LMFDB - Embedded newform 169.2.k.a.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(4,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("169.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.k (of order $78$, degree $24$, minimal)

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:	no
Analytic conductor:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			10.2
Character	$\chi$	$=$	169.10
Dual form			169.2.k.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.52063 - 0.514590i) q^{2} +(2.70717 - 0.439959i) q^{3} +(4.24882 + 1.81025i) q^{4} +(0.847165 - 3.43708i) q^{5} +(-7.05019 - 0.284113i) q^{6} +(0.693293 - 0.328971i) q^{7} +(-5.54370 - 3.82654i) q^{8} +(4.28962 - 1.43209i) q^{9} +O(q^{10})$	\(q+(-2.52063 - 0.514590i) q^{2} +(2.70717 - 0.439959i) q^{3} +(4.24882 + 1.81025i) q^{4} +(0.847165 - 3.43708i) q^{5} +(-7.05019 - 0.284113i) q^{6} +(0.693293 - 0.328971i) q^{7} +(-5.54370 - 3.82654i) q^{8} +(4.28962 - 1.43209i) q^{9} +(-3.90408 + 8.22767i) q^{10} +(-1.32084 + 3.95641i) q^{11} +(12.2987 + 3.03136i) q^{12} +(-2.08006 + 2.94505i) q^{13} +(-1.91682 + 0.472454i) q^{14} +(0.781249 - 9.67750i) q^{15} +(5.60600 + 5.83646i) q^{16} +(-2.29540 - 4.83746i) q^{17} +(-11.5495 + 1.40236i) q^{18} +(1.08266 + 0.625075i) q^{19} +(9.82143 - 13.0699i) q^{20} +(1.73213 - 1.19560i) q^{21} +(5.36529 - 9.29296i) q^{22} +(1.81759 + 3.14815i) q^{23} +(-16.6913 - 7.92012i) q^{24} +(-6.66857 - 3.49994i) q^{25} +(6.75857 - 6.35301i) q^{26} +(3.69710 - 1.94039i) q^{27} +(3.54119 - 0.142705i) q^{28} +(0.242243 - 1.18659i) q^{29} +(-6.94919 + 23.9914i) q^{30} +(1.61654 + 3.08006i) q^{31} +(-3.92682 - 6.20977i) q^{32} +(-1.83510 + 11.2918i) q^{33} +(3.29655 + 13.3746i) q^{34} +(-0.543369 - 2.66160i) q^{35} +(20.8183 + 1.68062i) q^{36} +(5.46268 - 8.63854i) q^{37} +(-2.40733 - 2.13271i) q^{38} +(-4.33540 + 8.88791i) q^{39} +(-17.8486 + 15.8125i) q^{40} +(1.11145 + 6.83901i) q^{41} +(-4.98131 + 2.12234i) q^{42} +(-4.94438 + 3.12664i) q^{43} +(-12.7741 + 14.4190i) q^{44} +(-1.28818 - 15.9570i) q^{45} +(-2.96146 - 8.87064i) q^{46} +(1.77845 + 0.215943i) q^{47} +(17.7442 + 13.3339i) q^{48} +(-4.05469 + 4.96609i) q^{49} +(15.0080 + 12.2536i) q^{50} +(-8.34234 - 12.0860i) q^{51} +(-14.1691 + 8.74754i) q^{52} +(0.439312 - 0.636453i) q^{53} +(-10.3175 + 2.98851i) q^{54} +(12.4795 + 7.89159i) q^{55} +(-5.10223 - 0.829193i) q^{56} +(3.20596 + 1.21586i) q^{57} +(-1.22121 + 2.86629i) q^{58} +(-3.29673 - 3.16655i) q^{59} +(20.8381 - 39.7037i) q^{60} +(7.51228 - 0.606454i) q^{61} +(-2.48973 - 8.59556i) q^{62} +(2.50285 - 2.40402i) q^{63} +(0.963174 + 2.53968i) q^{64} +(8.36023 + 9.64430i) q^{65} +(10.4363 - 27.5182i) q^{66} +(3.22636 + 7.57254i) q^{67} +(-0.995728 - 24.7087i) q^{68} +(6.30558 + 7.72294i) q^{69} +6.98852i q^{70} +(-7.05285 + 5.75847i) q^{71} +(-29.2603 - 8.47536i) q^{72} +(-7.64099 - 8.62490i) q^{73} +(-18.2147 + 18.9635i) q^{74} +(-19.5928 - 6.54104i) q^{75} +(3.46848 + 4.61571i) q^{76} +(0.385815 + 3.17747i) q^{77} +(15.5016 - 20.1722i) q^{78} +(0.238977 - 1.96816i) q^{79} +(24.8096 - 14.3238i) q^{80} +(-1.69109 + 1.27077i) q^{81} +(0.717741 - 17.8106i) q^{82} +(1.92766 - 0.731065i) q^{83} +(9.52385 - 1.94431i) q^{84} +(-18.5713 + 3.79137i) q^{85} +(14.0719 - 5.33676i) q^{86} +(0.133746 - 3.31887i) q^{87} +(22.4617 - 16.8789i) q^{88} +(-7.96181 + 4.59675i) q^{89} +(-4.96429 + 40.8846i) q^{90} +(-0.473255 + 2.72607i) q^{91} +(2.02364 + 16.6662i) q^{92} +(5.73136 + 7.62706i) q^{93} +(-4.37169 - 1.45949i) q^{94} +(3.06563 - 3.19165i) q^{95} +(-13.3626 - 15.0833i) q^{96} +(2.85521 + 0.827022i) q^{97} +(12.7759 - 10.4312i) q^{98} +18.8631i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) $ 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{78}\right)$

Coefficient data

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

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

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

$2$	−2.52063	−	0.514590i	−1.78235	−	0.363870i	−0.808052	−	0.589111i	$-0.799478\pi$
$2$	−2.52063	−	0.514590i	−1.78235	−	0.363870i	−0.974303	+	0.225241i	$0.927683\pi$
$3$	2.70717	−	0.439959i	1.56299	−	0.254010i	0.683507	−	0.729944i	$-0.260454\pi$
$3$	2.70717	−	0.439959i	1.56299	−	0.254010i	0.879481	+	0.475934i	$0.157890\pi$
$4$	4.24882	+	1.81025i	2.12441	+	0.905125i
$5$	0.847165	−	3.43708i	0.378864	−	1.53711i	−0.403907	−	0.914800i	$-0.632348\pi$
$5$	0.847165	−	3.43708i	0.378864	−	1.53711i	0.782771	−	0.622310i	$-0.213806\pi$
$6$	−7.05019	−	0.284113i	−2.87823	−	0.115989i
$7$	0.693293	−	0.328971i	0.262040	−	0.124340i	−0.293141	−	0.956069i	$-0.594700\pi$
$7$	0.693293	−	0.328971i	0.262040	−	0.124340i	0.555181	+	0.831730i	$0.312649\pi$
$8$	−5.54370	−	3.82654i	−1.96000	−	1.35289i
$9$	4.28962	−	1.43209i	1.42987	−	0.477362i
$10$	−3.90408	+	8.22767i	−1.23458	+	2.60182i
$11$	−1.32084	+	3.95641i	−0.398250	+	1.19290i	0.538416	+	0.842679i	$0.319023\pi$
$11$	−1.32084	+	3.95641i	−0.398250	+	1.19290i	−0.936666	+	0.350224i	$0.886105\pi$
$12$	12.2987	+	3.03136i	3.55034	+	0.875079i
$13$	−2.08006	+	2.94505i	−0.576906	+	0.816810i
$13$	−2.08006	+	2.94505i	−0.576906	+	0.816810i
$14$	−1.91682	+	0.472454i	−0.512292	+	0.126269i
$15$	0.781249	−	9.67750i	0.201718	−	2.49872i
$16$	5.60600	+	5.83646i	1.40150	+	1.45911i
$17$	−2.29540	−	4.83746i	−0.556717	−	1.17326i	−0.965447	−	0.260601i	$-0.916079\pi$
$17$	−2.29540	−	4.83746i	−0.556717	−	1.17326i	0.408730	−	0.912656i	$-0.365972\pi$
$18$	−11.5495	+	1.40236i	−2.72224	+	0.330540i
$19$	1.08266	+	0.625075i	0.248379	+	0.143402i	0.619022	−	0.785374i	$-0.287529\pi$
$19$	1.08266	+	0.625075i	0.248379	+	0.143402i	−0.370643	+	0.928776i	$0.620862\pi$
$20$	9.82143	−	13.0699i	2.19614	−	2.92253i
$21$	1.73213	−	1.19560i	0.377982	−	0.260902i
$22$	5.36529	−	9.29296i	1.14388	−	1.98127i
$23$	1.81759	+	3.14815i	0.378993	+	0.656435i	0.990916	−	0.134482i	$-0.0429371\pi$
$23$	1.81759	+	3.14815i	0.378993	+	0.656435i	−0.611923	+	0.790917i	$0.709604\pi$
$24$	−16.6913	−	7.92012i	−3.40710	−	1.61669i
$25$	−6.66857	−	3.49994i	−1.33371	−	0.699987i
$26$	6.75857	−	6.35301i	1.32546	−	1.24593i
$27$	3.69710	−	1.94039i	0.711508	−	0.373428i
$28$	3.54119	−	0.142705i	0.669223	−	0.0269688i
$29$	0.242243	−	1.18659i	0.0449835	−	0.220344i	−0.951085	−	0.308929i	$-0.900029\pi$
$29$	0.242243	−	1.18659i	0.0449835	−	0.220344i	0.996069	+	0.0885853i	$0.0282346\pi$
$30$	−6.94919	+	23.9914i	−1.26874	+	4.38021i
$31$	1.61654	+	3.08006i	0.290339	+	0.553196i	0.986315	−	0.164870i	$-0.0527203\pi$
$31$	1.61654	+	3.08006i	0.290339	+	0.553196i	−0.695976	+	0.718065i	$0.745028\pi$
$32$	−3.92682	−	6.20977i	−0.694171	−	1.09774i
$33$	−1.83510	+	11.2918i	−0.319450	+	1.96565i
$34$	3.29655	+	13.3746i	0.565354	+	2.29373i
$35$	−0.543369	−	2.66160i	−0.0918461	−	0.449892i
$36$	20.8183	+	1.68062i	3.46971	+	0.280104i
$37$	5.46268	−	8.63854i	0.898059	−	1.42017i	−0.00936740	−	0.999956i	$-0.502982\pi$
$37$	5.46268	−	8.63854i	0.898059	−	1.42017i	0.907427	−	0.420211i	$-0.138044\pi$
$38$	−2.40733	−	2.13271i	−0.390521	−	0.345971i
$39$	−4.33540	+	8.88791i	−0.694219	+	1.42321i
$40$	−17.8486	+	15.8125i	−2.82211	+	2.50017i
$41$	1.11145	+	6.83901i	0.173579	+	1.06807i	0.916893	+	0.399132i	$0.130688\pi$
$41$	1.11145	+	6.83901i	0.173579	+	1.06807i	−0.743315	+	0.668942i	$0.766747\pi$
$42$	−4.98131	+	2.12234i	−0.768632	+	0.327484i
$43$	−4.94438	+	3.12664i	−0.754011	+	0.476807i	−0.855354	−	0.518044i	$-0.826660\pi$
$43$	−4.94438	+	3.12664i	−0.754011	+	0.476807i	0.101343	+	0.994852i	$0.467686\pi$
$44$	−12.7741	+	14.4190i	−1.92577	+	2.17375i
$45$	−1.28818	−	15.9570i	−0.192031	−	2.37873i
$46$	−2.96146	−	8.87064i	−0.436643	−	1.30790i
$47$	1.77845	+	0.215943i	0.259414	+	0.0314985i	0.249210	−	0.968449i	$-0.419829\pi$
$47$	1.77845	+	0.215943i	0.259414	+	0.0314985i	0.0102035	+	0.999948i	$0.496752\pi$
$48$	17.7442	+	13.3339i	2.56116	+	1.92458i
$49$	−4.05469	+	4.96609i	−0.579241	+	0.709441i
$50$	15.0080	+	12.2536i	2.12245	+	1.73292i
$51$	−8.34234	−	12.0860i	−1.16816	−	1.69237i
$52$	−14.1691	+	8.74754i	−1.96490	+	1.21307i
$53$	0.439312	−	0.636453i	0.0603441	−	0.0874236i	−0.791650	−	0.610975i	$-0.790778\pi$
$53$	0.439312	−	0.636453i	0.0603441	−	0.0874236i	0.851994	+	0.523551i	$0.175393\pi$
$54$	−10.3175	+	2.98851i	−1.40404	+	0.406685i
$55$	12.4795	+	7.89159i	1.68274	+	1.06410i
$56$	−5.10223	−	0.829193i	−0.681814	−	0.110806i
$57$	3.20596	+	1.21586i	0.424640	+	0.161045i
$58$	−1.22121	+	2.86629i	−0.160353	+	0.376362i
$59$	−3.29673	−	3.16655i	−0.429197	−	0.412249i	0.446748	−	0.894660i	$-0.352582\pi$
$59$	−3.29673	−	3.16655i	−0.429197	−	0.412249i	−0.875945	+	0.482410i	$0.839761\pi$
$60$	20.8381	−	39.7037i	2.69019	−	5.12572i
$61$	7.51228	−	0.606454i	0.961849	−	0.0776485i	0.410444	−	0.911886i	$-0.365374\pi$
$61$	7.51228	−	0.606454i	0.961849	−	0.0776485i	0.551405	+	0.834237i	$0.314092\pi$
$62$	−2.48973	−	8.59556i	−0.316196	−	1.09164i
$63$	2.50285	−	2.40402i	0.315329	−	0.302878i
$64$	0.963174	+	2.53968i	0.120397	+	0.317460i
$65$	8.36023	+	9.64430i	1.03696	+	1.19623i
$66$	10.4363	−	27.5182i	1.28462	−	3.38725i
$67$	3.22636	+	7.57254i	0.394163	+	0.925133i	0.992313	+	0.123750i	$0.0394921\pi$
$67$	3.22636	+	7.57254i	0.394163	+	0.925133i	−0.598151	+	0.801383i	$0.704098\pi$
$68$	−0.995728	−	24.7087i	−0.120750	−	2.99637i
$69$	6.30558	+	7.72294i	0.759103	+	0.929732i
$70$			6.98852i			0.835287i
$71$	−7.05285	+	5.75847i	−0.837019	+	0.683405i	−0.950700	−	0.310112i	$-0.899633\pi$
$71$	−7.05285	+	5.75847i	−0.837019	+	0.683405i	0.113681	+	0.993517i	$0.463736\pi$
$72$	−29.2603	−	8.47536i	−3.44836	−	0.998831i
$73$	−7.64099	−	8.62490i	−0.894311	−	1.00947i	−0.999887	−	0.0150569i	$-0.995207\pi$
$73$	−7.64099	−	8.62490i	−0.894311	−	1.00947i	0.105576	−	0.994411i	$-0.466331\pi$
$74$	−18.2147	+	18.9635i	−2.11742	+	2.20446i
$75$	−19.5928	−	6.54104i	−2.26238	−	0.755294i
$76$	3.46848	+	4.61571i	0.397862	+	0.529459i
$77$	0.385815	+	3.17747i	0.0439677	+	0.362107i
$78$	15.5016	−	20.1722i	1.75521	−	2.28405i
$79$	0.238977	−	1.96816i	0.0268871	−	0.221435i	−0.973072	−	0.230502i	$-0.925963\pi$
$79$	0.238977	−	1.96816i	0.0268871	−	0.221435i	0.999959	+	0.00906720i	$0.00288622\pi$
$80$	24.8096	−	14.3238i	2.77380	−	1.60145i
$81$	−1.69109	+	1.27077i	−0.187899	+	0.141197i
$82$	0.717741	−	17.8106i	0.0792612	−	1.96685i
$83$	1.92766	−	0.731065i	0.211588	−	0.0802448i	−0.246534	−	0.969134i	$-0.579292\pi$
$83$	1.92766	−	0.731065i	0.211588	−	0.0802448i	0.458122	+	0.888889i	$0.348522\pi$
$84$	9.52385	−	1.94431i	1.03914	−	0.212141i
$85$	−18.5713	+	3.79137i	−2.01434	+	0.411231i
$86$	14.0719	−	5.33676i	1.51741	−	0.575478i
$87$	0.133746	−	3.31887i	0.0143391	−	0.355821i
$88$	22.4617	−	16.8789i	2.39443	−	1.79930i
$89$	−7.96181	+	4.59675i	−0.843950	+	0.487255i	−0.858605	−	0.512638i	$-0.828668\pi$
$89$	−7.96181	+	4.59675i	−0.843950	+	0.487255i	0.0146552	+	0.999893i	$0.495335\pi$
$90$	−4.96429	+	40.8846i	−0.523282	+	4.30961i
$91$	−0.473255	+	2.72607i	−0.0496106	+	0.285769i
$92$	2.02364	+	16.6662i	0.210979	+	1.73757i
$93$	5.73136	+	7.62706i	0.594314	+	0.790889i
$94$	−4.37169	−	1.45949i	−0.450906	−	0.150534i
$95$	3.06563	−	3.19165i	0.314527	−	0.327457i
$96$	−13.3626	−	15.0833i	−1.36382	−	1.53943i
$97$	2.85521	+	0.827022i	0.289903	+	0.0839714i	0.419983	−	0.907532i	$-0.362036\pi$
$97$	2.85521	+	0.827022i	0.289903	+	0.0839714i	−0.130080	+	0.991504i	$0.541523\pi$
$98$	12.7759	−	10.4312i	1.29056	−	1.05371i
$99$			18.8631i			1.89581i
$100$	−21.9978	−	26.9424i	−2.19978	−	2.69424i
$101$	0.686404	+	17.0329i	0.0682998	+	1.69484i	0.563543	+	0.826087i	$0.309438\pi$
$101$	0.686404	+	17.0329i	0.0682998	+	1.69484i	−0.495243	+	0.868755i	$0.664921\pi$
$102$	14.8086	+	34.7571i	1.46627	+	3.44147i
$103$	3.89565	−	10.2720i	0.383849	−	1.01213i	−0.594303	−	0.804241i	$-0.702572\pi$
$103$	3.89565	−	10.2720i	0.383849	−	1.01213i	0.978153	−	0.207887i	$-0.0666586\pi$
$104$	22.8006	−	8.36704i	2.23579	−	0.820456i
$105$	−2.64199	−	6.96635i	−0.257832	−	0.679846i
$106$	−1.43486	+	1.37820i	−0.139366	+	0.133862i
$107$	−0.279534	−	0.965063i	−0.0270236	−	0.0932962i	0.945873	−	0.324537i	$-0.105209\pi$
$107$	−0.279534	−	0.965063i	−0.0270236	−	0.0932962i	−0.972896	+	0.231241i	$0.925721\pi$
$108$	19.2209	−	1.55167i	1.84953	−	0.149310i
$109$	3.02369	−	5.76116i	0.289617	−	0.551819i	−0.696563	−	0.717496i	$-0.745288\pi$
$109$	3.02369	−	5.76116i	0.289617	−	0.551819i	0.986180	+	0.165676i	$0.0529807\pi$
$110$	−27.3954	−	26.3136i	−2.61205	−	2.50891i
$111$	10.9878	−	25.7894i	1.04292	−	2.44782i
$112$	5.80662	+	2.20216i	0.548674	+	0.208085i
$113$	4.91526	+	0.798807i	0.462388	+	0.0751454i	0.387143	−	0.922020i	$-0.373462\pi$
$113$	4.91526	+	0.798807i	0.462388	+	0.0751454i	0.0752453	+	0.997165i	$0.476026\pi$
$114$	−7.45537	−	4.71449i	−0.698259	−	0.441552i
$115$	12.3603	−	3.58019i	1.15260	−	0.333855i
$116$	3.17727	−	4.60307i	0.295002	−	0.427384i
$117$	−4.70512	+	15.6120i	−0.434989	+	1.44333i
$118$	6.68035	+	9.67816i	0.614976	+	0.890947i
$119$	−3.18277	−	2.59865i	−0.291764	−	0.238218i
$120$	−41.3624	+	50.6597i	−3.77585	+	4.62458i
$121$	−5.11470	−	3.84345i	−0.464973	−	0.349404i
$122$	−19.2478	−	2.33710i	−1.74261	−	0.211591i
$123$	6.01777	+	18.0254i	0.542604	+	1.62530i
$124$	1.29270	+	16.0130i	0.116088	+	1.43801i
$125$	−5.94185	+	6.70696i	−0.531455	+	0.599889i
$126$	−7.54584	+	4.77170i	−0.672237	+	0.425097i
$127$	19.2861	−	8.21702i	1.71136	−	0.729143i	0.711717	−	0.702467i	$-0.247918\pi$
$127$	19.2861	−	8.21702i	1.71136	−	0.729143i	0.999644	−	0.0266759i	$-0.00849221\pi$
$128$	1.23624	+	7.60686i	0.109269	+	0.672358i
$129$	−12.0097	+	10.6397i	−1.05740	+	0.936771i
$130$	−16.1102	−	28.6118i	−1.41296	−	2.50942i
$131$	−11.0305	−	9.77219i	−0.963741	−	0.853800i	0.0255624	−	0.999673i	$-0.491862\pi$
$131$	−11.0305	−	9.77219i	−0.963741	−	0.853800i	−0.989303	+	0.145873i	$0.953401\pi$
$132$	−28.2380	+	44.6549i	−2.45780	+	3.88671i
$133$	0.956233	+	0.0771951i	0.0829159	+	0.00669366i
$134$	−4.23570	−	20.7478i	−0.365909	−	1.79234i
$135$	−3.53722	−	14.3511i	−0.304436	−	1.23514i
$136$	−5.78571	+	35.6009i	−0.496120	+	3.05275i
$137$	−2.95050	−	4.66584i	−0.252078	−	0.398629i	0.695314	−	0.718707i	$-0.255266\pi$
$137$	−2.95050	−	4.66584i	−0.252078	−	0.398629i	−0.947391	+	0.320077i	$0.896291\pi$
$138$	−11.9199	−	22.7115i	−1.01469	−	1.93333i
$139$	−3.23217	+	11.1587i	−0.274149	+	0.946472i	0.698774	+	0.715342i	$0.253729\pi$
$139$	−3.23217	+	11.1587i	−0.274149	+	0.946472i	−0.972923	+	0.231130i	$0.925758\pi$
$140$	2.50948	−	12.2923i	0.212090	−	1.03889i
$141$	4.90958	−	0.197849i	0.413461	−	0.0166619i
$142$	20.7409	−	10.8857i	1.74054	−	0.913504i
$143$	−8.90440	−	12.1195i	−0.744623	−	1.01349i
$144$	32.4059	+	17.0079i	2.70049	+	1.41733i
$145$	−3.87318	−	1.83784i	−0.321650	−	0.152625i
$146$	14.8218	+	25.6722i	1.22666	+	2.12464i
$147$	−8.79187	+	15.2280i	−0.725141	+	1.25598i
$148$	38.8478	−	26.8147i	3.19327	−	2.20416i
$149$	1.18255	−	1.57369i	0.0968784	−	0.128922i	−0.748401	−	0.663247i	$-0.769178\pi$
$149$	1.18255	−	1.57369i	0.0968784	−	0.128922i	0.845279	+	0.534325i	$0.179434\pi$
$150$	46.0203	+	26.5698i	3.75754	+	2.16942i
$151$	3.99125	−	0.484625i	0.324803	−	0.0394382i	0.0434888	−	0.999054i	$-0.486153\pi$
$151$	3.99125	−	0.484625i	0.324803	−	0.0394382i	0.281314	+	0.959616i	$0.409230\pi$
$152$	−3.61008	−	7.60808i	−0.292816	−	0.617096i
$153$	−16.7741	−	17.4637i	−1.35610	−	1.41185i
$154$	0.662600	−	8.20777i	0.0533938	−	0.661401i
$155$	11.9559	−	2.94687i	0.960321	−	0.236698i
$156$	−34.5097	+	29.9149i	−2.76298	+	2.39511i
$157$	−17.3527	−	4.27705i	−1.38490	−	0.341346i	−0.524690	−	0.851293i	$-0.675819\pi$
$157$	−17.3527	−	4.27705i	−1.38490	−	0.341346i	−0.860206	+	0.509947i	$0.829665\pi$
$158$	−1.61517	+	4.83802i	−0.128496	+	0.384892i
$159$	0.909281	−	1.91627i	0.0721107	−	0.151970i
$160$	−24.6702	+	8.23611i	−1.95035	+	0.651122i
$161$	2.29577	+	1.58466i	0.180932	+	0.124888i
$162$	4.91655	−	2.33293i	0.386281	−	0.183292i
$163$	2.85111	+	0.114896i	0.223316	+	0.00899933i	0.151672	−	0.988431i	$-0.451534\pi$
$163$	2.85111	+	0.114896i	0.223316	+	0.00899933i	0.0716443	+	0.997430i	$0.477175\pi$
$164$	−7.65799	+	31.0697i	−0.597989	+	2.42614i
$165$	37.2563	+	15.8734i	2.90040	+	1.23574i
$166$	−5.23512	+	0.850790i	−0.406324	+	0.0660341i
$167$	6.33467	+	1.29323i	0.490192	+	0.100073i	0.438762	−	0.898603i	$-0.355417\pi$
$167$	6.33467	+	1.29323i	0.490192	+	0.100073i	0.0514295	+	0.998677i	$0.483622\pi$
$168$	−14.1774			−1.09381
$169$	−4.34666	−	12.2518i	−0.334359	−	0.942446i
$170$	48.7625			3.73991
$171$	5.53937	+	1.13087i	0.423606	+	0.0864798i
$172$	−26.6677	+	4.33393i	−2.03340	+	0.330459i
$173$	−3.47956	−	1.48250i	−0.264546	−	0.112712i	0.255621	−	0.966777i	$-0.417720\pi$
$173$	−3.47956	−	1.48250i	−0.264546	−	0.112712i	−0.520167	+	0.854065i	$0.674130\pi$
$174$	−2.04499	+	8.29683i	−0.155030	+	0.628981i
$175$	−5.77465	−	0.232710i	−0.436522	−	0.0175913i
$176$	−30.4961	+	14.4706i	−2.29873	+	1.09076i
$177$	−10.3180	−	7.12198i	−0.775546	−	0.535320i
$178$	22.4342	−	7.48964i	1.68152	−	0.561372i
$179$	1.12901	−	2.37935i	0.0843865	−	0.177841i	−0.856871	−	0.515532i	$-0.827595\pi$
$179$	1.12901	−	2.37935i	0.0843865	−	0.177841i	0.941257	+	0.337691i	$0.109646\pi$
$180$	23.4129	−	70.1303i	1.74510	−	5.22720i
$181$	−11.9418	−	2.94338i	−0.887624	−	0.218780i	−0.230960	−	0.972963i	$-0.574187\pi$
$181$	−11.9418	−	2.94338i	−0.887624	−	0.218780i	−0.656664	+	0.754183i	$0.728033\pi$
$182$	2.59571	−	6.62787i	0.192407	−	0.491290i
$183$	20.0702	−	4.94687i	1.48363	−	0.365683i
$184$	1.97038	−	24.4075i	0.145258	−	1.79934i
$185$	−25.0636	−	26.0939i	−1.84271	−	1.91847i
$186$	−10.5218	−	22.1743i	−0.771498	−	1.62590i
$187$	22.1709	−	2.69203i	1.62129	−	0.196861i
$188$	7.16540	+	4.13694i	0.522590	+	0.301718i
$189$	1.92484	−	2.56150i	0.140012	−	0.186322i
$190$	−9.36970	+	6.46744i	−0.679750	+	0.469197i
$191$	3.00455	−	5.20403i	0.217401	−	0.376550i	−0.736611	−	0.676316i	$-0.763575\pi$
$191$	3.00455	−	5.20403i	0.217401	−	0.376550i	0.954013	+	0.299766i	$0.0969086\pi$
$192$	3.72483	+	6.45160i	0.268817	+	0.465604i
$193$	−17.5927	−	8.34783i	−1.26635	−	0.600890i	−0.327380	−	0.944893i	$-0.606166\pi$
$193$	−17.5927	−	8.34783i	−1.26635	−	0.600890i	−0.938969	+	0.344003i	$0.888217\pi$
$194$	−6.77136	−	3.55388i	−0.486155	−	0.255154i
$195$	26.8757	+	22.4306i	1.92461	+	1.60629i
$196$	−26.2175	+	13.7600i	−1.87268	+	0.982857i
$197$	−14.0127	+	0.564693i	−0.998365	+	0.0402327i	−0.534063	−	0.845444i	$-0.679336\pi$
$197$	−14.0127	+	0.564693i	−0.998365	+	0.0402327i	−0.464302	+	0.885677i	$0.653695\pi$
$198$	9.70676	−	47.5469i	0.689829	−	3.37901i
$199$	−1.44641	+	4.99360i	−0.102534	+	0.353987i	−0.995337	−	0.0964598i	$-0.969248\pi$
$199$	−1.44641	+	4.99360i	−0.102534	+	0.353987i	0.892803	+	0.450447i	$0.148735\pi$
$200$	23.5759	+	44.9202i	1.66707	+	3.17633i
$201$	12.0659	+	19.0807i	0.851065	+	1.34585i
$202$	7.03482	−	43.2870i	0.494968	−	3.04566i
$203$	−0.222408	−	0.902343i	−0.0156100	−	0.0633321i
$204$	−13.5664	−	66.4528i	−0.949840	−	4.65262i
$205$	24.4478	+	1.97363i	1.70751	+	0.137844i
$206$	−15.1053	+	23.8872i	−1.05244	+	1.66430i
$207$	12.3052	+	10.9014i	0.855270	+	0.757703i
$208$	−28.8495	+	4.36974i	−2.00035	+	0.302987i
$209$	−3.90308	+	3.45783i	−0.269982	+	0.239183i
$210$	3.07466	+	18.9191i	0.212172	+	1.30554i
$211$	15.7305	−	6.70215i	1.08293	−	0.461395i	0.224581	−	0.974455i	$-0.427899\pi$
$211$	15.7305	−	6.70215i	1.08293	−	0.461395i	0.858353	+	0.513060i	$0.171488\pi$
$212$	3.01870	−	1.90891i	0.207325	−	0.131104i
$213$	−16.5598	+	18.6922i	−1.13466	+	1.28077i
$214$	0.207990	+	2.57641i	0.0142179	+	0.176120i
$215$	6.55780	+	19.6430i	0.447238	+	1.33964i
$216$	−27.9206	−	3.39018i	−1.89976	−	0.230672i
$217$	2.13399	+	1.60359i	0.144865	+	0.108859i
$218$	−10.5862	+	12.9658i	−0.716991	+	0.878155i
$219$	−24.4801	−	19.9874i	−1.65421	−	1.35062i
$220$	38.7375	+	56.1210i	2.61168	+	3.78368i
$221$	19.0212	+	3.30215i	1.27950	+	0.222126i
$222$	−40.9672	+	59.3513i	−2.74954	+	3.98340i
$223$	−12.9951	+	3.76406i	−0.870213	+	0.252060i	−0.683142	−	0.730286i	$-0.739387\pi$
$223$	−12.9951	+	3.76406i	−0.870213	+	0.252060i	−0.187072	+	0.982346i	$0.559900\pi$
$224$	−4.76528	−	3.01338i	−0.318393	−	0.201340i
$225$	−33.6179	−	5.46343i	−2.24119	−	0.364229i
$226$	−11.9785	−	4.54284i	−0.796797	−	0.302185i
$227$	1.66676	−	3.91203i	0.110627	−	0.259651i	−0.855460	−	0.517869i	$-0.826725\pi$
$227$	1.66676	−	3.91203i	0.110627	−	0.259651i	0.966086	+	0.258219i	$0.0831356\pi$
$228$	11.4205	+	10.9696i	0.756342	+	0.726477i
$229$	−4.43900	+	8.45781i	−0.293338	+	0.558908i	−0.986870	−	0.161517i	$-0.948361\pi$
$229$	−4.43900	+	8.45781i	−0.293338	+	0.558908i	0.693532	+	0.720426i	$0.256053\pi$
$230$	−32.9980	+	2.66387i	−2.17582	+	0.175651i
$231$	2.44243	+	8.43223i	0.160700	+	0.554800i
$232$	−5.88345	+	5.65113i	−0.386267	+	0.371015i
$233$	2.56489	+	6.76305i	0.168031	+	0.443062i	0.992409	−	0.122977i	$-0.0392443\pi$
$233$	2.56489	+	6.76305i	0.168031	+	0.443062i	−0.824378	+	0.566039i	$0.808475\pi$
$234$	19.8937	−	36.9309i	1.30049	−	2.41425i
$235$	2.24885	−	5.92974i	0.146699	−	0.386814i
$236$	−8.27493	−	19.4220i	−0.538652	−	1.26426i
$237$	−0.218954	−	5.43328i	−0.0142226	−	0.352930i
$238$	6.68535	+	8.18807i	0.433347	+	0.530754i
$239$		−	22.0313i		−	1.42508i	−0.701630	−	0.712542i	$-0.747544\pi$
$239$		−	22.0313i		−	1.42508i	0.701630	−	0.712542i	$-0.252456\pi$
$240$	60.8620	−	49.6923i	3.92863	−	3.20762i
$241$	20.6241	+	5.97385i	1.32852	+	0.384809i	0.865219	−	0.501394i	$-0.167179\pi$
$241$	20.6241	+	5.97385i	1.32852	+	0.384809i	0.463297	+	0.886203i	$0.346666\pi$
$242$	10.9145	+	12.3199i	0.701608	+	0.791952i
$243$	−12.6961	+	13.2181i	−0.814457	+	0.847940i
$244$	33.0161	+	11.0224i	2.11364	+	0.705637i
$245$	13.6339	+	18.1434i	0.871036	+	1.15914i
$246$	−5.89286	−	48.5321i	−0.375715	−	3.09429i
$247$	−4.09288	+	1.88830i	−0.260424	+	0.120149i
$248$	2.82436	−	23.2607i	0.179347	−	1.47706i
$249$	4.89688	−	2.82721i	0.310327	−	0.179167i
$250$	18.4285	−	13.8481i	1.16552	−	0.875834i
$251$	0.175478	−	4.35445i	0.0110761	−	0.274850i	−0.984155	−	0.177308i	$-0.943261\pi$
$251$	0.175478	−	4.35445i	0.0110761	−	0.274850i	0.995231	−	0.0975419i	$-0.0310980\pi$
$252$	14.9860	−	5.68345i	0.944031	−	0.358024i
$253$	−14.8561	+	3.03290i	−0.933998	+	0.190677i
$254$	−52.8414	+	10.7877i	−3.31557	+	0.676878i
$255$	−48.6078	+	18.4345i	−3.04394	+	1.15441i
$256$	1.01707	−	25.2382i	0.0635666	−	1.57739i
$257$	−1.49952	+	1.12681i	−0.0935372	+	0.0702886i	−0.646482	−	0.762929i	$-0.723760\pi$
$257$	−1.49952	+	1.12681i	−0.0935372	+	0.0702886i	0.552945	+	0.833218i	$0.313504\pi$
$258$	35.7471	−	20.6386i	2.22552	−	1.28490i
$259$	0.945404	−	7.78610i	0.0587445	−	0.483805i
$260$	18.0625	+	56.1110i	1.12019	+	3.47985i
$261$	−0.660162	−	5.43692i	−0.0408630	−	0.336537i
$262$	22.7752	+	30.3083i	1.40706	+	1.87245i
$263$	13.2744	+	4.43166i	0.818537	+	0.273268i	0.694943	−	0.719065i	$-0.255430\pi$
$263$	13.2744	+	4.43166i	0.818537	+	0.273268i	0.123594	+	0.992333i	$0.460558\pi$
$264$	53.3819	−	55.5764i	3.28543	−	3.42049i
$265$	−1.81537	−	2.04913i	−0.111517	−	0.125877i
$266$	−2.37059	−	0.686648i	−0.145350	−	0.0421011i
$267$	−19.5316	+	15.9471i	−1.19532	+	0.975945i
$268$			38.0149i			2.32213i
$269$	7.01851	+	8.59611i	0.427926	+	0.524114i	0.942893	−	0.333096i	$-0.108093\pi$
$269$	7.01851	+	8.59611i	0.427926	+	0.524114i	−0.514967	+	0.857210i	$0.672196\pi$
$270$	1.53110	+	37.9940i	0.0931801	+	2.31224i
$271$	−10.3476	−	24.2867i	−0.628571	−	1.47531i	−0.864038	−	0.503427i	$-0.832072\pi$
$271$	−10.3476	−	24.2867i	−0.628571	−	1.47531i	0.235467	−	0.971882i	$-0.424338\pi$
$272$	15.3656	−	40.5158i	0.931677	−	2.45663i
$273$	−0.0818288	+	7.58815i	−0.00495250	+	0.459256i
$274$	5.03612	+	13.2791i	0.304243	+	0.802223i
$275$	22.6553	−	21.7607i	1.36617	−	1.31222i
$276$	12.8108	+	44.2280i	0.771120	+	2.66221i
$277$	−22.2024	+	1.79237i	−1.33401	+	0.107693i	−0.726802	−	0.686847i	$-0.758994\pi$
$277$	−22.2024	+	1.79237i	−1.33401	+	0.107693i	−0.607213	+	0.794539i	$0.707712\pi$
$278$	13.8893	−	26.4638i	0.833024	−	1.58719i
$279$	11.3453	+	10.8973i	0.679224	+	0.652403i
$280$	−7.17244	+	16.8343i	−0.428635	+	1.00604i
$281$	−7.19074	−	2.72709i	−0.428963	−	0.162684i	0.130668	−	0.991426i	$-0.458288\pi$
$281$	−7.19074	−	2.72709i	−0.428963	−	0.162684i	−0.559631	+	0.828742i	$0.689057\pi$
$282$	−12.4771	−	2.02772i	−0.742998	−	0.120749i
$283$	−27.8806	−	17.6306i	−1.65733	−	1.04803i	−0.933837	−	0.357699i	$-0.883561\pi$
$283$	−27.8806	−	17.6306i	−1.65733	−	1.04803i	−0.723493	−	0.690332i	$-0.757464\pi$
$284$	−40.3905	+	11.6993i	−2.39674	+	0.694223i
$285$	6.89499	−	9.98911i	0.408424	−	0.591704i
$286$	16.2081	+	35.1310i	0.958405	+	2.07734i
$287$	3.02040	+	4.37580i	0.178288	+	0.258295i
$288$	−25.7375	−	21.0140i	−1.51660	−	1.23826i
$289$	−7.38057	+	9.03956i	−0.434151	+	0.531739i
$290$	8.81711	+	6.62563i	0.517758	+	0.389070i
$291$	8.09341	+	0.982718i	0.474444	+	0.0576080i
$292$	−16.8519	−	50.4777i	−0.986185	−	2.95399i
$293$	−0.150730	−	1.86712i	−0.00880572	−	0.109078i	0.990861	−	0.134885i	$-0.0430666\pi$
$293$	−0.150730	−	1.86712i	−0.00880572	−	0.109078i	−0.999667	+	0.0258068i	$0.991785\pi$
$294$	29.9972	−	33.8599i	1.74947	−	1.97475i
$295$	−13.6766	+	8.64853i	−0.796280	+	0.503537i
$296$	−63.3392	+	26.9863i	−3.68152	+	1.56855i
$297$	2.79368	+	17.1902i	0.162106	+	0.997477i
$298$	−3.79058	+	3.35816i	−0.219582	+	0.194533i
$299$	−13.0522	−	1.19547i	−0.754827	−	0.0691360i
$300$	−71.4053	−	63.2596i	−4.12259	−	3.65229i
$301$	−2.39933	+	3.79423i	−0.138295	+	0.218696i
$302$	−10.3098	−	0.832296i	−0.593265	−	0.0478933i
$303$	9.35201	+	45.8092i	0.537259	+	2.63167i
$304$	2.42117	+	9.82307i	0.138864	+	0.563392i
$305$	4.27971	−	26.3341i	0.245055	−	1.50789i
$306$	33.2946	+	52.6512i	1.90333	+	3.00987i
$307$	−3.60740	−	6.87333i	−0.205885	−	0.392282i	0.760516	−	0.649319i	$-0.224946\pi$
$307$	−3.60740	−	6.87333i	−0.205885	−	0.392282i	−0.966401	+	0.257037i	$0.917254\pi$
$308$	−4.11277	+	14.1989i	−0.234347	+	0.809058i
$309$	6.02695	−	29.5220i	0.342861	−	1.67945i
$310$	−31.6528	+	1.27557i	−1.79776	+	0.0724473i
$311$	8.84769	−	4.64362i	0.501706	−	0.263316i	−0.194830	−	0.980837i	$-0.562416\pi$
$311$	8.84769	−	4.64362i	0.501706	−	0.263316i	0.696537	+	0.717521i	$0.254723\pi$
$312$	58.0441	−	32.6824i	3.28610	−	1.85028i
$313$	15.3596	+	8.06135i	0.868177	+	0.455654i	0.839135	−	0.543924i	$-0.183062\pi$
$313$	15.3596	+	8.06135i	0.868177	+	0.455654i	0.0290421	+	0.999578i	$0.490754\pi$
$314$	41.5388	+	19.7104i	2.34417	+	1.11232i
$315$	−6.14249	−	10.6391i	−0.346090	−	0.599445i
$316$	4.57823	−	7.92972i	0.257545	−	0.446082i
$317$	24.3963	−	16.8395i	1.37023	−	0.945803i	0.370376	−	0.928882i	$-0.379229\pi$
$317$	24.3963	−	16.8395i	1.37023	−	0.945803i	0.999857	−	0.0169210i	$-0.00538639\pi$
$318$	−3.27806	+	4.36230i	−0.183824	+	0.244626i
$319$	4.37466	+	2.52571i	0.244934	+	0.141413i
$320$	9.54506	−	1.15898i	0.533585	−	0.0647890i
$321$	−1.18134	−	2.48961i	−0.0659357	−	0.138957i
$322$	−4.97134	−	5.17572i	−0.277042	−	0.288431i
$323$	0.538630	−	6.67213i	0.0299702	−	0.371247i
$324$	−9.48556	+	2.33798i	−0.526976	+	0.129888i
$325$	24.1785	−	12.3592i	1.34118	−	0.685565i
$326$	−7.12747	−	1.75676i	−0.394754	−	0.0972981i
$327$	5.65099	−	16.9268i	0.312500	−	0.936053i
$328$	20.0082	−	42.1664i	1.10477	−	2.32825i
$329$	1.30403	−	0.435348i	0.0718933	−	0.0240015i
$330$	−85.7410	−	59.1827i	−4.71989	−	3.25790i
$331$	−13.2647	+	6.29417i	−0.729092	+	0.345959i	−0.756790	−	0.653658i	$-0.773234\pi$
$331$	−13.2647	+	6.29417i	−0.729092	+	0.345959i	0.0276979	+	0.999616i	$0.491182\pi$
$332$	9.51368	+	0.383388i	0.522131	+	0.0210412i
$333$	11.0617	−	44.8791i	0.606178	−	2.45936i
$334$	−15.3019	−	6.51952i	−0.837282	−	0.356732i
$335$	28.7607	−	4.67407i	1.57137	−	0.255372i
$336$	16.6884	+	3.40696i	0.910427	+	0.185865i
$337$	2.02607			0.110367			0.0551836	−	0.998476i	$-0.482426\pi$
$337$	2.02607			0.110367			0.0551836	+	0.998476i	$0.482426\pi$
$338$	4.65168	+	33.1190i	0.253018	+	1.80144i
$339$	13.6579			0.741795
$340$	−85.7695	−	17.5100i	−4.65150	−	0.949611i
$341$	−14.3212	+	2.32742i	−0.775536	+	0.126037i
$342$	−13.3808	−	5.70101i	−0.723549	−	0.308275i
$343$	−2.46291	+	9.99242i	−0.132985	+	0.539540i
$344$	39.3744	+	1.58673i	2.12292	+	0.0855509i
$345$	31.8862	−	15.1302i	1.71670	−	0.814583i
$346$	8.00779	+	5.52738i	0.430502	+	0.297154i
$347$	22.7260	−	7.58704i	1.21999	−	0.407294i	0.367496	−	0.930025i	$-0.380215\pi$
$347$	22.7260	−	7.58704i	1.21999	−	0.407294i	0.852498	+	0.522731i	$0.175087\pi$
$348$	6.57626	−	13.8592i	0.352524	−	0.742930i
$349$	−10.0739	+	30.1750i	−0.539242	+	1.61523i	0.227853	+	0.973695i	$0.426829\pi$
$349$	−10.0739	+	30.1750i	−0.539242	+	1.61523i	−0.767096	+	0.641533i	$0.778299\pi$
$350$	14.4360	+	3.55816i	0.771637	+	0.190191i
$351$	−1.97566	+	14.9243i	−0.105453	+	0.796600i
$352$	29.7552	−	7.33399i	1.58595	−	0.390903i
$353$	−0.593543	+	7.35235i	−0.0315911	+	0.391326i	0.961569	+	0.274564i	$0.0885335\pi$
$353$	−0.593543	+	7.35235i	−0.0315911	+	0.391326i	−0.993160	+	0.116762i	$0.962749\pi$
$354$	22.3429	+	23.2614i	1.18751	+	1.23633i
$355$	13.8174	+	29.1196i	0.733353	+	1.54551i
$356$	−42.1495	+	5.11788i	−2.23392	+	0.271247i
$357$	−9.75962	−	5.63472i	−0.516534	−	0.298221i
$358$	−4.07022	+	5.41648i	−0.215118	+	0.286270i
$359$	27.4143	−	18.9227i	1.44687	−	0.998702i	0.452609	−	0.891709i	$-0.350493\pi$
$359$	27.4143	−	18.9227i	1.44687	−	0.998702i	0.994260	−	0.106993i	$-0.0341222\pi$
$360$	−53.9188	+	93.3902i	−2.84177	+	4.92209i
$361$	−8.71856	−	15.1010i	−0.458872	−	0.794789i
$362$	28.5861	+	13.5643i	1.50245	+	0.712923i
$363$	−15.5373	−	8.15463i	−0.815499	−	0.428007i
$364$	−6.94564	+	10.7258i	−0.364050	+	0.562187i
$365$	−36.1177	+	18.9560i	−1.89049	+	0.992203i
$366$	−53.1353	+	2.14128i	−2.77743	+	0.111926i
$367$	1.68062	−	8.23224i	0.0877279	−	0.429720i	−0.912078	−	0.410017i	$-0.865523\pi$
$367$	1.68062	−	8.23224i	0.0877279	−	0.429720i	0.999806	−	0.0197028i	$-0.00627201\pi$
$368$	−8.18468	+	28.2568i	−0.426656	+	1.47299i
$369$	14.5617	+	27.7451i	0.758054	+	1.44435i
$370$	49.7483	+	78.6707i	2.58629	+	4.08989i
$371$	0.0951968	−	0.585770i	0.00494237	−	0.0304116i
$372$	10.5446	+	42.7812i	0.546712	+	2.21810i
$373$	−1.58620	−	7.76973i	−0.0821304	−	0.402301i	−0.999985	−	0.00538569i	$-0.998286\pi$
$373$	−1.58620	−	7.76973i	−0.0821304	−	0.402301i	0.917855	−	0.396916i	$-0.129919\pi$
$374$	−57.2698	−	4.62330i	−2.96135	−	0.239065i
$375$	−13.1348	+	20.7711i	−0.678280	+	1.07261i
$376$	−9.03289	−	8.00244i	−0.465836	−	0.412694i
$377$	2.99068	+	3.18160i	0.154028	+	0.163861i
$378$	−6.16994	+	5.46609i	−0.317347	+	0.281145i
$379$	−0.299568	−	1.84332i	−0.0153878	−	0.0946847i	0.978220	−	0.207569i	$-0.0665552\pi$
$379$	−0.299568	−	1.84332i	−0.0153878	−	0.0946847i	−0.993608	+	0.112884i	$0.963991\pi$
$380$	18.8030	−	8.01120i	0.964572	−	0.410966i
$381$	48.5956	−	30.7300i	2.48963	−	1.57434i
$382$	−10.2513	+	11.5713i	−0.524502	+	0.592040i
$383$	0.273390	+	3.38655i	0.0139696	+	0.173044i	0.999980	+	0.00635939i	$0.00202427\pi$
$383$	0.273390	+	3.38655i	0.0139696	+	0.173044i	−0.986010	+	0.166685i	$0.946694\pi$
$384$	6.69341	+	20.0492i	0.341572	+	1.02313i
$385$	11.2481	+	1.36576i	0.573255	+	0.0696058i
$386$	40.0489	+	30.0948i	2.03844	+	1.53179i
$387$	−16.7319	+	20.4929i	−0.850531	+	1.04171i
$388$	10.6341	+	8.68251i	0.539867	+	0.440788i
$389$	4.45485	+	6.45397i	0.225870	+	0.327229i	0.919491	−	0.393111i	$-0.128601\pi$
$389$	4.45485	+	6.45397i	0.225870	+	0.327229i	−0.693621	+	0.720340i	$0.743986\pi$
$390$	−56.2011	−	70.3693i	−2.84585	−	3.56329i
$391$	11.0570	−	16.0188i	0.559175	−	0.810105i
$392$	41.4809	−	12.0151i	2.09510	−	0.606854i
$393$	−34.1609	−	21.6020i	−1.72319	−	1.08968i
$394$	35.6115	+	5.78743i	1.79408	+	0.291566i
$395$	−6.56226	−	2.48874i	−0.330183	−	0.125222i
$396$	−34.1469	+	80.1458i	−1.71595	+	4.02748i
$397$	−15.7582	−	15.1360i	−0.790881	−	0.759652i	0.183869	−	0.982951i	$-0.441138\pi$
$397$	−15.7582	−	15.1360i	−0.790881	−	0.759652i	−0.974750	+	0.223299i	$0.928317\pi$
$398$	6.21553	−	11.8427i	0.311556	−	0.593621i
$399$	2.62265	−	0.211722i	0.131297	−	0.0105994i
$400$	−16.9567	−	58.5415i	−0.847837	−	2.92707i
$401$	5.18459	−	4.97986i	0.258906	−	0.248683i	−0.552021	−	0.833830i	$-0.686143\pi$
$401$	5.18459	−	4.97986i	0.258906	−	0.248683i	0.810927	+	0.585148i	$0.198964\pi$
$402$	−20.5950	−	54.3045i	−1.02718	−	2.70846i
$403$	−12.4335	−	1.64593i	−0.619354	−	0.0819896i
$404$	−27.9175	+	73.6124i	−1.38895	+	3.66235i
$405$	2.93512	+	6.88898i	0.145847	+	0.342316i
$406$	0.0962703	+	2.38892i	0.00477781	+	0.118560i
$407$	26.9623	+	33.0228i	1.33647	+	1.63688i
$408$			98.9233i			4.89743i
$409$	25.0315	−	20.4376i	1.23773	−	1.01058i	0.238508	−	0.971141i	$-0.423342\pi$
$409$	25.0315	−	20.4376i	1.23773	−	1.01058i	0.999222	−	0.0394349i	$-0.0125558\pi$
$410$	−60.6083	−	17.5554i	−2.99323	−	0.867000i
$411$	−10.0403	−	11.3331i	−0.495251	−	0.559023i
$412$	35.1467	−	36.5916i	1.73156	−	1.80274i
$413$	−3.32730	−	1.11082i	−0.163726	−	0.0546597i
$414$	−25.4071	−	33.8107i	−1.24869	−	1.66170i
$415$	−0.879685	−	7.24486i	−0.0431821	−	0.355636i
$416$	26.4562	+	1.35203i	1.29712	+	0.0662888i
$417$	−3.84066	+	31.6307i	−0.188078	+	1.54896i
$418$	11.6176	−	6.70742i	0.568235	−	0.328070i
$419$	−24.9210	+	18.7269i	−1.21747	+	0.914870i	−0.998151	−	0.0607836i	$-0.980640\pi$
$419$	−24.9210	+	18.7269i	−1.21747	+	0.914870i	−0.219319	+	0.975653i	$0.570384\pi$
$420$	1.38552	−	34.3814i	0.0676066	−	1.67764i
$421$	32.8418	−	12.4553i	1.60061	−	0.607033i	0.616942	−	0.787008i	$-0.288371\pi$
$421$	32.8418	−	12.4553i	1.60061	−	0.607033i	0.983671	+	0.179976i	$0.0576020\pi$
$422$	−43.0997	+	8.79887i	−2.09806	+	0.428322i
$423$	7.93813	−	1.62058i	0.385965	−	0.0787953i
$424$	−4.87083	+	1.84726i	−0.236548	+	0.0897110i
$425$	−1.62374	+	40.2927i	−0.0787630	+	1.95448i
$426$	51.3600	−	38.5945i	2.48840	−	1.86991i
$427$	5.00870	−	2.89178i	0.242388	−	0.139943i
$428$	0.559319	−	4.60640i	0.0270357	−	0.222659i
$429$	−29.4379	−	28.8922i	−1.42127	−	1.39493i
$430$	−6.42169	−	52.8874i	−0.309681	−	2.55045i
$431$	−15.3617	−	20.4427i	−0.739946	−	0.984689i	−0.999819	−	0.0190465i	$-0.993937\pi$
$431$	−15.3617	−	20.4427i	−0.739946	−	0.984689i	0.259872	−	0.965643i	$-0.416319\pi$
$432$	32.0509	+	10.7002i	1.54205	+	0.514812i
$433$	−25.6862	+	26.7421i	−1.23440	+	1.28514i	−0.289733	+	0.957107i	$0.593567\pi$
$433$	−25.6862	+	26.7421i	−1.23440	+	1.28514i	−0.944665	+	0.328037i	$0.893613\pi$
$434$	−4.55381	−	5.14018i	−0.218590	−	0.246737i
$435$	−11.2939	−	3.27133i	−0.541503	−	0.156848i
$436$	23.2763	−	19.0045i	1.11473	−	0.910149i
$437$			4.54451i			0.217393i
$438$	51.4200	+	62.9780i	2.45694	+	3.00921i
$439$	0.996050	+	24.7167i	0.0475389	+	1.17966i	0.830291	+	0.557331i	$0.188174\pi$
$439$	0.996050	+	24.7167i	0.0475389	+	1.17966i	−0.782752	+	0.622334i	$0.786185\pi$
$440$	−38.9854	−	91.5021i	−1.85856	−	4.36219i
$441$	−10.2812	+	27.1093i	−0.489581	+	1.29092i
$442$	−46.2461	−	18.1116i	−2.19970	−	0.861481i
$443$	−9.04353	−	23.8458i	−0.429671	−	1.13295i	−0.958718	−	0.284357i	$-0.908220\pi$
$443$	−9.04353	−	23.8458i	−0.429671	−	1.13295i	0.529047	−	0.848592i	$-0.322549\pi$
$444$	93.3705	−	89.6836i	4.43117	−	4.25620i
$445$	9.05445	+	31.2596i	0.429222	+	1.48185i
$446$	34.6927	−	2.80068i	1.64275	−	0.132616i
$447$	2.50901	−	4.78053i	0.118672	−	0.226111i
$448$	1.50324	+	1.44389i	0.0710216	+	0.0682172i
$449$	12.6648	−	29.7254i	0.597689	−	1.40283i	−0.296455	−	0.955047i	$-0.595805\pi$
$449$	12.6648	−	29.7254i	0.597689	−	1.40283i	0.894144	−	0.447780i	$-0.147785\pi$
$450$	81.9268	+	31.0707i	3.86206	+	1.46469i
$451$	−28.5260	−	4.63593i	−1.34324	−	0.218297i
$452$	19.4380	+	12.2918i	0.914285	+	0.578159i
$453$	10.5918	−	3.06795i	0.497646	−	0.144145i
$454$	−6.21438	+	9.00308i	−0.291655	+	0.422536i
$455$	8.96879	+	3.93604i	0.420463	+	0.184525i
$456$	−13.1203	−	19.0081i	−0.614417	−	0.890136i
$457$	−17.4931	−	14.2826i	−0.818291	−	0.668114i	0.127877	−	0.991790i	$-0.459184\pi$
$457$	−17.4931	−	14.2826i	−0.818291	−	0.668114i	−0.946168	+	0.323676i	$0.895081\pi$
$458$	15.5414	−	19.0348i	0.726202	−	0.889436i
$459$	−17.8729	−	13.4306i	−0.834235	−	0.626887i
$460$	58.9975	+	7.16359i	2.75077	+	0.334004i
$461$	−9.57524	−	28.6814i	−0.445964	−	1.33582i	−0.896491	−	0.443061i	$-0.853892\pi$
$461$	−9.57524	−	28.6814i	−0.445964	−	1.33582i	0.450528	−	0.892762i	$-0.351236\pi$
$462$	−1.81731	−	22.5114i	−0.0845488	−	1.04732i
$463$	−26.2797	+	29.6637i	−1.22132	+	1.37859i	−0.318871	+	0.947798i	$0.603304\pi$
$463$	−26.2797	+	29.6637i	−1.22132	+	1.37859i	−0.902452	+	0.430790i	$0.858235\pi$
$464$	8.28348	−	5.23815i	0.384551	−	0.243175i
$465$	31.0702	−	13.2378i	1.44085	−	0.613888i
$466$	−2.98493	−	18.3670i	−0.138274	−	0.850835i
$467$	−20.2147	+	17.9087i	−0.935424	+	0.828714i	−0.985438	−	0.170035i	$-0.945612\pi$
$467$	−20.2147	+	17.9087i	−0.935424	+	0.828714i	0.0500137	+	0.998749i	$0.484074\pi$
$468$	−48.2528	+	57.8150i	−2.23049	+	2.67250i
$469$	4.72796	+	4.18861i	0.218317	+	0.193412i
$470$	−8.71992	+	13.7894i	−0.402220	+	0.636060i
$471$	−48.8585	−	3.94427i	−2.25128	−	0.181742i
$472$	6.15914	+	30.1695i	0.283497	+	1.38866i
$473$	−5.83950	−	23.6918i	−0.268501	−	1.08935i
$474$	−2.24401	+	13.8080i	−0.103071	+	0.634221i
$475$	−5.03208	−	7.95760i	−0.230888	−	0.365120i
$476$	−8.81880	−	16.8028i	−0.404209	−	0.770156i
$477$	0.973027	−	3.35928i	0.0445518	−	0.153811i
$478$	−11.3371	+	55.5327i	−0.518546	+	2.54001i
$479$	18.0473	−	0.727282i	0.824603	−	0.0332304i	0.375624	−	0.926772i	$-0.377429\pi$
$479$	18.0473	−	0.727282i	0.824603	−	0.0332304i	0.448980	+	0.893542i	$0.351788\pi$
$480$	−63.1629	+	33.1505i	−2.88298	+	1.51310i
$481$	14.0782	+	34.0566i	0.641911	+	1.55285i
$482$	−48.9117	−	25.6708i	−2.22787	−	1.16927i
$483$	6.91224	+	3.27990i	0.314518	+	0.149241i
$484$	−14.7738	−	25.5890i	−0.671537	−	1.16314i
$485$	5.26138	−	9.11297i	0.238907	−	0.413799i
$486$	38.8041	−	26.7846i	1.76019	−	1.21497i
$487$	−4.18259	+	5.56601i	−0.189531	+	0.252220i	−0.884199	−	0.467111i	$-0.845295\pi$
$487$	−4.18259	+	5.56601i	−0.189531	+	0.252220i	0.694668	+	0.719331i	$0.255551\pi$
$488$	−43.9665	−	25.3841i	−1.99027	−	1.14908i
$489$	7.76900	−	0.943327i	0.351326	−	0.0426587i
$490$	−25.0295	−	52.7486i	−1.13072	−	2.38294i
$491$	11.1397	+	11.5976i	0.502727	+	0.523394i	0.923411	−	0.383813i	$-0.125389\pi$
$491$	11.1397	+	11.5976i	0.502727	+	0.523394i	−0.420684	+	0.907207i	$0.638210\pi$
$492$	−7.06214	+	87.4803i	−0.318386	+	3.94392i
$493$	−6.29611	+	1.55185i	−0.283563	+	0.0698919i
$494$	11.2883	−	2.65354i	0.507886	−	0.119389i
$495$	64.8340	+	15.9801i	2.91407	+	0.718254i
$496$	−8.91433	+	26.7017i	−0.400265	+	1.19894i
$497$	−2.99532	+	6.31249i	−0.134358	+	0.283154i
$498$	−13.7981	+	4.60647i	−0.618306	+	0.206421i
$499$	20.7684	+	14.3354i	0.929720	+	0.641739i	0.933624	−	0.358253i	$-0.116628\pi$
$499$	20.7684	+	14.3354i	0.929720	+	0.641739i	−0.00390473	+	0.999992i	$0.501243\pi$
$500$	−37.3871	+	17.7404i	−1.67200	+	0.793375i
$501$	17.7180	+	0.714012i	0.791583	+	0.0318997i
$502$	−2.68307	+	10.8857i	−0.119751	+	0.485850i
$503$	8.12350	+	3.46110i	0.362209	+	0.154323i	0.565401	−	0.824816i	$-0.308721\pi$
$503$	8.12350	+	3.46110i	0.362209	+	0.154323i	−0.203192	+	0.979139i	$0.565132\pi$
$504$	−23.0741	+	3.74991i	−1.02780	+	0.167034i
$505$	59.1251	+	12.0705i	2.63103	+	0.537130i
$506$	39.0075			1.73410
$507$	−17.1575	−	31.2554i	−0.761990	−	1.38810i
$508$	96.8178			4.29559
$509$	27.4987	+	5.61391i	1.21886	+	0.248832i	0.766053	−	0.642777i	$-0.222218\pi$
$509$	27.4987	+	5.61391i	1.21886	+	0.248832i	0.452806	+	0.891609i	$0.350423\pi$
$510$	132.009	−	21.4535i	5.84544	−	0.949976i
$511$	−8.13479	−	3.46591i	−0.359862	−	0.153323i
$512$	−11.8623	+	48.1274i	−0.524246	+	2.12695i
$513$	5.21560	+	0.210181i	0.230274	+	0.00927973i
$514$	4.35957	−	2.06864i	0.192292	−	0.0912439i
$515$	−32.0054	−	22.0917i	−1.41033	−	0.973477i
$516$	−70.2875	+	23.4654i	−3.09423	+	1.03301i
$517$	−3.20342	+	6.75106i	−0.140886	+	0.296911i
$518$	−6.38967	+	19.1394i	−0.280746	+	0.840936i
$519$	−10.0720	−	2.48253i	−0.442112	−	0.108971i
$520$	−9.44232	−	85.4559i	−0.414073	−	3.74749i
$521$	1.80455	−	0.444780i	0.0790586	−	0.0194862i	−0.199588	−	0.979880i	$-0.563960\pi$
$521$	1.80455	−	0.444780i	0.0790586	−	0.0194862i	0.278647	+	0.960394i	$0.410114\pi$
$522$	−1.13376	+	14.0442i	−0.0496235	+	0.614697i
$523$	7.78777	+	8.10793i	0.340535	+	0.354535i	0.869345	−	0.494206i	$-0.164541\pi$
$523$	7.78777	+	8.10793i	0.340535	+	0.354535i	−0.528810	+	0.848740i	$0.677361\pi$
$524$	−29.1765	−	61.4882i	−1.27458	−	2.68613i
$525$	−15.7354	+	1.91062i	−0.686748	+	0.0833863i
$526$	−31.1795	−	18.0015i	−1.35949	−	0.784902i
$527$	11.1891	−	14.8899i	0.487403	−	0.648616i
$528$	−76.1918	+	52.5914i	−3.31582	+	2.28875i
$529$	4.89276	−	8.47450i	0.212728	−	0.368457i
$530$	3.52142	+	6.09928i	0.152961	+	0.264936i
$531$	−18.6765	−	8.86210i	−0.810490	−	0.384582i
$532$	3.92311	+	2.05901i	0.170089	+	0.0892694i
$533$	−22.4531	−	10.9523i	−0.972553	−	0.474397i
$534$	57.4382	−	30.1459i	2.48559	−	1.30454i
$535$	−3.55381	+	0.143214i	−0.153645	+	0.00619167i
$536$	11.0907	−	54.3257i	0.479044	−	2.34651i
$537$	2.00963	−	6.93803i	0.0867217	−	0.299398i
$538$	−13.2676	−	25.2793i	−0.572007	−	1.08987i
$539$	−14.2923	−	22.6014i	−0.615612	−	0.973513i
$540$	10.9500	−	67.3783i	0.471215	−	2.89950i
$541$	7.61264	+	30.8857i	0.327293	+	1.32788i	0.872104	+	0.489321i	$0.162755\pi$
$541$	7.61264	+	30.8857i	0.327293	+	1.32788i	−0.544811	+	0.838559i	$0.683398\pi$
$542$	13.5847	+	66.5424i	0.583514	+	2.85824i
$543$	−33.6234	−	2.71436i	−1.44292	−	0.116484i
$544$	−21.0259	+	33.2498i	−0.901478	+	1.42557i
$545$	−17.2400	−	15.2733i	−0.738482	−	0.654238i
$546$	4.11105	−	19.0848i	0.175937	−	0.816754i
$547$	23.5644	−	20.8763i	1.00754	−	0.892604i	0.0133159	−	0.999911i	$-0.495761\pi$
$547$	23.5644	−	20.8763i	1.00754	−	0.892604i	0.994226	+	0.107307i	$0.0342228\pi$
$548$	−4.08978	−	25.1654i	−0.174707	−	1.07501i
$549$	31.3564	−	13.3597i	1.33826	−	0.570178i
$550$	−68.3036	+	43.1926i	−2.91247	+	1.84174i
$551$	1.00397	−	1.13325i	0.0427707	−	0.0482781i
$552$	−5.40414	−	66.9423i	−0.230015	−	2.84925i
$553$	−0.481786	−	1.44313i	−0.0204876	−	0.0613679i
$554$	56.8865	+	6.90727i	2.41687	+	0.293462i
$555$	−79.3318	−	59.6139i	−3.36745	−	2.53047i
$556$	−33.9330	+	41.5604i	−1.43908	+	1.76255i
$557$	4.85709	+	3.96569i	0.205802	+	0.168032i	0.729741	−	0.683724i	$-0.239641\pi$
$557$	4.85709	+	3.96569i	0.205802	+	0.168032i	−0.523939	+	0.851756i	$0.675538\pi$
$558$	−22.9896	−	33.3062i	−0.973227	−	1.40996i
$559$	1.07652	−	21.0651i	0.0455320	−	0.890957i
$560$	12.4882	−	18.0923i	0.527722	−	0.764537i
$561$	58.8360	−	17.0421i	2.48406	−	0.719516i
$562$	16.7219	+	10.5743i	0.705369	+	0.446048i
$563$	−17.4600	−	2.83753i	−0.735852	−	0.119588i	−0.219075	−	0.975708i	$-0.570304\pi$
$563$	−17.4600	−	2.83753i	−0.735852	−	0.119588i	−0.516776	+	0.856120i	$0.672868\pi$
$564$	21.2181	+	8.04695i	0.893442	+	0.338838i
$565$	6.90960	−	16.2174i	0.290689	−	0.682272i
$566$	61.2041	+	58.7874i	2.57260	+	2.47102i
$567$	−0.754374	+	1.43734i	−0.0316807	+	0.0603626i
$568$	61.1339	−	4.93524i	2.56512	−	0.207078i
$569$	1.09472	+	3.77940i	0.0458929	+	0.158441i	0.980192	−	0.198049i	$-0.0634606\pi$
$569$	1.09472	+	3.77940i	0.0458929	+	0.158441i	−0.934299	+	0.356490i	$0.883973\pi$
$570$	−22.5200	+	21.6308i	−0.943260	+	0.906013i
$571$	11.6761	+	30.7874i	0.488631	+	1.28841i	0.921998	+	0.387195i	$0.126556\pi$
$571$	11.6761	+	30.7874i	0.488631	+	1.28841i	−0.433367	+	0.901217i	$0.642675\pi$
$572$	−15.8937	−	67.6129i	−0.664550	−	2.82704i
$573$	5.84428	−	15.4101i	0.244148	−	0.643766i
$574$	−5.36156	−	12.5840i	−0.223787	−	0.525248i
$575$	−1.10237	−	27.3551i	−0.0459721	−	1.14079i
$576$	7.76870	+	9.51492i	0.323696	+	0.396455i
$577$			36.6277i			1.52483i	0.647088	+	0.762416i	$0.275987\pi$
$577$			36.6277i			1.52483i	−0.647088	+	0.762416i	$0.724013\pi$
$578$	23.2554	−	18.9874i	0.967296	−	0.789772i
$579$	−51.2992	−	14.8590i	−2.13192	−	0.617518i
$580$	−13.1294	−	14.8201i	−0.545171	−	0.615371i
$581$	1.09593	−	1.14099i	0.0454670	−	0.0473361i
$582$	−19.8948	−	6.64186i	−0.824666	−	0.275314i
$583$	1.93781	+	2.57876i	0.0802558	+	0.106801i
$584$	9.35586	+	77.0525i	0.387148	+	3.18845i
$585$	49.6737	+	29.3978i	2.05376	+	1.21545i
$586$	−0.580869	+	4.78389i	−0.0239955	+	0.197621i
$587$	−28.5762	+	16.4985i	−1.17946	+	0.680964i	−0.955891	−	0.293723i	$-0.905106\pi$
$587$	−28.5762	+	16.4985i	−1.17946	+	0.680964i	−0.223574	+	0.974687i	$0.571772\pi$
$588$	−64.9215	+	48.7853i	−2.67732	+	2.01187i
$589$	−0.175102	+	4.34512i	−0.00721497	+	0.179038i
$590$	38.9240	−	14.7619i	1.60248	−	0.607739i
$591$	−37.6864	+	7.69374i	−1.55021	+	0.316478i
$592$	81.0422	−	16.5449i	3.33082	−	0.679991i
$593$	−2.47533	+	0.938767i	−0.101649	+	0.0385505i	−0.404905	−	0.914359i	$-0.632696\pi$
$593$	−2.47533	+	0.938767i	−0.101649	+	0.0385505i	0.303256	+	0.952909i	$0.401926\pi$
$594$	1.80408	−	44.7678i	0.0740223	−	1.83684i
$595$	−11.6281	+	8.73797i	−0.476706	+	0.358222i
$596$	7.87321	−	4.54560i	0.322499	−	0.186195i
$597$	−1.71872	+	14.1549i	−0.0703424	+	0.579322i
$598$	32.2845	+	9.72987i	1.32021	+	0.397884i
$599$	1.68642	+	13.8889i	0.0689051	+	0.567484i	0.985747	+	0.168234i	$0.0538065\pi$
$599$	1.68642	+	13.8889i	0.0689051	+	0.567484i	−0.916842	+	0.399250i	$0.869270\pi$
$600$	83.5872	+	111.234i	3.41243	+	4.54112i
$601$	−7.48676	−	2.49945i	−0.305391	−	0.101955i	0.159842	−	0.987143i	$-0.448901\pi$
$601$	−7.48676	−	2.49945i	−0.305391	−	0.101955i	−0.465233	+	0.885188i	$0.654030\pi$
$602$	8.00029	−	8.32919i	0.326068	−	0.339472i
$603$	24.6844	+	27.8629i	1.00523	+	1.13467i
$604$	17.8354	+	5.16608i	0.725711	+	0.210205i
$605$	−17.5432	+	14.3236i	−0.713234	+	0.582337i
$606$		−	120.280i		−	4.88606i
$607$	4.99788	+	6.12129i	0.202858	+	0.248455i	0.866007	−	0.500031i	$-0.166678\pi$
$607$	4.99788	+	6.12129i	0.202858	+	0.248455i	−0.663150	+	0.748487i	$0.730781\pi$
$608$	−0.369846	−	9.17764i	−0.0149992	−	0.372202i
$609$	−0.999090	−	2.34495i	−0.0404852	−	0.0950222i
$610$	−24.3388	+	64.1762i	−0.985450	+	2.59842i
$611$	−4.33525	+	4.78845i	−0.175386	+	0.193720i
$612$	−39.6563	−	104.565i	−1.60301	−	4.22680i
$613$	−25.6787	+	24.6647i	−1.03715	+	0.996199i	−0.999995	−	0.00311075i	$-0.999010\pi$
$613$	−25.6787	+	24.6647i	−1.03715	+	0.996199i	−0.0371575	+	0.999309i	$0.511830\pi$
$614$	5.55598	+	19.1815i	0.224221	+	0.774101i
$615$	67.0529	−	5.41307i	2.70383	−	0.218276i
$616$	10.0199	−	19.0913i	0.403713	−	0.769210i
$617$	17.2310	+	16.5506i	0.693695	+	0.666304i	0.954200	−	0.299169i	$-0.0967095\pi$
$617$	17.2310	+	16.5506i	0.693695	+	0.666304i	−0.260505	+	0.965473i	$0.583889\pi$
$618$	−30.3834	+	71.3125i	−1.22220	+	2.86861i
$619$	32.2977	+	12.2489i	1.29816	+	0.492326i	0.904320	−	0.426855i	$-0.140379\pi$
$619$	32.2977	+	12.2489i	1.29816	+	0.492326i	0.393836	+	0.919181i	$0.371148\pi$
$620$	56.1330	+	9.12250i	2.25436	+	0.366368i
$621$	12.8284	+	8.11222i	0.514788	+	0.325532i
$622$	−24.6913	+	7.15193i	−0.990032	+	0.286766i
$623$	−4.00766	+	5.80610i	−0.160564	+	0.232617i
$624$	−76.1782	+	24.5222i	−3.04957	+	0.981675i
$625$	−3.37247	−	4.88587i	−0.134899	−	0.195435i
$626$	−34.5676	−	28.2236i	−1.38160	−	1.12804i
$627$	−9.04502	+	11.0781i	−0.361223	+	0.442418i
$628$	−65.9858	−	49.5851i	−2.63312	−	1.97866i
$629$	−54.3276	−	6.59657i	−2.16618	−	0.263022i
$630$	10.0082	+	29.9781i	0.398735	+	1.19436i
$631$	−0.00175556	−	0.0217465i	−6.98879e−5	−	0.000865716i	0.996722	−	0.0808994i	$-0.0257793\pi$
$631$	−0.00175556	−	0.0217465i	−6.98879e−5	−	0.000865716i	−0.996792	+	0.0800337i	$0.974497\pi$
$632$	−8.85605	+	9.99642i	−0.352275	+	0.397636i
$633$	39.6366	−	25.0647i	1.57541	−	0.996232i
$634$	−70.1595	+	29.8922i	−2.78639	+	1.18717i
$635$	−11.9041	−	73.2489i	−0.472400	−	2.90680i
$636$	7.33230	−	6.49585i	0.290744	−	0.257577i
$637$	−6.19138	−	22.2710i	−0.245311	−	0.882411i
$638$	−9.72719	−	8.61754i	−0.385103	−	0.341172i
$639$	−22.0074	+	34.8020i	−0.870601	+	1.37674i
$640$	27.1927	+	2.19522i	1.07489	+	0.0867738i
$641$	−5.34113	−	26.1626i	−0.210962	−	1.03336i	−0.937966	−	0.346727i	$-0.887293\pi$
$641$	−5.34113	−	26.1626i	−0.210962	−	1.03336i	0.727004	−	0.686633i	$-0.240912\pi$
$642$	1.69658	+	6.88330i	0.0669587	+	0.271662i
$643$	0.517267	−	3.18287i	0.0203990	−	0.125520i	−0.974853	−	0.222847i	$-0.928465\pi$
$643$	0.517267	−	3.18287i	0.0203990	−	0.125520i	0.995253	+	0.0973265i	$0.0310291\pi$
$644$	6.88569	+	10.8888i	0.271334	+	0.429080i
$645$	26.3952	+	50.2919i	1.03931	+	1.98024i
$646$	−4.79110	+	16.5408i	−0.188503	+	0.650789i
$647$	4.66339	−	22.8428i	0.183337	−	0.898044i	−0.779175	−	0.626806i	$-0.784362\pi$
$647$	4.66339	−	22.8428i	0.183337	−	0.898044i	0.962512	−	0.271238i	$-0.0874330\pi$
$648$	14.2376	−	0.573755i	0.559305	−	0.0225392i
$649$	16.8826	−	8.86069i	0.662701	−	0.347812i
$650$	−67.3051	+	18.7109i	−2.63992	+	0.733902i
$651$	6.48259	+	3.40233i	0.254073	+	0.133348i
$652$	11.9058	+	5.64939i	0.466269	+	0.221247i
$653$	18.3075	+	31.7094i	0.716426	+	1.24089i	0.962407	+	0.271612i	$0.0875567\pi$
$653$	18.3075	+	31.7094i	0.716426	+	1.24089i	−0.245981	+	0.969275i	$0.579110\pi$
$654$	−22.9544	+	39.7582i	−0.897588	+	1.55467i
$655$	−42.9325	+	29.6342i	−1.67751	+	1.15790i
$656$	−33.6848	+	44.8264i	−1.31517	+	1.75018i
$657$	−45.1286	−	26.0550i	−1.76063	−	1.01650i
$658$	−3.51099	+	0.426312i	−0.136873	+	0.0166194i
$659$	11.1736	+	23.5478i	0.435261	+	0.917294i	0.996004	+	0.0893040i	$0.0284643\pi$
$659$	11.1736	+	23.5478i	0.435261	+	0.917294i	−0.560743	+	0.827990i	$0.689484\pi$
$660$	129.560	+	134.886i	5.04312	+	5.25045i
$661$	0.496974	−	6.15613i	0.0193301	−	0.239446i	−0.979876	−	0.199607i	$-0.936033\pi$
$661$	0.496974	−	6.15613i	0.0193301	−	0.239446i	0.999206	−	0.0398389i	$-0.0126845\pi$
$662$	36.6743	−	9.03939i	1.42539	−	0.351326i
$663$	52.9464	+	0.570962i	2.05627	+	0.0221743i
$664$	−13.4838	−	3.32347i	−0.523274	−	0.128975i
$665$	1.07541	−	3.22125i	0.0417027	−	0.124915i
$666$	−50.9768	+	107.431i	−1.97531	+	4.16288i
$667$	4.17585	−	1.39411i	0.161690	−	0.0539800i
$668$	24.5738	+	16.9620i	0.950788	+	0.656281i
$669$	−33.5239	+	15.9073i	−1.29611	+	0.615011i
$670$	−74.9004	−	3.01838i	−2.89365	−	0.116610i
$671$	−7.52317	+	30.5227i	−0.290429	+	1.17832i
$672$	−14.2262	−	6.06122i	−0.548788	−	0.233817i
$673$	18.9154	−	3.07406i	0.729137	−	0.118496i	0.215500	−	0.976504i	$-0.430862\pi$
$673$	18.9154	−	3.07406i	0.729137	−	0.118496i	0.513637	+	0.858008i	$0.328298\pi$
$674$	−5.10698	−	1.04260i	−0.196713	−	0.0401593i
$675$	−31.4456			−1.21034
$676$	3.71065	−	59.9242i	0.142717	−	2.30478i
$677$	−23.3100			−0.895877			−0.447939	−	0.894064i	$-0.647842\pi$
$677$	−23.3100			−0.895877			−0.447939	+	0.894064i	$0.647842\pi$
$678$	−34.4265	−	7.02822i	−1.32214	−	0.269917i
$679$	2.25156	−	0.365915i	0.0864071	−	0.0140425i
$680$	117.462	+	50.0458i	4.50445	+	1.91917i
$681$	2.79108	−	11.3239i	0.106954	−	0.433931i
$682$	37.2961	+	1.50298i	1.42814	+	0.0575522i
$683$	−32.1495	+	15.2551i	−1.23017	+	0.583721i	−0.929081	−	0.369877i	$-0.879400\pi$
$683$	−32.1495	+	15.2551i	−1.23017	+	0.583721i	−0.301084	+	0.953598i	$0.597349\pi$
$684$	21.4886	+	14.8325i	0.821637	+	0.567135i
$685$	−18.5364	+	6.18837i	−0.708240	+	0.236445i
$686$	11.3501	−	23.9198i	0.433348	−	0.913262i
$687$	−8.29607	+	24.8498i	−0.316515	+	0.948077i
$688$	−45.9666	−	11.3298i	−1.75246	−	0.431943i
$689$	0.960591	+	2.61766i	0.0365956	+	0.0997249i
$690$	−88.1593	+	21.7293i	−3.35617	+	0.827221i
$691$	−2.90979	+	36.0442i	−0.110693	+	1.37118i	0.668178	+	0.744001i	$0.267074\pi$
$691$	−2.90979	+	36.0442i	−0.110693	+	1.37118i	−0.778872	+	0.627183i	$0.784208\pi$
$692$	−12.1003	−	12.5977i	−0.459984	−	0.478894i
$693$	6.20542	+	13.0776i	0.235724	+	0.496778i
$694$	−61.1880	+	7.42957i	−2.32266	+	0.282022i
$695$	35.6153	+	20.5625i	1.35097	+	0.779981i
$696$	−13.4413	+	17.8871i	−0.509490	+	0.678008i
$697$	30.5322	−	21.0749i	1.15649	−	0.798268i
$698$	40.9203	−	70.8760i	1.54885	−	2.68270i
$699$	9.91905	+	17.1803i	0.375173	+	0.649819i
$700$	−24.1142	−	11.4423i	−0.911429	−	0.432479i
$701$	7.95953	+	4.17748i	0.300627	+	0.157781i	0.608292	−	0.793714i	$-0.291855\pi$
$701$	7.95953	+	4.17748i	0.300627	+	0.157781i	−0.307664	+	0.951495i	$0.599547\pi$
$702$	12.6598	−	36.6020i	0.477814	−	1.38145i
$703$	11.3140	−	5.93802i	0.426714	−	0.223957i
$704$	−11.3202	+	0.456190i	−0.426647	+	0.0171933i
$705$	3.47920	−	17.0423i	0.131034	−	0.641848i
$706$	5.27955	−	18.2271i	0.198698	−	0.685987i
$707$	6.07923	+	11.5830i	0.228633	+	0.435624i
$708$	−30.9466	−	48.9381i	−1.16304	−	1.83921i
$709$	0.702804	−	4.32453i	0.0263944	−	0.162411i	−0.970507	−	0.241073i	$-0.922501\pi$
$709$	0.702804	−	4.32453i	0.0263944	−	0.162411i	0.996901	+	0.0786619i	$0.0250648\pi$
$710$	−19.8439	−	80.5101i	−0.744730	−	3.02149i
$711$	−1.79345	−	8.78489i	−0.0672595	−	0.329459i
$712$	61.7275	+	4.98316i	2.31334	+	0.186752i
$713$	−6.75830	+	10.6874i	−0.253100	+	0.400246i
$714$	21.7008	+	19.2253i	0.812133	+	0.719487i
$715$	−49.1994	+	20.3379i	−1.83995	+	0.760594i
$716$	9.10419	−	8.06561i	0.340240	−	0.301426i
$717$	−9.69285	−	59.6425i	−0.361986	−	2.22739i
$718$	−78.8386	+	33.5900i	−2.94223	+	1.25357i
$719$	−4.50799	+	2.85068i	−0.168120	+	0.106312i	−0.615876	−	0.787843i	$-0.711198\pi$
$719$	−4.50799	+	2.85068i	−0.168120	+	0.106312i	0.447756	+	0.894156i	$0.352223\pi$
$720$	85.9109	−	96.9733i	3.20171	−	3.61398i
$721$	−0.678364	−	8.40304i	−0.0252636	−	0.312946i
$722$	14.2054	+	42.5505i	0.528672	+	1.58357i
$723$	58.4613	+	7.09849i	2.17420	+	0.263996i
$724$	−45.4101	−	34.1235i	−1.68765	−	1.26819i
$725$	−5.76839	+	7.06500i	−0.214233	+	0.262387i
$726$	34.9676	+	28.5502i	1.29777	+	1.05960i
$727$	−21.0380	−	30.4788i	−0.780255	−	1.13040i	−0.988337	−	0.152284i	$-0.951337\pi$
$727$	−21.0380	−	30.4788i	−0.780255	−	1.13040i	0.208081	−	0.978112i	$-0.433278\pi$
$728$	13.0550	−	13.3016i	0.483850	−	0.492989i
$729$	−24.9503	+	36.1467i	−0.924085	+	1.33877i
$730$	100.794	−	29.1953i	3.73055	−	1.08057i
$731$	26.4743	+	16.7413i	0.979188	+	0.619201i
$732$	94.2298	+	15.3138i	3.48283	+	0.566016i
$733$	−21.0175	−	7.97090i	−0.776301	−	0.294412i	−0.0655438	−	0.997850i	$-0.520878\pi$
$733$	−21.0175	−	7.97090i	−0.776301	−	0.294412i	−0.710757	+	0.703438i	$0.751647\pi$
$734$	−8.47246	+	19.8856i	−0.312724	+	0.733991i
$735$	44.8916	+	43.1190i	1.65585	+	1.59047i
$736$	12.4120	−	23.6490i	0.457512	−	0.871715i
$737$	−34.2216	+	2.76266i	−1.26057	+	0.101764i
$738$	−22.4274	−	77.4285i	−0.825565	−	2.85018i
$739$	14.2546	−	13.6917i	0.524363	−	0.503657i	−0.383147	−	0.923687i	$-0.625160\pi$
$739$	14.2546	−	13.6917i	0.524363	−	0.503657i	0.907510	+	0.420030i	$0.137980\pi$
$740$	−59.2539	−	156.240i	−2.17822	−	5.74349i
$741$	−10.2494	+	6.91265i	−0.376520	+	0.253943i
$742$	−0.541387	+	1.42752i	−0.0198750	+	0.0524059i
$743$	2.28412	+	5.36103i	0.0837962	+	0.196677i	0.956607	−	0.291382i	$-0.0941152\pi$
$743$	2.28412	+	5.36103i	0.0837962	+	0.196677i	−0.872810	+	0.488059i	$0.837705\pi$
$744$	−2.58771	−	64.2134i	−0.0948701	−	2.35418i
$745$	−4.40709	−	5.39770i	−0.161463	−	0.197756i
$746$			20.4009i			0.746929i
$747$	7.22199	−	5.89657i	0.264239	−	0.215744i
$748$	99.0731	+	28.6969i	3.62247	+	1.04926i
$749$	−0.511277	−	0.577113i	−0.0186817	−	0.0210872i
$750$	43.7967	−	45.5972i	1.59923	−	1.66497i
$751$	8.62844	+	2.88059i	0.314856	+	0.105114i	0.469704	−	0.882824i	$-0.344361\pi$
$751$	8.62844	+	2.88059i	0.314856	+	0.105114i	−0.154848	+	0.987938i	$0.549489\pi$
$752$	8.70964	+	11.5904i	0.317608	+	0.422659i
$753$	−1.44073	−	11.8655i	−0.0525030	−	0.432401i
$754$	−5.90117	−	9.55860i	−0.214908	−	0.348104i
$755$	1.71555	−	14.1288i	0.0624352	−	0.514200i
$756$	12.8153	−	7.39889i	0.466086	−	0.269095i
$757$	40.5390	−	30.4631i	1.47341	−	1.10720i	0.503429	−	0.864036i	$-0.332071\pi$
$757$	40.5390	−	30.4631i	1.47341	−	1.10720i	0.969985	−	0.243163i	$-0.0781849\pi$
$758$	−0.193452	+	4.80047i	−0.00702651	+	0.174361i
$759$	−38.8838	+	14.7467i	−1.41139	+	0.535271i
$760$	−29.2079	+	5.96284i	−1.05948	+	0.216295i
$761$	31.3080	−	6.39158i	1.13492	−	0.231695i	0.404394	−	0.914585i	$-0.367482\pi$
$761$	31.3080	−	6.39158i	1.13492	−	0.231695i	0.730521	+	0.682890i	$0.239277\pi$
$762$	−138.305	+	52.4521i	−5.01026	+	1.90014i
$763$	0.201045	−	4.98888i	0.00727832	−	0.180610i
$764$	22.1864	−	16.6720i	0.802674	−	0.603171i
$765$	−74.2345	+	42.8593i	−2.68395	+	1.54958i
$766$	1.05357	−	8.67692i	0.0380670	−	0.313510i
$767$	16.1830	−

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.k (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.52063 - 0.514590i) q^{2} +(2.70717 - 0.439959i) q^{3} +(4.24882 + 1.81025i) q^{4} +(0.847165 - 3.43708i) q^{5} +(-7.05019 - 0.284113i) q^{6} +(0.693293 - 0.328971i) q^{7} +(-5.54370 - 3.82654i) q^{8} +(4.28962 - 1.43209i) q^{9} +O(q^{10})\)	\(q+(-2.52063 - 0.514590i) q^{2} +(2.70717 - 0.439959i) q^{3} +(4.24882 + 1.81025i) q^{4} +(0.847165 - 3.43708i) q^{5} +(-7.05019 - 0.284113i) q^{6} +(0.693293 - 0.328971i) q^{7} +(-5.54370 - 3.82654i) q^{8} +(4.28962 - 1.43209i) q^{9} +(-3.90408 + 8.22767i) q^{10} +(-1.32084 + 3.95641i) q^{11} +(12.2987 + 3.03136i) q^{12} +(-2.08006 + 2.94505i) q^{13} +(-1.91682 + 0.472454i) q^{14} +(0.781249 - 9.67750i) q^{15} +(5.60600 + 5.83646i) q^{16} +(-2.29540 - 4.83746i) q^{17} +(-11.5495 + 1.40236i) q^{18} +(1.08266 + 0.625075i) q^{19} +(9.82143 - 13.0699i) q^{20} +(1.73213 - 1.19560i) q^{21} +(5.36529 - 9.29296i) q^{22} +(1.81759 + 3.14815i) q^{23} +(-16.6913 - 7.92012i) q^{24} +(-6.66857 - 3.49994i) q^{25} +(6.75857 - 6.35301i) q^{26} +(3.69710 - 1.94039i) q^{27} +(3.54119 - 0.142705i) q^{28} +(0.242243 - 1.18659i) q^{29} +(-6.94919 + 23.9914i) q^{30} +(1.61654 + 3.08006i) q^{31} +(-3.92682 - 6.20977i) q^{32} +(-1.83510 + 11.2918i) q^{33} +(3.29655 + 13.3746i) q^{34} +(-0.543369 - 2.66160i) q^{35} +(20.8183 + 1.68062i) q^{36} +(5.46268 - 8.63854i) q^{37} +(-2.40733 - 2.13271i) q^{38} +(-4.33540 + 8.88791i) q^{39} +(-17.8486 + 15.8125i) q^{40} +(1.11145 + 6.83901i) q^{41} +(-4.98131 + 2.12234i) q^{42} +(-4.94438 + 3.12664i) q^{43} +(-12.7741 + 14.4190i) q^{44} +(-1.28818 - 15.9570i) q^{45} +(-2.96146 - 8.87064i) q^{46} +(1.77845 + 0.215943i) q^{47} +(17.7442 + 13.3339i) q^{48} +(-4.05469 + 4.96609i) q^{49} +(15.0080 + 12.2536i) q^{50} +(-8.34234 - 12.0860i) q^{51} +(-14.1691 + 8.74754i) q^{52} +(0.439312 - 0.636453i) q^{53} +(-10.3175 + 2.98851i) q^{54} +(12.4795 + 7.89159i) q^{55} +(-5.10223 - 0.829193i) q^{56} +(3.20596 + 1.21586i) q^{57} +(-1.22121 + 2.86629i) q^{58} +(-3.29673 - 3.16655i) q^{59} +(20.8381 - 39.7037i) q^{60} +(7.51228 - 0.606454i) q^{61} +(-2.48973 - 8.59556i) q^{62} +(2.50285 - 2.40402i) q^{63} +(0.963174 + 2.53968i) q^{64} +(8.36023 + 9.64430i) q^{65} +(10.4363 - 27.5182i) q^{66} +(3.22636 + 7.57254i) q^{67} +(-0.995728 - 24.7087i) q^{68} +(6.30558 + 7.72294i) q^{69} +6.98852i q^{70} +(-7.05285 + 5.75847i) q^{71} +(-29.2603 - 8.47536i) q^{72} +(-7.64099 - 8.62490i) q^{73} +(-18.2147 + 18.9635i) q^{74} +(-19.5928 - 6.54104i) q^{75} +(3.46848 + 4.61571i) q^{76} +(0.385815 + 3.17747i) q^{77} +(15.5016 - 20.1722i) q^{78} +(0.238977 - 1.96816i) q^{79} +(24.8096 - 14.3238i) q^{80} +(-1.69109 + 1.27077i) q^{81} +(0.717741 - 17.8106i) q^{82} +(1.92766 - 0.731065i) q^{83} +(9.52385 - 1.94431i) q^{84} +(-18.5713 + 3.79137i) q^{85} +(14.0719 - 5.33676i) q^{86} +(0.133746 - 3.31887i) q^{87} +(22.4617 - 16.8789i) q^{88} +(-7.96181 + 4.59675i) q^{89} +(-4.96429 + 40.8846i) q^{90} +(-0.473255 + 2.72607i) q^{91} +(2.02364 + 16.6662i) q^{92} +(5.73136 + 7.62706i) q^{93} +(-4.37169 - 1.45949i) q^{94} +(3.06563 - 3.19165i) q^{95} +(-13.3626 - 15.0833i) q^{96} +(2.85521 + 0.827022i) q^{97} +(12.7759 - 10.4312i) q^{98} +18.8631i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

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