LMFDB - Embedded newform 6029.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, 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("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.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:	$48.1418073786$
Analytic rank:	$0$
Dimension:	$268$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51050 q^{2} +0.264508 q^{3} +4.30262 q^{4} +3.31299 q^{5} -0.664049 q^{6} +1.39465 q^{7} -5.78073 q^{8} -2.93004 q^{9} +O(q^{10})$	\(q-2.51050 q^{2} +0.264508 q^{3} +4.30262 q^{4} +3.31299 q^{5} -0.664049 q^{6} +1.39465 q^{7} -5.78073 q^{8} -2.93004 q^{9} -8.31726 q^{10} +4.55915 q^{11} +1.13808 q^{12} -4.70525 q^{13} -3.50128 q^{14} +0.876312 q^{15} +5.90730 q^{16} +6.18376 q^{17} +7.35586 q^{18} +6.82515 q^{19} +14.2545 q^{20} +0.368897 q^{21} -11.4458 q^{22} +2.32415 q^{23} -1.52905 q^{24} +5.97587 q^{25} +11.8125 q^{26} -1.56854 q^{27} +6.00066 q^{28} +5.20046 q^{29} -2.19998 q^{30} +7.82442 q^{31} -3.26882 q^{32} +1.20593 q^{33} -15.5243 q^{34} +4.62046 q^{35} -12.6068 q^{36} +8.70040 q^{37} -17.1346 q^{38} -1.24458 q^{39} -19.1515 q^{40} +5.22371 q^{41} -0.926117 q^{42} +7.60833 q^{43} +19.6163 q^{44} -9.70717 q^{45} -5.83479 q^{46} -7.58919 q^{47} +1.56253 q^{48} -5.05494 q^{49} -15.0024 q^{50} +1.63566 q^{51} -20.2449 q^{52} +8.59226 q^{53} +3.93783 q^{54} +15.1044 q^{55} -8.06211 q^{56} +1.80531 q^{57} -13.0558 q^{58} +13.8902 q^{59} +3.77044 q^{60} -7.34470 q^{61} -19.6432 q^{62} -4.08638 q^{63} -3.60822 q^{64} -15.5884 q^{65} -3.02750 q^{66} -14.3550 q^{67} +26.6064 q^{68} +0.614758 q^{69} -11.5997 q^{70} -6.75875 q^{71} +16.9377 q^{72} -13.6556 q^{73} -21.8424 q^{74} +1.58067 q^{75} +29.3660 q^{76} +6.35843 q^{77} +3.12451 q^{78} -11.9139 q^{79} +19.5708 q^{80} +8.37521 q^{81} -13.1141 q^{82} -8.24595 q^{83} +1.58722 q^{84} +20.4867 q^{85} -19.1007 q^{86} +1.37557 q^{87} -26.3552 q^{88} -3.18134 q^{89} +24.3699 q^{90} -6.56219 q^{91} +9.99995 q^{92} +2.06962 q^{93} +19.0527 q^{94} +22.6116 q^{95} -0.864630 q^{96} +8.10926 q^{97} +12.6904 q^{98} -13.3585 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) $ 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9 + 91 * q^10 + 49 * q^11 + 77 * q^12 + 45 * q^13 + 42 * q^14 + 37 * q^15 + 356 * q^16 + 40 * q^17 + 36 * q^18 + 245 * q^19 + 40 * q^20 + 66 * q^21 + 51 * q^22 + 26 * q^23 + 90 * q^24 + 314 * q^25 + 24 * q^26 + 160 * q^27 + 117 * q^28 + 54 * q^29 + 25 * q^30 + 181 * q^31 + 35 * q^32 + 49 * q^33 + 84 * q^34 + 73 * q^35 + 348 * q^36 + 77 * q^37 + 20 * q^38 + 96 * q^39 + 257 * q^40 + 62 * q^41 + 22 * q^42 + 199 * q^43 + 59 * q^44 + 60 * q^45 + 116 * q^46 + 41 * q^47 + 106 * q^48 + 381 * q^49 + 21 * q^50 + 248 * q^51 + 101 * q^52 + 4 * q^53 + 98 * q^54 + 136 * q^55 + 79 * q^56 + 47 * q^57 + 14 * q^58 + 170 * q^59 + 31 * q^60 + 247 * q^61 + 17 * q^62 + 143 * q^63 + 437 * q^64 + 29 * q^65 + 38 * q^66 + 114 * q^67 + 62 * q^68 + 101 * q^69 + 48 * q^70 + 64 * q^71 + 54 * q^72 + 115 * q^73 + 22 * q^74 + 250 * q^75 + 448 * q^76 + 8 * q^77 - 50 * q^78 + 271 * q^79 + 39 * q^80 + 336 * q^81 + 132 * q^82 + 74 * q^83 + 122 * q^84 + 58 * q^85 + 27 * q^86 + 105 * q^87 + 127 * q^88 + 63 * q^89 + 179 * q^90 + 406 * q^91 + 13 * q^92 + q^93 + 263 * q^94 + 76 * q^95 + 161 * q^96 + 123 * q^97 - 7 * q^98 + 180 * 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 $

$2$	−2.51050	−1.77519	−0.887596	−	0.460622i	$-0.847626\pi$
$2$	−2.51050	−1.77519	−0.887596	+	0.460622i	$0.847626\pi$
$3$	0.264508	0.152714	0.0763570	−	0.997081i	$-0.475671\pi$
$3$	0.264508	0.152714	0.0763570	+	0.997081i	$0.475671\pi$
$4$	4.30262	2.15131
$5$	3.31299	1.48161	0.740806	−	0.671719i	$-0.234444\pi$
$5$	3.31299	1.48161	0.740806	+	0.671719i	$0.234444\pi$
$6$	−0.664049	−0.271097
$7$	1.39465	0.527129	0.263565	−	0.964642i	$-0.415102\pi$
$7$	1.39465	0.527129	0.263565	+	0.964642i	$0.415102\pi$
$8$	−5.78073	−2.04380
$9$	−2.93004	−0.976678
$10$	−8.31726	−2.63015
$11$	4.55915	1.37464	0.687318	−	0.726357i	$-0.258788\pi$
$11$	4.55915	1.37464	0.687318	+	0.726357i	$0.258788\pi$
$12$	1.13808	0.328535
$13$	−4.70525	−1.30500	−0.652501	−	0.757788i	$-0.726280\pi$
$13$	−4.70525	−1.30500	−0.652501	+	0.757788i	$0.726280\pi$
$14$	−3.50128	−0.935756
$15$	0.876312	0.226263
$16$	5.90730	1.47682
$17$	6.18376	1.49978	0.749891	−	0.661562i	$-0.230106\pi$
$17$	6.18376	1.49978	0.749891	+	0.661562i	$0.230106\pi$
$18$	7.35586	1.73379
$19$	6.82515	1.56580	0.782899	−	0.622149i	$-0.213740\pi$
$19$	6.82515	1.56580	0.782899	+	0.622149i	$0.213740\pi$
$20$	14.2545	3.18741
$21$	0.368897	0.0805000
$22$	−11.4458	−2.44024
$23$	2.32415	0.484620	0.242310	−	0.970199i	$-0.422095\pi$
$23$	2.32415	0.484620	0.242310	+	0.970199i	$0.422095\pi$
$24$	−1.52905	−0.312116
$25$	5.97587	1.19517
$26$	11.8125	2.31663
$27$	−1.56854	−0.301866
$28$	6.00066	1.13402
$29$	5.20046	0.965702	0.482851	−	0.875702i	$-0.339601\pi$
$29$	5.20046	0.965702	0.482851	+	0.875702i	$0.339601\pi$
$30$	−2.19998	−0.401660
$31$	7.82442	1.40531	0.702653	−	0.711532i	$-0.251998\pi$
$31$	7.82442	1.40531	0.702653	+	0.711532i	$0.251998\pi$
$32$	−3.26882	−0.577851
$33$	1.20593	0.209926
$34$	−15.5243	−2.66240
$35$	4.62046	0.781001
$36$	−12.6068	−2.10114
$37$	8.70040	1.43034	0.715169	−	0.698952i	$-0.246350\pi$
$37$	8.70040	1.43034	0.715169	+	0.698952i	$0.246350\pi$
$38$	−17.1346	−2.77959
$39$	−1.24458	−0.199292
$40$	−19.1515	−3.02812
$41$	5.22371	0.815806	0.407903	−	0.913025i	$-0.366260\pi$
$41$	5.22371	0.815806	0.407903	+	0.913025i	$0.366260\pi$
$42$	−0.926117	−0.142903
$43$	7.60833	1.16026	0.580129	−	0.814524i	$-0.303002\pi$
$43$	7.60833	1.16026	0.580129	+	0.814524i	$0.303002\pi$
$44$	19.6163	2.95727
$45$	−9.70717	−1.44706
$46$	−5.83479	−0.860293
$47$	−7.58919	−1.10700	−0.553498	−	0.832850i	$-0.686707\pi$
$47$	−7.58919	−1.10700	−0.553498	+	0.832850i	$0.686707\pi$
$48$	1.56253	0.225532
$49$	−5.05494	−0.722135
$50$	−15.0024	−2.12167
$51$	1.63566	0.229038
$52$	−20.2449	−2.80746
$53$	8.59226	1.18024	0.590119	−	0.807317i	$-0.299081\pi$
$53$	8.59226	1.18024	0.590119	+	0.807317i	$0.299081\pi$
$54$	3.93783	0.535871
$55$	15.1044	2.03668
$56$	−8.06211	−1.07735
$57$	1.80531	0.239119
$58$	−13.0558	−1.71431
$59$	13.8902	1.80835	0.904175	−	0.427163i	$-0.140487\pi$
$59$	13.8902	1.80835	0.904175	+	0.427163i	$0.140487\pi$
$60$	3.77044	0.486762
$61$	−7.34470	−0.940392	−0.470196	−	0.882562i	$-0.655817\pi$
$61$	−7.34470	−0.940392	−0.470196	+	0.882562i	$0.655817\pi$
$62$	−19.6432	−2.49469
$63$	−4.08638	−0.514836
$64$	−3.60822	−0.451027
$65$	−15.5884	−1.93351
$66$	−3.02750	−0.372659
$67$	−14.3550	−1.75374	−0.876870	−	0.480728i	$-0.840373\pi$
$67$	−14.3550	−1.75374	−0.876870	+	0.480728i	$0.840373\pi$
$68$	26.6064	3.22649
$69$	0.614758	0.0740082
$70$	−11.5997	−1.38643
$71$	−6.75875	−0.802117	−0.401058	−	0.916053i	$-0.631358\pi$
$71$	−6.75875	−0.802117	−0.401058	+	0.916053i	$0.631358\pi$
$72$	16.9377	1.99613
$73$	−13.6556	−1.59826	−0.799132	−	0.601156i	$-0.794707\pi$
$73$	−13.6556	−1.59826	−0.799132	+	0.601156i	$0.794707\pi$
$74$	−21.8424	−2.53912
$75$	1.58067	0.182520
$76$	29.3660	3.36852
$77$	6.35843	0.724611
$78$	3.12451	0.353782
$79$	−11.9139	−1.34042	−0.670212	−	0.742170i	$-0.733797\pi$
$79$	−11.9139	−1.34042	−0.670212	+	0.742170i	$0.733797\pi$
$80$	19.5708	2.18808
$81$	8.37521	0.930579
$82$	−13.1141	−1.44821
$83$	−8.24595	−0.905111	−0.452555	−	0.891736i	$-0.649487\pi$
$83$	−8.24595	−0.905111	−0.452555	+	0.891736i	$0.649487\pi$
$84$	1.58722	0.173180
$85$	20.4867	2.22209
$86$	−19.1007	−2.05968
$87$	1.37557	0.147476
$88$	−26.3552	−2.80948
$89$	−3.18134	−0.337221	−0.168611	−	0.985683i	$-0.553928\pi$
$89$	−3.18134	−0.337221	−0.168611	+	0.985683i	$0.553928\pi$
$90$	24.3699	2.56881
$91$	−6.56219	−0.687904
$92$	9.99995	1.04257
$93$	2.06962	0.214610
$94$	19.0527	1.96513
$95$	22.6116	2.31991
$96$	−0.864630	−0.0882459
$97$	8.10926	0.823370	0.411685	−	0.911326i	$-0.364940\pi$
$97$	8.10926	0.823370	0.411685	+	0.911326i	$0.364940\pi$
$98$	12.6904	1.28193
$99$	−13.3585	−1.34258
$100$	25.7119	2.57119
$101$	−4.23942	−0.421838	−0.210919	−	0.977504i	$-0.567646\pi$
$101$	−4.23942	−0.421838	−0.210919	+	0.977504i	$0.567646\pi$
$102$	−4.10632	−0.406586
$103$	−0.699442	−0.0689180	−0.0344590	−	0.999406i	$-0.510971\pi$
$103$	−0.699442	−0.0689180	−0.0344590	+	0.999406i	$0.510971\pi$
$104$	27.1998	2.66716
$105$	1.22215	0.119270
$106$	−21.5709	−2.09515
$107$	−19.3481	−1.87045	−0.935227	−	0.354048i	$-0.884805\pi$
$107$	−19.3481	−1.87045	−0.935227	+	0.354048i	$0.884805\pi$
$108$	−6.74885	−0.649408
$109$	7.30577	0.699766	0.349883	−	0.936793i	$-0.386221\pi$
$109$	7.30577	0.699766	0.349883	+	0.936793i	$0.386221\pi$
$110$	−37.9196	−3.61550
$111$	2.30133	0.218433
$112$	8.23863	0.778477
$113$	−9.67861	−0.910487	−0.455244	−	0.890367i	$-0.650448\pi$
$113$	−9.67861	−0.910487	−0.455244	+	0.890367i	$0.650448\pi$
$114$	−4.53224	−0.424483
$115$	7.69989	0.718018
$116$	22.3756	2.07752
$117$	13.7865	1.27457
$118$	−34.8714	−3.21017
$119$	8.62419	0.790578
$120$	−5.06573	−0.462435
$121$	9.78586	0.889624
$122$	18.4389	1.66938
$123$	1.38171	0.124585
$124$	33.6655	3.02325
$125$	3.23306	0.289174
$126$	10.2589	0.913933
$127$	9.35630	0.830238	0.415119	−	0.909767i	$-0.363740\pi$
$127$	9.35630	0.830238	0.415119	+	0.909767i	$0.363740\pi$
$128$	15.5961	1.37851
$129$	2.01247	0.177188
$130$	39.1348	3.43235
$131$	−8.81569	−0.770230	−0.385115	−	0.922869i	$-0.625838\pi$
$131$	−8.81569	−0.770230	−0.385115	+	0.922869i	$0.625838\pi$
$132$	5.18867	0.451616
$133$	9.51872	0.825378
$134$	36.0382	3.11323
$135$	−5.19656	−0.447249
$136$	−35.7466	−3.06525
$137$	2.80944	0.240027	0.120014	−	0.992772i	$-0.461706\pi$
$137$	2.80944	0.240027	0.120014	+	0.992772i	$0.461706\pi$
$138$	−1.54335	−0.131379
$139$	3.69901	0.313746	0.156873	−	0.987619i	$-0.449859\pi$
$139$	3.69901	0.313746	0.156873	+	0.987619i	$0.449859\pi$
$140$	19.8801	1.68018
$141$	−2.00740	−0.169054
$142$	16.9679	1.42391
$143$	−21.4519	−1.79390
$144$	−17.3086	−1.44238
$145$	17.2291	1.43080
$146$	34.2823	2.83723
$147$	−1.33707	−0.110280
$148$	37.4345	3.07710
$149$	2.78313	0.228003	0.114002	−	0.993481i	$-0.463633\pi$
$149$	2.78313	0.228003	0.114002	+	0.993481i	$0.463633\pi$
$150$	−3.96827	−0.324008
$151$	13.2974	1.08213	0.541065	−	0.840981i	$-0.318021\pi$
$151$	13.2974	1.08213	0.541065	+	0.840981i	$0.318021\pi$
$152$	−39.4544	−3.20017
$153$	−18.1186	−1.46480
$154$	−15.9629	−1.28632
$155$	25.9222	2.08212
$156$	−5.35494	−0.428739
$157$	−7.14118	−0.569929	−0.284964	−	0.958538i	$-0.591982\pi$
$157$	−7.14118	−0.569929	−0.284964	+	0.958538i	$0.591982\pi$
$158$	29.9100	2.37951
$159$	2.27272	0.180239
$160$	−10.8296	−0.856151
$161$	3.24139	0.255457
$162$	−21.0260	−1.65196
$163$	−21.7812	−1.70603	−0.853016	−	0.521885i	$-0.825229\pi$
$163$	−21.7812	−1.70603	−0.853016	+	0.521885i	$0.825229\pi$
$164$	22.4756	1.75505
$165$	3.99524	0.311029
$166$	20.7015	1.60675
$167$	−10.8648	−0.840741	−0.420371	−	0.907353i	$-0.638100\pi$
$167$	−10.8648	−0.840741	−0.420371	+	0.907353i	$0.638100\pi$
$168$	−2.13250	−0.164526
$169$	9.13937	0.703028
$170$	−51.4319	−3.94465
$171$	−19.9979	−1.52928
$172$	32.7357	2.49608
$173$	12.7383	0.968476	0.484238	−	0.874936i	$-0.339097\pi$
$173$	12.7383	0.968476	0.484238	+	0.874936i	$0.339097\pi$
$174$	−3.45336	−0.261799
$175$	8.33427	0.630012
$176$	26.9323	2.03010
$177$	3.67407	0.276160
$178$	7.98676	0.598633
$179$	2.98350	0.222998	0.111499	−	0.993765i	$-0.464435\pi$
$179$	2.98350	0.222998	0.111499	+	0.993765i	$0.464435\pi$
$180$	−41.7662	−3.11307
$181$	1.06878	0.0794416	0.0397208	−	0.999211i	$-0.487353\pi$
$181$	1.06878	0.0794416	0.0397208	+	0.999211i	$0.487353\pi$
$182$	16.4744	1.22116
$183$	−1.94273	−0.143611
$184$	−13.4353	−0.990464
$185$	28.8243	2.11921
$186$	−5.19579	−0.380974
$187$	28.1927	2.06165
$188$	−32.6534	−2.38149
$189$	−2.18757	−0.159123
$190$	−56.7666	−4.11828
$191$	10.4159	0.753666	0.376833	−	0.926281i	$-0.377013\pi$
$191$	10.4159	0.753666	0.376833	+	0.926281i	$0.377013\pi$
$192$	−0.954404	−0.0688782
$193$	−3.83246	−0.275867	−0.137933	−	0.990442i	$-0.544046\pi$
$193$	−3.83246	−0.275867	−0.137933	+	0.990442i	$0.544046\pi$
$194$	−20.3583	−1.46164
$195$	−4.12327	−0.295273
$196$	−21.7495	−1.55354
$197$	14.6270	1.04213	0.521065	−	0.853517i	$-0.325535\pi$
$197$	14.6270	1.04213	0.521065	+	0.853517i	$0.325535\pi$
$198$	33.5365	2.38333
$199$	−11.9100	−0.844280	−0.422140	−	0.906531i	$-0.638721\pi$
$199$	−11.9100	−0.844280	−0.422140	+	0.906531i	$0.638721\pi$
$200$	−34.5449	−2.44270
$201$	−3.79701	−0.267821
$202$	10.6431	0.748844
$203$	7.25284	0.509050
$204$	7.03760	0.492731
$205$	17.3061	1.20871
$206$	1.75595	0.122343
$207$	−6.80985	−0.473318
$208$	−27.7953	−1.92726
$209$	31.1169	2.15240
$210$	−3.06821	−0.211727
$211$	−10.8905	−0.749730	−0.374865	−	0.927080i	$-0.622311\pi$
$211$	−10.8905	−0.749730	−0.374865	+	0.927080i	$0.622311\pi$
$212$	36.9692	2.53906
$213$	−1.78775	−0.122494
$214$	48.5735	3.32042
$215$	25.2063	1.71905
$216$	9.06733	0.616954
$217$	10.9123	0.740778
$218$	−18.3411	−1.24222
$219$	−3.61201	−0.244077
$220$	64.9885	4.38152
$221$	−29.0961	−1.95722
$222$	−5.77749	−0.387760
$223$	13.9871	0.936646	0.468323	−	0.883557i	$-0.344858\pi$
$223$	13.9871	0.936646	0.468323	+	0.883557i	$0.344858\pi$
$224$	−4.55887	−0.304602
$225$	−17.5095	−1.16730
$226$	24.2982	1.61629
$227$	−15.0445	−0.998539	−0.499269	−	0.866447i	$-0.666398\pi$
$227$	−15.0445	−0.998539	−0.499269	+	0.866447i	$0.666398\pi$
$228$	7.76756	0.514419
$229$	9.01118	0.595476	0.297738	−	0.954648i	$-0.403768\pi$
$229$	9.01118	0.595476	0.297738	+	0.954648i	$0.403768\pi$
$230$	−19.3306	−1.27462
$231$	1.68186	0.110658
$232$	−30.0625	−1.97370
$233$	−20.3381	−1.33239	−0.666196	−	0.745776i	$-0.732079\pi$
$233$	−20.3381	−1.33239	−0.666196	+	0.745776i	$0.732079\pi$
$234$	−34.6111	−2.26260
$235$	−25.1429	−1.64014
$236$	59.7642	3.89032
$237$	−3.15134	−0.204701
$238$	−21.6511	−1.40343
$239$	−1.43189	−0.0926215	−0.0463107	−	0.998927i	$-0.514746\pi$
$239$	−1.43189	−0.0926215	−0.0463107	+	0.998927i	$0.514746\pi$
$240$	5.17664	0.334151
$241$	−28.6119	−1.84305	−0.921526	−	0.388316i	$-0.873057\pi$
$241$	−28.6119	−1.84305	−0.921526	+	0.388316i	$0.873057\pi$
$242$	−24.5674	−1.57925
$243$	6.92095	0.443979
$244$	−31.6014	−2.02307
$245$	−16.7470	−1.06992
$246$	−3.46880	−0.221162
$247$	−32.1141	−2.04337
$248$	−45.2309	−2.87216
$249$	−2.18112	−0.138223
$250$	−8.11660	−0.513339
$251$	−25.4915	−1.60901	−0.804504	−	0.593948i	$-0.797569\pi$
$251$	−25.4915	−1.60901	−0.804504	+	0.593948i	$0.797569\pi$
$252$	−17.5821	−1.10757
$253$	10.5962	0.666176
$254$	−23.4890	−1.47383
$255$	5.41890	0.339345
$256$	−31.9375	−1.99610
$257$	25.4679	1.58864	0.794321	−	0.607498i	$-0.207827\pi$
$257$	25.4679	1.58864	0.794321	+	0.607498i	$0.207827\pi$
$258$	−5.05230	−0.314542
$259$	12.1340	0.753973
$260$	−67.0711	−4.15957
$261$	−15.2375	−0.943180
$262$	22.1318	1.36731
$263$	−23.3425	−1.43936	−0.719679	−	0.694307i	$-0.755711\pi$
$263$	−23.3425	−1.43936	−0.719679	+	0.694307i	$0.755711\pi$
$264$	−6.97118	−0.429046
$265$	28.4660	1.74865
$266$	−23.8968	−1.46520
$267$	−0.841490	−0.0514984
$268$	−61.7640	−3.77284
$269$	−19.5466	−1.19178	−0.595889	−	0.803067i	$-0.703200\pi$
$269$	−19.5466	−1.19178	−0.595889	+	0.803067i	$0.703200\pi$
$270$	13.0460	0.793953
$271$	24.4866	1.48746	0.743728	−	0.668483i	$-0.233056\pi$
$271$	24.4866	1.48746	0.743728	+	0.668483i	$0.233056\pi$
$272$	36.5293	2.21491
$273$	−1.73575	−0.105053
$274$	−7.05312	−0.426094
$275$	27.2449	1.64293
$276$	2.64507	0.159215
$277$	10.2926	0.618422	0.309211	−	0.950993i	$-0.399935\pi$
$277$	10.2926	0.618422	0.309211	+	0.950993i	$0.399935\pi$
$278$	−9.28636	−0.556959
$279$	−22.9258	−1.37253
$280$	−26.7097	−1.59621
$281$	10.7434	0.640897	0.320449	−	0.947266i	$-0.396166\pi$
$281$	10.7434	0.640897	0.320449	+	0.947266i	$0.396166\pi$
$282$	5.03959	0.300103
$283$	−12.2448	−0.727879	−0.363940	−	0.931423i	$-0.618569\pi$
$283$	−12.2448	−0.727879	−0.363940	+	0.931423i	$0.618569\pi$
$284$	−29.0804	−1.72560
$285$	5.98097	0.354282
$286$	53.8551	3.18452
$287$	7.28526	0.430035
$288$	9.57776	0.564375
$289$	21.2388	1.24934
$290$	−43.2536	−2.53994
$291$	2.14497	0.125740
$292$	−58.7547	−3.43836
$293$	0.569946	0.0332966	0.0166483	−	0.999861i	$-0.494700\pi$
$293$	0.569946	0.0332966	0.0166483	+	0.999861i	$0.494700\pi$
$294$	3.35673	0.195768
$295$	46.0180	2.67927
$296$	−50.2947	−2.92332
$297$	−7.15123	−0.414956
$298$	−6.98706	−0.404750
$299$	−10.9357	−0.632429
$300$	6.80102	0.392657
$301$	10.6110	0.611606
$302$	−33.3832	−1.92099
$303$	−1.12136	−0.0644206
$304$	40.3182	2.31241
$305$	−24.3329	−1.39330
$306$	45.4868	2.60031
$307$	29.6041	1.68959	0.844797	−	0.535087i	$-0.179721\pi$
$307$	29.6041	1.68959	0.844797	+	0.535087i	$0.179721\pi$
$308$	27.3579	1.55886
$309$	−0.185008	−0.0105247
$310$	−65.0777	−3.69616
$311$	−28.1143	−1.59421	−0.797107	−	0.603839i	$-0.793637\pi$
$311$	−28.1143	−1.59421	−0.797107	+	0.603839i	$0.793637\pi$
$312$	7.19457	0.407312
$313$	−12.9725	−0.733247	−0.366623	−	0.930369i	$-0.619486\pi$
$313$	−12.9725	−0.733247	−0.366623	+	0.930369i	$0.619486\pi$
$314$	17.9280	1.01173
$315$	−13.5381	−0.762787
$316$	−51.2612	−2.88367
$317$	−18.4963	−1.03886	−0.519428	−	0.854514i	$-0.673855\pi$
$317$	−18.4963	−1.03886	−0.519428	+	0.854514i	$0.673855\pi$
$318$	−5.70568	−0.319959
$319$	23.7097	1.32749
$320$	−11.9540	−0.668248
$321$	−5.11774	−0.285644
$322$	−8.13751	−0.453486
$323$	42.2051	2.34835
$324$	36.0354	2.00196
$325$	−28.1180	−1.55970
$326$	54.6816	3.02854
$327$	1.93244	0.106864
$328$	−30.1969	−1.66734
$329$	−10.5843	−0.583530
$330$	−10.0301	−0.552137
$331$	5.50234	0.302436	0.151218	−	0.988500i	$-0.451680\pi$
$331$	5.50234	0.302436	0.151218	+	0.988500i	$0.451680\pi$
$332$	−35.4792	−1.94717
$333$	−25.4925	−1.39698
$334$	27.2760	1.49248
$335$	−47.5578	−2.59836
$336$	2.17919	0.118884
$337$	−11.0434	−0.601572	−0.300786	−	0.953692i	$-0.597249\pi$
$337$	−11.0434	−0.601572	−0.300786	+	0.953692i	$0.597249\pi$
$338$	−22.9444	−1.24801
$339$	−2.56007	−0.139044
$340$	88.1465	4.78041
$341$	35.6727	1.93179
$342$	50.2049	2.71477
$343$	−16.8125	−0.907788
$344$	−43.9817	−2.37133
$345$	2.03669	0.109651
$346$	−31.9796	−1.71923
$347$	19.6614	1.05548	0.527740	−	0.849406i	$-0.323040\pi$
$347$	19.6614	1.05548	0.527740	+	0.849406i	$0.323040\pi$
$348$	5.91854	0.317267
$349$	23.3372	1.24921	0.624606	−	0.780940i	$-0.285260\pi$
$349$	23.3372	1.24921	0.624606	+	0.780940i	$0.285260\pi$
$350$	−20.9232	−1.11839
$351$	7.38039	0.393936
$352$	−14.9030	−0.794335
$353$	11.4973	0.611940	0.305970	−	0.952041i	$-0.401019\pi$
$353$	11.4973	0.611940	0.305970	+	0.952041i	$0.401019\pi$
$354$	−9.22377	−0.490238
$355$	−22.3917	−1.18843
$356$	−13.6881	−0.725467
$357$	2.28117	0.120732
$358$	−7.49009	−0.395864
$359$	31.6260	1.66916	0.834578	−	0.550889i	$-0.185711\pi$
$359$	31.6260	1.66916	0.834578	+	0.550889i	$0.185711\pi$
$360$	56.1145	2.95749
$361$	27.5827	1.45172
$362$	−2.68317	−0.141024
$363$	2.58844	0.135858
$364$	−28.2346	−1.47990
$365$	−45.2407	−2.36801
$366$	4.87724	0.254937
$367$	24.6172	1.28501	0.642503	−	0.766283i	$-0.277896\pi$
$367$	24.6172	1.28501	0.642503	+	0.766283i	$0.277896\pi$
$368$	13.7295	0.715698
$369$	−15.3057	−0.796780
$370$	−72.3635	−3.76200
$371$	11.9832	0.622138
$372$	8.90480	0.461693
$373$	21.0373	1.08927	0.544636	−	0.838673i	$-0.316668\pi$
$373$	21.0373	1.08927	0.544636	+	0.838673i	$0.316668\pi$
$374$	−70.7778	−3.65983
$375$	0.855171	0.0441608
$376$	43.8710	2.26248
$377$	−24.4695	−1.26024
$378$	5.49191	0.282473
$379$	23.8721	1.22623	0.613113	−	0.789995i	$-0.289917\pi$
$379$	23.8721	1.22623	0.613113	+	0.789995i	$0.289917\pi$
$380$	97.2893	4.99084
$381$	2.47482	0.126789
$382$	−26.1491	−1.33790
$383$	20.3321	1.03892	0.519461	−	0.854494i	$-0.326133\pi$
$383$	20.3321	1.03892	0.519461	+	0.854494i	$0.326133\pi$
$384$	4.12529	0.210518
$385$	21.0654	1.07359
$386$	9.62140	0.489717
$387$	−22.2927	−1.13320
$388$	34.8911	1.77132
$389$	−17.3947	−0.881944	−0.440972	−	0.897521i	$-0.645366\pi$
$389$	−17.3947	−0.881944	−0.440972	+	0.897521i	$0.645366\pi$
$390$	10.3515	0.524167
$391$	14.3720	0.726824
$392$	29.2213	1.47590
$393$	−2.33182	−0.117625
$394$	−36.7211	−1.84998
$395$	−39.4707	−1.98599
$396$	−57.4764	−2.88830
$397$	−11.6324	−0.583814	−0.291907	−	0.956447i	$-0.594290\pi$
$397$	−11.6324	−0.583814	−0.291907	+	0.956447i	$0.594290\pi$
$398$	29.9002	1.49876
$399$	2.51778	0.126047
$400$	35.3013	1.76506
$401$	−16.4480	−0.821375	−0.410687	−	0.911776i	$-0.634711\pi$
$401$	−16.4480	−0.821375	−0.410687	+	0.911776i	$0.634711\pi$
$402$	9.53241	0.475433
$403$	−36.8158	−1.83393
$404$	−18.2406	−0.907505
$405$	27.7470	1.37876
$406$	−18.2083	−0.903662
$407$	39.6665	1.96619
$408$	−9.45528	−0.468106
$409$	31.3349	1.54941	0.774705	−	0.632323i	$-0.217898\pi$
$409$	31.3349	1.54941	0.774705	+	0.632323i	$0.217898\pi$
$410$	−43.4469	−2.14569
$411$	0.743121	0.0366555
$412$	−3.00943	−0.148264
$413$	19.3720	0.953234
$414$	17.0962	0.840230
$415$	−27.3187	−1.34102
$416$	15.3806	0.754096
$417$	0.978418	0.0479133
$418$	−78.1191	−3.82093
$419$	28.0509	1.37037	0.685187	−	0.728367i	$-0.259720\pi$
$419$	28.0509	1.37037	0.685187	+	0.728367i	$0.259720\pi$
$420$	5.25845	0.256586
$421$	16.0668	0.783046	0.391523	−	0.920168i	$-0.371948\pi$
$421$	16.0668	0.783046	0.391523	+	0.920168i	$0.371948\pi$
$422$	27.3405	1.33091
$423$	22.2366	1.08118
$424$	−49.6695	−2.41217
$425$	36.9534	1.79250
$426$	4.48814	0.217451
$427$	−10.2433	−0.495708
$428$	−83.2476	−4.02393
$429$	−5.67422	−0.273954
$430$	−63.2804	−3.05165
$431$	−20.5123	−0.988041	−0.494020	−	0.869450i	$-0.664473\pi$
$431$	−20.5123	−0.988041	−0.494020	+	0.869450i	$0.664473\pi$
$432$	−9.26586	−0.445804
$433$	−8.98178	−0.431637	−0.215818	−	0.976434i	$-0.569242\pi$
$433$	−8.98178	−0.431637	−0.215818	+	0.976434i	$0.569242\pi$
$434$	−27.3955	−1.31502
$435$	4.55723	0.218503
$436$	31.4339	1.50541
$437$	15.8627	0.758816
$438$	9.06796	0.433284
$439$	32.7367	1.56244	0.781219	−	0.624257i	$-0.214598\pi$
$439$	32.7367	1.56244	0.781219	+	0.624257i	$0.214598\pi$
$440$	−87.3145	−4.16256
$441$	14.8112	0.705294
$442$	73.0459	3.47444
$443$	−30.5678	−1.45232	−0.726160	−	0.687525i	$-0.758697\pi$
$443$	−30.5678	−1.45232	−0.726160	+	0.687525i	$0.758697\pi$
$444$	9.90174	0.469916
$445$	−10.5397	−0.499631
$446$	−35.1147	−1.66273
$447$	0.736162	0.0348193
$448$	−5.03221	−0.237750
$449$	17.1630	0.809973	0.404986	−	0.914323i	$-0.367276\pi$
$449$	17.1630	0.809973	0.404986	+	0.914323i	$0.367276\pi$
$450$	43.9577	2.07219
$451$	23.8157	1.12144
$452$	−41.6434	−1.95874
$453$	3.51728	0.165256
$454$	37.7693	1.77260
$455$	−21.7404	−1.01921
$456$	−10.4360	−0.488711
$457$	−12.0928	−0.565679	−0.282839	−	0.959167i	$-0.591276\pi$
$457$	−12.0928	−0.565679	−0.282839	+	0.959167i	$0.591276\pi$
$458$	−22.6226	−1.05708
$459$	−9.69949	−0.452734
$460$	33.1297	1.54468
$461$	6.76593	0.315121	0.157560	−	0.987509i	$-0.449637\pi$
$461$	6.76593	0.315121	0.157560	+	0.987509i	$0.449637\pi$
$462$	−4.22231	−0.196440
$463$	−0.402040	−0.0186844	−0.00934218	−	0.999956i	$-0.502974\pi$
$463$	−0.402040	−0.0186844	−0.00934218	+	0.999956i	$0.502974\pi$
$464$	30.7207	1.42617
$465$	6.85663	0.317969
$466$	51.0588	2.36525
$467$	−24.3735	−1.12787	−0.563936	−	0.825819i	$-0.690713\pi$
$467$	−24.3735	−1.12787	−0.563936	+	0.825819i	$0.690713\pi$
$468$	59.3183	2.74199
$469$	−20.0202	−0.924447
$470$	63.1212	2.91156
$471$	−1.88890	−0.0870360
$472$	−80.2955	−3.69590
$473$	34.6875	1.59493
$474$	7.91144	0.363385
$475$	40.7863	1.87140
$476$	37.1066	1.70078
$477$	−25.1756	−1.15271
$478$	3.59477	0.164421
$479$	−33.4797	−1.52973	−0.764863	−	0.644193i	$-0.777193\pi$
$479$	−33.4797	−1.52973	−0.764863	+	0.644193i	$0.777193\pi$
$480$	−2.86451	−0.130746
$481$	−40.9376	−1.86659
$482$	71.8302	3.27177
$483$	0.857374	0.0390119
$484$	42.1049	1.91386
$485$	26.8659	1.21992
$486$	−17.3750	−0.788148
$487$	6.46774	0.293081	0.146541	−	0.989205i	$-0.453186\pi$
$487$	6.46774	0.293081	0.146541	+	0.989205i	$0.453186\pi$
$488$	42.4577	1.92197
$489$	−5.76130	−0.260535
$490$	42.0433	1.89932
$491$	−12.0948	−0.545828	−0.272914	−	0.962038i	$-0.587988\pi$
$491$	−12.0948	−0.545828	−0.272914	+	0.962038i	$0.587988\pi$
$492$	5.94499	0.268021
$493$	32.1584	1.44834
$494$	80.6224	3.62737
$495$	−44.2564	−1.98918
$496$	46.2212	2.07539
$497$	−9.42612	−0.422819
$498$	5.47571	0.245373
$499$	20.5470	0.919809	0.459905	−	0.887968i	$-0.347884\pi$
$499$	20.5470	0.919809	0.459905	+	0.887968i	$0.347884\pi$
$500$	13.9106	0.622102
$501$	−2.87382	−0.128393
$502$	63.9964	2.85630
$503$	9.45454	0.421557	0.210779	−	0.977534i	$-0.432400\pi$
$503$	9.45454	0.421557	0.210779	+	0.977534i	$0.432400\pi$
$504$	23.6223	1.05222
$505$	−14.0451	−0.625001
$506$	−26.6017	−1.18259
$507$	2.41744	0.107362
$508$	40.2566	1.78610
$509$	−34.1403	−1.51324	−0.756621	−	0.653853i	$-0.773151\pi$
$509$	−34.1403	−1.51324	−0.756621	+	0.653853i	$0.773151\pi$
$510$	−13.6042	−0.602403
$511$	−19.0448	−0.842491
$512$	48.9871	2.16495
$513$	−10.7056	−0.472662
$514$	−63.9372	−2.82015
$515$	−2.31724	−0.102110
$516$	8.65888	0.381186
$517$	−34.6002	−1.52172
$518$	−30.4625	−1.33845
$519$	3.36939	0.147900
$520$	90.1125	3.95169
$521$	−16.1085	−0.705724	−0.352862	−	0.935675i	$-0.614792\pi$
$521$	−16.1085	−0.705724	−0.352862	+	0.935675i	$0.614792\pi$
$522$	38.2539	1.67433
$523$	−17.9753	−0.786005	−0.393003	−	0.919537i	$-0.628564\pi$
$523$	−17.9753	−0.786005	−0.393003	+	0.919537i	$0.628564\pi$
$524$	−37.9305	−1.65700
$525$	2.20448	0.0962116
$526$	58.6013	2.55514
$527$	48.3843	2.10765
$528$	7.12381	0.310024
$529$	−17.5983	−0.765144
$530$	−71.4640	−3.10420
$531$	−40.6988	−1.76618
$532$	40.9554	1.77564
$533$	−24.5788	−1.06463
$534$	2.11256	0.0914196
$535$	−64.1001	−2.77129
$536$	82.9823	3.58429
$537$	0.789162	0.0340548
$538$	49.0718	2.11564
$539$	−23.0463	−0.992672
$540$	−22.3588	−0.962171
$541$	4.70284	0.202191	0.101095	−	0.994877i	$-0.467765\pi$
$541$	4.70284	0.202191	0.101095	+	0.994877i	$0.467765\pi$
$542$	−61.4737	−2.64052
$543$	0.282700	0.0121318
$544$	−20.2136	−0.866650
$545$	24.2039	1.03678
$546$	4.35761	0.186489
$547$	10.2660	0.438943	0.219471	−	0.975619i	$-0.429567\pi$
$547$	10.2660	0.438943	0.219471	+	0.975619i	$0.429567\pi$
$548$	12.0880	0.516373
$549$	21.5202	0.918461
$550$	−68.3984	−2.91652
$551$	35.4940	1.51209
$552$	−3.55375	−0.151258
$553$	−16.6158	−0.706577
$554$	−25.8396	−1.09782
$555$	7.62427	0.323632
$556$	15.9154	0.674964
$557$	−35.2407	−1.49320	−0.746599	−	0.665274i	$-0.768315\pi$
$557$	−35.2407	−1.49320	−0.746599	+	0.665274i	$0.768315\pi$
$558$	57.5553	2.43651
$559$	−35.7991	−1.51414
$560$	27.2945	1.15340
$561$	7.45720	0.314843
$562$	−26.9713	−1.13772
$563$	−6.39936	−0.269701	−0.134851	−	0.990866i	$-0.543055\pi$
$563$	−6.39936	−0.269701	−0.134851	+	0.990866i	$0.543055\pi$
$564$	−8.63709	−0.363687
$565$	−32.0651	−1.34899
$566$	30.7407	1.29213
$567$	11.6805	0.490535
$568$	39.0705	1.63936
$569$	22.5426	0.945033	0.472517	−	0.881322i	$-0.343346\pi$
$569$	22.5426	0.945033	0.472517	+	0.881322i	$0.343346\pi$
$570$	−15.0152	−0.628919
$571$	44.7003	1.87065	0.935324	−	0.353793i	$-0.115108\pi$
$571$	44.7003	1.87065	0.935324	+	0.353793i	$0.115108\pi$
$572$	−92.2996	−3.85924
$573$	2.75508	0.115095
$574$	−18.2897	−0.763396
$575$	13.8889	0.579205
$576$	10.5722	0.440509
$577$	−26.5891	−1.10692	−0.553459	−	0.832877i	$-0.686692\pi$
$577$	−26.5891	−1.10692	−0.553459	+	0.832877i	$0.686692\pi$
$578$	−53.3202	−2.21783
$579$	−1.01372	−0.0421287
$580$	74.1301	3.07809
$581$	−11.5002	−0.477110
$582$	−5.38494	−0.223213
$583$	39.1734	1.62240
$584$	78.9392	3.26653
$585$	45.6746	1.88841
$586$	−1.43085	−0.0591079
$587$	35.7979	1.47754	0.738769	−	0.673959i	$-0.235407\pi$
$587$	35.7979	1.47754	0.738769	+	0.673959i	$0.235407\pi$
$588$	−5.75292	−0.237247
$589$	53.4029	2.20043
$590$	−115.528	−4.75623
$591$	3.86896	0.159148
$592$	51.3959	2.11236
$593$	−4.75410	−0.195227	−0.0976137	−	0.995224i	$-0.531121\pi$
$593$	−4.75410	−0.195227	−0.0976137	+	0.995224i	$0.531121\pi$
$594$	17.9532	0.736628
$595$	28.5718	1.17133
$596$	11.9748	0.490506
$597$	−3.15030	−0.128933
$598$	27.4542	1.12268
$599$	5.58639	0.228254	0.114127	−	0.993466i	$-0.463593\pi$
$599$	5.58639	0.228254	0.114127	+	0.993466i	$0.463593\pi$
$600$	−9.13742	−0.373034
$601$	44.5183	1.81594	0.907970	−	0.419035i	$-0.137632\pi$
$601$	44.5183	1.81594	0.907970	+	0.419035i	$0.137632\pi$
$602$	−26.6389	−1.08572
$603$	42.0606	1.71284
$604$	57.2138	2.32800
$605$	32.4204	1.31808
$606$	2.81518	0.114359
$607$	22.6901	0.920963	0.460482	−	0.887669i	$-0.347677\pi$
$607$	22.6901	0.920963	0.460482	+	0.887669i	$0.347677\pi$
$608$	−22.3102	−0.904798
$609$	1.91844	0.0777390
$610$	61.0877	2.47337
$611$	35.7090	1.44463
$612$	−77.9576	−3.15125
$613$	−19.9537	−0.805923	−0.402962	−	0.915217i	$-0.632019\pi$
$613$	−19.9537	−0.805923	−0.402962	+	0.915217i	$0.632019\pi$
$614$	−74.3211	−2.99936
$615$	4.57760	0.184587
$616$	−36.7564	−1.48096
$617$	21.9824	0.884978	0.442489	−	0.896774i	$-0.354096\pi$
$617$	21.9824	0.884978	0.442489	+	0.896774i	$0.354096\pi$
$618$	0.464463	0.0186835
$619$	−2.39475	−0.0962532	−0.0481266	−	0.998841i	$-0.515325\pi$
$619$	−2.39475	−0.0962532	−0.0481266	+	0.998841i	$0.515325\pi$
$620$	111.533	4.47929
$621$	−3.64554	−0.146290
$622$	70.5809	2.83004
$623$	−4.43686	−0.177759
$624$	−7.35209	−0.294319
$625$	−19.1683	−0.766732
$626$	32.5674	1.30165
$627$	8.23068	0.328702
$628$	−30.7258	−1.22609
$629$	53.8012	2.14519
$630$	33.9875	1.35409
$631$	8.60045	0.342378	0.171189	−	0.985238i	$-0.445239\pi$
$631$	8.60045	0.342378	0.171189	+	0.985238i	$0.445239\pi$
$632$	68.8713	2.73955
$633$	−2.88061	−0.114494
$634$	46.4350	1.84417
$635$	30.9973	1.23009
$636$	9.77867	0.387749
$637$	23.7848	0.942387
$638$	−59.5233	−2.35655
$639$	19.8034	0.783410
$640$	51.6696	2.04242
$641$	−10.6206	−0.419487	−0.209744	−	0.977756i	$-0.567263\pi$
$641$	−10.6206	−0.419487	−0.209744	+	0.977756i	$0.567263\pi$
$642$	12.8481	0.507074
$643$	19.0382	0.750792	0.375396	−	0.926864i	$-0.377507\pi$
$643$	19.0382	0.750792	0.375396	+	0.926864i	$0.377507\pi$
$644$	13.9465	0.549568
$645$	6.66727	0.262524
$646$	−105.956	−4.16878
$647$	−6.99036	−0.274820	−0.137410	−	0.990514i	$-0.543878\pi$
$647$	−6.99036	−0.274820	−0.137410	+	0.990514i	$0.543878\pi$
$648$	−48.4149	−1.90192
$649$	63.3275	2.48582
$650$	70.5902	2.76878
$651$	2.88641	0.113127
$652$	−93.7160	−3.67020
$653$	−41.6398	−1.62949	−0.814746	−	0.579819i	$-0.803123\pi$
$653$	−41.6398	−1.62949	−0.814746	+	0.579819i	$0.803123\pi$
$654$	−4.85139	−0.189704
$655$	−29.2062	−1.14118
$656$	30.8580	1.20480
$657$	40.0113	1.56099
$658$	26.5719	1.03588
$659$	−23.9381	−0.932494	−0.466247	−	0.884655i	$-0.654394\pi$
$659$	−23.9381	−0.932494	−0.466247	+	0.884655i	$0.654394\pi$
$660$	17.1900	0.669120
$661$	−11.7613	−0.457460	−0.228730	−	0.973490i	$-0.573457\pi$
$661$	−11.7613	−0.457460	−0.228730	+	0.973490i	$0.573457\pi$
$662$	−13.8136	−0.536882
$663$	−7.69616	−0.298894
$664$	47.6676	1.84986
$665$	31.5354	1.22289
$666$	63.9989	2.47991
$667$	12.0867	0.467998
$668$	−46.7470	−1.80869
$669$	3.69971	0.143039
$670$	119.394	4.61259
$671$	−33.4856	−1.29270
$672$	−1.20586	−0.0465170
$673$	−5.10010	−0.196595	−0.0982973	−	0.995157i	$-0.531340\pi$
$673$	−5.10010	−0.196595	−0.0982973	+	0.995157i	$0.531340\pi$
$674$	27.7245	1.06791
$675$	−9.37342	−0.360783
$676$	39.3232	1.51243
$677$	−23.0863	−0.887279	−0.443640	−	0.896205i	$-0.646313\pi$
$677$	−23.0863	−0.887279	−0.443640	+	0.896205i	$0.646313\pi$
$678$	6.42707	0.246830
$679$	11.3096	0.434023
$680$	−118.428	−4.54151
$681$	−3.97940	−0.152491
$682$	−89.5564	−3.42929
$683$	33.7694	1.29215	0.646075	−	0.763274i	$-0.276409\pi$
$683$	33.7694	1.29215	0.646075	+	0.763274i	$0.276409\pi$
$684$	−86.0436	−3.28996
$685$	9.30765	0.355627
$686$	42.2077	1.61150
$687$	2.38353	0.0909375
$688$	44.9446	1.71350
$689$	−40.4287	−1.54021
$690$	−5.11310	−0.194652
$691$	8.02857	0.305421	0.152711	−	0.988271i	$-0.451200\pi$
$691$	8.02857	0.305421	0.152711	+	0.988271i	$0.451200\pi$
$692$	54.8081	2.08349
$693$	−18.6304	−0.707712
$694$	−49.3600	−1.87368
$695$	12.2548	0.464849
$696$	−7.95178	−0.301411
$697$	32.3021	1.22353
$698$	−58.5881	−2.21759
$699$	−5.37960	−0.203475
$700$	35.8592	1.35535
$701$	26.5561	1.00301	0.501506	−	0.865154i	$-0.332780\pi$
$701$	26.5561	1.00301	0.501506	+	0.865154i	$0.332780\pi$
$702$	−18.5285	−0.699312
$703$	59.3816	2.23962
$704$	−16.4504	−0.619998
$705$	−6.65050	−0.250472
$706$	−28.8640	−1.08631
$707$	−5.91252	−0.222363
$708$	15.8081	0.594106
$709$	5.15240	0.193502	0.0967511	−	0.995309i	$-0.469155\pi$
$709$	5.15240	0.193502	0.0967511	+	0.995309i	$0.469155\pi$
$710$	56.2143	2.10969
$711$	34.9083	1.30916
$712$	18.3905	0.689212
$713$	18.1852	0.681039
$714$	−5.72688	−0.214323
$715$	−71.0700	−2.65787
$716$	12.8369	0.479737
$717$	−0.378748	−0.0141446
$718$	−79.3971	−2.96307
$719$	−38.8576	−1.44914	−0.724572	−	0.689199i	$-0.757962\pi$
$719$	−38.8576	−1.44914	−0.724572	+	0.689199i	$0.757962\pi$
$720$	−57.3431	−2.13705
$721$	−0.975478	−0.0363287
$722$	−69.2465	−2.57709
$723$	−7.56808	−0.281460
$724$	4.59854	0.170903
$725$	31.0773	1.15418
$726$	−6.49829	−0.241174
$727$	−28.2293	−1.04697	−0.523484	−	0.852036i	$-0.675368\pi$
$727$	−28.2293	−1.04697	−0.523484	+	0.852036i	$0.675368\pi$
$728$	37.9342	1.40594
$729$	−23.2950	−0.862777
$730$	113.577	4.20367
$731$	47.0480	1.74013
$732$	−8.35884	−0.308952
$733$	12.9937	0.479934	0.239967	−	0.970781i	$-0.422863\pi$
$733$	12.9937	0.479934	0.239967	+	0.970781i	$0.422863\pi$
$734$	−61.8015	−2.28113
$735$	−4.42971	−0.163392
$736$	−7.59724	−0.280038
$737$	−65.4465	−2.41075
$738$	38.4249	1.41444
$739$	−21.6577	−0.796693	−0.398346	−	0.917235i	$-0.630416\pi$
$739$	−21.6577	−0.796693	−0.398346	+	0.917235i	$0.630416\pi$
$740$	124.020	4.55907
$741$	−8.49443	−0.312051
$742$	−30.0839	−1.10441
$743$	43.4857	1.59534	0.797668	−	0.603097i	$-0.206067\pi$
$743$	43.4857	1.59534	0.797668	+	0.603097i	$0.206067\pi$
$744$	−11.9639	−0.438619
$745$	9.22049	0.337812
$746$	−52.8142	−1.93367
$747$	24.1609	0.884002
$748$	121.302	4.43526
$749$	−26.9839	−0.985971
$750$	−2.14691	−0.0783940
$751$	−25.6617	−0.936409	−0.468205	−	0.883620i	$-0.655099\pi$
$751$	−25.6617	−0.936409	−0.468205	+	0.883620i	$0.655099\pi$
$752$	−44.8316	−1.63484
$753$	−6.74271	−0.245718
$754$	61.4307	2.23717
$755$	44.0542	1.60330
$756$	−9.41230	−0.342322
$757$	−13.4856	−0.490142	−0.245071	−	0.969505i	$-0.578811\pi$
$757$	−13.4856	−0.490142	−0.245071	+	0.969505i	$0.578811\pi$
$758$	−59.9309	−2.17679
$759$	2.80278	0.101734
$760$	−130.712	−4.74142
$761$	−1.86654	−0.0676622	−0.0338311	−	0.999428i	$-0.510771\pi$
$761$	−1.86654	−0.0676622	−0.0338311	+	0.999428i	$0.510771\pi$
$762$	−6.21304	−0.225075
$763$	10.1890	0.368867
$764$	44.8155	1.62137
$765$	−60.0267	−2.17027
$766$	−51.0438	−1.84429
$767$	−65.3568	−2.35990
$768$	−8.44775	−0.304832
$769$	48.9012	1.76342	0.881711	−	0.471790i	$-0.156392\pi$
$769$	48.9012	1.76342	0.881711	+	0.471790i	$0.156392\pi$
$770$	−52.8847	−1.90583
$771$	6.73647	0.242608
$772$	−16.4896	−0.593475
$773$	−42.0269	−1.51160	−0.755801	−	0.654802i	$-0.772752\pi$
$773$	−42.0269	−1.51160	−0.755801	+	0.654802i	$0.772752\pi$
$774$	55.9658	2.01165
$775$	46.7577	1.67959
$776$	−46.8774	−1.68280
$777$	3.20956	0.115142
$778$	43.6693	1.56562
$779$	35.6526	1.27739
$780$	−17.7409	−0.635224
$781$	−30.8142	−1.10262
$782$	−36.0809	−1.29025
$783$	−8.15716	−0.291513
$784$	−29.8611	−1.06647
$785$	−23.6586	−0.844413
$786$	5.85404	0.208807
$787$	−3.04299	−0.108471	−0.0542355	−	0.998528i	$-0.517272\pi$
$787$	−3.04299	−0.108471	−0.0542355	+	0.998528i	$0.517272\pi$
$788$	62.9344	2.24195
$789$	−6.17428	−0.219810
$790$	99.0914	3.52551
$791$	−13.4983	−0.479944
$792$	77.2218	2.74396
$793$	34.5586	1.22721
$794$	29.2032	1.03638
$795$	7.52950	0.267044
$796$	−51.2443	−1.81631
$797$	20.5916	0.729392	0.364696	−	0.931127i	$-0.381173\pi$
$797$	20.5916	0.729392	0.364696	+	0.931127i	$0.381173\pi$
$798$	−6.32089	−0.223757
$799$	−46.9297	−1.66025
$800$	−19.5341	−0.690633
$801$	9.32143	0.329357
$802$	41.2928	1.45810
$803$	−62.2578	−2.19703
$804$	−16.3371	−0.576165
$805$	10.7387	0.378489
$806$	92.4262	3.25557
$807$	−5.17024	−0.182001
$808$	24.5070	0.862152
$809$	29.4708	1.03614	0.518069	−	0.855339i	$-0.326651\pi$
$809$	29.4708	1.03614	0.518069	+	0.855339i	$0.326651\pi$
$810$	−69.6588	−2.44756
$811$	11.9496	0.419607	0.209803	−	0.977744i	$-0.432718\pi$
$811$	11.9496	0.419607	0.209803	+	0.977744i	$0.432718\pi$
$812$	31.2062	1.09512
$813$	6.47691	0.227155
$814$	−99.5827	−3.49037
$815$	−72.1606	−2.52768
$816$	9.66230	0.338248
$817$	51.9280	1.81673
$818$	−78.6662	−2.75050
$819$	19.2274	0.671861
$820$	74.4614	2.60031
$821$	−9.44398	−0.329597	−0.164799	−	0.986327i	$-0.552697\pi$
$821$	−9.44398	−0.329597	−0.164799	+	0.986327i	$0.552697\pi$
$822$	−1.86561	−0.0650705
$823$	−35.5386	−1.23880	−0.619399	−	0.785077i	$-0.712623\pi$
$823$	−35.5386	−1.23880	−0.619399	+	0.785077i	$0.712623\pi$
$824$	4.04328	0.140854
$825$	7.20651	0.250898
$826$	−48.6334	−1.69217
$827$	−53.9092	−1.87461	−0.937303	−	0.348514i	$-0.886686\pi$
$827$	−53.9092	−1.87461	−0.937303	+	0.348514i	$0.886686\pi$
$828$	−29.3002	−1.01825
$829$	2.64855	0.0919880	0.0459940	−	0.998942i	$-0.485354\pi$
$829$	2.64855	0.0919880	0.0459940	+	0.998942i	$0.485354\pi$
$830$	68.5837	2.38057
$831$	2.72248	0.0944417
$832$	16.9776	0.588591
$833$	−31.2585	−1.08304
$834$	−2.45632	−0.0850554
$835$	−35.9948	−1.24565
$836$	133.884	4.63048
$837$	−12.2729	−0.424215
$838$	−70.4218	−2.43268
$839$	−39.3623	−1.35894	−0.679468	−	0.733705i	$-0.737790\pi$
$839$	−39.3623	−1.35894	−0.679468	+	0.733705i	$0.737790\pi$
$840$	−7.06493	−0.243763
$841$	−1.95516	−0.0674194
$842$	−40.3356	−1.39006
$843$	2.84172	0.0978740
$844$	−46.8575	−1.61290
$845$	30.2786	1.04162
$846$	−55.8250	−1.91930
$847$	13.6479	0.468947
$848$	50.7570	1.74300
$849$	−3.23886	−0.111157
$850$	−92.7715	−3.18203
$851$	20.2211	0.693170
$852$	−7.69200	−0.263523
$853$	18.0279	0.617263	0.308632	−	0.951182i	$-0.400129\pi$
$853$	18.0279	0.617263	0.308632	+	0.951182i	$0.400129\pi$
$854$	25.7158	0.879978
$855$	−66.2529	−2.26580
$856$	111.846	3.82283
$857$	−11.7629	−0.401813	−0.200907	−	0.979610i	$-0.564389\pi$
$857$	−11.7629	−0.401813	−0.200907	+	0.979610i	$0.564389\pi$
$858$	14.2451	0.486321
$859$	12.7893	0.436364	0.218182	−	0.975908i	$-0.429987\pi$
$859$	12.7893	0.436364	0.218182	+	0.975908i	$0.429987\pi$
$860$	108.453	3.69822
$861$	1.92701	0.0656724
$862$	51.4961	1.75396
$863$	45.2491	1.54030	0.770148	−	0.637865i	$-0.220182\pi$
$863$	45.2491	1.54030	0.770148	+	0.637865i	$0.220182\pi$
$864$	5.12729	0.174434
$865$	42.2019	1.43491
$866$	22.5488	0.766239
$867$	5.61785	0.190792
$868$	46.9517	1.59364
$869$	−54.3175	−1.84260
$870$	−11.4409	−0.387884
$871$	67.5438	2.28863
$872$	−42.2327	−1.43018
$873$	−23.7604	−0.804168
$874$	−39.8234	−1.34705
$875$	4.50899	0.152432
$876$	−15.5411	−0.525086
$877$	19.1793	0.647639	0.323820	−	0.946119i	$-0.395033\pi$
$877$	19.1793	0.647639	0.323820	+	0.946119i	$0.395033\pi$
$878$	−82.1856	−2.77363
$879$	0.150755	0.00508485
$880$	89.2262	3.00782
$881$	42.9684	1.44764	0.723822	−	0.689987i	$-0.242384\pi$
$881$	42.9684	1.44764	0.723822	+	0.689987i	$0.242384\pi$
$882$	−37.1835	−1.25203
$883$	−37.3287	−1.25621	−0.628105	−	0.778129i	$-0.716169\pi$
$883$	−37.3287	−1.25621	−0.628105	+	0.778129i	$0.716169\pi$
$884$	−125.190	−4.21058
$885$	12.1722	0.409162
$886$	76.7406	2.57815
$887$	−21.6764	−0.727821	−0.363910	−	0.931434i	$-0.618559\pi$
$887$	−21.6764	−0.727821	−0.363910	+	0.931434i	$0.618559\pi$
$888$	−13.3034	−0.446432
$889$	13.0488	0.437642
$890$	26.4600	0.886941
$891$	38.1839	1.27921
$892$	60.1812	2.01502
$893$	−51.7974	−1.73333
$894$	−1.84814	−0.0618109
$895$	9.88431	0.330396
$896$	21.7511	0.726654
$897$	−2.89259	−0.0965808
$898$	−43.0878	−1.43786
$899$	40.6906	1.35711
$900$	−75.3368	−2.51123
$901$	53.1324	1.77010
$902$	−59.7893	−1.99077
$903$	2.80669	0.0934008
$904$	55.9495	1.86085
$905$	3.54084	0.117702
$906$	−8.83014	−0.293362
$907$	−44.4775	−1.47685	−0.738426	−	0.674335i	$-0.764431\pi$
$907$	−44.4775	−1.47685	−0.738426	+	0.674335i	$0.764431\pi$
$908$	−64.7308	−2.14817
$909$	12.4217	0.412000
$910$	54.5794	1.80929
$911$	11.1619	0.369809	0.184905	−	0.982756i	$-0.440802\pi$
$911$	11.1619	0.369809	0.184905	+	0.982756i	$0.440802\pi$
$912$	10.6645	0.353137
$913$	−37.5945	−1.24420
$914$	30.3591	1.00419
$915$	−6.43625	−0.212776
$916$	38.7717	1.28105
$917$	−12.2948	−0.406011
$918$	24.3506	0.803689
$919$	−53.5282	−1.76573	−0.882865	−	0.469626i	$-0.844389\pi$
$919$	−53.5282	−1.76573	−0.882865	+	0.469626i	$0.844389\pi$
$920$	−44.5110	−1.46748
$921$	7.83053	0.258025
$922$	−16.9859	−0.559400
$923$	31.8016	1.04676
$924$	7.23640	0.238060
$925$	51.9925	1.70950
$926$	1.00932	0.0331683
$927$	2.04939	0.0673108
$928$	−16.9994	−0.558032
$929$	34.2929	1.12511	0.562556	−	0.826759i	$-0.309818\pi$
$929$	34.2929	1.12511	0.562556	+	0.826759i	$0.309818\pi$
$930$	−17.2136	−0.564456
$931$	−34.5008	−1.13072
$932$	−87.5071	−2.86639
$933$	−7.43646	−0.243459
$934$	61.1897	2.00219
$935$	93.4020	3.05457
$936$	−79.6963	−2.60496
$937$	−27.7955	−0.908039	−0.454020	−	0.890992i	$-0.650010\pi$
$937$	−27.7955	−0.908039	−0.454020	+	0.890992i	$0.650010\pi$
$938$	50.2608	1.64107
$939$	−3.43132	−0.111977
$940$	−108.180	−3.52845
$941$	21.3738	0.696765	0.348382	−	0.937353i	$-0.386731\pi$
$941$	21.3738	0.696765	0.348382	+	0.937353i	$0.386731\pi$
$942$	4.74209	0.154506
$943$	12.1407	0.395356
$944$	82.0535	2.67061
$945$	−7.24740	−0.235758
$946$	−87.0831	−2.83131
$947$	−21.0439	−0.683834	−0.341917	−	0.939730i	$-0.611076\pi$
$947$	−21.0439	−0.683834	−0.341917	+	0.939730i	$0.611076\pi$
$948$	−13.5590	−0.440376
$949$	64.2529	2.08574
$950$	−102.394	−3.32210
$951$	−4.89243	−0.158648
$952$	−49.8541	−1.61578
$953$	13.7198	0.444427	0.222213	−	0.974998i	$-0.428672\pi$
$953$	13.7198	0.444427	0.222213	+	0.974998i	$0.428672\pi$
$954$	63.2034	2.04629
$955$	34.5076	1.11664
$956$	−6.16089	−0.199258
$957$	6.27142	0.202726
$958$	84.0508	2.71556
$959$	3.91820	0.126525
$960$	−3.16193	−0.102051
$961$	30.2215	0.974887
$962$	102.774	3.31356
$963$	56.6907	1.82683
$964$	−123.106	−3.96498
$965$	−12.6969	−0.408727
$966$	−2.15244	−0.0692536
$967$	−11.4132	−0.367023	−0.183511	−	0.983018i	$-0.558746\pi$
$967$	−11.4132	−0.367023	−0.183511	+	0.983018i	$0.558746\pi$
$968$	−56.5695	−1.81821
$969$	11.1636	0.358626
$970$	−67.4468	−2.16559
$971$	−1.05305	−0.0337939	−0.0168970	−	0.999857i	$-0.505379\pi$
$971$	−1.05305	−0.0337939	−0.0168970	+	0.999857i	$0.505379\pi$
$972$	29.7782	0.955136
$973$	5.15883	0.165385
$974$	−16.2373	−0.520276
$975$	−7.43744	−0.238189
$976$	−43.3873	−1.38879
$977$	−30.5238	−0.976543	−0.488272	−	0.872692i	$-0.662372\pi$
$977$	−30.5238	−0.976543	−0.488272	+	0.872692i	$0.662372\pi$
$978$	14.4637	0.462500
$979$	−14.5042	−0.463556
$980$	−72.0558	−2.30174
$981$	−21.4062	−0.683446
$982$	30.3639	0.968951
$983$	5.64666	0.180101	0.0900503	−	0.995937i	$-0.471297\pi$
$983$	5.64666	0.180101	0.0900503	+	0.995937i	$0.471297\pi$
$984$	−7.98732	−0.254626
$985$	48.4590	1.54403
$986$	−80.7337	−2.57109
$987$	−2.79963	−0.0891132
$988$	−138.175	−4.39592
$989$	17.6829	0.562284
$990$	111.106	3.53118
$991$	−52.5919	−1.67064	−0.835318	−	0.549767i	$-0.814717\pi$
$991$	−52.5919	−1.67064	−0.835318	+	0.549767i	$0.814717\pi$
$992$	−25.5766	−0.812058
$993$	1.45541	0.0461862
$994$	23.6643	0.750585
$995$	−39.4578	−1.25090
$996$	−9.38454	−0.297361
$997$	−10.7471	−0.340363	−0.170182	−	0.985413i	$-0.554435\pi$
$997$	−10.7471	−0.340363	−0.170182	+	0.985413i	$0.554435\pi$
$998$	−51.5832	−1.63284
$999$	−13.6470	−0.431771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.b.1.19	✓	268

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.b.1.19	✓	268	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51050 q^{2} +0.264508 q^{3} +4.30262 q^{4} +3.31299 q^{5} -0.664049 q^{6} +1.39465 q^{7} -5.78073 q^{8} -2.93004 q^{9} +O(q^{10})\)	\(q-2.51050 q^{2} +0.264508 q^{3} +4.30262 q^{4} +3.31299 q^{5} -0.664049 q^{6} +1.39465 q^{7} -5.78073 q^{8} -2.93004 q^{9} -8.31726 q^{10} +4.55915 q^{11} +1.13808 q^{12} -4.70525 q^{13} -3.50128 q^{14} +0.876312 q^{15} +5.90730 q^{16} +6.18376 q^{17} +7.35586 q^{18} +6.82515 q^{19} +14.2545 q^{20} +0.368897 q^{21} -11.4458 q^{22} +2.32415 q^{23} -1.52905 q^{24} +5.97587 q^{25} +11.8125 q^{26} -1.56854 q^{27} +6.00066 q^{28} +5.20046 q^{29} -2.19998 q^{30} +7.82442 q^{31} -3.26882 q^{32} +1.20593 q^{33} -15.5243 q^{34} +4.62046 q^{35} -12.6068 q^{36} +8.70040 q^{37} -17.1346 q^{38} -1.24458 q^{39} -19.1515 q^{40} +5.22371 q^{41} -0.926117 q^{42} +7.60833 q^{43} +19.6163 q^{44} -9.70717 q^{45} -5.83479 q^{46} -7.58919 q^{47} +1.56253 q^{48} -5.05494 q^{49} -15.0024 q^{50} +1.63566 q^{51} -20.2449 q^{52} +8.59226 q^{53} +3.93783 q^{54} +15.1044 q^{55} -8.06211 q^{56} +1.80531 q^{57} -13.0558 q^{58} +13.8902 q^{59} +3.77044 q^{60} -7.34470 q^{61} -19.6432 q^{62} -4.08638 q^{63} -3.60822 q^{64} -15.5884 q^{65} -3.02750 q^{66} -14.3550 q^{67} +26.6064 q^{68} +0.614758 q^{69} -11.5997 q^{70} -6.75875 q^{71} +16.9377 q^{72} -13.6556 q^{73} -21.8424 q^{74} +1.58067 q^{75} +29.3660 q^{76} +6.35843 q^{77} +3.12451 q^{78} -11.9139 q^{79} +19.5708 q^{80} +8.37521 q^{81} -13.1141 q^{82} -8.24595 q^{83} +1.58722 q^{84} +20.4867 q^{85} -19.1007 q^{86} +1.37557 q^{87} -26.3552 q^{88} -3.18134 q^{89} +24.3699 q^{90} -6.56219 q^{91} +9.99995 q^{92} +2.06962 q^{93} +19.0527 q^{94} +22.6116 q^{95} -0.864630 q^{96} +8.10926 q^{97} +12.6904 q^{98} -13.3585 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9 + 91 * q^10 + 49 * q^11 + 77 * q^12 + 45 * q^13 + 42 * q^14 + 37 * q^15 + 356 * q^16 + 40 * q^17 + 36 * q^18 + 245 * q^19 + 40 * q^20 + 66 * q^21 + 51 * q^22 + 26 * q^23 + 90 * q^24 + 314 * q^25 + 24 * q^26 + 160 * q^27 + 117 * q^28 + 54 * q^29 + 25 * q^30 + 181 * q^31 + 35 * q^32 + 49 * q^33 + 84 * q^34 + 73 * q^35 + 348 * q^36 + 77 * q^37 + 20 * q^38 + 96 * q^39 + 257 * q^40 + 62 * q^41 + 22 * q^42 + 199 * q^43 + 59 * q^44 + 60 * q^45 + 116 * q^46 + 41 * q^47 + 106 * q^48 + 381 * q^49 + 21 * q^50 + 248 * q^51 + 101 * q^52 + 4 * q^53 + 98 * q^54 + 136 * q^55 + 79 * q^56 + 47 * q^57 + 14 * q^58 + 170 * q^59 + 31 * q^60 + 247 * q^61 + 17 * q^62 + 143 * q^63 + 437 * q^64 + 29 * q^65 + 38 * q^66 + 114 * q^67 + 62 * q^68 + 101 * q^69 + 48 * q^70 + 64 * q^71 + 54 * q^72 + 115 * q^73 + 22 * q^74 + 250 * q^75 + 448 * q^76 + 8 * q^77 - 50 * q^78 + 271 * q^79 + 39 * q^80 + 336 * q^81 + 132 * q^82 + 74 * q^83 + 122 * q^84 + 58 * q^85 + 27 * q^86 + 105 * q^87 + 127 * q^88 + 63 * q^89 + 179 * q^90 + 406 * q^91 + 13 * q^92 + q^93 + 263 * q^94 + 76 * q^95 + 161 * q^96 + 123 * q^97 - 7 * q^98 + 180 * q^99

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