LMFDB - Embedded newform 363.2.e.j.202.1

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			202.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	363.202
Dual form			363.2.e.j.124.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 + 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +(0.309017 - 0.224514i) q^{5} +(1.30902 - 0.951057i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(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} +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} -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} -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} -0.381966 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} -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} +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} +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} +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} +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}+O(q^{10}) $ 4 * q + 3 * q^2 - q^3 + 3 * q^4 - q^5 + 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9	$ 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} - 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} - 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} - 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} - 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} - 5 q^{57} - 20 q^{59} + 3 q^{60} - 3 q^{61} + q^{62} + 3 q^{63} - 7 q^{64} + 14 q^{65} + 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} + 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} + 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}+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 - 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 - 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 - 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 - 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 - 5 * q^57 - 20 * q^59 + 3 * q^60 - 3 * q^61 + q^62 + 3 * q^63 - 7 * q^64 + 14 * q^65 + 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 + 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 + 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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	0.944915	−	0.327315i	$-0.106144\pi$
$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	−0.0193004	+	0.999814i	$0.506144\pi$
$3$	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	$-0.908125\pi$
$7$	−0.927051	−	2.85317i	−0.350392	−	1.07840i	0.608241	−	0.793752i	$-0.291875\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	0.618034			0.195440
$11$		0			0
$11$		0			0
$12$	0.618034			0.178411
$13$	5.04508	+	3.66547i	1.39925	+	1.01662i	0.994777	+	0.102070i	$0.0325466\pi$
$13$	5.04508	+	3.66547i	1.39925	+	1.01662i	0.404478	+	0.914548i	$0.367453\pi$
$14$	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	−0.646766	−	0.762688i	$-0.723879\pi$
$17$	−0.500000	+	0.363271i	−0.121268	+	0.0881062i	0.525498	+	0.850795i	$0.323879\pi$
$18$	−0.500000	−	1.53884i	−0.117851	−	0.362708i
$19$	0.263932	−	0.812299i	0.0605502	−	0.186354i	−0.916206	−	0.400707i	$-0.868764\pi$
$19$	0.263932	−	0.812299i	0.0605502	−	0.186354i	0.976756	+	0.214353i	$0.0687644\pi$
$20$	0.190983	+	0.138757i	0.0427051	+	0.0310271i
$21$	−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	$0.693254\pi$
$24$	−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	$0.0362980\pi$
$29$	1.38197	+	4.25325i	0.256625	+	0.789809i	−0.736881	+	0.676023i	$0.763702\pi$
$30$	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
$33$		0			0
$34$	−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	$0.253647\pi$
$41$	−1.83688	+	5.65334i	−0.286873	+	0.882903i	−0.985831	+	0.167741i	$0.946353\pi$
$42$	−3.92705	−	2.85317i	−0.605957	−	0.440254i
$43$	−1.76393			−0.268997			−0.134499	−	0.990914i	$-0.542942\pi$
$43$	−1.76393			−0.268997			−0.134499	+	0.990914i	$0.542942\pi$
$44$		0			0
$45$	−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
$55$		0			0
$56$	−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	−0.526853	−	0.849956i	$-0.676628\pi$
$61$	0.927051	−	0.673542i	0.118697	−	0.0862382i	0.645550	+	0.763718i	$0.276628\pi$
$62$	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
$66$		0			0
$67$	10.5623			1.29039			0.645196	−	0.764017i	$-0.276776\pi$
$67$	10.5623			1.29039			0.645196	+	0.764017i	$0.276776\pi$
$68$	−0.309017	−	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	0.926212	−	0.377003i	$-0.123045\pi$
$73$	−0.381966	−	1.17557i	−0.0447057	−	0.137590i	−0.970918	+	0.239412i	$0.923045\pi$
$74$	2.11803	−	6.51864i	0.246216	−	0.757776i
$75$	3.92705	+	2.85317i	0.453457	+	0.329456i
$76$	0.527864			0.0605502
$77$		0			0
$78$	10.0902			1.14249
$79$	0.427051	+	0.310271i	0.0480470	+	0.0349082i	0.611550	−	0.791206i	$-0.290547\pi$
$79$	0.427051	+	0.310271i	0.0480470	+	0.0349082i	−0.563503	+	0.826114i	$0.690547\pi$
$80$	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	−0.985476	−	0.169813i	$-0.945684\pi$
$83$	−10.2812	+	7.46969i	−1.12850	+	0.819906i	−0.143027	+	0.989719i	$0.545684\pi$
$84$	−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
$88$		0			0
$89$	9.47214			1.00404			0.502022	−	0.864855i	$-0.332590\pi$
$89$	9.47214			1.00404			0.502022	+	0.864855i	$0.332590\pi$
$90$	−0.500000	−	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
$99$		0			0
$100$	−3.00000			−0.300000
$101$	−2.42705	−	1.76336i	−0.241501	−	0.175460i	0.460451	−	0.887685i	$-0.347688\pi$
$101$	−2.42705	−	1.76336i	−0.241501	−	0.175460i	−0.701952	+	0.712225i	$0.747688\pi$
$102$	−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	−0.954521	−	0.298145i	$-0.903632\pi$
$107$	−0.0729490	+	0.224514i	−0.00705225	+	0.0217046i	0.947468	+	0.319849i	$0.103632\pi$
$108$	−0.500000	−	0.363271i	−0.0481125	−	0.0349558i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	−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
$121$		0			0
$122$	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	−0.181995	−	0.983299i	$-0.558255\pi$
$127$	7.85410	−	5.70634i	0.696939	−	0.506356i	0.878934	+	0.476944i	$0.158255\pi$
$128$	−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	$-0.293085\pi$
$131$	13.8541			1.21044			0.605219	+	0.796059i	$0.293085\pi$
$132$		0			0
$133$	−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	0.844561	−	0.535460i	$-0.179862\pi$
$139$	−1.80902	−	5.56758i	−0.153439	−	0.472236i	−0.997999	+	0.0632239i	$0.979862\pi$
$140$	0.218847	−	0.673542i	0.0184960	−	0.0569247i
$141$	0.500000	+	0.363271i	0.0421076	+	0.0305930i
$142$	−23.5623			−1.97730
$143$		0			0
$144$	−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	0.0333309	−	0.999444i	$-0.489388\pi$
$149$	12.1353	−	8.81678i	0.994159	−	0.722299i	0.960828	+	0.277146i	$0.0893885\pi$
$150$	2.42705	+	7.46969i	0.198168	+	0.609898i
$151$	−0.618034	+	1.90211i	−0.0502949	+	0.154792i	−0.973050	−	0.230596i	$-0.925932\pi$
$151$	−0.618034	+	1.90211i	−0.0502949	+	0.154792i	0.922755	+	0.385388i	$0.125932\pi$
$152$	−1.54508	−	1.12257i	−0.125323	−	0.0910524i
$153$	0.618034			0.0499651
$154$		0			0
$155$	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			0
$166$	−20.5623			−1.59594
$167$	−15.3992	−	11.1882i	−1.19162	−	0.865766i	−0.198190	−	0.980164i	$-0.563506\pi$
$167$	−15.3992	−	11.1882i	−1.19162	−	0.865766i	−0.993435	+	0.114398i	$0.963506\pi$
$168$	−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	$0.333593\pi$
$173$	−5.44427	+	16.7557i	−0.413920	+	1.27392i	−0.913213	+	0.407482i	$0.866407\pi$
$174$	5.85410	+	4.25325i	0.443798	+	0.322438i
$175$	14.5623			1.10081
$176$		0			0
$177$	−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
$187$		0			0
$188$	−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	−0.541365	−	0.840787i	$-0.682092\pi$
$193$	1.26393	−	0.918300i	0.0909798	−	0.0661007i	0.632345	+	0.774687i	$0.282092\pi$
$194$	−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	$-0.897127\pi$
$197$	−26.6180			−1.89646			−0.948228	+	0.317590i	$0.897127\pi$
$198$		0			0
$199$	−3.29180			−0.233349			−0.116675	−	0.993170i	$-0.537223\pi$
$199$	−3.29180			−0.233349			−0.116675	+	0.993170i	$0.537223\pi$
$200$	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
$209$		0			0
$210$	−1.85410			−0.127945
$211$	9.11803	+	6.62464i	0.627711	+	0.456059i	0.855607	−	0.517627i	$-0.173184\pi$
$211$	9.11803	+	6.62464i	0.627711	+	0.456059i	−0.227895	+	0.973686i	$0.573184\pi$
$212$	−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			0
$221$	−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	$-0.982316\pi$
$227$	−3.36475	−	10.3556i	−0.223326	−	0.687327i	0.775131	−	0.631800i	$-0.217684\pi$
$228$	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
$231$		0			0
$232$	10.0000			0.656532
$233$	7.01722	+	5.09831i	0.459713	+	0.334001i	0.793419	−	0.608676i	$-0.208299\pi$
$233$	7.01722	+	5.09831i	0.459713	+	0.334001i	−0.333705	+	0.942677i	$0.608299\pi$
$234$	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	$-0.707715\pi$
$239$	5.42705	−	16.7027i	0.351047	−	1.08041i	0.958266	−	0.285877i	$-0.0922848\pi$
$240$	−1.50000	−	1.08981i	−0.0968246	−	0.0703472i
$241$	−17.1246			−1.10309			−0.551547	−	0.834144i	$-0.685962\pi$
$241$	−17.1246			−1.10309			−0.551547	+	0.834144i	$0.685962\pi$
$242$		0			0
$243$	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
$253$		0			0
$254$	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	$-0.493387\pi$
$263$	0.673762			0.0415459			0.0207730	+	0.999784i	$0.493387\pi$
$264$		0			0
$265$	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	0.874795	−	0.484493i	$-0.160996\pi$
$271$	−1.93769	−	5.96361i	−0.117707	−	0.362263i	−0.992502	+	0.122229i	$0.960996\pi$
$272$	−0.927051	+	2.85317i	−0.0562107	+	0.172999i
$273$	−15.1353	−	10.9964i	−0.916027	−	0.665533i
$274$	2.38197			0.143900
$275$		0			0
$276$	−3.38197			−0.203570
$277$	8.44427	+	6.13512i	0.507367	+	0.368624i	0.811824	−	0.583902i	$-0.198475\pi$
$277$	8.44427	+	6.13512i	0.507367	+	0.368624i	−0.304457	+	0.952526i	$0.598475\pi$
$278$	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	−0.706924	−	0.707290i	$-0.749918\pi$
$281$	−4.23607	+	3.07768i	−0.252703	+	0.183599i	0.454221	+	0.890889i	$0.349918\pi$
$282$	0.309017	+	0.951057i	0.0184017	+	0.0566346i
$283$	6.85410	−	21.0948i	0.407434	−	1.25395i	−0.511412	−	0.859336i	$-0.670877\pi$
$283$	6.85410	−	21.0948i	0.407434	−	1.25395i	0.918846	−	0.394617i	$-0.129123\pi$
$284$	−7.28115	−	5.29007i	−0.432057	−	0.313908i
$285$	−0.326238			−0.0193247
$286$		0			0
$287$	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	$-0.924380\pi$
$293$	−5.54508	−	17.0660i	−0.323947	−	0.997007i	0.647966	−	0.761669i	$-0.275620\pi$
$294$	−1.00000	+	3.07768i	−0.0583212	+	0.179494i
$295$	−1.64590	−	1.19581i	−0.0958279	−	0.0696230i
$296$	−9.47214			−0.550557
$297$		0			0
$298$	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	$-0.311477\pi$
$307$	19.5623			1.11648			0.558240	+	0.829680i	$0.311477\pi$
$308$		0			0
$309$	−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
$319$		0			0
$320$	−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
$330$		0			0
$331$	−22.5967			−1.24203			−0.621015	−	0.783799i	$-0.713279\pi$
$331$	−22.5967			−1.24203			−0.621015	+	0.783799i	$0.713279\pi$
$332$	−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	$0.0217967\pi$
$337$	4.23607	+	13.0373i	0.230753	+	0.710186i	−0.766903	+	0.641763i	$0.778203\pi$
$338$	−12.9443	+	39.8384i	−0.704076	+	2.16692i
$339$	10.2812	+	7.46969i	0.558396	+	0.405698i
$340$	−0.145898			−0.00791243
$341$		0			0
$342$	−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	−0.652160	−	0.758081i	$-0.726137\pi$
$347$	−2.47214	+	1.79611i	−0.132711	+	0.0964203i	0.519449	+	0.854501i	$0.326137\pi$
$348$	0.854102	+	2.62866i	0.0457847	+	0.140911i
$349$	−9.30902	+	28.6502i	−0.498300	+	1.53361i	0.313449	+	0.949605i	$0.398515\pi$
$349$	−9.30902	+	28.6502i	−0.498300	+	1.53361i	−0.811750	+	0.584006i	$0.801485\pi$
$350$	19.0623	+	13.8496i	1.01892	+	0.740291i
$351$	−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	$0.512946\pi$
$354$	−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	$0.0503044\pi$
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	−0.706430	+	0.707783i	$0.749696\pi$
$360$	−0.263932	+	0.812299i	−0.0139104	+	0.0428119i
$361$	14.7812	+	10.7391i	0.777955	+	0.565218i
$362$	13.7984			0.725226
$363$		0			0
$364$	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	$-0.697080\pi$
$373$	−22.4164			−1.16068			−0.580339	+	0.814375i	$0.697080\pi$
$374$		0			0
$375$	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
$385$		0			0
$386$	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
$396$		0			0
$397$	−25.2918			−1.26936			−0.634679	−	0.772776i	$-0.718868\pi$
$397$	−25.2918			−1.26936			−0.634679	+	0.772776i	$0.718868\pi$
$398$	−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
$407$		0			0
$408$	1.38197			0.0684175
$409$	−23.4164	−	17.0130i	−1.15787	−	0.841240i	−0.168360	−	0.985726i	$-0.553847\pi$
$409$	−23.4164	−	17.0130i	−1.15787	−	0.841240i	−0.989507	+	0.144486i	$0.953847\pi$
$410$	−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
$418$		0			0
$419$	−21.5066			−1.05067			−0.525333	−	0.850897i	$-0.676059\pi$
$419$	−21.5066			−1.05067			−0.525333	+	0.850897i	$0.676059\pi$
$420$	−0.572949	−	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
$429$		0			0
$430$	−1.09017			−0.0525727
$431$	−1.20820	−	0.877812i	−0.0581971	−	0.0422827i	0.558306	−	0.829635i	$-0.311451\pi$
$431$	−1.20820	−	0.877812i	−0.0581971	−	0.0422827i	−0.616503	+	0.787352i	$0.711451\pi$
$432$	−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	$-0.630545\pi$
$439$	−16.7082			−0.797439			−0.398720	+	0.917073i	$0.630545\pi$
$440$		0			0
$441$	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
$451$		0			0
$452$	−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	0.243549	−	0.969889i	$-0.421688\pi$
$457$	26.5344	−	19.2784i	1.24123	−	0.901806i	0.997680	+	0.0680830i	$0.0216883\pi$
$458$	−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	$-0.425874\pi$
$461$	9.90983			0.461547			0.230773	+	0.973008i	$0.425874\pi$
$462$		0			0
$463$	8.79837			0.408895			0.204448	−	0.978878i	$-0.434460\pi$
$463$	8.79837			0.408895			0.204448	+	0.978878i	$0.434460\pi$
$464$	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
$473$		0			0
$474$	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	−0.854689	−	0.519140i	$-0.826252\pi$
$479$	−13.6803	+	9.93935i	−0.625071	+	0.454140i	0.229618	+	0.973281i	$0.426252\pi$
$480$	−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
$484$		0			0
$485$	−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	$0.101475\pi$
$491$	8.10081	+	24.9317i	0.365585	+	1.12515i	−0.584030	+	0.811732i	$0.698525\pi$
$492$	−1.13525	+	3.49396i	−0.0511812	+	0.157520i
$493$	−2.23607	−	1.62460i	−0.100707	−	0.0731682i
$494$	8.61803			0.387744
$495$		0			0
$496$	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	$-0.666143\pi$
$503$	9.29180	−	28.5972i	0.414301	−	1.27509i	0.912875	−	0.408239i	$-0.133857\pi$
$504$	5.42705	+	3.94298i	0.241740	+	0.175634i
$505$	−1.14590			−0.0509918
$506$		0			0
$507$	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
$517$		0			0
$518$	−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	0.239979	−	0.970778i	$-0.422859\pi$
$523$	28.2984	−	20.5600i	1.23740	−	0.899025i	0.997422	+	0.0717533i	$0.0228594\pi$
$524$	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
$528$		0			0
$529$	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
$539$		0			0
$540$	−0.236068			−0.0101587
$541$	−0.454915	−	0.330515i	−0.0195583	−	0.0142100i	0.577963	−	0.816063i	$-0.303848\pi$
$541$	−0.454915	−	0.330515i	−0.0195583	−	0.0142100i	−0.597521	+	0.801853i	$0.703848\pi$
$542$	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	$0.235993\pi$
$547$	−5.98936	+	18.4333i	−0.256086	+	0.788153i	−0.993614	+	0.112836i	$0.964007\pi$
$548$	0.736068	+	0.534785i	0.0314433	+	0.0228449i
$549$	−1.14590			−0.0489057
$550$		0			0
$551$	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	$-0.913583\pi$
$557$	−8.06231	−	24.8132i	−0.341611	−	1.05137i	0.621762	−	0.783206i	$-0.286417\pi$
$558$	1.92705	−	5.93085i	0.0815786	−	0.251073i
$559$	−8.89919	−	6.46564i	−0.376396	−	0.273467i
$560$	−5.56231			−0.235050
$561$		0			0
$562$	−8.47214			−0.357375
$563$	21.7533	+	15.8047i	0.916792	+	0.666088i	0.942723	−	0.333575i	$-0.108255\pi$
$563$	21.7533	+	15.8047i	0.916792	+	0.666088i	−0.0259316	+	0.999664i	$0.508255\pi$
$564$	−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	$0.353173\pi$
$569$	−10.5279	+	32.4014i	−0.441351	+	1.35834i	−0.886436	+	0.462851i	$0.846827\pi$
$570$	−0.427051	−	0.310271i	−0.0178872	−	0.0129958i
$571$	25.6869			1.07496			0.537482	−	0.843275i	$-0.319376\pi$
$571$	25.6869			1.07496			0.537482	+	0.843275i	$0.319376\pi$
$572$		0			0
$573$	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
$583$		0			0
$584$	−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	$-0.295225\pi$
$593$	29.2148			1.19971			0.599854	+	0.800110i	$0.295225\pi$
$594$		0			0
$595$	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	$0.0325540\pi$
$601$	6.12868	+	18.8621i	0.249994	+	0.769402i	−0.744781	+	0.667309i	$0.767446\pi$
$602$	−2.64590	+	8.14324i	−0.107839	+	0.331894i
$603$	−8.54508	−	6.20837i	−0.347983	−	0.252824i
$604$	−1.23607			−0.0502949
$605$		0			0
$606$	−4.85410			−0.197184
$607$	−1.88197	−	1.36733i	−0.0763866	−	0.0554981i	0.548937	−	0.835864i	$-0.315033\pi$
$607$	−1.88197	−	1.36733i	−0.0763866	−	0.0554981i	−0.625323	+	0.780366i	$0.715033\pi$
$608$	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	−0.969771	−	0.244016i	$-0.921535\pi$
$613$	−1.03444	+	3.18368i	−0.0417807	+	0.128588i	0.927990	+	0.372604i	$0.121535\pi$
$614$	25.6074	+	18.6049i	1.03343	+	0.750831i
$615$	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	$0.116002\pi$
$618$	−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
$627$		0			0
$628$	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
$638$		0			0
$639$	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
$649$		0			0
$650$	−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	$-0.631773\pi$
$659$	−20.6525			−0.804506			−0.402253	+	0.915528i	$0.631773\pi$
$660$		0			0
$661$	−21.0902			−0.820313			−0.410156	−	0.912015i	$-0.634526\pi$
$661$	−21.0902			−0.820313			−0.410156	+	0.912015i	$0.634526\pi$
$662$	−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
$671$		0			0
$672$	−10.1459			−0.391387
$673$	−11.6631	−	8.47375i	−0.449580	−	0.326639i	0.339850	−	0.940480i	$-0.389624\pi$
$673$	−11.6631	−	8.47375i	−0.449580	−	0.326639i	−0.789430	+	0.613841i	$0.789624\pi$
$674$	−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	−0.180790	−	0.983522i	$-0.557866\pi$
$677$	18.1803	−	13.2088i	0.698727	−	0.507655i	0.879517	+	0.475867i	$0.157866\pi$
$678$	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
$682$		0			0
$683$	−38.8885			−1.48803			−0.744014	−	0.668164i	$-0.767081\pi$
$683$	−38.8885			−1.48803			−0.744014	+	0.668164i	$0.767081\pi$
$684$	−0.427051	−	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
$693$		0			0
$694$	−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	$0.487623\pi$
$701$	−15.3541	+	47.2551i	−0.579916	+	1.78480i	−0.618792	+	0.785555i	$0.712377\pi$
$702$	−8.16312	−	5.93085i	−0.308097	−	0.223846i
$703$	−3.61803			−0.136457
$704$		0			0
$705$	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
$715$		0			0
$716$	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
$726$		0			0
$727$	32.1459			1.19223			0.596113	−	0.802901i	$-0.296711\pi$
$727$	32.1459			1.19223			0.596113	+	0.802901i	$0.296711\pi$
$728$	−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	$0.0480840\pi$
$733$	7.50658	+	23.1029i	0.277262	+	0.853324i	−0.711350	+	0.702838i	$0.751916\pi$
$734$	7.28115	−	22.4091i	0.268752	−	0.827134i
$735$	0.618034	+	0.449028i	0.0227965	+	0.0165626i
$736$	−18.5066			−0.682162
$737$		0			0
$738$	9.61803			0.354045
$739$	−20.2254	−	14.6946i	−0.744004	−	0.540551i	0.149958	−	0.988692i	$-0.452086\pi$
$739$	−20.2254	−	14.6946i	−0.744004	−	0.540551i	−0.893963	+	0.448142i	$0.852086\pi$
$740$	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	−0.381059	−	0.924551i	$-0.624441\pi$
$743$	10.3713	−	7.53521i	0.380487	−	0.276440i	0.761546	+	0.648111i	$0.224441\pi$
$744$	−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			0
$749$	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
$759$		0			0
$760$	−0.729490			−0.0264614
$761$	3.95492	+	2.87341i	0.143366	+	0.104161i	0.657156	−	0.753754i	$-0.271759\pi$
$761$	3.95492	+	2.87341i	0.143366	+	0.104161i	−0.513791	+	0.857916i	$0.671759\pi$
$762$	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	$-0.170577\pi$
$769$	47.6869			1.71963			0.859817	+	0.510602i	$0.170577\pi$
$770$		0			0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.30902 + 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +(0.309017 - 0.224514i) q^{5} +(1.30902 - 0.951057i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(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} +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} -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} -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} -0.381966 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} -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} +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} +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} +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} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - q^{3} + 3 q^{4} - q^{5} + 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - q^3 + 3 * q^4 - q^5 + 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9	\( 4 q + 3 q^{2} - q^{3} + 3 q^{4} - q^{5} + 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} - 2 q^{10} - 2 q^{12} + 9 q^{13} + 6 q^{14} + 4 q^{15} + 9 q^{16} - 2 q^{17} - 2 q^{18} + 10 q^{19} + 3 q^{20} - 12 q^{21} - 4 q^{23} - 5 q^{24} - 6 q^{25} + 8 q^{26} - q^{27} + 6 q^{28} + 10 q^{29} + 3 q^{30} + 8 q^{31} + 18 q^{32} - 4 q^{34} + 3 q^{35} + 3 q^{36} - 3 q^{37} + 9 q^{39} - 10 q^{40} - 23 q^{41} - 9 q^{42} - 16 q^{43} - 6 q^{45} - 13 q^{46} - 3 q^{47} - 6 q^{48} - 2 q^{49} - 12 q^{50} + 3 q^{51} - 7 q^{52} + 6 q^{53} - 2 q^{54} - 5 q^{57} - 20 q^{59} + 3 q^{60} - 3 q^{61} + q^{62} + 3 q^{63} - 7 q^{64} + 14 q^{65} + 2 q^{67} + q^{68} - 9 q^{69} - 9 q^{70} - 27 q^{71} - 5 q^{72} - 6 q^{73} + 4 q^{74} + 9 q^{75} + 20 q^{76} + 18 q^{78} - 5 q^{79} + 9 q^{80} - q^{81} - 11 q^{82} - 21 q^{83} - 9 q^{84} - 7 q^{85} - 7 q^{86} + 20 q^{89} - 2 q^{90} + 3 q^{91} + 7 q^{92} + 8 q^{93} - q^{94} - 25 q^{95} - 7 q^{96} - 33 q^{97} - 4 q^{98}+O(q^{100}) \) 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 - 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 - 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 - 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 - 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 - 5 * q^57 - 20 * q^59 + 3 * q^60 - 3 * q^61 + q^62 + 3 * q^63 - 7 * q^64 + 14 * q^65 + 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 + 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 + 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

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