LMFDB - Embedded newform 65.2.t.a.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(7,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 11]))

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

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

chi := DirichletCharacter("65.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.t (of order $12$, degree $4$, 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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.4
Root			$-0.274809i$ of defining polynomial
Character	$\chi$	$=$	65.7
Dual form			65.2.t.a.28.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.237991 - 0.137404i) q^{2} +(0.611610 + 2.28256i) q^{3} +(-0.962240 - 1.66665i) q^{4} +(1.45395 + 1.69883i) q^{5} +(0.168076 - 0.627267i) q^{6} +(-0.193052 - 0.334376i) q^{7} +1.07848i q^{8} +(-2.23793 + 1.29207i) q^{9} +O(q^{10})$	\(q+(-0.237991 - 0.137404i) q^{2} +(0.611610 + 2.28256i) q^{3} +(-0.962240 - 1.66665i) q^{4} +(1.45395 + 1.69883i) q^{5} +(0.168076 - 0.627267i) q^{6} +(-0.193052 - 0.334376i) q^{7} +1.07848i q^{8} +(-2.23793 + 1.29207i) q^{9} +(-0.112600 - 0.604086i) q^{10} +(-1.12873 - 4.21249i) q^{11} +(3.21571 - 3.21571i) q^{12} +(-1.35750 - 3.34024i) q^{13} +0.106105i q^{14} +(-2.98844 + 4.35775i) q^{15} +(-1.77629 + 3.07663i) q^{16} +(1.90527 + 0.510514i) q^{17} +0.710144 q^{18} +(-4.83947 - 1.29673i) q^{19} +(1.43231 - 4.05791i) q^{20} +(0.645159 - 0.645159i) q^{21} +(-0.310185 + 1.15763i) q^{22} +(0.322241 - 0.0863441i) q^{23} +(-2.46170 + 0.659609i) q^{24} +(-0.772064 + 4.94003i) q^{25} +(-0.135891 + 0.981474i) q^{26} +(0.694880 + 0.694880i) q^{27} +(-0.371524 + 0.643499i) q^{28} +(7.07031 + 4.08205i) q^{29} +(1.30999 - 0.626482i) q^{30} +(-2.54187 - 2.54187i) q^{31} +(2.71347 - 1.56662i) q^{32} +(8.92491 - 5.15280i) q^{33} +(-0.383290 - 0.383290i) q^{34} +(0.287361 - 0.814128i) q^{35} +(4.30685 + 2.48656i) q^{36} +(-2.41251 + 4.17859i) q^{37} +(0.973575 + 0.973575i) q^{38} +(6.79403 - 5.14149i) q^{39} +(-1.83216 + 1.56806i) q^{40} +(4.49768 - 1.20515i) q^{41} +(-0.242190 + 0.0648946i) q^{42} +(-1.76471 + 6.58600i) q^{43} +(-5.93462 + 5.93462i) q^{44} +(-5.44885 - 1.92327i) q^{45} +(-0.0885545 - 0.0237281i) q^{46} -9.83310 q^{47} +(-8.10898 - 2.17280i) q^{48} +(3.42546 - 5.93307i) q^{49} +(0.862526 - 1.06960i) q^{50} +4.66112i q^{51} +(-4.26077 + 5.47658i) q^{52} +(-7.17155 + 7.17155i) q^{53} +(-0.0698958 - 0.260855i) q^{54} +(5.51519 - 8.04227i) q^{55} +(0.360618 - 0.208203i) q^{56} -11.8395i q^{57} +(-1.12178 - 1.94298i) q^{58} +(-0.628209 + 2.34451i) q^{59} +(10.1384 + 0.787474i) q^{60} +(-5.32338 - 9.22037i) q^{61} +(0.255679 + 0.954209i) q^{62} +(0.864073 + 0.498873i) q^{63} +6.24413 q^{64} +(3.70078 - 7.16270i) q^{65} -2.83207 q^{66} +(5.52170 + 3.18796i) q^{67} +(-0.982475 - 3.66665i) q^{68} +(0.394171 + 0.682724i) q^{69} +(-0.180254 + 0.154271i) q^{70} +(-1.12684 + 4.20542i) q^{71} +(-1.39347 - 2.41357i) q^{72} -6.08593i q^{73} +(1.14831 - 0.662979i) q^{74} +(-11.7481 + 1.25909i) q^{75} +(2.49554 + 9.31346i) q^{76} +(-1.19065 + 1.19065i) q^{77} +(-2.32338 + 0.290100i) q^{78} -3.34944i q^{79} +(-7.80932 + 1.45564i) q^{80} +(-5.03732 + 8.72489i) q^{81} +(-1.23600 - 0.331185i) q^{82} +5.18834 q^{83} +(-1.69605 - 0.454456i) q^{84} +(1.90288 + 3.97899i) q^{85} +(1.32493 - 1.32493i) q^{86} +(-4.99324 + 18.6350i) q^{87} +(4.54309 - 1.21732i) q^{88} +(4.82829 - 1.29374i) q^{89} +(1.03251 + 1.20642i) q^{90} +(-0.854827 + 1.09875i) q^{91} +(-0.453978 - 0.453978i) q^{92} +(4.24734 - 7.35661i) q^{93} +(2.34019 + 1.35111i) q^{94} +(-4.83341 - 10.1068i) q^{95} +(5.23549 + 5.23549i) q^{96} +(12.7722 - 7.37402i) q^{97} +(-1.63046 + 0.941346i) q^{98} +(7.96886 + 7.96886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9	$ 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9} - 2 q^{10} - 16 q^{11} - 24 q^{12} - 4 q^{13} - 20 q^{15} - 2 q^{16} + 4 q^{17} - 20 q^{19} + 4 q^{21} + 16 q^{22} - 10 q^{23} + 32 q^{24} + 18 q^{25} - 24 q^{26} + 4 q^{27} + 18 q^{28} - 26 q^{30} + 48 q^{32} + 18 q^{33} + 2 q^{34} + 40 q^{35} + 36 q^{36} - 4 q^{37} - 8 q^{38} + 4 q^{39} - 16 q^{40} + 10 q^{41} + 40 q^{42} + 10 q^{43} - 36 q^{44} + 4 q^{46} - 40 q^{47} - 56 q^{48} + 18 q^{49} + 36 q^{50} - 30 q^{52} - 10 q^{53} - 48 q^{54} - 10 q^{55} - 16 q^{59} + 28 q^{60} - 16 q^{61} - 44 q^{62} - 36 q^{63} + 20 q^{64} - 14 q^{65} - 32 q^{66} + 18 q^{67} + 22 q^{68} - 16 q^{69} - 12 q^{70} - 16 q^{71} + 4 q^{72} + 18 q^{74} - 38 q^{75} - 64 q^{76} - 28 q^{77} + 68 q^{78} - 2 q^{80} - 14 q^{81} + 56 q^{82} + 48 q^{83} - 40 q^{84} - 26 q^{85} + 60 q^{86} - 34 q^{87} + 82 q^{88} - 6 q^{89} + 46 q^{90} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 48 q^{94} - 26 q^{95} + 56 q^{96} + 66 q^{97} - 30 q^{98} + 60 q^{99}+O(q^{100}) $ 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9 - 2 * q^10 - 16 * q^11 - 24 * q^12 - 4 * q^13 - 20 * q^15 - 2 * q^16 + 4 * q^17 - 20 * q^19 + 4 * q^21 + 16 * q^22 - 10 * q^23 + 32 * q^24 + 18 * q^25 - 24 * q^26 + 4 * q^27 + 18 * q^28 - 26 * q^30 + 48 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 + 36 * q^36 - 4 * q^37 - 8 * q^38 + 4 * q^39 - 16 * q^40 + 10 * q^41 + 40 * q^42 + 10 * q^43 - 36 * q^44 + 4 * q^46 - 40 * q^47 - 56 * q^48 + 18 * q^49 + 36 * q^50 - 30 * q^52 - 10 * q^53 - 48 * q^54 - 10 * q^55 - 16 * q^59 + 28 * q^60 - 16 * q^61 - 44 * q^62 - 36 * q^63 + 20 * q^64 - 14 * q^65 - 32 * q^66 + 18 * q^67 + 22 * q^68 - 16 * q^69 - 12 * q^70 - 16 * q^71 + 4 * q^72 + 18 * q^74 - 38 * q^75 - 64 * q^76 - 28 * q^77 + 68 * q^78 - 2 * q^80 - 14 * q^81 + 56 * q^82 + 48 * q^83 - 40 * q^84 - 26 * q^85 + 60 * q^86 - 34 * q^87 + 82 * q^88 - 6 * q^89 + 46 * q^90 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 48 * q^94 - 26 * q^95 + 56 * q^96 + 66 * q^97 - 30 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.237991	−	0.137404i	−0.168285	−	0.0971595i	0.413492	−	0.910508i	$-0.364309\pi$
$2$	−0.237991	−	0.137404i	−0.168285	−	0.0971595i	−0.581777	+	0.813348i	$0.697642\pi$
$3$	0.611610	+	2.28256i	0.353113	+	1.31784i	0.882842	+	0.469669i	$0.155627\pi$
$3$	0.611610	+	2.28256i	0.353113	+	1.31784i	−0.529729	+	0.848167i	$0.677707\pi$
$4$	−0.962240	−	1.66665i	−0.481120	−	0.833324i
$5$	1.45395	+	1.69883i	0.650226	+	0.759741i
$5$	1.45395	+	1.69883i	0.650226	+	0.759741i
$6$	0.168076	−	0.627267i	0.0686166	−	0.256081i
$7$	−0.193052	−	0.334376i	−0.0729667	−	0.126382i	0.827234	−	0.561858i	$-0.189913\pi$
$7$	−0.193052	−	0.334376i	−0.0729667	−	0.126382i	−0.900200	+	0.435476i	$0.856580\pi$
$8$			1.07848i			0.381301i
$9$	−2.23793	+	1.29207i	−0.745977	+	0.430690i
$10$	−0.112600	−	0.604086i	−0.0356073	−	0.191029i
$11$	−1.12873	−	4.21249i	−0.340326	−	1.27011i	−0.897979	−	0.440039i	$-0.854965\pi$
$11$	−1.12873	−	4.21249i	−0.340326	−	1.27011i	0.557653	−	0.830074i	$-0.311702\pi$
$12$	3.21571	−	3.21571i	0.928295	−	0.928295i
$13$	−1.35750	−	3.34024i	−0.376502	−	0.926416i
$13$	−1.35750	−	3.34024i	−0.376502	−	0.926416i
$14$			0.106105i			0.0283576i
$15$	−2.98844	+	4.35775i	−0.771611	+	1.12517i
$16$	−1.77629	+	3.07663i	−0.444073	+	0.769157i
$17$	1.90527	+	0.510514i	0.462095	+	0.123818i	0.482353	−	0.875977i	$-0.339782\pi$
$17$	1.90527	+	0.510514i	0.462095	+	0.123818i	−0.0202583	+	0.999795i	$0.506449\pi$
$18$	0.710144			0.167383
$19$	−4.83947	−	1.29673i	−1.11025	−	0.297491i	−0.343318	−	0.939219i	$-0.611551\pi$
$19$	−4.83947	−	1.29673i	−1.11025	−	0.297491i	−0.766932	+	0.641728i	$0.778218\pi$
$20$	1.43231	−	4.05791i	0.320274	−	0.907376i
$21$	0.645159	−	0.645159i	0.140785	−	0.140785i
$22$	−0.310185	+	1.15763i	−0.0661318	+	0.246807i
$23$	0.322241	−	0.0863441i	0.0671918	−	0.0180040i	−0.225067	−	0.974343i	$-0.572260\pi$
$23$	0.322241	−	0.0863441i	0.0671918	−	0.0180040i	0.292258	+	0.956339i	$0.405593\pi$
$24$	−2.46170	+	0.659609i	−0.502492	+	0.134642i
$25$	−0.772064	+	4.94003i	−0.154413	+	0.988006i
$26$	−0.135891	+	0.981474i	−0.0266504	+	0.192483i
$27$	0.694880	+	0.694880i	0.133730	+	0.133730i
$28$	−0.371524	+	0.643499i	−0.0702115	+	0.121610i
$29$	7.07031	+	4.08205i	1.31292	+	0.758017i	0.982579	−	0.185843i	$-0.0595016\pi$
$29$	7.07031	+	4.08205i	1.31292	+	0.758017i	0.330345	+	0.943860i	$0.392835\pi$
$30$	1.30999	−	0.626482i	0.239171	−	0.114379i
$31$	−2.54187	−	2.54187i	−0.456534	−	0.456534i	0.440982	−	0.897516i	$-0.354630\pi$
$31$	−2.54187	−	2.54187i	−0.456534	−	0.456534i	−0.897516	+	0.440982i	$0.854630\pi$
$32$	2.71347	−	1.56662i	0.479678	−	0.276942i
$33$	8.92491	−	5.15280i	1.55363	−	0.896987i
$34$	−0.383290	−	0.383290i	−0.0657336	−	0.0657336i
$35$	0.287361	−	0.814128i	0.0485728	−	0.137613i
$36$	4.30685	+	2.48656i	0.717809	+	0.414427i
$37$	−2.41251	+	4.17859i	−0.396614	+	0.686956i	−0.993306	−	0.115514i	$-0.963148\pi$
$37$	−2.41251	+	4.17859i	−0.396614	+	0.686956i	0.596691	+	0.802471i	$0.296482\pi$
$38$	0.973575	+	0.973575i	0.157935	+	0.157935i
$39$	6.79403	−	5.14149i	1.08792	−	0.823297i
$40$	−1.83216	+	1.56806i	−0.289690	+	0.247931i
$41$	4.49768	−	1.20515i	0.702419	−	0.188213i	0.110105	−	0.993920i	$-0.464881\pi$
$41$	4.49768	−	1.20515i	0.702419	−	0.188213i	0.592314	+	0.805707i	$0.298214\pi$
$42$	−0.242190	+	0.0648946i	−0.0373707	+	0.0100135i
$43$	−1.76471	+	6.58600i	−0.269116	+	1.00436i	0.690566	+	0.723269i	$0.257362\pi$
$43$	−1.76471	+	6.58600i	−0.269116	+	1.00436i	−0.959682	+	0.281087i	$0.909305\pi$
$44$	−5.93462	+	5.93462i	−0.894678	+	0.894678i
$45$	−5.44885	−	1.92327i	−0.812267	−	0.286704i
$46$	−0.0885545	−	0.0237281i	−0.0130566	−	0.00349852i
$47$	−9.83310			−1.43430			−0.717152	−	0.696917i	$-0.754555\pi$
$47$	−9.83310			−1.43430			−0.717152	+	0.696917i	$0.754555\pi$
$48$	−8.10898	−	2.17280i	−1.17043	−	0.313616i
$49$	3.42546	−	5.93307i	0.489352	−	0.847582i
$50$	0.862526	−	1.06960i	0.121980	−	0.151264i
$51$			4.66112i			0.652687i
$52$	−4.26077	+	5.47658i	−0.590862	+	0.759466i
$53$	−7.17155	+	7.17155i	−0.985088	+	0.985088i	−0.999890	−	0.0148021i	$-0.995288\pi$
$53$	−7.17155	+	7.17155i	−0.985088	+	0.985088i	0.0148021	+	0.999890i	$0.495288\pi$
$54$	−0.0698958	−	0.260855i	−0.00951161	−	0.0354978i
$55$	5.51519	−	8.04227i	0.743668	−	1.08442i
$56$	0.360618	−	0.208203i	0.0481896	−	0.0278223i
$57$		−	11.8395i		−	1.56818i
$58$	−1.12178	−	1.94298i	−0.147297	−	0.255126i
$59$	−0.628209	+	2.34451i	−0.0817858	+	0.305229i	−0.994686	−	0.102954i	$-0.967171\pi$
$59$	−0.628209	+	2.34451i	−0.0817858	+	0.305229i	0.912900	+	0.408183i	$0.133837\pi$
$60$	10.1384	+	0.787474i	1.30887	+	0.101662i
$61$	−5.32338	−	9.22037i	−0.681589	−	1.18055i	−0.974496	−	0.224406i	$-0.927956\pi$
$61$	−5.32338	−	9.22037i	−0.681589	−	1.18055i	0.292906	−	0.956141i	$-0.405378\pi$
$62$	0.255679	+	0.954209i	0.0324713	+	0.121185i
$63$	0.864073	+	0.498873i	0.108863	+	0.0628521i
$64$	6.24413			0.780516
$65$	3.70078	−	7.16270i	0.459025	−	0.888424i
$66$	−2.83207			−0.348603
$67$	5.52170	+	3.18796i	0.674583	+	0.389471i	0.797811	−	0.602908i	$-0.205991\pi$
$67$	5.52170	+	3.18796i	0.674583	+	0.389471i	−0.123228	+	0.992378i	$0.539325\pi$
$68$	−0.982475	−	3.66665i	−0.119143	−	0.444646i
$69$	0.394171	+	0.682724i	0.0474526	+	0.0821903i
$70$	−0.180254	+	0.154271i	−0.0215445	+	0.0184389i
$71$	−1.12684	+	4.20542i	−0.133731	+	0.499091i	−1.00000		0.000486883i	$-0.999845\pi$
$71$	−1.12684	+	4.20542i	−0.133731	+	0.499091i	0.866269	+	0.499578i	$0.166512\pi$
$72$	−1.39347	−	2.41357i	−0.164222	−	0.284442i
$73$		−	6.08593i		−	0.712304i	−0.934428	−	0.356152i	$-0.884088\pi$
$73$		−	6.08593i		−	0.712304i	0.934428	−	0.356152i	$-0.115912\pi$
$74$	1.14831	−	0.662979i	0.133489	−	0.0770697i
$75$	−11.7481	+	1.25909i	−1.35656	+	0.145387i
$76$	2.49554	+	9.31346i	0.286258	+	1.06833i
$77$	−1.19065	+	1.19065i	−0.135687	+	0.135687i
$78$	−2.32338	+	0.290100i	−0.263071	+	0.0328474i
$79$		−	3.34944i		−	0.376842i	−0.982088	−	0.188421i	$-0.939663\pi$
$79$		−	3.34944i		−	0.376842i	0.982088	−	0.188421i	$-0.0603369\pi$
$80$	−7.80932	+	1.45564i	−0.873108	+	0.162745i
$81$	−5.03732	+	8.72489i	−0.559702	+	0.969433i
$82$	−1.23600	−	0.331185i	−0.136493	−	0.0365733i
$83$	5.18834			0.569494			0.284747	−	0.958603i	$-0.408090\pi$
$83$	5.18834			0.569494			0.284747	+	0.958603i	$0.408090\pi$
$84$	−1.69605	−	0.454456i	−0.185054	−	0.0495852i
$85$	1.90288	+	3.97899i	0.206396	+	0.431582i
$86$	1.32493	−	1.32493i	0.142871	−	0.142871i
$87$	−4.99324	+	18.6350i	−0.535332	+	1.99788i
$88$	4.54309	−	1.21732i	0.484295	−	0.129766i
$89$	4.82829	−	1.29374i	0.511798	−	0.137136i	0.00632782	−	0.999980i	$-0.497986\pi$
$89$	4.82829	−	1.29374i	0.511798	−	0.137136i	0.505470	+	0.862844i	$0.331319\pi$
$90$	1.03251	+	1.20642i	0.108836	+	0.127167i
$91$	−0.854827	+	1.09875i	−0.0896102	+	0.115181i
$92$	−0.453978	−	0.453978i	−0.0473305	−	0.0473305i
$93$	4.24734	−	7.35661i	0.440429	−	0.762845i
$94$	2.34019	+	1.35111i	0.241372	+	0.139356i
$95$	−4.83341	−	10.1068i	−0.495898	−	1.03694i
$96$	5.23549	+	5.23549i	0.534345	+	0.534345i
$97$	12.7722	−	7.37402i	1.29682	−	0.748718i	0.316965	−	0.948437i	$-0.397336\pi$
$97$	12.7722	−	7.37402i	1.29682	−	0.748718i	0.979853	+	0.199719i	$0.0640030\pi$
$98$	−1.63046	+	0.941346i	−0.164701	+	0.0950903i
$99$	7.96886	+	7.96886i	0.800900	+	0.800900i
$100$	8.97621	−	3.46674i	0.897621	−	0.346674i
$101$	4.57218	+	2.63975i	0.454949	+	0.262665i	0.709918	−	0.704284i	$-0.248732\pi$
$101$	4.57218	+	2.63975i	0.454949	+	0.262665i	−0.254969	+	0.966949i	$0.582065\pi$
$102$	0.640458	−	1.10930i	0.0634147	−	0.109838i
$103$	−1.21001	−	1.21001i	−0.119226	−	0.119226i	0.644976	−	0.764203i	$-0.276867\pi$
$103$	−1.21001	−	1.21001i	−0.119226	−	0.119226i	−0.764203	+	0.644976i	$0.776867\pi$
$104$	3.60238	−	1.46404i	0.353243	−	0.143560i
$105$	2.03405	+	0.157989i	0.198503	+	0.0154181i
$106$	2.69217	−	0.721364i	0.261487	−	0.0700651i
$107$	−3.91480	+	1.04897i	−0.378458	+	0.101408i	−0.443033	−	0.896505i	$-0.646098\pi$
$107$	−3.91480	+	1.04897i	−0.378458	+	0.101408i	0.0645749	+	0.997913i	$0.479431\pi$
$108$	0.489479	−	1.82676i	0.0471002	−	0.175780i
$109$	−5.02898	+	5.02898i	−0.481689	+	0.481689i	−0.905671	−	0.423982i	$-0.860632\pi$
$109$	−5.02898	+	5.02898i	−0.481689	+	0.481689i	0.423982	+	0.905671i	$0.360632\pi$
$110$	−2.41761	+	1.15618i	−0.230510	+	0.110237i
$111$	−11.0134	−	2.95103i	−1.04535	−	0.280099i
$112$	1.37167			0.129610
$113$	3.83891	+	1.02863i	0.361134	+	0.0967655i	0.434824	−	0.900516i	$-0.356811\pi$
$113$	3.83891	+	1.02863i	0.361134	+	0.0967655i	−0.0736896	+	0.997281i	$0.523477\pi$
$114$	−1.62679	+	2.81769i	−0.152363	+	0.263901i
$115$	0.615206	+	0.421893i	0.0573682	+	0.0393417i
$116$		−	15.7116i		−	1.45879i
$117$	7.35381	+	5.72124i	0.679860	+	0.528929i
$118$	0.471653	−	0.471653i	0.0434192	−	0.0434192i
$119$	−0.197111	−	0.735630i	−0.0180692	−	0.0674351i
$120$	−4.69975	−	3.22297i	−0.429026	−	0.294216i
$121$	−6.94473	+	4.00954i	−0.631339	+	0.364504i
$122$			2.92582i			0.264892i
$123$	5.50165	+	9.52914i	0.496067	+	0.859213i
$124$	−1.79052	+	6.68231i	−0.160793	+	0.600089i
$125$	−9.51483	+	5.87095i	−0.851032	+	0.525113i
$126$	−0.137095	−	0.237455i	−0.0122134	−	0.0211542i
$127$	−2.95156	−	11.0154i	−0.261908	−	0.977455i	−0.964116	−	0.265483i	$-0.914469\pi$
$127$	−2.95156	−	11.0154i	−0.261908	−	0.977455i	0.702207	−	0.711972i	$-0.252198\pi$
$128$	−6.91298	−	3.99121i	−0.611027	−	0.352777i
$129$	−16.1123			−1.41860
$130$	−1.86494	+	1.19616i	−0.163566	+	0.104910i
$131$	20.8627			1.82279			0.911393	−	0.411536i	$-0.135008\pi$
$131$	20.8627			1.82279			0.911393	+	0.411536i	$0.135008\pi$
$132$	−17.1758	−	9.91645i	−1.49496	−	0.863117i
$133$	0.500673	+	1.86854i	0.0434138	+	0.162023i
$134$	−0.876078	−	1.51741i	−0.0756816	−	0.131084i
$135$	−0.170165	+	2.19080i	−0.0146454	+	0.188554i
$136$	−0.550580	+	2.05479i	−0.0472119	+	0.176197i
$137$	0.121975	+	0.211266i	0.0104210	+	0.0180497i	0.871189	−	0.490948i	$-0.163349\pi$
$137$	0.121975	+	0.211266i	0.0104210	+	0.0180497i	−0.860768	+	0.508998i	$0.830016\pi$
$138$		−	0.216643i		−	0.0184419i
$139$	10.1187	−	5.84202i	0.858255	−	0.495514i	−0.00517263	−	0.999987i	$-0.501647\pi$
$139$	10.1187	−	5.84202i	0.858255	−	0.495514i	0.863428	+	0.504473i	$0.168313\pi$
$140$	−1.63337	+	0.304457i	−0.138045	+	0.0257313i
$141$	−6.01402	−	22.4446i	−0.506472	−	1.89018i
$142$	0.846020	−	0.846020i	0.0709965	−	0.0709965i
$143$	−12.5385	+	9.48868i	−1.04852	+	0.793483i
$144$		−	9.18038i		−	0.765032i
$145$	3.34516	+	17.9464i	0.277800	+	1.49036i
$146$	−0.836233	+	1.44840i	−0.0692071	+	0.119870i
$147$	15.6376	+	4.19009i	1.28977	+	0.345593i
$148$	9.28566			0.763277
$149$	−2.44620	−	0.655457i	−0.200400	−	0.0536971i	0.157223	−	0.987563i	$-0.449746\pi$
$149$	−2.44620	−	0.655457i	−0.200400	−	0.0536971i	−0.357623	+	0.933866i	$0.616413\pi$
$150$	2.96895	+	1.31459i	0.242414	+	0.107336i
$151$	2.58498	−	2.58498i	0.210362	−	0.210362i	−0.594059	−	0.804421i	$-0.702475\pi$
$151$	2.58498	−	2.58498i	0.210362	−	0.210362i	0.804421	+	0.594059i	$0.202475\pi$
$152$	1.39850	−	5.21928i	0.113433	−	0.423339i
$153$	−4.92348	+	1.31924i	−0.398039	+	0.106654i
$154$	0.446964	−	0.119764i	0.0360174	−	0.00965083i
$155$	0.622463	−	8.01398i	0.0499974	−	0.643698i
$156$	−15.1066	−	6.37592i	−1.20949	−	0.510482i
$157$	−2.21767	−	2.21767i	−0.176990	−	0.176990i	0.613053	−	0.790042i	$-0.289941\pi$
$157$	−2.21767	−	2.21767i	−0.176990	−	0.176990i	−0.790042	+	0.613053i	$0.789941\pi$
$158$	−0.460228	+	0.797137i	−0.0366137	+	0.0634169i
$159$	−20.7557	−	11.9833i	−1.64603	−	0.950337i
$160$	6.60667	+	2.33194i	0.522303	+	0.184356i
$161$	−0.0910805	−	0.0910805i	−0.00717815	−	0.00717815i
$162$	2.39768	−	1.38430i	0.188379	−	0.108761i
$163$	−12.8283	+	7.40642i	−1.00479	+	0.580116i	−0.909662	−	0.415349i	$-0.863659\pi$
$163$	−12.8283	+	7.40642i	−1.00479	+	0.580116i	−0.0951279	+	0.995465i	$0.530326\pi$
$164$	−6.33641	−	6.33641i	−0.494790	−	0.494790i
$165$	21.7301	+	7.67002i	1.69169	+	0.597110i
$166$	−1.23478	−	0.712900i	−0.0958374	−	0.0553318i
$167$	−1.73406	+	3.00348i	−0.134186	+	0.232417i	−0.925286	−	0.379270i	$-0.876175\pi$
$167$	−1.73406	+	3.00348i	−0.134186	+	0.232417i	0.791100	+	0.611686i	$0.209509\pi$
$168$	0.695792	+	0.695792i	0.0536815	+	0.0536815i
$169$	−9.31440	+	9.06873i	−0.716492	+	0.697595i
$170$	0.0938613	−	1.20843i	0.00719883	−	0.0926823i
$171$	12.5059	−	3.35094i	0.956348	−	0.256253i
$172$	12.6746	−	3.39616i	0.966432	−	0.258955i
$173$	−1.01194	+	3.77661i	−0.0769362	+	0.287130i	−0.993665	−	0.112379i	$-0.964153\pi$
$173$	−1.01194	+	3.77661i	−0.0769362	+	0.287130i	0.916729	+	0.399509i	$0.130819\pi$
$174$	3.74888	−	3.74888i	0.284202	−	0.284202i
$175$	1.80087	−	0.695523i	0.136133	−	0.0525766i
$176$	14.9652	+	4.00992i	1.12805	+	0.302259i
$177$	−5.73569			−0.431121
$178$	−1.32686	−	0.355530i	−0.0994521	−	0.0266481i
$179$	−3.24880	+	5.62708i	−0.242827	+	0.420588i	−0.961518	−	0.274741i	$-0.911408\pi$
$179$	−3.24880	+	5.62708i	−0.242827	+	0.420588i	0.718692	+	0.695329i	$0.244741\pi$
$180$	2.03769	+	10.9320i	0.151881	+	0.814820i
$181$			11.9845i			0.890802i	0.895331	+	0.445401i	$0.146939\pi$
$181$			11.9845i			0.890802i	−0.895331	+	0.445401i	$0.853061\pi$
$182$	0.354415	−	0.144037i	0.0262710	−	0.0106767i
$183$	17.7902	−	17.7902i	1.31509	−	1.31509i
$184$	0.0931205	+	0.347530i	0.00686493	+	0.0256203i
$185$	−10.6064	+	1.97701i	−0.779798	+	0.145352i
$186$	−2.02166	+	1.16721i	−0.148235	+	0.0855837i
$187$		−	8.60214i		−	0.629051i
$188$	9.46180	+	16.3883i	0.690073	+	1.19524i
$189$	0.0982030	−	0.366499i	0.00714322	−	0.0266588i
$190$	−0.238412	+	3.06947i	−0.0172963	+	0.222683i
$191$	2.59646	+	4.49719i	0.187873	+	0.325405i	0.944541	−	0.328394i	$-0.106507\pi$
$191$	2.59646	+	4.49719i	0.187873	+	0.325405i	−0.756668	+	0.653799i	$0.773174\pi$
$192$	3.81897	+	14.2526i	0.275610	+	1.02859i
$193$	5.77996	+	3.33706i	0.416051	+	0.240207i	0.693386	−	0.720566i	$-0.256118\pi$
$193$	5.77996	+	3.33706i	0.416051	+	0.240207i	−0.277335	+	0.960773i	$0.589451\pi$
$194$	−4.05289			−0.290980
$195$	18.6127	+	4.06646i	1.33288	+	0.291205i
$196$	−13.1845			−0.941748
$197$	−16.9716	−	9.79857i	−1.20918	−	0.698119i	−0.246598	−	0.969118i	$-0.579313\pi$
$197$	−16.9716	−	9.79857i	−1.20918	−	0.698119i	−0.962580	+	0.270999i	$0.912646\pi$
$198$	−0.801563	−	2.99147i	−0.0569646	−	0.212595i
$199$	−7.35302	−	12.7358i	−0.521242	−	0.902817i	−0.999695	−	0.0247042i	$-0.992136\pi$
$199$	−7.35302	−	12.7358i	−0.521242	−	0.902817i	0.478453	−	0.878113i	$-0.341198\pi$
$200$	−5.32773	−	0.832657i	−0.376727	−	0.0588777i
$201$	−3.89957	+	14.5534i	−0.275054	+	1.02652i
$202$	−0.725425	−	1.25647i	−0.0510408	−	0.0884052i
$203$		−	3.15219i		−	0.221240i
$204$	7.76844	−	4.48511i	0.543900	−	0.314021i
$205$	8.58674	+	5.88858i	0.599724	+	0.411276i
$206$	0.121712	+	0.454234i	0.00848005	+	0.0316480i
$207$	−0.609590	+	0.609590i	−0.0423694	+	0.0423694i
$208$	12.6880	+	1.75673i	0.879754	+	0.121807i
$209$			21.8499i			1.51139i
$210$	−0.462377	−	0.317087i	−0.0319070	−	0.0218811i
$211$	10.7072	−	18.5453i	0.737111	−	1.27671i	−0.216679	−	0.976243i	$-0.569523\pi$
$211$	10.7072	−	18.5453i	0.737111	−	1.27671i	0.953791	−	0.300471i	$-0.0971440\pi$
$212$	18.8532	+	5.05170i	1.29484	+	0.346952i
$213$	−10.2883			−0.704943
$214$	1.07582	+	0.288265i	0.0735416	+	0.0197054i
$215$	−13.7543	+	6.57776i	−0.938037	+	0.448599i
$216$	−0.749414	+	0.749414i	−0.0509912	+	0.0509912i
$217$	−0.359227	+	1.34065i	−0.0243859	+	0.0910095i
$218$	1.88786	−	0.505850i	0.127862	−	0.0342605i
$219$	13.8915	−	3.72221i	0.938700	−	0.251524i
$220$	−18.7106	−	1.45329i	−1.26147	−	0.0979809i
$221$	−0.881153	−	7.05707i	−0.0592728	−	0.474710i
$222$	2.21561	+	2.21561i	0.148702	+	0.148702i
$223$	13.6678	−	23.6733i	0.915264	−	1.58528i	0.108749	−	0.994069i	$-0.465315\pi$
$223$	13.6678	−	23.6733i	0.915264	−	1.58528i	0.806515	−	0.591214i	$-0.201351\pi$
$224$	−1.04768	−	0.604878i	−0.0700010	−	0.0404151i
$225$	−4.65504	−	12.0530i	−0.310336	−	0.803534i
$226$	−0.772287	−	0.772287i	−0.0513718	−	0.0513718i
$227$	5.99928	−	3.46369i	0.398186	−	0.229893i	−0.287515	−	0.957776i	$-0.592829\pi$
$227$	5.99928	−	3.46369i	0.398186	−	0.229893i	0.685701	+	0.727883i	$0.259496\pi$
$228$	−19.7322	+	11.3924i	−1.30680	+	0.754481i
$229$	4.56825	+	4.56825i	0.301879	+	0.301879i	0.841749	−	0.539870i	$-0.181527\pi$
$229$	4.56825	+	4.56825i	0.301879	+	0.301879i	−0.539870	+	0.841749i	$0.681527\pi$
$230$	−0.0884436	−	0.184939i	−0.00583180	−	0.0121945i
$231$	−3.44594	−	1.98951i	−0.226726	−	0.130900i
$232$	−4.40241	+	7.62520i	−0.289032	+	0.500619i
$233$	5.49074	+	5.49074i	0.359711	+	0.359711i	0.863706	−	0.503996i	$-0.168137\pi$
$233$	5.49074	+	5.49074i	0.359711	+	0.359711i	−0.503996	+	0.863706i	$0.668137\pi$
$234$	−0.964019	−	2.37205i	−0.0630199	−	0.155066i
$235$	−14.2968	−	16.7048i	−0.932622	−	1.08970i
$236$	4.51196	−	1.20898i	0.293703	−	0.0786976i
$237$	7.64529	−	2.04855i	0.496615	−	0.133068i
$238$	−0.0541679	+	0.202157i	−0.00351119	+	0.0131039i
$239$	8.33949	−	8.33949i	0.539437	−	0.539437i	−0.383927	−	0.923363i	$-0.625429\pi$
$239$	8.33949	−	8.33949i	0.539437	−	0.539437i	0.923363	+	0.383927i	$0.125429\pi$
$240$	−8.09883	−	16.9349i	−0.522777	−	1.09315i
$241$	−1.40952	−	0.377680i	−0.0907952	−	0.0243285i	0.213135	−	0.977023i	$-0.431632\pi$
$241$	−1.40952	−	0.377680i	−0.0907952	−	0.0243285i	−0.303931	+	0.952694i	$0.598299\pi$
$242$	2.20371			0.141660
$243$	−20.1483	−	5.39872i	−1.29251	−	0.346328i
$244$	−10.2447	+	17.7444i	−0.655853	+	1.13597i
$245$	15.0597	−	2.80710i	0.962132	−	0.179339i
$246$		−	3.02380i		−	0.192791i
$247$	2.23817	+	17.9253i	0.142412	+	1.14056i
$248$	2.74136	−	2.74136i	0.174077	−	0.174077i
$249$	3.17324	+	11.8427i	0.201096	+	0.750500i
$250$	3.07114	−	0.0898555i	0.194236	−	0.00568296i
$251$	−11.2668	+	6.50488i	−0.711153	+	0.410585i	−0.811488	−	0.584369i	$-0.801342\pi$
$251$	−11.2668	+	6.50488i	−0.711153	+	0.410585i	0.100335	+	0.994954i	$0.468009\pi$
$252$		−	1.92014i		−	0.120958i
$253$	−0.727447	−	1.25997i	−0.0457342	−	0.0792139i
$254$	−0.811113	+	3.02712i	−0.0508938	+	0.189938i
$255$	−7.91846	+	6.77703i	−0.495873	+	0.424394i
$256$	−5.14731	−	8.91540i	−0.321707	−	0.557212i
$257$	−7.62518	−	28.4576i	−0.475646	−	1.77513i	−0.618922	−	0.785452i	$-0.712430\pi$
$257$	−7.62518	−	28.4576i	−0.475646	−	1.77513i	0.143276	−	0.989683i	$-0.454236\pi$
$258$	3.83458	+	2.21389i	0.238730	+	0.137831i
$259$	1.86296			0.115759
$260$	−15.4987	+	0.724344i	−0.961191	+	0.0449219i
$261$	−21.0972			−1.30588
$262$	−4.96515	−	2.86663i	−0.306748	−	0.177101i
$263$	−1.30768	−	4.88034i	−0.0806351	−	0.300934i	0.913817	−	0.406127i	$-0.133121\pi$
$263$	−1.30768	−	4.88034i	−0.0806351	−	0.300934i	−0.994452	+	0.105192i	$0.966454\pi$
$264$	5.55719	+	9.62534i	0.342022	+	0.592399i
$265$	−22.6103	−	1.75619i	−1.38894	−	0.107882i
$266$	0.137589	−	0.513490i	0.00843614	−	0.0314841i
$267$	5.90606	+	10.2296i	0.361445	+	0.626041i
$268$		−	12.2703i		−	0.749529i
$269$	7.49111	−	4.32499i	0.456741	−	0.263699i	−0.253932	−	0.967222i	$-0.581724\pi$
$269$	7.49111	−	4.32499i	0.456741	−	0.263699i	0.710673	+	0.703523i	$0.248391\pi$
$270$	0.341524	−	0.498011i	0.0207845	−	0.0303080i
$271$	5.96047	+	22.2448i	0.362073	+	1.35127i	0.871346	+	0.490669i	$0.163248\pi$
$271$	5.96047	+	22.2448i	0.362073	+	1.35127i	−0.509273	+	0.860605i	$0.670086\pi$
$272$	−4.95497	+	4.95497i	−0.300439	+	0.300439i
$273$	−3.03079	−	1.27918i	−0.183432	−	0.0774198i
$274$		−	0.0670394i		−	0.00405000i
$275$	21.6813	−	2.32366i	1.30743	−	0.140122i
$276$	0.758574	−	1.31389i	0.0456608	−	0.0790868i
$277$	−20.9037	−	5.60114i	−1.25598	−	0.336540i	−0.431338	−	0.902190i	$-0.641958\pi$
$277$	−20.9037	−	5.60114i	−1.25598	−	0.336540i	−0.824645	+	0.565650i	$0.808625\pi$
$278$	−3.21087			−0.192575
$279$	8.97282	+	2.40426i	0.537189	+	0.143939i
$280$	0.878021	+	0.309913i	0.0524718	+	0.0185208i
$281$	8.17717	−	8.17717i	0.487809	−	0.487809i	−0.419805	−	0.907614i	$-0.637902\pi$
$281$	8.17717	−	8.17717i	0.487809	−	0.487809i	0.907614	+	0.419805i	$0.137902\pi$
$282$	−1.65270	+	6.16797i	−0.0984171	+	0.367298i
$283$	−4.34603	+	1.16452i	−0.258345	+	0.0692233i	−0.385667	−	0.922638i	$-0.626029\pi$
$283$	−4.34603	+	1.16452i	−0.258345	+	0.0692233i	0.127322	+	0.991861i	$0.459362\pi$
$284$	8.09325	−	2.16858i	0.480246	−	0.128681i
$285$	20.1133	−	17.2140i	1.19141	−	1.01967i
$286$	4.28783	−	0.535383i	0.253545	−	0.0316579i
$287$	−1.27126	−	1.27126i	−0.0750400	−	0.0750400i
$288$	−4.04837	+	7.01198i	−0.238552	+	0.413185i
$289$	−11.3530	−	6.55467i	−0.667825	−	0.385569i
$290$	1.66979	−	4.73072i	0.0980534	−	0.277797i
$291$	24.6432	+	24.6432i	1.44461	+	1.44461i
$292$	−10.1431	+	5.85613i	−0.593580	+	0.342704i
$293$	11.3497	−	6.55274i	0.663056	−	0.382815i	−0.130385	−	0.991463i	$-0.541621\pi$
$293$	11.3497	−	6.55274i	0.663056	−	0.382815i	0.793440	+	0.608648i	$0.208288\pi$
$294$	−3.14588	−	3.14588i	−0.183472	−	0.183472i
$295$	−4.89631	+	2.34157i	−0.285074	+	0.136332i
$296$	−4.50653	−	2.60185i	−0.261937	−	0.151229i
$297$	2.14284	−	3.71150i	0.124340	−	0.215363i
$298$	0.492111	+	0.492111i	0.0285072	+	0.0285072i
$299$	−0.725851	−	0.959149i	−0.0419770	−	0.0554690i
$300$	13.4030	+	18.3684i	0.773821	+	1.06050i
$301$	2.54288	−	0.681363i	0.146569	−	0.0392731i
$302$	−0.970388	+	0.260015i	−0.0558396	+	0.0149622i
$303$	−3.22899	+	12.0508i	−0.185501	+	0.692298i
$304$	12.5859	−	12.5859i	0.721849	−	0.721849i
$305$	7.92394	−	22.4495i	0.453723	−	1.28545i
$306$	1.35301	+	0.362539i	0.0773466	+	0.0207250i
$307$	7.75447			0.442571			0.221285	−	0.975209i	$-0.428975\pi$
$307$	7.75447			0.442571			0.221285	+	0.975209i	$0.428975\pi$
$308$	3.13008	+	0.838703i	0.178353	+	0.0477896i
$309$	2.02187	−	3.50198i	0.115020	−	0.199221i
$310$	−1.24930	+	1.82173i	−0.0709552	+	0.103467i
$311$			11.6030i			0.657947i	0.944339	+	0.328974i	$0.106703\pi$
$311$			11.6030i			0.657947i	−0.944339	+	0.328974i	$0.893297\pi$
$312$	5.54500	+	7.32724i	0.313924	+	0.414823i
$313$	−10.1565	+	10.1565i	−0.574078	+	0.574078i	−0.933265	−	0.359188i	$-0.883054\pi$
$313$	−10.1565	+	10.1565i	−0.574078	+	0.574078i	0.359188	+	0.933265i	$0.383054\pi$
$314$	0.223069	+	0.832505i	0.0125885	+	0.0469810i
$315$	0.408817	+	2.19325i	0.0230342	+	0.123576i
$316$	−5.58234	+	3.22297i	−0.314031	+	0.181306i
$317$			21.7686i			1.22265i	0.791381	+	0.611323i	$0.209362\pi$
$317$			21.7686i			1.22265i	−0.791381	+	0.611323i	$0.790638\pi$
$318$	3.29311	+	5.70384i	0.184669	+	0.319855i
$319$	9.21508	−	34.3911i	0.515945	−	1.92553i
$320$	9.07864	+	10.6077i	0.507512	+	0.592990i
$321$	−4.78866	−	8.29420i	−0.267277	−	0.462937i
$322$	0.00916151	+	0.0341912i	0.000510551	+	0.00190540i
$323$	−8.55848	−	4.94124i	−0.476206	−	0.274938i
$324$	19.3884			1.07714
$325$	17.5490	−	4.12720i	0.973441	−	0.228936i
$326$	4.07070			0.225455
$327$	−14.5547	−	8.40318i	−0.804878	−	0.464697i
$328$	1.29973	+	4.85066i	0.0717656	+	0.267833i
$329$	1.89830	+	3.28795i	0.104657	+	0.181270i
$330$	−4.11768	−	4.81121i	−0.226671	−	0.264848i
$331$	−5.07792	+	18.9511i	−0.279108	+	1.04164i	0.673931	+	0.738795i	$0.264605\pi$
$331$	−5.07792	+	18.9511i	−0.279108	+	1.04164i	−0.953038	+	0.302850i	$0.902062\pi$
$332$	−4.99243	−	8.64714i	−0.273995	−	0.474573i
$333$		−	12.4685i		−	0.683272i
$334$	0.825383	−	0.476535i	0.0451630	−	0.0260748i
$335$	2.61247	+	14.0156i	0.142734	+	0.765753i
$336$	0.838924	+	3.13091i	0.0457671	+	0.170805i
$337$	−9.35946	+	9.35946i	−0.509842	+	0.509842i	−0.914478	−	0.404636i	$-0.867398\pi$
$337$	−9.35946	+	9.35946i	−0.509842	+	0.509842i	0.404636	+	0.914478i	$0.367398\pi$
$338$	3.46283	−	0.878441i	0.188353	−	0.0477809i
$339$			9.39165i			0.510084i
$340$	4.80055	−	7.00018i	0.260346	−	0.379638i
$341$	−7.83852	+	13.5767i	−0.424480	+	0.735220i
$342$	−3.43672	−	0.920867i	−0.185837	−	0.0497948i
$343$	−5.34789			−0.288759
$344$	−7.10288	−	1.90321i	−0.382962	−	0.102614i
$345$	−0.586730	+	1.66228i	−0.0315885	+	0.0894940i
$346$	0.759754	−	0.759754i	0.0408446	−	0.0408446i
$347$	−7.15698	+	26.7102i	−0.384207	+	1.43388i	0.455207	+	0.890386i	$0.349565\pi$
$347$	−7.15698	+	26.7102i	−0.384207	+	1.43388i	−0.839414	+	0.543493i	$0.817101\pi$
$348$	35.8627	−	9.60939i	1.92244	−	0.515118i
$349$	−28.5113	+	7.63958i	−1.52618	+	0.408938i	−0.921769	−	0.387739i	$-0.873256\pi$
$349$	−28.5113	+	7.63958i	−1.52618	+	0.408938i	−0.604406	+	0.796676i	$0.706590\pi$
$350$	−0.524160	−	0.0819196i	−0.0280175	−	0.00437878i
$351$	1.37777	−	3.26436i	0.0735398	−	0.174239i
$352$	−9.66215	−	9.66215i	−0.514994	−	0.514994i
$353$	−7.81777	+	13.5408i	−0.416098	+	0.720702i	−0.995543	−	0.0943088i	$-0.969936\pi$
$353$	−7.81777	+	13.5408i	−0.416098	+	0.720702i	0.579445	+	0.815011i	$0.303269\pi$
$354$	1.36504	+	0.788109i	0.0725513	+	0.0418875i
$355$	−8.78267	+	4.20015i	−0.466136	+	0.222921i
$356$	−6.80218	−	6.80218i	−0.360515	−	0.360515i
$357$	1.55856	−	0.899837i	0.0824879	−	0.0476244i
$358$	1.54637	−	0.892798i	0.0817282	−	0.0471858i
$359$	14.0592	+	14.0592i	0.742017	+	0.742017i	0.972966	−	0.230949i	$-0.0741830\pi$
$359$	14.0592	+	14.0592i	0.742017	+	0.742017i	−0.230949	+	0.972966i	$0.574183\pi$
$360$	2.07421	−	5.87648i	0.109320	−	0.309718i
$361$	5.28447	+	3.05099i	0.278130	+	0.160578i
$362$	1.64672	−	2.85221i	0.0865499	−	0.149909i
$363$	−13.3995	−	13.3995i	−0.703290	−	0.703290i
$364$	2.65378	+	0.367432i	0.139096	+	0.0192587i
$365$	10.3390	−	8.84863i	0.541167	−	0.463159i
$366$	−6.67836	+	1.78946i	−0.349084	+	0.0935367i
$367$	21.2746	−	5.70052i	1.11053	−	0.297565i	0.343483	−	0.939159i	$-0.388393\pi$
$367$	21.2746	−	5.70052i	1.11053	−	0.297565i	0.767045	+	0.641594i	$0.221727\pi$
$368$	−0.306745	+	1.14479i	−0.0159902	+	0.0596761i
$369$	−8.50836	+	8.50836i	−0.442928	+	0.442928i
$370$	2.79588	+	0.986854i	0.145351	+	0.0513041i
$371$	3.78247	+	1.01351i	0.196376	+	0.0526188i
$372$	−16.3479			−0.847597
$373$	1.12584	+	0.301668i	0.0582937	+	0.0156198i	0.287848	−	0.957676i	$-0.407060\pi$
$373$	1.12584	+	0.301668i	0.0582937	+	0.0156198i	−0.229554	+	0.973296i	$0.573727\pi$
$374$	−1.18197	+	2.04723i	−0.0611183	+	0.105860i
$375$	−19.2201	−	18.1274i	−0.992524	−	0.936096i
$376$		−	10.6048i		−	0.546901i
$377$	4.03708	−	29.1579i	0.207920	−	1.50171i
$378$	−0.0737299	+	0.0737299i	−0.00379226	+	0.00379226i
$379$	6.82640	+	25.4765i	0.350649	+	1.30864i	0.885873	+	0.463928i	$0.153560\pi$
$379$	6.82640	+	25.4765i	0.350649	+	1.30864i	−0.535224	+	0.844710i	$0.679773\pi$
$380$	−12.1936	+	17.7808i	−0.625520	+	0.912136i
$381$	23.3380	−	13.4742i	1.19564	−	0.690304i
$382$		−	1.42706i		−	0.0730146i
$383$	−16.4001	−	28.4058i	−0.838004	−	1.45147i	−0.891561	−	0.452901i	$-0.850389\pi$
$383$	−16.4001	−	28.4058i	−0.838004	−	1.45147i	0.0535563	−	0.998565i	$-0.482944\pi$
$384$	4.88213	−	18.2204i	0.249140	−	0.929804i
$385$	−3.75386	−	0.291570i	−0.191314	−	0.0148598i
$386$	−0.917054	−	1.58838i	−0.0466768	−	0.0808466i
$387$	−4.56027	−	17.0192i	−0.231812	−	0.865132i
$388$	−24.5798	−	14.1912i	−1.24785	−	0.720447i
$389$	9.36826			0.474989			0.237495	−	0.971389i	$-0.423674\pi$
$389$	9.36826			0.474989			0.237495	+	0.971389i	$0.423674\pi$
$390$	−3.87091	−	3.52525i	−0.196011	−	0.178508i
$391$	0.658034			0.0332782
$392$	6.39871	+	3.69430i	0.323184	+	0.186590i
$393$	12.7599	+	47.6205i	0.643650	+	2.40213i
$394$	2.69273	+	4.66395i	0.135658	+	0.234966i
$395$	5.69014	−	4.86992i	0.286302	−	0.245032i
$396$	5.61333	−	20.9492i	0.282080	−	1.05274i
$397$	5.82600	+	10.0909i	0.292399	+	0.506449i	0.974376	−	0.224924i	$-0.0722133\pi$
$397$	5.82600	+	10.0909i	0.292399	+	0.506449i	−0.681978	+	0.731373i	$0.738880\pi$
$398$			4.04135i			0.202574i
$399$	−3.95883	+	2.28563i	−0.198189	+	0.114425i
$400$	−13.8272	−	11.1503i	−0.691362	−	0.557515i
$401$	−5.33600	−	19.9142i	−0.266467	−	0.994469i	−0.961346	−	0.275342i	$-0.911209\pi$
$401$	−5.33600	−	19.9142i	−0.266467	−	0.994469i	0.694879	−	0.719126i	$-0.255458\pi$
$402$	2.92776	−	2.92776i	0.146024	−	0.146024i
$403$	−5.03988	+	11.9411i	−0.251054	+	0.594827i
$404$		−	10.1603i		−	0.505493i
$405$	−22.1461	+	4.12799i	−1.10045	+	0.205121i
$406$	−0.433124	+	0.750193i	−0.0214956	+	0.0372314i
$407$	20.3253	+	5.44616i	1.00749	+	0.269956i
$408$	−5.02693			−0.248870
$409$	4.40250	+	1.17965i	0.217689	+	0.0583297i	0.366015	−	0.930609i	$-0.380722\pi$
$409$	4.40250	+	1.17965i	0.217689	+	0.0583297i	−0.148326	+	0.988939i	$0.547388\pi$
$410$	−1.23445	−	2.58129i	−0.0609653	−	0.127481i
$411$	−0.407627	+	0.407627i	−0.0201067	+	0.0201067i
$412$	−0.852344	+	3.18099i	−0.0419920	+	0.156716i
$413$	0.905223	−	0.242554i	0.0445431	−	0.0119353i
$414$	0.228837	−	0.0613168i	0.0112467	−	0.00301355i
$415$	7.54358	+	8.81412i	0.370300	+	0.432668i
$416$	−8.91642	−	6.93695i	−0.437163	−	0.340112i
$417$	19.5234	+	19.5234i	0.956067	+	0.956067i
$418$	3.00227	−	5.20008i	0.146846	−	0.254344i
$419$	0.564687	+	0.326022i	0.0275868	+	0.0159272i	0.513730	−	0.857952i	$-0.328263\pi$
$419$	0.564687	+	0.326022i	0.0275868	+	0.0159272i	−0.486143	+	0.873879i	$0.661597\pi$
$420$	−1.69393	−	3.54206i	−0.0826553	−	0.172835i
$421$	−5.58095	−	5.58095i	−0.271999	−	0.271999i	0.557906	−	0.829904i	$-0.311605\pi$
$421$	−5.58095	−	5.58095i	−0.271999	−	0.271999i	−0.829904	+	0.557906i	$0.811605\pi$
$422$	−5.09642	+	2.94242i	−0.248090	+	0.143235i
$423$	22.0058	−	12.7051i	1.06996	−	0.617741i
$424$	−7.73438	−	7.73438i	−0.375615	−	0.375615i
$425$	−3.99295	+	9.01792i	−0.193686	+	0.437434i
$426$	2.44853	+	1.41366i	0.118631	+	0.0684919i
$427$	−2.05538	+	3.56002i	−0.0994667	+	0.172281i
$428$	5.51524	+	5.51524i	0.266589	+	0.266589i
$429$	−29.3271	−	22.8164i	−1.41593	−	1.10159i
$430$	4.17722	+	0.324454i	0.201443	+	0.0156466i
$431$	−34.5325	+	9.25295i	−1.66337	+	0.445699i	−0.963312	−	0.268385i	$-0.913510\pi$
$431$	−34.5325	+	9.25295i	−1.66337	+	0.445699i	−0.700060	+	0.714084i	$0.746843\pi$
$432$	−3.37220	+	0.903577i	−0.162245	+	0.0434734i
$433$	6.82761	−	25.4810i	0.328114	−	1.22454i	−0.583031	−	0.812450i	$-0.698133\pi$
$433$	6.82761	−	25.4810i	0.328114	−	1.22454i	0.911144	−	0.412087i	$-0.135200\pi$
$434$	0.269705	−	0.269705i	0.0129462	−	0.0129462i
$435$	−38.9177	+	18.6117i	−1.86596	+	0.892363i
$436$	13.2206	+	3.54246i	0.633154	+	0.169653i
$437$	−1.67144			−0.0799558
$438$	−3.81750	−	1.02290i	−0.182407	−	0.0488759i
$439$	−0.864675	+	1.49766i	−0.0412687	+	0.0714794i	−0.885922	−	0.463834i	$-0.846473\pi$
$439$	−0.864675	+	1.49766i	−0.0412687	+	0.0714794i	0.844653	+	0.535314i	$0.179807\pi$
$440$	8.67343	+	5.94803i	0.413490	+	0.283561i
$441$			17.7038i			0.843036i
$442$	−0.759965	+	1.80059i	−0.0361478	+	0.0856455i
$443$	2.86737	−	2.86737i	0.136233	−	0.136233i	−0.635702	−	0.771935i	$-0.719289\pi$
$443$	2.86737	−	2.86737i	0.136233	−	0.136233i	0.771935	+	0.635702i	$0.219289\pi$
$444$	5.67920	+	21.1951i	0.269523	+	1.00587i
$445$	9.21793	+	6.32143i	0.436972	+	0.299665i
$446$	−6.50564	+	3.75603i	−0.308051	+	0.177853i
$447$		−	5.98448i		−	0.283056i
$448$	−1.20544	−	2.08788i	−0.0569517	−	0.0986432i
$449$	−5.22508	+	19.5003i	−0.246587	+	0.920274i	0.725993	+	0.687702i	$0.241381\pi$
$449$	−5.22508	+	19.5003i	−0.246587	+	0.920274i	−0.972579	+	0.232571i	$0.925286\pi$
$450$	−0.548277	+	3.50813i	−0.0258460	+	0.165375i
$451$	−10.1534	−	17.5861i	−0.478103	−	0.828098i
$452$	−1.97958	−	7.38790i	−0.0931117	−	0.347497i
$453$	7.48135	+	4.31936i	0.351505	+	0.202941i
$454$	−1.90370			−0.0893452
$455$	−3.10947	+	0.145323i	−0.145774	+	0.00681286i
$456$	12.7686			0.597946
$457$	12.8012	+	7.39079i	0.598816	+	0.345727i	0.768576	−	0.639759i	$-0.220966\pi$
$457$	12.8012	+	7.39079i	0.598816	+	0.345727i	−0.169759	+	0.985486i	$0.554299\pi$
$458$	−0.459507	−	1.71490i	−0.0214713	−	0.0801321i
$459$	0.969184	+	1.67868i	0.0452377	+	0.0783539i
$460$	0.111172	−	1.43129i	0.00518341	−	0.0667344i
$461$	−1.57205	+	5.86696i	−0.0732175	+	0.273252i	−0.992823	−	0.119591i	$-0.961842\pi$
$461$	−1.57205	+	5.86696i	−0.0732175	+	0.273252i	0.919606	+	0.392843i	$0.128508\pi$
$462$	0.546735	+	0.946973i	0.0254364	+	0.0440572i
$463$			36.0148i			1.67375i	0.547396	+	0.836874i	$0.315619\pi$
$463$			36.0148i			1.67375i	−0.547396	+	0.836874i	$0.684381\pi$
$464$	−25.1179	+	14.5018i	−1.16607	+	0.673230i
$465$	18.6731	−	3.48062i	0.865943	−	0.161410i
$466$	−0.552297	−	2.06120i	−0.0255847	−	0.0954833i
$467$	7.68952	−	7.68952i	0.355829	−	0.355829i	−0.506444	−	0.862273i	$-0.669040\pi$
$467$	7.68952	−	7.68952i	0.355829	−	0.355829i	0.862273	+	0.506444i	$0.169040\pi$
$468$	2.45917	−	17.7614i	0.113675	−	0.821022i
$469$		−	2.46176i		−	0.113674i
$470$	1.10721	+	5.94004i	0.0510717	+	0.273993i
$471$	3.70562	−	6.41832i	0.170746	−	0.295741i
$472$	−2.52851	−	0.677511i	−0.116384	−	0.0311850i
$473$	29.7353			1.36723
$474$	−2.10099	−	0.562959i	−0.0965018	−	0.0258576i
$475$	10.1423	−	22.9060i	0.465360	−	1.05100i
$476$	−1.03637	+	1.03637i	−0.0475019	+	0.0475019i
$477$	6.78329	−	25.3156i	0.310586	−	1.15912i
$478$	−3.13061	+	0.838843i	−0.143191	+	0.0383678i
$479$	−8.87096	+	2.37697i	−0.405324	+	0.108606i	−0.455720	−	0.890123i	$-0.650618\pi$
$479$	−8.87096	+	2.37697i	−0.405324	+	0.108606i	0.0503960	+	0.998729i	$0.483952\pi$
$480$	−1.28208	+	16.5064i	−0.0585189	+	0.753408i
$481$	17.2325	+	2.38594i	0.785733	+	0.108789i
$482$	0.283559	+	0.283559i	0.0129157	+	0.0129157i
$483$	0.152191	−	0.263602i	0.00692492	−	0.0119943i
$484$	13.3650	+	7.71629i	0.607500	+	0.350740i
$485$	31.0973	+	10.9763i	1.41206	+	0.498410i
$486$	4.05331	+	4.05331i	0.183862	+	0.183862i
$487$	22.2840	−	12.8657i	1.00978	−	0.582998i	0.0986549	−	0.995122i	$-0.468546\pi$
$487$	22.2840	−	12.8657i	1.00978	−	0.582998i	0.911128	+	0.412123i	$0.135213\pi$
$488$	9.94399	−	5.74117i	0.450143	−	0.259890i
$489$	−24.7515	−	24.7515i	−1.11930	−	1.11930i
$490$	−3.96980	−	1.40121i	−0.179337	−	0.0633001i
$491$	11.4291	+	6.59859i	0.515788	+	0.297790i	0.735210	−	0.677840i	$-0.237084\pi$
$491$	11.4291	+	6.59859i	0.515788	+	0.297790i	−0.219422	+	0.975630i	$0.570417\pi$
$492$	10.5878	−	18.3386i	0.477336	−	0.826769i
$493$	11.3869	+	11.3869i	0.512839	+	0.512839i
$494$	1.93035	−	4.57360i	0.0868504	−	0.205776i
$495$	−1.95144	+	25.1241i	−0.0877108	+	1.12924i
$496$	12.3355	−	3.30529i	0.553881	−	0.148412i
$497$	1.62373	−	0.435076i	0.0728341	−	0.0195158i
$498$	0.872033	−	3.25447i	0.0390767	−	0.145836i
$499$	16.7683	−	16.7683i	0.750650	−	0.750650i	−0.223950	−	0.974601i	$-0.571895\pi$
$499$	16.7683	−	16.7683i	0.750650	−	0.750650i	0.974601	+	0.223950i	$0.0718954\pi$
$500$	18.9404	+	10.2086i	0.847039	+	0.456543i
$501$	−7.91620	−	2.12114i	−0.353670	−	0.0947655i
$502$	3.57520			0.159569
$503$	−7.28214	−	1.95124i	−0.324695	−	0.0870017i	0.0927898	−	0.995686i	$-0.470422\pi$
$503$	−7.28214	−	1.95124i	−0.324695	−	0.0870017i	−0.417485	+	0.908684i	$0.637088\pi$
$504$	−0.538025	+	0.931887i	−0.0239655	+	0.0415095i
$505$	2.16322	+	11.6054i	0.0962622	+	0.516435i
$506$			0.399817i			0.0177740i
$507$	−26.3967	−	15.7141i	−1.17232	−	0.697889i
$508$	−15.5186	+	15.5186i	−0.688528	+	0.688528i
$509$	−7.93327	−	29.6074i	−0.351636	−	1.31232i	−0.884666	−	0.466226i	$-0.845613\pi$
$509$	−7.93327	−	29.6074i	−0.351636	−	1.31232i	0.533030	−	0.846097i	$-0.321053\pi$
$510$	2.81572	−	0.524843i	0.124682	−	0.0232404i
$511$	−2.03499	+	1.17490i	−0.0900225	+	0.0519745i
$512$			18.7939i			0.830581i
$513$	−2.46178	−	4.26392i	−0.108690	−	0.188257i
$514$	−2.09547	+	7.82039i	−0.0924271	+	0.344942i
$515$	0.296312	−	3.81491i	0.0130571	−	0.168105i
$516$	15.5039	+	26.8535i	0.682519	+	1.18216i
$517$	11.0989	+	41.4218i	0.488131	+	1.82173i
$518$	−0.443368	−	0.255979i	−0.0194805	−	0.0112471i
$519$	−9.23923			−0.405557
$520$	7.72483	+	3.99122i	0.338756	+	0.175026i
$521$	−7.16076			−0.313719			−0.156859	−	0.987621i	$-0.550137\pi$
$521$	−7.16076			−0.313719			−0.156859	+	0.987621i	$0.550137\pi$
$522$	5.02094	+	2.89884i	0.219761	+	0.126879i
$523$	2.78390	+	10.3897i	0.121731	+	0.454308i	0.999702	−	0.0244065i	$-0.00776960\pi$
$523$	2.78390	+	10.3897i	0.121731	+	0.454308i	−0.877971	+	0.478714i	$0.841103\pi$
$524$	−20.0750	−	34.7709i	−0.876979	−	1.51897i
$525$	2.68900	+	3.68521i	0.117358	+	0.160836i
$526$	−0.359362	+	1.34116i	−0.0156689	+	0.0584773i
$527$	−3.54528	−	6.14061i	−0.154435	−	0.267489i
$528$			36.6115i			1.59331i
$529$	−19.8222	+	11.4444i	−0.861835	+	0.497581i
$530$	5.13975	+	3.52472i	0.223257	+	0.153104i
$531$	−1.62338	−	6.05854i	−0.0704487	−	0.262918i
$532$	2.63243	−	2.63243i	0.114130	−	0.114130i
$533$	−10.1311	−	13.3873i	−0.438826	−	0.579870i
$534$		−	3.24607i		−	0.140471i
$535$	−7.47394	−	5.12544i	−0.323127	−	0.221592i
$536$	−3.43815	+	5.95505i	−0.148505	+	0.257219i
$537$	−14.8311	−	3.97399i	−0.640011	−	0.171490i
$538$	−2.37709			−0.102484
$539$	−28.8594	−	7.73286i	−1.24306	−	0.333078i
$540$	3.81504	−	1.82447i	0.164173	−	0.0785129i
$541$	11.1986	−	11.1986i	0.481464	−	0.481464i	−0.424135	−	0.905599i	$-0.639422\pi$
$541$	11.1986	−	11.1986i	0.481464	−	0.481464i	0.905599	+	0.424135i	$0.139422\pi$
$542$	1.63799	−	6.11306i	0.0703576	−	0.262578i
$543$	−27.3554	+	7.32985i	−1.17393	+	0.314554i
$544$	5.96966	−	1.59957i	0.255947	−	0.0685808i
$545$	−15.8553	−	1.23152i	−0.679166	−	0.0527523i
$546$	0.545536	+	0.720878i	0.0233468	+	0.0308507i
$547$	−23.6205	−	23.6205i	−1.00994	−	1.00994i	−0.999950	−	0.00999077i	$-0.996820\pi$
$547$	−23.6205	−	23.6205i	−1.00994	−	1.00994i	−0.00999077	−	0.999950i	$-0.503180\pi$
$548$	0.234738	−	0.406578i	0.0100275	−	0.0173681i
$549$	23.8267	+	13.7564i	1.01690	+	0.587108i
$550$	−5.47923	−	2.42609i	−0.233635	−	0.103449i
$551$	−28.9232	−	28.9232i	−1.23217	−	1.23217i
$552$	−0.736305	+	0.425106i	−0.0313392	+	0.0180937i
$553$	−1.11997	+	0.646616i	−0.0476260	+	0.0274969i
$554$	4.20528	+	4.20528i	0.178665	+	0.178665i
$555$	−10.9996	−	23.0006i	−0.466908	−	0.976320i
$556$	−19.4732	−	11.2429i	−0.825847	−	0.476803i
$557$	−15.5732	+	26.9736i	−0.659859	+	1.14291i	0.320793	+	0.947149i	$0.396050\pi$
$557$	−15.5732	+	26.9736i	−0.659859	+	1.14291i	−0.980652	+	0.195759i	$0.937283\pi$
$558$	−1.80510	−	1.80510i	−0.0764159	−	0.0764159i
$559$	24.3944	−	3.04592i	1.03177	−	0.128829i
$560$	1.99433	+	2.33023i	0.0842759	+	0.0984702i
$561$	19.6349	−	5.26115i	0.828986	−	0.222126i
$562$	−3.06967	+	0.822517i	−0.129486	+	0.0346958i
$563$	−5.39509	+	20.1348i	−0.227376	+	0.848579i	0.754063	+	0.656802i	$0.228091\pi$
$563$	−5.39509	+	20.1348i	−0.227376	+	0.848579i	−0.981439	+	0.191776i	$0.938575\pi$
$564$	−31.6204	+	31.6204i	−1.33146	+	1.33146i
$565$	3.83410	+	8.01724i	0.161302	+	0.337288i
$566$	1.19433	+	0.320019i	0.0502013	+	0.0134514i
$567$	3.88985			0.163359
$568$	−4.53546	−	1.21527i	−0.190304	−	0.0509918i
$569$	20.8728	−	36.1527i	0.875031	−	1.51560i	0.0183019	−	0.999833i	$-0.494174\pi$
$569$	20.8728	−	36.1527i	0.875031	−	1.51560i	0.856729	−	0.515766i	$-0.172493\pi$
$570$	−7.15206	+	1.33313i	−0.299567	+	0.0558385i
$571$		−	19.2151i		−	0.804127i	−0.915612	−	0.402064i	$-0.868293\pi$
$571$		−	19.2151i		−	0.804127i	0.915612	−	0.402064i	$-0.131707\pi$
$572$	27.8793	+	11.7668i	1.16569	+	0.491996i
$573$	−8.67709	+	8.67709i	−0.362491	+	0.362491i
$574$	0.127872	+	0.477224i	0.00533727	+	0.0199190i
$575$	0.177752	+	1.65854i	0.00741278	+	0.0691660i
$576$	−13.9739	+	8.06785i	−0.582247	+	0.336160i
$577$		−	21.8168i		−	0.908243i	−0.890940	−	0.454122i	$-0.849953\pi$
$577$		−	21.8168i		−	0.908243i	0.890940	−	0.454122i	$-0.150047\pi$
$578$	1.80128	+	3.11991i	0.0749233	+	0.129771i
$579$	−4.08196	+	15.2341i	−0.169640	+	0.633107i
$580$	26.6914	−	22.8439i	1.10830	−	0.948542i
$581$	−1.00162	−	1.73485i	−0.0415541	−	0.0719738i
$582$	−2.47879	−	9.25095i	−0.102749	−	0.383464i
$583$	38.3048	+	22.1153i	1.58642	+	0.915922i
$584$	6.56356			0.271602
$585$	0.972630	+	20.8113i	0.0402133	+	0.860441i
$586$	−3.60150			−0.148777
$587$	5.07084	+	2.92765i	0.209296	+	0.120837i	0.600984	−	0.799261i	$-0.294775\pi$
$587$	5.07084	+	2.92765i	0.209296	+	0.120837i	−0.391688	+	0.920098i	$0.628109\pi$
$588$	−8.06375	−	30.0943i	−0.332543	−	1.24107i
$589$	9.00520	+	15.5975i	0.371053	+	0.642682i
$590$	1.48702	+	0.115500i	0.0612197	+	0.00475507i
$591$	11.9858	−	44.7316i	0.493030	−	1.84001i
$592$	−8.57065	−	14.8448i	−0.352252	−	0.610118i
$593$		−	45.6277i		−	1.87370i	−0.349727	−	0.936852i	$-0.613726\pi$
$593$		−	45.6277i		−	1.87370i	0.349727	−	0.936852i	$-0.386274\pi$
$594$	−1.01995	+	0.588870i	−0.0418492	+	0.0241616i
$595$	0.963122	−	1.40443i	0.0394842	−	0.0575759i
$596$	1.26141	+	4.70766i	0.0516695	+	0.192833i
$597$	24.5730	−	24.5730i	1.00571	−	1.00571i
$598$	0.0409550	+	0.328004i	0.00167477	+	0.0134131i
$599$		−	12.7240i		−	0.519888i	−0.965624	−	0.259944i	$-0.916296\pi$
$599$		−	12.7240i		−	0.519888i	0.965624	−	0.259944i	$-0.0837041\pi$
$600$	−1.35790	−	12.6701i	−0.0554362	−	0.517255i
$601$	12.3636	−	21.4144i	0.504321	−	0.873510i	−0.495666	−	0.868513i	$-0.665076\pi$
$601$	12.3636	−	21.4144i	0.504321	−	0.873510i	0.999988	−	0.00499702i	$-0.00159061\pi$
$602$	−0.698805	−	0.187244i	−0.0284812	−	0.00763151i
$603$	−16.4763			−0.670965
$604$	−6.79561	−	1.82088i	−0.276510	−	0.0740905i
$605$	−16.9088	−	5.96827i	−0.687442	−	0.242644i
$606$	2.42430	−	2.42430i	0.0984804	−	0.0984804i
$607$	1.13924	−	4.25169i	0.0462402	−	0.172571i	−0.938944	−	0.344070i	$-0.888194\pi$
$607$	1.13924	−	4.25169i	0.0462402	−	0.172571i	0.985184	+	0.171499i	$0.0548610\pi$
$608$	−15.1632	+	4.06298i	−0.614950	+	0.164775i
$609$	7.19505	−	1.92791i	0.291558	−	0.0781228i
$610$	−4.97048	+	4.25400i	−0.201249	+	0.172239i
$611$	13.3484	+	32.8449i	0.540019	+	1.32876i
$612$	6.93628	+	6.93628i	0.280382	+	0.280382i
$613$	−0.580288	+	1.00509i	−0.0234376	+	0.0405951i	−0.877506	−	0.479565i	$-0.840794\pi$
$613$	−0.580288	+	1.00509i	−0.0234376	+	0.0405951i	0.854069	+	0.520160i	$0.174128\pi$
$614$	−1.84550	−	1.06550i	−0.0744781	−	0.0430000i
$615$	−8.18929	+	23.2013i	−0.330224	+	0.935565i
$616$	−1.28409	−	1.28409i	−0.0517375	−	0.0517375i
$617$	−33.3212	+	19.2380i	−1.34146	+	0.774493i	−0.987022	−	0.160587i	$-0.948661\pi$
$617$	−33.3212	+	19.2380i	−1.34146	+	0.774493i	−0.354439	+	0.935079i	$0.615328\pi$
$618$	−0.962375	+	0.555628i	−0.0387124	+	0.0223506i
$619$	24.7229	+	24.7229i	0.993698	+	0.993698i	0.999980	−	0.00628240i	$-0.00199976\pi$
$619$	24.7229	+	24.7229i	0.993698	+	0.993698i	−0.00628240	+	0.999980i	$0.502000\pi$
$620$	−13.9554	+	6.67394i	−0.560464	+	0.268032i
$621$	0.283917	+	0.163920i	0.0113932	+	0.00657787i
$622$	1.59431	−	2.76142i	0.0639258	−	0.110723i
$623$	−1.36470	−	1.36470i	−0.0546757	−	0.0546757i
$624$	3.75027	+	30.0355i	0.150131	+	1.20238i
$625$	−23.8078	−	7.62804i	−0.952313	−	0.305122i
$626$	3.81269	−	1.02161i	0.152386	−	0.0408317i
$627$	−49.8736	+	13.3636i	−1.99176	+	0.533690i
$628$	−1.56215	+	5.83002i	−0.0623365	+	0.232643i
$629$	−6.72971	+	6.72971i	−0.268331	+	0.268331i
$630$	0.204067	−	0.578148i	0.00813024	−	0.0230340i
$631$	−7.05694	−	1.89090i	−0.280933	−	0.0752756i	0.115601	−	0.993296i	$-0.463120\pi$
$631$	−7.05694	−	1.89090i	−0.280933	−	0.0752756i	−0.396534	+	0.918020i	$0.629787\pi$
$632$	3.61231			0.143690
$633$	48.8794	+	13.0972i	1.94278	+	0.520567i
$634$	2.99110	−	5.18074i	0.118792	−	0.205753i
$635$	14.4218	−	21.0300i	0.572313	−	0.834549i
$636$			46.1232i			1.82891i
$637$	−24.4679	−	3.38773i	−0.969455	−	0.134227i
$638$	−6.91860	+	6.91860i	−0.273910	+	0.273910i
$639$	−2.91191	−	10.8674i	−0.115193	−	0.429907i
$640$	−3.27072	−	17.5470i	−0.129287	−	0.693607i
$641$	−7.19858	+	4.15610i	−0.284327	+	0.164156i	−0.635381	−	0.772199i	$-0.719157\pi$
$641$	−7.19858	+	4.15610i	−0.284327	+	0.164156i	0.351054	+	0.936355i	$0.385823\pi$
$642$			2.63193i			0.103874i
$643$	−5.57779	−	9.66101i	−0.219967	−	0.380993i	0.734831	−	0.678250i	$-0.237261\pi$
$643$	−5.57779	−	9.66101i	−0.219967	−	0.380993i	−0.954797	+	0.297257i	$0.903928\pi$
$644$	−0.0641579	+	0.239440i	−0.00252817	+	0.00943528i
$645$	−23.4264	−	27.3720i	−0.922414	−	1.07777i
$646$	1.35789	+	2.35194i	0.0534257	+	0.0925360i
$647$	10.8961	+	40.6647i	0.428369	+	1.59870i	0.756454	+	0.654047i	$0.226930\pi$
$647$	10.8961	+	40.6647i	0.428369	+	1.59870i	−0.328085	+	0.944648i	$0.606403\pi$
$648$	−9.40963	−	5.43265i	−0.369645	−	0.213415i
$649$	10.5853			0.415509
$650$	−4.74360	−	1.42907i	−0.186059	−	0.0560526i
$651$	−3.27983			−0.128547
$652$	24.6878	+	14.2535i	0.966849	+	0.558211i
$653$	−11.0577	−	41.2678i	−0.432721	−	1.61494i	−0.746463	−	0.665427i	$-0.768250\pi$
$653$	−11.0577	−	41.2678i	−0.432721	−	1.61494i	0.313742	−	0.949508i	$-0.398417\pi$
$654$	2.30926	+	3.99976i	0.0902994	+	0.156403i
$655$	30.3334	+	35.4423i	1.18522	+	1.38485i
$656$	−4.28140	+	15.9784i	−0.167160	+	0.623851i
$657$	7.86345	+	13.6199i	0.306782	+	0.531363i
$658$		−	1.04334i		−	0.0406735i
$659$	15.2491	−	8.80408i	0.594021	−	0.342958i	−0.172665	−	0.984981i	$-0.555238\pi$
$659$	15.2491	−	8.80408i	0.594021	−	0.342958i	0.766686	+	0.642023i	$0.221904\pi$
$660$	−8.12635	−	43.5968i	−0.316318	−	1.69700i
$661$	7.21232	+	26.9167i	0.280527	+	1.04694i	0.952047	+	0.305953i	$0.0989751\pi$
$661$	7.21232	+	26.9167i	0.280527	+	1.04694i	−0.671520	+	0.740987i	$0.734358\pi$
$662$	3.81246	−	3.81246i	0.148175	−	0.148175i
$663$	15.5692	−	6.32746i	0.604659	−	0.245738i
$664$			5.59552i			0.217148i
$665$	−2.44638	+	3.56732i	−0.0948665	+	0.138335i
$666$	−1.71323	+	2.96740i	−0.0663863	+	0.114985i
$667$	2.63080	+	0.704922i	0.101865	+	0.0272947i
$668$	6.67434			0.258238
$669$	62.3951	+	16.7187i	2.41234	+	0.646383i
$670$	1.30406	−	3.69455i	0.0503800	−	0.142733i
$671$	−32.8320	+	32.8320i	−1.26747	+	1.26747i
$672$	0.739899	−	2.76134i	0.0285422	−	0.106521i
$673$	7.05459	−	1.89027i	0.271934	−	0.0728646i	−0.120275	−	0.992741i	$-0.538378\pi$
$673$	7.05459	−	1.89027i	0.271934	−	0.0728646i	0.392209	+	0.919876i	$0.371711\pi$
$674$	3.51350	−	0.941440i	0.135335	−	0.0362629i
$675$	−3.96922	+	2.89624i	−0.152775	+	0.111476i
$676$	24.0771	+	6.79753i	0.926042	+	0.261444i
$677$	3.26988	+	3.26988i	0.125672	+	0.125672i	0.767145	−	0.641473i	$-0.221677\pi$
$677$	3.26988	+	3.26988i	0.125672	+	0.125672i	−0.641473	+	0.767145i	$0.721677\pi$
$678$	1.29045	−	2.23513i	0.0495595	−	0.0858397i
$679$	−4.93138	−	2.84713i	−0.189249	−	0.109263i
$680$	−4.29126	+	2.05222i	−0.164562	+	0.0786991i
$681$	11.5753	+	11.5753i	0.443566	+	0.443566i
$682$	3.73100	−	2.15409i	0.142867	−	0.0824845i
$683$	23.4651	−	13.5476i	0.897868	−	0.518384i	0.0213600	−	0.999772i	$-0.493200\pi$
$683$	23.4651	−	13.5476i	0.897868	−	0.518384i	0.876508	+	0.481388i	$0.159867\pi$
$684$	−17.6185	−	17.6185i	−0.673660	−	0.673660i
$685$	−0.181561	+	0.514385i	−0.00693709	+	0.0196536i
$686$	1.27275	+	0.734823i	0.0485939	+	0.0280557i
$687$	−7.63332	+	13.2213i	−0.291229	+	0.504424i
$688$	−17.1280	−	17.1280i	−0.653000	−	0.653000i
$689$	33.6901	+	14.2193i	1.28349	+	0.541714i
$690$	0.368040	−	0.314988i	0.0140111	−	0.0119914i
$691$	−12.1374	+	3.25221i	−0.461729	+	0.123720i	−0.482182	−	0.876071i	$-0.660156\pi$
$691$	−12.1374	+	3.25221i	−0.461729	+	0.123720i	0.0204532	+	0.999791i	$0.493489\pi$
$692$	7.26800	−	1.94746i	0.276288	−	0.0740311i
$693$	1.12619	−	4.20299i	0.0427804	−	0.159658i
$694$	5.37339	−	5.37339i	0.203971	−	0.203971i
$695$	24.6367	+	8.69594i	0.934522	+	0.329856i
$696$	−20.0975	−	5.38511i	−0.761795	−	0.204122i
$697$	9.18452			0.347889
$698$	7.83515	+	2.09942i	0.296565	+	0.0794643i
$699$	−9.17475	+	15.8911i	−0.347021	+	0.601058i
$700$	−2.89207	−	2.33217i	−0.109310	−	0.0881476i
$701$		−	39.3955i		−	1.48795i	−0.668208	−	0.743974i	$-0.732938\pi$
$701$		−	39.3955i		−	1.48795i	0.668208	−	0.743974i	$-0.267062\pi$
$702$	−0.776434	+	0.587578i	−0.0293046	+	0.0221767i
$703$	17.0938	−	17.0938i	0.644705	−	0.644705i
$704$	−7.04795	−	26.3033i	−0.265630	−	0.991343i
$705$	29.3856	−	42.8501i	1.10672	−	1.61383i
$706$	3.72112	−	2.14839i	0.140046	−	0.0808557i
$707$		−	2.03843i		−	0.0766631i
$708$	5.51911	+	9.55939i	0.207421	+	0.359264i
$709$	−6.62303	+	24.7175i	−0.248733	+	0.928285i	0.722737	+	0.691123i	$0.242884\pi$
$709$	−6.62303	+	24.7175i	−0.248733	+	0.928285i	−0.971470	+	0.237162i	$0.923783\pi$
$710$	2.66732	+	0.207176i	0.100103	+	0.00777519i
$711$	4.32771	+	7.49582i	0.162302	+	0.281115i
$712$	1.39527	+	5.20722i	0.0522900	+	0.195149i
$713$	−1.03857	−	0.599619i	−0.0388948	−	0.0224559i
$714$	−0.494566			−0.0185087
$715$	−34.3500	−	7.50470i	−1.28462	−	0.280660i
$716$	12.5045			0.467315
$717$	24.1359	+	13.9349i	0.901371	+	0.520407i
$718$	−1.41417	−	5.27777i	−0.0527765	−	0.196965i
$719$	4.34268	+	7.52174i	0.161955	+	0.280514i	0.935570	−	0.353142i	$-0.114887\pi$
$719$	4.34268	+	7.52174i	0.161955	+	0.280514i	−0.773615	+	0.633656i	$0.781554\pi$
$720$	15.5959	−	13.3478i	0.581226	−	0.497443i
$721$	−0.171004	+	0.638194i	−0.00636851	+	0.0237676i
$722$	−0.838438	−	1.45222i	−0.0312034	−	0.0540460i
$723$		−	3.44830i		−	0.128244i
$724$	19.9740	−	11.5320i	0.742327	−	0.428583i
$725$	−25.6242	+	31.7760i	−0.951658	+	1.18013i
$726$	1.34781	+	5.03011i	0.0500220	+	0.186685i
$727$	−17.4677	+	17.4677i	−0.647841	+	0.647841i	−0.952471	−	0.304630i	$-0.901467\pi$
$727$	−17.4677	+	17.4677i	−0.647841	+	0.647841i	0.304630	+	0.952471i	$0.401467\pi$
$728$	−1.18498	−	0.921915i	−0.0439184	−	0.0341684i
$729$		−	19.0676i		−	0.706209i
$730$	−3.67643	+	0.685277i	−0.136071	+	0.0253632i
$731$	−6.72450	+	11.6472i	−0.248715	+	0.430786i
$732$	−46.7685	−	12.5316i	−1.72861	−	0.463180i
$733$	−34.2413			−1.26473			−0.632365	−	0.774670i	$-0.717916\pi$
$733$	−34.2413			−1.26473			−0.632365	+	0.774670i	$0.717916\pi$
$734$	−5.84646	−	1.56655i	−0.215797	−	0.0578225i
$735$	15.6181	+	32.6579i	0.576081	+	1.20461i
$736$	0.739121	−	0.739121i	0.0272444	−	0.0272444i
$737$	7.19670	−	26.8584i	0.265094	−	0.989344i
$738$	3.19400	−	0.855830i	0.117573	−	0.0315035i
$739$	−27.2869	+	7.31150i	−1.00376	+	0.268958i	−0.723022	−	0.690825i	$-0.757247\pi$
$739$	−27.2869	+	7.31150i	−1.00376	+	0.268958i	−0.280743	+	0.959783i	$0.590581\pi$
$740$	13.5009	+	15.7748i	0.496302	+	0.579893i
$741$	−39.5467	+	16.0720i	−1.45278	+	0.590421i
$742$	−0.760935	−	0.760935i	−0.0279348	−	0.0279348i
$743$	−15.8384	+	27.4329i	−0.581055	+	1.00642i	0.414299	+	0.910141i	$0.364027\pi$
$743$	−15.8384	+	27.4329i	−0.581055	+	1.00642i	−0.995355	+	0.0962765i	$0.969307\pi$
$744$	7.93397	+	4.58068i	0.290873	+	0.167936i
$745$	−2.44314	−	5.10868i	−0.0895096	−	0.187168i
$746$	−0.226489	−	0.226489i	−0.00829237	−	0.00829237i
$747$	−11.6111	+	6.70370i	−0.424830	+	0.245275i
$748$	−14.3367	+	8.27733i	−0.524203	+	0.302649i
$749$	1.10651	+	1.10651i	0.0404309	+	0.0404309i
$750$	2.08344	+	6.95510i	0.0760764	+	0.253964i
$751$	2.11351	+	1.22024i	0.0771231	+	0.0445271i	0.538066	−	0.842903i	$-0.319155\pi$
$751$	2.11351	+	1.22024i	0.0771231	+	0.0445271i	−0.460943	+	0.887430i	$0.652489\pi$
$752$	17.4665	−	30.2528i	0.636936	−	1.10321i
$753$	−21.7387	−	21.7387i	−0.792201	−	0.792201i
$754$	−4.96721	+	6.38462i	−0.180895	+	0.232514i
$755$	8.14986	+	0.633018i	0.296604	+	0.0230379i
$756$	−0.705319	+	0.188990i	−0.0256522	+	0.00687349i
$757$	−41.2367	+	11.0493i	−1.49877	+	0.401595i	−0.912689	−	0.408655i	$-0.865998\pi$
$757$	−41.2367	+	11.0493i	−1.49877	+	0.401595i	−0.586084	+	0.810250i	$0.699331\pi$
$758$	1.87595	−	7.00115i	0.0681377	−	0.254293i
$759$	2.43105	−	2.43105i	0.0882416	−	0.0882416i
$760$	10.9000	−	5.21274i	0.395385	−	0.189086i
$761$	−38.5996	−	10.3427i	−1.39923	−	0.374923i	−0.521164	−	0.853457i	$-0.674502\pi$
$761$	−38.5996	−	10.3427i	−1.39923	−	0.374923i	−0.878069	+	0.478533i	$0.841169\pi$
$762$	−7.40565			−0.268279
$763$	2.65242	+	0.710715i	0.0960242	+	0.0257296i
$764$	4.99683	−	8.65476i	0.180779	−	0.313118i
$765$	−9.39965	−	6.44605i	−0.339845	−	0.233057i
$766$			9.01376i			0.325680i
$767$	8.68401	−	1.08429i	0.313561	−	0.0391516i
$768$	17.2018	−	17.2018i	0.620716	−	0.620716i
$769$	−9.91969	−	37.0208i	−0.357713	−	1.33500i	−0.877035	−	0.480426i	$-0.840482\pi$
$769$	−9.91969	−	37.0208i	−0.357713	−	1.33500i	0.519322	−	0.854579i	$-0.326184\pi$
$770$	0.853322	+	0.585187i	0.0307516	+	0.0210887i
$771$	60.2925	−	34.8099i	2.17138	−	1.25365i
$772$		−	12.8442i		−	0.462274i
$773$	7.28940	+	12.6256i	0.262181	+	0.454111i	0.966821	−	0.255454i	$-0.0822248\pi$
$773$	7.28940	+	12.6256i	0.262181	+	0.454111i	−0.704640	+	0.709565i	$0.748891\pi$
$774$	−1.25320	+	4.67701i	−0.0450454	+	0.168112i
$775$	14.5194	−	10.5945i	0.521553	−	0.380564i
$776$	7.95274	+	13.7745i	0.285487	+	0.494477i
$777$	1.13940	+	4.25231i	0.0408759	+	0.152551i
$778$	−2.22956	−	1.28724i	−0.0799337	−	0.0461497i
$779$	−23.3291			−0.835853
$780$	−11.1325	−	34.9338i	−0.398609	−	1.25083i
$781$	18.9872			0.679414
$782$	−0.156606	−	0.0904167i	−0.00560023	−	0.00323329i
$783$	2.07649	+	7.74955i	0.0742075	+	0.276946i
$784$	12.1692	+	21.0777i	0.434616	+	0.752777i
$785$	0.543072	−	6.99184i	0.0193831	−	0.249549i
$786$	3.50652	−	13.0865i	0.125073	−	0.466780i
$787$	−0.473902	−	0.820823i	−0.0168928	−	0.0292592i	0.857455	−	0.514558i	$-0.172044\pi$
$787$	−0.473902	−	0.820823i	−0.0168928	−	0.0292592i	−0.874348	+	0.485299i	$0.838711\pi$
$788$			37.7143i			1.34352i
$789$	10.3399	−	5.96972i	0.368109	−	0.212528i
$790$	−2.02335	+	0.377148i	−0.0719876	+	0.0134183i
$791$	−0.397158	−	1.48222i	−0.0141213	−	0.0527015i
$792$	−8.59426	+	8.59426i	−0.305384	+	0.305384i
$793$	−23.5718	+	30.2980i	−0.837058	+	1.07591i
$794$		−	3.20207i		−	0.113637i
$795$	−9.82008	−	52.6835i	−0.348283	−	1.86849i
$796$	−14.1507	+	24.5098i	−0.501560	+	0.868727i
$797$	−4.51774	−	1.21053i	−0.160027	−	0.0428790i	0.177916	−	0.984046i	$-0.443064\pi$
$797$	−4.51774	−	1.21053i	−0.160027	−	0.0428790i	−0.337943	+	0.941167i	$0.609731\pi$
$798$	1.25622			0.0444698
$799$	−18.7347	−	5.01994i	−0.662785	−	0.177593i
$800$	5.64419	+	14.6142i	0.199552	+	0.516688i
$801$	−9.13379	+	9.13379i	−0.322726	+	0.322726i
$802$	−1.46638	+	5.47260i	−0.0517796	+	0.193244i
$803$	−25.6369	+	6.86939i	−0.904707	+	0.242415i
$804$	28.0077	−	7.50465i	0.987756	−	0.264668i
$805$	0.0223041	−	0.287157i	0.000786117	−	0.0101210i
$806$	2.84020	−	2.14937i	0.100042	−	0.0757082i
$807$	14.4537	+	14.4537i	0.508794	+	0.508794i
$808$	−2.84692	+	4.93101i	−0.100154	+	0.173472i
$809$	21.1627	+	12.2183i	0.744040	+	0.429572i	0.823536	−	0.567263i	$-0.191998\pi$
$809$	21.1627	+	12.2183i	0.744040	+	0.429572i	−0.0794964	+	0.996835i	$0.525331\pi$
$810$	5.83779	+	2.06055i	0.205119	+	0.0724003i
$811$	−9.34795	−	9.34795i	−0.328251	−	0.328251i	0.523670	−	0.851921i	$-0.324562\pi$
$811$	−9.34795	−	9.34795i	−0.328251	−	0.328251i	−0.851921	+	0.523670i	$0.824562\pi$
$812$	−5.25359	+	3.03316i	−0.184365	+	0.106443i
$813$	−47.1295	+	27.2103i	−1.65291	+	0.954305i
$814$	−4.08893	−	4.08893i	−0.143317	−	0.143317i
$815$	−31.2340	−	11.0246i	−1.09408	−	0.386174i
$816$	−14.3405	−	8.27951i	−0.502019	−	0.289841i
$817$	17.0806	−	29.5844i	0.597573	−	1.03503i
$818$	−0.885667	−	0.885667i	−0.0309666	−	0.0309666i
$819$	0.493378	−	3.56343i	0.0172400	−	0.124516i
$820$	1.55168	−	19.9773i	0.0541871	−	0.697638i
$821$	−1.89876	+	0.508771i	−0.0662672	+	0.0177562i	−0.291800	−	0.956479i	$-0.594254\pi$
$821$	−1.89876	+	0.508771i	−0.0662672	+	0.0177562i	0.225533	+	0.974236i	$0.427588\pi$
$822$	0.153021	−	0.0410019i	0.00533723	−	0.00143011i
$823$	4.25627	−	15.8846i	0.148364	−	0.553703i	−0.851218	−	0.524812i	$-0.824136\pi$
$823$	4.25627	−	15.8846i	0.148364	−	0.553703i	0.999583	−	0.0288913i	$-0.00919767\pi$
$824$	1.30498	−	1.30498i	0.0454610	−	0.0454610i
$825$	18.5644	+	48.0676i	0.646329	+	1.67350i
$826$	−0.248763	−	0.0666558i	−0.00865557	−	0.00231925i
$827$	27.3262			0.950225			0.475113	−	0.879925i	$-0.342407\pi$
$827$	27.3262			0.950225			0.475113	+	0.879925i	$0.342407\pi$
$828$	1.60254	+	0.429400i	0.0556922	+	0.0149227i
$829$	7.27764	−	12.6052i	0.252763	−	0.437798i	−0.711523	−	0.702663i	$-0.751994\pi$
$829$	7.27764	−	12.6052i	0.252763	−	0.437798i	0.964286	+	0.264865i	$0.0853274\pi$
$830$	−0.584208	−	3.13420i	−0.0202782	−	0.108790i
$831$		−	51.1397i		−	1.77402i
$832$	−8.47639	−	20.8569i	−0.293866	−	0.723082i
$833$	9.55534	−	9.55534i	0.331073	−	0.331073i
$834$	−1.96380	−	7.32901i	−0.0680009	−	0.253783i
$835$	−7.62366	+	1.42103i	−0.263827	+	0.0491768i
$836$	36.4161	−	21.0248i	1.25948	−	0.727159i
$837$		−	3.53259i		−	0.122104i
$838$	−0.0895937	−	0.155181i	−0.00309496	−	0.00536063i
$839$	−6.33030	+	23.6250i	−0.218546	+	0.815625i	0.766342	+	0.642433i	$0.222075\pi$
$839$	−6.33030	+	23.6250i	−0.218546	+	0.815625i	−0.984888	+	0.173192i	$0.944592\pi$
$840$	−0.170388	+	2.19368i	−0.00587895	+	0.0756892i
$841$	18.8262	+	32.6080i	0.649180	+	1.12441i
$842$	0.561370	+	2.09506i	0.0193461	+	0.0722006i
$843$	23.6661	+	13.6636i	0.815104	+	0.470601i
$844$	−41.2114			−1.41856
$845$	−28.9489	−	2.63813i	−0.995873	−	0.0907544i
$846$	−6.98292			−0.240078
$847$	2.68139	+	1.54810i	0.0921335	+	0.0531933i
$848$	−9.32543	−	34.8030i	−0.320237	−	1.19514i
$849$	−5.31615	−	9.20784i	−0.182450	−	0.316012i
$850$	2.18939	−	1.59754i	0.0750954	−	0.0547951i
$851$	−0.416612	+	1.55482i	−0.0142813	+	0.0532985i
$852$	9.89982	+	17.1470i	0.339162	+	0.587446i
$853$		−	2.94669i		−	0.100893i	−0.998727	−	0.0504464i	$-0.983936\pi$
$853$		−	2.94669i		−	0.100893i	0.998727	−	0.0504464i	$-0.0160644\pi$
$854$	0.978324	−	0.564835i	0.0334775	−	0.0193283i
$855$	23.8756	+	16.3733i	0.816528	+	0.559955i
$856$	−1.13129	−	4.22204i	−0.0386667	−	0.144306i
$857$	−13.0632	+	13.0632i	−0.446229	+	0.446229i	−0.894099	−	0.447870i	$-0.852183\pi$
$857$	−13.0632	+	13.0632i	−0.446229	+	0.446229i	0.447870	+	0.894099i	$0.352183\pi$
$858$	3.84452	+	9.45978i	0.131250	+	0.322951i
$859$		−	3.08382i		−	0.105219i	−0.998615	−	0.0526093i	$-0.983246\pi$
$859$		−	3.08382i		−	0.105219i	0.998615	−	0.0526093i	$-0.0167538\pi$
$860$	24.1978	+	16.5942i	0.825137	+	0.565859i
$861$	2.12421	−	3.67923i	0.0723928	−	0.125388i
$862$	9.48982	+	2.54279i	0.323225	+	0.0866078i
$863$	50.9818			1.73544			0.867720	−	0.497053i	$-0.165585\pi$
$863$	50.9818			1.73544			0.867720	+	0.497053i	$0.165585\pi$
$864$	2.97415	+	0.796920i	0.101183	+	0.0271118i
$865$	−7.88713	+	3.77188i	−0.268170	+	0.128248i
$866$	−5.12611	+	5.12611i	−0.174192	+	0.174192i
$867$	8.01780	−	29.9228i	0.272299	−	1.01623i
$868$	2.58006	−	0.691326i	0.0875730	−	0.0234651i
$869$	−14.1095	+	3.78062i	−0.478631	+	0.128249i
$870$	11.8194	+	0.918039i	0.400715	+	0.0311244i
$871$	3.15284	−	22.7715i	0.106830	−	0.771581i
$872$	−5.42366	−	5.42366i	−0.183668	−	0.183668i
$873$	−19.0555	+	33.0051i	−0.644931	+	1.11705i
$874$	0.397788	+	0.229663i	0.0134554	+	0.00776846i
$875$	3.79996	+	2.04813i	0.128462	+	0.0692394i
$876$	−19.5706	−	19.5706i	−0.661228	−	0.661228i
$877$	−23.1824	+	13.3844i	−0.782814	+	0.451958i	−0.837427	−	0.546550i	$-0.815941\pi$
$877$	−23.1824	+	13.3844i	−0.782814	+	0.451958i	0.0546128	+	0.998508i	$0.482608\pi$
$878$	0.411570	−	0.237620i	0.0138898	−	0.00801929i
$879$	21.8986	+	21.8986i	0.738621	+	0.738621i
$880$	14.9465	+	31.2536i	0.503846	+	1.05356i
$881$	27.2630	+	15.7403i	0.918512	+	0.530303i	0.883160	−	0.469072i	$-0.155411\pi$
$881$	27.2630	+	15.7403i	0.918512	+	0.530303i	0.0353521	+	0.999375i	$0.488745\pi$
$882$	2.43257	−	4.21334i	0.0819089	−	0.141870i
$883$	27.3576	+	27.3576i	0.920657	+	0.920657i	0.997076	−	0.0764191i	$-0.0243487\pi$
$883$	27.3576	+	27.3576i	0.920657	+	0.920657i	−0.0764191	+	0.997076i	$0.524349\pi$
$884$	−10.9138	+	8.25917i	−0.367070	+	0.277786i
$885$	−8.33941	−	9.74398i	−0.280326	−	0.327540i
$886$	−1.07640	+	0.288420i	−0.0361623	+	0.00968965i
$887$	1.32670	−	0.355489i	0.0445463	−	0.0119362i	−0.236477	−	0.971637i	$-0.575993\pi$
$887$	1.32670	−	0.355489i	0.0445463	−	0.0119362i	0.281023	+	0.959701i	$0.409326\pi$
$888$	3.18263	−	11.8777i	0.106802	−	0.398591i
$889$	−3.11346	+	3.11346i	−0.104422	+	0.104422i
$890$	−1.32520	−	2.77103i	−0.0444206	−	0.0928851i
$891$	42.4393	+	11.3716i	1.42177	+	0.380962i
$892$	−52.6068			−1.76141
$893$	47.5870	+	12.7509i	1.59244	+	0.426692i
$894$	−0.822293	+	1.42425i	−0.0275016	+	0.0476341i
$895$	−14.2831	+	2.66233i	−0.477430	+	0.0889918i
$896$			3.08204i			0.102964i
$897$	1.74538	−	2.24342i	0.0582764	−	0.0749057i
$898$	3.92294	−	3.92294i	0.130910	−	0.130910i
$899$	−7.59580	−	28.3479i	−0.253334	−	0.945456i
$900$	−15.6089	+	19.3562i	−0.520296	+	0.645207i
$901$	−17.3249	+	10.0025i	−0.577176	+	0.333233i
$902$			5.58046i			0.185809i
$903$	3.11050	+	5.38754i	0.103511	+	0.179286i
$904$	−1.10936	+	4.14019i	−0.0368968	+	0.137701i
$905$	−20.3597	+	17.4249i	−0.676779	+	0.579223i
$906$	−1.18700	−	2.05594i	−0.0394354	−	0.0683040i
$907$	−6.02625	−	22.4903i	−0.200098	−	0.746777i	−0.990888	−	0.134689i	$-0.956996\pi$
$907$	−6.02625	−	22.4903i	−0.200098	−	0.746777i	0.790790	−	0.612088i	$-0.209670\pi$
$908$	−11.5455	−	6.66580i	−0.383151	−	0.221212i
$909$	−13.6430			−0.452508
$910$	0.759995	+	0.392669i	0.0251936	+	0.0130169i
$911$	2.89704			0.0959832			0.0479916	−	0.998848i	$-0.484718\pi$
$911$	2.89704			0.0959832			0.0479916	+	0.998848i	$0.484718\pi$
$912$	36.4256	+	21.0304i	1.20617	+	0.696385i
$913$	−5.85624	−	21.8558i	−0.193813	−	0.723322i
$914$	−2.03105	−	3.51789i	−0.0671813	−	0.116361i
$915$	56.0886	+	4.35653i	1.85423	+	0.144022i
$916$	3.21792	−	12.0094i	0.106323	−	0.396803i
$917$	−4.02759	−	6.97599i	−0.133003	−	0.230368i
$918$		−	0.532680i		−	0.0175811i
$919$	−14.3846	+	8.30494i	−0.474503	+	0.273955i	−0.718123	−	0.695916i	$-0.754998\pi$
$919$	−14.3846	+	8.30494i	−0.474503	+	0.273955i	0.243620	+	0.969871i	$0.421665\pi$
$920$	−0.455003	+	0.663488i	−0.0150010	+	0.0218745i
$921$	4.74271	+	17.7000i	0.156278	+	0.583236i
$922$	1.18028	−	1.18028i	0.0388704	−	0.0388704i
$923$	15.5768	−	1.94494i	0.512716	−	0.0640183i
$924$			7.65756i			0.251915i
$925$	−18.7798	−	15.1440i	−0.617475	−	0.497932i
$926$	4.94858	−	8.57120i	0.162621	−	0.281667i
$927$	4.27135	+	1.14451i	0.140290	+	0.0375905i
$928$	25.5801			0.839708
$929$	41.3672	+	11.0843i	1.35721	+	0.363664i	0.862792	−	0.505559i	$-0.168714\pi$
$929$	41.3672	+	11.0843i	1.35721	+	0.363664i	0.494420	+	0.869223i	$0.335380\pi$
$930$	−4.92228	−	1.73740i	−0.161408	−	0.0569717i
$931$	−24.2710	+	24.2710i	−0.795451	+	0.795451i
$932$	3.86773	−	14.4346i	0.126692	−	0.472820i
$933$	−26.4846	+	7.09653i	−0.867067	+	0.232330i
$934$	−2.88661	+	0.773465i	−0.0944528	+	0.0253086i
$935$	14.6136	−	12.5071i	0.477916	−	0.409025i
$936$	−6.17025	+	7.93095i	−0.201681	+	0.259231i
$937$	27.9881	+	27.9881i	0.914331	+	0.914331i	0.996609	−	0.0822783i	$-0.0262196\pi$
$937$	27.9881	+	27.9881i	0.914331	+	0.914331i	−0.0822783	+	0.996609i	$0.526220\pi$
$938$	−0.338257	+	0.585878i	−0.0110445	+	0.0191296i
$939$	−29.3945	−	16.9709i	−0.959254	−	0.553826i
$940$	−14.0840	+	39.9018i	−0.459371	+	1.30145i
$941$	−4.15042	−	4.15042i	−0.135300	−	0.135300i	0.636213	−	0.771513i	$-0.280500\pi$
$941$	−4.15042	−	4.15042i	−0.135300	−	0.135300i	−0.771513	+	0.636213i	$0.780500\pi$
$942$	−1.76381	+	1.01834i	−0.0574680	+	0.0331792i
$943$	1.34528	−	0.776696i	0.0438083	−	0.0252927i
$944$	−6.09729	−	6.09729i	−0.198450	−	0.198450i
$945$	0.765402	−	0.366040i	0.0248985	−	0.0119073i
$946$	−7.07675	−	4.08576i	−0.230085	−	0.132840i
$947$	12.4299	−	21.5292i	0.403918	−	0.699606i	−0.590277	−	0.807201i	$-0.700982\pi$
$947$	12.4299	−	21.5292i	0.403918	−	0.699606i	0.994195	+	0.107595i	$0.0343148\pi$
$948$	−10.7708	−	10.7708i	−0.349820	−	0.349820i
$949$	−20.3285	+	8.26164i	−0.659890	+	0.268184i
$950$	−5.56115	+	4.05783i	−0.180428	+	0.131653i
$951$	−49.6881	+	13.3139i	−1.61125	+	0.431732i
$952$	0.793363	−	0.212581i	0.0257130	−	0.00688979i
$953$	8.46463	−	31.5904i	0.274196	−	1.02331i	−0.682182	−	0.731182i	$-0.738969\pi$
$953$	8.46463	−	31.5904i	0.274196	−	1.02331i	0.956378	−	0.292131i	$-0.0943645\pi$
$954$	−5.09284	+	5.09284i	−0.164887	+	0.164887i
$955$	−3.86486	+	10.9496i	−0.125064	+	0.354322i
$956$	−21.9236	−	5.87441i	−0.709059	−	0.189992i
$957$	84.1358			2.71973
$958$	2.43782	+	0.653211i	0.0787622	+	0.0211043i
$959$	0.0470949	−	0.0815707i	0.00152077	−	0.00263405i
$960$	−18.6602	+	27.2103i	−0.602254	+	0.878209i
$961$		−	18.0777i		−	0.583153i
$962$	−3.77334	−	2.93565i	−0.121657	−	0.0946491i
$963$	7.40571	−	7.40571i	0.238646	−	0.238646i
$964$	0.726837	+	2.71259i	0.0234098	+	0.0873667i
$965$	2.73466	+	14.6711i	0.0880318	+	0.472280i
$966$	−0.0724402	+	0.0418234i	−0.00233072	+	0.00134564i
$967$			30.0090i			0.965023i	0.875890	+	0.482512i	$0.160275\pi$
$967$			30.0090i			0.965023i	−0.875890	+	0.482512i	$0.839725\pi$
$968$	−4.32422	−	7.48976i	−0.138986	−	0.240730i
$969$	6.04422	−	22.5573i	0.194168	−	0.724646i
$970$	−5.89269	−	6.88518i	−0.189203	−	0.221070i
$971$	3.13659	+	5.43273i	0.100658	+	0.174345i	0.911956	−	0.410288i	$-0.134572\pi$
$971$	3.13659	+	5.43273i	0.100658	+	0.174345i	−0.811298	+	0.584633i	$0.801239\pi$
$972$	10.3897	+	38.7750i	0.333251	+	1.24371i
$973$	−3.90686	−	2.25563i	−0.125248	−	0.0723120i
$974$	−7.07119			−0.226575
$975$	20.1537	+	37.5323i	0.645435	+	1.20200i
$976$	37.8235			1.21070
$977$	13.4772	+	7.78106i	0.431174	+	0.248938i	0.699847	−	0.714293i	$-0.253252\pi$
$977$	13.4772	+	7.78106i	0.431174	+	0.248938i	−0.268673	+	0.963231i	$0.586585\pi$
$978$	2.48968	+	9.29160i	0.0796111	+	0.297113i
$979$	−10.8997	−	18.8788i	−0.348356	−	0.603370i
$980$	−19.1695	−	22.3982i	−0.612349	−	0.715484i
$981$	4.75672	−	17.7523i	0.151870	−	0.566788i
$982$	−1.81335	−	3.14082i	−0.0578663	−	0.100227i
$983$		−	53.4558i		−	1.70498i	−0.522746	−	0.852488i	$-0.675093\pi$
$983$		−	53.4558i		−	1.70498i	0.522746	−	0.852488i	$-0.324907\pi$
$984$	−10.2770	+	5.93342i	−0.327619	+	0.189151i
$985$	−8.02974	−	43.0786i	−0.255849	−	1.37260i
$986$	−1.14537	−	4.27459i	−0.0364761	−	0.136131i
$987$	−6.34391	+	6.34391i	−0.201929	+	0.201929i
$988$	27.7215	−	20.9787i	0.881939	−	0.667421i
$989$			2.27465i			0.0723297i
$990$	3.91658	−	5.71117i	0.124477	−	0.181513i
$991$	11.8198	−	20.4726i	0.375470	−	0.650333i	−0.614927	−	0.788584i	$-0.710815\pi$
$991$	11.8198	−	20.4726i	0.375470	−	0.650333i	0.990397	+	0.138251i	$0.0441480\pi$
$992$	−10.8795	−	2.91514i	−0.345423	−	0.0925558i
$993$	−46.3626			−1.47127
$994$	−0.446214	−	0.119563i	−0.0141531	−	0.00379230i
$995$	10.9451	−	31.0088i	0.346983	−	0.983044i
$996$	16.6842	−	16.6842i	0.528658	−	0.528658i
$997$	13.3882	−	49.9653i	0.424007	−	1.58242i	−0.342075	−	0.939673i	$-0.611130\pi$
$997$	13.3882	−	49.9653i	0.424007	−	1.58242i	0.766082	−	0.642743i	$-0.222204\pi$
$998$	−6.29473	+	1.68667i	−0.199256	+	0.0533905i
$999$	−4.58002	+	1.22721i	−0.144906	+	0.0388273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.t.a.7.4	yes	20
3.2	odd	2		585.2.dp.a.397.2		20
5.2	odd	4		325.2.s.b.293.2		20
5.3	odd	4		65.2.o.a.33.4	yes	20
5.4	even	2		325.2.x.b.7.2		20
13.2	odd	12		65.2.o.a.2.4	✓	20
13.3	even	3		845.2.t.f.427.2		20
13.4	even	6		845.2.f.d.437.6		20
13.5	odd	4		845.2.o.e.357.4		20
13.6	odd	12		845.2.k.e.577.5		20
13.7	odd	12		845.2.k.d.577.6		20
13.8	odd	4		845.2.o.f.357.2		20
13.9	even	3		845.2.f.e.437.5		20
13.10	even	6		845.2.t.e.427.4		20
13.11	odd	12		845.2.o.g.587.2		20
13.12	even	2		845.2.t.g.657.2		20
15.8	even	4		585.2.cf.a.163.2		20
39.2	even	12		585.2.cf.a.262.2		20
65.2	even	12		325.2.x.b.93.2		20
65.3	odd	12		845.2.o.e.258.4		20
65.8	even	4		845.2.t.e.188.4		20
65.18	even	4		845.2.t.f.188.2		20
65.23	odd	12		845.2.o.f.258.2		20
65.28	even	12	inner	65.2.t.a.28.4	yes	20
65.33	even	12		845.2.f.d.408.5		20
65.38	odd	4		845.2.o.g.488.2		20
65.43	odd	12		845.2.k.d.268.6		20
65.48	odd	12		845.2.k.e.268.5		20
65.54	odd	12		325.2.s.b.132.2		20
65.58	even	12		845.2.f.e.408.6		20
65.63	even	12		845.2.t.g.418.2		20
195.158	odd	12		585.2.dp.a.28.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.4	✓	20	13.2	odd	12
65.2.o.a.33.4	yes	20	5.3	odd	4
65.2.t.a.7.4	yes	20	1.1	even	1	trivial
65.2.t.a.28.4	yes	20	65.28	even	12	inner
325.2.s.b.132.2		20	65.54	odd	12
325.2.s.b.293.2		20	5.2	odd	4
325.2.x.b.7.2		20	5.4	even	2
325.2.x.b.93.2		20	65.2	even	12
585.2.cf.a.163.2		20	15.8	even	4
585.2.cf.a.262.2		20	39.2	even	12
585.2.dp.a.28.2		20	195.158	odd	12
585.2.dp.a.397.2		20	3.2	odd	2
845.2.f.d.408.5		20	65.33	even	12
845.2.f.d.437.6		20	13.4	even	6
845.2.f.e.408.6		20	65.58	even	12
845.2.f.e.437.5		20	13.9	even	3
845.2.k.d.268.6		20	65.43	odd	12
845.2.k.d.577.6		20	13.7	odd	12
845.2.k.e.268.5		20	65.48	odd	12
845.2.k.e.577.5		20	13.6	odd	12
845.2.o.e.258.4		20	65.3	odd	12
845.2.o.e.357.4		20	13.5	odd	4
845.2.o.f.258.2		20	65.23	odd	12
845.2.o.f.357.2		20	13.8	odd	4
845.2.o.g.488.2		20	65.38	odd	4
845.2.o.g.587.2		20	13.11	odd	12
845.2.t.e.188.4		20	65.8	even	4
845.2.t.e.427.4		20	13.10	even	6
845.2.t.f.188.2		20	65.18	even	4
845.2.t.f.427.2		20	13.3	even	3
845.2.t.g.418.2		20	65.63	even	12
845.2.t.g.657.2		20	13.12	even	2

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.237991 - 0.137404i) q^{2} +(0.611610 + 2.28256i) q^{3} +(-0.962240 - 1.66665i) q^{4} +(1.45395 + 1.69883i) q^{5} +(0.168076 - 0.627267i) q^{6} +(-0.193052 - 0.334376i) q^{7} +1.07848i q^{8} +(-2.23793 + 1.29207i) q^{9} +O(q^{10})\)	\(q+(-0.237991 - 0.137404i) q^{2} +(0.611610 + 2.28256i) q^{3} +(-0.962240 - 1.66665i) q^{4} +(1.45395 + 1.69883i) q^{5} +(0.168076 - 0.627267i) q^{6} +(-0.193052 - 0.334376i) q^{7} +1.07848i q^{8} +(-2.23793 + 1.29207i) q^{9} +(-0.112600 - 0.604086i) q^{10} +(-1.12873 - 4.21249i) q^{11} +(3.21571 - 3.21571i) q^{12} +(-1.35750 - 3.34024i) q^{13} +0.106105i q^{14} +(-2.98844 + 4.35775i) q^{15} +(-1.77629 + 3.07663i) q^{16} +(1.90527 + 0.510514i) q^{17} +0.710144 q^{18} +(-4.83947 - 1.29673i) q^{19} +(1.43231 - 4.05791i) q^{20} +(0.645159 - 0.645159i) q^{21} +(-0.310185 + 1.15763i) q^{22} +(0.322241 - 0.0863441i) q^{23} +(-2.46170 + 0.659609i) q^{24} +(-0.772064 + 4.94003i) q^{25} +(-0.135891 + 0.981474i) q^{26} +(0.694880 + 0.694880i) q^{27} +(-0.371524 + 0.643499i) q^{28} +(7.07031 + 4.08205i) q^{29} +(1.30999 - 0.626482i) q^{30} +(-2.54187 - 2.54187i) q^{31} +(2.71347 - 1.56662i) q^{32} +(8.92491 - 5.15280i) q^{33} +(-0.383290 - 0.383290i) q^{34} +(0.287361 - 0.814128i) q^{35} +(4.30685 + 2.48656i) q^{36} +(-2.41251 + 4.17859i) q^{37} +(0.973575 + 0.973575i) q^{38} +(6.79403 - 5.14149i) q^{39} +(-1.83216 + 1.56806i) q^{40} +(4.49768 - 1.20515i) q^{41} +(-0.242190 + 0.0648946i) q^{42} +(-1.76471 + 6.58600i) q^{43} +(-5.93462 + 5.93462i) q^{44} +(-5.44885 - 1.92327i) q^{45} +(-0.0885545 - 0.0237281i) q^{46} -9.83310 q^{47} +(-8.10898 - 2.17280i) q^{48} +(3.42546 - 5.93307i) q^{49} +(0.862526 - 1.06960i) q^{50} +4.66112i q^{51} +(-4.26077 + 5.47658i) q^{52} +(-7.17155 + 7.17155i) q^{53} +(-0.0698958 - 0.260855i) q^{54} +(5.51519 - 8.04227i) q^{55} +(0.360618 - 0.208203i) q^{56} -11.8395i q^{57} +(-1.12178 - 1.94298i) q^{58} +(-0.628209 + 2.34451i) q^{59} +(10.1384 + 0.787474i) q^{60} +(-5.32338 - 9.22037i) q^{61} +(0.255679 + 0.954209i) q^{62} +(0.864073 + 0.498873i) q^{63} +6.24413 q^{64} +(3.70078 - 7.16270i) q^{65} -2.83207 q^{66} +(5.52170 + 3.18796i) q^{67} +(-0.982475 - 3.66665i) q^{68} +(0.394171 + 0.682724i) q^{69} +(-0.180254 + 0.154271i) q^{70} +(-1.12684 + 4.20542i) q^{71} +(-1.39347 - 2.41357i) q^{72} -6.08593i q^{73} +(1.14831 - 0.662979i) q^{74} +(-11.7481 + 1.25909i) q^{75} +(2.49554 + 9.31346i) q^{76} +(-1.19065 + 1.19065i) q^{77} +(-2.32338 + 0.290100i) q^{78} -3.34944i q^{79} +(-7.80932 + 1.45564i) q^{80} +(-5.03732 + 8.72489i) q^{81} +(-1.23600 - 0.331185i) q^{82} +5.18834 q^{83} +(-1.69605 - 0.454456i) q^{84} +(1.90288 + 3.97899i) q^{85} +(1.32493 - 1.32493i) q^{86} +(-4.99324 + 18.6350i) q^{87} +(4.54309 - 1.21732i) q^{88} +(4.82829 - 1.29374i) q^{89} +(1.03251 + 1.20642i) q^{90} +(-0.854827 + 1.09875i) q^{91} +(-0.453978 - 0.453978i) q^{92} +(4.24734 - 7.35661i) q^{93} +(2.34019 + 1.35111i) q^{94} +(-4.83341 - 10.1068i) q^{95} +(5.23549 + 5.23549i) q^{96} +(12.7722 - 7.37402i) q^{97} +(-1.63046 + 0.941346i) q^{98} +(7.96886 + 7.96886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9	\( 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9} - 2 q^{10} - 16 q^{11} - 24 q^{12} - 4 q^{13} - 20 q^{15} - 2 q^{16} + 4 q^{17} - 20 q^{19} + 4 q^{21} + 16 q^{22} - 10 q^{23} + 32 q^{24} + 18 q^{25} - 24 q^{26} + 4 q^{27} + 18 q^{28} - 26 q^{30} + 48 q^{32} + 18 q^{33} + 2 q^{34} + 40 q^{35} + 36 q^{36} - 4 q^{37} - 8 q^{38} + 4 q^{39} - 16 q^{40} + 10 q^{41} + 40 q^{42} + 10 q^{43} - 36 q^{44} + 4 q^{46} - 40 q^{47} - 56 q^{48} + 18 q^{49} + 36 q^{50} - 30 q^{52} - 10 q^{53} - 48 q^{54} - 10 q^{55} - 16 q^{59} + 28 q^{60} - 16 q^{61} - 44 q^{62} - 36 q^{63} + 20 q^{64} - 14 q^{65} - 32 q^{66} + 18 q^{67} + 22 q^{68} - 16 q^{69} - 12 q^{70} - 16 q^{71} + 4 q^{72} + 18 q^{74} - 38 q^{75} - 64 q^{76} - 28 q^{77} + 68 q^{78} - 2 q^{80} - 14 q^{81} + 56 q^{82} + 48 q^{83} - 40 q^{84} - 26 q^{85} + 60 q^{86} - 34 q^{87} + 82 q^{88} - 6 q^{89} + 46 q^{90} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 48 q^{94} - 26 q^{95} + 56 q^{96} + 66 q^{97} - 30 q^{98} + 60 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9 - 2 * q^10 - 16 * q^11 - 24 * q^12 - 4 * q^13 - 20 * q^15 - 2 * q^16 + 4 * q^17 - 20 * q^19 + 4 * q^21 + 16 * q^22 - 10 * q^23 + 32 * q^24 + 18 * q^25 - 24 * q^26 + 4 * q^27 + 18 * q^28 - 26 * q^30 + 48 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 + 36 * q^36 - 4 * q^37 - 8 * q^38 + 4 * q^39 - 16 * q^40 + 10 * q^41 + 40 * q^42 + 10 * q^43 - 36 * q^44 + 4 * q^46 - 40 * q^47 - 56 * q^48 + 18 * q^49 + 36 * q^50 - 30 * q^52 - 10 * q^53 - 48 * q^54 - 10 * q^55 - 16 * q^59 + 28 * q^60 - 16 * q^61 - 44 * q^62 - 36 * q^63 + 20 * q^64 - 14 * q^65 - 32 * q^66 + 18 * q^67 + 22 * q^68 - 16 * q^69 - 12 * q^70 - 16 * q^71 + 4 * q^72 + 18 * q^74 - 38 * q^75 - 64 * q^76 - 28 * q^77 + 68 * q^78 - 2 * q^80 - 14 * q^81 + 56 * q^82 + 48 * q^83 - 40 * q^84 - 26 * q^85 + 60 * q^86 - 34 * q^87 + 82 * q^88 - 6 * q^89 + 46 * q^90 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 48 * q^94 - 26 * q^95 + 56 * q^96 + 66 * q^97 - 30 * q^98 + 60 * q^99

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