LMFDB - Embedded newform 363.2.e.h.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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			130.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	363.130
Dual form			363.2.e.h.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+(0.500000 - 1.53884i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.118034 - 0.363271i) q^{5} +(0.500000 + 1.53884i) q^{6} +(-2.42705 - 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.618034 q^{10} +0.618034 q^{12} +(1.92705 - 5.93085i) q^{13} +(-3.92705 + 2.85317i) q^{14} +(0.309017 + 0.224514i) q^{15} +(-1.50000 - 4.61653i) q^{16} +(-0.190983 - 0.587785i) q^{17} +(-1.30902 - 0.951057i) q^{18} +(0.690983 - 0.502029i) q^{19} +(-0.0729490 + 0.224514i) q^{20} +3.00000 q^{21} -5.47214 q^{23} +(-0.690983 + 2.12663i) q^{24} +(3.92705 - 2.85317i) q^{25} +(-8.16312 - 5.93085i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.572949 + 1.76336i) q^{28} +(3.61803 + 2.62866i) q^{29} +(0.500000 - 0.363271i) q^{30} +(-1.19098 + 3.66547i) q^{31} -3.38197 q^{32} -1.00000 q^{34} +(-0.354102 + 1.08981i) q^{35} +(-0.500000 + 0.363271i) q^{36} +(3.42705 + 2.48990i) q^{37} +(-0.427051 - 1.31433i) q^{38} +(1.92705 + 5.93085i) q^{39} +(-0.690983 - 0.502029i) q^{40} +(-4.80902 + 3.49396i) q^{41} +(1.50000 - 4.61653i) q^{42} +1.76393 q^{43} -0.381966 q^{45} +(-2.73607 + 8.42075i) q^{46} +(0.500000 - 0.363271i) q^{47} +(3.92705 + 2.85317i) q^{48} +(0.618034 + 1.90211i) q^{49} +(-2.42705 - 7.46969i) q^{50} +(0.500000 + 0.363271i) q^{51} +(-3.11803 + 2.26538i) q^{52} +(-2.28115 + 7.02067i) q^{53} +1.61803 q^{54} -6.70820 q^{56} +(-0.263932 + 0.812299i) q^{57} +(5.85410 - 4.25325i) q^{58} +(4.30902 + 3.13068i) q^{59} +(-0.0729490 - 0.224514i) q^{60} +(0.354102 + 1.08981i) q^{61} +(5.04508 + 3.66547i) q^{62} +(-2.42705 + 1.76336i) q^{63} +(1.30902 - 4.02874i) q^{64} -2.38197 q^{65} +10.5623 q^{67} +(-0.118034 + 0.363271i) q^{68} +(4.42705 - 3.21644i) q^{69} +(1.50000 + 1.08981i) q^{70} +(4.50000 + 13.8496i) q^{71} +(-0.690983 - 2.12663i) q^{72} +(-1.00000 - 0.726543i) q^{73} +(5.54508 - 4.02874i) q^{74} +(-1.50000 + 4.61653i) q^{75} -0.527864 q^{76} +10.0902 q^{78} +(0.163119 - 0.502029i) q^{79} +(-1.50000 + 1.08981i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(2.97214 + 9.14729i) q^{82} +(-3.92705 - 12.0862i) q^{83} +(-1.50000 - 1.08981i) q^{84} +(-0.190983 + 0.138757i) q^{85} +(0.881966 - 2.71441i) q^{86} -4.47214 q^{87} +9.47214 q^{89} +(-0.190983 + 0.587785i) q^{90} +(-15.1353 + 10.9964i) q^{91} +(2.73607 + 1.98787i) q^{92} +(-1.19098 - 3.66547i) q^{93} +(-0.309017 - 0.951057i) q^{94} +(-0.263932 - 0.191758i) q^{95} +(2.73607 - 1.98787i) q^{96} +(4.64590 - 14.2986i) q^{97} +3.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 5 q^{8} - q^{9} + 2 q^{10} - 2 q^{12} + q^{13} - 9 q^{14} - q^{15} - 6 q^{16} - 3 q^{17} - 3 q^{18} + 5 q^{19} - 7 q^{20} + 12 q^{21}+ \cdots + 4 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 5 * q^8 - q^9 + 2 * q^10 - 2 * q^12 + q^13 - 9 * q^14 - q^15 - 6 * q^16 - 3 * q^17 - 3 * q^18 + 5 * q^19 - 7 * q^20 + 12 * q^21 - 4 * q^23 - 5 * q^24 + 9 * q^25 - 17 * q^26 - q^27 + 9 * q^28 + 10 * q^29 + 2 * q^30 - 7 * q^31 - 18 * q^32 - 4 * q^34 + 12 * q^35 - 2 * q^36 + 7 * q^37 + 5 * q^38 + q^39 - 5 * q^40 - 17 * q^41 + 6 * q^42 + 16 * q^43 - 6 * q^45 - 2 * q^46 + 2 * q^47 + 9 * q^48 - 2 * q^49 - 3 * q^50 + 2 * q^51 - 8 * q^52 + 11 * q^53 + 2 * q^54 - 10 * q^57 + 10 * q^58 + 15 * q^59 - 7 * q^60 - 12 * q^61 + 9 * q^62 - 3 * q^63 + 3 * q^64 - 14 * q^65 + 2 * q^67 + 4 * q^68 + 11 * q^69 + 6 * q^70 + 18 * q^71 - 5 * q^72 - 4 * q^73 + 11 * q^74 - 6 * q^75 - 20 * q^76 + 18 * q^78 - 15 * q^79 - 6 * q^80 - q^81 - 6 * q^82 - 9 * q^83 - 6 * q^84 - 3 * q^85 + 8 * q^86 + 20 * q^89 - 3 * q^90 - 27 * q^91 + 2 * q^92 - 7 * q^93 + q^94 - 10 * q^95 + 2 * q^96 + 32 * q^97 + 4 * q^98

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 $

$2$	0.500000	−	1.53884i	0.353553	−	1.08813i	−0.603290	−	0.797522i	$-0.706144\pi$
$2$	0.500000	−	1.53884i	0.353553	−	1.08813i	0.956844	−	0.290604i	$-0.0938561\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.500000	−	0.363271i	−0.250000	−	0.181636i
$5$	−0.118034	−	0.363271i	−0.0527864	−	0.162460i	0.921188	−	0.389118i	$-0.127220\pi$
$5$	−0.118034	−	0.363271i	−0.0527864	−	0.162460i	−0.973974	+	0.226658i	$0.927220\pi$
$6$	0.500000	+	1.53884i	0.204124	+	0.628230i
$7$	−2.42705	−	1.76336i	−0.917339	−	0.666486i	0.0255212	−	0.999674i	$-0.491875\pi$
$7$	−2.42705	−	1.76336i	−0.917339	−	0.666486i	−0.942860	+	0.333188i	$0.891875\pi$
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.618034			−0.195440
$11$		0			0
$11$		0			0
$12$	0.618034			0.178411
$13$	1.92705	−	5.93085i	0.534468	−	1.64492i	−0.210329	−	0.977631i	$-0.567453\pi$
$13$	1.92705	−	5.93085i	0.534468	−	1.64492i	0.744796	−	0.667292i	$-0.232547\pi$
$14$	−3.92705	+	2.85317i	−1.04955	+	0.762542i
$15$	0.309017	+	0.224514i	0.0797878	+	0.0579693i
$16$	−1.50000	−	4.61653i	−0.375000	−	1.15413i
$17$	−0.190983	−	0.587785i	−0.0463202	−	0.142559i	0.925222	−	0.379427i	$-0.123879\pi$
$17$	−0.190983	−	0.587785i	−0.0463202	−	0.142559i	−0.971542	+	0.236868i	$0.923879\pi$
$18$	−1.30902	−	0.951057i	−0.308538	−	0.224166i
$19$	0.690983	−	0.502029i	0.158522	−	0.115173i	−0.505696	−	0.862712i	$-0.668764\pi$
$19$	0.690983	−	0.502029i	0.158522	−	0.115173i	0.664219	+	0.747538i	$0.268764\pi$
$20$	−0.0729490	+	0.224514i	−0.0163119	+	0.0502029i
$21$	3.00000			0.654654
$22$		0			0
$23$	−5.47214			−1.14102			−0.570510	−	0.821291i	$-0.693254\pi$
$23$	−5.47214			−1.14102			−0.570510	+	0.821291i	$0.693254\pi$
$24$	−0.690983	+	2.12663i	−0.141046	+	0.434096i
$25$	3.92705	−	2.85317i	0.785410	−	0.570634i
$26$	−8.16312	−	5.93085i	−1.60092	−	1.16314i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	0.572949	+	1.76336i	0.108277	+	0.333243i
$29$	3.61803	+	2.62866i	0.671852	+	0.488129i	0.870645	−	0.491912i	$-0.163702\pi$
$29$	3.61803	+	2.62866i	0.671852	+	0.488129i	−0.198793	+	0.980042i	$0.563702\pi$
$30$	0.500000	−	0.363271i	0.0912871	−	0.0663240i
$31$	−1.19098	+	3.66547i	−0.213907	+	0.658338i	0.785323	+	0.619087i	$0.212497\pi$
$31$	−1.19098	+	3.66547i	−0.213907	+	0.658338i	−0.999229	+	0.0392508i	$0.987503\pi$
$32$	−3.38197			−0.597853
$33$		0			0
$34$	−1.00000			−0.171499
$35$	−0.354102	+	1.08981i	−0.0598542	+	0.184212i
$36$	−0.500000	+	0.363271i	−0.0833333	+	0.0605452i
$37$	3.42705	+	2.48990i	0.563404	+	0.409337i	0.832703	−	0.553720i	$-0.186792\pi$
$37$	3.42705	+	2.48990i	0.563404	+	0.409337i	−0.269299	+	0.963057i	$0.586792\pi$
$38$	−0.427051	−	1.31433i	−0.0692768	−	0.213212i
$39$	1.92705	+	5.93085i	0.308575	+	0.949697i
$40$	−0.690983	−	0.502029i	−0.109254	−	0.0793777i
$41$	−4.80902	+	3.49396i	−0.751042	+	0.545664i	−0.896150	−	0.443752i	$-0.853647\pi$
$41$	−4.80902	+	3.49396i	−0.751042	+	0.545664i	0.145107	+	0.989416i	$0.453647\pi$
$42$	1.50000	−	4.61653i	0.231455	−	0.712345i
$43$	1.76393			0.268997			0.134499	−	0.990914i	$-0.457058\pi$
$43$	1.76393			0.268997			0.134499	+	0.990914i	$0.457058\pi$
$44$		0			0
$45$	−0.381966			−0.0569401
$46$	−2.73607	+	8.42075i	−0.403411	+	1.24157i
$47$	0.500000	−	0.363271i	0.0729325	−	0.0529886i	−0.550722	−	0.834689i	$-0.685647\pi$
$47$	0.500000	−	0.363271i	0.0729325	−	0.0529886i	0.623654	+	0.781700i	$0.285647\pi$
$48$	3.92705	+	2.85317i	0.566821	+	0.411820i
$49$	0.618034	+	1.90211i	0.0882906	+	0.271730i
$50$	−2.42705	−	7.46969i	−0.343237	−	1.05637i
$51$	0.500000	+	0.363271i	0.0700140	+	0.0508682i
$52$	−3.11803	+	2.26538i	−0.432394	+	0.314152i
$53$	−2.28115	+	7.02067i	−0.313340	+	0.964363i	0.663092	+	0.748538i	$0.269244\pi$
$53$	−2.28115	+	7.02067i	−0.313340	+	0.964363i	−0.976432	+	0.215825i	$0.930756\pi$
$54$	1.61803			0.220187
$55$		0			0
$56$	−6.70820			−0.896421
$57$	−0.263932	+	0.812299i	−0.0349587	+	0.107592i
$58$	5.85410	−	4.25325i	0.768681	−	0.558480i
$59$	4.30902	+	3.13068i	0.560986	+	0.407580i	0.831820	−	0.555046i	$-0.187299\pi$
$59$	4.30902	+	3.13068i	0.560986	+	0.407580i	−0.270834	+	0.962626i	$0.587299\pi$
$60$	−0.0729490	−	0.224514i	−0.00941768	−	0.0289846i
$61$	0.354102	+	1.08981i	0.0453381	+	0.139536i	0.971163	−	0.238416i	$-0.0766282\pi$
$61$	0.354102	+	1.08981i	0.0453381	+	0.139536i	−0.925825	+	0.377953i	$0.876628\pi$
$62$	5.04508	+	3.66547i	0.640726	+	0.465515i
$63$	−2.42705	+	1.76336i	−0.305780	+	0.222162i
$64$	1.30902	−	4.02874i	0.163627	−	0.503593i
$65$	−2.38197			−0.295447
$66$		0			0
$67$	10.5623			1.29039			0.645196	−	0.764017i	$-0.276776\pi$
$67$	10.5623			1.29039			0.645196	+	0.764017i	$0.276776\pi$
$68$	−0.118034	+	0.363271i	−0.0143137	+	0.0440531i
$69$	4.42705	−	3.21644i	0.532954	−	0.387214i
$70$	1.50000	+	1.08981i	0.179284	+	0.130258i
$71$	4.50000	+	13.8496i	0.534052	+	1.64364i	0.745689	+	0.666294i	$0.232120\pi$
$71$	4.50000	+	13.8496i	0.534052	+	1.64364i	−0.211637	+	0.977348i	$0.567880\pi$
$72$	−0.690983	−	2.12663i	−0.0814331	−	0.250625i
$73$	−1.00000	−	0.726543i	−0.117041	−	0.0850354i	0.527725	−	0.849415i	$-0.323045\pi$
$73$	−1.00000	−	0.726543i	−0.117041	−	0.0850354i	−0.644766	+	0.764380i	$0.723045\pi$
$74$	5.54508	−	4.02874i	0.644603	−	0.468332i
$75$	−1.50000	+	4.61653i	−0.173205	+	0.533070i
$76$	−0.527864			−0.0605502
$77$		0			0
$78$	10.0902			1.14249
$79$	0.163119	−	0.502029i	0.0183523	−	0.0564826i	−0.941461	−	0.337122i	$-0.890547\pi$
$79$	0.163119	−	0.502029i	0.0183523	−	0.0564826i	0.959813	+	0.280639i	$0.0905465\pi$
$80$	−1.50000	+	1.08981i	−0.167705	+	0.121845i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	2.97214	+	9.14729i	0.328218	+	1.01015i
$83$	−3.92705	−	12.0862i	−0.431050	−	1.32664i	−0.897081	−	0.441867i	$-0.854316\pi$
$83$	−3.92705	−	12.0862i	−0.431050	−	1.32664i	0.466031	−	0.884768i	$-0.345684\pi$
$84$	−1.50000	−	1.08981i	−0.163663	−	0.118908i
$85$	−0.190983	+	0.138757i	−0.0207150	+	0.0150503i
$86$	0.881966	−	2.71441i	0.0951048	−	0.292703i
$87$	−4.47214			−0.479463
$88$		0			0
$89$	9.47214			1.00404			0.502022	−	0.864855i	$-0.332590\pi$
$89$	9.47214			1.00404			0.502022	+	0.864855i	$0.332590\pi$
$90$	−0.190983	+	0.587785i	−0.0201314	+	0.0619580i
$91$	−15.1353	+	10.9964i	−1.58661	+	1.15274i
$92$	2.73607	+	1.98787i	0.285255	+	0.207250i
$93$	−1.19098	−	3.66547i	−0.123499	−	0.380091i
$94$	−0.309017	−	0.951057i	−0.0318727	−	0.0980940i
$95$	−0.263932	−	0.191758i	−0.0270789	−	0.0196739i
$96$	2.73607	−	1.98787i	0.279249	−	0.202886i
$97$	4.64590	−	14.2986i	0.471719	−	1.45180i	−0.378612	−	0.925556i	$-0.623598\pi$
$97$	4.64590	−	14.2986i	0.471719	−	1.45180i	0.850331	−	0.526248i	$-0.176402\pi$
$98$	3.23607			0.326892
$99$		0			0
$100$	−3.00000			−0.300000
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	−0.986526	−	0.163605i	$-0.947688\pi$
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	0.894281	+	0.447506i	$0.147688\pi$
$102$	0.809017	−	0.587785i	0.0801046	−	0.0581994i
$103$	4.85410	+	3.52671i	0.478289	+	0.347497i	0.800663	−	0.599115i	$-0.204481\pi$
$103$	4.85410	+	3.52671i	0.478289	+	0.347497i	−0.322374	+	0.946612i	$0.604481\pi$
$104$	−4.30902	−	13.2618i	−0.422534	−	1.30043i
$105$	−0.354102	−	1.08981i	−0.0345568	−	0.106355i
$106$	9.66312	+	7.02067i	0.938565	+	0.681907i
$107$	−0.190983	+	0.138757i	−0.0184630	+	0.0134142i	−0.596978	−	0.802257i	$-0.703632\pi$
$107$	−0.190983	+	0.138757i	−0.0184630	+	0.0134142i	0.578515	+	0.815671i	$0.303632\pi$
$108$	0.190983	−	0.587785i	0.0183773	−	0.0565597i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	−4.23607			−0.402070
$112$	−4.50000	+	13.8496i	−0.425210	+	1.30866i
$113$	10.2812	−	7.46969i	0.967170	−	0.702690i	0.0123648	−	0.999924i	$-0.496064\pi$
$113$	10.2812	−	7.46969i	0.967170	−	0.702690i	0.954805	+	0.297234i	$0.0960641\pi$
$114$	1.11803	+	0.812299i	0.104713	+	0.0760788i
$115$	0.645898	+	1.98787i	0.0602303	+	0.185370i
$116$	−0.854102	−	2.62866i	−0.0793014	−	0.244065i
$117$	−5.04508	−	3.66547i	−0.466418	−	0.338873i
$118$	6.97214	−	5.06555i	0.641837	−	0.466322i
$119$	−0.572949	+	1.76336i	−0.0525222	+	0.161647i
$120$	0.854102			0.0779685
$121$		0			0
$122$	1.85410			0.167863
$123$	1.83688	−	5.65334i	0.165626	−	0.509744i
$124$	1.92705	−	1.40008i	0.173054	−	0.125731i
$125$	−3.04508	−	2.21238i	−0.272361	−	0.197882i
$126$	1.50000	+	4.61653i	0.133631	+	0.411273i
$127$	3.00000	+	9.23305i	0.266207	+	0.819301i	0.991413	+	0.130769i	$0.0417445\pi$
$127$	3.00000	+	9.23305i	0.266207	+	0.819301i	−0.725206	+	0.688532i	$0.758255\pi$
$128$	−11.0172	−	8.00448i	−0.973794	−	0.707503i
$129$	−1.42705	+	1.03681i	−0.125645	+	0.0912863i
$130$	−1.19098	+	3.66547i	−0.104456	+	0.321483i
$131$	−13.8541			−1.21044			−0.605219	−	0.796059i	$-0.706915\pi$
$131$	−13.8541			−1.21044			−0.605219	+	0.796059i	$0.706915\pi$
$132$		0			0
$133$	−2.56231			−0.222180
$134$	5.28115	−	16.2537i	0.456222	−	1.40411i
$135$	0.309017	−	0.224514i	0.0265959	−	0.0193231i
$136$	−1.11803	−	0.812299i	−0.0958706	−	0.0696541i
$137$	−0.454915	−	1.40008i	−0.0388660	−	0.119617i	0.929741	−	0.368214i	$-0.120031\pi$
$137$	−0.454915	−	1.40008i	−0.0388660	−	0.119617i	−0.968607	+	0.248597i	$0.920031\pi$
$138$	−2.73607	−	8.42075i	−0.232910	−	0.716822i
$139$	−4.73607	−	3.44095i	−0.401708	−	0.291858i	0.368528	−	0.929617i	$-0.379862\pi$
$139$	−4.73607	−	3.44095i	−0.401708	−	0.291858i	−0.770236	+	0.637759i	$0.779862\pi$
$140$	0.572949	−	0.416272i	0.0484230	−	0.0351814i
$141$	−0.190983	+	0.587785i	−0.0160837	+	0.0495004i
$142$	23.5623			1.97730
$143$		0			0
$144$	−4.85410			−0.404508
$145$	0.527864	−	1.62460i	0.0438367	−	0.134916i
$146$	−1.61803	+	1.17557i	−0.133909	+	0.0972909i
$147$	−1.61803	−	1.17557i	−0.133453	−	0.0969594i
$148$	−0.809017	−	2.48990i	−0.0665008	−	0.204668i
$149$	4.63525	+	14.2658i	0.379735	+	1.16870i	0.940228	+	0.340545i	$0.110612\pi$
$149$	4.63525	+	14.2658i	0.379735	+	1.16870i	−0.560493	+	0.828159i	$0.689388\pi$
$150$	6.35410	+	4.61653i	0.518810	+	0.376938i
$151$	−1.61803	+	1.17557i	−0.131674	+	0.0956666i	−0.651673	−	0.758500i	$-0.725932\pi$
$151$	−1.61803	+	1.17557i	−0.131674	+	0.0956666i	0.519999	+	0.854167i	$0.325932\pi$
$152$	0.590170	−	1.81636i	0.0478691	−	0.147326i
$153$	−0.618034			−0.0499651
$154$		0			0
$155$	1.47214			0.118245
$156$	1.19098	−	3.66547i	0.0953550	−	0.293472i
$157$	−7.85410	+	5.70634i	−0.626826	+	0.455415i	−0.855299	−	0.518135i	$-0.826627\pi$
$157$	−7.85410	+	5.70634i	−0.626826	+	0.455415i	0.228473	+	0.973550i	$0.426627\pi$
$158$	−0.690983	−	0.502029i	−0.0549717	−	0.0399392i
$159$	−2.28115	−	7.02067i	−0.180907	−	0.556775i
$160$	0.399187	+	1.22857i	0.0315585	+	0.0971271i
$161$	13.2812	+	9.64932i	1.04670	+	0.760473i
$162$	−1.30902	+	0.951057i	−0.102846	+	0.0747221i
$163$	−4.71885	+	14.5231i	−0.369609	+	1.13754i	0.577436	+	0.816436i	$0.304053\pi$
$163$	−4.71885	+	14.5231i	−0.369609	+	1.13754i	−0.947045	+	0.321102i	$0.895947\pi$
$164$	3.67376			0.286873
$165$		0			0
$166$	−20.5623			−1.59594
$167$	−5.88197	+	18.1028i	−0.455160	+	1.40084i	0.415787	+	0.909462i	$0.363506\pi$
$167$	−5.88197	+	18.1028i	−0.455160	+	1.40084i	−0.870947	+	0.491377i	$0.836494\pi$
$168$	5.42705	−	3.94298i	0.418706	−	0.304208i
$169$	−20.9443	−	15.2169i	−1.61110	−	1.17053i
$170$	0.118034	+	0.363271i	0.00905279	+	0.0278616i
$171$	−0.263932	−	0.812299i	−0.0201834	−	0.0621181i
$172$	−0.881966	−	0.640786i	−0.0672493	−	0.0488595i
$173$	−14.2533	+	10.3556i	−1.08366	+	0.787323i	−0.978317	−	0.207113i	$-0.933593\pi$
$173$	−14.2533	+	10.3556i	−1.08366	+	0.787323i	−0.105340	+	0.994436i	$0.533593\pi$
$174$	−2.23607	+	6.88191i	−0.169516	+	0.521716i
$175$	−14.5623			−1.10081
$176$		0			0
$177$	−5.32624			−0.400345
$178$	4.73607	−	14.5761i	0.354983	−	1.09253i
$179$	−1.80902	+	1.31433i	−0.135212	+	0.0982375i	−0.653335	−	0.757069i	$-0.726631\pi$
$179$	−1.80902	+	1.31433i	−0.135212	+	0.0982375i	0.518123	+	0.855306i	$0.326631\pi$
$180$	0.190983	+	0.138757i	0.0142350	+	0.0103424i
$181$	−2.63525	−	8.11048i	−0.195877	−	0.602847i	−0.999965	−	0.00833738i	$-0.997346\pi$
$181$	−2.63525	−	8.11048i	−0.195877	−	0.602847i	0.804088	−	0.594510i	$-0.202654\pi$
$182$	9.35410	+	28.7890i	0.693372	+	2.13398i
$183$	−0.927051	−	0.673542i	−0.0685296	−	0.0497897i
$184$	−9.89919	+	7.19218i	−0.729778	+	0.530215i
$185$	0.500000	−	1.53884i	0.0367607	−	0.113138i
$186$	−6.23607			−0.457251
$187$		0			0
$188$	−0.381966			−0.0278577
$189$	0.927051	−	2.85317i	0.0674330	−	0.207538i
$190$	−0.427051	+	0.310271i	−0.0309815	+	0.0225094i
$191$	−1.19098	−	0.865300i	−0.0861765	−	0.0626109i	0.543863	−	0.839174i	$-0.316961\pi$
$191$	−1.19098	−	0.865300i	−0.0861765	−	0.0626109i	−0.630039	+	0.776563i	$0.716961\pi$
$192$	1.30902	+	4.02874i	0.0944702	+	0.290749i
$193$	0.482779	+	1.48584i	0.0347512	+	0.106953i	0.966927	−	0.255052i	$-0.0820924\pi$
$193$	0.482779	+	1.48584i	0.0347512	+	0.106953i	−0.932176	+	0.362005i	$0.882092\pi$
$194$	−19.6803	−	14.2986i	−1.41297	−	1.02658i
$195$	1.92705	−	1.40008i	0.137999	−	0.100262i
$196$	0.381966	−	1.17557i	0.0272833	−	0.0839693i
$197$	26.6180			1.89646			0.948228	−	0.317590i	$-0.102873\pi$
$197$	26.6180			1.89646			0.948228	+	0.317590i	$0.102873\pi$
$198$		0			0
$199$	−3.29180			−0.233349			−0.116675	−	0.993170i	$-0.537223\pi$
$199$	−3.29180			−0.233349			−0.116675	+	0.993170i	$0.537223\pi$
$200$	3.35410	−	10.3229i	0.237171	−	0.729937i
$201$	−8.54508	+	6.20837i	−0.602724	+	0.437904i
$202$	3.92705	+	2.85317i	0.276306	+	0.200748i
$203$	−4.14590	−	12.7598i	−0.290985	−	0.895560i
$204$	−0.118034	−	0.363271i	−0.00826403	−	0.0254341i
$205$	1.83688	+	1.33457i	0.128293	+	0.0932106i
$206$	7.85410	−	5.70634i	0.547221	−	0.397579i
$207$	−1.69098	+	5.20431i	−0.117531	+	0.361725i
$208$	−30.2705			−2.09888
$209$		0			0
$210$	−1.85410			−0.127945
$211$	3.48278	−	10.7189i	0.239764	−	0.737919i	−0.756689	−	0.653775i	$-0.773184\pi$
$211$	3.48278	−	10.7189i	0.239764	−	0.737919i	0.996454	−	0.0841442i	$-0.0268156\pi$
$212$	3.69098	−	2.68166i	0.253498	−	0.184177i
$213$	−11.7812	−	8.55951i	−0.807231	−	0.586488i
$214$	0.118034	+	0.363271i	0.00806864	+	0.0248327i
$215$	−0.208204	−	0.640786i	−0.0141994	−	0.0437012i
$216$	1.80902	+	1.31433i	0.123088	+	0.0894287i
$217$	9.35410	−	6.79615i	0.634998	−	0.461353i
$218$		0			0
$219$	1.23607			0.0835257
$220$		0			0
$221$	−3.85410			−0.259255
$222$	−2.11803	+	6.51864i	−0.142153	+	0.437502i
$223$	10.2812	−	7.46969i	0.688477	−	0.500208i	−0.187682	−	0.982230i	$-0.560097\pi$
$223$	10.2812	−	7.46969i	0.688477	−	0.500208i	0.876159	+	0.482022i	$0.160097\pi$
$224$	8.20820	+	5.96361i	0.548434	+	0.398460i
$225$	−1.50000	−	4.61653i	−0.100000	−	0.307768i
$226$	−6.35410	−	19.5559i	−0.422669	−	1.30084i
$227$	−8.80902	−	6.40013i	−0.584675	−	0.424791i	0.255731	−	0.966748i	$-0.417684\pi$
$227$	−8.80902	−	6.40013i	−0.584675	−	0.424791i	−0.840406	+	0.541957i	$0.817684\pi$
$228$	0.427051	−	0.310271i	0.0282821	−	0.0205482i
$229$	3.09017	−	9.51057i	0.204204	−	0.628476i	−0.795541	−	0.605900i	$-0.792813\pi$
$229$	3.09017	−	9.51057i	0.204204	−	0.628476i	0.999745	−	0.0225760i	$-0.00718678\pi$
$230$	3.38197			0.223000
$231$		0			0
$232$	10.0000			0.656532
$233$	2.68034	−	8.24924i	0.175595	−	0.540426i	−0.824065	−	0.566495i	$-0.808299\pi$
$233$	2.68034	−	8.24924i	0.175595	−	0.540426i	0.999660	+	0.0260694i	$0.00829908\pi$
$234$	−8.16312	+	5.93085i	−0.533640	+	0.387712i
$235$	−0.190983	−	0.138757i	−0.0124584	−	0.00905153i
$236$	−1.01722	−	3.13068i	−0.0662154	−	0.203790i
$237$	0.163119	+	0.502029i	0.0105957	+	0.0326103i
$238$	2.42705	+	1.76336i	0.157322	+	0.114301i
$239$	14.2082	−	10.3229i	0.919052	−	0.667731i	−0.0242356	−	0.999706i	$-0.507715\pi$
$239$	14.2082	−	10.3229i	0.919052	−	0.667731i	0.943288	+	0.331976i	$0.107715\pi$
$240$	0.572949	−	1.76336i	0.0369837	−	0.113824i
$241$	17.1246			1.10309			0.551547	−	0.834144i	$-0.314038\pi$
$241$	17.1246			1.10309			0.551547	+	0.834144i	$0.314038\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	0.218847	−	0.673542i	0.0140102	−	0.0431191i
$245$	0.618034	−	0.449028i	0.0394847	−	0.0286873i
$246$	−7.78115	−	5.65334i	−0.496108	−	0.360444i
$247$	−1.64590	−	5.06555i	−0.104726	−	0.322313i
$248$	2.66312	+	8.19624i	0.169108	+	0.520462i
$249$	10.2812	+	7.46969i	0.651542	+	0.473373i
$250$	−4.92705	+	3.57971i	−0.311614	+	0.226401i
$251$	5.19098	−	15.9762i	0.327652	−	1.00841i	−0.642577	−	0.766221i	$-0.722135\pi$
$251$	5.19098	−	15.9762i	0.327652	−	1.00841i	0.970229	−	0.242188i	$-0.0778651\pi$
$252$	1.85410			0.116797
$253$		0			0
$254$	15.7082			0.985620
$255$	0.0729490	−	0.224514i	0.00456824	−	0.0140596i
$256$	−10.9721	+	7.97172i	−0.685758	+	0.498233i
$257$	22.1074	+	16.0620i	1.37902	+	1.00192i	0.996971	+	0.0777760i	$0.0247819\pi$
$257$	22.1074	+	16.0620i	1.37902	+	1.00192i	0.382050	+	0.924142i	$0.375218\pi$
$258$	0.881966	+	2.71441i	0.0549088	+	0.168992i
$259$	−3.92705	−	12.0862i	−0.244015	−	0.751001i
$260$	1.19098	+	0.865300i	0.0738616	+	0.0536636i
$261$	3.61803	−	2.62866i	0.223951	−	0.162710i
$262$	−6.92705	+	21.3193i	−0.427955	+	1.31711i
$263$	−0.673762			−0.0415459			−0.0207730	−	0.999784i	$-0.506613\pi$
$263$	−0.673762			−0.0415459			−0.0207730	+	0.999784i	$0.506613\pi$
$264$		0			0
$265$	2.81966			0.173210
$266$	−1.28115	+	3.94298i	−0.0785525	+	0.241760i
$267$	−7.66312	+	5.56758i	−0.468975	+	0.340730i
$268$	−5.28115	−	3.83698i	−0.322598	−	0.234381i
$269$	7.56231	+	23.2744i	0.461082	+	1.41906i	0.863844	+	0.503760i	$0.168050\pi$
$269$	7.56231	+	23.2744i	0.461082	+	1.41906i	−0.402762	+	0.915305i	$0.631950\pi$
$270$	−0.190983	−	0.587785i	−0.0116229	−	0.0357715i
$271$	−5.07295	−	3.68571i	−0.308160	−	0.223891i	0.422947	−	0.906155i	$-0.360996\pi$
$271$	−5.07295	−	3.68571i	−0.308160	−	0.223891i	−0.731106	+	0.682263i	$0.760996\pi$
$272$	−2.42705	+	1.76336i	−0.147162	+	0.106919i
$273$	5.78115	−	17.7926i	0.349891	−	1.07685i
$274$	−2.38197			−0.143900
$275$		0			0
$276$	−3.38197			−0.203570
$277$	3.22542	−	9.92684i	0.193797	−	0.596446i	−0.806192	−	0.591655i	$-0.798475\pi$
$277$	3.22542	−	9.92684i	0.193797	−	0.596446i	0.999989	−	0.00479118i	$-0.00152509\pi$
$278$	−7.66312	+	5.56758i	−0.459603	+	0.333921i
$279$	3.11803	+	2.26538i	0.186672	+	0.135625i
$280$	0.791796	+	2.43690i	0.0473189	+	0.145632i
$281$	−1.61803	−	4.97980i	−0.0965238	−	0.297070i	0.891124	−	0.453760i	$-0.149918\pi$
$281$	−1.61803	−	4.97980i	−0.0965238	−	0.297070i	−0.987648	+	0.156690i	$0.949918\pi$
$282$	0.809017	+	0.587785i	0.0481763	+	0.0350021i
$283$	17.9443	−	13.0373i	1.06668	−	0.774986i	0.0913644	−	0.995818i	$-0.470877\pi$
$283$	17.9443	−	13.0373i	1.06668	−	0.774986i	0.975312	+	0.220832i	$0.0708772\pi$
$284$	2.78115	−	8.55951i	0.165031	−	0.507913i
$285$	0.326238			0.0193247
$286$		0			0
$287$	17.8328			1.05264
$288$	−1.04508	+	3.21644i	−0.0615822	+	0.189531i
$289$	13.4443	−	9.76784i	0.790840	−	0.574579i
$290$	−2.23607	−	1.62460i	−0.131306	−	0.0953997i
$291$	4.64590	+	14.2986i	0.272347	+	0.838199i
$292$	0.236068	+	0.726543i	0.0138148	+	0.0425177i
$293$	−14.5172	−	10.5474i	−0.848105	−	0.616184i	0.0765178	−	0.997068i	$-0.475620\pi$
$293$	−14.5172	−	10.5474i	−0.848105	−	0.616184i	−0.924623	+	0.380884i	$0.875620\pi$
$294$	−2.61803	+	1.90211i	−0.152687	+	0.110933i
$295$	0.628677	−	1.93487i	0.0366030	−	0.112652i
$296$	9.47214			0.550557
$297$		0			0
$298$	24.2705			1.40595
$299$	−10.5451	+	32.4544i	−0.609838	+	1.87689i
$300$	2.42705	−	1.76336i	0.140126	−	0.101807i
$301$	−4.28115	−	3.11044i	−0.246762	−	0.179283i
$302$	1.00000	+	3.07768i	0.0575435	+	0.177101i
$303$	−0.927051	−	2.85317i	−0.0532577	−	0.163910i
$304$	−3.35410	−	2.43690i	−0.192371	−	0.139766i
$305$	0.354102	−	0.257270i	0.0202758	−	0.0147312i
$306$	−0.309017	+	0.951057i	−0.0176653	+	0.0543683i
$307$	−19.5623			−1.11648			−0.558240	−	0.829680i	$-0.688523\pi$
$307$	−19.5623			−1.11648			−0.558240	+	0.829680i	$0.688523\pi$
$308$		0			0
$309$	−6.00000			−0.341328
$310$	0.736068	−	2.26538i	0.0418059	−	0.128665i
$311$	−9.28115	+	6.74315i	−0.526286	+	0.382369i	−0.818967	−	0.573841i	$-0.805453\pi$
$311$	−9.28115	+	6.74315i	−0.526286	+	0.382369i	0.292681	+	0.956210i	$0.405453\pi$
$312$	11.2812	+	8.19624i	0.638670	+	0.464021i
$313$	−8.60081	−	26.4706i	−0.486147	−	1.49621i	−0.830313	−	0.557297i	$-0.811838\pi$
$313$	−8.60081	−	26.4706i	−0.486147	−	1.49621i	0.344166	−	0.938909i	$-0.388162\pi$
$314$	4.85410	+	14.9394i	0.273933	+	0.843079i
$315$	0.927051	+	0.673542i	0.0522334	+	0.0379498i
$316$	−0.263932	+	0.191758i	−0.0148473	+	0.0107872i
$317$	7.83688	−	24.1194i	0.440163	−	1.35468i	−0.447539	−	0.894264i	$-0.647699\pi$
$317$	7.83688	−	24.1194i	0.440163	−	1.35468i	0.887702	−	0.460418i	$-0.152301\pi$
$318$	−11.9443			−0.669802
$319$		0			0
$320$	−1.61803			−0.0904508
$321$	0.0729490	−	0.224514i	0.00407162	−	0.0125311i
$322$	21.4894	−	15.6129i	1.19756	−	0.870075i
$323$	−0.427051	−	0.310271i	−0.0237618	−	0.0172639i
$324$	0.190983	+	0.587785i	0.0106102	+	0.0326547i
$325$	−9.35410	−	28.7890i	−0.518872	−	1.59692i
$326$	19.9894	+	14.5231i	1.10711	+	0.804361i
$327$		0			0
$328$	−4.10739	+	12.6412i	−0.226793	+	0.697996i
$329$	−1.85410			−0.102220
$330$		0			0
$331$	−22.5967			−1.24203			−0.621015	−	0.783799i	$-0.713279\pi$
$331$	−22.5967			−1.24203			−0.621015	+	0.783799i	$0.713279\pi$
$332$	−2.42705	+	7.46969i	−0.133202	+	0.409953i
$333$	3.42705	−	2.48990i	0.187801	−	0.136446i
$334$	24.9164	+	18.1028i	1.36337	+	0.990543i
$335$	−1.24671	−	3.83698i	−0.0681151	−	0.209637i
$336$	−4.50000	−	13.8496i	−0.245495	−	0.755556i
$337$	11.0902	+	8.05748i	0.604120	+	0.438919i	0.847339	−	0.531053i	$-0.178203\pi$
$337$	11.0902	+	8.05748i	0.604120	+	0.438919i	−0.243219	+	0.969971i	$0.578203\pi$
$338$	−33.8885	+	24.6215i	−1.84329	+	1.33923i
$339$	−3.92705	+	12.0862i	−0.213288	+	0.656433i
$340$	0.145898			0.00791243
$341$		0			0
$342$	−1.38197			−0.0747282
$343$	−4.63525	+	14.2658i	−0.250280	+	0.770283i
$344$	3.19098	−	2.31838i	0.172046	−	0.124999i
$345$	−1.69098	−	1.22857i	−0.0910395	−	0.0661440i
$346$	8.80902	+	27.1114i	0.473576	+	1.45752i
$347$	−0.944272	−	2.90617i	−0.0506912	−	0.156011i	0.922507	−	0.385982i	$-0.126137\pi$
$347$	−0.944272	−	2.90617i	−0.0506912	−	0.156011i	−0.973198	+	0.229970i	$0.926137\pi$
$348$	2.23607	+	1.62460i	0.119866	+	0.0870876i
$349$	−24.3713	+	17.7068i	−1.30457	+	0.947823i	−0.999989	−	0.00466403i	$-0.998515\pi$
$349$	−24.3713	+	17.7068i	−1.30457	+	0.947823i	−0.304578	+	0.952487i	$0.598515\pi$
$350$	−7.28115	+	22.4091i	−0.389194	+	1.19782i
$351$	6.23607			0.332857
$352$		0			0
$353$	−1.52786			−0.0813200			−0.0406600	−	0.999173i	$-0.512946\pi$
$353$	−1.52786			−0.0813200			−0.0406600	+	0.999173i	$0.512946\pi$
$354$	−2.66312	+	8.19624i	−0.141543	+	0.435625i
$355$	4.50000	−	3.26944i	0.238835	−	0.173524i
$356$	−4.73607	−	3.44095i	−0.251011	−	0.182370i
$357$	−0.572949	−	1.76336i	−0.0303237	−	0.0933267i
$358$	1.11803	+	3.44095i	0.0590899	+	0.181860i
$359$	13.9443	+	10.1311i	0.735951	+	0.534699i	0.891440	−	0.453138i	$-0.149696\pi$
$359$	13.9443	+	10.1311i	0.735951	+	0.534699i	−0.155490	+	0.987838i	$0.549696\pi$
$360$	−0.690983	+	0.502029i	−0.0364180	+	0.0264592i
$361$	−5.64590	+	17.3763i	−0.297153	+	0.914541i
$362$	−13.7984			−0.725226
$363$		0			0
$364$	11.5623			0.606029
$365$	−0.145898	+	0.449028i	−0.00763665	+	0.0235032i
$366$	−1.50000	+	1.08981i	−0.0784063	+	0.0569655i
$367$	11.7812	+	8.55951i	0.614971	+	0.446803i	0.851161	−	0.524904i	$-0.175899\pi$
$367$	11.7812	+	8.55951i	0.614971	+	0.446803i	−0.236190	+	0.971707i	$0.575899\pi$
$368$	8.20820	+	25.2623i	0.427882	+	1.31689i
$369$	1.83688	+	5.65334i	0.0956242	+	0.294301i
$370$	−2.11803	−	1.53884i	−0.110111	−	0.0800006i
$371$	17.9164	−	13.0170i	0.930174	−	0.675811i
$372$	−0.736068	+	2.26538i	−0.0381633	+	0.117455i
$373$	22.4164			1.16068			0.580339	−	0.814375i	$-0.302920\pi$
$373$	22.4164			1.16068			0.580339	+	0.814375i	$0.302920\pi$
$374$		0			0
$375$	3.76393			0.194369
$376$	0.427051	−	1.31433i	0.0220235	−	0.0677813i
$377$	22.5623	−	16.3925i	1.16202	−	0.844255i
$378$	−3.92705	−	2.85317i	−0.201986	−	0.146751i
$379$	8.78115	+	27.0256i	0.451058	+	1.38821i	0.875702	+	0.482852i	$0.160399\pi$
$379$	8.78115	+	27.0256i	0.451058	+	1.38821i	−0.424644	+	0.905360i	$0.639601\pi$
$380$	0.0623059	+	0.191758i	0.00319623	+	0.00983697i
$381$	−7.85410	−	5.70634i	−0.402378	−	0.292345i
$382$	−1.92705	+	1.40008i	−0.0985965	+	0.0716346i
$383$	−2.74671	+	8.45351i	−0.140350	+	0.431954i	−0.996384	−	0.0849664i	$-0.972922\pi$
$383$	−2.74671	+	8.45351i	−0.140350	+	0.431954i	0.856033	+	0.516920i	$0.172922\pi$
$384$	13.6180			0.694942
$385$		0			0
$386$	2.52786			0.128665
$387$	0.545085	−	1.67760i	0.0277082	−	0.0852772i
$388$	−7.51722	+	5.46158i	−0.381629	+	0.277270i
$389$	7.50000	+	5.44907i	0.380265	+	0.276279i	0.761455	−	0.648218i	$-0.224485\pi$
$389$	7.50000	+	5.44907i	0.380265	+	0.276279i	−0.381190	+	0.924497i	$0.624485\pi$
$390$	−1.19098	−	3.66547i	−0.0603078	−	0.185608i
$391$	1.04508	+	3.21644i	0.0528522	+	0.162662i
$392$	3.61803	+	2.62866i	0.182738	+	0.132767i
$393$	11.2082	−	8.14324i	0.565379	−	0.410772i
$394$	13.3090	−	40.9609i	0.670499	−	2.06358i
$395$	−0.201626			−0.0101449
$396$		0			0
$397$	−25.2918			−1.26936			−0.634679	−	0.772776i	$-0.718868\pi$
$397$	−25.2918			−1.26936			−0.634679	+	0.772776i	$0.718868\pi$
$398$	−1.64590	+	5.06555i	−0.0825014	+	0.253913i
$399$	2.07295	−	1.50609i	0.103777	−	0.0753986i
$400$	−19.0623	−	13.8496i	−0.953115	−	0.692479i
$401$	−4.60739	−	14.1801i	−0.230082	−	0.708120i	−0.997736	−	0.0672551i	$-0.978576\pi$
$401$	−4.60739	−	14.1801i	−0.230082	−	0.708120i	0.767654	−	0.640865i	$-0.221424\pi$
$402$	5.28115	+	16.2537i	0.263400	+	0.810662i
$403$	19.4443	+	14.1271i	0.968588	+	0.703721i
$404$	1.50000	−	1.08981i	0.0746278	−	0.0542203i
$405$	−0.118034	+	0.363271i	−0.00586516	+	0.0180511i
$406$	−21.7082			−1.07736
$407$		0			0
$408$	1.38197			0.0684175
$409$	−8.94427	+	27.5276i	−0.442266	+	1.36115i	0.443189	+	0.896428i	$0.353847\pi$
$409$	−8.94427	+	27.5276i	−0.442266	+	1.36115i	−0.885455	+	0.464726i	$0.846153\pi$
$410$	2.97214	−	2.15938i	0.146783	−	0.106644i
$411$	1.19098	+	0.865300i	0.0587469	+	0.0426821i
$412$	−1.14590	−	3.52671i	−0.0564543	−	0.173749i
$413$	−4.93769	−	15.1967i	−0.242968	−	0.747779i
$414$	7.16312	+	5.20431i	0.352048	+	0.255778i
$415$	−3.92705	+	2.85317i	−0.192771	+	0.140057i
$416$	−6.51722	+	20.0579i	−0.319533	+	0.983422i
$417$	5.85410			0.286677
$418$		0			0
$419$	−21.5066			−1.05067			−0.525333	−	0.850897i	$-0.676059\pi$
$419$	−21.5066			−1.05067			−0.525333	+	0.850897i	$0.676059\pi$
$420$	−0.218847	+	0.673542i	−0.0106786	+	0.0328655i
$421$	3.01722	−	2.19214i	0.147050	−	0.106838i	−0.511828	−	0.859088i	$-0.671031\pi$
$421$	3.01722	−	2.19214i	0.147050	−	0.106838i	0.658878	+	0.752250i	$0.271031\pi$
$422$	−14.7533	−	10.7189i	−0.718179	−	0.521787i
$423$	−0.190983	−	0.587785i	−0.00928591	−	0.0285791i
$424$	5.10081	+	15.6987i	0.247717	+	0.762396i
$425$	−2.42705	−	1.76336i	−0.117729	−	0.0855353i
$426$	−19.0623	+	13.8496i	−0.923572	+	0.671014i
$427$	1.06231	−	3.26944i	0.0514086	−	0.158219i
$428$	0.145898			0.00705225
$429$		0			0
$430$	−1.09017			−0.0525727
$431$	−0.461493	+	1.42033i	−0.0222293	+	0.0684148i	−0.961556	−	0.274610i	$-0.911451\pi$
$431$	−0.461493	+	1.42033i	−0.0222293	+	0.0684148i	0.939326	+	0.343024i	$0.111451\pi$
$432$	3.92705	−	2.85317i	0.188940	−	0.137273i
$433$	4.85410	+	3.52671i	0.233273	+	0.169483i	0.698281	−	0.715824i	$-0.253949\pi$
$433$	4.85410	+	3.52671i	0.233273	+	0.169483i	−0.465008	+	0.885307i	$0.653949\pi$
$434$	−5.78115	−	17.7926i	−0.277504	−	0.854070i
$435$	0.527864	+	1.62460i	0.0253091	+	0.0778935i
$436$		0			0
$437$	−3.78115	+	2.74717i	−0.180877	+	0.131415i
$438$	0.618034	−	1.90211i	0.0295308	−	0.0908865i
$439$	16.7082			0.797439			0.398720	−	0.917073i	$-0.369455\pi$
$439$	16.7082			0.797439			0.398720	+	0.917073i	$0.369455\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$	−1.92705	+	5.93085i	−0.0916605	+	0.282102i
$443$	0.708204	−	0.514540i	0.0336478	−	0.0244465i	−0.570834	−	0.821065i	$-0.693380\pi$
$443$	0.708204	−	0.514540i	0.0336478	−	0.0244465i	0.604482	+	0.796619i	$0.293380\pi$
$444$	2.11803	+	1.53884i	0.100517	+	0.0730302i
$445$	−1.11803	−	3.44095i	−0.0529999	−	0.163117i
$446$	−6.35410	−	19.5559i	−0.300875	−	0.925999i
$447$	−12.1353	−	8.81678i	−0.573978	−	0.417019i
$448$	−10.2812	+	7.46969i	−0.485739	+	0.352910i
$449$	−4.79837	+	14.7679i	−0.226449	+	0.696939i	0.771692	+	0.635996i	$0.219411\pi$
$449$	−4.79837	+	14.7679i	−0.226449	+	0.696939i	−0.998141	+	0.0609427i	$0.980589\pi$
$450$	−7.85410			−0.370246
$451$		0			0
$452$	−7.85410			−0.369426
$453$	0.618034	−	1.90211i	0.0290378	−	0.0893691i
$454$	−14.2533	+	10.3556i	−0.668940	+	0.486013i
$455$	5.78115	+	4.20025i	0.271025	+	0.196911i
$456$	0.590170	+	1.81636i	0.0276372	+	0.0850587i
$457$	10.1353	+	31.1931i	0.474107	+	1.45915i	0.847158	+	0.531341i	$0.178312\pi$
$457$	10.1353	+	31.1931i	0.474107	+	1.45915i	−0.373051	+	0.927811i	$0.621688\pi$
$458$	−13.0902	−	9.51057i	−0.611663	−	0.444400i
$459$	0.500000	−	0.363271i	0.0233380	−	0.0169561i
$460$	0.399187	−	1.22857i	0.0186122	−	0.0572824i
$461$	−9.90983			−0.461547			−0.230773	−	0.973008i	$-0.574126\pi$
$461$	−9.90983			−0.461547			−0.230773	+	0.973008i	$0.574126\pi$
$462$		0			0
$463$	8.79837			0.408895			0.204448	−	0.978878i	$-0.434460\pi$
$463$	8.79837			0.408895			0.204448	+	0.978878i	$0.434460\pi$
$464$	6.70820	−	20.6457i	0.311421	−	0.958454i
$465$	−1.19098	+	0.865300i	−0.0552305	+	0.0401273i
$466$	−11.3541	−	8.24924i	−0.525969	−	0.382139i
$467$	−4.39919	−	13.5393i	−0.203570	−	0.626524i	−0.999769	−	0.0214895i	$-0.993159\pi$
$467$	−4.39919	−	13.5393i	−0.203570	−	0.626524i	0.796199	−	0.605035i	$-0.206841\pi$
$468$	1.19098	+	3.66547i	0.0550532	+	0.169436i
$469$	−25.6353	−	18.6251i	−1.18373	−	0.860027i
$470$	−0.309017	+	0.224514i	−0.0142539	+	0.0103561i
$471$	3.00000	−	9.23305i	0.138233	−	0.425437i
$472$	11.9098			0.548194
$473$		0			0
$474$	0.854102			0.0392302
$475$	1.28115	−	3.94298i	0.0587833	−	0.180916i
$476$	0.927051	−	0.673542i	0.0424913	−	0.0308717i
$477$	5.97214	+	4.33901i	0.273445	+	0.198670i
$478$	−8.78115	−	27.0256i	−0.401641	−	1.23612i
$479$	−5.22542	−	16.0822i	−0.238756	−	0.734815i	−0.996601	−	0.0823803i	$-0.973748\pi$
$479$	−5.22542	−	16.0822i	−0.238756	−	0.734815i	0.757845	−	0.652434i	$-0.226252\pi$
$480$	−1.04508	−	0.759299i	−0.0477014	−	0.0346571i
$481$	21.3713	−	15.5272i	0.974448	−	0.707978i
$482$	8.56231	−	26.3521i	0.390002	−	1.20030i
$483$	−16.4164			−0.746972
$484$		0			0
$485$	−5.74265			−0.260760
$486$	0.500000	−	1.53884i	0.0226805	−	0.0698033i
$487$	−31.6976	+	23.0296i	−1.43635	+	1.04357i	−0.447565	+	0.894252i	$0.647709\pi$
$487$	−31.6976	+	23.0296i	−1.43635	+	1.04357i	−0.988789	+	0.149320i	$0.952291\pi$
$488$	2.07295	+	1.50609i	0.0938380	+	0.0681773i
$489$	−4.71885	−	14.5231i	−0.213394	−	0.656758i
$490$	−0.381966	−	1.17557i	−0.0172555	−	0.0531069i
$491$	21.2082	+	15.4087i	0.957113	+	0.695383i	0.952478	−	0.304606i	$-0.0985248\pi$
$491$	21.2082	+	15.4087i	0.957113	+	0.695383i	0.00463443	+	0.999989i	$0.498525\pi$
$492$	−2.97214	+	2.15938i	−0.133994	+	0.0973525i
$493$	0.854102	−	2.62866i	0.0384668	−	0.118389i
$494$	−8.61803			−0.387744
$495$		0			0
$496$	18.7082			0.840023
$497$	13.5000	−	41.5487i	0.605558	−	1.86372i
$498$	16.6353	−	12.0862i	0.745444	−	0.541596i
$499$	−2.07295	−	1.50609i	−0.0927979	−	0.0674217i	0.540419	−	0.841396i	$-0.318266\pi$
$499$	−2.07295	−	1.50609i	−0.0927979	−	0.0674217i	−0.633217	+	0.773975i	$0.718266\pi$
$500$	0.718847	+	2.21238i	0.0321478	+	0.0989408i
$501$	−5.88197	−	18.1028i	−0.262787	−	0.808775i
$502$	−21.9894	−	15.9762i	−0.981433	−	0.713053i
$503$	24.3262	−	17.6740i	1.08465	−	0.788047i	0.106165	−	0.994349i	$-0.466143\pi$
$503$	24.3262	−	17.6740i	1.08465	−	0.788047i	0.978488	+	0.206302i	$0.0661429\pi$
$504$	−2.07295	+	6.37988i	−0.0923365	+	0.284182i
$505$	1.14590			0.0509918
$506$		0			0
$507$	25.8885			1.14975
$508$	1.85410	−	5.70634i	0.0822625	−	0.253178i
$509$	−17.2984	+	12.5680i	−0.766737	+	0.557067i	−0.900969	−	0.433883i	$-0.857143\pi$
$509$	−17.2984	+	12.5680i	−0.766737	+	0.557067i	0.134232	+	0.990950i	$0.457143\pi$
$510$	−0.309017	−	0.224514i	−0.0136835	−	0.00994165i
$511$	1.14590	+	3.52671i	0.0506915	+	0.156013i
$512$	−1.63525	−	5.03280i	−0.0722687	−	0.222420i
$513$	0.690983	+	0.502029i	0.0305076	+	0.0221651i
$514$	35.7705	−	25.9888i	1.57777	−	1.14632i
$515$	0.708204	−	2.17963i	0.0312072	−	0.0960459i
$516$	1.09017			0.0479921
$517$		0			0
$518$	−20.5623			−0.903456
$519$	5.44427	−	16.7557i	0.238977	−	0.735496i
$520$	−4.30902	+	3.13068i	−0.188963	+	0.137290i
$521$	−31.4164	−	22.8254i	−1.37638	−	0.999997i	−0.997208	−	0.0746698i	$-0.976210\pi$
$521$	−31.4164	−	22.8254i	−1.37638	−	0.999997i	−0.379170	−	0.925327i	$-0.623790\pi$
$522$	−2.23607	−	6.88191i	−0.0978700	−	0.301213i
$523$	10.8090	+	33.2667i	0.472645	+	1.45465i	0.849107	+	0.528221i	$0.177141\pi$
$523$	10.8090	+	33.2667i	0.472645	+	1.45465i	−0.376462	+	0.926432i	$0.622859\pi$
$524$	6.92705	+	5.03280i	0.302610	+	0.219859i
$525$	11.7812	−	8.55951i	0.514172	−	0.373568i
$526$	−0.336881	+	1.03681i	−0.0146887	+	0.0452072i
$527$	2.38197			0.103760
$528$		0			0
$529$	6.94427			0.301925
$530$	1.40983	−	4.33901i	0.0612391	−	0.188475i
$531$	4.30902	−	3.13068i	0.186995	−	0.135860i
$532$	1.28115	+	0.930812i	0.0555450	+	0.0403558i
$533$	11.4549	+	35.2546i	0.496167	+	1.52705i
$534$	4.73607	+	14.5761i	0.204950	+	0.630770i
$535$	0.0729490	+	0.0530006i	0.00315386	+	0.00229141i
$536$	19.1074	−	13.8823i	0.825314	−	0.599625i
$537$	0.690983	−	2.12663i	0.0298181	−	0.0917707i
$538$	39.5967			1.70714
$539$		0			0
$540$	−0.236068			−0.0101587
$541$	−0.173762	+	0.534785i	−0.00747062	+	0.0229922i	−0.954722	−	0.297498i	$-0.903848\pi$
$541$	−0.173762	+	0.534785i	−0.00747062	+	0.0229922i	0.947252	+	0.320491i	$0.103848\pi$
$542$	−8.20820	+	5.96361i	−0.352573	+	0.256159i
$543$	6.89919	+	5.01255i	0.296072	+	0.215109i
$544$	0.645898	+	1.98787i	0.0276926	+	0.0852292i
$545$		0			0
$546$	−24.4894	−	17.7926i	−1.04805	−	0.761451i
$547$	−15.6803	+	11.3924i	−0.670443	+	0.487105i	−0.870173	−	0.492746i	$-0.835993\pi$
$547$	−15.6803	+	11.3924i	−0.670443	+	0.487105i	0.199731	+	0.979851i	$0.435993\pi$
$548$	−0.281153	+	0.865300i	−0.0120103	+	0.0369638i
$549$	1.14590			0.0489057
$550$		0			0
$551$	3.81966			0.162723
$552$	3.78115	−	11.6372i	0.160937	−	0.495312i
$553$	−1.28115	+	0.930812i	−0.0544802	+	0.0395822i
$554$	−13.6631	−	9.92684i	−0.580490	−	0.421751i
$555$	0.500000	+	1.53884i	0.0212238	+	0.0653202i
$556$	1.11803	+	3.44095i	0.0474152	+	0.145929i
$557$	−21.1074	−	15.3354i	−0.894349	−	0.649782i	0.0426594	−	0.999090i	$-0.486417\pi$
$557$	−21.1074	−	15.3354i	−0.894349	−	0.649782i	−0.937008	+	0.349307i	$0.886417\pi$
$558$	5.04508	−	3.66547i	0.213575	−	0.155172i
$559$	3.39919	−	10.4616i	0.143770	−	0.442479i
$560$	5.56231			0.235050
$561$		0			0
$562$	−8.47214			−0.357375
$563$	8.30902	−	25.5725i	0.350183	−	1.07775i	−0.608567	−	0.793503i	$-0.708255\pi$
$563$	8.30902	−	25.5725i	0.350183	−	1.07775i	0.958750	−	0.284251i	$-0.0917448\pi$
$564$	0.309017	−	0.224514i	0.0130120	−	0.00945374i
$565$	−3.92705	−	2.85317i	−0.165212	−	0.120034i
$566$	−11.0902	−	34.1320i	−0.466155	−	1.43468i
$567$	0.927051	+	2.85317i	0.0389325	+	0.119822i
$568$	26.3435	+	19.1396i	1.10535	+	0.803082i
$569$	−27.5623	+	20.0252i	−1.15547	+	0.839500i	−0.989199	−	0.146580i	$-0.953173\pi$
$569$	−27.5623	+	20.0252i	−1.15547	+	0.839500i	−0.166273	+	0.986080i	$0.553173\pi$
$570$	0.163119	−	0.502029i	0.00683230	−	0.0210277i
$571$	−25.6869			−1.07496			−0.537482	−	0.843275i	$-0.680624\pi$
$571$	−25.6869			−1.07496			−0.537482	+	0.843275i	$0.680624\pi$
$572$		0			0
$573$	1.47214			0.0614994
$574$	8.91641	−	27.4419i	0.372164	−	1.14540i
$575$	−21.4894	+	15.6129i	−0.896168	+	0.651104i
$576$	−3.42705	−	2.48990i	−0.142794	−	0.103746i
$577$	4.70820	+	14.4904i	0.196005	+	0.603242i	0.999963	+	0.00855598i	$0.00272349\pi$
$577$	4.70820	+	14.4904i	0.196005	+	0.603242i	−0.803958	+	0.594686i	$0.797277\pi$
$578$	−8.30902	−	25.5725i	−0.345610	−	1.06368i
$579$	−1.26393	−	0.918300i	−0.0525272	−	0.0381633i
$580$	−0.854102	+	0.620541i	−0.0354647	+	0.0257666i
$581$	−11.7812	+	36.2587i	−0.488765	+	1.50426i
$582$	24.3262			1.00836
$583$		0			0
$584$	−2.76393			−0.114372
$585$	−0.736068	+	2.26538i	−0.0304327	+	0.0936621i
$586$	−23.4894	+	17.0660i	−0.970336	+	0.704991i
$587$	−19.6631	−	14.2861i	−0.811584	−	0.589650i	0.102706	−	0.994712i	$-0.467250\pi$
$587$	−19.6631	−	14.2861i	−0.811584	−	0.589650i	−0.914289	+	0.405062i	$0.867250\pi$
$588$	0.381966	+	1.17557i	0.0157520	+	0.0484797i
$589$	1.01722	+	3.13068i	0.0419139	+	0.128998i
$590$	−2.66312	−	1.93487i	−0.109639	−	0.0796573i
$591$	−21.5344	+	15.6457i	−0.885809	+	0.643578i
$592$	6.35410	−	19.5559i	0.261152	−	0.803743i
$593$	−29.2148			−1.19971			−0.599854	−	0.800110i	$-0.704775\pi$
$593$	−29.2148			−1.19971			−0.599854	+	0.800110i	$0.704775\pi$
$594$		0			0
$595$	0.708204			0.0290335
$596$	2.86475	−	8.81678i	0.117345	−	0.361149i
$597$	2.66312	−	1.93487i	0.108994	−	0.0791889i
$598$	44.6697	+	32.4544i	1.82668	+	1.32716i
$599$	−6.70820	−	20.6457i	−0.274090	−	0.843562i	−0.989459	−	0.144815i	$-0.953741\pi$
$599$	−6.70820	−	20.6457i	−0.274090	−	0.843562i	0.715369	−	0.698747i	$-0.246259\pi$
$600$	3.35410	+	10.3229i	0.136931	+	0.421429i
$601$	16.0451	+	11.6574i	0.654493	+	0.475517i	0.864799	−	0.502119i	$-0.167446\pi$
$601$	16.0451	+	11.6574i	0.654493	+	0.475517i	−0.210306	+	0.977636i	$0.567446\pi$
$602$	−6.92705	+	5.03280i	−0.282326	+	0.205121i
$603$	3.26393	−	10.0453i	0.132918	−	0.409078i
$604$	1.23607			0.0502949
$605$		0			0
$606$	−4.85410			−0.197184
$607$	−0.718847	+	2.21238i	−0.0291771	+	0.0897979i	−0.964585	−	0.263774i	$-0.915033\pi$
$607$	−0.718847	+	2.21238i	−0.0291771	+	0.0897979i	0.935408	+	0.353571i	$0.115033\pi$
$608$	−2.33688	+	1.69784i	−0.0947730	+	0.0688566i
$609$	10.8541	+	7.88597i	0.439830	+	0.319555i
$610$	−0.218847	−	0.673542i	−0.00886086	−	0.0272709i
$611$	−1.19098	−	3.66547i	−0.0481820	−	0.148289i
$612$	0.309017	+	0.224514i	0.0124913	+	0.00907544i
$613$	−2.70820	+	1.96763i	−0.109383	+	0.0794716i	−0.641132	−	0.767430i	$-0.721535\pi$
$613$	−2.70820	+	1.96763i	−0.109383	+	0.0794716i	0.531749	+	0.846902i	$0.321535\pi$
$614$	−9.78115	+	30.1033i	−0.394735	+	1.21487i
$615$	−2.27051			−0.0915558
$616$		0			0
$617$	46.4164			1.86865			0.934327	−	0.356417i	$-0.116002\pi$
$617$	46.4164			1.86865			0.934327	+	0.356417i	$0.116002\pi$
$618$	−3.00000	+	9.23305i	−0.120678	+	0.371408i
$619$	25.2254	−	18.3273i	1.01390	−	0.736638i	0.0488729	−	0.998805i	$-0.484437\pi$
$619$	25.2254	−	18.3273i	1.01390	−	0.736638i	0.965023	+	0.262167i	$0.0844371\pi$
$620$	−0.736068	−	0.534785i	−0.0295612	−	0.0214775i
$621$	−1.69098	−	5.20431i	−0.0678568	−	0.208842i
$622$	5.73607	+	17.6538i	0.229995	+	0.707853i
$623$	−22.9894	−	16.7027i	−0.921049	−	0.669181i
$624$	24.4894	−	17.7926i	0.980359	−	0.712272i
$625$	7.05573	−	21.7153i	0.282229	−	0.868612i
$626$	−45.0344			−1.79994
$627$		0			0
$628$	6.00000			0.239426
$629$	0.809017	−	2.48990i	0.0322576	−	0.0992787i
$630$	1.50000	−	1.08981i	0.0597614	−	0.0434192i
$631$	−10.2984	−	7.48221i	−0.409972	−	0.297862i	0.363619	−	0.931548i	$-0.381541\pi$
$631$	−10.2984	−	7.48221i	−0.409972	−	0.297862i	−0.773590	+	0.633686i	$0.781541\pi$
$632$	−0.364745	−	1.12257i	−0.0145088	−	0.0446534i
$633$	3.48278	+	10.7189i	0.138428	+	0.426038i
$634$	−33.1976	−	24.1194i	−1.31844	−	0.957905i
$635$	3.00000	−	2.17963i	0.119051	−	0.0864959i
$636$	−1.40983	+	4.33901i	−0.0559034	+	0.172053i
$637$	12.4721			0.494164
$638$		0			0
$639$	14.5623			0.576076
$640$	−1.60739	+	4.94704i	−0.0635377	+	0.195549i
$641$	5.45492	−	3.96323i	0.215456	−	0.156538i	−0.474823	−	0.880081i	$-0.657488\pi$
$641$	5.45492	−	3.96323i	0.215456	−	0.156538i	0.690279	+	0.723543i	$0.257488\pi$
$642$	−0.309017	−	0.224514i	−0.0121959	−	0.00886086i
$643$	−5.69756	−	17.5353i	−0.224690	−	0.691524i	−0.998323	−	0.0578904i	$-0.981563\pi$
$643$	−5.69756	−	17.5353i	−0.224690	−	0.691524i	0.773633	−	0.633634i	$-0.218437\pi$
$644$	−3.13525	−	9.64932i	−0.123546	−	0.380237i
$645$	0.545085	+	0.396027i	0.0214627	+	0.0155936i
$646$	−0.690983	+	0.502029i	−0.0271864	+	0.0197520i
$647$	0.989357	−	3.04493i	0.0388956	−	0.119708i	−0.929723	−	0.368259i	$-0.879954\pi$
$647$	0.989357	−	3.04493i	0.0388956	−	0.119708i	0.968619	+	0.248550i	$0.0799541\pi$
$648$	−2.23607			−0.0878410
$649$		0			0
$650$	−48.9787			−1.92110
$651$	−3.57295	+	10.9964i	−0.140035	+	0.430983i
$652$	7.63525	−	5.54734i	0.299020	−	0.217250i
$653$	−17.7705	−	12.9110i	−0.695414	−	0.505248i	0.183022	−	0.983109i	$-0.441412\pi$
$653$	−17.7705	−	12.9110i	−0.695414	−	0.505248i	−0.878435	+	0.477861i	$0.841412\pi$
$654$		0			0
$655$	1.63525	+	5.03280i	0.0638947	+	0.196648i
$656$	23.3435	+	16.9600i	0.911409	+	0.662177i
$657$	−1.00000	+	0.726543i	−0.0390137	+	0.0283451i
$658$	−0.927051	+	2.85317i	−0.0361402	+	0.111228i
$659$	20.6525			0.804506			0.402253	−	0.915528i	$-0.368227\pi$
$659$	20.6525			0.804506			0.402253	+	0.915528i	$0.368227\pi$
$660$		0			0
$661$	−21.0902			−0.820313			−0.410156	−	0.912015i	$-0.634526\pi$
$661$	−21.0902			−0.820313			−0.410156	+	0.912015i	$0.634526\pi$
$662$	−11.2984	+	34.7728i	−0.439124	+	1.35148i
$663$	3.11803	−	2.26538i	0.121094	−	0.0879802i
$664$	−22.9894	−	16.7027i	−0.892160	−	0.648192i
$665$	0.302439	+	0.930812i	0.0117281	+	0.0360953i
$666$	−2.11803	−	6.51864i	−0.0820721	−	0.252592i
$667$	−19.7984	−	14.3844i	−0.766596	−	0.556965i
$668$	9.51722	−	6.91467i	0.368232	−	0.267536i
$669$	−3.92705	+	12.0862i	−0.151829	+	0.467280i
$670$	−6.52786			−0.252193
$671$		0			0
$672$	−10.1459			−0.391387
$673$	−4.45492	+	13.7108i	−0.171724	+	0.528513i	−0.999469	−	0.0325922i	$-0.989624\pi$
$673$	−4.45492	+	13.7108i	−0.171724	+	0.528513i	0.827744	+	0.561105i	$0.189624\pi$
$674$	17.9443	−	13.0373i	0.691188	−	0.502177i
$675$	3.92705	+	2.85317i	0.151152	+	0.109819i
$676$	4.94427	+	15.2169i	0.190164	+	0.585266i
$677$	6.94427	+	21.3723i	0.266890	+	0.821403i	0.991252	+	0.131983i	$0.0421345\pi$
$677$	6.94427	+	21.3723i	0.266890	+	0.821403i	−0.724362	+	0.689420i	$0.757866\pi$
$678$	16.6353	+	12.0862i	0.638873	+	0.464168i
$679$	−36.4894	+	26.5111i	−1.40033	+	1.01740i
$680$	−0.163119	+	0.502029i	−0.00625533	+	0.0192519i
$681$	10.8885			0.417250
$682$		0			0
$683$	−38.8885			−1.48803			−0.744014	−	0.668164i	$-0.767081\pi$
$683$	−38.8885			−1.48803			−0.744014	+	0.668164i	$0.767081\pi$
$684$	−0.163119	+	0.502029i	−0.00623701	+	0.0191955i
$685$	−0.454915	+	0.330515i	−0.0173814	+	0.0126283i
$686$	19.6353	+	14.2658i	0.749678	+	0.544673i
$687$	3.09017	+	9.51057i	0.117897	+	0.362851i
$688$	−2.64590	−	8.14324i	−0.100874	−	0.310458i
$689$	37.2426	+	27.0584i	1.41883	+	1.03084i
$690$	−2.73607	+	1.98787i	−0.104160	+	0.0756769i
$691$	−12.2705	+	37.7647i	−0.466792	+	1.43664i	0.389922	+	0.920848i	$0.372502\pi$
$691$	−12.2705	+	37.7647i	−0.466792	+	1.43664i	−0.856715	+	0.515791i	$0.827498\pi$
$692$	10.8885			0.413920
$693$		0			0
$694$	−4.94427			−0.187682
$695$	−0.690983	+	2.12663i	−0.0262105	+	0.0806676i
$696$	−8.09017	+	5.87785i	−0.306657	+	0.222799i
$697$	2.97214	+	2.15938i	0.112578	+	0.0817925i
$698$	15.0623	+	46.3570i	0.570117	+	1.75464i
$699$	2.68034	+	8.24924i	0.101380	+	0.312015i
$700$	7.28115	+	5.29007i	0.275202	+	0.199946i
$701$	−40.1976	+	29.2052i	−1.51824	+	1.10307i	−0.555890	+	0.831256i	$0.687623\pi$
$701$	−40.1976	+	29.2052i	−1.51824	+	1.10307i	−0.962351	+	0.271811i	$0.912377\pi$
$702$	3.11803	−	9.59632i	0.117683	−	0.362190i
$703$	3.61803			0.136457
$704$		0			0
$705$	0.236068			0.00889083
$706$	−0.763932	+	2.35114i	−0.0287510	+	0.0884864i
$707$	7.28115	−	5.29007i	0.273836	−	0.198953i
$708$	2.66312	+	1.93487i	0.100086	+	0.0727168i
$709$	1.93363	+	5.95110i	0.0726190	+	0.223498i	0.980778	−	0.195127i	$-0.0625120\pi$
$709$	1.93363	+	5.95110i	0.0726190	+	0.223498i	−0.908159	+	0.418625i	$0.862512\pi$
$710$	−2.78115	−	8.55951i	−0.104375	−	0.321233i
$711$	−0.427051	−	0.310271i	−0.0160157	−	0.0116361i
$712$	17.1353	−	12.4495i	0.642171	−	0.466564i
$713$	6.51722	−	20.0579i	0.244072	−	0.751176i
$714$	−3.00000			−0.112272
$715$		0			0
$716$	1.38197			0.0516465
$717$	−5.42705	+	16.7027i	−0.202677	+	0.623775i
$718$	22.5623	−	16.3925i	0.842018	−	0.611762i
$719$	22.9894	+	16.7027i	0.857358	+	0.622907i	0.927165	−	0.374653i	$-0.122238\pi$
$719$	22.9894	+	16.7027i	0.857358	+	0.622907i	−0.0698067	+	0.997561i	$0.522238\pi$
$720$	0.572949	+	1.76336i	0.0213525	+	0.0657164i
$721$	−5.56231	−	17.1190i	−0.207151	−	0.637546i
$722$	23.9164	+	17.3763i	0.890077	+	0.646678i
$723$	−13.8541	+	10.0656i	−0.515240	+	0.374343i
$724$	−1.62868	+	5.01255i	−0.0605293	+	0.186290i
$725$	21.7082			0.806222
$726$		0			0
$727$	32.1459			1.19223			0.596113	−	0.802901i	$-0.296711\pi$
$727$	32.1459			1.19223			0.596113	+	0.802901i	$0.296711\pi$
$728$	−12.9271	+	39.7854i	−0.479108	+	1.47454i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	0.618034	+	0.449028i	0.0228745	+	0.0166193i
$731$	−0.336881	−	1.03681i	−0.0124600	−	0.0383479i
$732$	0.218847	+	0.673542i	0.00808882	+	0.0248948i
$733$	19.6525	+	14.2784i	0.725881	+	0.527383i	0.888258	−	0.459346i	$-0.151916\pi$
$733$	19.6525	+	14.2784i	0.725881	+	0.527383i	−0.162377	+	0.986729i	$0.551916\pi$
$734$	19.0623	−	13.8496i	0.703603	−	0.511197i
$735$	−0.236068	+	0.726543i	−0.00870750	+	0.0267989i
$736$	18.5066			0.682162
$737$		0			0
$738$	9.61803			0.354045
$739$	−7.72542	+	23.7764i	−0.284184	+	0.874629i	0.702458	+	0.711726i	$0.252086\pi$
$739$	−7.72542	+	23.7764i	−0.284184	+	0.874629i	−0.986642	+	0.162904i	$0.947914\pi$
$740$	−0.809017	+	0.587785i	−0.0297401	+	0.0216074i
$741$	4.30902	+	3.13068i	0.158296	+	0.115009i
$742$	−11.0729	−	34.0790i	−0.406501	−	1.25108i
$743$	3.96149	+	12.1922i	0.145333	+	0.447289i	0.997054	−	0.0767070i	$-0.0244406\pi$
$743$	3.96149	+	12.1922i	0.145333	+	0.447289i	−0.851721	+	0.523996i	$0.824441\pi$
$744$	−6.97214	−	5.06555i	−0.255611	−	0.185712i
$745$	4.63525	−	3.36771i	0.169823	−	0.123383i
$746$	11.2082	−	34.4953i	0.410362	−	1.26296i
$747$	−12.7082			−0.464969
$748$		0			0
$749$	0.708204			0.0258772
$750$	1.88197	−	5.79210i	0.0687197	−	0.211497i
$751$	42.8156	−	31.1074i	1.56236	−	1.13512i	0.628325	−	0.777951i	$-0.283741\pi$
$751$	42.8156	−	31.1074i	1.56236	−	1.13512i	0.934039	−	0.357172i	$-0.116259\pi$
$752$	−2.42705	−	1.76336i	−0.0885054	−	0.0643030i
$753$	5.19098	+	15.9762i	0.189170	+	0.582205i
$754$	−13.9443	−	42.9161i	−0.507820	−	1.56291i
$755$	0.618034	+	0.449028i	0.0224926	+	0.0163418i
$756$	−1.50000	+	1.08981i	−0.0545545	+	0.0396361i
$757$	−4.92705	+	15.1639i	−0.179077	+	0.551141i	−0.999796	−	0.0201900i	$-0.993573\pi$
$757$	−4.92705	+	15.1639i	−0.179077	+	0.551141i	0.820719	+	0.571331i	$0.193573\pi$
$758$	45.9787			1.67002
$759$		0			0
$760$	−0.729490			−0.0264614
$761$	1.51064	−	4.64928i	0.0547608	−	0.168536i	−0.919935	−	0.392070i	$-0.871759\pi$
$761$	1.51064	−	4.64928i	0.0547608	−	0.168536i	0.974696	+	0.223533i	$0.0717592\pi$
$762$	−12.7082	+	9.23305i	−0.460370	+	0.334478i
$763$		0			0
$764$	0.281153	+	0.865300i	0.0101718	+	0.0313054i
$765$	0.0729490	+	0.224514i	0.00263748	+	0.00811732i
$766$	11.6353	+	8.45351i	0.420399	+	0.305438i
$767$	26.8713	−	19.5232i	0.970267	−	0.704940i
$768$	4.19098	−	12.8985i	0.151229	−	0.465435i
$769$	−47.6869			−1.71963			−0.859817	−	0.510602i	$-0.829423\pi$
$769$	−47.6869			−1.71963			−0.859817	+	0.510602i	$0.829423\pi$
$770$		0			0
$771$	−27.3262			−0.984130
$772$	0.298374	−	0.918300i	0.0107387	−	0.0330504i
$773$	−39.8435	+	28.9480i	−1.43307	+	1.04119i	−0.443635	+	0.896208i	$0.646311\pi$
$773$	−39.8435	+	28.9480i	−1.43307	+	1.04119i	−0.989435	+	0.144978i	$0.953689\pi$
$774$	−2.30902	−	1.67760i	−0.0829959	−	0.0603001i
$775$	5.78115	+	17.7926i	0.207665	+	0.639128i
$776$	−10.3885	−	31.9727i	−0.372927	−	1.14775i
$777$	10.2812	+	7.46969i	0.368834	+	0.267974i
$778$	12.1353	−	8.81678i	0.435070	−	0.316097i
$779$	−1.56888	+	4.82853i	−0.0562111	+	0.173000i
$780$	−1.47214			−0.0527109
$781$		0			0
$782$	5.47214			0.195683
$783$	−1.38197	+	4.25325i	−0.0493874	+	0.151999i
$784$	7.85410	−	5.70634i	0.280504	−	0.203798i
$785$	3.00000	+	2.17963i	0.107075	+	0.0777942i
$786$	−6.92705	−	21.3193i	−0.247080	−	0.760433i
$787$	−7.32624	−	22.5478i	−0.261152	−	0.803744i	−0.992555	−	0.121798i	$-0.961134\pi$
$787$	−7.32624	−	22.5478i	−0.261152	−	0.803744i	0.731403	−	0.681946i	$-0.238866\pi$
$788$	−13.3090	−	9.66957i	−0.474114	−	0.344464i
$789$	0.545085	−	0.396027i	0.0194055	−	0.0140989i
$790$	−0.100813	+	0.310271i	−0.00358677	+	0.0110389i
$791$	−38.1246			−1.35556
$792$		0			0
$793$	7.14590			0.253758
$794$	−12.6459	+	38.9201i	−0.448786	+	1.38122i
$795$	−2.28115	+	1.65735i	−0.0809042	+	0.0587803i
$796$	1.64590	+	1.19581i	0.0583373	+	0.0423845i
$797$	4.70820	+	14.4904i	0.166773	+	0.513275i	0.999163	−	0.0409162i	$-0.0130277\pi$
$797$	4.70820	+	14.4904i	0.166773	+	0.513275i	−0.832389	+	0.554191i	$0.813028\pi$
$798$	−1.28115	−	3.94298i	−0.0453523	−	0.139580i
$799$	−0.309017	−	0.224514i	−0.0109322	−	0.00794273i
$800$	−13.2812	+	9.64932i	−0.469560	+	0.341155i
$801$	2.92705	−	9.00854i	0.103422	−	0.318301i
$802$	−24.1246			−0.851870
$803$		0			0
$804$	6.52786			0.230220
$805$	1.93769	−	5.96361i	0.0682947	−	0.210190i
$806$	31.4615	−	22.8581i	1.10818	−	0.805143i
$807$	−19.7984	−	14.3844i	−0.696936	−	0.506353i
$808$	2.07295	+	6.37988i	0.0729261	+	0.224443i
$809$	7.82624	+	24.0867i	0.275156	+	0.846843i	0.989178	+	0.146720i	$0.0468715\pi$
$809$	7.82624	+	24.0867i	0.275156	+	0.846843i	−0.714022	+	0.700123i	$0.753128\pi$
$810$	0.500000	+	0.363271i	0.0175682	+	0.0127641i
$811$	−37.0066	+	26.8869i	−1.29948	+	0.944125i	−0.999950	−	0.00996294i	$-0.996829\pi$
$811$	−37.0066	+	26.8869i	−1.29948	+	0.944125i	−0.299526	+	0.954088i	$0.596829\pi$
$812$	−2.56231	+	7.88597i	−0.0899193	+	0.276743i
$813$	6.27051			0.219916
$814$		0			0
$815$	5.83282			0.204315
$816$	0.927051	−	2.85317i	0.0324533	−	0.0998809i
$817$	1.21885	−	0.885544i	0.0426421	−	0.0309813i
$818$	37.8885	+	27.5276i	1.32474	+	0.962481i
$819$	5.78115	+	17.7926i	0.202010	+	0.621722i
$820$	−0.433629	−	1.33457i	−0.0151430	−	0.0466053i
$821$	−10.9894	−	7.98424i	−0.383531	−	0.278652i	0.379268	−	0.925287i	$-0.376176\pi$
$821$	−10.9894	−	7.98424i	−0.383531	−	0.278652i	−0.762800	+	0.646635i	$0.776176\pi$
$822$	1.92705	−	1.40008i	0.0672136	−	0.0488336i
$823$	−8.19756	+	25.2295i	−0.285749	+	0.879445i	0.700424	+	0.713727i	$0.252994\pi$
$823$	−8.19756	+	25.2295i	−0.285749	+	0.879445i	−0.986173	+	0.165718i	$0.947006\pi$
$824$	13.4164			0.467383
$825$		0			0
$826$	−25.8541			−0.899579
$827$	3.97871	−	12.2452i	0.138353	−	0.425808i	−0.857743	−	0.514079i	$-0.828134\pi$
$827$	3.97871	−	12.2452i	0.138353	−	0.425808i	0.996097	+	0.0882705i	$0.0281340\pi$
$828$	2.73607	−	1.98787i	0.0950849	−	0.0690832i
$829$	34.5344	+	25.0907i	1.19943	+	0.871437i	0.994229	−	0.107282i	$-0.0342148\pi$
$829$	34.5344	+	25.0907i	1.19943	+	0.871437i	0.205202	+	0.978720i	$0.434215\pi$
$830$	2.42705	+	7.46969i	0.0842442	+	0.259277i
$831$	3.22542	+	9.92684i	0.111889	+	0.344358i
$832$	−21.3713	−	15.5272i	−0.740917	−	0.538308i
$833$	1.00000	−	0.726543i	0.0346479	−	0.0251732i
$834$	2.92705	−	9.00854i	0.101355	−	0.311940i
$835$	7.27051			0.251606
$836$		0			0
$837$	−3.85410			−0.133217
$838$	−10.7533	+	33.0952i	−0.371466	+	1.14326i
$839$	18.8435	−	13.6906i	0.650548	−	0.472651i	−0.212910	−	0.977072i	$-0.568294\pi$
$839$	18.8435	−	13.6906i	0.650548	−	0.472651i	0.863458	+	0.504421i	$0.168294\pi$
$840$	−2.07295	−	1.50609i	−0.0715235	−	0.0519649i
$841$	−2.78115	−	8.55951i	−0.0959018	−	0.295155i
$842$	−1.86475	−	5.73910i	−0.0642634	−	0.197782i
$843$	4.23607	+	3.07768i	0.145898	+	0.106001i
$844$	−5.63525	+	4.09425i	−0.193973	+	0.140930i
$845$	−3.05573	+	9.40456i	−0.105120	+	0.323527i
$846$	−1.00000			−0.0343807
$847$		0			0
$848$	35.8328			1.23050
$849$	−6.85410	+	21.0948i	−0.235232	+	0.723970i
$850$	−3.92705	+	2.85317i	−0.134697	+	0.0978629i
$851$	−18.7533	−	13.6251i	−0.642854	−	0.467061i
$852$	2.78115	+	8.55951i	0.0952807	+	0.293244i
$853$	2.45492	+	7.55545i	0.0840547	+	0.258694i	0.984247	−	0.176799i	$-0.0565742\pi$
$853$	2.45492	+	7.55545i	0.0840547	+	0.258694i	−0.900192	+	0.435493i	$0.856574\pi$
$854$	−4.50000	−	3.26944i	−0.153987	−	0.111878i
$855$	−0.263932	+	0.191758i	−0.00902628	+	0.00655798i
$856$	−0.163119	+	0.502029i	−0.00557529	+	0.0171590i
$857$	−41.7214			−1.42517			−0.712587	−	0.701584i	$-0.752477\pi$
$857$	−41.7214			−1.42517			−0.712587	+	0.701584i	$0.752477\pi$
$858$		0			0
$859$	42.8885			1.46334			0.731669	−	0.681660i	$-0.238742\pi$
$859$	42.8885			1.46334			0.731669	+	0.681660i	$0.238742\pi$
$860$	−0.128677	+	0.396027i	−0.00438785	+	0.0135044i
$861$	−14.4271	+	10.4819i	−0.491673	+	0.357221i
$862$	1.95492	+	1.42033i	0.0665847	+	0.0483766i
$863$	−7.38197	−	22.7194i	−0.251285	−	0.773376i	−0.994539	−	0.104366i	$-0.966719\pi$
$863$	−7.38197	−	22.7194i	−0.251285	−	0.773376i	0.743254	−	0.669009i	$-0.233281\pi$
$864$	−1.04508	−	3.21644i	−0.0355545	−	0.109426i
$865$	5.44427	+	3.95550i	0.185111	+	0.134491i
$866$	7.85410	−	5.70634i	0.266893	−	0.193909i
$867$	−5.13525	+	15.8047i	−0.174402	+	0.536755i
$868$	−7.14590			−0.242548
$869$		0			0
$870$	2.76393			0.0937061
$871$	20.3541	−	62.6435i	0.689672	−	2.12259i
$872$		0			0
$873$	−12.1631	−	8.83702i	−0.411659	−	0.299088i
$874$	2.33688	+	7.19218i	0.0790462	+	0.243279i
$875$	3.48936	+	10.7391i	0.117962	+	0.363049i
$876$	−0.618034	−	0.449028i	−0.0208814	−	0.0151712i
$877$	16.5172	−	12.0005i	0.557747	−	0.405227i	−0.272887	−	0.962046i	$-0.587978\pi$
$877$	16.5172	−	12.0005i	0.557747	−	0.405227i	0.830634	+	0.556819i	$0.187978\pi$
$878$	8.35410	−	25.7113i	0.281937	−	0.867714i
$879$	17.9443			0.605245
$880$		0			0
$881$	25.0902			0.845309			0.422655	−	0.906291i	$-0.361098\pi$
$881$	25.0902			0.845309			0.422655	+	0.906291i	$0.361098\pi$
$882$	1.00000	−	3.07768i	0.0336718	−	0.103631i
$883$	−30.2705	+	21.9928i	−1.01868	+	0.740117i	−0.966013	−	0.258495i	$-0.916774\pi$
$883$	−30.2705	+	21.9928i	−1.01868	+	0.740117i	−0.0526711	+	0.998612i	$0.516774\pi$
$884$	1.92705	+	1.40008i	0.0648137	+	0.0470899i
$885$	0.628677	+	1.93487i	0.0211327	+	0.0650399i
$886$	−0.437694	−	1.34708i	−0.0147046	−	0.0452562i
$887$	−2.42705	−	1.76336i	−0.0814924	−	0.0592077i	0.546293	−	0.837594i	$-0.316038\pi$
$887$	−2.42705	−	1.76336i	−0.0814924	−	0.0592077i	−0.627785	+	0.778386i	$0.716038\pi$
$888$	−7.66312	+	5.56758i	−0.257157	+	0.186836i
$889$	9.00000	−	27.6992i	0.301850	−	0.929000i
$890$	−5.85410			−0.196230
$891$		0			0
$892$	−7.85410			−0.262975
$893$	0.163119	−	0.502029i	0.00545857	−	0.0167997i
$894$	−19.6353	+	14.2658i	−0.656701	+	0.477121i
$895$	0.690983	+	0.502029i	0.0230970	+	0.0167810i
$896$	12.6246	+	38.8546i	0.421759	+	1.29804i
$897$	−10.5451	−	32.4544i	−0.352090	−	1.08362i
$898$	20.3262	+	14.7679i	0.678295	+	0.492810i
$899$	−13.9443	+	10.1311i	−0.465068	+	0.337891i
$900$	−0.927051	+	2.85317i	−0.0309017	+	0.0951057i
$901$	4.56231			0.151992
$902$		0			0
$903$	5.29180			0.176100
$904$	8.78115	−	27.0256i	0.292057	−	0.898858i
$905$	−2.63525	+	1.91462i	−0.0875988	+	0.0636443i
$906$	−2.61803	−	1.90211i	−0.0869784	−	0.0631935i
$907$	1.22949	+	3.78398i	0.0408246	+	0.125645i	0.969392	−	0.245520i	$-0.0789586\pi$
$907$	1.22949	+	3.78398i	0.0408246	+	0.125645i	−0.928567	+	0.371165i	$0.878959\pi$
$908$	2.07953	+	6.40013i	0.0690115	+	0.212396i
$909$	2.42705	+	1.76336i	0.0805002	+	0.0584868i
$910$	9.35410	−	6.79615i	0.310085	−	0.225290i
$911$	11.1074	−	34.1850i	0.368004	−	1.13260i	−0.580074	−	0.814564i	$-0.696976\pi$
$911$	11.1074	−	34.1850i	0.368004	−	1.13260i	0.948078	−	0.318037i	$-0.103024\pi$
$912$	4.14590			0.137284
$913$		0			0
$914$	53.0689			1.75536
$915$	−0.135255	+	0.416272i	−0.00447139	+	0.0137615i
$916$	−5.00000	+	3.63271i	−0.165205	+	0.120028i
$917$	33.6246	+	24.4297i	1.11038	+	0.806740i
$918$	−0.309017	−	0.951057i	−0.0101991	−	0.0313895i
$919$	−14.5106	−	44.6592i	−0.478662	−	1.47317i	−0.840955	−	0.541106i	$-0.818006\pi$
$919$	−14.5106	−	44.6592i	−0.478662	−	1.47317i	0.362293	−	0.932064i	$-0.381994\pi$
$920$	3.78115	+	2.74717i	0.124661	+	0.0905715i
$921$	15.8262	−	11.4984i	0.521492	−	0.378886i
$922$	−4.95492	+	15.2497i	−0.163181	+	0.502221i
$923$	90.8115			2.98910
$924$		0			0
$925$	20.5623			0.676084
$926$	4.39919	−	13.5393i	0.144566	−	0.444929i
$927$	4.85410	−	3.52671i	0.159430	−	0.115832i
$928$	−12.2361	−	8.89002i	−0.401669	−	0.291829i
$929$	0.892609	+	2.74717i	0.0292856	+	0.0901317i	0.964631	−	0.263604i	$-0.0849112\pi$
$929$	0.892609	+	2.74717i	0.0292856	+	0.0901317i	−0.935345	+	0.353736i	$0.884911\pi$
$930$	0.736068	+	2.26538i	0.0241366	+	0.0742849i
$931$	1.38197	+	1.00406i	0.0452921	+	0.0329066i
$932$	−4.33688	+	3.15093i	−0.142059	+	0.103212i
$933$	3.54508	−	10.9106i	0.116061	−	0.357199i
$934$	−23.0344			−0.753710
$935$		0			0
$936$	−13.9443			−0.455783
$937$	10.0729	−	31.0013i	0.329069	−	1.01277i	−0.640501	−	0.767957i	$-0.721273\pi$
$937$	10.0729	−	31.0013i	0.329069	−	1.01277i	0.969570	−	0.244813i	$-0.0787266\pi$
$938$	−41.4787	+	30.1360i	−1.35433	+	0.983977i
$939$	22.5172	+	16.3597i	0.734822	+	0.533879i
$940$	0.0450850	+	0.138757i	0.00147051	+	0.00452576i
$941$	10.3926	+	31.9852i	0.338789	+	1.04269i	0.964825	+	0.262892i	$0.0846764\pi$
$941$	10.3926	+	31.9852i	0.338789	+	1.04269i	−0.626036	+	0.779794i	$0.715324\pi$
$942$	−12.7082	−	9.23305i	−0.414056	−	0.300829i
$943$	26.3156	−	19.1194i	0.856954	−	0.622613i
$944$	7.98936	−	24.5887i	0.260031	−	0.800294i
$945$	−1.14590			−0.0372761
$946$		0			0
$947$	2.67376			0.0868856			0.0434428	−	0.999056i	$-0.486167\pi$
$947$	2.67376			0.0868856			0.0434428	+	0.999056i	$0.486167\pi$
$948$	0.100813	−	0.310271i	0.00327426	−	0.0100771i
$949$	−6.23607	+	4.53077i	−0.202431	+	0.147075i
$950$	−5.42705	−	3.94298i	−0.176077	−	0.127927i
$951$	7.83688	+	24.1194i	0.254128	+	0.782126i
$952$	1.28115	+	3.94298i	0.0415224	+	0.127793i
$953$	−48.6869	−	35.3731i	−1.57712	−	1.14585i	−0.919900	−	0.392152i	$-0.871731\pi$
$953$	−48.6869	−	35.3731i	−1.57712	−	1.14585i	−0.657223	−	0.753696i	$-0.728269\pi$
$954$	9.66312	−	7.02067i	0.312855	−	0.227302i
$955$	−0.173762	+	0.534785i	−0.00562281	+	0.0173052i
$956$	−10.8541			−0.351047
$957$		0			0
$958$	−27.3607			−0.883983
$959$	−1.36475	+	4.20025i	−0.0440699	+	0.135633i
$960$	1.30902	−	0.951057i	0.0422483	−	0.0306952i
$961$	13.0623	+	9.49032i	0.421365	+	0.306139i
$962$	−13.2082	−	40.6507i	−0.425850	−	1.31063i
$963$	0.0729490	+	0.224514i	0.00235075	+	0.00723486i
$964$	−8.56231	−	6.22088i	−0.275773	−	0.200361i
$965$	0.482779	−	0.350760i	0.0155412	−	0.0112913i
$966$	−8.20820	+	25.2623i	−0.264095	+	0.812800i
$967$	25.6869			0.826036			0.413018	−	0.910723i	$-0.364475\pi$
$967$	25.6869			0.826036			0.413018	+	0.910723i	$0.364475\pi$
$968$		0			0
$969$	0.527864			0.0169574
$970$	−2.87132	+	8.83702i	−0.0921926	+	0.283740i
$971$	27.3262	−	19.8537i	0.876941	−	0.637135i	−0.0554996	−	0.998459i	$-0.517675\pi$
$971$	27.3262	−	19.8537i	0.876941	−	0.637135i	0.932440	+	0.361324i	$0.117675\pi$
$972$	−0.500000	−	0.363271i	−0.0160375	−	0.0116519i
$973$	5.42705	+	16.7027i	0.173983	+	0.535465i
$974$	19.5902	+	60.2923i	0.627710	+	1.93189i
$975$	24.4894	+	17.7926i	0.784287	+	0.569818i
$976$	4.50000	−	3.26944i	0.144041	−	0.104652i
$977$	−15.2533	+	46.9448i	−0.487996	+	1.50190i	0.339598	+	0.940571i	$0.389709\pi$
$977$	−15.2533	+	46.9448i	−0.487996	+	1.50190i	−0.827594	+	0.561327i	$0.810291\pi$
$978$	−24.7082			−0.790081
$979$		0			0
$980$	−0.472136			−0.0150818
$981$		0			0
$982$	34.3156	−	24.9317i	1.09505	−	0.795604i
$983$	−28.5623	−	20.7517i	−0.910996	−	0.661877i	0.0302705	−	0.999542i	$-0.490363\pi$
$983$	−28.5623	−	20.7517i	−0.910996	−	0.661877i	−0.941267	+	0.337664i	$0.890363\pi$
$984$	−4.10739	−	12.6412i	−0.130939	−	0.402988i
$985$	−3.14183	−	9.66957i	−0.100107	−	0.308098i
$986$	−3.61803	−	2.62866i	−0.115222	−	0.0837134i
$987$	1.50000	−	1.08981i	0.0477455	−	0.0346892i
$988$	−1.01722	+	3.13068i	−0.0323621	+	0.0996003i
$989$	−9.65248			−0.306931
$990$		0			0
$991$	−12.2705			−0.389786			−0.194893	−	0.980825i	$-0.562436\pi$
$991$	−12.2705			−0.389786			−0.194893	+	0.980825i	$0.562436\pi$
$992$	4.02786	−	12.3965i	0.127885	−	0.393589i
$993$	18.2812	−	13.2820i	0.580135	−	0.421493i
$994$	−57.1869	−	41.5487i	−1.81386	−	1.31785i
$995$	0.388544	+	1.19581i	0.0123177	+	0.0379099i
$996$	−2.42705	−	7.46969i	−0.0769041	−	0.236686i
$997$	−27.4894	−	19.9722i	−0.870597	−	0.632526i	0.0601503	−	0.998189i	$-0.480842\pi$
$997$	−27.4894	−	19.9722i	−0.870597	−	0.632526i	−0.930747	+	0.365664i	$0.880842\pi$
$998$	−3.35410	+	2.43690i	−0.106172	+	0.0771386i
$999$	−1.30902	+	4.02874i	−0.0414155	+	0.127464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.e.h.130.1		4
11.2	odd	10		363.2.e.j.124.1		4
11.3	even	5		33.2.e.a.4.1	✓	4
11.4	even	5		363.2.a.h.1.2		2
11.5	even	5	inner	363.2.e.h.148.1		4
11.6	odd	10		363.2.e.c.148.1		4
11.7	odd	10		363.2.a.e.1.1		2
11.8	odd	10		363.2.e.j.202.1		4
11.9	even	5		33.2.e.a.25.1	yes	4
11.10	odd	2		363.2.e.c.130.1		4
33.14	odd	10		99.2.f.b.37.1		4
33.20	odd	10		99.2.f.b.91.1		4
33.26	odd	10		1089.2.a.m.1.1		2
33.29	even	10		1089.2.a.s.1.2		2
44.3	odd	10		528.2.y.f.433.1		4
44.7	even	10		5808.2.a.bm.1.2		2
44.15	odd	10		5808.2.a.bl.1.2		2
44.31	odd	10		528.2.y.f.289.1		4
55.3	odd	20		825.2.bx.b.499.1		8
55.4	even	10		9075.2.a.x.1.1		2
55.9	even	10		825.2.n.f.751.1		4
55.14	even	10		825.2.n.f.301.1		4
55.29	odd	10		9075.2.a.bv.1.2		2
55.42	odd	20		825.2.bx.b.124.1		8
55.47	odd	20		825.2.bx.b.499.2		8
55.53	odd	20		825.2.bx.b.124.2		8
99.14	odd	30		891.2.n.a.136.1		8
99.20	odd	30		891.2.n.a.190.1		8
99.25	even	15		891.2.n.d.433.1		8
99.31	even	15		891.2.n.d.784.1		8
99.47	odd	30		891.2.n.a.433.1		8
99.58	even	15		891.2.n.d.136.1		8
99.86	odd	30		891.2.n.a.784.1		8
99.97	even	15		891.2.n.d.190.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.4.1	✓	4	11.3	even	5
33.2.e.a.25.1	yes	4	11.9	even	5
99.2.f.b.37.1		4	33.14	odd	10
99.2.f.b.91.1		4	33.20	odd	10
363.2.a.e.1.1		2	11.7	odd	10
363.2.a.h.1.2		2	11.4	even	5
363.2.e.c.130.1		4	11.10	odd	2
363.2.e.c.148.1		4	11.6	odd	10
363.2.e.h.130.1		4	1.1	even	1	trivial
363.2.e.h.148.1		4	11.5	even	5	inner
363.2.e.j.124.1		4	11.2	odd	10
363.2.e.j.202.1		4	11.8	odd	10
528.2.y.f.289.1		4	44.31	odd	10
528.2.y.f.433.1		4	44.3	odd	10
825.2.n.f.301.1		4	55.14	even	10
825.2.n.f.751.1		4	55.9	even	10
825.2.bx.b.124.1		8	55.42	odd	20
825.2.bx.b.124.2		8	55.53	odd	20
825.2.bx.b.499.1		8	55.3	odd	20
825.2.bx.b.499.2		8	55.47	odd	20
891.2.n.a.136.1		8	99.14	odd	30
891.2.n.a.190.1		8	99.20	odd	30
891.2.n.a.433.1		8	99.47	odd	30
891.2.n.a.784.1		8	99.86	odd	30
891.2.n.d.136.1		8	99.58	even	15
891.2.n.d.190.1		8	99.97	even	15
891.2.n.d.433.1		8	99.25	even	15
891.2.n.d.784.1		8	99.31	even	15
1089.2.a.m.1.1		2	33.26	odd	10
1089.2.a.s.1.2		2	33.29	even	10
5808.2.a.bl.1.2		2	44.15	odd	10
5808.2.a.bm.1.2		2	44.7	even	10
9075.2.a.x.1.1		2	55.4	even	10
9075.2.a.bv.1.2		2	55.29	odd	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 $\F_{q}$
Belyi maps

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+(0.500000 - 1.53884i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.118034 - 0.363271i) q^{5} +(0.500000 + 1.53884i) q^{6} +(-2.42705 - 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.618034 q^{10} +0.618034 q^{12} +(1.92705 - 5.93085i) q^{13} +(-3.92705 + 2.85317i) q^{14} +(0.309017 + 0.224514i) q^{15} +(-1.50000 - 4.61653i) q^{16} +(-0.190983 - 0.587785i) q^{17} +(-1.30902 - 0.951057i) q^{18} +(0.690983 - 0.502029i) q^{19} +(-0.0729490 + 0.224514i) q^{20} +3.00000 q^{21} -5.47214 q^{23} +(-0.690983 + 2.12663i) q^{24} +(3.92705 - 2.85317i) q^{25} +(-8.16312 - 5.93085i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.572949 + 1.76336i) q^{28} +(3.61803 + 2.62866i) q^{29} +(0.500000 - 0.363271i) q^{30} +(-1.19098 + 3.66547i) q^{31} -3.38197 q^{32} -1.00000 q^{34} +(-0.354102 + 1.08981i) q^{35} +(-0.500000 + 0.363271i) q^{36} +(3.42705 + 2.48990i) q^{37} +(-0.427051 - 1.31433i) q^{38} +(1.92705 + 5.93085i) q^{39} +(-0.690983 - 0.502029i) q^{40} +(-4.80902 + 3.49396i) q^{41} +(1.50000 - 4.61653i) q^{42} +1.76393 q^{43} -0.381966 q^{45} +(-2.73607 + 8.42075i) q^{46} +(0.500000 - 0.363271i) q^{47} +(3.92705 + 2.85317i) q^{48} +(0.618034 + 1.90211i) q^{49} +(-2.42705 - 7.46969i) q^{50} +(0.500000 + 0.363271i) q^{51} +(-3.11803 + 2.26538i) q^{52} +(-2.28115 + 7.02067i) q^{53} +1.61803 q^{54} -6.70820 q^{56} +(-0.263932 + 0.812299i) q^{57} +(5.85410 - 4.25325i) q^{58} +(4.30902 + 3.13068i) q^{59} +(-0.0729490 - 0.224514i) q^{60} +(0.354102 + 1.08981i) q^{61} +(5.04508 + 3.66547i) q^{62} +(-2.42705 + 1.76336i) q^{63} +(1.30902 - 4.02874i) q^{64} -2.38197 q^{65} +10.5623 q^{67} +(-0.118034 + 0.363271i) q^{68} +(4.42705 - 3.21644i) q^{69} +(1.50000 + 1.08981i) q^{70} +(4.50000 + 13.8496i) q^{71} +(-0.690983 - 2.12663i) q^{72} +(-1.00000 - 0.726543i) q^{73} +(5.54508 - 4.02874i) q^{74} +(-1.50000 + 4.61653i) q^{75} -0.527864 q^{76} +10.0902 q^{78} +(0.163119 - 0.502029i) q^{79} +(-1.50000 + 1.08981i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(2.97214 + 9.14729i) q^{82} +(-3.92705 - 12.0862i) q^{83} +(-1.50000 - 1.08981i) q^{84} +(-0.190983 + 0.138757i) q^{85} +(0.881966 - 2.71441i) q^{86} -4.47214 q^{87} +9.47214 q^{89} +(-0.190983 + 0.587785i) q^{90} +(-15.1353 + 10.9964i) q^{91} +(2.73607 + 1.98787i) q^{92} +(-1.19098 - 3.66547i) q^{93} +(-0.309017 - 0.951057i) q^{94} +(-0.263932 - 0.191758i) q^{95} +(2.73607 - 1.98787i) q^{96} +(4.64590 - 14.2986i) q^{97} +3.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 5 q^{8} - q^{9} + 2 q^{10} - 2 q^{12} + q^{13} - 9 q^{14} - q^{15} - 6 q^{16} - 3 q^{17} - 3 q^{18} + 5 q^{19} - 7 q^{20} + 12 q^{21}+ \cdots + 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 5 * q^8 - q^9 + 2 * q^10 - 2 * q^12 + q^13 - 9 * q^14 - q^15 - 6 * q^16 - 3 * q^17 - 3 * q^18 + 5 * q^19 - 7 * q^20 + 12 * q^21 - 4 * q^23 - 5 * q^24 + 9 * q^25 - 17 * q^26 - q^27 + 9 * q^28 + 10 * q^29 + 2 * q^30 - 7 * q^31 - 18 * q^32 - 4 * q^34 + 12 * q^35 - 2 * q^36 + 7 * q^37 + 5 * q^38 + q^39 - 5 * q^40 - 17 * q^41 + 6 * q^42 + 16 * q^43 - 6 * q^45 - 2 * q^46 + 2 * q^47 + 9 * q^48 - 2 * q^49 - 3 * q^50 + 2 * q^51 - 8 * q^52 + 11 * q^53 + 2 * q^54 - 10 * q^57 + 10 * q^58 + 15 * q^59 - 7 * q^60 - 12 * q^61 + 9 * q^62 - 3 * q^63 + 3 * q^64 - 14 * q^65 + 2 * q^67 + 4 * q^68 + 11 * q^69 + 6 * q^70 + 18 * q^71 - 5 * q^72 - 4 * q^73 + 11 * q^74 - 6 * q^75 - 20 * q^76 + 18 * q^78 - 15 * q^79 - 6 * q^80 - q^81 - 6 * q^82 - 9 * q^83 - 6 * q^84 - 3 * q^85 + 8 * q^86 + 20 * q^89 - 3 * q^90 - 27 * q^91 + 2 * q^92 - 7 * q^93 + q^94 - 10 * q^95 + 2 * q^96 + 32 * q^97 + 4 * q^98

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