LMFDB - Embedded newform 8006.2.a.c.1.7

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:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.10076 q^{3} +1.00000 q^{4} -2.40718 q^{5} +3.10076 q^{6} -4.08337 q^{7} -1.00000 q^{8} +6.61471 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.10076 q^{3} +1.00000 q^{4} -2.40718 q^{5} +3.10076 q^{6} -4.08337 q^{7} -1.00000 q^{8} +6.61471 q^{9} +2.40718 q^{10} +4.11222 q^{11} -3.10076 q^{12} -4.82737 q^{13} +4.08337 q^{14} +7.46408 q^{15} +1.00000 q^{16} -0.682284 q^{17} -6.61471 q^{18} -1.43659 q^{19} -2.40718 q^{20} +12.6615 q^{21} -4.11222 q^{22} +4.67947 q^{23} +3.10076 q^{24} +0.794507 q^{25} +4.82737 q^{26} -11.2083 q^{27} -4.08337 q^{28} +6.13357 q^{29} -7.46408 q^{30} +7.90996 q^{31} -1.00000 q^{32} -12.7510 q^{33} +0.682284 q^{34} +9.82939 q^{35} +6.61471 q^{36} -6.33970 q^{37} +1.43659 q^{38} +14.9685 q^{39} +2.40718 q^{40} -1.98784 q^{41} -12.6615 q^{42} +3.25327 q^{43} +4.11222 q^{44} -15.9228 q^{45} -4.67947 q^{46} -2.95920 q^{47} -3.10076 q^{48} +9.67389 q^{49} -0.794507 q^{50} +2.11560 q^{51} -4.82737 q^{52} +8.18323 q^{53} +11.2083 q^{54} -9.89886 q^{55} +4.08337 q^{56} +4.45451 q^{57} -6.13357 q^{58} +4.45630 q^{59} +7.46408 q^{60} -9.76853 q^{61} -7.90996 q^{62} -27.0103 q^{63} +1.00000 q^{64} +11.6203 q^{65} +12.7510 q^{66} +1.12779 q^{67} -0.682284 q^{68} -14.5099 q^{69} -9.82939 q^{70} -2.14819 q^{71} -6.61471 q^{72} +8.32283 q^{73} +6.33970 q^{74} -2.46358 q^{75} -1.43659 q^{76} -16.7917 q^{77} -14.9685 q^{78} -12.0685 q^{79} -2.40718 q^{80} +14.9102 q^{81} +1.98784 q^{82} +5.61556 q^{83} +12.6615 q^{84} +1.64238 q^{85} -3.25327 q^{86} -19.0187 q^{87} -4.11222 q^{88} -11.3071 q^{89} +15.9228 q^{90} +19.7119 q^{91} +4.67947 q^{92} -24.5269 q^{93} +2.95920 q^{94} +3.45812 q^{95} +3.10076 q^{96} -6.56206 q^{97} -9.67389 q^{98} +27.2012 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) $ 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9} - 10 q^{10} + 4 q^{11} - 2 q^{12} + 40 q^{13} - 8 q^{14} + 15 q^{15} + 92 q^{16} - 14 q^{17} - 104 q^{18} + 64 q^{19} + 10 q^{20} + 54 q^{21} - 4 q^{22} - 49 q^{23} + 2 q^{24} + 116 q^{25} - 40 q^{26} - 8 q^{27} + 8 q^{28} + 39 q^{29} - 15 q^{30} + 53 q^{31} - 92 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} + 104 q^{36} + 58 q^{37} - 64 q^{38} + 58 q^{39} - 10 q^{40} + 27 q^{41} - 54 q^{42} + 40 q^{43} + 4 q^{44} + 43 q^{45} + 49 q^{46} - 28 q^{47} - 2 q^{48} + 148 q^{49} - 116 q^{50} + 48 q^{51} + 40 q^{52} + 32 q^{53} + 8 q^{54} + 36 q^{55} - 8 q^{56} + 48 q^{57} - 39 q^{58} + 8 q^{59} + 15 q^{60} + 99 q^{61} - 53 q^{62} + 92 q^{64} + 13 q^{65} - q^{66} + 48 q^{67} - 14 q^{68} + 63 q^{69} + 22 q^{70} - 13 q^{71} - 104 q^{72} + 49 q^{73} - 58 q^{74} + 16 q^{75} + 64 q^{76} + 41 q^{77} - 58 q^{78} + 143 q^{79} + 10 q^{80} + 124 q^{81} - 27 q^{82} - 24 q^{83} + 54 q^{84} + 121 q^{85} - 40 q^{86} + 5 q^{87} - 4 q^{88} + 25 q^{89} - 43 q^{90} + 67 q^{91} - 49 q^{92} + 43 q^{93} + 28 q^{94} - 38 q^{95} + 2 q^{96} + 74 q^{97} - 148 q^{98} + 86 q^{99}+O(q^{100}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9 - 10 * q^10 + 4 * q^11 - 2 * q^12 + 40 * q^13 - 8 * q^14 + 15 * q^15 + 92 * q^16 - 14 * q^17 - 104 * q^18 + 64 * q^19 + 10 * q^20 + 54 * q^21 - 4 * q^22 - 49 * q^23 + 2 * q^24 + 116 * q^25 - 40 * q^26 - 8 * q^27 + 8 * q^28 + 39 * q^29 - 15 * q^30 + 53 * q^31 - 92 * q^32 + q^33 + 14 * q^34 - 22 * q^35 + 104 * q^36 + 58 * q^37 - 64 * q^38 + 58 * q^39 - 10 * q^40 + 27 * q^41 - 54 * q^42 + 40 * q^43 + 4 * q^44 + 43 * q^45 + 49 * q^46 - 28 * q^47 - 2 * q^48 + 148 * q^49 - 116 * q^50 + 48 * q^51 + 40 * q^52 + 32 * q^53 + 8 * q^54 + 36 * q^55 - 8 * q^56 + 48 * q^57 - 39 * q^58 + 8 * q^59 + 15 * q^60 + 99 * q^61 - 53 * q^62 + 92 * q^64 + 13 * q^65 - q^66 + 48 * q^67 - 14 * q^68 + 63 * q^69 + 22 * q^70 - 13 * q^71 - 104 * q^72 + 49 * q^73 - 58 * q^74 + 16 * q^75 + 64 * q^76 + 41 * q^77 - 58 * q^78 + 143 * q^79 + 10 * q^80 + 124 * q^81 - 27 * q^82 - 24 * q^83 + 54 * q^84 + 121 * q^85 - 40 * q^86 + 5 * q^87 - 4 * q^88 + 25 * q^89 - 43 * q^90 + 67 * q^91 - 49 * q^92 + 43 * q^93 + 28 * q^94 - 38 * q^95 + 2 * q^96 + 74 * q^97 - 148 * q^98 + 86 * 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
$3$	−3.10076	−1.79022	−0.895112	−	0.445841i	$-0.852905\pi$
$3$	−3.10076	−1.79022	−0.895112	+	0.445841i	$0.852905\pi$
$4$	1.00000	0.500000
$5$	−2.40718	−1.07652	−0.538261	−	0.842778i	$-0.680919\pi$
$5$	−2.40718	−1.07652	−0.538261	+	0.842778i	$0.680919\pi$
$6$	3.10076	1.26588
$7$	−4.08337	−1.54337	−0.771684	−	0.636006i	$-0.780585\pi$
$7$	−4.08337	−1.54337	−0.771684	+	0.636006i	$0.780585\pi$
$8$	−1.00000	−0.353553
$9$	6.61471	2.20490
$10$	2.40718	0.761217
$11$	4.11222	1.23988	0.619941	−	0.784648i	$-0.287156\pi$
$11$	4.11222	1.23988	0.619941	+	0.784648i	$0.287156\pi$
$12$	−3.10076	−0.895112
$13$	−4.82737	−1.33887	−0.669436	−	0.742870i	$-0.733464\pi$
$13$	−4.82737	−1.33887	−0.669436	+	0.742870i	$0.733464\pi$
$14$	4.08337	1.09133
$15$	7.46408	1.92722
$16$	1.00000	0.250000
$17$	−0.682284	−0.165478	−0.0827391	−	0.996571i	$-0.526367\pi$
$17$	−0.682284	−0.165478	−0.0827391	+	0.996571i	$0.526367\pi$
$18$	−6.61471	−1.55910
$19$	−1.43659	−0.329576	−0.164788	−	0.986329i	$-0.552694\pi$
$19$	−1.43659	−0.329576	−0.164788	+	0.986329i	$0.552694\pi$
$20$	−2.40718	−0.538261
$21$	12.6615	2.76297
$22$	−4.11222	−0.876729
$23$	4.67947	0.975738	0.487869	−	0.872917i	$-0.337774\pi$
$23$	4.67947	0.975738	0.487869	+	0.872917i	$0.337774\pi$
$24$	3.10076	0.632940
$25$	0.794507	0.158901
$26$	4.82737	0.946725
$27$	−11.2083	−2.15704
$28$	−4.08337	−0.771684
$29$	6.13357	1.13898	0.569488	−	0.822000i	$-0.307142\pi$
$29$	6.13357	1.13898	0.569488	+	0.822000i	$0.307142\pi$
$30$	−7.46408	−1.36275
$31$	7.90996	1.42067	0.710336	−	0.703863i	$-0.248543\pi$
$31$	7.90996	1.42067	0.710336	+	0.703863i	$0.248543\pi$
$32$	−1.00000	−0.176777
$33$	−12.7510	−2.21967
$34$	0.682284	0.117011
$35$	9.82939	1.66147
$36$	6.61471	1.10245
$37$	−6.33970	−1.04224	−0.521120	−	0.853483i	$-0.674486\pi$
$37$	−6.33970	−1.04224	−0.521120	+	0.853483i	$0.674486\pi$
$38$	1.43659	0.233045
$39$	14.9685	2.39688
$40$	2.40718	0.380608
$41$	−1.98784	−0.310449	−0.155224	−	0.987879i	$-0.549610\pi$
$41$	−1.98784	−0.310449	−0.155224	+	0.987879i	$0.549610\pi$
$42$	−12.6615	−1.95372
$43$	3.25327	0.496119	0.248060	−	0.968745i	$-0.420207\pi$
$43$	3.25327	0.496119	0.248060	+	0.968745i	$0.420207\pi$
$44$	4.11222	0.619941
$45$	−15.9228	−2.37363
$46$	−4.67947	−0.689951
$47$	−2.95920	−0.431644	−0.215822	−	0.976433i	$-0.569243\pi$
$47$	−2.95920	−0.431644	−0.215822	+	0.976433i	$0.569243\pi$
$48$	−3.10076	−0.447556
$49$	9.67389	1.38198
$50$	−0.794507	−0.112360
$51$	2.11560	0.296243
$52$	−4.82737	−0.669436
$53$	8.18323	1.12405	0.562026	−	0.827119i	$-0.310022\pi$
$53$	8.18323	1.12405	0.562026	+	0.827119i	$0.310022\pi$
$54$	11.2083	1.52526
$55$	−9.89886	−1.33476
$56$	4.08337	0.545663
$57$	4.45451	0.590014
$58$	−6.13357	−0.805377
$59$	4.45630	0.580161	0.290080	−	0.957002i	$-0.406318\pi$
$59$	4.45630	0.580161	0.290080	+	0.957002i	$0.406318\pi$
$60$	7.46408	0.963608
$61$	−9.76853	−1.25073	−0.625366	−	0.780331i	$-0.715050\pi$
$61$	−9.76853	−1.25073	−0.625366	+	0.780331i	$0.715050\pi$
$62$	−7.90996	−1.00457
$63$	−27.0103	−3.40297
$64$	1.00000	0.125000
$65$	11.6203	1.44133
$66$	12.7510	1.56954
$67$	1.12779	0.137781	0.0688907	−	0.997624i	$-0.478054\pi$
$67$	1.12779	0.137781	0.0688907	+	0.997624i	$0.478054\pi$
$68$	−0.682284	−0.0827391
$69$	−14.5099	−1.74679
$70$	−9.82939	−1.17484
$71$	−2.14819	−0.254943	−0.127472	−	0.991842i	$-0.540686\pi$
$71$	−2.14819	−0.254943	−0.127472	+	0.991842i	$0.540686\pi$
$72$	−6.61471	−0.779551
$73$	8.32283	0.974113	0.487057	−	0.873370i	$-0.338071\pi$
$73$	8.32283	0.974113	0.487057	+	0.873370i	$0.338071\pi$
$74$	6.33970	0.736975
$75$	−2.46358	−0.284469
$76$	−1.43659	−0.164788
$77$	−16.7917	−1.91359
$78$	−14.9685	−1.69485
$79$	−12.0685	−1.35781	−0.678904	−	0.734227i	$-0.737545\pi$
$79$	−12.0685	−1.35781	−0.678904	+	0.734227i	$0.737545\pi$
$80$	−2.40718	−0.269131
$81$	14.9102	1.65669
$82$	1.98784	0.219520
$83$	5.61556	0.616388	0.308194	−	0.951324i	$-0.400275\pi$
$83$	5.61556	0.616388	0.308194	+	0.951324i	$0.400275\pi$
$84$	12.6615	1.38149
$85$	1.64238	0.178141
$86$	−3.25327	−0.350809
$87$	−19.0187	−2.03902
$88$	−4.11222	−0.438365
$89$	−11.3071	−1.19855	−0.599273	−	0.800545i	$-0.704544\pi$
$89$	−11.3071	−1.19855	−0.599273	+	0.800545i	$0.704544\pi$
$90$	15.9228	1.67841
$91$	19.7119	2.06637
$92$	4.67947	0.487869
$93$	−24.5269	−2.54332
$94$	2.95920	0.305218
$95$	3.45812	0.354796
$96$	3.10076	0.316470
$97$	−6.56206	−0.666276	−0.333138	−	0.942878i	$-0.608107\pi$
$97$	−6.56206	−0.666276	−0.333138	+	0.942878i	$0.608107\pi$
$98$	−9.67389	−0.977211
$99$	27.2012	2.73382
$100$	0.794507	0.0794507
$101$	16.1160	1.60360	0.801800	−	0.597592i	$-0.203876\pi$
$101$	16.1160	1.60360	0.801800	+	0.597592i	$0.203876\pi$
$102$	−2.11560	−0.209476
$103$	−2.90639	−0.286375	−0.143187	−	0.989696i	$-0.545735\pi$
$103$	−2.90639	−0.286375	−0.143187	+	0.989696i	$0.545735\pi$
$104$	4.82737	0.473363
$105$	−30.4786	−2.97440
$106$	−8.18323	−0.794825
$107$	7.54815	0.729707	0.364854	−	0.931065i	$-0.381119\pi$
$107$	7.54815	0.729707	0.364854	+	0.931065i	$0.381119\pi$
$108$	−11.2083	−1.07852
$109$	0.227099	0.0217522	0.0108761	−	0.999941i	$-0.496538\pi$
$109$	0.227099	0.0217522	0.0108761	+	0.999941i	$0.496538\pi$
$110$	9.89886	0.943819
$111$	19.6579	1.86584
$112$	−4.08337	−0.385842
$113$	−4.18703	−0.393883	−0.196941	−	0.980415i	$-0.563101\pi$
$113$	−4.18703	−0.393883	−0.196941	+	0.980415i	$0.563101\pi$
$114$	−4.45451	−0.417203
$115$	−11.2643	−1.05040
$116$	6.13357	0.569488
$117$	−31.9316	−2.95208
$118$	−4.45630	−0.410236
$119$	2.78602	0.255394
$120$	−7.46408	−0.681374
$121$	5.91039	0.537308
$122$	9.76853	0.884402
$123$	6.16382	0.555773
$124$	7.90996	0.710336
$125$	10.1234	0.905462
$126$	27.0103	2.40627
$127$	−2.74272	−0.243377	−0.121689	−	0.992568i	$-0.538831\pi$
$127$	−2.74272	−0.243377	−0.121689	+	0.992568i	$0.538831\pi$
$128$	−1.00000	−0.0883883
$129$	−10.0876	−0.888164
$130$	−11.6203	−1.01917
$131$	−21.0730	−1.84116	−0.920578	−	0.390559i	$-0.872282\pi$
$131$	−21.0730	−1.84116	−0.920578	+	0.390559i	$0.872282\pi$
$132$	−12.7510	−1.10983
$133$	5.86611	0.508656
$134$	−1.12779	−0.0974262
$135$	26.9804	2.32211
$136$	0.682284	0.0585054
$137$	1.02721	0.0877605	0.0438802	−	0.999037i	$-0.486028\pi$
$137$	1.02721	0.0877605	0.0438802	+	0.999037i	$0.486028\pi$
$138$	14.5099	1.23517
$139$	−19.1258	−1.62223	−0.811116	−	0.584885i	$-0.801139\pi$
$139$	−19.1258	−1.62223	−0.811116	+	0.584885i	$0.801139\pi$
$140$	9.82939	0.830735
$141$	9.17577	0.772739
$142$	2.14819	0.180272
$143$	−19.8512	−1.66004
$144$	6.61471	0.551225
$145$	−14.7646	−1.22613
$146$	−8.32283	−0.688802
$147$	−29.9964	−2.47406
$148$	−6.33970	−0.521120
$149$	−1.33508	−0.109374	−0.0546871	−	0.998504i	$-0.517416\pi$
$149$	−1.33508	−0.109374	−0.0546871	+	0.998504i	$0.517416\pi$
$150$	2.46358	0.201150
$151$	−5.78166	−0.470505	−0.235253	−	0.971934i	$-0.575592\pi$
$151$	−5.78166	−0.470505	−0.235253	+	0.971934i	$0.575592\pi$
$152$	1.43659	0.116523
$153$	−4.51311	−0.364863
$154$	16.7917	1.35312
$155$	−19.0407	−1.52939
$156$	14.9685	1.19844
$157$	−5.05538	−0.403463	−0.201732	−	0.979441i	$-0.564657\pi$
$157$	−5.05538	−0.403463	−0.201732	+	0.979441i	$0.564657\pi$
$158$	12.0685	0.960115
$159$	−25.3742	−2.01231
$160$	2.40718	0.190304
$161$	−19.1080	−1.50592
$162$	−14.9102	−1.17146
$163$	−16.0770	−1.25925	−0.629623	−	0.776901i	$-0.716791\pi$
$163$	−16.0770	−1.25925	−0.629623	+	0.776901i	$0.716791\pi$
$164$	−1.98784	−0.155224
$165$	30.6940	2.38952
$166$	−5.61556	−0.435852
$167$	−15.6666	−1.21231	−0.606157	−	0.795345i	$-0.707290\pi$
$167$	−15.6666	−1.21231	−0.606157	+	0.795345i	$0.707290\pi$
$168$	−12.6615	−0.976859
$169$	10.3035	0.792577
$170$	−1.64238	−0.125965
$171$	−9.50260	−0.726682
$172$	3.25327	0.248060
$173$	13.9136	1.05783	0.528915	−	0.848675i	$-0.322599\pi$
$173$	13.9136	1.05783	0.528915	+	0.848675i	$0.322599\pi$
$174$	19.0187	1.44181
$175$	−3.24427	−0.245243
$176$	4.11222	0.309971
$177$	−13.8179	−1.03862
$178$	11.3071	0.847500
$179$	−10.3193	−0.771300	−0.385650	−	0.922645i	$-0.626023\pi$
$179$	−10.3193	−0.771300	−0.385650	+	0.922645i	$0.626023\pi$
$180$	−15.9228	−1.18681
$181$	7.66022	0.569379	0.284690	−	0.958620i	$-0.408109\pi$
$181$	7.66022	0.569379	0.284690	+	0.958620i	$0.408109\pi$
$182$	−19.7119	−1.46115
$183$	30.2899	2.23909
$184$	−4.67947	−0.344975
$185$	15.2608	1.12200
$186$	24.5269	1.79840
$187$	−2.80571	−0.205174
$188$	−2.95920	−0.215822
$189$	45.7677	3.32911
$190$	−3.45812	−0.250878
$191$	−13.9253	−1.00760	−0.503798	−	0.863822i	$-0.668064\pi$
$191$	−13.9253	−1.00760	−0.503798	+	0.863822i	$0.668064\pi$
$192$	−3.10076	−0.223778
$193$	6.22997	0.448443	0.224221	−	0.974538i	$-0.428016\pi$
$193$	6.22997	0.448443	0.224221	+	0.974538i	$0.428016\pi$
$194$	6.56206	0.471128
$195$	−36.0319	−2.58030
$196$	9.67389	0.690992
$197$	16.3145	1.16236	0.581179	−	0.813776i	$-0.302592\pi$
$197$	16.3145	1.16236	0.581179	+	0.813776i	$0.302592\pi$
$198$	−27.2012	−1.93310
$199$	−15.1578	−1.07451	−0.537256	−	0.843419i	$-0.680539\pi$
$199$	−15.1578	−1.07451	−0.537256	+	0.843419i	$0.680539\pi$
$200$	−0.794507	−0.0561801
$201$	−3.49700	−0.246660
$202$	−16.1160	−1.13392
$203$	−25.0456	−1.75786
$204$	2.11560	0.148122
$205$	4.78509	0.334205
$206$	2.90639	0.202498
$207$	30.9533	2.15141
$208$	−4.82737	−0.334718
$209$	−5.90757	−0.408635
$210$	30.4786	2.10322
$211$	−1.38732	−0.0955070	−0.0477535	−	0.998859i	$-0.515206\pi$
$211$	−1.38732	−0.0955070	−0.0477535	+	0.998859i	$0.515206\pi$
$212$	8.18323	0.562026
$213$	6.66102	0.456405
$214$	−7.54815	−0.515981
$215$	−7.83120	−0.534084
$216$	11.2083	0.762630
$217$	−32.2993	−2.19262
$218$	−0.227099	−0.0153811
$219$	−25.8071	−1.74388
$220$	−9.89886	−0.667381
$221$	3.29364	0.221554
$222$	−19.6579	−1.31935
$223$	−22.1087	−1.48051	−0.740254	−	0.672328i	$-0.765295\pi$
$223$	−22.1087	−1.48051	−0.740254	+	0.672328i	$0.765295\pi$
$224$	4.08337	0.272831
$225$	5.25543	0.350362
$226$	4.18703	0.278517
$227$	−16.6497	−1.10508	−0.552539	−	0.833487i	$-0.686341\pi$
$227$	−16.6497	−1.10508	−0.552539	+	0.833487i	$0.686341\pi$
$228$	4.45451	0.295007
$229$	26.8635	1.77519	0.887597	−	0.460622i	$-0.152373\pi$
$229$	26.8635	1.77519	0.887597	+	0.460622i	$0.152373\pi$
$230$	11.2643	0.742748
$231$	52.0671	3.42576
$232$	−6.13357	−0.402689
$233$	−2.45681	−0.160951	−0.0804754	−	0.996757i	$-0.525644\pi$
$233$	−2.45681	−0.160951	−0.0804754	+	0.996757i	$0.525644\pi$
$234$	31.9316	2.08744
$235$	7.12333	0.464675
$236$	4.45630	0.290080
$237$	37.4214	2.43078
$238$	−2.78602	−0.180591
$239$	5.30684	0.343271	0.171636	−	0.985161i	$-0.445095\pi$
$239$	5.30684	0.343271	0.171636	+	0.985161i	$0.445095\pi$
$240$	7.46408	0.481804
$241$	26.1496	1.68445	0.842223	−	0.539129i	$-0.181246\pi$
$241$	26.1496	1.68445	0.842223	+	0.539129i	$0.181246\pi$
$242$	−5.91039	−0.379934
$243$	−12.6080	−0.808802
$244$	−9.76853	−0.625366
$245$	−23.2868	−1.48774
$246$	−6.16382	−0.392991
$247$	6.93494	0.441259
$248$	−7.90996	−0.502283
$249$	−17.4125	−1.10347
$250$	−10.1234	−0.640258
$251$	−0.376037	−0.0237352	−0.0118676	−	0.999930i	$-0.503778\pi$
$251$	−0.376037	−0.0237352	−0.0118676	+	0.999930i	$0.503778\pi$
$252$	−27.0103	−1.70149
$253$	19.2430	1.20980
$254$	2.74272	0.172094
$255$	−5.09263	−0.318913
$256$	1.00000	0.0625000
$257$	−6.84293	−0.426850	−0.213425	−	0.976959i	$-0.568462\pi$
$257$	−6.84293	−0.426850	−0.213425	+	0.976959i	$0.568462\pi$
$258$	10.0876	0.628027
$259$	25.8873	1.60856
$260$	11.6203	0.720663
$261$	40.5718	2.51133
$262$	21.0730	1.30189
$263$	−8.65987	−0.533990	−0.266995	−	0.963698i	$-0.586031\pi$
$263$	−8.65987	−0.533990	−0.266995	+	0.963698i	$0.586031\pi$
$264$	12.7510	0.784771
$265$	−19.6985	−1.21007
$266$	−5.86611	−0.359674
$267$	35.0605	2.14567
$268$	1.12779	0.0688907
$269$	−14.0352	−0.855744	−0.427872	−	0.903839i	$-0.640737\pi$
$269$	−14.0352	−0.855744	−0.427872	+	0.903839i	$0.640737\pi$
$270$	−26.9804	−1.64198
$271$	4.36444	0.265121	0.132560	−	0.991175i	$-0.457680\pi$
$271$	4.36444	0.265121	0.132560	+	0.991175i	$0.457680\pi$
$272$	−0.682284	−0.0413696
$273$	−61.1219	−3.69927
$274$	−1.02721	−0.0620560
$275$	3.26719	0.197019
$276$	−14.5099	−0.873395
$277$	3.09385	0.185892	0.0929458	−	0.995671i	$-0.470372\pi$
$277$	3.09385	0.185892	0.0929458	+	0.995671i	$0.470372\pi$
$278$	19.1258	1.14709
$279$	52.3221	3.13244
$280$	−9.82939	−0.587419
$281$	−19.0960	−1.13917	−0.569585	−	0.821932i	$-0.692896\pi$
$281$	−19.0960	−1.13917	−0.569585	+	0.821932i	$0.692896\pi$
$282$	−9.17577	−0.546409
$283$	−14.5000	−0.861935	−0.430967	−	0.902367i	$-0.641828\pi$
$283$	−14.5000	−0.861935	−0.430967	+	0.902367i	$0.641828\pi$
$284$	−2.14819	−0.127472
$285$	−10.7228	−0.635164
$286$	19.8512	1.17383
$287$	8.11709	0.479136
$288$	−6.61471	−0.389775
$289$	−16.5345	−0.972617
$290$	14.7646	0.867007
$291$	20.3474	1.19278
$292$	8.32283	0.487057
$293$	12.4670	0.728328	0.364164	−	0.931335i	$-0.381355\pi$
$293$	12.4670	0.728328	0.364164	+	0.931335i	$0.381355\pi$
$294$	29.9964	1.74943
$295$	−10.7271	−0.624556
$296$	6.33970	0.368488
$297$	−46.0912	−2.67448
$298$	1.33508	0.0773393
$299$	−22.5896	−1.30639
$300$	−2.46358	−0.142235
$301$	−13.2843	−0.765694
$302$	5.78166	0.332697
$303$	−49.9718	−2.87080
$304$	−1.43659	−0.0823939
$305$	23.5146	1.34644
$306$	4.51311	0.257997
$307$	−10.4794	−0.598089	−0.299045	−	0.954239i	$-0.596668\pi$
$307$	−10.4794	−0.598089	−0.299045	+	0.954239i	$0.596668\pi$
$308$	−16.7917	−0.956797
$309$	9.01200	0.512675
$310$	19.0407	1.08144
$311$	9.78242	0.554710	0.277355	−	0.960767i	$-0.410542\pi$
$311$	9.78242	0.554710	0.277355	+	0.960767i	$0.410542\pi$
$312$	−14.9685	−0.847425
$313$	−20.4726	−1.15718	−0.578589	−	0.815619i	$-0.696396\pi$
$313$	−20.4726	−1.15718	−0.578589	+	0.815619i	$0.696396\pi$
$314$	5.05538	0.285291
$315$	65.0185	3.66338
$316$	−12.0685	−0.678904
$317$	21.1177	1.18609	0.593043	−	0.805171i	$-0.297926\pi$
$317$	21.1177	1.18609	0.593043	+	0.805171i	$0.297926\pi$
$318$	25.3742	1.42292
$319$	25.2226	1.41220
$320$	−2.40718	−0.134565
$321$	−23.4050	−1.30634
$322$	19.1080	1.06485
$323$	0.980161	0.0545376
$324$	14.9102	0.828345
$325$	−3.83538	−0.212749
$326$	16.0770	0.890421
$327$	−0.704180	−0.0389412
$328$	1.98784	0.109760
$329$	12.0835	0.666186
$330$	−30.6940	−1.68965
$331$	12.7883	0.702906	0.351453	−	0.936206i	$-0.385688\pi$
$331$	12.7883	0.702906	0.351453	+	0.936206i	$0.385688\pi$
$332$	5.61556	0.308194
$333$	−41.9353	−2.29804
$334$	15.6666	0.857236
$335$	−2.71479	−0.148325
$336$	12.6615	0.690744
$337$	23.4297	1.27630	0.638150	−	0.769912i	$-0.279700\pi$
$337$	23.4297	1.27630	0.638150	+	0.769912i	$0.279700\pi$
$338$	−10.3035	−0.560437
$339$	12.9830	0.705139
$340$	1.64238	0.0890706
$341$	32.5275	1.76147
$342$	9.50260	0.513842
$343$	−10.9185	−0.589543
$344$	−3.25327	−0.175405
$345$	34.9280	1.88046
$346$	−13.9136	−0.747999
$347$	10.5274	0.565140	0.282570	−	0.959247i	$-0.408813\pi$
$347$	10.5274	0.565140	0.282570	+	0.959247i	$0.408813\pi$
$348$	−19.0187	−1.01951
$349$	4.33812	0.232214	0.116107	−	0.993237i	$-0.462958\pi$
$349$	4.33812	0.232214	0.116107	+	0.993237i	$0.462958\pi$
$350$	3.24427	0.173413
$351$	54.1068	2.88801
$352$	−4.11222	−0.219182
$353$	−18.6017	−0.990068	−0.495034	−	0.868874i	$-0.664844\pi$
$353$	−18.6017	−0.990068	−0.495034	+	0.868874i	$0.664844\pi$
$354$	13.8179	0.734414
$355$	5.17108	0.274452
$356$	−11.3071	−0.599273
$357$	−8.63877	−0.457212
$358$	10.3193	0.545391
$359$	20.4746	1.08061	0.540304	−	0.841470i	$-0.318309\pi$
$359$	20.4746	1.08061	0.540304	+	0.841470i	$0.318309\pi$
$360$	15.9228	0.839204
$361$	−16.9362	−0.891380
$362$	−7.66022	−0.402612
$363$	−18.3267	−0.961902
$364$	19.7119	1.03319
$365$	−20.0345	−1.04866
$366$	−30.2899	−1.58328
$367$	−2.68022	−0.139907	−0.0699533	−	0.997550i	$-0.522285\pi$
$367$	−2.68022	−0.139907	−0.0699533	+	0.997550i	$0.522285\pi$
$368$	4.67947	0.243934
$369$	−13.1490	−0.684509
$370$	−15.2608	−0.793371
$371$	−33.4151	−1.73483
$372$	−24.5269	−1.27166
$373$	15.9257	0.824603	0.412301	−	0.911048i	$-0.364725\pi$
$373$	15.9257	0.824603	0.412301	+	0.911048i	$0.364725\pi$
$374$	2.80571	0.145080
$375$	−31.3901	−1.62098
$376$	2.95920	0.152609
$377$	−29.6090	−1.52494
$378$	−45.7677	−2.35404
$379$	−5.93370	−0.304794	−0.152397	−	0.988319i	$-0.548699\pi$
$379$	−5.93370	−0.304794	−0.152397	+	0.988319i	$0.548699\pi$
$380$	3.45812	0.177398
$381$	8.50451	0.435699
$382$	13.9253	0.712478
$383$	24.4882	1.25129	0.625645	−	0.780108i	$-0.284836\pi$
$383$	24.4882	1.25129	0.625645	+	0.780108i	$0.284836\pi$
$384$	3.10076	0.158235
$385$	40.4207	2.06003
$386$	−6.22997	−0.317097
$387$	21.5194	1.09389
$388$	−6.56206	−0.333138
$389$	34.0842	1.72814	0.864068	−	0.503376i	$-0.167909\pi$
$389$	34.0842	1.72814	0.864068	+	0.503376i	$0.167909\pi$
$390$	36.0319	1.82454
$391$	−3.19273	−0.161463
$392$	−9.67389	−0.488605
$393$	65.3423	3.29608
$394$	−16.3145	−0.821912
$395$	29.0509	1.46171
$396$	27.2012	1.36691
$397$	−30.1668	−1.51403	−0.757015	−	0.653398i	$-0.773343\pi$
$397$	−30.1668	−1.51403	−0.757015	+	0.653398i	$0.773343\pi$
$398$	15.1578	0.759794
$399$	−18.1894	−0.910609
$400$	0.794507	0.0397254
$401$	−19.3878	−0.968179	−0.484090	−	0.875018i	$-0.660849\pi$
$401$	−19.3878	−0.968179	−0.484090	+	0.875018i	$0.660849\pi$
$402$	3.49700	0.174415
$403$	−38.1843	−1.90210
$404$	16.1160	0.801800
$405$	−35.8915	−1.78346
$406$	25.0456	1.24299
$407$	−26.0703	−1.29226
$408$	−2.11560	−0.104738
$409$	0.892288	0.0441208	0.0220604	−	0.999757i	$-0.492977\pi$
$409$	0.892288	0.0441208	0.0220604	+	0.999757i	$0.492977\pi$
$410$	−4.78509	−0.236319
$411$	−3.18513	−0.157111
$412$	−2.90639	−0.143187
$413$	−18.1967	−0.895402
$414$	−30.9533	−1.52127
$415$	−13.5177	−0.663556
$416$	4.82737	0.236681
$417$	59.3046	2.90416
$418$	5.90757	0.288949
$419$	−8.86226	−0.432950	−0.216475	−	0.976288i	$-0.569456\pi$
$419$	−8.86226	−0.432950	−0.216475	+	0.976288i	$0.569456\pi$
$420$	−30.4786	−1.48720
$421$	25.2235	1.22932	0.614658	−	0.788794i	$-0.289294\pi$
$421$	25.2235	1.22932	0.614658	+	0.788794i	$0.289294\pi$
$422$	1.38732	0.0675337
$423$	−19.5743	−0.951733
$424$	−8.18323	−0.397413
$425$	−0.542080	−0.0262947
$426$	−6.66102	−0.322727
$427$	39.8885	1.93034
$428$	7.54815	0.364854
$429$	61.5539	2.97185
$430$	7.83120	0.377654
$431$	0.753558	0.0362976	0.0181488	−	0.999835i	$-0.494223\pi$
$431$	0.753558	0.0362976	0.0181488	+	0.999835i	$0.494223\pi$
$432$	−11.2083	−0.539261
$433$	23.2515	1.11739	0.558697	−	0.829372i	$-0.311301\pi$
$433$	23.2515	1.11739	0.558697	+	0.829372i	$0.311301\pi$
$434$	32.2993	1.55042
$435$	45.7815	2.19505
$436$	0.227099	0.0108761
$437$	−6.72247	−0.321579
$438$	25.8071	1.23311
$439$	39.4573	1.88319	0.941597	−	0.336741i	$-0.109325\pi$
$439$	39.4573	1.88319	0.941597	+	0.336741i	$0.109325\pi$
$440$	9.89886	0.471910
$441$	63.9899	3.04714
$442$	−3.29364	−0.156662
$443$	−17.2831	−0.821144	−0.410572	−	0.911828i	$-0.634671\pi$
$443$	−17.2831	−0.821144	−0.410572	+	0.911828i	$0.634671\pi$
$444$	19.6579	0.932922
$445$	27.2181	1.29026
$446$	22.1087	1.04688
$447$	4.13977	0.195804
$448$	−4.08337	−0.192921
$449$	34.1339	1.61088	0.805438	−	0.592680i	$-0.201930\pi$
$449$	34.1339	1.61088	0.805438	+	0.592680i	$0.201930\pi$
$450$	−5.25543	−0.247743
$451$	−8.17445	−0.384920
$452$	−4.18703	−0.196941
$453$	17.9275	0.842309
$454$	16.6497	0.781408
$455$	−47.4501	−2.22450
$456$	−4.45451	−0.208601
$457$	−27.0437	−1.26505	−0.632525	−	0.774540i	$-0.717981\pi$
$457$	−27.0437	−1.26505	−0.632525	+	0.774540i	$0.717981\pi$
$458$	−26.8635	−1.25525
$459$	7.64727	0.356944
$460$	−11.2643	−0.525202
$461$	−5.60542	−0.261070	−0.130535	−	0.991444i	$-0.541670\pi$
$461$	−5.60542	−0.261070	−0.130535	+	0.991444i	$0.541670\pi$
$462$	−52.0671	−2.42238
$463$	6.05289	0.281302	0.140651	−	0.990059i	$-0.455081\pi$
$463$	6.05289	0.281302	0.140651	+	0.990059i	$0.455081\pi$
$464$	6.13357	0.284744
$465$	59.0406	2.73794
$466$	2.45681	0.113809
$467$	−38.3843	−1.77621	−0.888106	−	0.459639i	$-0.847979\pi$
$467$	−38.3843	−1.77621	−0.888106	+	0.459639i	$0.847979\pi$
$468$	−31.9316	−1.47604
$469$	−4.60518	−0.212647
$470$	−7.12333	−0.328575
$471$	15.6755	0.722289
$472$	−4.45630	−0.205118
$473$	13.3782	0.615129
$474$	−37.4214	−1.71882
$475$	−1.14138	−0.0523700
$476$	2.78602	0.127697
$477$	54.1296	2.47843
$478$	−5.30684	−0.242729
$479$	−18.5554	−0.847820	−0.423910	−	0.905704i	$-0.639343\pi$
$479$	−18.5554	−0.847820	−0.423910	+	0.905704i	$0.639343\pi$
$480$	−7.46408	−0.340687
$481$	30.6041	1.39543
$482$	−26.1496	−1.19108
$483$	59.2493	2.69594
$484$	5.91039	0.268654
$485$	15.7960	0.717261
$486$	12.6080	0.571910
$487$	3.21170	0.145536	0.0727679	−	0.997349i	$-0.476817\pi$
$487$	3.21170	0.145536	0.0727679	+	0.997349i	$0.476817\pi$
$488$	9.76853	0.442201
$489$	49.8508	2.25433
$490$	23.2868	1.05199
$491$	−31.8690	−1.43823	−0.719114	−	0.694892i	$-0.755452\pi$
$491$	−31.8690	−1.43823	−0.719114	+	0.694892i	$0.755452\pi$
$492$	6.16382	0.277886
$493$	−4.18484	−0.188476
$494$	−6.93494	−0.312017
$495$	−65.4780	−2.94302
$496$	7.90996	0.355168
$497$	8.77185	0.393471
$498$	17.4125	0.780273
$499$	−16.5250	−0.739762	−0.369881	−	0.929079i	$-0.620601\pi$
$499$	−16.5250	−0.739762	−0.369881	+	0.929079i	$0.620601\pi$
$500$	10.1234	0.452731
$501$	48.5782	2.17032
$502$	0.376037	0.0167834
$503$	26.6229	1.18706	0.593529	−	0.804813i	$-0.297734\pi$
$503$	26.6229	1.18706	0.593529	+	0.804813i	$0.297734\pi$
$504$	27.0103	1.20313
$505$	−38.7941	−1.72631
$506$	−19.2430	−0.855458
$507$	−31.9487	−1.41889
$508$	−2.74272	−0.121689
$509$	−4.12559	−0.182864	−0.0914319	−	0.995811i	$-0.529144\pi$
$509$	−4.12559	−0.182864	−0.0914319	+	0.995811i	$0.529144\pi$
$510$	5.09263	0.225505
$511$	−33.9852	−1.50342
$512$	−1.00000	−0.0441942
$513$	16.1017	0.710909
$514$	6.84293	0.301829
$515$	6.99619	0.308289
$516$	−10.0876	−0.444082
$517$	−12.1689	−0.535188
$518$	−25.8873	−1.13742
$519$	−43.1427	−1.89375
$520$	−11.6203	−0.509586
$521$	−14.8413	−0.650209	−0.325104	−	0.945678i	$-0.605399\pi$
$521$	−14.8413	−0.650209	−0.325104	+	0.945678i	$0.605399\pi$
$522$	−40.5718	−1.77578
$523$	16.1060	0.704267	0.352133	−	0.935950i	$-0.385456\pi$
$523$	16.1060	0.704267	0.352133	+	0.935950i	$0.385456\pi$
$524$	−21.0730	−0.920578
$525$	10.0597	0.439041
$526$	8.65987	0.377588
$527$	−5.39684	−0.235090
$528$	−12.7510	−0.554917
$529$	−1.10252	−0.0479357
$530$	19.6985	0.855648
$531$	29.4771	1.27920
$532$	5.86611	0.254328
$533$	9.59605	0.415651
$534$	−35.0605	−1.51722
$535$	−18.1697	−0.785547
$536$	−1.12779	−0.0487131
$537$	31.9976	1.38080
$538$	14.0352	0.605103
$539$	39.7812	1.71350
$540$	26.9804	1.16105
$541$	−3.33569	−0.143413	−0.0717063	−	0.997426i	$-0.522844\pi$
$541$	−3.33569	−0.143413	−0.0717063	+	0.997426i	$0.522844\pi$
$542$	−4.36444	−0.187469
$543$	−23.7525	−1.01932
$544$	0.682284	0.0292527
$545$	−0.546668	−0.0234167
$546$	61.1219	2.61578
$547$	26.5255	1.13415	0.567075	−	0.823666i	$-0.308075\pi$
$547$	26.5255	1.13415	0.567075	+	0.823666i	$0.308075\pi$
$548$	1.02721	0.0438802
$549$	−64.6160	−2.75774
$550$	−3.26719	−0.139314
$551$	−8.81141	−0.375379
$552$	14.5099	0.617583
$553$	49.2800	2.09560
$554$	−3.09385	−0.131445
$555$	−47.3200	−2.00862
$556$	−19.1258	−0.811116
$557$	−28.2541	−1.19717	−0.598583	−	0.801061i	$-0.704269\pi$
$557$	−28.2541	−1.19717	−0.598583	+	0.801061i	$0.704269\pi$
$558$	−52.3221	−2.21497
$559$	−15.7047	−0.664240
$560$	9.82939	0.415368
$561$	8.69982	0.367307
$562$	19.0960	0.805515
$563$	−8.53693	−0.359789	−0.179894	−	0.983686i	$-0.557576\pi$
$563$	−8.53693	−0.359789	−0.179894	+	0.983686i	$0.557576\pi$
$564$	9.17577	0.386370
$565$	10.0789	0.424024
$566$	14.5000	0.609480
$567$	−60.8839	−2.55688
$568$	2.14819	0.0901360
$569$	−41.8407	−1.75405	−0.877026	−	0.480442i	$-0.840476\pi$
$569$	−41.8407	−1.75405	−0.877026	+	0.480442i	$0.840476\pi$
$570$	10.7228	0.449129
$571$	26.5513	1.11114	0.555568	−	0.831471i	$-0.312501\pi$
$571$	26.5513	1.11114	0.555568	+	0.831471i	$0.312501\pi$
$572$	−19.8512	−0.830022
$573$	43.1789	1.80382
$574$	−8.11709	−0.338801
$575$	3.71788	0.155046
$576$	6.61471	0.275613
$577$	6.53072	0.271877	0.135939	−	0.990717i	$-0.456595\pi$
$577$	6.53072	0.271877	0.135939	+	0.990717i	$0.456595\pi$
$578$	16.5345	0.687744
$579$	−19.3176	−0.802813
$580$	−14.7646	−0.613067
$581$	−22.9304	−0.951313
$582$	−20.3474	−0.843425
$583$	33.6513	1.39369
$584$	−8.32283	−0.344401
$585$	76.8651	3.17798
$586$	−12.4670	−0.515005
$587$	19.3553	0.798877	0.399439	−	0.916760i	$-0.369205\pi$
$587$	19.3553	0.798877	0.399439	+	0.916760i	$0.369205\pi$
$588$	−29.9964	−1.23703
$589$	−11.3633	−0.468219
$590$	10.7271	0.441628
$591$	−50.5873	−2.08088
$592$	−6.33970	−0.260560
$593$	15.3407	0.629967	0.314984	−	0.949097i	$-0.398001\pi$
$593$	15.3407	0.629967	0.314984	+	0.949097i	$0.398001\pi$
$594$	46.0912	1.89114
$595$	−6.70644	−0.274937
$596$	−1.33508	−0.0546871
$597$	47.0008	1.92362
$598$	22.5896	0.923756
$599$	−0.329560	−0.0134655	−0.00673273	−	0.999977i	$-0.502143\pi$
$599$	−0.329560	−0.0134655	−0.00673273	+	0.999977i	$0.502143\pi$
$600$	2.46358	0.100575
$601$	34.5499	1.40932	0.704660	−	0.709546i	$-0.251100\pi$
$601$	34.5499	1.40932	0.704660	+	0.709546i	$0.251100\pi$
$602$	13.2843	0.541428
$603$	7.46000	0.303795
$604$	−5.78166	−0.235253
$605$	−14.2274	−0.578425
$606$	49.9718	2.02997
$607$	28.1220	1.14144	0.570719	−	0.821145i	$-0.306664\pi$
$607$	28.1220	1.14144	0.570719	+	0.821145i	$0.306664\pi$
$608$	1.43659	0.0582613
$609$	77.6605	3.14696
$610$	−23.5146	−0.952078
$611$	14.2852	0.577916
$612$	−4.51311	−0.182432
$613$	41.5948	1.68000	0.839999	−	0.542588i	$-0.182555\pi$
$613$	41.5948	1.68000	0.839999	+	0.542588i	$0.182555\pi$
$614$	10.4794	0.422913
$615$	−14.8374	−0.598302
$616$	16.7917	0.676558
$617$	−17.1905	−0.692063	−0.346032	−	0.938223i	$-0.612471\pi$
$617$	−17.1905	−0.692063	−0.346032	+	0.938223i	$0.612471\pi$
$618$	−9.01200	−0.362516
$619$	21.5061	0.864402	0.432201	−	0.901777i	$-0.357737\pi$
$619$	21.5061	0.864402	0.432201	+	0.901777i	$0.357737\pi$
$620$	−19.0407	−0.764693
$621$	−52.4491	−2.10471
$622$	−9.78242	−0.392239
$623$	46.1709	1.84980
$624$	14.9685	0.599220
$625$	−28.3413	−1.13365
$626$	20.4726	0.818248
$627$	18.3179	0.731548
$628$	−5.05538	−0.201732
$629$	4.32548	0.172468
$630$	−65.0185	−2.59040
$631$	−24.8911	−0.990898	−0.495449	−	0.868637i	$-0.664997\pi$
$631$	−24.8911	−0.990898	−0.495449	+	0.868637i	$0.664997\pi$
$632$	12.0685	0.480058
$633$	4.30174	0.170979
$634$	−21.1177	−0.838690
$635$	6.60222	0.262001
$636$	−25.3742	−1.00615
$637$	−46.6995	−1.85030
$638$	−25.2226	−0.998573
$639$	−14.2096	−0.562125
$640$	2.40718	0.0951521
$641$	14.4553	0.570950	0.285475	−	0.958386i	$-0.407849\pi$
$641$	14.4553	0.570950	0.285475	+	0.958386i	$0.407849\pi$
$642$	23.4050	0.923722
$643$	42.6357	1.68139	0.840694	−	0.541510i	$-0.182147\pi$
$643$	42.6357	1.68139	0.840694	+	0.541510i	$0.182147\pi$
$644$	−19.1080	−0.752961
$645$	24.2827	0.956129
$646$	−0.980161	−0.0385639
$647$	−32.9797	−1.29657	−0.648283	−	0.761400i	$-0.724512\pi$
$647$	−32.9797	−1.29657	−0.648283	+	0.761400i	$0.724512\pi$
$648$	−14.9102	−0.585728
$649$	18.3253	0.719331
$650$	3.83538	0.150436
$651$	100.152	3.92528
$652$	−16.0770	−0.629623
$653$	47.6769	1.86574	0.932871	−	0.360211i	$-0.117295\pi$
$653$	47.6769	1.86574	0.932871	+	0.360211i	$0.117295\pi$
$654$	0.704180	0.0275356
$655$	50.7264	1.98205
$656$	−1.98784	−0.0776122
$657$	55.0530	2.14782
$658$	−12.0835	−0.471064
$659$	−33.1525	−1.29144	−0.645718	−	0.763576i	$-0.723442\pi$
$659$	−33.1525	−1.29144	−0.645718	+	0.763576i	$0.723442\pi$
$660$	30.6940	1.19476
$661$	−0.628606	−0.0244500	−0.0122250	−	0.999925i	$-0.503891\pi$
$661$	−0.628606	−0.0244500	−0.0122250	+	0.999925i	$0.503891\pi$
$662$	−12.7883	−0.497030
$663$	−10.2128	−0.396632
$664$	−5.61556	−0.217926
$665$	−14.1208	−0.547580
$666$	41.9353	1.62496
$667$	28.7019	1.11134
$668$	−15.6666	−0.606157
$669$	68.5537	2.65044
$670$	2.71479	0.104882
$671$	−40.1704	−1.55076
$672$	−12.6615	−0.488429
$673$	−22.5352	−0.868670	−0.434335	−	0.900752i	$-0.643017\pi$
$673$	−22.5352	−0.868670	−0.434335	+	0.900752i	$0.643017\pi$
$674$	−23.4297	−0.902480
$675$	−8.90510	−0.342757
$676$	10.3035	0.396289
$677$	25.7902	0.991197	0.495598	−	0.868552i	$-0.334949\pi$
$677$	25.7902	0.991197	0.495598	+	0.868552i	$0.334949\pi$
$678$	−12.9830	−0.498608
$679$	26.7953	1.02831
$680$	−1.64238	−0.0629824
$681$	51.6266	1.97834
$682$	−32.5275	−1.24554
$683$	45.2026	1.72963	0.864815	−	0.502091i	$-0.167436\pi$
$683$	45.2026	1.72963	0.864815	+	0.502091i	$0.167436\pi$
$684$	−9.50260	−0.363341
$685$	−2.47268	−0.0944761
$686$	10.9185	0.416870
$687$	−83.2974	−3.17799
$688$	3.25327	0.124030
$689$	−39.5035	−1.50496
$690$	−34.9280	−1.32968
$691$	17.4119	0.662380	0.331190	−	0.943564i	$-0.392550\pi$
$691$	17.4119	0.662380	0.331190	+	0.943564i	$0.392550\pi$
$692$	13.9136	0.528915
$693$	−111.072	−4.21929
$694$	−10.5274	−0.399615
$695$	46.0393	1.74637
$696$	19.0187	0.720903
$697$	1.35627	0.0513725
$698$	−4.33812	−0.164200
$699$	7.61796	0.288138
$700$	−3.24427	−0.122622
$701$	45.2652	1.70964	0.854822	−	0.518921i	$-0.173666\pi$
$701$	45.2652	1.70964	0.854822	+	0.518921i	$0.173666\pi$
$702$	−54.1068	−2.04213
$703$	9.10753	0.343497
$704$	4.11222	0.154985
$705$	−22.0877	−0.831872
$706$	18.6017	0.700084
$707$	−65.8075	−2.47495
$708$	−13.8179	−0.519309
$709$	−32.9984	−1.23928	−0.619641	−	0.784885i	$-0.712722\pi$
$709$	−32.9984	−1.23928	−0.619641	+	0.784885i	$0.712722\pi$
$710$	−5.17108	−0.194067
$711$	−79.8293	−2.99383
$712$	11.3071	0.423750
$713$	37.0145	1.38620
$714$	8.63877	0.323298
$715$	47.7855	1.78707
$716$	−10.3193	−0.385650
$717$	−16.4552	−0.614532
$718$	−20.4746	−0.764106
$719$	22.2361	0.829266	0.414633	−	0.909989i	$-0.363910\pi$
$719$	22.2361	0.829266	0.414633	+	0.909989i	$0.363910\pi$
$720$	−15.9228	−0.593407
$721$	11.8678	0.441982
$722$	16.9362	0.630301
$723$	−81.0838	−3.01554
$724$	7.66022	0.284690
$725$	4.87317	0.180985
$726$	18.3267	0.680167
$727$	10.5495	0.391258	0.195629	−	0.980678i	$-0.437325\pi$
$727$	10.5495	0.391258	0.195629	+	0.980678i	$0.437325\pi$
$728$	−19.7119	−0.730573
$729$	−5.63633	−0.208753
$730$	20.0345	0.741511
$731$	−2.21966	−0.0820969
$732$	30.2899	1.11955
$733$	−16.7518	−0.618743	−0.309371	−	0.950941i	$-0.600119\pi$
$733$	−16.7518	−0.618743	−0.309371	+	0.950941i	$0.600119\pi$
$734$	2.68022	0.0989289
$735$	72.2067	2.66338
$736$	−4.67947	−0.172488
$737$	4.63772	0.170833
$738$	13.1490	0.484021
$739$	27.6387	1.01671	0.508353	−	0.861149i	$-0.330254\pi$
$739$	27.6387	1.01671	0.508353	+	0.861149i	$0.330254\pi$
$740$	15.2608	0.560998
$741$	−21.5036	−0.789953
$742$	33.4151	1.22671
$743$	−32.9675	−1.20946	−0.604730	−	0.796430i	$-0.706719\pi$
$743$	−32.9675	−1.20946	−0.604730	+	0.796430i	$0.706719\pi$
$744$	24.5269	0.899199
$745$	3.21378	0.117744
$746$	−15.9257	−0.583082
$747$	37.1453	1.35907
$748$	−2.80571	−0.102587
$749$	−30.8219	−1.12621
$750$	31.3901	1.14621
$751$	10.1222	0.369366	0.184683	−	0.982798i	$-0.440874\pi$
$751$	10.1222	0.369366	0.184683	+	0.982798i	$0.440874\pi$
$752$	−2.95920	−0.107911
$753$	1.16600	0.0424914
$754$	29.6090	1.07830
$755$	13.9175	0.506509
$756$	45.7677	1.66456
$757$	−20.2129	−0.734650	−0.367325	−	0.930093i	$-0.619726\pi$
$757$	−20.2129	−0.734650	−0.367325	+	0.930093i	$0.619726\pi$
$758$	5.93370	0.215522
$759$	−59.6681	−2.16581
$760$	−3.45812	−0.125439
$761$	−1.97876	−0.0717299	−0.0358650	−	0.999357i	$-0.511419\pi$
$761$	−1.97876	−0.0717299	−0.0358650	+	0.999357i	$0.511419\pi$
$762$	−8.50451	−0.308086
$763$	−0.927329	−0.0335716
$764$	−13.9253	−0.503798
$765$	10.8639	0.392784
$766$	−24.4882	−0.884796
$767$	−21.5122	−0.776761
$768$	−3.10076	−0.111889
$769$	9.58038	0.345477	0.172739	−	0.984968i	$-0.444738\pi$
$769$	9.58038	0.345477	0.172739	+	0.984968i	$0.444738\pi$
$770$	−40.4207	−1.45666
$771$	21.2183	0.764157
$772$	6.22997	0.224221
$773$	−46.6014	−1.67614	−0.838068	−	0.545566i	$-0.816315\pi$
$773$	−46.6014	−1.67614	−0.838068	+	0.545566i	$0.816315\pi$
$774$	−21.5194	−0.773500
$775$	6.28452	0.225747
$776$	6.56206	0.235564
$777$	−80.2704	−2.87968
$778$	−34.0842	−1.22198
$779$	2.85571	0.102316
$780$	−36.0319	−1.29015
$781$	−8.83384	−0.316100
$782$	3.19273	0.114172
$783$	−68.7471	−2.45682
$784$	9.67389	0.345496
$785$	12.1692	0.434337
$786$	−65.3423	−2.33068
$787$	−23.5333	−0.838870	−0.419435	−	0.907785i	$-0.637772\pi$
$787$	−23.5333	−0.838870	−0.419435	+	0.907785i	$0.637772\pi$
$788$	16.3145	0.581179
$789$	26.8522	0.955963
$790$	−29.0509	−1.03359
$791$	17.0972	0.607906
$792$	−27.2012	−0.966551
$793$	47.1563	1.67457
$794$	30.1668	1.07058
$795$	61.0803	2.16629
$796$	−15.1578	−0.537256
$797$	46.2293	1.63753	0.818763	−	0.574132i	$-0.194660\pi$
$797$	46.2293	1.63753	0.818763	+	0.574132i	$0.194660\pi$
$798$	18.1894	0.643898
$799$	2.01902	0.0714277
$800$	−0.794507	−0.0280901
$801$	−74.7929	−2.64268
$802$	19.3878	0.684606
$803$	34.2253	1.20779
$804$	−3.49700	−0.123330
$805$	45.9964	1.62116
$806$	38.1843	1.34499
$807$	43.5199	1.53197
$808$	−16.1160	−0.566958
$809$	−48.9598	−1.72133	−0.860667	−	0.509168i	$-0.829953\pi$
$809$	−48.9598	−1.72133	−0.860667	+	0.509168i	$0.829953\pi$
$810$	35.8915	1.26110
$811$	−40.1723	−1.41064	−0.705321	−	0.708888i	$-0.749197\pi$
$811$	−40.1723	−1.41064	−0.705321	+	0.708888i	$0.749197\pi$
$812$	−25.0456	−0.878929
$813$	−13.5331	−0.474625
$814$	26.0703	0.913763
$815$	38.7001	1.35561
$816$	2.11560	0.0740608
$817$	−4.67360	−0.163509
$818$	−0.892288	−0.0311981
$819$	130.389	4.55615
$820$	4.78509	0.167103
$821$	−13.9728	−0.487653	−0.243826	−	0.969819i	$-0.578403\pi$
$821$	−13.9728	−0.487653	−0.243826	+	0.969819i	$0.578403\pi$
$822$	3.18513	0.111094
$823$	−39.6987	−1.38381	−0.691905	−	0.721989i	$-0.743228\pi$
$823$	−39.6987	−1.38381	−0.691905	+	0.721989i	$0.743228\pi$
$824$	2.90639	0.101249
$825$	−10.1308	−0.352708
$826$	18.1967	0.633144
$827$	−26.1779	−0.910294	−0.455147	−	0.890416i	$-0.650413\pi$
$827$	−26.1779	−0.910294	−0.455147	+	0.890416i	$0.650413\pi$
$828$	30.9533	1.07570
$829$	36.1125	1.25424	0.627120	−	0.778923i	$-0.284234\pi$
$829$	36.1125	1.25424	0.627120	+	0.778923i	$0.284234\pi$
$830$	13.5177	0.469205
$831$	−9.59329	−0.332788
$832$	−4.82737	−0.167359
$833$	−6.60035	−0.228688
$834$	−59.3046	−2.05355
$835$	37.7122	1.30508
$836$	−5.90757	−0.204317
$837$	−88.6575	−3.06445
$838$	8.86226	0.306142
$839$	−24.9978	−0.863020	−0.431510	−	0.902108i	$-0.642019\pi$
$839$	−24.9978	−0.863020	−0.431510	+	0.902108i	$0.642019\pi$
$840$	30.4786	1.05161
$841$	8.62071	0.297266
$842$	−25.2235	−0.869258
$843$	59.2120	2.03937
$844$	−1.38732	−0.0477535
$845$	−24.8024	−0.853227
$846$	19.5743	0.672977
$847$	−24.1343	−0.829264
$848$	8.18323	0.281013
$849$	44.9610	1.54306
$850$	0.542080	0.0185932
$851$	−29.6665	−1.01695
$852$	6.66102	0.228203
$853$	−12.6863	−0.434372	−0.217186	−	0.976130i	$-0.569688\pi$
$853$	−12.6863	−0.434372	−0.217186	+	0.976130i	$0.569688\pi$
$854$	−39.8885	−1.36496
$855$	22.8744	0.782290
$856$	−7.54815	−0.257991
$857$	33.6969	1.15106	0.575532	−	0.817779i	$-0.304795\pi$
$857$	33.6969	1.15106	0.575532	+	0.817779i	$0.304795\pi$
$858$	−61.5539	−2.10141
$859$	−49.0927	−1.67502	−0.837510	−	0.546422i	$-0.815990\pi$
$859$	−49.0927	−1.67502	−0.837510	+	0.546422i	$0.815990\pi$
$860$	−7.83120	−0.267042
$861$	−25.1691	−0.857762
$862$	−0.753558	−0.0256663
$863$	16.0831	0.547476	0.273738	−	0.961804i	$-0.411740\pi$
$863$	16.0831	0.547476	0.273738	+	0.961804i	$0.411740\pi$
$864$	11.2083	0.381315
$865$	−33.4925	−1.13878
$866$	−23.2515	−0.790117
$867$	51.2695	1.74120
$868$	−32.2993	−1.09631
$869$	−49.6282	−1.68352
$870$	−45.7815	−1.55214
$871$	−5.44426	−0.184472
$872$	−0.227099	−0.00769055
$873$	−43.4061	−1.46907
$874$	6.72247	0.227391
$875$	−41.3374	−1.39746
$876$	−25.8071	−0.871940
$877$	−22.8921	−0.773010	−0.386505	−	0.922287i	$-0.626318\pi$
$877$	−22.8921	−0.773010	−0.386505	+	0.922287i	$0.626318\pi$
$878$	−39.4573	−1.33162
$879$	−38.6570	−1.30387
$880$	−9.89886	−0.333690
$881$	−54.2800	−1.82874	−0.914370	−	0.404879i	$-0.867314\pi$
$881$	−54.2800	−1.82874	−0.914370	+	0.404879i	$0.867314\pi$
$882$	−63.9899	−2.15465
$883$	36.8371	1.23967	0.619834	−	0.784733i	$-0.287200\pi$
$883$	36.8371	1.23967	0.619834	+	0.784733i	$0.287200\pi$
$884$	3.29364	0.110777
$885$	33.2622	1.11810
$886$	17.2831	0.580637
$887$	−39.8511	−1.33807	−0.669034	−	0.743232i	$-0.733292\pi$
$887$	−39.8511	−1.33807	−0.669034	+	0.743232i	$0.733292\pi$
$888$	−19.6579	−0.659676
$889$	11.1995	0.375620
$890$	−27.2181	−0.912354
$891$	61.3141	2.05410
$892$	−22.1087	−0.740254
$893$	4.25115	0.142259
$894$	−4.13977	−0.138455
$895$	24.8404	0.830322
$896$	4.08337	0.136416
$897$	70.0448	2.33873
$898$	−34.1339	−1.13906
$899$	48.5163	1.61811
$900$	5.25543	0.175181
$901$	−5.58329	−0.186006
$902$	8.17445	0.272179
$903$	41.1914	1.37076
$904$	4.18703	0.139259
$905$	−18.4395	−0.612950
$906$	−17.9275	−0.595603
$907$	−29.3335	−0.974002	−0.487001	−	0.873401i	$-0.661909\pi$
$907$	−29.3335	−0.974002	−0.487001	+	0.873401i	$0.661909\pi$
$908$	−16.6497	−0.552539
$909$	106.603	3.53578
$910$	47.4501	1.57296
$911$	26.3776	0.873928	0.436964	−	0.899479i	$-0.356054\pi$
$911$	26.3776	0.873928	0.436964	+	0.899479i	$0.356054\pi$
$912$	4.45451	0.147504
$913$	23.0924	0.764248
$914$	27.0437	0.894525
$915$	−72.9131	−2.41043
$916$	26.8635	0.887597
$917$	86.0488	2.84158
$918$	−7.64727	−0.252398
$919$	43.7022	1.44160	0.720801	−	0.693142i	$-0.243774\pi$
$919$	43.7022	1.44160	0.720801	+	0.693142i	$0.243774\pi$
$920$	11.2643	0.371374
$921$	32.4940	1.07071
$922$	5.60542	0.184605
$923$	10.3701	0.341336
$924$	52.0671	1.71288
$925$	−5.03694	−0.165614
$926$	−6.05289	−0.198910
$927$	−19.2249	−0.631428
$928$	−6.13357	−0.201344
$929$	−21.3545	−0.700618	−0.350309	−	0.936634i	$-0.613923\pi$
$929$	−21.3545	−0.700618	−0.350309	+	0.936634i	$0.613923\pi$
$930$	−59.0406	−1.93602
$931$	−13.8974	−0.455468
$932$	−2.45681	−0.0804754
$933$	−30.3329	−0.993055
$934$	38.3843	1.25597
$935$	6.75384	0.220874
$936$	31.9316	1.04372
$937$	−35.8715	−1.17187	−0.585935	−	0.810358i	$-0.699273\pi$
$937$	−35.8715	−1.17187	−0.585935	+	0.810358i	$0.699273\pi$
$938$	4.60518	0.150364
$939$	63.4805	2.07161
$940$	7.12333	0.232337
$941$	25.7527	0.839513	0.419756	−	0.907637i	$-0.362116\pi$
$941$	25.7527	0.839513	0.419756	+	0.907637i	$0.362116\pi$
$942$	−15.6755	−0.510736
$943$	−9.30205	−0.302916
$944$	4.45630	0.145040
$945$	−110.171	−3.58387
$946$	−13.3782	−0.434962
$947$	22.0684	0.717128	0.358564	−	0.933505i	$-0.383266\pi$
$947$	22.0684	0.717128	0.358564	+	0.933505i	$0.383266\pi$
$948$	37.4214	1.21539
$949$	−40.1774	−1.30421
$950$	1.14138	0.0370312
$951$	−65.4808	−2.12336
$952$	−2.78602	−0.0902954
$953$	51.3480	1.66333	0.831663	−	0.555281i	$-0.187389\pi$
$953$	51.3480	1.66333	0.831663	+	0.555281i	$0.187389\pi$
$954$	−54.1296	−1.75251
$955$	33.5206	1.08470
$956$	5.30684	0.171636
$957$	−78.2093	−2.52815
$958$	18.5554	0.599499
$959$	−4.19448	−0.135447
$960$	7.46408	0.240902
$961$	31.5675	1.01831
$962$	−30.6041	−0.986715
$963$	49.9288	1.60893
$964$	26.1496	0.842223
$965$	−14.9966	−0.482759
$966$	−59.2493	−1.90632
$967$	53.5471	1.72196	0.860979	−	0.508640i	$-0.169852\pi$
$967$	53.5471	1.72196	0.860979	+	0.508640i	$0.169852\pi$
$968$	−5.91039	−0.189967
$969$	−3.03924	−0.0976345
$970$	−15.7960	−0.507180
$971$	14.2153	0.456190	0.228095	−	0.973639i	$-0.426750\pi$
$971$	14.2153	0.456190	0.228095	+	0.973639i	$0.426750\pi$
$972$	−12.6080	−0.404401
$973$	78.0978	2.50370
$974$	−3.21170	−0.102909
$975$	11.8926	0.380868
$976$	−9.76853	−0.312683
$977$	39.0551	1.24948	0.624742	−	0.780831i	$-0.285204\pi$
$977$	39.0551	1.24948	0.624742	+	0.780831i	$0.285204\pi$
$978$	−49.8508	−1.59405
$979$	−46.4972	−1.48606
$980$	−23.2868	−0.743869
$981$	1.50219	0.0479614
$982$	31.8690	1.01698
$983$	−13.1744	−0.420199	−0.210100	−	0.977680i	$-0.567379\pi$
$983$	−13.1744	−0.420199	−0.210100	+	0.977680i	$0.567379\pi$
$984$	−6.16382	−0.196495
$985$	−39.2719	−1.25131
$986$	4.18484	0.133272
$987$	−37.4681	−1.19262
$988$	6.93494	0.220630
$989$	15.2236	0.484082
$990$	65.4780	2.08103
$991$	13.6809	0.434588	0.217294	−	0.976106i	$-0.430277\pi$
$991$	13.6809	0.434588	0.217294	+	0.976106i	$0.430277\pi$
$992$	−7.90996	−0.251142
$993$	−39.6533	−1.25836
$994$	−8.77185	−0.278226
$995$	36.4876	1.15674
$996$	−17.4125	−0.551736
$997$	26.7332	0.846650	0.423325	−	0.905978i	$-0.360863\pi$
$997$	26.7332	0.846650	0.423325	+	0.905978i	$0.360863\pi$
$998$	16.5250	0.523090
$999$	71.0575	2.24816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.c.1.7	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.c.1.7	✓	92	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.10076 q^{3} +1.00000 q^{4} -2.40718 q^{5} +3.10076 q^{6} -4.08337 q^{7} -1.00000 q^{8} +6.61471 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.10076 q^{3} +1.00000 q^{4} -2.40718 q^{5} +3.10076 q^{6} -4.08337 q^{7} -1.00000 q^{8} +6.61471 q^{9} +2.40718 q^{10} +4.11222 q^{11} -3.10076 q^{12} -4.82737 q^{13} +4.08337 q^{14} +7.46408 q^{15} +1.00000 q^{16} -0.682284 q^{17} -6.61471 q^{18} -1.43659 q^{19} -2.40718 q^{20} +12.6615 q^{21} -4.11222 q^{22} +4.67947 q^{23} +3.10076 q^{24} +0.794507 q^{25} +4.82737 q^{26} -11.2083 q^{27} -4.08337 q^{28} +6.13357 q^{29} -7.46408 q^{30} +7.90996 q^{31} -1.00000 q^{32} -12.7510 q^{33} +0.682284 q^{34} +9.82939 q^{35} +6.61471 q^{36} -6.33970 q^{37} +1.43659 q^{38} +14.9685 q^{39} +2.40718 q^{40} -1.98784 q^{41} -12.6615 q^{42} +3.25327 q^{43} +4.11222 q^{44} -15.9228 q^{45} -4.67947 q^{46} -2.95920 q^{47} -3.10076 q^{48} +9.67389 q^{49} -0.794507 q^{50} +2.11560 q^{51} -4.82737 q^{52} +8.18323 q^{53} +11.2083 q^{54} -9.89886 q^{55} +4.08337 q^{56} +4.45451 q^{57} -6.13357 q^{58} +4.45630 q^{59} +7.46408 q^{60} -9.76853 q^{61} -7.90996 q^{62} -27.0103 q^{63} +1.00000 q^{64} +11.6203 q^{65} +12.7510 q^{66} +1.12779 q^{67} -0.682284 q^{68} -14.5099 q^{69} -9.82939 q^{70} -2.14819 q^{71} -6.61471 q^{72} +8.32283 q^{73} +6.33970 q^{74} -2.46358 q^{75} -1.43659 q^{76} -16.7917 q^{77} -14.9685 q^{78} -12.0685 q^{79} -2.40718 q^{80} +14.9102 q^{81} +1.98784 q^{82} +5.61556 q^{83} +12.6615 q^{84} +1.64238 q^{85} -3.25327 q^{86} -19.0187 q^{87} -4.11222 q^{88} -11.3071 q^{89} +15.9228 q^{90} +19.7119 q^{91} +4.67947 q^{92} -24.5269 q^{93} +2.95920 q^{94} +3.45812 q^{95} +3.10076 q^{96} -6.56206 q^{97} -9.67389 q^{98} +27.2012 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9} - 10 q^{10} + 4 q^{11} - 2 q^{12} + 40 q^{13} - 8 q^{14} + 15 q^{15} + 92 q^{16} - 14 q^{17} - 104 q^{18} + 64 q^{19} + 10 q^{20} + 54 q^{21} - 4 q^{22} - 49 q^{23} + 2 q^{24} + 116 q^{25} - 40 q^{26} - 8 q^{27} + 8 q^{28} + 39 q^{29} - 15 q^{30} + 53 q^{31} - 92 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} + 104 q^{36} + 58 q^{37} - 64 q^{38} + 58 q^{39} - 10 q^{40} + 27 q^{41} - 54 q^{42} + 40 q^{43} + 4 q^{44} + 43 q^{45} + 49 q^{46} - 28 q^{47} - 2 q^{48} + 148 q^{49} - 116 q^{50} + 48 q^{51} + 40 q^{52} + 32 q^{53} + 8 q^{54} + 36 q^{55} - 8 q^{56} + 48 q^{57} - 39 q^{58} + 8 q^{59} + 15 q^{60} + 99 q^{61} - 53 q^{62} + 92 q^{64} + 13 q^{65} - q^{66} + 48 q^{67} - 14 q^{68} + 63 q^{69} + 22 q^{70} - 13 q^{71} - 104 q^{72} + 49 q^{73} - 58 q^{74} + 16 q^{75} + 64 q^{76} + 41 q^{77} - 58 q^{78} + 143 q^{79} + 10 q^{80} + 124 q^{81} - 27 q^{82} - 24 q^{83} + 54 q^{84} + 121 q^{85} - 40 q^{86} + 5 q^{87} - 4 q^{88} + 25 q^{89} - 43 q^{90} + 67 q^{91} - 49 q^{92} + 43 q^{93} + 28 q^{94} - 38 q^{95} + 2 q^{96} + 74 q^{97} - 148 q^{98} + 86 q^{99}+O(q^{100}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9 - 10 * q^10 + 4 * q^11 - 2 * q^12 + 40 * q^13 - 8 * q^14 + 15 * q^15 + 92 * q^16 - 14 * q^17 - 104 * q^18 + 64 * q^19 + 10 * q^20 + 54 * q^21 - 4 * q^22 - 49 * q^23 + 2 * q^24 + 116 * q^25 - 40 * q^26 - 8 * q^27 + 8 * q^28 + 39 * q^29 - 15 * q^30 + 53 * q^31 - 92 * q^32 + q^33 + 14 * q^34 - 22 * q^35 + 104 * q^36 + 58 * q^37 - 64 * q^38 + 58 * q^39 - 10 * q^40 + 27 * q^41 - 54 * q^42 + 40 * q^43 + 4 * q^44 + 43 * q^45 + 49 * q^46 - 28 * q^47 - 2 * q^48 + 148 * q^49 - 116 * q^50 + 48 * q^51 + 40 * q^52 + 32 * q^53 + 8 * q^54 + 36 * q^55 - 8 * q^56 + 48 * q^57 - 39 * q^58 + 8 * q^59 + 15 * q^60 + 99 * q^61 - 53 * q^62 + 92 * q^64 + 13 * q^65 - q^66 + 48 * q^67 - 14 * q^68 + 63 * q^69 + 22 * q^70 - 13 * q^71 - 104 * q^72 + 49 * q^73 - 58 * q^74 + 16 * q^75 + 64 * q^76 + 41 * q^77 - 58 * q^78 + 143 * q^79 + 10 * q^80 + 124 * q^81 - 27 * q^82 - 24 * q^83 + 54 * q^84 + 121 * q^85 - 40 * q^86 + 5 * q^87 - 4 * q^88 + 25 * q^89 - 43 * q^90 + 67 * q^91 - 49 * q^92 + 43 * q^93 + 28 * q^94 - 38 * q^95 + 2 * q^96 + 74 * q^97 - 148 * q^98 + 86 * q^99

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