LMFDB - Embedded newform 930.4.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,4,Mod(1,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("930.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	930.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:	$54.8717763053$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 672x^{4} + 1206x^{3} + 93339x^{2} - 70713x - 2871288 $ x^6 - x^5 - 672x^4 + 1206x^3 + 93339x^2 - 70713x - 2871288
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$6.81581$ of defining polynomial
Character	$\chi$	$=$	930.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +2.44538 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +2.44538 q^{7} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} +25.5849 q^{11} +12.0000 q^{12} -73.9816 q^{13} +4.89076 q^{14} +15.0000 q^{15} +16.0000 q^{16} +53.6928 q^{17} +18.0000 q^{18} -33.0348 q^{19} +20.0000 q^{20} +7.33613 q^{21} +51.1697 q^{22} +189.245 q^{23} +24.0000 q^{24} +25.0000 q^{25} -147.963 q^{26} +27.0000 q^{27} +9.78151 q^{28} +247.924 q^{29} +30.0000 q^{30} +31.0000 q^{31} +32.0000 q^{32} +76.7546 q^{33} +107.386 q^{34} +12.2269 q^{35} +36.0000 q^{36} -91.1934 q^{37} -66.0695 q^{38} -221.945 q^{39} +40.0000 q^{40} +510.900 q^{41} +14.6723 q^{42} +156.464 q^{43} +102.339 q^{44} +45.0000 q^{45} +378.489 q^{46} -174.564 q^{47} +48.0000 q^{48} -337.020 q^{49} +50.0000 q^{50} +161.078 q^{51} -295.926 q^{52} +202.359 q^{53} +54.0000 q^{54} +127.924 q^{55} +19.5630 q^{56} -99.1043 q^{57} +495.849 q^{58} -603.488 q^{59} +60.0000 q^{60} -545.131 q^{61} +62.0000 q^{62} +22.0084 q^{63} +64.0000 q^{64} -369.908 q^{65} +153.509 q^{66} +947.654 q^{67} +214.771 q^{68} +567.734 q^{69} +24.4538 q^{70} +486.293 q^{71} +72.0000 q^{72} -979.470 q^{73} -182.387 q^{74} +75.0000 q^{75} -132.139 q^{76} +62.5647 q^{77} -443.890 q^{78} +212.849 q^{79} +80.0000 q^{80} +81.0000 q^{81} +1021.80 q^{82} +291.538 q^{83} +29.3445 q^{84} +268.464 q^{85} +312.929 q^{86} +743.773 q^{87} +204.679 q^{88} -243.897 q^{89} +90.0000 q^{90} -180.913 q^{91} +756.979 q^{92} +93.0000 q^{93} -349.127 q^{94} -165.174 q^{95} +96.0000 q^{96} +683.601 q^{97} -674.040 q^{98} +230.264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 30 q^{5} + 36 q^{6} + 21 q^{7} + 48 q^{8} + 54 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 30 * q^5 + 36 * q^6 + 21 * q^7 + 48 * q^8 + 54 * q^9	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 30 q^{5} + 36 q^{6} + 21 q^{7} + 48 q^{8} + 54 q^{9} + 60 q^{10} + 59 q^{11} + 72 q^{12} + 106 q^{13} + 42 q^{14} + 90 q^{15} + 96 q^{16} + 118 q^{17} + 108 q^{18} + 31 q^{19} + 120 q^{20} + 63 q^{21} + 118 q^{22} + 187 q^{23} + 144 q^{24} + 150 q^{25} + 212 q^{26} + 162 q^{27} + 84 q^{28} + 332 q^{29} + 180 q^{30} + 186 q^{31} + 192 q^{32} + 177 q^{33} + 236 q^{34} + 105 q^{35} + 216 q^{36} + 374 q^{37} + 62 q^{38} + 318 q^{39} + 240 q^{40} + 212 q^{41} + 126 q^{42} - 201 q^{43} + 236 q^{44} + 270 q^{45} + 374 q^{46} + 176 q^{47} + 288 q^{48} + 711 q^{49} + 300 q^{50} + 354 q^{51} + 424 q^{52} + 91 q^{53} + 324 q^{54} + 295 q^{55} + 168 q^{56} + 93 q^{57} + 664 q^{58} + 478 q^{59} + 360 q^{60} + 446 q^{61} + 372 q^{62} + 189 q^{63} + 384 q^{64} + 530 q^{65} + 354 q^{66} + 692 q^{67} + 472 q^{68} + 561 q^{69} + 210 q^{70} + 877 q^{71} + 432 q^{72} - 181 q^{73} + 748 q^{74} + 450 q^{75} + 124 q^{76} + 1079 q^{77} + 636 q^{78} - 259 q^{79} + 480 q^{80} + 486 q^{81} + 424 q^{82} + 290 q^{83} + 252 q^{84} + 590 q^{85} - 402 q^{86} + 996 q^{87} + 472 q^{88} + 87 q^{89} + 540 q^{90} - 954 q^{91} + 748 q^{92} + 558 q^{93} + 352 q^{94} + 155 q^{95} + 576 q^{96} - 434 q^{97} + 1422 q^{98} + 531 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 30 * q^5 + 36 * q^6 + 21 * q^7 + 48 * q^8 + 54 * q^9 + 60 * q^10 + 59 * q^11 + 72 * q^12 + 106 * q^13 + 42 * q^14 + 90 * q^15 + 96 * q^16 + 118 * q^17 + 108 * q^18 + 31 * q^19 + 120 * q^20 + 63 * q^21 + 118 * q^22 + 187 * q^23 + 144 * q^24 + 150 * q^25 + 212 * q^26 + 162 * q^27 + 84 * q^28 + 332 * q^29 + 180 * q^30 + 186 * q^31 + 192 * q^32 + 177 * q^33 + 236 * q^34 + 105 * q^35 + 216 * q^36 + 374 * q^37 + 62 * q^38 + 318 * q^39 + 240 * q^40 + 212 * q^41 + 126 * q^42 - 201 * q^43 + 236 * q^44 + 270 * q^45 + 374 * q^46 + 176 * q^47 + 288 * q^48 + 711 * q^49 + 300 * q^50 + 354 * q^51 + 424 * q^52 + 91 * q^53 + 324 * q^54 + 295 * q^55 + 168 * q^56 + 93 * q^57 + 664 * q^58 + 478 * q^59 + 360 * q^60 + 446 * q^61 + 372 * q^62 + 189 * q^63 + 384 * q^64 + 530 * q^65 + 354 * q^66 + 692 * q^67 + 472 * q^68 + 561 * q^69 + 210 * q^70 + 877 * q^71 + 432 * q^72 - 181 * q^73 + 748 * q^74 + 450 * q^75 + 124 * q^76 + 1079 * q^77 + 636 * q^78 - 259 * q^79 + 480 * q^80 + 486 * q^81 + 424 * q^82 + 290 * q^83 + 252 * q^84 + 590 * q^85 - 402 * q^86 + 996 * q^87 + 472 * q^88 + 87 * q^89 + 540 * q^90 - 954 * q^91 + 748 * q^92 + 558 * q^93 + 352 * q^94 + 155 * q^95 + 576 * q^96 - 434 * q^97 + 1422 * q^98 + 531 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	6.00000	0.408248
$7$	2.44538	0.132038	0.0660190	−	0.997818i	$-0.478970\pi$
$7$	2.44538	0.132038	0.0660190	+	0.997818i	$0.478970\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	10.0000	0.316228
$11$	25.5849	0.701284	0.350642	−	0.936510i	$-0.385963\pi$
$11$	25.5849	0.701284	0.350642	+	0.936510i	$0.385963\pi$
$12$	12.0000	0.288675
$13$	−73.9816	−1.57837	−0.789185	−	0.614156i	$-0.789497\pi$
$13$	−73.9816	−1.57837	−0.789185	+	0.614156i	$0.789497\pi$
$14$	4.89076	0.0933650
$15$	15.0000	0.258199
$16$	16.0000	0.250000
$17$	53.6928	0.766024	0.383012	−	0.923743i	$-0.374887\pi$
$17$	53.6928	0.766024	0.383012	+	0.923743i	$0.374887\pi$
$18$	18.0000	0.235702
$19$	−33.0348	−0.398879	−0.199439	−	0.979910i	$-0.563912\pi$
$19$	−33.0348	−0.398879	−0.199439	+	0.979910i	$0.563912\pi$
$20$	20.0000	0.223607
$21$	7.33613	0.0762322
$22$	51.1697	0.495883
$23$	189.245	1.71566	0.857832	−	0.513931i	$-0.171811\pi$
$23$	189.245	1.71566	0.857832	+	0.513931i	$0.171811\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	−147.963	−1.11608
$27$	27.0000	0.192450
$28$	9.78151	0.0660190
$29$	247.924	1.58753	0.793765	−	0.608224i	$-0.208118\pi$
$29$	247.924	1.58753	0.793765	+	0.608224i	$0.208118\pi$
$30$	30.0000	0.182574
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	32.0000	0.176777
$33$	76.7546	0.404887
$34$	107.386	0.541661
$35$	12.2269	0.0590492
$36$	36.0000	0.166667
$37$	−91.1934	−0.405192	−0.202596	−	0.979262i	$-0.564938\pi$
$37$	−91.1934	−0.405192	−0.202596	+	0.979262i	$0.564938\pi$
$38$	−66.0695	−0.282050
$39$	−221.945	−0.911272
$40$	40.0000	0.158114
$41$	510.900	1.94608	0.973039	−	0.230640i	$-0.0740819\pi$
$41$	510.900	1.94608	0.973039	+	0.230640i	$0.0740819\pi$
$42$	14.6723	0.0539043
$43$	156.464	0.554897	0.277449	−	0.960740i	$-0.410511\pi$
$43$	156.464	0.554897	0.277449	+	0.960740i	$0.410511\pi$
$44$	102.339	0.350642
$45$	45.0000	0.149071
$46$	378.489	1.21316
$47$	−174.564	−0.541760	−0.270880	−	0.962613i	$-0.587315\pi$
$47$	−174.564	−0.541760	−0.270880	+	0.962613i	$0.587315\pi$
$48$	48.0000	0.144338
$49$	−337.020	−0.982566
$50$	50.0000	0.141421
$51$	161.078	0.442264
$52$	−295.926	−0.789185
$53$	202.359	0.524457	0.262228	−	0.965006i	$-0.415543\pi$
$53$	202.359	0.524457	0.262228	+	0.965006i	$0.415543\pi$
$54$	54.0000	0.136083
$55$	127.924	0.313624
$56$	19.5630	0.0466825
$57$	−99.1043	−0.230293
$58$	495.849	1.12255
$59$	−603.488	−1.33165	−0.665826	−	0.746107i	$-0.731921\pi$
$59$	−603.488	−1.33165	−0.665826	+	0.746107i	$0.731921\pi$
$60$	60.0000	0.129099
$61$	−545.131	−1.14421	−0.572105	−	0.820180i	$-0.693873\pi$
$61$	−545.131	−1.14421	−0.572105	+	0.820180i	$0.693873\pi$
$62$	62.0000	0.127000
$63$	22.0084	0.0440127
$64$	64.0000	0.125000
$65$	−369.908	−0.705868
$66$	153.509	0.286298
$67$	947.654	1.72798	0.863988	−	0.503513i	$-0.167959\pi$
$67$	947.654	1.72798	0.863988	+	0.503513i	$0.167959\pi$
$68$	214.771	0.383012
$69$	567.734	0.990539
$70$	24.4538	0.0417541
$71$	486.293	0.812850	0.406425	−	0.913684i	$-0.366775\pi$
$71$	486.293	0.812850	0.406425	+	0.913684i	$0.366775\pi$
$72$	72.0000	0.117851
$73$	−979.470	−1.57039	−0.785194	−	0.619250i	$-0.787437\pi$
$73$	−979.470	−1.57039	−0.785194	+	0.619250i	$0.787437\pi$
$74$	−182.387	−0.286514
$75$	75.0000	0.115470
$76$	−132.139	−0.199439
$77$	62.5647	0.0925962
$78$	−443.890	−0.644367
$79$	212.849	0.303131	0.151565	−	0.988447i	$-0.451569\pi$
$79$	212.849	0.303131	0.151565	+	0.988447i	$0.451569\pi$
$80$	80.0000	0.111803
$81$	81.0000	0.111111
$82$	1021.80	1.37609
$83$	291.538	0.385547	0.192774	−	0.981243i	$-0.438252\pi$
$83$	291.538	0.385547	0.192774	+	0.981243i	$0.438252\pi$
$84$	29.3445	0.0381161
$85$	268.464	0.342576
$86$	312.929	0.392372
$87$	743.773	0.916561
$88$	204.679	0.247941
$89$	−243.897	−0.290484	−0.145242	−	0.989396i	$-0.546396\pi$
$89$	−243.897	−0.290484	−0.145242	+	0.989396i	$0.546396\pi$
$90$	90.0000	0.105409
$91$	−180.913	−0.208405
$92$	756.979	0.857832
$93$	93.0000	0.103695
$94$	−349.127	−0.383082
$95$	−165.174	−0.178384
$96$	96.0000	0.102062
$97$	683.601	0.715558	0.357779	−	0.933806i	$-0.383534\pi$
$97$	683.601	0.715558	0.357779	+	0.933806i	$0.383534\pi$
$98$	−674.040	−0.694779
$99$	230.264	0.233761
$100$	100.000	0.100000
$101$	−1191.24	−1.17359	−0.586797	−	0.809734i	$-0.699611\pi$
$101$	−1191.24	−1.17359	−0.586797	+	0.809734i	$0.699611\pi$
$102$	322.157	0.312728
$103$	1073.42	1.02687	0.513433	−	0.858130i	$-0.328374\pi$
$103$	1073.42	1.02687	0.513433	+	0.858130i	$0.328374\pi$
$104$	−591.853	−0.558038
$105$	36.6807	0.0340921
$106$	404.719	0.370847
$107$	−451.707	−0.408114	−0.204057	−	0.978959i	$-0.565413\pi$
$107$	−451.707	−0.408114	−0.204057	+	0.978959i	$0.565413\pi$
$108$	108.000	0.0962250
$109$	44.9693	0.0395163	0.0197582	−	0.999805i	$-0.493710\pi$
$109$	44.9693	0.0395163	0.0197582	+	0.999805i	$0.493710\pi$
$110$	255.849	0.221765
$111$	−273.580	−0.233938
$112$	39.1261	0.0330095
$113$	1670.02	1.39029	0.695143	−	0.718871i	$-0.255341\pi$
$113$	1670.02	1.39029	0.695143	+	0.718871i	$0.255341\pi$
$114$	−198.209	−0.162842
$115$	946.224	0.767268
$116$	991.697	0.793765
$117$	−665.834	−0.526123
$118$	−1206.98	−0.941620
$119$	131.299	0.101144
$120$	120.000	0.0912871
$121$	−676.415	−0.508201
$122$	−1090.26	−0.809079
$123$	1532.70	1.12357
$124$	124.000	0.0898027
$125$	125.000	0.0894427
$126$	44.0168	0.0311217
$127$	770.540	0.538381	0.269190	−	0.963087i	$-0.413244\pi$
$127$	770.540	0.538381	0.269190	+	0.963087i	$0.413244\pi$
$128$	128.000	0.0883883
$129$	469.393	0.320370
$130$	−739.816	−0.499124
$131$	1058.09	0.705694	0.352847	−	0.935681i	$-0.385214\pi$
$131$	1058.09	0.705694	0.352847	+	0.935681i	$0.385214\pi$
$132$	307.018	0.202443
$133$	−80.7825	−0.0526672
$134$	1895.31	1.22186
$135$	135.000	0.0860663
$136$	429.542	0.270830
$137$	−2424.25	−1.51181	−0.755903	−	0.654683i	$-0.772802\pi$
$137$	−2424.25	−1.51181	−0.755903	+	0.654683i	$0.772802\pi$
$138$	1135.47	0.700417
$139$	−2843.82	−1.73532	−0.867660	−	0.497158i	$-0.834377\pi$
$139$	−2843.82	−1.73532	−0.867660	+	0.497158i	$0.834377\pi$
$140$	48.9076	0.0295246
$141$	−523.691	−0.312785
$142$	972.586	0.574772
$143$	−1892.81	−1.10689
$144$	144.000	0.0833333
$145$	1239.62	0.709965
$146$	−1958.94	−1.11043
$147$	−1011.06	−0.567285
$148$	−364.774	−0.202596
$149$	2566.83	1.41129	0.705647	−	0.708564i	$-0.250657\pi$
$149$	2566.83	1.41129	0.705647	+	0.708564i	$0.250657\pi$
$150$	150.000	0.0816497
$151$	−2458.82	−1.32514	−0.662570	−	0.749000i	$-0.730534\pi$
$151$	−2458.82	−1.32514	−0.662570	+	0.749000i	$0.730534\pi$
$152$	−264.278	−0.141025
$153$	483.235	0.255341
$154$	125.129	0.0654754
$155$	155.000	0.0803219
$156$	−887.779	−0.455636
$157$	−1942.26	−0.987318	−0.493659	−	0.869656i	$-0.664341\pi$
$157$	−1942.26	−0.987318	−0.493659	+	0.869656i	$0.664341\pi$
$158$	425.697	0.214346
$159$	607.078	0.302795
$160$	160.000	0.0790569
$161$	462.775	0.226533
$162$	162.000	0.0785674
$163$	603.363	0.289933	0.144966	−	0.989437i	$-0.453693\pi$
$163$	603.363	0.289933	0.144966	+	0.989437i	$0.453693\pi$
$164$	2043.60	0.973039
$165$	383.773	0.181071
$166$	583.076	0.272623
$167$	−1295.33	−0.600216	−0.300108	−	0.953905i	$-0.597023\pi$
$167$	−1295.33	−0.600216	−0.300108	+	0.953905i	$0.597023\pi$
$168$	58.6891	0.0269521
$169$	3276.28	1.49125
$170$	536.928	0.242238
$171$	−297.313	−0.132960
$172$	625.857	0.277449
$173$	−2070.93	−0.910117	−0.455058	−	0.890462i	$-0.650382\pi$
$173$	−2070.93	−0.910117	−0.455058	+	0.890462i	$0.650382\pi$
$174$	1487.55	0.648107
$175$	61.1345	0.0264076
$176$	409.358	0.175321
$177$	−1810.46	−0.768830
$178$	−487.794	−0.205403
$179$	2533.04	1.05770	0.528851	−	0.848715i	$-0.322623\pi$
$179$	2533.04	1.05770	0.528851	+	0.848715i	$0.322623\pi$
$180$	180.000	0.0745356
$181$	4014.25	1.64849	0.824245	−	0.566233i	$-0.191600\pi$
$181$	4014.25	1.64849	0.824245	+	0.566233i	$0.191600\pi$
$182$	−361.826	−0.147364
$183$	−1635.39	−0.660610
$184$	1513.96	0.606579
$185$	−455.967	−0.181207
$186$	186.000	0.0733236
$187$	1373.72	0.537201
$188$	−698.255	−0.270880
$189$	66.0252	0.0254107
$190$	−330.348	−0.126137
$191$	−2067.36	−0.783190	−0.391595	−	0.920138i	$-0.628077\pi$
$191$	−2067.36	−0.783190	−0.391595	+	0.920138i	$0.628077\pi$
$192$	192.000	0.0721688
$193$	−3057.25	−1.14024	−0.570119	−	0.821562i	$-0.693103\pi$
$193$	−3057.25	−1.14024	−0.570119	+	0.821562i	$0.693103\pi$
$194$	1367.20	0.505976
$195$	−1109.72	−0.407533
$196$	−1348.08	−0.491283
$197$	2787.04	1.00796	0.503980	−	0.863715i	$-0.331868\pi$
$197$	2787.04	1.00796	0.503980	+	0.863715i	$0.331868\pi$
$198$	460.527	0.165294
$199$	−1938.80	−0.690644	−0.345322	−	0.938484i	$-0.612230\pi$
$199$	−1938.80	−0.690644	−0.345322	+	0.938484i	$0.612230\pi$
$200$	200.000	0.0707107
$201$	2842.96	0.997647
$202$	−2382.48	−0.829856
$203$	606.269	0.209614
$204$	644.313	0.221132
$205$	2554.50	0.870313
$206$	2146.84	0.726103
$207$	1703.20	0.571888
$208$	−1183.71	−0.394592
$209$	−845.190	−0.279727
$210$	73.3613	0.0241067
$211$	2488.01	0.811762	0.405881	−	0.913926i	$-0.366965\pi$
$211$	2488.01	0.811762	0.405881	+	0.913926i	$0.366965\pi$
$212$	809.438	0.262228
$213$	1458.88	0.469299
$214$	−903.414	−0.288580
$215$	782.321	0.248158
$216$	216.000	0.0680414
$217$	75.8067	0.0237147
$218$	89.9387	0.0279423
$219$	−2938.41	−0.906664
$220$	511.697	0.156812
$221$	−3972.28	−1.20907
$222$	−547.160	−0.165419
$223$	−3279.34	−0.984756	−0.492378	−	0.870381i	$-0.663872\pi$
$223$	−3279.34	−0.984756	−0.492378	+	0.870381i	$0.663872\pi$
$224$	78.2521	0.0233412
$225$	225.000	0.0666667
$226$	3340.04	0.983081
$227$	4909.37	1.43545	0.717724	−	0.696328i	$-0.245184\pi$
$227$	4909.37	1.43545	0.717724	+	0.696328i	$0.245184\pi$
$228$	−396.417	−0.115146
$229$	−2606.02	−0.752012	−0.376006	−	0.926617i	$-0.622703\pi$
$229$	−2606.02	−0.752012	−0.376006	+	0.926617i	$0.622703\pi$
$230$	1892.45	0.542540
$231$	187.694	0.0534604
$232$	1983.39	0.561277
$233$	−2226.54	−0.626031	−0.313016	−	0.949748i	$-0.601339\pi$
$233$	−2226.54	−0.626031	−0.313016	+	0.949748i	$0.601339\pi$
$234$	−1331.67	−0.372025
$235$	−872.818	−0.242283
$236$	−2413.95	−0.665826
$237$	638.546	0.175013
$238$	262.598	0.0715198
$239$	−7066.01	−1.91239	−0.956197	−	0.292724i	$-0.905438\pi$
$239$	−7066.01	−1.91239	−0.956197	+	0.292724i	$0.905438\pi$
$240$	240.000	0.0645497
$241$	−3654.41	−0.976769	−0.488385	−	0.872629i	$-0.662414\pi$
$241$	−3654.41	−0.976769	−0.488385	+	0.872629i	$0.662414\pi$
$242$	−1352.83	−0.359352
$243$	243.000	0.0641500
$244$	−2180.52	−0.572105
$245$	−1685.10	−0.439417
$246$	3065.40	0.794483
$247$	2443.96	0.629578
$248$	248.000	0.0635001
$249$	874.613	0.222596
$250$	250.000	0.0632456
$251$	4367.97	1.09842	0.549211	−	0.835684i	$-0.314928\pi$
$251$	4367.97	1.09842	0.549211	+	0.835684i	$0.314928\pi$
$252$	88.0336	0.0220063
$253$	4841.80	1.20317
$254$	1541.08	0.380693
$255$	805.392	0.197787
$256$	256.000	0.0625000
$257$	−3779.64	−0.917384	−0.458692	−	0.888595i	$-0.651682\pi$
$257$	−3779.64	−0.917384	−0.458692	+	0.888595i	$0.651682\pi$
$258$	938.786	0.226536
$259$	−223.002	−0.0535007
$260$	−1479.63	−0.352934
$261$	2231.32	0.529177
$262$	2116.18	0.499001
$263$	−1879.52	−0.440671	−0.220335	−	0.975424i	$-0.570715\pi$
$263$	−1879.52	−0.440671	−0.220335	+	0.975424i	$0.570715\pi$
$264$	614.037	0.143149
$265$	1011.80	0.234544
$266$	−161.565	−0.0372413
$267$	−731.691	−0.167711
$268$	3790.61	0.863988
$269$	1011.61	0.229289	0.114645	−	0.993407i	$-0.463427\pi$
$269$	1011.61	0.229289	0.114645	+	0.993407i	$0.463427\pi$
$270$	270.000	0.0608581
$271$	−398.386	−0.0892996	−0.0446498	−	0.999003i	$-0.514217\pi$
$271$	−398.386	−0.0892996	−0.0446498	+	0.999003i	$0.514217\pi$
$272$	859.084	0.191506
$273$	−542.739	−0.120323
$274$	−4848.50	−1.06901
$275$	639.621	0.140257
$276$	2270.94	0.495269
$277$	−4166.76	−0.903813	−0.451906	−	0.892065i	$-0.649256\pi$
$277$	−4166.76	−0.903813	−0.451906	+	0.892065i	$0.649256\pi$
$278$	−5687.64	−1.22706
$279$	279.000	0.0598684
$280$	97.8151	0.0208770
$281$	1459.02	0.309743	0.154871	−	0.987935i	$-0.450504\pi$
$281$	1459.02	0.309743	0.154871	+	0.987935i	$0.450504\pi$
$282$	−1047.38	−0.221173
$283$	−271.785	−0.0570881	−0.0285440	−	0.999593i	$-0.509087\pi$
$283$	−271.785	−0.0570881	−0.0285440	+	0.999593i	$0.509087\pi$
$284$	1945.17	0.406425
$285$	−495.521	−0.102990
$286$	−3785.62	−0.782686
$287$	1249.34	0.256956
$288$	288.000	0.0589256
$289$	−2030.09	−0.413207
$290$	2479.24	0.502021
$291$	2050.80	0.413128
$292$	−3917.88	−0.785194
$293$	−1882.47	−0.375341	−0.187670	−	0.982232i	$-0.560094\pi$
$293$	−1882.47	−0.375341	−0.187670	+	0.982232i	$0.560094\pi$
$294$	−2022.12	−0.401131
$295$	−3017.44	−0.595533
$296$	−729.547	−0.143257
$297$	690.791	0.134962
$298$	5133.65	0.997935
$299$	−14000.6	−2.70795
$300$	300.000	0.0577350
$301$	382.614	0.0732675
$302$	−4917.64	−0.937015
$303$	−3573.72	−0.677574
$304$	−528.556	−0.0997197
$305$	−2725.65	−0.511706
$306$	966.470	0.180554
$307$	−8459.14	−1.57260	−0.786301	−	0.617844i	$-0.788006\pi$
$307$	−8459.14	−1.57260	−0.786301	+	0.617844i	$0.788006\pi$
$308$	250.259	0.0462981
$309$	3220.26	0.592861
$310$	310.000	0.0567962
$311$	−7134.59	−1.30085	−0.650427	−	0.759569i	$-0.725410\pi$
$311$	−7134.59	−1.30085	−0.650427	+	0.759569i	$0.725410\pi$
$312$	−1775.56	−0.322183
$313$	249.274	0.0450154	0.0225077	−	0.999747i	$-0.492835\pi$
$313$	249.274	0.0450154	0.0225077	+	0.999747i	$0.492835\pi$
$314$	−3884.51	−0.698139
$315$	110.042	0.0196831
$316$	851.395	0.151565
$317$	6398.74	1.13372	0.566859	−	0.823815i	$-0.308158\pi$
$317$	6398.74	1.13372	0.566859	+	0.823815i	$0.308158\pi$
$318$	1214.16	0.214109
$319$	6343.11	1.11331
$320$	320.000	0.0559017
$321$	−1355.12	−0.235625
$322$	925.550	0.160183
$323$	−1773.73	−0.305551
$324$	324.000	0.0555556
$325$	−1849.54	−0.315674
$326$	1206.73	0.205014
$327$	134.908	0.0228148
$328$	4087.20	0.688043
$329$	−426.874	−0.0715329
$330$	767.546	0.128036
$331$	11605.9	1.92724	0.963621	−	0.267272i	$-0.0861224\pi$
$331$	11605.9	1.92724	0.963621	+	0.267272i	$0.0861224\pi$
$332$	1166.15	0.192774
$333$	−820.741	−0.135064
$334$	−2590.67	−0.424417
$335$	4738.27	0.772774
$336$	117.378	0.0190580
$337$	5240.65	0.847111	0.423555	−	0.905870i	$-0.360782\pi$
$337$	5240.65	0.847111	0.423555	+	0.905870i	$0.360782\pi$
$338$	6552.55	1.05447
$339$	5010.06	0.802682
$340$	1073.86	0.171288
$341$	793.131	0.125954
$342$	−594.626	−0.0940166
$343$	−1662.91	−0.261774
$344$	1251.71	0.196186
$345$	2838.67	0.442982
$346$	−4141.87	−0.643550
$347$	4135.14	0.639729	0.319865	−	0.947463i	$-0.396363\pi$
$347$	4135.14	0.639729	0.319865	+	0.947463i	$0.396363\pi$
$348$	2975.09	0.458281
$349$	3225.63	0.494739	0.247370	−	0.968921i	$-0.420434\pi$
$349$	3225.63	0.494739	0.247370	+	0.968921i	$0.420434\pi$
$350$	122.269	0.0186730
$351$	−1997.50	−0.303757
$352$	818.715	0.123971
$353$	5673.97	0.855510	0.427755	−	0.903895i	$-0.359305\pi$
$353$	5673.97	0.855510	0.427755	+	0.903895i	$0.359305\pi$
$354$	−3620.93	−0.543645
$355$	2431.46	0.363518
$356$	−975.588	−0.145242
$357$	393.897	0.0583957
$358$	5066.09	0.747908
$359$	−3638.27	−0.534876	−0.267438	−	0.963575i	$-0.586177\pi$
$359$	−3638.27	−0.534876	−0.267438	+	0.963575i	$0.586177\pi$
$360$	360.000	0.0527046
$361$	−5767.70	−0.840896
$362$	8028.50	1.16566
$363$	−2029.25	−0.293410
$364$	−723.652	−0.104202
$365$	−4897.35	−0.702299
$366$	−3270.78	−0.467122
$367$	6355.75	0.903998	0.451999	−	0.892018i	$-0.350711\pi$
$367$	6355.75	0.903998	0.451999	+	0.892018i	$0.350711\pi$
$368$	3027.92	0.428916
$369$	4598.10	0.648693
$370$	−911.934	−0.128133
$371$	494.845	0.0692482
$372$	372.000	0.0518476
$373$	−6764.52	−0.939018	−0.469509	−	0.882928i	$-0.655569\pi$
$373$	−6764.52	−0.939018	−0.469509	+	0.882928i	$0.655569\pi$
$374$	2747.44	0.379858
$375$	375.000	0.0516398
$376$	−1396.51	−0.191541
$377$	−18341.8	−2.50571
$378$	132.050	0.0179681
$379$	−12958.3	−1.75626	−0.878132	−	0.478418i	$-0.841210\pi$
$379$	−12958.3	−1.75626	−0.878132	+	0.478418i	$0.841210\pi$
$380$	−660.695	−0.0891920
$381$	2311.62	0.310834
$382$	−4134.73	−0.553799
$383$	−14238.5	−1.89961	−0.949807	−	0.312837i	$-0.898721\pi$
$383$	−14238.5	−1.89961	−0.949807	+	0.312837i	$0.898721\pi$
$384$	384.000	0.0510310
$385$	312.823	0.0414103
$386$	−6114.50	−0.806269
$387$	1408.18	0.184966
$388$	2734.40	0.357779
$389$	−5078.21	−0.661890	−0.330945	−	0.943650i	$-0.607368\pi$
$389$	−5078.21	−0.661890	−0.330945	+	0.943650i	$0.607368\pi$
$390$	−2219.45	−0.288170
$391$	10161.1	1.31424
$392$	−2696.16	−0.347390
$393$	3174.27	0.407432
$394$	5574.07	0.712736
$395$	1064.24	0.135564
$396$	921.055	0.116881
$397$	5605.98	0.708706	0.354353	−	0.935112i	$-0.384701\pi$
$397$	5605.98	0.708706	0.354353	+	0.935112i	$0.384701\pi$
$398$	−3877.61	−0.488359
$399$	−242.347	−0.0304074
$400$	400.000	0.0500000
$401$	10893.1	1.35655	0.678275	−	0.734809i	$-0.262728\pi$
$401$	10893.1	1.35655	0.678275	+	0.734809i	$0.262728\pi$
$402$	5685.92	0.705443
$403$	−2293.43	−0.283484
$404$	−4764.96	−0.586797
$405$	405.000	0.0496904
$406$	1212.54	0.148220
$407$	−2333.17	−0.284155
$408$	1288.63	0.156364
$409$	−9782.29	−1.18265	−0.591324	−	0.806434i	$-0.701395\pi$
$409$	−9782.29	−1.18265	−0.591324	+	0.806434i	$0.701395\pi$
$410$	5109.00	0.615404
$411$	−7272.75	−0.872842
$412$	4293.68	0.513433
$413$	−1475.76	−0.175829
$414$	3406.40	0.404386
$415$	1457.69	0.172422
$416$	−2367.41	−0.279019
$417$	−8531.45	−1.00189
$418$	−1690.38	−0.197797
$419$	−13863.9	−1.61645	−0.808227	−	0.588870i	$-0.799573\pi$
$419$	−13863.9	−1.61645	−0.808227	+	0.588870i	$0.799573\pi$
$420$	146.723	0.0170460
$421$	−7130.19	−0.825426	−0.412713	−	0.910861i	$-0.635419\pi$
$421$	−7130.19	−0.825426	−0.412713	+	0.910861i	$0.635419\pi$
$422$	4976.02	0.574002
$423$	−1571.07	−0.180587
$424$	1618.88	0.185423
$425$	1342.32	0.153205
$426$	2917.76	0.331845
$427$	−1333.05	−0.151079
$428$	−1806.83	−0.204057
$429$	−5678.43	−0.639061
$430$	1564.64	0.175474
$431$	−6925.07	−0.773941	−0.386971	−	0.922092i	$-0.626479\pi$
$431$	−6925.07	−0.773941	−0.386971	+	0.922092i	$0.626479\pi$
$432$	432.000	0.0481125
$433$	−9692.31	−1.07571	−0.537855	−	0.843037i	$-0.680765\pi$
$433$	−9692.31	−1.07571	−0.537855	+	0.843037i	$0.680765\pi$
$434$	151.613	0.0167688
$435$	3718.86	0.409899
$436$	179.877	0.0197582
$437$	−6251.65	−0.684341
$438$	−5876.82	−0.641108
$439$	−10781.8	−1.17218	−0.586090	−	0.810246i	$-0.699334\pi$
$439$	−10781.8	−1.17218	−0.586090	+	0.810246i	$0.699334\pi$
$440$	1023.39	0.110883
$441$	−3033.18	−0.327522
$442$	−7944.55	−0.854941
$443$	−10148.7	−1.08844	−0.544221	−	0.838942i	$-0.683175\pi$
$443$	−10148.7	−1.08844	−0.544221	+	0.838942i	$0.683175\pi$
$444$	−1094.32	−0.116969
$445$	−1219.49	−0.129908
$446$	−6558.67	−0.696328
$447$	7700.48	0.814810
$448$	156.504	0.0165048
$449$	11420.8	1.20040	0.600202	−	0.799848i	$-0.295087\pi$
$449$	11420.8	1.20040	0.600202	+	0.799848i	$0.295087\pi$
$450$	450.000	0.0471405
$451$	13071.3	1.36475
$452$	6680.09	0.695143
$453$	−7376.47	−0.765070
$454$	9818.75	1.01501
$455$	−904.565	−0.0932015
$456$	−792.834	−0.0814208
$457$	5757.93	0.589376	0.294688	−	0.955594i	$-0.404784\pi$
$457$	5757.93	0.589376	0.294688	+	0.955594i	$0.404784\pi$
$458$	−5212.04	−0.531753
$459$	1449.70	0.147421
$460$	3784.89	0.383634
$461$	9211.87	0.930671	0.465336	−	0.885134i	$-0.345934\pi$
$461$	9211.87	0.930671	0.465336	+	0.885134i	$0.345934\pi$
$462$	375.388	0.0378022
$463$	−14762.8	−1.48182	−0.740912	−	0.671602i	$-0.765606\pi$
$463$	−14762.8	−1.48182	−0.740912	+	0.671602i	$0.765606\pi$
$464$	3966.79	0.396883
$465$	465.000	0.0463739
$466$	−4453.07	−0.442671
$467$	−12130.2	−1.20197	−0.600984	−	0.799261i	$-0.705225\pi$
$467$	−12130.2	−1.20197	−0.600984	+	0.799261i	$0.705225\pi$
$468$	−2663.34	−0.263062
$469$	2317.37	0.228158
$470$	−1745.64	−0.171320
$471$	−5826.77	−0.570028
$472$	−4827.91	−0.470810
$473$	4003.12	0.389141
$474$	1277.09	0.123753
$475$	−825.869	−0.0797757
$476$	525.197	0.0505722
$477$	1821.23	0.174819
$478$	−14132.0	−1.35227
$479$	8766.82	0.836255	0.418128	−	0.908388i	$-0.362687\pi$
$479$	8766.82	0.836255	0.418128	+	0.908388i	$0.362687\pi$
$480$	480.000	0.0456435
$481$	6746.63	0.639543
$482$	−7308.82	−0.690680
$483$	1388.32	0.130789
$484$	−2705.66	−0.254100
$485$	3418.00	0.320007
$486$	486.000	0.0453609
$487$	12505.0	1.16356	0.581780	−	0.813346i	$-0.302356\pi$
$487$	12505.0	1.16356	0.581780	+	0.813346i	$0.302356\pi$
$488$	−4361.04	−0.404539
$489$	1810.09	0.167393
$490$	−3370.20	−0.310715
$491$	18476.4	1.69822	0.849112	−	0.528212i	$-0.177137\pi$
$491$	18476.4	1.69822	0.849112	+	0.528212i	$0.177137\pi$
$492$	6130.80	0.561784
$493$	13311.7	1.21609
$494$	4887.93	0.445179
$495$	1151.32	0.104541
$496$	496.000	0.0449013
$497$	1189.17	0.107327
$498$	1749.23	0.157399
$499$	5274.85	0.473216	0.236608	−	0.971605i	$-0.423964\pi$
$499$	5274.85	0.473216	0.236608	+	0.971605i	$0.423964\pi$
$500$	500.000	0.0447214
$501$	−3886.00	−0.346535
$502$	8735.94	0.776701
$503$	−9066.66	−0.803702	−0.401851	−	0.915705i	$-0.631633\pi$
$503$	−9066.66	−0.803702	−0.401851	+	0.915705i	$0.631633\pi$
$504$	176.067	0.0155608
$505$	−5956.21	−0.524847
$506$	9683.60	0.850768
$507$	9828.83	0.860974
$508$	3082.16	0.269190
$509$	−18461.5	−1.60764	−0.803822	−	0.594870i	$-0.797204\pi$
$509$	−18461.5	−1.60764	−0.803822	+	0.594870i	$0.797204\pi$
$510$	1610.78	0.139856
$511$	−2395.18	−0.207351
$512$	512.000	0.0441942
$513$	−891.939	−0.0767642
$514$	−7559.28	−0.648688
$515$	5367.09	0.459228
$516$	1877.57	0.160185
$517$	−4466.19	−0.379928
$518$	−446.005	−0.0378307
$519$	−6212.80	−0.525456
$520$	−2959.26	−0.249562
$521$	−6099.03	−0.512867	−0.256433	−	0.966562i	$-0.582547\pi$
$521$	−6099.03	−0.512867	−0.256433	+	0.966562i	$0.582547\pi$
$522$	4462.64	0.374185
$523$	22537.9	1.88435	0.942173	−	0.335126i	$-0.108779\pi$
$523$	22537.9	1.88435	0.942173	+	0.335126i	$0.108779\pi$
$524$	4232.37	0.352847
$525$	183.403	0.0152464
$526$	−3759.05	−0.311601
$527$	1664.48	0.137582
$528$	1228.07	0.101222
$529$	23646.6	1.94350
$530$	2023.59	0.165848
$531$	−5431.39	−0.443884
$532$	−323.130	−0.0263336
$533$	−37797.2	−3.07163
$534$	−1463.38	−0.118589
$535$	−2258.54	−0.182514
$536$	7581.23	0.610931
$537$	7599.13	0.610664
$538$	2023.22	0.162132
$539$	−8622.61	−0.689058
$540$	540.000	0.0430331
$541$	−6891.60	−0.547676	−0.273838	−	0.961776i	$-0.588293\pi$
$541$	−6891.60	−0.547676	−0.273838	+	0.961776i	$0.588293\pi$
$542$	−796.771	−0.0631444
$543$	12042.7	0.951756
$544$	1718.17	0.135415
$545$	224.847	0.0176722
$546$	−1085.48	−0.0850809
$547$	−1319.26	−0.103122	−0.0515608	−	0.998670i	$-0.516420\pi$
$547$	−1319.26	−0.103122	−0.0515608	+	0.998670i	$0.516420\pi$
$548$	−9697.00	−0.755903
$549$	−4906.18	−0.381403
$550$	1279.24	0.0991765
$551$	−8190.12	−0.633232
$552$	4541.87	0.350208
$553$	520.495	0.0400248
$554$	−8333.51	−0.639092
$555$	−1367.90	−0.104620
$556$	−11375.3	−0.867660
$557$	3855.78	0.293311	0.146656	−	0.989188i	$-0.453149\pi$
$557$	3855.78	0.293311	0.146656	+	0.989188i	$0.453149\pi$
$558$	558.000	0.0423334
$559$	−11575.5	−0.875833
$560$	195.630	0.0147623
$561$	4121.17	0.310153
$562$	2918.04	0.219021
$563$	5179.51	0.387727	0.193863	−	0.981029i	$-0.437898\pi$
$563$	5179.51	0.387727	0.193863	+	0.981029i	$0.437898\pi$
$564$	−2094.76	−0.156393
$565$	8350.11	0.621755
$566$	−543.569	−0.0403674
$567$	198.076	0.0146709
$568$	3890.34	0.287386
$569$	−15576.2	−1.14761	−0.573805	−	0.818992i	$-0.694533\pi$
$569$	−15576.2	−1.14761	−0.573805	+	0.818992i	$0.694533\pi$
$570$	−991.043	−0.0728249
$571$	1771.25	0.129815	0.0649077	−	0.997891i	$-0.479325\pi$
$571$	1771.25	0.129815	0.0649077	+	0.997891i	$0.479325\pi$
$572$	−7571.23	−0.553443
$573$	−6202.09	−0.452175
$574$	2498.69	0.181696
$575$	4731.12	0.343133
$576$	576.000	0.0416667
$577$	12576.0	0.907356	0.453678	−	0.891166i	$-0.350112\pi$
$577$	12576.0	0.907356	0.453678	+	0.891166i	$0.350112\pi$
$578$	−4060.17	−0.292181
$579$	−9171.75	−0.658316
$580$	4958.49	0.354983
$581$	712.920	0.0509069
$582$	4101.61	0.292125
$583$	5177.34	0.367793
$584$	−7835.76	−0.555216
$585$	−3329.17	−0.235289
$586$	−3764.93	−0.265406
$587$	−15443.6	−1.08590	−0.542950	−	0.839765i	$-0.682693\pi$
$587$	−15443.6	−1.08590	−0.542950	+	0.839765i	$0.682693\pi$
$588$	−4044.24	−0.283642
$589$	−1024.08	−0.0716407
$590$	−6034.88	−0.421105
$591$	8361.11	0.581946
$592$	−1459.09	−0.101298
$593$	20137.0	1.39448	0.697240	−	0.716838i	$-0.254411\pi$
$593$	20137.0	1.39448	0.697240	+	0.716838i	$0.254411\pi$
$594$	1381.58	0.0954327
$595$	656.496	0.0452331
$596$	10267.3	0.705647
$597$	−5816.41	−0.398744
$598$	−28001.3	−1.91481
$599$	−16776.1	−1.14433	−0.572165	−	0.820138i	$-0.693896\pi$
$599$	−16776.1	−1.14433	−0.572165	+	0.820138i	$0.693896\pi$
$600$	600.000	0.0408248
$601$	−18367.2	−1.24661	−0.623307	−	0.781977i	$-0.714211\pi$
$601$	−18367.2	−1.24661	−0.623307	+	0.781977i	$0.714211\pi$
$602$	765.229	0.0518080
$603$	8528.88	0.575992
$604$	−9835.29	−0.662570
$605$	−3382.08	−0.227274
$606$	−7147.45	−0.479117
$607$	−14200.7	−0.949571	−0.474785	−	0.880102i	$-0.657474\pi$
$607$	−14200.7	−0.949571	−0.474785	+	0.880102i	$0.657474\pi$
$608$	−1057.11	−0.0705125
$609$	1818.81	0.121021
$610$	−5451.31	−0.361831
$611$	12914.5	0.855098
$612$	1932.94	0.127671
$613$	18346.8	1.20884	0.604422	−	0.796664i	$-0.293404\pi$
$613$	18346.8	1.20884	0.604422	+	0.796664i	$0.293404\pi$
$614$	−16918.3	−1.11200
$615$	7663.50	0.502475
$616$	500.517	0.0327377
$617$	10557.4	0.688858	0.344429	−	0.938812i	$-0.388072\pi$
$617$	10557.4	0.688858	0.344429	+	0.938812i	$0.388072\pi$
$618$	6440.51	0.419216
$619$	7759.01	0.503814	0.251907	−	0.967751i	$-0.418942\pi$
$619$	7759.01	0.503814	0.251907	+	0.967751i	$0.418942\pi$
$620$	620.000	0.0401610
$621$	5109.61	0.330180
$622$	−14269.2	−0.919842
$623$	−596.421	−0.0383549
$624$	−3551.12	−0.227818
$625$	625.000	0.0400000
$626$	498.548	0.0318307
$627$	−2535.57	−0.161501
$628$	−7769.03	−0.493659
$629$	−4896.43	−0.310387
$630$	220.084	0.0139180
$631$	8875.60	0.559956	0.279978	−	0.960006i	$-0.409673\pi$
$631$	8875.60	0.559956	0.279978	+	0.960006i	$0.409673\pi$
$632$	1702.79	0.107173
$633$	7464.03	0.468671
$634$	12797.5	0.801660
$635$	3852.70	0.240771
$636$	2428.31	0.151398
$637$	24933.3	1.55085
$638$	12686.2	0.787229
$639$	4376.64	0.270950
$640$	640.000	0.0395285
$641$	−11601.8	−0.714892	−0.357446	−	0.933934i	$-0.616352\pi$
$641$	−11601.8	−0.714892	−0.357446	+	0.933934i	$0.616352\pi$
$642$	−2710.24	−0.166612
$643$	10434.7	0.639978	0.319989	−	0.947421i	$-0.396321\pi$
$643$	10434.7	0.639978	0.319989	+	0.947421i	$0.396321\pi$
$644$	1851.10	0.113266
$645$	2346.96	0.143274
$646$	−3547.46	−0.216057
$647$	266.614	0.0162004	0.00810020	−	0.999967i	$-0.497422\pi$
$647$	266.614	0.0162004	0.00810020	+	0.999967i	$0.497422\pi$
$648$	648.000	0.0392837
$649$	−15440.2	−0.933866
$650$	−3699.08	−0.223215
$651$	227.420	0.0136917
$652$	2413.45	0.144966
$653$	−29461.1	−1.76554	−0.882772	−	0.469801i	$-0.844326\pi$
$653$	−29461.1	−1.76554	−0.882772	+	0.469801i	$0.844326\pi$
$654$	269.816	0.0161325
$655$	5290.46	0.315596
$656$	8174.40	0.486520
$657$	−8815.23	−0.523463
$658$	−853.749	−0.0505814
$659$	1254.83	0.0741750	0.0370875	−	0.999312i	$-0.488192\pi$
$659$	1254.83	0.0741750	0.0370875	+	0.999312i	$0.488192\pi$
$660$	1535.09	0.0905354
$661$	18334.4	1.07886	0.539428	−	0.842032i	$-0.318640\pi$
$661$	18334.4	1.07886	0.539428	+	0.842032i	$0.318640\pi$
$662$	23211.8	1.36277
$663$	−11916.8	−0.698056
$664$	2332.30	0.136312
$665$	−403.912	−0.0235535
$666$	−1641.48	−0.0955047
$667$	46918.4	2.72367
$668$	−5181.34	−0.300108
$669$	−9838.01	−0.568549
$670$	9476.54	0.546434
$671$	−13947.1	−0.802416
$672$	234.756	0.0134761
$673$	15829.7	0.906671	0.453335	−	0.891340i	$-0.350234\pi$
$673$	15829.7	0.906671	0.453335	+	0.891340i	$0.350234\pi$
$674$	10481.3	0.598998
$675$	675.000	0.0384900
$676$	13105.1	0.745625
$677$	541.232	0.0307256	0.0153628	−	0.999882i	$-0.495110\pi$
$677$	541.232	0.0307256	0.0153628	+	0.999882i	$0.495110\pi$
$678$	10020.1	0.567582
$679$	1671.66	0.0944809
$680$	2147.71	0.121119
$681$	14728.1	0.828756
$682$	1586.26	0.0890632
$683$	−13184.9	−0.738662	−0.369331	−	0.929298i	$-0.620413\pi$
$683$	−13184.9	−0.738662	−0.369331	+	0.929298i	$0.620413\pi$
$684$	−1189.25	−0.0664798
$685$	−12121.2	−0.676101
$686$	−3325.81	−0.185102
$687$	−7818.06	−0.434174
$688$	2503.43	0.138724
$689$	−14970.9	−0.827786
$690$	5677.34	0.313236
$691$	−5195.02	−0.286002	−0.143001	−	0.989723i	$-0.545675\pi$
$691$	−5195.02	−0.286002	−0.143001	+	0.989723i	$0.545675\pi$
$692$	−8283.74	−0.455058
$693$	563.082	0.0308654
$694$	8270.29	0.452357
$695$	−14219.1	−0.776059
$696$	5950.18	0.324053
$697$	27431.7	1.49074
$698$	6451.26	0.349833
$699$	−6679.61	−0.361439
$700$	244.538	0.0132038
$701$	−32351.9	−1.74310	−0.871550	−	0.490307i	$-0.836885\pi$
$701$	−32351.9	−1.74310	−0.871550	+	0.490307i	$0.836885\pi$
$702$	−3995.01	−0.214789
$703$	3012.55	0.161622
$704$	1637.43	0.0876605
$705$	−2618.46	−0.139882
$706$	11347.9	0.604937
$707$	−2913.04	−0.154959
$708$	−7241.86	−0.384415
$709$	−33464.7	−1.77263	−0.886315	−	0.463084i	$-0.846743\pi$
$709$	−33464.7	−1.77263	−0.886315	+	0.463084i	$0.846743\pi$
$710$	4862.93	0.257046
$711$	1915.64	0.101044
$712$	−1951.18	−0.102701
$713$	5866.59	0.308142
$714$	787.795	0.0412920
$715$	−9464.04	−0.495014
$716$	10132.2	0.528851
$717$	−21198.0	−1.10412
$718$	−7276.54	−0.378215
$719$	10075.9	0.522627	0.261314	−	0.965254i	$-0.415844\pi$
$719$	10075.9	0.522627	0.261314	+	0.965254i	$0.415844\pi$
$720$	720.000	0.0372678
$721$	2624.92	0.135585
$722$	−11535.4	−0.594603
$723$	−10963.2	−0.563938
$724$	16057.0	0.824245
$725$	6198.11	0.317506
$726$	−4058.49	−0.207472
$727$	12903.7	0.658285	0.329143	−	0.944280i	$-0.393240\pi$
$727$	12903.7	0.658285	0.329143	+	0.944280i	$0.393240\pi$
$728$	−1447.30	−0.0736822
$729$	729.000	0.0370370
$730$	−9794.70	−0.496600
$731$	8401.00	0.425065
$732$	−6541.57	−0.330305
$733$	31168.9	1.57060	0.785299	−	0.619116i	$-0.212509\pi$
$733$	31168.9	1.57060	0.785299	+	0.619116i	$0.212509\pi$
$734$	12711.5	0.639223
$735$	−5055.30	−0.253697
$736$	6055.83	0.303289
$737$	24245.6	1.21180
$738$	9196.20	0.458695
$739$	−22238.0	−1.10695	−0.553477	−	0.832865i	$-0.686699\pi$
$739$	−22238.0	−1.10695	−0.553477	+	0.832865i	$0.686699\pi$
$740$	−1823.87	−0.0906037
$741$	7331.89	0.363487
$742$	989.691	0.0489659
$743$	−15875.3	−0.783862	−0.391931	−	0.919995i	$-0.628193\pi$
$743$	−15875.3	−0.783862	−0.391931	+	0.919995i	$0.628193\pi$
$744$	744.000	0.0366618
$745$	12834.1	0.631149
$746$	−13529.0	−0.663986
$747$	2623.84	0.128516
$748$	5494.89	0.268600
$749$	−1104.59	−0.0538865
$750$	750.000	0.0365148
$751$	−10630.6	−0.516530	−0.258265	−	0.966074i	$-0.583151\pi$
$751$	−10630.6	−0.516530	−0.258265	+	0.966074i	$0.583151\pi$
$752$	−2793.02	−0.135440
$753$	13103.9	0.634174
$754$	−36683.7	−1.77180
$755$	−12294.1	−0.592620
$756$	264.101	0.0127054
$757$	20830.9	1.00015	0.500074	−	0.865983i	$-0.333306\pi$
$757$	20830.9	1.00015	0.500074	+	0.865983i	$0.333306\pi$
$758$	−25916.6	−1.24187
$759$	14525.4	0.694649
$760$	−1321.39	−0.0630683
$761$	29971.0	1.42766	0.713828	−	0.700321i	$-0.246960\pi$
$761$	29971.0	1.42766	0.713828	+	0.700321i	$0.246960\pi$
$762$	4623.24	0.219793
$763$	109.967	0.00521766
$764$	−8269.46	−0.391595
$765$	2416.17	0.114192
$766$	−28476.9	−1.34323
$767$	44647.0	2.10184
$768$	768.000	0.0360844
$769$	9120.99	0.427713	0.213856	−	0.976865i	$-0.431398\pi$
$769$	9120.99	0.427713	0.213856	+	0.976865i	$0.431398\pi$
$770$	625.647	0.0292815
$771$	−11338.9	−0.529652
$772$	−12229.0	−0.570119
$773$	35982.7	1.67427	0.837134	−	0.546997i	$-0.184229\pi$
$773$	35982.7	1.67427	0.837134	+	0.546997i	$0.184229\pi$
$774$	2816.36	0.130791
$775$	775.000	0.0359211
$776$	5468.81	0.252988
$777$	−669.007	−0.0308887
$778$	−10156.4	−0.468027
$779$	−16877.5	−0.776249
$780$	−4438.90	−0.203767
$781$	12441.7	0.570039
$782$	20322.1	0.929308
$783$	6693.96	0.305520
$784$	−5392.32	−0.245641
$785$	−9711.28	−0.441542
$786$	6348.55	0.288098
$787$	9228.04	0.417972	0.208986	−	0.977919i	$-0.432984\pi$
$787$	9228.04	0.417972	0.208986	+	0.977919i	$0.432984\pi$
$788$	11148.1	0.503980
$789$	−5638.57	−0.254421
$790$	2128.49	0.0958584
$791$	4083.83	0.183571
$792$	1842.11	0.0826471
$793$	40329.6	1.80599
$794$	11212.0	0.501130
$795$	3035.39	0.135414
$796$	−7755.22	−0.345322
$797$	30021.8	1.33429	0.667143	−	0.744930i	$-0.267517\pi$
$797$	30021.8	1.33429	0.667143	+	0.744930i	$0.267517\pi$
$798$	−484.695	−0.0215013
$799$	−9372.81	−0.415001
$800$	800.000	0.0353553
$801$	−2195.07	−0.0968279
$802$	21786.2	0.959225
$803$	−25059.6	−1.10129
$804$	11371.8	0.498823
$805$	2313.87	0.101309
$806$	−4586.86	−0.200453
$807$	3034.82	0.132380
$808$	−9529.93	−0.414928
$809$	−11939.2	−0.518864	−0.259432	−	0.965761i	$-0.583535\pi$
$809$	−11939.2	−0.518864	−0.259432	+	0.965761i	$0.583535\pi$
$810$	810.000	0.0351364
$811$	−2711.44	−0.117400	−0.0587002	−	0.998276i	$-0.518696\pi$
$811$	−2711.44	−0.117400	−0.0587002	+	0.998276i	$0.518696\pi$
$812$	2425.07	0.104807
$813$	−1195.16	−0.0515572
$814$	−4666.34	−0.200928
$815$	3016.82	0.129662
$816$	2577.25	0.110566
$817$	−5168.76	−0.221337
$818$	−19564.6	−0.836259
$819$	−1628.22	−0.0694683
$820$	10218.0	0.435156
$821$	37216.4	1.58205	0.791025	−	0.611784i	$-0.209548\pi$
$821$	37216.4	1.58205	0.791025	+	0.611784i	$0.209548\pi$
$822$	−14545.5	−0.617193
$823$	36906.6	1.56316	0.781581	−	0.623804i	$-0.214414\pi$
$823$	36906.6	1.56316	0.781581	+	0.623804i	$0.214414\pi$
$824$	8587.35	0.363052
$825$	1918.86	0.0809773
$826$	−2951.51	−0.124330
$827$	30490.7	1.28206	0.641031	−	0.767515i	$-0.278507\pi$
$827$	30490.7	1.28206	0.641031	+	0.767515i	$0.278507\pi$
$828$	6812.81	0.285944
$829$	−2829.90	−0.118560	−0.0592802	−	0.998241i	$-0.518881\pi$
$829$	−2829.90	−0.118560	−0.0592802	+	0.998241i	$0.518881\pi$
$830$	2915.38	0.121921
$831$	−12500.3	−0.521816
$832$	−4734.82	−0.197296
$833$	−18095.5	−0.752669
$834$	−17062.9	−0.708441
$835$	−6476.67	−0.268425
$836$	−3380.76	−0.139864
$837$	837.000	0.0345651
$838$	−27727.8	−1.14301
$839$	−12405.9	−0.510487	−0.255243	−	0.966877i	$-0.582156\pi$
$839$	−12405.9	−0.510487	−0.255243	+	0.966877i	$0.582156\pi$
$840$	293.445	0.0120534
$841$	37077.5	1.52025
$842$	−14260.4	−0.583664
$843$	4377.06	0.178830
$844$	9952.04	0.405881
$845$	16381.4	0.666907
$846$	−3142.15	−0.127694
$847$	−1654.09	−0.0671018
$848$	3237.75	0.131114
$849$	−815.354	−0.0329598
$850$	2684.64	0.108332
$851$	−17257.9	−0.695173
$852$	5835.51	0.234650
$853$	−17092.3	−0.686082	−0.343041	−	0.939320i	$-0.611457\pi$
$853$	−17092.3	−0.686082	−0.343041	+	0.939320i	$0.611457\pi$
$854$	−2666.10	−0.106829
$855$	−1486.56	−0.0594613
$856$	−3613.66	−0.144290
$857$	26842.1	1.06991	0.534953	−	0.844882i	$-0.320329\pi$
$857$	26842.1	1.06991	0.534953	+	0.844882i	$0.320329\pi$
$858$	−11356.9	−0.451884
$859$	−8013.83	−0.318310	−0.159155	−	0.987254i	$-0.550877\pi$
$859$	−8013.83	−0.318310	−0.159155	+	0.987254i	$0.550877\pi$
$860$	3129.29	0.124079
$861$	3748.03	0.148354
$862$	−13850.1	−0.547259
$863$	39046.9	1.54018	0.770088	−	0.637938i	$-0.220212\pi$
$863$	39046.9	1.54018	0.770088	+	0.637938i	$0.220212\pi$
$864$	864.000	0.0340207
$865$	−10354.7	−0.407017
$866$	−19384.6	−0.760642
$867$	−6090.26	−0.238565
$868$	303.227	0.0118574
$869$	5445.70	0.212581
$870$	7437.73	0.289842
$871$	−70108.9	−2.72738
$872$	359.755	0.0139711
$873$	6152.41	0.238519
$874$	−12503.3	−0.483902
$875$	305.672	0.0118098
$876$	−11753.6	−0.453332
$877$	36958.8	1.42305	0.711523	−	0.702663i	$-0.248006\pi$
$877$	36958.8	1.42305	0.711523	+	0.702663i	$0.248006\pi$
$878$	−21563.6	−0.828856
$879$	−5647.40	−0.216703
$880$	2046.79	0.0784059
$881$	39877.7	1.52499	0.762493	−	0.646996i	$-0.223975\pi$
$881$	39877.7	1.52499	0.762493	+	0.646996i	$0.223975\pi$
$882$	−6066.36	−0.231593
$883$	−43041.6	−1.64039	−0.820195	−	0.572084i	$-0.806135\pi$
$883$	−43041.6	−1.64039	−0.820195	+	0.572084i	$0.806135\pi$
$884$	−15889.1	−0.604535
$885$	−9052.32	−0.343831
$886$	−20297.4	−0.769645
$887$	29387.3	1.11243	0.556217	−	0.831037i	$-0.312252\pi$
$887$	29387.3	1.11243	0.556217	+	0.831037i	$0.312252\pi$
$888$	−2188.64	−0.0827095
$889$	1884.26	0.0710867
$890$	−2438.97	−0.0918590
$891$	2072.37	0.0779204
$892$	−13117.3	−0.492378
$893$	5766.67	0.216097
$894$	15401.0	0.576158
$895$	12665.2	0.473019
$896$	313.008	0.0116706
$897$	−42001.9	−1.56344
$898$	22841.6	0.848814
$899$	7685.65	0.285129
$900$	900.000	0.0333333
$901$	10865.2	0.401746
$902$	26142.6	0.965027
$903$	1147.84	0.0423010
$904$	13360.2	0.491541
$905$	20071.2	0.737227
$906$	−14752.9	−0.540986
$907$	−34944.2	−1.27928	−0.639638	−	0.768676i	$-0.720916\pi$
$907$	−34944.2	−1.27928	−0.639638	+	0.768676i	$0.720916\pi$
$908$	19637.5	0.717724
$909$	−10721.2	−0.391198
$910$	−1809.13	−0.0659034
$911$	45341.9	1.64901	0.824503	−	0.565857i	$-0.191455\pi$
$911$	45341.9	1.64901	0.824503	+	0.565857i	$0.191455\pi$
$912$	−1585.67	−0.0575732
$913$	7458.95	0.270378
$914$	11515.9	0.416751
$915$	−8176.96	−0.295434
$916$	−10424.1	−0.376006
$917$	2587.43	0.0931784
$918$	2899.41	0.104243
$919$	−3650.63	−0.131037	−0.0655186	−	0.997851i	$-0.520870\pi$
$919$	−3650.63	−0.131037	−0.0655186	+	0.997851i	$0.520870\pi$
$920$	7569.79	0.271270
$921$	−25377.4	−0.907942
$922$	18423.7	0.658084
$923$	−35976.7	−1.28298
$924$	750.776	0.0267302
$925$	−2279.84	−0.0810384
$926$	−29525.5	−1.04781
$927$	9660.77	0.342288
$928$	7933.58	0.280638
$929$	−29123.7	−1.02854	−0.514271	−	0.857627i	$-0.671938\pi$
$929$	−29123.7	−1.02854	−0.514271	+	0.857627i	$0.671938\pi$
$930$	930.000	0.0327913
$931$	11133.4	0.391925
$932$	−8906.15	−0.313016
$933$	−21403.8	−0.751048
$934$	−24260.4	−0.849920
$935$	6868.61	0.240243
$936$	−5326.68	−0.186013
$937$	52326.9	1.82438	0.912191	−	0.409766i	$-0.134390\pi$
$937$	52326.9	1.82438	0.912191	+	0.409766i	$0.134390\pi$
$938$	4634.74	0.161332
$939$	747.823	0.0259896
$940$	−3491.27	−0.121141
$941$	13912.1	0.481957	0.240978	−	0.970531i	$-0.422532\pi$
$941$	13912.1	0.481957	0.240978	+	0.970531i	$0.422532\pi$
$942$	−11653.5	−0.403071
$943$	96685.2	3.33881
$944$	−9655.81	−0.332913
$945$	330.126	0.0113640
$946$	8006.23	0.275164
$947$	−12838.5	−0.440543	−0.220272	−	0.975439i	$-0.570694\pi$
$947$	−12838.5	−0.440543	−0.220272	+	0.975439i	$0.570694\pi$
$948$	2554.18	0.0875064
$949$	72462.8	2.47865
$950$	−1651.74	−0.0564100
$951$	19196.2	0.654553
$952$	1050.39	0.0357599
$953$	1549.16	0.0526572	0.0263286	−	0.999653i	$-0.491618\pi$
$953$	1549.16	0.0526572	0.0263286	+	0.999653i	$0.491618\pi$
$954$	3642.47	0.123616
$955$	−10336.8	−0.350253
$956$	−28264.0	−0.956197
$957$	19029.3	0.642770
$958$	17533.6	0.591322
$959$	−5928.21	−0.199616
$960$	960.000	0.0322749
$961$	961.000	0.0322581
$962$	13493.3	0.452225
$963$	−4065.36	−0.136038
$964$	−14617.6	−0.488385
$965$	−15286.3	−0.509930
$966$	2776.65	0.0924816
$967$	−3167.52	−0.105337	−0.0526684	−	0.998612i	$-0.516773\pi$
$967$	−3167.52	−0.105337	−0.0526684	+	0.998612i	$0.516773\pi$
$968$	−5411.32	−0.179676
$969$	−5321.18	−0.176410
$970$	6836.01	0.226279
$971$	40596.9	1.34173	0.670864	−	0.741581i	$-0.265924\pi$
$971$	40596.9	1.34173	0.670864	+	0.741581i	$0.265924\pi$
$972$	972.000	0.0320750
$973$	−6954.21	−0.229128
$974$	25009.9	0.822762
$975$	−5548.62	−0.182254
$976$	−8722.09	−0.286053
$977$	39879.3	1.30589	0.652944	−	0.757406i	$-0.273534\pi$
$977$	39879.3	1.30589	0.652944	+	0.757406i	$0.273534\pi$
$978$	3620.18	0.118365
$979$	−6240.07	−0.203712
$980$	−6740.40	−0.219708
$981$	404.724	0.0131721
$982$	36952.8	1.20083
$983$	14386.3	0.466789	0.233394	−	0.972382i	$-0.425017\pi$
$983$	14386.3	0.466789	0.233394	+	0.972382i	$0.425017\pi$
$984$	12261.6	0.397242
$985$	13935.2	0.450774
$986$	26623.5	0.859903
$987$	−1280.62	−0.0412996
$988$	9775.86	0.314789
$989$	29610.0	0.952017
$990$	2302.64	0.0739218
$991$	−40955.3	−1.31280	−0.656402	−	0.754411i	$-0.727923\pi$
$991$	−40955.3	−1.31280	−0.656402	+	0.754411i	$0.727923\pi$
$992$	992.000	0.0317500
$993$	34817.7	1.11269
$994$	2378.34	0.0758917
$995$	−9694.02	−0.308865
$996$	3498.45	0.111298
$997$	40691.4	1.29259	0.646294	−	0.763089i	$-0.276318\pi$
$997$	40691.4	1.29259	0.646294	+	0.763089i	$0.276318\pi$
$998$	10549.7	0.334614
$999$	−2462.22	−0.0779792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.4.a.r.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.4.a.r.1.3	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	930.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +2.44538 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +2.44538 q^{7} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} +25.5849 q^{11} +12.0000 q^{12} -73.9816 q^{13} +4.89076 q^{14} +15.0000 q^{15} +16.0000 q^{16} +53.6928 q^{17} +18.0000 q^{18} -33.0348 q^{19} +20.0000 q^{20} +7.33613 q^{21} +51.1697 q^{22} +189.245 q^{23} +24.0000 q^{24} +25.0000 q^{25} -147.963 q^{26} +27.0000 q^{27} +9.78151 q^{28} +247.924 q^{29} +30.0000 q^{30} +31.0000 q^{31} +32.0000 q^{32} +76.7546 q^{33} +107.386 q^{34} +12.2269 q^{35} +36.0000 q^{36} -91.1934 q^{37} -66.0695 q^{38} -221.945 q^{39} +40.0000 q^{40} +510.900 q^{41} +14.6723 q^{42} +156.464 q^{43} +102.339 q^{44} +45.0000 q^{45} +378.489 q^{46} -174.564 q^{47} +48.0000 q^{48} -337.020 q^{49} +50.0000 q^{50} +161.078 q^{51} -295.926 q^{52} +202.359 q^{53} +54.0000 q^{54} +127.924 q^{55} +19.5630 q^{56} -99.1043 q^{57} +495.849 q^{58} -603.488 q^{59} +60.0000 q^{60} -545.131 q^{61} +62.0000 q^{62} +22.0084 q^{63} +64.0000 q^{64} -369.908 q^{65} +153.509 q^{66} +947.654 q^{67} +214.771 q^{68} +567.734 q^{69} +24.4538 q^{70} +486.293 q^{71} +72.0000 q^{72} -979.470 q^{73} -182.387 q^{74} +75.0000 q^{75} -132.139 q^{76} +62.5647 q^{77} -443.890 q^{78} +212.849 q^{79} +80.0000 q^{80} +81.0000 q^{81} +1021.80 q^{82} +291.538 q^{83} +29.3445 q^{84} +268.464 q^{85} +312.929 q^{86} +743.773 q^{87} +204.679 q^{88} -243.897 q^{89} +90.0000 q^{90} -180.913 q^{91} +756.979 q^{92} +93.0000 q^{93} -349.127 q^{94} -165.174 q^{95} +96.0000 q^{96} +683.601 q^{97} -674.040 q^{98} +230.264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 30 q^{5} + 36 q^{6} + 21 q^{7} + 48 q^{8} + 54 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 30 * q^5 + 36 * q^6 + 21 * q^7 + 48 * q^8 + 54 * q^9	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 30 q^{5} + 36 q^{6} + 21 q^{7} + 48 q^{8} + 54 q^{9} + 60 q^{10} + 59 q^{11} + 72 q^{12} + 106 q^{13} + 42 q^{14} + 90 q^{15} + 96 q^{16} + 118 q^{17} + 108 q^{18} + 31 q^{19} + 120 q^{20} + 63 q^{21} + 118 q^{22} + 187 q^{23} + 144 q^{24} + 150 q^{25} + 212 q^{26} + 162 q^{27} + 84 q^{28} + 332 q^{29} + 180 q^{30} + 186 q^{31} + 192 q^{32} + 177 q^{33} + 236 q^{34} + 105 q^{35} + 216 q^{36} + 374 q^{37} + 62 q^{38} + 318 q^{39} + 240 q^{40} + 212 q^{41} + 126 q^{42} - 201 q^{43} + 236 q^{44} + 270 q^{45} + 374 q^{46} + 176 q^{47} + 288 q^{48} + 711 q^{49} + 300 q^{50} + 354 q^{51} + 424 q^{52} + 91 q^{53} + 324 q^{54} + 295 q^{55} + 168 q^{56} + 93 q^{57} + 664 q^{58} + 478 q^{59} + 360 q^{60} + 446 q^{61} + 372 q^{62} + 189 q^{63} + 384 q^{64} + 530 q^{65} + 354 q^{66} + 692 q^{67} + 472 q^{68} + 561 q^{69} + 210 q^{70} + 877 q^{71} + 432 q^{72} - 181 q^{73} + 748 q^{74} + 450 q^{75} + 124 q^{76} + 1079 q^{77} + 636 q^{78} - 259 q^{79} + 480 q^{80} + 486 q^{81} + 424 q^{82} + 290 q^{83} + 252 q^{84} + 590 q^{85} - 402 q^{86} + 996 q^{87} + 472 q^{88} + 87 q^{89} + 540 q^{90} - 954 q^{91} + 748 q^{92} + 558 q^{93} + 352 q^{94} + 155 q^{95} + 576 q^{96} - 434 q^{97} + 1422 q^{98} + 531 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 30 * q^5 + 36 * q^6 + 21 * q^7 + 48 * q^8 + 54 * q^9 + 60 * q^10 + 59 * q^11 + 72 * q^12 + 106 * q^13 + 42 * q^14 + 90 * q^15 + 96 * q^16 + 118 * q^17 + 108 * q^18 + 31 * q^19 + 120 * q^20 + 63 * q^21 + 118 * q^22 + 187 * q^23 + 144 * q^24 + 150 * q^25 + 212 * q^26 + 162 * q^27 + 84 * q^28 + 332 * q^29 + 180 * q^30 + 186 * q^31 + 192 * q^32 + 177 * q^33 + 236 * q^34 + 105 * q^35 + 216 * q^36 + 374 * q^37 + 62 * q^38 + 318 * q^39 + 240 * q^40 + 212 * q^41 + 126 * q^42 - 201 * q^43 + 236 * q^44 + 270 * q^45 + 374 * q^46 + 176 * q^47 + 288 * q^48 + 711 * q^49 + 300 * q^50 + 354 * q^51 + 424 * q^52 + 91 * q^53 + 324 * q^54 + 295 * q^55 + 168 * q^56 + 93 * q^57 + 664 * q^58 + 478 * q^59 + 360 * q^60 + 446 * q^61 + 372 * q^62 + 189 * q^63 + 384 * q^64 + 530 * q^65 + 354 * q^66 + 692 * q^67 + 472 * q^68 + 561 * q^69 + 210 * q^70 + 877 * q^71 + 432 * q^72 - 181 * q^73 + 748 * q^74 + 450 * q^75 + 124 * q^76 + 1079 * q^77 + 636 * q^78 - 259 * q^79 + 480 * q^80 + 486 * q^81 + 424 * q^82 + 290 * q^83 + 252 * q^84 + 590 * q^85 - 402 * q^86 + 996 * q^87 + 472 * q^88 + 87 * q^89 + 540 * q^90 - 954 * q^91 + 748 * q^92 + 558 * q^93 + 352 * q^94 + 155 * q^95 + 576 * q^96 - 434 * q^97 + 1422 * q^98 + 531 * q^99

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