LMFDB - Embedded newform 8007.2.a.j.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:	$0$
Dimension:	$64$
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)

$f(q)$	$=$	$q+1.33241 q^{2} -1.00000 q^{3} -0.224694 q^{4} +1.51914 q^{5} -1.33241 q^{6} +0.436093 q^{7} -2.96420 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.33241 q^{2} -1.00000 q^{3} -0.224694 q^{4} +1.51914 q^{5} -1.33241 q^{6} +0.436093 q^{7} -2.96420 q^{8} +1.00000 q^{9} +2.02411 q^{10} +0.644895 q^{11} +0.224694 q^{12} -4.27285 q^{13} +0.581054 q^{14} -1.51914 q^{15} -3.50013 q^{16} +1.00000 q^{17} +1.33241 q^{18} +0.0690924 q^{19} -0.341341 q^{20} -0.436093 q^{21} +0.859262 q^{22} -5.04440 q^{23} +2.96420 q^{24} -2.69221 q^{25} -5.69317 q^{26} -1.00000 q^{27} -0.0979874 q^{28} +3.48239 q^{29} -2.02411 q^{30} +10.4362 q^{31} +1.26480 q^{32} -0.644895 q^{33} +1.33241 q^{34} +0.662487 q^{35} -0.224694 q^{36} +7.73226 q^{37} +0.0920591 q^{38} +4.27285 q^{39} -4.50303 q^{40} -10.1901 q^{41} -0.581054 q^{42} +10.6846 q^{43} -0.144904 q^{44} +1.51914 q^{45} -6.72119 q^{46} -11.7878 q^{47} +3.50013 q^{48} -6.80982 q^{49} -3.58712 q^{50} -1.00000 q^{51} +0.960081 q^{52} -4.85638 q^{53} -1.33241 q^{54} +0.979686 q^{55} -1.29267 q^{56} -0.0690924 q^{57} +4.63995 q^{58} +8.79634 q^{59} +0.341341 q^{60} +2.96388 q^{61} +13.9052 q^{62} +0.436093 q^{63} +8.68548 q^{64} -6.49105 q^{65} -0.859262 q^{66} +12.2496 q^{67} -0.224694 q^{68} +5.04440 q^{69} +0.882702 q^{70} +3.15767 q^{71} -2.96420 q^{72} -12.8384 q^{73} +10.3025 q^{74} +2.69221 q^{75} -0.0155246 q^{76} +0.281235 q^{77} +5.69317 q^{78} +11.5914 q^{79} -5.31718 q^{80} +1.00000 q^{81} -13.5773 q^{82} +1.99179 q^{83} +0.0979874 q^{84} +1.51914 q^{85} +14.2362 q^{86} -3.48239 q^{87} -1.91160 q^{88} +12.3432 q^{89} +2.02411 q^{90} -1.86336 q^{91} +1.13344 q^{92} -10.4362 q^{93} -15.7061 q^{94} +0.104961 q^{95} -1.26480 q^{96} +12.5841 q^{97} -9.07345 q^{98} +0.644895 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	1.33241	0.942153	0.471077	−	0.882092i	$-0.343865\pi$
$2$	1.33241	0.942153	0.471077	+	0.882092i	$0.343865\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.224694	−0.112347
$5$	1.51914	0.679380	0.339690	−	0.940537i	$-0.389678\pi$
$5$	1.51914	0.679380	0.339690	+	0.940537i	$0.389678\pi$
$6$	−1.33241	−0.543953
$7$	0.436093	0.164828	0.0824139	−	0.996598i	$-0.473737\pi$
$7$	0.436093	0.164828	0.0824139	+	0.996598i	$0.473737\pi$
$8$	−2.96420	−1.04800
$9$	1.00000	0.333333
$10$	2.02411	0.640080
$11$	0.644895	0.194443	0.0972216	−	0.995263i	$-0.469004\pi$
$11$	0.644895	0.194443	0.0972216	+	0.995263i	$0.469004\pi$
$12$	0.224694	0.0648634
$13$	−4.27285	−1.18507	−0.592537	−	0.805543i	$-0.701874\pi$
$13$	−4.27285	−1.18507	−0.592537	+	0.805543i	$0.701874\pi$
$14$	0.581054	0.155293
$15$	−1.51914	−0.392240
$16$	−3.50013	−0.875031
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.33241	0.314051
$19$	0.0690924	0.0158509	0.00792544	−	0.999969i	$-0.497477\pi$
$19$	0.0690924	0.0158509	0.00792544	+	0.999969i	$0.497477\pi$
$20$	−0.341341	−0.0763262
$21$	−0.436093	−0.0951634
$22$	0.859262	0.183195
$23$	−5.04440	−1.05183	−0.525915	−	0.850537i	$-0.676277\pi$
$23$	−5.04440	−1.05183	−0.525915	+	0.850537i	$0.676277\pi$
$24$	2.96420	0.605064
$25$	−2.69221	−0.538443
$26$	−5.69317	−1.11652
$27$	−1.00000	−0.192450
$28$	−0.0979874	−0.0185179
$29$	3.48239	0.646663	0.323331	−	0.946286i	$-0.395197\pi$
$29$	3.48239	0.646663	0.323331	+	0.946286i	$0.395197\pi$
$30$	−2.02411	−0.369550
$31$	10.4362	1.87439	0.937197	−	0.348800i	$-0.113411\pi$
$31$	10.4362	1.87439	0.937197	+	0.348800i	$0.113411\pi$
$32$	1.26480	0.223588
$33$	−0.644895	−0.112262
$34$	1.33241	0.228506
$35$	0.662487	0.111981
$36$	−0.224694	−0.0374489
$37$	7.73226	1.27118	0.635588	−	0.772028i	$-0.280758\pi$
$37$	7.73226	1.27118	0.635588	+	0.772028i	$0.280758\pi$
$38$	0.0920591	0.0149340
$39$	4.27285	0.684203
$40$	−4.50303	−0.711991
$41$	−10.1901	−1.59142	−0.795712	−	0.605675i	$-0.792903\pi$
$41$	−10.1901	−1.59142	−0.795712	+	0.605675i	$0.792903\pi$
$42$	−0.581054	−0.0896585
$43$	10.6846	1.62938	0.814690	−	0.579897i	$-0.196907\pi$
$43$	10.6846	1.62938	0.814690	+	0.579897i	$0.196907\pi$
$44$	−0.144904	−0.0218451
$45$	1.51914	0.226460
$46$	−6.72119	−0.990986
$47$	−11.7878	−1.71942	−0.859711	−	0.510780i	$-0.829357\pi$
$47$	−11.7878	−1.71942	−0.859711	+	0.510780i	$0.829357\pi$
$48$	3.50013	0.505200
$49$	−6.80982	−0.972832
$50$	−3.58712	−0.507296
$51$	−1.00000	−0.140028
$52$	0.960081	0.133139
$53$	−4.85638	−0.667076	−0.333538	−	0.942737i	$-0.608242\pi$
$53$	−4.85638	−0.667076	−0.333538	+	0.942737i	$0.608242\pi$
$54$	−1.33241	−0.181318
$55$	0.979686	0.132101
$56$	−1.29267	−0.172740
$57$	−0.0690924	−0.00915151
$58$	4.63995	0.609256
$59$	8.79634	1.14519	0.572593	−	0.819840i	$-0.305938\pi$
$59$	8.79634	1.14519	0.572593	+	0.819840i	$0.305938\pi$
$60$	0.341341	0.0440669
$61$	2.96388	0.379486	0.189743	−	0.981834i	$-0.439235\pi$
$61$	2.96388	0.379486	0.189743	+	0.981834i	$0.439235\pi$
$62$	13.9052	1.76597
$63$	0.436093	0.0549426
$64$	8.68548	1.08569
$65$	−6.49105	−0.805116
$66$	−0.859262	−0.105768
$67$	12.2496	1.49652	0.748262	−	0.663404i	$-0.230889\pi$
$67$	12.2496	1.49652	0.748262	+	0.663404i	$0.230889\pi$
$68$	−0.224694	−0.0272481
$69$	5.04440	0.607275
$70$	0.882702	0.105503
$71$	3.15767	0.374746	0.187373	−	0.982289i	$-0.440003\pi$
$71$	3.15767	0.374746	0.187373	+	0.982289i	$0.440003\pi$
$72$	−2.96420	−0.349334
$73$	−12.8384	−1.50262	−0.751312	−	0.659947i	$-0.770579\pi$
$73$	−12.8384	−1.50262	−0.751312	+	0.659947i	$0.770579\pi$
$74$	10.3025	1.19764
$75$	2.69221	0.310870
$76$	−0.0155246	−0.00178079
$77$	0.281235	0.0320496
$78$	5.69317	0.644624
$79$	11.5914	1.30413	0.652066	−	0.758162i	$-0.273903\pi$
$79$	11.5914	1.30413	0.652066	+	0.758162i	$0.273903\pi$
$80$	−5.31718	−0.594479
$81$	1.00000	0.111111
$82$	−13.5773	−1.49937
$83$	1.99179	0.218627	0.109314	−	0.994007i	$-0.465135\pi$
$83$	1.99179	0.218627	0.109314	+	0.994007i	$0.465135\pi$
$84$	0.0979874	0.0106913
$85$	1.51914	0.164774
$86$	14.2362	1.53513
$87$	−3.48239	−0.373351
$88$	−1.91160	−0.203777
$89$	12.3432	1.30837	0.654186	−	0.756334i	$-0.273011\pi$
$89$	12.3432	1.30837	0.654186	+	0.756334i	$0.273011\pi$
$90$	2.02411	0.213360
$91$	−1.86336	−0.195333
$92$	1.13344	0.118170
$93$	−10.4362	−1.08218
$94$	−15.7061	−1.61996
$95$	0.104961	0.0107688
$96$	−1.26480	−0.129088
$97$	12.5841	1.27772	0.638862	−	0.769322i	$-0.279406\pi$
$97$	12.5841	1.27772	0.638862	+	0.769322i	$0.279406\pi$
$98$	−9.07345	−0.916557
$99$	0.644895	0.0648144
$100$	0.604923	0.0604923
$101$	−14.5211	−1.44490	−0.722450	−	0.691424i	$-0.756984\pi$
$101$	−14.5211	−1.44490	−0.722450	+	0.691424i	$0.756984\pi$
$102$	−1.33241	−0.131928
$103$	−8.85705	−0.872711	−0.436356	−	0.899774i	$-0.643731\pi$
$103$	−8.85705	−0.872711	−0.436356	+	0.899774i	$0.643731\pi$
$104$	12.6655	1.24196
$105$	−0.662487	−0.0646521
$106$	−6.47068	−0.628488
$107$	17.9402	1.73435	0.867173	−	0.498007i	$-0.165934\pi$
$107$	17.9402	1.73435	0.867173	+	0.498007i	$0.165934\pi$
$108$	0.224694	0.0216211
$109$	0.909858	0.0871486	0.0435743	−	0.999050i	$-0.486125\pi$
$109$	0.909858	0.0871486	0.0435743	+	0.999050i	$0.486125\pi$
$110$	1.30534	0.124459
$111$	−7.73226	−0.733914
$112$	−1.52638	−0.144230
$113$	16.2524	1.52889	0.764447	−	0.644687i	$-0.223012\pi$
$113$	16.2524	1.52889	0.764447	+	0.644687i	$0.223012\pi$
$114$	−0.0920591	−0.00862212
$115$	−7.66315	−0.714593
$116$	−0.782470	−0.0726505
$117$	−4.27285	−0.395025
$118$	11.7203	1.07894
$119$	0.436093	0.0399766
$120$	4.50303	0.411068
$121$	−10.5841	−0.962192
$122$	3.94909	0.357534
$123$	10.1901	0.918809
$124$	−2.34494	−0.210582
$125$	−11.6855	−1.04519
$126$	0.581054	0.0517644
$127$	1.02495	0.0909499	0.0454750	−	0.998965i	$-0.485520\pi$
$127$	1.02495	0.0909499	0.0454750	+	0.998965i	$0.485520\pi$
$128$	9.04299	0.799295
$129$	−10.6846	−0.940722
$130$	−8.64871	−0.758542
$131$	15.5677	1.36016	0.680080	−	0.733138i	$-0.261945\pi$
$131$	15.5677	1.36016	0.680080	+	0.733138i	$0.261945\pi$
$132$	0.144904	0.0126123
$133$	0.0301307	0.00261267
$134$	16.3214	1.40995
$135$	−1.51914	−0.130747
$136$	−2.96420	−0.254178
$137$	19.5999	1.67453	0.837266	−	0.546796i	$-0.184153\pi$
$137$	19.5999	1.67453	0.837266	+	0.546796i	$0.184153\pi$
$138$	6.72119	0.572146
$139$	6.50841	0.552036	0.276018	−	0.961152i	$-0.410985\pi$
$139$	6.50841	0.552036	0.276018	+	0.961152i	$0.410985\pi$
$140$	−0.148857	−0.0125807
$141$	11.7878	0.992709
$142$	4.20729	0.353068
$143$	−2.75554	−0.230430
$144$	−3.50013	−0.291677
$145$	5.29023	0.439330
$146$	−17.1060	−1.41570
$147$	6.80982	0.561665
$148$	−1.73739	−0.142813
$149$	3.05970	0.250660	0.125330	−	0.992115i	$-0.460001\pi$
$149$	3.05970	0.250660	0.125330	+	0.992115i	$0.460001\pi$
$150$	3.58712	0.292887
$151$	−21.4844	−1.74838	−0.874188	−	0.485587i	$-0.838606\pi$
$151$	−21.4844	−1.74838	−0.874188	+	0.485587i	$0.838606\pi$
$152$	−0.204803	−0.0166117
$153$	1.00000	0.0808452
$154$	0.374719	0.0301957
$155$	15.8540	1.27343
$156$	−0.960081	−0.0768680
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	15.4444	1.22869
$159$	4.85638	0.385136
$160$	1.92141	0.151901
$161$	−2.19983	−0.173371
$162$	1.33241	0.104684
$163$	20.8114	1.63008	0.815039	−	0.579406i	$-0.196715\pi$
$163$	20.8114	1.63008	0.815039	+	0.579406i	$0.196715\pi$
$164$	2.28965	0.178791
$165$	−0.979686	−0.0762684
$166$	2.65387	0.205980
$167$	−17.6036	−1.36221	−0.681103	−	0.732187i	$-0.738500\pi$
$167$	−17.6036	−1.36221	−0.681103	+	0.732187i	$0.738500\pi$
$168$	1.29267	0.0997314
$169$	5.25721	0.404400
$170$	2.02411	0.155242
$171$	0.0690924	0.00528362
$172$	−2.40075	−0.183056
$173$	−11.9941	−0.911894	−0.455947	−	0.890007i	$-0.650699\pi$
$173$	−11.9941	−0.911894	−0.455947	+	0.890007i	$0.650699\pi$
$174$	−4.63995	−0.351754
$175$	−1.17406	−0.0887504
$176$	−2.25721	−0.170144
$177$	−8.79634	−0.661173
$178$	16.4461	1.23269
$179$	−5.86533	−0.438395	−0.219198	−	0.975681i	$-0.570344\pi$
$179$	−5.86533	−0.438395	−0.219198	+	0.975681i	$0.570344\pi$
$180$	−0.341341	−0.0254421
$181$	22.6585	1.68419	0.842096	−	0.539328i	$-0.181322\pi$
$181$	22.6585	1.68419	0.842096	+	0.539328i	$0.181322\pi$
$182$	−2.48275	−0.184034
$183$	−2.96388	−0.219096
$184$	14.9526	1.10232
$185$	11.7464	0.863612
$186$	−13.9052	−1.01958
$187$	0.644895	0.0471594
$188$	2.64864	0.193172
$189$	−0.436093	−0.0317211
$190$	0.139851	0.0101458
$191$	9.79991	0.709097	0.354548	−	0.935038i	$-0.384635\pi$
$191$	9.79991	0.709097	0.354548	+	0.935038i	$0.384635\pi$
$192$	−8.68548	−0.626821
$193$	26.8386	1.93189	0.965943	−	0.258753i	$-0.0833117\pi$
$193$	26.8386	1.93189	0.965943	+	0.258753i	$0.0833117\pi$
$194$	16.7672	1.20381
$195$	6.49105	0.464834
$196$	1.53012	0.109295
$197$	8.30023	0.591367	0.295683	−	0.955286i	$-0.404453\pi$
$197$	8.30023	0.591367	0.295683	+	0.955286i	$0.404453\pi$
$198$	0.859262	0.0610651
$199$	−0.934425	−0.0662396	−0.0331198	−	0.999451i	$-0.510544\pi$
$199$	−0.934425	−0.0662396	−0.0331198	+	0.999451i	$0.510544\pi$
$200$	7.98025	0.564289
$201$	−12.2496	−0.864018
$202$	−19.3479	−1.36132
$203$	1.51865	0.106588
$204$	0.224694	0.0157317
$205$	−15.4802	−1.08118
$206$	−11.8012	−0.822228
$207$	−5.04440	−0.350610
$208$	14.9555	1.03698
$209$	0.0445573	0.00308209
$210$	−0.882702	−0.0609122
$211$	−14.6922	−1.01145	−0.505727	−	0.862694i	$-0.668776\pi$
$211$	−14.6922	−1.01145	−0.505727	+	0.862694i	$0.668776\pi$
$212$	1.09120	0.0749438
$213$	−3.15767	−0.216360
$214$	23.9037	1.63402
$215$	16.2313	1.10697
$216$	2.96420	0.201688
$217$	4.55115	0.308952
$218$	1.21230	0.0821074
$219$	12.8384	0.867541
$220$	−0.220129	−0.0148411
$221$	−4.27285	−0.287423
$222$	−10.3025	−0.691460
$223$	−16.1617	−1.08227	−0.541134	−	0.840936i	$-0.682005\pi$
$223$	−16.1617	−1.08227	−0.541134	+	0.840936i	$0.682005\pi$
$224$	0.551572	0.0368534
$225$	−2.69221	−0.179481
$226$	21.6547	1.44045
$227$	2.63734	0.175046	0.0875230	−	0.996162i	$-0.472105\pi$
$227$	2.63734	0.175046	0.0875230	+	0.996162i	$0.472105\pi$
$228$	0.0155246	0.00102814
$229$	−6.96871	−0.460505	−0.230253	−	0.973131i	$-0.573955\pi$
$229$	−6.96871	−0.460505	−0.230253	+	0.973131i	$0.573955\pi$
$230$	−10.2104	−0.673256
$231$	−0.281235	−0.0185039
$232$	−10.3225	−0.677704
$233$	−24.9729	−1.63603	−0.818013	−	0.575200i	$-0.804924\pi$
$233$	−24.9729	−1.63603	−0.818013	+	0.575200i	$0.804924\pi$
$234$	−5.69317	−0.372174
$235$	−17.9073	−1.16814
$236$	−1.97648	−0.128658
$237$	−11.5914	−0.752941
$238$	0.581054	0.0376641
$239$	−19.7786	−1.27937	−0.639684	−	0.768638i	$-0.720935\pi$
$239$	−19.7786	−1.27937	−0.639684	+	0.768638i	$0.720935\pi$
$240$	5.31718	0.343222
$241$	17.3177	1.11553	0.557767	−	0.829998i	$-0.311658\pi$
$241$	17.3177	1.11553	0.557767	+	0.829998i	$0.311658\pi$
$242$	−14.1023	−0.906532
$243$	−1.00000	−0.0641500
$244$	−0.665965	−0.0426340
$245$	−10.3451	−0.660922
$246$	13.5773	0.865659
$247$	−0.295221	−0.0187845
$248$	−30.9349	−1.96437
$249$	−1.99179	−0.126224
$250$	−15.5699	−0.984727
$251$	9.90439	0.625159	0.312580	−	0.949892i	$-0.398807\pi$
$251$	9.90439	0.625159	0.312580	+	0.949892i	$0.398807\pi$
$252$	−0.0979874	−0.00617263
$253$	−3.25311	−0.204521
$254$	1.36565	0.0856888
$255$	−1.51914	−0.0951322
$256$	−5.32203	−0.332627
$257$	20.3087	1.26682	0.633412	−	0.773815i	$-0.281654\pi$
$257$	20.3087	1.26682	0.633412	+	0.773815i	$0.281654\pi$
$258$	−14.2362	−0.886305
$259$	3.37199	0.209525
$260$	1.45850	0.0904521
$261$	3.48239	0.215554
$262$	20.7425	1.28148
$263$	−6.46294	−0.398522	−0.199261	−	0.979946i	$-0.563854\pi$
$263$	−6.46294	−0.398522	−0.199261	+	0.979946i	$0.563854\pi$
$264$	1.91160	0.117651
$265$	−7.37752	−0.453198
$266$	0.0401464	0.00246153
$267$	−12.3432	−0.755389
$268$	−2.75240	−0.168130
$269$	2.08536	0.127147	0.0635733	−	0.997977i	$-0.479750\pi$
$269$	2.08536	0.127147	0.0635733	+	0.997977i	$0.479750\pi$
$270$	−2.02411	−0.123183
$271$	−28.0606	−1.70456	−0.852280	−	0.523085i	$-0.824781\pi$
$271$	−28.0606	−1.70456	−0.852280	+	0.523085i	$0.824781\pi$
$272$	−3.50013	−0.212226
$273$	1.86336	0.112776
$274$	26.1150	1.57767
$275$	−1.73620	−0.104697
$276$	−1.13344	−0.0682254
$277$	−4.80531	−0.288723	−0.144362	−	0.989525i	$-0.546113\pi$
$277$	−4.80531	−0.288723	−0.144362	+	0.989525i	$0.546113\pi$
$278$	8.67185	0.520103
$279$	10.4362	0.624798
$280$	−1.96374	−0.117356
$281$	16.3661	0.976322	0.488161	−	0.872754i	$-0.337668\pi$
$281$	16.3661	0.976322	0.488161	+	0.872754i	$0.337668\pi$
$282$	15.7061	0.935284
$283$	32.3411	1.92248	0.961240	−	0.275711i	$-0.0889134\pi$
$283$	32.3411	1.92248	0.961240	+	0.275711i	$0.0889134\pi$
$284$	−0.709507	−0.0421015
$285$	−0.104961	−0.00621735
$286$	−3.67149	−0.217100
$287$	−4.44383	−0.262311
$288$	1.26480	0.0745292
$289$	1.00000	0.0588235
$290$	7.04874	0.413916
$291$	−12.5841	−0.737694
$292$	2.88471	0.168815
$293$	17.9838	1.05063	0.525313	−	0.850909i	$-0.323948\pi$
$293$	17.9838	1.05063	0.525313	+	0.850909i	$0.323948\pi$
$294$	9.07345	0.529174
$295$	13.3629	0.778016
$296$	−22.9199	−1.33219
$297$	−0.644895	−0.0374206
$298$	4.07676	0.236160
$299$	21.5540	1.24650
$300$	−0.604923	−0.0349253
$301$	4.65946	0.268567
$302$	−28.6260	−1.64724
$303$	14.5211	0.834213
$304$	−0.241832	−0.0138700
$305$	4.50255	0.257815
$306$	1.33241	0.0761686
$307$	−26.8183	−1.53060	−0.765301	−	0.643673i	$-0.777410\pi$
$307$	−26.8183	−1.53060	−0.765301	+	0.643673i	$0.777410\pi$
$308$	−0.0631916	−0.00360067
$309$	8.85705	0.503860
$310$	21.1240	1.19976
$311$	−14.8353	−0.841234	−0.420617	−	0.907238i	$-0.638186\pi$
$311$	−14.8353	−0.841234	−0.420617	+	0.907238i	$0.638186\pi$
$312$	−12.6655	−0.717046
$313$	22.2795	1.25931	0.629655	−	0.776875i	$-0.283196\pi$
$313$	22.2795	1.25931	0.629655	+	0.776875i	$0.283196\pi$
$314$	−1.33241	−0.0751920
$315$	0.662487	0.0373269
$316$	−2.60451	−0.146515
$317$	23.0816	1.29639	0.648195	−	0.761474i	$-0.275524\pi$
$317$	23.0816	1.29639	0.648195	+	0.761474i	$0.275524\pi$
$318$	6.47068	0.362857
$319$	2.24577	0.125739
$320$	13.1945	0.737593
$321$	−17.9402	−1.00133
$322$	−2.93107	−0.163342
$323$	0.0690924	0.00384440
$324$	−0.224694	−0.0124830
$325$	11.5034	0.638095
$326$	27.7293	1.53578
$327$	−0.909858	−0.0503153
$328$	30.2054	1.66781
$329$	−5.14057	−0.283409
$330$	−1.30534	−0.0718566
$331$	22.7342	1.24958	0.624792	−	0.780791i	$-0.285184\pi$
$331$	22.7342	1.24958	0.624792	+	0.780791i	$0.285184\pi$
$332$	−0.447542	−0.0245621
$333$	7.73226	0.423725
$334$	−23.4551	−1.28341
$335$	18.6088	1.01671
$336$	1.52638	0.0832710
$337$	18.8832	1.02863	0.514317	−	0.857600i	$-0.328046\pi$
$337$	18.8832	1.02863	0.514317	+	0.857600i	$0.328046\pi$
$338$	7.00473	0.381007
$339$	−16.2524	−0.882707
$340$	−0.341341	−0.0185118
$341$	6.73024	0.364463
$342$	0.0920591	0.00497799
$343$	−6.02237	−0.325178
$344$	−31.6711	−1.70759
$345$	7.66315	0.412570
$346$	−15.9810	−0.859144
$347$	29.1051	1.56244	0.781221	−	0.624255i	$-0.214597\pi$
$347$	29.1051	1.56244	0.781221	+	0.624255i	$0.214597\pi$
$348$	0.782470	0.0419448
$349$	8.15932	0.436758	0.218379	−	0.975864i	$-0.429923\pi$
$349$	8.15932	0.436758	0.218379	+	0.975864i	$0.429923\pi$
$350$	−1.56432	−0.0836165
$351$	4.27285	0.228068
$352$	0.815665	0.0434751
$353$	−0.759625	−0.0404307	−0.0202154	−	0.999796i	$-0.506435\pi$
$353$	−0.759625	−0.0404307	−0.0202154	+	0.999796i	$0.506435\pi$
$354$	−11.7203	−0.622927
$355$	4.79694	0.254595
$356$	−2.77343	−0.146991
$357$	−0.436093	−0.0230805
$358$	−7.81500	−0.413035
$359$	9.17693	0.484340	0.242170	−	0.970234i	$-0.422141\pi$
$359$	9.17693	0.484340	0.242170	+	0.970234i	$0.422141\pi$
$360$	−4.50303	−0.237330
$361$	−18.9952	−0.999749
$362$	30.1903	1.58677
$363$	10.5841	0.555522
$364$	0.418685	0.0219451
$365$	−19.5034	−1.02085
$366$	−3.94909	−0.206422
$367$	−4.43002	−0.231245	−0.115623	−	0.993293i	$-0.536886\pi$
$367$	−4.43002	−0.231245	−0.115623	+	0.993293i	$0.536886\pi$
$368$	17.6560	0.920385
$369$	−10.1901	−0.530475
$370$	15.6510	0.813655
$371$	−2.11784	−0.109953
$372$	2.34494	0.121580
$373$	33.3422	1.72639	0.863196	−	0.504870i	$-0.168459\pi$
$373$	33.3422	1.72639	0.863196	+	0.504870i	$0.168459\pi$
$374$	0.859262	0.0444314
$375$	11.6855	0.603439
$376$	34.9412	1.80196
$377$	−14.8797	−0.766343
$378$	−0.581054	−0.0298862
$379$	−17.6929	−0.908822	−0.454411	−	0.890792i	$-0.650150\pi$
$379$	−17.6929	−0.908822	−0.454411	+	0.890792i	$0.650150\pi$
$380$	−0.0235841	−0.00120984
$381$	−1.02495	−0.0525100
$382$	13.0575	0.668078
$383$	−7.16233	−0.365978	−0.182989	−	0.983115i	$-0.558577\pi$
$383$	−7.16233	−0.365978	−0.182989	+	0.983115i	$0.558577\pi$
$384$	−9.04299	−0.461473
$385$	0.427235	0.0217739
$386$	35.7600	1.82013
$387$	10.6846	0.543126
$388$	−2.82757	−0.143548
$389$	−16.6936	−0.846397	−0.423198	−	0.906037i	$-0.639093\pi$
$389$	−16.6936	−0.846397	−0.423198	+	0.906037i	$0.639093\pi$
$390$	8.64871	0.437945
$391$	−5.04440	−0.255106
$392$	20.1856	1.01953
$393$	−15.5677	−0.785288
$394$	11.0593	0.557158
$395$	17.6089	0.886001
$396$	−0.144904	−0.00728169
$397$	27.3997	1.37515	0.687575	−	0.726114i	$-0.258675\pi$
$397$	27.3997	1.37515	0.687575	+	0.726114i	$0.258675\pi$
$398$	−1.24503	−0.0624079
$399$	−0.0301307	−0.00150842
$400$	9.42309	0.471154
$401$	21.2306	1.06021	0.530103	−	0.847933i	$-0.322153\pi$
$401$	21.2306	1.06021	0.530103	+	0.847933i	$0.322153\pi$
$402$	−16.3214	−0.814038
$403$	−44.5922	−2.22130
$404$	3.26279	0.162330
$405$	1.51914	0.0754867
$406$	2.02345	0.100422
$407$	4.98650	0.247172
$408$	2.96420	0.146750
$409$	32.4002	1.60209	0.801044	−	0.598606i	$-0.204278\pi$
$409$	32.4002	1.60209	0.801044	+	0.598606i	$0.204278\pi$
$410$	−20.6259	−1.01864
$411$	−19.5999	−0.966791
$412$	1.99012	0.0980463
$413$	3.83603	0.188758
$414$	−6.72119	−0.330329
$415$	3.02580	0.148531
$416$	−5.40430	−0.264968
$417$	−6.50841	−0.318718
$418$	0.0593684	0.00290381
$419$	3.94304	0.192630	0.0963152	−	0.995351i	$-0.469294\pi$
$419$	3.94304	0.192630	0.0963152	+	0.995351i	$0.469294\pi$
$420$	0.148857	0.00726346
$421$	27.1580	1.32360	0.661799	−	0.749681i	$-0.269793\pi$
$421$	27.1580	1.32360	0.661799	+	0.749681i	$0.269793\pi$
$422$	−19.5760	−0.952944
$423$	−11.7878	−0.573141
$424$	14.3953	0.699096
$425$	−2.69221	−0.130592
$426$	−4.20729	−0.203844
$427$	1.29253	0.0625498
$428$	−4.03105	−0.194848
$429$	2.75554	0.133039
$430$	21.6267	1.04293
$431$	−22.8215	−1.09927	−0.549636	−	0.835404i	$-0.685234\pi$
$431$	−22.8215	−1.09927	−0.549636	+	0.835404i	$0.685234\pi$
$432$	3.50013	0.168400
$433$	10.2525	0.492705	0.246353	−	0.969180i	$-0.420768\pi$
$433$	10.2525	0.492705	0.246353	+	0.969180i	$0.420768\pi$
$434$	6.06398	0.291081
$435$	−5.29023	−0.253647
$436$	−0.204439	−0.00979087
$437$	−0.348530	−0.0166724
$438$	17.1060	0.817356
$439$	−13.6861	−0.653202	−0.326601	−	0.945162i	$-0.605903\pi$
$439$	−13.6861	−0.653202	−0.326601	+	0.945162i	$0.605903\pi$
$440$	−2.90398	−0.138442
$441$	−6.80982	−0.324277
$442$	−5.69317	−0.270796
$443$	−25.6442	−1.21839	−0.609196	−	0.793019i	$-0.708508\pi$
$443$	−25.6442	−1.21839	−0.609196	+	0.793019i	$0.708508\pi$
$444$	1.73739	0.0824529
$445$	18.7510	0.888882
$446$	−21.5340	−1.01966
$447$	−3.05970	−0.144719
$448$	3.78768	0.178951
$449$	25.0929	1.18421	0.592103	−	0.805862i	$-0.298298\pi$
$449$	25.0929	1.18421	0.592103	+	0.805862i	$0.298298\pi$
$450$	−3.58712	−0.169099
$451$	−6.57153	−0.309441
$452$	−3.65180	−0.171766
$453$	21.4844	1.00943
$454$	3.51400	0.164920
$455$	−2.83070	−0.132705
$456$	0.204803	0.00959079
$457$	−10.5843	−0.495111	−0.247556	−	0.968874i	$-0.579627\pi$
$457$	−10.5843	−0.495111	−0.247556	+	0.968874i	$0.579627\pi$
$458$	−9.28515	−0.433867
$459$	−1.00000	−0.0466760
$460$	1.72186	0.0802822
$461$	−3.23520	−0.150678	−0.0753392	−	0.997158i	$-0.524004\pi$
$461$	−3.23520	−0.150678	−0.0753392	+	0.997158i	$0.524004\pi$
$462$	−0.374719	−0.0174335
$463$	28.8069	1.33877	0.669384	−	0.742916i	$-0.266558\pi$
$463$	28.8069	1.33877	0.669384	+	0.742916i	$0.266558\pi$
$464$	−12.1888	−0.565850
$465$	−15.8540	−0.735213
$466$	−33.2740	−1.54139
$467$	42.5869	1.97068	0.985342	−	0.170589i	$-0.0545670\pi$
$467$	42.5869	1.97068	0.985342	+	0.170589i	$0.0545670\pi$
$468$	0.960081	0.0443798
$469$	5.34196	0.246669
$470$	−23.8598	−1.10057
$471$	1.00000	0.0460776
$472$	−26.0741	−1.20016
$473$	6.89042	0.316822
$474$	−15.4444	−0.709386
$475$	−0.186011	−0.00853479
$476$	−0.0979874	−0.00449125
$477$	−4.85638	−0.222359
$478$	−26.3531	−1.20536
$479$	−7.67898	−0.350862	−0.175431	−	0.984492i	$-0.556132\pi$
$479$	−7.67898	−0.350862	−0.175431	+	0.984492i	$0.556132\pi$
$480$	−1.92141	−0.0877000
$481$	−33.0388	−1.50644
$482$	23.0743	1.05100
$483$	2.19983	0.100096
$484$	2.37818	0.108099
$485$	19.1170	0.868059
$486$	−1.33241	−0.0604392
$487$	9.63471	0.436591	0.218295	−	0.975883i	$-0.429950\pi$
$487$	9.63471	0.436591	0.218295	+	0.975883i	$0.429950\pi$
$488$	−8.78552	−0.397702
$489$	−20.8114	−0.941126
$490$	−13.7838	−0.622690
$491$	−7.80857	−0.352396	−0.176198	−	0.984355i	$-0.556380\pi$
$491$	−7.80857	−0.352396	−0.176198	+	0.984355i	$0.556380\pi$
$492$	−2.28965	−0.103225
$493$	3.48239	0.156839
$494$	−0.393354	−0.0176978
$495$	0.979686	0.0440336
$496$	−36.5280	−1.64015
$497$	1.37704	0.0617686
$498$	−2.65387	−0.118923
$499$	−28.3439	−1.26885	−0.634423	−	0.772986i	$-0.718762\pi$
$499$	−28.3439	−1.26885	−0.634423	+	0.772986i	$0.718762\pi$
$500$	2.62567	0.117423
$501$	17.6036	0.786470
$502$	13.1967	0.588996
$503$	36.7429	1.63828	0.819142	−	0.573591i	$-0.194450\pi$
$503$	36.7429	1.63828	0.819142	+	0.573591i	$0.194450\pi$
$504$	−1.29267	−0.0575799
$505$	−22.0595	−0.981636
$506$	−4.33446	−0.192690
$507$	−5.25721	−0.233481
$508$	−0.230301	−0.0102179
$509$	24.2530	1.07499	0.537497	−	0.843265i	$-0.319370\pi$
$509$	24.2530	1.07499	0.537497	+	0.843265i	$0.319370\pi$
$510$	−2.02411	−0.0896292
$511$	−5.59875	−0.247674
$512$	−25.1771	−1.11268
$513$	−0.0690924	−0.00305050
$514$	27.0595	1.19354
$515$	−13.4551	−0.592903
$516$	2.40075	0.105687
$517$	−7.60187	−0.334330
$518$	4.49286	0.197405
$519$	11.9941	0.526482
$520$	19.2407	0.843762
$521$	21.1975	0.928679	0.464339	−	0.885657i	$-0.346292\pi$
$521$	21.1975	0.928679	0.464339	+	0.885657i	$0.346292\pi$
$522$	4.63995	0.203085
$523$	−29.5010	−1.28999	−0.644995	−	0.764187i	$-0.723141\pi$
$523$	−29.5010	−1.28999	−0.644995	+	0.764187i	$0.723141\pi$
$524$	−3.49797	−0.152810
$525$	1.17406	0.0512401
$526$	−8.61126	−0.375469
$527$	10.4362	0.454607
$528$	2.25721	0.0982326
$529$	2.44600	0.106348
$530$	−9.82986	−0.426982
$531$	8.79634	0.381729
$532$	−0.00677018	−0.000293525 0
$533$	43.5406	1.88595
$534$	−16.4461	−0.711693
$535$	27.2537	1.17828
$536$	−36.3101	−1.56836
$537$	5.86533	0.253107
$538$	2.77854	0.119792
$539$	−4.39162	−0.189160
$540$	0.341341	0.0146890
$541$	−11.3171	−0.486559	−0.243280	−	0.969956i	$-0.578223\pi$
$541$	−11.3171	−0.486559	−0.243280	+	0.969956i	$0.578223\pi$
$542$	−37.3881	−1.60596
$543$	−22.6585	−0.972369
$544$	1.26480	0.0542279
$545$	1.38220	0.0592070
$546$	2.48275	0.106252
$547$	23.8565	1.02003	0.510015	−	0.860165i	$-0.329640\pi$
$547$	23.8565	1.02003	0.510015	+	0.860165i	$0.329640\pi$
$548$	−4.40397	−0.188128
$549$	2.96388	0.126495
$550$	−2.31332	−0.0986402
$551$	0.240606	0.0102502
$552$	−14.9526	−0.636425
$553$	5.05492	0.214957
$554$	−6.40263	−0.272022
$555$	−11.7464	−0.498606
$556$	−1.46240	−0.0620195
$557$	−8.30474	−0.351883	−0.175942	−	0.984401i	$-0.556297\pi$
$557$	−8.30474	−0.351883	−0.175942	+	0.984401i	$0.556297\pi$
$558$	13.9052	0.588656
$559$	−45.6534	−1.93093
$560$	−2.31879	−0.0979867
$561$	−0.644895	−0.0272275
$562$	21.8063	0.919845
$563$	−5.20056	−0.219178	−0.109589	−	0.993977i	$-0.534953\pi$
$563$	−5.20056	−0.219178	−0.109589	+	0.993977i	$0.534953\pi$
$564$	−2.64864	−0.111528
$565$	24.6896	1.03870
$566$	43.0915	1.81127
$567$	0.436093	0.0183142
$568$	−9.35994	−0.392734
$569$	20.9422	0.877943	0.438971	−	0.898501i	$-0.355343\pi$
$569$	20.9422	0.877943	0.438971	+	0.898501i	$0.355343\pi$
$570$	−0.139851	−0.00585770
$571$	−11.5455	−0.483164	−0.241582	−	0.970380i	$-0.577666\pi$
$571$	−11.5455	−0.483164	−0.241582	+	0.970380i	$0.577666\pi$
$572$	0.619151	0.0258880
$573$	−9.79991	−0.409397
$574$	−5.92099	−0.247137
$575$	13.5806	0.566351
$576$	8.68548	0.361895
$577$	25.2478	1.05108	0.525539	−	0.850769i	$-0.323864\pi$
$577$	25.2478	1.05108	0.525539	+	0.850769i	$0.323864\pi$
$578$	1.33241	0.0554208
$579$	−26.8386	−1.11538
$580$	−1.18868	−0.0493573
$581$	0.868606	0.0360358
$582$	−16.7672	−0.695021
$583$	−3.13186	−0.129708
$584$	38.0556	1.57475
$585$	−6.49105	−0.268372
$586$	23.9617	0.989850
$587$	20.7881	0.858017	0.429008	−	0.903300i	$-0.358863\pi$
$587$	20.7881	0.858017	0.429008	+	0.903300i	$0.358863\pi$
$588$	−1.53012	−0.0631012
$589$	0.721061	0.0297108
$590$	17.8048	0.733011
$591$	−8.30023	−0.341426
$592$	−27.0639	−1.11232
$593$	−38.2341	−1.57008	−0.785042	−	0.619442i	$-0.787359\pi$
$593$	−38.2341	−1.57008	−0.785042	+	0.619442i	$0.787359\pi$
$594$	−0.859262	−0.0352560
$595$	0.662487	0.0271593
$596$	−0.687494	−0.0281609
$597$	0.934425	0.0382435
$598$	28.7186	1.17439
$599$	0.0581685	0.00237670	0.00118835	−	0.999999i	$-0.499622\pi$
$599$	0.0581685	0.00237670	0.00118835	+	0.999999i	$0.499622\pi$
$600$	−7.98025	−0.325792
$601$	−33.6355	−1.37202	−0.686010	−	0.727592i	$-0.740639\pi$
$601$	−33.6355	−1.37202	−0.686010	+	0.727592i	$0.740639\pi$
$602$	6.20830	0.253031
$603$	12.2496	0.498841
$604$	4.82741	0.196424
$605$	−16.0787	−0.653694
$606$	19.3479	0.785957
$607$	5.43712	0.220686	0.110343	−	0.993894i	$-0.464805\pi$
$607$	5.43712	0.220686	0.110343	+	0.993894i	$0.464805\pi$
$608$	0.0873882	0.00354406
$609$	−1.51865	−0.0615386
$610$	5.99922	0.242901
$611$	50.3673	2.03764
$612$	−0.224694	−0.00908270
$613$	23.3190	0.941844	0.470922	−	0.882175i	$-0.343921\pi$
$613$	23.3190	0.941844	0.470922	+	0.882175i	$0.343921\pi$
$614$	−35.7329	−1.44206
$615$	15.4802	0.624220
$616$	−0.833634	−0.0335881
$617$	−24.1565	−0.972506	−0.486253	−	0.873818i	$-0.661637\pi$
$617$	−24.1565	−0.972506	−0.486253	+	0.873818i	$0.661637\pi$
$618$	11.8012	0.474714
$619$	11.9495	0.480292	0.240146	−	0.970737i	$-0.422805\pi$
$619$	11.9495	0.480292	0.240146	+	0.970737i	$0.422805\pi$
$620$	−3.56230	−0.143065
$621$	5.04440	0.202425
$622$	−19.7667	−0.792572
$623$	5.38277	0.215656
$624$	−14.9555	−0.598699
$625$	−4.29091	−0.171636
$626$	29.6853	1.18646
$627$	−0.0445573	−0.00177945
$628$	0.224694	0.00896625
$629$	7.73226	0.308306
$630$	0.882702	0.0351677
$631$	−35.8385	−1.42671	−0.713355	−	0.700803i	$-0.752825\pi$
$631$	−35.8385	−1.42671	−0.713355	+	0.700803i	$0.752825\pi$
$632$	−34.3591	−1.36673
$633$	14.6922	0.583963
$634$	30.7540	1.22140
$635$	1.55705	0.0617896
$636$	−1.09120	−0.0432688
$637$	29.0973	1.15288
$638$	2.99228	0.118466
$639$	3.15767	0.124915
$640$	13.7376	0.543025
$641$	−0.455528	−0.0179923	−0.00899614	−	0.999960i	$-0.502864\pi$
$641$	−0.455528	−0.0179923	−0.00899614	+	0.999960i	$0.502864\pi$
$642$	−23.9037	−0.943402
$643$	−13.2675	−0.523220	−0.261610	−	0.965174i	$-0.584253\pi$
$643$	−13.2675	−0.523220	−0.261610	+	0.965174i	$0.584253\pi$
$644$	0.494288	0.0194777
$645$	−16.2313	−0.639108
$646$	0.0920591	0.00362202
$647$	18.2556	0.717703	0.358852	−	0.933395i	$-0.383168\pi$
$647$	18.2556	0.717703	0.358852	+	0.933395i	$0.383168\pi$
$648$	−2.96420	−0.116445
$649$	5.67272	0.222674
$650$	15.3272	0.601183
$651$	−4.55115	−0.178374
$652$	−4.67620	−0.183134
$653$	21.4090	0.837801	0.418900	−	0.908032i	$-0.362416\pi$
$653$	21.4090	0.837801	0.418900	+	0.908032i	$0.362416\pi$
$654$	−1.21230	−0.0474047
$655$	23.6496	0.924065
$656$	35.6666	1.39255
$657$	−12.8384	−0.500875
$658$	−6.84933	−0.267015
$659$	−30.5377	−1.18958	−0.594790	−	0.803881i	$-0.702765\pi$
$659$	−30.5377	−1.18958	−0.594790	+	0.803881i	$0.702765\pi$
$660$	0.220129	0.00856851
$661$	−9.54856	−0.371396	−0.185698	−	0.982607i	$-0.559455\pi$
$661$	−9.54856	−0.371396	−0.185698	+	0.982607i	$0.559455\pi$
$662$	30.2912	1.17730
$663$	4.27285	0.165944
$664$	−5.90405	−0.229122
$665$	0.0457728	0.00177499
$666$	10.3025	0.399214
$667$	−17.5666	−0.680180
$668$	3.95541	0.153040
$669$	16.1617	0.624848
$670$	24.7945	0.957895
$671$	1.91139	0.0737884
$672$	−0.551572	−0.0212773
$673$	10.7184	0.413163	0.206582	−	0.978429i	$-0.433766\pi$
$673$	10.7184	0.413163	0.206582	+	0.978429i	$0.433766\pi$
$674$	25.1601	0.969131
$675$	2.69221	0.103623
$676$	−1.18126	−0.0454331
$677$	−22.7224	−0.873291	−0.436646	−	0.899634i	$-0.643834\pi$
$677$	−22.7224	−0.873291	−0.436646	+	0.899634i	$0.643834\pi$
$678$	−21.6547	−0.831645
$679$	5.48785	0.210604
$680$	−4.50303	−0.172683
$681$	−2.63734	−0.101063
$682$	8.96742	0.343380
$683$	−26.5163	−1.01462	−0.507310	−	0.861764i	$-0.669360\pi$
$683$	−26.5163	−1.01462	−0.507310	+	0.861764i	$0.669360\pi$
$684$	−0.0155246	−0.000593598 0
$685$	29.7750	1.13764
$686$	−8.02425	−0.306367
$687$	6.96871	0.265873
$688$	−37.3973	−1.42576
$689$	20.7506	0.790534
$690$	10.2104	0.388704
$691$	9.42542	0.358560	0.179280	−	0.983798i	$-0.442623\pi$
$691$	9.42542	0.358560	0.179280	+	0.983798i	$0.442623\pi$
$692$	2.69500	0.102448
$693$	0.281235	0.0106832
$694$	38.7798	1.47206
$695$	9.88718	0.375042
$696$	10.3225	0.391272
$697$	−10.1901	−0.385977
$698$	10.8715	0.411493
$699$	24.9729	0.944560
$700$	0.263803	0.00997082
$701$	−16.9989	−0.642041	−0.321021	−	0.947072i	$-0.604026\pi$
$701$	−16.9989	−0.642041	−0.321021	+	0.947072i	$0.604026\pi$
$702$	5.69317	0.214875
$703$	0.534240	0.0201493
$704$	5.60122	0.211104
$705$	17.9073	0.674427
$706$	−1.01213	−0.0380920
$707$	−6.33254	−0.238160
$708$	1.97648	0.0742807
$709$	19.0783	0.716499	0.358249	−	0.933626i	$-0.383374\pi$
$709$	19.0783	0.716499	0.358249	+	0.933626i	$0.383374\pi$
$710$	6.39147	0.239867
$711$	11.5914	0.434710
$712$	−36.5875	−1.37118
$713$	−52.6443	−1.97155
$714$	−0.581054	−0.0217454
$715$	−4.18605	−0.156549
$716$	1.31790	0.0492523
$717$	19.7786	0.738644
$718$	12.2274	0.456322
$719$	−9.16641	−0.341849	−0.170925	−	0.985284i	$-0.554675\pi$
$719$	−9.16641	−0.341849	−0.170925	+	0.985284i	$0.554675\pi$
$720$	−5.31718	−0.198160
$721$	−3.86250	−0.143847
$722$	−25.3094	−0.941917
$723$	−17.3177	−0.644054
$724$	−5.09122	−0.189214
$725$	−9.37533	−0.348191
$726$	14.1023	0.523387
$727$	−28.7611	−1.06669	−0.533345	−	0.845898i	$-0.679065\pi$
$727$	−28.7611	−1.06669	−0.533345	+	0.845898i	$0.679065\pi$
$728$	5.52336	0.204709
$729$	1.00000	0.0370370
$730$	−25.9864	−0.961800
$731$	10.6846	0.395182
$732$	0.665965	0.0246148
$733$	−10.5294	−0.388911	−0.194456	−	0.980911i	$-0.562294\pi$
$733$	−10.5294	−0.388911	−0.194456	+	0.980911i	$0.562294\pi$
$734$	−5.90259	−0.217868
$735$	10.3451	0.381584
$736$	−6.38017	−0.235176
$737$	7.89969	0.290989
$738$	−13.5773	−0.499788
$739$	−23.7096	−0.872172	−0.436086	−	0.899905i	$-0.643636\pi$
$739$	−23.7096	−0.872172	−0.436086	+	0.899905i	$0.643636\pi$
$740$	−2.63934	−0.0970240
$741$	0.295221	0.0108452
$742$	−2.82182	−0.103592
$743$	−31.7700	−1.16553	−0.582764	−	0.812642i	$-0.698029\pi$
$743$	−31.7700	−1.16553	−0.582764	+	0.812642i	$0.698029\pi$
$744$	30.9349	1.13413
$745$	4.64811	0.170293
$746$	44.4253	1.62653
$747$	1.99179	0.0728757
$748$	−0.144904	−0.00529821
$749$	7.82361	0.285869
$750$	15.5699	0.568532
$751$	21.2377	0.774974	0.387487	−	0.921875i	$-0.373343\pi$
$751$	21.2377	0.774974	0.387487	+	0.921875i	$0.373343\pi$
$752$	41.2587	1.50455
$753$	−9.90439	−0.360936
$754$	−19.8258	−0.722013
$755$	−32.6378	−1.18781
$756$	0.0979874	0.00356377
$757$	−23.5676	−0.856580	−0.428290	−	0.903641i	$-0.640884\pi$
$757$	−23.5676	−0.856580	−0.428290	+	0.903641i	$0.640884\pi$
$758$	−23.5741	−0.856250
$759$	3.25311	0.118080
$760$	−0.311125	−0.0112857
$761$	1.52448	0.0552624	0.0276312	−	0.999618i	$-0.491204\pi$
$761$	1.52448	0.0552624	0.0276312	+	0.999618i	$0.491204\pi$
$762$	−1.36565	−0.0494724
$763$	0.396783	0.0143645
$764$	−2.20198	−0.0796648
$765$	1.51914	0.0549246
$766$	−9.54314	−0.344808
$767$	−37.5854	−1.35713
$768$	5.32203	0.192042
$769$	−0.0123132	−0.000444024 0	−0.000222012	−	1.00000i	$-0.500071\pi$
$769$	−0.0123132	−0.000444024 0	−0.000222012		1.00000i	$0.500071\pi$
$770$	0.569250	0.0205143
$771$	−20.3087	−0.731401
$772$	−6.03047	−0.217041
$773$	33.6529	1.21041	0.605205	−	0.796070i	$-0.293091\pi$
$773$	33.6529	1.21041	0.605205	+	0.796070i	$0.293091\pi$
$774$	14.2362	0.511708
$775$	−28.0965	−1.00925
$776$	−37.3018	−1.33906
$777$	−3.37199	−0.120969
$778$	−22.2426	−0.797436
$779$	−0.704057	−0.0252255
$780$	−1.45850	−0.0522226
$781$	2.03636	0.0728668
$782$	−6.72119	−0.240349
$783$	−3.48239	−0.124450
$784$	23.8352	0.851258
$785$	−1.51914	−0.0542204
$786$	−20.7425	−0.739862
$787$	12.8897	0.459469	0.229734	−	0.973253i	$-0.426214\pi$
$787$	12.8897	0.459469	0.229734	+	0.973253i	$0.426214\pi$
$788$	−1.86501	−0.0664381
$789$	6.46294	0.230087
$790$	23.4622	0.834749
$791$	7.08755	0.252004
$792$	−1.91160	−0.0679256
$793$	−12.6642	−0.449719
$794$	36.5075	1.29560
$795$	7.37752	0.261654
$796$	0.209959	0.00744181
$797$	−32.8001	−1.16184	−0.580920	−	0.813961i	$-0.697307\pi$
$797$	−32.8001	−1.16184	−0.580920	+	0.813961i	$0.697307\pi$
$798$	−0.0401464	−0.00142117
$799$	−11.7878	−0.417021
$800$	−3.40512	−0.120389
$801$	12.3432	0.436124
$802$	28.2878	0.998878
$803$	−8.27944	−0.292175
$804$	2.75240	0.0970697
$805$	−3.34185	−0.117785
$806$	−59.4149	−2.09280
$807$	−2.08536	−0.0734081
$808$	43.0433	1.51426
$809$	−36.6693	−1.28922	−0.644612	−	0.764510i	$-0.722981\pi$
$809$	−36.6693	−1.28922	−0.644612	+	0.764510i	$0.722981\pi$
$810$	2.02411	0.0711200
$811$	28.2305	0.991306	0.495653	−	0.868521i	$-0.334929\pi$
$811$	28.2305	0.991306	0.495653	+	0.868521i	$0.334929\pi$
$812$	−0.341230	−0.0119748
$813$	28.0606	0.984129
$814$	6.64404	0.232874
$815$	31.6155	1.10744
$816$	3.50013	0.122529
$817$	0.738221	0.0258271
$818$	43.1702	1.50941
$819$	−1.86336	−0.0651111
$820$	3.47829	0.121467
$821$	−53.1113	−1.85360	−0.926799	−	0.375557i	$-0.877451\pi$
$821$	−53.1113	−1.85360	−0.926799	+	0.375557i	$0.877451\pi$
$822$	−26.1150	−0.910866
$823$	2.21202	0.0771062	0.0385531	−	0.999257i	$-0.487725\pi$
$823$	2.21202	0.0771062	0.0385531	+	0.999257i	$0.487725\pi$
$824$	26.2540	0.914603
$825$	1.73620	0.0604466
$826$	5.11114	0.177839
$827$	−38.1381	−1.32619	−0.663095	−	0.748535i	$-0.730758\pi$
$827$	−38.1381	−1.32619	−0.663095	+	0.748535i	$0.730758\pi$
$828$	1.13344	0.0393899
$829$	−1.82936	−0.0635364	−0.0317682	−	0.999495i	$-0.510114\pi$
$829$	−1.82936	−0.0635364	−0.0317682	+	0.999495i	$0.510114\pi$
$830$	4.03160	0.139939
$831$	4.80531	0.166694
$832$	−37.1117	−1.28662
$833$	−6.80982	−0.235946
$834$	−8.67185	−0.300281
$835$	−26.7423	−0.925456
$836$	−0.0100117	−0.000346263 0
$837$	−10.4362	−0.360727
$838$	5.25374	0.181487
$839$	−40.9582	−1.41403	−0.707017	−	0.707197i	$-0.749959\pi$
$839$	−40.9582	−1.41403	−0.707017	+	0.707197i	$0.749959\pi$
$840$	1.96374	0.0677555
$841$	−16.8730	−0.581827
$842$	36.1854	1.24703
$843$	−16.3661	−0.563680
$844$	3.30125	0.113634
$845$	7.98643	0.274742
$846$	−15.7061	−0.539987
$847$	−4.61566	−0.158596
$848$	16.9980	0.583712
$849$	−32.3411	−1.10994
$850$	−3.58712	−0.123037
$851$	−39.0046	−1.33706
$852$	0.709507	0.0243073
$853$	14.4275	0.493989	0.246995	−	0.969017i	$-0.420557\pi$
$853$	14.4275	0.493989	0.246995	+	0.969017i	$0.420557\pi$
$854$	1.72217	0.0589315
$855$	0.104961	0.00358959
$856$	−53.1783	−1.81760
$857$	24.1991	0.826626	0.413313	−	0.910589i	$-0.364372\pi$
$857$	24.1991	0.826626	0.413313	+	0.910589i	$0.364372\pi$
$858$	3.67149	0.125343
$859$	−41.5674	−1.41826	−0.709131	−	0.705076i	$-0.750913\pi$
$859$	−41.5674	−1.41826	−0.709131	+	0.705076i	$0.750913\pi$
$860$	−3.64708	−0.124364
$861$	4.44383	0.151445
$862$	−30.4075	−1.03568
$863$	46.2346	1.57385	0.786923	−	0.617052i	$-0.211673\pi$
$863$	46.2346	1.57385	0.786923	+	0.617052i	$0.211673\pi$
$864$	−1.26480	−0.0430294
$865$	−18.2207	−0.619522
$866$	13.6605	0.464204
$867$	−1.00000	−0.0339618
$868$	−1.02261	−0.0347098
$869$	7.47522	0.253579
$870$	−7.04874	−0.238975
$871$	−52.3405	−1.77349
$872$	−2.69700	−0.0913319
$873$	12.5841	0.425908
$874$	−0.464383	−0.0157080
$875$	−5.09599	−0.172276
$876$	−2.88471	−0.0974654
$877$	−20.3058	−0.685677	−0.342839	−	0.939394i	$-0.611388\pi$
$877$	−20.3058	−0.685677	−0.342839	+	0.939394i	$0.611388\pi$
$878$	−18.2354	−0.615416
$879$	−17.9838	−0.606579
$880$	−3.42902	−0.115592
$881$	0.985727	0.0332100	0.0166050	−	0.999862i	$-0.494714\pi$
$881$	0.985727	0.0332100	0.0166050	+	0.999862i	$0.494714\pi$
$882$	−9.07345	−0.305519
$883$	−40.6621	−1.36839	−0.684194	−	0.729300i	$-0.739846\pi$
$883$	−40.6621	−1.36839	−0.684194	+	0.729300i	$0.739846\pi$
$884$	0.960081	0.0322910
$885$	−13.3629	−0.449188
$886$	−34.1685	−1.14791
$887$	−8.83561	−0.296671	−0.148335	−	0.988937i	$-0.547392\pi$
$887$	−8.83561	−0.296671	−0.148335	+	0.988937i	$0.547392\pi$
$888$	22.9199	0.769143
$889$	0.446976	0.0149911
$890$	24.9839	0.837463
$891$	0.644895	0.0216048
$892$	3.63143	0.121589
$893$	−0.814445	−0.0272543
$894$	−4.07676	−0.136347
$895$	−8.91025	−0.297837
$896$	3.94359	0.131746
$897$	−21.5540	−0.719665
$898$	33.4339	1.11570
$899$	36.3428	1.21210
$900$	0.604923	0.0201641
$901$	−4.85638	−0.161790
$902$	−8.75595	−0.291541
$903$	−4.65946	−0.155057
$904$	−48.1752	−1.60228
$905$	34.4214	1.14421
$906$	28.6260	0.951034
$907$	−22.2271	−0.738037	−0.369019	−	0.929422i	$-0.620306\pi$
$907$	−22.2271	−0.738037	−0.369019	+	0.929422i	$0.620306\pi$
$908$	−0.592592	−0.0196659
$909$	−14.5211	−0.481633
$910$	−3.77165	−0.125029
$911$	2.70456	0.0896060	0.0448030	−	0.998996i	$-0.485734\pi$
$911$	2.70456	0.0896060	0.0448030	+	0.998996i	$0.485734\pi$
$912$	0.241832	0.00800786
$913$	1.28449	0.0425105
$914$	−14.1025	−0.466471
$915$	−4.50255	−0.148850
$916$	1.56582	0.0517363
$917$	6.78899	0.224192
$918$	−1.33241	−0.0439760
$919$	41.2347	1.36021	0.680103	−	0.733116i	$-0.261935\pi$
$919$	41.2347	1.36021	0.680103	+	0.733116i	$0.261935\pi$
$920$	22.7151	0.748894
$921$	26.8183	0.883693
$922$	−4.31060	−0.141962
$923$	−13.4922	−0.444102
$924$	0.0631916	0.00207885
$925$	−20.8169	−0.684456
$926$	38.3825	1.26133
$927$	−8.85705	−0.290904
$928$	4.40453	0.144586
$929$	−55.9093	−1.83433	−0.917163	−	0.398513i	$-0.869526\pi$
$929$	−55.9093	−1.83433	−0.917163	+	0.398513i	$0.869526\pi$
$930$	−21.1240	−0.692683
$931$	−0.470507	−0.0154202
$932$	5.61124	0.183802
$933$	14.8353	0.485687
$934$	56.7430	1.85669
$935$	0.979686	0.0320391
$936$	12.6655	0.413986
$937$	−56.2456	−1.83746	−0.918732	−	0.394881i	$-0.870786\pi$
$937$	−56.2456	−1.83746	−0.918732	+	0.394881i	$0.870786\pi$
$938$	7.11766	0.232400
$939$	−22.2795	−0.727063
$940$	4.02365	0.131237
$941$	−38.8406	−1.26617	−0.633084	−	0.774083i	$-0.718211\pi$
$941$	−38.8406	−1.26617	−0.633084	+	0.774083i	$0.718211\pi$
$942$	1.33241	0.0434121
$943$	51.4029	1.67391
$944$	−30.7883	−1.00207
$945$	−0.662487	−0.0215507
$946$	9.18083	0.298495
$947$	50.0396	1.62607	0.813034	−	0.582216i	$-0.197814\pi$
$947$	50.0396	1.62607	0.813034	+	0.582216i	$0.197814\pi$
$948$	2.60451	0.0845905
$949$	54.8566	1.78072
$950$	−0.247843	−0.00804108
$951$	−23.0816	−0.748472
$952$	−1.29267	−0.0418956
$953$	−12.2339	−0.396293	−0.198147	−	0.980172i	$-0.563492\pi$
$953$	−12.2339	−0.396293	−0.198147	+	0.980172i	$0.563492\pi$
$954$	−6.47068	−0.209496
$955$	14.8874	0.481746
$956$	4.44411	0.143733
$957$	−2.24577	−0.0725955
$958$	−10.2315	−0.330565
$959$	8.54738	0.276009
$960$	−13.1945	−0.425849
$961$	77.9140	2.51335
$962$	−44.0211	−1.41930
$963$	17.9402	0.578115
$964$	−3.89119	−0.125327
$965$	40.7716	1.31249
$966$	2.93107	0.0943056
$967$	12.8828	0.414282	0.207141	−	0.978311i	$-0.433584\pi$
$967$	12.8828	0.414282	0.207141	+	0.978311i	$0.433584\pi$
$968$	31.3734	1.00838
$969$	−0.0690924	−0.00221957
$970$	25.4716	0.817845
$971$	−35.7269	−1.14653	−0.573266	−	0.819370i	$-0.694324\pi$
$971$	−35.7269	−1.14653	−0.573266	+	0.819370i	$0.694324\pi$
$972$	0.224694	0.00720705
$973$	2.83827	0.0909909
$974$	12.8374	0.411335
$975$	−11.5034	−0.368404
$976$	−10.3739	−0.332062
$977$	−25.3246	−0.810206	−0.405103	−	0.914271i	$-0.632764\pi$
$977$	−25.3246	−0.810206	−0.405103	+	0.914271i	$0.632764\pi$
$978$	−27.7293	−0.886685
$979$	7.96004	0.254404
$980$	2.32447	0.0742525
$981$	0.909858	0.0290495
$982$	−10.4042	−0.332011
$983$	8.41059	0.268256	0.134128	−	0.990964i	$-0.457177\pi$
$983$	8.41059	0.268256	0.134128	+	0.990964i	$0.457177\pi$
$984$	−30.2054	−0.962913
$985$	12.6092	0.401763
$986$	4.63995	0.147766
$987$	5.14057	0.163626
$988$	0.0663343	0.00211037
$989$	−53.8972	−1.71383
$990$	1.30534	0.0414864
$991$	44.8213	1.42379	0.711897	−	0.702283i	$-0.247836\pi$
$991$	44.8213	1.42379	0.711897	+	0.702283i	$0.247836\pi$
$992$	13.1997	0.419091
$993$	−22.7342	−0.721448
$994$	1.83477	0.0581955
$995$	−1.41952	−0.0450019
$996$	0.447542	0.0141809
$997$	−40.1512	−1.27160	−0.635801	−	0.771853i	$-0.719330\pi$
$997$	−40.1512	−1.27160	−0.635801	+	0.771853i	$0.719330\pi$
$998$	−37.7656	−1.19545
$999$	−7.73226	−0.244638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.44	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.44	✓	64	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)

\(f(q)\)	\(=\)	\(q+1.33241 q^{2} -1.00000 q^{3} -0.224694 q^{4} +1.51914 q^{5} -1.33241 q^{6} +0.436093 q^{7} -2.96420 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.33241 q^{2} -1.00000 q^{3} -0.224694 q^{4} +1.51914 q^{5} -1.33241 q^{6} +0.436093 q^{7} -2.96420 q^{8} +1.00000 q^{9} +2.02411 q^{10} +0.644895 q^{11} +0.224694 q^{12} -4.27285 q^{13} +0.581054 q^{14} -1.51914 q^{15} -3.50013 q^{16} +1.00000 q^{17} +1.33241 q^{18} +0.0690924 q^{19} -0.341341 q^{20} -0.436093 q^{21} +0.859262 q^{22} -5.04440 q^{23} +2.96420 q^{24} -2.69221 q^{25} -5.69317 q^{26} -1.00000 q^{27} -0.0979874 q^{28} +3.48239 q^{29} -2.02411 q^{30} +10.4362 q^{31} +1.26480 q^{32} -0.644895 q^{33} +1.33241 q^{34} +0.662487 q^{35} -0.224694 q^{36} +7.73226 q^{37} +0.0920591 q^{38} +4.27285 q^{39} -4.50303 q^{40} -10.1901 q^{41} -0.581054 q^{42} +10.6846 q^{43} -0.144904 q^{44} +1.51914 q^{45} -6.72119 q^{46} -11.7878 q^{47} +3.50013 q^{48} -6.80982 q^{49} -3.58712 q^{50} -1.00000 q^{51} +0.960081 q^{52} -4.85638 q^{53} -1.33241 q^{54} +0.979686 q^{55} -1.29267 q^{56} -0.0690924 q^{57} +4.63995 q^{58} +8.79634 q^{59} +0.341341 q^{60} +2.96388 q^{61} +13.9052 q^{62} +0.436093 q^{63} +8.68548 q^{64} -6.49105 q^{65} -0.859262 q^{66} +12.2496 q^{67} -0.224694 q^{68} +5.04440 q^{69} +0.882702 q^{70} +3.15767 q^{71} -2.96420 q^{72} -12.8384 q^{73} +10.3025 q^{74} +2.69221 q^{75} -0.0155246 q^{76} +0.281235 q^{77} +5.69317 q^{78} +11.5914 q^{79} -5.31718 q^{80} +1.00000 q^{81} -13.5773 q^{82} +1.99179 q^{83} +0.0979874 q^{84} +1.51914 q^{85} +14.2362 q^{86} -3.48239 q^{87} -1.91160 q^{88} +12.3432 q^{89} +2.02411 q^{90} -1.86336 q^{91} +1.13344 q^{92} -10.4362 q^{93} -15.7061 q^{94} +0.104961 q^{95} -1.26480 q^{96} +12.5841 q^{97} -9.07345 q^{98} +0.644895 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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