LMFDB - Embedded newform 675.2.l.f.151.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.8
Character	$\chi$	$=$	675.151
Dual form			675.2.l.f.76.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.672508 + 0.564301i) q^{2} +(1.45527 + 0.939248i) q^{3} +(-0.213465 - 1.21062i) q^{4} +(0.448662 + 1.45286i) q^{6} +(-0.0883715 + 0.501180i) q^{7} +(1.41750 - 2.45517i) q^{8} +(1.23563 + 2.73372i) q^{9} +O(q^{10})$	\(q+(0.672508 + 0.564301i) q^{2} +(1.45527 + 0.939248i) q^{3} +(-0.213465 - 1.21062i) q^{4} +(0.448662 + 1.45286i) q^{6} +(-0.0883715 + 0.501180i) q^{7} +(1.41750 - 2.45517i) q^{8} +(1.23563 + 2.73372i) q^{9} +(2.28041 - 0.830001i) q^{11} +(0.826424 - 1.96228i) q^{12} +(4.85915 - 4.07731i) q^{13} +(-0.342247 + 0.287179i) q^{14} +(0.0284139 - 0.0103418i) q^{16} +(-2.86909 - 4.96942i) q^{17} +(-0.711675 + 2.53572i) q^{18} +(-1.94493 + 3.36871i) q^{19} +(-0.599337 + 0.646349i) q^{21} +(2.00197 + 0.728656i) q^{22} +(1.12370 + 6.37282i) q^{23} +(4.36886 - 2.24156i) q^{24} +5.56865 q^{26} +(-0.769474 + 5.13886i) q^{27} +0.625603 q^{28} +(-0.324767 - 0.272512i) q^{29} +(1.47718 + 8.37750i) q^{31} +(-5.30309 - 1.93017i) q^{32} +(4.09819 + 0.933994i) q^{33} +(0.874759 - 4.96101i) q^{34} +(3.04574 - 2.07943i) q^{36} +(-1.19190 - 2.06443i) q^{37} +(-3.20895 + 1.16796i) q^{38} +(10.9010 - 1.36964i) q^{39} +(0.938033 - 0.787103i) q^{41} +(-0.767795 + 0.0964687i) q^{42} +(2.34944 - 0.855127i) q^{43} +(-1.49160 - 2.58353i) q^{44} +(-2.84049 + 4.91988i) q^{46} +(0.143949 - 0.816377i) q^{47} +(0.0510634 + 0.0116376i) q^{48} +(6.33448 + 2.30556i) q^{49} +(0.492208 - 9.92664i) q^{51} +(-5.97334 - 5.01222i) q^{52} -8.88536 q^{53} +(-3.41735 + 3.02171i) q^{54} +(1.10522 + 0.927387i) q^{56} +(-5.99445 + 3.07562i) q^{57} +(-0.0646297 - 0.366533i) q^{58} +(-6.58000 - 2.39492i) q^{59} +(0.558258 - 3.16604i) q^{61} +(-3.73402 + 6.46751i) q^{62} +(-1.47928 + 0.377687i) q^{63} +(-2.50742 - 4.34297i) q^{64} +(2.22901 + 2.94073i) q^{66} +(-5.32923 + 4.47176i) q^{67} +(-5.40363 + 4.53418i) q^{68} +(-4.35037 + 10.3296i) q^{69} +(-1.59927 - 2.77002i) q^{71} +(8.46325 + 0.841362i) q^{72} +(5.99262 - 10.3795i) q^{73} +(0.363398 - 2.06093i) q^{74} +(4.49341 + 1.63547i) q^{76} +(0.214457 + 1.21624i) q^{77} +(8.10390 + 5.23035i) q^{78} +(2.06451 + 1.73233i) q^{79} +(-5.94646 + 6.75571i) q^{81} +1.07500 q^{82} +(-6.00558 - 5.03928i) q^{83} +(0.910421 + 0.587596i) q^{84} +(2.06257 + 0.750714i) q^{86} +(-0.216668 - 0.701616i) q^{87} +(1.19467 - 6.77532i) q^{88} +(-9.24733 + 16.0168i) q^{89} +(1.61406 + 2.79563i) q^{91} +(7.47519 - 2.72075i) q^{92} +(-5.71886 + 13.5790i) q^{93} +(0.557490 - 0.467789i) q^{94} +(-5.90453 - 7.78984i) q^{96} +(7.86099 - 2.86117i) q^{97} +(2.95896 + 5.12506i) q^{98} +(5.08672 + 5.20843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.672508	+	0.564301i	0.475535	+	0.399021i	0.848809	−	0.528700i	$-0.177320\pi$
$2$	0.672508	+	0.564301i	0.475535	+	0.399021i	−0.373274	+	0.927721i	$0.621765\pi$
$3$	1.45527	+	0.939248i	0.840201	+	0.542275i
$3$	1.45527	+	0.939248i	0.840201	+	0.542275i
$4$	−0.213465	−	1.21062i	−0.106733	−	0.605310i
$5$		0			0
$5$		0			0
$6$	0.448662	+	1.45286i	0.183166	+	0.593129i
$7$	−0.0883715	+	0.501180i	−0.0334013	+	0.189428i	−0.996943	−	0.0781292i	$-0.975105\pi$
$7$	−0.0883715	+	0.501180i	−0.0334013	+	0.189428i	0.963542	+	0.267557i	$0.0862165\pi$
$8$	1.41750	−	2.45517i	0.501160	−	0.868035i
$9$	1.23563	+	2.73372i	0.411875	+	0.911240i
$10$		0			0
$11$	2.28041	−	0.830001i	0.687569	−	0.250255i	0.0254752	−	0.999675i	$-0.491890\pi$
$11$	2.28041	−	0.830001i	0.687569	−	0.250255i	0.662094	+	0.749421i	$0.269668\pi$
$12$	0.826424	−	1.96228i	0.238568	−	0.566461i
$13$	4.85915	−	4.07731i	1.34769	−	1.13084i	0.368107	−	0.929784i	$-0.380006\pi$
$13$	4.85915	−	4.07731i	1.34769	−	1.13084i	0.979579	−	0.201059i	$-0.0644383\pi$
$14$	−0.342247	+	0.287179i	−0.0914694	+	0.0767519i
$15$		0			0
$16$	0.0284139	−	0.0103418i	0.00710347	−	0.00258545i
$17$	−2.86909	−	4.96942i	−0.695857	−	1.20526i	−0.969891	−	0.243540i	$-0.921691\pi$
$17$	−2.86909	−	4.96942i	−0.695857	−	1.20526i	0.274033	−	0.961720i	$-0.411642\pi$
$18$	−0.711675	+	2.53572i	−0.167743	+	0.597674i
$19$	−1.94493	+	3.36871i	−0.446197	+	0.772835i	−0.998135	−	0.0610497i	$-0.980555\pi$
$19$	−1.94493	+	3.36871i	−0.446197	+	0.772835i	0.551938	+	0.833885i	$0.313889\pi$
$20$		0			0
$21$	−0.599337	+	0.646349i	−0.130786	+	0.141045i
$22$	2.00197	+	0.728656i	0.426820	+	0.155350i
$23$	1.12370	+	6.37282i	0.234308	+	1.32882i	0.844067	+	0.536238i	$0.180155\pi$
$23$	1.12370	+	6.37282i	0.234308	+	1.32882i	−0.609760	+	0.792586i	$0.708734\pi$
$24$	4.36886	−	2.24156i	0.891789	−	0.457557i
$25$		0			0
$26$	5.56865			1.09210
$27$	−0.769474	+	5.13886i	−0.148085	+	0.988975i
$28$	0.625603			0.118228
$29$	−0.324767	−	0.272512i	−0.0603078	−	0.0506042i	0.612136	−	0.790753i	$-0.290311\pi$
$29$	−0.324767	−	0.272512i	−0.0603078	−	0.0506042i	−0.672443	+	0.740149i	$0.734755\pi$
$30$		0			0
$31$	1.47718	+	8.37750i	0.265309	+	1.50464i	0.768153	+	0.640266i	$0.221176\pi$
$31$	1.47718	+	8.37750i	0.265309	+	1.50464i	−0.502844	+	0.864377i	$0.667713\pi$
$32$	−5.30309	−	1.93017i	−0.937464	−	0.341209i
$33$	4.09819	+	0.933994i	0.713403	+	0.162588i
$34$	0.874759	−	4.96101i	0.150020	−	0.850806i
$35$		0			0
$36$	3.04574	−	2.07943i	0.507623	−	0.346571i
$37$	−1.19190	−	2.06443i	−0.195947	−	0.339390i	0.751264	−	0.660002i	$-0.229445\pi$
$37$	−1.19190	−	2.06443i	−0.195947	−	0.339390i	−0.947210	+	0.320612i	$0.896111\pi$
$38$	−3.20895	+	1.16796i	−0.520560	+	0.189468i
$39$	10.9010	−	1.36964i	1.74555	−	0.219318i
$40$		0			0
$41$	0.938033	−	0.787103i	0.146496	−	0.122925i	−0.566594	−	0.823997i	$-0.691739\pi$
$41$	0.938033	−	0.787103i	0.146496	−	0.122925i	0.713090	+	0.701072i	$0.247295\pi$
$42$	−0.767795	+	0.0964687i	−0.118473	+	0.0148854i
$43$	2.34944	−	0.855127i	0.358287	−	0.130406i	−0.156604	−	0.987661i	$-0.550055\pi$
$43$	2.34944	−	0.855127i	0.358287	−	0.130406i	0.514891	+	0.857256i	$0.327832\pi$
$44$	−1.49160	−	2.58353i	−0.224868	−	0.389482i
$45$		0			0
$46$	−2.84049	+	4.91988i	−0.418808	+	0.725396i
$47$	0.143949	−	0.816377i	0.0209972	−	0.119081i	−0.972508	−	0.232871i	$-0.925188\pi$
$47$	0.143949	−	0.816377i	0.0209972	−	0.119081i	0.993505	+	0.113790i	$0.0362991\pi$
$48$	0.0510634	+	0.0116376i	0.00737037	+	0.00167974i
$49$	6.33448	+	2.30556i	0.904925	+	0.329366i
$50$		0			0
$51$	0.492208	−	9.92664i	0.0689229	−	1.39001i
$52$	−5.97334	−	5.01222i	−0.828353	−	0.695070i
$53$	−8.88536			−1.22050			−0.610249	−	0.792210i	$-0.708931\pi$
$53$	−8.88536			−1.22050			−0.610249	+	0.792210i	$0.708931\pi$
$54$	−3.41735	+	3.02171i	−0.465042	+	0.411203i
$55$		0			0
$56$	1.10522	+	0.927387i	0.147691	+	0.123927i
$57$	−5.99445	+	3.07562i	−0.793984	+	0.407376i
$58$	−0.0646297	−	0.366533i	−0.00848630	−	0.0481282i
$59$	−6.58000	−	2.39492i	−0.856643	−	0.311792i	−0.123897	−	0.992295i	$-0.539539\pi$
$59$	−6.58000	−	2.39492i	−0.856643	−	0.311792i	−0.732746	+	0.680503i	$0.761762\pi$
$60$		0			0
$61$	0.558258	−	3.16604i	0.0714776	−	0.405369i	−0.927986	−	0.372615i	$-0.878461\pi$
$61$	0.558258	−	3.16604i	0.0714776	−	0.405369i	0.999463	−	0.0327541i	$-0.0104278\pi$
$62$	−3.73402	+	6.46751i	−0.474221	+	0.821375i
$63$	−1.47928	+	0.377687i	−0.186372	+	0.0475841i
$64$	−2.50742	−	4.34297i	−0.313427	−	0.542871i
$65$		0			0
$66$	2.22901	+	2.94073i	0.274372	+	0.361979i
$67$	−5.32923	+	4.47176i	−0.651070	+	0.546312i	−0.907395	−	0.420278i	$-0.861932\pi$
$67$	−5.32923	+	4.47176i	−0.651070	+	0.546312i	0.256326	+	0.966590i	$0.417488\pi$
$68$	−5.40363	+	4.53418i	−0.655286	+	0.549850i
$69$	−4.35037	+	10.3296i	−0.523723	+	1.24354i
$70$		0			0
$71$	−1.59927	−	2.77002i	−0.189799	−	0.328741i	0.755384	−	0.655282i	$-0.227450\pi$
$71$	−1.59927	−	2.77002i	−0.189799	−	0.328741i	−0.945183	+	0.326541i	$0.894117\pi$
$72$	8.46325	+	0.841362i	0.997404	+	0.0991554i
$73$	5.99262	−	10.3795i	0.701383	−	1.21483i	−0.266598	−	0.963808i	$-0.585899\pi$
$73$	5.99262	−	10.3795i	0.701383	−	1.21483i	0.967981	−	0.251024i	$-0.0807672\pi$
$74$	0.363398	−	2.06093i	0.0422442	−	0.239579i
$75$		0			0
$76$	4.49341	+	1.63547i	0.515429	+	0.187601i
$77$	0.214457	+	1.21624i	0.0244396	+	0.138604i
$78$	8.10390	+	5.23035i	0.917585	+	0.592220i
$79$	2.06451	+	1.73233i	0.232276	+	0.194903i	0.751495	−	0.659738i	$-0.229333\pi$
$79$	2.06451	+	1.73233i	0.232276	+	0.194903i	−0.519220	+	0.854641i	$0.673777\pi$
$80$		0			0
$81$	−5.94646	+	6.75571i	−0.660718	+	0.750634i
$82$	1.07500			0.118714
$83$	−6.00558	−	5.03928i	−0.659198	−	0.553133i	0.250648	−	0.968078i	$-0.419356\pi$
$83$	−6.00558	−	5.03928i	−0.659198	−	0.553133i	−0.909846	+	0.414945i	$0.863801\pi$
$84$	0.910421	+	0.587596i	0.0993351	+	0.0641120i
$85$		0			0
$86$	2.06257	+	0.750714i	0.222412	+	0.0809515i
$87$	−0.216668	−	0.701616i	−0.0232292	−	0.0752211i
$88$	1.19467	−	6.77532i	0.127353	−	0.722252i
$89$	−9.24733	+	16.0168i	−0.980215	+	1.69778i	−0.318690	+	0.947859i	$0.603243\pi$
$89$	−9.24733	+	16.0168i	−0.980215	+	1.69778i	−0.661525	+	0.749923i	$0.730091\pi$
$90$		0			0
$91$	1.61406	+	2.79563i	0.169199	+	0.293061i
$92$	7.47519	−	2.72075i	0.779343	−	0.283658i
$93$	−5.71886	+	13.5790i	−0.593018	+	1.40807i
$94$	0.557490	−	0.467789i	0.0575007	−	0.0482488i
$95$		0			0
$96$	−5.90453	−	7.78984i	−0.602629	−	0.795047i
$97$	7.86099	−	2.86117i	0.798163	−	0.290508i	0.0894380	−	0.995992i	$-0.471493\pi$
$97$	7.86099	−	2.86117i	0.798163	−	0.290508i	0.708725	+	0.705485i	$0.249271\pi$
$98$	2.95896	+	5.12506i	0.298900	+	0.517710i
$99$	5.08672	+	5.20843i	0.511235	+	0.523467i
$100$		0			0
$101$	0.772822	−	4.38289i	0.0768986	−	0.436114i	−0.921914	−	0.387395i	$-0.873375\pi$
$101$	0.772822	−	4.38289i	0.0768986	−	0.436114i	0.998813	−	0.0487190i	$-0.0155139\pi$
$102$	5.93263	−	6.39799i	0.587418	−	0.633496i
$103$	−10.4849	−	3.81618i	−1.03310	−	0.376019i	−0.230842	−	0.972991i	$-0.574148\pi$
$103$	−10.4849	−	3.81618i	−1.03310	−	0.376019i	−0.802262	+	0.596972i	$0.796370\pi$
$104$	−3.12269	−	17.7096i	−0.306204	−	1.73657i
$105$		0			0
$106$	−5.97548	−	5.01402i	−0.580390	−	0.487005i
$107$	−11.5176			−1.11345			−0.556724	−	0.830698i	$-0.687942\pi$
$107$	−11.5176			−1.11345			−0.556724	+	0.830698i	$0.687942\pi$
$108$	6.38547	−	0.165427i	0.614442	−	0.0159182i
$109$	−16.8148			−1.61057			−0.805285	−	0.592888i	$-0.797988\pi$
$109$	−16.8148			−1.61057			−0.805285	+	0.592888i	$0.797988\pi$
$110$		0			0
$111$	0.204476	−	4.12379i	0.0194080	−	0.391413i
$112$	0.00267213	+	0.0151544i	0.000252492	+	0.00143195i
$113$	−10.0593	−	3.66129i	−0.946301	−	0.344425i	−0.177650	−	0.984094i	$-0.556849\pi$
$113$	−10.0593	−	3.66129i	−0.946301	−	0.344425i	−0.768651	+	0.639668i	$0.779072\pi$
$114$	−5.76689	−	1.31430i	−0.540119	−	0.123095i
$115$		0			0
$116$	−0.260582	+	0.451342i	−0.0241945	+	0.0419060i
$117$	17.1503	+	8.24553i	1.58555	+	0.762300i
$118$	−3.07364	−	5.32371i	−0.282952	−	0.490087i
$119$	2.74412	−	0.998777i	0.251553	−	0.0915577i
$120$		0			0
$121$	−3.91512	+	3.28518i	−0.355920	+	0.298653i
$122$	2.16203	−	1.81416i	0.195741	−	0.164246i
$123$	2.10438	−	0.264402i	0.189745	−	0.0238404i
$124$	9.82665	−	3.57661i	0.882459	−	0.321189i
$125$		0			0
$126$	−1.20796	−	0.580762i	−0.107613	−	0.0517384i
$127$	3.89640	−	6.74877i	0.345750	−	0.598857i	−0.639740	−	0.768592i	$-0.720958\pi$
$127$	3.89640	−	6.74877i	0.345750	−	0.598857i	0.985490	+	0.169735i	$0.0542912\pi$
$128$	−1.19546	+	6.77978i	−0.105664	+	0.599253i
$129$	4.22225	+	0.962268i	0.371748	+	0.0847230i
$130$		0			0
$131$	1.52245	+	8.63426i	0.133017	+	0.754378i	0.976220	+	0.216783i	$0.0695563\pi$
$131$	1.52245	+	8.63426i	0.133017	+	0.754378i	−0.843203	+	0.537596i	$0.819333\pi$
$132$	0.255892	−	5.16073i	0.0222726	−	0.449184i
$133$	−1.51645	−	1.27246i	−0.131493	−	0.110336i
$134$	−6.10737			−0.527597
$135$		0			0
$136$	−16.2677			−1.39494
$137$	12.2406	+	10.2711i	1.04579	+	0.877519i	0.992644	−	0.121068i	$-0.0386319\pi$
$137$	12.2406	+	10.2711i	1.04579	+	0.877519i	0.0531421	+	0.998587i	$0.483076\pi$
$138$	−8.75467	+	4.49182i	−0.745247	+	0.382369i
$139$	−0.582428	−	3.30311i	−0.0494009	−	0.280167i	0.950093	−	0.311966i	$-0.100987\pi$
$139$	−0.582428	−	3.30311i	−0.0494009	−	0.280167i	−0.999494	+	0.0317992i	$0.989876\pi$
$140$		0			0
$141$	0.976266	−	1.05285i	0.0822164	−	0.0886656i
$142$	0.487603	−	2.76534i	0.0409188	−	0.232062i
$143$	7.69668	−	13.3310i	0.643629	−	1.11480i
$144$	0.0633805	+	0.0648970i	0.00528171	+	0.00540808i
$145$		0			0
$146$	9.88727	−	3.59867i	0.818276	−	0.297828i
$147$	7.05288	+	9.30486i	0.581712	+	0.767452i
$148$	−2.24481	+	1.88362i	−0.184522	+	0.154833i
$149$	−1.64045	+	1.37650i	−0.134391	+	0.112767i	−0.707505	−	0.706708i	$-0.750179\pi$
$149$	−1.64045	+	1.37650i	−0.134391	+	0.112767i	0.573114	+	0.819475i	$0.305735\pi$
$150$		0			0
$151$	−14.8096	+	5.39026i	−1.20519	+	0.438653i	−0.865032	−	0.501716i	$-0.832702\pi$
$151$	−14.8096	+	5.39026i	−1.20519	+	0.438653i	−0.340156	+	0.940369i	$0.610480\pi$
$152$	5.51385	+	9.55027i	0.447232	+	0.774629i
$153$	10.0399	−	13.9836i	0.811675	−	1.13051i
$154$	−0.542104	+	0.938952i	−0.0436840	+	0.0756629i
$155$		0			0
$156$	−3.98510	−	12.9046i	−0.319063	−	1.03319i
$157$	20.5892	+	7.49385i	1.64320	+	0.598074i	0.987594	−	0.157032i	$-0.0501925\pi$
$157$	20.5892	+	7.49385i	1.64320	+	0.598074i	0.655602	+	0.755106i	$0.272415\pi$
$158$	0.410845	+	2.33002i	0.0326851	+	0.185366i
$159$	−12.9306	−	8.34556i	−1.02546	−	0.661846i
$160$		0			0
$161$	−3.29323			−0.259543
$162$	−7.81130	+	1.18767i	−0.613714	+	0.0933125i
$163$	19.9707			1.56423			0.782115	−	0.623134i	$-0.214141\pi$
$163$	19.9707			1.56423			0.782115	+	0.623134i	$0.214141\pi$
$164$	−1.15312	−	0.967584i	−0.0900436	−	0.0755556i
$165$		0			0
$166$	−1.19513	−	6.77791i	−0.0927600	−	0.526068i
$167$	−16.2833	−	5.92664i	−1.26004	−	0.458617i	−0.376258	−	0.926515i	$-0.622789\pi$
$167$	−16.2833	−	5.92664i	−1.26004	−	0.458617i	−0.883783	+	0.467897i	$0.845012\pi$
$168$	0.737343	+	2.38767i	0.0568873	+	0.184213i
$169$	4.72945	−	26.8220i	0.363804	−	2.06323i
$170$		0			0
$171$	−11.6123	−	1.15442i	−0.888016	−	0.0882808i
$172$	−1.53676	−	2.66174i	−0.117177	−	0.202956i
$173$	−13.4604	+	4.89919i	−1.02338	+	0.372478i	−0.798555	−	0.601922i	$-0.794402\pi$
$173$	−13.4604	+	4.89919i	−1.02338	+	0.372478i	−0.224821	+	0.974400i	$0.572180\pi$
$174$	0.250212	−	0.594109i	0.0189685	−	0.0450393i
$175$		0			0
$176$	0.0562116	−	0.0471671i	0.00423711	−	0.00355535i
$177$	−7.32625	−	9.66551i	−0.550675	−	0.726505i
$178$	−15.2572	+	5.55318i	−1.14358	+	0.416228i
$179$	12.1807	+	21.0976i	0.910428	+	1.57691i	0.813460	+	0.581621i	$0.197581\pi$
$179$	12.1807	+	21.0976i	0.910428	+	1.57691i	0.0969684	+	0.995287i	$0.469085\pi$
$180$		0			0
$181$	2.03955	−	3.53261i	0.151599	−	0.262577i	−0.780217	−	0.625509i	$-0.784891\pi$
$181$	2.03955	−	3.53261i	0.151599	−	0.262577i	0.931815	+	0.362933i	$0.118225\pi$
$182$	−0.492110	+	2.79090i	−0.0364776	+	0.206875i
$183$	3.78611	−	4.08310i	0.279877	−	0.301831i
$184$	17.2392	+	6.27456i	1.27089	+	0.462567i
$185$		0			0
$186$	−11.5086	+	5.90481i	−0.843852	+	0.432962i
$187$	−10.6673	−	8.95095i	−0.780072	−	0.654558i
$188$	−1.01905			−0.0743219
$189$	−2.50749	−	0.839774i	−0.182393	−	0.0610845i
$190$		0			0
$191$	5.70298	+	4.78537i	0.412653	+	0.346257i	0.825360	−	0.564607i	$-0.190972\pi$
$191$	5.70298	+	4.78537i	0.412653	+	0.346257i	−0.412707	+	0.910864i	$0.635417\pi$
$192$	0.430160	−	8.67528i	0.0310441	−	0.626085i
$193$	−1.60633	−	9.10995i	−0.115626	−	0.655749i	−0.986438	−	0.164133i	$-0.947517\pi$
$193$	−1.60633	−	9.10995i	−0.115626	−	0.655749i	0.870812	−	0.491616i	$-0.163594\pi$
$194$	6.90115	+	2.51181i	0.495473	+	0.180338i
$195$		0			0
$196$	1.43897	−	8.16081i	0.102784	−	0.582915i
$197$	4.51987	−	7.82865i	0.322028	−	0.557768i	−0.658879	−	0.752249i	$-0.728969\pi$
$197$	4.51987	−	7.82865i	0.322028	−	0.557768i	0.980906	+	0.194481i	$0.0623023\pi$
$198$	0.481737	+	6.37316i	0.0342356	+	0.452921i
$199$	3.66921	+	6.35527i	0.260104	+	0.450513i	0.966269	−	0.257534i	$-0.0829099\pi$
$199$	3.66921	+	6.35527i	0.260104	+	0.450513i	−0.706166	+	0.708047i	$0.749577\pi$
$200$		0			0
$201$	−11.9556	+	1.50214i	−0.843281	+	0.105953i
$202$	2.99300	−	2.51143i	0.210587	−	0.176703i
$203$	0.165278	−	0.138684i	0.0116002	−	0.00973374i
$204$	−12.1225	+	1.52311i	−0.848742	+	0.106639i
$205$		0			0
$206$	−4.89768	−	8.48303i	−0.341238	−	0.591041i
$207$	−16.0330	+	10.9463i	−1.11437	+	0.760820i
$208$	0.0959005	−	0.166105i	0.00664950	−	0.0115173i
$209$	−1.63919	+	9.29633i	−0.113385	+	0.643041i
$210$		0			0
$211$	15.6493	+	5.69586i	1.07734	+	0.392119i	0.818917	−	0.573913i	$-0.194575\pi$
$211$	15.6493	+	5.69586i	1.07734	+	0.392119i	0.258423	+	0.966032i	$0.416797\pi$
$212$	1.89671	+	10.7568i	0.130267	+	0.738780i
$213$	0.274364	−	5.53325i	0.0187991	−	0.379132i
$214$	−7.74568	−	6.49940i	−0.529484	−	0.444290i
$215$		0			0
$216$	11.5261	+	9.17350i	0.784250	+	0.624178i
$217$	−4.32917			−0.293883
$218$	−11.3081	−	9.48864i	−0.765882	−	0.642652i
$219$	18.4698	−	9.47646i	1.24808	−	0.640360i
$220$		0			0
$221$	−34.2032	−	12.4490i	−2.30076	−	0.837407i
$222$	2.46457	−	2.65790i	0.165411	−	0.178386i
$223$	−1.47210	+	8.34872i	−0.0985794	+	0.559072i	0.895012	+	0.446042i	$0.147167\pi$
$223$	−1.47210	+	8.34872i	−0.0985794	+	0.559072i	−0.993592	+	0.113030i	$0.963944\pi$
$224$	1.43600	−	2.48723i	0.0959470	−	0.166185i
$225$		0			0
$226$	−4.69890	−	8.13874i	−0.312566	−	0.541381i
$227$	9.11223	−	3.31658i	0.604800	−	0.220129i	−0.0214263	−	0.999770i	$-0.506821\pi$
$227$	9.11223	−	3.31658i	0.604800	−	0.220129i	0.626227	+	0.779641i	$0.284599\pi$
$228$	5.00301	+	6.60047i	0.331333	+	0.437127i
$229$	0.120012	−	0.100702i	0.00793060	−	0.00665457i	−0.638814	−	0.769361i	$-0.720575\pi$
$229$	0.120012	−	0.100702i	0.00793060	−	0.00665457i	0.646744	+	0.762707i	$0.276130\pi$
$230$		0			0
$231$	−0.830262	+	1.97139i	−0.0546272	+	0.129708i
$232$	−1.12942	+	0.411076i	−0.0741501	+	0.0269884i
$233$	−8.14148	−	14.1015i	−0.533366	−	0.923818i	−0.999241	−	0.0389667i	$-0.987593\pi$
$233$	−8.14148	−	14.1015i	−0.533366	−	0.923818i	0.465874	−	0.884851i	$-0.345740\pi$
$234$	6.88077	+	15.2231i	0.449810	+	0.995168i
$235$		0			0
$236$	−1.49474	+	8.47711i	−0.0972995	+	0.551813i
$237$	1.37734	+	4.46010i	0.0894676	+	0.289715i
$238$	2.40905	+	0.876823i	0.156156	+	0.0568360i
$239$	−3.50159	−	19.8585i	−0.226499	−	1.28454i	−0.859798	−	0.510634i	$-0.829411\pi$
$239$	−3.50159	−	19.8585i	−0.226499	−	1.28454i	0.633299	−	0.773907i	$-0.281700\pi$
$240$		0			0
$241$	20.2060	+	16.9549i	1.30158	+	1.09216i	0.989869	+	0.141984i	$0.0453481\pi$
$241$	20.2060	+	16.9549i	1.30158	+	1.09216i	0.311716	+	0.950175i	$0.399096\pi$
$242$	−4.48678			−0.288421
$243$	−14.9990	+	4.24618i	−0.962186	+	0.272393i
$244$	−3.95204			−0.253003
$245$		0			0
$246$	1.56441	+	1.00969i	0.0997434	+	0.0643755i
$247$	4.28460	+	24.2991i	0.272622	+	1.54612i
$248$	22.6621	+	8.24833i	1.43905	+	0.523770i
$249$	−4.00661	−	12.9742i	−0.253908	−	0.822209i
$250$		0			0
$251$	−10.6490	+	18.4446i	−0.672160	+	1.16422i	0.305130	+	0.952311i	$0.401300\pi$
$251$	−10.6490	+	18.4446i	−0.672160	+	1.16422i	−0.977290	+	0.211905i	$0.932033\pi$
$252$	0.773011	+	1.71022i	0.0486951	+	0.107734i
$253$	7.85194	+	13.6000i	0.493647	+	0.855022i
$254$	6.42871	−	2.33986i	0.403373	−	0.146816i
$255$		0			0
$256$	−12.3130	+	10.3318i	−0.769560	+	0.645737i
$257$	8.82228	−	7.40277i	0.550319	−	0.461772i	−0.324730	−	0.945807i	$-0.605274\pi$
$257$	8.82228	−	7.40277i	0.550319	−	0.461772i	0.875049	+	0.484034i	$0.160829\pi$
$258$	2.29649	+	3.02976i	0.142973	+	0.188624i
$259$	1.13998	−	0.414918i	0.0708348	−	0.0257818i
$260$		0			0
$261$	0.343681	−	1.22455i	0.0212733	−	0.0757975i
$262$	−3.84846	+	6.66573i	−0.237759	+	0.411810i
$263$	1.87867	−	10.6545i	0.115844	−	0.656983i	−0.870485	−	0.492195i	$-0.836195\pi$
$263$	1.87867	−	10.6545i	0.115844	−	0.656983i	0.986329	−	0.164789i	$-0.0526942\pi$
$264$	8.10228	−	8.73784i	0.498661	−	0.537777i
$265$		0			0
$266$	−0.301779	−	1.71147i	−0.0185033	−	0.104937i
$267$	−28.5012	+	14.6233i	−1.74424	+	0.894932i
$268$	6.55121	+	5.49712i	0.400179	+	0.335790i
$269$	−27.5918			−1.68230			−0.841152	−	0.540798i	$-0.818122\pi$
$269$	−27.5918			−1.68230			−0.841152	+	0.540798i	$0.818122\pi$
$270$		0			0
$271$	22.2930			1.35421			0.677103	−	0.735889i	$-0.263235\pi$
$271$	22.2930			1.35421			0.677103	+	0.735889i	$0.263235\pi$
$272$	−0.132915	−	0.111529i	−0.00805914	−	0.00676242i
$273$	−0.276899	+	5.58439i	−0.0167587	+	0.337983i
$274$	2.43592	+	13.8148i	0.147159	+	0.834582i
$275$		0			0
$276$	13.4339	+	3.06164i	0.808625	+	0.184289i
$277$	3.55616	−	20.1680i	0.213669	−	1.21178i	−0.669532	−	0.742783i	$-0.733505\pi$
$277$	3.55616	−	20.1680i	0.213669	−	1.21178i	0.883201	−	0.468994i	$-0.155383\pi$
$278$	1.47226	−	2.55004i	0.0883006	−	0.152941i
$279$	−21.0765	+	14.3896i	−1.26182	+	0.861486i
$280$		0			0
$281$	14.8184	−	5.39346i	0.883993	−	0.321747i	0.140173	−	0.990127i	$-0.455234\pi$
$281$	14.8184	−	5.39346i	0.883993	−	0.321747i	0.743820	+	0.668380i	$0.233012\pi$
$282$	1.25067	−	0.157139i	0.0744763	−	0.00935749i
$283$	−8.09200	+	6.78999i	−0.481019	+	0.403623i	−0.850795	−	0.525498i	$-0.823879\pi$
$283$	−8.09200	+	6.78999i	−0.481019	+	0.403623i	0.369776	+	0.929121i	$0.379435\pi$
$284$	−3.01206	+	2.52742i	−0.178733	+	0.149975i
$285$		0			0
$286$	12.6988	−	4.62199i	0.750896	−	0.273304i
$287$	0.311585	+	0.539681i	0.0183923	+	0.0318564i
$288$	−1.27610	−	16.8821i	−0.0751946	−	0.994790i
$289$	−7.96339	+	13.7930i	−0.468435	+	0.811353i
$290$		0			0
$291$	14.1272	+	3.21965i	0.828152	+	0.188739i
$292$	−13.8449	−	5.03913i	−0.810211	−	0.294893i
$293$	2.86499	+	16.2482i	0.167375	+	0.949229i	0.946582	+	0.322463i	$0.104511\pi$
$293$	2.86499	+	16.2482i	0.167375	+	0.949229i	−0.779207	+	0.626766i	$0.784378\pi$
$294$	−0.507624	+	10.2375i	−0.0296052	+	0.597066i
$295$		0			0
$296$	−6.75804			−0.392803
$297$	2.51055	+	12.3574i	0.145677	+	0.717048i
$298$	−1.87998			−0.108904
$299$	31.4442	+	26.3848i	1.81846	+	1.52587i
$300$		0			0
$301$	0.220949	+	1.25306i	0.0127353	+	0.0722253i
$302$	−13.0013	−	4.73209i	−0.748142	−	0.272301i
$303$	5.24129	−	5.65242i	0.301104	−	0.324723i
$304$	−0.0204243	+	0.115832i	−0.00117142	+	0.00664343i
$305$		0			0
$306$	14.6429	−	3.73860i	0.837078	−	0.213721i
$307$	7.16633	+	12.4125i	0.409004	+	0.708416i	0.994778	−	0.102058i	$-0.0325428\pi$
$307$	7.16633	+	12.4125i	0.409004	+	0.708416i	−0.585774	+	0.810474i	$0.699209\pi$
$308$	1.42663	−	0.519251i	0.0812898	−	0.0295871i
$309$	−11.6740	−	15.4015i	−0.664109	−	0.876158i
$310$		0			0
$311$	24.3502	−	20.4322i	1.38077	−	1.15861i	0.411846	−	0.911253i	$-0.364884\pi$
$311$	24.3502	−	20.4322i	1.38077	−	1.15861i	0.968926	−	0.247352i	$-0.0795605\pi$
$312$	12.0894	−	28.7053i	0.684427	−	1.62512i
$313$	−16.0443	+	5.83964i	−0.906876	+	0.330076i	−0.753005	−	0.658015i	$-0.771396\pi$
$313$	−16.0443	+	5.83964i	−0.906876	+	0.330076i	−0.153871	+	0.988091i	$0.549174\pi$
$314$	9.61761	+	16.6582i	0.542753	+	0.940076i
$315$		0			0
$316$	1.65650	−	2.86914i	0.0931852	−	0.161401i
$317$	2.37080	−	13.4455i	0.133157	−	0.755173i	−0.842968	−	0.537964i	$-0.819194\pi$
$317$	2.37080	−	13.4455i	0.133157	−	0.755173i	0.976125	−	0.217209i	$-0.0696952\pi$
$318$	−3.98653	−	12.9092i	−0.223553	−	0.723913i
$319$	−0.966788	−	0.351882i	−0.0541297	−	0.0197016i
$320$		0			0
$321$	−16.7612	−	10.8179i	−0.935520	−	0.603795i
$322$	−2.21472	−	1.85837i	−0.123422	−	0.103563i
$323$	22.3207			1.24196
$324$	9.44796	+	5.75680i	0.524887	+	0.319822i
$325$		0			0
$326$	13.4305	+	11.2695i	0.743846	+	0.624161i
$327$	−24.4701	−	15.7933i	−1.35320	−	0.873372i
$328$	−0.602818	−	3.41875i	−0.0332851	−	0.188769i
$329$	0.396431	+	0.144289i	0.0218559	+	0.00795491i
$330$		0			0
$331$	4.91646	−	27.8827i	0.270233	−	1.53257i	−0.483474	−	0.875359i	$-0.660625\pi$
$331$	4.91646	−	27.8827i	0.270233	−	1.53257i	0.753707	−	0.657211i	$-0.228264\pi$
$332$	−4.81867	+	8.34619i	−0.264459	+	0.458057i
$333$	4.17083	−	5.80917i	0.228560	−	0.318341i
$334$	−7.60625	−	13.1744i	−0.416196	−	0.720872i
$335$		0			0
$336$	−0.0103451	+	0.0245635i	−0.000564369	+	0.00134005i
$337$	13.2795	−	11.1428i	0.723379	−	0.606987i	−0.204938	−	0.978775i	$-0.565699\pi$
$337$	13.2795	−	11.1428i	0.723379	−	0.606987i	0.928318	+	0.371787i	$0.121255\pi$
$338$	18.3163	−	15.3692i	0.996276	−	0.835975i
$339$	−11.2002	−	14.7764i	−0.608310	−	0.802542i
$340$		0			0
$341$	10.3219	+	17.8781i	0.558963	+	0.968152i
$342$	−7.15794	−	7.32921i	−0.387057	−	0.396318i
$343$	−3.49648	+	6.05608i	−0.188792	+	0.326997i
$344$	1.23084	−	6.98043i	0.0663623	−	0.376359i
$345$		0			0
$346$	−11.8168	−	4.30098i	−0.635278	−	0.231222i
$347$	0.584994	+	3.31767i	0.0314041	+	0.178102i	0.996475	−	0.0838860i	$-0.0267331\pi$
$347$	0.584994	+	3.31767i	0.0314041	+	0.178102i	−0.965071	+	0.261988i	$0.915622\pi$
$348$	−0.803140	+	0.412073i	−0.0430528	+	0.0220894i
$349$	5.25034	+	4.40556i	0.281045	+	0.235824i	0.772402	−	0.635133i	$-0.219055\pi$
$349$	5.25034	+	4.40556i	0.281045	+	0.235824i	−0.491358	+	0.870958i	$0.663499\pi$
$350$		0			0
$351$	17.2138	+	28.1079i	0.918802	+	1.50029i
$352$	−13.6953			−0.729960
$353$	23.3547	+	19.5969i	1.24304	+	1.04304i	0.997280	+	0.0737074i	$0.0234831\pi$
$353$	23.3547	+	19.5969i	1.24304	+	1.04304i	0.245763	+	0.969330i	$0.420961\pi$
$354$	0.527300	−	10.6344i	0.0280257	−	0.565209i
$355$		0			0
$356$	21.3643	+	7.77597i	1.13231	+	0.412126i
$357$	4.93153	+	1.12392i	0.261004	+	0.0594840i
$358$	−3.71378	+	21.0619i	−0.196279	+	1.11316i
$359$	7.50154	−	12.9931i	0.395916	−	0.685747i	−0.597301	−	0.802017i	$-0.703760\pi$
$359$	7.50154	−	12.9931i	0.395916	−	0.685747i	0.993218	+	0.116270i	$0.0370937\pi$
$360$		0			0
$361$	1.93452	+	3.35069i	0.101817	+	0.176352i
$362$	3.36507	−	1.22479i	0.176864	−	0.0643733i
$363$	−8.78316	+	1.10355i	−0.460996	+	0.0579214i
$364$	3.03990	−	2.55078i	0.159334	−	0.133697i
$365$		0			0
$366$	4.85029	−	0.609409i	0.253529	−	0.0318543i
$367$	15.5982	−	5.67728i	0.814219	−	0.296351i	0.0988534	−	0.995102i	$-0.468483\pi$
$367$	15.5982	−	5.67728i	0.814219	−	0.296351i	0.715365	+	0.698751i	$0.246260\pi$
$368$	0.0978351	+	0.169455i	0.00510000	+	0.00883347i
$369$	3.31078	+	1.59176i	0.172352	+	0.0828635i
$370$		0			0
$371$	0.785213	−	4.45316i	0.0407662	−	0.231197i
$372$	17.6598	+	4.02473i	0.915616	+	0.208673i
$373$	−6.57037	−	2.39142i	−0.340201	−	0.123823i	0.166269	−	0.986080i	$-0.446828\pi$
$373$	−6.57037	−	2.39142i	−0.340201	−	0.123823i	−0.506470	+	0.862257i	$0.669050\pi$
$374$	−2.12283	−	12.0392i	−0.109769	−	0.622531i
$375$		0			0
$376$	−1.80030	−	1.51063i	−0.0928434	−	0.0779048i
$377$	−2.68921			−0.138501
$378$	−1.21243	−	1.97974i	−0.0623604	−	0.101827i
$379$	−13.7794			−0.707801			−0.353901	−	0.935283i	$-0.615145\pi$
$379$	−13.7794			−0.707801			−0.353901	+	0.935283i	$0.615145\pi$
$380$		0			0
$381$	12.0091	−	6.16160i	0.615245	−	0.315668i
$382$	1.13491	+	6.43640i	0.0580671	+	0.329315i
$383$	−9.64267	−	3.50965i	−0.492718	−	0.179335i	0.0836981	−	0.996491i	$-0.473327\pi$
$383$	−9.64267	−	3.50965i	−0.492718	−	0.179335i	−0.576416	+	0.817157i	$0.695549\pi$
$384$	−8.10761	+	8.74358i	−0.413740	+	0.446194i
$385$		0			0
$386$	4.06049	−	7.03297i	0.206673	−	0.357969i
$387$	5.24071	+	5.36610i	0.266400	+	0.272774i
$388$	−5.14184	−	8.90592i	−0.261037	−	0.452130i
$389$	36.0005	−	13.1031i	1.82530	−	0.664354i	0.831185	−	0.555996i	$-0.187663\pi$
$389$	36.0005	−	13.1031i	1.82530	−	0.664354i	0.994112	−	0.108358i	$-0.0345594\pi$
$390$		0			0
$391$	28.4452	−	23.8683i	1.43853	−	1.20707i
$392$	14.6396	−	12.2841i	0.739414	−	0.620442i
$393$	−5.89413	+	13.9951i	−0.297320	+	0.705961i
$394$	7.45737	−	2.71426i	0.375697	−	0.136742i
$395$		0			0
$396$	5.21960	−	7.26991i	0.262295	−	0.365327i
$397$	−15.9911	+	27.6975i	−0.802573	+	1.39010i	0.115345	+	0.993326i	$0.463203\pi$
$397$	−15.9911	+	27.6975i	−0.802573	+	1.39010i	−0.917917	+	0.396771i	$0.870131\pi$
$398$	−1.11871	+	6.34451i	−0.0560758	+	0.318022i
$399$	−1.01170	−	3.27609i	−0.0506483	−	0.164010i
$400$		0			0
$401$	−0.893312	−	5.06623i	−0.0446099	−	0.252995i	0.954345	−	0.298707i	$-0.0965554\pi$
$401$	−0.893312	−	5.06623i	−0.0446099	−	0.252995i	−0.998955	+	0.0457121i	$0.985444\pi$
$402$	−8.88788	−	5.73634i	−0.443287	−	0.286103i
$403$	41.3355	+	34.6846i	2.05907	+	1.72776i
$404$	−5.47099			−0.272192
$405$		0			0
$406$	0.189410			0.00940028
$407$	−4.43149	−	3.71846i	−0.219661	−	0.184317i
$408$	−23.6739	−	15.2794i	−1.17203	−	0.756444i
$409$	4.07496	+	23.1102i	0.201494	+	1.14273i	0.902863	+	0.429929i	$0.141462\pi$
$409$	4.07496	+	23.1102i	0.201494	+	1.14273i	−0.701369	+	0.712799i	$0.747427\pi$
$410$		0			0
$411$	8.16630	+	26.4442i	0.402814	+	1.30440i
$412$	−2.38179	+	13.5078i	−0.117342	+	0.665482i
$413$	1.78177	−	3.08612i	0.0876752	−	0.151858i
$414$	−16.9594	−	1.68599i	−0.833507	−	0.0828618i
$415$		0			0
$416$	−33.6384	+	12.2434i	−1.64926	+	0.600281i
$417$	2.25485	−	5.35397i	0.110421	−	0.262185i
$418$	−6.34831	+	5.32686i	−0.310506	+	0.260545i
$419$	−7.14090	+	5.99192i	−0.348856	+	0.292725i	−0.800330	−	0.599559i	$-0.795343\pi$
$419$	−7.14090	+	5.99192i	−0.348856	+	0.292725i	0.451475	+	0.892284i	$0.350898\pi$
$420$		0			0
$421$	−22.7017	+	8.26276i	−1.10641	+	0.402702i	−0.829677	−	0.558243i	$-0.811476\pi$
$421$	−22.7017	+	8.26276i	−1.10641	+	0.402702i	−0.276738	+	0.960945i	$0.589253\pi$
$422$	7.31007	+	12.6614i	0.355849	+	0.616348i
$423$	2.40961	−	0.615219i	0.117159	−	0.0299130i
$424$	−12.5950	+	21.8151i	−0.611665	+	1.05943i
$425$		0			0
$426$	3.30693	−	3.56633i	0.160221	−	0.172789i
$427$	1.53742	+	0.559575i	0.0744009	+	0.0270797i
$428$	2.45860	+	13.9434i	0.118841	+	0.673982i
$429$	23.7219	−	12.1712i	1.14530	−	0.587630i
$430$		0			0
$431$	−10.5453			−0.507950			−0.253975	−	0.967211i	$-0.581738\pi$
$431$	−10.5453			−0.507950			−0.253975	+	0.967211i	$0.581738\pi$
$432$	0.0312814	+	0.153973i	0.00150503	+	0.00740802i
$433$	−4.12615			−0.198290			−0.0991451	−	0.995073i	$-0.531611\pi$
$433$	−4.12615			−0.198290			−0.0991451	+	0.995073i	$0.531611\pi$
$434$	−2.91141	−	2.44296i	−0.139752	−	0.117266i
$435$		0			0
$436$	3.58938	+	20.3564i	0.171900	+	0.974894i
$437$	−23.6537	−	8.60924i	−1.13151	−	0.411836i
$438$	17.7687	+	4.04956i	0.849021	+	0.193495i
$439$	−2.08794	+	11.8413i	−0.0996517	+	0.565153i	0.893571	+	0.448923i	$0.148192\pi$
$439$	−2.08794	+	11.8413i	−0.0996517	+	0.565153i	−0.993222	+	0.116230i	$0.962919\pi$
$440$		0			0
$441$	1.52428	+	20.1655i	0.0725847	+	0.960262i
$442$	−15.9770	−	27.6729i	−0.759948	−	1.31627i
$443$	31.8626	−	11.5970i	1.51384	−	0.550992i	0.554237	−	0.832359i	$-0.313010\pi$
$443$	31.8626	−	11.5970i	1.51384	−	0.550992i	0.959600	+	0.281367i	$0.0907877\pi$
$444$	−5.03599	+	0.632742i	−0.238998	+	0.0300286i
$445$		0			0
$446$	−5.70120	+	4.78387i	−0.269960	+	0.226523i
$447$	−3.68018	+	0.462392i	−0.174066	+	0.0218704i
$448$	2.39819	−	0.872871i	0.113304	−	0.0412393i
$449$	0.297582	+	0.515427i	0.0140438	+	0.0243245i	0.872962	−	0.487788i	$-0.162196\pi$
$449$	0.297582	+	0.515427i	0.0140438	+	0.0243245i	−0.858918	+	0.512113i	$0.828863\pi$
$450$		0			0
$451$	1.48580	−	2.57349i	0.0699638	−	0.121181i
$452$	−2.28512	+	12.9596i	−0.107483	+	0.609567i
$453$	−26.6148	−	6.06562i	−1.25047	−	0.284988i
$454$	7.99960	+	2.91162i	0.375440	+	0.136649i
$455$		0			0
$456$	−0.945929	+	19.0771i	−0.0442972	+	0.893367i
$457$	6.79746	+	5.70374i	0.317972	+	0.266810i	0.787778	−	0.615960i	$-0.211232\pi$
$457$	6.79746	+	5.70374i	0.317972	+	0.266810i	−0.469806	+	0.882770i	$0.655676\pi$
$458$	0.137535			0.00642659
$459$	27.7448	−	10.9200i	1.29502	−	0.509704i
$460$		0			0
$461$	−19.2142	−	16.1226i	−0.894895	−	0.750906i	0.0742911	−	0.997237i	$-0.476331\pi$
$461$	−19.2142	−	16.1226i	−0.894895	−	0.750906i	−0.969186	+	0.246331i	$0.920775\pi$
$462$	−1.67082	+	0.857259i	−0.0777335	+	0.0398833i
$463$	−1.99238	−	11.2994i	−0.0925939	−	0.525126i	−0.995458	−	0.0952002i	$-0.969651\pi$
$463$	−1.99238	−	11.2994i	−0.0925939	−	0.525126i	0.902864	−	0.429926i	$-0.141460\pi$
$464$	−0.0120462	−	0.00438444i	−0.000559229	−	0.000203543i
$465$		0			0
$466$	2.48226	−	14.0776i	0.114989	−	0.652132i
$467$	0.328021	−	0.568149i	0.0151790	−	0.0262908i	−0.858336	−	0.513088i	$-0.828502\pi$
$467$	0.328021	−	0.568149i	0.0151790	−	0.0262908i	0.873515	+	0.486797i	$0.161835\pi$
$468$	6.32122	−	22.5227i	0.292198	−	1.04111i
$469$	−1.77020	−	3.06608i	−0.0817403	−	0.141578i
$470$		0			0
$471$	22.9243	+	30.2439i	1.05629	+	1.39357i
$472$	−15.2071	+	12.7602i	−0.699962	+	0.587338i
$473$	4.64793	−	3.90008i	0.213712	−	0.179326i
$474$	−1.59057	+	3.77669i	−0.0730575	+	0.173469i
$475$		0			0
$476$	−1.79491	−	3.10888i	−0.0822697	−	0.142495i
$477$	−10.9790	−	24.2901i	−0.502693	−	1.11217i
$478$	8.85134	−	15.3310i	0.404851	−	0.701223i
$479$	3.87971	−	22.0029i	0.177269	−	1.00534i	−0.758224	−	0.651994i	$-0.773933\pi$
$479$	3.87971	−	22.0029i	0.177269	−	1.00534i	0.935493	−	0.353346i	$-0.114956\pi$
$480$		0			0
$481$	−14.2089	−	5.17162i	−0.647871	−	0.235806i
$482$	4.02106	+	22.8046i	0.183154	+	1.03872i
$483$	−4.79254	−	3.09316i	−0.218068	−	0.140744i
$484$	4.81285	+	4.03846i	0.218766	+	0.183566i
$485$		0			0
$486$	−12.4831	−	5.60836i	−0.566244	−	0.254401i
$487$	−28.3011			−1.28245			−0.641224	−	0.767354i	$-0.721573\pi$
$487$	−28.3011			−1.28245			−0.641224	+	0.767354i	$0.721573\pi$
$488$	−6.98184	−	5.85846i	−0.316053	−	0.265200i
$489$	29.0628	+	18.7575i	1.31427	+	0.848243i
$490$		0			0
$491$	−40.2634	−	14.6547i	−1.81706	−	0.661357i	−0.995879	−	0.0906928i	$-0.971092\pi$
$491$	−40.2634	−	14.6547i	−1.81706	−	0.661357i	−0.821184	−	0.570664i	$-0.806686\pi$
$492$	−0.769302	−	2.49116i	−0.0346828	−	0.112310i
$493$	−0.422438	+	2.39577i	−0.0190257	+	0.107900i
$494$	−10.8306	+	18.7592i	−0.487293	+	0.844015i
$495$		0			0
$496$	0.128611	+	0.222761i	0.00577480	+	0.0100022i
$497$	1.52961	−	0.556732i	0.0686124	−	0.0249729i
$498$	4.62691	−	10.9862i	0.207337	−	0.492304i
$499$	−3.09802	+	2.59955i	−0.138686	+	0.116372i	−0.709492	−	0.704714i	$-0.751076\pi$
$499$	−3.09802	+	2.59955i	−0.138686	+	0.116372i	0.570805	+	0.821085i	$0.306631\pi$
$500$		0			0
$501$	−18.1300	−	23.9189i	−0.809991	−	1.06862i
$502$	−17.5699	+	6.39492i	−0.784183	+	0.285419i
$503$	11.9697	+	20.7321i	0.533702	+	0.924399i	0.999225	+	0.0393633i	$0.0125330\pi$
$503$	11.9697	+	20.7321i	0.533702	+	0.924399i	−0.465523	+	0.885036i	$0.654134\pi$
$504$	−1.16958	+	4.16726i	−0.0520974	+	0.185624i
$505$		0			0
$506$	−2.39398	+	13.5769i	−0.106425	+	0.603569i
$507$	32.0752	−	34.5912i	1.42451	−	1.53625i
$508$	−9.00195	−	3.27644i	−0.399397	−	0.145369i
$509$	−4.85069	−	27.5096i	−0.215003	−	1.21934i	−0.880901	−	0.473300i	$-0.843063\pi$
$509$	−4.85069	−	27.5096i	−0.215003	−	1.21934i	0.665898	−	0.746043i	$-0.268049\pi$
$510$		0			0
$511$	4.67243	+	3.92064i	0.206696	+	0.173439i
$512$	−0.342088			−0.0151183
$513$	−15.8148	−	12.5868i	−0.698239	−	0.555723i
$514$	10.1105			0.445953
$515$		0			0
$516$	0.263639	−	5.31695i	0.0116060	−	0.234066i
$517$	−0.349331	−	1.98115i	−0.0153635	−	0.0871310i
$518$	1.00078	+	0.364256i	0.0439719	+	0.0160045i
$519$	−24.1901	−	5.51302i	−1.06183	−	0.241995i
$520$		0			0
$521$	−6.07222	+	10.5174i	−0.266029	+	0.460775i	−0.967833	−	0.251595i	$-0.919045\pi$
$521$	−6.07222	+	10.5174i	−0.266029	+	0.460775i	0.701804	+	0.712370i	$0.252378\pi$
$522$	0.922142	−	0.629577i	0.0403610	−	0.0275559i
$523$	11.2405	+	19.4691i	0.491512	+	0.851324i	0.999952	−	0.00977335i	$-0.00311100\pi$
$523$	11.2405	+	19.4691i	0.491512	+	0.851324i	−0.508440	+	0.861097i	$0.669778\pi$
$524$	10.1278	−	3.68622i	0.442436	−	0.161033i
$525$		0			0
$526$	7.27576	−	6.10509i	0.317238	−	0.266195i
$527$	37.3931	−	31.3765i	1.62887	−	1.36678i
$528$	0.126105	−	0.0158443i	0.00548800	−	0.000689534i
$529$	−17.7371	+	6.45579i	−0.771180	+	0.280687i
$530$		0			0
$531$	−1.58336	−	20.9471i	−0.0687119	−	0.909027i
$532$	−1.21675	+	2.10748i	−0.0527529	+	0.0913706i
$533$	1.34878	−	7.64931i	0.0584221	−	0.331328i
$534$	−27.4192	−	6.24895i	−1.18655	−	0.270419i
$535$		0			0
$536$	3.42478	+	19.4229i	0.147928	+	0.838941i
$537$	−2.08966	+	42.1434i	−0.0901756	+	1.81862i
$538$	−18.5557	−	15.5701i	−0.799995	−	0.671276i
$539$	16.3588			0.704624
$540$		0			0
$541$	−22.1510			−0.952347			−0.476173	−	0.879351i	$-0.657977\pi$
$541$	−22.1510			−0.952347			−0.476173	+	0.879351i	$0.657977\pi$
$542$	14.9922	+	12.5800i	0.643972	+	0.540357i
$543$	6.28609	−	3.22525i	0.269762	−	0.138409i
$544$	5.62326	+	31.8911i	0.241095	+	1.36732i
$545$		0			0
$546$	−3.33750	+	3.59929i	−0.142832	+	0.154036i
$547$	−1.66357	+	9.43459i	−0.0711292	+	0.403394i	0.928367	+	0.371664i	$0.121213\pi$
$547$	−1.66357	+	9.43459i	−0.0711292	+	0.403394i	−0.999496	+	0.0317297i	$0.989898\pi$
$548$	9.82146	−	17.0113i	0.419552	−	0.726685i
$549$	9.34486	−	2.38591i	0.398829	−	0.101828i
$550$		0			0
$551$	1.54966	−	0.564031i	0.0660179	−	0.0240285i
$552$	19.1943	+	25.3231i	0.816966	+	1.07782i
$553$	−1.05065	+	0.881604i	−0.0446784	+	0.0374896i
$554$	13.7724	−	11.5564i	0.585132	−	0.490984i
$555$		0			0
$556$	−3.87449	+	1.41020i	−0.164315	+	0.0598058i
$557$	0.0452561	+	0.0783859i	0.00191756	+	0.00332132i	0.866983	−	0.498338i	$-0.166056\pi$
$557$	0.0452561	+	0.0783859i	0.00191756	+	0.00332132i	−0.865065	+	0.501660i	$0.832723\pi$
$558$	−22.2942	−	2.21635i	−0.943790	−	0.0938255i
$559$	7.92967	−	13.7346i	0.335389	−	0.580911i
$560$		0			0
$561$	−7.11668	−	23.0453i	−0.300467	−	0.972975i
$562$	13.0090	+	4.73491i	0.548753	+	0.199730i
$563$	2.55509	+	14.4906i	0.107684	+	0.610707i	0.990114	+	0.140263i	$0.0447949\pi$
$563$	2.55509	+	14.4906i	0.107684	+	0.610707i	−0.882430	+	0.470443i	$0.844094\pi$
$564$	−1.48299	−	0.957142i	−0.0624453	−	0.0403029i
$565$		0			0
$566$	−9.27354			−0.389796
$567$	−2.86033	−	3.57726i	−0.120122	−	0.150231i
$568$	−9.06785			−0.380479
$569$	−5.30885	−	4.45466i	−0.222559	−	0.186749i	0.524690	−	0.851293i	$-0.324181\pi$
$569$	−5.30885	−	4.45466i	−0.222559	−	0.186749i	−0.747249	+	0.664544i	$0.768626\pi$
$570$		0			0
$571$	−5.14921	−	29.2026i	−0.215488	−	1.22209i	−0.880058	−	0.474866i	$-0.842497\pi$
$571$	−5.14921	−	29.2026i	−0.215488	−	1.22209i	0.664570	−	0.747226i	$-0.268615\pi$
$572$	−17.7818	−	6.47205i	−0.743495	−	0.270610i
$573$	3.80473	+	12.3205i	0.158945	+	0.514697i
$574$	−0.0949993	+	0.538768i	−0.00396519	+	0.0224877i
$575$		0			0
$576$	8.77425	−	12.2209i	0.365594	−	0.509202i
$577$	2.30175	+	3.98675i	0.0958231	+	0.165970i	0.909952	−	0.414714i	$-0.136118\pi$
$577$	2.30175	+	3.98675i	0.0958231	+	0.165970i	−0.814129	+	0.580684i	$0.802785\pi$
$578$	−13.1389	+	4.78215i	−0.546505	+	0.198911i
$579$	6.21886	−	14.7662i	0.258447	−	0.613662i
$580$		0			0
$581$	3.05631	−	2.56455i	0.126797	−	0.106395i
$582$	7.68382	+	10.1373i	0.318505	+	0.420203i
$583$	−20.2623	+	7.37486i	−0.839177	+	0.305435i
$584$	−16.9890	−	29.4259i	−0.703011	−	1.21765i
$585$		0			0
$586$	−7.24214	+	12.5438i	−0.299170	+	0.518178i
$587$	1.69338	−	9.60364i	0.0698933	−	0.396384i	−0.929712	−	0.368288i	$-0.879944\pi$
$587$	1.69338	−	9.60364i	0.0698933	−	0.396384i	0.999605	−	0.0280969i	$-0.00894470\pi$
$588$	9.75911	−	10.5246i	0.402459	−	0.434028i
$589$	−31.0944	−	11.3174i	−1.28122	−	0.466327i
$590$		0			0
$591$	13.9307	−	7.14752i	0.573032	−	0.294010i
$592$	−0.0552163	−	0.0463320i	−0.00226938	−	0.00190423i
$593$	1.52185			0.0624948			0.0312474	−	0.999512i	$-0.490052\pi$
$593$	1.52185			0.0624948			0.0312474	+	0.999512i	$0.490052\pi$
$594$	−5.28492	+	9.72714i	−0.216843	+	0.399110i
$595$		0			0
$596$	2.01660	+	1.69213i	0.0826032	+	0.0693123i
$597$	−0.629473	+	12.6949i	−0.0257626	+	0.519569i
$598$	6.25749	+	35.4880i	0.255888	+	1.45121i
$599$	24.2758	+	8.83566i	0.991881	+	0.361015i	0.786448	−	0.617656i	$-0.211918\pi$
$599$	24.2758	+	8.83566i	0.991881	+	0.361015i	0.205433	+	0.978671i	$0.434140\pi$
$600$		0			0
$601$	−2.97450	+	16.8692i	−0.121332	+	0.688109i	0.862087	+	0.506761i	$0.169157\pi$
$601$	−2.97450	+	16.8692i	−0.121332	+	0.688109i	−0.983419	+	0.181348i	$0.941954\pi$
$602$	−0.558515	+	0.967376i	−0.0227634	+	0.0394273i
$603$	−18.8095	−	9.04322i	−0.765981	−	0.368268i
$604$	9.68689	+	16.7782i	0.394154	+	0.682695i
$605$		0			0
$606$	6.71448	−	0.843633i	0.272757	−	0.0342703i
$607$	9.63781	−	8.08708i	0.391187	−	0.328244i	−0.425889	−	0.904776i	$-0.640038\pi$
$607$	9.63781	−	8.08708i	0.391187	−	0.328244i	0.817075	+	0.576531i	$0.195594\pi$
$608$	16.8163	−	14.1106i	0.681991	−	0.572259i
$609$	0.370783	−	0.0465866i	0.0150249	−	0.00188779i
$610$		0			0
$611$	−2.62915	−	4.55382i	−0.106364	−	0.184228i
$612$	−19.0720	−	9.16946i	−0.770942	−	0.370653i
$613$	−11.7819	+	20.4069i	−0.475867	+	0.824226i	−0.999618	−	0.0276453i	$-0.991199\pi$
$613$	−11.7819	+	20.4069i	−0.475867	+	0.824226i	0.523750	+	0.851872i	$0.324532\pi$
$614$	−2.18495	+	12.3914i	−0.0881773	+	0.500078i
$615$		0			0
$616$	3.29008	+	1.19749i	0.132561	+	0.0482483i
$617$	2.01505	+	11.4279i	0.0811229	+	0.460071i	0.998126	+	0.0611910i	$0.0194899\pi$
$617$	2.01505	+	11.4279i	0.0811229	+	0.460071i	−0.917003	+	0.398880i	$0.869399\pi$
$618$	0.840222	−	16.9452i	0.0337987	−	0.681638i
$619$	−15.1620	−	12.7224i	−0.609411	−	0.511357i	0.285044	−	0.958514i	$-0.407992\pi$
$619$	−15.1620	−	12.7224i	−0.609411	−	0.511357i	−0.894455	+	0.447158i	$0.852436\pi$
$620$		0			0
$621$	−33.6137	+	0.870823i	−1.34887	+	0.0349449i
$622$	27.9056			1.11891
$623$	−7.21012	−	6.05001i	−0.288867	−	0.242388i
$624$	0.295575	−	0.151653i	0.0118325	−	0.00607097i
$625$		0			0
$626$	−14.0852	−	5.12660i	−0.562959	−	0.204900i
$627$	−11.1170	+	11.9891i	−0.443972	+	0.478797i
$628$	4.67714	−	26.5254i	0.186638	−	1.05848i
$629$	−6.83933	+	11.8461i	−0.272702	+	0.472334i
$630$		0			0
$631$	−7.28122	−	12.6114i	−0.289861	−	0.502054i	0.683916	−	0.729561i	$-0.260276\pi$
$631$	−7.28122	−	12.6114i	−0.289861	−	0.502054i	−0.973776	+	0.227508i	$0.926942\pi$
$632$	7.17962	−	2.61317i	0.285590	−	0.103946i
$633$	17.4241	+	22.9876i	0.692545	+	0.913673i
$634$	9.18168	−	7.70434i	0.364651	−	0.305979i
$635$		0			0
$636$	−7.34307	+	17.4355i	−0.291172	+	0.691364i
$637$	40.1807	−	14.6246i	1.59202	−	0.579446i
$638$	−0.451605	−	0.782203i	−0.0178792	−	0.0309677i
$639$	5.59637	−	7.79468i	0.221389	−	0.308353i
$640$		0			0
$641$	3.38084	−	19.1737i	0.133535	−	0.757315i	−0.842334	−	0.538957i	$-0.818819\pi$
$641$	3.38084	−	19.1737i	0.133535	−	0.757315i	0.975869	−	0.218358i	$-0.0700702\pi$
$642$	−5.16751	−	16.7335i	−0.203945	−	0.660418i
$643$	2.97050	+	1.08118i	0.117145	+	0.0426374i	0.399928	−	0.916547i	$-0.369035\pi$
$643$	2.97050	+	1.08118i	0.117145	+	0.0426374i	−0.282782	+	0.959184i	$0.591257\pi$
$644$	0.702989	+	3.98685i	0.0277017	+	0.157104i
$645$		0			0
$646$	15.0109	+	12.5956i	0.590594	+	0.495567i
$647$	18.5045			0.727489			0.363744	−	0.931499i	$-0.381498\pi$
$647$	18.5045			0.727489			0.363744	+	0.931499i	$0.381498\pi$
$648$	8.15736	+	24.1758i	0.320451	+	0.949714i
$649$	−16.9929			−0.667029
$650$		0			0
$651$	−6.30012	−	4.06617i	−0.246921	−	0.159366i
$652$	−4.26306	−	24.1770i	−0.166954	−	0.946844i
$653$	−10.6618	−	3.88059i	−0.417230	−	0.151859i	0.124870	−	0.992173i	$-0.460149\pi$
$653$	−10.6618	−	3.88059i	−0.417230	−	0.151859i	−0.542100	+	0.840314i	$0.682371\pi$
$654$	−7.54418	−	24.4297i	−0.295001	−	0.955276i
$655$		0			0
$656$	0.0185131	−	0.0320656i	0.000722815	−	0.00125195i
$657$	35.7794	+	3.55695i	1.39589	+	0.138770i
$658$	0.185180	+	0.320742i	0.00721908	+	0.0125038i
$659$	−24.1280	+	8.78187i	−0.939893	+	0.342093i	−0.766124	−	0.642693i	$-0.777817\pi$
$659$	−24.1280	+	8.78187i	−0.939893	+	0.342093i	−0.173769	+	0.984786i	$0.555595\pi$
$660$		0			0
$661$	−6.15873	+	5.16779i	−0.239547	+	0.201004i	−0.754655	−	0.656121i	$-0.772196\pi$
$661$	−6.15873	+	5.16779i	−0.239547	+	0.201004i	0.515109	+	0.857125i	$0.327752\pi$
$662$	19.0406	−	15.9770i	0.740033	−	0.620962i
$663$	−38.0823	−	50.2419i	−1.47899	−	1.95123i
$664$	−20.8852	+	7.60159i	−0.810502	+	0.294999i
$665$		0			0
$666$	6.08304	−	1.55311i	0.235713	−	0.0601819i
$667$	1.37173	−	2.37590i	0.0531135	−	0.0919954i
$668$	−3.69900	+	20.9781i	−0.143118	+	0.811665i
$669$	−9.98383	+	10.7670i	−0.385997	+	0.416275i
$670$		0			0
$671$	−1.35476	−	7.68321i	−0.0522999	−	0.296607i
$672$	4.42590	−	2.27083i	0.170733	−	0.0875992i
$673$	−10.4677	−	8.78341i	−0.403499	−	0.338576i	0.418346	−	0.908288i	$-0.362610\pi$
$673$	−10.4677	−	8.78341i	−0.403499	−	0.338576i	−0.821844	+	0.569712i	$0.807055\pi$
$674$	15.2185			0.586193
$675$		0			0
$676$	−33.4809			−1.28773
$677$	−33.6430	−	28.2299i	−1.29301	−	1.08496i	−0.991308	−	0.131558i	$-0.958002\pi$
$677$	−33.6430	−	28.2299i	−1.29301	−	1.08496i	−0.301698	−	0.953404i	$-0.597553\pi$
$678$	0.806121	−	16.2575i	0.0309589	−	0.624366i
$679$	0.739271	+	4.19262i	0.0283706	+	0.160898i
$680$		0			0
$681$	16.3759	+	3.73213i	0.627524	+	0.143015i
$682$	−3.14705	+	17.8478i	−0.120507	+	0.683428i
$683$	−2.15285	+	3.72885i	−0.0823767	+	0.142681i	−0.904270	−	0.426960i	$-0.859584\pi$
$683$	−2.15285	+	3.72885i	−0.0823767	+	0.142681i	0.821894	+	0.569641i	$0.192918\pi$
$684$	1.08126	+	14.3045i	0.0413429	+	0.546948i
$685$		0			0
$686$	−5.76886	+	2.09969i	−0.220256	+	0.0801667i
$687$	0.269234	−	0.0338276i	0.0102719	−	0.00129060i
$688$	0.0579132	−	0.0485949i	0.00220792	−	0.00185266i
$689$	−43.1753	+	36.2284i	−1.64485	+	1.38019i
$690$		0			0
$691$	21.9927	−	8.00468i	0.836641	−	0.304512i	0.112059	−	0.993702i	$-0.464255\pi$
$691$	21.9927	−	8.00468i	0.836641	−	0.304512i	0.724581	+	0.689189i	$0.242033\pi$
$692$	8.80438	+	15.2496i	0.334692	+	0.579704i
$693$	−3.05988	+	2.08909i	−0.116235	+	0.0793578i
$694$	−1.47875	+	2.56127i	−0.0561326	+	0.0972245i
$695$		0			0
$696$	−2.02971	−	0.462580i	−0.0769361	−	0.0175341i
$697$	−6.60275	−	2.40320i	−0.250097	−	0.0910279i
$698$	1.04484	+	5.92555i	0.0395476	+	0.224286i
$699$	1.39671	−	28.1683i	0.0528286	−	1.06542i
$700$		0			0
$701$	15.0287			0.567624			0.283812	−	0.958880i	$-0.408401\pi$
$701$	15.0287			0.567624			0.283812	+	0.958880i	$0.408401\pi$
$702$	−4.28493	+	28.6165i	−0.161724	+	1.08006i
$703$	9.27261			0.349723
$704$	−9.32261	−	7.82260i	−0.351359	−	0.294825i
$705$		0			0
$706$	4.64765	+	26.3581i	0.174917	+	0.992002i
$707$	2.12832	+	0.774645i	0.0800437	+	0.0291335i
$708$	−10.1374	+	10.9326i	−0.380986	+	0.410871i
$709$	4.68507	−	26.5704i	0.175952	−	0.997871i	−0.761088	−	0.648648i	$-0.775335\pi$
$709$	4.68507	−	26.5704i	0.175952	−	0.997871i	0.937040	−	0.349223i	$-0.113554\pi$
$710$		0			0
$711$	−2.18475	+	7.78432i	−0.0819345	+	0.291935i
$712$	26.2161	+	45.4076i	0.982489	+	1.70172i
$713$	−51.7284	+	18.8276i	−1.93724	+	0.705098i
$714$	2.68227	+	3.53871i	0.100381	+	0.132433i
$715$		0			0
$716$	22.9410	−	19.2498i	0.857347	−	0.719399i
$717$	13.5563	−	32.1884i	0.506270	−	1.20210i
$718$	12.3768	−	4.50480i	0.461900	−	0.168118i
$719$	−21.0623	−	36.4809i	−0.785490	−	1.36051i	−0.928706	−	0.370817i	$-0.879078\pi$
$719$	−21.0623	−	36.4809i	−0.785490	−	1.36051i	0.143216	−	0.989691i	$-0.454255\pi$
$720$		0			0
$721$	2.83915	−	4.91756i	0.105736	−	0.183139i
$722$	−0.589817	+	3.34502i	−0.0219507	+	0.124489i
$723$	13.4804	+	43.6524i	0.501342	+	1.62345i
$724$	−4.71202	−	1.71503i	−0.175121	−	0.0637388i
$725$		0			0
$726$	−6.52948	−	4.21420i	−0.242332	−	0.156404i
$727$	7.96369	+	6.68233i	0.295357	+	0.247834i	0.778409	−	0.627758i	$-0.216027\pi$
$727$	7.96369	+	6.68233i	0.295357	+	0.247834i	−0.483052	+	0.875592i	$0.660472\pi$
$728$	9.15166			0.339183
$729$	−25.8158	−	7.90844i	−0.956142	−	0.292905i
$730$		0			0
$731$	−10.9902	−	9.22191i	−0.406489	−	0.341085i
$732$	−5.75128	−	3.71194i	−0.212574	−	0.137197i
$733$	−7.78456	−	44.1484i	−0.287529	−	1.63066i	−0.696108	−	0.717937i	$-0.745087\pi$
$733$	−7.78456	−	44.1484i	−0.287529	−	1.63066i	0.408579	−	0.912723i	$-0.366024\pi$
$734$	13.6936	+	4.98406i	0.505440	+	0.183965i
$735$		0			0
$736$	6.34152	−	35.9646i	0.233752	−	1.32567i
$737$	−8.44127	+	14.6207i	−0.310938	+	0.538561i
$738$	1.32830	+	2.93875i	0.0488952	+	0.108177i
$739$	8.15749	+	14.1292i	0.300078	+	0.519751i	0.976153	−	0.217082i	$-0.0696539\pi$
$739$	8.15749	+	14.1292i	0.300078	+	0.519751i	−0.676075	+	0.736833i	$0.736321\pi$
$740$		0			0
$741$	−16.5877	+	39.3861i	−0.609364	+	1.44689i
$742$	3.04099	−	2.55169i	0.111638	−	0.0936755i
$743$	8.85961	−	7.43409i	0.325028	−	0.272730i	−0.465643	−	0.884973i	$-0.654177\pi$
$743$	8.85961	−	7.43409i	0.325028	−	0.272730i	0.790670	+	0.612242i	$0.209732\pi$
$744$	25.2323	+	33.2889i	0.925060	+	1.22043i
$745$		0			0
$746$	−3.06915	−	5.31592i	−0.112369	−	0.194630i
$747$	6.35534	−	22.6442i	0.232530	−	0.828509i
$748$	−8.55910	+	14.8248i	−0.312952	+	0.542049i
$749$	1.01783	−	5.77239i	0.0371906	−	0.210918i
$750$		0			0
$751$	−17.9955	−	6.54983i	−0.656666	−	0.239007i	−0.00786953	−	0.999969i	$-0.502505\pi$
$751$	−17.9955	−	6.54983i	−0.656666	−	0.239007i	−0.648796	+	0.760962i	$0.724727\pi$
$752$	−0.00435265	−	0.0246851i	−0.000158725	−	0.000900174i
$753$	−32.8213	+	16.8399i	−1.19607	+	0.613679i
$754$	−1.80852	−	1.51753i	−0.0658623	−	0.0552650i
$755$		0			0
$756$	−0.481385	+	3.21489i	−0.0175078	+	0.116924i
$757$	−8.63554			−0.313864			−0.156932	−	0.987609i	$-0.550160\pi$
$757$	−8.63554			−0.313864			−0.156932	+	0.987609i	$0.550160\pi$
$758$	−9.26677	−	7.77575i	−0.336584	−	0.282428i
$759$	−1.34704	+	27.1665i	−0.0488945	+	0.986083i
$760$		0			0
$761$	−1.00649	−	0.366334i	−0.0364854	−	0.0132796i	0.323713	−	0.946155i	$-0.395069\pi$
$761$	−1.00649	−	0.366334i	−0.0364854	−	0.0132796i	−0.360198	+	0.932876i	$0.617291\pi$
$762$	11.5532	+	2.63302i	0.418529	+	0.0953844i
$763$	1.48595	−	8.42726i	0.0537951	−	0.305087i
$764$	4.57588	−	7.92566i	0.165550	−	0.286740i
$765$		0			0
$766$	−4.50428	−	7.80164i	−0.162746	−	0.281885i
$767$	−41.7380	+	15.1914i	−1.50707	+	0.548530i
$768$	−27.6228	+	3.47064i	−0.996752	+	0.125236i
$769$	7.27290	−	6.10268i	0.262267	−	0.220068i	−0.502166	−	0.864771i	$-0.667463\pi$
$769$	7.27290	−	6.10268i	0.262267	−	0.220068i	0.764433	+	0.644703i	$0.223019\pi$
$770$		0			0
$771$	19.7918	−	2.48672i	0.712786	−	0.0895572i
$772$	−10.6858	+	3.88931i	−0.384590	+	0.139979i
$773$	−0.387381	−	0.670964i	−0.0139331	−	0.0241329i	0.858975	−	0.512018i	$-0.171102\pi$
$773$	−0.387381	−	0.670964i	−0.0139331	−	0.0241329i	−0.872908	+	0.487885i	$0.837769\pi$
$774$	0.496320	+	6.56609i	0.0178399	+	0.236013i
$775$		0			0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.672508 + 0.564301i) q^{2} +(1.45527 + 0.939248i) q^{3} +(-0.213465 - 1.21062i) q^{4} +(0.448662 + 1.45286i) q^{6} +(-0.0883715 + 0.501180i) q^{7} +(1.41750 - 2.45517i) q^{8} +(1.23563 + 2.73372i) q^{9} +O(q^{10})\)	\(q+(0.672508 + 0.564301i) q^{2} +(1.45527 + 0.939248i) q^{3} +(-0.213465 - 1.21062i) q^{4} +(0.448662 + 1.45286i) q^{6} +(-0.0883715 + 0.501180i) q^{7} +(1.41750 - 2.45517i) q^{8} +(1.23563 + 2.73372i) q^{9} +(2.28041 - 0.830001i) q^{11} +(0.826424 - 1.96228i) q^{12} +(4.85915 - 4.07731i) q^{13} +(-0.342247 + 0.287179i) q^{14} +(0.0284139 - 0.0103418i) q^{16} +(-2.86909 - 4.96942i) q^{17} +(-0.711675 + 2.53572i) q^{18} +(-1.94493 + 3.36871i) q^{19} +(-0.599337 + 0.646349i) q^{21} +(2.00197 + 0.728656i) q^{22} +(1.12370 + 6.37282i) q^{23} +(4.36886 - 2.24156i) q^{24} +5.56865 q^{26} +(-0.769474 + 5.13886i) q^{27} +0.625603 q^{28} +(-0.324767 - 0.272512i) q^{29} +(1.47718 + 8.37750i) q^{31} +(-5.30309 - 1.93017i) q^{32} +(4.09819 + 0.933994i) q^{33} +(0.874759 - 4.96101i) q^{34} +(3.04574 - 2.07943i) q^{36} +(-1.19190 - 2.06443i) q^{37} +(-3.20895 + 1.16796i) q^{38} +(10.9010 - 1.36964i) q^{39} +(0.938033 - 0.787103i) q^{41} +(-0.767795 + 0.0964687i) q^{42} +(2.34944 - 0.855127i) q^{43} +(-1.49160 - 2.58353i) q^{44} +(-2.84049 + 4.91988i) q^{46} +(0.143949 - 0.816377i) q^{47} +(0.0510634 + 0.0116376i) q^{48} +(6.33448 + 2.30556i) q^{49} +(0.492208 - 9.92664i) q^{51} +(-5.97334 - 5.01222i) q^{52} -8.88536 q^{53} +(-3.41735 + 3.02171i) q^{54} +(1.10522 + 0.927387i) q^{56} +(-5.99445 + 3.07562i) q^{57} +(-0.0646297 - 0.366533i) q^{58} +(-6.58000 - 2.39492i) q^{59} +(0.558258 - 3.16604i) q^{61} +(-3.73402 + 6.46751i) q^{62} +(-1.47928 + 0.377687i) q^{63} +(-2.50742 - 4.34297i) q^{64} +(2.22901 + 2.94073i) q^{66} +(-5.32923 + 4.47176i) q^{67} +(-5.40363 + 4.53418i) q^{68} +(-4.35037 + 10.3296i) q^{69} +(-1.59927 - 2.77002i) q^{71} +(8.46325 + 0.841362i) q^{72} +(5.99262 - 10.3795i) q^{73} +(0.363398 - 2.06093i) q^{74} +(4.49341 + 1.63547i) q^{76} +(0.214457 + 1.21624i) q^{77} +(8.10390 + 5.23035i) q^{78} +(2.06451 + 1.73233i) q^{79} +(-5.94646 + 6.75571i) q^{81} +1.07500 q^{82} +(-6.00558 - 5.03928i) q^{83} +(0.910421 + 0.587596i) q^{84} +(2.06257 + 0.750714i) q^{86} +(-0.216668 - 0.701616i) q^{87} +(1.19467 - 6.77532i) q^{88} +(-9.24733 + 16.0168i) q^{89} +(1.61406 + 2.79563i) q^{91} +(7.47519 - 2.72075i) q^{92} +(-5.71886 + 13.5790i) q^{93} +(0.557490 - 0.467789i) q^{94} +(-5.90453 - 7.78984i) q^{96} +(7.86099 - 2.86117i) q^{97} +(2.95896 + 5.12506i) q^{98} +(5.08672 + 5.20843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

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