LMFDB - Embedded newform 169.2.k.a.127.11

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			127.11
Character	$\chi$	$=$	169.127
Dual form			169.2.k.a.4.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10078 - 0.0443599i) q^{2} +(-0.581947 - 2.00912i) q^{3} +(-0.783766 + 0.0632721i) q^{4} +(1.05138 - 0.398737i) q^{5} +(-0.729720 - 2.18578i) q^{6} +(1.23850 - 2.90687i) q^{7} +(-3.04723 + 0.370001i) q^{8} +(-1.16231 + 0.735002i) q^{9} +O(q^{10})$	\(q+(1.10078 - 0.0443599i) q^{2} +(-0.581947 - 2.00912i) q^{3} +(-0.783766 + 0.0632721i) q^{4} +(1.05138 - 0.398737i) q^{5} +(-0.729720 - 2.18578i) q^{6} +(1.23850 - 2.90687i) q^{7} +(-3.04723 + 0.370001i) q^{8} +(-1.16231 + 0.735002i) q^{9} +(1.13965 - 0.485561i) q^{10} +(-2.18262 + 3.45154i) q^{11} +(0.583231 + 1.53785i) q^{12} +(1.57196 - 3.24483i) q^{13} +(1.23437 - 3.25476i) q^{14} +(-1.41296 - 1.88031i) q^{15} +(-1.78565 + 0.290196i) q^{16} +(5.19062 + 2.21152i) q^{17} +(-1.24685 + 0.860636i) q^{18} +(6.10663 + 3.52566i) q^{19} +(-0.798810 + 0.379040i) q^{20} +(-6.56098 - 0.796647i) q^{21} +(-2.24947 + 3.89620i) q^{22} +(-2.04500 - 3.54205i) q^{23} +(2.51670 + 5.90691i) q^{24} +(-2.79614 + 2.47716i) q^{25} +(1.58644 - 3.64158i) q^{26} +(-2.54387 - 2.25367i) q^{27} +(-0.786771 + 2.35667i) q^{28} +(0.373616 + 9.27118i) q^{29} +(-1.63877 - 2.00713i) q^{30} +(-2.81240 + 3.17454i) q^{31} +(4.06241 - 0.829348i) q^{32} +(8.20470 + 2.37652i) q^{33} +(5.81184 + 2.20414i) q^{34} +(0.143063 - 3.55007i) q^{35} +(0.864476 - 0.649611i) q^{36} +(3.22361 + 0.658105i) q^{37} +(6.87845 + 3.61009i) q^{38} +(-7.43404 - 1.26992i) q^{39} +(-3.05627 + 1.60406i) q^{40} +(6.24401 - 1.80860i) q^{41} +(-7.25753 - 0.585889i) q^{42} +(-0.411297 - 2.01466i) q^{43} +(1.49228 - 2.84329i) q^{44} +(-0.928964 + 1.23623i) q^{45} +(-2.40822 - 3.80830i) q^{46} +(-8.30806 - 5.73464i) q^{47} +(1.62219 + 3.41870i) q^{48} +(-2.06693 - 2.15190i) q^{49} +(-2.96805 + 2.85085i) q^{50} +(1.42253 - 11.7155i) q^{51} +(-1.02674 + 2.64265i) q^{52} +(0.290857 + 2.39543i) q^{53} +(-2.90021 - 2.36795i) q^{54} +(-0.918514 + 4.49918i) q^{55} +(-2.69845 + 9.31614i) q^{56} +(3.52973 - 14.3207i) q^{57} +(0.822538 + 10.1890i) q^{58} +(-1.13988 + 7.01397i) q^{59} +(1.22640 + 1.38432i) q^{60} +(-7.11055 - 5.34323i) q^{61} +(-2.95501 + 3.61923i) q^{62} +(0.697029 + 4.28899i) q^{63} +(7.94805 - 1.95902i) q^{64} +(0.358894 - 4.03837i) q^{65} +(9.13700 + 2.25207i) q^{66} +(1.03676 - 12.8426i) q^{67} +(-4.20816 - 1.40489i) q^{68} +(-5.92630 + 6.16993i) q^{69} -3.91419i q^{70} +(-1.98407 - 1.90572i) q^{71} +(3.26988 - 2.66978i) q^{72} +(-2.71437 - 5.17180i) q^{73} +(3.57768 + 0.581429i) q^{74} +(6.60411 + 4.17619i) q^{75} +(-5.00924 - 2.37691i) q^{76} +(7.32998 + 10.6193i) q^{77} +(-8.23958 - 1.06813i) q^{78} +(0.0925711 - 0.134112i) q^{79} +(-1.76169 + 1.01711i) q^{80} +(-4.81612 + 10.1497i) q^{81} +(6.79305 - 2.26785i) q^{82} +(1.34744 + 5.46679i) q^{83} +(5.19267 + 0.209258i) q^{84} +(6.33915 + 0.255459i) q^{85} +(-0.542118 - 2.19946i) q^{86} +(18.4095 - 6.14598i) q^{87} +(5.37387 - 11.3252i) q^{88} +(0.105560 - 0.0609451i) q^{89} +(-0.967747 + 1.40202i) q^{90} +(-7.48544 - 8.58820i) q^{91} +(1.82691 + 2.64674i) q^{92} +(8.01470 + 3.80302i) q^{93} +(-9.39973 - 5.94403i) q^{94} +(7.82622 + 1.27189i) q^{95} +(-4.03037 - 7.67922i) q^{96} +(-7.83403 + 6.39629i) q^{97} +(-2.37069 - 2.27708i) q^{98} -5.61599i 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{77}{78}\right)$

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 $

$2$	1.10078	−	0.0443599i	0.778369	−	0.0313672i	0.352099	−	0.935963i	$-0.385468\pi$
$2$	1.10078	−	0.0443599i	0.778369	−	0.0313672i	0.426271	+	0.904596i	$0.359827\pi$
$3$	−0.581947	−	2.00912i	−0.335988	−	1.15996i	−0.933641	−	0.358209i	$-0.883387\pi$
$3$	−0.581947	−	2.00912i	−0.335988	−	1.15996i	0.597654	−	0.801754i	$-0.296100\pi$
$4$	−0.783766	+	0.0632721i	−0.391883	+	0.0316360i
$5$	1.05138	−	0.398737i	0.470193	−	0.178321i	−0.108116	−	0.994138i	$-0.534482\pi$
$5$	1.05138	−	0.398737i	0.470193	−	0.178321i	0.578309	+	0.815817i	$0.303713\pi$
$6$	−0.729720	−	2.18578i	−0.297907	−	0.892341i
$7$	1.23850	−	2.90687i	0.468109	−	1.09869i	−0.503902	−	0.863761i	$-0.668103\pi$
$7$	1.23850	−	2.90687i	0.468109	−	1.09869i	0.972012	−	0.234932i	$-0.0754868\pi$
$8$	−3.04723	+	0.370001i	−1.07736	+	0.130815i
$9$	−1.16231	+	0.735002i	−0.387438	+	0.245001i
$10$	1.13965	−	0.485561i	0.360390	−	0.153548i
$11$	−2.18262	+	3.45154i	−0.658084	+	1.04068i	0.336986	+	0.941509i	$0.390592\pi$
$11$	−2.18262	+	3.45154i	−0.658084	+	1.04068i	−0.995071	+	0.0991676i	$0.968382\pi$
$12$	0.583231	+	1.53785i	0.168364	+	0.443940i
$13$	1.57196	−	3.24483i	0.435982	−	0.899955i
$13$	1.57196	−	3.24483i	0.435982	−	0.899955i
$14$	1.23437	−	3.25476i	0.329899	−	0.869872i
$15$	−1.41296	−	1.88031i	−0.364825	−	0.485493i
$16$	−1.78565	+	0.290196i	−0.446413	+	0.0725491i
$17$	5.19062	+	2.21152i	1.25891	+	0.536372i	0.915312	−	0.402745i	$-0.131944\pi$
$17$	5.19062	+	2.21152i	1.25891	+	0.536372i	0.343599	+	0.939117i	$0.388354\pi$
$18$	−1.24685	+	0.860636i	−0.293884	+	0.202854i
$19$	6.10663	+	3.52566i	1.40096	+	0.808843i	0.994491	−	0.104824i	$-0.0334278\pi$
$19$	6.10663	+	3.52566i	1.40096	+	0.808843i	0.406466	+	0.913666i	$0.366761\pi$
$20$	−0.798810	+	0.379040i	−0.178619	+	0.0847559i
$21$	−6.56098	−	0.796647i	−1.43172	−	0.173843i
$22$	−2.24947	+	3.89620i	−0.479589	+	0.830673i
$23$	−2.04500	−	3.54205i	−0.426412	−	0.738568i	0.570139	−	0.821548i	$-0.306889\pi$
$23$	−2.04500	−	3.54205i	−0.426412	−	0.738568i	−0.996551	+	0.0829805i	$0.973556\pi$
$24$	2.51670	+	5.90691i	0.513719	+	1.20574i
$25$	−2.79614	+	2.47716i	−0.559227	+	0.495432i
$26$	1.58644	−	3.64158i	0.311126	−	0.714173i
$27$	−2.54387	−	2.25367i	−0.489568	−	0.433719i
$28$	−0.786771	+	2.35667i	−0.148686	+	0.445368i
$29$	0.373616	+	9.27118i	0.0693787	+	1.72162i	0.542025	+	0.840363i	$0.317658\pi$
$29$	0.373616	+	9.27118i	0.0693787	+	1.72162i	−0.472646	+	0.881252i	$0.656701\pi$
$30$	−1.63877	−	2.00713i	−0.299197	−	0.366450i
$31$	−2.81240	+	3.17454i	−0.505122	+	0.570165i	−0.944657	−	0.328061i	$-0.893605\pi$
$31$	−2.81240	+	3.17454i	−0.505122	+	0.570165i	0.439535	+	0.898226i	$0.355143\pi$
$32$	4.06241	−	0.829348i	0.718140	−	0.146609i
$33$	8.20470	+	2.37652i	1.42826	+	0.413699i
$34$	5.81184	+	2.20414i	0.996722	+	0.378007i
$35$	0.143063	−	3.55007i	0.0241821	−	0.600072i
$36$	0.864476	−	0.649611i	0.144079	−	0.108269i
$37$	3.22361	+	0.658105i	0.529958	+	0.108192i	0.457551	−	0.889183i	$-0.348727\pi$
$37$	3.22361	+	0.658105i	0.529958	+	0.108192i	0.0724072	+	0.997375i	$0.476932\pi$
$38$	6.87845	+	3.61009i	1.11583	+	0.585634i
$39$	−7.43404	−	1.26992i	−1.19040	−	0.203350i
$40$	−3.05627	+	1.60406i	−0.483239	+	0.253624i
$41$	6.24401	−	1.80860i	0.975150	−	0.282456i	0.247868	−	0.968794i	$-0.420270\pi$
$41$	6.24401	−	1.80860i	0.975150	−	0.282456i	0.727282	+	0.686338i	$0.240783\pi$
$42$	−7.25753	−	0.585889i	−1.11986	−	0.0904046i
$43$	−0.411297	−	2.01466i	−0.0627222	−	0.307233i	0.936312	−	0.351169i	$-0.114216\pi$
$43$	−0.411297	−	2.01466i	−0.0627222	−	0.307233i	−0.999034	+	0.0439352i	$0.986010\pi$
$44$	1.49228	−	2.84329i	0.224969	−	0.428643i
$45$	−0.928964	+	1.23623i	−0.138482	+	0.184286i
$46$	−2.40822	−	3.80830i	−0.355073	−	0.561503i
$47$	−8.30806	−	5.73464i	−1.21185	−	0.836483i	−0.221516	−	0.975157i	$-0.571101\pi$
$47$	−8.30806	−	5.73464i	−1.21185	−	0.836483i	−0.990338	+	0.138674i	$0.955716\pi$
$48$	1.62219	+	3.41870i	0.234143	+	0.493447i
$49$	−2.06693	−	2.15190i	−0.295275	−	0.307414i
$50$	−2.96805	+	2.85085i	−0.419745	+	0.403171i
$51$	1.42253	−	11.7155i	0.199193	−	1.64050i
$52$	−1.02674	+	2.64265i	−0.142383	+	0.366470i
$53$	0.290857	+	2.39543i	0.0399523	+	0.329037i	0.998958	+	0.0456486i	$0.0145355\pi$
$53$	0.290857	+	2.39543i	0.0399523	+	0.329037i	−0.959005	+	0.283388i	$0.908541\pi$
$54$	−2.90021	−	2.36795i	−0.394669	−	0.322237i
$55$	−0.918514	+	4.49918i	−0.123852	+	0.606669i
$56$	−2.69845	+	9.31614i	−0.360596	+	1.24492i
$57$	3.52973	−	14.3207i	0.467524	−	1.89682i
$58$	0.822538	+	10.1890i	0.108005	+	1.33788i
$59$	−1.13988	+	7.01397i	−0.148400	+	0.913141i	0.800907	+	0.598789i	$0.204351\pi$
$59$	−1.13988	+	7.01397i	−0.148400	+	0.913141i	−0.949307	+	0.314352i	$0.898213\pi$
$60$	1.22640	+	1.38432i	0.158328	+	0.178715i
$61$	−7.11055	−	5.34323i	−0.910412	−	0.684130i	0.0386388	−	0.999253i	$-0.487698\pi$
$61$	−7.11055	−	5.34323i	−0.910412	−	0.684130i	−0.949051	+	0.315123i	$0.897954\pi$
$62$	−2.95501	+	3.61923i	−0.375287	+	0.459643i
$63$	0.697029	+	4.28899i	0.0878174	+	0.540362i
$64$	7.94805	−	1.95902i	0.993507	−	0.244877i
$65$	0.358894	−	4.03837i	0.0445153	−	0.500898i
$66$	9.13700	+	2.25207i	1.12469	+	0.277210i
$67$	1.03676	−	12.8426i	0.126661	−	1.56897i	−0.551572	−	0.834127i	$-0.685972\pi$
$67$	1.03676	−	12.8426i	0.126661	−	1.56897i	0.678233	−	0.734847i	$-0.262746\pi$
$68$	−4.20816	−	1.40489i	−0.510314	−	0.170368i
$69$	−5.92630	+	6.16993i	−0.713443	+	0.742772i
$70$		−	3.91419i		−	0.467836i
$71$	−1.98407	−	1.90572i	−0.235465	−	0.226168i	0.565699	−	0.824612i	$-0.308606\pi$
$71$	−1.98407	−	1.90572i	−0.235465	−	0.226168i	−0.801165	+	0.598444i	$0.795786\pi$
$72$	3.26988	−	2.66978i	0.385359	−	0.314636i
$73$	−2.71437	−	5.17180i	−0.317693	−	0.605314i	0.673278	−	0.739389i	$-0.264886\pi$
$73$	−2.71437	−	5.17180i	−0.317693	−	0.605314i	−0.990971	+	0.134076i	$0.957193\pi$
$74$	3.57768	+	0.581429i	0.415897	+	0.0675898i
$75$	6.60411	+	4.17619i	0.762577	+	0.482224i
$76$	−5.00924	−	2.37691i	−0.574599	−	0.272651i
$77$	7.32998	+	10.6193i	0.835329	+	1.21018i
$78$	−8.23958	−	1.06813i	−0.932949	−	0.120942i
$79$	0.0925711	−	0.134112i	0.0104151	−	0.0150888i	−0.817742	−	0.575585i	$-0.804774\pi$
$79$	0.0925711	−	0.134112i	0.0104151	−	0.0150888i	0.828157	+	0.560496i	$0.189390\pi$
$80$	−1.76169	+	1.01711i	−0.196963	+	0.113717i
$81$	−4.81612	+	10.1497i	−0.535124	+	1.12775i
$82$	6.79305	−	2.26785i	0.750167	−	0.250442i
$83$	1.34744	+	5.46679i	0.147901	+	0.600058i	0.997374	+	0.0724257i	$0.0230740\pi$
$83$	1.34744	+	5.46679i	0.147901	+	0.600058i	−0.849473	+	0.527632i	$0.823080\pi$
$84$	5.19267	+	0.209258i	0.566567	+	0.0228319i
$85$	6.33915	+	0.255459i	0.687578	+	0.0277084i
$86$	−0.542118	−	2.19946i	−0.0584580	−	0.237174i
$87$	18.4095	−	6.14598i	1.97370	−	0.658918i
$88$	5.37387	−	11.3252i	0.572856	−	1.20727i
$89$	0.105560	−	0.0609451i	0.0111893	−	0.00646017i	−0.494395	−	0.869237i	$-0.664610\pi$
$89$	0.105560	−	0.0609451i	0.0111893	−	0.00646017i	0.505584	+	0.862777i	$0.331277\pi$
$90$	−0.967747	+	1.40202i	−0.102009	+	0.147786i
$91$	−7.48544	−	8.58820i	−0.784687	−	0.900288i
$92$	1.82691	+	2.64674i	0.190469	+	0.275942i
$93$	8.01470	+	3.80302i	0.831085	+	0.394355i
$94$	−9.39973	−	5.94403i	−0.969508	−	0.613080i
$95$	7.82622	+	1.27189i	0.802954	+	0.130493i
$96$	−4.03037	−	7.67922i	−0.411348	−	0.783758i
$97$	−7.83403	+	6.39629i	−0.795425	+	0.649445i	−0.940430	−	0.339986i	$-0.889578\pi$
$97$	−7.83403	+	6.39629i	−0.795425	+	0.649445i	0.145005	+	0.989431i	$0.453680\pi$
$98$	−2.37069	−	2.27708i	−0.239476	−	0.230020i
$99$		−	5.61599i		−	0.564429i
$100$	2.03478	−	2.11843i	0.203478	−	0.211843i
$101$	−2.38825	−	0.797313i	−0.237639	−	0.0793356i	0.195354	−	0.980733i	$-0.437414\pi$
$101$	−2.38825	−	0.797313i	−0.237639	−	0.0793356i	−0.432993	+	0.901397i	$0.642543\pi$
$102$	1.04619	−	12.9593i	0.103588	−	1.28317i
$103$	−9.61166	−	2.36906i	−0.947065	−	0.233431i	−0.264608	−	0.964356i	$-0.585243\pi$
$103$	−9.61166	−	2.36906i	−0.947065	−	0.233431i	−0.682457	+	0.730925i	$0.739089\pi$
$104$	−3.58952	+	10.4694i	−0.351982	+	1.02661i
$105$	−7.21576	+	1.77852i	−0.704186	+	0.173566i
$106$	0.426431	+	2.62393i	0.0414186	+	0.254859i
$107$	−1.44079	+	1.76465i	−0.139286	+	0.170595i	−0.839537	−	0.543302i	$-0.817174\pi$
$107$	−1.44079	+	1.76465i	−0.139286	+	0.170595i	0.700251	+	0.713897i	$0.253071\pi$
$108$	2.13639	+	1.60539i	0.205574	+	0.154479i
$109$	−0.378270	−	0.426978i	−0.0362317	−	0.0408971i	0.730116	−	0.683324i	$-0.239466\pi$
$109$	−0.378270	−	0.426978i	−0.0362317	−	0.0408971i	−0.766347	+	0.642427i	$0.777928\pi$
$110$	−0.811499	+	4.99335i	−0.0773734	+	0.476098i
$111$	−0.553763	−	6.85959i	−0.0525609	−	0.651083i
$112$	−1.36797	+	5.55006i	−0.129261	+	0.524431i
$113$	−3.72797	+	12.8704i	−0.350698	+	1.21075i	0.570383	+	0.821379i	$0.306795\pi$
$113$	−3.72797	+	12.8704i	−0.350698	+	1.21075i	−0.921081	+	0.389371i	$0.872692\pi$
$114$	3.25019	−	15.9205i	0.304408	−	1.49109i
$115$	−3.56243	−	2.90863i	−0.332198	−	0.271231i
$116$	−0.879434	−	7.24279i	−0.0816534	−	0.672476i
$117$	0.557854	+	4.92690i	0.0515737	+	0.455492i
$118$	−0.943619	+	7.77140i	−0.0868672	+	0.715416i
$119$	12.8572	−	12.3495i	1.17862	−	1.13208i
$120$	5.00133	+	5.20693i	0.456557	+	0.475326i
$121$	−2.43365	−	5.12882i	−0.221241	−	0.466256i
$122$	−8.06417	−	5.56630i	−0.730096	−	0.503949i
$123$	−7.26737	−	11.4924i	−0.655276	−	1.03624i
$124$	2.00340	−	2.66604i	0.179911	−	0.239418i
$125$	−4.56488	+	8.69765i	−0.408295	+	0.777942i
$126$	0.957535	+	4.69032i	0.0853040	+	0.417847i
$127$	4.08739	+	0.329968i	0.362697	+	0.0292799i	0.260472	−	0.965481i	$-0.416122\pi$
$127$	4.08739	+	0.329968i	0.362697	+	0.0292799i	0.102225	+	0.994761i	$0.467404\pi$
$128$	0.697144	−	0.201930i	0.0616194	−	0.0178483i
$129$	−3.80834	+	1.99877i	−0.335306	+	0.175982i
$130$	0.215921	−	4.46127i	0.0189376	−	0.391279i
$131$	16.6305	+	8.72838i	1.45302	+	0.762602i	0.992172	−	0.124879i	$-0.0398543\pi$
$131$	16.6305	+	8.72838i	1.45302	+	0.762602i	0.460844	+	0.887481i	$0.347547\pi$
$132$	−6.58093	−	1.34351i	−0.572797	−	0.116937i
$133$	17.8117	−	13.3846i	1.54447	−	1.16059i
$134$	0.571550	−	14.1829i	0.0493744	−	1.22521i
$135$	−3.57321	−	1.35514i	−0.307533	−	0.116632i
$136$	−16.6353	−	4.81847i	−1.42646	−	0.413180i
$137$	−2.36521	+	0.482861i	−0.202073	+	0.0412536i	−0.299996	−	0.953940i	$-0.596985\pi$
$137$	−2.36521	+	0.482861i	−0.202073	+	0.0412536i	0.0979227	+	0.995194i	$0.468780\pi$
$138$	−6.24986	+	7.05463i	−0.532023	+	0.600530i
$139$	12.6389	+	15.4799i	1.07202	+	1.31299i	0.947142	+	0.320814i	$0.103956\pi$
$139$	12.6389	+	15.4799i	1.07202	+	1.31299i	0.124878	+	0.992172i	$0.460146\pi$
$140$	0.112493	+	2.79148i	0.00950736	+	0.235923i
$141$	−6.68670	+	20.0291i	−0.563121	+	1.68675i
$142$	−2.26856	−	2.00977i	−0.190373	−	0.168656i
$143$	7.76868	+	12.5079i	0.649650	+	1.04596i
$144$	1.86219	−	1.64976i	0.155182	−	0.137480i
$145$	4.08958	+	9.59860i	0.339621	+	0.797120i
$146$	−3.21735	−	5.57261i	−0.266269	−	0.461192i
$147$	−3.12057	+	5.40499i	−0.257380	+	0.445796i
$148$	−2.56819	−	0.311835i	−0.211104	−	0.0256327i
$149$	6.52264	−	3.09503i	0.534356	−	0.253555i	−0.142340	−	0.989818i	$-0.545463\pi$
$149$	6.52264	−	3.09503i	0.534356	−	0.253555i	0.676696	+	0.736263i	$0.263411\pi$
$150$	7.45493	+	4.30410i	0.608692	+	0.351429i
$151$	−12.6196	+	8.71070i	−1.02697	+	0.708866i	−0.957416	−	0.288712i	$-0.906773\pi$
$151$	−12.6196	+	8.71070i	−1.02697	+	0.708866i	−0.0695542	+	0.997578i	$0.522158\pi$
$152$	−19.9128	−	8.48405i	−1.61514	−	0.688147i
$153$	−7.65860	+	1.24464i	−0.619161	+	0.100623i
$154$	8.53977	+	11.3644i	0.688154	+	0.915767i
$155$	−1.69110	+	4.45907i	−0.135833	+	0.358161i
$156$	5.90690	+	0.524952i	0.472930	+	0.0420298i
$157$	1.97306	+	5.20253i	0.157467	+	0.415207i	0.990411	−	0.138150i	$-0.0441156\pi$
$157$	1.97306	+	5.20253i	0.157467	+	0.415207i	−0.832944	+	0.553357i	$0.813346\pi$
$158$	0.0959512	−	0.151735i	0.00763347	−	0.0120714i
$159$	4.64342	−	1.97838i	0.368247	−	0.156896i
$160$	3.94047	−	2.49180i	0.311521	−	0.196994i
$161$	−12.8290	+	1.55772i	−1.01107	+	0.122766i
$162$	−4.85124	+	11.3863i	−0.381150	+	0.894591i
$163$	−0.629153	−	1.88454i	−0.0492791	−	0.147609i	0.921021	−	0.389512i	$-0.127356\pi$
$163$	−0.629153	−	1.88454i	−0.0492791	−	0.147609i	−0.970300	+	0.241904i	$0.922228\pi$
$164$	−4.77940	+	1.81259i	−0.373209	+	0.141539i
$165$	9.57390	−	0.772885i	0.745327	−	0.0601690i
$166$	1.72574	+	5.95796i	0.133944	+	0.462427i
$167$	−4.15733	+	0.167535i	−0.321704	+	0.0129642i	−0.200593	−	0.979675i	$-0.564287\pi$
$167$	−4.15733	+	0.167535i	−0.321704	+	0.0129642i	−0.121111	+	0.992639i	$0.538646\pi$
$168$	20.2876			1.56522
$169$	−8.05790	−	10.2015i	−0.619839	−	0.784729i
$170$	6.98935			0.536058
$171$	−9.68918	+	0.390461i	−0.740950	+	0.0298593i
$172$	0.449832	+	1.55300i	0.0342994	+	0.118415i
$173$	14.8594	−	1.19958i	1.12974	−	0.0912020i	0.498572	−	0.866848i	$-0.333858\pi$
$173$	14.8594	−	1.19958i	1.12974	−	0.0912020i	0.631168	+	0.775646i	$0.282576\pi$
$174$	19.9921	−	7.58201i	1.51560	−	0.574791i
$175$	3.73776	+	11.1960i	0.282548	+	0.846336i
$176$	2.89577	−	6.79662i	0.218277	−	0.512315i
$177$	14.7552	−	1.79161i	1.10907	−	0.134666i
$178$	0.113495	−	0.0717698i	0.00850680	−	0.00537937i
$179$	−7.79198	+	3.31985i	−0.582400	+	0.248137i	−0.663013	−	0.748608i	$-0.730722\pi$
$179$	−7.79198	+	3.31985i	−0.582400	+	0.248137i	0.0806130	+	0.996745i	$0.474312\pi$
$180$	0.649872	−	1.02769i	0.0484386	−	0.0765995i
$181$	−0.755880	−	1.99309i	−0.0561841	−	0.148145i	0.903986	−	0.427563i	$-0.140628\pi$
$181$	−0.755880	−	1.99309i	−0.0561841	−	0.148145i	−0.960170	+	0.279418i	$0.909859\pi$
$182$	−8.62079	−	9.12167i	−0.639016	−	0.676143i
$183$	−6.59720	+	17.3954i	−0.487679	+	1.28590i
$184$	7.54215	+	10.0368i	0.556015	+	0.739921i
$185$	3.65166	−	0.593453i	0.268476	−	0.0436315i
$186$	8.99112	+	3.83076i	0.659261	+	0.280885i
$187$	−18.9623	+	13.0887i	−1.38666	+	0.957142i
$188$	6.87441	+	3.96894i	0.501368	+	0.289465i
$189$	−9.70171	+	4.60352i	−0.705696	+	0.334857i
$190$	8.67137	+	1.05290i	0.629087	+	0.0763850i
$191$	7.56804	−	13.1082i	0.547604	−	0.948478i	−0.450834	−	0.892608i	$-0.648873\pi$
$191$	7.56804	−	13.1082i	0.547604	−	0.948478i	0.998438	−	0.0558700i	$-0.0177932\pi$
$192$	−8.56125	−	14.8285i	−0.617855	−	1.07016i
$193$	−6.43564	−	15.1050i	−0.463248	−	1.08728i	−0.973794	−	0.227432i	$-0.926967\pi$
$193$	−6.43564	−	15.1050i	−0.463248	−	1.08728i	0.510546	−	0.859850i	$-0.329443\pi$
$194$	−8.33980	+	7.38842i	−0.598763	+	0.530458i
$195$	−8.32240	+	1.62906i	−0.595979	+	0.116659i
$196$	1.75614	+	1.55581i	0.125439	+	0.111129i
$197$	−2.43805	+	7.30286i	−0.173704	+	0.520307i	−0.999015	−	0.0443712i	$-0.985872\pi$
$197$	−2.43805	+	7.30286i	−0.173704	+	0.520307i	0.825311	+	0.564678i	$0.191000\pi$
$198$	−0.249125	−	6.18197i	−0.0177045	−	0.439334i
$199$	−3.11261	−	3.81225i	−0.220647	−	0.270243i	0.652405	−	0.757870i	$-0.273760\pi$
$199$	−3.11261	−	3.81225i	−0.220647	−	0.270243i	−0.873052	+	0.487627i	$0.837863\pi$
$200$	7.60392	−	8.58305i	0.537678	−	0.606913i
$201$	−26.4056	+	5.39075i	−1.86251	+	0.380234i
$202$	−2.66430	−	0.771724i	−0.187460	−	0.0542983i
$203$	27.4128	+	10.3963i	1.92400	+	0.729678i
$204$	−0.373659	+	9.27225i	−0.0261614	+	0.649187i
$205$	5.84369	−	4.39125i	0.408141	−	0.306698i
$206$	−10.6854	−	2.18144i	−0.744488	−	0.151988i
$207$	4.98034	+	2.61389i	0.346158	+	0.181678i
$208$	−1.86533	+	6.25032i	−0.129337	+	0.433382i
$209$	−25.4974	+	13.3821i	−1.76369	+	0.925657i
$210$	−7.86407	+	2.27786i	−0.542672	+	0.157187i
$211$	5.40996	+	0.436737i	0.372437	+	0.0300662i	0.265268	−	0.964175i	$-0.414539\pi$
$211$	5.40996	+	0.436737i	0.372437	+	0.0300662i	0.107169	+	0.994241i	$0.465822\pi$
$212$	−0.379528	−	1.85905i	−0.0260661	−	0.127680i
$213$	−2.67419	+	5.09525i	−0.183233	+	0.349121i
$214$	−1.50771	+	2.00640i	−0.103065	+	0.137155i
$215$	−1.23575	−	1.95419i	−0.0842776	−	0.133274i
$216$	8.58562	+	5.92622i	0.584177	+	0.403228i
$217$	5.74482	+	12.1070i	0.389984	+	0.821873i
$218$	−0.435332	−	0.453229i	−0.0294844	−	0.0306965i
$219$	−8.81113	+	8.46320i	−0.595401	+	0.571890i
$220$	0.435227	−	3.58442i	0.0293430	−	0.241661i
$221$	15.3354	−	13.3663i	1.03157	−	0.899115i
$222$	−0.913862	−	7.52633i	−0.0613344	−	0.505134i
$223$	−19.2073	−	15.6823i	−1.28621	−	1.05016i	−0.995637	−	0.0933106i	$-0.970255\pi$
$223$	−19.2073	−	15.6823i	−1.28621	−	1.05016i	−0.290578	−	0.956851i	$-0.593848\pi$
$224$	2.62050	−	12.8361i	0.175089	−	0.857645i
$225$	1.42927	−	4.93440i	0.0952845	−	0.328960i
$226$	−3.53274	+	14.3329i	−0.234995	+	0.953411i
$227$	−0.189861	−	2.35185i	−0.0126015	−	0.156098i	0.987396	−	0.158268i	$-0.0505911\pi$
$227$	−0.189861	−	2.35185i	−0.0126015	−	0.156098i	−0.999998	+	0.00217070i	$0.999309\pi$
$228$	−1.86038	+	11.4474i	−0.123207	+	0.758121i
$229$	−17.7848	−	20.0749i	−1.17525	−	1.32659i	−0.934484	−	0.356006i	$-0.884138\pi$
$229$	−17.7848	−	20.0749i	−1.17525	−	1.32659i	−0.240771	−	0.970582i	$-0.577400\pi$
$230$	−4.05048	−	3.04374i	−0.267081	−	0.200698i
$231$	17.0698	−	20.9067i	1.12311	−	1.37556i
$232$	−4.56884	−	28.1132i	−0.299959	−	1.84572i
$233$	−0.154252	+	0.0380196i	−0.0101054	+	0.00249075i	−0.244365	−	0.969683i	$-0.578580\pi$
$233$	−0.154252	+	0.0380196i	−0.0101054	+	0.00249075i	0.234260	+	0.972174i	$0.424733\pi$
$234$	0.832632	+	5.39869i	0.0544309	+	0.352924i
$235$	−11.0216	−	2.71657i	−0.718968	−	0.177210i
$236$	0.449611	−	5.56943i	0.0292672	−	0.362539i
$237$	−0.323319	−	0.107940i	−0.0210018	−	0.00701143i
$238$	13.6051	−	14.1644i	0.881888	−	0.918143i
$239$			0.752656i			0.0486853i	0.999704	+	0.0243426i	$0.00774927\pi$
$239$			0.752656i			0.0486853i	−0.999704	+	0.0243426i	$0.992251\pi$
$240$	3.06871	+	2.94754i	0.198084	+	0.190263i
$241$	14.3328	−	11.7024i	0.923258	−	0.753817i	−0.0462360	−	0.998931i	$-0.514723\pi$
$241$	14.3328	−	11.7024i	0.923258	−	0.753817i	0.969494	+	0.245113i	$0.0788252\pi$
$242$	−2.90643	−	5.53774i	−0.186832	−	0.355980i
$243$	13.1310	+	2.13400i	0.842357	+	0.136896i
$244$	5.91108	+	3.73794i	0.378418	+	0.239297i
$245$	−3.03118	−	1.43831i	−0.193655	−	0.0918903i
$246$	−8.50958	−	12.3282i	−0.542551	−	0.786020i
$247$	21.0395	−	14.2728i	1.33871	−	0.908157i
$248$	7.39545	−	10.7142i	0.469611	−	0.680349i
$249$	10.1993	−	5.88855i	0.646353	−	0.373172i
$250$	−4.63910	+	9.77670i	−0.293403	+	0.618333i
$251$	−6.33247	+	2.11409i	−0.399702	+	0.133440i	−0.509411	−	0.860524i	$-0.670137\pi$
$251$	−6.33247	+	2.11409i	−0.399702	+	0.133440i	0.109708	+	0.993964i	$0.465008\pi$
$252$	−0.817681	−	3.31746i	−0.0515090	−	0.208980i
$253$	16.6890	+	0.672542i	1.04923	+	0.0422824i
$254$	4.51395	+	0.181906i	0.283231	+	0.0114138i
$255$	−3.17581	−	12.8848i	−0.198877	−	0.806875i
$256$	−14.7708	+	4.93123i	−0.923178	+	0.308202i
$257$	−7.87968	+	16.6061i	−0.491521	+	1.03586i	0.494491	+	0.869183i	$0.335355\pi$
$257$	−7.87968	+	16.6061i	−0.491521	+	1.03586i	−0.986012	+	0.166676i	$0.946697\pi$
$258$	−4.10348	+	2.36915i	−0.255472	+	0.147497i
$259$	5.90547	−	8.55554i	0.366948	−	0.531616i
$260$	−0.0257727	+	3.18784i	−0.00159835	+	0.197701i
$261$	−7.24860	−	10.5014i	−0.448677	−	0.650021i
$262$	18.6938	+	8.87029i	1.15490	+	0.548009i
$263$	−14.2101	−	8.98595i	−0.876235	−	0.554098i	0.0189355	−	0.999821i	$-0.493972\pi$
$263$	−14.2101	−	8.98595i	−0.876235	−	0.554098i	−0.895171	+	0.445723i	$0.852947\pi$
$264$	−25.8809	−	4.20606i	−1.59286	−	0.258865i
$265$	1.26095	+	2.40254i	0.0774594	+	0.147587i
$266$	19.0130	−	15.5237i	1.16576	−	0.951816i
$267$	−0.183876	−	0.176615i	−0.0112530	−	0.0108087i
$268$			10.1312i			0.618861i
$269$	12.2248	−	12.7274i	0.745362	−	0.776004i	−0.235256	−	0.971933i	$-0.575593\pi$
$269$	12.2248	−	12.7274i	0.745362	−	0.776004i	0.980618	+	0.195929i	$0.0627723\pi$
$270$	−3.99343	−	1.33320i	−0.243032	−	0.0811361i
$271$	2.35539	−	29.1767i	0.143080	−	1.77236i	−0.384762	−	0.923016i	$-0.625716\pi$
$271$	2.35539	−	29.1767i	0.143080	−	1.77236i	0.527842	−	0.849343i	$-0.323001\pi$
$272$	−9.91041	−	2.44270i	−0.600907	−	0.148110i
$273$	−12.8986	+	20.0370i	−0.780656	+	1.21269i
$274$	−2.58215	+	0.636444i	−0.155994	+	0.0384490i
$275$	−2.44711	−	15.0577i	−0.147566	−	0.908011i
$276$	4.25444	−	5.21075i	0.256087	−	0.313650i
$277$	22.6162	+	16.9950i	1.35888	+	1.02113i	0.996006	+	0.0892893i	$0.0284596\pi$
$277$	22.6162	+	16.9950i	1.35888	+	1.02113i	0.362870	+	0.931840i	$0.381797\pi$
$278$	14.5994	+	16.4793i	0.875612	+	0.988362i
$279$	0.935593	−	5.75693i	0.0560125	−	0.344659i
$280$	0.877583	+	10.8708i	0.0524456	+	0.649655i
$281$	5.14904	−	20.8905i	0.307166	−	1.24622i	−0.591038	−	0.806644i	$-0.701282\pi$
$281$	5.14904	−	20.8905i	0.307166	−	1.24622i	0.898204	−	0.439578i	$-0.144872\pi$
$282$	−6.47209	+	22.3443i	−0.385408	+	1.33058i
$283$	−4.35232	+	21.3191i	−0.258719	+	1.26729i	0.617959	+	0.786210i	$0.287960\pi$
$283$	−4.35232	+	21.3191i	−0.258719	+	1.26729i	−0.876678	+	0.481078i	$0.840246\pi$
$284$	1.67562	+	1.36810i	0.0994299	+	0.0811820i
$285$	−1.99909	−	16.4640i	−0.118416	−	0.975241i
$286$	9.10646	+	13.4238i	0.538476	+	0.793768i
$287$	2.47585	−	20.3905i	0.146145	−	1.20361i
$288$	−4.11222	+	3.94985i	−0.242315	+	0.232747i
$289$	10.2754	+	10.6979i	0.604438	+	0.629286i
$290$	4.92752	+	10.3845i	0.289354	+	0.609801i
$291$	17.4099	+	12.0172i	1.02058	+	0.704459i
$292$	2.45466	+	3.88174i	0.143648	+	0.227161i
$293$	0.216822	−	0.288538i	0.0126669	−	0.0168565i	−0.793065	−	0.609137i	$-0.791516\pi$
$293$	0.216822	−	0.288538i	0.0126669	−	0.0168565i	0.805732	+	0.592281i	$0.201772\pi$
$294$	−3.19530	+	6.08813i	−0.186354	+	0.355067i
$295$	1.59828	+	7.82889i	0.0930554	+	0.455815i
$296$	−10.0666	−	0.812658i	−0.585108	−	0.0472348i
$297$	13.3309	−	3.86135i	0.773539	−	0.224058i
$298$	7.04270	−	3.69629i	0.407973	−	0.214121i
$299$	−14.7080	+	1.06775i	−0.850586	+	0.0617494i
$300$	−5.44031	−	2.85529i	−0.314096	−	0.164850i
$301$	−6.36575	−	1.29958i	−0.366916	−	0.0749064i
$302$	−13.5050	+	10.1484i	−0.777127	+	0.583973i
$303$	−0.212062	+	5.26226i	−0.0121826	+	0.302309i
$304$	−11.9274	−	4.52348i	−0.684085	−	0.259439i
$305$	−9.60646	−	2.78254i	−0.550064	−	0.159328i
$306$	−8.37522	+	1.70981i	−0.478779	+	0.0977435i
$307$	0.288491	−	0.325639i	0.0164650	−	0.0185852i	−0.740221	−	0.672364i	$-0.765279\pi$
$307$	0.288491	−	0.325639i	0.0164650	−	0.0185852i	0.756686	+	0.653779i	$0.226817\pi$
$308$	−6.41689	−	7.85927i	−0.365636	−	0.447823i
$309$	0.833763	+	20.6896i	0.0474311	+	1.17699i
$310$	−1.66373	+	4.98348i	−0.0944935	+	0.283042i
$311$	10.5956	+	9.38686i	0.600820	+	0.532280i	0.907782	−	0.419441i	$-0.137774\pi$
$311$	10.5956	+	9.38686i	0.600820	+	0.532280i	−0.306962	+	0.951722i	$0.599313\pi$
$312$	23.1231	+	1.11914i	1.30909	+	0.0633587i
$313$	0.0489166	−	0.0433363i	0.00276493	−	0.00244951i	−0.661739	−	0.749734i	$-0.730181\pi$
$313$	0.0489166	−	0.0433363i	0.00276493	−	0.00244951i	0.664504	+	0.747285i	$0.268643\pi$
$314$	2.40269	+	5.63932i	0.135592	+	0.318245i
$315$	2.44303	+	4.23144i	0.137649	+	0.238415i
$316$	−0.0640685	+	0.110970i	−0.00360413	+	0.00624254i
$317$	−1.24934	−	0.151698i	−0.0701700	−	0.00852018i	0.0853764	−	0.996349i	$-0.472791\pi$
$317$	−1.24934	−	0.151698i	−0.0701700	−	0.00852018i	−0.155546	+	0.987829i	$0.549714\pi$
$318$	5.02363	−	2.38374i	0.281711	−	0.133674i
$319$	−32.8153	−	18.9459i	−1.83730	−	1.06077i
$320$	7.57532	−	5.22887i	0.423473	−	0.292303i
$321$	4.38384	+	1.86778i	0.244682	+	0.104249i
$322$	−14.0528	+	2.28380i	−0.783132	+	0.127271i
$323$	23.9001	+	31.8053i	1.32984	+	1.76969i
$324$	3.13251	−	8.25975i	0.174028	−	0.458875i
$325$	3.64257	+	12.9670i	0.202053	+	0.719279i
$326$	−0.776157	−	2.04656i	−0.0429874	−	0.113348i
$327$	−0.637715	+	1.00847i	−0.0352657	+	0.0557683i
$328$	−18.3577	+	7.82150i	−1.01364	+	0.431870i
$329$	−26.9594	+	17.0481i	−1.48632	+	0.939890i
$330$	10.5045	−	1.27547i	0.578252	−	0.0702125i
$331$	9.87205	−	23.1706i	0.542617	−	1.27357i	−0.392670	−	0.919679i	$-0.628449\pi$
$331$	9.87205	−	23.1706i	0.542617	−	1.27357i	0.935287	−	0.353890i	$-0.115141\pi$
$332$	−1.40197	−	4.19943i	−0.0769433	−	0.230473i
$333$	−4.23055	+	1.60444i	−0.231833	+	0.0879226i
$334$	−4.56888	+	0.368838i	−0.249998	+	0.0201819i
$335$	−4.03079	−	13.9159i	−0.220226	−	0.760307i
$336$	11.9468	−	0.481439i	0.651751	−	0.0262647i
$337$	−17.9808			−0.979477			−0.489738	−	0.871869i	$-0.662908\pi$
$337$	−17.9808			−0.979477			−0.489738	+	0.871869i	$0.662908\pi$
$338$	−9.32252	−	10.8721i	−0.507078	−	0.591366i
$339$	28.0277			1.52226
$340$	−4.98457	+	0.200871i	−0.270326	+	0.0108938i
$341$	−4.81865	−	16.6359i	−0.260945	−	0.900885i
$342$	−10.6483	+	0.859623i	−0.575796	+	0.0464831i
$343$	11.8655	−	4.49998i	0.640676	−	0.242976i
$344$	1.99874	+	5.98696i	0.107765	+	0.322795i
$345$	−3.77063	+	8.85000i	−0.203004	+	0.476468i
$346$	16.3037	−	1.97963i	0.876494	−	0.106426i
$347$	−10.6099	+	6.70931i	−0.569571	+	0.360175i	−0.787997	−	0.615679i	$-0.788882\pi$
$347$	−10.6099	+	6.70931i	−0.569571	+	0.360175i	0.218427	+	0.975853i	$0.429908\pi$
$348$	−14.0398	+	5.98181i	−0.752614	+	0.320659i
$349$	−8.09141	+	12.7955i	−0.433123	+	0.684930i	−0.989261	−	0.146161i	$-0.953308\pi$
$349$	−8.09141	+	12.7955i	−0.433123	+	0.684930i	0.556138	+	0.831090i	$0.312283\pi$
$350$	4.61111	+	12.1585i	0.246474	+	0.649899i
$351$	−11.3116	+	4.71176i	−0.603771	+	0.251495i
$352$	−6.00418	+	15.8317i	−0.320024	+	0.843833i
$353$	−21.1152	−	28.0993i	−1.12385	−	1.49557i	−0.844633	−	0.535346i	$-0.820181\pi$
$353$	−21.1152	−	28.0993i	−1.12385	−	1.49557i	−0.279218	−	0.960228i	$-0.590075\pi$
$354$	16.1628	−	2.62671i	0.859042	−	0.139608i
$355$	−2.84590	−	1.21252i	−0.151045	−	0.0643541i
$356$	−0.0788782	+	0.0544457i	−0.00418054	+	0.00288562i
$357$	−32.2938	−	18.6448i	−1.70917	−	0.986788i
$358$	−8.42998	+	4.00008i	−0.445539	+	0.211411i
$359$	12.6427	+	1.53510i	0.667255	+	0.0810194i	0.447153	−	0.894458i	$-0.352438\pi$
$359$	12.6427	+	1.53510i	0.667255	+	0.0810194i	0.220102	+	0.975477i	$0.429361\pi$
$360$	2.37336	−	4.11078i	0.125087	−	0.216657i
$361$	15.3606	+	26.6053i	0.808452	+	1.40028i
$362$	−0.920471	−	2.16043i	−0.0483789	−	0.113549i
$363$	−8.88813	+	7.87419i	−0.466506	+	0.413288i
$364$	6.41022	+	6.25752i	0.335987	+	0.327983i
$365$	−4.91604	−	4.35523i	−0.257317	−	0.227963i
$366$	−6.49041	+	19.4411i	−0.339259	+	1.01621i
$367$	1.09184	+	27.0938i	0.0569938	+	1.41429i	0.734420	+	0.678695i	$0.237454\pi$
$367$	1.09184	+	27.0938i	0.0569938	+	1.41429i	−0.677426	+	0.735590i	$0.736905\pi$
$368$	4.67955	+	5.73141i	0.243938	+	0.298770i
$369$	−5.92816	+	6.69151i	−0.308608	+	0.348346i
$370$	3.99335	−	0.815249i	0.207604	−	0.0423828i
$371$	7.32341	+	2.12125i	0.380213	+	0.110130i
$372$	−6.52227	−	2.47357i	−0.338164	−	0.128249i
$373$	1.52877	−	37.9361i	0.0791569	−	1.96426i	−0.144272	−	0.989538i	$-0.546084\pi$
$373$	1.52877	−	37.9361i	0.0791569	−	1.96426i	0.223429	−	0.974720i	$-0.428275\pi$
$374$	−20.2927	+	15.2490i	−1.04931	+	0.788505i
$375$	20.1311	+	4.10979i	1.03957	+	0.212229i
$376$	27.4384	+	14.4008i	1.41503	+	0.742663i
$377$	30.6708	+	13.3616i	1.57962	+	0.688156i
$378$	−10.4752	+	5.49783i	−0.538788	+	0.282778i
$379$	12.1981	−	3.53322i	0.626574	−	0.181490i	0.0502847	−	0.998735i	$-0.483987\pi$
$379$	12.1981	−	3.53322i	0.626574	−	0.181490i	0.576290	+	0.817245i	$0.304500\pi$
$380$	−6.21440	−	0.501678i	−0.318792	−	0.0257355i
$381$	−1.71570	−	8.40406i	−0.0878981	−	0.430553i
$382$	7.74926	−	14.7650i	0.396487	−	0.755443i
$383$	−8.16470	+	10.8652i	−0.417197	+	0.555188i	−0.958298	−	0.285769i	$-0.907751\pi$
$383$	−8.16470	+	10.8652i	−0.417197	+	0.555188i	0.541102	+	0.840957i	$0.318007\pi$
$384$	−0.811403	−	1.28313i	−0.0414067	−	0.0654795i
$385$	11.9409	+	8.24224i	0.608567	+	0.420063i
$386$	−7.75428	−	16.3418i	−0.394683	−	0.831776i
$387$	1.95884	+	2.03937i	0.0995733	+	0.103667i
$388$	5.73534	−	5.50886i	0.291168	−	0.279670i
$389$	0.720535	−	5.93414i	0.0365326	−	0.300873i	−0.962978	−	0.269581i	$-0.913115\pi$
$389$	0.720535	−	5.93414i	0.0365326	−	0.300873i	0.999510	−	0.0312917i	$-0.00996209\pi$
$390$	−9.08887	+	2.16241i	−0.460233	+	0.109498i
$391$	−2.78153	−	22.9080i	−0.140668	−	1.15851i
$392$	7.09460	+	5.79256i	0.358332	+	0.292569i
$393$	7.85822	−	38.4921i	0.396395	−	1.94167i
$394$	−2.35981	+	8.14699i	−0.118885	+	0.410440i
$395$	0.0438521	−	0.177915i	0.00220644	−	0.00895188i
$396$	0.355336	+	4.40162i	0.0178563	+	0.221190i
$397$	−3.31681	+	20.4091i	−0.166466	+	1.02431i	0.760549	+	0.649281i	$0.224930\pi$
$397$	−3.31681	+	20.4091i	−0.166466	+	1.02431i	−0.927015	+	0.375025i	$0.877634\pi$
$398$	−3.59541	−	4.05838i	−0.180222	−	0.203428i
$399$	−37.2567	−	27.9966i	−1.86517	−	1.40158i
$400$	4.27406	−	5.23477i	0.213703	−	0.261739i
$401$	−1.36220	−	8.38197i	−0.0680252	−	0.418576i	−0.998620	−	0.0525239i	$-0.983273\pi$
$401$	−1.36220	−	8.38197i	−0.0680252	−	0.418576i	0.930595	−	0.366052i	$-0.119291\pi$
$402$	−28.8277	+	7.10538i	−1.43779	+	0.354384i
$403$	5.87990	+	14.1160i	0.292899	+	0.703169i
$404$	1.92227	+	0.473797i	0.0956366	+	0.0235723i
$405$	−1.01650	+	12.5916i	−0.0505104	+	0.625684i
$406$	30.6367	+	10.2280i	1.52047	+	0.507608i
$407$	−9.30738	+	9.69001i	−0.461350	+	0.480316i
$408$			36.2263i			1.79347i
$409$	10.8980	+	10.4677i	0.538872	+	0.517594i	0.912002	−	0.410185i	$-0.134536\pi$
$409$	10.8980	+	10.4677i	0.538872	+	0.517594i	−0.373130	+	0.927779i	$0.621715\pi$
$410$	6.23782	−	5.09303i	0.308064	−	0.251527i
$411$	2.34655	+	4.47098i	0.115747	+	0.220537i
$412$	7.68319	+	1.24864i	0.378523	+	0.0615160i
$413$	18.9769	+	12.0003i	0.933794	+	0.590496i
$414$	5.59822	+	2.65639i	0.275137	+	0.130554i
$415$	3.59649	+	5.21042i	0.176545	+	0.255769i
$416$	3.69484	−	14.4856i	0.181155	−	0.710213i
$417$	23.7457	−	34.4016i	1.16283	−	1.68465i
$418$	−27.4734	+	15.8618i	−1.34377	+	0.775825i
$419$	−5.68021	+	11.9708i	−0.277496	+	0.584811i	−0.993571	−	0.113213i	$-0.963886\pi$
$419$	−5.68021	+	11.9708i	−0.277496	+	0.584811i	0.716075	+	0.698024i	$0.245937\pi$
$420$	5.54293	−	1.85050i	0.270467	−	0.0902953i
$421$	−2.49604	−	10.1268i	−0.121650	−	0.493551i	−0.999883	−	0.0153187i	$-0.995124\pi$
$421$	−2.49604	−	10.1268i	−0.121650	−	0.493551i	0.878233	−	0.478233i	$-0.158722\pi$
$422$	5.97455	+	0.240766i	0.290836	+	0.0117203i
$423$	13.8715	+	0.559004i	0.674457	+	0.0271797i
$424$	−1.77262	−	7.19179i	−0.0860859	−	0.349264i
$425$	−19.9920	+	6.67430i	−0.969753	+	0.323751i
$426$	−2.71767	+	5.72738i	−0.131672	+	0.277492i
$427$	−24.3385	+	14.0518i	−1.17782	+	0.680016i
$428$	1.01759	−	1.47423i	0.0491870	−	0.0712597i
$429$	20.6089	−	22.8871i	0.995005	−	1.10500i
$430$	−1.44698	−	2.09631i	−0.0697795	−	0.101093i
$431$	3.44001	+	1.63231i	0.165700	+	0.0786254i	0.509736	−	0.860331i	$-0.329743\pi$
$431$	3.44001	+	1.63231i	0.165700	+	0.0786254i	−0.344036	+	0.938956i	$0.611794\pi$
$432$	5.19647	+	3.28605i	0.250015	+	0.158100i
$433$	9.80514	+	1.59349i	0.471205	+	0.0765783i	0.391377	−	0.920230i	$-0.371999\pi$
$433$	9.80514	+	1.59349i	0.471205	+	0.0765783i	0.0798279	+	0.996809i	$0.474563\pi$
$434$	6.86085	+	13.0723i	0.329331	+	0.627488i
$435$	16.9048	−	13.8023i	0.810522	−	0.661771i
$436$	0.323490	+	0.310717i	0.0154924	+	0.0148806i
$437$		−	28.8400i		−	1.37960i
$438$	−9.32369	+	9.70698i	−0.445503	+	0.463818i
$439$	13.9169	+	4.64616i	0.664219	+	0.221749i	0.628733	−	0.777621i	$-0.283574\pi$
$439$	13.9169	+	4.64616i	0.664219	+	0.221749i	0.0354862	+	0.999370i	$0.488702\pi$
$440$	1.13422	−	14.0499i	0.0540720	−	0.669802i
$441$	3.98407	+	0.981984i	0.189717	+	0.0467611i
$442$	16.2880	−	15.3936i	0.774742	−	0.732201i
$443$	12.6929	−	3.12851i	0.603056	−	0.148640i	0.0740447	−	0.997255i	$-0.476409\pi$
$443$	12.6929	−	3.12851i	0.603056	−	0.148640i	0.529011	+	0.848615i	$0.322563\pi$
$444$	0.868041	+	5.34127i	0.0411954	+	0.253485i
$445$	0.0866830	−	0.106167i	0.00410917	−	0.00503282i
$446$	−21.8387	−	16.4107i	−1.03409	−	0.777069i
$447$	−10.0141	−	11.3036i	−0.473651	−	0.534642i
$448$	4.14906	−	25.5302i	0.196025	−	1.20619i
$449$	−2.59648	−	32.1632i	−0.122536	−	1.51788i	−0.707440	−	0.706773i	$-0.750150\pi$
$449$	−2.59648	−	32.1632i	−0.122536	−	1.51788i	0.584904	−	0.811102i	$-0.301132\pi$
$450$	1.35442	−	5.49509i	0.0638479	−	0.259041i
$451$	−7.38584	+	25.4989i	−0.347786	+	1.20070i
$452$	2.10751	−	10.3233i	0.0991292	−	0.485567i
$453$	24.8448	+	20.2851i	1.16731	+	0.953078i
$454$	−0.313323	−	2.58044i	−0.0147050	−	0.121106i
$455$	−11.2945	−	6.04477i	−0.529495	−	0.283383i
$456$	−5.45723	+	44.9444i	−0.255558	+	2.10471i
$457$	−19.9100	+	19.1239i	−0.931353	+	0.894576i	−0.994638	−	0.103419i	$-0.967022\pi$
$457$	−19.9100	+	19.1239i	−0.931353	+	0.894576i	0.0632853	+	0.997995i	$0.479842\pi$
$458$	−20.4677	−	21.3091i	−0.956393	−	0.995711i
$459$	−8.22024	−	17.3238i	−0.383688	−	0.808605i
$460$	2.97614	+	2.05428i	0.138763	+	0.0957815i
$461$	2.38145	+	3.76597i	0.110915	+	0.175399i	0.896086	−	0.443881i	$-0.146399\pi$
$461$	2.38145	+	3.76597i	0.110915	+	0.175399i	−0.785170	+	0.619280i	$0.787425\pi$
$462$	17.8626	−	23.7709i	0.831045	−	1.10592i
$463$	−8.95065	+	17.0540i	−0.415972	+	0.792568i	−0.999814	−	0.0192993i	$-0.993856\pi$
$463$	−8.95065	+	17.0540i	−0.415972	+	0.792568i	0.583842	+	0.811867i	$0.301549\pi$
$464$	−3.35761	−	16.4467i	−0.155873	−	0.763517i
$465$	9.94293	+	0.802676i	0.461092	+	0.0372232i
$466$	−0.168111	+	0.0486938i	−0.00778758	+	0.00225570i
$467$	−3.12465	+	1.63994i	−0.144592	+	0.0758875i	−0.535467	−	0.844556i	$-0.679865\pi$
$467$	−3.12465	+	1.63994i	−0.144592	+	0.0758875i	0.390876	+	0.920443i	$0.372172\pi$
$468$	−0.748963	−	3.82624i	−0.0346208	−	0.176868i
$469$	−36.0477	−	18.9193i	−1.66453	−	0.873613i
$470$	−12.2528	−	2.50143i	−0.565181	−	0.115383i
$471$	9.30427	−	6.99171i	0.428718	−	0.322161i
$472$	0.878306	−	21.7949i	0.0404273	−	1.00319i
$473$	7.85139	+	2.97764i	0.361007	+	0.136912i
$474$	−0.360691	−	0.104475i	−0.0165671	−	0.00479872i
$475$	−25.8086	+	5.26886i	−1.18418	+	0.241752i
$476$	−9.29564	+	10.4926i	−0.426065	+	0.480928i
$477$	−2.09871	−	2.57045i	−0.0960933	−	0.117693i
$478$	0.0333878	+	0.828509i	0.00152712	+	0.0378951i
$479$	6.28232	−	18.8178i	0.287046	−	0.859809i	−0.701997	−	0.712180i	$-0.747708\pi$
$479$	6.28232	−	18.8178i	0.287046	−	0.859809i	0.989043	−	0.147628i	$-0.0471640\pi$
$480$	−7.29946	−	6.46676i	−0.333173	−	0.295166i
$481$	7.20282	−	9.42557i	0.328420	−	0.429769i
$482$	15.2582	−	13.5176i	0.694991	−	0.615708i
$483$	10.5954	+	24.8684i	0.482110	+	1.13155i
$484$	2.23192	+	3.86581i	0.101451	+	0.175719i
$485$	−5.68613	+	9.84867i	−0.258194	+	0.447205i
$486$	14.5491	+	1.76658i	0.659959	+	0.0801335i
$487$	−5.62287	+	2.66808i	−0.254797	+	0.120902i	−0.551807	−	0.833972i	$-0.686062\pi$
$487$	−5.62287	+	2.66808i	−0.254797	+	0.120902i	0.297011	+	0.954874i	$0.404010\pi$
$488$	23.6445	+	13.6511i	1.07033	+	0.617958i
$489$	−3.42013	+	2.36075i	−0.154664	+	0.106757i
$490$	−3.40046	−	1.44880i	−0.153617	−	0.0654502i
$491$	−30.6672	+	4.98391i	−1.38399	+	0.224921i	−0.806384	−	0.591393i	$-0.798578\pi$
$491$	−30.6672	+	4.98391i	−1.38399	+	0.224921i	−0.577609	+	0.816313i	$0.696014\pi$
$492$	6.42306	+	8.54754i	0.289574	+	0.385353i
$493$	−18.5641	+	48.9495i	−0.836084	+	2.20457i
$494$	22.5268	−	16.6445i	1.01353	−	0.748873i
$495$	−2.23931	−	5.90457i	−0.100649	−	0.265390i
$496$	4.10072	−	6.48477i	0.184128	−	0.291175i
$497$	−7.99695	+	3.40718i	−0.358712	+	0.152833i
$498$	10.9659	−	6.93444i	0.491396	−	0.310740i
$499$	−8.43207	+	1.02384i	−0.377471	+	0.0458333i	−0.307074	−	0.951686i	$-0.599350\pi$
$499$	−8.43207	+	1.02384i	−0.377471	+	0.0458333i	−0.0703976	+	0.997519i	$0.522427\pi$
$500$	3.02748	−	7.10575i	0.135393	−	0.317779i
$501$	2.75595	+	8.25507i	0.123127	+	0.368809i
$502$	−6.87688	+	2.60806i	−0.306930	+	0.116403i
$503$	−7.27333	+	0.587164i	−0.324302	+	0.0261803i	−0.241546	−	0.970389i	$-0.577654\pi$
$503$	−7.27333	+	0.587164i	−0.324302	+	0.0261803i	−0.0827562	+	0.996570i	$0.526372\pi$
$504$	−3.71094	−	12.8116i	−0.165298	−	0.570676i
$505$	−2.82888	+	0.114000i	−0.125884	+	0.00507293i
$506$	18.4007			0.818011
$507$	−15.8067	+	22.1260i	−0.701999	+	0.982649i
$508$	−3.22443			−0.143061
$509$	20.2344	−	0.815417i	0.896872	−	0.0361427i	0.412453	−	0.910979i	$-0.364672\pi$
$509$	20.2344	−	0.815417i	0.896872	−	0.0361427i	0.484419	+	0.874836i	$0.339031\pi$
$510$	−4.06743	−	14.0424i	−0.180109	−	0.621808i
$511$	−18.3955	+	1.48504i	−0.813769	+	0.0656942i
$512$	−17.3980	+	6.59818i	−0.768889	+	0.291601i
$513$	−7.58878	−	22.7312i	−0.335053	−	1.00361i
$514$	−7.93715	+	18.6292i	−0.350093	+	0.821698i
$515$	−11.0502	+	1.34174i	−0.486929	+	0.0591239i
$516$	2.85838	−	1.80753i	0.125833	−	0.0795721i
$517$	37.9266	−	16.1590i	1.66801	−	0.710673i
$518$	6.12110	−	9.67974i	0.268945	−	0.425303i
$519$	−11.0575	−	29.1562i	−0.485369	−	1.27981i
$520$	0.400566	+	12.4386i	0.0175660	+	0.545469i
$521$	11.5275	−	30.3954i	0.505027	−	1.33165i	−0.403942	−	0.914784i	$-0.632360\pi$
$521$	11.5275	−	30.3954i	0.505027	−	1.33165i	0.908969	−	0.416863i	$-0.136870\pi$
$522$	−8.44495	−	11.2382i	−0.369626	−	0.491882i
$523$	17.0715	−	2.77438i	0.746483	−	0.121315i	0.224741	−	0.974419i	$-0.427847\pi$
$523$	17.0715	−	2.77438i	0.746483	−	0.121315i	0.521742	+	0.853103i	$0.325282\pi$
$524$	−13.5867	−	5.78875i	−0.593538	−	0.252883i
$525$	20.3188	−	14.0251i	0.886786	−	0.612104i
$526$	−16.0409	−	9.26120i	−0.699415	−	0.403807i
$527$	−21.6187	+	10.2582i	−0.941724	+	0.446854i
$528$	−15.3404	−	1.86266i	−0.667605	−	0.0810619i
$529$	3.13593	−	5.43160i	0.136345	−	0.236156i
$530$	1.49460	+	2.58873i	0.0649214	+	0.112447i
$531$	−3.83038	−	8.99024i	−0.166225	−	0.390143i
$532$	−13.1133	+	11.6174i	−0.568535	+	0.503678i
$533$	3.94671	−	23.1038i	0.170951	−	1.00074i
$534$	−0.210242	−	0.186258i	−0.00909806	−	0.00806017i
$535$	−0.811193	+	2.42982i	−0.0350709	+	0.105050i
$536$	1.59252	+	39.5180i	0.0687864	+	1.70692i
$537$	11.2045	+	13.7230i	0.483509	+	0.592191i
$538$	12.8923	−	14.5524i	0.555826	−	0.627398i
$539$	11.9387	−	2.43730i	0.514235	−	0.104982i
$540$	2.88630	+	0.836027i	0.124207	+	0.0359769i
$541$	18.3785	+	6.97006i	0.790156	+	0.299666i	0.716473	−	0.697615i	$-0.245755\pi$
$541$	18.3785	+	6.97006i	0.790156	+	0.299666i	0.0736830	+	0.997282i	$0.476525\pi$
$542$	1.29849	−	32.2216i	0.0557748	−	1.38404i
$543$	−3.56447	+	2.67853i	−0.152966	+	0.114947i
$544$	22.9206	+	4.67927i	0.982712	+	0.200622i
$545$	−0.567959	−	0.298088i	−0.0243287	−	0.0127687i
$546$	−13.3096	+	22.6285i	−0.569600	+	0.968410i
$547$	12.4517	−	6.53517i	0.532397	−	0.279424i	−0.177026	−	0.984206i	$-0.556648\pi$
$547$	12.4517	−	6.53517i	0.532397	−	0.279424i	0.709423	+	0.704783i	$0.248955\pi$
$548$	1.82322	−	0.528101i	0.0778839	−	0.0225594i
$549$	12.1920	+	0.984237i	0.520340	+	0.0420062i
$550$	−3.36169	−	16.4666i	−0.143343	−	0.702139i
$551$	−30.4055	+	57.9329i	−1.29532	+	2.46802i
$552$	15.7759	−	20.9939i	0.671467	−	0.893561i
$553$	−0.275198	−	0.435190i	−0.0117026	−	0.0185062i
$554$	25.6494	+	17.7045i	1.08974	+	0.752191i
$555$	−3.31739	−	6.99125i	−0.140815	−	0.296762i
$556$	−10.8854	−	11.3329i	−0.461644	−	0.480622i
$557$	−18.1383	+	17.4221i	−0.768545	+	0.738197i	−0.970475	−	0.241203i	$-0.922458\pi$
$557$	−18.1383	+	17.4221i	−0.768545	+	0.738197i	0.201930	+	0.979400i	$0.435279\pi$
$558$	0.774505	−	6.37862i	0.0327874	−	0.270029i
$559$	−7.18379	−	1.83238i	−0.303842	−	0.0775013i
$560$	0.774758	+	6.38070i	0.0327395	+	0.269634i
$561$	37.3318	+	30.4805i	1.57615	+	1.28689i
$562$	4.74126	−	23.2242i	0.199998	−	0.979655i
$563$	3.73577	−	12.8974i	0.157444	−	0.543559i	−0.842544	−	0.538628i	$-0.818943\pi$
$563$	3.73577	−	12.8974i	0.157444	−	0.543559i	0.999988	−	0.00493174i	$-0.00156983\pi$
$564$	3.97352	−	16.1212i	0.167315	−	0.678825i
$565$	1.21240	+	15.0183i	0.0510060	+	0.631823i
$566$	−3.84524	+	23.6607i	−0.161627	+	0.994533i
$567$	23.5392	+	26.5703i	0.988554	+	1.11585i
$568$	6.75103	+	5.07307i	0.283267	+	0.212861i
$569$	6.73725	−	8.25163i	0.282440	−	0.345926i	−0.613827	−	0.789440i	$-0.710371\pi$
$569$	6.73725	−	8.25163i	0.282440	−	0.345926i	0.896268	+	0.443514i	$0.146268\pi$
$570$	−2.93089	−	18.0345i	−0.122762	−	0.755383i
$571$	−37.7826	+	9.31256i	−1.58115	+	0.389719i	−0.929506	−	0.368806i	$-0.879767\pi$
$571$	−37.7826	+	9.31256i	−1.58115	+	0.389719i	−0.651644	+	0.758525i	$0.725920\pi$
$572$	−6.88022	−	9.31172i	−0.287677	−	0.389343i
$573$	−30.7401	−	7.57676i	−1.28419	−	0.316524i
$574$	1.82085	−	22.5552i	0.0760007	−	0.941437i
$575$	14.4923	+	4.83825i	0.604372	+	0.201769i
$576$	−7.79824	+	8.11883i	−0.324927	+	0.338285i
$577$		−	19.9882i		−	0.832121i	−0.909337	−	0.416061i	$-0.863410\pi$
$577$		−	19.9882i		−	0.832121i	0.909337	−	0.416061i	$-0.136590\pi$
$578$	11.7856	+	11.3202i	0.490215	+	0.470857i
$579$	−26.6025	+	21.7203i	−1.10556	+	0.902664i
$580$	−3.81260	−	7.26429i	−0.158309	−	0.301633i
$581$	17.5600	+	2.85379i	0.728513	+	0.118395i
$582$	19.6975	+	12.4560i	0.816489	+	0.516316i
$583$	−8.90273	−	4.22440i	−0.368713	−	0.174957i
$584$	10.1849	+	14.7553i	0.421453	+	0.610580i
$585$	2.55106	+	4.95763i	0.105473	+	0.204973i
$586$	0.225874	−	0.327235i	0.00933076	−	0.0135179i
$587$	−19.5306	+	11.2760i	−0.806115	+	0.465411i	−0.845605	−	0.533809i	$-0.820760\pi$
$587$	−19.5306	+	11.2760i	−0.806115	+	0.465411i	0.0394896	+	0.999220i	$0.487427\pi$
$588$	2.10381	−	4.43369i	0.0867597	−	0.182842i
$589$	−28.3667	+	9.47018i	−1.16883	+	0.390212i
$590$	2.10664	+	8.54698i	0.0867291	+	0.351874i
$591$	16.0911	+	0.648449i	0.661900	+	0.0266736i
$592$	−5.94722	−	0.239665i	−0.244429	−	0.00985016i
$593$	−0.545441	−	2.21294i	−0.0223986	−	0.0908746i	0.958679	−	0.284491i	$-0.0918245\pi$
$593$	−0.545441	−	2.21294i	−0.0223986	−	0.0908746i	−0.981077	+	0.193616i	$0.937978\pi$
$594$	14.5031	−	4.84186i	0.595071	−	0.198664i
$595$	8.59363	−	18.1107i	0.352305	−	0.742466i
$596$	−4.91639	+	2.83848i	−0.201383	+	0.116269i
$597$	−5.84788	+	8.47212i	−0.239338	+	0.346741i
$598$	−16.1429	+	1.82780i	−0.660133	+	0.0747443i
$599$	24.0024	+	34.7735i	0.980711	+	1.42081i	0.905844	+	0.423612i	$0.139238\pi$
$599$	24.0024	+	34.7735i	0.980711	+	1.42081i	0.0748678	+	0.997193i	$0.476147\pi$
$600$	−21.6694	−	10.2823i	−0.884650	−	0.419772i
$601$	−5.95993	−	3.76883i	−0.243110	−	0.153734i	0.407354	−	0.913270i	$-0.366451\pi$
$601$	−5.95993	−	3.76883i	−0.243110	−	0.153734i	−0.650465	+	0.759537i	$0.725426\pi$
$602$	−7.06495	−	1.14817i	−0.287946	−	0.0467957i
$603$	8.23430	+	15.6892i	0.335327	+	0.638912i
$604$	9.33968	−	7.62561i	0.380026	−	0.310282i
$605$	−4.60376	−	4.42197i	−0.187169	−	0.179779i
$606$			5.80199i			0.235690i
$607$	21.4240	−	22.3048i	0.869574	−	0.905323i	−0.126667	−	0.991945i	$-0.540428\pi$
$607$	21.4240	−	22.3048i	0.869574	−	0.905323i	0.996241	+	0.0866225i	$0.0276074\pi$
$608$	27.7317	+	9.25819i	1.12467	+	0.375469i
$609$	4.93457	−	61.1256i	0.199959	−	2.47694i
$610$	−10.6980	−	2.63683i	−0.433151	−	0.106762i
$611$	−31.6679	+	17.9437i	−1.28114	+	0.725923i
$612$	5.92379	−	1.46008i	0.239455	−	0.0590204i
$613$	2.09999	+	12.9217i	0.0848177	+	0.521904i	0.994340	+	0.106248i	$0.0338839\pi$
$613$	2.09999	+	12.9217i	0.0848177	+	0.521904i	−0.909522	+	0.415656i	$0.863552\pi$
$614$	0.303120	−	0.371254i	0.0122329	−	0.0149826i
$615$	−12.2233	−	9.18518i	−0.492889	−	0.370382i
$616$	−26.2653	−	29.6474i	−1.05826	−	1.19453i
$617$	0.115470	−	0.710516i	0.00464865	−	0.0286043i	−0.984622	−	0.174697i	$-0.944106\pi$
$617$	0.115470	−	0.710516i	0.00464865	−	0.0286043i	0.989271	+	0.146092i	$0.0466696\pi$
$618$	1.83558	+	22.7377i	0.0738378	+	0.914646i
$619$	−4.02308	+	16.3223i	−0.161701	+	0.656047i	0.833003	+	0.553268i	$0.186620\pi$
$619$	−4.02308	+	16.3223i	−0.161701	+	0.656047i	−0.994704	+	0.102779i	$0.967227\pi$
$620$	1.04329	−	3.60187i	0.0418997	−	0.144654i
$621$	−2.78039	+	13.6193i	−0.111573	+	0.546523i
$622$	12.0798	+	9.86285i	0.484356	+	0.395464i
$623$	−0.0464232	−	0.382330i	−0.00185991	−	0.0153177i
$624$	13.6431	+	0.110300i	0.546162	+	0.00441555i
$625$	0.920022	−	7.57706i	0.0368009	−	0.303082i
$626$	0.0519240	−	0.0498737i	0.00207530	−	0.00199335i
$627$	41.7243	+	43.4395i	1.66631	+	1.73481i
$628$	−1.87559	−	3.95272i	−0.0748442	−	0.157731i
$629$	15.2771	+	10.5450i	0.609139	+	0.420458i
$630$	2.87694	+	4.54952i	0.114620	+	0.181257i
$631$	21.5094	−	28.6238i	0.856276	−	1.13950i	−0.132661	−	0.991161i	$-0.542352\pi$
$631$	21.5094	−	28.6238i	0.856276	−	1.13950i	0.988937	−	0.148335i	$-0.0473914\pi$
$632$	−0.232464	+	0.442922i	−0.00924691	+	0.0176185i
$633$	−2.27086	−	11.1234i	−0.0902584	−	0.442115i
$634$	−1.38198	−	0.111565i	−0.0548854	−	0.00443081i
$635$	4.42899	−	1.28287i	0.175759	−	0.0509092i
$636$	−3.51418	+	1.84438i	−0.139346	+	0.0731346i
$637$	−10.2317	+	3.32414i	−0.405394	+	0.131707i
$638$	−36.9628	−	19.3996i	−1.46337	−	0.768037i
$639$	3.70682	+	0.756752i	0.146639	+	0.0299366i
$640$	0.652449	−	0.490284i	0.0257903	−	0.0193802i
$641$	−2.00857	+	49.8422i	−0.0793338	+	1.96865i	0.132043	+	0.991244i	$0.457846\pi$
$641$	−2.00857	+	49.8422i	−0.0793338	+	1.96865i	−0.211377	+	0.977405i	$0.567795\pi$
$642$	4.90850	+	1.86155i	0.193723	+	0.0734695i
$643$	22.4306	+	6.49710i	0.884577	+	0.256221i	0.689255	−	0.724519i	$-0.257938\pi$
$643$	22.4306	+	6.49710i	0.884577	+	0.256221i	0.195321	+	0.980739i	$0.437425\pi$
$644$	9.95637	−	2.03261i	0.392336	−	0.0800959i
$645$	−3.20704	+	3.62000i	−0.126277	+	0.142538i
$646$	27.7197	+	33.9504i	1.09062	+	1.33576i
$647$	1.38067	+	34.2609i	0.0542796	+	1.34693i	0.765260	+	0.643722i	$0.222611\pi$
$647$	1.38067	+	34.2609i	0.0542796	+	1.34693i	−0.710980	+	0.703212i	$0.751748\pi$
$648$	10.9204	−	32.7106i	0.428994	−	1.28499i
$649$	−21.7210	−	19.2432i	−0.852625	−	0.755360i
$650$	4.58488	+	14.1122i	0.179834	+	0.553527i
$651$	20.9811	−	18.5876i	0.822313	−	0.728506i
$652$	0.612348	+	1.43723i	0.0239814	+	0.0562864i
$653$	−20.9795	−	36.3375i	−0.820989	−	1.42200i	−0.904946	−	0.425526i	$-0.860089\pi$
$653$	−20.9795	−	36.3375i	−0.820989	−	1.42200i	0.0839567	−	0.996469i	$-0.473244\pi$
$654$	−0.657249	+	1.13839i	−0.0257005	+	0.0445145i
$655$	20.9654	+	2.54566i	0.819186	+	0.0994672i
$656$	−10.6248	+	5.04151i	−0.414827	+	0.196838i
$657$	6.95623	+	4.01618i	0.271388	+	0.156686i
$658$	−28.9201	+	19.9621i	−1.12742	+	0.778203i
$659$	−23.9410	−	10.2003i	−0.932609	−	0.397348i	−0.128419	−	0.991720i	$-0.540990\pi$
$659$	−23.9410	−	10.2003i	−0.932609	−	0.397348i	−0.804190	+	0.594372i	$0.797400\pi$
$660$	−7.45479	+	1.21152i	−0.290177	+	0.0471584i
$661$	−18.0684	−	24.0446i	−0.702778	−	0.935227i	0.297029	−	0.954868i	$-0.404004\pi$
$661$	−18.0684	−	24.0446i	−0.702778	−	0.935227i	−0.999807	+	0.0196410i	$0.993748\pi$
$662$	9.83911	−	25.9436i	0.382408	−	1.00833i
$663$	−35.7789	−	23.0322i	−1.38954	−	0.894496i
$664$	−6.12868	−	16.1600i	−0.237839	−	0.627130i
$665$	13.3900	−	21.1746i	0.519241	−	0.821115i
$666$	−4.58573	+	1.95380i	−0.177694	+	0.0757082i
$667$	32.0749	−	20.2829i	1.24195	−	0.785359i
$668$	3.24777	−	0.394351i	0.125660	−	0.0152579i
$669$	−20.3298	+	47.7159i	−0.785997	+	1.84480i
$670$	−5.05432	−	15.1395i	−0.195266	−	0.584892i
$671$	33.9620	−	12.8801i	1.31109	−	0.497230i
$672$	−27.3141	+	2.20502i	−1.05366	+	0.0850606i
$673$	−5.93007	−	20.4730i	−0.228587	−	0.789175i	−0.990020	−	0.140930i	$-0.954991\pi$
$673$	−5.93007	−	20.4730i	−0.228587	−	0.789175i	0.761432	−	0.648245i	$-0.224497\pi$
$674$	−19.7929	+	0.797627i	−0.762394	+	0.0307234i
$675$	12.6957			0.488658
$676$	6.96098	+	7.48573i	0.267730	+	0.287913i
$677$	−20.0506			−0.770608			−0.385304	−	0.922790i	$-0.625903\pi$
$677$	−20.0506			−0.770608			−0.385304	+	0.922790i	$0.625903\pi$
$678$	30.8523	−	1.24331i	1.18488	−	0.0477489i
$679$	8.89071	+	30.6943i	0.341194	+	1.17794i
$680$	−19.4114	+	1.56705i	−0.744392	+	0.0600935i
$681$	−4.61465	+	1.75010i	−0.176834	+	0.0670641i
$682$	−6.04224	−	18.0987i	−0.231370	−	0.693036i
$683$	1.01570	−	2.38392i	0.0388645	−	0.0912183i	−0.899416	−	0.437094i	$-0.856008\pi$
$683$	1.01570	−	2.38392i	0.0388645	−	0.0912183i	0.938280	+	0.345875i	$0.112418\pi$
$684$	7.56934	−	0.919084i	0.289421	−	0.0351421i
$685$	−2.29421	+	1.45077i	−0.0876571	+	0.0554310i
$686$	12.8617	−	5.47984i	0.491061	−	0.209221i
$687$	−29.9830	+	47.4143i	−1.14392	+	1.80897i
$688$	1.31908	+	3.47813i	0.0502895	+	0.132602i
$689$	8.22997	+	2.82172i	0.313537	+	0.107499i
$690$	−3.75805	+	9.90917i	−0.143067	+	0.377236i
$691$	10.1737	+	13.5388i	0.387027	+	0.515040i	0.950344	−	0.311201i	$-0.100731\pi$
$691$	10.1737	+	13.5388i	0.387027	+	0.515040i	−0.563317	+	0.826241i	$0.690475\pi$
$692$	−11.5704	+	1.88037i	−0.439840	+	0.0714810i
$693$	−16.3250	−	6.95541i	−0.620134	−	0.264214i
$694$	−11.3816	+	7.85613i	−0.432039	+	0.298215i
$695$	19.4608	+	11.2357i	0.738189	+	0.426194i
$696$	−53.8238	+	25.5397i	−2.04019	+	0.968080i
$697$	36.4100	+	4.42098i	1.37913	+	0.167456i
$698$	−8.33926	+	14.4440i	−0.315645	+	0.546714i
$699$	0.166152	+	0.287784i	0.00628445	+	0.0108850i
$700$	−3.63792	−	8.53852i	−0.137501	−	0.322726i
$701$	−20.7571	+	18.3892i	−0.783984	+	0.694550i	−0.956910	−	0.290385i	$-0.906217\pi$
$701$	−20.7571	+	18.3892i	−0.783984	+	0.694550i	0.172925	+	0.984935i	$0.444678\pi$
$702$	−12.2426	+	5.68840i	−0.462068	+	0.214695i
$703$	17.3651	+	15.3842i	0.654938	+	0.580225i
$704$	−10.5859	+	31.7088i	−0.398973	+	1.19507i
$705$	0.956065	+	23.7245i	0.0360075	+	0.893517i
$706$	−24.4897	−	29.9945i	−0.921683	−	1.12886i
$707$	−5.27553	+	5.95484i	−0.198407	+	0.223955i
$708$	−11.4513	+	2.33780i	−0.430365	+	0.0878597i
$709$	4.03142	+	1.16771i	0.151403	+	0.0438544i	0.353054	−	0.935603i	$-0.385143\pi$
$709$	4.03142	+	1.16771i	0.151403	+	0.0438544i	−0.201651	+	0.979458i	$0.564631\pi$
$710$	−3.18650	−	1.20848i	−0.119587	−	0.0453534i
$711$	−0.00902369	+	0.223920i	−0.000338415	+	0.00839767i
$712$	−0.299116	+	0.224771i	−0.0112098	+	0.00842365i
$713$	16.9957	+	3.46971i	0.636496	+	0.129942i
$714$	−36.3754	−	19.0913i	−1.36132	−	0.714473i
$715$	13.1552	+	10.0529i	0.491978	+	0.375959i
$716$	5.89703	−	3.09500i	0.220382	−	0.115666i
$717$	1.51217	−	0.438007i	0.0564732	−	0.0163577i
$718$	13.9849	+	1.12898i	0.521912	+	0.0421331i
$719$	−0.119586	−	0.585769i	−0.00445979	−	0.0218455i	0.977500	−	0.210936i	$-0.0676512\pi$
$719$	−0.119586	−	0.585769i	−0.00445979	−	0.0218455i	−0.981960	+	0.189091i	$0.939446\pi$
$720$	1.30006	−	2.47705i	0.0484503	−	0.0923143i
$721$	−18.7906	+	25.0058i	−0.699799	+	0.931263i
$722$	18.0889	+	28.6052i	0.673197	+	1.06458i
$723$	−31.8524	−	21.9861i	−1.18460	−	0.817673i
$724$	0.718540	+	1.51429i	0.0267043	+	0.0562782i
$725$	−24.0109	−	24.9980i	−0.891742	−	0.928402i
$726$	−9.43458	+	9.06203i	−0.350150	+	0.336324i
$727$	2.80420	−	23.0947i	0.104002	−	0.856533i	−0.843576	−	0.537009i	$-0.819554\pi$
$727$	2.80420	−	23.0947i	0.104002	−	0.856533i	0.947578	−	0.319524i	$-0.103523\pi$
$728$	25.9875	+	23.4006i	0.963160	+	0.867284i
$729$	0.708360	+	5.83387i	0.0262356	+	0.216069i
$730$	−5.60467	−	4.57607i	−0.207438	−	0.169368i
$731$	2.32058	−	11.3670i	0.0858298	−	0.420422i
$732$	4.07002	−	14.0513i	0.150432	−	0.519352i
$733$	6.85464	−	27.8103i	0.253182	−	1.02720i	−0.697390	−	0.716692i	$-0.745655\pi$
$733$	6.85464	−	27.8103i	0.253182	−	1.02720i	0.950571	−	0.310506i	$-0.100499\pi$
$734$	2.40376	+	29.7759i	0.0887244	+	1.09905i
$735$	−1.12575	+	6.92701i	−0.0415238	+	0.255506i
$736$	−11.2452	−	12.6932i	−0.414505	−	0.467879i
$737$	42.0639	+	31.6089i	1.54944	+	1.16433i
$738$	−6.22877	+	7.62886i	−0.229284	+	0.280822i
$739$	3.54807	+	21.8321i	0.130518	+	0.803108i	0.966937	+	0.255017i	$0.0820811\pi$
$739$	3.54807	+	21.8321i	0.130518	+	0.803108i	−0.836419	+	0.548091i	$0.815355\pi$
$740$	−2.82450	+	0.696176i	−0.103831	+	0.0255919i
$741$	−40.9196	−	33.9649i	−1.50322	−	1.24773i
$742$	8.15557	+	2.01017i	0.299400	+	0.0737955i
$743$	0.184228	−	2.28207i	0.00675865	−	0.0837209i	−0.992499	−	0.122256i	$-0.960987\pi$
$743$	0.184228	−	2.28207i	0.00675865	−	0.0837209i	0.999257	+	0.0385351i	$0.0122691\pi$
$744$	−25.8297	−	8.62323i	−0.946964	−	0.316143i
$745$	5.62370	−	5.85489i	0.206036	−	0.214507i
$746$		−	41.8272i		−	1.53140i
$747$	−5.58425	−	5.36375i	−0.204317	−	0.196249i
$748$	14.0338	−	11.4583i	0.513128	−	0.418956i
$749$	3.34518	+	6.37370i	0.122230	+	0.232890i
$750$	22.3422	+	3.63097i	0.815823	+	0.132584i
$751$	−18.1820	−	11.4976i	−0.663471	−	0.419553i	0.159841	−	0.987143i	$-0.448902\pi$
$751$	−18.1820	−	11.4976i	−0.663471	−	0.419553i	−0.823312	+	0.567589i	$0.807876\pi$
$752$	16.4995	+	7.82909i	0.601673	+	0.285497i
$753$	7.93262	+	11.4924i	0.289081	+	0.418806i
$754$	34.3545	+	13.3476i	1.25112	+	0.486091i
$755$	−9.79479	+	14.1902i	−0.356469	+	0.516434i
$756$	7.31259	−	4.22193i	0.265956	−	0.153550i
$757$	18.5939	−	39.1858i	0.675806	−	1.42423i	−0.218077	−	0.975932i	$-0.569978\pi$
$757$	18.5939	−	39.1858i	0.675806	−	1.42423i	0.893883	−	0.448300i	$-0.147970\pi$
$758$	13.2707	−	4.43041i	0.482013	−	0.160920i
$759$	−8.36088	−	33.9214i	−0.303481	−	1.23127i
$760$	−24.3189	−	0.980018i	−0.882139	−	0.0355490i
$761$	15.0291	+	0.605651i	0.544804	+	0.0219548i	0.311143	−	0.950363i	$-0.399288\pi$
$761$	15.0291	+	0.605651i	0.544804	+	0.0219548i	0.233661	+	0.972318i	$0.424929\pi$
$762$	−2.26141	−	9.17492i	−0.0819224	−	0.332372i
$763$	−1.70966	+	0.570767i	−0.0618937	+	0.0206632i
$764$	−5.10218	+	10.7526i	−0.184590	+	0.389016i
$765$	−7.55584	+	4.36237i	−0.273182	+	0.157722i
$766$	−8.50556	+	12.3224i	−0.307318	+	0.445227i

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)

\(f(q)\)	\(=\)	\(q+(1.10078 - 0.0443599i) q^{2} +(-0.581947 - 2.00912i) q^{3} +(-0.783766 + 0.0632721i) q^{4} +(1.05138 - 0.398737i) q^{5} +(-0.729720 - 2.18578i) q^{6} +(1.23850 - 2.90687i) q^{7} +(-3.04723 + 0.370001i) q^{8} +(-1.16231 + 0.735002i) q^{9} +O(q^{10})\)	\(q+(1.10078 - 0.0443599i) q^{2} +(-0.581947 - 2.00912i) q^{3} +(-0.783766 + 0.0632721i) q^{4} +(1.05138 - 0.398737i) q^{5} +(-0.729720 - 2.18578i) q^{6} +(1.23850 - 2.90687i) q^{7} +(-3.04723 + 0.370001i) q^{8} +(-1.16231 + 0.735002i) q^{9} +(1.13965 - 0.485561i) q^{10} +(-2.18262 + 3.45154i) q^{11} +(0.583231 + 1.53785i) q^{12} +(1.57196 - 3.24483i) q^{13} +(1.23437 - 3.25476i) q^{14} +(-1.41296 - 1.88031i) q^{15} +(-1.78565 + 0.290196i) q^{16} +(5.19062 + 2.21152i) q^{17} +(-1.24685 + 0.860636i) q^{18} +(6.10663 + 3.52566i) q^{19} +(-0.798810 + 0.379040i) q^{20} +(-6.56098 - 0.796647i) q^{21} +(-2.24947 + 3.89620i) q^{22} +(-2.04500 - 3.54205i) q^{23} +(2.51670 + 5.90691i) q^{24} +(-2.79614 + 2.47716i) q^{25} +(1.58644 - 3.64158i) q^{26} +(-2.54387 - 2.25367i) q^{27} +(-0.786771 + 2.35667i) q^{28} +(0.373616 + 9.27118i) q^{29} +(-1.63877 - 2.00713i) q^{30} +(-2.81240 + 3.17454i) q^{31} +(4.06241 - 0.829348i) q^{32} +(8.20470 + 2.37652i) q^{33} +(5.81184 + 2.20414i) q^{34} +(0.143063 - 3.55007i) q^{35} +(0.864476 - 0.649611i) q^{36} +(3.22361 + 0.658105i) q^{37} +(6.87845 + 3.61009i) q^{38} +(-7.43404 - 1.26992i) q^{39} +(-3.05627 + 1.60406i) q^{40} +(6.24401 - 1.80860i) q^{41} +(-7.25753 - 0.585889i) q^{42} +(-0.411297 - 2.01466i) q^{43} +(1.49228 - 2.84329i) q^{44} +(-0.928964 + 1.23623i) q^{45} +(-2.40822 - 3.80830i) q^{46} +(-8.30806 - 5.73464i) q^{47} +(1.62219 + 3.41870i) q^{48} +(-2.06693 - 2.15190i) q^{49} +(-2.96805 + 2.85085i) q^{50} +(1.42253 - 11.7155i) q^{51} +(-1.02674 + 2.64265i) q^{52} +(0.290857 + 2.39543i) q^{53} +(-2.90021 - 2.36795i) q^{54} +(-0.918514 + 4.49918i) q^{55} +(-2.69845 + 9.31614i) q^{56} +(3.52973 - 14.3207i) q^{57} +(0.822538 + 10.1890i) q^{58} +(-1.13988 + 7.01397i) q^{59} +(1.22640 + 1.38432i) q^{60} +(-7.11055 - 5.34323i) q^{61} +(-2.95501 + 3.61923i) q^{62} +(0.697029 + 4.28899i) q^{63} +(7.94805 - 1.95902i) q^{64} +(0.358894 - 4.03837i) q^{65} +(9.13700 + 2.25207i) q^{66} +(1.03676 - 12.8426i) q^{67} +(-4.20816 - 1.40489i) q^{68} +(-5.92630 + 6.16993i) q^{69} -3.91419i q^{70} +(-1.98407 - 1.90572i) q^{71} +(3.26988 - 2.66978i) q^{72} +(-2.71437 - 5.17180i) q^{73} +(3.57768 + 0.581429i) q^{74} +(6.60411 + 4.17619i) q^{75} +(-5.00924 - 2.37691i) q^{76} +(7.32998 + 10.6193i) q^{77} +(-8.23958 - 1.06813i) q^{78} +(0.0925711 - 0.134112i) q^{79} +(-1.76169 + 1.01711i) q^{80} +(-4.81612 + 10.1497i) q^{81} +(6.79305 - 2.26785i) q^{82} +(1.34744 + 5.46679i) q^{83} +(5.19267 + 0.209258i) q^{84} +(6.33915 + 0.255459i) q^{85} +(-0.542118 - 2.19946i) q^{86} +(18.4095 - 6.14598i) q^{87} +(5.37387 - 11.3252i) q^{88} +(0.105560 - 0.0609451i) q^{89} +(-0.967747 + 1.40202i) q^{90} +(-7.48544 - 8.58820i) q^{91} +(1.82691 + 2.64674i) q^{92} +(8.01470 + 3.80302i) q^{93} +(-9.39973 - 5.94403i) q^{94} +(7.82622 + 1.27189i) q^{95} +(-4.03037 - 7.67922i) q^{96} +(-7.83403 + 6.39629i) q^{97} +(-2.37069 - 2.27708i) q^{98} -5.61599i 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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