LMFDB - Embedded newform 153.2.s.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

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

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

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	153.11
Dual form			153.2.s.a.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34967 - 1.75893i) q^{2} +(-0.353226 - 1.69565i) q^{3} +(-0.754572 + 2.81610i) q^{4} +(-1.95144 - 0.127904i) q^{5} +(-2.50579 + 2.90987i) q^{6} +(-0.0117682 - 0.179547i) q^{7} +(1.87511 - 0.776696i) q^{8} +(-2.75046 + 1.19790i) q^{9} +O(q^{10})$	\(q+(-1.34967 - 1.75893i) q^{2} +(-0.353226 - 1.69565i) q^{3} +(-0.754572 + 2.81610i) q^{4} +(-1.95144 - 0.127904i) q^{5} +(-2.50579 + 2.90987i) q^{6} +(-0.0117682 - 0.179547i) q^{7} +(1.87511 - 0.776696i) q^{8} +(-2.75046 + 1.19790i) q^{9} +(2.40883 + 3.60506i) q^{10} +(-1.93619 - 1.69800i) q^{11} +(5.04166 + 0.284770i) q^{12} +(1.09295 + 0.292855i) q^{13} +(-0.299928 + 0.263030i) q^{14} +(0.472418 + 3.35413i) q^{15} +(1.15275 + 0.665543i) q^{16} +(4.05247 + 0.759899i) q^{17} +(5.81924 + 3.22110i) q^{18} +(-5.72485 - 2.37131i) q^{19} +(1.83269 - 5.39893i) q^{20} +(-0.300293 + 0.0833756i) q^{21} +(-0.373425 + 5.69736i) q^{22} +(-1.13485 - 3.34316i) q^{23} +(-1.97934 - 2.90518i) q^{24} +(-1.16548 - 0.153438i) q^{25} +(-0.960014 - 2.31768i) q^{26} +(3.00275 + 4.24070i) q^{27} +(0.514504 + 0.102341i) q^{28} +(-5.61452 + 2.76878i) q^{29} +(5.26207 - 5.35793i) q^{30} +(-3.35223 - 3.82248i) q^{31} +(-0.915032 - 6.95036i) q^{32} +(-2.19529 + 3.88289i) q^{33} +(-4.13291 - 8.15362i) q^{34} +0.351881i q^{35} +(-1.29797 - 8.64948i) q^{36} +(-1.71395 - 8.61661i) q^{37} +(3.55571 + 13.2701i) q^{38} +(0.110521 - 1.95671i) q^{39} +(-3.75850 + 1.27584i) q^{40} +(3.19018 - 6.46904i) q^{41} +(0.551949 + 0.415664i) q^{42} +(0.244602 - 1.85793i) q^{43} +(6.24273 - 4.17126i) q^{44} +(5.52057 - 1.98582i) q^{45} +(-4.34870 + 6.50829i) q^{46} +(0.820877 - 0.219953i) q^{47} +(0.721345 - 2.18976i) q^{48} +(6.90802 - 0.909457i) q^{49} +(1.30313 + 2.25709i) q^{50} +(-0.142917 - 7.14000i) q^{51} +(-1.64942 + 2.85688i) q^{52} +(-4.44864 + 10.7400i) q^{53} +(3.40635 - 11.0052i) q^{54} +(3.56118 + 3.56118i) q^{55} +(-0.161521 - 0.327531i) q^{56} +(-1.99875 + 10.5450i) q^{57} +(12.4478 + 6.13860i) q^{58} +(-2.50879 - 1.92506i) q^{59} +(-9.80205 - 1.20056i) q^{60} +(-10.8317 + 0.709946i) q^{61} +(-2.19906 + 11.0554i) q^{62} +(0.247447 + 0.479742i) q^{63} +(-9.10774 + 9.10774i) q^{64} +(-2.09537 - 0.711281i) q^{65} +(9.79264 - 1.37926i) q^{66} +(9.11090 - 5.26018i) q^{67} +(-5.19783 + 10.8388i) q^{68} +(-5.26798 + 3.10520i) q^{69} +(0.618933 - 0.474924i) q^{70} +(12.6361 - 2.51348i) q^{71} +(-4.22702 + 4.38246i) q^{72} +(8.59520 + 5.74313i) q^{73} +(-12.8427 + 14.6443i) q^{74} +(0.151500 + 2.03045i) q^{75} +(10.9977 - 14.3324i) q^{76} +(-0.282086 + 0.367621i) q^{77} +(-3.59087 + 2.44651i) q^{78} +(4.22913 - 4.82239i) q^{79} +(-2.16440 - 1.44621i) q^{80} +(6.13009 - 6.58954i) q^{81} +(-15.6843 + 3.11980i) q^{82} +(7.40903 - 5.68515i) q^{83} +(-0.00820131 - 0.908568i) q^{84} +(-7.81095 - 2.00122i) q^{85} +(-3.59810 + 2.07737i) q^{86} +(6.67807 + 8.54227i) q^{87} +(-4.94941 - 1.68010i) q^{88} +(-10.2745 + 10.2745i) q^{89} +(-10.9439 - 7.03007i) q^{90} +(0.0397194 - 0.199683i) q^{91} +(10.2710 - 0.673197i) q^{92} +(-5.29750 + 7.03441i) q^{93} +(-1.49480 - 1.14700i) q^{94} +(10.8684 + 5.35969i) q^{95} +(-11.4622 + 4.00662i) q^{96} +(-1.17141 - 2.37538i) q^{97} +(-10.9232 - 10.9232i) q^{98} +(7.35945 + 2.35092i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.34967	−	1.75893i	−0.954363	−	1.24375i	−0.969808	−	0.243869i	$-0.921583\pi$
$2$	−1.34967	−	1.75893i	−0.954363	−	1.24375i	0.0154457	−	0.999881i	$-0.495083\pi$
$3$	−0.353226	−	1.69565i	−0.203935	−	0.978984i
$3$	−0.353226	−	1.69565i	−0.203935	−	0.978984i
$4$	−0.754572	+	2.81610i	−0.377286	+	1.40805i
$5$	−1.95144	−	0.127904i	−0.872709	−	0.0572004i	−0.377536	−	0.925995i	$-0.623229\pi$
$5$	−1.95144	−	0.127904i	−0.872709	−	0.0572004i	−0.495173	+	0.868795i	$0.664895\pi$
$6$	−2.50579	+	2.90987i	−1.02298	+	1.18795i
$7$	−0.0117682	−	0.179547i	−0.00444795	−	0.0678626i	0.995058	−	0.0992966i	$-0.0316593\pi$
$7$	−0.0117682	−	0.179547i	−0.00444795	−	0.0678626i	−0.999506	+	0.0314340i	$0.989993\pi$
$8$	1.87511	−	0.776696i	0.662952	−	0.274604i
$9$	−2.75046	+	1.19790i	−0.916821	+	0.399299i
$10$	2.40883	+	3.60506i	0.761738	+	1.14002i
$11$	−1.93619	−	1.69800i	−0.583784	−	0.511965i	0.315734	−	0.948848i	$-0.397749\pi$
$11$	−1.93619	−	1.69800i	−0.583784	−	0.511965i	−0.899519	+	0.436882i	$0.856083\pi$
$12$	5.04166	+	0.284770i	1.45540	+	0.0822060i
$13$	1.09295	+	0.292855i	0.303130	+	0.0812234i	0.407178	−	0.913349i	$-0.366513\pi$
$13$	1.09295	+	0.292855i	0.303130	+	0.0812234i	−0.104048	+	0.994572i	$0.533180\pi$
$14$	−0.299928	+	0.263030i	−0.0801591	+	0.0702976i
$15$	0.472418	+	3.35413i	0.121978	+	0.866033i
$16$	1.15275	+	0.665543i	0.288188	+	0.166386i
$17$	4.05247	+	0.759899i	0.982870	+	0.184303i
$17$	4.05247	+	0.759899i	0.982870	+	0.184303i
$18$	5.81924	+	3.22110i	1.37161	+	0.759220i
$19$	−5.72485	−	2.37131i	−1.31337	−	0.544016i	−0.387505	−	0.921868i	$-0.626663\pi$
$19$	−5.72485	−	2.37131i	−1.31337	−	0.544016i	−0.925866	+	0.377852i	$0.876663\pi$
$20$	1.83269	−	5.39893i	0.409802	−	1.20724i
$21$	−0.300293	+	0.0833756i	−0.0655293	+	0.0181940i
$22$	−0.373425	+	5.69736i	−0.0796145	+	1.21468i
$23$	−1.13485	−	3.34316i	−0.236633	−	0.697098i	−0.998765	−	0.0496766i	$-0.984181\pi$
$23$	−1.13485	−	3.34316i	−0.236633	−	0.697098i	0.762133	−	0.647421i	$-0.224152\pi$
$24$	−1.97934	−	2.90518i	−0.404032	−	0.593018i
$25$	−1.16548	−	0.153438i	−0.233096	−	0.0306877i
$26$	−0.960014	−	2.31768i	−0.188274	−	0.454534i
$27$	3.00275	+	4.24070i	0.577879	+	0.816122i
$28$	0.514504	+	0.102341i	0.0972320	+	0.0193407i
$29$	−5.61452	+	2.76878i	−1.04259	+	0.514149i	−0.881201	−	0.472742i	$-0.843264\pi$
$29$	−5.61452	+	2.76878i	−1.04259	+	0.514149i	−0.161390	+	0.986891i	$0.551598\pi$
$30$	5.26207	−	5.35793i	0.960718	−	0.978220i
$31$	−3.35223	−	3.82248i	−0.602078	−	0.686538i	0.367863	−	0.929880i	$-0.380090\pi$
$31$	−3.35223	−	3.82248i	−0.602078	−	0.686538i	−0.969941	+	0.243342i	$0.921756\pi$
$32$	−0.915032	−	6.95036i	−0.161756	−	1.22866i
$33$	−2.19529	+	3.88289i	−0.382152	+	0.675924i
$34$	−4.13291	−	8.15362i	−0.708788	−	1.39833i
$35$			0.351881i			0.0594787i
$36$	−1.29797	−	8.64948i	−0.216329	−	1.44158i
$37$	−1.71395	−	8.61661i	−0.281772	−	1.41656i	−0.819324	−	0.573331i	$-0.805651\pi$
$37$	−1.71395	−	8.61661i	−0.281772	−	1.41656i	0.537552	−	0.843230i	$-0.319349\pi$
$38$	3.55571	+	13.2701i	0.576812	+	2.15269i
$39$	0.110521	−	1.95671i	0.0176976	−	0.313324i
$40$	−3.75850	+	1.27584i	−0.594271	+	0.201728i
$41$	3.19018	−	6.46904i	0.498222	−	1.01029i	−0.491974	−	0.870610i	$-0.663724\pi$
$41$	3.19018	−	6.46904i	0.498222	−	1.01029i	0.990196	−	0.139685i	$-0.0446089\pi$
$42$	0.551949	+	0.415664i	0.0851675	+	0.0641383i
$43$	0.244602	−	1.85793i	0.0373014	−	0.283332i	−0.962621	−	0.270853i	$-0.912694\pi$
$43$	0.244602	−	1.85793i	0.0373014	−	0.283332i	0.999922	−	0.0124794i	$-0.00397241\pi$
$44$	6.24273	−	4.17126i	0.941126	−	0.628840i
$45$	5.52057	−	1.98582i	0.822958	−	0.296029i
$46$	−4.34870	+	6.50829i	−0.641181	+	0.959596i
$47$	0.820877	−	0.219953i	0.119737	−	0.0320835i	−0.198453	−	0.980110i	$-0.563592\pi$
$47$	0.820877	−	0.219953i	0.119737	−	0.0320835i	0.318190	+	0.948027i	$0.396925\pi$
$48$	0.721345	−	2.18976i	0.104117	−	0.316064i
$49$	6.90802	−	0.909457i	0.986859	−	0.129922i
$50$	1.30313	+	2.25709i	0.184290	+	0.319200i
$51$	−0.142917	−	7.14000i	−0.0200123	−	0.999800i
$52$	−1.64942	+	2.85688i	−0.228733	+	0.396178i
$53$	−4.44864	+	10.7400i	−0.611068	+	1.47525i	0.250761	+	0.968049i	$0.419319\pi$
$53$	−4.44864	+	10.7400i	−0.611068	+	1.47525i	−0.861829	+	0.507199i	$0.830681\pi$
$54$	3.40635	−	11.0052i	0.463545	−	1.49761i
$55$	3.56118	+	3.56118i	0.480189	+	0.480189i
$56$	−0.161521	−	0.327531i	−0.0215841	−	0.0437682i
$57$	−1.99875	+	10.5450i	−0.264741	+	1.39671i
$58$	12.4478	+	6.13860i	1.63448	+	0.806037i
$59$	−2.50879	−	1.92506i	−0.326616	−	0.250622i	0.432416	−	0.901674i	$-0.357661\pi$
$59$	−2.50879	−	1.92506i	−0.326616	−	0.250622i	−0.759033	+	0.651053i	$0.774328\pi$
$60$	−9.80205	−	1.20056i	−1.26544	−	0.154991i
$61$	−10.8317	+	0.709946i	−1.38685	+	0.0908993i	−0.740458	−	0.672102i	$-0.765391\pi$
$61$	−10.8317	+	0.709946i	−1.38685	+	0.0908993i	−0.646397	+	0.763002i	$0.723725\pi$
$62$	−2.19906	+	11.0554i	−0.279281	+	1.40404i
$63$	0.247447	+	0.479742i	0.0311754	+	0.0604418i
$64$	−9.10774	+	9.10774i	−1.13847	+	1.13847i
$65$	−2.09537	−	0.711281i	−0.259898	−	0.0882236i
$66$	9.79264	−	1.37926i	1.20539	−	0.169775i
$67$	9.11090	−	5.26018i	1.11307	−	0.642633i	0.173450	−	0.984843i	$-0.444508\pi$
$67$	9.11090	−	5.26018i	1.11307	−	0.642633i	0.939624	+	0.342209i	$0.111175\pi$
$68$	−5.19783	+	10.8388i	−0.630330	+	1.31439i
$69$	−5.26798	+	3.10520i	−0.634190	+	0.373822i
$70$	0.618933	−	0.474924i	0.0739766	−	0.0567642i
$71$	12.6361	−	2.51348i	1.49963	−	0.298295i	0.624056	−	0.781380i	$-0.285484\pi$
$71$	12.6361	−	2.51348i	1.49963	−	0.298295i	0.875574	+	0.483085i	$0.160484\pi$
$72$	−4.22702	+	4.38246i	−0.498159	+	0.516478i
$73$	8.59520	+	5.74313i	1.00599	+	0.672182i	0.945377	−	0.325979i	$-0.105694\pi$
$73$	8.59520	+	5.74313i	1.00599	+	0.672182i	0.0606148	+	0.998161i	$0.480694\pi$
$74$	−12.8427	+	14.6443i	−1.49294	+	1.70237i
$75$	0.151500	+	2.03045i	0.0174937	+	0.234456i
$76$	10.9977	−	14.3324i	1.26152	−	1.64404i
$77$	−0.282086	+	0.367621i	−0.0321466	+	0.0418943i
$78$	−3.59087	+	2.44651i	−0.406586	+	0.277013i
$79$	4.22913	−	4.82239i	0.475814	−	0.542562i	−0.463285	−	0.886209i	$-0.653329\pi$
$79$	4.22913	−	4.82239i	0.475814	−	0.542562i	0.939099	+	0.343648i	$0.111663\pi$
$80$	−2.16440	−	1.44621i	−0.241987	−	0.161691i
$81$	6.13009	−	6.58954i	0.681121	−	0.732171i
$82$	−15.6843	+	3.11980i	−1.73204	+	0.344524i
$83$	7.40903	−	5.68515i	0.813246	−	0.624026i	−0.116099	−	0.993238i	$-0.537039\pi$
$83$	7.40903	−	5.68515i	0.813246	−	0.624026i	0.929345	+	0.369212i	$0.120372\pi$
$84$	−0.00820131	−	0.908568i	−0.000894837	−	0.0991329i
$85$	−7.81095	−	2.00122i	−0.847217	−	0.217063i
$86$	−3.59810	+	2.07737i	−0.387994	+	0.224008i
$87$	6.67807	+	8.54227i	0.715965	+	0.915827i
$88$	−4.94941	−	1.68010i	−0.527609	−	0.179099i
$89$	−10.2745	+	10.2745i	−1.08909	+	1.08909i	−0.0934682	+	0.995622i	$0.529795\pi$
$89$	−10.2745	+	10.2745i	−1.08909	+	1.08909i	−0.995622	+	0.0934682i	$0.970205\pi$
$90$	−10.9439	−	7.03007i	−1.15359	−	0.741034i
$91$	0.0397194	−	0.199683i	0.00416373	−	0.0209325i
$92$	10.2710	−	0.673197i	1.07083	−	0.0701857i
$93$	−5.29750	+	7.03441i	−0.549325	+	0.729434i
$94$	−1.49480	−	1.14700i	−0.154176	−	0.118304i
$95$	10.8684	+	5.35969i	1.11507	+	0.549893i
$96$	−11.4622	+	4.00662i	−1.16985	+	0.408924i
$97$	−1.17141	−	2.37538i	−0.118938	−	0.241183i	0.829259	−	0.558864i	$-0.188763\pi$
$97$	−1.17141	−	2.37538i	−0.118938	−	0.241183i	−0.948198	+	0.317681i	$0.897096\pi$
$98$	−10.9232	−	10.9232i	−1.10341	−	1.10341i
$99$	7.35945	+	2.35092i	0.739653	+	0.236276i
$100$	1.31154	−	3.16633i	0.131154	−	0.316633i
$101$	−1.04532	+	1.81054i	−0.104013	+	0.180155i	−0.913334	−	0.407210i	$-0.866502\pi$
$101$	−1.04532	+	1.81054i	−0.104013	+	0.180155i	0.809322	+	0.587366i	$0.199835\pi$
$102$	−12.3658	+	9.88804i	−1.22440	+	0.979062i
$103$	−1.50429	−	2.60551i	−0.148222	−	0.256728i	0.782348	−	0.622841i	$-0.214022\pi$
$103$	−1.50429	−	2.60551i	−0.148222	−	0.256728i	−0.930570	+	0.366113i	$0.880688\pi$
$104$	2.27686	−	0.299755i	0.223265	−	0.0293934i
$105$	0.596667	−	0.124293i	0.0582287	−	0.0121298i
$106$	24.8950	−	6.67060i	2.41802	−	0.647906i
$107$	4.92541	−	7.37140i	0.476158	−	0.712620i	−0.513177	−	0.858283i	$-0.671531\pi$
$107$	4.92541	−	7.37140i	0.476158	−	0.712620i	0.989334	+	0.145663i	$0.0465314\pi$
$108$	−14.2080	+	5.25613i	−1.36717	+	0.505772i
$109$	7.29495	−	4.87433i	0.698729	−	0.466876i	−0.154783	−	0.987948i	$-0.549468\pi$
$109$	7.29495	−	4.87433i	0.698729	−	0.466876i	0.853512	+	0.521073i	$0.174468\pi$
$110$	1.45743	−	11.0703i	0.138960	−	1.05551i
$111$	−14.0053	+	5.94987i	−1.32933	+	0.564737i
$112$	0.105931	−	0.214806i	0.0100095	−	0.0202973i
$113$	7.41375	−	2.51663i	0.697427	−	0.236745i	0.0498637	−	0.998756i	$-0.484121\pi$
$113$	7.41375	−	2.51663i	0.697427	−	0.236745i	0.647564	+	0.762011i	$0.275788\pi$
$114$	21.2455	−	10.7166i	1.98982	−	1.00370i
$115$	1.78699	+	6.66912i	0.166637	+	0.621899i
$116$	−3.56059	−	17.9003i	−0.330593	−	1.66200i
$117$	−3.35693	+	0.503754i	−0.310348	+	0.0465721i
$118$			7.01098i			0.645413i
$119$	0.0887478	−	0.736554i	0.00813550	−	0.0675198i
$120$	3.49098	+	5.92245i	0.318681	+	0.540643i
$121$	−0.570133	−	4.33059i	−0.0518303	−	0.393690i
$122$	15.8680	+	18.0939i	1.43662	+	1.63815i
$123$	−12.0961	−	3.12439i	−1.09067	−	0.281717i
$124$	13.2940	−	6.55587i	1.19384	−	0.588734i
$125$	11.8450	+	2.35611i	1.05945	+	0.210737i
$126$	0.509858	−	1.08274i	0.0454218	−	0.0964578i
$127$	0.494267	+	1.19327i	0.0438591	+	0.105885i	0.944291	−	0.329112i	$-0.106749\pi$
$127$	0.494267	+	1.19327i	0.0438591	+	0.105885i	−0.900432	+	0.434997i	$0.856749\pi$
$128$	14.4116	+	1.89732i	1.27382	+	0.167701i
$129$	−3.23681	+	0.241512i	−0.284985	+	0.0212639i
$130$	1.57697	+	4.64559i	0.138309	+	0.407445i
$131$	0.955788	−	14.5825i	0.0835076	−	1.27408i	−0.726298	−	0.687380i	$-0.758761\pi$
$131$	0.955788	−	14.5825i	0.0835076	−	1.27408i	0.809805	−	0.586699i	$-0.199573\pi$
$132$	−9.27809	−	9.11209i	−0.807554	−	0.793105i
$133$	−0.358392	+	1.05579i	−0.0310765	+	0.0915485i
$134$	−21.5490	−	8.92589i	−1.86155	−	0.771080i
$135$	−5.31727	−	8.65951i	−0.457638	−	0.745292i
$136$	8.18905	−	1.72265i	0.702205	−	0.147716i
$137$	−15.0426	−	8.68484i	−1.28517	−	0.741996i	−0.307385	−	0.951585i	$-0.599454\pi$
$137$	−15.0426	−	8.68484i	−1.28517	−	0.741996i	−0.977789	+	0.209589i	$0.932787\pi$
$138$	12.5719	+	5.07498i	1.07019	+	0.432011i
$139$	−15.5913	+	13.6732i	−1.32244	+	1.15975i	−0.347400	+	0.937717i	$0.612935\pi$
$139$	−15.5913	+	13.6732i	−1.32244	+	1.15975i	−0.975040	+	0.222031i	$0.928731\pi$
$140$	−0.990931	−	0.265519i	−0.0837490	−	0.0224405i
$141$	−0.662919	−	1.31423i	−0.0558279	−	0.110678i
$142$	−21.4756	−	18.8336i	−1.80219	−	1.58048i
$143$	−1.61890	−	2.42285i	−0.135379	−	0.202609i
$144$	−3.96786	−	0.449671i	−0.330655	−	0.0374726i
$145$	11.3105	−	4.68497i	0.939288	−	0.389066i
$146$	−1.49896	−	22.8697i	−0.124055	−	1.89271i
$147$	−3.98221	−	11.3923i	−0.328447	−	0.939624i
$148$	25.5585	+	1.67519i	2.10090	+	0.137700i
$149$	−4.46321	+	16.6569i	−0.365640	+	1.36459i	0.500911	+	0.865499i	$0.332999\pi$
$149$	−4.46321	+	16.6569i	−0.365640	+	1.36459i	−0.866551	+	0.499089i	$0.833668\pi$
$150$	3.36693	−	3.00692i	0.274909	−	0.245514i
$151$	9.72605	+	12.6752i	0.791494	+	1.03150i	0.998585	+	0.0531739i	$0.0169338\pi$
$151$	9.72605	+	12.6752i	0.791494	+	1.03150i	−0.207091	+	0.978322i	$0.566400\pi$
$152$	−12.5765			−1.02009
$153$	−12.0565	+	2.76437i	−0.974707	+	0.223486i
$154$	1.02734			0.0827856
$155$	6.05275	+	7.88809i	0.486168	+	0.633587i
$156$	5.42689	+	1.78772i	0.434499	+	0.143132i
$157$	−3.02040	+	11.2723i	−0.241054	+	0.899625i	0.734272	+	0.678855i	$0.237524\pi$
$157$	−3.02040	+	11.2723i	−0.241054	+	0.899625i	−0.975326	+	0.220770i	$0.929143\pi$
$158$	−14.1902	−	0.930073i	−1.12891	−	0.0739926i
$159$	19.7826	+	3.74970i	1.56886	+	0.297371i
$160$	0.896649	+	13.6802i	0.0708863	+	1.08152i
$161$	−0.586901	+	0.243102i	−0.0462543	+	0.0191592i
$162$	−19.8641	−	1.88866i	−1.56067	−	0.148387i
$163$	−6.58170	−	9.85021i	−0.515518	−	0.771528i	0.478806	−	0.877921i	$-0.341070\pi$
$163$	−6.58170	−	9.85021i	−0.515518	−	0.771528i	−0.994324	+	0.106393i	$0.966070\pi$
$164$	15.8103	+	13.8652i	1.23457	+	1.08269i
$165$	4.78061	−	7.29642i	0.372170	−	0.568025i
$166$	−19.9995	−	5.35885i	−1.55226	−	0.415928i
$167$	−3.29375	+	2.88854i	−0.254878	+	0.223522i	−0.777244	−	0.629200i	$-0.783383\pi$
$167$	−3.29375	+	2.88854i	−0.254878	+	0.223522i	0.522366	+	0.852721i	$0.325049\pi$
$168$	−0.498325	+	0.389575i	−0.0384466	+	0.0300564i
$169$	−10.1496	−	5.85985i	−0.780735	−	0.450757i
$170$	7.02222	+	16.4399i	0.538580	+	1.26088i
$171$	18.5866	−	0.335576i	1.42135	−	0.0256621i
$172$	5.04756	+	2.09077i	0.384873	+	0.159420i
$173$	3.42167	−	10.0799i	0.260145	−	0.766363i	−0.735865	−	0.677128i	$-0.763224\pi$
$173$	3.42167	−	10.0799i	0.260145	−	0.766363i	0.996011	−	0.0892350i	$-0.0284422\pi$
$174$	6.01201	−	23.2755i	0.455770	−	1.76451i
$175$	−0.0138339	+	0.211065i	−0.00104575	+	0.0159550i
$176$	−1.10187	−	3.24599i	−0.0830563	−	0.244676i
$177$	−2.37806	+	4.93401i	−0.178746	+	0.370863i
$178$	31.9392	+	4.20487i	2.39394	+	0.315169i
$179$	2.62459	+	6.33632i	0.196171	+	0.473599i	0.991103	−	0.133100i	$-0.0424932\pi$
$179$	2.62459	+	6.33632i	0.196171	+	0.473599i	−0.794931	+	0.606699i	$0.792493\pi$
$180$	1.42661	+	17.0449i	0.106333	+	1.27045i
$181$	3.12720	+	0.622039i	0.232443	+	0.0462358i	0.309937	−	0.950757i	$-0.399692\pi$
$181$	3.12720	+	0.622039i	0.232443	+	0.0462358i	−0.0774943	+	0.996993i	$0.524692\pi$
$182$	−0.404836	+	0.199643i	−0.0300084	+	0.0147985i
$183$	5.02985	+	18.1160i	0.371817	+	1.33917i
$184$	−4.72459	−	5.38737i	−0.348302	−	0.397162i
$185$	2.24257	+	17.0340i	0.164877	+	1.25236i
$186$	19.5229	−	0.176226i	1.43149	−	0.0129215i
$187$	−6.55607	−	8.35240i	−0.479427	−	0.610788i
$188$			2.47764i			0.180701i
$189$	0.726069	−	0.589041i	0.0528138	−	0.0428464i
$190$	−5.24144	−	26.3505i	−0.380254	−	1.91167i
$191$	0.447519	+	1.67016i	0.0323814	+	0.120849i	0.980225	−	0.197888i	$-0.0634081\pi$
$191$	0.447519	+	1.67016i	0.0323814	+	0.120849i	−0.947843	+	0.318737i	$0.896741\pi$
$192$	18.6606	+	12.2265i	1.34672	+	0.882369i
$193$	−1.00906	+	0.342529i	−0.0726335	+	0.0246558i	−0.357520	−	0.933906i	$-0.616378\pi$
$193$	−1.00906	+	0.342529i	−0.0726335	+	0.0246558i	0.284886	+	0.958561i	$0.408044\pi$
$194$	−2.59710	+	5.26640i	−0.186461	+	0.378105i
$195$	−0.465946	+	3.80425i	−0.0333671	+	0.272428i
$196$	−2.65147	+	20.1399i	−0.189391	+	1.43857i
$197$	7.44534	−	4.97482i	0.530459	−	0.354441i	−0.261317	−	0.965253i	$-0.584157\pi$
$197$	7.44534	−	4.97482i	0.530459	−	0.354441i	0.791776	+	0.610812i	$0.209157\pi$
$198$	−5.79776	−	16.1177i	−0.412029	−	1.14544i
$199$	−9.78402	+	14.6428i	−0.693571	+	1.03800i	0.302814	+	0.953050i	$0.402074\pi$
$199$	−9.78402	+	14.6428i	−0.693571	+	1.03800i	−0.996385	+	0.0849521i	$0.972926\pi$
$200$	−2.30458	+	0.617511i	−0.162958	+	0.0436646i
$201$	−12.1376	−	13.5909i	−0.856123	−	0.958626i
$202$	4.59544	−	0.605001i	0.323334	−	0.0425677i
$203$	0.563200	+	0.975490i	0.0395289	+	0.0684660i
$204$	20.2148	+	4.98517i	1.41532	+	0.349032i
$205$	−7.05285	+	12.2159i	−0.492592	+	0.853195i
$206$	−2.55260	+	6.16252i	−0.177848	+	0.429363i
$207$	7.12613	+	7.83581i	0.495300	+	0.544626i
$208$	1.06500	+	1.06500i	0.0738442	+	0.0738442i
$209$	7.05794	+	14.3121i	0.488208	+	0.989988i
$210$	−1.02393	−	0.881738i	−0.0706577	−	0.0608457i
$211$	−9.64475	−	4.75626i	−0.663972	−	0.327435i	0.0788863	−	0.996884i	$-0.474864\pi$
$211$	−9.64475	−	4.75626i	−0.663972	−	0.327435i	−0.742858	+	0.669449i	$0.766530\pi$
$212$	−26.8880	−	20.6319i	−1.84668	−	1.41700i
$213$	−8.72538	−	20.5386i	−0.597853	−	1.40728i
$214$	−19.6135	+	1.28553i	−1.34075	+	0.0878773i
$215$	−0.714962	+	3.59436i	−0.0487600	+	0.245133i
$216$	8.92422	+	5.61955i	0.607216	+	0.382362i
$217$	−0.646868	+	0.646868i	−0.0439122	+	0.0439122i
$218$	−18.4194	−	6.25254i	−1.24752	−	0.423475i
$219$	6.70229	−	16.6031i	0.452899	−	1.12193i
$220$	−12.7158	+	7.34147i	−0.857299	+	0.494962i
$221$	4.20662	+	2.01732i	0.282968	+	0.135700i
$222$	29.3680	+	16.6040i	1.97105	+	1.11439i
$223$	−12.8414	+	9.85358i	−0.859926	+	0.659844i	−0.941570	−	0.336817i	$-0.890650\pi$
$223$	−12.8414	+	9.85358i	−0.859926	+	0.659844i	0.0816442	+	0.996662i	$0.473983\pi$
$224$	−1.23715	+	0.246085i	−0.0826606	+	0.0164422i
$225$	3.38941	−	0.974098i	0.225961	−	0.0649399i
$226$	−14.4327	−	9.64363i	−0.960050	−	0.641485i
$227$	4.28085	−	4.88137i	0.284130	−	0.323988i	−0.592116	−	0.805853i	$-0.701707\pi$
$227$	4.28085	−	4.88137i	0.284130	−	0.323988i	0.876245	+	0.481865i	$0.160040\pi$
$228$	−28.1875	−	13.5856i	−1.86676	−	0.899728i
$229$	−7.17119	+	9.34567i	−0.473885	+	0.617579i	−0.967736	−	0.251968i	$-0.918922\pi$
$229$	−7.17119	+	9.34567i	−0.473885	+	0.617579i	0.493850	+	0.869547i	$0.335589\pi$
$230$	9.31865	−	12.1443i	0.614454	−	0.800772i
$231$	0.722997	+	0.348465i	0.0475697	+	0.0229273i
$232$	−8.37736	+	9.55254i	−0.550000	+	0.627155i
$233$	−6.04447	−	4.03878i	−0.395986	−	0.264589i	0.341596	−	0.939847i	$-0.389033\pi$
$233$	−6.04447	−	4.03878i	−0.395986	−	0.264589i	−0.737582	+	0.675257i	$0.764033\pi$
$234$	5.41682	+	5.22469i	0.354109	+	0.341549i
$235$	−1.63002	+	0.324231i	−0.106331	+	0.0211505i
$236$	7.31422	−	5.61240i	0.476115	−	0.365336i
$237$	−9.67093	−	5.46772i	−0.628195	−	0.355167i
$238$	−1.41533	+	0.838006i	−0.0917420	+	0.0543199i
$239$	10.7534	−	6.20850i	0.695582	−	0.401595i	−0.110118	−	0.993919i	$-0.535123\pi$
$239$	10.7534	−	6.20850i	0.695582	−	0.401595i	0.805700	+	0.592324i	$0.201789\pi$
$240$	−1.68774	+	4.18090i	−0.108943	+	0.269876i
$241$	−1.63570	−	0.555247i	−0.105365	−	0.0357666i	0.268259	−	0.963347i	$-0.413552\pi$
$241$	−1.63570	−	0.555247i	−0.105365	−	0.0357666i	−0.373624	+	0.927580i	$0.621885\pi$
$242$	−6.84770	+	6.84770i	−0.440187	+	0.440187i
$243$	−13.3389	−	8.06689i	−0.855688	−	0.517491i
$244$	6.17400	−	31.0388i	0.395250	−	1.98706i
$245$	−13.5969	+	0.891186i	−0.868672	+	0.0569358i
$246$	10.8302	+	25.4931i	0.690507	+	1.62538i
$247$	−5.56253	−	4.26828i	−0.353935	−	0.271584i
$248$	−9.25471	−	4.56392i	−0.587674	−	0.289809i
$249$	−12.2571	−	10.5550i	−0.776761	−	0.668895i
$250$	−11.8426	−	24.0144i	−0.748992	−	1.51881i
$251$	−9.98125	−	9.98125i	−0.630011	−	0.630011i	0.318060	−	0.948071i	$-0.396969\pi$
$251$	−9.98125	−	9.98125i	−0.630011	−	0.630011i	−0.948071	+	0.318060i	$0.896969\pi$
$252$	−1.53772	+	0.334837i	−0.0968671	+	0.0210927i
$253$	−3.47939	+	8.39998i	−0.218747	+	0.528102i
$254$	1.43177	−	2.47990i	0.0898372	−	0.155603i
$255$	−0.634341	+	13.9515i	−0.0397240	+	0.873679i
$256$	−3.23340	−	5.60042i	−0.202088	−	0.350026i
$257$	21.5760	−	2.84054i	1.34588	−	0.177188i	0.577082	−	0.816686i	$-0.304191\pi$
$257$	21.5760	−	2.84054i	1.34588	−	0.177188i	0.768793	+	0.639498i	$0.220858\pi$
$258$	4.79343	+	5.36735i	0.298426	+	0.334156i
$259$	−1.52692	+	0.409137i	−0.0948782	+	0.0254225i
$260$	3.58414	−	5.36405i	0.222279	−	0.332664i
$261$	12.1258	−	14.3410i	0.750570	−	0.887688i
$262$	−26.9396	+	18.0004i	−1.66433	+	1.11207i
$263$	0.165254	−	1.25523i	0.0101900	−	0.0774008i	−0.985594	−	0.169127i	$-0.945905\pi$
$263$	0.165254	−	1.25523i	0.0101900	−	0.0774008i	0.995784	+	0.0917263i	$0.0292385\pi$
$264$	−1.10060	+	8.98592i	−0.0677371	+	0.553045i
$265$	10.0549	−	20.3894i	0.617669	−	1.25251i
$266$	2.34077	−	0.794583i	0.143522	−	0.0487190i
$267$	21.0511	+	13.7927i	1.28831	+	0.844099i
$268$	7.93837	+	29.6264i	0.484913	+	1.80972i
$269$	1.32171	+	6.64467i	0.0805859	+	0.405133i	0.999932	+	0.0116823i	$0.00371868\pi$
$269$	1.32171	+	6.64467i	0.0805859	+	0.405133i	−0.919346	+	0.393450i	$0.871281\pi$
$270$	−8.05487	+	21.0402i	−0.490204	+	1.28047i
$271$			2.35757i			0.143212i	0.997433	+	0.0716060i	$0.0228124\pi$
$271$			2.35757i			0.143212i	−0.997433	+	0.0716060i	$0.977188\pi$
$272$	4.16576	+	3.57307i	0.252586	+	0.216649i
$273$	−0.352622	+	0.00318299i	−0.0213417	+	0.000192644i
$274$	5.02656	+	38.1805i	0.303665	+	2.30657i
$275$	1.99606	+	2.27607i	0.120367	+	0.137252i
$276$	−4.76949	−	17.1782i	−0.287090	−	1.03401i
$277$	16.8755	−	8.32207i	1.01395	−	0.500025i	0.142128	−	0.989848i	$-0.454605\pi$
$277$	16.8755	−	8.32207i	1.01395	−	0.500025i	0.871822	+	0.489824i	$0.162939\pi$
$278$	45.0934	+	8.96964i	2.70452	+	0.537963i
$279$	13.7991	+	6.49797i	0.826131	+	0.389024i
$280$	0.273304	+	0.659815i	0.0163331	+	0.0394315i
$281$	19.5159	+	2.56931i	1.16422	+	0.153272i	0.687770	−	0.725929i	$-0.258590\pi$
$281$	19.5159	+	2.56931i	1.16422	+	0.153272i	0.476450	+	0.879201i	$0.341923\pi$
$282$	−1.41691	+	2.93980i	−0.0843755	+	0.175063i
$283$	−4.89539	−	14.4214i	−0.291001	−	0.857260i	−0.989866	−	0.142007i	$-0.954645\pi$
$283$	−4.89539	−	14.4214i	−0.291001	−	0.857260i	0.698865	−	0.715254i	$-0.253689\pi$
$284$	−2.45664	+	37.4811i	−0.145775	+	2.22410i
$285$	5.24917	−	20.3222i	0.310934	−	1.20378i
$286$	−2.07664	+	6.11758i	−0.122794	+	0.361740i
$287$	−1.19904	−	0.496660i	−0.0707773	−	0.0293169i
$288$	10.8426	+	18.0206i	0.638905	+	1.06187i
$289$	15.8451	+	6.15894i	0.932065	+	0.362291i
$290$	−23.5060	−	13.5712i	−1.38032	−	0.796929i
$291$	−3.61404	+	2.82534i	−0.211859	+	0.165624i
$292$	−22.6589	+	19.8713i	−1.32601	+	1.16288i
$293$	−32.1677	−	8.61931i	−1.87926	−	0.503545i	−0.999610	−	0.0279169i	$-0.991113\pi$
$293$	−32.1677	−	8.61931i	−1.87926	−	0.503545i	−0.879646	−	0.475628i	$-0.842221\pi$
$294$	−14.6636	+	22.3803i	−0.855199	+	1.30525i
$295$	4.64952	+	4.07752i	0.270705	+	0.237402i
$296$	−9.90633	−	14.8259i	−0.575794	−	0.861736i
$297$	1.38678	−	13.3095i	0.0804693	−	0.772294i
$298$	35.3222	−	14.6309i	2.04616	−	0.847547i
$299$	−0.261273	−	3.98626i	−0.0151098	−	0.230531i
$300$	−5.83226	−	1.10548i	−0.336726	−	0.0638248i
$301$	−0.336466	−	0.0220531i	−0.0193936	−	0.00127112i
$302$	9.16783	−	34.2148i	0.527550	−	1.96884i
$303$	3.43928	+	1.13296i	0.197581	+	0.0650869i
$304$	−5.02114	−	6.54367i	−0.287982	−	0.375305i
$305$	21.2281			1.21552
$306$	21.1346	+	17.4754i	1.20818	+	0.999005i
$307$	30.4740			1.73925			0.869623	−	0.493717i	$-0.164362\pi$
$307$	30.4740			1.73925			0.869623	+	0.493717i	$0.164362\pi$
$308$	−0.822404	−	1.07178i	−0.0468608	−	0.0610702i
$309$	−3.88668	+	3.47109i	−0.221105	+	0.197463i
$310$	5.70536	−	21.2927i	0.324042	−	1.20934i
$311$	−24.7700	−	1.62351i	−1.40458	−	0.0920608i	−0.655826	−	0.754912i	$-0.727679\pi$
$311$	−24.7700	−	1.62351i	−1.40458	−	0.0920608i	−0.748751	+	0.662851i	$0.769346\pi$
$312$	−1.31253	−	3.75488i	−0.0743072	−	0.212578i
$313$	0.612141	+	9.33946i	0.0346002	+	0.527898i	0.979617	+	0.200875i	$0.0643786\pi$
$313$	0.612141	+	9.33946i	0.0346002	+	0.527898i	−0.945017	+	0.327022i	$0.893955\pi$
$314$	23.9037	−	9.90122i	1.34896	−	0.558758i
$315$	−0.421517	−	0.967835i	−0.0237498	−	0.0545313i
$316$	10.3892	+	15.5485i	0.584436	+	0.874670i
$317$	−15.5685	−	13.6532i	−0.874415	−	0.766842i	0.0991926	−	0.995068i	$-0.468374\pi$
$317$	−15.5685	−	13.6532i	−0.874415	−	0.766842i	−0.973608	+	0.228226i	$0.926707\pi$
$318$	−20.1046	−	39.8570i	−1.12741	−	2.23507i
$319$	15.5722	+	4.17255i	0.871875	+	0.233618i
$320$	18.9381	−	16.6083i	1.05867	−	0.928430i
$321$	−14.2391	−	5.74801i	−0.794749	−	0.320823i
$322$	1.21972	+	0.704208i	0.0679726	+	0.0392440i
$323$	−21.3979	−	13.9600i	−1.19061	−	0.776754i
$324$	13.9312	+	22.2352i	0.773956	+	1.23529i
$325$	−1.22888	−	0.509018i	−0.0681659	−	0.0282352i
$326$	−8.44266	+	24.8713i	−0.467596	+	1.37749i
$327$	−10.8419	−	10.6479i	−0.599560	−	0.588832i
$328$	0.957457	−	14.6080i	0.0528667	−	0.806590i
$329$	−0.0491523	−	0.144798i	−0.00270985	−	0.00798297i
$330$	−19.2861	+	1.43902i	−1.06167	+	0.0792154i
$331$	8.27842	+	1.08987i	0.455023	+	0.0599049i	0.354555	−	0.935035i	$-0.384633\pi$
$331$	8.27842	+	1.08987i	0.455023	+	0.0599049i	0.100468	+	0.994940i	$0.467966\pi$
$332$	10.4193	+	25.1544i	0.571833	+	1.38053i
$333$	15.0360	+	21.6465i	0.823965	+	1.18622i
$334$	9.52621	+	1.89488i	0.521251	+	0.103683i
$335$	−18.4521	+	9.09959i	−1.00815	+	0.497164i
$336$	−0.401654	−	0.103746i	−0.0219120	−	0.00565983i
$337$	18.5479	+	21.1499i	1.01037	+	1.15211i	0.988327	+	0.152350i	$0.0486842\pi$
$337$	18.5479	+	21.1499i	1.01037	+	1.15211i	0.0220446	+	0.999757i	$0.492982\pi$
$338$	3.39153	+	25.7612i	0.184475	+	1.40122i
$339$	−6.88606	−	11.6822i	−0.373999	−	0.634490i
$340$	11.5296	−	20.4864i	0.625278	−	1.11103i
$341$			13.0931i			0.709033i
$342$	−25.6760	−	32.2395i	−1.38840	−	1.74331i
$343$	−0.490307	−	2.46494i	−0.0264741	−	0.133094i
$344$	−0.984396	−	3.67382i	−0.0530751	−	0.198079i
$345$	10.6773	−	5.38581i	0.574846	−	0.289962i
$346$	−22.3480	+	7.58612i	−1.20144	+	0.407833i
$347$	9.05383	−	18.3593i	0.486035	−	0.985581i	−0.506341	−	0.862333i	$-0.669002\pi$
$347$	9.05383	−	18.3593i	0.486035	−	0.985581i	0.992376	−	0.123248i	$-0.0393310\pi$
$348$	−29.0950	+	12.3604i	−1.55965	+	0.662585i
$349$	0.495926	−	3.76693i	0.0265463	−	0.201639i	−0.973032	−	0.230669i	$-0.925909\pi$
$349$	0.495926	−	3.76693i	0.0265463	−	0.201639i	0.999579	+	0.0290300i	$0.00924185\pi$
$350$	0.389919	−	0.260536i	0.0208420	−	0.0139262i
$351$	2.03995	+	5.51424i	0.108884	+	0.294328i
$352$	−10.0300	+	15.0110i	−0.534601	+	0.800087i
$353$	2.62096	−	0.702285i	0.139500	−	0.0373789i	−0.188393	−	0.982094i	$-0.560328\pi$
$353$	2.62096	−	0.702285i	0.139500	−	0.0373789i	0.327893	+	0.944715i	$0.393661\pi$
$354$	11.8882	−	2.47646i	0.631849	−	0.131622i
$355$	−24.9800	+	3.28868i	−1.32580	+	0.174545i
$356$	−21.1811	−	36.6867i	−1.12260	−	1.94439i
$357$	−1.28029	+	0.109685i	−0.0677600	+	0.00580514i
$358$	7.60279	−	13.1684i	0.401820	−	0.695973i
$359$	9.40229	−	22.6991i	0.496234	−	1.19802i	−0.455263	−	0.890357i	$-0.650455\pi$
$359$	9.40229	−	22.6991i	0.496234	−	1.19802i	0.951497	−	0.307658i	$-0.0995453\pi$
$360$	8.80930	−	8.01144i	0.464291	−	0.422240i
$361$	13.7158	+	13.7158i	0.721883	+	0.721883i
$362$	−3.12658	−	6.34007i	−0.164329	−	0.333227i
$363$	−7.14178	+	2.49642i	−0.374846	+	0.131028i
$364$	0.532356	+	0.262529i	0.0279030	+	0.0137603i
$365$	−16.0384	−	12.3067i	−0.839489	−	0.644162i
$366$	25.0760	−	33.2978i	1.31075	−	1.74050i
$367$	3.46805	−	0.227308i	0.181031	−	0.0118654i	0.0253819	−	0.999678i	$-0.491920\pi$
$367$	3.46805	−	0.227308i	0.181031	−	0.0118654i	0.155649	+	0.987812i	$0.450253\pi$
$368$	0.916814	−	4.60914i	0.0477922	−	0.240268i
$369$	−1.02523	+	21.6144i	−0.0533711	+	1.12520i
$370$	26.9348	−	26.9348i	1.40027	−	1.40027i
$371$	1.98069	+	0.672353i	0.102832	+	0.0349068i
$372$	−15.8122	−	20.2263i	−0.819827	−	1.04868i
$373$	26.9296	−	15.5478i	1.39436	−	0.805035i	0.400567	−	0.916267i	$-0.368813\pi$
$373$	26.9296	−	15.5478i	1.39436	−	0.805035i	0.993794	+	0.111232i	$0.0354797\pi$
$374$	−5.84272	+	22.8047i	−0.302120	+	1.17920i
$375$	−0.188812	−	20.9172i	−0.00975019	−	1.08016i
$376$	1.36840	−	1.05001i	0.0705697	−	0.0541501i
$377$	−6.94725	+	1.38189i	−0.357802	+	0.0711711i
$378$	−2.01604	−	0.482091i	−0.103694	−	0.0247961i
$379$	−21.4947	−	14.3623i	−1.10411	−	0.737740i	−0.136610	−	0.990625i	$-0.543621\pi$
$379$	−21.4947	−	14.3623i	−1.10411	−	0.737740i	−0.967496	+	0.252885i	$0.918621\pi$
$380$	−23.2944	+	26.5622i	−1.19498	+	1.36261i
$381$	1.84877	−	1.25960i	0.0947155	−	0.0645311i
$382$	2.33369	−	3.04133i	0.119402	−	0.155608i
$383$	−1.28123	+	1.66973i	−0.0654677	+	0.0853192i	−0.824939	−	0.565221i	$-0.808791\pi$
$383$	−1.28123	+	1.66973i	−0.0654677	+	0.0853192i	0.759472	+	0.650540i	$0.225458\pi$
$384$	−1.87336	−	25.1072i	−0.0955994	−	1.28125i
$385$	0.597492	−	0.681309i	0.0304510	−	0.0347227i
$386$	1.96438	+	1.31256i	0.0999843	+	0.0668074i
$387$	1.55285	+	5.40319i	0.0789356	+	0.274659i
$388$	7.57321	−	1.50640i	0.384471	−	0.0764761i
$389$	−0.831473	+	0.638012i	−0.0421573	+	0.0323485i	−0.629625	−	0.776899i	$-0.716792\pi$
$389$	−0.831473	+	0.638012i	−0.0421573	+	0.0323485i	0.587468	+	0.809248i	$0.300125\pi$
$390$	7.32028	−	4.31493i	0.370677	−	0.218495i
$391$	−2.05849	−	14.4105i	−0.104102	−	0.728768i
$392$	12.2469	−	7.07076i	0.618563	−	0.357128i
$393$	−25.0644	+	3.53024i	−1.26433	+	0.178077i
$394$	−18.7991	−	6.38144i	−0.947086	−	0.321492i
$395$	−8.86967	+	8.86967i	−0.446282	+	0.446282i
$396$	−12.1737	+	18.9510i	−0.611749	+	0.952325i
$397$	−2.28690	+	11.4970i	−0.114776	+	0.577020i	0.880003	+	0.474969i	$0.157541\pi$
$397$	−2.28690	+	11.4970i	−0.114776	+	0.577020i	−0.994779	+	0.102051i	$0.967459\pi$
$398$	38.9609	−	2.55363i	1.95293	−	0.128002i
$399$	1.91684	+	0.234775i	0.0959621	+	0.0117535i
$400$	−1.24139	−	0.952554i	−0.0620696	−	0.0476277i
$401$	−7.60544	−	3.75059i	−0.379798	−	0.187295i	0.242362	−	0.970186i	$-0.422078\pi$
$401$	−7.60544	−	3.75059i	−0.379798	−	0.187295i	−0.622160	+	0.782890i	$0.713745\pi$
$402$	−7.52352	+	39.6925i	−0.375239	+	1.97968i
$403$	−2.54438	−	5.15950i	−0.126745	−	0.257013i
$404$	−4.30989	−	4.30989i	−0.214425	−	0.214425i
$405$	−12.8053	+	12.0750i	−0.636301	+	0.600012i
$406$	0.955682	−	2.30722i	0.0474297	−	0.114505i
$407$	−11.3124	+	19.5937i	−0.560736	+	0.971224i
$408$	−5.81360	−	13.2773i	−0.287816	−	0.657324i
$409$	−17.0137	−	29.4686i	−0.841274	−	1.45713i	−0.888818	−	0.458261i	$-0.848473\pi$
$409$	−17.0137	−	29.4686i	−0.841274	−	1.45713i	0.0475435	−	0.998869i	$-0.484861\pi$
$410$	31.0059	−	4.08200i	1.53127	−	0.201596i
$411$	−9.41302	+	28.5747i	−0.464310	+	1.40948i
$412$	8.47247	−	2.27019i	0.417408	−	0.111844i
$413$	−0.316116	+	0.473101i	−0.0155550	+	0.0232798i
$414$	4.16468	−	23.1101i	0.204683	−	1.13580i
$415$	−15.1854	+	10.1466i	−0.745422	+	0.498075i
$416$	1.03536	−	7.86437i	0.0507629	−	0.385583i
$417$	28.6923	+	21.6077i	1.40507	+	1.05813i
$418$	15.6480	−	31.7311i	0.765370	−	1.55202i
$419$	10.6162	−	3.60372i	0.518637	−	0.176053i	−0.0498332	−	0.998758i	$-0.515869\pi$
$419$	10.6162	−	3.60372i	0.518637	−	0.176053i	0.568470	+	0.822704i	$0.307536\pi$
$420$	−0.100205	+	1.77406i	−0.00488950	+	0.0865653i
$421$	8.76493	+	32.7112i	0.427176	+	1.59424i	0.759124	+	0.650946i	$0.225628\pi$
$421$	8.76493	+	32.7112i	0.427176	+	1.59424i	−0.331948	+	0.943298i	$0.607706\pi$
$422$	4.65133	+	23.3838i	0.226423	+	1.13831i
$423$	−1.99431	+	1.58830i	−0.0969667	+	0.0772257i
$424$			23.5939i			1.14582i
$425$	−4.60648	−	1.50745i	−0.223447	−	0.0731222i
$426$	−24.3495	+	43.0677i	−1.17974	+	2.08664i
$427$	0.254938	+	1.93645i	0.0123373	+	0.0937112i
$428$	17.0420	+	19.4327i	0.823757	+	0.939315i
$429$	−3.53647	+	3.60090i	−0.170743	+	0.173853i
$430$	7.28717	−	3.59364i	0.351419	−	0.173301i
$431$	−7.57077	−	1.50592i	−0.364671	−	0.0725376i	0.00935382	−	0.999956i	$-0.497023\pi$
$431$	−7.57077	−	1.50592i	−0.364671	−	0.0725376i	−0.374025	+	0.927419i	$0.622023\pi$
$432$	0.639066	+	6.88694i	0.0307471	+	0.331348i
$433$	−9.03116	−	21.8032i	−0.434010	−	1.04779i	−0.977982	−	0.208689i	$-0.933080\pi$
$433$	−9.03116	−	21.8032i	−0.434010	−	1.04779i	0.543972	−	0.839103i	$-0.316920\pi$
$434$	2.01085	+	0.264734i	0.0965240	+	0.0127076i
$435$	−11.9392	−	17.5238i	−0.572443	−	0.840204i
$436$	8.22203	+	24.2213i	0.393764	+	1.15999i
$437$	−1.43083	+	21.8302i	−0.0684457	+	1.04428i
$438$	−38.2495	+	10.6199i	−1.82763	+	0.507437i
$439$	−0.107673	+	0.317195i	−0.00513896	+	0.0151389i	−0.949469	−	0.313860i	$-0.898378\pi$
$439$	−0.107673	+	0.317195i	−0.00513896	+	0.0151389i	0.944330	+	0.328999i	$0.106711\pi$
$440$	9.44356	+	3.91165i	0.450204	+	0.186481i
$441$	−17.9108	+	10.7765i	−0.852895	+	0.513167i
$442$	−2.12923	−	10.1219i	−0.101277	−	0.481447i
$443$	−0.140494	−	0.0811141i	−0.00667506	−	0.00385385i	0.496659	−	0.867946i	$-0.334560\pi$
$443$	−0.140494	−	0.0811141i	−0.00667506	−	0.00385385i	−0.503334	+	0.864092i	$0.667893\pi$
$444$	−6.18739	−	43.9300i	−0.293641	−	2.08483i
$445$	21.3641	−	18.7358i	1.01276	−	0.888162i
$446$	34.6635	+	9.28804i	1.64136	+	0.439802i
$447$	29.8208	+	1.68438i	1.41048	+	0.0796686i
$448$	1.74245	+	1.52809i	0.0823232	+	0.0721955i
$449$	−7.85643	−	11.7580i	−0.370768	−	0.554893i	0.598431	−	0.801175i	$-0.295791\pi$
$449$	−7.85643	−	11.7580i	−0.370768	−	0.554893i	−0.969198	+	0.246282i	$0.920791\pi$
$450$	−6.28797	−	4.64702i	−0.296418	−	0.219063i
$451$	−17.1612	+	7.10841i	−0.808090	+	0.334722i
$452$	1.49287	+	22.7768i	0.0702189	+	1.07133i
$453$	18.0573	−	20.9692i	0.848405	−	0.985219i
$454$	−14.3637	−	0.941447i	−0.674122	−	0.0441843i
$455$	−0.103050	+	0.384588i	−0.00483106	+	0.0180298i
$456$	4.44236	+	21.3254i	0.208032	+	0.998653i
$457$	10.6853	+	13.9253i	0.499835	+	0.651398i	0.973333	−	0.229397i	$-0.0736754\pi$
$457$	10.6853	+	13.9253i	0.499835	+	0.651398i	−0.473498	+	0.880795i	$0.657009\pi$
$458$	26.1171			1.22037
$459$	8.94606	+	19.4671i	0.417567	+	0.908646i
$460$	−20.1293			−0.938534
$461$	10.7959	+	14.0695i	0.502816	+	0.655283i	0.973946	−	0.226781i	$-0.0728203\pi$
$461$	10.7959	+	14.0695i	0.502816	+	0.655283i	−0.471130	+	0.882064i	$0.656154\pi$
$462$	−0.362884	−	1.74201i	−0.0168829	−	0.0810458i
$463$	−4.86211	+	18.1457i	−0.225962	+	0.843300i	0.756056	+	0.654508i	$0.227124\pi$
$463$	−4.86211	+	18.1457i	−0.225962	+	0.843300i	−0.982017	+	0.188792i	$0.939543\pi$
$464$	−8.31490	−	0.544988i	−0.386010	−	0.0253004i
$465$	11.2375	−	13.0496i	0.521125	−	0.605162i
$466$	1.05412	+	16.0828i	0.0488313	+	0.745022i
$467$	−24.8403	+	10.2892i	−1.14947	+	0.476127i	−0.874357	−	0.485284i	$-0.838716\pi$
$467$	−24.8403	+	10.2892i	−1.14947	+	0.476127i	−0.275116	+	0.961411i	$0.588716\pi$
$468$	1.11442	−	9.83357i	0.0515142	−	0.454557i
$469$	−1.05167	−	1.57394i	−0.0485617	−	0.0726777i
$470$	2.77029	+	2.42948i	0.127784	+	0.112064i
$471$	20.1807	+	1.13988i	0.929878	+	0.0525227i
$472$	−6.19944	−	1.66114i	−0.285352	−	0.0764600i
$473$	−3.62836	+	3.18199i	−0.166832	+	0.146308i
$474$	3.43526	+	24.3901i	0.157787	+	1.12027i
$475$	6.30835	+	3.64213i	0.289447	+	0.167112i
$476$	2.00724	+	0.805706i	0.0920019	+	0.0369295i
$477$	−0.629549	−	34.8689i	−0.0288251	−	1.59654i
$478$	−25.4339	−	10.5351i	−1.16332	−	0.481863i
$479$	−3.82788	+	11.2766i	−0.174900	+	0.515239i	−0.998663	−	0.0516953i	$-0.983538\pi$
$479$	−3.82788	+	11.2766i	−0.174900	+	0.515239i	0.823763	+	0.566935i	$0.191871\pi$
$480$	22.8802	−	6.35261i	1.04433	−	0.289956i
$481$	0.650156	−	9.91947i	0.0296446	−	0.452289i
$482$	1.23103	+	3.62649i	0.0560717	+	0.165182i
$483$	0.619526	+	0.909309i	0.0281894	+	0.0413750i
$484$	12.6256	+	1.66219i	0.573890	+	0.0755541i
$485$	1.98210	+	4.78522i	0.0900027	+	0.217286i
$486$	3.81402	+	34.3498i	0.173007	+	1.55814i
$487$	−15.6673	−	3.11643i	−0.709955	−	0.141219i	−0.173113	−	0.984902i	$-0.555383\pi$
$487$	−15.6673	−	3.11643i	−0.709955	−	0.141219i	−0.536842	+	0.843683i	$0.680383\pi$
$488$	−19.7592	+	9.74416i	−0.894457	+	0.441097i
$489$	−14.3777	+	14.6396i	−0.650181	+	0.662026i
$490$	19.9189	+	22.7131i	0.899842	+	1.02607i
$491$	−1.32514	−	10.0654i	−0.0598026	−	0.454245i	−0.994981	−	0.100068i	$-0.968094\pi$
$491$	−1.32514	−	10.0654i	−0.0598026	−	0.454245i	0.935178	−	0.354178i	$-0.115239\pi$
$492$	17.9260	−	31.7062i	0.808165	−	1.42943i
$493$	−24.8567	+	6.95393i	−1.11949	+	0.313189i
$494$			15.5449i			0.699396i
$495$	−14.0608	−	5.52897i	−0.631986	−	0.248509i
$496$	−1.32027	−	6.63743i	−0.0592818	−	0.298029i
$497$	−0.599992	−	2.23920i	−0.0269133	−	0.100442i
$498$	−2.02239	+	35.8051i	−0.0906256	+	1.60446i
$499$	−11.6617	+	3.95862i	−0.522050	+	0.177212i	−0.570011	−	0.821637i	$-0.693061\pi$
$499$	−11.6617	+	3.95862i	−0.522050	+	0.177212i	0.0479610	+	0.998849i	$0.484728\pi$
$500$	−15.5729	+	31.5788i	−0.696442	+	1.41225i
$501$	6.06139	+	4.56474i	0.270803	+	0.203937i
$502$	−4.08487	+	31.0277i	−0.182317	+	1.38483i
$503$	−16.6358	+	11.1157i	−0.741753	+	0.495623i	−0.868116	−	0.496361i	$-0.834669\pi$
$503$	−16.6358	+	11.1157i	−0.741753	+	0.495623i	0.126364	+	0.991984i	$0.459669\pi$
$504$	0.836605	+	0.707377i	0.0372653	+	0.0315091i
$505$	2.27144	−	3.39945i	0.101078	−	0.151274i
$506$	19.4710	−	5.21724i	0.865591	−	0.231934i
$507$	−6.35117	+	19.2799i	−0.282065	+	0.856253i
$508$	−3.73331	+	0.491500i	−0.165639	+	0.0218068i
$509$	10.4673	+	18.1299i	0.463956	+	0.803596i	0.999154	−	0.0411314i	$-0.0130962\pi$
$509$	10.4673	+	18.1299i	0.463956	+	0.803596i	−0.535198	+	0.844727i	$0.679763\pi$
$510$	25.3959	−	17.7142i	1.12455	−	0.784400i
$511$	0.930014	−	1.61083i	0.0411414	−	0.0712590i
$512$	5.63865	−	13.6129i	0.249196	−	0.601611i
$513$	−7.13428	−	31.3978i	−0.314986	−	1.38625i
$514$	−34.1169	−	34.1169i	−1.50483	−	1.50483i
$515$	2.60227	+	5.27689i	0.114670	+	0.232527i
$516$	1.76228	−	9.29741i	0.0775801	−	0.409296i
$517$	−1.96286	−	0.967974i	−0.0863263	−	0.0425714i
$518$	2.78048	+	2.13354i	0.122167	+	0.0937424i
$519$	−18.3007	−	2.24147i	−0.803310	−	0.0983897i
$520$	−4.48149	+	0.293733i	−0.196526	+	0.0128810i
$521$	−3.88666	+	19.5396i	−0.170278	+	0.856044i	0.797322	+	0.603554i	$0.206249\pi$
$521$	−3.88666	+	19.5396i	−0.170278	+	0.856044i	−0.967600	+	0.252490i	$0.918751\pi$
$522$	−41.5907	−	1.97276i	−1.82038	−	0.0863452i
$523$	14.6139	−	14.6139i	0.639022	−	0.639022i	−0.311292	−	0.950314i	$-0.600762\pi$
$523$	14.6139	−	14.6139i	0.639022	−	0.639022i	0.950314	+	0.311292i	$0.100762\pi$
$524$	40.3446	+	13.6951i	1.76246	+	0.598275i
$525$	0.362779	−	0.0510961i	0.0158330	−	0.00223002i
$526$	−2.43090	+	1.40348i	−0.105992	+	0.0611946i
$527$	−10.6801	−	18.0379i	−0.465233	−	0.785742i
$528$	−5.11486	+	3.01495i	−0.222596	+	0.131209i
$529$	8.35828	−	6.41353i	0.363403	−	0.278849i
$530$	−49.4343	+	9.83309i	−2.14729	+	0.427122i
$531$	9.20635	+	2.28954i	0.399521	+	0.0993575i
$532$	−2.70277	−	1.80594i	−0.117180	−	0.0782972i
$533$	5.38120	−	6.13609i	0.233086	−	0.265783i
$534$	−4.15176	−	55.6430i	−0.179664	−	2.40791i
$535$	−10.5545	+	13.7548i	−0.456309	+	0.594674i
$536$	12.9984	−	16.9398i	0.561445	−	0.731689i
$537$	9.81711	−	6.68854i	0.423640	−	0.288632i
$538$	9.90362	−	11.2929i	0.426975	−	0.486872i
$539$	−14.9195	−	9.96890i	−0.642629	−	0.429391i
$540$	28.3983	−	8.43975i	1.22207	−	0.363189i
$541$	33.0365	−	6.57136i	1.42035	−	0.282525i	0.575619	−	0.817718i	$-0.304761\pi$
$541$	33.0365	−	6.57136i	1.42035	−	0.282525i	0.844730	+	0.535193i	$0.179761\pi$
$542$	4.14679	−	3.18194i	0.178120	−	0.136676i
$543$	−0.0498483	−	5.52236i	−0.00213920	−	0.236987i
$544$	1.57343	−	28.8615i	0.0674601	−	1.23743i
$545$	−14.8591	+	8.57889i	−0.636492	+	0.367479i
$546$	0.481523	+	0.615941i	0.0206073	+	0.0263599i
$547$	28.8511	+	9.79364i	1.23359	+	0.418746i	0.860691	−	0.509128i	$-0.170032\pi$
$547$	28.8511	+	9.79364i	1.23359	+	0.418746i	0.372895	+	0.927874i	$0.378365\pi$
$548$	35.8081	−	35.8081i	1.52965	−	1.52965i
$549$	28.9417	−	14.9279i	1.23520	−	0.637108i
$550$	1.30941	−	6.58287i	0.0558336	−	0.280695i
$551$	38.7079	−	2.53705i	1.64901	−	0.108082i
$552$	−7.46624	+	9.91422i	−0.317784	+	0.421977i
$553$	−0.915618	−	0.702578i	−0.0389360	−	0.0298767i
$554$	−37.4143	−	18.4507i	−1.58958	−	0.783895i
$555$	28.0915	−	9.81945i	1.19242	−	0.416813i
$556$	−26.7404	−	54.2242i	−1.13405	−	2.29962i
$557$	−13.7661	−	13.7661i	−0.583287	−	0.583287i	0.352518	−	0.935805i	$-0.385325\pi$
$557$	−13.7661	−	13.7661i	−0.583287	−	0.583287i	−0.935805	+	0.352518i	$0.885325\pi$
$558$	−7.19482	−	33.0418i	−0.304581	−	1.39877i
$559$	0.811444	−	1.95900i	0.0343204	−	0.0828568i
$560$	−0.234192	+	0.405632i	−0.00989640	+	0.0171411i
$561$	−11.8470	+	14.0671i	−0.500180	+	0.593913i
$562$	−21.8208	−	37.7947i	−0.920455	−	1.59428i
$563$	10.1212	−	1.33248i	0.426556	−	0.0561572i	0.0858078	−	0.996312i	$-0.472653\pi$
$563$	10.1212	−	1.33248i	0.426556	−	0.0561572i	0.340748	+	0.940155i	$0.389320\pi$
$564$	4.20121	−	0.875168i	0.176903	−	0.0368512i
$565$	−14.7894	+	3.96280i	−0.622193	+	0.166716i
$566$	−18.7589	+	28.0747i	−0.788497	+	1.18007i
$567$	−1.25527	−	1.02310i	−0.0527166	−	0.0429660i
$568$	21.7419	−	14.5275i	0.912269	−	0.609559i
$569$	−3.07036	+	23.3217i	−0.128716	+	0.977698i	0.798190	+	0.602406i	$0.205791\pi$
$569$	−3.07036	+	23.3217i	−0.128716	+	0.977698i	−0.926906	+	0.375292i	$0.877542\pi$
$570$	−42.8299	+	18.1954i	−1.79395	+	0.762119i
$571$	−2.86002	+	5.79956i	−0.119688	+	0.242704i	−0.948469	−	0.316869i	$-0.897368\pi$
$571$	−2.86002	+	5.79956i	−0.119688	+	0.242704i	0.828781	+	0.559573i	$0.189035\pi$
$572$	8.04457	−	2.73076i	0.336360	−	0.114179i
$573$	2.67394	−	1.34878i	0.111705	−	0.0563462i
$574$	0.744727	+	2.77936i	0.0310843	+	0.116008i
$575$	0.809677	+	4.07052i	0.0337659	+	0.169752i
$576$	14.1404	−	35.9606i	0.589182	−	1.49836i
$577$		−	18.2911i		−	0.761468i	−0.924685	−	0.380734i	$-0.875671\pi$
$577$		−	18.2911i		−	0.761468i	0.924685	−	0.380734i	$-0.124329\pi$
$578$	−10.5526	−	36.1829i	−0.438929	−	1.50501i
$579$	0.937234	+	1.59002i	0.0389501	+	0.0660789i
$580$	4.65875	+	35.3867i	0.193444	+	1.46935i
$581$	−1.10794	−	1.26337i	−0.0459653	−	0.0524134i
$582$	9.84734	+	2.54355i	0.408185	+	0.105433i
$583$	26.8499	−	13.2409i	1.11201	−	0.548382i
$584$	20.5776	+	4.09314i	0.851508	+	0.169375i
$585$	6.61527	−	0.553680i	0.273508	−	0.0228918i
$586$	28.2551	+	68.2139i	1.16721	+	2.81789i
$587$	−24.5328	−	3.22980i	−1.01258	−	0.133308i	−0.394063	−	0.919083i	$-0.628931\pi$
$587$	−24.5328	−	3.22980i	−1.01258	−	0.133308i	−0.618512	+	0.785775i	$0.712264\pi$
$588$	35.0868	−	2.61798i	1.44696	−	0.107964i
$589$	10.1267	+	29.8323i	0.417264	+	1.22922i
$590$	0.896731	−	13.6815i	0.0369178	−	0.563257i
$591$	−11.0654	−	10.8675i	−0.455171	−	0.447028i
$592$	3.75896	−	11.0735i	0.154492	−	0.455119i
$593$	12.7576	+	5.28436i	0.523890	+	0.217003i	0.628925	−	0.777466i	$-0.283495\pi$
$593$	12.7576	+	5.28436i	0.523890	+	0.217003i	−0.105034	+	0.994469i	$0.533495\pi$
$594$	−25.2821	+	15.5242i	−1.03734	+	0.636965i
$595$	−0.267394	+	1.42599i	−0.0109621	+	0.0584598i
$596$	−43.5397	−	25.1377i	−1.78346	−	1.02968i
$597$	28.2851	+	11.4180i	1.15763	+	0.467310i
$598$	−6.65891	+	5.83970i	−0.272303	+	0.238803i
$599$	−8.76070	−	2.34742i	−0.357952	−	0.0959130i	0.0753612	−	0.997156i	$-0.475989\pi$
$599$	−8.76070	−	2.34742i	−0.357952	−	0.0959130i	−0.433313	+	0.901243i	$0.642656\pi$
$600$	1.86112	+	3.68964i	0.0759799	+	0.150629i
$601$	−4.92450	−	4.31867i	−0.200875	−	0.176162i	0.552999	−	0.833182i	$-0.313483\pi$
$601$	−4.92450	−	4.31867i	−0.200875	−	0.176162i	−0.753873	+	0.657020i	$0.771817\pi$
$602$	0.415329	+	0.621584i	0.0169275	+	0.0253339i
$603$	−18.7580	+	25.3818i	−0.763887	+	1.03363i
$604$	−43.0337	+	17.8251i	−1.75102	+	0.725295i
$605$	0.558679	+	8.52379i	0.0227135	+	0.346542i
$606$	−2.64910	−	7.57856i	−0.107612	−	0.307858i
$607$	20.2426	+	1.32677i	0.821623	+	0.0538520i	0.470415	−	0.882446i	$-0.344104\pi$
$607$	20.2426	+	1.32677i	0.821623	+	0.0538520i	0.351208	+	0.936298i	$0.385771\pi$
$608$	−11.2430	+	41.9596i	−0.455965	+	1.70169i
$609$	1.45515	−	1.29956i	0.0589658	−	0.0526608i
$610$	−28.6510	−	37.3388i	−1.16005	−	1.51180i
$611$	0.961592			0.0389019
$612$	1.31272	−	36.0381i	0.0530636	−	1.45675i
$613$	29.3144			1.18400			0.591998	−	0.805939i	$-0.298339\pi$
$613$	29.3144			1.18400			0.591998	+	0.805939i	$0.298339\pi$
$614$	−41.1300	−	53.6016i	−1.65987	−	2.16319i
$615$	23.2051	+	7.64419i	0.935721	+	0.308244i
$616$	−0.243412	+	0.908425i	−0.00980734	+	0.0366015i
$617$	16.5267	+	1.08322i	0.665339	+	0.0436086i	0.394331	−	0.918968i	$-0.370976\pi$
$617$	16.5267	+	1.08322i	0.665339	+	0.0436086i	0.271008	+	0.962577i	$0.412643\pi$
$618$	11.3511	+	2.15155i	0.456609	+	0.0865482i
$619$	−2.57733	−	39.3224i	−0.103592	−	1.58050i	−0.661079	−	0.750316i	$-0.729901\pi$
$619$	−2.57733	−	39.3224i	−0.103592	−	1.58050i	0.557487	−	0.830185i	$-0.311765\pi$
$620$	−26.7809	+	11.0930i	−1.07555	+	0.445506i
$621$	10.7697	−	14.8512i	0.432172	−	0.595959i
$622$	30.5757	+	45.7598i	1.22597	+	1.83480i
$623$	1.96566	+	1.72384i	0.0787527	+	0.0690643i
$624$	1.42968	−	2.18204i	0.0572329	−	0.0873517i
$625$	−17.1359	−	4.59156i	−0.685437	−	0.183662i
$626$	15.6012	−	13.6819i	0.623551	−	0.546840i
$627$	21.7753	−	17.0232i	0.869620	−	0.679842i
$628$	−29.4647	−	17.0115i	−1.17577	−	0.678832i
$629$	−0.397986	−	36.2210i	−0.0158687	−	1.44423i
$630$	−1.13344	+	2.04768i	−0.0451574	+	0.0815814i
$631$	−29.7616	−	12.3276i	−1.18479	−	0.490756i	−0.298735	−	0.954336i	$-0.596565\pi$
$631$	−29.7616	−	12.3276i	−1.18479	−	0.490756i	−0.886055	+	0.463580i	$0.846565\pi$
$632$	4.18454	−	12.3273i	0.166452	−	0.490352i
$633$	−4.65818	+	18.0342i	−0.185146	+	0.716793i
$634$	−3.00263	+	45.8113i	−0.119250	+	1.81940i
$635$	−0.811907	−	2.39180i	−0.0322195	−	0.0949157i
$636$	−25.4869	+	52.8804i	−1.01062	+	2.09684i
$637$	7.81646	+	1.02906i	0.309699	+	0.0407727i
$638$	−13.6781	−	33.0219i	−0.541522	−	1.30735i
$639$	−31.7442	+	22.0500i	−1.25578	+	0.872283i
$640$	−27.8807	−	5.54581i	−1.10208	−	0.219217i
$641$	35.0362	−	17.2779i	1.38384	−	0.682437i	0.410517	−	0.911853i	$-0.365348\pi$
$641$	35.0362	−	17.2779i	1.38384	−	0.682437i	0.973328	+	0.229416i	$0.0736817\pi$
$642$	9.10780	+	32.8035i	0.359456	+	1.29465i
$643$	14.8667	+	16.9522i	0.586283	+	0.668528i	0.966589	−	0.256333i	$-0.0825143\pi$
$643$	14.8667	+	16.9522i	0.586283	+	0.668528i	−0.380305	+	0.924861i	$0.624181\pi$
$644$	−0.241742	−	1.83621i	−0.00952596	−	0.0723568i
$645$	6.34731	−	0.0572949i	0.249925	−	0.00225598i
$646$	4.32549	+	56.4787i	0.170184	+	2.22212i
$647$			16.3636i			0.643321i	0.946855	+	0.321661i	$0.104241\pi$
$647$			16.3636i			0.643321i	−0.946855	+	0.321661i	$0.895759\pi$
$648$	6.37653	−	17.1173i	0.250494	−	0.672432i
$649$	1.58875	+	7.98720i	0.0623640	+	0.313525i
$650$	0.763257	+	2.84851i	0.0299374	+	0.111728i
$651$	1.32535	+	0.868371i	0.0519446	+	0.0340341i
$652$	32.7055	−	11.1020i	1.28085	−	0.434789i
$653$	−4.90517	+	9.94669i	−0.191954	+	0.389244i	−0.971479	−	0.237127i	$-0.923794\pi$
$653$	−4.90517	+	9.94669i	−0.191954	+	0.389244i	0.779525	+	0.626372i	$0.215461\pi$
$654$	−4.09591	+	33.4414i	−0.160163	+	1.30766i
$655$	−3.73032	+	28.3346i	−0.145756	+	1.10712i
$656$	7.98292	−	5.33401i	0.311681	−	0.208258i
$657$	−30.5204	−	5.50010i	−1.19072	−	0.214579i
$658$	−0.188350	+	0.281885i	−0.00734263	+	0.0109890i
$659$	33.5342	−	8.98545i	1.30631	−	0.350023i	0.462474	−	0.886633i	$-0.346962\pi$
$659$	33.5342	−	8.98545i	1.30631	−	0.350023i	0.843831	+	0.536609i	$0.180295\pi$
$660$	16.9401	+	18.9684i	0.659393	+	0.738342i
$661$	1.98237	−	0.260984i	0.0771052	−	0.0101511i	−0.0918749	−	0.995771i	$-0.529286\pi$
$661$	1.98237	−	0.260984i	0.0771052	−	0.0101511i	0.168980	+	0.985619i	$0.445953\pi$
$662$	−9.25614	−	16.0321i	−0.359750	−	0.623106i
$663$	1.93479	−	7.84552i	0.0751408	−	0.304695i
$664$	9.47711	−	16.4148i	0.367783	−	0.637019i
$665$	0.834418	−	2.01446i	0.0323574	−	0.0781176i
$666$	17.7810	−	55.6629i	0.689001	−	2.15689i
$667$	15.6281	+	15.6281i	0.605123	+	0.605123i
$668$	−5.64904	−	11.4551i	−0.218568	−	0.443212i
$669$	21.2442	+	18.2940i	0.821346	+	0.707289i
$670$	40.9099	+	20.1745i	1.58049	+	0.779409i
$671$	22.1777	+	17.0176i	0.856162	+	0.656956i
$672$	0.854268	+	2.01085i	0.0329541	+	0.0775703i
$673$	0.643710	−	0.0421910i	0.0248132	−	0.00162634i	−0.0529915	−	0.998595i	$-0.516876\pi$
$673$	0.643710	−	0.0421910i	0.0248132	−	0.00162634i	0.0778047	+	0.996969i	$0.475209\pi$
$674$	12.1675	−	61.1699i	0.468673	−	2.35618i
$675$	−2.84896	−	5.40319i	−0.109657	−	0.207969i
$676$	24.1605	−	24.1605i	0.929249	−	0.929249i
$677$	−17.7234	−	6.01630i	−0.681167	−	0.231225i	−0.0406553	−	0.999173i	$-0.512945\pi$
$677$	−17.7234	−	6.01630i	−0.681167	−	0.231225i	−0.640512	+	0.767948i	$0.721278\pi$
$678$	−11.2542	+	27.8792i	−0.432216	+	1.07069i
$679$	−0.412708	+	0.238277i	−0.0158383	+	0.00914423i
$680$	−16.2007	+	2.31422i	−0.621270	+	0.0887465i
$681$	−9.78920	−	5.53459i	−0.375123	−	0.212086i
$682$	23.0299	−	17.6714i	0.881860	−	0.676675i
$683$	11.2368	−	2.23513i	0.429962	−	0.0855248i	0.0246352	−	0.999697i	$-0.492158\pi$
$683$	11.2368	−	2.23513i	0.429962	−	0.0855248i	0.405327	+	0.914172i	$0.367158\pi$
$684$	−13.0799	+	52.5949i	−0.500122	+	2.01101i
$685$	28.2438	+	18.8719i	1.07914	+	0.721059i
$686$	−3.67390	+	4.18928i	−0.140270	+	0.159947i
$687$	18.3800	+	8.85869i	0.701242	+	0.337980i
$688$	1.51850	−	1.97895i	0.0578923	−	0.0754467i
$689$	−8.00740	+	10.4354i	−0.305058	+	0.397559i
$690$	−23.8841	−	11.5115i	−0.909252	−	0.438235i
$691$	−32.6252	+	37.2019i	−1.24112	+	1.41523i	−0.366503	+	0.930417i	$0.619445\pi$
$691$	−32.6252	+	37.2019i	−1.24112	+	1.41523i	−0.874619	+	0.484811i	$0.838888\pi$
$692$	25.8042	+	17.2418i	0.980928	+	0.655435i
$693$	0.335494	−	1.34904i	0.0127444	−	0.0512457i
$694$	−44.5125	+	8.85408i	−1.68967	+	0.336096i
$695$	32.1743	−	24.6882i	1.22044	−	0.936478i
$696$	19.1569	+	10.8309i	0.726140	+	0.410543i
$697$	17.8439	−	23.7914i	0.675888	−	0.901164i
$698$	−7.29509	+	4.21182i	−0.276123	+	0.159420i
$699$	−4.71330	+	11.6759i	−0.178273	+	0.441623i
$700$	−0.583941	−	0.198221i	−0.0220709	−	0.00749206i
$701$	34.6398	−	34.6398i	1.30833	−	1.30833i	0.385706	−	0.922622i	$-0.373958\pi$
$701$	34.6398	−	34.6398i	1.30833	−	1.30833i	0.922622	−	0.385706i	$-0.126042\pi$
$702$	6.94589	−	11.0305i	0.262156	−	0.416321i
$703$	−10.6205	+	53.3931i	−0.400561	+	2.01376i
$704$	33.0993	−	2.16944i	1.24748	−	0.0817639i
$705$	1.12555	+	2.64942i	0.0423906	+	0.0997829i
$706$	−4.77271	−	3.66223i	−0.179623	−	0.137830i
$707$	0.337379	+	0.166377i	0.0126885	+	0.00625725i
$708$	−12.1002	−	10.4199i	−0.454755	−	0.391605i
$709$	−13.1710	−	26.7082i	−0.494648	−	1.00305i	−0.990866	−	0.134850i	$-0.956945\pi$
$709$	−13.1710	−	26.7082i	−0.494648	−	1.00305i	0.496218	−	0.868198i	$-0.334722\pi$
$710$	39.4994	+	39.4994i	1.48239	+	1.48239i
$711$	−5.85532	+	18.3299i	−0.219592	+	0.687424i
$712$	−11.2856	+	27.2459i	−0.422946	+	1.02108i
$713$	−8.97490	+	15.5450i	−0.336113	+	0.582164i
$714$	1.92090	+	2.10389i	0.0718877	+	0.0787362i
$715$	2.84928	+	4.93510i	0.106557	+	0.184562i
$716$	−19.8242	+	2.60990i	−0.740864	+	0.0975365i
$717$	−14.3258	−	16.0411i	−0.535009	−	0.599065i
$718$	−52.6162	+	14.0985i	−1.96362	+	0.526150i
$719$	11.7055	−	17.5185i	0.436541	−	0.653330i	−0.546342	−	0.837562i	$-0.683980\pi$
$719$	11.7055	−	17.5185i	0.436541	−	0.653330i	0.982883	+	0.184233i	$0.0589800\pi$
$720$	7.68551	+	1.38501i	0.286422	+	0.0516162i
$721$	−0.450110	+	0.300754i	−0.0167630	+	0.0112007i
$722$	5.61325	−	42.6369i	0.208903	−	1.58678i
$723$	−0.363731	+	2.96971i	−0.0135273	+	0.110445i
$724$	−4.11142	+	8.33714i	−0.152800	+	0.309847i
$725$	6.96846	−	2.36547i	0.258802	−	0.0878514i
$726$	14.0301	+	9.19252i	0.520706	+	0.341167i
$727$	−10.3764	−	38.7252i	−0.384838	−	1.43624i	−0.838421	−	0.545022i	$-0.816521\pi$
$727$	−10.3764	−	38.7252i	−0.384838	−	1.43624i	0.453583	−	0.891214i	$-0.350146\pi$
$728$	−0.0806147	−	0.405278i	−0.00298778	−	0.0150206i
$729$	−8.96700	+	25.4675i	−0.332111	+	0.943240i
$730$			44.8204i			1.65888i
$731$	2.40309	−	7.34336i	0.0888813	−	0.271604i
$732$	−54.8118	+	0.494766i	−2.02590	+	0.0182871i
$733$	−2.91192	−	22.1183i	−0.107554	−	0.816957i	−0.957164	−	0.289545i	$-0.906496\pi$
$733$	−2.91192	−	22.1183i	−0.107554	−	0.816957i	0.849610	−	0.527412i	$-0.176837\pi$
$734$	−5.08055	−	5.79326i	−0.187527	−	0.213833i
$735$	6.31391	+	22.7408i	0.232892	+	0.838805i
$736$	−22.1978	+	10.9467i	−0.818220	+	0.403501i
$737$	−26.5722	−	5.28555i	−0.978801	−	0.194696i
$738$	39.4018	−	27.3690i	1.45040	−	1.00747i
$739$	−14.4782	−	34.9535i	−0.532590	−	1.28579i	−0.929803	−	0.368059i	$-0.880023\pi$
$739$	−14.4782	−	34.9535i	−0.532590	−	1.28579i	0.397213	−	0.917727i	$-0.369977\pi$
$740$	−49.6616	−	6.53807i	−1.82560	−	0.240344i
$741$	−5.27268	+	10.9398i	−0.193697	+	0.401883i
$742$	−1.49066	−	4.39134i	−0.0547238	−	0.161211i
$743$	0.696178	−	10.6216i	0.0255403	−	0.389669i	−0.965883	−	0.258979i	$-0.916614\pi$
$743$	0.696178	−	10.6216i	0.0255403	−	0.389669i	0.991423	−	0.130690i	$-0.0417194\pi$
$744$	−4.46980	+	17.3048i	−0.163871	+	0.634426i
$745$	10.8401	−	31.9341i	0.397152	−	1.16997i
$746$	−63.6936	−	26.3828i	−2.33199	−	0.965941i
$747$	−13.5680	+	24.5120i	−0.496428	+	0.896848i
$748$	28.4682	−	12.1601i	1.04090	−	0.444616i
$749$	−1.38148	−	0.797598i	−0.0504782	−	0.0291436i
$750$	−36.5369	+	28.5634i	−1.33414	+	1.04299i
$751$	−30.3621	+	26.6268i	−1.10793	+	0.971627i	−0.999747	−	0.0225045i	$-0.992836\pi$
$751$	−30.3621	+	26.6268i	−1.10793	+	0.971627i	−0.108181	+	0.994131i	$0.534503\pi$
$752$	1.09266	+	0.292777i	0.0398451	+	0.0106765i
$753$	−13.3991	+	20.4503i	−0.488289	+	0.745252i
$754$	11.8072	+	10.3546i	0.429991	+	0.377092i
$755$	−17.3585	−	25.9789i	−0.631742	−	0.945469i
$756$	1.11093	+	2.48916i	0.0404040	+	0.0905298i
$757$	−19.5481	+	8.09711i	−0.710489	+	0.294294i	−0.708507	−	0.705704i	$-0.750631\pi$
$757$	−19.5481	+	8.09711i	−0.710489	+	0.294294i	−0.00198230	+	0.999998i	$0.500631\pi$
$758$	3.74856	+	57.1919i	0.136154	+	2.07730i
$759$	15.4724	+	2.93273i	0.561614	+	0.106451i
$760$	24.5423	+	1.60859i	0.890242	+	0.0583495i
$761$	−1.82056	+	6.79443i	−0.0659953	+	0.246298i	−0.991041	−	0.133558i	$-0.957360\pi$
$761$	−1.82056	+	6.79443i	−0.0659953	+	0.246298i	0.925046	+	0.379856i	$0.124026\pi$
$762$	−4.71078	−	1.55182i	−0.170653	−	0.0562164i
$763$	−0.961021	−	1.25243i	−0.0347913	−	0.0453409i
$764$	−5.04104			−0.182378
$765$	23.8810	−	3.85242i	0.863419	−	0.139285i
$766$	4.66617			0.168596
$767$	−2.17822	−	2.83871i	−0.0786509	−	0.102500i
$768$	−8.35423	+	7.46094i	−0.301457	+	0.269223i
$769$	3.55676	−	13.2740i	0.128260	−	0.478673i	−0.871675	−	0.490085i	$-0.836966\pi$
$769$	3.55676	−	13.2740i	0.128260	−	0.478673i	0.999935	+	0.0114118i	$0.00363256\pi$
$770$	−2.00479	−	0.131401i	−0.0722477	−	0.00473536i
$771$	−12.4378	−	35.5820i	−0.447935	−	1.28146i
$772$	−0.203189	−	3.10007i	−0.00731294	−	0.111574i
$773$	0.300425	−	0.124440i	0.0108055	−	0.00447580i	−0.377274	−	0.926102i	$-0.623139\pi$
$773$	0.300425	−	0.124440i	0.0108055	−	0.00447580i	0.388080	+	0.921626i	$0.373139\pi$
$774$	7.40798	−	10.0239i	0.266274	−	0.360301i
$775$	3.32044	+	4.96939i	0.119274	+	0.178506i
$776$	−4.04146	−	3.54427i	−0.145080	−	0.127232i
$777$	1.23310	+	2.44461i	0.0442373	+	0.0876997i
$778$	2.24443	+	0.601394i	0.0804668	+	0.0215610i
$779$	−33.6034	+	29.4694i	−1.20397	+	1.05585i
$780$	−10.3616	−	4.18273i	−0.371004	−	0.149766i
$781$	−28.7338	−	16.5895i	−1.02818	−	0.593618i
$782$	−22.5687	+	23.0701i	−0.807054	+	0.824986i
$783$	−28.6005	−	15.4955i	−1.02210	−	0.553766i
$784$	8.56852	+	3.54920i	0.306019	+	0.126757i
$785$	7.33588	−	21.6108i	0.261829	−	0.771322i
$786$	40.0382	+	39.3219i	1.42812	+	1.40256i
$787$	−1.88469	+	28.7548i	−0.0671818	+	1.02500i	0.822603	+	0.568616i	$0.192521\pi$
$787$	−1.88469	+	28.7548i	−0.0671818	+	1.02500i	−0.889785	+	0.456380i	$0.849146\pi$
$788$	8.39154	+	24.7207i	0.298936	+	0.880638i
$789$	−2.18680	+	0.163167i	−0.0778522	+	0.00580889i
$790$	27.5723	+	3.62996i	0.980977	+	0.129148i
$791$	−0.539101	−	1.30150i	−0.0191682	−	0.0462762i
$792$	15.6257	−	1.30783i	0.555237	−	0.0464718i
$793$	−12.0464	−	2.39618i	−0.427780	−	0.0850908i
$794$	23.3090	−	11.4947i	0.827207	−	0.407933i
$795$	−38.1249	−	9.84758i	−1.35215	−	0.349258i
$796$	−33.8529	−	38.6018i	−1.19988	−	1.36821i
$797$	1.25938	+	9.56593i	0.0446095	+	0.338843i	0.999167	+	0.0408150i	$0.0129954\pi$
$797$	1.25938	+	9.56593i	0.0446095	+	0.338843i	−0.954557	+	0.298028i	$0.903671\pi$
$798$	−2.17416	−	3.68846i	−0.0769643	−	0.130570i
$799$	3.49372	−	0.267572i	0.123599	−	0.00946600i
$800$			8.24091i			0.291360i
$801$	15.9518	−	40.5673i	0.563628	−	1.43337i
$802$	3.66784	+	18.4395i	0.129516	+	0.651121i
$803$	−6.89016	−	25.7144i	−0.243148	−	0.907442i
$804$	47.4320	−	23.9255i	1.67280	−	0.843788i
$805$	1.17639	−	0.399332i	0.0414624	−	0.0140746i
$806$	−5.64110	+	11.4390i	−0.198699	+	0.402923i
$807$	10.8002	−	4.58822i	0.380184	−	0.161513i
$808$	−0.553843	+	4.20686i	−0.0194841	+	0.147997i
$809$	7.78611	−	5.20251i	0.273745	−	0.182911i	−0.411119	−	0.911582i	$-0.634862\pi$
$809$	7.78611	−	5.20251i	0.273745	−	0.182911i	0.684864	+	0.728671i	$0.259862\pi$
$810$	38.5220	+	6.22631i	1.35353	+	0.218770i
$811$	−15.7832	+	23.6213i	−0.554225	+	0.829456i	−0.997767	−	0.0667978i	$-0.978722\pi$
$811$	−15.7832	+	23.6213i	−0.554225	+	0.829456i	0.443542	+	0.896254i	$0.353722\pi$
$812$	−3.17205	+	0.849949i	−0.111317	+	0.0298274i
$813$	3.99761	−	0.832755i	0.140202	−	0.0292060i
$814$	49.7320	−	6.54734i	1.74310	−	0.229484i
$815$	11.5839	+	20.0639i	0.405766	+	0.702807i
$816$	4.58723	−	8.32578i	0.160585	−	0.291461i
$817$	−5.80605	+	10.0564i	−0.203128	+	0.351828i
$818$	−28.8702	+	69.6989i	−1.00942	+	2.43696i
$819$	0.129953	+	0.596800i	0.00454092	+	0.0208539i
$820$	−29.0793	−	29.0793i	−1.01549	−	1.01549i
$821$	−14.2531	−	28.9024i	−0.497436	−	1.00870i	−0.990346	−	0.138619i	$-0.955734\pi$
$821$	−14.2531	−	28.9024i	−0.497436	−	1.00870i	0.492910	−	0.870080i	$-0.335933\pi$
$822$	62.9653	−	22.0096i	2.19617	−	0.767674i
$823$	10.3016	+	5.08020i	0.359092	+	0.177085i	0.612882	−	0.790175i	$-0.290010\pi$
$823$	10.3016	+	5.08020i	0.359092	+	0.177085i	−0.253789	+	0.967260i	$0.581677\pi$
$824$	−4.84440	−	3.71724i	−0.168763	−	0.129496i
$825$	3.15436	−	4.18859i	0.109821	−	0.145828i
$826$	1.25880	−	0.0825063i	0.0437994	−	0.00287076i
$827$	−5.08115	+	25.5447i	−0.176689	+	0.888275i	0.786116	+	0.618079i	$0.212089\pi$
$827$	−5.08115	+	25.5447i	−0.176689	+	0.888275i	−0.962805	+	0.270196i	$0.912911\pi$
$828$	−27.4436	+	14.1552i	−0.953731	+	0.491927i
$829$	5.16068	−	5.16068i	0.179238	−	0.179238i	−0.611786	−	0.791023i	$-0.709549\pi$
$829$	5.16068	−	5.16068i	0.179238	−	0.179238i	0.791023	+	0.611786i	$0.209549\pi$
$830$	38.3424	+	13.0155i	1.33088	+	0.451774i
$831$	−20.0722	−	25.6754i	−0.696296	−	0.890668i
$832$	−12.6216	+	7.28706i	−0.437574	+	0.252634i
$833$	28.6857	+	1.56384i	0.993899	+	0.0541839i
$834$	−0.718800	−	79.6310i	−0.0248900	−	2.75739i
$835$	6.79699	−	5.21552i	0.235220	−	0.180490i
$836$	−45.6300	+	9.07637i	−1.57815	+	0.313913i
$837$	6.14409	−	25.6937i	0.212371	−	0.888105i
$838$	−20.6671	−	13.8093i	−0.713934	−	0.477035i
$839$	−3.04825	+	3.47586i	−0.105237	+	0.120000i	−0.802060	−	0.597243i	$-0.796263\pi$
$839$	−3.04825	+	3.47586i	−0.105237	+	0.120000i	0.696823	+	0.717243i	$0.254596\pi$
$840$	1.02228	−	0.696493i	0.0352719	−	0.0240313i
$841$	6.20267	−	8.08347i	0.213885	−	0.278740i
$842$	45.7068	−	59.5662i	1.57516	−	2.05279i
$843$	−2.53686	−	33.9997i	−0.0873741	−	1.17101i
$844$	20.6718	−	23.5716i	0.711551	−	0.811369i
$845$	19.0567	+	12.7333i	0.655571	+	0.438038i
$846$	5.48537	+	1.36416i	0.188591	+	0.0469009i
$847$	−0.770837	+	0.153329i	−0.0264863	+	0.00526845i
$848$	−12.2761	+	9.41978i	−0.421563	+	0.323477i
$849$	−22.7244	+	13.3949i	−0.779899	+	0.459711i
$850$	3.56574	+	10.1370i	0.122304	+	0.347698i
$851$	−26.8616	+	15.5086i	−0.920805	+	0.531627i
$852$	64.4226	−	9.07370i	2.20708	−	0.310860i
$853$	−23.6855	−	8.04013i	−0.810975	−	0.275289i	−0.115010	−	0.993364i	$-0.536690\pi$
$853$	−23.6855	−	8.04013i	−0.810975	−	0.275289i	−0.695965	+	0.718075i	$0.745023\pi$
$854$	3.06199	−	3.06199i	0.104779	−	0.104779i
$855$	−36.3134	−	1.72244i	−1.24189	−	0.0589062i
$856$	3.51035	−	17.6477i	0.119981	−	0.603187i
$857$	−6.28588	+	0.411999i	−0.214722	+	0.0140736i	−0.172384	−	0.985030i	$-0.555147\pi$
$857$	−6.28588	+	0.411999i	−0.214722	+	0.0140736i	−0.0423374	+	0.999103i	$0.513480\pi$
$858$	11.1068	+	1.36036i	0.379180	+	0.0464421i
$859$	29.0570	+	22.2962i	0.991412	+	0.760737i	0.971006	−	0.239054i	$-0.0768374\pi$
$859$	29.0570	+	22.2962i	0.991412	+	0.760737i	0.0204061	+	0.999792i	$0.493504\pi$
$860$	−9.58257	−	4.72560i	−0.326763	−	0.161142i
$861$	−0.418628	+	2.20859i	−0.0142668	+	0.0752686i
$862$	7.56925	+	15.3489i	0.257810	+	0.522787i
$863$	33.6934	+	33.6934i	1.14694	+	1.14694i	0.987152	+	0.159784i	$0.0510798\pi$
$863$	33.6934	+	33.6934i	1.14694	+	1.14694i	0.159784	+	0.987152i	$0.448920\pi$
$864$	26.7267	−	24.7506i	0.909262	−	0.842031i
$865$	−7.96644	+	19.2327i	−0.270867	+	0.653931i
$866$	−26.1610	+	45.3123i	−0.888989	+	1.53977i
$867$	4.84651	−	29.0433i	0.164596	−	0.986361i
$868$	−1.33354	−	2.30975i	−0.0452631	−	0.0783981i
$869$	−16.3768	+	2.15605i	−0.555545	+	0.0731389i
$870$	−14.7091	+	44.6517i	−0.498685	+	1.51383i
$871$	11.4982	−	3.08094i	0.389603	−	0.104394i
$872$	9.89296	−	14.8059i	0.335018	−	0.501390i
$873$	6.06736	+	5.13016i	0.205349	+	0.173630i
$874$	40.3289	−	26.9469i	1.36414	−	0.911492i
$875$	0.283640	−	2.15446i	0.00958879	−	0.0728341i
$876$	41.6986	+	31.4025i	1.40886	+	1.06099i
$877$	−4.84549	+	9.82567i	−0.163620	+	0.331789i	−0.963207	−	0.268762i	$-0.913386\pi$
$877$	−4.84549	+	9.82567i	−0.163620	+	0.331789i	0.799586	+	0.600551i	$0.205052\pi$
$878$	0.703247	−	0.238720i	0.0237334	−	0.00805641i
$879$	−3.25286	+	57.5897i	−0.109716	+	1.94245i
$880$	1.73505	+	6.47528i	0.0584884	+	0.218282i
$881$	2.51851	+	12.6614i	0.0848506	+	0.426573i	0.999739	+	0.0228649i	$0.00727877\pi$
$881$	2.51851	+	12.6614i	0.0848506	+	0.426573i	−0.914888	+	0.403708i	$0.867721\pi$
$882$	43.1288	+	16.9590i	1.45222	+	0.571040i
$883$		−	57.1259i		−	1.92244i	−0.275781	−	0.961220i	$-0.588937\pi$
$883$		−	57.1259i		−	1.92244i	0.275781	−	0.961220i	$-0.411063\pi$
$884$	−8.85517	+	10.3240i	−0.297832	+	0.347235i
$885$	5.27171	−	9.32424i	0.177207	−	0.313431i
$886$	0.0469467	+	0.356596i	0.00157721	+	0.0119801i
$887$	23.9561	+	27.3167i	0.804367	+	0.917205i	0.997958	−	0.0638772i	$-0.0203466\pi$
$887$	23.9561	+	27.3167i	0.804367	+	0.917205i	−0.193590	+	0.981082i	$0.562013\pi$
$888$	−21.6403	+	22.0346i	−0.726202	+	0.739432i
$889$	0.208431	−	0.102787i	0.00699056	−	0.00344736i
$890$	−61.7895	−	12.2907i	−2.07119	−	0.411985i
$891$	−23.0581	+	2.34975i	−0.772474	+	0.0787197i
$892$	−18.0589	−	43.5980i	−0.604656	−	1.45977i
$893$	−5.22097	−	0.687354i	−0.174713	−	0.0230014i
$894$	−37.2857	−	54.7261i	−1.24702	−	1.83031i
$895$	−4.31128	−	12.7006i	−0.144110	−	0.424535i
$896$	0.171062	−	2.60990i	0.00571477	−	0.0871905i
$897$	−6.66701	+	1.85108i	−0.222605	+	0.0618057i
$898$	−10.0778	+	29.6883i	−0.336301	+	0.990711i
$899$	29.4048	+	12.1798i	0.980703	+	0.406221i
$900$	0.185602	+	10.2800i	0.00618673	+	0.342665i
$901$	−26.1893	+	40.1429i	−0.872492	+	1.33736i
$902$	35.6652	+	20.5913i	1.18752	+	0.685616i
$903$	0.0814542	+	0.578319i	0.00271062	+	0.0192452i
$904$	11.9470	−	10.4772i	0.397350	−	0.348466i
$905$	−6.02297	−	1.61385i	−0.200210	−	0.0536462i
$906$	−61.2547	−	3.45987i	−2.03505	−	0.114947i
$907$	1.94677	+	1.70727i	0.0646414	+	0.0566890i	0.691057	−	0.722800i	$-0.257145\pi$
$907$	1.94677	+	1.70727i	0.0646414	+	0.0566890i	−0.626416	+	0.779489i	$0.715479\pi$
$908$	10.5162	+	15.7386i	0.348993	+	0.522305i
$909$	0.706263	−	6.23200i	0.0234252	−	0.206702i
$910$	0.815547	−	0.337810i	0.0270351	−	0.0111983i
$911$	2.98519	+	45.5452i	0.0989037	+	1.50898i	0.702497	+	0.711687i	$0.252068\pi$
$911$	2.98519	+	45.5452i	0.0989037	+	1.50898i	−0.603593	+	0.797292i	$0.706265\pi$
$912$	−9.32218	+	10.8255i	−0.308688	+	0.358468i
$913$	−23.9987	−	1.57296i	−0.794240	−	0.0520572i
$914$	10.0720	−	37.5892i	0.333152	−	1.24334i
$915$	−7.49833	−	35.9955i	−0.247887	−	1.18997i
$916$	−20.9072	−	27.2468i	−0.690792	−	0.900258i
$917$	−2.62950			−0.0868337
$918$	22.1670	−	42.0097i	0.731619	−	1.38653i
$919$	12.2132			0.402876			0.201438	−	0.979501i	$-0.435439\pi$
$919$	12.2132			0.402876			0.201438	+	0.979501i	$0.435439\pi$
$920$	8.53068	+	11.1174i	0.281248	+	0.366530i
$921$	−10.7642	−	51.6733i	−0.354693	−	1.70269i
$922$	10.1763	−	37.9785i	0.335139	−	1.25075i
$923$	14.5467	+	0.953443i	0.478811	+	0.0313829i
$924$	−1.52687	+	1.77309i	−0.0502302	+	0.0583304i
$925$	0.675457	+	10.3055i	0.0222089	+	0.338842i
$926$	38.4791	−	15.9386i	1.26450	−	0.523774i
$927$	7.25862	+	5.36437i	0.238405	+	0.176189i
$928$	24.3815	+	36.4894i	0.800361	+	1.19782i
$929$	41.2496	+	36.1750i	1.35336	+	1.18686i	0.964040	+	0.265758i	$0.0856221\pi$
$929$	41.2496	+	36.1750i	1.35336	+	1.18686i	0.389316	+	0.921104i	$0.372711\pi$
$930$	−38.1202	−	2.15316i	−1.25001	−	0.0706049i
$931$	−41.7040	−	11.1745i	−1.36679	−	0.366231i
$932$	15.9346	−	13.9743i	0.521955	−	0.457742i
$933$	5.99650	+	42.5747i	0.196317	+	1.39383i
$934$	51.6243	+	29.8053i	1.68920	+	0.975258i
$935$	11.7255	+	17.1377i	0.383463	+	0.560464i
$936$	−5.90335	+	3.55191i	−0.192957	+	0.116098i
$937$	−42.4638	−	17.5891i	−1.38723	−	0.574610i	−0.440826	−	0.897593i	$-0.645314\pi$
$937$	−42.4638	−	17.5891i	−1.38723	−	0.574610i	−0.946405	+	0.322983i	$0.895314\pi$
$938$	−1.34903	+	3.97411i	−0.0440474	+	0.129759i
$939$	15.6202	−	4.33692i	0.509747	−	0.141530i
$940$	0.316900	−	4.83496i	0.0103361	−	0.157699i
$941$	−15.2193	−	44.8347i	−0.496136	−	1.46157i	−0.850255	−	0.526370i	$-0.823553\pi$
$941$	−15.2193	−	44.8347i	−0.496136	−	1.46157i	0.354119	−	0.935200i	$-0.384781\pi$
$942$	−25.2324	−	37.0349i	−0.822116	−	1.20666i
$943$	−25.2474	−	3.32389i	−0.822170	−	0.108241i
$944$	−1.61080	−	3.88883i	−0.0524272	−	0.126571i
$945$	−1.49222	+	1.05661i	−0.0485419	+	0.0343715i
$946$	10.4940	+	2.08738i	0.341189	+	0.0678667i
$947$	−22.5952	+	11.1427i	−0.734245	+	0.362090i	−0.770660	−	0.637247i	$-0.780073\pi$
$947$	−22.5952	+	11.1427i	−0.734245	+	0.362090i	0.0364142	+	0.999337i	$0.488406\pi$
$948$	22.6951	−	23.1085i	0.737102	−	0.750530i
$949$	7.71222	+	8.79410i	0.250349	+	0.285469i
$950$	−2.10797	−	16.0116i	−0.0683916	−	0.519486i
$951$	−17.6519	+	31.2215i	−0.572402	+	1.01243i
$952$	−0.405667	−	1.45005i	−0.0131477	−	0.0469964i
$953$		−	8.03487i		−	0.260275i	−0.991496	−	0.130138i	$-0.958458\pi$
$953$		−	8.03487i		−	0.260275i	0.991496	−	0.130138i	$-0.0415419\pi$
$954$	−60.4822	+	48.1689i	−1.95818	+	1.55953i
$955$	−0.659685	−	3.31646i	−0.0213469	−	0.107318i
$956$	9.36952	+	34.9675i	0.303032	+	1.13093i
$957$	1.57469	−	27.8788i	0.0509025	−	0.901195i
$958$	25.0010	−	8.48671i	0.807747	−	0.274193i
$959$	−1.38232	+	2.80306i	−0.0446374	+	0.0905156i
$960$	−34.8512	−	26.2459i	−1.12482	−	0.847083i
$961$	0.672367	−	5.10714i	0.0216893	−	0.164746i
$962$	−18.3251	+	12.2445i	−0.590825	+	0.394777i
$963$	−4.71699	+	26.1749i	−0.152003	+	0.843474i
$964$	2.79789	−	4.18733i	0.0901138	−	0.134865i
$965$	2.01292	−	0.539361i	0.0647982	−	0.0173626i
$966$	0.763252	−	2.31697i	0.0245572	−	0.0745473i
$967$	29.2929	−	3.85648i	0.941996	−	0.124016i	0.356141	−	0.934432i	$-0.384092\pi$
$967$	29.2929	−	3.85648i	0.941996	−	0.124016i	0.585855	+	0.810416i	$0.300759\pi$
$968$	−4.43262	−	7.67752i	−0.142470	−	0.246765i
$969$	−16.1130	+	41.2143i	−0.517624	+	1.32399i
$970$	5.74167	−	9.94486i	0.184354	−	0.319310i
$971$	4.64743	−	11.2199i	0.149143	−	0.360064i	−0.831597	−	0.555379i	$-0.812573\pi$
$971$	4.64743	−	11.2199i	0.149143	−	0.360064i	0.980740	+	0.195316i	$0.0625731\pi$
$972$	32.7823	−	31.4765i	1.05149	−	1.00961i
$973$	2.63848	+	2.63848i	0.0845856	+	0.0845856i
$974$	15.6642	+	31.7639i	0.501914	+	1.01778i
$975$	−0.429045	+	2.26355i	−0.0137404	+	0.0724915i
$976$	−12.9588	−	6.39055i	−0.414800	−	0.204557i
$977$	−26.3002	−	20.1808i	−0.841417	−	0.645642i	0.0954087	−	0.995438i	$-0.469584\pi$
$977$	−26.3002	−	20.1808i	−0.841417	−	0.645642i	−0.936826	+	0.349796i	$0.886251\pi$
$978$	45.1552	+	5.53062i	1.44390	+	0.176850i
$979$	37.3393	−	2.44735i	1.19337	−	0.0782176i
$980$	7.75015	−	38.9626i	0.247569	−	1.24462i
$981$	−14.2255	+	22.1452i	−0.454186	+	0.707043i
$982$	−15.9158	+	15.9158i	−0.507894	+	0.507894i
$983$	−37.4498	−	12.7125i	−1.19446	−	0.405466i	−0.347787	−	0.937574i	$-0.613067\pi$
$983$	−37.4498	−	12.7125i	−1.19446	−	0.405466i	−0.846677	+	0.532108i	$0.821400\pi$
$984$	−25.1082	+	3.53641i	−0.800421	+	0.112736i
$985$	−15.1654	+	8.75575i	−0.483210	+	0.278981i
$986$	45.7799	+	34.3356i	1.45793	+	1.09347i
$987$	−0.228165	+	0.134491i	−0.00726257	+	0.00428091i
$988$	16.2172	−	12.4439i	0.515939	−	0.395894i
$989$	−6.48896	+	1.29074i	−0.206337	+	0.0410430i
$990$	9.25244	+	32.1942i	0.294062	+	1.02320i
$991$	−39.0754	−	26.1093i	−1.24127	−	0.829390i	−0.250924	−	0.968007i	$-0.580734\pi$
$991$	−39.0754	−	26.1093i	−1.24127	−	0.829390i	−0.990346	+	0.138616i	$0.955734\pi$
$992$	−23.5002	+	26.7969i	−0.746133	+	0.850802i
$993$	−1.07611	−	14.4223i	−0.0341492	−	0.457677i
$994$	−3.12880	+	4.07753i	−0.0992395	+	0.129331i
$995$	20.9658	−	27.3231i	0.664659	−	0.866201i
$996$	38.9727	−	26.5527i	1.23490	−	0.841354i
$997$	−15.7116	+	17.9157i	−0.497593	+	0.567396i	−0.945057	−	0.326906i	$-0.893994\pi$
$997$	−15.7116	+	17.9157i	−0.497593	+	0.567396i	0.447464	+	0.894302i	$0.352327\pi$
$998$	22.7024	+	15.1693i	0.718632	+	0.480175i
$999$	31.3938	−	33.1418i	0.993257	−	1.04856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.11.3	✓	256
3.2	odd	2		459.2.y.a.62.14		256
9.4	even	3		459.2.y.a.368.14		256
9.5	odd	6	inner	153.2.s.a.113.3	yes	256
17.14	odd	16	inner	153.2.s.a.65.3	yes	256
51.14	even	16		459.2.y.a.116.14		256
153.14	even	48	inner	153.2.s.a.14.3	yes	256
153.31	odd	48		459.2.y.a.422.14		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.3	✓	256	1.1	even	1	trivial
153.2.s.a.14.3	yes	256	153.14	even	48	inner
153.2.s.a.65.3	yes	256	17.14	odd	16	inner
153.2.s.a.113.3	yes	256	9.5	odd	6	inner
459.2.y.a.62.14		256	3.2	odd	2
459.2.y.a.116.14		256	51.14	even	16
459.2.y.a.368.14		256	9.4	even	3
459.2.y.a.422.14		256	153.31	odd	48

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34967 - 1.75893i) q^{2} +(-0.353226 - 1.69565i) q^{3} +(-0.754572 + 2.81610i) q^{4} +(-1.95144 - 0.127904i) q^{5} +(-2.50579 + 2.90987i) q^{6} +(-0.0117682 - 0.179547i) q^{7} +(1.87511 - 0.776696i) q^{8} +(-2.75046 + 1.19790i) q^{9} +O(q^{10})\)	\(q+(-1.34967 - 1.75893i) q^{2} +(-0.353226 - 1.69565i) q^{3} +(-0.754572 + 2.81610i) q^{4} +(-1.95144 - 0.127904i) q^{5} +(-2.50579 + 2.90987i) q^{6} +(-0.0117682 - 0.179547i) q^{7} +(1.87511 - 0.776696i) q^{8} +(-2.75046 + 1.19790i) q^{9} +(2.40883 + 3.60506i) q^{10} +(-1.93619 - 1.69800i) q^{11} +(5.04166 + 0.284770i) q^{12} +(1.09295 + 0.292855i) q^{13} +(-0.299928 + 0.263030i) q^{14} +(0.472418 + 3.35413i) q^{15} +(1.15275 + 0.665543i) q^{16} +(4.05247 + 0.759899i) q^{17} +(5.81924 + 3.22110i) q^{18} +(-5.72485 - 2.37131i) q^{19} +(1.83269 - 5.39893i) q^{20} +(-0.300293 + 0.0833756i) q^{21} +(-0.373425 + 5.69736i) q^{22} +(-1.13485 - 3.34316i) q^{23} +(-1.97934 - 2.90518i) q^{24} +(-1.16548 - 0.153438i) q^{25} +(-0.960014 - 2.31768i) q^{26} +(3.00275 + 4.24070i) q^{27} +(0.514504 + 0.102341i) q^{28} +(-5.61452 + 2.76878i) q^{29} +(5.26207 - 5.35793i) q^{30} +(-3.35223 - 3.82248i) q^{31} +(-0.915032 - 6.95036i) q^{32} +(-2.19529 + 3.88289i) q^{33} +(-4.13291 - 8.15362i) q^{34} +0.351881i q^{35} +(-1.29797 - 8.64948i) q^{36} +(-1.71395 - 8.61661i) q^{37} +(3.55571 + 13.2701i) q^{38} +(0.110521 - 1.95671i) q^{39} +(-3.75850 + 1.27584i) q^{40} +(3.19018 - 6.46904i) q^{41} +(0.551949 + 0.415664i) q^{42} +(0.244602 - 1.85793i) q^{43} +(6.24273 - 4.17126i) q^{44} +(5.52057 - 1.98582i) q^{45} +(-4.34870 + 6.50829i) q^{46} +(0.820877 - 0.219953i) q^{47} +(0.721345 - 2.18976i) q^{48} +(6.90802 - 0.909457i) q^{49} +(1.30313 + 2.25709i) q^{50} +(-0.142917 - 7.14000i) q^{51} +(-1.64942 + 2.85688i) q^{52} +(-4.44864 + 10.7400i) q^{53} +(3.40635 - 11.0052i) q^{54} +(3.56118 + 3.56118i) q^{55} +(-0.161521 - 0.327531i) q^{56} +(-1.99875 + 10.5450i) q^{57} +(12.4478 + 6.13860i) q^{58} +(-2.50879 - 1.92506i) q^{59} +(-9.80205 - 1.20056i) q^{60} +(-10.8317 + 0.709946i) q^{61} +(-2.19906 + 11.0554i) q^{62} +(0.247447 + 0.479742i) q^{63} +(-9.10774 + 9.10774i) q^{64} +(-2.09537 - 0.711281i) q^{65} +(9.79264 - 1.37926i) q^{66} +(9.11090 - 5.26018i) q^{67} +(-5.19783 + 10.8388i) q^{68} +(-5.26798 + 3.10520i) q^{69} +(0.618933 - 0.474924i) q^{70} +(12.6361 - 2.51348i) q^{71} +(-4.22702 + 4.38246i) q^{72} +(8.59520 + 5.74313i) q^{73} +(-12.8427 + 14.6443i) q^{74} +(0.151500 + 2.03045i) q^{75} +(10.9977 - 14.3324i) q^{76} +(-0.282086 + 0.367621i) q^{77} +(-3.59087 + 2.44651i) q^{78} +(4.22913 - 4.82239i) q^{79} +(-2.16440 - 1.44621i) q^{80} +(6.13009 - 6.58954i) q^{81} +(-15.6843 + 3.11980i) q^{82} +(7.40903 - 5.68515i) q^{83} +(-0.00820131 - 0.908568i) q^{84} +(-7.81095 - 2.00122i) q^{85} +(-3.59810 + 2.07737i) q^{86} +(6.67807 + 8.54227i) q^{87} +(-4.94941 - 1.68010i) q^{88} +(-10.2745 + 10.2745i) q^{89} +(-10.9439 - 7.03007i) q^{90} +(0.0397194 - 0.199683i) q^{91} +(10.2710 - 0.673197i) q^{92} +(-5.29750 + 7.03441i) q^{93} +(-1.49480 - 1.14700i) q^{94} +(10.8684 + 5.35969i) q^{95} +(-11.4622 + 4.00662i) q^{96} +(-1.17141 - 2.37538i) q^{97} +(-10.9232 - 10.9232i) q^{98} +(7.35945 + 2.35092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

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