LMFDB - Embedded newform 729.2.i.a.10.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(10,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(162))

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

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

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

chi := DirichletCharacter("729.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, 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:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			10.13
Character	$\chi$	$=$	729.10
Dual form			729.2.i.a.73.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.172340 + 0.0269534i) q^{2} +(-1.87552 - 0.601362i) q^{4} +(3.61353 + 1.64255i) q^{5} +(-0.239963 - 1.75684i) q^{7} +(-0.618779 - 0.310762i) q^{8} +O(q^{10})$	\(q+(0.172340 + 0.0269534i) q^{2} +(-1.87552 - 0.601362i) q^{4} +(3.61353 + 1.64255i) q^{5} +(-0.239963 - 1.75684i) q^{7} +(-0.618779 - 0.310762i) q^{8} +(0.578482 + 0.380474i) q^{10} +(2.47725 - 0.192547i) q^{11} +(-2.01751 - 5.89640i) q^{13} +(0.00599773 - 0.309241i) q^{14} +(3.10644 + 2.22035i) q^{16} +(0.176605 - 0.409417i) q^{17} +(0.151680 - 0.203742i) q^{19} +(-5.78949 - 5.25368i) q^{20} +(0.432118 + 0.0335868i) q^{22} +(1.85192 + 1.43535i) q^{23} +(7.07202 + 8.10364i) q^{25} +(-0.188769 - 1.07056i) q^{26} +(-0.606441 + 3.43930i) q^{28} +(-1.33639 + 0.806516i) q^{29} +(7.13954 - 0.277047i) q^{31} +(1.46421 + 1.43609i) q^{32} +(0.0414713 - 0.0657986i) q^{34} +(2.01859 - 6.74255i) q^{35} +(-0.487313 + 0.516522i) q^{37} +(0.0316321 - 0.0310245i) q^{38} +(-1.72553 - 2.13933i) q^{40} +(2.87367 - 7.44299i) q^{41} +(-2.22695 - 8.64553i) q^{43} +(-4.76192 - 1.12860i) q^{44} +(0.280472 + 0.297283i) q^{46} +(8.95827 + 0.347622i) q^{47} +(3.71469 - 1.03405i) q^{49} +(1.00037 + 1.58719i) q^{50} +(0.238017 + 12.2721i) q^{52} +(-12.1664 + 4.42821i) q^{53} +(9.26787 + 3.37323i) q^{55} +(-0.397476 + 1.16167i) q^{56} +(-0.252052 + 0.102974i) q^{58} +(2.27902 + 4.76617i) q^{59} +(1.91821 - 0.615051i) q^{61} +(1.23789 + 0.144689i) q^{62} +(-4.34670 - 5.83863i) q^{64} +(2.39480 - 24.6207i) q^{65} +(3.75857 + 2.26831i) q^{67} +(-0.577434 + 0.661666i) q^{68} +(0.529617 - 1.10760i) q^{70} +(0.190370 - 3.26853i) q^{71} +(-11.5763 + 7.61387i) q^{73} +(-0.0979054 + 0.0758824i) q^{74} +(-0.407002 + 0.290908i) q^{76} +(-0.932722 - 4.30592i) q^{77} +(8.50403 - 10.5433i) q^{79} +(7.57817 + 13.1258i) q^{80} +(0.695861 - 1.20527i) q^{82} +(0.695186 + 1.80058i) q^{83} +(1.31066 - 1.18936i) q^{85} +(-0.150764 - 1.54999i) q^{86} +(-1.59270 - 0.650691i) q^{88} +(0.669466 + 11.4943i) q^{89} +(-9.87491 + 4.95936i) q^{91} +(-2.61016 - 3.80570i) q^{92} +(1.53450 + 0.301365i) q^{94} +(0.882758 - 0.487085i) q^{95} +(1.84689 - 0.839514i) q^{97} +(0.668060 - 0.0780850i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{81}\right)$

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 $

$2$	0.172340	+	0.0269534i	0.121863	+	0.0190590i	0.215156	−	0.976580i	$-0.430974\pi$
$2$	0.172340	+	0.0269534i	0.121863	+	0.0190590i	−0.0932934	+	0.995639i	$0.529739\pi$
$3$		0			0
$3$		0			0
$4$	−1.87552	−	0.601362i	−0.937761	−	0.300681i
$5$	3.61353	+	1.64255i	1.61602	+	0.734571i	0.998642	−	0.0520956i	$-0.0165901\pi$
$5$	3.61353	+	1.64255i	1.61602	+	0.734571i	0.617378	+	0.786667i	$0.288195\pi$
$6$		0			0
$7$	−0.239963	−	1.75684i	−0.0906975	−	0.664023i	−0.978866	−	0.204505i	$-0.934442\pi$
$7$	−0.239963	−	1.75684i	−0.0906975	−	0.664023i	0.888168	−	0.459519i	$-0.151978\pi$
$8$	−0.618779	−	0.310762i	−0.218771	−	0.109871i
$9$		0			0
$10$	0.578482	+	0.380474i	0.182932	+	0.120316i
$11$	2.47725	−	0.192547i	0.746918	−	0.0580551i	0.301609	−	0.953432i	$-0.402476\pi$
$11$	2.47725	−	0.192547i	0.746918	−	0.0580551i	0.445309	+	0.895377i	$0.353094\pi$
$12$		0			0
$13$	−2.01751	−	5.89640i	−0.559557	−	1.63537i	−0.755793	−	0.654810i	$-0.772748\pi$
$13$	−2.01751	−	5.89640i	−0.559557	−	1.63537i	0.196236	−	0.980557i	$-0.437128\pi$
$14$	0.00599773	−	0.309241i	0.00160296	−	0.0826482i
$15$		0			0
$16$	3.10644	+	2.22035i	0.776609	+	0.555087i
$17$	0.176605	−	0.409417i	0.0428330	−	0.0992981i	−0.895456	−	0.445149i	$-0.853151\pi$
$17$	0.176605	−	0.409417i	0.0428330	−	0.0992981i	0.938289	+	0.345851i	$0.112410\pi$
$18$		0			0
$19$	0.151680	−	0.203742i	0.0347978	−	0.0467416i	−0.784384	−	0.620276i	$-0.787021\pi$
$19$	0.151680	−	0.203742i	0.0347978	−	0.0467416i	0.819182	+	0.573534i	$0.194428\pi$
$20$	−5.78949	−	5.25368i	−1.29457	−	1.17476i
$21$		0			0
$22$	0.432118	+	0.0335868i	0.0921278	+	0.00716074i
$23$	1.85192	+	1.43535i	0.386153	+	0.299291i	0.787118	−	0.616802i	$-0.211572\pi$
$23$	1.85192	+	1.43535i	0.386153	+	0.299291i	−0.400965	+	0.916093i	$0.631325\pi$
$24$		0			0
$25$	7.07202	+	8.10364i	1.41440	+	1.62073i
$26$	−0.188769	−	1.07056i	−0.0370207	−	0.209955i
$27$		0			0
$28$	−0.606441	+	3.43930i	−0.114607	+	0.649966i
$29$	−1.33639	+	0.806516i	−0.248162	+	0.149766i	−0.635325	−	0.772245i	$-0.719134\pi$
$29$	−1.33639	+	0.806516i	−0.248162	+	0.149766i	0.387164	+	0.922011i	$0.373455\pi$
$30$		0			0
$31$	7.13954	−	0.277047i	1.28230	−	0.0497591i	0.611409	−	0.791315i	$-0.290603\pi$
$31$	7.13954	−	0.277047i	1.28230	−	0.0497591i	0.670891	+	0.741556i	$0.265912\pi$
$32$	1.46421	+	1.43609i	0.258838	+	0.253867i
$33$		0			0
$34$	0.0414713	−	0.0657986i	0.00711226	−	0.0112844i
$35$	2.01859	−	6.74255i	0.341203	−	1.13970i
$36$		0			0
$37$	−0.487313	+	0.516522i	−0.0801138	+	0.0849156i	−0.766190	−	0.642614i	$-0.777850\pi$
$37$	−0.487313	+	0.516522i	−0.0801138	+	0.0849156i	0.686077	+	0.727529i	$0.259331\pi$
$38$	0.0316321	−	0.0310245i	0.00513140	−	0.00503284i
$39$		0			0
$40$	−1.72553	−	2.13933i	−0.272831	−	0.338257i
$41$	2.87367	−	7.44299i	0.448792	−	1.16240i	−0.505316	−	0.862934i	$-0.668624\pi$
$41$	2.87367	−	7.44299i	0.448792	−	1.16240i	0.954107	−	0.299465i	$-0.0968081\pi$
$42$		0			0
$43$	−2.22695	−	8.64553i	−0.339606	−	1.31843i	−0.879179	−	0.476492i	$-0.841908\pi$
$43$	−2.22695	−	8.64553i	−0.339606	−	1.31843i	0.539573	−	0.841939i	$-0.318586\pi$
$44$	−4.76192	−	1.12860i	−0.717886	−	0.170142i
$45$		0			0
$46$	0.280472	+	0.297283i	0.0413534	+	0.0438320i
$47$	8.95827	+	0.347622i	1.30670	+	0.0507058i	0.682688	−	0.730710i	$-0.260811\pi$
$47$	8.95827	+	0.347622i	1.30670	+	0.0507058i	0.624011	+	0.781416i	$0.285502\pi$
$48$		0			0
$49$	3.71469	−	1.03405i	0.530670	−	0.147722i
$50$	1.00037	+	1.58719i	0.141474	+	0.224463i
$51$		0			0
$52$	0.238017	+	12.2721i	0.0330070	+	1.70183i
$53$	−12.1664	+	4.42821i	−1.67118	+	0.608261i	−0.992060	−	0.125763i	$-0.959862\pi$
$53$	−12.1664	+	4.42821i	−1.67118	+	0.608261i	−0.679123	+	0.734024i	$0.737640\pi$
$54$		0			0
$55$	9.26787	+	3.37323i	1.24968	+	0.454846i
$56$	−0.397476	+	1.16167i	−0.0531150	+	0.155234i
$57$		0			0
$58$	−0.252052	+	0.102974i	−0.0330960	+	0.0135212i
$59$	2.27902	+	4.76617i	0.296703	+	0.620503i	0.995494	−	0.0948236i	$-0.0302287\pi$
$59$	2.27902	+	4.76617i	0.296703	+	0.620503i	−0.698791	+	0.715326i	$0.746278\pi$
$60$		0			0
$61$	1.91821	−	0.615051i	0.245602	−	0.0787492i	−0.179975	−	0.983671i	$-0.557602\pi$
$61$	1.91821	−	0.615051i	0.245602	−	0.0787492i	0.425578	+	0.904922i	$0.360071\pi$
$62$	1.23789	+	0.144689i	0.157213	+	0.0183755i
$63$		0			0
$64$	−4.34670	−	5.83863i	−0.543338	−	0.729829i
$65$	2.39480	−	24.6207i	0.297038	−	3.05382i
$66$		0			0
$67$	3.75857	+	2.26831i	0.459183	+	0.277118i	0.727366	−	0.686250i	$-0.240744\pi$
$67$	3.75857	+	2.26831i	0.459183	+	0.277118i	−0.268183	+	0.963368i	$0.586423\pi$
$68$	−0.577434	+	0.661666i	−0.0700242	+	0.0802388i
$69$		0			0
$70$	0.529617	−	1.10760i	0.0633014	−	0.132384i
$71$	0.190370	−	3.26853i	0.0225928	−	0.387904i	−0.967990	−	0.250989i	$-0.919244\pi$
$71$	0.190370	−	3.26853i	0.0225928	−	0.387904i	0.990583	−	0.136915i	$-0.0437187\pi$
$72$		0			0
$73$	−11.5763	+	7.61387i	−1.35491	+	0.891137i	−0.999057	−	0.0434064i	$-0.986179\pi$
$73$	−11.5763	+	7.61387i	−1.35491	+	0.891137i	−0.355850	+	0.934543i	$0.615809\pi$
$74$	−0.0979054	+	0.0758824i	−0.0113813	+	0.00882115i
$75$		0			0
$76$	−0.407002	+	0.290908i	−0.0466864	+	0.0333694i
$77$	−0.932722	−	4.30592i	−0.106294	−	0.490705i
$78$		0			0
$79$	8.50403	−	10.5433i	0.956779	−	1.18622i	−0.0256671	−	0.999671i	$-0.508171\pi$
$79$	8.50403	−	10.5433i	0.956779	−	1.18622i	0.982446	−	0.186549i	$-0.0597302\pi$
$80$	7.57817	+	13.1258i	0.847265	+	1.46751i
$81$		0			0
$82$	0.695861	−	1.20527i	0.0768450	−	0.133099i
$83$	0.695186	+	1.80058i	0.0763066	+	0.197639i	0.965788	−	0.259332i	$-0.0835023\pi$
$83$	0.695186	+	1.80058i	0.0763066	+	0.197639i	−0.889482	+	0.456971i	$0.848934\pi$
$84$		0			0
$85$	1.31066	−	1.18936i	0.142161	−	0.129004i
$86$	−0.150764	−	1.54999i	−0.0162573	−	0.167140i
$87$		0			0
$88$	−1.59270	−	0.650691i	−0.169783	−	0.0693639i
$89$	0.669466	+	11.4943i	0.0709633	+	1.21839i	0.826367	+	0.563133i	$0.190404\pi$
$89$	0.669466	+	11.4943i	0.0709633	+	1.21839i	−0.755403	+	0.655260i	$0.772559\pi$
$90$		0			0
$91$	−9.87491	+	4.95936i	−1.03517	+	0.519883i
$92$	−2.61016	−	3.80570i	−0.272128	−	0.396772i
$93$		0			0
$94$	1.53450	+	0.301365i	0.158271	+	0.0310834i
$95$	0.882758	−	0.487085i	0.0905691	−	0.0499739i
$96$		0			0
$97$	1.84689	−	0.839514i	0.187523	−	0.0852398i	−0.317848	−	0.948142i	$-0.602960\pi$
$97$	1.84689	−	0.839514i	0.187523	−	0.0852398i	0.505372	+	0.862902i	$0.331355\pi$
$98$	0.668060	−	0.0780850i	0.0674842	−	0.00788777i
$99$		0			0
$100$	−8.39051	−	19.4514i	−0.839051	−	1.94514i
$101$	−0.843492	+	3.89399i	−0.0839306	+	0.387467i	−0.999905	−	0.0137696i	$-0.995617\pi$
$101$	−0.843492	+	3.89399i	−0.0839306	+	0.387467i	0.915975	+	0.401236i	$0.131419\pi$
$102$		0			0
$103$	−8.11677	+	11.8345i	−0.799769	+	1.16609i	0.183336	+	0.983050i	$0.441310\pi$
$103$	−8.11677	+	11.8345i	−0.799769	+	1.16609i	−0.983105	+	0.183041i	$0.941406\pi$
$104$	−0.583986	+	4.27553i	−0.0572646	+	0.419251i
$105$		0			0
$106$	−2.21611	+	0.435230i	−0.215248	+	0.0422732i
$107$	−10.0621	+	8.44307i	−0.972736	+	0.816222i	−0.982978	−	0.183725i	$-0.941184\pi$
$107$	−10.0621	+	8.44307i	−0.972736	+	0.816222i	0.0102420	+	0.999948i	$0.496740\pi$
$108$		0			0
$109$	−4.44337	−	3.72843i	−0.425598	−	0.357119i	0.404690	−	0.914454i	$-0.367380\pi$
$109$	−4.44337	−	3.72843i	−0.425598	−	0.357119i	−0.830288	+	0.557335i	$0.811824\pi$
$110$	1.50630	+	0.831142i	0.143620	+	0.0792463i
$111$		0			0
$112$	3.15537	−	5.99031i	0.298154	−	0.566031i
$113$	−2.62806	+	10.2028i	−0.247227	+	0.959796i	0.717503	+	0.696556i	$0.245285\pi$
$113$	−2.62806	+	10.2028i	−0.247227	+	0.959796i	−0.964730	+	0.263240i	$0.915209\pi$
$114$		0			0
$115$	4.33435	+	8.22856i	0.404180	+	0.767317i
$116$	2.99144	−	0.708984i	0.277748	−	0.0658275i
$117$		0			0
$118$	0.264301	+	0.882828i	0.0243309	+	0.0812709i
$119$	−0.761659	−	0.212022i	−0.0698211	−	0.0194360i
$120$		0			0
$121$	−4.76821	+	0.745735i	−0.433474	+	0.0677941i
$122$	0.347162	−	0.0542952i	0.0314306	−	0.00491566i
$123$		0			0
$124$	−13.5570	−	3.77384i	−1.21745	−	0.338901i
$125$	6.55224	+	21.8860i	0.586050	+	1.95754i
$126$		0			0
$127$	−11.0268	+	2.61340i	−0.978471	+	0.231902i	−0.688582	−	0.725158i	$-0.741767\pi$
$127$	−11.0268	+	2.61340i	−0.978471	+	0.231902i	−0.289889	+	0.957060i	$0.593618\pi$
$128$	−2.50337	−	4.75253i	−0.221269	−	0.420068i
$129$		0			0
$130$	1.07633	−	4.17857i	0.0944005	−	0.366485i
$131$	3.03312	−	5.75823i	0.265005	−	0.503099i	−0.715746	−	0.698360i	$-0.753913\pi$
$131$	3.03312	−	5.75823i	0.265005	−	0.503099i	0.980751	+	0.195261i	$0.0625554\pi$
$132$		0			0
$133$	−0.394340	−	0.217588i	−0.0341936	−	0.0188672i
$134$	0.586613	+	0.492226i	0.0506756	+	0.0425219i
$135$		0			0
$136$	−0.236511	+	0.198456i	−0.0202806	+	0.0170175i
$137$	−18.1184	+	3.55833i	−1.54796	+	0.304009i	−0.892438	−	0.451169i	$-0.851007\pi$
$137$	−18.1184	+	3.55833i	−1.54796	+	0.304009i	−0.655519	+	0.755178i	$0.727550\pi$
$138$		0			0
$139$	1.24780	−	9.13549i	0.105837	−	0.774862i	−0.858993	−	0.511987i	$-0.828910\pi$
$139$	1.24780	−	9.13549i	0.105837	−	0.774862i	0.964830	−	0.262875i	$-0.0846707\pi$
$140$	−7.84061	+	11.4319i	−0.662653	+	0.966171i
$141$		0			0
$142$	0.120907	−	0.558167i	0.0101463	−	0.0468403i
$143$	−6.13321	−	14.2184i	−0.512885	−	1.18900i
$144$		0			0
$145$	−6.15383	+	0.719280i	−0.511048	+	0.0597330i
$146$	−2.20028	+	1.00015i	−0.182097	+	0.0827731i
$147$		0			0
$148$	1.22458	−	0.675696i	0.100660	−	0.0555419i
$149$	−17.3304	−	3.40358i	−1.41976	−	0.278832i	−0.576835	−	0.816861i	$-0.695712\pi$
$149$	−17.3304	−	3.40358i	−1.41976	−	0.278832i	−0.842927	+	0.538029i	$0.819169\pi$
$150$		0			0
$151$	10.8254	+	15.7839i	0.880963	+	1.28447i	0.957801	+	0.287431i	$0.0928013\pi$
$151$	10.8254	+	15.7839i	0.880963	+	1.28447i	−0.0768386	+	0.997044i	$0.524483\pi$
$152$	−0.157172	+	0.0789347i	−0.0127483	+	0.00640245i
$153$		0			0
$154$	−0.0446856	−	0.767221i	−0.00360086	−	0.0618245i
$155$	26.2540	+	10.7259i	2.10877	+	0.861529i
$156$		0			0
$157$	0.000263734		0.00271142i	2.10482e−5		0.000216395i	0.995313	−	0.0967027i	$-0.0308296\pi$
$157$	0.000263734		0.00271142i	2.10482e−5		0.000216395i	−0.995292	+	0.0969191i	$0.969101\pi$
$158$	1.74976	−	1.58782i	0.139204	−	0.126321i
$159$		0			0
$160$	2.93212	+	7.59439i	0.231805	+	0.600389i
$161$	2.07729	−	3.59796i	0.163713	−	0.283559i
$162$		0			0
$163$	2.53449	+	4.38987i	0.198517	+	0.343841i	0.948048	−	0.318128i	$-0.103054\pi$
$163$	2.53449	+	4.38987i	0.198517	+	0.343841i	−0.749531	+	0.661969i	$0.769721\pi$
$164$	−9.86555	+	12.2314i	−0.770370	+	0.955109i
$165$		0			0
$166$	0.0712764	+	0.329049i	0.00553212	+	0.0255391i
$167$	18.3087	−	13.0862i	1.41677	−	1.01264i	0.422426	−	0.906397i	$-0.361179\pi$
$167$	18.3087	−	13.0862i	1.41677	−	1.01264i	0.994340	−	0.106246i	$-0.0338832\pi$
$168$		0			0
$169$	−20.4221	+	15.8283i	−1.57093	+	1.21756i
$170$	0.257935	−	0.169647i	0.0197827	−	0.0130113i
$171$		0			0
$172$	−1.02241	+	17.5541i	−0.0779579	+	1.33849i
$173$	−7.77822	+	16.2668i	−0.591367	+	1.23674i	0.361222	+	0.932480i	$0.382360\pi$
$173$	−7.77822	+	16.2668i	−0.591367	+	1.23674i	−0.952589	+	0.304260i	$0.901591\pi$
$174$		0			0
$175$	12.5398	−	14.3690i	0.947918	−	1.08619i
$176$	8.12293	+	4.90221i	0.612289	+	0.369518i
$177$		0			0
$178$	−0.194435	+	1.99897i	−0.0145735	+	0.149829i
$179$	−4.33614	−	5.82445i	−0.324099	−	0.435340i	0.609975	−	0.792421i	$-0.291180\pi$
$179$	−4.33614	−	5.82445i	−0.324099	−	0.435340i	−0.934074	+	0.357081i	$0.883772\pi$
$180$		0			0
$181$	−6.77130	−	0.791451i	−0.503306	−	0.0588281i	−0.139348	−	0.990243i	$-0.544501\pi$
$181$	−6.77130	−	0.791451i	−0.503306	−	0.0588281i	−0.363958	+	0.931415i	$0.618575\pi$
$182$	−1.83551	+	0.588533i	−0.136057	+	0.0436249i
$183$		0			0
$184$	−0.699879	−	1.46367i	−0.0515957	−	0.107903i
$185$	−2.60933	+	1.06603i	−0.191842	+	0.0783761i
$186$		0			0
$187$	0.358663	−	1.04823i	0.0262280	−	0.0766542i
$188$	−16.5924	−	6.03913i	−1.21012	−	0.440449i
$189$		0			0
$190$	0.165263	−	0.0601508i	0.0119894	−	0.00436379i
$191$	−0.172105	−	8.87367i	−0.0124531	−	0.642076i	−0.953094	−	0.302674i	$-0.902121\pi$
$191$	−0.172105	−	8.87367i	−0.0124531	−	0.642076i	0.940641	−	0.339403i	$-0.110225\pi$
$192$		0			0
$193$	−5.41189	−	8.58655i	−0.389556	−	0.618073i	0.592743	−	0.805392i	$-0.298045\pi$
$193$	−5.41189	−	8.58655i	−0.389556	−	0.618073i	−0.982299	+	0.187318i	$0.940020\pi$
$194$	0.340920	−	0.0949016i	0.0244766	−	0.00681354i
$195$		0			0
$196$	−7.58882	−	0.294481i	−0.542059	−	0.0210343i
$197$	9.93884	+	10.5346i	0.708113	+	0.750556i	0.977145	−	0.212575i	$-0.0681851\pi$
$197$	9.93884	+	10.5346i	0.708113	+	0.750556i	−0.269032	+	0.963131i	$0.586704\pi$
$198$		0			0
$199$	10.8744	+	2.57729i	0.770868	+	0.182699i	0.597186	−	0.802103i	$-0.296285\pi$
$199$	10.8744	+	2.57729i	0.770868	+	0.182699i	0.173682	+	0.984802i	$0.444434\pi$
$200$	−1.85771	−	7.21208i	−0.131360	−	0.509971i
$201$		0			0
$202$	−0.250323	+	0.648354i	−0.0176127	+	0.0456180i
$203$	1.73760	+	2.15429i	0.121956	+	0.151202i
$204$		0			0
$205$	22.6096	−	22.1753i	1.57912	−	1.54879i
$206$	−1.71782	+	1.82079i	−0.119686	+	0.126860i
$207$		0			0
$208$	6.82478	−	22.7964i	0.473214	−	1.58064i
$209$	0.336520	−	0.533925i	0.0232775	−	0.0369323i
$210$		0			0
$211$	1.97368	+	1.93577i	0.135874	+	0.133264i	0.764977	−	0.644058i	$-0.222751\pi$
$211$	1.97368	+	1.93577i	0.135874	+	0.133264i	−0.629103	+	0.777322i	$0.716578\pi$
$212$	25.4813	−	0.988790i	1.75006	−	0.0679104i
$213$		0			0
$214$	−1.96166	+	1.18387i	−0.134096	+	0.0809276i
$215$	6.15359	−	34.8988i	0.419672	−	2.38008i
$216$		0			0
$217$	−2.19995	−	12.4766i	−0.149343	−	0.846964i
$218$	−0.665276	−	0.762321i	−0.0450581	−	0.0516309i
$219$		0			0
$220$	−15.3536	−	11.8999i	−1.03514	−	0.802292i
$221$	−2.77039	−	0.215332i	−0.186356	−	0.0144848i
$222$		0			0
$223$	−13.4955	−	12.2466i	−0.903729	−	0.820090i	0.0805430	−	0.996751i	$-0.474335\pi$
$223$	−13.4955	−	12.2466i	−0.903729	−	0.820090i	−0.984272	+	0.176661i	$0.943470\pi$
$224$	2.17162	−	2.91699i	0.145097	−	0.194900i
$225$		0			0
$226$	−0.727919	+	1.68751i	−0.0484205	+	0.112251i
$227$	−13.0618	−	9.33601i	−0.866942	−	0.619653i	0.0586070	−	0.998281i	$-0.481334\pi$
$227$	−13.0618	−	9.33601i	−0.866942	−	0.619653i	−0.925549	+	0.378628i	$0.876396\pi$
$228$		0			0
$229$	−0.129079	+	6.65526i	−0.00852976	+	0.439792i	0.971066	+	0.238813i	$0.0767581\pi$
$229$	−0.129079	+	6.65526i	−0.00852976	+	0.439792i	−0.979595	+	0.200979i	$0.935588\pi$
$230$	0.525192	+	1.53493i	0.0346301	+	0.101210i
$231$		0			0
$232$	1.07757	−	0.0837550i	0.0707457	−	0.00549879i
$233$	−2.13674	−	1.40535i	−0.139982	−	0.0920678i	0.477586	−	0.878585i	$-0.341512\pi$
$233$	−2.13674	−	1.40535i	−0.139982	−	0.0920678i	−0.617569	+	0.786517i	$0.711882\pi$
$234$		0			0
$235$	31.8000	+	15.9706i	2.07440	+	1.04180i
$236$	−1.40816	−	10.3096i	−0.0916636	−	0.671096i
$237$		0			0
$238$	−0.125549	−	0.0570691i	−0.00813815	−	0.00369924i
$239$	−7.88090	−	2.52691i	−0.509773	−	0.163452i	0.0392986	−	0.999228i	$-0.487488\pi$
$239$	−7.88090	−	2.52691i	−0.509773	−	0.163452i	−0.549071	+	0.835775i	$0.685019\pi$
$240$		0			0
$241$	1.04597	+	0.163587i	0.0673769	+	0.0105376i	0.188117	−	0.982147i	$-0.439761\pi$
$241$	1.04597	+	0.163587i	0.0673769	+	0.0105376i	−0.120740	+	0.992684i	$0.538527\pi$
$242$	−0.841852			−0.0541163
$243$		0			0
$244$	−3.96752			−0.253995
$245$	15.1216	+	2.36498i	0.966086	+	0.151093i
$246$		0			0
$247$	−1.50736	−	0.483316i	−0.0959111	−	0.0307526i
$248$	−4.50389	−	2.04727i	−0.285998	−	0.130002i
$249$		0			0
$250$	0.539308	+	3.94843i	0.0341088	+	0.249721i
$251$	0.0338418	+	0.0169960i	0.00213608	+	0.00107278i	0.449867	−	0.893096i	$-0.351471\pi$
$251$	0.0338418	+	0.0169960i	0.00213608	+	0.00107278i	−0.447731	+	0.894168i	$0.647768\pi$
$252$		0			0
$253$	4.86404	+	3.19913i	0.305800	+	0.201128i
$254$	−1.97080	+	0.153182i	−0.123659	+	0.00961152i
$255$		0			0
$256$	4.40957	+	12.8874i	0.275598	+	0.805465i
$257$	−0.462516	+	23.8472i	−0.0288509	+	1.48755i	0.653725	+	0.756732i	$0.273205\pi$
$257$	−0.462516	+	23.8472i	−0.0288509	+	1.48755i	−0.682576	+	0.730815i	$0.739140\pi$
$258$		0			0
$259$	1.02438	+	0.732185i	0.0636521	+	0.0454958i
$260$	−19.2974	+	44.7365i	−1.19678	+	2.77444i
$261$		0			0
$262$	0.677931	−	0.910619i	0.0418827	−	0.0562582i
$263$	3.84840	+	3.49223i	0.237302	+	0.215340i	0.781977	−	0.623307i	$-0.214211\pi$
$263$	3.84840	+	3.49223i	0.237302	+	0.215340i	−0.544675	+	0.838647i	$0.683347\pi$
$264$		0			0
$265$	−51.2372	−	3.98247i	−3.14748	−	0.244641i
$266$	−0.0620957	−	0.0481278i	−0.00380733	−	0.00295090i
$267$		0			0
$268$	−5.68521	−	6.51453i	−0.347279	−	0.397938i
$269$	−4.75230	−	26.9517i	−0.289753	−	1.64327i	−0.687796	−	0.725904i	$-0.741421\pi$
$269$	−4.75230	−	26.9517i	−0.289753	−	1.64327i	0.398043	−	0.917367i	$-0.369690\pi$
$270$		0			0
$271$	−4.27031	+	24.2181i	−0.259403	+	1.47115i	0.525111	+	0.851034i	$0.324024\pi$
$271$	−4.27031	+	24.2181i	−0.259403	+	1.47115i	−0.784514	+	0.620112i	$0.787087\pi$
$272$	1.45766	−	0.879702i	0.0883836	−	0.0533398i
$273$		0			0
$274$	−3.21842	+	0.124890i	−0.194432	+	0.00754485i
$275$	19.0795	+	18.7130i	1.15054	+	1.12844i
$276$		0			0
$277$	−1.83251	+	2.90747i	−0.110105	+	0.174693i	−0.896518	−	0.443008i	$-0.853911\pi$
$277$	−1.83251	+	2.90747i	−0.110105	+	0.174693i	0.786413	+	0.617701i	$0.211936\pi$
$278$	0.461278	−	1.54078i	0.0276656	−	0.0924096i
$279$		0			0
$280$	−3.34439	+	3.54485i	−0.199866	+	0.211845i
$281$	−8.25038	+	8.09191i	−0.492176	+	0.482723i	−0.903392	−	0.428815i	$-0.858931\pi$
$281$	−8.25038	+	8.09191i	−0.492176	+	0.482723i	0.411216	+	0.911538i	$0.365104\pi$
$282$		0			0
$283$	14.4781	+	17.9500i	0.860631	+	1.06702i	0.997080	+	0.0763682i	$0.0243325\pi$
$283$	14.4781	+	17.9500i	0.860631	+	1.06702i	−0.136448	+	0.990647i	$0.543569\pi$
$284$	−2.32262	+	6.01572i	−0.137822	+	0.356968i
$285$		0			0
$286$	−0.673761	−	2.61570i	−0.0398403	−	0.154670i
$287$	−13.7657	−	3.26253i	−0.812564	−	0.192581i
$288$		0			0
$289$	11.5297	+	12.2207i	0.678216	+	0.718867i
$290$	−1.07994	−	0.0419065i	−0.0634161	−	0.00246083i
$291$		0			0
$292$	26.2904	−	7.31842i	1.53853	−	0.428278i
$293$	−0.209085	−	0.331737i	−0.0122149	−	0.0193803i	0.839823	−	0.542860i	$-0.182658\pi$
$293$	−0.209085	−	0.331737i	−0.0122149	−	0.0193803i	−0.852038	+	0.523479i	$0.824634\pi$
$294$		0			0
$295$	0.406637	+	20.9661i	0.0236753	+	1.22069i
$296$	0.462055	−	0.168174i	0.0268564	−	0.00977492i
$297$		0			0
$298$	−2.89498	−	1.05369i	−0.167701	−	0.0610384i
$299$	4.72711	−	13.8155i	0.273376	−	0.798972i
$300$		0			0
$301$	−14.6544	+	5.98700i	−0.844668	+	0.345085i
$302$	1.44022	+	3.01197i	0.0828756	+	0.173320i
$303$		0			0
$304$	0.923563	−	0.296129i	0.0529700	−	0.0169841i
$305$	7.94178	+	0.928261i	0.454745	+	0.0531521i
$306$		0			0
$307$	5.99188	+	8.04850i	0.341975	+	0.459352i	0.939525	−	0.342479i	$-0.111267\pi$
$307$	5.99188	+	8.04850i	0.341975	+	0.459352i	−0.597551	+	0.801831i	$0.703859\pi$
$308$	−0.840078	+	8.63675i	−0.0478679	+	0.492125i
$309$		0			0
$310$	4.23551	+	2.55614i	0.240561	+	0.145179i
$311$	−2.38164	+	2.72906i	−0.135051	+	0.154751i	−0.816978	−	0.576669i	$-0.804352\pi$
$311$	−2.38164	+	2.72906i	−0.135051	+	0.154751i	0.681927	+	0.731420i	$0.261142\pi$
$312$		0			0
$313$	3.24250	−	6.78112i	0.183277	−	0.383292i	−0.789938	−	0.613186i	$-0.789888\pi$
$313$	3.24250	−	6.78112i	0.183277	−	0.383292i	0.973216	+	0.229895i	$0.0738382\pi$
$314$	−2.76303e−5	0	0.000474394i	−1.55927e−6	0	2.67716e-5i
$315$		0			0
$316$	−22.2899	+	14.6603i	−1.25390	+	0.824705i
$317$	11.3961	−	8.83266i	0.640070	−	0.496092i	−0.240101	−	0.970748i	$-0.577181\pi$
$317$	11.3961	−	8.83266i	0.640070	−	0.496092i	0.880171	+	0.474656i	$0.157428\pi$
$318$		0			0
$319$	−3.15528	+	2.25526i	−0.176662	+	0.126270i
$320$	−6.11668	−	28.2378i	−0.341933	−	1.57854i
$321$		0			0
$322$	0.454976	−	0.564082i	0.0253548	−	0.0314351i
$323$	−0.0566279	−	0.0980823i	−0.00315086	−	0.00545745i
$324$		0			0
$325$	33.5144	−	58.0486i	1.85904	−	3.21996i
$326$	0.318472	+	0.824862i	0.0176385	+	0.0456849i
$327$		0			0
$328$	−4.09117	+	3.71254i	−0.225897	+	0.204990i
$329$	−1.53894	−	15.8217i	−0.0848444	−	0.872277i
$330$		0			0
$331$	1.00299	+	0.409767i	0.0551294	+	0.0225228i	0.405597	−	0.914052i	$-0.367064\pi$
$331$	1.00299	+	0.409767i	0.0551294	+	0.0225228i	−0.350467	+	0.936575i	$0.613977\pi$
$332$	−0.221038	−	3.79508i	−0.0121310	−	0.208282i
$333$		0			0
$334$	3.50803	−	1.76180i	0.191951	−	0.0964012i
$335$	9.85590	+	14.3703i	0.538486	+	0.785131i
$336$		0			0
$337$	22.0367	+	4.32787i	1.20042	+	0.235754i	0.752665	−	0.658404i	$-0.228768\pi$
$337$	22.0367	+	4.32787i	1.20042	+	0.235754i	0.447751	+	0.894158i	$0.352225\pi$
$338$	−3.94616	+	2.17740i	−0.214643	+	0.118435i
$339$		0			0
$340$	−3.17340	+	1.44249i	−0.172102	+	0.0782298i
$341$	17.6331	−	2.06101i	0.954884	−	0.111610i
$342$		0			0
$343$	−7.62423	−	17.6749i	−0.411670	−	0.954357i
$344$	−1.30872	+	6.04173i	−0.0705615	+	0.325748i
$345$		0			0
$346$	−1.77894	+	2.59376i	−0.0956365	+	0.139441i
$347$	3.43196	−	25.1264i	0.184237	−	1.34886i	−0.633713	−	0.773568i	$-0.718470\pi$
$347$	3.43196	−	25.1264i	0.184237	−	1.34886i	0.817950	−	0.575289i	$-0.195110\pi$
$348$		0			0
$349$	6.22130	−	1.22182i	0.333018	−	0.0654027i	−0.0234083	−	0.999726i	$-0.507452\pi$
$349$	6.22130	−	1.22182i	0.333018	−	0.0654027i	0.356427	+	0.934323i	$0.383995\pi$
$350$	2.54839	−	2.13836i	0.136217	−	0.114300i
$351$		0			0
$352$	3.90372	+	3.27561i	0.208069	+	0.174591i
$353$	−10.1334	−	5.59138i	−0.539347	−	0.297599i	0.189953	−	0.981793i	$-0.439167\pi$
$353$	−10.1334	−	5.59138i	−0.539347	−	0.297599i	−0.729300	+	0.684194i	$0.760154\pi$
$354$		0			0
$355$	6.05664	−	11.4983i	0.321453	−	0.610264i
$356$	5.65663	−	21.9604i	0.299801	−	1.16390i
$357$		0			0
$358$	−0.590301	−	1.12066i	−0.0311984	−	0.0592286i
$359$	0.697874	−	0.165399i	0.0368324	−	0.00872944i	−0.212158	−	0.977235i	$-0.568049\pi$
$359$	0.697874	−	0.165399i	0.0368324	−	0.00872944i	0.248991	+	0.968506i	$0.419901\pi$
$360$		0			0
$361$	5.43076	+	18.1400i	0.285829	+	0.954736i
$362$	−1.14563	−	0.318908i	−0.0602130	−	0.0167614i
$363$		0			0
$364$	21.5030	−	3.36300i	1.12706	−	0.176269i
$365$	−54.3376	+	8.49825i	−2.84416	+	0.444819i
$366$		0			0
$367$	16.9014	+	4.70484i	0.882248	+	0.245591i	0.679531	−	0.733647i	$-0.262183\pi$
$367$	16.9014	+	4.70484i	0.882248	+	0.245591i	0.202717	+	0.979237i	$0.435023\pi$
$368$	2.56591	+	8.57073i	0.133757	+	0.446780i
$369$		0			0
$370$	−0.478425	+	0.113389i	−0.0248721	+	0.00589480i
$371$	10.6991	+	20.3118i	0.555472	+	1.05454i
$372$		0			0
$373$	0.892322	−	3.46421i	0.0462027	−	0.179370i	−0.941127	−	0.338054i	$-0.890231\pi$
$373$	0.892322	−	3.46421i	0.0462027	−	0.179370i	0.987329	+	0.158684i	$0.0507252\pi$
$374$	0.0900652	−	0.170985i	0.00465716	−	0.00884140i
$375$		0			0
$376$	−5.43516	−	2.99900i	−0.280297	−	0.154661i
$377$	7.45173	+	6.25274i	0.383783	+	0.322033i
$378$		0			0
$379$	−20.8871	+	17.5264i	−1.07290	+	0.900268i	−0.995312	−	0.0967171i	$-0.969166\pi$
$379$	−20.8871	+	17.5264i	−1.07290	+	0.900268i	−0.0775863	+	0.996986i	$0.524721\pi$
$380$	−1.94855	+	0.382682i	−0.0999583	+	0.0196312i
$381$		0			0
$382$	0.209515	−	1.53392i	0.0107197	−	0.0784824i
$383$	−16.5310	+	24.1028i	−0.844694	+	1.23159i	0.126180	+	0.992007i	$0.459728\pi$
$383$	−16.5310	+	24.1028i	−0.844694	+	1.23159i	−0.970875	+	0.239587i	$0.922988\pi$
$384$		0			0
$385$	3.70228	−	17.0916i	0.188686	−	0.871070i
$386$	−0.701246	−	1.62567i	−0.0356925	−	0.0827445i
$387$		0			0
$388$	−3.96873	+	0.463878i	−0.201482	+	0.0235498i
$389$	27.8628	−	12.6652i	1.41270	−	0.642152i	0.445297	−	0.895383i	$-0.353098\pi$
$389$	27.8628	−	12.6652i	1.41270	−	0.642152i	0.967406	+	0.253231i	$0.0814933\pi$
$390$		0			0
$391$	0.914715	−	0.504718i	0.0462591	−	0.0255247i
$392$	−2.61992	−	0.514535i	−0.132326	−	0.0259879i
$393$		0			0
$394$	1.42891	+	2.08341i	0.0719876	+	0.104961i
$395$	48.0476	−	24.1304i	2.41754	−	1.21413i
$396$		0			0
$397$	−1.60485	−	27.5542i	−0.0805450	−	1.38290i	−0.760351	−	0.649513i	$-0.774973\pi$
$397$	−1.60485	−	27.5542i	−0.0805450	−	1.38290i	0.679806	−	0.733392i	$-0.262064\pi$
$398$	1.80463	+	0.737272i	0.0904579	+	0.0369561i
$399$		0			0
$400$	3.97589	+	40.8758i	0.198795	+	2.04379i
$401$	4.57338	−	4.15012i	0.228384	−	0.207247i	−0.549779	−	0.835310i	$-0.685288\pi$
$401$	4.57338	−	4.15012i	0.228384	−	0.207247i	0.778162	+	0.628063i	$0.216152\pi$
$402$		0			0
$403$	−16.0377	−	41.5387i	−0.798894	−	2.06919i
$404$	3.92368	−	6.79602i	0.195211	−	0.338115i
$405$		0			0
$406$	0.241393	+	0.418104i	0.0119801	+	0.0207502i
$407$	−1.10774	+	1.37338i	−0.0549086	+	0.0680760i
$408$		0			0
$409$	−2.42335	−	11.1874i	−0.119827	−	0.553182i	−0.997292	−	0.0735420i	$-0.976570\pi$
$409$	−2.42335	−	11.1874i	−0.119827	−	0.553182i	0.877465	−	0.479640i	$-0.159233\pi$
$410$	4.49423	−	3.21228i	0.221954	−	0.158643i
$411$		0			0
$412$	22.3400	−	17.3148i	1.10061	−	0.853039i
$413$	7.82652	−	5.14758i	0.385118	−	0.253296i
$414$		0			0
$415$	−0.445464	+	7.64832i	−0.0218670	+	0.375441i
$416$	5.51368	−	11.5309i	0.270331	−	0.565348i
$417$		0			0
$418$	0.0723868	−	0.0829461i	0.00354055	−	0.00405702i
$419$	12.1631	+	7.34046i	0.594206	+	0.358605i	0.781694	−	0.623662i	$-0.214356\pi$
$419$	12.1631	+	7.34046i	0.594206	+	0.358605i	−0.187488	+	0.982267i	$0.560035\pi$
$420$		0			0
$421$	2.00654	−	20.6290i	0.0977928	−	1.00540i	−0.810127	−	0.586254i	$-0.800602\pi$
$421$	2.00654	−	20.6290i	0.0977928	−	1.00540i	0.907920	−	0.419144i	$-0.137670\pi$
$422$	0.287967	+	0.386807i	0.0140180	+	0.0188295i
$423$		0			0
$424$	8.90443	+	1.04078i	0.432438	+	0.0505447i
$425$	4.56672	−	1.46426i	0.221518	−	0.0710270i
$426$		0			0
$427$	−1.54085	−	3.22241i	−0.0745668	−	0.155943i
$428$	23.9489	−	9.78422i	1.15762	−	0.472938i
$429$		0			0
$430$	2.00115	−	5.84858i	0.0965040	−	0.282044i
$431$	2.93489	+	1.06821i	0.141369	+	0.0514540i	0.411735	−	0.911303i	$-0.364923\pi$
$431$	2.93489	+	1.06821i	0.141369	+	0.0514540i	−0.270367	+	0.962757i	$0.587145\pi$
$432$		0			0
$433$	28.4450	−	10.3531i	1.36698	−	0.497540i	0.448774	−	0.893645i	$-0.351861\pi$
$433$	28.4450	−	10.3531i	1.36698	−	0.497540i	0.918205	+	0.396105i	$0.129638\pi$
$434$	−0.0428532	−	2.20950i	−0.00205702	−	0.106059i
$435$		0			0
$436$	6.09151	+	9.66483i	0.291730	+	0.462862i
$437$	0.573341	−	0.159600i	0.0274266	−	0.00763472i
$438$		0			0
$439$	−16.0842	−	0.624139i	−0.767655	−	0.0297885i	−0.348027	−	0.937484i	$-0.613148\pi$
$439$	−16.0842	−	0.624139i	−0.767655	−	0.0297885i	−0.419628	+	0.907696i	$0.637840\pi$
$440$	−4.68649	−	4.96739i	−0.223420	−	0.236811i
$441$		0			0
$442$	−0.471644	−	0.111782i	−0.0224338	−	0.00531691i
$443$	−2.00521	−	7.78469i	−0.0952702	−	0.369862i	0.902933	−	0.429781i	$-0.141409\pi$
$443$	−2.00521	−	7.78469i	−0.0952702	−	0.369862i	−0.998203	+	0.0599197i	$0.980916\pi$
$444$		0			0
$445$	−16.4608	+	42.6346i	−0.780318	+	2.02107i
$446$	−1.99573	−	2.47432i	−0.0945006	−	0.117162i
$447$		0			0
$448$	−9.21450	+	9.03752i	−0.435344	+	0.426982i
$449$	−2.52229	+	2.67347i	−0.119034	+	0.126169i	−0.784150	−	0.620571i	$-0.786901\pi$
$449$	−2.52229	+	2.67347i	−0.119034	+	0.126169i	0.665116	+	0.746740i	$0.268382\pi$
$450$		0			0
$451$	5.68566	−	18.9914i	0.267727	−	0.894271i
$452$	11.0645	−	17.5551i	0.520433	−	0.825722i
$453$		0			0
$454$	−1.99943	−	1.96102i	−0.0938378	−	0.0920355i
$455$	−43.8293	+	1.70078i	−2.05475	+	0.0797336i
$456$		0			0
$457$	−5.45102	+	3.28970i	−0.254988	+	0.153886i	−0.638432	−	0.769678i	$-0.720417\pi$
$457$	−5.45102	+	3.28970i	−0.254988	+	0.153886i	0.383444	+	0.923564i	$0.374738\pi$
$458$	−0.201627	+	1.14349i	−0.00942143	+	0.0534316i
$459$		0			0
$460$	−3.18082	−	18.0393i	−0.148307	−	0.841089i
$461$	9.41358	+	10.7868i	0.438434	+	0.502390i	0.929546	−	0.368707i	$-0.120199\pi$
$461$	9.41358	+	10.7868i	0.438434	+	0.502390i	−0.491112	+	0.871097i	$0.663409\pi$
$462$		0			0
$463$	12.0511	+	9.34032i	0.560063	+	0.434081i	0.852895	−	0.522083i	$-0.174845\pi$
$463$	12.0511	+	9.34032i	0.560063	+	0.434081i	−0.292832	+	0.956164i	$0.594598\pi$
$464$	−5.94216	−	0.461861i	−0.275858	−	0.0214414i
$465$		0			0
$466$	−0.330365	−	0.299790i	−0.0153039	−	0.0138875i
$467$	7.59189	−	10.1977i	0.351311	−	0.471892i	−0.590981	−	0.806686i	$-0.701259\pi$
$467$	7.59189	−	10.1977i	0.351311	−	0.471892i	0.942292	+	0.334794i	$0.108667\pi$
$468$		0			0
$469$	3.08314	−	7.14753i	0.142366	−	0.330042i
$470$	5.04994	+	3.60948i	0.232936	+	0.166493i
$471$		0			0
$472$	0.0709360	−	3.65744i	0.00326509	−	0.168347i
$473$	−7.18136	−	20.9883i	−0.330199	−	0.965044i
$474$		0			0
$475$	2.72374	−	0.211706i	0.124974	−	0.00971372i
$476$	1.30100	+	0.855684i	0.0596315	+	0.0392202i
$477$		0			0
$478$	−1.29008	−	0.647904i	−0.0590070	−	0.0296344i
$479$	3.87034	+	28.3359i	0.176840	+	1.29470i	0.838502	+	0.544898i	$0.183432\pi$
$479$	3.87034	+	28.3359i	0.176840	+	1.29470i	−0.661662	+	0.749803i	$0.730148\pi$
$480$		0			0
$481$	4.02878	+	1.83130i	0.183696	+	0.0835003i
$482$	0.175853	+	0.0563850i	0.00800989	+	0.00256827i
$483$		0			0
$484$	9.39134	+	1.46878i	0.426879	+	0.0667627i
$485$	8.05274			0.365656
$486$		0			0
$487$	0.819346			0.0371281			0.0185640	−	0.999828i	$-0.494091\pi$
$487$	0.819346			0.0371281			0.0185640	+	0.999828i	$0.494091\pi$
$488$	−1.37809	−	0.215529i	−0.0623830	−	0.00975652i
$489$		0			0
$490$	2.54231	+	0.815160i	0.114850	+	0.0368252i
$491$	−3.23681	−	1.47131i	−0.146075	−	0.0663993i	0.339439	−	0.940628i	$-0.389763\pi$
$491$	−3.23681	−	1.47131i	−0.146075	−	0.0663993i	−0.485514	+	0.874229i	$0.661368\pi$
$492$		0			0
$493$	0.0941877	+	0.689576i	0.00424200	+	0.0310569i
$494$	−0.246751	−	0.123923i	−0.0111019	−	0.00557556i
$495$		0			0
$496$	22.7937	+	14.9916i	1.02347	+	0.673144i
$497$	−5.78798	+	0.449877i	−0.259626	+	0.0201797i
$498$		0			0
$499$	0.565415	+	1.65249i	0.0253115	+	0.0739755i	0.958081	−	0.286499i	$-0.0924914\pi$
$499$	0.565415	+	1.65249i	0.0253115	+	0.0739755i	−0.932769	+	0.360474i	$0.882615\pi$
$500$	0.872540	−	44.9880i	0.0390212	−	2.01192i
$501$		0			0
$502$	0.00537419	+	0.00384124i	0.000239862	+	0.000171443i
$503$	−4.21004	+	9.75997i	−0.187716	+	0.435175i	−0.985921	−	0.167211i	$-0.946524\pi$
$503$	−4.21004	+	9.75997i	−0.187716	+	0.435175i	0.798205	+	0.602386i	$0.205783\pi$
$504$		0			0
$505$	−9.44406	+	12.6856i	−0.420255	+	0.564501i
$506$	0.752040	+	0.682440i	0.0334323	+	0.0303382i
$507$		0			0
$508$	22.2526	+	1.72961i	0.987300	+	0.0767390i
$509$	−5.63976	−	4.37114i	−0.249978	−	0.193748i	0.479903	−	0.877321i	$-0.340672\pi$
$509$	−5.63976	−	4.37114i	−0.249978	−	0.193748i	−0.729881	+	0.683574i	$0.760425\pi$
$510$		0			0
$511$	16.1543	+	18.5107i	0.714622	+	0.818866i
$512$	2.27810	+	12.9197i	0.100679	+	0.570977i
$513$		0			0
$514$	−0.722474	+	4.09735i	−0.0318669	+	0.180726i
$515$	−48.7690	+	29.4322i	−2.14902	+	1.29694i
$516$		0			0
$517$	22.2588	−	0.863742i	0.978940	−	0.0379873i
$518$	0.156807	+	0.153795i	0.00688970	+	0.00675737i
$519$		0			0
$520$	−9.13304	+	14.4905i	−0.400510	+	0.635453i
$521$	6.94966	−	23.2135i	0.304470	−	1.01700i	−0.659658	−	0.751566i	$-0.729299\pi$
$521$	6.94966	−	23.2135i	0.304470	−	1.01700i	0.964129	−	0.265436i	$-0.0855158\pi$
$522$		0			0
$523$	−1.11762	+	1.18461i	−0.0488702	+	0.0517994i	−0.751347	−	0.659907i	$-0.770596\pi$
$523$	−1.11762	+	1.18461i	−0.0488702	+	0.0517994i	0.702477	+	0.711706i	$0.252077\pi$
$524$	−9.15146	+	8.97569i	−0.399783	+	0.392105i
$525$		0			0
$526$	0.569104	+	0.705578i	0.0248141	+	0.0307647i
$527$	1.14745	−	2.97198i	0.0499838	−	0.129461i
$528$		0			0
$529$	−4.36775	−	16.9567i	−0.189902	−	0.737246i
$530$	−8.72286	−	2.06736i	−0.378897	−	0.0898002i
$531$		0			0
$532$	0.608744	+	0.645231i	0.0263924	+	0.0279743i
$533$	−49.6845	−	1.92798i	−2.15207	−	0.0835103i
$534$		0			0
$535$	−50.2277	+	13.9818i	−2.17153	+	0.604488i
$536$	−1.62082	−	2.57161i	−0.0700088	−	0.111076i
$537$		0			0
$538$	−0.0925709	−	4.77293i	−0.00399101	−	0.205776i
$539$	9.00310	−	3.27686i	0.387791	−	0.141144i
$540$		0			0
$541$	16.7526	+	6.09746i	0.720253	+	0.262150i	0.676033	−	0.736871i	$-0.263698\pi$
$541$	16.7526	+	6.09746i	0.720253	+	0.262150i	0.0442195	+	0.999022i	$0.485920\pi$
$542$	−1.38870	+	4.05864i	−0.0596500	+	0.174334i
$543$		0			0
$544$	0.846545	−	0.345852i	0.0362953	−	0.0148283i
$545$	−9.93213	−	20.7713i	−0.425446	−	0.889744i
$546$		0			0
$547$	−30.8212	+	9.88242i	−1.31782	+	0.422542i	−0.879338	−	0.476199i	$-0.842014\pi$
$547$	−30.8212	+	9.88242i	−1.31782	+	0.422542i	−0.438481	+	0.898740i	$0.644483\pi$
$548$	36.1213	+	4.22197i	1.54302	+	0.180354i
$549$		0			0
$550$	2.78377	+	3.73925i	0.118700	+	0.159442i
$551$	−0.0383830	+	0.394612i	−0.00163517	+	0.0168110i
$552$		0			0
$553$	−20.5636	−	12.4102i	−0.874455	−	0.527736i
$554$	−0.394181	+	0.451681i	−0.0167471	+	0.0191901i
$555$		0			0
$556$	−7.83401	+	16.3834i	−0.332236	+	0.694812i
$557$	−2.10640	+	36.1655i	−0.0892512	+	1.53238i	0.595351	+	0.803466i	$0.297013\pi$
$557$	−2.10640	+	36.1655i	−0.0892512	+	1.53238i	−0.684602	+	0.728917i	$0.740024\pi$
$558$		0			0
$559$	−46.4846	+	30.5734i	−1.96609	+	1.29312i
$560$	21.2414	−	16.4633i	0.897613	−	0.695703i
$561$		0			0
$562$	−1.63997	+	1.17218i	−0.0691780	+	0.0494455i
$563$	3.41754	+	15.7771i	0.144032	+	0.664926i	0.991064	+	0.133384i	$0.0425845\pi$
$563$	3.41754	+	15.7771i	0.144032	+	0.664926i	−0.847032	+	0.531541i	$0.821613\pi$
$564$		0			0
$565$	−26.2552	+	32.5513i	−1.10456	+	1.36944i
$566$	2.01133	+	3.48373i	0.0845425	+	0.146432i
$567$		0			0
$568$	−1.13353	+	1.96334i	−0.0475621	+	0.0823799i
$569$	6.32998	+	16.3951i	0.265367	+	0.687317i	0.999961	+	0.00881057i	$0.00280453\pi$
$569$	6.32998	+	16.3951i	0.265367	+	0.687317i	−0.734594	+	0.678506i	$0.762628\pi$
$570$		0			0
$571$	9.62320	−	8.73259i	0.402718	−	0.365447i	−0.445330	−	0.895367i	$-0.646914\pi$
$571$	9.62320	−	8.73259i	0.402718	−	0.365447i	0.848048	+	0.529919i	$0.177778\pi$
$572$	2.95258	+	30.3551i	0.123453	+	1.26921i
$573$		0			0
$574$	−2.28444	−	0.933297i	−0.0953508	−	0.0389551i
$575$	1.46529	+	25.1581i	0.0611070	+	1.04917i
$576$		0			0
$577$	29.9421	−	15.0375i	1.24651	−	0.626020i	0.301624	−	0.953427i	$-0.402471\pi$
$577$	29.9421	−	15.0375i	1.24651	−	0.626020i	0.944883	+	0.327407i	$0.106175\pi$
$578$	1.65763	+	2.41688i	0.0689483	+	0.100529i
$579$		0			0
$580$	11.9742	+	2.35166i	0.497201	+	0.0976472i
$581$	2.99651	−	1.65340i	0.124316	−	0.0685947i
$582$		0			0
$583$	−29.2865	+	13.3124i	−1.21292	+	0.551342i
$584$	9.52930	−	1.11382i	0.394325	−	0.0460900i
$585$		0			0
$586$	−0.0270923	−	0.0628069i	−0.00111917	−	0.00259453i
$587$	−7.11711	+	32.8562i	−0.293755	+	1.35612i	0.556980	+	0.830526i	$0.311960\pi$
$587$	−7.11711	+	32.8562i	−0.293755	+	1.35612i	−0.850734	+	0.525596i	$0.823842\pi$
$588$		0			0
$589$	1.02648	−	1.49665i	0.0422954	−	0.0616683i
$590$	−0.495029	+	3.62425i	−0.0203800	+	0.149208i
$591$		0			0
$592$	−2.66066	+	0.522537i	−0.109353	+	0.0214761i
$593$	−22.8590	+	19.1809i	−0.938705	+	0.787667i	−0.977359	−	0.211586i	$-0.932137\pi$
$593$	−22.8590	+	19.1809i	−0.938705	+	0.787667i	0.0386547	+	0.999253i	$0.487693\pi$
$594$		0			0
$595$	−2.40402	−	2.01721i	−0.0985552	−	0.0826976i
$596$	30.4567	+	16.8053i	1.24756	+	0.688373i
$597$		0			0
$598$	1.18704	−	2.25355i	0.0485419	−	0.0921545i
$599$	−5.87134	+	22.7939i	−0.239896	+	0.931335i	0.729129	+	0.684376i	$0.239925\pi$
$599$	−5.87134	+	22.7939i	−0.239896	+	0.931335i	−0.969026	+	0.246959i	$0.920569\pi$
$600$		0			0
$601$	−15.9233	−	30.2296i	−0.649524	−	1.23309i	−0.959329	−	0.282290i	$-0.908906\pi$
$601$	−15.9233	−	30.2296i	−0.649524	−	1.23309i	0.309806	−	0.950800i	$-0.399736\pi$
$602$	−2.68691	+	0.636810i	−0.109510	+	0.0259544i
$603$		0			0
$604$	−10.8115	−	36.1130i	−0.439915	−	1.46942i
$605$	−18.4550	−	5.13730i	−0.750302	−	0.208861i
$606$		0			0
$607$	−41.4020	+	6.47515i	−1.68045	+	0.262818i	−0.921515	−	0.388344i	$-0.873047\pi$
$607$	−41.4020	+	6.47515i	−1.68045	+	0.262818i	−0.758939	+	0.651162i	$0.774282\pi$
$608$	0.514683	−	0.0804950i	0.0208732	−	0.00326450i
$609$		0			0
$610$	1.34366	+	0.374034i	0.0544034	+	0.0151442i
$611$	−16.0237	−	53.5229i	−0.648250	−	2.16530i
$612$		0			0
$613$	−0.819618	+	0.194253i	−0.0331041	+	0.00784581i	−0.247135	−	0.968981i	$-0.579489\pi$
$613$	−0.819618	+	0.194253i	−0.0331041	+	0.00784581i	0.214030	+	0.976827i	$0.431341\pi$
$614$	0.815705	+	1.54858i	0.0329192	+	0.0624955i
$615$		0			0
$616$	−0.760971	+	2.95427i	−0.0306604	+	0.119031i
$617$	−7.70007	+	14.6182i	−0.309993	+	0.588508i	−0.989393	−	0.145260i	$-0.953598\pi$
$617$	−7.70007	+	14.6182i	−0.309993	+	0.588508i	0.679400	+	0.733768i	$0.262240\pi$
$618$		0			0
$619$	34.7440	+	19.1709i	1.39648	+	0.770544i	0.989724	−	0.142993i	$-0.0456726\pi$
$619$	34.7440	+	19.1709i	1.39648	+	0.770544i	0.406755	+	0.913537i	$0.366660\pi$
$620$	−42.7898	−	35.9049i	−1.71848	−	1.44198i
$621$		0			0
$622$	−0.484009	+	0.406132i	−0.0194070	+	0.0162844i
$623$	20.0330	−	3.93435i	0.802605	−	0.157626i
$624$		0			0
$625$	−4.99434	+	36.5650i	−0.199774	+	1.46260i
$626$	0.741586	−	1.08126i	0.0296397	−	0.0432158i
$627$		0			0
$628$	0.00113591	−	0.00524393i	4.53276e−5	−	0.000209255i
$629$	0.125411	+	0.290734i	0.00500045	+	0.0115923i
$630$		0			0
$631$	41.9203	−	4.89978i	1.66882	−	0.195057i	0.771436	−	0.636307i	$-0.219539\pi$
$631$	41.9203	−	4.89978i	1.66882	−	0.195057i	0.897384	+	0.441250i	$0.145465\pi$
$632$	−8.53859	+	3.88127i	−0.339647	+	0.154389i
$633$		0			0
$634$	2.20207	−	1.21505i	0.0874555	−	0.0482559i
$635$	−44.1384	−	8.66849i	−1.75158	−	0.343999i
$636$		0			0
$637$	−13.5916	−	19.8171i	−0.538520	−	0.785181i
$638$	−0.604567	+	0.303625i	−0.0239350	+	0.0120206i
$639$		0			0
$640$	−1.23973	−	21.2853i	−0.0490046	−	0.841377i
$641$	−8.27868	−	3.38221i	−0.326988	−	0.133589i	0.208761	−	0.977967i	$-0.433057\pi$
$641$	−8.27868	−	3.38221i	−0.326988	−	0.133589i	−0.535749	+	0.844377i	$0.679971\pi$
$642$		0			0
$643$	−0.318795	−	3.27750i	−0.0125721	−	0.129252i	0.986916	−	0.161233i	$-0.0515469\pi$
$643$	−0.318795	−	3.27750i	−0.0125721	−	0.129252i	−0.999488	+	0.0319805i	$0.989819\pi$
$644$	−6.05967	+	5.49886i	−0.238785	+	0.216685i
$645$		0			0
$646$	−0.00711557	−	0.0184298i	−0.000279958	−	0.000725110i
$647$	−0.584702	+	1.01273i	−0.0229870	+	0.0398147i	−0.877290	−	0.479961i	$-0.840651\pi$
$647$	−0.584702	+	1.01273i	−0.0229870	+	0.0398147i	0.854303	+	0.519775i	$0.173984\pi$
$648$		0			0
$649$	6.56341	+	11.3682i	0.257636	+	0.446239i
$650$	7.34047	−	9.10076i	0.287917	−	0.356961i
$651$		0			0
$652$	−2.11360	−	9.75744i	−0.0827748	−	0.382131i
$653$	10.4435	−	7.46456i	0.408686	−	0.292111i	−0.358508	−	0.933527i	$-0.616714\pi$
$653$	10.4435	−	7.46456i	0.408686	−	0.292111i	0.767193	+	0.641416i	$0.221653\pi$
$654$		0			0
$655$	20.4185	−	15.8255i	0.797815	−	0.618354i
$656$	25.4529	−	16.7406i	0.993768	−	0.653611i
$657$		0			0
$658$	0.161228	−	2.76818i	0.00628533	−	0.107915i
$659$	3.04019	−	6.35802i	0.118429	−	0.247673i	−0.834413	−	0.551139i	$-0.814193\pi$
$659$	3.04019	−	6.35802i	0.118429	−	0.247673i	0.952842	+	0.303466i	$0.0981439\pi$
$660$		0			0
$661$	−16.3368	+	18.7198i	−0.635426	+	0.728118i	−0.977355	−	0.211608i	$-0.932130\pi$
$661$	−16.3368	+	18.7198i	−0.635426	+	0.728118i	0.341928	+	0.939726i	$0.388920\pi$
$662$	0.161811	+	0.0976532i	0.00628894	+	0.00379540i
$663$		0			0
$664$	0.129385	−	1.33020i	0.00502112	−	0.0516217i
$665$	−1.06756	−	1.43398i	−0.0413982	−	0.0556075i
$666$		0			0
$667$	−3.63253	−	0.424581i	−0.140652	−	0.0164399i
$668$	−42.2078	+	13.5334i	−1.63307	+	0.523623i
$669$		0			0
$670$	1.31124	+	2.74222i	0.0506574	+	0.105941i
$671$	4.63347	−	1.89298i	0.178873	−	0.0730776i
$672$		0			0
$673$	−2.38787	+	6.97882i	−0.0920457	+	0.269014i	−0.982561	−	0.185939i	$-0.940467\pi$
$673$	−2.38787	+	6.97882i	−0.0920457	+	0.269014i	0.890516	+	0.454953i	$0.150344\pi$
$674$	3.68115	+	1.33983i	0.141793	+	0.0516083i
$675$		0			0
$676$	47.8206	−	17.4053i	1.83925	−	0.669433i
$677$	0.722290	+	37.2411i	0.0277598	+	1.43129i	0.712075	+	0.702104i	$0.247756\pi$
$677$	0.722290	+	37.2411i	0.0277598	+	1.43129i	−0.684315	+	0.729187i	$0.739899\pi$
$678$		0			0
$679$	−1.91808	−	3.04324i	−0.0736091	−	0.116789i
$680$	−1.18061	+	0.328646i	−0.0452745	+	0.0126030i
$681$		0			0
$682$	3.09443	+	0.120078i	0.118492	+	0.00459802i
$683$	−7.33243	−	7.77192i	−0.280568	−	0.297384i	0.571730	−	0.820442i	$-0.306273\pi$
$683$	−7.33243	−	7.77192i	−0.280568	−	0.297384i	−0.852297	+	0.523058i	$0.824791\pi$
$684$		0			0
$685$	−71.3161	−	16.9022i	−2.72485	−	0.645801i
$686$	−0.837556	−	3.25159i	−0.0319780	−	0.124146i
$687$		0			0
$688$	12.2782	−	31.8014i	0.468103	−	1.21242i
$689$	50.6563	+	62.8040i	1.92985	+	2.39264i
$690$		0			0
$691$	22.7397	−	22.3029i	0.865058	−	0.848443i	−0.124553	−	0.992213i	$-0.539750\pi$
$691$	22.7397	−	22.3029i	0.865058	−	0.848443i	0.989611	+	0.143770i	$0.0459225\pi$
$692$	24.3704	−	25.8311i	0.926425	−	0.981953i
$693$		0			0
$694$	1.26871	−	4.23778i	0.0481595	−	0.160864i
$695$	19.5145	−	30.9618i	0.740226	−	1.17445i
$696$		0			0
$697$	−2.53978	−	2.49100i	−0.0962010	−	0.0943532i
$698$	1.10511	−	0.0428832i	0.0418290	−	0.00162315i
$699$		0			0
$700$	−32.1596	+	19.4084i	−1.21552	+	0.733569i
$701$	−0.866197	+	4.91245i	−0.0327158	+	0.185541i	−0.996786	−	0.0801057i	$-0.974474\pi$
$701$	−0.866197	+	4.91245i	−0.0327158	+	0.185541i	0.964071	+	0.265646i	$0.0855853\pi$
$702$		0			0
$703$	0.0313214	+	0.177632i	0.00118131	+	0.00669953i
$704$	−11.8921	−	13.6268i	−0.448199	−	0.513579i
$705$		0			0
$706$	−1.59568	−	1.23675i	−0.0600543	−	0.0465456i
$707$	7.04353	+	0.547466i	0.264899	+	0.0205896i
$708$		0			0
$709$	22.9152	+	20.7945i	0.860600	+	0.780952i	0.977221	−	0.212224i	$-0.0680706\pi$
$709$	22.9152	+	20.7945i	0.860600	+	0.780952i	−0.116622	+	0.993176i	$0.537206\pi$
$710$	1.35372	−	1.81836i	0.0508041	−	0.0682418i
$711$		0			0
$712$	3.15774	−	7.32047i	0.118341	−	0.274346i
$713$	13.6195	+	9.73467i	0.510056	+	0.364566i
$714$		0			0
$715$	1.19187	−	61.4526i	0.0445735	−	2.29820i
$716$	4.62993	+	13.5315i	0.173029	+	0.505695i
$717$		0			0
$718$	0.124730	−	0.00969474i	0.00465486	−	0.000361805i
$719$	−33.2272	−	21.8539i	−1.23917	−	0.815013i	−0.250940	−	0.968003i	$-0.580740\pi$
$719$	−33.2272	−	21.8539i	−1.23917	−	0.815013i	−0.988228	+	0.152990i	$0.951110\pi$
$720$		0			0
$721$	22.7391	+	11.4200i	0.846849	+	0.425304i
$722$	0.447000	+	3.27262i	0.0166356	+	0.121794i
$723$		0			0
$724$	12.2238	+	5.55638i	0.454293	+	0.206501i
$725$	−15.9867	−	5.12593i	−0.593731	−	0.190372i
$726$		0			0
$727$	−35.0870	−	5.48750i	−1.30130	−	0.203520i	−0.534372	−	0.845249i	$-0.679452\pi$
$727$	−35.0870	−	5.48750i	−1.30130	−	0.203520i	−0.766931	+	0.641729i	$0.778217\pi$
$728$	7.65157			0.283586
$729$		0			0
$730$	−9.59358			−0.355074
$731$	−3.93292	−	0.615097i	−0.145464	−	0.0227502i
$732$		0			0
$733$	−50.0361	−	16.0434i	−1.84812	−	0.592577i	−0.997798	−	0.0663213i	$-0.978874\pi$
$733$	−50.0361	−	16.0434i	−1.84812	−	0.592577i	−0.850326	−	0.526256i	$-0.823595\pi$
$734$	2.78598	+	1.26638i	0.102832	+	0.0467430i
$735$		0			0
$736$	0.650319	+	4.76118i	0.0239711	+	0.175499i
$737$	9.74767	+	4.89546i	0.359060	+	0.180327i
$738$		0			0
$739$	−19.0508	−	12.5299i	−0.700796	−	0.460921i	0.148449	−	0.988920i	$-0.452572\pi$
$739$	−19.0508	−	12.5299i	−0.700796	−	0.460921i	−0.849245	+	0.527999i	$0.822942\pi$
$740$	5.53493	−	0.430209i	0.203468	−	0.0158148i
$741$		0			0
$742$	1.29641	+	3.78891i	0.0475928	+	0.139095i
$743$	0.830654	−	42.8283i	0.0304737	−	1.57122i	−0.603183	−	0.797603i	$-0.706101\pi$
$743$	0.830654	−	42.8283i	0.0304737	−	1.57122i	0.633656	−	0.773615i	$-0.281553\pi$
$744$		0			0
$745$	−57.0334	−	40.7650i	−2.08954	−	1.49351i
$746$	0.247155	−	0.572969i	0.00904897	−	0.0209779i
$747$		0			0
$748$	−1.30305	+	1.75029i	−0.0476441	+	0.0639971i
$749$	17.2476	+	15.6514i	0.630215	+	0.571890i
$750$		0			0
$751$	19.7729	+	1.53687i	0.721522	+	0.0560811i	0.433002	−	0.901393i	$-0.357454\pi$
$751$	19.7729	+	1.53687i	0.721522	+	0.0560811i	0.288520	+	0.957474i	$0.406837\pi$
$752$	27.0565	+	20.9703i	0.986647	+	0.764709i
$753$		0			0
$754$	1.11570	+	1.27844i	0.0406312	+	0.0465582i
$755$	13.1922	+	74.8169i	0.480115	+	2.72287i
$756$		0			0
$757$	−1.33943	+	7.59626i	−0.0486822	+	0.276091i	−0.999426	−	0.0338884i	$-0.989211\pi$
$757$	−1.33943	+	7.59626i	−0.0486822	+	0.276091i	0.950743	+	0.309979i	$0.100322\pi$
$758$	−4.07207	+	2.45751i	−0.147904	+	0.0892607i
$759$		0			0
$760$	−0.697600	+	0.0270701i	−0.0253046	+	0.000981934i
$761$	35.7218	+	35.0357i	1.29491	+	1.27004i	0.942503	+	0.334199i	$0.108466\pi$
$761$	35.7218	+	35.0357i	1.29491	+	1.27004i	0.352412	+	0.935845i	$0.385362\pi$
$762$		0			0
$763$	−5.48402	+	8.70099i	−0.198535	+	0.314997i
$764$	−5.01350	+	16.7463i	−0.181382	+	0.605858i
$765$		0			0
$766$	−3.49860	+	3.70830i	−0.126410	+	0.133986i
$767$	23.5053	−	23.0538i	0.848727	−	0.832426i
$768$		0			0
$769$	−8.98138	−	11.1352i	−0.323877	−	0.401544i	0.590087	−	0.807339i	$-0.299093\pi$
$769$	−8.98138	−	11.1352i	−0.323877	−	0.401544i	−0.913964	+	0.405795i	$0.866995\pi$
$770$	1.09873	−	2.84578i	0.0395954	−	0.102555i
$771$		0			0
$772$	4.98649	+	19.3588i	0.179468	+	0.696737i
$773$	−14.0288	−	3.32488i	−0.504579	−	0.119587i	−0.0295602	−	0.999563i	$-0.509411\pi$
$773$	−14.0288	−	3.32488i	−0.504579	−	0.119587i	−0.475019	+	0.879976i	$0.657559\pi$
$774$		0			0
$775$	52.7361	+	55.8970i	1.89434	+	2.00788i
$776$	−1.40371	−	0.0544702i	−0.0503901	−	0.00195537i
$777$		0			0
$778$	5.14325	−	1.43172i	0.184394	−	0.0513297i
$779$	−1.08057	−	1.71444i	−0.0387154	−	0.0614262i
$780$		0			0
$781$	−0.157751	−	8.13362i	−0.00564479	−	0.291044i
$782$	0.171246	−	0.0623283i	0.00612373	−	0.00222885i
$783$		0			0
$784$	13.8354	+	5.03568i	0.494122	+	0.179846i
$785$	−0.00350064	+	0.0102310i	−0.000124943	+	0.000365160i
$786$		0			0
$787$	5.38829	−	2.20136i	0.192072	−	0.0784700i	−0.280123	−	0.959964i	$-0.590375\pi$
$787$	5.38829	−	2.20136i	0.192072	−	0.0784700i	0.472195	+	0.881494i	$0.343462\pi$
$788$	−12.3054	−	25.7346i	−0.438363	−	0.916758i
$789$		0			0
$790$	8.93090	−	2.86358i	0.317747	−	0.101882i
$791$	18.5553	+	2.16880i	0.659750	+	0.0771137i
$792$		0			0
$793$	−7.49661	−	10.0697i	−0.266212	−	0.357585i
$794$	0.466101	−	4.79193i	0.0165413	−	0.170059i
$795$		0			0
$796$	−18.8453	−	11.3732i	−0.667955	−	0.403113i
$797$	8.82763	−	10.1153i	0.312691	−	0.358304i	−0.575481	−	0.817815i	$-0.695185\pi$
$797$	8.82763	−	10.1153i	0.312691	−	0.358304i	0.888172	+	0.459511i	$0.151975\pi$
$798$		0			0
$799$	1.72440	−	3.60627i	0.0610049	−	0.127581i
$800$	−1.28260	+	22.0215i	−0.0453469	+	0.778576i
$801$		0			0
$802$	0.900035	−	0.591962i	0.0317813	−	0.0209029i
$803$	−27.2114	+	21.0904i	−0.960270	+	0.744265i
$804$		0			0
$805$	13.4162	−	9.58931i	0.472858	−	0.337979i
$806$	−1.64432	−	7.59103i	−0.0579187	−	0.267383i
$807$		0			0
$808$	1.73204	−	2.14739i	0.0609330	−	0.0755451i
$809$	−12.2313	−	21.1853i	−0.430030	−	0.744834i	0.566845	−	0.823824i	$-0.308164\pi$
$809$	−12.2313	−	21.1853i	−0.430030	−	0.744834i	−0.996875	+	0.0789900i	$0.974830\pi$
$810$		0			0
$811$	−18.0651	+	31.2897i	−0.634352	+	1.09873i	0.352300	+	0.935887i	$0.385400\pi$
$811$	−18.0651	+	31.2897i	−0.634352	+	1.09873i	−0.986652	+	0.162843i	$0.947934\pi$
$812$	−1.96341	−	5.08535i	−0.0689021	−	0.178461i
$813$		0			0
$814$	−0.227925	+	0.206831i	−0.00798876	+	0.00724942i
$815$	1.94788	+	20.0260i	0.0682313	+	0.701479i
$816$		0			0
$817$	−2.09924	−	0.857635i	−0.0734432	−	0.0300048i
$818$	−0.116100	−	1.99335i	−0.00405933	−	0.0696960i
$819$		0			0
$820$	−55.7401	+	27.9937i	−1.94653	+	0.977584i
$821$	14.3328	+	20.8977i	0.500218	+	0.729336i	0.989775	−	0.142635i	$-0.0455576\pi$
$821$	14.3328	+	20.8977i	0.500218	+	0.729336i	−0.489557	+	0.871971i	$0.662842\pi$
$822$		0			0
$823$	2.28925	+	0.449593i	0.0797981	+	0.0156718i	0.232452	−	0.972608i	$-0.425325\pi$
$823$	2.28925	+	0.449593i	0.0797981	+	0.0156718i	−0.152654	+	0.988280i	$0.548782\pi$
$824$	8.70021	−	4.80057i	0.303086	−	0.167236i
$825$		0			0
$826$	1.48757	−	0.676181i	0.0517590	−	0.0235274i
$827$	−23.5883	+	2.75707i	−0.820244	+	0.0958728i	−0.515856	−	0.856675i	$-0.672526\pi$
$827$	−23.5883	+	2.75707i	−0.820244	+	0.0958728i	−0.304388	+	0.952548i	$0.598452\pi$
$828$		0			0
$829$	−13.6218	−	31.5788i	−0.473104	−	1.09678i	−0.973023	−	0.230706i	$-0.925896\pi$
$829$	−13.6218	−	31.5788i	−0.473104	−	1.09678i	0.499920	−	0.866072i	$-0.333363\pi$
$830$	−0.282920	+	1.30610i	−0.00982028	+	0.0453355i
$831$		0			0
$832$	−25.6574	+	37.4094i	−0.889510	+	1.29694i
$833$	0.232674	−	1.70348i	0.00806168	−	0.0590219i
$834$		0			0
$835$	87.6537	−	17.2146i	3.03338	−	0.595737i
$836$	−0.952232	+	0.799017i	−0.0329336	+	0.0276346i
$837$		0			0
$838$	1.89833	+	1.59289i	0.0655768	+	0.0550255i
$839$	−4.28108	−	2.36220i	−0.147799	−	0.0815522i	0.407489	−	0.913210i	$-0.366404\pi$
$839$	−4.28108	−	2.36220i	−0.147799	−	0.0815522i	−0.555288	+	0.831658i	$0.687392\pi$
$840$		0			0
$841$	−12.3798	+	23.5024i	−0.426889	+	0.810429i
$842$	0.901830	−	3.50112i	0.0310791	−	0.120656i
$843$		0			0
$844$	−2.53758	−	4.81747i	−0.0873470	−	0.165824i
$845$	−99.7946	+	23.6517i	−3.43304	+	0.813645i
$846$		0			0
$847$	2.45433	+	8.19804i	0.0843318	+	0.281688i
$848$	−47.6263	−	13.2577i	−1.63549	−	0.455271i
$849$		0			0
$850$	0.826494	−	0.129261i	0.0283485	−	0.00443362i
$851$	−1.64385	+	0.257094i	−0.0563506	+	0.00881308i
$852$		0			0
$853$	−2.60451	−	0.725016i	−0.0891769	−	0.0248241i	0.223297	−	0.974751i	$-0.428318\pi$
$853$	−2.60451	−	0.725016i	−0.0891769	−	0.0248241i	−0.312474	+	0.949926i	$0.601158\pi$
$854$	−0.178694	−	0.596880i	−0.00611479	−	0.0204248i
$855$		0			0
$856$	8.84998	−	2.09748i	0.302486	−	0.0716905i
$857$	−26.4515	−	50.2169i	−0.903565	−	1.71538i	−0.668979	−	0.743281i	$-0.733269\pi$
$857$	−26.4515	−	50.2169i	−0.903565	−	1.71538i	−0.234586	−	0.972095i	$-0.575373\pi$
$858$		0			0
$859$	1.84703	−	7.17062i	0.0630199	−	0.244658i	−0.929122	−	0.369772i	$-0.879436\pi$
$859$	1.84703	−	7.17062i	0.0630199	−	0.244658i	0.992142	+	0.125114i	$0.0399296\pi$
$860$	−32.5280	+	61.7529i	−1.10919	+	2.10575i
$861$		0			0
$862$	0.477006	+	0.263201i	0.0162469	+	0.00896465i
$863$	−0.550643	−	0.462045i	−0.0187441	−	0.0157282i	0.633367	−	0.773851i	$-0.281672\pi$
$863$	−0.550643	−	0.462045i	−0.0187441	−	0.0157282i	−0.652112	+	0.758123i	$0.726117\pi$
$864$		0			0
$865$	−54.8258	+	46.0043i	−1.86413	+	1.56419i
$866$	5.18125	−	1.01757i	0.176066	−	0.0345783i
$867$		0			0
$868$	−3.37686	+	24.7230i	−0.114618	+	0.839154i
$869$	19.0365	−	27.7559i	0.645769	−	0.941554i
$870$		0			0
$871$	5.79190	−	26.7384i	0.196251	−	0.905996i
$872$	1.59081	+	3.68791i	0.0538716	+	0.124888i
$873$		0			0
$874$	0.103111	−	0.0120520i	0.00348779	−	0.000407664i
$875$	36.8779	−	16.7631i	1.24670	−	0.566696i
$876$		0			0
$877$	10.0285	−	5.53348i	0.338637	−	0.186852i	−0.304674	−	0.952457i	$-0.598548\pi$
$877$	10.0285	−	5.53348i	0.338637	−	0.186852i	0.643312	+	0.765604i	$0.277560\pi$
$878$	−2.75512	−	0.541087i	−0.0929807	−	0.0182608i
$879$		0			0
$880$	21.3003	+	31.0566i	0.718033	+	1.04692i
$881$	23.2184	−	11.6607i	0.782248	−	0.392860i	−0.0124053	−	0.999923i	$-0.503949\pi$
$881$	23.2184	−	11.6607i	0.782248	−	0.392860i	0.794654	+	0.607063i	$0.207653\pi$
$882$		0			0
$883$	−2.14964	−	36.9079i	−0.0723411	−	1.24205i	−0.817802	−	0.575500i	$-0.804808\pi$
$883$	−2.14964	−	36.9079i	−0.0723411	−	1.24205i	0.745461	−	0.666550i	$-0.232230\pi$
$884$	5.06643	+	2.06986i	0.170402	+	0.0696171i
$885$		0			0
$886$	−0.135753	−	1.39566i	−0.00456069	−	0.0468880i
$887$	11.9320	−	10.8277i	0.400636	−	0.363558i	−0.446637	−	0.894715i	$-0.647378\pi$
$887$	11.9320	−	10.8277i	0.400636	−	0.363558i	0.847273	+	0.531157i	$0.178243\pi$
$888$		0			0
$889$	7.23736	+	18.7452i	0.242733	+	0.628695i
$890$	−3.98600	+	6.90396i	−0.133611	+	0.231421i
$891$		0			0
$892$	17.9466	+	31.0844i	0.600896	+	1.04078i
$893$	1.42962	−	1.77245i	0.0478404	−	0.0593127i
$894$		0			0
$895$	−6.10183	−	28.1692i	−0.203962	−	0.941592i
$896$	−7.74872	+	5.53845i	−0.258867	+	0.185027i
$897$		0			0
$898$	−0.506750	+	0.392761i	−0.0169105	+	0.0131066i
$899$	−9.31778	+	6.12840i	−0.310765	+	0.204394i
$900$		0			0
$901$	−0.335667	+	5.76317i	−0.0111827	+	0.191999i
$902$	1.49175	−	3.11973i	0.0496698	−	0.103876i
$903$		0			0
$904$	4.79683	−	5.49656i	0.159540	−	0.182813i
$905$	−23.1683	−	13.9821i	−0.770140	−	0.464782i
$906$		0			0
$907$	−2.10813	+	21.6734i	−0.0699992	+	0.719654i	0.892983	+	0.450090i	$0.148608\pi$
$907$	−2.10813	+	21.6734i	−0.0699992	+	0.719654i	−0.962982	+	0.269564i	$0.913120\pi$
$908$	18.8834	+	25.3647i	0.626666	+	0.841759i
$909$		0			0
$910$	−7.59937	−	0.888238i	−0.251917	−	0.0294448i
$911$	45.8109	−	14.6887i	1.51778	−	0.486658i	0.574460	−	0.818533i	$-0.305212\pi$
$911$	45.8109	−	14.6887i	1.51778	−	0.486658i	0.943323	+	0.331875i	$0.107681\pi$
$912$		0			0
$913$	2.06884	+	4.32662i	0.0684687	+	0.143190i
$914$	−1.02810	+	0.420023i	−0.0340064	+	0.0138931i
$915$		0			0
$916$	4.24431	−	12.4045i	0.140236	−	0.409855i
$917$	−10.8441	−	3.94694i	−0.358105	−	0.130340i
$918$		0			0
$919$	6.31244	−	2.29754i	0.208228	−	0.0757888i	−0.235800	−	0.971802i	$-0.575771\pi$
$919$	6.31244	−	2.29754i	0.208228	−	0.0757888i	0.444028	+	0.896013i	$0.353549\pi$
$920$	−0.124877	−	6.43861i	−0.00411706	−	0.212275i
$921$		0			0
$922$	1.33159	+	2.11271i	0.0438537	+	0.0695786i
$923$	−19.6567	+	5.47180i	−0.647007	+	0.180107i
$924$		0			0
$925$	−7.63199	−	0.296156i	−0.250938	−	0.00973755i
$926$	1.82513	+	1.93453i	0.0599775	+	0.0635725i
$927$		0			0
$928$	−3.11499	−	0.738265i	−0.102254	−	0.0242347i
$929$	−5.85245	−	22.7206i	−0.192013	−	0.745439i	−0.989796	−	0.142494i	$-0.954488\pi$
$929$	−5.85245	−	22.7206i	−0.192013	−	0.745439i	0.797783	−	0.602945i	$-0.206006\pi$
$930$		0			0
$931$	0.352765	−	0.913684i	0.0115614	−	0.0299448i
$932$	3.16237	+	3.92072i	0.103587	+	0.128427i
$933$		0			0
$934$	1.58325	−	1.55284i	0.0518054	−	0.0508104i
$935$	3.01781	−	3.19869i	0.0986930	−	0.104608i
$936$		0			0
$937$	−7.27085	+	24.2863i	−0.237528	+	0.793400i	0.753229	+	0.657758i	$0.228495\pi$
$937$	−7.27085	+	24.2863i	−0.237528	+	0.793400i	−0.990758	+	0.135642i	$0.956690\pi$
$938$	0.723998	−	1.14870i	0.0236394	−	0.0375064i
$939$		0			0
$940$	−50.0375	−	49.0764i	−1.63204	−	1.60070i
$941$	−30.5584	+	1.18580i	−0.996175	+	0.0386561i	−0.531702	−	0.846931i	$-0.678448\pi$
$941$	−30.5584	+	1.18580i	−0.996175	+	0.0386561i	−0.464473	+	0.885587i	$0.653756\pi$
$942$		0			0
$943$	16.0051	−	9.65912i	0.521198	−	0.314544i
$944$	−3.50292	+	19.8660i	−0.114010	+	0.646584i
$945$		0			0
$946$	−0.671926	−	3.81068i	−0.0218462	−	0.123896i
$947$	−17.6931	−	20.2741i	−0.574950	−	0.658819i	0.390135	−	0.920758i	$-0.372428\pi$
$947$	−17.6931	−	20.2741i	−0.574950	−	0.658819i	−0.965085	+	0.261938i	$0.915638\pi$
$948$		0			0
$949$	68.2498	+	52.8976i	2.21548	+	1.71713i
$950$	0.475114	+	0.0369288i	0.0154147	+	0.00119813i
$951$		0			0
$952$	0.405410	+	0.367890i	0.0131394	+	0.0119234i
$953$	−2.35388	+	3.16181i	−0.0762496	+	0.102421i	−0.838612	−	0.544730i	$-0.816632\pi$
$953$	−2.35388	+	3.16181i	−0.0762496	+	0.102421i	0.762362	+	0.647151i	$0.224040\pi$
$954$		0			0
$955$	13.9536	−	32.3480i	0.451526	−	1.04676i
$956$	13.2612	+	9.47854i	0.428898	+	0.306558i
$957$		0			0
$958$	−0.0967367	+	4.98772i	−0.00312542	+	0.161146i
$959$	10.5992	+	30.9772i	0.342265	+	1.00031i
$960$		0			0
$961$	19.9895	−	1.55371i	0.644824	−	0.0501197i
$962$	0.644958	+	0.424196i	0.0207943	+	0.0136766i
$963$		0			0
$964$	−1.86337	−	0.935818i	−0.0600150	−	0.0301407i
$965$	−5.45219	−	39.9171i	−0.175512	−	1.28498i
$966$		0			0
$967$	36.9571	+	16.7991i	1.18846	+	0.540222i	0.907726	−	0.419563i	$-0.137817\pi$
$967$	36.9571	+	16.7991i	1.18846	+	0.540222i	0.280735	+	0.959785i	$0.409422\pi$
$968$	3.18222	+	1.02034i	0.102280	+	0.0327948i
$969$		0			0
$970$	1.38781	+	0.217049i	0.0445598	+	0.00696902i
$971$	18.1242			0.581633			0.290817	−	0.956779i	$-0.406073\pi$
$971$	18.1242			0.581633			0.290817	+	0.956779i	$0.406073\pi$
$972$		0			0
$973$	−16.3490			−0.524126
$974$	0.141206	+	0.0220842i	0.00452452	+	0.000707623i
$975$		0			0
$976$	7.32444	+	2.34849i	0.234450	+	0.0751732i
$977$	−52.6028	−	23.9109i	−1.68291	−	0.764977i	−0.999386	−	0.0350512i	$-0.988841\pi$
$977$	−52.6028	−	23.9109i	−1.68291	−	0.764977i	−0.683526	−	0.729926i	$-0.739555\pi$
$978$		0			0
$979$	3.87162	+	28.3453i	0.123738	+	0.905920i
$980$	−26.9387	−	13.5291i	−0.860526	−	0.432173i
$981$		0			0
$982$	−0.518174	−	0.340808i	−0.0165356	−	0.0108756i
$983$	−7.50233	+	0.583127i	−0.239287	+	0.0185989i	−0.196576	−	0.980489i	$-0.562982\pi$
$983$	−7.50233	+	0.583127i	−0.239287	+	0.0185989i	−0.0427112	+	0.999087i	$0.513600\pi$
$984$		0			0
$985$	18.6108	+	54.3920i	0.592988	+	1.73307i
$986$	−0.00235416	+	0.121380i	−7.49718e−5	+	0.00386552i
$987$		0			0
$988$	2.53644	+	1.81294i	0.0806949	+	0.0576772i
$989$	8.28522	−	19.2073i	0.263455	−	0.610757i
$990$		0			0
$991$	−6.87075	+	9.22902i	−0.218257	+	0.293169i	−0.897744	−	0.440518i	$-0.854795\pi$
$991$	−6.87075	+	9.22902i	−0.218257	+	0.293169i	0.679487	+	0.733687i	$0.262202\pi$
$992$	10.8517	+	9.84735i	0.344540	+	0.312654i
$993$		0			0
$994$	−1.00962	−	0.0784741i	−0.0320233	−	0.00248905i
$995$	35.0618	+	27.1749i	1.11153	+	0.861503i
$996$		0			0
$997$	0.0347315	+	0.0397978i	0.00109996	+	0.00126041i	0.753986	−	0.656891i	$-0.228129\pi$
$997$	0.0347315	+	0.0397978i	0.00109996	+	0.00126041i	−0.752886	+	0.658151i	$0.771339\pi$
$998$	0.0529032	+	0.300029i	0.00167462	+	0.00949726i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.10.13		1404
3.2	odd	2		243.2.i.a.13.14	✓	1404
243.56	odd	162		243.2.i.a.187.14	yes	1404
243.187	even	81	inner	729.2.i.a.73.13		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.13.14	✓	1404	3.2	odd	2
243.2.i.a.187.14	yes	1404	243.56	odd	162
729.2.i.a.10.13		1404	1.1	even	1	trivial
729.2.i.a.73.13		1404	243.187	even	81	inner

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.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.172340 + 0.0269534i) q^{2} +(-1.87552 - 0.601362i) q^{4} +(3.61353 + 1.64255i) q^{5} +(-0.239963 - 1.75684i) q^{7} +(-0.618779 - 0.310762i) q^{8} +O(q^{10})\)	\(q+(0.172340 + 0.0269534i) q^{2} +(-1.87552 - 0.601362i) q^{4} +(3.61353 + 1.64255i) q^{5} +(-0.239963 - 1.75684i) q^{7} +(-0.618779 - 0.310762i) q^{8} +(0.578482 + 0.380474i) q^{10} +(2.47725 - 0.192547i) q^{11} +(-2.01751 - 5.89640i) q^{13} +(0.00599773 - 0.309241i) q^{14} +(3.10644 + 2.22035i) q^{16} +(0.176605 - 0.409417i) q^{17} +(0.151680 - 0.203742i) q^{19} +(-5.78949 - 5.25368i) q^{20} +(0.432118 + 0.0335868i) q^{22} +(1.85192 + 1.43535i) q^{23} +(7.07202 + 8.10364i) q^{25} +(-0.188769 - 1.07056i) q^{26} +(-0.606441 + 3.43930i) q^{28} +(-1.33639 + 0.806516i) q^{29} +(7.13954 - 0.277047i) q^{31} +(1.46421 + 1.43609i) q^{32} +(0.0414713 - 0.0657986i) q^{34} +(2.01859 - 6.74255i) q^{35} +(-0.487313 + 0.516522i) q^{37} +(0.0316321 - 0.0310245i) q^{38} +(-1.72553 - 2.13933i) q^{40} +(2.87367 - 7.44299i) q^{41} +(-2.22695 - 8.64553i) q^{43} +(-4.76192 - 1.12860i) q^{44} +(0.280472 + 0.297283i) q^{46} +(8.95827 + 0.347622i) q^{47} +(3.71469 - 1.03405i) q^{49} +(1.00037 + 1.58719i) q^{50} +(0.238017 + 12.2721i) q^{52} +(-12.1664 + 4.42821i) q^{53} +(9.26787 + 3.37323i) q^{55} +(-0.397476 + 1.16167i) q^{56} +(-0.252052 + 0.102974i) q^{58} +(2.27902 + 4.76617i) q^{59} +(1.91821 - 0.615051i) q^{61} +(1.23789 + 0.144689i) q^{62} +(-4.34670 - 5.83863i) q^{64} +(2.39480 - 24.6207i) q^{65} +(3.75857 + 2.26831i) q^{67} +(-0.577434 + 0.661666i) q^{68} +(0.529617 - 1.10760i) q^{70} +(0.190370 - 3.26853i) q^{71} +(-11.5763 + 7.61387i) q^{73} +(-0.0979054 + 0.0758824i) q^{74} +(-0.407002 + 0.290908i) q^{76} +(-0.932722 - 4.30592i) q^{77} +(8.50403 - 10.5433i) q^{79} +(7.57817 + 13.1258i) q^{80} +(0.695861 - 1.20527i) q^{82} +(0.695186 + 1.80058i) q^{83} +(1.31066 - 1.18936i) q^{85} +(-0.150764 - 1.54999i) q^{86} +(-1.59270 - 0.650691i) q^{88} +(0.669466 + 11.4943i) q^{89} +(-9.87491 + 4.95936i) q^{91} +(-2.61016 - 3.80570i) q^{92} +(1.53450 + 0.301365i) q^{94} +(0.882758 - 0.487085i) q^{95} +(1.84689 - 0.839514i) q^{97} +(0.668060 - 0.0780850i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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