LMFDB - Embedded newform 8007.2.a.e.1.44

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:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.44
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)

$f(q)$	$=$	$q+2.33434 q^{2} +1.00000 q^{3} +3.44916 q^{4} -3.01300 q^{5} +2.33434 q^{6} +0.805971 q^{7} +3.38285 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.33434 q^{2} +1.00000 q^{3} +3.44916 q^{4} -3.01300 q^{5} +2.33434 q^{6} +0.805971 q^{7} +3.38285 q^{8} +1.00000 q^{9} -7.03338 q^{10} +0.210193 q^{11} +3.44916 q^{12} -2.50157 q^{13} +1.88141 q^{14} -3.01300 q^{15} +0.998405 q^{16} -1.00000 q^{17} +2.33434 q^{18} +1.78533 q^{19} -10.3923 q^{20} +0.805971 q^{21} +0.490663 q^{22} -1.54799 q^{23} +3.38285 q^{24} +4.07816 q^{25} -5.83952 q^{26} +1.00000 q^{27} +2.77993 q^{28} -7.23400 q^{29} -7.03338 q^{30} -7.38077 q^{31} -4.43508 q^{32} +0.210193 q^{33} -2.33434 q^{34} -2.42839 q^{35} +3.44916 q^{36} -10.0586 q^{37} +4.16757 q^{38} -2.50157 q^{39} -10.1925 q^{40} -8.23202 q^{41} +1.88141 q^{42} +10.4057 q^{43} +0.724991 q^{44} -3.01300 q^{45} -3.61354 q^{46} +11.1683 q^{47} +0.998405 q^{48} -6.35041 q^{49} +9.51984 q^{50} -1.00000 q^{51} -8.62831 q^{52} +10.4577 q^{53} +2.33434 q^{54} -0.633312 q^{55} +2.72648 q^{56} +1.78533 q^{57} -16.8867 q^{58} -7.17161 q^{59} -10.3923 q^{60} +5.34097 q^{61} -17.2293 q^{62} +0.805971 q^{63} -12.3498 q^{64} +7.53722 q^{65} +0.490663 q^{66} -12.4841 q^{67} -3.44916 q^{68} -1.54799 q^{69} -5.66870 q^{70} -11.5697 q^{71} +3.38285 q^{72} +1.18077 q^{73} -23.4802 q^{74} +4.07816 q^{75} +6.15788 q^{76} +0.169410 q^{77} -5.83952 q^{78} +10.8894 q^{79} -3.00819 q^{80} +1.00000 q^{81} -19.2164 q^{82} +8.24034 q^{83} +2.77993 q^{84} +3.01300 q^{85} +24.2905 q^{86} -7.23400 q^{87} +0.711051 q^{88} -9.83273 q^{89} -7.03338 q^{90} -2.01619 q^{91} -5.33928 q^{92} -7.38077 q^{93} +26.0707 q^{94} -5.37919 q^{95} -4.43508 q^{96} +10.5645 q^{97} -14.8240 q^{98} +0.210193 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	2.33434	1.65063	0.825315	−	0.564672i	$-0.190997\pi$
$2$	2.33434	1.65063	0.825315	+	0.564672i	$0.190997\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.44916	1.72458
$5$	−3.01300	−1.34745	−0.673727	−	0.738980i	$-0.735308\pi$
$5$	−3.01300	−1.34745	−0.673727	+	0.738980i	$0.735308\pi$
$6$	2.33434	0.952992
$7$	0.805971	0.304629	0.152314	−	0.988332i	$-0.451327\pi$
$7$	0.805971	0.304629	0.152314	+	0.988332i	$0.451327\pi$
$8$	3.38285	1.19602
$9$	1.00000	0.333333
$10$	−7.03338	−2.22415
$11$	0.210193	0.0633756	0.0316878	−	0.999498i	$-0.489912\pi$
$11$	0.210193	0.0633756	0.0316878	+	0.999498i	$0.489912\pi$
$12$	3.44916	0.995688
$13$	−2.50157	−0.693810	−0.346905	−	0.937900i	$-0.612767\pi$
$13$	−2.50157	−0.693810	−0.346905	+	0.937900i	$0.612767\pi$
$14$	1.88141	0.502829
$15$	−3.01300	−0.777953
$16$	0.998405	0.249601
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.33434	0.550210
$19$	1.78533	0.409582	0.204791	−	0.978806i	$-0.434349\pi$
$19$	1.78533	0.409582	0.204791	+	0.978806i	$0.434349\pi$
$20$	−10.3923	−2.32380
$21$	0.805971	0.175877
$22$	0.490663	0.104610
$23$	−1.54799	−0.322778	−0.161389	−	0.986891i	$-0.551597\pi$
$23$	−1.54799	−0.322778	−0.161389	+	0.986891i	$0.551597\pi$
$24$	3.38285	0.690521
$25$	4.07816	0.815633
$26$	−5.83952	−1.14522
$27$	1.00000	0.192450
$28$	2.77993	0.525357
$29$	−7.23400	−1.34332	−0.671660	−	0.740859i	$-0.734419\pi$
$29$	−7.23400	−1.34332	−0.671660	+	0.740859i	$0.734419\pi$
$30$	−7.03338	−1.28411
$31$	−7.38077	−1.32563	−0.662813	−	0.748785i	$-0.730638\pi$
$31$	−7.38077	−1.32563	−0.662813	+	0.748785i	$0.730638\pi$
$32$	−4.43508	−0.784018
$33$	0.210193	0.0365899
$34$	−2.33434	−0.400337
$35$	−2.42839	−0.410473
$36$	3.44916	0.574861
$37$	−10.0586	−1.65362	−0.826811	−	0.562480i	$-0.809847\pi$
$37$	−10.0586	−1.65362	−0.826811	+	0.562480i	$0.809847\pi$
$38$	4.16757	0.676068
$39$	−2.50157	−0.400571
$40$	−10.1925	−1.61158
$41$	−8.23202	−1.28563	−0.642813	−	0.766023i	$-0.722233\pi$
$41$	−8.23202	−1.28563	−0.642813	+	0.766023i	$0.722233\pi$
$42$	1.88141	0.290309
$43$	10.4057	1.58686	0.793429	−	0.608663i	$-0.208294\pi$
$43$	10.4057	1.58686	0.793429	+	0.608663i	$0.208294\pi$
$44$	0.724991	0.109296
$45$	−3.01300	−0.449151
$46$	−3.61354	−0.532788
$47$	11.1683	1.62907	0.814533	−	0.580118i	$-0.196993\pi$
$47$	11.1683	1.62907	0.814533	+	0.580118i	$0.196993\pi$
$48$	0.998405	0.144107
$49$	−6.35041	−0.907201
$50$	9.51984	1.34631
$51$	−1.00000	−0.140028
$52$	−8.62831	−1.19653
$53$	10.4577	1.43648	0.718238	−	0.695798i	$-0.244949\pi$
$53$	10.4577	1.43648	0.718238	+	0.695798i	$0.244949\pi$
$54$	2.33434	0.317664
$55$	−0.633312	−0.0853957
$56$	2.72648	0.364341
$57$	1.78533	0.236472
$58$	−16.8867	−2.21733
$59$	−7.17161	−0.933663	−0.466832	−	0.884346i	$-0.654605\pi$
$59$	−7.17161	−0.933663	−0.466832	+	0.884346i	$0.654605\pi$
$60$	−10.3923	−1.34164
$61$	5.34097	0.683841	0.341921	−	0.939729i	$-0.388923\pi$
$61$	5.34097	0.683841	0.341921	+	0.939729i	$0.388923\pi$
$62$	−17.2293	−2.18812
$63$	0.805971	0.101543
$64$	−12.3498	−1.54373
$65$	7.53722	0.934877
$66$	0.490663	0.0603965
$67$	−12.4841	−1.52518	−0.762588	−	0.646885i	$-0.776071\pi$
$67$	−12.4841	−1.52518	−0.762588	+	0.646885i	$0.776071\pi$
$68$	−3.44916	−0.418273
$69$	−1.54799	−0.186356
$70$	−5.66870	−0.677539
$71$	−11.5697	−1.37307	−0.686533	−	0.727098i	$-0.740868\pi$
$71$	−11.5697	−1.37307	−0.686533	+	0.727098i	$0.740868\pi$
$72$	3.38285	0.398672
$73$	1.18077	0.138199	0.0690993	−	0.997610i	$-0.477987\pi$
$73$	1.18077	0.138199	0.0690993	+	0.997610i	$0.477987\pi$
$74$	−23.4802	−2.72952
$75$	4.07816	0.470906
$76$	6.15788	0.706358
$77$	0.169410	0.0193060
$78$	−5.83952	−0.661195
$79$	10.8894	1.22516	0.612579	−	0.790409i	$-0.290132\pi$
$79$	10.8894	1.22516	0.612579	+	0.790409i	$0.290132\pi$
$80$	−3.00819	−0.336326
$81$	1.00000	0.111111
$82$	−19.2164	−2.12209
$83$	8.24034	0.904495	0.452247	−	0.891893i	$-0.350622\pi$
$83$	8.24034	0.904495	0.452247	+	0.891893i	$0.350622\pi$
$84$	2.77993	0.303315
$85$	3.01300	0.326806
$86$	24.2905	2.61932
$87$	−7.23400	−0.775567
$88$	0.711051	0.0757983
$89$	−9.83273	−1.04227	−0.521134	−	0.853475i	$-0.674491\pi$
$89$	−9.83273	−1.04227	−0.521134	+	0.853475i	$0.674491\pi$
$90$	−7.03338	−0.741383
$91$	−2.01619	−0.211354
$92$	−5.33928	−0.556658
$93$	−7.38077	−0.765350
$94$	26.0707	2.68899
$95$	−5.37919	−0.551893
$96$	−4.43508	−0.452653
$97$	10.5645	1.07266	0.536332	−	0.844007i	$-0.319809\pi$
$97$	10.5645	1.07266	0.536332	+	0.844007i	$0.319809\pi$
$98$	−14.8240	−1.49745
$99$	0.210193	0.0211252
$100$	14.0663	1.40663
$101$	−12.9343	−1.28701	−0.643506	−	0.765441i	$-0.722521\pi$
$101$	−12.9343	−1.28701	−0.643506	+	0.765441i	$0.722521\pi$
$102$	−2.33434	−0.231135
$103$	1.18927	0.117182	0.0585909	−	0.998282i	$-0.481339\pi$
$103$	1.18927	0.117182	0.0585909	+	0.998282i	$0.481339\pi$
$104$	−8.46242	−0.829808
$105$	−2.42839	−0.236987
$106$	24.4119	2.37109
$107$	−0.460731	−0.0445406	−0.0222703	−	0.999752i	$-0.507089\pi$
$107$	−0.460731	−0.0445406	−0.0222703	+	0.999752i	$0.507089\pi$
$108$	3.44916	0.331896
$109$	8.68386	0.831763	0.415882	−	0.909419i	$-0.363473\pi$
$109$	8.68386	0.831763	0.415882	+	0.909419i	$0.363473\pi$
$110$	−1.47837	−0.140957
$111$	−10.0586	−0.954719
$112$	0.804686	0.0760357
$113$	−14.0081	−1.31778	−0.658888	−	0.752241i	$-0.728973\pi$
$113$	−14.0081	−1.31778	−0.658888	+	0.752241i	$0.728973\pi$
$114$	4.16757	0.390328
$115$	4.66410	0.434929
$116$	−24.9513	−2.31667
$117$	−2.50157	−0.231270
$118$	−16.7410	−1.54113
$119$	−0.805971	−0.0738833
$120$	−10.1925	−0.930445
$121$	−10.9558	−0.995984
$122$	12.4677	1.12877
$123$	−8.23202	−0.742256
$124$	−25.4575	−2.28615
$125$	2.77749	0.248427
$126$	1.88141	0.167610
$127$	2.09797	0.186164	0.0930822	−	0.995658i	$-0.470328\pi$
$127$	2.09797	0.186164	0.0930822	+	0.995658i	$0.470328\pi$
$128$	−19.9585	−1.76410
$129$	10.4057	0.916173
$130$	17.5945	1.54314
$131$	−13.7280	−1.19942	−0.599708	−	0.800219i	$-0.704717\pi$
$131$	−13.7280	−1.19942	−0.599708	+	0.800219i	$0.704717\pi$
$132$	0.724991	0.0631023
$133$	1.43892	0.124770
$134$	−29.1422	−2.51750
$135$	−3.01300	−0.259318
$136$	−3.38285	−0.290077
$137$	14.6945	1.25543	0.627717	−	0.778442i	$-0.283990\pi$
$137$	14.6945	1.25543	0.627717	+	0.778442i	$0.283990\pi$
$138$	−3.61354	−0.307605
$139$	11.5687	0.981243	0.490622	−	0.871373i	$-0.336770\pi$
$139$	11.5687	0.981243	0.490622	+	0.871373i	$0.336770\pi$
$140$	−8.37592	−0.707894
$141$	11.1683	0.940541
$142$	−27.0076	−2.26643
$143$	−0.525812	−0.0439706
$144$	0.998405	0.0832004
$145$	21.7960	1.81006
$146$	2.75632	0.228115
$147$	−6.35041	−0.523773
$148$	−34.6937	−2.85181
$149$	2.16182	0.177103	0.0885515	−	0.996072i	$-0.471776\pi$
$149$	2.16182	0.177103	0.0885515	+	0.996072i	$0.471776\pi$
$150$	9.51984	0.777291
$151$	−13.9815	−1.13780	−0.568901	−	0.822406i	$-0.692631\pi$
$151$	−13.9815	−1.13780	−0.568901	+	0.822406i	$0.692631\pi$
$152$	6.03949	0.489867
$153$	−1.00000	−0.0808452
$154$	0.395460	0.0318671
$155$	22.2383	1.78622
$156$	−8.62831	−0.690818
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	25.4197	2.02228
$159$	10.4577	0.829349
$160$	13.3629	1.05643
$161$	−1.24764	−0.0983275
$162$	2.33434	0.183403
$163$	−20.4399	−1.60098	−0.800490	−	0.599346i	$-0.795427\pi$
$163$	−20.4399	−1.60098	−0.800490	+	0.599346i	$0.795427\pi$
$164$	−28.3936	−2.21717
$165$	−0.633312	−0.0493032
$166$	19.2358	1.49299
$167$	−7.74487	−0.599316	−0.299658	−	0.954047i	$-0.596873\pi$
$167$	−7.74487	−0.599316	−0.299658	+	0.954047i	$0.596873\pi$
$168$	2.72648	0.210352
$169$	−6.74217	−0.518628
$170$	7.03338	0.539435
$171$	1.78533	0.136527
$172$	35.8911	2.73667
$173$	23.6620	1.79899	0.899493	−	0.436936i	$-0.143936\pi$
$173$	23.6620	1.79899	0.899493	+	0.436936i	$0.143936\pi$
$174$	−16.8867	−1.28017
$175$	3.28688	0.248465
$176$	0.209858	0.0158186
$177$	−7.17161	−0.539051
$178$	−22.9530	−1.72040
$179$	7.66328	0.572781	0.286390	−	0.958113i	$-0.407545\pi$
$179$	7.66328	0.572781	0.286390	+	0.958113i	$0.407545\pi$
$180$	−10.3923	−0.774598
$181$	−6.29563	−0.467950	−0.233975	−	0.972243i	$-0.575173\pi$
$181$	−6.29563	−0.467950	−0.233975	+	0.972243i	$0.575173\pi$
$182$	−4.70648	−0.348868
$183$	5.34097	0.394816
$184$	−5.23662	−0.386049
$185$	30.3065	2.22818
$186$	−17.2293	−1.26331
$187$	−0.210193	−0.0153708
$188$	38.5213	2.80946
$189$	0.805971	0.0586258
$190$	−12.5569	−0.910971
$191$	−9.23979	−0.668567	−0.334284	−	0.942472i	$-0.608494\pi$
$191$	−9.23979	−0.668567	−0.334284	+	0.942472i	$0.608494\pi$
$192$	−12.3498	−0.891270
$193$	7.42968	0.534800	0.267400	−	0.963586i	$-0.413835\pi$
$193$	7.42968	0.534800	0.267400	+	0.963586i	$0.413835\pi$
$194$	24.6612	1.77057
$195$	7.53722	0.539751
$196$	−21.9036	−1.56454
$197$	−15.7636	−1.12311	−0.561554	−	0.827440i	$-0.689796\pi$
$197$	−15.7636	−1.12311	−0.561554	+	0.827440i	$0.689796\pi$
$198$	0.490663	0.0348699
$199$	4.79962	0.340236	0.170118	−	0.985424i	$-0.445585\pi$
$199$	4.79962	0.340236	0.170118	+	0.985424i	$0.445585\pi$
$200$	13.7958	0.975511
$201$	−12.4841	−0.880560
$202$	−30.1932	−2.12438
$203$	−5.83040	−0.409214
$204$	−3.44916	−0.241490
$205$	24.8031	1.73232
$206$	2.77615	0.193424
$207$	−1.54799	−0.107593
$208$	−2.49758	−0.173176
$209$	0.375263	0.0259575
$210$	−5.66870	−0.391177
$211$	−8.65142	−0.595589	−0.297794	−	0.954630i	$-0.596251\pi$
$211$	−8.65142	−0.595589	−0.297794	+	0.954630i	$0.596251\pi$
$212$	36.0703	2.47732
$213$	−11.5697	−0.792740
$214$	−1.07551	−0.0735200
$215$	−31.3524	−2.13822
$216$	3.38285	0.230174
$217$	−5.94869	−0.403823
$218$	20.2711	1.37293
$219$	1.18077	0.0797889
$220$	−2.18440	−0.147272
$221$	2.50157	0.168274
$222$	−23.4802	−1.57589
$223$	13.6820	0.916213	0.458107	−	0.888897i	$-0.348528\pi$
$223$	13.6820	0.916213	0.458107	+	0.888897i	$0.348528\pi$
$224$	−3.57454	−0.238834
$225$	4.07816	0.271878
$226$	−32.6998	−2.17516
$227$	−21.3227	−1.41524	−0.707619	−	0.706594i	$-0.750231\pi$
$227$	−21.3227	−1.41524	−0.707619	+	0.706594i	$0.750231\pi$
$228$	6.15788	0.407816
$229$	1.64624	0.108787	0.0543933	−	0.998520i	$-0.482678\pi$
$229$	1.64624	0.108787	0.0543933	+	0.998520i	$0.482678\pi$
$230$	10.8876	0.717908
$231$	0.169410	0.0111463
$232$	−24.4715	−1.60663
$233$	−4.81556	−0.315478	−0.157739	−	0.987481i	$-0.550420\pi$
$233$	−4.81556	−0.315478	−0.157739	+	0.987481i	$0.550420\pi$
$234$	−5.83952	−0.381741
$235$	−33.6501	−2.19509
$236$	−24.7360	−1.61018
$237$	10.8894	0.707346
$238$	−1.88141	−0.121954
$239$	12.7659	0.825758	0.412879	−	0.910786i	$-0.364523\pi$
$239$	12.7659	0.825758	0.412879	+	0.910786i	$0.364523\pi$
$240$	−3.00819	−0.194178
$241$	−12.1817	−0.784690	−0.392345	−	0.919818i	$-0.628336\pi$
$241$	−12.1817	−0.784690	−0.392345	+	0.919818i	$0.628336\pi$
$242$	−25.5747	−1.64400
$243$	1.00000	0.0641500
$244$	18.4219	1.17934
$245$	19.1338	1.22241
$246$	−19.2164	−1.22519
$247$	−4.46611	−0.284172
$248$	−24.9680	−1.58547
$249$	8.24034	0.522210
$250$	6.48363	0.410061
$251$	−29.7706	−1.87910	−0.939551	−	0.342409i	$-0.888757\pi$
$251$	−29.7706	−1.87910	−0.939551	+	0.342409i	$0.888757\pi$
$252$	2.77993	0.175119
$253$	−0.325377	−0.0204563
$254$	4.89738	0.307289
$255$	3.01300	0.188681
$256$	−21.8905	−1.36816
$257$	6.89417	0.430046	0.215023	−	0.976609i	$-0.431017\pi$
$257$	6.89417	0.430046	0.215023	+	0.976609i	$0.431017\pi$
$258$	24.2905	1.51226
$259$	−8.10693	−0.503740
$260$	25.9971	1.61227
$261$	−7.23400	−0.447774
$262$	−32.0458	−1.97979
$263$	6.05378	0.373292	0.186646	−	0.982427i	$-0.440238\pi$
$263$	6.05378	0.373292	0.186646	+	0.982427i	$0.440238\pi$
$264$	0.711051	0.0437622
$265$	−31.5090	−1.93558
$266$	3.35894	0.205950
$267$	−9.83273	−0.601754
$268$	−43.0597	−2.63029
$269$	4.60492	0.280767	0.140384	−	0.990097i	$-0.455166\pi$
$269$	4.60492	0.280767	0.140384	+	0.990097i	$0.455166\pi$
$270$	−7.03338	−0.428038
$271$	21.2581	1.29134	0.645668	−	0.763618i	$-0.276579\pi$
$271$	21.2581	1.29134	0.645668	+	0.763618i	$0.276579\pi$
$272$	−0.998405	−0.0605372
$273$	−2.01619	−0.122025
$274$	34.3020	2.07226
$275$	0.857202	0.0516912
$276$	−5.33928	−0.321387
$277$	1.12974	0.0678794	0.0339397	−	0.999424i	$-0.489195\pi$
$277$	1.12974	0.0678794	0.0339397	+	0.999424i	$0.489195\pi$
$278$	27.0053	1.61967
$279$	−7.38077	−0.441875
$280$	−8.21488	−0.490933
$281$	−29.5848	−1.76488	−0.882441	−	0.470423i	$-0.844101\pi$
$281$	−29.5848	−1.76488	−0.882441	+	0.470423i	$0.844101\pi$
$282$	26.0707	1.55249
$283$	−17.6514	−1.04926	−0.524632	−	0.851329i	$-0.675797\pi$
$283$	−17.6514	−1.04926	−0.524632	+	0.851329i	$0.675797\pi$
$284$	−39.9057	−2.36797
$285$	−5.37919	−0.318635
$286$	−1.22743	−0.0725792
$287$	−6.63477	−0.391638
$288$	−4.43508	−0.261339
$289$	1.00000	0.0588235
$290$	50.8795	2.98775
$291$	10.5645	0.619303
$292$	4.07266	0.238335
$293$	8.64625	0.505119	0.252560	−	0.967581i	$-0.418728\pi$
$293$	8.64625	0.505119	0.252560	+	0.967581i	$0.418728\pi$
$294$	−14.8240	−0.864556
$295$	21.6080	1.25807
$296$	−34.0267	−1.97776
$297$	0.210193	0.0121966
$298$	5.04643	0.292332
$299$	3.87240	0.223947
$300$	14.0663	0.812115
$301$	8.38672	0.483402
$302$	−32.6377	−1.87809
$303$	−12.9343	−0.743057
$304$	1.78248	0.102232
$305$	−16.0923	−0.921445
$306$	−2.33434	−0.133446
$307$	16.6426	0.949844	0.474922	−	0.880028i	$-0.342476\pi$
$307$	16.6426	0.949844	0.474922	+	0.880028i	$0.342476\pi$
$308$	0.584322	0.0332948
$309$	1.18927	0.0676549
$310$	51.9118	2.94839
$311$	14.2059	0.805544	0.402772	−	0.915300i	$-0.368047\pi$
$311$	14.2059	0.805544	0.402772	+	0.915300i	$0.368047\pi$
$312$	−8.46242	−0.479090
$313$	−9.53976	−0.539219	−0.269609	−	0.962970i	$-0.586895\pi$
$313$	−9.53976	−0.539219	−0.269609	+	0.962970i	$0.586895\pi$
$314$	2.33434	0.131735
$315$	−2.42839	−0.136824
$316$	37.5595	2.11289
$317$	4.23111	0.237643	0.118822	−	0.992916i	$-0.462088\pi$
$317$	4.23111	0.237643	0.118822	+	0.992916i	$0.462088\pi$
$318$	24.4119	1.36895
$319$	−1.52054	−0.0851338
$320$	37.2099	2.08010
$321$	−0.460731	−0.0257155
$322$	−2.91241	−0.162302
$323$	−1.78533	−0.0993382
$324$	3.44916	0.191620
$325$	−10.2018	−0.565894
$326$	−47.7139	−2.64263
$327$	8.68386	0.480219
$328$	−27.8477	−1.53763
$329$	9.00134	0.496260
$330$	−1.47837	−0.0813815
$331$	9.99683	0.549476	0.274738	−	0.961519i	$-0.411409\pi$
$331$	9.99683	0.549476	0.274738	+	0.961519i	$0.411409\pi$
$332$	28.4223	1.55988
$333$	−10.0586	−0.551207
$334$	−18.0792	−0.989249
$335$	37.6146	2.05510
$336$	0.804686	0.0438992
$337$	35.1802	1.91639	0.958195	−	0.286117i	$-0.0923645\pi$
$337$	35.1802	1.91639	0.958195	+	0.286117i	$0.0923645\pi$
$338$	−15.7385	−0.856064
$339$	−14.0081	−0.760818
$340$	10.3923	0.563603
$341$	−1.55139	−0.0840123
$342$	4.16757	0.225356
$343$	−10.7600	−0.580988
$344$	35.2010	1.89791
$345$	4.66410	0.251106
$346$	55.2352	2.96946
$347$	12.5869	0.675699	0.337850	−	0.941200i	$-0.390300\pi$
$347$	12.5869	0.675699	0.337850	+	0.941200i	$0.390300\pi$
$348$	−24.9513	−1.33753
$349$	21.8636	1.17033	0.585166	−	0.810914i	$-0.301029\pi$
$349$	21.8636	1.17033	0.585166	+	0.810914i	$0.301029\pi$
$350$	7.67271	0.410124
$351$	−2.50157	−0.133524
$352$	−0.932222	−0.0496876
$353$	−19.0946	−1.01630	−0.508151	−	0.861268i	$-0.669671\pi$
$353$	−19.0946	−1.01630	−0.508151	+	0.861268i	$0.669671\pi$
$354$	−16.7410	−0.889774
$355$	34.8594	1.85014
$356$	−33.9147	−1.79748
$357$	−0.805971	−0.0426565
$358$	17.8887	0.945449
$359$	−21.0810	−1.11261	−0.556307	−	0.830977i	$-0.687782\pi$
$359$	−21.0810	−1.11261	−0.556307	+	0.830977i	$0.687782\pi$
$360$	−10.1925	−0.537193
$361$	−15.8126	−0.832243
$362$	−14.6962	−0.772413
$363$	−10.9558	−0.575031
$364$	−6.95417	−0.364498
$365$	−3.55765	−0.186216
$366$	12.4677	0.651695
$367$	22.4163	1.17012	0.585060	−	0.810990i	$-0.301071\pi$
$367$	22.4163	1.17012	0.585060	+	0.810990i	$0.301071\pi$
$368$	−1.54552	−0.0805659
$369$	−8.23202	−0.428542
$370$	70.7459	3.67790
$371$	8.42860	0.437591
$372$	−25.4575	−1.31991
$373$	22.3743	1.15849	0.579247	−	0.815152i	$-0.303347\pi$
$373$	22.3743	1.15849	0.579247	+	0.815152i	$0.303347\pi$
$374$	−0.490663	−0.0253716
$375$	2.77749	0.143429
$376$	37.7807	1.94839
$377$	18.0963	0.932009
$378$	1.88141	0.0967695
$379$	−4.61512	−0.237063	−0.118531	−	0.992950i	$-0.537819\pi$
$379$	−4.61512	−0.237063	−0.118531	+	0.992950i	$0.537819\pi$
$380$	−18.5537	−0.951784
$381$	2.09797	0.107482
$382$	−21.5688	−1.10356
$383$	28.6156	1.46219	0.731095	−	0.682276i	$-0.239010\pi$
$383$	28.6156	1.46219	0.731095	+	0.682276i	$0.239010\pi$
$384$	−19.9585	−1.01851
$385$	−0.510431	−0.0260140
$386$	17.3434	0.882757
$387$	10.4057	0.528953
$388$	36.4388	1.84990
$389$	−11.1433	−0.564988	−0.282494	−	0.959269i	$-0.591162\pi$
$389$	−11.1433	−0.564988	−0.282494	+	0.959269i	$0.591162\pi$
$390$	17.5945	0.890930
$391$	1.54799	0.0782853
$392$	−21.4825	−1.08503
$393$	−13.7280	−0.692484
$394$	−36.7976	−1.85384
$395$	−32.8099	−1.65085
$396$	0.724991	0.0364321
$397$	15.8714	0.796560	0.398280	−	0.917264i	$-0.369607\pi$
$397$	15.8714	0.796560	0.398280	+	0.917264i	$0.369607\pi$
$398$	11.2040	0.561604
$399$	1.43892	0.0720362
$400$	4.07166	0.203583
$401$	12.3380	0.616129	0.308065	−	0.951365i	$-0.400319\pi$
$401$	12.3380	0.616129	0.308065	+	0.951365i	$0.400319\pi$
$402$	−29.1422	−1.45348
$403$	18.4635	0.919732
$404$	−44.6126	−2.21956
$405$	−3.01300	−0.149717
$406$	−13.6102	−0.675461
$407$	−2.11425	−0.104799
$408$	−3.38285	−0.167476
$409$	−19.0994	−0.944403	−0.472201	−	0.881491i	$-0.656540\pi$
$409$	−19.0994	−0.944403	−0.472201	+	0.881491i	$0.656540\pi$
$410$	57.8989	2.85942
$411$	14.6945	0.724825
$412$	4.10197	0.202090
$413$	−5.78011	−0.284420
$414$	−3.61354	−0.177596
$415$	−24.8281	−1.21877
$416$	11.0946	0.543959
$417$	11.5687	0.566521
$418$	0.875994	0.0428463
$419$	−39.2009	−1.91509	−0.957545	−	0.288283i	$-0.906916\pi$
$419$	−39.2009	−1.91509	−0.957545	+	0.288283i	$0.906916\pi$
$420$	−8.37592	−0.408703
$421$	0.356212	0.0173607	0.00868036	−	0.999962i	$-0.497237\pi$
$421$	0.356212	0.0173607	0.00868036	+	0.999962i	$0.497237\pi$
$422$	−20.1954	−0.983097
$423$	11.1683	0.543022
$424$	35.3768	1.71805
$425$	−4.07816	−0.197820
$426$	−27.0076	−1.30852
$427$	4.30467	0.208318
$428$	−1.58914	−0.0768139
$429$	−0.525812	−0.0253864
$430$	−73.1874	−3.52941
$431$	23.0133	1.10851	0.554256	−	0.832346i	$-0.313003\pi$
$431$	23.0133	1.10851	0.554256	+	0.832346i	$0.313003\pi$
$432$	0.998405	0.0480358
$433$	36.9862	1.77744	0.888722	−	0.458447i	$-0.151594\pi$
$433$	36.9862	1.77744	0.888722	+	0.458447i	$0.151594\pi$
$434$	−13.8863	−0.666563
$435$	21.7960	1.04504
$436$	29.9521	1.43444
$437$	−2.76367	−0.132204
$438$	2.75632	0.131702
$439$	12.5687	0.599871	0.299935	−	0.953960i	$-0.403035\pi$
$439$	12.5687	0.599871	0.299935	+	0.953960i	$0.403035\pi$
$440$	−2.14240	−0.102135
$441$	−6.35041	−0.302400
$442$	5.83952	0.277757
$443$	12.1228	0.575973	0.287986	−	0.957635i	$-0.407014\pi$
$443$	12.1228	0.575973	0.287986	+	0.957635i	$0.407014\pi$
$444$	−34.6937	−1.64649
$445$	29.6260	1.40441
$446$	31.9385	1.51233
$447$	2.16182	0.102251
$448$	−9.95359	−0.470263
$449$	−12.7054	−0.599603	−0.299802	−	0.954002i	$-0.596921\pi$
$449$	−12.7054	−0.599603	−0.299802	+	0.954002i	$0.596921\pi$
$450$	9.51984	0.448769
$451$	−1.73031	−0.0814773
$452$	−48.3164	−2.27261
$453$	−13.9815	−0.656910
$454$	−49.7746	−2.33604
$455$	6.07478	0.284790
$456$	6.03949	0.282825
$457$	4.74661	0.222037	0.111019	−	0.993818i	$-0.464589\pi$
$457$	4.74661	0.222037	0.111019	+	0.993818i	$0.464589\pi$
$458$	3.84289	0.179567
$459$	−1.00000	−0.0466760
$460$	16.0872	0.750071
$461$	13.2043	0.614983	0.307492	−	0.951551i	$-0.400510\pi$
$461$	13.2043	0.614983	0.307492	+	0.951551i	$0.400510\pi$
$462$	0.395460	0.0183985
$463$	28.9153	1.34381	0.671904	−	0.740639i	$-0.265477\pi$
$463$	28.9153	1.34381	0.671904	+	0.740639i	$0.265477\pi$
$464$	−7.22246	−0.335295
$465$	22.2383	1.03127
$466$	−11.2412	−0.520738
$467$	−13.9397	−0.645054	−0.322527	−	0.946560i	$-0.604532\pi$
$467$	−13.9397	−0.645054	−0.322527	+	0.946560i	$0.604532\pi$
$468$	−8.62831	−0.398844
$469$	−10.0618	−0.464612
$470$	−78.5509	−3.62328
$471$	1.00000	0.0460776
$472$	−24.2605	−1.11668
$473$	2.18721	0.100568
$474$	25.4197	1.16757
$475$	7.28085	0.334068
$476$	−2.77993	−0.127418
$477$	10.4577	0.478825
$478$	29.8000	1.36302
$479$	35.8323	1.63722	0.818609	−	0.574351i	$-0.194746\pi$
$479$	35.8323	1.63722	0.818609	+	0.574351i	$0.194746\pi$
$480$	13.3629	0.609929
$481$	25.1622	1.14730
$482$	−28.4362	−1.29523
$483$	−1.24764	−0.0567694
$484$	−37.7884	−1.71766
$485$	−31.8309	−1.44537
$486$	2.33434	0.105888
$487$	−1.20338	−0.0545305	−0.0272652	−	0.999628i	$-0.508680\pi$
$487$	−1.20338	−0.0545305	−0.0272652	+	0.999628i	$0.508680\pi$
$488$	18.0677	0.817886
$489$	−20.4399	−0.924326
$490$	44.6648	2.01775
$491$	−27.1922	−1.22717	−0.613584	−	0.789630i	$-0.710273\pi$
$491$	−27.1922	−1.22717	−0.613584	+	0.789630i	$0.710273\pi$
$492$	−28.3936	−1.28008
$493$	7.23400	0.325803
$494$	−10.4254	−0.469063
$495$	−0.633312	−0.0284652
$496$	−7.36900	−0.330878
$497$	−9.32482	−0.418275
$498$	19.2358	0.861976
$499$	−37.2496	−1.66752	−0.833762	−	0.552125i	$-0.813817\pi$
$499$	−37.2496	−1.66752	−0.833762	+	0.552125i	$0.813817\pi$
$500$	9.58003	0.428432
$501$	−7.74487	−0.346015
$502$	−69.4948	−3.10170
$503$	−27.7338	−1.23659	−0.618295	−	0.785946i	$-0.712176\pi$
$503$	−27.7338	−1.23659	−0.618295	+	0.785946i	$0.712176\pi$
$504$	2.72648	0.121447
$505$	38.9711	1.73419
$506$	−0.759542	−0.0337658
$507$	−6.74217	−0.299430
$508$	7.23623	0.321056
$509$	34.7406	1.53985	0.769925	−	0.638135i	$-0.220294\pi$
$509$	34.7406	1.53985	0.769925	+	0.638135i	$0.220294\pi$
$510$	7.03338	0.311443
$511$	0.951666	0.0420992
$512$	−11.1829	−0.494219
$513$	1.78533	0.0788241
$514$	16.0934	0.709848
$515$	−3.58325	−0.157897
$516$	35.8911	1.58002
$517$	2.34750	0.103243
$518$	−18.9244	−0.831489
$519$	23.6620	1.03864
$520$	25.4973	1.11813
$521$	32.3325	1.41651	0.708256	−	0.705956i	$-0.249482\pi$
$521$	32.3325	1.41651	0.708256	+	0.705956i	$0.249482\pi$
$522$	−16.8867	−0.739109
$523$	11.4691	0.501510	0.250755	−	0.968051i	$-0.419321\pi$
$523$	11.4691	0.501510	0.250755	+	0.968051i	$0.419321\pi$
$524$	−47.3500	−2.06849
$525$	3.28688	0.143451
$526$	14.1316	0.616167
$527$	7.38077	0.321511
$528$	0.209858	0.00913289
$529$	−20.6037	−0.895814
$530$	−73.5529	−3.19494
$531$	−7.17161	−0.311221
$532$	4.96308	0.215177
$533$	20.5929	0.891980
$534$	−22.9530	−0.993273
$535$	1.38818	0.0600164
$536$	−42.2318	−1.82414
$537$	7.66328	0.330695
$538$	10.7495	0.463443
$539$	−1.33481	−0.0574944
$540$	−10.3923	−0.447215
$541$	−23.0579	−0.991337	−0.495669	−	0.868512i	$-0.665077\pi$
$541$	−23.0579	−0.991337	−0.495669	+	0.868512i	$0.665077\pi$
$542$	49.6237	2.13152
$543$	−6.29563	−0.270171
$544$	4.43508	0.190152
$545$	−26.1645	−1.12076
$546$	−4.70648	−0.201419
$547$	37.0974	1.58617	0.793086	−	0.609110i	$-0.208473\pi$
$547$	37.0974	1.58617	0.793086	+	0.609110i	$0.208473\pi$
$548$	50.6837	2.16510
$549$	5.34097	0.227947
$550$	2.00100	0.0853231
$551$	−12.9151	−0.550200
$552$	−5.23662	−0.222885
$553$	8.77658	0.373218
$554$	2.63720	0.112044
$555$	30.3065	1.28644
$556$	39.9023	1.69223
$557$	7.00635	0.296868	0.148434	−	0.988922i	$-0.452577\pi$
$557$	7.00635	0.296868	0.148434	+	0.988922i	$0.452577\pi$
$558$	−17.2293	−0.729373
$559$	−26.0306	−1.10098
$560$	−2.42452	−0.102455
$561$	−0.210193	−0.00887436
$562$	−69.0611	−2.91317
$563$	−29.9681	−1.26300	−0.631502	−	0.775375i	$-0.717561\pi$
$563$	−29.9681	−1.26300	−0.631502	+	0.775375i	$0.717561\pi$
$564$	38.5213	1.62204
$565$	42.2065	1.77564
$566$	−41.2043	−1.73195
$567$	0.805971	0.0338476
$568$	−39.1384	−1.64221
$569$	−22.8734	−0.958901	−0.479450	−	0.877569i	$-0.659164\pi$
$569$	−22.8734	−0.958901	−0.479450	+	0.877569i	$0.659164\pi$
$570$	−12.5569	−0.525949
$571$	−17.6045	−0.736727	−0.368364	−	0.929682i	$-0.620082\pi$
$571$	−17.6045	−0.736727	−0.368364	+	0.929682i	$0.620082\pi$
$572$	−1.81361	−0.0758309
$573$	−9.23979	−0.385998
$574$	−15.4878	−0.646450
$575$	−6.31296	−0.263269
$576$	−12.3498	−0.514575
$577$	8.44725	0.351663	0.175832	−	0.984420i	$-0.443739\pi$
$577$	8.44725	0.351663	0.175832	+	0.984420i	$0.443739\pi$
$578$	2.33434	0.0970959
$579$	7.42968	0.308767
$580$	75.1781	3.12160
$581$	6.64148	0.275535
$582$	24.6612	1.02224
$583$	2.19814	0.0910375
$584$	3.99436	0.165288
$585$	7.53722	0.311626
$586$	20.1833	0.833766
$587$	23.7706	0.981116	0.490558	−	0.871408i	$-0.336793\pi$
$587$	23.7706	0.981116	0.490558	+	0.871408i	$0.336793\pi$
$588$	−21.9036	−0.903290
$589$	−13.1771	−0.542952
$590$	50.4406	2.07661
$591$	−15.7636	−0.648427
$592$	−10.0425	−0.412746
$593$	45.7958	1.88061	0.940304	−	0.340336i	$-0.110541\pi$
$593$	45.7958	1.88061	0.940304	+	0.340336i	$0.110541\pi$
$594$	0.490663	0.0201322
$595$	2.42839	0.0995543
$596$	7.45647	0.305429
$597$	4.79962	0.196436
$598$	9.03952	0.369653
$599$	−40.4504	−1.65276	−0.826380	−	0.563113i	$-0.809604\pi$
$599$	−40.4504	−1.65276	−0.826380	+	0.563113i	$0.809604\pi$
$600$	13.7958	0.563211
$601$	−30.7754	−1.25535	−0.627677	−	0.778474i	$-0.715994\pi$
$601$	−30.7754	−1.25535	−0.627677	+	0.778474i	$0.715994\pi$
$602$	19.5775	0.797919
$603$	−12.4841	−0.508392
$604$	−48.2246	−1.96223
$605$	33.0099	1.34204
$606$	−30.1932	−1.22651
$607$	2.40352	0.0975560	0.0487780	−	0.998810i	$-0.484467\pi$
$607$	2.40352	0.0975560	0.0487780	+	0.998810i	$0.484467\pi$
$608$	−7.91806	−0.321120
$609$	−5.83040	−0.236260
$610$	−37.5651	−1.52097
$611$	−27.9383	−1.13026
$612$	−3.44916	−0.139424
$613$	38.7499	1.56509	0.782547	−	0.622591i	$-0.213920\pi$
$613$	38.7499	1.56509	0.782547	+	0.622591i	$0.213920\pi$
$614$	38.8496	1.56784
$615$	24.8031	1.00016
$616$	0.573087	0.0230903
$617$	−8.25971	−0.332523	−0.166262	−	0.986082i	$-0.553170\pi$
$617$	−8.25971	−0.332523	−0.166262	+	0.986082i	$0.553170\pi$
$618$	2.77615	0.111673
$619$	38.1020	1.53145	0.765724	−	0.643169i	$-0.222381\pi$
$619$	38.1020	1.53145	0.765724	+	0.643169i	$0.222381\pi$
$620$	76.7034	3.08048
$621$	−1.54799	−0.0621187
$622$	33.1615	1.32966
$623$	−7.92490	−0.317504
$624$	−2.49758	−0.0999831
$625$	−28.7594	−1.15038
$626$	−22.2691	−0.890051
$627$	0.375263	0.0149866
$628$	3.44916	0.137637
$629$	10.0586	0.401062
$630$	−5.66870	−0.225846
$631$	29.5729	1.17728	0.588639	−	0.808396i	$-0.299664\pi$
$631$	29.5729	1.17728	0.588639	+	0.808396i	$0.299664\pi$
$632$	36.8374	1.46531
$633$	−8.65142	−0.343863
$634$	9.87688	0.392261
$635$	−6.32117	−0.250848
$636$	36.0703	1.43028
$637$	15.8860	0.629425
$638$	−3.54946	−0.140524
$639$	−11.5697	−0.457689
$640$	60.1351	2.37705
$641$	−2.70994	−0.107036	−0.0535180	−	0.998567i	$-0.517043\pi$
$641$	−2.70994	−0.107036	−0.0535180	+	0.998567i	$0.517043\pi$
$642$	−1.07551	−0.0424468
$643$	37.4984	1.47879	0.739396	−	0.673271i	$-0.235111\pi$
$643$	37.4984	1.47879	0.739396	+	0.673271i	$0.235111\pi$
$644$	−4.30330	−0.169574
$645$	−31.3524	−1.23450
$646$	−4.16757	−0.163971
$647$	−24.2480	−0.953286	−0.476643	−	0.879097i	$-0.658147\pi$
$647$	−24.2480	−0.953286	−0.476643	+	0.879097i	$0.658147\pi$
$648$	3.38285	0.132891
$649$	−1.50742	−0.0591715
$650$	−23.8145	−0.934082
$651$	−5.94869	−0.233148
$652$	−70.5007	−2.76102
$653$	−37.9146	−1.48371	−0.741856	−	0.670559i	$-0.766054\pi$
$653$	−37.9146	−1.48371	−0.741856	+	0.670559i	$0.766054\pi$
$654$	20.2711	0.792664
$655$	41.3623	1.61616
$656$	−8.21889	−0.320894
$657$	1.18077	0.0460662
$658$	21.0122	0.819142
$659$	−51.0527	−1.98873	−0.994366	−	0.106003i	$-0.966195\pi$
$659$	−51.0527	−1.98873	−0.994366	+	0.106003i	$0.966195\pi$
$660$	−2.18440	−0.0850275
$661$	46.3119	1.80132	0.900662	−	0.434521i	$-0.143082\pi$
$661$	46.3119	1.80132	0.900662	+	0.434521i	$0.143082\pi$
$662$	23.3360	0.906981
$663$	2.50157	0.0971528
$664$	27.8758	1.08179
$665$	−4.33547	−0.168122
$666$	−23.4802	−0.909840
$667$	11.1982	0.433595
$668$	−26.7133	−1.03357
$669$	13.6820	0.528976
$670$	87.8054	3.39222
$671$	1.12264	0.0433389
$672$	−3.57454	−0.137891
$673$	−16.0357	−0.618133	−0.309066	−	0.951040i	$-0.600017\pi$
$673$	−16.0357	−0.618133	−0.309066	+	0.951040i	$0.600017\pi$
$674$	82.1228	3.16325
$675$	4.07816	0.156969
$676$	−23.2548	−0.894417
$677$	−0.442477	−0.0170058	−0.00850289	−	0.999964i	$-0.502707\pi$
$677$	−0.442477	−0.0170058	−0.00850289	+	0.999964i	$0.502707\pi$
$678$	−32.6998	−1.25583
$679$	8.51470	0.326764
$680$	10.1925	0.390865
$681$	−21.3227	−0.817089
$682$	−3.62147	−0.138673
$683$	35.3839	1.35393	0.676963	−	0.736017i	$-0.263296\pi$
$683$	35.3839	1.35393	0.676963	+	0.736017i	$0.263296\pi$
$684$	6.15788	0.235453
$685$	−44.2744	−1.69164
$686$	−25.1177	−0.958997
$687$	1.64624	0.0628080
$688$	10.3891	0.396082
$689$	−26.1606	−0.996640
$690$	10.8876	0.414484
$691$	−19.4329	−0.739263	−0.369632	−	0.929178i	$-0.620516\pi$
$691$	−19.4329	−0.739263	−0.369632	+	0.929178i	$0.620516\pi$
$692$	81.6140	3.10250
$693$	0.169410	0.00643534
$694$	29.3821	1.11533
$695$	−34.8564	−1.32218
$696$	−24.4715	−0.927591
$697$	8.23202	0.311810
$698$	51.0372	1.93179
$699$	−4.81556	−0.182141
$700$	11.3370	0.428498
$701$	−9.59954	−0.362570	−0.181285	−	0.983431i	$-0.558026\pi$
$701$	−9.59954	−0.362570	−0.181285	+	0.983431i	$0.558026\pi$
$702$	−5.83952	−0.220398
$703$	−17.9579	−0.677294
$704$	−2.59584	−0.0978345
$705$	−33.6501	−1.26734
$706$	−44.5734	−1.67754
$707$	−10.4247	−0.392061
$708$	−24.7360	−0.929637
$709$	41.9921	1.57705	0.788524	−	0.615004i	$-0.210846\pi$
$709$	41.9921	1.57705	0.788524	+	0.615004i	$0.210846\pi$
$710$	81.3738	3.05391
$711$	10.8894	0.408386
$712$	−33.2626	−1.24657
$713$	11.4254	0.427884
$714$	−1.88141	−0.0704102
$715$	1.58427	0.0592484
$716$	26.4319	0.987807
$717$	12.7659	0.476752
$718$	−49.2103	−1.83651
$719$	−34.8735	−1.30056	−0.650282	−	0.759693i	$-0.725349\pi$
$719$	−34.8735	−1.30056	−0.650282	+	0.759693i	$0.725349\pi$
$720$	−3.00819	−0.112109
$721$	0.958513	0.0356969
$722$	−36.9121	−1.37373
$723$	−12.1817	−0.453041
$724$	−21.7146	−0.807018
$725$	−29.5014	−1.09566
$726$	−25.5747	−0.949164
$727$	−16.1988	−0.600779	−0.300389	−	0.953817i	$-0.597117\pi$
$727$	−16.1988	−0.600779	−0.300389	+	0.953817i	$0.597117\pi$
$728$	−6.82047	−0.252783
$729$	1.00000	0.0370370
$730$	−8.30479	−0.307374
$731$	−10.4057	−0.384870
$732$	18.4219	0.680893
$733$	−21.7530	−0.803464	−0.401732	−	0.915757i	$-0.631592\pi$
$733$	−21.7530	−0.803464	−0.401732	+	0.915757i	$0.631592\pi$
$734$	52.3273	1.93144
$735$	19.1338	0.705760
$736$	6.86546	0.253064
$737$	−2.62407	−0.0966589
$738$	−19.2164	−0.707365
$739$	−8.99049	−0.330720	−0.165360	−	0.986233i	$-0.552879\pi$
$739$	−8.99049	−0.330720	−0.165360	+	0.986233i	$0.552879\pi$
$740$	104.532	3.84268
$741$	−4.46611	−0.164067
$742$	19.6753	0.722302
$743$	−35.9387	−1.31846	−0.659232	−	0.751940i	$-0.729118\pi$
$743$	−35.9387	−1.31846	−0.659232	+	0.751940i	$0.729118\pi$
$744$	−24.9680	−0.915373
$745$	−6.51356	−0.238638
$746$	52.2292	1.91225
$747$	8.24034	0.301498
$748$	−0.724991	−0.0265083
$749$	−0.371336	−0.0135683
$750$	6.48363	0.236749
$751$	31.1926	1.13823	0.569116	−	0.822257i	$-0.307285\pi$
$751$	31.1926	1.13823	0.569116	+	0.822257i	$0.307285\pi$
$752$	11.1505	0.406617
$753$	−29.7706	−1.08490
$754$	42.2431	1.53840
$755$	42.1264	1.53314
$756$	2.77993	0.101105
$757$	44.5491	1.61917	0.809583	−	0.587005i	$-0.199693\pi$
$757$	44.5491	1.61917	0.809583	+	0.587005i	$0.199693\pi$
$758$	−10.7733	−0.391303
$759$	−0.325377	−0.0118104
$760$	−18.1970	−0.660073
$761$	4.11217	0.149066	0.0745330	−	0.997219i	$-0.476253\pi$
$761$	4.11217	0.149066	0.0745330	+	0.997219i	$0.476253\pi$
$762$	4.89738	0.177413
$763$	6.99894	0.253379
$764$	−31.8695	−1.15300
$765$	3.01300	0.108935
$766$	66.7987	2.41354
$767$	17.9402	0.647785
$768$	−21.8905	−0.789906
$769$	−9.10726	−0.328416	−0.164208	−	0.986426i	$-0.552507\pi$
$769$	−9.10726	−0.328416	−0.164208	+	0.986426i	$0.552507\pi$
$770$	−1.19152	−0.0429395
$771$	6.89417	0.248287
$772$	25.6262	0.922307
$773$	−41.9843	−1.51007	−0.755035	−	0.655684i	$-0.772380\pi$
$773$	−41.9843	−1.51007	−0.755035	+	0.655684i	$0.772380\pi$
$774$	24.2905	0.873106
$775$	−30.1000	−1.08122
$776$	35.7382	1.28293
$777$	−8.10693	−0.290835
$778$	−26.0123	−0.932586
$779$	−14.6968	−0.526569
$780$	25.9971	0.930845
$781$	−2.43186	−0.0870189
$782$	3.61354	0.129220
$783$	−7.23400	−0.258522
$784$	−6.34028	−0.226439
$785$	−3.01300	−0.107539
$786$	−32.0458	−1.14303
$787$	−32.2848	−1.15083	−0.575414	−	0.817862i	$-0.695159\pi$
$787$	−32.2848	−1.15083	−0.575414	+	0.817862i	$0.695159\pi$
$788$	−54.3712	−1.93689
$789$	6.05378	0.215520
$790$	−76.5896	−2.72494
$791$	−11.2902	−0.401432
$792$	0.711051	0.0252661
$793$	−13.3608	−0.474456
$794$	37.0492	1.31483
$795$	−31.5090	−1.11751
$796$	16.5547	0.586765
$797$	−4.73632	−0.167769	−0.0838845	−	0.996475i	$-0.526733\pi$
$797$	−4.73632	−0.167769	−0.0838845	+	0.996475i	$0.526733\pi$
$798$	3.35894	0.118905
$799$	−11.1683	−0.395106
$800$	−18.0870	−0.639471
$801$	−9.83273	−0.347423
$802$	28.8011	1.01700
$803$	0.248189	0.00875842
$804$	−43.0597	−1.51860
$805$	3.75913	0.132492
$806$	43.1001	1.51814
$807$	4.60492	0.162101
$808$	−43.7548	−1.53929
$809$	−17.7046	−0.622460	−0.311230	−	0.950335i	$-0.600741\pi$
$809$	−17.7046	−0.622460	−0.311230	+	0.950335i	$0.600741\pi$
$810$	−7.03338	−0.247128
$811$	−11.8186	−0.415008	−0.207504	−	0.978234i	$-0.566534\pi$
$811$	−11.8186	−0.415008	−0.207504	+	0.978234i	$0.566534\pi$
$812$	−20.1100	−0.705723
$813$	21.2581	0.745553
$814$	−4.93538	−0.172985
$815$	61.5855	2.15725
$816$	−0.998405	−0.0349512
$817$	18.5776	0.649948
$818$	−44.5845	−1.55886
$819$	−2.01619	−0.0704514
$820$	85.5499	2.98753
$821$	18.5887	0.648751	0.324376	−	0.945928i	$-0.394846\pi$
$821$	18.5887	0.648751	0.324376	+	0.945928i	$0.394846\pi$
$822$	34.3020	1.19642
$823$	−43.8139	−1.52726	−0.763629	−	0.645655i	$-0.776584\pi$
$823$	−43.8139	−1.52726	−0.763629	+	0.645655i	$0.776584\pi$
$824$	4.02310	0.140151
$825$	0.857202	0.0298439
$826$	−13.4928	−0.469473
$827$	42.9585	1.49381	0.746907	−	0.664929i	$-0.231538\pi$
$827$	42.9585	1.49381	0.746907	+	0.664929i	$0.231538\pi$
$828$	−5.33928	−0.185553
$829$	−11.7202	−0.407059	−0.203529	−	0.979069i	$-0.565241\pi$
$829$	−11.7202	−0.407059	−0.203529	+	0.979069i	$0.565241\pi$
$830$	−57.9574	−2.01173
$831$	1.12974	0.0391902
$832$	30.8938	1.07105
$833$	6.35041	0.220029
$834$	27.0053	0.935117
$835$	23.3353	0.807550
$836$	1.29434	0.0447658
$837$	−7.38077	−0.255117
$838$	−91.5085	−3.16111
$839$	38.1403	1.31675	0.658375	−	0.752690i	$-0.271244\pi$
$839$	38.1403	1.31675	0.658375	+	0.752690i	$0.271244\pi$
$840$	−8.21488	−0.283440
$841$	23.3308	0.804510
$842$	0.831522	0.0286562
$843$	−29.5848	−1.01895
$844$	−29.8402	−1.02714
$845$	20.3141	0.698828
$846$	26.0707	0.896328
$847$	−8.83008	−0.303405
$848$	10.4410	0.358546
$849$	−17.6514	−0.605793
$850$	−9.51984	−0.326528
$851$	15.5706	0.533754
$852$	−39.9057	−1.36715
$853$	−17.7907	−0.609141	−0.304570	−	0.952490i	$-0.598513\pi$
$853$	−17.7907	−0.609141	−0.304570	+	0.952490i	$0.598513\pi$
$854$	10.0486	0.343855
$855$	−5.37919	−0.183964
$856$	−1.55858	−0.0532713
$857$	23.0846	0.788555	0.394278	−	0.918991i	$-0.370995\pi$
$857$	23.0846	0.788555	0.394278	+	0.918991i	$0.370995\pi$
$858$	−1.22743	−0.0419036
$859$	−43.0125	−1.46757	−0.733784	−	0.679383i	$-0.762247\pi$
$859$	−43.0125	−1.46757	−0.733784	+	0.679383i	$0.762247\pi$
$860$	−108.140	−3.68753
$861$	−6.63477	−0.226112
$862$	53.7210	1.82974
$863$	23.2619	0.791844	0.395922	−	0.918284i	$-0.370425\pi$
$863$	23.2619	0.791844	0.395922	+	0.918284i	$0.370425\pi$
$864$	−4.43508	−0.150884
$865$	−71.2935	−2.42405
$866$	86.3385	2.93390
$867$	1.00000	0.0339618
$868$	−20.5180	−0.696427
$869$	2.28889	0.0776452
$870$	50.8795	1.72498
$871$	31.2298	1.05818
$872$	29.3762	0.994803
$873$	10.5645	0.357555
$874$	−6.45136	−0.218220
$875$	2.23858	0.0756778
$876$	4.07266	0.137603
$877$	48.7521	1.64624	0.823121	−	0.567866i	$-0.192231\pi$
$877$	48.7521	1.64624	0.823121	+	0.567866i	$0.192231\pi$
$878$	29.3396	0.990165
$879$	8.64625	0.291631
$880$	−0.632302	−0.0213149
$881$	−47.7849	−1.60991	−0.804957	−	0.593334i	$-0.797811\pi$
$881$	−47.7849	−1.60991	−0.804957	+	0.593334i	$0.797811\pi$
$882$	−14.8240	−0.499152
$883$	38.5348	1.29680	0.648400	−	0.761300i	$-0.275438\pi$
$883$	38.5348	1.29680	0.648400	+	0.761300i	$0.275438\pi$
$884$	8.62831	0.290202
$885$	21.6080	0.726346
$886$	28.2988	0.950718
$887$	−45.6170	−1.53167	−0.765835	−	0.643037i	$-0.777674\pi$
$887$	−45.6170	−1.53167	−0.765835	+	0.643037i	$0.777674\pi$
$888$	−34.0267	−1.14186
$889$	1.69090	0.0567110
$890$	69.1573	2.31816
$891$	0.210193	0.00704173
$892$	47.1914	1.58008
$893$	19.9391	0.667236
$894$	5.04643	0.168778
$895$	−23.0895	−0.771795
$896$	−16.0860	−0.537396
$897$	3.87240	0.129296
$898$	−29.6587	−0.989724
$899$	53.3925	1.78074
$900$	14.0663	0.468875
$901$	−10.4577	−0.348396
$902$	−4.03915	−0.134489
$903$	8.38672	0.279092
$904$	−47.3874	−1.57608
$905$	18.9687	0.630541
$906$	−32.6377	−1.08432
$907$	−34.7499	−1.15385	−0.576927	−	0.816796i	$-0.695748\pi$
$907$	−34.7499	−1.15385	−0.576927	+	0.816796i	$0.695748\pi$
$908$	−73.5456	−2.44070
$909$	−12.9343	−0.429004
$910$	14.1806	0.470083
$911$	50.9296	1.68737	0.843687	−	0.536836i	$-0.180381\pi$
$911$	50.9296	1.68737	0.843687	+	0.536836i	$0.180381\pi$
$912$	1.78248	0.0590238
$913$	1.73206	0.0573229
$914$	11.0802	0.366501
$915$	−16.0923	−0.531996
$916$	5.67815	0.187611
$917$	−11.0643	−0.365377
$918$	−2.33434	−0.0770448
$919$	−24.1295	−0.795957	−0.397979	−	0.917395i	$-0.630288\pi$
$919$	−24.1295	−0.795957	−0.397979	+	0.917395i	$0.630288\pi$
$920$	15.7779	0.520183
$921$	16.6426	0.548393
$922$	30.8233	1.01511
$923$	28.9423	0.952647
$924$	0.584322	0.0192228
$925$	−41.0206	−1.34875
$926$	67.4982	2.21813
$927$	1.18927	0.0390606
$928$	32.0833	1.05319
$929$	35.5707	1.16704	0.583518	−	0.812100i	$-0.301676\pi$
$929$	35.5707	1.16704	0.583518	+	0.812100i	$0.301676\pi$
$930$	51.9118	1.70225
$931$	−11.3376	−0.371573
$932$	−16.6097	−0.544068
$933$	14.2059	0.465081
$934$	−32.5402	−1.06475
$935$	0.633312	0.0207115
$936$	−8.46242	−0.276603
$937$	8.00653	0.261562	0.130781	−	0.991411i	$-0.458252\pi$
$937$	8.00653	0.261562	0.130781	+	0.991411i	$0.458252\pi$
$938$	−23.4878	−0.766903
$939$	−9.53976	−0.311318
$940$	−116.065	−3.78561
$941$	24.5049	0.798838	0.399419	−	0.916768i	$-0.369212\pi$
$941$	24.5049	0.798838	0.399419	+	0.916768i	$0.369212\pi$
$942$	2.33434	0.0760571
$943$	12.7431	0.414972
$944$	−7.16017	−0.233044
$945$	−2.42839	−0.0789956
$946$	5.10571	0.166001
$947$	−18.7833	−0.610375	−0.305188	−	0.952292i	$-0.598719\pi$
$947$	−18.7833	−0.610375	−0.305188	+	0.952292i	$0.598719\pi$
$948$	37.5595	1.21988
$949$	−2.95377	−0.0958834
$950$	16.9960	0.551423
$951$	4.23111	0.137203
$952$	−2.72648	−0.0883657
$953$	−9.02456	−0.292334	−0.146167	−	0.989260i	$-0.546694\pi$
$953$	−9.02456	−0.292334	−0.146167	+	0.989260i	$0.546694\pi$
$954$	24.4119	0.790363
$955$	27.8395	0.900864
$956$	44.0317	1.42409
$957$	−1.52054	−0.0491520
$958$	83.6448	2.70244
$959$	11.8433	0.382441
$960$	37.2099	1.20095
$961$	23.4758	0.757284
$962$	58.7373	1.89377
$963$	−0.460731	−0.0148469
$964$	−42.0165	−1.35326
$965$	−22.3856	−0.720618
$966$	−2.91241	−0.0937054
$967$	5.02954	0.161739	0.0808696	−	0.996725i	$-0.474230\pi$
$967$	5.02954	0.161739	0.0808696	+	0.996725i	$0.474230\pi$
$968$	−37.0619	−1.19121
$969$	−1.78533	−0.0573529
$970$	−74.3043	−2.38577
$971$	44.4677	1.42704	0.713518	−	0.700637i	$-0.247101\pi$
$971$	44.4677	1.42704	0.713518	+	0.700637i	$0.247101\pi$
$972$	3.44916	0.110632
$973$	9.32403	0.298915
$974$	−2.80911	−0.0900097
$975$	−10.2018	−0.326719
$976$	5.33245	0.170688
$977$	5.87955	0.188103	0.0940517	−	0.995567i	$-0.470018\pi$
$977$	5.87955	0.188103	0.0940517	+	0.995567i	$0.470018\pi$
$978$	−47.7139	−1.52572
$979$	−2.06677	−0.0660544
$980$	65.9955	2.10815
$981$	8.68386	0.277254
$982$	−63.4760	−2.02560
$983$	42.6059	1.35892	0.679459	−	0.733714i	$-0.262215\pi$
$983$	42.6059	1.35892	0.679459	+	0.733714i	$0.262215\pi$
$984$	−27.8477	−0.887752
$985$	47.4957	1.51334
$986$	16.8867	0.537781
$987$	9.00134	0.286516
$988$	−15.4043	−0.490078
$989$	−16.1080	−0.512204
$990$	−1.47837	−0.0469856
$991$	−34.1905	−1.08610	−0.543049	−	0.839701i	$-0.682730\pi$
$991$	−34.1905	−1.08610	−0.543049	+	0.839701i	$0.682730\pi$
$992$	32.7343	1.03931
$993$	9.99683	0.317240
$994$	−21.7673	−0.690418
$995$	−14.4613	−0.458453
$996$	28.4223	0.900594
$997$	−42.0504	−1.33175	−0.665875	−	0.746063i	$-0.731942\pi$
$997$	−42.0504	−1.33175	−0.665875	+	0.746063i	$0.731942\pi$
$998$	−86.9535	−2.75246
$999$	−10.0586	−0.318240

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.44	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.44	✓	46	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)

\(f(q)\)	\(=\)	\(q+2.33434 q^{2} +1.00000 q^{3} +3.44916 q^{4} -3.01300 q^{5} +2.33434 q^{6} +0.805971 q^{7} +3.38285 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.33434 q^{2} +1.00000 q^{3} +3.44916 q^{4} -3.01300 q^{5} +2.33434 q^{6} +0.805971 q^{7} +3.38285 q^{8} +1.00000 q^{9} -7.03338 q^{10} +0.210193 q^{11} +3.44916 q^{12} -2.50157 q^{13} +1.88141 q^{14} -3.01300 q^{15} +0.998405 q^{16} -1.00000 q^{17} +2.33434 q^{18} +1.78533 q^{19} -10.3923 q^{20} +0.805971 q^{21} +0.490663 q^{22} -1.54799 q^{23} +3.38285 q^{24} +4.07816 q^{25} -5.83952 q^{26} +1.00000 q^{27} +2.77993 q^{28} -7.23400 q^{29} -7.03338 q^{30} -7.38077 q^{31} -4.43508 q^{32} +0.210193 q^{33} -2.33434 q^{34} -2.42839 q^{35} +3.44916 q^{36} -10.0586 q^{37} +4.16757 q^{38} -2.50157 q^{39} -10.1925 q^{40} -8.23202 q^{41} +1.88141 q^{42} +10.4057 q^{43} +0.724991 q^{44} -3.01300 q^{45} -3.61354 q^{46} +11.1683 q^{47} +0.998405 q^{48} -6.35041 q^{49} +9.51984 q^{50} -1.00000 q^{51} -8.62831 q^{52} +10.4577 q^{53} +2.33434 q^{54} -0.633312 q^{55} +2.72648 q^{56} +1.78533 q^{57} -16.8867 q^{58} -7.17161 q^{59} -10.3923 q^{60} +5.34097 q^{61} -17.2293 q^{62} +0.805971 q^{63} -12.3498 q^{64} +7.53722 q^{65} +0.490663 q^{66} -12.4841 q^{67} -3.44916 q^{68} -1.54799 q^{69} -5.66870 q^{70} -11.5697 q^{71} +3.38285 q^{72} +1.18077 q^{73} -23.4802 q^{74} +4.07816 q^{75} +6.15788 q^{76} +0.169410 q^{77} -5.83952 q^{78} +10.8894 q^{79} -3.00819 q^{80} +1.00000 q^{81} -19.2164 q^{82} +8.24034 q^{83} +2.77993 q^{84} +3.01300 q^{85} +24.2905 q^{86} -7.23400 q^{87} +0.711051 q^{88} -9.83273 q^{89} -7.03338 q^{90} -2.01619 q^{91} -5.33928 q^{92} -7.38077 q^{93} +26.0707 q^{94} -5.37919 q^{95} -4.43508 q^{96} +10.5645 q^{97} -14.8240 q^{98} +0.210193 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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