LMFDB - Embedded newform 729.2.c.a.487.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.4
Root			$1.37340i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.a.244.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0864880 - 0.149802i) q^{2} +(0.985040 + 1.70614i) q^{4} +(-1.86828 - 3.23596i) q^{5} +(-1.51575 + 2.62535i) q^{7} +0.686728 q^{8} +O(q^{10})$	\(q+(0.0864880 - 0.149802i) q^{2} +(0.985040 + 1.70614i) q^{4} +(-1.86828 - 3.23596i) q^{5} +(-1.51575 + 2.62535i) q^{7} +0.686728 q^{8} -0.646335 q^{10} +(-1.24585 + 2.15787i) q^{11} +(0.382569 + 0.662630i) q^{13} +(0.262188 + 0.454123i) q^{14} +(-1.91069 + 3.30940i) q^{16} -4.62278 q^{17} -0.611844 q^{19} +(3.68066 - 6.37509i) q^{20} +(0.215502 + 0.373260i) q^{22} +(3.26219 + 5.65028i) q^{23} +(-4.48095 + 7.76123i) q^{25} +0.132351 q^{26} -5.97229 q^{28} +(-3.27545 + 5.67324i) q^{29} +(-3.27521 - 5.67283i) q^{31} +(1.01723 + 1.76190i) q^{32} +(-0.399815 + 0.692500i) q^{34} +11.3274 q^{35} +4.95969 q^{37} +(-0.0529171 + 0.0916552i) q^{38} +(-1.28300 - 2.22222i) q^{40} +(2.63012 + 4.55550i) q^{41} +(-2.78529 + 4.82426i) q^{43} -4.90884 q^{44} +1.12856 q^{46} +(0.553808 - 0.959223i) q^{47} +(-1.09499 - 1.89658i) q^{49} +(0.775096 + 1.34251i) q^{50} +(-0.753692 + 1.30543i) q^{52} -8.84310 q^{53} +9.31038 q^{55} +(-1.04091 + 1.80290i) q^{56} +(0.566573 + 0.981334i) q^{58} +(-5.92588 - 10.2639i) q^{59} +(-4.09350 + 7.09015i) q^{61} -1.13307 q^{62} -7.29083 q^{64} +(1.42949 - 2.47596i) q^{65} +(0.606169 + 1.04992i) q^{67} +(-4.55362 - 7.88711i) q^{68} +(0.979682 - 1.69686i) q^{70} +4.91946 q^{71} +4.29945 q^{73} +(0.428953 - 0.742969i) q^{74} +(-0.602691 - 1.04389i) q^{76} +(-3.77679 - 6.54158i) q^{77} +(5.89730 - 10.2144i) q^{79} +14.2788 q^{80} +0.909895 q^{82} +(4.50804 - 7.80815i) q^{83} +(8.63666 + 14.9591i) q^{85} +(0.481788 + 0.834481i) q^{86} +(-0.855559 + 1.48187i) q^{88} -7.53885 q^{89} -2.31952 q^{91} +(-6.42677 + 11.1315i) q^{92} +(-0.0957954 - 0.165923i) q^{94} +(1.14310 + 1.97990i) q^{95} +(0.474177 - 0.821299i) q^{97} -0.378814 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8	$ 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 15 q^{16} - 18 q^{17} + 24 q^{19} + 21 q^{20} - 3 q^{22} + 12 q^{23} - 9 q^{25} + 48 q^{26} + 6 q^{28} - 21 q^{29} - 15 q^{31} + 60 q^{35} + 6 q^{37} - 15 q^{38} - 3 q^{40} + 12 q^{41} - 6 q^{43} - 66 q^{44} - 6 q^{46} + 15 q^{47} - 12 q^{49} + 24 q^{50} - 3 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} + 15 q^{58} - 6 q^{59} - 24 q^{61} - 60 q^{62} + 12 q^{64} + 15 q^{65} - 15 q^{67} - 36 q^{68} + 15 q^{70} + 24 q^{73} - 24 q^{74} - 9 q^{76} - 15 q^{77} - 24 q^{79} - 42 q^{80} - 42 q^{82} + 6 q^{83} + 18 q^{85} + 30 q^{86} + 21 q^{88} - 18 q^{89} + 36 q^{91} - 6 q^{92} + 6 q^{94} + 33 q^{95} + 21 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^13 - 24 * q^14 - 15 * q^16 - 18 * q^17 + 24 * q^19 + 21 * q^20 - 3 * q^22 + 12 * q^23 - 9 * q^25 + 48 * q^26 + 6 * q^28 - 21 * q^29 - 15 * q^31 + 60 * q^35 + 6 * q^37 - 15 * q^38 - 3 * q^40 + 12 * q^41 - 6 * q^43 - 66 * q^44 - 6 * q^46 + 15 * q^47 - 12 * q^49 + 24 * q^50 - 3 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 + 15 * q^58 - 6 * q^59 - 24 * q^61 - 60 * q^62 + 12 * q^64 + 15 * q^65 - 15 * q^67 - 36 * q^68 + 15 * q^70 + 24 * q^73 - 24 * q^74 - 9 * q^76 - 15 * q^77 - 24 * q^79 - 42 * q^80 - 42 * q^82 + 6 * q^83 + 18 * q^85 + 30 * q^86 + 21 * q^88 - 18 * q^89 + 36 * q^91 - 6 * q^92 + 6 * q^94 + 33 * q^95 + 21 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.0864880	−	0.149802i	0.0611562	−	0.105926i	−0.833826	−	0.552027i	$-0.813855\pi$
$2$	0.0864880	−	0.149802i	0.0611562	−	0.105926i	0.894982	+	0.446101i	$0.147188\pi$
$3$		0			0
$3$		0			0
$4$	0.985040	+	1.70614i	0.492520	+	0.853069i
$5$	−1.86828	−	3.23596i	−0.835521	−	1.44716i	−0.893606	−	0.448853i	$-0.851833\pi$
$5$	−1.86828	−	3.23596i	−0.835521	−	1.44716i	0.0580849	−	0.998312i	$-0.481501\pi$
$6$		0			0
$7$	−1.51575	+	2.62535i	−0.572899	+	0.992291i	0.423367	+	0.905958i	$0.360848\pi$
$7$	−1.51575	+	2.62535i	−0.572899	+	0.992291i	−0.996266	+	0.0863324i	$0.972485\pi$
$8$	0.686728			0.242795
$9$		0			0
$10$	−0.646335			−0.204389
$11$	−1.24585	+	2.15787i	−0.375637	+	0.650623i	−0.990422	−	0.138072i	$-0.955909\pi$
$11$	−1.24585	+	2.15787i	−0.375637	+	0.650623i	0.614785	+	0.788695i	$0.289243\pi$
$12$		0			0
$13$	0.382569	+	0.662630i	0.106106	+	0.183780i	0.914189	−	0.405287i	$-0.132828\pi$
$13$	0.382569	+	0.662630i	0.106106	+	0.183780i	−0.808084	+	0.589068i	$0.799495\pi$
$14$	0.262188	+	0.454123i	0.0700727	+	0.121369i
$15$		0			0
$16$	−1.91069	+	3.30940i	−0.477671	+	0.827351i
$17$	−4.62278			−1.12119			−0.560595	−	0.828090i	$-0.689427\pi$
$17$	−4.62278			−1.12119			−0.560595	+	0.828090i	$0.689427\pi$
$18$		0			0
$19$	−0.611844			−0.140367			−0.0701833	−	0.997534i	$-0.522358\pi$
$19$	−0.611844			−0.140367			−0.0701833	+	0.997534i	$0.522358\pi$
$20$	3.68066	−	6.37509i	0.823021	−	1.42551i
$21$		0			0
$22$	0.215502	+	0.373260i	0.0459451	+	0.0795793i
$23$	3.26219	+	5.65028i	0.680213	+	1.17816i	0.974916	+	0.222575i	$0.0714462\pi$
$23$	3.26219	+	5.65028i	0.680213	+	1.17816i	−0.294702	+	0.955589i	$0.595221\pi$
$24$		0			0
$25$	−4.48095	+	7.76123i	−0.896190	+	1.55225i
$26$	0.132351			0.0259561
$27$		0			0
$28$	−5.97229			−1.12866
$29$	−3.27545	+	5.67324i	−0.608235	+	1.05349i	0.383296	+	0.923626i	$0.374789\pi$
$29$	−3.27545	+	5.67324i	−0.608235	+	1.05349i	−0.991531	+	0.129869i	$0.958544\pi$
$30$		0			0
$31$	−3.27521	−	5.67283i	−0.588246	−	1.01887i	−0.994462	−	0.105094i	$-0.966486\pi$
$31$	−3.27521	−	5.67283i	−0.588246	−	1.01887i	0.406217	−	0.913777i	$-0.366848\pi$
$32$	1.01723	+	1.76190i	0.179823	+	0.311462i
$33$		0			0
$34$	−0.399815	+	0.692500i	−0.0685677	+	0.118763i
$35$	11.3274			1.91468
$36$		0			0
$37$	4.95969			0.815368			0.407684	−	0.913123i	$-0.366337\pi$
$37$	4.95969			0.815368			0.407684	+	0.913123i	$0.366337\pi$
$38$	−0.0529171	+	0.0916552i	−0.00858429	+	0.0148684i
$39$		0			0
$40$	−1.28300	−	2.22222i	−0.202860	−	0.351364i
$41$	2.63012	+	4.55550i	0.410756	+	0.711450i	0.994973	−	0.100148i	$-0.0319316\pi$
$41$	2.63012	+	4.55550i	0.410756	+	0.711450i	−0.584217	+	0.811598i	$0.698598\pi$
$42$		0			0
$43$	−2.78529	+	4.82426i	−0.424752	+	0.735692i	−0.996397	−	0.0848086i	$-0.972972\pi$
$43$	−2.78529	+	4.82426i	−0.424752	+	0.735692i	0.571645	+	0.820501i	$0.306305\pi$
$44$	−4.90884			−0.740035
$45$		0			0
$46$	1.12856			0.166397
$47$	0.553808	−	0.959223i	0.0807812	−	0.139917i	−0.822805	−	0.568324i	$-0.807592\pi$
$47$	0.553808	−	0.959223i	0.0807812	−	0.139917i	0.903586	+	0.428407i	$0.140925\pi$
$48$		0			0
$49$	−1.09499	−	1.89658i	−0.156427	−	0.270940i
$50$	0.775096	+	1.34251i	0.109615	+	0.189859i
$51$		0			0
$52$	−0.753692	+	1.30543i	−0.104518	+	0.181031i
$53$	−8.84310			−1.21469			−0.607346	−	0.794437i	$-0.707766\pi$
$53$	−8.84310			−1.21469			−0.607346	+	0.794437i	$0.707766\pi$
$54$		0			0
$55$	9.31038			1.25541
$56$	−1.04091	+	1.80290i	−0.139097	+	0.240923i
$57$		0			0
$58$	0.566573	+	0.981334i	0.0743947	+	0.128855i
$59$	−5.92588	−	10.2639i	−0.771484	−	1.33625i	−0.936750	−	0.350000i	$-0.886182\pi$
$59$	−5.92588	−	10.2639i	−0.771484	−	1.33625i	0.165266	−	0.986249i	$-0.447152\pi$
$60$		0			0
$61$	−4.09350	+	7.09015i	−0.524119	+	0.907801i	0.475486	+	0.879723i	$0.342272\pi$
$61$	−4.09350	+	7.09015i	−0.524119	+	0.907801i	−0.999606	+	0.0280781i	$0.991061\pi$
$62$	−1.13307			−0.143900
$63$		0			0
$64$	−7.29083			−0.911354
$65$	1.42949	−	2.47596i	0.177307	−	0.307105i
$66$		0			0
$67$	0.606169	+	1.04992i	0.0740553	+	0.128268i	0.900675	−	0.434493i	$-0.143073\pi$
$67$	0.606169	+	1.04992i	0.0740553	+	0.128268i	−0.826620	+	0.562761i	$0.809739\pi$
$68$	−4.55362	−	7.88711i	−0.552208	−	0.956452i
$69$		0			0
$70$	0.979682	−	1.69686i	0.117094	−	0.202813i
$71$	4.91946			0.583833			0.291916	−	0.956444i	$-0.405707\pi$
$71$	4.91946			0.583833			0.291916	+	0.956444i	$0.405707\pi$
$72$		0			0
$73$	4.29945			0.503213			0.251606	−	0.967830i	$-0.419041\pi$
$73$	4.29945			0.503213			0.251606	+	0.967830i	$0.419041\pi$
$74$	0.428953	−	0.742969i	0.0498648	−	0.0863684i
$75$		0			0
$76$	−0.602691	−	1.04389i	−0.0691333	−	0.119742i
$77$	−3.77679	−	6.54158i	−0.430405	−	0.745483i
$78$		0			0
$79$	5.89730	−	10.2144i	0.663498	−	1.14921i	−0.316192	−	0.948695i	$-0.602404\pi$
$79$	5.89730	−	10.2144i	0.663498	−	1.14921i	0.979690	−	0.200518i	$-0.0642624\pi$
$80$	14.2788			1.59642
$81$		0			0
$82$	0.909895			0.100481
$83$	4.50804	−	7.80815i	0.494821	−	0.857056i	−0.505161	−	0.863025i	$-0.668567\pi$
$83$	4.50804	−	7.80815i	0.494821	−	0.857056i	0.999982	+	0.00596962i	$0.00190020\pi$
$84$		0			0
$85$	8.63666	+	14.9591i	0.936777	+	1.62255i
$86$	0.481788	+	0.834481i	0.0519525	+	0.0899844i
$87$		0			0
$88$	−0.855559	+	1.48187i	−0.0912029	+	0.157968i
$89$	−7.53885			−0.799117			−0.399558	−	0.916708i	$-0.630837\pi$
$89$	−7.53885			−0.799117			−0.399558	+	0.916708i	$0.630837\pi$
$90$		0			0
$91$	−2.31952			−0.243151
$92$	−6.42677	+	11.1315i	−0.670037	+	1.16054i
$93$		0			0
$94$	−0.0957954	−	0.165923i	−0.00988055	−	0.0171136i
$95$	1.14310	+	1.97990i	0.117279	+	0.203134i
$96$		0			0
$97$	0.474177	−	0.821299i	0.0481454	−	0.0833903i	−0.840948	−	0.541115i	$-0.818002\pi$
$97$	0.474177	−	0.821299i	0.0481454	−	0.0833903i	0.889094	+	0.457725i	$0.151336\pi$
$98$	−0.378814			−0.0382659
$99$		0			0
$100$	−17.6557			−1.76557
$101$	−2.80408	+	4.85680i	−0.279016	+	0.483270i	−0.971140	−	0.238508i	$-0.923342\pi$
$101$	−2.80408	+	4.85680i	−0.279016	+	0.483270i	0.692124	+	0.721778i	$0.256675\pi$
$102$		0			0
$103$	4.71251	+	8.16231i	0.464337	+	0.804256i	0.999171	−	0.0407012i	$-0.0129592\pi$
$103$	4.71251	+	8.16231i	0.464337	+	0.804256i	−0.534834	+	0.844957i	$0.679626\pi$
$104$	0.262721	+	0.455046i	0.0257619	+	0.0446210i
$105$		0			0
$106$	−0.764821	+	1.32471i	−0.0742860	+	0.128667i
$107$	1.27825			0.123573			0.0617864	−	0.998089i	$-0.480320\pi$
$107$	1.27825			0.123573			0.0617864	+	0.998089i	$0.480320\pi$
$108$		0			0
$109$	−7.40689			−0.709451			−0.354726	−	0.934970i	$-0.615426\pi$
$109$	−7.40689			−0.709451			−0.354726	+	0.934970i	$0.615426\pi$
$110$	0.805236	−	1.39471i	0.0767762	−	0.132980i
$111$		0			0
$112$	−5.79224	−	10.0325i	−0.547315	−	0.947978i
$113$	4.67598	+	8.09904i	0.439879	+	0.761893i	0.997680	−	0.0680818i	$-0.0216879\pi$
$113$	4.67598	+	8.09904i	0.439879	+	0.761893i	−0.557800	+	0.829975i	$0.688355\pi$
$114$		0			0
$115$	12.1894	−	21.1126i	1.13666	−	1.96876i
$116$	−12.9058			−1.19827
$117$		0			0
$118$	−2.05007			−0.188724
$119$	7.00698	−	12.1364i	0.642329	−	1.11255i
$120$		0			0
$121$	2.39573	+	4.14952i	0.217793	+	0.377229i
$122$	0.708077	+	1.22643i	0.0641063	+	0.111035i
$123$		0			0
$124$	6.45243	−	11.1759i	0.579445	−	1.00363i
$125$	14.8039			1.32410
$126$		0			0
$127$	20.7968			1.84542			0.922710	−	0.385496i	$-0.125970\pi$
$127$	20.7968			1.84542			0.922710	+	0.385496i	$0.125970\pi$
$128$	−2.66503	+	4.61597i	−0.235558	+	0.407998i
$129$		0			0
$130$	−0.247268	−	0.428281i	−0.0216868	−	0.0375627i
$131$	−0.327915	−	0.567965i	−0.0286501	−	0.0496233i	0.851345	−	0.524606i	$-0.175788\pi$
$131$	−0.327915	−	0.567965i	−0.0286501	−	0.0496233i	−0.879995	+	0.474983i	$0.842454\pi$
$132$		0			0
$133$	0.927402	−	1.60631i	0.0804159	−	0.139284i
$134$	0.209705			0.0181158
$135$		0			0
$136$	−3.17460			−0.272219
$137$	4.29380	−	7.43708i	0.366844	−	0.635393i	−0.622226	−	0.782838i	$-0.713772\pi$
$137$	4.29380	−	7.43708i	0.366844	−	0.635393i	0.989070	+	0.147445i	$0.0471049\pi$
$138$		0			0
$139$	−6.72307	−	11.6447i	−0.570243	−	0.987691i	−0.996541	−	0.0831074i	$-0.973516\pi$
$139$	−6.72307	−	11.6447i	−0.570243	−	0.987691i	0.426297	−	0.904583i	$-0.359818\pi$
$140$	11.1579	+	19.3261i	0.943016	+	1.63335i
$141$		0			0
$142$	0.425474	−	0.736943i	0.0357050	−	0.0618429i
$143$	−1.90649			−0.159429
$144$		0			0
$145$	24.4778			2.03277
$146$	0.371851	−	0.644064i	0.0307746	−	0.0533031i
$147$		0			0
$148$	4.88549	+	8.46192i	0.401585	+	0.695565i
$149$	4.81103	+	8.33295i	0.394135	+	0.682662i	0.992990	−	0.118195i	$-0.0377108\pi$
$149$	4.81103	+	8.33295i	0.394135	+	0.682662i	−0.598855	+	0.800857i	$0.704377\pi$
$150$		0			0
$151$	3.56410	−	6.17320i	0.290042	−	0.502368i	−0.683777	−	0.729691i	$-0.739664\pi$
$151$	3.56410	−	6.17320i	0.290042	−	0.502368i	0.973819	+	0.227323i	$0.0729972\pi$
$152$	−0.420170			−0.0340803
$153$		0			0
$154$	−1.30659			−0.105288
$155$	−12.2380	+	21.1969i	−0.982983	+	1.70258i
$156$		0			0
$157$	−3.84288	−	6.65607i	−0.306696	−	0.531212i	0.670942	−	0.741510i	$-0.265890\pi$
$157$	−3.84288	−	6.65607i	−0.306696	−	0.531212i	−0.977637	+	0.210298i	$0.932557\pi$
$158$	−1.02009	−	1.76685i	−0.0811541	−	0.140563i
$159$		0			0
$160$	3.80095	−	6.58343i	0.300491	−	0.520466i
$161$	−19.7786			−1.55877
$162$		0			0
$163$	1.04750			0.0820465			0.0410232	−	0.999158i	$-0.486938\pi$
$163$	1.04750			0.0820465			0.0410232	+	0.999158i	$0.486938\pi$
$164$	−5.18154	+	8.97470i	−0.404611	+	0.700806i
$165$		0			0
$166$	−0.779782	−	1.35062i	−0.0605228	−	0.104829i
$167$	4.17704	+	7.23484i	0.323229	+	0.559849i	0.981152	−	0.193236i	$-0.0618983\pi$
$167$	4.17704	+	7.23484i	0.323229	+	0.559849i	−0.657923	+	0.753085i	$0.728565\pi$
$168$		0			0
$169$	6.20728	−	10.7513i	0.477483	−	0.827025i
$170$	2.98787			0.229159
$171$		0			0
$172$	−10.9745			−0.836796
$173$	10.9229	−	18.9190i	0.830452	−	1.43839i	−0.0672277	−	0.997738i	$-0.521415\pi$
$173$	10.9229	−	18.9190i	0.830452	−	1.43839i	0.897680	−	0.440648i	$-0.145251\pi$
$174$		0			0
$175$	−13.5840	−	23.5282i	−1.02685	−	1.77856i
$176$	−4.76085	−	8.24603i	−0.358862	−	0.621568i
$177$		0			0
$178$	−0.652020	+	1.12933i	−0.0488710	+	0.0846470i
$179$	9.08866			0.679319			0.339659	−	0.940549i	$-0.389688\pi$
$179$	9.08866			0.679319			0.339659	+	0.940549i	$0.389688\pi$
$180$		0			0
$181$	−7.13077			−0.530026			−0.265013	−	0.964245i	$-0.585376\pi$
$181$	−7.13077			−0.530026			−0.265013	+	0.964245i	$0.585376\pi$
$182$	−0.200610	+	0.347467i	−0.0148702	+	0.0257560i
$183$		0			0
$184$	2.24024	+	3.88020i	0.165152	+	0.286052i
$185$	−9.26609	−	16.0493i	−0.681257	−	1.17997i
$186$		0			0
$187$	5.75929	−	9.97537i	0.421161	−	0.729472i
$188$	2.18209			0.159145
$189$		0			0
$190$	0.395456			0.0286894
$191$	5.97781	−	10.3539i	0.432539	−	0.749180i	−0.564552	−	0.825398i	$-0.690951\pi$
$191$	5.97781	−	10.3539i	0.432539	−	0.749180i	0.997091	+	0.0762174i	$0.0242843\pi$
$192$		0			0
$193$	4.43682	+	7.68479i	0.319369	+	0.553164i	0.980357	−	0.197233i	$-0.0631957\pi$
$193$	4.43682	+	7.68479i	0.319369	+	0.553164i	−0.660987	+	0.750397i	$0.729862\pi$
$194$	−0.0820212	−	0.142065i	−0.00588878	−	0.0101997i
$195$		0			0
$196$	2.15722	−	3.73641i	0.154087	−	0.266886i
$197$	−7.39790			−0.527079			−0.263539	−	0.964649i	$-0.584890\pi$
$197$	−7.39790			−0.527079			−0.263539	+	0.964649i	$0.584890\pi$
$198$		0			0
$199$	−10.3837			−0.736084			−0.368042	−	0.929809i	$-0.619972\pi$
$199$	−10.3837			−0.736084			−0.368042	+	0.929809i	$0.619972\pi$
$200$	−3.07719	+	5.32986i	−0.217591	+	0.376878i
$201$		0			0
$202$	0.485038	+	0.840110i	0.0341271	+	0.0591099i
$203$	−9.92951	−	17.1984i	−0.696915	−	1.20709i
$204$		0			0
$205$	9.82761	−	17.0219i	0.686390	−	1.18886i
$206$	1.63030			0.113588
$207$		0			0
$208$	−2.92388			−0.202735
$209$	0.762265	−	1.32028i	0.0527269	−	0.0913257i
$210$		0			0
$211$	−10.4306	−	18.0663i	−0.718070	−	1.24373i	−0.961763	−	0.273882i	$-0.911692\pi$
$211$	−10.4306	−	18.0663i	−0.718070	−	1.24373i	0.243693	−	0.969852i	$-0.421641\pi$
$212$	−8.71080	−	15.0875i	−0.598260	−	1.03622i
$213$		0			0
$214$	0.110553	−	0.191483i	0.00755724	−	0.0130895i
$215$	20.8148			1.41956
$216$		0			0
$217$	19.8576			1.34802
$218$	−0.640607	+	1.10956i	−0.0433874	+	0.0751491i
$219$		0			0
$220$	9.17109	+	15.8848i	0.618315	+	1.07095i
$221$	−1.76854	−	3.06319i	−0.118965	−	0.206053i
$222$		0			0
$223$	−11.7892	+	20.4196i	−0.789466	+	1.36740i	0.136828	+	0.990595i	$0.456309\pi$
$223$	−11.7892	+	20.4196i	−0.789466	+	1.36740i	−0.926294	+	0.376801i	$0.877024\pi$
$224$	−6.16747			−0.412081
$225$		0			0
$226$	1.61766			0.107605
$227$	−5.24207	+	9.07952i	−0.347928	+	0.602629i	−0.985881	−	0.167446i	$-0.946448\pi$
$227$	−5.24207	+	9.07952i	−0.347928	+	0.602629i	0.637953	+	0.770075i	$0.279781\pi$
$228$		0			0
$229$	6.94121	+	12.0225i	0.458688	+	0.794471i	0.998892	−	0.0470633i	$-0.0149862\pi$
$229$	6.94121	+	12.0225i	0.458688	+	0.794471i	−0.540204	+	0.841534i	$0.681653\pi$
$230$	−2.10847	−	3.65197i	−0.139028	−	0.240804i
$231$		0			0
$232$	−2.24934	+	3.89597i	−0.147676	+	0.255783i
$233$	−7.59964			−0.497869			−0.248935	−	0.968520i	$-0.580080\pi$
$233$	−7.59964			−0.497869			−0.248935	+	0.968520i	$0.580080\pi$
$234$		0			0
$235$	−4.13868			−0.269977
$236$	11.6745	−	20.2207i	0.759942	−	1.31626i
$237$		0			0
$238$	−1.21204	−	2.09931i	−0.0785648	−	0.136078i
$239$	8.27934	+	14.3402i	0.535546	+	0.927593i	0.999137	+	0.0415436i	$0.0132275\pi$
$239$	8.27934	+	14.3402i	0.535546	+	0.927593i	−0.463591	+	0.886050i	$0.653439\pi$
$240$		0			0
$241$	7.25924	−	12.5734i	0.467609	−	0.809923i	−0.531706	−	0.846929i	$-0.678449\pi$
$241$	7.25924	−	12.5734i	0.467609	−	0.809923i	0.999315	+	0.0370064i	$0.0117822\pi$
$242$	0.828806			0.0532776
$243$		0			0
$244$	−16.1290			−1.03256
$245$	−4.09150	+	7.08668i	−0.261396	+	0.452751i
$246$		0			0
$247$	−0.234073	−	0.405426i	−0.0148937	−	0.0257966i
$248$	−2.24918	−	3.89570i	−0.142823	−	0.247377i
$249$		0			0
$250$	1.28036	−	2.21765i	0.0809769	−	0.140256i
$251$	−9.05181			−0.571345			−0.285673	−	0.958327i	$-0.592217\pi$
$251$	−9.05181			−0.571345			−0.285673	+	0.958327i	$0.592217\pi$
$252$		0			0
$253$	−16.2568			−1.02205
$254$	1.79867	−	3.11540i	0.112859	−	0.195477i
$255$		0			0
$256$	−6.82984	−	11.8296i	−0.426865	−	0.739352i
$257$	4.84994	+	8.40034i	0.302531	+	0.523999i	0.976709	−	0.214570i	$-0.0688351\pi$
$257$	4.84994	+	8.40034i	0.302531	+	0.523999i	−0.674178	+	0.738569i	$0.735502\pi$
$258$		0			0
$259$	−7.51764	+	13.0209i	−0.467124	+	0.809082i
$260$	5.63243			0.349309
$261$		0			0
$262$	−0.113443			−0.00700852
$263$	−13.4276	+	23.2573i	−0.827983	+	1.43411i	0.0716358	+	0.997431i	$0.477178\pi$
$263$	−13.4276	+	23.2573i	−0.827983	+	1.43411i	−0.899618	+	0.436677i	$0.856155\pi$
$264$		0			0
$265$	16.5214	+	28.6159i	1.01490	+	1.75786i
$266$	−0.160418	−	0.277852i	−0.00983587	−	0.0170362i
$267$		0			0
$268$	−1.19420	+	2.06842i	−0.0729474	+	0.126349i
$269$	−11.7388			−0.715729			−0.357865	−	0.933774i	$-0.616495\pi$
$269$	−11.7388			−0.715729			−0.357865	+	0.933774i	$0.616495\pi$
$270$		0			0
$271$	0.144576			0.00878238			0.00439119	−	0.999990i	$-0.498602\pi$
$271$	0.144576			0.00878238			0.00439119	+	0.999990i	$0.498602\pi$
$272$	8.83268	−	15.2987i	0.535560	−	0.927617i
$273$		0			0
$274$	−0.742724	−	1.28644i	−0.0448696	−	0.0777165i
$275$	−11.1652	−	19.3386i	−0.673285	−	1.16616i
$276$		0			0
$277$	0.507212	−	0.878518i	0.0304754	−	0.0527850i	−0.850385	−	0.526160i	$-0.823631\pi$
$277$	0.507212	−	0.878518i	0.0304754	−	0.0527850i	0.880861	+	0.473375i	$0.156965\pi$
$278$	−2.32586			−0.139496
$279$		0			0
$280$	7.77883			0.464874
$281$	−13.7647	+	23.8412i	−0.821135	+	1.42225i	0.0837029	+	0.996491i	$0.473325\pi$
$281$	−13.7647	+	23.8412i	−0.821135	+	1.42225i	−0.904838	+	0.425756i	$0.860008\pi$
$282$		0			0
$283$	13.4014	+	23.2120i	0.796633	+	1.37981i	0.921797	+	0.387673i	$0.126721\pi$
$283$	13.4014	+	23.2120i	0.796633	+	1.37981i	−0.125164	+	0.992136i	$0.539946\pi$
$284$	4.84587	+	8.39329i	0.287549	+	0.498050i
$285$		0			0
$286$	−0.164889	+	0.285596i	−0.00975007	+	0.0168876i
$287$	−15.9464			−0.941286
$288$		0			0
$289$	4.37012			0.257066
$290$	2.11704	−	3.66682i	0.124317	−	0.215323i
$291$		0			0
$292$	4.23513	+	7.33546i	0.247842	+	0.429275i
$293$	9.32863	+	16.1577i	0.544984	+	0.943941i	0.998608	+	0.0527472i	$0.0167977\pi$
$293$	9.32863	+	16.1577i	0.544984	+	0.943941i	−0.453624	+	0.891193i	$0.649869\pi$
$294$		0			0
$295$	−22.1424	+	38.3518i	−1.28918	+	2.23293i
$296$	3.40596			0.197967
$297$		0			0
$298$	1.66439			0.0964153
$299$	−2.49603	+	4.32324i	−0.144349	+	0.250020i
$300$		0			0
$301$	−8.44359	−	14.6247i	−0.486680	−	0.842955i
$302$	−0.616504	−	1.06782i	−0.0354758	−	0.0614459i
$303$		0			0
$304$	1.16904	−	2.02484i	0.0670491	−	0.116132i
$305$	30.5913			1.75165
$306$		0			0
$307$	33.7893			1.92845			0.964227	−	0.265077i	$-0.0853973\pi$
$307$	33.7893			1.92845			0.964227	+	0.265077i	$0.0853973\pi$
$308$	7.44057	−	12.8874i	0.423966	−	0.734330i
$309$		0			0
$310$	2.11689	+	3.66655i	0.120231	+	0.208246i
$311$	17.3433	+	30.0395i	0.983448	+	1.70338i	0.648642	+	0.761094i	$0.275337\pi$
$311$	17.3433	+	30.0395i	0.983448	+	1.70338i	0.334806	+	0.942287i	$0.391329\pi$
$312$		0			0
$313$	−1.67019	+	2.89285i	−0.0944047	+	0.163514i	−0.909360	−	0.416010i	$-0.863428\pi$
$313$	−1.67019	+	2.89285i	−0.0944047	+	0.163514i	0.814955	+	0.579524i	$0.196761\pi$
$314$	−1.32945			−0.0750254
$315$		0			0
$316$	23.2363			1.30714
$317$	15.5164	−	26.8752i	0.871488	−	1.50946i	0.0110301	−	0.999939i	$-0.496489\pi$
$317$	15.5164	−	26.8752i	0.871488	−	1.50946i	0.860458	−	0.509522i	$-0.170178\pi$
$318$		0			0
$319$	−8.16142	−	14.1360i	−0.456952	−	0.791463i
$320$	13.6213	+	23.5928i	0.761455	+	1.31888i
$321$		0			0
$322$	−1.71061	+	2.96287i	−0.0953288	+	0.165114i
$323$	2.82842			0.157378
$324$		0			0
$325$	−6.85710			−0.380363
$326$	0.0905961	−	0.156917i	0.00501765	−	0.00869083i
$327$		0			0
$328$	1.80618	+	3.12839i	0.0997295	+	0.172736i
$329$	1.67887	+	2.90788i	0.0925590	+	0.160317i
$330$		0			0
$331$	−1.63584	+	2.83336i	−0.0899138	+	0.155735i	−0.907475	−	0.420107i	$-0.861992\pi$
$331$	−1.63584	+	2.83336i	−0.0899138	+	0.155735i	0.817561	+	0.575842i	$0.195326\pi$
$332$	17.7624			0.974837
$333$		0			0
$334$	1.44505			0.0790699
$335$	2.26499	−	3.92308i	0.123750	−	0.214341i
$336$		0			0
$337$	−3.18290	−	5.51295i	−0.173384	−	0.300310i	0.766217	−	0.642582i	$-0.222137\pi$
$337$	−3.18290	−	5.51295i	−0.173384	−	0.300310i	−0.939601	+	0.342272i	$0.888803\pi$
$338$	−1.07371	−	1.85972i	−0.0584021	−	0.101155i
$339$		0			0
$340$	−17.0149	+	29.4707i	−0.922763	+	1.59827i
$341$	16.3217			0.883868
$342$		0			0
$343$	−14.5816			−0.787331
$344$	−1.91273	+	3.31295i	−0.103128	+	0.178623i
$345$		0			0
$346$	−1.88940	−	3.27253i	−0.101575	−	0.175932i
$347$	4.39620	+	7.61445i	0.236001	+	0.408765i	0.959563	−	0.281494i	$-0.0908299\pi$
$347$	4.39620	+	7.61445i	0.236001	+	0.408765i	−0.723562	+	0.690259i	$0.757497\pi$
$348$		0			0
$349$	−7.20011	+	12.4710i	−0.385413	+	0.667555i	−0.991826	−	0.127595i	$-0.959274\pi$
$349$	−7.20011	+	12.4710i	−0.385413	+	0.667555i	0.606413	+	0.795150i	$0.292608\pi$
$350$	−4.69941			−0.251194
$351$		0			0
$352$	−5.06926			−0.270192
$353$	−16.6002	+	28.7525i	−0.883542	+	1.53034i	−0.0361653	+	0.999346i	$0.511514\pi$
$353$	−16.6002	+	28.7525i	−0.883542	+	1.53034i	−0.847376	+	0.530993i	$0.821819\pi$
$354$		0			0
$355$	−9.19094	−	15.9192i	−0.487804	−	0.844902i
$356$	−7.42607	−	12.8623i	−0.393581	−	0.681702i
$357$		0			0
$358$	0.786060	−	1.36150i	0.0415446	−	0.0719573i
$359$	4.94514			0.260995			0.130497	−	0.991449i	$-0.458343\pi$
$359$	4.94514			0.260995			0.130497	+	0.991449i	$0.458343\pi$
$360$		0			0
$361$	−18.6256			−0.980297
$362$	−0.616726	+	1.06820i	−0.0324144	+	0.0561434i
$363$		0			0
$364$	−2.28482	−	3.95742i	−0.119757	−	0.207425i
$365$	−8.03258	−	13.9128i	−0.420445	−	0.728231i
$366$		0			0
$367$	1.24623	−	2.15853i	0.0650525	−	0.112674i	−0.831665	−	0.555278i	$-0.812612\pi$
$367$	1.24623	−	2.15853i	0.0650525	−	0.112674i	0.896717	+	0.442604i	$0.145945\pi$
$368$	−24.9321			−1.29967
$369$		0			0
$370$	−3.20562			−0.166652
$371$	13.4039	−	23.2163i	0.695896	−	1.20533i
$372$		0			0
$373$	14.0238	+	24.2899i	0.726124	+	1.25768i	0.958510	+	0.285060i	$0.0920136\pi$
$373$	14.0238	+	24.2899i	0.726124	+	1.25768i	−0.232385	+	0.972624i	$0.574653\pi$
$374$	−0.996218	−	1.72550i	−0.0515132	−	0.0892235i
$375$		0			0
$376$	0.380316	−	0.658726i	0.0196133	−	0.0339712i
$377$	−5.01234			−0.258149
$378$		0			0
$379$	5.13991			0.264019			0.132010	−	0.991248i	$-0.457857\pi$
$379$	5.13991			0.264019			0.132010	+	0.991248i	$0.457857\pi$
$380$	−2.25199	+	3.90056i	−0.115525	+	0.200095i
$381$		0			0
$382$	−1.03402	−	1.79097i	−0.0529050	−	0.0916341i
$383$	0.0223364	+	0.0386879i	0.00114134	+	0.00197686i	0.866596	−	0.499011i	$-0.166303\pi$
$383$	0.0223364	+	0.0386879i	0.00114134	+	0.00197686i	−0.865454	+	0.500988i	$0.832970\pi$
$384$		0			0
$385$	−14.1122	+	24.4430i	−0.719224	+	1.24573i
$386$	1.53493			0.0781256
$387$		0			0
$388$	1.86833			0.0948502
$389$	−10.4911	+	18.1712i	−0.531921	+	0.921315i	0.467384	+	0.884054i	$0.345197\pi$
$389$	−10.4911	+	18.1712i	−0.531921	+	0.921315i	−0.999306	+	0.0372607i	$0.988137\pi$
$390$		0			0
$391$	−15.0804	−	26.1200i	−0.762648	−	1.32095i
$392$	−0.751960	−	1.30243i	−0.0379797	−	0.0657828i
$393$		0			0
$394$	−0.639830	+	1.10822i	−0.0322341	+	0.0558312i
$395$	−44.0713			−2.21747
$396$		0			0
$397$	−0.00245641			−0.000123284			−6.16419e−5	−	1.00000i	$-0.500020\pi$
$397$	−0.00245641			−0.000123284			−6.16419e−5		1.00000i	$0.500020\pi$
$398$	−0.898069	+	1.55550i	−0.0450161	+	0.0779703i
$399$		0			0
$400$	−17.1234	−	29.6586i	−0.856169	−	1.48293i
$401$	−12.6282	−	21.8726i	−0.630620	−	1.09227i	−0.987425	−	0.158088i	$-0.949467\pi$
$401$	−12.6282	−	21.8726i	−0.630620	−	1.09227i	0.356805	−	0.934179i	$-0.383866\pi$
$402$		0			0
$403$	2.50599	−	4.34051i	0.124832	−	0.216216i
$404$	−11.0485			−0.549684
$405$		0			0
$406$	−3.43513			−0.170483
$407$	−6.17902	+	10.7024i	−0.306283	+	0.530497i
$408$		0			0
$409$	11.6443	+	20.1685i	0.575772	+	0.997267i	0.995957	+	0.0898282i	$0.0286318\pi$
$409$	11.6443	+	20.1685i	0.575772	+	0.997267i	−0.420185	+	0.907438i	$0.638035\pi$
$410$	−1.69994	−	2.94438i	−0.0839540	−	0.145413i
$411$		0			0
$412$	−9.28402	+	16.0804i	−0.457391	+	0.792224i
$413$	35.9286			1.76793
$414$		0			0
$415$	−33.6891			−1.65373
$416$	−0.778323	+	1.34809i	−0.0381604	+	0.0660958i
$417$		0			0
$418$	−0.131853	−	0.228377i	−0.00644916	−	0.0111703i
$419$	−15.6442	−	27.0965i	−0.764268	−	1.32375i	−0.940633	−	0.339427i	$-0.889767\pi$
$419$	−15.6442	−	27.0965i	−0.764268	−	1.32375i	0.176364	−	0.984325i	$-0.443566\pi$
$420$		0			0
$421$	−15.2648	+	26.4394i	−0.743960	+	1.28858i	0.206719	+	0.978400i	$0.433722\pi$
$421$	−15.2648	+	26.4394i	−0.743960	+	1.28858i	−0.950679	+	0.310177i	$0.899612\pi$
$422$	−3.60848			−0.175658
$423$		0			0
$424$	−6.07280			−0.294921
$425$	20.7145	−	35.8785i	1.00480	−	1.74036i
$426$		0			0
$427$	−12.4094	−	21.4938i	−0.600535	−	1.04016i
$428$	1.25912	+	2.18087i	0.0608620	+	0.105416i
$429$		0			0
$430$	1.80023	−	3.11809i	0.0868148	−	0.150368i
$431$	12.4246			0.598474			0.299237	−	0.954179i	$-0.403268\pi$
$431$	12.4246			0.598474			0.299237	+	0.954179i	$0.403268\pi$
$432$		0			0
$433$	−0.760649			−0.0365545			−0.0182772	−	0.999833i	$-0.505818\pi$
$433$	−0.760649			−0.0365545			−0.0182772	+	0.999833i	$0.505818\pi$
$434$	1.71744	−	2.97470i	0.0824399	−	0.142790i
$435$		0			0
$436$	−7.29608	−	12.6372i	−0.349419	−	0.605211i
$437$	−1.99595	−	3.45709i	−0.0954792	−	0.165375i
$438$		0			0
$439$	−15.0547	+	26.0755i	−0.718521	+	1.24451i	0.243065	+	0.970010i	$0.421847\pi$
$439$	−15.0547	+	26.0755i	−0.718521	+	1.24451i	−0.961586	+	0.274504i	$0.911486\pi$
$440$	6.39370			0.304808
$441$		0			0
$442$	−0.611828			−0.0291017
$443$	6.83079	−	11.8313i	0.324541	−	0.562121i	−0.656879	−	0.753996i	$-0.728124\pi$
$443$	6.83079	−	11.8313i	0.324541	−	0.562121i	0.981419	+	0.191875i	$0.0614570\pi$
$444$		0			0
$445$	14.0847	+	24.3954i	0.667679	+	1.15645i
$446$	2.03926	+	3.53209i	0.0965616	+	0.167250i
$447$		0			0
$448$	11.0511	−	19.1410i	0.522114	−	0.904328i
$449$	21.9989			1.03819			0.519097	−	0.854715i	$-0.326268\pi$
$449$	21.9989			1.03819			0.519097	+	0.854715i	$0.326268\pi$
$450$		0			0
$451$	−13.1069			−0.617181
$452$	−9.21205	+	15.9557i	−0.433299	+	0.750495i
$453$		0			0
$454$	0.906751	+	1.57054i	0.0425559	+	0.0737091i
$455$	4.33351	+	7.50586i	0.203158	+	0.351880i
$456$		0			0
$457$	0.744414	−	1.28936i	0.0348222	−	0.0603138i	−0.848089	−	0.529854i	$-0.822247\pi$
$457$	0.744414	−	1.28936i	0.0348222	−	0.0603138i	0.882911	+	0.469540i	$0.155580\pi$
$458$	2.40132			0.112206
$459$		0			0
$460$	48.0281			2.23932
$461$	−3.55667	+	6.16033i	−0.165651	+	0.286915i	−0.936886	−	0.349635i	$-0.886306\pi$
$461$	−3.55667	+	6.16033i	−0.165651	+	0.286915i	0.771236	+	0.636550i	$0.219639\pi$
$462$		0			0
$463$	13.2704	+	22.9849i	0.616726	+	1.06820i	0.990079	+	0.140512i	$0.0448748\pi$
$463$	13.2704	+	22.9849i	0.616726	+	1.06820i	−0.373353	+	0.927689i	$0.621792\pi$
$464$	−12.5167	−	21.6796i	−0.581073	−	1.00645i
$465$		0			0
$466$	−0.657278	+	1.13844i	−0.0304478	+	0.0527371i
$467$	−26.1519			−1.21017			−0.605084	−	0.796162i	$-0.706860\pi$
$467$	−26.1519			−1.21017			−0.605084	+	0.796162i	$0.706860\pi$
$468$		0			0
$469$	−3.67520			−0.169705
$470$	−0.357946	+	0.619980i	−0.0165108	+	0.0285975i
$471$		0			0
$472$	−4.06947	−	7.04852i	−0.187312	−	0.324435i
$473$	−6.94009	−	12.0206i	−0.319106	−	0.552707i
$474$		0			0
$475$	2.74164	−	4.74866i	0.125795	−	0.217884i
$476$	27.6086			1.26544
$477$		0			0
$478$	2.86425			0.131008
$479$	−5.20327	+	9.01234i	−0.237744	+	0.411784i	−0.960067	−	0.279772i	$-0.909741\pi$
$479$	−5.20327	+	9.01234i	−0.237744	+	0.411784i	0.722323	+	0.691556i	$0.243074\pi$
$480$		0			0
$481$	1.89742	+	3.28644i	0.0865151	+	0.149849i
$482$	−1.25567	−	2.17489i	−0.0571944	−	0.0990636i
$483$		0			0
$484$	−4.71977	+	8.17488i	−0.214535	+	0.371585i
$485$	−3.54358			−0.160906
$486$		0			0
$487$	−18.4664			−0.836791			−0.418396	−	0.908265i	$-0.637407\pi$
$487$	−18.4664			−0.836791			−0.418396	+	0.908265i	$0.637407\pi$
$488$	−2.81112	+	4.86901i	−0.127254	+	0.220410i
$489$		0			0
$490$	0.707730	+	1.22582i	0.0319720	+	0.0553771i
$491$	−8.48695	−	14.6998i	−0.383011	−	0.663394i	0.608480	−	0.793569i	$-0.291779\pi$
$491$	−8.48695	−	14.6998i	−0.383011	−	0.663394i	−0.991491	+	0.130175i	$0.958446\pi$
$492$		0			0
$493$	15.1417	−	26.2262i	0.681947	−	1.18117i
$494$	−0.0809779			−0.00364337
$495$		0			0
$496$	25.0316			1.12395
$497$	−7.45667	+	12.9153i	−0.334477	+	0.579332i
$498$		0			0
$499$	−12.3231	−	21.3442i	−0.551657	−	0.955498i	−0.998155	−	0.0607136i	$-0.980662\pi$
$499$	−12.3231	−	21.3442i	−0.551657	−	0.955498i	0.446498	−	0.894785i	$-0.352671\pi$
$500$	14.5824	+	25.2575i	0.652145	+	1.12955i
$501$		0			0
$502$	−0.782873	+	1.35598i	−0.0349413	+	0.0605201i
$503$	−40.1137			−1.78858			−0.894291	−	0.447485i	$-0.852320\pi$
$503$	−40.1137			−1.78858			−0.894291	+	0.447485i	$0.852320\pi$
$504$		0			0
$505$	20.9552			0.932495
$506$	−1.40601	+	2.43529i	−0.0625050	+	0.108262i
$507$		0			0
$508$	20.4857	+	35.4823i	0.908905	+	1.57427i
$509$	2.47426	+	4.28554i	0.109670	+	0.189953i	0.915636	−	0.402007i	$-0.131687\pi$
$509$	2.47426	+	4.28554i	0.109670	+	0.189953i	−0.805967	+	0.591961i	$0.798354\pi$
$510$		0			0
$511$	−6.51689	+	11.2876i	−0.288290	+	0.499333i
$512$	−13.0229			−0.575537
$513$		0			0
$514$	1.67785			0.0740066
$515$	17.6086	−	30.4990i	0.775927	−	1.34395i
$516$		0			0
$517$	1.37992	+	2.39009i	0.0606889	+	0.105116i
$518$	1.30037	+	2.25231i	0.0571350	+	0.0989608i
$519$		0			0
$520$	0.981674	−	1.70031i	0.0430493	−	0.0745635i
$521$	−7.73958			−0.339077			−0.169539	−	0.985524i	$-0.554228\pi$
$521$	−7.73958			−0.339077			−0.169539	+	0.985524i	$0.554228\pi$
$522$		0			0
$523$	36.0140			1.57478			0.787391	−	0.616453i	$-0.211431\pi$
$523$	36.0140			1.57478			0.787391	+	0.616453i	$0.211431\pi$
$524$	0.646018	−	1.11894i	0.0282214	−	0.0488810i
$525$		0			0
$526$	2.32266	+	4.02296i	0.101273	+	0.175409i
$527$	15.1406	+	26.2243i	0.659535	+	1.14235i
$528$		0			0
$529$	−9.78374	+	16.9459i	−0.425380	+	0.736780i
$530$	5.71561			0.248270
$531$		0			0
$532$	3.65411			0.158426
$533$	−2.01241	+	3.48559i	−0.0871670	+	0.150978i
$534$		0			0
$535$	−2.38812	−	4.13635i	−0.103248	−	0.178830i
$536$	0.416273	+	0.721007i	0.0179803	+	0.0311427i
$537$		0			0
$538$	−1.01527	+	1.75849i	−0.0437713	+	0.0758141i
$539$	5.45676			0.235039
$540$		0			0
$541$	−24.4147			−1.04967			−0.524834	−	0.851204i	$-0.675873\pi$
$541$	−24.4147			−1.04967			−0.524834	+	0.851204i	$0.675873\pi$
$542$	0.0125041	−	0.0216577i	0.000537097	−	0.000930280i
$543$		0			0
$544$	−4.70244	−	8.14486i	−0.201615	−	0.349208i
$545$	13.8381	+	23.9684i	0.592761	+	1.02669i
$546$		0			0
$547$	14.1809	−	24.5620i	0.606331	−	1.05020i	−0.385509	−	0.922704i	$-0.625974\pi$
$547$	14.1809	−	24.5620i	0.606331	−	1.05020i	0.991840	−	0.127492i	$-0.0406927\pi$
$548$	16.9183			0.722712
$549$		0			0
$550$	−3.86261			−0.164702
$551$	2.00406	−	3.47114i	0.0853759	−	0.147875i
$552$		0			0
$553$	17.8777	+	30.9650i	0.760235	+	1.31677i
$554$	−0.0877355	−	0.151962i	−0.00372753	−	0.00645626i
$555$		0			0
$556$	13.2450	−	22.9410i	0.561712	−	0.972914i
$557$	36.9373			1.56508			0.782542	−	0.622598i	$-0.213923\pi$
$557$	36.9373			1.56508			0.782542	+	0.622598i	$0.213923\pi$
$558$		0			0
$559$	−4.26226			−0.180274
$560$	−21.6431	+	37.4869i	−0.914586	+	1.58411i
$561$		0			0
$562$	2.38097	+	4.12396i	0.100435	+	0.173959i
$563$	11.3877	+	19.7241i	0.479935	+	0.831271i	0.999735	−	0.0230164i	$-0.00732700\pi$
$563$	11.3877	+	19.7241i	0.479935	+	0.831271i	−0.519800	+	0.854288i	$0.673994\pi$
$564$		0			0
$565$	17.4721	−	30.2626i	0.735057	−	1.27316i
$566$	4.63625			0.194876
$567$		0			0
$568$	3.37833			0.141752
$569$	15.4344	−	26.7331i	0.647043	−	1.12071i	−0.336783	−	0.941582i	$-0.609339\pi$
$569$	15.4344	−	26.7331i	0.647043	−	1.12071i	0.983826	−	0.179129i	$-0.0573279\pi$
$570$		0			0
$571$	−6.41025	−	11.1029i	−0.268260	−	0.464641i	0.700152	−	0.713994i	$-0.253115\pi$
$571$	−6.41025	−	11.1029i	−0.268260	−	0.464641i	−0.968413	+	0.249353i	$0.919782\pi$
$572$	−1.87797	−	3.25274i	−0.0785219	−	0.136004i
$573$		0			0
$574$	−1.37917	+	2.38880i	−0.0575655	+	0.0997064i
$575$	−58.4708			−2.43840
$576$		0			0
$577$	−23.5264			−0.979417			−0.489708	−	0.871886i	$-0.662897\pi$
$577$	−23.5264			−0.979417			−0.489708	+	0.871886i	$0.662897\pi$
$578$	0.377963	−	0.654651i	0.0157212	−	0.0272299i
$579$		0			0
$580$	24.1116	+	41.7626i	1.00118	+	1.73410i
$581$	13.6661	+	23.6704i	0.566965	+	0.982013i
$582$		0			0
$583$	11.0172	−	19.0823i	0.456284	−	0.790307i
$584$	2.95255			0.122178
$585$		0			0
$586$	3.22726			0.133317
$587$	5.69372	−	9.86181i	0.235005	−	0.407041i	−0.724269	−	0.689517i	$-0.757823\pi$
$587$	5.69372	−	9.86181i	0.235005	−	0.407041i	0.959274	+	0.282477i	$0.0911560\pi$
$588$		0			0
$589$	2.00392	+	3.47089i	0.0825700	+	0.143016i
$590$	3.83011	+	6.63394i	0.157683	+	0.273115i
$591$		0			0
$592$	−9.47640	+	16.4136i	−0.389478	+	0.674595i
$593$	37.7324			1.54948			0.774742	−	0.632277i	$-0.217880\pi$
$593$	37.7324			1.54948			0.774742	+	0.632277i	$0.217880\pi$
$594$		0			0
$595$	−52.3640			−2.14672
$596$	−9.47812	+	16.4166i	−0.388239	+	0.672449i
$597$		0			0
$598$	0.431753	+	0.747817i	0.0176557	+	0.0305805i
$599$	23.6791	+	41.0134i	0.967502	+	1.67576i	0.702738	+	0.711449i	$0.251961\pi$
$599$	23.6791	+	41.0134i	0.967502	+	1.67576i	0.264764	+	0.964313i	$0.414706\pi$
$600$		0			0
$601$	15.5537	−	26.9398i	0.634449	−	1.09890i	−0.352182	−	0.935932i	$-0.614560\pi$
$601$	15.5537	−	26.9398i	0.634449	−	1.09890i	0.986631	−	0.162967i	$-0.0521065\pi$
$602$	−2.92108			−0.119054
$603$		0			0
$604$	14.0431			0.571407
$605$	8.95178	−	15.5049i	0.363942	−	0.630365i
$606$		0			0
$607$	−14.7432	−	25.5360i	−0.598409	−	1.03647i	−0.993056	−	0.117642i	$-0.962467\pi$
$607$	−14.7432	−	25.5360i	−0.598409	−	1.03647i	0.394647	−	0.918833i	$-0.370867\pi$
$608$	−0.622386	−	1.07801i	−0.0252411	−	0.0437189i
$609$		0			0
$610$	2.64578	−	4.58262i	0.107124	−	0.185545i
$611$	0.847480			0.0342854
$612$		0			0
$613$	−6.10428			−0.246550			−0.123275	−	0.992373i	$-0.539340\pi$
$613$	−6.10428			−0.246550			−0.123275	+	0.992373i	$0.539340\pi$
$614$	2.92236	−	5.06168i	0.117937	−	0.204273i
$615$		0			0
$616$	−2.59363	−	4.49229i	−0.104500	−	0.181000i
$617$	−9.56005	−	16.5585i	−0.384873	−	0.666620i	0.606878	−	0.794795i	$-0.292422\pi$
$617$	−9.56005	−	16.5585i	−0.384873	−	0.666620i	−0.991752	+	0.128175i	$0.959088\pi$
$618$		0			0
$619$	3.37693	−	5.84901i	0.135730	−	0.235092i	−0.790146	−	0.612919i	$-0.789995\pi$
$619$	3.37693	−	5.84901i	0.135730	−	0.235092i	0.925876	+	0.377827i	$0.123329\pi$
$620$	−48.2198			−1.93655
$621$		0			0
$622$	5.99994			0.240576
$623$	11.4270	−	19.7922i	0.457813	−	0.792956i
$624$		0			0
$625$	−5.25307	−	9.09859i	−0.210123	−	0.363944i
$626$	0.288903	+	0.500394i	0.0115469	+	0.0199998i
$627$		0			0
$628$	7.57079	−	13.1130i	0.302107	−	0.523265i
$629$	−22.9276			−0.914182
$630$		0			0
$631$	−0.456907			−0.0181892			−0.00909458	−	0.999959i	$-0.502895\pi$
$631$	−0.456907			−0.0181892			−0.00909458	+	0.999959i	$0.502895\pi$
$632$	4.04984	−	7.01454i	0.161094	−	0.279023i
$633$		0			0
$634$	−2.68396	−	4.64876i	−0.106594	−	0.184626i
$635$	−38.8543	−	67.2976i	−1.54189	−	2.67062i
$636$		0			0
$637$	0.837819	−	1.45114i	0.0331956	−	0.0574964i
$638$	−2.82346			−0.111782
$639$		0			0
$640$	19.9161			0.787253
$641$	1.43552	−	2.48639i	0.0566994	−	0.0982063i	−0.836282	−	0.548299i	$-0.815276\pi$
$641$	1.43552	−	2.48639i	0.0566994	−	0.0982063i	0.892982	+	0.450092i	$0.148609\pi$
$642$		0			0
$643$	0.851422	+	1.47471i	0.0335768	+	0.0581567i	0.882325	−	0.470640i	$-0.155977\pi$
$643$	0.851422	+	1.47471i	0.0335768	+	0.0581567i	−0.848749	+	0.528796i	$0.822643\pi$
$644$	−19.4827	−	33.7451i	−0.767727	−	1.32974i
$645$		0			0
$646$	0.244624	−	0.423702i	0.00962462	−	0.0166703i
$647$	36.1004			1.41925			0.709626	−	0.704579i	$-0.248864\pi$
$647$	36.1004			1.41925			0.709626	+	0.704579i	$0.248864\pi$
$648$		0			0
$649$	29.5310			1.15919
$650$	−0.593056	+	1.02720i	−0.0232616	+	0.0402902i
$651$		0			0
$652$	1.03183	+	1.78718i	0.0404095	+	0.0699914i
$653$	21.7840	+	37.7310i	0.852473	+	1.47653i	0.878969	+	0.476878i	$0.158232\pi$
$653$	21.7840	+	37.7310i	0.852473	+	1.47653i	−0.0264960	+	0.999649i	$0.508435\pi$
$654$		0			0
$655$	−1.22527	+	2.12224i	−0.0478754	+	0.0829227i
$656$	−20.1013			−0.784825
$657$		0			0
$658$	0.580807			0.0226422
$659$	−12.7405	+	22.0672i	−0.496299	+	0.859615i	−0.999991	−	0.00426823i	$-0.998641\pi$
$659$	−12.7405	+	22.0672i	−0.496299	+	0.859615i	0.503692	+	0.863883i	$0.331975\pi$
$660$		0			0
$661$	−17.0836	−	29.5897i	−0.664475	−	1.15090i	−0.979427	−	0.201797i	$-0.935322\pi$
$661$	−17.0836	−	29.5897i	−0.664475	−	1.15090i	0.314952	−	0.949107i	$-0.398011\pi$
$662$	0.282961	+	0.490102i	0.0109976	+	0.0190484i
$663$		0			0
$664$	3.09580	−	5.36207i	0.120140	−	0.208089i
$665$	−6.93059			−0.268757
$666$		0			0
$667$	−42.7405			−1.65492
$668$	−8.22910	+	14.2532i	−0.318393	+	0.551473i
$669$		0			0
$670$	−0.391789	−	0.678598i	−0.0151361	−	0.0262165i
$671$	−10.1998	−	17.6665i	−0.393757	−	0.682008i
$672$		0			0
$673$	14.7719	−	25.5856i	0.569413	−	0.986253i	−0.427211	−	0.904152i	$-0.640504\pi$
$673$	14.7719	−	25.5856i	0.569413	−	0.986253i	0.996624	−	0.0821009i	$-0.0261630\pi$
$674$	−1.10113			−0.0424140
$675$		0			0
$676$	24.4577			0.940680
$677$	−20.3901	+	35.3167i	−0.783656	+	1.35733i	0.146143	+	0.989264i	$0.453314\pi$
$677$	−20.3901	+	35.3167i	−0.783656	+	1.35733i	−0.929799	+	0.368068i	$0.880019\pi$
$678$		0			0
$679$	1.43747	+	2.48977i	0.0551649	+	0.0955484i
$680$	5.93104	+	10.2729i	0.227445	+	0.393946i
$681$		0			0
$682$	1.41163	−	2.44501i	0.0540540	−	0.0936243i
$683$	31.6426			1.21077			0.605384	−	0.795933i	$-0.293019\pi$
$683$	31.6426			1.21077			0.605384	+	0.795933i	$0.293019\pi$
$684$		0			0
$685$	−32.0881			−1.22602
$686$	−1.26113	+	2.18434i	−0.0481502	+	0.0833986i
$687$		0			0
$688$	−10.6436	−	18.4353i	−0.405784	−	0.702839i
$689$	−3.38310	−	5.85970i	−0.128886	−	0.223237i
$690$		0			0
$691$	14.2924	−	24.7551i	0.543708	−	0.941729i	−0.454979	−	0.890502i	$-0.650353\pi$
$691$	14.2924	−	24.7551i	0.543708	−	0.941729i	0.998687	−	0.0512273i	$-0.0163133\pi$
$692$	43.0379			1.63606
$693$		0			0
$694$	1.52088			0.0577316
$695$	−25.1212	+	43.5112i	−0.952900	+	1.65047i
$696$		0			0
$697$	−12.1585	−	21.0591i	−0.460535	−	0.797670i
$698$	1.24545	+	2.15718i	0.0471408	+	0.0816503i
$699$		0			0
$700$	26.7615	−	46.3523i	1.01149	−	1.75195i
$701$	−7.52982			−0.284397			−0.142199	−	0.989838i	$-0.545417\pi$
$701$	−7.52982			−0.284397			−0.142199	+	0.989838i	$0.545417\pi$
$702$		0			0
$703$	−3.03455			−0.114450
$704$	9.08327	−	15.7327i	0.342338	−	0.592948i
$705$		0			0
$706$	2.87144	+	4.97348i	0.108068	+	0.187180i
$707$	−8.50055	−	14.7234i	−0.319696	−	0.553730i
$708$		0			0
$709$	−4.00699	+	6.94032i	−0.150486	+	0.260649i	−0.931406	−	0.363982i	$-0.881417\pi$
$709$	−4.00699	+	6.94032i	−0.150486	+	0.260649i	0.780920	+	0.624631i	$0.214750\pi$
$710$	−3.17962			−0.119329
$711$		0			0
$712$	−5.17714			−0.194022
$713$	21.3687	−	37.0117i	0.800265	−	1.38610i
$714$		0			0
$715$	3.56187	+	6.16933i	0.133206	+	0.230720i
$716$	8.95269	+	15.5065i	0.334578	+	0.579506i
$717$		0			0
$718$	0.427695	−	0.740790i	0.0159615	−	0.0276460i
$719$	26.9826			1.00628			0.503140	−	0.864205i	$-0.332178\pi$
$719$	26.9826			1.00628			0.503140	+	0.864205i	$0.332178\pi$
$720$		0			0
$721$	−28.5719			−1.06407
$722$	−1.61089	+	2.79015i	−0.0599513	+	0.103839i
$723$		0			0
$724$	−7.02409	−	12.1661i	−0.261048	−	0.452149i
$725$	−29.3542	−	50.8430i	−1.09019	−	1.88826i
$726$		0			0
$727$	7.34717	−	12.7257i	0.272491	−	0.471969i	−0.697008	−	0.717064i	$-0.745486\pi$
$727$	7.34717	−	12.7257i	0.272491	−	0.471969i	0.969499	+	0.245095i	$0.0788190\pi$
$728$	−1.59288			−0.0590360
$729$		0			0
$730$	−2.77889			−0.102851
$731$	12.8758	−	22.3015i	0.476228	−	0.824851i
$732$		0			0
$733$	15.6719	+	27.1445i	0.578854	+	1.00261i	0.995611	+	0.0935872i	$0.0298334\pi$
$733$	15.6719	+	27.1445i	0.578854	+	1.00261i	−0.416757	+	0.909018i	$0.636833\pi$
$734$	−0.215567	−	0.373373i	−0.00795673	−	0.0137815i
$735$		0			0
$736$	−6.63680	+	11.4953i	−0.244636	+	0.423721i
$737$	−3.02078			−0.111272
$738$		0			0
$739$	0.482909			0.0177641			0.00888205	−	0.999961i	$-0.497173\pi$
$739$	0.482909			0.0177641			0.00888205	+	0.999961i	$0.497173\pi$
$740$	18.2549	−	31.6185i	0.671065	−	1.16232i
$741$		0			0
$742$	−2.31855	−	4.01585i	−0.0851168	−	0.147427i
$743$	−21.5254	−	37.2830i	−0.789689	−	1.36778i	−0.926157	−	0.377137i	$-0.876908\pi$
$743$	−21.5254	−	37.2830i	−0.789689	−	1.36778i	0.136468	−	0.990644i	$-0.456425\pi$
$744$		0			0
$745$	17.9767	−	31.1366i	0.658616	−	1.14076i
$746$	4.85156			0.177628
$747$		0			0
$748$	22.6925			0.829720
$749$	−1.93750	+	3.35585i	−0.0707947	+	0.122620i
$750$		0			0
$751$	−21.9608	−	38.0372i	−0.801361	−	1.38800i	−0.918720	−	0.394909i	$-0.870776\pi$
$751$	−21.9608	−	38.0372i	−0.801361	−	1.38800i	0.117359	−	0.993090i	$-0.462557\pi$
$752$	2.11631	+	3.66555i	0.0771737	+	0.133669i
$753$		0			0
$754$	−0.433507	+	0.750857i	−0.0157874	+	0.0273446i
$755$	−26.6350			−0.969346
$756$		0			0
$757$	22.4143			0.814661			0.407331	−	0.913281i	$-0.366460\pi$
$757$	22.4143			0.814661			0.407331	+	0.913281i	$0.366460\pi$
$758$	0.444540	−	0.769966i	0.0161464	−	0.0279664i
$759$		0			0
$760$	0.784997	+	1.35965i	0.0284748	+	0.0493198i
$761$	4.99837	+	8.65743i	0.181191	+	0.313832i	0.942286	−	0.334808i	$-0.108672\pi$
$761$	4.99837	+	8.65743i	0.181191	+	0.313832i	−0.761096	+	0.648640i	$0.775338\pi$
$762$		0			0
$763$	11.2270	−	19.4457i	0.406444	−	0.703982i
$764$	23.5535			0.852137
$765$		0			0
$766$	0.00772733			0.000279200
$767$	4.53412	−	7.85332i	0.163718	−	0.283567i
$768$		0			0
$769$	3.74810	+	6.49189i	0.135160	+	0.234104i	0.925658	−	0.378360i	$-0.123512\pi$
$769$	3.74810	+	6.49189i	0.135160	+	0.234104i	−0.790499	+	0.612464i	$0.790179\pi$
$770$	2.44107	+	4.22806i	0.0879701	+	0.152369i
$771$		0			0
$772$	−8.74088	+	15.1397i	−0.314591	+	0.544888i
$773$	−19.8391			−0.713562			−0.356781	−	0.934188i	$-0.616126\pi$
$773$	−19.8391			−0.713562			−0.356781	+	0.934188i	$0.616126\pi$
$774$		0			0
$775$	58.7043			2.10872
$776$	0.325631	−	0.564009i	0.0116895	−	0.0202467i
$777$		0			0
$778$	1.81471	+	3.14318i	0.0650606	+	0.112688i
$779$	−1.60922	−	2.78726i	−0.0576564	−	0.0998638i
$780$		0			0
$781$	−6.12890	+	10.6156i	−0.219309	+	0.379855i
$782$	−5.21709			−0.186563
$783$		0			0
$784$	8.36872			0.298883
$785$	−14.3592	+	24.8708i	−0.512501	+	0.887678i
$786$		0			0
$787$	−19.8641	−	34.4057i	−0.708080	−	1.22643i	−0.965569	−	0.260149i	$-0.916228\pi$
$787$	−19.8641	−	34.4057i	−0.708080	−	1.22643i	0.257489	−	0.966281i	$-0.417105\pi$
$788$	−7.28723	−	12.6218i	−0.259597	−	0.449635i
$789$		0			0
$790$	−3.81164	+	6.60195i	−0.135612	+	0.234887i
$791$	−28.3505			−1.00803
$792$		0			0
$793$	−6.26419			−0.222448
$794$	−0.000212450	0	0.000367974i	−7.53957e−6	0	1.30589e-5i
$795$		0			0
$796$	−10.2284	−	17.7161i	−0.362536	−	0.627931i
$797$	4.55298	+	7.88599i	0.161275	+	0.279336i	0.935326	−	0.353787i	$-0.115106\pi$
$797$	4.55298	+	7.88599i	0.161275	+	0.279336i	−0.774051	+	0.633123i	$0.781773\pi$
$798$		0			0
$799$	−2.56013	+	4.43428i	−0.0905710	+	0.156874i
$800$	−18.2326			−0.644621
$801$		0			0
$802$	−4.36874			−0.154265
$803$	−5.35646	+	9.27766i	−0.189025	+	0.327402i
$804$		0			0
$805$	36.9520	+	64.0028i	1.30239	+	2.25580i
$806$	−0.433476	−	0.750803i	−0.0152686	−	0.0264459i
$807$		0			0
$808$	−1.92564	+	3.33530i	−0.0677437	+	0.117336i
$809$	3.01910			0.106146			0.0530730	−	0.998591i	$-0.483098\pi$
$809$	3.01910			0.106146			0.0530730	+	0.998591i	$0.483098\pi$
$810$		0			0
$811$	33.1722			1.16483			0.582416	−	0.812891i	$-0.302107\pi$
$811$	33.1722			1.16483			0.582416	+	0.812891i	$0.302107\pi$
$812$	19.5619	−	33.8822i	0.686489	−	1.18903i
$813$		0			0
$814$	1.06882	+	1.85125i	0.0374622	+	0.0648864i
$815$	−1.95702	−	3.38966i	−0.0685516	−	0.118735i
$816$		0			0
$817$	1.70416	−	2.95169i	0.0596210	−	0.103267i
$818$	4.02836			0.140848
$819$		0			0
$820$	38.7223			1.35224
$821$	−21.3810	+	37.0329i	−0.746201	+	1.29246i	0.203430	+	0.979089i	$0.434791\pi$
$821$	−21.3810	+	37.0329i	−0.746201	+	1.29246i	−0.949631	+	0.313369i	$0.898542\pi$
$822$		0			0
$823$	17.6144	+	30.5091i	0.614000	+	1.06348i	0.990559	+	0.137087i	$0.0437740\pi$
$823$	17.6144	+	30.5091i	0.614000	+	1.06348i	−0.376559	+	0.926393i	$0.622893\pi$
$824$	3.23621	+	5.60529i	0.112739	+	0.195269i
$825$		0			0
$826$	3.10739	−	5.38216i	0.108120	−	0.187269i
$827$	26.0380			0.905429			0.452714	−	0.891656i	$-0.350456\pi$
$827$	26.0380			0.905429			0.452714	+	0.891656i	$0.350456\pi$
$828$		0			0
$829$	−7.90268			−0.274471			−0.137236	−	0.990538i	$-0.543822\pi$
$829$	−7.90268			−0.274471			−0.137236	+	0.990538i	$0.543822\pi$
$830$	−2.91370	+	5.04668i	−0.101136	+	0.175173i
$831$		0			0
$832$	−2.78925	−	4.83112i	−0.0966998	−	0.167489i
$833$	5.06190	+	8.76746i	0.175384	+	0.303775i
$834$		0			0
$835$	15.6078	−	27.0334i	0.540129	−	0.935531i
$836$	3.00344			0.103876
$837$		0			0
$838$	−5.41213			−0.186959
$839$	−2.57420	+	4.45864i	−0.0888711	+	0.153929i	−0.907034	−	0.421057i	$-0.861659\pi$
$839$	−2.57420	+	4.45864i	−0.0888711	+	0.153929i	0.818163	+	0.574986i	$0.194993\pi$
$840$		0			0
$841$	−6.95710	−	12.0500i	−0.239900	−	0.415519i
$842$	2.64044	+	4.57338i	0.0909956	+	0.157609i
$843$		0			0
$844$	20.5491	−	35.5920i	0.707328	−	1.22513i
$845$	−46.3878			−1.59579
$846$		0			0
$847$	−14.5253			−0.499094
$848$	16.8964	−	29.2654i	0.580224	−	1.00498i
$849$		0			0
$850$	−3.58310	−	6.20612i	−0.122899	−	0.212868i
$851$	16.1794	+	28.0236i	0.554624	+	0.960637i
$852$		0			0
$853$	−12.9952	+	22.5084i	−0.444948	+	0.770673i	−0.998049	−	0.0624418i	$-0.980111\pi$
$853$	−12.9952	+	22.5084i	−0.444948	+	0.770673i	0.553100	+	0.833115i	$0.313445\pi$
$854$	−4.29307			−0.146906
$855$		0			0
$856$	0.877808			0.0300028
$857$	2.05957	−	3.56727i	0.0703535	−	0.121856i	−0.828703	−	0.559689i	$-0.810921\pi$
$857$	2.05957	−	3.56727i	0.0703535	−	0.121856i	0.899056	+	0.437833i	$0.144254\pi$
$858$		0			0
$859$	3.21471	+	5.56805i	0.109685	+	0.189979i	0.915642	−	0.401994i	$-0.131683\pi$
$859$	3.21471	+	5.56805i	0.109685	+	0.189979i	−0.805958	+	0.591973i	$0.798349\pi$
$860$	20.5034	+	35.5129i	0.699160	+	1.21098i
$861$		0			0
$862$	1.07458	−	1.86123i	0.0366004	−	0.0633938i
$863$	29.6195			1.00826			0.504129	−	0.863628i	$-0.331813\pi$
$863$	29.6195			1.00826			0.504129	+	0.863628i	$0.331813\pi$
$864$		0			0
$865$	−81.6282			−2.77544
$866$	−0.0657870	+	0.113946i	−0.00223553	+	0.00387206i
$867$		0			0
$868$	19.5605	+	33.8798i	0.663927	+	1.14996i
$869$	14.6943	+	25.4512i	0.498469	+	0.863374i
$870$		0			0
$871$	−0.463803	+	0.803331i	−0.0157154	+	0.0272198i
$872$	−5.08652			−0.172251
$873$		0			0
$874$	−0.690503			−0.0233566
$875$	−22.4390	+	38.8654i	−0.758576	+	1.31389i
$876$		0			0
$877$	15.9338	+	27.5982i	0.538048	+	0.931926i	0.999009	+	0.0445057i	$0.0141713\pi$
$877$	15.9338	+	27.5982i	0.538048	+	0.931926i	−0.460962	+	0.887420i	$0.652495\pi$
$878$	2.60410	+	4.51043i	0.0878840	+	0.152220i
$879$		0			0
$880$	−17.7892	+	30.8118i	−0.599674	+	1.03867i
$881$	34.7864			1.17198			0.585991	−	0.810317i	$-0.300705\pi$
$881$	34.7864			1.17198			0.585991	+	0.810317i	$0.300705\pi$
$882$		0			0
$883$	−30.3764			−1.02225			−0.511124	−	0.859507i	$-0.670771\pi$
$883$	−30.3764			−1.02225			−0.511124	+	0.859507i	$0.670771\pi$
$884$	3.48415	−	6.03473i	0.117185	−	0.202970i
$885$		0			0
$886$	−1.18156	−	2.04653i	−0.0396954	−	0.0687544i
$887$	25.0138	+	43.3252i	0.839882	+	1.45472i	0.889993	+	0.455974i	$0.150709\pi$
$887$	25.0138	+	43.3252i	0.839882	+	1.45472i	−0.0501110	+	0.998744i	$0.515958\pi$
$888$		0			0
$889$	−31.5228	+	54.5990i	−1.05724	+	1.83119i
$890$	4.87263			0.163331
$891$		0			0
$892$	−46.4515			−1.55531
$893$	−0.338844	+	0.586895i	−0.0113390	+	0.0196397i
$894$		0			0
$895$	−16.9802	−	29.4105i	−0.567585	−	0.983086i
$896$	−8.07903	−	13.9933i	−0.269902	−	0.467483i
$897$		0			0
$898$	1.90264	−	3.29547i	0.0634920	−	0.109971i
$899$	42.9111			1.43117
$900$		0			0
$901$	40.8797			1.36190
$902$	−1.13359	+	1.96344i	−0.0377444	+	0.0653753i
$903$		0			0
$904$	3.21113	+	5.56184i	0.106801	+	0.184984i
$905$	13.3223	+	23.0749i	0.442848	+	0.767035i
$906$		0			0
$907$	22.0322	−	38.1608i	0.731566	−	1.26711i	−0.224648	−	0.974440i	$-0.572123\pi$
$907$	22.0322	−	38.1608i	0.731566	−	1.26711i	0.956214	−	0.292669i	$-0.0945434\pi$
$908$	−20.6546			−0.685446
$909$		0			0
$910$	1.49919			0.0496975
$911$	18.5891	−	32.1973i	0.615885	−	1.06674i	−0.374343	−	0.927290i	$-0.622132\pi$
$911$	18.5891	−	32.1973i	0.615885	−	1.06674i	0.990228	−	0.139455i	$-0.0445349\pi$
$912$		0			0
$913$	11.2327	+	19.4555i	0.371747	+	0.643884i
$914$	−0.128766	−	0.223029i	−0.00425919	−	0.00737713i
$915$		0			0
$916$	−13.6747	+	23.6853i	−0.451826	+	0.782585i
$917$	1.98815			0.0656544
$918$		0			0
$919$	12.3976			0.408958			0.204479	−	0.978871i	$-0.434450\pi$
$919$	12.3976			0.408958			0.204479	+	0.978871i	$0.434450\pi$
$920$	8.37078	−	14.4986i	0.275977	−	0.478005i
$921$		0			0
$922$	0.615218	+	1.06559i	0.0202611	+	0.0350933i
$923$	1.88204	+	3.25978i	0.0619480	+	0.107297i
$924$		0			0
$925$	−22.2241	+	38.4933i	−0.730724	+	1.26565i
$926$	4.59091			0.150867
$927$		0			0
$928$	−13.3275			−0.437498
$929$	−16.6941	+	28.9150i	−0.547716	+	0.948672i	0.450715	+	0.892668i	$0.351169\pi$
$929$	−16.6941	+	28.9150i	−0.547716	+	0.948672i	−0.998431	+	0.0560035i	$0.982164\pi$
$930$		0			0
$931$	0.669963	+	1.16041i	0.0219571	+	0.0380309i
$932$	−7.48595	−	12.9660i	−0.245210	−	0.424717i
$933$		0			0
$934$	−2.26183	+	3.91760i	−0.0740093	+	0.128188i
$935$	−43.0399			−1.40755
$936$		0			0
$937$	−24.8441			−0.811620			−0.405810	−	0.913957i	$-0.633011\pi$
$937$	−24.8441			−0.811620			−0.405810	+	0.913957i	$0.633011\pi$
$938$	−0.317861	+	0.550551i	−0.0103785	+	0.0179761i
$939$		0			0
$940$	−4.07676	−	7.06116i	−0.132969	−	0.230309i
$941$	−12.7149	−	22.0229i	−0.414495	−	0.717927i	0.580880	−	0.813989i	$-0.302709\pi$
$941$	−12.7149	−	22.0229i	−0.414495	−	0.717927i	−0.995375	+	0.0960624i	$0.969375\pi$
$942$		0			0
$943$	−17.1599	+	29.7218i	−0.558803	+	0.967875i
$944$	45.2900			1.47406
$945$		0			0
$946$	−2.40094			−0.0780612
$947$	−8.31507	+	14.4021i	−0.270204	+	0.468006i	−0.968914	−	0.247398i	$-0.920424\pi$
$947$	−8.31507	+	14.4021i	−0.270204	+	0.468006i	0.698710	+	0.715405i	$0.253758\pi$
$948$		0			0
$949$	1.64484	+	2.84894i	0.0533937	+	0.0924806i
$950$	−0.474238	−	0.821404i	−0.0153863	−	0.0266499i
$951$		0			0
$952$	4.81189	−	8.33444i	0.155954	−	0.270121i
$953$	14.2671			0.462158			0.231079	−	0.972935i	$-0.425774\pi$
$953$	14.2671			0.462158			0.231079	+	0.972935i	$0.425774\pi$
$954$		0			0
$955$	−44.6730			−1.44558
$956$	−16.3110	+	28.2514i	−0.527534	+	0.913716i
$957$		0			0
$958$	0.900041	+	1.55892i	0.0290790	+	0.0503663i
$959$	13.0167	+	22.5455i	0.420330	+	0.728032i
$960$		0			0
$961$	−5.95404	+	10.3127i	−0.192066	+	0.332668i
$962$	0.656418			0.0211638
$963$		0			0
$964$	28.6026			0.921227
$965$	16.5784	−	28.7147i	0.533679	−	0.924359i
$966$		0			0
$967$	19.5424	+	33.8484i	0.628440	+	1.08849i	0.987865	+	0.155317i	$0.0496398\pi$
$967$	19.5424	+	33.8484i	0.628440	+	1.08849i	−0.359424	+	0.933174i	$0.617027\pi$
$968$	1.64521	+	2.84959i	0.0528791	+	0.0915893i
$969$		0			0
$970$	−0.306477	+	0.530835i	−0.00984040	+	0.0170441i
$971$	−4.40370			−0.141321			−0.0706607	−	0.997500i	$-0.522511\pi$
$971$	−4.40370			−0.141321			−0.0706607	+	0.997500i	$0.522511\pi$
$972$		0			0
$973$	40.7619			1.30677
$974$	−1.59712	+	2.76629i	−0.0511750	+	0.0886377i
$975$		0			0
$976$	−15.6428	−	27.0941i	−0.500714	−	0.867261i
$977$	−21.0633	−	36.4827i	−0.673874	−	1.16718i	−0.976797	−	0.214169i	$-0.931296\pi$
$977$	−21.0633	−	36.4827i	−0.673874	−	1.16718i	0.302923	−	0.953015i	$-0.402038\pi$
$978$		0			0
$979$	9.39226	−	16.2679i	0.300178	−	0.519924i
$980$	−16.1211			−0.514971
$981$		0			0
$982$	−2.93608			−0.0936939
$983$	10.2131	−	17.6896i	0.325746	−	0.564209i	−0.655917	−	0.754833i	$-0.727718\pi$
$983$	10.2131	−	17.6896i	0.325746	−	0.564209i	0.981663	+	0.190624i	$0.0610511\pi$
$984$		0			0
$985$	13.8214	+	23.9393i	0.440385	+	0.762770i
$986$	−2.61915	−	4.53649i	−0.0834106	−	0.144471i
$987$		0			0
$988$	0.461142	−	0.798721i	0.0146709	−	0.0254107i
$989$	−36.3445			−1.15569
$990$		0			0
$991$	0.0680712			0.00216235			0.00108118	−	0.999999i	$-0.499656\pi$
$991$	0.0680712			0.00216235			0.00108118	+	0.999999i	$0.499656\pi$
$992$	6.66329	−	11.5412i	0.211560	−	0.366432i
$993$		0			0
$994$	1.28982	+	2.23404i	0.0409107	+	0.0708595i
$995$	19.3998	+	33.6014i	0.615014	+	1.06524i
$996$		0			0
$997$	−5.32305	+	9.21980i	−0.168583	+	0.291994i	−0.937922	−	0.346847i	$-0.887252\pi$
$997$	−5.32305	+	9.21980i	−0.168583	+	0.291994i	0.769339	+	0.638841i	$0.220586\pi$
$998$	−4.26319			−0.134949
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.a.487.4		12
3.2	odd	2		729.2.c.d.487.3		12
9.2	odd	6		729.2.a.b.1.4	✓	6
9.4	even	3	inner	729.2.c.a.244.4		12
9.5	odd	6		729.2.c.d.244.3		12
9.7	even	3		729.2.a.e.1.3	yes	6
27.2	odd	18		729.2.e.j.325.2		12
27.4	even	9		729.2.e.k.163.2		12
27.5	odd	18		729.2.e.j.406.2		12
27.7	even	9		729.2.e.l.82.1		12
27.11	odd	18		729.2.e.t.568.1		12
27.13	even	9		729.2.e.l.649.1		12
27.14	odd	18		729.2.e.s.649.2		12
27.16	even	9		729.2.e.k.568.2		12
27.20	odd	18		729.2.e.s.82.2		12
27.22	even	9		729.2.e.u.406.1		12
27.23	odd	18		729.2.e.t.163.1		12
27.25	even	9		729.2.e.u.325.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.4	✓	6	9.2	odd	6
729.2.a.e.1.3	yes	6	9.7	even	3
729.2.c.a.244.4		12	9.4	even	3	inner
729.2.c.a.487.4		12	1.1	even	1	trivial
729.2.c.d.244.3		12	9.5	odd	6
729.2.c.d.487.3		12	3.2	odd	2
729.2.e.j.325.2		12	27.2	odd	18
729.2.e.j.406.2		12	27.5	odd	18
729.2.e.k.163.2		12	27.4	even	9
729.2.e.k.568.2		12	27.16	even	9
729.2.e.l.82.1		12	27.7	even	9
729.2.e.l.649.1		12	27.13	even	9
729.2.e.s.82.2		12	27.20	odd	18
729.2.e.s.649.2		12	27.14	odd	18
729.2.e.t.163.1		12	27.23	odd	18
729.2.e.t.568.1		12	27.11	odd	18
729.2.e.u.325.1		12	27.25	even	9
729.2.e.u.406.1		12	27.22	even	9

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0864880 - 0.149802i) q^{2} +(0.985040 + 1.70614i) q^{4} +(-1.86828 - 3.23596i) q^{5} +(-1.51575 + 2.62535i) q^{7} +0.686728 q^{8} +O(q^{10})\)	\(q+(0.0864880 - 0.149802i) q^{2} +(0.985040 + 1.70614i) q^{4} +(-1.86828 - 3.23596i) q^{5} +(-1.51575 + 2.62535i) q^{7} +0.686728 q^{8} -0.646335 q^{10} +(-1.24585 + 2.15787i) q^{11} +(0.382569 + 0.662630i) q^{13} +(0.262188 + 0.454123i) q^{14} +(-1.91069 + 3.30940i) q^{16} -4.62278 q^{17} -0.611844 q^{19} +(3.68066 - 6.37509i) q^{20} +(0.215502 + 0.373260i) q^{22} +(3.26219 + 5.65028i) q^{23} +(-4.48095 + 7.76123i) q^{25} +0.132351 q^{26} -5.97229 q^{28} +(-3.27545 + 5.67324i) q^{29} +(-3.27521 - 5.67283i) q^{31} +(1.01723 + 1.76190i) q^{32} +(-0.399815 + 0.692500i) q^{34} +11.3274 q^{35} +4.95969 q^{37} +(-0.0529171 + 0.0916552i) q^{38} +(-1.28300 - 2.22222i) q^{40} +(2.63012 + 4.55550i) q^{41} +(-2.78529 + 4.82426i) q^{43} -4.90884 q^{44} +1.12856 q^{46} +(0.553808 - 0.959223i) q^{47} +(-1.09499 - 1.89658i) q^{49} +(0.775096 + 1.34251i) q^{50} +(-0.753692 + 1.30543i) q^{52} -8.84310 q^{53} +9.31038 q^{55} +(-1.04091 + 1.80290i) q^{56} +(0.566573 + 0.981334i) q^{58} +(-5.92588 - 10.2639i) q^{59} +(-4.09350 + 7.09015i) q^{61} -1.13307 q^{62} -7.29083 q^{64} +(1.42949 - 2.47596i) q^{65} +(0.606169 + 1.04992i) q^{67} +(-4.55362 - 7.88711i) q^{68} +(0.979682 - 1.69686i) q^{70} +4.91946 q^{71} +4.29945 q^{73} +(0.428953 - 0.742969i) q^{74} +(-0.602691 - 1.04389i) q^{76} +(-3.77679 - 6.54158i) q^{77} +(5.89730 - 10.2144i) q^{79} +14.2788 q^{80} +0.909895 q^{82} +(4.50804 - 7.80815i) q^{83} +(8.63666 + 14.9591i) q^{85} +(0.481788 + 0.834481i) q^{86} +(-0.855559 + 1.48187i) q^{88} -7.53885 q^{89} -2.31952 q^{91} +(-6.42677 + 11.1315i) q^{92} +(-0.0957954 - 0.165923i) q^{94} +(1.14310 + 1.97990i) q^{95} +(0.474177 - 0.821299i) q^{97} -0.378814 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8	\( 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 15 q^{16} - 18 q^{17} + 24 q^{19} + 21 q^{20} - 3 q^{22} + 12 q^{23} - 9 q^{25} + 48 q^{26} + 6 q^{28} - 21 q^{29} - 15 q^{31} + 60 q^{35} + 6 q^{37} - 15 q^{38} - 3 q^{40} + 12 q^{41} - 6 q^{43} - 66 q^{44} - 6 q^{46} + 15 q^{47} - 12 q^{49} + 24 q^{50} - 3 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} + 15 q^{58} - 6 q^{59} - 24 q^{61} - 60 q^{62} + 12 q^{64} + 15 q^{65} - 15 q^{67} - 36 q^{68} + 15 q^{70} + 24 q^{73} - 24 q^{74} - 9 q^{76} - 15 q^{77} - 24 q^{79} - 42 q^{80} - 42 q^{82} + 6 q^{83} + 18 q^{85} + 30 q^{86} + 21 q^{88} - 18 q^{89} + 36 q^{91} - 6 q^{92} + 6 q^{94} + 33 q^{95} + 21 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^13 - 24 * q^14 - 15 * q^16 - 18 * q^17 + 24 * q^19 + 21 * q^20 - 3 * q^22 + 12 * q^23 - 9 * q^25 + 48 * q^26 + 6 * q^28 - 21 * q^29 - 15 * q^31 + 60 * q^35 + 6 * q^37 - 15 * q^38 - 3 * q^40 + 12 * q^41 - 6 * q^43 - 66 * q^44 - 6 * q^46 + 15 * q^47 - 12 * q^49 + 24 * q^50 - 3 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 + 15 * q^58 - 6 * q^59 - 24 * q^61 - 60 * q^62 + 12 * q^64 + 15 * q^65 - 15 * q^67 - 36 * q^68 + 15 * q^70 + 24 * q^73 - 24 * q^74 - 9 * q^76 - 15 * q^77 - 24 * q^79 - 42 * q^80 - 42 * q^82 + 6 * q^83 + 18 * q^85 + 30 * q^86 + 21 * q^88 - 18 * q^89 + 36 * q^91 - 6 * q^92 + 6 * q^94 + 33 * q^95 + 21 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more