LMFDB - Embedded newform 6010.2.a.h.1.3

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:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.81740 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.81740 q^{6} -2.15395 q^{7} +1.00000 q^{8} +4.93776 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.81740 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.81740 q^{6} -2.15395 q^{7} +1.00000 q^{8} +4.93776 q^{9} -1.00000 q^{10} -6.40793 q^{11} -2.81740 q^{12} -1.28870 q^{13} -2.15395 q^{14} +2.81740 q^{15} +1.00000 q^{16} -2.94492 q^{17} +4.93776 q^{18} -3.06941 q^{19} -1.00000 q^{20} +6.06853 q^{21} -6.40793 q^{22} -6.87778 q^{23} -2.81740 q^{24} +1.00000 q^{25} -1.28870 q^{26} -5.45946 q^{27} -2.15395 q^{28} -4.94628 q^{29} +2.81740 q^{30} -9.82353 q^{31} +1.00000 q^{32} +18.0537 q^{33} -2.94492 q^{34} +2.15395 q^{35} +4.93776 q^{36} +4.65833 q^{37} -3.06941 q^{38} +3.63079 q^{39} -1.00000 q^{40} +1.22863 q^{41} +6.06853 q^{42} -4.10688 q^{43} -6.40793 q^{44} -4.93776 q^{45} -6.87778 q^{46} +10.5581 q^{47} -2.81740 q^{48} -2.36052 q^{49} +1.00000 q^{50} +8.29704 q^{51} -1.28870 q^{52} -0.167913 q^{53} -5.45946 q^{54} +6.40793 q^{55} -2.15395 q^{56} +8.64776 q^{57} -4.94628 q^{58} -2.37436 q^{59} +2.81740 q^{60} -1.06496 q^{61} -9.82353 q^{62} -10.6357 q^{63} +1.00000 q^{64} +1.28870 q^{65} +18.0537 q^{66} -4.65290 q^{67} -2.94492 q^{68} +19.3775 q^{69} +2.15395 q^{70} -11.9049 q^{71} +4.93776 q^{72} -15.0550 q^{73} +4.65833 q^{74} -2.81740 q^{75} -3.06941 q^{76} +13.8023 q^{77} +3.63079 q^{78} +5.30025 q^{79} -1.00000 q^{80} +0.568210 q^{81} +1.22863 q^{82} -9.02153 q^{83} +6.06853 q^{84} +2.94492 q^{85} -4.10688 q^{86} +13.9357 q^{87} -6.40793 q^{88} +6.22434 q^{89} -4.93776 q^{90} +2.77579 q^{91} -6.87778 q^{92} +27.6768 q^{93} +10.5581 q^{94} +3.06941 q^{95} -2.81740 q^{96} +9.19358 q^{97} -2.36052 q^{98} -31.6408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9 - 28 * q^10 + 4 * q^11 + 4 * q^12 + 22 * q^13 + 10 * q^14 - 4 * q^15 + 28 * q^16 + 15 * q^17 + 40 * q^18 - 11 * q^19 - 28 * q^20 + 18 * q^21 + 4 * q^22 + 23 * q^23 + 4 * q^24 + 28 * q^25 + 22 * q^26 + 19 * q^27 + 10 * q^28 + 19 * q^29 - 4 * q^30 + 7 * q^31 + 28 * q^32 + 33 * q^33 + 15 * q^34 - 10 * q^35 + 40 * q^36 + 22 * q^37 - 11 * q^38 + 8 * q^39 - 28 * q^40 + 41 * q^41 + 18 * q^42 + 7 * q^43 + 4 * q^44 - 40 * q^45 + 23 * q^46 + 51 * q^47 + 4 * q^48 + 60 * q^49 + 28 * q^50 - 5 * q^51 + 22 * q^52 + 25 * q^53 + 19 * q^54 - 4 * q^55 + 10 * q^56 + 8 * q^57 + 19 * q^58 + 32 * q^59 - 4 * q^60 + 24 * q^61 + 7 * q^62 + 33 * q^63 + 28 * q^64 - 22 * q^65 + 33 * q^66 + 3 * q^67 + 15 * q^68 + 43 * q^69 - 10 * q^70 + 8 * q^71 + 40 * q^72 + 47 * q^73 + 22 * q^74 + 4 * q^75 - 11 * q^76 + 46 * q^77 + 8 * q^78 - 22 * q^79 - 28 * q^80 + 76 * q^81 + 41 * q^82 + 36 * q^83 + 18 * q^84 - 15 * q^85 + 7 * q^86 + 72 * q^87 + 4 * q^88 + 70 * q^89 - 40 * q^90 - 21 * q^91 + 23 * q^92 + 24 * q^93 + 51 * q^94 + 11 * q^95 + 4 * q^96 + 43 * q^97 + 60 * q^98 - 9 * 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
$3$	−2.81740	−1.62663	−0.813314	−	0.581825i	$-0.802339\pi$
$3$	−2.81740	−1.62663	−0.813314	+	0.581825i	$0.802339\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.81740	−1.15020
$7$	−2.15395	−0.814115	−0.407057	−	0.913403i	$-0.633445\pi$
$7$	−2.15395	−0.814115	−0.407057	+	0.913403i	$0.633445\pi$
$8$	1.00000	0.353553
$9$	4.93776	1.64592
$10$	−1.00000	−0.316228
$11$	−6.40793	−1.93206	−0.966032	−	0.258422i	$-0.916797\pi$
$11$	−6.40793	−1.93206	−0.966032	+	0.258422i	$0.916797\pi$
$12$	−2.81740	−0.813314
$13$	−1.28870	−0.357422	−0.178711	−	0.983902i	$-0.557193\pi$
$13$	−1.28870	−0.357422	−0.178711	+	0.983902i	$0.557193\pi$
$14$	−2.15395	−0.575666
$15$	2.81740	0.727450
$16$	1.00000	0.250000
$17$	−2.94492	−0.714249	−0.357124	−	0.934057i	$-0.616243\pi$
$17$	−2.94492	−0.714249	−0.357124	+	0.934057i	$0.616243\pi$
$18$	4.93776	1.16384
$19$	−3.06941	−0.704170	−0.352085	−	0.935968i	$-0.614527\pi$
$19$	−3.06941	−0.704170	−0.352085	+	0.935968i	$0.614527\pi$
$20$	−1.00000	−0.223607
$21$	6.06853	1.32426
$22$	−6.40793	−1.36618
$23$	−6.87778	−1.43412	−0.717058	−	0.697013i	$-0.754512\pi$
$23$	−6.87778	−1.43412	−0.717058	+	0.697013i	$0.754512\pi$
$24$	−2.81740	−0.575100
$25$	1.00000	0.200000
$26$	−1.28870	−0.252735
$27$	−5.45946	−1.05067
$28$	−2.15395	−0.407057
$29$	−4.94628	−0.918501	−0.459250	−	0.888307i	$-0.651882\pi$
$29$	−4.94628	−0.918501	−0.459250	+	0.888307i	$0.651882\pi$
$30$	2.81740	0.514385
$31$	−9.82353	−1.76436	−0.882179	−	0.470914i	$-0.843924\pi$
$31$	−9.82353	−1.76436	−0.882179	+	0.470914i	$0.843924\pi$
$32$	1.00000	0.176777
$33$	18.0537	3.14275
$34$	−2.94492	−0.505050
$35$	2.15395	0.364083
$36$	4.93776	0.822960
$37$	4.65833	0.765825	0.382913	−	0.923785i	$-0.374921\pi$
$37$	4.65833	0.765825	0.382913	+	0.923785i	$0.374921\pi$
$38$	−3.06941	−0.497923
$39$	3.63079	0.581392
$40$	−1.00000	−0.158114
$41$	1.22863	0.191880	0.0959401	−	0.995387i	$-0.469414\pi$
$41$	1.22863	0.191880	0.0959401	+	0.995387i	$0.469414\pi$
$42$	6.06853	0.936395
$43$	−4.10688	−0.626294	−0.313147	−	0.949705i	$-0.601383\pi$
$43$	−4.10688	−0.626294	−0.313147	+	0.949705i	$0.601383\pi$
$44$	−6.40793	−0.966032
$45$	−4.93776	−0.736078
$46$	−6.87778	−1.01407
$47$	10.5581	1.54006	0.770031	−	0.638006i	$-0.220241\pi$
$47$	10.5581	1.54006	0.770031	+	0.638006i	$0.220241\pi$
$48$	−2.81740	−0.406657
$49$	−2.36052	−0.337217
$50$	1.00000	0.141421
$51$	8.29704	1.16182
$52$	−1.28870	−0.178711
$53$	−0.167913	−0.0230646	−0.0115323	−	0.999934i	$-0.503671\pi$
$53$	−0.167913	−0.0230646	−0.0115323	+	0.999934i	$0.503671\pi$
$54$	−5.45946	−0.742938
$55$	6.40793	0.864045
$56$	−2.15395	−0.287833
$57$	8.64776	1.14542
$58$	−4.94628	−0.649478
$59$	−2.37436	−0.309116	−0.154558	−	0.987984i	$-0.549395\pi$
$59$	−2.37436	−0.309116	−0.154558	+	0.987984i	$0.549395\pi$
$60$	2.81740	0.363725
$61$	−1.06496	−0.136354	−0.0681769	−	0.997673i	$-0.521718\pi$
$61$	−1.06496	−0.136354	−0.0681769	+	0.997673i	$0.521718\pi$
$62$	−9.82353	−1.24759
$63$	−10.6357	−1.33997
$64$	1.00000	0.125000
$65$	1.28870	0.159844
$66$	18.0537	2.22226
$67$	−4.65290	−0.568442	−0.284221	−	0.958759i	$-0.591735\pi$
$67$	−4.65290	−0.568442	−0.284221	+	0.958759i	$0.591735\pi$
$68$	−2.94492	−0.357124
$69$	19.3775	2.33278
$70$	2.15395	0.257446
$71$	−11.9049	−1.41285	−0.706427	−	0.707786i	$-0.749694\pi$
$71$	−11.9049	−1.41285	−0.706427	+	0.707786i	$0.749694\pi$
$72$	4.93776	0.581921
$73$	−15.0550	−1.76206	−0.881028	−	0.473063i	$-0.843148\pi$
$73$	−15.0550	−1.76206	−0.881028	+	0.473063i	$0.843148\pi$
$74$	4.65833	0.541520
$75$	−2.81740	−0.325326
$76$	−3.06941	−0.352085
$77$	13.8023	1.57292
$78$	3.63079	0.411106
$79$	5.30025	0.596324	0.298162	−	0.954515i	$-0.403626\pi$
$79$	5.30025	0.596324	0.298162	+	0.954515i	$0.403626\pi$
$80$	−1.00000	−0.111803
$81$	0.568210	0.0631344
$82$	1.22863	0.135680
$83$	−9.02153	−0.990241	−0.495121	−	0.868824i	$-0.664876\pi$
$83$	−9.02153	−0.990241	−0.495121	+	0.868824i	$0.664876\pi$
$84$	6.06853	0.662131
$85$	2.94492	0.319422
$86$	−4.10688	−0.442857
$87$	13.9357	1.49406
$88$	−6.40793	−0.683088
$89$	6.22434	0.659779	0.329889	−	0.944020i	$-0.392989\pi$
$89$	6.22434	0.659779	0.329889	+	0.944020i	$0.392989\pi$
$90$	−4.93776	−0.520486
$91$	2.77579	0.290982
$92$	−6.87778	−0.717058
$93$	27.6768	2.86996
$94$	10.5581	1.08899
$95$	3.06941	0.314914
$96$	−2.81740	−0.287550
$97$	9.19358	0.933467	0.466733	−	0.884398i	$-0.345431\pi$
$97$	9.19358	0.933467	0.466733	+	0.884398i	$0.345431\pi$
$98$	−2.36052	−0.238448
$99$	−31.6408	−3.18002
$100$	1.00000	0.100000
$101$	7.65033	0.761237	0.380618	−	0.924732i	$-0.375711\pi$
$101$	7.65033	0.761237	0.380618	+	0.924732i	$0.375711\pi$
$102$	8.29704	0.821529
$103$	−12.5996	−1.24147	−0.620736	−	0.784020i	$-0.713166\pi$
$103$	−12.5996	−1.24147	−0.620736	+	0.784020i	$0.713166\pi$
$104$	−1.28870	−0.126368
$105$	−6.06853	−0.592228
$106$	−0.167913	−0.0163091
$107$	−6.49399	−0.627798	−0.313899	−	0.949456i	$-0.601635\pi$
$107$	−6.49399	−0.627798	−0.313899	+	0.949456i	$0.601635\pi$
$108$	−5.45946	−0.525337
$109$	−12.2455	−1.17290	−0.586451	−	0.809984i	$-0.699475\pi$
$109$	−12.2455	−1.17290	−0.586451	+	0.809984i	$0.699475\pi$
$110$	6.40793	0.610972
$111$	−13.1244	−1.24571
$112$	−2.15395	−0.203529
$113$	−1.65607	−0.155790	−0.0778950	−	0.996962i	$-0.524820\pi$
$113$	−1.65607	−0.155790	−0.0778950	+	0.996962i	$0.524820\pi$
$114$	8.64776	0.809937
$115$	6.87778	0.641357
$116$	−4.94628	−0.459250
$117$	−6.36331	−0.588288
$118$	−2.37436	−0.218578
$119$	6.34320	0.581480
$120$	2.81740	0.257193
$121$	30.0616	2.73287
$122$	−1.06496	−0.0964167
$123$	−3.46155	−0.312118
$124$	−9.82353	−0.882179
$125$	−1.00000	−0.0894427
$126$	−10.6357	−0.947501
$127$	18.2212	1.61687	0.808433	−	0.588588i	$-0.200316\pi$
$127$	18.2212	1.61687	0.808433	+	0.588588i	$0.200316\pi$
$128$	1.00000	0.0883883
$129$	11.5708	1.01875
$130$	1.28870	0.113027
$131$	19.6414	1.71607	0.858037	−	0.513588i	$-0.171684\pi$
$131$	19.6414	1.71607	0.858037	+	0.513588i	$0.171684\pi$
$132$	18.0537	1.57138
$133$	6.61133	0.573275
$134$	−4.65290	−0.401949
$135$	5.45946	0.469875
$136$	−2.94492	−0.252525
$137$	−10.0163	−0.855751	−0.427876	−	0.903838i	$-0.640738\pi$
$137$	−10.0163	−0.855751	−0.427876	+	0.903838i	$0.640738\pi$
$138$	19.3775	1.64952
$139$	−5.11539	−0.433881	−0.216941	−	0.976185i	$-0.569608\pi$
$139$	−5.11539	−0.433881	−0.216941	+	0.976185i	$0.569608\pi$
$140$	2.15395	0.182042
$141$	−29.7465	−2.50511
$142$	−11.9049	−0.999038
$143$	8.25792	0.690562
$144$	4.93776	0.411480
$145$	4.94628	0.410766
$146$	−15.0550	−1.24596
$147$	6.65053	0.548527
$148$	4.65833	0.382913
$149$	−15.1533	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$149$	−15.1533	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$150$	−2.81740	−0.230040
$151$	−18.8856	−1.53689	−0.768443	−	0.639919i	$-0.778968\pi$
$151$	−18.8856	−1.53689	−0.768443	+	0.639919i	$0.778968\pi$
$152$	−3.06941	−0.248962
$153$	−14.5413	−1.17560
$154$	13.8023	1.11222
$155$	9.82353	0.789045
$156$	3.63079	0.290696
$157$	13.4127	1.07045	0.535225	−	0.844709i	$-0.320227\pi$
$157$	13.4127	1.07045	0.535225	+	0.844709i	$0.320227\pi$
$158$	5.30025	0.421665
$159$	0.473078	0.0375175
$160$	−1.00000	−0.0790569
$161$	14.8144	1.16754
$162$	0.568210	0.0446428
$163$	−10.8775	−0.851990	−0.425995	−	0.904726i	$-0.640076\pi$
$163$	−10.8775	−0.851990	−0.425995	+	0.904726i	$0.640076\pi$
$164$	1.22863	0.0959401
$165$	−18.0537	−1.40548
$166$	−9.02153	−0.700206
$167$	−2.20593	−0.170700	−0.0853500	−	0.996351i	$-0.527201\pi$
$167$	−2.20593	−0.170700	−0.0853500	+	0.996351i	$0.527201\pi$
$168$	6.06853	0.468198
$169$	−11.3392	−0.872250
$170$	2.94492	0.225865
$171$	−15.1560	−1.15901
$172$	−4.10688	−0.313147
$173$	−6.78697	−0.516004	−0.258002	−	0.966144i	$-0.583064\pi$
$173$	−6.78697	−0.516004	−0.258002	+	0.966144i	$0.583064\pi$
$174$	13.9357	1.05646
$175$	−2.15395	−0.162823
$176$	−6.40793	−0.483016
$177$	6.68954	0.502817
$178$	6.22434	0.466534
$179$	10.3462	0.773313	0.386657	−	0.922224i	$-0.373630\pi$
$179$	10.3462	0.773313	0.386657	+	0.922224i	$0.373630\pi$
$180$	−4.93776	−0.368039
$181$	−25.0091	−1.85891	−0.929456	−	0.368932i	$-0.879723\pi$
$181$	−25.0091	−1.85891	−0.929456	+	0.368932i	$0.879723\pi$
$182$	2.77579	0.205756
$183$	3.00041	0.221797
$184$	−6.87778	−0.507037
$185$	−4.65833	−0.342487
$186$	27.6768	2.02936
$187$	18.8709	1.37997
$188$	10.5581	0.770031
$189$	11.7594	0.855369
$190$	3.06941	0.222678
$191$	0.749630	0.0542414	0.0271207	−	0.999632i	$-0.491366\pi$
$191$	0.749630	0.0542414	0.0271207	+	0.999632i	$0.491366\pi$
$192$	−2.81740	−0.203329
$193$	26.6374	1.91740	0.958699	−	0.284421i	$-0.0918014\pi$
$193$	26.6374	1.91740	0.958699	+	0.284421i	$0.0918014\pi$
$194$	9.19358	0.660061
$195$	−3.63079	−0.260007
$196$	−2.36052	−0.168608
$197$	17.9589	1.27952	0.639761	−	0.768574i	$-0.279033\pi$
$197$	17.9589	1.27952	0.639761	+	0.768574i	$0.279033\pi$
$198$	−31.6408	−2.24862
$199$	9.86336	0.699195	0.349598	−	0.936900i	$-0.386318\pi$
$199$	9.86336	0.699195	0.349598	+	0.936900i	$0.386318\pi$
$200$	1.00000	0.0707107
$201$	13.1091	0.924644
$202$	7.65033	0.538276
$203$	10.6540	0.747765
$204$	8.29704	0.580909
$205$	−1.22863	−0.0858114
$206$	−12.5996	−0.877853
$207$	−33.9609	−2.36044
$208$	−1.28870	−0.0893554
$209$	19.6685	1.36050
$210$	−6.06853	−0.418769
$211$	−26.3645	−1.81501	−0.907503	−	0.420046i	$-0.862014\pi$
$211$	−26.3645	−1.81501	−0.907503	+	0.420046i	$0.862014\pi$
$212$	−0.167913	−0.0115323
$213$	33.5409	2.29819
$214$	−6.49399	−0.443920
$215$	4.10688	0.280087
$216$	−5.45946	−0.371469
$217$	21.1594	1.43639
$218$	−12.2455	−0.829367
$219$	42.4161	2.86621
$220$	6.40793	0.432023
$221$	3.79513	0.255288
$222$	−13.1244	−0.880852
$223$	21.7264	1.45491	0.727455	−	0.686156i	$-0.240703\pi$
$223$	21.7264	1.45491	0.727455	+	0.686156i	$0.240703\pi$
$224$	−2.15395	−0.143917
$225$	4.93776	0.329184
$226$	−1.65607	−0.110160
$227$	27.9651	1.85611	0.928055	−	0.372444i	$-0.121480\pi$
$227$	27.9651	1.85611	0.928055	+	0.372444i	$0.121480\pi$
$228$	8.64776	0.572712
$229$	−10.4870	−0.693002	−0.346501	−	0.938050i	$-0.612630\pi$
$229$	−10.4870	−0.693002	−0.346501	+	0.938050i	$0.612630\pi$
$230$	6.87778	0.453508
$231$	−38.8868	−2.55856
$232$	−4.94628	−0.324739
$233$	12.7444	0.834915	0.417457	−	0.908697i	$-0.362921\pi$
$233$	12.7444	0.834915	0.417457	+	0.908697i	$0.362921\pi$
$234$	−6.36331	−0.415982
$235$	−10.5581	−0.688737
$236$	−2.37436	−0.154558
$237$	−14.9329	−0.969998
$238$	6.34320	0.411169
$239$	7.17401	0.464048	0.232024	−	0.972710i	$-0.425465\pi$
$239$	7.17401	0.464048	0.232024	+	0.972710i	$0.425465\pi$
$240$	2.81740	0.181863
$241$	20.3891	1.31337	0.656687	−	0.754163i	$-0.271957\pi$
$241$	20.3891	1.31337	0.656687	+	0.754163i	$0.271957\pi$
$242$	30.0616	1.93243
$243$	14.7775	0.947977
$244$	−1.06496	−0.0681769
$245$	2.36052	0.150808
$246$	−3.46155	−0.220701
$247$	3.95555	0.251686
$248$	−9.82353	−0.623795
$249$	25.4173	1.61075
$250$	−1.00000	−0.0632456
$251$	5.17996	0.326956	0.163478	−	0.986547i	$-0.447729\pi$
$251$	5.17996	0.326956	0.163478	+	0.986547i	$0.447729\pi$
$252$	−10.6357	−0.669984
$253$	44.0724	2.77081
$254$	18.2212	1.14330
$255$	−8.29704	−0.519580
$256$	1.00000	0.0625000
$257$	26.9043	1.67825	0.839123	−	0.543941i	$-0.183069\pi$
$257$	26.9043	1.67825	0.839123	+	0.543941i	$0.183069\pi$
$258$	11.5708	0.720364
$259$	−10.0338	−0.623470
$260$	1.28870	0.0799219
$261$	−24.4235	−1.51178
$262$	19.6414	1.21345
$263$	25.5070	1.57283	0.786413	−	0.617701i	$-0.211936\pi$
$263$	25.5070	1.57283	0.786413	+	0.617701i	$0.211936\pi$
$264$	18.0537	1.11113
$265$	0.167913	0.0103148
$266$	6.61133	0.405367
$267$	−17.5365	−1.07321
$268$	−4.65290	−0.284221
$269$	15.4185	0.940081	0.470041	−	0.882645i	$-0.344239\pi$
$269$	15.4185	0.940081	0.470041	+	0.882645i	$0.344239\pi$
$270$	5.45946	0.332252
$271$	−29.0605	−1.76530	−0.882650	−	0.470031i	$-0.844243\pi$
$271$	−29.0605	−1.76530	−0.882650	+	0.470031i	$0.844243\pi$
$272$	−2.94492	−0.178562
$273$	−7.82053	−0.473320
$274$	−10.0163	−0.605107
$275$	−6.40793	−0.386413
$276$	19.3775	1.16639
$277$	−23.4085	−1.40648	−0.703240	−	0.710952i	$-0.748264\pi$
$277$	−23.4085	−1.40648	−0.703240	+	0.710952i	$0.748264\pi$
$278$	−5.11539	−0.306801
$279$	−48.5063	−2.90399
$280$	2.15395	0.128723
$281$	−22.0851	−1.31749	−0.658744	−	0.752367i	$-0.728912\pi$
$281$	−22.0851	−1.31749	−0.658744	+	0.752367i	$0.728912\pi$
$282$	−29.7465	−1.77138
$283$	−13.1767	−0.783273	−0.391637	−	0.920120i	$-0.628091\pi$
$283$	−13.1767	−0.783273	−0.391637	+	0.920120i	$0.628091\pi$
$284$	−11.9049	−0.706427
$285$	−8.64776	−0.512249
$286$	8.25792	0.488301
$287$	−2.64641	−0.156212
$288$	4.93776	0.290960
$289$	−8.32743	−0.489849
$290$	4.94628	0.290455
$291$	−25.9020	−1.51840
$292$	−15.0550	−0.881028
$293$	3.30285	0.192955	0.0964773	−	0.995335i	$-0.469242\pi$
$293$	3.30285	0.192955	0.0964773	+	0.995335i	$0.469242\pi$
$294$	6.65053	0.387867
$295$	2.37436	0.138241
$296$	4.65833	0.270760
$297$	34.9838	2.02997
$298$	−15.1533	−0.877807
$299$	8.86341	0.512584
$300$	−2.81740	−0.162663
$301$	8.84601	0.509875
$302$	−18.8856	−1.08674
$303$	−21.5541	−1.23825
$304$	−3.06941	−0.176043
$305$	1.06496	0.0609792
$306$	−14.5413	−0.831272
$307$	−24.0510	−1.37266	−0.686332	−	0.727288i	$-0.740780\pi$
$307$	−24.0510	−1.37266	−0.686332	+	0.727288i	$0.740780\pi$
$308$	13.8023	0.786461
$309$	35.4980	2.01941
$310$	9.82353	0.557939
$311$	−6.59799	−0.374138	−0.187069	−	0.982347i	$-0.559899\pi$
$311$	−6.59799	−0.374138	−0.187069	+	0.982347i	$0.559899\pi$
$312$	3.63079	0.205553
$313$	24.4231	1.38048	0.690239	−	0.723582i	$-0.257505\pi$
$313$	24.4231	1.38048	0.690239	+	0.723582i	$0.257505\pi$
$314$	13.4127	0.756923
$315$	10.6357	0.599252
$316$	5.30025	0.298162
$317$	−15.8344	−0.889351	−0.444675	−	0.895692i	$-0.646681\pi$
$317$	−15.8344	−0.889351	−0.444675	+	0.895692i	$0.646681\pi$
$318$	0.473078	0.0265289
$319$	31.6954	1.77460
$320$	−1.00000	−0.0559017
$321$	18.2962	1.02119
$322$	14.8144	0.825573
$323$	9.03916	0.502953
$324$	0.568210	0.0315672
$325$	−1.28870	−0.0714843
$326$	−10.8775	−0.602448
$327$	34.5004	1.90788
$328$	1.22863	0.0678399
$329$	−22.7417	−1.25379
$330$	−18.0537	−0.993825
$331$	17.3544	0.953884	0.476942	−	0.878935i	$-0.341745\pi$
$331$	17.3544	0.953884	0.476942	+	0.878935i	$0.341745\pi$
$332$	−9.02153	−0.495121
$333$	23.0017	1.26049
$334$	−2.20593	−0.120703
$335$	4.65290	0.254215
$336$	6.06853	0.331066
$337$	−1.09879	−0.0598549	−0.0299275	−	0.999552i	$-0.509528\pi$
$337$	−1.09879	−0.0598549	−0.0299275	+	0.999552i	$0.509528\pi$
$338$	−11.3392	−0.616774
$339$	4.66582	0.253413
$340$	2.94492	0.159711
$341$	62.9485	3.40885
$342$	−15.1560	−0.819543
$343$	20.1620	1.08865
$344$	−4.10688	−0.221428
$345$	−19.3775	−1.04325
$346$	−6.78697	−0.364870
$347$	−24.5598	−1.31844	−0.659218	−	0.751952i	$-0.729113\pi$
$347$	−24.5598	−1.31844	−0.659218	+	0.751952i	$0.729113\pi$
$348$	13.9357	0.747030
$349$	−11.9905	−0.641838	−0.320919	−	0.947107i	$-0.603992\pi$
$349$	−11.9905	−0.641838	−0.320919	+	0.947107i	$0.603992\pi$
$350$	−2.15395	−0.115133
$351$	7.03562	0.375533
$352$	−6.40793	−0.341544
$353$	1.12445	0.0598485	0.0299243	−	0.999552i	$-0.490473\pi$
$353$	1.12445	0.0598485	0.0299243	+	0.999552i	$0.490473\pi$
$354$	6.68954	0.355545
$355$	11.9049	0.631847
$356$	6.22434	0.329889
$357$	−17.8714	−0.945853
$358$	10.3462	0.546815
$359$	11.0048	0.580809	0.290405	−	0.956904i	$-0.406210\pi$
$359$	11.0048	0.580809	0.290405	+	0.956904i	$0.406210\pi$
$360$	−4.93776	−0.260243
$361$	−9.57874	−0.504144
$362$	−25.0091	−1.31445
$363$	−84.6956	−4.44537
$364$	2.77579	0.145491
$365$	15.0550	0.788016
$366$	3.00041	0.156834
$367$	0.0436956	0.00228089	0.00114045	−	0.999999i	$-0.499637\pi$
$367$	0.0436956	0.00228089	0.00114045	+	0.999999i	$0.499637\pi$
$368$	−6.87778	−0.358529
$369$	6.06669	0.315819
$370$	−4.65833	−0.242175
$371$	0.361675	0.0187772
$372$	27.6768	1.43498
$373$	14.8404	0.768409	0.384204	−	0.923248i	$-0.374476\pi$
$373$	14.8404	0.768409	0.384204	+	0.923248i	$0.374476\pi$
$374$	18.8709	0.975789
$375$	2.81740	0.145490
$376$	10.5581	0.544494
$377$	6.37428	0.328292
$378$	11.7594	0.604837
$379$	−19.9665	−1.02561	−0.512806	−	0.858505i	$-0.671394\pi$
$379$	−19.9665	−1.02561	−0.512806	+	0.858505i	$0.671394\pi$
$380$	3.06941	0.157457
$381$	−51.3364	−2.63004
$382$	0.749630	0.0383544
$383$	3.31029	0.169148	0.0845740	−	0.996417i	$-0.473047\pi$
$383$	3.31029	0.169148	0.0845740	+	0.996417i	$0.473047\pi$
$384$	−2.81740	−0.143775
$385$	−13.8023	−0.703432
$386$	26.6374	1.35581
$387$	−20.2788	−1.03083
$388$	9.19358	0.466733
$389$	8.37614	0.424687	0.212344	−	0.977195i	$-0.431890\pi$
$389$	8.37614	0.424687	0.212344	+	0.977195i	$0.431890\pi$
$390$	−3.63079	−0.183852
$391$	20.2545	1.02432
$392$	−2.36052	−0.119224
$393$	−55.3377	−2.79142
$394$	17.9589	0.904758
$395$	−5.30025	−0.266684
$396$	−31.6408	−1.59001
$397$	−20.3635	−1.02202	−0.511008	−	0.859576i	$-0.670728\pi$
$397$	−20.3635	−1.02202	−0.511008	+	0.859576i	$0.670728\pi$
$398$	9.86336	0.494406
$399$	−18.6268	−0.932506
$400$	1.00000	0.0500000
$401$	−15.2245	−0.760275	−0.380138	−	0.924930i	$-0.624123\pi$
$401$	−15.2245	−0.760275	−0.380138	+	0.924930i	$0.624123\pi$
$402$	13.1091	0.653822
$403$	12.6596	0.630620
$404$	7.65033	0.380618
$405$	−0.568210	−0.0282346
$406$	10.6540	0.528750
$407$	−29.8503	−1.47962
$408$	8.29704	0.410764
$409$	−16.1380	−0.797975	−0.398987	−	0.916956i	$-0.630638\pi$
$409$	−16.1380	−0.797975	−0.398987	+	0.916956i	$0.630638\pi$
$410$	−1.22863	−0.0606778
$411$	28.2200	1.39199
$412$	−12.5996	−0.620736
$413$	5.11425	0.251656
$414$	−33.9609	−1.66909
$415$	9.02153	0.442849
$416$	−1.28870	−0.0631838
$417$	14.4121	0.705764
$418$	19.6685	0.962020
$419$	0.829843	0.0405405	0.0202702	−	0.999795i	$-0.493547\pi$
$419$	0.829843	0.0405405	0.0202702	+	0.999795i	$0.493547\pi$
$420$	−6.06853	−0.296114
$421$	−19.8399	−0.966938	−0.483469	−	0.875362i	$-0.660623\pi$
$421$	−19.8399	−0.966938	−0.483469	+	0.875362i	$0.660623\pi$
$422$	−26.3645	−1.28340
$423$	52.1336	2.53482
$424$	−0.167913	−0.00815457
$425$	−2.94492	−0.142850
$426$	33.5409	1.62506
$427$	2.29386	0.111008
$428$	−6.49399	−0.313899
$429$	−23.2659	−1.12329
$430$	4.10688	0.198052
$431$	25.6523	1.23563	0.617813	−	0.786325i	$-0.288019\pi$
$431$	25.6523	1.23563	0.617813	+	0.786325i	$0.288019\pi$
$432$	−5.45946	−0.262668
$433$	−18.2084	−0.875039	−0.437520	−	0.899209i	$-0.644143\pi$
$433$	−18.2084	−0.875039	−0.437520	+	0.899209i	$0.644143\pi$
$434$	21.1594	1.01568
$435$	−13.9357	−0.668164
$436$	−12.2455	−0.586451
$437$	21.1107	1.00986
$438$	42.4161	2.02672
$439$	26.5697	1.26810	0.634052	−	0.773291i	$-0.281391\pi$
$439$	26.5697	1.26810	0.634052	+	0.773291i	$0.281391\pi$
$440$	6.40793	0.305486
$441$	−11.6557	−0.555032
$442$	3.79513	0.180516
$443$	−6.75515	−0.320947	−0.160473	−	0.987040i	$-0.551302\pi$
$443$	−6.75515	−0.320947	−0.160473	+	0.987040i	$0.551302\pi$
$444$	−13.1244	−0.622857
$445$	−6.22434	−0.295062
$446$	21.7264	1.02878
$447$	42.6929	2.01931
$448$	−2.15395	−0.101764
$449$	2.76680	0.130573	0.0652867	−	0.997867i	$-0.479204\pi$
$449$	2.76680	0.130573	0.0652867	+	0.997867i	$0.479204\pi$
$450$	4.93776	0.232768
$451$	−7.87299	−0.370725
$452$	−1.65607	−0.0778950
$453$	53.2082	2.49994
$454$	27.9651	1.31247
$455$	−2.77579	−0.130131
$456$	8.64776	0.404968
$457$	−9.91544	−0.463825	−0.231912	−	0.972737i	$-0.574498\pi$
$457$	−9.91544	−0.463825	−0.231912	+	0.972737i	$0.574498\pi$
$458$	−10.4870	−0.490026
$459$	16.0777	0.750442
$460$	6.87778	0.320678
$461$	9.63573	0.448781	0.224390	−	0.974499i	$-0.427961\pi$
$461$	9.63573	0.448781	0.224390	+	0.974499i	$0.427961\pi$
$462$	−38.8868	−1.80918
$463$	−23.7718	−1.10477	−0.552385	−	0.833589i	$-0.686282\pi$
$463$	−23.7718	−1.10477	−0.552385	+	0.833589i	$0.686282\pi$
$464$	−4.94628	−0.229625
$465$	−27.6768	−1.28348
$466$	12.7444	0.590374
$467$	12.6756	0.586557	0.293279	−	0.956027i	$-0.405254\pi$
$467$	12.6756	0.586557	0.293279	+	0.956027i	$0.405254\pi$
$468$	−6.36331	−0.294144
$469$	10.0221	0.462777
$470$	−10.5581	−0.487011
$471$	−37.7890	−1.74123
$472$	−2.37436	−0.109289
$473$	26.3166	1.21004
$474$	−14.9329	−0.685892
$475$	−3.06941	−0.140834
$476$	6.34320	0.290740
$477$	−0.829114	−0.0379625
$478$	7.17401	0.328132
$479$	−39.6685	−1.81250	−0.906250	−	0.422742i	$-0.861068\pi$
$479$	−39.6685	−1.81250	−0.906250	+	0.422742i	$0.861068\pi$
$480$	2.81740	0.128596
$481$	−6.00320	−0.273722
$482$	20.3891	0.928696
$483$	−41.7381	−1.89915
$484$	30.0616	1.36644
$485$	−9.19358	−0.417459
$486$	14.7775	0.670321
$487$	16.3850	0.742474	0.371237	−	0.928538i	$-0.378934\pi$
$487$	16.3850	0.742474	0.371237	+	0.928538i	$0.378934\pi$
$488$	−1.06496	−0.0482083
$489$	30.6462	1.38587
$490$	2.36052	0.106637
$491$	−9.49351	−0.428436	−0.214218	−	0.976786i	$-0.568720\pi$
$491$	−9.49351	−0.428436	−0.214218	+	0.976786i	$0.568720\pi$
$492$	−3.46155	−0.156059
$493$	14.5664	0.656038
$494$	3.95555	0.177969
$495$	31.6408	1.42215
$496$	−9.82353	−0.441090
$497$	25.6425	1.15022
$498$	25.4173	1.13898
$499$	−16.3628	−0.732500	−0.366250	−	0.930517i	$-0.619358\pi$
$499$	−16.3628	−0.732500	−0.366250	+	0.930517i	$0.619358\pi$
$500$	−1.00000	−0.0447214
$501$	6.21499	0.277665
$502$	5.17996	0.231193
$503$	14.7179	0.656237	0.328118	−	0.944637i	$-0.393586\pi$
$503$	14.7179	0.656237	0.328118	+	0.944637i	$0.393586\pi$
$504$	−10.6357	−0.473750
$505$	−7.65033	−0.340435
$506$	44.0724	1.95926
$507$	31.9472	1.41883
$508$	18.2212	0.808433
$509$	−8.01828	−0.355404	−0.177702	−	0.984084i	$-0.556866\pi$
$509$	−8.01828	−0.355404	−0.177702	+	0.984084i	$0.556866\pi$
$510$	−8.29704	−0.367399
$511$	32.4277	1.43452
$512$	1.00000	0.0441942
$513$	16.7573	0.739853
$514$	26.9043	1.18670
$515$	12.5996	0.555203
$516$	11.5708	0.509374
$517$	−67.6558	−2.97550
$518$	−10.0338	−0.440860
$519$	19.1216	0.839346
$520$	1.28870	0.0565133
$521$	−4.16053	−0.182276	−0.0911381	−	0.995838i	$-0.529050\pi$
$521$	−4.16053	−0.182276	−0.0911381	+	0.995838i	$0.529050\pi$
$522$	−24.4235	−1.06899
$523$	14.2317	0.622311	0.311155	−	0.950359i	$-0.399284\pi$
$523$	14.2317	0.622311	0.311155	+	0.950359i	$0.399284\pi$
$524$	19.6414	0.858037
$525$	6.06853	0.264853
$526$	25.5070	1.11216
$527$	28.9295	1.26019
$528$	18.0537	0.785688
$529$	24.3039	1.05669
$530$	0.167913	0.00729367
$531$	−11.7240	−0.508780
$532$	6.61133	0.286638
$533$	−1.58334	−0.0685821
$534$	−17.5365	−0.758877
$535$	6.49399	0.280760
$536$	−4.65290	−0.200975
$537$	−29.1495	−1.25789
$538$	15.4185	0.664738
$539$	15.1260	0.651525
$540$	5.45946	0.234938
$541$	7.25216	0.311795	0.155897	−	0.987773i	$-0.450173\pi$
$541$	7.25216	0.311795	0.155897	+	0.987773i	$0.450173\pi$
$542$	−29.0605	−1.24826
$543$	70.4608	3.02376
$544$	−2.94492	−0.126263
$545$	12.2455	0.524538
$546$	−7.82053	−0.334688
$547$	2.52420	0.107927	0.0539634	−	0.998543i	$-0.482815\pi$
$547$	2.52420	0.107927	0.0539634	+	0.998543i	$0.482815\pi$
$548$	−10.0163	−0.427876
$549$	−5.25850	−0.224427
$550$	−6.40793	−0.273235
$551$	15.1821	0.646781
$552$	19.3775	0.824761
$553$	−11.4164	−0.485477
$554$	−23.4085	−0.994532
$555$	13.1244	0.557100
$556$	−5.11539	−0.216941
$557$	11.9962	0.508294	0.254147	−	0.967166i	$-0.418205\pi$
$557$	11.9962	0.508294	0.254147	+	0.967166i	$0.418205\pi$
$558$	−48.5063	−2.05343
$559$	5.29255	0.223851
$560$	2.15395	0.0910208
$561$	−53.1668	−2.24471
$562$	−22.0851	−0.931605
$563$	−19.7357	−0.831759	−0.415880	−	0.909420i	$-0.636526\pi$
$563$	−19.7357	−0.831759	−0.415880	+	0.909420i	$0.636526\pi$
$564$	−29.7465	−1.25255
$565$	1.65607	0.0696714
$566$	−13.1767	−0.553858
$567$	−1.22389	−0.0513987
$568$	−11.9049	−0.499519
$569$	6.94147	0.291002	0.145501	−	0.989358i	$-0.453521\pi$
$569$	6.94147	0.291002	0.145501	+	0.989358i	$0.453521\pi$
$570$	−8.64776	−0.362215
$571$	−22.3033	−0.933362	−0.466681	−	0.884426i	$-0.654550\pi$
$571$	−22.3033	−0.933362	−0.466681	+	0.884426i	$0.654550\pi$
$572$	8.25792	0.345281
$573$	−2.11201	−0.0882305
$574$	−2.64641	−0.110459
$575$	−6.87778	−0.286823
$576$	4.93776	0.205740
$577$	23.8766	0.993997	0.496999	−	0.867751i	$-0.334435\pi$
$577$	23.8766	0.993997	0.496999	+	0.867751i	$0.334435\pi$
$578$	−8.32743	−0.346375
$579$	−75.0482	−3.11890
$580$	4.94628	0.205383
$581$	19.4319	0.806170
$582$	−25.9020	−1.07367
$583$	1.07597	0.0445623
$584$	−15.0550	−0.622981
$585$	6.36331	0.263090
$586$	3.30285	0.136439
$587$	21.7526	0.897824	0.448912	−	0.893576i	$-0.351812\pi$
$587$	21.7526	0.897824	0.448912	+	0.893576i	$0.351812\pi$
$588$	6.65053	0.274263
$589$	30.1524	1.24241
$590$	2.37436	0.0977511
$591$	−50.5976	−2.08131
$592$	4.65833	0.191456
$593$	−25.6272	−1.05238	−0.526192	−	0.850366i	$-0.676381\pi$
$593$	−25.6272	−1.05238	−0.526192	+	0.850366i	$0.676381\pi$
$594$	34.9838	1.43540
$595$	−6.34320	−0.260046
$596$	−15.1533	−0.620703
$597$	−27.7891	−1.13733
$598$	8.86341	0.362452
$599$	2.55442	0.104371	0.0521854	−	0.998637i	$-0.483381\pi$
$599$	2.55442	0.104371	0.0521854	+	0.998637i	$0.483381\pi$
$600$	−2.81740	−0.115020
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	8.84601	0.360536
$603$	−22.9749	−0.935610
$604$	−18.8856	−0.768443
$605$	−30.0616	−1.22218
$606$	−21.5541	−0.875574
$607$	22.8633	0.927992	0.463996	−	0.885837i	$-0.346415\pi$
$607$	22.8633	0.927992	0.463996	+	0.885837i	$0.346415\pi$
$608$	−3.06941	−0.124481
$609$	−30.0167	−1.21634
$610$	1.06496	0.0431188
$611$	−13.6063	−0.550452
$612$	−14.5413	−0.587798
$613$	−21.1024	−0.852316	−0.426158	−	0.904649i	$-0.640133\pi$
$613$	−21.1024	−0.852316	−0.426158	+	0.904649i	$0.640133\pi$
$614$	−24.0510	−0.970621
$615$	3.46155	0.139583
$616$	13.8023	0.556112
$617$	22.4594	0.904183	0.452092	−	0.891972i	$-0.350678\pi$
$617$	22.4594	0.904183	0.452092	+	0.891972i	$0.350678\pi$
$618$	35.4980	1.42794
$619$	11.2318	0.451443	0.225721	−	0.974192i	$-0.427526\pi$
$619$	11.2318	0.451443	0.225721	+	0.974192i	$0.427526\pi$
$620$	9.82353	0.394522
$621$	37.5490	1.50679
$622$	−6.59799	−0.264555
$623$	−13.4069	−0.537136
$624$	3.63079	0.145348
$625$	1.00000	0.0400000
$626$	24.4231	0.976145
$627$	−55.4142	−2.21303
$628$	13.4127	0.535225
$629$	−13.7184	−0.546990
$630$	10.6357	0.423735
$631$	8.28345	0.329759	0.164880	−	0.986314i	$-0.447276\pi$
$631$	8.28345	0.329759	0.164880	+	0.986314i	$0.447276\pi$
$632$	5.30025	0.210832
$633$	74.2794	2.95234
$634$	−15.8344	−0.628866
$635$	−18.2212	−0.723085
$636$	0.473078	0.0187588
$637$	3.04200	0.120529
$638$	31.6954	1.25483
$639$	−58.7836	−2.32544
$640$	−1.00000	−0.0395285
$641$	0.353398	0.0139584	0.00697919	−	0.999976i	$-0.497778\pi$
$641$	0.353398	0.0139584	0.00697919	+	0.999976i	$0.497778\pi$
$642$	18.2962	0.722093
$643$	29.9711	1.18194	0.590971	−	0.806692i	$-0.298745\pi$
$643$	29.9711	1.18194	0.590971	+	0.806692i	$0.298745\pi$
$644$	14.8144	0.583768
$645$	−11.5708	−0.455598
$646$	9.03916	0.355641
$647$	−20.0328	−0.787571	−0.393785	−	0.919202i	$-0.628835\pi$
$647$	−20.0328	−0.787571	−0.393785	+	0.919202i	$0.628835\pi$
$648$	0.568210	0.0223214
$649$	15.2148	0.597232
$650$	−1.28870	−0.0505471
$651$	−59.6144	−2.33647
$652$	−10.8775	−0.425995
$653$	−10.6454	−0.416585	−0.208292	−	0.978067i	$-0.566791\pi$
$653$	−10.6454	−0.416585	−0.208292	+	0.978067i	$0.566791\pi$
$654$	34.5004	1.34907
$655$	−19.6414	−0.767452
$656$	1.22863	0.0479700
$657$	−74.3381	−2.90021
$658$	−22.7417	−0.886562
$659$	12.0516	0.469466	0.234733	−	0.972060i	$-0.424578\pi$
$659$	12.0516	0.469466	0.234733	+	0.972060i	$0.424578\pi$
$660$	−18.0537	−0.702740
$661$	−7.94455	−0.309007	−0.154504	−	0.987992i	$-0.549378\pi$
$661$	−7.94455	−0.309007	−0.154504	+	0.987992i	$0.549378\pi$
$662$	17.3544	0.674498
$663$	−10.6924	−0.415259
$664$	−9.02153	−0.350103
$665$	−6.61133	−0.256377
$666$	23.0017	0.891299
$667$	34.0194	1.31724
$668$	−2.20593	−0.0853500
$669$	−61.2121	−2.36660
$670$	4.65290	0.179757
$671$	6.82417	0.263444
$672$	6.06853	0.234099
$673$	−4.90713	−0.189156	−0.0945779	−	0.995517i	$-0.530150\pi$
$673$	−4.90713	−0.189156	−0.0945779	+	0.995517i	$0.530150\pi$
$674$	−1.09879	−0.0423238
$675$	−5.45946	−0.210135
$676$	−11.3392	−0.436125
$677$	−32.8446	−1.26232	−0.631160	−	0.775653i	$-0.717421\pi$
$677$	−32.8446	−1.26232	−0.631160	+	0.775653i	$0.717421\pi$
$678$	4.66582	0.179190
$679$	−19.8025	−0.759949
$680$	2.94492	0.112933
$681$	−78.7890	−3.01920
$682$	62.9485	2.41042
$683$	−39.7025	−1.51917	−0.759587	−	0.650406i	$-0.774599\pi$
$683$	−39.7025	−1.51917	−0.759587	+	0.650406i	$0.774599\pi$
$684$	−15.1560	−0.579504
$685$	10.0163	0.382704
$686$	20.1620	0.769791
$687$	29.5462	1.12726
$688$	−4.10688	−0.156574
$689$	0.216390	0.00824379
$690$	−19.3775	−0.737688
$691$	−19.4788	−0.741008	−0.370504	−	0.928831i	$-0.620815\pi$
$691$	−19.4788	−0.741008	−0.370504	+	0.928831i	$0.620815\pi$
$692$	−6.78697	−0.258002
$693$	68.1527	2.58891
$694$	−24.5598	−0.932275
$695$	5.11539	0.194038
$696$	13.9357	0.528230
$697$	−3.61823	−0.137050
$698$	−11.9905	−0.453848
$699$	−35.9062	−1.35810
$700$	−2.15395	−0.0814115
$701$	−14.0614	−0.531092	−0.265546	−	0.964098i	$-0.585552\pi$
$701$	−14.0614	−0.531092	−0.265546	+	0.964098i	$0.585552\pi$
$702$	7.03562	0.265542
$703$	−14.2983	−0.539271
$704$	−6.40793	−0.241508
$705$	29.7465	1.12032
$706$	1.12445	0.0423193
$707$	−16.4784	−0.619734
$708$	6.68954	0.251408
$709$	−40.0130	−1.50272	−0.751359	−	0.659894i	$-0.770601\pi$
$709$	−40.0130	−1.50272	−0.751359	+	0.659894i	$0.770601\pi$
$710$	11.9049	0.446783
$711$	26.1714	0.981503
$712$	6.22434	0.233267
$713$	67.5641	2.53030
$714$	−17.8714	−0.668819
$715$	−8.25792	−0.308829
$716$	10.3462	0.386657
$717$	−20.2121	−0.754834
$718$	11.0048	0.410694
$719$	−37.4084	−1.39510	−0.697550	−	0.716536i	$-0.745726\pi$
$719$	−37.4084	−1.39510	−0.697550	+	0.716536i	$0.745726\pi$
$720$	−4.93776	−0.184020
$721$	27.1388	1.01070
$722$	−9.57874	−0.356484
$723$	−57.4442	−2.13637
$724$	−25.0091	−0.929456
$725$	−4.94628	−0.183700
$726$	−84.6956	−3.14335
$727$	−41.5872	−1.54238	−0.771192	−	0.636603i	$-0.780339\pi$
$727$	−41.5872	−1.54238	−0.771192	+	0.636603i	$0.780339\pi$
$728$	2.77579	0.102878
$729$	−43.3388	−1.60514
$730$	15.0550	0.557211
$731$	12.0945	0.447330
$732$	3.00041	0.110898
$733$	33.3725	1.23264	0.616321	−	0.787495i	$-0.288622\pi$
$733$	33.3725	1.23264	0.616321	+	0.787495i	$0.288622\pi$
$734$	0.0436956	0.00161283
$735$	−6.65053	−0.245309
$736$	−6.87778	−0.253518
$737$	29.8155	1.09827
$738$	6.06669	0.223318
$739$	−1.87632	−0.0690216	−0.0345108	−	0.999404i	$-0.510987\pi$
$739$	−1.87632	−0.0690216	−0.0345108	+	0.999404i	$0.510987\pi$
$740$	−4.65833	−0.171244
$741$	−11.1444	−0.409399
$742$	0.361675	0.0132775
$743$	−3.25903	−0.119562	−0.0597811	−	0.998212i	$-0.519040\pi$
$743$	−3.25903	−0.119562	−0.0597811	+	0.998212i	$0.519040\pi$
$744$	27.6768	1.01468
$745$	15.1533	0.555174
$746$	14.8404	0.543347
$747$	−44.5462	−1.62986
$748$	18.8709	0.689987
$749$	13.9877	0.511099
$750$	2.81740	0.102877
$751$	−13.4707	−0.491552	−0.245776	−	0.969327i	$-0.579043\pi$
$751$	−13.4707	−0.491552	−0.245776	+	0.969327i	$0.579043\pi$
$752$	10.5581	0.385016
$753$	−14.5940	−0.531836
$754$	6.37428	0.232138
$755$	18.8856	0.687316
$756$	11.7594	0.427684
$757$	−40.7214	−1.48004	−0.740022	−	0.672583i	$-0.765185\pi$
$757$	−40.7214	−1.48004	−0.740022	+	0.672583i	$0.765185\pi$
$758$	−19.9665	−0.725217
$759$	−124.170	−4.50707
$760$	3.06941	0.111339
$761$	32.5723	1.18074	0.590372	−	0.807131i	$-0.298981\pi$
$761$	32.5723	1.18074	0.590372	+	0.807131i	$0.298981\pi$
$762$	−51.3364	−1.85972
$763$	26.3761	0.954878
$764$	0.749630	0.0271207
$765$	14.5413	0.525743
$766$	3.31029	0.119606
$767$	3.05985	0.110485
$768$	−2.81740	−0.101664
$769$	52.8469	1.90571	0.952854	−	0.303429i	$-0.0981314\pi$
$769$	52.8469	1.90571	0.952854	+	0.303429i	$0.0981314\pi$
$770$	−13.8023	−0.497402
$771$	−75.8004	−2.72988
$772$	26.6374	0.958699
$773$	−52.7311	−1.89661	−0.948303	−	0.317367i	$-0.897201\pi$
$773$	−52.7311	−1.89661	−0.948303	+	0.317367i	$0.897201\pi$
$774$	−20.2788	−0.728907
$775$	−9.82353	−0.352872
$776$	9.19358	0.330030
$777$	28.2692	1.01415
$778$	8.37614	0.300299
$779$	−3.77117	−0.135116
$780$	−3.63079	−0.130003
$781$	76.2859	2.72972
$782$	20.2545	0.724301
$783$	27.0040	0.965044
$784$	−2.36052	−0.0843042
$785$	−13.4127	−0.478720
$786$	−55.3377	−1.97383
$787$	−34.6961	−1.23678	−0.618392	−	0.785870i	$-0.712215\pi$
$787$	−34.6961	−1.23678	−0.618392	+	0.785870i	$0.712215\pi$
$788$	17.9589	0.639761
$789$	−71.8634	−2.55841
$790$	−5.30025	−0.188574
$791$	3.56709	0.126831
$792$	−31.6408	−1.12431
$793$	1.37241	0.0487358
$794$	−20.3635	−0.722674
$795$	−0.473078	−0.0167784
$796$	9.86336	0.349598
$797$	−29.8354	−1.05682	−0.528412	−	0.848988i	$-0.677212\pi$
$797$	−29.8354	−1.05682	−0.528412	+	0.848988i	$0.677212\pi$
$798$	−18.6268	−0.659381
$799$	−31.0929	−1.09999
$800$	1.00000	0.0353553
$801$	30.7343	1.08594
$802$	−15.2245	−0.537596
$803$	96.4715	3.40441
$804$	13.1091	0.462322
$805$	−14.8144	−0.522138
$806$	12.6596	0.445916
$807$	−43.4401	−1.52916
$808$	7.65033	0.269138
$809$	−37.1496	−1.30611	−0.653055	−	0.757310i	$-0.726513\pi$
$809$	−37.1496	−1.30611	−0.653055	+	0.757310i	$0.726513\pi$
$810$	−0.568210	−0.0199649
$811$	−23.4270	−0.822634	−0.411317	−	0.911492i	$-0.634931\pi$
$811$	−23.4270	−0.822634	−0.411317	+	0.911492i	$0.634931\pi$
$812$	10.6540	0.373883
$813$	81.8752	2.87149
$814$	−29.8503	−1.04625
$815$	10.8775	0.381021
$816$	8.29704	0.290454
$817$	12.6057	0.441018
$818$	−16.1380	−0.564253
$819$	13.7062	0.478934
$820$	−1.22863	−0.0429057
$821$	−17.1064	−0.597016	−0.298508	−	0.954407i	$-0.596489\pi$
$821$	−17.1064	−0.597016	−0.298508	+	0.954407i	$0.596489\pi$
$822$	28.2200	0.984285
$823$	38.9537	1.35784	0.678920	−	0.734212i	$-0.262448\pi$
$823$	38.9537	1.35784	0.678920	+	0.734212i	$0.262448\pi$
$824$	−12.5996	−0.438926
$825$	18.0537	0.628550
$826$	5.11425	0.177948
$827$	−51.0588	−1.77549	−0.887744	−	0.460337i	$-0.847729\pi$
$827$	−51.0588	−1.77549	−0.887744	+	0.460337i	$0.847729\pi$
$828$	−33.9609	−1.18022
$829$	17.4985	0.607747	0.303874	−	0.952712i	$-0.401720\pi$
$829$	17.4985	0.607747	0.303874	+	0.952712i	$0.401720\pi$
$830$	9.02153	0.313142
$831$	65.9512	2.28782
$832$	−1.28870	−0.0446777
$833$	6.95154	0.240857
$834$	14.4121	0.499051
$835$	2.20593	0.0763394
$836$	19.6685	0.680251
$837$	53.6312	1.85376
$838$	0.829843	0.0286664
$839$	−11.9537	−0.412688	−0.206344	−	0.978480i	$-0.566157\pi$
$839$	−11.9537	−0.412688	−0.206344	+	0.978480i	$0.566157\pi$
$840$	−6.06853	−0.209384
$841$	−4.53433	−0.156356
$842$	−19.8399	−0.683728
$843$	62.2227	2.14306
$844$	−26.3645	−0.907503
$845$	11.3392	0.390082
$846$	52.1336	1.79239
$847$	−64.7510	−2.22487
$848$	−0.167913	−0.00576615
$849$	37.1241	1.27409
$850$	−2.94492	−0.101010
$851$	−32.0390	−1.09828
$852$	33.5409	1.14909
$853$	−28.8618	−0.988210	−0.494105	−	0.869402i	$-0.664504\pi$
$853$	−28.8618	−0.988210	−0.494105	+	0.869402i	$0.664504\pi$
$854$	2.29386	0.0784942
$855$	15.1560	0.518324
$856$	−6.49399	−0.221960
$857$	22.3472	0.763364	0.381682	−	0.924294i	$-0.375345\pi$
$857$	22.3472	0.763364	0.381682	+	0.924294i	$0.375345\pi$
$858$	−23.2659	−0.794284
$859$	−40.5226	−1.38261	−0.691306	−	0.722562i	$-0.742964\pi$
$859$	−40.5226	−1.38261	−0.691306	+	0.722562i	$0.742964\pi$
$860$	4.10688	0.140044
$861$	7.45600	0.254100
$862$	25.6523	0.873720
$863$	−36.8496	−1.25438	−0.627188	−	0.778868i	$-0.715794\pi$
$863$	−36.8496	−1.25438	−0.627188	+	0.778868i	$0.715794\pi$
$864$	−5.45946	−0.185735
$865$	6.78697	0.230764
$866$	−18.2084	−0.618746
$867$	23.4617	0.796802
$868$	21.1594	0.718195
$869$	−33.9636	−1.15214
$870$	−13.9357	−0.472463
$871$	5.99620	0.203173
$872$	−12.2455	−0.414684
$873$	45.3957	1.53641
$874$	21.1107	0.714080
$875$	2.15395	0.0728167
$876$	42.4161	1.43311
$877$	−11.4042	−0.385093	−0.192546	−	0.981288i	$-0.561675\pi$
$877$	−11.4042	−0.385093	−0.192546	+	0.981288i	$0.561675\pi$
$878$	26.5697	0.896684
$879$	−9.30546	−0.313865
$880$	6.40793	0.216011
$881$	21.6146	0.728214	0.364107	−	0.931357i	$-0.381374\pi$
$881$	21.6146	0.728214	0.364107	+	0.931357i	$0.381374\pi$
$882$	−11.6557	−0.392467
$883$	43.9314	1.47841	0.739205	−	0.673480i	$-0.235201\pi$
$883$	43.9314	1.47841	0.739205	+	0.673480i	$0.235201\pi$
$884$	3.79513	0.127644
$885$	−6.68954	−0.224867
$886$	−6.75515	−0.226944
$887$	41.6772	1.39938	0.699692	−	0.714445i	$-0.253321\pi$
$887$	41.6772	1.39938	0.699692	+	0.714445i	$0.253321\pi$
$888$	−13.1244	−0.440426
$889$	−39.2474	−1.31632
$890$	−6.22434	−0.208640
$891$	−3.64105	−0.121980
$892$	21.7264	0.727455
$893$	−32.4072	−1.08447
$894$	42.6929	1.42787
$895$	−10.3462	−0.345836
$896$	−2.15395	−0.0719583
$897$	−24.9718	−0.833785
$898$	2.76680	0.0923293
$899$	48.5899	1.62056
$900$	4.93776	0.164592
$901$	0.494490	0.0164739
$902$	−7.87299	−0.262142
$903$	−24.9228	−0.829378
$904$	−1.65607	−0.0550801
$905$	25.0091	0.831331
$906$	53.2082	1.76773
$907$	−5.05295	−0.167780	−0.0838902	−	0.996475i	$-0.526734\pi$
$907$	−5.05295	−0.167780	−0.0838902	+	0.996475i	$0.526734\pi$
$908$	27.9651	0.928055
$909$	37.7755	1.25294
$910$	−2.77579	−0.0920167
$911$	55.3176	1.83276	0.916378	−	0.400315i	$-0.131099\pi$
$911$	55.3176	1.83276	0.916378	+	0.400315i	$0.131099\pi$
$912$	8.64776	0.286356
$913$	57.8093	1.91321
$914$	−9.91544	−0.327974
$915$	−3.00041	−0.0991906
$916$	−10.4870	−0.346501
$917$	−42.3064	−1.39708
$918$	16.0777	0.530643
$919$	30.3079	0.999766	0.499883	−	0.866093i	$-0.333376\pi$
$919$	30.3079	0.999766	0.499883	+	0.866093i	$0.333376\pi$
$920$	6.87778	0.226754
$921$	67.7615	2.23282
$922$	9.63573	0.317336
$923$	15.3419	0.504984
$924$	−38.8868	−1.27928
$925$	4.65833	0.153165
$926$	−23.7718	−0.781190
$927$	−62.2136	−2.04336
$928$	−4.94628	−0.162370
$929$	12.2805	0.402910	0.201455	−	0.979498i	$-0.435433\pi$
$929$	12.2805	0.402910	0.201455	+	0.979498i	$0.435433\pi$
$930$	−27.6768	−0.907560
$931$	7.24539	0.237458
$932$	12.7444	0.417457
$933$	18.5892	0.608583
$934$	12.6756	0.414759
$935$	−18.8709	−0.617143
$936$	−6.36331	−0.207991
$937$	−33.8725	−1.10657	−0.553283	−	0.832993i	$-0.686625\pi$
$937$	−33.8725	−1.10657	−0.553283	+	0.832993i	$0.686625\pi$
$938$	10.0221	0.327233
$939$	−68.8098	−2.24552
$940$	−10.5581	−0.344368
$941$	−43.5304	−1.41905	−0.709525	−	0.704680i	$-0.751091\pi$
$941$	−43.5304	−1.41905	−0.709525	+	0.704680i	$0.751091\pi$
$942$	−37.7890	−1.23123
$943$	−8.45027	−0.275179
$944$	−2.37436	−0.0772790
$945$	−11.7594	−0.382533
$946$	26.3166	0.855628
$947$	−32.2791	−1.04893	−0.524465	−	0.851432i	$-0.675734\pi$
$947$	−32.2791	−1.04893	−0.524465	+	0.851432i	$0.675734\pi$
$948$	−14.9329	−0.484999
$949$	19.4014	0.629797
$950$	−3.06941	−0.0995847
$951$	44.6120	1.44664
$952$	6.34320	0.205584
$953$	−17.2247	−0.557962	−0.278981	−	0.960297i	$-0.589997\pi$
$953$	−17.2247	−0.557962	−0.278981	+	0.960297i	$0.589997\pi$
$954$	−0.829114	−0.0268435
$955$	−0.749630	−0.0242575
$956$	7.17401	0.232024
$957$	−89.2988	−2.88662
$958$	−39.6685	−1.28163
$959$	21.5746	0.696680
$960$	2.81740	0.0909313
$961$	65.5017	2.11296
$962$	−6.00320	−0.193551
$963$	−32.0658	−1.03331
$964$	20.3891	0.656687
$965$	−26.6374	−0.857487
$966$	−41.7381	−1.34290
$967$	−28.7641	−0.924991	−0.462495	−	0.886622i	$-0.653046\pi$
$967$	−28.7641	−0.924991	−0.462495	+	0.886622i	$0.653046\pi$
$968$	30.0616	0.966216
$969$	−25.4670	−0.818117
$970$	−9.19358	−0.295188
$971$	−27.3926	−0.879071	−0.439535	−	0.898225i	$-0.644857\pi$
$971$	−27.3926	−0.879071	−0.439535	+	0.898225i	$0.644857\pi$
$972$	14.7775	0.473988
$973$	11.0183	0.353229
$974$	16.3850	0.525008
$975$	3.63079	0.116278
$976$	−1.06496	−0.0340884
$977$	−38.8406	−1.24262	−0.621311	−	0.783564i	$-0.713400\pi$
$977$	−38.8406	−1.24262	−0.621311	+	0.783564i	$0.713400\pi$
$978$	30.6462	0.979959
$979$	−39.8851	−1.27473
$980$	2.36052	0.0754040
$981$	−60.4652	−1.93050
$982$	−9.49351	−0.302950
$983$	−24.3257	−0.775871	−0.387935	−	0.921687i	$-0.626812\pi$
$983$	−24.3257	−0.775871	−0.387935	+	0.921687i	$0.626812\pi$
$984$	−3.46155	−0.110350
$985$	−17.9589	−0.572219
$986$	14.5664	0.463889
$987$	64.0724	2.03945
$988$	3.95555	0.125843
$989$	28.2463	0.898179
$990$	31.6408	1.00561
$991$	−22.3331	−0.709433	−0.354717	−	0.934974i	$-0.615423\pi$
$991$	−22.3331	−0.709433	−0.354717	+	0.934974i	$0.615423\pi$
$992$	−9.82353	−0.311897
$993$	−48.8943	−1.55162
$994$	25.6425	0.813332
$995$	−9.86336	−0.312690
$996$	25.4173	0.805377
$997$	21.6461	0.685539	0.342769	−	0.939420i	$-0.388635\pi$
$997$	21.6461	0.685539	0.342769	+	0.939420i	$0.388635\pi$
$998$	−16.3628	−0.517955
$999$	−25.4320	−0.804632

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.h.1.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.h.1.3	✓	28	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.81740 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.81740 q^{6} -2.15395 q^{7} +1.00000 q^{8} +4.93776 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.81740 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.81740 q^{6} -2.15395 q^{7} +1.00000 q^{8} +4.93776 q^{9} -1.00000 q^{10} -6.40793 q^{11} -2.81740 q^{12} -1.28870 q^{13} -2.15395 q^{14} +2.81740 q^{15} +1.00000 q^{16} -2.94492 q^{17} +4.93776 q^{18} -3.06941 q^{19} -1.00000 q^{20} +6.06853 q^{21} -6.40793 q^{22} -6.87778 q^{23} -2.81740 q^{24} +1.00000 q^{25} -1.28870 q^{26} -5.45946 q^{27} -2.15395 q^{28} -4.94628 q^{29} +2.81740 q^{30} -9.82353 q^{31} +1.00000 q^{32} +18.0537 q^{33} -2.94492 q^{34} +2.15395 q^{35} +4.93776 q^{36} +4.65833 q^{37} -3.06941 q^{38} +3.63079 q^{39} -1.00000 q^{40} +1.22863 q^{41} +6.06853 q^{42} -4.10688 q^{43} -6.40793 q^{44} -4.93776 q^{45} -6.87778 q^{46} +10.5581 q^{47} -2.81740 q^{48} -2.36052 q^{49} +1.00000 q^{50} +8.29704 q^{51} -1.28870 q^{52} -0.167913 q^{53} -5.45946 q^{54} +6.40793 q^{55} -2.15395 q^{56} +8.64776 q^{57} -4.94628 q^{58} -2.37436 q^{59} +2.81740 q^{60} -1.06496 q^{61} -9.82353 q^{62} -10.6357 q^{63} +1.00000 q^{64} +1.28870 q^{65} +18.0537 q^{66} -4.65290 q^{67} -2.94492 q^{68} +19.3775 q^{69} +2.15395 q^{70} -11.9049 q^{71} +4.93776 q^{72} -15.0550 q^{73} +4.65833 q^{74} -2.81740 q^{75} -3.06941 q^{76} +13.8023 q^{77} +3.63079 q^{78} +5.30025 q^{79} -1.00000 q^{80} +0.568210 q^{81} +1.22863 q^{82} -9.02153 q^{83} +6.06853 q^{84} +2.94492 q^{85} -4.10688 q^{86} +13.9357 q^{87} -6.40793 q^{88} +6.22434 q^{89} -4.93776 q^{90} +2.77579 q^{91} -6.87778 q^{92} +27.6768 q^{93} +10.5581 q^{94} +3.06941 q^{95} -2.81740 q^{96} +9.19358 q^{97} -2.36052 q^{98} -31.6408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9 - 28 * q^10 + 4 * q^11 + 4 * q^12 + 22 * q^13 + 10 * q^14 - 4 * q^15 + 28 * q^16 + 15 * q^17 + 40 * q^18 - 11 * q^19 - 28 * q^20 + 18 * q^21 + 4 * q^22 + 23 * q^23 + 4 * q^24 + 28 * q^25 + 22 * q^26 + 19 * q^27 + 10 * q^28 + 19 * q^29 - 4 * q^30 + 7 * q^31 + 28 * q^32 + 33 * q^33 + 15 * q^34 - 10 * q^35 + 40 * q^36 + 22 * q^37 - 11 * q^38 + 8 * q^39 - 28 * q^40 + 41 * q^41 + 18 * q^42 + 7 * q^43 + 4 * q^44 - 40 * q^45 + 23 * q^46 + 51 * q^47 + 4 * q^48 + 60 * q^49 + 28 * q^50 - 5 * q^51 + 22 * q^52 + 25 * q^53 + 19 * q^54 - 4 * q^55 + 10 * q^56 + 8 * q^57 + 19 * q^58 + 32 * q^59 - 4 * q^60 + 24 * q^61 + 7 * q^62 + 33 * q^63 + 28 * q^64 - 22 * q^65 + 33 * q^66 + 3 * q^67 + 15 * q^68 + 43 * q^69 - 10 * q^70 + 8 * q^71 + 40 * q^72 + 47 * q^73 + 22 * q^74 + 4 * q^75 - 11 * q^76 + 46 * q^77 + 8 * q^78 - 22 * q^79 - 28 * q^80 + 76 * q^81 + 41 * q^82 + 36 * q^83 + 18 * q^84 - 15 * q^85 + 7 * q^86 + 72 * q^87 + 4 * q^88 + 70 * q^89 - 40 * q^90 - 21 * q^91 + 23 * q^92 + 24 * q^93 + 51 * q^94 + 11 * q^95 + 4 * q^96 + 43 * q^97 + 60 * q^98 - 9 * q^99

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