LMFDB - Embedded newform 6037.2.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, 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("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74252 q^{2} -0.770641 q^{3} +5.52143 q^{4} +3.66315 q^{5} +2.11350 q^{6} -4.05510 q^{7} -9.65761 q^{8} -2.40611 q^{9} +O(q^{10})$	\(q-2.74252 q^{2} -0.770641 q^{3} +5.52143 q^{4} +3.66315 q^{5} +2.11350 q^{6} -4.05510 q^{7} -9.65761 q^{8} -2.40611 q^{9} -10.0463 q^{10} +2.59243 q^{11} -4.25504 q^{12} +6.34752 q^{13} +11.1212 q^{14} -2.82297 q^{15} +15.4434 q^{16} +4.25605 q^{17} +6.59882 q^{18} +0.846401 q^{19} +20.2258 q^{20} +3.12503 q^{21} -7.10979 q^{22} -5.33234 q^{23} +7.44255 q^{24} +8.41865 q^{25} -17.4082 q^{26} +4.16617 q^{27} -22.3900 q^{28} +3.49174 q^{29} +7.74206 q^{30} -7.25555 q^{31} -23.0386 q^{32} -1.99783 q^{33} -11.6723 q^{34} -14.8545 q^{35} -13.2852 q^{36} -1.03499 q^{37} -2.32128 q^{38} -4.89166 q^{39} -35.3773 q^{40} -1.78110 q^{41} -8.57046 q^{42} -9.45036 q^{43} +14.3139 q^{44} -8.81395 q^{45} +14.6241 q^{46} -8.19747 q^{47} -11.9013 q^{48} +9.44388 q^{49} -23.0884 q^{50} -3.27988 q^{51} +35.0474 q^{52} -8.23944 q^{53} -11.4258 q^{54} +9.49644 q^{55} +39.1626 q^{56} -0.652271 q^{57} -9.57617 q^{58} -5.27460 q^{59} -15.5868 q^{60} -3.18583 q^{61} +19.8985 q^{62} +9.75704 q^{63} +32.2971 q^{64} +23.2519 q^{65} +5.47909 q^{66} -11.6463 q^{67} +23.4995 q^{68} +4.10932 q^{69} +40.7387 q^{70} +0.924976 q^{71} +23.2373 q^{72} -2.53596 q^{73} +2.83848 q^{74} -6.48776 q^{75} +4.67335 q^{76} -10.5126 q^{77} +13.4155 q^{78} -4.32093 q^{79} +56.5713 q^{80} +4.00772 q^{81} +4.88470 q^{82} +0.825528 q^{83} +17.2546 q^{84} +15.5905 q^{85} +25.9178 q^{86} -2.69087 q^{87} -25.0367 q^{88} +12.6211 q^{89} +24.1725 q^{90} -25.7399 q^{91} -29.4422 q^{92} +5.59142 q^{93} +22.4818 q^{94} +3.10049 q^{95} +17.7545 q^{96} -0.300325 q^{97} -25.9001 q^{98} -6.23767 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) $ 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * 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 $

$2$	−2.74252	−1.93926	−0.969628	−	0.244583i	$-0.921349\pi$
$2$	−2.74252	−1.93926	−0.969628	+	0.244583i	$0.921349\pi$
$3$	−0.770641	−0.444930	−0.222465	−	0.974941i	$-0.571410\pi$
$3$	−0.770641	−0.444930	−0.222465	+	0.974941i	$0.571410\pi$
$4$	5.52143	2.76072
$5$	3.66315	1.63821	0.819105	−	0.573644i	$-0.194471\pi$
$5$	3.66315	1.63821	0.819105	+	0.573644i	$0.194471\pi$
$6$	2.11350	0.862833
$7$	−4.05510	−1.53269	−0.766343	−	0.642432i	$-0.777926\pi$
$7$	−4.05510	−1.53269	−0.766343	+	0.642432i	$0.777926\pi$
$8$	−9.65761	−3.41448
$9$	−2.40611	−0.802038
$10$	−10.0463	−3.17691
$11$	2.59243	0.781646	0.390823	−	0.920466i	$-0.372190\pi$
$11$	2.59243	0.781646	0.390823	+	0.920466i	$0.372190\pi$
$12$	−4.25504	−1.22832
$13$	6.34752	1.76049	0.880243	−	0.474523i	$-0.157379\pi$
$13$	6.34752	1.76049	0.880243	+	0.474523i	$0.157379\pi$
$14$	11.1212	2.97227
$15$	−2.82297	−0.728888
$16$	15.4434	3.86084
$17$	4.25605	1.03224	0.516122	−	0.856515i	$-0.327375\pi$
$17$	4.25605	1.03224	0.516122	+	0.856515i	$0.327375\pi$
$18$	6.59882	1.55536
$19$	0.846401	0.194178	0.0970889	−	0.995276i	$-0.469047\pi$
$19$	0.846401	0.194178	0.0970889	+	0.995276i	$0.469047\pi$
$20$	20.2258	4.52263
$21$	3.12503	0.681937
$22$	−7.10979	−1.51581
$23$	−5.33234	−1.11187	−0.555935	−	0.831226i	$-0.687640\pi$
$23$	−5.33234	−1.11187	−0.555935	+	0.831226i	$0.687640\pi$
$24$	7.44255	1.51920
$25$	8.41865	1.68373
$26$	−17.4082	−3.41404
$27$	4.16617	0.801780
$28$	−22.3900	−4.23131
$29$	3.49174	0.648399	0.324200	−	0.945989i	$-0.394905\pi$
$29$	3.49174	0.648399	0.324200	+	0.945989i	$0.394905\pi$
$30$	7.74206	1.41350
$31$	−7.25555	−1.30313	−0.651567	−	0.758591i	$-0.725888\pi$
$31$	−7.25555	−1.30313	−0.651567	+	0.758591i	$0.725888\pi$
$32$	−23.0386	−4.07268
$33$	−1.99783	−0.347777
$34$	−11.6723	−2.00179
$35$	−14.8545	−2.51086
$36$	−13.2852	−2.21420
$37$	−1.03499	−0.170151	−0.0850754	−	0.996375i	$-0.527113\pi$
$37$	−1.03499	−0.170151	−0.0850754	+	0.996375i	$0.527113\pi$
$38$	−2.32128	−0.376561
$39$	−4.89166	−0.783293
$40$	−35.3773	−5.59364
$41$	−1.78110	−0.278160	−0.139080	−	0.990281i	$-0.544415\pi$
$41$	−1.78110	−0.278160	−0.139080	+	0.990281i	$0.544415\pi$
$42$	−8.57046	−1.32245
$43$	−9.45036	−1.44117	−0.720583	−	0.693369i	$-0.756126\pi$
$43$	−9.45036	−1.44117	−0.720583	+	0.693369i	$0.756126\pi$
$44$	14.3139	2.15790
$45$	−8.81395	−1.31391
$46$	14.6241	2.15620
$47$	−8.19747	−1.19572	−0.597862	−	0.801599i	$-0.703983\pi$
$47$	−8.19747	−1.19572	−0.597862	+	0.801599i	$0.703983\pi$
$48$	−11.9013	−1.71780
$49$	9.44388	1.34913
$50$	−23.0884	−3.26519
$51$	−3.27988	−0.459276
$52$	35.0474	4.86020
$53$	−8.23944	−1.13177	−0.565887	−	0.824483i	$-0.691466\pi$
$53$	−8.23944	−1.13177	−0.565887	+	0.824483i	$0.691466\pi$
$54$	−11.4258	−1.55486
$55$	9.49644	1.28050
$56$	39.1626	5.23333
$57$	−0.652271	−0.0863955
$58$	−9.57617	−1.25741
$59$	−5.27460	−0.686694	−0.343347	−	0.939209i	$-0.611561\pi$
$59$	−5.27460	−0.686694	−0.343347	+	0.939209i	$0.611561\pi$
$60$	−15.5868	−2.01225
$61$	−3.18583	−0.407904	−0.203952	−	0.978981i	$-0.565379\pi$
$61$	−3.18583	−0.407904	−0.203952	+	0.978981i	$0.565379\pi$
$62$	19.8985	2.52711
$63$	9.75704	1.22927
$64$	32.2971	4.03713
$65$	23.2519	2.88405
$66$	5.47909	0.674430
$67$	−11.6463	−1.42282	−0.711412	−	0.702775i	$-0.751944\pi$
$67$	−11.6463	−1.42282	−0.711412	+	0.702775i	$0.751944\pi$
$68$	23.4995	2.84973
$69$	4.10932	0.494704
$70$	40.7387	4.86920
$71$	0.924976	0.109774	0.0548872	−	0.998493i	$-0.482520\pi$
$71$	0.924976	0.109774	0.0548872	+	0.998493i	$0.482520\pi$
$72$	23.2373	2.73854
$73$	−2.53596	−0.296812	−0.148406	−	0.988927i	$-0.547414\pi$
$73$	−2.53596	−0.296812	−0.148406	+	0.988927i	$0.547414\pi$
$74$	2.83848	0.329966
$75$	−6.48776	−0.749142
$76$	4.67335	0.536070
$77$	−10.5126	−1.19802
$78$	13.4155	1.51901
$79$	−4.32093	−0.486143	−0.243071	−	0.970008i	$-0.578155\pi$
$79$	−4.32093	−0.486143	−0.243071	+	0.970008i	$0.578155\pi$
$80$	56.5713	6.32487
$81$	4.00772	0.445302
$82$	4.88470	0.539424
$83$	0.825528	0.0906134	0.0453067	−	0.998973i	$-0.485573\pi$
$83$	0.825528	0.0906134	0.0453067	+	0.998973i	$0.485573\pi$
$84$	17.2546	1.88264
$85$	15.5905	1.69103
$86$	25.9178	2.79479
$87$	−2.69087	−0.288492
$88$	−25.0367	−2.66892
$89$	12.6211	1.33784	0.668918	−	0.743337i	$-0.266758\pi$
$89$	12.6211	1.33784	0.668918	+	0.743337i	$0.266758\pi$
$90$	24.1725	2.54800
$91$	−25.7399	−2.69827
$92$	−29.4422	−3.06956
$93$	5.59142	0.579803
$94$	22.4818	2.31882
$95$	3.10049	0.318104
$96$	17.7545	1.81206
$97$	−0.300325	−0.0304934	−0.0152467	−	0.999884i	$-0.504853\pi$
$97$	−0.300325	−0.0304934	−0.0152467	+	0.999884i	$0.504853\pi$
$98$	−25.9001	−2.61630
$99$	−6.23767	−0.626909
$100$	46.4830	4.64830
$101$	−19.1113	−1.90164	−0.950821	−	0.309742i	$-0.899757\pi$
$101$	−19.1113	−1.90164	−0.950821	+	0.309742i	$0.899757\pi$
$102$	8.99516	0.890653
$103$	−3.86385	−0.380716	−0.190358	−	0.981715i	$-0.560965\pi$
$103$	−3.86385	−0.380716	−0.190358	+	0.981715i	$0.560965\pi$
$104$	−61.3019	−6.01115
$105$	11.4474	1.11716
$106$	22.5969	2.19480
$107$	10.3742	1.00291	0.501455	−	0.865184i	$-0.332798\pi$
$107$	10.3742	1.00291	0.501455	+	0.865184i	$0.332798\pi$
$108$	23.0032	2.21349
$109$	5.11892	0.490303	0.245152	−	0.969485i	$-0.421162\pi$
$109$	5.11892	0.490303	0.245152	+	0.969485i	$0.421162\pi$
$110$	−26.0442	−2.48322
$111$	0.797603	0.0757052
$112$	−62.6245	−5.91746
$113$	−4.05006	−0.380998	−0.190499	−	0.981687i	$-0.561011\pi$
$113$	−4.05006	−0.380998	−0.190499	+	0.981687i	$0.561011\pi$
$114$	1.78887	0.167543
$115$	−19.5332	−1.82148
$116$	19.2794	1.79005
$117$	−15.2729	−1.41198
$118$	14.4657	1.33168
$119$	−17.2587	−1.58210
$120$	27.2632	2.48878
$121$	−4.27933	−0.389030
$122$	8.73721	0.791030
$123$	1.37258	0.123762
$124$	−40.0610	−3.59759
$125$	12.5230	1.12009
$126$	−26.7589	−2.38387
$127$	−12.1681	−1.07975	−0.539873	−	0.841747i	$-0.681528\pi$
$127$	−12.1681	−1.07975	−0.539873	+	0.841747i	$0.681528\pi$
$128$	−42.4983	−3.75635
$129$	7.28283	0.641218
$130$	−63.7689	−5.59291
$131$	9.53692	0.833244	0.416622	−	0.909080i	$-0.363214\pi$
$131$	9.53692	0.833244	0.416622	+	0.909080i	$0.363214\pi$
$132$	−11.0309	−0.960115
$133$	−3.43225	−0.297614
$134$	31.9403	2.75922
$135$	15.2613	1.31348
$136$	−41.1033	−3.52458
$137$	8.69336	0.742724	0.371362	−	0.928488i	$-0.378891\pi$
$137$	8.69336	0.742724	0.371362	+	0.928488i	$0.378891\pi$
$138$	−11.2699	−0.959358
$139$	−15.5933	−1.32260	−0.661302	−	0.750120i	$-0.729996\pi$
$139$	−15.5933	−1.32260	−0.661302	+	0.750120i	$0.729996\pi$
$140$	−82.0179	−6.93177
$141$	6.31731	0.532013
$142$	−2.53677	−0.212881
$143$	16.4555	1.37608
$144$	−37.1585	−3.09654
$145$	12.7907	1.06221
$146$	6.95493	0.575594
$147$	−7.27784	−0.600266
$148$	−5.71461	−0.469738
$149$	−9.72913	−0.797042	−0.398521	−	0.917159i	$-0.630476\pi$
$149$	−9.72913	−0.797042	−0.398521	+	0.917159i	$0.630476\pi$
$150$	17.7928	1.45278
$151$	24.4730	1.99158	0.995790	−	0.0916602i	$-0.0292173\pi$
$151$	24.4730	1.99158	0.995790	+	0.0916602i	$0.0292173\pi$
$152$	−8.17422	−0.663017
$153$	−10.2405	−0.827898
$154$	28.8309	2.32326
$155$	−26.5781	−2.13481
$156$	−27.0090	−2.16245
$157$	14.9690	1.19466	0.597330	−	0.801996i	$-0.296228\pi$
$157$	14.9690	1.19466	0.597330	+	0.801996i	$0.296228\pi$
$158$	11.8503	0.942755
$159$	6.34965	0.503560
$160$	−84.3936	−6.67190
$161$	21.6232	1.70415
$162$	−10.9913	−0.863555
$163$	11.2376	0.880196	0.440098	−	0.897950i	$-0.354944\pi$
$163$	11.2376	0.880196	0.440098	+	0.897950i	$0.354944\pi$
$164$	−9.83420	−0.767922
$165$	−7.31834	−0.569732
$166$	−2.26403	−0.175723
$167$	2.78845	0.215777	0.107889	−	0.994163i	$-0.465591\pi$
$167$	2.78845	0.215777	0.107889	+	0.994163i	$0.465591\pi$
$168$	−30.1803	−2.32846
$169$	27.2911	2.09931
$170$	−42.7574	−3.27934
$171$	−2.03654	−0.155738
$172$	−52.1795	−3.97865
$173$	−23.4357	−1.78178	−0.890892	−	0.454216i	$-0.849920\pi$
$173$	−23.4357	−1.78178	−0.890892	+	0.454216i	$0.849920\pi$
$174$	7.37978	0.559460
$175$	−34.1385	−2.58063
$176$	40.0358	3.01781
$177$	4.06482	0.305531
$178$	−34.6137	−2.59441
$179$	−12.9171	−0.965467	−0.482733	−	0.875767i	$-0.660356\pi$
$179$	−12.9171	−0.965467	−0.482733	+	0.875767i	$0.660356\pi$
$180$	−48.6656	−3.62732
$181$	15.0526	1.11885	0.559424	−	0.828882i	$-0.311022\pi$
$181$	15.0526	1.11885	0.559424	+	0.828882i	$0.311022\pi$
$182$	70.5922	5.23264
$183$	2.45513	0.181488
$184$	51.4977	3.79646
$185$	−3.79131	−0.278743
$186$	−15.3346	−1.12439
$187$	11.0335	0.806849
$188$	−45.2618	−3.30106
$189$	−16.8943	−1.22888
$190$	−8.50318	−0.616885
$191$	22.4369	1.62347	0.811737	−	0.584023i	$-0.198522\pi$
$191$	22.4369	1.62347	0.811737	+	0.584023i	$0.198522\pi$
$192$	−24.8894	−1.79624
$193$	−7.37484	−0.530853	−0.265426	−	0.964131i	$-0.585513\pi$
$193$	−7.37484	−0.530853	−0.265426	+	0.964131i	$0.585513\pi$
$194$	0.823649	0.0591346
$195$	−17.9189	−1.28320
$196$	52.1437	3.72455
$197$	−14.9068	−1.06206	−0.531032	−	0.847352i	$-0.678195\pi$
$197$	−14.9068	−1.06206	−0.531032	+	0.847352i	$0.678195\pi$
$198$	17.1070	1.21574
$199$	24.8169	1.75922	0.879610	−	0.475695i	$-0.157803\pi$
$199$	24.8169	1.75922	0.879610	+	0.475695i	$0.157803\pi$
$200$	−81.3041	−5.74907
$201$	8.97512	0.633056
$202$	52.4131	3.68777
$203$	−14.1594	−0.993792
$204$	−18.1097	−1.26793
$205$	−6.52442	−0.455685
$206$	10.5967	0.738306
$207$	12.8302	0.891761
$208$	98.0271	6.79696
$209$	2.19423	0.151778
$210$	−31.3949	−2.16645
$211$	2.00392	0.137955	0.0689777	−	0.997618i	$-0.478026\pi$
$211$	2.00392	0.137955	0.0689777	+	0.997618i	$0.478026\pi$
$212$	−45.4935	−3.12451
$213$	−0.712824	−0.0488419
$214$	−28.4514	−1.94490
$215$	−34.6181	−2.36093
$216$	−40.2353	−2.73766
$217$	29.4220	1.99730
$218$	−14.0388	−0.950824
$219$	1.95431	0.132060
$220$	52.4340	3.53510
$221$	27.0154	1.81725
$222$	−2.18745	−0.146812
$223$	−1.58320	−0.106019	−0.0530094	−	0.998594i	$-0.516881\pi$
$223$	−1.58320	−0.106019	−0.0530094	+	0.998594i	$0.516881\pi$
$224$	93.4238	6.24214
$225$	−20.2562	−1.35042
$226$	11.1074	0.738852
$227$	−15.2188	−1.01011	−0.505054	−	0.863088i	$-0.668527\pi$
$227$	−15.2188	−1.01011	−0.505054	+	0.863088i	$0.668527\pi$
$228$	−3.60147	−0.238513
$229$	−1.72057	−0.113699	−0.0568493	−	0.998383i	$-0.518105\pi$
$229$	−1.72057	−0.113699	−0.0568493	+	0.998383i	$0.518105\pi$
$230$	53.5701	3.53231
$231$	8.10141	0.533033
$232$	−33.7218	−2.21395
$233$	−20.1880	−1.32256	−0.661281	−	0.750138i	$-0.729987\pi$
$233$	−20.1880	−1.32256	−0.661281	+	0.750138i	$0.729987\pi$
$234$	41.8862	2.73818
$235$	−30.0286	−1.95885
$236$	−29.1233	−1.89577
$237$	3.32988	0.216299
$238$	47.3325	3.06811
$239$	−24.0573	−1.55614	−0.778068	−	0.628180i	$-0.783800\pi$
$239$	−24.0573	−1.55614	−0.778068	+	0.628180i	$0.783800\pi$
$240$	−43.5962	−2.81412
$241$	−15.8997	−1.02419	−0.512096	−	0.858928i	$-0.671131\pi$
$241$	−15.8997	−1.02419	−0.512096	+	0.858928i	$0.671131\pi$
$242$	11.7362	0.754429
$243$	−15.5870	−0.999908
$244$	−17.5903	−1.12611
$245$	34.5943	2.21015
$246$	−3.76435	−0.240006
$247$	5.37255	0.341847
$248$	70.0713	4.44953
$249$	−0.636185	−0.0403166
$250$	−34.3447	−2.17215
$251$	1.28143	0.0808831	0.0404416	−	0.999182i	$-0.487124\pi$
$251$	1.28143	0.0808831	0.0404416	+	0.999182i	$0.487124\pi$
$252$	53.8729	3.39367
$253$	−13.8237	−0.869088
$254$	33.3713	2.09390
$255$	−12.0147	−0.752390
$256$	51.9585	3.24740
$257$	11.0863	0.691542	0.345771	−	0.938319i	$-0.387617\pi$
$257$	11.0863	0.691542	0.345771	+	0.938319i	$0.387617\pi$
$258$	−19.9733	−1.24349
$259$	4.19698	0.260788
$260$	128.384	7.96203
$261$	−8.40151	−0.520041
$262$	−26.1552	−1.61587
$263$	−27.1817	−1.67610	−0.838049	−	0.545595i	$-0.816304\pi$
$263$	−27.1817	−1.67610	−0.838049	+	0.545595i	$0.816304\pi$
$264$	19.2943	1.18748
$265$	−30.1823	−1.85408
$266$	9.41302	0.577149
$267$	−9.72634	−0.595243
$268$	−64.3043	−3.92801
$269$	24.7477	1.50890	0.754448	−	0.656360i	$-0.227905\pi$
$269$	24.7477	1.50890	0.754448	+	0.656360i	$0.227905\pi$
$270$	−41.8545	−2.54718
$271$	23.5008	1.42757	0.713785	−	0.700364i	$-0.246979\pi$
$271$	23.5008	1.42757	0.713785	+	0.700364i	$0.246979\pi$
$272$	65.7277	3.98533
$273$	19.8362	1.20054
$274$	−23.8418	−1.44033
$275$	21.8247	1.31608
$276$	22.6893	1.36574
$277$	−26.6014	−1.59832	−0.799162	−	0.601115i	$-0.794723\pi$
$277$	−26.6014	−1.59832	−0.799162	+	0.601115i	$0.794723\pi$
$278$	42.7649	2.56487
$279$	17.4577	1.04516
$280$	143.459	8.57329
$281$	−0.0513758	−0.00306482	−0.00153241	−	0.999999i	$-0.500488\pi$
$281$	−0.0513758	−0.00306482	−0.00153241	+	0.999999i	$0.500488\pi$
$282$	−17.3254	−1.03171
$283$	31.5351	1.87456	0.937282	−	0.348572i	$-0.113333\pi$
$283$	31.5351	1.87456	0.937282	+	0.348572i	$0.113333\pi$
$284$	5.10719	0.303056
$285$	−2.38937	−0.141534
$286$	−45.1296	−2.66857
$287$	7.22253	0.426332
$288$	55.4334	3.26644
$289$	1.11395	0.0655264
$290$	−35.0789	−2.05991
$291$	0.231443	0.0135674
$292$	−14.0021	−0.819413
$293$	17.8549	1.04310	0.521548	−	0.853222i	$-0.325355\pi$
$293$	17.8549	1.04310	0.521548	+	0.853222i	$0.325355\pi$
$294$	19.9596	1.16407
$295$	−19.3216	−1.12495
$296$	9.99551	0.580977
$297$	10.8005	0.626708
$298$	26.6824	1.54567
$299$	−33.8472	−1.95743
$300$	−35.8217	−2.06817
$301$	38.3222	2.20885
$302$	−67.1176	−3.86219
$303$	14.7279	0.846097
$304$	13.0713	0.749690
$305$	−11.6702	−0.668232
$306$	28.0849	1.60551
$307$	−32.0613	−1.82984	−0.914918	−	0.403639i	$-0.867745\pi$
$307$	−32.0613	−1.82984	−0.914918	+	0.403639i	$0.867745\pi$
$308$	−58.0444	−3.30739
$309$	2.97764	0.169392
$310$	72.8912	4.13994
$311$	27.5302	1.56109	0.780547	−	0.625097i	$-0.214940\pi$
$311$	27.5302	1.56109	0.780547	+	0.625097i	$0.214940\pi$
$312$	47.2418	2.67454
$313$	−10.8428	−0.612872	−0.306436	−	0.951891i	$-0.599136\pi$
$313$	−10.8428	−0.612872	−0.306436	+	0.951891i	$0.599136\pi$
$314$	−41.0530	−2.31675
$315$	35.7415	2.01380
$316$	−23.8577	−1.34210
$317$	−19.2889	−1.08337	−0.541687	−	0.840580i	$-0.682214\pi$
$317$	−19.2889	−1.08337	−0.541687	+	0.840580i	$0.682214\pi$
$318$	−17.4141	−0.976532
$319$	9.05207	0.506818
$320$	118.309	6.61367
$321$	−7.99477	−0.446225
$322$	−59.3021	−3.30478
$323$	3.60233	0.200439
$324$	22.1283	1.22935
$325$	53.4376	2.96419
$326$	−30.8194	−1.70693
$327$	−3.94485	−0.218151
$328$	17.2011	0.949774
$329$	33.2416	1.83267
$330$	20.0707	1.10486
$331$	0.181405	0.00997093	0.00498546	−	0.999988i	$-0.498413\pi$
$331$	0.181405	0.00997093	0.00498546	+	0.999988i	$0.498413\pi$
$332$	4.55810	0.250158
$333$	2.49030	0.136467
$334$	−7.64740	−0.418447
$335$	−42.6622	−2.33088
$336$	48.2610	2.63285
$337$	−8.97450	−0.488872	−0.244436	−	0.969665i	$-0.578603\pi$
$337$	−8.97450	−0.488872	−0.244436	+	0.969665i	$0.578603\pi$
$338$	−74.8464	−4.07111
$339$	3.12114	0.169517
$340$	86.0821	4.66846
$341$	−18.8095	−1.01859
$342$	5.58525	0.302016
$343$	−9.91018	−0.535099
$344$	91.2679	4.92084
$345$	15.0530	0.810429
$346$	64.2730	3.45534
$347$	−3.85894	−0.207159	−0.103579	−	0.994621i	$-0.533030\pi$
$347$	−3.85894	−0.207159	−0.103579	+	0.994621i	$0.533030\pi$
$348$	−14.8575	−0.796445
$349$	−24.7676	−1.32578	−0.662889	−	0.748717i	$-0.730670\pi$
$349$	−24.7676	−1.32578	−0.662889	+	0.748717i	$0.730670\pi$
$350$	93.6257	5.00450
$351$	26.4449	1.41152
$352$	−59.7258	−3.18339
$353$	28.1340	1.49742	0.748711	−	0.662896i	$-0.230673\pi$
$353$	28.1340	1.49742	0.748711	+	0.662896i	$0.230673\pi$
$354$	−11.1479	−0.592502
$355$	3.38832	0.179834
$356$	69.6866	3.69338
$357$	13.3003	0.703925
$358$	35.4253	1.87229
$359$	−19.8871	−1.04960	−0.524801	−	0.851225i	$-0.675860\pi$
$359$	−19.8871	−1.04960	−0.524801	+	0.851225i	$0.675860\pi$
$360$	85.1217	4.48631
$361$	−18.2836	−0.962295
$362$	−41.2820	−2.16973
$363$	3.29782	0.173091
$364$	−142.121	−7.44917
$365$	−9.28959	−0.486240
$366$	−6.73325	−0.351953
$367$	31.1363	1.62530	0.812650	−	0.582752i	$-0.198024\pi$
$367$	31.1363	1.62530	0.812650	+	0.582752i	$0.198024\pi$
$368$	−82.3493	−4.29275
$369$	4.28552	0.223095
$370$	10.3978	0.540554
$371$	33.4118	1.73465
$372$	30.8726	1.60067
$373$	9.49899	0.491839	0.245919	−	0.969290i	$-0.420910\pi$
$373$	9.49899	0.491839	0.245919	+	0.969290i	$0.420910\pi$
$374$	−30.2596	−1.56469
$375$	−9.65076	−0.498363
$376$	79.1681	4.08278
$377$	22.1639	1.14150
$378$	46.3329	2.38311
$379$	5.75318	0.295521	0.147761	−	0.989023i	$-0.452794\pi$
$379$	5.75318	0.295521	0.147761	+	0.989023i	$0.452794\pi$
$380$	17.1192	0.878195
$381$	9.37725	0.480411
$382$	−61.5336	−3.14833
$383$	−37.0803	−1.89472	−0.947358	−	0.320175i	$-0.896258\pi$
$383$	−37.0803	−1.89472	−0.947358	+	0.320175i	$0.896258\pi$
$384$	32.7509	1.67131
$385$	−38.5091	−1.96260
$386$	20.2257	1.02946
$387$	22.7386	1.15587
$388$	−1.65823	−0.0841837
$389$	−16.7894	−0.851258	−0.425629	−	0.904898i	$-0.639947\pi$
$389$	−16.7894	−0.851258	−0.425629	+	0.904898i	$0.639947\pi$
$390$	49.1429	2.48845
$391$	−22.6947	−1.14772
$392$	−91.2053	−4.60656
$393$	−7.34954	−0.370735
$394$	40.8822	2.05961
$395$	−15.8282	−0.796404
$396$	−34.4409	−1.73072
$397$	−15.5897	−0.782426	−0.391213	−	0.920300i	$-0.627944\pi$
$397$	−15.5897	−0.782426	−0.391213	+	0.920300i	$0.627944\pi$
$398$	−68.0608	−3.41158
$399$	2.64503	0.132417
$400$	130.012	6.50062
$401$	−25.4530	−1.27106	−0.635532	−	0.772075i	$-0.719219\pi$
$401$	−25.4530	−1.27106	−0.635532	+	0.772075i	$0.719219\pi$
$402$	−24.6145	−1.22766
$403$	−46.0547	−2.29415
$404$	−105.522	−5.24989
$405$	14.6809	0.729498
$406$	38.8324	1.92722
$407$	−2.68313	−0.132998
$408$	31.6759	1.56819
$409$	7.40151	0.365981	0.182991	−	0.983115i	$-0.441422\pi$
$409$	7.40151	0.365981	0.182991	+	0.983115i	$0.441422\pi$
$410$	17.8934	0.883690
$411$	−6.69946	−0.330460
$412$	−21.3340	−1.05105
$413$	21.3890	1.05249
$414$	−35.1872	−1.72935
$415$	3.02403	0.148444
$416$	−146.238	−7.16990
$417$	12.0168	0.588465
$418$	−6.01774	−0.294337
$419$	−9.43829	−0.461091	−0.230545	−	0.973062i	$-0.574051\pi$
$419$	−9.43829	−0.461091	−0.230545	+	0.973062i	$0.574051\pi$
$420$	63.2063	3.08415
$421$	−15.3466	−0.747948	−0.373974	−	0.927439i	$-0.622005\pi$
$421$	−15.3466	−0.747948	−0.373974	+	0.927439i	$0.622005\pi$
$422$	−5.49579	−0.267531
$423$	19.7240	0.959016
$424$	79.5734	3.86442
$425$	35.8302	1.73802
$426$	1.95494	0.0947170
$427$	12.9189	0.625188
$428$	57.2804	2.76875
$429$	−12.6813	−0.612257
$430$	94.9409	4.57845
$431$	−19.8785	−0.957514	−0.478757	−	0.877947i	$-0.658913\pi$
$431$	−19.8785	−0.957514	−0.478757	+	0.877947i	$0.658913\pi$
$432$	64.3397	3.09554
$433$	−4.66180	−0.224032	−0.112016	−	0.993706i	$-0.535731\pi$
$433$	−4.66180	−0.224032	−0.112016	+	0.993706i	$0.535731\pi$
$434$	−80.6905	−3.87327
$435$	−9.85707	−0.472610
$436$	28.2638	1.35359
$437$	−4.51330	−0.215900
$438$	−5.35975	−0.256099
$439$	31.9512	1.52495	0.762475	−	0.647018i	$-0.223984\pi$
$439$	31.9512	1.52495	0.762475	+	0.647018i	$0.223984\pi$
$440$	−91.7130	−4.37224
$441$	−22.7230	−1.08205
$442$	−74.0903	−3.52412
$443$	4.66859	0.221811	0.110906	−	0.993831i	$-0.464625\pi$
$443$	4.66859	0.221811	0.110906	+	0.993831i	$0.464625\pi$
$444$	4.40391	0.209001
$445$	46.2330	2.19165
$446$	4.34196	0.205598
$447$	7.49767	0.354627
$448$	−130.968	−6.18765
$449$	−29.2328	−1.37958	−0.689791	−	0.724009i	$-0.742297\pi$
$449$	−29.2328	−1.37958	−0.689791	+	0.724009i	$0.742297\pi$
$450$	55.5532	2.61880
$451$	−4.61736	−0.217423
$452$	−22.3621	−1.05183
$453$	−18.8599	−0.886113
$454$	41.7379	1.95886
$455$	−94.2890	−4.42034
$456$	6.29939	0.294996
$457$	8.41776	0.393766	0.196883	−	0.980427i	$-0.436918\pi$
$457$	8.41776	0.393766	0.196883	+	0.980427i	$0.436918\pi$
$458$	4.71871	0.220491
$459$	17.7314	0.827632
$460$	−107.851	−5.02858
$461$	5.54030	0.258037	0.129019	−	0.991642i	$-0.458817\pi$
$461$	5.54030	0.258037	0.129019	+	0.991642i	$0.458817\pi$
$462$	−22.2183	−1.03369
$463$	27.5174	1.27884	0.639421	−	0.768857i	$-0.279174\pi$
$463$	27.5174	1.27884	0.639421	+	0.768857i	$0.279174\pi$
$464$	53.9242	2.50337
$465$	20.4822	0.949839
$466$	55.3661	2.56479
$467$	−21.6474	−1.00172	−0.500862	−	0.865527i	$-0.666984\pi$
$467$	−21.6474	−1.00172	−0.500862	+	0.865527i	$0.666984\pi$
$468$	−84.3281	−3.89807
$469$	47.2270	2.18074
$470$	82.3540	3.79871
$471$	−11.5358	−0.531540
$472$	50.9400	2.34470
$473$	−24.4994	−1.12648
$474$	−9.13229	−0.419460
$475$	7.12556	0.326943
$476$	−95.2929	−4.36774
$477$	19.8250	0.907726
$478$	65.9776	3.01775
$479$	4.44885	0.203273	0.101637	−	0.994822i	$-0.467592\pi$
$479$	4.44885	0.203273	0.101637	+	0.994822i	$0.467592\pi$
$480$	65.0372	2.96853
$481$	−6.56961	−0.299548
$482$	43.6054	1.98617
$483$	−16.6637	−0.758225
$484$	−23.6280	−1.07400
$485$	−1.10014	−0.0499546
$486$	42.7478	1.93908
$487$	39.0243	1.76836	0.884180	−	0.467146i	$-0.154718\pi$
$487$	39.0243	1.76836	0.884180	+	0.467146i	$0.154718\pi$
$488$	30.7675	1.39278
$489$	−8.66015	−0.391625
$490$	−94.8757	−4.28605
$491$	−15.8720	−0.716295	−0.358147	−	0.933665i	$-0.616591\pi$
$491$	−15.8720	−0.716295	−0.358147	+	0.933665i	$0.616591\pi$
$492$	7.57864	0.341671
$493$	14.8610	0.669306
$494$	−14.7344	−0.662930
$495$	−22.8495	−1.02701
$496$	−112.050	−5.03119
$497$	−3.75088	−0.168250
$498$	1.74475	0.0781842
$499$	−11.2494	−0.503591	−0.251796	−	0.967780i	$-0.581021\pi$
$499$	−11.2494	−0.503591	−0.251796	+	0.967780i	$0.581021\pi$
$500$	69.1451	3.09226
$501$	−2.14890	−0.0960056
$502$	−3.51435	−0.156853
$503$	−31.6877	−1.41289	−0.706443	−	0.707770i	$-0.749701\pi$
$503$	−31.6877	−1.41289	−0.706443	+	0.707770i	$0.749701\pi$
$504$	−94.2297	−4.19733
$505$	−70.0074	−3.11529
$506$	37.9118	1.68539
$507$	−21.0316	−0.934046
$508$	−67.1854	−2.98087
$509$	−14.7447	−0.653545	−0.326773	−	0.945103i	$-0.605961\pi$
$509$	−14.7447	−0.653545	−0.326773	+	0.945103i	$0.605961\pi$
$510$	32.9506	1.45908
$511$	10.2836	0.454919
$512$	−57.5007	−2.54120
$513$	3.52625	0.155688
$514$	−30.4043	−1.34108
$515$	−14.1538	−0.623693
$516$	40.2117	1.77022
$517$	−21.2513	−0.934633
$518$	−11.5103	−0.505735
$519$	18.0605	0.792768
$520$	−224.558	−9.84752
$521$	6.64834	0.291269	0.145634	−	0.989338i	$-0.453478\pi$
$521$	6.64834	0.291269	0.145634	+	0.989338i	$0.453478\pi$
$522$	23.0413	1.00849
$523$	32.5221	1.42209	0.711045	−	0.703146i	$-0.248222\pi$
$523$	32.5221	1.42209	0.711045	+	0.703146i	$0.248222\pi$
$524$	52.6575	2.30035
$525$	26.3085	1.14820
$526$	74.5466	3.25039
$527$	−30.8800	−1.34515
$528$	−30.8532	−1.34271
$529$	5.43386	0.236255
$530$	82.7757	3.59555
$531$	12.6913	0.550754
$532$	−18.9509	−0.821627
$533$	−11.3055	−0.489698
$534$	26.6747	1.15433
$535$	38.0022	1.64298
$536$	112.476	4.85821
$537$	9.95442	0.429565
$538$	−67.8712	−2.92614
$539$	24.4826	1.05454
$540$	84.2643	3.62616
$541$	10.2760	0.441800	0.220900	−	0.975297i	$-0.429101\pi$
$541$	10.2760	0.441800	0.220900	+	0.975297i	$0.429101\pi$
$542$	−64.4514	−2.76843
$543$	−11.6001	−0.497809
$544$	−98.0532	−4.20400
$545$	18.7514	0.803220
$546$	−54.4012	−2.32816
$547$	7.44109	0.318158	0.159079	−	0.987266i	$-0.449148\pi$
$547$	7.44109	0.318158	0.159079	+	0.987266i	$0.449148\pi$
$548$	47.9998	2.05045
$549$	7.66547	0.327154
$550$	−59.8548	−2.55222
$551$	2.95541	0.125905
$552$	−39.6862	−1.68916
$553$	17.5218	0.745104
$554$	72.9550	3.09956
$555$	2.92174	0.124021
$556$	−86.0972	−3.65133
$557$	−20.9640	−0.888274	−0.444137	−	0.895959i	$-0.646490\pi$
$557$	−20.9640	−0.888274	−0.444137	+	0.895959i	$0.646490\pi$
$558$	−47.8780	−2.02684
$559$	−59.9864	−2.53715
$560$	−229.403	−9.69403
$561$	−8.50286	−0.358991
$562$	0.140899	0.00594348
$563$	−3.80421	−0.160328	−0.0801642	−	0.996782i	$-0.525544\pi$
$563$	−3.80421	−0.160328	−0.0801642	+	0.996782i	$0.525544\pi$
$564$	34.8806	1.46874
$565$	−14.8360	−0.624154
$566$	−86.4856	−3.63526
$567$	−16.2517	−0.682508
$568$	−8.93306	−0.374823
$569$	−14.6303	−0.613336	−0.306668	−	0.951817i	$-0.599214\pi$
$569$	−14.6303	−0.613336	−0.306668	+	0.951817i	$0.599214\pi$
$570$	6.55289	0.274471
$571$	12.5245	0.524135	0.262068	−	0.965050i	$-0.415596\pi$
$571$	12.5245	0.524135	0.262068	+	0.965050i	$0.415596\pi$
$572$	90.8579	3.79896
$573$	−17.2908	−0.722332
$574$	−19.8080	−0.826768
$575$	−44.8911	−1.87209
$576$	−77.7104	−3.23793
$577$	−17.9445	−0.747041	−0.373521	−	0.927622i	$-0.621849\pi$
$577$	−17.9445	−0.747041	−0.373521	+	0.927622i	$0.621849\pi$
$578$	−3.05503	−0.127073
$579$	5.68335	0.236192
$580$	70.6233	2.93247
$581$	−3.34760	−0.138882
$582$	−0.634738	−0.0263107
$583$	−21.3601	−0.884647
$584$	24.4913	1.01346
$585$	−55.9467	−2.31311
$586$	−48.9676	−2.02283
$587$	−8.47030	−0.349607	−0.174803	−	0.984603i	$-0.555929\pi$
$587$	−8.47030	−0.349607	−0.174803	+	0.984603i	$0.555929\pi$
$588$	−40.1841	−1.65716
$589$	−6.14110	−0.253040
$590$	52.9900	2.18156
$591$	11.4878	0.472543
$592$	−15.9837	−0.656926
$593$	3.88405	0.159499	0.0797495	−	0.996815i	$-0.474588\pi$
$593$	3.88405	0.159499	0.0797495	+	0.996815i	$0.474588\pi$
$594$	−29.6206	−1.21535
$595$	−63.2213	−2.59182
$596$	−53.7188	−2.20041
$597$	−19.1249	−0.782729
$598$	92.8266	3.79596
$599$	22.3942	0.915003	0.457502	−	0.889209i	$-0.348744\pi$
$599$	22.3942	0.915003	0.457502	+	0.889209i	$0.348744\pi$
$600$	62.6563	2.55793
$601$	−13.0388	−0.531864	−0.265932	−	0.963992i	$-0.585680\pi$
$601$	−13.0388	−0.531864	−0.265932	+	0.963992i	$0.585680\pi$
$602$	−105.100	−4.28354
$603$	28.0223	1.14116
$604$	135.126	5.49819
$605$	−15.6758	−0.637312
$606$	−40.3916	−1.64080
$607$	−26.5976	−1.07957	−0.539783	−	0.841805i	$-0.681494\pi$
$607$	−26.5976	−1.07957	−0.539783	+	0.841805i	$0.681494\pi$
$608$	−19.4999	−0.790824
$609$	10.9118	0.442168
$610$	32.0057	1.29587
$611$	−52.0337	−2.10506
$612$	−56.5424	−2.28559
$613$	39.6224	1.60033	0.800167	−	0.599777i	$-0.204744\pi$
$613$	39.6224	1.60033	0.800167	+	0.599777i	$0.204744\pi$
$614$	87.9289	3.54852
$615$	5.02798	0.202748
$616$	101.526	4.09061
$617$	3.51376	0.141459	0.0707293	−	0.997496i	$-0.477467\pi$
$617$	3.51376	0.141459	0.0707293	+	0.997496i	$0.477467\pi$
$618$	−8.16624	−0.328494
$619$	−25.5021	−1.02502	−0.512509	−	0.858682i	$-0.671284\pi$
$619$	−25.5021	−1.02502	−0.512509	+	0.858682i	$0.671284\pi$
$620$	−146.749	−5.89360
$621$	−22.2154	−0.891475
$622$	−75.5022	−3.02736
$623$	−51.1799	−2.05048
$624$	−75.5437	−3.02417
$625$	3.78047	0.151219
$626$	29.7366	1.18852
$627$	−1.69097	−0.0675307
$628$	82.6506	3.29812
$629$	−4.40496	−0.175637
$630$	−98.0219	−3.90528
$631$	39.8096	1.58479	0.792397	−	0.610006i	$-0.208833\pi$
$631$	39.8096	1.58479	0.792397	+	0.610006i	$0.208833\pi$
$632$	41.7299	1.65993
$633$	−1.54430	−0.0613804
$634$	52.9004	2.10094
$635$	−44.5736	−1.76885
$636$	35.0592	1.39019
$637$	59.9452	2.37512
$638$	−24.8255	−0.982851
$639$	−2.22560	−0.0880433
$640$	−155.678	−6.15370
$641$	−27.8160	−1.09867	−0.549333	−	0.835603i	$-0.685118\pi$
$641$	−27.8160	−1.09867	−0.549333	+	0.835603i	$0.685118\pi$
$642$	21.9258	0.865344
$643$	18.5276	0.730659	0.365329	−	0.930878i	$-0.380956\pi$
$643$	18.5276	0.730659	0.365329	+	0.930878i	$0.380956\pi$
$644$	119.391	4.70467
$645$	26.6781	1.05045
$646$	−9.87946	−0.388702
$647$	−22.1440	−0.870569	−0.435285	−	0.900293i	$-0.643352\pi$
$647$	−22.1440	−0.870569	−0.435285	+	0.900293i	$0.643352\pi$
$648$	−38.7050	−1.52048
$649$	−13.6740	−0.536752
$650$	−146.554	−5.74832
$651$	−22.6738	−0.888656
$652$	62.0476	2.42997
$653$	21.7889	0.852664	0.426332	−	0.904567i	$-0.359805\pi$
$653$	21.7889	0.852664	0.426332	+	0.904567i	$0.359805\pi$
$654$	10.8188	0.423050
$655$	34.9351	1.36503
$656$	−27.5061	−1.07393
$657$	6.10180	0.238054
$658$	−91.1659	−3.55402
$659$	40.5368	1.57909	0.789545	−	0.613692i	$-0.210316\pi$
$659$	40.5368	1.57909	0.789545	+	0.613692i	$0.210316\pi$
$660$	−40.4077	−1.57287
$661$	−20.4497	−0.795403	−0.397701	−	0.917515i	$-0.630192\pi$
$661$	−20.4497	−0.795403	−0.397701	+	0.917515i	$0.630192\pi$
$662$	−0.497508	−0.0193362
$663$	−20.8191	−0.808549
$664$	−7.97263	−0.309398
$665$	−12.5728	−0.487553
$666$	−6.82970	−0.264645
$667$	−18.6191	−0.720935
$668$	15.3963	0.595699
$669$	1.22008	0.0471709
$670$	117.002	4.52018
$671$	−8.25903	−0.318836
$672$	−71.9962	−2.77731
$673$	−15.9930	−0.616484	−0.308242	−	0.951308i	$-0.599741\pi$
$673$	−15.9930	−0.616484	−0.308242	+	0.951308i	$0.599741\pi$
$674$	24.6128	0.948048
$675$	35.0735	1.34998
$676$	150.686	5.79561
$677$	22.3986	0.860849	0.430424	−	0.902627i	$-0.358364\pi$
$677$	22.3986	0.860849	0.430424	+	0.902627i	$0.358364\pi$
$678$	−8.55980	−0.328737
$679$	1.21785	0.0467368
$680$	−150.567	−5.77400
$681$	11.7282	0.449427
$682$	51.5854	1.97531
$683$	−16.7979	−0.642753	−0.321377	−	0.946951i	$-0.604146\pi$
$683$	−16.7979	−0.642753	−0.321377	+	0.946951i	$0.604146\pi$
$684$	−11.2446	−0.429948
$685$	31.8451	1.21674
$686$	27.1789	1.03769
$687$	1.32594	0.0505879
$688$	−145.945	−5.56411
$689$	−52.3001	−1.99247
$690$	−41.2833	−1.57163
$691$	−32.7889	−1.24735	−0.623675	−	0.781684i	$-0.714361\pi$
$691$	−32.7889	−1.24735	−0.623675	+	0.781684i	$0.714361\pi$
$692$	−129.399	−4.91900
$693$	25.2944	0.960855
$694$	10.5832	0.401734
$695$	−57.1204	−2.16670
$696$	25.9874	0.985051
$697$	−7.58043	−0.287129
$698$	67.9257	2.57103
$699$	15.5577	0.588447
$700$	−188.494	−7.12439
$701$	−42.4247	−1.60236	−0.801179	−	0.598425i	$-0.795794\pi$
$701$	−42.4247	−1.60236	−0.801179	+	0.598425i	$0.795794\pi$
$702$	−72.5257	−2.73730
$703$	−0.876015	−0.0330395
$704$	83.7277	3.15561
$705$	23.1412	0.871549
$706$	−77.1582	−2.90389
$707$	77.4982	2.91462
$708$	22.4436	0.843483
$709$	17.4304	0.654611	0.327305	−	0.944919i	$-0.393859\pi$
$709$	17.4304	0.654611	0.327305	+	0.944919i	$0.393859\pi$
$710$	−9.29256	−0.348744
$711$	10.3966	0.389905
$712$	−121.890	−4.56801
$713$	38.6890	1.44892
$714$	−36.4763	−1.36509
$715$	60.2789	2.25430
$716$	−71.3207	−2.66538
$717$	18.5395	0.692371
$718$	54.5409	2.03545
$719$	7.87554	0.293708	0.146854	−	0.989158i	$-0.453085\pi$
$719$	7.87554	0.293708	0.146854	+	0.989158i	$0.453085\pi$
$720$	−136.117	−5.07278
$721$	15.6683	0.583518
$722$	50.1432	1.86614
$723$	12.2530	0.455693
$724$	83.1117	3.08882
$725$	29.3957	1.09173
$726$	−9.04436	−0.335668
$727$	8.08019	0.299678	0.149839	−	0.988710i	$-0.452125\pi$
$727$	8.08019	0.299678	0.149839	+	0.988710i	$0.452125\pi$
$728$	248.586	9.21320
$729$	−0.0111596	−0.000413320 0
$730$	25.4769	0.942943
$731$	−40.2212	−1.48763
$732$	13.5558	0.501038
$733$	−11.6344	−0.429725	−0.214863	−	0.976644i	$-0.568930\pi$
$733$	−11.6344	−0.429725	−0.214863	+	0.976644i	$0.568930\pi$
$734$	−85.3920	−3.15187
$735$	−26.6598	−0.983361
$736$	122.849	4.52829
$737$	−30.1922	−1.11214
$738$	−11.7531	−0.432639
$739$	12.5210	0.460591	0.230296	−	0.973121i	$-0.426031\pi$
$739$	12.5210	0.460591	0.230296	+	0.973121i	$0.426031\pi$
$740$	−20.9335	−0.769530
$741$	−4.14031	−0.152098
$742$	−91.6327	−3.36394
$743$	−39.7708	−1.45905	−0.729525	−	0.683955i	$-0.760259\pi$
$743$	−39.7708	−1.45905	−0.729525	+	0.683955i	$0.760259\pi$
$744$	−53.9998	−1.97973
$745$	−35.6393	−1.30572
$746$	−26.0512	−0.953802
$747$	−1.98631	−0.0726754
$748$	60.9207	2.22748
$749$	−42.0684	−1.53715
$750$	26.4674	0.966454
$751$	52.5012	1.91580	0.957898	−	0.287108i	$-0.0926938\pi$
$751$	52.5012	1.91580	0.957898	+	0.287108i	$0.0926938\pi$
$752$	−126.597	−4.61650
$753$	−0.987522	−0.0359873
$754$	−60.7850	−2.21366
$755$	89.6481	3.26263
$756$	−93.2805	−3.39258
$757$	−5.98472	−0.217518	−0.108759	−	0.994068i	$-0.534688\pi$
$757$	−5.98472	−0.217518	−0.108759	+	0.994068i	$0.534688\pi$
$758$	−15.7782	−0.573091
$759$	10.6531	0.386683
$760$	−29.9434	−1.08616
$761$	−48.2787	−1.75010	−0.875050	−	0.484032i	$-0.839172\pi$
$761$	−48.2787	−1.75010	−0.875050	+	0.484032i	$0.839172\pi$
$762$	−25.7173	−0.931640
$763$	−20.7577	−0.751481
$764$	123.884	4.48195
$765$	−37.5126	−1.35627
$766$	101.694	3.67434
$767$	−33.4806	−1.20892
$768$	−40.0413	−1.44487
$769$	23.1701	0.835537	0.417768	−	0.908554i	$-0.362812\pi$
$769$	23.1701	0.835537	0.417768	+	0.908554i	$0.362812\pi$
$770$	105.612	3.80599
$771$	−8.54352	−0.307687
$772$	−40.7197	−1.46553
$773$	−21.0936	−0.758683	−0.379342	−	0.925257i	$-0.623849\pi$
$773$	−21.0936	−0.758683	−0.379342	+	0.925257i	$0.623849\pi$
$774$	−62.3612	−2.24153
$775$	−61.0819	−2.19413
$776$	2.90043	0.104119
$777$	−3.23437	−0.116032
$778$	46.0454	1.65081
$779$	−1.50752	−0.0540126
$780$	−98.9379	−3.54254
$781$	2.39793	0.0858048
$782$	62.2407	2.22572
$783$	14.5472	0.519873
$784$	145.845	5.20876
$785$	54.8338	1.95710
$786$	20.1563	0.718951
$787$	−47.0737	−1.67799	−0.838997	−	0.544135i	$-0.816858\pi$
$787$	−47.0737	−1.67799	−0.838997	+	0.544135i	$0.816858\pi$
$788$	−82.3067	−2.93206
$789$	20.9474	0.745746
$790$	43.4092	1.54443
$791$	16.4234	0.583950
$792$	60.2410	2.14057
$793$	−20.2221	−0.718109
$794$	42.7552	1.51732
$795$	23.2597	0.824937
$796$	137.025	4.85671
$797$	37.6118	1.33228	0.666140	−	0.745827i	$-0.267945\pi$
$797$	37.6118	1.33228	0.666140	+	0.745827i	$0.267945\pi$
$798$	−7.25405	−0.256791
$799$	−34.8889	−1.23428
$800$	−193.954	−6.85730
$801$	−30.3678	−1.07299
$802$	69.8055	2.46492
$803$	−6.57429	−0.232002
$804$	49.5555	1.74769
$805$	79.2090	2.79175
$806$	126.306	4.44895
$807$	−19.0716	−0.671352
$808$	184.569	6.49312
$809$	11.4666	0.403143	0.201571	−	0.979474i	$-0.435395\pi$
$809$	11.4666	0.403143	0.201571	+	0.979474i	$0.435395\pi$
$810$	−40.2626	−1.41468
$811$	28.3235	0.994572	0.497286	−	0.867587i	$-0.334330\pi$
$811$	28.3235	0.994572	0.497286	+	0.867587i	$0.334330\pi$
$812$	−78.1800	−2.74358
$813$	−18.1107	−0.635169
$814$	7.35854	0.257917
$815$	41.1650	1.44195
$816$	−50.6524	−1.77319
$817$	−7.99880	−0.279843
$818$	−20.2988	−0.709731
$819$	61.9330	2.16412
$820$	−36.0241	−1.25802
$821$	−30.8938	−1.07820	−0.539100	−	0.842241i	$-0.681236\pi$
$821$	−30.8938	−1.07820	−0.539100	+	0.842241i	$0.681236\pi$
$822$	18.3734	0.640847
$823$	−0.0869889	−0.00303224	−0.00151612	−	0.999999i	$-0.500483\pi$
$823$	−0.0869889	−0.00303224	−0.00151612	+	0.999999i	$0.500483\pi$
$824$	37.3155	1.29995
$825$	−16.8190	−0.585563
$826$	−58.6600	−2.04104
$827$	−9.31853	−0.324037	−0.162019	−	0.986788i	$-0.551800\pi$
$827$	−9.31853	−0.324037	−0.162019	+	0.986788i	$0.551800\pi$
$828$	70.8412	2.46190
$829$	24.5372	0.852211	0.426106	−	0.904673i	$-0.359885\pi$
$829$	24.5372	0.852211	0.426106	+	0.904673i	$0.359885\pi$
$830$	−8.29347	−0.287871
$831$	20.5001	0.711142
$832$	205.006	7.10731
$833$	40.1936	1.39263
$834$	−32.9564	−1.14119
$835$	10.2145	0.353488
$836$	12.1153	0.419017
$837$	−30.2278	−1.04483
$838$	25.8847	0.894173
$839$	−12.9060	−0.445565	−0.222782	−	0.974868i	$-0.571514\pi$
$839$	−12.9060	−0.445565	−0.222782	+	0.974868i	$0.571514\pi$
$840$	−110.555	−3.81451
$841$	−16.8078	−0.579579
$842$	42.0884	1.45046
$843$	0.0395923	0.00136363
$844$	11.0645	0.380856
$845$	99.9712	3.43911
$846$	−54.0937	−1.85978
$847$	17.3531	0.596260
$848$	−127.245	−4.36960
$849$	−24.3022	−0.834049
$850$	−98.2652	−3.37047
$851$	5.51891	0.189186
$852$	−3.93581	−0.134839
$853$	−11.4936	−0.393532	−0.196766	−	0.980450i	$-0.563044\pi$
$853$	−11.4936	−0.393532	−0.196766	+	0.980450i	$0.563044\pi$
$854$	−35.4303	−1.21240
$855$	−7.46014	−0.255131
$856$	−100.190	−3.42442
$857$	−18.8806	−0.644950	−0.322475	−	0.946578i	$-0.604515\pi$
$857$	−18.8806	−0.644950	−0.322475	+	0.946578i	$0.604515\pi$
$858$	34.7787	1.18732
$859$	−14.7641	−0.503744	−0.251872	−	0.967761i	$-0.581046\pi$
$859$	−14.7641	−0.503744	−0.251872	+	0.967761i	$0.581046\pi$
$860$	−191.141	−6.51787
$861$	−5.56598	−0.189688
$862$	54.5173	1.85687
$863$	6.57596	0.223848	0.111924	−	0.993717i	$-0.464299\pi$
$863$	6.57596	0.223848	0.111924	+	0.993717i	$0.464299\pi$
$864$	−95.9826	−3.26539
$865$	−85.8485	−2.91894
$866$	12.7851	0.434455
$867$	−0.858455	−0.0291546
$868$	162.452	5.51397
$869$	−11.2017	−0.379991
$870$	27.0332	0.916513
$871$	−73.9252	−2.50486
$872$	−49.4365	−1.67413
$873$	0.722617	0.0244569
$874$	12.3778	0.418686
$875$	−50.7822	−1.71675
$876$	10.7906	0.364581
$877$	8.13706	0.274769	0.137384	−	0.990518i	$-0.456130\pi$
$877$	8.13706	0.274769	0.137384	+	0.990518i	$0.456130\pi$
$878$	−87.6270	−2.95727
$879$	−13.7597	−0.464104
$880$	146.657	4.94381
$881$	−22.0333	−0.742320	−0.371160	−	0.928569i	$-0.621040\pi$
$881$	−22.0333	−0.742320	−0.371160	+	0.928569i	$0.621040\pi$
$882$	62.3184	2.09837
$883$	−5.70537	−0.192001	−0.0960005	−	0.995381i	$-0.530605\pi$
$883$	−5.70537	−0.192001	−0.0960005	+	0.995381i	$0.530605\pi$
$884$	149.164	5.01691
$885$	14.8900	0.500523
$886$	−12.8037	−0.430149
$887$	30.1648	1.01284	0.506418	−	0.862288i	$-0.330969\pi$
$887$	30.1648	1.01284	0.506418	+	0.862288i	$0.330969\pi$
$888$	−7.70295	−0.258494
$889$	49.3430	1.65491
$890$	−126.795	−4.25018
$891$	10.3897	0.348068
$892$	−8.74153	−0.292688
$893$	−6.93835	−0.232183
$894$	−20.5625	−0.687714
$895$	−47.3171	−1.58164
$896$	172.335	5.75731
$897$	26.0840	0.870919
$898$	80.1717	2.67536
$899$	−25.3345	−0.844951
$900$	−111.843	−3.72811
$901$	−35.0675	−1.16827
$902$	12.6632	0.421639
$903$	−29.5326	−0.982785
$904$	39.1139	1.30091
$905$	55.1397	1.83291
$906$	51.7236	1.71840
$907$	58.8431	1.95385	0.976927	−	0.213575i	$-0.0685108\pi$
$907$	58.8431	1.95385	0.976927	+	0.213575i	$0.0685108\pi$
$908$	−84.0296	−2.78862
$909$	45.9838	1.52519
$910$	258.590	8.57217
$911$	39.6708	1.31435	0.657176	−	0.753737i	$-0.271751\pi$
$911$	39.6708	1.31435	0.657176	+	0.753737i	$0.271751\pi$
$912$	−10.0733	−0.333559
$913$	2.14012	0.0708276
$914$	−23.0859	−0.763614
$915$	8.99350	0.297316
$916$	−9.50003	−0.313890
$917$	−38.6732	−1.27710
$918$	−48.6288	−1.60499
$919$	−17.6363	−0.581767	−0.290884	−	0.956758i	$-0.593949\pi$
$919$	−17.6363	−0.581767	−0.290884	+	0.956758i	$0.593949\pi$
$920$	188.644	6.21940
$921$	24.7078	0.814148
$922$	−15.1944	−0.500401
$923$	5.87131	0.193256
$924$	44.7314	1.47155
$925$	−8.71320	−0.286488
$926$	−75.4671	−2.48000
$927$	9.29685	0.305349
$928$	−80.4446	−2.64072
$929$	−46.1961	−1.51564	−0.757822	−	0.652461i	$-0.773737\pi$
$929$	−46.1961	−1.51564	−0.757822	+	0.652461i	$0.773737\pi$
$930$	−56.1729	−1.84198
$931$	7.99331	0.261970
$932$	−111.467	−3.65122
$933$	−21.2159	−0.694577
$934$	59.3686	1.94260
$935$	40.4173	1.32179
$936$	147.499	4.82117
$937$	−20.0392	−0.654652	−0.327326	−	0.944911i	$-0.606148\pi$
$937$	−20.0392	−0.654652	−0.327326	+	0.944911i	$0.606148\pi$
$938$	−129.521	−4.22902
$939$	8.35591	0.272685
$940$	−165.801	−5.40782
$941$	40.7791	1.32936	0.664681	−	0.747127i	$-0.268567\pi$
$941$	40.7791	1.32936	0.664681	+	0.747127i	$0.268567\pi$
$942$	31.6371	1.03079
$943$	9.49741	0.309278
$944$	−81.4575	−2.65122
$945$	−61.8862	−2.01316
$946$	67.1901	2.18454
$947$	−44.1486	−1.43464	−0.717318	−	0.696746i	$-0.754630\pi$
$947$	−44.1486	−1.43464	−0.717318	+	0.696746i	$0.754630\pi$
$948$	18.3857	0.597141
$949$	−16.0971	−0.522533
$950$	−19.5420	−0.634027
$951$	14.8648	0.482026
$952$	166.678	5.40207
$953$	53.7106	1.73986	0.869928	−	0.493179i	$-0.164165\pi$
$953$	53.7106	1.73986	0.869928	+	0.493179i	$0.164165\pi$
$954$	−54.3706	−1.76031
$955$	82.1895	2.65959
$956$	−132.831	−4.29605
$957$	−6.97589	−0.225499
$958$	−12.2011	−0.394199
$959$	−35.2525	−1.13836
$960$	−91.1736	−2.94262
$961$	21.6429	0.698159
$962$	18.0173	0.580901
$963$	−24.9615	−0.804372
$964$	−87.7893	−2.82750
$965$	−27.0151	−0.869648
$966$	45.7006	1.47039
$967$	44.6528	1.43594	0.717968	−	0.696076i	$-0.245072\pi$
$967$	44.6528	1.43594	0.717968	+	0.696076i	$0.245072\pi$
$968$	41.3281	1.32834
$969$	−2.77610	−0.0891811
$970$	3.01715	0.0968748
$971$	−18.7032	−0.600216	−0.300108	−	0.953905i	$-0.597023\pi$
$971$	−18.7032	−0.600216	−0.300108	+	0.953905i	$0.597023\pi$
$972$	−86.0627	−2.76046
$973$	63.2323	2.02714
$974$	−107.025	−3.42930
$975$	−41.1812	−1.31885
$976$	−49.1999	−1.57485
$977$	41.3973	1.32442	0.662208	−	0.749320i	$-0.269620\pi$
$977$	41.3973	1.32442	0.662208	+	0.749320i	$0.269620\pi$
$978$	23.7507	0.759462
$979$	32.7193	1.04571
$980$	191.010	6.10160
$981$	−12.3167	−0.393242
$982$	43.5294	1.38908
$983$	23.5982	0.752666	0.376333	−	0.926485i	$-0.377185\pi$
$983$	23.5982	0.752666	0.376333	+	0.926485i	$0.377185\pi$
$984$	−13.2559	−0.422582
$985$	−54.6057	−1.73988
$986$	−40.7566	−1.29796
$987$	−25.6173	−0.815409
$988$	29.6642	0.943744
$989$	50.3925	1.60239
$990$	62.6653	1.99163
$991$	22.5548	0.716478	0.358239	−	0.933630i	$-0.383377\pi$
$991$	22.5548	0.716478	0.358239	+	0.933630i	$0.383377\pi$
$992$	167.157	5.30725
$993$	−0.139798	−0.00443636
$994$	10.2869	0.326279
$995$	90.9078	2.88197
$996$	−3.51265	−0.111303
$997$	−46.2107	−1.46351	−0.731754	−	0.681569i	$-0.761298\pi$
$997$	−46.2107	−1.46351	−0.731754	+	0.681569i	$0.761298\pi$
$998$	30.8517	0.976593
$999$	−4.31193	−0.136424

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.7	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.7	✓	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74252 q^{2} -0.770641 q^{3} +5.52143 q^{4} +3.66315 q^{5} +2.11350 q^{6} -4.05510 q^{7} -9.65761 q^{8} -2.40611 q^{9} +O(q^{10})\)	\(q-2.74252 q^{2} -0.770641 q^{3} +5.52143 q^{4} +3.66315 q^{5} +2.11350 q^{6} -4.05510 q^{7} -9.65761 q^{8} -2.40611 q^{9} -10.0463 q^{10} +2.59243 q^{11} -4.25504 q^{12} +6.34752 q^{13} +11.1212 q^{14} -2.82297 q^{15} +15.4434 q^{16} +4.25605 q^{17} +6.59882 q^{18} +0.846401 q^{19} +20.2258 q^{20} +3.12503 q^{21} -7.10979 q^{22} -5.33234 q^{23} +7.44255 q^{24} +8.41865 q^{25} -17.4082 q^{26} +4.16617 q^{27} -22.3900 q^{28} +3.49174 q^{29} +7.74206 q^{30} -7.25555 q^{31} -23.0386 q^{32} -1.99783 q^{33} -11.6723 q^{34} -14.8545 q^{35} -13.2852 q^{36} -1.03499 q^{37} -2.32128 q^{38} -4.89166 q^{39} -35.3773 q^{40} -1.78110 q^{41} -8.57046 q^{42} -9.45036 q^{43} +14.3139 q^{44} -8.81395 q^{45} +14.6241 q^{46} -8.19747 q^{47} -11.9013 q^{48} +9.44388 q^{49} -23.0884 q^{50} -3.27988 q^{51} +35.0474 q^{52} -8.23944 q^{53} -11.4258 q^{54} +9.49644 q^{55} +39.1626 q^{56} -0.652271 q^{57} -9.57617 q^{58} -5.27460 q^{59} -15.5868 q^{60} -3.18583 q^{61} +19.8985 q^{62} +9.75704 q^{63} +32.2971 q^{64} +23.2519 q^{65} +5.47909 q^{66} -11.6463 q^{67} +23.4995 q^{68} +4.10932 q^{69} +40.7387 q^{70} +0.924976 q^{71} +23.2373 q^{72} -2.53596 q^{73} +2.83848 q^{74} -6.48776 q^{75} +4.67335 q^{76} -10.5126 q^{77} +13.4155 q^{78} -4.32093 q^{79} +56.5713 q^{80} +4.00772 q^{81} +4.88470 q^{82} +0.825528 q^{83} +17.2546 q^{84} +15.5905 q^{85} +25.9178 q^{86} -2.69087 q^{87} -25.0367 q^{88} +12.6211 q^{89} +24.1725 q^{90} -25.7399 q^{91} -29.4422 q^{92} +5.59142 q^{93} +22.4818 q^{94} +3.10049 q^{95} +17.7545 q^{96} -0.300325 q^{97} -25.9001 q^{98} -6.23767 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * q^99

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