LMFDB - Embedded newform 33.2.e.a.4.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [33,2,Mod(4,33)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("33.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.263506326670$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			4.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	33.4
Dual form			33.2.e.a.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30902 - 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +(0.309017 - 0.224514i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(0.927051 + 2.85317i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} -0.618034 q^{10} +(2.80902 + 1.76336i) q^{11} +0.618034 q^{12} +(-5.04508 - 3.66547i) q^{13} +(1.50000 - 4.61653i) q^{14} +(-0.118034 - 0.363271i) q^{15} +(3.92705 - 2.85317i) q^{16} +(0.500000 - 0.363271i) q^{17} +(0.500000 + 1.53884i) q^{18} +(-0.263932 + 0.812299i) q^{19} +(0.190983 + 0.138757i) q^{20} +3.00000 q^{21} +(-2.00000 - 4.97980i) q^{22} -5.47214 q^{23} +(1.80902 + 1.31433i) q^{24} +(-1.50000 + 4.61653i) q^{25} +(3.11803 + 9.59632i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.50000 + 1.08981i) q^{28} +(-1.38197 - 4.25325i) q^{29} +(-0.190983 + 0.587785i) q^{30} +(3.11803 + 2.26538i) q^{31} -3.38197 q^{32} +(2.54508 - 2.12663i) q^{33} -1.00000 q^{34} +(0.927051 + 0.673542i) q^{35} +(0.190983 - 0.587785i) q^{36} +(-1.30902 - 4.02874i) q^{37} +(1.11803 - 0.812299i) q^{38} +(-5.04508 + 3.66547i) q^{39} +(0.263932 + 0.812299i) q^{40} +(1.83688 - 5.65334i) q^{41} +(-3.92705 - 2.85317i) q^{42} +1.76393 q^{43} +(-0.500000 + 1.98787i) q^{44} -0.381966 q^{45} +(7.16312 + 5.20431i) q^{46} +(-0.190983 + 0.587785i) q^{47} +(-1.50000 - 4.61653i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(6.35410 - 4.61653i) q^{50} +(-0.190983 - 0.587785i) q^{51} +(1.19098 - 3.66547i) q^{52} +(5.97214 + 4.33901i) q^{53} +1.61803 q^{54} +(1.26393 - 0.0857567i) q^{55} -6.70820 q^{56} +(0.690983 + 0.502029i) q^{57} +(-2.23607 + 6.88191i) q^{58} +(-1.64590 - 5.06555i) q^{59} +(0.190983 - 0.138757i) q^{60} +(-0.927051 + 0.673542i) q^{61} +(-1.92705 - 5.93085i) q^{62} +(0.927051 - 2.85317i) q^{63} +(-3.42705 - 2.48990i) q^{64} -2.38197 q^{65} +(-5.35410 + 0.363271i) q^{66} +10.5623 q^{67} +(0.309017 + 0.224514i) q^{68} +(-1.69098 + 5.20431i) q^{69} +(-0.572949 - 1.76336i) q^{70} +(-11.7812 + 8.55951i) q^{71} +(1.80902 - 1.31433i) q^{72} +(0.381966 + 1.17557i) q^{73} +(-2.11803 + 6.51864i) q^{74} +(3.92705 + 2.85317i) q^{75} -0.527864 q^{76} +(-2.42705 + 9.64932i) q^{77} +10.0902 q^{78} +(-0.427051 - 0.310271i) q^{79} +(0.572949 - 1.76336i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-7.78115 + 5.65334i) q^{82} +(10.2812 - 7.46969i) q^{83} +(0.572949 + 1.76336i) q^{84} +(0.0729490 - 0.224514i) q^{85} +(-2.30902 - 1.67760i) q^{86} -4.47214 q^{87} +(-5.69098 + 4.75528i) q^{88} +9.47214 q^{89} +(0.500000 + 0.363271i) q^{90} +(5.78115 - 17.7926i) q^{91} +(-1.04508 - 3.21644i) q^{92} +(3.11803 - 2.26538i) q^{93} +(0.809017 - 0.587785i) q^{94} +(0.100813 + 0.310271i) q^{95} +(-1.04508 + 3.21644i) q^{96} +(-12.1631 - 8.83702i) q^{97} +3.23607 q^{98} +(-1.23607 - 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - q^{3} + 3 q^{4} - q^{5} - 3 q^{6} - 3 q^{7} - 5 q^{8} - q^{9} + 2 q^{10} + 9 q^{11} - 2 q^{12} - 9 q^{13} + 6 q^{14} + 4 q^{15} + 9 q^{16} + 2 q^{17} + 2 q^{18} - 10 q^{19} + 3 q^{20}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - q^3 + 3 * q^4 - q^5 - 3 * q^6 - 3 * q^7 - 5 * q^8 - q^9 + 2 * q^10 + 9 * q^11 - 2 * q^12 - 9 * q^13 + 6 * q^14 + 4 * q^15 + 9 * q^16 + 2 * q^17 + 2 * q^18 - 10 * q^19 + 3 * q^20 + 12 * q^21 - 8 * q^22 - 4 * q^23 + 5 * q^24 - 6 * q^25 + 8 * q^26 - q^27 - 6 * q^28 - 10 * q^29 - 3 * q^30 + 8 * q^31 - 18 * q^32 - q^33 - 4 * q^34 - 3 * q^35 + 3 * q^36 - 3 * q^37 - 9 * q^39 + 10 * q^40 + 23 * q^41 - 9 * q^42 + 16 * q^43 - 2 * q^44 - 6 * q^45 + 13 * q^46 - 3 * q^47 - 6 * q^48 - 2 * q^49 + 12 * q^50 - 3 * q^51 + 7 * q^52 + 6 * q^53 + 2 * q^54 + 14 * q^55 + 5 * q^57 - 20 * q^59 + 3 * q^60 + 3 * q^61 - q^62 - 3 * q^63 - 7 * q^64 - 14 * q^65 - 8 * q^66 + 2 * q^67 - q^68 - 9 * q^69 - 9 * q^70 - 27 * q^71 + 5 * q^72 + 6 * q^73 - 4 * q^74 + 9 * q^75 - 20 * q^76 - 3 * q^77 + 18 * q^78 + 5 * q^79 + 9 * q^80 - q^81 - 11 * q^82 + 21 * q^83 + 9 * q^84 + 7 * q^85 - 7 * q^86 - 25 * q^88 + 20 * q^89 + 2 * q^90 + 3 * q^91 + 7 * q^92 + 8 * q^93 + q^94 + 25 * q^95 + 7 * q^96 - 33 * q^97 + 4 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.30902	−	0.951057i	−0.925615	−	0.672499i	0.0193004	−	0.999814i	$-0.493856\pi$
$2$	−1.30902	−	0.951057i	−0.925615	−	0.672499i	−0.944915	+	0.327315i	$0.893856\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	0.190983	+	0.587785i	0.0954915	+	0.293893i
$5$	0.309017	−	0.224514i	0.138197	−	0.100406i	−0.516539	−	0.856264i	$-0.672780\pi$
$5$	0.309017	−	0.224514i	0.138197	−	0.100406i	0.654736	+	0.755858i	$0.272780\pi$
$6$	−1.30902	+	0.951057i	−0.534404	+	0.388267i
$7$	0.927051	+	2.85317i	0.350392	+	1.07840i	0.958633	+	0.284644i	$0.0918755\pi$
$7$	0.927051	+	2.85317i	0.350392	+	1.07840i	−0.608241	+	0.793752i	$0.708125\pi$
$8$	−0.690983	+	2.12663i	−0.244299	+	0.751876i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−0.618034			−0.195440
$11$	2.80902	+	1.76336i	0.846950	+	0.531672i
$11$	2.80902	+	1.76336i	0.846950	+	0.531672i
$12$	0.618034			0.178411
$13$	−5.04508	−	3.66547i	−1.39925	−	1.01662i	−0.994777	−	0.102070i	$-0.967453\pi$
$13$	−5.04508	−	3.66547i	−1.39925	−	1.01662i	−0.404478	−	0.914548i	$-0.632547\pi$
$14$	1.50000	−	4.61653i	0.400892	−	1.23382i
$15$	−0.118034	−	0.363271i	−0.0304762	−	0.0937962i
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$	0.500000	−	0.363271i	0.121268	−	0.0881062i	−0.525498	−	0.850795i	$-0.676121\pi$
$17$	0.500000	−	0.363271i	0.121268	−	0.0881062i	0.646766	+	0.762688i	$0.276121\pi$
$18$	0.500000	+	1.53884i	0.117851	+	0.362708i
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	−0.976756	−	0.214353i	$-0.931236\pi$
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	0.916206	+	0.400707i	$0.131236\pi$
$20$	0.190983	+	0.138757i	0.0427051	+	0.0310271i
$21$	3.00000			0.654654
$22$	−2.00000	−	4.97980i	−0.426401	−	1.06170i
$23$	−5.47214			−1.14102			−0.570510	−	0.821291i	$-0.693254\pi$
$23$	−5.47214			−1.14102			−0.570510	+	0.821291i	$0.693254\pi$
$24$	1.80902	+	1.31433i	0.369264	+	0.268286i
$25$	−1.50000	+	4.61653i	−0.300000	+	0.923305i
$26$	3.11803	+	9.59632i	0.611497	+	1.88199i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−1.50000	+	1.08981i	−0.283473	+	0.205955i
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	−0.993505	−	0.113787i	$-0.963702\pi$
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	0.736881	−	0.676023i	$-0.236298\pi$
$30$	−0.190983	+	0.587785i	−0.0348686	+	0.107314i
$31$	3.11803	+	2.26538i	0.560015	+	0.406875i	0.831465	−	0.555578i	$-0.187503\pi$
$31$	3.11803	+	2.26538i	0.560015	+	0.406875i	−0.271449	+	0.962453i	$0.587503\pi$
$32$	−3.38197			−0.597853
$33$	2.54508	−	2.12663i	0.443042	−	0.370198i
$34$	−1.00000			−0.171499
$35$	0.927051	+	0.673542i	0.156700	+	0.113849i
$36$	0.190983	−	0.587785i	0.0318305	−	0.0979642i
$37$	−1.30902	−	4.02874i	−0.215201	−	0.662321i	−0.999139	−	0.0414819i	$-0.986792\pi$
$37$	−1.30902	−	4.02874i	−0.215201	−	0.662321i	0.783938	−	0.620839i	$-0.213208\pi$
$38$	1.11803	−	0.812299i	0.181369	−	0.131772i
$39$	−5.04508	+	3.66547i	−0.807860	+	0.586945i
$40$	0.263932	+	0.812299i	0.0417313	+	0.128436i
$41$	1.83688	−	5.65334i	0.286873	−	0.882903i	−0.698958	−	0.715162i	$-0.746353\pi$
$41$	1.83688	−	5.65334i	0.286873	−	0.882903i	0.985831	−	0.167741i	$-0.0536472\pi$
$42$	−3.92705	−	2.85317i	−0.605957	−	0.440254i
$43$	1.76393			0.268997			0.134499	−	0.990914i	$-0.457058\pi$
$43$	1.76393			0.268997			0.134499	+	0.990914i	$0.457058\pi$
$44$	−0.500000	+	1.98787i	−0.0753778	+	0.299683i
$45$	−0.381966			−0.0569401
$46$	7.16312	+	5.20431i	1.05614	+	0.767334i
$47$	−0.190983	+	0.587785i	−0.0278577	+	0.0857373i	−0.964019	−	0.265834i	$-0.914353\pi$
$47$	−0.190983	+	0.587785i	−0.0278577	+	0.0857373i	0.936161	+	0.351572i	$0.114353\pi$
$48$	−1.50000	−	4.61653i	−0.216506	−	0.666338i
$49$	−1.61803	+	1.17557i	−0.231148	+	0.167939i
$50$	6.35410	−	4.61653i	0.898606	−	0.652875i
$51$	−0.190983	−	0.587785i	−0.0267430	−	0.0823064i
$52$	1.19098	−	3.66547i	0.165160	−	0.508309i
$53$	5.97214	+	4.33901i	0.820336	+	0.596009i	0.916809	−	0.399327i	$-0.130756\pi$
$53$	5.97214	+	4.33901i	0.820336	+	0.596009i	−0.0964728	+	0.995336i	$0.530756\pi$
$54$	1.61803			0.220187
$55$	1.26393	−	0.0857567i	0.170429	−	0.0115634i
$56$	−6.70820			−0.896421
$57$	0.690983	+	0.502029i	0.0915229	+	0.0664953i
$58$	−2.23607	+	6.88191i	−0.293610	+	0.903639i
$59$	−1.64590	−	5.06555i	−0.214278	−	0.659479i	−0.999204	−	0.0398899i	$-0.987299\pi$
$59$	−1.64590	−	5.06555i	−0.214278	−	0.659479i	0.784926	−	0.619589i	$-0.212701\pi$
$60$	0.190983	−	0.138757i	0.0246558	−	0.0179135i
$61$	−0.927051	+	0.673542i	−0.118697	+	0.0862382i	−0.645550	−	0.763718i	$-0.723372\pi$
$61$	−0.927051	+	0.673542i	−0.118697	+	0.0862382i	0.526853	+	0.849956i	$0.323372\pi$
$62$	−1.92705	−	5.93085i	−0.244736	−	0.753219i
$63$	0.927051	−	2.85317i	0.116797	−	0.359466i
$64$	−3.42705	−	2.48990i	−0.428381	−	0.311237i
$65$	−2.38197			−0.295447
$66$	−5.35410	+	0.363271i	−0.659044	+	0.0447156i
$67$	10.5623			1.29039			0.645196	−	0.764017i	$-0.276776\pi$
$67$	10.5623			1.29039			0.645196	+	0.764017i	$0.276776\pi$
$68$	0.309017	+	0.224514i	0.0374738	+	0.0272263i
$69$	−1.69098	+	5.20431i	−0.203570	+	0.626525i
$70$	−0.572949	−	1.76336i	−0.0684805	−	0.210761i
$71$	−11.7812	+	8.55951i	−1.39817	+	1.01583i	−0.403253	+	0.915089i	$0.632120\pi$
$71$	−11.7812	+	8.55951i	−1.39817	+	1.01583i	−0.994913	+	0.100738i	$0.967880\pi$
$72$	1.80902	−	1.31433i	0.213195	−	0.154895i
$73$	0.381966	+	1.17557i	0.0447057	+	0.137590i	0.970918	−	0.239412i	$-0.0769548\pi$
$73$	0.381966	+	1.17557i	0.0447057	+	0.137590i	−0.926212	+	0.377003i	$0.876955\pi$
$74$	−2.11803	+	6.51864i	−0.246216	+	0.757776i
$75$	3.92705	+	2.85317i	0.453457	+	0.329456i
$76$	−0.527864			−0.0605502
$77$	−2.42705	+	9.64932i	−0.276588	+	1.09964i
$78$	10.0902			1.14249
$79$	−0.427051	−	0.310271i	−0.0480470	−	0.0349082i	0.563503	−	0.826114i	$-0.309453\pi$
$79$	−0.427051	−	0.310271i	−0.0480470	−	0.0349082i	−0.611550	+	0.791206i	$0.709453\pi$
$80$	0.572949	−	1.76336i	0.0640576	−	0.197149i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−7.78115	+	5.65334i	−0.859285	+	0.624307i
$83$	10.2812	−	7.46969i	1.12850	−	0.819906i	0.143027	−	0.989719i	$-0.454316\pi$
$83$	10.2812	−	7.46969i	1.12850	−	0.819906i	0.985476	+	0.169813i	$0.0543165\pi$
$84$	0.572949	+	1.76336i	0.0625139	+	0.192398i
$85$	0.0729490	−	0.224514i	0.00791243	−	0.0243520i
$86$	−2.30902	−	1.67760i	−0.248988	−	0.180900i
$87$	−4.47214			−0.479463
$88$	−5.69098	+	4.75528i	−0.606661	+	0.506915i
$89$	9.47214			1.00404			0.502022	−	0.864855i	$-0.332590\pi$
$89$	9.47214			1.00404			0.502022	+	0.864855i	$0.332590\pi$
$90$	0.500000	+	0.363271i	0.0527046	+	0.0382922i
$91$	5.78115	−	17.7926i	0.606029	−	1.86517i
$92$	−1.04508	−	3.21644i	−0.108958	−	0.335337i
$93$	3.11803	−	2.26538i	0.323325	−	0.234909i
$94$	0.809017	−	0.587785i	0.0834437	−	0.0606254i
$95$	0.100813	+	0.310271i	0.0103432	+	0.0318331i
$96$	−1.04508	+	3.21644i	−0.106664	+	0.328277i
$97$	−12.1631	−	8.83702i	−1.23498	−	0.897264i	−0.237724	−	0.971333i	$-0.576402\pi$
$97$	−12.1631	−	8.83702i	−1.23498	−	0.897264i	−0.997253	+	0.0740689i	$0.976402\pi$
$98$	3.23607			0.326892
$99$	−1.23607	−	3.07768i	−0.124230	−	0.309319i
$100$	−3.00000			−0.300000
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	0.701952	−	0.712225i	$-0.252312\pi$
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	−0.460451	+	0.887685i	$0.652312\pi$
$102$	−0.309017	+	0.951057i	−0.0305972	+	0.0941686i
$103$	−1.85410	−	5.70634i	−0.182690	−	0.562262i	0.817211	−	0.576339i	$-0.195519\pi$
$103$	−1.85410	−	5.70634i	−0.182690	−	0.562262i	−0.999901	+	0.0140765i	$0.995519\pi$
$104$	11.2812	−	8.19624i	1.10621	−	0.803707i
$105$	0.927051	−	0.673542i	0.0904709	−	0.0657310i
$106$	−3.69098	−	11.3597i	−0.358500	−	1.10335i
$107$	0.0729490	−	0.224514i	0.00705225	−	0.0217046i	−0.947468	−	0.319849i	$-0.896368\pi$
$107$	0.0729490	−	0.224514i	0.00705225	−	0.0217046i	0.954521	+	0.298145i	$0.0963678\pi$
$108$	−0.500000	−	0.363271i	−0.0481125	−	0.0349558i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	−1.73607	−	1.08981i	−0.165528	−	0.103910i
$111$	−4.23607			−0.402070
$112$	11.7812	+	8.55951i	1.11321	+	0.808798i
$113$	−3.92705	+	12.0862i	−0.369426	+	1.13698i	0.577737	+	0.816223i	$0.303936\pi$
$113$	−3.92705	+	12.0862i	−0.369426	+	1.13698i	−0.947163	+	0.320753i	$0.896064\pi$
$114$	−0.427051	−	1.31433i	−0.0399970	−	0.123098i
$115$	−1.69098	+	1.22857i	−0.157685	+	0.114565i
$116$	2.23607	−	1.62460i	0.207614	−	0.150840i
$117$	1.92705	+	5.93085i	0.178156	+	0.548308i
$118$	−2.66312	+	8.19624i	−0.245160	+	0.754525i
$119$	1.50000	+	1.08981i	0.137505	+	0.0999031i
$120$	0.854102			0.0779685
$121$	4.78115	+	9.90659i	0.434650	+	0.900599i
$122$	1.85410			0.167863
$123$	−4.80902	−	3.49396i	−0.433614	−	0.315039i
$124$	−0.736068	+	2.26538i	−0.0661009	+	0.203438i
$125$	1.16312	+	3.57971i	0.104033	+	0.320179i
$126$	−3.92705	+	2.85317i	−0.349850	+	0.254181i
$127$	−7.85410	+	5.70634i	−0.696939	+	0.506356i	−0.878934	−	0.476944i	$-0.841745\pi$
$127$	−7.85410	+	5.70634i	−0.696939	+	0.506356i	0.181995	+	0.983299i	$0.441745\pi$
$128$	4.20820	+	12.9515i	0.371956	+	1.14476i
$129$	0.545085	−	1.67760i	0.0479921	−	0.147704i
$130$	3.11803	+	2.26538i	0.273470	+	0.198687i
$131$	−13.8541			−1.21044			−0.605219	−	0.796059i	$-0.706915\pi$
$131$	−13.8541			−1.21044			−0.605219	+	0.796059i	$0.706915\pi$
$132$	1.73607	+	1.08981i	0.151105	+	0.0948561i
$133$	−2.56231			−0.222180
$134$	−13.8262	−	10.0453i	−1.19441	−	0.867786i
$135$	−0.118034	+	0.363271i	−0.0101587	+	0.0312654i
$136$	0.427051	+	1.31433i	0.0366193	+	0.112703i
$137$	1.19098	−	0.865300i	0.101753	−	0.0739276i	−0.535746	−	0.844379i	$-0.679969\pi$
$137$	1.19098	−	0.865300i	0.101753	−	0.0739276i	0.637498	+	0.770452i	$0.279969\pi$
$138$	7.16312	−	5.20431i	0.609765	−	0.443020i
$139$	1.80902	+	5.56758i	0.153439	+	0.472236i	0.997999	−	0.0632239i	$-0.0201382\pi$
$139$	1.80902	+	5.56758i	0.153439	+	0.472236i	−0.844561	+	0.535460i	$0.820138\pi$
$140$	−0.218847	+	0.673542i	−0.0184960	+	0.0569247i
$141$	0.500000	+	0.363271i	0.0421076	+	0.0305930i
$142$	23.5623			1.97730
$143$	−7.70820	−	19.1926i	−0.644592	−	1.60497i
$144$	−4.85410			−0.404508
$145$	−1.38197	−	1.00406i	−0.114766	−	0.0833824i
$146$	0.618034	−	1.90211i	0.0511489	−	0.157420i
$147$	0.618034	+	1.90211i	0.0509746	+	0.156884i
$148$	2.11803	−	1.53884i	0.174101	−	0.126492i
$149$	−12.1353	+	8.81678i	−0.994159	+	0.722299i	−0.960828	−	0.277146i	$-0.910612\pi$
$149$	−12.1353	+	8.81678i	−0.994159	+	0.722299i	−0.0333309	+	0.999444i	$0.510612\pi$
$150$	−2.42705	−	7.46969i	−0.198168	−	0.609898i
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	−0.922755	−	0.385388i	$-0.874068\pi$
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	0.973050	+	0.230596i	$0.0740676\pi$
$152$	−1.54508	−	1.12257i	−0.125323	−	0.0910524i
$153$	−0.618034			−0.0499651
$154$	12.3541	−	10.3229i	0.995522	−	0.831840i
$155$	1.47214			0.118245
$156$	−3.11803	−	2.26538i	−0.249643	−	0.181376i
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	−0.757077	−	0.653325i	$-0.773373\pi$
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	0.996503	−	0.0835524i	$-0.0266266\pi$
$158$	0.263932	+	0.812299i	0.0209973	+	0.0646231i
$159$	5.97214	−	4.33901i	0.473621	−	0.344106i
$160$	−1.04508	+	0.759299i	−0.0826212	+	0.0600278i
$161$	−5.07295	−	15.6129i	−0.399804	−	1.23047i
$162$	0.500000	−	1.53884i	0.0392837	−	0.120903i
$163$	12.3541	+	8.97578i	0.967648	+	0.703037i	0.954914	−	0.296882i	$-0.0959467\pi$
$163$	12.3541	+	8.97578i	0.967648	+	0.703037i	0.0127336	+	0.999919i	$0.495947\pi$
$164$	3.67376			0.286873
$165$	0.309017	−	1.22857i	0.0240569	−	0.0956441i
$166$	−20.5623			−1.59594
$167$	15.3992	+	11.1882i	1.19162	+	0.865766i	0.993435	−	0.114398i	$-0.0364938\pi$
$167$	15.3992	+	11.1882i	1.19162	+	0.865766i	0.198190	+	0.980164i	$0.436494\pi$
$168$	−2.07295	+	6.37988i	−0.159931	+	0.492219i
$169$	8.00000	+	24.6215i	0.615385	+	1.89396i
$170$	−0.309017	+	0.224514i	−0.0237005	+	0.0172194i
$171$	0.690983	−	0.502029i	0.0528408	−	0.0383911i
$172$	0.336881	+	1.03681i	0.0256869	+	0.0790563i
$173$	5.44427	−	16.7557i	0.413920	−	1.27392i	−0.499293	−	0.866433i	$-0.666407\pi$
$173$	5.44427	−	16.7557i	0.413920	−	1.27392i	0.913213	−	0.407482i	$-0.133593\pi$
$174$	5.85410	+	4.25325i	0.443798	+	0.322438i
$175$	−14.5623			−1.10081
$176$	16.0623	−	1.08981i	1.21074	−	0.0821478i
$177$	−5.32624			−0.400345
$178$	−12.3992	−	9.00854i	−0.929358	−	0.675218i
$179$	0.690983	−	2.12663i	0.0516465	−	0.158952i	−0.921907	−	0.387412i	$-0.873369\pi$
$179$	0.690983	−	2.12663i	0.0516465	−	0.158952i	0.973553	+	0.228460i	$0.0733691\pi$
$180$	−0.0729490	−	0.224514i	−0.00543730	−	0.0167343i
$181$	6.89919	−	5.01255i	0.512813	−	0.372580i	−0.301077	−	0.953600i	$-0.597346\pi$
$181$	6.89919	−	5.01255i	0.512813	−	0.372580i	0.813889	+	0.581020i	$0.197346\pi$
$182$	−24.4894	+	17.7926i	−1.81527	+	1.31887i
$183$	0.354102	+	1.08981i	0.0261760	+	0.0805614i
$184$	3.78115	−	11.6372i	0.278750	−	0.857905i
$185$	−1.30902	−	0.951057i	−0.0962408	−	0.0699231i
$186$	−6.23607			−0.457251
$187$	2.04508	−	0.138757i	0.149551	−	0.0101469i
$188$	−0.381966			−0.0278577
$189$	−2.42705	−	1.76336i	−0.176542	−	0.128265i
$190$	0.163119	−	0.502029i	0.0118339	−	0.0364210i
$191$	0.454915	+	1.40008i	0.0329165	+	0.101307i	0.966165	−	0.257925i	$-0.0830388\pi$
$191$	0.454915	+	1.40008i	0.0329165	+	0.101307i	−0.933248	+	0.359232i	$0.883039\pi$
$192$	−3.42705	+	2.48990i	−0.247326	+	0.179693i
$193$	−1.26393	+	0.918300i	−0.0909798	+	0.0661007i	−0.632345	−	0.774687i	$-0.717908\pi$
$193$	−1.26393	+	0.918300i	−0.0909798	+	0.0661007i	0.541365	+	0.840787i	$0.317908\pi$
$194$	7.51722	+	23.1356i	0.539705	+	1.66104i
$195$	−0.736068	+	2.26538i	−0.0527109	+	0.162228i
$196$	−1.00000	−	0.726543i	−0.0714286	−	0.0518959i
$197$	26.6180			1.89646			0.948228	−	0.317590i	$-0.102873\pi$
$197$	26.6180			1.89646			0.948228	+	0.317590i	$0.102873\pi$
$198$	−1.30902	+	5.20431i	−0.0930278	+	0.369854i
$199$	−3.29180			−0.233349			−0.116675	−	0.993170i	$-0.537223\pi$
$199$	−3.29180			−0.233349			−0.116675	+	0.993170i	$0.537223\pi$
$200$	−8.78115	−	6.37988i	−0.620921	−	0.451126i
$201$	3.26393	−	10.0453i	0.230220	−	0.708544i
$202$	−1.50000	−	4.61653i	−0.105540	−	0.324818i
$203$	10.8541	−	7.88597i	0.761809	−	0.553486i
$204$	0.309017	−	0.224514i	0.0216355	−	0.0157191i
$205$	−0.701626	−	2.15938i	−0.0490037	−	0.150818i
$206$	−3.00000	+	9.23305i	−0.209020	+	0.643297i
$207$	4.42705	+	3.21644i	0.307701	+	0.223558i
$208$	−30.2705			−2.09888
$209$	−2.17376	+	1.81636i	−0.150362	+	0.125640i
$210$	−1.85410			−0.127945
$211$	−9.11803	−	6.62464i	−0.627711	−	0.456059i	0.227895	−	0.973686i	$-0.426816\pi$
$211$	−9.11803	−	6.62464i	−0.627711	−	0.456059i	−0.855607	+	0.517627i	$0.826816\pi$
$212$	−1.40983	+	4.33901i	−0.0968275	+	0.298004i
$213$	4.50000	+	13.8496i	0.308335	+	0.948957i
$214$	−0.309017	+	0.224514i	−0.0211240	+	0.0153475i
$215$	0.545085	−	0.396027i	0.0371745	−	0.0270088i
$216$	−0.690983	−	2.12663i	−0.0470154	−	0.144699i
$217$	−3.57295	+	10.9964i	−0.242548	+	0.746485i
$218$		0			0
$219$	1.23607			0.0835257
$220$	0.291796	+	0.726543i	0.0196729	+	0.0489835i
$221$	−3.85410			−0.259255
$222$	5.54508	+	4.02874i	0.372162	+	0.270391i
$223$	−3.92705	+	12.0862i	−0.262975	+	0.809353i	0.729178	+	0.684324i	$0.239903\pi$
$223$	−3.92705	+	12.0862i	−0.262975	+	0.809353i	−0.992153	+	0.125029i	$0.960097\pi$
$224$	−3.13525	−	9.64932i	−0.209483	−	0.644722i
$225$	3.92705	−	2.85317i	0.261803	−	0.190211i
$226$	16.6353	−	12.0862i	1.10656	−	0.803963i
$227$	3.36475	+	10.3556i	0.223326	+	0.687327i	0.998457	+	0.0555264i	$0.0176837\pi$
$227$	3.36475	+	10.3556i	0.223326	+	0.687327i	−0.775131	+	0.631800i	$0.782316\pi$
$228$	−0.163119	+	0.502029i	−0.0108028	+	0.0332477i
$229$	−8.09017	−	5.87785i	−0.534613	−	0.388419i	0.287467	−	0.957790i	$-0.407187\pi$
$229$	−8.09017	−	5.87785i	−0.534613	−	0.388419i	−0.822081	+	0.569371i	$0.807187\pi$
$230$	3.38197			0.223000
$231$	8.42705	+	5.29007i	0.554459	+	0.348061i
$232$	10.0000			0.656532
$233$	−7.01722	−	5.09831i	−0.459713	−	0.334001i	0.333705	−	0.942677i	$-0.391701\pi$
$233$	−7.01722	−	5.09831i	−0.459713	−	0.334001i	−0.793419	+	0.608676i	$0.791701\pi$
$234$	3.11803	−	9.59632i	0.203832	−	0.627331i
$235$	0.0729490	+	0.224514i	0.00475867	+	0.0146457i
$236$	2.66312	−	1.93487i	0.173354	−	0.125949i
$237$	−0.427051	+	0.310271i	−0.0277399	+	0.0201542i
$238$	−0.927051	−	2.85317i	−0.0600918	−	0.184944i
$239$	−5.42705	+	16.7027i	−0.351047	+	1.08041i	0.607220	+	0.794534i	$0.292285\pi$
$239$	−5.42705	+	16.7027i	−0.351047	+	1.08041i	−0.958266	+	0.285877i	$0.907715\pi$
$240$	−1.50000	−	1.08981i	−0.0968246	−	0.0703472i
$241$	17.1246			1.10309			0.551547	−	0.834144i	$-0.314038\pi$
$241$	17.1246			1.10309			0.551547	+	0.834144i	$0.314038\pi$
$242$	3.16312	−	17.5150i	0.203333	−	1.12591i
$243$	1.00000			0.0641500
$244$	−0.572949	−	0.416272i	−0.0366793	−	0.0266491i
$245$	−0.236068	+	0.726543i	−0.0150818	+	0.0464171i
$246$	2.97214	+	9.14729i	0.189496	+	0.583210i
$247$	4.30902	−	3.13068i	0.274176	−	0.199201i
$248$	−6.97214	+	5.06555i	−0.442731	+	0.321663i
$249$	−3.92705	−	12.0862i	−0.248867	−	0.765933i
$250$	1.88197	−	5.79210i	0.119026	−	0.366324i
$251$	−13.5902	−	9.87384i	−0.857804	−	0.623231i	0.0694827	−	0.997583i	$-0.477865\pi$
$251$	−13.5902	−	9.87384i	−0.857804	−	0.623231i	−0.927287	+	0.374352i	$0.877865\pi$
$252$	1.85410			0.116797
$253$	−15.3713	−	9.64932i	−0.966387	−	0.606648i
$254$	15.7082			0.985620
$255$	−0.190983	−	0.138757i	−0.0119598	−	0.00868932i
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$	−8.44427	−	25.9888i	−0.526739	−	1.62114i	−0.760851	−	0.648927i	$-0.775218\pi$
$257$	−8.44427	−	25.9888i	−0.526739	−	1.62114i	0.234112	−	0.972210i	$-0.424782\pi$
$258$	−2.30902	+	1.67760i	−0.143753	+	0.104443i
$259$	10.2812	−	7.46969i	0.638840	−	0.464144i
$260$	−0.454915	−	1.40008i	−0.0282126	−	0.0868296i
$261$	−1.38197	+	4.25325i	−0.0855415	+	0.263270i
$262$	18.1353	+	13.1760i	1.12040	+	0.814018i
$263$	−0.673762			−0.0415459			−0.0207730	−	0.999784i	$-0.506613\pi$
$263$	−0.673762			−0.0415459			−0.0207730	+	0.999784i	$0.506613\pi$
$264$	2.76393	+	6.88191i	0.170108	+	0.423552i
$265$	2.81966			0.173210
$266$	3.35410	+	2.43690i	0.205653	+	0.149416i
$267$	2.92705	−	9.00854i	0.179133	−	0.551313i
$268$	2.01722	+	6.20837i	0.123221	+	0.379236i
$269$	−19.7984	+	14.3844i	−1.20713	+	0.877030i	−0.994967	−	0.100205i	$-0.968050\pi$
$269$	−19.7984	+	14.3844i	−1.20713	+	0.877030i	−0.212161	+	0.977235i	$0.568050\pi$
$270$	0.500000	−	0.363271i	0.0304290	−	0.0221080i
$271$	1.93769	+	5.96361i	0.117707	+	0.362263i	0.992502	−	0.122229i	$-0.0390043\pi$
$271$	1.93769	+	5.96361i	0.117707	+	0.362263i	−0.874795	+	0.484493i	$0.839004\pi$
$272$	0.927051	−	2.85317i	0.0562107	−	0.172999i
$273$	−15.1353	−	10.9964i	−0.916027	−	0.665533i
$274$	−2.38197			−0.143900
$275$	−12.3541	+	10.3229i	−0.744980	+	0.622492i
$276$	−3.38197			−0.203570
$277$	−8.44427	−	6.13512i	−0.507367	−	0.368624i	0.304457	−	0.952526i	$-0.401525\pi$
$277$	−8.44427	−	6.13512i	−0.507367	−	0.368624i	−0.811824	+	0.583902i	$0.801525\pi$
$278$	2.92705	−	9.00854i	0.175553	−	0.540296i
$279$	−1.19098	−	3.66547i	−0.0713023	−	0.219446i
$280$	−2.07295	+	1.50609i	−0.123882	+	0.0900058i
$281$	4.23607	−	3.07768i	0.252703	−	0.183599i	−0.454221	−	0.890889i	$-0.650082\pi$
$281$	4.23607	−	3.07768i	0.252703	−	0.183599i	0.706924	+	0.707290i	$0.250082\pi$
$282$	−0.309017	−	0.951057i	−0.0184017	−	0.0566346i
$283$	−6.85410	+	21.0948i	−0.407434	+	1.25395i	0.511412	+	0.859336i	$0.329123\pi$
$283$	−6.85410	+	21.0948i	−0.407434	+	1.25395i	−0.918846	+	0.394617i	$0.870877\pi$
$284$	−7.28115	−	5.29007i	−0.432057	−	0.313908i
$285$	0.326238			0.0193247
$286$	−8.16312	+	32.4544i	−0.482695	+	1.91907i
$287$	17.8328			1.05264
$288$	2.73607	+	1.98787i	0.161224	+	0.117136i
$289$	−5.13525	+	15.8047i	−0.302074	+	0.929688i
$290$	0.854102	+	2.62866i	0.0501546	+	0.154360i
$291$	−12.1631	+	8.83702i	−0.713015	+	0.518035i
$292$	−0.618034	+	0.449028i	−0.0361677	+	0.0262774i
$293$	5.54508	+	17.0660i	0.323947	+	0.997007i	0.971914	+	0.235338i	$0.0756198\pi$
$293$	5.54508	+	17.0660i	0.323947	+	0.997007i	−0.647966	+	0.761669i	$0.724380\pi$
$294$	1.00000	−	3.07768i	0.0583212	−	0.179494i
$295$	−1.64590	−	1.19581i	−0.0958279	−	0.0696230i
$296$	9.47214			0.550557
$297$	−3.30902	+	0.224514i	−0.192009	+	0.0130276i
$298$	24.2705			1.40595
$299$	27.6074	+	20.0579i	1.59658	+	1.15998i
$300$	−0.927051	+	2.85317i	−0.0535233	+	0.164728i
$301$	1.63525	+	5.03280i	0.0942545	+	0.290086i
$302$	−2.61803	+	1.90211i	−0.150651	+	0.109454i
$303$	2.42705	−	1.76336i	0.139430	−	0.101302i
$304$	1.28115	+	3.94298i	0.0734792	+	0.226146i
$305$	−0.135255	+	0.416272i	−0.00774467	+	0.0238357i
$306$	0.809017	+	0.587785i	0.0462484	+	0.0336014i
$307$	−19.5623			−1.11648			−0.558240	−	0.829680i	$-0.688523\pi$
$307$	−19.5623			−1.11648			−0.558240	+	0.829680i	$0.688523\pi$
$308$	−6.13525	+	0.416272i	−0.349589	+	0.0237193i
$309$	−6.00000			−0.341328
$310$	−1.92705	−	1.40008i	−0.109449	−	0.0795195i
$311$	3.54508	−	10.9106i	0.201023	−	0.618686i	−0.798830	−	0.601557i	$-0.794547\pi$
$311$	3.54508	−	10.9106i	0.201023	−	0.618686i	0.999853	−	0.0171293i	$-0.00545269\pi$
$312$	−4.30902	−	13.2618i	−0.243950	−	0.750801i
$313$	22.5172	−	16.3597i	1.27275	−	0.924706i	0.273440	−	0.961889i	$-0.411838\pi$
$313$	22.5172	−	16.3597i	1.27275	−	0.924706i	0.999308	+	0.0371831i	$0.0118385\pi$
$314$	−12.7082	+	9.23305i	−0.717165	+	0.521051i
$315$	−0.354102	−	1.08981i	−0.0199514	−	0.0614041i
$316$	0.100813	−	0.310271i	0.00567118	−	0.0174541i
$317$	−20.5172	−	14.9066i	−1.15236	−	0.837240i	−0.163569	−	0.986532i	$-0.552301\pi$
$317$	−20.5172	−	14.9066i	−1.15236	−	0.837240i	−0.988793	+	0.149292i	$0.952301\pi$
$318$	−11.9443			−0.669802
$319$	3.61803	−	14.3844i	0.202571	−	0.805370i
$320$	−1.61803			−0.0904508
$321$	−0.190983	−	0.138757i	−0.0106596	−	0.00774468i
$322$	−8.20820	+	25.2623i	−0.457425	+	1.40781i
$323$	0.163119	+	0.502029i	0.00907618	+	0.0279336i
$324$	−0.500000	+	0.363271i	−0.0277778	+	0.0201817i
$325$	24.4894	−	17.7926i	1.35843	−	0.986954i
$326$	−7.63525	−	23.4989i	−0.422878	−	1.30148i
$327$		0			0
$328$	10.7533	+	7.81272i	0.593751	+	0.431385i
$329$	−1.85410			−0.102220
$330$	−1.57295	+	1.31433i	−0.0865880	+	0.0723514i
$331$	−22.5967			−1.24203			−0.621015	−	0.783799i	$-0.713279\pi$
$331$	−22.5967			−1.24203			−0.621015	+	0.783799i	$0.713279\pi$
$332$	6.35410	+	4.61653i	0.348727	+	0.253365i
$333$	−1.30902	+	4.02874i	−0.0717337	+	0.220774i
$334$	−9.51722	−	29.2910i	−0.520759	−	1.60273i
$335$	3.26393	−	2.37139i	0.178328	−	0.129563i
$336$	11.7812	−	8.55951i	0.642715	−	0.466959i
$337$	−4.23607	−	13.0373i	−0.230753	−	0.710186i	−0.997656	−	0.0684228i	$-0.978203\pi$
$337$	−4.23607	−	13.0373i	−0.230753	−	0.710186i	0.766903	−	0.641763i	$-0.221797\pi$
$338$	12.9443	−	39.8384i	0.704076	−	2.16692i
$339$	10.2812	+	7.46969i	0.558396	+	0.405698i
$340$	0.145898			0.00791243
$341$	4.76393	+	11.8617i	0.257981	+	0.642347i
$342$	−1.38197			−0.0747282
$343$	12.1353	+	8.81678i	0.655242	+	0.476061i
$344$	−1.21885	+	3.75123i	−0.0657158	+	0.202253i
$345$	0.645898	+	1.98787i	0.0347740	+	0.107023i
$346$	−23.0623	+	16.7557i	−1.23984	+	0.900794i
$347$	2.47214	−	1.79611i	0.132711	−	0.0964203i	−0.519449	−	0.854501i	$-0.673863\pi$
$347$	2.47214	−	1.79611i	0.132711	−	0.0964203i	0.652160	+	0.758081i	$0.273863\pi$
$348$	−0.854102	−	2.62866i	−0.0457847	−	0.140911i
$349$	9.30902	−	28.6502i	0.498300	−	1.53361i	−0.313449	−	0.949605i	$-0.601485\pi$
$349$	9.30902	−	28.6502i	0.498300	−	1.53361i	0.811750	−	0.584006i	$-0.198515\pi$
$350$	19.0623	+	13.8496i	1.01892	+	0.740291i
$351$	6.23607			0.332857
$352$	−9.50000	−	5.96361i	−0.506352	−	0.317861i
$353$	−1.52786			−0.0813200			−0.0406600	−	0.999173i	$-0.512946\pi$
$353$	−1.52786			−0.0813200			−0.0406600	+	0.999173i	$0.512946\pi$
$354$	6.97214	+	5.06555i	0.370565	+	0.269231i
$355$	−1.71885	+	5.29007i	−0.0912269	+	0.280768i
$356$	1.80902	+	5.56758i	0.0958777	+	0.295081i
$357$	1.50000	−	1.08981i	0.0793884	−	0.0576791i
$358$	−2.92705	+	2.12663i	−0.154699	+	0.112396i
$359$	−5.32624	−	16.3925i	−0.281108	−	0.865162i	−0.987538	−	0.157379i	$-0.949696\pi$
$359$	−5.32624	−	16.3925i	−0.281108	−	0.865162i	0.706430	−	0.707783i	$-0.250304\pi$
$360$	0.263932	−	0.812299i	0.0139104	−	0.0428119i
$361$	14.7812	+	10.7391i	0.777955	+	0.565218i
$362$	−13.7984			−0.725226
$363$	10.8992	−	1.48584i	0.572059	−	0.0779864i
$364$	11.5623			0.606029
$365$	0.381966	+	0.277515i	0.0199930	+	0.0145258i
$366$	0.572949	−	1.76336i	0.0299485	−	0.0921721i
$367$	−4.50000	−	13.8496i	−0.234898	−	0.722942i	−0.997135	−	0.0756437i	$-0.975899\pi$
$367$	−4.50000	−	13.8496i	−0.234898	−	0.722942i	0.762237	−	0.647298i	$-0.224101\pi$
$368$	−21.4894	+	15.6129i	−1.12021	+	0.813880i
$369$	−4.80902	+	3.49396i	−0.250347	+	0.181888i
$370$	0.809017	+	2.48990i	0.0420588	+	0.129444i
$371$	−6.84346	+	21.0620i	−0.355295	+	1.09348i
$372$	1.92705	+	1.40008i	0.0999129	+	0.0725910i
$373$	22.4164			1.16068			0.580339	−	0.814375i	$-0.302920\pi$
$373$	22.4164			1.16068			0.580339	+	0.814375i	$0.302920\pi$
$374$	−2.80902	−	1.76336i	−0.145251	−	0.0911810i
$375$	3.76393			0.194369
$376$	−1.11803	−	0.812299i	−0.0576582	−	0.0418911i
$377$	−8.61803	+	26.5236i	−0.443851	+	1.36603i
$378$	1.50000	+	4.61653i	0.0771517	+	0.237448i
$379$	−22.9894	+	16.7027i	−1.18088	+	0.857962i	−0.992271	−	0.124089i	$-0.960399\pi$
$379$	−22.9894	+	16.7027i	−1.18088	+	0.857962i	−0.188613	+	0.982052i	$0.560399\pi$
$380$	−0.163119	+	0.118513i	−0.00836783	+	0.00607958i
$381$	3.00000	+	9.23305i	0.153695	+	0.473024i
$382$	0.736068	−	2.26538i	0.0376605	−	0.115907i
$383$	7.19098	+	5.22455i	0.367442	+	0.266962i	0.756149	−	0.654399i	$-0.227078\pi$
$383$	7.19098	+	5.22455i	0.367442	+	0.266962i	−0.388707	+	0.921361i	$0.627078\pi$
$384$	13.6180			0.694942
$385$	1.41641	+	3.52671i	0.0721868	+	0.179738i
$386$	2.52786			0.128665
$387$	−1.42705	−	1.03681i	−0.0725411	−	0.0527042i
$388$	2.87132	−	8.83702i	0.145769	−	0.448632i
$389$	−2.86475	−	8.81678i	−0.145248	−	0.447028i	0.851795	−	0.523876i	$-0.175515\pi$
$389$	−2.86475	−	8.81678i	−0.145248	−	0.447028i	−0.997043	+	0.0768476i	$0.975515\pi$
$390$	3.11803	−	2.26538i	0.157888	−	0.114712i
$391$	−2.73607	+	1.98787i	−0.138369	+	0.100531i
$392$	−1.38197	−	4.25325i	−0.0697998	−	0.214822i
$393$	−4.28115	+	13.1760i	−0.215956	+	0.664643i
$394$	−34.8435	−	25.3153i	−1.75539	−	1.27536i
$395$	−0.201626			−0.0101449
$396$	1.57295	−	1.31433i	0.0790437	−	0.0660475i
$397$	−25.2918			−1.26936			−0.634679	−	0.772776i	$-0.718868\pi$
$397$	−25.2918			−1.26936			−0.634679	+	0.772776i	$0.718868\pi$
$398$	4.30902	+	3.13068i	0.215992	+	0.156927i
$399$	−0.791796	+	2.43690i	−0.0396394	+	0.121997i
$400$	7.28115	+	22.4091i	0.364058	+	1.12045i
$401$	12.0623	−	8.76378i	0.602363	−	0.437642i	−0.244354	−	0.969686i	$-0.578576\pi$
$401$	12.0623	−	8.76378i	0.602363	−	0.437642i	0.846717	+	0.532044i	$0.178576\pi$
$402$	−13.8262	+	10.0453i	−0.689590	+	0.501017i
$403$	−7.42705	−	22.8581i	−0.369968	−	1.13864i
$404$	−0.572949	+	1.76336i	−0.0285053	+	0.0877302i
$405$	0.309017	+	0.224514i	0.0153552	+	0.0111562i
$406$	−21.7082			−1.07736
$407$	3.42705	−	13.6251i	0.169873	−	0.675369i
$408$	1.38197			0.0684175
$409$	23.4164	+	17.0130i	1.15787	+	0.841240i	0.989507	−	0.144486i	$-0.0461529\pi$
$409$	23.4164	+	17.0130i	1.15787	+	0.841240i	0.168360	+	0.985726i	$0.446153\pi$
$410$	−1.13525	+	3.49396i	−0.0560662	+	0.172554i
$411$	−0.454915	−	1.40008i	−0.0224393	−	0.0690611i
$412$	3.00000	−	2.17963i	0.147799	−	0.107383i
$413$	12.9271	−	9.39205i	0.636099	−	0.462153i
$414$	−2.73607	−	8.42075i	−0.134470	−	0.413857i
$415$	1.50000	−	4.61653i	0.0736321	−	0.226616i
$416$	17.0623	+	12.3965i	0.836548	+	0.607788i
$417$	5.85410			0.286677
$418$	4.57295	−	0.310271i	0.223670	−	0.0151758i
$419$	−21.5066			−1.05067			−0.525333	−	0.850897i	$-0.676059\pi$
$419$	−21.5066			−1.05067			−0.525333	+	0.850897i	$0.676059\pi$
$420$	0.572949	+	0.416272i	0.0279570	+	0.0203120i
$421$	−1.15248	+	3.54696i	−0.0561682	+	0.172868i	−0.975205	−	0.221304i	$-0.928969\pi$
$421$	−1.15248	+	3.54696i	−0.0561682	+	0.172868i	0.919037	+	0.394172i	$0.128969\pi$
$422$	5.63525	+	17.3435i	0.274320	+	0.844270i
$423$	0.500000	−	0.363271i	0.0243108	−	0.0176629i
$424$	−13.3541	+	9.70232i	−0.648533	+	0.471186i
$425$	0.927051	+	2.85317i	0.0449686	+	0.138399i
$426$	7.28115	−	22.4091i	0.352773	−	1.08572i
$427$	−2.78115	−	2.02063i	−0.134589	−	0.0977849i
$428$	0.145898			0.00705225
$429$	−20.6353	+	1.40008i	−0.996279	+	0.0675967i
$430$	−1.09017			−0.0525727
$431$	1.20820	+	0.877812i	0.0581971	+	0.0422827i	0.616503	−	0.787352i	$-0.288549\pi$
$431$	1.20820	+	0.877812i	0.0581971	+	0.0422827i	−0.558306	+	0.829635i	$0.688549\pi$
$432$	−1.50000	+	4.61653i	−0.0721688	+	0.222113i
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	0.896569	−	0.442903i	$-0.146051\pi$
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	−0.985672	+	0.168674i	$0.946051\pi$
$434$	15.1353	−	10.9964i	0.726515	−	0.527844i
$435$	−1.38197	+	1.00406i	−0.0662602	+	0.0481409i
$436$		0			0
$437$	1.44427	−	4.44501i	0.0690889	−	0.212634i
$438$	−1.61803	−	1.17557i	−0.0773127	−	0.0561709i
$439$	16.7082			0.797439			0.398720	−	0.917073i	$-0.369455\pi$
$439$	16.7082			0.797439			0.398720	+	0.917073i	$0.369455\pi$
$440$	−0.690983	+	2.74717i	−0.0329413	+	0.130966i
$441$	2.00000			0.0952381
$442$	5.04508	+	3.66547i	0.239970	+	0.174349i
$443$	−0.270510	+	0.832544i	−0.0128523	+	0.0395553i	−0.957277	−	0.289172i	$-0.906620\pi$
$443$	−0.270510	+	0.832544i	−0.0128523	+	0.0395553i	0.944425	+	0.328728i	$0.106620\pi$
$444$	−0.809017	−	2.48990i	−0.0383942	−	0.118165i
$445$	2.92705	−	2.12663i	0.138756	−	0.100812i
$446$	16.6353	−	12.0862i	0.787702	−	0.572299i
$447$	4.63525	+	14.2658i	0.219240	+	0.674751i
$448$	3.92705	−	12.0862i	0.185536	−	0.571020i
$449$	12.5623	+	9.12705i	0.592852	+	0.430732i	0.843334	−	0.537389i	$-0.180589\pi$
$449$	12.5623	+	9.12705i	0.592852	+	0.430732i	−0.250483	+	0.968121i	$0.580589\pi$
$450$	−7.85410			−0.370246
$451$	15.1287	−	12.6412i	0.712382	−	0.595253i
$452$	−7.85410			−0.369426
$453$	−1.61803	−	1.17557i	−0.0760219	−	0.0552331i
$454$	5.44427	−	16.7557i	0.255512	−	0.786386i
$455$	−2.20820	−	6.79615i	−0.103522	−	0.318609i
$456$	−1.54508	+	1.12257i	−0.0723552	+	0.0525692i
$457$	−26.5344	+	19.2784i	−1.24123	+	0.901806i	−0.997680	−	0.0680830i	$-0.978312\pi$
$457$	−26.5344	+	19.2784i	−1.24123	+	0.901806i	−0.243549	+	0.969889i	$0.578312\pi$
$458$	5.00000	+	15.3884i	0.233635	+	0.719054i
$459$	−0.190983	+	0.587785i	−0.00891432	+	0.0274355i
$460$	−1.04508	−	0.759299i	−0.0487273	−	0.0354025i
$461$	−9.90983			−0.461547			−0.230773	−	0.973008i	$-0.574126\pi$
$461$	−9.90983			−0.461547			−0.230773	+	0.973008i	$0.574126\pi$
$462$	−6.00000	−	14.9394i	−0.279145	−	0.695043i
$463$	8.79837			0.408895			0.204448	−	0.978878i	$-0.434460\pi$
$463$	8.79837			0.408895			0.204448	+	0.978878i	$0.434460\pi$
$464$	−17.5623	−	12.7598i	−0.815310	−	0.592357i
$465$	0.454915	−	1.40008i	0.0210962	−	0.0649274i
$466$	4.33688	+	13.3475i	0.200902	+	0.618313i
$467$	11.5172	−	8.36775i	0.532953	−	0.387213i	−0.288508	−	0.957478i	$-0.593159\pi$
$467$	11.5172	−	8.36775i	0.532953	−	0.387213i	0.821461	+	0.570264i	$0.193159\pi$
$468$	−3.11803	+	2.26538i	−0.144131	+	0.104717i
$469$	9.79180	+	30.1360i	0.452143	+	1.39155i
$470$	0.118034	−	0.363271i	0.00544450	−	0.0167565i
$471$	−7.85410	−	5.70634i	−0.361898	−	0.262934i
$472$	11.9098			0.548194
$473$	4.95492	+	3.11044i	0.227827	+	0.143018i
$474$	0.854102			0.0392302
$475$	−3.35410	−	2.43690i	−0.153897	−	0.111813i
$476$	−0.354102	+	1.08981i	−0.0162302	+	0.0499515i
$477$	−2.28115	−	7.02067i	−0.104447	−	0.321454i
$478$	22.9894	−	16.7027i	1.05151	−	0.763966i
$479$	13.6803	−	9.93935i	0.625071	−	0.454140i	−0.229618	−	0.973281i	$-0.573748\pi$
$479$	13.6803	−	9.93935i	0.625071	−	0.454140i	0.854689	+	0.519140i	$0.173748\pi$
$480$	0.399187	+	1.22857i	0.0182203	+	0.0560763i
$481$	−8.16312	+	25.1235i	−0.372206	+	1.14553i
$482$	−22.4164	−	16.2865i	−1.02104	−	0.741829i
$483$	−16.4164			−0.746972
$484$	−4.90983	+	4.70228i	−0.223174	+	0.213740i
$485$	−5.74265			−0.260760
$486$	−1.30902	−	0.951057i	−0.0593782	−	0.0431408i
$487$	12.1074	−	37.2627i	0.548638	−	1.68853i	−0.163540	−	0.986537i	$-0.552291\pi$
$487$	12.1074	−	37.2627i	0.548638	−	1.68853i	0.712179	−	0.701998i	$-0.247709\pi$
$488$	−0.791796	−	2.43690i	−0.0358429	−	0.110313i
$489$	12.3541	−	8.97578i	0.558672	−	0.405899i
$490$	1.00000	−	0.726543i	0.0451754	−	0.0328218i
$491$	−8.10081	−	24.9317i	−0.365585	−	1.12515i	−0.949614	−	0.313421i	$-0.898525\pi$
$491$	−8.10081	−	24.9317i	−0.365585	−	1.12515i	0.584030	−	0.811732i	$-0.301475\pi$
$492$	1.13525	−	3.49396i	0.0511812	−	0.157520i
$493$	−2.23607	−	1.62460i	−0.100707	−	0.0731682i
$494$	−8.61803			−0.387744
$495$	−1.07295	−	0.673542i	−0.0482255	−	0.0302735i
$496$	18.7082			0.840023
$497$	−35.3435	−	25.6785i	−1.58537	−	1.15184i
$498$	−6.35410	+	19.5559i	−0.284734	+	0.876322i
$499$	0.791796	+	2.43690i	0.0354457	+	0.109091i	0.967214	−	0.253963i	$-0.0817342\pi$
$499$	0.791796	+	2.43690i	0.0354457	+	0.109091i	−0.931768	+	0.363054i	$0.881734\pi$
$500$	−1.88197	+	1.36733i	−0.0841641	+	0.0611488i
$501$	15.3992	−	11.1882i	0.687985	−	0.499850i
$502$	8.39919	+	25.8500i	0.374874	+	1.15374i
$503$	−9.29180	+	28.5972i	−0.414301	+	1.27509i	0.498574	+	0.866847i	$0.333857\pi$
$503$	−9.29180	+	28.5972i	−0.414301	+	1.27509i	−0.912875	+	0.408239i	$0.866143\pi$
$504$	5.42705	+	3.94298i	0.241740	+	0.175634i
$505$	1.14590			0.0509918
$506$	10.9443	+	27.2501i	0.486532	+	1.21142i
$507$	25.8885			1.14975
$508$	−4.85410	−	3.52671i	−0.215366	−	0.156473i
$509$	6.60739	−	20.3355i	0.292867	−	0.901353i	−0.691062	−	0.722796i	$-0.742857\pi$
$509$	6.60739	−	20.3355i	0.292867	−	0.901353i	0.983929	−	0.178558i	$-0.0571432\pi$
$510$	0.118034	+	0.363271i	0.00522663	+	0.0160859i
$511$	−3.00000	+	2.17963i	−0.132712	+	0.0964210i
$512$	4.28115	−	3.11044i	0.189202	−	0.137463i
$513$	−0.263932	−	0.812299i	−0.0116529	−	0.0358639i
$514$	−13.6631	+	42.0508i	−0.602654	+	1.85478i
$515$	−1.85410	−	1.34708i	−0.0817015	−	0.0593596i
$516$	1.09017			0.0479921
$517$	−1.57295	+	1.31433i	−0.0691782	+	0.0578041i
$518$	−20.5623			−0.903456
$519$	−14.2533	−	10.3556i	−0.625650	−	0.454561i
$520$	1.64590	−	5.06555i	0.0721774	−	0.222139i
$521$	12.0000	+	36.9322i	0.525730	+	1.61803i	0.762869	+	0.646553i	$0.223790\pi$
$521$	12.0000	+	36.9322i	0.525730	+	1.61803i	−0.237139	+	0.971476i	$0.576210\pi$
$522$	5.85410	−	4.25325i	0.256227	−	0.186160i
$523$	−28.2984	+	20.5600i	−1.23740	+	0.899025i	−0.997422	−	0.0717533i	$-0.977141\pi$
$523$	−28.2984	+	20.5600i	−1.23740	+	0.899025i	−0.239979	+	0.970778i	$0.577141\pi$
$524$	−2.64590	−	8.14324i	−0.115587	−	0.355739i
$525$	−4.50000	+	13.8496i	−0.196396	+	0.604445i
$526$	0.881966	+	0.640786i	0.0384555	+	0.0279396i
$527$	2.38197			0.103760
$528$	3.92705	−	15.6129i	0.170903	−	0.679466i
$529$	6.94427			0.301925
$530$	−3.69098	−	2.68166i	−0.160326	−	0.116484i
$531$	−1.64590	+	5.06555i	−0.0714259	+	0.219826i
$532$	−0.489357	−	1.50609i	−0.0212163	−	0.0652971i
$533$	−29.9894	+	21.7885i	−1.29898	+	0.943767i
$534$	−12.3992	+	9.00854i	−0.536565	+	0.389838i
$535$	−0.0278640	−	0.0857567i	−0.00120467	−	0.00370759i
$536$	−7.29837	+	22.4621i	−0.315242	+	0.970214i
$537$	−1.80902	−	1.31433i	−0.0780648	−	0.0567174i
$538$	39.5967			1.70714
$539$	−6.61803	+	0.449028i	−0.285059	+	0.0193410i
$540$	−0.236068			−0.0101587
$541$	0.454915	+	0.330515i	0.0195583	+	0.0142100i	0.597521	−	0.801853i	$-0.296152\pi$
$541$	0.454915	+	0.330515i	0.0195583	+	0.0142100i	−0.577963	+	0.816063i	$0.696152\pi$
$542$	3.13525	−	9.64932i	0.134671	−	0.414474i
$543$	−2.63525	−	8.11048i	−0.113090	−	0.348054i
$544$	−1.69098	+	1.22857i	−0.0725003	+	0.0526745i
$545$		0			0
$546$	9.35410	+	28.7890i	0.400319	+	1.23205i
$547$	5.98936	−	18.4333i	0.256086	−	0.788153i	−0.737527	−	0.675317i	$-0.764007\pi$
$547$	5.98936	−	18.4333i	0.256086	−	0.788153i	0.993614	−	0.112836i	$-0.0359933\pi$
$548$	0.736068	+	0.534785i	0.0314433	+	0.0228449i
$549$	1.14590			0.0489057
$550$	25.9894	−	1.76336i	1.10819	−	0.0751897i
$551$	3.81966			0.162723
$552$	−9.89919	−	7.19218i	−0.421337	−	0.306120i
$553$	0.489357	−	1.50609i	0.0208096	−	0.0640453i
$554$	5.21885	+	16.0620i	0.221728	+	0.682407i
$555$	−1.30902	+	0.951057i	−0.0555647	+	0.0403701i
$556$	−2.92705	+	2.12663i	−0.124135	+	0.0901891i
$557$	8.06231	+	24.8132i	0.341611	+	1.05137i	0.963373	+	0.268164i	$0.0864170\pi$
$557$	8.06231	+	24.8132i	0.341611	+	1.05137i	−0.621762	+	0.783206i	$0.713583\pi$
$558$	−1.92705	+	5.93085i	−0.0815786	+	0.251073i
$559$	−8.89919	−	6.46564i	−0.376396	−	0.273467i
$560$	5.56231			0.235050
$561$	0.500000	−	1.98787i	0.0211100	−	0.0839279i
$562$	−8.47214			−0.357375
$563$	−21.7533	−	15.8047i	−0.916792	−	0.666088i	0.0259316	−	0.999664i	$-0.491745\pi$
$563$	−21.7533	−	15.8047i	−0.916792	−	0.666088i	−0.942723	+	0.333575i	$0.891745\pi$
$564$	−0.118034	+	0.363271i	−0.00497013	+	0.0152965i
$565$	1.50000	+	4.61653i	0.0631055	+	0.194219i
$566$	29.0344	−	21.0948i	1.22041	−	0.886679i
$567$	−2.42705	+	1.76336i	−0.101927	+	0.0740540i
$568$	−10.0623	−	30.9686i	−0.422205	−	1.29941i
$569$	10.5279	−	32.4014i	0.441351	−	1.35834i	−0.445085	−	0.895488i	$-0.646827\pi$
$569$	10.5279	−	32.4014i	0.441351	−	1.35834i	0.886436	−	0.462851i	$-0.153173\pi$
$570$	−0.427051	−	0.310271i	−0.0178872	−	0.0129958i
$571$	−25.6869			−1.07496			−0.537482	−	0.843275i	$-0.680624\pi$
$571$	−25.6869			−1.07496			−0.537482	+	0.843275i	$0.680624\pi$
$572$	9.80902	−	8.19624i	0.410136	−	0.342702i
$573$	1.47214			0.0614994
$574$	−23.3435	−	16.9600i	−0.974337	−	0.707897i
$575$	8.20820	−	25.2623i	0.342306	−	1.05351i
$576$	1.30902	+	4.02874i	0.0545424	+	0.167864i
$577$	−12.3262	+	8.95554i	−0.513148	+	0.372824i	−0.814016	−	0.580842i	$-0.802723\pi$
$577$	−12.3262	+	8.95554i	−0.513148	+	0.372824i	0.300868	+	0.953666i	$0.402723\pi$
$578$	21.7533	−	15.8047i	0.904818	−	0.657388i
$579$	0.482779	+	1.48584i	0.0200636	+	0.0617495i
$580$	0.326238	−	1.00406i	0.0135463	−	0.0416912i
$581$	30.8435	+	22.4091i	1.27960	+	0.929685i
$582$	24.3262			1.00836
$583$	9.12461	+	22.7194i	0.377903	+	0.940940i
$584$	−2.76393			−0.114372
$585$	1.92705	+	1.40008i	0.0796738	+	0.0578864i
$586$	8.97214	−	27.6134i	0.370636	−	1.14070i
$587$	7.51064	+	23.1154i	0.309997	+	0.954074i	0.977765	+	0.209704i	$0.0672500\pi$
$587$	7.51064	+	23.1154i	0.309997	+	0.954074i	−0.667767	+	0.744370i	$0.732750\pi$
$588$	−1.00000	+	0.726543i	−0.0412393	+	0.0299621i
$589$	−2.66312	+	1.93487i	−0.109732	+	0.0797249i
$590$	1.01722	+	3.13068i	0.0418783	+	0.128888i
$591$	8.22542	−	25.3153i	0.338349	−	1.04133i
$592$	−16.6353	−	12.0862i	−0.683705	−	0.496741i
$593$	−29.2148			−1.19971			−0.599854	−	0.800110i	$-0.704775\pi$
$593$	−29.2148			−1.19971			−0.599854	+	0.800110i	$0.704775\pi$
$594$	4.54508	+	2.85317i	0.186487	+	0.117067i
$595$	0.708204			0.0290335
$596$	−7.50000	−	5.44907i	−0.307212	−	0.223203i
$597$	−1.01722	+	3.13068i	−0.0416321	+	0.128130i
$598$	−17.0623	−	52.5124i	−0.697730	−	2.14739i
$599$	17.5623	−	12.7598i	0.717576	−	0.521350i	−0.168033	−	0.985781i	$-0.553741\pi$
$599$	17.5623	−	12.7598i	0.717576	−	0.521350i	0.885609	+	0.464432i	$0.153741\pi$
$600$	−8.78115	+	6.37988i	−0.358489	+	0.260458i
$601$	−6.12868	−	18.8621i	−0.249994	−	0.769402i	−0.994775	−	0.102093i	$-0.967446\pi$
$601$	−6.12868	−	18.8621i	−0.249994	−	0.769402i	0.744781	−	0.667309i	$-0.232554\pi$
$602$	2.64590	−	8.14324i	0.107839	−	0.331894i
$603$	−8.54508	−	6.20837i	−0.347983	−	0.252824i
$604$	1.23607			0.0502949
$605$	3.70163	+	1.98787i	0.150493	+	0.0808184i
$606$	−4.85410			−0.197184
$607$	1.88197	+	1.36733i	0.0763866	+	0.0554981i	0.625323	−	0.780366i	$-0.284967\pi$
$607$	1.88197	+	1.36733i	0.0763866	+	0.0554981i	−0.548937	+	0.835864i	$0.684967\pi$
$608$	0.892609	−	2.74717i	0.0362001	−	0.111412i
$609$	−4.14590	−	12.7598i	−0.168000	−	0.517052i
$610$	0.572949	−	0.416272i	0.0231980	−	0.0168544i
$611$	3.11803	−	2.26538i	0.126142	−	0.0916476i
$612$	−0.118034	−	0.363271i	−0.00477124	−	0.0146844i
$613$	1.03444	−	3.18368i	0.0417807	−	0.128588i	−0.927990	−	0.372604i	$-0.878465\pi$
$613$	1.03444	−	3.18368i	0.0417807	−	0.128588i	0.969771	+	0.244016i	$0.0784650\pi$
$614$	25.6074	+	18.6049i	1.03343	+	0.750831i
$615$	−2.27051			−0.0915558
$616$	−18.8435	−	11.8290i	−0.759225	−	0.476602i
$617$	46.4164			1.86865			0.934327	−	0.356417i	$-0.116002\pi$
$617$	46.4164			1.86865			0.934327	+	0.356417i	$0.116002\pi$
$618$	7.85410	+	5.70634i	0.315938	+	0.229543i
$619$	−9.63525	+	29.6543i	−0.387274	+	1.19191i	0.547544	+	0.836777i	$0.315563\pi$
$619$	−9.63525	+	29.6543i	−0.387274	+	1.19191i	−0.934817	+	0.355129i	$0.884437\pi$
$620$	0.281153	+	0.865300i	0.0112914	+	0.0347513i
$621$	4.42705	−	3.21644i	0.177651	−	0.129071i
$622$	−15.0172	+	10.9106i	−0.602136	+	0.437477i
$623$	8.78115	+	27.0256i	0.351809	+	1.08276i
$624$	−9.35410	+	28.7890i	−0.374464	+	1.15248i
$625$	−18.4721	−	13.4208i	−0.738885	−	0.536832i
$626$	−45.0344			−1.79994
$627$	1.05573	+	2.62866i	0.0421617	+	0.104978i
$628$	6.00000			0.239426
$629$	−2.11803	−	1.53884i	−0.0844515	−	0.0613576i
$630$	−0.572949	+	1.76336i	−0.0228268	+	0.0702538i
$631$	3.93363	+	12.1065i	0.156595	+	0.481951i	0.998319	−	0.0579577i	$-0.0184589\pi$
$631$	3.93363	+	12.1065i	0.156595	+	0.481951i	−0.841724	+	0.539908i	$0.818459\pi$
$632$	0.954915	−	0.693786i	0.0379845	−	0.0275973i
$633$	−9.11803	+	6.62464i	−0.362409	+	0.263306i
$634$	12.6803	+	39.0261i	0.503601	+	1.54992i
$635$	−1.14590	+	3.52671i	−0.0454736	+	0.139953i
$636$	3.69098	+	2.68166i	0.146357	+	0.106335i
$637$	12.4721			0.494164
$638$	−18.4164	+	15.3884i	−0.729113	+	0.609233i
$639$	14.5623			0.576076
$640$	4.20820	+	3.05744i	0.166344	+	0.120856i
$641$	−2.08359	+	6.41264i	−0.0822969	+	0.253284i	−0.983736	−	0.179623i	$-0.942512\pi$
$641$	−2.08359	+	6.41264i	−0.0822969	+	0.253284i	0.901439	+	0.432907i	$0.142512\pi$
$642$	0.118034	+	0.363271i	0.00465843	+	0.0143372i
$643$	14.9164	−	10.8374i	0.588246	−	0.427386i	−0.253442	−	0.967351i	$-0.581563\pi$
$643$	14.9164	−	10.8374i	0.588246	−	0.427386i	0.841687	+	0.539965i	$0.181563\pi$
$644$	8.20820	−	5.96361i	0.323449	−	0.234999i
$645$	−0.208204	−	0.640786i	−0.00819802	−	0.0252309i
$646$	0.263932	−	0.812299i	0.0103843	−	0.0319595i
$647$	−2.59017	−	1.88187i	−0.101830	−	0.0739839i	0.535705	−	0.844405i	$-0.320046\pi$
$647$	−2.59017	−	1.88187i	−0.101830	−	0.0739839i	−0.637535	+	0.770421i	$0.720046\pi$
$648$	−2.23607			−0.0878410
$649$	4.30902	−	17.1315i	0.169144	−	0.672471i
$650$	−48.9787			−1.92110
$651$	9.35410	+	6.79615i	0.366616	+	0.266362i
$652$	−2.91641	+	8.97578i	−0.114215	+	0.351519i
$653$	6.78773	+	20.8905i	0.265624	+	0.817508i	0.991549	+	0.129734i	$0.0414122\pi$
$653$	6.78773	+	20.8905i	0.265624	+	0.817508i	−0.725924	+	0.687774i	$0.758588\pi$
$654$		0			0
$655$	−4.28115	+	3.11044i	−0.167278	+	0.121535i
$656$	−8.91641	−	27.4419i	−0.348127	−	1.07143i
$657$	0.381966	−	1.17557i	0.0149019	−	0.0458634i
$658$	2.42705	+	1.76336i	0.0946163	+	0.0687428i
$659$	20.6525			0.804506			0.402253	−	0.915528i	$-0.368227\pi$
$659$	20.6525			0.804506			0.402253	+	0.915528i	$0.368227\pi$
$660$	0.781153	−	0.0530006i	0.0304063	−	0.00206304i
$661$	−21.0902			−0.820313			−0.410156	−	0.912015i	$-0.634526\pi$
$661$	−21.0902			−0.820313			−0.410156	+	0.912015i	$0.634526\pi$
$662$	29.5795	+	21.4908i	1.14964	+	0.835263i
$663$	−1.19098	+	3.66547i	−0.0462539	+	0.142355i
$664$	8.78115	+	27.0256i	0.340775	+	1.04880i
$665$	−0.791796	+	0.575274i	−0.0307045	+	0.0223082i
$666$	5.54508	−	4.02874i	0.214868	−	0.156111i
$667$	7.56231	+	23.2744i	0.292814	+	0.901188i
$668$	−3.63525	+	11.1882i	−0.140652	+	0.432883i
$669$	10.2812	+	7.46969i	0.397492	+	0.288795i
$670$	−6.52786			−0.252193
$671$	−3.79180	+	0.257270i	−0.146381	+	0.00993180i
$672$	−10.1459			−0.391387
$673$	11.6631	+	8.47375i	0.449580	+	0.326639i	0.789430	−	0.613841i	$-0.210376\pi$
$673$	11.6631	+	8.47375i	0.449580	+	0.326639i	−0.339850	+	0.940480i	$0.610376\pi$
$674$	−6.85410	+	21.0948i	−0.264010	+	0.812540i
$675$	−1.50000	−	4.61653i	−0.0577350	−	0.177690i
$676$	−12.9443	+	9.40456i	−0.497857	+	0.361714i
$677$	−18.1803	+	13.2088i	−0.698727	+	0.507655i	−0.879517	−	0.475867i	$-0.842134\pi$
$677$	−18.1803	+	13.2088i	−0.698727	+	0.507655i	0.180790	+	0.983522i	$0.442134\pi$
$678$	−6.35410	−	19.5559i	−0.244028	−	0.751040i
$679$	13.9377	−	42.8958i	0.534880	−	1.64619i
$680$	0.427051	+	0.310271i	0.0163767	+	0.0118983i
$681$	10.8885			0.417250
$682$	5.04508	−	20.0579i	0.193186	−	0.768058i
$683$	−38.8885			−1.48803			−0.744014	−	0.668164i	$-0.767081\pi$
$683$	−38.8885			−1.48803			−0.744014	+	0.668164i	$0.767081\pi$
$684$	0.427051	+	0.310271i	0.0163287	+	0.0118635i
$685$	0.173762	−	0.534785i	0.00663911	−	0.0204331i
$686$	−7.50000	−	23.0826i	−0.286351	−	0.881299i
$687$	−8.09017	+	5.87785i	−0.308659	+	0.224254i
$688$	6.92705	−	5.03280i	0.264091	−	0.191874i
$689$	−14.2254	−	43.7814i	−0.541946	−	1.66794i
$690$	1.04508	−	3.21644i	0.0397857	−	0.122448i
$691$	32.1246	+	23.3399i	1.22208	+	0.887892i	0.996271	−	0.0862806i	$-0.0274981\pi$
$691$	32.1246	+	23.3399i	1.22208	+	0.887892i	0.225807	+	0.974172i	$0.427498\pi$
$692$	10.8885			0.413920
$693$	7.63525	−	6.37988i	0.290039	−	0.242352i
$694$	−4.94427			−0.187682
$695$	1.80902	+	1.31433i	0.0686199	+	0.0498553i
$696$	3.09017	−	9.51057i	0.117133	−	0.360497i
$697$	−1.13525	−	3.49396i	−0.0430008	−	0.132343i
$698$	−39.4336	+	28.6502i	−1.49258	+	1.08443i
$699$	−7.01722	+	5.09831i	−0.265416	+	0.192836i
$700$	−2.78115	−	8.55951i	−0.105118	−	0.323519i
$701$	15.3541	−	47.2551i	0.579916	−	1.78480i	−0.0388752	−	0.999244i	$-0.512377\pi$
$701$	15.3541	−	47.2551i	0.579916	−	1.78480i	0.618792	−	0.785555i	$-0.287623\pi$
$702$	−8.16312	−	5.93085i	−0.308097	−	0.223846i
$703$	3.61803			0.136457
$704$	−5.23607	−	13.0373i	−0.197342	−	0.491361i
$705$	0.236068			0.00889083
$706$	2.00000	+	1.45309i	0.0752710	+	0.0546876i
$707$	−2.78115	+	8.55951i	−0.104596	+	0.321913i
$708$	−1.01722	−	3.13068i	−0.0382295	−	0.117658i
$709$	−5.06231	+	3.67798i	−0.190119	+	0.138129i	−0.678773	−	0.734348i	$-0.737488\pi$
$709$	−5.06231	+	3.67798i	−0.190119	+	0.138129i	0.488654	+	0.872478i	$0.337488\pi$
$710$	7.28115	−	5.29007i	0.273257	−	0.198533i
$711$	0.163119	+	0.502029i	0.00611744	+	0.0188275i
$712$	−6.54508	+	20.1437i	−0.245287	+	0.754917i
$713$	−17.0623	−	12.3965i	−0.638988	−	0.464252i
$714$	−3.00000			−0.112272
$715$	−6.69098	−	4.20025i	−0.250229	−	0.157081i
$716$	1.38197			0.0516465
$717$	14.2082	+	10.3229i	0.530615	+	0.385514i
$718$	−8.61803	+	26.5236i	−0.321622	+	0.989851i
$719$	−8.78115	−	27.0256i	−0.327482	−	1.00789i	−0.970308	−	0.241873i	$-0.922238\pi$
$719$	−8.78115	−	27.0256i	−0.327482	−	1.00789i	0.642826	−	0.766012i	$-0.277762\pi$
$720$	−1.50000	+	1.08981i	−0.0559017	+	0.0406150i
$721$	14.5623	−	10.5801i	0.542329	−	0.394025i
$722$	−9.13525	−	28.1154i	−0.339979	−	1.04635i
$723$	5.29180	−	16.2865i	0.196804	−	0.605700i
$724$	4.26393	+	3.09793i	0.158468	+	0.115134i
$725$	21.7082			0.806222
$726$	−15.6803	−	8.42075i	−0.581952	−	0.312523i
$727$	32.1459			1.19223			0.596113	−	0.802901i	$-0.296711\pi$
$727$	32.1459			1.19223			0.596113	+	0.802901i	$0.296711\pi$
$728$	33.8435	+	24.5887i	1.25432	+	0.911318i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−0.236068	−	0.726543i	−0.00873727	−	0.0268905i
$731$	0.881966	−	0.640786i	0.0326207	−	0.0237003i
$732$	−0.572949	+	0.416272i	−0.0211768	+	0.0153858i
$733$	−7.50658	−	23.1029i	−0.277262	−	0.853324i	−0.988612	−	0.150486i	$-0.951916\pi$
$733$	−7.50658	−	23.1029i	−0.277262	−	0.853324i	0.711350	−	0.702838i	$-0.248084\pi$
$734$	−7.28115	+	22.4091i	−0.268752	+	0.827134i
$735$	0.618034	+	0.449028i	0.0227965	+	0.0165626i
$736$	18.5066			0.682162
$737$	29.6697	+	18.6251i	1.09290	+	0.686064i
$738$	9.61803			0.354045
$739$	20.2254	+	14.6946i	0.744004	+	0.540551i	0.893963	−	0.448142i	$-0.147914\pi$
$739$	20.2254	+	14.6946i	0.744004	+	0.540551i	−0.149958	+	0.988692i	$0.547914\pi$
$740$	0.309017	−	0.951057i	0.0113597	−	0.0349615i
$741$	−1.64590	−	5.06555i	−0.0604636	−	0.186088i
$742$	28.9894	−	21.0620i	1.06423	−	0.773210i
$743$	−10.3713	+	7.53521i	−0.380487	+	0.276440i	−0.761546	−	0.648111i	$-0.775559\pi$
$743$	−10.3713	+	7.53521i	−0.380487	+	0.276440i	0.381059	+	0.924551i	$0.375559\pi$
$744$	2.66312	+	8.19624i	0.0976347	+	0.300489i
$745$	−1.77051	+	5.44907i	−0.0648665	+	0.199638i
$746$	−29.3435	−	21.3193i	−1.07434	−	0.780554i
$747$	−12.7082			−0.464969
$748$	0.472136	+	1.17557i	0.0172630	+	0.0429831i
$749$	0.708204			0.0258772
$750$	−4.92705	−	3.57971i	−0.179910	−	0.130713i
$751$	−16.3541	+	50.3328i	−0.596770	+	1.83667i	−0.0510571	+	0.998696i	$0.516259\pi$
$751$	−16.3541	+	50.3328i	−0.596770	+	1.83667i	−0.545713	+	0.837972i	$0.683741\pi$
$752$	0.927051	+	2.85317i	0.0338061	+	0.104044i
$753$	−13.5902	+	9.87384i	−0.495253	+	0.359823i
$754$	36.5066	−	26.5236i	1.32949	−	0.965932i
$755$	−0.236068	−	0.726543i	−0.00859139	−	0.0264416i
$756$	0.572949	−	1.76336i	0.0208380	−	0.0641326i
$757$	12.8992	+	9.37181i	0.468829	+	0.340624i	0.796985	−	0.603999i	$-0.206427\pi$
$757$	12.8992	+	9.37181i	0.468829	+	0.340624i	−0.328156	+	0.944624i	$0.606427\pi$
$758$	45.9787			1.67002
$759$	−13.9271	+	11.6372i	−0.505520	+	0.422403i
$760$	−0.729490			−0.0264614
$761$	−3.95492	−	2.87341i	−0.143366	−	0.104161i	0.513791	−	0.857916i	$-0.328241\pi$
$761$	−3.95492	−	2.87341i	−0.143366	−	0.104161i	−0.657156	+	0.753754i	$0.728241\pi$
$762$	4.85410	−	14.9394i	0.175846	−	0.541197i
$763$		0			0
$764$	−0.736068	+	0.534785i	−0.0266300	+	0.0193478i
$765$	−0.190983	+	0.138757i	−0.00690501	+	0.00501678i
$766$	−4.44427	−	13.6781i	−0.160578	−	0.494208i
$767$	−10.2639	+	31.5891i	−0.370609	+	1.14062i
$768$	−10.9721	−	7.97172i	−0.395923	−	0.287655i
$769$	−47.6869			−1.71963			−0.859817	−	0.510602i	$-0.829423\pi$
$769$	−47.6869			−1.71963			−0.859817	+	0.510602i	$0.829423\pi$
$770$	1.50000	−	5.96361i	0.0540562	−	0.214914i
$771$	−27.3262			−0.984130
$772$	−0.781153	−	0.567541i	−0.0281143	−	0.0204262i
$773$	15.2188	−	46.8388i	0.547384	−	1.68467i	−0.167870	−	0.985809i	$-0.553689\pi$
$773$	15.2188	−	46.8388i	0.547384	−	1.68467i	0.715253	−	0.698865i	$-0.246311\pi$
$774$	0.881966	+	2.71441i	0.0317016	+	0.0975675i
$775$	−15.1353	+	10.9964i	−0.543674	+	0.395003i
$776$	27.1976	−	19.7602i	0.976336	−	0.709349i
$777$	−3.92705	−	12.0862i	−0.140882	−	0.433591i
$778$	−4.63525	+	14.2658i	−0.166182	+	0.511455i
$779$	4.10739	+	2.98419i	0.147163	+	0.106920i
$780$	−1.47214			−0.0527109
$781$	−48.1869	+	3.26944i	−1.72426	+	0.116990i
$782$	5.47214			0.195683
$783$	3.61803	+	2.62866i	0.129298	+	0.0939405i
$784$	−3.00000	+	9.23305i	−0.107143	+	0.329752i
$785$	−1.14590	−	3.52671i	−0.0408989	−	0.125874i
$786$	18.1353	−	13.1760i	0.646863	−	0.469974i
$787$	19.1803	−	13.9353i	0.683705	−	0.496741i	−0.190880	−	0.981613i	$-0.561134\pi$
$787$	19.1803	−	13.9353i	0.683705	−	0.496741i	0.874585	+	0.484873i	$0.161134\pi$
$788$	5.08359	+	15.6457i	0.181095	+	0.557355i
$789$	−0.208204	+	0.640786i	−0.00741226	+	0.0228126i
$790$	0.263932	+	0.191758i	0.00939028	+	0.00682244i
$791$	−38.1246			−1.35556
$792$	7.39919	−	0.502029i	0.262919	−	0.0178388i
$793$	7.14590			0.253758
$794$	33.1074	+	24.0539i	1.17494	+	0.853642i
$795$	0.871323	−	2.68166i	0.0309026	−	0.0951085i
$796$	−0.628677	−	1.93487i	−0.0222829	−	0.0685796i
$797$	−12.3262	+	8.95554i	−0.436618	+	0.317221i	−0.784290	−	0.620395i	$-0.786972\pi$
$797$	−12.3262	+	8.95554i	−0.436618	+	0.317221i	0.347672	+	0.937616i	$0.386972\pi$
$798$	3.35410	−	2.43690i	0.118734	−	0.0862652i
$799$	0.118034	+	0.363271i	0.00417574	+	0.0128516i
$800$	5.07295	−	15.6129i	0.179356	−	0.552000i
$801$	−7.66312	−	5.56758i	−0.270763	−	0.196721i
$802$	−24.1246			−0.851870
$803$	−1.00000	+	3.97574i	−0.0352892	+	0.140301i
$804$	6.52786			0.230220
$805$	−5.07295	−	3.68571i	−0.178798	−	0.129904i
$806$	−12.0172	+	36.9852i	−0.423289	+	1.30275i
$807$	7.56231	+	23.2744i	0.266206	+	0.819297i
$808$	−5.42705	+	3.94298i	−0.190923	+	0.138714i
$809$	−20.4894	+	14.8864i	−0.720367	+	0.523378i	−0.886502	−	0.462726i	$-0.846872\pi$
$809$	−20.4894	+	14.8864i	−0.720367	+	0.523378i	0.166134	+	0.986103i	$0.446872\pi$
$810$	−0.190983	−	0.587785i	−0.00671046	−	0.0206527i
$811$	14.1353	−	43.5038i	0.496356	−	1.52763i	−0.318477	−	0.947931i	$-0.603171\pi$
$811$	14.1353	−	43.5038i	0.496356	−	1.52763i	0.814833	−	0.579696i	$-0.196829\pi$
$812$	6.70820	+	4.87380i	0.235412	+	0.171037i
$813$	6.27051			0.219916
$814$	−17.4443	+	14.5761i	−0.611421	+	0.510893i
$815$	5.83282			0.204315
$816$	−2.42705	−	1.76336i	−0.0849638	−	0.0617298i
$817$	−0.465558	+	1.43284i	−0.0162878	+	0.0501287i
$818$	−14.4721	−	44.5407i	−0.506006	−	1.55733i
$819$	−15.1353	+	10.9964i	−0.528869	+	0.384246i
$820$	1.13525	−	0.824811i	0.0396448	−	0.0288036i
$821$	4.19756	+	12.9188i	0.146496	+	0.450868i	0.997200	−	0.0747763i	$-0.0238243\pi$
$821$	4.19756	+	12.9188i	0.146496	+	0.450868i	−0.850704	+	0.525644i	$0.823824\pi$
$822$	−0.736068	+	2.26538i	−0.0256733	+	0.0790144i
$823$	21.4615	+	15.5927i	0.748101	+	0.543527i	0.895238	−	0.445589i	$-0.147006\pi$
$823$	21.4615	+	15.5927i	0.748101	+	0.543527i	−0.147137	+	0.989116i	$0.547006\pi$
$824$	13.4164			0.467383
$825$	6.00000	+	14.9394i	0.208893	+	0.520123i
$826$	−25.8541			−0.899579
$827$	−10.4164	−	7.56796i	−0.362214	−	0.263164i	0.391761	−	0.920067i	$-0.371866\pi$
$827$	−10.4164	−	7.56796i	−0.362214	−	0.263164i	−0.753975	+	0.656903i	$0.771866\pi$
$828$	−1.04508	+	3.21644i	−0.0363192	+	0.111779i
$829$	−13.1910	−	40.5977i	−0.458142	−	1.41002i	−0.867407	−	0.497600i	$-0.834215\pi$
$829$	−13.1910	−	40.5977i	−0.458142	−	1.41002i	0.409265	−	0.912416i	$-0.365785\pi$
$830$	−6.35410	+	4.61653i	−0.220554	+	0.160242i
$831$	−8.44427	+	6.13512i	−0.292929	+	0.212825i
$832$	8.16312	+	25.1235i	0.283005	+	0.871001i
$833$	−0.381966	+	1.17557i	−0.0132343	+	0.0407311i
$834$	−7.66312	−	5.56758i	−0.265352	−	0.192790i
$835$	7.27051			0.251606
$836$	−1.48278	−	0.930812i	−0.0512830	−	0.0321928i
$837$	−3.85410			−0.133217
$838$	28.1525	+	20.4540i	0.972511	+	0.706571i
$839$	−7.19756	+	22.1518i	−0.248487	+	0.764766i	0.746556	+	0.665323i	$0.231706\pi$
$839$	−7.19756	+	22.1518i	−0.248487	+	0.764766i	−0.995043	+	0.0994428i	$0.968294\pi$
$840$	0.791796	+	2.43690i	0.0273196	+	0.0840810i
$841$	7.28115	−	5.29007i	0.251074	−	0.182416i
$842$	4.88197	−	3.54696i	0.168244	−	0.122236i
$843$	−1.61803	−	4.97980i	−0.0557281	−	0.171513i
$844$	2.15248	−	6.62464i	0.0740913	−	0.228029i
$845$	8.00000	+	5.81234i	0.275208	+	0.199951i
$846$	−1.00000			−0.0343807
$847$	−23.8328	+	22.8254i	−0.818905	+	0.784289i
$848$	35.8328			1.23050
$849$	17.9443	+	13.0373i	0.615846	+	0.447438i
$850$	1.50000	−	4.61653i	0.0514496	−	0.158346i
$851$	7.16312	+	22.0458i	0.245549	+	0.755721i
$852$	−7.28115	+	5.29007i	−0.249448	+	0.181235i
$853$	−6.42705	+	4.66953i	−0.220058	+	0.159882i	−0.692353	−	0.721559i	$-0.743426\pi$
$853$	−6.42705	+	4.66953i	−0.220058	+	0.159882i	0.472295	+	0.881441i	$0.343426\pi$
$854$	1.71885	+	5.29007i	0.0588177	+	0.181022i
$855$	0.100813	−	0.310271i	0.00344773	−	0.0106110i
$856$	0.427051	+	0.310271i	0.0145963	+	0.0106048i
$857$	−41.7214			−1.42517			−0.712587	−	0.701584i	$-0.752477\pi$
$857$	−41.7214			−1.42517			−0.712587	+	0.701584i	$0.752477\pi$
$858$	28.3435	+	17.7926i	0.967630	+	0.607428i
$859$	42.8885			1.46334			0.731669	−	0.681660i	$-0.238742\pi$
$859$	42.8885			1.46334			0.731669	+	0.681660i	$0.238742\pi$
$860$	0.336881	+	0.244758i	0.0114875	+	0.00834619i
$861$	5.51064	−	16.9600i	0.187802	−	0.577996i
$862$	−0.746711	−	2.29814i	−0.0254331	−	0.0782750i
$863$	19.3262	−	14.0413i	0.657873	−	0.477973i	−0.208071	−	0.978114i	$-0.566719\pi$
$863$	19.3262	−	14.0413i	0.657873	−	0.477973i	0.865944	+	0.500141i	$0.166719\pi$
$864$	2.73607	−	1.98787i	0.0930829	−	0.0676287i
$865$	−2.07953	−	6.40013i	−0.0707060	−	0.217611i
$866$	−3.00000	+	9.23305i	−0.101944	+	0.313752i
$867$	13.4443	+	9.76784i	0.456591	+	0.331733i
$868$	−7.14590			−0.242548
$869$	−0.652476	−	1.62460i	−0.0221337	−	0.0551107i
$870$	2.76393			0.0937061
$871$	−53.2877	−	38.7158i	−1.80559	−	1.31183i
$872$		0			0
$873$	4.64590	+	14.2986i	0.157240	+	0.483934i
$874$	−6.11803	+	4.44501i	−0.206946	+	0.150355i
$875$	−9.13525	+	6.63715i	−0.308828	+	0.224377i
$876$	0.236068	+	0.726543i	0.00797600	+	0.0245476i
$877$	−6.30902	+	19.4172i	−0.213040	+	0.655671i	0.786247	+	0.617913i	$0.212022\pi$
$877$	−6.30902	+	19.4172i	−0.213040	+	0.655671i	−0.999287	+	0.0377579i	$0.987978\pi$
$878$	−21.8713	−	15.8904i	−0.738121	−	0.536277i
$879$	17.9443			0.605245
$880$	4.71885	−	3.94298i	0.159072	−	0.132918i
$881$	25.0902			0.845309			0.422655	−	0.906291i	$-0.361098\pi$
$881$	25.0902			0.845309			0.422655	+	0.906291i	$0.361098\pi$
$882$	−2.61803	−	1.90211i	−0.0881538	−	0.0640475i
$883$	11.5623	−	35.5851i	0.389103	−	1.19753i	−0.544358	−	0.838853i	$-0.683226\pi$
$883$	11.5623	−	35.5851i	0.389103	−	1.19753i	0.933460	−	0.358681i	$-0.116774\pi$
$884$	−0.736068	−	2.26538i	−0.0247566	−	0.0761931i
$885$	−1.64590	+	1.19581i	−0.0553263	+	0.0401969i
$886$	1.14590	−	0.832544i	0.0384972	−	0.0279699i
$887$	0.927051	+	2.85317i	0.0311273	+	0.0958001i	0.965413	−	0.260725i	$-0.0839615\pi$
$887$	0.927051	+	2.85317i	0.0311273	+	0.0958001i	−0.934286	+	0.356525i	$0.883962\pi$
$888$	2.92705	−	9.00854i	0.0982254	−	0.302307i
$889$	−23.5623	−	17.1190i	−0.790254	−	0.574153i
$890$	−5.85410			−0.196230
$891$	−0.809017	+	3.21644i	−0.0271031	+	0.107755i
$892$	−7.85410			−0.262975
$893$	−0.427051	−	0.310271i	−0.0142907	−	0.0103828i
$894$	7.50000	−	23.0826i	0.250838	−	0.771999i
$895$	−0.263932	−	0.812299i	−0.00882227	−	0.0271522i
$896$	−33.0517	+	24.0134i	−1.10418	+	0.802233i
$897$	27.6074	−	20.0579i	0.921784	−	0.669715i
$898$	−7.76393	−	23.8949i	−0.259086	−	0.797384i
$899$	5.32624	−	16.3925i	0.177640	−	0.546720i
$900$	2.42705	+	1.76336i	0.0809017	+	0.0587785i
$901$	4.56231			0.151992
$902$	−31.8262	+	2.15938i	−1.05970	+	0.0718996i
$903$	5.29180			0.176100
$904$	−22.9894	−	16.7027i	−0.764615	−	0.555525i
$905$	1.00658	−	3.09793i	0.0334598	−	0.102979i
$906$	1.00000	+	3.07768i	0.0332228	+	0.102249i
$907$	−3.21885	+	2.33863i	−0.106880	+	0.0776529i	−0.639942	−	0.768424i	$-0.721041\pi$
$907$	−3.21885	+	2.33863i	−0.106880	+	0.0776529i	0.533061	+	0.846077i	$0.321041\pi$
$908$	−5.44427	+	3.95550i	−0.180675	+	0.131268i
$909$	−0.927051	−	2.85317i	−0.0307483	−	0.0946337i
$910$	−3.57295	+	10.9964i	−0.118442	+	0.364527i
$911$	−29.0795	−	21.1275i	−0.963448	−	0.699986i	−0.00949880	−	0.999955i	$-0.503024\pi$
$911$	−29.0795	−	21.1275i	−0.963448	−	0.699986i	−0.953949	+	0.299969i	$0.903024\pi$
$912$	4.14590			0.137284
$913$	42.0517	−	2.85317i	1.39171	−	0.0944261i
$914$	53.0689			1.75536
$915$	0.354102	+	0.257270i	0.0117062	+	0.00850509i
$916$	1.90983	−	5.87785i	0.0631026	−	0.194210i
$917$	−12.8435	−	39.5281i	−0.424128	−	1.30533i
$918$	0.809017	−	0.587785i	0.0267015	−	0.0193998i
$919$	37.9894	−	27.6009i	1.25315	−	0.910469i	0.254753	−	0.967006i	$-0.418006\pi$
$919$	37.9894	−	27.6009i	1.25315	−	0.910469i	0.998400	+	0.0565371i	$0.0180059\pi$
$920$	−1.44427	−	4.44501i	−0.0476162	−	0.146548i
$921$	−6.04508	+	18.6049i	−0.199192	+	0.613051i
$922$	12.9721	+	9.42481i	0.427215	+	0.310390i
$923$	90.8115			2.98910
$924$	−1.50000	+	5.96361i	−0.0493464	+	0.196188i
$925$	20.5623			0.676084
$926$	−11.5172	−	8.36775i	−0.378479	−	0.274981i
$927$	−1.85410	+	5.70634i	−0.0608967	+	0.187421i
$928$	4.67376	+	14.3844i	0.153424	+	0.472190i
$929$	−2.33688	+	1.69784i	−0.0766706	+	0.0557044i	−0.625460	−	0.780256i	$-0.715089\pi$
$929$	−2.33688	+	1.69784i	−0.0766706	+	0.0557044i	0.548790	+	0.835960i	$0.315089\pi$
$930$	−1.92705	+	1.40008i	−0.0631905	+	0.0459106i
$931$	−0.527864	−	1.62460i	−0.0173000	−	0.0532441i
$932$	1.65654	−	5.09831i	0.0542618	−	0.167001i
$933$	−9.28115	−	6.74315i	−0.303851	−	0.220761i
$934$	−23.0344			−0.753710
$935$	0.600813	−	0.502029i	0.0196487	−	0.0164181i
$936$	−13.9443			−0.455783
$937$	−26.3713	−	19.1599i	−0.861514	−	0.625926i	0.0667827	−	0.997768i	$-0.478727\pi$
$937$	−26.3713	−	19.1599i	−0.861514	−	0.625926i	−0.928296	+	0.371841i	$0.878727\pi$
$938$	15.8435	−	48.7612i	0.517307	−	1.59211i
$939$	−8.60081	−	26.4706i	−0.280677	−	0.863835i
$940$	−0.118034	+	0.0857567i	−0.00384984	+	0.00279708i
$941$	−27.2082	+	19.7679i	−0.886962	+	0.644416i	−0.935084	−	0.354426i	$-0.884676\pi$
$941$	−27.2082	+	19.7679i	−0.886962	+	0.644416i	0.0481221	+	0.998841i	$0.484676\pi$
$942$	4.85410	+	14.9394i	0.158155	+	0.486752i
$943$	−10.0517	+	30.9358i	−0.327327	+	1.00741i
$944$	−20.9164	−	15.1967i	−0.680771	−	0.494609i
$945$	−1.14590			−0.0372761
$946$	−3.52786	−	8.78402i	−0.114701	−	0.285593i
$947$	2.67376			0.0868856			0.0434428	−	0.999056i	$-0.486167\pi$
$947$	2.67376			0.0868856			0.0434428	+	0.999056i	$0.486167\pi$
$948$	−0.263932	−	0.191758i	−0.00857211	−	0.00622801i
$949$	2.38197	−	7.33094i	0.0773219	−	0.237972i
$950$	2.07295	+	6.37988i	0.0672553	+	0.206991i
$951$	−20.5172	+	14.9066i	−0.665316	+	0.483381i
$952$	−3.35410	+	2.43690i	−0.108707	+	0.0789803i
$953$	18.5967	+	57.2349i	0.602408	+	1.85402i	0.513714	+	0.857961i	$0.328269\pi$
$953$	18.5967	+	57.2349i	0.602408	+	1.85402i	0.0886937	+	0.996059i	$0.471731\pi$
$954$	−3.69098	+	11.3597i	−0.119500	+	0.367783i
$955$	0.454915	+	0.330515i	0.0147207	+	0.0106952i
$956$	−10.8541			−0.351047
$957$	−12.5623	−	7.88597i	−0.406082	−	0.254917i
$958$	−27.3607			−0.883983
$959$	3.57295	+	2.59590i	0.115377	+	0.0838260i
$960$	−0.500000	+	1.53884i	−0.0161374	+	0.0496659i
$961$	−4.98936	−	15.3557i	−0.160947	−	0.495344i
$962$	34.5795	−	25.1235i	1.11489	−	0.810014i
$963$	−0.190983	+	0.138757i	−0.00615434	+	0.00447139i
$964$	3.27051	+	10.0656i	0.105336	+	0.324191i
$965$	−0.184405	+	0.567541i	−0.00593621	+	0.0182698i
$966$	21.4894	+	15.6129i	0.691409	+	0.502338i
$967$	25.6869			0.826036			0.413018	−	0.910723i	$-0.364475\pi$
$967$	25.6869			0.826036			0.413018	+	0.910723i	$0.364475\pi$
$968$	−24.3713	+	3.32244i	−0.783324	+	0.106787i
$969$	0.527864			0.0169574
$970$	7.51722	+	5.46158i	0.241363	+	0.175361i
$971$	−10.4377	+	32.1239i	−0.334962	+	1.03091i	0.631779	+	0.775148i	$0.282325\pi$
$971$	−10.4377	+	32.1239i	−0.334962	+	1.03091i	−0.966741	+	0.255757i	$0.917675\pi$
$972$	0.190983	+	0.587785i	0.00612578	+	0.0188532i
$973$	−14.2082	+	10.3229i	−0.455494	+	0.330936i
$974$	−51.2877	+	37.2627i	−1.64336	+	1.19397i
$975$	−9.35410	−	28.7890i	−0.299571	−	0.921985i
$976$	−1.71885	+	5.29007i	−0.0550190	+	0.169331i
$977$	39.9336	+	29.0135i	1.27759	+	0.928223i	0.999477	−	0.0323250i	$-0.0102912\pi$
$977$	39.9336	+	29.0135i	1.27759	+	0.928223i	0.278113	+	0.960548i	$0.410291\pi$
$978$	−24.7082			−0.790081
$979$	26.6074	+	16.7027i	0.850376	+	0.533822i
$980$	−0.472136			−0.0150818
$981$		0			0
$982$	−13.1074	+	40.3404i	−0.418274	+	1.28731i
$983$	10.9098	+	33.5770i	0.347970	+	1.07094i	0.959975	+	0.280086i	$0.0903631\pi$
$983$	10.9098	+	33.5770i	0.347970	+	1.07094i	−0.612005	+	0.790854i	$0.709637\pi$
$984$	10.7533	−	7.81272i	0.342802	−	0.249060i
$985$	8.22542	−	5.97612i	0.262084	−	0.190415i
$986$	1.38197	+	4.25325i	0.0440108	+	0.135451i
$987$	−0.572949	+	1.76336i	−0.0182372	+	0.0561282i
$988$	2.66312	+	1.93487i	0.0847251	+	0.0615564i
$989$	−9.65248			−0.306931
$990$	0.763932	+	1.90211i	0.0242794	+	0.0604531i
$991$	−12.2705			−0.389786			−0.194893	−	0.980825i	$-0.562436\pi$
$991$	−12.2705			−0.389786			−0.194893	+	0.980825i	$0.562436\pi$
$992$	−10.5451	−	7.66145i	−0.334807	−	0.243251i
$993$	−6.98278	+	21.4908i	−0.221592	+	0.681989i
$994$	21.8435	+	67.2273i	0.692832	+	2.13232i
$995$	−1.01722	+	0.739054i	−0.0322481	+	0.0234296i
$996$	6.35410	−	4.61653i	0.201337	−	0.146280i
$997$	10.5000	+	32.3157i	0.332538	+	1.02345i	0.967922	+	0.251251i	$0.0808420\pi$
$997$	10.5000	+	32.3157i	0.332538	+	1.02345i	−0.635384	+	0.772197i	$0.719158\pi$
$998$	1.28115	−	3.94298i	0.0405542	−	0.124813i
$999$	3.42705	+	2.48990i	0.108427	+	0.0787769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.2.e.a.4.1	✓	4
3.2	odd	2		99.2.f.b.37.1		4
4.3	odd	2		528.2.y.f.433.1		4
5.2	odd	4		825.2.bx.b.499.2		8
5.3	odd	4		825.2.bx.b.499.1		8
5.4	even	2		825.2.n.f.301.1		4
9.2	odd	6		891.2.n.a.433.1		8
9.4	even	3		891.2.n.d.136.1		8
9.5	odd	6		891.2.n.a.136.1		8
9.7	even	3		891.2.n.d.433.1		8
11.2	odd	10		363.2.e.c.148.1		4
11.3	even	5	inner	33.2.e.a.25.1	yes	4
11.4	even	5		363.2.e.h.130.1		4
11.5	even	5		363.2.a.h.1.2		2
11.6	odd	10		363.2.a.e.1.1		2
11.7	odd	10		363.2.e.c.130.1		4
11.8	odd	10		363.2.e.j.124.1		4
11.9	even	5		363.2.e.h.148.1		4
11.10	odd	2		363.2.e.j.202.1		4
33.5	odd	10		1089.2.a.m.1.1		2
33.14	odd	10		99.2.f.b.91.1		4
33.17	even	10		1089.2.a.s.1.2		2
44.3	odd	10		528.2.y.f.289.1		4
44.27	odd	10		5808.2.a.bl.1.2		2
44.39	even	10		5808.2.a.bm.1.2		2
55.3	odd	20		825.2.bx.b.124.2		8
55.14	even	10		825.2.n.f.751.1		4
55.39	odd	10		9075.2.a.bv.1.2		2
55.47	odd	20		825.2.bx.b.124.1		8
55.49	even	10		9075.2.a.x.1.1		2
99.14	odd	30		891.2.n.a.784.1		8
99.25	even	15		891.2.n.d.190.1		8
99.47	odd	30		891.2.n.a.190.1		8
99.58	even	15		891.2.n.d.784.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.4.1	✓	4	1.1	even	1	trivial
33.2.e.a.25.1	yes	4	11.3	even	5	inner
99.2.f.b.37.1		4	3.2	odd	2
99.2.f.b.91.1		4	33.14	odd	10
363.2.a.e.1.1		2	11.6	odd	10
363.2.a.h.1.2		2	11.5	even	5
363.2.e.c.130.1		4	11.7	odd	10
363.2.e.c.148.1		4	11.2	odd	10
363.2.e.h.130.1		4	11.4	even	5
363.2.e.h.148.1		4	11.9	even	5
363.2.e.j.124.1		4	11.8	odd	10
363.2.e.j.202.1		4	11.10	odd	2
528.2.y.f.289.1		4	44.3	odd	10
528.2.y.f.433.1		4	4.3	odd	2
825.2.n.f.301.1		4	5.4	even	2
825.2.n.f.751.1		4	55.14	even	10
825.2.bx.b.124.1		8	55.47	odd	20
825.2.bx.b.124.2		8	55.3	odd	20
825.2.bx.b.499.1		8	5.3	odd	4
825.2.bx.b.499.2		8	5.2	odd	4
891.2.n.a.136.1		8	9.5	odd	6
891.2.n.a.190.1		8	99.47	odd	30
891.2.n.a.433.1		8	9.2	odd	6
891.2.n.a.784.1		8	99.14	odd	30
891.2.n.d.136.1		8	9.4	even	3
891.2.n.d.190.1		8	99.25	even	15
891.2.n.d.433.1		8	9.7	even	3
891.2.n.d.784.1		8	99.58	even	15
1089.2.a.m.1.1		2	33.5	odd	10
1089.2.a.s.1.2		2	33.17	even	10
5808.2.a.bl.1.2		2	44.27	odd	10
5808.2.a.bm.1.2		2	44.39	even	10
9075.2.a.x.1.1		2	55.49	even	10
9075.2.a.bv.1.2		2	55.39	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 - 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +(0.309017 - 0.224514i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(0.927051 + 2.85317i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} -0.618034 q^{10} +(2.80902 + 1.76336i) q^{11} +0.618034 q^{12} +(-5.04508 - 3.66547i) q^{13} +(1.50000 - 4.61653i) q^{14} +(-0.118034 - 0.363271i) q^{15} +(3.92705 - 2.85317i) q^{16} +(0.500000 - 0.363271i) q^{17} +(0.500000 + 1.53884i) q^{18} +(-0.263932 + 0.812299i) q^{19} +(0.190983 + 0.138757i) q^{20} +3.00000 q^{21} +(-2.00000 - 4.97980i) q^{22} -5.47214 q^{23} +(1.80902 + 1.31433i) q^{24} +(-1.50000 + 4.61653i) q^{25} +(3.11803 + 9.59632i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.50000 + 1.08981i) q^{28} +(-1.38197 - 4.25325i) q^{29} +(-0.190983 + 0.587785i) q^{30} +(3.11803 + 2.26538i) q^{31} -3.38197 q^{32} +(2.54508 - 2.12663i) q^{33} -1.00000 q^{34} +(0.927051 + 0.673542i) q^{35} +(0.190983 - 0.587785i) q^{36} +(-1.30902 - 4.02874i) q^{37} +(1.11803 - 0.812299i) q^{38} +(-5.04508 + 3.66547i) q^{39} +(0.263932 + 0.812299i) q^{40} +(1.83688 - 5.65334i) q^{41} +(-3.92705 - 2.85317i) q^{42} +1.76393 q^{43} +(-0.500000 + 1.98787i) q^{44} -0.381966 q^{45} +(7.16312 + 5.20431i) q^{46} +(-0.190983 + 0.587785i) q^{47} +(-1.50000 - 4.61653i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(6.35410 - 4.61653i) q^{50} +(-0.190983 - 0.587785i) q^{51} +(1.19098 - 3.66547i) q^{52} +(5.97214 + 4.33901i) q^{53} +1.61803 q^{54} +(1.26393 - 0.0857567i) q^{55} -6.70820 q^{56} +(0.690983 + 0.502029i) q^{57} +(-2.23607 + 6.88191i) q^{58} +(-1.64590 - 5.06555i) q^{59} +(0.190983 - 0.138757i) q^{60} +(-0.927051 + 0.673542i) q^{61} +(-1.92705 - 5.93085i) q^{62} +(0.927051 - 2.85317i) q^{63} +(-3.42705 - 2.48990i) q^{64} -2.38197 q^{65} +(-5.35410 + 0.363271i) q^{66} +10.5623 q^{67} +(0.309017 + 0.224514i) q^{68} +(-1.69098 + 5.20431i) q^{69} +(-0.572949 - 1.76336i) q^{70} +(-11.7812 + 8.55951i) q^{71} +(1.80902 - 1.31433i) q^{72} +(0.381966 + 1.17557i) q^{73} +(-2.11803 + 6.51864i) q^{74} +(3.92705 + 2.85317i) q^{75} -0.527864 q^{76} +(-2.42705 + 9.64932i) q^{77} +10.0902 q^{78} +(-0.427051 - 0.310271i) q^{79} +(0.572949 - 1.76336i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-7.78115 + 5.65334i) q^{82} +(10.2812 - 7.46969i) q^{83} +(0.572949 + 1.76336i) q^{84} +(0.0729490 - 0.224514i) q^{85} +(-2.30902 - 1.67760i) q^{86} -4.47214 q^{87} +(-5.69098 + 4.75528i) q^{88} +9.47214 q^{89} +(0.500000 + 0.363271i) q^{90} +(5.78115 - 17.7926i) q^{91} +(-1.04508 - 3.21644i) q^{92} +(3.11803 - 2.26538i) q^{93} +(0.809017 - 0.587785i) q^{94} +(0.100813 + 0.310271i) q^{95} +(-1.04508 + 3.21644i) q^{96} +(-12.1631 - 8.83702i) q^{97} +3.23607 q^{98} +(-1.23607 - 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - q^{3} + 3 q^{4} - q^{5} - 3 q^{6} - 3 q^{7} - 5 q^{8} - q^{9} + 2 q^{10} + 9 q^{11} - 2 q^{12} - 9 q^{13} + 6 q^{14} + 4 q^{15} + 9 q^{16} + 2 q^{17} + 2 q^{18} - 10 q^{19} + 3 q^{20}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - q^3 + 3 * q^4 - q^5 - 3 * q^6 - 3 * q^7 - 5 * q^8 - q^9 + 2 * q^10 + 9 * q^11 - 2 * q^12 - 9 * q^13 + 6 * q^14 + 4 * q^15 + 9 * q^16 + 2 * q^17 + 2 * q^18 - 10 * q^19 + 3 * q^20 + 12 * q^21 - 8 * q^22 - 4 * q^23 + 5 * q^24 - 6 * q^25 + 8 * q^26 - q^27 - 6 * q^28 - 10 * q^29 - 3 * q^30 + 8 * q^31 - 18 * q^32 - q^33 - 4 * q^34 - 3 * q^35 + 3 * q^36 - 3 * q^37 - 9 * q^39 + 10 * q^40 + 23 * q^41 - 9 * q^42 + 16 * q^43 - 2 * q^44 - 6 * q^45 + 13 * q^46 - 3 * q^47 - 6 * q^48 - 2 * q^49 + 12 * q^50 - 3 * q^51 + 7 * q^52 + 6 * q^53 + 2 * q^54 + 14 * q^55 + 5 * q^57 - 20 * q^59 + 3 * q^60 + 3 * q^61 - q^62 - 3 * q^63 - 7 * q^64 - 14 * q^65 - 8 * q^66 + 2 * q^67 - q^68 - 9 * q^69 - 9 * q^70 - 27 * q^71 + 5 * q^72 + 6 * q^73 - 4 * q^74 + 9 * q^75 - 20 * q^76 - 3 * q^77 + 18 * q^78 + 5 * q^79 + 9 * q^80 - q^81 - 11 * q^82 + 21 * q^83 + 9 * q^84 + 7 * q^85 - 7 * q^86 - 25 * q^88 + 20 * q^89 + 2 * q^90 + 3 * q^91 + 7 * q^92 + 8 * q^93 + q^94 + 25 * q^95 + 7 * q^96 - 33 * q^97 + 4 * q^98 + 4 * q^99

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