LMFDB - Embedded newform 4034.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.58772 q^{3} +1.00000 q^{4} -1.78395 q^{5} -2.58772 q^{6} -0.188589 q^{7} +1.00000 q^{8} +3.69628 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.58772 q^{3} +1.00000 q^{4} -1.78395 q^{5} -2.58772 q^{6} -0.188589 q^{7} +1.00000 q^{8} +3.69628 q^{9} -1.78395 q^{10} -4.86180 q^{11} -2.58772 q^{12} +5.13586 q^{13} -0.188589 q^{14} +4.61637 q^{15} +1.00000 q^{16} -4.65888 q^{17} +3.69628 q^{18} -2.98794 q^{19} -1.78395 q^{20} +0.488016 q^{21} -4.86180 q^{22} -1.55744 q^{23} -2.58772 q^{24} -1.81751 q^{25} +5.13586 q^{26} -1.80179 q^{27} -0.188589 q^{28} -4.32676 q^{29} +4.61637 q^{30} +0.532625 q^{31} +1.00000 q^{32} +12.5810 q^{33} -4.65888 q^{34} +0.336434 q^{35} +3.69628 q^{36} +9.81373 q^{37} -2.98794 q^{38} -13.2902 q^{39} -1.78395 q^{40} +9.33695 q^{41} +0.488016 q^{42} -0.538781 q^{43} -4.86180 q^{44} -6.59400 q^{45} -1.55744 q^{46} -9.10544 q^{47} -2.58772 q^{48} -6.96443 q^{49} -1.81751 q^{50} +12.0559 q^{51} +5.13586 q^{52} -4.35604 q^{53} -1.80179 q^{54} +8.67322 q^{55} -0.188589 q^{56} +7.73195 q^{57} -4.32676 q^{58} -9.08011 q^{59} +4.61637 q^{60} -3.15788 q^{61} +0.532625 q^{62} -0.697079 q^{63} +1.00000 q^{64} -9.16214 q^{65} +12.5810 q^{66} +6.33901 q^{67} -4.65888 q^{68} +4.03020 q^{69} +0.336434 q^{70} +3.02151 q^{71} +3.69628 q^{72} -0.972022 q^{73} +9.81373 q^{74} +4.70320 q^{75} -2.98794 q^{76} +0.916883 q^{77} -13.2902 q^{78} +7.94337 q^{79} -1.78395 q^{80} -6.42633 q^{81} +9.33695 q^{82} +3.66356 q^{83} +0.488016 q^{84} +8.31123 q^{85} -0.538781 q^{86} +11.1964 q^{87} -4.86180 q^{88} +1.04812 q^{89} -6.59400 q^{90} -0.968568 q^{91} -1.55744 q^{92} -1.37828 q^{93} -9.10544 q^{94} +5.33035 q^{95} -2.58772 q^{96} +9.63424 q^{97} -6.96443 q^{98} -17.9706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.58772	−1.49402	−0.747010	−	0.664813i	$-0.768511\pi$
$3$	−2.58772	−1.49402	−0.747010	+	0.664813i	$0.768511\pi$
$4$	1.00000	0.500000
$5$	−1.78395	−0.797808	−0.398904	−	0.916993i	$-0.630609\pi$
$5$	−1.78395	−0.797808	−0.398904	+	0.916993i	$0.630609\pi$
$6$	−2.58772	−1.05643
$7$	−0.188589	−0.0712800	−0.0356400	−	0.999365i	$-0.511347\pi$
$7$	−0.188589	−0.0712800	−0.0356400	+	0.999365i	$0.511347\pi$
$8$	1.00000	0.353553
$9$	3.69628	1.23209
$10$	−1.78395	−0.564136
$11$	−4.86180	−1.46589	−0.732944	−	0.680289i	$-0.761854\pi$
$11$	−4.86180	−1.46589	−0.732944	+	0.680289i	$0.761854\pi$
$12$	−2.58772	−0.747010
$13$	5.13586	1.42443	0.712216	−	0.701960i	$-0.247692\pi$
$13$	5.13586	1.42443	0.712216	+	0.701960i	$0.247692\pi$
$14$	−0.188589	−0.0504026
$15$	4.61637	1.19194
$16$	1.00000	0.250000
$17$	−4.65888	−1.12994	−0.564972	−	0.825110i	$-0.691113\pi$
$17$	−4.65888	−1.12994	−0.564972	+	0.825110i	$0.691113\pi$
$18$	3.69628	0.871223
$19$	−2.98794	−0.685481	−0.342740	−	0.939430i	$-0.611355\pi$
$19$	−2.98794	−0.685481	−0.342740	+	0.939430i	$0.611355\pi$
$20$	−1.78395	−0.398904
$21$	0.488016	0.106494
$22$	−4.86180	−1.03654
$23$	−1.55744	−0.324748	−0.162374	−	0.986729i	$-0.551915\pi$
$23$	−1.55744	−0.324748	−0.162374	+	0.986729i	$0.551915\pi$
$24$	−2.58772	−0.528216
$25$	−1.81751	−0.363502
$26$	5.13586	1.00723
$27$	−1.80179	−0.346754
$28$	−0.188589	−0.0356400
$29$	−4.32676	−0.803459	−0.401730	−	0.915758i	$-0.631591\pi$
$29$	−4.32676	−0.803459	−0.401730	+	0.915758i	$0.631591\pi$
$30$	4.61637	0.842830
$31$	0.532625	0.0956623	0.0478312	−	0.998855i	$-0.484769\pi$
$31$	0.532625	0.0956623	0.0478312	+	0.998855i	$0.484769\pi$
$32$	1.00000	0.176777
$33$	12.5810	2.19006
$34$	−4.65888	−0.798992
$35$	0.336434	0.0568678
$36$	3.69628	0.616047
$37$	9.81373	1.61337	0.806684	−	0.590984i	$-0.201260\pi$
$37$	9.81373	1.61337	0.806684	+	0.590984i	$0.201260\pi$
$38$	−2.98794	−0.484708
$39$	−13.2902	−2.12813
$40$	−1.78395	−0.282068
$41$	9.33695	1.45819	0.729093	−	0.684414i	$-0.239942\pi$
$41$	9.33695	1.45819	0.729093	+	0.684414i	$0.239942\pi$
$42$	0.488016	0.0753025
$43$	−0.538781	−0.0821633	−0.0410817	−	0.999156i	$-0.513080\pi$
$43$	−0.538781	−0.0821633	−0.0410817	+	0.999156i	$0.513080\pi$
$44$	−4.86180	−0.732944
$45$	−6.59400	−0.982976
$46$	−1.55744	−0.229631
$47$	−9.10544	−1.32817	−0.664083	−	0.747659i	$-0.731178\pi$
$47$	−9.10544	−1.32817	−0.664083	+	0.747659i	$0.731178\pi$
$48$	−2.58772	−0.373505
$49$	−6.96443	−0.994919
$50$	−1.81751	−0.257035
$51$	12.0559	1.68816
$52$	5.13586	0.712216
$53$	−4.35604	−0.598348	−0.299174	−	0.954199i	$-0.596711\pi$
$53$	−4.35604	−0.598348	−0.299174	+	0.954199i	$0.596711\pi$
$54$	−1.80179	−0.245192
$55$	8.67322	1.16950
$56$	−0.188589	−0.0252013
$57$	7.73195	1.02412
$58$	−4.32676	−0.568132
$59$	−9.08011	−1.18213	−0.591065	−	0.806624i	$-0.701292\pi$
$59$	−9.08011	−1.18213	−0.591065	+	0.806624i	$0.701292\pi$
$60$	4.61637	0.595971
$61$	−3.15788	−0.404325	−0.202162	−	0.979352i	$-0.564797\pi$
$61$	−3.15788	−0.404325	−0.202162	+	0.979352i	$0.564797\pi$
$62$	0.532625	0.0676435
$63$	−0.697079	−0.0878237
$64$	1.00000	0.125000
$65$	−9.16214	−1.13642
$66$	12.5810	1.54861
$67$	6.33901	0.774433	0.387217	−	0.921989i	$-0.373437\pi$
$67$	6.33901	0.774433	0.387217	+	0.921989i	$0.373437\pi$
$68$	−4.65888	−0.564972
$69$	4.03020	0.485179
$70$	0.336434	0.0402116
$71$	3.02151	0.358588	0.179294	−	0.983796i	$-0.442619\pi$
$71$	3.02151	0.358588	0.179294	+	0.983796i	$0.442619\pi$
$72$	3.69628	0.435611
$73$	−0.972022	−0.113767	−0.0568833	−	0.998381i	$-0.518116\pi$
$73$	−0.972022	−0.113767	−0.0568833	+	0.998381i	$0.518116\pi$
$74$	9.81373	1.14082
$75$	4.70320	0.543079
$76$	−2.98794	−0.342740
$77$	0.916883	0.104488
$78$	−13.2902	−1.50481
$79$	7.94337	0.893699	0.446850	−	0.894609i	$-0.352546\pi$
$79$	7.94337	0.893699	0.446850	+	0.894609i	$0.352546\pi$
$80$	−1.78395	−0.199452
$81$	−6.42633	−0.714037
$82$	9.33695	1.03109
$83$	3.66356	0.402127	0.201064	−	0.979578i	$-0.435560\pi$
$83$	3.66356	0.402127	0.201064	+	0.979578i	$0.435560\pi$
$84$	0.488016	0.0532469
$85$	8.31123	0.901479
$86$	−0.538781	−0.0580982
$87$	11.1964	1.20038
$88$	−4.86180	−0.518269
$89$	1.04812	0.111100	0.0555501	−	0.998456i	$-0.482309\pi$
$89$	1.04812	0.111100	0.0555501	+	0.998456i	$0.482309\pi$
$90$	−6.59400	−0.695069
$91$	−0.968568	−0.101534
$92$	−1.55744	−0.162374
$93$	−1.37828	−0.142921
$94$	−9.10544	−0.939155
$95$	5.33035	0.546882
$96$	−2.58772	−0.264108
$97$	9.63424	0.978209	0.489104	−	0.872225i	$-0.337324\pi$
$97$	9.63424	0.978209	0.489104	+	0.872225i	$0.337324\pi$
$98$	−6.96443	−0.703514
$99$	−17.9706	−1.80611
$100$	−1.81751	−0.181751
$101$	13.1079	1.30429	0.652145	−	0.758094i	$-0.273869\pi$
$101$	13.1079	1.30429	0.652145	+	0.758094i	$0.273869\pi$
$102$	12.0559	1.19371
$103$	6.04571	0.595701	0.297851	−	0.954612i	$-0.403730\pi$
$103$	6.04571	0.595701	0.297851	+	0.954612i	$0.403730\pi$
$104$	5.13586	0.503613
$105$	−0.870597	−0.0849616
$106$	−4.35604	−0.423096
$107$	−11.8997	−1.15039	−0.575194	−	0.818017i	$-0.695074\pi$
$107$	−11.8997	−1.15039	−0.575194	+	0.818017i	$0.695074\pi$
$108$	−1.80179	−0.173377
$109$	11.9472	1.14433	0.572165	−	0.820138i	$-0.306104\pi$
$109$	11.9472	1.14433	0.572165	+	0.820138i	$0.306104\pi$
$110$	8.67322	0.826959
$111$	−25.3952	−2.41040
$112$	−0.188589	−0.0178200
$113$	−1.70874	−0.160745	−0.0803726	−	0.996765i	$-0.525611\pi$
$113$	−1.70874	−0.160745	−0.0803726	+	0.996765i	$0.525611\pi$
$114$	7.73195	0.724163
$115$	2.77839	0.259086
$116$	−4.32676	−0.401730
$117$	18.9836	1.75504
$118$	−9.08011	−0.835892
$119$	0.878615	0.0805425
$120$	4.61637	0.421415
$121$	12.6371	1.14883
$122$	−3.15788	−0.285901
$123$	−24.1614	−2.17856
$124$	0.532625	0.0478312
$125$	12.1621	1.08781
$126$	−0.697079	−0.0621008
$127$	−17.9684	−1.59444	−0.797220	−	0.603689i	$-0.793697\pi$
$127$	−17.9684	−1.59444	−0.797220	+	0.603689i	$0.793697\pi$
$128$	1.00000	0.0883883
$129$	1.39421	0.122754
$130$	−9.16214	−0.803573
$131$	12.7471	1.11372	0.556860	−	0.830607i	$-0.312006\pi$
$131$	12.7471	1.11372	0.556860	+	0.830607i	$0.312006\pi$
$132$	12.5810	1.09503
$133$	0.563493	0.0488611
$134$	6.33901	0.547607
$135$	3.21431	0.276643
$136$	−4.65888	−0.399496
$137$	1.53024	0.130737	0.0653686	−	0.997861i	$-0.479178\pi$
$137$	1.53024	0.130737	0.0653686	+	0.997861i	$0.479178\pi$
$138$	4.03020	0.343074
$139$	−13.2088	−1.12035	−0.560177	−	0.828373i	$-0.689267\pi$
$139$	−13.2088	−1.12035	−0.560177	+	0.828373i	$0.689267\pi$
$140$	0.336434	0.0284339
$141$	23.5623	1.98430
$142$	3.02151	0.253560
$143$	−24.9695	−2.08806
$144$	3.69628	0.308024
$145$	7.71874	0.641007
$146$	−0.972022	−0.0804451
$147$	18.0220	1.48643
$148$	9.81373	0.806684
$149$	4.94589	0.405183	0.202591	−	0.979263i	$-0.435064\pi$
$149$	4.94589	0.405183	0.202591	+	0.979263i	$0.435064\pi$
$150$	4.70320	0.384015
$151$	6.32400	0.514640	0.257320	−	0.966326i	$-0.417161\pi$
$151$	6.32400	0.514640	0.257320	+	0.966326i	$0.417161\pi$
$152$	−2.98794	−0.242354
$153$	−17.2206	−1.39220
$154$	0.916883	0.0738845
$155$	−0.950179	−0.0763202
$156$	−13.2902	−1.06406
$157$	8.30268	0.662626	0.331313	−	0.943521i	$-0.392508\pi$
$157$	8.30268	0.662626	0.331313	+	0.943521i	$0.392508\pi$
$158$	7.94337	0.631941
$159$	11.2722	0.893943
$160$	−1.78395	−0.141034
$161$	0.293715	0.0231480
$162$	−6.42633	−0.504900
$163$	21.5519	1.68808	0.844039	−	0.536282i	$-0.180171\pi$
$163$	21.5519	1.68808	0.844039	+	0.536282i	$0.180171\pi$
$164$	9.33695	0.729093
$165$	−22.4439	−1.74725
$166$	3.66356	0.284347
$167$	19.9134	1.54094	0.770472	−	0.637474i	$-0.220021\pi$
$167$	19.9134	1.54094	0.770472	+	0.637474i	$0.220021\pi$
$168$	0.488016	0.0376512
$169$	13.3771	1.02901
$170$	8.31123	0.637442
$171$	−11.0443	−0.844577
$172$	−0.538781	−0.0410817
$173$	24.7307	1.88024	0.940119	−	0.340848i	$-0.110714\pi$
$173$	24.7307	1.88024	0.940119	+	0.340848i	$0.110714\pi$
$174$	11.1964	0.848800
$175$	0.342763	0.0259104
$176$	−4.86180	−0.366472
$177$	23.4968	1.76613
$178$	1.04812	0.0785597
$179$	9.85095	0.736295	0.368147	−	0.929767i	$-0.379992\pi$
$179$	9.85095	0.736295	0.368147	+	0.929767i	$0.379992\pi$
$180$	−6.59400	−0.491488
$181$	12.5456	0.932508	0.466254	−	0.884651i	$-0.345603\pi$
$181$	12.5456	0.932508	0.466254	+	0.884651i	$0.345603\pi$
$182$	−0.968568	−0.0717951
$183$	8.17170	0.604069
$184$	−1.55744	−0.114816
$185$	−17.5072	−1.28716
$186$	−1.37828	−0.101061
$187$	22.6505	1.65637
$188$	−9.10544	−0.664083
$189$	0.339798	0.0247167
$190$	5.33035	0.386704
$191$	−15.3966	−1.11406	−0.557030	−	0.830492i	$-0.688059\pi$
$191$	−15.3966	−1.11406	−0.557030	+	0.830492i	$0.688059\pi$
$192$	−2.58772	−0.186752
$193$	16.3836	1.17932	0.589659	−	0.807652i	$-0.299262\pi$
$193$	16.3836	1.17932	0.589659	+	0.807652i	$0.299262\pi$
$194$	9.63424	0.691698
$195$	23.7090	1.69784
$196$	−6.96443	−0.497460
$197$	18.7570	1.33638	0.668191	−	0.743990i	$-0.267069\pi$
$197$	18.7570	1.33638	0.668191	+	0.743990i	$0.267069\pi$
$198$	−17.9706	−1.27711
$199$	−2.48325	−0.176033	−0.0880163	−	0.996119i	$-0.528053\pi$
$199$	−2.48325	−0.176033	−0.0880163	+	0.996119i	$0.528053\pi$
$200$	−1.81751	−0.128517
$201$	−16.4036	−1.15702
$202$	13.1079	0.922272
$203$	0.815980	0.0572706
$204$	12.0559	0.844080
$205$	−16.6567	−1.16335
$206$	6.04571	0.421224
$207$	−5.75672	−0.400120
$208$	5.13586	0.356108
$209$	14.5268	1.00484
$210$	−0.870597	−0.0600769
$211$	1.99921	0.137632	0.0688158	−	0.997629i	$-0.478078\pi$
$211$	1.99921	0.137632	0.0688158	+	0.997629i	$0.478078\pi$
$212$	−4.35604	−0.299174
$213$	−7.81883	−0.535737
$214$	−11.8997	−0.813448
$215$	0.961160	0.0655506
$216$	−1.80179	−0.122596
$217$	−0.100447	−0.00681881
$218$	11.9472	0.809164
$219$	2.51532	0.169969
$220$	8.67322	0.584749
$221$	−23.9274	−1.60953
$222$	−25.3952	−1.70441
$223$	14.3800	0.962955	0.481478	−	0.876458i	$-0.340100\pi$
$223$	14.3800	0.962955	0.481478	+	0.876458i	$0.340100\pi$
$224$	−0.188589	−0.0126006
$225$	−6.71803	−0.447869
$226$	−1.70874	−0.113664
$227$	21.3775	1.41888	0.709438	−	0.704768i	$-0.248949\pi$
$227$	21.3775	1.41888	0.709438	+	0.704768i	$0.248949\pi$
$228$	7.73195	0.512061
$229$	20.4269	1.34985	0.674924	−	0.737887i	$-0.264177\pi$
$229$	20.4269	1.34985	0.674924	+	0.737887i	$0.264177\pi$
$230$	2.77839	0.183202
$231$	−2.37263	−0.156108
$232$	−4.32676	−0.284066
$233$	−21.3711	−1.40007	−0.700033	−	0.714110i	$-0.746831\pi$
$233$	−21.3711	−1.40007	−0.700033	+	0.714110i	$0.746831\pi$
$234$	18.9836	1.24100
$235$	16.2437	1.05962
$236$	−9.08011	−0.591065
$237$	−20.5552	−1.33520
$238$	0.878615	0.0569521
$239$	9.90077	0.640428	0.320214	−	0.947345i	$-0.396245\pi$
$239$	9.90077	0.640428	0.320214	+	0.947345i	$0.396245\pi$
$240$	4.61637	0.297985
$241$	−15.2985	−0.985461	−0.492731	−	0.870182i	$-0.664001\pi$
$241$	−15.2985	−0.985461	−0.492731	+	0.870182i	$0.664001\pi$
$242$	12.6371	0.812342
$243$	22.0349	1.41354
$244$	−3.15788	−0.202162
$245$	12.4242	0.793755
$246$	−24.1614	−1.54047
$247$	−15.3457	−0.976421
$248$	0.532625	0.0338217
$249$	−9.48025	−0.600786
$250$	12.1621	0.769200
$251$	0.687735	0.0434095	0.0217047	−	0.999764i	$-0.493091\pi$
$251$	0.687735	0.0434095	0.0217047	+	0.999764i	$0.493091\pi$
$252$	−0.697079	−0.0439119
$253$	7.57194	0.476044
$254$	−17.9684	−1.12744
$255$	−21.5071	−1.34683
$256$	1.00000	0.0625000
$257$	−10.9865	−0.685320	−0.342660	−	0.939460i	$-0.611328\pi$
$257$	−10.9865	−0.685320	−0.342660	+	0.939460i	$0.611328\pi$
$258$	1.39421	0.0867999
$259$	−1.85076	−0.115001
$260$	−9.16214	−0.568212
$261$	−15.9929	−0.989938
$262$	12.7471	0.787518
$263$	−23.6982	−1.46129	−0.730647	−	0.682755i	$-0.760782\pi$
$263$	−23.6982	−1.46129	−0.730647	+	0.682755i	$0.760782\pi$
$264$	12.5810	0.774305
$265$	7.77097	0.477367
$266$	0.563493	0.0345500
$267$	−2.71223	−0.165986
$268$	6.33901	0.387217
$269$	−19.9262	−1.21492	−0.607462	−	0.794349i	$-0.707812\pi$
$269$	−19.9262	−1.21492	−0.607462	+	0.794349i	$0.707812\pi$
$270$	3.21431	0.195616
$271$	17.5399	1.06548	0.532738	−	0.846280i	$-0.321163\pi$
$271$	17.5399	1.06548	0.532738	+	0.846280i	$0.321163\pi$
$272$	−4.65888	−0.282486
$273$	2.50638	0.151693
$274$	1.53024	0.0924452
$275$	8.83636	0.532853
$276$	4.03020	0.242590
$277$	−5.49191	−0.329977	−0.164988	−	0.986296i	$-0.552759\pi$
$277$	−5.49191	−0.329977	−0.164988	+	0.986296i	$0.552759\pi$
$278$	−13.2088	−0.792209
$279$	1.96873	0.117865
$280$	0.336434	0.0201058
$281$	−7.19172	−0.429022	−0.214511	−	0.976722i	$-0.568816\pi$
$281$	−7.19172	−0.429022	−0.214511	+	0.976722i	$0.568816\pi$
$282$	23.5623	1.40312
$283$	−17.3016	−1.02848	−0.514238	−	0.857648i	$-0.671925\pi$
$283$	−17.3016	−1.02848	−0.514238	+	0.857648i	$0.671925\pi$
$284$	3.02151	0.179294
$285$	−13.7934	−0.817053
$286$	−24.9695	−1.47648
$287$	−1.76085	−0.103940
$288$	3.69628	0.217806
$289$	4.70518	0.276775
$290$	7.71874	0.453260
$291$	−24.9307	−1.46146
$292$	−0.972022	−0.0568833
$293$	3.35447	0.195970	0.0979850	−	0.995188i	$-0.468760\pi$
$293$	3.35447	0.195970	0.0979850	+	0.995188i	$0.468760\pi$
$294$	18.0220	1.05106
$295$	16.1985	0.943113
$296$	9.81373	0.570411
$297$	8.75993	0.508303
$298$	4.94589	0.286508
$299$	−7.99877	−0.462581
$300$	4.70320	0.271539
$301$	0.101608	0.00585660
$302$	6.32400	0.363905
$303$	−33.9197	−1.94863
$304$	−2.98794	−0.171370
$305$	5.63351	0.322574
$306$	−17.2206	−0.984434
$307$	9.72930	0.555281	0.277640	−	0.960685i	$-0.410448\pi$
$307$	9.72930	0.555281	0.277640	+	0.960685i	$0.410448\pi$
$308$	0.916883	0.0522442
$309$	−15.6446	−0.889989
$310$	−0.950179	−0.0539665
$311$	−20.2205	−1.14660	−0.573299	−	0.819346i	$-0.694337\pi$
$311$	−20.2205	−1.14660	−0.573299	+	0.819346i	$0.694337\pi$
$312$	−13.2902	−0.752407
$313$	24.0688	1.36045	0.680225	−	0.733003i	$-0.261882\pi$
$313$	24.0688	1.36045	0.680225	+	0.733003i	$0.261882\pi$
$314$	8.30268	0.468547
$315$	1.24356	0.0700665
$316$	7.94337	0.446850
$317$	−2.06845	−0.116176	−0.0580878	−	0.998311i	$-0.518500\pi$
$317$	−2.06845	−0.116176	−0.0580878	+	0.998311i	$0.518500\pi$
$318$	11.2722	0.632113
$319$	21.0358	1.17778
$320$	−1.78395	−0.0997260
$321$	30.7931	1.71870
$322$	0.293715	0.0163681
$323$	13.9205	0.774555
$324$	−6.42633	−0.357019
$325$	−9.33448	−0.517784
$326$	21.5519	1.19365
$327$	−30.9159	−1.70965
$328$	9.33695	0.515547
$329$	1.71719	0.0946716
$330$	−22.4439	−1.23549
$331$	−12.5101	−0.687618	−0.343809	−	0.939040i	$-0.611717\pi$
$331$	−12.5101	−0.687618	−0.343809	+	0.939040i	$0.611717\pi$
$332$	3.66356	0.201064
$333$	36.2743	1.98782
$334$	19.9134	1.08961
$335$	−11.3085	−0.617849
$336$	0.488016	0.0266234
$337$	−6.72045	−0.366086	−0.183043	−	0.983105i	$-0.558595\pi$
$337$	−6.72045	−0.366086	−0.183043	+	0.983105i	$0.558595\pi$
$338$	13.3771	0.727618
$339$	4.42175	0.240156
$340$	8.31123	0.450740
$341$	−2.58952	−0.140230
$342$	−11.0443	−0.597206
$343$	2.63354	0.142198
$344$	−0.538781	−0.0290491
$345$	−7.18970	−0.387080
$346$	24.7307	1.32953
$347$	−17.9500	−0.963608	−0.481804	−	0.876279i	$-0.660018\pi$
$347$	−17.9500	−0.963608	−0.481804	+	0.876279i	$0.660018\pi$
$348$	11.1964	0.600192
$349$	−17.5499	−0.939424	−0.469712	−	0.882820i	$-0.655642\pi$
$349$	−17.5499	−0.939424	−0.469712	+	0.882820i	$0.655642\pi$
$350$	0.342763	0.0183214
$351$	−9.25374	−0.493928
$352$	−4.86180	−0.259135
$353$	−5.78118	−0.307701	−0.153851	−	0.988094i	$-0.549167\pi$
$353$	−5.78118	−0.307701	−0.153851	+	0.988094i	$0.549167\pi$
$354$	23.4968	1.24884
$355$	−5.39024	−0.286084
$356$	1.04812	0.0555501
$357$	−2.27361	−0.120332
$358$	9.85095	0.520639
$359$	11.2088	0.591578	0.295789	−	0.955253i	$-0.404418\pi$
$359$	11.2088	0.591578	0.295789	+	0.955253i	$0.404418\pi$
$360$	−6.59400	−0.347534
$361$	−10.0722	−0.530116
$362$	12.5456	0.659383
$363$	−32.7012	−1.71637
$364$	−0.968568	−0.0507668
$365$	1.73404	0.0907639
$366$	8.17170	0.427142
$367$	20.5509	1.07275	0.536373	−	0.843981i	$-0.319794\pi$
$367$	20.5509	1.07275	0.536373	+	0.843981i	$0.319794\pi$
$368$	−1.55744	−0.0811869
$369$	34.5120	1.79662
$370$	−17.5072	−0.910158
$371$	0.821502	0.0426502
$372$	−1.37828	−0.0714607
$373$	28.2339	1.46189	0.730947	−	0.682434i	$-0.239079\pi$
$373$	28.2339	1.46189	0.730947	+	0.682434i	$0.239079\pi$
$374$	22.6505	1.17123
$375$	−31.4721	−1.62521
$376$	−9.10544	−0.469577
$377$	−22.2217	−1.14447
$378$	0.339798	0.0174773
$379$	−14.4738	−0.743469	−0.371735	−	0.928339i	$-0.621237\pi$
$379$	−14.4738	−0.743469	−0.371735	+	0.928339i	$0.621237\pi$
$380$	5.33035	0.273441
$381$	46.4972	2.38212
$382$	−15.3966	−0.787760
$383$	37.0287	1.89208	0.946038	−	0.324056i	$-0.105047\pi$
$383$	37.0287	1.89208	0.946038	+	0.324056i	$0.105047\pi$
$384$	−2.58772	−0.132054
$385$	−1.63568	−0.0833618
$386$	16.3836	0.833903
$387$	−1.99149	−0.101233
$388$	9.63424	0.489104
$389$	11.8961	0.603156	0.301578	−	0.953442i	$-0.402487\pi$
$389$	11.8961	0.603156	0.301578	+	0.953442i	$0.402487\pi$
$390$	23.7090	1.20055
$391$	7.25591	0.366947
$392$	−6.96443	−0.351757
$393$	−32.9859	−1.66392
$394$	18.7570	0.944964
$395$	−14.1706	−0.713001
$396$	−17.9706	−0.903056
$397$	25.1716	1.26333	0.631664	−	0.775243i	$-0.282372\pi$
$397$	25.1716	1.26333	0.631664	+	0.775243i	$0.282372\pi$
$398$	−2.48325	−0.124474
$399$	−1.45816	−0.0729994
$400$	−1.81751	−0.0908755
$401$	−9.88914	−0.493840	−0.246920	−	0.969036i	$-0.579418\pi$
$401$	−9.88914	−0.493840	−0.246920	+	0.969036i	$0.579418\pi$
$402$	−16.4036	−0.818136
$403$	2.73549	0.136264
$404$	13.1079	0.652145
$405$	11.4643	0.569665
$406$	0.815980	0.0404964
$407$	−47.7124	−2.36501
$408$	12.0559	0.596855
$409$	17.5995	0.870239	0.435120	−	0.900373i	$-0.356706\pi$
$409$	17.5995	0.870239	0.435120	+	0.900373i	$0.356706\pi$
$410$	−16.6567	−0.822615
$411$	−3.95983	−0.195324
$412$	6.04571	0.297851
$413$	1.71241	0.0842623
$414$	−5.75672	−0.282928
$415$	−6.53561	−0.320821
$416$	5.13586	0.251806
$417$	34.1806	1.67383
$418$	14.5268	0.710527
$419$	−10.5762	−0.516683	−0.258342	−	0.966054i	$-0.583176\pi$
$419$	−10.5762	−0.516683	−0.258342	+	0.966054i	$0.583176\pi$
$420$	−0.870597	−0.0424808
$421$	−25.9219	−1.26335	−0.631677	−	0.775231i	$-0.717633\pi$
$421$	−25.9219	−1.26335	−0.631677	+	0.775231i	$0.717633\pi$
$422$	1.99921	0.0973202
$423$	−33.6563	−1.63643
$424$	−4.35604	−0.211548
$425$	8.46756	0.410737
$426$	−7.81883	−0.378823
$427$	0.595542	0.0288203
$428$	−11.8997	−0.575194
$429$	64.6141	3.11960
$430$	0.961160	0.0463513
$431$	16.8848	0.813311	0.406656	−	0.913582i	$-0.366695\pi$
$431$	16.8848	0.813311	0.406656	+	0.913582i	$0.366695\pi$
$432$	−1.80179	−0.0866886
$433$	−35.1768	−1.69049	−0.845244	−	0.534380i	$-0.820545\pi$
$433$	−35.1768	−1.69049	−0.845244	+	0.534380i	$0.820545\pi$
$434$	−0.100447	−0.00482163
$435$	−19.9739	−0.957676
$436$	11.9472	0.572165
$437$	4.65352	0.222608
$438$	2.51532	0.120187
$439$	−12.5185	−0.597477	−0.298739	−	0.954335i	$-0.596566\pi$
$439$	−12.5185	−0.597477	−0.298739	+	0.954335i	$0.596566\pi$
$440$	8.67322	0.413480
$441$	−25.7425	−1.22583
$442$	−23.9274	−1.13811
$443$	−40.9333	−1.94480	−0.972400	−	0.233318i	$-0.925042\pi$
$443$	−40.9333	−1.94480	−0.972400	+	0.233318i	$0.925042\pi$
$444$	−25.3952	−1.20520
$445$	−1.86979	−0.0886367
$446$	14.3800	0.680912
$447$	−12.7986	−0.605351
$448$	−0.188589	−0.00891000
$449$	1.33855	0.0631702	0.0315851	−	0.999501i	$-0.489944\pi$
$449$	1.33855	0.0631702	0.0315851	+	0.999501i	$0.489944\pi$
$450$	−6.71803	−0.316691
$451$	−45.3944	−2.13754
$452$	−1.70874	−0.0803726
$453$	−16.3647	−0.768882
$454$	21.3775	1.00330
$455$	1.72788	0.0810043
$456$	7.73195	0.362082
$457$	−20.2618	−0.947805	−0.473902	−	0.880577i	$-0.657155\pi$
$457$	−20.2618	−0.947805	−0.473902	+	0.880577i	$0.657155\pi$
$458$	20.4269	0.954486
$459$	8.39432	0.391813
$460$	2.77839	0.129543
$461$	−7.41470	−0.345337	−0.172669	−	0.984980i	$-0.555239\pi$
$461$	−7.41470	−0.345337	−0.172669	+	0.984980i	$0.555239\pi$
$462$	−2.37263	−0.110385
$463$	2.77160	0.128807	0.0644035	−	0.997924i	$-0.479486\pi$
$463$	2.77160	0.128807	0.0644035	+	0.997924i	$0.479486\pi$
$464$	−4.32676	−0.200865
$465$	2.45879	0.114024
$466$	−21.3711	−0.989996
$467$	−29.9082	−1.38398	−0.691992	−	0.721905i	$-0.743267\pi$
$467$	−29.9082	−1.38398	−0.691992	+	0.721905i	$0.743267\pi$
$468$	18.9836	0.877518
$469$	−1.19547	−0.0552016
$470$	16.2437	0.749265
$471$	−21.4850	−0.989976
$472$	−9.08011	−0.417946
$473$	2.61944	0.120442
$474$	−20.5552	−0.944132
$475$	5.43061	0.249174
$476$	0.878615	0.0402712
$477$	−16.1012	−0.737221
$478$	9.90077	0.452851
$479$	−8.86741	−0.405162	−0.202581	−	0.979265i	$-0.564933\pi$
$479$	−8.86741	−0.405162	−0.202581	+	0.979265i	$0.564933\pi$
$480$	4.61637	0.210707
$481$	50.4020	2.29813
$482$	−15.2985	−0.696826
$483$	−0.760053	−0.0345836
$484$	12.6371	0.574413
$485$	−17.1870	−0.780423
$486$	22.0349	0.999524
$487$	−17.1123	−0.775430	−0.387715	−	0.921779i	$-0.626736\pi$
$487$	−17.1123	−0.775430	−0.387715	+	0.921779i	$0.626736\pi$
$488$	−3.15788	−0.142950
$489$	−55.7703	−2.52202
$490$	12.4242	0.561269
$491$	19.7307	0.890433	0.445217	−	0.895423i	$-0.353127\pi$
$491$	19.7307	0.890433	0.445217	+	0.895423i	$0.353127\pi$
$492$	−24.1614	−1.08928
$493$	20.1579	0.907865
$494$	−15.3457	−0.690434
$495$	32.0587	1.44093
$496$	0.532625	0.0239156
$497$	−0.569825	−0.0255601
$498$	−9.48025	−0.424820
$499$	−11.5043	−0.515003	−0.257502	−	0.966278i	$-0.582899\pi$
$499$	−11.5043	−0.515003	−0.257502	+	0.966278i	$0.582899\pi$
$500$	12.1621	0.543907
$501$	−51.5302	−2.30220
$502$	0.687735	0.0306951
$503$	37.0855	1.65356	0.826781	−	0.562524i	$-0.190170\pi$
$503$	37.0855	1.65356	0.826781	+	0.562524i	$0.190170\pi$
$504$	−0.697079	−0.0310504
$505$	−23.3840	−1.04057
$506$	7.57194	0.336614
$507$	−34.6161	−1.53736
$508$	−17.9684	−0.797220
$509$	39.4830	1.75005	0.875026	−	0.484076i	$-0.160844\pi$
$509$	39.4830	1.75005	0.875026	+	0.484076i	$0.160844\pi$
$510$	−21.5071	−0.952351
$511$	0.183313	0.00810928
$512$	1.00000	0.0441942
$513$	5.38364	0.237693
$514$	−10.9865	−0.484594
$515$	−10.7853	−0.475255
$516$	1.39421	0.0613768
$517$	44.2688	1.94694
$518$	−1.85076	−0.0813179
$519$	−63.9960	−2.80911
$520$	−9.16214	−0.401786
$521$	22.3360	0.978560	0.489280	−	0.872127i	$-0.337260\pi$
$521$	22.3360	0.978560	0.489280	+	0.872127i	$0.337260\pi$
$522$	−15.9929	−0.699992
$523$	7.71401	0.337310	0.168655	−	0.985675i	$-0.446058\pi$
$523$	7.71401	0.337310	0.168655	+	0.985675i	$0.446058\pi$
$524$	12.7471	0.556860
$525$	−0.886973	−0.0387107
$526$	−23.6982	−1.03329
$527$	−2.48144	−0.108093
$528$	12.5810	0.547516
$529$	−20.5744	−0.894539
$530$	7.77097	0.337549
$531$	−33.5627	−1.45650
$532$	0.563493	0.0244305
$533$	47.9533	2.07709
$534$	−2.71223	−0.117370
$535$	21.2285	0.917790
$536$	6.33901	0.273804
$537$	−25.4915	−1.10004
$538$	−19.9262	−0.859081
$539$	33.8597	1.45844
$540$	3.21431	0.138322
$541$	11.1053	0.477454	0.238727	−	0.971087i	$-0.423270\pi$
$541$	11.1053	0.477454	0.238727	+	0.971087i	$0.423270\pi$
$542$	17.5399	0.753405
$543$	−32.4645	−1.39319
$544$	−4.65888	−0.199748
$545$	−21.3132	−0.912956
$546$	2.50638	0.107263
$547$	−18.2371	−0.779761	−0.389880	−	0.920865i	$-0.627484\pi$
$547$	−18.2371	−0.779761	−0.389880	+	0.920865i	$0.627484\pi$
$548$	1.53024	0.0653686
$549$	−11.6724	−0.498167
$550$	8.83636	0.376784
$551$	12.9281	0.550756
$552$	4.03020	0.171537
$553$	−1.49803	−0.0637029
$554$	−5.49191	−0.233329
$555$	45.3038	1.92304
$556$	−13.2088	−0.560177
$557$	6.38777	0.270658	0.135329	−	0.990801i	$-0.456791\pi$
$557$	6.38777	0.270658	0.135329	+	0.990801i	$0.456791\pi$
$558$	1.96873	0.0833432
$559$	−2.76710	−0.117036
$560$	0.336434	0.0142169
$561$	−58.6132	−2.47465
$562$	−7.19172	−0.303365
$563$	−0.608978	−0.0256654	−0.0128327	−	0.999918i	$-0.504085\pi$
$563$	−0.608978	−0.0256654	−0.0128327	+	0.999918i	$0.504085\pi$
$564$	23.5623	0.992152
$565$	3.04832	0.128244
$566$	−17.3016	−0.727242
$567$	1.21194	0.0508966
$568$	3.02151	0.126780
$569$	34.4563	1.44448	0.722242	−	0.691641i	$-0.243112\pi$
$569$	34.4563	1.44448	0.722242	+	0.691641i	$0.243112\pi$
$570$	−13.7934	−0.577744
$571$	44.0686	1.84422	0.922108	−	0.386933i	$-0.126466\pi$
$571$	44.0686	1.84422	0.922108	+	0.386933i	$0.126466\pi$
$572$	−24.9695	−1.04403
$573$	39.8421	1.66443
$574$	−1.76085	−0.0734964
$575$	2.83065	0.118046
$576$	3.69628	0.154012
$577$	−15.4184	−0.641877	−0.320939	−	0.947100i	$-0.603998\pi$
$577$	−15.4184	−0.641877	−0.320939	+	0.947100i	$0.603998\pi$
$578$	4.70518	0.195710
$579$	−42.3961	−1.76192
$580$	7.71874	0.320503
$581$	−0.690907	−0.0286637
$582$	−24.9307	−1.03341
$583$	21.1782	0.877110
$584$	−0.972022	−0.0402225
$585$	−33.8659	−1.40018
$586$	3.35447	0.138572
$587$	−25.1760	−1.03912	−0.519562	−	0.854433i	$-0.673905\pi$
$587$	−25.1760	−1.03912	−0.519562	+	0.854433i	$0.673905\pi$
$588$	18.0220	0.743214
$589$	−1.59145	−0.0655747
$590$	16.1985	0.666882
$591$	−48.5378	−1.99658
$592$	9.81373	0.403342
$593$	−27.7690	−1.14033	−0.570167	−	0.821529i	$-0.693122\pi$
$593$	−27.7690	−1.14033	−0.570167	+	0.821529i	$0.693122\pi$
$594$	8.75993	0.359424
$595$	−1.56741	−0.0642575
$596$	4.94589	0.202591
$597$	6.42594	0.262996
$598$	−7.99877	−0.327094
$599$	22.9439	0.937461	0.468731	−	0.883341i	$-0.344712\pi$
$599$	22.9439	0.937461	0.468731	+	0.883341i	$0.344712\pi$
$600$	4.70320	0.192007
$601$	−5.69708	−0.232389	−0.116194	−	0.993227i	$-0.537070\pi$
$601$	−5.69708	−0.232389	−0.116194	+	0.993227i	$0.537070\pi$
$602$	0.101608	0.00414124
$603$	23.4308	0.954175
$604$	6.32400	0.257320
$605$	−22.5440	−0.916543
$606$	−33.9197	−1.37789
$607$	−1.86678	−0.0757701	−0.0378851	−	0.999282i	$-0.512062\pi$
$607$	−1.86678	−0.0757701	−0.0378851	+	0.999282i	$0.512062\pi$
$608$	−2.98794	−0.121177
$609$	−2.11153	−0.0855634
$610$	5.63351	0.228094
$611$	−46.7643	−1.89188
$612$	−17.2206	−0.696100
$613$	−2.67093	−0.107878	−0.0539389	−	0.998544i	$-0.517178\pi$
$613$	−2.67093	−0.107878	−0.0539389	+	0.998544i	$0.517178\pi$
$614$	9.72930	0.392643
$615$	43.1028	1.73807
$616$	0.916883	0.0369423
$617$	−17.1812	−0.691690	−0.345845	−	0.938292i	$-0.612408\pi$
$617$	−17.1812	−0.691690	−0.345845	+	0.938292i	$0.612408\pi$
$618$	−15.6446	−0.629318
$619$	24.5804	0.987971	0.493985	−	0.869470i	$-0.335540\pi$
$619$	24.5804	0.987971	0.493985	+	0.869470i	$0.335540\pi$
$620$	−0.950179	−0.0381601
$621$	2.80617	0.112608
$622$	−20.2205	−0.810767
$623$	−0.197664	−0.00791922
$624$	−13.2902	−0.532032
$625$	−12.6091	−0.504364
$626$	24.0688	0.961984
$627$	−37.5912	−1.50125
$628$	8.30268	0.331313
$629$	−45.7210	−1.82302
$630$	1.24356	0.0495445
$631$	25.8175	1.02778	0.513890	−	0.857856i	$-0.328204\pi$
$631$	25.8175	1.02778	0.513890	+	0.857856i	$0.328204\pi$
$632$	7.94337	0.315970
$633$	−5.17340	−0.205624
$634$	−2.06845	−0.0821486
$635$	32.0548	1.27206
$636$	11.2722	0.446972
$637$	−35.7684	−1.41719
$638$	21.0358	0.832817
$639$	11.1684	0.441814
$640$	−1.78395	−0.0705170
$641$	−2.84770	−0.112477	−0.0562387	−	0.998417i	$-0.517911\pi$
$641$	−2.84770	−0.112477	−0.0562387	+	0.998417i	$0.517911\pi$
$642$	30.7931	1.21531
$643$	−7.33837	−0.289397	−0.144699	−	0.989476i	$-0.546221\pi$
$643$	−7.33837	−0.289397	−0.144699	+	0.989476i	$0.546221\pi$
$644$	0.293715	0.0115740
$645$	−2.48721	−0.0979339
$646$	13.9205	0.547693
$647$	−24.3978	−0.959175	−0.479588	−	0.877494i	$-0.659214\pi$
$647$	−24.3978	−0.959175	−0.479588	+	0.877494i	$0.659214\pi$
$648$	−6.42633	−0.252450
$649$	44.1457	1.73287
$650$	−9.33448	−0.366128
$651$	0.259929	0.0101874
$652$	21.5519	0.844039
$653$	49.6987	1.94486	0.972430	−	0.233197i	$-0.0749187\pi$
$653$	49.6987	1.94486	0.972430	+	0.233197i	$0.0749187\pi$
$654$	−30.9159	−1.20891
$655$	−22.7402	−0.888534
$656$	9.33695	0.364547
$657$	−3.59287	−0.140171
$658$	1.71719	0.0669430
$659$	−2.60897	−0.101631	−0.0508155	−	0.998708i	$-0.516182\pi$
$659$	−2.60897	−0.101631	−0.0508155	+	0.998708i	$0.516182\pi$
$660$	−22.4439	−0.873626
$661$	−13.1593	−0.511837	−0.255919	−	0.966698i	$-0.582378\pi$
$661$	−13.1593	−0.511837	−0.255919	+	0.966698i	$0.582378\pi$
$662$	−12.5101	−0.486219
$663$	61.9173	2.40467
$664$	3.66356	0.142174
$665$	−1.00525	−0.0389818
$666$	36.2743	1.40560
$667$	6.73865	0.260922
$668$	19.9134	0.770472
$669$	−37.2114	−1.43867
$670$	−11.3085	−0.436885
$671$	15.3530	0.592695
$672$	0.488016	0.0188256
$673$	−35.2053	−1.35706	−0.678532	−	0.734571i	$-0.737384\pi$
$673$	−35.2053	−1.35706	−0.678532	+	0.734571i	$0.737384\pi$
$674$	−6.72045	−0.258862
$675$	3.27477	0.126046
$676$	13.3771	0.514503
$677$	−13.0763	−0.502565	−0.251282	−	0.967914i	$-0.580852\pi$
$677$	−13.0763	−0.502565	−0.251282	+	0.967914i	$0.580852\pi$
$678$	4.42175	0.169816
$679$	−1.81691	−0.0697267
$680$	8.31123	0.318721
$681$	−55.3190	−2.11983
$682$	−2.58952	−0.0991577
$683$	−40.4784	−1.54886	−0.774432	−	0.632657i	$-0.781964\pi$
$683$	−40.4784	−1.54886	−0.774432	+	0.632657i	$0.781964\pi$
$684$	−11.0443	−0.422289
$685$	−2.72988	−0.104303
$686$	2.63354	0.100549
$687$	−52.8591	−2.01670
$688$	−0.538781	−0.0205408
$689$	−22.3720	−0.852306
$690$	−7.18970	−0.273707
$691$	−8.91225	−0.339038	−0.169519	−	0.985527i	$-0.554221\pi$
$691$	−8.91225	−0.339038	−0.169519	+	0.985527i	$0.554221\pi$
$692$	24.7307	0.940119
$693$	3.38906	0.128740
$694$	−17.9500	−0.681374
$695$	23.5638	0.893827
$696$	11.1964	0.424400
$697$	−43.4997	−1.64767
$698$	−17.5499	−0.664273
$699$	55.3023	2.09173
$700$	0.342763	0.0129552
$701$	50.3952	1.90340	0.951700	−	0.307028i	$-0.0993346\pi$
$701$	50.3952	1.90340	0.951700	+	0.307028i	$0.0993346\pi$
$702$	−9.25374	−0.349260
$703$	−29.3228	−1.10593
$704$	−4.86180	−0.183236
$705$	−42.0341	−1.58309
$706$	−5.78118	−0.217578
$707$	−2.47202	−0.0929698
$708$	23.4968	0.883063
$709$	41.7789	1.56904	0.784519	−	0.620105i	$-0.212910\pi$
$709$	41.7789	1.56904	0.784519	+	0.620105i	$0.212910\pi$
$710$	−5.39024	−0.202292
$711$	29.3610	1.10112
$712$	1.04812	0.0392798
$713$	−0.829529	−0.0310661
$714$	−2.27361	−0.0850876
$715$	44.5445	1.66587
$716$	9.85095	0.368147
$717$	−25.6204	−0.956812
$718$	11.2088	0.418309
$719$	−16.3394	−0.609355	−0.304678	−	0.952456i	$-0.598549\pi$
$719$	−16.3394	−0.609355	−0.304678	+	0.952456i	$0.598549\pi$
$720$	−6.59400	−0.245744
$721$	−1.14016	−0.0424616
$722$	−10.0722	−0.374849
$723$	39.5881	1.47230
$724$	12.5456	0.466254
$725$	7.86393	0.292059
$726$	−32.7012	−1.21366
$727$	−14.9533	−0.554586	−0.277293	−	0.960785i	$-0.589437\pi$
$727$	−14.9533	−0.554586	−0.277293	+	0.960785i	$0.589437\pi$
$728$	−0.968568	−0.0358975
$729$	−37.7411	−1.39782
$730$	1.73404	0.0641798
$731$	2.51012	0.0928400
$732$	8.17170	0.302035
$733$	4.31730	0.159463	0.0797315	−	0.996816i	$-0.474594\pi$
$733$	4.31730	0.159463	0.0797315	+	0.996816i	$0.474594\pi$
$734$	20.5509	0.758547
$735$	−32.1504	−1.18589
$736$	−1.55744	−0.0574078
$737$	−30.8190	−1.13523
$738$	34.5120	1.27041
$739$	−28.6425	−1.05363	−0.526816	−	0.849979i	$-0.676614\pi$
$739$	−28.6425	−1.05363	−0.526816	+	0.849979i	$0.676614\pi$
$740$	−17.5072	−0.643579
$741$	39.7102	1.45879
$742$	0.821502	0.0301583
$743$	50.6615	1.85859	0.929295	−	0.369339i	$-0.120416\pi$
$743$	50.6615	1.85859	0.929295	+	0.369339i	$0.120416\pi$
$744$	−1.37828	−0.0505303
$745$	−8.82323	−0.323258
$746$	28.2339	1.03372
$747$	13.5415	0.495459
$748$	22.6505	0.828186
$749$	2.24416	0.0819997
$750$	−31.4721	−1.14920
$751$	−46.6551	−1.70247	−0.851235	−	0.524785i	$-0.824146\pi$
$751$	−46.6551	−1.70247	−0.851235	+	0.524785i	$0.824146\pi$
$752$	−9.10544	−0.332041
$753$	−1.77967	−0.0648546
$754$	−22.2217	−0.809265
$755$	−11.2817	−0.410584
$756$	0.339798	0.0123583
$757$	−14.0526	−0.510751	−0.255376	−	0.966842i	$-0.582199\pi$
$757$	−14.0526	−0.510751	−0.255376	+	0.966842i	$0.582199\pi$
$758$	−14.4738	−0.525712
$759$	−19.5940	−0.711218
$760$	5.33035	0.193352
$761$	52.8641	1.91632	0.958161	−	0.286230i	$-0.0924020\pi$
$761$	52.8641	1.91632	0.958161	+	0.286230i	$0.0924020\pi$
$762$	46.4972	1.68442
$763$	−2.25311	−0.0815679
$764$	−15.3966	−0.557030
$765$	30.7207	1.11071
$766$	37.0287	1.33790
$767$	−46.6342	−1.68386
$768$	−2.58772	−0.0933762
$769$	48.6194	1.75326	0.876631	−	0.481163i	$-0.159786\pi$
$769$	48.6194	1.75326	0.876631	+	0.481163i	$0.159786\pi$
$770$	−1.63568	−0.0589457
$771$	28.4300	1.02388
$772$	16.3836	0.589659
$773$	20.9686	0.754188	0.377094	−	0.926175i	$-0.376923\pi$
$773$	20.9686	0.754188	0.377094	+	0.926175i	$0.376923\pi$
$774$	−1.99149	−0.0715825
$775$	−0.968051	−0.0347734
$776$	9.63424	0.345849
$777$	4.78925	0.171814
$778$	11.8961	0.426496
$779$	−27.8983	−0.999559
$780$	23.7090	0.848920
$781$	−14.6900	−0.525649
$782$	7.25591	0.259471
$783$	7.79591	0.278603
$784$	−6.96443	−0.248730
$785$	−14.8116	−0.528648
$786$	−32.9859	−1.17657
$787$	29.3425	1.04595	0.522974	−	0.852349i	$-0.324822\pi$
$787$	29.3425	1.04595	0.522974	+	0.852349i	$0.324822\pi$
$788$	18.7570	0.668191
$789$	61.3243	2.18320
$790$	−14.1706	−0.504168
$791$	0.322251	0.0114579
$792$	−17.9706	−0.638557
$793$	−16.2184	−0.575933
$794$	25.1716	0.893307
$795$	−20.1091	−0.713195
$796$	−2.48325	−0.0880163
$797$	−4.91715	−0.174175	−0.0870873	−	0.996201i	$-0.527756\pi$
$797$	−4.91715	−0.174175	−0.0870873	+	0.996201i	$0.527756\pi$
$798$	−1.45816	−0.0516184
$799$	42.4212	1.50075
$800$	−1.81751	−0.0642587
$801$	3.87414	0.136886
$802$	−9.88914	−0.349198
$803$	4.72577	0.166769
$804$	−16.4036	−0.578509
$805$	−0.523975	−0.0184677
$806$	2.73549	0.0963535
$807$	51.5635	1.81512
$808$	13.1079	0.461136
$809$	51.7736	1.82026	0.910132	−	0.414319i	$-0.135980\pi$
$809$	51.7736	1.82026	0.910132	+	0.414319i	$0.135980\pi$
$810$	11.4643	0.402814
$811$	−9.24815	−0.324746	−0.162373	−	0.986729i	$-0.551915\pi$
$811$	−9.24815	−0.324746	−0.162373	+	0.986729i	$0.551915\pi$
$812$	0.815980	0.0286353
$813$	−45.3884	−1.59184
$814$	−47.7124	−1.67232
$815$	−38.4477	−1.34676
$816$	12.0559	0.422040
$817$	1.60985	0.0563214
$818$	17.5995	0.615352
$819$	−3.58010	−0.125099
$820$	−16.6567	−0.581677
$821$	17.2285	0.601277	0.300639	−	0.953738i	$-0.402800\pi$
$821$	17.2285	0.601277	0.300639	+	0.953738i	$0.402800\pi$
$822$	−3.95983	−0.138115
$823$	−23.0732	−0.804282	−0.402141	−	0.915578i	$-0.631734\pi$
$823$	−23.0732	−0.804282	−0.402141	+	0.915578i	$0.631734\pi$
$824$	6.04571	0.210612
$825$	−22.8660	−0.796093
$826$	1.71241	0.0595824
$827$	−5.07334	−0.176417	−0.0882087	−	0.996102i	$-0.528114\pi$
$827$	−5.07334	−0.176417	−0.0882087	+	0.996102i	$0.528114\pi$
$828$	−5.75672	−0.200060
$829$	13.6574	0.474343	0.237171	−	0.971468i	$-0.423780\pi$
$829$	13.6574	0.474343	0.237171	+	0.971468i	$0.423780\pi$
$830$	−6.53561	−0.226854
$831$	14.2115	0.492992
$832$	5.13586	0.178054
$833$	32.4465	1.12420
$834$	34.1806	1.18358
$835$	−35.5246	−1.22938
$836$	14.5268	0.502419
$837$	−0.959678	−0.0331713
$838$	−10.5762	−0.365350
$839$	29.8396	1.03018	0.515089	−	0.857137i	$-0.327759\pi$
$839$	29.8396	1.03018	0.515089	+	0.857137i	$0.327759\pi$
$840$	−0.870597	−0.0300385
$841$	−10.2791	−0.354453
$842$	−25.9219	−0.893327
$843$	18.6102	0.640968
$844$	1.99921	0.0688158
$845$	−23.8641	−0.820950
$846$	−33.6563	−1.15713
$847$	−2.38322	−0.0818883
$848$	−4.35604	−0.149587
$849$	44.7717	1.53656
$850$	8.46756	0.290435
$851$	−15.2842	−0.523937
$852$	−7.81883	−0.267869
$853$	−3.57858	−0.122528	−0.0612640	−	0.998122i	$-0.519513\pi$
$853$	−3.57858	−0.122528	−0.0612640	+	0.998122i	$0.519513\pi$
$854$	0.595542	0.0203790
$855$	19.7025	0.673811
$856$	−11.8997	−0.406724
$857$	−33.0036	−1.12738	−0.563690	−	0.825986i	$-0.690619\pi$
$857$	−33.0036	−1.12738	−0.563690	+	0.825986i	$0.690619\pi$
$858$	64.6141	2.20589
$859$	−10.3417	−0.352854	−0.176427	−	0.984314i	$-0.556454\pi$
$859$	−10.3417	−0.352854	−0.176427	+	0.984314i	$0.556454\pi$
$860$	0.961160	0.0327753
$861$	4.55658	0.155288
$862$	16.8848	0.575098
$863$	−53.7026	−1.82806	−0.914029	−	0.405649i	$-0.867045\pi$
$863$	−53.7026	−1.82806	−0.914029	+	0.405649i	$0.867045\pi$
$864$	−1.80179	−0.0612981
$865$	−44.1183	−1.50007
$866$	−35.1768	−1.19536
$867$	−12.1757	−0.413508
$868$	−0.100447	−0.00340941
$869$	−38.6191	−1.31006
$870$	−19.9739	−0.677179
$871$	32.5563	1.10313
$872$	11.9472	0.404582
$873$	35.6109	1.20525
$874$	4.65352	0.157408
$875$	−2.29364	−0.0775393
$876$	2.51532	0.0849847
$877$	17.2688	0.583126	0.291563	−	0.956552i	$-0.405825\pi$
$877$	17.2688	0.583126	0.291563	+	0.956552i	$0.405825\pi$
$878$	−12.5185	−0.422480
$879$	−8.68042	−0.292783
$880$	8.67322	0.292374
$881$	40.3331	1.35886	0.679429	−	0.733741i	$-0.262228\pi$
$881$	40.3331	1.35886	0.679429	+	0.733741i	$0.262228\pi$
$882$	−25.7425	−0.866796
$883$	27.5690	0.927771	0.463885	−	0.885895i	$-0.346455\pi$
$883$	27.5690	0.927771	0.463885	+	0.885895i	$0.346455\pi$
$884$	−23.9274	−0.804765
$885$	−41.9172	−1.40903
$886$	−40.9333	−1.37518
$887$	21.7101	0.728953	0.364476	−	0.931213i	$-0.381248\pi$
$887$	21.7101	0.728953	0.364476	+	0.931213i	$0.381248\pi$
$888$	−25.3952	−0.852206
$889$	3.38865	0.113652
$890$	−1.86979	−0.0626756
$891$	31.2435	1.04670
$892$	14.3800	0.481478
$893$	27.2065	0.910431
$894$	−12.7986	−0.428048
$895$	−17.5736	−0.587422
$896$	−0.188589	−0.00630032
$897$	20.6986	0.691105
$898$	1.33855	0.0446681
$899$	−2.30454	−0.0768608
$900$	−6.71803	−0.223934
$901$	20.2943	0.676100
$902$	−45.3944	−1.51147
$903$	−0.262934	−0.00874988
$904$	−1.70874	−0.0568320
$905$	−22.3808	−0.743963
$906$	−16.3647	−0.543682
$907$	−4.57008	−0.151747	−0.0758735	−	0.997117i	$-0.524175\pi$
$907$	−4.57008	−0.151747	−0.0758735	+	0.997117i	$0.524175\pi$
$908$	21.3775	0.709438
$909$	48.4507	1.60701
$910$	1.72788	0.0572787
$911$	39.9399	1.32327	0.661634	−	0.749827i	$-0.269863\pi$
$911$	39.9399	1.32327	0.661634	+	0.749827i	$0.269863\pi$
$912$	7.73195	0.256030
$913$	−17.8115	−0.589474
$914$	−20.2618	−0.670199
$915$	−14.5779	−0.481932
$916$	20.4269	0.674924
$917$	−2.40396	−0.0793859
$918$	8.39432	0.277054
$919$	−26.2921	−0.867298	−0.433649	−	0.901082i	$-0.642774\pi$
$919$	−26.2921	−0.867298	−0.433649	+	0.901082i	$0.642774\pi$
$920$	2.77839	0.0916009
$921$	−25.1767	−0.829600
$922$	−7.41470	−0.244190
$923$	15.5181	0.510784
$924$	−2.37263	−0.0780539
$925$	−17.8365	−0.586462
$926$	2.77160	0.0910803
$927$	22.3467	0.733960
$928$	−4.32676	−0.142033
$929$	−24.3855	−0.800062	−0.400031	−	0.916502i	$-0.631001\pi$
$929$	−24.3855	−0.800062	−0.400031	+	0.916502i	$0.631001\pi$
$930$	2.45879	0.0806270
$931$	20.8093	0.681998
$932$	−21.3711	−0.700033
$933$	52.3249	1.71304
$934$	−29.9082	−0.978625
$935$	−40.4075	−1.32147
$936$	18.9836	0.620499
$937$	−4.28486	−0.139980	−0.0699901	−	0.997548i	$-0.522297\pi$
$937$	−4.28486	−0.139980	−0.0699901	+	0.997548i	$0.522297\pi$
$938$	−1.19547	−0.0390334
$939$	−62.2833	−2.03254
$940$	16.2437	0.529811
$941$	−29.8128	−0.971869	−0.485934	−	0.873995i	$-0.661521\pi$
$941$	−29.8128	−0.971869	−0.485934	+	0.873995i	$0.661521\pi$
$942$	−21.4850	−0.700019
$943$	−14.5417	−0.473543
$944$	−9.08011	−0.295533
$945$	−0.606183	−0.0197192
$946$	2.61944	0.0851655
$947$	−20.4756	−0.665368	−0.332684	−	0.943038i	$-0.607954\pi$
$947$	−20.4756	−0.665368	−0.332684	+	0.943038i	$0.607954\pi$
$948$	−20.5552	−0.667602
$949$	−4.99217	−0.162053
$950$	5.43061	0.176192
$951$	5.35256	0.173569
$952$	0.878615	0.0284761
$953$	−16.9026	−0.547530	−0.273765	−	0.961797i	$-0.588269\pi$
$953$	−16.9026	−0.547530	−0.273765	+	0.961797i	$0.588269\pi$
$954$	−16.1012	−0.521294
$955$	27.4669	0.888807
$956$	9.90077	0.320214
$957$	−54.4348	−1.75963
$958$	−8.86741	−0.286493
$959$	−0.288587	−0.00931895
$960$	4.61637	0.148993
$961$	−30.7163	−0.990849
$962$	50.4020	1.62502
$963$	−43.9847	−1.41739
$964$	−15.2985	−0.492731
$965$	−29.2276	−0.940869
$966$	−0.760053	−0.0244543
$967$	1.78408	0.0573722	0.0286861	−	0.999588i	$-0.490868\pi$
$967$	1.78408	0.0573722	0.0286861	+	0.999588i	$0.490868\pi$
$968$	12.6371	0.406171
$969$	−36.0222	−1.15720
$970$	−17.1870	−0.551842
$971$	34.0379	1.09233	0.546165	−	0.837678i	$-0.316087\pi$
$971$	34.0379	1.09233	0.546165	+	0.837678i	$0.316087\pi$
$972$	22.0349	0.706770
$973$	2.49103	0.0798588
$974$	−17.1123	−0.548312
$975$	24.1550	0.773579
$976$	−3.15788	−0.101081
$977$	6.94628	0.222231	0.111116	−	0.993807i	$-0.464558\pi$
$977$	6.94628	0.222231	0.111116	+	0.993807i	$0.464558\pi$
$978$	−55.7703	−1.78334
$979$	−5.09573	−0.162860
$980$	12.4242	0.396877
$981$	44.1601	1.40992
$982$	19.7307	0.629631
$983$	−37.0341	−1.18120	−0.590602	−	0.806963i	$-0.701110\pi$
$983$	−37.0341	−1.18120	−0.590602	+	0.806963i	$0.701110\pi$
$984$	−24.1614	−0.770237
$985$	−33.4616	−1.06618
$986$	20.1579	0.641957
$987$	−4.44360	−0.141441
$988$	−15.3457	−0.488210
$989$	0.839116	0.0266823
$990$	32.0587	1.01889
$991$	−5.32775	−0.169241	−0.0846207	−	0.996413i	$-0.526968\pi$
$991$	−5.32775	−0.169241	−0.0846207	+	0.996413i	$0.526968\pi$
$992$	0.532625	0.0169109
$993$	32.3726	1.02731
$994$	−0.569825	−0.0180737
$995$	4.43000	0.140440
$996$	−9.48025	−0.300393
$997$	−24.1495	−0.764823	−0.382412	−	0.923992i	$-0.624906\pi$
$997$	−24.1495	−0.764823	−0.382412	+	0.923992i	$0.624906\pi$
$998$	−11.5043	−0.364162
$999$	−17.6823	−0.559442

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.6	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.6	✓	52	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.58772 q^{3} +1.00000 q^{4} -1.78395 q^{5} -2.58772 q^{6} -0.188589 q^{7} +1.00000 q^{8} +3.69628 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.58772 q^{3} +1.00000 q^{4} -1.78395 q^{5} -2.58772 q^{6} -0.188589 q^{7} +1.00000 q^{8} +3.69628 q^{9} -1.78395 q^{10} -4.86180 q^{11} -2.58772 q^{12} +5.13586 q^{13} -0.188589 q^{14} +4.61637 q^{15} +1.00000 q^{16} -4.65888 q^{17} +3.69628 q^{18} -2.98794 q^{19} -1.78395 q^{20} +0.488016 q^{21} -4.86180 q^{22} -1.55744 q^{23} -2.58772 q^{24} -1.81751 q^{25} +5.13586 q^{26} -1.80179 q^{27} -0.188589 q^{28} -4.32676 q^{29} +4.61637 q^{30} +0.532625 q^{31} +1.00000 q^{32} +12.5810 q^{33} -4.65888 q^{34} +0.336434 q^{35} +3.69628 q^{36} +9.81373 q^{37} -2.98794 q^{38} -13.2902 q^{39} -1.78395 q^{40} +9.33695 q^{41} +0.488016 q^{42} -0.538781 q^{43} -4.86180 q^{44} -6.59400 q^{45} -1.55744 q^{46} -9.10544 q^{47} -2.58772 q^{48} -6.96443 q^{49} -1.81751 q^{50} +12.0559 q^{51} +5.13586 q^{52} -4.35604 q^{53} -1.80179 q^{54} +8.67322 q^{55} -0.188589 q^{56} +7.73195 q^{57} -4.32676 q^{58} -9.08011 q^{59} +4.61637 q^{60} -3.15788 q^{61} +0.532625 q^{62} -0.697079 q^{63} +1.00000 q^{64} -9.16214 q^{65} +12.5810 q^{66} +6.33901 q^{67} -4.65888 q^{68} +4.03020 q^{69} +0.336434 q^{70} +3.02151 q^{71} +3.69628 q^{72} -0.972022 q^{73} +9.81373 q^{74} +4.70320 q^{75} -2.98794 q^{76} +0.916883 q^{77} -13.2902 q^{78} +7.94337 q^{79} -1.78395 q^{80} -6.42633 q^{81} +9.33695 q^{82} +3.66356 q^{83} +0.488016 q^{84} +8.31123 q^{85} -0.538781 q^{86} +11.1964 q^{87} -4.86180 q^{88} +1.04812 q^{89} -6.59400 q^{90} -0.968568 q^{91} -1.55744 q^{92} -1.37828 q^{93} -9.10544 q^{94} +5.33035 q^{95} -2.58772 q^{96} +9.63424 q^{97} -6.96443 q^{98} -17.9706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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