LMFDB - Embedded newform 552.2.bf.a.5.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(5,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 11, 1]))

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

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

chi := DirichletCharacter("552.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bf (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$92$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.17
Character	$\chi$	$=$	552.5
Dual form			552.2.bf.a.221.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18573 - 0.770749i) q^{2} +(1.67663 - 0.434625i) q^{3} +(0.811892 + 1.82779i) q^{4} +(3.15950 + 0.454268i) q^{5} +(-2.32301 - 0.776919i) q^{6} +(0.966873 - 0.441556i) q^{7} +(0.446090 - 2.79303i) q^{8} +(2.62220 - 1.45741i) q^{9} +O(q^{10})$	\(q+(-1.18573 - 0.770749i) q^{2} +(1.67663 - 0.434625i) q^{3} +(0.811892 + 1.82779i) q^{4} +(3.15950 + 0.454268i) q^{5} +(-2.32301 - 0.776919i) q^{6} +(0.966873 - 0.441556i) q^{7} +(0.446090 - 2.79303i) q^{8} +(2.62220 - 1.45741i) q^{9} +(-3.39618 - 2.97382i) q^{10} +(-1.45838 - 4.96677i) q^{11} +(2.15565 + 2.71167i) q^{12} +(-5.38000 - 2.45696i) q^{13} +(-1.48678 - 0.221652i) q^{14} +(5.49477 - 0.611557i) q^{15} +(-2.68166 + 2.96794i) q^{16} +(-1.57359 + 1.01129i) q^{17} +(-4.23251 - 0.292969i) q^{18} +(1.16859 + 0.751005i) q^{19} +(1.73487 + 6.14374i) q^{20} +(1.42918 - 1.16055i) q^{21} +(-2.09890 + 7.01327i) q^{22} +(4.68944 - 1.00455i) q^{23} +(-0.465989 - 4.87677i) q^{24} +(4.97864 + 1.46186i) q^{25} +(4.48550 + 7.05992i) q^{26} +(3.76305 - 3.58322i) q^{27} +(1.59207 + 1.40875i) q^{28} +(-1.58834 + 1.02077i) q^{29} +(-6.98664 - 3.50995i) q^{30} +(5.21351 + 6.01671i) q^{31} +(5.46726 - 1.45227i) q^{32} +(-4.60384 - 7.69361i) q^{33} +(2.64530 + 0.0137365i) q^{34} +(3.25542 - 0.955879i) q^{35} +(4.79280 + 3.60959i) q^{36} +(0.881073 + 6.12800i) q^{37} +(-0.806787 - 1.79117i) q^{38} +(-10.0882 - 1.78115i) q^{39} +(2.67821 - 8.62194i) q^{40} +(-8.01106 - 1.15182i) q^{41} +(-2.58911 + 0.274560i) q^{42} +(-2.14799 + 2.47891i) q^{43} +(7.89419 - 6.69809i) q^{44} +(8.94692 - 3.41352i) q^{45} +(-6.33465 - 2.42327i) q^{46} +7.43194i q^{47} +(-3.20623 + 6.14167i) q^{48} +(-3.84415 + 4.43639i) q^{49} +(-4.77657 - 5.57065i) q^{50} +(-2.19881 + 2.37948i) q^{51} +(0.122848 - 11.8283i) q^{52} +(1.31544 - 0.600740i) q^{53} +(-7.22371 + 1.34835i) q^{54} +(-2.35150 - 16.3550i) q^{55} +(-0.801966 - 2.89748i) q^{56} +(2.28570 + 0.751264i) q^{57} +(2.67009 + 0.0138653i) q^{58} +(-0.468756 + 1.02643i) q^{59} +(5.57896 + 9.54679i) q^{60} +(8.03054 + 9.26774i) q^{61} +(-1.54442 - 11.1525i) q^{62} +(1.89181 - 2.56698i) q^{63} +(-7.60201 - 2.49188i) q^{64} +(-15.8820 - 10.2068i) q^{65} +(-0.470948 + 12.6709i) q^{66} +(3.53167 + 1.03699i) q^{67} +(-3.12601 - 2.05515i) q^{68} +(7.42588 - 3.72241i) q^{69} +(-4.59678 - 1.37571i) q^{70} +(1.09880 - 3.74217i) q^{71} +(-2.90086 - 7.97402i) q^{72} +(-0.799168 - 0.513594i) q^{73} +(3.67844 - 7.94521i) q^{74} +(8.98272 + 0.287166i) q^{75} +(-0.423917 + 2.74567i) q^{76} +(-3.60317 - 4.15828i) q^{77} +(10.5890 + 9.88739i) q^{78} +(4.02179 + 1.83669i) q^{79} +(-9.82097 + 8.15903i) q^{80} +(4.75190 - 7.64326i) q^{81} +(8.61116 + 7.54025i) q^{82} +(-14.2163 + 2.04399i) q^{83} +(3.28160 + 1.67000i) q^{84} +(-5.43117 + 2.48033i) q^{85} +(4.45755 - 1.28375i) q^{86} +(-2.21942 + 2.40178i) q^{87} +(-14.5229 + 1.85766i) q^{88} +(6.78673 - 7.83230i) q^{89} +(-13.2396 - 2.84833i) q^{90} -6.28667 q^{91} +(5.64343 + 7.75575i) q^{92} +(11.3562 + 7.82190i) q^{93} +(5.72816 - 8.81225i) q^{94} +(3.35100 + 2.90366i) q^{95} +(8.53539 - 4.81114i) q^{96} +(-7.60162 - 1.09295i) q^{97} +(7.97746 - 2.29746i) q^{98} +(-11.0628 - 10.8984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) $ 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9	$ 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) $ 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9 - 22 * q^10 - 12 * q^12 - 22 * q^15 - 30 * q^16 - 10 * q^18 - 14 * q^24 + 40 * q^25 - 22 * q^28 - 11 * q^30 - 20 * q^31 - 22 * q^33 - 18 * q^36 - 42 * q^39 - 176 * q^40 - 11 * q^42 + 90 * q^46 - 64 * q^48 + 32 * q^49 - 90 * q^52 + 21 * q^54 - 76 * q^55 - 22 * q^57 + 76 * q^58 - 11 * q^60 - 22 * q^63 - 28 * q^64 - 44 * q^66 - 116 * q^70 - 79 * q^72 - 36 * q^73 - 22 * q^76 - 134 * q^78 - 44 * q^79 - 34 * q^81 - 40 * q^82 - 165 * q^84 - 18 * q^87 - 22 * q^88 - 198 * q^90 + 88 * q^94 - 231 * q^96 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.18573	−	0.770749i	−0.838435	−	0.545002i
$2$	−1.18573	−	0.770749i	−0.838435	−	0.545002i
$3$	1.67663	−	0.434625i	0.968005	−	0.250931i
$3$	1.67663	−	0.434625i	0.968005	−	0.250931i
$4$	0.811892	+	1.82779i	0.405946	+	0.913897i
$5$	3.15950	+	0.454268i	1.41297	+	0.203155i	0.806164	−	0.591693i	$-0.201540\pi$
$5$	3.15950	+	0.454268i	1.41297	+	0.203155i	0.606809	+	0.794847i	$0.292449\pi$
$6$	−2.32301	−	0.776919i	−0.948367	−	0.317176i
$7$	0.966873	−	0.441556i	0.365444	−	0.166893i	−0.224226	−	0.974537i	$-0.571985\pi$
$7$	0.966873	−	0.441556i	0.365444	−	0.166893i	0.589669	+	0.807645i	$0.299258\pi$
$8$	0.446090	−	2.79303i	0.157717	−	0.987484i
$9$	2.62220	−	1.45741i	0.874068	−	0.485804i
$10$	−3.39618	−	2.97382i	−1.07397	−	0.940405i
$11$	−1.45838	−	4.96677i	−0.439717	−	1.49754i	−0.819835	−	0.572600i	$-0.805935\pi$
$11$	−1.45838	−	4.96677i	−0.439717	−	1.49754i	0.380119	−	0.924938i	$-0.375883\pi$
$12$	2.15565	+	2.71167i	0.622282	+	0.782793i
$13$	−5.38000	−	2.45696i	−1.49214	−	0.681439i	−0.508417	−	0.861111i	$-0.669769\pi$
$13$	−5.38000	−	2.45696i	−1.49214	−	0.681439i	−0.983727	+	0.179672i	$0.942497\pi$
$14$	−1.48678	−	0.221652i	−0.397357	−	0.0592390i
$15$	5.49477	−	0.611557i	1.41874	−	0.157903i
$16$	−2.68166	+	2.96794i	−0.670416	+	0.741985i
$17$	−1.57359	+	1.01129i	−0.381652	+	0.245273i	−0.717374	−	0.696688i	$-0.754656\pi$
$17$	−1.57359	+	1.01129i	−0.381652	+	0.245273i	0.335722	+	0.941961i	$0.391020\pi$
$18$	−4.23251	−	0.292969i	−0.997613	−	0.0690534i
$19$	1.16859	+	0.751005i	0.268092	+	0.172292i	0.667779	−	0.744359i	$-0.267245\pi$
$19$	1.16859	+	0.751005i	0.268092	+	0.172292i	−0.399687	+	0.916652i	$0.630881\pi$
$20$	1.73487	+	6.14374i	0.387928	+	1.37378i
$21$	1.42918	−	1.16055i	0.311873	−	0.253254i
$22$	−2.09890	+	7.01327i	−0.447487	+	1.49523i
$23$	4.68944	−	1.00455i	0.977817	−	0.209463i
$23$	4.68944	−	1.00455i	0.977817	−	0.209463i
$24$	−0.465989	−	4.87677i	−0.0951195	−	0.995466i
$25$	4.97864	+	1.46186i	0.995728	+	0.292372i
$26$	4.48550	+	7.05992i	0.879680	+	1.38456i
$27$	3.76305	−	3.58322i	0.724199	−	0.689591i
$28$	1.59207	+	1.40875i	0.300873	+	0.266229i
$29$	−1.58834	+	1.02077i	−0.294948	+	0.189551i	−0.679743	−	0.733451i	$-0.737909\pi$
$29$	−1.58834	+	1.02077i	−0.294948	+	0.189551i	0.384795	+	0.923002i	$0.374272\pi$
$30$	−6.98664	−	3.50995i	−1.27558	−	0.640826i
$31$	5.21351	+	6.01671i	0.936373	+	1.08063i	0.996595	+	0.0824475i	$0.0262737\pi$
$31$	5.21351	+	6.01671i	0.936373	+	1.08063i	−0.0602220	+	0.998185i	$0.519181\pi$
$32$	5.46726	−	1.45227i	0.966484	−	0.256728i
$33$	−4.60384	−	7.69361i	−0.801426	−	1.33929i
$34$	2.64530	+	0.0137365i	0.453665	+	0.00235580i
$35$	3.25542	−	0.955879i	0.550267	−	0.161573i
$36$	4.79280	+	3.60959i	0.798799	+	0.601598i
$37$	0.881073	+	6.12800i	0.144848	+	1.00744i	0.924488	+	0.381210i	$0.124493\pi$
$37$	0.881073	+	6.12800i	0.144848	+	1.00744i	−0.779641	+	0.626227i	$0.784598\pi$
$38$	−0.806787	−	1.79117i	−0.130878	−	0.290567i
$39$	−10.0882	−	1.78115i	−1.61540	−	0.285212i
$40$	2.67821	−	8.62194i	0.423462	−	1.36325i
$41$	−8.01106	−	1.15182i	−1.25112	−	0.179883i	−0.515268	−	0.857029i	$-0.672308\pi$
$41$	−8.01106	−	1.15182i	−1.25112	−	0.179883i	−0.735849	+	0.677146i	$0.763217\pi$
$42$	−2.58911	+	0.274560i	−0.399509	+	0.0423655i
$43$	−2.14799	+	2.47891i	−0.327565	+	0.378031i	−0.895514	−	0.445034i	$-0.853192\pi$
$43$	−2.14799	+	2.47891i	−0.327565	+	0.378031i	0.567949	+	0.823064i	$0.307737\pi$
$44$	7.89419	−	6.69809i	1.19009	−	1.00977i
$45$	8.94692	−	3.41352i	1.33373	−	0.508857i
$46$	−6.33465	−	2.42327i	−0.933993	−	0.357291i
$47$			7.43194i			1.08406i	0.840359	+	0.542030i	$0.182344\pi$
$47$			7.43194i			1.08406i	−0.840359	+	0.542030i	$0.817656\pi$
$48$	−3.20623	+	6.14167i	−0.462779	+	0.886474i
$49$	−3.84415	+	4.43639i	−0.549165	+	0.633770i
$50$	−4.77657	−	5.57065i	−0.675509	−	0.787808i
$51$	−2.19881	+	2.37948i	−0.307895	+	0.333194i
$52$	0.122848	−	11.8283i	0.0170359	−	1.64029i
$53$	1.31544	−	0.600740i	0.180689	−	0.0825180i	−0.323016	−	0.946393i	$-0.604697\pi$
$53$	1.31544	−	0.600740i	0.180689	−	0.0825180i	0.503706	+	0.863875i	$0.331970\pi$
$54$	−7.22371	+	1.34835i	−0.983022	+	0.183488i
$55$	−2.35150	−	16.3550i	−0.317076	−	2.20531i
$56$	−0.801966	−	2.89748i	−0.107167	−	0.387192i
$57$	2.28570	+	0.751264i	0.302748	+	0.0995074i
$58$	2.67009	+	0.0138653i	0.350600	+	0.00182060i
$59$	−0.468756	+	1.02643i	−0.0610268	+	0.133630i	−0.937688	−	0.347478i	$-0.887038\pi$
$59$	−0.468756	+	1.02643i	−0.0610268	+	0.133630i	0.876661	+	0.481108i	$0.159765\pi$
$60$	5.57896	+	9.54679i	0.720240	+	1.23248i
$61$	8.03054	+	9.26774i	1.02821	+	1.18661i	0.982232	+	0.187670i	$0.0600934\pi$
$61$	8.03054	+	9.26774i	1.02821	+	1.18661i	0.0459733	+	0.998943i	$0.485361\pi$
$62$	−1.54442	−	11.1525i	−0.196141	−	1.41637i
$63$	1.89181	−	2.56698i	0.238345	−	0.323409i
$64$	−7.60201	−	2.49188i	−0.950251	−	0.311486i
$65$	−15.8820	−	10.2068i	−1.96992	−	1.26599i
$66$	−0.470948	+	12.6709i	−0.0579698	+	1.55968i
$67$	3.53167	+	1.03699i	0.431462	+	0.126689i	0.490250	−	0.871582i	$-0.336905\pi$
$67$	3.53167	+	1.03699i	0.431462	+	0.126689i	−0.0587881	+	0.998270i	$0.518724\pi$
$68$	−3.12601	−	2.05515i	−0.379085	−	0.249224i
$69$	7.42588	−	3.72241i	0.893971	−	0.448125i
$70$	−4.59678	−	1.37571i	−0.549421	−	0.164428i
$71$	1.09880	−	3.74217i	0.130403	−	0.444114i	−0.868242	−	0.496141i	$-0.834750\pi$
$71$	1.09880	−	3.74217i	0.130403	−	0.444114i	0.998646	+	0.0520271i	$0.0165682\pi$
$72$	−2.90086	−	7.97402i	−0.341869	−	0.939748i
$73$	−0.799168	−	0.513594i	−0.0935355	−	0.0601116i	0.493037	−	0.870008i	$-0.335887\pi$
$73$	−0.799168	−	0.513594i	−0.0935355	−	0.0601116i	−0.586572	+	0.809897i	$0.699523\pi$
$74$	3.67844	−	7.94521i	0.427610	−	0.923612i
$75$	8.98272	+	0.287166i	1.03723	+	0.0331590i
$76$	−0.423917	+	2.74567i	−0.0486266	+	0.314950i
$77$	−3.60317	−	4.15828i	−0.410619	−	0.473880i
$78$	10.5890	+	9.88739i	1.19896	+	1.11953i
$79$	4.02179	+	1.83669i	0.452486	+	0.206644i	0.628604	−	0.777726i	$-0.283627\pi$
$79$	4.02179	+	1.83669i	0.452486	+	0.206644i	−0.176118	+	0.984369i	$0.556354\pi$
$80$	−9.82097	+	8.15903i	−1.09802	+	0.912207i
$81$	4.75190	−	7.64326i	0.527988	−	0.849252i
$82$	8.61116	+	7.54025i	0.950943	+	0.832682i
$83$	−14.2163	+	2.04399i	−1.56044	+	0.224357i	−0.867795	−	0.496922i	$-0.834463\pi$
$83$	−14.2163	+	2.04399i	−1.56044	+	0.224357i	−0.692644	+	0.721280i	$0.743554\pi$
$84$	3.28160	+	1.67000i	0.358051	+	0.182212i
$85$	−5.43117	+	2.48033i	−0.589093	+	0.269030i
$86$	4.45755	−	1.28375i	0.480669	−	0.138430i
$87$	−2.21942	+	2.40178i	−0.237947	+	0.257498i
$88$	−14.5229	+	1.85766i	−1.54815	+	0.198027i
$89$	6.78673	−	7.83230i	0.719391	−	0.830222i	−0.271842	−	0.962342i	$-0.587633\pi$
$89$	6.78673	−	7.83230i	0.719391	−	0.830222i	0.991234	+	0.132120i	$0.0421784\pi$
$90$	−13.2396	−	2.84833i	−1.39557	−	0.300240i
$91$	−6.28667			−0.659022
$92$	5.64343	+	7.75575i	0.588368	+	0.808593i
$93$	11.3562	+	7.82190i	1.17758	+	0.811093i
$94$	5.72816	−	8.81225i	0.590815	−	0.908914i
$95$	3.35100	+	2.90366i	0.343805	+	0.297909i
$96$	8.53539	−	4.81114i	0.871140	−	0.491035i
$97$	−7.60162	−	1.09295i	−0.771828	−	0.110972i	−0.254861	−	0.966978i	$-0.582030\pi$
$97$	−7.60162	−	1.09295i	−0.771828	−	0.110972i	−0.516967	+	0.856005i	$0.672939\pi$
$98$	7.97746	−	2.29746i	0.805845	−	0.232079i
$99$	−11.0628	−	10.8984i	−1.11185	−	1.09533i
$100$	1.37013	+	10.2868i	0.137013	+	1.02868i
$101$	1.10295	+	7.67120i	0.109748	+	0.763313i	0.968156	+	0.250346i	$0.0805445\pi$
$101$	1.10295	+	7.67120i	0.109748	+	0.763313i	−0.858408	+	0.512967i	$0.828546\pi$
$102$	4.44117	−	1.12668i	0.439741	−	0.111558i
$103$	1.66083	+	5.65628i	0.163647	+	0.557330i	0.999959	+	0.00907627i	$0.00288910\pi$
$103$	1.66083	+	5.65628i	0.163647	+	0.557330i	−0.836312	+	0.548254i	$0.815293\pi$
$104$	−9.26233	+	13.9305i	−0.908247	+	1.36599i
$105$	5.04271	−	3.01755i	0.492118	−	0.294482i
$106$	−2.02277	−	0.301559i	−0.196468	−	0.0292900i
$107$	14.6499	−	12.6942i	1.41626	−	1.22720i	0.479352	−	0.877623i	$-0.340872\pi$
$107$	14.6499	−	12.6942i	1.41626	−	1.22720i	0.936909	−	0.349574i	$-0.113674\pi$
$108$	9.60458	+	3.96889i	0.924201	+	0.381906i
$109$	0.644837	−	0.414412i	0.0617642	−	0.0396934i	−0.509394	−	0.860533i	$-0.670131\pi$
$109$	0.644837	−	0.414412i	0.0617642	−	0.0396934i	0.571159	+	0.820840i	$0.306494\pi$
$110$	−9.81739	+	21.2050i	−0.936051	+	2.02182i
$111$	4.14062	+	9.89148i	0.393010	+	0.938857i
$112$	−1.28232	+	4.05373i	−0.121167	+	0.383041i
$113$	−0.511394	−	0.150159i	−0.0481079	−	0.0141257i	0.257590	−	0.966254i	$-0.417072\pi$
$113$	−0.511394	−	0.150159i	−0.0481079	−	0.0141257i	−0.305698	+	0.952129i	$0.598890\pi$
$114$	−2.13117	−	2.65249i	−0.199603	−	0.248429i
$115$	15.2726	−	1.04361i	1.42418	−	0.0973172i
$116$	−3.15531	−	2.07441i	−0.292963	−	0.192604i
$117$	−17.6883	+	1.39822i	−1.63528	+	0.129266i
$118$	1.34694	−	0.855774i	0.123996	−	0.0787804i
$119$	−1.07493	+	1.67262i	−0.0985382	+	0.153328i
$120$	0.743066	−	15.6198i	0.0678324	−	1.42589i
$121$	−13.2882	+	8.53978i	−1.20801	+	0.776343i
$122$	−2.37892	−	17.1785i	−0.215377	−	1.55527i
$123$	−13.9322	+	1.55063i	−1.25623	+	0.139815i
$124$	−6.76450	+	14.4141i	−0.607470	+	1.29443i
$125$	0.548254	+	0.250379i	0.0490374	+	0.0223946i
$126$	−4.22167	+	1.58563i	−0.376096	+	0.141259i
$127$	9.66424	−	2.83768i	0.857563	−	0.251803i	0.176746	−	0.984257i	$-0.443443\pi$
$127$	9.66424	−	2.83768i	0.857563	−	0.251803i	0.680817	+	0.732453i	$0.261625\pi$
$128$	7.09328	+	8.81393i	0.626963	+	0.779049i
$129$	−2.52400	+	5.08980i	−0.222225	+	0.448132i
$130$	10.9649	+	24.3435i	0.961683	+	2.13506i
$131$	7.76606	+	17.0053i	0.678524	+	1.48576i	0.864200	+	0.503149i	$0.167825\pi$
$131$	7.76606	+	17.0053i	0.678524	+	1.48576i	−0.185675	+	0.982611i	$0.559447\pi$
$132$	10.3245	−	14.6613i	0.898634	−	1.27610i
$133$	1.46149	+	0.210130i	0.126727	+	0.0182206i
$134$	−3.38833	−	3.95162i	−0.292707	−	0.341368i
$135$	13.5171	−	9.61177i	1.16337	−	0.827249i
$136$	2.12259	+	4.84622i	0.182010	+	0.415560i
$137$	−20.8156			−1.77839			−0.889197	−	0.457525i	$-0.848736\pi$
$137$	−20.8156			−1.77839			−0.889197	+	0.457525i	$0.848736\pi$
$138$	−11.6741	−	1.30973i	−0.993765	−	0.111492i
$139$			2.75564i			0.233730i	0.993148	+	0.116865i	$0.0372845\pi$
$139$			2.75564i			0.233730i	−0.993148	+	0.116865i	$0.962715\pi$
$140$	4.39020	+	5.17418i	0.371040	+	0.437298i
$141$	3.23010	+	12.4606i	0.272024	+	1.04938i
$142$	−4.18715	+	3.59029i	−0.351378	+	0.301290i
$143$	−4.35712	+	30.3044i	−0.364360	+	2.53418i
$144$	−2.70635	+	11.6908i	−0.225529	+	0.974236i
$145$	−5.48208	+	2.50358i	−0.455262	+	0.207911i
$146$	0.551742	+	1.22494i	0.0456625	+	0.101377i
$147$	−4.51707	+	9.10897i	−0.372562	+	0.751295i
$148$	−10.4854	+	6.58569i	−0.861894	+	0.541341i
$149$	3.84792	+	13.1048i	0.315234	+	1.07359i	0.952902	+	0.303278i	$0.0980811\pi$
$149$	3.84792	+	13.1048i	0.315234	+	1.07359i	−0.637668	+	0.770311i	$0.720101\pi$
$150$	−10.4297	−	7.26392i	−0.851582	−	0.593097i
$151$	0.787976	−	1.72543i	0.0641245	−	0.140413i	−0.874856	−	0.484382i	$-0.839044\pi$
$151$	0.787976	−	1.72543i	0.0641245	−	0.140413i	0.938981	+	0.343969i	$0.111772\pi$
$152$	2.61887	−	2.92888i	0.212419	−	0.237563i
$153$	−2.65242	+	4.94517i	−0.214435	+	0.399794i
$154$	1.06738	+	7.70772i	0.0860121	+	0.621106i
$155$	13.7389	+	21.3781i	1.10353	+	1.71713i
$156$	−4.93491	−	19.8852i	−0.395109	−	1.59209i
$157$	−16.8034	−	10.7989i	−1.34106	−	0.861846i	−0.344036	−	0.938957i	$-0.611794\pi$
$157$	−16.8034	−	10.7989i	−1.34106	−	0.861846i	−0.997023	+	0.0771109i	$0.975430\pi$
$158$	−3.35311	−	5.27760i	−0.266759	−	0.419863i
$159$	1.94441	−	1.57894i	0.154202	−	0.125218i
$160$	17.9335	−	2.10487i	1.41777	−	0.166404i
$161$	4.09053	−	3.04192i	0.322379	−	0.239737i
$162$	−11.5255	+	5.40030i	−0.905528	+	0.424287i
$163$	6.86756	−	23.3888i	0.537909	−	1.83195i	−0.0167325	−	0.999860i	$-0.505326\pi$
$163$	6.86756	−	23.3888i	0.537909	−	1.83195i	0.554641	−	0.832090i	$-0.312855\pi$
$164$	−4.39883	−	15.5777i	−0.343491	−	1.21642i
$165$	−11.0509	−	26.3994i	−0.860311	−	2.05519i
$166$	18.4320	+	8.53357i	1.43060	+	0.662333i
$167$	−5.71969	−	8.90002i	−0.442603	−	0.688704i	0.546246	−	0.837625i	$-0.316056\pi$
$167$	−5.71969	−	8.90002i	−0.442603	−	0.688704i	−0.988849	+	0.148921i	$0.952420\pi$
$168$	−2.60392	−	4.50945i	−0.200897	−	0.347912i
$169$	14.3946	+	16.6122i	1.10727	+	1.27786i
$170$	8.35159	+	1.24508i	0.640538	+	0.0954929i
$171$	4.15880	+	0.266175i	0.318031	+	0.0203549i
$172$	−6.27488	−	1.91348i	−0.478455	−	0.145901i
$173$	−23.7645	+	6.97790i	−1.80678	+	0.530520i	−0.998316	−	0.0580183i	$-0.981522\pi$
$173$	−23.7645	+	6.97790i	−1.80678	+	0.530520i	−0.808469	+	0.588538i	$0.799704\pi$
$174$	4.48280	−	1.13724i	0.339840	−	0.0862141i
$175$	5.45921	−	0.784915i	0.412677	−	0.0593340i
$176$	18.6520	+	8.99084i	1.40594	+	0.677710i
$177$	−0.339819	+	1.92468i	−0.0255424	+	0.144668i
$178$	−14.0839	+	4.05610i	−1.05564	+	0.304017i
$179$	0.227632	−	1.58321i	0.0170140	−	0.118335i	−0.979544	−	0.201228i	$-0.935507\pi$
$179$	0.227632	−	1.58321i	0.0170140	−	0.118335i	0.996558	+	0.0828929i	$0.0264159\pi$
$180$	13.5031	+	13.5817i	1.00646	+	1.01232i
$181$	9.29756	−	10.7300i	0.691082	−	0.797551i	−0.296437	−	0.955053i	$-0.595798\pi$
$181$	9.29756	−	10.7300i	0.691082	−	0.797551i	0.987519	+	0.157501i	$0.0503438\pi$
$182$	7.45426	+	4.84544i	0.552547	+	0.359168i
$183$	17.4923	+	12.0483i	1.29307	+	0.890639i
$184$	−0.713818	−	13.5459i	−0.0526233	−	0.998614i
$185$			19.7617i			1.45291i
$186$	−7.43656	−	18.0274i	−0.545275	−	1.32183i
$187$	7.31772	+	6.34084i	0.535125	+	0.463688i
$188$	−13.5841	+	6.03393i	−0.990719	+	0.440070i
$189$	2.05620	−	5.12612i	0.149566	−	0.372870i
$190$	−1.73537	−	6.02572i	−0.125897	−	0.437151i
$191$	−6.02692	−	13.1971i	−0.436093	−	0.954910i	−0.992299	−	0.123865i	$-0.960471\pi$
$191$	−6.02692	−	13.1971i	−0.436093	−	0.954910i	0.556206	−	0.831044i	$-0.312256\pi$
$192$	−13.8288	−	0.873958i	−0.998009	−	0.0630725i
$193$	−2.14425	−	14.9136i	−0.154346	−	1.07350i	−0.908825	−	0.417178i	$-0.863019\pi$
$193$	−2.14425	−	14.9136i	−0.154346	−	1.07350i	0.754478	−	0.656325i	$-0.227890\pi$
$194$	8.17105	+	7.15488i	0.586647	+	0.513691i
$195$	−31.0644	−	10.2103i	−2.22457	−	0.731173i
$196$	−11.2298	−	3.42445i	−0.802132	−	0.244604i
$197$	2.64733	−	5.79685i	0.188615	−	0.413009i	−0.791574	−	0.611073i	$-0.790738\pi$
$197$	2.64733	−	5.79685i	0.188615	−	0.413009i	0.980189	+	0.198064i	$0.0634655\pi$
$198$	4.71748	+	21.4492i	0.335257	+	1.52433i
$199$	−12.8515	+	11.1359i	−0.911019	+	0.789402i	−0.978055	−	0.208348i	$-0.933191\pi$
$199$	−12.8515	+	11.1359i	−0.911019	+	0.789402i	0.0670360	+	0.997751i	$0.478646\pi$
$200$	6.30394	−	13.2534i	0.445756	−	0.937154i
$201$	6.37202	+	0.203705i	0.449447	+	0.0143682i
$202$	4.60477	−	9.94604i	0.323991	−	0.699801i
$203$	−1.08500	+	1.68829i	−0.0761521	+	0.118495i
$204$	−6.13440	−	2.08709i	−0.429494	−	0.146126i
$205$	−24.7877	−	7.27834i	−1.73125	−	0.508341i
$206$	2.39028	−	7.98689i	0.166539	−	0.556473i
$207$	10.8326	−	9.46859i	0.752920	−	0.658112i
$208$	21.7195	−	9.37878i	1.50598	−	0.650301i
$209$	2.02583	−	6.89935i	0.140130	−	0.477238i
$210$	−8.30504	−	0.308679i	−0.573102	−	0.0213009i
$211$	−0.102277	+	0.159146i	−0.00704103	+	0.0109561i	−0.844756	−	0.535151i	$-0.820255\pi$
$211$	−0.102277	+	0.159146i	−0.00704103	+	0.0109561i	0.837715	+	0.546107i	$0.183891\pi$
$212$	2.16602	+	1.91661i	0.148763	+	0.131633i
$213$	0.215847	−	6.75181i	0.0147896	−	0.462626i
$214$	−27.1548	+	3.76046i	−1.85627	+	0.257060i
$215$	−7.91267	+	6.85637i	−0.539640	+	0.467600i
$216$	−8.32938	−	12.1087i	−0.566742	−	0.823895i
$217$	7.69751	+	3.51534i	0.522541	+	0.238637i
$218$	−1.08401	−	0.00562905i	−0.0734183	−	0.000381247i
$219$	−1.56313	−	0.513771i	−0.105627	−	0.0347174i
$220$	27.9845	−	17.5766i	1.88671	−	1.18501i
$221$	10.9506	−	1.57446i	0.736619	−	0.105910i
$222$	2.71421	−	14.9200i	0.182166	−	1.00136i
$223$	−5.87793	−	12.8709i	−0.393615	−	0.861897i	−0.997878	−	0.0651117i	$-0.979260\pi$
$223$	−5.87793	−	12.8709i	−0.393615	−	0.861897i	0.604263	−	0.796785i	$-0.293468\pi$
$224$	4.64488	−	3.81827i	0.310349	−	0.255119i
$225$	15.1855	−	3.42264i	1.01237	−	0.228176i
$226$	0.490638	+	0.572203i	0.0326368	+	0.0380624i
$227$	2.04813	+	1.77472i	0.135939	+	0.117792i	0.720177	−	0.693791i	$-0.244061\pi$
$227$	2.04813	+	1.77472i	0.135939	+	0.117792i	−0.584237	+	0.811583i	$0.698606\pi$
$228$	0.482582	+	4.78773i	0.0319598	+	0.317075i
$229$	−1.49217			−0.0986052			−0.0493026	−	0.998784i	$-0.515700\pi$
$229$	−1.49217			−0.0986052			−0.0493026	+	0.998784i	$0.515700\pi$
$230$	−18.9135	−	10.5339i	−1.24712	−	0.694588i
$231$	−7.84849	−	5.40589i	−0.516393	−	0.355681i
$232$	2.14248	+	4.89164i	0.140661	+	0.321152i
$233$	6.53167	+	5.65972i	0.427904	+	0.370781i	0.842023	−	0.539442i	$-0.181365\pi$
$233$	6.53167	+	5.65972i	0.427904	+	0.370781i	−0.414119	+	0.910223i	$0.635910\pi$
$234$	22.0511	+	11.9753i	1.44153	+	0.782850i
$235$	−3.37609	+	23.4812i	−0.220232	+	1.53175i
$236$	−2.25669	−	0.0234377i	−0.146898	−	0.00152567i
$237$	7.54133	+	1.33149i	0.489862	+	0.0864894i
$238$	2.56373	−	1.15477i	0.166182	−	0.0748524i
$239$	1.83648	−	0.264046i	0.118792	−	0.0170797i	−0.0826624	−	0.996578i	$-0.526342\pi$
$239$	1.83648	−	0.264046i	0.118792	−	0.0170797i	0.201454	+	0.979498i	$0.435433\pi$
$240$	−12.9201	+	17.9481i	−0.833986	+	1.15855i
$241$	0.302917	+	1.03164i	0.0195126	+	0.0664538i	0.968674	−	0.248337i	$-0.0798839\pi$
$241$	0.302917	+	1.03164i	0.0195126	+	0.0664538i	−0.949161	+	0.314790i	$0.898066\pi$
$242$	22.3381	+	0.115998i	1.43595	+	0.00745662i
$243$	4.64524	−	14.8802i	0.297992	−	0.954568i
$244$	−10.4196	+	22.2026i	−0.667046	+	1.42137i
$245$	−14.1609	+	12.2705i	−0.904708	+	0.783934i
$246$	17.7149	+	8.89963i	1.12946	+	0.567419i
$247$	−4.44181	−	6.91159i	−0.282625	−	0.439774i
$248$	19.1305	−	11.8775i	1.21479	−	0.754220i
$249$	−22.9471	+	9.60577i	−1.45421	+	0.608741i
$250$	−0.457100	−	0.719448i	−0.0289095	−	0.0455019i
$251$	−3.97610	+	13.5413i	−0.250969	+	0.854722i	0.733578	+	0.679605i	$0.237849\pi$
$251$	−3.97610	+	13.5413i	−0.250969	+	0.854722i	−0.984548	+	0.175117i	$0.943969\pi$
$252$	6.22786	+	1.37372i	0.392318	+	0.0865365i
$253$	−11.8283	−	21.8264i	−0.743641	−	1.37221i
$254$	−13.6463	−	4.08400i	−0.856244	−	0.256253i
$255$	−8.02807	+	6.51913i	−0.502737	+	0.408244i
$256$	−1.61735	−	15.9180i	−0.101085	−	0.994878i
$257$	3.63840	−	5.66146i	0.226957	−	0.353152i	−0.709035	−	0.705173i	$-0.750869\pi$
$257$	3.63840	−	5.66146i	0.226957	−	0.353152i	0.935992	+	0.352021i	$0.114506\pi$
$258$	6.91572	−	4.08974i	0.430554	−	0.254616i
$259$	3.55774	+	5.53595i	0.221067	+	0.343987i
$260$	5.76137	−	37.3158i	0.357305	−	2.31423i
$261$	−2.67728	+	4.99153i	−0.165719	+	0.308968i
$262$	3.89840	−	26.1493i	0.240844	−	1.61551i
$263$	−2.37306	+	5.19628i	−0.146329	+	0.320416i	−0.968577	−	0.248713i	$-0.919992\pi$
$263$	−2.37306	+	5.19628i	−0.146329	+	0.320416i	0.822248	+	0.569129i	$0.192720\pi$
$264$	−23.5422	+	9.42661i	−1.44892	+	0.580168i
$265$	4.42902	−	1.30048i	0.272073	−	0.0798878i
$266$	−1.57096	−	1.37560i	−0.0963220	−	0.0843432i
$267$	7.97474	−	16.0816i	0.488046	−	0.984176i
$268$	0.971925	+	7.29709i	0.0593698	+	0.445741i
$269$	8.33133	+	18.2431i	0.507970	+	1.11230i	0.973796	+	0.227423i	$0.0730299\pi$
$269$	8.33133	+	18.2431i	0.507970	+	1.11230i	−0.465826	+	0.884876i	$0.654243\pi$
$270$	−23.4358	+	0.978628i	−1.42626	+	0.0595574i
$271$	1.84365	−	12.8229i	0.111994	−	0.778934i	−0.853982	−	0.520302i	$-0.825819\pi$
$271$	1.84365	−	12.8229i	0.111994	−	0.778934i	0.965976	−	0.258632i	$-0.0832716\pi$
$272$	1.21841	−	7.38227i	0.0738769	−	0.447616i
$273$	−10.5404	+	2.73234i	−0.637936	+	0.165369i
$274$	24.6816	+	16.0436i	1.49107	+	0.969228i
$275$		−	26.8597i		−	1.61970i
$276$	12.8328	+	10.5508i	0.772444	+	0.635083i
$277$			12.7415i			0.765562i	0.923839	+	0.382781i	$0.125034\pi$
$277$			12.7415i			0.765562i	−0.923839	+	0.382781i	$0.874966\pi$
$278$	2.12391	−	3.26743i	0.127383	−	0.195967i
$279$	22.4397	+	8.17880i	1.34343	+	0.489652i
$280$	−1.21758	−	9.51890i	−0.0727645	−	0.568863i
$281$	0.637448	−	4.43355i	0.0380270	−	0.264483i	−0.961934	−	0.273281i	$-0.911891\pi$
$281$	0.637448	−	4.43355i	0.0380270	−	0.264483i	0.999961	+	0.00879737i	$0.00280033\pi$
$282$	5.77401	−	17.2645i	0.343837	−	1.02809i
$283$	1.40692	+	3.08072i	0.0836327	+	0.183130i	0.946828	−	0.321740i	$-0.104268\pi$
$283$	1.40692	+	3.08072i	0.0836327	+	0.183130i	−0.863195	+	0.504870i	$0.831540\pi$
$284$	7.73202	−	1.02985i	0.458811	−	0.0611106i
$285$	6.88040	+	3.41194i	0.407559	+	0.202106i
$286$	28.5234	−	32.5745i	1.68663	−	1.92617i
$287$	−8.25427	+	2.42367i	−0.487234	+	0.143065i
$288$	12.2197	−	11.7762i	0.720052	−	0.693920i
$289$	−5.60856	+	12.2810i	−0.329915	+	0.722414i
$290$	8.42987	+	1.25675i	0.495019	+	0.0737987i
$291$	−13.2202	+	1.47138i	−0.774980	+	0.0862537i
$292$	0.289907	−	1.87770i	0.0169655	−	0.109884i
$293$	−3.51413	−	5.46810i	−0.205298	−	0.319450i	0.723302	−	0.690531i	$-0.242623\pi$
$293$	−3.51413	−	5.46810i	−0.205298	−	0.319450i	−0.928600	+	0.371082i	$0.878987\pi$
$294$	12.3767	−	7.31920i	0.721826	−	0.426865i
$295$	−1.94731	+	3.03008i	−0.113377	+	0.176418i
$296$	17.5087	+	0.272778i	1.01767	+	0.0158549i
$297$	−23.2850	−	13.4645i	−1.35113	−	0.781290i
$298$	5.53795	−	18.5045i	0.320805	−	1.07194i
$299$	−27.6974	−	6.11732i	−1.60178	−	0.353774i
$300$	6.76811	+	16.6517i	0.390757	+	0.961387i
$301$	−0.982254	+	3.34525i	−0.0566162	+	0.192817i
$302$	−2.26419	+	1.43855i	−0.130290	+	0.0827793i
$303$	5.18334	+	12.3824i	0.297775	+	0.711352i
$304$	−5.36270	+	1.45435i	−0.307572	+	0.0834129i
$305$	21.1625	+	32.9295i	1.21176	+	1.88554i
$306$	6.95653	−	3.81927i	0.397678	−	0.218333i
$307$	18.4424	−	15.9804i	1.05256	−	0.912050i	0.0562986	−	0.998414i	$-0.482070\pi$
$307$	18.4424	−	15.9804i	1.05256	−	0.912050i	0.996264	+	0.0863636i	$0.0275247\pi$
$308$	4.67510	−	9.96193i	0.266388	−	0.567634i
$309$	5.24297	+	8.76168i	0.298262	+	0.498434i
$310$	0.186619	−	35.9379i	0.0105992	−	2.04113i
$311$	−7.53709	−	25.6690i	−0.427389	−	1.45555i	−0.838968	−	0.544180i	$-0.816841\pi$
$311$	−7.53709	−	25.6690i	−0.427389	−	1.45555i	0.411579	−	0.911374i	$-0.364977\pi$
$312$	−9.47502	+	27.3819i	−0.536418	+	1.55020i
$313$	−11.6370	+	1.67315i	−0.657765	+	0.0945723i	−0.463112	−	0.886300i	$-0.653267\pi$
$313$	−11.6370	+	1.67315i	−0.657765	+	0.0945723i	−0.194653	+	0.980872i	$0.562358\pi$
$314$	11.6010	+	25.7557i	0.654682	+	1.45348i
$315$	7.14327	−	7.25100i	0.402478	−	0.408548i
$316$	−0.0918341	+	8.84219i	−0.00516607	+	0.497412i
$317$	2.66230	−	18.5167i	0.149530	−	1.04000i	−0.767461	−	0.641095i	$-0.778480\pi$
$317$	2.66230	−	18.5167i	0.149530	−	1.04000i	0.916991	−	0.398907i	$-0.130611\pi$
$318$	−3.52250	+	0.373540i	−0.197532	+	0.0209471i
$319$	7.38631	+	6.40027i	0.413554	+	0.358347i
$320$	−22.8866	−	11.3265i	−1.27940	−	0.633169i
$321$	19.0453	−	27.6508i	1.06301	−	1.54332i
$322$	−7.19481	+	0.454113i	−0.400951	+	0.0253067i
$323$	−2.59836			−0.144577
$324$	17.8283	+	2.47999i	0.990463	+	0.137777i
$325$	−23.1933	−	20.0971i	−1.28654	−	1.11479i
$326$	−26.1699	+	22.4395i	−1.44942	+	1.24281i
$327$	0.901043	−	0.975079i	0.0498278	−	0.0539220i
$328$	−6.79071	+	21.8613i	−0.374954	+	1.20709i
$329$	3.28162	+	7.18574i	0.180922	+	0.396163i
$330$	−7.24396	+	39.8199i	−0.398767	+	2.19201i
$331$	1.87868	−	0.270114i	0.103262	−	0.0148468i	−0.0904902	−	0.995897i	$-0.528843\pi$
$331$	1.87868	−	0.270114i	0.103262	−	0.0148468i	0.193752	+	0.981051i	$0.437934\pi$
$332$	−15.2781	−	24.3249i	−0.838493	−	1.33500i
$333$	11.2414	+	14.7848i	0.616024	+	0.810201i
$334$	−0.0776919	+	14.9614i	−0.00425111	+	0.818653i
$335$	10.6872	+	4.88070i	0.583907	+	0.266661i
$336$	−0.388125	+	7.35394i	−0.0211739	+	0.401191i
$337$	25.6895	−	22.2601i	1.39940	−	1.21259i	0.452208	−	0.891913i	$-0.350637\pi$
$337$	25.6895	−	22.2601i	1.39940	−	1.21259i	0.947190	−	0.320673i	$-0.103909\pi$
$338$	−4.26415	−	30.7921i	−0.231939	−	1.67487i
$339$	−0.922683	−	0.0294970i	−0.0501132	−	0.00160205i
$340$	−8.94306	−	7.91330i	−0.485005	−	0.429159i
$341$	22.2804	−	34.6689i	1.20655	−	1.87743i
$342$	−4.72604	−	3.52100i	−0.255555	−	0.190394i
$343$	−3.85412	+	13.1259i	−0.208103	+	0.708734i
$344$	5.96547	+	7.10521i	0.321637	+	0.383087i
$345$	25.1531	−	8.38762i	1.35420	−	0.451574i
$346$	33.5564	+	10.0426i	1.80401	+	0.539895i
$347$	7.15627	+	2.10127i	0.384168	+	0.112802i	0.468114	−	0.883668i	$-0.344934\pi$
$347$	7.15627	+	2.10127i	0.384168	+	0.112802i	−0.0839450	+	0.996470i	$0.526752\pi$
$348$	−6.19190	−	2.10665i	−0.331920	−	0.112929i
$349$	−14.5562	+	22.6500i	−0.779178	+	1.21242i	0.193690	+	0.981063i	$0.437955\pi$
$349$	−14.5562	+	22.6500i	−0.779178	+	1.21242i	−0.972868	+	0.231362i	$0.925682\pi$
$350$	−7.07809	−	3.27698i	−0.378340	−	0.175162i
$351$	−29.0490	+	10.0321i	−1.55052	+	0.535472i
$352$	−15.1864	−	25.0366i	−0.809439	−	1.33446i
$353$	23.8810	−	20.6930i	1.27105	−	1.10138i	0.281147	−	0.959665i	$-0.409285\pi$
$353$	23.8810	−	20.6930i	1.27105	−	1.10138i	0.989908	−	0.141710i	$-0.0452602\pi$
$354$	1.88638	−	2.02023i	0.100260	−	0.107374i
$355$	5.17161	−	11.3242i	0.274480	−	0.601028i
$356$	19.8259	+	6.04576i	1.05077	+	0.320425i
$357$	−1.07530	+	3.27155i	−0.0569107	+	0.173149i
$358$	−1.49017	+	1.70181i	−0.0787579	+	0.0899435i
$359$	−1.07362	−	7.46716i	−0.0566633	−	0.394102i	−0.998341	−	0.0575846i	$-0.981660\pi$
$359$	−1.07362	−	7.46716i	−0.0566633	−	0.394102i	0.941677	−	0.336517i	$-0.109249\pi$
$360$	−5.54292	−	26.5117i	−0.292137	−	1.39729i
$361$	−7.09130	−	15.5278i	−0.373226	−	0.817251i
$362$	−19.2945	+	5.55670i	−1.01409	+	0.292054i
$363$	−18.5678	+	20.0934i	−0.974555	+	1.05463i
$364$	−5.10409	−	11.4907i	−0.267527	−	0.602278i
$365$	−2.29166	−	1.98574i	−0.119951	−	0.103938i
$366$	−11.4548	−	27.7682i	−0.598751	−	1.45147i
$367$		−	7.88612i		−	0.411652i	−0.978589	−	0.205826i	$-0.934012\pi$
$367$		−	7.88612i		−	0.411652i	0.978589	−	0.205826i	$-0.0659881\pi$
$368$	−9.59407	+	16.6119i	−0.500126	+	0.865953i
$369$	−22.6853	+	8.65512i	−1.18095	+	0.450568i
$370$	15.2313	−	23.4319i	0.791838	−	1.21817i
$371$	1.00660	−	1.16168i	0.0522601	−	0.0603113i
$372$	−5.07686	+	27.1072i	−0.263223	+	1.40545i
$373$	−3.63454	+	25.2788i	−0.188189	+	1.30888i	0.648503	+	0.761212i	$0.275395\pi$
$373$	−3.63454	+	25.2788i	−0.188189	+	1.30888i	−0.836693	+	0.547673i	$0.815514\pi$
$374$	−3.78961	−	13.1586i	−0.195956	−	0.680416i
$375$	1.02804	+	0.181510i	0.0530879	+	0.00937312i
$376$	20.7576	+	3.31532i	1.07049	+	0.170974i
$377$	11.0533	−	1.58922i	0.569273	−	0.0818490i
$378$	−6.38903	+	4.49336i	−0.328616	+	0.231113i
$379$	−19.7556	+	5.80078i	−1.01478	+	0.297966i	−0.746507	−	0.665377i	$-0.768271\pi$
$379$	−19.7556	+	5.80078i	−1.01478	+	0.297966i	−0.268272	+	0.963343i	$0.586453\pi$
$380$	−2.58664	+	8.48239i	−0.132692	+	0.435137i
$381$	14.9701	−	8.95806i	0.766940	−	0.458935i
$382$	−3.02539	+	20.2934i	−0.154792	+	1.03830i
$383$	−4.31480	−	4.97954i	−0.220476	−	0.254443i	0.634727	−	0.772737i	$-0.281113\pi$
$383$	−4.31480	−	4.97954i	−0.220476	−	0.254443i	−0.855202	+	0.518294i	$0.826567\pi$
$384$	15.7236	+	11.6948i	0.802391	+	0.596799i
$385$	−9.49526	−	14.7749i	−0.483923	−	0.752999i
$386$	−8.95214	+	19.3361i	−0.455652	+	0.984181i
$387$	−2.01967	+	9.63072i	−0.102665	+	0.489557i
$388$	−4.17401	−	14.7816i	−0.211903	−	0.750420i
$389$	−1.11359	+	3.79255i	−0.0564614	+	0.192290i	−0.982894	−	0.184170i	$-0.941040\pi$
$389$	−1.11359	+	3.79255i	−0.0564614	+	0.192290i	0.926433	+	0.376460i	$0.122859\pi$
$390$	28.9643	+	36.0495i	1.46667	+	1.82544i
$391$	−6.36339	+	6.32312i	−0.321810	+	0.319774i
$392$	10.6761	+	12.7159i	0.539225	+	0.642248i
$393$	20.4118	+	25.1363i	1.02964	+	1.26796i
$394$	−7.60693	+	4.83305i	−0.383232	+	0.243485i
$395$	11.8725	+	7.62999i	0.597370	+	0.383907i
$396$	10.9383	−	29.0688i	0.549670	−	1.46076i
$397$	−4.20568	−	6.54417i	−0.211077	−	0.328443i	0.719530	−	0.694461i	$-0.244357\pi$
$397$	−4.20568	−	6.54417i	−0.211077	−	0.328443i	−0.930608	+	0.366018i	$0.880721\pi$
$398$	23.8213	−	3.29883i	1.19406	−	0.165355i
$399$	2.54170	−	0.282887i	0.127244	−	0.0141621i
$400$	−17.6898	+	10.8561i	−0.884488	+	0.542805i
$401$	−10.9377	+	23.9503i	−0.546204	+	1.19602i	0.412328	+	0.911035i	$0.364716\pi$
$401$	−10.9377	+	23.9503i	−0.546204	+	1.19602i	−0.958532	+	0.284985i	$0.908012\pi$
$402$	−7.39846	−	5.15277i	−0.369002	−	0.256997i
$403$	−13.2658	−	45.1793i	−0.660818	−	2.25054i
$404$	−13.1259	+	8.24416i	−0.653038	+	0.410162i
$405$	18.4857	−	21.9903i	0.918563	−	1.09271i
$406$	2.58776	−	1.16559i	0.128429	−	0.0578473i
$407$	29.1514	−	13.3130i	1.44498	−	0.659901i
$408$	5.66509	+	7.20280i	0.280464	+	0.356592i
$409$	−1.99225	+	13.8564i	−0.0985104	+	0.685155i	0.879393	+	0.476097i	$0.157949\pi$
$409$	−1.99225	+	13.8564i	−0.0985104	+	0.685155i	−0.977903	+	0.209058i	$0.932960\pi$
$410$	23.7817	+	27.7352i	1.17449	+	1.36975i
$411$	−34.9001	+	9.04696i	−1.72149	+	0.446253i
$412$	−8.99011	+	7.62795i	−0.442911	+	0.375802i
$413$			1.19941i			0.0590192i
$414$	−20.1424	+	2.87791i	−0.989947	+	0.141441i
$415$	−45.8449			−2.25044
$416$	−32.9820	−	5.61962i	−1.61708	−	0.275524i
$417$	1.19767	+	4.62020i	0.0586501	+	0.226252i
$418$	−7.71975	+	6.61933i	−0.377585	+	0.323762i
$419$	−35.5415	−	5.11010i	−1.73632	−	0.249645i	−0.799801	−	0.600266i	$-0.795061\pi$
$419$	−35.5415	−	5.11010i	−1.73632	−	0.249645i	−0.936517	+	0.350621i	$0.885971\pi$
$420$	9.60958	+	6.76711i	0.468900	+	0.330201i
$421$	10.7379	+	23.5126i	0.523332	+	1.14594i	0.968163	+	0.250322i	$0.0805364\pi$
$421$	10.7379	+	23.5126i	0.523332	+	1.14594i	−0.444831	+	0.895614i	$0.646736\pi$
$422$	0.243934	−	0.109874i	0.0118745	−	0.00534856i
$423$	10.8314	+	19.4881i	0.526641	+	0.947542i
$424$	−1.09108	−	3.94204i	−0.0529875	−	0.191442i
$425$	−9.31271	+	2.73446i	−0.451733	+	0.132641i
$426$	−5.45989	+	7.83943i	−0.264532	+	0.379822i
$427$	11.8567	+	5.41479i	0.573788	+	0.262040i
$428$	35.0966	+	16.4707i	1.69646	+	0.796141i
$429$	5.86575	+	52.7031i	0.283201	+	2.54453i
$430$	14.6668	−	2.03109i	0.707296	−	0.0979478i
$431$	−1.16575	+	0.749184i	−0.0561524	+	0.0360869i	−0.568416	−	0.822741i	$-0.692443\pi$
$431$	−1.16575	+	0.749184i	−0.0561524	+	0.0360869i	0.512263	+	0.858828i	$0.328807\pi$
$432$	0.543563	+	20.7775i	0.0261522	+	0.999658i
$433$	−13.2499	+	20.6173i	−0.636750	+	0.990803i	0.361540	+	0.932356i	$0.382251\pi$
$433$	−13.2499	+	20.6173i	−0.636750	+	0.990803i	−0.998291	+	0.0584463i	$0.981385\pi$
$434$	−6.41770	−	10.1011i	−0.308059	−	0.484867i
$435$	−8.10332	+	6.58023i	−0.388524	+	0.315498i
$436$	1.28100	+	0.842173i	0.0613486	+	0.0403327i
$437$	6.23444	+	2.34789i	0.298234	+	0.112315i
$438$	1.45746	+	1.81398i	0.0696401	+	0.0866751i
$439$	−12.1655	−	3.57210i	−0.580626	−	0.170487i	−0.0217858	−	0.999763i	$-0.506935\pi$
$439$	−12.1655	−	3.57210i	−0.580626	−	0.170487i	−0.558840	+	0.829276i	$0.688753\pi$
$440$	−46.7290	−	0.728017i	−2.22772	−	0.0347069i
$441$	−3.61450	+	17.2356i	−0.172119	+	0.820744i
$442$	−14.1980	−	6.57331i	−0.675328	−	0.312660i
$443$	−8.57219	+	5.50901i	−0.407277	+	0.261741i	−0.728201	−	0.685364i	$-0.759643\pi$
$443$	−8.57219	+	5.50901i	−0.407277	+	0.261741i	0.320924	+	0.947105i	$0.396007\pi$
$444$	−14.7179	+	15.5990i	−0.698478	+	0.740296i
$445$	25.0006	−	21.6632i	1.18514	−	1.02693i
$446$	−2.95060	+	19.7917i	−0.139715	+	0.937165i
$447$	12.1472	+	20.2996i	0.574545	+	0.960138i
$448$	−8.45048	+	0.947377i	−0.399248	+	0.0447594i
$449$	−6.46487	−	22.0173i	−0.305096	−	1.03906i	−0.959217	−	0.282671i	$-0.908779\pi$
$449$	−6.46487	−	22.0173i	−0.305096	−	1.03906i	0.654121	−	0.756390i	$-0.273039\pi$
$450$	−20.6439	−	7.64593i	−0.973162	−	0.360433i
$451$	5.96232	+	41.4689i	0.280755	+	1.95269i
$452$	−0.140737	−	1.05663i	−0.00661971	−	0.0496999i
$453$	0.571234	−	3.23538i	0.0268389	−	0.152011i
$454$	−1.06066	−	3.68292i	−0.0497793	−	0.172848i
$455$	−19.8627	−	2.85583i	−0.931180	−	0.133883i
$456$	3.11793	−	6.04889i	0.146010	−	0.283265i
$457$	5.31811	+	4.60816i	0.248770	+	0.215561i	0.770316	−	0.637663i	$-0.220099\pi$
$457$	5.31811	+	4.60816i	0.248770	+	0.215561i	−0.521545	+	0.853224i	$0.674644\pi$
$458$	1.76930	+	1.15009i	0.0826741	+	0.0537400i
$459$	−2.29784	+	9.44405i	−0.107254	+	0.440811i
$460$	14.3072	+	27.0680i	0.667079	+	1.26205i
$461$	24.6982			1.15031			0.575156	−	0.818044i	$-0.304941\pi$
$461$	24.6982			1.15031			0.575156	+	0.818044i	$0.304941\pi$
$462$	5.13957	+	12.4591i	0.239115	+	0.579651i
$463$	−12.8043	+	14.7770i	−0.595068	+	0.686745i	−0.970774	−	0.239994i	$-0.922855\pi$
$463$	−12.8043	+	14.7770i	−0.595068	+	0.686745i	0.375706	+	0.926739i	$0.377400\pi$
$464$	1.22983	−	7.45146i	0.0570934	−	0.345925i
$465$	32.3266	+	29.8721i	1.49911	+	1.38528i
$466$	−3.38254	−	11.7452i	−0.156693	−	0.544084i
$467$	−26.7932	+	12.2360i	−1.23984	+	0.566217i	−0.923926	−	0.382571i	$-0.875039\pi$
$467$	−26.7932	+	12.2360i	−1.23984	+	0.566217i	−0.315915	+	0.948787i	$0.602312\pi$
$468$	−16.9166	−	31.1953i	−0.781971	−	1.44200i
$469$	3.87257	−	0.556791i	0.178818	−	0.0257102i
$470$	22.1013	−	25.2402i	1.01946	−	1.16424i
$471$	−32.8666	−	10.8026i	−1.51441	−	0.497758i
$472$	2.65775	+	1.76713i	0.122333	+	0.0813387i
$473$	15.4448	+	7.05338i	0.710151	+	0.324315i
$474$	−7.91571	−	7.39126i	−0.363581	−	0.339492i
$475$	4.72011	+	5.44729i	0.216573	+	0.249939i
$476$	−3.92992	−	0.606759i	−0.180128	−	0.0278108i
$477$	2.57382	−	3.49240i	0.117847	−	0.159906i
$478$	−2.38108	−	1.10238i	−0.108908	−	0.0504217i
$479$	−25.8823	−	16.6335i	−1.18259	−	0.760006i	−0.206731	−	0.978398i	$-0.566282\pi$
$479$	−25.8823	−	16.6335i	−1.18259	−	0.760006i	−0.975861	+	0.218392i	$0.929919\pi$
$480$	29.1532	−	11.3234i	1.33065	−	0.516842i
$481$	10.3161	−	35.1334i	0.470374	−	1.60195i
$482$	0.435959	−	1.45671i	0.0198574	−	0.0663515i
$483$	5.53623	−	6.87804i	0.251907	−	0.312962i
$484$	−26.3975	−	17.3546i	−1.19989	−	0.788847i
$485$	−23.5209	−	6.90635i	−1.06803	−	0.313601i
$486$	−16.9769	+	14.0636i	−0.770089	+	0.637937i
$487$	17.7860	+	11.4304i	0.805961	+	0.517960i	0.877556	−	0.479474i	$-0.159173\pi$
$487$	17.7860	+	11.4304i	0.805961	+	0.517960i	−0.0715951	+	0.997434i	$0.522809\pi$
$488$	29.4674	−	18.2953i	1.33393	−	0.828188i
$489$	1.34905	−	42.1992i	0.0610063	−	1.90831i
$490$	26.2485	−	3.63494i	1.18578	−	0.164210i
$491$	−9.25413	−	10.6798i	−0.417633	−	0.481974i	0.507481	−	0.861663i	$-0.330577\pi$
$491$	−9.25413	−	10.6798i	−0.417633	−	0.481974i	−0.925114	+	0.379689i	$0.876031\pi$
$492$	−14.1457	−	24.2063i	−0.637737	−	1.09130i
$493$	1.46712	−	3.21254i	0.0660757	−	0.144686i
$494$	−0.0603341	+	11.6188i	−0.00271456	+	0.522753i
$495$	−30.0021	−	39.4591i	−1.34849	−	1.77355i
$496$	−31.8381	−	0.661406i	−1.42957	−	0.0296980i
$497$	−0.589977	−	4.10338i	−0.0264641	−	0.184062i
$498$	34.6126	+	6.29666i	1.55103	+	0.282160i
$499$	33.3058	−	15.2102i	1.49097	−	0.680904i	0.507447	−	0.861683i	$-0.330589\pi$
$499$	33.3058	−	15.2102i	1.49097	−	0.680904i	0.983524	+	0.180779i	$0.0578620\pi$
$500$	−0.0125189	+	1.20538i	−0.000559864	+	0.0539061i
$501$	−13.4580	−	12.4361i	−0.601259	−	0.555606i
$502$	15.1515	−	12.9918i	0.676246	−	0.579850i
$503$	−9.31266	+	10.7474i	−0.415231	+	0.479202i	−0.924378	−	0.381477i	$-0.875415\pi$
$503$	−9.31266	+	10.7474i	−0.415231	+	0.479202i	0.509147	+	0.860679i	$0.329961\pi$
$504$	−6.32574	−	6.42898i	−0.281771	−	0.286369i
$505$			24.7382i			1.10084i
$506$	−2.79751	+	34.9968i	−0.124364	+	1.55580i
$507$	31.3545	+	21.5964i	1.39250	+	0.959128i
$508$	13.0330	+	15.3604i	0.578246	+	0.681506i
$509$	18.3187	−	21.1409i	0.811961	−	0.937052i	−0.187013	−	0.982358i	$-0.559881\pi$
$509$	18.3187	−	21.1409i	0.811961	−	0.937052i	0.998973	+	0.0453051i	$0.0144260\pi$
$510$	14.5437	−	1.54227i	0.644006	−	0.0682929i
$511$	−0.999475	−	0.143703i	−0.0442142	−	0.00635704i
$512$	−10.3511	+	20.1210i	−0.457458	+	0.889231i
$513$	7.08847	−	1.36124i	0.312963	−	0.0601001i
$514$	−8.67771	+	3.90864i	−0.382757	+	0.172403i
$515$	2.67794	+	18.6255i	0.118004	+	0.820738i
$516$	−11.3523	−	0.480982i	−0.499758	−	0.0211741i
$517$	36.9127	−	10.8386i	1.62342	−	0.476679i
$518$	0.0483256	−	9.30625i	0.00212331	−	0.408893i
$519$	−36.8117	+	22.0280i	−1.61585	+	0.966924i
$520$	−35.5925	+	39.8058i	−1.56084	+	1.74560i
$521$	−0.242262	−	0.279586i	−0.0106137	−	0.0122489i	0.750418	−	0.660964i	$-0.229852\pi$
$521$	−0.242262	−	0.279586i	−0.0106137	−	0.0122489i	−0.761032	+	0.648715i	$0.775307\pi$
$522$	7.02174	−	3.85507i	0.307333	−	0.168732i
$523$	12.1829	−	7.82946i	0.532720	−	0.342358i	−0.246466	−	0.969151i	$-0.579269\pi$
$523$	12.1829	−	7.82946i	0.532720	−	0.342358i	0.779186	+	0.626793i	$0.215633\pi$
$524$	−24.7770	+	28.0012i	−1.08239	+	1.22324i
$525$	8.81195	−	3.68872i	0.384585	−	0.160989i
$526$	6.81882	−	4.33233i	0.297315	−	0.188898i
$527$	−14.2886	−	4.19550i	−0.622419	−	0.182759i
$528$	35.1801	+	6.96774i	1.53102	+	0.303232i
$529$	20.9818	−	9.42155i	0.912251	−	0.409633i
$530$	−6.25395	−	1.87166i	−0.271654	−	0.0812995i
$531$	0.266762	+	3.37468i	0.0115765	+	0.146449i
$532$	0.802494	+	2.84190i	0.0347925	+	0.123212i
$533$	40.2695	+	25.8797i	1.74427	+	1.12097i
$534$	−21.8507	+	12.9218i	−0.945573	+	0.559182i
$535$	52.0530	−	33.4525i	2.25045	−	1.44628i
$536$	4.47179	−	9.40146i	0.193152	−	0.406081i
$537$	−0.306448	−	2.75340i	−0.0132242	−	0.118818i
$538$	4.18215	−	28.0526i	0.180305	−	1.20943i
$539$	27.6407	+	12.6231i	1.19057	+	0.543716i
$540$	28.5428	+	16.9028i	1.22828	+	0.727379i
$541$	0.733265	+	2.49727i	0.0315255	+	0.107366i	0.973753	−	0.227608i	$-0.0730905\pi$
$541$	0.733265	+	2.49727i	0.0315255	+	0.107366i	−0.942227	+	0.334974i	$0.891272\pi$
$542$	−12.0693	+	13.7834i	−0.518420	+	0.592049i
$543$	10.9251	−	22.0312i	0.468841	−	0.945447i
$544$	−7.13457	+	7.81426i	−0.305892	+	0.335033i
$545$	2.22562	−	1.01641i	0.0953351	−	0.0435381i
$546$	14.6040	+	4.88423i	0.624994	+	0.209026i
$547$	2.67534	+	0.384656i	0.114389	+	0.0164467i	0.199272	−	0.979944i	$-0.436142\pi$
$547$	2.67534	+	0.384656i	0.114389	+	0.0164467i	−0.0848823	+	0.996391i	$0.527051\pi$
$548$	−16.9000	−	38.0466i	−0.721931	−	1.62527i
$549$	34.5646	+	12.5981i	1.47518	+	0.537673i
$550$	−20.7021	+	31.8482i	−0.882740	+	1.35801i
$551$	−2.62272			−0.111732
$552$	−7.08418	−	22.4012i	−0.301523	−	0.953459i
$553$	4.69956			0.199846
$554$	9.82050	−	15.1079i	0.417233	−	0.641874i
$555$	8.58891	+	33.1331i	0.364579	+	1.40642i
$556$	−5.03674	+	2.23728i	−0.213605	+	0.0948818i
$557$	−16.8027	−	2.41587i	−0.711954	−	0.102364i	−0.223184	−	0.974776i	$-0.571645\pi$
$557$	−16.8027	−	2.41587i	−0.711954	−	0.102364i	−0.488770	+	0.872413i	$0.662554\pi$
$558$	−20.3035	−	26.9932i	−0.859517	−	1.14271i
$559$	17.6468	−	8.05902i	0.746379	−	0.340860i
$560$	−5.89296	+	12.2253i	−0.249023	+	0.516611i
$561$	15.0250	+	7.45081i	0.634357	+	0.314573i
$562$	−4.17299	+	4.76566i	−0.176027	+	0.201027i
$563$	−10.1306	−	34.5016i	−0.426953	−	1.45407i	−0.839614	−	0.543184i	$-0.817219\pi$
$563$	−10.1306	−	34.5016i	−0.426953	−	1.45407i	0.412661	−	0.910885i	$-0.364600\pi$
$564$	−20.1530	+	16.0207i	−0.848595	+	0.674591i
$565$	−1.54754	−	0.706737i	−0.0651054	−	0.0297326i
$566$	0.706245	−	4.73728i	0.0296857	−	0.199123i
$567$	1.21955	−	9.48829i	0.0512163	−	0.398471i
$568$	−9.96181	−	4.73832i	−0.417988	−	0.198816i
$569$	0.245797	−	0.157964i	0.0103043	−	0.00662220i	−0.535479	−	0.844549i	$-0.679869\pi$
$569$	0.245797	−	0.157964i	0.0103043	−	0.00662220i	0.545783	+	0.837927i	$0.316232\pi$
$570$	−5.52851	−	9.34869i	−0.231564	−	0.391573i
$571$	30.4873	+	19.5930i	1.27585	+	0.819941i	0.990370	−	0.138443i	$-0.0442096\pi$
$571$	30.4873	+	19.5930i	1.27585	+	0.819941i	0.285483	+	0.958384i	$0.407846\pi$
$572$	−58.9277	+	16.6400i	−2.46389	+	0.695752i
$573$	−15.8407	−	19.5073i	−0.661756	−	0.814928i
$574$	11.6553	+	3.48816i	0.486485	+	0.145593i
$575$	24.8156	+	1.85403i	1.03488	+	0.0773182i
$576$	−23.5657	+	4.54504i	−0.981905	+	0.189377i
$577$	11.4767	+	3.36987i	0.477782	+	0.140290i	0.511752	−	0.859133i	$-0.328997\pi$
$577$	11.4767	+	3.36987i	0.477782	+	0.140290i	−0.0339696	+	0.999423i	$0.510815\pi$
$578$	16.1158	−	10.2391i	0.670329	−	0.425892i
$579$	−10.0769	−	24.0727i	−0.418783	−	1.00043i
$580$	−9.02688	−	7.98747i	−0.374821	−	0.331662i
$581$	−12.8428	+	8.25356i	−0.532809	+	0.342416i
$582$	16.8096	+	8.44478i	0.696778	+	0.350047i
$583$	−4.90214	−	5.65737i	−0.203026	−	0.234304i
$584$	−1.79098	+	2.00299i	−0.0741114	+	0.0828843i
$585$	−56.5213	−	3.61752i	−2.33687	−	0.149566i
$586$	−0.0477332	+	9.19218i	−0.00197184	+	0.379725i
$587$	32.5422	−	9.55524i	1.34316	−	0.394387i	0.470363	−	0.882473i	$-0.344123\pi$
$587$	32.5422	−	9.55524i	1.34316	−	0.394387i	0.872795	+	0.488086i	$0.162305\pi$
$588$	−20.3167	−	0.860791i	−0.837846	−	0.0354984i
$589$	1.57386	+	10.9464i	0.0648496	+	0.451039i
$590$	4.64441	−	2.09195i	0.191207	−	0.0861242i
$591$	1.91915	−	10.8698i	0.0789435	−	0.447124i
$592$	−20.5503	−	13.8183i	−0.844612	−	0.567927i
$593$	−31.4674	−	4.52433i	−1.29221	−	0.185792i	−0.538293	−	0.842758i	$-0.680930\pi$
$593$	−31.4674	−	4.52433i	−1.29221	−	0.185792i	−0.753920	+	0.656966i	$0.771840\pi$
$594$	17.2318	+	33.9121i	0.707031	+	1.39143i
$595$	−4.15605	+	4.79633i	−0.170381	+	0.196630i
$596$	−20.8288	+	17.6729i	−0.853182	+	0.723911i
$597$	−16.7073	+	24.2564i	−0.683786	+	0.992748i
$598$	28.1265	+	28.6012i	1.15018	+	1.16959i
$599$			9.46996i			0.386932i	0.981107	+	0.193466i	$0.0619730\pi$
$599$			9.46996i			0.386932i	−0.981107	+	0.193466i	$0.938027\pi$
$600$	4.80916	−	24.9609i	0.196333	−	1.01902i
$601$	23.6893	−	27.3389i	0.966307	−	1.11518i	−0.0269957	−	0.999636i	$-0.508594\pi$
$601$	23.6893	−	27.3389i	0.966307	−	1.11518i	0.993303	−	0.115542i	$-0.0368605\pi$
$602$	3.74303	−	3.20948i	0.152555	−	0.130809i
$603$	10.7721	−	2.42790i	0.438673	−	0.0988716i
$604$	3.79347	+	0.0393987i	0.154354	+	0.00160311i
$605$	−45.8633	+	20.9451i	−1.86461	+	0.851538i
$606$	3.39773	−	18.6772i	0.138023	−	0.758710i
$607$	−6.50166	−	45.2200i	−0.263894	−	1.83542i	−0.502826	−	0.864388i	$-0.667706\pi$
$607$	−6.50166	−	45.2200i	−0.263894	−	1.83542i	0.238931	−	0.971036i	$-0.423203\pi$
$608$	7.47963	+	2.40883i	0.303339	+	0.0976909i
$609$	−1.08537	+	3.30222i	−0.0439816	+	0.133813i
$610$	0.287455	−	55.3563i	0.0116387	−	2.24131i
$611$	18.2600	−	39.9839i	0.738721	−	1.61757i
$612$	−11.1922	−	0.833130i	−0.452419	−	0.0336773i
$613$	−5.65182	−	6.52254i	−0.228275	−	0.263443i	0.630045	−	0.776559i	$-0.283037\pi$
$613$	−5.65182	−	6.52254i	−0.228275	−	0.263443i	−0.858319	+	0.513116i	$0.828491\pi$
$614$	−34.1845	+	4.73394i	−1.37957	+	0.191046i
$615$	−44.7233	−	1.42975i	−1.80342	−	0.0576529i
$616$	−13.2215	+	8.20879i	−0.532711	+	0.330742i
$617$	31.1290	+	20.0054i	1.25321	+	0.805388i	0.987339	−	0.158622i	$-0.0507050\pi$
$617$	31.1290	+	20.0054i	1.25321	+	0.805388i	0.265868	+	0.964009i	$0.414341\pi$
$618$	0.536328	−	14.4300i	0.0215743	−	0.580458i
$619$	11.8319	+	3.47417i	0.475566	+	0.139639i	0.510727	−	0.859743i	$-0.329376\pi$
$619$	11.8319	+	3.47417i	0.475566	+	0.139639i	−0.0351611	+	0.999382i	$0.511194\pi$
$620$	−27.9203	+	42.4686i	−1.12131	+	1.70558i
$621$	14.0471	−	20.5835i	0.563690	−	0.825987i
$622$	−10.8474	+	36.2456i	−0.434942	+	1.45332i
$623$	3.10350	−	10.5696i	0.124339	−	0.423460i
$624$	32.3394	−	25.1646i	1.29461	−	1.00739i
$625$	−20.2071	−	12.9863i	−0.808284	−	0.519453i
$626$	15.0879	+	6.98534i	0.603035	+	0.279190i
$627$	0.397951	−	12.4482i	0.0158926	−	0.497132i
$628$	6.09561	−	39.4807i	0.243241	−	1.57545i
$629$	−7.58362	−	8.75196i	−0.302379	−	0.348964i
$630$	−14.0587	+	3.09203i	−0.560111	+	0.123190i
$631$	−7.18424	−	3.28093i	−0.286000	−	0.130612i	0.267250	−	0.963627i	$-0.413885\pi$
$631$	−7.18424	−	3.28093i	−0.286000	−	0.130612i	−0.553250	+	0.833015i	$0.686612\pi$
$632$	6.92400	−	10.4136i	0.275422	−	0.414232i
$633$	−0.102312	+	0.311281i	−0.00406654	+	0.0123723i
$634$	−17.4285	+	19.9038i	−0.692174	+	0.790480i
$635$	31.8233	−	4.57550i	1.26287	−	0.181573i
$636$	4.46463	+	2.27205i	0.177034	+	0.0900927i
$637$	31.5816	−	14.4228i	1.25131	−	0.571454i
$638$	−3.82513	−	13.2820i	−0.151438	−	0.525838i
$639$	−2.57261	−	11.4141i	−0.101771	−	0.451536i
$640$	18.4074	+	31.0699i	0.727615	+	1.22815i
$641$	3.47068	−	4.00538i	0.137084	−	0.158203i	−0.683057	−	0.730365i	$-0.739350\pi$
$641$	3.47068	−	4.00538i	0.137084	−	0.158203i	0.820140	+	0.572162i	$0.193895\pi$
$642$	−43.8943	+	18.1071i	−1.73237	+	0.714629i
$643$	−10.0786			−0.397462			−0.198731	−	0.980054i	$-0.563682\pi$
$643$	−10.0786			−0.397462			−0.198731	+	0.980054i	$0.563682\pi$
$644$	8.88108	+	5.00694i	0.349964	+	0.197301i
$645$	−10.2867	+	14.9347i	−0.405039	+	0.588052i
$646$	3.08095	+	2.00269i	0.121218	+	0.0787946i
$647$	9.57802	+	8.29940i	0.376551	+	0.326283i	0.822489	−	0.568780i	$-0.192585\pi$
$647$	9.57802	+	8.29940i	0.376551	+	0.326283i	−0.445939	+	0.895064i	$0.647130\pi$
$648$	−19.2281	−	16.6818i	−0.755350	−	0.655322i
$649$	5.78167	+	0.831279i	0.226951	+	0.0326306i
$650$	12.0111	+	41.7060i	0.471114	+	1.63584i
$651$	14.4338	+	2.54840i	0.565704	+	0.0998798i
$652$	48.3256	−	6.43665i	1.89258	−	0.252079i
$653$	−4.06994	−	28.3070i	−0.159269	−	1.10774i	−0.899985	−	0.435922i	$-0.856423\pi$
$653$	−4.06994	−	28.3070i	−0.159269	−	1.10774i	0.740716	−	0.671819i	$-0.234487\pi$
$654$	−1.81993	+	0.461699i	−0.0711649	+	0.0180538i
$655$	16.8119	+	57.2562i	0.656897	+	2.23718i
$656$	24.9015	−	20.6876i	0.972240	−	0.807714i
$657$	−2.84410	−	0.182030i	−0.110959	−	0.00710168i
$658$	1.64731	−	11.0496i	0.0642186	−	0.430759i
$659$	−5.83484	+	5.05592i	−0.227293	+	0.196951i	−0.761061	−	0.648681i	$-0.775321\pi$
$659$	−5.83484	+	5.05592i	−0.227293	+	0.196951i	0.533768	+	0.845631i	$0.320776\pi$
$660$	39.2805	−	41.6322i	1.52899	−	1.62053i
$661$	−38.5401	+	24.7682i	−1.49904	+	0.963372i	−0.504017	+	0.863694i	$0.668145\pi$
$661$	−38.5401	+	24.7682i	−1.49904	+	0.963372i	−0.995020	+	0.0996781i	$0.968219\pi$
$662$	−2.43579	−	1.12771i	−0.0946698	−	0.0438298i
$663$	17.6759	−	7.39921i	0.686475	−	0.287362i
$664$	−0.632814	+	40.6183i	−0.0245580	+	1.57629i
$665$	4.52212	+	1.32781i	0.175360	+	0.0514904i
$666$	−1.93384	−	26.1950i	−0.0749349	−	1.01503i
$667$	−6.42304	+	6.38239i	−0.248701	+	0.247127i
$668$	11.6236	−	17.6803i	0.449732	−	0.684070i
$669$	−15.4491	−	19.0250i	−0.597298	−	0.735550i
$670$	−8.91035	−	14.0244i	−0.344237	−	0.541808i
$671$	34.3192	−	53.4017i	1.32488	−	2.06155i
$672$	6.12826	−	8.42061i	0.236403	−	0.324832i
$673$	−4.79105	+	3.07902i	−0.184681	+	0.118687i	−0.629715	−	0.776827i	$-0.716828\pi$
$673$	−4.79105	+	3.07902i	−0.184681	+	0.118687i	0.445033	+	0.895514i	$0.353192\pi$
$674$	−47.6177	+	6.59420i	−1.83417	+	0.253999i
$675$	23.9730	−	12.3385i	0.922722	−	0.474910i
$676$	−18.6769	+	39.7976i	−0.718341	+	1.53068i
$677$	−19.7048	−	8.99887i	−0.757316	−	0.345855i	−0.000946951	−	1.00000i	$-0.500301\pi$
$677$	−19.7048	−	8.99887i	−0.757316	−	0.345855i	−0.756369	+	0.654145i	$0.773029\pi$
$678$	1.07131	+	0.746132i	0.0411436	+	0.0286550i
$679$	−7.83240	+	2.29980i	−0.300580	+	0.0882583i
$680$	4.50484	+	16.2759i	0.172753	+	0.624151i
$681$	4.20530	+	2.08538i	0.161148	+	0.0799120i
$682$	−53.1394	+	23.9353i	−2.03481	+	0.916528i
$683$	4.20547	+	9.20870i	0.160918	+	0.352361i	0.972866	−	0.231368i	$-0.0743202\pi$
$683$	4.20547	+	9.20870i	0.160918	+	0.352361i	−0.811948	+	0.583729i	$0.801593\pi$
$684$	2.88998	+	7.81753i	0.110501	+	0.298911i
$685$	−65.7668	−	9.45585i	−2.51282	−	0.361289i
$686$	14.6867	−	12.5932i	0.560742	−	0.480811i
$687$	−2.50182	+	0.648533i	−0.0954504	+	0.0247431i
$688$	−1.59708	−	13.0227i	−0.0608881	−	0.496486i
$689$	−8.55305			−0.325845
$690$	−36.2894	−	9.44128i	−1.38151	−	0.359423i
$691$		−	34.1044i		−	1.29739i	−0.761047	−	0.648696i	$-0.775314\pi$
$691$		−	34.1044i		−	1.29739i	0.761047	−	0.648696i	$-0.224686\pi$
$692$	−32.0484	−	37.7714i	−1.21830	−	1.43585i
$693$	−15.5086	−	5.65255i	−0.589122	−	0.214723i
$694$	−6.86582	−	8.00722i	−0.260623	−	0.303950i
$695$	−1.25180	+	8.70645i	−0.0474834	+	0.330254i
$696$	5.71819	+	7.27031i	0.216747	+	0.275580i
$697$	13.7710	−	6.28899i	0.521613	−	0.238212i
$698$	34.7172	−	15.6374i	1.31406	−	0.591886i
$699$	13.4111	+	6.65046i	0.507253	+	0.251543i
$700$	5.86695	+	9.34104i	0.221750	+	0.353058i
$701$	−4.53047	−	15.4294i	−0.171113	−	0.582759i	−0.999737	−	0.0229520i	$-0.992694\pi$
$701$	−4.53047	−	15.4294i	−0.171113	−	0.582759i	0.828623	−	0.559807i	$-0.189125\pi$
$702$	42.1764	+	10.4942i	1.59185	+	0.396080i
$703$	−3.57255	+	7.82279i	−0.134741	+	0.295042i
$704$	−1.29004	+	41.3915i	−0.0486201	+	1.56000i
$705$	4.54505	+	40.8368i	0.171177	+	1.53800i
$706$	−44.2653	+	6.12996i	−1.66595	+	0.230704i
$707$	4.45368	+	6.93006i	0.167498	+	0.260632i
$708$	−3.79382	+	0.941515i	−0.142581	+	0.0353843i
$709$	3.11500	+	2.00189i	0.116986	+	0.0751825i	0.597825	−	0.801626i	$-0.296032\pi$
$709$	3.11500	+	2.00189i	0.116986	+	0.0751825i	−0.480839	+	0.876809i	$0.659668\pi$
$710$	−14.8603	+	9.44143i	−0.557696	+	0.354331i
$711$	13.2228	−	1.04523i	0.495892	−	0.0391993i
$712$	−18.8483	−	22.4494i	−0.706371	−	0.841328i
$713$	30.4925	+	22.9778i	1.14195	+	0.860525i
$714$	3.79655	−	3.05038i	0.142082	−	0.114158i
$715$	−27.5326	+	93.7676i	−1.02966	+	3.50671i
$716$	3.07860	−	0.869334i	0.115053	−	0.0324885i
$717$	2.96434	−	1.24089i	0.110705	−	0.0463418i
$718$	−4.48229	+	9.68149i	−0.167278	+	0.361310i
$719$	13.7112	+	21.3351i	0.511343	+	0.795665i	0.996911	−	0.0785337i	$-0.0250238\pi$
$719$	13.7112	+	21.3351i	0.511343	+	0.795665i	−0.485569	+	0.874198i	$0.661387\pi$
$720$	−13.8615	+	35.7078i	−0.516588	+	1.33075i
$721$	4.10338	+	4.73556i	0.152818	+	0.176361i
$722$	−3.55969	+	23.8773i	−0.132478	+	0.888621i
$723$	0.956257	+	1.59803i	0.0355636	+	0.0594313i
$724$	27.1608	+	8.28247i	1.00942	+	0.307815i
$725$	−9.40000	+	2.76009i	−0.349107	+	0.102507i
$726$	37.5033	−	9.51422i	1.39188	−	0.353106i
$727$	−10.9683	+	1.57700i	−0.406792	+	0.0584879i	−0.342674	−	0.939454i	$-0.611333\pi$
$727$	−10.9683	+	1.57700i	−0.406792	+	0.0584879i	−0.0641182	+	0.997942i	$0.520423\pi$
$728$	−2.80442	+	17.5588i	−0.103939	+	0.650774i
$729$	1.32105	−	26.9677i	0.0489276	−	0.998802i
$730$	1.18678	+	4.12084i	0.0439247	+	0.152519i
$731$	0.873170	−	6.07303i	0.0322954	−	0.224619i
$732$	−7.82006	+	41.7542i	−0.289038	+	1.54328i
$733$	25.7265	−	29.6900i	0.950230	−	1.09662i	−0.0449922	−	0.998987i	$-0.514326\pi$
$733$	25.7265	−	29.6900i	0.950230	−	1.09662i	0.995222	−	0.0976365i	$-0.0311283\pi$
$734$	−6.07822	+	9.35078i	−0.224351	+	0.345144i
$735$	−18.4096	+	26.7278i	−0.679049	+	0.985871i
$736$	24.1795	−	12.3025i	0.891269	−	0.453476i
$737$		−	19.0533i		−	0.701838i
$738$	33.5695	+	7.22207i	1.23571	+	0.265848i
$739$	32.1912	+	27.8938i	1.18417	+	1.02609i	0.999059	+	0.0433727i	$0.0138103\pi$
$739$	32.1912	+	27.8938i	1.18417	+	1.02609i	0.185112	+	0.982717i	$0.440735\pi$
$740$	−36.1203	+	16.0443i	−1.32781	+	0.589802i
$741$	−10.4512	−	9.65768i	−0.383935	−	0.354784i
$742$	−2.08891	+	0.601596i	−0.0766864	+	0.0220853i
$743$	6.04961	+	13.2468i	0.221939	+	0.485978i	0.987546	−	0.157330i	$-0.0502887\pi$
$743$	6.04961	+	13.2468i	0.221939	+	0.485978i	−0.765607	+	0.643308i	$0.777561\pi$
$744$	26.9126	−	28.2288i	0.986665	−	1.03492i
$745$	6.20443	+	43.1527i	0.227313	+	1.58099i
$746$	23.7932	−	27.1724i	0.871129	−	0.994851i
$747$	−34.2990	+	26.0787i	−1.25494	+	0.954171i
$748$	−5.64856	+	18.5234i	−0.206532	+	0.677281i
$749$	8.55939	−	18.7425i	0.312753	−	0.684835i
$750$	−1.07908	−	1.00758i	−0.0394024	−	0.0367918i
$751$	−15.0056	+	13.0024i	−0.547561	+	0.474465i	−0.884160	−	0.467183i	$-0.845269\pi$
$751$	−15.0056	+	13.0024i	−0.547561	+	0.474465i	0.336599	+	0.941648i	$0.390723\pi$
$752$	−22.0576	−	19.9300i	−0.804357	−	0.726771i
$753$	−0.781059	+	24.4320i	−0.0284634	+	0.890351i
$754$	−14.3310	−	6.63492i	−0.521906	−	0.241630i
$755$	3.27342	−	5.09354i	0.119132	−	0.185373i
$756$	11.0389	−	0.403549i	0.401481	−	0.0146769i
$757$	30.7079	+	9.01665i	1.11610	+	0.327716i	0.787229	−	0.616660i	$-0.211515\pi$
$757$	30.7079	+	9.01665i	1.11610	+	0.327716i	0.328868	+	0.944376i	$0.393333\pi$
$758$	27.8957	+	8.34851i	1.01322	+	0.303232i
$759$	−29.3181	−	31.4540i	−1.06418	−	1.14171i
$760$	9.60484	−	8.06413i	0.348404	−	0.292517i
$761$	−8.37394	+	28.5190i	−0.303555	+	1.03381i	0.656575	+	0.754261i	$0.272004\pi$
$761$	−8.37394	+	28.5190i	−0.303555	+	1.03381i	−0.960130	+	0.279553i	$0.909814\pi$
$762$	−24.6548	−	0.916362i	−0.893150	−	0.0331963i
$763$	0.440490	−	0.685415i	0.0159468	−	0.0248137i
$764$	19.2284	−	21.7306i	0.695659	−	0.786185i
$765$	−10.6268	+	14.4194i	−0.384211	+	0.521334i
$766$	1.27819	+	9.23000i	0.0461829	+	0.333493i
$767$	5.04382	−	4.37049i	0.182122	−	0.157809i
$768$	−9.63008	−	25.9858i	−0.347496	−	0.937682i
$769$	11.5041	+	5.25375i	0.414849	+	0.189455i	0.611895	−	0.790939i	$-0.290408\pi$
$769$	11.5041	+	5.25375i	0.414849	+	0.189455i	−0.197046	+	0.980394i	$0.563135\pi$
$770$	−0.128976	+	24.8375i	−0.00464798	+	0.895080i
$771$	3.63965	−	11.0735i	0.131079	−	0.398803i
$772$	25.5181	−	16.0275i	0.918415	−	0.576841i
$773$	2.15890	−	0.310402i	0.0776501	−	0.0111644i	−0.103380	−	0.994642i	$-0.532966\pi$
$773$	2.15890	−	0.310402i	0.0776501	−	0.0111644i	0.181030	+	0.983478i	$0.442057\pi$
$774$	9.81764	−	9.86273i	0.352888	−	0.354509i
$775$	17.1606	+	37.5764i	0.616426	+	1.34979i
$776$	−6.44365	+	20.7440i	−0.231313	+	0.744666i
$777$	8.37109	+	7.73549i	0.300311	+	0.277509i
$778$	4.24352	−	3.63863i	0.152138	−	0.130451i
$779$	−8.49660	−	7.36234i	−0.304422	−	0.263783i
$780$	−6.55867	−	65.0690i	−0.234838	−	2.32984i
$781$	−20.1889			−0.722417
$782$	12.4188	−	2.59291i	0.444095	−	0.0927224i
$783$	−2.31938	+	9.53258i	−0.0828878	+	0.340666i
$784$	−2.85822	−	23.3061i	−0.102079	−	0.832362i
$785$	−48.1848	−	41.7524i	−1.71979	−	1.49021i
$786$	−4.82894	−	45.5372i	−0.172243	−	1.62426i
$787$	1.48514	−	10.3294i	0.0529396	−	0.368203i	−0.946080	−	0.323933i	$-0.894995\pi$
$787$	1.48514	−	10.3294i	0.0529396	−	0.368203i	0.999020	−	0.0442700i	$-0.0140962\pi$
$788$	12.7448	+	0.132366i	0.454015	+	0.00471535i
$789$	−1.72032	+	9.74364i	−0.0612451	+	0.346883i
$790$	−8.19672	−	18.1978i	−0.291626	−	0.647449i
$791$	−0.560756	+	0.0806246i	−0.0199382	+	0.00286668i
$792$	−35.3746	+	26.0370i	−1.25698	+	0.925184i
$793$	−20.4338	−	69.5912i	−0.725626	−	2.47126i
$794$	−0.0571268	+	11.0011i	−0.00202735	+	0.390415i
$795$	6.86063	−	4.10539i	0.243322	−	0.145603i
$796$	−30.7881	−	14.4488i	−1.09126	−	0.512123i
$797$	21.1861	−	18.3579i	0.750450	−	0.650269i	−0.193220	−	0.981155i	$-0.561893\pi$
$797$	21.1861	−	18.3579i	0.750450	−	0.650269i	0.943670	+	0.330887i	$0.107348\pi$
$798$	−3.23180	−	1.62359i	−0.114404	−	0.0574745i
$799$	−7.51583	−	11.6949i	−0.265891	−	0.413734i
$800$	29.3425	+	0.762015i	1.03741	+	0.0269413i
$801$	6.38128	−	30.4289i	0.225471	−	1.07515i
$802$	31.4288	−	19.9682i	1.10979	−	0.705103i
$803$	−1.38542	+	4.71830i	−0.0488903	+	0.166505i
$804$	4.80106	+	11.8121i	0.169320	+	0.416581i
$805$	14.3059	−	7.75277i	0.504217	−	0.273249i
$806$	−19.0923	+	63.7949i	−0.672496	+	2.24708i
$807$	21.8975	+	26.9659i	0.770827	+	0.949246i
$808$	21.9179	+	0.341471i	0.771069	+	0.0120129i
$809$	−10.9123	+	16.9799i	−0.383658	+	0.596983i	−0.978347	−	0.206973i	$-0.933639\pi$
$809$	−10.9123	+	16.9799i	−0.383658	+	0.596983i	0.594689	+	0.803956i	$0.297275\pi$
$810$	−38.8680	+	11.8266i	−1.36568	+	0.415544i
$811$	−23.3574	−	36.3448i	−0.820189	−	1.27624i	−0.958283	−	0.285820i	$-0.907734\pi$
$811$	−23.3574	−	36.3448i	−0.820189	−	1.27624i	0.138094	−	0.990419i	$-0.455902\pi$
$812$	−3.96676	−	0.612446i	−0.139206	−	0.0214927i
$813$	−2.48201	−	22.3006i	−0.0870478	−	0.782115i
$814$	−44.8266	−	6.68286i	−1.57117	−	0.234234i
$815$	32.3229	−	70.7772i	1.13222	−	2.47922i
$816$	−1.16569	−	12.9069i	−0.0408073	−	0.451832i
$817$	−4.37179	+	1.28367i	−0.152949	+	0.0449100i
$818$	13.0421	−	14.8944i	0.456005	−	0.520769i
$819$	−16.4849	+	9.16227i	−0.576030	+	0.320156i
$820$	−6.82165	−	51.2161i	−0.238222	−	1.78854i
$821$	3.39054	+	7.42424i	0.118331	+	0.259108i	0.959524	−	0.281626i	$-0.0908738\pi$
$821$	3.39054	+	7.42424i	0.118331	+	0.259108i	−0.841194	+	0.540734i	$0.818147\pi$
$822$	48.3549	+	16.1720i	1.68657	+	0.564063i
$823$	4.80208	−	33.3992i	0.167390	−	1.16422i	−0.716863	−	0.697214i	$-0.754423\pi$
$823$	4.80208	−	33.3992i	0.167390	−	1.16422i	0.884253	−	0.467008i	$-0.154668\pi$
$824$	16.5390	−	2.11555i	0.576165	−	0.0736985i
$825$	−11.6739	−	45.0339i	−0.406432	−	1.56788i
$826$	0.924446	−	1.42217i	0.0321656	−	0.0494837i
$827$		−	34.0967i		−	1.18566i	−0.805328	−	0.592830i	$-0.798011\pi$
$827$		−	34.0967i		−	1.18566i	0.805328	−	0.592830i	$-0.201989\pi$
$828$	26.1015	+	12.1124i	0.907092	+	0.420933i
$829$		−	6.53521i		−	0.226977i	−0.993539	−	0.113489i	$-0.963797\pi$
$829$		−	6.53521i		−	0.226977i	0.993539	−	0.113489i	$-0.0362025\pi$
$830$	54.3595	+	35.3349i	1.88684	+	1.22649i
$831$	5.53777	+	21.3628i	0.192103	+	0.741068i
$832$	34.7763	+	32.0842i	1.20565	+	1.11232i
$833$	1.56267	−	10.8686i	0.0541433	−	0.376575i
$834$	2.14091	−	6.40139i	0.0741335	−	0.221662i
$835$	−14.0284	−	30.7179i	−0.485473	−	1.06304i
$836$	14.2553	−	1.89872i	0.493031	−	0.0656686i
$837$	41.1779	+	3.96000i	1.42332	+	0.136878i
$838$	38.2039	+	33.4528i	1.31973	+	1.15561i
$839$	1.39600	−	0.409903i	0.0481954	−	0.0141514i	−0.257546	−	0.966266i	$-0.582914\pi$
$839$	1.39600	−	0.409903i	0.0481954	−	0.0141514i	0.305741	+	0.952115i	$0.401096\pi$
$840$	−6.17859	−	15.4305i	−0.213182	−	0.532403i
$841$	−10.5662	+	23.1367i	−0.364351	+	0.797816i
$842$	5.39019	−	36.1558i	0.185758	−	1.24601i
$843$	−0.858162	−	7.71049i	−0.0295567	−	0.265563i
$844$	−0.373924	−	0.0577318i	−0.0128710	−	0.00198721i
$845$	37.9332	+	59.0253i	1.30494	+	2.03053i
$846$	2.17733	−	31.4558i	0.0748580	−	1.08147i
$847$	−9.07717	+	14.1243i	−0.311895	+	0.485318i
$848$	−1.74460	+	5.51512i	−0.0599098	+	0.189390i
$849$	3.69785	+	4.55377i	0.126910	+	0.156285i
$850$	13.1499	+	3.93545i	0.451038	+	0.134985i
$851$	10.2876	+	27.8518i	0.352655	+	0.954748i
$852$	12.5162	−	5.08721i	0.428797	−	0.174285i
$853$	−8.04230	+	27.3896i	−0.275363	+	0.937801i	0.699432	+	0.714699i	$0.253436\pi$
$853$	−8.04230	+	27.3896i	−0.275363	+	0.937801i	−0.974795	+	0.223102i	$0.928382\pi$
$854$	−9.88540	−	15.5590i	−0.338271	−	0.532419i
$855$	13.0188	+	2.73019i	0.445234	+	0.0933705i
$856$	−28.9201	−	46.5804i	−0.988470	−	1.59208i
$857$	−17.7706	−	27.6516i	−0.607032	−	0.944560i	−0.999691	−	0.0248757i	$-0.992081\pi$
$857$	−17.7706	−	27.6516i	−0.607032	−	0.944560i	0.392659	−	0.919684i	$-0.371555\pi$
$858$	33.6657	−	67.0125i	1.14933	−	2.28777i
$859$	−1.05412	+	0.913400i	−0.0359661	+	0.0311648i	−0.672658	−	0.739953i	$-0.734848\pi$
$859$	−1.05412	+	0.913400i	−0.0359661	+	0.0311648i	0.636692	+	0.771118i	$0.280302\pi$
$860$	−18.9563	−	8.89611i	−0.646403	−	0.303355i
$861$	−12.7860	+	7.65112i	−0.435746	+	0.260749i
$862$	1.95970	+	0.0101763i	0.0667475	+	0.000346607i
$863$	10.5466	+	35.9184i	0.359010	+	1.22268i	0.919027	+	0.394194i	$0.128976\pi$
$863$	10.5466	+	35.9184i	0.359010	+	1.22268i	−0.560017	+	0.828481i	$0.689205\pi$
$864$	15.3697	−	25.0554i	0.522889	−	0.852401i
$865$	−78.2540	+	11.2512i	−2.66072	+	0.382553i
$866$	31.6015	−	14.2341i	1.07386	−	0.483693i
$867$	−4.06586	+	23.0284i	−0.138084	+	0.782086i
$868$	−0.175766	+	16.9235i	−0.00596590	+	0.574422i
$869$	3.25713	−	22.6539i	0.110491	−	0.768480i
$870$	14.6800	−	1.55673i	0.497699	−	0.0527780i
$871$	−16.4525	−	14.2562i	−0.557473	−	0.483053i
$872$	−0.869808	−	1.98591i	−0.0294554	−	0.0672515i
$873$	−21.5259	+	8.21277i	−0.728541	+	0.277960i
$874$	−5.58270	−	7.58915i	−0.188838	−	0.256707i
$875$	0.640649			0.0216579
$876$	−0.330026	−	3.27421i	−0.0111506	−	0.110625i
$877$	−18.1874	−	15.7595i	−0.614146	−	0.532160i	0.291295	−	0.956633i	$-0.405914\pi$
$877$	−18.1874	−	15.7595i	−0.614146	−	0.532160i	−0.905441	+	0.424473i	$0.860459\pi$
$878$	11.6717	+	13.6120i	0.393901	+	0.459384i
$879$	−8.26848	−	7.64067i	−0.278889	−	0.257713i
$880$	54.8467	+	36.8796i	1.84888	+	1.24321i
$881$	20.9261	+	45.8218i	0.705019	+	1.54378i	0.833777	+	0.552101i	$0.186174\pi$
$881$	20.9261	+	45.8218i	0.705019	+	1.54378i	−0.128758	+	0.991676i	$0.541099\pi$
$882$	17.5702	−	17.6509i	0.591618	−	0.594335i
$883$	−55.8516	+	8.03024i	−1.87955	+	0.270239i	−0.984456	−	0.175629i	$-0.943804\pi$
$883$	−55.8516	+	8.03024i	−1.87955	+	0.270239i	−0.895099	+	0.445868i	$0.852895\pi$
$884$	11.7685	+	18.7372i	0.395818	+	0.630200i
$885$	−1.94798	+	5.92668i	−0.0654807	+	0.199223i
$886$	14.4103	+	0.0748301i	0.484124	+	0.00251397i
$887$	30.7284	+	14.0332i	1.03176	+	0.471189i	0.858027	−	0.513604i	$-0.171690\pi$
$887$	30.7284	+	14.0332i	1.03176	+	0.471189i	0.173732	+	0.984793i	$0.444417\pi$
$888$	29.4743	−	7.15237i	0.989091	−	0.240018i
$889$	8.09110	−	7.01098i	0.271367	−	0.235141i
$890$	−46.3408	+	6.41737i	−1.55335	+	0.215111i
$891$	−44.8924	−	12.4548i	−1.50395	−	0.417252i
$892$	18.7531	−	21.1934i	0.627899	−	0.709607i
$893$	−5.58143	+	8.68487i	−0.186775	+	0.290628i
$894$	1.24260	−	33.4322i	0.0415587	−	1.11814i
$895$	1.43841	−	4.89876i	0.0480806	−	0.163748i
$896$	10.7501	+	5.38987i	0.359137	+	0.180063i
$897$	−49.0971	+	1.78144i	−1.63930	+	0.0594806i
$898$	−9.30426	+	31.0893i	−0.310487	+	1.03746i
$899$	−14.4225	−	4.23482i	−0.481017	−	0.141239i
$900$	18.5849	+	24.9772i	0.619496	+	0.832574i
$901$	−1.46244	+	2.27560i	−0.0487210	+	0.0758114i
$902$	24.8924	−	53.7662i	0.828827	−	1.79022i
$903$	−0.192953	+	6.03567i	−0.00642106	+	0.200855i
$904$	−0.647525	+	1.36135i	−0.0215364	+	0.0452779i
$905$	34.2499	−	29.6777i	1.13851	−	0.986522i
$906$	−3.17099	+	3.39600i	−0.105349	+	0.112824i
$907$	−2.36570	+	5.18017i	−0.0785519	+	0.172005i	−0.944833	−	0.327552i	$-0.893776\pi$
$907$	−2.36570	+	5.18017i	−0.0785519	+	0.172005i	0.866281	+	0.499557i	$0.166504\pi$
$908$	−1.58096	+	5.18444i	−0.0524658	+	0.172052i
$909$	14.0723	+	18.5080i	0.466748	+	0.613871i
$910$	21.3506	+	18.6954i	0.707767	+	0.619747i
$911$	1.01264	+	7.04306i	0.0335502	+	0.233347i	0.999696	−	0.0246492i	$-0.00784688\pi$
$911$	1.01264	+	7.04306i	0.0335502	+	0.233347i	−0.966146	+	0.257996i	$0.916938\pi$
$912$	−8.35918	+	4.76918i	−0.276800	+	0.157923i
$913$	30.8847	+	67.6281i	1.02213	+	2.23816i
$914$	−2.75408	−	9.56295i	−0.0910967	−	0.316314i
$915$	49.7937	+	46.0129i	1.64613	+	1.52114i
$916$	−1.21148	−	2.72738i	−0.0400284	−	0.0901150i
$917$	15.0176	+	13.0128i	0.495925	+	0.429721i
$918$	10.0036	−	9.42700i	0.330168	−	0.311137i
$919$			25.2882i			0.834182i	0.908865	+	0.417091i	$0.136950\pi$
$919$			25.2882i			0.834182i	−0.908865	+	0.417091i	$0.863050\pi$
$920$	3.89814	−	43.1225i	0.128518	−	1.42171i
$921$	23.9756	−	34.8088i	0.790024	−	1.14699i
$922$	−29.2853	−	19.0361i	−0.964461	−	0.626922i
$923$	−15.1059	+	17.4332i	−0.497217	+	0.573819i
$924$	3.50873	−	18.7344i	0.115429	−	0.616317i
$925$	−4.57173	+	31.7971i	−0.150318	+	1.04548i
$926$	26.5718	−	7.65253i	0.873203	−	0.251478i
$927$	12.5986	+	12.4114i	0.413792	+	0.407644i
$928$	−7.20145	+	7.88750i	−0.236399	+	0.258920i
$929$	39.6267	−	5.69746i	1.30011	−	0.186928i	0.542733	−	0.839906i	$-0.317390\pi$
$929$	39.6267	−	5.69746i	1.30011	−	0.186928i	0.757377	+	0.652978i	$0.226481\pi$
$930$	−15.3066	−	60.3357i	−0.501923	−	1.97849i
$931$	−7.82398	+	2.29733i	−0.256421	+	0.0752919i
$932$	−5.04180	+	16.5336i	−0.165150	+	0.541577i
$933$	−23.7933	−	39.7617i	−0.778958	−	1.30174i
$934$	41.2003	+	6.14224i	1.34812	+	0.200980i
$935$	20.2399	+	23.3581i	0.661916	+	0.763892i
$936$	−3.98528	+	50.0276i	−0.130263	+	1.63520i
$937$	−0.293317	−	0.456409i	−0.00958223	−	0.0149102i	0.836429	−	0.548075i	$-0.184639\pi$
$937$	−0.293317	−	0.456409i	−0.00958223	−	0.0149102i	−0.846012	+	0.533164i	$0.821003\pi$
$938$	−5.02095	−	2.32457i	−0.163940	−	0.0759001i
$939$	−18.7839	+	7.86302i	−0.612989	+	0.256600i
$940$	−45.6599	+	12.8934i	−1.48926	+	0.420537i
$941$	−12.6834	+	43.1956i	−0.413466	+	1.40813i	0.445123	+	0.895470i	$0.353160\pi$
$941$	−12.6834	+	43.1956i	−0.413466	+	1.40813i	−0.858588	+	0.512665i	$0.828658\pi$
$942$	30.6447	+	38.1409i	0.998459	+	1.24270i
$943$	−38.7245	+	2.64612i	−1.26104	+	0.0861695i
$944$	−1.78935	−	4.14379i	−0.0582382	−	0.134869i
$945$	8.82519	−	15.2619i	0.287083	−	0.496470i
$946$	−12.8769	−	20.2674i	−0.418663	−	0.658950i
$947$	−15.5453	−	9.99034i	−0.505153	−	0.324642i	0.263121	−	0.964763i	$-0.415248\pi$
$947$	−15.5453	−	9.99034i	−0.505153	−	0.324642i	−0.768275	+	0.640120i	$0.778884\pi$
$948$	3.68906	+	14.8650i	0.119815	+	0.482794i
$949$	3.03764	+	4.72666i	0.0986061	+	0.153434i
$950$	−1.39826	−	10.0970i	−0.0453654	−	0.327590i
$951$	−3.58412	−	32.2029i	−0.116223	−	1.04425i
$952$	4.19215	+	3.74843i	0.135868	+	0.121487i
$953$	0.943180	−	2.06528i	0.0305526	−	0.0669009i	−0.893740	−	0.448584i	$-0.851928\pi$
$953$	0.943180	−	2.06528i	0.0305526	−	0.0669009i	0.924293	+	0.381684i	$0.124656\pi$
$954$	−5.74360	+	2.15726i	−0.185956	+	0.0698438i
$955$	−13.0470	−	44.4342i	−0.422193	−	1.43786i
$956$	1.97364	+	3.14233i	0.0638322	+	0.101630i
$957$	15.1659	+	7.52064i	0.490242	+	0.243108i
$958$	17.8690	+	39.6716i	0.577322	+	1.28173i
$959$	−20.1260	+	9.19124i	−0.649903	+	0.296801i
$960$	−43.2952	−	9.04326i	−1.39735	−	0.291870i
$961$	−4.60836	+	32.0518i	−0.148657	+	1.03393i
$962$	−39.3111	+	33.7075i	−1.26744	+	1.08677i
$963$	19.9143	−	54.6378i	0.641730	−	1.76068i
$964$	−1.63969	+	1.39125i	−0.0528109	+	0.0448091i
$965$		−	48.0936i		−	1.54819i
$966$	−11.8657	+	3.88842i	−0.381772	+	0.125108i
$967$	34.7425			1.11724			0.558622	−	0.829422i	$-0.311330\pi$
$967$	34.7425			1.11724			0.558622	+	0.829422i	$0.311330\pi$
$968$	17.9241	+	40.9237i	0.576103	+	1.31534i
$969$	−4.35650	+	1.12931i	−0.139951	+	0.0362787i
$970$	22.5662	+	26.3177i	0.724558	+	0.845011i
$971$	9.80923	+	1.41035i	0.314793	+	0.0452604i	0.297901	−	0.954597i	$-0.403714\pi$
$971$	9.80923	+	1.41035i	0.314793	+	0.0452604i	0.0168925	+	0.999857i	$0.494623\pi$
$972$	30.9695	−	3.59060i	0.993346	−	0.115169i
$973$	1.21677	+	2.66435i	0.0390078	+	0.0854152i
$974$	−12.2794	−	27.2618i	−0.393457	−	0.873526i
$975$	−47.6215	−	23.6152i	−1.52511	−	0.756291i
$976$	−49.0413	−	1.01879i	−1.56977	−	0.0326106i
$977$	−27.5401	+	8.08649i	−0.881084	+	0.258710i	−0.690823	−	0.723024i	$-0.742752\pi$
$977$	−27.5401	+	8.08649i	−0.881084	+	0.258710i	−0.190261	+	0.981734i	$0.560933\pi$
$978$	−34.1246	+	48.9969i	−1.09118	+	1.56675i
$979$	−48.7988	−	22.2857i	−1.55962	−	0.712253i
$980$	−33.9251	−	15.9209i	−1.08370	−	0.508576i
$981$	1.08693	−	2.02647i	0.0347029	−	0.0647001i
$982$	2.74139	+	19.7960i	0.0874811	+	0.631714i
$983$	−22.4414	+	14.4222i	−0.715771	+	0.459998i	−0.847163	−	0.531332i	$-0.821692\pi$
$983$	−22.4414	+	14.4222i	−0.715771	+	0.459998i	0.131393	+	0.991330i	$0.458055\pi$
$984$	−1.88408	+	39.6048i	−0.0600622	+	1.26255i
$985$	10.9976	−	17.1126i	0.350412	−	0.545252i
$986$	−4.21566	+	2.67841i	−0.134254	+	0.0852980i
$987$	8.62518	+	10.6216i	0.274542	+	0.338089i
$988$	9.02669	−	13.7302i	0.287177	−	0.436815i
$989$	−7.58269	+	13.7825i	−0.241115	+	0.438257i
$990$	5.16123	+	69.9118i	0.164035	+	2.22194i
$991$	29.2747	+	8.59581i	0.929940	+	0.273055i	0.711412	−	0.702776i	$-0.248056\pi$
$991$	29.2747	+	8.59581i	0.929940	+	0.273055i	0.218528	+	0.975831i	$0.429874\pi$
$992$	37.2415	+	25.3234i	1.18242	+	0.804020i
$993$	3.03247	−	1.26940i	0.0962324	−	0.0402833i
$994$	−2.46313	+	5.32021i	−0.0781256	+	0.168747i
$995$	−45.6630	+	29.3459i	−1.44762	+	0.930326i
$996$	−36.1879	−	34.1438i	−1.14666	−	1.08189i
$997$	−3.49002	+	3.02412i	−0.110530	+	0.0957748i	−0.708372	−	0.705839i	$-0.750570\pi$
$997$	−3.49002	+	3.02412i	−0.110530	+	0.0957748i	0.597842	+	0.801614i	$0.296025\pi$
$998$	−51.2148	−	7.63522i	−1.62118	−	0.241689i
$999$	25.2735	+	19.9029i	0.799618	+	0.629699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bf.a.5.17	yes	920
3.2	odd	2	inner	552.2.bf.a.5.76	yes	920
8.5	even	2	inner	552.2.bf.a.5.92	yes	920
23.14	odd	22	inner	552.2.bf.a.221.1	yes	920
24.5	odd	2	inner	552.2.bf.a.5.1	✓	920
69.14	even	22	inner	552.2.bf.a.221.92	yes	920
184.37	odd	22	inner	552.2.bf.a.221.76	yes	920
552.221	even	22	inner	552.2.bf.a.221.17	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bf.a.5.1	✓	920	24.5	odd	2	inner
552.2.bf.a.5.17	yes	920	1.1	even	1	trivial
552.2.bf.a.5.76	yes	920	3.2	odd	2	inner
552.2.bf.a.5.92	yes	920	8.5	even	2	inner
552.2.bf.a.221.1	yes	920	23.14	odd	22	inner
552.2.bf.a.221.17	yes	920	552.221	even	22	inner
552.2.bf.a.221.76	yes	920	184.37	odd	22	inner
552.2.bf.a.221.92	yes	920	69.14	even	22	inner

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bf (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18573 - 0.770749i) q^{2} +(1.67663 - 0.434625i) q^{3} +(0.811892 + 1.82779i) q^{4} +(3.15950 + 0.454268i) q^{5} +(-2.32301 - 0.776919i) q^{6} +(0.966873 - 0.441556i) q^{7} +(0.446090 - 2.79303i) q^{8} +(2.62220 - 1.45741i) q^{9} +O(q^{10})\)	\(q+(-1.18573 - 0.770749i) q^{2} +(1.67663 - 0.434625i) q^{3} +(0.811892 + 1.82779i) q^{4} +(3.15950 + 0.454268i) q^{5} +(-2.32301 - 0.776919i) q^{6} +(0.966873 - 0.441556i) q^{7} +(0.446090 - 2.79303i) q^{8} +(2.62220 - 1.45741i) q^{9} +(-3.39618 - 2.97382i) q^{10} +(-1.45838 - 4.96677i) q^{11} +(2.15565 + 2.71167i) q^{12} +(-5.38000 - 2.45696i) q^{13} +(-1.48678 - 0.221652i) q^{14} +(5.49477 - 0.611557i) q^{15} +(-2.68166 + 2.96794i) q^{16} +(-1.57359 + 1.01129i) q^{17} +(-4.23251 - 0.292969i) q^{18} +(1.16859 + 0.751005i) q^{19} +(1.73487 + 6.14374i) q^{20} +(1.42918 - 1.16055i) q^{21} +(-2.09890 + 7.01327i) q^{22} +(4.68944 - 1.00455i) q^{23} +(-0.465989 - 4.87677i) q^{24} +(4.97864 + 1.46186i) q^{25} +(4.48550 + 7.05992i) q^{26} +(3.76305 - 3.58322i) q^{27} +(1.59207 + 1.40875i) q^{28} +(-1.58834 + 1.02077i) q^{29} +(-6.98664 - 3.50995i) q^{30} +(5.21351 + 6.01671i) q^{31} +(5.46726 - 1.45227i) q^{32} +(-4.60384 - 7.69361i) q^{33} +(2.64530 + 0.0137365i) q^{34} +(3.25542 - 0.955879i) q^{35} +(4.79280 + 3.60959i) q^{36} +(0.881073 + 6.12800i) q^{37} +(-0.806787 - 1.79117i) q^{38} +(-10.0882 - 1.78115i) q^{39} +(2.67821 - 8.62194i) q^{40} +(-8.01106 - 1.15182i) q^{41} +(-2.58911 + 0.274560i) q^{42} +(-2.14799 + 2.47891i) q^{43} +(7.89419 - 6.69809i) q^{44} +(8.94692 - 3.41352i) q^{45} +(-6.33465 - 2.42327i) q^{46} +7.43194i q^{47} +(-3.20623 + 6.14167i) q^{48} +(-3.84415 + 4.43639i) q^{49} +(-4.77657 - 5.57065i) q^{50} +(-2.19881 + 2.37948i) q^{51} +(0.122848 - 11.8283i) q^{52} +(1.31544 - 0.600740i) q^{53} +(-7.22371 + 1.34835i) q^{54} +(-2.35150 - 16.3550i) q^{55} +(-0.801966 - 2.89748i) q^{56} +(2.28570 + 0.751264i) q^{57} +(2.67009 + 0.0138653i) q^{58} +(-0.468756 + 1.02643i) q^{59} +(5.57896 + 9.54679i) q^{60} +(8.03054 + 9.26774i) q^{61} +(-1.54442 - 11.1525i) q^{62} +(1.89181 - 2.56698i) q^{63} +(-7.60201 - 2.49188i) q^{64} +(-15.8820 - 10.2068i) q^{65} +(-0.470948 + 12.6709i) q^{66} +(3.53167 + 1.03699i) q^{67} +(-3.12601 - 2.05515i) q^{68} +(7.42588 - 3.72241i) q^{69} +(-4.59678 - 1.37571i) q^{70} +(1.09880 - 3.74217i) q^{71} +(-2.90086 - 7.97402i) q^{72} +(-0.799168 - 0.513594i) q^{73} +(3.67844 - 7.94521i) q^{74} +(8.98272 + 0.287166i) q^{75} +(-0.423917 + 2.74567i) q^{76} +(-3.60317 - 4.15828i) q^{77} +(10.5890 + 9.88739i) q^{78} +(4.02179 + 1.83669i) q^{79} +(-9.82097 + 8.15903i) q^{80} +(4.75190 - 7.64326i) q^{81} +(8.61116 + 7.54025i) q^{82} +(-14.2163 + 2.04399i) q^{83} +(3.28160 + 1.67000i) q^{84} +(-5.43117 + 2.48033i) q^{85} +(4.45755 - 1.28375i) q^{86} +(-2.21942 + 2.40178i) q^{87} +(-14.5229 + 1.85766i) q^{88} +(6.78673 - 7.83230i) q^{89} +(-13.2396 - 2.84833i) q^{90} -6.28667 q^{91} +(5.64343 + 7.75575i) q^{92} +(11.3562 + 7.82190i) q^{93} +(5.72816 - 8.81225i) q^{94} +(3.35100 + 2.90366i) q^{95} +(8.53539 - 4.81114i) q^{96} +(-7.60162 - 1.09295i) q^{97} +(7.97746 - 2.29746i) q^{98} +(-11.0628 - 10.8984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) \) 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9	\( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) \) 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9 - 22 * q^10 - 12 * q^12 - 22 * q^15 - 30 * q^16 - 10 * q^18 - 14 * q^24 + 40 * q^25 - 22 * q^28 - 11 * q^30 - 20 * q^31 - 22 * q^33 - 18 * q^36 - 42 * q^39 - 176 * q^40 - 11 * q^42 + 90 * q^46 - 64 * q^48 + 32 * q^49 - 90 * q^52 + 21 * q^54 - 76 * q^55 - 22 * q^57 + 76 * q^58 - 11 * q^60 - 22 * q^63 - 28 * q^64 - 44 * q^66 - 116 * q^70 - 79 * q^72 - 36 * q^73 - 22 * q^76 - 134 * q^78 - 44 * q^79 - 34 * q^81 - 40 * q^82 - 165 * q^84 - 18 * q^87 - 22 * q^88 - 198 * q^90 + 88 * q^94 - 231 * q^96 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more