LMFDB - Embedded newform 8014.2.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$91$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.85455 q^{3} +1.00000 q^{4} -2.30346 q^{5} +2.85455 q^{6} +3.17509 q^{7} -1.00000 q^{8} +5.14844 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.85455 q^{3} +1.00000 q^{4} -2.30346 q^{5} +2.85455 q^{6} +3.17509 q^{7} -1.00000 q^{8} +5.14844 q^{9} +2.30346 q^{10} +0.413956 q^{11} -2.85455 q^{12} -0.672208 q^{13} -3.17509 q^{14} +6.57535 q^{15} +1.00000 q^{16} -4.90655 q^{17} -5.14844 q^{18} -4.05918 q^{19} -2.30346 q^{20} -9.06345 q^{21} -0.413956 q^{22} -3.18964 q^{23} +2.85455 q^{24} +0.305950 q^{25} +0.672208 q^{26} -6.13284 q^{27} +3.17509 q^{28} +8.43607 q^{29} -6.57535 q^{30} -9.73017 q^{31} -1.00000 q^{32} -1.18166 q^{33} +4.90655 q^{34} -7.31371 q^{35} +5.14844 q^{36} -0.281784 q^{37} +4.05918 q^{38} +1.91885 q^{39} +2.30346 q^{40} +11.3819 q^{41} +9.06345 q^{42} -0.672064 q^{43} +0.413956 q^{44} -11.8593 q^{45} +3.18964 q^{46} -4.25377 q^{47} -2.85455 q^{48} +3.08121 q^{49} -0.305950 q^{50} +14.0060 q^{51} -0.672208 q^{52} +0.287120 q^{53} +6.13284 q^{54} -0.953533 q^{55} -3.17509 q^{56} +11.5871 q^{57} -8.43607 q^{58} +2.51707 q^{59} +6.57535 q^{60} -14.4708 q^{61} +9.73017 q^{62} +16.3468 q^{63} +1.00000 q^{64} +1.54841 q^{65} +1.18166 q^{66} -2.18572 q^{67} -4.90655 q^{68} +9.10497 q^{69} +7.31371 q^{70} +1.58520 q^{71} -5.14844 q^{72} -11.6259 q^{73} +0.281784 q^{74} -0.873349 q^{75} -4.05918 q^{76} +1.31435 q^{77} -1.91885 q^{78} +13.8719 q^{79} -2.30346 q^{80} +2.06115 q^{81} -11.3819 q^{82} -10.9091 q^{83} -9.06345 q^{84} +11.3021 q^{85} +0.672064 q^{86} -24.0812 q^{87} -0.413956 q^{88} +7.83590 q^{89} +11.8593 q^{90} -2.13432 q^{91} -3.18964 q^{92} +27.7752 q^{93} +4.25377 q^{94} +9.35017 q^{95} +2.85455 q^{96} +11.4406 q^{97} -3.08121 q^{98} +2.13123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) $ 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * 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
$3$	−2.85455	−1.64807	−0.824037	−	0.566536i	$-0.808283\pi$
$3$	−2.85455	−1.64807	−0.824037	+	0.566536i	$0.808283\pi$
$4$	1.00000	0.500000
$5$	−2.30346	−1.03014	−0.515070	−	0.857148i	$-0.672234\pi$
$5$	−2.30346	−1.03014	−0.515070	+	0.857148i	$0.672234\pi$
$6$	2.85455	1.16536
$7$	3.17509	1.20007	0.600036	−	0.799973i	$-0.295153\pi$
$7$	3.17509	1.20007	0.600036	+	0.799973i	$0.295153\pi$
$8$	−1.00000	−0.353553
$9$	5.14844	1.71615
$10$	2.30346	0.728420
$11$	0.413956	0.124812	0.0624062	−	0.998051i	$-0.480123\pi$
$11$	0.413956	0.124812	0.0624062	+	0.998051i	$0.480123\pi$
$12$	−2.85455	−0.824037
$13$	−0.672208	−0.186437	−0.0932185	−	0.995646i	$-0.529715\pi$
$13$	−0.672208	−0.186437	−0.0932185	+	0.995646i	$0.529715\pi$
$14$	−3.17509	−0.848579
$15$	6.57535	1.69775
$16$	1.00000	0.250000
$17$	−4.90655	−1.19001	−0.595007	−	0.803720i	$-0.702851\pi$
$17$	−4.90655	−1.19001	−0.595007	+	0.803720i	$0.702851\pi$
$18$	−5.14844	−1.21350
$19$	−4.05918	−0.931239	−0.465619	−	0.884985i	$-0.654168\pi$
$19$	−4.05918	−0.931239	−0.465619	+	0.884985i	$0.654168\pi$
$20$	−2.30346	−0.515070
$21$	−9.06345	−1.97781
$22$	−0.413956	−0.0882557
$23$	−3.18964	−0.665085	−0.332543	−	0.943088i	$-0.607907\pi$
$23$	−3.18964	−0.665085	−0.332543	+	0.943088i	$0.607907\pi$
$24$	2.85455	0.582682
$25$	0.305950	0.0611900
$26$	0.672208	0.131831
$27$	−6.13284	−1.18027
$28$	3.17509	0.600036
$29$	8.43607	1.56654	0.783269	−	0.621683i	$-0.213551\pi$
$29$	8.43607	1.56654	0.783269	+	0.621683i	$0.213551\pi$
$30$	−6.57535	−1.20049
$31$	−9.73017	−1.74759	−0.873795	−	0.486294i	$-0.838348\pi$
$31$	−9.73017	−1.74759	−0.873795	+	0.486294i	$0.838348\pi$
$32$	−1.00000	−0.176777
$33$	−1.18166	−0.205700
$34$	4.90655	0.841467
$35$	−7.31371	−1.23624
$36$	5.14844	0.858074
$37$	−0.281784	−0.0463250	−0.0231625	−	0.999732i	$-0.507374\pi$
$37$	−0.281784	−0.0463250	−0.0231625	+	0.999732i	$0.507374\pi$
$38$	4.05918	0.658485
$39$	1.91885	0.307262
$40$	2.30346	0.364210
$41$	11.3819	1.77756	0.888779	−	0.458335i	$-0.151554\pi$
$41$	11.3819	1.77756	0.888779	+	0.458335i	$0.151554\pi$
$42$	9.06345	1.39852
$43$	−0.672064	−0.102489	−0.0512444	−	0.998686i	$-0.516319\pi$
$43$	−0.672064	−0.102489	−0.0512444	+	0.998686i	$0.516319\pi$
$44$	0.413956	0.0624062
$45$	−11.8593	−1.76787
$46$	3.18964	0.470286
$47$	−4.25377	−0.620476	−0.310238	−	0.950659i	$-0.600409\pi$
$47$	−4.25377	−0.620476	−0.310238	+	0.950659i	$0.600409\pi$
$48$	−2.85455	−0.412019
$49$	3.08121	0.440173
$50$	−0.305950	−0.0432678
$51$	14.0060	1.96123
$52$	−0.672208	−0.0932185
$53$	0.287120	0.0394390	0.0197195	−	0.999806i	$-0.493723\pi$
$53$	0.287120	0.0394390	0.0197195	+	0.999806i	$0.493723\pi$
$54$	6.13284	0.834574
$55$	−0.953533	−0.128574
$56$	−3.17509	−0.424289
$57$	11.5871	1.53475
$58$	−8.43607	−1.10771
$59$	2.51707	0.327695	0.163848	−	0.986486i	$-0.447609\pi$
$59$	2.51707	0.327695	0.163848	+	0.986486i	$0.447609\pi$
$60$	6.57535	0.848874
$61$	−14.4708	−1.85280	−0.926400	−	0.376540i	$-0.877114\pi$
$61$	−14.4708	−1.85280	−0.926400	+	0.376540i	$0.877114\pi$
$62$	9.73017	1.23573
$63$	16.3468	2.05950
$64$	1.00000	0.125000
$65$	1.54841	0.192056
$66$	1.18166	0.145452
$67$	−2.18572	−0.267028	−0.133514	−	0.991047i	$-0.542626\pi$
$67$	−2.18572	−0.267028	−0.133514	+	0.991047i	$0.542626\pi$
$68$	−4.90655	−0.595007
$69$	9.10497	1.09611
$70$	7.31371	0.874156
$71$	1.58520	0.188129	0.0940645	−	0.995566i	$-0.470014\pi$
$71$	1.58520	0.188129	0.0940645	+	0.995566i	$0.470014\pi$
$72$	−5.14844	−0.606750
$73$	−11.6259	−1.36070	−0.680352	−	0.732885i	$-0.738173\pi$
$73$	−11.6259	−1.36070	−0.680352	+	0.732885i	$0.738173\pi$
$74$	0.281784	0.0327567
$75$	−0.873349	−0.100846
$76$	−4.05918	−0.465619
$77$	1.31435	0.149784
$78$	−1.91885	−0.217267
$79$	13.8719	1.56071	0.780353	−	0.625340i	$-0.215040\pi$
$79$	13.8719	1.56071	0.780353	+	0.625340i	$0.215040\pi$
$80$	−2.30346	−0.257535
$81$	2.06115	0.229017
$82$	−11.3819	−1.25692
$83$	−10.9091	−1.19743	−0.598716	−	0.800961i	$-0.704322\pi$
$83$	−10.9091	−1.19743	−0.598716	+	0.800961i	$0.704322\pi$
$84$	−9.06345	−0.988904
$85$	11.3021	1.22588
$86$	0.672064	0.0724705
$87$	−24.0812	−2.58177
$88$	−0.413956	−0.0441279
$89$	7.83590	0.830603	0.415302	−	0.909684i	$-0.363676\pi$
$89$	7.83590	0.830603	0.415302	+	0.909684i	$0.363676\pi$
$90$	11.8593	1.25008
$91$	−2.13432	−0.223738
$92$	−3.18964	−0.332543
$93$	27.7752	2.88016
$94$	4.25377	0.438743
$95$	9.35017	0.959307
$96$	2.85455	0.291341
$97$	11.4406	1.16161	0.580807	−	0.814041i	$-0.302737\pi$
$97$	11.4406	1.16161	0.580807	+	0.814041i	$0.302737\pi$
$98$	−3.08121	−0.311249
$99$	2.13123	0.214197
$100$	0.305950	0.0305950
$101$	16.2393	1.61587	0.807937	−	0.589268i	$-0.200584\pi$
$101$	16.2393	1.61587	0.807937	+	0.589268i	$0.200584\pi$
$102$	−14.0060	−1.38680
$103$	9.71683	0.957427	0.478714	−	0.877971i	$-0.341103\pi$
$103$	9.71683	0.957427	0.478714	+	0.877971i	$0.341103\pi$
$104$	0.672208	0.0659154
$105$	20.8773	2.03742
$106$	−0.287120	−0.0278876
$107$	11.7121	1.13225	0.566123	−	0.824321i	$-0.308443\pi$
$107$	11.7121	1.13225	0.566123	+	0.824321i	$0.308443\pi$
$108$	−6.13284	−0.590133
$109$	−15.5267	−1.48719	−0.743595	−	0.668631i	$-0.766881\pi$
$109$	−15.5267	−1.48719	−0.743595	+	0.668631i	$0.766881\pi$
$110$	0.953533	0.0909158
$111$	0.804366	0.0763470
$112$	3.17509	0.300018
$113$	2.49326	0.234546	0.117273	−	0.993100i	$-0.462585\pi$
$113$	2.49326	0.234546	0.117273	+	0.993100i	$0.462585\pi$
$114$	−11.5871	−1.08523
$115$	7.34722	0.685131
$116$	8.43607	0.783269
$117$	−3.46082	−0.319953
$118$	−2.51707	−0.231715
$119$	−15.5788	−1.42810
$120$	−6.57535	−0.600245
$121$	−10.8286	−0.984422
$122$	14.4708	1.31013
$123$	−32.4903	−2.92955
$124$	−9.73017	−0.873795
$125$	10.8126	0.967106
$126$	−16.3468	−1.45629
$127$	−2.93521	−0.260458	−0.130229	−	0.991484i	$-0.541571\pi$
$127$	−2.93521	−0.260458	−0.130229	+	0.991484i	$0.541571\pi$
$128$	−1.00000	−0.0883883
$129$	1.91844	0.168909
$130$	−1.54841	−0.135804
$131$	2.35723	0.205952	0.102976	−	0.994684i	$-0.467163\pi$
$131$	2.35723	0.205952	0.102976	+	0.994684i	$0.467163\pi$
$132$	−1.18166	−0.102850
$133$	−12.8883	−1.11755
$134$	2.18572	0.188818
$135$	14.1268	1.21584
$136$	4.90655	0.420734
$137$	−1.35681	−0.115920	−0.0579602	−	0.998319i	$-0.518460\pi$
$137$	−1.35681	−0.115920	−0.0579602	+	0.998319i	$0.518460\pi$
$138$	−9.10497	−0.775067
$139$	−2.83325	−0.240313	−0.120156	−	0.992755i	$-0.538340\pi$
$139$	−2.83325	−0.240313	−0.120156	+	0.992755i	$0.538340\pi$
$140$	−7.31371	−0.618121
$141$	12.1426	1.02259
$142$	−1.58520	−0.133027
$143$	−0.278265	−0.0232696
$144$	5.14844	0.429037
$145$	−19.4322	−1.61376
$146$	11.6259	0.962164
$147$	−8.79546	−0.725437
$148$	−0.281784	−0.0231625
$149$	−18.3430	−1.50272	−0.751359	−	0.659894i	$-0.770601\pi$
$149$	−18.3430	−1.50272	−0.751359	+	0.659894i	$0.770601\pi$
$150$	0.873349	0.0713086
$151$	7.55158	0.614539	0.307269	−	0.951623i	$-0.400585\pi$
$151$	7.55158	0.614539	0.307269	+	0.951623i	$0.400585\pi$
$152$	4.05918	0.329243
$153$	−25.2611	−2.04224
$154$	−1.31435	−0.105913
$155$	22.4131	1.80026
$156$	1.91885	0.153631
$157$	−18.5097	−1.47723	−0.738617	−	0.674125i	$-0.764521\pi$
$157$	−18.5097	−1.47723	−0.738617	+	0.674125i	$0.764521\pi$
$158$	−13.8719	−1.10359
$159$	−0.819598	−0.0649984
$160$	2.30346	0.182105
$161$	−10.1274	−0.798150
$162$	−2.06115	−0.161939
$163$	−1.46622	−0.114844	−0.0574218	−	0.998350i	$-0.518288\pi$
$163$	−1.46622	−0.114844	−0.0574218	+	0.998350i	$0.518288\pi$
$164$	11.3819	0.888779
$165$	2.72191	0.211900
$166$	10.9091	0.846712
$167$	−19.2262	−1.48777	−0.743885	−	0.668308i	$-0.767019\pi$
$167$	−19.2262	−1.48777	−0.743885	+	0.668308i	$0.767019\pi$
$168$	9.06345	0.699261
$169$	−12.5481	−0.965241
$170$	−11.3021	−0.866829
$171$	−20.8984	−1.59814
$172$	−0.672064	−0.0512444
$173$	−12.3908	−0.942055	−0.471028	−	0.882118i	$-0.656117\pi$
$173$	−12.3908	−0.942055	−0.471028	+	0.882118i	$0.656117\pi$
$174$	24.0812	1.82559
$175$	0.971419	0.0734324
$176$	0.413956	0.0312031
$177$	−7.18511	−0.540066
$178$	−7.83590	−0.587325
$179$	−19.9492	−1.49108	−0.745538	−	0.666463i	$-0.767807\pi$
$179$	−19.9492	−1.49108	−0.745538	+	0.666463i	$0.767807\pi$
$180$	−11.8593	−0.883937
$181$	−0.795424	−0.0591234	−0.0295617	−	0.999563i	$-0.509411\pi$
$181$	−0.795424	−0.0591234	−0.0295617	+	0.999563i	$0.509411\pi$
$182$	2.13432	0.158206
$183$	41.3077	3.05355
$184$	3.18964	0.235143
$185$	0.649079	0.0477213
$186$	−27.7752	−2.03658
$187$	−2.03110	−0.148529
$188$	−4.25377	−0.310238
$189$	−19.4723	−1.41640
$190$	−9.35017	−0.678333
$191$	8.91160	0.644821	0.322410	−	0.946600i	$-0.395507\pi$
$191$	8.91160	0.644821	0.322410	+	0.946600i	$0.395507\pi$
$192$	−2.85455	−0.206009
$193$	−3.52444	−0.253694	−0.126847	−	0.991922i	$-0.540486\pi$
$193$	−3.52444	−0.253694	−0.126847	+	0.991922i	$0.540486\pi$
$194$	−11.4406	−0.821385
$195$	−4.42000	−0.316523
$196$	3.08121	0.220086
$197$	−20.2260	−1.44104	−0.720520	−	0.693434i	$-0.756097\pi$
$197$	−20.2260	−1.44104	−0.720520	+	0.693434i	$0.756097\pi$
$198$	−2.13123	−0.151460
$199$	−23.1259	−1.63935	−0.819676	−	0.572827i	$-0.805847\pi$
$199$	−23.1259	−1.63935	−0.819676	+	0.572827i	$0.805847\pi$
$200$	−0.305950	−0.0216339
$201$	6.23925	0.440083
$202$	−16.2393	−1.14260
$203$	26.7853	1.87996
$204$	14.0060	0.980616
$205$	−26.2179	−1.83114
$206$	−9.71683	−0.677003
$207$	−16.4217	−1.14138
$208$	−0.672208	−0.0466092
$209$	−1.68032	−0.116230
$210$	−20.8773	−1.44067
$211$	0.849949	0.0585129	0.0292565	−	0.999572i	$-0.490686\pi$
$211$	0.849949	0.0585129	0.0292565	+	0.999572i	$0.490686\pi$
$212$	0.287120	0.0197195
$213$	−4.52504	−0.310051
$214$	−11.7121	−0.800619
$215$	1.54808	0.105578
$216$	6.13284	0.417287
$217$	−30.8942	−2.09723
$218$	15.5267	1.05160
$219$	33.1866	2.24254
$220$	−0.953533	−0.0642872
$221$	3.29822	0.221863
$222$	−0.804366	−0.0539855
$223$	25.9787	1.73966	0.869832	−	0.493347i	$-0.164227\pi$
$223$	25.9787	1.73966	0.869832	+	0.493347i	$0.164227\pi$
$224$	−3.17509	−0.212145
$225$	1.57517	0.105011
$226$	−2.49326	−0.165849
$227$	−22.9333	−1.52214	−0.761068	−	0.648672i	$-0.775325\pi$
$227$	−22.9333	−1.52214	−0.761068	+	0.648672i	$0.775325\pi$
$228$	11.5871	0.767375
$229$	22.9824	1.51872	0.759359	−	0.650671i	$-0.225512\pi$
$229$	22.9824	1.51872	0.759359	+	0.650671i	$0.225512\pi$
$230$	−7.34722	−0.484461
$231$	−3.75187	−0.246855
$232$	−8.43607	−0.553855
$233$	28.0038	1.83459	0.917296	−	0.398207i	$-0.130367\pi$
$233$	28.0038	1.83459	0.917296	+	0.398207i	$0.130367\pi$
$234$	3.46082	0.226241
$235$	9.79841	0.639178
$236$	2.51707	0.163848
$237$	−39.5979	−2.57216
$238$	15.5788	1.00982
$239$	21.5230	1.39221	0.696105	−	0.717940i	$-0.254915\pi$
$239$	21.5230	1.39221	0.696105	+	0.717940i	$0.254915\pi$
$240$	6.57535	0.424437
$241$	−20.6101	−1.32761	−0.663806	−	0.747905i	$-0.731060\pi$
$241$	−20.6101	−1.32761	−0.663806	+	0.747905i	$0.731060\pi$
$242$	10.8286	0.696091
$243$	12.5149	0.802829
$244$	−14.4708	−0.926400
$245$	−7.09745	−0.453440
$246$	32.4903	2.07150
$247$	2.72861	0.173617
$248$	9.73017	0.617866
$249$	31.1406	1.97346
$250$	−10.8126	−0.683848
$251$	−3.38753	−0.213819	−0.106909	−	0.994269i	$-0.534095\pi$
$251$	−3.38753	−0.213819	−0.106909	+	0.994269i	$0.534095\pi$
$252$	16.3468	1.02975
$253$	−1.32037	−0.0830109
$254$	2.93521	0.184172
$255$	−32.2623	−2.02034
$256$	1.00000	0.0625000
$257$	14.7628	0.920881	0.460441	−	0.887691i	$-0.347691\pi$
$257$	14.7628	0.920881	0.460441	+	0.887691i	$0.347691\pi$
$258$	−1.91844	−0.119437
$259$	−0.894690	−0.0555933
$260$	1.54841	0.0960281
$261$	43.4326	2.68841
$262$	−2.35723	−0.145630
$263$	−12.0749	−0.744573	−0.372287	−	0.928118i	$-0.621426\pi$
$263$	−12.0749	−0.744573	−0.372287	+	0.928118i	$0.621426\pi$
$264$	1.18166	0.0727260
$265$	−0.661371	−0.0406277
$266$	12.8883	0.790230
$267$	−22.3679	−1.36890
$268$	−2.18572	−0.133514
$269$	−2.08695	−0.127244	−0.0636219	−	0.997974i	$-0.520265\pi$
$269$	−2.08695	−0.127244	−0.0636219	+	0.997974i	$0.520265\pi$
$270$	−14.1268	−0.859728
$271$	−14.4015	−0.874831	−0.437416	−	0.899259i	$-0.644106\pi$
$271$	−14.4015	−0.874831	−0.437416	+	0.899259i	$0.644106\pi$
$272$	−4.90655	−0.297504
$273$	6.09252	0.368736
$274$	1.35681	0.0819681
$275$	0.126650	0.00763727
$276$	9.10497	0.548055
$277$	2.46601	0.148168	0.0740841	−	0.997252i	$-0.476397\pi$
$277$	2.46601	0.148168	0.0740841	+	0.997252i	$0.476397\pi$
$278$	2.83325	0.169927
$279$	−50.0952	−2.99912
$280$	7.31371	0.437078
$281$	23.0612	1.37571	0.687857	−	0.725846i	$-0.258552\pi$
$281$	23.0612	1.37571	0.687857	+	0.725846i	$0.258552\pi$
$282$	−12.1426	−0.723081
$283$	−29.4036	−1.74786	−0.873932	−	0.486048i	$-0.838438\pi$
$283$	−29.4036	−1.74786	−0.873932	+	0.486048i	$0.838438\pi$
$284$	1.58520	0.0940645
$285$	−26.6905	−1.58101
$286$	0.278265	0.0164541
$287$	36.1387	2.13320
$288$	−5.14844	−0.303375
$289$	7.07427	0.416133
$290$	19.4322	1.14110
$291$	−32.6577	−1.91443
$292$	−11.6259	−0.680352
$293$	3.91444	0.228684	0.114342	−	0.993441i	$-0.463524\pi$
$293$	3.91444	0.228684	0.114342	+	0.993441i	$0.463524\pi$
$294$	8.79546	0.512961
$295$	−5.79799	−0.337572
$296$	0.281784	0.0163784
$297$	−2.53873	−0.147312
$298$	18.3430	1.06258
$299$	2.14410	0.123996
$300$	−0.873349	−0.0504228
$301$	−2.13386	−0.122994
$302$	−7.55158	−0.434545
$303$	−46.3560	−2.66308
$304$	−4.05918	−0.232810
$305$	33.3331	1.90865
$306$	25.2611	1.44408
$307$	−31.5132	−1.79855	−0.899277	−	0.437379i	$-0.855907\pi$
$307$	−31.5132	−1.79855	−0.899277	+	0.437379i	$0.855907\pi$
$308$	1.31435	0.0748920
$309$	−27.7372	−1.57791
$310$	−22.4131	−1.27298
$311$	30.0903	1.70626	0.853132	−	0.521695i	$-0.174700\pi$
$311$	30.0903	1.70626	0.853132	+	0.521695i	$0.174700\pi$
$312$	−1.91885	−0.108633
$313$	25.7827	1.45733	0.728663	−	0.684872i	$-0.240142\pi$
$313$	25.7827	1.45733	0.728663	+	0.684872i	$0.240142\pi$
$314$	18.5097	1.04456
$315$	−37.6542	−2.12158
$316$	13.8719	0.780353
$317$	−7.92759	−0.445258	−0.222629	−	0.974903i	$-0.571464\pi$
$317$	−7.92759	−0.445258	−0.222629	+	0.974903i	$0.571464\pi$
$318$	0.819598	0.0459608
$319$	3.49216	0.195524
$320$	−2.30346	−0.128768
$321$	−33.4326	−1.86603
$322$	10.1274	0.564377
$323$	19.9166	1.10819
$324$	2.06115	0.114508
$325$	−0.205662	−0.0114081
$326$	1.46622	0.0812067
$327$	44.3217	2.45100
$328$	−11.3819	−0.628462
$329$	−13.5061	−0.744616
$330$	−2.72191	−0.149836
$331$	20.7642	1.14130	0.570651	−	0.821193i	$-0.306691\pi$
$331$	20.7642	1.14130	0.570651	+	0.821193i	$0.306691\pi$
$332$	−10.9091	−0.598716
$333$	−1.45075	−0.0795005
$334$	19.2262	1.05201
$335$	5.03473	0.275077
$336$	−9.06345	−0.494452
$337$	−6.56444	−0.357588	−0.178794	−	0.983887i	$-0.557220\pi$
$337$	−6.56444	−0.357588	−0.178794	+	0.983887i	$0.557220\pi$
$338$	12.5481	0.682529
$339$	−7.11712	−0.386549
$340$	11.3021	0.612941
$341$	−4.02786	−0.218121
$342$	20.8984	1.13006
$343$	−12.4425	−0.671833
$344$	0.672064	0.0362352
$345$	−20.9730	−1.12915
$346$	12.3908	0.666134
$347$	−13.8558	−0.743816	−0.371908	−	0.928270i	$-0.621296\pi$
$347$	−13.8558	−0.743816	−0.371908	+	0.928270i	$0.621296\pi$
$348$	−24.0812	−1.29089
$349$	18.7434	1.00331	0.501657	−	0.865067i	$-0.332724\pi$
$349$	18.7434	1.00331	0.501657	+	0.865067i	$0.332724\pi$
$350$	−0.971419	−0.0519245
$351$	4.12254	0.220045
$352$	−0.413956	−0.0220639
$353$	29.6464	1.57792	0.788961	−	0.614444i	$-0.210620\pi$
$353$	29.6464	1.57792	0.788961	+	0.614444i	$0.210620\pi$
$354$	7.18511	0.381884
$355$	−3.65146	−0.193799
$356$	7.83590	0.415302
$357$	44.4703	2.35362
$358$	19.9492	1.05435
$359$	−16.2499	−0.857639	−0.428819	−	0.903390i	$-0.641070\pi$
$359$	−16.2499	−0.857639	−0.428819	+	0.903390i	$0.641070\pi$
$360$	11.8593	0.625038
$361$	−2.52309	−0.132794
$362$	0.795424	0.0418066
$363$	30.9109	1.62240
$364$	−2.13432	−0.111869
$365$	26.7798	1.40172
$366$	−41.3077	−2.15919
$367$	29.2518	1.52693	0.763465	−	0.645849i	$-0.223496\pi$
$367$	29.2518	1.52693	0.763465	+	0.645849i	$0.223496\pi$
$368$	−3.18964	−0.166271
$369$	58.5992	3.05055
$370$	−0.649079	−0.0337440
$371$	0.911633	0.0473296
$372$	27.7752	1.44008
$373$	4.54286	0.235220	0.117610	−	0.993060i	$-0.462477\pi$
$373$	4.54286	0.235220	0.117610	+	0.993060i	$0.462477\pi$
$374$	2.03110	0.105026
$375$	−30.8650	−1.59386
$376$	4.25377	0.219371
$377$	−5.67079	−0.292061
$378$	19.4723	1.00155
$379$	12.3231	0.632993	0.316496	−	0.948594i	$-0.397493\pi$
$379$	12.3231	0.632993	0.316496	+	0.948594i	$0.397493\pi$
$380$	9.35017	0.479654
$381$	8.37871	0.429254
$382$	−8.91160	−0.455957
$383$	−31.2445	−1.59652	−0.798259	−	0.602315i	$-0.794245\pi$
$383$	−31.2445	−1.59652	−0.798259	+	0.602315i	$0.794245\pi$
$384$	2.85455	0.145671
$385$	−3.02756	−0.154299
$386$	3.52444	0.179389
$387$	−3.46008	−0.175886
$388$	11.4406	0.580807
$389$	−4.14582	−0.210201	−0.105101	−	0.994462i	$-0.533517\pi$
$389$	−4.14582	−0.210201	−0.105101	+	0.994462i	$0.533517\pi$
$390$	4.42000	0.223816
$391$	15.6501	0.791461
$392$	−3.08121	−0.155625
$393$	−6.72883	−0.339425
$394$	20.2260	1.01897
$395$	−31.9533	−1.60775
$396$	2.13123	0.107098
$397$	−17.7326	−0.889976	−0.444988	−	0.895537i	$-0.646792\pi$
$397$	−17.7326	−0.889976	−0.444988	+	0.895537i	$0.646792\pi$
$398$	23.1259	1.15920
$399$	36.7902	1.84181
$400$	0.305950	0.0152975
$401$	33.8246	1.68912	0.844560	−	0.535461i	$-0.179862\pi$
$401$	33.8246	1.68912	0.844560	+	0.535461i	$0.179862\pi$
$402$	−6.23925	−0.311185
$403$	6.54070	0.325815
$404$	16.2393	0.807937
$405$	−4.74778	−0.235919
$406$	−26.7853	−1.32933
$407$	−0.116646	−0.00578194
$408$	−14.0060	−0.693400
$409$	19.7549	0.976817	0.488409	−	0.872615i	$-0.337578\pi$
$409$	19.7549	0.976817	0.488409	+	0.872615i	$0.337578\pi$
$410$	26.2179	1.29481
$411$	3.87309	0.191045
$412$	9.71683	0.478714
$413$	7.99194	0.393258
$414$	16.4217	0.807081
$415$	25.1288	1.23352
$416$	0.672208	0.0329577
$417$	8.08764	0.396054
$418$	1.68032	0.0821872
$419$	16.1326	0.788131	0.394066	−	0.919082i	$-0.371068\pi$
$419$	16.1326	0.788131	0.394066	+	0.919082i	$0.371068\pi$
$420$	20.8773	1.01871
$421$	−11.7260	−0.571489	−0.285745	−	0.958306i	$-0.592241\pi$
$421$	−11.7260	−0.571489	−0.285745	+	0.958306i	$0.592241\pi$
$422$	−0.849949	−0.0413749
$423$	−21.9003	−1.06483
$424$	−0.287120	−0.0139438
$425$	−1.50116	−0.0728169
$426$	4.52504	0.219239
$427$	−45.9462	−2.22349
$428$	11.7121	0.566123
$429$	0.794319	0.0383501
$430$	−1.54808	−0.0746548
$431$	25.3571	1.22141	0.610705	−	0.791859i	$-0.290886\pi$
$431$	25.3571	1.22141	0.610705	+	0.791859i	$0.290886\pi$
$432$	−6.13284	−0.295066
$433$	−6.05304	−0.290890	−0.145445	−	0.989366i	$-0.546461\pi$
$433$	−6.05304	−0.290890	−0.145445	+	0.989366i	$0.546461\pi$
$434$	30.8942	1.48297
$435$	55.4701	2.65959
$436$	−15.5267	−0.743595
$437$	12.9473	0.619353
$438$	−33.1866	−1.58572
$439$	8.04523	0.383978	0.191989	−	0.981397i	$-0.438506\pi$
$439$	8.04523	0.383978	0.191989	+	0.981397i	$0.438506\pi$
$440$	0.953533	0.0454579
$441$	15.8634	0.755401
$442$	−3.29822	−0.156881
$443$	−22.1143	−1.05068	−0.525342	−	0.850891i	$-0.676063\pi$
$443$	−22.1143	−1.05068	−0.525342	+	0.850891i	$0.676063\pi$
$444$	0.804366	0.0381735
$445$	−18.0497	−0.855638
$446$	−25.9787	−1.23013
$447$	52.3610	2.47659
$448$	3.17509	0.150009
$449$	33.2077	1.56717	0.783583	−	0.621287i	$-0.213390\pi$
$449$	33.2077	1.56717	0.783583	+	0.621287i	$0.213390\pi$
$450$	−1.57517	−0.0742540
$451$	4.71162	0.221862
$452$	2.49326	0.117273
$453$	−21.5563	−1.01281
$454$	22.9333	1.07631
$455$	4.91633	0.230481
$456$	−11.5871	−0.542616
$457$	25.2302	1.18022	0.590110	−	0.807323i	$-0.299085\pi$
$457$	25.2302	1.18022	0.590110	+	0.807323i	$0.299085\pi$
$458$	−22.9824	−1.07390
$459$	30.0911	1.40453
$460$	7.34722	0.342566
$461$	−33.2214	−1.54728	−0.773638	−	0.633628i	$-0.781565\pi$
$461$	−33.2214	−1.54728	−0.773638	+	0.633628i	$0.781565\pi$
$462$	3.75187	0.174553
$463$	12.0866	0.561710	0.280855	−	0.959750i	$-0.409382\pi$
$463$	12.0866	0.561710	0.280855	+	0.959750i	$0.409382\pi$
$464$	8.43607	0.391635
$465$	−63.9793	−2.96697
$466$	−28.0038	−1.29725
$467$	10.2671	0.475103	0.237552	−	0.971375i	$-0.423655\pi$
$467$	10.2671	0.475103	0.237552	+	0.971375i	$0.423655\pi$
$468$	−3.46082	−0.159977
$469$	−6.93987	−0.320453
$470$	−9.79841	−0.451967
$471$	52.8368	2.43459
$472$	−2.51707	−0.115858
$473$	−0.278205	−0.0127919
$474$	39.5979	1.81879
$475$	−1.24190	−0.0569825
$476$	−15.5788	−0.714051
$477$	1.47822	0.0676831
$478$	−21.5230	−0.984441
$479$	−14.1229	−0.645293	−0.322646	−	0.946520i	$-0.604572\pi$
$479$	−14.1229	−0.645293	−0.322646	+	0.946520i	$0.604572\pi$
$480$	−6.57535	−0.300122
$481$	0.189417	0.00863669
$482$	20.6101	0.938764
$483$	28.9091	1.31541
$484$	−10.8286	−0.492211
$485$	−26.3529	−1.19663
$486$	−12.5149	−0.567686
$487$	41.6404	1.88691	0.943454	−	0.331503i	$-0.107556\pi$
$487$	41.6404	1.88691	0.943454	+	0.331503i	$0.107556\pi$
$488$	14.4708	0.655064
$489$	4.18541	0.189271
$490$	7.09745	0.320630
$491$	22.6235	1.02098	0.510492	−	0.859883i	$-0.329463\pi$
$491$	22.6235	1.02098	0.510492	+	0.859883i	$0.329463\pi$
$492$	−32.4903	−1.46477
$493$	−41.3920	−1.86420
$494$	−2.72861	−0.122766
$495$	−4.90921	−0.220653
$496$	−9.73017	−0.436898
$497$	5.03317	0.225768
$498$	−31.1406	−1.39544
$499$	−6.46447	−0.289389	−0.144695	−	0.989476i	$-0.546220\pi$
$499$	−6.46447	−0.289389	−0.144695	+	0.989476i	$0.546220\pi$
$500$	10.8126	0.483553
$501$	54.8822	2.45195
$502$	3.38753	0.151193
$503$	−6.33814	−0.282603	−0.141302	−	0.989967i	$-0.545129\pi$
$503$	−6.33814	−0.282603	−0.141302	+	0.989967i	$0.545129\pi$
$504$	−16.3468	−0.728144
$505$	−37.4067	−1.66458
$506$	1.32037	0.0586976
$507$	35.8193	1.59079
$508$	−2.93521	−0.130229
$509$	8.64833	0.383331	0.191665	−	0.981460i	$-0.438611\pi$
$509$	8.64833	0.383331	0.191665	+	0.981460i	$0.438611\pi$
$510$	32.2623	1.42860
$511$	−36.9132	−1.63294
$512$	−1.00000	−0.0441942
$513$	24.8943	1.09911
$514$	−14.7628	−0.651161
$515$	−22.3824	−0.986285
$516$	1.91844	0.0844545
$517$	−1.76087	−0.0774431
$518$	0.894690	0.0393104
$519$	35.3701	1.55258
$520$	−1.54841	−0.0679021
$521$	−19.1778	−0.840194	−0.420097	−	0.907479i	$-0.638004\pi$
$521$	−19.1778	−0.840194	−0.420097	+	0.907479i	$0.638004\pi$
$522$	−43.4326	−1.90099
$523$	−14.3291	−0.626569	−0.313285	−	0.949659i	$-0.601429\pi$
$523$	−14.3291	−0.626569	−0.313285	+	0.949659i	$0.601429\pi$
$524$	2.35723	0.102976
$525$	−2.77296	−0.121022
$526$	12.0749	0.526493
$527$	47.7416	2.07966
$528$	−1.18166	−0.0514250
$529$	−12.8262	−0.557662
$530$	0.661371	0.0287281
$531$	12.9590	0.562373
$532$	−12.8883	−0.558777
$533$	−7.65102	−0.331403
$534$	22.3679	0.967956
$535$	−26.9783	−1.16637
$536$	2.18572	0.0944088
$537$	56.9461	2.45740
$538$	2.08695	0.0899749
$539$	1.27548	0.0549390
$540$	14.1268	0.607920
$541$	8.28473	0.356188	0.178094	−	0.984013i	$-0.443007\pi$
$541$	8.28473	0.356188	0.178094	+	0.984013i	$0.443007\pi$
$542$	14.4015	0.618599
$543$	2.27058	0.0974398
$544$	4.90655	0.210367
$545$	35.7652	1.53201
$546$	−6.09252	−0.260736
$547$	−41.3780	−1.76919	−0.884597	−	0.466357i	$-0.845566\pi$
$547$	−41.3780	−1.76919	−0.884597	+	0.466357i	$0.845566\pi$
$548$	−1.35681	−0.0579602
$549$	−74.5023	−3.17968
$550$	−0.126650	−0.00540037
$551$	−34.2435	−1.45882
$552$	−9.10497	−0.387533
$553$	44.0444	1.87296
$554$	−2.46601	−0.104771
$555$	−1.85283	−0.0786482
$556$	−2.83325	−0.120156
$557$	−4.62133	−0.195812	−0.0979059	−	0.995196i	$-0.531214\pi$
$557$	−4.62133	−0.195812	−0.0979059	+	0.995196i	$0.531214\pi$
$558$	50.0952	2.12070
$559$	0.451766	0.0191077
$560$	−7.31371	−0.309061
$561$	5.79787	0.244786
$562$	−23.0612	−0.972777
$563$	0.799597	0.0336990	0.0168495	−	0.999858i	$-0.494636\pi$
$563$	0.799597	0.0336990	0.0168495	+	0.999858i	$0.494636\pi$
$564$	12.1426	0.511295
$565$	−5.74313	−0.241615
$566$	29.4036	1.23593
$567$	6.54434	0.274836
$568$	−1.58520	−0.0665137
$569$	28.7200	1.20401	0.602003	−	0.798494i	$-0.294370\pi$
$569$	28.7200	1.20401	0.602003	+	0.798494i	$0.294370\pi$
$570$	26.6905	1.11794
$571$	21.6214	0.904829	0.452414	−	0.891808i	$-0.350563\pi$
$571$	21.6214	0.904829	0.452414	+	0.891808i	$0.350563\pi$
$572$	−0.278265	−0.0116348
$573$	−25.4386	−1.06271
$574$	−36.1387	−1.50840
$575$	−0.975869	−0.0406965
$576$	5.14844	0.214519
$577$	34.0812	1.41882	0.709409	−	0.704797i	$-0.248962\pi$
$577$	34.0812	1.41882	0.709409	+	0.704797i	$0.248962\pi$
$578$	−7.07427	−0.294251
$579$	10.0607	0.418107
$580$	−19.4322	−0.806878
$581$	−34.6375	−1.43700
$582$	32.6577	1.35370
$583$	0.118855	0.00492248
$584$	11.6259	0.481082
$585$	7.97189	0.329597
$586$	−3.91444	−0.161704
$587$	38.8078	1.60177	0.800885	−	0.598819i	$-0.204363\pi$
$587$	38.8078	1.60177	0.800885	+	0.598819i	$0.204363\pi$
$588$	−8.79546	−0.362719
$589$	39.4965	1.62742
$590$	5.79799	0.238700
$591$	57.7360	2.37494
$592$	−0.281784	−0.0115812
$593$	42.1518	1.73097	0.865484	−	0.500937i	$-0.167011\pi$
$593$	42.1518	1.73097	0.865484	+	0.500937i	$0.167011\pi$
$594$	2.53873	0.104165
$595$	35.8851	1.47115
$596$	−18.3430	−0.751359
$597$	66.0140	2.70178
$598$	−2.14410	−0.0876787
$599$	−2.06618	−0.0844219	−0.0422110	−	0.999109i	$-0.513440\pi$
$599$	−2.06618	−0.0844219	−0.0422110	+	0.999109i	$0.513440\pi$
$600$	0.873349	0.0356543
$601$	−6.75696	−0.275622	−0.137811	−	0.990459i	$-0.544007\pi$
$601$	−6.75696	−0.275622	−0.137811	+	0.990459i	$0.544007\pi$
$602$	2.13386	0.0869698
$603$	−11.2531	−0.458260
$604$	7.55158	0.307269
$605$	24.9434	1.01409
$606$	46.3560	1.88308
$607$	−31.7072	−1.28695	−0.643477	−	0.765465i	$-0.722509\pi$
$607$	−31.7072	−1.28695	−0.643477	+	0.765465i	$0.722509\pi$
$608$	4.05918	0.164621
$609$	−76.4599	−3.09831
$610$	−33.3331	−1.34962
$611$	2.85942	0.115680
$612$	−25.2611	−1.02112
$613$	33.0986	1.33684	0.668420	−	0.743784i	$-0.266971\pi$
$613$	33.0986	1.33684	0.668420	+	0.743784i	$0.266971\pi$
$614$	31.5132	1.27177
$615$	74.8402	3.01785
$616$	−1.31435	−0.0529566
$617$	−7.89936	−0.318016	−0.159008	−	0.987277i	$-0.550830\pi$
$617$	−7.89936	−0.318016	−0.159008	+	0.987277i	$0.550830\pi$
$618$	27.7372	1.11575
$619$	−13.1969	−0.530427	−0.265214	−	0.964190i	$-0.585442\pi$
$619$	−13.1969	−0.530427	−0.265214	+	0.964190i	$0.585442\pi$
$620$	22.4131	0.900132
$621$	19.5615	0.784977
$622$	−30.0903	−1.20651
$623$	24.8797	0.996784
$624$	1.91885	0.0768155
$625$	−26.4361	−1.05745
$626$	−25.7827	−1.03049
$627$	4.79656	0.191556
$628$	−18.5097	−0.738617
$629$	1.38259	0.0551274
$630$	37.6542	1.50018
$631$	−12.9440	−0.515294	−0.257647	−	0.966239i	$-0.582947\pi$
$631$	−12.9440	−0.515294	−0.257647	+	0.966239i	$0.582947\pi$
$632$	−13.8719	−0.551793
$633$	−2.42622	−0.0964336
$634$	7.92759	0.314845
$635$	6.76116	0.268308
$636$	−0.819598	−0.0324992
$637$	−2.07121	−0.0820644
$638$	−3.49216	−0.138256
$639$	8.16133	0.322857
$640$	2.30346	0.0910524
$641$	−1.82741	−0.0721783	−0.0360891	−	0.999349i	$-0.511490\pi$
$641$	−1.82741	−0.0721783	−0.0360891	+	0.999349i	$0.511490\pi$
$642$	33.4326	1.31948
$643$	18.5168	0.730231	0.365115	−	0.930962i	$-0.381030\pi$
$643$	18.5168	0.730231	0.365115	+	0.930962i	$0.381030\pi$
$644$	−10.1274	−0.399075
$645$	−4.41905	−0.174000
$646$	−19.9166	−0.783607
$647$	−33.4600	−1.31545	−0.657725	−	0.753258i	$-0.728481\pi$
$647$	−33.4600	−1.31545	−0.657725	+	0.753258i	$0.728481\pi$
$648$	−2.06115	−0.0809696
$649$	1.04196	0.0409004
$650$	0.205662	0.00806672
$651$	88.1889	3.45640
$652$	−1.46622	−0.0574218
$653$	40.5859	1.58825	0.794125	−	0.607755i	$-0.207930\pi$
$653$	40.5859	1.58825	0.794125	+	0.607755i	$0.207930\pi$
$654$	−44.3217	−1.73312
$655$	−5.42980	−0.212160
$656$	11.3819	0.444390
$657$	−59.8551	−2.33517
$658$	13.5061	0.526523
$659$	−4.34073	−0.169091	−0.0845454	−	0.996420i	$-0.526944\pi$
$659$	−4.34073	−0.169091	−0.0845454	+	0.996420i	$0.526944\pi$
$660$	2.72191	0.105950
$661$	24.6045	0.957003	0.478501	−	0.878087i	$-0.341180\pi$
$661$	24.6045	0.957003	0.478501	+	0.878087i	$0.341180\pi$
$662$	−20.7642	−0.807023
$663$	−9.41494	−0.365646
$664$	10.9091	0.423356
$665$	29.6876	1.15124
$666$	1.45075	0.0562154
$667$	−26.9080	−1.04188
$668$	−19.2262	−0.743885
$669$	−74.1575	−2.86710
$670$	−5.03473	−0.194509
$671$	−5.99029	−0.231253
$672$	9.06345	0.349630
$673$	20.9384	0.807117	0.403559	−	0.914954i	$-0.367773\pi$
$673$	20.9384	0.807117	0.403559	+	0.914954i	$0.367773\pi$
$674$	6.56444	0.252853
$675$	−1.87634	−0.0722204
$676$	−12.5481	−0.482621
$677$	−25.3677	−0.974960	−0.487480	−	0.873134i	$-0.662084\pi$
$677$	−25.3677	−0.974960	−0.487480	+	0.873134i	$0.662084\pi$
$678$	7.11712	0.273332
$679$	36.3249	1.39402
$680$	−11.3021	−0.433415
$681$	65.4642	2.50859
$682$	4.02786	0.154235
$683$	−43.0303	−1.64651	−0.823254	−	0.567673i	$-0.807844\pi$
$683$	−43.0303	−1.64651	−0.823254	+	0.567673i	$0.807844\pi$
$684$	−20.8984	−0.799072
$685$	3.12537	0.119414
$686$	12.4425	0.475058
$687$	−65.6043	−2.50296
$688$	−0.672064	−0.0256222
$689$	−0.193004	−0.00735288
$690$	20.9730	0.798428
$691$	−40.9023	−1.55600	−0.777998	−	0.628267i	$-0.783764\pi$
$691$	−40.9023	−1.55600	−0.777998	+	0.628267i	$0.783764\pi$
$692$	−12.3908	−0.471028
$693$	6.76685	0.257051
$694$	13.8558	0.525958
$695$	6.52629	0.247556
$696$	24.0812	0.912794
$697$	−55.8461	−2.11532
$698$	−18.7434	−0.709449
$699$	−79.9383	−3.02354
$700$	0.971419	0.0367162
$701$	50.4493	1.90545	0.952723	−	0.303842i	$-0.0982694\pi$
$701$	50.4493	1.90545	0.952723	+	0.303842i	$0.0982694\pi$
$702$	−4.12254	−0.155595
$703$	1.14381	0.0431396
$704$	0.413956	0.0156016
$705$	−27.9700	−1.05341
$706$	−29.6464	−1.11576
$707$	51.5614	1.93917
$708$	−7.18511	−0.270033
$709$	12.3419	0.463510	0.231755	−	0.972774i	$-0.425553\pi$
$709$	12.3419	0.463510	0.231755	+	0.972774i	$0.425553\pi$
$710$	3.65146	0.137037
$711$	71.4185	2.67840
$712$	−7.83590	−0.293663
$713$	31.0357	1.16230
$714$	−44.4703	−1.66426
$715$	0.640973	0.0239710
$716$	−19.9492	−0.745538
$717$	−61.4386	−2.29446
$718$	16.2499	0.606442
$719$	14.7376	0.549620	0.274810	−	0.961499i	$-0.411385\pi$
$719$	14.7376	0.549620	0.274810	+	0.961499i	$0.411385\pi$
$720$	−11.8593	−0.441969
$721$	30.8518	1.14898
$722$	2.52309	0.0938995
$723$	58.8325	2.18800
$724$	−0.795424	−0.0295617
$725$	2.58101	0.0958564
$726$	−30.9109	−1.14721
$727$	−29.0902	−1.07890	−0.539448	−	0.842019i	$-0.681367\pi$
$727$	−29.0902	−1.07890	−0.539448	+	0.842019i	$0.681367\pi$
$728$	2.13432	0.0791032
$729$	−41.9077	−1.55214
$730$	−26.7798	−0.991164
$731$	3.29752	0.121963
$732$	41.3077	1.52678
$733$	30.2623	1.11776	0.558882	−	0.829247i	$-0.311230\pi$
$733$	30.2623	1.11776	0.558882	+	0.829247i	$0.311230\pi$
$734$	−29.2518	−1.07970
$735$	20.2600	0.747302
$736$	3.18964	0.117572
$737$	−0.904793	−0.0333285
$738$	−58.5992	−2.15707
$739$	53.0471	1.95137	0.975684	−	0.219182i	$-0.0703389\pi$
$739$	53.0471	1.95137	0.975684	+	0.219182i	$0.0703389\pi$
$740$	0.649079	0.0238606
$741$	−7.78895	−0.286134
$742$	−0.911633	−0.0334671
$743$	−44.0810	−1.61717	−0.808587	−	0.588376i	$-0.799767\pi$
$743$	−44.0810	−1.61717	−0.808587	+	0.588376i	$0.799767\pi$
$744$	−27.7752	−1.01829
$745$	42.2525	1.54801
$746$	−4.54286	−0.166326
$747$	−56.1650	−2.05497
$748$	−2.03110	−0.0742643
$749$	37.1868	1.35878
$750$	30.8650	1.12703
$751$	43.9612	1.60417	0.802083	−	0.597212i	$-0.203725\pi$
$751$	43.9612	1.60417	0.802083	+	0.597212i	$0.203725\pi$
$752$	−4.25377	−0.155119
$753$	9.66985	0.352389
$754$	5.67079	0.206518
$755$	−17.3948	−0.633061
$756$	−19.4723	−0.708202
$757$	−36.6385	−1.33165	−0.665825	−	0.746108i	$-0.731920\pi$
$757$	−36.6385	−1.33165	−0.665825	+	0.746108i	$0.731920\pi$
$758$	−12.3231	−0.447594
$759$	3.76906	0.136808
$760$	−9.35017	−0.339166
$761$	−26.3628	−0.955651	−0.477825	−	0.878455i	$-0.658575\pi$
$761$	−26.3628	−0.955651	−0.477825	+	0.878455i	$0.658575\pi$
$762$	−8.37871	−0.303528
$763$	−49.2987	−1.78473
$764$	8.91160	0.322410
$765$	58.1881	2.10380
$766$	31.2445	1.12891
$767$	−1.69200	−0.0610945
$768$	−2.85455	−0.103005
$769$	29.7379	1.07237	0.536187	−	0.844099i	$-0.319864\pi$
$769$	29.7379	1.07237	0.536187	+	0.844099i	$0.319864\pi$
$770$	3.02756	0.109106
$771$	−42.1413	−1.51768
$772$	−3.52444	−0.126847
$773$	18.2124	0.655054	0.327527	−	0.944842i	$-0.393785\pi$
$773$	18.2124	0.655054	0.327527	+	0.944842i	$0.393785\pi$
$774$	3.46008	0.124370
$775$	−2.97694	−0.106935
$776$	−11.4406	−0.410692
$777$	2.55393	0.0916219
$778$	4.14582	0.148635
$779$	−46.2013	−1.65533
$780$	−4.42000	−0.158261
$781$	0.656205	0.0234809
$782$	−15.6501	−0.559647
$783$	−51.7370	−1.84893
$784$	3.08121	0.110043
$785$	42.6364	1.52176
$786$	6.72883	0.240009
$787$	39.2856	1.40038	0.700190	−	0.713956i	$-0.253099\pi$
$787$	39.2856	1.40038	0.700190	+	0.713956i	$0.253099\pi$
$788$	−20.2260	−0.720520
$789$	34.4685	1.22711
$790$	31.9533	1.13685
$791$	7.91632	0.281472
$792$	−2.13123	−0.0757300
$793$	9.72741	0.345430
$794$	17.7326	0.629308
$795$	1.88792	0.0669575
$796$	−23.1259	−0.819676
$797$	−30.1692	−1.06865	−0.534324	−	0.845280i	$-0.679434\pi$
$797$	−30.1692	−1.06865	−0.534324	+	0.845280i	$0.679434\pi$
$798$	−36.7902	−1.30236
$799$	20.8714	0.738375
$800$	−0.305950	−0.0108170
$801$	40.3427	1.42544
$802$	−33.8246	−1.19439
$803$	−4.81260	−0.169833
$804$	6.23925	0.220041
$805$	23.3281	0.822207
$806$	−6.54070	−0.230386
$807$	5.95731	0.209707
$808$	−16.2393	−0.571298
$809$	45.9915	1.61698	0.808488	−	0.588512i	$-0.200286\pi$
$809$	45.9915	1.61698	0.808488	+	0.588512i	$0.200286\pi$
$810$	4.74778	0.166820
$811$	−11.6077	−0.407601	−0.203801	−	0.979012i	$-0.565329\pi$
$811$	−11.6077	−0.407601	−0.203801	+	0.979012i	$0.565329\pi$
$812$	26.7853	0.939980
$813$	41.1099	1.44179
$814$	0.116646	0.00408845
$815$	3.37740	0.118305
$816$	14.0060	0.490308
$817$	2.72803	0.0954415
$818$	−19.7549	−0.690714
$819$	−10.9884	−0.383967
$820$	−26.2179	−0.915568
$821$	−26.6636	−0.930568	−0.465284	−	0.885162i	$-0.654048\pi$
$821$	−26.6636	−0.930568	−0.465284	+	0.885162i	$0.654048\pi$
$822$	−3.87309	−0.135090
$823$	26.7455	0.932290	0.466145	−	0.884708i	$-0.345643\pi$
$823$	26.7455	0.932290	0.466145	+	0.884708i	$0.345643\pi$
$824$	−9.71683	−0.338502
$825$	−0.361528	−0.0125868
$826$	−7.99194	−0.278075
$827$	36.1612	1.25745	0.628725	−	0.777628i	$-0.283577\pi$
$827$	36.1612	1.25745	0.628725	+	0.777628i	$0.283577\pi$
$828$	−16.4217	−0.570692
$829$	7.14980	0.248323	0.124161	−	0.992262i	$-0.460376\pi$
$829$	7.14980	0.248323	0.124161	+	0.992262i	$0.460376\pi$
$830$	−25.1288	−0.872233
$831$	−7.03935	−0.244192
$832$	−0.672208	−0.0233046
$833$	−15.1181	−0.523812
$834$	−8.08764	−0.280052
$835$	44.2869	1.53261
$836$	−1.68032	−0.0581151
$837$	59.6736	2.06262
$838$	−16.1326	−0.557293
$839$	−15.9902	−0.552042	−0.276021	−	0.961152i	$-0.589016\pi$
$839$	−15.9902	−0.552042	−0.276021	+	0.961152i	$0.589016\pi$
$840$	−20.8773	−0.720337
$841$	42.1673	1.45404
$842$	11.7260	0.404104
$843$	−65.8292	−2.26728
$844$	0.849949	0.0292565
$845$	28.9042	0.994334
$846$	21.9003	0.752948
$847$	−34.3819	−1.18138
$848$	0.287120	0.00985974
$849$	83.9340	2.88061
$850$	1.50116	0.0514893
$851$	0.898788	0.0308101
$852$	−4.52504	−0.155025
$853$	−6.15311	−0.210679	−0.105339	−	0.994436i	$-0.533593\pi$
$853$	−6.15311	−0.210679	−0.105339	+	0.994436i	$0.533593\pi$
$854$	45.9462	1.57225
$855$	48.1388	1.64631
$856$	−11.7121	−0.400310
$857$	51.2830	1.75180	0.875898	−	0.482497i	$-0.160270\pi$
$857$	51.2830	1.75180	0.875898	+	0.482497i	$0.160270\pi$
$858$	−0.794319	−0.0271176
$859$	−54.4323	−1.85721	−0.928604	−	0.371073i	$-0.878990\pi$
$859$	−54.4323	−1.85721	−0.928604	+	0.371073i	$0.878990\pi$
$860$	1.54808	0.0527889
$861$	−103.160	−3.51567
$862$	−25.3571	−0.863667
$863$	17.0004	0.578700	0.289350	−	0.957223i	$-0.406561\pi$
$863$	17.0004	0.578700	0.289350	+	0.957223i	$0.406561\pi$
$864$	6.13284	0.208643
$865$	28.5418	0.970449
$866$	6.05304	0.205691
$867$	−20.1938	−0.685819
$868$	−30.8942	−1.04862
$869$	5.74234	0.194795
$870$	−55.4701	−1.88061
$871$	1.46926	0.0497840
$872$	15.5267	0.525801
$873$	58.9011	1.99350
$874$	−12.9473	−0.437949
$875$	34.3309	1.16060
$876$	33.1866	1.12127
$877$	39.4717	1.33286	0.666432	−	0.745566i	$-0.267821\pi$
$877$	39.4717	1.33286	0.666432	+	0.745566i	$0.267821\pi$
$878$	−8.04523	−0.271513
$879$	−11.1740	−0.376888
$880$	−0.953533	−0.0321436
$881$	−55.4807	−1.86919	−0.934596	−	0.355711i	$-0.884239\pi$
$881$	−55.4807	−1.86919	−0.934596	+	0.355711i	$0.884239\pi$
$882$	−15.8634	−0.534149
$883$	37.4063	1.25882	0.629411	−	0.777072i	$-0.283296\pi$
$883$	37.4063	1.25882	0.629411	+	0.777072i	$0.283296\pi$
$884$	3.29822	0.110931
$885$	16.5506	0.556344
$886$	22.1143	0.742946
$887$	−40.4595	−1.35850	−0.679248	−	0.733909i	$-0.737694\pi$
$887$	−40.4595	−1.35850	−0.679248	+	0.733909i	$0.737694\pi$
$888$	−0.804366	−0.0269927
$889$	−9.31957	−0.312568
$890$	18.0497	0.605028
$891$	0.853225	0.0285841
$892$	25.9787	0.869832
$893$	17.2668	0.577812
$894$	−52.3610	−1.75121
$895$	45.9524	1.53602
$896$	−3.17509	−0.106072
$897$	−6.12043	−0.204355
$898$	−33.2077	−1.10815
$899$	−82.0844	−2.73767
$900$	1.57517	0.0525055
$901$	−1.40877	−0.0469329
$902$	−4.71162	−0.156880
$903$	6.09122	0.202703
$904$	−2.49326	−0.0829245
$905$	1.83223	0.0609054
$906$	21.5563	0.716162
$907$	−27.2665	−0.905371	−0.452685	−	0.891670i	$-0.649534\pi$
$907$	−27.2665	−0.905371	−0.452685	+	0.891670i	$0.649534\pi$
$908$	−22.9333	−0.761068
$909$	83.6073	2.77308
$910$	−4.91633	−0.162975
$911$	56.1186	1.85929	0.929646	−	0.368455i	$-0.120113\pi$
$911$	56.1186	1.85929	0.929646	+	0.368455i	$0.120113\pi$
$912$	11.5871	0.383688
$913$	−4.51590	−0.149454
$914$	−25.2302	−0.834541
$915$	−95.1508	−3.14559
$916$	22.9824	0.759359
$917$	7.48443	0.247158
$918$	−30.0911	−0.993154
$919$	−36.9629	−1.21929	−0.609647	−	0.792673i	$-0.708689\pi$
$919$	−36.9629	−1.21929	−0.609647	+	0.792673i	$0.708689\pi$
$920$	−7.34722	−0.242231
$921$	89.9560	2.96415
$922$	33.2214	1.09409
$923$	−1.06559	−0.0350742
$924$	−3.75187	−0.123428
$925$	−0.0862117	−0.00283462
$926$	−12.0866	−0.397189
$927$	50.0265	1.64309
$928$	−8.43607	−0.276928
$929$	−31.4682	−1.03244	−0.516218	−	0.856457i	$-0.672661\pi$
$929$	−31.4682	−1.03244	−0.516218	+	0.856457i	$0.672661\pi$
$930$	63.9793	2.09796
$931$	−12.5072	−0.409906
$932$	28.0038	0.917296
$933$	−85.8942	−2.81205
$934$	−10.2671	−0.335949
$935$	4.67856	0.153005
$936$	3.46082	0.113121
$937$	20.8829	0.682214	0.341107	−	0.940024i	$-0.389198\pi$
$937$	20.8829	0.682214	0.341107	+	0.940024i	$0.389198\pi$
$938$	6.93987	0.226595
$939$	−73.5981	−2.40178
$940$	9.79841	0.319589
$941$	−25.7251	−0.838616	−0.419308	−	0.907844i	$-0.637727\pi$
$941$	−25.7251	−0.838616	−0.419308	+	0.907844i	$0.637727\pi$
$942$	−52.8368	−1.72152
$943$	−36.3042	−1.18223
$944$	2.51707	0.0819238
$945$	44.8538	1.45909
$946$	0.278205	0.00904522
$947$	21.1626	0.687692	0.343846	−	0.939026i	$-0.388270\pi$
$947$	21.1626	0.687692	0.343846	+	0.939026i	$0.388270\pi$
$948$	−39.5979	−1.28608
$949$	7.81500	0.253686
$950$	1.24190	0.0402927
$951$	22.6297	0.733818
$952$	15.5788	0.504910
$953$	−31.2721	−1.01300	−0.506502	−	0.862239i	$-0.669062\pi$
$953$	−31.2721	−1.01300	−0.506502	+	0.862239i	$0.669062\pi$
$954$	−1.47822	−0.0478592
$955$	−20.5276	−0.664256
$956$	21.5230	0.696105
$957$	−9.96854	−0.322237
$958$	14.1229	0.456291
$959$	−4.30801	−0.139113
$960$	6.57535	0.212219
$961$	63.6762	2.05407
$962$	−0.189417	−0.00610706
$963$	60.2988	1.94310
$964$	−20.6101	−0.663806
$965$	8.11842	0.261341
$966$	−28.9091	−0.930136
$967$	37.7483	1.21390	0.606952	−	0.794738i	$-0.292392\pi$
$967$	37.7483	1.21390	0.606952	+	0.794738i	$0.292392\pi$
$968$	10.8286	0.348046
$969$	−56.8528	−1.82638
$970$	26.3529	0.846142
$971$	−9.61896	−0.308687	−0.154344	−	0.988017i	$-0.549326\pi$
$971$	−9.61896	−0.308687	−0.154344	+	0.988017i	$0.549326\pi$
$972$	12.5149	0.401415
$973$	−8.99582	−0.288393
$974$	−41.6404	−1.33425
$975$	0.587072	0.0188013
$976$	−14.4708	−0.463200
$977$	−36.0571	−1.15357	−0.576785	−	0.816896i	$-0.695693\pi$
$977$	−36.0571	−1.15357	−0.576785	+	0.816896i	$0.695693\pi$
$978$	−4.18541	−0.133835
$979$	3.24372	0.103670
$980$	−7.09745	−0.226720
$981$	−79.9384	−2.55224
$982$	−22.6235	−0.721945
$983$	14.6200	0.466304	0.233152	−	0.972440i	$-0.425096\pi$
$983$	14.6200	0.466304	0.233152	+	0.972440i	$0.425096\pi$
$984$	32.4903	1.03575
$985$	46.5898	1.48447
$986$	41.3920	1.31819
$987$	38.5538	1.22718
$988$	2.72861	0.0868087
$989$	2.14364	0.0681638
$990$	4.90921	0.156025
$991$	−20.9053	−0.664078	−0.332039	−	0.943266i	$-0.607736\pi$
$991$	−20.9053	−0.664078	−0.332039	+	0.943266i	$0.607736\pi$
$992$	9.73017	0.308933
$993$	−59.2723	−1.88095
$994$	−5.03317	−0.159642
$995$	53.2697	1.68876
$996$	31.1406	0.986728
$997$	12.2711	0.388629	0.194314	−	0.980939i	$-0.437752\pi$
$997$	12.2711	0.388629	0.194314	+	0.980939i	$0.437752\pi$
$998$	6.46447	0.204629
$999$	1.72813	0.0546758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.e.1.12	✓	91

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.e.1.12	✓	91	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.85455 q^{3} +1.00000 q^{4} -2.30346 q^{5} +2.85455 q^{6} +3.17509 q^{7} -1.00000 q^{8} +5.14844 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.85455 q^{3} +1.00000 q^{4} -2.30346 q^{5} +2.85455 q^{6} +3.17509 q^{7} -1.00000 q^{8} +5.14844 q^{9} +2.30346 q^{10} +0.413956 q^{11} -2.85455 q^{12} -0.672208 q^{13} -3.17509 q^{14} +6.57535 q^{15} +1.00000 q^{16} -4.90655 q^{17} -5.14844 q^{18} -4.05918 q^{19} -2.30346 q^{20} -9.06345 q^{21} -0.413956 q^{22} -3.18964 q^{23} +2.85455 q^{24} +0.305950 q^{25} +0.672208 q^{26} -6.13284 q^{27} +3.17509 q^{28} +8.43607 q^{29} -6.57535 q^{30} -9.73017 q^{31} -1.00000 q^{32} -1.18166 q^{33} +4.90655 q^{34} -7.31371 q^{35} +5.14844 q^{36} -0.281784 q^{37} +4.05918 q^{38} +1.91885 q^{39} +2.30346 q^{40} +11.3819 q^{41} +9.06345 q^{42} -0.672064 q^{43} +0.413956 q^{44} -11.8593 q^{45} +3.18964 q^{46} -4.25377 q^{47} -2.85455 q^{48} +3.08121 q^{49} -0.305950 q^{50} +14.0060 q^{51} -0.672208 q^{52} +0.287120 q^{53} +6.13284 q^{54} -0.953533 q^{55} -3.17509 q^{56} +11.5871 q^{57} -8.43607 q^{58} +2.51707 q^{59} +6.57535 q^{60} -14.4708 q^{61} +9.73017 q^{62} +16.3468 q^{63} +1.00000 q^{64} +1.54841 q^{65} +1.18166 q^{66} -2.18572 q^{67} -4.90655 q^{68} +9.10497 q^{69} +7.31371 q^{70} +1.58520 q^{71} -5.14844 q^{72} -11.6259 q^{73} +0.281784 q^{74} -0.873349 q^{75} -4.05918 q^{76} +1.31435 q^{77} -1.91885 q^{78} +13.8719 q^{79} -2.30346 q^{80} +2.06115 q^{81} -11.3819 q^{82} -10.9091 q^{83} -9.06345 q^{84} +11.3021 q^{85} +0.672064 q^{86} -24.0812 q^{87} -0.413956 q^{88} +7.83590 q^{89} +11.8593 q^{90} -2.13432 q^{91} -3.18964 q^{92} +27.7752 q^{93} +4.25377 q^{94} +9.35017 q^{95} +2.85455 q^{96} +11.4406 q^{97} -3.08121 q^{98} +2.13123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * q^99

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