LMFDB - Embedded newform 882.2.l.a.509.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(227,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("882.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.1
Root			$-1.62181 + 0.608059i$ of defining polynomial
Character	$\chi$	$=$	882.509
Dual form			882.2.l.a.227.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.33750 - 1.10050i) q^{3} -1.00000 q^{4} +(-1.94556 - 3.36980i) q^{5} +(-1.10050 + 1.33750i) q^{6} +1.00000i q^{8} +(0.577806 + 2.94383i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.33750 - 1.10050i) q^{3} -1.00000 q^{4} +(-1.94556 - 3.36980i) q^{5} +(-1.10050 + 1.33750i) q^{6} +1.00000i q^{8} +(0.577806 + 2.94383i) q^{9} +(-3.36980 + 1.94556i) q^{10} +(-3.41614 - 1.97231i) q^{11} +(1.33750 + 1.10050i) q^{12} +(-2.46687 - 1.42425i) q^{13} +(-1.10628 + 6.64819i) q^{15} +1.00000 q^{16} +(0.371058 + 0.642692i) q^{17} +(2.94383 - 0.577806i) q^{18} +(-1.54563 - 0.892369i) q^{19} +(1.94556 + 3.36980i) q^{20} +(-1.97231 + 3.41614i) q^{22} +(5.41535 - 3.12656i) q^{23} +(1.10050 - 1.33750i) q^{24} +(-5.07039 + 8.78217i) q^{25} +(-1.42425 + 2.46687i) q^{26} +(2.46687 - 4.57324i) q^{27} +(-2.50079 + 1.44383i) q^{29} +(6.64819 + 1.10628i) q^{30} +3.51174i q^{31} -1.00000i q^{32} +(2.39856 + 6.39742i) q^{33} +(0.642692 - 0.371058i) q^{34} +(-0.577806 - 2.94383i) q^{36} +(-1.50079 + 2.59944i) q^{37} +(-0.892369 + 1.54563i) q^{38} +(1.73205 + 4.61971i) q^{39} +(3.36980 - 1.94556i) q^{40} +(5.24705 - 9.08816i) q^{41} +(0.471521 + 0.816699i) q^{43} +(3.41614 + 1.97231i) q^{44} +(8.79598 - 7.67448i) q^{45} +(-3.12656 - 5.41535i) q^{46} +2.18525 q^{47} +(-1.33750 - 1.10050i) q^{48} +(8.78217 + 5.07039i) q^{50} +(0.210992 - 1.26795i) q^{51} +(2.46687 + 1.42425i) q^{52} +(-4.57324 - 2.46687i) q^{54} +15.3490i q^{55} +(1.08523 + 2.89450i) q^{57} +(1.44383 + 2.50079i) q^{58} +0.0211346 q^{59} +(1.10628 - 6.64819i) q^{60} +2.46911i q^{61} +3.51174 q^{62} -1.00000 q^{64} +11.0838i q^{65} +(6.39742 - 2.39856i) q^{66} +13.4493 q^{67} +(-0.371058 - 0.642692i) q^{68} +(-10.6838 - 1.77782i) q^{69} -1.94304i q^{71} +(-2.94383 + 0.577806i) q^{72} +(-4.20443 + 2.42743i) q^{73} +(2.59944 + 1.50079i) q^{74} +(16.4464 - 6.16618i) q^{75} +(1.54563 + 0.892369i) q^{76} +(4.61971 - 1.73205i) q^{78} +3.63613 q^{79} +(-1.94556 - 3.36980i) q^{80} +(-8.33228 + 3.40192i) q^{81} +(-9.08816 - 5.24705i) q^{82} +(4.02998 + 6.98012i) q^{83} +(1.44383 - 2.50079i) q^{85} +(0.816699 - 0.471521i) q^{86} +(4.93374 + 0.820992i) q^{87} +(1.97231 - 3.41614i) q^{88} +(-4.63323 + 8.02499i) q^{89} +(-7.67448 - 8.79598i) q^{90} +(-5.41535 + 3.12656i) q^{92} +(3.86466 - 4.69694i) q^{93} -2.18525i q^{94} +6.94462i q^{95} +(-1.10050 + 1.33750i) q^{96} +(-16.2983 + 9.40980i) q^{97} +(3.83228 - 11.1962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 12 * q^9	$ 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 12 * q^9 + 12 * q^11 + 16 * q^16 + 12 * q^18 + 48 * q^23 - 8 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 + 60 * q^50 + 24 * q^51 + 48 * q^57 - 12 * q^58 - 16 * q^64 + 56 * q^67 - 12 * q^72 - 36 * q^74 - 24 * q^78 + 8 * q^79 - 12 * q^85 + 24 * q^86 - 48 * q^92 + 84 * q^93 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.33750	−	1.10050i	−0.772205	−	0.635373i
$3$	−1.33750	−	1.10050i	−0.772205	−	0.635373i
$4$	−1.00000			−0.500000
$5$	−1.94556	−	3.36980i	−0.870080	−	1.50702i	−0.861913	−	0.507056i	$-0.830734\pi$
$5$	−1.94556	−	3.36980i	−0.870080	−	1.50702i	−0.00816625	−	0.999967i	$-0.502599\pi$
$6$	−1.10050	+	1.33750i	−0.449277	+	0.546032i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.577806	+	2.94383i	0.192602	+	0.981277i
$10$	−3.36980	+	1.94556i	−1.06563	+	0.615239i
$11$	−3.41614	−	1.97231i	−1.03001	−	0.594674i	−0.113019	−	0.993593i	$-0.536052\pi$
$11$	−3.41614	−	1.97231i	−1.03001	−	0.594674i	−0.916986	+	0.398919i	$0.869385\pi$
$12$	1.33750	+	1.10050i	0.386103	+	0.317687i
$13$	−2.46687	−	1.42425i	−0.684186	−	0.395015i	0.117244	−	0.993103i	$-0.462594\pi$
$13$	−2.46687	−	1.42425i	−0.684186	−	0.395015i	−0.801430	+	0.598088i	$0.795927\pi$
$14$		0			0
$15$	−1.10628	+	6.64819i	−0.285641	+	1.71656i
$16$	1.00000			0.250000
$17$	0.371058	+	0.642692i	0.0899949	+	0.155876i	0.907509	−	0.420033i	$-0.137982\pi$
$17$	0.371058	+	0.642692i	0.0899949	+	0.155876i	−0.817514	+	0.575909i	$0.804648\pi$
$18$	2.94383	−	0.577806i	0.693868	−	0.136190i
$19$	−1.54563	−	0.892369i	−0.354591	−	0.204723i	0.312114	−	0.950045i	$-0.398963\pi$
$19$	−1.54563	−	0.892369i	−0.354591	−	0.204723i	−0.666706	+	0.745321i	$0.732296\pi$
$20$	1.94556	+	3.36980i	0.435040	+	0.753511i
$21$		0			0
$22$	−1.97231	+	3.41614i	−0.420498	+	0.728324i
$23$	5.41535	−	3.12656i	1.12918	−	0.651932i	0.185451	−	0.982654i	$-0.440626\pi$
$23$	5.41535	−	3.12656i	1.12918	−	0.651932i	0.943728	+	0.330722i	$0.107292\pi$
$24$	1.10050	−	1.33750i	0.224638	−	0.273016i
$25$	−5.07039	+	8.78217i	−1.01408	+	1.75643i
$26$	−1.42425	+	2.46687i	−0.279318	+	0.483793i
$27$	2.46687	−	4.57324i	0.474749	−	0.880121i
$28$		0			0
$29$	−2.50079	+	1.44383i	−0.464385	+	0.268113i	−0.713886	−	0.700262i	$-0.753067\pi$
$29$	−2.50079	+	1.44383i	−0.464385	+	0.268113i	0.249501	+	0.968374i	$0.419733\pi$
$30$	6.64819	+	1.10628i	1.21379	+	0.201979i
$31$			3.51174i			0.630726i	0.948971	+	0.315363i	$0.102126\pi$
$31$			3.51174i			0.630726i	−0.948971	+	0.315363i	$0.897874\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.39856	+	6.39742i	0.417536	+	1.11365i
$34$	0.642692	−	0.371058i	0.110221	−	0.0636360i
$35$		0			0
$36$	−0.577806	−	2.94383i	−0.0963009	−	0.490638i
$37$	−1.50079	+	2.59944i	−0.246728	+	0.427346i	−0.962616	−	0.270870i	$-0.912689\pi$
$37$	−1.50079	+	2.59944i	−0.246728	+	0.427346i	0.715888	+	0.698215i	$0.246022\pi$
$38$	−0.892369	+	1.54563i	−0.144761	+	0.250734i
$39$	1.73205	+	4.61971i	0.277350	+	0.739746i
$40$	3.36980	−	1.94556i	0.532813	−	0.307620i
$41$	5.24705	−	9.08816i	0.819452	−	1.41933i	−0.0866345	−	0.996240i	$-0.527611\pi$
$41$	5.24705	−	9.08816i	0.819452	−	1.41933i	0.906087	−	0.423092i	$-0.139055\pi$
$42$		0			0
$43$	0.471521	+	0.816699i	0.0719063	+	0.124545i	0.899737	−	0.436433i	$-0.143758\pi$
$43$	0.471521	+	0.816699i	0.0719063	+	0.124545i	−0.827830	+	0.560978i	$0.810425\pi$
$44$	3.41614	+	1.97231i	0.515003	+	0.297337i
$45$	8.79598	−	7.67448i	1.31123	−	1.14404i
$46$	−3.12656	−	5.41535i	−0.460985	−	0.798450i
$47$	2.18525			0.318752			0.159376	−	0.987218i	$-0.449052\pi$
$47$	2.18525			0.318752			0.159376	+	0.987218i	$0.449052\pi$
$48$	−1.33750	−	1.10050i	−0.193051	−	0.158843i
$49$		0			0
$50$	8.78217	+	5.07039i	1.24199	+	0.717061i
$51$	0.210992	−	1.26795i	0.0295447	−	0.177548i
$52$	2.46687	+	1.42425i	0.342093	+	0.197507i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	−4.57324	−	2.46687i	−0.622340	−	0.335698i
$55$			15.3490i			2.06965i
$56$		0			0
$57$	1.08523	+	2.89450i	0.143742	+	0.383386i
$58$	1.44383	+	2.50079i	0.189584	+	0.328370i
$59$	0.0211346			0.00275149			0.00137575	−	0.999999i	$-0.499562\pi$
$59$	0.0211346			0.00275149			0.00137575	+	0.999999i	$0.499562\pi$
$60$	1.10628	−	6.64819i	0.142821	−	0.858278i
$61$			2.46911i			0.316138i	0.987428	+	0.158069i	$0.0505268\pi$
$61$			2.46911i			0.316138i	−0.987428	+	0.158069i	$0.949473\pi$
$62$	3.51174			0.445991
$63$		0			0
$64$	−1.00000			−0.125000
$65$			11.0838i			1.37478i
$66$	6.39742	−	2.39856i	0.787468	−	0.295242i
$67$	13.4493			1.64309			0.821544	−	0.570144i	$-0.193113\pi$
$67$	13.4493			1.64309			0.821544	+	0.570144i	$0.193113\pi$
$68$	−0.371058	−	0.642692i	−0.0449974	−	0.0779379i
$69$	−10.6838	−	1.77782i	−1.28618	−	0.214025i
$70$		0			0
$71$		−	1.94304i		−	0.230597i	−0.993331	−	0.115298i	$-0.963218\pi$
$71$		−	1.94304i		−	0.230597i	0.993331	−	0.115298i	$-0.0367824\pi$
$72$	−2.94383	+	0.577806i	−0.346934	+	0.0680950i
$73$	−4.20443	+	2.42743i	−0.492092	+	0.284109i	−0.725442	−	0.688284i	$-0.758364\pi$
$73$	−4.20443	+	2.42743i	−0.492092	+	0.284109i	0.233350	+	0.972393i	$0.425031\pi$
$74$	2.59944	+	1.50079i	0.302179	+	0.174463i
$75$	16.4464	−	6.16618i	1.89907	−	0.712009i
$76$	1.54563	+	0.892369i	0.177296	+	0.102362i
$77$		0			0
$78$	4.61971	−	1.73205i	0.523079	−	0.196116i
$79$	3.63613			0.409096			0.204548	−	0.978856i	$-0.434427\pi$
$79$	3.63613			0.409096			0.204548	+	0.978856i	$0.434427\pi$
$80$	−1.94556	−	3.36980i	−0.217520	−	0.376756i
$81$	−8.33228	+	3.40192i	−0.925809	+	0.377992i
$82$	−9.08816	−	5.24705i	−1.00362	−	0.579440i
$83$	4.02998	+	6.98012i	0.442347	+	0.766168i	0.997863	−	0.0653378i	$-0.0208125\pi$
$83$	4.02998	+	6.98012i	0.442347	+	0.766168i	−0.555516	+	0.831506i	$0.687479\pi$
$84$		0			0
$85$	1.44383	−	2.50079i	0.156605	−	0.271249i
$86$	0.816699	−	0.471521i	0.0880669	−	0.0508454i
$87$	4.93374	+	0.820992i	0.528952	+	0.0880196i
$88$	1.97231	−	3.41614i	0.210249	−	0.364162i
$89$	−4.63323	+	8.02499i	−0.491122	+	0.850647i	−0.999948	−	0.0102218i	$-0.996746\pi$
$89$	−4.63323	+	8.02499i	−0.491122	+	0.850647i	0.508826	+	0.860869i	$0.330080\pi$
$90$	−7.67448	−	8.79598i	−0.808962	−	0.927178i
$91$		0			0
$92$	−5.41535	+	3.12656i	−0.564589	+	0.325966i
$93$	3.86466	−	4.69694i	0.400747	−	0.487050i
$94$		−	2.18525i		−	0.225392i
$95$			6.94462i			0.712503i
$96$	−1.10050	+	1.33750i	−0.112319	+	0.136508i
$97$	−16.2983	+	9.40980i	−1.65484	+	0.955421i	−0.679794	+	0.733403i	$0.737931\pi$
$97$	−16.2983	+	9.40980i	−1.65484	+	0.955421i	−0.975043	+	0.222018i	$0.928736\pi$
$98$		0			0
$99$	3.83228	−	11.1962i	0.385159	−	1.12526i
$100$	5.07039	−	8.78217i	0.507039	−	0.878217i
$101$	−4.14079	+	7.17206i	−0.412024	+	0.713647i	−0.995111	−	0.0987631i	$-0.968511\pi$
$101$	−4.14079	+	7.17206i	−0.412024	+	0.713647i	0.583087	+	0.812410i	$0.301845\pi$
$102$	−1.26795	−	0.210992i	−0.125546	−	0.0208913i
$103$	−14.7646	+	8.52435i	−1.45480	+	0.839929i	−0.998748	−	0.0500247i	$-0.984070\pi$
$103$	−14.7646	+	8.52435i	−1.45480	+	0.839929i	−0.456051	+	0.889953i	$0.650737\pi$
$104$	1.42425	−	2.46687i	0.139659	−	0.241896i
$105$		0			0
$106$		0			0
$107$	−12.4161	−	7.16846i	−1.20031	−	0.693001i	−0.239689	−	0.970850i	$-0.577045\pi$
$107$	−12.4161	−	7.16846i	−1.20031	−	0.693001i	−0.960625	+	0.277848i	$0.910379\pi$
$108$	−2.46687	+	4.57324i	−0.237374	+	0.440061i
$109$	−5.63998	−	9.76874i	−0.540212	−	0.935675i	−0.998891	−	0.0470733i	$-0.985011\pi$
$109$	−5.63998	−	9.76874i	−0.540212	−	0.935675i	0.458679	−	0.888602i	$-0.348323\pi$
$110$	15.3490			1.46347
$111$	4.86799	−	1.82513i	0.462049	−	0.173234i
$112$		0			0
$113$	−8.51501	−	4.91614i	−0.801024	−	0.462472i	0.0428049	−	0.999083i	$-0.486371\pi$
$113$	−8.51501	−	4.91614i	−0.801024	−	0.462472i	−0.843829	+	0.536612i	$0.819704\pi$
$114$	2.89450	−	1.08523i	0.271095	−	0.101641i
$115$	−21.0718	−	12.1658i	−1.96495	−	1.13447i
$116$	2.50079	−	1.44383i	0.232192	−	0.134056i
$117$	2.76737	−	8.08498i	0.255844	−	0.747457i
$118$		−	0.0211346i		−	0.00194560i
$119$		0			0
$120$	−6.64819	−	1.10628i	−0.606894	−	0.100989i
$121$	2.28001	+	3.94910i	0.207274	+	0.359009i
$122$	2.46911			0.223543
$123$	−17.0194	+	6.38103i	−1.53459	+	0.575358i
$124$		−	3.51174i		−	0.315363i
$125$	20.0033			1.78915
$126$		0			0
$127$	2.94462			0.261293			0.130646	−	0.991429i	$-0.458295\pi$
$127$	2.94462			0.261293			0.130646	+	0.991429i	$0.458295\pi$
$128$			1.00000i			0.0883883i
$129$	0.268117	−	1.61124i	0.0236064	−	0.141862i
$130$	11.0838			0.972115
$131$	−7.53255	−	13.0468i	−0.658122	−	1.13990i	−0.981101	−	0.193495i	$-0.938018\pi$
$131$	−7.53255	−	13.0468i	−0.658122	−	1.13990i	0.322979	−	0.946406i	$-0.395316\pi$
$132$	−2.39856	−	6.39742i	−0.208768	−	0.556824i
$133$		0			0
$134$		−	13.4493i		−	1.16184i
$135$	−20.2104	+	0.584648i	−1.73943	+	0.0503185i
$136$	−0.642692	+	0.371058i	−0.0551104	+	0.0318180i
$137$	13.6139	+	7.85997i	1.16311	+	0.671523i	0.952048	−	0.305950i	$-0.0989739\pi$
$137$	13.6139	+	7.85997i	1.16311	+	0.671523i	0.211064	+	0.977472i	$0.432307\pi$
$138$	−1.77782	+	10.6838i	−0.151338	+	0.909465i
$139$	−2.86373	−	1.65337i	−0.242898	−	0.140237i	0.373610	−	0.927586i	$-0.378120\pi$
$139$	−2.86373	−	1.65337i	−0.242898	−	0.140237i	−0.616508	+	0.787349i	$0.711453\pi$
$140$		0			0
$141$	−2.92277	−	2.40487i	−0.246142	−	0.202526i
$142$	−1.94304			−0.163056
$143$	5.61811	+	9.73085i	0.469810	+	0.813735i
$144$	0.577806	+	2.94383i	0.0481505	+	0.245319i
$145$	9.73085	+	5.61811i	0.808103	+	0.466559i
$146$	2.42743	+	4.20443i	0.200896	+	0.347961i
$147$		0			0
$148$	1.50079	−	2.59944i	0.123364	−	0.213673i
$149$	−9.52765	+	5.50079i	−0.780535	+	0.450642i	−0.836620	−	0.547784i	$-0.815472\pi$
$149$	−9.52765	+	5.50079i	−0.780535	+	0.450642i	0.0560848	+	0.998426i	$0.482138\pi$
$150$	−6.16618	−	16.4464i	−0.503467	−	1.34284i
$151$	0.719988	−	1.24706i	0.0585918	−	0.101484i	−0.835242	−	0.549883i	$-0.814672\pi$
$151$	0.719988	−	1.24706i	0.0585918	−	0.101484i	0.893834	+	0.448399i	$0.148006\pi$
$152$	0.892369	−	1.54563i	0.0723807	−	0.125367i
$153$	−1.67758	+	1.46368i	−0.135624	+	0.118332i
$154$		0			0
$155$	11.8339	−	6.83228i	0.950518	−	0.548782i
$156$	−1.73205	−	4.61971i	−0.138675	−	0.369873i
$157$			16.6071i			1.32539i	0.748890	+	0.662695i	$0.230587\pi$
$157$			16.6071i			1.32539i	−0.748890	+	0.662695i	$0.769413\pi$
$158$		−	3.63613i		−	0.289275i
$159$		0			0
$160$	−3.36980	+	1.94556i	−0.266406	+	0.153810i
$161$		0			0
$162$	3.40192	+	8.33228i	0.267280	+	0.654646i
$163$	6.19773	−	10.7348i	0.485444	−	0.840813i	−0.514416	−	0.857541i	$-0.671991\pi$
$163$	6.19773	−	10.7348i	0.485444	−	0.840813i	0.999860	+	0.0167274i	$0.00532476\pi$
$164$	−5.24705	+	9.08816i	−0.409726	+	0.709666i
$165$	16.8915	−	20.5292i	1.31500	−	1.59820i
$166$	6.98012	−	4.02998i	0.541763	−	0.312787i
$167$	5.86087	−	10.1513i	0.453528	−	0.785534i	−0.545074	−	0.838388i	$-0.683498\pi$
$167$	5.86087	−	10.1513i	0.453528	−	0.785534i	0.998602	+	0.0528541i	$0.0168318\pi$
$168$		0			0
$169$	−2.44304	−	4.23147i	−0.187926	−	0.325498i
$170$	−2.50079	−	1.44383i	−0.191802	−	0.110737i
$171$	1.73391	−	5.06568i	0.132595	−	0.387383i
$172$	−0.471521	−	0.816699i	−0.0359532	−	0.0622727i
$173$	−16.7710			−1.27507			−0.637536	−	0.770420i	$-0.720046\pi$
$173$	−16.7710			−1.27507			−0.637536	+	0.770420i	$0.720046\pi$
$174$	0.820992	−	4.93374i	0.0622393	−	0.374026i
$175$		0			0
$176$	−3.41614	−	1.97231i	−0.257501	−	0.148668i
$177$	−0.0282675	−	0.0232586i	−0.00212472	−	0.00174822i
$178$	8.02499	+	4.63323i	0.601499	+	0.347275i
$179$	−5.00158	+	2.88766i	−0.373835	+	0.215834i	−0.675133	−	0.737696i	$-0.735914\pi$
$179$	−5.00158	+	2.88766i	−0.373835	+	0.215834i	0.301297	+	0.953530i	$0.402580\pi$
$180$	−8.79598	+	7.67448i	−0.655614	+	0.572022i
$181$		−	5.53310i		−	0.411272i	−0.978629	−	0.205636i	$-0.934074\pi$
$181$		−	5.53310i		−	0.411272i	0.978629	−	0.205636i	$-0.0659263\pi$
$182$		0			0
$183$	2.71726	−	3.30244i	0.200865	−	0.244123i
$184$	3.12656	+	5.41535i	0.230493	+	0.399225i
$185$	11.6795			0.858692
$186$	−4.69694	−	3.86466i	−0.344396	−	0.283371i
$187$		−	2.92737i		−	0.214070i
$188$	−2.18525			−0.159376
$189$		0			0
$190$	6.94462			0.503816
$191$		−	6.21372i		−	0.449609i	−0.974404	−	0.224805i	$-0.927826\pi$
$191$		−	6.21372i		−	0.449609i	0.974404	−	0.224805i	$-0.0721744\pi$
$192$	1.33750	+	1.10050i	0.0965257	+	0.0794216i
$193$	−7.80542			−0.561847			−0.280923	−	0.959730i	$-0.590641\pi$
$193$	−7.80542			−0.561847			−0.280923	+	0.959730i	$0.590641\pi$
$194$	9.40980	+	16.2983i	0.675584	+	1.17015i
$195$	12.1977	−	14.8246i	0.873497	−	1.06161i
$196$		0			0
$197$			12.7737i			0.910092i	0.890468	+	0.455046i	$0.150377\pi$
$197$			12.7737i			0.910092i	−0.890468	+	0.455046i	$0.849623\pi$
$198$	−11.1962	−	3.83228i	−0.795676	−	0.272348i
$199$	−1.56925	+	0.906005i	−0.111241	+	0.0642250i	−0.554588	−	0.832125i	$-0.687124\pi$
$199$	−1.56925	+	0.906005i	−0.111241	+	0.0642250i	0.443347	+	0.896350i	$0.353791\pi$
$200$	−8.78217	−	5.07039i	−0.620993	−	0.358530i
$201$	−17.9884	−	14.8009i	−1.26880	−	1.04397i
$202$	7.17206	+	4.14079i	0.504624	+	0.291345i
$203$		0			0
$204$	−0.210992	+	1.26795i	−0.0147724	+	0.0887742i
$205$	−40.8338			−2.85195
$206$	8.52435	+	14.7646i	0.593919	+	1.02870i
$207$	12.3331	+	14.1353i	0.857208	+	0.982474i
$208$	−2.46687	−	1.42425i	−0.171047	−	0.0987537i
$209$	3.52006	+	6.09692i	0.243487	+	0.421732i
$210$		0			0
$211$	−1.88766	+	3.26953i	−0.129952	+	0.225083i	−0.923658	−	0.383218i	$-0.874816\pi$
$211$	−1.88766	+	3.26953i	−0.129952	+	0.225083i	0.793706	+	0.608302i	$0.208149\pi$
$212$		0			0
$213$	−2.13832	+	2.59882i	−0.146515	+	0.178068i
$214$	−7.16846	+	12.4161i	−0.490026	+	0.848750i
$215$	1.83474	−	3.17787i	0.125128	−	0.216729i
$216$	4.57324	+	2.46687i	0.311170	+	0.167849i
$217$		0			0
$218$	−9.76874	+	5.63998i	−0.661622	+	0.381988i
$219$	8.29481	+	1.38029i	0.560511	+	0.0932712i
$220$		−	15.3490i		−	1.03483i
$221$		−	2.11392i		−	0.142197i
$222$	−1.82513	−	4.86799i	−0.122495	−	0.326718i
$223$	−11.0662	+	6.38910i	−0.741051	+	0.427846i	−0.822451	−	0.568836i	$-0.807394\pi$
$223$	−11.0662	+	6.38910i	−0.741051	+	0.427846i	0.0814006	+	0.996681i	$0.474061\pi$
$224$		0			0
$225$	−28.7829	−	9.85197i	−1.91886	−	0.656798i
$226$	−4.91614	+	8.51501i	−0.327017	+	0.566410i
$227$	9.99110	−	17.3051i	0.663133	−	1.14858i	−0.316655	−	0.948541i	$-0.602560\pi$
$227$	9.99110	−	17.3051i	0.663133	−	1.14858i	0.979788	−	0.200039i	$-0.0641068\pi$
$228$	−1.08523	−	2.89450i	−0.0718708	−	0.191693i
$229$	8.77402	−	5.06568i	0.579804	−	0.334750i	−0.181252	−	0.983437i	$-0.558015\pi$
$229$	8.77402	−	5.06568i	0.579804	−	0.334750i	0.761055	+	0.648687i	$0.224682\pi$
$230$	−12.1658	+	21.0718i	−0.802188	+	1.38943i
$231$		0			0
$232$	−1.44383	−	2.50079i	−0.0947921	−	0.164185i
$233$	−6.33070	−	3.65503i	−0.414738	−	0.239449i	0.278085	−	0.960556i	$-0.410300\pi$
$233$	−6.33070	−	3.65503i	−0.414738	−	0.239449i	−0.692824	+	0.721107i	$0.743634\pi$
$234$	−8.08498	−	2.76737i	−0.528532	−	0.180909i
$235$	−4.25153	−	7.36387i	−0.277339	−	0.480366i
$236$	−0.0211346			−0.00137575
$237$	−4.86332	−	4.00156i	−0.315906	−	0.259929i
$238$		0			0
$239$	7.28317	+	4.20494i	0.471109	+	0.271995i	0.716704	−	0.697378i	$-0.245650\pi$
$239$	7.28317	+	4.20494i	0.471109	+	0.271995i	−0.245595	+	0.969373i	$0.578983\pi$
$240$	−1.10628	+	6.64819i	−0.0714103	+	0.429139i
$241$	−7.75277	−	4.47607i	−0.499400	−	0.288329i	0.229066	−	0.973411i	$-0.426433\pi$
$241$	−7.75277	−	4.47607i	−0.499400	−	0.288329i	−0.728466	+	0.685082i	$0.759766\pi$
$242$	3.94910	−	2.28001i	0.253858	−	0.146565i
$243$	14.8882	+	4.61960i	0.955080	+	0.296347i
$244$		−	2.46911i		−	0.158069i
$245$		0			0
$246$	6.38103	+	17.0194i	0.406840	+	1.08512i
$247$	2.54191	+	4.40271i	0.161738	+	0.280138i
$248$	−3.51174			−0.222995
$249$	2.29153	−	13.7709i	0.145220	−	0.872695i
$250$		−	20.0033i		−	1.26512i
$251$	−12.6432			−0.798033			−0.399017	−	0.916944i	$-0.630648\pi$
$251$	−12.6432			−0.798033			−0.399017	+	0.916944i	$0.630648\pi$
$252$		0			0
$253$	−24.6661			−1.55075
$254$		−	2.94462i		−	0.184762i
$255$	−4.68324	+	1.75587i	−0.293276	+	0.109957i
$256$	1.00000			0.0625000
$257$	8.15329	+	14.1219i	0.508588	+	0.880900i	0.999951	+	0.00994523i	$0.00316572\pi$
$257$	8.15329	+	14.1219i	0.508588	+	0.880900i	−0.491362	+	0.870955i	$0.663501\pi$
$258$	−1.61124	−	0.268117i	−0.100312	−	0.0166922i
$259$		0			0
$260$		−	11.0838i		−	0.687389i
$261$	−5.69536	−	6.52765i	−0.352534	−	0.404051i
$262$	−13.0468	+	7.53255i	−0.806032	+	0.465363i
$263$	−20.5434	−	11.8608i	−1.26676	−	0.731366i	−0.292389	−	0.956300i	$-0.594450\pi$
$263$	−20.5434	−	11.8608i	−1.26676	−	0.731366i	−0.974374	+	0.224934i	$0.927783\pi$
$264$	−6.39742	+	2.39856i	−0.393734	+	0.147621i
$265$		0			0
$266$		0			0
$267$	15.0284	−	5.63455i	0.919725	−	0.344829i
$268$	−13.4493			−0.821544
$269$	3.64144	+	6.30716i	0.222022	+	0.384554i	0.955422	−	0.295244i	$-0.0954009\pi$
$269$	3.64144	+	6.30716i	0.222022	+	0.384554i	−0.733400	+	0.679798i	$0.762068\pi$
$270$	0.584648	+	20.2104i	0.0355805	+	1.22996i
$271$	19.6483	+	11.3440i	1.19355	+	0.689097i	0.959110	−	0.283033i	$-0.0913407\pi$
$271$	19.6483	+	11.3440i	1.19355	+	0.689097i	0.234441	+	0.972130i	$0.424674\pi$
$272$	0.371058	+	0.642692i	0.0224987	+	0.0389689i
$273$		0			0
$274$	7.85997	−	13.6139i	0.474838	−	0.822444i
$275$	34.6423	−	20.0007i	2.08901	−	1.20609i
$276$	10.6838	+	1.77782i	0.643089	+	0.107012i
$277$	−12.0838	+	20.9298i	−0.726046	+	1.25755i	0.232496	+	0.972597i	$0.425311\pi$
$277$	−12.0838	+	20.9298i	−0.726046	+	1.25755i	−0.958542	+	0.284951i	$0.908023\pi$
$278$	−1.65337	+	2.86373i	−0.0991628	+	0.171755i
$279$	−10.3380	+	2.02910i	−0.618917	+	0.121479i
$280$		0			0
$281$	−4.11229	+	2.37423i	−0.245319	+	0.141635i	−0.617619	−	0.786478i	$-0.711903\pi$
$281$	−4.11229	+	2.37423i	−0.245319	+	0.141635i	0.372300	+	0.928112i	$0.378569\pi$
$282$	−2.40487	+	2.92277i	−0.143208	+	0.174049i
$283$		−	29.3853i		−	1.74677i	−0.487027	−	0.873387i	$-0.661919\pi$
$283$		−	29.3853i		−	1.74677i	0.487027	−	0.873387i	$-0.338081\pi$
$284$			1.94304i			0.115298i
$285$	7.64254	−	9.28842i	0.452705	−	0.550198i
$286$	9.73085	−	5.61811i	0.575398	−	0.332206i
$287$		0			0
$288$	2.94383	−	0.577806i	0.173467	−	0.0340475i
$289$	8.22463	−	14.2455i	0.483802	−	0.837969i
$290$	5.61811	−	9.73085i	0.329907	−	0.571415i
$291$	32.1544	+	5.35061i	1.88492	+	0.313658i
$292$	4.20443	−	2.42743i	0.246046	−	0.142055i
$293$	−3.31206	+	5.73666i	−0.193493	+	0.335139i	−0.946405	−	0.322981i	$-0.895315\pi$
$293$	−3.31206	+	5.73666i	−0.193493	+	0.335139i	0.752913	+	0.658121i	$0.228648\pi$
$294$		0			0
$295$	−0.0411186	−	0.0712195i	−0.00239402	−	0.00414656i
$296$	−2.59944	−	1.50079i	−0.151090	−	0.0872316i
$297$	−17.4470	+	10.7574i	−1.01238	+	0.624209i
$298$	5.50079	+	9.52765i	0.318652	+	0.551922i
$299$	−17.8119			−1.03009
$300$	−16.4464	+	6.16618i	−0.949533	+	0.356005i
$301$		0			0
$302$	−1.24706	−	0.719988i	−0.0717600	−	0.0414307i
$303$	13.4311	−	5.03569i	0.771599	−	0.289293i
$304$	−1.54563	−	0.892369i	−0.0886479	−	0.0511809i
$305$	8.32043	−	4.80380i	0.476426	−	0.275065i
$306$	1.46368	+	1.67758i	0.0836733	+	0.0959007i
$307$			21.7242i			1.23987i	0.784655	+	0.619933i	$0.212840\pi$
$307$			21.7242i			1.23987i	−0.784655	+	0.619933i	$0.787160\pi$
$308$		0			0
$309$	29.1287	+	4.84712i	1.65707	+	0.275743i
$310$	−6.83228	−	11.8339i	−0.388048	−	0.672118i
$311$	6.29800			0.357127			0.178563	−	0.983928i	$-0.442855\pi$
$311$	6.29800			0.357127			0.178563	+	0.983928i	$0.442855\pi$
$312$	−4.61971	+	1.73205i	−0.261540	+	0.0980581i
$313$			22.2191i			1.25590i	0.778256	+	0.627948i	$0.216105\pi$
$313$			22.2191i			1.25590i	−0.778256	+	0.627948i	$0.783895\pi$
$314$	16.6071			0.937192
$315$		0			0
$316$	−3.63613			−0.204548
$317$			15.6614i			0.879632i	0.898088	+	0.439816i	$0.144956\pi$
$317$			15.6614i			0.879632i	−0.898088	+	0.439816i	$0.855044\pi$
$318$		0			0
$319$	11.3907			0.637758
$320$	1.94556	+	3.36980i	0.108760	+	0.188378i
$321$	8.71769	+	23.2518i	0.486574	+	1.29779i
$322$		0			0
$323$		−	1.32448i		−	0.0736963i
$324$	8.33228	−	3.40192i	0.462905	−	0.188996i
$325$	25.0159	−	14.4430i	1.38763	−	0.801151i
$326$	−10.7348	−	6.19773i	−0.594545	−	0.343260i
$327$	−3.20701	+	19.2725i	−0.177348	+	1.06577i
$328$	9.08816	+	5.24705i	0.501810	+	0.289720i
$329$		0			0
$330$	−20.5292	−	16.8915i	−1.13010	−	0.929847i
$331$	1.27226			0.0699296			0.0349648	−	0.999389i	$-0.488868\pi$
$331$	1.27226			0.0699296			0.0349648	+	0.999389i	$0.488868\pi$
$332$	−4.02998	−	6.98012i	−0.221174	−	0.383084i
$333$	−8.51948	−	2.91610i	−0.466865	−	0.159801i
$334$	−10.1513	−	5.86087i	−0.555456	−	0.320693i
$335$	−26.1663	−	45.3214i	−1.42962	−	2.47617i
$336$		0			0
$337$	−3.78001	+	6.54717i	−0.205910	+	0.356647i	−0.950422	−	0.310962i	$-0.899349\pi$
$337$	−3.78001	+	6.54717i	−0.205910	+	0.356647i	0.744512	+	0.667609i	$0.232682\pi$
$338$	−4.23147	+	2.44304i	−0.230162	+	0.132884i
$339$	5.97860	+	15.9461i	0.324713	+	0.866072i
$340$	−1.44383	+	2.50079i	−0.0783027	+	0.135624i
$341$	6.92623	−	11.9966i	0.375076	−	0.649651i
$342$	−5.06568	−	1.73391i	−0.273921	−	0.0937592i
$343$		0			0
$344$	−0.816699	+	0.471521i	−0.0440334	+	0.0254227i
$345$	14.7950	+	39.4612i	0.796537	+	2.12452i
$346$			16.7710i			0.901613i
$347$		−	22.1091i		−	1.18688i	−0.804879	−	0.593439i	$-0.797770\pi$
$347$		−	22.1091i		−	1.18688i	0.804879	−	0.593439i	$-0.202230\pi$
$348$	−4.93374	−	0.820992i	−0.264476	−	0.0440098i
$349$	12.7682	−	7.37173i	0.683467	−	0.394600i	−0.117693	−	0.993050i	$-0.537550\pi$
$349$	12.7682	−	7.37173i	0.683467	−	0.394600i	0.801160	+	0.598450i	$0.204217\pi$
$350$		0			0
$351$	−12.5989	+	7.76816i	−0.672478	+	0.414634i
$352$	−1.97231	+	3.41614i	−0.105124	+	0.182081i
$353$	−8.63881	+	14.9629i	−0.459798	+	0.796393i	−0.998950	−	0.0458154i	$-0.985411\pi$
$353$	−8.63881	+	14.9629i	−0.459798	+	0.796393i	0.539152	+	0.842208i	$0.318745\pi$
$354$	−0.0232586	+	0.0282675i	−0.00123618	+	0.00150240i
$355$	−6.54767	+	3.78030i	−0.347514	+	0.200638i
$356$	4.63323	−	8.02499i	0.245561	−	0.425324i
$357$		0			0
$358$	2.88766	+	5.00158i	0.152618	+	0.264342i
$359$	−9.45088	−	5.45647i	−0.498799	−	0.287982i	0.229419	−	0.973328i	$-0.426318\pi$
$359$	−9.45088	−	5.45647i	−0.498799	−	0.287982i	−0.728217	+	0.685346i	$0.759651\pi$
$360$	7.67448	+	8.79598i	0.404481	+	0.463589i
$361$	−7.90736	−	13.6959i	−0.416177	−	0.720839i
$362$	−5.53310			−0.290813
$363$	1.29646	−	7.79106i	0.0680466	−	0.408925i
$364$		0			0
$365$	16.3599	+	9.44541i	0.856318	+	0.494395i
$366$	−3.30244	−	2.71726i	−0.172621	−	0.142033i
$367$	30.9407	+	17.8636i	1.61509	+	0.932472i	0.988166	+	0.153391i	$0.0490194\pi$
$367$	30.9407	+	17.8636i	1.61509	+	0.932472i	0.626923	+	0.779081i	$0.284314\pi$
$368$	5.41535	−	3.12656i	0.282295	−	0.162983i
$369$	29.7858	+	10.1952i	1.55059	+	0.530743i
$370$		−	11.6795i		−	0.607187i
$371$		0			0
$372$	−3.86466	+	4.69694i	−0.200373	+	0.243525i
$373$	16.0300	+	27.7648i	0.830003	+	1.43761i	0.898035	+	0.439923i	$0.144994\pi$
$373$	16.0300	+	27.7648i	0.830003	+	1.43761i	−0.0680328	+	0.997683i	$0.521672\pi$
$374$	−2.92737			−0.151371
$375$	−26.7544	−	22.0136i	−1.38159	−	1.13678i
$376$			2.18525i			0.112696i
$377$	8.22549			0.423634
$378$		0			0
$379$	34.8891			1.79214			0.896068	−	0.443918i	$-0.146412\pi$
$379$	34.8891			1.79214			0.896068	+	0.443918i	$0.146412\pi$
$380$		−	6.94462i		−	0.356251i
$381$	−3.93842	−	3.24055i	−0.201772	−	0.166018i
$382$	−6.21372			−0.317922
$383$	8.76711	+	15.1851i	0.447978	+	0.775921i	0.998254	−	0.0590616i	$-0.0188108\pi$
$383$	8.76711	+	15.1851i	0.447978	+	0.775921i	−0.550276	+	0.834983i	$0.685477\pi$
$384$	1.10050	−	1.33750i	0.0561596	−	0.0682539i
$385$		0			0
$386$			7.80542i			0.397286i
$387$	−2.13178	+	1.85997i	−0.108364	+	0.0945477i
$388$	16.2983	−	9.40980i	0.827418	−	0.477710i
$389$	6.60060	+	3.81086i	0.334664	+	0.193218i	0.657910	−	0.753097i	$-0.271441\pi$
$389$	6.60060	+	3.81086i	0.334664	+	0.193218i	−0.323246	+	0.946315i	$0.604774\pi$
$390$	−14.8246	−	12.1977i	−0.750672	−	0.617656i
$391$	4.01882	+	2.32027i	0.203241	+	0.117341i
$392$		0			0
$393$	−4.28317	+	25.7396i	−0.216057	+	1.29839i
$394$	12.7737			0.643532
$395$	−7.07430	−	12.2530i	−0.355947	−	0.616517i
$396$	−3.83228	+	11.1962i	−0.192579	+	0.562628i
$397$	−32.6032	−	18.8234i	−1.63631	−	0.944722i	−0.982090	−	0.188414i	$-0.939665\pi$
$397$	−32.6032	−	18.8234i	−1.63631	−	0.944722i	−0.654216	−	0.756307i	$-0.727001\pi$
$398$	0.906005	+	1.56925i	0.0454139	+	0.0786592i
$399$		0			0
$400$	−5.07039	+	8.78217i	−0.253519	+	0.439108i
$401$	−18.5689	+	10.7207i	−0.927284	+	0.535368i	−0.885952	−	0.463778i	$-0.846494\pi$
$401$	−18.5689	+	10.7207i	−0.927284	+	0.535368i	−0.0413326	+	0.999145i	$0.513160\pi$
$402$	−14.8009	+	17.9884i	−0.738202	+	0.897178i
$403$	5.00158	−	8.66299i	0.249146	−	0.431534i
$404$	4.14079	−	7.17206i	0.206012	−	0.356823i
$405$	27.6747	+	21.4595i	1.37517	+	1.06633i
$406$		0			0
$407$	10.2538	−	5.92004i	0.508262	−	0.293445i
$408$	1.26795	+	0.210992i	0.0627728	+	0.0104456i
$409$		−	29.5703i		−	1.46216i	−0.682293	−	0.731079i	$-0.739017\pi$
$409$		−	29.5703i		−	1.46216i	0.682293	−	0.731079i	$-0.260983\pi$
$410$			40.8338i			2.01664i
$411$	−9.55865	−	25.4947i	−0.471493	−	1.25756i
$412$	14.7646	−	8.52435i	0.727400	−	0.419964i
$413$		0			0
$414$	14.1353	−	12.3331i	0.694714	−	0.606137i
$415$	15.6811	−	27.1605i	0.769755	−	1.33325i
$416$	−1.42425	+	2.46687i	−0.0698294	+	0.120948i
$417$	2.01070	+	5.36291i	0.0984642	+	0.262623i
$418$	6.09692	−	3.52006i	0.298210	−	0.172172i
$419$	−3.56481	+	6.17443i	−0.174152	+	0.301641i	−0.939868	−	0.341539i	$-0.889052\pi$
$419$	−3.56481	+	6.17443i	−0.174152	+	0.301641i	0.765715	+	0.643180i	$0.222385\pi$
$420$		0			0
$421$	−2.31007	−	4.00115i	−0.112586	−	0.195004i	0.804226	−	0.594323i	$-0.202580\pi$
$421$	−2.31007	−	4.00115i	−0.112586	−	0.195004i	−0.916812	+	0.399319i	$0.869247\pi$
$422$	3.26953	+	1.88766i	0.159158	+	0.0918899i
$423$	1.26265	+	6.43301i	0.0613922	+	0.312784i
$424$		0			0
$425$	−7.52564			−0.365047
$426$	2.59882	+	2.13832i	0.125913	+	0.103602i
$427$		0			0
$428$	12.4161	+	7.16846i	0.600157	+	0.346501i
$429$	3.19458	−	19.1977i	0.154236	−	0.926875i
$430$	−3.17787	−	1.83474i	−0.153250	−	0.0884792i
$431$	−3.47078	+	2.00385i	−0.167181	+	0.0965223i	−0.581256	−	0.813721i	$-0.697439\pi$
$431$	−3.47078	+	2.00385i	−0.167181	+	0.0965223i	0.414075	+	0.910243i	$0.364105\pi$
$432$	2.46687	−	4.57324i	0.118687	−	0.220030i
$433$		−	29.4125i		−	1.41348i	−0.707475	−	0.706738i	$-0.750166\pi$
$433$		−	29.4125i		−	1.41348i	0.707475	−	0.706738i	$-0.249834\pi$
$434$		0			0
$435$	−6.83228	−	18.2230i	−0.327583	−	0.873726i
$436$	5.63998	+	9.76874i	0.270106	+	0.467838i
$437$	−11.1602			−0.533863
$438$	1.38029	−	8.29481i	0.0659527	−	0.396341i
$439$		−	21.3769i		−	1.02027i	−0.860096	−	0.510133i	$-0.829596\pi$
$439$		−	21.3769i		−	1.02027i	0.860096	−	0.510133i	$-0.170404\pi$
$440$	−15.3490			−0.731733
$441$		0			0
$442$	−2.11392			−0.100549
$443$			5.83386i			0.277175i	0.990350	+	0.138587i	$0.0442562\pi$
$443$			5.83386i			0.277175i	−0.990350	+	0.138587i	$0.955744\pi$
$444$	−4.86799	+	1.82513i	−0.231024	+	0.0866171i
$445$	36.0569			1.70926
$446$	6.38910	+	11.0662i	0.302533	+	0.524002i
$447$	18.7968	+	3.12786i	0.889059	+	0.147943i
$448$		0			0
$449$		−	22.5823i		−	1.06573i	−0.846202	−	0.532863i	$-0.821116\pi$
$449$		−	22.5823i		−	1.06573i	0.846202	−	0.532863i	$-0.178884\pi$
$450$	−9.85197	+	28.7829i	−0.464427	+	1.35684i
$451$	−35.8493	+	20.6976i	−1.68808	+	0.974613i
$452$	8.51501	+	4.91614i	0.400512	+	0.231236i
$453$	−2.33537	+	0.875590i	−0.109725	+	0.0411388i
$454$	−17.3051	−	9.99110i	−0.812168	−	0.468906i
$455$		0			0
$456$	−2.89450	+	1.08523i	−0.135548	+	0.0508203i
$457$	39.8623			1.86468			0.932340	−	0.361584i	$-0.117764\pi$
$457$	39.8623			1.86468			0.932340	+	0.361584i	$0.117764\pi$
$458$	−5.06568	−	8.77402i	−0.236704	−	0.409983i
$459$	3.85454	−	0.111505i	0.179915	−	0.00520459i
$460$	21.0718	+	12.1658i	0.982476	+	0.567233i
$461$	−3.68254	−	6.37834i	−0.171513	−	0.297069i	0.767436	−	0.641125i	$-0.221532\pi$
$461$	−3.68254	−	6.37834i	−0.171513	−	0.297069i	−0.938949	+	0.344056i	$0.888199\pi$
$462$		0			0
$463$	−14.3457	+	24.8475i	−0.666702	+	1.15476i	0.312119	+	0.950043i	$0.398961\pi$
$463$	−14.3457	+	24.8475i	−0.666702	+	1.15476i	−0.978821	+	0.204718i	$0.934372\pi$
$464$	−2.50079	+	1.44383i	−0.116096	+	0.0670282i
$465$	−23.3467	−	3.88498i	−1.08268	−	0.180162i
$466$	−3.65503	+	6.33070i	−0.169316	+	0.293264i
$467$	6.83519	−	11.8389i	0.316295	−	0.547839i	−0.663417	−	0.748250i	$-0.730894\pi$
$467$	6.83519	−	11.8389i	0.316295	−	0.547839i	0.979712	+	0.200411i	$0.0642278\pi$
$468$	−2.76737	+	8.08498i	−0.127922	+	0.373728i
$469$		0			0
$470$	−7.36387	+	4.25153i	−0.339670	+	0.196109i
$471$	18.2761	−	22.2119i	0.842117	−	1.02347i
$472$			0.0211346i			0.000972799i
$473$		−	3.71994i		−	0.171043i
$474$	−4.00156	+	4.86332i	−0.183798	+	0.223380i
$475$	15.6739	−	9.04931i	0.719166	−	0.415211i
$476$		0			0
$477$		0			0
$478$	4.20494	−	7.28317i	0.192329	−	0.333124i
$479$	5.20537	−	9.01596i	0.237839	−	0.411950i	−0.722255	−	0.691627i	$-0.756894\pi$
$479$	5.20537	−	9.01596i	0.237839	−	0.411950i	0.960094	+	0.279677i	$0.0902275\pi$
$480$	6.64819	+	1.10628i	0.303447	+	0.0504947i
$481$	7.40449	−	4.27499i	0.337616	−	0.194923i
$482$	−4.47607	+	7.75277i	−0.203879	+	0.353129i
$483$		0			0
$484$	−2.28001	−	3.94910i	−0.103637	−	0.179504i
$485$	63.4184	+	36.6146i	2.87968	+	1.66258i
$486$	4.61960	−	14.8882i	0.209549	−	0.675344i
$487$	−1.16925	−	2.02520i	−0.0529838	−	0.0917707i	0.838317	−	0.545183i	$-0.183540\pi$
$487$	−1.16925	−	2.02520i	−0.0529838	−	0.0917707i	−0.891301	+	0.453412i	$0.850207\pi$
$488$	−2.46911			−0.111772
$489$	−20.1031	+	7.53716i	−0.909092	+	0.340842i
$490$		0			0
$491$	−29.3448	−	16.9422i	−1.32431	−	0.764591i	−0.339898	−	0.940462i	$-0.610392\pi$
$491$	−29.3448	−	16.9422i	−1.32431	−	0.764591i	−0.984413	+	0.175871i	$0.943726\pi$
$492$	17.0194	−	6.38103i	0.767295	−	0.287679i
$493$	−1.85588	−	1.07149i	−0.0835845	−	0.0482575i
$494$	4.40271	−	2.54191i	0.198087	−	0.114366i
$495$	−45.1848	+	8.86872i	−2.03090	+	0.398619i
$496$			3.51174i			0.157682i
$497$		0			0
$498$	−13.7709	−	2.29153i	−0.617088	−	0.102686i
$499$	8.30223	+	14.3799i	0.371659	+	0.643732i	0.989821	−	0.142319i	$-0.0454558\pi$
$499$	8.30223	+	14.3799i	0.371659	+	0.643732i	−0.618162	+	0.786051i	$0.712123\pi$
$500$	−20.0033			−0.894576
$501$	−19.0104	+	7.12751i	−0.849324	+	0.318434i
$502$			12.6432i			0.564295i
$503$	−35.3661			−1.57690			−0.788449	−	0.615100i	$-0.789115\pi$
$503$	−35.3661			−1.57690			−0.788449	+	0.615100i	$0.789115\pi$
$504$		0			0
$505$	32.2246			1.43398
$506$			24.6661i			1.09654i
$507$	−1.38916	+	8.34816i	−0.0616950	+	0.370755i
$508$	−2.94462			−0.130646
$509$	−18.5291	−	32.0933i	−0.821287	−	1.42251i	−0.904724	−	0.425998i	$-0.859923\pi$
$509$	−18.5291	−	32.0933i	−0.821287	−	1.42251i	0.0834371	−	0.996513i	$-0.473410\pi$
$510$	1.75587	+	4.68324i	0.0777511	+	0.207377i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−7.89388	+	4.86718i	−0.348523	+	0.214891i
$514$	14.1219	−	8.15329i	0.622891	−	0.359626i
$515$	57.4507	+	33.1692i	2.53158	+	1.46161i
$516$	−0.268117	+	1.61124i	−0.0118032	+	0.0709310i
$517$	−7.46513	−	4.30999i	−0.328316	−	0.189553i
$518$		0			0
$519$	22.4311	+	18.4564i	0.984618	+	0.810147i
$520$	−11.0838			−0.486057
$521$	−0.891547	−	1.54420i	−0.0390594	−	0.0676528i	0.845835	−	0.533445i	$-0.179103\pi$
$521$	−0.891547	−	1.54420i	−0.0390594	−	0.0676528i	−0.884894	+	0.465792i	$0.845769\pi$
$522$	−6.52765	+	5.69536i	−0.285707	+	0.249279i
$523$	20.8312	+	12.0269i	0.910886	+	0.525901i	0.880716	−	0.473644i	$-0.157062\pi$
$523$	20.8312	+	12.0269i	0.910886	+	0.525901i	0.0301702	+	0.999545i	$0.490395\pi$
$524$	7.53255	+	13.0468i	0.329061	+	0.569950i
$525$		0			0
$526$	−11.8608	+	20.5434i	−0.517154	+	0.895737i
$527$	−2.25696	+	1.30306i	−0.0983149	+	0.0567621i
$528$	2.39856	+	6.39742i	0.104384	+	0.278412i
$529$	8.05069	−	13.9442i	0.350030	−	0.606270i
$530$		0			0
$531$	0.0122117	+	0.0622167i	0.000529942	+	0.00269998i
$532$		0			0
$533$	−25.8876	+	14.9462i	−1.12132	+	0.647392i
$534$	−5.63455	−	15.0284i	−0.243831	−	0.650344i
$535$			55.7866i			2.41187i
$536$			13.4493i			0.580920i
$537$	9.86747	+	1.64198i	0.425813	+	0.0708569i
$538$	6.30716	−	3.64144i	0.271921	−	0.156994i
$539$		0			0
$540$	20.2104	−	0.584648i	0.869716	−	0.0251592i
$541$	−15.0016	+	25.9835i	−0.644968	+	1.11712i	0.339341	+	0.940664i	$0.389796\pi$
$541$	−15.0016	+	25.9835i	−0.644968	+	1.11712i	−0.984309	+	0.176454i	$0.943537\pi$
$542$	11.3440	−	19.6483i	0.487265	−	0.843968i
$543$	−6.08917	+	7.40051i	−0.261311	+	0.317586i
$544$	0.642692	−	0.371058i	0.0275552	−	0.0159090i
$545$	−21.9458	+	38.0113i	−0.940056	+	1.62822i
$546$		0			0
$547$	−10.7816	−	18.6743i	−0.460987	−	0.798454i	0.538023	−	0.842930i	$-0.319171\pi$
$547$	−10.7816	−	18.6743i	−0.460987	−	0.798454i	−0.999010	+	0.0444765i	$0.985838\pi$
$548$	−13.6139	−	7.85997i	−0.581556	−	0.335761i
$549$	−7.26865	+	1.42667i	−0.310219	+	0.0608887i
$550$	−20.0007	−	34.6423i	−0.852835	−	1.47715i
$551$	5.15372			0.219556
$552$	1.77782	−	10.6838i	0.0756692	−	0.454733i
$553$		0			0
$554$	20.9298	+	12.0838i	0.889221	+	0.513392i
$555$	−15.6213	−	12.8533i	−0.663087	−	0.545590i
$556$	2.86373	+	1.65337i	0.121449	+	0.0701187i
$557$	−31.9976	+	18.4738i	−1.35578	+	0.782762i	−0.989052	−	0.147565i	$-0.952856\pi$
$557$	−31.9976	+	18.4738i	−1.35578	+	0.782762i	−0.366731	+	0.930327i	$0.619523\pi$
$558$	2.02910	+	10.3380i	0.0858987	+	0.437640i
$559$		−	2.68625i		−	0.113616i
$560$		0			0
$561$	−3.22157	+	3.91535i	−0.136015	+	0.165306i
$562$	2.37423	+	4.11229i	0.100151	+	0.173467i
$563$	−15.1684			−0.639273			−0.319637	−	0.947540i	$-0.603561\pi$
$563$	−15.1684			−0.639273			−0.319637	+	0.947540i	$0.603561\pi$
$564$	2.92277	+	2.40487i	0.123071	+	0.101263i
$565$			38.2585i			1.60955i
$566$	−29.3853			−1.23516
$567$		0			0
$568$	1.94304			0.0815282
$569$		−	36.7292i		−	1.53977i	−0.638183	−	0.769885i	$-0.720314\pi$
$569$		−	36.7292i		−	1.53977i	0.638183	−	0.769885i	$-0.279686\pi$
$570$	−9.28842	−	7.64254i	−0.389049	−	0.320111i
$571$	11.2277			0.469866			0.234933	−	0.972012i	$-0.424513\pi$
$571$	11.2277			0.469866			0.234933	+	0.972012i	$0.424513\pi$
$572$	−5.61811	−	9.73085i	−0.234905	−	0.406867i
$573$	−6.83819	+	8.31085i	−0.285670	+	0.347191i
$574$		0			0
$575$			63.4114i			2.64444i
$576$	−0.577806	−	2.94383i	−0.0240752	−	0.122660i
$577$	31.6545	−	18.2757i	1.31780	−	0.760829i	0.334422	−	0.942424i	$-0.391459\pi$
$577$	31.6545	−	18.2757i	1.31780	−	0.760829i	0.983374	+	0.181594i	$0.0581257\pi$
$578$	−14.2455	−	8.22463i	−0.592534	−	0.342100i
$579$	10.4397	+	8.58986i	0.433861	+	0.356982i
$580$	−9.73085	−	5.61811i	−0.404052	−	0.233279i
$581$		0			0
$582$	5.35061	−	32.1544i	0.221790	−	1.33284i
$583$		0			0
$584$	−2.42743	−	4.20443i	−0.100448	−	0.173981i
$585$	−32.6289	+	6.40429i	−1.34904	+	0.264785i
$586$	5.73666	+	3.31206i	0.236979	+	0.136820i
$587$	4.99738	+	8.65571i	0.206264	+	0.357259i	0.950535	−	0.310619i	$-0.100536\pi$
$587$	4.99738	+	8.65571i	0.206264	+	0.357259i	−0.744271	+	0.667878i	$0.767203\pi$
$588$		0			0
$589$	3.13376	−	5.42784i	0.129124	−	0.223650i
$590$	−0.0712195	+	0.0411186i	−0.00293206	+	0.00169283i
$591$	14.0575	−	17.0849i	0.578248	−	0.702778i
$592$	−1.50079	+	2.59944i	−0.0616820	+	0.106836i
$593$	−3.89111	+	6.73961i	−0.159789	+	0.276763i	−0.934792	−	0.355194i	$-0.884415\pi$
$593$	−3.89111	+	6.73961i	−0.159789	+	0.276763i	0.775004	+	0.631957i	$0.217748\pi$
$594$	10.7574	+	17.4470i	0.441382	+	0.715860i
$595$		0			0
$596$	9.52765	−	5.50079i	0.390268	−	0.225321i
$597$	3.09592	+	0.515173i	0.126708	+	0.0210846i
$598$			17.8119i			0.728385i
$599$		−	25.0124i		−	1.02198i	−0.859586	−	0.510990i	$-0.829279\pi$
$599$		−	25.0124i		−	1.02198i	0.859586	−	0.510990i	$-0.170721\pi$
$600$	6.16618	+	16.4464i	0.251733	+	0.671421i
$601$	25.9925	−	15.0068i	1.06026	−	0.612139i	0.134753	−	0.990879i	$-0.456976\pi$
$601$	25.9925	−	15.0068i	1.06026	−	0.612139i	0.925503	+	0.378740i	$0.123643\pi$
$602$		0			0
$603$	7.77106	+	39.5924i	0.316462	+	1.61233i
$604$	−0.719988	+	1.24706i	−0.0292959	+	0.0507420i
$605$	8.87179	−	15.3664i	0.360689	−	0.624732i
$606$	−5.03569	−	13.4311i	−0.204561	−	0.545603i
$607$	−3.96882	+	2.29140i	−0.161089	+	0.0930050i	−0.578378	−	0.815769i	$-0.696314\pi$
$607$	−3.96882	+	2.29140i	−0.161089	+	0.0930050i	0.417288	+	0.908774i	$0.362981\pi$
$608$	−0.892369	+	1.54563i	−0.0361903	+	0.0626835i
$609$		0			0
$610$	−4.80380	−	8.32043i	−0.194500	−	0.336884i
$611$	−5.39073	−	3.11234i	−0.218085	−	0.125912i
$612$	1.67758	−	1.46368i	0.0678120	−	0.0591659i
$613$	−15.2761	−	26.4590i	−0.616996	−	1.06867i	−0.990031	−	0.140852i	$-0.955016\pi$
$613$	−15.2761	−	26.4590i	−0.616996	−	1.06867i	0.373034	−	0.927818i	$-0.378317\pi$
$614$	21.7242			0.876717
$615$	54.6151	+	44.9375i	2.20229	+	1.81206i
$616$		0			0
$617$	−28.2484	−	16.3092i	−1.13724	−	0.656585i	−0.191493	−	0.981494i	$-0.561333\pi$
$617$	−28.2484	−	16.3092i	−1.13724	−	0.656585i	−0.945745	+	0.324909i	$0.894666\pi$
$618$	4.84712	−	29.1287i	0.194980	−	1.17173i
$619$	17.3244	+	10.0023i	0.696327	+	0.402024i	0.805978	−	0.591946i	$-0.201640\pi$
$619$	17.3244	+	10.0023i	0.696327	+	0.402024i	−0.109651	+	0.993970i	$0.534973\pi$
$620$	−11.8339	+	6.83228i	−0.475259	+	0.274391i
$621$	−0.939542	−	32.4785i	−0.0377025	−	1.30332i
$622$		−	6.29800i		−	0.252527i
$623$		0			0
$624$	1.73205	+	4.61971i	0.0693375	+	0.184937i
$625$	−13.5657	−	23.4965i	−0.542628	−	0.939859i
$626$	22.2191			0.888052
$627$	2.00158	−	12.0284i	0.0799353	−	0.480369i
$628$		−	16.6071i		−	0.662695i
$629$	−2.22752			−0.0888171
$630$		0			0
$631$	6.09634			0.242692			0.121346	−	0.992610i	$-0.461279\pi$
$631$	6.09634			0.242692			0.121346	+	0.992610i	$0.461279\pi$
$632$			3.63613i			0.144637i
$633$	6.12285	−	2.29562i	0.243362	−	0.0912426i
$634$	15.6614			0.621994
$635$	−5.72893	−	9.92279i	−0.227345	−	0.393774i
$636$		0			0
$637$		0			0
$638$		−	11.3907i		−	0.450963i
$639$	5.71999	−	1.12270i	0.226279	−	0.0444134i
$640$	3.36980	−	1.94556i	0.133203	−	0.0769049i
$641$	−28.9612	−	16.7207i	−1.14390	−	0.660429i	−0.196504	−	0.980503i	$-0.562959\pi$
$641$	−28.9612	−	16.7207i	−1.14390	−	0.660429i	−0.947393	+	0.320074i	$0.896292\pi$
$642$	23.2518	−	8.71769i	0.917674	−	0.344060i
$643$	−16.6022	−	9.58527i	−0.654726	−	0.378006i	0.135539	−	0.990772i	$-0.456724\pi$
$643$	−16.6022	−	9.58527i	−0.654726	−	0.378006i	−0.790264	+	0.612766i	$0.790057\pi$
$644$		0			0
$645$	−5.95121	+	2.23126i	−0.234328	+	0.0878559i
$646$	−1.32448			−0.0521111
$647$	−22.3025	−	38.6290i	−0.876800	−	1.51866i	−0.854832	−	0.518904i	$-0.826340\pi$
$647$	−22.3025	−	38.6290i	−0.876800	−	1.51866i	−0.0219681	−	0.999759i	$-0.506993\pi$
$648$	−3.40192	−	8.33228i	−0.133640	−	0.327323i
$649$	−0.0721988	−	0.0416840i	−0.00283405	−	0.00163624i
$650$	−14.4430	−	25.0159i	−0.566500	−	0.981206i
$651$		0			0
$652$	−6.19773	+	10.7348i	−0.242722	+	0.420407i
$653$	0.564755	−	0.326061i	0.0221006	−	0.0127598i	−0.488909	−	0.872335i	$-0.662605\pi$
$653$	0.564755	−	0.326061i	0.0221006	−	0.0127598i	0.511010	+	0.859575i	$0.329272\pi$
$654$	19.2725	+	3.20701i	0.753613	+	0.125404i
$655$	−29.3100	+	50.7664i	−1.14524	+	1.98361i
$656$	5.24705	−	9.08816i	0.204863	−	0.354833i
$657$	−9.57529	−	10.9746i	−0.373568	−	0.428158i
$658$		0			0
$659$	26.2738	−	15.1692i	1.02348	−	0.590908i	0.108372	−	0.994110i	$-0.465436\pi$
$659$	26.2738	−	15.1692i	1.02348	−	0.590908i	0.915111	+	0.403202i	$0.132103\pi$
$660$	−16.8915	+	20.5292i	−0.657501	+	0.799099i
$661$		−	12.8176i		−	0.498548i	−0.968433	−	0.249274i	$-0.919808\pi$
$661$		−	12.8176i		−	0.498548i	0.968433	−	0.249274i	$-0.0801919\pi$
$662$		−	1.27226i		−	0.0494477i
$663$	−2.32636	+	2.82736i	−0.0903484	+	0.109806i
$664$	−6.98012	+	4.02998i	−0.270881	+	0.156393i
$665$		0			0
$666$	−2.91610	+	8.51948i	−0.112996	+	0.330123i
$667$	−9.02843	+	15.6377i	−0.349582	+	0.605494i
$668$	−5.86087	+	10.1513i	−0.226764	+	0.392767i
$669$	21.8323	+	3.63297i	0.844085	+	0.140459i
$670$	−45.3214	+	26.1663i	−1.75092	+	1.01089i
$671$	4.86986	−	8.43484i	0.187999	−	0.325623i
$672$		0			0
$673$	11.2246	+	19.4416i	0.432678	+	0.749420i	0.997103	−	0.0760644i	$-0.0242355\pi$
$673$	11.2246	+	19.4416i	0.432678	+	0.749420i	−0.564425	+	0.825484i	$0.690902\pi$
$674$	6.54717	+	3.78001i	0.252188	+	0.145601i
$675$	27.6550	+	44.8526i	1.06444	+	1.72638i
$676$	2.44304	+	4.23147i	0.0939632	+	0.162749i
$677$	51.1807			1.96703			0.983516	−	0.180820i	$-0.0578752\pi$
$677$	51.1807			1.96703			0.983516	+	0.180820i	$0.0578752\pi$
$678$	15.9461	−	5.97860i	0.612406	−	0.229607i
$679$		0			0
$680$	2.50079	+	1.44383i	0.0959009	+	0.0553684i
$681$	−32.4073	+	12.1503i	−1.24185	+	0.465602i
$682$	−11.9966	−	6.92623i	−0.459373	−	0.265219i
$683$	−12.6107	+	7.28080i	−0.482536	+	0.278592i	−0.721473	−	0.692443i	$-0.756534\pi$
$683$	−12.6107	+	7.28080i	−0.482536	+	0.278592i	0.238937	+	0.971035i	$0.423201\pi$
$684$	−1.73391	+	5.06568i	−0.0662977	+	0.193691i
$685$		−	61.1681i		−	2.33711i
$686$		0			0
$687$	−17.3100	−	2.88045i	−0.660419	−	0.109896i
$688$	0.471521	+	0.816699i	0.0179766	+	0.0311363i
$689$		0			0
$690$	39.4612	−	14.7950i	1.50226	−	0.563237i
$691$			24.4515i			0.930180i	0.885263	+	0.465090i	$0.153978\pi$
$691$			24.4515i			0.930180i	−0.885263	+	0.465090i	$0.846022\pi$
$692$	16.7710			0.637536
$693$		0			0
$694$	−22.1091			−0.839250
$695$			12.8669i			0.488071i
$696$	−0.820992	+	4.93374i	−0.0311196	+	0.187013i
$697$	7.78785			0.294986
$698$	−7.37173	−	12.7682i	−0.279024	−	0.483284i
$699$	4.44495	+	11.8555i	0.168123	+	0.448417i
$700$		0			0
$701$		−	2.21697i		−	0.0837337i	−0.999123	−	0.0418669i	$-0.986669\pi$
$701$		−	2.21697i		−	0.0837337i	0.999123	−	0.0418669i	$-0.0133305\pi$
$702$	7.76816	+	12.5989i	0.293190	+	0.475514i
$703$	4.63932	−	2.67851i	0.174975	−	0.101022i
$704$	3.41614	+	1.97231i	0.128751	+	0.0743342i
$705$	−2.41751	+	14.5280i	−0.0910487	+	0.547155i
$706$	14.9629	+	8.63881i	0.563135	+	0.325126i
$707$		0			0
$708$	0.0282675	+	0.0232586i	0.00106236	+	0.000874112i
$709$	−24.3923			−0.916072			−0.458036	−	0.888934i	$-0.651447\pi$
$709$	−24.3923			−0.916072			−0.458036	+	0.888934i	$0.651447\pi$
$710$	3.78030	+	6.54767i	0.141872	+	0.245730i
$711$	2.10098	+	10.7041i	0.0787927	+	0.401437i
$712$	−8.02499	−	4.63323i	−0.300749	−	0.173638i
$713$	10.9796	+	19.0173i	0.411190	+	0.712203i
$714$		0			0
$715$	21.8607	−	37.8639i	0.817544	−	1.41603i
$716$	5.00158	−	2.88766i	0.186918	−	0.107917i
$717$	−5.11370	−	13.6392i	−0.190975	−	0.509366i
$718$	−5.45647	+	9.45088i	−0.203634	+	0.352704i
$719$	−1.11376	+	1.92909i	−0.0415363	+	0.0719429i	−0.886046	−	0.463597i	$-0.846559\pi$
$719$	−1.11376	+	1.92909i	−0.0415363	+	0.0719429i	0.844510	+	0.535540i	$0.179892\pi$
$720$	8.79598	−	7.67448i	0.327807	−	0.286011i
$721$		0			0
$722$	−13.6959	+	7.90736i	−0.509710	+	0.294281i
$723$	5.44342	+	14.5186i	0.202443	+	0.539954i
$724$			5.53310i			0.205636i
$725$		−	29.2831i		−	1.08755i
$726$	−7.79106	−	1.29646i	−0.289153	−	0.0481162i
$727$	−10.4880	+	6.05523i	−0.388977	+	0.224576i	−0.681717	−	0.731616i	$-0.738766\pi$
$727$	−10.4880	+	6.05523i	−0.388977	+	0.224576i	0.292740	+	0.956192i	$0.405433\pi$
$728$		0			0
$729$	−14.8291	−	22.5632i	−0.549227	−	0.835673i
$730$	9.44541	−	16.3599i	0.349590	−	0.605508i
$731$	−0.349924	+	0.606086i	−0.0129424	+	0.0224169i
$732$	−2.71726	+	3.30244i	−0.100433	+	0.122062i
$733$	13.5673	−	7.83306i	0.501118	−	0.289321i	−0.228057	−	0.973648i	$-0.573237\pi$
$733$	13.5673	−	7.83306i	0.501118	−	0.289321i	0.729175	+	0.684327i	$0.239904\pi$
$734$	17.8636	−	30.9407i	0.659357	−	1.14204i
$735$		0			0
$736$	−3.12656	−	5.41535i	−0.115246	−	0.199613i
$737$	−45.9446	−	26.5261i	−1.69239	−	0.977102i
$738$	10.1952	−	29.7858i	0.375292	−	1.09643i
$739$	4.05227	+	7.01874i	0.149065	+	0.258188i	0.930882	−	0.365319i	$-0.119040\pi$
$739$	4.05227	+	7.01874i	0.149065	+	0.258188i	−0.781817	+	0.623508i	$0.785707\pi$
$740$	−11.6795			−0.429346
$741$	1.44538	−	8.68599i	0.0530974	−	0.319088i
$742$		0			0
$743$	−10.5429	−	6.08697i	−0.386783	−	0.223309i	0.293982	−	0.955811i	$-0.405019\pi$
$743$	−10.5429	−	6.08697i	−0.386783	−	0.223309i	−0.680765	+	0.732502i	$0.738353\pi$
$744$	4.69694	+	3.86466i	0.172198	+	0.141685i
$745$	37.0732	+	21.4042i	1.35826	+	0.784189i
$746$	27.7648	−	16.0300i	1.01654	−	0.586900i
$747$	−18.2198	+	15.8967i	−0.666626	+	0.581631i
$748$			2.92737i			0.107035i
$749$		0			0
$750$	−22.0136	+	26.7544i	−0.803824	+	0.976934i
$751$	−17.3062	−	29.9752i	−0.631511	−	1.09381i	−0.987243	−	0.159221i	$-0.949102\pi$
$751$	−17.3062	−	29.9752i	−0.631511	−	1.09381i	0.355732	−	0.934588i	$-0.384232\pi$
$752$	2.18525			0.0796879
$753$	16.9103	+	13.9139i	0.616246	+	0.507049i
$754$		−	8.22549i		−	0.299555i
$755$	−5.60311			−0.203918
$756$		0			0
$757$	−39.0553			−1.41949			−0.709744	−	0.704459i	$-0.751190\pi$
$757$	−39.0553			−1.41949			−0.709744	+	0.704459i	$0.751190\pi$
$758$		−	34.8891i		−	1.26723i
$759$	32.9909	+	27.1451i	1.19749	+	0.985303i
$760$	−6.94462			−0.251908
$761$	−5.11262	−	8.85532i	−0.185332	−	0.321005i	0.758356	−	0.651840i	$-0.226003\pi$
$761$	−5.11262	−	8.85532i	−0.185332	−	0.321005i	−0.943688	+	0.330835i	$0.892670\pi$
$762$	−3.24055	+	3.93842i	−0.117393	+	0.142674i
$763$		0			0
$764$			6.21372i			0.224805i
$765$	8.19615	+	2.80542i	0.296333	+	0.101430i
$766$	15.1851	−	8.76711i	0.548659	−	0.316769i
$767$	−0.0521363	−	0.0301009i	−0.00188253	−	0.00108688i
$768$	−1.33750	−	1.10050i	−0.0482628	−	0.0397108i
$769$	26.6746	+	15.4006i	0.961910	+	0.555359i	0.896760	−	0.442517i	$-0.145914\pi$
$769$	26.6746	+	15.4006i	0.961910	+	0.555359i	0.0651494	+	0.997876i	$0.479248\pi$
$770$		0			0
$771$	4.63613	−	27.8607i	0.166966	−	1.00338i
$772$	7.80542			0.280923
$773$	−17.8916	−	30.9892i	−0.643518	−	1.11461i	−0.984642	−	0.174587i	$-0.944141\pi$
$773$	−17.8916	−	30.9892i	−0.643518	−	1.11461i	0.341124	−	0.940018i	$-0.389192\pi$
$774$	1.85997	+	2.13178i	0.0668553	+	0.0766251i
$775$	−30.8406	−	17.8059i	−1.10783	−	0.639605i
$776$	−9.40980	−	16.2983i	−0.337792	−	0.585073i
$777$		0			0
$778$	3.81086	−	6.60060i	0.136626	−	0.236643i
$779$	−16.2200	+	9.36461i	−0.581141	+	0.335522i
$780$	−12.1977	+	14.8246i	−0.436749	+	0.530805i
$781$	−3.83228	+	6.63771i	−0.137130	+	0.237516i
$782$	2.32027	−	4.01882i	0.0829727	−	0.143713i
$783$	0.433877	+	14.9985i	0.0155055	+	0.536001i
$784$		0			0
$785$	55.9626	−	32.3100i	1.99739	−	1.15319i
$786$	25.7396	+	4.28317i	0.918101	+	0.152775i
$787$			15.3413i			0.546857i	0.961892	+	0.273429i	$0.0881578\pi$
$787$			15.3413i			0.546857i	−0.961892	+	0.273429i	$0.911842\pi$
$788$		−	12.7737i		−	0.455046i
$789$	14.4241	+	38.4718i	0.513511	+	1.36963i
$790$	−12.2530	+	7.07430i	−0.435944	+	0.251692i
$791$		0			0
$792$	11.1962	+	3.83228i	0.397838	+	0.136174i
$793$	3.51663	−	6.09098i	0.124879	−	0.216297i
$794$	−18.8234	+	32.6032i	−0.668019	+	1.15704i
$795$		0			0
$796$	1.56925	−	0.906005i	0.0556205	−	0.0321125i
$797$	17.5200	−	30.3455i	0.620590	−	1.07489i	−0.368786	−	0.929514i	$-0.620226\pi$
$797$	17.5200	−	30.3455i	0.620590	−	1.07489i	0.989376	−	0.145379i	$-0.0464402\pi$
$798$		0			0
$799$	0.810856	+	1.40444i	0.0286860	+	0.0496857i
$800$	8.78217	+	5.07039i	0.310496	+	0.179265i
$801$	−26.3013	−	9.00256i	−0.929312	−	0.318090i
$802$	10.7207	+	18.5689i	0.378562	+	0.655689i
$803$	19.1506			0.675809
$804$	17.9884	+	14.8009i	0.634401	+	0.521987i
$805$		0			0
$806$	−8.66299	−	5.00158i	−0.305141	−	0.176173i
$807$	2.07060	−	12.4432i	0.0728885	−	0.438022i
$808$	−7.17206	−	4.14079i	−0.252312	−	0.145673i
$809$	23.6360	−	13.6462i	0.830997	−	0.479777i	−0.0231967	−	0.999731i	$-0.507384\pi$
$809$	23.6360	−	13.6462i	0.830997	−	0.479777i	0.854194	+	0.519954i	$0.174051\pi$
$810$	21.4595	−	27.6747i	0.754011	−	0.972391i
$811$			27.7628i			0.974883i	0.873156	+	0.487442i	$0.162070\pi$
$811$			27.7628i			0.974883i	−0.873156	+	0.487442i	$0.837930\pi$
$812$		0			0
$813$	−13.7956	−	36.7955i	−0.483833	−	1.29047i
$814$	−5.92004	−	10.2538i	−0.207497	−	0.359396i
$815$	−48.2322			−1.68950
$816$	0.210992	−	1.26795i	0.00738618	−	0.0443871i
$817$		−	1.68308i		−	0.0588836i
$818$	−29.5703			−1.03390
$819$		0			0
$820$	40.8338			1.42598
$821$		−	44.4523i		−	1.55140i	−0.631104	−	0.775698i	$-0.717398\pi$
$821$		−	44.4523i		−	1.55140i	0.631104	−	0.775698i	$-0.282602\pi$
$822$	−25.4947	+	9.55865i	−0.889231	+	0.333396i
$823$	−51.1153			−1.78177			−0.890884	−	0.454231i	$-0.849914\pi$
$823$	−51.1153			−1.78177			−0.890884	+	0.454231i	$0.849914\pi$
$824$	−8.52435	−	14.7646i	−0.296960	−	0.514349i
$825$	−68.3448	−	11.3728i	−2.37946	−	0.395951i
$826$		0			0
$827$		−	14.5414i		−	0.505653i	−0.967512	−	0.252826i	$-0.918640\pi$
$827$		−	14.5414i		−	0.505653i	0.967512	−	0.252826i	$-0.0813601\pi$
$828$	−12.3331	−	14.1353i	−0.428604	−	0.491237i
$829$	−24.2211	+	13.9841i	−0.841234	+	0.485686i	−0.857683	−	0.514178i	$-0.828097\pi$
$829$	−24.2211	+	13.9841i	−0.841234	+	0.485686i	0.0164497	+	0.999865i	$0.494764\pi$
$830$	−27.1605	−	15.6811i	−0.942754	−	0.544299i
$831$	39.1953	−	14.6953i	1.35967	−	0.509775i
$832$	2.46687	+	1.42425i	0.0855233	+	0.0493769i
$833$		0			0
$834$	5.36291	−	2.01070i	0.185703	−	0.0696247i
$835$	−45.6107			−1.57842
$836$	−3.52006	−	6.09692i	−0.121744	−	0.210866i
$837$	16.0600	+	8.66299i	0.555116	+	0.299437i
$838$	6.17443	+	3.56481i	0.213292	+	0.123144i
$839$	0.499354	+	0.864906i	0.0172396	+	0.0298599i	0.874517	−	0.484996i	$-0.161179\pi$
$839$	0.499354	+	0.864906i	0.0172396	+	0.0298599i	−0.857277	+	0.514856i	$0.827846\pi$
$840$		0			0
$841$	−10.3307	+	17.8933i	−0.356231	+	0.617011i
$842$	−4.00115	+	2.31007i	−0.137889	+	0.0796102i
$843$	8.11303	+	1.35004i	0.279428	+	0.0464978i
$844$	1.88766	−	3.26953i	0.0649760	−	0.112542i
$845$	−9.50616	+	16.4651i	−0.327022	+	0.566418i
$846$	6.43301	−	1.26265i	0.221172	−	0.0434108i
$847$		0			0
$848$		0			0
$849$	−32.3385	+	39.3028i	−1.10985	+	1.34887i
$850$			7.52564i			0.258127i
$851$			18.7692i			0.643400i
$852$	2.13832	−	2.59882i	0.0732575	−	0.0890340i
$853$	−8.48739	+	4.90020i	−0.290603	+	0.167780i	−0.638214	−	0.769859i	$-0.720326\pi$
$853$	−8.48739	+	4.90020i	−0.290603	+	0.167780i	0.347611	+	0.937639i	$0.386993\pi$
$854$		0			0
$855$	−20.4438	+	4.01264i	−0.699163	+	0.137229i
$856$	7.16846	−	12.4161i	0.245013	−	0.424375i
$857$	−3.85002	+	6.66842i	−0.131514	+	0.227789i	−0.924260	−	0.381763i	$-0.875317\pi$
$857$	−3.85002	+	6.66842i	−0.131514	+	0.227789i	0.792746	+	0.609552i	$0.208651\pi$
$858$	−19.1977	−	3.19458i	−0.655400	−	0.109061i
$859$	−16.4022	+	9.46979i	−0.559634	+	0.323105i	−0.752999	−	0.658022i	$-0.771393\pi$
$859$	−16.4022	+	9.46979i	−0.559634	+	0.323105i	0.193364	+	0.981127i	$0.438060\pi$
$860$	−1.83474	+	3.17787i	−0.0625642	+	0.108364i
$861$		0			0
$862$	2.00385	+	3.47078i	0.0682515	+	0.118215i
$863$	−15.1156	−	8.72700i	−0.514541	−	0.297070i	0.220157	−	0.975464i	$-0.429343\pi$
$863$	−15.1156	−	8.72700i	−0.514541	−	0.297070i	−0.734698	+	0.678394i	$0.762676\pi$
$864$	−4.57324	−	2.46687i	−0.155585	−	0.0839245i
$865$	32.6289	+	56.5149i	1.10942	+	1.92156i
$866$	−29.4125			−0.999479
$867$	−26.6776	+	10.0021i	−0.906018	+	0.339690i
$868$		0			0
$869$	−12.4215	−	7.17157i	−0.421371	−	0.243279i
$870$	−18.2230	+	6.83228i	−0.617818	+	0.231636i
$871$	−33.1776	−	19.1551i	−1.12418	−	0.649045i
$872$	9.76874	−	5.63998i	0.330811	−	0.190994i
$873$	−37.1181	−	42.5423i	−1.25626	−	1.43984i
$874$			11.1602i			0.377498i
$875$		0			0
$876$	−8.29481	−	1.38029i	−0.280256	−	0.0466356i
$877$	−0.196152	−	0.339746i	−0.00662360	−	0.0114724i	0.862695	−	0.505725i	$-0.168775\pi$
$877$	−0.196152	−	0.339746i	−0.00662360	−	0.0114724i	−0.869318	+	0.494253i	$0.835442\pi$
$878$	−21.3769			−0.721436
$879$	10.7431	−	4.02786i	0.362355	−	0.135856i
$880$			15.3490i			0.517414i
$881$	−37.0259			−1.24744			−0.623718	−	0.781650i	$-0.714378\pi$
$881$	−37.0259			−1.24744			−0.623718	+	0.781650i	$0.714378\pi$
$882$		0			0
$883$	−29.9586			−1.00819			−0.504094	−	0.863649i	$-0.668174\pi$
$883$	−29.9586			−1.00819			−0.504094	+	0.863649i	$0.668174\pi$
$884$			2.11392i			0.0710987i
$885$	−0.0233809	+	0.140507i	−0.000785940	+	0.00472309i
$886$	5.83386			0.195992
$887$	14.4930	+	25.1026i	0.486626	+	0.842861i	0.999882	−	0.0153745i	$-0.00489405\pi$
$887$	14.4930	+	25.1026i	0.486626	+	0.842861i	−0.513256	+	0.858236i	$0.671561\pi$
$888$	1.82513	+	4.86799i	0.0612475	+	0.163359i
$889$		0			0
$890$		−	36.0569i		−	1.20863i
$891$	35.1739	+	4.81239i	1.17837	+	0.161221i
$892$	11.0662	−	6.38910i	0.370525	−	0.213923i
$893$	−3.37759	−	1.95005i	−0.113027	−	0.0652560i
$894$	3.12786	−	18.7968i	0.104611	−	0.628660i
$895$	19.4617	+	11.2362i	0.650533	+	0.375586i
$896$		0			0
$897$	23.8235	+	19.6020i	0.795442	+	0.654492i
$898$	−22.5823			−0.753582
$899$	−5.07035	−	8.78211i	−0.169106	−	0.292900i
$900$	28.7829	+	9.85197i	0.959430	+	0.328399i
$901$		0			0
$902$	20.6976	+	35.8493i	0.689156	+	1.19365i
$903$		0			0
$904$	4.91614	−	8.51501i	0.163508	−	0.283205i
$905$	−18.6455	+	10.7650i	−0.619796	+	0.357839i
$906$	0.875590	+	2.33537i	0.0290895	+	0.0775874i
$907$	1.94773	−	3.37357i	0.0646733	−	0.112017i	−0.831876	−	0.554962i	$-0.812733\pi$
$907$	1.94773	−	3.37357i	0.0646733	−	0.112017i	0.896549	+	0.442945i	$0.146066\pi$
$908$	−9.99110	+	17.3051i	−0.331566	+	0.574290i
$909$	−23.5059	−	8.04573i	−0.779642	−	0.266860i
$910$		0			0
$911$	1.32768	−	0.766538i	0.0439881	−	0.0253966i	−0.477845	−	0.878444i	$-0.658582\pi$
$911$	1.32768	−	0.766538i	0.0439881	−	0.0253966i	0.521833	+	0.853048i	$0.325248\pi$
$912$	1.08523	+	2.89450i	0.0359354	+	0.0958466i
$913$		−	31.7935i		−	1.05221i
$914$		−	39.8623i		−	1.31853i
$915$	−16.4151	−	2.73154i	−0.542668	−	0.0903020i
$916$	−8.77402	+	5.06568i	−0.289902	+	0.167375i
$917$		0			0
$918$	−0.111505	−	3.85454i	−0.00368020	−	0.127219i
$919$	−14.1266	+	24.4679i	−0.465992	+	0.807122i	−0.999246	−	0.0388335i	$-0.987636\pi$
$919$	−14.1266	+	24.4679i	−0.465992	+	0.807122i	0.533254	+	0.845955i	$0.320969\pi$
$920$	12.1658	−	21.0718i	0.401094	−	0.694715i
$921$	23.9074	−	29.0561i	0.787777	−	0.957430i
$922$	−6.37834	+	3.68254i	−0.210059	+	0.121278i
$923$	−2.76737	+	4.79323i	−0.0910892	+	0.157771i
$924$		0			0
$925$	−15.2192	−	26.3603i	−0.500403	−	0.866723i
$926$	24.8475	+	14.3457i	0.816539	+	0.471429i
$927$	−33.6253	−	38.5391i	−1.10440	−	1.26579i
$928$	1.44383	+	2.50079i	0.0473961	+	0.0820924i
$929$	3.28726			0.107851			0.0539257	−	0.998545i	$-0.482827\pi$
$929$	3.28726			0.107851			0.0539257	+	0.998545i	$0.482827\pi$
$930$	−3.88498	+	23.3467i	−0.127393	+	0.765568i
$931$		0			0
$932$	6.33070	+	3.65503i	0.207369	+	0.119725i
$933$	−8.42356	−	6.93093i	−0.275775	−	0.226909i
$934$	−11.8389	−	6.83519i	−0.387380	−	0.223654i
$935$	−9.86466	+	5.69536i	−0.322609	+	0.186258i
$936$	8.08498	+	2.76737i	0.264266	+	0.0904544i
$937$		−	35.5084i		−	1.16001i	−0.814613	−	0.580005i	$-0.803051\pi$
$937$		−	35.5084i		−	1.16001i	0.814613	−	0.580005i	$-0.196949\pi$
$938$		0			0
$939$	24.4520	−	29.7180i	0.797962	−	0.969809i
$940$	4.25153	+	7.36387i	0.138670	+	0.240183i
$941$	12.4988			0.407450			0.203725	−	0.979028i	$-0.434695\pi$
$941$	12.4988			0.407450			0.203725	+	0.979028i	$0.434695\pi$
$942$	−22.2119	−	18.2761i	−0.723704	−	0.595466i
$943$		−	65.6208i		−	2.13691i
$944$	0.0211346			0.000687873
$945$		0			0
$946$	−3.71994			−0.120946
$947$			36.1154i			1.17359i	0.809734	+	0.586796i	$0.199611\pi$
$947$			36.1154i			1.17359i	−0.809734	+	0.586796i	$0.800389\pi$
$948$	4.86332	+	4.00156i	0.157953	+	0.129964i
$949$	13.8290			0.448910
$950$	−9.04931	−	15.6739i	−0.293598	−	0.508527i
$951$	17.2354	−	20.9471i	0.558895	−	0.679257i
$952$		0			0
$953$			45.2925i			1.46717i	0.679599	+	0.733584i	$0.262154\pi$
$953$			45.2925i			1.46717i	−0.679599	+	0.733584i	$0.737846\pi$
$954$		0			0
$955$	−20.9390	+	12.0892i	−0.677571	+	0.391196i
$956$	−7.28317	−	4.20494i	−0.235554	−	0.135997i
$957$	−15.2351	−	12.5355i	−0.492480	−	0.405215i
$958$	−9.01596	−	5.20537i	−0.291293	−	0.168178i
$959$		0			0
$960$	1.10628	−	6.64819i	0.0357052	−	0.214569i
$961$	18.6677			0.602184
$962$	−4.27499	−	7.40449i	−0.137831	−	0.238730i
$963$	13.9286	−	40.6930i	0.448844	−	1.31131i
$964$	7.75277	+	4.47607i	0.249700	+	0.144164i
$965$	15.1859	+	26.3028i	0.488851	+	0.846716i
$966$		0			0
$967$	12.0000	−	20.7845i	0.385893	−	0.668385i	−0.606000	−	0.795465i	$-0.707227\pi$
$967$	12.0000	−	20.7845i	0.385893	−	0.668385i	0.991893	+	0.127079i	$0.0405602\pi$
$968$	−3.94910	+	2.28001i	−0.126929	+	0.0732824i
$969$	−1.45759	+	1.77150i	−0.0468246	+	0.0569086i
$970$	36.6146	−	63.4184i	1.17562	−	2.03624i
$971$	−16.6813	+	28.8928i	−0.535328	+	0.927215i	0.463819	+	0.885930i	$0.346479\pi$
$971$	−16.6813	+	28.8928i	−0.535328	+	0.927215i	−0.999147	+	0.0412855i	$0.986855\pi$
$972$	−14.8882	−	4.61960i	−0.477540	−	0.148174i
$973$		0			0
$974$	−2.02520	+	1.16925i	−0.0648917	+	0.0374652i
$975$	−49.3533	−	8.21257i	−1.58057	−	0.263013i
$976$			2.46911i			0.0790344i
$977$			34.5077i			1.10400i	0.833844	+	0.552000i	$0.186135\pi$
$977$			34.5077i			1.10400i	−0.833844	+	0.552000i	$0.813865\pi$
$978$	7.53716	+	20.1031i	0.241012	+	0.642825i
$979$	31.6555	−	18.2763i	1.01172	−	0.584114i
$980$		0			0
$981$	25.4987	−	22.2476i	0.814111	−	0.710311i
$982$	−16.9422	+	29.3448i	−0.540648	+	0.936429i
$983$	1.20651	−	2.08973i	0.0384817	−	0.0666522i	−0.846143	−	0.532956i	$-0.821081\pi$
$983$	1.20651	−	2.08973i	0.0384817	−	0.0666522i	0.884625	+	0.466304i	$0.154415\pi$
$984$	−6.38103	−	17.0194i	−0.203420	−	0.542560i
$985$	43.0450	−	24.8521i	1.37153	−	0.791852i
$986$	−1.07149	+	1.85588i	−0.0341232	+	0.0591032i
$987$		0			0
$988$	−2.54191	−	4.40271i	−0.0808688	−	0.140069i
$989$	5.10691	+	2.94847i	0.162390	+	0.0937560i
$990$	8.86872	+	45.1848i	0.281866	+	1.43607i
$991$	−24.2991	−	42.0873i	−0.771887	−	1.33695i	−0.936528	−	0.350594i	$-0.885980\pi$
$991$	−24.2991	−	42.0873i	−0.771887	−	1.33695i	0.164641	−	0.986354i	$-0.447353\pi$
$992$	3.51174			0.111498
$993$	−1.70164	−	1.40012i	−0.0540000	−	0.0444314i
$994$		0			0
$995$	6.10612	+	3.52537i	0.193577	+	0.111762i
$996$	−2.29153	+	13.7709i	−0.0726099	+	0.436347i
$997$	38.8449	+	22.4271i	1.23023	+	0.710274i	0.967078	−	0.254481i	$-0.0819045\pi$
$997$	38.8449	+	22.4271i	1.23023	+	0.710274i	0.263152	+	0.964754i	$0.415238\pi$
$998$	14.3799	−	8.30223i	0.455187	−	0.262802i
$999$	8.18564	+	13.2760i	0.258982	+	0.420033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.l.a.509.1		16
3.2	odd	2		2646.2.l.b.1097.8		16
7.2	even	3		126.2.m.a.41.4	yes	16
7.3	odd	6		882.2.t.b.815.7		16
7.4	even	3		882.2.t.b.815.6		16
7.5	odd	6		126.2.m.a.41.1	✓	16
7.6	odd	2	inner	882.2.l.a.509.4		16
9.2	odd	6		882.2.t.b.803.7		16
9.7	even	3		2646.2.t.a.1979.4		16
21.2	odd	6		378.2.m.a.125.8		16
21.5	even	6		378.2.m.a.125.5		16
21.11	odd	6		2646.2.t.a.2285.1		16
21.17	even	6		2646.2.t.a.2285.4		16
21.20	even	2		2646.2.l.b.1097.5		16
28.19	even	6		1008.2.cc.b.545.7		16
28.23	odd	6		1008.2.cc.b.545.2		16
63.2	odd	6		126.2.m.a.83.1	yes	16
63.5	even	6		1134.2.d.a.1133.16		16
63.11	odd	6	inner	882.2.l.a.227.8		16
63.16	even	3		378.2.m.a.251.5		16
63.20	even	6		882.2.t.b.803.6		16
63.23	odd	6		1134.2.d.a.1133.9		16
63.25	even	3		2646.2.l.b.521.1		16
63.34	odd	6		2646.2.t.a.1979.1		16
63.38	even	6	inner	882.2.l.a.227.5		16
63.40	odd	6		1134.2.d.a.1133.1		16
63.47	even	6		126.2.m.a.83.4	yes	16
63.52	odd	6		2646.2.l.b.521.4		16
63.58	even	3		1134.2.d.a.1133.8		16
63.61	odd	6		378.2.m.a.251.8		16
84.23	even	6		3024.2.cc.b.881.8		16
84.47	odd	6		3024.2.cc.b.881.1		16
252.47	odd	6		1008.2.cc.b.209.2		16
252.79	odd	6		3024.2.cc.b.2897.1		16
252.187	even	6		3024.2.cc.b.2897.8		16
252.191	even	6		1008.2.cc.b.209.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.1	✓	16	7.5	odd	6
126.2.m.a.41.4	yes	16	7.2	even	3
126.2.m.a.83.1	yes	16	63.2	odd	6
126.2.m.a.83.4	yes	16	63.47	even	6
378.2.m.a.125.5		16	21.5	even	6
378.2.m.a.125.8		16	21.2	odd	6
378.2.m.a.251.5		16	63.16	even	3
378.2.m.a.251.8		16	63.61	odd	6
882.2.l.a.227.5		16	63.38	even	6	inner
882.2.l.a.227.8		16	63.11	odd	6	inner
882.2.l.a.509.1		16	1.1	even	1	trivial
882.2.l.a.509.4		16	7.6	odd	2	inner
882.2.t.b.803.6		16	63.20	even	6
882.2.t.b.803.7		16	9.2	odd	6
882.2.t.b.815.6		16	7.4	even	3
882.2.t.b.815.7		16	7.3	odd	6
1008.2.cc.b.209.2		16	252.47	odd	6
1008.2.cc.b.209.7		16	252.191	even	6
1008.2.cc.b.545.2		16	28.23	odd	6
1008.2.cc.b.545.7		16	28.19	even	6
1134.2.d.a.1133.1		16	63.40	odd	6
1134.2.d.a.1133.8		16	63.58	even	3
1134.2.d.a.1133.9		16	63.23	odd	6
1134.2.d.a.1133.16		16	63.5	even	6
2646.2.l.b.521.1		16	63.25	even	3
2646.2.l.b.521.4		16	63.52	odd	6
2646.2.l.b.1097.5		16	21.20	even	2
2646.2.l.b.1097.8		16	3.2	odd	2
2646.2.t.a.1979.1		16	63.34	odd	6
2646.2.t.a.1979.4		16	9.7	even	3
2646.2.t.a.2285.1		16	21.11	odd	6
2646.2.t.a.2285.4		16	21.17	even	6
3024.2.cc.b.881.1		16	84.47	odd	6
3024.2.cc.b.881.8		16	84.23	even	6
3024.2.cc.b.2897.1		16	252.79	odd	6
3024.2.cc.b.2897.8		16	252.187	even	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.33750 - 1.10050i) q^{3} -1.00000 q^{4} +(-1.94556 - 3.36980i) q^{5} +(-1.10050 + 1.33750i) q^{6} +1.00000i q^{8} +(0.577806 + 2.94383i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.33750 - 1.10050i) q^{3} -1.00000 q^{4} +(-1.94556 - 3.36980i) q^{5} +(-1.10050 + 1.33750i) q^{6} +1.00000i q^{8} +(0.577806 + 2.94383i) q^{9} +(-3.36980 + 1.94556i) q^{10} +(-3.41614 - 1.97231i) q^{11} +(1.33750 + 1.10050i) q^{12} +(-2.46687 - 1.42425i) q^{13} +(-1.10628 + 6.64819i) q^{15} +1.00000 q^{16} +(0.371058 + 0.642692i) q^{17} +(2.94383 - 0.577806i) q^{18} +(-1.54563 - 0.892369i) q^{19} +(1.94556 + 3.36980i) q^{20} +(-1.97231 + 3.41614i) q^{22} +(5.41535 - 3.12656i) q^{23} +(1.10050 - 1.33750i) q^{24} +(-5.07039 + 8.78217i) q^{25} +(-1.42425 + 2.46687i) q^{26} +(2.46687 - 4.57324i) q^{27} +(-2.50079 + 1.44383i) q^{29} +(6.64819 + 1.10628i) q^{30} +3.51174i q^{31} -1.00000i q^{32} +(2.39856 + 6.39742i) q^{33} +(0.642692 - 0.371058i) q^{34} +(-0.577806 - 2.94383i) q^{36} +(-1.50079 + 2.59944i) q^{37} +(-0.892369 + 1.54563i) q^{38} +(1.73205 + 4.61971i) q^{39} +(3.36980 - 1.94556i) q^{40} +(5.24705 - 9.08816i) q^{41} +(0.471521 + 0.816699i) q^{43} +(3.41614 + 1.97231i) q^{44} +(8.79598 - 7.67448i) q^{45} +(-3.12656 - 5.41535i) q^{46} +2.18525 q^{47} +(-1.33750 - 1.10050i) q^{48} +(8.78217 + 5.07039i) q^{50} +(0.210992 - 1.26795i) q^{51} +(2.46687 + 1.42425i) q^{52} +(-4.57324 - 2.46687i) q^{54} +15.3490i q^{55} +(1.08523 + 2.89450i) q^{57} +(1.44383 + 2.50079i) q^{58} +0.0211346 q^{59} +(1.10628 - 6.64819i) q^{60} +2.46911i q^{61} +3.51174 q^{62} -1.00000 q^{64} +11.0838i q^{65} +(6.39742 - 2.39856i) q^{66} +13.4493 q^{67} +(-0.371058 - 0.642692i) q^{68} +(-10.6838 - 1.77782i) q^{69} -1.94304i q^{71} +(-2.94383 + 0.577806i) q^{72} +(-4.20443 + 2.42743i) q^{73} +(2.59944 + 1.50079i) q^{74} +(16.4464 - 6.16618i) q^{75} +(1.54563 + 0.892369i) q^{76} +(4.61971 - 1.73205i) q^{78} +3.63613 q^{79} +(-1.94556 - 3.36980i) q^{80} +(-8.33228 + 3.40192i) q^{81} +(-9.08816 - 5.24705i) q^{82} +(4.02998 + 6.98012i) q^{83} +(1.44383 - 2.50079i) q^{85} +(0.816699 - 0.471521i) q^{86} +(4.93374 + 0.820992i) q^{87} +(1.97231 - 3.41614i) q^{88} +(-4.63323 + 8.02499i) q^{89} +(-7.67448 - 8.79598i) q^{90} +(-5.41535 + 3.12656i) q^{92} +(3.86466 - 4.69694i) q^{93} -2.18525i q^{94} +6.94462i q^{95} +(-1.10050 + 1.33750i) q^{96} +(-16.2983 + 9.40980i) q^{97} +(3.83228 - 11.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 12 * q^9	\( 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 12 * q^9 + 12 * q^11 + 16 * q^16 + 12 * q^18 + 48 * q^23 - 8 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 + 60 * q^50 + 24 * q^51 + 48 * q^57 - 12 * q^58 - 16 * q^64 + 56 * q^67 - 12 * q^72 - 36 * q^74 - 24 * q^78 + 8 * q^79 - 12 * q^85 + 24 * q^86 - 48 * q^92 + 84 * q^93 - 72 * q^99

Introduction

L-functions

Modular forms

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