LMFDB - Embedded newform 363.2.e.m.130.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, not 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			130.1
Root			$1.40126 - 1.01807i$ of defining polynomial
Character	$\chi$	$=$	363.130
Dual form			363.2.e.m.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.535233 + 1.64728i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.927051 - 2.85317i) q^{5} +(0.535233 + 1.64728i) q^{6} +(-2.80252 - 2.03615i) q^{7} +(-1.40126 + 1.01807i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.535233 + 1.64728i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.927051 - 2.85317i) q^{5} +(0.535233 + 1.64728i) q^{6} +(-2.80252 - 2.03615i) q^{7} +(-1.40126 + 1.01807i) q^{8} +(0.309017 - 0.951057i) q^{9} +5.19615 q^{10} -1.00000 q^{12} +(0.535233 - 1.64728i) q^{13} +(4.85410 - 3.52671i) q^{14} +(-2.42705 - 1.76336i) q^{15} +(-1.54508 - 4.75528i) q^{16} +(-0.535233 - 1.64728i) q^{17} +(1.40126 + 1.01807i) q^{18} +(5.60503 - 4.07230i) q^{19} +(-0.927051 + 2.85317i) q^{20} -3.46410 q^{21} -6.00000 q^{23} +(-0.535233 + 1.64728i) q^{24} +(-3.23607 + 2.35114i) q^{25} +(2.42705 + 1.76336i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.07047 + 3.29456i) q^{28} +(-1.40126 - 1.01807i) q^{29} +(4.20378 - 3.05422i) q^{30} +(1.23607 - 3.80423i) q^{31} +5.19615 q^{32} +3.00000 q^{34} +(-3.21140 + 9.88367i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(8.89919 + 6.46564i) q^{37} +(3.70820 + 11.4127i) q^{38} +(-0.535233 - 1.64728i) q^{39} +(4.20378 + 3.05422i) q^{40} +(-1.40126 + 1.01807i) q^{41} +(1.85410 - 5.70634i) q^{42} -3.46410 q^{43} -3.00000 q^{45} +(3.21140 - 9.88367i) q^{46} +(-4.04508 - 2.93893i) q^{48} +(1.54508 + 4.75528i) q^{49} +(-2.14093 - 6.58911i) q^{50} +(-1.40126 - 1.01807i) q^{51} +(-1.40126 + 1.01807i) q^{52} +(-2.78115 + 8.55951i) q^{53} +1.73205 q^{54} +6.00000 q^{56} +(2.14093 - 6.58911i) q^{57} +(2.42705 - 1.76336i) q^{58} +(4.85410 + 3.52671i) q^{59} +(0.927051 + 2.85317i) q^{60} +(5.60503 + 4.07230i) q^{62} +(-2.80252 + 2.03615i) q^{63} +(0.309017 - 0.951057i) q^{64} -5.19615 q^{65} -2.00000 q^{67} +(-0.535233 + 1.64728i) q^{68} +(-4.85410 + 3.52671i) q^{69} +(-14.5623 - 10.5801i) q^{70} +(-1.85410 - 5.70634i) q^{71} +(0.535233 + 1.64728i) q^{72} +(5.60503 + 4.07230i) q^{73} +(-15.4138 + 11.1988i) q^{74} +(-1.23607 + 3.80423i) q^{75} -6.92820 q^{76} +3.00000 q^{78} +(-12.1353 + 8.81678i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.927051 - 2.85317i) q^{82} +(2.80252 + 2.03615i) q^{84} +(-4.20378 + 3.05422i) q^{85} +(1.85410 - 5.70634i) q^{86} -1.73205 q^{87} +9.00000 q^{89} +(1.60570 - 4.94183i) q^{90} +(-4.85410 + 3.52671i) q^{91} +(4.85410 + 3.52671i) q^{92} +(-1.23607 - 3.80423i) q^{93} +(-16.8151 - 12.2169i) q^{95} +(4.20378 - 3.05422i) q^{96} +(-2.16312 + 6.65740i) q^{97} -8.66025 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 2 * q^4 + 6 * q^5 - 2 * q^9	$ 8 q + 2 q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{9} - 8 q^{12} + 12 q^{14} - 6 q^{15} + 10 q^{16} + 6 q^{20} - 48 q^{23} - 8 q^{25} + 6 q^{26} + 2 q^{27} - 8 q^{31} + 24 q^{34} - 2 q^{36} + 22 q^{37} - 24 q^{38} - 12 q^{42} - 24 q^{45} - 10 q^{48} - 10 q^{49} + 18 q^{53} + 48 q^{56} + 6 q^{58} + 12 q^{59} - 6 q^{60} - 2 q^{64} - 16 q^{67} - 12 q^{69} - 36 q^{70} + 12 q^{71} + 8 q^{75} + 24 q^{78} - 30 q^{80} - 2 q^{81} + 6 q^{82} - 12 q^{86} + 72 q^{89} - 12 q^{91} + 12 q^{92} + 8 q^{93} + 14 q^{97}+O(q^{100}) $ 8 * q + 2 * q^3 - 2 * q^4 + 6 * q^5 - 2 * q^9 - 8 * q^12 + 12 * q^14 - 6 * q^15 + 10 * q^16 + 6 * q^20 - 48 * q^23 - 8 * q^25 + 6 * q^26 + 2 * q^27 - 8 * q^31 + 24 * q^34 - 2 * q^36 + 22 * q^37 - 24 * q^38 - 12 * q^42 - 24 * q^45 - 10 * q^48 - 10 * q^49 + 18 * q^53 + 48 * q^56 + 6 * q^58 + 12 * q^59 - 6 * q^60 - 2 * q^64 - 16 * q^67 - 12 * q^69 - 36 * q^70 + 12 * q^71 + 8 * q^75 + 24 * q^78 - 30 * q^80 - 2 * q^81 + 6 * q^82 - 12 * q^86 + 72 * q^89 - 12 * q^91 + 12 * q^92 + 8 * q^93 + 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.535233	+	1.64728i	−0.378467	+	1.16480i	0.562643	+	0.826700i	$0.309785\pi$
$2$	−0.535233	+	1.64728i	−0.378467	+	1.16480i	−0.941110	+	0.338101i	$0.890215\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.927051	−	2.85317i	−0.414590	−	1.27598i	−0.912617	−	0.408815i	$-0.865942\pi$
$5$	−0.927051	−	2.85317i	−0.414590	−	1.27598i	0.498027	−	0.867161i	$-0.334058\pi$
$6$	0.535233	+	1.64728i	0.218508	+	0.672499i
$7$	−2.80252	−	2.03615i	−1.05925	−	0.769592i	−0.0853021	−	0.996355i	$-0.527186\pi$
$7$	−2.80252	−	2.03615i	−1.05925	−	0.769592i	−0.973950	+	0.226764i	$0.927186\pi$
$8$	−1.40126	+	1.01807i	−0.495420	+	0.359943i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	5.19615			1.64317
$11$		0			0
$11$		0			0
$12$	−1.00000			−0.288675
$13$	0.535233	−	1.64728i	0.148447	−	0.456873i	−0.848991	−	0.528407i	$-0.822790\pi$
$13$	0.535233	−	1.64728i	0.148447	−	0.456873i	0.997438	+	0.0715342i	$0.0227895\pi$
$14$	4.85410	−	3.52671i	1.29731	−	0.942553i
$15$	−2.42705	−	1.76336i	−0.626662	−	0.455296i
$16$	−1.54508	−	4.75528i	−0.386271	−	1.18882i
$17$	−0.535233	−	1.64728i	−0.129813	−	0.399524i	0.864934	−	0.501885i	$-0.167360\pi$
$17$	−0.535233	−	1.64728i	−0.129813	−	0.399524i	−0.994747	+	0.102362i	$0.967360\pi$
$18$	1.40126	+	1.01807i	0.330280	+	0.239962i
$19$	5.60503	−	4.07230i	1.28588	−	0.934249i	0.286169	−	0.958179i	$-0.407618\pi$
$19$	5.60503	−	4.07230i	1.28588	−	0.934249i	0.999714	+	0.0239303i	$0.00761799\pi$
$20$	−0.927051	+	2.85317i	−0.207295	+	0.637988i
$21$	−3.46410			−0.755929
$22$		0			0
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	−0.535233	+	1.64728i	−0.109254	+	0.336249i
$25$	−3.23607	+	2.35114i	−0.647214	+	0.470228i
$26$	2.42705	+	1.76336i	0.475984	+	0.345823i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	1.07047	+	3.29456i	0.202299	+	0.622613i
$29$	−1.40126	−	1.01807i	−0.260207	−	0.189052i	0.450031	−	0.893013i	$-0.351413\pi$
$29$	−1.40126	−	1.01807i	−0.260207	−	0.189052i	−0.710238	+	0.703961i	$0.751413\pi$
$30$	4.20378	−	3.05422i	0.767501	−	0.557622i
$31$	1.23607	−	3.80423i	0.222004	−	0.683259i	−0.776578	−	0.630022i	$-0.783046\pi$
$31$	1.23607	−	3.80423i	0.222004	−	0.683259i	0.998582	−	0.0532375i	$-0.0169540\pi$
$32$	5.19615			0.918559
$33$		0			0
$34$	3.00000			0.514496
$35$	−3.21140	+	9.88367i	−0.542825	+	1.67065i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	8.89919	+	6.46564i	1.46302	+	1.06294i	0.982564	+	0.185924i	$0.0595278\pi$
$37$	8.89919	+	6.46564i	1.46302	+	1.06294i	0.480453	+	0.877020i	$0.340472\pi$
$38$	3.70820	+	11.4127i	0.601550	+	1.85138i
$39$	−0.535233	−	1.64728i	−0.0857059	−	0.263776i
$40$	4.20378	+	3.05422i	0.664675	+	0.482915i
$41$	−1.40126	+	1.01807i	−0.218840	+	0.158996i	−0.691804	−	0.722085i	$-0.743184\pi$
$41$	−1.40126	+	1.01807i	−0.218840	+	0.158996i	0.472964	+	0.881082i	$0.343184\pi$
$42$	1.85410	−	5.70634i	0.286094	−	0.880507i
$43$	−3.46410			−0.528271			−0.264135	−	0.964486i	$-0.585087\pi$
$43$	−3.46410			−0.528271			−0.264135	+	0.964486i	$0.585087\pi$
$44$		0			0
$45$	−3.00000			−0.447214
$46$	3.21140	−	9.88367i	0.473495	−	1.45727i
$47$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$47$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$48$	−4.04508	−	2.93893i	−0.583858	−	0.424197i
$49$	1.54508	+	4.75528i	0.220726	+	0.679326i
$50$	−2.14093	−	6.58911i	−0.302774	−	0.931841i
$51$	−1.40126	−	1.01807i	−0.196215	−	0.142559i
$52$	−1.40126	+	1.01807i	−0.194320	+	0.141181i
$53$	−2.78115	+	8.55951i	−0.382021	+	1.17574i	0.556598	+	0.830782i	$0.312106\pi$
$53$	−2.78115	+	8.55951i	−0.382021	+	1.17574i	−0.938619	+	0.344957i	$0.887894\pi$
$54$	1.73205			0.235702
$55$		0			0
$56$	6.00000			0.801784
$57$	2.14093	−	6.58911i	0.283573	−	0.872749i
$58$	2.42705	−	1.76336i	0.318687	−	0.231540i
$59$	4.85410	+	3.52671i	0.631950	+	0.459139i	0.857075	−	0.515191i	$-0.172279\pi$
$59$	4.85410	+	3.52671i	0.631950	+	0.459139i	−0.225125	+	0.974330i	$0.572279\pi$
$60$	0.927051	+	2.85317i	0.119682	+	0.368343i
$61$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$61$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$62$	5.60503	+	4.07230i	0.711840	+	0.517182i
$63$	−2.80252	+	2.03615i	−0.353084	+	0.256531i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−5.19615			−0.644503
$66$		0			0
$67$	−2.00000			−0.244339			−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000			−0.244339			−0.122169	+	0.992509i	$0.538985\pi$
$68$	−0.535233	+	1.64728i	−0.0649066	+	0.199762i
$69$	−4.85410	+	3.52671i	−0.584365	+	0.424566i
$70$	−14.5623	−	10.5801i	−1.74053	−	1.26457i
$71$	−1.85410	−	5.70634i	−0.220041	−	0.677218i	−0.998757	−	0.0498409i	$-0.984129\pi$
$71$	−1.85410	−	5.70634i	−0.220041	−	0.677218i	0.778716	−	0.627377i	$-0.215871\pi$
$72$	0.535233	+	1.64728i	0.0630778	+	0.194134i
$73$	5.60503	+	4.07230i	0.656020	+	0.476626i	0.865316	−	0.501226i	$-0.167117\pi$
$73$	5.60503	+	4.07230i	0.656020	+	0.476626i	−0.209297	+	0.977852i	$0.567117\pi$
$74$	−15.4138	+	11.1988i	−1.79182	+	1.30184i
$75$	−1.23607	+	3.80423i	−0.142729	+	0.439274i
$76$	−6.92820			−0.794719
$77$		0			0
$78$	3.00000			0.339683
$79$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$79$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$80$	−12.1353	+	8.81678i	−1.35676	+	0.985746i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.927051	−	2.85317i	−0.102376	−	0.315080i
$83$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$83$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$84$	2.80252	+	2.03615i	0.305780	+	0.222162i
$85$	−4.20378	+	3.05422i	−0.455963	+	0.331277i
$86$	1.85410	−	5.70634i	0.199933	−	0.615330i
$87$	−1.73205			−0.185695
$88$		0			0
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$	1.60570	−	4.94183i	0.169256	−	0.520915i
$91$	−4.85410	+	3.52671i	−0.508848	+	0.369700i
$92$	4.85410	+	3.52671i	0.506075	+	0.367685i
$93$	−1.23607	−	3.80423i	−0.128174	−	0.394480i
$94$		0			0
$95$	−16.8151	−	12.2169i	−1.72519	−	1.25343i
$96$	4.20378	−	3.05422i	0.429046	−	0.311720i
$97$	−2.16312	+	6.65740i	−0.219631	+	0.675956i	0.779161	+	0.626824i	$0.215646\pi$
$97$	−2.16312	+	6.65740i	−0.219631	+	0.675956i	−0.998792	+	0.0491321i	$0.984354\pi$
$98$	−8.66025			−0.874818
$99$		0			0
$100$	4.00000			0.400000
$101$	4.28187	−	13.1782i	0.426061	−	1.31128i	−0.475913	−	0.879493i	$-0.657882\pi$
$101$	4.28187	−	13.1782i	0.426061	−	1.31128i	0.901974	−	0.431790i	$-0.142118\pi$
$102$	2.42705	−	1.76336i	0.240314	−	0.174598i
$103$	−11.3262	−	8.22899i	−1.11601	−	0.810827i	−0.132408	−	0.991195i	$-0.542271\pi$
$103$	−11.3262	−	8.22899i	−1.11601	−	0.810827i	−0.983599	+	0.180368i	$0.942271\pi$
$104$	0.927051	+	2.85317i	0.0909048	+	0.279776i
$105$	3.21140	+	9.88367i	0.313400	+	0.964547i
$106$	−12.6113	−	9.16267i	−1.22492	−	0.889957i
$107$	2.80252	−	2.03615i	0.270930	−	0.196842i	−0.444022	−	0.896016i	$-0.646449\pi$
$107$	2.80252	−	2.03615i	0.270930	−	0.196842i	0.714951	+	0.699174i	$0.246449\pi$
$108$	−0.309017	+	0.951057i	−0.0297352	+	0.0915155i
$109$	−15.5885			−1.49310			−0.746552	−	0.665327i	$-0.768292\pi$
$109$	−15.5885			−1.49310			−0.746552	+	0.665327i	$0.768292\pi$
$110$		0			0
$111$	11.0000			1.04407
$112$	−5.35233	+	16.4728i	−0.505748	+	1.55653i
$113$	16.9894	−	12.3435i	1.59822	−	1.16118i	0.707417	−	0.706796i	$-0.249860\pi$
$113$	16.9894	−	12.3435i	1.59822	−	1.16118i	0.890807	−	0.454382i	$-0.150140\pi$
$114$	9.70820	+	7.05342i	0.909257	+	0.660614i
$115$	5.56231	+	17.1190i	0.518688	+	1.59636i
$116$	0.535233	+	1.64728i	0.0496951	+	0.152946i
$117$	−1.40126	−	1.01807i	−0.129546	−	0.0941210i
$118$	−8.40755	+	6.10844i	−0.773978	+	0.562328i
$119$	−1.85410	+	5.70634i	−0.169965	+	0.523099i
$120$	5.19615			0.474342
$121$		0			0
$122$		0			0
$123$	−0.535233	+	1.64728i	−0.0482603	+	0.148530i
$124$	−3.23607	+	2.35114i	−0.290607	+	0.211139i
$125$	−2.42705	−	1.76336i	−0.217082	−	0.157719i
$126$	−1.85410	−	5.70634i	−0.165177	−	0.508361i
$127$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$127$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$128$	9.80881	+	7.12652i	0.866984	+	0.629901i
$129$	−2.80252	+	2.03615i	−0.246748	+	0.179273i
$130$	2.78115	−	8.55951i	0.243923	−	0.750719i
$131$	17.3205			1.51330			0.756650	−	0.653820i	$-0.226835\pi$
$131$	17.3205			1.51330			0.756650	+	0.653820i	$0.226835\pi$
$132$		0			0
$133$	−24.0000			−2.08106
$134$	1.07047	−	3.29456i	0.0924742	−	0.284606i
$135$	−2.42705	+	1.76336i	−0.208887	+	0.151765i
$136$	2.42705	+	1.76336i	0.208118	+	0.151207i
$137$	−1.85410	−	5.70634i	−0.158407	−	0.487525i	0.840083	−	0.542457i	$-0.182506\pi$
$137$	−1.85410	−	5.70634i	−0.158407	−	0.487525i	−0.998490	+	0.0549317i	$0.982506\pi$
$138$	−3.21140	−	9.88367i	−0.273372	−	0.841354i
$139$	8.40755	+	6.10844i	0.713119	+	0.518111i	0.884178	−	0.467149i	$-0.154719\pi$
$139$	8.40755	+	6.10844i	0.713119	+	0.518111i	−0.171059	+	0.985261i	$0.554719\pi$
$140$	8.40755	−	6.10844i	0.710568	−	0.516258i
$141$		0			0
$142$	10.3923			0.872103
$143$		0			0
$144$	−5.00000			−0.416667
$145$	−1.60570	+	4.94183i	−0.133346	+	0.410397i
$146$	−9.70820	+	7.05342i	−0.803457	+	0.583745i
$147$	4.04508	+	2.93893i	0.333633	+	0.242399i
$148$	−3.39919	−	10.4616i	−0.279411	−	0.859940i
$149$	3.74663	+	11.5309i	0.306936	+	0.944652i	0.978948	+	0.204111i	$0.0654305\pi$
$149$	3.74663	+	11.5309i	0.306936	+	0.944652i	−0.672012	+	0.740541i	$0.734570\pi$
$150$	−5.60503	−	4.07230i	−0.457649	−	0.332502i
$151$	11.2101	−	8.14459i	0.912262	−	0.662797i	−0.0293236	−	0.999570i	$-0.509335\pi$
$151$	11.2101	−	8.14459i	0.912262	−	0.662797i	0.941586	+	0.336773i	$0.109335\pi$
$152$	−3.70820	+	11.4127i	−0.300775	+	0.925690i
$153$	−1.73205			−0.140028
$154$		0			0
$155$	−12.0000			−0.963863
$156$	−0.535233	+	1.64728i	−0.0428529	+	0.131888i
$157$	11.3262	−	8.22899i	0.903932	−	0.656745i	−0.0355408	−	0.999368i	$-0.511315\pi$
$157$	11.3262	−	8.22899i	0.903932	−	0.656745i	0.939473	+	0.342623i	$0.111315\pi$
$158$		0			0
$159$	2.78115	+	8.55951i	0.220560	+	0.678813i
$160$	−4.81710	−	14.8255i	−0.380825	−	1.17206i
$161$	16.8151	+	12.2169i	1.32522	+	0.962826i
$162$	1.40126	−	1.01807i	0.110093	−	0.0799874i
$163$	0.618034	−	1.90211i	0.0484082	−	0.148985i	−0.923931	−	0.382560i	$-0.875042\pi$
$163$	0.618034	−	1.90211i	0.0484082	−	0.148985i	0.972339	+	0.233575i	$0.0750425\pi$
$164$	1.73205			0.135250
$165$		0			0
$166$		0			0
$167$	1.07047	−	3.29456i	0.0828352	−	0.254940i	−0.901058	−	0.433699i	$-0.857208\pi$
$167$	1.07047	−	3.29456i	0.0828352	−	0.254940i	0.983893	+	0.178759i	$0.0572081\pi$
$168$	4.85410	−	3.52671i	0.374502	−	0.272092i
$169$	8.09017	+	5.87785i	0.622321	+	0.452143i
$170$	−2.78115	−	8.55951i	−0.213305	−	0.656484i
$171$	−2.14093	−	6.58911i	−0.163721	−	0.503882i
$172$	2.80252	+	2.03615i	0.213690	+	0.155255i
$173$	16.8151	−	12.2169i	1.27843	−	0.928833i	0.278924	−	0.960313i	$-0.410022\pi$
$173$	16.8151	−	12.2169i	1.27843	−	0.928833i	0.999504	+	0.0314804i	$0.0100222\pi$
$174$	0.927051	−	2.85317i	0.0702796	−	0.216298i
$175$	13.8564			1.04745
$176$		0			0
$177$	6.00000			0.450988
$178$	−4.81710	+	14.8255i	−0.361057	+	1.11122i
$179$	−9.70820	+	7.05342i	−0.725625	+	0.527198i	−0.888176	−	0.459503i	$-0.848028\pi$
$179$	−9.70820	+	7.05342i	−0.725625	+	0.527198i	0.162551	+	0.986700i	$0.448028\pi$
$180$	2.42705	+	1.76336i	0.180902	+	0.131433i
$181$	−2.16312	−	6.65740i	−0.160783	−	0.494840i	0.837918	−	0.545797i	$-0.183773\pi$
$181$	−2.16312	−	6.65740i	−0.160783	−	0.494840i	−0.998701	+	0.0509566i	$0.983773\pi$
$182$	−3.21140	−	9.88367i	−0.238045	−	0.732626i
$183$		0			0
$184$	8.40755	−	6.10844i	0.619813	−	0.450320i
$185$	10.1976	−	31.3849i	0.749740	−	2.30746i
$186$	6.92820			0.508001
$187$		0			0
$188$		0			0
$189$	−1.07047	+	3.29456i	−0.0778650	+	0.239644i
$190$	29.1246	−	21.1603i	2.11292	−	1.53513i
$191$	−9.70820	−	7.05342i	−0.702461	−	0.510368i	0.178272	−	0.983981i	$-0.442949\pi$
$191$	−9.70820	−	7.05342i	−0.702461	−	0.510368i	−0.880733	+	0.473614i	$0.842949\pi$
$192$	−0.309017	−	0.951057i	−0.0223014	−	0.0686366i
$193$	1.60570	+	4.94183i	0.115581	+	0.355721i	0.992068	−	0.125705i	$-0.0401191\pi$
$193$	1.60570	+	4.94183i	0.115581	+	0.355721i	−0.876487	+	0.481426i	$0.840119\pi$
$194$	−9.80881	−	7.12652i	−0.704232	−	0.511654i
$195$	−4.20378	+	3.05422i	−0.301039	+	0.218717i
$196$	1.54508	−	4.75528i	0.110363	−	0.339663i
$197$	19.0526			1.35744			0.678719	−	0.734398i	$-0.262535\pi$
$197$	19.0526			1.35744			0.678719	+	0.734398i	$0.262535\pi$
$198$		0			0
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$	2.14093	−	6.58911i	0.151387	−	0.465921i
$201$	−1.61803	+	1.17557i	−0.114127	+	0.0829184i
$202$	19.4164	+	14.1068i	1.36613	+	0.992554i
$203$	1.85410	+	5.70634i	0.130132	+	0.400506i
$204$	0.535233	+	1.64728i	0.0374738	+	0.115333i
$205$	4.20378	+	3.05422i	0.293604	+	0.213316i
$206$	19.6176	−	14.2530i	1.36682	−	0.993056i
$207$	−1.85410	+	5.70634i	−0.128869	+	0.396618i
$208$	−8.66025			−0.600481
$209$		0			0
$210$	−18.0000			−1.24212
$211$	5.35233	−	16.4728i	0.368470	−	1.13403i	−0.579310	−	0.815107i	$-0.696678\pi$
$211$	5.35233	−	16.4728i	0.368470	−	1.13403i	0.947780	−	0.318926i	$-0.103322\pi$
$212$	7.28115	−	5.29007i	0.500072	−	0.363323i
$213$	−4.85410	−	3.52671i	−0.332598	−	0.241646i
$214$	1.85410	+	5.70634i	0.126744	+	0.390077i
$215$	3.21140	+	9.88367i	0.219016	+	0.674061i
$216$	1.40126	+	1.01807i	0.0953436	+	0.0692712i
$217$	−11.2101	+	8.14459i	−0.760989	+	0.552891i
$218$	8.34346	−	25.6785i	0.565090	−	1.73917i
$219$	6.92820			0.468165
$220$		0			0
$221$	−3.00000			−0.201802
$222$	−5.88756	+	18.1201i	−0.395147	+	1.21614i
$223$	−16.1803	+	11.7557i	−1.08352	+	0.787220i	−0.978293	−	0.207228i	$-0.933556\pi$
$223$	−16.1803	+	11.7557i	−1.08352	+	0.787220i	−0.105223	+	0.994449i	$0.533556\pi$
$224$	−14.5623	−	10.5801i	−0.972985	−	0.706915i
$225$	1.23607	+	3.80423i	0.0824045	+	0.253615i
$226$	11.2399	+	34.5928i	0.747667	+	2.30108i
$227$	−19.6176	−	14.2530i	−1.30207	−	0.946007i	−0.302094	−	0.953278i	$-0.597686\pi$
$227$	−19.6176	−	14.2530i	−1.30207	−	0.946007i	−0.999974	+	0.00727112i	$0.997686\pi$
$228$	−5.60503	+	4.07230i	−0.371202	+	0.269694i
$229$	−7.10739	+	21.8743i	−0.469670	+	1.44549i	0.383344	+	0.923606i	$0.374772\pi$
$229$	−7.10739	+	21.8743i	−0.469670	+	1.44549i	−0.853014	+	0.521889i	$0.825228\pi$
$230$	−31.1769			−2.05574
$231$		0			0
$232$	3.00000			0.196960
$233$	−9.09896	+	28.0037i	−0.596093	+	1.83459i	−0.0468838	+	0.998900i	$0.514929\pi$
$233$	−9.09896	+	28.0037i	−0.596093	+	1.83459i	−0.549209	+	0.835685i	$0.685071\pi$
$234$	2.42705	−	1.76336i	0.158661	−	0.115274i
$235$		0			0
$236$	−1.85410	−	5.70634i	−0.120692	−	0.371451i
$237$		0			0
$238$	−8.40755	−	6.10844i	−0.544981	−	0.395952i
$239$	−5.60503	+	4.07230i	−0.362560	+	0.263415i	−0.754119	−	0.656738i	$-0.771936\pi$
$239$	−5.60503	+	4.07230i	−0.362560	+	0.263415i	0.391559	+	0.920153i	$0.371936\pi$
$240$	−4.63525	+	14.2658i	−0.299204	+	0.920857i
$241$	20.7846			1.33885			0.669427	−	0.742878i	$-0.266540\pi$
$241$	20.7846			1.33885			0.669427	+	0.742878i	$0.266540\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	12.1353	−	8.81678i	0.775293	−	0.563283i
$246$	−2.42705	−	1.76336i	−0.154743	−	0.112427i
$247$	−3.70820	−	11.4127i	−0.235947	−	0.726171i
$248$	2.14093	+	6.58911i	0.135949	+	0.418409i
$249$		0			0
$250$	4.20378	−	3.05422i	0.265870	−	0.193166i
$251$	−1.85410	+	5.70634i	−0.117030	+	0.360181i	−0.992365	−	0.123336i	$-0.960641\pi$
$251$	−1.85410	+	5.70634i	−0.117030	+	0.360181i	0.875335	+	0.483517i	$0.160641\pi$
$252$	3.46410			0.218218
$253$		0			0
$254$		0			0
$255$	−1.60570	+	4.94183i	−0.100553	+	0.309470i
$256$	−15.3713	+	11.1679i	−0.960708	+	0.697995i
$257$	−7.28115	−	5.29007i	−0.454186	−	0.329985i	0.337060	−	0.941483i	$-0.390567\pi$
$257$	−7.28115	−	5.29007i	−0.454186	−	0.329985i	−0.791246	+	0.611498i	$0.790567\pi$
$258$	−1.85410	−	5.70634i	−0.115431	−	0.355261i
$259$	−11.7751	−	36.2401i	−0.731671	−	2.25185i
$260$	4.20378	+	3.05422i	0.260707	+	0.189415i
$261$	−1.40126	+	1.01807i	−0.0867357	+	0.0630172i
$262$	−9.27051	+	28.5317i	−0.572734	+	1.76269i
$263$	−13.8564			−0.854423			−0.427211	−	0.904152i	$-0.640504\pi$
$263$	−13.8564			−0.854423			−0.427211	+	0.904152i	$0.640504\pi$
$264$		0			0
$265$	27.0000			1.65860
$266$	12.8456	−	39.5347i	0.787614	−	2.42403i
$267$	7.28115	−	5.29007i	0.445599	−	0.323747i
$268$	1.61803	+	1.17557i	0.0988372	+	0.0718094i
$269$	−6.48936	−	19.9722i	−0.395663	−	1.21773i	−0.928444	−	0.371472i	$-0.878853\pi$
$269$	−6.48936	−	19.9722i	−0.395663	−	1.21773i	0.532781	−	0.846253i	$-0.321147\pi$
$270$	−1.60570	−	4.94183i	−0.0977198	−	0.300750i
$271$	−2.80252	−	2.03615i	−0.170241	−	0.123687i	0.499402	−	0.866370i	$-0.333553\pi$
$271$	−2.80252	−	2.03615i	−0.170241	−	0.123687i	−0.669643	+	0.742683i	$0.733553\pi$
$272$	−7.00629	+	5.09037i	−0.424819	+	0.308649i
$273$	−1.85410	+	5.70634i	−0.112215	+	0.345363i
$274$	10.3923			0.627822
$275$		0			0
$276$	6.00000			0.361158
$277$	1.60570	−	4.94183i	0.0964771	−	0.296926i	−0.891159	−	0.453692i	$-0.850107\pi$
$277$	1.60570	−	4.94183i	0.0964771	−	0.296926i	0.987636	+	0.156766i	$0.0501067\pi$
$278$	−14.5623	+	10.5801i	−0.873389	+	0.634554i
$279$	−3.23607	−	2.35114i	−0.193738	−	0.140759i
$280$	−5.56231	−	17.1190i	−0.332411	−	1.02306i
$281$	2.14093	+	6.58911i	0.127717	+	0.393074i	0.994386	−	0.105810i	$-0.0337435\pi$
$281$	2.14093	+	6.58911i	0.127717	+	0.393074i	−0.866669	+	0.498884i	$0.833744\pi$
$282$		0			0
$283$	−25.2227	+	18.3253i	−1.49933	+	1.08933i	−0.528684	+	0.848819i	$0.677314\pi$
$283$	−25.2227	+	18.3253i	−1.49933	+	1.08933i	−0.970647	+	0.240509i	$0.922686\pi$
$284$	−1.85410	+	5.70634i	−0.110021	+	0.338609i
$285$	−20.7846			−1.23117
$286$		0			0
$287$	6.00000			0.354169
$288$	1.60570	−	4.94183i	0.0946167	−	0.291200i
$289$	11.3262	−	8.22899i	0.666249	−	0.484058i
$290$	−7.28115	−	5.29007i	−0.427564	−	0.310643i
$291$	2.16312	+	6.65740i	0.126804	+	0.390263i
$292$	−2.14093	−	6.58911i	−0.125289	−	0.385599i
$293$	15.4138	+	11.1988i	0.900486	+	0.654242i	0.938591	−	0.345032i	$-0.112132\pi$
$293$	15.4138	+	11.1988i	0.900486	+	0.654242i	−0.0381045	+	0.999274i	$0.512132\pi$
$294$	−7.00629	+	5.09037i	−0.408615	+	0.296876i
$295$	5.56231	−	17.1190i	0.323850	−	0.996708i
$296$	−19.0526			−1.10741
$297$		0			0
$298$	−21.0000			−1.21650
$299$	−3.21140	+	9.88367i	−0.185720	+	0.571587i
$300$	3.23607	−	2.35114i	0.186834	−	0.135743i
$301$	9.70820	+	7.05342i	0.559572	+	0.406553i
$302$	7.41641	+	22.8254i	0.426766	+	1.31345i
$303$	−4.28187	−	13.1782i	−0.245987	−	0.757069i
$304$	−28.0252	−	20.3615i	−1.60735	−	1.16781i
$305$		0			0
$306$	0.927051	−	2.85317i	0.0529960	−	0.163105i
$307$	−3.46410			−0.197707			−0.0988534	−	0.995102i	$-0.531517\pi$
$307$	−3.46410			−0.197707			−0.0988534	+	0.995102i	$0.531517\pi$
$308$		0			0
$309$	−14.0000			−0.796432
$310$	6.42280	−	19.7673i	0.364790	−	1.12271i
$311$	−9.70820	+	7.05342i	−0.550502	+	0.399963i	−0.827970	−	0.560772i	$-0.810505\pi$
$311$	−9.70820	+	7.05342i	−0.550502	+	0.399963i	0.277469	+	0.960735i	$0.410505\pi$
$312$	2.42705	+	1.76336i	0.137405	+	0.0998304i
$313$	2.16312	+	6.65740i	0.122267	+	0.376298i	0.993393	−	0.114760i	$-0.0366100\pi$
$313$	2.16312	+	6.65740i	0.122267	+	0.376298i	−0.871126	+	0.491059i	$0.836610\pi$
$314$	7.49326	+	23.0619i	0.422869	+	1.30146i
$315$	8.40755	+	6.10844i	0.473712	+	0.344172i
$316$		0			0
$317$	1.85410	−	5.70634i	0.104137	−	0.320500i	−0.885390	−	0.464849i	$-0.846109\pi$
$317$	1.85410	−	5.70634i	0.104137	−	0.320500i	0.989527	+	0.144349i	$0.0461087\pi$
$318$	−15.5885			−0.874157
$319$		0			0
$320$	−3.00000			−0.167705
$321$	1.07047	−	3.29456i	0.0597476	−	0.183884i
$322$	−29.1246	+	21.1603i	−1.62305	+	1.17922i
$323$	−9.70820	−	7.05342i	−0.540179	−	0.392463i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	2.14093	+	6.58911i	0.118758	+	0.365498i
$326$	2.80252	+	2.03615i	0.155217	+	0.112772i
$327$	−12.6113	+	9.16267i	−0.697408	+	0.506697i
$328$	0.927051	−	2.85317i	0.0511878	−	0.157540i
$329$		0			0
$330$		0			0
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$		0			0
$333$	8.89919	−	6.46564i	0.487672	−	0.354315i
$334$	4.85410	+	3.52671i	0.265605	+	0.192973i
$335$	1.85410	+	5.70634i	0.101300	+	0.311771i
$336$	5.35233	+	16.4728i	0.291994	+	0.898664i
$337$	−9.80881	−	7.12652i	−0.534320	−	0.388206i	0.287651	−	0.957735i	$-0.407126\pi$
$337$	−9.80881	−	7.12652i	−0.534320	−	0.388206i	−0.821971	+	0.569529i	$0.807126\pi$
$338$	−14.0126	+	10.1807i	−0.762184	+	0.553759i
$339$	6.48936	−	19.9722i	0.352453	−	1.08474i
$340$	5.19615			0.281801
$341$		0			0
$342$	12.0000			0.648886
$343$	−2.14093	+	6.58911i	−0.115599	+	0.355779i
$344$	4.85410	−	3.52671i	0.261716	−	0.190148i
$345$	14.5623	+	10.5801i	0.784008	+	0.569615i
$346$	11.1246	+	34.2380i	0.598063	+	1.84065i
$347$	−8.56373	−	26.3565i	−0.459725	−	1.41489i	−0.865497	−	0.500914i	$-0.832997\pi$
$347$	−8.56373	−	26.3565i	−0.459725	−	1.41489i	0.405772	−	0.913974i	$-0.367003\pi$
$348$	1.40126	+	1.01807i	0.0751153	+	0.0545745i
$349$	−1.40126	+	1.01807i	−0.0750076	+	0.0544962i	−0.624657	−	0.780899i	$-0.714761\pi$
$349$	−1.40126	+	1.01807i	−0.0750076	+	0.0544962i	0.549650	+	0.835395i	$0.314761\pi$
$350$	−7.41641	+	22.8254i	−0.396424	+	1.22007i
$351$	−1.73205			−0.0924500
$352$		0			0
$353$	21.0000			1.11772			0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000			1.11772			0.558859	+	0.829263i	$0.311239\pi$
$354$	−3.21140	+	9.88367i	−0.170684	+	0.525311i
$355$	−14.5623	+	10.5801i	−0.772887	+	0.561535i
$356$	−7.28115	−	5.29007i	−0.385900	−	0.280373i
$357$	1.85410	+	5.70634i	0.0981295	+	0.302011i
$358$	−6.42280	−	19.7673i	−0.339455	−	1.04474i
$359$	25.2227	+	18.3253i	1.33120	+	0.967174i	0.999719	+	0.0237124i	$0.00754859\pi$
$359$	25.2227	+	18.3253i	1.33120	+	0.967174i	0.331482	+	0.943462i	$0.392451\pi$
$360$	4.20378	−	3.05422i	0.221558	−	0.160972i
$361$	8.96149	−	27.5806i	0.471658	−	1.45161i
$362$	12.1244			0.637242
$363$		0			0
$364$	6.00000			0.314485
$365$	6.42280	−	19.7673i	0.336185	−	1.03467i
$366$		0			0
$367$	−21.0344	−	15.2824i	−1.09799	−	0.797736i	−0.117258	−	0.993101i	$-0.537411\pi$
$367$	−21.0344	−	15.2824i	−1.09799	−	0.797736i	−0.980730	+	0.195366i	$0.937411\pi$
$368$	9.27051	+	28.5317i	0.483259	+	1.48732i
$369$	0.535233	+	1.64728i	0.0278631	+	0.0857539i
$370$	46.2415	+	33.5964i	2.40398	+	1.74660i
$371$	25.2227	−	18.3253i	1.30949	−	0.951404i
$372$	−1.23607	+	3.80423i	−0.0640871	+	0.197240i
$373$	−20.7846			−1.07619			−0.538093	−	0.842885i	$-0.680855\pi$
$373$	−20.7846			−1.07619			−0.538093	+	0.842885i	$0.680855\pi$
$374$		0			0
$375$	−3.00000			−0.154919
$376$		0			0
$377$	−2.42705	+	1.76336i	−0.124999	+	0.0908174i
$378$	−4.85410	−	3.52671i	−0.249668	−	0.181394i
$379$	4.32624	+	13.3148i	0.222224	+	0.683935i	0.998562	+	0.0536176i	$0.0170752\pi$
$379$	4.32624	+	13.3148i	0.222224	+	0.683935i	−0.776338	+	0.630317i	$0.782925\pi$
$380$	6.42280	+	19.7673i	0.329483	+	1.01404i
$381$		0			0
$382$	16.8151	−	12.2169i	0.860335	−	0.625070i
$383$	1.85410	−	5.70634i	0.0947402	−	0.291580i	−0.892446	−	0.451155i	$-0.851012\pi$
$383$	1.85410	−	5.70634i	0.0947402	−	0.291580i	0.987186	+	0.159575i	$0.0510122\pi$
$384$	12.1244			0.618718
$385$		0			0
$386$	−9.00000			−0.458088
$387$	−1.07047	+	3.29456i	−0.0544149	+	0.167472i
$388$	5.66312	−	4.11450i	0.287501	−	0.208882i
$389$	21.8435	+	15.8702i	1.10751	+	0.804651i	0.982269	−	0.187476i	$-0.0600305\pi$
$389$	21.8435	+	15.8702i	1.10751	+	0.804651i	0.125238	+	0.992127i	$0.460031\pi$
$390$	−2.78115	−	8.55951i	−0.140829	−	0.433428i
$391$	3.21140	+	9.88367i	0.162407	+	0.499839i
$392$	−7.00629	−	5.09037i	−0.353871	−	0.257102i
$393$	14.0126	−	10.1807i	0.706841	−	0.513550i
$394$	−10.1976	+	31.3849i	−0.513746	+	1.58115i
$395$		0			0
$396$		0			0
$397$	11.0000			0.552074			0.276037	−	0.961147i	$-0.410979\pi$
$397$	11.0000			0.552074			0.276037	+	0.961147i	$0.410979\pi$
$398$	−5.35233	+	16.4728i	−0.268288	+	0.825706i
$399$	−19.4164	+	14.1068i	−0.972036	+	0.706226i
$400$	16.1803	+	11.7557i	0.809017	+	0.587785i
$401$	0.927051	+	2.85317i	0.0462947	+	0.142480i	0.971532	−	0.236909i	$-0.0761342\pi$
$401$	0.927051	+	2.85317i	0.0462947	+	0.142480i	−0.925237	+	0.379389i	$0.876134\pi$
$402$	−1.07047	−	3.29456i	−0.0533900	−	0.164318i
$403$	−5.60503	−	4.07230i	−0.279207	−	0.202855i
$404$	−11.2101	+	8.14459i	−0.557722	+	0.405209i
$405$	−0.927051	+	2.85317i	−0.0460655	+	0.141775i
$406$	−10.3923			−0.515761
$407$		0			0
$408$	3.00000			0.148522
$409$	−0.535233	+	1.64728i	−0.0264656	+	0.0814527i	−0.963417	−	0.268007i	$-0.913635\pi$
$409$	−0.535233	+	1.64728i	−0.0264656	+	0.0814527i	0.936951	+	0.349460i	$0.113635\pi$
$410$	−7.28115	+	5.29007i	−0.359591	+	0.261258i
$411$	−4.85410	−	3.52671i	−0.239435	−	0.173960i
$412$	4.32624	+	13.3148i	0.213138	+	0.655973i
$413$	−6.42280	−	19.7673i	−0.316045	−	0.972687i
$414$	−8.40755	−	6.10844i	−0.413209	−	0.300214i
$415$		0			0
$416$	2.78115	−	8.55951i	0.136357	−	0.419664i
$417$	10.3923			0.508913
$418$		0			0
$419$	−30.0000			−1.46560			−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$420$	3.21140	−	9.88367i	0.156700	−	0.482274i
$421$	−5.66312	+	4.11450i	−0.276004	+	0.200528i	−0.717172	−	0.696896i	$-0.754564\pi$
$421$	−5.66312	+	4.11450i	−0.276004	+	0.200528i	0.441169	+	0.897424i	$0.354564\pi$
$422$	24.2705	+	17.6336i	1.18147	+	0.858388i
$423$		0			0
$424$	−4.81710	−	14.8255i	−0.233939	−	0.719990i
$425$	5.60503	+	4.07230i	0.271884	+	0.197535i
$426$	8.40755	−	6.10844i	0.407347	−	0.295955i
$427$		0			0
$428$	−3.46410			−0.167444
$429$		0			0
$430$	−18.0000			−0.868037
$431$	5.35233	−	16.4728i	0.257813	−	0.793466i	−0.735450	−	0.677579i	$-0.763029\pi$
$431$	5.35233	−	16.4728i	0.257813	−	0.793466i	0.993262	−	0.115887i	$-0.0369709\pi$
$432$	−4.04508	+	2.93893i	−0.194619	+	0.141399i
$433$	15.3713	+	11.1679i	0.738699	+	0.536696i	0.892303	−	0.451436i	$-0.149088\pi$
$433$	15.3713	+	11.1679i	0.738699	+	0.536696i	−0.153605	+	0.988132i	$0.549088\pi$
$434$	−7.41641	−	22.8254i	−0.355999	−	1.09565i
$435$	1.60570	+	4.94183i	0.0769874	+	0.236943i
$436$	12.6113	+	9.16267i	0.603973	+	0.438812i
$437$	−33.6302	+	24.4338i	−1.60875	+	1.16883i
$438$	−3.70820	+	11.4127i	−0.177185	+	0.545319i
$439$	6.92820			0.330665			0.165333	−	0.986238i	$-0.447130\pi$
$439$	6.92820			0.330665			0.165333	+	0.986238i	$0.447130\pi$
$440$		0			0
$441$	5.00000			0.238095
$442$	1.60570	−	4.94183i	0.0763753	−	0.235059i
$443$	14.5623	−	10.5801i	0.691876	−	0.502677i	−0.185400	−	0.982663i	$-0.559358\pi$
$443$	14.5623	−	10.5801i	0.691876	−	0.502677i	0.877276	+	0.479986i	$0.159358\pi$
$444$	−8.89919	−	6.46564i	−0.422337	−	0.306846i
$445$	−8.34346	−	25.6785i	−0.395518	−	1.21728i
$446$	−10.7047	−	32.9456i	−0.506880	−	1.56002i
$447$	9.80881	+	7.12652i	0.463941	+	0.337073i
$448$	−2.80252	+	2.03615i	−0.132406	+	0.0961989i
$449$	6.48936	−	19.9722i	0.306252	−	0.942546i	−0.672955	−	0.739683i	$-0.734975\pi$
$449$	6.48936	−	19.9722i	0.306252	−	0.942546i	0.979207	−	0.202863i	$-0.0650245\pi$
$450$	−6.92820			−0.326599
$451$		0			0
$452$	−21.0000			−0.987757
$453$	4.28187	−	13.1782i	0.201180	−	0.619167i
$454$	33.9787	−	24.6870i	1.59470	−	1.15862i
$455$	14.5623	+	10.5801i	0.682691	+	0.496004i
$456$	3.70820	+	11.4127i	0.173653	+	0.534448i
$457$	9.09896	+	28.0037i	0.425632	+	1.30996i	0.902388	+	0.430924i	$0.141812\pi$
$457$	9.09896	+	28.0037i	0.425632	+	1.30996i	−0.476757	+	0.879035i	$0.658188\pi$
$458$	−32.2289	−	23.4157i	−1.50596	−	1.09414i
$459$	−1.40126	+	1.01807i	−0.0654051	+	0.0475196i
$460$	5.56231	−	17.1190i	0.259344	−	0.798178i
$461$	15.5885			0.726027			0.363013	−	0.931784i	$-0.381748\pi$
$461$	15.5885			0.726027			0.363013	+	0.931784i	$0.381748\pi$
$462$		0			0
$463$	−34.0000			−1.58011			−0.790057	−	0.613033i	$-0.789949\pi$
$463$	−34.0000			−1.58011			−0.790057	+	0.613033i	$0.789949\pi$
$464$	−2.67617	+	8.23639i	−0.124238	+	0.382365i
$465$	−9.70820	+	7.05342i	−0.450207	+	0.327095i
$466$	−41.2599	−	29.9770i	−1.91133	−	1.38866i
$467$	−5.56231	−	17.1190i	−0.257393	−	0.792174i	−0.993349	−	0.115144i	$-0.963267\pi$
$467$	−5.56231	−	17.1190i	−0.257393	−	0.792174i	0.735956	−	0.677029i	$-0.236733\pi$
$468$	0.535233	+	1.64728i	0.0247412	+	0.0761455i
$469$	5.60503	+	4.07230i	0.258816	+	0.188041i
$470$		0			0
$471$	4.32624	−	13.3148i	0.199343	−	0.613513i
$472$	−10.3923			−0.478345
$473$		0			0
$474$		0			0
$475$	−8.56373	+	26.3565i	−0.392931	+	1.20932i
$476$	4.85410	−	3.52671i	0.222487	−	0.161647i
$477$	7.28115	+	5.29007i	0.333381	+	0.242216i
$478$	−3.70820	−	11.4127i	−0.169609	−	0.522004i
$479$	−7.49326	−	23.0619i	−0.342376	−	1.05372i	−0.962974	−	0.269596i	$-0.913110\pi$
$479$	−7.49326	−	23.0619i	−0.342376	−	1.05372i	0.620598	−	0.784129i	$-0.286890\pi$
$480$	−12.6113	−	9.16267i	−0.575626	−	0.418217i
$481$	15.4138	−	11.1988i	0.702811	−	0.510622i
$482$	−11.1246	+	34.2380i	−0.506712	+	1.55950i
$483$	20.7846			0.945732
$484$		0			0
$485$	21.0000			0.953561
$486$	0.535233	−	1.64728i	0.0242787	−	0.0747221i
$487$	30.7426	−	22.3358i	1.39308	−	1.01213i	0.397563	−	0.917575i	$-0.369856\pi$
$487$	30.7426	−	22.3358i	1.39308	−	1.01213i	0.995519	−	0.0945586i	$-0.0301440\pi$
$488$		0			0
$489$	−0.618034	−	1.90211i	−0.0279485	−	0.0860165i
$490$	8.02850	+	24.7092i	0.362691	+	1.11625i
$491$	−16.8151	−	12.2169i	−0.758855	−	0.551340i	0.139704	−	0.990193i	$-0.455385\pi$
$491$	−16.8151	−	12.2169i	−0.758855	−	0.551340i	−0.898559	+	0.438853i	$0.855385\pi$
$492$	1.40126	−	1.01807i	0.0631736	−	0.0458983i
$493$	−0.927051	+	2.85317i	−0.0417523	+	0.128500i
$494$	20.7846			0.935144
$495$		0			0
$496$	−20.0000			−0.898027
$497$	−6.42280	+	19.7673i	−0.288102	+	0.886686i
$498$		0			0
$499$	−17.7984	−	12.9313i	−0.796765	−	0.578883i	0.113199	−	0.993572i	$-0.463890\pi$
$499$	−17.7984	−	12.9313i	−0.796765	−	0.578883i	−0.909963	+	0.414689i	$0.863890\pi$
$500$	0.927051	+	2.85317i	0.0414590	+	0.127598i
$501$	−1.07047	−	3.29456i	−0.0478249	−	0.147190i
$502$	−8.40755	−	6.10844i	−0.375247	−	0.272633i
$503$	25.2227	−	18.3253i	1.12462	−	0.817086i	0.139719	−	0.990191i	$-0.455380\pi$
$503$	25.2227	−	18.3253i	1.12462	−	0.817086i	0.984903	+	0.173105i	$0.0553800\pi$
$504$	1.85410	−	5.70634i	0.0825883	−	0.254181i
$505$	−41.5692			−1.84981
$506$		0			0
$507$	10.0000			0.444116
$508$		0			0
$509$	−14.5623	+	10.5801i	−0.645463	+	0.468956i	−0.861723	−	0.507380i	$-0.830614\pi$
$509$	−14.5623	+	10.5801i	−0.645463	+	0.468956i	0.216260	+	0.976336i	$0.430614\pi$
$510$	−7.28115	−	5.29007i	−0.322415	−	0.234248i
$511$	−7.41641	−	22.8254i	−0.328083	−	1.00973i
$512$	−2.67617	−	8.23639i	−0.118271	−	0.364000i
$513$	−5.60503	−	4.07230i	−0.247468	−	0.179796i
$514$	12.6113	−	9.16267i	0.556262	−	0.404148i
$515$	−12.9787	+	39.9444i	−0.571910	+	1.76016i
$516$	3.46410			0.152499
$517$		0			0
$518$	66.0000			2.89987
$519$	6.42280	−	19.7673i	0.281930	−	0.867690i
$520$	7.28115	−	5.29007i	0.319300	−	0.231985i
$521$	−4.85410	−	3.52671i	−0.212662	−	0.154508i	0.476355	−	0.879253i	$-0.341958\pi$
$521$	−4.85410	−	3.52671i	−0.212662	−	0.154508i	−0.689017	+	0.724745i	$0.741958\pi$
$522$	−0.927051	−	2.85317i	−0.0405759	−	0.124880i
$523$	12.8456	+	39.5347i	0.561699	+	1.72873i	0.677562	+	0.735466i	$0.263037\pi$
$523$	12.8456	+	39.5347i	0.561699	+	1.72873i	−0.115863	+	0.993265i	$0.536963\pi$
$524$	−14.0126	−	10.1807i	−0.612143	−	0.444748i
$525$	11.2101	−	8.14459i	0.489247	−	0.355459i
$526$	7.41641	−	22.8254i	0.323371	−	0.995233i
$527$	−6.92820			−0.301797
$528$		0			0
$529$	13.0000			0.565217
$530$	−14.4513	+	44.4765i	−0.627724	+	1.93194i
$531$	4.85410	−	3.52671i	0.210650	−	0.153046i
$532$	19.4164	+	14.1068i	0.841808	+	0.611609i
$533$	0.927051	+	2.85317i	0.0401550	+	0.123584i
$534$	4.81710	+	14.8255i	0.208456	+	0.641562i
$535$	−8.40755	−	6.10844i	−0.363490	−	0.264091i
$536$	2.80252	−	2.03615i	0.121050	−	0.0879482i
$537$	−3.70820	+	11.4127i	−0.160021	+	0.492493i
$538$	36.3731			1.56815
$539$		0			0
$540$	3.00000			0.129099
$541$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$541$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$542$	4.85410	−	3.52671i	0.208502	−	0.151485i
$543$	−5.66312	−	4.11450i	−0.243028	−	0.176570i
$544$	−2.78115	−	8.55951i	−0.119241	−	0.366986i
$545$	14.4513	+	44.4765i	0.619025	+	1.90516i
$546$	−8.40755	−	6.10844i	−0.359810	−	0.261417i
$547$	−28.0252	+	20.3615i	−1.19827	+	0.870594i	−0.994113	−	0.108344i	$-0.965445\pi$
$547$	−28.0252	+	20.3615i	−1.19827	+	0.870594i	−0.204156	+	0.978938i	$0.565445\pi$
$548$	−1.85410	+	5.70634i	−0.0792033	+	0.243763i
$549$		0			0
$550$		0			0
$551$	−12.0000			−0.511217
$552$	3.21140	−	9.88367i	0.136686	−	0.420677i
$553$		0			0
$554$	7.28115	+	5.29007i	0.309347	+	0.224753i
$555$	−10.1976	−	31.3849i	−0.432862	−	1.33221i
$556$	−3.21140	−	9.88367i	−0.136194	−	0.419161i
$557$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$557$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$558$	5.60503	−	4.07230i	0.237280	−	0.172394i
$559$	−1.85410	+	5.70634i	−0.0784202	+	0.241352i
$560$	51.9615			2.19578
$561$		0			0
$562$	−12.0000			−0.506189
$563$	−5.35233	+	16.4728i	−0.225574	+	0.694245i	0.772659	+	0.634821i	$0.218926\pi$
$563$	−5.35233	+	16.4728i	−0.225574	+	0.694245i	−0.998233	+	0.0594237i	$0.981074\pi$
$564$		0			0
$565$	−50.9681	−	37.0305i	−2.14424	−	1.55788i
$566$	−16.6869	−	51.3571i	−0.701403	−	2.15870i
$567$	1.07047	+	3.29456i	0.0449554	+	0.138358i
$568$	8.40755	+	6.10844i	0.352773	+	0.256305i
$569$	−22.4201	+	16.2892i	−0.939901	+	0.682878i	−0.948397	−	0.317086i	$-0.897296\pi$
$569$	−22.4201	+	16.2892i	−0.939901	+	0.682878i	0.00849582	+	0.999964i	$0.497296\pi$
$570$	11.1246	−	34.2380i	0.465959	−	1.43407i
$571$	−3.46410			−0.144968			−0.0724841	−	0.997370i	$-0.523093\pi$
$571$	−3.46410			−0.144968			−0.0724841	+	0.997370i	$0.523093\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$	−3.21140	+	9.88367i	−0.134041	+	0.412536i
$575$	19.4164	−	14.1068i	0.809720	−	0.588296i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	4.01722	+	12.3637i	0.167239	+	0.514709i	0.999194	−	0.0401338i	$-0.0127784\pi$
$577$	4.01722	+	12.3637i	0.167239	+	0.514709i	−0.831955	+	0.554843i	$0.812778\pi$
$578$	7.49326	+	23.0619i	0.311679	+	0.959248i
$579$	4.20378	+	3.05422i	0.174703	+	0.126929i
$580$	4.20378	−	3.05422i	0.174552	−	0.126820i
$581$		0			0
$582$	−12.1244			−0.502571
$583$		0			0
$584$	−12.0000			−0.496564
$585$	−1.60570	+	4.94183i	−0.0663875	+	0.204320i
$586$	−26.6976	+	19.3969i	−1.10287	+	0.801279i
$587$	9.70820	+	7.05342i	0.400700	+	0.291126i	0.769826	−	0.638254i	$-0.220343\pi$
$587$	9.70820	+	7.05342i	0.400700	+	0.291126i	−0.369126	+	0.929379i	$0.620343\pi$
$588$	−1.54508	−	4.75528i	−0.0637182	−	0.196105i
$589$	−8.56373	−	26.3565i	−0.352862	−	1.08600i
$590$	25.2227	+	18.3253i	1.03840	+	0.754442i
$591$	15.4138	−	11.1988i	0.634041	−	0.460658i
$592$	16.9959	−	52.3081i	0.698529	−	2.14985i
$593$	22.5167			0.924648			0.462324	−	0.886711i	$-0.347016\pi$
$593$	22.5167			0.924648			0.462324	+	0.886711i	$0.347016\pi$
$594$		0			0
$595$	18.0000			0.737928
$596$	3.74663	−	11.5309i	0.153468	−	0.472326i
$597$	8.09017	−	5.87785i	0.331109	−	0.240564i
$598$	−14.5623	−	10.5801i	−0.595497	−	0.432654i
$599$	7.41641	+	22.8254i	0.303026	+	0.932619i	0.980406	+	0.196986i	$0.0631152\pi$
$599$	7.41641	+	22.8254i	0.303026	+	0.932619i	−0.677380	+	0.735633i	$0.736885\pi$
$600$	−2.14093	−	6.58911i	−0.0874032	−	0.268999i
$601$	−18.2164	−	13.2350i	−0.743061	−	0.539865i	0.150607	−	0.988594i	$-0.451877\pi$
$601$	−18.2164	−	13.2350i	−0.743061	−	0.539865i	−0.893668	+	0.448728i	$0.851877\pi$
$602$	−16.8151	+	12.2169i	−0.685332	+	0.497923i
$603$	−0.618034	+	1.90211i	−0.0251683	+	0.0774600i
$604$	−13.8564			−0.563809
$605$		0			0
$606$	24.0000			0.974933
$607$	−6.42280	+	19.7673i	−0.260693	+	0.802332i	0.731961	+	0.681347i	$0.238605\pi$
$607$	−6.42280	+	19.7673i	−0.260693	+	0.802332i	−0.992654	+	0.120985i	$0.961395\pi$
$608$	29.1246	−	21.1603i	1.18116	−	0.858162i
$609$	4.85410	+	3.52671i	0.196698	+	0.142910i
$610$		0			0
$611$		0			0
$612$	1.40126	+	1.01807i	0.0566425	+	0.0411532i
$613$	15.4138	−	11.1988i	0.622559	−	0.452316i	−0.231255	−	0.972893i	$-0.574283\pi$
$613$	15.4138	−	11.1988i	0.622559	−	0.452316i	0.853815	+	0.520577i	$0.174283\pi$
$614$	1.85410	−	5.70634i	0.0748255	−	0.230289i
$615$	5.19615			0.209529
$616$		0			0
$617$	−9.00000			−0.362326			−0.181163	−	0.983453i	$-0.557986\pi$
$617$	−9.00000			−0.362326			−0.181163	+	0.983453i	$0.557986\pi$
$618$	7.49326	−	23.0619i	0.301423	−	0.927685i
$619$	8.09017	−	5.87785i	0.325171	−	0.236251i	−0.413208	−	0.910637i	$-0.635592\pi$
$619$	8.09017	−	5.87785i	0.325171	−	0.236251i	0.738379	+	0.674386i	$0.235592\pi$
$620$	9.70820	+	7.05342i	0.389891	+	0.283272i
$621$	1.85410	+	5.70634i	0.0744025	+	0.228988i
$622$	−6.42280	−	19.7673i	−0.257531	−	0.792598i
$623$	−25.2227	−	18.3253i	−1.01052	−	0.734189i
$624$	−7.00629	+	5.09037i	−0.280476	+	0.203778i
$625$	−8.96149	+	27.5806i	−0.358460	+	1.10323i
$626$	−12.1244			−0.484587
$627$		0			0
$628$	−14.0000			−0.558661
$629$	5.88756	−	18.1201i	0.234753	−	0.722494i
$630$	−14.5623	+	10.5801i	−0.580176	+	0.421523i
$631$	11.3262	+	8.22899i	0.450890	+	0.327591i	0.789947	−	0.613175i	$-0.210108\pi$
$631$	11.3262	+	8.22899i	0.450890	+	0.327591i	−0.339057	+	0.940766i	$0.610108\pi$
$632$		0			0
$633$	−5.35233	−	16.4728i	−0.212736	−	0.654734i
$634$	8.40755	+	6.10844i	0.333907	+	0.242597i
$635$		0			0
$636$	2.78115	−	8.55951i	0.110280	−	0.339407i
$637$	8.66025			0.343132
$638$		0			0
$639$	−6.00000			−0.237356
$640$	11.2399	−	34.5928i	0.444296	−	1.36740i
$641$	12.1353	−	8.81678i	0.479314	−	0.348242i	−0.321746	−	0.946826i	$-0.604270\pi$
$641$	12.1353	−	8.81678i	0.479314	−	0.348242i	0.801060	+	0.598584i	$0.204270\pi$
$642$	4.85410	+	3.52671i	0.191576	+	0.139188i
$643$	−4.94427	−	15.2169i	−0.194983	−	0.600096i	−0.999977	−	0.00681282i	$-0.997831\pi$
$643$	−4.94427	−	15.2169i	−0.194983	−	0.600096i	0.804994	−	0.593283i	$-0.202169\pi$
$644$	−6.42280	−	19.7673i	−0.253094	−	0.778942i
$645$	8.40755	+	6.10844i	0.331047	+	0.240520i
$646$	16.8151	−	12.2169i	0.661581	−	0.480667i
$647$	−3.70820	+	11.4127i	−0.145785	+	0.448679i	−0.997111	−	0.0759575i	$-0.975799\pi$
$647$	−3.70820	+	11.4127i	−0.145785	+	0.448679i	0.851327	+	0.524636i	$0.175799\pi$
$648$	1.73205			0.0680414
$649$		0			0
$650$	−12.0000			−0.470679
$651$	−4.28187	+	13.1782i	−0.167820	+	0.516495i
$652$	−1.61803	+	1.17557i	−0.0633671	+	0.0460389i
$653$	24.2705	+	17.6336i	0.949778	+	0.690054i	0.950754	−	0.309945i	$-0.100311\pi$
$653$	24.2705	+	17.6336i	0.949778	+	0.690054i	−0.000976014		1.00000i	$0.500311\pi$
$654$	−8.34346	−	25.6785i	−0.326255	−	1.00411i
$655$	−16.0570	−	49.4183i	−0.627399	−	1.93093i
$656$	7.00629	+	5.09037i	0.273550	+	0.198746i
$657$	5.60503	−	4.07230i	0.218673	−	0.158875i
$658$		0			0
$659$	−13.8564			−0.539769			−0.269884	−	0.962893i	$-0.586986\pi$
$659$	−13.8564			−0.539769			−0.269884	+	0.962893i	$0.586986\pi$
$660$		0			0
$661$	−41.0000			−1.59472			−0.797358	−	0.603507i	$-0.793769\pi$
$661$	−41.0000			−1.59472			−0.797358	+	0.603507i	$0.793769\pi$
$662$	−10.7047	+	32.9456i	−0.416049	+	1.28047i
$663$	−2.42705	+	1.76336i	−0.0942588	+	0.0684831i
$664$		0			0
$665$	22.2492	+	68.4761i	0.862788	+	2.65539i
$666$	5.88756	+	18.1201i	0.228138	+	0.702138i
$667$	8.40755	+	6.10844i	0.325542	+	0.236520i
$668$	−2.80252	+	2.03615i	−0.108433	+	0.0787809i
$669$	−6.18034	+	19.0211i	−0.238946	+	0.735399i
$670$	−10.3923			−0.401490
$671$		0			0
$672$	−18.0000			−0.694365
$673$	6.42280	−	19.7673i	0.247581	−	0.761975i	−0.747621	−	0.664126i	$-0.768804\pi$
$673$	6.42280	−	19.7673i	0.247581	−	0.761975i	0.995201	−	0.0978489i	$-0.0311962\pi$
$674$	16.9894	−	12.3435i	0.654406	−	0.475453i
$675$	3.23607	+	2.35114i	0.124556	+	0.0904955i
$676$	−3.09017	−	9.51057i	−0.118853	−	0.365791i
$677$	−10.1694	−	31.2983i	−0.390843	−	1.20289i	−0.932152	−	0.362067i	$-0.882071\pi$
$677$	−10.1694	−	31.2983i	−0.390843	−	1.20289i	0.541309	−	0.840824i	$-0.317929\pi$
$678$	29.4264	+	21.3796i	1.13012	+	0.821077i
$679$	19.6176	−	14.2530i	0.752855	−	0.546981i
$680$	2.78115	−	8.55951i	0.106652	−	0.328242i
$681$	−24.2487			−0.929213
$682$		0			0
$683$	−6.00000			−0.229584			−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000			−0.229584			−0.114792	+	0.993390i	$0.536620\pi$
$684$	−2.14093	+	6.58911i	−0.0818606	+	0.251941i
$685$	−14.5623	+	10.5801i	−0.556397	+	0.404246i
$686$	−9.70820	−	7.05342i	−0.370661	−	0.269301i
$687$	7.10739	+	21.8743i	0.271164	+	0.834557i
$688$	5.35233	+	16.4728i	0.204056	+	0.628019i
$689$	12.6113	+	9.16267i	0.480453	+	0.349070i
$690$	−25.2227	+	18.3253i	−0.960210	+	0.697633i
$691$	−3.09017	+	9.51057i	−0.117556	+	0.361799i	−0.992471	−	0.122476i	$-0.960917\pi$
$691$	−3.09017	+	9.51057i	−0.117556	+	0.361799i	0.874916	+	0.484275i	$0.160917\pi$
$692$	−20.7846			−0.790112
$693$		0			0
$694$	48.0000			1.82206
$695$	9.63420	−	29.6510i	0.365446	−	1.12473i
$696$	2.42705	−	1.76336i	0.0919971	−	0.0668398i
$697$	2.42705	+	1.76336i	0.0919311	+	0.0667919i
$698$	−0.927051	−	2.85317i	−0.0350894	−	0.107994i
$699$	9.09896	+	28.0037i	0.344154	+	1.05920i
$700$	−11.2101	−	8.14459i	−0.423701	−	0.307837i
$701$	−32.2289	+	23.4157i	−1.21727	+	0.884399i	−0.995871	−	0.0907843i	$-0.971063\pi$
$701$	−32.2289	+	23.4157i	−1.21727	+	0.884399i	−0.221400	+	0.975183i	$0.571063\pi$
$702$	0.927051	−	2.85317i	0.0349893	−	0.107686i
$703$	76.2102			2.87432
$704$		0			0
$705$		0			0
$706$	−11.2399	+	34.5928i	−0.423019	+	1.30192i
$707$	−38.8328	+	28.2137i	−1.46046	+	1.06109i
$708$	−4.85410	−	3.52671i	−0.182428	−	0.132542i
$709$	6.79837	+	20.9232i	0.255318	+	0.785789i	0.993767	+	0.111479i	$0.0355588\pi$
$709$	6.79837	+	20.9232i	0.255318	+	0.785789i	−0.738448	+	0.674310i	$0.764441\pi$
$710$	−9.63420	−	29.6510i	−0.361565	−	1.11278i
$711$		0			0
$712$	−12.6113	+	9.16267i	−0.472629	+	0.343385i
$713$	−7.41641	+	22.8254i	−0.277747	+	0.854816i
$714$	−10.3923			−0.388922
$715$		0			0
$716$	12.0000			0.448461
$717$	−2.14093	+	6.58911i	−0.0799546	+	0.246075i
$718$	−43.6869	+	31.7404i	−1.63038	+	1.18454i
$719$	24.2705	+	17.6336i	0.905137	+	0.657621i	0.939780	−	0.341779i	$-0.111029\pi$
$719$	24.2705	+	17.6336i	0.905137	+	0.657621i	−0.0346431	+	0.999400i	$0.511029\pi$
$720$	4.63525	+	14.2658i	0.172746	+	0.531657i
$721$	14.9865	+	46.1238i	0.558127	+	1.71774i
$722$	40.6365	+	29.5241i	1.51233	+	1.09877i
$723$	16.8151	−	12.2169i	0.625360	−	0.454351i
$724$	−2.16312	+	6.65740i	−0.0803917	+	0.247420i
$725$	6.92820			0.257307
$726$		0			0
$727$	−2.00000			−0.0741759			−0.0370879	−	0.999312i	$-0.511808\pi$
$727$	−2.00000			−0.0741759			−0.0370879	+	0.999312i	$0.511808\pi$
$728$	3.21140	−	9.88367i	0.119022	−	0.366313i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	29.1246	+	21.1603i	1.07795	+	0.783177i
$731$	1.85410	+	5.70634i	0.0685764	+	0.211057i
$732$		0			0
$733$	7.00629	+	5.09037i	0.258783	+	0.188017i	0.709610	−	0.704594i	$-0.248871\pi$
$733$	7.00629	+	5.09037i	0.258783	+	0.188017i	−0.450827	+	0.892611i	$0.648871\pi$
$734$	36.4327	−	26.4699i	1.34476	−	0.977023i
$735$	4.63525	−	14.2658i	0.170974	−	0.526204i
$736$	−31.1769			−1.14920
$737$		0			0
$738$	−3.00000			−0.110432
$739$	8.56373	−	26.3565i	0.315022	−	0.969538i	−0.660724	−	0.750629i	$-0.729750\pi$
$739$	8.56373	−	26.3565i	0.315022	−	0.969538i	0.975745	−	0.218908i	$-0.0702496\pi$
$740$	−26.6976	+	19.3969i	−0.981422	+	0.713045i
$741$	−9.70820	−	7.05342i	−0.356640	−	0.259114i
$742$	16.6869	+	51.3571i	0.612596	+	1.88538i
$743$	16.0570	+	49.4183i	0.589074	+	1.81298i	0.582255	+	0.813007i	$0.302171\pi$
$743$	16.0570	+	49.4183i	0.589074	+	1.81298i	0.00681943	+	0.999977i	$0.497829\pi$
$744$	5.60503	+	4.07230i	0.205491	+	0.149298i
$745$	29.4264	−	21.3796i	1.07810	−	0.783286i
$746$	11.1246	−	34.2380i	0.407301	−	1.25354i
$747$		0			0
$748$		0			0
$749$	−12.0000			−0.438470
$750$	1.60570	−	4.94183i	0.0586319	−	0.180450i
$751$	1.61803	−	1.17557i	0.0590429	−	0.0428972i	−0.557872	−	0.829927i	$-0.688382\pi$
$751$	1.61803	−	1.17557i	0.0590429	−	0.0428972i	0.616915	+	0.787030i	$0.288382\pi$
$752$		0			0
$753$	1.85410	+	5.70634i	0.0675672	+	0.207951i
$754$	−1.60570	−	4.94183i	−0.0584761	−	0.179971i
$755$	−33.6302	−	24.4338i	−1.22393	−	0.889236i
$756$	2.80252	−	2.03615i	0.101927	−	0.0740540i
$757$	−5.25329	+	16.1680i	−0.190934	+	0.587635i	−1.00000		8.33163e-5i	$-0.999973\pi$
$757$	−5.25329	+	16.1680i	−0.190934	+	0.587635i	0.809066	+	0.587718i	$0.199973\pi$
$758$	−24.2487			−0.880753
$759$		0			0
$760$	36.0000			1.30586
$761$	−10.1694	+	31.2983i	−0.368642	+	1.13456i	0.579028	+	0.815308i	$0.303432\pi$
$761$	−10.1694	+	31.2983i	−0.368642	+	1.13456i	−0.947669	+	0.319254i	$0.896568\pi$
$762$		0			0
$763$	43.6869	+	31.7404i	1.58157	+	1.14908i
$764$	3.70820	+	11.4127i	0.134158	+	0.412896i
$765$	1.60570	+	4.94183i	0.0580542	+	0.178672i
$766$	8.40755	+	6.10844i	0.303777	+	0.220707i
$767$	8.40755	−	6.10844i	0.303579	−	0.220563i
$768$	−5.87132	+	18.0701i	−0.211863	+	0.652048i
$769$	−25.9808			−0.936890			−0.468445	−	0.883493i	$-0.655186\pi$
$769$	−25.9808			−0.936890			−0.468445	+	0.883493i	$0.655186\pi$
$770$		0			0
$771$	−9.00000			−0.324127
$772$	1.60570	−	4.94183i	0.0577904	−	0.177861i
$773$	−14.5623	+	10.5801i	−0.523770	+	0.380541i	−0.818022	−	0.575187i	$-0.804929\pi$
$773$	−14.5623	+	10.5801i	−0.523770	+	0.380541i	0.294252	+	0.955728i	$0.404929\pi$
$774$	−4.85410	−	3.52671i	−0.174477	−	0.126765i
$775$	4.94427	+	15.2169i	0.177603	+	0.546607i
$776$	−3.74663	−	11.5309i	−0.134496	−	0.413937i
$777$	−30.8277	−	22.3976i	−1.10594	−	0.803510i
$778$	−37.8340	+	27.4880i	−1.35641	+	0.985492i
$779$	−3.70820	+	11.4127i	−0.132860	+	0.408902i
$780$	5.19615			0.186052
$781$		0			0
$782$	−18.0000			−0.643679
$783$	−0.535233	+	1.64728i	−0.0191277	+	0.0588689i
$784$	20.2254	−	14.6946i	0.722337	−	0.524808i
$785$	−33.9787	−	24.6870i	−1.21275	−	0.881116i
$786$	9.27051	+	28.5317i	0.330668	+	1.01769i
$787$	2.14093	+	6.58911i	0.0763160	+	0.234877i	0.981936	−	0.189214i	$-0.0605939\pi$
$787$	2.14093	+	6.58911i	0.0763160	+	0.234877i	−0.905620	+	0.424090i	$0.860594\pi$
$788$	−15.4138	−	11.1988i	−0.549095	−	0.398941i
$789$	−11.2101	+	8.14459i	−0.399089	+	0.289955i
$790$		0			0
$791$	−72.7461			−2.58655
$792$		0			0
$793$		0			0
$794$	−5.88756	+	18.1201i	−0.208942	+	0.643057i
$795$	21.8435	−	15.8702i	0.774708	−	0.562858i
$796$	−8.09017	−	5.87785i	−0.286748	−	0.208335i
$797$	−12.9787	−	39.9444i	−0.459730	−	1.41490i	−0.865492	−	0.500924i	$-0.832994\pi$
$797$	−12.9787	−	39.9444i	−0.459730	−	1.41490i	0.405762	−	0.913979i	$-0.367006\pi$
$798$	−12.8456	−	39.5347i	−0.454729	−	1.39951i
$799$		0			0
$800$	−16.8151	+	12.2169i	−0.594504	+	0.431932i
$801$	2.78115	−	8.55951i	0.0982672	−	0.302435i
$802$	−5.19615			−0.183483
$803$		0			0
$804$	2.00000			0.0705346
$805$	19.2684	−	59.3020i	0.679122	−	2.09012i
$806$	9.70820	−	7.05342i	0.341957	−	0.248446i
$807$	−16.9894	−	12.3435i	−0.598054	−	0.434511i
$808$	7.41641	+	22.8254i	0.260908	+	0.802993i
$809$	−6.42280	−	19.7673i	−0.225814	−	0.694983i	−0.998208	−	0.0598395i	$-0.980941\pi$
$809$	−6.42280	−	19.7673i	−0.225814	−	0.694983i	0.772394	−	0.635143i	$-0.219059\pi$
$810$	−4.20378	−	3.05422i	−0.147706	−	0.107314i
$811$	−22.4201	+	16.2892i	−0.787277	+	0.571991i	−0.907154	−	0.420798i	$-0.861750\pi$
$811$	−22.4201	+	16.2892i	−0.787277	+	0.571991i	0.119877	+	0.992789i	$0.461750\pi$
$812$	1.85410	−	5.70634i	0.0650662	−	0.200253i
$813$	−3.46410			−0.121491
$814$		0			0
$815$	−6.00000			−0.210171
$816$	−2.67617	+	8.23639i	−0.0936845	+	0.288331i
$817$	−19.4164	+	14.1068i	−0.679294	+	0.493536i
$818$	−2.42705	−	1.76336i	−0.0848598	−	0.0616543i
$819$	1.85410	+	5.70634i	0.0647876	+	0.199396i
$820$	−1.60570	−	4.94183i	−0.0560735	−	0.172576i
$821$	44.8403	+	32.5784i	1.56494	+	1.13699i	0.931811	+	0.362943i	$0.118228\pi$
$821$	44.8403	+	32.5784i	1.56494	+	1.13699i	0.633125	+	0.774049i	$0.281772\pi$
$822$	8.40755	−	6.10844i	0.293247	−	0.213056i
$823$	4.32624	−	13.3148i	0.150803	−	0.464124i	−0.846908	−	0.531739i	$-0.821539\pi$
$823$	4.32624	−	13.3148i	0.150803	−	0.464124i	0.997712	+	0.0676144i	$0.0215388\pi$
$824$	24.2487			0.844744
$825$		0			0
$826$	36.0000			1.25260
$827$	11.7751	−	36.2401i	0.409461	−	1.26019i	−0.507651	−	0.861563i	$-0.669486\pi$
$827$	11.7751	−	36.2401i	0.409461	−	1.26019i	0.917112	−	0.398629i	$-0.130514\pi$
$828$	4.85410	−	3.52671i	0.168692	−	0.122562i
$829$	−8.89919	−	6.46564i	−0.309082	−	0.224561i	0.422421	−	0.906400i	$-0.361180\pi$
$829$	−8.89919	−	6.46564i	−0.309082	−	0.224561i	−0.731502	+	0.681839i	$0.761180\pi$
$830$		0			0
$831$	−1.60570	−	4.94183i	−0.0557011	−	0.171430i
$832$	−1.40126	−	1.01807i	−0.0485799	−	0.0352954i
$833$	7.00629	−	5.09037i	0.242754	−	0.176371i
$834$	−5.56231	+	17.1190i	−0.192607	+	0.592783i
$835$	−10.3923			−0.359641
$836$		0			0
$837$	−4.00000			−0.138260
$838$	16.0570	−	49.4183i	0.554680	−	1.70713i
$839$	−19.4164	+	14.1068i	−0.670329	+	0.487022i	−0.870135	−	0.492813i	$-0.835969\pi$
$839$	−19.4164	+	14.1068i	−0.670329	+	0.487022i	0.199806	+	0.979835i	$0.435969\pi$
$840$	−14.5623	−	10.5801i	−0.502447	−	0.365049i
$841$	−8.03444	−	24.7275i	−0.277050	−	0.852671i
$842$	−3.74663	−	11.5309i	−0.129117	−	0.397383i
$843$	5.60503	+	4.07230i	0.193048	+	0.140257i
$844$	−14.0126	+	10.1807i	−0.482333	+	0.350435i
$845$	9.27051	−	28.5317i	0.318915	−	0.981520i
$846$		0			0
$847$		0			0
$848$	45.0000			1.54531
$849$	−9.63420	+	29.6510i	−0.330645	+	1.01762i
$850$	−9.70820	+	7.05342i	−0.332989	+	0.241930i
$851$	−53.3951	−	38.7938i	−1.83036	−	1.32984i
$852$	1.85410	+	5.70634i	0.0635205	+	0.195496i
$853$	−2.67617	−	8.23639i	−0.0916302	−	0.282009i	0.894731	−	0.446606i	$-0.147367\pi$
$853$	−2.67617	−	8.23639i	−0.0916302	−	0.282009i	−0.986361	+	0.164598i	$0.947367\pi$
$854$		0			0
$855$	−16.8151	+	12.2169i	−0.575064	+	0.417809i
$856$	−1.85410	+	5.70634i	−0.0633719	+	0.195039i
$857$	−41.5692			−1.41998			−0.709989	−	0.704213i	$-0.751300\pi$
$857$	−41.5692			−1.41998			−0.709989	+	0.704213i	$0.751300\pi$
$858$		0			0
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$	3.21140	−	9.88367i	0.109508	−	0.337030i
$861$	4.85410	−	3.52671i	0.165427	−	0.120190i
$862$	24.2705	+	17.6336i	0.826657	+	0.600601i
$863$	1.85410	+	5.70634i	0.0631144	+	0.194246i	0.977642	−	0.210278i	$-0.0674370\pi$
$863$	1.85410	+	5.70634i	0.0631144	+	0.194246i	−0.914527	+	0.404524i	$0.867437\pi$
$864$	−1.60570	−	4.94183i	−0.0546270	−	0.168125i
$865$	−50.4453	−	36.6507i	−1.71519	−	1.24616i
$866$	−26.6239	+	19.3434i	−0.904717	+	0.657316i
$867$	4.32624	−	13.3148i	0.146927	−	0.452194i
$868$	13.8564			0.470317
$869$		0			0
$870$	−9.00000			−0.305129
$871$	−1.07047	+	3.29456i	−0.0362714	+	0.111632i
$872$	21.8435	−	15.8702i	0.739713	−	0.537433i
$873$	5.66312	+	4.11450i	0.191668	+	0.139255i
$874$	−22.2492	−	68.4761i	−0.752591	−	2.31624i
$875$	3.21140	+	9.88367i	0.108565	+	0.334129i
$876$	−5.60503	−	4.07230i	−0.189377	−	0.137590i
$877$	−15.4138	+	11.1988i	−0.520489	+	0.378157i	−0.816788	−	0.576938i	$-0.804247\pi$
$877$	−15.4138	+	11.1988i	−0.520489	+	0.378157i	0.296299	+	0.955095i	$0.404247\pi$
$878$	−3.70820	+	11.4127i	−0.125146	+	0.385159i
$879$	19.0526			0.642627
$880$		0			0
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$	−2.67617	+	8.23639i	−0.0901112	+	0.277334i
$883$	−3.23607	+	2.35114i	−0.108902	+	0.0791222i	−0.640904	−	0.767621i	$-0.721440\pi$
$883$	−3.23607	+	2.35114i	−0.108902	+	0.0791222i	0.532001	+	0.846744i	$0.321440\pi$
$884$	2.42705	+	1.76336i	0.0816306	+	0.0593081i
$885$	−5.56231	−	17.1190i	−0.186975	−	0.575449i
$886$	9.63420	+	29.6510i	0.323667	+	0.996145i
$887$	25.2227	+	18.3253i	0.846894	+	0.615304i	0.924288	−	0.381696i	$-0.124660\pi$
$887$	25.2227	+	18.3253i	0.846894	+	0.615304i	−0.0773940	+	0.997001i	$0.524660\pi$
$888$	−15.4138	+	11.1988i	−0.517255	+	0.375808i
$889$		0			0
$890$	46.7654			1.56758
$891$		0			0
$892$	20.0000			0.669650
$893$		0			0
$894$	−16.9894	+	12.3435i	−0.568209	+	0.412828i
$895$	29.1246	+	21.1603i	0.973528	+	0.707310i
$896$	−12.9787	−	39.9444i	−0.433588	−	1.33445i
$897$	3.21140	+	9.88367i	0.107225	+	0.330006i
$898$	29.4264	+	21.3796i	0.981973	+	0.713445i
$899$	−5.60503	+	4.07230i	−0.186938	+	0.135819i
$900$	1.23607	−	3.80423i	0.0412023	−	0.126808i
$901$	15.5885			0.519327
$902$		0			0
$903$	12.0000			0.399335
$904$	−11.2399	+	34.5928i	−0.373833	+	1.15054i
$905$	−16.9894	+	12.3435i	−0.564745	+	0.410312i
$906$	19.4164	+	14.1068i	0.645067	+	0.468669i
$907$	−6.79837	−	20.9232i	−0.225736	−	0.694745i	−0.998216	−	0.0597055i	$-0.980984\pi$
$907$	−6.79837	−	20.9232i	−0.225736	−	0.694745i	0.772480	−	0.635039i	$-0.219016\pi$
$908$	7.49326	+	23.0619i	0.248673	+	0.765336i
$909$	−11.2101	−	8.14459i	−0.371814	−	0.270139i
$910$	−25.2227	+	18.3253i	−0.836123	+	0.607479i
$911$	−9.27051	+	28.5317i	−0.307146	+	0.945297i	0.671722	+	0.740803i	$0.265555\pi$
$911$	−9.27051	+	28.5317i	−0.307146	+	0.945297i	−0.978868	+	0.204494i	$0.934445\pi$
$912$	−34.6410			−1.14708
$913$		0			0
$914$	−51.0000			−1.68693
$915$		0			0
$916$	18.6074	−	13.5191i	0.614805	−	0.446682i
$917$	−48.5410	−	35.2671i	−1.60297	−	1.16462i
$918$	−0.927051	−	2.85317i	−0.0305972	−	0.0941686i
$919$	7.49326	+	23.0619i	0.247180	+	0.760742i	0.995270	+	0.0971448i	$0.0309710\pi$
$919$	7.49326	+	23.0619i	0.247180	+	0.760742i	−0.748090	+	0.663597i	$0.769029\pi$
$920$	−25.2227	−	18.3253i	−0.831566	−	0.604168i
$921$	−2.80252	+	2.03615i	−0.0923461	+	0.0670934i
$922$	−8.34346	+	25.6785i	−0.274777	+	0.845677i
$923$	−10.3923			−0.342067
$924$		0			0
$925$	−44.0000			−1.44671
$926$	18.1979	−	56.0075i	0.598021	−	1.84052i
$927$	−11.3262	+	8.22899i	−0.372002	+	0.270276i
$928$	−7.28115	−	5.29007i	−0.239016	−	0.173655i
$929$	12.0517	+	37.0912i	0.395402	+	1.21692i	0.928648	+	0.370962i	$0.120972\pi$
$929$	12.0517	+	37.0912i	0.395402	+	1.21692i	−0.533246	+	0.845960i	$0.679028\pi$
$930$	−6.42280	−	19.7673i	−0.210612	−	0.648197i
$931$	28.0252	+	20.3615i	0.918488	+	0.667321i
$932$	23.8214	−	17.3073i	0.780296	−	0.566918i
$933$	−3.70820	+	11.4127i	−0.121401	+	0.373634i
$934$	31.1769			1.02014
$935$		0			0
$936$	3.00000			0.0980581
$937$	−15.5218	+	47.7711i	−0.507074	+	1.56061i	0.290182	+	0.956971i	$0.406284\pi$
$937$	−15.5218	+	47.7711i	−0.507074	+	1.56061i	−0.797256	+	0.603641i	$0.793716\pi$
$938$	−9.70820	+	7.05342i	−0.316984	+	0.230302i
$939$	5.66312	+	4.11450i	0.184809	+	0.134272i
$940$		0			0
$941$	−9.09896	−	28.0037i	−0.296618	−	0.912895i	−0.982673	−	0.185346i	$-0.940659\pi$
$941$	−9.09896	−	28.0037i	−0.296618	−	0.912895i	0.686056	−	0.727549i	$-0.259341\pi$
$942$	19.6176	+	14.2530i	0.639177	+	0.464389i
$943$	8.40755	−	6.10844i	0.273788	−	0.198918i
$944$	9.27051	−	28.5317i	0.301729	−	0.928628i
$945$	10.3923			0.338062
$946$		0			0
$947$	54.0000			1.75476			0.877382	−	0.479792i	$-0.159288\pi$
$947$	54.0000			1.75476			0.877382	+	0.479792i	$0.159288\pi$
$948$		0			0
$949$	9.70820	−	7.05342i	0.315142	−	0.228964i
$950$	−38.8328	−	28.2137i	−1.25990	−	0.915373i
$951$	−1.85410	−	5.70634i	−0.0601234	−	0.185041i
$952$	−3.21140	−	9.88367i	−0.104082	−	0.320332i
$953$	−46.2415	−	33.5964i	−1.49791	−	1.08830i	−0.971204	−	0.238248i	$-0.923427\pi$
$953$	−46.2415	−	33.5964i	−1.49791	−	1.08830i	−0.526706	−	0.850048i	$-0.676573\pi$
$954$	−12.6113	+	9.16267i	−0.408307	+	0.296652i
$955$	−11.1246	+	34.2380i	−0.359984	+	1.10792i
$956$	6.92820			0.224074
$957$		0			0
$958$	42.0000			1.35696
$959$	−6.42280	+	19.7673i	−0.207403	+	0.638321i
$960$	−2.42705	+	1.76336i	−0.0783327	+	0.0569121i
$961$	12.1353	+	8.81678i	0.391460	+	0.284412i
$962$	10.1976	+	31.3849i	0.328783	+	1.01189i
$963$	−1.07047	−	3.29456i	−0.0344953	−	0.106166i
$964$	−16.8151	−	12.2169i	−0.541578	−	0.393479i
$965$	12.6113	−	9.16267i	0.405973	−	0.294957i
$966$	−11.1246	+	34.2380i	−0.357929	+	1.10159i
$967$	−10.3923			−0.334194			−0.167097	−	0.985940i	$-0.553439\pi$
$967$	−10.3923			−0.334194			−0.167097	+	0.985940i	$0.553439\pi$
$968$		0			0
$969$	−12.0000			−0.385496
$970$	−11.2399	+	34.5928i	−0.360891	+	1.11071i
$971$	33.9787	−	24.6870i	1.09043	−	0.792243i	0.110957	−	0.993825i	$-0.464608\pi$
$971$	33.9787	−	24.6870i	1.09043	−	0.792243i	0.979472	+	0.201582i	$0.0646083\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	−11.1246	−	34.2380i	−0.356639	−	1.09762i
$974$	20.3389	+	62.5966i	0.651699	+	2.00572i
$975$	5.60503	+	4.07230i	0.179505	+	0.130418i
$976$		0			0
$977$	−2.78115	+	8.55951i	−0.0889770	+	0.273843i	−0.985637	−	0.168876i	$-0.945986\pi$
$977$	−2.78115	+	8.55951i	−0.0889770	+	0.273843i	0.896660	+	0.442719i	$0.145986\pi$
$978$	3.46410			0.110770
$979$		0			0
$980$	−15.0000			−0.479157
$981$	−4.81710	+	14.8255i	−0.153798	+	0.473342i
$982$	29.1246	−	21.1603i	0.929404	−	0.675251i
$983$	29.1246	+	21.1603i	0.928931	+	0.674908i	0.945731	−	0.324951i	$-0.105348\pi$
$983$	29.1246	+	21.1603i	0.928931	+	0.674908i	−0.0168000	+	0.999859i	$0.505348\pi$
$984$	−0.927051	−	2.85317i	−0.0295533	−	0.0909557i
$985$	−17.6627	−	54.3602i	−0.562780	−	1.73206i
$986$	−4.20378	−	3.05422i	−0.133875	−	0.0972662i
$987$		0			0
$988$	−3.70820	+	11.4127i	−0.117974	+	0.363086i
$989$	20.7846			0.660912
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$	6.42280	−	19.7673i	0.203924	−	0.627614i
$993$	16.1803	−	11.7557i	0.513468	−	0.373056i
$994$	−29.1246	−	21.1603i	−0.923777	−	0.671163i
$995$	−9.27051	−	28.5317i	−0.293895	−	0.904516i
$996$		0			0
$997$	−1.40126	−	1.01807i	−0.0443783	−	0.0322427i	0.565375	−	0.824834i	$-0.308731\pi$
$997$	−1.40126	−	1.01807i	−0.0443783	−	0.0322427i	−0.609753	+	0.792591i	$0.708731\pi$
$998$	30.8277	−	22.3976i	0.975833	−	0.708984i
$999$	3.39919	−	10.4616i	0.107546	−	0.330991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.e.m.130.1		8
11.2	odd	10	inner	363.2.e.m.124.1		8
11.3	even	5	inner	363.2.e.m.202.2		8
11.4	even	5		363.2.a.f.1.1	✓	2
11.5	even	5	inner	363.2.e.m.148.1		8
11.6	odd	10	inner	363.2.e.m.148.2		8
11.7	odd	10		363.2.a.f.1.2	yes	2
11.8	odd	10	inner	363.2.e.m.202.1		8
11.9	even	5	inner	363.2.e.m.124.2		8
11.10	odd	2	inner	363.2.e.m.130.2		8
33.26	odd	10		1089.2.a.o.1.2		2
33.29	even	10		1089.2.a.o.1.1		2
44.7	even	10		5808.2.a.ca.1.2		2
44.15	odd	10		5808.2.a.ca.1.1		2
55.4	even	10		9075.2.a.bo.1.2		2
55.29	odd	10		9075.2.a.bo.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.a.f.1.1	✓	2	11.4	even	5
363.2.a.f.1.2	yes	2	11.7	odd	10
363.2.e.m.124.1		8	11.2	odd	10	inner
363.2.e.m.124.2		8	11.9	even	5	inner
363.2.e.m.130.1		8	1.1	even	1	trivial
363.2.e.m.130.2		8	11.10	odd	2	inner
363.2.e.m.148.1		8	11.5	even	5	inner
363.2.e.m.148.2		8	11.6	odd	10	inner
363.2.e.m.202.1		8	11.8	odd	10	inner
363.2.e.m.202.2		8	11.3	even	5	inner
1089.2.a.o.1.1		2	33.29	even	10
1089.2.a.o.1.2		2	33.26	odd	10
5808.2.a.ca.1.1		2	44.15	odd	10
5808.2.a.ca.1.2		2	44.7	even	10
9075.2.a.bo.1.1		2	55.29	odd	10
9075.2.a.bo.1.2		2	55.4	even	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.535233 + 1.64728i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.927051 - 2.85317i) q^{5} +(0.535233 + 1.64728i) q^{6} +(-2.80252 - 2.03615i) q^{7} +(-1.40126 + 1.01807i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.535233 + 1.64728i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.927051 - 2.85317i) q^{5} +(0.535233 + 1.64728i) q^{6} +(-2.80252 - 2.03615i) q^{7} +(-1.40126 + 1.01807i) q^{8} +(0.309017 - 0.951057i) q^{9} +5.19615 q^{10} -1.00000 q^{12} +(0.535233 - 1.64728i) q^{13} +(4.85410 - 3.52671i) q^{14} +(-2.42705 - 1.76336i) q^{15} +(-1.54508 - 4.75528i) q^{16} +(-0.535233 - 1.64728i) q^{17} +(1.40126 + 1.01807i) q^{18} +(5.60503 - 4.07230i) q^{19} +(-0.927051 + 2.85317i) q^{20} -3.46410 q^{21} -6.00000 q^{23} +(-0.535233 + 1.64728i) q^{24} +(-3.23607 + 2.35114i) q^{25} +(2.42705 + 1.76336i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.07047 + 3.29456i) q^{28} +(-1.40126 - 1.01807i) q^{29} +(4.20378 - 3.05422i) q^{30} +(1.23607 - 3.80423i) q^{31} +5.19615 q^{32} +3.00000 q^{34} +(-3.21140 + 9.88367i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(8.89919 + 6.46564i) q^{37} +(3.70820 + 11.4127i) q^{38} +(-0.535233 - 1.64728i) q^{39} +(4.20378 + 3.05422i) q^{40} +(-1.40126 + 1.01807i) q^{41} +(1.85410 - 5.70634i) q^{42} -3.46410 q^{43} -3.00000 q^{45} +(3.21140 - 9.88367i) q^{46} +(-4.04508 - 2.93893i) q^{48} +(1.54508 + 4.75528i) q^{49} +(-2.14093 - 6.58911i) q^{50} +(-1.40126 - 1.01807i) q^{51} +(-1.40126 + 1.01807i) q^{52} +(-2.78115 + 8.55951i) q^{53} +1.73205 q^{54} +6.00000 q^{56} +(2.14093 - 6.58911i) q^{57} +(2.42705 - 1.76336i) q^{58} +(4.85410 + 3.52671i) q^{59} +(0.927051 + 2.85317i) q^{60} +(5.60503 + 4.07230i) q^{62} +(-2.80252 + 2.03615i) q^{63} +(0.309017 - 0.951057i) q^{64} -5.19615 q^{65} -2.00000 q^{67} +(-0.535233 + 1.64728i) q^{68} +(-4.85410 + 3.52671i) q^{69} +(-14.5623 - 10.5801i) q^{70} +(-1.85410 - 5.70634i) q^{71} +(0.535233 + 1.64728i) q^{72} +(5.60503 + 4.07230i) q^{73} +(-15.4138 + 11.1988i) q^{74} +(-1.23607 + 3.80423i) q^{75} -6.92820 q^{76} +3.00000 q^{78} +(-12.1353 + 8.81678i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.927051 - 2.85317i) q^{82} +(2.80252 + 2.03615i) q^{84} +(-4.20378 + 3.05422i) q^{85} +(1.85410 - 5.70634i) q^{86} -1.73205 q^{87} +9.00000 q^{89} +(1.60570 - 4.94183i) q^{90} +(-4.85410 + 3.52671i) q^{91} +(4.85410 + 3.52671i) q^{92} +(-1.23607 - 3.80423i) q^{93} +(-16.8151 - 12.2169i) q^{95} +(4.20378 - 3.05422i) q^{96} +(-2.16312 + 6.65740i) q^{97} -8.66025 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 2 * q^4 + 6 * q^5 - 2 * q^9	\( 8 q + 2 q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{9} - 8 q^{12} + 12 q^{14} - 6 q^{15} + 10 q^{16} + 6 q^{20} - 48 q^{23} - 8 q^{25} + 6 q^{26} + 2 q^{27} - 8 q^{31} + 24 q^{34} - 2 q^{36} + 22 q^{37} - 24 q^{38} - 12 q^{42} - 24 q^{45} - 10 q^{48} - 10 q^{49} + 18 q^{53} + 48 q^{56} + 6 q^{58} + 12 q^{59} - 6 q^{60} - 2 q^{64} - 16 q^{67} - 12 q^{69} - 36 q^{70} + 12 q^{71} + 8 q^{75} + 24 q^{78} - 30 q^{80} - 2 q^{81} + 6 q^{82} - 12 q^{86} + 72 q^{89} - 12 q^{91} + 12 q^{92} + 8 q^{93} + 14 q^{97}+O(q^{100}) \) 8 * q + 2 * q^3 - 2 * q^4 + 6 * q^5 - 2 * q^9 - 8 * q^12 + 12 * q^14 - 6 * q^15 + 10 * q^16 + 6 * q^20 - 48 * q^23 - 8 * q^25 + 6 * q^26 + 2 * q^27 - 8 * q^31 + 24 * q^34 - 2 * q^36 + 22 * q^37 - 24 * q^38 - 12 * q^42 - 24 * q^45 - 10 * q^48 - 10 * q^49 + 18 * q^53 + 48 * q^56 + 6 * q^58 + 12 * q^59 - 6 * q^60 - 2 * q^64 - 16 * q^67 - 12 * q^69 - 36 * q^70 + 12 * q^71 + 8 * q^75 + 24 * q^78 - 30 * q^80 - 2 * q^81 + 6 * q^82 - 12 * q^86 + 72 * q^89 - 12 * q^91 + 12 * q^92 + 8 * q^93 + 14 * q^97

Introduction

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