LMFDB - Embedded newform 8007.2.a.c.1.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.35
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.24169 q^{2} -1.00000 q^{3} +3.02517 q^{4} +2.80284 q^{5} -2.24169 q^{6} -1.91992 q^{7} +2.29811 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.24169 q^{2} -1.00000 q^{3} +3.02517 q^{4} +2.80284 q^{5} -2.24169 q^{6} -1.91992 q^{7} +2.29811 q^{8} +1.00000 q^{9} +6.28309 q^{10} +0.785297 q^{11} -3.02517 q^{12} -6.00076 q^{13} -4.30386 q^{14} -2.80284 q^{15} -0.898696 q^{16} +1.00000 q^{17} +2.24169 q^{18} +3.83009 q^{19} +8.47906 q^{20} +1.91992 q^{21} +1.76039 q^{22} -5.66658 q^{23} -2.29811 q^{24} +2.85591 q^{25} -13.4518 q^{26} -1.00000 q^{27} -5.80807 q^{28} -4.03029 q^{29} -6.28309 q^{30} -8.03212 q^{31} -6.61081 q^{32} -0.785297 q^{33} +2.24169 q^{34} -5.38122 q^{35} +3.02517 q^{36} +2.70378 q^{37} +8.58586 q^{38} +6.00076 q^{39} +6.44122 q^{40} -2.83108 q^{41} +4.30386 q^{42} -2.91875 q^{43} +2.37565 q^{44} +2.80284 q^{45} -12.7027 q^{46} +3.74023 q^{47} +0.898696 q^{48} -3.31392 q^{49} +6.40207 q^{50} -1.00000 q^{51} -18.1533 q^{52} -7.34892 q^{53} -2.24169 q^{54} +2.20106 q^{55} -4.41217 q^{56} -3.83009 q^{57} -9.03466 q^{58} -0.402590 q^{59} -8.47906 q^{60} +1.15857 q^{61} -18.0055 q^{62} -1.91992 q^{63} -13.0220 q^{64} -16.8192 q^{65} -1.76039 q^{66} -6.92692 q^{67} +3.02517 q^{68} +5.66658 q^{69} -12.0630 q^{70} +15.3264 q^{71} +2.29811 q^{72} -6.75202 q^{73} +6.06103 q^{74} -2.85591 q^{75} +11.5867 q^{76} -1.50770 q^{77} +13.4518 q^{78} +6.24448 q^{79} -2.51890 q^{80} +1.00000 q^{81} -6.34639 q^{82} +4.64860 q^{83} +5.80807 q^{84} +2.80284 q^{85} -6.54293 q^{86} +4.03029 q^{87} +1.80470 q^{88} -1.52421 q^{89} +6.28309 q^{90} +11.5210 q^{91} -17.1423 q^{92} +8.03212 q^{93} +8.38442 q^{94} +10.7351 q^{95} +6.61081 q^{96} -7.11823 q^{97} -7.42877 q^{98} +0.785297 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.24169	1.58511	0.792557	−	0.609798i	$-0.208750\pi$
$2$	2.24169	1.58511	0.792557	+	0.609798i	$0.208750\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.02517	1.51258
$5$	2.80284	1.25347	0.626734	−	0.779233i	$-0.284391\pi$
$5$	2.80284	1.25347	0.626734	+	0.779233i	$0.284391\pi$
$6$	−2.24169	−0.915166
$7$	−1.91992	−0.725661	−0.362830	−	0.931855i	$-0.618190\pi$
$7$	−1.91992	−0.725661	−0.362830	+	0.931855i	$0.618190\pi$
$8$	2.29811	0.812503
$9$	1.00000	0.333333
$10$	6.28309	1.98689
$11$	0.785297	0.236776	0.118388	−	0.992967i	$-0.462227\pi$
$11$	0.785297	0.236776	0.118388	+	0.992967i	$0.462227\pi$
$12$	−3.02517	−0.873291
$13$	−6.00076	−1.66431	−0.832156	−	0.554542i	$-0.812894\pi$
$13$	−6.00076	−1.66431	−0.832156	+	0.554542i	$0.812894\pi$
$14$	−4.30386	−1.15025
$15$	−2.80284	−0.723690
$16$	−0.898696	−0.224674
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.24169	0.528371
$19$	3.83009	0.878682	0.439341	−	0.898320i	$-0.355212\pi$
$19$	3.83009	0.878682	0.439341	+	0.898320i	$0.355212\pi$
$20$	8.47906	1.89598
$21$	1.91992	0.418960
$22$	1.76039	0.375317
$23$	−5.66658	−1.18156	−0.590782	−	0.806831i	$-0.701181\pi$
$23$	−5.66658	−1.18156	−0.590782	+	0.806831i	$0.701181\pi$
$24$	−2.29811	−0.469099
$25$	2.85591	0.571183
$26$	−13.4518	−2.63812
$27$	−1.00000	−0.192450
$28$	−5.80807	−1.09762
$29$	−4.03029	−0.748407	−0.374203	−	0.927347i	$-0.622084\pi$
$29$	−4.03029	−0.748407	−0.374203	+	0.927347i	$0.622084\pi$
$30$	−6.28309	−1.14713
$31$	−8.03212	−1.44261	−0.721305	−	0.692617i	$-0.756458\pi$
$31$	−8.03212	−1.44261	−0.721305	+	0.692617i	$0.756458\pi$
$32$	−6.61081	−1.16864
$33$	−0.785297	−0.136703
$34$	2.24169	0.384446
$35$	−5.38122	−0.909592
$36$	3.02517	0.504195
$37$	2.70378	0.444499	0.222249	−	0.974990i	$-0.428660\pi$
$37$	2.70378	0.444499	0.222249	+	0.974990i	$0.428660\pi$
$38$	8.58586	1.39281
$39$	6.00076	0.960891
$40$	6.44122	1.01845
$41$	−2.83108	−0.442140	−0.221070	−	0.975258i	$-0.570955\pi$
$41$	−2.83108	−0.442140	−0.221070	+	0.975258i	$0.570955\pi$
$42$	4.30386	0.664099
$43$	−2.91875	−0.445105	−0.222552	−	0.974921i	$-0.571439\pi$
$43$	−2.91875	−0.445105	−0.222552	+	0.974921i	$0.571439\pi$
$44$	2.37565	0.358143
$45$	2.80284	0.417823
$46$	−12.7027	−1.87291
$47$	3.74023	0.545568	0.272784	−	0.962075i	$-0.412056\pi$
$47$	3.74023	0.545568	0.272784	+	0.962075i	$0.412056\pi$
$48$	0.898696	0.129716
$49$	−3.31392	−0.473417
$50$	6.40207	0.905389
$51$	−1.00000	−0.140028
$52$	−18.1533	−2.51741
$53$	−7.34892	−1.00945	−0.504726	−	0.863280i	$-0.668406\pi$
$53$	−7.34892	−1.00945	−0.504726	+	0.863280i	$0.668406\pi$
$54$	−2.24169	−0.305055
$55$	2.20106	0.296791
$56$	−4.41217	−0.589602
$57$	−3.83009	−0.507307
$58$	−9.03466	−1.18631
$59$	−0.402590	−0.0524128	−0.0262064	−	0.999657i	$-0.508343\pi$
$59$	−0.402590	−0.0524128	−0.0262064	+	0.999657i	$0.508343\pi$
$60$	−8.47906	−1.09464
$61$	1.15857	0.148339	0.0741697	−	0.997246i	$-0.476369\pi$
$61$	1.15857	0.148339	0.0741697	+	0.997246i	$0.476369\pi$
$62$	−18.0055	−2.28670
$63$	−1.91992	−0.241887
$64$	−13.0220	−1.62775
$65$	−16.8192	−2.08616
$66$	−1.76039	−0.216689
$67$	−6.92692	−0.846257	−0.423129	−	0.906070i	$-0.639068\pi$
$67$	−6.92692	−0.846257	−0.423129	+	0.906070i	$0.639068\pi$
$68$	3.02517	0.366855
$69$	5.66658	0.682176
$70$	−12.0630	−1.44181
$71$	15.3264	1.81891	0.909457	−	0.415798i	$-0.136498\pi$
$71$	15.3264	1.81891	0.909457	+	0.415798i	$0.136498\pi$
$72$	2.29811	0.270834
$73$	−6.75202	−0.790264	−0.395132	−	0.918624i	$-0.629301\pi$
$73$	−6.75202	−0.790264	−0.395132	+	0.918624i	$0.629301\pi$
$74$	6.06103	0.704580
$75$	−2.85591	−0.329772
$76$	11.5867	1.32908
$77$	−1.50770	−0.171819
$78$	13.4518	1.52312
$79$	6.24448	0.702559	0.351280	−	0.936271i	$-0.385747\pi$
$79$	6.24448	0.702559	0.351280	+	0.936271i	$0.385747\pi$
$80$	−2.51890	−0.281622
$81$	1.00000	0.111111
$82$	−6.34639	−0.700841
$83$	4.64860	0.510250	0.255125	−	0.966908i	$-0.417883\pi$
$83$	4.64860	0.510250	0.255125	+	0.966908i	$0.417883\pi$
$84$	5.80807	0.633713
$85$	2.80284	0.304011
$86$	−6.54293	−0.705542
$87$	4.03029	0.432093
$88$	1.80470	0.192381
$89$	−1.52421	−0.161566	−0.0807831	−	0.996732i	$-0.525742\pi$
$89$	−1.52421	−0.161566	−0.0807831	+	0.996732i	$0.525742\pi$
$90$	6.28309	0.662296
$91$	11.5210	1.20773
$92$	−17.1423	−1.78721
$93$	8.03212	0.832892
$94$	8.38442	0.864787
$95$	10.7351	1.10140
$96$	6.61081	0.674713
$97$	−7.11823	−0.722746	−0.361373	−	0.932421i	$-0.617692\pi$
$97$	−7.11823	−0.722746	−0.361373	+	0.932421i	$0.617692\pi$
$98$	−7.42877	−0.750419
$99$	0.785297	0.0789253
$100$	8.63961	0.863961
$101$	6.24785	0.621684	0.310842	−	0.950462i	$-0.399389\pi$
$101$	6.24785	0.621684	0.310842	+	0.950462i	$0.399389\pi$
$102$	−2.24169	−0.221960
$103$	2.56948	0.253178	0.126589	−	0.991955i	$-0.459597\pi$
$103$	2.56948	0.253178	0.126589	+	0.991955i	$0.459597\pi$
$104$	−13.7904	−1.35226
$105$	5.38122	0.525153
$106$	−16.4740	−1.60010
$107$	−6.51642	−0.629966	−0.314983	−	0.949097i	$-0.601999\pi$
$107$	−6.51642	−0.629966	−0.314983	+	0.949097i	$0.601999\pi$
$108$	−3.02517	−0.291097
$109$	8.53829	0.817820	0.408910	−	0.912575i	$-0.365909\pi$
$109$	8.53829	0.817820	0.408910	+	0.912575i	$0.365909\pi$
$110$	4.93409	0.470447
$111$	−2.70378	−0.256631
$112$	1.72542	0.163037
$113$	4.80278	0.451807	0.225904	−	0.974150i	$-0.427467\pi$
$113$	4.80278	0.451807	0.225904	+	0.974150i	$0.427467\pi$
$114$	−8.58586	−0.804139
$115$	−15.8825	−1.48105
$116$	−12.1923	−1.13203
$117$	−6.00076	−0.554771
$118$	−0.902482	−0.0830802
$119$	−1.91992	−0.175999
$120$	−6.44122	−0.588001
$121$	−10.3833	−0.943937
$122$	2.59715	0.235135
$123$	2.83108	0.255269
$124$	−24.2985	−2.18207
$125$	−6.00953	−0.537509
$126$	−4.30386	−0.383418
$127$	−5.79443	−0.514173	−0.257086	−	0.966388i	$-0.582763\pi$
$127$	−5.79443	−0.514173	−0.257086	+	0.966388i	$0.582763\pi$
$128$	−15.9696	−1.41153
$129$	2.91875	0.256981
$130$	−37.7034	−3.30680
$131$	1.33833	0.116931	0.0584654	−	0.998289i	$-0.481379\pi$
$131$	1.33833	0.116931	0.0584654	+	0.998289i	$0.481379\pi$
$132$	−2.37565	−0.206774
$133$	−7.35345	−0.637625
$134$	−15.5280	−1.34141
$135$	−2.80284	−0.241230
$136$	2.29811	0.197061
$137$	−8.80425	−0.752197	−0.376099	−	0.926580i	$-0.622735\pi$
$137$	−8.80425	−0.752197	−0.376099	+	0.926580i	$0.622735\pi$
$138$	12.7027	1.08133
$139$	−22.9810	−1.94922	−0.974611	−	0.223907i	$-0.928119\pi$
$139$	−22.9810	−1.94922	−0.974611	+	0.223907i	$0.928119\pi$
$140$	−16.2791	−1.37583
$141$	−3.74023	−0.314984
$142$	34.3571	2.88318
$143$	−4.71238	−0.394069
$144$	−0.898696	−0.0748914
$145$	−11.2963	−0.938104
$146$	−15.1359	−1.25266
$147$	3.31392	0.273327
$148$	8.17938	0.672341
$149$	13.1375	1.07626	0.538131	−	0.842861i	$-0.319130\pi$
$149$	13.1375	1.07626	0.538131	+	0.842861i	$0.319130\pi$
$150$	−6.40207	−0.522727
$151$	8.61536	0.701108	0.350554	−	0.936543i	$-0.385993\pi$
$151$	8.61536	0.701108	0.350554	+	0.936543i	$0.385993\pi$
$152$	8.80194	0.713932
$153$	1.00000	0.0808452
$154$	−3.37980	−0.272352
$155$	−22.5127	−1.80827
$156$	18.1533	1.45343
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	13.9982	1.11364
$159$	7.34892	0.582807
$160$	−18.5290	−1.46485
$161$	10.8794	0.857414
$162$	2.24169	0.176124
$163$	15.9706	1.25091	0.625456	−	0.780259i	$-0.284913\pi$
$163$	15.9706	1.25091	0.625456	+	0.780259i	$0.284913\pi$
$164$	−8.56448	−0.668773
$165$	−2.20106	−0.171352
$166$	10.4207	0.808804
$167$	−10.4871	−0.811515	−0.405758	−	0.913981i	$-0.632992\pi$
$167$	−10.4871	−0.811515	−0.405758	+	0.913981i	$0.632992\pi$
$168$	4.41217	0.340407
$169$	23.0091	1.76993
$170$	6.28309	0.481891
$171$	3.83009	0.292894
$172$	−8.82970	−0.673259
$173$	1.21634	0.0924770	0.0462385	−	0.998930i	$-0.485277\pi$
$173$	1.21634	0.0924770	0.0462385	+	0.998930i	$0.485277\pi$
$174$	9.03466	0.684916
$175$	−5.48312	−0.414485
$176$	−0.705743	−0.0531974
$177$	0.402590	0.0302605
$178$	−3.41681	−0.256101
$179$	−12.9207	−0.965740	−0.482870	−	0.875692i	$-0.660406\pi$
$179$	−12.9207	−0.965740	−0.482870	+	0.875692i	$0.660406\pi$
$180$	8.47906	0.631992
$181$	5.55402	0.412827	0.206413	−	0.978465i	$-0.433821\pi$
$181$	5.55402	0.412827	0.206413	+	0.978465i	$0.433821\pi$
$182$	25.8264	1.91438
$183$	−1.15857	−0.0856438
$184$	−13.0224	−0.960024
$185$	7.57826	0.557165
$186$	18.0055	1.32023
$187$	0.785297	0.0574266
$188$	11.3148	0.825217
$189$	1.91992	0.139653
$190$	24.0648	1.74584
$191$	−20.5649	−1.48802	−0.744012	−	0.668166i	$-0.767080\pi$
$191$	−20.5649	−1.48802	−0.744012	+	0.668166i	$0.767080\pi$
$192$	13.0220	0.939781
$193$	9.51401	0.684834	0.342417	−	0.939548i	$-0.388755\pi$
$193$	9.51401	0.684834	0.342417	+	0.939548i	$0.388755\pi$
$194$	−15.9568	−1.14563
$195$	16.8192	1.20445
$196$	−10.0252	−0.716083
$197$	−6.31380	−0.449840	−0.224920	−	0.974377i	$-0.572212\pi$
$197$	−6.31380	−0.449840	−0.224920	+	0.974377i	$0.572212\pi$
$198$	1.76039	0.125106
$199$	−16.9760	−1.20339	−0.601697	−	0.798725i	$-0.705508\pi$
$199$	−16.9760	−1.20339	−0.601697	+	0.798725i	$0.705508\pi$
$200$	6.56319	0.464088
$201$	6.92692	0.488587
$202$	14.0057	0.985440
$203$	7.73783	0.543089
$204$	−3.02517	−0.211804
$205$	−7.93505	−0.554208
$206$	5.75997	0.401316
$207$	−5.66658	−0.393854
$208$	5.39286	0.373928
$209$	3.00775	0.208051
$210$	12.0630	0.832428
$211$	13.7778	0.948504	0.474252	−	0.880389i	$-0.342718\pi$
$211$	13.7778	0.948504	0.474252	+	0.880389i	$0.342718\pi$
$212$	−22.2317	−1.52688
$213$	−15.3264	−1.05015
$214$	−14.6078	−0.998568
$215$	−8.18079	−0.557925
$216$	−2.29811	−0.156366
$217$	15.4210	1.04685
$218$	19.1402	1.29634
$219$	6.75202	0.456259
$220$	6.65858	0.448921
$221$	−6.00076	−0.403655
$222$	−6.06103	−0.406790
$223$	18.4352	1.23451	0.617257	−	0.786761i	$-0.288244\pi$
$223$	18.4352	1.23451	0.617257	+	0.786761i	$0.288244\pi$
$224$	12.6922	0.848034
$225$	2.85591	0.190394
$226$	10.7663	0.716166
$227$	−14.0586	−0.933105	−0.466553	−	0.884493i	$-0.654504\pi$
$227$	−14.0586	−0.933105	−0.466553	+	0.884493i	$0.654504\pi$
$228$	−11.5867	−0.767345
$229$	6.80994	0.450014	0.225007	−	0.974357i	$-0.427760\pi$
$229$	6.80994	0.450014	0.225007	+	0.974357i	$0.427760\pi$
$230$	−35.6036	−2.34764
$231$	1.50770	0.0991997
$232$	−9.26204	−0.608083
$233$	−14.6362	−0.958851	−0.479425	−	0.877583i	$-0.659155\pi$
$233$	−14.6362	−0.958851	−0.479425	+	0.877583i	$0.659155\pi$
$234$	−13.4518	−0.879374
$235$	10.4833	0.683852
$236$	−1.21790	−0.0792787
$237$	−6.24448	−0.405623
$238$	−4.30386	−0.278978
$239$	1.06519	0.0689012	0.0344506	−	0.999406i	$-0.489032\pi$
$239$	1.06519	0.0689012	0.0344506	+	0.999406i	$0.489032\pi$
$240$	2.51890	0.162594
$241$	22.8798	1.47382	0.736909	−	0.675992i	$-0.236284\pi$
$241$	22.8798	1.47382	0.736909	+	0.675992i	$0.236284\pi$
$242$	−23.2761	−1.49625
$243$	−1.00000	−0.0641500
$244$	3.50486	0.224376
$245$	−9.28838	−0.593413
$246$	6.34639	0.404631
$247$	−22.9834	−1.46240
$248$	−18.4587	−1.17213
$249$	−4.64860	−0.294593
$250$	−13.4715	−0.852013
$251$	5.54067	0.349724	0.174862	−	0.984593i	$-0.444052\pi$
$251$	5.54067	0.349724	0.174862	+	0.984593i	$0.444052\pi$
$252$	−5.80807	−0.365874
$253$	−4.44995	−0.279766
$254$	−12.9893	−0.815022
$255$	−2.80284	−0.175521
$256$	−9.75493	−0.609683
$257$	−4.99623	−0.311656	−0.155828	−	0.987784i	$-0.549805\pi$
$257$	−4.99623	−0.311656	−0.155828	+	0.987784i	$0.549805\pi$
$258$	6.54293	0.407345
$259$	−5.19103	−0.322555
$260$	−50.8808	−3.15550
$261$	−4.03029	−0.249469
$262$	3.00013	0.185349
$263$	2.59967	0.160302	0.0801512	−	0.996783i	$-0.474460\pi$
$263$	2.59967	0.160302	0.0801512	+	0.996783i	$0.474460\pi$
$264$	−1.80470	−0.111071
$265$	−20.5979	−1.26532
$266$	−16.4841	−1.01071
$267$	1.52421	0.0932802
$268$	−20.9551	−1.28004
$269$	2.95757	0.180327	0.0901633	−	0.995927i	$-0.471261\pi$
$269$	2.95757	0.180327	0.0901633	+	0.995927i	$0.471261\pi$
$270$	−6.28309	−0.382377
$271$	13.4729	0.818418	0.409209	−	0.912441i	$-0.365805\pi$
$271$	13.4729	0.818418	0.409209	+	0.912441i	$0.365805\pi$
$272$	−0.898696	−0.0544915
$273$	−11.5210	−0.697281
$274$	−19.7364	−1.19232
$275$	2.24274	0.135242
$276$	17.1423	1.03185
$277$	−4.18735	−0.251594	−0.125797	−	0.992056i	$-0.540149\pi$
$277$	−4.18735	−0.251594	−0.125797	+	0.992056i	$0.540149\pi$
$278$	−51.5162	−3.08974
$279$	−8.03212	−0.480870
$280$	−12.3666	−0.739047
$281$	7.27664	0.434088	0.217044	−	0.976162i	$-0.430359\pi$
$281$	7.27664	0.434088	0.217044	+	0.976162i	$0.430359\pi$
$282$	−8.38442	−0.499285
$283$	3.68981	0.219337	0.109668	−	0.993968i	$-0.465021\pi$
$283$	3.68981	0.219337	0.109668	+	0.993968i	$0.465021\pi$
$284$	46.3650	2.75126
$285$	−10.7351	−0.635894
$286$	−10.5637	−0.624644
$287$	5.43543	0.320843
$288$	−6.61081	−0.389546
$289$	1.00000	0.0588235
$290$	−25.3227	−1.48700
$291$	7.11823	0.417278
$292$	−20.4260	−1.19534
$293$	−26.5601	−1.55166	−0.775829	−	0.630944i	$-0.782668\pi$
$293$	−26.5601	−1.55166	−0.775829	+	0.630944i	$0.782668\pi$
$294$	7.42877	0.433255
$295$	−1.12840	−0.0656977
$296$	6.21357	0.361156
$297$	−0.785297	−0.0455675
$298$	29.4501	1.70600
$299$	34.0038	1.96649
$300$	−8.63961	−0.498808
$301$	5.60376	0.322995
$302$	19.3130	1.11134
$303$	−6.24785	−0.358929
$304$	−3.44208	−0.197417
$305$	3.24728	0.185939
$306$	2.24169	0.128149
$307$	11.5944	0.661729	0.330864	−	0.943678i	$-0.392660\pi$
$307$	11.5944	0.661729	0.330864	+	0.943678i	$0.392660\pi$
$308$	−4.56106	−0.259891
$309$	−2.56948	−0.146172
$310$	−50.4666	−2.86631
$311$	25.7781	1.46174	0.730870	−	0.682516i	$-0.239114\pi$
$311$	25.7781	1.46174	0.730870	+	0.682516i	$0.239114\pi$
$312$	13.7904	0.780727
$313$	8.70954	0.492292	0.246146	−	0.969233i	$-0.420836\pi$
$313$	8.70954	0.492292	0.246146	+	0.969233i	$0.420836\pi$
$314$	2.24169	0.126506
$315$	−5.38122	−0.303197
$316$	18.8906	1.06268
$317$	−26.4697	−1.48669	−0.743344	−	0.668909i	$-0.766761\pi$
$317$	−26.4697	−1.48669	−0.743344	+	0.668909i	$0.766761\pi$
$318$	16.4740	0.923816
$319$	−3.16498	−0.177205
$320$	−36.4985	−2.04033
$321$	6.51642	0.363711
$322$	24.3881	1.35910
$323$	3.83009	0.213112
$324$	3.02517	0.168065
$325$	−17.1377	−0.950626
$326$	35.8011	1.98284
$327$	−8.53829	−0.472169
$328$	−6.50611	−0.359240
$329$	−7.18092	−0.395897
$330$	−4.93409	−0.271613
$331$	10.7212	0.589289	0.294645	−	0.955607i	$-0.404799\pi$
$331$	10.7212	0.589289	0.294645	+	0.955607i	$0.404799\pi$
$332$	14.0628	0.771796
$333$	2.70378	0.148166
$334$	−23.5088	−1.28634
$335$	−19.4150	−1.06076
$336$	−1.72542	−0.0941295
$337$	−15.0852	−0.821741	−0.410870	−	0.911694i	$-0.634775\pi$
$337$	−15.0852	−0.821741	−0.410870	+	0.911694i	$0.634775\pi$
$338$	51.5793	2.80555
$339$	−4.80278	−0.260851
$340$	8.47906	0.459842
$341$	−6.30760	−0.341575
$342$	8.58586	0.464270
$343$	19.8019	1.06920
$344$	−6.70759	−0.361649
$345$	15.8825	0.855086
$346$	2.72667	0.146586
$347$	27.6963	1.48682	0.743408	−	0.668838i	$-0.233208\pi$
$347$	27.6963	1.48682	0.743408	+	0.668838i	$0.233208\pi$
$348$	12.1923	0.653577
$349$	−14.1794	−0.759008	−0.379504	−	0.925190i	$-0.623905\pi$
$349$	−14.1794	−0.759008	−0.379504	+	0.925190i	$0.623905\pi$
$350$	−12.2914	−0.657005
$351$	6.00076	0.320297
$352$	−5.19145	−0.276705
$353$	−31.7257	−1.68859	−0.844294	−	0.535881i	$-0.819980\pi$
$353$	−31.7257	−1.68859	−0.844294	+	0.535881i	$0.819980\pi$
$354$	0.902482	0.0479664
$355$	42.9576	2.27995
$356$	−4.61100	−0.244382
$357$	1.91992	0.101613
$358$	−28.9642	−1.53081
$359$	20.1235	1.06208	0.531039	−	0.847348i	$-0.321802\pi$
$359$	20.1235	1.06208	0.531039	+	0.847348i	$0.321802\pi$
$360$	6.44122	0.339482
$361$	−4.33044	−0.227918
$362$	12.4504	0.654377
$363$	10.3833	0.544982
$364$	34.8529	1.82679
$365$	−18.9248	−0.990570
$366$	−2.59715	−0.135755
$367$	−19.1666	−1.00049	−0.500244	−	0.865885i	$-0.666756\pi$
$367$	−19.1666	−1.00049	−0.500244	+	0.865885i	$0.666756\pi$
$368$	5.09253	0.265467
$369$	−2.83108	−0.147380
$370$	16.9881	0.883169
$371$	14.1093	0.732519
$372$	24.2985	1.25982
$373$	−25.3725	−1.31374	−0.656870	−	0.754004i	$-0.728120\pi$
$373$	−25.3725	−1.31374	−0.656870	+	0.754004i	$0.728120\pi$
$374$	1.76039	0.0910276
$375$	6.00953	0.310331
$376$	8.59544	0.443276
$377$	24.1848	1.24558
$378$	4.30386	0.221366
$379$	17.8517	0.916982	0.458491	−	0.888699i	$-0.348390\pi$
$379$	17.8517	0.916982	0.458491	+	0.888699i	$0.348390\pi$
$380$	32.4755	1.66596
$381$	5.79443	0.296858
$382$	−46.1001	−2.35869
$383$	−30.9555	−1.58175	−0.790876	−	0.611976i	$-0.790375\pi$
$383$	−30.9555	−1.58175	−0.790876	+	0.611976i	$0.790375\pi$
$384$	15.9696	0.814946
$385$	−4.22586	−0.215370
$386$	21.3275	1.08554
$387$	−2.91875	−0.148368
$388$	−21.5338	−1.09321
$389$	−15.5770	−0.789787	−0.394894	−	0.918727i	$-0.629219\pi$
$389$	−15.5770	−0.789787	−0.394894	+	0.918727i	$0.629219\pi$
$390$	37.7034	1.90918
$391$	−5.66658	−0.286571
$392$	−7.61574	−0.384653
$393$	−1.33833	−0.0675100
$394$	−14.1536	−0.713047
$395$	17.5023	0.880635
$396$	2.37565	0.119381
$397$	7.34593	0.368682	0.184341	−	0.982862i	$-0.440985\pi$
$397$	7.34593	0.368682	0.184341	+	0.982862i	$0.440985\pi$
$398$	−38.0548	−1.90751
$399$	7.35345	0.368133
$400$	−2.56660	−0.128330
$401$	5.37051	0.268190	0.134095	−	0.990968i	$-0.457187\pi$
$401$	5.37051	0.268190	0.134095	+	0.990968i	$0.457187\pi$
$402$	15.5280	0.774466
$403$	48.1988	2.40095
$404$	18.9008	0.940349
$405$	2.80284	0.139274
$406$	17.3458	0.860858
$407$	2.12327	0.105247
$408$	−2.29811	−0.113773
$409$	2.46697	0.121984	0.0609919	−	0.998138i	$-0.480574\pi$
$409$	2.46697	0.121984	0.0609919	+	0.998138i	$0.480574\pi$
$410$	−17.7879	−0.878482
$411$	8.80425	0.434281
$412$	7.77310	0.382953
$413$	0.772940	0.0380339
$414$	−12.7027	−0.624304
$415$	13.0293	0.639582
$416$	39.6699	1.94498
$417$	22.9810	1.12538
$418$	6.74245	0.329784
$419$	−5.28332	−0.258107	−0.129054	−	0.991638i	$-0.541194\pi$
$419$	−5.28332	−0.258107	−0.129054	+	0.991638i	$0.541194\pi$
$420$	16.2791	0.794339
$421$	14.7725	0.719970	0.359985	−	0.932958i	$-0.382782\pi$
$421$	14.7725	0.719970	0.359985	+	0.932958i	$0.382782\pi$
$422$	30.8856	1.50349
$423$	3.74023	0.181856
$424$	−16.8886	−0.820183
$425$	2.85591	0.138532
$426$	−34.3571	−1.66461
$427$	−2.22435	−0.107644
$428$	−19.7133	−0.952877
$429$	4.71238	0.227516
$430$	−18.3388	−0.884374
$431$	−14.0943	−0.678901	−0.339450	−	0.940624i	$-0.610241\pi$
$431$	−14.0943	−0.678901	−0.339450	+	0.940624i	$0.610241\pi$
$432$	0.898696	0.0432386
$433$	9.59451	0.461082	0.230541	−	0.973063i	$-0.425950\pi$
$433$	9.59451	0.461082	0.230541	+	0.973063i	$0.425950\pi$
$434$	34.5691	1.65937
$435$	11.2963	0.541615
$436$	25.8298	1.23702
$437$	−21.7035	−1.03822
$438$	15.1359	0.723222
$439$	7.34729	0.350667	0.175333	−	0.984509i	$-0.443900\pi$
$439$	7.34729	0.350667	0.175333	+	0.984509i	$0.443900\pi$
$440$	5.05827	0.241144
$441$	−3.31392	−0.157806
$442$	−13.4518	−0.639839
$443$	35.2832	1.67636	0.838178	−	0.545396i	$-0.183621\pi$
$443$	35.2832	1.67636	0.838178	+	0.545396i	$0.183621\pi$
$444$	−8.17938	−0.388176
$445$	−4.27212	−0.202518
$446$	41.3261	1.95685
$447$	−13.1375	−0.621381
$448$	25.0011	1.18119
$449$	−0.586275	−0.0276680	−0.0138340	−	0.999904i	$-0.504404\pi$
$449$	−0.586275	−0.0276680	−0.0138340	+	0.999904i	$0.504404\pi$
$450$	6.40207	0.301796
$451$	−2.22323	−0.104688
$452$	14.5292	0.683396
$453$	−8.61536	−0.404785
$454$	−31.5151	−1.47908
$455$	32.2914	1.51385
$456$	−8.80194	−0.412189
$457$	−1.46772	−0.0686573	−0.0343286	−	0.999411i	$-0.510929\pi$
$457$	−1.46772	−0.0686573	−0.0343286	+	0.999411i	$0.510929\pi$
$458$	15.2658	0.713323
$459$	−1.00000	−0.0466760
$460$	−48.0473	−2.24022
$461$	−11.1344	−0.518581	−0.259290	−	0.965799i	$-0.583489\pi$
$461$	−11.1344	−0.518581	−0.259290	+	0.965799i	$0.583489\pi$
$462$	3.37980	0.157243
$463$	1.17698	0.0546990	0.0273495	−	0.999626i	$-0.491293\pi$
$463$	1.17698	0.0546990	0.0273495	+	0.999626i	$0.491293\pi$
$464$	3.62201	0.168148
$465$	22.5127	1.04400
$466$	−32.8098	−1.51989
$467$	15.3745	0.711448	0.355724	−	0.934591i	$-0.384234\pi$
$467$	15.3745	0.711448	0.355724	+	0.934591i	$0.384234\pi$
$468$	−18.1533	−0.839137
$469$	13.2991	0.614096
$470$	23.5002	1.08398
$471$	−1.00000	−0.0460776
$472$	−0.925195	−0.0425855
$473$	−2.29208	−0.105390
$474$	−13.9982	−0.642958
$475$	10.9384	0.501888
$476$	−5.80807	−0.266213
$477$	−7.34892	−0.336484
$478$	2.38782	0.109216
$479$	37.6275	1.71924	0.859622	−	0.510931i	$-0.170699\pi$
$479$	37.6275	1.71924	0.859622	+	0.510931i	$0.170699\pi$
$480$	18.5290	0.845731
$481$	−16.2247	−0.739784
$482$	51.2894	2.33617
$483$	−10.8794	−0.495028
$484$	−31.4112	−1.42778
$485$	−19.9512	−0.905940
$486$	−2.24169	−0.101685
$487$	2.26963	0.102847	0.0514234	−	0.998677i	$-0.483624\pi$
$487$	2.26963	0.102847	0.0514234	+	0.998677i	$0.483624\pi$
$488$	2.66251	0.120526
$489$	−15.9706	−0.722215
$490$	−20.8217	−0.940627
$491$	−42.6418	−1.92440	−0.962200	−	0.272345i	$-0.912201\pi$
$491$	−42.6418	−1.92440	−0.962200	+	0.272345i	$0.912201\pi$
$492$	8.56448	0.386116
$493$	−4.03029	−0.181515
$494$	−51.5217	−2.31807
$495$	2.20106	0.0989304
$496$	7.21844	0.324117
$497$	−29.4255	−1.31991
$498$	−10.4207	−0.466963
$499$	−34.7360	−1.55500	−0.777498	−	0.628886i	$-0.783511\pi$
$499$	−34.7360	−1.55500	−0.777498	+	0.628886i	$0.783511\pi$
$500$	−18.1798	−0.813028
$501$	10.4871	0.468529
$502$	12.4205	0.554352
$503$	−1.77026	−0.0789319	−0.0394659	−	0.999221i	$-0.512566\pi$
$503$	−1.77026	−0.0789319	−0.0394659	+	0.999221i	$0.512566\pi$
$504$	−4.41217	−0.196534
$505$	17.5117	0.779261
$506$	−9.97539	−0.443460
$507$	−23.0091	−1.02187
$508$	−17.5291	−0.777730
$509$	−30.2526	−1.34092	−0.670461	−	0.741945i	$-0.733904\pi$
$509$	−30.2526	−1.34092	−0.670461	+	0.741945i	$0.733904\pi$
$510$	−6.28309	−0.278220
$511$	12.9633	0.573463
$512$	10.0717	0.445111
$513$	−3.83009	−0.169102
$514$	−11.2000	−0.494011
$515$	7.20184	0.317351
$516$	8.82970	0.388706
$517$	2.93719	0.129177
$518$	−11.6367	−0.511286
$519$	−1.21634	−0.0533916
$520$	−38.6523	−1.69501
$521$	−1.09078	−0.0477880	−0.0238940	−	0.999714i	$-0.507606\pi$
$521$	−1.09078	−0.0477880	−0.0238940	+	0.999714i	$0.507606\pi$
$522$	−9.03466	−0.395437
$523$	15.4511	0.675628	0.337814	−	0.941213i	$-0.390313\pi$
$523$	15.4511	0.675628	0.337814	+	0.941213i	$0.390313\pi$
$524$	4.04868	0.176868
$525$	5.48312	0.239303
$526$	5.82765	0.254097
$527$	−8.03212	−0.349885
$528$	0.705743	0.0307135
$529$	9.11011	0.396092
$530$	−46.1740	−2.00567
$531$	−0.402590	−0.0174709
$532$	−22.2454	−0.964461
$533$	16.9886	0.735858
$534$	3.41681	0.147860
$535$	−18.2645	−0.789643
$536$	−15.9188	−0.687587
$537$	12.9207	0.557570
$538$	6.62996	0.285838
$539$	−2.60241	−0.112094
$540$	−8.47906	−0.364881
$541$	33.3863	1.43539	0.717695	−	0.696358i	$-0.245197\pi$
$541$	33.3863	1.43539	0.717695	+	0.696358i	$0.245197\pi$
$542$	30.2020	1.29729
$543$	−5.55402	−0.238346
$544$	−6.61081	−0.283436
$545$	23.9315	1.02511
$546$	−25.8264	−1.10527
$547$	−18.2934	−0.782169	−0.391084	−	0.920355i	$-0.627900\pi$
$547$	−18.2934	−0.782169	−0.391084	+	0.920355i	$0.627900\pi$
$548$	−26.6343	−1.13776
$549$	1.15857	0.0494465
$550$	5.02752	0.214374
$551$	−15.4364	−0.657612
$552$	13.0224	0.554270
$553$	−11.9889	−0.509819
$554$	−9.38674	−0.398804
$555$	−7.57826	−0.321679
$556$	−69.5213	−2.94836
$557$	−41.0071	−1.73753	−0.868763	−	0.495228i	$-0.835085\pi$
$557$	−41.0071	−1.73753	−0.868763	+	0.495228i	$0.835085\pi$
$558$	−18.0055	−0.762234
$559$	17.5147	0.740794
$560$	4.83608	0.204362
$561$	−0.785297	−0.0331553
$562$	16.3120	0.688078
$563$	7.34321	0.309479	0.154740	−	0.987955i	$-0.450546\pi$
$563$	7.34321	0.309479	0.154740	+	0.987955i	$0.450546\pi$
$564$	−11.3148	−0.476439
$565$	13.4614	0.566326
$566$	8.27142	0.347674
$567$	−1.91992	−0.0806289
$568$	35.2218	1.47787
$569$	−44.3381	−1.85875	−0.929374	−	0.369139i	$-0.879653\pi$
$569$	−44.3381	−1.85875	−0.929374	+	0.369139i	$0.879653\pi$
$570$	−24.0648	−1.00796
$571$	−45.4208	−1.90080	−0.950401	−	0.311029i	$-0.899326\pi$
$571$	−45.4208	−1.90080	−0.950401	+	0.311029i	$0.899326\pi$
$572$	−14.2557	−0.596062
$573$	20.5649	0.859112
$574$	12.1845	0.508573
$575$	−16.1833	−0.674888
$576$	−13.0220	−0.542583
$577$	−14.4094	−0.599872	−0.299936	−	0.953959i	$-0.596965\pi$
$577$	−14.4094	−0.599872	−0.299936	+	0.953959i	$0.596965\pi$
$578$	2.24169	0.0932420
$579$	−9.51401	−0.395389
$580$	−34.1731	−1.41896
$581$	−8.92493	−0.370268
$582$	15.9568	0.661433
$583$	−5.77109	−0.239014
$584$	−15.5168	−0.642092
$585$	−16.8192	−0.695387
$586$	−59.5395	−2.45955
$587$	−16.4601	−0.679382	−0.339691	−	0.940537i	$-0.610322\pi$
$587$	−16.4601	−0.679382	−0.339691	+	0.940537i	$0.610322\pi$
$588$	10.0252	0.413430
$589$	−30.7637	−1.26760
$590$	−2.52951	−0.104138
$591$	6.31380	0.259715
$592$	−2.42988	−0.0998673
$593$	−2.54090	−0.104342	−0.0521712	−	0.998638i	$-0.516614\pi$
$593$	−2.54090	−0.104342	−0.0521712	+	0.998638i	$0.516614\pi$
$594$	−1.76039	−0.0722297
$595$	−5.38122	−0.220609
$596$	39.7430	1.62794
$597$	16.9760	0.694779
$598$	76.2259	3.11711
$599$	−21.1011	−0.862166	−0.431083	−	0.902312i	$-0.641868\pi$
$599$	−21.1011	−0.862166	−0.431083	+	0.902312i	$0.641868\pi$
$600$	−6.56319	−0.267941
$601$	−1.54771	−0.0631325	−0.0315662	−	0.999502i	$-0.510050\pi$
$601$	−1.54771	−0.0631325	−0.0315662	+	0.999502i	$0.510050\pi$
$602$	12.5619	0.511984
$603$	−6.92692	−0.282086
$604$	26.0629	1.06048
$605$	−29.1028	−1.18320
$606$	−14.0057	−0.568944
$607$	−5.60944	−0.227680	−0.113840	−	0.993499i	$-0.536315\pi$
$607$	−5.60944	−0.227680	−0.113840	+	0.993499i	$0.536315\pi$
$608$	−25.3200	−1.02686
$609$	−7.73783	−0.313553
$610$	7.27939	0.294734
$611$	−22.4442	−0.907995
$612$	3.02517	0.122285
$613$	5.38354	0.217439	0.108720	−	0.994072i	$-0.465325\pi$
$613$	5.38354	0.217439	0.108720	+	0.994072i	$0.465325\pi$
$614$	25.9911	1.04892
$615$	7.93505	0.319972
$616$	−3.46487	−0.139603
$617$	−8.99472	−0.362114	−0.181057	−	0.983473i	$-0.557952\pi$
$617$	−8.99472	−0.362114	−0.181057	+	0.983473i	$0.557952\pi$
$618$	−5.75997	−0.231700
$619$	4.94574	0.198786	0.0993930	−	0.995048i	$-0.468310\pi$
$619$	4.94574	0.198786	0.0993930	+	0.995048i	$0.468310\pi$
$620$	−68.1048	−2.73516
$621$	5.66658	0.227392
$622$	57.7864	2.31702
$623$	2.92636	0.117242
$624$	−5.39286	−0.215887
$625$	−31.1233	−1.24493
$626$	19.5241	0.780339
$627$	−3.00775	−0.120118
$628$	3.02517	0.120717
$629$	2.70378	0.107807
$630$	−12.0630	−0.480602
$631$	19.4335	0.773635	0.386817	−	0.922156i	$-0.373574\pi$
$631$	19.4335	0.773635	0.386817	+	0.922156i	$0.373574\pi$
$632$	14.3505	0.570832
$633$	−13.7778	−0.547619
$634$	−59.3369	−2.35657
$635$	−16.2409	−0.644499
$636$	22.2317	0.881545
$637$	19.8860	0.787913
$638$	−7.09489	−0.280890
$639$	15.3264	0.606305
$640$	−44.7603	−1.76931
$641$	20.9975	0.829352	0.414676	−	0.909969i	$-0.363895\pi$
$641$	20.9975	0.829352	0.414676	+	0.909969i	$0.363895\pi$
$642$	14.6078	0.576523
$643$	39.4522	1.55584	0.777922	−	0.628361i	$-0.216274\pi$
$643$	39.4522	1.55584	0.777922	+	0.628361i	$0.216274\pi$
$644$	32.9119	1.29691
$645$	8.18079	0.322118
$646$	8.58586	0.337806
$647$	18.0593	0.709985	0.354993	−	0.934869i	$-0.384483\pi$
$647$	18.0593	0.709985	0.354993	+	0.934869i	$0.384483\pi$
$648$	2.29811	0.0902781
$649$	−0.316153	−0.0124101
$650$	−38.4173	−1.50685
$651$	−15.4210	−0.604397
$652$	48.3137	1.89211
$653$	−8.67596	−0.339517	−0.169758	−	0.985486i	$-0.554299\pi$
$653$	−8.67596	−0.339517	−0.169758	+	0.985486i	$0.554299\pi$
$654$	−19.1402	−0.748441
$655$	3.75114	0.146569
$656$	2.54428	0.0993373
$657$	−6.75202	−0.263421
$658$	−16.0974	−0.627542
$659$	−0.112495	−0.00438220	−0.00219110	−	0.999998i	$-0.500697\pi$
$659$	−0.112495	−0.00438220	−0.00219110	+	0.999998i	$0.500697\pi$
$660$	−6.65858	−0.259185
$661$	32.3767	1.25931	0.629653	−	0.776877i	$-0.283197\pi$
$661$	32.3767	1.25931	0.629653	+	0.776877i	$0.283197\pi$
$662$	24.0335	0.934090
$663$	6.00076	0.233050
$664$	10.6830	0.414580
$665$	−20.6105	−0.799242
$666$	6.06103	0.234860
$667$	22.8380	0.884290
$668$	−31.7252	−1.22749
$669$	−18.4352	−0.712747
$670$	−43.5225	−1.68142
$671$	0.909820	0.0351232
$672$	−12.6922	−0.489613
$673$	1.30771	0.0504084	0.0252042	−	0.999682i	$-0.491976\pi$
$673$	1.30771	0.0504084	0.0252042	+	0.999682i	$0.491976\pi$
$674$	−33.8162	−1.30255
$675$	−2.85591	−0.109924
$676$	69.6065	2.67717
$677$	19.1955	0.737744	0.368872	−	0.929480i	$-0.379744\pi$
$677$	19.1955	0.737744	0.368872	+	0.929480i	$0.379744\pi$
$678$	−10.7663	−0.413478
$679$	13.6664	0.524468
$680$	6.44122	0.247010
$681$	14.0586	0.538729
$682$	−14.1397	−0.541436
$683$	44.3008	1.69512	0.847562	−	0.530696i	$-0.178069\pi$
$683$	44.3008	1.69512	0.847562	+	0.530696i	$0.178069\pi$
$684$	11.5867	0.443027
$685$	−24.6769	−0.942856
$686$	44.3896	1.69480
$687$	−6.80994	−0.259816
$688$	2.62307	0.100004
$689$	44.0991	1.68004
$690$	35.6036	1.35541
$691$	−36.3575	−1.38311	−0.691553	−	0.722326i	$-0.743073\pi$
$691$	−36.3575	−1.38311	−0.691553	+	0.722326i	$0.743073\pi$
$692$	3.67965	0.139879
$693$	−1.50770	−0.0572730
$694$	62.0865	2.35677
$695$	−64.4120	−2.44329
$696$	9.26204	0.351077
$697$	−2.83108	−0.107235
$698$	−31.7859	−1.20311
$699$	14.6362	0.553593
$700$	−16.5873	−0.626943
$701$	34.8999	1.31815	0.659076	−	0.752076i	$-0.270948\pi$
$701$	34.8999	1.31815	0.659076	+	0.752076i	$0.270948\pi$
$702$	13.4518	0.507707
$703$	10.3557	0.390573
$704$	−10.2261	−0.385412
$705$	−10.4833	−0.394822
$706$	−71.1191	−2.67660
$707$	−11.9954	−0.451132
$708$	1.21790	0.0457716
$709$	−40.5957	−1.52460	−0.762302	−	0.647221i	$-0.775931\pi$
$709$	−40.5957	−1.52460	−0.762302	+	0.647221i	$0.775931\pi$
$710$	96.2975	3.61398
$711$	6.24448	0.234186
$712$	−3.50280	−0.131273
$713$	45.5146	1.70454
$714$	4.30386	0.161068
$715$	−13.2080	−0.493953
$716$	−39.0873	−1.46076
$717$	−1.06519	−0.0397801
$718$	45.1106	1.68351
$719$	30.5391	1.13892	0.569458	−	0.822020i	$-0.307153\pi$
$719$	30.5391	1.13892	0.569458	+	0.822020i	$0.307153\pi$
$720$	−2.51890	−0.0938740
$721$	−4.93319	−0.183721
$722$	−9.70750	−0.361276
$723$	−22.8798	−0.850910
$724$	16.8018	0.624435
$725$	−11.5102	−0.427477
$726$	23.2761	0.863859
$727$	22.2438	0.824975	0.412488	−	0.910963i	$-0.364660\pi$
$727$	22.2438	0.824975	0.412488	+	0.910963i	$0.364660\pi$
$728$	26.4764	0.981281
$729$	1.00000	0.0370370
$730$	−42.4236	−1.57017
$731$	−2.91875	−0.107954
$732$	−3.50486	−0.129543
$733$	−36.2092	−1.33742	−0.668709	−	0.743524i	$-0.733153\pi$
$733$	−36.2092	−1.33742	−0.668709	+	0.743524i	$0.733153\pi$
$734$	−42.9655	−1.58589
$735$	9.28838	0.342607
$736$	37.4607	1.38082
$737$	−5.43969	−0.200373
$738$	−6.34639	−0.233614
$739$	−48.5862	−1.78727	−0.893637	−	0.448791i	$-0.851855\pi$
$739$	−48.5862	−1.78727	−0.893637	+	0.448791i	$0.851855\pi$
$740$	22.9255	0.842758
$741$	22.9834	0.844318
$742$	31.6287	1.16113
$743$	−15.0347	−0.551571	−0.275785	−	0.961219i	$-0.588938\pi$
$743$	−15.0347	−0.551571	−0.275785	+	0.961219i	$0.588938\pi$
$744$	18.4587	0.676727
$745$	36.8222	1.34906
$746$	−56.8773	−2.08243
$747$	4.64860	0.170083
$748$	2.37565	0.0868625
$749$	12.5110	0.457142
$750$	13.4715	0.491910
$751$	25.7568	0.939880	0.469940	−	0.882698i	$-0.344276\pi$
$751$	25.7568	0.939880	0.469940	+	0.882698i	$0.344276\pi$
$752$	−3.36133	−0.122575
$753$	−5.54067	−0.201913
$754$	54.2149	1.97439
$755$	24.1475	0.878816
$756$	5.80807	0.211238
$757$	28.3319	1.02974	0.514870	−	0.857268i	$-0.327840\pi$
$757$	28.3319	1.02974	0.514870	+	0.857268i	$0.327840\pi$
$758$	40.0180	1.45352
$759$	4.44995	0.161523
$760$	24.6704	0.894891
$761$	34.8073	1.26176	0.630881	−	0.775879i	$-0.282693\pi$
$761$	34.8073	1.26176	0.630881	+	0.775879i	$0.282693\pi$
$762$	12.9893	0.470553
$763$	−16.3928	−0.593460
$764$	−62.2123	−2.25076
$765$	2.80284	0.101337
$766$	−69.3926	−2.50726
$767$	2.41585	0.0872312
$768$	9.75493	0.352001
$769$	−22.3327	−0.805339	−0.402670	−	0.915345i	$-0.631918\pi$
$769$	−22.3327	−0.805339	−0.402670	+	0.915345i	$0.631918\pi$
$770$	−9.47305	−0.341385
$771$	4.99623	0.179935
$772$	28.7815	1.03587
$773$	23.2380	0.835814	0.417907	−	0.908490i	$-0.362764\pi$
$773$	23.2380	0.835814	0.417907	+	0.908490i	$0.362764\pi$
$774$	−6.54293	−0.235181
$775$	−22.9390	−0.823994
$776$	−16.3584	−0.587234
$777$	5.19103	0.186227
$778$	−34.9189	−1.25190
$779$	−10.8433	−0.388500
$780$	50.8808	1.82183
$781$	12.0358	0.430675
$782$	−12.7027	−0.454248
$783$	4.03029	0.144031
$784$	2.97821	0.106365
$785$	2.80284	0.100038
$786$	−3.00013	−0.107011
$787$	10.5862	0.377357	0.188679	−	0.982039i	$-0.439580\pi$
$787$	10.5862	0.377357	0.188679	+	0.982039i	$0.439580\pi$
$788$	−19.1003	−0.680420
$789$	−2.59967	−0.0925506
$790$	39.2347	1.39591
$791$	−9.22094	−0.327859
$792$	1.80470	0.0641271
$793$	−6.95229	−0.246883
$794$	16.4673	0.584402
$795$	20.5979	0.730531
$796$	−51.3551	−1.82023
$797$	10.8199	0.383262	0.191631	−	0.981467i	$-0.438622\pi$
$797$	10.8199	0.383262	0.191631	+	0.981467i	$0.438622\pi$
$798$	16.4841	0.583532
$799$	3.74023	0.132320
$800$	−18.8799	−0.667505
$801$	−1.52421	−0.0538554
$802$	12.0390	0.425112
$803$	−5.30234	−0.187115
$804$	20.9551	0.739029
$805$	30.4931	1.07474
$806$	108.047	3.80578
$807$	−2.95757	−0.104112
$808$	14.3582	0.505120
$809$	3.93755	0.138437	0.0692185	−	0.997602i	$-0.477949\pi$
$809$	3.93755	0.138437	0.0692185	+	0.997602i	$0.477949\pi$
$810$	6.28309	0.220765
$811$	9.51851	0.334240	0.167120	−	0.985937i	$-0.446553\pi$
$811$	9.51851	0.334240	0.167120	+	0.985937i	$0.446553\pi$
$812$	23.4082	0.821468
$813$	−13.4729	−0.472514
$814$	4.75971	0.166828
$815$	44.7630	1.56798
$816$	0.898696	0.0314607
$817$	−11.1791	−0.391106
$818$	5.53018	0.193358
$819$	11.5210	0.402575
$820$	−24.0049	−0.838286
$821$	−22.3478	−0.779944	−0.389972	−	0.920827i	$-0.627515\pi$
$821$	−22.3478	−0.779944	−0.389972	+	0.920827i	$0.627515\pi$
$822$	19.7364	0.688385
$823$	33.0388	1.15166	0.575831	−	0.817569i	$-0.304679\pi$
$823$	33.0388	1.15166	0.575831	+	0.817569i	$0.304679\pi$
$824$	5.90493	0.205708
$825$	−2.24274	−0.0780822
$826$	1.73269	0.0602880
$827$	28.4832	0.990460	0.495230	−	0.868762i	$-0.335084\pi$
$827$	28.4832	0.990460	0.495230	+	0.868762i	$0.335084\pi$
$828$	−17.1423	−0.595738
$829$	−37.5661	−1.30472	−0.652362	−	0.757908i	$-0.726222\pi$
$829$	−37.5661	−1.30472	−0.652362	+	0.757908i	$0.726222\pi$
$830$	29.2076	1.01381
$831$	4.18735	0.145258
$832$	78.1418	2.70908
$833$	−3.31392	−0.114820
$834$	51.5162	1.78386
$835$	−29.3936	−1.01721
$836$	9.09896	0.314694
$837$	8.03212	0.277631
$838$	−11.8436	−0.409129
$839$	36.9805	1.27671	0.638355	−	0.769742i	$-0.279615\pi$
$839$	36.9805	1.27671	0.638355	+	0.769742i	$0.279615\pi$
$840$	12.3666	0.426689
$841$	−12.7567	−0.439887
$842$	33.1154	1.14123
$843$	−7.27664	−0.250621
$844$	41.6802	1.43469
$845$	64.4910	2.21856
$846$	8.38442	0.288262
$847$	19.9351	0.684978
$848$	6.60445	0.226798
$849$	−3.68981	−0.126634
$850$	6.40207	0.219589
$851$	−15.3212	−0.525203
$852$	−46.3650	−1.58844
$853$	8.96218	0.306859	0.153430	−	0.988160i	$-0.450968\pi$
$853$	8.96218	0.306859	0.153430	+	0.988160i	$0.450968\pi$
$854$	−4.98631	−0.170628
$855$	10.7351	0.367133
$856$	−14.9754	−0.511850
$857$	−19.2496	−0.657555	−0.328777	−	0.944407i	$-0.606637\pi$
$857$	−19.2496	−0.657555	−0.328777	+	0.944407i	$0.606637\pi$
$858$	10.5637	0.360638
$859$	−16.4478	−0.561192	−0.280596	−	0.959826i	$-0.590532\pi$
$859$	−16.4478	−0.561192	−0.280596	+	0.959826i	$0.590532\pi$
$860$	−24.7482	−0.843908
$861$	−5.43543	−0.185239
$862$	−31.5951	−1.07613
$863$	−24.8778	−0.846851	−0.423425	−	0.905931i	$-0.639172\pi$
$863$	−24.8778	−0.846851	−0.423425	+	0.905931i	$0.639172\pi$
$864$	6.61081	0.224904
$865$	3.40922	0.115917
$866$	21.5079	0.730868
$867$	−1.00000	−0.0339618
$868$	46.6511	1.58344
$869$	4.90377	0.166349
$870$	25.3227	0.858521
$871$	41.5668	1.40844
$872$	19.6219	0.664481
$873$	−7.11823	−0.240915
$874$	−48.6524	−1.64569
$875$	11.5378	0.390049
$876$	20.4260	0.690130
$877$	−3.59939	−0.121543	−0.0607713	−	0.998152i	$-0.519356\pi$
$877$	−3.59939	−0.121543	−0.0607713	+	0.998152i	$0.519356\pi$
$878$	16.4703	0.555847
$879$	26.5601	0.895850
$880$	−1.97809	−0.0666813
$881$	−5.20265	−0.175282	−0.0876408	−	0.996152i	$-0.527933\pi$
$881$	−5.20265	−0.175282	−0.0876408	+	0.996152i	$0.527933\pi$
$882$	−7.42877	−0.250140
$883$	32.6696	1.09942	0.549710	−	0.835355i	$-0.314738\pi$
$883$	32.6696	1.09942	0.549710	+	0.835355i	$0.314738\pi$
$884$	−18.1533	−0.610562
$885$	1.12840	0.0379306
$886$	79.0940	2.65722
$887$	−26.7980	−0.899788	−0.449894	−	0.893082i	$-0.648538\pi$
$887$	−26.7980	−0.899788	−0.449894	+	0.893082i	$0.648538\pi$
$888$	−6.21357	−0.208514
$889$	11.1248	0.373115
$890$	−9.57677	−0.321014
$891$	0.785297	0.0263084
$892$	55.7697	1.86731
$893$	14.3254	0.479381
$894$	−29.4501	−0.984959
$895$	−36.2147	−1.21052
$896$	30.6603	1.02429
$897$	−34.0038	−1.13535
$898$	−1.31425	−0.0438570
$899$	32.3718	1.07966
$900$	8.63961	0.287987
$901$	−7.34892	−0.244828
$902$	−4.98380	−0.165942
$903$	−5.60376	−0.186481
$904$	11.0373	0.367095
$905$	15.5670	0.517465
$906$	−19.3130	−0.641630
$907$	34.7555	1.15404	0.577018	−	0.816731i	$-0.304216\pi$
$907$	34.7555	1.15404	0.577018	+	0.816731i	$0.304216\pi$
$908$	−42.5298	−1.41140
$909$	6.24785	0.207228
$910$	72.3873	2.39962
$911$	15.4162	0.510763	0.255381	−	0.966840i	$-0.417799\pi$
$911$	15.4162	0.510763	0.255381	+	0.966840i	$0.417799\pi$
$912$	3.44208	0.113979
$913$	3.65053	0.120815
$914$	−3.29018	−0.108830
$915$	−3.24728	−0.107352
$916$	20.6012	0.680683
$917$	−2.56949	−0.0848520
$918$	−2.24169	−0.0739867
$919$	−20.4696	−0.675229	−0.337614	−	0.941285i	$-0.609620\pi$
$919$	−20.4696	−0.675229	−0.337614	+	0.941285i	$0.609620\pi$
$920$	−36.4997	−1.20336
$921$	−11.5944	−0.382049
$922$	−24.9599	−0.822009
$923$	−91.9703	−3.02724
$924$	4.56106	0.150048
$925$	7.72176	0.253890
$926$	2.63843	0.0867041
$927$	2.56948	0.0843927
$928$	26.6435	0.874616
$929$	10.8214	0.355039	0.177520	−	0.984117i	$-0.443193\pi$
$929$	10.8214	0.355039	0.177520	+	0.984117i	$0.443193\pi$
$930$	50.4666	1.65486
$931$	−12.6926	−0.415983
$932$	−44.2770	−1.45034
$933$	−25.7781	−0.843937
$934$	34.4649	1.12772
$935$	2.20106	0.0719824
$936$	−13.7904	−0.450753
$937$	1.80712	0.0590360	0.0295180	−	0.999564i	$-0.490603\pi$
$937$	1.80712	0.0590360	0.0295180	+	0.999564i	$0.490603\pi$
$938$	29.8125	0.973411
$939$	−8.70954	−0.284225
$940$	31.7136	1.03438
$941$	22.5348	0.734613	0.367306	−	0.930100i	$-0.380280\pi$
$941$	22.5348	0.734613	0.367306	+	0.930100i	$0.380280\pi$
$942$	−2.24169	−0.0730382
$943$	16.0425	0.522416
$944$	0.361806	0.0117758
$945$	5.38122	0.175051
$946$	−5.13814	−0.167055
$947$	4.34111	0.141067	0.0705336	−	0.997509i	$-0.477530\pi$
$947$	4.34111	0.141067	0.0705336	+	0.997509i	$0.477530\pi$
$948$	−18.8906	−0.613538
$949$	40.5172	1.31525
$950$	24.5205	0.795549
$951$	26.4697	0.858340
$952$	−4.41217	−0.142999
$953$	13.8010	0.447057	0.223528	−	0.974697i	$-0.428242\pi$
$953$	13.8010	0.447057	0.223528	+	0.974697i	$0.428242\pi$
$954$	−16.4740	−0.533365
$955$	−57.6402	−1.86519
$956$	3.22237	0.104219
$957$	3.16498	0.102309
$958$	84.3491	2.72520
$959$	16.9034	0.545840
$960$	36.4985	1.17799
$961$	33.5149	1.08113
$962$	−36.3708	−1.17264
$963$	−6.51642	−0.209989
$964$	69.2153	2.22927
$965$	26.6663	0.858417
$966$	−24.3881	−0.784676
$967$	36.4234	1.17130	0.585648	−	0.810565i	$-0.300840\pi$
$967$	36.4234	1.17130	0.585648	+	0.810565i	$0.300840\pi$
$968$	−23.8619	−0.766952
$969$	−3.83009	−0.123040
$970$	−44.7245	−1.43602
$971$	1.14126	0.0366247	0.0183123	−	0.999832i	$-0.494171\pi$
$971$	1.14126	0.0366247	0.0183123	+	0.999832i	$0.494171\pi$
$972$	−3.02517	−0.0970323
$973$	44.1216	1.41447
$974$	5.08780	0.163024
$975$	17.1377	0.548844
$976$	−1.04120	−0.0333280
$977$	−50.6349	−1.61995	−0.809977	−	0.586462i	$-0.800520\pi$
$977$	−50.6349	−1.61995	−0.809977	+	0.586462i	$0.800520\pi$
$978$	−35.8011	−1.14479
$979$	−1.19696	−0.0382550
$980$	−28.0989	−0.897587
$981$	8.53829	0.272607
$982$	−95.5897	−3.05039
$983$	27.4430	0.875296	0.437648	−	0.899146i	$-0.355812\pi$
$983$	27.4430	0.875296	0.437648	+	0.899146i	$0.355812\pi$
$984$	6.50611	0.207407
$985$	−17.6966	−0.563860
$986$	−9.03466	−0.287722
$987$	7.18092	0.228571
$988$	−69.5287	−2.21200
$989$	16.5393	0.525920
$990$	4.93409	0.156816
$991$	34.8382	1.10667	0.553336	−	0.832958i	$-0.313354\pi$
$991$	34.8382	1.10667	0.553336	+	0.832958i	$0.313354\pi$
$992$	53.0988	1.68589
$993$	−10.7212	−0.340226
$994$	−65.9628	−2.09221
$995$	−47.5809	−1.50842
$996$	−14.0628	−0.445597
$997$	3.06594	0.0970991	0.0485496	−	0.998821i	$-0.484540\pi$
$997$	3.06594	0.0970991	0.0485496	+	0.998821i	$0.484540\pi$
$998$	−77.8672	−2.46484
$999$	−2.70378	−0.0855438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.35	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.35	✓	39	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+2.24169 q^{2} -1.00000 q^{3} +3.02517 q^{4} +2.80284 q^{5} -2.24169 q^{6} -1.91992 q^{7} +2.29811 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.24169 q^{2} -1.00000 q^{3} +3.02517 q^{4} +2.80284 q^{5} -2.24169 q^{6} -1.91992 q^{7} +2.29811 q^{8} +1.00000 q^{9} +6.28309 q^{10} +0.785297 q^{11} -3.02517 q^{12} -6.00076 q^{13} -4.30386 q^{14} -2.80284 q^{15} -0.898696 q^{16} +1.00000 q^{17} +2.24169 q^{18} +3.83009 q^{19} +8.47906 q^{20} +1.91992 q^{21} +1.76039 q^{22} -5.66658 q^{23} -2.29811 q^{24} +2.85591 q^{25} -13.4518 q^{26} -1.00000 q^{27} -5.80807 q^{28} -4.03029 q^{29} -6.28309 q^{30} -8.03212 q^{31} -6.61081 q^{32} -0.785297 q^{33} +2.24169 q^{34} -5.38122 q^{35} +3.02517 q^{36} +2.70378 q^{37} +8.58586 q^{38} +6.00076 q^{39} +6.44122 q^{40} -2.83108 q^{41} +4.30386 q^{42} -2.91875 q^{43} +2.37565 q^{44} +2.80284 q^{45} -12.7027 q^{46} +3.74023 q^{47} +0.898696 q^{48} -3.31392 q^{49} +6.40207 q^{50} -1.00000 q^{51} -18.1533 q^{52} -7.34892 q^{53} -2.24169 q^{54} +2.20106 q^{55} -4.41217 q^{56} -3.83009 q^{57} -9.03466 q^{58} -0.402590 q^{59} -8.47906 q^{60} +1.15857 q^{61} -18.0055 q^{62} -1.91992 q^{63} -13.0220 q^{64} -16.8192 q^{65} -1.76039 q^{66} -6.92692 q^{67} +3.02517 q^{68} +5.66658 q^{69} -12.0630 q^{70} +15.3264 q^{71} +2.29811 q^{72} -6.75202 q^{73} +6.06103 q^{74} -2.85591 q^{75} +11.5867 q^{76} -1.50770 q^{77} +13.4518 q^{78} +6.24448 q^{79} -2.51890 q^{80} +1.00000 q^{81} -6.34639 q^{82} +4.64860 q^{83} +5.80807 q^{84} +2.80284 q^{85} -6.54293 q^{86} +4.03029 q^{87} +1.80470 q^{88} -1.52421 q^{89} +6.28309 q^{90} +11.5210 q^{91} -17.1423 q^{92} +8.03212 q^{93} +8.38442 q^{94} +10.7351 q^{95} +6.61081 q^{96} -7.11823 q^{97} -7.42877 q^{98} +0.785297 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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