LMFDB - Embedded newform 6043.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.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:	$48.2535979415$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55204 q^{2} -3.15051 q^{3} +4.51292 q^{4} -4.10943 q^{5} +8.04024 q^{6} -3.50763 q^{7} -6.41307 q^{8} +6.92573 q^{9} +O(q^{10})$	\(q-2.55204 q^{2} -3.15051 q^{3} +4.51292 q^{4} -4.10943 q^{5} +8.04024 q^{6} -3.50763 q^{7} -6.41307 q^{8} +6.92573 q^{9} +10.4874 q^{10} +6.03427 q^{11} -14.2180 q^{12} -3.72813 q^{13} +8.95162 q^{14} +12.9468 q^{15} +7.34059 q^{16} +2.02972 q^{17} -17.6748 q^{18} -6.71693 q^{19} -18.5455 q^{20} +11.0508 q^{21} -15.3997 q^{22} +1.18275 q^{23} +20.2045 q^{24} +11.8874 q^{25} +9.51434 q^{26} -12.3681 q^{27} -15.8296 q^{28} -9.57421 q^{29} -33.0408 q^{30} +7.03140 q^{31} -5.90736 q^{32} -19.0110 q^{33} -5.17992 q^{34} +14.4144 q^{35} +31.2553 q^{36} -1.49410 q^{37} +17.1419 q^{38} +11.7455 q^{39} +26.3541 q^{40} -7.11124 q^{41} -28.2022 q^{42} -5.30293 q^{43} +27.2321 q^{44} -28.4608 q^{45} -3.01844 q^{46} -0.415395 q^{47} -23.1266 q^{48} +5.30347 q^{49} -30.3372 q^{50} -6.39464 q^{51} -16.8247 q^{52} -6.99664 q^{53} +31.5638 q^{54} -24.7974 q^{55} +22.4947 q^{56} +21.1618 q^{57} +24.4338 q^{58} -10.4162 q^{59} +58.4279 q^{60} +3.39737 q^{61} -17.9444 q^{62} -24.2929 q^{63} +0.394637 q^{64} +15.3205 q^{65} +48.5170 q^{66} -1.54471 q^{67} +9.15994 q^{68} -3.72628 q^{69} -36.7860 q^{70} +1.12825 q^{71} -44.4152 q^{72} +7.00511 q^{73} +3.81300 q^{74} -37.4514 q^{75} -30.3130 q^{76} -21.1660 q^{77} -29.9751 q^{78} -4.68477 q^{79} -30.1656 q^{80} +18.1886 q^{81} +18.1482 q^{82} -10.8033 q^{83} +49.8715 q^{84} -8.34097 q^{85} +13.5333 q^{86} +30.1637 q^{87} -38.6982 q^{88} -0.101119 q^{89} +72.6332 q^{90} +13.0769 q^{91} +5.33767 q^{92} -22.1525 q^{93} +1.06010 q^{94} +27.6028 q^{95} +18.6112 q^{96} +13.3302 q^{97} -13.5347 q^{98} +41.7917 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) $ 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9} - 24 q^{10} - 37 q^{11} - 74 q^{12} - 113 q^{13} - 35 q^{14} - 34 q^{15} + 218 q^{16} - 125 q^{17} - 108 q^{18} - 46 q^{19} - 157 q^{20} - 113 q^{21} - 16 q^{22} - 60 q^{23} - 49 q^{24} + 208 q^{25} - 52 q^{26} - 90 q^{27} - 70 q^{28} - 137 q^{29} - 26 q^{30} - 36 q^{31} - 258 q^{32} - 153 q^{33} - 23 q^{34} - 77 q^{35} + 180 q^{36} - 108 q^{37} - 122 q^{38} - 32 q^{39} - 57 q^{40} - 186 q^{41} - 28 q^{42} - 54 q^{43} - 90 q^{44} - 233 q^{45} - 42 q^{46} - 188 q^{47} - 149 q^{48} + 189 q^{49} - 146 q^{50} - 34 q^{51} - 195 q^{52} - 196 q^{53} - 36 q^{54} - 57 q^{55} - 63 q^{56} - 76 q^{57} - 24 q^{58} - 137 q^{59} - 73 q^{60} - 96 q^{61} - 167 q^{62} - 113 q^{63} + 224 q^{64} - 131 q^{65} - 11 q^{66} - 71 q^{67} - 260 q^{68} - 162 q^{69} - 48 q^{70} - 77 q^{71} - 290 q^{72} - 160 q^{73} - 34 q^{74} - 100 q^{75} - 84 q^{76} - 416 q^{77} - 59 q^{78} - 17 q^{79} - 268 q^{80} + 147 q^{81} - 28 q^{82} - 238 q^{83} - 184 q^{84} - 108 q^{85} - 61 q^{86} - 127 q^{87} - 47 q^{88} - 183 q^{89} - 56 q^{90} - 14 q^{91} - 109 q^{92} - 206 q^{93} + q^{94} - 84 q^{95} - 54 q^{96} - 127 q^{97} - 294 q^{98} - 66 q^{99}+O(q^{100}) \) 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9 - 24 * q^10 - 37 * q^11 - 74 * q^12 - 113 * q^13 - 35 * q^14 - 34 * q^15 + 218 * q^16 - 125 * q^17 - 108 * q^18 - 46 * q^19 - 157 * q^20 - 113 * q^21 - 16 * q^22 - 60 * q^23 - 49 * q^24 + 208 * q^25 - 52 * q^26 - 90 * q^27 - 70 * q^28 - 137 * q^29 - 26 * q^30 - 36 * q^31 - 258 * q^32 - 153 * q^33 - 23 * q^34 - 77 * q^35 + 180 * q^36 - 108 * q^37 - 122 * q^38 - 32 * q^39 - 57 * q^40 - 186 * q^41 - 28 * q^42 - 54 * q^43 - 90 * q^44 - 233 * q^45 - 42 * q^46 - 188 * q^47 - 149 * q^48 + 189 * q^49 - 146 * q^50 - 34 * q^51 - 195 * q^52 - 196 * q^53 - 36 * q^54 - 57 * q^55 - 63 * q^56 - 76 * q^57 - 24 * q^58 - 137 * q^59 - 73 * q^60 - 96 * q^61 - 167 * q^62 - 113 * q^63 + 224 * q^64 - 131 * q^65 - 11 * q^66 - 71 * q^67 - 260 * q^68 - 162 * q^69 - 48 * q^70 - 77 * q^71 - 290 * q^72 - 160 * q^73 - 34 * q^74 - 100 * q^75 - 84 * q^76 - 416 * q^77 - 59 * q^78 - 17 * q^79 - 268 * q^80 + 147 * q^81 - 28 * q^82 - 238 * q^83 - 184 * q^84 - 108 * q^85 - 61 * q^86 - 127 * q^87 - 47 * q^88 - 183 * q^89 - 56 * q^90 - 14 * q^91 - 109 * q^92 - 206 * q^93 + q^94 - 84 * q^95 - 54 * q^96 - 127 * q^97 - 294 * q^98 - 66 * 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 $

$2$	−2.55204	−1.80457	−0.902283	−	0.431144i	$-0.858110\pi$
$2$	−2.55204	−1.80457	−0.902283	+	0.431144i	$0.858110\pi$
$3$	−3.15051	−1.81895	−0.909475	−	0.415759i	$-0.863516\pi$
$3$	−3.15051	−1.81895	−0.909475	+	0.415759i	$0.863516\pi$
$4$	4.51292	2.25646
$5$	−4.10943	−1.83779	−0.918896	−	0.394499i	$-0.870918\pi$
$5$	−4.10943	−1.83779	−0.918896	+	0.394499i	$0.870918\pi$
$6$	8.04024	3.28241
$7$	−3.50763	−1.32576	−0.662880	−	0.748726i	$-0.730666\pi$
$7$	−3.50763	−1.32576	−0.662880	+	0.748726i	$0.730666\pi$
$8$	−6.41307	−2.26736
$9$	6.92573	2.30858
$10$	10.4874	3.31642
$11$	6.03427	1.81940	0.909700	−	0.415266i	$-0.136312\pi$
$11$	6.03427	1.81940	0.909700	+	0.415266i	$0.136312\pi$
$12$	−14.2180	−4.10439
$13$	−3.72813	−1.03400	−0.516999	−	0.855986i	$-0.672951\pi$
$13$	−3.72813	−1.03400	−0.516999	+	0.855986i	$0.672951\pi$
$14$	8.95162	2.39242
$15$	12.9468	3.34285
$16$	7.34059	1.83515
$17$	2.02972	0.492278	0.246139	−	0.969235i	$-0.420838\pi$
$17$	2.02972	0.492278	0.246139	+	0.969235i	$0.420838\pi$
$18$	−17.6748	−4.16598
$19$	−6.71693	−1.54097	−0.770485	−	0.637458i	$-0.779986\pi$
$19$	−6.71693	−1.54097	−0.770485	+	0.637458i	$0.779986\pi$
$20$	−18.5455	−4.14690
$21$	11.0508	2.41149
$22$	−15.3997	−3.28323
$23$	1.18275	0.246621	0.123311	−	0.992368i	$-0.460649\pi$
$23$	1.18275	0.246621	0.123311	+	0.992368i	$0.460649\pi$
$24$	20.2045	4.12422
$25$	11.8874	2.37748
$26$	9.51434	1.86592
$27$	−12.3681	−2.38024
$28$	−15.8296	−2.99152
$29$	−9.57421	−1.77789	−0.888943	−	0.458018i	$-0.848560\pi$
$29$	−9.57421	−1.77789	−0.888943	+	0.458018i	$0.848560\pi$
$30$	−33.0408	−6.03240
$31$	7.03140	1.26288	0.631438	−	0.775426i	$-0.282465\pi$
$31$	7.03140	1.26288	0.631438	+	0.775426i	$0.282465\pi$
$32$	−5.90736	−1.04428
$33$	−19.0110	−3.30940
$34$	−5.17992	−0.888349
$35$	14.4144	2.43647
$36$	31.2553	5.20921
$37$	−1.49410	−0.245628	−0.122814	−	0.992430i	$-0.539192\pi$
$37$	−1.49410	−0.245628	−0.122814	+	0.992430i	$0.539192\pi$
$38$	17.1419	2.78078
$39$	11.7455	1.88079
$40$	26.3541	4.16694
$41$	−7.11124	−1.11059	−0.555295	−	0.831654i	$-0.687394\pi$
$41$	−7.11124	−1.11059	−0.555295	+	0.831654i	$0.687394\pi$
$42$	−28.2022	−4.35169
$43$	−5.30293	−0.808690	−0.404345	−	0.914607i	$-0.632500\pi$
$43$	−5.30293	−0.808690	−0.404345	+	0.914607i	$0.632500\pi$
$44$	27.2321	4.10540
$45$	−28.4608	−4.24269
$46$	−3.01844	−0.445045
$47$	−0.415395	−0.0605915	−0.0302958	−	0.999541i	$-0.509645\pi$
$47$	−0.415395	−0.0605915	−0.0302958	+	0.999541i	$0.509645\pi$
$48$	−23.1266	−3.33804
$49$	5.30347	0.757639
$50$	−30.3372	−4.29032
$51$	−6.39464	−0.895429
$52$	−16.8247	−2.33317
$53$	−6.99664	−0.961062	−0.480531	−	0.876978i	$-0.659556\pi$
$53$	−6.99664	−0.961062	−0.480531	+	0.876978i	$0.659556\pi$
$54$	31.5638	4.29529
$55$	−24.7974	−3.34368
$56$	22.4947	3.00598
$57$	21.1618	2.80295
$58$	24.4338	3.20831
$59$	−10.4162	−1.35608	−0.678040	−	0.735025i	$-0.737170\pi$
$59$	−10.4162	−1.35608	−0.678040	+	0.735025i	$0.737170\pi$
$60$	58.4279	7.54301
$61$	3.39737	0.434988	0.217494	−	0.976062i	$-0.430212\pi$
$61$	3.39737	0.434988	0.217494	+	0.976062i	$0.430212\pi$
$62$	−17.9444	−2.27894
$63$	−24.2929	−3.06062
$64$	0.394637	0.0493297
$65$	15.3205	1.90027
$66$	48.5170	5.97202
$67$	−1.54471	−0.188717	−0.0943584	−	0.995538i	$-0.530080\pi$
$67$	−1.54471	−0.188717	−0.0943584	+	0.995538i	$0.530080\pi$
$68$	9.15994	1.11081
$69$	−3.72628	−0.448592
$70$	−36.7860	−4.39677
$71$	1.12825	0.133899	0.0669494	−	0.997756i	$-0.478673\pi$
$71$	1.12825	0.133899	0.0669494	+	0.997756i	$0.478673\pi$
$72$	−44.4152	−5.23438
$73$	7.00511	0.819886	0.409943	−	0.912111i	$-0.365549\pi$
$73$	7.00511	0.819886	0.409943	+	0.912111i	$0.365549\pi$
$74$	3.81300	0.443252
$75$	−37.4514	−4.32452
$76$	−30.3130	−3.47713
$77$	−21.1660	−2.41209
$78$	−29.9751	−3.39401
$79$	−4.68477	−0.527078	−0.263539	−	0.964649i	$-0.584890\pi$
$79$	−4.68477	−0.527078	−0.263539	+	0.964649i	$0.584890\pi$
$80$	−30.1656	−3.37262
$81$	18.1886	2.02095
$82$	18.1482	2.00413
$83$	−10.8033	−1.18581	−0.592906	−	0.805272i	$-0.702019\pi$
$83$	−10.8033	−1.18581	−0.592906	+	0.805272i	$0.702019\pi$
$84$	49.8715	5.44143
$85$	−8.34097	−0.904705
$86$	13.5333	1.45933
$87$	30.1637	3.23389
$88$	−38.6982	−4.12524
$89$	−0.101119	−0.0107186	−0.00535928	−	0.999986i	$-0.501706\pi$
$89$	−0.101119	−0.0107186	−0.00535928	+	0.999986i	$0.501706\pi$
$90$	72.6332	7.65621
$91$	13.0769	1.37083
$92$	5.33767	0.556491
$93$	−22.1525	−2.29711
$94$	1.06010	0.109341
$95$	27.6028	2.83198
$96$	18.6112	1.89950
$97$	13.3302	1.35348	0.676738	−	0.736224i	$-0.263393\pi$
$97$	13.3302	1.35348	0.676738	+	0.736224i	$0.263393\pi$
$98$	−13.5347	−1.36721
$99$	41.7917	4.20023
$100$	53.6469	5.36469
$101$	14.5284	1.44563	0.722815	−	0.691042i	$-0.242848\pi$
$101$	14.5284	1.44563	0.722815	+	0.691042i	$0.242848\pi$
$102$	16.3194	1.61586
$103$	13.7087	1.35075	0.675377	−	0.737472i	$-0.263981\pi$
$103$	13.7087	1.35075	0.675377	+	0.737472i	$0.263981\pi$
$104$	23.9088	2.34445
$105$	−45.4126	−4.43182
$106$	17.8557	1.73430
$107$	−14.1169	−1.36474	−0.682369	−	0.731008i	$-0.739050\pi$
$107$	−14.1169	−1.36474	−0.682369	+	0.731008i	$0.739050\pi$
$108$	−55.8161	−5.37091
$109$	3.48638	0.333934	0.166967	−	0.985962i	$-0.446603\pi$
$109$	3.48638	0.333934	0.166967	+	0.985962i	$0.446603\pi$
$110$	63.2840	6.03389
$111$	4.70718	0.446785
$112$	−25.7481	−2.43297
$113$	−2.54748	−0.239647	−0.119823	−	0.992795i	$-0.538233\pi$
$113$	−2.54748	−0.239647	−0.119823	+	0.992795i	$0.538233\pi$
$114$	−54.0057	−5.05810
$115$	−4.86045	−0.453239
$116$	−43.2076	−4.01173
$117$	−25.8200	−2.38706
$118$	26.5827	2.44713
$119$	−7.11949	−0.652643
$120$	−83.0288	−7.57946
$121$	25.4124	2.31022
$122$	−8.67022	−0.784965
$123$	22.4041	2.02011
$124$	31.7321	2.84963
$125$	−28.3033	−2.53153
$126$	61.9965	5.52309
$127$	10.9550	0.972098	0.486049	−	0.873932i	$-0.338438\pi$
$127$	10.9550	0.972098	0.486049	+	0.873932i	$0.338438\pi$
$128$	10.8076	0.955264
$129$	16.7070	1.47097
$130$	−39.0985	−3.42917
$131$	−4.93952	−0.431568	−0.215784	−	0.976441i	$-0.569231\pi$
$131$	−4.93952	−0.431568	−0.215784	+	0.976441i	$0.569231\pi$
$132$	−85.7952	−7.46752
$133$	23.5605	2.04296
$134$	3.94218	0.340552
$135$	50.8257	4.37438
$136$	−13.0167	−1.11617
$137$	2.59463	0.221674	0.110837	−	0.993839i	$-0.464647\pi$
$137$	2.59463	0.221674	0.110837	+	0.993839i	$0.464647\pi$
$138$	9.50963	0.809514
$139$	−8.91137	−0.755852	−0.377926	−	0.925836i	$-0.623363\pi$
$139$	−8.91137	−0.755852	−0.377926	+	0.925836i	$0.623363\pi$
$140$	65.0508	5.49780
$141$	1.30871	0.110213
$142$	−2.87935	−0.241629
$143$	−22.4965	−1.88125
$144$	50.8390	4.23658
$145$	39.3445	3.26739
$146$	−17.8773	−1.47954
$147$	−16.7087	−1.37811
$148$	−6.74274	−0.554250
$149$	−4.41479	−0.361674	−0.180837	−	0.983513i	$-0.557881\pi$
$149$	−4.41479	−0.361674	−0.180837	+	0.983513i	$0.557881\pi$
$150$	95.5776	7.80388
$151$	7.61818	0.619958	0.309979	−	0.950743i	$-0.399678\pi$
$151$	7.61818	0.619958	0.309979	+	0.950743i	$0.399678\pi$
$152$	43.0762	3.49394
$153$	14.0573	1.13646
$154$	54.0165	4.35277
$155$	−28.8950	−2.32090
$156$	53.0066	4.24392
$157$	4.85728	0.387653	0.193826	−	0.981036i	$-0.437910\pi$
$157$	4.85728	0.387653	0.193826	+	0.981036i	$0.437910\pi$
$158$	11.9557	0.951147
$159$	22.0430	1.74812
$160$	24.2759	1.91918
$161$	−4.14867	−0.326961
$162$	−46.4180	−3.64694
$163$	13.3140	1.04284	0.521418	−	0.853302i	$-0.325403\pi$
$163$	13.3140	1.04284	0.521418	+	0.853302i	$0.325403\pi$
$164$	−32.0924	−2.50600
$165$	78.1245	6.08198
$166$	27.5704	2.13988
$167$	−22.4715	−1.73890	−0.869449	−	0.494023i	$-0.835526\pi$
$167$	−22.4715	−1.73890	−0.869449	+	0.494023i	$0.835526\pi$
$168$	−70.8698	−5.46772
$169$	0.898950	0.0691500
$170$	21.2865	1.63260
$171$	−46.5197	−3.55745
$172$	−23.9317	−1.82478
$173$	−14.8713	−1.13064	−0.565322	−	0.824870i	$-0.691248\pi$
$173$	−14.8713	−1.13064	−0.565322	+	0.824870i	$0.691248\pi$
$174$	−76.9790	−5.83576
$175$	−41.6966	−3.15197
$176$	44.2951	3.33887
$177$	32.8165	2.46664
$178$	0.258059	0.0193423
$179$	7.39970	0.553079	0.276540	−	0.961002i	$-0.410812\pi$
$179$	7.39970	0.553079	0.276540	+	0.961002i	$0.410812\pi$
$180$	−128.441	−9.57345
$181$	−4.28306	−0.318357	−0.159179	−	0.987250i	$-0.550885\pi$
$181$	−4.28306	−0.318357	−0.159179	+	0.987250i	$0.550885\pi$
$182$	−33.3728	−2.47376
$183$	−10.7034	−0.791222
$184$	−7.58509	−0.559180
$185$	6.13989	0.451414
$186$	56.5341	4.14528
$187$	12.2478	0.895651
$188$	−1.87464	−0.136722
$189$	43.3826	3.15562
$190$	−70.4434	−5.11050
$191$	13.6153	0.985172	0.492586	−	0.870264i	$-0.336052\pi$
$191$	13.6153	0.985172	0.492586	+	0.870264i	$0.336052\pi$
$192$	−1.24331	−0.0897282
$193$	13.7603	0.990487	0.495244	−	0.868754i	$-0.335079\pi$
$193$	13.7603	0.990487	0.495244	+	0.868754i	$0.335079\pi$
$194$	−34.0192	−2.44244
$195$	−48.2674	−3.45650
$196$	23.9341	1.70958
$197$	14.1426	1.00762	0.503811	−	0.863814i	$-0.331931\pi$
$197$	14.1426	1.00762	0.503811	+	0.863814i	$0.331931\pi$
$198$	−106.654	−7.57958
$199$	−10.1553	−0.719894	−0.359947	−	0.932973i	$-0.617205\pi$
$199$	−10.1553	−0.719894	−0.359947	+	0.932973i	$0.617205\pi$
$200$	−76.2348	−5.39061
$201$	4.86664	0.343267
$202$	−37.0771	−2.60873
$203$	33.5828	2.35705
$204$	−28.8585	−2.02050
$205$	29.2231	2.04103
$206$	−34.9851	−2.43753
$207$	8.19144	0.569345
$208$	−27.3667	−1.89754
$209$	−40.5317	−2.80364
$210$	115.895	7.99751
$211$	18.9737	1.30620	0.653100	−	0.757272i	$-0.273468\pi$
$211$	18.9737	1.30620	0.653100	+	0.757272i	$0.273468\pi$
$212$	−31.5752	−2.16860
$213$	−3.55457	−0.243555
$214$	36.0270	2.46276
$215$	21.7920	1.48620
$216$	79.3173	5.39686
$217$	−24.6635	−1.67427
$218$	−8.89738	−0.602607
$219$	−22.0697	−1.49133
$220$	−111.909	−7.54488
$221$	−7.56704	−0.509014
$222$	−12.0129	−0.806254
$223$	−28.3083	−1.89566	−0.947832	−	0.318771i	$-0.896730\pi$
$223$	−28.3083	−1.89566	−0.947832	+	0.318771i	$0.896730\pi$
$224$	20.7208	1.38447
$225$	82.3290	5.48860
$226$	6.50127	0.432458
$227$	23.0272	1.52837	0.764185	−	0.644997i	$-0.223141\pi$
$227$	23.0272	1.52837	0.764185	+	0.644997i	$0.223141\pi$
$228$	95.5014	6.32473
$229$	−1.59219	−0.105215	−0.0526073	−	0.998615i	$-0.516753\pi$
$229$	−1.59219	−0.105215	−0.0526073	+	0.998615i	$0.516753\pi$
$230$	12.4041	0.817900
$231$	66.6837	4.38746
$232$	61.4001	4.03111
$233$	−17.9805	−1.17794	−0.588972	−	0.808154i	$-0.700467\pi$
$233$	−17.9805	−1.17794	−0.588972	+	0.808154i	$0.700467\pi$
$234$	65.8938	4.30761
$235$	1.70704	0.111355
$236$	−47.0076	−3.05994
$237$	14.7594	0.958728
$238$	18.1692	1.17774
$239$	23.5446	1.52297	0.761487	−	0.648180i	$-0.224469\pi$
$239$	23.5446	1.52297	0.761487	+	0.648180i	$0.224469\pi$
$240$	95.0373	6.13463
$241$	15.2226	0.980572	0.490286	−	0.871562i	$-0.336892\pi$
$241$	15.2226	0.980572	0.490286	+	0.871562i	$0.336892\pi$
$242$	−64.8534	−4.16894
$243$	−20.1991	−1.29577
$244$	15.3320	0.981533
$245$	−21.7942	−1.39238
$246$	−57.1761	−3.64541
$247$	25.0416	1.59336
$248$	−45.0929	−2.86340
$249$	34.0358	2.15693
$250$	72.2312	4.56830
$251$	29.8005	1.88099	0.940496	−	0.339805i	$-0.110361\pi$
$251$	29.8005	1.88099	0.940496	+	0.339805i	$0.110361\pi$
$252$	−109.632	−6.90616
$253$	7.13706	0.448703
$254$	−27.9576	−1.75422
$255$	26.2783	1.64561
$256$	−28.3707	−1.77317
$257$	4.15778	0.259355	0.129678	−	0.991556i	$-0.458606\pi$
$257$	4.15778	0.259355	0.129678	+	0.991556i	$0.458606\pi$
$258$	−42.6369	−2.65446
$259$	5.24074	0.325644
$260$	69.1401	4.28789
$261$	−66.3084	−4.10439
$262$	12.6059	0.778793
$263$	13.0420	0.804206	0.402103	−	0.915594i	$-0.368279\pi$
$263$	13.0420	0.804206	0.402103	+	0.915594i	$0.368279\pi$
$264$	121.919	7.50360
$265$	28.7522	1.76623
$266$	−60.1274	−3.68665
$267$	0.318576	0.0194965
$268$	−6.97117	−0.425832
$269$	−8.68142	−0.529315	−0.264658	−	0.964342i	$-0.585259\pi$
$269$	−8.68142	−0.529315	−0.264658	+	0.964342i	$0.585259\pi$
$270$	−129.709	−7.89386
$271$	−1.82376	−0.110786	−0.0553928	−	0.998465i	$-0.517641\pi$
$271$	−1.82376	−0.110786	−0.0553928	+	0.998465i	$0.517641\pi$
$272$	14.8993	0.903404
$273$	−41.1989	−2.49347
$274$	−6.62160	−0.400025
$275$	71.7318	4.32559
$276$	−16.8164	−1.01223
$277$	23.2889	1.39929	0.699647	−	0.714489i	$-0.253341\pi$
$277$	23.2889	1.39929	0.699647	+	0.714489i	$0.253341\pi$
$278$	22.7422	1.36399
$279$	48.6976	2.91545
$280$	−92.4403	−5.52437
$281$	0.391162	0.0233348	0.0116674	−	0.999932i	$-0.496286\pi$
$281$	0.391162	0.0233348	0.0116674	+	0.999932i	$0.496286\pi$
$282$	−3.33987	−0.198887
$283$	12.5963	0.748772	0.374386	−	0.927273i	$-0.377854\pi$
$283$	12.5963	0.748772	0.374386	+	0.927273i	$0.377854\pi$
$284$	5.09171	0.302137
$285$	−86.9628	−5.15123
$286$	57.4121	3.39485
$287$	24.9436	1.47237
$288$	−40.9128	−2.41081
$289$	−12.8803	−0.757662
$290$	−100.409	−5.89621
$291$	−41.9970	−2.46191
$292$	31.6135	1.85004
$293$	−18.6208	−1.08784	−0.543920	−	0.839137i	$-0.683060\pi$
$293$	−18.6208	−1.08784	−0.543920	+	0.839137i	$0.683060\pi$
$294$	42.6412	2.48688
$295$	42.8048	2.49219
$296$	9.58176	0.556928
$297$	−74.6322	−4.33060
$298$	11.2667	0.652664
$299$	−4.40946	−0.255006
$300$	−169.015	−9.75810
$301$	18.6007	1.07213
$302$	−19.4419	−1.11876
$303$	−45.7719	−2.62953
$304$	−49.3063	−2.82791
$305$	−13.9612	−0.799418
$306$	−35.8747	−2.05082
$307$	10.8758	0.620714	0.310357	−	0.950620i	$-0.399551\pi$
$307$	10.8758	0.620714	0.310357	+	0.950620i	$0.399551\pi$
$308$	−95.5203	−5.44278
$309$	−43.1893	−2.45695
$310$	73.7413	4.18823
$311$	−0.242991	−0.0137788	−0.00688938	−	0.999976i	$-0.502193\pi$
$311$	−0.242991	−0.0137788	−0.00688938	+	0.999976i	$0.502193\pi$
$312$	−75.3249	−4.26443
$313$	−19.2805	−1.08980	−0.544900	−	0.838501i	$-0.683432\pi$
$313$	−19.2805	−1.08980	−0.544900	+	0.838501i	$0.683432\pi$
$314$	−12.3960	−0.699545
$315$	99.8300	5.62478
$316$	−21.1420	−1.18933
$317$	−5.01232	−0.281520	−0.140760	−	0.990044i	$-0.544955\pi$
$317$	−5.01232	−0.281520	−0.140760	+	0.990044i	$0.544955\pi$
$318$	−56.2546	−3.15460
$319$	−57.7733	−3.23469
$320$	−1.62173	−0.0906577
$321$	44.4756	2.48239
$322$	10.5876	0.590022
$323$	−13.6335	−0.758586
$324$	82.0836	4.56020
$325$	−44.3178	−2.45831
$326$	−33.9780	−1.88187
$327$	−10.9839	−0.607410
$328$	45.6049	2.51811
$329$	1.45705	0.0803298
$330$	−199.377	−10.9753
$331$	7.21938	0.396813	0.198406	−	0.980120i	$-0.436423\pi$
$331$	7.21938	0.396813	0.198406	+	0.980120i	$0.436423\pi$
$332$	−48.7542	−2.67574
$333$	−10.3477	−0.567052
$334$	57.3482	3.13796
$335$	6.34789	0.346823
$336$	81.1197	4.42544
$337$	18.9020	1.02966	0.514828	−	0.857294i	$-0.327856\pi$
$337$	18.9020	1.02966	0.514828	+	0.857294i	$0.327856\pi$
$338$	−2.29416	−0.124786
$339$	8.02586	0.435905
$340$	−37.6421	−2.04143
$341$	42.4293	2.29768
$342$	118.720	6.41965
$343$	5.95080	0.321313
$344$	34.0081	1.83359
$345$	15.3129	0.824419
$346$	37.9522	2.04032
$347$	19.4497	1.04412	0.522058	−	0.852910i	$-0.325164\pi$
$347$	19.4497	1.04412	0.522058	+	0.852910i	$0.325164\pi$
$348$	136.126	7.29713
$349$	21.3433	1.14248	0.571239	−	0.820784i	$-0.306463\pi$
$349$	21.3433	1.14248	0.571239	+	0.820784i	$0.306463\pi$
$350$	106.412	5.68794
$351$	46.1098	2.46116
$352$	−35.6466	−1.89997
$353$	36.2604	1.92995	0.964974	−	0.262344i	$-0.0844954\pi$
$353$	36.2604	1.92995	0.964974	+	0.262344i	$0.0844954\pi$
$354$	−83.7491	−4.45121
$355$	−4.63647	−0.246078
$356$	−0.456340	−0.0241860
$357$	22.4301	1.18712
$358$	−18.8843	−0.998068
$359$	−22.1518	−1.16913	−0.584564	−	0.811348i	$-0.698734\pi$
$359$	−22.1518	−1.16913	−0.584564	+	0.811348i	$0.698734\pi$
$360$	182.521	9.61971
$361$	26.1172	1.37459
$362$	10.9306	0.574497
$363$	−80.0620	−4.20217
$364$	59.0150	3.09323
$365$	−28.7870	−1.50678
$366$	27.3157	1.42781
$367$	−37.9225	−1.97954	−0.989770	−	0.142672i	$-0.954431\pi$
$367$	−37.9225	−1.97954	−0.989770	+	0.142672i	$0.954431\pi$
$368$	8.68212	0.452587
$369$	−49.2506	−2.56388
$370$	−15.6693	−0.814606
$371$	24.5416	1.27414
$372$	−99.9725	−5.18333
$373$	19.4498	1.00707	0.503537	−	0.863974i	$-0.332032\pi$
$373$	19.4498	1.00707	0.503537	+	0.863974i	$0.332032\pi$
$374$	−31.2570	−1.61626
$375$	89.1700	4.60472
$376$	2.66396	0.137383
$377$	35.6939	1.83833
$378$	−110.714	−5.69453
$379$	26.6587	1.36937	0.684683	−	0.728841i	$-0.259940\pi$
$379$	26.6587	1.36937	0.684683	+	0.728841i	$0.259940\pi$
$380$	124.569	6.39025
$381$	−34.5138	−1.76820
$382$	−34.7469	−1.77781
$383$	−3.84085	−0.196258	−0.0981292	−	0.995174i	$-0.531286\pi$
$383$	−3.84085	−0.196258	−0.0981292	+	0.995174i	$0.531286\pi$
$384$	−34.0494	−1.73758
$385$	86.9801	4.43292
$386$	−35.1168	−1.78740
$387$	−36.7267	−1.86692
$388$	60.1581	3.05406
$389$	−2.59464	−0.131553	−0.0657767	−	0.997834i	$-0.520953\pi$
$389$	−2.59464	−0.131553	−0.0657767	+	0.997834i	$0.520953\pi$
$390$	123.180	6.23748
$391$	2.40065	0.121406
$392$	−34.0115	−1.71784
$393$	15.5620	0.785000
$394$	−36.0926	−1.81832
$395$	19.2517	0.968660
$396$	188.603	9.47764
$397$	−37.3322	−1.87365	−0.936826	−	0.349796i	$-0.886251\pi$
$397$	−37.3322	−1.87365	−0.936826	+	0.349796i	$0.886251\pi$
$398$	25.9169	1.29910
$399$	−74.2277	−3.71603
$400$	87.2606	4.36303
$401$	−6.55742	−0.327462	−0.163731	−	0.986505i	$-0.552353\pi$
$401$	−6.55742	−0.327462	−0.163731	+	0.986505i	$0.552353\pi$
$402$	−12.4199	−0.619447
$403$	−26.2140	−1.30581
$404$	65.5655	3.26200
$405$	−74.7447	−3.71409
$406$	−85.7047	−4.25345
$407$	−9.01579	−0.446896
$408$	41.0093	2.03026
$409$	−26.0965	−1.29039	−0.645196	−	0.764017i	$-0.723224\pi$
$409$	−26.0965	−1.29039	−0.645196	+	0.764017i	$0.723224\pi$
$410$	−74.5787	−3.68318
$411$	−8.17441	−0.403214
$412$	61.8661	3.04792
$413$	36.5363	1.79784
$414$	−20.9049	−1.02742
$415$	44.3952	2.17928
$416$	22.0234	1.07979
$417$	28.0754	1.37486
$418$	103.439	5.05935
$419$	27.1996	1.32879	0.664394	−	0.747382i	$-0.268690\pi$
$419$	27.1996	1.32879	0.664394	+	0.747382i	$0.268690\pi$
$420$	−204.943	−10.0002
$421$	−4.28863	−0.209015	−0.104507	−	0.994524i	$-0.533327\pi$
$421$	−4.28863	−0.209015	−0.104507	+	0.994524i	$0.533327\pi$
$422$	−48.4216	−2.35712
$423$	−2.87691	−0.139880
$424$	44.8699	2.17908
$425$	24.1281	1.17038
$426$	9.07142	0.439512
$427$	−11.9167	−0.576690
$428$	−63.7086	−3.07947
$429$	70.8756	3.42191
$430$	−55.6142	−2.68195
$431$	0.956874	0.0460910	0.0230455	−	0.999734i	$-0.492664\pi$
$431$	0.956874	0.0460910	0.0230455	+	0.999734i	$0.492664\pi$
$432$	−90.7890	−4.36809
$433$	9.68949	0.465647	0.232824	−	0.972519i	$-0.425204\pi$
$433$	9.68949	0.465647	0.232824	+	0.972519i	$0.425204\pi$
$434$	62.9424	3.02133
$435$	−123.955	−5.94321
$436$	15.7337	0.753509
$437$	−7.94448	−0.380036
$438$	56.3227	2.69120
$439$	−2.16857	−0.103500	−0.0517501	−	0.998660i	$-0.516480\pi$
$439$	−2.16857	−0.103500	−0.0517501	+	0.998660i	$0.516480\pi$
$440$	159.027	7.58134
$441$	36.7304	1.74907
$442$	19.3114	0.918550
$443$	24.7313	1.17502	0.587510	−	0.809217i	$-0.300108\pi$
$443$	24.7313	1.17502	0.587510	+	0.809217i	$0.300108\pi$
$444$	21.2431	1.00815
$445$	0.415540	0.0196985
$446$	72.2440	3.42085
$447$	13.9089	0.657866
$448$	−1.38424	−0.0653993
$449$	−33.2385	−1.56862	−0.784310	−	0.620369i	$-0.786983\pi$
$449$	−33.2385	−1.56862	−0.784310	+	0.620369i	$0.786983\pi$
$450$	−210.107	−9.90454
$451$	−42.9111	−2.02061
$452$	−11.4966	−0.540753
$453$	−24.0012	−1.12767
$454$	−58.7665	−2.75805
$455$	−53.7386	−2.51930
$456$	−135.712	−6.35530
$457$	−39.7266	−1.85833	−0.929165	−	0.369665i	$-0.879473\pi$
$457$	−39.7266	−1.85833	−0.929165	+	0.369665i	$0.879473\pi$
$458$	4.06333	0.189867
$459$	−25.1037	−1.17174
$460$	−21.9348	−1.02271
$461$	−22.8060	−1.06218	−0.531092	−	0.847314i	$-0.678218\pi$
$461$	−22.8060	−1.06218	−0.531092	+	0.847314i	$0.678218\pi$
$462$	−170.180	−7.91747
$463$	18.9770	0.881938	0.440969	−	0.897522i	$-0.354635\pi$
$463$	18.9770	0.881938	0.440969	+	0.897522i	$0.354635\pi$
$464$	−70.2804	−3.26268
$465$	91.0342	4.22161
$466$	45.8870	2.12568
$467$	23.6118	1.09262	0.546312	−	0.837582i	$-0.316031\pi$
$467$	23.6118	1.09262	0.546312	+	0.837582i	$0.316031\pi$
$468$	−116.524	−5.38631
$469$	5.41829	0.250193
$470$	−4.35643	−0.200947
$471$	−15.3029	−0.705121
$472$	66.8001	3.07472
$473$	−31.9993	−1.47133
$474$	−37.6667	−1.73009
$475$	−79.8469	−3.66363
$476$	−32.1297	−1.47266
$477$	−48.4568	−2.21869
$478$	−60.0869	−2.74831
$479$	−23.0799	−1.05455	−0.527275	−	0.849695i	$-0.676786\pi$
$479$	−23.0799	−1.05455	−0.527275	+	0.849695i	$0.676786\pi$
$480$	−76.4814	−3.49088
$481$	5.57019	0.253979
$482$	−38.8486	−1.76951
$483$	13.0704	0.594725
$484$	114.684	5.21291
$485$	−54.7795	−2.48741
$486$	51.5490	2.33831
$487$	−11.8757	−0.538138	−0.269069	−	0.963121i	$-0.586716\pi$
$487$	−11.8757	−0.538138	−0.269069	+	0.963121i	$0.586716\pi$
$488$	−21.7876	−0.986276
$489$	−41.9460	−1.89687
$490$	55.6198	2.51265
$491$	−9.37985	−0.423306	−0.211653	−	0.977345i	$-0.567885\pi$
$491$	−9.37985	−0.423306	−0.211653	+	0.977345i	$0.567885\pi$
$492$	101.108	4.55829
$493$	−19.4329	−0.875215
$494$	−63.9072	−2.87532
$495$	−171.740	−7.71914
$496$	51.6146	2.31757
$497$	−3.95749	−0.177518
$498$	−86.8608	−3.89233
$499$	18.4658	0.826642	0.413321	−	0.910585i	$-0.364369\pi$
$499$	18.4658	0.826642	0.413321	+	0.910585i	$0.364369\pi$
$500$	−127.731	−5.71228
$501$	70.7968	3.16297
$502$	−76.0522	−3.39437
$503$	25.4030	1.13266	0.566331	−	0.824178i	$-0.308362\pi$
$503$	25.4030	1.13266	0.566331	+	0.824178i	$0.308362\pi$
$504$	155.792	6.93954
$505$	−59.7034	−2.65677
$506$	−18.2141	−0.809714
$507$	−2.83215	−0.125780
$508$	49.4390	2.19350
$509$	−42.9603	−1.90418	−0.952091	−	0.305815i	$-0.901071\pi$
$509$	−42.9603	−1.90418	−0.952091	+	0.305815i	$0.901071\pi$
$510$	−67.0634	−2.96962
$511$	−24.5713	−1.08697
$512$	50.7880	2.24453
$513$	83.0755	3.66787
$514$	−10.6108	−0.468024
$515$	−56.3348	−2.48241
$516$	75.3971	3.31917
$517$	−2.50660	−0.110240
$518$	−13.3746	−0.587646
$519$	46.8522	2.05659
$520$	−98.2514	−4.30861
$521$	29.0375	1.27216	0.636078	−	0.771625i	$-0.280556\pi$
$521$	29.0375	1.27216	0.636078	+	0.771625i	$0.280556\pi$
$522$	169.222	7.40664
$523$	−9.96091	−0.435560	−0.217780	−	0.975998i	$-0.569882\pi$
$523$	−9.96091	−0.435560	−0.217780	+	0.975998i	$0.569882\pi$
$524$	−22.2916	−0.973815
$525$	131.366	5.73327
$526$	−33.2838	−1.45124
$527$	14.2717	0.621687
$528$	−139.552	−6.07323
$529$	−21.6011	−0.939178
$530$	−73.3768	−3.18728
$531$	−72.1401	−3.13061
$532$	106.327	4.60985
$533$	26.5116	1.14835
$534$	−0.813019	−0.0351828
$535$	58.0126	2.50810
$536$	9.90636	0.427890
$537$	−23.3128	−1.00602
$538$	22.1553	0.955184
$539$	32.0026	1.37845
$540$	229.372	9.87061
$541$	−4.88033	−0.209822	−0.104911	−	0.994482i	$-0.533456\pi$
$541$	−4.88033	−0.209822	−0.104911	+	0.994482i	$0.533456\pi$
$542$	4.65431	0.199920
$543$	13.4938	0.579076
$544$	−11.9903	−0.514078
$545$	−14.3270	−0.613702
$546$	105.141	4.49964
$547$	−6.19013	−0.264671	−0.132335	−	0.991205i	$-0.542248\pi$
$547$	−6.19013	−0.264671	−0.132335	+	0.991205i	$0.542248\pi$
$548$	11.7093	0.500198
$549$	23.5293	1.00420
$550$	−183.063	−7.80581
$551$	64.3093	2.73967
$552$	23.8969	1.01712
$553$	16.4325	0.698779
$554$	−59.4342	−2.52512
$555$	−19.3438	−0.821099
$556$	−40.2163	−1.70555
$557$	25.2451	1.06967	0.534834	−	0.844957i	$-0.320374\pi$
$557$	25.2451	1.06967	0.534834	+	0.844957i	$0.320374\pi$
$558$	−124.278	−5.26112
$559$	19.7700	0.836183
$560$	105.810	4.47129
$561$	−38.5870	−1.62914
$562$	−0.998262	−0.0421091
$563$	−33.4496	−1.40973	−0.704866	−	0.709341i	$-0.748993\pi$
$563$	−33.4496	−1.40973	−0.704866	+	0.709341i	$0.748993\pi$
$564$	5.90609	0.248691
$565$	10.4687	0.440421
$566$	−32.1463	−1.35121
$567$	−63.7988	−2.67930
$568$	−7.23556	−0.303597
$569$	41.7981	1.75227	0.876134	−	0.482068i	$-0.160114\pi$
$569$	41.7981	1.75227	0.876134	+	0.482068i	$0.160114\pi$
$570$	221.933	9.29574
$571$	42.4761	1.77757	0.888786	−	0.458323i	$-0.151550\pi$
$571$	42.4761	1.77757	0.888786	+	0.458323i	$0.151550\pi$
$572$	−101.525	−4.24497
$573$	−42.8953	−1.79198
$574$	−63.6571	−2.65700
$575$	14.0599	0.586338
$576$	2.73315	0.113881
$577$	27.5323	1.14618	0.573092	−	0.819491i	$-0.305744\pi$
$577$	27.5323	1.14618	0.573092	+	0.819491i	$0.305744\pi$
$578$	32.8710	1.36725
$579$	−43.3520	−1.80165
$580$	177.559	7.37272
$581$	37.8939	1.57210
$582$	107.178	4.44267
$583$	−42.2196	−1.74856
$584$	−44.9242	−1.85898
$585$	106.106	4.38693
$586$	47.5211	1.96308
$587$	5.98771	0.247139	0.123570	−	0.992336i	$-0.460566\pi$
$587$	5.98771	0.247139	0.123570	+	0.992336i	$0.460566\pi$
$588$	−75.4048	−3.10964
$589$	−47.2294	−1.94605
$590$	−109.240	−4.49733
$591$	−44.5566	−1.83281
$592$	−10.9676	−0.450764
$593$	−29.3529	−1.20538	−0.602689	−	0.797977i	$-0.705904\pi$
$593$	−29.3529	−1.20538	−0.602689	+	0.797977i	$0.705904\pi$
$594$	190.465	7.81486
$595$	29.2570	1.19942
$596$	−19.9236	−0.816102
$597$	31.9946	1.30945
$598$	11.2531	0.460175
$599$	−24.2602	−0.991244	−0.495622	−	0.868538i	$-0.665060\pi$
$599$	−24.2602	−0.991244	−0.495622	+	0.868538i	$0.665060\pi$
$600$	240.179	9.80526
$601$	15.8212	0.645360	0.322680	−	0.946508i	$-0.395416\pi$
$601$	15.8212	0.645360	0.322680	+	0.946508i	$0.395416\pi$
$602$	−47.4698	−1.93473
$603$	−10.6983	−0.435668
$604$	34.3802	1.39891
$605$	−104.430	−4.24570
$606$	116.812	4.74516
$607$	35.9056	1.45736	0.728681	−	0.684853i	$-0.240134\pi$
$607$	35.9056	1.45736	0.728681	+	0.684853i	$0.240134\pi$
$608$	39.6793	1.60921
$609$	−105.803	−4.28735
$610$	35.6297	1.44260
$611$	1.54865	0.0626515
$612$	63.4393	2.56438
$613$	−27.7701	−1.12162	−0.560811	−	0.827944i	$-0.689511\pi$
$613$	−27.7701	−1.12162	−0.560811	+	0.827944i	$0.689511\pi$
$614$	−27.7555	−1.12012
$615$	−92.0679	−3.71254
$616$	135.739	5.46908
$617$	−4.20798	−0.169407	−0.0847035	−	0.996406i	$-0.526994\pi$
$617$	−4.20798	−0.169407	−0.0847035	+	0.996406i	$0.526994\pi$
$618$	110.221	4.43374
$619$	7.94081	0.319168	0.159584	−	0.987184i	$-0.448985\pi$
$619$	7.94081	0.319168	0.159584	+	0.987184i	$0.448985\pi$
$620$	−130.401	−5.23703
$621$	−14.6284	−0.587017
$622$	0.620123	0.0248647
$623$	0.354687	0.0142102
$624$	86.2191	3.45153
$625$	56.8734	2.27494
$626$	49.2047	1.96661
$627$	127.696	5.09968
$628$	21.9205	0.874723
$629$	−3.03259	−0.120917
$630$	−254.770	−10.1503
$631$	−27.7063	−1.10297	−0.551485	−	0.834185i	$-0.685938\pi$
$631$	−27.7063	−1.10297	−0.551485	+	0.834185i	$0.685938\pi$
$632$	30.0438	1.19508
$633$	−59.7768	−2.37591
$634$	12.7917	0.508022
$635$	−45.0187	−1.78651
$636$	99.4782	3.94457
$637$	−19.7720	−0.783396
$638$	147.440	5.83720
$639$	7.81397	0.309116
$640$	−44.4130	−1.75558
$641$	−3.92501	−0.155028	−0.0775142	−	0.996991i	$-0.524698\pi$
$641$	−3.92501	−0.155028	−0.0775142	+	0.996991i	$0.524698\pi$
$642$	−113.504	−4.47963
$643$	32.3105	1.27420	0.637100	−	0.770781i	$-0.280134\pi$
$643$	32.3105	1.27420	0.637100	+	0.770781i	$0.280134\pi$
$644$	−18.7226	−0.737773
$645$	−68.6561	−2.70333
$646$	34.7932	1.36892
$647$	1.76519	0.0693968	0.0346984	−	0.999398i	$-0.488953\pi$
$647$	1.76519	0.0693968	0.0346984	+	0.999398i	$0.488953\pi$
$648$	−116.645	−4.58223
$649$	−62.8544	−2.46725
$650$	113.101	4.43618
$651$	77.7028	3.04541
$652$	60.0851	2.35312
$653$	25.9905	1.01709	0.508543	−	0.861037i	$-0.330184\pi$
$653$	25.9905	1.01709	0.508543	+	0.861037i	$0.330184\pi$
$654$	28.0313	1.09611
$655$	20.2986	0.793132
$656$	−52.2007	−2.03810
$657$	48.5155	1.89277
$658$	−3.71846	−0.144960
$659$	32.9821	1.28480	0.642400	−	0.766370i	$-0.277939\pi$
$659$	32.9821	1.28480	0.642400	+	0.766370i	$0.277939\pi$
$660$	352.569	13.7237
$661$	−28.5798	−1.11162	−0.555812	−	0.831308i	$-0.687593\pi$
$661$	−28.5798	−1.11162	−0.555812	+	0.831308i	$0.687593\pi$
$662$	−18.4242	−0.716075
$663$	23.8401	0.925871
$664$	69.2821	2.68867
$665$	−96.8202	−3.75453
$666$	26.4078	1.02328
$667$	−11.3239	−0.438465
$668$	−101.412	−3.92375
$669$	89.1857	3.44812
$670$	−16.2001	−0.625864
$671$	20.5006	0.791418
$672$	−65.2812	−2.51828
$673$	−10.1347	−0.390664	−0.195332	−	0.980737i	$-0.562578\pi$
$673$	−10.1347	−0.390664	−0.195332	+	0.980737i	$0.562578\pi$
$674$	−48.2386	−1.85808
$675$	−147.024	−5.65897
$676$	4.05689	0.156034
$677$	5.70274	0.219174	0.109587	−	0.993977i	$-0.465047\pi$
$677$	5.70274	0.219174	0.109587	+	0.993977i	$0.465047\pi$
$678$	−20.4823	−0.786619
$679$	−46.7574	−1.79438
$680$	53.4913	2.05130
$681$	−72.5476	−2.78003
$682$	−108.281	−4.14631
$683$	43.7091	1.67248	0.836241	−	0.548362i	$-0.184748\pi$
$683$	43.7091	1.67248	0.836241	+	0.548362i	$0.184748\pi$
$684$	−209.939	−8.02724
$685$	−10.6624	−0.407391
$686$	−15.1867	−0.579830
$687$	5.01620	0.191380
$688$	−38.9267	−1.48407
$689$	26.0844	0.993735
$690$	−39.0792	−1.48772
$691$	28.8311	1.09679	0.548393	−	0.836221i	$-0.315240\pi$
$691$	28.8311	1.09679	0.548393	+	0.836221i	$0.315240\pi$
$692$	−67.1130	−2.55125
$693$	−146.590	−5.56849
$694$	−49.6365	−1.88418
$695$	36.6206	1.38910
$696$	−193.442	−7.33239
$697$	−14.4338	−0.546719
$698$	−54.4689	−2.06168
$699$	56.6479	2.14262
$700$	−188.173	−7.11229
$701$	−47.5546	−1.79611	−0.898056	−	0.439882i	$-0.855020\pi$
$701$	−47.5546	−1.79611	−0.898056	+	0.439882i	$0.855020\pi$
$702$	−117.674	−4.44132
$703$	10.0358	0.378506
$704$	2.38135	0.0897504
$705$	−5.37804	−0.202549
$706$	−92.5382	−3.48272
$707$	−50.9602	−1.91656
$708$	148.098	5.56587
$709$	11.6442	0.437307	0.218653	−	0.975803i	$-0.429834\pi$
$709$	11.6442	0.437307	0.218653	+	0.975803i	$0.429834\pi$
$710$	11.8325	0.444065
$711$	−32.4455	−1.21680
$712$	0.648481	0.0243029
$713$	8.31642	0.311452
$714$	−57.2424	−2.14224
$715$	92.4479	3.45735
$716$	33.3942	1.24800
$717$	−74.1776	−2.77021
$718$	56.5324	2.10977
$719$	−20.3617	−0.759362	−0.379681	−	0.925117i	$-0.623966\pi$
$719$	−20.3617	−0.759362	−0.379681	+	0.925117i	$0.623966\pi$
$720$	−208.919	−7.78596
$721$	−48.0849	−1.79078
$722$	−66.6521	−2.48053
$723$	−47.9589	−1.78361
$724$	−19.3291	−0.718360
$725$	−113.813	−4.22689
$726$	204.322	7.58309
$727$	16.6804	0.618641	0.309321	−	0.950958i	$-0.399898\pi$
$727$	16.6804	0.618641	0.309321	+	0.950958i	$0.399898\pi$
$728$	−83.8631	−3.10817
$729$	9.07189	0.335996
$730$	73.4656	2.71908
$731$	−10.7634	−0.398100
$732$	−48.3038	−1.78536
$733$	−16.6227	−0.613973	−0.306986	−	0.951714i	$-0.599321\pi$
$733$	−16.6227	−0.613973	−0.306986	+	0.951714i	$0.599321\pi$
$734$	96.7799	3.57221
$735$	68.6630	2.53267
$736$	−6.98695	−0.257543
$737$	−9.32122	−0.343351
$738$	125.689	4.62669
$739$	33.0670	1.21639	0.608194	−	0.793789i	$-0.291894\pi$
$739$	33.0670	1.21639	0.608194	+	0.793789i	$0.291894\pi$
$740$	27.7088	1.01860
$741$	−78.8939	−2.89824
$742$	−62.6312	−2.29926
$743$	−28.1290	−1.03195	−0.515977	−	0.856603i	$-0.672571\pi$
$743$	−28.1290	−1.03195	−0.515977	+	0.856603i	$0.672571\pi$
$744$	142.066	5.20838
$745$	18.1423	0.664681
$746$	−49.6368	−1.81733
$747$	−74.8205	−2.73754
$748$	55.2735	2.02100
$749$	49.5170	1.80931
$750$	−227.565	−8.30952
$751$	5.31797	0.194056	0.0970278	−	0.995282i	$-0.469066\pi$
$751$	5.31797	0.194056	0.0970278	+	0.995282i	$0.469066\pi$
$752$	−3.04924	−0.111194
$753$	−93.8869	−3.42143
$754$	−91.0923	−3.31739
$755$	−31.3064	−1.13935
$756$	195.782	7.12053
$757$	−28.7147	−1.04366	−0.521828	−	0.853051i	$-0.674750\pi$
$757$	−28.7147	−1.04366	−0.521828	+	0.853051i	$0.674750\pi$
$758$	−68.0342	−2.47111
$759$	−22.4854	−0.816168
$760$	−177.018	−6.42113
$761$	6.77539	0.245608	0.122804	−	0.992431i	$-0.460811\pi$
$761$	6.77539	0.245608	0.122804	+	0.992431i	$0.460811\pi$
$762$	88.0807	3.19083
$763$	−12.2289	−0.442717
$764$	61.4449	2.22300
$765$	−57.7673	−2.08858
$766$	9.80202	0.354161
$767$	38.8331	1.40218
$768$	89.3822	3.22530
$769$	31.3643	1.13102	0.565512	−	0.824740i	$-0.308679\pi$
$769$	31.3643	1.13102	0.565512	+	0.824740i	$0.308679\pi$
$770$	−221.977	−7.99949
$771$	−13.0991	−0.471754
$772$	62.0990	2.23499
$773$	−7.98910	−0.287348	−0.143674	−	0.989625i	$-0.545892\pi$
$773$	−7.98910	−0.287348	−0.143674	+	0.989625i	$0.545892\pi$
$774$	93.7281	3.36899
$775$	83.5851	3.00246
$776$	−85.4875	−3.06882
$777$	−16.5110	−0.592330
$778$	6.62163	0.237397
$779$	47.7657	1.71138
$780$	−217.827	−7.79945
$781$	6.80817	0.243616
$782$	−6.12657	−0.219086
$783$	118.415	4.23179
$784$	38.9306	1.39038
$785$	−19.9606	−0.712425
$786$	−39.7149	−1.41658
$787$	−9.85610	−0.351332	−0.175666	−	0.984450i	$-0.556208\pi$
$787$	−9.85610	−0.351332	−0.175666	+	0.984450i	$0.556208\pi$
$788$	63.8246	2.27366
$789$	−41.0891	−1.46281
$790$	−49.1312	−1.74801
$791$	8.93561	0.317714
$792$	−268.013	−9.52344
$793$	−12.6658	−0.449777
$794$	95.2734	3.38113
$795$	−90.5841	−3.21269
$796$	−45.8303	−1.62441
$797$	21.3584	0.756553	0.378277	−	0.925693i	$-0.376517\pi$
$797$	21.3584	0.756553	0.378277	+	0.925693i	$0.376517\pi$
$798$	189.432	6.70583
$799$	−0.843133	−0.0298279
$800$	−70.2232	−2.48276
$801$	−0.700321	−0.0247446
$802$	16.7348	0.590927
$803$	42.2707	1.49170
$804$	21.9628	0.774567
$805$	17.0486	0.600886
$806$	66.8991	2.35642
$807$	27.3509	0.962798
$808$	−93.1717	−3.27777
$809$	−7.85925	−0.276316	−0.138158	−	0.990410i	$-0.544118\pi$
$809$	−7.85925	−0.276316	−0.138158	+	0.990410i	$0.544118\pi$
$810$	190.752	6.70232
$811$	−41.2361	−1.44800	−0.723998	−	0.689802i	$-0.757698\pi$
$811$	−41.2361	−1.44800	−0.723998	+	0.689802i	$0.757698\pi$
$812$	151.556	5.31859
$813$	5.74578	0.201513
$814$	23.0087	0.806453
$815$	−54.7131	−1.91652
$816$	−46.9405	−1.64325
$817$	35.6194	1.24617
$818$	66.5995	2.32860
$819$	90.5671	3.16467
$820$	131.882	4.60551
$821$	−21.9134	−0.764782	−0.382391	−	0.924001i	$-0.624899\pi$
$821$	−21.9134	−0.764782	−0.382391	+	0.924001i	$0.624899\pi$
$822$	20.8614	0.727626
$823$	51.5676	1.79753	0.898766	−	0.438428i	$-0.144464\pi$
$823$	51.5676	1.79753	0.898766	+	0.438428i	$0.144464\pi$
$824$	−87.9146	−3.06265
$825$	−225.992	−7.86803
$826$	−93.2422	−3.24431
$827$	−5.49296	−0.191009	−0.0955045	−	0.995429i	$-0.530446\pi$
$827$	−5.49296	−0.191009	−0.0955045	+	0.995429i	$0.530446\pi$
$828$	36.9673	1.28470
$829$	15.0984	0.524390	0.262195	−	0.965015i	$-0.415554\pi$
$829$	15.0984	0.524390	0.262195	+	0.965015i	$0.415554\pi$
$830$	−113.299	−3.93265
$831$	−73.3720	−2.54525
$832$	−1.47126	−0.0510067
$833$	10.7645	0.372969
$834$	−71.6496	−2.48102
$835$	92.3451	3.19573
$836$	−182.916	−6.32630
$837$	−86.9648	−3.00594
$838$	−69.4146	−2.39789
$839$	22.5561	0.778724	0.389362	−	0.921085i	$-0.372696\pi$
$839$	22.5561	0.778724	0.389362	+	0.921085i	$0.372696\pi$
$840$	291.234	10.0485
$841$	62.6655	2.16088
$842$	10.9448	0.377181
$843$	−1.23236	−0.0424448
$844$	85.6266	2.94739
$845$	−3.69417	−0.127083
$846$	7.34200	0.252423
$847$	−89.1372	−3.06279
$848$	−51.3595	−1.76369
$849$	−39.6848	−1.36198
$850$	−61.5758	−2.11203
$851$	−1.76715	−0.0605772
$852$	−16.0415	−0.549572
$853$	−9.17259	−0.314063	−0.157032	−	0.987594i	$-0.550193\pi$
$853$	−9.17259	−0.314063	−0.157032	+	0.987594i	$0.550193\pi$
$854$	30.4119	1.04068
$855$	191.169	6.53785
$856$	90.5330	3.09435
$857$	−11.0327	−0.376870	−0.188435	−	0.982086i	$-0.560342\pi$
$857$	−11.0327	−0.376870	−0.188435	+	0.982086i	$0.560342\pi$
$858$	−180.878	−6.17506
$859$	35.0254	1.19505	0.597526	−	0.801850i	$-0.296151\pi$
$859$	35.0254	1.19505	0.597526	+	0.801850i	$0.296151\pi$
$860$	98.3456	3.35356
$861$	−78.5852	−2.67817
$862$	−2.44198	−0.0831743
$863$	−26.2934	−0.895036	−0.447518	−	0.894275i	$-0.647692\pi$
$863$	−26.2934	−0.895036	−0.447518	+	0.894275i	$0.647692\pi$
$864$	73.0626	2.48564
$865$	61.1126	2.07789
$866$	−24.7280	−0.840291
$867$	40.5794	1.37815
$868$	−111.305	−3.77792
$869$	−28.2692	−0.958966
$870$	316.340	10.7249
$871$	5.75890	0.195133
$872$	−22.3584	−0.757151
$873$	92.3214	3.12461
$874$	20.2746	0.685800
$875$	99.2776	3.35619
$876$	−99.5986	−3.36513
$877$	28.0878	0.948459	0.474229	−	0.880401i	$-0.342727\pi$
$877$	28.0878	0.948459	0.474229	+	0.880401i	$0.342727\pi$
$878$	5.53428	0.186773
$879$	58.6651	1.97873
$880$	−182.028	−6.13615
$881$	−29.7351	−1.00180	−0.500900	−	0.865505i	$-0.666998\pi$
$881$	−29.7351	−1.00180	−0.500900	+	0.865505i	$0.666998\pi$
$882$	−93.7376	−3.15631
$883$	−11.7565	−0.395636	−0.197818	−	0.980239i	$-0.563386\pi$
$883$	−11.7565	−0.395636	−0.197818	+	0.980239i	$0.563386\pi$
$884$	−34.1494	−1.14857
$885$	−134.857	−4.53317
$886$	−63.1154	−2.12040
$887$	−35.8139	−1.20251	−0.601257	−	0.799056i	$-0.705333\pi$
$887$	−35.8139	−1.20251	−0.601257	+	0.799056i	$0.705333\pi$
$888$	−30.1875	−1.01302
$889$	−38.4260	−1.28877
$890$	−1.06048	−0.0355472
$891$	109.755	3.67692
$892$	−127.753	−4.27749
$893$	2.79018	0.0933697
$894$	−35.4960	−1.18716
$895$	−30.4085	−1.01645
$896$	−37.9090	−1.26645
$897$	13.8921	0.463843
$898$	84.8259	2.83068
$899$	−67.3201	−2.24525
$900$	371.544	12.3848
$901$	−14.2012	−0.473110
$902$	109.511	3.64632
$903$	−58.6018	−1.95015
$904$	16.3372	0.543366
$905$	17.6009	0.585075
$906$	61.2520	2.03496
$907$	5.90469	0.196062	0.0980310	−	0.995183i	$-0.468746\pi$
$907$	5.90469	0.196062	0.0980310	+	0.995183i	$0.468746\pi$
$908$	103.920	3.44871
$909$	100.620	3.33735
$910$	137.143	4.54625
$911$	−22.6333	−0.749874	−0.374937	−	0.927050i	$-0.622336\pi$
$911$	−22.6333	−0.749874	−0.374937	+	0.927050i	$0.622336\pi$
$912$	155.340	5.14382
$913$	−65.1898	−2.15747
$914$	101.384	3.35348
$915$	43.9851	1.45410
$916$	−7.18540	−0.237412
$917$	17.3260	0.572155
$918$	64.0656	2.11448
$919$	−20.8265	−0.687004	−0.343502	−	0.939152i	$-0.611613\pi$
$919$	−20.8265	−0.687004	−0.343502	+	0.939152i	$0.611613\pi$
$920$	31.1704	1.02766
$921$	−34.2643	−1.12905
$922$	58.2020	1.91678
$923$	−4.20627	−0.138451
$924$	300.938	9.90013
$925$	−17.7610	−0.583977
$926$	−48.4302	−1.59152
$927$	94.9425	3.11832
$928$	56.5583	1.85662
$929$	11.5201	0.377962	0.188981	−	0.981981i	$-0.439482\pi$
$929$	11.5201	0.377962	0.188981	+	0.981981i	$0.439482\pi$
$930$	−232.323	−7.61817
$931$	−35.6230	−1.16750
$932$	−81.1446	−2.65798
$933$	0.765547	0.0250629
$934$	−60.2583	−1.97171
$935$	−50.3316	−1.64602
$936$	165.586	5.41234
$937$	−23.6248	−0.771789	−0.385895	−	0.922543i	$-0.626107\pi$
$937$	−23.6248	−0.771789	−0.385895	+	0.922543i	$0.626107\pi$
$938$	−13.8277	−0.451490
$939$	60.7435	1.98229
$940$	7.70371	0.251267
$941$	−34.1527	−1.11334	−0.556672	−	0.830732i	$-0.687922\pi$
$941$	−34.1527	−1.11334	−0.556672	+	0.830732i	$0.687922\pi$
$942$	39.0537	1.27244
$943$	−8.41085	−0.273895
$944$	−76.4614	−2.48861
$945$	−178.278	−5.79938
$946$	81.6636	2.65511
$947$	−24.6416	−0.800744	−0.400372	−	0.916353i	$-0.631119\pi$
$947$	−24.6416	−0.800744	−0.400372	+	0.916353i	$0.631119\pi$
$948$	66.6081	2.16333
$949$	−26.1159	−0.847759
$950$	203.773	6.61126
$951$	15.7914	0.512071
$952$	45.6578	1.47978
$953$	12.3716	0.400756	0.200378	−	0.979719i	$-0.435783\pi$
$953$	12.3716	0.400756	0.200378	+	0.979719i	$0.435783\pi$
$954$	123.664	4.00377
$955$	−55.9513	−1.81054
$956$	106.255	3.43653
$957$	182.016	5.88373
$958$	58.9010	1.90300
$959$	−9.10099	−0.293886
$960$	5.10930	0.164902
$961$	18.4405	0.594856
$962$	−14.2154	−0.458322
$963$	−97.7702	−3.15060
$964$	68.6982	2.21262
$965$	−56.5469	−1.82031
$966$	−33.3563	−1.07322
$967$	5.24910	0.168800	0.0843999	−	0.996432i	$-0.473103\pi$
$967$	5.24910	0.168800	0.0843999	+	0.996432i	$0.473103\pi$
$968$	−162.971	−5.23810
$969$	42.9524	1.37983
$970$	139.800	4.48870
$971$	23.4937	0.753950	0.376975	−	0.926223i	$-0.376964\pi$
$971$	23.4937	0.753950	0.376975	+	0.926223i	$0.376964\pi$
$972$	−91.1570	−2.92386
$973$	31.2578	1.00208
$974$	30.3072	0.971106
$975$	139.624	4.47154
$976$	24.9387	0.798268
$977$	−43.1571	−1.38072	−0.690360	−	0.723466i	$-0.742548\pi$
$977$	−43.1571	−1.38072	−0.690360	+	0.723466i	$0.742548\pi$
$978$	107.048	3.42302
$979$	−0.610177	−0.0195013
$980$	−98.3556	−3.14185
$981$	24.1457	0.770914
$982$	23.9378	0.763885
$983$	20.8051	0.663579	0.331790	−	0.943353i	$-0.392348\pi$
$983$	20.8051	0.663579	0.331790	+	0.943353i	$0.392348\pi$
$984$	−143.679	−4.58031
$985$	−58.1182	−1.85180
$986$	49.5936	1.57938
$987$	−4.59046	−0.146116
$988$	113.011	3.59535
$989$	−6.27207	−0.199440
$990$	438.288	13.9297
$991$	41.9594	1.33288	0.666442	−	0.745557i	$-0.267816\pi$
$991$	41.9594	1.33288	0.666442	+	0.745557i	$0.267816\pi$
$992$	−41.5370	−1.31880
$993$	−22.7447	−0.721783
$994$	10.0997	0.320342
$995$	41.7327	1.32302
$996$	153.601	4.86703
$997$	47.7181	1.51125	0.755623	−	0.655006i	$-0.227334\pi$
$997$	47.7181	1.51125	0.755623	+	0.655006i	$0.227334\pi$
$998$	−47.1255	−1.49173
$999$	18.4791	0.584653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.b.1.17	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.b.1.17	✓	243	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:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55204 q^{2} -3.15051 q^{3} +4.51292 q^{4} -4.10943 q^{5} +8.04024 q^{6} -3.50763 q^{7} -6.41307 q^{8} +6.92573 q^{9} +O(q^{10})\)	\(q-2.55204 q^{2} -3.15051 q^{3} +4.51292 q^{4} -4.10943 q^{5} +8.04024 q^{6} -3.50763 q^{7} -6.41307 q^{8} +6.92573 q^{9} +10.4874 q^{10} +6.03427 q^{11} -14.2180 q^{12} -3.72813 q^{13} +8.95162 q^{14} +12.9468 q^{15} +7.34059 q^{16} +2.02972 q^{17} -17.6748 q^{18} -6.71693 q^{19} -18.5455 q^{20} +11.0508 q^{21} -15.3997 q^{22} +1.18275 q^{23} +20.2045 q^{24} +11.8874 q^{25} +9.51434 q^{26} -12.3681 q^{27} -15.8296 q^{28} -9.57421 q^{29} -33.0408 q^{30} +7.03140 q^{31} -5.90736 q^{32} -19.0110 q^{33} -5.17992 q^{34} +14.4144 q^{35} +31.2553 q^{36} -1.49410 q^{37} +17.1419 q^{38} +11.7455 q^{39} +26.3541 q^{40} -7.11124 q^{41} -28.2022 q^{42} -5.30293 q^{43} +27.2321 q^{44} -28.4608 q^{45} -3.01844 q^{46} -0.415395 q^{47} -23.1266 q^{48} +5.30347 q^{49} -30.3372 q^{50} -6.39464 q^{51} -16.8247 q^{52} -6.99664 q^{53} +31.5638 q^{54} -24.7974 q^{55} +22.4947 q^{56} +21.1618 q^{57} +24.4338 q^{58} -10.4162 q^{59} +58.4279 q^{60} +3.39737 q^{61} -17.9444 q^{62} -24.2929 q^{63} +0.394637 q^{64} +15.3205 q^{65} +48.5170 q^{66} -1.54471 q^{67} +9.15994 q^{68} -3.72628 q^{69} -36.7860 q^{70} +1.12825 q^{71} -44.4152 q^{72} +7.00511 q^{73} +3.81300 q^{74} -37.4514 q^{75} -30.3130 q^{76} -21.1660 q^{77} -29.9751 q^{78} -4.68477 q^{79} -30.1656 q^{80} +18.1886 q^{81} +18.1482 q^{82} -10.8033 q^{83} +49.8715 q^{84} -8.34097 q^{85} +13.5333 q^{86} +30.1637 q^{87} -38.6982 q^{88} -0.101119 q^{89} +72.6332 q^{90} +13.0769 q^{91} +5.33767 q^{92} -22.1525 q^{93} +1.06010 q^{94} +27.6028 q^{95} +18.6112 q^{96} +13.3302 q^{97} -13.5347 q^{98} +41.7917 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) \) 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9} - 24 q^{10} - 37 q^{11} - 74 q^{12} - 113 q^{13} - 35 q^{14} - 34 q^{15} + 218 q^{16} - 125 q^{17} - 108 q^{18} - 46 q^{19} - 157 q^{20} - 113 q^{21} - 16 q^{22} - 60 q^{23} - 49 q^{24} + 208 q^{25} - 52 q^{26} - 90 q^{27} - 70 q^{28} - 137 q^{29} - 26 q^{30} - 36 q^{31} - 258 q^{32} - 153 q^{33} - 23 q^{34} - 77 q^{35} + 180 q^{36} - 108 q^{37} - 122 q^{38} - 32 q^{39} - 57 q^{40} - 186 q^{41} - 28 q^{42} - 54 q^{43} - 90 q^{44} - 233 q^{45} - 42 q^{46} - 188 q^{47} - 149 q^{48} + 189 q^{49} - 146 q^{50} - 34 q^{51} - 195 q^{52} - 196 q^{53} - 36 q^{54} - 57 q^{55} - 63 q^{56} - 76 q^{57} - 24 q^{58} - 137 q^{59} - 73 q^{60} - 96 q^{61} - 167 q^{62} - 113 q^{63} + 224 q^{64} - 131 q^{65} - 11 q^{66} - 71 q^{67} - 260 q^{68} - 162 q^{69} - 48 q^{70} - 77 q^{71} - 290 q^{72} - 160 q^{73} - 34 q^{74} - 100 q^{75} - 84 q^{76} - 416 q^{77} - 59 q^{78} - 17 q^{79} - 268 q^{80} + 147 q^{81} - 28 q^{82} - 238 q^{83} - 184 q^{84} - 108 q^{85} - 61 q^{86} - 127 q^{87} - 47 q^{88} - 183 q^{89} - 56 q^{90} - 14 q^{91} - 109 q^{92} - 206 q^{93} + q^{94} - 84 q^{95} - 54 q^{96} - 127 q^{97} - 294 q^{98} - 66 q^{99}+O(q^{100}) \) 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9 - 24 * q^10 - 37 * q^11 - 74 * q^12 - 113 * q^13 - 35 * q^14 - 34 * q^15 + 218 * q^16 - 125 * q^17 - 108 * q^18 - 46 * q^19 - 157 * q^20 - 113 * q^21 - 16 * q^22 - 60 * q^23 - 49 * q^24 + 208 * q^25 - 52 * q^26 - 90 * q^27 - 70 * q^28 - 137 * q^29 - 26 * q^30 - 36 * q^31 - 258 * q^32 - 153 * q^33 - 23 * q^34 - 77 * q^35 + 180 * q^36 - 108 * q^37 - 122 * q^38 - 32 * q^39 - 57 * q^40 - 186 * q^41 - 28 * q^42 - 54 * q^43 - 90 * q^44 - 233 * q^45 - 42 * q^46 - 188 * q^47 - 149 * q^48 + 189 * q^49 - 146 * q^50 - 34 * q^51 - 195 * q^52 - 196 * q^53 - 36 * q^54 - 57 * q^55 - 63 * q^56 - 76 * q^57 - 24 * q^58 - 137 * q^59 - 73 * q^60 - 96 * q^61 - 167 * q^62 - 113 * q^63 + 224 * q^64 - 131 * q^65 - 11 * q^66 - 71 * q^67 - 260 * q^68 - 162 * q^69 - 48 * q^70 - 77 * q^71 - 290 * q^72 - 160 * q^73 - 34 * q^74 - 100 * q^75 - 84 * q^76 - 416 * q^77 - 59 * q^78 - 17 * q^79 - 268 * q^80 + 147 * q^81 - 28 * q^82 - 238 * q^83 - 184 * q^84 - 108 * q^85 - 61 * q^86 - 127 * q^87 - 47 * q^88 - 183 * q^89 - 56 * q^90 - 14 * q^91 - 109 * q^92 - 206 * q^93 + q^94 - 84 * q^95 - 54 * q^96 - 127 * q^97 - 294 * q^98 - 66 * q^99

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