LMFDB - Embedded newform 8002.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, 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("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$95$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.18851 q^{3} +1.00000 q^{4} +0.351128 q^{5} -3.18851 q^{6} -0.0577605 q^{7} +1.00000 q^{8} +7.16662 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.18851 q^{3} +1.00000 q^{4} +0.351128 q^{5} -3.18851 q^{6} -0.0577605 q^{7} +1.00000 q^{8} +7.16662 q^{9} +0.351128 q^{10} -5.39977 q^{11} -3.18851 q^{12} -2.94715 q^{13} -0.0577605 q^{14} -1.11958 q^{15} +1.00000 q^{16} +1.40569 q^{17} +7.16662 q^{18} +2.23189 q^{19} +0.351128 q^{20} +0.184170 q^{21} -5.39977 q^{22} -3.39309 q^{23} -3.18851 q^{24} -4.87671 q^{25} -2.94715 q^{26} -13.2853 q^{27} -0.0577605 q^{28} -1.15446 q^{29} -1.11958 q^{30} +1.29701 q^{31} +1.00000 q^{32} +17.2173 q^{33} +1.40569 q^{34} -0.0202813 q^{35} +7.16662 q^{36} +4.71740 q^{37} +2.23189 q^{38} +9.39703 q^{39} +0.351128 q^{40} -5.17881 q^{41} +0.184170 q^{42} -0.286042 q^{43} -5.39977 q^{44} +2.51640 q^{45} -3.39309 q^{46} -1.17549 q^{47} -3.18851 q^{48} -6.99666 q^{49} -4.87671 q^{50} -4.48205 q^{51} -2.94715 q^{52} +5.97850 q^{53} -13.2853 q^{54} -1.89601 q^{55} -0.0577605 q^{56} -7.11642 q^{57} -1.15446 q^{58} -13.6214 q^{59} -1.11958 q^{60} +13.7140 q^{61} +1.29701 q^{62} -0.413948 q^{63} +1.00000 q^{64} -1.03483 q^{65} +17.2173 q^{66} +2.35374 q^{67} +1.40569 q^{68} +10.8189 q^{69} -0.0202813 q^{70} +13.1128 q^{71} +7.16662 q^{72} +5.12587 q^{73} +4.71740 q^{74} +15.5495 q^{75} +2.23189 q^{76} +0.311894 q^{77} +9.39703 q^{78} -12.8323 q^{79} +0.351128 q^{80} +20.8606 q^{81} -5.17881 q^{82} +13.1076 q^{83} +0.184170 q^{84} +0.493576 q^{85} -0.286042 q^{86} +3.68101 q^{87} -5.39977 q^{88} -2.12644 q^{89} +2.51640 q^{90} +0.170229 q^{91} -3.39309 q^{92} -4.13555 q^{93} -1.17549 q^{94} +0.783680 q^{95} -3.18851 q^{96} -7.02327 q^{97} -6.99666 q^{98} -38.6981 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) $ 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9 + 36 * q^10 + 40 * q^11 + 24 * q^12 + 52 * q^13 + 21 * q^14 + 15 * q^15 + 95 * q^16 + 84 * q^17 + 121 * q^18 + 37 * q^19 + 36 * q^20 + 36 * q^21 + 40 * q^22 + 37 * q^23 + 24 * q^24 + 133 * q^25 + 52 * q^26 + 93 * q^27 + 21 * q^28 + 66 * q^29 + 15 * q^30 + 10 * q^31 + 95 * q^32 + 63 * q^33 + 84 * q^34 + 55 * q^35 + 121 * q^36 + 49 * q^37 + 37 * q^38 + 14 * q^39 + 36 * q^40 + 98 * q^41 + 36 * q^42 + 37 * q^43 + 40 * q^44 + 97 * q^45 + 37 * q^46 + 91 * q^47 + 24 * q^48 + 170 * q^49 + 133 * q^50 + 22 * q^51 + 52 * q^52 + 70 * q^53 + 93 * q^54 - q^55 + 21 * q^56 + 50 * q^57 + 66 * q^58 + 72 * q^59 + 15 * q^60 + 97 * q^61 + 10 * q^62 + 75 * q^63 + 95 * q^64 + 75 * q^65 + 63 * q^66 + 39 * q^67 + 84 * q^68 + 65 * q^69 + 55 * q^70 + 28 * q^71 + 121 * q^72 + 117 * q^73 + 49 * q^74 + 62 * q^75 + 37 * q^76 + 92 * q^77 + 14 * q^78 + q^79 + 36 * q^80 + 155 * q^81 + 98 * q^82 + 117 * q^83 + 36 * q^84 + 81 * q^85 + 37 * q^86 + 46 * q^87 + 40 * q^88 + 90 * q^89 + 97 * q^90 + 65 * q^91 + 37 * q^92 + 36 * q^93 + 91 * q^94 + 38 * q^95 + 24 * q^96 + 111 * q^97 + 170 * q^98 + 97 * 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
$3$	−3.18851	−1.84089	−0.920445	−	0.390873i	$-0.872173\pi$
$3$	−3.18851	−1.84089	−0.920445	+	0.390873i	$0.872173\pi$
$4$	1.00000	0.500000
$5$	0.351128	0.157029	0.0785146	−	0.996913i	$-0.474982\pi$
$5$	0.351128	0.157029	0.0785146	+	0.996913i	$0.474982\pi$
$6$	−3.18851	−1.30171
$7$	−0.0577605	−0.0218314	−0.0109157	−	0.999940i	$-0.503475\pi$
$7$	−0.0577605	−0.0218314	−0.0109157	+	0.999940i	$0.503475\pi$
$8$	1.00000	0.353553
$9$	7.16662	2.38887
$10$	0.351128	0.111036
$11$	−5.39977	−1.62809	−0.814047	−	0.580799i	$-0.802740\pi$
$11$	−5.39977	−1.62809	−0.814047	+	0.580799i	$0.802740\pi$
$12$	−3.18851	−0.920445
$13$	−2.94715	−0.817393	−0.408696	−	0.912670i	$-0.634017\pi$
$13$	−2.94715	−0.817393	−0.408696	+	0.912670i	$0.634017\pi$
$14$	−0.0577605	−0.0154371
$15$	−1.11958	−0.289074
$16$	1.00000	0.250000
$17$	1.40569	0.340929	0.170464	−	0.985364i	$-0.445473\pi$
$17$	1.40569	0.340929	0.170464	+	0.985364i	$0.445473\pi$
$18$	7.16662	1.68919
$19$	2.23189	0.512031	0.256015	−	0.966673i	$-0.417590\pi$
$19$	2.23189	0.512031	0.256015	+	0.966673i	$0.417590\pi$
$20$	0.351128	0.0785146
$21$	0.184170	0.0401892
$22$	−5.39977	−1.15124
$23$	−3.39309	−0.707509	−0.353754	−	0.935338i	$-0.615095\pi$
$23$	−3.39309	−0.707509	−0.353754	+	0.935338i	$0.615095\pi$
$24$	−3.18851	−0.650853
$25$	−4.87671	−0.975342
$26$	−2.94715	−0.577984
$27$	−13.2853	−2.55676
$28$	−0.0577605	−0.0109157
$29$	−1.15446	−0.214378	−0.107189	−	0.994239i	$-0.534185\pi$
$29$	−1.15446	−0.214378	−0.107189	+	0.994239i	$0.534185\pi$
$30$	−1.11958	−0.204406
$31$	1.29701	0.232951	0.116475	−	0.993194i	$-0.462840\pi$
$31$	1.29701	0.232951	0.116475	+	0.993194i	$0.462840\pi$
$32$	1.00000	0.176777
$33$	17.2173	2.99714
$34$	1.40569	0.241073
$35$	−0.0202813	−0.00342817
$36$	7.16662	1.19444
$37$	4.71740	0.775536	0.387768	−	0.921757i	$-0.373246\pi$
$37$	4.71740	0.775536	0.387768	+	0.921757i	$0.373246\pi$
$38$	2.23189	0.362061
$39$	9.39703	1.50473
$40$	0.351128	0.0555182
$41$	−5.17881	−0.808795	−0.404397	−	0.914583i	$-0.632519\pi$
$41$	−5.17881	−0.808795	−0.404397	+	0.914583i	$0.632519\pi$
$42$	0.184170	0.0284181
$43$	−0.286042	−0.0436210	−0.0218105	−	0.999762i	$-0.506943\pi$
$43$	−0.286042	−0.0436210	−0.0218105	+	0.999762i	$0.506943\pi$
$44$	−5.39977	−0.814047
$45$	2.51640	0.375123
$46$	−3.39309	−0.500284
$47$	−1.17549	−0.171463	−0.0857315	−	0.996318i	$-0.527323\pi$
$47$	−1.17549	−0.171463	−0.0857315	+	0.996318i	$0.527323\pi$
$48$	−3.18851	−0.460222
$49$	−6.99666	−0.999523
$50$	−4.87671	−0.689671
$51$	−4.48205	−0.627612
$52$	−2.94715	−0.408696
$53$	5.97850	0.821210	0.410605	−	0.911813i	$-0.365318\pi$
$53$	5.97850	0.821210	0.410605	+	0.911813i	$0.365318\pi$
$54$	−13.2853	−1.80790
$55$	−1.89601	−0.255658
$56$	−0.0577605	−0.00771857
$57$	−7.11642	−0.942592
$58$	−1.15446	−0.151588
$59$	−13.6214	−1.77335	−0.886676	−	0.462392i	$-0.846991\pi$
$59$	−13.6214	−1.77335	−0.886676	+	0.462392i	$0.846991\pi$
$60$	−1.11958	−0.144537
$61$	13.7140	1.75590	0.877949	−	0.478755i	$-0.158912\pi$
$61$	13.7140	1.75590	0.877949	+	0.478755i	$0.158912\pi$
$62$	1.29701	0.164721
$63$	−0.413948	−0.0521525
$64$	1.00000	0.125000
$65$	−1.03483	−0.128355
$66$	17.2173	2.11930
$67$	2.35374	0.287555	0.143777	−	0.989610i	$-0.454075\pi$
$67$	2.35374	0.287555	0.143777	+	0.989610i	$0.454075\pi$
$68$	1.40569	0.170464
$69$	10.8189	1.30245
$70$	−0.0202813	−0.00242408
$71$	13.1128	1.55620	0.778102	−	0.628138i	$-0.216183\pi$
$71$	13.1128	1.55620	0.778102	+	0.628138i	$0.216183\pi$
$72$	7.16662	0.844594
$73$	5.12587	0.599938	0.299969	−	0.953949i	$-0.403024\pi$
$73$	5.12587	0.599938	0.299969	+	0.953949i	$0.403024\pi$
$74$	4.71740	0.548387
$75$	15.5495	1.79550
$76$	2.23189	0.256015
$77$	0.311894	0.0355436
$78$	9.39703	1.06400
$79$	−12.8323	−1.44375	−0.721876	−	0.692023i	$-0.756720\pi$
$79$	−12.8323	−1.44375	−0.721876	+	0.692023i	$0.756720\pi$
$80$	0.351128	0.0392573
$81$	20.8606	2.31784
$82$	−5.17881	−0.571904
$83$	13.1076	1.43875	0.719374	−	0.694623i	$-0.244429\pi$
$83$	13.1076	1.43875	0.719374	+	0.694623i	$0.244429\pi$
$84$	0.184170	0.0200946
$85$	0.493576	0.0535358
$86$	−0.286042	−0.0308447
$87$	3.68101	0.394645
$88$	−5.39977	−0.575618
$89$	−2.12644	−0.225402	−0.112701	−	0.993629i	$-0.535950\pi$
$89$	−2.12644	−0.225402	−0.112701	+	0.993629i	$0.535950\pi$
$90$	2.51640	0.265252
$91$	0.170229	0.0178448
$92$	−3.39309	−0.353754
$93$	−4.13555	−0.428837
$94$	−1.17549	−0.121243
$95$	0.783680	0.0804039
$96$	−3.18851	−0.325426
$97$	−7.02327	−0.713105	−0.356552	−	0.934275i	$-0.616048\pi$
$97$	−7.02327	−0.713105	−0.356552	+	0.934275i	$0.616048\pi$
$98$	−6.99666	−0.706770
$99$	−38.6981	−3.88931
$100$	−4.87671	−0.487671
$101$	4.51023	0.448785	0.224392	−	0.974499i	$-0.427960\pi$
$101$	4.51023	0.448785	0.224392	+	0.974499i	$0.427960\pi$
$102$	−4.48205	−0.443789
$103$	−10.1297	−0.998111	−0.499055	−	0.866570i	$-0.666320\pi$
$103$	−10.1297	−0.998111	−0.499055	+	0.866570i	$0.666320\pi$
$104$	−2.94715	−0.288992
$105$	0.0646673	0.00631089
$106$	5.97850	0.580683
$107$	−1.07318	−0.103749	−0.0518743	−	0.998654i	$-0.516520\pi$
$107$	−1.07318	−0.103749	−0.0518743	+	0.998654i	$0.516520\pi$
$108$	−13.2853	−1.27838
$109$	0.281014	0.0269162	0.0134581	−	0.999909i	$-0.495716\pi$
$109$	0.281014	0.0269162	0.0134581	+	0.999909i	$0.495716\pi$
$110$	−1.89601	−0.180778
$111$	−15.0415	−1.42768
$112$	−0.0577605	−0.00545786
$113$	−7.95563	−0.748402	−0.374201	−	0.927348i	$-0.622083\pi$
$113$	−7.95563	−0.748402	−0.374201	+	0.927348i	$0.622083\pi$
$114$	−7.11642	−0.666513
$115$	−1.19141	−0.111100
$116$	−1.15446	−0.107189
$117$	−21.1211	−1.95265
$118$	−13.6214	−1.25395
$119$	−0.0811932	−0.00744296
$120$	−1.11958	−0.102203
$121$	18.1576	1.65069
$122$	13.7140	1.24161
$123$	16.5127	1.48890
$124$	1.29701	0.116475
$125$	−3.46799	−0.310187
$126$	−0.413948	−0.0368774
$127$	−14.1315	−1.25397	−0.626984	−	0.779032i	$-0.715711\pi$
$127$	−14.1315	−1.25397	−0.626984	+	0.779032i	$0.715711\pi$
$128$	1.00000	0.0883883
$129$	0.912050	0.0803015
$130$	−1.03483	−0.0907604
$131$	0.707092	0.0617789	0.0308895	−	0.999523i	$-0.490166\pi$
$131$	0.707092	0.0617789	0.0308895	+	0.999523i	$0.490166\pi$
$132$	17.2173	1.49857
$133$	−0.128915	−0.0111784
$134$	2.35374	0.203332
$135$	−4.66485	−0.401486
$136$	1.40569	0.120537
$137$	3.86278	0.330019	0.165010	−	0.986292i	$-0.447234\pi$
$137$	3.86278	0.330019	0.165010	+	0.986292i	$0.447234\pi$
$138$	10.8189	0.920968
$139$	6.77937	0.575019	0.287509	−	0.957778i	$-0.407173\pi$
$139$	6.77937	0.575019	0.287509	+	0.957778i	$0.407173\pi$
$140$	−0.0202813	−0.00171409
$141$	3.74807	0.315644
$142$	13.1128	1.10040
$143$	15.9140	1.33079
$144$	7.16662	0.597218
$145$	−0.405363	−0.0336636
$146$	5.12587	0.424220
$147$	22.3090	1.84001
$148$	4.71740	0.387768
$149$	21.1638	1.73380	0.866902	−	0.498479i	$-0.166108\pi$
$149$	21.1638	1.73380	0.866902	+	0.498479i	$0.166108\pi$
$150$	15.5495	1.26961
$151$	−7.04888	−0.573630	−0.286815	−	0.957986i	$-0.592596\pi$
$151$	−7.04888	−0.573630	−0.286815	+	0.957986i	$0.592596\pi$
$152$	2.23189	0.181030
$153$	10.0740	0.814436
$154$	0.311894	0.0251331
$155$	0.455418	0.0365801
$156$	9.39703	0.752365
$157$	4.24638	0.338898	0.169449	−	0.985539i	$-0.445801\pi$
$157$	4.24638	0.338898	0.169449	+	0.985539i	$0.445801\pi$
$158$	−12.8323	−1.02089
$159$	−19.0625	−1.51176
$160$	0.351128	0.0277591
$161$	0.195987	0.0154459
$162$	20.8606	1.63896
$163$	−11.8806	−0.930560	−0.465280	−	0.885163i	$-0.654046\pi$
$163$	−11.8806	−0.930560	−0.465280	+	0.885163i	$0.654046\pi$
$164$	−5.17881	−0.404397
$165$	6.04546	0.470639
$166$	13.1076	1.01735
$167$	1.85125	0.143254	0.0716271	−	0.997431i	$-0.477181\pi$
$167$	1.85125	0.143254	0.0716271	+	0.997431i	$0.477181\pi$
$168$	0.184170	0.0142090
$169$	−4.31430	−0.331869
$170$	0.493576	0.0378555
$171$	15.9951	1.22318
$172$	−0.286042	−0.0218105
$173$	15.6743	1.19169	0.595846	−	0.803099i	$-0.296817\pi$
$173$	15.6743	1.19169	0.595846	+	0.803099i	$0.296817\pi$
$174$	3.68101	0.279056
$175$	0.281681	0.0212931
$176$	−5.39977	−0.407023
$177$	43.4319	3.26454
$178$	−2.12644	−0.159384
$179$	−7.68540	−0.574434	−0.287217	−	0.957866i	$-0.592730\pi$
$179$	−7.68540	−0.574434	−0.287217	+	0.957866i	$0.592730\pi$
$180$	2.51640	0.187562
$181$	−16.4273	−1.22103	−0.610517	−	0.792003i	$-0.709038\pi$
$181$	−16.4273	−1.22103	−0.610517	+	0.792003i	$0.709038\pi$
$182$	0.170229	0.0126182
$183$	−43.7273	−3.23241
$184$	−3.39309	−0.250142
$185$	1.65641	0.121782
$186$	−4.13555	−0.303233
$187$	−7.59039	−0.555064
$188$	−1.17549	−0.0857315
$189$	0.767367	0.0558177
$190$	0.783680	0.0568541
$191$	13.8275	1.00052	0.500260	−	0.865875i	$-0.333238\pi$
$191$	13.8275	1.00052	0.500260	+	0.865875i	$0.333238\pi$
$192$	−3.18851	−0.230111
$193$	−6.05409	−0.435783	−0.217891	−	0.975973i	$-0.569918\pi$
$193$	−6.05409	−0.435783	−0.217891	+	0.975973i	$0.569918\pi$
$194$	−7.02327	−0.504241
$195$	3.29956	0.236287
$196$	−6.99666	−0.499762
$197$	22.4666	1.60068	0.800339	−	0.599547i	$-0.204653\pi$
$197$	22.4666	1.60068	0.800339	+	0.599547i	$0.204653\pi$
$198$	−38.6981	−2.75016
$199$	6.05225	0.429033	0.214516	−	0.976720i	$-0.431182\pi$
$199$	6.05225	0.429033	0.214516	+	0.976720i	$0.431182\pi$
$200$	−4.87671	−0.344835
$201$	−7.50492	−0.529356
$202$	4.51023	0.317339
$203$	0.0666821	0.00468017
$204$	−4.48205	−0.313806
$205$	−1.81843	−0.127004
$206$	−10.1297	−0.705771
$207$	−24.3170	−1.69015
$208$	−2.94715	−0.204348
$209$	−12.0517	−0.833634
$210$	0.0646673	0.00446247
$211$	19.8703	1.36793	0.683965	−	0.729514i	$-0.260254\pi$
$211$	19.8703	1.36793	0.683965	+	0.729514i	$0.260254\pi$
$212$	5.97850	0.410605
$213$	−41.8104	−2.86480
$214$	−1.07318	−0.0733614
$215$	−0.100438	−0.00684978
$216$	−13.2853	−0.903952
$217$	−0.0749163	−0.00508565
$218$	0.281014	0.0190327
$219$	−16.3439	−1.10442
$220$	−1.89601	−0.127829
$221$	−4.14277	−0.278673
$222$	−15.0415	−1.00952
$223$	5.42391	0.363212	0.181606	−	0.983371i	$-0.441870\pi$
$223$	5.42391	0.363212	0.181606	+	0.983371i	$0.441870\pi$
$224$	−0.0577605	−0.00385929
$225$	−34.9495	−2.32997
$226$	−7.95563	−0.529200
$227$	−5.46374	−0.362641	−0.181321	−	0.983424i	$-0.558037\pi$
$227$	−5.46374	−0.362641	−0.181321	+	0.983424i	$0.558037\pi$
$228$	−7.11642	−0.471296
$229$	21.7380	1.43649	0.718244	−	0.695792i	$-0.244946\pi$
$229$	21.7380	1.43649	0.718244	+	0.695792i	$0.244946\pi$
$230$	−1.19141	−0.0785593
$231$	−0.994478	−0.0654318
$232$	−1.15446	−0.0757939
$233$	3.81272	0.249779	0.124890	−	0.992171i	$-0.460142\pi$
$233$	3.81272	0.249779	0.124890	+	0.992171i	$0.460142\pi$
$234$	−21.1211	−1.38073
$235$	−0.412748	−0.0269247
$236$	−13.6214	−0.886676
$237$	40.9161	2.65779
$238$	−0.0811932	−0.00526297
$239$	1.27478	0.0824584	0.0412292	−	0.999150i	$-0.486873\pi$
$239$	1.27478	0.0824584	0.0412292	+	0.999150i	$0.486873\pi$
$240$	−1.11958	−0.0722684
$241$	−4.69522	−0.302446	−0.151223	−	0.988500i	$-0.548321\pi$
$241$	−4.69522	−0.302446	−0.151223	+	0.988500i	$0.548321\pi$
$242$	18.1576	1.16721
$243$	−26.6582	−1.71013
$244$	13.7140	0.877949
$245$	−2.45673	−0.156954
$246$	16.5127	1.05281
$247$	−6.57772	−0.418530
$248$	1.29701	0.0823605
$249$	−41.7938	−2.64858
$250$	−3.46799	−0.219335
$251$	−25.6637	−1.61988	−0.809938	−	0.586515i	$-0.800500\pi$
$251$	−25.6637	−1.61988	−0.809938	+	0.586515i	$0.800500\pi$
$252$	−0.413948	−0.0260762
$253$	18.3219	1.15189
$254$	−14.1315	−0.886689
$255$	−1.57377	−0.0985535
$256$	1.00000	0.0625000
$257$	−1.13831	−0.0710056	−0.0355028	−	0.999370i	$-0.511303\pi$
$257$	−1.13831	−0.0710056	−0.0355028	+	0.999370i	$0.511303\pi$
$258$	0.912050	0.0567817
$259$	−0.272479	−0.0169311
$260$	−1.03483	−0.0641773
$261$	−8.27357	−0.512121
$262$	0.707092	0.0436843
$263$	−6.71461	−0.414040	−0.207020	−	0.978337i	$-0.566377\pi$
$263$	−6.71461	−0.414040	−0.207020	+	0.978337i	$0.566377\pi$
$264$	17.2173	1.05965
$265$	2.09922	0.128954
$266$	−0.128915	−0.00790430
$267$	6.78019	0.414941
$268$	2.35374	0.143777
$269$	27.5133	1.67751	0.838757	−	0.544506i	$-0.183283\pi$
$269$	27.5133	1.67751	0.838757	+	0.544506i	$0.183283\pi$
$270$	−4.66485	−0.283894
$271$	19.4083	1.17897	0.589484	−	0.807780i	$-0.299331\pi$
$271$	19.4083	1.17897	0.589484	+	0.807780i	$0.299331\pi$
$272$	1.40569	0.0852322
$273$	−0.542777	−0.0328504
$274$	3.86278	0.233359
$275$	26.3331	1.58795
$276$	10.8189	0.651223
$277$	26.2861	1.57938	0.789689	−	0.613508i	$-0.210242\pi$
$277$	26.2861	1.57938	0.789689	+	0.613508i	$0.210242\pi$
$278$	6.77937	0.406600
$279$	9.29521	0.556490
$280$	−0.0202813	−0.00121204
$281$	−2.89238	−0.172545	−0.0862724	−	0.996272i	$-0.527496\pi$
$281$	−2.89238	−0.172545	−0.0862724	+	0.996272i	$0.527496\pi$
$282$	3.74807	0.223194
$283$	13.0373	0.774990	0.387495	−	0.921872i	$-0.373340\pi$
$283$	13.0373	0.774990	0.387495	+	0.921872i	$0.373340\pi$
$284$	13.1128	0.778102
$285$	−2.49877	−0.148015
$286$	15.9140	0.941012
$287$	0.299131	0.0176571
$288$	7.16662	0.422297
$289$	−15.0240	−0.883767
$290$	−0.405363	−0.0238037
$291$	22.3938	1.31275
$292$	5.12587	0.299969
$293$	7.12259	0.416106	0.208053	−	0.978118i	$-0.433287\pi$
$293$	7.12259	0.416106	0.208053	+	0.978118i	$0.433287\pi$
$294$	22.3090	1.30108
$295$	−4.78285	−0.278468
$296$	4.71740	0.274193
$297$	71.7377	4.16265
$298$	21.1638	1.22598
$299$	9.99996	0.578313
$300$	15.5495	0.897748
$301$	0.0165220	0.000952310 0
$302$	−7.04888	−0.405617
$303$	−14.3809	−0.826163
$304$	2.23189	0.128008
$305$	4.81537	0.275727
$306$	10.0740	0.575893
$307$	−25.4107	−1.45026	−0.725132	−	0.688610i	$-0.758221\pi$
$307$	−25.4107	−1.45026	−0.725132	+	0.688610i	$0.758221\pi$
$308$	0.311894	0.0177718
$309$	32.2987	1.83741
$310$	0.455418	0.0258660
$311$	10.4586	0.593053	0.296527	−	0.955025i	$-0.404172\pi$
$311$	10.4586	0.593053	0.296527	+	0.955025i	$0.404172\pi$
$312$	9.39703	0.532002
$313$	16.9977	0.960769	0.480385	−	0.877058i	$-0.340497\pi$
$313$	16.9977	0.960769	0.480385	+	0.877058i	$0.340497\pi$
$314$	4.24638	0.239637
$315$	−0.145349	−0.00818947
$316$	−12.8323	−0.721876
$317$	29.2313	1.64180	0.820898	−	0.571075i	$-0.193473\pi$
$317$	29.2313	1.64180	0.820898	+	0.571075i	$0.193473\pi$
$318$	−19.0625	−1.06897
$319$	6.23382	0.349027
$320$	0.351128	0.0196287
$321$	3.42186	0.190990
$322$	0.195987	0.0109219
$323$	3.13734	0.174566
$324$	20.8606	1.15892
$325$	14.3724	0.797237
$326$	−11.8806	−0.658005
$327$	−0.896017	−0.0495498
$328$	−5.17881	−0.285952
$329$	0.0678970	0.00374328
$330$	6.04546	0.332792
$331$	−26.9945	−1.48375	−0.741877	−	0.670536i	$-0.766064\pi$
$331$	−26.9945	−1.48375	−0.741877	+	0.670536i	$0.766064\pi$
$332$	13.1076	0.719374
$333$	33.8078	1.85266
$334$	1.85125	0.101296
$335$	0.826463	0.0451545
$336$	0.184170	0.0100473
$337$	2.68441	0.146229	0.0731146	−	0.997324i	$-0.476706\pi$
$337$	2.68441	0.146229	0.0731146	+	0.997324i	$0.476706\pi$
$338$	−4.31430	−0.234667
$339$	25.3666	1.37773
$340$	0.493576	0.0267679
$341$	−7.00359	−0.379266
$342$	15.9951	0.864917
$343$	0.808455	0.0436524
$344$	−0.286042	−0.0154224
$345$	3.79883	0.204522
$346$	15.6743	0.842653
$347$	14.8292	0.796071	0.398036	−	0.917370i	$-0.369692\pi$
$347$	14.8292	0.796071	0.398036	+	0.917370i	$0.369692\pi$
$348$	3.68101	0.197323
$349$	−7.10975	−0.380576	−0.190288	−	0.981728i	$-0.560942\pi$
$349$	−7.10975	−0.380576	−0.190288	+	0.981728i	$0.560942\pi$
$350$	0.281681	0.0150565
$351$	39.1539	2.08988
$352$	−5.39977	−0.287809
$353$	10.3876	0.552874	0.276437	−	0.961032i	$-0.410846\pi$
$353$	10.3876	0.552874	0.276437	+	0.961032i	$0.410846\pi$
$354$	43.4319	2.30838
$355$	4.60428	0.244370
$356$	−2.12644	−0.112701
$357$	0.258885	0.0137017
$358$	−7.68540	−0.406186
$359$	−18.1410	−0.957446	−0.478723	−	0.877966i	$-0.658900\pi$
$359$	−18.1410	−0.957446	−0.478723	+	0.877966i	$0.658900\pi$
$360$	2.51640	0.132626
$361$	−14.0187	−0.737824
$362$	−16.4273	−0.863402
$363$	−57.8956	−3.03873
$364$	0.170229	0.00892242
$365$	1.79984	0.0942078
$366$	−43.7273	−2.28566
$367$	27.0323	1.41107	0.705536	−	0.708674i	$-0.250706\pi$
$367$	27.0323	1.41107	0.705536	+	0.708674i	$0.250706\pi$
$368$	−3.39309	−0.176877
$369$	−37.1146	−1.93211
$370$	1.65641	0.0861128
$371$	−0.345321	−0.0179282
$372$	−4.13555	−0.214418
$373$	0.767008	0.0397142	0.0198571	−	0.999803i	$-0.493679\pi$
$373$	0.767008	0.0397142	0.0198571	+	0.999803i	$0.493679\pi$
$374$	−7.59039	−0.392490
$375$	11.0577	0.571019
$376$	−1.17549	−0.0606213
$377$	3.40237	0.175231
$378$	0.767367	0.0394691
$379$	27.2575	1.40012	0.700062	−	0.714082i	$-0.253156\pi$
$379$	27.2575	1.40012	0.700062	+	0.714082i	$0.253156\pi$
$380$	0.783680	0.0402019
$381$	45.0585	2.30841
$382$	13.8275	0.707475
$383$	0.117402	0.00599897	0.00299948	−	0.999996i	$-0.499045\pi$
$383$	0.117402	0.00599897	0.00299948	+	0.999996i	$0.499045\pi$
$384$	−3.18851	−0.162713
$385$	0.109515	0.00558139
$386$	−6.05409	−0.308145
$387$	−2.04996	−0.104205
$388$	−7.02327	−0.356552
$389$	35.1150	1.78040	0.890201	−	0.455569i	$-0.150564\pi$
$389$	35.1150	1.78040	0.890201	+	0.455569i	$0.150564\pi$
$390$	3.29956	0.167080
$391$	−4.76962	−0.241210
$392$	−6.99666	−0.353385
$393$	−2.25457	−0.113728
$394$	22.4666	1.13185
$395$	−4.50580	−0.226711
$396$	−38.6981	−1.94465
$397$	−1.31606	−0.0660512	−0.0330256	−	0.999455i	$-0.510514\pi$
$397$	−1.31606	−0.0660512	−0.0330256	+	0.999455i	$0.510514\pi$
$398$	6.05225	0.303372
$399$	0.411048	0.0205781
$400$	−4.87671	−0.243835
$401$	−13.3230	−0.665320	−0.332660	−	0.943047i	$-0.607946\pi$
$401$	−13.3230	−0.665320	−0.332660	+	0.943047i	$0.607946\pi$
$402$	−7.50492	−0.374311
$403$	−3.82250	−0.190412
$404$	4.51023	0.224392
$405$	7.32473	0.363969
$406$	0.0666821	0.00330938
$407$	−25.4729	−1.26264
$408$	−4.48205	−0.221895
$409$	−15.3892	−0.760947	−0.380473	−	0.924792i	$-0.624239\pi$
$409$	−15.3892	−0.760947	−0.380473	+	0.924792i	$0.624239\pi$
$410$	−1.81843	−0.0898057
$411$	−12.3165	−0.607529
$412$	−10.1297	−0.499055
$413$	0.786777	0.0387148
$414$	−24.3170	−1.19512
$415$	4.60245	0.225926
$416$	−2.94715	−0.144496
$417$	−21.6161	−1.05855
$418$	−12.0517	−0.589468
$419$	1.41036	0.0689004	0.0344502	−	0.999406i	$-0.489032\pi$
$419$	1.41036	0.0689004	0.0344502	+	0.999406i	$0.489032\pi$
$420$	0.0646673	0.00315544
$421$	29.2210	1.42414	0.712072	−	0.702107i	$-0.247757\pi$
$421$	29.2210	1.42414	0.712072	+	0.702107i	$0.247757\pi$
$422$	19.8703	0.967273
$423$	−8.42430	−0.409603
$424$	5.97850	0.290342
$425$	−6.85512	−0.332522
$426$	−41.8104	−2.02572
$427$	−0.792128	−0.0383337
$428$	−1.07318	−0.0518743
$429$	−50.7419	−2.44984
$430$	−0.100438	−0.00484353
$431$	16.0748	0.774296	0.387148	−	0.922018i	$-0.373460\pi$
$431$	16.0748	0.774296	0.387148	+	0.922018i	$0.373460\pi$
$432$	−13.2853	−0.639190
$433$	26.8635	1.29098	0.645488	−	0.763771i	$-0.276654\pi$
$433$	26.8635	1.29098	0.645488	+	0.763771i	$0.276654\pi$
$434$	−0.0749163	−0.00359610
$435$	1.29251	0.0619709
$436$	0.281014	0.0134581
$437$	−7.57301	−0.362266
$438$	−16.3439	−0.780942
$439$	41.7094	1.99068	0.995341	−	0.0964163i	$-0.0307380\pi$
$439$	41.7094	1.99068	0.995341	+	0.0964163i	$0.0307380\pi$
$440$	−1.89601	−0.0903889
$441$	−50.1424	−2.38773
$442$	−4.14277	−0.197051
$443$	13.0661	0.620791	0.310395	−	0.950608i	$-0.399539\pi$
$443$	13.0661	0.620791	0.310395	+	0.950608i	$0.399539\pi$
$444$	−15.0415	−0.713838
$445$	−0.746653	−0.0353948
$446$	5.42391	0.256829
$447$	−67.4810	−3.19174
$448$	−0.0577605	−0.00272893
$449$	−5.58863	−0.263744	−0.131872	−	0.991267i	$-0.542099\pi$
$449$	−5.58863	−0.263744	−0.131872	+	0.991267i	$0.542099\pi$
$450$	−34.9495	−1.64754
$451$	27.9644	1.31679
$452$	−7.95563	−0.374201
$453$	22.4754	1.05599
$454$	−5.46374	−0.256426
$455$	0.0597722	0.00280216
$456$	−7.11642	−0.333257
$457$	24.8788	1.16378	0.581891	−	0.813267i	$-0.302313\pi$
$457$	24.8788	1.16378	0.581891	+	0.813267i	$0.302313\pi$
$458$	21.7380	1.01575
$459$	−18.6750	−0.871674
$460$	−1.19141	−0.0555498
$461$	−17.8233	−0.830113	−0.415056	−	0.909796i	$-0.636238\pi$
$461$	−17.8233	−0.830113	−0.415056	+	0.909796i	$0.636238\pi$
$462$	−0.994478	−0.0462673
$463$	−22.1977	−1.03161	−0.515806	−	0.856705i	$-0.672508\pi$
$463$	−22.1977	−1.03161	−0.515806	+	0.856705i	$0.672508\pi$
$464$	−1.15446	−0.0535944
$465$	−1.45211	−0.0673399
$466$	3.81272	0.176621
$467$	24.2826	1.12366	0.561831	−	0.827252i	$-0.310097\pi$
$467$	24.2826	1.12366	0.561831	+	0.827252i	$0.310097\pi$
$468$	−21.1211	−0.976324
$469$	−0.135953	−0.00627773
$470$	−0.412748	−0.0190386
$471$	−13.5396	−0.623874
$472$	−13.6214	−0.626974
$473$	1.54456	0.0710191
$474$	40.9161	1.87934
$475$	−10.8843	−0.499405
$476$	−0.0811932	−0.00372148
$477$	42.8456	1.96177
$478$	1.27478	0.0583069
$479$	30.5985	1.39808	0.699041	−	0.715082i	$-0.253611\pi$
$479$	30.5985	1.39808	0.699041	+	0.715082i	$0.253611\pi$
$480$	−1.11958	−0.0511015
$481$	−13.9029	−0.633917
$482$	−4.69522	−0.213862
$483$	−0.624907	−0.0284342
$484$	18.1576	0.825344
$485$	−2.46607	−0.111978
$486$	−26.6582	−1.20924
$487$	13.6485	0.618472	0.309236	−	0.950985i	$-0.399927\pi$
$487$	13.6485	0.618472	0.309236	+	0.950985i	$0.399927\pi$
$488$	13.7140	0.620803
$489$	37.8814	1.71306
$490$	−2.45673	−0.110984
$491$	−24.4442	−1.10315	−0.551576	−	0.834124i	$-0.685973\pi$
$491$	−24.4442	−1.10315	−0.551576	+	0.834124i	$0.685973\pi$
$492$	16.5127	0.744451
$493$	−1.62281	−0.0730875
$494$	−6.57772	−0.295946
$495$	−13.5880	−0.610735
$496$	1.29701	0.0582377
$497$	−0.757403	−0.0339742
$498$	−41.7938	−1.87283
$499$	11.2997	0.505843	0.252921	−	0.967487i	$-0.418609\pi$
$499$	11.2997	0.505843	0.252921	+	0.967487i	$0.418609\pi$
$500$	−3.46799	−0.155093
$501$	−5.90274	−0.263715
$502$	−25.6637	−1.14543
$503$	23.5004	1.04783	0.523915	−	0.851770i	$-0.324471\pi$
$503$	23.5004	1.04783	0.523915	+	0.851770i	$0.324471\pi$
$504$	−0.413948	−0.0184387
$505$	1.58367	0.0704724
$506$	18.3219	0.814510
$507$	13.7562	0.610934
$508$	−14.1315	−0.626984
$509$	21.2474	0.941775	0.470888	−	0.882193i	$-0.343934\pi$
$509$	21.2474	0.941775	0.470888	+	0.882193i	$0.343934\pi$
$510$	−1.57377	−0.0696879
$511$	−0.296073	−0.0130975
$512$	1.00000	0.0441942
$513$	−29.6514	−1.30914
$514$	−1.13831	−0.0502086
$515$	−3.55683	−0.156733
$516$	0.912050	0.0401508
$517$	6.34739	0.279158
$518$	−0.272479	−0.0119721
$519$	−49.9776	−2.19377
$520$	−1.03483	−0.0453802
$521$	17.0571	0.747284	0.373642	−	0.927573i	$-0.378109\pi$
$521$	17.0571	0.747284	0.373642	+	0.927573i	$0.378109\pi$
$522$	−8.27357	−0.362124
$523$	−5.59900	−0.244827	−0.122414	−	0.992479i	$-0.539063\pi$
$523$	−5.59900	−0.244827	−0.122414	+	0.992479i	$0.539063\pi$
$524$	0.707092	0.0308895
$525$	−0.898144	−0.0391982
$526$	−6.71461	−0.292771
$527$	1.82320	0.0794197
$528$	17.2173	0.749285
$529$	−11.4869	−0.499431
$530$	2.09922	0.0911842
$531$	−97.6192	−4.23631
$532$	−0.128915	−0.00558918
$533$	15.2628	0.661103
$534$	6.78019	0.293407
$535$	−0.376825	−0.0162916
$536$	2.35374	0.101666
$537$	24.5050	1.05747
$538$	27.5133	1.18618
$539$	37.7804	1.62732
$540$	−4.66485	−0.200743
$541$	−23.7142	−1.01955	−0.509776	−	0.860307i	$-0.670272\pi$
$541$	−23.7142	−1.01955	−0.509776	+	0.860307i	$0.670272\pi$
$542$	19.4083	0.833657
$543$	52.3788	2.24779
$544$	1.40569	0.0602683
$545$	0.0986719	0.00422664
$546$	−0.542777	−0.0232287
$547$	−8.36756	−0.357771	−0.178886	−	0.983870i	$-0.557249\pi$
$547$	−8.36756	−0.357771	−0.178886	+	0.983870i	$0.557249\pi$
$548$	3.86278	0.165010
$549$	98.2830	4.19462
$550$	26.3331	1.12285
$551$	−2.57663	−0.109768
$552$	10.8189	0.460484
$553$	0.741203	0.0315191
$554$	26.2861	1.11679
$555$	−5.28149	−0.224187
$556$	6.77937	0.287509
$557$	4.90317	0.207754	0.103877	−	0.994590i	$-0.466875\pi$
$557$	4.90317	0.207754	0.103877	+	0.994590i	$0.466875\pi$
$558$	9.29521	0.393498
$559$	0.843010	0.0356555
$560$	−0.0202813	−0.000857043 0
$561$	24.2021	1.02181
$562$	−2.89238	−0.122008
$563$	10.6522	0.448937	0.224469	−	0.974481i	$-0.427935\pi$
$563$	10.6522	0.448937	0.224469	+	0.974481i	$0.427935\pi$
$564$	3.74807	0.157822
$565$	−2.79344	−0.117521
$566$	13.0373	0.548001
$567$	−1.20492	−0.0506018
$568$	13.1128	0.550201
$569$	−19.4633	−0.815944	−0.407972	−	0.912994i	$-0.633764\pi$
$569$	−19.4633	−0.815944	−0.407972	+	0.912994i	$0.633764\pi$
$570$	−2.49877	−0.104662
$571$	−25.0752	−1.04937	−0.524683	−	0.851298i	$-0.675816\pi$
$571$	−25.0752	−1.04937	−0.524683	+	0.851298i	$0.675816\pi$
$572$	15.9140	0.665396
$573$	−44.0891	−1.84185
$574$	0.299131	0.0124855
$575$	16.5471	0.690063
$576$	7.16662	0.298609
$577$	13.2555	0.551833	0.275917	−	0.961182i	$-0.411019\pi$
$577$	13.2555	0.551833	0.275917	+	0.961182i	$0.411019\pi$
$578$	−15.0240	−0.624918
$579$	19.3035	0.802228
$580$	−0.405363	−0.0168318
$581$	−0.757103	−0.0314099
$582$	22.3938	0.928252
$583$	−32.2825	−1.33701
$584$	5.12587	0.212110
$585$	−7.41622	−0.306623
$586$	7.12259	0.294232
$587$	34.4376	1.42139	0.710695	−	0.703500i	$-0.248381\pi$
$587$	34.4376	1.42139	0.710695	+	0.703500i	$0.248381\pi$
$588$	22.3090	0.920006
$589$	2.89480	0.119278
$590$	−4.78285	−0.196907
$591$	−71.6350	−2.94667
$592$	4.71740	0.193884
$593$	10.8940	0.447363	0.223682	−	0.974662i	$-0.428192\pi$
$593$	10.8940	0.447363	0.223682	+	0.974662i	$0.428192\pi$
$594$	71.7377	2.94344
$595$	−0.0285092	−0.00116876
$596$	21.1638	0.866902
$597$	−19.2977	−0.789802
$598$	9.99996	0.408929
$599$	−29.0404	−1.18656	−0.593279	−	0.804997i	$-0.702167\pi$
$599$	−29.0404	−1.18656	−0.593279	+	0.804997i	$0.702167\pi$
$600$	15.5495	0.634804
$601$	15.1014	0.616001	0.308000	−	0.951386i	$-0.400340\pi$
$601$	15.1014	0.616001	0.308000	+	0.951386i	$0.400340\pi$
$602$	0.0165220	0.000673385 0
$603$	16.8683	0.686932
$604$	−7.04888	−0.286815
$605$	6.37563	0.259206
$606$	−14.3809	−0.584185
$607$	−15.9137	−0.645917	−0.322958	−	0.946413i	$-0.604677\pi$
$607$	−15.9137	−0.645917	−0.322958	+	0.946413i	$0.604677\pi$
$608$	2.23189	0.0905151
$609$	−0.212617	−0.00861567
$610$	4.81537	0.194969
$611$	3.46435	0.140153
$612$	10.0740	0.407218
$613$	39.7223	1.60437	0.802183	−	0.597078i	$-0.203672\pi$
$613$	39.7223	1.60437	0.802183	+	0.597078i	$0.203672\pi$
$614$	−25.4107	−1.02549
$615$	5.79808	0.233801
$616$	0.311894	0.0125666
$617$	−2.21589	−0.0892084	−0.0446042	−	0.999005i	$-0.514203\pi$
$617$	−2.21589	−0.0892084	−0.0446042	+	0.999005i	$0.514203\pi$
$618$	32.2987	1.29925
$619$	18.8139	0.756195	0.378098	−	0.925766i	$-0.376578\pi$
$619$	18.8139	0.756195	0.378098	+	0.925766i	$0.376578\pi$
$620$	0.455418	0.0182900
$621$	45.0783	1.80893
$622$	10.4586	0.419352
$623$	0.122824	0.00492085
$624$	9.39703	0.376182
$625$	23.1658	0.926633
$626$	16.9977	0.679366
$627$	38.4270	1.53463
$628$	4.24638	0.169449
$629$	6.63118	0.264403
$630$	−0.145349	−0.00579083
$631$	5.99589	0.238693	0.119346	−	0.992853i	$-0.461920\pi$
$631$	5.99589	0.238693	0.119346	+	0.992853i	$0.461920\pi$
$632$	−12.8323	−0.510443
$633$	−63.3569	−2.51821
$634$	29.2313	1.16093
$635$	−4.96197	−0.196910
$636$	−19.0625	−0.755878
$637$	20.6202	0.817003
$638$	6.23382	0.246799
$639$	93.9745	3.71757
$640$	0.351128	0.0138796
$641$	18.2986	0.722752	0.361376	−	0.932420i	$-0.382307\pi$
$641$	18.2986	0.722752	0.361376	+	0.932420i	$0.382307\pi$
$642$	3.42186	0.135050
$643$	−32.0443	−1.26370	−0.631852	−	0.775089i	$-0.717705\pi$
$643$	−32.0443	−1.26370	−0.631852	+	0.775089i	$0.717705\pi$
$644$	0.195987	0.00772296
$645$	0.320246	0.0126097
$646$	3.13734	0.123437
$647$	11.3474	0.446113	0.223057	−	0.974806i	$-0.428397\pi$
$647$	11.3474	0.446113	0.223057	+	0.974806i	$0.428397\pi$
$648$	20.8606	0.819481
$649$	73.5523	2.88718
$650$	14.3724	0.563732
$651$	0.238871	0.00936211
$652$	−11.8806	−0.465280
$653$	−35.1173	−1.37424	−0.687122	−	0.726542i	$-0.741126\pi$
$653$	−35.1173	−1.37424	−0.687122	+	0.726542i	$0.741126\pi$
$654$	−0.896017	−0.0350370
$655$	0.248280	0.00970110
$656$	−5.17881	−0.202199
$657$	36.7352	1.43318
$658$	0.0678970	0.00264690
$659$	−30.4714	−1.18700	−0.593500	−	0.804834i	$-0.702254\pi$
$659$	−30.4714	−1.18700	−0.593500	+	0.804834i	$0.702254\pi$
$660$	6.04546	0.235319
$661$	17.1357	0.666502	0.333251	−	0.942838i	$-0.391854\pi$
$661$	17.1357	0.666502	0.333251	+	0.942838i	$0.391854\pi$
$662$	−26.9945	−1.04917
$663$	13.2093	0.513006
$664$	13.1076	0.508674
$665$	−0.0452657	−0.00175533
$666$	33.8078	1.31003
$667$	3.91719	0.151674
$668$	1.85125	0.0716271
$669$	−17.2942	−0.668633
$670$	0.826463	0.0319291
$671$	−74.0525	−2.85876
$672$	0.184170	0.00710452
$673$	−12.6930	−0.489280	−0.244640	−	0.969614i	$-0.578670\pi$
$673$	−12.6930	−0.489280	−0.244640	+	0.969614i	$0.578670\pi$
$674$	2.68441	0.103400
$675$	64.7886	2.49372
$676$	−4.31430	−0.165935
$677$	8.51830	0.327385	0.163692	−	0.986511i	$-0.447660\pi$
$677$	8.51830	0.327385	0.163692	+	0.986511i	$0.447660\pi$
$678$	25.3666	0.974199
$679$	0.405668	0.0155681
$680$	0.493576	0.0189278
$681$	17.4212	0.667583
$682$	−7.00359	−0.268181
$683$	−21.4559	−0.820986	−0.410493	−	0.911864i	$-0.634643\pi$
$683$	−21.4559	−0.820986	−0.410493	+	0.911864i	$0.634643\pi$
$684$	15.9951	0.611588
$685$	1.35633	0.0518227
$686$	0.808455	0.0308669
$687$	−69.3119	−2.64441
$688$	−0.286042	−0.0109053
$689$	−17.6195	−0.671251
$690$	3.79883	0.144619
$691$	44.0980	1.67757	0.838784	−	0.544465i	$-0.183267\pi$
$691$	44.0980	1.67757	0.838784	+	0.544465i	$0.183267\pi$
$692$	15.6743	0.595846
$693$	2.23522	0.0849091
$694$	14.8292	0.562907
$695$	2.38043	0.0902948
$696$	3.68101	0.139528
$697$	−7.27979	−0.275742
$698$	−7.10975	−0.269108
$699$	−12.1569	−0.459816
$700$	0.281681	0.0106465
$701$	2.34658	0.0886289	0.0443145	−	0.999018i	$-0.485890\pi$
$701$	2.34658	0.0886289	0.0443145	+	0.999018i	$0.485890\pi$
$702$	39.1539	1.47777
$703$	10.5287	0.397098
$704$	−5.39977	−0.203512
$705$	1.31605	0.0495654
$706$	10.3876	0.390941
$707$	−0.260513	−0.00979761
$708$	43.4319	1.63227
$709$	−33.3449	−1.25229	−0.626146	−	0.779706i	$-0.715369\pi$
$709$	−33.3449	−1.25229	−0.626146	+	0.779706i	$0.715369\pi$
$710$	4.60428	0.172795
$711$	−91.9645	−3.44894
$712$	−2.12644	−0.0796918
$713$	−4.40089	−0.164815
$714$	0.258885	0.00968855
$715$	5.58784	0.208973
$716$	−7.68540	−0.287217
$717$	−4.06464	−0.151797
$718$	−18.1410	−0.677017
$719$	17.2023	0.641536	0.320768	−	0.947158i	$-0.396059\pi$
$719$	17.2023	0.641536	0.320768	+	0.947158i	$0.396059\pi$
$720$	2.51640	0.0937808
$721$	0.585098	0.0217902
$722$	−14.0187	−0.521721
$723$	14.9708	0.556770
$724$	−16.4273	−0.610517
$725$	5.62996	0.209091
$726$	−57.8956	−2.14871
$727$	−9.96483	−0.369575	−0.184788	−	0.982778i	$-0.559160\pi$
$727$	−9.96483	−0.369575	−0.184788	+	0.982778i	$0.559160\pi$
$728$	0.170229	0.00630911
$729$	22.4185	0.830314
$730$	1.79984	0.0666150
$731$	−0.402086	−0.0148717
$732$	−43.7273	−1.61621
$733$	−23.7230	−0.876229	−0.438114	−	0.898919i	$-0.644354\pi$
$733$	−23.7230	−0.876229	−0.438114	+	0.898919i	$0.644354\pi$
$734$	27.0323	0.997779
$735$	7.83330	0.288936
$736$	−3.39309	−0.125071
$737$	−12.7096	−0.468166
$738$	−37.1146	−1.36621
$739$	−5.03039	−0.185046	−0.0925230	−	0.995711i	$-0.529493\pi$
$739$	−5.03039	−0.185046	−0.0925230	+	0.995711i	$0.529493\pi$
$740$	1.65641	0.0608909
$741$	20.9732	0.770468
$742$	−0.345321	−0.0126771
$743$	43.6231	1.60038	0.800188	−	0.599749i	$-0.204733\pi$
$743$	43.6231	1.60038	0.800188	+	0.599749i	$0.204733\pi$
$744$	−4.13555	−0.151617
$745$	7.43120	0.272258
$746$	0.767008	0.0280822
$747$	93.9373	3.43699
$748$	−7.59039	−0.277532
$749$	0.0619877	0.00226498
$750$	11.0577	0.403771
$751$	−5.59970	−0.204336	−0.102168	−	0.994767i	$-0.532578\pi$
$751$	−5.59970	−0.204336	−0.102168	+	0.994767i	$0.532578\pi$
$752$	−1.17549	−0.0428658
$753$	81.8290	2.98201
$754$	3.40237	0.123907
$755$	−2.47506	−0.0900766
$756$	0.767367	0.0279089
$757$	−11.2975	−0.410615	−0.205308	−	0.978697i	$-0.565819\pi$
$757$	−11.2975	−0.410615	−0.205308	+	0.978697i	$0.565819\pi$
$758$	27.2575	0.990038
$759$	−58.4197	−2.12050
$760$	0.783680	0.0284271
$761$	−21.4931	−0.779125	−0.389563	−	0.921000i	$-0.627374\pi$
$761$	−21.4931	−0.779125	−0.389563	+	0.921000i	$0.627374\pi$
$762$	45.0585	1.63230
$763$	−0.0162315	−0.000587620 0
$764$	13.8275	0.500260
$765$	3.53727	0.127890
$766$	0.117402	0.00424191
$767$	40.1442	1.44952
$768$	−3.18851	−0.115056
$769$	−47.7414	−1.72160	−0.860799	−	0.508945i	$-0.830036\pi$
$769$	−47.7414	−1.72160	−0.860799	+	0.508945i	$0.830036\pi$
$770$	0.109515	0.00394664
$771$	3.62951	0.130714
$772$	−6.05409	−0.217891
$773$	30.9234	1.11224	0.556118	−	0.831103i	$-0.312290\pi$
$773$	30.9234	1.11224	0.556118	+	0.831103i	$0.312290\pi$
$774$	−2.04996	−0.0736842
$775$	−6.32516	−0.227207
$776$	−7.02327	−0.252121
$777$	0.868804	0.0311682
$778$	35.1150	1.25893
$779$	−11.5586	−0.414128
$780$	3.29956	0.118143
$781$	−70.8062	−2.53365
$782$	−4.76962	−0.170561
$783$	15.3374	0.548112
$784$	−6.99666	−0.249881
$785$	1.49102	0.0532169
$786$	−2.25457	−0.0804180
$787$	19.2563	0.686412	0.343206	−	0.939260i	$-0.388487\pi$
$787$	19.2563	0.686412	0.343206	+	0.939260i	$0.388487\pi$
$788$	22.4666	0.800339
$789$	21.4096	0.762202
$790$	−4.50580	−0.160309
$791$	0.459521	0.0163387
$792$	−38.6981	−1.37508
$793$	−40.4172	−1.43526
$794$	−1.31606	−0.0467052
$795$	−6.69339	−0.237390
$796$	6.05225	0.214516
$797$	46.9113	1.66168	0.830842	−	0.556508i	$-0.187859\pi$
$797$	46.9113	1.66168	0.830842	+	0.556508i	$0.187859\pi$
$798$	0.411048	0.0145509
$799$	−1.65237	−0.0584567
$800$	−4.87671	−0.172418
$801$	−15.2394	−0.538457
$802$	−13.3230	−0.470452
$803$	−27.6786	−0.976755
$804$	−7.50492	−0.264678
$805$	0.0688165	0.00242546
$806$	−3.82250	−0.134642
$807$	−87.7264	−3.08812
$808$	4.51023	0.158669
$809$	42.4935	1.49399	0.746996	−	0.664829i	$-0.231496\pi$
$809$	42.4935	1.49399	0.746996	+	0.664829i	$0.231496\pi$
$810$	7.32473	0.257365
$811$	36.5707	1.28417	0.642085	−	0.766633i	$-0.278070\pi$
$811$	36.5707	1.28417	0.642085	+	0.766633i	$0.278070\pi$
$812$	0.0666821	0.00234008
$813$	−61.8835	−2.17035
$814$	−25.4729	−0.892825
$815$	−4.17161	−0.146125
$816$	−4.48205	−0.156903
$817$	−0.638415	−0.0223353
$818$	−15.3892	−0.538071
$819$	1.21997	0.0426291
$820$	−1.81843	−0.0635022
$821$	−15.6227	−0.545236	−0.272618	−	0.962122i	$-0.587889\pi$
$821$	−15.6227	−0.545236	−0.272618	+	0.962122i	$0.587889\pi$
$822$	−12.3165	−0.429588
$823$	6.63032	0.231118	0.115559	−	0.993301i	$-0.463134\pi$
$823$	6.63032	0.231118	0.115559	+	0.993301i	$0.463134\pi$
$824$	−10.1297	−0.352885
$825$	−83.9635	−2.92324
$826$	0.786777	0.0273755
$827$	20.6878	0.719386	0.359693	−	0.933071i	$-0.382881\pi$
$827$	20.6878	0.719386	0.359693	+	0.933071i	$0.382881\pi$
$828$	−24.3170	−0.845074
$829$	21.5821	0.749578	0.374789	−	0.927110i	$-0.377715\pi$
$829$	21.5821	0.749578	0.374789	+	0.927110i	$0.377715\pi$
$830$	4.60245	0.159753
$831$	−83.8135	−2.90746
$832$	−2.94715	−0.102174
$833$	−9.83511	−0.340766
$834$	−21.6161	−0.748505
$835$	0.650027	0.0224951
$836$	−12.0517	−0.416817
$837$	−17.2313	−0.595599
$838$	1.41036	0.0487199
$839$	9.59206	0.331155	0.165577	−	0.986197i	$-0.447051\pi$
$839$	9.59206	0.331155	0.165577	+	0.986197i	$0.447051\pi$
$840$	0.0646673	0.00223124
$841$	−27.6672	−0.954042
$842$	29.2210	1.00702
$843$	9.22239	0.317636
$844$	19.8703	0.683965
$845$	−1.51487	−0.0521132
$846$	−8.42430	−0.289633
$847$	−1.04879	−0.0360369
$848$	5.97850	0.205302
$849$	−41.5698	−1.42667
$850$	−6.85512	−0.235129
$851$	−16.0066	−0.548698
$852$	−41.8104	−1.43240
$853$	−40.7052	−1.39372	−0.696860	−	0.717207i	$-0.745420\pi$
$853$	−40.7052	−1.39372	−0.696860	+	0.717207i	$0.745420\pi$
$854$	−0.792128	−0.0271060
$855$	5.61633	0.192075
$856$	−1.07318	−0.0366807
$857$	11.5869	0.395802	0.197901	−	0.980222i	$-0.436588\pi$
$857$	11.5869	0.395802	0.197901	+	0.980222i	$0.436588\pi$
$858$	−50.7419	−1.73230
$859$	−47.8901	−1.63399	−0.816994	−	0.576646i	$-0.804361\pi$
$859$	−47.8901	−1.63399	−0.816994	+	0.576646i	$0.804361\pi$
$860$	−0.100438	−0.00342489
$861$	−0.953783	−0.0325048
$862$	16.0748	0.547510
$863$	−21.3403	−0.726433	−0.363217	−	0.931705i	$-0.618322\pi$
$863$	−21.3403	−0.726433	−0.363217	+	0.931705i	$0.618322\pi$
$864$	−13.2853	−0.451976
$865$	5.50367	0.187130
$866$	26.8635	0.912858
$867$	47.9044	1.62692
$868$	−0.0749163	−0.00254282
$869$	69.2917	2.35056
$870$	1.29251	0.0438200
$871$	−6.93682	−0.235045
$872$	0.281014	0.00951633
$873$	−50.3331	−1.70352
$874$	−7.57301	−0.256161
$875$	0.200313	0.00677181
$876$	−16.3439	−0.552210
$877$	−43.0067	−1.45223	−0.726117	−	0.687571i	$-0.758677\pi$
$877$	−43.0067	−1.45223	−0.726117	+	0.687571i	$0.758677\pi$
$878$	41.7094	1.40762
$879$	−22.7105	−0.766006
$880$	−1.89601	−0.0639146
$881$	30.2420	1.01888	0.509439	−	0.860507i	$-0.329853\pi$
$881$	30.2420	1.01888	0.509439	+	0.860507i	$0.329853\pi$
$882$	−50.1424	−1.68838
$883$	28.6454	0.963995	0.481997	−	0.876173i	$-0.339912\pi$
$883$	28.6454	0.963995	0.481997	+	0.876173i	$0.339912\pi$
$884$	−4.14277	−0.139336
$885$	15.2502	0.512629
$886$	13.0661	0.438965
$887$	−3.39221	−0.113899	−0.0569497	−	0.998377i	$-0.518137\pi$
$887$	−3.39221	−0.113899	−0.0569497	+	0.998377i	$0.518137\pi$
$888$	−15.0415	−0.504760
$889$	0.816242	0.0273759
$890$	−0.746653	−0.0250279
$891$	−112.642	−3.77366
$892$	5.42391	0.181606
$893$	−2.62357	−0.0877944
$894$	−67.4810	−2.25690
$895$	−2.69856	−0.0902029
$896$	−0.0577605	−0.00192964
$897$	−31.8850	−1.06461
$898$	−5.58863	−0.186495
$899$	−1.49735	−0.0499394
$900$	−34.9495	−1.16498
$901$	8.40389	0.279974
$902$	27.9644	0.931114
$903$	−0.0526805	−0.00175310
$904$	−7.95563	−0.264600
$905$	−5.76810	−0.191738
$906$	22.4754	0.746697
$907$	13.6645	0.453724	0.226862	−	0.973927i	$-0.427153\pi$
$907$	13.6645	0.453724	0.226862	+	0.973927i	$0.427153\pi$
$908$	−5.46374	−0.181321
$909$	32.3231	1.07209
$910$	0.0597722	0.00198143
$911$	6.15264	0.203846	0.101923	−	0.994792i	$-0.467500\pi$
$911$	6.15264	0.203846	0.101923	+	0.994792i	$0.467500\pi$
$912$	−7.11642	−0.235648
$913$	−70.7782	−2.34242
$914$	24.8788	0.822919
$915$	−15.3539	−0.507583
$916$	21.7380	0.718244
$917$	−0.0408420	−0.00134872
$918$	−18.6750	−0.616367
$919$	17.0845	0.563567	0.281783	−	0.959478i	$-0.409074\pi$
$919$	17.0845	0.563567	0.281783	+	0.959478i	$0.409074\pi$
$920$	−1.19141	−0.0392796
$921$	81.0223	2.66977
$922$	−17.8233	−0.586978
$923$	−38.6454	−1.27203
$924$	−0.994478	−0.0327159
$925$	−23.0054	−0.756413
$926$	−22.1977	−0.729460
$927$	−72.5958	−2.38436
$928$	−1.15446	−0.0378970
$929$	−12.9380	−0.424481	−0.212240	−	0.977217i	$-0.568076\pi$
$929$	−12.9380	−0.424481	−0.212240	+	0.977217i	$0.568076\pi$
$930$	−1.45211	−0.0476165
$931$	−15.6158	−0.511787
$932$	3.81272	0.124890
$933$	−33.3474	−1.09175
$934$	24.2826	0.794550
$935$	−2.66520	−0.0871613
$936$	−21.1211	−0.690365
$937$	31.5824	1.03175	0.515876	−	0.856664i	$-0.327467\pi$
$937$	31.5824	1.03175	0.515876	+	0.856664i	$0.327467\pi$
$938$	−0.135953	−0.00443902
$939$	−54.1975	−1.76867
$940$	−0.412748	−0.0134624
$941$	−12.6455	−0.412230	−0.206115	−	0.978528i	$-0.566082\pi$
$941$	−12.6455	−0.412230	−0.206115	+	0.978528i	$0.566082\pi$
$942$	−13.5396	−0.441145
$943$	17.5722	0.572230
$944$	−13.6214	−0.443338
$945$	0.269444	0.00876502
$946$	1.54456	0.0502181
$947$	35.1989	1.14381	0.571905	−	0.820320i	$-0.306205\pi$
$947$	35.1989	1.14381	0.571905	+	0.820320i	$0.306205\pi$
$948$	40.9161	1.32889
$949$	−15.1067	−0.490385
$950$	−10.8843	−0.353133
$951$	−93.2045	−3.02236
$952$	−0.0811932	−0.00263149
$953$	−34.3557	−1.11289	−0.556444	−	0.830885i	$-0.687835\pi$
$953$	−34.3557	−1.11289	−0.556444	+	0.830885i	$0.687835\pi$
$954$	42.8456	1.38718
$955$	4.85522	0.157111
$956$	1.27478	0.0412292
$957$	−19.8766	−0.642520
$958$	30.5985	0.988593
$959$	−0.223116	−0.00720479
$960$	−1.11958	−0.0361342
$961$	−29.3178	−0.945734
$962$	−13.9029	−0.448247
$963$	−7.69111	−0.247842
$964$	−4.69522	−0.151223
$965$	−2.12576	−0.0684307
$966$	−0.624907	−0.0201060
$967$	34.4154	1.10672	0.553362	−	0.832941i	$-0.313345\pi$
$967$	34.4154	1.10672	0.553362	+	0.832941i	$0.313345\pi$
$968$	18.1576	0.583606
$969$	−10.0034	−0.321357
$970$	−2.46607	−0.0791807
$971$	−33.3164	−1.06917	−0.534587	−	0.845114i	$-0.679533\pi$
$971$	−33.3164	−1.06917	−0.534587	+	0.845114i	$0.679533\pi$
$972$	−26.6582	−0.855064
$973$	−0.391580	−0.0125535
$974$	13.6485	0.437326
$975$	−45.8266	−1.46763
$976$	13.7140	0.438974
$977$	0.876320	0.0280360	0.0140180	−	0.999902i	$-0.495538\pi$
$977$	0.876320	0.0280360	0.0140180	+	0.999902i	$0.495538\pi$
$978$	37.8814	1.21132
$979$	11.4823	0.366976
$980$	−2.45673	−0.0784772
$981$	2.01392	0.0642995
$982$	−24.4442	−0.780047
$983$	−53.2709	−1.69908	−0.849539	−	0.527526i	$-0.823120\pi$
$983$	−53.2709	−1.69908	−0.849539	+	0.527526i	$0.823120\pi$
$984$	16.5127	0.526406
$985$	7.88865	0.251353
$986$	−1.62281	−0.0516807
$987$	−0.216490	−0.00689097
$988$	−6.57772	−0.209265
$989$	0.970568	0.0308623
$990$	−13.5880	−0.431855
$991$	−35.6003	−1.13088	−0.565441	−	0.824789i	$-0.691294\pi$
$991$	−35.6003	−1.13088	−0.565441	+	0.824789i	$0.691294\pi$
$992$	1.29701	0.0411803
$993$	86.0725	2.73143
$994$	−0.757403	−0.0240234
$995$	2.12512	0.0673707
$996$	−41.7938	−1.32429
$997$	4.23464	0.134112	0.0670562	−	0.997749i	$-0.478639\pi$
$997$	4.23464	0.134112	0.0670562	+	0.997749i	$0.478639\pi$
$998$	11.2997	0.357685
$999$	−62.6722	−1.98286

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.g.1.2	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.g.1.2	✓	95	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.18851 q^{3} +1.00000 q^{4} +0.351128 q^{5} -3.18851 q^{6} -0.0577605 q^{7} +1.00000 q^{8} +7.16662 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.18851 q^{3} +1.00000 q^{4} +0.351128 q^{5} -3.18851 q^{6} -0.0577605 q^{7} +1.00000 q^{8} +7.16662 q^{9} +0.351128 q^{10} -5.39977 q^{11} -3.18851 q^{12} -2.94715 q^{13} -0.0577605 q^{14} -1.11958 q^{15} +1.00000 q^{16} +1.40569 q^{17} +7.16662 q^{18} +2.23189 q^{19} +0.351128 q^{20} +0.184170 q^{21} -5.39977 q^{22} -3.39309 q^{23} -3.18851 q^{24} -4.87671 q^{25} -2.94715 q^{26} -13.2853 q^{27} -0.0577605 q^{28} -1.15446 q^{29} -1.11958 q^{30} +1.29701 q^{31} +1.00000 q^{32} +17.2173 q^{33} +1.40569 q^{34} -0.0202813 q^{35} +7.16662 q^{36} +4.71740 q^{37} +2.23189 q^{38} +9.39703 q^{39} +0.351128 q^{40} -5.17881 q^{41} +0.184170 q^{42} -0.286042 q^{43} -5.39977 q^{44} +2.51640 q^{45} -3.39309 q^{46} -1.17549 q^{47} -3.18851 q^{48} -6.99666 q^{49} -4.87671 q^{50} -4.48205 q^{51} -2.94715 q^{52} +5.97850 q^{53} -13.2853 q^{54} -1.89601 q^{55} -0.0577605 q^{56} -7.11642 q^{57} -1.15446 q^{58} -13.6214 q^{59} -1.11958 q^{60} +13.7140 q^{61} +1.29701 q^{62} -0.413948 q^{63} +1.00000 q^{64} -1.03483 q^{65} +17.2173 q^{66} +2.35374 q^{67} +1.40569 q^{68} +10.8189 q^{69} -0.0202813 q^{70} +13.1128 q^{71} +7.16662 q^{72} +5.12587 q^{73} +4.71740 q^{74} +15.5495 q^{75} +2.23189 q^{76} +0.311894 q^{77} +9.39703 q^{78} -12.8323 q^{79} +0.351128 q^{80} +20.8606 q^{81} -5.17881 q^{82} +13.1076 q^{83} +0.184170 q^{84} +0.493576 q^{85} -0.286042 q^{86} +3.68101 q^{87} -5.39977 q^{88} -2.12644 q^{89} +2.51640 q^{90} +0.170229 q^{91} -3.39309 q^{92} -4.13555 q^{93} -1.17549 q^{94} +0.783680 q^{95} -3.18851 q^{96} -7.02327 q^{97} -6.99666 q^{98} -38.6981 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9 + 36 * q^10 + 40 * q^11 + 24 * q^12 + 52 * q^13 + 21 * q^14 + 15 * q^15 + 95 * q^16 + 84 * q^17 + 121 * q^18 + 37 * q^19 + 36 * q^20 + 36 * q^21 + 40 * q^22 + 37 * q^23 + 24 * q^24 + 133 * q^25 + 52 * q^26 + 93 * q^27 + 21 * q^28 + 66 * q^29 + 15 * q^30 + 10 * q^31 + 95 * q^32 + 63 * q^33 + 84 * q^34 + 55 * q^35 + 121 * q^36 + 49 * q^37 + 37 * q^38 + 14 * q^39 + 36 * q^40 + 98 * q^41 + 36 * q^42 + 37 * q^43 + 40 * q^44 + 97 * q^45 + 37 * q^46 + 91 * q^47 + 24 * q^48 + 170 * q^49 + 133 * q^50 + 22 * q^51 + 52 * q^52 + 70 * q^53 + 93 * q^54 - q^55 + 21 * q^56 + 50 * q^57 + 66 * q^58 + 72 * q^59 + 15 * q^60 + 97 * q^61 + 10 * q^62 + 75 * q^63 + 95 * q^64 + 75 * q^65 + 63 * q^66 + 39 * q^67 + 84 * q^68 + 65 * q^69 + 55 * q^70 + 28 * q^71 + 121 * q^72 + 117 * q^73 + 49 * q^74 + 62 * q^75 + 37 * q^76 + 92 * q^77 + 14 * q^78 + q^79 + 36 * q^80 + 155 * q^81 + 98 * q^82 + 117 * q^83 + 36 * q^84 + 81 * q^85 + 37 * q^86 + 46 * q^87 + 40 * q^88 + 90 * q^89 + 97 * q^90 + 65 * q^91 + 37 * q^92 + 36 * q^93 + 91 * q^94 + 38 * q^95 + 24 * q^96 + 111 * q^97 + 170 * q^98 + 97 * q^99

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