LMFDB - Embedded newform 882.2.t.b.803.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(803,882)]

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, 5]))

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

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

chi := DirichletCharacter("882.803");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.t (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			803.3
Root			$-1.69547 - 0.354107i$ of defining polynomial
Character	$\chi$	$=$	882.803
Dual form			882.2.t.b.815.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.15440 + 1.29126i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.79035 q^{5} +(-1.64537 - 0.541068i) q^{6} +1.00000i q^{8} +(-0.334727 + 2.98127i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.15440 + 1.29126i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.79035 q^{5} +(-1.64537 - 0.541068i) q^{6} +1.00000i q^{8} +(-0.334727 + 2.98127i) q^{9} +(1.55049 - 0.895175i) q^{10} +2.40150i q^{11} +(1.69547 - 0.354107i) q^{12} +(4.23601 - 2.44566i) q^{13} +(-2.06678 - 2.31181i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.83233 + 3.17369i) q^{17} +(-1.20075 - 2.74922i) q^{18} +(2.61281 + 1.50851i) q^{19} +(-0.895175 + 1.55049i) q^{20} +(-1.20075 - 2.07976i) q^{22} +3.76638i q^{23} +(-1.29126 + 1.15440i) q^{24} -1.79465 q^{25} +(-2.44566 + 4.23601i) q^{26} +(-4.23601 + 3.00935i) q^{27} +(-5.68202 - 3.28052i) q^{29} +(2.94579 + 0.968701i) q^{30} +(-4.02408 - 2.32330i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.10098 + 2.77229i) q^{33} +(-3.17369 - 1.83233i) q^{34} +(2.41449 + 1.78052i) q^{36} +(-4.68202 + 8.10950i) q^{37} -3.01701 q^{38} +(8.04805 + 2.64654i) q^{39} -1.79035i q^{40} +(4.04094 + 6.99911i) q^{41} +(-3.48127 + 6.02973i) q^{43} +(2.07976 + 1.20075i) q^{44} +(0.599278 - 5.33751i) q^{45} +(-1.88319 - 3.26178i) q^{46} +(-2.56802 - 4.44794i) q^{47} +(0.541068 - 1.64537i) q^{48} +(1.55421 - 0.897324i) q^{50} +(-1.98283 + 6.02973i) q^{51} -4.89133i q^{52} +(2.16382 - 4.72418i) q^{54} -4.29953i q^{55} +(1.06834 + 5.11524i) q^{57} +6.56103 q^{58} +(-7.29501 + 12.6353i) q^{59} +(-3.03548 + 0.633975i) q^{60} +(9.81058 - 5.66414i) q^{61} +4.64661 q^{62} -1.00000 q^{64} +(-7.58394 + 4.37859i) q^{65} +(1.29938 - 3.95136i) q^{66} +(-0.285115 + 0.493834i) q^{67} +3.66466 q^{68} +(-4.86340 + 4.34791i) q^{69} +5.96254i q^{71} +(-2.98127 - 0.334727i) q^{72} +(10.7226 - 6.19070i) q^{73} -9.36404i q^{74} +(-2.07174 - 2.31737i) q^{75} +(2.61281 - 1.50851i) q^{76} +(-8.29308 + 1.73205i) q^{78} +(-1.51831 - 2.62979i) q^{79} +(0.895175 + 1.55049i) q^{80} +(-8.77592 - 1.99582i) q^{81} +(-6.99911 - 4.04094i) q^{82} +(7.00270 - 12.1290i) q^{83} +(-3.28052 - 5.68202i) q^{85} -6.96254i q^{86} +(-2.32330 - 11.1240i) q^{87} -2.40150 q^{88} +(-1.87432 + 3.24641i) q^{89} +(2.14977 + 4.92206i) q^{90} +(3.26178 + 1.88319i) q^{92} +(-1.64539 - 7.87817i) q^{93} +(4.44794 + 2.56802i) q^{94} +(-4.67784 - 2.70075i) q^{95} +(0.354107 + 1.69547i) q^{96} +(-4.77256 - 2.75544i) q^{97} +(-7.15953 - 0.803848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 36 q^{39} + 4 q^{43} + 12 q^{44} - 12 q^{46} + 60 q^{50} - 36 q^{51} + 48 q^{57} + 24 q^{58} - 24 q^{60} - 16 q^{64} - 84 q^{65} - 28 q^{67} + 12 q^{72} - 24 q^{78} - 4 q^{79} - 36 q^{81} - 12 q^{85} - 48 q^{92} + 12 q^{93} - 12 q^{95} - 72 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 36 * q^39 + 4 * q^43 + 12 * q^44 - 12 * q^46 + 60 * q^50 - 36 * q^51 + 48 * q^57 + 24 * q^58 - 24 * q^60 - 16 * q^64 - 84 * q^65 - 28 * q^67 + 12 * q^72 - 24 * q^78 - 4 * q^79 - 36 * q^81 - 12 * q^85 - 48 * q^92 + 12 * q^93 - 12 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.15440	+	1.29126i	0.666492	+	0.745512i
$3$	1.15440	+	1.29126i	0.666492	+	0.745512i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.79035			−0.800669			−0.400334	−	0.916369i	$-0.631106\pi$
$5$	−1.79035			−0.800669			−0.400334	+	0.916369i	$0.631106\pi$
$6$	−1.64537	−	0.541068i	−0.671720	−	0.220890i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−0.334727	+	2.98127i	−0.111576	+	0.993756i
$10$	1.55049	−	0.895175i	0.490307	−	0.283079i
$11$			2.40150i			0.724081i	0.932162	+	0.362040i	$0.117920\pi$
$11$			2.40150i			0.724081i	−0.932162	+	0.362040i	$0.882080\pi$
$12$	1.69547	−	0.354107i	0.489439	−	0.102222i
$13$	4.23601	−	2.44566i	1.17486	−	0.678305i	0.220039	−	0.975491i	$-0.429382\pi$
$13$	4.23601	−	2.44566i	1.17486	−	0.678305i	0.954820	+	0.297186i	$0.0960482\pi$
$14$		0			0
$15$	−2.06678	−	2.31181i	−0.533640	−	0.596908i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.83233	+	3.17369i	0.444406	+	0.769734i	0.998011	−	0.0630460i	$-0.0200815\pi$
$17$	1.83233	+	3.17369i	0.444406	+	0.769734i	−0.553605	+	0.832780i	$0.686748\pi$
$18$	−1.20075	−	2.74922i	−0.283020	−	0.647997i
$19$	2.61281	+	1.50851i	0.599419	+	0.346075i	0.768813	−	0.639474i	$-0.220848\pi$
$19$	2.61281	+	1.50851i	0.599419	+	0.346075i	−0.169394	+	0.985548i	$0.554181\pi$
$20$	−0.895175	+	1.55049i	−0.200167	+	0.346700i
$21$		0			0
$22$	−1.20075	−	2.07976i	−0.256001	−	0.443407i
$23$			3.76638i			0.785345i	0.919678	+	0.392673i	$0.128449\pi$
$23$			3.76638i			0.785345i	−0.919678	+	0.392673i	$0.871551\pi$
$24$	−1.29126	+	1.15440i	−0.263578	+	0.235641i
$25$	−1.79465			−0.358930
$26$	−2.44566	+	4.23601i	−0.479634	+	0.830750i
$27$	−4.23601	+	3.00935i	−0.815221	+	0.579150i
$28$		0			0
$29$	−5.68202	−	3.28052i	−1.05512	−	0.609176i	−0.131045	−	0.991376i	$-0.541833\pi$
$29$	−5.68202	−	3.28052i	−1.05512	−	0.609176i	−0.924080	+	0.382200i	$0.875167\pi$
$30$	2.94579	+	0.968701i	0.537825	+	0.176860i
$31$	−4.02408	−	2.32330i	−0.722746	−	0.417278i	0.0930163	−	0.995665i	$-0.470349\pi$
$31$	−4.02408	−	2.32330i	−0.722746	−	0.417278i	−0.815763	+	0.578387i	$0.803682\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−3.10098	+	2.77229i	−0.539811	+	0.482594i
$34$	−3.17369	−	1.83233i	−0.544284	−	0.314242i
$35$		0			0
$36$	2.41449	+	1.78052i	0.402415	+	0.296753i
$37$	−4.68202	+	8.10950i	−0.769719	+	1.33319i	0.167996	+	0.985788i	$0.446271\pi$
$37$	−4.68202	+	8.10950i	−0.769719	+	1.33319i	−0.937715	+	0.347405i	$0.887063\pi$
$38$	−3.01701			−0.489424
$39$	8.04805	+	2.64654i	1.28872	+	0.423786i
$40$		−	1.79035i		−	0.283079i
$41$	4.04094	+	6.99911i	0.631088	+	1.09308i	0.987330	+	0.158683i	$0.0507248\pi$
$41$	4.04094	+	6.99911i	0.631088	+	1.09308i	−0.356241	+	0.934394i	$0.615942\pi$
$42$		0			0
$43$	−3.48127	+	6.02973i	−0.530888	+	0.919526i	0.468462	+	0.883484i	$0.344808\pi$
$43$	−3.48127	+	6.02973i	−0.530888	+	0.919526i	−0.999350	+	0.0360419i	$0.988525\pi$
$44$	2.07976	+	1.20075i	0.313536	+	0.181020i
$45$	0.599278	−	5.33751i	0.0893351	−	0.795669i
$46$	−1.88319	−	3.26178i	−0.277661	−	0.480924i
$47$	−2.56802	−	4.44794i	−0.374584	−	0.648799i	0.615680	−	0.787996i	$-0.288881\pi$
$47$	−2.56802	−	4.44794i	−0.374584	−	0.648799i	−0.990265	+	0.139197i	$0.955548\pi$
$48$	0.541068	−	1.64537i	0.0780965	−	0.237489i
$49$		0			0
$50$	1.55421	−	0.897324i	0.219799	−	0.126901i
$51$	−1.98283	+	6.02973i	−0.277652	+	0.844331i
$52$		−	4.89133i		−	0.678305i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	2.16382	−	4.72418i	0.294458	−	0.642880i
$55$		−	4.29953i		−	0.579749i
$56$		0			0
$57$	1.06834	+	5.11524i	0.141506	+	0.677530i
$58$	6.56103			0.861506
$59$	−7.29501	+	12.6353i	−0.949729	+	1.64498i	−0.203735	+	0.979026i	$0.565308\pi$
$59$	−7.29501	+	12.6353i	−0.949729	+	1.64498i	−0.745994	+	0.665953i	$0.768025\pi$
$60$	−3.03548	+	0.633975i	−0.391879	+	0.0818458i
$61$	9.81058	−	5.66414i	1.25612	−	0.725219i	0.283799	−	0.958884i	$-0.408405\pi$
$61$	9.81058	−	5.66414i	1.25612	−	0.725219i	0.972317	+	0.233665i	$0.0750718\pi$
$62$	4.64661			0.590120
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−7.58394	+	4.37859i	−0.940672	+	0.543097i
$66$	1.29938	−	3.95136i	0.159942	−	0.486379i
$67$	−0.285115	+	0.493834i	−0.0348324	+	0.0603315i	−0.882916	−	0.469531i	$-0.844423\pi$
$67$	−0.285115	+	0.493834i	−0.0348324	+	0.0603315i	0.848084	+	0.529862i	$0.177756\pi$
$68$	3.66466			0.444406
$69$	−4.86340	+	4.34791i	−0.585484	+	0.523427i
$70$		0			0
$71$			5.96254i			0.707623i	0.935317	+	0.353811i	$0.115115\pi$
$71$			5.96254i			0.707623i	−0.935317	+	0.353811i	$0.884885\pi$
$72$	−2.98127	−	0.334727i	−0.351346	−	0.0394479i
$73$	10.7226	−	6.19070i	1.25499	−	0.724567i	0.282891	−	0.959152i	$-0.408706\pi$
$73$	10.7226	−	6.19070i	1.25499	−	0.724567i	0.972096	+	0.234585i	$0.0753731\pi$
$74$		−	9.36404i		−	1.08855i
$75$	−2.07174	−	2.31737i	−0.239224	−	0.267586i
$76$	2.61281	−	1.50851i	0.299710	−	0.173037i
$77$		0			0
$78$	−8.29308	+	1.73205i	−0.939007	+	0.196116i
$79$	−1.51831	−	2.62979i	−0.170824	−	0.295875i	0.767884	−	0.640588i	$-0.221309\pi$
$79$	−1.51831	−	2.62979i	−0.170824	−	0.295875i	−0.938708	+	0.344713i	$0.887976\pi$
$80$	0.895175	+	1.55049i	0.100084	+	0.173350i
$81$	−8.77592	−	1.99582i	−0.975102	−	0.221758i
$82$	−6.99911	−	4.04094i	−0.772922	−	0.446247i
$83$	7.00270	−	12.1290i	0.768646	−	1.33133i	−0.169651	−	0.985504i	$-0.554264\pi$
$83$	7.00270	−	12.1290i	0.768646	−	1.33133i	0.938297	−	0.345830i	$-0.112403\pi$
$84$		0			0
$85$	−3.28052	−	5.68202i	−0.355822	−	0.616302i
$86$		−	6.96254i		−	0.750790i
$87$	−2.32330	−	11.1240i	−0.249084	−	1.19262i
$88$	−2.40150			−0.256001
$89$	−1.87432	+	3.24641i	−0.198677	+	0.344119i	−0.948100	−	0.317973i	$-0.896998\pi$
$89$	−1.87432	+	3.24641i	−0.198677	+	0.344119i	0.749423	+	0.662092i	$0.230331\pi$
$90$	2.14977	+	4.92206i	0.226605	+	0.518831i
$91$		0			0
$92$	3.26178	+	1.88319i	0.340064	+	0.196336i
$93$	−1.64539	−	7.87817i	−0.170619	−	0.816928i
$94$	4.44794	+	2.56802i	0.458770	+	0.264871i
$95$	−4.67784	−	2.70075i	−0.479936	−	0.277091i
$96$	0.354107	+	1.69547i	0.0361409	+	0.173043i
$97$	−4.77256	−	2.75544i	−0.484580	−	0.279772i	0.237743	−	0.971328i	$-0.423592\pi$
$97$	−4.77256	−	2.75544i	−0.484580	−	0.279772i	−0.722323	+	0.691556i	$0.756926\pi$
$98$		0			0
$99$	−7.15953	−	0.803848i	−0.719560	−	0.0807897i
$100$	−0.897324	+	1.55421i	−0.0897324	+	0.155421i
$101$	−0.250324			−0.0249082			−0.0124541	−	0.999922i	$-0.503964\pi$
$101$	−0.250324			−0.0249082			−0.0124541	+	0.999922i	$0.503964\pi$
$102$	−1.29768	−	6.21332i	−0.128490	−	0.615210i
$103$		−	0.167931i		−	0.0165468i	−0.999966	−	0.00827339i	$-0.997366\pi$
$103$		−	0.167931i		−	0.0165468i	0.999966	−	0.00827339i	$-0.00263353\pi$
$104$	2.44566	+	4.23601i	0.239817	+	0.415375i
$105$		0			0
$106$		0			0
$107$	6.92024	+	3.99540i	0.669004	+	0.386250i	0.795699	−	0.605692i	$-0.207104\pi$
$107$	6.92024	+	3.99540i	0.669004	+	0.386250i	−0.126695	+	0.991942i	$0.540437\pi$
$108$	0.488168	+	5.17317i	0.0469740	+	0.497789i
$109$	9.47667	+	16.4141i	0.907700	+	1.57218i	0.817251	+	0.576282i	$0.195497\pi$
$109$	9.47667	+	16.4141i	0.907700	+	1.57218i	0.0904491	+	0.995901i	$0.471170\pi$
$110$	2.14977	+	3.72350i	0.204972	+	0.355022i
$111$	−15.8764	+	3.31587i	−1.50692	+	0.314728i
$112$		0			0
$113$	−1.00418	+	0.579764i	−0.0944653	+	0.0545396i	−0.546488	−	0.837467i	$-0.684036\pi$
$113$	−1.00418	+	0.579764i	−0.0944653	+	0.0545396i	0.452023	+	0.892006i	$0.350702\pi$
$114$	−3.48283	−	3.89576i	−0.326197	−	0.364871i
$115$		−	6.74314i		−	0.628801i
$116$	−5.68202	+	3.28052i	−0.527562	+	0.304588i
$117$	5.87327	+	13.4473i	0.542984	+	1.24320i
$118$		−	14.5900i		−	1.34312i
$119$		0			0
$120$	2.31181	−	2.06678i	0.211039	−	0.188670i
$121$	5.23278			0.475707
$122$	−5.66414	+	9.81058i	−0.512807	+	0.888208i
$123$	−4.37285	+	13.2977i	−0.394286	+	1.19901i
$124$	−4.02408	+	2.32330i	−0.361373	+	0.208639i
$125$	12.1648			1.08805
$126$		0			0
$127$	1.40150			0.124363			0.0621817	−	0.998065i	$-0.480194\pi$
$127$	1.40150			0.124363			0.0621817	+	0.998065i	$0.480194\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−11.8047	+	2.46548i	−1.03935	+	0.217073i
$130$	4.37859	−	7.58394i	0.384028	−	0.665156i
$131$	−10.4918			−0.916671			−0.458335	−	0.888779i	$-0.651554\pi$
$131$	−10.4918			−0.916671			−0.458335	+	0.888779i	$0.651554\pi$
$132$	0.850388	+	4.07167i	0.0740168	+	0.354393i
$133$		0			0
$134$		−	0.570231i		−	0.0492604i
$135$	7.58394	−	5.38779i	0.652722	−	0.463707i
$136$	−3.17369	+	1.83233i	−0.272142	+	0.157121i
$137$			4.72056i			0.403305i	0.979457	+	0.201652i	$0.0646311\pi$
$137$			4.72056i			0.403305i	−0.979457	+	0.201652i	$0.935369\pi$
$138$	2.03787	−	6.19710i	0.173475	−	0.527532i
$139$	2.04707	−	1.18187i	0.173630	−	0.100245i	−0.410666	−	0.911786i	$-0.634704\pi$
$139$	2.04707	−	1.18187i	0.173630	−	0.100245i	0.584296	+	0.811540i	$0.301371\pi$
$140$		0			0
$141$	2.77895	−	8.45070i	0.234030	−	0.711677i
$142$	−2.98127	−	5.16371i	−0.250182	−	0.433329i
$143$	5.87327	+	10.1728i	0.491148	+	0.850692i
$144$	2.74922	−	1.20075i	0.229101	−	0.100063i
$145$	10.1728	+	5.87327i	0.844805	+	0.487749i
$146$	−6.19070	+	10.7226i	−0.512346	+	0.887410i
$147$		0			0
$148$	4.68202	+	8.10950i	0.384860	+	0.666597i
$149$		−	17.3640i		−	1.42252i	−0.702930	−	0.711259i	$-0.748125\pi$
$149$		−	17.3640i		−	1.42252i	0.702930	−	0.711259i	$-0.251875\pi$
$150$	2.95286	+	0.971027i	0.241100	+	0.0792840i
$151$	−11.2328			−0.914110			−0.457055	−	0.889438i	$-0.651096\pi$
$151$	−11.2328			−0.914110			−0.457055	+	0.889438i	$0.651096\pi$
$152$	−1.50851	+	2.61281i	−0.122356	+	0.211927i
$153$	−10.0750	+	4.40035i	−0.814512	+	0.355748i
$154$		0			0
$155$	7.20451	+	4.15953i	0.578680	+	0.334101i
$156$	6.31599	−	5.64654i	0.505684	−	0.452085i
$157$	11.9885	+	6.92154i	0.956783	+	0.552399i	0.895181	−	0.445702i	$-0.147046\pi$
$157$	11.9885	+	6.92154i	0.956783	+	0.552399i	0.0616014	+	0.998101i	$0.480379\pi$
$158$	2.62979	+	1.51831i	0.209215	+	0.120790i
$159$		0			0
$160$	−1.55049	−	0.895175i	−0.122577	−	0.0707698i
$161$		0			0
$162$	8.59808	−	2.65953i	0.675529	−	0.208952i
$163$	2.16789	−	3.75489i	0.169802	−	0.294106i	−0.768548	−	0.639792i	$-0.779020\pi$
$163$	2.16789	−	3.75489i	0.169802	−	0.294106i	0.938350	+	0.345686i	$0.112354\pi$
$164$	8.08188			0.631088
$165$	5.55183	−	4.96337i	0.432210	−	0.386398i
$166$			14.0054i			1.08703i
$167$	6.20756	+	10.7518i	0.480355	+	0.832000i	0.999746	−	0.0225370i	$-0.00717435\pi$
$167$	6.20756	+	10.7518i	0.480355	+	0.832000i	−0.519391	+	0.854537i	$0.673841\pi$
$168$		0			0
$169$	5.46254	−	9.46139i	0.420195	−	0.727799i
$170$	5.68202	+	3.28052i	0.435791	+	0.251604i
$171$	−5.37184	+	7.28454i	−0.410795	+	0.557063i
$172$	3.48127	+	6.02973i	0.265444	+	0.459763i
$173$	−8.70908	−	15.0846i	−0.662139	−	1.14686i	−0.980052	−	0.198739i	$-0.936315\pi$
$173$	−8.70908	−	15.0846i	−0.662139	−	1.14686i	0.317913	−	0.948120i	$-0.397018\pi$
$174$	7.57405	+	8.47203i	0.574187	+	0.642263i
$175$		0			0
$176$	2.07976	−	1.20075i	0.156768	−	0.0905101i
$177$	−24.7369	+	5.16642i	−1.85934	+	0.388332i
$178$		−	3.74863i		−	0.280972i
$179$	11.3640	−	6.56103i	0.849388	−	0.490395i	−0.0110562	−	0.999939i	$-0.503519\pi$
$179$	11.3640	−	6.56103i	0.849388	−	0.490395i	0.860444	+	0.509544i	$0.170186\pi$
$180$	−4.32278	−	3.18775i	−0.322201	−	0.237601i
$181$		−	13.3577i		−	0.992873i	−0.868073	−	0.496437i	$-0.834641\pi$
$181$		−	13.3577i		−	0.992873i	0.868073	−	0.496437i	$-0.165359\pi$
$182$		0			0
$183$	18.6392	+	6.12937i	1.37785	+	0.453096i
$184$	−3.76638			−0.277661
$185$	8.38245	−	14.5188i	0.616290	−	1.06745i
$186$	5.36404	+	6.00000i	0.393310	+	0.439941i
$187$	−7.62164	+	4.40035i	−0.557349	+	0.321786i
$188$	−5.13604			−0.374584
$189$		0			0
$190$	5.40150			0.391866
$191$	8.01361	−	4.62666i	0.579845	−	0.334774i	−0.181227	−	0.983441i	$-0.558007\pi$
$191$	8.01361	−	4.62666i	0.579845	−	0.334774i	0.761072	+	0.648668i	$0.224674\pi$
$192$	−1.15440	−	1.29126i	−0.0833116	−	0.0931890i
$193$	12.2801	−	21.2698i	0.883941	−	1.53103i	0.0370176	−	0.999315i	$-0.488214\pi$
$193$	12.2801	−	21.2698i	0.883941	−	1.53103i	0.846923	−	0.531716i	$-0.178452\pi$
$194$	5.51087			0.395658
$195$	−14.4088	−	4.73823i	−1.03184	−	0.339312i
$196$		0			0
$197$		−	12.4861i		−	0.889598i	−0.895630	−	0.444799i	$-0.853275\pi$
$197$		−	12.4861i		−	0.889598i	0.895630	−	0.444799i	$-0.146725\pi$
$198$	6.60226	−	2.88361i	0.469202	−	0.204929i
$199$	−0.155144	+	0.0895727i	−0.0109979	+	0.00634964i	−0.505489	−	0.862833i	$-0.668688\pi$
$199$	−0.155144	+	0.0895727i	−0.0109979	+	0.00634964i	0.494491	+	0.869183i	$0.335355\pi$
$200$		−	1.79465i		−	0.126901i
$201$	−0.966808	+	0.201923i	−0.0681934	+	0.0142425i
$202$	0.216787	−	0.125162i	0.0152531	−	0.00880637i
$203$		0			0
$204$	4.23048	+	4.73205i	0.296193	+	0.331310i
$205$	−7.23469	−	12.5309i	−0.505293	−	0.875193i
$206$	0.0839657	+	0.145433i	0.00585017	+	0.0101328i
$207$	−11.2286	−	1.26071i	−0.780441	−	0.0876253i
$208$	−4.23601	−	2.44566i	−0.293715	−	0.169576i
$209$	−3.62268	+	6.27467i	−0.250586	+	0.434028i
$210$		0			0
$211$	7.56103	+	13.0961i	0.520523	+	0.901572i	0.999715	+	0.0238622i	$0.00759629\pi$
$211$	7.56103	+	13.0961i	0.520523	+	0.901572i	−0.479192	+	0.877710i	$0.659070\pi$
$212$		0			0
$213$	−7.69921	+	6.88314i	−0.527541	+	0.471625i
$214$	−7.99080			−0.546240
$215$	6.23269	−	10.7953i	0.425066	−	0.736235i
$216$	−3.00935	−	4.23601i	−0.204760	−	0.288224i
$217$		0			0
$218$	−16.4141	−	9.47667i	−1.11170	−	0.641841i
$219$	20.3720	+	6.69919i	1.37661	+	0.452689i
$220$	−3.72350	−	2.14977i	−0.251039	−	0.144937i
$221$	15.5236	+	8.96254i	1.04423	+	0.602885i
$222$	12.0914	−	10.8098i	0.811525	−	0.725509i
$223$	7.27049	+	4.19762i	0.486868	+	0.281093i	0.723274	−	0.690561i	$-0.242636\pi$
$223$	7.27049	+	4.19762i	0.486868	+	0.281093i	−0.236406	+	0.971654i	$0.575970\pi$
$224$		0			0
$225$	0.600717	−	5.35033i	0.0400478	−	0.356688i
$226$	0.579764	−	1.00418i	0.0385653	−	0.0667971i
$227$	2.42522			0.160967			0.0804836	−	0.996756i	$-0.474354\pi$
$227$	2.42522			0.160967			0.0804836	+	0.996756i	$0.474354\pi$
$228$	4.96410	+	1.63241i	0.328756	+	0.108109i
$229$		−	2.01975i		−	0.133469i	−0.997771	−	0.0667344i	$-0.978742\pi$
$229$		−	2.01975i		−	0.133469i	0.997771	−	0.0667344i	$-0.0212580\pi$
$230$	3.37157	+	5.83973i	0.222315	+	0.385061i
$231$		0			0
$232$	3.28052	−	5.68202i	0.215376	−	0.373043i
$233$	−11.0236	−	6.36446i	−0.722178	−	0.416950i	0.0933759	−	0.995631i	$-0.470234\pi$
$233$	−11.0236	−	6.36446i	−0.722178	−	0.416950i	−0.815554	+	0.578681i	$0.803568\pi$
$234$	−11.8101	−	8.70908i	−0.772048	−	0.569331i
$235$	4.59766	+	7.96337i	0.299918	+	0.519473i
$236$	7.29501	+	12.6353i	0.474864	+	0.822489i
$237$	1.64302	−	4.99637i	0.106726	−	0.324549i
$238$		0			0
$239$	15.1117	−	8.72474i	0.977494	−	0.564356i	0.0759814	−	0.997109i	$-0.475791\pi$
$239$	15.1117	−	8.72474i	0.977494	−	0.564356i	0.901513	+	0.432753i	$0.142458\pi$
$240$	−0.968701	+	2.94579i	−0.0625294	+	0.190150i
$241$			11.4332i			0.736476i	0.929732	+	0.368238i	$0.120039\pi$
$241$			11.4332i			0.736476i	−0.929732	+	0.368238i	$0.879961\pi$
$242$	−4.53172	+	2.61639i	−0.291310	+	0.168188i
$243$	−7.55378	−	13.6360i	−0.484575	−	0.874750i
$244$		−	11.3283i		−	0.725219i
$245$		0			0
$246$	−2.86185	−	13.7026i	−0.182465	−	0.873643i
$247$	14.7572			0.938977
$248$	2.32330	−	4.02408i	0.147530	−	0.255529i
$249$	23.7457	−	4.95940i	1.50482	−	0.314289i
$250$	−10.5350	+	6.08240i	−0.666293	+	0.384685i
$251$	27.3560			1.72669			0.863347	−	0.504611i	$-0.168364\pi$
$251$	27.3560			1.72669			0.863347	+	0.504611i	$0.168364\pi$
$252$		0			0
$253$	−9.04499			−0.568653
$254$	−1.21374	+	0.700752i	−0.0761567	+	0.0439691i
$255$	3.54997	−	10.7953i	0.222307	−	0.676030i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.49673			0.218120			0.109060	−	0.994035i	$-0.465216\pi$
$257$	3.49673			0.218120			0.109060	+	0.994035i	$0.465216\pi$
$258$	8.99047	−	8.03754i	0.559722	−	0.500396i
$259$		0			0
$260$			8.75718i			0.543097i
$261$	11.6820	−	15.8415i	0.723099	−	0.980567i
$262$	9.08614	−	5.24589i	0.561344	−	0.324092i
$263$			9.64348i			0.594643i	0.954777	+	0.297321i	$0.0960932\pi$
$263$			9.64348i			0.594643i	−0.954777	+	0.297321i	$0.903907\pi$
$264$	−2.77229	−	3.10098i	−0.170623	−	0.190852i
$265$		0			0
$266$		0			0
$267$	−6.35568	+	1.32741i	−0.388961	+	0.0812365i
$268$	0.285115	+	0.493834i	0.0174162	+	0.0301657i
$269$	−3.45554	−	5.98517i	−0.210688	−	0.364922i	0.741242	−	0.671238i	$-0.234237\pi$
$269$	−3.45554	−	5.98517i	−0.210688	−	0.364922i	−0.951930	+	0.306316i	$0.900904\pi$
$270$	−3.87399	+	8.45794i	−0.235764	+	0.514734i
$271$	17.8672	+	10.3156i	1.08535	+	0.626629i	0.932335	−	0.361595i	$-0.117768\pi$
$271$	17.8672	+	10.3156i	1.08535	+	0.626629i	0.153017	+	0.988224i	$0.451101\pi$
$272$	1.83233	−	3.17369i	0.111101	−	0.192433i
$273$		0			0
$274$	−2.36028	−	4.08812i	−0.142590	−	0.246973i
$275$		−	4.30986i		−	0.259894i
$276$	1.33370	+	6.38578i	0.0802794	+	0.384379i
$277$	−15.5144			−0.932168			−0.466084	−	0.884740i	$-0.654336\pi$
$277$	−15.5144			−0.932168			−0.466084	+	0.884740i	$0.654336\pi$
$278$	−1.18187	+	2.04707i	−0.0708841	+	0.122775i
$279$	8.27336	−	11.2192i	0.495313	−	0.671675i
$280$		0			0
$281$	11.7759	+	6.79883i	0.702492	+	0.405584i	0.808275	−	0.588805i	$-0.200401\pi$
$281$	11.7759	+	6.79883i	0.702492	+	0.405584i	−0.105783	+	0.994389i	$0.533735\pi$
$282$	1.81871	+	8.70799i	0.108302	+	0.518553i
$283$	−4.71796	−	2.72392i	−0.280454	−	0.161920i	0.353175	−	0.935557i	$-0.385102\pi$
$283$	−4.71796	−	2.72392i	−0.280454	−	0.161920i	−0.633629	+	0.773637i	$0.718435\pi$
$284$	5.16371	+	2.98127i	0.306410	+	0.176906i
$285$	−1.91271	−	9.15807i	−0.113299	−	0.542477i
$286$	−10.1728	−	5.87327i	−0.601530	−	0.347294i
$287$		0			0
$288$	−1.78052	+	2.41449i	−0.104918	+	0.142275i
$289$	1.78512	−	3.09191i	0.105007	−	0.181877i
$290$	−11.7465			−0.689781
$291$	−1.95144	−	9.34351i	−0.114395	−	0.547726i
$292$		−	12.3814i		−	0.724567i
$293$	−12.2311	−	21.1849i	−0.714550	−	1.23764i	−0.963133	−	0.269026i	$-0.913298\pi$
$293$	−12.2311	−	21.1849i	−0.714550	−	1.23764i	0.248583	−	0.968610i	$-0.420035\pi$
$294$		0			0
$295$	13.0606	−	22.6216i	0.760418	−	1.31708i
$296$	−8.10950	−	4.68202i	−0.471355	−	0.272137i
$297$	−7.22697	−	10.1728i	−0.419351	−	0.590286i
$298$	8.68202	+	15.0377i	0.502936	+	0.871111i
$299$	9.21130	+	15.9544i	0.532703	+	0.922670i
$300$	−3.04277	+	0.635497i	−0.175674	+	0.0366904i
$301$		0			0
$302$	9.72787	−	5.61639i	0.559776	−	0.323187i
$303$	−0.288974	−	0.323235i	−0.0166011	−	0.0185693i
$304$		−	3.01701i		−	0.173037i
$305$	−17.5644	+	10.1408i	−1.00573	+	0.580660i
$306$	6.52499	−	8.84830i	0.373009	−	0.505824i
$307$			31.2223i			1.78195i	0.454053	+	0.890975i	$0.349978\pi$
$307$			31.2223i			1.78195i	−0.454053	+	0.890975i	$0.650022\pi$
$308$		0			0
$309$	0.216844	−	0.193860i	0.0123358	−	0.0110283i
$310$	−8.31905			−0.472491
$311$	5.45501	−	9.44836i	0.309325	−	0.535767i	−0.668889	−	0.743362i	$-0.733230\pi$
$311$	5.45501	−	9.44836i	0.309325	−	0.535767i	0.978215	+	0.207594i	$0.0665634\pi$
$312$	−2.64654	+	8.04805i	−0.149831	+	0.455631i
$313$	2.96532	−	1.71203i	0.167610	−	0.0967694i	−0.413849	−	0.910346i	$-0.635816\pi$
$313$	2.96532	−	1.71203i	0.167610	−	0.0967694i	0.581458	+	0.813576i	$0.302482\pi$
$314$	−13.8431			−0.781210
$315$		0			0
$316$	−3.03663			−0.170824
$317$	−16.4953	+	9.52357i	−0.926468	+	0.534897i	−0.885693	−	0.464272i	$-0.846316\pi$
$317$	−16.4953	+	9.52357i	−0.926468	+	0.534897i	−0.0407755	+	0.999168i	$0.512983\pi$
$318$		0			0
$319$	7.87817	−	13.6454i	0.441093	−	0.763995i
$320$	1.79035			0.100084
$321$	2.82960	+	13.5481i	0.157933	+	0.756183i
$322$		0			0
$323$			11.0563i			0.615191i
$324$	−6.11639	+	6.60226i	−0.339799	+	0.366792i
$325$	−7.60215	+	4.38910i	−0.421692	+	0.243464i
$326$			4.33577i			0.240136i
$327$	−10.2550	+	31.1853i	−0.567105	+	1.72455i
$328$	−6.99911	+	4.04094i	−0.386461	+	0.223123i
$329$		0			0
$330$	−2.32634	+	7.07432i	−0.128061	+	0.389429i
$331$	−0.0366251	−	0.0634366i	−0.00201310	−	0.00348679i	0.865017	−	0.501742i	$-0.167307\pi$
$331$	−0.0366251	−	0.0634366i	−0.00201310	−	0.00348679i	−0.867030	+	0.498256i	$0.833974\pi$
$332$	−7.00270	−	12.1290i	−0.384323	−	0.665667i
$333$	−22.6094	−	16.6728i	−1.23899	−	0.913665i
$334$	−10.7518	−	6.20756i	−0.588313	−	0.339663i
$335$	0.510456	−	0.884136i	0.0278892	−	0.0483055i
$336$		0			0
$337$	1.11639	+	1.93364i	0.0608136	+	0.105332i	0.894829	−	0.446408i	$-0.147297\pi$
$337$	1.11639	+	1.93364i	0.0608136	+	0.105332i	−0.834016	+	0.551741i	$0.813964\pi$
$338$			10.9251i			0.594246i
$339$	−1.90785	−	0.627383i	−0.103620	−	0.0340748i
$340$	−6.56103			−0.355822
$341$	5.57943	−	9.66385i	0.302143	−	0.523327i
$342$	1.00987	−	8.99452i	0.0546077	−	0.486368i
$343$		0			0
$344$	−6.02973	−	3.48127i	−0.325101	−	0.187697i
$345$	8.70718	−	7.78428i	0.468779	−	0.419091i
$346$	15.0846	+	8.70908i	0.810952	+	0.468203i
$347$	−27.5751	−	15.9205i	−1.48031	−	0.854656i	−0.480556	−	0.876964i	$-0.659565\pi$
$347$	−27.5751	−	15.9205i	−1.48031	−	0.854656i	−0.999751	+	0.0223084i	$0.992898\pi$
$348$	−10.7953	−	3.54997i	−0.578690	−	0.190298i
$349$	12.7613	+	7.36772i	0.683095	+	0.394385i	0.801020	−	0.598637i	$-0.204291\pi$
$349$	12.7613	+	7.36772i	0.683095	+	0.394385i	−0.117925	+	0.993022i	$0.537624\pi$
$350$		0			0
$351$	−10.5839	+	23.1075i	−0.564929	+	1.23339i
$352$	−1.20075	+	2.07976i	−0.0640003	+	0.110852i
$353$	−2.15957			−0.114943			−0.0574713	−	0.998347i	$-0.518304\pi$
$353$	−2.15957			−0.114943			−0.0574713	+	0.998347i	$0.518304\pi$
$354$	18.8396	−	16.8427i	1.00131	−	0.895179i
$355$		−	10.6750i		−	0.566571i
$356$	1.87432	+	3.24641i	0.0993385	+	0.172059i
$357$		0			0
$358$	−6.56103	+	11.3640i	−0.346761	+	0.600608i
$359$	28.2712	+	16.3224i	1.49210	+	0.861463i	0.999959	−	0.00905364i	$-0.00288190\pi$
$359$	28.2712	+	16.3224i	1.49210	+	0.861463i	0.492139	+	0.870517i	$0.336215\pi$
$360$	5.33751	+	0.599278i	0.281312	+	0.0315847i
$361$	−4.94882	−	8.57161i	−0.260464	−	0.451138i
$362$	6.67887	+	11.5681i	0.351034	+	0.608008i
$363$	6.04071	+	6.75690i	0.317055	+	0.354645i
$364$		0			0
$365$	−19.1972	+	11.0835i	−1.00483	+	0.580138i
$366$	−19.2067	+	4.01142i	−1.00395	+	0.209680i
$367$			29.7003i			1.55034i	0.631751	+	0.775171i	$0.282336\pi$
$367$			29.7003i			1.55034i	−0.631751	+	0.775171i	$0.717664\pi$
$368$	3.26178	−	1.88319i	0.170032	−	0.0981682i
$369$	−22.2188	+	9.70433i	−1.15667	+	0.505187i
$370$			16.7649i			0.871566i
$371$		0			0
$372$	−7.64539	−	2.51413i	−0.396395	−	0.130352i
$373$	−2.01672			−0.104422			−0.0522109	−	0.998636i	$-0.516627\pi$
$373$	−2.01672			−0.104422			−0.0522109	+	0.998636i	$0.516627\pi$
$374$	4.40035	−	7.62164i	0.227537	−	0.394105i
$375$	14.0430	+	15.7080i	0.725179	+	0.811156i
$376$	4.44794	−	2.56802i	0.229385	−	0.132436i
$377$	−32.0921			−1.65283
$378$		0			0
$379$	−18.8709			−0.969332			−0.484666	−	0.874699i	$-0.661059\pi$
$379$	−18.8709			−0.969332			−0.484666	+	0.874699i	$0.661059\pi$
$380$	−4.67784	+	2.70075i	−0.239968	+	0.138546i
$381$	1.61789	+	1.80971i	0.0828873	+	0.0927144i
$382$	−4.62666	+	8.01361i	−0.236721	+	0.410012i
$383$	−0.836511			−0.0427437			−0.0213719	−	0.999772i	$-0.506803\pi$
$383$	−0.836511			−0.0427437			−0.0213719	+	0.999772i	$0.506803\pi$
$384$	1.64537	+	0.541068i	0.0839650	+	0.0276113i
$385$		0			0
$386$			24.5602i			1.25008i
$387$	−16.8110	−	12.3969i	−0.854550	−	0.630170i
$388$	−4.77256	+	2.75544i	−0.242290	+	0.139886i
$389$		−	24.8219i		−	1.25852i	−0.777195	−	0.629260i	$-0.783358\pi$
$389$		−	24.8219i		−	1.25852i	0.777195	−	0.629260i	$-0.216642\pi$
$390$	14.8475	−	3.10098i	0.751833	−	0.157024i
$391$	−11.9533	+	6.90127i	−0.604507	+	0.349012i
$392$		0			0
$393$	−12.1117	−	13.5477i	−0.610954	−	0.683389i
$394$	6.24305	+	10.8133i	0.314520	+	0.544765i
$395$	2.71831	+	4.70825i	0.136773	+	0.236898i
$396$	−4.27592	+	5.79841i	−0.214873	+	0.291381i
$397$	−2.62744	−	1.51695i	−0.131867	−	0.0761336i	0.432615	−	0.901579i	$-0.357591\pi$
$397$	−2.62744	−	1.51695i	−0.131867	−	0.0761336i	−0.564482	+	0.825445i	$0.690924\pi$
$398$	0.0895727	−	0.155144i	0.00448987	−	0.00777669i
$399$		0			0
$400$	0.897324	+	1.55421i	0.0448662	+	0.0777105i
$401$			13.0771i			0.653038i	0.945191	+	0.326519i	$0.105876\pi$
$401$			13.0771i			0.653038i	−0.945191	+	0.326519i	$0.894124\pi$
$402$	0.736319	−	0.658274i	0.0367242	−	0.0328317i
$403$	−22.7281			−1.13217
$404$	−0.125162	+	0.216787i	−0.00622705	+	0.0107856i
$405$	15.7120	+	3.57322i	0.780733	+	0.177555i
$406$		0			0
$407$	−19.4750	−	11.2439i	−0.965339	−	0.557339i
$408$	−6.02973	−	1.98283i	−0.298516	−	0.0981649i
$409$	4.82124	+	2.78354i	0.238395	+	0.137637i	0.614439	−	0.788965i	$-0.289382\pi$
$409$	4.82124	+	2.78354i	0.238395	+	0.137637i	−0.376044	+	0.926602i	$0.622716\pi$
$410$	12.5309	+	7.23469i	0.618855	+	0.357296i
$411$	−6.09549	+	5.44941i	−0.300668	+	0.268799i
$412$	−0.145433	−	0.0839657i	−0.00716496	−	0.00413669i
$413$		0			0
$414$	10.3546	−	4.52249i	0.508901	−	0.222268i
$415$	−12.5373	+	21.7152i	−0.615431	+	1.06596i
$416$	4.89133			0.239817
$417$	3.88924	+	1.27895i	0.190457	+	0.0626304i
$418$		−	7.24536i		−	0.354382i
$419$	−8.19938	−	14.2017i	−0.400566	−	0.693800i	0.593228	−	0.805034i	$-0.297853\pi$
$419$	−8.19938	−	14.2017i	−0.400566	−	0.693800i	−0.993794	+	0.111234i	$0.964520\pi$
$420$		0			0
$421$	−7.72892	+	13.3869i	−0.376684	+	0.652437i	−0.990578	−	0.136952i	$-0.956269\pi$
$421$	−7.72892	+	13.3869i	−0.376684	+	0.652437i	0.613893	+	0.789389i	$0.289603\pi$
$422$	−13.0961	−	7.56103i	−0.637508	−	0.368065i
$423$	14.1201	−	6.16711i	0.686543	−	0.299855i
$424$		0			0
$425$	−3.28839	−	5.69566i	−0.159510	−	0.276280i
$426$	3.22614	−	9.81058i	0.156307	−	0.475324i
$427$		0			0
$428$	6.92024	−	3.99540i	0.334502	−	0.193125i
$429$	−6.35568	+	19.3274i	−0.306855	+	0.933136i
$430$			12.4654i			0.601134i
$431$	21.6737	−	12.5133i	1.04398	−	0.602744i	0.123024	−	0.992404i	$-0.460741\pi$
$431$	21.6737	−	12.5133i	1.04398	−	0.602744i	0.920959	+	0.389660i	$0.127407\pi$
$432$	4.72418	+	2.16382i	0.227292	+	0.104107i
$433$			2.25168i			0.108209i	0.998535	+	0.0541044i	$0.0172304\pi$
$433$			2.25168i			0.108209i	−0.998535	+	0.0541044i	$0.982770\pi$
$434$		0			0
$435$	4.15953	+	19.9159i	0.199434	+	0.954893i
$436$	18.9533			0.907700
$437$	−5.68161	+	9.84084i	−0.271788	+	0.470751i
$438$	−20.9923	+	4.38434i	−1.00305	+	0.209492i
$439$	16.2293	−	9.37000i	0.774583	−	0.447206i	−0.0599239	−	0.998203i	$-0.519086\pi$
$439$	16.2293	−	9.37000i	0.774583	−	0.447206i	0.834507	+	0.550997i	$0.185752\pi$
$440$	4.29953			0.204972
$441$		0			0
$442$	−17.9251			−0.852609
$443$	1.04314	−	0.602256i	0.0495610	−	0.0286141i	−0.475015	−	0.879978i	$-0.657557\pi$
$443$	1.04314	−	0.602256i	0.0495610	−	0.0286141i	0.524576	+	0.851364i	$0.324224\pi$
$444$	−5.06658	+	15.4073i	−0.240449	+	0.731199i
$445$	3.35568	−	5.81221i	0.159074	−	0.275525i
$446$	−8.39524			−0.397526
$447$	22.4216	−	20.0450i	1.06050	−	0.948097i
$448$		0			0
$449$		−	26.8022i		−	1.26487i	−0.774612	−	0.632436i	$-0.782055\pi$
$449$		−	26.8022i		−	1.26487i	0.774612	−	0.632436i	$-0.217945\pi$
$450$	2.15493	+	4.93388i	0.101584	+	0.232585i
$451$	−16.8084	+	9.70433i	−0.791476	+	0.456959i
$452$			1.15953i			0.0545396i
$453$	−12.9671	−	14.5045i	−0.609248	−	0.681480i
$454$	−2.10030	+	1.21261i	−0.0985719	+	0.0569105i
$455$		0			0
$456$	−5.11524	+	1.06834i	−0.239543	+	0.0500298i
$457$	−6.92442	−	11.9934i	−0.323911	−	0.561030i	0.657381	−	0.753559i	$-0.271664\pi$
$457$	−6.92442	−	11.9934i	−0.323911	−	0.561030i	−0.981291	+	0.192529i	$0.938331\pi$
$458$	1.00987	+	1.74915i	0.0471883	+	0.0817326i
$459$	−17.3125	−	7.92967i	−0.808080	−	0.370125i
$460$	−5.83973	−	3.37157i	−0.272279	−	0.157200i
$461$	−2.40241	+	4.16110i	−0.111892	+	0.193802i	−0.916533	−	0.399959i	$-0.869024\pi$
$461$	−2.40241	+	4.16110i	−0.111892	+	0.193802i	0.804641	+	0.593761i	$0.202358\pi$
$462$		0			0
$463$	10.5194	+	18.2201i	0.488877	+	0.846760i	0.999918	−	0.0127960i	$-0.00407321\pi$
$463$	10.5194	+	18.2201i	0.488877	+	0.846760i	−0.511041	+	0.859556i	$0.670740\pi$
$464$			6.56103i			0.304588i
$465$	2.94583	+	14.1047i	0.136610	+	0.654089i
$466$	12.7289			0.589656
$467$	2.91151	−	5.04288i	0.134729	−	0.233357i	−0.790765	−	0.612120i	$-0.790317\pi$
$467$	2.91151	−	5.04288i	0.134729	−	0.233357i	0.925494	+	0.378763i	$0.123650\pi$
$468$	14.5824	+	1.63726i	0.674070	+	0.0756823i
$469$		0			0
$470$	−7.96337	−	4.59766i	−0.367323	−	0.212074i
$471$	4.90192	+	23.4705i	0.225869	+	1.08146i
$472$	−12.6353	−	7.29501i	−0.581588	−	0.335780i
$473$	−14.4804	−	8.36028i	−0.665811	−	0.384406i
$474$	1.07529	+	5.14850i	0.0493897	+	0.236478i
$475$	−4.68907	−	2.70724i	−0.215149	−	0.124217i
$476$		0			0
$477$		0			0
$478$	−8.72474	+	15.1117i	−0.399060	+	0.691193i
$479$	26.9561			1.23166			0.615828	−	0.787881i	$-0.288822\pi$
$479$	26.9561			1.23166			0.615828	+	0.787881i	$0.288822\pi$
$480$	−0.633975	−	3.03548i	−0.0289368	−	0.138550i
$481$			45.8026i			2.08842i
$482$	−5.71659	−	9.90142i	−0.260383	−	0.450997i
$483$		0			0
$484$	2.61639	−	4.53172i	0.118927	−	0.205987i
$485$	8.54455	+	4.93320i	0.387988	+	0.224005i
$486$	13.3598	+	8.03223i	0.606011	+	0.364349i
$487$	6.81338	+	11.8011i	0.308744	+	0.534760i	0.978088	−	0.208193i	$-0.0667581\pi$
$487$	6.81338	+	11.8011i	0.308744	+	0.534760i	−0.669344	+	0.742953i	$0.733425\pi$
$488$	5.66414	+	9.81058i	0.256404	+	0.444104i
$489$	7.35116	−	1.53533i	0.332431	−	0.0694299i
$490$		0			0
$491$	−33.7430	+	19.4815i	−1.52280	+	0.879188i	−0.523162	+	0.852234i	$0.675248\pi$
$491$	−33.7430	+	19.4815i	−1.52280	+	0.879188i	−0.999637	+	0.0269544i	$0.991419\pi$
$492$	9.32971	+	10.4358i	0.420616	+	0.470484i
$493$		−	24.0440i		−	1.08289i
$494$	−12.7801	+	7.37859i	−0.575004	+	0.331979i
$495$	12.8181	+	1.43917i	0.576129	+	0.0646858i
$496$			4.64661i			0.208639i
$497$		0			0
$498$	−18.0847	+	16.1678i	−0.810393	+	0.724497i
$499$	26.0097			1.16435			0.582176	−	0.813063i	$-0.302201\pi$
$499$	26.0097			1.16435			0.582176	+	0.813063i	$0.302201\pi$
$500$	6.08240	−	10.5350i	0.272013	−	0.471141i
$501$	−6.71743	+	20.4275i	−0.300113	+	0.912632i
$502$	−23.6910	+	13.6780i	−1.05738	+	0.610478i
$503$	−10.5271			−0.469378			−0.234689	−	0.972070i	$-0.575407\pi$
$503$	−10.5271			−0.469378			−0.234689	+	0.972070i	$0.575407\pi$
$504$		0			0
$505$	0.448168			0.0199432
$506$	7.83319	−	4.52249i	0.348228	−	0.201049i
$507$	18.5231	−	3.86864i	0.822640	−	0.171812i
$508$	0.700752	−	1.21374i	0.0310908	−	0.0538509i
$509$	0.938871			0.0416147			0.0208074	−	0.999784i	$-0.493376\pi$
$509$	0.938871			0.0416147			0.0208074	+	0.999784i	$0.493376\pi$
$510$	2.32330	+	11.1240i	0.102878	+	0.492580i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−15.6075	+	1.47281i	−0.689088	+	0.0650261i
$514$	−3.02826	+	1.74837i	−0.133571	+	0.0771172i
$515$			0.300656i			0.0132485i
$516$	−3.76721	+	11.4560i	−0.165842	+	0.504320i
$517$	10.6818	−	6.16711i	0.469783	−	0.271229i
$518$		0			0
$519$	9.42442	−	28.6593i	0.413686	−	1.25801i
$520$	−4.37859	−	7.58394i	−0.192014	−	0.332578i
$521$	−19.7527	−	34.2127i	−0.865382	−	1.49889i	−0.866667	−	0.498887i	$-0.833742\pi$
$521$	−19.7527	−	34.2127i	−0.865382	−	1.49889i	0.00128461	−	0.999999i	$-0.499591\pi$
$522$	−2.19615	+	19.5602i	−0.0961230	+	0.856126i
$523$	−21.0697	−	12.1646i	−0.921315	−	0.531922i	−0.0372609	−	0.999306i	$-0.511863\pi$
$523$	−21.0697	−	12.1646i	−0.921315	−	0.531922i	−0.884054	+	0.467384i	$0.845197\pi$
$524$	−5.24589	+	9.08614i	−0.229168	+	0.396930i
$525$		0			0
$526$	−4.82174	−	8.35150i	−0.210238	−	0.364143i
$527$		−	17.0283i		−	0.741763i
$528$	3.95136	+	1.29938i	0.171961	+	0.0565482i
$529$	8.81436			0.383233
$530$		0			0
$531$	−35.2274	−	25.9777i	−1.52874	−	1.12734i
$532$		0			0
$533$	34.2349	+	19.7655i	1.48288	+	0.856141i
$534$	4.84047	−	4.32741i	0.209468	−	0.187266i
$535$	−12.3896	−	7.15316i	−0.535651	−	0.309258i
$536$	−0.493834	−	0.285115i	−0.0213304	−	0.0123151i
$537$	21.5907	+	7.09993i	0.931706	+	0.306385i
$538$	5.98517	+	3.45554i	0.258039	+	0.148979i
$539$		0			0
$540$	−0.873992	−	9.26178i	−0.0376106	−	0.398564i
$541$	−21.3640	+	37.0036i	−0.918512	+	1.59091i	−0.116835	+	0.993151i	$0.537275\pi$
$541$	−21.3640	+	37.0036i	−0.918512	+	1.59091i	−0.801677	+	0.597758i	$0.796058\pi$
$542$	−20.6312			−0.886187
$543$	17.2484	−	15.4202i	0.740199	−	0.661743i
$544$			3.66466i			0.157121i
$545$	−16.9665	−	29.3869i	−0.726767	−	1.25880i
$546$		0			0
$547$	−12.2477	+	21.2136i	−0.523672	+	0.907026i	0.475949	+	0.879473i	$0.342105\pi$
$547$	−12.2477	+	21.2136i	−0.523672	+	0.907026i	−0.999620	+	0.0275530i	$0.991229\pi$
$548$	4.08812	+	2.36028i	0.174636	+	0.100826i
$549$	13.6025	+	31.1439i	0.580539	+	1.32919i
$550$	2.15493	+	3.73244i	0.0918864	+	0.159152i
$551$	−9.89735	−	17.1427i	−0.421641	−	0.730304i
$552$	−4.34791	−	4.86340i	−0.185059	−	0.207000i
$553$		0			0
$554$	13.4358	−	7.75718i	0.570834	−	0.329571i
$555$	28.4243	−	5.93656i	1.20655	−	0.251993i
$556$		−	2.36375i		−	0.100245i
$557$	2.20344	−	1.27216i	0.0933627	−	0.0539030i	−0.452592	−	0.891718i	$-0.649501\pi$
$557$	2.20344	−	1.27216i	0.0933627	−	0.0539030i	0.545954	+	0.837815i	$0.316167\pi$
$558$	−1.55534	+	13.8528i	−0.0658430	+	0.586435i
$559$			34.0560i			1.44042i
$560$		0			0
$561$	−14.4804	−	4.76178i	−0.611364	−	0.201043i
$562$	−13.5977			−0.573583
$563$	7.90707	−	13.6954i	0.333243	−	0.577194i	−0.649902	−	0.760018i	$-0.725190\pi$
$563$	7.90707	−	13.6954i	0.333243	−	0.577194i	0.983146	+	0.182823i	$0.0585236\pi$
$564$	−5.92904	−	6.63199i	−0.249658	−	0.279257i
$565$	1.79783	−	1.03798i	0.0756354	−	0.0436681i
$566$	5.44783			0.228990
$567$		0			0
$568$	−5.96254			−0.250182
$569$	5.52793	−	3.19155i	0.231743	−	0.133797i	−0.379633	−	0.925137i	$-0.623950\pi$
$569$	5.52793	−	3.19155i	0.231743	−	0.133797i	0.611376	+	0.791340i	$0.290616\pi$
$570$	6.23549	+	6.97477i	0.261176	+	0.292141i
$571$	3.91188	−	6.77557i	0.163707	−	0.283549i	−0.772488	−	0.635029i	$-0.780988\pi$
$571$	3.91188	−	6.77557i	0.163707	−	0.283549i	0.936195	+	0.351480i	$0.114322\pi$
$572$	11.7465			0.491148
$573$	15.2252	+	5.00668i	0.636040	+	0.209157i
$574$		0			0
$575$		−	6.75933i		−	0.281884i
$576$	0.334727	−	2.98127i	0.0139469	−	0.124219i
$577$	−12.4012	+	7.15986i	−0.516270	+	0.298069i	−0.735407	−	0.677625i	$-0.763009\pi$
$577$	−12.4012	+	7.15986i	−0.516270	+	0.298069i	0.219137	+	0.975694i	$0.429676\pi$
$578$			3.57023i			0.148502i
$579$	41.6410	−	8.69693i	1.73054	−	0.361432i
$580$	10.1728	−	5.87327i	0.422403	−	0.243874i
$581$		0			0
$582$	6.36175	+	7.11600i	0.263703	+	0.294968i
$583$		0			0
$584$	6.19070	+	10.7226i	0.256173	+	0.443705i
$585$	−10.5152	−	24.0754i	−0.434750	−	0.995395i
$586$	21.1849	+	12.2311i	0.875141	+	0.505263i
$587$	2.37575	−	4.11492i	0.0980577	−	0.169841i	−0.812823	−	0.582511i	$-0.802070\pi$
$587$	2.37575	−	4.11492i	0.0980577	−	0.169841i	0.910881	+	0.412670i	$0.135404\pi$
$588$		0			0
$589$	−7.00943	−	12.1407i	−0.288819	−	0.500249i
$590$			26.1212i			1.07539i
$591$	16.1229	−	14.4139i	0.663206	−	0.592910i
$592$	9.36404			0.384860
$593$	1.79035	−	3.10098i	0.0735208	−	0.127342i	−0.826921	−	0.562318i	$-0.809910\pi$
$593$	1.79035	−	3.10098i	0.0735208	−	0.127342i	0.900442	+	0.434976i	$0.143243\pi$
$594$	11.3451	+	5.19642i	0.465497	+	0.213212i
$595$		0			0
$596$	−15.0377	−	8.68202i	−0.615968	−	0.355629i
$597$	−0.294761	−	0.0969299i	−0.0120638	−	0.00396708i
$598$	−15.9544	−	9.21130i	−0.652426	−	0.376678i
$599$	13.0471	+	7.53277i	0.533091	+	0.307780i	0.742274	−	0.670096i	$-0.233747\pi$
$599$	13.0471	+	7.53277i	0.533091	+	0.307780i	−0.209183	+	0.977877i	$0.567080\pi$
$600$	2.31737	−	2.07174i	0.0946060	−	0.0845784i
$601$	19.8704	+	11.4722i	0.810530	+	0.467960i	0.847140	−	0.531370i	$-0.178322\pi$
$601$	19.8704	+	11.4722i	0.810530	+	0.467960i	−0.0366096	+	0.999330i	$0.511656\pi$
$602$		0			0
$603$	−1.37682	−	1.01531i	−0.0560683	−	0.0413464i
$604$	−5.61639	+	9.72787i	−0.228528	+	0.395821i
$605$	−9.36850			−0.380884
$606$	0.411876	+	0.135442i	0.0167313	+	0.00550197i
$607$		−	24.4832i		−	0.993741i	−0.867825	−	0.496870i	$-0.834482\pi$
$607$		−	24.4832i		−	0.993741i	0.867825	−	0.496870i	$-0.165518\pi$
$608$	1.50851	+	2.61281i	0.0611780	+	0.105963i
$609$		0			0
$610$	10.1408	−	17.5644i	0.410589	−	0.711161i
$611$	−21.7563	−	12.5610i	−0.880167	−	0.508165i
$612$	−1.22666	+	10.9253i	−0.0495848	+	0.441631i
$613$	0.440043	+	0.762177i	0.0177732	+	0.0307840i	0.874775	−	0.484529i	$-0.161009\pi$
$613$	0.440043	+	0.762177i	0.0177732	+	0.0307840i	−0.857002	+	0.515313i	$0.827676\pi$
$614$	−15.6111	−	27.0393i	−0.630014	−	1.09122i
$615$	7.82892	−	23.8075i	0.315693	−	0.960011i
$616$		0			0
$617$	−11.7607	+	6.79005i	−0.473468	+	0.273357i	−0.717690	−	0.696362i	$-0.754801\pi$
$617$	−11.7607	+	6.79005i	−0.473468	+	0.273357i	0.244222	+	0.969719i	$0.421467\pi$
$618$	−0.0908623	+	0.276309i	−0.00365502	+	0.0111148i
$619$		−	35.4869i		−	1.42634i	−0.700992	−	0.713169i	$-0.747259\pi$
$619$		−	35.4869i		−	1.42634i	0.700992	−	0.713169i	$-0.252741\pi$
$620$	7.20451	−	4.15953i	0.289340	−	0.167051i
$621$	−11.3344	−	15.9544i	−0.454833	−	0.640230i
$622$			10.9100i			0.437452i
$623$		0			0
$624$	−1.73205	−	8.29308i	−0.0693375	−	0.331989i
$625$	−12.8060			−0.512240
$626$	−1.71203	+	2.96532i	−0.0684263	+	0.118518i
$627$	−12.2843	+	2.56563i	−0.490587	+	0.102461i
$628$	11.9885	−	6.92154i	0.478391	−	0.276199i
$629$	−34.3161			−1.36827
$630$		0			0
$631$	26.9822			1.07415			0.537073	−	0.843536i	$-0.319530\pi$
$631$	26.9822			1.07415			0.537073	+	0.843536i	$0.319530\pi$
$632$	2.62979	−	1.51831i	0.104608	−	0.0603952i
$633$	−8.18207	+	24.8814i	−0.325208	+	0.988947i
$634$	9.52357	−	16.4953i	0.378229	−	0.655112i
$635$	−2.50918			−0.0995739
$636$		0			0
$637$		0			0
$638$			15.7563i			0.623800i
$639$	−17.7759	−	1.99582i	−0.703204	−	0.0789534i
$640$	−1.55049	+	0.895175i	−0.0612884	+	0.0353849i
$641$		−	1.07708i		−	0.0425420i	−0.999774	−	0.0212710i	$-0.993229\pi$
$641$		−	1.07708i		−	0.0425420i	0.999774	−	0.0212710i	$-0.00677128\pi$
$642$	−9.22457	−	10.3182i	−0.364065	−	0.407228i
$643$	−33.3126	+	19.2330i	−1.31372	+	0.758477i	−0.982710	−	0.185150i	$-0.940723\pi$
$643$	−33.3126	+	19.2330i	−1.31372	+	0.758477i	−0.331010	+	0.943627i	$0.607389\pi$
$644$		0			0
$645$	21.1346	−	4.41407i	0.832175	−	0.173804i
$646$	−5.52817	−	9.57507i	−0.217503	−	0.376726i
$647$	−4.47605	−	7.75275i	−0.175972	−	0.304792i	0.764525	−	0.644594i	$-0.222973\pi$
$647$	−4.47605	−	7.75275i	−0.175972	−	0.304792i	−0.940497	+	0.339802i	$0.889640\pi$
$648$	1.99582	−	8.77592i	0.0784032	−	0.344751i
$649$	−30.3438	−	17.5190i	−1.19110	−	0.687680i
$650$	4.38910	−	7.60215i	0.172155	−	0.298181i
$651$		0			0
$652$	−2.16789	−	3.75489i	−0.0849010	−	0.147053i
$653$		−	11.3846i		−	0.445513i	−0.974874	−	0.222757i	$-0.928494\pi$
$653$		−	11.3846i		−	0.445513i	0.974874	−	0.222757i	$-0.0715055\pi$
$654$	−6.71150	−	32.1348i	−0.262440	−	1.25657i
$655$	18.7839			0.733949
$656$	4.04094	−	6.99911i	0.157772	−	0.273269i
$657$	14.8670	+	34.0392i	0.580017	+	1.32799i
$658$		0			0
$659$	31.4373	+	18.1503i	1.22462	+	0.707036i	0.965900	−	0.258915i	$-0.0833650\pi$
$659$	31.4373	+	18.1503i	1.22462	+	0.707036i	0.258723	+	0.965952i	$0.416698\pi$
$660$	−1.52249	−	7.28972i	−0.0592629	−	0.283752i
$661$	−31.2425	−	18.0379i	−1.21519	−	0.701593i	−0.251308	−	0.967907i	$-0.580861\pi$
$661$	−31.2425	−	18.0379i	−1.21519	−	0.701593i	−0.963886	+	0.266315i	$0.914194\pi$
$662$	0.0634366	+	0.0366251i	0.00246553	+	0.00142348i
$663$	6.34739	+	30.3914i	0.246512	+	1.18030i
$664$	12.1290	+	7.00270i	0.470698	+	0.271757i
$665$		0			0
$666$	27.9167	+	3.13439i	1.08175	+	0.121455i
$667$	12.3557	−	21.4007i	0.478414	−	0.828637i
$668$	12.4151			0.480355
$669$	2.97281	+	14.2339i	0.114935	+	0.550313i
$670$			1.02091i			0.0394413i
$671$	13.6025	+	23.5602i	0.525117	+	0.909530i
$672$		0			0
$673$	4.78512	−	8.28806i	0.184453	−	0.319481i	−0.758939	−	0.651161i	$-0.774282\pi$
$673$	4.78512	−	8.28806i	0.184453	−	0.319481i	0.943392	+	0.331680i	$0.107615\pi$
$674$	−1.93364	−	1.11639i	−0.0744811	−	0.0430017i
$675$	7.60215	−	5.40073i	0.292607	−	0.207874i
$676$	−5.46254	−	9.46139i	−0.210098	−	0.363900i
$677$	−7.81408	−	13.5344i	−0.300320	−	0.520169i	0.675889	−	0.737004i	$-0.263760\pi$
$677$	−7.81408	−	13.5344i	−0.300320	−	0.520169i	−0.976208	+	0.216835i	$0.930427\pi$
$678$	1.96594	−	0.410596i	0.0755015	−	0.0157689i
$679$		0			0
$680$	5.68202	−	3.28052i	0.217896	−	0.125802i
$681$	2.79967	+	3.13160i	0.107283	+	0.120003i
$682$			11.1589i			0.427294i
$683$	−9.63996	+	5.56563i	−0.368863	+	0.212963i	−0.672961	−	0.739678i	$-0.734978\pi$
$683$	−9.63996	+	5.56563i	−0.368863	+	0.212963i	0.304099	+	0.952640i	$0.401645\pi$
$684$	3.62268	+	8.29442i	0.138517	+	0.317145i
$685$		−	8.45145i		−	0.322913i
$686$		0			0
$687$	2.60803	−	2.33159i	0.0995025	−	0.0889559i
$688$	6.96254			0.265444
$689$		0			0
$690$	−3.64850	+	11.0950i	−0.138896	+	0.422378i
$691$	2.61903	−	1.51210i	0.0996324	−	0.0575228i	−0.449356	−	0.893353i	$-0.648346\pi$
$691$	2.61903	−	1.51210i	0.0996324	−	0.0575228i	0.548988	+	0.835830i	$0.315013\pi$
$692$	−17.4182			−0.662139
$693$		0			0
$694$	31.8409			1.20867
$695$	−3.66497	+	2.11597i	−0.139020	+	0.0802633i
$696$	11.1240	−	2.32330i	0.421655	−	0.0880646i
$697$	−14.8087	+	25.6494i	−0.560919	+	0.971540i
$698$	−14.7354			−0.557745
$699$	−4.50739	−	21.5815i	−0.170485	−	0.816286i
$700$		0			0
$701$		−	50.1486i		−	1.89409i	−0.321103	−	0.947044i	$-0.604054\pi$
$701$		−	50.1486i		−	1.89409i	0.321103	−	0.947044i	$-0.395946\pi$
$702$	−2.38779	−	25.3037i	−0.0901214	−	0.955025i
$703$	−24.4664	+	14.1257i	−0.922769	+	0.532761i
$704$		−	2.40150i		−	0.0905101i
$705$	−4.97529	+	15.1297i	−0.187380	+	0.569817i
$706$	1.87025	−	1.07979i	0.0703876	−	0.0406383i
$707$		0			0
$708$	−7.89419	+	24.0060i	−0.296682	+	0.902200i
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	0.897908	−	0.440183i	$-0.145086\pi$
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	−0.830163	+	0.557520i	$0.811753\pi$
$710$	5.33751	+	9.24484i	0.200313	+	0.346953i
$711$	8.34834	−	3.64623i	0.313087	−	0.136744i
$712$	−3.24641	−	1.87432i	−0.121664	−	0.0702429i
$713$	8.75046	−	15.1562i	0.327707	−	0.567605i
$714$		0			0
$715$	−10.5152	−	18.2129i	−0.393246	−	0.681123i
$716$		−	13.1221i		−	0.490395i
$717$	28.7109	+	9.44136i	1.07223	+	0.352594i
$718$	−32.6448			−1.21829
$719$	−17.1580	+	29.7186i	−0.639887	+	1.10832i	0.345571	+	0.938393i	$0.387685\pi$
$719$	−17.1580	+	29.7186i	−0.639887	+	1.10832i	−0.985457	+	0.169924i	$0.945648\pi$
$720$	−4.92206	+	2.14977i	−0.183434	+	0.0801171i
$721$		0			0
$722$	8.57161	+	4.94882i	0.319002	+	0.184176i
$723$	−14.7633	+	13.1984i	−0.549051	+	0.490855i
$724$	−11.5681	−	6.67887i	−0.429927	−	0.248218i
$725$	10.1972	+	5.88737i	0.378716	+	0.218651i
$726$	−8.60986	−	2.83129i	−0.319542	−	0.105079i
$727$	−19.4757	−	11.2443i	−0.722315	−	0.417029i	0.0932892	−	0.995639i	$-0.470262\pi$
$727$	−19.4757	−	11.2443i	−0.722315	−	0.417029i	−0.815604	+	0.578610i	$0.803595\pi$
$728$		0			0
$729$	8.88761	−	25.4953i	0.329171	−	0.944270i
$730$	11.0835	−	19.1972i	0.410220	−	0.710521i
$731$	−25.5154			−0.943720
$732$	14.6278	−	13.0774i	0.540659	−	0.483353i
$733$		−	31.1845i		−	1.15182i	−0.817512	−	0.575912i	$-0.804647\pi$
$733$		−	31.1845i		−	1.15182i	0.817512	−	0.575912i	$-0.195353\pi$
$734$	−14.8501	−	25.7212i	−0.548129	−	0.949387i
$735$		0			0
$736$	−1.88319	+	3.26178i	−0.0694154	+	0.120231i
$737$	−1.18595	−	0.684706i	−0.0436849	−	0.0252215i
$738$	14.3899	−	19.5136i	0.529700	−	0.718306i
$739$	−2.04314	−	3.53882i	−0.0751581	−	0.130178i	0.825997	−	0.563675i	$-0.190613\pi$
$739$	−2.04314	−	3.53882i	−0.0751581	−	0.130178i	−0.901155	+	0.433497i	$0.857279\pi$
$740$	−8.38245	−	14.5188i	−0.308145	−	0.533723i
$741$	17.0357	+	19.0554i	0.625821	+	0.700018i
$742$		0			0
$743$	−1.78246	+	1.02910i	−0.0653921	+	0.0377542i	−0.532340	−	0.846531i	$-0.678687\pi$
$743$	−1.78246	+	1.02910i	−0.0653921	+	0.0377542i	0.466947	+	0.884285i	$0.345354\pi$
$744$	7.87817	−	1.64539i	0.288828	−	0.0603231i
$745$			31.0877i			1.13897i
$746$	1.74653	−	1.00836i	0.0639450	−	0.0369187i
$747$	33.8159	+	24.9368i	1.23726	+	0.912391i
$748$			8.80071i			0.321786i
$749$		0			0
$750$	−20.0156	−	6.58198i	−0.730866	−	0.240340i
$751$	23.8105			0.868859			0.434429	−	0.900706i	$-0.356950\pi$
$751$	23.8105			0.868859			0.434429	+	0.900706i	$0.356950\pi$
$752$	−2.56802	+	4.44794i	−0.0936461	+	0.162200i
$753$	31.5797	+	35.3238i	1.15083	+	1.28727i
$754$	27.7926	−	16.0461i	1.01215	−	0.584363i
$755$	20.1106			0.731900
$756$		0			0
$757$	10.0754			0.366197			0.183098	−	0.983095i	$-0.441387\pi$
$757$	10.0754			0.366197			0.183098	+	0.983095i	$0.441387\pi$
$758$	16.3427	−	9.43544i	0.593592	−	0.342711i
$759$	−10.4415	−	11.6795i	−0.379003	−	0.423938i
$760$	2.70075	−	4.67784i	0.0979666	−	0.169683i
$761$	27.8735			1.01041			0.505207	−	0.862998i	$-0.331416\pi$
$761$	27.8735			1.01041			0.505207	+	0.862998i	$0.331416\pi$
$762$	−2.30599	−	0.758309i	−0.0835374	−	0.0274707i
$763$		0			0
$764$		−	9.25333i		−	0.334774i
$765$	18.0377	−	7.87817i	0.652154	−	0.284836i
$766$	0.724440	−	0.418256i	0.0261751	−	0.0151122i
$767$			71.3645i			2.57682i
$768$	−1.69547	+	0.354107i	−0.0611799	+	0.0127777i
$769$	6.21166	−	3.58631i	0.223998	−	0.129326i	−0.383802	−	0.923415i	$-0.625385\pi$
$769$	6.21166	−	3.58631i	0.223998	−	0.129326i	0.607800	+	0.794090i	$0.292052\pi$
$770$		0			0
$771$	4.03663	+	4.51521i	0.145376	+	0.162611i
$772$	−12.2801	−	21.2698i	−0.441970	−	0.765515i
$773$	−1.07077	−	1.85462i	−0.0385128	−	0.0667061i	0.846127	−	0.532982i	$-0.178929\pi$
$773$	−1.07077	−	1.85462i	−0.0385128	−	0.0667061i	−0.884639	+	0.466276i	$0.845595\pi$
$774$	20.7572	+	2.33055i	0.746102	+	0.0837698i
$775$	7.22181	+	4.16951i	0.259415	+	0.149773i
$776$	2.75544	−	4.77256i	0.0989144	−	0.171325i
$777$		0			0
$778$	12.4109	+	21.4964i	0.444954	+	0.770682i
$779$			24.3831i			0.873615i
$780$	−11.3078	+	10.1093i	−0.404886	+	0.361970i
$781$	−14.3191			−0.512376
$782$	6.90127	−	11.9533i	0.246789	−	0.427451i
$783$	33.9413	−	3.20289i	1.21296	−	0.114462i
$784$		0			0
$785$	−21.4635	−	12.3920i	−0.766066	−	0.442288i
$786$	17.2629	+	5.67677i	0.615746	+	0.202484i
$787$	15.8961	+	9.17759i	0.566633	+	0.327146i	0.755804	−	0.654798i	$-0.227247\pi$
$787$	15.8961	+	9.17759i	0.566633	+	0.327146i	−0.189170	+	0.981944i	$0.560580\pi$
$788$	−10.8133	−	6.24305i	−0.385207	−	0.222400i
$789$	−12.4523	+	11.1324i	−0.443313	+	0.396325i
$790$	−4.70825	−	2.71831i	−0.167512	−	0.0967131i
$791$		0			0
$792$	0.803848	−	7.15953i	0.0285635	−	0.254403i
$793$	27.7052	−	47.9868i	0.983839	−	1.70406i
$794$	3.03390			0.107669
$795$		0			0
$796$			0.179145i			0.00634964i
$797$	−12.4226	−	21.5166i	−0.440031	−	0.762156i	0.557660	−	0.830069i	$-0.311699\pi$
$797$	−12.4226	−	21.5166i	−0.440031	−	0.762156i	−0.997691	+	0.0679130i	$0.978366\pi$
$798$		0			0
$799$	9.41094	−	16.3002i	0.332935	−	0.576660i
$800$	−1.55421	−	0.897324i	−0.0549497	−	0.0317252i
$801$	−9.05103	−	6.67450i	−0.319803	−	0.235832i
$802$	−6.53854	−	11.3251i	−0.230884	−	0.399903i
$803$	14.8670	+	25.7504i	0.524645	+	0.908712i
$804$	−0.308534	+	0.938241i	−0.0108811	+	0.0330892i
$805$		0			0
$806$	19.6831	−	11.3640i	0.693307	−	0.400281i
$807$	3.73936	−	11.3713i	0.131632	−	0.400288i
$808$		−	0.250324i		−	0.00880637i
$809$	32.7237	−	18.8930i	1.15050	−	0.664244i	0.201494	−	0.979490i	$-0.435420\pi$
$809$	32.7237	−	18.8930i	1.15050	−	0.664244i	0.949010	+	0.315246i	$0.102087\pi$
$810$	−15.3936	+	4.76148i	−0.540875	+	0.167301i
$811$			36.5165i			1.28227i	0.767429	+	0.641134i	$0.221536\pi$
$811$			36.5165i			1.28227i	−0.767429	+	0.641134i	$0.778464\pi$
$812$		0			0
$813$	7.30565	+	34.9795i	0.256220	+	1.22679i
$814$	22.4878			0.788196
$815$	−3.88128	+	6.72257i	−0.135955	+	0.235481i
$816$	6.21332	−	1.29768i	0.217510	−	0.0454280i
$817$	−18.1918	+	10.5030i	−0.636449	+	0.367454i
$818$	−5.56709			−0.194649
$819$		0			0
$820$	−14.4694			−0.505293
$821$	5.52142	−	3.18779i	0.192699	−	0.111255i	−0.400547	−	0.916276i	$-0.631180\pi$
$821$	5.52142	−	3.18779i	0.192699	−	0.111255i	0.593245	+	0.805022i	$0.297846\pi$
$822$	2.55414	−	7.76707i	0.0890860	−	0.270908i
$823$	−14.0293	+	24.2995i	−0.489032	+	0.847028i	−0.999920	−	0.0126187i	$-0.995983\pi$
$823$	−14.0293	+	24.2995i	−0.489032	+	0.847028i	0.510888	+	0.859647i	$0.329317\pi$
$824$	0.167931			0.00585017
$825$	5.56516	−	4.97529i	0.193754	−	0.173217i
$826$		0			0
$827$			0.581579i			0.0202235i	0.999949	+	0.0101117i	$0.00321872\pi$
$827$			0.581579i			0.0202235i	−0.999949	+	0.0101117i	$0.996781\pi$
$828$	−6.70610	+	9.09390i	−0.233053	+	0.316035i
$829$	44.9680	−	25.9623i	1.56180	−	0.901708i	0.564729	−	0.825276i	$-0.308981\pi$
$829$	44.9680	−	25.9623i	1.56180	−	0.901708i	0.997075	−	0.0764314i	$-0.0243526\pi$
$830$		−	25.0746i		−	0.870351i
$831$	−17.9098	−	20.0331i	−0.621283	−	0.694942i
$832$	−4.23601	+	2.44566i	−0.146857	+	0.0847881i
$833$		0			0
$834$	−4.00766	+	0.837019i	−0.138774	+	0.0289836i
$835$	−11.1137	−	19.2495i	−0.384606	−	0.666156i
$836$	3.62268	+	6.27467i	0.125293	+	0.217014i
$837$	24.0377	−	2.26833i	0.830864	−	0.0784049i
$838$	14.2017	+	8.19938i	0.490591	+	0.283243i
$839$	3.33038	−	5.76838i	0.114977	−	0.199147i	−0.802793	−	0.596257i	$-0.796654\pi$
$839$	3.33038	−	5.76838i	0.114977	−	0.199147i	0.917771	+	0.397111i	$0.129987\pi$
$840$		0			0
$841$	7.02357	+	12.1652i	0.242192	+	0.419489i
$842$		−	15.4578i		−	0.532712i
$843$	4.81502	+	23.0544i	0.165838	+	0.794035i
$844$	15.1221			0.520523
$845$	−9.77985	+	16.9392i	−0.336437	+	0.582726i
$846$	−9.14481	+	12.4009i	−0.314405	+	0.426353i
$847$		0			0
$848$		0			0
$849$	−1.92911	−	9.23662i	−0.0662070	−	0.317000i
$850$	5.69566	+	3.28839i	0.195360	+	0.112791i
$851$	−30.5435	−	17.6343i	−1.04702	−	0.604495i
$852$	2.11137	+	10.1093i	0.0723345	+	0.346338i
$853$	19.2287	+	11.1017i	0.658378	+	0.380115i	0.791659	−	0.610964i	$-0.209218\pi$
$853$	19.2287	+	11.1017i	0.658378	+	0.380115i	−0.133281	+	0.991078i	$0.542551\pi$
$854$		0			0
$855$	9.61746	−	13.0419i	0.328910	−	0.446023i
$856$	−3.99540	+	6.92024i	−0.136560	+	0.236529i
$857$	−15.2966			−0.522522			−0.261261	−	0.965268i	$-0.584138\pi$
$857$	−15.2966			−0.522522			−0.261261	+	0.965268i	$0.584138\pi$
$858$	−4.15953	−	19.9159i	−0.142004	−	0.679917i
$859$		−	4.25646i		−	0.145229i	−0.997360	−	0.0726143i	$-0.976866\pi$
$859$		−	4.25646i		−	0.145229i	0.997360	−	0.0726143i	$-0.0231342\pi$
$860$	−6.23269	−	10.7953i	−0.212533	−	0.368118i
$861$		0			0
$862$	−12.5133	+	21.6737i	−0.426204	+	0.738208i
$863$	−20.4922	−	11.8312i	−0.697562	−	0.402738i	0.108876	−	0.994055i	$-0.465275\pi$
$863$	−20.4922	−	11.8312i	−0.697562	−	0.402738i	−0.806439	+	0.591317i	$0.798608\pi$
$864$	−5.17317	+	0.488168i	−0.175995	+	0.0166078i
$865$	15.5923	+	27.0067i	0.530154	+	0.918254i
$866$	−1.12584	−	1.95001i	−0.0382576	−	0.0662641i
$867$	6.05321	−	1.26424i	0.205578	−	0.0429359i
$868$		0			0
$869$	6.31546	−	3.64623i	0.214237	−	0.123690i
$870$	−13.5602	−	15.1679i	−0.459734	−	0.514240i
$871$			2.78919i			0.0945079i
$872$	−16.4141	+	9.47667i	−0.555851	+	0.320920i
$873$	9.81220	−	13.3060i	0.332093	−	0.450338i
$874$		−	11.3632i		−	0.384367i
$875$		0			0
$876$	15.9877	−	14.2931i	0.540173	−	0.482918i
$877$	−20.3923			−0.688599			−0.344300	−	0.938860i	$-0.611884\pi$
$877$	−20.3923			−0.688599			−0.344300	+	0.938860i	$0.611884\pi$
$878$	−9.37000	+	16.2293i	−0.316222	+	0.547713i
$879$	13.2357	−	40.2495i	0.446430	−	1.35758i
$880$	−3.72350	+	2.14977i	−0.125519	+	0.0724686i
$881$	−32.4586			−1.09356			−0.546780	−	0.837276i	$-0.684147\pi$
$881$	−32.4586			−1.09356			−0.546780	+	0.837276i	$0.684147\pi$
$882$		0			0
$883$	−24.8311			−0.835632			−0.417816	−	0.908532i	$-0.637204\pi$
$883$	−24.8311			−0.835632			−0.417816	+	0.908532i	$0.637204\pi$
$884$	15.5236	−	8.96254i	0.522114	−	0.301443i
$885$	44.2877	−	9.24970i	1.48871	−	0.310925i
$886$	−0.602256	+	1.04314i	−0.0202332	+	0.0350449i
$887$	−9.72119			−0.326405			−0.163203	−	0.986593i	$-0.552182\pi$
$887$	−9.72119			−0.326405			−0.163203	+	0.986593i	$0.552182\pi$
$888$	−3.31587	−	15.8764i	−0.111273	−	0.532778i
$889$		0			0
$890$			6.71136i			0.224965i
$891$	4.79297	−	21.0754i	0.160571	−	0.706052i
$892$	7.27049	−	4.19762i	0.243434	−	0.140547i
$893$		−	15.4955i		−	0.518537i
$894$	−9.39513	+	28.5703i	−0.314220	+	0.955533i
$895$	−20.3456	+	11.7465i	−0.680079	+	0.392644i
$896$		0			0
$897$	−9.96789	+	30.3120i	−0.332818	+	1.01209i
$898$	13.4011	+	23.2114i	0.447200	+	0.774573i
$899$	15.2433	+	26.4021i	0.508392	+	0.880560i
$900$	−4.33316	−	3.19540i	−0.144439	−	0.106513i
$901$		0			0
$902$	9.70433	−	16.8084i	0.323119	−	0.559658i
$903$		0			0
$904$	−0.579764	−	1.00418i	−0.0192827	−	0.0333985i
$905$			23.9150i			0.794963i
$906$	18.4821	+	6.07770i	0.614026	+	0.201918i
$907$	−16.0863			−0.534136			−0.267068	−	0.963678i	$-0.586055\pi$
$907$	−16.0863			−0.534136			−0.267068	+	0.963678i	$0.586055\pi$
$908$	1.21261	−	2.10030i	0.0402418	−	0.0697009i
$909$	0.0837902	−	0.746284i	0.00277915	−	0.0247527i
$910$		0			0
$911$	27.0087	+	15.5935i	0.894838	+	0.516635i	0.875522	−	0.483179i	$-0.160518\pi$
$911$	27.0087	+	15.5935i	0.894838	+	0.516635i	0.0193161	+	0.999813i	$0.493851\pi$
$912$	3.89576	−	3.48283i	0.129001	−	0.115328i
$913$	29.1279	+	16.8170i	0.963993	+	0.556562i
$914$	11.9934	+	6.92442i	0.396708	+	0.229039i
$915$	−33.3707	−	10.9737i	−1.10320	−	0.362780i
$916$	−1.74915	−	1.00987i	−0.0577936	−	0.0333672i
$917$		0			0
$918$	18.9579	−	1.78897i	0.625705	−	0.0590449i
$919$	−12.8832	+	22.3143i	−0.424977	+	0.736082i	−0.996418	−	0.0845609i	$-0.973051\pi$
$919$	−12.8832	+	22.3143i	−0.424977	+	0.736082i	0.571441	+	0.820643i	$0.306385\pi$
$920$	6.74314			0.222315
$921$	−40.3162	+	36.0430i	−1.32846	+	1.18766i
$922$		−	4.80483i		−	0.158239i
$923$	14.5824	+	25.2574i	0.479984	+	0.831357i
$924$		0			0
$925$	8.40258	−	14.5537i	0.276275	−	0.478522i
$926$	−18.2201	−	10.5194i	−0.598750	−	0.345689i
$927$	0.500648	+	0.0562111i	0.0164435	+	0.00184622i
$928$	−3.28052	−	5.68202i	−0.107688	−	0.186521i
$929$	27.3744	+	47.4138i	0.898124	+	1.55560i	0.829891	+	0.557926i	$0.188403\pi$
$929$	27.3744	+	47.4138i	0.898124	+	1.55560i	0.0682329	+	0.997669i	$0.478264\pi$
$930$	−9.60351	−	10.7421i	−0.314911	−	0.352247i
$931$		0			0
$932$	−11.0236	+	6.36446i	−0.361089	+	0.208475i
$933$	18.4976	−	3.86331i	0.605584	−	0.126479i
$934$			5.82302i			0.190535i
$935$	13.6454	−	7.87817i	0.446252	−	0.257644i
$936$	−13.4473	+	5.87327i	−0.439539	+	0.191974i
$937$		−	58.2065i		−	1.90152i	−0.309924	−	0.950761i	$-0.600304\pi$
$937$		−	58.2065i		−	1.90152i	0.309924	−	0.950761i	$-0.399696\pi$
$938$		0			0
$939$	5.63384	+	1.85265i	0.183853	+	0.0604588i
$940$	9.19531			0.299918
$941$	−16.6658	+	28.8660i	−0.543289	+	0.941005i	0.455423	+	0.890275i	$0.349488\pi$
$941$	−16.6658	+	28.8660i	−0.543289	+	0.941005i	−0.998712	+	0.0507297i	$0.983845\pi$
$942$	−15.9804	−	17.8751i	−0.520671	−	0.582401i
$943$	−26.3613	+	15.2197i	−0.858443	+	0.495622i
$944$	14.5900			0.474864
$945$		0			0
$946$	16.7206			0.543632
$947$	6.59497	−	3.80761i	0.214308	−	0.123731i	−0.389004	−	0.921236i	$-0.627181\pi$
$947$	6.59497	−	3.80761i	0.214308	−	0.123731i	0.603312	+	0.797505i	$0.293847\pi$
$948$	−3.50548	−	3.92109i	−0.113853	−	0.127351i
$949$	30.2808	−	52.4478i	0.982955	−	1.70253i
$950$	5.41447			0.175669
$951$	−31.3396	−	10.3058i	−1.01626	−	0.334188i
$952$		0			0
$953$			55.7861i			1.80709i	0.428495	+	0.903544i	$0.359044\pi$
$953$			55.7861i			1.80709i	−0.428495	+	0.903544i	$0.640956\pi$
$954$		0			0
$955$	−14.3472	+	8.28334i	−0.464264	+	0.268043i
$956$		−	17.4495i		−	0.564356i
$957$	26.7144	−	5.57943i	0.863553	−	0.180357i
$958$	−23.3447	+	13.4781i	−0.754232	+	0.435456i
$959$		0			0
$960$	2.06678	+	2.31181i	0.0667050	+	0.0746135i
$961$	−4.70451	−	8.14845i	−0.151758	−	0.262853i
$962$	−22.9013	−	39.6662i	−0.738367	−	1.27889i
$963$	−14.2277	+	19.2937i	−0.458483	+	0.621731i
$964$	9.90142	+	5.71659i	0.318903	+	0.184119i
$965$	−21.9857	+	38.0803i	−0.707744	+	1.22585i
$966$		0			0
$967$	−13.3369	−	23.1003i	−0.428887	−	0.742855i	0.567887	−	0.823106i	$-0.307761\pi$
$967$	−13.3369	−	23.1003i	−0.428887	−	0.742855i	−0.996775	+	0.0802517i	$0.974428\pi$
$968$			5.23278i			0.168188i
$969$	−14.2766	+	12.7634i	−0.458632	+	0.410020i
$970$	−9.86639			−0.316791
$971$	−4.29971	+	7.44731i	−0.137984	+	0.238996i	−0.926733	−	0.375719i	$-0.877396\pi$
$971$	−4.29971	+	7.44731i	−0.137984	+	0.238996i	0.788749	+	0.614715i	$0.210729\pi$
$972$	−15.5860	−	0.276237i	−0.499921	−	0.00886031i
$973$		0			0
$974$	−11.8011	−	6.81338i	−0.378132	−	0.218315i
$975$	−14.4434	−	4.74961i	−0.462559	−	0.152109i
$976$	−9.81058	−	5.66414i	−0.314029	−	0.181305i
$977$	12.7973	+	7.38854i	0.409423	+	0.236380i	0.690542	−	0.723293i	$-0.257372\pi$
$977$	12.7973	+	7.38854i	0.409423	+	0.236380i	−0.281119	+	0.959673i	$0.590705\pi$
$978$	−5.59863	+	5.00521i	−0.179024	+	0.160049i
$979$	−7.79627	−	4.50118i	−0.249170	−	0.143858i
$980$		0			0
$981$	−52.1068	+	22.7583i	−1.66364	+	0.726615i
$982$	19.4815	−	33.7430i	0.621680	−	1.07678i
$983$	20.5135			0.654280			0.327140	−	0.944976i	$-0.393915\pi$
$983$	20.5135			0.654280			0.327140	+	0.944976i	$0.393915\pi$
$984$	−13.2977	−	4.37285i	−0.423915	−	0.139401i
$985$			22.3545i			0.712273i
$986$	12.0220	+	20.8227i	0.382858	+	0.663130i
$987$		0			0
$988$	7.37859	−	12.7801i	0.234744	−	0.406589i
$989$	−22.7103	−	13.1118i	−0.722145	−	0.416931i
$990$	−11.8203	+	5.16267i	−0.375675	+	0.164080i
$991$	4.64647	+	8.04792i	0.147600	+	0.255651i	0.930340	−	0.366698i	$-0.119512\pi$
$991$	4.64647	+	8.04792i	0.147600	+	0.255651i	−0.782740	+	0.622349i	$0.786179\pi$
$992$	−2.32330	−	4.02408i	−0.0737650	−	0.127765i
$993$	0.0396334	−	0.120524i	0.00125773	−	0.00382471i
$994$		0			0
$995$	0.277763	−	0.160366i	0.00880567	−	0.00508396i
$996$	7.57788	−	23.0441i	0.240114	−	0.730179i
$997$		−	0.0199668i		−	0.000632354i	−1.00000		0.000316177i	$-0.999899\pi$
$997$		−	0.0199668i		−	0.000632354i	1.00000		0.000316177i	$-0.000100642\pi$
$998$	−22.5250	+	13.0048i	−0.713018	+	0.411661i
$999$	−4.57123	−	48.4418i	−0.144627	−	1.53263i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.t.b.803.3		16
3.2	odd	2		2646.2.t.a.1979.8		16
7.2	even	3		126.2.m.a.83.5	yes	16
7.3	odd	6		882.2.l.a.227.2		16
7.4	even	3		882.2.l.a.227.3		16
7.5	odd	6		126.2.m.a.83.8	yes	16
7.6	odd	2	inner	882.2.t.b.803.2		16
9.4	even	3		2646.2.l.b.1097.4		16
9.5	odd	6		882.2.l.a.509.6		16
21.2	odd	6		378.2.m.a.251.1		16
21.5	even	6		378.2.m.a.251.4		16
21.11	odd	6		2646.2.l.b.521.5		16
21.17	even	6		2646.2.l.b.521.8		16
21.20	even	2		2646.2.t.a.1979.5		16
28.19	even	6		1008.2.cc.b.209.1		16
28.23	odd	6		1008.2.cc.b.209.8		16
63.2	odd	6		1134.2.d.a.1133.14		16
63.4	even	3		2646.2.t.a.2285.5		16
63.5	even	6		126.2.m.a.41.5	✓	16
63.13	odd	6		2646.2.l.b.1097.1		16
63.16	even	3		1134.2.d.a.1133.3		16
63.23	odd	6		126.2.m.a.41.8	yes	16
63.31	odd	6		2646.2.t.a.2285.8		16
63.32	odd	6	inner	882.2.t.b.815.2		16
63.40	odd	6		378.2.m.a.125.1		16
63.41	even	6		882.2.l.a.509.7		16
63.47	even	6		1134.2.d.a.1133.11		16
63.58	even	3		378.2.m.a.125.4		16
63.59	even	6	inner	882.2.t.b.815.3		16
63.61	odd	6		1134.2.d.a.1133.6		16
84.23	even	6		3024.2.cc.b.2897.3		16
84.47	odd	6		3024.2.cc.b.2897.6		16
252.23	even	6		1008.2.cc.b.545.1		16
252.103	even	6		3024.2.cc.b.881.3		16
252.131	odd	6		1008.2.cc.b.545.8		16
252.247	odd	6		3024.2.cc.b.881.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.5	✓	16	63.5	even	6
126.2.m.a.41.8	yes	16	63.23	odd	6
126.2.m.a.83.5	yes	16	7.2	even	3
126.2.m.a.83.8	yes	16	7.5	odd	6
378.2.m.a.125.1		16	63.40	odd	6
378.2.m.a.125.4		16	63.58	even	3
378.2.m.a.251.1		16	21.2	odd	6
378.2.m.a.251.4		16	21.5	even	6
882.2.l.a.227.2		16	7.3	odd	6
882.2.l.a.227.3		16	7.4	even	3
882.2.l.a.509.6		16	9.5	odd	6
882.2.l.a.509.7		16	63.41	even	6
882.2.t.b.803.2		16	7.6	odd	2	inner
882.2.t.b.803.3		16	1.1	even	1	trivial
882.2.t.b.815.2		16	63.32	odd	6	inner
882.2.t.b.815.3		16	63.59	even	6	inner
1008.2.cc.b.209.1		16	28.19	even	6
1008.2.cc.b.209.8		16	28.23	odd	6
1008.2.cc.b.545.1		16	252.23	even	6
1008.2.cc.b.545.8		16	252.131	odd	6
1134.2.d.a.1133.3		16	63.16	even	3
1134.2.d.a.1133.6		16	63.61	odd	6
1134.2.d.a.1133.11		16	63.47	even	6
1134.2.d.a.1133.14		16	63.2	odd	6
2646.2.l.b.521.5		16	21.11	odd	6
2646.2.l.b.521.8		16	21.17	even	6
2646.2.l.b.1097.1		16	63.13	odd	6
2646.2.l.b.1097.4		16	9.4	even	3
2646.2.t.a.1979.5		16	21.20	even	2
2646.2.t.a.1979.8		16	3.2	odd	2
2646.2.t.a.2285.5		16	63.4	even	3
2646.2.t.a.2285.8		16	63.31	odd	6
3024.2.cc.b.881.3		16	252.103	even	6
3024.2.cc.b.881.6		16	252.247	odd	6
3024.2.cc.b.2897.3		16	84.23	even	6
3024.2.cc.b.2897.6		16	84.47	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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.15440 + 1.29126i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.79035 q^{5} +(-1.64537 - 0.541068i) q^{6} +1.00000i q^{8} +(-0.334727 + 2.98127i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.15440 + 1.29126i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.79035 q^{5} +(-1.64537 - 0.541068i) q^{6} +1.00000i q^{8} +(-0.334727 + 2.98127i) q^{9} +(1.55049 - 0.895175i) q^{10} +2.40150i q^{11} +(1.69547 - 0.354107i) q^{12} +(4.23601 - 2.44566i) q^{13} +(-2.06678 - 2.31181i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.83233 + 3.17369i) q^{17} +(-1.20075 - 2.74922i) q^{18} +(2.61281 + 1.50851i) q^{19} +(-0.895175 + 1.55049i) q^{20} +(-1.20075 - 2.07976i) q^{22} +3.76638i q^{23} +(-1.29126 + 1.15440i) q^{24} -1.79465 q^{25} +(-2.44566 + 4.23601i) q^{26} +(-4.23601 + 3.00935i) q^{27} +(-5.68202 - 3.28052i) q^{29} +(2.94579 + 0.968701i) q^{30} +(-4.02408 - 2.32330i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.10098 + 2.77229i) q^{33} +(-3.17369 - 1.83233i) q^{34} +(2.41449 + 1.78052i) q^{36} +(-4.68202 + 8.10950i) q^{37} -3.01701 q^{38} +(8.04805 + 2.64654i) q^{39} -1.79035i q^{40} +(4.04094 + 6.99911i) q^{41} +(-3.48127 + 6.02973i) q^{43} +(2.07976 + 1.20075i) q^{44} +(0.599278 - 5.33751i) q^{45} +(-1.88319 - 3.26178i) q^{46} +(-2.56802 - 4.44794i) q^{47} +(0.541068 - 1.64537i) q^{48} +(1.55421 - 0.897324i) q^{50} +(-1.98283 + 6.02973i) q^{51} -4.89133i q^{52} +(2.16382 - 4.72418i) q^{54} -4.29953i q^{55} +(1.06834 + 5.11524i) q^{57} +6.56103 q^{58} +(-7.29501 + 12.6353i) q^{59} +(-3.03548 + 0.633975i) q^{60} +(9.81058 - 5.66414i) q^{61} +4.64661 q^{62} -1.00000 q^{64} +(-7.58394 + 4.37859i) q^{65} +(1.29938 - 3.95136i) q^{66} +(-0.285115 + 0.493834i) q^{67} +3.66466 q^{68} +(-4.86340 + 4.34791i) q^{69} +5.96254i q^{71} +(-2.98127 - 0.334727i) q^{72} +(10.7226 - 6.19070i) q^{73} -9.36404i q^{74} +(-2.07174 - 2.31737i) q^{75} +(2.61281 - 1.50851i) q^{76} +(-8.29308 + 1.73205i) q^{78} +(-1.51831 - 2.62979i) q^{79} +(0.895175 + 1.55049i) q^{80} +(-8.77592 - 1.99582i) q^{81} +(-6.99911 - 4.04094i) q^{82} +(7.00270 - 12.1290i) q^{83} +(-3.28052 - 5.68202i) q^{85} -6.96254i q^{86} +(-2.32330 - 11.1240i) q^{87} -2.40150 q^{88} +(-1.87432 + 3.24641i) q^{89} +(2.14977 + 4.92206i) q^{90} +(3.26178 + 1.88319i) q^{92} +(-1.64539 - 7.87817i) q^{93} +(4.44794 + 2.56802i) q^{94} +(-4.67784 - 2.70075i) q^{95} +(0.354107 + 1.69547i) q^{96} +(-4.77256 - 2.75544i) q^{97} +(-7.15953 - 0.803848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 36 q^{39} + 4 q^{43} + 12 q^{44} - 12 q^{46} + 60 q^{50} - 36 q^{51} + 48 q^{57} + 24 q^{58} - 24 q^{60} - 16 q^{64} - 84 q^{65} - 28 q^{67} + 12 q^{72} - 24 q^{78} - 4 q^{79} - 36 q^{81} - 12 q^{85} - 48 q^{92} + 12 q^{93} - 12 q^{95} - 72 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 36 * q^39 + 4 * q^43 + 12 * q^44 - 12 * q^46 + 60 * q^50 - 36 * q^51 + 48 * q^57 + 24 * q^58 - 24 * q^60 - 16 * q^64 - 84 * q^65 - 28 * q^67 + 12 * q^72 - 24 * q^78 - 4 * q^79 - 36 * q^81 - 12 * q^85 - 48 * q^92 + 12 * q^93 - 12 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

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