LMFDB - Embedded newform 6010.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.14296 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.14296 q^{6} +0.736597 q^{7} -1.00000 q^{8} +1.59228 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.14296 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.14296 q^{6} +0.736597 q^{7} -1.00000 q^{8} +1.59228 q^{9} +1.00000 q^{10} -3.15712 q^{11} -2.14296 q^{12} -4.66538 q^{13} -0.736597 q^{14} +2.14296 q^{15} +1.00000 q^{16} +3.14164 q^{17} -1.59228 q^{18} -4.01979 q^{19} -1.00000 q^{20} -1.57850 q^{21} +3.15712 q^{22} -7.10860 q^{23} +2.14296 q^{24} +1.00000 q^{25} +4.66538 q^{26} +3.01668 q^{27} +0.736597 q^{28} -2.80984 q^{29} -2.14296 q^{30} -5.72133 q^{31} -1.00000 q^{32} +6.76559 q^{33} -3.14164 q^{34} -0.736597 q^{35} +1.59228 q^{36} -7.97212 q^{37} +4.01979 q^{38} +9.99774 q^{39} +1.00000 q^{40} -10.3736 q^{41} +1.57850 q^{42} +10.0395 q^{43} -3.15712 q^{44} -1.59228 q^{45} +7.10860 q^{46} -8.43542 q^{47} -2.14296 q^{48} -6.45743 q^{49} -1.00000 q^{50} -6.73241 q^{51} -4.66538 q^{52} +7.83253 q^{53} -3.01668 q^{54} +3.15712 q^{55} -0.736597 q^{56} +8.61426 q^{57} +2.80984 q^{58} +2.06051 q^{59} +2.14296 q^{60} +4.47293 q^{61} +5.72133 q^{62} +1.17287 q^{63} +1.00000 q^{64} +4.66538 q^{65} -6.76559 q^{66} -8.16901 q^{67} +3.14164 q^{68} +15.2335 q^{69} +0.736597 q^{70} +9.31937 q^{71} -1.59228 q^{72} -8.97252 q^{73} +7.97212 q^{74} -2.14296 q^{75} -4.01979 q^{76} -2.32553 q^{77} -9.99774 q^{78} -15.5710 q^{79} -1.00000 q^{80} -11.2415 q^{81} +10.3736 q^{82} +15.7876 q^{83} -1.57850 q^{84} -3.14164 q^{85} -10.0395 q^{86} +6.02137 q^{87} +3.15712 q^{88} -6.08980 q^{89} +1.59228 q^{90} -3.43651 q^{91} -7.10860 q^{92} +12.2606 q^{93} +8.43542 q^{94} +4.01979 q^{95} +2.14296 q^{96} -17.7555 q^{97} +6.45743 q^{98} -5.02703 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 21 q^{2} + 8 q^{3} + 21 q^{4} - 21 q^{5} - 8 q^{6} - 21 q^{8} + 15 q^{9}+O(q^{10}) $ 21 * q - 21 * q^2 + 8 * q^3 + 21 * q^4 - 21 * q^5 - 8 * q^6 - 21 * q^8 + 15 * q^9	\( 21 q - 21 q^{2} + 8 q^{3} + 21 q^{4} - 21 q^{5} - 8 q^{6} - 21 q^{8} + 15 q^{9} + 21 q^{10} + 8 q^{11} + 8 q^{12} + 2 q^{13} - 8 q^{15} + 21 q^{16} + 25 q^{17} - 15 q^{18} - 11 q^{19} - 21 q^{20} - 8 q^{21} - 8 q^{22} + 15 q^{23} - 8 q^{24} + 21 q^{25} - 2 q^{26} + 29 q^{27} + 3 q^{29} + 8 q^{30} - 19 q^{31} - 21 q^{32} + 11 q^{33} - 25 q^{34} + 15 q^{36} - 8 q^{37} + 11 q^{38} - 2 q^{39} + 21 q^{40} + 15 q^{41} + 8 q^{42} + 19 q^{43} + 8 q^{44} - 15 q^{45} - 15 q^{46} + 19 q^{47} + 8 q^{48} - 15 q^{49} - 21 q^{50} + 13 q^{51} + 2 q^{52} + 45 q^{53} - 29 q^{54} - 8 q^{55} + 22 q^{57} - 3 q^{58} + 34 q^{59} - 8 q^{60} - 26 q^{61} + 19 q^{62} + 5 q^{63} + 21 q^{64} - 2 q^{65} - 11 q^{66} + 19 q^{67} + 25 q^{68} - 3 q^{69} + 10 q^{71} - 15 q^{72} - 17 q^{73} + 8 q^{74} + 8 q^{75} - 11 q^{76} + 42 q^{77} + 2 q^{78} - 42 q^{79} - 21 q^{80} + q^{81} - 15 q^{82} + 76 q^{83} - 8 q^{84} - 25 q^{85} - 19 q^{86} + 6 q^{87} - 8 q^{88} + 14 q^{89} + 15 q^{90} - 19 q^{91} + 15 q^{92} + 2 q^{93} - 19 q^{94} + 11 q^{95} - 8 q^{96} - 9 q^{97} + 15 q^{98} + 21 q^{99}+O(q^{100}) \) 21 * q - 21 * q^2 + 8 * q^3 + 21 * q^4 - 21 * q^5 - 8 * q^6 - 21 * q^8 + 15 * q^9 + 21 * q^10 + 8 * q^11 + 8 * q^12 + 2 * q^13 - 8 * q^15 + 21 * q^16 + 25 * q^17 - 15 * q^18 - 11 * q^19 - 21 * q^20 - 8 * q^21 - 8 * q^22 + 15 * q^23 - 8 * q^24 + 21 * q^25 - 2 * q^26 + 29 * q^27 + 3 * q^29 + 8 * q^30 - 19 * q^31 - 21 * q^32 + 11 * q^33 - 25 * q^34 + 15 * q^36 - 8 * q^37 + 11 * q^38 - 2 * q^39 + 21 * q^40 + 15 * q^41 + 8 * q^42 + 19 * q^43 + 8 * q^44 - 15 * q^45 - 15 * q^46 + 19 * q^47 + 8 * q^48 - 15 * q^49 - 21 * q^50 + 13 * q^51 + 2 * q^52 + 45 * q^53 - 29 * q^54 - 8 * q^55 + 22 * q^57 - 3 * q^58 + 34 * q^59 - 8 * q^60 - 26 * q^61 + 19 * q^62 + 5 * q^63 + 21 * q^64 - 2 * q^65 - 11 * q^66 + 19 * q^67 + 25 * q^68 - 3 * q^69 + 10 * q^71 - 15 * q^72 - 17 * q^73 + 8 * q^74 + 8 * q^75 - 11 * q^76 + 42 * q^77 + 2 * q^78 - 42 * q^79 - 21 * q^80 + q^81 - 15 * q^82 + 76 * q^83 - 8 * q^84 - 25 * q^85 - 19 * q^86 + 6 * q^87 - 8 * q^88 + 14 * q^89 + 15 * q^90 - 19 * q^91 + 15 * q^92 + 2 * q^93 - 19 * q^94 + 11 * q^95 - 8 * q^96 - 9 * q^97 + 15 * q^98 + 21 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.14296	−1.23724	−0.618620	−	0.785691i	$-0.712308\pi$
$3$	−2.14296	−1.23724	−0.618620	+	0.785691i	$0.712308\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.14296	0.874860
$7$	0.736597	0.278407	0.139204	−	0.990264i	$-0.455546\pi$
$7$	0.736597	0.278407	0.139204	+	0.990264i	$0.455546\pi$
$8$	−1.00000	−0.353553
$9$	1.59228	0.530761
$10$	1.00000	0.316228
$11$	−3.15712	−0.951908	−0.475954	−	0.879470i	$-0.657897\pi$
$11$	−3.15712	−0.951908	−0.475954	+	0.879470i	$0.657897\pi$
$12$	−2.14296	−0.618620
$13$	−4.66538	−1.29394	−0.646972	−	0.762514i	$-0.723965\pi$
$13$	−4.66538	−1.29394	−0.646972	+	0.762514i	$0.723965\pi$
$14$	−0.736597	−0.196864
$15$	2.14296	0.553310
$16$	1.00000	0.250000
$17$	3.14164	0.761959	0.380980	−	0.924583i	$-0.375587\pi$
$17$	3.14164	0.761959	0.380980	+	0.924583i	$0.375587\pi$
$18$	−1.59228	−0.375305
$19$	−4.01979	−0.922204	−0.461102	−	0.887347i	$-0.652546\pi$
$19$	−4.01979	−0.922204	−0.461102	+	0.887347i	$0.652546\pi$
$20$	−1.00000	−0.223607
$21$	−1.57850	−0.344457
$22$	3.15712	0.673101
$23$	−7.10860	−1.48225	−0.741123	−	0.671369i	$-0.765707\pi$
$23$	−7.10860	−1.48225	−0.741123	+	0.671369i	$0.765707\pi$
$24$	2.14296	0.437430
$25$	1.00000	0.200000
$26$	4.66538	0.914957
$27$	3.01668	0.580561
$28$	0.736597	0.139204
$29$	−2.80984	−0.521773	−0.260887	−	0.965369i	$-0.584015\pi$
$29$	−2.80984	−0.521773	−0.260887	+	0.965369i	$0.584015\pi$
$30$	−2.14296	−0.391249
$31$	−5.72133	−1.02758	−0.513791	−	0.857916i	$-0.671759\pi$
$31$	−5.72133	−1.02758	−0.513791	+	0.857916i	$0.671759\pi$
$32$	−1.00000	−0.176777
$33$	6.76559	1.17774
$34$	−3.14164	−0.538787
$35$	−0.736597	−0.124508
$36$	1.59228	0.265381
$37$	−7.97212	−1.31061	−0.655304	−	0.755365i	$-0.727460\pi$
$37$	−7.97212	−1.31061	−0.655304	+	0.755365i	$0.727460\pi$
$38$	4.01979	0.652097
$39$	9.99774	1.60092
$40$	1.00000	0.158114
$41$	−10.3736	−1.62008	−0.810039	−	0.586376i	$-0.800554\pi$
$41$	−10.3736	−1.62008	−0.810039	+	0.586376i	$0.800554\pi$
$42$	1.57850	0.243568
$43$	10.0395	1.53101	0.765507	−	0.643428i	$-0.222488\pi$
$43$	10.0395	1.53101	0.765507	+	0.643428i	$0.222488\pi$
$44$	−3.15712	−0.475954
$45$	−1.59228	−0.237364
$46$	7.10860	1.04811
$47$	−8.43542	−1.23043	−0.615217	−	0.788358i	$-0.710931\pi$
$47$	−8.43542	−1.23043	−0.615217	+	0.788358i	$0.710931\pi$
$48$	−2.14296	−0.309310
$49$	−6.45743	−0.922489
$50$	−1.00000	−0.141421
$51$	−6.73241	−0.942726
$52$	−4.66538	−0.646972
$53$	7.83253	1.07588	0.537940	−	0.842983i	$-0.319203\pi$
$53$	7.83253	1.07588	0.537940	+	0.842983i	$0.319203\pi$
$54$	−3.01668	−0.410518
$55$	3.15712	0.425706
$56$	−0.736597	−0.0984319
$57$	8.61426	1.14099
$58$	2.80984	0.368949
$59$	2.06051	0.268256	0.134128	−	0.990964i	$-0.457177\pi$
$59$	2.06051	0.268256	0.134128	+	0.990964i	$0.457177\pi$
$60$	2.14296	0.276655
$61$	4.47293	0.572700	0.286350	−	0.958125i	$-0.407558\pi$
$61$	4.47293	0.572700	0.286350	+	0.958125i	$0.407558\pi$
$62$	5.72133	0.726610
$63$	1.17287	0.147768
$64$	1.00000	0.125000
$65$	4.66538	0.578670
$66$	−6.76559	−0.832787
$67$	−8.16901	−0.998003	−0.499002	−	0.866601i	$-0.666300\pi$
$67$	−8.16901	−0.998003	−0.499002	+	0.866601i	$0.666300\pi$
$68$	3.14164	0.380980
$69$	15.2335	1.83389
$70$	0.736597	0.0880401
$71$	9.31937	1.10601	0.553003	−	0.833179i	$-0.313482\pi$
$71$	9.31937	1.10601	0.553003	+	0.833179i	$0.313482\pi$
$72$	−1.59228	−0.187652
$73$	−8.97252	−1.05015	−0.525077	−	0.851055i	$-0.675963\pi$
$73$	−8.97252	−1.05015	−0.525077	+	0.851055i	$0.675963\pi$
$74$	7.97212	0.926740
$75$	−2.14296	−0.247448
$76$	−4.01979	−0.461102
$77$	−2.32553	−0.265018
$78$	−9.99774	−1.13202
$79$	−15.5710	−1.75187	−0.875937	−	0.482425i	$-0.839756\pi$
$79$	−15.5710	−1.75187	−0.875937	+	0.482425i	$0.839756\pi$
$80$	−1.00000	−0.111803
$81$	−11.2415	−1.24905
$82$	10.3736	1.14557
$83$	15.7876	1.73291	0.866455	−	0.499255i	$-0.166393\pi$
$83$	15.7876	1.73291	0.866455	+	0.499255i	$0.166393\pi$
$84$	−1.57850	−0.172228
$85$	−3.14164	−0.340759
$86$	−10.0395	−1.08259
$87$	6.02137	0.645558
$88$	3.15712	0.336550
$89$	−6.08980	−0.645517	−0.322759	−	0.946481i	$-0.604610\pi$
$89$	−6.08980	−0.645517	−0.322759	+	0.946481i	$0.604610\pi$
$90$	1.59228	0.167841
$91$	−3.43651	−0.360244
$92$	−7.10860	−0.741123
$93$	12.2606	1.27136
$94$	8.43542	0.870048
$95$	4.01979	0.412422
$96$	2.14296	0.218715
$97$	−17.7555	−1.80280	−0.901399	−	0.432990i	$-0.857459\pi$
$97$	−17.7555	−1.80280	−0.901399	+	0.432990i	$0.857459\pi$
$98$	6.45743	0.652298
$99$	−5.02703	−0.505236
$100$	1.00000	0.100000
$101$	−14.1340	−1.40638	−0.703192	−	0.711000i	$-0.748242\pi$
$101$	−14.1340	−1.40638	−0.703192	+	0.711000i	$0.748242\pi$
$102$	6.73241	0.666608
$103$	5.56725	0.548558	0.274279	−	0.961650i	$-0.411561\pi$
$103$	5.56725	0.548558	0.274279	+	0.961650i	$0.411561\pi$
$104$	4.66538	0.457478
$105$	1.57850	0.154046
$106$	−7.83253	−0.760763
$107$	−12.2074	−1.18013	−0.590067	−	0.807354i	$-0.700899\pi$
$107$	−12.2074	−1.18013	−0.590067	+	0.807354i	$0.700899\pi$
$108$	3.01668	0.290280
$109$	−3.43406	−0.328923	−0.164461	−	0.986384i	$-0.552589\pi$
$109$	−3.43406	−0.328923	−0.164461	+	0.986384i	$0.552589\pi$
$110$	−3.15712	−0.301020
$111$	17.0839	1.62154
$112$	0.736597	0.0696018
$113$	17.4959	1.64587	0.822937	−	0.568133i	$-0.192334\pi$
$113$	17.4959	1.64587	0.822937	+	0.568133i	$0.192334\pi$
$114$	−8.61426	−0.806800
$115$	7.10860	0.662881
$116$	−2.80984	−0.260887
$117$	−7.42861	−0.686776
$118$	−2.06051	−0.189686
$119$	2.31412	0.212135
$120$	−2.14296	−0.195625
$121$	−1.03258	−0.0938712
$122$	−4.47293	−0.404960
$123$	22.2301	2.00442
$124$	−5.72133	−0.513791
$125$	−1.00000	−0.0894427
$126$	−1.17287	−0.104488
$127$	10.1949	0.904652	0.452326	−	0.891853i	$-0.350594\pi$
$127$	10.1949	0.904652	0.452326	+	0.891853i	$0.350594\pi$
$128$	−1.00000	−0.0883883
$129$	−21.5143	−1.89423
$130$	−4.66538	−0.409181
$131$	15.1027	1.31953	0.659764	−	0.751473i	$-0.270656\pi$
$131$	15.1027	1.31953	0.659764	+	0.751473i	$0.270656\pi$
$132$	6.76559	0.588869
$133$	−2.96097	−0.256748
$134$	8.16901	0.705695
$135$	−3.01668	−0.259635
$136$	−3.14164	−0.269393
$137$	−14.6783	−1.25405	−0.627026	−	0.778998i	$-0.715728\pi$
$137$	−14.6783	−1.25405	−0.627026	+	0.778998i	$0.715728\pi$
$138$	−15.2335	−1.29676
$139$	1.17572	0.0997236	0.0498618	−	0.998756i	$-0.484122\pi$
$139$	1.17572	0.0997236	0.0498618	+	0.998756i	$0.484122\pi$
$140$	−0.736597	−0.0622538
$141$	18.0768	1.52234
$142$	−9.31937	−0.782064
$143$	14.7292	1.23172
$144$	1.59228	0.132690
$145$	2.80984	0.233344
$146$	8.97252	0.742571
$147$	13.8380	1.14134
$148$	−7.97212	−0.655304
$149$	−4.18473	−0.342826	−0.171413	−	0.985199i	$-0.554833\pi$
$149$	−4.18473	−0.342826	−0.171413	+	0.985199i	$0.554833\pi$
$150$	2.14296	0.174972
$151$	−15.7280	−1.27993	−0.639963	−	0.768406i	$-0.721050\pi$
$151$	−15.7280	−1.27993	−0.639963	+	0.768406i	$0.721050\pi$
$152$	4.01979	0.326048
$153$	5.00238	0.404418
$154$	2.32553	0.187396
$155$	5.72133	0.459548
$156$	9.99774	0.800460
$157$	6.05642	0.483355	0.241678	−	0.970357i	$-0.422302\pi$
$157$	6.05642	0.483355	0.241678	+	0.970357i	$0.422302\pi$
$158$	15.5710	1.23876
$159$	−16.7848	−1.33112
$160$	1.00000	0.0790569
$161$	−5.23617	−0.412668
$162$	11.2415	0.883214
$163$	−21.4761	−1.68214	−0.841068	−	0.540929i	$-0.818073\pi$
$163$	−21.4761	−1.68214	−0.841068	+	0.540929i	$0.818073\pi$
$164$	−10.3736	−0.810039
$165$	−6.76559	−0.526700
$166$	−15.7876	−1.22535
$167$	5.52017	0.427164	0.213582	−	0.976925i	$-0.431487\pi$
$167$	5.52017	0.427164	0.213582	+	0.976925i	$0.431487\pi$
$168$	1.57850	0.121784
$169$	8.76580	0.674293
$170$	3.14164	0.240953
$171$	−6.40065	−0.489470
$172$	10.0395	0.765507
$173$	12.1974	0.927351	0.463676	−	0.886005i	$-0.346530\pi$
$173$	12.1974	0.927351	0.463676	+	0.886005i	$0.346530\pi$
$174$	−6.02137	−0.456479
$175$	0.736597	0.0556815
$176$	−3.15712	−0.237977
$177$	−4.41560	−0.331897
$178$	6.08980	0.456450
$179$	−6.54798	−0.489419	−0.244709	−	0.969596i	$-0.578693\pi$
$179$	−6.54798	−0.489419	−0.244709	+	0.969596i	$0.578693\pi$
$180$	−1.59228	−0.118682
$181$	−13.3931	−0.995504	−0.497752	−	0.867319i	$-0.665841\pi$
$181$	−13.3931	−0.995504	−0.497752	+	0.867319i	$0.665841\pi$
$182$	3.43651	0.254731
$183$	−9.58532	−0.708567
$184$	7.10860	0.524053
$185$	7.97212	0.586122
$186$	−12.2606	−0.898990
$187$	−9.91854	−0.725315
$188$	−8.43542	−0.615217
$189$	2.22208	0.161632
$190$	−4.01979	−0.291626
$191$	−7.17995	−0.519523	−0.259762	−	0.965673i	$-0.583644\pi$
$191$	−7.17995	−0.519523	−0.259762	+	0.965673i	$0.583644\pi$
$192$	−2.14296	−0.154655
$193$	14.3466	1.03269	0.516347	−	0.856380i	$-0.327292\pi$
$193$	14.3466	1.03269	0.516347	+	0.856380i	$0.327292\pi$
$194$	17.7555	1.27477
$195$	−9.99774	−0.715953
$196$	−6.45743	−0.461245
$197$	−20.7117	−1.47565	−0.737825	−	0.674993i	$-0.764147\pi$
$197$	−20.7117	−1.47565	−0.737825	+	0.674993i	$0.764147\pi$
$198$	5.02703	0.357256
$199$	−2.30944	−0.163712	−0.0818558	−	0.996644i	$-0.526085\pi$
$199$	−2.30944	−0.163712	−0.0818558	+	0.996644i	$0.526085\pi$
$200$	−1.00000	−0.0707107
$201$	17.5059	1.23477
$202$	14.1340	0.994463
$203$	−2.06972	−0.145266
$204$	−6.73241	−0.471363
$205$	10.3736	0.724521
$206$	−5.56725	−0.387889
$207$	−11.3189	−0.786719
$208$	−4.66538	−0.323486
$209$	12.6910	0.877853
$210$	−1.57850	−0.108927
$211$	−12.0649	−0.830579	−0.415290	−	0.909689i	$-0.636320\pi$
$211$	−12.0649	−0.830579	−0.415290	+	0.909689i	$0.636320\pi$
$212$	7.83253	0.537940
$213$	−19.9711	−1.36839
$214$	12.2074	0.834481
$215$	−10.0395	−0.684690
$216$	−3.01668	−0.205259
$217$	−4.21431	−0.286086
$218$	3.43406	0.232584
$219$	19.2278	1.29929
$220$	3.15712	0.212853
$221$	−14.6569	−0.985933
$222$	−17.0839	−1.14660
$223$	8.86581	0.593699	0.296849	−	0.954924i	$-0.404064\pi$
$223$	8.86581	0.593699	0.296849	+	0.954924i	$0.404064\pi$
$224$	−0.736597	−0.0492159
$225$	1.59228	0.106152
$226$	−17.4959	−1.16381
$227$	−5.87659	−0.390043	−0.195022	−	0.980799i	$-0.562478\pi$
$227$	−5.87659	−0.390043	−0.195022	+	0.980799i	$0.562478\pi$
$228$	8.61426	0.570493
$229$	−6.27352	−0.414566	−0.207283	−	0.978281i	$-0.566462\pi$
$229$	−6.27352	−0.414566	−0.207283	+	0.978281i	$0.566462\pi$
$230$	−7.10860	−0.468727
$231$	4.98351	0.327891
$232$	2.80984	0.184475
$233$	−15.2330	−0.997948	−0.498974	−	0.866617i	$-0.666290\pi$
$233$	−15.2330	−0.997948	−0.498974	+	0.866617i	$0.666290\pi$
$234$	7.42861	0.485624
$235$	8.43542	0.550266
$236$	2.06051	0.134128
$237$	33.3680	2.16749
$238$	−2.31412	−0.150002
$239$	−23.8799	−1.54466	−0.772330	−	0.635222i	$-0.780909\pi$
$239$	−23.8799	−1.54466	−0.772330	+	0.635222i	$0.780909\pi$
$240$	2.14296	0.138328
$241$	−16.3410	−1.05262	−0.526308	−	0.850294i	$-0.676424\pi$
$241$	−16.3410	−1.05262	−0.526308	+	0.850294i	$0.676424\pi$
$242$	1.03258	0.0663769
$243$	15.0400	0.964818
$244$	4.47293	0.286350
$245$	6.45743	0.412550
$246$	−22.2301	−1.41734
$247$	18.7539	1.19328
$248$	5.72133	0.363305
$249$	−33.8322	−2.14403
$250$	1.00000	0.0632456
$251$	−7.09340	−0.447732	−0.223866	−	0.974620i	$-0.571868\pi$
$251$	−7.09340	−0.447732	−0.223866	+	0.974620i	$0.571868\pi$
$252$	1.17287	0.0738839
$253$	22.4427	1.41096
$254$	−10.1949	−0.639686
$255$	6.73241	0.421600
$256$	1.00000	0.0625000
$257$	24.3092	1.51636	0.758182	−	0.652043i	$-0.226088\pi$
$257$	24.3092	1.51636	0.758182	+	0.652043i	$0.226088\pi$
$258$	21.5143	1.33942
$259$	−5.87224	−0.364883
$260$	4.66538	0.289335
$261$	−4.47405	−0.276937
$262$	−15.1027	−0.933047
$263$	−0.431138	−0.0265851	−0.0132925	−	0.999912i	$-0.504231\pi$
$263$	−0.431138	−0.0265851	−0.0132925	+	0.999912i	$0.504231\pi$
$264$	−6.76559	−0.416393
$265$	−7.83253	−0.481148
$266$	2.96097	0.181548
$267$	13.0502	0.798660
$268$	−8.16901	−0.499002
$269$	7.22774	0.440683	0.220342	−	0.975423i	$-0.429283\pi$
$269$	7.22774	0.440683	0.220342	+	0.975423i	$0.429283\pi$
$270$	3.01668	0.183589
$271$	−9.52488	−0.578595	−0.289298	−	0.957239i	$-0.593422\pi$
$271$	−9.52488	−0.578595	−0.289298	+	0.957239i	$0.593422\pi$
$272$	3.14164	0.190490
$273$	7.36430	0.445708
$274$	14.6783	0.886749
$275$	−3.15712	−0.190382
$276$	15.2335	0.916947
$277$	19.9210	1.19694	0.598468	−	0.801147i	$-0.295776\pi$
$277$	19.9210	1.19694	0.598468	+	0.801147i	$0.295776\pi$
$278$	−1.17572	−0.0705152
$279$	−9.10998	−0.545400
$280$	0.736597	0.0440201
$281$	26.6999	1.59278	0.796391	−	0.604782i	$-0.206740\pi$
$281$	26.6999	1.59278	0.796391	+	0.604782i	$0.206740\pi$
$282$	−18.0768	−1.07646
$283$	7.84636	0.466418	0.233209	−	0.972427i	$-0.425077\pi$
$283$	7.84636	0.466418	0.233209	+	0.972427i	$0.425077\pi$
$284$	9.31937	0.553003
$285$	−8.61426	−0.510265
$286$	−14.7292	−0.870955
$287$	−7.64113	−0.451041
$288$	−1.59228	−0.0938262
$289$	−7.13011	−0.419418
$290$	−2.80984	−0.164999
$291$	38.0493	2.23049
$292$	−8.97252	−0.525077
$293$	−3.76786	−0.220121	−0.110060	−	0.993925i	$-0.535104\pi$
$293$	−3.76786	−0.220121	−0.110060	+	0.993925i	$0.535104\pi$
$294$	−13.8380	−0.807049
$295$	−2.06051	−0.119968
$296$	7.97212	0.463370
$297$	−9.52403	−0.552640
$298$	4.18473	0.242415
$299$	33.1644	1.91794
$300$	−2.14296	−0.123724
$301$	7.39508	0.426246
$302$	15.7280	0.905044
$303$	30.2886	1.74003
$304$	−4.01979	−0.230551
$305$	−4.47293	−0.256119
$306$	−5.00238	−0.285967
$307$	9.59769	0.547769	0.273885	−	0.961763i	$-0.411691\pi$
$307$	9.59769	0.547769	0.273885	+	0.961763i	$0.411691\pi$
$308$	−2.32553	−0.132509
$309$	−11.9304	−0.678697
$310$	−5.72133	−0.324950
$311$	4.00013	0.226827	0.113413	−	0.993548i	$-0.463822\pi$
$311$	4.00013	0.226827	0.113413	+	0.993548i	$0.463822\pi$
$312$	−9.99774	−0.566010
$313$	−6.13589	−0.346821	−0.173410	−	0.984850i	$-0.555479\pi$
$313$	−6.13589	−0.346821	−0.173410	+	0.984850i	$0.555479\pi$
$314$	−6.05642	−0.341784
$315$	−1.17287	−0.0660838
$316$	−15.5710	−0.875937
$317$	−14.6446	−0.822520	−0.411260	−	0.911518i	$-0.634911\pi$
$317$	−14.6446	−0.822520	−0.411260	+	0.911518i	$0.634911\pi$
$318$	16.7848	0.941245
$319$	8.87099	0.496680
$320$	−1.00000	−0.0559017
$321$	26.1600	1.46011
$322$	5.23617	0.291801
$323$	−12.6287	−0.702682
$324$	−11.2415	−0.624527
$325$	−4.66538	−0.258789
$326$	21.4761	1.18945
$327$	7.35905	0.406956
$328$	10.3736	0.572784
$329$	−6.21351	−0.342562
$330$	6.76559	0.372433
$331$	28.6390	1.57414	0.787071	−	0.616863i	$-0.211597\pi$
$331$	28.6390	1.57414	0.787071	+	0.616863i	$0.211597\pi$
$332$	15.7876	0.866455
$333$	−12.6939	−0.695620
$334$	−5.52017	−0.302050
$335$	8.16901	0.446321
$336$	−1.57850	−0.0861141
$337$	14.7214	0.801927	0.400963	−	0.916094i	$-0.368675\pi$
$337$	14.7214	0.801927	0.400963	+	0.916094i	$0.368675\pi$
$338$	−8.76580	−0.476797
$339$	−37.4930	−2.03634
$340$	−3.14164	−0.170379
$341$	18.0629	0.978163
$342$	6.40065	0.346108
$343$	−9.91269	−0.535235
$344$	−10.0395	−0.541295
$345$	−15.2335	−0.820142
$346$	−12.1974	−0.655736
$347$	32.0717	1.72170	0.860849	−	0.508860i	$-0.169933\pi$
$347$	32.0717	1.72170	0.860849	+	0.508860i	$0.169933\pi$
$348$	6.02137	0.322779
$349$	−5.43075	−0.290701	−0.145351	−	0.989380i	$-0.546431\pi$
$349$	−5.43075	−0.290701	−0.145351	+	0.989380i	$0.546431\pi$
$350$	−0.736597	−0.0393727
$351$	−14.0740	−0.751213
$352$	3.15712	0.168275
$353$	−1.82256	−0.0970050	−0.0485025	−	0.998823i	$-0.515445\pi$
$353$	−1.82256	−0.0970050	−0.0485025	+	0.998823i	$0.515445\pi$
$354$	4.41560	0.234686
$355$	−9.31937	−0.494621
$356$	−6.08980	−0.322759
$357$	−4.95907	−0.262462
$358$	6.54798	0.346071
$359$	−25.8553	−1.36459	−0.682296	−	0.731076i	$-0.739019\pi$
$359$	−25.8553	−1.36459	−0.682296	+	0.731076i	$0.739019\pi$
$360$	1.59228	0.0839207
$361$	−2.84126	−0.149540
$362$	13.3931	0.703928
$363$	2.21279	0.116141
$364$	−3.43651	−0.180122
$365$	8.97252	0.469643
$366$	9.58532	0.501033
$367$	−8.23813	−0.430027	−0.215013	−	0.976611i	$-0.568980\pi$
$367$	−8.23813	−0.430027	−0.215013	+	0.976611i	$0.568980\pi$
$368$	−7.10860	−0.370562
$369$	−16.5176	−0.859874
$370$	−7.97212	−0.414451
$371$	5.76942	0.299533
$372$	12.2606	0.635682
$373$	−18.7443	−0.970543	−0.485271	−	0.874364i	$-0.661279\pi$
$373$	−18.7443	−0.970543	−0.485271	+	0.874364i	$0.661279\pi$
$374$	9.91854	0.512875
$375$	2.14296	0.110662
$376$	8.43542	0.435024
$377$	13.1090	0.675146
$378$	−2.22208	−0.114291
$379$	21.3593	1.09715	0.548577	−	0.836100i	$-0.315170\pi$
$379$	21.3593	1.09715	0.548577	+	0.836100i	$0.315170\pi$
$380$	4.01979	0.206211
$381$	−21.8473	−1.11927
$382$	7.17995	0.367358
$383$	24.9272	1.27372	0.636860	−	0.770979i	$-0.280233\pi$
$383$	24.9272	1.27372	0.636860	+	0.770979i	$0.280233\pi$
$384$	2.14296	0.109358
$385$	2.32553	0.118520
$386$	−14.3466	−0.730225
$387$	15.9858	0.812603
$388$	−17.7555	−0.901399
$389$	2.11348	0.107158	0.0535788	−	0.998564i	$-0.482937\pi$
$389$	2.11348	0.107158	0.0535788	+	0.998564i	$0.482937\pi$
$390$	9.99774	0.506255
$391$	−22.3327	−1.12941
$392$	6.45743	0.326149
$393$	−32.3645	−1.63257
$394$	20.7117	1.04344
$395$	15.5710	0.783462
$396$	−5.02703	−0.252618
$397$	−13.0699	−0.655959	−0.327979	−	0.944685i	$-0.606368\pi$
$397$	−13.0699	−0.655959	−0.327979	+	0.944685i	$0.606368\pi$
$398$	2.30944	0.115762
$399$	6.34524	0.317659
$400$	1.00000	0.0500000
$401$	29.6893	1.48261	0.741307	−	0.671166i	$-0.234206\pi$
$401$	29.6893	1.48261	0.741307	+	0.671166i	$0.234206\pi$
$402$	−17.5059	−0.873113
$403$	26.6922	1.32963
$404$	−14.1340	−0.703192
$405$	11.2415	0.558594
$406$	2.06972	0.102718
$407$	25.1690	1.24758
$408$	6.73241	0.333304
$409$	−4.03673	−0.199603	−0.0998017	−	0.995007i	$-0.531821\pi$
$409$	−4.03673	−0.199603	−0.0998017	+	0.995007i	$0.531821\pi$
$410$	−10.3736	−0.512313
$411$	31.4550	1.55156
$412$	5.56725	0.274279
$413$	1.51777	0.0746844
$414$	11.3189	0.556294
$415$	−15.7876	−0.774981
$416$	4.66538	0.228739
$417$	−2.51953	−0.123382
$418$	−12.6910	−0.620736
$419$	39.1232	1.91129	0.955647	−	0.294516i	$-0.0951583\pi$
$419$	39.1232	1.91129	0.955647	+	0.294516i	$0.0951583\pi$
$420$	1.57850	0.0770228
$421$	9.80007	0.477626	0.238813	−	0.971066i	$-0.423242\pi$
$421$	9.80007	0.477626	0.238813	+	0.971066i	$0.423242\pi$
$422$	12.0649	0.587308
$423$	−13.4316	−0.653066
$424$	−7.83253	−0.380381
$425$	3.14164	0.152392
$426$	19.9711	0.967601
$427$	3.29475	0.159444
$428$	−12.2074	−0.590067
$429$	−31.5641	−1.52393
$430$	10.0395	0.484149
$431$	9.30372	0.448145	0.224072	−	0.974573i	$-0.428065\pi$
$431$	9.30372	0.448145	0.224072	+	0.974573i	$0.428065\pi$
$432$	3.01668	0.145140
$433$	11.2128	0.538851	0.269426	−	0.963021i	$-0.413166\pi$
$433$	11.2128	0.538851	0.269426	+	0.963021i	$0.413166\pi$
$434$	4.21431	0.202293
$435$	−6.02137	−0.288703
$436$	−3.43406	−0.164461
$437$	28.5751	1.36693
$438$	−19.2278	−0.918738
$439$	25.9606	1.23903	0.619516	−	0.784984i	$-0.287329\pi$
$439$	25.9606	1.23903	0.619516	+	0.784984i	$0.287329\pi$
$440$	−3.15712	−0.150510
$441$	−10.2821	−0.489622
$442$	14.6569	0.697160
$443$	−3.75852	−0.178573	−0.0892864	−	0.996006i	$-0.528459\pi$
$443$	−3.75852	−0.178573	−0.0892864	+	0.996006i	$0.528459\pi$
$444$	17.0839	0.810768
$445$	6.08980	0.288684
$446$	−8.86581	−0.419808
$447$	8.96772	0.424158
$448$	0.736597	0.0348009
$449$	−40.5643	−1.91435	−0.957173	−	0.289516i	$-0.906506\pi$
$449$	−40.5643	−1.91435	−0.957173	+	0.289516i	$0.906506\pi$
$450$	−1.59228	−0.0750610
$451$	32.7506	1.54216
$452$	17.4959	0.822937
$453$	33.7045	1.58357
$454$	5.87659	0.275802
$455$	3.43651	0.161106
$456$	−8.61426	−0.403400
$457$	10.9802	0.513632	0.256816	−	0.966460i	$-0.417327\pi$
$457$	10.9802	0.513632	0.256816	+	0.966460i	$0.417327\pi$
$458$	6.27352	0.293142
$459$	9.47732	0.442364
$460$	7.10860	0.331440
$461$	5.09029	0.237078	0.118539	−	0.992949i	$-0.462179\pi$
$461$	5.09029	0.237078	0.118539	+	0.992949i	$0.462179\pi$
$462$	−4.98351	−0.231854
$463$	12.7025	0.590334	0.295167	−	0.955446i	$-0.404625\pi$
$463$	12.7025	0.590334	0.295167	+	0.955446i	$0.404625\pi$
$464$	−2.80984	−0.130443
$465$	−12.2606	−0.568571
$466$	15.2330	0.705655
$467$	9.88392	0.457373	0.228687	−	0.973500i	$-0.426557\pi$
$467$	9.88392	0.457373	0.228687	+	0.973500i	$0.426557\pi$
$468$	−7.42861	−0.343388
$469$	−6.01726	−0.277851
$470$	−8.43542	−0.389097
$471$	−12.9787	−0.598026
$472$	−2.06051	−0.0948428
$473$	−31.6960	−1.45738
$474$	−33.3680	−1.53265
$475$	−4.01979	−0.184441
$476$	2.31412	0.106068
$477$	12.4716	0.571036
$478$	23.8799	1.09224
$479$	−4.77224	−0.218049	−0.109025	−	0.994039i	$-0.534773\pi$
$479$	−4.77224	−0.218049	−0.109025	+	0.994039i	$0.534773\pi$
$480$	−2.14296	−0.0978124
$481$	37.1930	1.69585
$482$	16.3410	0.744313
$483$	11.2209	0.510569
$484$	−1.03258	−0.0469356
$485$	17.7555	0.806236
$486$	−15.0400	−0.682229
$487$	0.963447	0.0436580	0.0218290	−	0.999762i	$-0.493051\pi$
$487$	0.963447	0.0436580	0.0218290	+	0.999762i	$0.493051\pi$
$488$	−4.47293	−0.202480
$489$	46.0224	2.08121
$490$	−6.45743	−0.291717
$491$	31.5297	1.42292	0.711459	−	0.702728i	$-0.248035\pi$
$491$	31.5297	1.42292	0.711459	+	0.702728i	$0.248035\pi$
$492$	22.2301	1.00221
$493$	−8.82749	−0.397570
$494$	−18.7539	−0.843777
$495$	5.02703	0.225948
$496$	−5.72133	−0.256895
$497$	6.86462	0.307920
$498$	33.8322	1.51605
$499$	28.3383	1.26860	0.634298	−	0.773089i	$-0.281289\pi$
$499$	28.3383	1.26860	0.634298	+	0.773089i	$0.281289\pi$
$500$	−1.00000	−0.0447214
$501$	−11.8295	−0.528504
$502$	7.09340	0.316594
$503$	−19.2281	−0.857338	−0.428669	−	0.903462i	$-0.641017\pi$
$503$	−19.2281	−0.857338	−0.428669	+	0.903462i	$0.641017\pi$
$504$	−1.17287	−0.0522438
$505$	14.1340	0.628954
$506$	−22.4427	−0.997701
$507$	−18.7848	−0.834261
$508$	10.1949	0.452326
$509$	29.6406	1.31380	0.656899	−	0.753979i	$-0.271868\pi$
$509$	29.6406	1.31380	0.656899	+	0.753979i	$0.271868\pi$
$510$	−6.73241	−0.298116
$511$	−6.60913	−0.292371
$512$	−1.00000	−0.0441942
$513$	−12.1264	−0.535395
$514$	−24.3092	−1.07223
$515$	−5.56725	−0.245323
$516$	−21.5143	−0.947115
$517$	26.6317	1.17126
$518$	5.87224	0.258011
$519$	−26.1386	−1.14736
$520$	−4.66538	−0.204591
$521$	−7.06813	−0.309660	−0.154830	−	0.987941i	$-0.549483\pi$
$521$	−7.06813	−0.309660	−0.154830	+	0.987941i	$0.549483\pi$
$522$	4.47405	0.195824
$523$	28.9340	1.26520	0.632598	−	0.774481i	$-0.281989\pi$
$523$	28.9340	1.26520	0.632598	+	0.774481i	$0.281989\pi$
$524$	15.1027	0.659764
$525$	−1.57850	−0.0688913
$526$	0.431138	0.0187985
$527$	−17.9744	−0.782975
$528$	6.76559	0.294435
$529$	27.5323	1.19705
$530$	7.83253	0.340223
$531$	3.28092	0.142380
$532$	−2.96097	−0.128374
$533$	48.3966	2.09629
$534$	−13.0502	−0.564738
$535$	12.2074	0.527772
$536$	8.16901	0.352847
$537$	14.0321	0.605528
$538$	−7.22774	−0.311610
$539$	20.3869	0.878125
$540$	−3.01668	−0.129817
$541$	2.18518	0.0939482	0.0469741	−	0.998896i	$-0.485042\pi$
$541$	2.18518	0.0939482	0.0469741	+	0.998896i	$0.485042\pi$
$542$	9.52488	0.409128
$543$	28.7010	1.23168
$544$	−3.14164	−0.134697
$545$	3.43406	0.147099
$546$	−7.36430	−0.315163
$547$	−25.6177	−1.09533	−0.547667	−	0.836697i	$-0.684484\pi$
$547$	−25.6177	−1.09533	−0.547667	+	0.836697i	$0.684484\pi$
$548$	−14.6783	−0.627026
$549$	7.12218	0.303967
$550$	3.15712	0.134620
$551$	11.2950	0.481181
$552$	−15.2335	−0.648379
$553$	−11.4695	−0.487735
$554$	−19.9210	−0.846362
$555$	−17.0839	−0.725173
$556$	1.17572	0.0498618
$557$	−20.9176	−0.886306	−0.443153	−	0.896446i	$-0.646140\pi$
$557$	−20.9176	−0.886306	−0.443153	+	0.896446i	$0.646140\pi$
$558$	9.10998	0.385656
$559$	−46.8383	−1.98105
$560$	−0.736597	−0.0311269
$561$	21.2550	0.897388
$562$	−26.6999	−1.12627
$563$	33.7960	1.42433	0.712167	−	0.702010i	$-0.247714\pi$
$563$	33.7960	1.42433	0.712167	+	0.702010i	$0.247714\pi$
$564$	18.0768	0.761170
$565$	−17.4959	−0.736057
$566$	−7.84636	−0.329807
$567$	−8.28044	−0.347746
$568$	−9.31937	−0.391032
$569$	18.9228	0.793285	0.396642	−	0.917973i	$-0.370175\pi$
$569$	18.9228	0.793285	0.396642	+	0.917973i	$0.370175\pi$
$570$	8.61426	0.360812
$571$	−46.6961	−1.95417	−0.977084	−	0.212852i	$-0.931725\pi$
$571$	−46.6961	−1.95417	−0.977084	+	0.212852i	$0.931725\pi$
$572$	14.7292	0.615858
$573$	15.3864	0.642774
$574$	7.64113	0.318934
$575$	−7.10860	−0.296449
$576$	1.59228	0.0663452
$577$	−20.2305	−0.842209	−0.421104	−	0.907012i	$-0.638357\pi$
$577$	−20.2305	−0.842209	−0.421104	+	0.907012i	$0.638357\pi$
$578$	7.13011	0.296573
$579$	−30.7443	−1.27769
$580$	2.80984	0.116672
$581$	11.6291	0.482455
$582$	−38.0493	−1.57720
$583$	−24.7283	−1.02414
$584$	8.97252	0.371286
$585$	7.42861	0.307135
$586$	3.76786	0.155649
$587$	32.3018	1.33324	0.666619	−	0.745399i	$-0.267741\pi$
$587$	32.3018	1.33324	0.666619	+	0.745399i	$0.267741\pi$
$588$	13.8380	0.570670
$589$	22.9986	0.947639
$590$	2.06051	0.0848300
$591$	44.3844	1.82573
$592$	−7.97212	−0.327652
$593$	4.03651	0.165760	0.0828799	−	0.996560i	$-0.473588\pi$
$593$	4.03651	0.165760	0.0828799	+	0.996560i	$0.473588\pi$
$594$	9.52403	0.390776
$595$	−2.31412	−0.0948697
$596$	−4.18473	−0.171413
$597$	4.94903	0.202550
$598$	−33.1644	−1.35619
$599$	17.7830	0.726594	0.363297	−	0.931673i	$-0.381651\pi$
$599$	17.7830	0.726594	0.363297	+	0.931673i	$0.381651\pi$
$600$	2.14296	0.0874860
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	−7.39508	−0.301401
$603$	−13.0074	−0.529701
$604$	−15.7280	−0.639963
$605$	1.03258	0.0419805
$606$	−30.2886	−1.23039
$607$	−41.7377	−1.69408	−0.847040	−	0.531529i	$-0.821618\pi$
$607$	−41.7377	−1.69408	−0.847040	+	0.531529i	$0.821618\pi$
$608$	4.01979	0.163024
$609$	4.43532	0.179728
$610$	4.47293	0.181104
$611$	39.3545	1.59211
$612$	5.00238	0.202209
$613$	16.3315	0.659623	0.329812	−	0.944047i	$-0.393015\pi$
$613$	16.3315	0.659623	0.329812	+	0.944047i	$0.393015\pi$
$614$	−9.59769	−0.387331
$615$	−22.2301	−0.896405
$616$	2.32553	0.0936981
$617$	−28.9374	−1.16497	−0.582487	−	0.812840i	$-0.697920\pi$
$617$	−28.9374	−1.16497	−0.582487	+	0.812840i	$0.697920\pi$
$618$	11.9304	0.479912
$619$	−4.64048	−0.186517	−0.0932583	−	0.995642i	$-0.529728\pi$
$619$	−4.64048	−0.186517	−0.0932583	+	0.995642i	$0.529728\pi$
$620$	5.72133	0.229774
$621$	−21.4444	−0.860534
$622$	−4.00013	−0.160391
$623$	−4.48573	−0.179717
$624$	9.99774	0.400230
$625$	1.00000	0.0400000
$626$	6.13589	0.245239
$627$	−27.1963	−1.08611
$628$	6.05642	0.241678
$629$	−25.0455	−0.998630
$630$	1.17287	0.0467283
$631$	−38.8504	−1.54661	−0.773305	−	0.634035i	$-0.781398\pi$
$631$	−38.8504	−1.54661	−0.773305	+	0.634035i	$0.781398\pi$
$632$	15.5710	0.619381
$633$	25.8545	1.02763
$634$	14.6446	0.581609
$635$	−10.1949	−0.404573
$636$	−16.7848	−0.665561
$637$	30.1264	1.19365
$638$	−8.87099	−0.351206
$639$	14.8391	0.587025
$640$	1.00000	0.0395285
$641$	−19.3171	−0.762978	−0.381489	−	0.924373i	$-0.624589\pi$
$641$	−19.3171	−0.762978	−0.381489	+	0.924373i	$0.624589\pi$
$642$	−26.1600	−1.03245
$643$	3.88125	0.153062	0.0765309	−	0.997067i	$-0.475616\pi$
$643$	3.88125	0.153062	0.0765309	+	0.997067i	$0.475616\pi$
$644$	−5.23617	−0.206334
$645$	21.5143	0.847126
$646$	12.6287	0.496871
$647$	7.09591	0.278969	0.139485	−	0.990224i	$-0.455455\pi$
$647$	7.09591	0.278969	0.139485	+	0.990224i	$0.455455\pi$
$648$	11.2415	0.441607
$649$	−6.50529	−0.255355
$650$	4.66538	0.182991
$651$	9.03111	0.353957
$652$	−21.4761	−0.841068
$653$	44.8000	1.75316	0.876581	−	0.481255i	$-0.159819\pi$
$653$	44.8000	1.75316	0.876581	+	0.481255i	$0.159819\pi$
$654$	−7.35905	−0.287762
$655$	−15.1027	−0.590111
$656$	−10.3736	−0.405019
$657$	−14.2868	−0.557381
$658$	6.21351	0.242228
$659$	18.1165	0.705720	0.352860	−	0.935676i	$-0.385209\pi$
$659$	18.1165	0.705720	0.352860	+	0.935676i	$0.385209\pi$
$660$	−6.76559	−0.263350
$661$	15.1010	0.587359	0.293680	−	0.955904i	$-0.405120\pi$
$661$	15.1010	0.587359	0.293680	+	0.955904i	$0.405120\pi$
$662$	−28.6390	−1.11309
$663$	31.4093	1.21984
$664$	−15.7876	−0.612676
$665$	2.96097	0.114821
$666$	12.6939	0.491878
$667$	19.9740	0.773397
$668$	5.52017	0.213582
$669$	−18.9991	−0.734547
$670$	−8.16901	−0.315596
$671$	−14.1216	−0.545158
$672$	1.57850	0.0608919
$673$	11.5445	0.445006	0.222503	−	0.974932i	$-0.428577\pi$
$673$	11.5445	0.445006	0.222503	+	0.974932i	$0.428577\pi$
$674$	−14.7214	−0.567048
$675$	3.01668	0.116112
$676$	8.76580	0.337146
$677$	5.22090	0.200656	0.100328	−	0.994954i	$-0.468011\pi$
$677$	5.22090	0.200656	0.100328	+	0.994954i	$0.468011\pi$
$678$	37.4930	1.43991
$679$	−13.0786	−0.501912
$680$	3.14164	0.120476
$681$	12.5933	0.482577
$682$	−18.0629	−0.691665
$683$	40.5236	1.55059	0.775295	−	0.631599i	$-0.217601\pi$
$683$	40.5236	1.55059	0.775295	+	0.631599i	$0.217601\pi$
$684$	−6.40065	−0.244735
$685$	14.6783	0.560829
$686$	9.91269	0.378468
$687$	13.4439	0.512917
$688$	10.0395	0.382753
$689$	−36.5418	−1.39213
$690$	15.2335	0.579928
$691$	18.8301	0.716332	0.358166	−	0.933658i	$-0.383402\pi$
$691$	18.8301	0.716332	0.358166	+	0.933658i	$0.383402\pi$
$692$	12.1974	0.463676
$693$	−3.70290	−0.140661
$694$	−32.0717	−1.21742
$695$	−1.17572	−0.0445978
$696$	−6.02137	−0.228239
$697$	−32.5900	−1.23443
$698$	5.43075	0.205557
$699$	32.6437	1.23470
$700$	0.736597	0.0278407
$701$	−38.9301	−1.47037	−0.735186	−	0.677866i	$-0.762905\pi$
$701$	−38.9301	−1.47037	−0.735186	+	0.677866i	$0.762905\pi$
$702$	14.0740	0.531188
$703$	32.0463	1.20865
$704$	−3.15712	−0.118988
$705$	−18.0768	−0.680811
$706$	1.82256	0.0685929
$707$	−10.4110	−0.391547
$708$	−4.41560	−0.165948
$709$	15.8921	0.596841	0.298421	−	0.954434i	$-0.403540\pi$
$709$	15.8921	0.596841	0.298421	+	0.954434i	$0.403540\pi$
$710$	9.31937	0.349750
$711$	−24.7934	−0.929827
$712$	6.08980	0.228225
$713$	40.6707	1.52313
$714$	4.95907	0.185589
$715$	−14.7292	−0.550840
$716$	−6.54798	−0.244709
$717$	51.1736	1.91111
$718$	25.8553	0.964913
$719$	−20.8768	−0.778572	−0.389286	−	0.921117i	$-0.627278\pi$
$719$	−20.8768	−0.778572	−0.389286	+	0.921117i	$0.627278\pi$
$720$	−1.59228	−0.0593409
$721$	4.10082	0.152723
$722$	2.84126	0.105741
$723$	35.0182	1.30234
$724$	−13.3931	−0.497752
$725$	−2.80984	−0.104355
$726$	−2.21279	−0.0821242
$727$	−3.27559	−0.121485	−0.0607425	−	0.998153i	$-0.519347\pi$
$727$	−3.27559	−0.121485	−0.0607425	+	0.998153i	$0.519347\pi$
$728$	3.43651	0.127365
$729$	1.49427	0.0553432
$730$	−8.97252	−0.332088
$731$	31.5406	1.16657
$732$	−9.58532	−0.354284
$733$	−47.3900	−1.75039	−0.875196	−	0.483769i	$-0.839267\pi$
$733$	−47.3900	−1.75039	−0.875196	+	0.483769i	$0.839267\pi$
$734$	8.23813	0.304075
$735$	−13.8380	−0.510423
$736$	7.10860	0.262027
$737$	25.7905	0.950007
$738$	16.5176	0.608023
$739$	−49.8496	−1.83375	−0.916874	−	0.399176i	$-0.869296\pi$
$739$	−49.8496	−1.83375	−0.916874	+	0.399176i	$0.869296\pi$
$740$	7.97212	0.293061
$741$	−40.1888	−1.47637
$742$	−5.76942	−0.211802
$743$	9.39024	0.344494	0.172247	−	0.985054i	$-0.444897\pi$
$743$	9.39024	0.344494	0.172247	+	0.985054i	$0.444897\pi$
$744$	−12.2606	−0.449495
$745$	4.18473	0.153317
$746$	18.7443	0.686277
$747$	25.1383	0.919762
$748$	−9.91854	−0.362658
$749$	−8.99193	−0.328558
$750$	−2.14296	−0.0782499
$751$	3.92141	0.143094	0.0715472	−	0.997437i	$-0.477206\pi$
$751$	3.92141	0.143094	0.0715472	+	0.997437i	$0.477206\pi$
$752$	−8.43542	−0.307608
$753$	15.2009	0.553951
$754$	−13.1090	−0.477400
$755$	15.7280	0.572400
$756$	2.22208	0.0808162
$757$	35.4154	1.28719	0.643597	−	0.765365i	$-0.277441\pi$
$757$	35.4154	1.28719	0.643597	+	0.765365i	$0.277441\pi$
$758$	−21.3593	−0.775805
$759$	−48.0939	−1.74570
$760$	−4.01979	−0.145813
$761$	47.8165	1.73335	0.866673	−	0.498877i	$-0.166254\pi$
$761$	47.8165	1.73335	0.866673	+	0.498877i	$0.166254\pi$
$762$	21.8473	0.791445
$763$	−2.52951	−0.0915746
$764$	−7.17995	−0.259762
$765$	−5.00238	−0.180861
$766$	−24.9272	−0.900656
$767$	−9.61308	−0.347108
$768$	−2.14296	−0.0773275
$769$	−26.8548	−0.968410	−0.484205	−	0.874955i	$-0.660891\pi$
$769$	−26.8548	−0.968410	−0.484205	+	0.874955i	$0.660891\pi$
$770$	−2.32553	−0.0838061
$771$	−52.0936	−1.87611
$772$	14.3466	0.516347
$773$	−46.8908	−1.68654	−0.843272	−	0.537488i	$-0.819373\pi$
$773$	−46.8908	−1.68654	−0.843272	+	0.537488i	$0.819373\pi$
$774$	−15.9858	−0.574597
$775$	−5.72133	−0.205516
$776$	17.7555	0.637385
$777$	12.5840	0.451448
$778$	−2.11348	−0.0757718
$779$	41.6996	1.49404
$780$	−9.99774	−0.357976
$781$	−29.4224	−1.05282
$782$	22.3327	0.798615
$783$	−8.47638	−0.302921
$784$	−6.45743	−0.230622
$785$	−6.05642	−0.216163
$786$	32.3645	1.15440
$787$	−20.9834	−0.747978	−0.373989	−	0.927433i	$-0.622010\pi$
$787$	−20.9834	−0.747978	−0.373989	+	0.927433i	$0.622010\pi$
$788$	−20.7117	−0.737825
$789$	0.923911	0.0328921
$790$	−15.5710	−0.553991
$791$	12.8874	0.458223
$792$	5.02703	0.178628
$793$	−20.8679	−0.741042
$794$	13.0699	0.463833
$795$	16.7848	0.595296
$796$	−2.30944	−0.0818558
$797$	21.7525	0.770514	0.385257	−	0.922809i	$-0.374113\pi$
$797$	21.7525	0.770514	0.385257	+	0.922809i	$0.374113\pi$
$798$	−6.34524	−0.224619
$799$	−26.5011	−0.937540
$800$	−1.00000	−0.0353553
$801$	−9.69669	−0.342616
$802$	−29.6893	−1.04837
$803$	28.3273	0.999650
$804$	17.5059	0.617384
$805$	5.23617	0.184551
$806$	−26.6922	−0.940193
$807$	−15.4888	−0.545230
$808$	14.1340	0.497232
$809$	−2.18991	−0.0769932	−0.0384966	−	0.999259i	$-0.512257\pi$
$809$	−2.18991	−0.0769932	−0.0384966	+	0.999259i	$0.512257\pi$
$810$	−11.2415	−0.394985
$811$	10.7749	0.378359	0.189180	−	0.981943i	$-0.439417\pi$
$811$	10.7749	0.378359	0.189180	+	0.981943i	$0.439417\pi$
$812$	−2.06972	−0.0726328
$813$	20.4114	0.715861
$814$	−25.1690	−0.882171
$815$	21.4761	0.752274
$816$	−6.73241	−0.235682
$817$	−40.3568	−1.41191
$818$	4.03673	0.141141
$819$	−5.47189	−0.191203
$820$	10.3736	0.362260
$821$	−46.2372	−1.61369	−0.806845	−	0.590763i	$-0.798827\pi$
$821$	−46.2372	−1.61369	−0.806845	+	0.590763i	$0.798827\pi$
$822$	−31.4550	−1.09712
$823$	−18.1597	−0.633006	−0.316503	−	0.948591i	$-0.602509\pi$
$823$	−18.1597	−0.633006	−0.316503	+	0.948591i	$0.602509\pi$
$824$	−5.56725	−0.193945
$825$	6.76559	0.235548
$826$	−1.51777	−0.0528099
$827$	−3.22987	−0.112313	−0.0561567	−	0.998422i	$-0.517885\pi$
$827$	−3.22987	−0.112313	−0.0561567	+	0.998422i	$0.517885\pi$
$828$	−11.3189	−0.393359
$829$	2.96612	0.103018	0.0515088	−	0.998673i	$-0.483597\pi$
$829$	2.96612	0.103018	0.0515088	+	0.998673i	$0.483597\pi$
$830$	15.7876	0.547994
$831$	−42.6899	−1.48090
$832$	−4.66538	−0.161743
$833$	−20.2869	−0.702899
$834$	2.51953	0.0872442
$835$	−5.52017	−0.191033
$836$	12.6910	0.438927
$837$	−17.2594	−0.596573
$838$	−39.1232	−1.35149
$839$	46.7222	1.61303	0.806514	−	0.591214i	$-0.201351\pi$
$839$	46.7222	1.61303	0.806514	+	0.591214i	$0.201351\pi$
$840$	−1.57850	−0.0544634
$841$	−21.1048	−0.727753
$842$	−9.80007	−0.337733
$843$	−57.2169	−1.97065
$844$	−12.0649	−0.415290
$845$	−8.76580	−0.301553
$846$	13.4316	0.461788
$847$	−0.760597	−0.0261344
$848$	7.83253	0.268970
$849$	−16.8145	−0.577071
$850$	−3.14164	−0.107757
$851$	56.6706	1.94264
$852$	−19.9711	−0.684197
$853$	−21.2710	−0.728306	−0.364153	−	0.931339i	$-0.618641\pi$
$853$	−21.2710	−0.728306	−0.364153	+	0.931339i	$0.618641\pi$
$854$	−3.29475	−0.112744
$855$	6.40065	0.218898
$856$	12.2074	0.417240
$857$	−20.0645	−0.685391	−0.342696	−	0.939447i	$-0.611340\pi$
$857$	−20.0645	−0.685391	−0.342696	+	0.939447i	$0.611340\pi$
$858$	31.5641	1.07758
$859$	−8.78364	−0.299694	−0.149847	−	0.988709i	$-0.547878\pi$
$859$	−8.78364	−0.299694	−0.149847	+	0.988709i	$0.547878\pi$
$860$	−10.0395	−0.342345
$861$	16.3746	0.558046
$862$	−9.30372	−0.316886
$863$	15.1021	0.514083	0.257041	−	0.966400i	$-0.417252\pi$
$863$	15.1021	0.514083	0.257041	+	0.966400i	$0.417252\pi$
$864$	−3.01668	−0.102630
$865$	−12.1974	−0.414724
$866$	−11.2128	−0.381025
$867$	15.2795	0.518920
$868$	−4.21431	−0.143043
$869$	49.1595	1.66762
$870$	6.02137	0.204144
$871$	38.1116	1.29136
$872$	3.43406	0.116292
$873$	−28.2718	−0.956855
$874$	−28.5751	−0.966568
$875$	−0.736597	−0.0249015
$876$	19.2278	0.649646
$877$	−36.3730	−1.22823	−0.614115	−	0.789217i	$-0.710487\pi$
$877$	−36.3730	−1.22823	−0.614115	+	0.789217i	$0.710487\pi$
$878$	−25.9606	−0.876128
$879$	8.07439	0.272342
$880$	3.15712	0.106427
$881$	−46.5628	−1.56874	−0.784371	−	0.620292i	$-0.787014\pi$
$881$	−46.5628	−1.56874	−0.784371	+	0.620292i	$0.787014\pi$
$882$	10.2821	0.346215
$883$	−26.4906	−0.891480	−0.445740	−	0.895163i	$-0.647059\pi$
$883$	−26.4906	−0.891480	−0.445740	+	0.895163i	$0.647059\pi$
$884$	−14.6569	−0.492967
$885$	4.41560	0.148429
$886$	3.75852	0.126270
$887$	−37.8911	−1.27226	−0.636129	−	0.771582i	$-0.719466\pi$
$887$	−37.8911	−1.27226	−0.636129	+	0.771582i	$0.719466\pi$
$888$	−17.0839	−0.573300
$889$	7.50954	0.251862
$890$	−6.08980	−0.204131
$891$	35.4907	1.18898
$892$	8.86581	0.296849
$893$	33.9087	1.13471
$894$	−8.96772	−0.299925
$895$	6.54798	0.218875
$896$	−0.736597	−0.0246080
$897$	−71.0700	−2.37296
$898$	40.5643	1.35365
$899$	16.0760	0.536164
$900$	1.59228	0.0530761
$901$	24.6070	0.819777
$902$	−32.7506	−1.09048
$903$	−15.8474	−0.527368
$904$	−17.4959	−0.581904
$905$	13.3931	0.445203
$906$	−33.7045	−1.11976
$907$	−27.8282	−0.924019	−0.462009	−	0.886875i	$-0.652871\pi$
$907$	−27.8282	−0.924019	−0.462009	+	0.886875i	$0.652871\pi$
$908$	−5.87659	−0.195022
$909$	−22.5053	−0.746454
$910$	−3.43651	−0.113919
$911$	9.80608	0.324890	0.162445	−	0.986718i	$-0.448062\pi$
$911$	9.80608	0.324890	0.162445	+	0.986718i	$0.448062\pi$
$912$	8.61426	0.285247
$913$	−49.8433	−1.64957
$914$	−10.9802	−0.363193
$915$	9.58532	0.316881
$916$	−6.27352	−0.207283
$917$	11.1246	0.367366
$918$	−9.47732	−0.312798
$919$	3.59770	0.118677	0.0593386	−	0.998238i	$-0.481101\pi$
$919$	3.59770	0.118677	0.0593386	+	0.998238i	$0.481101\pi$
$920$	−7.10860	−0.234364
$921$	−20.5675	−0.677722
$922$	−5.09029	−0.167640
$923$	−43.4785	−1.43111
$924$	4.98351	0.163945
$925$	−7.97212	−0.262122
$926$	−12.7025	−0.417429
$927$	8.86465	0.291153
$928$	2.80984	0.0922374
$929$	−21.9392	−0.719801	−0.359901	−	0.932991i	$-0.617189\pi$
$929$	−21.9392	−0.719801	−0.359901	+	0.932991i	$0.617189\pi$
$930$	12.2606	0.402041
$931$	25.9575	0.850723
$932$	−15.2330	−0.498974
$933$	−8.57213	−0.280639
$934$	−9.88392	−0.323412
$935$	9.91854	0.324371
$936$	7.42861	0.242812
$937$	43.5668	1.42327	0.711633	−	0.702552i	$-0.247956\pi$
$937$	43.5668	1.42327	0.711633	+	0.702552i	$0.247956\pi$
$938$	6.01726	0.196471
$939$	13.1490	0.429100
$940$	8.43542	0.275133
$941$	23.9417	0.780478	0.390239	−	0.920714i	$-0.372392\pi$
$941$	23.9417	0.780478	0.390239	+	0.920714i	$0.372392\pi$
$942$	12.9787	0.422868
$943$	73.7415	2.40135
$944$	2.06051	0.0670640
$945$	−2.22208	−0.0722842
$946$	31.6960	1.03053
$947$	−56.2049	−1.82641	−0.913206	−	0.407498i	$-0.866401\pi$
$947$	−56.2049	−1.82641	−0.913206	+	0.407498i	$0.866401\pi$
$948$	33.3680	1.08374
$949$	41.8602	1.35884
$950$	4.01979	0.130419
$951$	31.3827	1.01765
$952$	−2.31412	−0.0750011
$953$	13.3214	0.431524	0.215762	−	0.976446i	$-0.430776\pi$
$953$	13.3214	0.431524	0.215762	+	0.976446i	$0.430776\pi$
$954$	−12.4716	−0.403783
$955$	7.17995	0.232338
$956$	−23.8799	−0.772330
$957$	−19.0102	−0.614512
$958$	4.77224	0.154184
$959$	−10.8120	−0.349137
$960$	2.14296	0.0691638
$961$	1.73361	0.0559229
$962$	−37.1930	−1.19915
$963$	−19.4376	−0.626369
$964$	−16.3410	−0.526308
$965$	−14.3466	−0.461835
$966$	−11.2209	−0.361027
$967$	4.92304	0.158314	0.0791572	−	0.996862i	$-0.474777\pi$
$967$	4.92304	0.158314	0.0791572	+	0.996862i	$0.474777\pi$
$968$	1.03258	0.0331885
$969$	27.0629	0.869386
$970$	−17.7555	−0.570095
$971$	24.1991	0.776585	0.388292	−	0.921536i	$-0.373065\pi$
$971$	24.1991	0.776585	0.388292	+	0.921536i	$0.373065\pi$
$972$	15.0400	0.482409
$973$	0.866034	0.0277638
$974$	−0.963447	−0.0308708
$975$	9.99774	0.320184
$976$	4.47293	0.143175
$977$	11.4315	0.365728	0.182864	−	0.983138i	$-0.441463\pi$
$977$	11.4315	0.365728	0.182864	+	0.983138i	$0.441463\pi$
$978$	−46.0224	−1.47163
$979$	19.2262	0.614473
$980$	6.45743	0.206275
$981$	−5.46799	−0.174580
$982$	−31.5297	−1.00615
$983$	21.0272	0.670663	0.335332	−	0.942100i	$-0.391152\pi$
$983$	21.0272	0.670663	0.335332	+	0.942100i	$0.391152\pi$
$984$	−22.2301	−0.708671
$985$	20.7117	0.659930
$986$	8.82749	0.281124
$987$	13.3153	0.423831
$988$	18.7539	0.596640
$989$	−71.3670	−2.26934
$990$	−5.02703	−0.159770
$991$	−8.97600	−0.285132	−0.142566	−	0.989785i	$-0.545535\pi$
$991$	−8.97600	−0.285132	−0.142566	+	0.989785i	$0.545535\pi$
$992$	5.72133	0.181652
$993$	−61.3722	−1.94759
$994$	−6.86462	−0.217733
$995$	2.30944	0.0732141
$996$	−33.8322	−1.07201
$997$	43.9438	1.39172	0.695858	−	0.718180i	$-0.255024\pi$
$997$	43.9438	1.39172	0.695858	+	0.718180i	$0.255024\pi$
$998$	−28.3383	−0.897033
$999$	−24.0493	−0.760888

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.e.1.2	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.e.1.2	✓	21	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.14296 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.14296 q^{6} +0.736597 q^{7} -1.00000 q^{8} +1.59228 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.14296 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.14296 q^{6} +0.736597 q^{7} -1.00000 q^{8} +1.59228 q^{9} +1.00000 q^{10} -3.15712 q^{11} -2.14296 q^{12} -4.66538 q^{13} -0.736597 q^{14} +2.14296 q^{15} +1.00000 q^{16} +3.14164 q^{17} -1.59228 q^{18} -4.01979 q^{19} -1.00000 q^{20} -1.57850 q^{21} +3.15712 q^{22} -7.10860 q^{23} +2.14296 q^{24} +1.00000 q^{25} +4.66538 q^{26} +3.01668 q^{27} +0.736597 q^{28} -2.80984 q^{29} -2.14296 q^{30} -5.72133 q^{31} -1.00000 q^{32} +6.76559 q^{33} -3.14164 q^{34} -0.736597 q^{35} +1.59228 q^{36} -7.97212 q^{37} +4.01979 q^{38} +9.99774 q^{39} +1.00000 q^{40} -10.3736 q^{41} +1.57850 q^{42} +10.0395 q^{43} -3.15712 q^{44} -1.59228 q^{45} +7.10860 q^{46} -8.43542 q^{47} -2.14296 q^{48} -6.45743 q^{49} -1.00000 q^{50} -6.73241 q^{51} -4.66538 q^{52} +7.83253 q^{53} -3.01668 q^{54} +3.15712 q^{55} -0.736597 q^{56} +8.61426 q^{57} +2.80984 q^{58} +2.06051 q^{59} +2.14296 q^{60} +4.47293 q^{61} +5.72133 q^{62} +1.17287 q^{63} +1.00000 q^{64} +4.66538 q^{65} -6.76559 q^{66} -8.16901 q^{67} +3.14164 q^{68} +15.2335 q^{69} +0.736597 q^{70} +9.31937 q^{71} -1.59228 q^{72} -8.97252 q^{73} +7.97212 q^{74} -2.14296 q^{75} -4.01979 q^{76} -2.32553 q^{77} -9.99774 q^{78} -15.5710 q^{79} -1.00000 q^{80} -11.2415 q^{81} +10.3736 q^{82} +15.7876 q^{83} -1.57850 q^{84} -3.14164 q^{85} -10.0395 q^{86} +6.02137 q^{87} +3.15712 q^{88} -6.08980 q^{89} +1.59228 q^{90} -3.43651 q^{91} -7.10860 q^{92} +12.2606 q^{93} +8.43542 q^{94} +4.01979 q^{95} +2.14296 q^{96} -17.7555 q^{97} +6.45743 q^{98} -5.02703 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 21 q^{2} + 8 q^{3} + 21 q^{4} - 21 q^{5} - 8 q^{6} - 21 q^{8} + 15 q^{9}+O(q^{10}) \) 21 * q - 21 * q^2 + 8 * q^3 + 21 * q^4 - 21 * q^5 - 8 * q^6 - 21 * q^8 + 15 * q^9	\( 21 q - 21 q^{2} + 8 q^{3} + 21 q^{4} - 21 q^{5} - 8 q^{6} - 21 q^{8} + 15 q^{9} + 21 q^{10} + 8 q^{11} + 8 q^{12} + 2 q^{13} - 8 q^{15} + 21 q^{16} + 25 q^{17} - 15 q^{18} - 11 q^{19} - 21 q^{20} - 8 q^{21} - 8 q^{22} + 15 q^{23} - 8 q^{24} + 21 q^{25} - 2 q^{26} + 29 q^{27} + 3 q^{29} + 8 q^{30} - 19 q^{31} - 21 q^{32} + 11 q^{33} - 25 q^{34} + 15 q^{36} - 8 q^{37} + 11 q^{38} - 2 q^{39} + 21 q^{40} + 15 q^{41} + 8 q^{42} + 19 q^{43} + 8 q^{44} - 15 q^{45} - 15 q^{46} + 19 q^{47} + 8 q^{48} - 15 q^{49} - 21 q^{50} + 13 q^{51} + 2 q^{52} + 45 q^{53} - 29 q^{54} - 8 q^{55} + 22 q^{57} - 3 q^{58} + 34 q^{59} - 8 q^{60} - 26 q^{61} + 19 q^{62} + 5 q^{63} + 21 q^{64} - 2 q^{65} - 11 q^{66} + 19 q^{67} + 25 q^{68} - 3 q^{69} + 10 q^{71} - 15 q^{72} - 17 q^{73} + 8 q^{74} + 8 q^{75} - 11 q^{76} + 42 q^{77} + 2 q^{78} - 42 q^{79} - 21 q^{80} + q^{81} - 15 q^{82} + 76 q^{83} - 8 q^{84} - 25 q^{85} - 19 q^{86} + 6 q^{87} - 8 q^{88} + 14 q^{89} + 15 q^{90} - 19 q^{91} + 15 q^{92} + 2 q^{93} - 19 q^{94} + 11 q^{95} - 8 q^{96} - 9 q^{97} + 15 q^{98} + 21 q^{99}+O(q^{100}) \) 21 * q - 21 * q^2 + 8 * q^3 + 21 * q^4 - 21 * q^5 - 8 * q^6 - 21 * q^8 + 15 * q^9 + 21 * q^10 + 8 * q^11 + 8 * q^12 + 2 * q^13 - 8 * q^15 + 21 * q^16 + 25 * q^17 - 15 * q^18 - 11 * q^19 - 21 * q^20 - 8 * q^21 - 8 * q^22 + 15 * q^23 - 8 * q^24 + 21 * q^25 - 2 * q^26 + 29 * q^27 + 3 * q^29 + 8 * q^30 - 19 * q^31 - 21 * q^32 + 11 * q^33 - 25 * q^34 + 15 * q^36 - 8 * q^37 + 11 * q^38 - 2 * q^39 + 21 * q^40 + 15 * q^41 + 8 * q^42 + 19 * q^43 + 8 * q^44 - 15 * q^45 - 15 * q^46 + 19 * q^47 + 8 * q^48 - 15 * q^49 - 21 * q^50 + 13 * q^51 + 2 * q^52 + 45 * q^53 - 29 * q^54 - 8 * q^55 + 22 * q^57 - 3 * q^58 + 34 * q^59 - 8 * q^60 - 26 * q^61 + 19 * q^62 + 5 * q^63 + 21 * q^64 - 2 * q^65 - 11 * q^66 + 19 * q^67 + 25 * q^68 - 3 * q^69 + 10 * q^71 - 15 * q^72 - 17 * q^73 + 8 * q^74 + 8 * q^75 - 11 * q^76 + 42 * q^77 + 2 * q^78 - 42 * q^79 - 21 * q^80 + q^81 - 15 * q^82 + 76 * q^83 - 8 * q^84 - 25 * q^85 - 19 * q^86 + 6 * q^87 - 8 * q^88 + 14 * q^89 + 15 * q^90 - 19 * q^91 + 15 * q^92 + 2 * q^93 - 19 * q^94 + 11 * q^95 - 8 * q^96 - 9 * q^97 + 15 * q^98 + 21 * q^99

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