LMFDB - Embedded newform 8014.2.a.e.1.1

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			1.1
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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.44800 q^{3} +1.00000 q^{4} -2.43856 q^{5} +3.44800 q^{6} +4.30446 q^{7} -1.00000 q^{8} +8.88870 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.44800 q^{3} +1.00000 q^{4} -2.43856 q^{5} +3.44800 q^{6} +4.30446 q^{7} -1.00000 q^{8} +8.88870 q^{9} +2.43856 q^{10} -0.100094 q^{11} -3.44800 q^{12} -0.689835 q^{13} -4.30446 q^{14} +8.40815 q^{15} +1.00000 q^{16} +7.90962 q^{17} -8.88870 q^{18} -7.30178 q^{19} -2.43856 q^{20} -14.8418 q^{21} +0.100094 q^{22} +4.22271 q^{23} +3.44800 q^{24} +0.946569 q^{25} +0.689835 q^{26} -20.3042 q^{27} +4.30446 q^{28} +2.33912 q^{29} -8.40815 q^{30} +4.26837 q^{31} -1.00000 q^{32} +0.345124 q^{33} -7.90962 q^{34} -10.4967 q^{35} +8.88870 q^{36} +10.8993 q^{37} +7.30178 q^{38} +2.37855 q^{39} +2.43856 q^{40} +0.474474 q^{41} +14.8418 q^{42} +8.50378 q^{43} -0.100094 q^{44} -21.6756 q^{45} -4.22271 q^{46} +7.41936 q^{47} -3.44800 q^{48} +11.5284 q^{49} -0.946569 q^{50} -27.2724 q^{51} -0.689835 q^{52} +4.26923 q^{53} +20.3042 q^{54} +0.244085 q^{55} -4.30446 q^{56} +25.1765 q^{57} -2.33912 q^{58} +2.46114 q^{59} +8.40815 q^{60} +8.47839 q^{61} -4.26837 q^{62} +38.2610 q^{63} +1.00000 q^{64} +1.68220 q^{65} -0.345124 q^{66} -7.84511 q^{67} +7.90962 q^{68} -14.5599 q^{69} +10.4967 q^{70} +7.65727 q^{71} -8.88870 q^{72} +7.79692 q^{73} -10.8993 q^{74} -3.26377 q^{75} -7.30178 q^{76} -0.430851 q^{77} -2.37855 q^{78} -3.65290 q^{79} -2.43856 q^{80} +43.3428 q^{81} -0.474474 q^{82} +16.8768 q^{83} -14.8418 q^{84} -19.2881 q^{85} -8.50378 q^{86} -8.06528 q^{87} +0.100094 q^{88} +12.4095 q^{89} +21.6756 q^{90} -2.96937 q^{91} +4.22271 q^{92} -14.7173 q^{93} -7.41936 q^{94} +17.8058 q^{95} +3.44800 q^{96} -15.9280 q^{97} -11.5284 q^{98} -0.889706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.44800	−1.99070	−0.995352	−	0.0963084i	$-0.969296\pi$
$3$	−3.44800	−1.99070	−0.995352	+	0.0963084i	$0.969296\pi$
$4$	1.00000	0.500000
$5$	−2.43856	−1.09056	−0.545278	−	0.838255i	$-0.683576\pi$
$5$	−2.43856	−1.09056	−0.545278	+	0.838255i	$0.683576\pi$
$6$	3.44800	1.40764
$7$	4.30446	1.62693	0.813467	−	0.581612i	$-0.197578\pi$
$7$	4.30446	1.62693	0.813467	+	0.581612i	$0.197578\pi$
$8$	−1.00000	−0.353553
$9$	8.88870	2.96290
$10$	2.43856	0.771140
$11$	−0.100094	−0.0301795	−0.0150898	−	0.999886i	$-0.504803\pi$
$11$	−0.100094	−0.0301795	−0.0150898	+	0.999886i	$0.504803\pi$
$12$	−3.44800	−0.995352
$13$	−0.689835	−0.191326	−0.0956629	−	0.995414i	$-0.530497\pi$
$13$	−0.689835	−0.191326	−0.0956629	+	0.995414i	$0.530497\pi$
$14$	−4.30446	−1.15042
$15$	8.40815	2.17097
$16$	1.00000	0.250000
$17$	7.90962	1.91836	0.959182	−	0.282788i	$-0.0912594\pi$
$17$	7.90962	1.91836	0.959182	+	0.282788i	$0.0912594\pi$
$18$	−8.88870	−2.09509
$19$	−7.30178	−1.67514	−0.837572	−	0.546327i	$-0.816026\pi$
$19$	−7.30178	−1.67514	−0.837572	+	0.546327i	$0.816026\pi$
$20$	−2.43856	−0.545278
$21$	−14.8418	−3.23874
$22$	0.100094	0.0213401
$23$	4.22271	0.880496	0.440248	−	0.897876i	$-0.354891\pi$
$23$	4.22271	0.880496	0.440248	+	0.897876i	$0.354891\pi$
$24$	3.44800	0.703820
$25$	0.946569	0.189314
$26$	0.689835	0.135288
$27$	−20.3042	−3.90755
$28$	4.30446	0.813467
$29$	2.33912	0.434364	0.217182	−	0.976131i	$-0.430314\pi$
$29$	2.33912	0.434364	0.217182	+	0.976131i	$0.430314\pi$
$30$	−8.40815	−1.53511
$31$	4.26837	0.766622	0.383311	−	0.923619i	$-0.374784\pi$
$31$	4.26837	0.766622	0.383311	+	0.923619i	$0.374784\pi$
$32$	−1.00000	−0.176777
$33$	0.345124	0.0600784
$34$	−7.90962	−1.35649
$35$	−10.4967	−1.77426
$36$	8.88870	1.48145
$37$	10.8993	1.79183	0.895914	−	0.444228i	$-0.146522\pi$
$37$	10.8993	1.79183	0.895914	+	0.444228i	$0.146522\pi$
$38$	7.30178	1.18451
$39$	2.37855	0.380873
$40$	2.43856	0.385570
$41$	0.474474	0.0741003	0.0370502	−	0.999313i	$-0.488204\pi$
$41$	0.474474	0.0741003	0.0370502	+	0.999313i	$0.488204\pi$
$42$	14.8418	2.29014
$43$	8.50378	1.29681	0.648407	−	0.761293i	$-0.275435\pi$
$43$	8.50378	1.29681	0.648407	+	0.761293i	$0.275435\pi$
$44$	−0.100094	−0.0150898
$45$	−21.6756	−3.23121
$46$	−4.22271	−0.622605
$47$	7.41936	1.08222	0.541112	−	0.840950i	$-0.318003\pi$
$47$	7.41936	1.08222	0.541112	+	0.840950i	$0.318003\pi$
$48$	−3.44800	−0.497676
$49$	11.5284	1.64691
$50$	−0.946569	−0.133865
$51$	−27.2724	−3.81889
$52$	−0.689835	−0.0956629
$53$	4.26923	0.586424	0.293212	−	0.956047i	$-0.405276\pi$
$53$	4.26923	0.586424	0.293212	+	0.956047i	$0.405276\pi$
$54$	20.3042	2.76305
$55$	0.244085	0.0329125
$56$	−4.30446	−0.575208
$57$	25.1765	3.33471
$58$	−2.33912	−0.307141
$59$	2.46114	0.320413	0.160206	−	0.987084i	$-0.448784\pi$
$59$	2.46114	0.320413	0.160206	+	0.987084i	$0.448784\pi$
$60$	8.40815	1.08549
$61$	8.47839	1.08555	0.542773	−	0.839879i	$-0.317374\pi$
$61$	8.47839	1.08555	0.542773	+	0.839879i	$0.317374\pi$
$62$	−4.26837	−0.542083
$63$	38.2610	4.82044
$64$	1.00000	0.125000
$65$	1.68220	0.208652
$66$	−0.345124	−0.0424819
$67$	−7.84511	−0.958433	−0.479217	−	0.877697i	$-0.659079\pi$
$67$	−7.84511	−0.958433	−0.479217	+	0.877697i	$0.659079\pi$
$68$	7.90962	0.959182
$69$	−14.5599	−1.75281
$70$	10.4967	1.25459
$71$	7.65727	0.908751	0.454375	−	0.890810i	$-0.349862\pi$
$71$	7.65727	0.908751	0.454375	+	0.890810i	$0.349862\pi$
$72$	−8.88870	−1.04754
$73$	7.79692	0.912561	0.456280	−	0.889836i	$-0.349181\pi$
$73$	7.79692	0.912561	0.456280	+	0.889836i	$0.349181\pi$
$74$	−10.8993	−1.26701
$75$	−3.26377	−0.376868
$76$	−7.30178	−0.837572
$77$	−0.430851	−0.0491001
$78$	−2.37855	−0.269318
$79$	−3.65290	−0.410983	−0.205492	−	0.978659i	$-0.565879\pi$
$79$	−3.65290	−0.410983	−0.205492	+	0.978659i	$0.565879\pi$
$80$	−2.43856	−0.272639
$81$	43.3428	4.81587
$82$	−0.474474	−0.0523968
$83$	16.8768	1.85247	0.926233	−	0.376952i	$-0.123028\pi$
$83$	16.8768	1.85247	0.926233	+	0.376952i	$0.123028\pi$
$84$	−14.8418	−1.61937
$85$	−19.2881	−2.09209
$86$	−8.50378	−0.916987
$87$	−8.06528	−0.864689
$88$	0.100094	0.0106701
$89$	12.4095	1.31540	0.657702	−	0.753278i	$-0.271529\pi$
$89$	12.4095	1.31540	0.657702	+	0.753278i	$0.271529\pi$
$90$	21.6756	2.28481
$91$	−2.96937	−0.311274
$92$	4.22271	0.440248
$93$	−14.7173	−1.52612
$94$	−7.41936	−0.765248
$95$	17.8058	1.82684
$96$	3.44800	0.351910
$97$	−15.9280	−1.61724	−0.808620	−	0.588332i	$-0.799785\pi$
$97$	−15.9280	−1.61724	−0.808620	+	0.588332i	$0.799785\pi$
$98$	−11.5284	−1.16454
$99$	−0.889706	−0.0894188
$100$	0.946569	0.0946569
$101$	0.489886	0.0487455	0.0243727	−	0.999703i	$-0.492241\pi$
$101$	0.489886	0.0487455	0.0243727	+	0.999703i	$0.492241\pi$
$102$	27.2724	2.70037
$103$	−8.31852	−0.819648	−0.409824	−	0.912165i	$-0.634410\pi$
$103$	−8.31852	−0.819648	−0.409824	+	0.912165i	$0.634410\pi$
$104$	0.689835	0.0676439
$105$	36.1925	3.53203
$106$	−4.26923	−0.414664
$107$	−6.02589	−0.582544	−0.291272	−	0.956640i	$-0.594079\pi$
$107$	−6.02589	−0.582544	−0.291272	+	0.956640i	$0.594079\pi$
$108$	−20.3042	−1.95377
$109$	6.99709	0.670199	0.335100	−	0.942183i	$-0.391230\pi$
$109$	6.99709	0.670199	0.335100	+	0.942183i	$0.391230\pi$
$110$	−0.244085	−0.0232726
$111$	−37.5806	−3.56700
$112$	4.30446	0.406733
$113$	2.14753	0.202022	0.101011	−	0.994885i	$-0.467792\pi$
$113$	2.14753	0.202022	0.101011	+	0.994885i	$0.467792\pi$
$114$	−25.1765	−2.35800
$115$	−10.2973	−0.960231
$116$	2.33912	0.217182
$117$	−6.13173	−0.566879
$118$	−2.46114	−0.226566
$119$	34.0466	3.12105
$120$	−8.40815	−0.767555
$121$	−10.9900	−0.999089
$122$	−8.47839	−0.767597
$123$	−1.63598	−0.147512
$124$	4.26837	0.383311
$125$	9.88453	0.884099
$126$	−38.2610	−3.40856
$127$	−7.47892	−0.663646	−0.331823	−	0.943342i	$-0.607664\pi$
$127$	−7.47892	−0.663646	−0.331823	+	0.943342i	$0.607664\pi$
$128$	−1.00000	−0.0883883
$129$	−29.3210	−2.58157
$130$	−1.68220	−0.147539
$131$	−7.41263	−0.647645	−0.323822	−	0.946118i	$-0.604968\pi$
$131$	−7.41263	−0.647645	−0.323822	+	0.946118i	$0.604968\pi$
$132$	0.345124	0.0300392
$133$	−31.4302	−2.72535
$134$	7.84511	0.677715
$135$	49.5130	4.26140
$136$	−7.90962	−0.678244
$137$	−16.0645	−1.37248	−0.686242	−	0.727373i	$-0.740741\pi$
$137$	−16.0645	−1.37248	−0.686242	+	0.727373i	$0.740741\pi$
$138$	14.5599	1.23942
$139$	2.02937	0.172129	0.0860643	−	0.996290i	$-0.472571\pi$
$139$	2.02937	0.172129	0.0860643	+	0.996290i	$0.472571\pi$
$140$	−10.4967	−0.887131
$141$	−25.5819	−2.15439
$142$	−7.65727	−0.642584
$143$	0.0690484	0.00577412
$144$	8.88870	0.740725
$145$	−5.70408	−0.473698
$146$	−7.79692	−0.645278
$147$	−39.7499	−3.27851
$148$	10.8993	0.895914
$149$	13.6870	1.12128	0.560641	−	0.828059i	$-0.310555\pi$
$149$	13.6870	1.12128	0.560641	+	0.828059i	$0.310555\pi$
$150$	3.26377	0.266486
$151$	−5.25959	−0.428019	−0.214009	−	0.976832i	$-0.568652\pi$
$151$	−5.25959	−0.428019	−0.214009	+	0.976832i	$0.568652\pi$
$152$	7.30178	0.592253
$153$	70.3062	5.68392
$154$	0.430851	0.0347190
$155$	−10.4087	−0.836044
$156$	2.37855	0.190436
$157$	17.0465	1.36046	0.680230	−	0.732999i	$-0.261880\pi$
$157$	17.0465	1.36046	0.680230	+	0.732999i	$0.261880\pi$
$158$	3.65290	0.290609
$159$	−14.7203	−1.16740
$160$	2.43856	0.192785
$161$	18.1765	1.43251
$162$	−43.3428	−3.40533
$163$	17.4777	1.36896	0.684478	−	0.729034i	$-0.260030\pi$
$163$	17.4777	1.36896	0.684478	+	0.729034i	$0.260030\pi$
$164$	0.474474	0.0370502
$165$	−0.841606	−0.0655190
$166$	−16.8768	−1.30989
$167$	−10.8328	−0.838269	−0.419134	−	0.907924i	$-0.637666\pi$
$167$	−10.8328	−0.838269	−0.419134	+	0.907924i	$0.637666\pi$
$168$	14.8418	1.14507
$169$	−12.5241	−0.963394
$170$	19.2881	1.47933
$171$	−64.9033	−4.96328
$172$	8.50378	0.648407
$173$	−10.8157	−0.822300	−0.411150	−	0.911568i	$-0.634873\pi$
$173$	−10.8157	−0.822300	−0.411150	+	0.911568i	$0.634873\pi$
$174$	8.06528	0.611428
$175$	4.07447	0.308001
$176$	−0.100094	−0.00754488
$177$	−8.48600	−0.637847
$178$	−12.4095	−0.930131
$179$	18.2001	1.36034	0.680170	−	0.733054i	$-0.261906\pi$
$179$	18.2001	1.36034	0.680170	+	0.733054i	$0.261906\pi$
$180$	−21.6756	−1.61560
$181$	10.8754	0.808362	0.404181	−	0.914679i	$-0.367557\pi$
$181$	10.8754	0.808362	0.404181	+	0.914679i	$0.367557\pi$
$182$	2.96937	0.220104
$183$	−29.2335	−2.16100
$184$	−4.22271	−0.311302
$185$	−26.5785	−1.95409
$186$	14.7173	1.07913
$187$	−0.791706	−0.0578953
$188$	7.41936	0.541112
$189$	−87.3987	−6.35732
$190$	−17.8058	−1.29177
$191$	−3.54455	−0.256475	−0.128237	−	0.991743i	$-0.540932\pi$
$191$	−3.54455	−0.256475	−0.128237	+	0.991743i	$0.540932\pi$
$192$	−3.44800	−0.248838
$193$	−2.16971	−0.156179	−0.0780897	−	0.996946i	$-0.524882\pi$
$193$	−2.16971	−0.156179	−0.0780897	+	0.996946i	$0.524882\pi$
$194$	15.9280	1.14356
$195$	−5.80024	−0.415363
$196$	11.5284	0.823456
$197$	−3.88832	−0.277032	−0.138516	−	0.990360i	$-0.544233\pi$
$197$	−3.88832	−0.277032	−0.138516	+	0.990360i	$0.544233\pi$
$198$	0.889706	0.0632287
$199$	−16.6556	−1.18069	−0.590344	−	0.807152i	$-0.701008\pi$
$199$	−16.6556	−1.18069	−0.590344	+	0.807152i	$0.701008\pi$
$200$	−0.946569	−0.0669325
$201$	27.0499	1.90796
$202$	−0.489886	−0.0344682
$203$	10.0687	0.706681
$204$	−27.2724	−1.90945
$205$	−1.15703	−0.0808106
$206$	8.31852	0.579578
$207$	37.5344	2.60882
$208$	−0.689835	−0.0478315
$209$	0.730866	0.0505550
$210$	−36.1925	−2.49752
$211$	8.24008	0.567270	0.283635	−	0.958932i	$-0.408460\pi$
$211$	8.24008	0.567270	0.283635	+	0.958932i	$0.408460\pi$
$212$	4.26923	0.293212
$213$	−26.4023	−1.80905
$214$	6.02589	0.411921
$215$	−20.7370	−1.41425
$216$	20.3042	1.38153
$217$	18.3730	1.24724
$218$	−6.99709	−0.473902
$219$	−26.8838	−1.81664
$220$	0.244085	0.0164562
$221$	−5.45633	−0.367033
$222$	37.5806	2.52225
$223$	−10.9860	−0.735674	−0.367837	−	0.929890i	$-0.619902\pi$
$223$	−10.9860	−0.735674	−0.367837	+	0.929890i	$0.619902\pi$
$224$	−4.30446	−0.287604
$225$	8.41376	0.560918
$226$	−2.14753	−0.142851
$227$	20.2592	1.34465	0.672324	−	0.740257i	$-0.265296\pi$
$227$	20.2592	1.34465	0.672324	+	0.740257i	$0.265296\pi$
$228$	25.1765	1.66736
$229$	−2.09798	−0.138639	−0.0693193	−	0.997595i	$-0.522083\pi$
$229$	−2.09798	−0.138639	−0.0693193	+	0.997595i	$0.522083\pi$
$230$	10.2973	0.678986
$231$	1.48557	0.0977436
$232$	−2.33912	−0.153571
$233$	−3.58268	−0.234709	−0.117355	−	0.993090i	$-0.537441\pi$
$233$	−3.58268	−0.234709	−0.117355	+	0.993090i	$0.537441\pi$
$234$	6.13173	0.400844
$235$	−18.0925	−1.18023
$236$	2.46114	0.160206
$237$	12.5952	0.818146
$238$	−34.0466	−2.20692
$239$	15.2190	0.984433	0.492217	−	0.870473i	$-0.336187\pi$
$239$	15.2190	0.984433	0.492217	+	0.870473i	$0.336187\pi$
$240$	8.40815	0.542744
$241$	−18.4846	−1.19070	−0.595348	−	0.803468i	$-0.702986\pi$
$241$	−18.4846	−1.19070	−0.595348	+	0.803468i	$0.702986\pi$
$242$	10.9900	0.706463
$243$	−88.5334	−5.67942
$244$	8.47839	0.542773
$245$	−28.1126	−1.79605
$246$	1.63598	0.104307
$247$	5.03703	0.320498
$248$	−4.26837	−0.271042
$249$	−58.1911	−3.68771
$250$	−9.88453	−0.625153
$251$	−26.6029	−1.67916	−0.839580	−	0.543237i	$-0.817199\pi$
$251$	−26.6029	−1.67916	−0.839580	+	0.543237i	$0.817199\pi$
$252$	38.2610	2.41022
$253$	−0.422668	−0.0265729
$254$	7.47892	0.469269
$255$	66.5053	4.16472
$256$	1.00000	0.0625000
$257$	2.47266	0.154240	0.0771201	−	0.997022i	$-0.475428\pi$
$257$	2.47266	0.154240	0.0771201	+	0.997022i	$0.475428\pi$
$258$	29.3210	1.82545
$259$	46.9155	2.91518
$260$	1.68220	0.104326
$261$	20.7917	1.28698
$262$	7.41263	0.457954
$263$	−1.66376	−0.102592	−0.0512959	−	0.998683i	$-0.516335\pi$
$263$	−1.66376	−0.102592	−0.0512959	+	0.998683i	$0.516335\pi$
$264$	−0.345124	−0.0212409
$265$	−10.4108	−0.639528
$266$	31.4302	1.92711
$267$	−42.7879	−2.61858
$268$	−7.84511	−0.479217
$269$	−7.09445	−0.432556	−0.216278	−	0.976332i	$-0.569392\pi$
$269$	−7.09445	−0.432556	−0.216278	+	0.976332i	$0.569392\pi$
$270$	−49.5130	−3.01327
$271$	13.6818	0.831107	0.415554	−	0.909569i	$-0.363588\pi$
$271$	13.6818	0.831107	0.415554	+	0.909569i	$0.363588\pi$
$272$	7.90962	0.479591
$273$	10.2384	0.619655
$274$	16.0645	0.970492
$275$	−0.0947460	−0.00571340
$276$	−14.5599	−0.876403
$277$	−13.1517	−0.790210	−0.395105	−	0.918636i	$-0.629292\pi$
$277$	−13.1517	−0.790210	−0.395105	+	0.918636i	$0.629292\pi$
$278$	−2.02937	−0.121713
$279$	37.9402	2.27142
$280$	10.4967	0.627297
$281$	15.7644	0.940428	0.470214	−	0.882552i	$-0.344177\pi$
$281$	15.7644	0.940428	0.470214	+	0.882552i	$0.344177\pi$
$282$	25.5819	1.52338
$283$	−20.8460	−1.23916	−0.619582	−	0.784932i	$-0.712698\pi$
$283$	−20.8460	−1.23916	−0.619582	+	0.784932i	$0.712698\pi$
$284$	7.65727	0.454375
$285$	−61.3945	−3.63670
$286$	−0.0690484	−0.00408292
$287$	2.04235	0.120556
$288$	−8.88870	−0.523771
$289$	45.5621	2.68012
$290$	5.70408	0.334955
$291$	54.9196	3.21944
$292$	7.79692	0.456280
$293$	14.6082	0.853420	0.426710	−	0.904389i	$-0.359673\pi$
$293$	14.6082	0.853420	0.426710	+	0.904389i	$0.359673\pi$
$294$	39.7499	2.31826
$295$	−6.00163	−0.349428
$296$	−10.8993	−0.633507
$297$	2.03233	0.117928
$298$	−13.6870	−0.792866
$299$	−2.91297	−0.168462
$300$	−3.26377	−0.188434
$301$	36.6042	2.10983
$302$	5.25959	0.302655
$303$	−1.68913	−0.0970377
$304$	−7.30178	−0.418786
$305$	−20.6750	−1.18385
$306$	−70.3062	−4.01914
$307$	−12.9345	−0.738211	−0.369105	−	0.929388i	$-0.620336\pi$
$307$	−12.9345	−0.738211	−0.369105	+	0.929388i	$0.620336\pi$
$308$	−0.430851	−0.0245500
$309$	28.6822	1.63168
$310$	10.4087	0.591173
$311$	−3.58268	−0.203155	−0.101578	−	0.994828i	$-0.532389\pi$
$311$	−3.58268	−0.203155	−0.101578	+	0.994828i	$0.532389\pi$
$312$	−2.37855	−0.134659
$313$	−2.90901	−0.164427	−0.0822136	−	0.996615i	$-0.526199\pi$
$313$	−2.90901	−0.164427	−0.0822136	+	0.996615i	$0.526199\pi$
$314$	−17.0465	−0.961990
$315$	−93.3018	−5.25696
$316$	−3.65290	−0.205492
$317$	−23.8279	−1.33831	−0.669155	−	0.743123i	$-0.733344\pi$
$317$	−23.8279	−1.33831	−0.669155	+	0.743123i	$0.733344\pi$
$318$	14.7203	0.825473
$319$	−0.234132	−0.0131089
$320$	−2.43856	−0.136320
$321$	20.7772	1.15967
$322$	−18.1765	−1.01294
$323$	−57.7543	−3.21354
$324$	43.3428	2.40794
$325$	−0.652976	−0.0362206
$326$	−17.4777	−0.967998
$327$	−24.1259	−1.33417
$328$	−0.474474	−0.0261984
$329$	31.9363	1.76071
$330$	0.841606	0.0463289
$331$	−15.5668	−0.855630	−0.427815	−	0.903866i	$-0.640716\pi$
$331$	−15.5668	−0.855630	−0.427815	+	0.903866i	$0.640716\pi$
$332$	16.8768	0.926233
$333$	96.8802	5.30900
$334$	10.8328	0.592745
$335$	19.1308	1.04523
$336$	−14.8418	−0.809685
$337$	−29.7880	−1.62266	−0.811328	−	0.584591i	$-0.801255\pi$
$337$	−29.7880	−1.62266	−0.811328	+	0.584591i	$0.801255\pi$
$338$	12.5241	0.681223
$339$	−7.40467	−0.402166
$340$	−19.2881	−1.04604
$341$	−0.427239	−0.0231363
$342$	64.9033	3.50957
$343$	19.4922	1.05248
$344$	−8.50378	−0.458493
$345$	35.5052	1.91153
$346$	10.8157	0.581454
$347$	9.54784	0.512555	0.256277	−	0.966603i	$-0.417504\pi$
$347$	9.54784	0.512555	0.256277	+	0.966603i	$0.417504\pi$
$348$	−8.06528	−0.432345
$349$	0.378070	0.0202376	0.0101188	−	0.999949i	$-0.496779\pi$
$349$	0.378070	0.0202376	0.0101188	+	0.999949i	$0.496779\pi$
$350$	−4.07447	−0.217790
$351$	14.0066	0.747615
$352$	0.100094	0.00533503
$353$	−10.7476	−0.572039	−0.286019	−	0.958224i	$-0.592332\pi$
$353$	−10.7476	−0.572039	−0.286019	+	0.958224i	$0.592332\pi$
$354$	8.48600	0.451026
$355$	−18.6727	−0.991044
$356$	12.4095	0.657702
$357$	−117.393	−6.21309
$358$	−18.2001	−0.961906
$359$	27.9325	1.47422	0.737109	−	0.675774i	$-0.236190\pi$
$359$	27.9325	1.47422	0.737109	+	0.675774i	$0.236190\pi$
$360$	21.6756	1.14240
$361$	34.3161	1.80611
$362$	−10.8754	−0.571598
$363$	37.8934	1.98889
$364$	−2.96937	−0.155637
$365$	−19.0133	−0.995199
$366$	29.2335	1.52806
$367$	0.200577	0.0104700	0.00523501	−	0.999986i	$-0.498334\pi$
$367$	0.200577	0.0104700	0.00523501	+	0.999986i	$0.498334\pi$
$368$	4.22271	0.220124
$369$	4.21745	0.219552
$370$	26.5785	1.38175
$371$	18.3767	0.954072
$372$	−14.7173	−0.763058
$373$	27.3706	1.41719	0.708597	−	0.705614i	$-0.249329\pi$
$373$	27.3706	1.41719	0.708597	+	0.705614i	$0.249329\pi$
$374$	0.791706	0.0409382
$375$	−34.0818	−1.75998
$376$	−7.41936	−0.382624
$377$	−1.61361	−0.0831050
$378$	87.3987	4.49530
$379$	3.86848	0.198710	0.0993552	−	0.995052i	$-0.468322\pi$
$379$	3.86848	0.198710	0.0993552	+	0.995052i	$0.468322\pi$
$380$	17.8058	0.913420
$381$	25.7873	1.32112
$382$	3.54455	0.181355
$383$	−8.88178	−0.453838	−0.226919	−	0.973914i	$-0.572865\pi$
$383$	−8.88178	−0.453838	−0.226919	+	0.973914i	$0.572865\pi$
$384$	3.44800	0.175955
$385$	1.05066	0.0535464
$386$	2.16971	0.110436
$387$	75.5876	3.84233
$388$	−15.9280	−0.808620
$389$	21.2070	1.07524	0.537620	−	0.843187i	$-0.319323\pi$
$389$	21.2070	1.07524	0.537620	+	0.843187i	$0.319323\pi$
$390$	5.80024	0.293706
$391$	33.4000	1.68911
$392$	−11.5284	−0.582271
$393$	25.5588	1.28927
$394$	3.88832	0.195891
$395$	8.90781	0.448201
$396$	−0.889706	−0.0447094
$397$	−25.7290	−1.29130	−0.645650	−	0.763634i	$-0.723413\pi$
$397$	−25.7290	−1.29130	−0.645650	+	0.763634i	$0.723413\pi$
$398$	16.6556	0.834872
$399$	108.371	5.42536
$400$	0.946569	0.0473284
$401$	22.3427	1.11574	0.557870	−	0.829929i	$-0.311619\pi$
$401$	22.3427	1.11574	0.557870	+	0.829929i	$0.311619\pi$
$402$	−27.0499	−1.34913
$403$	−2.94447	−0.146675
$404$	0.489886	0.0243727
$405$	−105.694	−5.25198
$406$	−10.0687	−0.499699
$407$	−1.09095	−0.0540765
$408$	27.2724	1.35018
$409$	12.4867	0.617428	0.308714	−	0.951155i	$-0.400101\pi$
$409$	12.4867	0.617428	0.308714	+	0.951155i	$0.400101\pi$
$410$	1.15703	0.0571417
$411$	55.3904	2.73221
$412$	−8.31852	−0.409824
$413$	10.5939	0.521290
$414$	−37.5344	−1.84471
$415$	−41.1550	−2.02022
$416$	0.689835	0.0338219
$417$	−6.99726	−0.342657
$418$	−0.730866	−0.0357478
$419$	−0.661323	−0.0323077	−0.0161539	−	0.999870i	$-0.505142\pi$
$419$	−0.661323	−0.0323077	−0.0161539	+	0.999870i	$0.505142\pi$
$420$	36.1925	1.76602
$421$	13.9812	0.681403	0.340702	−	0.940171i	$-0.389335\pi$
$421$	13.9812	0.681403	0.340702	+	0.940171i	$0.389335\pi$
$422$	−8.24008	−0.401121
$423$	65.9484	3.20652
$424$	−4.26923	−0.207332
$425$	7.48700	0.363173
$426$	26.4023	1.27919
$427$	36.4949	1.76611
$428$	−6.02589	−0.291272
$429$	−0.238079	−0.0114946
$430$	20.7370	1.00003
$431$	28.8634	1.39030	0.695151	−	0.718864i	$-0.255338\pi$
$431$	28.8634	1.39030	0.695151	+	0.718864i	$0.255338\pi$
$432$	−20.3042	−0.976887
$433$	−35.2602	−1.69450	−0.847249	−	0.531197i	$-0.821743\pi$
$433$	−35.2602	−1.69450	−0.847249	+	0.531197i	$0.821743\pi$
$434$	−18.3730	−0.881933
$435$	19.6677	0.942992
$436$	6.99709	0.335100
$437$	−30.8333	−1.47496
$438$	26.8838	1.28456
$439$	−19.4485	−0.928228	−0.464114	−	0.885776i	$-0.653627\pi$
$439$	−19.4485	−0.928228	−0.464114	+	0.885776i	$0.653627\pi$
$440$	−0.244085	−0.0116363
$441$	102.472	4.87963
$442$	5.45633	0.259531
$443$	3.82654	0.181804	0.0909022	−	0.995860i	$-0.471025\pi$
$443$	3.82654	0.181804	0.0909022	+	0.995860i	$0.471025\pi$
$444$	−37.5806	−1.78350
$445$	−30.2613	−1.43452
$446$	10.9860	0.520200
$447$	−47.1927	−2.23214
$448$	4.30446	0.203367
$449$	−12.1502	−0.573402	−0.286701	−	0.958020i	$-0.592559\pi$
$449$	−12.1502	−0.573402	−0.286701	+	0.958020i	$0.592559\pi$
$450$	−8.41376	−0.396629
$451$	−0.0474920	−0.00223631
$452$	2.14753	0.101011
$453$	18.1350	0.852059
$454$	−20.2592	−0.950810
$455$	7.24098	0.339462
$456$	−25.1765	−1.17900
$457$	−4.65990	−0.217981	−0.108990	−	0.994043i	$-0.534762\pi$
$457$	−4.65990	−0.217981	−0.108990	+	0.994043i	$0.534762\pi$
$458$	2.09798	0.0980323
$459$	−160.599	−7.49610
$460$	−10.2973	−0.480115
$461$	−34.4457	−1.60430	−0.802148	−	0.597126i	$-0.796309\pi$
$461$	−34.4457	−1.60430	−0.802148	+	0.597126i	$0.796309\pi$
$462$	−1.48557	−0.0691152
$463$	16.0192	0.744475	0.372237	−	0.928138i	$-0.378591\pi$
$463$	16.0192	0.744475	0.372237	+	0.928138i	$0.378591\pi$
$464$	2.33912	0.108591
$465$	35.8891	1.66432
$466$	3.58268	0.165964
$467$	−30.5947	−1.41575	−0.707877	−	0.706336i	$-0.750347\pi$
$467$	−30.5947	−1.41575	−0.707877	+	0.706336i	$0.750347\pi$
$468$	−6.13173	−0.283440
$469$	−33.7690	−1.55931
$470$	18.0925	0.834546
$471$	−58.7763	−2.70827
$472$	−2.46114	−0.113283
$473$	−0.851179	−0.0391372
$474$	−12.5952	−0.578517
$475$	−6.91164	−0.317128
$476$	34.0466	1.56053
$477$	37.9479	1.73751
$478$	−15.2190	−0.696099
$479$	−18.7102	−0.854890	−0.427445	−	0.904041i	$-0.640586\pi$
$479$	−18.7102	−0.854890	−0.427445	+	0.904041i	$0.640586\pi$
$480$	−8.40815	−0.383778
$481$	−7.51869	−0.342823
$482$	18.4846	0.841949
$483$	−62.6725	−2.85170
$484$	−10.9900	−0.499545
$485$	38.8413	1.76369
$486$	88.5334	4.01596
$487$	−19.1891	−0.869543	−0.434772	−	0.900541i	$-0.643171\pi$
$487$	−19.1891	−0.869543	−0.434772	+	0.900541i	$0.643171\pi$
$488$	−8.47839	−0.383799
$489$	−60.2630	−2.72518
$490$	28.1126	1.27000
$491$	−22.3913	−1.01051	−0.505254	−	0.862971i	$-0.668601\pi$
$491$	−22.3913	−1.01051	−0.505254	+	0.862971i	$0.668601\pi$
$492$	−1.63598	−0.0737559
$493$	18.5015	0.833268
$494$	−5.03703	−0.226627
$495$	2.16960	0.0975163
$496$	4.26837	0.191655
$497$	32.9604	1.47848
$498$	58.1911	2.60760
$499$	8.62712	0.386203	0.193101	−	0.981179i	$-0.438145\pi$
$499$	8.62712	0.386203	0.193101	+	0.981179i	$0.438145\pi$
$500$	9.88453	0.442050
$501$	37.3515	1.66874
$502$	26.6029	1.18734
$503$	40.7363	1.81634	0.908172	−	0.418598i	$-0.137478\pi$
$503$	40.7363	1.81634	0.908172	+	0.418598i	$0.137478\pi$
$504$	−38.2610	−1.70428
$505$	−1.19462	−0.0531597
$506$	0.422668	0.0187899
$507$	43.1832	1.91783
$508$	−7.47892	−0.331823
$509$	−17.7437	−0.786477	−0.393239	−	0.919436i	$-0.628645\pi$
$509$	−17.7437	−0.786477	−0.393239	+	0.919436i	$0.628645\pi$
$510$	−66.5053	−2.94490
$511$	33.5616	1.48468
$512$	−1.00000	−0.0441942
$513$	148.257	6.54571
$514$	−2.47266	−0.109064
$515$	20.2852	0.893872
$516$	−29.3210	−1.29079
$517$	−0.742634	−0.0326610
$518$	−46.9155	−2.06135
$519$	37.2924	1.63696
$520$	−1.68220	−0.0737695
$521$	−15.6366	−0.685051	−0.342526	−	0.939509i	$-0.611282\pi$
$521$	−15.6366	−0.685051	−0.342526	+	0.939509i	$0.611282\pi$
$522$	−20.7917	−0.910029
$523$	−2.66424	−0.116499	−0.0582495	−	0.998302i	$-0.518552\pi$
$523$	−2.66424	−0.116499	−0.0582495	+	0.998302i	$0.518552\pi$
$524$	−7.41263	−0.323822
$525$	−14.0488	−0.613138
$526$	1.66376	0.0725433
$527$	33.7612	1.47066
$528$	0.345124	0.0150196
$529$	−5.16872	−0.224727
$530$	10.4108	0.452215
$531$	21.8763	0.949351
$532$	−31.4302	−1.36267
$533$	−0.327309	−0.0141773
$534$	42.7879	1.85161
$535$	14.6945	0.635298
$536$	7.84511	0.338857
$537$	−62.7540	−2.70803
$538$	7.09445	0.305864
$539$	−1.15392	−0.0497030
$540$	49.5130	2.13070
$541$	6.31865	0.271660	0.135830	−	0.990732i	$-0.456630\pi$
$541$	6.31865	0.271660	0.135830	+	0.990732i	$0.456630\pi$
$542$	−13.6818	−0.587682
$543$	−37.4984	−1.60921
$544$	−7.90962	−0.339122
$545$	−17.0628	−0.730890
$546$	−10.2384	−0.438162
$547$	−29.6202	−1.26647	−0.633235	−	0.773960i	$-0.718273\pi$
$547$	−29.6202	−1.26647	−0.633235	+	0.773960i	$0.718273\pi$
$548$	−16.0645	−0.686242
$549$	75.3618	3.21636
$550$	0.0947460	0.00403998
$551$	−17.0797	−0.727622
$552$	14.5599	0.619711
$553$	−15.7238	−0.668643
$554$	13.1517	0.558763
$555$	91.6426	3.89001
$556$	2.02937	0.0860643
$557$	4.21674	0.178669	0.0893346	−	0.996002i	$-0.471526\pi$
$557$	4.21674	0.178669	0.0893346	+	0.996002i	$0.471526\pi$
$558$	−37.9402	−1.60614
$559$	−5.86621	−0.248114
$560$	−10.4967	−0.443566
$561$	2.72980	0.115252
$562$	−15.7644	−0.664983
$563$	−11.0845	−0.467156	−0.233578	−	0.972338i	$-0.575043\pi$
$563$	−11.0845	−0.467156	−0.233578	+	0.972338i	$0.575043\pi$
$564$	−25.5819	−1.07719
$565$	−5.23687	−0.220317
$566$	20.8460	0.876222
$567$	186.568	7.83510
$568$	−7.65727	−0.321292
$569$	−22.2664	−0.933456	−0.466728	−	0.884401i	$-0.654567\pi$
$569$	−22.2664	−0.933456	−0.466728	+	0.884401i	$0.654567\pi$
$570$	61.3945	2.57153
$571$	16.2903	0.681726	0.340863	−	0.940113i	$-0.389281\pi$
$571$	16.2903	0.681726	0.340863	+	0.940113i	$0.389281\pi$
$572$	0.0690484	0.00288706
$573$	12.2216	0.510565
$574$	−2.04235	−0.0852462
$575$	3.99709	0.166690
$576$	8.88870	0.370362
$577$	−3.96874	−0.165221	−0.0826103	−	0.996582i	$-0.526326\pi$
$577$	−3.96874	−0.165221	−0.0826103	+	0.996582i	$0.526326\pi$
$578$	−45.5621	−1.89513
$579$	7.48117	0.310907
$580$	−5.70408	−0.236849
$581$	72.6454	3.01384
$582$	−54.9196	−2.27649
$583$	−0.427325	−0.0176980
$584$	−7.79692	−0.322639
$585$	14.9526	0.618214
$586$	−14.6082	−0.603459
$587$	−34.3721	−1.41869	−0.709344	−	0.704862i	$-0.751009\pi$
$587$	−34.3721	−1.41869	−0.709344	+	0.704862i	$0.751009\pi$
$588$	−39.7499	−1.63926
$589$	−31.1667	−1.28420
$590$	6.00163	0.247083
$591$	13.4069	0.551488
$592$	10.8993	0.447957
$593$	4.22941	0.173681	0.0868406	−	0.996222i	$-0.472323\pi$
$593$	4.22941	0.173681	0.0868406	+	0.996222i	$0.472323\pi$
$594$	−2.03233	−0.0833876
$595$	−83.0248	−3.40368
$596$	13.6870	0.560641
$597$	57.4287	2.35040
$598$	2.91297	0.119120
$599$	6.23323	0.254683	0.127342	−	0.991859i	$-0.459356\pi$
$599$	6.23323	0.254683	0.127342	+	0.991859i	$0.459356\pi$
$600$	3.26377	0.133243
$601$	33.0806	1.34939	0.674693	−	0.738098i	$-0.264276\pi$
$601$	33.0806	1.34939	0.674693	+	0.738098i	$0.264276\pi$
$602$	−36.6042	−1.49188
$603$	−69.7328	−2.83974
$604$	−5.25959	−0.214009
$605$	26.7997	1.08956
$606$	1.68913	0.0686160
$607$	9.65561	0.391909	0.195955	−	0.980613i	$-0.437219\pi$
$607$	9.65561	0.391909	0.195955	+	0.980613i	$0.437219\pi$
$608$	7.30178	0.296126
$609$	−34.7167	−1.40679
$610$	20.6750	0.837108
$611$	−5.11813	−0.207057
$612$	70.3062	2.84196
$613$	17.2790	0.697892	0.348946	−	0.937143i	$-0.386540\pi$
$613$	17.2790	0.697892	0.348946	+	0.937143i	$0.386540\pi$
$614$	12.9345	0.521994
$615$	3.98944	0.160870
$616$	0.430851	0.0173595
$617$	29.7302	1.19689	0.598446	−	0.801163i	$-0.295785\pi$
$617$	29.7302	1.19689	0.598446	+	0.801163i	$0.295785\pi$
$618$	−28.6822	−1.15377
$619$	−43.8109	−1.76091	−0.880455	−	0.474131i	$-0.842762\pi$
$619$	−43.8109	−1.76091	−0.880455	+	0.474131i	$0.842762\pi$
$620$	−10.4087	−0.418022
$621$	−85.7388	−3.44058
$622$	3.58268	0.143653
$623$	53.4162	2.14007
$624$	2.37855	0.0952182
$625$	−28.8369	−1.15347
$626$	2.90901	0.116268
$627$	−2.52002	−0.100640
$628$	17.0465	0.680230
$629$	86.2090	3.43738
$630$	93.3018	3.71723
$631$	19.7371	0.785720	0.392860	−	0.919598i	$-0.371486\pi$
$631$	19.7371	0.785720	0.392860	+	0.919598i	$0.371486\pi$
$632$	3.65290	0.145305
$633$	−28.4118	−1.12927
$634$	23.8279	0.946328
$635$	18.2378	0.723744
$636$	−14.7203	−0.583698
$637$	−7.95268	−0.315097
$638$	0.234132	0.00926938
$639$	68.0632	2.69254
$640$	2.43856	0.0963925
$641$	23.8737	0.942954	0.471477	−	0.881878i	$-0.343721\pi$
$641$	23.8737	0.942954	0.471477	+	0.881878i	$0.343721\pi$
$642$	−20.7772	−0.820013
$643$	−20.7038	−0.816477	−0.408238	−	0.912875i	$-0.633857\pi$
$643$	−20.7038	−0.816477	−0.408238	+	0.912875i	$0.633857\pi$
$644$	18.1765	0.716254
$645$	71.5011	2.81535
$646$	57.7543	2.27231
$647$	29.0195	1.14088	0.570438	−	0.821341i	$-0.306774\pi$
$647$	29.0195	1.14088	0.570438	+	0.821341i	$0.306774\pi$
$648$	−43.3428	−1.70267
$649$	−0.246345	−0.00966990
$650$	0.652976	0.0256118
$651$	−63.3502	−2.48289
$652$	17.4777	0.684478
$653$	47.9963	1.87824	0.939120	−	0.343588i	$-0.111642\pi$
$653$	47.9963	1.87824	0.939120	+	0.343588i	$0.111642\pi$
$654$	24.1259	0.943399
$655$	18.0761	0.706293
$656$	0.474474	0.0185251
$657$	69.3045	2.70383
$658$	−31.9363	−1.24501
$659$	45.7314	1.78144	0.890721	−	0.454550i	$-0.150200\pi$
$659$	45.7314	1.78144	0.890721	+	0.454550i	$0.150200\pi$
$660$	−0.841606	−0.0327595
$661$	33.4826	1.30232	0.651161	−	0.758940i	$-0.274282\pi$
$661$	33.4826	1.30232	0.651161	+	0.758940i	$0.274282\pi$
$662$	15.5668	0.605022
$663$	18.8134	0.730653
$664$	−16.8768	−0.654945
$665$	76.6445	2.97215
$666$	−96.8802	−3.75403
$667$	9.87743	0.382455
$668$	−10.8328	−0.419134
$669$	37.8796	1.46451
$670$	−19.1308	−0.739086
$671$	−0.848637	−0.0327613
$672$	14.8418	0.572534
$673$	20.1252	0.775770	0.387885	−	0.921708i	$-0.373206\pi$
$673$	20.1252	0.775770	0.387885	+	0.921708i	$0.373206\pi$
$674$	29.7880	1.14739
$675$	−19.2193	−0.739753
$676$	−12.5241	−0.481697
$677$	48.3297	1.85746	0.928731	−	0.370754i	$-0.120901\pi$
$677$	48.3297	1.85746	0.928731	+	0.370754i	$0.120901\pi$
$678$	7.40467	0.284375
$679$	−68.5613	−2.63114
$680$	19.2881	0.739664
$681$	−69.8536	−2.67680
$682$	0.427239	0.0163598
$683$	−44.3631	−1.69751	−0.848754	−	0.528788i	$-0.822647\pi$
$683$	−44.3631	−1.69751	−0.848754	+	0.528788i	$0.822647\pi$
$684$	−64.9033	−2.48164
$685$	39.1742	1.49677
$686$	−19.4922	−0.744218
$687$	7.23384	0.275988
$688$	8.50378	0.324204
$689$	−2.94506	−0.112198
$690$	−35.5052	−1.35166
$691$	−35.2452	−1.34079	−0.670394	−	0.742005i	$-0.733875\pi$
$691$	−35.2452	−1.34079	−0.670394	+	0.742005i	$0.733875\pi$
$692$	−10.8157	−0.411150
$693$	−3.82971	−0.145478
$694$	−9.54784	−0.362431
$695$	−4.94873	−0.187716
$696$	8.06528	0.305714
$697$	3.75291	0.142151
$698$	−0.378070	−0.0143102
$699$	12.3531	0.467236
$700$	4.07447	0.154000
$701$	31.6357	1.19486	0.597432	−	0.801920i	$-0.296188\pi$
$701$	31.6357	1.19486	0.597432	+	0.801920i	$0.296188\pi$
$702$	−14.0066	−0.528644
$703$	−79.5841	−3.00157
$704$	−0.100094	−0.00377244
$705$	62.3830	2.34948
$706$	10.7476	0.404492
$707$	2.10869	0.0793056
$708$	−8.48600	−0.318923
$709$	−37.3007	−1.40086	−0.700428	−	0.713723i	$-0.747007\pi$
$709$	−37.3007	−1.40086	−0.700428	+	0.713723i	$0.747007\pi$
$710$	18.6727	0.700774
$711$	−32.4695	−1.21770
$712$	−12.4095	−0.465065
$713$	18.0241	0.675007
$714$	117.393	4.39332
$715$	−0.168379	−0.00629701
$716$	18.2001	0.680170
$717$	−52.4750	−1.95971
$718$	−27.9325	−1.04243
$719$	−10.7342	−0.400318	−0.200159	−	0.979763i	$-0.564146\pi$
$719$	−10.7342	−0.400318	−0.200159	+	0.979763i	$0.564146\pi$
$720$	−21.6756	−0.807802
$721$	−35.8067	−1.33351
$722$	−34.3161	−1.27711
$723$	63.7348	2.37032
$724$	10.8754	0.404181
$725$	2.21414	0.0822310
$726$	−37.8934	−1.40636
$727$	−29.8752	−1.10801	−0.554005	−	0.832513i	$-0.686901\pi$
$727$	−29.8752	−1.10801	−0.554005	+	0.832513i	$0.686901\pi$
$728$	2.96937	0.110052
$729$	175.235	6.49017
$730$	19.0133	0.703712
$731$	67.2617	2.48776
$732$	−29.2335	−1.08050
$733$	33.1003	1.22259	0.611294	−	0.791404i	$-0.290649\pi$
$733$	33.1003	1.22259	0.611294	+	0.791404i	$0.290649\pi$
$734$	−0.200577	−0.00740342
$735$	96.9324	3.57540
$736$	−4.22271	−0.155651
$737$	0.785250	0.0289250
$738$	−4.21745	−0.155247
$739$	−37.7163	−1.38742	−0.693708	−	0.720256i	$-0.744024\pi$
$739$	−37.7163	−1.38742	−0.693708	+	0.720256i	$0.744024\pi$
$740$	−26.5785	−0.977045
$741$	−17.3677	−0.638017
$742$	−18.3767	−0.674631
$743$	−13.0151	−0.477478	−0.238739	−	0.971084i	$-0.576734\pi$
$743$	−13.0151	−0.477478	−0.238739	+	0.971084i	$0.576734\pi$
$744$	14.7173	0.539563
$745$	−33.3765	−1.22282
$746$	−27.3706	−1.00211
$747$	150.012	5.48867
$748$	−0.791706	−0.0289477
$749$	−25.9382	−0.947761
$750$	34.0818	1.24449
$751$	15.4644	0.564303	0.282151	−	0.959370i	$-0.408952\pi$
$751$	15.4644	0.564303	0.282151	+	0.959370i	$0.408952\pi$
$752$	7.41936	0.270556
$753$	91.7267	3.34271
$754$	1.61361	0.0587641
$755$	12.8258	0.466779
$756$	−87.3987	−3.17866
$757$	13.9528	0.507124	0.253562	−	0.967319i	$-0.418398\pi$
$757$	13.9528	0.507124	0.253562	+	0.967319i	$0.418398\pi$
$758$	−3.86848	−0.140510
$759$	1.45736	0.0528988
$760$	−17.8058	−0.645885
$761$	−30.6902	−1.11252	−0.556259	−	0.831009i	$-0.687764\pi$
$761$	−30.6902	−1.11252	−0.556259	+	0.831009i	$0.687764\pi$
$762$	−25.7873	−0.934175
$763$	30.1187	1.09037
$764$	−3.54455	−0.128237
$765$	−171.446	−6.19864
$766$	8.88178	0.320912
$767$	−1.69778	−0.0613032
$768$	−3.44800	−0.124419
$769$	−4.46264	−0.160927	−0.0804634	−	0.996758i	$-0.525640\pi$
$769$	−4.46264	−0.160927	−0.0804634	+	0.996758i	$0.525640\pi$
$770$	−1.05066	−0.0378630
$771$	−8.52572	−0.307046
$772$	−2.16971	−0.0780897
$773$	−37.9289	−1.36421	−0.682103	−	0.731256i	$-0.738935\pi$
$773$	−37.9289	−1.36421	−0.682103	+	0.731256i	$0.738935\pi$
$774$	−75.5876	−2.71694
$775$	4.04030	0.145132
$776$	15.9280	0.571780
$777$	−161.764	−5.80327
$778$	−21.2070	−0.760310
$779$	−3.46450	−0.124129
$780$	−5.80024	−0.207682
$781$	−0.766448	−0.0274257
$782$	−33.4000	−1.19438
$783$	−47.4940	−1.69730
$784$	11.5284	0.411728
$785$	−41.5689	−1.48366
$786$	−25.5588	−0.911650
$787$	−16.3768	−0.583770	−0.291885	−	0.956453i	$-0.594282\pi$
$787$	−16.3768	−0.583770	−0.291885	+	0.956453i	$0.594282\pi$
$788$	−3.88832	−0.138516
$789$	5.73664	0.204230
$790$	−8.90781	−0.316926
$791$	9.24394	0.328677
$792$	0.889706	0.0316143
$793$	−5.84869	−0.207693
$794$	25.7290	0.913086
$795$	35.8963	1.27311
$796$	−16.6556	−0.590344
$797$	39.1966	1.38841	0.694207	−	0.719775i	$-0.255755\pi$
$797$	39.1966	1.38841	0.694207	+	0.719775i	$0.255755\pi$
$798$	−108.371	−3.83631
$799$	58.6843	2.07610
$800$	−0.946569	−0.0334663
$801$	110.304	3.89741
$802$	−22.3427	−0.788947
$803$	−0.780426	−0.0275406
$804$	27.0499	0.953978
$805$	−44.3244	−1.56223
$806$	2.94447	0.103715
$807$	24.4617	0.861091
$808$	−0.489886	−0.0172341
$809$	3.71032	0.130448	0.0652239	−	0.997871i	$-0.479224\pi$
$809$	3.71032	0.130448	0.0652239	+	0.997871i	$0.479224\pi$
$810$	105.694	3.71371
$811$	43.0790	1.51271	0.756355	−	0.654162i	$-0.226978\pi$
$811$	43.0790	1.51271	0.756355	+	0.654162i	$0.226978\pi$
$812$	10.0687	0.353340
$813$	−47.1747	−1.65449
$814$	1.09095	0.0382379
$815$	−42.6203	−1.49292
$816$	−27.2724	−0.954724
$817$	−62.0928	−2.17235
$818$	−12.4867	−0.436587
$819$	−26.3938	−0.922274
$820$	−1.15703	−0.0404053
$821$	−3.28174	−0.114534	−0.0572668	−	0.998359i	$-0.518239\pi$
$821$	−3.28174	−0.114534	−0.0572668	+	0.998359i	$0.518239\pi$
$822$	−55.3904	−1.93196
$823$	−5.56654	−0.194038	−0.0970188	−	0.995283i	$-0.530931\pi$
$823$	−5.56654	−0.194038	−0.0970188	+	0.995283i	$0.530931\pi$
$824$	8.31852	0.289789
$825$	0.326684	0.0113737
$826$	−10.5939	−0.368608
$827$	−16.5249	−0.574627	−0.287313	−	0.957837i	$-0.592762\pi$
$827$	−16.5249	−0.574627	−0.287313	+	0.957837i	$0.592762\pi$
$828$	37.5344	1.30441
$829$	6.58447	0.228688	0.114344	−	0.993441i	$-0.463523\pi$
$829$	6.58447	0.228688	0.114344	+	0.993441i	$0.463523\pi$
$830$	41.1550	1.42851
$831$	45.3471	1.57307
$832$	−0.689835	−0.0239157
$833$	91.1851	3.15938
$834$	6.99726	0.242295
$835$	26.4165	0.914179
$836$	0.730866	0.0252775
$837$	−86.6659	−2.99561
$838$	0.661323	0.0228450
$839$	35.8056	1.23615	0.618074	−	0.786120i	$-0.287913\pi$
$839$	35.8056	1.23615	0.618074	+	0.786120i	$0.287913\pi$
$840$	−36.1925	−1.24876
$841$	−23.5285	−0.811328
$842$	−13.9812	−0.481825
$843$	−54.3558	−1.87211
$844$	8.24008	0.283635
$845$	30.5408	1.05064
$846$	−65.9484	−2.26735
$847$	−47.3059	−1.62545
$848$	4.26923	0.146606
$849$	71.8769	2.46681
$850$	−7.48700	−0.256802
$851$	46.0244	1.57770
$852$	−26.4023	−0.904527
$853$	30.0148	1.02769	0.513844	−	0.857884i	$-0.328221\pi$
$853$	30.0148	1.02769	0.513844	+	0.857884i	$0.328221\pi$
$854$	−36.4949	−1.24883
$855$	158.271	5.41274
$856$	6.02589	0.205961
$857$	−43.3335	−1.48025	−0.740123	−	0.672472i	$-0.765233\pi$
$857$	−43.3335	−1.48025	−0.740123	+	0.672472i	$0.765233\pi$
$858$	0.238079	0.00812788
$859$	48.8743	1.66757	0.833784	−	0.552090i	$-0.186170\pi$
$859$	48.8743	1.66757	0.833784	+	0.552090i	$0.186170\pi$
$860$	−20.7370	−0.707125
$861$	−7.04203	−0.239992
$862$	−28.8634	−0.983092
$863$	5.28219	0.179808	0.0899040	−	0.995950i	$-0.471344\pi$
$863$	5.28219	0.179808	0.0899040	+	0.995950i	$0.471344\pi$
$864$	20.3042	0.690764
$865$	26.3746	0.896765
$866$	35.2602	1.19819
$867$	−157.098	−5.33533
$868$	18.3730	0.623621
$869$	0.365634	0.0124033
$870$	−19.6677	−0.666796
$871$	5.41184	0.183373
$872$	−6.99709	−0.236951
$873$	−141.579	−4.79172
$874$	30.8333	1.04295
$875$	42.5476	1.43837
$876$	−26.8838	−0.908319
$877$	−10.4764	−0.353764	−0.176882	−	0.984232i	$-0.556601\pi$
$877$	−10.4764	−0.353764	−0.176882	+	0.984232i	$0.556601\pi$
$878$	19.4485	0.656356
$879$	−50.3690	−1.69891
$880$	0.244085	0.00822812
$881$	−37.1097	−1.25026	−0.625129	−	0.780522i	$-0.714954\pi$
$881$	−37.1097	−1.25026	−0.625129	+	0.780522i	$0.714954\pi$
$882$	−102.472	−3.45042
$883$	−30.9212	−1.04058	−0.520291	−	0.853989i	$-0.674176\pi$
$883$	−30.9212	−1.04058	−0.520291	+	0.853989i	$0.674176\pi$
$884$	−5.45633	−0.183516
$885$	20.6936	0.695608
$886$	−3.82654	−0.128555
$887$	9.07331	0.304652	0.152326	−	0.988330i	$-0.451324\pi$
$887$	9.07331	0.304652	0.152326	+	0.988330i	$0.451324\pi$
$888$	37.5806	1.26112
$889$	−32.1927	−1.07971
$890$	30.2613	1.01436
$891$	−4.33836	−0.145341
$892$	−10.9860	−0.367837
$893$	−54.1745	−1.81288
$894$	47.1927	1.57836
$895$	−44.3821	−1.48353
$896$	−4.30446	−0.143802
$897$	10.0439	0.335357
$898$	12.1502	0.405456
$899$	9.98423	0.332993
$900$	8.41376	0.280459
$901$	33.7680	1.12497
$902$	0.0474920	0.00158131
$903$	−126.211	−4.20005
$904$	−2.14753	−0.0714257
$905$	−26.5203	−0.881565
$906$	−18.1350	−0.602496
$907$	49.6219	1.64767	0.823834	−	0.566831i	$-0.191831\pi$
$907$	49.6219	1.64767	0.823834	+	0.566831i	$0.191831\pi$
$908$	20.2592	0.672324
$909$	4.35445	0.144428
$910$	−7.24098	−0.240036
$911$	44.2726	1.46682	0.733409	−	0.679788i	$-0.237928\pi$
$911$	44.2726	1.46682	0.733409	+	0.679788i	$0.237928\pi$
$912$	25.1765	0.833679
$913$	−1.68926	−0.0559065
$914$	4.65990	0.154136
$915$	71.2875	2.35669
$916$	−2.09798	−0.0693193
$917$	−31.9074	−1.05367
$918$	160.599	5.30055
$919$	−31.9693	−1.05457	−0.527285	−	0.849688i	$-0.676790\pi$
$919$	−31.9693	−1.05457	−0.527285	+	0.849688i	$0.676790\pi$
$920$	10.2973	0.339493
$921$	44.5981	1.46956
$922$	34.4457	1.13441
$923$	−5.28225	−0.173868
$924$	1.48557	0.0488718
$925$	10.3169	0.339218
$926$	−16.0192	−0.526423
$927$	−73.9408	−2.42853
$928$	−2.33912	−0.0767854
$929$	9.88040	0.324165	0.162083	−	0.986777i	$-0.448179\pi$
$929$	9.88040	0.324165	0.162083	+	0.986777i	$0.448179\pi$
$930$	−35.8891	−1.17685
$931$	−84.1778	−2.75881
$932$	−3.58268	−0.117355
$933$	12.3531	0.404422
$934$	30.5947	1.00109
$935$	1.93062	0.0631381
$936$	6.13173	0.200422
$937$	5.81135	0.189849	0.0949243	−	0.995484i	$-0.469739\pi$
$937$	5.81135	0.189849	0.0949243	+	0.995484i	$0.469739\pi$
$938$	33.7690	1.10260
$939$	10.0303	0.327326
$940$	−18.0925	−0.590113
$941$	−24.6208	−0.802614	−0.401307	−	0.915944i	$-0.631444\pi$
$941$	−24.6208	−0.802614	−0.401307	+	0.915944i	$0.631444\pi$
$942$	58.7763	1.91504
$943$	2.00356	0.0652450
$944$	2.46114	0.0801032
$945$	213.127	6.93302
$946$	0.851179	0.0276742
$947$	4.36426	0.141819	0.0709096	−	0.997483i	$-0.477410\pi$
$947$	4.36426	0.141819	0.0709096	+	0.997483i	$0.477410\pi$
$948$	12.5952	0.409073
$949$	−5.37859	−0.174596
$950$	6.91164	0.224243
$951$	82.1587	2.66418
$952$	−34.0466	−1.10346
$953$	−10.8565	−0.351677	−0.175838	−	0.984419i	$-0.556264\pi$
$953$	−10.8565	−0.351677	−0.175838	+	0.984419i	$0.556264\pi$
$954$	−37.9479	−1.22861
$955$	8.64360	0.279700
$956$	15.2190	0.492217
$957$	0.807287	0.0260959
$958$	18.7102	0.604499
$959$	−69.1490	−2.23294
$960$	8.40815	0.271372
$961$	−12.7810	−0.412291
$962$	7.51869	0.242412
$963$	−53.5623	−1.72602
$964$	−18.4846	−0.595348
$965$	5.29097	0.170322
$966$	62.6725	2.01646
$967$	−16.2446	−0.522390	−0.261195	−	0.965286i	$-0.584117\pi$
$967$	−16.2446	−0.522390	−0.261195	+	0.965286i	$0.584117\pi$
$968$	10.9900	0.353231
$969$	199.137	6.39720
$970$	−38.8413	−1.24712
$971$	−37.6439	−1.20805	−0.604026	−	0.796965i	$-0.706438\pi$
$971$	−37.6439	−1.20805	−0.604026	+	0.796965i	$0.706438\pi$
$972$	−88.5334	−2.83971
$973$	8.73533	0.280042
$974$	19.1891	0.614860
$975$	2.25146	0.0721045
$976$	8.47839	0.271387
$977$	48.1894	1.54172	0.770858	−	0.637007i	$-0.219828\pi$
$977$	48.1894	1.54172	0.770858	+	0.637007i	$0.219828\pi$
$978$	60.2630	1.92700
$979$	−1.24212	−0.0396982
$980$	−28.1126	−0.898025
$981$	62.1950	1.98573
$982$	22.3913	0.714537
$983$	−54.3685	−1.73409	−0.867043	−	0.498233i	$-0.833982\pi$
$983$	−54.3685	−1.73409	−0.867043	+	0.498233i	$0.833982\pi$
$984$	1.63598	0.0521533
$985$	9.48191	0.302119
$986$	−18.5015	−0.589209
$987$	−110.116	−3.50504
$988$	5.03703	0.160249
$989$	35.9090	1.14184
$990$	−2.16960	−0.0689544
$991$	−38.2754	−1.21586	−0.607930	−	0.793991i	$-0.708000\pi$
$991$	−38.2754	−1.21586	−0.607930	+	0.793991i	$0.708000\pi$
$992$	−4.26837	−0.135521
$993$	53.6744	1.70330
$994$	−32.9604	−1.04544
$995$	40.6158	1.28761
$996$	−58.1911	−1.84385
$997$	20.9768	0.664343	0.332171	−	0.943219i	$-0.392219\pi$
$997$	20.9768	0.664343	0.332171	+	0.943219i	$0.392219\pi$
$998$	−8.62712	−0.273087
$999$	−221.301	−7.00165

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.e.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.44800 q^{3} +1.00000 q^{4} -2.43856 q^{5} +3.44800 q^{6} +4.30446 q^{7} -1.00000 q^{8} +8.88870 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.44800 q^{3} +1.00000 q^{4} -2.43856 q^{5} +3.44800 q^{6} +4.30446 q^{7} -1.00000 q^{8} +8.88870 q^{9} +2.43856 q^{10} -0.100094 q^{11} -3.44800 q^{12} -0.689835 q^{13} -4.30446 q^{14} +8.40815 q^{15} +1.00000 q^{16} +7.90962 q^{17} -8.88870 q^{18} -7.30178 q^{19} -2.43856 q^{20} -14.8418 q^{21} +0.100094 q^{22} +4.22271 q^{23} +3.44800 q^{24} +0.946569 q^{25} +0.689835 q^{26} -20.3042 q^{27} +4.30446 q^{28} +2.33912 q^{29} -8.40815 q^{30} +4.26837 q^{31} -1.00000 q^{32} +0.345124 q^{33} -7.90962 q^{34} -10.4967 q^{35} +8.88870 q^{36} +10.8993 q^{37} +7.30178 q^{38} +2.37855 q^{39} +2.43856 q^{40} +0.474474 q^{41} +14.8418 q^{42} +8.50378 q^{43} -0.100094 q^{44} -21.6756 q^{45} -4.22271 q^{46} +7.41936 q^{47} -3.44800 q^{48} +11.5284 q^{49} -0.946569 q^{50} -27.2724 q^{51} -0.689835 q^{52} +4.26923 q^{53} +20.3042 q^{54} +0.244085 q^{55} -4.30446 q^{56} +25.1765 q^{57} -2.33912 q^{58} +2.46114 q^{59} +8.40815 q^{60} +8.47839 q^{61} -4.26837 q^{62} +38.2610 q^{63} +1.00000 q^{64} +1.68220 q^{65} -0.345124 q^{66} -7.84511 q^{67} +7.90962 q^{68} -14.5599 q^{69} +10.4967 q^{70} +7.65727 q^{71} -8.88870 q^{72} +7.79692 q^{73} -10.8993 q^{74} -3.26377 q^{75} -7.30178 q^{76} -0.430851 q^{77} -2.37855 q^{78} -3.65290 q^{79} -2.43856 q^{80} +43.3428 q^{81} -0.474474 q^{82} +16.8768 q^{83} -14.8418 q^{84} -19.2881 q^{85} -8.50378 q^{86} -8.06528 q^{87} +0.100094 q^{88} +12.4095 q^{89} +21.6756 q^{90} -2.96937 q^{91} +4.22271 q^{92} -14.7173 q^{93} -7.41936 q^{94} +17.8058 q^{95} +3.44800 q^{96} -15.9280 q^{97} -11.5284 q^{98} -0.889706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) \) 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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