LMFDB - Embedded newform 6023.2.a.c.1.106

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.106
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.77544 q^{2} -1.73439 q^{3} +1.15220 q^{4} +0.320872 q^{5} -3.07930 q^{6} -4.28215 q^{7} -1.50522 q^{8} +0.00809141 q^{9} +O(q^{10})$	\(q+1.77544 q^{2} -1.73439 q^{3} +1.15220 q^{4} +0.320872 q^{5} -3.07930 q^{6} -4.28215 q^{7} -1.50522 q^{8} +0.00809141 q^{9} +0.569690 q^{10} -4.70266 q^{11} -1.99836 q^{12} -6.93300 q^{13} -7.60271 q^{14} -0.556515 q^{15} -4.97684 q^{16} -1.58184 q^{17} +0.0143658 q^{18} +1.00000 q^{19} +0.369708 q^{20} +7.42689 q^{21} -8.34931 q^{22} +6.09289 q^{23} +2.61064 q^{24} -4.89704 q^{25} -12.3092 q^{26} +5.18912 q^{27} -4.93388 q^{28} -7.91007 q^{29} -0.988061 q^{30} -1.68480 q^{31} -5.82564 q^{32} +8.15623 q^{33} -2.80846 q^{34} -1.37402 q^{35} +0.00932291 q^{36} -4.36576 q^{37} +1.77544 q^{38} +12.0245 q^{39} -0.482984 q^{40} +5.75576 q^{41} +13.1860 q^{42} -2.46683 q^{43} -5.41840 q^{44} +0.00259631 q^{45} +10.8176 q^{46} -4.33894 q^{47} +8.63175 q^{48} +11.3368 q^{49} -8.69442 q^{50} +2.74351 q^{51} -7.98819 q^{52} -10.2804 q^{53} +9.21299 q^{54} -1.50895 q^{55} +6.44559 q^{56} -1.73439 q^{57} -14.0439 q^{58} -0.199937 q^{59} -0.641216 q^{60} +0.396990 q^{61} -2.99126 q^{62} -0.0346486 q^{63} -0.389422 q^{64} -2.22461 q^{65} +14.4809 q^{66} +6.23140 q^{67} -1.82259 q^{68} -10.5674 q^{69} -2.43950 q^{70} -0.427896 q^{71} -0.0121794 q^{72} +7.10971 q^{73} -7.75116 q^{74} +8.49335 q^{75} +1.15220 q^{76} +20.1375 q^{77} +21.3488 q^{78} -15.2922 q^{79} -1.59693 q^{80} -9.02421 q^{81} +10.2190 q^{82} -8.44947 q^{83} +8.55725 q^{84} -0.507567 q^{85} -4.37971 q^{86} +13.7191 q^{87} +7.07856 q^{88} +17.1053 q^{89} +0.00460960 q^{90} +29.6881 q^{91} +7.02021 q^{92} +2.92209 q^{93} -7.70354 q^{94} +0.320872 q^{95} +10.1039 q^{96} +14.8267 q^{97} +20.1278 q^{98} -0.0380512 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * 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 $

$2$	1.77544	1.25543	0.627714	−	0.778444i	$-0.283991\pi$
$2$	1.77544	1.25543	0.627714	+	0.778444i	$0.283991\pi$
$3$	−1.73439	−1.00135	−0.500674	−	0.865636i	$-0.666914\pi$
$3$	−1.73439	−1.00135	−0.500674	+	0.865636i	$0.666914\pi$
$4$	1.15220	0.576099
$5$	0.320872	0.143498	0.0717491	−	0.997423i	$-0.477142\pi$
$5$	0.320872	0.143498	0.0717491	+	0.997423i	$0.477142\pi$
$6$	−3.07930	−1.25712
$7$	−4.28215	−1.61850	−0.809250	−	0.587464i	$-0.800126\pi$
$7$	−4.28215	−1.61850	−0.809250	+	0.587464i	$0.800126\pi$
$8$	−1.50522	−0.532177
$9$	0.00809141	0.00269714
$10$	0.569690	0.180152
$11$	−4.70266	−1.41791	−0.708953	−	0.705256i	$-0.750832\pi$
$11$	−4.70266	−1.41791	−0.708953	+	0.705256i	$0.750832\pi$
$12$	−1.99836	−0.576875
$13$	−6.93300	−1.92287	−0.961435	−	0.275034i	$-0.911311\pi$
$13$	−6.93300	−1.92287	−0.961435	+	0.275034i	$0.911311\pi$
$14$	−7.60271	−2.03191
$15$	−0.556515	−0.143692
$16$	−4.97684	−1.24421
$17$	−1.58184	−0.383652	−0.191826	−	0.981429i	$-0.561441\pi$
$17$	−1.58184	−0.383652	−0.191826	+	0.981429i	$0.561441\pi$
$18$	0.0143658	0.00338606
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.369708	0.0826692
$21$	7.42689	1.62068
$22$	−8.34931	−1.78008
$23$	6.09289	1.27045	0.635227	−	0.772325i	$-0.280906\pi$
$23$	6.09289	1.27045	0.635227	+	0.772325i	$0.280906\pi$
$24$	2.61064	0.532894
$25$	−4.89704	−0.979408
$26$	−12.3092	−2.41402
$27$	5.18912	0.998647
$28$	−4.93388	−0.932416
$29$	−7.91007	−1.46886	−0.734431	−	0.678683i	$-0.762551\pi$
$29$	−7.91007	−1.46886	−0.734431	+	0.678683i	$0.762551\pi$
$30$	−0.988061	−0.180395
$31$	−1.68480	−0.302599	−0.151299	−	0.988488i	$-0.548346\pi$
$31$	−1.68480	−0.302599	−0.151299	+	0.988488i	$0.548346\pi$
$32$	−5.82564	−1.02984
$33$	8.15623	1.41982
$34$	−2.80846	−0.481647
$35$	−1.37402	−0.232252
$36$	0.00932291	0.00155382
$37$	−4.36576	−0.717727	−0.358863	−	0.933390i	$-0.616836\pi$
$37$	−4.36576	−0.717727	−0.358863	+	0.933390i	$0.616836\pi$
$38$	1.77544	0.288015
$39$	12.0245	1.92546
$40$	−0.482984	−0.0763665
$41$	5.75576	0.898899	0.449450	−	0.893306i	$-0.351620\pi$
$41$	5.75576	0.898899	0.449450	+	0.893306i	$0.351620\pi$
$42$	13.1860	2.03465
$43$	−2.46683	−0.376188	−0.188094	−	0.982151i	$-0.560231\pi$
$43$	−2.46683	−0.376188	−0.188094	+	0.982151i	$0.560231\pi$
$44$	−5.41840	−0.816854
$45$	0.00259631	0.000387035 0
$46$	10.8176	1.59496
$47$	−4.33894	−0.632899	−0.316450	−	0.948609i	$-0.602491\pi$
$47$	−4.33894	−0.632899	−0.316450	+	0.948609i	$0.602491\pi$
$48$	8.63175	1.24589
$49$	11.3368	1.61954
$50$	−8.69442	−1.22958
$51$	2.74351	0.384169
$52$	−7.98819	−1.10776
$53$	−10.2804	−1.41212	−0.706059	−	0.708153i	$-0.749529\pi$
$53$	−10.2804	−1.41212	−0.706059	+	0.708153i	$0.749529\pi$
$54$	9.21299	1.25373
$55$	−1.50895	−0.203467
$56$	6.44559	0.861329
$57$	−1.73439	−0.229725
$58$	−14.0439	−1.84405
$59$	−0.199937	−0.0260295	−0.0130148	−	0.999915i	$-0.504143\pi$
$59$	−0.199937	−0.0260295	−0.0130148	+	0.999915i	$0.504143\pi$
$60$	−0.641216	−0.0827806
$61$	0.396990	0.0508293	0.0254147	−	0.999677i	$-0.491909\pi$
$61$	0.396990	0.0508293	0.0254147	+	0.999677i	$0.491909\pi$
$62$	−2.99126	−0.379891
$63$	−0.0346486	−0.00436532
$64$	−0.389422	−0.0486777
$65$	−2.22461	−0.275928
$66$	14.4809	1.78248
$67$	6.23140	0.761286	0.380643	−	0.924722i	$-0.375703\pi$
$67$	6.23140	0.761286	0.380643	+	0.924722i	$0.375703\pi$
$68$	−1.82259	−0.221021
$69$	−10.5674	−1.27217
$70$	−2.43950	−0.291576
$71$	−0.427896	−0.0507820	−0.0253910	−	0.999678i	$-0.508083\pi$
$71$	−0.427896	−0.0507820	−0.0253910	+	0.999678i	$0.508083\pi$
$72$	−0.0121794	−0.00143535
$73$	7.10971	0.832128	0.416064	−	0.909335i	$-0.363409\pi$
$73$	7.10971	0.832128	0.416064	+	0.909335i	$0.363409\pi$
$74$	−7.75116	−0.901054
$75$	8.49335	0.980728
$76$	1.15220	0.132166
$77$	20.1375	2.29488
$78$	21.3488	2.41728
$79$	−15.2922	−1.72051	−0.860254	−	0.509866i	$-0.829695\pi$
$79$	−15.2922	−1.72051	−0.860254	+	0.509866i	$0.829695\pi$
$80$	−1.59693	−0.178542
$81$	−9.02421	−1.00269
$82$	10.2190	1.12850
$83$	−8.44947	−0.927450	−0.463725	−	0.885979i	$-0.653487\pi$
$83$	−8.44947	−0.927450	−0.463725	+	0.885979i	$0.653487\pi$
$84$	8.55725	0.933673
$85$	−0.507567	−0.0550534
$86$	−4.37971	−0.472277
$87$	13.7191	1.47084
$88$	7.07856	0.754577
$89$	17.1053	1.81315	0.906577	−	0.422040i	$-0.138686\pi$
$89$	17.1053	1.81315	0.906577	+	0.422040i	$0.138686\pi$
$90$	0.00460960	0.000485894 0
$91$	29.6881	3.11216
$92$	7.02021	0.731908
$93$	2.92209	0.303007
$94$	−7.70354	−0.794560
$95$	0.320872	0.0329208
$96$	10.1039	1.03123
$97$	14.8267	1.50542	0.752711	−	0.658351i	$-0.228746\pi$
$97$	14.8267	1.50542	0.752711	+	0.658351i	$0.228746\pi$
$98$	20.1278	2.03322
$99$	−0.0380512	−0.00382429
$100$	−5.64236	−0.564236
$101$	−1.27908	−0.127274	−0.0636368	−	0.997973i	$-0.520270\pi$
$101$	−1.27908	−0.127274	−0.0636368	+	0.997973i	$0.520270\pi$
$102$	4.87095	0.482296
$103$	0.847362	0.0834931	0.0417465	−	0.999128i	$-0.486708\pi$
$103$	0.847362	0.0834931	0.0417465	+	0.999128i	$0.486708\pi$
$104$	10.4357	1.02331
$105$	2.38308	0.232565
$106$	−18.2522	−1.77281
$107$	−19.4565	−1.88093	−0.940463	−	0.339895i	$-0.889608\pi$
$107$	−19.4565	−1.88093	−0.940463	+	0.339895i	$0.889608\pi$
$108$	5.97890	0.575320
$109$	−13.7119	−1.31337	−0.656683	−	0.754167i	$-0.728041\pi$
$109$	−13.7119	−1.31337	−0.656683	+	0.754167i	$0.728041\pi$
$110$	−2.67906	−0.255438
$111$	7.57191	0.718694
$112$	21.3115	2.01375
$113$	1.48986	0.140154	0.0700769	−	0.997542i	$-0.477676\pi$
$113$	1.48986	0.140154	0.0700769	+	0.997542i	$0.477676\pi$
$114$	−3.07930	−0.288403
$115$	1.95504	0.182308
$116$	−9.11396	−0.846210
$117$	−0.0560978	−0.00518624
$118$	−0.354976	−0.0326782
$119$	6.77366	0.620941
$120$	0.837680	0.0764694
$121$	11.1150	1.01046
$122$	0.704832	0.0638125
$123$	−9.98271	−0.900111
$124$	−1.94122	−0.174327
$125$	−3.17568	−0.284042
$126$	−0.0615167	−0.00548034
$127$	8.88001	0.787973	0.393987	−	0.919116i	$-0.371096\pi$
$127$	8.88001	0.787973	0.393987	+	0.919116i	$0.371096\pi$
$128$	10.9599	0.968726
$129$	4.27843	0.376695
$130$	−3.94966	−0.346408
$131$	−6.98439	−0.610229	−0.305115	−	0.952316i	$-0.598695\pi$
$131$	−6.98439	−0.610229	−0.305115	+	0.952316i	$0.598695\pi$
$132$	9.39759	0.817955
$133$	−4.28215	−0.371309
$134$	11.0635	0.955740
$135$	1.66504	0.143304
$136$	2.38102	0.204171
$137$	−10.1226	−0.864834	−0.432417	−	0.901674i	$-0.642339\pi$
$137$	−10.1226	−0.864834	−0.432417	+	0.901674i	$0.642339\pi$
$138$	−18.7618	−1.59711
$139$	−17.5511	−1.48867	−0.744334	−	0.667807i	$-0.767233\pi$
$139$	−17.5511	−1.48867	−0.744334	+	0.667807i	$0.767233\pi$
$140$	−1.58314	−0.133800
$141$	7.52539	0.633752
$142$	−0.759706	−0.0637531
$143$	32.6036	2.72645
$144$	−0.0402696	−0.00335580
$145$	−2.53812	−0.210779
$146$	12.6229	1.04468
$147$	−19.6624	−1.62172
$148$	−5.03022	−0.413482
$149$	12.6836	1.03908	0.519541	−	0.854446i	$-0.326103\pi$
$149$	12.6836	1.03908	0.519541	+	0.854446i	$0.326103\pi$
$150$	15.0795	1.23123
$151$	−18.6518	−1.51786	−0.758931	−	0.651171i	$-0.774278\pi$
$151$	−18.6518	−1.51786	−0.758931	+	0.651171i	$0.774278\pi$
$152$	−1.50522	−0.122090
$153$	−0.0127993	−0.00103476
$154$	35.7530	2.88106
$155$	−0.540604	−0.0434224
$156$	13.8546	1.10926
$157$	−22.1105	−1.76461	−0.882305	−	0.470678i	$-0.844009\pi$
$157$	−22.1105	−1.76461	−0.882305	+	0.470678i	$0.844009\pi$
$158$	−27.1504	−2.15997
$159$	17.8301	1.41402
$160$	−1.86928	−0.147780
$161$	−26.0906	−2.05623
$162$	−16.0220	−1.25880
$163$	−14.2739	−1.11802	−0.559008	−	0.829163i	$-0.688818\pi$
$163$	−14.2739	−1.11802	−0.559008	+	0.829163i	$0.688818\pi$
$164$	6.63178	0.517855
$165$	2.61710	0.203741
$166$	−15.0016	−1.16435
$167$	−13.2314	−1.02388	−0.511940	−	0.859021i	$-0.671073\pi$
$167$	−13.2314	−1.02388	−0.511940	+	0.859021i	$0.671073\pi$
$168$	−11.1791	−0.862489
$169$	35.0665	2.69743
$170$	−0.901157	−0.0691156
$171$	0.00809141	0.000618766 0
$172$	−2.84227	−0.216721
$173$	21.4839	1.63339	0.816697	−	0.577067i	$-0.195803\pi$
$173$	21.4839	1.63339	0.816697	+	0.577067i	$0.195803\pi$
$174$	24.3575	1.84654
$175$	20.9699	1.58517
$176$	23.4044	1.76417
$177$	0.346767	0.0260646
$178$	30.3694	2.27628
$179$	−2.11993	−0.158451	−0.0792254	−	0.996857i	$-0.525245\pi$
$179$	−2.11993	−0.158451	−0.0792254	+	0.996857i	$0.525245\pi$
$180$	0.00299146	0.000222970 0
$181$	−22.8009	−1.69478	−0.847388	−	0.530974i	$-0.821826\pi$
$181$	−22.8009	−1.69478	−0.847388	+	0.530974i	$0.821826\pi$
$182$	52.7096	3.90710
$183$	−0.688533	−0.0508978
$184$	−9.17116	−0.676107
$185$	−1.40085	−0.102993
$186$	5.18800	0.380403
$187$	7.43885	0.543982
$188$	−4.99932	−0.364613
$189$	−22.2206	−1.61631
$190$	0.569690	0.0413296
$191$	−11.8292	−0.855931	−0.427965	−	0.903795i	$-0.640770\pi$
$191$	−11.8292	−0.855931	−0.427965	+	0.903795i	$0.640770\pi$
$192$	0.675407	0.0487433
$193$	−3.00307	−0.216165	−0.108083	−	0.994142i	$-0.534471\pi$
$193$	−3.00307	−0.216165	−0.108083	+	0.994142i	$0.534471\pi$
$194$	26.3239	1.88995
$195$	3.85832	0.276300
$196$	13.0622	0.933017
$197$	10.7639	0.766893	0.383446	−	0.923563i	$-0.374737\pi$
$197$	10.7639	0.766893	0.383446	+	0.923563i	$0.374737\pi$
$198$	−0.0675577	−0.00480112
$199$	−15.5556	−1.10271	−0.551354	−	0.834271i	$-0.685889\pi$
$199$	−15.5556	−1.10271	−0.551354	+	0.834271i	$0.685889\pi$
$200$	7.37114	0.521219
$201$	−10.8076	−0.762312
$202$	−2.27094	−0.159783
$203$	33.8721	2.37735
$204$	3.16107	0.221319
$205$	1.84686	0.128990
$206$	1.50444	0.104820
$207$	0.0493001	0.00342659
$208$	34.5044	2.39245
$209$	−4.70266	−0.325290
$210$	4.23103	0.291968
$211$	18.1263	1.24786	0.623932	−	0.781479i	$-0.285534\pi$
$211$	18.1263	1.24786	0.623932	+	0.781479i	$0.285534\pi$
$212$	−11.8450	−0.813519
$213$	0.742137	0.0508504
$214$	−34.5438	−2.36137
$215$	−0.791536	−0.0539823
$216$	−7.81079	−0.531457
$217$	7.21456	0.489756
$218$	−24.3448	−1.64884
$219$	−12.3310	−0.833250
$220$	−1.73861	−0.117217
$221$	10.9669	0.737712
$222$	13.4435	0.902268
$223$	14.0553	0.941211	0.470606	−	0.882344i	$-0.344035\pi$
$223$	14.0553	0.941211	0.470606	+	0.882344i	$0.344035\pi$
$224$	24.9463	1.66679
$225$	−0.0396240	−0.00264160
$226$	2.64515	0.175953
$227$	0.957283	0.0635371	0.0317686	−	0.999495i	$-0.489886\pi$
$227$	0.957283	0.0635371	0.0317686	+	0.999495i	$0.489886\pi$
$228$	−1.99836	−0.132344
$229$	−16.5536	−1.09389	−0.546945	−	0.837168i	$-0.684209\pi$
$229$	−16.5536	−1.09389	−0.546945	+	0.837168i	$0.684209\pi$
$230$	3.47106	0.228875
$231$	−34.9262	−2.29797
$232$	11.9064	0.781695
$233$	−6.96215	−0.456106	−0.228053	−	0.973649i	$-0.573236\pi$
$233$	−6.96215	−0.456106	−0.228053	+	0.973649i	$0.573236\pi$
$234$	−0.0995984	−0.00651095
$235$	−1.39224	−0.0908200
$236$	−0.230367	−0.0149956
$237$	26.5226	1.72283
$238$	12.0263	0.779546
$239$	23.3767	1.51212	0.756058	−	0.654505i	$-0.227123\pi$
$239$	23.3767	1.51212	0.756058	+	0.654505i	$0.227123\pi$
$240$	2.76969	0.178782
$241$	−14.1783	−0.913305	−0.456652	−	0.889645i	$-0.650952\pi$
$241$	−14.1783	−0.913305	−0.456652	+	0.889645i	$0.650952\pi$
$242$	19.7341	1.26856
$243$	0.0840882	0.00539426
$244$	0.457411	0.0292827
$245$	3.63766	0.232401
$246$	−17.7237	−1.13002
$247$	−6.93300	−0.441136
$248$	2.53600	0.161036
$249$	14.6546	0.928700
$250$	−5.63824	−0.356594
$251$	−18.6256	−1.17564	−0.587820	−	0.808992i	$-0.700014\pi$
$251$	−18.6256	−1.17564	−0.587820	+	0.808992i	$0.700014\pi$
$252$	−0.0399221	−0.00251486
$253$	−28.6528	−1.80139
$254$	15.7659	0.989243
$255$	0.880317	0.0551276
$256$	20.2375	1.26484
$257$	1.09163	0.0680943	0.0340471	−	0.999420i	$-0.489160\pi$
$257$	1.09163	0.0680943	0.0340471	+	0.999420i	$0.489160\pi$
$258$	7.59611	0.472913
$259$	18.6948	1.16164
$260$	−2.56319	−0.158962
$261$	−0.0640036	−0.00396172
$262$	−12.4004	−0.766098
$263$	−9.05368	−0.558274	−0.279137	−	0.960251i	$-0.590048\pi$
$263$	−9.05368	−0.558274	−0.279137	+	0.960251i	$0.590048\pi$
$264$	−12.2769	−0.755594
$265$	−3.29868	−0.202636
$266$	−7.60271	−0.466152
$267$	−29.6671	−1.81560
$268$	7.17980	0.438576
$269$	−12.3836	−0.755042	−0.377521	−	0.926001i	$-0.623223\pi$
$269$	−12.3836	−0.755042	−0.377521	+	0.926001i	$0.623223\pi$
$270$	2.95619	0.179908
$271$	−10.8607	−0.659742	−0.329871	−	0.944026i	$-0.607005\pi$
$271$	−10.8607	−0.659742	−0.329871	+	0.944026i	$0.607005\pi$
$272$	7.87254	0.477343
$273$	−51.4907	−3.11636
$274$	−17.9721	−1.08574
$275$	23.0291	1.38871
$276$	−12.1758	−0.732894
$277$	4.77836	0.287104	0.143552	−	0.989643i	$-0.454148\pi$
$277$	4.77836	0.287104	0.143552	+	0.989643i	$0.454148\pi$
$278$	−31.1611	−1.86892
$279$	−0.0136324	−0.000816151 0
$280$	2.06821	0.123599
$281$	2.58020	0.153922	0.0769610	−	0.997034i	$-0.475478\pi$
$281$	2.58020	0.153922	0.0769610	+	0.997034i	$0.475478\pi$
$282$	13.3609	0.795630
$283$	−14.2665	−0.848054	−0.424027	−	0.905650i	$-0.639384\pi$
$283$	−14.2665	−0.848054	−0.424027	+	0.905650i	$0.639384\pi$
$284$	−0.493021	−0.0292554
$285$	−0.556515	−0.0329651
$286$	57.8858	3.42286
$287$	−24.6470	−1.45487
$288$	−0.0471377	−0.00277761
$289$	−14.4978	−0.852811
$290$	−4.50628	−0.264618
$291$	−25.7152	−1.50745
$292$	8.19179	0.479388
$293$	−15.0208	−0.877525	−0.438762	−	0.898603i	$-0.644583\pi$
$293$	−15.0208	−0.877525	−0.438762	+	0.898603i	$0.644583\pi$
$294$	−34.9094	−2.03596
$295$	−0.0641541	−0.00373519
$296$	6.57145	0.381958
$297$	−24.4027	−1.41599
$298$	22.5190	1.30449
$299$	−42.2420	−2.44292
$300$	9.78603	0.564997
$301$	10.5633	0.608860
$302$	−33.1152	−1.90557
$303$	2.21842	0.127445
$304$	−4.97684	−0.285441
$305$	0.127383	0.00729392
$306$	−0.0227244	−0.00129907
$307$	0.512604	0.0292559	0.0146279	−	0.999893i	$-0.495344\pi$
$307$	0.512604	0.0292559	0.0146279	+	0.999893i	$0.495344\pi$
$308$	23.2024	1.32208
$309$	−1.46965	−0.0836056
$310$	−0.959813	−0.0545137
$311$	2.42346	0.137422	0.0687109	−	0.997637i	$-0.478111\pi$
$311$	2.42346	0.137422	0.0687109	+	0.997637i	$0.478111\pi$
$312$	−18.0996	−1.02469
$313$	29.0713	1.64321	0.821603	−	0.570060i	$-0.193080\pi$
$313$	29.0713	1.64321	0.821603	+	0.570060i	$0.193080\pi$
$314$	−39.2559	−2.21534
$315$	−0.0111178	−0.000626415 0
$316$	−17.6196	−0.991183
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	31.6564	1.77520
$319$	37.1984	2.08271
$320$	−0.124954	−0.00698517
$321$	33.7450	1.88346
$322$	−46.3225	−2.58145
$323$	−1.58184	−0.0880158
$324$	−10.3977	−0.577649
$325$	33.9512	1.88327
$326$	−25.3424	−1.40359
$327$	23.7818	1.31514
$328$	−8.66371	−0.478374
$329$	18.5800	1.02435
$330$	4.64652	0.255782
$331$	22.2086	1.22069	0.610347	−	0.792135i	$-0.291030\pi$
$331$	22.2086	1.22069	0.610347	+	0.792135i	$0.291030\pi$
$332$	−9.73546	−0.534303
$333$	−0.0353252	−0.00193581
$334$	−23.4917	−1.28541
$335$	1.99948	0.109243
$336$	−36.9624	−2.01647
$337$	3.24196	0.176601	0.0883004	−	0.996094i	$-0.471856\pi$
$337$	3.24196	0.176601	0.0883004	+	0.996094i	$0.471856\pi$
$338$	62.2586	3.38642
$339$	−2.58398	−0.140343
$340$	−0.584818	−0.0317162
$341$	7.92304	0.429057
$342$	0.0143658	0.000776816 0
$343$	−18.5708	−1.00273
$344$	3.71313	0.200199
$345$	−3.39079	−0.182554
$346$	38.1435	2.05061
$347$	31.3982	1.68554	0.842772	−	0.538270i	$-0.180922\pi$
$347$	31.3982	1.68554	0.842772	+	0.538270i	$0.180922\pi$
$348$	15.8071	0.847351
$349$	−19.0310	−1.01871	−0.509354	−	0.860557i	$-0.670116\pi$
$349$	−19.0310	−1.01871	−0.509354	+	0.860557i	$0.670116\pi$
$350$	37.2308	1.99007
$351$	−35.9762	−1.92027
$352$	27.3960	1.46021
$353$	28.9237	1.53946	0.769728	−	0.638372i	$-0.220392\pi$
$353$	28.9237	1.53946	0.769728	+	0.638372i	$0.220392\pi$
$354$	0.615666	0.0327223
$355$	−0.137300	−0.00728712
$356$	19.7087	1.04456
$357$	−11.7481	−0.621777
$358$	−3.76381	−0.198923
$359$	−10.0229	−0.528990	−0.264495	−	0.964387i	$-0.585205\pi$
$359$	−10.0229	−0.528990	−0.264495	+	0.964387i	$0.585205\pi$
$360$	−0.00390802	−0.000205971 0
$361$	1.00000	0.0526316
$362$	−40.4817	−2.12767
$363$	−19.2777	−1.01182
$364$	34.2066	1.79291
$365$	2.28131	0.119409
$366$	−1.22245	−0.0638985
$367$	−36.0500	−1.88179	−0.940897	−	0.338692i	$-0.890015\pi$
$367$	−36.0500	−1.88179	−0.940897	+	0.338692i	$0.890015\pi$
$368$	−30.3233	−1.58071
$369$	0.0465723	0.00242446
$370$	−2.48713	−0.129300
$371$	44.0221	2.28551
$372$	3.36683	0.174562
$373$	−16.3927	−0.848782	−0.424391	−	0.905479i	$-0.639512\pi$
$373$	−16.3927	−0.848782	−0.424391	+	0.905479i	$0.639512\pi$
$374$	13.2072	0.682931
$375$	5.50786	0.284424
$376$	6.53108	0.336815
$377$	54.8405	2.82443
$378$	−39.4514	−2.02916
$379$	−38.4576	−1.97543	−0.987716	−	0.156260i	$-0.950056\pi$
$379$	−38.4576	−1.97543	−0.987716	+	0.156260i	$0.950056\pi$
$380$	0.369708	0.0189656
$381$	−15.4013	−0.789035
$382$	−21.0021	−1.07456
$383$	9.96030	0.508947	0.254474	−	0.967080i	$-0.418098\pi$
$383$	9.96030	0.508947	0.254474	+	0.967080i	$0.418098\pi$
$384$	−19.0087	−0.970032
$385$	6.46156	0.329311
$386$	−5.33177	−0.271380
$387$	−0.0199601	−0.00101463
$388$	17.0833	0.867272
$389$	−14.3521	−0.727682	−0.363841	−	0.931461i	$-0.618535\pi$
$389$	−14.3521	−0.727682	−0.363841	+	0.931461i	$0.618535\pi$
$390$	6.85023	0.346875
$391$	−9.63796	−0.487412
$392$	−17.0644	−0.861883
$393$	12.1136	0.611051
$394$	19.1106	0.962779
$395$	−4.90684	−0.246890
$396$	−0.0438425	−0.00220317
$397$	25.0409	1.25677	0.628383	−	0.777904i	$-0.283717\pi$
$397$	25.0409	1.25677	0.628383	+	0.777904i	$0.283717\pi$
$398$	−27.6181	−1.38437
$399$	7.42689	0.371810
$400$	24.3718	1.21859
$401$	23.8416	1.19059	0.595296	−	0.803507i	$-0.297035\pi$
$401$	23.8416	1.19059	0.595296	+	0.803507i	$0.297035\pi$
$402$	−19.1884	−0.957028
$403$	11.6807	0.581858
$404$	−1.47376	−0.0733222
$405$	−2.89561	−0.143884
$406$	60.1379	2.98460
$407$	20.5307	1.01767
$408$	−4.12960	−0.204446
$409$	−28.4042	−1.40450	−0.702249	−	0.711931i	$-0.747821\pi$
$409$	−28.4042	−1.40450	−0.702249	+	0.711931i	$0.747821\pi$
$410$	3.27900	0.161938
$411$	17.5565	0.865999
$412$	0.976329	0.0481003
$413$	0.856159	0.0421288
$414$	0.0875295	0.00430184
$415$	−2.71120	−0.133087
$416$	40.3892	1.98024
$417$	30.4404	1.49067
$418$	−8.34931	−0.408378
$419$	19.4885	0.952074	0.476037	−	0.879425i	$-0.342073\pi$
$419$	19.4885	0.952074	0.476037	+	0.879425i	$0.342073\pi$
$420$	2.74578	0.133980
$421$	−34.1673	−1.66521	−0.832606	−	0.553865i	$-0.813152\pi$
$421$	−34.1673	−1.66521	−0.832606	+	0.553865i	$0.813152\pi$
$422$	32.1821	1.56660
$423$	−0.0351082	−0.00170702
$424$	15.4743	0.751496
$425$	7.74632	0.375752
$426$	1.31762	0.0638390
$427$	−1.69997	−0.0822672
$428$	−22.4177	−1.08360
$429$	−56.5471	−2.73012
$430$	−1.40533	−0.0677709
$431$	−3.13099	−0.150814	−0.0754071	−	0.997153i	$-0.524026\pi$
$431$	−3.13099	−0.150814	−0.0754071	+	0.997153i	$0.524026\pi$
$432$	−25.8254	−1.24253
$433$	32.7495	1.57384	0.786921	−	0.617054i	$-0.211674\pi$
$433$	32.7495	1.57384	0.786921	+	0.617054i	$0.211674\pi$
$434$	12.8090	0.614853
$435$	4.40207	0.211063
$436$	−15.7989	−0.756629
$437$	6.09289	0.291462
$438$	−21.8929	−1.04609
$439$	0.817962	0.0390392	0.0195196	−	0.999809i	$-0.493786\pi$
$439$	0.817962	0.0390392	0.0195196	+	0.999809i	$0.493786\pi$
$440$	2.27131	0.108281
$441$	0.0917307	0.00436813
$442$	19.4711	0.926145
$443$	19.2071	0.912555	0.456277	−	0.889838i	$-0.349182\pi$
$443$	19.2071	0.912555	0.456277	+	0.889838i	$0.349182\pi$
$444$	8.72434	0.414039
$445$	5.48860	0.260185
$446$	24.9544	1.18162
$447$	−21.9983	−1.04048
$448$	1.66756	0.0787849
$449$	32.8486	1.55022	0.775111	−	0.631825i	$-0.217694\pi$
$449$	32.8486	1.55022	0.775111	+	0.631825i	$0.217694\pi$
$450$	−0.0703501	−0.00331634
$451$	−27.0674	−1.27455
$452$	1.71661	0.0807425
$453$	32.3494	1.51991
$454$	1.69960	0.0797663
$455$	9.52609	0.446590
$456$	2.61064	0.122254
$457$	19.5908	0.916418	0.458209	−	0.888844i	$-0.348491\pi$
$457$	19.5908	0.916418	0.458209	+	0.888844i	$0.348491\pi$
$458$	−29.3899	−1.37330
$459$	−8.20835	−0.383133
$460$	2.25259	0.105027
$461$	23.0780	1.07485	0.537424	−	0.843312i	$-0.319397\pi$
$461$	23.0780	1.07485	0.537424	+	0.843312i	$0.319397\pi$
$462$	−62.0094	−2.88494
$463$	35.8876	1.66784	0.833919	−	0.551886i	$-0.186092\pi$
$463$	35.8876	1.66784	0.833919	+	0.551886i	$0.186092\pi$
$464$	39.3671	1.82757
$465$	0.937616	0.0434809
$466$	−12.3609	−0.572608
$467$	−15.3683	−0.711161	−0.355581	−	0.934646i	$-0.615717\pi$
$467$	−15.3683	−0.711161	−0.355581	+	0.934646i	$0.615717\pi$
$468$	−0.0646358	−0.00298779
$469$	−26.6838	−1.23214
$470$	−2.47185	−0.114018
$471$	38.3481	1.76699
$472$	0.300950	0.0138523
$473$	11.6007	0.533399
$474$	47.0893	2.16288
$475$	−4.89704	−0.224692
$476$	7.80460	0.357723
$477$	−0.0831827	−0.00380868
$478$	41.5041	1.89835
$479$	−41.6270	−1.90198	−0.950992	−	0.309215i	$-0.899934\pi$
$479$	−41.6270	−1.90198	−0.950992	+	0.309215i	$0.899934\pi$
$480$	3.24206	0.147979
$481$	30.2678	1.38009
$482$	−25.1728	−1.14659
$483$	45.2512	2.05900
$484$	12.8067	0.582124
$485$	4.75747	0.216025
$486$	0.149294	0.00677211
$487$	−25.9620	−1.17645	−0.588225	−	0.808698i	$-0.700173\pi$
$487$	−25.9620	−1.17645	−0.588225	+	0.808698i	$0.700173\pi$
$488$	−0.597558	−0.0270502
$489$	24.7564	1.11952
$490$	6.45846	0.291763
$491$	15.4654	0.697943	0.348971	−	0.937133i	$-0.386531\pi$
$491$	15.4654	0.697943	0.348971	+	0.937133i	$0.386531\pi$
$492$	−11.5021	−0.518553
$493$	12.5124	0.563532
$494$	−12.3092	−0.553815
$495$	−0.0122096	−0.000548779 0
$496$	8.38497	0.376496
$497$	1.83232	0.0821906
$498$	26.0185	1.16592
$499$	12.5288	0.560868	0.280434	−	0.959873i	$-0.409522\pi$
$499$	12.5288	0.560868	0.280434	+	0.959873i	$0.409522\pi$
$500$	−3.65902	−0.163636
$501$	22.9484	1.02526
$502$	−33.0687	−1.47593
$503$	−14.3697	−0.640712	−0.320356	−	0.947297i	$-0.603802\pi$
$503$	−14.3697	−0.640712	−0.320356	+	0.947297i	$0.603802\pi$
$504$	0.0521540	0.00232312
$505$	−0.410422	−0.0182635
$506$	−50.8714	−2.26151
$507$	−60.8189	−2.70106
$508$	10.2315	0.453951
$509$	−22.0226	−0.976133	−0.488067	−	0.872806i	$-0.662298\pi$
$509$	−22.0226	−0.976133	−0.488067	+	0.872806i	$0.662298\pi$
$510$	1.56295	0.0692087
$511$	−30.4448	−1.34680
$512$	14.0108	0.619194
$513$	5.18912	0.229105
$514$	1.93813	0.0854875
$515$	0.271895	0.0119811
$516$	4.92960	0.217013
$517$	20.4046	0.897392
$518$	33.1916	1.45836
$519$	−37.2614	−1.63559
$520$	3.34853	0.146843
$521$	−20.4863	−0.897522	−0.448761	−	0.893652i	$-0.648135\pi$
$521$	−20.4863	−0.897522	−0.448761	+	0.893652i	$0.648135\pi$
$522$	−0.113635	−0.00497366
$523$	17.3120	0.757001	0.378500	−	0.925601i	$-0.376440\pi$
$523$	17.3120	0.757001	0.378500	+	0.925601i	$0.376440\pi$
$524$	−8.04740	−0.351552
$525$	−36.3698	−1.58731
$526$	−16.0743	−0.700872
$527$	2.66508	0.116093
$528$	−40.5922	−1.76655
$529$	14.1233	0.614055
$530$	−5.85662	−0.254395
$531$	−0.00161777	−7.02053e−5 0
$532$	−4.93388	−0.213911
$533$	−39.9047	−1.72847
$534$	−52.6723	−2.27935
$535$	−6.24303	−0.269910
$536$	−9.37965	−0.405139
$537$	3.67677	0.158664
$538$	−21.9864	−0.947901
$539$	−53.3131	−2.29636
$540$	1.91846	0.0825574
$541$	31.3341	1.34716	0.673580	−	0.739115i	$-0.264756\pi$
$541$	31.3341	1.34716	0.673580	+	0.739115i	$0.264756\pi$
$542$	−19.2826	−0.828259
$543$	39.5455	1.69706
$544$	9.21522	0.395099
$545$	−4.39978	−0.188466
$546$	−91.4188	−3.91236
$547$	−6.52268	−0.278889	−0.139445	−	0.990230i	$-0.544532\pi$
$547$	−6.52268	−0.278889	−0.139445	+	0.990230i	$0.544532\pi$
$548$	−11.6633	−0.498230
$549$	0.00321221	0.000137094 0
$550$	40.8869	1.74342
$551$	−7.91007	−0.336980
$552$	15.9063	0.677018
$553$	65.4835	2.78464
$554$	8.48371	0.360438
$555$	2.42961	0.103131
$556$	−20.2224	−0.857620
$557$	−14.9294	−0.632579	−0.316289	−	0.948663i	$-0.602437\pi$
$557$	−14.9294	−0.632579	−0.316289	+	0.948663i	$0.602437\pi$
$558$	−0.0242036	−0.00102462
$559$	17.1025	0.723360
$560$	6.83828	0.288970
$561$	−12.9018	−0.544715
$562$	4.58100	0.193238
$563$	−5.60226	−0.236107	−0.118054	−	0.993007i	$-0.537665\pi$
$563$	−5.60226	−0.236107	−0.118054	+	0.993007i	$0.537665\pi$
$564$	8.67074	0.365104
$565$	0.478053	0.0201118
$566$	−25.3293	−1.06467
$567$	38.6430	1.62285
$568$	0.644080	0.0270250
$569$	−20.1627	−0.845266	−0.422633	−	0.906301i	$-0.638894\pi$
$569$	−20.1627	−0.845266	−0.422633	+	0.906301i	$0.638894\pi$
$570$	−0.988061	−0.0413853
$571$	−11.3715	−0.475882	−0.237941	−	0.971280i	$-0.576472\pi$
$571$	−11.3715	−0.475882	−0.237941	+	0.971280i	$0.576472\pi$
$572$	37.5658	1.57070
$573$	20.5164	0.857084
$574$	−43.7594	−1.82648
$575$	−29.8371	−1.24429
$576$	−0.00315097	−0.000131291 0
$577$	−9.91922	−0.412943	−0.206471	−	0.978453i	$-0.566198\pi$
$577$	−9.91922	−0.412943	−0.206471	+	0.978453i	$0.566198\pi$
$578$	−25.7400	−1.07064
$579$	5.20847	0.216457
$580$	−2.92441	−0.121430
$581$	36.1819	1.50108
$582$	−45.6558	−1.89250
$583$	48.3451	2.00225
$584$	−10.7017	−0.442840
$585$	−0.0180002	−0.000744217 0
$586$	−26.6686	−1.10167
$587$	11.9583	0.493572	0.246786	−	0.969070i	$-0.420626\pi$
$587$	11.9583	0.493572	0.246786	+	0.969070i	$0.420626\pi$
$588$	−22.6549	−0.934274
$589$	−1.68480	−0.0694209
$590$	−0.113902	−0.00468927
$591$	−18.6687	−0.767926
$592$	21.7277	0.893002
$593$	−26.7437	−1.09823	−0.549117	−	0.835746i	$-0.685036\pi$
$593$	−26.7437	−1.09823	−0.549117	+	0.835746i	$0.685036\pi$
$594$	−43.3256	−1.77767
$595$	2.17348	0.0891039
$596$	14.6140	0.598614
$597$	26.9794	1.10419
$598$	−74.9983	−3.06691
$599$	−33.5294	−1.36997	−0.684987	−	0.728555i	$-0.740192\pi$
$599$	−33.5294	−1.36997	−0.684987	+	0.728555i	$0.740192\pi$
$600$	−12.7844	−0.521921
$601$	17.7937	0.725822	0.362911	−	0.931824i	$-0.381783\pi$
$601$	17.7937	0.725822	0.362911	+	0.931824i	$0.381783\pi$
$602$	18.7546	0.764380
$603$	0.0504208	0.00205329
$604$	−21.4906	−0.874439
$605$	3.56650	0.144999
$606$	3.93868	0.159998
$607$	−36.4718	−1.48034	−0.740171	−	0.672418i	$-0.765256\pi$
$607$	−36.4718	−1.48034	−0.740171	+	0.672418i	$0.765256\pi$
$608$	−5.82564	−0.236261
$609$	−58.7472	−2.38056
$610$	0.226161	0.00915699
$611$	30.0819	1.21698
$612$	−0.0147473	−0.000596125 0
$613$	4.51026	0.182168	0.0910839	−	0.995843i	$-0.470967\pi$
$613$	4.51026	0.182168	0.0910839	+	0.995843i	$0.470967\pi$
$614$	0.910100	0.0367286
$615$	−3.20317	−0.129164
$616$	−30.3114	−1.22128
$617$	−12.6493	−0.509242	−0.254621	−	0.967041i	$-0.581951\pi$
$617$	−12.6493	−0.509242	−0.254621	+	0.967041i	$0.581951\pi$
$618$	−2.60928	−0.104961
$619$	15.1674	0.609630	0.304815	−	0.952412i	$-0.401405\pi$
$619$	15.1674	0.609630	0.304815	+	0.952412i	$0.401405\pi$
$620$	−0.622883	−0.0250156
$621$	31.6167	1.26874
$622$	4.30272	0.172523
$623$	−73.2473	−2.93459
$624$	−59.8439	−2.39568
$625$	23.4662	0.938649
$626$	51.6144	2.06293
$627$	8.15623	0.325728
$628$	−25.4757	−1.01659
$629$	6.90592	0.275357
$630$	−0.0197390	−0.000786419 0
$631$	7.54874	0.300511	0.150255	−	0.988647i	$-0.451990\pi$
$631$	7.54874	0.300511	0.150255	+	0.988647i	$0.451990\pi$
$632$	23.0182	0.915615
$633$	−31.4379	−1.24955
$634$	−1.77544	−0.0705119
$635$	2.84934	0.113073
$636$	20.5438	0.814616
$637$	−78.5980	−3.11417
$638$	66.0436	2.61469
$639$	−0.00346229	−0.000136966 0
$640$	3.51672	0.139011
$641$	−20.7917	−0.821223	−0.410611	−	0.911810i	$-0.634685\pi$
$641$	−20.7917	−0.821223	−0.410611	+	0.911810i	$0.634685\pi$
$642$	59.9123	2.36455
$643$	−20.7645	−0.818870	−0.409435	−	0.912339i	$-0.634274\pi$
$643$	−20.7645	−0.818870	−0.409435	+	0.912339i	$0.634274\pi$
$644$	−30.0616	−1.18459
$645$	1.37283	0.0540550
$646$	−2.80846	−0.110497
$647$	9.00726	0.354112	0.177056	−	0.984201i	$-0.443343\pi$
$647$	9.00726	0.354112	0.177056	+	0.984201i	$0.443343\pi$
$648$	13.5835	0.533609
$649$	0.940235	0.0369075
$650$	60.2784	2.36431
$651$	−12.5128	−0.490416
$652$	−16.4463	−0.644087
$653$	−9.69384	−0.379349	−0.189675	−	0.981847i	$-0.560743\pi$
$653$	−9.69384	−0.379349	−0.189675	+	0.981847i	$0.560743\pi$
$654$	42.2232	1.65106
$655$	−2.24109	−0.0875668
$656$	−28.6455	−1.11842
$657$	0.0575276	0.00224437
$658$	32.9877	1.28599
$659$	−30.8280	−1.20089	−0.600444	−	0.799667i	$-0.705009\pi$
$659$	−30.8280	−1.20089	−0.600444	+	0.799667i	$0.705009\pi$
$660$	3.01542	0.117375
$661$	6.92463	0.269337	0.134668	−	0.990891i	$-0.457003\pi$
$661$	6.92463	0.269337	0.134668	+	0.990891i	$0.457003\pi$
$662$	39.4300	1.53249
$663$	−19.0208	−0.738707
$664$	12.7183	0.493567
$665$	−1.37402	−0.0532822
$666$	−0.0627178	−0.00243027
$667$	−48.1951	−1.86612
$668$	−15.2452	−0.589856
$669$	−24.3773	−0.942480
$670$	3.54996	0.137147
$671$	−1.86691	−0.0720712
$672$	−43.2664	−1.66904
$673$	−39.0934	−1.50694	−0.753471	−	0.657481i	$-0.771622\pi$
$673$	−39.0934	−1.50694	−0.753471	+	0.657481i	$0.771622\pi$
$674$	5.75592	0.221710
$675$	−25.4113	−0.978083
$676$	40.4036	1.55398
$677$	43.0258	1.65361	0.826807	−	0.562485i	$-0.190155\pi$
$677$	43.0258	1.65361	0.826807	+	0.562485i	$0.190155\pi$
$678$	−4.58772	−0.176190
$679$	−63.4901	−2.43653
$680$	0.764002	0.0292981
$681$	−1.66030	−0.0636227
$682$	14.0669	0.538650
$683$	21.9423	0.839598	0.419799	−	0.907617i	$-0.362101\pi$
$683$	21.9423	0.839598	0.419799	+	0.907617i	$0.362101\pi$
$684$	0.00932291	0.000356470 0
$685$	−3.24806	−0.124102
$686$	−32.9714	−1.25885
$687$	28.7103	1.09536
$688$	12.2770	0.468056
$689$	71.2738	2.71532
$690$	−6.02015	−0.229183
$691$	−19.7157	−0.750019	−0.375010	−	0.927021i	$-0.622361\pi$
$691$	−19.7157	−0.750019	−0.375010	+	0.927021i	$0.622361\pi$
$692$	24.7537	0.940996
$693$	0.162941	0.00618961
$694$	55.7457	2.11608
$695$	−5.63167	−0.213621
$696$	−20.6503	−0.782748
$697$	−9.10468	−0.344864
$698$	−33.7885	−1.27891
$699$	12.0751	0.456720
$700$	24.1614	0.913216
$701$	2.85712	0.107912	0.0539560	−	0.998543i	$-0.482817\pi$
$701$	2.85712	0.107912	0.0539560	+	0.998543i	$0.482817\pi$
$702$	−63.8737	−2.41076
$703$	−4.36576	−0.164658
$704$	1.83132	0.0690204
$705$	2.41469	0.0909424
$706$	51.3525	1.93268
$707$	5.47722	0.205992
$708$	0.399545	0.0150158
$709$	28.2291	1.06016	0.530082	−	0.847946i	$-0.322161\pi$
$709$	28.2291	1.06016	0.530082	+	0.847946i	$0.322161\pi$
$710$	−0.243768	−0.00914846
$711$	−0.123736	−0.00464045
$712$	−25.7473	−0.964919
$713$	−10.2653	−0.384438
$714$	−20.8582	−0.780597
$715$	10.4616	0.391241
$716$	−2.44258	−0.0912833
$717$	−40.5443	−1.51415
$718$	−17.7952	−0.664109
$719$	23.8660	0.890051	0.445026	−	0.895518i	$-0.353195\pi$
$719$	23.8660	0.890051	0.445026	+	0.895518i	$0.353195\pi$
$720$	−0.0129214	−0.000481552 0
$721$	−3.62853	−0.135134
$722$	1.77544	0.0660751
$723$	24.5906	0.914536
$724$	−26.2711	−0.976359
$725$	38.7359	1.43862
$726$	−34.2265	−1.27027
$727$	23.2441	0.862077	0.431038	−	0.902334i	$-0.358147\pi$
$727$	23.2441	0.862077	0.431038	+	0.902334i	$0.358147\pi$
$728$	−44.6873	−1.65622
$729$	26.9268	0.997288
$730$	4.05033	0.149909
$731$	3.90212	0.144325
$732$	−0.793326	−0.0293222
$733$	−22.5886	−0.834329	−0.417164	−	0.908831i	$-0.636976\pi$
$733$	−22.5886	−0.834329	−0.417164	+	0.908831i	$0.636976\pi$
$734$	−64.0047	−2.36246
$735$	−6.30910	−0.232715
$736$	−35.4950	−1.30836
$737$	−29.3042	−1.07943
$738$	0.0826864	0.00304373
$739$	1.52665	0.0561588	0.0280794	−	0.999606i	$-0.491061\pi$
$739$	1.52665	0.0561588	0.0280794	+	0.999606i	$0.491061\pi$
$740$	−1.61406	−0.0593339
$741$	12.0245	0.441731
$742$	78.1587	2.86930
$743$	−17.1098	−0.627697	−0.313848	−	0.949473i	$-0.601618\pi$
$743$	−17.1098	−0.627697	−0.313848	+	0.949473i	$0.601618\pi$
$744$	−4.39840	−0.161253
$745$	4.06981	0.149106
$746$	−29.1043	−1.06558
$747$	−0.0683681	−0.00250146
$748$	8.57103	0.313388
$749$	83.3154	3.04428
$750$	9.77888	0.357074
$751$	12.2998	0.448827	0.224414	−	0.974494i	$-0.427953\pi$
$751$	12.2998	0.448827	0.224414	+	0.974494i	$0.427953\pi$
$752$	21.5942	0.787459
$753$	32.3040	1.17722
$754$	97.3662	3.54587
$755$	−5.98484	−0.217811
$756$	−25.6025	−0.931155
$757$	−47.2976	−1.71906	−0.859530	−	0.511085i	$-0.829244\pi$
$757$	−47.2976	−1.71906	−0.859530	+	0.511085i	$0.829244\pi$
$758$	−68.2792	−2.48001
$759$	49.6950	1.80381
$760$	−0.482984	−0.0175197
$761$	−9.09484	−0.329688	−0.164844	−	0.986320i	$-0.552712\pi$
$761$	−9.09484	−0.329688	−0.164844	+	0.986320i	$0.552712\pi$
$762$	−27.3442	−0.990576
$763$	58.7166	2.12568
$764$	−13.6296	−0.493101
$765$	−0.00410694	−0.000148487 0
$766$	17.6839	0.638947
$767$	1.38616	0.0500514
$768$	−35.0996	−1.26655
$769$	15.5823	0.561914	0.280957	−	0.959720i	$-0.409348\pi$
$769$	15.5823	0.561914	0.280957	+	0.959720i	$0.409348\pi$
$770$	11.4721	0.413427
$771$	−1.89331	−0.0681861
$772$	−3.46013	−0.124533
$773$	−6.08378	−0.218818	−0.109409	−	0.993997i	$-0.534896\pi$
$773$	−6.08378	−0.218818	−0.109409	+	0.993997i	$0.534896\pi$
$774$	−0.0354381	−0.00127380
$775$	8.25053	0.296368
$776$	−22.3175	−0.801151
$777$	−32.4240	−1.16321
$778$	−25.4814	−0.913552
$779$	5.75576	0.206222
$780$	4.44555	0.159176
$781$	2.01225	0.0720041
$782$	−17.1116	−0.611911
$783$	−41.0463	−1.46687
$784$	−56.4214	−2.01505
$785$	−7.09464	−0.253218
$786$	21.5070	0.767131
$787$	−22.8250	−0.813623	−0.406811	−	0.913512i	$-0.633359\pi$
$787$	−22.8250	−0.813623	−0.406811	+	0.913512i	$0.633359\pi$
$788$	12.4021	0.441806
$789$	15.7026	0.559026
$790$	−8.71181	−0.309952
$791$	−6.37978	−0.226839
$792$	0.0572756	0.00203520
$793$	−2.75233	−0.0977381
$794$	44.4587	1.57778
$795$	5.72118	0.202909
$796$	−17.9232	−0.635269
$797$	28.9169	1.02429	0.512145	−	0.858899i	$-0.328851\pi$
$797$	28.9169	1.02429	0.512145	+	0.858899i	$0.328851\pi$
$798$	13.1860	0.466780
$799$	6.86350	0.242813
$800$	28.5284	1.00863
$801$	0.138406	0.00489033
$802$	42.3294	1.49470
$803$	−33.4346	−1.17988
$804$	−12.4525	−0.439167
$805$	−8.37175	−0.295066
$806$	20.7384	0.730480
$807$	21.4779	0.756060
$808$	1.92531	0.0677321
$809$	36.5974	1.28670	0.643348	−	0.765574i	$-0.277545\pi$
$809$	36.5974	1.28670	0.643348	+	0.765574i	$0.277545\pi$
$810$	−5.14100	−0.180636
$811$	−24.8555	−0.872794	−0.436397	−	0.899754i	$-0.643746\pi$
$811$	−24.8555	−0.872794	−0.436397	+	0.899754i	$0.643746\pi$
$812$	39.0273	1.36959
$813$	18.8367	0.660631
$814$	36.4511	1.27761
$815$	−4.58008	−0.160433
$816$	−13.6540	−0.477986
$817$	−2.46683	−0.0863034
$818$	−50.4301	−1.76325
$819$	0.240219	0.00839393
$820$	2.12795	0.0743113
$821$	17.2935	0.603549	0.301774	−	0.953379i	$-0.402421\pi$
$821$	17.2935	0.603549	0.301774	+	0.953379i	$0.402421\pi$
$822$	31.1706	1.08720
$823$	−33.6410	−1.17265	−0.586326	−	0.810075i	$-0.699426\pi$
$823$	−33.6410	−1.17265	−0.586326	+	0.810075i	$0.699426\pi$
$824$	−1.27547	−0.0444331
$825$	−39.9414	−1.39058
$826$	1.52006	0.0528897
$827$	−22.9433	−0.797818	−0.398909	−	0.916991i	$-0.630611\pi$
$827$	−22.9433	−0.797818	−0.398909	+	0.916991i	$0.630611\pi$
$828$	0.0568034	0.00197406
$829$	−35.8524	−1.24521	−0.622603	−	0.782538i	$-0.713925\pi$
$829$	−35.8524	−1.24521	−0.622603	+	0.782538i	$0.713925\pi$
$830$	−4.81358	−0.167082
$831$	−8.28752	−0.287491
$832$	2.69986	0.0936009
$833$	−17.9330	−0.621340
$834$	54.0453	1.87143
$835$	−4.24560	−0.146925
$836$	−5.41840	−0.187399
$837$	−8.74262	−0.302189
$838$	34.6007	1.19526
$839$	−11.7156	−0.404466	−0.202233	−	0.979337i	$-0.564820\pi$
$839$	−11.7156	−0.404466	−0.202233	+	0.979337i	$0.564820\pi$
$840$	−3.58707	−0.123766
$841$	33.5692	1.15756
$842$	−60.6621	−2.09055
$843$	−4.47507	−0.154129
$844$	20.8850	0.718893
$845$	11.2519	0.387076
$846$	−0.0623325	−0.00214304
$847$	−47.5962	−1.63543
$848$	51.1637	1.75697
$849$	24.7436	0.849196
$850$	13.7532	0.471729
$851$	−26.6001	−0.911839
$852$	0.855089	0.0292949
$853$	−30.1645	−1.03281	−0.516407	−	0.856343i	$-0.672731\pi$
$853$	−30.1645	−1.03281	−0.516407	+	0.856343i	$0.672731\pi$
$854$	−3.01820	−0.103281
$855$	0.00259631	8.87918e−5 0
$856$	29.2863	1.00099
$857$	−5.92386	−0.202355	−0.101178	−	0.994868i	$-0.532261\pi$
$857$	−5.92386	−0.202355	−0.101178	+	0.994868i	$0.532261\pi$
$858$	−100.396	−3.42747
$859$	−15.0443	−0.513306	−0.256653	−	0.966504i	$-0.582620\pi$
$859$	−15.0443	−0.513306	−0.256653	+	0.966504i	$0.582620\pi$
$860$	−0.912006	−0.0310992
$861$	42.7474	1.45683
$862$	−5.55889	−0.189336
$863$	7.75140	0.263861	0.131930	−	0.991259i	$-0.457882\pi$
$863$	7.75140	0.263861	0.131930	+	0.991259i	$0.457882\pi$
$864$	−30.2300	−1.02844
$865$	6.89359	0.234389
$866$	58.1449	1.97584
$867$	25.1448	0.853961
$868$	8.31260	0.282148
$869$	71.9141	2.43952
$870$	7.81563	0.264975
$871$	−43.2023	−1.46385
$872$	20.6395	0.698943
$873$	0.119969	0.00406033
$874$	10.8176	0.365910
$875$	13.5987	0.459721
$876$	−14.2077	−0.480034
$877$	−1.38905	−0.0469050	−0.0234525	−	0.999725i	$-0.507466\pi$
$877$	−1.38905	−0.0469050	−0.0234525	+	0.999725i	$0.507466\pi$
$878$	1.45225	0.0490109
$879$	26.0519	0.878707
$880$	7.50981	0.253156
$881$	35.6276	1.20032	0.600162	−	0.799878i	$-0.295103\pi$
$881$	35.6276	1.20032	0.600162	+	0.799878i	$0.295103\pi$
$882$	0.162863	0.00548387
$883$	−49.7436	−1.67401	−0.837003	−	0.547198i	$-0.815695\pi$
$883$	−49.7436	−1.67401	−0.837003	+	0.547198i	$0.815695\pi$
$884$	12.6360	0.424995
$885$	0.111268	0.00374023
$886$	34.1010	1.14565
$887$	−34.1933	−1.14810	−0.574049	−	0.818821i	$-0.694628\pi$
$887$	−34.1933	−1.14810	−0.574049	+	0.818821i	$0.694628\pi$
$888$	−11.3974	−0.382472
$889$	−38.0255	−1.27533
$890$	9.74469	0.326643
$891$	42.4378	1.42172
$892$	16.1945	0.542231
$893$	−4.33894	−0.145197
$894$	−39.0566	−1.30625
$895$	−0.680225	−0.0227374
$896$	−46.9319	−1.56788
$897$	73.2639	2.44621
$898$	58.3209	1.94619
$899$	13.3269	0.444476
$900$	−0.0456547	−0.00152182
$901$	16.2619	0.541762
$902$	−48.0567	−1.60011
$903$	−18.3209	−0.609680
$904$	−2.24257	−0.0745867
$905$	−7.31616	−0.243198
$906$	57.4345	1.90813
$907$	37.1044	1.23203	0.616015	−	0.787734i	$-0.288746\pi$
$907$	37.1044	1.23203	0.616015	+	0.787734i	$0.288746\pi$
$908$	1.10298	0.0366037
$909$	−0.0103496	−0.000343274 0
$910$	16.9130	0.560662
$911$	49.3399	1.63470	0.817352	−	0.576139i	$-0.195441\pi$
$911$	49.3399	1.63470	0.817352	+	0.576139i	$0.195441\pi$
$912$	8.63175	0.285826
$913$	39.7350	1.31504
$914$	34.7823	1.15050
$915$	−0.220931	−0.00730375
$916$	−19.0730	−0.630189
$917$	29.9082	0.987656
$918$	−14.5735	−0.480996
$919$	−6.20438	−0.204664	−0.102332	−	0.994750i	$-0.532630\pi$
$919$	−6.20438	−0.204664	−0.102332	+	0.994750i	$0.532630\pi$
$920$	−2.94277	−0.0970202
$921$	−0.889053	−0.0292953
$922$	40.9736	1.34939
$923$	2.96661	0.0976471
$924$	−40.2419	−1.32386
$925$	21.3793	0.702947
$926$	63.7164	2.09385
$927$	0.00685636	0.000225192 0
$928$	46.0812	1.51269
$929$	8.17643	0.268260	0.134130	−	0.990964i	$-0.457176\pi$
$929$	8.17643	0.268260	0.134130	+	0.990964i	$0.457176\pi$
$930$	1.66468	0.0545872
$931$	11.3368	0.371548
$932$	−8.02178	−0.262762
$933$	−4.20321	−0.137607
$934$	−27.2856	−0.892812
$935$	2.38692	0.0780605
$936$	0.0844397	0.00276000
$937$	18.0800	0.590647	0.295324	−	0.955397i	$-0.404573\pi$
$937$	18.0800	0.590647	0.295324	+	0.955397i	$0.404573\pi$
$938$	−47.3755	−1.54687
$939$	−50.4208	−1.64542
$940$	−1.60414	−0.0523213
$941$	−31.9490	−1.04151	−0.520754	−	0.853707i	$-0.674349\pi$
$941$	−31.9490	−1.04151	−0.520754	+	0.853707i	$0.674349\pi$
$942$	68.0849	2.21833
$943$	35.0692	1.14201
$944$	0.995052	0.0323862
$945$	−7.12996	−0.231938
$946$	20.5963	0.669644
$947$	−45.9496	−1.49316	−0.746581	−	0.665295i	$-0.768306\pi$
$947$	−45.9496	−1.49316	−0.746581	+	0.665295i	$0.768306\pi$
$948$	30.5593	0.992519
$949$	−49.2916	−1.60007
$950$	−8.69442	−0.282084
$951$	1.73439	0.0562413
$952$	−10.1959	−0.330450
$953$	3.22191	0.104368	0.0521840	−	0.998637i	$-0.483382\pi$
$953$	3.22191	0.104368	0.0521840	+	0.998637i	$0.483382\pi$
$954$	−0.147686	−0.00478152
$955$	−3.79566	−0.122825
$956$	26.9346	0.871128
$957$	−64.5163	−2.08552
$958$	−73.9063	−2.38780
$959$	43.3466	1.39973
$960$	0.216719	0.00699458
$961$	−28.1615	−0.908434
$962$	53.7388	1.73261
$963$	−0.157430	−0.00507312
$964$	−16.3362	−0.526154
$965$	−0.963600	−0.0310194
$966$	80.3410	2.58493
$967$	−30.4531	−0.979306	−0.489653	−	0.871917i	$-0.662877\pi$
$967$	−30.4531	−0.979306	−0.489653	+	0.871917i	$0.662877\pi$
$968$	−16.7306	−0.537742
$969$	2.74351	0.0881344
$970$	8.44661	0.271204
$971$	12.2347	0.392629	0.196315	−	0.980541i	$-0.437103\pi$
$971$	12.2347	0.392629	0.196315	+	0.980541i	$0.437103\pi$
$972$	0.0968863	0.00310763
$973$	75.1566	2.40941
$974$	−46.0940	−1.47695
$975$	−58.8845	−1.88581
$976$	−1.97575	−0.0632423
$977$	4.83637	0.154729	0.0773646	−	0.997003i	$-0.475349\pi$
$977$	4.83637	0.154729	0.0773646	+	0.997003i	$0.475349\pi$
$978$	43.9535	1.40548
$979$	−80.4403	−2.57088
$980$	4.19130	0.133886
$981$	−0.110949	−0.00354233
$982$	27.4579	0.876217
$983$	35.7117	1.13903	0.569513	−	0.821983i	$-0.307132\pi$
$983$	35.7117	1.13903	0.569513	+	0.821983i	$0.307132\pi$
$984$	15.0262	0.479018
$985$	3.45382	0.110048
$986$	22.2151	0.707474
$987$	−32.2248	−1.02573
$988$	−7.98819	−0.254138
$989$	−15.0301	−0.477930
$990$	−0.0216774	−0.000688952 0
$991$	−17.1318	−0.544209	−0.272104	−	0.962268i	$-0.587720\pi$
$991$	−17.1318	−0.544209	−0.272104	+	0.962268i	$0.587720\pi$
$992$	9.81503	0.311628
$993$	−38.5182	−1.22234
$994$	3.25317	0.103184
$995$	−4.99136	−0.158237
$996$	16.8850	0.535023
$997$	50.7157	1.60618	0.803092	−	0.595855i	$-0.203187\pi$
$997$	50.7157	1.60618	0.803092	+	0.595855i	$0.203187\pi$
$998$	22.2442	0.704129
$999$	−22.6545	−0.716755

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.106	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.106	✓	138	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q+1.77544 q^{2} -1.73439 q^{3} +1.15220 q^{4} +0.320872 q^{5} -3.07930 q^{6} -4.28215 q^{7} -1.50522 q^{8} +0.00809141 q^{9} +O(q^{10})\)	\(q+1.77544 q^{2} -1.73439 q^{3} +1.15220 q^{4} +0.320872 q^{5} -3.07930 q^{6} -4.28215 q^{7} -1.50522 q^{8} +0.00809141 q^{9} +0.569690 q^{10} -4.70266 q^{11} -1.99836 q^{12} -6.93300 q^{13} -7.60271 q^{14} -0.556515 q^{15} -4.97684 q^{16} -1.58184 q^{17} +0.0143658 q^{18} +1.00000 q^{19} +0.369708 q^{20} +7.42689 q^{21} -8.34931 q^{22} +6.09289 q^{23} +2.61064 q^{24} -4.89704 q^{25} -12.3092 q^{26} +5.18912 q^{27} -4.93388 q^{28} -7.91007 q^{29} -0.988061 q^{30} -1.68480 q^{31} -5.82564 q^{32} +8.15623 q^{33} -2.80846 q^{34} -1.37402 q^{35} +0.00932291 q^{36} -4.36576 q^{37} +1.77544 q^{38} +12.0245 q^{39} -0.482984 q^{40} +5.75576 q^{41} +13.1860 q^{42} -2.46683 q^{43} -5.41840 q^{44} +0.00259631 q^{45} +10.8176 q^{46} -4.33894 q^{47} +8.63175 q^{48} +11.3368 q^{49} -8.69442 q^{50} +2.74351 q^{51} -7.98819 q^{52} -10.2804 q^{53} +9.21299 q^{54} -1.50895 q^{55} +6.44559 q^{56} -1.73439 q^{57} -14.0439 q^{58} -0.199937 q^{59} -0.641216 q^{60} +0.396990 q^{61} -2.99126 q^{62} -0.0346486 q^{63} -0.389422 q^{64} -2.22461 q^{65} +14.4809 q^{66} +6.23140 q^{67} -1.82259 q^{68} -10.5674 q^{69} -2.43950 q^{70} -0.427896 q^{71} -0.0121794 q^{72} +7.10971 q^{73} -7.75116 q^{74} +8.49335 q^{75} +1.15220 q^{76} +20.1375 q^{77} +21.3488 q^{78} -15.2922 q^{79} -1.59693 q^{80} -9.02421 q^{81} +10.2190 q^{82} -8.44947 q^{83} +8.55725 q^{84} -0.507567 q^{85} -4.37971 q^{86} +13.7191 q^{87} +7.07856 q^{88} +17.1053 q^{89} +0.00460960 q^{90} +29.6881 q^{91} +7.02021 q^{92} +2.92209 q^{93} -7.70354 q^{94} +0.320872 q^{95} +10.1039 q^{96} +14.8267 q^{97} +20.1278 q^{98} -0.0380512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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