LMFDB - Embedded newform 8021.2.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39849 q^{2} +2.44398 q^{3} +3.75277 q^{4} -3.07733 q^{5} -5.86187 q^{6} +3.93094 q^{7} -4.20400 q^{8} +2.97305 q^{9} +O(q^{10})$	\(q-2.39849 q^{2} +2.44398 q^{3} +3.75277 q^{4} -3.07733 q^{5} -5.86187 q^{6} +3.93094 q^{7} -4.20400 q^{8} +2.97305 q^{9} +7.38096 q^{10} -3.84902 q^{11} +9.17169 q^{12} +1.00000 q^{13} -9.42833 q^{14} -7.52095 q^{15} +2.57772 q^{16} +2.52034 q^{17} -7.13084 q^{18} -0.852482 q^{19} -11.5485 q^{20} +9.60714 q^{21} +9.23185 q^{22} +0.964453 q^{23} -10.2745 q^{24} +4.46999 q^{25} -2.39849 q^{26} -0.0658687 q^{27} +14.7519 q^{28} +5.17548 q^{29} +18.0389 q^{30} +5.71398 q^{31} +2.22534 q^{32} -9.40694 q^{33} -6.04501 q^{34} -12.0968 q^{35} +11.1572 q^{36} +10.2790 q^{37} +2.04467 q^{38} +2.44398 q^{39} +12.9371 q^{40} +6.54877 q^{41} -23.0427 q^{42} +2.99731 q^{43} -14.4445 q^{44} -9.14906 q^{45} -2.31323 q^{46} -9.73042 q^{47} +6.29991 q^{48} +8.45228 q^{49} -10.7212 q^{50} +6.15966 q^{51} +3.75277 q^{52} -0.00793395 q^{53} +0.157986 q^{54} +11.8447 q^{55} -16.5257 q^{56} -2.08345 q^{57} -12.4133 q^{58} -10.2313 q^{59} -28.2244 q^{60} +7.78575 q^{61} -13.7049 q^{62} +11.6869 q^{63} -10.4929 q^{64} -3.07733 q^{65} +22.5625 q^{66} -3.23411 q^{67} +9.45824 q^{68} +2.35711 q^{69} +29.0141 q^{70} -6.48975 q^{71} -12.4987 q^{72} +7.30201 q^{73} -24.6540 q^{74} +10.9246 q^{75} -3.19916 q^{76} -15.1303 q^{77} -5.86187 q^{78} -14.2361 q^{79} -7.93252 q^{80} -9.08013 q^{81} -15.7072 q^{82} -5.48460 q^{83} +36.0534 q^{84} -7.75592 q^{85} -7.18902 q^{86} +12.6488 q^{87} +16.1813 q^{88} -15.2511 q^{89} +21.9440 q^{90} +3.93094 q^{91} +3.61937 q^{92} +13.9649 q^{93} +23.3383 q^{94} +2.62337 q^{95} +5.43870 q^{96} +4.52055 q^{97} -20.2727 q^{98} -11.4433 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) $ 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * 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 $

$2$	−2.39849	−1.69599	−0.847995	−	0.530004i	$-0.822190\pi$
$2$	−2.39849	−1.69599	−0.847995	+	0.530004i	$0.822190\pi$
$3$	2.44398	1.41103	0.705517	−	0.708693i	$-0.250715\pi$
$3$	2.44398	1.41103	0.705517	+	0.708693i	$0.250715\pi$
$4$	3.75277	1.87638
$5$	−3.07733	−1.37623	−0.688113	−	0.725604i	$-0.741561\pi$
$5$	−3.07733	−1.37623	−0.688113	+	0.725604i	$0.741561\pi$
$6$	−5.86187	−2.39310
$7$	3.93094	1.48576	0.742878	−	0.669427i	$-0.233460\pi$
$7$	3.93094	1.48576	0.742878	+	0.669427i	$0.233460\pi$
$8$	−4.20400	−1.48634
$9$	2.97305	0.991016
$10$	7.38096	2.33407
$11$	−3.84902	−1.16052	−0.580262	−	0.814430i	$-0.697050\pi$
$11$	−3.84902	−1.16052	−0.580262	+	0.814430i	$0.697050\pi$
$12$	9.17169	2.64764
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−9.42833	−2.51983
$15$	−7.52095	−1.94190
$16$	2.57772	0.644431
$17$	2.52034	0.611272	0.305636	−	0.952148i	$-0.401131\pi$
$17$	2.52034	0.611272	0.305636	+	0.952148i	$0.401131\pi$
$18$	−7.13084	−1.68075
$19$	−0.852482	−0.195573	−0.0977864	−	0.995207i	$-0.531176\pi$
$19$	−0.852482	−0.195573	−0.0977864	+	0.995207i	$0.531176\pi$
$20$	−11.5485	−2.58233
$21$	9.60714	2.09645
$22$	9.23185	1.96824
$23$	0.964453	0.201102	0.100551	−	0.994932i	$-0.467939\pi$
$23$	0.964453	0.201102	0.100551	+	0.994932i	$0.467939\pi$
$24$	−10.2745	−2.09727
$25$	4.46999	0.893997
$26$	−2.39849	−0.470383
$27$	−0.0658687	−0.0126764
$28$	14.7519	2.78785
$29$	5.17548	0.961062	0.480531	−	0.876978i	$-0.340444\pi$
$29$	5.17548	0.961062	0.480531	+	0.876978i	$0.340444\pi$
$30$	18.0389	3.29345
$31$	5.71398	1.02626	0.513130	−	0.858311i	$-0.328486\pi$
$31$	5.71398	1.02626	0.513130	+	0.858311i	$0.328486\pi$
$32$	2.22534	0.393389
$33$	−9.40694	−1.63754
$34$	−6.04501	−1.03671
$35$	−12.0968	−2.04473
$36$	11.1572	1.85953
$37$	10.2790	1.68985	0.844925	−	0.534885i	$-0.179645\pi$
$37$	10.2790	1.68985	0.844925	+	0.534885i	$0.179645\pi$
$38$	2.04467	0.331689
$39$	2.44398	0.391350
$40$	12.9371	2.04554
$41$	6.54877	1.02275	0.511373	−	0.859359i	$-0.329137\pi$
$41$	6.54877	1.02275	0.511373	+	0.859359i	$0.329137\pi$
$42$	−23.0427	−3.55556
$43$	2.99731	0.457085	0.228543	−	0.973534i	$-0.426604\pi$
$43$	2.99731	0.457085	0.228543	+	0.973534i	$0.426604\pi$
$44$	−14.4445	−2.17759
$45$	−9.14906	−1.36386
$46$	−2.31323	−0.341068
$47$	−9.73042	−1.41933	−0.709664	−	0.704541i	$-0.751153\pi$
$47$	−9.73042	−1.41933	−0.709664	+	0.704541i	$0.751153\pi$
$48$	6.29991	0.909314
$49$	8.45228	1.20747
$50$	−10.7212	−1.51621
$51$	6.15966	0.862525
$52$	3.75277	0.520415
$53$	−0.00793395	−0.00108981	−0.000544906	−	1.00000i	$-0.500173\pi$
$53$	−0.00793395	−0.00108981	−0.000544906		1.00000i	$0.500173\pi$
$54$	0.157986	0.0214991
$55$	11.8447	1.59714
$56$	−16.5257	−2.20833
$57$	−2.08345	−0.275960
$58$	−12.4133	−1.62995
$59$	−10.2313	−1.33200	−0.666001	−	0.745951i	$-0.731995\pi$
$59$	−10.2313	−1.33200	−0.666001	+	0.745951i	$0.731995\pi$
$60$	−28.2244	−3.64375
$61$	7.78575	0.996864	0.498432	−	0.866929i	$-0.333909\pi$
$61$	7.78575	0.996864	0.498432	+	0.866929i	$0.333909\pi$
$62$	−13.7049	−1.74053
$63$	11.6869	1.47241
$64$	−10.4929	−1.31161
$65$	−3.07733	−0.381696
$66$	22.5625	2.77725
$67$	−3.23411	−0.395109	−0.197555	−	0.980292i	$-0.563300\pi$
$67$	−3.23411	−0.395109	−0.197555	+	0.980292i	$0.563300\pi$
$68$	9.45824	1.14698
$69$	2.35711	0.283762
$70$	29.0141	3.46785
$71$	−6.48975	−0.770192	−0.385096	−	0.922877i	$-0.625832\pi$
$71$	−6.48975	−0.770192	−0.385096	+	0.922877i	$0.625832\pi$
$72$	−12.4987	−1.47298
$73$	7.30201	0.854635	0.427318	−	0.904102i	$-0.359459\pi$
$73$	7.30201	0.854635	0.427318	+	0.904102i	$0.359459\pi$
$74$	−24.6540	−2.86597
$75$	10.9246	1.26146
$76$	−3.19916	−0.366969
$77$	−15.1303	−1.72425
$78$	−5.86187	−0.663726
$79$	−14.2361	−1.60169	−0.800843	−	0.598875i	$-0.795615\pi$
$79$	−14.2361	−1.60169	−0.800843	+	0.598875i	$0.795615\pi$
$80$	−7.93252	−0.886883
$81$	−9.08013	−1.00890
$82$	−15.7072	−1.73457
$83$	−5.48460	−0.602013	−0.301006	−	0.953622i	$-0.597323\pi$
$83$	−5.48460	−0.602013	−0.301006	+	0.953622i	$0.597323\pi$
$84$	36.0534	3.93375
$85$	−7.75592	−0.841248
$86$	−7.18902	−0.775212
$87$	12.6488	1.35609
$88$	16.1813	1.72493
$89$	−15.2511	−1.61661	−0.808307	−	0.588762i	$-0.799616\pi$
$89$	−15.2511	−1.61661	−0.808307	+	0.588762i	$0.799616\pi$
$90$	21.9440	2.31310
$91$	3.93094	0.412074
$92$	3.61937	0.377345
$93$	13.9649	1.44809
$94$	23.3383	2.40717
$95$	2.62337	0.269152
$96$	5.43870	0.555085
$97$	4.52055	0.458993	0.229496	−	0.973310i	$-0.426292\pi$
$97$	4.52055	0.458993	0.229496	+	0.973310i	$0.426292\pi$
$98$	−20.2727	−2.04786
$99$	−11.4433	−1.15010
$100$	16.7748	1.67748
$101$	15.2849	1.52091	0.760454	−	0.649392i	$-0.224976\pi$
$101$	15.2849	1.52091	0.760454	+	0.649392i	$0.224976\pi$
$102$	−14.7739	−1.46283
$103$	−0.901971	−0.0888739	−0.0444369	−	0.999012i	$-0.514149\pi$
$103$	−0.901971	−0.0888739	−0.0444369	+	0.999012i	$0.514149\pi$
$104$	−4.20400	−0.412236
$105$	−29.5644	−2.88519
$106$	0.0190295	0.00184831
$107$	14.2277	1.37545	0.687723	−	0.725973i	$-0.258611\pi$
$107$	14.2277	1.37545	0.687723	+	0.725973i	$0.258611\pi$
$108$	−0.247190	−0.0237859
$109$	−15.8764	−1.52068	−0.760339	−	0.649526i	$-0.774967\pi$
$109$	−15.8764	−1.52068	−0.760339	+	0.649526i	$0.774967\pi$
$110$	−28.4095	−2.70874
$111$	25.1216	2.38443
$112$	10.1329	0.957467
$113$	6.53416	0.614682	0.307341	−	0.951599i	$-0.400561\pi$
$113$	6.53416	0.614682	0.307341	+	0.951599i	$0.400561\pi$
$114$	4.99714	0.468025
$115$	−2.96794	−0.276762
$116$	19.4224	1.80332
$117$	2.97305	0.274858
$118$	24.5397	2.25906
$119$	9.90729	0.908200
$120$	31.6181	2.88632
$121$	3.81495	0.346814
$122$	−18.6741	−1.69067
$123$	16.0051	1.44313
$124$	21.4432	1.92566
$125$	1.63103	0.145884
$126$	−28.0309	−2.49719
$127$	15.0761	1.33778	0.668892	−	0.743360i	$-0.266769\pi$
$127$	15.0761	1.33778	0.668892	+	0.743360i	$0.266769\pi$
$128$	20.7165	1.83110
$129$	7.32537	0.644963
$130$	7.38096	0.647353
$131$	21.1064	1.84407	0.922036	−	0.387105i	$-0.126525\pi$
$131$	21.1064	1.84407	0.922036	+	0.387105i	$0.126525\pi$
$132$	−35.3020	−3.07265
$133$	−3.35105	−0.290573
$134$	7.75699	0.670102
$135$	0.202700	0.0174456
$136$	−10.5955	−0.908556
$137$	−1.44821	−0.123729	−0.0618647	−	0.998085i	$-0.519705\pi$
$137$	−1.44821	−0.123729	−0.0618647	+	0.998085i	$0.519705\pi$
$138$	−5.65350	−0.481258
$139$	11.0909	0.940716	0.470358	−	0.882476i	$-0.344125\pi$
$139$	11.0909	0.940716	0.470358	+	0.882476i	$0.344125\pi$
$140$	−45.3965	−3.83671
$141$	−23.7810	−2.00272
$142$	15.5656	1.30624
$143$	−3.84902	−0.321871
$144$	7.66370	0.638642
$145$	−15.9267	−1.32264
$146$	−17.5138	−1.44945
$147$	20.6572	1.70378
$148$	38.5745	3.17081
$149$	1.10840	0.0908038	0.0454019	−	0.998969i	$-0.485543\pi$
$149$	1.10840	0.0908038	0.0454019	+	0.998969i	$0.485543\pi$
$150$	−26.2025	−2.13942
$151$	−16.2839	−1.32517	−0.662583	−	0.748988i	$-0.730540\pi$
$151$	−16.2839	−1.32517	−0.662583	+	0.748988i	$0.730540\pi$
$152$	3.58383	0.290687
$153$	7.49309	0.605780
$154$	36.2898	2.92432
$155$	−17.5838	−1.41237
$156$	9.17169	0.734323
$157$	6.52134	0.520460	0.260230	−	0.965547i	$-0.416202\pi$
$157$	6.52134	0.520460	0.260230	+	0.965547i	$0.416202\pi$
$158$	34.1452	2.71644
$159$	−0.0193904	−0.00153776
$160$	−6.84812	−0.541392
$161$	3.79121	0.298789
$162$	21.7786	1.71109
$163$	−15.6027	−1.22210	−0.611049	−	0.791593i	$-0.709252\pi$
$163$	−15.6027	−1.22210	−0.611049	+	0.791593i	$0.709252\pi$
$164$	24.5760	1.91906
$165$	28.9483	2.25362
$166$	13.1548	1.02101
$167$	−8.98580	−0.695342	−0.347671	−	0.937617i	$-0.613027\pi$
$167$	−8.98580	−0.695342	−0.347671	+	0.937617i	$0.613027\pi$
$168$	−40.3884	−3.11603
$169$	1.00000	0.0769231
$170$	18.6025	1.42675
$171$	−2.53447	−0.193816
$172$	11.2482	0.857667
$173$	−0.111503	−0.00847740	−0.00423870	−	0.999991i	$-0.501349\pi$
$173$	−0.111503	−0.00847740	−0.00423870	+	0.999991i	$0.501349\pi$
$174$	−30.3380	−2.29992
$175$	17.5712	1.32826
$176$	−9.92171	−0.747877
$177$	−25.0051	−1.87950
$178$	36.5797	2.74176
$179$	−7.23190	−0.540538	−0.270269	−	0.962785i	$-0.587113\pi$
$179$	−7.23190	−0.540538	−0.270269	+	0.962785i	$0.587113\pi$
$180$	−34.3343	−2.55913
$181$	13.5693	1.00860	0.504298	−	0.863530i	$-0.331751\pi$
$181$	13.5693	1.00860	0.504298	+	0.863530i	$0.331751\pi$
$182$	−9.42833	−0.698874
$183$	19.0282	1.40661
$184$	−4.05456	−0.298906
$185$	−31.6318	−2.32561
$186$	−33.4946	−2.45594
$187$	−9.70083	−0.709395
$188$	−36.5160	−2.66320
$189$	−0.258926	−0.0188341
$190$	−6.29214	−0.456480
$191$	−4.69042	−0.339387	−0.169694	−	0.985497i	$-0.554278\pi$
$191$	−4.69042	−0.339387	−0.169694	+	0.985497i	$0.554278\pi$
$192$	−25.6445	−1.85073
$193$	−2.89621	−0.208474	−0.104237	−	0.994553i	$-0.533240\pi$
$193$	−2.89621	−0.208474	−0.104237	+	0.994553i	$0.533240\pi$
$194$	−10.8425	−0.778447
$195$	−7.52095	−0.538586
$196$	31.7194	2.26567
$197$	22.8885	1.63074	0.815368	−	0.578944i	$-0.196535\pi$
$197$	22.8885	1.63074	0.815368	+	0.578944i	$0.196535\pi$
$198$	27.4467	1.95055
$199$	10.2917	0.729557	0.364778	−	0.931094i	$-0.381145\pi$
$199$	10.2917	0.729557	0.364778	+	0.931094i	$0.381145\pi$
$200$	−18.7918	−1.32878
$201$	−7.90410	−0.557513
$202$	−36.6608	−2.57945
$203$	20.3445	1.42790
$204$	23.1158	1.61843
$205$	−20.1528	−1.40753
$206$	2.16337	0.150729
$207$	2.86737	0.199296
$208$	2.57772	0.178733
$209$	3.28122	0.226967
$210$	70.9100	4.89325
$211$	−7.43852	−0.512089	−0.256044	−	0.966665i	$-0.582419\pi$
$211$	−7.43852	−0.512089	−0.256044	+	0.966665i	$0.582419\pi$
$212$	−0.0297742	−0.00204490
$213$	−15.8608	−1.08677
$214$	−34.1251	−2.33274
$215$	−9.22372	−0.629053
$216$	0.276912	0.0188415
$217$	22.4613	1.52477
$218$	38.0793	2.57906
$219$	17.8460	1.20592
$220$	44.4505	2.99685
$221$	2.52034	0.169536
$222$	−60.2539	−4.04398
$223$	11.4142	0.764351	0.382176	−	0.924090i	$-0.375175\pi$
$223$	11.4142	0.764351	0.382176	+	0.924090i	$0.375175\pi$
$224$	8.74769	0.584479
$225$	13.2895	0.885966
$226$	−15.6721	−1.04250
$227$	28.9383	1.92070	0.960352	−	0.278791i	$-0.0899335\pi$
$227$	28.9383	1.92070	0.960352	+	0.278791i	$0.0899335\pi$
$228$	−7.81870	−0.517806
$229$	−21.5560	−1.42446	−0.712229	−	0.701948i	$-0.752314\pi$
$229$	−21.5560	−1.42446	−0.712229	+	0.701948i	$0.752314\pi$
$230$	7.11859	0.469386
$231$	−36.9781	−2.43298
$232$	−21.7577	−1.42846
$233$	17.1574	1.12402	0.562010	−	0.827130i	$-0.310028\pi$
$233$	17.1574	1.12402	0.562010	+	0.827130i	$0.310028\pi$
$234$	−7.13084	−0.466157
$235$	29.9437	1.95331
$236$	−38.3957	−2.49935
$237$	−34.7927	−2.26003
$238$	−23.7626	−1.54030
$239$	26.3979	1.70754	0.853769	−	0.520653i	$-0.174311\pi$
$239$	26.3979	1.70754	0.853769	+	0.520653i	$0.174311\pi$
$240$	−19.3869	−1.25142
$241$	−13.4642	−0.867308	−0.433654	−	0.901079i	$-0.642776\pi$
$241$	−13.4642	−0.867308	−0.433654	+	0.901079i	$0.642776\pi$
$242$	−9.15014	−0.588193
$243$	−21.9941	−1.41092
$244$	29.2181	1.87050
$245$	−26.0105	−1.66175
$246$	−38.3881	−2.44753
$247$	−0.852482	−0.0542421
$248$	−24.0216	−1.52537
$249$	−13.4043	−0.849460
$250$	−3.91201	−0.247417
$251$	−8.31788	−0.525020	−0.262510	−	0.964929i	$-0.584550\pi$
$251$	−8.31788	−0.525020	−0.262510	+	0.964929i	$0.584550\pi$
$252$	43.8581	2.76280
$253$	−3.71220	−0.233384
$254$	−36.1598	−2.26887
$255$	−18.9553	−1.18703
$256$	−28.7025	−1.79391
$257$	−11.8677	−0.740289	−0.370145	−	0.928974i	$-0.620692\pi$
$257$	−11.8677	−0.740289	−0.370145	+	0.928974i	$0.620692\pi$
$258$	−17.5698	−1.09385
$259$	40.4059	2.51070
$260$	−11.5485	−0.716209
$261$	15.3869	0.952428
$262$	−50.6235	−3.12753
$263$	15.8418	0.976846	0.488423	−	0.872607i	$-0.337572\pi$
$263$	15.8418	0.976846	0.488423	+	0.872607i	$0.337572\pi$
$264$	39.5467	2.43393
$265$	0.0244154	0.00149983
$266$	8.03748	0.492809
$267$	−37.2734	−2.28110
$268$	−12.1369	−0.741376
$269$	12.1837	0.742851	0.371425	−	0.928463i	$-0.378869\pi$
$269$	12.1837	0.742851	0.371425	+	0.928463i	$0.378869\pi$
$270$	−0.486174	−0.0295876
$271$	25.6906	1.56059	0.780295	−	0.625411i	$-0.215069\pi$
$271$	25.6906	1.56059	0.780295	+	0.625411i	$0.215069\pi$
$272$	6.49674	0.393922
$273$	9.60714	0.581451
$274$	3.47353	0.209844
$275$	−17.2051	−1.03750
$276$	8.84567	0.532447
$277$	8.26900	0.496836	0.248418	−	0.968653i	$-0.420089\pi$
$277$	8.26900	0.496836	0.248418	+	0.968653i	$0.420089\pi$
$278$	−26.6014	−1.59544
$279$	16.9879	1.01704
$280$	50.8550	3.03917
$281$	−5.89540	−0.351690	−0.175845	−	0.984418i	$-0.556266\pi$
$281$	−5.89540	−0.351690	−0.175845	+	0.984418i	$0.556266\pi$
$282$	57.0385	3.39659
$283$	2.63425	0.156590	0.0782950	−	0.996930i	$-0.475052\pi$
$283$	2.63425	0.156590	0.0782950	+	0.996930i	$0.475052\pi$
$284$	−24.3545	−1.44517
$285$	6.41147	0.379783
$286$	9.23185	0.545890
$287$	25.7428	1.51955
$288$	6.61605	0.389855
$289$	−10.6479	−0.626347
$290$	38.2000	2.24318
$291$	11.0481	0.647654
$292$	27.4027	1.60362
$293$	−20.3120	−1.18664	−0.593321	−	0.804966i	$-0.702184\pi$
$293$	−20.3120	−1.18664	−0.593321	+	0.804966i	$0.702184\pi$
$294$	−49.5462	−2.88959
$295$	31.4851	1.83313
$296$	−43.2127	−2.51169
$297$	0.253530	0.0147113
$298$	−2.65849	−0.154002
$299$	0.964453	0.0557758
$300$	40.9974	2.36698
$301$	11.7822	0.679117
$302$	39.0569	2.24747
$303$	37.3561	2.14605
$304$	−2.19746	−0.126033
$305$	−23.9594	−1.37191
$306$	−17.9721	−1.02740
$307$	6.68064	0.381284	0.190642	−	0.981660i	$-0.438943\pi$
$307$	6.68064	0.381284	0.190642	+	0.981660i	$0.438943\pi$
$308$	−56.7803	−3.23536
$309$	−2.20440	−0.125404
$310$	42.1747	2.39536
$311$	12.1096	0.686675	0.343337	−	0.939212i	$-0.388443\pi$
$311$	12.1096	0.686675	0.343337	+	0.939212i	$0.388443\pi$
$312$	−10.2745	−0.581679
$313$	18.7612	1.06045	0.530224	−	0.847858i	$-0.322108\pi$
$313$	18.7612	1.06045	0.530224	+	0.847858i	$0.322108\pi$
$314$	−15.6414	−0.882694
$315$	−35.9644	−2.02637
$316$	−53.4247	−3.00538
$317$	9.33996	0.524584	0.262292	−	0.964988i	$-0.415522\pi$
$317$	9.33996	0.524584	0.262292	+	0.964988i	$0.415522\pi$
$318$	0.0465078	0.00260803
$319$	−19.9205	−1.11533
$320$	32.2902	1.80508
$321$	34.7723	1.94080
$322$	−9.09318	−0.506743
$323$	−2.14854	−0.119548
$324$	−34.0756	−1.89309
$325$	4.46999	0.247950
$326$	37.4230	2.07267
$327$	−38.8015	−2.14573
$328$	−27.5310	−1.52015
$329$	−38.2497	−2.10877
$330$	−69.4322	−3.82212
$331$	−3.11387	−0.171154	−0.0855770	−	0.996332i	$-0.527273\pi$
$331$	−3.11387	−0.171154	−0.0855770	+	0.996332i	$0.527273\pi$
$332$	−20.5824	−1.12961
$333$	30.5598	1.67467
$334$	21.5524	1.17929
$335$	9.95243	0.543760
$336$	24.7646	1.35102
$337$	−3.90605	−0.212776	−0.106388	−	0.994325i	$-0.533929\pi$
$337$	−3.90605	−0.212776	−0.106388	+	0.994325i	$0.533929\pi$
$338$	−2.39849	−0.130461
$339$	15.9694	0.867337
$340$	−29.1062	−1.57850
$341$	−21.9932	−1.19100
$342$	6.07891	0.328710
$343$	5.70883	0.308248
$344$	−12.6007	−0.679383
$345$	−7.25360	−0.390521
$346$	0.267439	0.0143776
$347$	9.30816	0.499688	0.249844	−	0.968286i	$-0.419621\pi$
$347$	9.30816	0.499688	0.249844	+	0.968286i	$0.419621\pi$
$348$	47.4679	2.54455
$349$	27.4005	1.46671	0.733357	−	0.679844i	$-0.237952\pi$
$349$	27.4005	1.46671	0.733357	+	0.679844i	$0.237952\pi$
$350$	−42.1445	−2.25272
$351$	−0.0658687	−0.00351581
$352$	−8.56539	−0.456537
$353$	10.0528	0.535057	0.267529	−	0.963550i	$-0.413793\pi$
$353$	10.0528	0.535057	0.267529	+	0.963550i	$0.413793\pi$
$354$	59.9746	3.18761
$355$	19.9711	1.05996
$356$	−57.2338	−3.03339
$357$	24.2132	1.28150
$358$	17.3457	0.916747
$359$	8.81229	0.465095	0.232547	−	0.972585i	$-0.425294\pi$
$359$	8.81229	0.465095	0.232547	+	0.972585i	$0.425294\pi$
$360$	38.4626	2.02716
$361$	−18.2733	−0.961751
$362$	−32.5458	−1.71057
$363$	9.32368	0.489366
$364$	14.7519	0.773210
$365$	−22.4707	−1.17617
$366$	−45.6391	−2.38559
$367$	4.37829	0.228545	0.114272	−	0.993449i	$-0.463546\pi$
$367$	4.37829	0.228545	0.114272	+	0.993449i	$0.463546\pi$
$368$	2.48609	0.129597
$369$	19.4698	1.01356
$370$	75.8686	3.94422
$371$	−0.0311879	−0.00161919
$372$	52.4069	2.71717
$373$	4.68566	0.242614	0.121307	−	0.992615i	$-0.461291\pi$
$373$	4.68566	0.242614	0.121307	+	0.992615i	$0.461291\pi$
$374$	23.2674	1.20313
$375$	3.98621	0.205847
$376$	40.9067	2.10960
$377$	5.17548	0.266551
$378$	0.621032	0.0319424
$379$	19.3309	0.992962	0.496481	−	0.868048i	$-0.334625\pi$
$379$	19.3309	0.992962	0.496481	+	0.868048i	$0.334625\pi$
$380$	9.84490	0.505033
$381$	36.8456	1.88766
$382$	11.2499	0.575597
$383$	27.8784	1.42452	0.712260	−	0.701916i	$-0.247672\pi$
$383$	27.8784	1.42452	0.712260	+	0.701916i	$0.247672\pi$
$384$	50.6308	2.58374
$385$	46.5609	2.37296
$386$	6.94653	0.353569
$387$	8.91115	0.452979
$388$	16.9646	0.861246
$389$	−8.88605	−0.450541	−0.225270	−	0.974296i	$-0.572327\pi$
$389$	−8.88605	−0.450541	−0.225270	+	0.974296i	$0.572327\pi$
$390$	18.0389	0.913437
$391$	2.43075	0.122928
$392$	−35.5334	−1.79471
$393$	51.5836	2.60205
$394$	−54.8978	−2.76571
$395$	43.8092	2.20428
$396$	−42.9441	−2.15802
$397$	17.3066	0.868594	0.434297	−	0.900770i	$-0.356997\pi$
$397$	17.3066	0.868594	0.434297	+	0.900770i	$0.356997\pi$
$398$	−24.6845	−1.23732
$399$	−8.18992	−0.410009
$400$	11.5224	0.576120
$401$	8.89776	0.444333	0.222166	−	0.975009i	$-0.428687\pi$
$401$	8.89776	0.444333	0.222166	+	0.975009i	$0.428687\pi$
$402$	18.9579	0.945536
$403$	5.71398	0.284634
$404$	57.3608	2.85381
$405$	27.9426	1.38848
$406$	−48.7961	−2.42171
$407$	−39.5639	−1.96111
$408$	−25.8952	−1.28200
$409$	5.42301	0.268151	0.134075	−	0.990971i	$-0.457194\pi$
$409$	5.42301	0.268151	0.134075	+	0.990971i	$0.457194\pi$
$410$	48.3362	2.38716
$411$	−3.53941	−0.174586
$412$	−3.38489	−0.166761
$413$	−40.2186	−1.97903
$414$	−6.87735	−0.338004
$415$	16.8779	0.828506
$416$	2.22534	0.109106
$417$	27.1059	1.32738
$418$	−7.86998	−0.384933
$419$	5.61034	0.274083	0.137041	−	0.990565i	$-0.456241\pi$
$419$	5.61034	0.274083	0.137041	+	0.990565i	$0.456241\pi$
$420$	−110.948	−5.41372
$421$	−36.2532	−1.76687	−0.883436	−	0.468552i	$-0.844776\pi$
$421$	−36.2532	−1.76687	−0.883436	+	0.468552i	$0.844776\pi$
$422$	17.8412	0.868497
$423$	−28.9290	−1.40658
$424$	0.0333543	0.00161983
$425$	11.2659	0.546475
$426$	38.0421	1.84315
$427$	30.6053	1.48110
$428$	53.3933	2.58086
$429$	−9.40694	−0.454171
$430$	22.1230	1.06687
$431$	−14.4018	−0.693712	−0.346856	−	0.937918i	$-0.612751\pi$
$431$	−14.4018	−0.693712	−0.346856	+	0.937918i	$0.612751\pi$
$432$	−0.169791	−0.00816909
$433$	5.13439	0.246743	0.123371	−	0.992361i	$-0.460629\pi$
$433$	5.13439	0.246743	0.123371	+	0.992361i	$0.460629\pi$
$434$	−53.8733	−2.58600
$435$	−38.9245	−1.86629
$436$	−59.5802	−2.85338
$437$	−0.822178	−0.0393301
$438$	−42.8034	−2.04523
$439$	0.497810	0.0237592	0.0118796	−	0.999929i	$-0.496219\pi$
$439$	0.497810	0.0237592	0.0118796	+	0.999929i	$0.496219\pi$
$440$	−49.7952	−2.37389
$441$	25.1290	1.19662
$442$	−6.04501	−0.287532
$443$	32.0714	1.52376	0.761880	−	0.647718i	$-0.224277\pi$
$443$	32.0714	1.52376	0.761880	+	0.647718i	$0.224277\pi$
$444$	94.2754	4.47411
$445$	46.9327	2.22483
$446$	−27.3769	−1.29633
$447$	2.70891	0.128127
$448$	−41.2470	−1.94874
$449$	−6.26470	−0.295649	−0.147825	−	0.989014i	$-0.547227\pi$
$449$	−6.26470	−0.295649	−0.147825	+	0.989014i	$0.547227\pi$
$450$	−31.8747	−1.50259
$451$	−25.2064	−1.18692
$452$	24.5212	1.15338
$453$	−39.7976	−1.86985
$454$	−69.4083	−3.25750
$455$	−12.0968	−0.567107
$456$	8.75882	0.410169
$457$	−22.6792	−1.06089	−0.530443	−	0.847720i	$-0.677975\pi$
$457$	−22.6792	−1.06089	−0.530443	+	0.847720i	$0.677975\pi$
$458$	51.7018	2.41587
$459$	−0.166011	−0.00774875
$460$	−11.1380	−0.519312
$461$	32.2834	1.50359	0.751794	−	0.659398i	$-0.229189\pi$
$461$	32.2834	1.50359	0.751794	+	0.659398i	$0.229189\pi$
$462$	88.6917	4.12631
$463$	29.5185	1.37184	0.685920	−	0.727677i	$-0.259400\pi$
$463$	29.5185	1.37184	0.685920	+	0.727677i	$0.259400\pi$
$464$	13.3410	0.619338
$465$	−42.9745	−1.99290
$466$	−41.1520	−1.90633
$467$	−19.3869	−0.897118	−0.448559	−	0.893753i	$-0.648063\pi$
$467$	−19.3869	−0.897118	−0.448559	+	0.893753i	$0.648063\pi$
$468$	11.1572	0.515740
$469$	−12.7131	−0.587036
$470$	−71.8199	−3.31280
$471$	15.9380	0.734386
$472$	43.0124	1.97980
$473$	−11.5367	−0.530458
$474$	83.4501	3.83299
$475$	−3.81058	−0.174841
$476$	37.1798	1.70413
$477$	−0.0235880	−0.00108002
$478$	−63.3151	−2.89597
$479$	23.4681	1.07229	0.536143	−	0.844127i	$-0.319881\pi$
$479$	23.4681	1.07229	0.536143	+	0.844127i	$0.319881\pi$
$480$	−16.7367	−0.763922
$481$	10.2790	0.468680
$482$	32.2939	1.47095
$483$	9.26564	0.421601
$484$	14.3166	0.650756
$485$	−13.9113	−0.631677
$486$	52.7526	2.39291
$487$	3.10710	0.140796	0.0703981	−	0.997519i	$-0.477573\pi$
$487$	3.10710	0.140796	0.0703981	+	0.997519i	$0.477573\pi$
$488$	−32.7313	−1.48168
$489$	−38.1327	−1.72442
$490$	62.3860	2.81831
$491$	−34.3957	−1.55226	−0.776128	−	0.630575i	$-0.782819\pi$
$491$	−34.3957	−1.55226	−0.776128	+	0.630575i	$0.782819\pi$
$492$	60.0633	2.70786
$493$	13.0439	0.587470
$494$	2.04467	0.0919941
$495$	35.2149	1.58279
$496$	14.7291	0.661354
$497$	−25.5108	−1.14432
$498$	32.1500	1.44068
$499$	15.4085	0.689778	0.344889	−	0.938643i	$-0.387917\pi$
$499$	15.4085	0.689778	0.344889	+	0.938643i	$0.387917\pi$
$500$	6.12087	0.273734
$501$	−21.9611	−0.981151
$502$	19.9504	0.890429
$503$	−19.5741	−0.872766	−0.436383	−	0.899761i	$-0.643741\pi$
$503$	−19.5741	−0.872766	−0.436383	+	0.899761i	$0.643741\pi$
$504$	−49.1316	−2.18849
$505$	−47.0369	−2.09311
$506$	8.90368	0.395817
$507$	2.44398	0.108541
$508$	56.5769	2.51020
$509$	−44.2591	−1.96175	−0.980876	−	0.194633i	$-0.937648\pi$
$509$	−44.2591	−1.96175	−0.980876	+	0.194633i	$0.937648\pi$
$510$	45.4642	2.01319
$511$	28.7037	1.26978
$512$	27.4098	1.21135
$513$	0.0561519	0.00247917
$514$	28.4647	1.25552
$515$	2.77567	0.122310
$516$	27.4904	1.21020
$517$	37.4526	1.64716
$518$	−96.9134	−4.25813
$519$	−0.272511	−0.0119619
$520$	12.9371	0.567330
$521$	−4.45711	−0.195270	−0.0976349	−	0.995222i	$-0.531128\pi$
$521$	−4.45711	−0.195270	−0.0976349	+	0.995222i	$0.531128\pi$
$522$	−36.9055	−1.61531
$523$	25.2398	1.10366	0.551829	−	0.833957i	$-0.313930\pi$
$523$	25.2398	1.10366	0.551829	+	0.833957i	$0.313930\pi$
$524$	79.2072	3.46018
$525$	42.9438	1.87422
$526$	−37.9964	−1.65672
$527$	14.4012	0.627324
$528$	−24.2485	−1.05528
$529$	−22.0698	−0.959558
$530$	−0.0585602	−0.00254369
$531$	−30.4181	−1.32004
$532$	−12.5757	−0.545227
$533$	6.54877	0.283659
$534$	89.4000	3.86872
$535$	−43.7834	−1.89292
$536$	13.5962	0.587266
$537$	−17.6746	−0.762717
$538$	−29.2224	−1.25987
$539$	−32.5330	−1.40130
$540$	0.760686	0.0327347
$541$	36.5733	1.57241	0.786204	−	0.617967i	$-0.212044\pi$
$541$	36.5733	1.57241	0.786204	+	0.617967i	$0.212044\pi$
$542$	−61.6186	−2.64675
$543$	33.1631	1.42316
$544$	5.60861	0.240467
$545$	48.8568	2.09280
$546$	−23.0427	−0.986135
$547$	−17.0618	−0.729510	−0.364755	−	0.931104i	$-0.618847\pi$
$547$	−17.0618	−0.729510	−0.364755	+	0.931104i	$0.618847\pi$
$548$	−5.43481	−0.232164
$549$	23.1474	0.987908
$550$	41.2662	1.75960
$551$	−4.41200	−0.187958
$552$	−9.90927	−0.421766
$553$	−55.9612	−2.37971
$554$	−19.8331	−0.842629
$555$	−77.3075	−3.28152
$556$	41.6215	1.76514
$557$	13.6514	0.578430	0.289215	−	0.957264i	$-0.406606\pi$
$557$	13.6514	0.578430	0.289215	+	0.957264i	$0.406606\pi$
$558$	−40.7454	−1.72489
$559$	2.99731	0.126773
$560$	−31.1823	−1.31769
$561$	−23.7087	−1.00098
$562$	14.1401	0.596463
$563$	−15.4895	−0.652804	−0.326402	−	0.945231i	$-0.605836\pi$
$563$	−15.4895	−0.652804	−0.326402	+	0.945231i	$0.605836\pi$
$564$	−89.2444	−3.75787
$565$	−20.1078	−0.845941
$566$	−6.31823	−0.265575
$567$	−35.6934	−1.49898
$568$	27.2829	1.14476
$569$	−35.9338	−1.50642	−0.753211	−	0.657779i	$-0.771496\pi$
$569$	−35.9338	−1.50642	−0.753211	+	0.657779i	$0.771496\pi$
$570$	−15.3779	−0.644108
$571$	−2.83539	−0.118657	−0.0593287	−	0.998239i	$-0.518896\pi$
$571$	−2.83539	−0.118657	−0.0593287	+	0.998239i	$0.518896\pi$
$572$	−14.4445	−0.603954
$573$	−11.4633	−0.478887
$574$	−61.7440	−2.57714
$575$	4.31109	0.179785
$576$	−31.1960	−1.29983
$577$	29.1694	1.21434	0.607169	−	0.794573i	$-0.292305\pi$
$577$	29.1694	1.21434	0.607169	+	0.794573i	$0.292305\pi$
$578$	25.5389	1.06228
$579$	−7.07828	−0.294163
$580$	−59.7691	−2.48178
$581$	−21.5596	−0.894444
$582$	−26.4989	−1.09841
$583$	0.0305379	0.00126475
$584$	−30.6976	−1.27028
$585$	−9.14906	−0.378267
$586$	48.7183	2.01253
$587$	32.7200	1.35050	0.675250	−	0.737589i	$-0.264036\pi$
$587$	32.7200	1.35050	0.675250	+	0.737589i	$0.264036\pi$
$588$	77.5218	3.19694
$589$	−4.87106	−0.200709
$590$	−75.5168	−3.10898
$591$	55.9390	2.30102
$592$	26.4963	1.08899
$593$	−13.0128	−0.534374	−0.267187	−	0.963645i	$-0.586094\pi$
$593$	−13.0128	−0.534374	−0.267187	+	0.963645i	$0.586094\pi$
$594$	−0.608090	−0.0249502
$595$	−30.4881	−1.24989
$596$	4.15957	0.170383
$597$	25.1526	1.02943
$598$	−2.31323	−0.0945951
$599$	17.9946	0.735239	0.367619	−	0.929976i	$-0.380173\pi$
$599$	17.9946	0.735239	0.367619	+	0.929976i	$0.380173\pi$
$600$	−45.9269	−1.87496
$601$	−4.56781	−0.186325	−0.0931624	−	0.995651i	$-0.529698\pi$
$601$	−4.56781	−0.186325	−0.0931624	+	0.995651i	$0.529698\pi$
$602$	−28.2596	−1.15178
$603$	−9.61516	−0.391560
$604$	−61.1098	−2.48652
$605$	−11.7399	−0.477294
$606$	−89.5984	−3.63968
$607$	−0.500988	−0.0203345	−0.0101672	−	0.999948i	$-0.503236\pi$
$607$	−0.500988	−0.0203345	−0.0101672	+	0.999948i	$0.503236\pi$
$608$	−1.89706	−0.0769361
$609$	49.7216	2.01482
$610$	57.4664	2.32675
$611$	−9.73042	−0.393651
$612$	28.1198	1.13668
$613$	18.1222	0.731949	0.365974	−	0.930625i	$-0.380736\pi$
$613$	18.1222	0.731949	0.365974	+	0.930625i	$0.380736\pi$
$614$	−16.0235	−0.646655
$615$	−49.2530	−1.98607
$616$	63.6076	2.56282
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	5.28724	0.212684
$619$	−37.4786	−1.50639	−0.753197	−	0.657795i	$-0.771489\pi$
$619$	−37.4786	−1.50639	−0.753197	+	0.657795i	$0.771489\pi$
$620$	−65.9880	−2.65014
$621$	−0.0635273	−0.00254926
$622$	−29.0449	−1.16459
$623$	−59.9512	−2.40189
$624$	6.29991	0.252198
$625$	−27.3692	−1.09477
$626$	−44.9987	−1.79851
$627$	8.01924	0.320258
$628$	24.4731	0.976582
$629$	25.9064	1.03296
$630$	86.2604	3.43670
$631$	−7.35691	−0.292874	−0.146437	−	0.989220i	$-0.546781\pi$
$631$	−7.35691	−0.292874	−0.146437	+	0.989220i	$0.546781\pi$
$632$	59.8485	2.38065
$633$	−18.1796	−0.722574
$634$	−22.4018	−0.889690
$635$	−46.3941	−1.84109
$636$	−0.0727677	−0.00288543
$637$	8.45228	0.334892
$638$	47.7792	1.89160
$639$	−19.2943	−0.763272
$640$	−63.7516	−2.52000
$641$	−39.7859	−1.57145	−0.785725	−	0.618577i	$-0.787710\pi$
$641$	−39.7859	−1.57145	−0.785725	+	0.618577i	$0.787710\pi$
$642$	−83.4011	−3.29158
$643$	31.0906	1.22609	0.613046	−	0.790047i	$-0.289944\pi$
$643$	31.0906	1.22609	0.613046	+	0.790047i	$0.289944\pi$
$644$	14.2275	0.560642
$645$	−22.5426	−0.887615
$646$	5.15326	0.202752
$647$	25.4768	1.00160	0.500798	−	0.865564i	$-0.333040\pi$
$647$	25.4768	1.00160	0.500798	+	0.865564i	$0.333040\pi$
$648$	38.1728	1.49957
$649$	39.3805	1.54582
$650$	−10.7212	−0.420521
$651$	54.8950	2.15151
$652$	−58.5533	−2.29312
$653$	−17.8264	−0.697602	−0.348801	−	0.937197i	$-0.613411\pi$
$653$	−17.8264	−0.697602	−0.348801	+	0.937197i	$0.613411\pi$
$654$	93.0652	3.63914
$655$	−64.9513	−2.53786
$656$	16.8809	0.659090
$657$	21.7092	0.846957
$658$	91.7416	3.57646
$659$	6.28480	0.244821	0.122411	−	0.992480i	$-0.460938\pi$
$659$	6.28480	0.244821	0.122411	+	0.992480i	$0.460938\pi$
$660$	108.636	4.22866
$661$	21.0754	0.819738	0.409869	−	0.912144i	$-0.365574\pi$
$661$	21.0754	0.819738	0.409869	+	0.912144i	$0.365574\pi$
$662$	7.46861	0.290276
$663$	6.15966	0.239221
$664$	23.0572	0.894794
$665$	10.3123	0.399894
$666$	−73.2975	−2.84022
$667$	4.99150	0.193272
$668$	−33.7216	−1.30473
$669$	27.8961	1.07853
$670$	−23.8708	−0.922211
$671$	−29.9675	−1.15688
$672$	21.3792	0.824720
$673$	42.1679	1.62545	0.812727	−	0.582645i	$-0.197982\pi$
$673$	42.1679	1.62545	0.812727	+	0.582645i	$0.197982\pi$
$674$	9.36863	0.360866
$675$	−0.294432	−0.0113327
$676$	3.75277	0.144337
$677$	−34.7640	−1.33609	−0.668045	−	0.744121i	$-0.732869\pi$
$677$	−34.7640	−1.33609	−0.668045	+	0.744121i	$0.732869\pi$
$678$	−38.3024	−1.47100
$679$	17.7700	0.681951
$680$	32.6059	1.25038
$681$	70.7247	2.71018
$682$	52.7506	2.01992
$683$	26.8507	1.02741	0.513707	−	0.857966i	$-0.328272\pi$
$683$	26.8507	1.02741	0.513707	+	0.857966i	$0.328272\pi$
$684$	−9.51127	−0.363673
$685$	4.45664	0.170279
$686$	−13.6926	−0.522786
$687$	−52.6824	−2.00996
$688$	7.72624	0.294560
$689$	−0.00793395	−0.000302259 0
$690$	17.3977	0.662320
$691$	5.04774	0.192025	0.0960126	−	0.995380i	$-0.469391\pi$
$691$	5.04774	0.192025	0.0960126	+	0.995380i	$0.469391\pi$
$692$	−0.418444	−0.0159069
$693$	−44.9830	−1.70876
$694$	−22.3255	−0.847466
$695$	−34.1303	−1.29464
$696$	−53.1754	−2.01561
$697$	16.5051	0.625176
$698$	−65.7198	−2.48753
$699$	41.9324	1.58603
$700$	65.9408	2.49233
$701$	−14.7665	−0.557723	−0.278862	−	0.960331i	$-0.589957\pi$
$701$	−14.7665	−0.557723	−0.278862	+	0.960331i	$0.589957\pi$
$702$	0.157986	0.00596278
$703$	−8.76262	−0.330488
$704$	40.3874	1.52216
$705$	73.1820	2.75619
$706$	−24.1116	−0.907452
$707$	60.0842	2.25970
$708$	−93.8383	−3.52666
$709$	−42.2864	−1.58810	−0.794050	−	0.607852i	$-0.792031\pi$
$709$	−42.2864	−1.58810	−0.794050	+	0.607852i	$0.792031\pi$
$710$	−47.9006	−1.79768
$711$	−42.3246	−1.58730
$712$	64.1156	2.40283
$713$	5.51086	0.206383
$714$	−58.0753	−2.17341
$715$	11.8447	0.442967
$716$	−27.1396	−1.01426
$717$	64.5160	2.40939
$718$	−21.1362	−0.788797
$719$	−44.8482	−1.67256	−0.836278	−	0.548306i	$-0.815273\pi$
$719$	−44.8482	−1.67256	−0.836278	+	0.548306i	$0.815273\pi$
$720$	−23.5838	−0.878915
$721$	−3.54559	−0.132045
$722$	43.8283	1.63112
$723$	−32.9064	−1.22380
$724$	50.9223	1.89251
$725$	23.1343	0.859187
$726$	−22.3628	−0.829960
$727$	15.8181	0.586662	0.293331	−	0.956011i	$-0.405236\pi$
$727$	15.8181	0.586662	0.293331	+	0.956011i	$0.405236\pi$
$728$	−16.5257	−0.612482
$729$	−26.5127	−0.981952
$730$	53.8958	1.99477
$731$	7.55423	0.279403
$732$	71.4086	2.63934
$733$	6.85170	0.253073	0.126537	−	0.991962i	$-0.459614\pi$
$733$	6.85170	0.253073	0.126537	+	0.991962i	$0.459614\pi$
$734$	−10.5013	−0.387610
$735$	−63.5692	−2.34478
$736$	2.14624	0.0791114
$737$	12.4481	0.458533
$738$	−46.6982	−1.71898
$739$	36.1124	1.32842	0.664208	−	0.747548i	$-0.268769\pi$
$739$	36.1124	1.32842	0.664208	+	0.747548i	$0.268769\pi$
$740$	−118.707	−4.36374
$741$	−2.08345	−0.0765374
$742$	0.0748038	0.00274614
$743$	35.9783	1.31991	0.659957	−	0.751303i	$-0.270574\pi$
$743$	35.9783	1.31991	0.659957	+	0.751303i	$0.270574\pi$
$744$	−58.7082	−2.15235
$745$	−3.41092	−0.124967
$746$	−11.2385	−0.411472
$747$	−16.3060	−0.596605
$748$	−36.4049	−1.33110
$749$	55.9283	2.04358
$750$	−9.56089	−0.349114
$751$	−12.5400	−0.457592	−0.228796	−	0.973474i	$-0.573479\pi$
$751$	−12.5400	−0.457592	−0.228796	+	0.973474i	$0.573479\pi$
$752$	−25.0823	−0.914659
$753$	−20.3287	−0.740821
$754$	−12.4133	−0.452067
$755$	50.1111	1.82373
$756$	−0.971688	−0.0353400
$757$	28.8900	1.05002	0.525012	−	0.851095i	$-0.324061\pi$
$757$	28.8900	1.05002	0.525012	+	0.851095i	$0.324061\pi$
$758$	−46.3650	−1.68405
$759$	−9.07255	−0.329313
$760$	−11.0286	−0.400051
$761$	19.3662	0.702023	0.351012	−	0.936371i	$-0.385838\pi$
$761$	19.3662	0.702023	0.351012	+	0.936371i	$0.385838\pi$
$762$	−88.3739	−3.20145
$763$	−62.4090	−2.25936
$764$	−17.6021	−0.636820
$765$	−23.0587	−0.833690
$766$	−66.8662	−2.41597
$767$	−10.2313	−0.369431
$768$	−70.1485	−2.53127
$769$	34.6260	1.24864	0.624322	−	0.781167i	$-0.285375\pi$
$769$	34.6260	1.24864	0.624322	+	0.781167i	$0.285375\pi$
$770$	−111.676	−4.02452
$771$	−29.0045	−1.04457
$772$	−10.8688	−0.391176
$773$	−37.0354	−1.33207	−0.666034	−	0.745921i	$-0.732010\pi$
$773$	−37.0354	−1.33207	−0.666034	+	0.745921i	$0.732010\pi$
$774$	−21.3733	−0.768248
$775$	25.5414	0.917474
$776$	−19.0044	−0.682218
$777$	98.7514	3.54269
$778$	21.3131	0.764113
$779$	−5.58271	−0.200021
$780$	−28.2244	−1.01059
$781$	24.9792	0.893825
$782$	−5.83013	−0.208485
$783$	−0.340902	−0.0121828
$784$	21.7877	0.778131
$785$	−20.0683	−0.716270
$786$	−123.723	−4.41305
$787$	46.1220	1.64407	0.822036	−	0.569435i	$-0.192838\pi$
$787$	46.1220	1.64407	0.822036	+	0.569435i	$0.192838\pi$
$788$	85.8951	3.05988
$789$	38.7170	1.37836
$790$	−105.076	−3.73844
$791$	25.6854	0.913267
$792$	48.1077	1.70943
$793$	7.78575	0.276480
$794$	−41.5098	−1.47313
$795$	0.0596708	0.00211631
$796$	38.6222	1.36893
$797$	41.9080	1.48446	0.742229	−	0.670147i	$-0.233769\pi$
$797$	41.9080	1.48446	0.742229	+	0.670147i	$0.233769\pi$
$798$	19.6435	0.695371
$799$	−24.5239	−0.867594
$800$	9.94725	0.351688
$801$	−45.3423	−1.60209
$802$	−21.3412	−0.753584
$803$	−28.1056	−0.991824
$804$	−29.6623	−1.04611
$805$	−11.6668	−0.411201
$806$	−13.7049	−0.482736
$807$	29.7766	1.04819
$808$	−64.2578	−2.26058
$809$	8.04324	0.282785	0.141393	−	0.989954i	$-0.454842\pi$
$809$	8.04324	0.282785	0.141393	+	0.989954i	$0.454842\pi$
$810$	−67.0201	−2.35485
$811$	−22.2906	−0.782728	−0.391364	−	0.920236i	$-0.627997\pi$
$811$	−22.2906	−0.782728	−0.391364	+	0.920236i	$0.627997\pi$
$812$	76.3481	2.67929
$813$	62.7873	2.20205
$814$	94.8937	3.32602
$815$	48.0147	1.68188
$816$	15.8779	0.555838
$817$	−2.55515	−0.0893934
$818$	−13.0070	−0.454781
$819$	11.6869	0.408372
$820$	−75.6286	−2.64107
$821$	−17.7246	−0.618592	−0.309296	−	0.950966i	$-0.600093\pi$
$821$	−17.7246	−0.618592	−0.309296	+	0.950966i	$0.600093\pi$
$822$	8.48925	0.296097
$823$	−8.57987	−0.299076	−0.149538	−	0.988756i	$-0.547779\pi$
$823$	−8.57987	−0.299076	−0.149538	+	0.988756i	$0.547779\pi$
$824$	3.79188	0.132097
$825$	−42.0489	−1.46395
$826$	96.4640	3.35641
$827$	14.7739	0.513739	0.256869	−	0.966446i	$-0.417309\pi$
$827$	14.7739	0.513739	0.256869	+	0.966446i	$0.417309\pi$
$828$	10.7606	0.373955
$829$	−23.7057	−0.823335	−0.411667	−	0.911334i	$-0.635053\pi$
$829$	−23.7057	−0.823335	−0.411667	+	0.911334i	$0.635053\pi$
$830$	−40.4816	−1.40514
$831$	20.2093	0.701052
$832$	−10.4929	−0.363776
$833$	21.3026	0.738091
$834$	−65.0133	−2.25123
$835$	27.6523	0.956947
$836$	12.3136	0.425876
$837$	−0.376372	−0.0130093
$838$	−13.4564	−0.464842
$839$	7.85196	0.271080	0.135540	−	0.990772i	$-0.456723\pi$
$839$	7.85196	0.271080	0.135540	+	0.990772i	$0.456723\pi$
$840$	124.289	4.28837
$841$	−2.21443	−0.0763597
$842$	86.9530	2.99660
$843$	−14.4083	−0.496247
$844$	−27.9150	−0.960875
$845$	−3.07733	−0.105864
$846$	69.3860	2.38554
$847$	14.9963	0.515281
$848$	−0.0204515	−0.000702308 0
$849$	6.43806	0.220954
$850$	−27.0211	−0.926817
$851$	9.91357	0.339833
$852$	−59.5220	−2.03919
$853$	2.91985	0.0999736	0.0499868	−	0.998750i	$-0.484082\pi$
$853$	2.91985	0.0999736	0.0499868	+	0.998750i	$0.484082\pi$
$854$	−73.4066	−2.51192
$855$	7.79941	0.266734
$856$	−59.8133	−2.04438
$857$	34.3211	1.17239	0.586193	−	0.810171i	$-0.300626\pi$
$857$	34.3211	1.17239	0.586193	+	0.810171i	$0.300626\pi$
$858$	22.5625	0.770270
$859$	−22.4815	−0.767058	−0.383529	−	0.923529i	$-0.625291\pi$
$859$	−22.4815	−0.767058	−0.383529	+	0.923529i	$0.625291\pi$
$860$	−34.6145	−1.18034
$861$	62.9150	2.14414
$862$	34.5427	1.17653
$863$	−10.7474	−0.365844	−0.182922	−	0.983127i	$-0.558556\pi$
$863$	−10.7474	−0.365844	−0.182922	+	0.983127i	$0.558556\pi$
$864$	−0.146580	−0.00498677
$865$	0.343132	0.0116668
$866$	−12.3148	−0.418474
$867$	−26.0233	−0.883797
$868$	84.2920	2.86106
$869$	54.7950	1.85879
$870$	93.3601	3.16521
$871$	−3.23411	−0.109584
$872$	66.7441	2.26024
$873$	13.4398	0.454869
$874$	1.97199	0.0667035
$875$	6.41148	0.216747
$876$	66.9718	2.26277
$877$	−37.5065	−1.26650	−0.633252	−	0.773946i	$-0.718280\pi$
$877$	−37.5065	−1.26650	−0.633252	+	0.773946i	$0.718280\pi$
$878$	−1.19399	−0.0402953
$879$	−49.6423	−1.67439
$880$	30.5324	1.02925
$881$	−26.3410	−0.887451	−0.443725	−	0.896163i	$-0.646343\pi$
$881$	−26.3410	−0.887451	−0.443725	+	0.896163i	$0.646343\pi$
$882$	−60.2718	−2.02946
$883$	20.0409	0.674428	0.337214	−	0.941428i	$-0.390515\pi$
$883$	20.0409	0.674428	0.337214	+	0.941428i	$0.390515\pi$
$884$	9.45824	0.318115
$885$	76.9491	2.58662
$886$	−76.9231	−2.58428
$887$	27.0397	0.907905	0.453953	−	0.891026i	$-0.350014\pi$
$887$	27.0397	0.907905	0.453953	+	0.891026i	$0.350014\pi$
$888$	−105.611	−3.54408
$889$	59.2631	1.98762
$890$	−112.568	−3.77328
$891$	34.9496	1.17086
$892$	42.8348	1.43422
$893$	8.29500	0.277582
$894$	−6.49731	−0.217303
$895$	22.2550	0.743902
$896$	81.4353	2.72056
$897$	2.35711	0.0787015
$898$	15.0258	0.501418
$899$	29.5726	0.986300
$900$	49.8723	1.66241
$901$	−0.0199962	−0.000666171 0
$902$	60.4572	2.01301
$903$	28.7956	0.958257
$904$	−27.4696	−0.913625
$905$	−41.7572	−1.38806
$906$	95.4543	3.17126
$907$	−6.42601	−0.213372	−0.106686	−	0.994293i	$-0.534024\pi$
$907$	−6.42601	−0.213372	−0.106686	+	0.994293i	$0.534024\pi$
$908$	108.599	3.60398
$909$	45.4429	1.50724
$910$	29.0141	0.961809
$911$	26.2851	0.870864	0.435432	−	0.900222i	$-0.356596\pi$
$911$	26.2851	0.870864	0.435432	+	0.900222i	$0.356596\pi$
$912$	−5.37056	−0.177837
$913$	21.1103	0.698650
$914$	54.3958	1.79925
$915$	−58.5563	−1.93581
$916$	−80.8945	−2.67283
$917$	82.9678	2.73984
$918$	0.398177	0.0131418
$919$	40.6952	1.34241	0.671206	−	0.741271i	$-0.265777\pi$
$919$	40.6952	1.34241	0.671206	+	0.741271i	$0.265777\pi$
$920$	12.4772	0.411362
$921$	16.3274	0.538005
$922$	−77.4315	−2.55007
$923$	−6.48975	−0.213613
$924$	−138.770	−4.56520
$925$	45.9468	1.51072
$926$	−70.7998	−2.32663
$927$	−2.68160	−0.0880754
$928$	11.5172	0.378071
$929$	−25.9170	−0.850310	−0.425155	−	0.905121i	$-0.639780\pi$
$929$	−25.9170	−0.850310	−0.425155	+	0.905121i	$0.639780\pi$
$930$	103.074	3.37993
$931$	−7.20542	−0.236148
$932$	64.3878	2.10909
$933$	29.5958	0.968921
$934$	46.4993	1.52150
$935$	29.8527	0.976287
$936$	−12.4987	−0.408532
$937$	−28.8943	−0.943936	−0.471968	−	0.881616i	$-0.656456\pi$
$937$	−28.8943	−0.943936	−0.471968	+	0.881616i	$0.656456\pi$
$938$	30.4922	0.995607
$939$	45.8521	1.49633
$940$	112.372	3.66517
$941$	−24.6460	−0.803435	−0.401718	−	0.915764i	$-0.631587\pi$
$941$	−24.6460	−0.803435	−0.401718	+	0.915764i	$0.631587\pi$
$942$	−38.2273	−1.24551
$943$	6.31598	0.205677
$944$	−26.3735	−0.858383
$945$	0.796801	0.0259200
$946$	27.6707	0.899652
$947$	0.427788	0.0139012	0.00695062	−	0.999976i	$-0.497788\pi$
$947$	0.427788	0.0139012	0.00695062	+	0.999976i	$0.497788\pi$
$948$	−130.569	−4.24069
$949$	7.30201	0.237033
$950$	9.13965	0.296529
$951$	22.8267	0.740206
$952$	−41.6502	−1.34989
$953$	−19.2792	−0.624516	−0.312258	−	0.949997i	$-0.601085\pi$
$953$	−19.2792	−0.624516	−0.312258	+	0.949997i	$0.601085\pi$
$954$	0.0565757	0.00183170
$955$	14.4340	0.467073
$956$	99.0651	3.20399
$957$	−48.6854	−1.57377
$958$	−56.2882	−1.81859
$959$	−5.69284	−0.183832
$960$	78.9167	2.54703
$961$	1.64955	0.0532113
$962$	−24.6540	−0.794877
$963$	42.2997	1.36309
$964$	−50.5282	−1.62740
$965$	8.91260	0.286907
$966$	−22.2236	−0.715032
$967$	52.7552	1.69649	0.848247	−	0.529601i	$-0.177658\pi$
$967$	52.7552	1.69649	0.848247	+	0.529601i	$0.177658\pi$
$968$	−16.0381	−0.515483
$969$	−5.25100	−0.168686
$970$	33.3660	1.07132
$971$	4.65780	0.149476	0.0747380	−	0.997203i	$-0.476188\pi$
$971$	4.65780	0.149476	0.0747380	+	0.997203i	$0.476188\pi$
$972$	−82.5386	−2.64743
$973$	43.5976	1.39767
$974$	−7.45236	−0.238789
$975$	10.9246	0.349866
$976$	20.0695	0.642410
$977$	16.2028	0.518372	0.259186	−	0.965827i	$-0.416546\pi$
$977$	16.2028	0.518372	0.259186	+	0.965827i	$0.416546\pi$
$978$	91.4611	2.92460
$979$	58.7018	1.87612
$980$	−97.6113	−3.11808
$981$	−47.2012	−1.50702
$982$	82.4978	2.63261
$983$	10.8661	0.346574	0.173287	−	0.984871i	$-0.444561\pi$
$983$	10.8661	0.346574	0.173287	+	0.984871i	$0.444561\pi$
$984$	−67.2853	−2.14498
$985$	−70.4354	−2.24426
$986$	−31.2858	−0.996343
$987$	−93.4815	−2.97555
$988$	−3.19916	−0.101779
$989$	2.89076	0.0919209
$990$	−84.4627	−2.68440
$991$	−48.1512	−1.52957	−0.764787	−	0.644283i	$-0.777156\pi$
$991$	−48.1512	−1.52957	−0.764787	+	0.644283i	$0.777156\pi$
$992$	12.7156	0.403719
$993$	−7.61025	−0.241504
$994$	61.1875	1.94075
$995$	−31.6709	−1.00403
$996$	−50.3031	−1.59391
$997$	−50.8636	−1.61087	−0.805434	−	0.592686i	$-0.798068\pi$
$997$	−50.8636	−1.61087	−0.805434	+	0.592686i	$0.798068\pi$
$998$	−36.9571	−1.16986
$999$	−0.677061	−0.0214213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.d.1.19	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.d.1.19	✓	174	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.39849 q^{2} +2.44398 q^{3} +3.75277 q^{4} -3.07733 q^{5} -5.86187 q^{6} +3.93094 q^{7} -4.20400 q^{8} +2.97305 q^{9} +O(q^{10})\)	\(q-2.39849 q^{2} +2.44398 q^{3} +3.75277 q^{4} -3.07733 q^{5} -5.86187 q^{6} +3.93094 q^{7} -4.20400 q^{8} +2.97305 q^{9} +7.38096 q^{10} -3.84902 q^{11} +9.17169 q^{12} +1.00000 q^{13} -9.42833 q^{14} -7.52095 q^{15} +2.57772 q^{16} +2.52034 q^{17} -7.13084 q^{18} -0.852482 q^{19} -11.5485 q^{20} +9.60714 q^{21} +9.23185 q^{22} +0.964453 q^{23} -10.2745 q^{24} +4.46999 q^{25} -2.39849 q^{26} -0.0658687 q^{27} +14.7519 q^{28} +5.17548 q^{29} +18.0389 q^{30} +5.71398 q^{31} +2.22534 q^{32} -9.40694 q^{33} -6.04501 q^{34} -12.0968 q^{35} +11.1572 q^{36} +10.2790 q^{37} +2.04467 q^{38} +2.44398 q^{39} +12.9371 q^{40} +6.54877 q^{41} -23.0427 q^{42} +2.99731 q^{43} -14.4445 q^{44} -9.14906 q^{45} -2.31323 q^{46} -9.73042 q^{47} +6.29991 q^{48} +8.45228 q^{49} -10.7212 q^{50} +6.15966 q^{51} +3.75277 q^{52} -0.00793395 q^{53} +0.157986 q^{54} +11.8447 q^{55} -16.5257 q^{56} -2.08345 q^{57} -12.4133 q^{58} -10.2313 q^{59} -28.2244 q^{60} +7.78575 q^{61} -13.7049 q^{62} +11.6869 q^{63} -10.4929 q^{64} -3.07733 q^{65} +22.5625 q^{66} -3.23411 q^{67} +9.45824 q^{68} +2.35711 q^{69} +29.0141 q^{70} -6.48975 q^{71} -12.4987 q^{72} +7.30201 q^{73} -24.6540 q^{74} +10.9246 q^{75} -3.19916 q^{76} -15.1303 q^{77} -5.86187 q^{78} -14.2361 q^{79} -7.93252 q^{80} -9.08013 q^{81} -15.7072 q^{82} -5.48460 q^{83} +36.0534 q^{84} -7.75592 q^{85} -7.18902 q^{86} +12.6488 q^{87} +16.1813 q^{88} -15.2511 q^{89} +21.9440 q^{90} +3.93094 q^{91} +3.61937 q^{92} +13.9649 q^{93} +23.3383 q^{94} +2.62337 q^{95} +5.43870 q^{96} +4.52055 q^{97} -20.2727 q^{98} -11.4433 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * q^99

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