$642$	−6175.09	−0.379613
$643$	23969.9	1.47011	0.735055	−	0.678007i	$-0.237156\pi$
$643$	23969.9	1.47011	0.735055	+	0.678007i	$0.237156\pi$
$644$	15476.9	0.947009
$645$	−15222.5	−0.929282
$646$	1094.11	0.0666364
$647$	8314.25	0.505204	0.252602	−	0.967570i	$-0.418714\pi$
$647$	8314.25	0.505204	0.252602	+	0.967570i	$0.418714\pi$
$648$	3919.97	0.237641
$649$	0	0
$650$	8590.04	0.518353
$651$	−12777.9	−0.769287
$652$	13272.9	0.797249
$653$	−30079.3	−1.80260	−0.901298	−	0.433200i	$-0.857384\pi$
$653$	−30079.3	−1.80260	−0.901298	+	0.433200i	$0.857384\pi$
$654$	7902.84	0.472516
$655$	−3877.38	−0.231300
$656$	−4049.94	−0.241042
$657$	38926.3	2.31151
$658$	−21728.4	−1.28733
$659$	−10041.6	−0.593572	−0.296786	−	0.954944i	$-0.595915\pi$
$659$	−10041.6	−0.593572	−0.296786	+	0.954944i	$0.595915\pi$
$660$	0	0
$661$	1402.50	0.0825281	0.0412640	−	0.999148i	$-0.486862\pi$
$661$	1402.50	0.0825281	0.0412640	+	0.999148i	$0.486862\pi$
$662$	−619.741	−0.0363851
$663$	−8569.17	−0.501959
$664$	−4297.93	−0.251193
$665$	7130.31	0.415792
$666$	−15129.8	−0.880279
$667$	−26555.1	−1.54155
$668$	−12062.4	−0.698665
$669$	−20601.4	−1.19057
$670$	15503.6	0.893963
$671$	0	0
$672$	5441.49	0.312366
$673$	20385.4	1.16761	0.583803	−	0.811895i	$-0.301564\pi$
$673$	20385.4	1.16761	0.583803	+	0.811895i	$0.301564\pi$
$674$	−22329.3	−1.27610
$675$	−5352.98	−0.305239
$676$	−1033.94	−0.0588271
$677$	−7385.00	−0.419245	−0.209622	−	0.977782i	$-0.567223\pi$
$677$	−7385.00	−0.419245	−0.209622	+	0.977782i	$0.567223\pi$
$678$	24023.3	1.36078
$679$	−3910.68	−0.221028
$680$	2973.42	0.167685
$681$	−1958.19	−0.110188
$682$	0	0
$683$	−25844.0	−1.44787	−0.723935	−	0.689868i	$-0.757668\pi$
$683$	−25844.0	−1.44787	−0.723935	+	0.689868i	$0.757668\pi$
$684$	2988.33	0.167049
$685$	−31082.8	−1.73374
$686$	9236.56	0.514072
$687$	−14055.9	−0.780591
$688$	2089.97	0.115813
$689$	−569.822	−0.0315073
$690$	41428.9	2.28576
$691$	8438.80	0.464583	0.232292	−	0.972646i	$-0.425378\pi$
$691$	8438.80	0.464583	0.232292	+	0.972646i	$0.425378\pi$
$692$	−8837.64	−0.485486
$693$	0	0
$694$	−5030.97	−0.275177
$695$	2587.23	0.141208
$696$	−9336.45	−0.508473
$697$	6306.39	0.342714
$698$	22753.2	1.23384
$699$	−24845.3	−1.34440
$700$	8493.89	0.458627
$701$	−12983.4	−0.699536	−0.349768	−	0.936836i	$-0.613740\pi$
$701$	−12983.4	−0.699536	−0.349768	+	0.936836i	$0.613740\pi$
$702$	−4832.03	−0.259791
$703$	4881.90	0.261912
$704$	0	0
$705$	−58163.2	−3.10717
$706$	−12420.2	−0.662095
$707$	−8940.83	−0.475608
$708$	−1111.20	−0.0589848
$709$	−17918.6	−0.949150	−0.474575	−	0.880215i	$-0.657398\pi$
$709$	−17918.6	−0.949150	−0.474575	+	0.880215i	$0.657398\pi$
$710$	−2340.61	−0.123721
$711$	26285.4	1.38647
$712$	−5336.71	−0.280901
$713$	13356.7	0.701560
$714$	−8473.24	−0.444122
$715$	0	0
$716$	−9087.33	−0.474315
$717$	−39166.9	−2.04005
$718$	4975.01	0.258587
$719$	3517.35	0.182441	0.0912204	−	0.995831i	$-0.470923\pi$
$719$	3517.35	0.182441	0.0912204	+	0.995831i	$0.470923\pi$
$720$	8121.30	0.420366
$721$	29771.0	1.53777
$722$	12753.8	0.657404
$723$	−47449.9	−2.44078
$724$	−2497.74	−0.128215
$725$	−14573.7	−0.746559
$726$	0	0
$727$	−29438.9	−1.50183	−0.750913	−	0.660401i	$-0.770386\pi$
$727$	−29438.9	−1.50183	−0.750913	+	0.660401i	$0.770386\pi$
$728$	7667.26	0.390340
$729$	−28245.8	−1.43503
$730$	−34134.8	−1.73066
$731$	−3254.41	−0.164663
$732$	−16821.8	−0.849385
$733$	3435.90	0.173135	0.0865673	−	0.996246i	$-0.472410\pi$
$733$	3435.90	0.173135	0.0865673	+	0.996246i	$0.472410\pi$
$734$	−13439.1	−0.675810
$735$	−15247.7	−0.765199
$736$	−5687.97	−0.284866
$737$	0	0
$738$	17224.6	0.859143
$739$	−33601.8	−1.67261	−0.836307	−	0.548262i	$-0.815290\pi$
$739$	−33601.8	−1.67261	−0.836307	+	0.548262i	$0.815290\pi$
$740$	13267.4	0.659079
$741$	7552.04	0.374401
$742$	−563.444	−0.0278769
$743$	−1193.70	−0.0589404	−0.0294702	−	0.999566i	$-0.509382\pi$
$743$	−1193.70	−0.0589404	−0.0294702	+	0.999566i	$0.509382\pi$
$744$	4696.06	0.231406
$745$	−6699.06	−0.329443
$746$	17228.7	0.845562
$747$	18279.4	0.895324
$748$	0	0
$749$	−8603.54	−0.419715
$750$	−6397.73	−0.311483
$751$	24509.4	1.19089	0.595446	−	0.803396i	$-0.296976\pi$
$751$	24509.4	1.19089	0.595446	+	0.803396i	$0.296976\pi$
$752$	7985.50	0.387235
$753$	43509.4	2.10567
$754$	−13155.4	−0.635400
$755$	425.701	0.0205203
$756$	−4777.94	−0.229857
$757$	10803.8	0.518721	0.259360	−	0.965781i	$-0.416488\pi$
$757$	10803.8	0.518721	0.259360	+	0.965781i	$0.416488\pi$
$758$	16018.2	0.767555
$759$	0	0
$760$	−2620.49	−0.125073
$761$	8175.91	0.389457	0.194728	−	0.980857i	$-0.437617\pi$
$761$	8175.91	0.389457	0.194728	+	0.980857i	$0.437617\pi$
$762$	−10894.9	−0.517951
$763$	11010.8	0.522432
$764$	−5376.79	−0.254615
$765$	−12646.1	−0.597676
$766$	−16023.9	−0.755831
$767$	−1565.72	−0.0737089
$768$	−1999.82	−0.0939615
$769$	−28895.9	−1.35502	−0.677511	−	0.735513i	$-0.736941\pi$
$769$	−28895.9	−1.35502	−0.677511	+	0.735513i	$0.736941\pi$
$770$	0	0
$771$	46144.8	2.15547
$772$	18495.0	0.862243
$773$	−17996.8	−0.837387	−0.418693	−	0.908128i	$-0.637512\pi$
$773$	−17996.8	−0.837387	−0.418693	+	0.908128i	$0.637512\pi$
$774$	−8888.77	−0.412791
$775$	7330.32	0.339759
$776$	1437.23	0.0664866
$777$	−37807.5	−1.74561
$778$	−16059.2	−0.740039
$779$	−5557.85	−0.255623
$780$	20524.0	0.942148
$781$	0	0
$782$	8857.06	0.405023
$783$	8197.94	0.374164
$784$	2093.43	0.0953640
$785$	25716.8	1.16926
$786$	−4060.74	−0.184277
$787$	−15876.7	−0.719114	−0.359557	−	0.933123i	$-0.617072\pi$
$787$	−15876.7	−0.719114	−0.359557	+	0.933123i	$0.617072\pi$
$788$	2658.76	0.120196
$789$	53540.1	2.41582
$790$	−23049.9	−1.03807
$791$	33470.8	1.50453
$792$	0	0
$793$	−23702.5	−1.06141
$794$	−8869.99	−0.396454
$795$	−1508.24	−0.0672854
$796$	−12171.3	−0.541959
$797$	16497.7	0.733223	0.366611	−	0.930374i	$-0.380518\pi$
$797$	16497.7	0.733223	0.366611	+	0.930374i	$0.380518\pi$
$798$	7467.51	0.331262
$799$	−12434.7	−0.550572
$800$	−3121.63	−0.137958
$801$	22697.3	1.00121
$802$	7858.41	0.345998
$803$	0	0
$804$	16236.7	0.712221
$805$	57721.5	2.52722
$806$	6616.93	0.289170
$807$	−8603.65	−0.375295
$808$	3285.88	0.143066
$809$	−9102.95	−0.395603	−0.197801	−	0.980242i	$-0.563380\pi$
$809$	−9102.95	−0.395603	−0.197801	+	0.980242i	$0.563380\pi$
$810$	14619.7	0.634176
$811$	36576.2	1.58368	0.791841	−	0.610728i	$-0.209123\pi$
$811$	36576.2	1.58368	0.791841	+	0.610728i	$0.209123\pi$
$812$	−13008.1	−0.562188
$813$	20089.6	0.866633
$814$	0	0
$815$	49501.7	2.12757
$816$	3114.04	0.133595
$817$	2868.13	0.122819
$818$	29128.4	1.24505
$819$	−32609.3	−1.39128
$820$	−15104.4	−0.643254
$821$	−3644.21	−0.154913	−0.0774567	−	0.996996i	$-0.524680\pi$
$821$	−3644.21	−0.154913	−0.0774567	+	0.996996i	$0.524680\pi$
$822$	−32552.8	−1.38128
$823$	−16895.9	−0.715618	−0.357809	−	0.933795i	$-0.616476\pi$
$823$	−16895.9	−0.715618	−0.357809	+	0.933795i	$0.616476\pi$
$824$	−10941.3	−0.462570
$825$	0	0
$826$	−1548.19	−0.0652160
$827$	−38778.1	−1.63053	−0.815263	−	0.579090i	$-0.803408\pi$
$827$	−38778.1	−1.63053	−0.815263	+	0.579090i	$0.803408\pi$
$828$	24191.3	1.01534
$829$	−12394.3	−0.519267	−0.259634	−	0.965707i	$-0.583602\pi$
$829$	−12394.3	−0.519267	−0.259634	+	0.965707i	$0.583602\pi$
$830$	−16029.3	−0.670343
$831$	57339.5	2.39361
$832$	−2817.83	−0.117417
$833$	−3259.80	−0.135589
$834$	2709.59	0.112500
$835$	−44987.1	−1.86448
$836$	0	0
$837$	−4123.41	−0.170282
$838$	−8057.55	−0.332152
$839$	24563.8	1.01077	0.505386	−	0.862893i	$-0.331350\pi$
$839$	24563.8	1.01077	0.505386	+	0.862893i	$0.331350\pi$
$840$	20294.2	0.833591
$841$	−2069.74	−0.0848635
$842$	17055.2	0.698054
$843$	58533.5	2.39146
$844$	10366.4	0.422781
$845$	−3856.13	−0.156988
$846$	−33962.8	−1.38022
$847$	0	0
$848$	207.074	0.00838554
$849$	50730.7	2.05073
$850$	4860.86	0.196148
$851$	39520.1	1.59193
$852$	−2451.30	−0.0985684
$853$	−12207.6	−0.490013	−0.245007	−	0.969521i	$-0.578790\pi$
$853$	−12207.6	−0.490013	−0.245007	+	0.969521i	$0.578790\pi$
$854$	−23437.2	−0.939114
$855$	11145.1	0.445794
$856$	3161.93	0.126253
$857$	7281.72	0.290244	0.145122	−	0.989414i	$-0.453643\pi$
$857$	7281.72	0.290244	0.145122	+	0.989414i	$0.453643\pi$
$858$	0	0
$859$	5927.39	0.235437	0.117718	−	0.993047i	$-0.462442\pi$
$859$	5927.39	0.235437	0.117718	+	0.993047i	$0.462442\pi$
$860$	7794.62	0.309063
$861$	43042.4	1.70369
$862$	−26830.4	−1.06015
$863$	−38561.9	−1.52104	−0.760522	−	0.649312i	$-0.775057\pi$
$863$	−38561.9	−1.52104	−0.760522	+	0.649312i	$0.775057\pi$
$864$	1755.96	0.0691424
$865$	−32960.3	−1.29559
$866$	−8264.62	−0.324299
$867$	33530.4	1.31344
$868$	6542.86	0.255852
$869$	0	0
$870$	−34820.6	−1.35693
$871$	22878.2	0.890009
$872$	−4046.61	−0.157151
$873$	−6112.63	−0.236977
$874$	−7805.76	−0.302098
$875$	−8913.73	−0.344388
$876$	−35749.0	−1.37882
$877$	28512.7	1.09784	0.548919	−	0.835875i	$-0.315039\pi$
$877$	28512.7	1.09784	0.548919	+	0.835875i	$0.315039\pi$
$878$	−6716.91	−0.258183
$879$	20973.7	0.804809
$880$	0	0
$881$	40747.6	1.55826	0.779128	−	0.626865i	$-0.215662\pi$
$881$	40747.6	1.55826	0.779128	+	0.626865i	$0.215662\pi$
$882$	−8903.48	−0.339905
$883$	−3595.59	−0.137034	−0.0685171	−	0.997650i	$-0.521827\pi$
$883$	−3595.59	−0.137034	−0.0685171	+	0.997650i	$0.521827\pi$
$884$	4387.80	0.166943
$885$	−4144.24	−0.157409
$886$	883.499	0.0335008
$887$	−7715.30	−0.292057	−0.146028	−	0.989280i	$-0.546649\pi$
$887$	−7715.30	−0.292057	−0.146028	+	0.989280i	$0.546649\pi$
$888$	13894.8	0.525089
$889$	−15179.4	−0.572667
$890$	−19903.5	−0.749624
$891$	0	0
$892$	10548.8	0.395965
$893$	10958.7	0.410660
$894$	−7015.87	−0.262467
$895$	−33891.5	−1.26577
$896$	−2786.29	−0.103888
$897$	61135.5	2.27565
$898$	816.957	0.0303588
$899$	−11226.2	−0.416478
$900$	13276.5	0.491721
$901$	−322.446	−0.0119226
$902$	0	0
$903$	−22212.0	−0.818571
$904$	−12301.0	−0.452572
$905$	−9315.41	−0.342160
$906$	445.833	0.0163486
$907$	−33713.7	−1.23423	−0.617114	−	0.786874i	$-0.711698\pi$
$907$	−33713.7	−1.23423	−0.617114	+	0.786874i	$0.711698\pi$
$908$	1002.68	0.0366466
$909$	−13975.1	−0.509927
$910$	28595.3	1.04168
$911$	15030.7	0.546642	0.273321	−	0.961923i	$-0.411878\pi$
$911$	15030.7	0.546642	0.273321	+	0.961923i	$0.411878\pi$
$912$	−2744.42	−0.0996455
$913$	0	0
$914$	−3045.69	−0.110222
$915$	−62737.3	−2.26670
$916$	7197.25	0.259611
$917$	−5657.69	−0.203744
$918$	−2734.31	−0.0983067
$919$	−17090.7	−0.613460	−0.306730	−	0.951797i	$-0.599235\pi$
$919$	−17090.7	−0.613460	−0.306730	+	0.951797i	$0.599235\pi$
$920$	−21213.5	−0.760204
$921$	−65085.4	−2.32860
$922$	27722.7	0.990237
$923$	−3453.98	−0.123173
$924$	0	0
$925$	21689.1	0.770955
$926$	13004.5	0.461506
$927$	46533.9	1.64873
$928$	4780.68	0.169109
$929$	13160.3	0.464773	0.232386	−	0.972624i	$-0.425347\pi$
$929$	13160.3	0.464773	0.232386	+	0.972624i	$0.425347\pi$
$930$	17514.1	0.617539
$931$	2872.87	0.101133
$932$	12721.9	0.447124
$933$	39218.1	1.37614
$934$	−847.946	−0.0297063
$935$	0	0
$936$	11984.4	0.418506
$937$	4056.29	0.141423	0.0707114	−	0.997497i	$-0.477473\pi$
$937$	4056.29	0.141423	0.0707114	+	0.997497i	$0.477473\pi$
$938$	22622.1	0.787460
$939$	−23607.9	−0.820463
$940$	29782.2	1.03339
$941$	33397.6	1.15699	0.578497	−	0.815684i	$-0.303639\pi$
$941$	33397.6	1.15699	0.578497	+	0.815684i	$0.303639\pi$
$942$	26933.0	0.931553
$943$	−44992.1	−1.55370
$944$	568.982	0.0196173
$945$	−17819.5	−0.613405
$946$	0	0
$947$	25660.8	0.880533	0.440267	−	0.897867i	$-0.354884\pi$
$947$	25660.8	0.880533	0.440267	+	0.897867i	$0.354884\pi$
$948$	−24139.9	−0.827034
$949$	−50371.7	−1.72301
$950$	−4283.90	−0.146303
$951$	82337.7	2.80755
$952$	4338.68	0.147707
$953$	48852.8	1.66054	0.830271	−	0.557359i	$-0.188185\pi$
$953$	48852.8	1.66054	0.830271	+	0.557359i	$0.188185\pi$
$954$	−880.696	−0.0298885
$955$	−20052.9	−0.679474
$956$	20055.2	0.678485
$957$	0	0
$958$	−9114.68	−0.307392
$959$	−45354.6	−1.52719
$960$	−7458.42	−0.250749
$961$	−24144.4	−0.810461
$962$	19578.3	0.656164
$963$	−13447.8	−0.450001
$964$	24296.5	0.811761
$965$	68977.9	2.30101
$966$	60451.2	2.01344
$967$	−48861.8	−1.62491	−0.812456	−	0.583023i	$-0.801870\pi$
$967$	−48861.8	−1.62491	−0.812456	+	0.583023i	$0.801870\pi$
$968$	0	0
$969$	4273.48	0.141676
$970$	5360.20	0.177429
$971$	34887.5	1.15303	0.576516	−	0.817086i	$-0.304412\pi$
$971$	34887.5	1.15303	0.576516	+	0.817086i	$0.304412\pi$
$972$	21237.4	0.700813
$973$	3775.17	0.124385
$974$	13417.8	0.441412
$975$	33551.9	1.10207
$976$	8613.49	0.282491
$977$	−19012.4	−0.622580	−0.311290	−	0.950315i	$-0.600761\pi$
$977$	−19012.4	−0.622580	−0.311290	+	0.950315i	$0.600761\pi$
$978$	51842.7	1.69504
$979$	0	0
$980$	7807.52	0.254492
$981$	17210.5	0.560130
$982$	−29055.3	−0.944187
$983$	−7447.89	−0.241659	−0.120829	−	0.992673i	$-0.538555\pi$
$983$	−7447.89	−0.241659	−0.120829	+	0.992673i	$0.538555\pi$
$984$	−15818.7	−0.512481
$985$	9915.95	0.320760
$986$	−7444.27	−0.240440
$987$	−84869.1	−2.73699
$988$	−3866.98	−0.124519
$989$	23218.2	0.746506
$990$	0	0
$991$	5313.37	0.170318	0.0851588	−	0.996367i	$-0.472860\pi$
$991$	5313.37	0.170318	0.0851588	+	0.996367i	$0.472860\pi$
$992$	−2404.60	−0.0769617
$993$	−2420.65	−0.0773586
$994$	−3415.32	−0.108981
$995$	−45393.2	−1.44629
$996$	−16787.3	−0.534063
$997$	53523.9	1.70022	0.850110	−	0.526604i	$-0.176535\pi$
$997$	53523.9	1.70022	0.850110	+	0.526604i	$0.176535\pi$
$998$	19399.1	0.615297
$999$	−12200.4	−0.386391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.4.a.n.1.1		4
3.2	odd	2		2178.4.a.by.1.1		4
4.3	odd	2		1936.4.a.bn.1.4		4
11.2	odd	10		242.4.c.n.81.1		8
11.3	even	5		22.4.c.b.9.2	yes	8
11.4	even	5		22.4.c.b.5.2	✓	8
11.5	even	5		242.4.c.r.3.1		8
11.6	odd	10		242.4.c.n.3.1		8
11.7	odd	10		242.4.c.q.27.2		8
11.8	odd	10		242.4.c.q.9.2		8
11.9	even	5		242.4.c.r.81.1		8
11.10	odd	2		242.4.a.o.1.1		4
33.14	odd	10		198.4.f.d.163.1		8
33.26	odd	10		198.4.f.d.181.1		8
33.32	even	2		2178.4.a.bt.1.1		4
44.3	odd	10		176.4.m.b.97.1		8
44.15	odd	10		176.4.m.b.49.1		8
44.43	even	2		1936.4.a.bm.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.b.5.2	✓	8	11.4	even	5
22.4.c.b.9.2	yes	8	11.3	even	5
176.4.m.b.49.1		8	44.15	odd	10
176.4.m.b.97.1		8	44.3	odd	10
198.4.f.d.163.1		8	33.14	odd	10
198.4.f.d.181.1		8	33.26	odd	10
242.4.a.n.1.1		4	1.1	even	1	trivial
242.4.a.o.1.1		4	11.10	odd	2
242.4.c.n.3.1		8	11.6	odd	10
242.4.c.n.81.1		8	11.2	odd	10
242.4.c.q.9.2		8	11.8	odd	10
242.4.c.q.27.2		8	11.7	odd	10
242.4.c.r.3.1		8	11.5	even	5
242.4.c.r.81.1		8	11.9	even	5
1936.4.a.bm.1.4		4	44.43	even	2
1936.4.a.bn.1.4		4	4.3	odd	2
2178.4.a.bt.1.1		4	33.32	even	2
2178.4.a.by.1.1		4	3.2	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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	242.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -7.81182 q^{3} +4.00000 q^{4} +14.9181 q^{5} +15.6236 q^{6} +21.7679 q^{7} -8.00000 q^{8} +34.0245 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -7.81182 q^{3} +4.00000 q^{4} +14.9181 q^{5} +15.6236 q^{6} +21.7679 q^{7} -8.00000 q^{8} +34.0245 q^{9} -29.8363 q^{10} -31.2473 q^{12} -44.0286 q^{13} -43.5357 q^{14} -116.538 q^{15} +16.0000 q^{16} -24.9145 q^{17} -68.0489 q^{18} +21.9573 q^{19} +59.6725 q^{20} -170.046 q^{21} +177.749 q^{23} +62.4945 q^{24} +97.5508 q^{25} +88.0571 q^{26} -54.8738 q^{27} +87.0714 q^{28} -149.396 q^{29} +233.075 q^{30} +75.1436 q^{31} -32.0000 q^{32} +49.8290 q^{34} +324.736 q^{35} +136.098 q^{36} +222.336 q^{37} -43.9145 q^{38} +343.943 q^{39} -119.345 q^{40} -253.121 q^{41} +340.093 q^{42} +130.623 q^{43} +507.582 q^{45} -355.498 q^{46} +499.093 q^{47} -124.989 q^{48} +130.839 q^{49} -195.102 q^{50} +194.627 q^{51} -176.114 q^{52} +12.9421 q^{53} +109.748 q^{54} -174.143 q^{56} -171.526 q^{57} +298.793 q^{58} +35.5614 q^{59} -466.151 q^{60} +538.343 q^{61} -150.287 q^{62} +740.639 q^{63} +64.0000 q^{64} -656.824 q^{65} -519.621 q^{67} -99.6580 q^{68} -1388.54 q^{69} -649.472 q^{70} +78.4486 q^{71} -272.196 q^{72} +1144.07 q^{73} -444.673 q^{74} -762.049 q^{75} +87.8290 q^{76} -687.886 q^{78} +772.546 q^{79} +238.690 q^{80} -489.997 q^{81} +506.243 q^{82} +537.242 q^{83} -680.186 q^{84} -371.678 q^{85} -261.247 q^{86} +1167.06 q^{87} +667.089 q^{89} -1015.16 q^{90} -958.407 q^{91} +710.996 q^{92} -587.008 q^{93} -998.187 q^{94} +327.561 q^{95} +249.978 q^{96} -179.654 q^{97} -261.679 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 4 q^{3} + 16 q^{4} + 25 q^{5} - 8 q^{6} - 3 q^{7} - 32 q^{8} + 102 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 + 4 * q^3 + 16 * q^4 + 25 * q^5 - 8 * q^6 - 3 * q^7 - 32 * q^8 + 102 * q^9	\( 4 q - 8 q^{2} + 4 q^{3} + 16 q^{4} + 25 q^{5} - 8 q^{6} - 3 q^{7} - 32 q^{8} + 102 q^{9} - 50 q^{10} + 16 q^{12} + 41 q^{13} + 6 q^{14} + 68 q^{15} + 64 q^{16} - 52 q^{17} - 204 q^{18} - 16 q^{19} + 100 q^{20} - 25 q^{21} + 314 q^{23} - 32 q^{24} - 21 q^{25} - 82 q^{26} + 286 q^{27} - 12 q^{28} - 561 q^{29} - 136 q^{30} + 199 q^{31} - 128 q^{32} + 104 q^{34} + 714 q^{35} + 408 q^{36} + 357 q^{37} + 32 q^{38} + 1038 q^{39} - 200 q^{40} - 32 q^{41} + 50 q^{42} + 721 q^{43} + 1326 q^{45} - 628 q^{46} + 403 q^{47} + 64 q^{48} + 823 q^{49} + 42 q^{50} + 174 q^{51} + 164 q^{52} - 133 q^{53} - 572 q^{54} + 24 q^{56} + 1031 q^{57} + 1122 q^{58} + 1016 q^{59} + 272 q^{60} + 919 q^{61} - 398 q^{62} + 1367 q^{63} + 256 q^{64} - 69 q^{65} + 289 q^{67} - 208 q^{68} - 1620 q^{69} - 1428 q^{70} - 1205 q^{71} - 816 q^{72} + 1234 q^{73} - 714 q^{74} - 911 q^{75} - 64 q^{76} - 2076 q^{78} + 603 q^{79} + 400 q^{80} - 1400 q^{81} + 64 q^{82} - 1514 q^{83} - 100 q^{84} - 717 q^{85} - 1442 q^{86} + 1061 q^{87} - 1101 q^{89} - 2652 q^{90} - 2306 q^{91} + 1256 q^{92} - 2298 q^{93} - 806 q^{94} + 1766 q^{95} - 128 q^{96} + 2116 q^{97} - 1646 q^{98}+O(q^{100}) \) 4 * q - 8 * q^2 + 4 * q^3 + 16 * q^4 + 25 * q^5 - 8 * q^6 - 3 * q^7 - 32 * q^8 + 102 * q^9 - 50 * q^10 + 16 * q^12 + 41 * q^13 + 6 * q^14 + 68 * q^15 + 64 * q^16 - 52 * q^17 - 204 * q^18 - 16 * q^19 + 100 * q^20 - 25 * q^21 + 314 * q^23 - 32 * q^24 - 21 * q^25 - 82 * q^26 + 286 * q^27 - 12 * q^28 - 561 * q^29 - 136 * q^30 + 199 * q^31 - 128 * q^32 + 104 * q^34 + 714 * q^35 + 408 * q^36 + 357 * q^37 + 32 * q^38 + 1038 * q^39 - 200 * q^40 - 32 * q^41 + 50 * q^42 + 721 * q^43 + 1326 * q^45 - 628 * q^46 + 403 * q^47 + 64 * q^48 + 823 * q^49 + 42 * q^50 + 174 * q^51 + 164 * q^52 - 133 * q^53 - 572 * q^54 + 24 * q^56 + 1031 * q^57 + 1122 * q^58 + 1016 * q^59 + 272 * q^60 + 919 * q^61 - 398 * q^62 + 1367 * q^63 + 256 * q^64 - 69 * q^65 + 289 * q^67 - 208 * q^68 - 1620 * q^69 - 1428 * q^70 - 1205 * q^71 - 816 * q^72 + 1234 * q^73 - 714 * q^74 - 911 * q^75 - 64 * q^76 - 2076 * q^78 + 603 * q^79 + 400 * q^80 - 1400 * q^81 + 64 * q^82 - 1514 * q^83 - 100 * q^84 - 717 * q^85 - 1442 * q^86 + 1061 * q^87 - 1101 * q^89 - 2652 * q^90 - 2306 * q^91 + 1256 * q^92 - 2298 * q^93 - 806 * q^94 + 1766 * q^95 - 128 * q^96 + 2116 * q^97 - 1646 * q^98

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