LMFDB - Embedded newform 882.2.g.l.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(361,882)]

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([0, 4]))

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

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

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.2.g.l.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.41421 - 2.44949i) q^{5} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.41421 - 2.44949i) q^{5} -1.00000 q^{8} +(1.41421 - 2.44949i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-0.500000 - 0.866025i) q^{16} +(0.707107 - 1.22474i) q^{17} +(-3.53553 - 6.12372i) q^{19} +2.82843 q^{20} -2.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.50000 + 2.59808i) q^{25} -2.00000 q^{29} +(4.24264 - 7.34847i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.41421 q^{34} +(-5.00000 - 8.66025i) q^{37} +(3.53553 - 6.12372i) q^{38} +(1.41421 + 2.44949i) q^{40} -9.89949 q^{41} +2.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(2.00000 - 3.46410i) q^{46} +(-1.41421 - 2.44949i) q^{47} -3.00000 q^{50} +(-1.00000 + 1.73205i) q^{53} +5.65685 q^{55} +(-1.00000 - 1.73205i) q^{58} +(0.707107 - 1.22474i) q^{59} +(1.41421 + 2.44949i) q^{61} +8.48528 q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{67} +(0.707107 + 1.22474i) q^{68} +12.0000 q^{71} +(-0.707107 + 1.22474i) q^{73} +(5.00000 - 8.66025i) q^{74} +7.07107 q^{76} +(2.00000 + 3.46410i) q^{79} +(-1.41421 + 2.44949i) q^{80} +(-4.94975 - 8.57321i) q^{82} +9.89949 q^{83} -4.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(1.00000 - 1.73205i) q^{88} +(3.53553 + 6.12372i) q^{89} +4.00000 q^{92} +(1.41421 - 2.44949i) q^{94} +(-10.0000 + 17.3205i) q^{95} -9.89949 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 4 q^{11} - 2 q^{16} - 8 q^{22} - 8 q^{23} - 6 q^{25} - 8 q^{29} + 2 q^{32} - 20 q^{37} + 8 q^{43} - 4 q^{44} + 8 q^{46} - 12 q^{50} - 4 q^{53} - 4 q^{58} + 4 q^{64} - 24 q^{67} + 48 q^{71} + 20 q^{74} + 8 q^{79} - 16 q^{85} + 4 q^{86} + 4 q^{88} + 16 q^{92} - 40 q^{95}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 4 * q^11 - 2 * q^16 - 8 * q^22 - 8 * q^23 - 6 * q^25 - 8 * q^29 + 2 * q^32 - 20 * q^37 + 8 * q^43 - 4 * q^44 + 8 * q^46 - 12 * q^50 - 4 * q^53 - 4 * q^58 + 4 * q^64 - 24 * q^67 + 48 * q^71 + 20 * q^74 + 8 * q^79 - 16 * q^85 + 4 * q^86 + 4 * q^88 + 16 * q^92 - 40 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.41421	−	2.44949i	−0.632456	−	1.09545i	−0.987048	−	0.160424i	$-0.948714\pi$
$5$	−1.41421	−	2.44949i	−0.632456	−	1.09545i	0.354593	−	0.935021i	$-0.384620\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.41421	−	2.44949i	0.447214	−	0.774597i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.707107	−	1.22474i	0.171499	−	0.297044i	−0.767445	−	0.641114i	$-0.778472\pi$
$17$	0.707107	−	1.22474i	0.171499	−	0.297044i	0.938944	+	0.344070i	$0.111806\pi$
$18$		0			0
$19$	−3.53553	−	6.12372i	−0.811107	−	1.40488i	−0.912090	−	0.409991i	$-0.865532\pi$
$19$	−3.53553	−	6.12372i	−0.811107	−	1.40488i	0.100983	−	0.994888i	$-0.467801\pi$
$20$	2.82843			0.632456
$21$		0			0
$22$	−2.00000			−0.426401
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	−1.50000	+	2.59808i	−0.300000	+	0.519615i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	4.24264	−	7.34847i	0.762001	−	1.31982i	−0.179817	−	0.983700i	$-0.557551\pi$
$31$	4.24264	−	7.34847i	0.762001	−	1.31982i	0.941818	−	0.336124i	$-0.109116\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	1.41421			0.242536
$35$		0			0
$36$		0			0
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	0.0821995	−	0.996616i	$-0.473806\pi$
$38$	3.53553	−	6.12372i	0.573539	−	0.993399i
$39$		0			0
$40$	1.41421	+	2.44949i	0.223607	+	0.387298i
$41$	−9.89949			−1.54604			−0.773021	−	0.634381i	$-0.781255\pi$
$41$	−9.89949			−1.54604			−0.773021	+	0.634381i	$0.781255\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$		0			0
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	−1.41421	−	2.44949i	−0.206284	−	0.357295i	0.744257	−	0.667893i	$-0.232804\pi$
$47$	−1.41421	−	2.44949i	−0.206284	−	0.357295i	−0.950541	+	0.310599i	$0.899470\pi$
$48$		0			0
$49$		0			0
$50$	−3.00000			−0.424264
$51$		0			0
$52$		0			0
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$		0			0
$55$	5.65685			0.762770
$56$		0			0
$57$		0			0
$58$	−1.00000	−	1.73205i	−0.131306	−	0.227429i
$59$	0.707107	−	1.22474i	0.0920575	−	0.159448i	−0.816319	−	0.577601i	$-0.803989\pi$
$59$	0.707107	−	1.22474i	0.0920575	−	0.159448i	0.908377	+	0.418153i	$0.137322\pi$
$60$		0			0
$61$	1.41421	+	2.44949i	0.181071	+	0.313625i	0.942246	−	0.334922i	$-0.108710\pi$
$61$	1.41421	+	2.44949i	0.181071	+	0.313625i	−0.761174	+	0.648547i	$0.775377\pi$
$62$	8.48528			1.07763
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	0.222571	+	0.974916i	$0.428555\pi$
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	−0.955588	+	0.294706i	$0.904778\pi$
$68$	0.707107	+	1.22474i	0.0857493	+	0.148522i
$69$		0			0
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−0.707107	+	1.22474i	−0.0827606	+	0.143346i	−0.904435	−	0.426612i	$-0.859707\pi$
$73$	−0.707107	+	1.22474i	−0.0827606	+	0.143346i	0.821674	+	0.569958i	$0.193040\pi$
$74$	5.00000	−	8.66025i	0.581238	−	1.00673i
$75$		0			0
$76$	7.07107			0.811107
$77$		0			0
$78$		0			0
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−1.41421	+	2.44949i	−0.158114	+	0.273861i
$81$		0			0
$82$	−4.94975	−	8.57321i	−0.546608	−	0.946753i
$83$	9.89949			1.08661			0.543305	−	0.839535i	$-0.317173\pi$
$83$	9.89949			1.08661			0.543305	+	0.839535i	$0.317173\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$		0			0
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	3.53553	+	6.12372i	0.374766	+	0.649113i	0.990292	−	0.139003i	$-0.0443898\pi$
$89$	3.53553	+	6.12372i	0.374766	+	0.649113i	−0.615526	+	0.788116i	$0.711056\pi$
$90$		0			0
$91$		0			0
$92$	4.00000			0.417029
$93$		0			0
$94$	1.41421	−	2.44949i	0.145865	−	0.252646i
$95$	−10.0000	+	17.3205i	−1.02598	+	1.77705i
$96$		0			0
$97$	−9.89949			−1.00514			−0.502571	−	0.864536i	$-0.667612\pi$
$97$	−9.89949			−1.00514			−0.502571	+	0.864536i	$0.667612\pi$
$98$		0			0
$99$		0			0
$100$	−1.50000	−	2.59808i	−0.150000	−	0.259808i
$101$	−4.24264	+	7.34847i	−0.422159	+	0.731200i	−0.996150	−	0.0876610i	$-0.972061\pi$
$101$	−4.24264	+	7.34847i	−0.422159	+	0.731200i	0.573992	+	0.818861i	$0.305394\pi$
$102$		0			0
$103$	1.41421	+	2.44949i	0.139347	+	0.241355i	0.927249	−	0.374444i	$-0.122166\pi$
$103$	1.41421	+	2.44949i	0.139347	+	0.241355i	−0.787903	+	0.615800i	$0.788833\pi$
$104$		0			0
$105$		0			0
$106$	−2.00000			−0.194257
$107$	−2.00000	−	3.46410i	−0.193347	−	0.334887i	0.753010	−	0.658009i	$-0.228601\pi$
$107$	−2.00000	−	3.46410i	−0.193347	−	0.334887i	−0.946357	+	0.323122i	$0.895268\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	2.82843	+	4.89898i	0.269680	+	0.467099i
$111$		0			0
$112$		0			0
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$	−5.65685	+	9.79796i	−0.527504	+	0.913664i
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$		0			0
$118$	1.41421			0.130189
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−1.41421	+	2.44949i	−0.128037	+	0.221766i
$123$		0			0
$124$	4.24264	+	7.34847i	0.381000	+	0.659912i
$125$	−5.65685			−0.505964
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−6.36396	−	11.0227i	−0.556022	−	0.963058i	−0.997823	−	0.0659452i	$-0.978994\pi$
$131$	−6.36396	−	11.0227i	−0.556022	−	0.963058i	0.441801	−	0.897113i	$-0.354340\pi$
$132$		0			0
$133$		0			0
$134$	−12.0000			−1.03664
$135$		0			0
$136$	−0.707107	+	1.22474i	−0.0606339	+	0.105021i
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	−9.89949			−0.839664			−0.419832	−	0.907602i	$-0.637911\pi$
$139$	−9.89949			−0.839664			−0.419832	+	0.907602i	$0.637911\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	+	10.3923i	0.503509	+	0.872103i
$143$		0			0
$144$		0			0
$145$	2.82843	+	4.89898i	0.234888	+	0.406838i
$146$	−1.41421			−0.117041
$147$		0			0
$148$	10.0000			0.821995
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	3.53553	+	6.12372i	0.286770	+	0.496700i
$153$		0			0
$154$		0			0
$155$	−24.0000			−1.92773
$156$		0			0
$157$	−5.65685	+	9.79796i	−0.451466	+	0.781962i	−0.998477	−	0.0551630i	$-0.982432\pi$
$157$	−5.65685	+	9.79796i	−0.451466	+	0.781962i	0.547011	+	0.837125i	$0.315765\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$		0			0
$160$	−2.82843			−0.223607
$161$		0			0
$162$		0			0
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	0.601035	−	0.799223i	$-0.294755\pi$
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	−0.992665	+	0.120900i	$0.961422\pi$
$164$	4.94975	−	8.57321i	0.386510	−	0.669456i
$165$		0			0
$166$	4.94975	+	8.57321i	0.384175	+	0.665410i
$167$	−19.7990			−1.53209			−0.766046	−	0.642786i	$-0.777779\pi$
$167$	−19.7990			−1.53209			−0.766046	+	0.642786i	$0.777779\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	−2.00000	−	3.46410i	−0.153393	−	0.265684i
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	8.48528	+	14.6969i	0.645124	+	1.11739i	0.984273	+	0.176655i	$0.0565276\pi$
$173$	8.48528	+	14.6969i	0.645124	+	1.11739i	−0.339149	+	0.940733i	$0.610139\pi$
$174$		0			0
$175$		0			0
$176$	2.00000			0.150756
$177$		0			0
$178$	−3.53553	+	6.12372i	−0.264999	+	0.458993i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	−14.1421	+	24.4949i	−1.03975	+	1.80090i
$186$		0			0
$187$	1.41421	+	2.44949i	0.103418	+	0.179124i
$188$	2.82843			0.206284
$189$		0			0
$190$	−20.0000			−1.45095
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$		0			0
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	−0.420096	−	0.907480i	$-0.638004\pi$
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	0.995948	−	0.0899262i	$-0.0286631\pi$
$194$	−4.94975	−	8.57321i	−0.355371	−	0.615521i
$195$		0			0
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	4.24264	−	7.34847i	0.300753	−	0.520919i	−0.675554	−	0.737311i	$-0.736095\pi$
$199$	4.24264	−	7.34847i	0.300753	−	0.520919i	0.976307	+	0.216391i	$0.0694287\pi$
$200$	1.50000	−	2.59808i	0.106066	−	0.183712i
$201$		0			0
$202$	−8.48528			−0.597022
$203$		0			0
$204$		0			0
$205$	14.0000	+	24.2487i	0.977802	+	1.69360i
$206$	−1.41421	+	2.44949i	−0.0985329	+	0.170664i
$207$		0			0
$208$		0			0
$209$	14.1421			0.978232
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$	−1.00000	−	1.73205i	−0.0686803	−	0.118958i
$213$		0			0
$214$	2.00000	−	3.46410i	0.136717	−	0.236801i
$215$	−2.82843	−	4.89898i	−0.192897	−	0.334108i
$216$		0			0
$217$		0			0
$218$	2.00000			0.135457
$219$		0			0
$220$	−2.82843	+	4.89898i	−0.190693	+	0.330289i
$221$		0			0
$222$		0			0
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$		0			0
$225$		0			0
$226$	6.00000	+	10.3923i	0.399114	+	0.691286i
$227$	10.6066	−	18.3712i	0.703985	−	1.21934i	−0.263072	−	0.964776i	$-0.584736\pi$
$227$	10.6066	−	18.3712i	0.703985	−	1.21934i	0.967057	−	0.254561i	$-0.0819311\pi$
$228$		0			0
$229$	−8.48528	−	14.6969i	−0.560723	−	0.971201i	−0.997434	−	0.0715988i	$-0.977190\pi$
$229$	−8.48528	−	14.6969i	−0.560723	−	0.971201i	0.436710	−	0.899602i	$-0.356143\pi$
$230$	−11.3137			−0.746004
$231$		0			0
$232$	2.00000			0.131306
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	0.928312	+	0.371802i	$0.121260\pi$
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	−0.142166	+	0.989843i	$0.545407\pi$
$234$		0			0
$235$	−4.00000	+	6.92820i	−0.260931	+	0.451946i
$236$	0.707107	+	1.22474i	0.0460287	+	0.0797241i
$237$		0			0
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	−10.6066	+	18.3712i	−0.683231	+	1.18339i	0.290758	+	0.956797i	$0.406093\pi$
$241$	−10.6066	+	18.3712i	−0.683231	+	1.18339i	−0.973989	+	0.226595i	$0.927241\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$		0			0
$244$	−2.82843			−0.181071
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−4.24264	+	7.34847i	−0.269408	+	0.466628i
$249$		0			0
$250$	−2.82843	−	4.89898i	−0.178885	−	0.309839i
$251$	9.89949			0.624851			0.312425	−	0.949942i	$-0.398859\pi$
$251$	9.89949			0.624851			0.312425	+	0.949942i	$0.398859\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$	8.00000	+	13.8564i	0.501965	+	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.36396	−	11.0227i	−0.396973	−	0.687577i	0.596378	−	0.802704i	$-0.296606\pi$
$257$	−6.36396	−	11.0227i	−0.396973	−	0.687577i	−0.993351	+	0.115126i	$0.963273\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	6.36396	−	11.0227i	0.393167	−	0.680985i
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$		0			0
$265$	5.65685			0.347498
$266$		0			0
$267$		0			0
$268$	−6.00000	−	10.3923i	−0.366508	−	0.634811i
$269$	5.65685	−	9.79796i	0.344904	−	0.597392i	−0.640432	−	0.768015i	$-0.721245\pi$
$269$	5.65685	−	9.79796i	0.344904	−	0.597392i	0.985336	+	0.170623i	$0.0545780\pi$
$270$		0			0
$271$	11.3137	+	19.5959i	0.687259	+	1.19037i	0.972721	+	0.231977i	$0.0745195\pi$
$271$	11.3137	+	19.5959i	0.687259	+	1.19037i	−0.285462	+	0.958390i	$0.592147\pi$
$272$	−1.41421			−0.0857493
$273$		0			0
$274$	12.0000			0.724947
$275$	−3.00000	−	5.19615i	−0.180907	−	0.313340i
$276$		0			0
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$	−4.94975	−	8.57321i	−0.296866	−	0.514187i
$279$		0			0
$280$		0			0
$281$	−16.0000			−0.954480			−0.477240	−	0.878773i	$-0.658363\pi$
$281$	−16.0000			−0.954480			−0.477240	+	0.878773i	$0.658363\pi$
$282$		0			0
$283$	−0.707107	+	1.22474i	−0.0420331	+	0.0728035i	−0.886277	−	0.463156i	$-0.846717\pi$
$283$	−0.707107	+	1.22474i	−0.0420331	+	0.0728035i	0.844243	+	0.535960i	$0.180050\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.50000	+	12.9904i	0.441176	+	0.764140i
$290$	−2.82843	+	4.89898i	−0.166091	+	0.287678i
$291$		0			0
$292$	−0.707107	−	1.22474i	−0.0413803	−	0.0716728i
$293$	−19.7990			−1.15667			−0.578335	−	0.815800i	$-0.696297\pi$
$293$	−19.7990			−1.15667			−0.578335	+	0.815800i	$0.696297\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	5.00000	+	8.66025i	0.290619	+	0.503367i
$297$		0			0
$298$	−5.00000	+	8.66025i	−0.289642	+	0.501675i
$299$		0			0
$300$		0			0
$301$		0			0
$302$	16.0000			0.920697
$303$		0			0
$304$	−3.53553	+	6.12372i	−0.202777	+	0.351220i
$305$	4.00000	−	6.92820i	0.229039	−	0.396708i
$306$		0			0
$307$	9.89949			0.564994			0.282497	−	0.959268i	$-0.408837\pi$
$307$	9.89949			0.564994			0.282497	+	0.959268i	$0.408837\pi$
$308$		0			0
$309$		0			0
$310$	−12.0000	−	20.7846i	−0.681554	−	1.18049i
$311$	5.65685	−	9.79796i	0.320771	−	0.555591i	−0.659877	−	0.751374i	$-0.729391\pi$
$311$	5.65685	−	9.79796i	0.320771	−	0.555591i	0.980647	+	0.195783i	$0.0627248\pi$
$312$		0			0
$313$	6.36396	+	11.0227i	0.359712	+	0.623040i	0.987913	−	0.155012i	$-0.0495415\pi$
$313$	6.36396	+	11.0227i	0.359712	+	0.623040i	−0.628200	+	0.778052i	$0.716208\pi$
$314$	−11.3137			−0.638470
$315$		0			0
$316$	−4.00000			−0.225018
$317$	5.00000	+	8.66025i	0.280828	+	0.486408i	0.971589	−	0.236675i	$-0.0760576\pi$
$317$	5.00000	+	8.66025i	0.280828	+	0.486408i	−0.690761	+	0.723083i	$0.742724\pi$
$318$		0			0
$319$	2.00000	−	3.46410i	0.111979	−	0.193952i
$320$	−1.41421	−	2.44949i	−0.0790569	−	0.136931i
$321$		0			0
$322$		0			0
$323$	−10.0000			−0.556415
$324$		0			0
$325$		0			0
$326$	5.00000	−	8.66025i	0.276924	−	0.479647i
$327$		0			0
$328$	9.89949			0.546608
$329$		0			0
$330$		0			0
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$	−4.94975	+	8.57321i	−0.271653	+	0.470516i
$333$		0			0
$334$	−9.89949	−	17.1464i	−0.541676	−	0.938211i
$335$	33.9411			1.85440
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	−6.50000	−	11.2583i	−0.353553	−	0.612372i
$339$		0			0
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$	8.48528	+	14.6969i	0.459504	+	0.795884i
$342$		0			0
$343$		0			0
$344$	−2.00000			−0.107833
$345$		0			0
$346$	−8.48528	+	14.6969i	−0.456172	+	0.790112i
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	0.110885	+	0.993833i	$0.464631\pi$
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	−0.916127	+	0.400887i	$0.868702\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$		0			0
$351$		0			0
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	0.707107	−	1.22474i	0.0376355	−	0.0651866i	−0.846594	−	0.532239i	$-0.821351\pi$
$353$	0.707107	−	1.22474i	0.0376355	−	0.0651866i	0.884230	+	0.467052i	$0.154684\pi$
$354$		0			0
$355$	−16.9706	−	29.3939i	−0.900704	−	1.56007i
$356$	−7.07107			−0.374766
$357$		0			0
$358$	12.0000			0.634220
$359$	−16.0000	−	27.7128i	−0.844448	−	1.46263i	−0.886100	−	0.463494i	$-0.846596\pi$
$359$	−16.0000	−	27.7128i	−0.844448	−	1.46263i	0.0416523	−	0.999132i	$-0.486738\pi$
$360$		0			0
$361$	−15.5000	+	26.8468i	−0.815789	+	1.41299i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.00000			0.209370
$366$		0			0
$367$	14.1421	−	24.4949i	0.738213	−	1.27862i	−0.215086	−	0.976595i	$-0.569003\pi$
$367$	14.1421	−	24.4949i	0.738213	−	1.27862i	0.953299	−	0.302028i	$-0.0976636\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$		0			0
$370$	−28.2843			−1.47043
$371$		0			0
$372$		0			0
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	0.707055	−	0.707159i	$-0.250023\pi$
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	−0.965945	+	0.258748i	$0.916690\pi$
$374$	−1.41421	+	2.44949i	−0.0731272	+	0.126660i
$375$		0			0
$376$	1.41421	+	2.44949i	0.0729325	+	0.126323i
$377$		0			0
$378$		0			0
$379$	−26.0000			−1.33553			−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000			−1.33553			−0.667765	+	0.744372i	$0.732749\pi$
$380$	−10.0000	−	17.3205i	−0.512989	−	0.888523i
$381$		0			0
$382$	2.00000	−	3.46410i	0.102329	−	0.177239i
$383$	18.3848	+	31.8434i	0.939418	+	1.62712i	0.766559	+	0.642173i	$0.221967\pi$
$383$	18.3848	+	31.8434i	0.939418	+	1.62712i	0.172859	+	0.984947i	$0.444700\pi$
$384$		0			0
$385$		0			0
$386$	16.0000			0.814379
$387$		0			0
$388$	4.94975	−	8.57321i	0.251285	−	0.435239i
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	−0.321716	−	0.946836i	$-0.604260\pi$
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	0.980842	−	0.194804i	$-0.0624070\pi$
$390$		0			0
$391$	−5.65685			−0.286079
$392$		0			0
$393$		0			0
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$	5.65685	−	9.79796i	0.284627	−	0.492989i
$396$		0			0
$397$	11.3137	+	19.5959i	0.567819	+	0.983491i	0.996781	+	0.0801687i	$0.0255459\pi$
$397$	11.3137	+	19.5959i	0.567819	+	0.983491i	−0.428963	+	0.903322i	$0.641121\pi$
$398$	8.48528			0.425329
$399$		0			0
$400$	3.00000			0.150000
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		0			0
$403$		0			0
$404$	−4.24264	−	7.34847i	−0.211079	−	0.365600i
$405$		0			0
$406$		0			0
$407$	20.0000			0.991363
$408$		0			0
$409$	19.0919	−	33.0681i	0.944033	−	1.63511i	0.186357	−	0.982482i	$-0.440332\pi$
$409$	19.0919	−	33.0681i	0.944033	−	1.63511i	0.757676	−	0.652631i	$-0.226335\pi$
$410$	−14.0000	+	24.2487i	−0.691411	+	1.19756i
$411$		0			0
$412$	−2.82843			−0.139347
$413$		0			0
$414$		0			0
$415$	−14.0000	−	24.2487i	−0.687233	−	1.19032i
$416$		0			0
$417$		0			0
$418$	7.07107	+	12.2474i	0.345857	+	0.599042i
$419$	−9.89949			−0.483622			−0.241811	−	0.970323i	$-0.577741\pi$
$419$	−9.89949			−0.483622			−0.241811	+	0.970323i	$0.577741\pi$
$420$		0			0
$421$	30.0000			1.46211			0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000			1.46211			0.731055	+	0.682318i	$0.239028\pi$
$422$	−6.00000	−	10.3923i	−0.292075	−	0.505889i
$423$		0			0
$424$	1.00000	−	1.73205i	0.0485643	−	0.0841158i
$425$	2.12132	+	3.67423i	0.102899	+	0.178227i
$426$		0			0
$427$		0			0
$428$	4.00000			0.193347
$429$		0			0
$430$	2.82843	−	4.89898i	0.136399	−	0.236250i
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	29.6985			1.42722			0.713609	−	0.700544i	$-0.247059\pi$
$433$	29.6985			1.42722			0.713609	+	0.700544i	$0.247059\pi$
$434$		0			0
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−14.1421	+	24.4949i	−0.676510	+	1.17175i
$438$		0			0
$439$	−8.48528	−	14.6969i	−0.404980	−	0.701447i	0.589339	−	0.807886i	$-0.299388\pi$
$439$	−8.48528	−	14.6969i	−0.404980	−	0.701447i	−0.994319	+	0.106439i	$0.966055\pi$
$440$	−5.65685			−0.269680
$441$		0			0
$442$		0			0
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	0.814595	−	0.580030i	$-0.196959\pi$
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	−0.909618	+	0.415445i	$0.863626\pi$
$444$		0			0
$445$	10.0000	−	17.3205i	0.474045	−	0.821071i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	9.89949	−	17.1464i	0.466149	−	0.807394i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$		0			0
$454$	21.2132			0.995585
$455$		0			0
$456$		0			0
$457$	−12.0000	−	20.7846i	−0.561336	−	0.972263i	−0.997380	−	0.0723376i	$-0.976954\pi$
$457$	−12.0000	−	20.7846i	−0.561336	−	0.972263i	0.436044	−	0.899925i	$-0.356379\pi$
$458$	8.48528	−	14.6969i	0.396491	−	0.686743i
$459$		0			0
$460$	−5.65685	−	9.79796i	−0.263752	−	0.456832i
$461$	39.5980			1.84426			0.922131	−	0.386878i	$-0.126447\pi$
$461$	39.5980			1.84426			0.922131	+	0.386878i	$0.126447\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	−16.2635	−	28.1691i	−0.752583	−	1.30351i	−0.946567	−	0.322507i	$-0.895474\pi$
$467$	−16.2635	−	28.1691i	−0.752583	−	1.30351i	0.193984	−	0.981005i	$-0.437859\pi$
$468$		0			0
$469$		0			0
$470$	−8.00000			−0.369012
$471$		0			0
$472$	−0.707107	+	1.22474i	−0.0325472	+	0.0563735i
$473$	−2.00000	+	3.46410i	−0.0919601	+	0.159280i
$474$		0			0
$475$	21.2132			0.973329
$476$		0			0
$477$		0			0
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	15.5563	−	26.9444i	0.710788	−	1.23112i	−0.253774	−	0.967264i	$-0.581672\pi$
$479$	15.5563	−	26.9444i	0.710788	−	1.23112i	0.964562	−	0.263857i	$-0.0849947\pi$
$480$		0			0
$481$		0			0
$482$	−21.2132			−0.966235
$483$		0			0
$484$	−7.00000			−0.318182
$485$	14.0000	+	24.2487i	0.635707	+	1.10108i
$486$		0			0
$487$	−6.00000	+	10.3923i	−0.271886	+	0.470920i	−0.969345	−	0.245705i	$-0.920981\pi$
$487$	−6.00000	+	10.3923i	−0.271886	+	0.470920i	0.697459	+	0.716625i	$0.254314\pi$
$488$	−1.41421	−	2.44949i	−0.0640184	−	0.110883i
$489$		0			0
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	−1.41421	+	2.44949i	−0.0636930	+	0.110319i
$494$		0			0
$495$		0			0
$496$	−8.48528			−0.381000
$497$		0			0
$498$		0			0
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	2.82843	−	4.89898i	0.126491	−	0.219089i
$501$		0			0
$502$	4.94975	+	8.57321i	0.220918	+	0.382641i
$503$	39.5980			1.76559			0.882793	−	0.469762i	$-0.155660\pi$
$503$	39.5980			1.76559			0.882793	+	0.469762i	$0.155660\pi$
$504$		0			0
$505$	24.0000			1.06799
$506$	4.00000	+	6.92820i	0.177822	+	0.307996i
$507$		0			0
$508$	−8.00000	+	13.8564i	−0.354943	+	0.614779i
$509$	−11.3137	−	19.5959i	−0.501471	−	0.868574i	−0.999999	−	0.00169976i	$-0.999459\pi$
$509$	−11.3137	−	19.5959i	−0.501471	−	0.868574i	0.498527	−	0.866874i	$-0.333874\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	6.36396	−	11.0227i	0.280702	−	0.486191i
$515$	4.00000	−	6.92820i	0.176261	−	0.305293i
$516$		0			0
$517$	5.65685			0.248788
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.707107	−	1.22474i	0.0309789	−	0.0536570i	−0.850120	−	0.526589i	$-0.823471\pi$
$521$	0.707107	−	1.22474i	0.0309789	−	0.0536570i	0.881099	+	0.472931i	$0.156804\pi$
$522$		0			0
$523$	6.36396	+	11.0227i	0.278277	+	0.481989i	0.970957	−	0.239256i	$-0.0769035\pi$
$523$	6.36396	+	11.0227i	0.278277	+	0.481989i	−0.692680	+	0.721245i	$0.743570\pi$
$524$	12.7279			0.556022
$525$		0			0
$526$	12.0000			0.523225
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	2.82843	+	4.89898i	0.122859	+	0.212798i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−5.65685	+	9.79796i	−0.244567	+	0.423603i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$		0			0
$538$	11.3137			0.487769
$539$		0			0
$540$		0			0
$541$	−5.00000	−	8.66025i	−0.214967	−	0.372333i	0.738296	−	0.674477i	$-0.235631\pi$
$541$	−5.00000	−	8.66025i	−0.214967	−	0.372333i	−0.953262	+	0.302144i	$0.902298\pi$
$542$	−11.3137	+	19.5959i	−0.485965	+	0.841717i
$543$		0			0
$544$	−0.707107	−	1.22474i	−0.0303170	−	0.0525105i
$545$	−5.65685			−0.242313
$546$		0			0
$547$	−26.0000			−1.11168			−0.555840	−	0.831289i	$-0.687603\pi$
$547$	−26.0000			−1.11168			−0.555840	+	0.831289i	$0.687603\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$		0			0
$550$	3.00000	−	5.19615i	0.127920	−	0.221565i
$551$	7.07107	+	12.2474i	0.301238	+	0.521759i
$552$		0			0
$553$		0			0
$554$	2.00000			0.0849719
$555$		0			0
$556$	4.94975	−	8.57321i	0.209916	−	0.363585i
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	0.350824	+	0.936442i	$0.385902\pi$
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	−0.986394	+	0.164399i	$0.947432\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−8.00000	−	13.8564i	−0.337460	−	0.584497i
$563$	0.707107	−	1.22474i	0.0298010	−	0.0516168i	−0.850740	−	0.525586i	$-0.823846\pi$
$563$	0.707107	−	1.22474i	0.0298010	−	0.0516168i	0.880541	+	0.473970i	$0.157179\pi$
$564$		0			0
$565$	−16.9706	−	29.3939i	−0.713957	−	1.23661i
$566$	−1.41421			−0.0594438
$567$		0			0
$568$	−12.0000			−0.503509
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	0.951592	−	0.307364i	$-0.0994469\pi$
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	−0.741981	+	0.670421i	$0.766114\pi$
$570$		0			0
$571$	1.00000	−	1.73205i	0.0418487	−	0.0724841i	−0.844342	−	0.535804i	$-0.820009\pi$
$571$	1.00000	−	1.73205i	0.0418487	−	0.0724841i	0.886191	+	0.463320i	$0.153342\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	−10.6066	+	18.3712i	−0.441559	+	0.764802i	−0.997805	−	0.0662152i	$-0.978908\pi$
$577$	−10.6066	+	18.3712i	−0.441559	+	0.764802i	0.556247	+	0.831017i	$0.312241\pi$
$578$	−7.50000	+	12.9904i	−0.311959	+	0.540329i
$579$		0			0
$580$	−5.65685			−0.234888
$581$		0			0
$582$		0			0
$583$	−2.00000	−	3.46410i	−0.0828315	−	0.143468i
$584$	0.707107	−	1.22474i	0.0292603	−	0.0506803i
$585$		0			0
$586$	−9.89949	−	17.1464i	−0.408944	−	0.708312i
$587$	−29.6985			−1.22579			−0.612894	−	0.790165i	$-0.709995\pi$
$587$	−29.6985			−1.22579			−0.612894	+	0.790165i	$0.709995\pi$
$588$		0			0
$589$	−60.0000			−2.47226
$590$	−2.00000	−	3.46410i	−0.0823387	−	0.142615i
$591$		0			0
$592$	−5.00000	+	8.66025i	−0.205499	+	0.355934i
$593$	3.53553	+	6.12372i	0.145187	+	0.251471i	0.929443	−	0.368967i	$-0.120288\pi$
$593$	3.53553	+	6.12372i	0.145187	+	0.251471i	−0.784256	+	0.620438i	$0.786955\pi$
$594$		0			0
$595$		0			0
$596$	−10.0000			−0.409616
$597$		0			0
$598$		0			0
$599$	−8.00000	+	13.8564i	−0.326871	+	0.566157i	−0.981889	−	0.189456i	$-0.939328\pi$
$599$	−8.00000	+	13.8564i	−0.326871	+	0.566157i	0.655018	+	0.755613i	$0.272661\pi$
$600$		0			0
$601$	−29.6985			−1.21143			−0.605713	−	0.795683i	$-0.707112\pi$
$601$	−29.6985			−1.21143			−0.605713	+	0.795683i	$0.707112\pi$
$602$		0			0
$603$		0			0
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$	9.89949	−	17.1464i	0.402472	−	0.697101i
$606$		0			0
$607$	−8.48528	−	14.6969i	−0.344407	−	0.596530i	0.640839	−	0.767675i	$-0.278587\pi$
$607$	−8.48528	−	14.6969i	−0.344407	−	0.596530i	−0.985246	+	0.171145i	$0.945253\pi$
$608$	−7.07107			−0.286770
$609$		0			0
$610$	8.00000			0.323911
$611$		0			0
$612$		0			0
$613$	15.0000	−	25.9808i	0.605844	−	1.04935i	−0.386073	−	0.922468i	$-0.626169\pi$
$613$	15.0000	−	25.9808i	0.605844	−	1.04935i	0.991917	−	0.126885i	$-0.0404979\pi$
$614$	4.94975	+	8.57321i	0.199756	+	0.345987i
$615$		0			0
$616$		0			0
$617$	26.0000			1.04672			0.523360	−	0.852111i	$-0.324678\pi$
$617$	26.0000			1.04672			0.523360	+	0.852111i	$0.324678\pi$
$618$		0			0
$619$	9.19239	−	15.9217i	0.369473	−	0.639946i	−0.620010	−	0.784594i	$-0.712871\pi$
$619$	9.19239	−	15.9217i	0.369473	−	0.639946i	0.989483	+	0.144647i	$0.0462048\pi$
$620$	12.0000	−	20.7846i	0.481932	−	0.834730i
$621$		0			0
$622$	11.3137			0.453638
$623$		0			0
$624$		0			0
$625$	15.5000	+	26.8468i	0.620000	+	1.07387i
$626$	−6.36396	+	11.0227i	−0.254355	+	0.440556i
$627$		0			0
$628$	−5.65685	−	9.79796i	−0.225733	−	0.390981i
$629$	−14.1421			−0.563884
$630$		0			0
$631$	44.0000			1.75161			0.875806	−	0.482663i	$-0.160330\pi$
$631$	44.0000			1.75161			0.875806	+	0.482663i	$0.160330\pi$
$632$	−2.00000	−	3.46410i	−0.0795557	−	0.137795i
$633$		0			0
$634$	−5.00000	+	8.66025i	−0.198575	+	0.343943i
$635$	−22.6274	−	39.1918i	−0.897942	−	1.55528i
$636$		0			0
$637$		0			0
$638$	4.00000			0.158362
$639$		0			0
$640$	1.41421	−	2.44949i	0.0559017	−	0.0968246i
$641$	13.0000	−	22.5167i	0.513469	−	0.889355i	−0.486409	−	0.873731i	$-0.661693\pi$
$641$	13.0000	−	22.5167i	0.513469	−	0.889355i	0.999878	−	0.0156233i	$-0.00497325\pi$
$642$		0			0
$643$	−9.89949			−0.390398			−0.195199	−	0.980764i	$-0.562535\pi$
$643$	−9.89949			−0.390398			−0.195199	+	0.980764i	$0.562535\pi$
$644$		0			0
$645$		0			0
$646$	−5.00000	−	8.66025i	−0.196722	−	0.340733i
$647$	−4.24264	+	7.34847i	−0.166795	+	0.288898i	−0.937291	−	0.348547i	$-0.886675\pi$
$647$	−4.24264	+	7.34847i	−0.166795	+	0.288898i	0.770496	+	0.637445i	$0.220009\pi$
$648$		0			0
$649$	1.41421	+	2.44949i	0.0555127	+	0.0961509i
$650$		0			0
$651$		0			0
$652$	10.0000			0.391630
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$		0			0
$655$	−18.0000	+	31.1769i	−0.703318	+	1.21818i
$656$	4.94975	+	8.57321i	0.193255	+	0.334728i
$657$		0			0
$658$		0			0
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$		0			0
$661$	4.24264	−	7.34847i	0.165020	−	0.285822i	−0.771643	−	0.636056i	$-0.780565\pi$
$661$	4.24264	−	7.34847i	0.165020	−	0.285822i	0.936662	+	0.350234i	$0.113898\pi$
$662$	5.00000	−	8.66025i	0.194331	−	0.336590i
$663$		0			0
$664$	−9.89949			−0.384175
$665$		0			0
$666$		0			0
$667$	4.00000	+	6.92820i	0.154881	+	0.268261i
$668$	9.89949	−	17.1464i	0.383023	−	0.663415i
$669$		0			0
$670$	16.9706	+	29.3939i	0.655630	+	1.13558i
$671$	−5.65685			−0.218380
$672$		0			0
$673$	−12.0000			−0.462566			−0.231283	−	0.972887i	$-0.574292\pi$
$673$	−12.0000			−0.462566			−0.231283	+	0.972887i	$0.574292\pi$
$674$	1.00000	+	1.73205i	0.0385186	+	0.0667161i
$675$		0			0
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	8.48528	+	14.6969i	0.326116	+	0.564849i	0.981738	−	0.190240i	$-0.0609267\pi$
$677$	8.48528	+	14.6969i	0.326116	+	0.564849i	−0.655622	+	0.755090i	$0.727593\pi$
$678$		0			0
$679$		0			0
$680$	4.00000			0.153393
$681$		0			0
$682$	−8.48528	+	14.6969i	−0.324918	+	0.562775i
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$		0			0
$685$	−33.9411			−1.29682
$686$		0			0
$687$		0			0
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$		0			0
$690$		0			0
$691$	6.36396	+	11.0227i	0.242096	+	0.419323i	0.961311	−	0.275464i	$-0.0888316\pi$
$691$	6.36396	+	11.0227i	0.242096	+	0.419323i	−0.719215	+	0.694788i	$0.755498\pi$
$692$	−16.9706			−0.645124
$693$		0			0
$694$	−30.0000			−1.13878
$695$	14.0000	+	24.2487i	0.531050	+	0.919806i
$696$		0			0
$697$	−7.00000	+	12.1244i	−0.265144	+	0.459243i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	−35.3553	+	61.2372i	−1.33345	+	2.30961i
$704$	−1.00000	+	1.73205i	−0.0376889	+	0.0652791i
$705$		0			0
$706$	1.41421			0.0532246
$707$		0			0
$708$		0			0
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	0.756730	−	0.653727i	$-0.226796\pi$
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	−0.944509	+	0.328484i	$0.893462\pi$
$710$	16.9706	−	29.3939i	0.636894	−	1.10313i
$711$		0			0
$712$	−3.53553	−	6.12372i	−0.132500	−	0.229496i
$713$	−33.9411			−1.27111
$714$		0			0
$715$		0			0
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	16.0000	−	27.7128i	0.597115	−	1.03423i
$719$	−1.41421	−	2.44949i	−0.0527413	−	0.0913506i	0.838449	−	0.544979i	$-0.183463\pi$
$719$	−1.41421	−	2.44949i	−0.0527413	−	0.0913506i	−0.891191	+	0.453629i	$0.850129\pi$
$720$		0			0
$721$		0			0
$722$	−31.0000			−1.15370
$723$		0			0
$724$		0			0
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$		0			0
$727$	19.7990			0.734304			0.367152	−	0.930161i	$-0.380333\pi$
$727$	19.7990			0.734304			0.367152	+	0.930161i	$0.380333\pi$
$728$		0			0
$729$		0			0
$730$	2.00000	+	3.46410i	0.0740233	+	0.128212i
$731$	1.41421	−	2.44949i	0.0523066	−	0.0905977i
$732$		0			0
$733$	21.2132	+	36.7423i	0.783528	+	1.35711i	0.929875	+	0.367876i	$0.119915\pi$
$733$	21.2132	+	36.7423i	0.783528	+	1.35711i	−0.146347	+	0.989233i	$0.546752\pi$
$734$	28.2843			1.04399
$735$		0			0
$736$	−4.00000			−0.147442
$737$	−12.0000	−	20.7846i	−0.442026	−	0.765611i
$738$		0			0
$739$	15.0000	−	25.9808i	0.551784	−	0.955718i	−0.446362	−	0.894852i	$-0.647281\pi$
$739$	15.0000	−	25.9808i	0.551784	−	0.955718i	0.998146	−	0.0608653i	$-0.0193860\pi$
$740$	−14.1421	−	24.4949i	−0.519875	−	0.900450i
$741$		0			0
$742$		0			0
$743$	−16.0000			−0.586983			−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000			−0.586983			−0.293492	+	0.955962i	$0.594817\pi$
$744$		0			0
$745$	14.1421	−	24.4949i	0.518128	−	0.897424i
$746$	5.00000	−	8.66025i	0.183063	−	0.317074i
$747$		0			0
$748$	−2.82843			−0.103418
$749$		0			0
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	−1.41421	+	2.44949i	−0.0515711	+	0.0893237i
$753$		0			0
$754$		0			0
$755$	−45.2548			−1.64699
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−13.0000	−	22.5167i	−0.472181	−	0.817842i
$759$		0			0
$760$	10.0000	−	17.3205i	0.362738	−	0.628281i
$761$	3.53553	+	6.12372i	0.128163	+	0.221985i	0.922965	−	0.384884i	$-0.125759\pi$
$761$	3.53553	+	6.12372i	0.128163	+	0.221985i	−0.794802	+	0.606869i	$0.792425\pi$
$762$		0			0
$763$		0			0
$764$	4.00000			0.144715
$765$		0			0
$766$	−18.3848	+	31.8434i	−0.664269	+	1.15055i
$767$		0			0
$768$		0			0
$769$	−29.6985			−1.07095			−0.535477	−	0.844550i	$-0.679868\pi$
$769$	−29.6985			−1.07095			−0.535477	+	0.844550i	$0.679868\pi$
$770$		0			0
$771$		0			0
$772$	8.00000	+	13.8564i	0.287926	+	0.498703i
$773$	−24.0416	+	41.6413i	−0.864717	+	1.49773i	0.00261021	+	0.999997i	$0.499169\pi$
$773$	−24.0416	+	41.6413i	−0.864717	+	1.49773i	−0.867328	+	0.497738i	$0.834164\pi$
$774$		0			0
$775$	12.7279	+	22.0454i	0.457200	+	0.791894i
$776$	9.89949			0.355371
$777$		0			0
$778$	26.0000			0.932145
$779$	35.0000	+	60.6218i	1.25401	+	2.17200i
$780$		0			0
$781$	−12.0000	+	20.7846i	−0.429394	+	0.743732i
$782$	−2.82843	−	4.89898i	−0.101144	−	0.175187i
$783$		0			0
$784$		0			0
$785$	32.0000			1.14213
$786$		0			0
$787$	−0.707107	+	1.22474i	−0.0252056	+	0.0436574i	−0.878353	−	0.478012i	$-0.841357\pi$
$787$	−0.707107	+	1.22474i	−0.0252056	+	0.0436574i	0.853147	+	0.521670i	$0.174691\pi$
$788$	1.00000	−	1.73205i	0.0356235	−	0.0617018i
$789$		0			0
$790$	11.3137			0.402524
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−11.3137	+	19.5959i	−0.401508	+	0.695433i
$795$		0			0
$796$	4.24264	+	7.34847i	0.150376	+	0.260460i
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$	−4.00000			−0.141510
$800$	1.50000	+	2.59808i	0.0530330	+	0.0918559i
$801$		0			0
$802$	9.00000	−	15.5885i	0.317801	−	0.550448i
$803$	−1.41421	−	2.44949i	−0.0499065	−	0.0864406i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	4.24264	−	7.34847i	0.149256	−	0.258518i
$809$	−8.00000	+	13.8564i	−0.281265	+	0.487165i	−0.971697	−	0.236232i	$-0.924087\pi$
$809$	−8.00000	+	13.8564i	−0.281265	+	0.487165i	0.690432	+	0.723398i	$0.257421\pi$
$810$		0			0
$811$	29.6985			1.04285			0.521427	−	0.853296i	$-0.325400\pi$
$811$	29.6985			1.04285			0.521427	+	0.853296i	$0.325400\pi$
$812$		0			0
$813$		0			0
$814$	10.0000	+	17.3205i	0.350500	+	0.607083i
$815$	−14.1421	+	24.4949i	−0.495377	+	0.858019i
$816$		0			0
$817$	−7.07107	−	12.2474i	−0.247385	−	0.428484i
$818$	38.1838			1.33506
$819$		0			0
$820$	−28.0000			−0.977802
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$		0			0
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$	−1.41421	−	2.44949i	−0.0492665	−	0.0853320i
$825$		0			0
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−15.5563	+	26.9444i	−0.540294	+	0.935817i	0.458593	+	0.888647i	$0.348354\pi$
$829$	−15.5563	+	26.9444i	−0.540294	+	0.935817i	−0.998887	+	0.0471706i	$0.984980\pi$
$830$	14.0000	−	24.2487i	0.485947	−	0.841685i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	28.0000	+	48.4974i	0.968980	+	1.67832i
$836$	−7.07107	+	12.2474i	−0.244558	+	0.423587i
$837$		0			0
$838$	−4.94975	−	8.57321i	−0.170986	−	0.296157i
$839$	19.7990			0.683537			0.341769	−	0.939784i	$-0.388974\pi$
$839$	19.7990			0.683537			0.341769	+	0.939784i	$0.388974\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	15.0000	+	25.9808i	0.516934	+	0.895356i
$843$		0			0
$844$	6.00000	−	10.3923i	0.206529	−	0.357718i
$845$	18.3848	+	31.8434i	0.632456	+	1.09545i
$846$		0			0
$847$		0			0
$848$	2.00000			0.0686803
$849$		0			0
$850$	−2.12132	+	3.67423i	−0.0727607	+	0.126025i
$851$	−20.0000	+	34.6410i	−0.685591	+	1.18748i
$852$		0			0
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$		0			0
$855$		0			0
$856$	2.00000	+	3.46410i	0.0683586	+	0.118401i
$857$	−9.19239	+	15.9217i	−0.314006	+	0.543874i	−0.979226	−	0.202773i	$-0.935005\pi$
$857$	−9.19239	+	15.9217i	−0.314006	+	0.543874i	0.665220	+	0.746648i	$0.268338\pi$
$858$		0			0
$859$	−13.4350	−	23.2702i	−0.458397	−	0.793967i	0.540479	−	0.841357i	$-0.318243\pi$
$859$	−13.4350	−	23.2702i	−0.458397	−	0.793967i	−0.998876	+	0.0473900i	$0.984910\pi$
$860$	5.65685			0.192897
$861$		0			0
$862$	12.0000			0.408722
$863$	−2.00000	−	3.46410i	−0.0680808	−	0.117919i	0.829976	−	0.557800i	$-0.188354\pi$
$863$	−2.00000	−	3.46410i	−0.0680808	−	0.117919i	−0.898056	+	0.439880i	$0.855021\pi$
$864$		0			0
$865$	24.0000	−	41.5692i	0.816024	−	1.41340i
$866$	14.8492	+	25.7196i	0.504598	+	0.873989i
$867$		0			0
$868$		0			0
$869$	−8.00000			−0.271381
$870$		0			0
$871$		0			0
$872$	−1.00000	+	1.73205i	−0.0338643	+	0.0586546i
$873$		0			0
$874$	−28.2843			−0.956730
$875$		0			0
$876$		0			0
$877$	23.0000	+	39.8372i	0.776655	+	1.34521i	0.933860	+	0.357640i	$0.116418\pi$
$877$	23.0000	+	39.8372i	0.776655	+	1.34521i	−0.157205	+	0.987566i	$0.550248\pi$
$878$	8.48528	−	14.6969i	0.286364	−	0.495998i
$879$		0			0
$880$	−2.82843	−	4.89898i	−0.0953463	−	0.165145i
$881$	29.6985			1.00057			0.500284	−	0.865862i	$-0.333229\pi$
$881$	29.6985			1.00057			0.500284	+	0.865862i	$0.333229\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$		0			0
$885$		0			0
$886$	2.00000	−	3.46410i	0.0671913	−	0.116379i
$887$	18.3848	+	31.8434i	0.617300	+	1.06920i	0.989976	+	0.141234i	$0.0451070\pi$
$887$	18.3848	+	31.8434i	0.617300	+	1.06920i	−0.372676	+	0.927962i	$0.621560\pi$
$888$		0			0
$889$		0			0
$890$	20.0000			0.670402
$891$		0			0
$892$		0			0
$893$	−10.0000	+	17.3205i	−0.334637	+	0.579609i
$894$		0			0
$895$	−33.9411			−1.13453
$896$		0			0
$897$		0			0
$898$	−15.0000	−	25.9808i	−0.500556	−	0.866989i
$899$	−8.48528	+	14.6969i	−0.283000	+	0.490170i
$900$		0			0
$901$	1.41421	+	2.44949i	0.0471143	+	0.0816043i
$902$	19.7990			0.659234
$903$		0			0
$904$	−12.0000			−0.399114
$905$		0			0
$906$		0			0
$907$	22.0000	−	38.1051i	0.730498	−	1.26526i	−0.226173	−	0.974087i	$-0.572621\pi$
$907$	22.0000	−	38.1051i	0.730498	−	1.26526i	0.956671	−	0.291172i	$-0.0940453\pi$
$908$	10.6066	+	18.3712i	0.351992	+	0.609669i
$909$		0			0
$910$		0			0
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$		0			0
$913$	−9.89949	+	17.1464i	−0.327625	+	0.567464i
$914$	12.0000	−	20.7846i	0.396925	−	0.687494i
$915$		0			0
$916$	16.9706			0.560723
$917$		0			0
$918$		0			0
$919$	16.0000	+	27.7128i	0.527791	+	0.914161i	0.999475	+	0.0323936i	$0.0103130\pi$
$919$	16.0000	+	27.7128i	0.527791	+	0.914161i	−0.471684	+	0.881768i	$0.656354\pi$
$920$	5.65685	−	9.79796i	0.186501	−	0.323029i
$921$		0			0
$922$	19.7990	+	34.2929i	0.652045	+	1.12938i
$923$		0			0
$924$		0			0
$925$	30.0000			0.986394
$926$	8.00000	+	13.8564i	0.262896	+	0.455350i
$927$		0			0
$928$	−1.00000	+	1.73205i	−0.0328266	+	0.0568574i
$929$	−16.2635	−	28.1691i	−0.533587	−	0.924199i	−0.999230	−	0.0392269i	$-0.987510\pi$
$929$	−16.2635	−	28.1691i	−0.533587	−	0.924199i	0.465644	−	0.884972i	$-0.345823\pi$
$930$		0			0
$931$		0			0
$932$	−24.0000			−0.786146
$933$		0			0
$934$	16.2635	−	28.1691i	0.532157	−	0.921722i
$935$	4.00000	−	6.92820i	0.130814	−	0.226576i
$936$		0			0
$937$	−9.89949			−0.323402			−0.161701	−	0.986840i	$-0.551698\pi$
$937$	−9.89949			−0.323402			−0.161701	+	0.986840i	$0.551698\pi$
$938$		0			0
$939$		0			0
$940$	−4.00000	−	6.92820i	−0.130466	−	0.225973i
$941$	15.5563	−	26.9444i	0.507122	−	0.878362i	−0.492844	−	0.870118i	$-0.664043\pi$
$941$	15.5563	−	26.9444i	0.507122	−	0.878362i	0.999966	−	0.00824396i	$-0.00262416\pi$
$942$		0			0
$943$	19.7990	+	34.2929i	0.644744	+	1.11673i
$944$	−1.41421			−0.0460287
$945$		0			0
$946$	−4.00000			−0.130051
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$		0			0
$949$		0			0
$950$	10.6066	+	18.3712i	0.344124	+	0.596040i
$951$		0			0
$952$		0			0
$953$	26.0000			0.842223			0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000			0.842223			0.421111	+	0.907009i	$0.361640\pi$
$954$		0			0
$955$	−5.65685	+	9.79796i	−0.183052	+	0.317055i
$956$	−6.00000	+	10.3923i	−0.194054	+	0.336111i
$957$		0			0
$958$	31.1127			1.00521
$959$		0			0
$960$		0			0
$961$	−20.5000	−	35.5070i	−0.661290	−	1.14539i
$962$		0			0
$963$		0			0
$964$	−10.6066	−	18.3712i	−0.341616	−	0.591696i
$965$	−45.2548			−1.45680
$966$		0			0
$967$	−12.0000			−0.385894			−0.192947	−	0.981209i	$-0.561805\pi$
$967$	−12.0000			−0.385894			−0.192947	+	0.981209i	$0.561805\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$		0			0
$970$	−14.0000	+	24.2487i	−0.449513	+	0.778579i
$971$	−16.2635	−	28.1691i	−0.521919	−	0.903990i	−0.999675	−	0.0254978i	$-0.991883\pi$
$971$	−16.2635	−	28.1691i	−0.521919	−	0.903990i	0.477756	−	0.878493i	$-0.341450\pi$
$972$		0			0
$973$		0			0
$974$	−12.0000			−0.384505
$975$		0			0
$976$	1.41421	−	2.44949i	0.0452679	−	0.0784063i
$977$	6.00000	−	10.3923i	0.191957	−	0.332479i	−0.753942	−	0.656941i	$-0.771850\pi$
$977$	6.00000	−	10.3923i	0.191957	−	0.332479i	0.945899	+	0.324462i	$0.105183\pi$
$978$		0			0
$979$	−14.1421			−0.451985
$980$		0			0
$981$		0			0
$982$	6.00000	+	10.3923i	0.191468	+	0.331632i
$983$	−24.0416	+	41.6413i	−0.766809	+	1.32815i	0.172476	+	0.985014i	$0.444823\pi$
$983$	−24.0416	+	41.6413i	−0.766809	+	1.32815i	−0.939285	+	0.343138i	$0.888510\pi$
$984$		0			0
$985$	2.82843	+	4.89898i	0.0901212	+	0.156094i
$986$	−2.82843			−0.0900755
$987$		0			0
$988$		0			0
$989$	−4.00000	−	6.92820i	−0.127193	−	0.220304i
$990$		0			0
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$	−4.24264	−	7.34847i	−0.134704	−	0.233314i
$993$		0			0
$994$		0			0
$995$	−24.0000			−0.760851
$996$		0			0
$997$	−15.5563	+	26.9444i	−0.492675	+	0.853337i	−0.999964	−	0.00843818i	$-0.997314\pi$
$997$	−15.5563	+	26.9444i	−0.492675	+	0.853337i	0.507290	+	0.861775i	$0.330647\pi$
$998$	−2.00000	+	3.46410i	−0.0633089	+	0.109654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.g.l.361.1		4
3.2	odd	2		98.2.c.c.67.1		4
7.2	even	3	inner	882.2.g.l.667.1		4
7.3	odd	6		882.2.a.n.1.1		2
7.4	even	3		882.2.a.n.1.2		2
7.5	odd	6	inner	882.2.g.l.667.2		4
7.6	odd	2	inner	882.2.g.l.361.2		4
12.11	even	2		784.2.i.m.753.2		4
21.2	odd	6		98.2.c.c.79.1		4
21.5	even	6		98.2.c.c.79.2		4
21.11	odd	6		98.2.a.b.1.2	yes	2
21.17	even	6		98.2.a.b.1.1	✓	2
21.20	even	2		98.2.c.c.67.2		4
28.3	even	6		7056.2.a.cl.1.1		2
28.11	odd	6		7056.2.a.cl.1.2		2
84.11	even	6		784.2.a.l.1.1		2
84.23	even	6		784.2.i.m.177.2		4
84.47	odd	6		784.2.i.m.177.1		4
84.59	odd	6		784.2.a.l.1.2		2
84.83	odd	2		784.2.i.m.753.1		4
105.17	odd	12		2450.2.c.v.99.4		4
105.32	even	12		2450.2.c.v.99.3		4
105.38	odd	12		2450.2.c.v.99.1		4
105.53	even	12		2450.2.c.v.99.2		4
105.59	even	6		2450.2.a.bj.1.2		2
105.74	odd	6		2450.2.a.bj.1.1		2
168.11	even	6		3136.2.a.bm.1.2		2
168.53	odd	6		3136.2.a.bn.1.1		2
168.59	odd	6		3136.2.a.bm.1.1		2
168.101	even	6		3136.2.a.bn.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.a.b.1.1	✓	2	21.17	even	6
98.2.a.b.1.2	yes	2	21.11	odd	6
98.2.c.c.67.1		4	3.2	odd	2
98.2.c.c.67.2		4	21.20	even	2
98.2.c.c.79.1		4	21.2	odd	6
98.2.c.c.79.2		4	21.5	even	6
784.2.a.l.1.1		2	84.11	even	6
784.2.a.l.1.2		2	84.59	odd	6
784.2.i.m.177.1		4	84.47	odd	6
784.2.i.m.177.2		4	84.23	even	6
784.2.i.m.753.1		4	84.83	odd	2
784.2.i.m.753.2		4	12.11	even	2
882.2.a.n.1.1		2	7.3	odd	6
882.2.a.n.1.2		2	7.4	even	3
882.2.g.l.361.1		4	1.1	even	1	trivial
882.2.g.l.361.2		4	7.6	odd	2	inner
882.2.g.l.667.1		4	7.2	even	3	inner
882.2.g.l.667.2		4	7.5	odd	6	inner
2450.2.a.bj.1.1		2	105.74	odd	6
2450.2.a.bj.1.2		2	105.59	even	6
2450.2.c.v.99.1		4	105.38	odd	12
2450.2.c.v.99.2		4	105.53	even	12
2450.2.c.v.99.3		4	105.32	even	12
2450.2.c.v.99.4		4	105.17	odd	12
3136.2.a.bm.1.1		2	168.59	odd	6
3136.2.a.bm.1.2		2	168.11	even	6
3136.2.a.bn.1.1		2	168.53	odd	6
3136.2.a.bn.1.2		2	168.101	even	6
7056.2.a.cl.1.1		2	28.3	even	6
7056.2.a.cl.1.2		2	28.11	odd	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.41421 - 2.44949i) q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.41421 - 2.44949i) q^{5} -1.00000 q^{8} +(1.41421 - 2.44949i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-0.500000 - 0.866025i) q^{16} +(0.707107 - 1.22474i) q^{17} +(-3.53553 - 6.12372i) q^{19} +2.82843 q^{20} -2.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.50000 + 2.59808i) q^{25} -2.00000 q^{29} +(4.24264 - 7.34847i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.41421 q^{34} +(-5.00000 - 8.66025i) q^{37} +(3.53553 - 6.12372i) q^{38} +(1.41421 + 2.44949i) q^{40} -9.89949 q^{41} +2.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(2.00000 - 3.46410i) q^{46} +(-1.41421 - 2.44949i) q^{47} -3.00000 q^{50} +(-1.00000 + 1.73205i) q^{53} +5.65685 q^{55} +(-1.00000 - 1.73205i) q^{58} +(0.707107 - 1.22474i) q^{59} +(1.41421 + 2.44949i) q^{61} +8.48528 q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{67} +(0.707107 + 1.22474i) q^{68} +12.0000 q^{71} +(-0.707107 + 1.22474i) q^{73} +(5.00000 - 8.66025i) q^{74} +7.07107 q^{76} +(2.00000 + 3.46410i) q^{79} +(-1.41421 + 2.44949i) q^{80} +(-4.94975 - 8.57321i) q^{82} +9.89949 q^{83} -4.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(1.00000 - 1.73205i) q^{88} +(3.53553 + 6.12372i) q^{89} +4.00000 q^{92} +(1.41421 - 2.44949i) q^{94} +(-10.0000 + 17.3205i) q^{95} -9.89949 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 4 q^{11} - 2 q^{16} - 8 q^{22} - 8 q^{23} - 6 q^{25} - 8 q^{29} + 2 q^{32} - 20 q^{37} + 8 q^{43} - 4 q^{44} + 8 q^{46} - 12 q^{50} - 4 q^{53} - 4 q^{58} + 4 q^{64} - 24 q^{67} + 48 q^{71} + 20 q^{74} + 8 q^{79} - 16 q^{85} + 4 q^{86} + 4 q^{88} + 16 q^{92} - 40 q^{95}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 4 * q^11 - 2 * q^16 - 8 * q^22 - 8 * q^23 - 6 * q^25 - 8 * q^29 + 2 * q^32 - 20 * q^37 + 8 * q^43 - 4 * q^44 + 8 * q^46 - 12 * q^50 - 4 * q^53 - 4 * q^58 + 4 * q^64 - 24 * q^67 + 48 * q^71 + 20 * q^74 + 8 * q^79 - 16 * q^85 + 4 * q^86 + 4 * q^88 + 16 * q^92 - 40 * q^95

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