LMFDB - Embedded newform 8006.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$1$
Dimension:	$75$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.68989 q^{3} +1.00000 q^{4} -1.33052 q^{5} +2.68989 q^{6} +1.26652 q^{7} -1.00000 q^{8} +4.23551 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.68989 q^{3} +1.00000 q^{4} -1.33052 q^{5} +2.68989 q^{6} +1.26652 q^{7} -1.00000 q^{8} +4.23551 q^{9} +1.33052 q^{10} -0.113630 q^{11} -2.68989 q^{12} +5.76551 q^{13} -1.26652 q^{14} +3.57896 q^{15} +1.00000 q^{16} -0.579807 q^{17} -4.23551 q^{18} +1.49274 q^{19} -1.33052 q^{20} -3.40681 q^{21} +0.113630 q^{22} +1.55184 q^{23} +2.68989 q^{24} -3.22971 q^{25} -5.76551 q^{26} -3.32337 q^{27} +1.26652 q^{28} +4.03795 q^{29} -3.57896 q^{30} -0.783038 q^{31} -1.00000 q^{32} +0.305653 q^{33} +0.579807 q^{34} -1.68514 q^{35} +4.23551 q^{36} -6.81811 q^{37} -1.49274 q^{38} -15.5086 q^{39} +1.33052 q^{40} +2.89617 q^{41} +3.40681 q^{42} -6.93847 q^{43} -0.113630 q^{44} -5.63544 q^{45} -1.55184 q^{46} -4.22450 q^{47} -2.68989 q^{48} -5.39592 q^{49} +3.22971 q^{50} +1.55962 q^{51} +5.76551 q^{52} +2.71801 q^{53} +3.32337 q^{54} +0.151188 q^{55} -1.26652 q^{56} -4.01530 q^{57} -4.03795 q^{58} -0.764961 q^{59} +3.57896 q^{60} -6.44172 q^{61} +0.783038 q^{62} +5.36437 q^{63} +1.00000 q^{64} -7.67114 q^{65} -0.305653 q^{66} +3.98176 q^{67} -0.579807 q^{68} -4.17427 q^{69} +1.68514 q^{70} +5.05911 q^{71} -4.23551 q^{72} -8.99396 q^{73} +6.81811 q^{74} +8.68756 q^{75} +1.49274 q^{76} -0.143916 q^{77} +15.5086 q^{78} -6.40212 q^{79} -1.33052 q^{80} -3.76701 q^{81} -2.89617 q^{82} +16.6817 q^{83} -3.40681 q^{84} +0.771447 q^{85} +6.93847 q^{86} -10.8616 q^{87} +0.113630 q^{88} +0.299356 q^{89} +5.63544 q^{90} +7.30215 q^{91} +1.55184 q^{92} +2.10629 q^{93} +4.22450 q^{94} -1.98612 q^{95} +2.68989 q^{96} +6.70496 q^{97} +5.39592 q^{98} -0.481282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) $ 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9 + 9 * q^10 - 5 * q^11 + q^12 - 35 * q^13 + 8 * q^14 - 21 * q^15 + 75 * q^16 + 4 * q^17 - 66 * q^18 - 59 * q^19 - 9 * q^20 - 62 * q^21 + 5 * q^22 + 43 * q^23 - q^24 + 44 * q^25 + 35 * q^26 + 4 * q^27 - 8 * q^28 - 38 * q^29 + 21 * q^30 - 51 * q^31 - 75 * q^32 - 19 * q^33 - 4 * q^34 + 14 * q^35 + 66 * q^36 - 63 * q^37 + 59 * q^38 - 34 * q^39 + 9 * q^40 - 27 * q^41 + 62 * q^42 - 39 * q^43 - 5 * q^44 - 52 * q^45 - 43 * q^46 + 40 * q^47 + q^48 + 29 * q^49 - 44 * q^50 - 34 * q^51 - 35 * q^52 - 39 * q^53 - 4 * q^54 - 48 * q^55 + 8 * q^56 - 28 * q^57 + 38 * q^58 + 5 * q^59 - 21 * q^60 - 98 * q^61 + 51 * q^62 + 2 * q^63 + 75 * q^64 - q^65 + 19 * q^66 - 59 * q^67 + 4 * q^68 - 69 * q^69 - 14 * q^70 - 9 * q^71 - 66 * q^72 - 51 * q^73 + 63 * q^74 - q^75 - 59 * q^76 - 25 * q^77 + 34 * q^78 - 139 * q^79 - 9 * q^80 + 23 * q^81 + 27 * q^82 + 31 * q^83 - 62 * q^84 - 149 * q^85 + 39 * q^86 + q^87 + 5 * q^88 - 39 * q^89 + 52 * q^90 - 93 * q^91 + 43 * q^92 - 83 * q^93 - 40 * q^94 + 2 * q^95 - q^96 - 70 * q^97 - 29 * q^98 - 61 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.68989	−1.55301	−0.776504	−	0.630112i	$-0.783009\pi$
$3$	−2.68989	−1.55301	−0.776504	+	0.630112i	$0.783009\pi$
$4$	1.00000	0.500000
$5$	−1.33052	−0.595028	−0.297514	−	0.954717i	$-0.596157\pi$
$5$	−1.33052	−0.595028	−0.297514	+	0.954717i	$0.596157\pi$
$6$	2.68989	1.09814
$7$	1.26652	0.478701	0.239350	−	0.970933i	$-0.423066\pi$
$7$	1.26652	0.478701	0.239350	+	0.970933i	$0.423066\pi$
$8$	−1.00000	−0.353553
$9$	4.23551	1.41184
$10$	1.33052	0.420748
$11$	−0.113630	−0.0342608	−0.0171304	−	0.999853i	$-0.505453\pi$
$11$	−0.113630	−0.0342608	−0.0171304	+	0.999853i	$0.505453\pi$
$12$	−2.68989	−0.776504
$13$	5.76551	1.59906	0.799532	−	0.600624i	$-0.205081\pi$
$13$	5.76551	1.59906	0.799532	+	0.600624i	$0.205081\pi$
$14$	−1.26652	−0.338493
$15$	3.57896	0.924083
$16$	1.00000	0.250000
$17$	−0.579807	−0.140624	−0.0703119	−	0.997525i	$-0.522399\pi$
$17$	−0.579807	−0.140624	−0.0703119	+	0.997525i	$0.522399\pi$
$18$	−4.23551	−0.998318
$19$	1.49274	0.342458	0.171229	−	0.985231i	$-0.445226\pi$
$19$	1.49274	0.342458	0.171229	+	0.985231i	$0.445226\pi$
$20$	−1.33052	−0.297514
$21$	−3.40681	−0.743427
$22$	0.113630	0.0242261
$23$	1.55184	0.323580	0.161790	−	0.986825i	$-0.448273\pi$
$23$	1.55184	0.323580	0.161790	+	0.986825i	$0.448273\pi$
$24$	2.68989	0.549071
$25$	−3.22971	−0.645942
$26$	−5.76551	−1.13071
$27$	−3.32337	−0.639583
$28$	1.26652	0.239350
$29$	4.03795	0.749828	0.374914	−	0.927060i	$-0.377672\pi$
$29$	4.03795	0.749828	0.374914	+	0.927060i	$0.377672\pi$
$30$	−3.57896	−0.653426
$31$	−0.783038	−0.140638	−0.0703189	−	0.997525i	$-0.522402\pi$
$31$	−0.783038	−0.140638	−0.0703189	+	0.997525i	$0.522402\pi$
$32$	−1.00000	−0.176777
$33$	0.305653	0.0532074
$34$	0.579807	0.0994361
$35$	−1.68514	−0.284840
$36$	4.23551	0.705918
$37$	−6.81811	−1.12089	−0.560445	−	0.828191i	$-0.689370\pi$
$37$	−6.81811	−1.12089	−0.560445	+	0.828191i	$0.689370\pi$
$38$	−1.49274	−0.242154
$39$	−15.5086	−2.48336
$40$	1.33052	0.210374
$41$	2.89617	0.452305	0.226153	−	0.974092i	$-0.427385\pi$
$41$	2.89617	0.452305	0.226153	+	0.974092i	$0.427385\pi$
$42$	3.40681	0.525682
$43$	−6.93847	−1.05811	−0.529054	−	0.848588i	$-0.677453\pi$
$43$	−6.93847	−1.05811	−0.529054	+	0.848588i	$0.677453\pi$
$44$	−0.113630	−0.0171304
$45$	−5.63544	−0.840081
$46$	−1.55184	−0.228806
$47$	−4.22450	−0.616207	−0.308103	−	0.951353i	$-0.599694\pi$
$47$	−4.22450	−0.616207	−0.308103	+	0.951353i	$0.599694\pi$
$48$	−2.68989	−0.388252
$49$	−5.39592	−0.770845
$50$	3.22971	0.456750
$51$	1.55962	0.218390
$52$	5.76551	0.799532
$53$	2.71801	0.373348	0.186674	−	0.982422i	$-0.440229\pi$
$53$	2.71801	0.373348	0.186674	+	0.982422i	$0.440229\pi$
$54$	3.32337	0.452254
$55$	0.151188	0.0203862
$56$	−1.26652	−0.169246
$57$	−4.01530	−0.531839
$58$	−4.03795	−0.530208
$59$	−0.764961	−0.0995894	−0.0497947	−	0.998759i	$-0.515857\pi$
$59$	−0.764961	−0.0995894	−0.0497947	+	0.998759i	$0.515857\pi$
$60$	3.57896	0.462042
$61$	−6.44172	−0.824778	−0.412389	−	0.911008i	$-0.635305\pi$
$61$	−6.44172	−0.824778	−0.412389	+	0.911008i	$0.635305\pi$
$62$	0.783038	0.0994459
$63$	5.36437	0.675847
$64$	1.00000	0.125000
$65$	−7.67114	−0.951488
$66$	−0.305653	−0.0376233
$67$	3.98176	0.486450	0.243225	−	0.969970i	$-0.421795\pi$
$67$	3.98176	0.486450	0.243225	+	0.969970i	$0.421795\pi$
$68$	−0.579807	−0.0703119
$69$	−4.17427	−0.502523
$70$	1.68514	0.201413
$71$	5.05911	0.600405	0.300203	−	0.953875i	$-0.402946\pi$
$71$	5.05911	0.600405	0.300203	+	0.953875i	$0.402946\pi$
$72$	−4.23551	−0.499159
$73$	−8.99396	−1.05266	−0.526332	−	0.850279i	$-0.676433\pi$
$73$	−8.99396	−1.05266	−0.526332	+	0.850279i	$0.676433\pi$
$74$	6.81811	0.792589
$75$	8.68756	1.00315
$76$	1.49274	0.171229
$77$	−0.143916	−0.0164007
$78$	15.5086	1.75600
$79$	−6.40212	−0.720294	−0.360147	−	0.932895i	$-0.617274\pi$
$79$	−6.40212	−0.720294	−0.360147	+	0.932895i	$0.617274\pi$
$80$	−1.33052	−0.148757
$81$	−3.76701	−0.418557
$82$	−2.89617	−0.319828
$83$	16.6817	1.83106	0.915528	−	0.402255i	$-0.131774\pi$
$83$	16.6817	1.83106	0.915528	+	0.402255i	$0.131774\pi$
$84$	−3.40681	−0.371713
$85$	0.771447	0.0836751
$86$	6.93847	0.748195
$87$	−10.8616	−1.16449
$88$	0.113630	0.0121130
$89$	0.299356	0.0317317	0.0158658	−	0.999874i	$-0.494950\pi$
$89$	0.299356	0.0317317	0.0158658	+	0.999874i	$0.494950\pi$
$90$	5.63544	0.594027
$91$	7.30215	0.765473
$92$	1.55184	0.161790
$93$	2.10629	0.218412
$94$	4.22450	0.435724
$95$	−1.98612	−0.203772
$96$	2.68989	0.274536
$97$	6.70496	0.680785	0.340393	−	0.940283i	$-0.389440\pi$
$97$	6.70496	0.680785	0.340393	+	0.940283i	$0.389440\pi$
$98$	5.39592	0.545070
$99$	−0.481282	−0.0483707
$100$	−3.22971	−0.322971
$101$	−19.5920	−1.94948	−0.974739	−	0.223349i	$-0.928301\pi$
$101$	−19.5920	−1.94948	−0.974739	+	0.223349i	$0.928301\pi$
$102$	−1.55962	−0.154425
$103$	−15.0345	−1.48139	−0.740695	−	0.671841i	$-0.765504\pi$
$103$	−15.0345	−1.48139	−0.740695	+	0.671841i	$0.765504\pi$
$104$	−5.76551	−0.565354
$105$	4.53284	0.442360
$106$	−2.71801	−0.263997
$107$	4.72735	0.457010	0.228505	−	0.973543i	$-0.426616\pi$
$107$	4.72735	0.457010	0.228505	+	0.973543i	$0.426616\pi$
$108$	−3.32337	−0.319792
$109$	−0.875700	−0.0838768	−0.0419384	−	0.999120i	$-0.513353\pi$
$109$	−0.875700	−0.0838768	−0.0419384	+	0.999120i	$0.513353\pi$
$110$	−0.151188	−0.0144152
$111$	18.3400	1.74075
$112$	1.26652	0.119675
$113$	17.3476	1.63192	0.815961	−	0.578107i	$-0.196208\pi$
$113$	17.3476	1.63192	0.815961	+	0.578107i	$0.196208\pi$
$114$	4.01530	0.376067
$115$	−2.06475	−0.192539
$116$	4.03795	0.374914
$117$	24.4198	2.25761
$118$	0.764961	0.0704203
$119$	−0.734340	−0.0673168
$120$	−3.57896	−0.326713
$121$	−10.9871	−0.998826
$122$	6.44172	0.583206
$123$	−7.79037	−0.702434
$124$	−0.783038	−0.0703189
$125$	10.9498	0.979381
$126$	−5.36437	−0.477896
$127$	3.82092	0.339052	0.169526	−	0.985526i	$-0.445776\pi$
$127$	3.82092	0.339052	0.169526	+	0.985526i	$0.445776\pi$
$128$	−1.00000	−0.0883883
$129$	18.6637	1.64325
$130$	7.67114	0.672803
$131$	−7.68286	−0.671254	−0.335627	−	0.941995i	$-0.608948\pi$
$131$	−7.68286	−0.671254	−0.335627	+	0.941995i	$0.608948\pi$
$132$	0.305653	0.0266037
$133$	1.89059	0.163935
$134$	−3.98176	−0.343972
$135$	4.42182	0.380570
$136$	0.579807	0.0497181
$137$	−13.7983	−1.17887	−0.589434	−	0.807817i	$-0.700649\pi$
$137$	−13.7983	−1.17887	−0.589434	+	0.807817i	$0.700649\pi$
$138$	4.17427	0.355337
$139$	11.9709	1.01536	0.507680	−	0.861546i	$-0.330503\pi$
$139$	11.9709	1.01536	0.507680	+	0.861546i	$0.330503\pi$
$140$	−1.68514	−0.142420
$141$	11.3634	0.956974
$142$	−5.05911	−0.424551
$143$	−0.655137	−0.0547853
$144$	4.23551	0.352959
$145$	−5.37258	−0.446168
$146$	8.99396	0.744346
$147$	14.5144	1.19713
$148$	−6.81811	−0.560445
$149$	5.97349	0.489367	0.244684	−	0.969603i	$-0.421316\pi$
$149$	5.97349	0.489367	0.244684	+	0.969603i	$0.421316\pi$
$150$	−8.68756	−0.709336
$151$	14.5950	1.18773	0.593864	−	0.804565i	$-0.297602\pi$
$151$	14.5950	1.18773	0.593864	+	0.804565i	$0.297602\pi$
$152$	−1.49274	−0.121077
$153$	−2.45578	−0.198538
$154$	0.143916	0.0115970
$155$	1.04185	0.0836834
$156$	−15.5086	−1.24168
$157$	−7.19197	−0.573982	−0.286991	−	0.957933i	$-0.592655\pi$
$157$	−7.19197	−0.573982	−0.286991	+	0.957933i	$0.592655\pi$
$158$	6.40212	0.509325
$159$	−7.31115	−0.579812
$160$	1.33052	0.105187
$161$	1.96544	0.154898
$162$	3.76701	0.295964
$163$	−13.5595	−1.06206	−0.531031	−	0.847353i	$-0.678195\pi$
$163$	−13.5595	−1.06206	−0.531031	+	0.847353i	$0.678195\pi$
$164$	2.89617	0.226153
$165$	−0.406678	−0.0316599
$166$	−16.6817	−1.29475
$167$	7.72904	0.598091	0.299046	−	0.954239i	$-0.403332\pi$
$167$	7.72904	0.598091	0.299046	+	0.954239i	$0.403332\pi$
$168$	3.40681	0.262841
$169$	20.2411	1.55700
$170$	−0.771447	−0.0591673
$171$	6.32250	0.483494
$172$	−6.93847	−0.529054
$173$	−7.08619	−0.538753	−0.269376	−	0.963035i	$-0.586818\pi$
$173$	−7.08619	−0.538753	−0.269376	+	0.963035i	$0.586818\pi$
$174$	10.8616	0.823418
$175$	−4.09050	−0.309213
$176$	−0.113630	−0.00856521
$177$	2.05766	0.154663
$178$	−0.299356	−0.0224377
$179$	24.1189	1.80273	0.901365	−	0.433061i	$-0.142566\pi$
$179$	24.1189	1.80273	0.901365	+	0.433061i	$0.142566\pi$
$180$	−5.63544	−0.420041
$181$	−24.8395	−1.84630	−0.923152	−	0.384436i	$-0.874396\pi$
$181$	−24.8395	−1.84630	−0.923152	+	0.384436i	$0.874396\pi$
$182$	−7.30215	−0.541271
$183$	17.3275	1.28089
$184$	−1.55184	−0.114403
$185$	9.07165	0.666961
$186$	−2.10629	−0.154440
$187$	0.0658837	0.00481789
$188$	−4.22450	−0.308103
$189$	−4.20913	−0.306169
$190$	1.98612	0.144088
$191$	−13.5066	−0.977305	−0.488652	−	0.872479i	$-0.662511\pi$
$191$	−13.5066	−0.977305	−0.488652	+	0.872479i	$0.662511\pi$
$192$	−2.68989	−0.194126
$193$	3.76390	0.270931	0.135466	−	0.990782i	$-0.456747\pi$
$193$	3.76390	0.270931	0.135466	+	0.990782i	$0.456747\pi$
$194$	−6.70496	−0.481388
$195$	20.6345	1.47767
$196$	−5.39592	−0.385423
$197$	13.7427	0.979125	0.489563	−	0.871968i	$-0.337156\pi$
$197$	13.7427	0.979125	0.489563	+	0.871968i	$0.337156\pi$
$198$	0.481282	0.0342032
$199$	−12.4376	−0.881682	−0.440841	−	0.897585i	$-0.645320\pi$
$199$	−12.4376	−0.881682	−0.440841	+	0.897585i	$0.645320\pi$
$200$	3.22971	0.228375
$201$	−10.7105	−0.755461
$202$	19.5920	1.37849
$203$	5.11415	0.358943
$204$	1.55962	0.109195
$205$	−3.85342	−0.269134
$206$	15.0345	1.04750
$207$	6.57281	0.456842
$208$	5.76551	0.399766
$209$	−0.169620	−0.0117329
$210$	−4.53284	−0.312795
$211$	−28.5817	−1.96765	−0.983824	−	0.179137i	$-0.942669\pi$
$211$	−28.5817	−1.96765	−0.983824	+	0.179137i	$0.942669\pi$
$212$	2.71801	0.186674
$213$	−13.6084	−0.932435
$214$	−4.72735	−0.323155
$215$	9.23180	0.629603
$216$	3.32337	0.226127
$217$	−0.991736	−0.0673234
$218$	0.875700	0.0593099
$219$	24.1928	1.63480
$220$	0.151188	0.0101931
$221$	−3.34288	−0.224867
$222$	−18.3400	−1.23090
$223$	−0.0892539	−0.00597688	−0.00298844	−	0.999996i	$-0.500951\pi$
$223$	−0.0892539	−0.00597688	−0.00298844	+	0.999996i	$0.500951\pi$
$224$	−1.26652	−0.0846232
$225$	−13.6795	−0.911963
$226$	−17.3476	−1.15394
$227$	14.2120	0.943285	0.471643	−	0.881790i	$-0.343661\pi$
$227$	14.2120	0.943285	0.471643	+	0.881790i	$0.343661\pi$
$228$	−4.01530	−0.265920
$229$	16.1104	1.06461	0.532304	−	0.846553i	$-0.321326\pi$
$229$	16.1104	1.06461	0.532304	+	0.846553i	$0.321326\pi$
$230$	2.06475	0.136146
$231$	0.387117	0.0254704
$232$	−4.03795	−0.265104
$233$	16.8575	1.10437	0.552186	−	0.833721i	$-0.313794\pi$
$233$	16.8575	1.10437	0.552186	+	0.833721i	$0.313794\pi$
$234$	−24.4198	−1.59637
$235$	5.62080	0.366660
$236$	−0.764961	−0.0497947
$237$	17.2210	1.11862
$238$	0.734340	0.0476002
$239$	16.0928	1.04096	0.520478	−	0.853875i	$-0.325754\pi$
$239$	16.0928	1.04096	0.520478	+	0.853875i	$0.325754\pi$
$240$	3.57896	0.231021
$241$	16.3522	1.05334	0.526669	−	0.850071i	$-0.323441\pi$
$241$	16.3522	1.05334	0.526669	+	0.850071i	$0.323441\pi$
$242$	10.9871	0.706277
$243$	20.1030	1.28961
$244$	−6.44172	−0.412389
$245$	7.17939	0.458675
$246$	7.79037	0.496696
$247$	8.60639	0.547611
$248$	0.783038	0.0497230
$249$	−44.8719	−2.84364
$250$	−10.9498	−0.692527
$251$	25.9333	1.63689	0.818446	−	0.574583i	$-0.194836\pi$
$251$	25.9333	1.63689	0.818446	+	0.574583i	$0.194836\pi$
$252$	5.36437	0.337923
$253$	−0.176336	−0.0110861
$254$	−3.82092	−0.239746
$255$	−2.07511	−0.129948
$256$	1.00000	0.0625000
$257$	−0.719936	−0.0449084	−0.0224542	−	0.999748i	$-0.507148\pi$
$257$	−0.719936	−0.0449084	−0.0224542	+	0.999748i	$0.507148\pi$
$258$	−18.6637	−1.16195
$259$	−8.63530	−0.536571
$260$	−7.67114	−0.475744
$261$	17.1027	1.05863
$262$	7.68286	0.474649
$263$	11.0625	0.682146	0.341073	−	0.940037i	$-0.389210\pi$
$263$	11.0625	0.682146	0.341073	+	0.940037i	$0.389210\pi$
$264$	−0.305653	−0.0188116
$265$	−3.61638	−0.222152
$266$	−1.89059	−0.115919
$267$	−0.805235	−0.0492796
$268$	3.98176	0.243225
$269$	−27.1714	−1.65667	−0.828335	−	0.560233i	$-0.810712\pi$
$269$	−27.1714	−1.65667	−0.828335	+	0.560233i	$0.810712\pi$
$270$	−4.42182	−0.269104
$271$	15.5986	0.947550	0.473775	−	0.880646i	$-0.342891\pi$
$271$	15.5986	0.947550	0.473775	+	0.880646i	$0.342891\pi$
$272$	−0.579807	−0.0351560
$273$	−19.6420	−1.18879
$274$	13.7983	0.833585
$275$	0.366993	0.0221305
$276$	−4.17427	−0.251262
$277$	−0.150364	−0.00903449	−0.00451725	−	0.999990i	$-0.501438\pi$
$277$	−0.150364	−0.00903449	−0.00451725	+	0.999990i	$0.501438\pi$
$278$	−11.9709	−0.717968
$279$	−3.31656	−0.198557
$280$	1.68514	0.100706
$281$	−3.71250	−0.221469	−0.110735	−	0.993850i	$-0.535320\pi$
$281$	−3.71250	−0.221469	−0.110735	+	0.993850i	$0.535320\pi$
$282$	−11.3634	−0.676683
$283$	−15.1672	−0.901598	−0.450799	−	0.892625i	$-0.648861\pi$
$283$	−15.1672	−0.901598	−0.450799	+	0.892625i	$0.648861\pi$
$284$	5.05911	0.300203
$285$	5.34245	0.316459
$286$	0.655137	0.0387390
$287$	3.66806	0.216519
$288$	−4.23551	−0.249580
$289$	−16.6638	−0.980225
$290$	5.37258	0.315489
$291$	−18.0356	−1.05727
$292$	−8.99396	−0.526332
$293$	−11.8466	−0.692086	−0.346043	−	0.938219i	$-0.612475\pi$
$293$	−11.8466	−0.692086	−0.346043	+	0.938219i	$0.612475\pi$
$294$	−14.5144	−0.846498
$295$	1.01780	0.0592585
$296$	6.81811	0.396295
$297$	0.377636	0.0219127
$298$	−5.97349	−0.346035
$299$	8.94713	0.517426
$300$	8.68756	0.501577
$301$	−8.78774	−0.506517
$302$	−14.5950	−0.839850
$303$	52.7003	3.02755
$304$	1.49274	0.0856144
$305$	8.57085	0.490766
$306$	2.45578	0.140387
$307$	−10.7991	−0.616336	−0.308168	−	0.951332i	$-0.599716\pi$
$307$	−10.7991	−0.616336	−0.308168	+	0.951332i	$0.599716\pi$
$308$	−0.143916	−0.00820035
$309$	40.4411	2.30061
$310$	−1.04185	−0.0591731
$311$	17.5241	0.993699	0.496849	−	0.867837i	$-0.334490\pi$
$311$	17.5241	0.993699	0.496849	+	0.867837i	$0.334490\pi$
$312$	15.5086	0.878000
$313$	−15.3221	−0.866058	−0.433029	−	0.901380i	$-0.642555\pi$
$313$	−15.3221	−0.866058	−0.433029	+	0.901380i	$0.642555\pi$
$314$	7.19197	0.405867
$315$	−7.13741	−0.402148
$316$	−6.40212	−0.360147
$317$	−22.9097	−1.28674	−0.643368	−	0.765557i	$-0.722463\pi$
$317$	−22.9097	−1.28674	−0.643368	+	0.765557i	$0.722463\pi$
$318$	7.31115	0.409989
$319$	−0.458833	−0.0256897
$320$	−1.33052	−0.0743785
$321$	−12.7160	−0.709740
$322$	−1.96544	−0.109530
$323$	−0.865500	−0.0481577
$324$	−3.76701	−0.209278
$325$	−18.6209	−1.03290
$326$	13.5595	0.750991
$327$	2.35554	0.130261
$328$	−2.89617	−0.159914
$329$	−5.35043	−0.294979
$330$	0.406678	0.0223869
$331$	0.883605	0.0485673	0.0242837	−	0.999705i	$-0.492270\pi$
$331$	0.883605	0.0485673	0.0242837	+	0.999705i	$0.492270\pi$
$332$	16.6817	0.915528
$333$	−28.8782	−1.58251
$334$	−7.72904	−0.422914
$335$	−5.29783	−0.289451
$336$	−3.40681	−0.185857
$337$	35.2814	1.92190	0.960949	−	0.276724i	$-0.0892489\pi$
$337$	35.2814	1.92190	0.960949	+	0.276724i	$0.0892489\pi$
$338$	−20.2411	−1.10097
$339$	−46.6631	−2.53439
$340$	0.771447	0.0418376
$341$	0.0889769	0.00481837
$342$	−6.32250	−0.341882
$343$	−15.6997	−0.847705
$344$	6.93847	0.374097
$345$	5.55396	0.299015
$346$	7.08619	0.380956
$347$	−24.9113	−1.33731	−0.668655	−	0.743573i	$-0.733130\pi$
$347$	−24.9113	−1.33731	−0.668655	+	0.743573i	$0.733130\pi$
$348$	−10.8616	−0.582244
$349$	−20.0872	−1.07524	−0.537621	−	0.843186i	$-0.680677\pi$
$349$	−20.0872	−1.07524	−0.537621	+	0.843186i	$0.680677\pi$
$350$	4.09050	0.218647
$351$	−19.1609	−1.02273
$352$	0.113630	0.00605652
$353$	26.7689	1.42476	0.712382	−	0.701792i	$-0.247617\pi$
$353$	26.7689	1.42476	0.712382	+	0.701792i	$0.247617\pi$
$354$	−2.05766	−0.109363
$355$	−6.73126	−0.357258
$356$	0.299356	0.0158658
$357$	1.97529	0.104544
$358$	−24.1189	−1.27472
$359$	−35.3550	−1.86597	−0.932983	−	0.359922i	$-0.882803\pi$
$359$	−35.3550	−1.86597	−0.932983	+	0.359922i	$0.882803\pi$
$360$	5.63544	0.297014
$361$	−16.7717	−0.882723
$362$	24.8395	1.30553
$363$	29.5541	1.55119
$364$	7.30215	0.382737
$365$	11.9667	0.626364
$366$	−17.3275	−0.905724
$367$	13.5206	0.705767	0.352884	−	0.935667i	$-0.385201\pi$
$367$	13.5206	0.705767	0.352884	+	0.935667i	$0.385201\pi$
$368$	1.55184	0.0808951
$369$	12.2667	0.638581
$370$	−9.07165	−0.471613
$371$	3.44243	0.178722
$372$	2.10629	0.109206
$373$	−8.32203	−0.430898	−0.215449	−	0.976515i	$-0.569122\pi$
$373$	−8.32203	−0.430898	−0.215449	+	0.976515i	$0.569122\pi$
$374$	−0.0658837	−0.00340676
$375$	−29.4538	−1.52099
$376$	4.22450	0.217862
$377$	23.2808	1.19902
$378$	4.20913	0.216494
$379$	−23.0765	−1.18536	−0.592681	−	0.805438i	$-0.701930\pi$
$379$	−23.0765	−1.18536	−0.592681	+	0.805438i	$0.701930\pi$
$380$	−1.98612	−0.101886
$381$	−10.2779	−0.526551
$382$	13.5066	0.691059
$383$	19.0785	0.974866	0.487433	−	0.873160i	$-0.337933\pi$
$383$	19.0785	0.974866	0.487433	+	0.873160i	$0.337933\pi$
$384$	2.68989	0.137268
$385$	0.191483	0.00975887
$386$	−3.76390	−0.191577
$387$	−29.3879	−1.49387
$388$	6.70496	0.340393
$389$	26.9211	1.36495	0.682477	−	0.730907i	$-0.260903\pi$
$389$	26.9211	1.36495	0.682477	+	0.730907i	$0.260903\pi$
$390$	−20.6345	−1.04487
$391$	−0.899766	−0.0455031
$392$	5.39592	0.272535
$393$	20.6660	1.04246
$394$	−13.7427	−0.692346
$395$	8.51816	0.428595
$396$	−0.481282	−0.0241853
$397$	−15.5807	−0.781971	−0.390985	−	0.920397i	$-0.627866\pi$
$397$	−15.5807	−0.781971	−0.390985	+	0.920397i	$0.627866\pi$
$398$	12.4376	0.623443
$399$	−5.08547	−0.254592
$400$	−3.22971	−0.161485
$401$	12.4782	0.623131	0.311566	−	0.950225i	$-0.399147\pi$
$401$	12.4782	0.623131	0.311566	+	0.950225i	$0.399147\pi$
$402$	10.7105	0.534191
$403$	−4.51461	−0.224889
$404$	−19.5920	−0.974739
$405$	5.01209	0.249053
$406$	−5.11415	−0.253811
$407$	0.774745	0.0384027
$408$	−1.55962	−0.0772126
$409$	26.9575	1.33296	0.666481	−	0.745522i	$-0.267800\pi$
$409$	26.9575	1.33296	0.666481	+	0.745522i	$0.267800\pi$
$410$	3.85342	0.190307
$411$	37.1159	1.83079
$412$	−15.0345	−0.740695
$413$	−0.968841	−0.0476735
$414$	−6.57281	−0.323036
$415$	−22.1954	−1.08953
$416$	−5.76551	−0.282677
$417$	−32.2005	−1.57686
$418$	0.169620	0.00829640
$419$	−26.8750	−1.31293	−0.656465	−	0.754357i	$-0.727949\pi$
$419$	−26.8750	−1.31293	−0.656465	+	0.754357i	$0.727949\pi$
$420$	4.53284	0.221180
$421$	−17.8020	−0.867614	−0.433807	−	0.901006i	$-0.642830\pi$
$421$	−17.8020	−0.867614	−0.433807	+	0.901006i	$0.642830\pi$
$422$	28.5817	1.39134
$423$	−17.8929	−0.869982
$424$	−2.71801	−0.131998
$425$	1.87261	0.0908349
$426$	13.6084	0.659331
$427$	−8.15859	−0.394822
$428$	4.72735	0.228505
$429$	1.76224	0.0850820
$430$	−9.23180	−0.445197
$431$	10.0675	0.484935	0.242467	−	0.970160i	$-0.422043\pi$
$431$	10.0675	0.484935	0.242467	+	0.970160i	$0.422043\pi$
$432$	−3.32337	−0.159896
$433$	−11.7466	−0.564507	−0.282254	−	0.959340i	$-0.591082\pi$
$433$	−11.7466	−0.564507	−0.282254	+	0.959340i	$0.591082\pi$
$434$	0.991736	0.0476049
$435$	14.4516	0.692903
$436$	−0.875700	−0.0419384
$437$	2.31649	0.110813
$438$	−24.1928	−1.15597
$439$	−2.45754	−0.117292	−0.0586459	−	0.998279i	$-0.518678\pi$
$439$	−2.45754	−0.117292	−0.0586459	+	0.998279i	$0.518678\pi$
$440$	−0.151188	−0.00720759
$441$	−22.8544	−1.08831
$442$	3.34288	0.159005
$443$	−23.1720	−1.10093	−0.550466	−	0.834857i	$-0.685550\pi$
$443$	−23.1720	−1.10093	−0.550466	+	0.834857i	$0.685550\pi$
$444$	18.3400	0.870376
$445$	−0.398300	−0.0188812
$446$	0.0892539	0.00422629
$447$	−16.0680	−0.759992
$448$	1.26652	0.0598376
$449$	−19.2977	−0.910716	−0.455358	−	0.890308i	$-0.650489\pi$
$449$	−19.2977	−0.910716	−0.455358	+	0.890308i	$0.650489\pi$
$450$	13.6795	0.644855
$451$	−0.329092	−0.0154964
$452$	17.3476	0.815961
$453$	−39.2591	−1.84455
$454$	−14.2120	−0.667003
$455$	−9.71568	−0.455478
$456$	4.01530	0.188034
$457$	−9.52738	−0.445672	−0.222836	−	0.974856i	$-0.571531\pi$
$457$	−9.52738	−0.445672	−0.222836	+	0.974856i	$0.571531\pi$
$458$	−16.1104	−0.752792
$459$	1.92692	0.0899407
$460$	−2.06475	−0.0962697
$461$	−29.0571	−1.35333	−0.676663	−	0.736293i	$-0.736575\pi$
$461$	−29.0571	−1.35333	−0.676663	+	0.736293i	$0.736575\pi$
$462$	−0.387117	−0.0180103
$463$	−8.73027	−0.405730	−0.202865	−	0.979207i	$-0.565025\pi$
$463$	−8.73027	−0.405730	−0.202865	+	0.979207i	$0.565025\pi$
$464$	4.03795	0.187457
$465$	−2.80246	−0.129961
$466$	−16.8575	−0.780909
$467$	−33.7547	−1.56198	−0.780991	−	0.624542i	$-0.785286\pi$
$467$	−33.7547	−1.56198	−0.780991	+	0.624542i	$0.785286\pi$
$468$	24.4198	1.12881
$469$	5.04300	0.232864
$470$	−5.62080	−0.259268
$471$	19.3456	0.891399
$472$	0.764961	0.0352102
$473$	0.788421	0.0362516
$474$	−17.2210	−0.790986
$475$	−4.82111	−0.221208
$476$	−0.734340	−0.0336584
$477$	11.5122	0.527105
$478$	−16.0928	−0.736068
$479$	7.02756	0.321097	0.160549	−	0.987028i	$-0.448674\pi$
$479$	7.02756	0.321097	0.160549	+	0.987028i	$0.448674\pi$
$480$	−3.57896	−0.163356
$481$	−39.3099	−1.79238
$482$	−16.3522	−0.744822
$483$	−5.28681	−0.240558
$484$	−10.9871	−0.499413
$485$	−8.92110	−0.405086
$486$	−20.1030	−0.911889
$487$	36.7091	1.66345	0.831725	−	0.555188i	$-0.187354\pi$
$487$	36.7091	1.66345	0.831725	+	0.555188i	$0.187354\pi$
$488$	6.44172	0.291603
$489$	36.4735	1.64939
$490$	−7.17939	−0.324332
$491$	−41.2369	−1.86099	−0.930497	−	0.366300i	$-0.880624\pi$
$491$	−41.2369	−1.86099	−0.930497	+	0.366300i	$0.880624\pi$
$492$	−7.79037	−0.351217
$493$	−2.34123	−0.105444
$494$	−8.60639	−0.387220
$495$	0.640357	0.0287819
$496$	−0.783038	−0.0351594
$497$	6.40748	0.287415
$498$	44.8719	2.01076
$499$	41.5129	1.85837	0.929186	−	0.369612i	$-0.120509\pi$
$499$	41.5129	1.85837	0.929186	+	0.369612i	$0.120509\pi$
$500$	10.9498	0.489691
$501$	−20.7903	−0.928840
$502$	−25.9333	−1.15746
$503$	−20.1288	−0.897497	−0.448749	−	0.893658i	$-0.648130\pi$
$503$	−20.1288	−0.897497	−0.448749	+	0.893658i	$0.648130\pi$
$504$	−5.36437	−0.238948
$505$	26.0676	1.15999
$506$	0.176336	0.00783908
$507$	−54.4462	−2.41804
$508$	3.82092	0.169526
$509$	28.4764	1.26220	0.631098	−	0.775703i	$-0.282605\pi$
$509$	28.4764	1.26220	0.631098	+	0.775703i	$0.282605\pi$
$510$	2.07511	0.0918872
$511$	−11.3911	−0.503911
$512$	−1.00000	−0.0441942
$513$	−4.96092	−0.219030
$514$	0.719936	0.0317550
$515$	20.0037	0.881469
$516$	18.6637	0.821625
$517$	0.480032	0.0211118
$518$	8.63530	0.379413
$519$	19.0611	0.836688
$520$	7.67114	0.336402
$521$	−5.76046	−0.252370	−0.126185	−	0.992007i	$-0.540273\pi$
$521$	−5.76046	−0.252370	−0.126185	+	0.992007i	$0.540273\pi$
$522$	−17.1027	−0.748567
$523$	36.3778	1.59069	0.795346	−	0.606156i	$-0.207289\pi$
$523$	36.3778	1.59069	0.795346	+	0.606156i	$0.207289\pi$
$524$	−7.68286	−0.335627
$525$	11.0030	0.480210
$526$	−11.0625	−0.482350
$527$	0.454011	0.0197770
$528$	0.305653	0.0133018
$529$	−20.5918	−0.895296
$530$	3.61638	0.157085
$531$	−3.24000	−0.140604
$532$	1.89059	0.0819674
$533$	16.6979	0.723265
$534$	0.805235	0.0348459
$535$	−6.28984	−0.271934
$536$	−3.98176	−0.171986
$537$	−64.8771	−2.79965
$538$	27.1714	1.17144
$539$	0.613140	0.0264098
$540$	4.42182	0.190285
$541$	−7.08479	−0.304599	−0.152299	−	0.988334i	$-0.548668\pi$
$541$	−7.08479	−0.304599	−0.152299	+	0.988334i	$0.548668\pi$
$542$	−15.5986	−0.670019
$543$	66.8154	2.86732
$544$	0.579807	0.0248590
$545$	1.16514	0.0499090
$546$	19.6420	0.840599
$547$	31.4522	1.34480	0.672400	−	0.740188i	$-0.265263\pi$
$547$	31.4522	1.34480	0.672400	+	0.740188i	$0.265263\pi$
$548$	−13.7983	−0.589434
$549$	−27.2839	−1.16445
$550$	−0.366993	−0.0156486
$551$	6.02759	0.256784
$552$	4.17427	0.177669
$553$	−8.10843	−0.344806
$554$	0.150364	0.00638835
$555$	−24.4017	−1.03580
$556$	11.9709	0.507680
$557$	−19.5875	−0.829951	−0.414975	−	0.909833i	$-0.636210\pi$
$557$	−19.5875	−0.829951	−0.414975	+	0.909833i	$0.636210\pi$
$558$	3.31656	0.140401
$559$	−40.0038	−1.69198
$560$	−1.68514	−0.0712101
$561$	−0.177220	−0.00748223
$562$	3.71250	0.156602
$563$	−15.0018	−0.632249	−0.316125	−	0.948718i	$-0.602382\pi$
$563$	−15.0018	−0.632249	−0.316125	+	0.948718i	$0.602382\pi$
$564$	11.3634	0.478487
$565$	−23.0813	−0.971039
$566$	15.1672	0.637526
$567$	−4.77101	−0.200363
$568$	−5.05911	−0.212275
$569$	−29.0578	−1.21817	−0.609083	−	0.793106i	$-0.708463\pi$
$569$	−29.0578	−1.21817	−0.609083	+	0.793106i	$0.708463\pi$
$570$	−5.34245	−0.223770
$571$	−27.4460	−1.14858	−0.574290	−	0.818652i	$-0.694722\pi$
$571$	−27.4460	−1.14858	−0.574290	+	0.818652i	$0.694722\pi$
$572$	−0.655137	−0.0273926
$573$	36.3313	1.51776
$574$	−3.66806	−0.153102
$575$	−5.01198	−0.209014
$576$	4.23551	0.176479
$577$	47.8333	1.99133	0.995664	−	0.0930218i	$-0.0296526\pi$
$577$	47.8333	1.99133	0.995664	+	0.0930218i	$0.0296526\pi$
$578$	16.6638	0.693124
$579$	−10.1245	−0.420758
$580$	−5.37258	−0.223084
$581$	21.1278	0.876528
$582$	18.0356	0.747599
$583$	−0.308849	−0.0127912
$584$	8.99396	0.372173
$585$	−32.4911	−1.34334
$586$	11.8466	0.489379
$587$	−35.5006	−1.46527	−0.732634	−	0.680623i	$-0.761709\pi$
$587$	−35.5006	−1.46527	−0.732634	+	0.680623i	$0.761709\pi$
$588$	14.5144	0.598565
$589$	−1.16887	−0.0481625
$590$	−1.01780	−0.0419021
$591$	−36.9663	−1.52059
$592$	−6.81811	−0.280223
$593$	−3.20400	−0.131572	−0.0657862	−	0.997834i	$-0.520956\pi$
$593$	−3.20400	−0.131572	−0.0657862	+	0.997834i	$0.520956\pi$
$594$	−0.377636	−0.0154946
$595$	0.977055	0.0400554
$596$	5.97349	0.244684
$597$	33.4559	1.36926
$598$	−8.94713	−0.365875
$599$	30.3110	1.23848	0.619238	−	0.785203i	$-0.287442\pi$
$599$	30.3110	1.23848	0.619238	+	0.785203i	$0.287442\pi$
$600$	−8.68756	−0.354668
$601$	−18.7191	−0.763567	−0.381783	−	0.924252i	$-0.624690\pi$
$601$	−18.7191	−0.763567	−0.381783	+	0.924252i	$0.624690\pi$
$602$	8.78774	0.358162
$603$	16.8648	0.686787
$604$	14.5950	0.593864
$605$	14.6186	0.594329
$606$	−52.7003	−2.14080
$607$	−11.7606	−0.477347	−0.238674	−	0.971100i	$-0.576713\pi$
$607$	−11.7606	−0.477347	−0.238674	+	0.971100i	$0.576713\pi$
$608$	−1.49274	−0.0605385
$609$	−13.7565	−0.557442
$610$	−8.57085	−0.347024
$611$	−24.3564	−0.985354
$612$	−2.45578	−0.0992689
$613$	15.8680	0.640901	0.320451	−	0.947265i	$-0.396166\pi$
$613$	15.8680	0.640901	0.320451	+	0.947265i	$0.396166\pi$
$614$	10.7991	0.435816
$615$	10.3653	0.417968
$616$	0.143916	0.00579852
$617$	1.90505	0.0766945	0.0383473	−	0.999264i	$-0.487791\pi$
$617$	1.90505	0.0766945	0.0383473	+	0.999264i	$0.487791\pi$
$618$	−40.4411	−1.62678
$619$	15.2144	0.611517	0.305758	−	0.952109i	$-0.401090\pi$
$619$	15.2144	0.611517	0.305758	+	0.952109i	$0.401090\pi$
$620$	1.04185	0.0418417
$621$	−5.15733	−0.206957
$622$	−17.5241	−0.702651
$623$	0.379142	0.0151900
$624$	−15.5086	−0.620840
$625$	1.57957	0.0631826
$626$	15.3221	0.612395
$627$	0.456260	0.0182213
$628$	−7.19197	−0.286991
$629$	3.95319	0.157624
$630$	7.13741	0.284361
$631$	18.4650	0.735080	0.367540	−	0.930008i	$-0.380200\pi$
$631$	18.4650	0.735080	0.367540	+	0.930008i	$0.380200\pi$
$632$	6.40212	0.254663
$633$	76.8817	3.05577
$634$	22.9097	0.909860
$635$	−5.08383	−0.201746
$636$	−7.31115	−0.289906
$637$	−31.1102	−1.23263
$638$	0.458833	0.0181654
$639$	21.4279	0.847674
$640$	1.33052	0.0525935
$641$	−13.7979	−0.544985	−0.272492	−	0.962158i	$-0.587848\pi$
$641$	−13.7979	−0.544985	−0.272492	+	0.962158i	$0.587848\pi$
$642$	12.7160	0.501862
$643$	−6.67048	−0.263058	−0.131529	−	0.991312i	$-0.541989\pi$
$643$	−6.67048	−0.263058	−0.131529	+	0.991312i	$0.541989\pi$
$644$	1.96544	0.0774491
$645$	−24.8325	−0.977779
$646$	0.865500	0.0340526
$647$	42.1527	1.65719	0.828596	−	0.559846i	$-0.189140\pi$
$647$	42.1527	1.65719	0.828596	+	0.559846i	$0.189140\pi$
$648$	3.76701	0.147982
$649$	0.0869228	0.00341202
$650$	18.6209	0.730372
$651$	2.66766	0.104554
$652$	−13.5595	−0.531031
$653$	−17.6252	−0.689727	−0.344863	−	0.938653i	$-0.612075\pi$
$653$	−17.6252	−0.689727	−0.344863	+	0.938653i	$0.612075\pi$
$654$	−2.35554	−0.0921087
$655$	10.2222	0.399415
$656$	2.89617	0.113076
$657$	−38.0940	−1.48619
$658$	5.35043	0.208582
$659$	−20.6109	−0.802887	−0.401444	−	0.915884i	$-0.631491\pi$
$659$	−20.6109	−0.802887	−0.401444	+	0.915884i	$0.631491\pi$
$660$	−0.406678	−0.0158299
$661$	−26.9024	−1.04638	−0.523191	−	0.852216i	$-0.675259\pi$
$661$	−26.9024	−1.04638	−0.523191	+	0.852216i	$0.675259\pi$
$662$	−0.883605	−0.0343423
$663$	8.99198	0.349220
$664$	−16.6817	−0.647376
$665$	−2.51547	−0.0975457
$666$	28.8782	1.11901
$667$	6.26623	0.242630
$668$	7.72904	0.299046
$669$	0.240083	0.00928215
$670$	5.29783	0.204673
$671$	0.731975	0.0282576
$672$	3.40681	0.131420
$673$	−17.8291	−0.687263	−0.343632	−	0.939105i	$-0.611657\pi$
$673$	−17.8291	−0.687263	−0.343632	+	0.939105i	$0.611657\pi$
$674$	−35.2814	−1.35899
$675$	10.7335	0.413134
$676$	20.2411	0.778502
$677$	−29.8581	−1.14754	−0.573771	−	0.819016i	$-0.694520\pi$
$677$	−29.8581	−1.14754	−0.573771	+	0.819016i	$0.694520\pi$
$678$	46.6631	1.79208
$679$	8.49199	0.325892
$680$	−0.771447	−0.0295836
$681$	−38.2288	−1.46493
$682$	−0.0889769	−0.00340710
$683$	−7.67686	−0.293747	−0.146873	−	0.989155i	$-0.546921\pi$
$683$	−7.67686	−0.293747	−0.146873	+	0.989155i	$0.546921\pi$
$684$	6.32250	0.241747
$685$	18.3589	0.701459
$686$	15.6997	0.599418
$687$	−43.3353	−1.65335
$688$	−6.93847	−0.264527
$689$	15.6707	0.597007
$690$	−5.55396	−0.211436
$691$	−41.5993	−1.58251	−0.791255	−	0.611486i	$-0.790572\pi$
$691$	−41.5993	−1.58251	−0.791255	+	0.611486i	$0.790572\pi$
$692$	−7.08619	−0.269376
$693$	−0.609555	−0.0231551
$694$	24.9113	0.945621
$695$	−15.9276	−0.604168
$696$	10.8616	0.411709
$697$	−1.67922	−0.0636049
$698$	20.0872	0.760311
$699$	−45.3448	−1.71510
$700$	−4.09050	−0.154606
$701$	−31.9209	−1.20564	−0.602818	−	0.797879i	$-0.705956\pi$
$701$	−31.9209	−1.20564	−0.602818	+	0.797879i	$0.705956\pi$
$702$	19.1609	0.723183
$703$	−10.1777	−0.383857
$704$	−0.113630	−0.00428261
$705$	−15.1193	−0.569426
$706$	−26.7689	−1.00746
$707$	−24.8137	−0.933216
$708$	2.05766	0.0773316
$709$	−35.8457	−1.34621	−0.673107	−	0.739545i	$-0.735041\pi$
$709$	−35.8457	−1.34621	−0.673107	+	0.739545i	$0.735041\pi$
$710$	6.73126	0.252620
$711$	−27.1162	−1.01694
$712$	−0.299356	−0.0112188
$713$	−1.21515	−0.0455076
$714$	−1.97529	−0.0739234
$715$	0.871674	0.0325988
$716$	24.1189	0.901365
$717$	−43.2879	−1.61661
$718$	35.3550	1.31944
$719$	6.28764	0.234489	0.117245	−	0.993103i	$-0.462594\pi$
$719$	6.28764	0.234489	0.117245	+	0.993103i	$0.462594\pi$
$720$	−5.63544	−0.210020
$721$	−19.0415	−0.709143
$722$	16.7717	0.624179
$723$	−43.9856	−1.63584
$724$	−24.8395	−0.923152
$725$	−13.0414	−0.484345
$726$	−29.5541	−1.09685
$727$	−14.4860	−0.537255	−0.268628	−	0.963244i	$-0.586570\pi$
$727$	−14.4860	−0.537255	−0.268628	+	0.963244i	$0.586570\pi$
$728$	−7.30215	−0.270636
$729$	−42.7737	−1.58421
$730$	−11.9667	−0.442906
$731$	4.02298	0.148795
$732$	17.3275	0.640443
$733$	50.6820	1.87198	0.935991	−	0.352024i	$-0.114506\pi$
$733$	50.6820	1.87198	0.935991	+	0.352024i	$0.114506\pi$
$734$	−13.5206	−0.499053
$735$	−19.3118	−0.712325
$736$	−1.55184	−0.0572015
$737$	−0.452449	−0.0166662
$738$	−12.2667	−0.451545
$739$	−30.3786	−1.11749	−0.558747	−	0.829338i	$-0.688718\pi$
$739$	−30.3786	−1.11749	−0.558747	+	0.829338i	$0.688718\pi$
$740$	9.07165	0.333481
$741$	−23.1502	−0.850445
$742$	−3.44243	−0.126375
$743$	51.0067	1.87125	0.935627	−	0.352989i	$-0.114835\pi$
$743$	51.0067	1.87125	0.935627	+	0.352989i	$0.114835\pi$
$744$	−2.10629	−0.0772202
$745$	−7.94787	−0.291187
$746$	8.32203	0.304691
$747$	70.6555	2.58515
$748$	0.0658837	0.00240895
$749$	5.98730	0.218771
$750$	29.4538	1.07550
$751$	4.14247	0.151161	0.0755803	−	0.997140i	$-0.475919\pi$
$751$	4.14247	0.151161	0.0755803	+	0.997140i	$0.475919\pi$
$752$	−4.22450	−0.154052
$753$	−69.7576	−2.54211
$754$	−23.2808	−0.847837
$755$	−19.4190	−0.706731
$756$	−4.20913	−0.153085
$757$	−4.85058	−0.176297	−0.0881486	−	0.996107i	$-0.528095\pi$
$757$	−4.85058	−0.176297	−0.0881486	+	0.996107i	$0.528095\pi$
$758$	23.0765	0.838177
$759$	0.474324	0.0172169
$760$	1.98612	0.0720442
$761$	40.9789	1.48548	0.742742	−	0.669578i	$-0.233525\pi$
$761$	40.9789	1.48548	0.742742	+	0.669578i	$0.233525\pi$
$762$	10.2779	0.372328
$763$	−1.10909	−0.0401519
$764$	−13.5066	−0.488652
$765$	3.26747	0.118135
$766$	−19.0785	−0.689334
$767$	−4.41039	−0.159250
$768$	−2.68989	−0.0970630
$769$	−17.8484	−0.643630	−0.321815	−	0.946803i	$-0.604293\pi$
$769$	−17.8484	−0.643630	−0.321815	+	0.946803i	$0.604293\pi$
$770$	−0.191483	−0.00690056
$771$	1.93655	0.0697431
$772$	3.76390	0.135466
$773$	22.5139	0.809768	0.404884	−	0.914368i	$-0.367312\pi$
$773$	22.5139	0.809768	0.404884	+	0.914368i	$0.367312\pi$
$774$	29.3879	1.05633
$775$	2.52898	0.0908438
$776$	−6.70496	−0.240694
$777$	23.2280	0.833300
$778$	−26.9211	−0.965168
$779$	4.32322	0.154895
$780$	20.6345	0.738834
$781$	−0.574868	−0.0205704
$782$	0.899766	0.0321756
$783$	−13.4196	−0.479577
$784$	−5.39592	−0.192711
$785$	9.56909	0.341535
$786$	−20.6660	−0.737133
$787$	24.7134	0.880936	0.440468	−	0.897768i	$-0.354813\pi$
$787$	24.7134	0.880936	0.440468	+	0.897768i	$0.354813\pi$
$788$	13.7427	0.489563
$789$	−29.7570	−1.05938
$790$	−8.51816	−0.303063
$791$	21.9711	0.781203
$792$	0.481282	0.0171016
$793$	−37.1398	−1.31887
$794$	15.5807	0.552937
$795$	9.72766	0.345004
$796$	−12.4376	−0.440841
$797$	−29.8763	−1.05827	−0.529136	−	0.848537i	$-0.677484\pi$
$797$	−29.8763	−1.05827	−0.529136	+	0.848537i	$0.677484\pi$
$798$	5.08547	0.180024
$799$	2.44940	0.0866534
$800$	3.22971	0.114187
$801$	1.26792	0.0447999
$802$	−12.4782	−0.440620
$803$	1.02199	0.0360651
$804$	−10.7105	−0.377730
$805$	−2.61506	−0.0921688
$806$	4.51461	0.159020
$807$	73.0881	2.57282
$808$	19.5920	0.689244
$809$	−53.7953	−1.89134	−0.945672	−	0.325124i	$-0.894594\pi$
$809$	−53.7953	−1.89134	−0.945672	+	0.325124i	$0.894594\pi$
$810$	−5.01209	−0.176107
$811$	35.0926	1.23227	0.616135	−	0.787641i	$-0.288698\pi$
$811$	35.0926	1.23227	0.616135	+	0.787641i	$0.288698\pi$
$812$	5.11415	0.179472
$813$	−41.9586	−1.47155
$814$	−0.774745	−0.0271548
$815$	18.0412	0.631956
$816$	1.55962	0.0545975
$817$	−10.3573	−0.362357
$818$	−26.9575	−0.942546
$819$	30.9283	1.08072
$820$	−3.85342	−0.134567
$821$	−30.8999	−1.07841	−0.539207	−	0.842173i	$-0.681276\pi$
$821$	−30.8999	−1.07841	−0.539207	+	0.842173i	$0.681276\pi$
$822$	−37.1159	−1.29456
$823$	27.4389	0.956460	0.478230	−	0.878235i	$-0.341279\pi$
$823$	27.4389	0.956460	0.478230	+	0.878235i	$0.341279\pi$
$824$	15.0345	0.523751
$825$	−0.987171	−0.0343689
$826$	0.968841	0.0337103
$827$	5.89858	0.205114	0.102557	−	0.994727i	$-0.467298\pi$
$827$	5.89858	0.205114	0.102557	+	0.994727i	$0.467298\pi$
$828$	6.57281	0.228421
$829$	−17.5080	−0.608077	−0.304039	−	0.952660i	$-0.598335\pi$
$829$	−17.5080	−0.608077	−0.304039	+	0.952660i	$0.598335\pi$
$830$	22.1954	0.770413
$831$	0.404462	0.0140306
$832$	5.76551	0.199883
$833$	3.12859	0.108399
$834$	32.2005	1.11501
$835$	−10.2837	−0.355881
$836$	−0.169620	−0.00586644
$837$	2.60233	0.0899496
$838$	26.8750	0.928381
$839$	−44.4634	−1.53505	−0.767524	−	0.641021i	$-0.778511\pi$
$839$	−44.4634	−1.53505	−0.767524	+	0.641021i	$0.778511\pi$
$840$	−4.53284	−0.156398
$841$	−12.6950	−0.437758
$842$	17.8020	0.613496
$843$	9.98621	0.343943
$844$	−28.5817	−0.983824
$845$	−26.9312	−0.926461
$846$	17.8929	0.615171
$847$	−13.9154	−0.478139
$848$	2.71801	0.0933369
$849$	40.7982	1.40019
$850$	−1.87261	−0.0642299
$851$	−10.5806	−0.362698
$852$	−13.6084	−0.466217
$853$	19.4573	0.666206	0.333103	−	0.942890i	$-0.391904\pi$
$853$	19.4573	0.666206	0.333103	+	0.942890i	$0.391904\pi$
$854$	8.15859	0.279181
$855$	−8.41223	−0.287692
$856$	−4.72735	−0.161577
$857$	−25.8012	−0.881352	−0.440676	−	0.897666i	$-0.645261\pi$
$857$	−25.8012	−0.881352	−0.440676	+	0.897666i	$0.645261\pi$
$858$	−1.76224	−0.0601620
$859$	13.0795	0.446266	0.223133	−	0.974788i	$-0.428372\pi$
$859$	13.0795	0.446266	0.223133	+	0.974788i	$0.428372\pi$
$860$	9.23180	0.314802
$861$	−9.86669	−0.336256
$862$	−10.0675	−0.342901
$863$	−16.7772	−0.571101	−0.285550	−	0.958364i	$-0.592176\pi$
$863$	−16.7772	−0.571101	−0.285550	+	0.958364i	$0.592176\pi$
$864$	3.32337	0.113063
$865$	9.42833	0.320573
$866$	11.7466	0.399167
$867$	44.8238	1.52230
$868$	−0.991736	−0.0336617
$869$	0.727475	0.0246779
$870$	−14.4516	−0.489957
$871$	22.9569	0.777864
$872$	0.875700	0.0296549
$873$	28.3989	0.961156
$874$	−2.31649	−0.0783563
$875$	13.8682	0.468831
$876$	24.1928	0.817398
$877$	−52.7118	−1.77995	−0.889976	−	0.456008i	$-0.849279\pi$
$877$	−52.7118	−1.77995	−0.889976	+	0.456008i	$0.849279\pi$
$878$	2.45754	0.0829378
$879$	31.8661	1.07482
$880$	0.151188	0.00509654
$881$	−18.4856	−0.622797	−0.311398	−	0.950279i	$-0.600797\pi$
$881$	−18.4856	−0.622797	−0.311398	+	0.950279i	$0.600797\pi$
$882$	22.8544	0.769549
$883$	−17.6769	−0.594874	−0.297437	−	0.954741i	$-0.596132\pi$
$883$	−17.6769	−0.594874	−0.297437	+	0.954741i	$0.596132\pi$
$884$	−3.34288	−0.112433
$885$	−2.73776	−0.0920289
$886$	23.1720	0.778477
$887$	−46.8752	−1.57392	−0.786958	−	0.617007i	$-0.788345\pi$
$887$	−46.8752	−1.57392	−0.786958	+	0.617007i	$0.788345\pi$
$888$	−18.3400	−0.615449
$889$	4.83929	0.162305
$890$	0.398300	0.0133511
$891$	0.428047	0.0143401
$892$	−0.0892539	−0.00298844
$893$	−6.30607	−0.211025
$894$	16.0680	0.537395
$895$	−32.0907	−1.07267
$896$	−1.26652	−0.0423116
$897$	−24.0668	−0.803566
$898$	19.2977	0.643973
$899$	−3.16186	−0.105454
$900$	−13.6795	−0.455982
$901$	−1.57592	−0.0525016
$902$	0.329092	0.0109576
$903$	23.6381	0.786625
$904$	−17.3476	−0.576972
$905$	33.0495	1.09860
$906$	39.2591	1.30429
$907$	16.6665	0.553403	0.276701	−	0.960956i	$-0.410759\pi$
$907$	16.6665	0.553403	0.276701	+	0.960956i	$0.410759\pi$
$908$	14.2120	0.471643
$909$	−82.9820	−2.75234
$910$	9.71568	0.322072
$911$	53.9153	1.78629	0.893147	−	0.449765i	$-0.148492\pi$
$911$	53.9153	1.78629	0.893147	+	0.449765i	$0.148492\pi$
$912$	−4.01530	−0.132960
$913$	−1.89555	−0.0627335
$914$	9.52738	0.315138
$915$	−23.0547	−0.762163
$916$	16.1104	0.532304
$917$	−9.73052	−0.321330
$918$	−1.92692	−0.0635977
$919$	10.9912	0.362565	0.181283	−	0.983431i	$-0.441975\pi$
$919$	10.9912	0.362565	0.181283	+	0.983431i	$0.441975\pi$
$920$	2.06475	0.0680729
$921$	29.0484	0.957176
$922$	29.0571	0.956946
$923$	29.1683	0.960087
$924$	0.387117	0.0127352
$925$	22.0205	0.724030
$926$	8.73027	0.286894
$927$	−63.6786	−2.09148
$928$	−4.03795	−0.132552
$929$	2.29902	0.0754284	0.0377142	−	0.999289i	$-0.487992\pi$
$929$	2.29902	0.0754284	0.0377142	+	0.999289i	$0.487992\pi$
$930$	2.80246	0.0918963
$931$	−8.05469	−0.263982
$932$	16.8575	0.552186
$933$	−47.1378	−1.54322
$934$	33.7547	1.10449
$935$	−0.0876598	−0.00286678
$936$	−24.4198	−0.798187
$937$	4.75818	0.155443	0.0777216	−	0.996975i	$-0.475235\pi$
$937$	4.75818	0.155443	0.0777216	+	0.996975i	$0.475235\pi$
$938$	−5.04300	−0.164660
$939$	41.2148	1.34500
$940$	5.62080	0.183330
$941$	−45.2436	−1.47490	−0.737450	−	0.675401i	$-0.763970\pi$
$941$	−45.2436	−1.47490	−0.737450	+	0.675401i	$0.763970\pi$
$942$	−19.3456	−0.630314
$943$	4.49438	0.146357
$944$	−0.764961	−0.0248974
$945$	5.60034	0.182179
$946$	−0.788421	−0.0256338
$947$	−17.6135	−0.572363	−0.286182	−	0.958175i	$-0.592386\pi$
$947$	−17.6135	−0.572363	−0.286182	+	0.958175i	$0.592386\pi$
$948$	17.2210	0.559312
$949$	−51.8547	−1.68328
$950$	4.82111	0.156417
$951$	61.6245	1.99831
$952$	0.734340	0.0238001
$953$	−25.8679	−0.837943	−0.418971	−	0.907999i	$-0.637609\pi$
$953$	−25.8679	−0.837943	−0.418971	+	0.907999i	$0.637609\pi$
$954$	−11.5122	−0.372720
$955$	17.9709	0.581524
$956$	16.0928	0.520478
$957$	1.23421	0.0398964
$958$	−7.02756	−0.227050
$959$	−17.4759	−0.564325
$960$	3.57896	0.115510
$961$	−30.3869	−0.980221
$962$	39.3099	1.26740
$963$	20.0227	0.645223
$964$	16.3522	0.526669
$965$	−5.00795	−0.161212
$966$	5.28681	0.170100
$967$	−17.4467	−0.561048	−0.280524	−	0.959847i	$-0.590508\pi$
$967$	−17.4467	−0.561048	−0.280524	+	0.959847i	$0.590508\pi$
$968$	10.9871	0.353138
$969$	2.32810	0.0747893
$970$	8.92110	0.286439
$971$	−38.5315	−1.23653	−0.618267	−	0.785968i	$-0.712165\pi$
$971$	−38.5315	−1.23653	−0.618267	+	0.785968i	$0.712165\pi$
$972$	20.1030	0.644803
$973$	15.1615	0.486054
$974$	−36.7091	−1.17624
$975$	50.0882	1.60411
$976$	−6.44172	−0.206194
$977$	5.78155	0.184968	0.0924840	−	0.995714i	$-0.470519\pi$
$977$	5.78155	0.184968	0.0924840	+	0.995714i	$0.470519\pi$
$978$	−36.4735	−1.16629
$979$	−0.0340159	−0.00108715
$980$	7.17939	0.229337
$981$	−3.70903	−0.118420
$982$	41.2369	1.31592
$983$	−27.4752	−0.876323	−0.438161	−	0.898896i	$-0.644370\pi$
$983$	−27.4752	−0.876323	−0.438161	+	0.898896i	$0.644370\pi$
$984$	7.79037	0.248348
$985$	−18.2849	−0.582607
$986$	2.34123	0.0745599
$987$	14.3921	0.458105
$988$	8.60639	0.273806
$989$	−10.7674	−0.342383
$990$	−0.640357	−0.0203519
$991$	1.88598	0.0599102	0.0299551	−	0.999551i	$-0.490464\pi$
$991$	1.88598	0.0599102	0.0299551	+	0.999551i	$0.490464\pi$
$992$	0.783038	0.0248615
$993$	−2.37680	−0.0754255
$994$	−6.40748	−0.203233
$995$	16.5486	0.524625
$996$	−44.8719	−1.42182
$997$	19.1931	0.607851	0.303926	−	0.952696i	$-0.401703\pi$
$997$	19.1931	0.607851	0.303926	+	0.952696i	$0.401703\pi$
$998$	−41.5129	−1.31407
$999$	22.6591	0.716903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.b.1.9	✓	75

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.b.1.9	✓	75	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.68989 q^{3} +1.00000 q^{4} -1.33052 q^{5} +2.68989 q^{6} +1.26652 q^{7} -1.00000 q^{8} +4.23551 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.68989 q^{3} +1.00000 q^{4} -1.33052 q^{5} +2.68989 q^{6} +1.26652 q^{7} -1.00000 q^{8} +4.23551 q^{9} +1.33052 q^{10} -0.113630 q^{11} -2.68989 q^{12} +5.76551 q^{13} -1.26652 q^{14} +3.57896 q^{15} +1.00000 q^{16} -0.579807 q^{17} -4.23551 q^{18} +1.49274 q^{19} -1.33052 q^{20} -3.40681 q^{21} +0.113630 q^{22} +1.55184 q^{23} +2.68989 q^{24} -3.22971 q^{25} -5.76551 q^{26} -3.32337 q^{27} +1.26652 q^{28} +4.03795 q^{29} -3.57896 q^{30} -0.783038 q^{31} -1.00000 q^{32} +0.305653 q^{33} +0.579807 q^{34} -1.68514 q^{35} +4.23551 q^{36} -6.81811 q^{37} -1.49274 q^{38} -15.5086 q^{39} +1.33052 q^{40} +2.89617 q^{41} +3.40681 q^{42} -6.93847 q^{43} -0.113630 q^{44} -5.63544 q^{45} -1.55184 q^{46} -4.22450 q^{47} -2.68989 q^{48} -5.39592 q^{49} +3.22971 q^{50} +1.55962 q^{51} +5.76551 q^{52} +2.71801 q^{53} +3.32337 q^{54} +0.151188 q^{55} -1.26652 q^{56} -4.01530 q^{57} -4.03795 q^{58} -0.764961 q^{59} +3.57896 q^{60} -6.44172 q^{61} +0.783038 q^{62} +5.36437 q^{63} +1.00000 q^{64} -7.67114 q^{65} -0.305653 q^{66} +3.98176 q^{67} -0.579807 q^{68} -4.17427 q^{69} +1.68514 q^{70} +5.05911 q^{71} -4.23551 q^{72} -8.99396 q^{73} +6.81811 q^{74} +8.68756 q^{75} +1.49274 q^{76} -0.143916 q^{77} +15.5086 q^{78} -6.40212 q^{79} -1.33052 q^{80} -3.76701 q^{81} -2.89617 q^{82} +16.6817 q^{83} -3.40681 q^{84} +0.771447 q^{85} +6.93847 q^{86} -10.8616 q^{87} +0.113630 q^{88} +0.299356 q^{89} +5.63544 q^{90} +7.30215 q^{91} +1.55184 q^{92} +2.10629 q^{93} +4.22450 q^{94} -1.98612 q^{95} +2.68989 q^{96} +6.70496 q^{97} +5.39592 q^{98} -0.481282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9 + 9 * q^10 - 5 * q^11 + q^12 - 35 * q^13 + 8 * q^14 - 21 * q^15 + 75 * q^16 + 4 * q^17 - 66 * q^18 - 59 * q^19 - 9 * q^20 - 62 * q^21 + 5 * q^22 + 43 * q^23 - q^24 + 44 * q^25 + 35 * q^26 + 4 * q^27 - 8 * q^28 - 38 * q^29 + 21 * q^30 - 51 * q^31 - 75 * q^32 - 19 * q^33 - 4 * q^34 + 14 * q^35 + 66 * q^36 - 63 * q^37 + 59 * q^38 - 34 * q^39 + 9 * q^40 - 27 * q^41 + 62 * q^42 - 39 * q^43 - 5 * q^44 - 52 * q^45 - 43 * q^46 + 40 * q^47 + q^48 + 29 * q^49 - 44 * q^50 - 34 * q^51 - 35 * q^52 - 39 * q^53 - 4 * q^54 - 48 * q^55 + 8 * q^56 - 28 * q^57 + 38 * q^58 + 5 * q^59 - 21 * q^60 - 98 * q^61 + 51 * q^62 + 2 * q^63 + 75 * q^64 - q^65 + 19 * q^66 - 59 * q^67 + 4 * q^68 - 69 * q^69 - 14 * q^70 - 9 * q^71 - 66 * q^72 - 51 * q^73 + 63 * q^74 - q^75 - 59 * q^76 - 25 * q^77 + 34 * q^78 - 139 * q^79 - 9 * q^80 + 23 * q^81 + 27 * q^82 + 31 * q^83 - 62 * q^84 - 149 * q^85 + 39 * q^86 + q^87 + 5 * q^88 - 39 * q^89 + 52 * q^90 - 93 * q^91 + 43 * q^92 - 83 * q^93 - 40 * q^94 + 2 * q^95 - q^96 - 70 * q^97 - 29 * q^98 - 61 * q^99

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