LMFDB - Embedded newform 882.2.l.a.509.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("882.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			509.7
Root			$1.69547 + 0.354107i$ of defining polynomial
Character	$\chi$	$=$	882.509
Dual form			882.2.l.a.227.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.541068 + 1.64537i) q^{3} -1.00000 q^{4} +(0.895175 + 1.55049i) q^{5} +(-1.64537 + 0.541068i) q^{6} -1.00000i q^{8} +(-2.41449 + 1.78052i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.541068 + 1.64537i) q^{3} -1.00000 q^{4} +(0.895175 + 1.55049i) q^{5} +(-1.64537 + 0.541068i) q^{6} -1.00000i q^{8} +(-2.41449 + 1.78052i) q^{9} +(-1.55049 + 0.895175i) q^{10} +(2.07976 + 1.20075i) q^{11} +(-0.541068 - 1.64537i) q^{12} +(4.23601 + 2.44566i) q^{13} +(-2.06678 + 2.31181i) q^{15} +1.00000 q^{16} +(1.83233 + 3.17369i) q^{17} +(-1.78052 - 2.41449i) q^{18} +(-2.61281 - 1.50851i) q^{19} +(-0.895175 - 1.55049i) q^{20} +(-1.20075 + 2.07976i) q^{22} +(-3.26178 + 1.88319i) q^{23} +(1.64537 - 0.541068i) q^{24} +(0.897324 - 1.55421i) q^{25} +(-2.44566 + 4.23601i) q^{26} +(-4.23601 - 3.00935i) q^{27} +(-5.68202 + 3.28052i) q^{29} +(-2.31181 - 2.06678i) q^{30} -4.64661i q^{31} +1.00000i q^{32} +(-0.850388 + 4.07167i) q^{33} +(-3.17369 + 1.83233i) q^{34} +(2.41449 - 1.78052i) q^{36} +(-4.68202 + 8.10950i) q^{37} +(1.50851 - 2.61281i) q^{38} +(-1.73205 + 8.29308i) q^{39} +(1.55049 - 0.895175i) q^{40} +(4.04094 - 6.99911i) q^{41} +(-3.48127 - 6.02973i) q^{43} +(-2.07976 - 1.20075i) q^{44} +(-4.92206 - 2.14977i) q^{45} +(-1.88319 - 3.26178i) q^{46} +5.13604 q^{47} +(0.541068 + 1.64537i) q^{48} +(1.55421 + 0.897324i) q^{50} +(-4.23048 + 4.73205i) q^{51} +(-4.23601 - 2.44566i) q^{52} +(3.00935 - 4.23601i) q^{54} +4.29953i q^{55} +(1.06834 - 5.11524i) q^{57} +(-3.28052 - 5.68202i) q^{58} +14.5900 q^{59} +(2.06678 - 2.31181i) q^{60} -11.3283i q^{61} +4.64661 q^{62} -1.00000 q^{64} +8.75718i q^{65} +(-4.07167 - 0.850388i) q^{66} +0.570231 q^{67} +(-1.83233 - 3.17369i) q^{68} +(-4.86340 - 4.34791i) q^{69} -5.96254i q^{71} +(1.78052 + 2.41449i) q^{72} +(-10.7226 + 6.19070i) q^{73} +(-8.10950 - 4.68202i) q^{74} +(3.04277 + 0.635497i) q^{75} +(2.61281 + 1.50851i) q^{76} +(-8.29308 - 1.73205i) q^{78} +3.03663 q^{79} +(0.895175 + 1.55049i) q^{80} +(2.65953 - 8.59808i) q^{81} +(6.99911 + 4.04094i) q^{82} +(7.00270 + 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} +(6.02973 - 3.48127i) q^{86} +(-8.47203 - 7.57405i) q^{87} +(1.20075 - 2.07976i) q^{88} +(-1.87432 + 3.24641i) q^{89} +(2.14977 - 4.92206i) q^{90} +(3.26178 - 1.88319i) q^{92} +(7.64539 - 2.51413i) q^{93} +5.13604i q^{94} -5.40150i q^{95} +(-1.64537 + 0.541068i) q^{96} +(-4.77256 + 2.75544i) q^{97} +(-7.15953 + 0.803848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 12 * q^9	$ 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 12 * q^9 + 12 * q^11 + 16 * q^16 + 12 * q^18 + 48 * q^23 - 8 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 + 60 * q^50 + 24 * q^51 + 48 * q^57 - 12 * q^58 - 16 * q^64 + 56 * q^67 - 12 * q^72 - 36 * q^74 - 24 * q^78 + 8 * q^79 - 12 * q^85 + 24 * q^86 - 48 * q^92 + 84 * q^93 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.541068	+	1.64537i	0.312386	+	0.949955i
$3$	0.541068	+	1.64537i	0.312386	+	0.949955i
$4$	−1.00000			−0.500000
$5$	0.895175	+	1.55049i	0.400334	+	0.693399i	0.993766	−	0.111485i	$-0.0355607\pi$
$5$	0.895175	+	1.55049i	0.400334	+	0.693399i	−0.593432	+	0.804884i	$0.702227\pi$
$6$	−1.64537	+	0.541068i	−0.671720	+	0.220890i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−2.41449	+	1.78052i	−0.804830	+	0.593505i
$10$	−1.55049	+	0.895175i	−0.490307	+	0.283079i
$11$	2.07976	+	1.20075i	0.627072	+	0.362040i	0.779617	−	0.626256i	$-0.215414\pi$
$11$	2.07976	+	1.20075i	0.627072	+	0.362040i	−0.152545	+	0.988297i	$0.548747\pi$
$12$	−0.541068	−	1.64537i	−0.156193	−	0.474978i
$13$	4.23601	+	2.44566i	1.17486	+	0.678305i	0.954820	−	0.297186i	$-0.0960482\pi$
$13$	4.23601	+	2.44566i	1.17486	+	0.678305i	0.220039	+	0.975491i	$0.429382\pi$
$14$		0			0
$15$	−2.06678	+	2.31181i	−0.533640	+	0.596908i
$16$	1.00000			0.250000
$17$	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	$0.686748\pi$
$18$	−1.78052	−	2.41449i	−0.419672	−	0.569101i
$19$	−2.61281	−	1.50851i	−0.599419	−	0.346075i	0.169394	−	0.985548i	$-0.445819\pi$
$19$	−2.61281	−	1.50851i	−0.599419	−	0.346075i	−0.768813	+	0.639474i	$0.779152\pi$
$20$	−0.895175	−	1.55049i	−0.200167	−	0.346700i
$21$		0			0
$22$	−1.20075	+	2.07976i	−0.256001	+	0.443407i
$23$	−3.26178	+	1.88319i	−0.680129	+	0.392673i	−0.799904	−	0.600128i	$-0.795116\pi$
$23$	−3.26178	+	1.88319i	−0.680129	+	0.392673i	0.119775	+	0.992801i	$0.461783\pi$
$24$	1.64537	−	0.541068i	0.335860	−	0.110445i
$25$	0.897324	−	1.55421i	0.179465	−	0.310842i
$26$	−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	−0.924080	−	0.382200i	$-0.875167\pi$
$29$	−5.68202	+	3.28052i	−1.05512	+	0.609176i	−0.131045	+	0.991376i	$0.541833\pi$
$30$	−2.31181	−	2.06678i	−0.422078	−	0.377340i
$31$		−	4.64661i		−	0.834556i	−0.908779	−	0.417278i	$-0.862984\pi$
$31$		−	4.64661i		−	0.834556i	0.908779	−	0.417278i	$-0.137016\pi$
$32$			1.00000i			0.176777i
$33$	−0.850388	+	4.07167i	−0.148034	+	0.708787i
$34$	−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	$0.887063\pi$
$38$	1.50851	−	2.61281i	0.244712	−	0.423853i
$39$	−1.73205	+	8.29308i	−0.277350	+	1.32796i
$40$	1.55049	−	0.895175i	0.245154	−	0.141540i
$41$	4.04094	−	6.99911i	0.631088	−	1.09308i	−0.356241	−	0.934394i	$-0.615942\pi$
$41$	4.04094	−	6.99911i	0.631088	−	1.09308i	0.987330	−	0.158683i	$-0.0507248\pi$
$42$		0			0
$43$	−3.48127	−	6.02973i	−0.530888	−	0.919526i	−0.999350	−	0.0360419i	$-0.988525\pi$
$43$	−3.48127	−	6.02973i	−0.530888	−	0.919526i	0.468462	−	0.883484i	$-0.344808\pi$
$44$	−2.07976	−	1.20075i	−0.313536	−	0.181020i
$45$	−4.92206	−	2.14977i	−0.733737	−	0.320468i
$46$	−1.88319	−	3.26178i	−0.277661	−	0.480924i
$47$	5.13604			0.749169			0.374584	−	0.927193i	$-0.377785\pi$
$47$	5.13604			0.749169			0.374584	+	0.927193i	$0.377785\pi$
$48$	0.541068	+	1.64537i	0.0780965	+	0.237489i
$49$		0			0
$50$	1.55421	+	0.897324i	0.219799	+	0.126901i
$51$	−4.23048	+	4.73205i	−0.592386	+	0.662620i
$52$	−4.23601	−	2.44566i	−0.587429	−	0.339152i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	3.00935	−	4.23601i	0.409521	−	0.576448i
$55$			4.29953i			0.579749i
$56$		0			0
$57$	1.06834	−	5.11524i	0.141506	−	0.677530i
$58$	−3.28052	−	5.68202i	−0.430753	−	0.746086i
$59$	14.5900			1.89946			0.949729	−	0.313073i	$-0.101359\pi$
$59$	14.5900			1.89946			0.949729	+	0.313073i	$0.101359\pi$
$60$	2.06678	−	2.31181i	0.266820	−	0.298454i
$61$		−	11.3283i		−	1.45044i	−0.688518	−	0.725219i	$-0.741738\pi$
$61$		−	11.3283i		−	1.45044i	0.688518	−	0.725219i	$-0.258262\pi$
$62$	4.64661			0.590120
$63$		0			0
$64$	−1.00000			−0.125000
$65$			8.75718i			1.08619i
$66$	−4.07167	−	0.850388i	−0.501188	−	0.104676i
$67$	0.570231			0.0696648			0.0348324	−	0.999393i	$-0.488910\pi$
$67$	0.570231			0.0696648			0.0348324	+	0.999393i	$0.488910\pi$
$68$	−1.83233	−	3.17369i	−0.222203	−	0.384867i
$69$	−4.86340	−	4.34791i	−0.585484	−	0.523427i
$70$		0			0
$71$		−	5.96254i		−	0.707623i	−0.935317	−	0.353811i	$-0.884885\pi$
$71$		−	5.96254i		−	0.707623i	0.935317	−	0.353811i	$-0.115115\pi$
$72$	1.78052	+	2.41449i	0.209836	+	0.284550i
$73$	−10.7226	+	6.19070i	−1.25499	+	0.724567i	−0.972096	−	0.234585i	$-0.924627\pi$
$73$	−10.7226	+	6.19070i	−1.25499	+	0.724567i	−0.282891	+	0.959152i	$0.591294\pi$
$74$	−8.10950	−	4.68202i	−0.942710	−	0.544274i
$75$	3.04277	+	0.635497i	0.351348	+	0.0733808i
$76$	2.61281	+	1.50851i	0.299710	+	0.173037i
$77$		0			0
$78$	−8.29308	−	1.73205i	−0.939007	−	0.196116i
$79$	3.03663			0.341647			0.170824	−	0.985302i	$-0.445357\pi$
$79$	3.03663			0.341647			0.170824	+	0.985302i	$0.445357\pi$
$80$	0.895175	+	1.55049i	0.100084	+	0.173350i
$81$	2.65953	−	8.59808i	0.295503	−	0.955342i
$82$	6.99911	+	4.04094i	0.772922	+	0.446247i
$83$	7.00270	+	12.1290i	0.768646	+	1.33133i	0.938297	+	0.345830i	$0.112403\pi$
$83$	7.00270	+	12.1290i	0.768646	+	1.33133i	−0.169651	+	0.985504i	$0.554264\pi$
$84$		0			0
$85$	−3.28052	+	5.68202i	−0.355822	+	0.616302i
$86$	6.02973	−	3.48127i	0.650203	−	0.375395i
$87$	−8.47203	−	7.57405i	−0.908296	−	0.812023i
$88$	1.20075	−	2.07976i	0.128001	−	0.221704i
$89$	−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
$93$	7.64539	−	2.51413i	0.792791	−	0.260703i
$94$			5.13604i			0.529742i
$95$		−	5.40150i		−	0.554183i
$96$	−1.64537	+	0.541068i	−0.167930	+	0.0552225i
$97$	−4.77256	+	2.75544i	−0.484580	+	0.279772i	−0.722323	−	0.691556i	$-0.756926\pi$
$97$	−4.77256	+	2.75544i	−0.484580	+	0.279772i	0.237743	+	0.971328i	$0.423592\pi$
$98$		0			0
$99$	−7.15953	+	0.803848i	−0.719560	+	0.0807897i
$100$	−0.897324	+	1.55421i	−0.0897324	+	0.155421i
$101$	0.125162	−	0.216787i	0.0124541	−	0.0215711i	−0.859731	−	0.510747i	$-0.829369\pi$
$101$	0.125162	−	0.216787i	0.0124541	−	0.0215711i	0.872185	+	0.489176i	$0.162702\pi$
$102$	−4.73205	−	4.23048i	−0.468543	−	0.418880i
$103$	0.145433	−	0.0839657i	0.0143299	−	0.00827339i	−0.492818	−	0.870132i	$-0.664033\pi$
$103$	0.145433	−	0.0839657i	0.0143299	−	0.00827339i	0.507148	+	0.861859i	$0.330700\pi$
$104$	2.44566	−	4.23601i	0.239817	−	0.415375i
$105$		0			0
$106$		0			0
$107$	−6.92024	−	3.99540i	−0.669004	−	0.386250i	0.126695	−	0.991942i	$-0.459563\pi$
$107$	−6.92024	−	3.99540i	−0.669004	−	0.386250i	−0.795699	+	0.605692i	$0.792896\pi$
$108$	4.23601	+	3.00935i	0.407611	+	0.289575i
$109$	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	$0.471170\pi$
$110$	−4.29953			−0.409944
$111$	−15.8764	−	3.31587i	−1.50692	−	0.314728i
$112$		0			0
$113$	−1.00418	−	0.579764i	−0.0944653	−	0.0545396i	0.452023	−	0.892006i	$-0.350702\pi$
$113$	−1.00418	−	0.579764i	−0.0944653	−	0.0545396i	−0.546488	+	0.837467i	$0.684036\pi$
$114$	5.11524	+	1.06834i	0.479086	+	0.100060i
$115$	−5.83973	−	3.37157i	−0.544558	−	0.314401i
$116$	5.68202	−	3.28052i	0.527562	−	0.304588i
$117$	−14.5824	+	1.63726i	−1.34814	+	0.151365i
$118$			14.5900i			1.34312i
$119$		0			0
$120$	2.31181	+	2.06678i	0.211039	+	0.188670i
$121$	−2.61639	−	4.53172i	−0.237854	−	0.411974i
$122$	11.3283			1.02561
$123$	13.7026	+	2.86185i	1.23552	+	0.258044i
$124$			4.64661i			0.417278i
$125$	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	$0.480194\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	8.03754	−	8.99047i	0.707666	−	0.791567i
$130$	−8.75718			−0.768056
$131$	5.24589	+	9.08614i	0.458335	+	0.793860i	0.998873	−	0.0474597i	$-0.0151126\pi$
$131$	5.24589	+	9.08614i	0.458335	+	0.793860i	−0.540538	+	0.841320i	$0.681779\pi$
$132$	0.850388	−	4.07167i	0.0740168	−	0.354393i
$133$		0			0
$134$			0.570231i			0.0492604i
$135$	0.873992	−	9.26178i	0.0752213	−	0.797127i
$136$	3.17369	−	1.83233i	0.272142	−	0.157121i
$137$	4.08812	+	2.36028i	0.349272	+	0.201652i	0.664365	−	0.747409i	$-0.268702\pi$
$137$	4.08812	+	2.36028i	0.349272	+	0.201652i	−0.315093	+	0.949061i	$0.602036\pi$
$138$	4.34791	−	4.86340i	0.370119	−	0.414000i
$139$	2.04707	+	1.18187i	0.173630	+	0.100245i	0.584296	−	0.811540i	$-0.301371\pi$
$139$	2.04707	+	1.18187i	0.173630	+	0.100245i	−0.410666	+	0.911786i	$0.634704\pi$
$140$		0			0
$141$	2.77895	+	8.45070i	0.234030	+	0.711677i
$142$	5.96254			0.500365
$143$	5.87327	+	10.1728i	0.491148	+	0.850692i
$144$	−2.41449	+	1.78052i	−0.201208	+	0.148376i
$145$	−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
$149$	15.0377	−	8.68202i	1.23194	−	0.711259i	0.264503	−	0.964385i	$-0.414792\pi$
$149$	15.0377	−	8.68202i	1.23194	−	0.711259i	0.967433	+	0.253126i	$0.0814587\pi$
$150$	−0.635497	+	3.04277i	−0.0518881	+	0.248441i
$151$	5.61639	−	9.72787i	0.457055	−	0.791643i	−0.541749	−	0.840541i	$-0.682238\pi$
$151$	5.61639	−	9.72787i	0.457055	−	0.791643i	0.998804	+	0.0488977i	$0.0155708\pi$
$152$	−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
$156$	1.73205	−	8.29308i	0.138675	−	0.663978i
$157$			13.8431i			1.10480i	0.833580	+	0.552399i	$0.186287\pi$
$157$			13.8431i			1.10480i	−0.833580	+	0.552399i	$0.813713\pi$
$158$			3.03663i			0.241581i
$159$		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	$0.112354\pi$
$164$	−4.04094	+	6.99911i	−0.315544	+	0.546539i
$165$	−7.07432	+	2.32634i	−0.550735	+	0.181105i
$166$	−12.1290	+	7.00270i	−0.941395	+	0.543515i
$167$	6.20756	−	10.7518i	0.480355	−	0.832000i	−0.519391	−	0.854537i	$-0.673841\pi$
$167$	6.20756	−	10.7518i	0.480355	−	0.832000i	0.999746	+	0.0225370i	$0.00717435\pi$
$168$		0			0
$169$	5.46254	+	9.46139i	0.420195	+	0.727799i
$170$	−5.68202	−	3.28052i	−0.435791	−	0.251604i
$171$	8.99452	−	1.00987i	0.687828	−	0.0772270i
$172$	3.48127	+	6.02973i	0.265444	+	0.459763i
$173$	17.4182			1.32428			0.662139	−	0.749381i	$-0.269649\pi$
$173$	17.4182			1.32428			0.662139	+	0.749381i	$0.269649\pi$
$174$	7.57405	−	8.47203i	0.574187	−	0.642263i
$175$		0			0
$176$	2.07976	+	1.20075i	0.156768	+	0.0905101i
$177$	7.89419	+	24.0060i	0.593364	+	1.80440i
$178$	−3.24641	−	1.87432i	−0.243329	−	0.140486i
$179$	−11.3640	+	6.56103i	−0.849388	+	0.490395i	−0.860444	−	0.509544i	$-0.829814\pi$
$179$	−11.3640	+	6.56103i	−0.849388	+	0.490395i	0.0110562	+	0.999939i	$0.496481\pi$
$180$	4.92206	+	2.14977i	0.366869	+	0.160234i
$181$			13.3577i			0.992873i	0.868073	+	0.496437i	$0.165359\pi$
$181$			13.3577i			0.992873i	−0.868073	+	0.496437i	$0.834641\pi$
$182$		0			0
$183$	18.6392	−	6.12937i	1.37785	−	0.453096i
$184$	1.88319	+	3.26178i	0.138831	+	0.240462i
$185$	−16.7649			−1.23258
$186$	2.51413	+	7.64539i	0.184345	+	0.560588i
$187$			8.80071i			0.643572i
$188$	−5.13604			−0.374584
$189$		0			0
$190$	5.40150			0.391866
$191$		−	9.25333i		−	0.669547i	−0.942299	−	0.334774i	$-0.891340\pi$
$191$		−	9.25333i		−	0.669547i	0.942299	−	0.334774i	$-0.108660\pi$
$192$	−0.541068	−	1.64537i	−0.0390482	−	0.118744i
$193$	−24.5602			−1.76788			−0.883941	−	0.467599i	$-0.845119\pi$
$193$	−24.5602			−1.76788			−0.883941	+	0.467599i	$0.845119\pi$
$194$	−2.75544	−	4.77256i	−0.197829	−	0.342650i
$195$	−14.4088	+	4.73823i	−1.03184	+	0.339312i
$196$		0			0
$197$			12.4861i			0.889598i	0.895630	+	0.444799i	$0.146725\pi$
$197$			12.4861i			0.889598i	−0.895630	+	0.444799i	$0.853275\pi$
$198$	−0.803848	−	7.15953i	−0.0571270	−	0.508805i
$199$	0.155144	−	0.0895727i	0.0109979	−	0.00634964i	−0.494491	−	0.869183i	$-0.664645\pi$
$199$	0.155144	−	0.0895727i	0.0109979	−	0.00634964i	0.505489	+	0.862833i	$0.331312\pi$
$200$	−1.55421	−	0.897324i	−0.109899	−	0.0634504i
$201$	0.308534	+	0.938241i	0.0217623	+	0.0661784i
$202$	0.216787	+	0.125162i	0.0152531	+	0.00880637i
$203$		0			0
$204$	4.23048	−	4.73205i	0.296193	−	0.331310i
$205$	14.4694			1.01059
$206$	0.0839657	+	0.145433i	0.00585017	+	0.0101328i
$207$	4.52249	−	10.3546i	0.314335	−	0.719695i
$208$	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	−0.479192	−	0.877710i	$-0.659070\pi$
$211$	7.56103	−	13.0961i	0.520523	−	0.901572i	0.999715	−	0.0238622i	$-0.00759629\pi$
$212$		0			0
$213$	9.81058	−	3.22614i	0.672210	−	0.221051i
$214$	3.99540	−	6.92024i	0.273120	−	0.473058i
$215$	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
$219$	−15.9877	−	14.2931i	−1.08035	−	0.965837i
$220$		−	4.29953i		−	0.289874i
$221$			17.9251i			1.20577i
$222$	3.31587	−	15.8764i	0.222547	−	1.06556i
$223$	7.27049	−	4.19762i	0.486868	−	0.281093i	−0.236406	−	0.971654i	$-0.575970\pi$
$223$	7.27049	−	4.19762i	0.486868	−	0.281093i	0.723274	+	0.690561i	$0.242636\pi$
$224$		0			0
$225$	0.600717	+	5.35033i	0.0400478	+	0.356688i
$226$	0.579764	−	1.00418i	0.0385653	−	0.0667971i
$227$	−1.21261	+	2.10030i	−0.0804836	+	0.139402i	−0.903458	−	0.428677i	$-0.858980\pi$
$227$	−1.21261	+	2.10030i	−0.0804836	+	0.139402i	0.822974	+	0.568079i	$0.192313\pi$
$228$	−1.06834	+	5.11524i	−0.0707528	+	0.338765i
$229$	1.74915	−	1.00987i	0.115587	−	0.0667344i	−0.441092	−	0.897462i	$-0.645409\pi$
$229$	1.74915	−	1.00987i	0.115587	−	0.0667344i	0.556679	+	0.830728i	$0.312075\pi$
$230$	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	0.815554	−	0.578681i	$-0.196432\pi$
$233$	11.0236	+	6.36446i	0.722178	+	0.416950i	−0.0933759	+	0.995631i	$0.529766\pi$
$234$	−1.63726	−	14.5824i	−0.107031	−	0.953278i
$235$	4.59766	+	7.96337i	0.299918	+	0.519473i
$236$	−14.5900			−0.949729
$237$	1.64302	+	4.99637i	0.106726	+	0.324549i
$238$		0			0
$239$	15.1117	+	8.72474i	0.977494	+	0.564356i	0.901513	−	0.432753i	$-0.142458\pi$
$239$	15.1117	+	8.72474i	0.977494	+	0.564356i	0.0759814	+	0.997109i	$0.475791\pi$
$240$	−2.06678	+	2.31181i	−0.133410	+	0.149227i
$241$	9.90142	+	5.71659i	0.637807	+	0.368238i	0.783769	−	0.621052i	$-0.213295\pi$
$241$	9.90142	+	5.71659i	0.637807	+	0.368238i	−0.145963	+	0.989290i	$0.546628\pi$
$242$	4.53172	−	2.61639i	0.291310	−	0.168188i
$243$	15.5860	−	0.276237i	0.999843	−	0.0177206i
$244$			11.3283i			0.725219i
$245$		0			0
$246$	−2.86185	+	13.7026i	−0.182465	+	0.873643i
$247$	−7.37859	−	12.7801i	−0.469489	−	0.813178i
$248$	−4.64661			−0.295060
$249$	−16.1678	+	18.0847i	−1.02459	+	1.14607i
$250$			12.1648i			0.769369i
$251$	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
$254$			1.40150i			0.0879382i
$255$	−11.1240	−	2.32330i	−0.696613	−	0.145491i
$256$	1.00000			0.0625000
$257$	−1.74837	−	3.02826i	−0.109060	−	0.188898i	0.806330	−	0.591466i	$-0.201451\pi$
$257$	−1.74837	−	3.02826i	−0.109060	−	0.188898i	−0.915390	+	0.402569i	$0.868117\pi$
$258$	8.99047	+	8.03754i	0.559722	+	0.500396i
$259$		0			0
$260$		−	8.75718i		−	0.543097i
$261$	7.87817	−	18.0377i	0.487647	−	1.11651i
$262$	−9.08614	+	5.24589i	−0.561344	+	0.324092i
$263$	8.35150	+	4.82174i	0.514976	+	0.297321i	0.734877	−	0.678201i	$-0.237240\pi$
$263$	8.35150	+	4.82174i	0.514976	+	0.297321i	−0.219901	+	0.975522i	$0.570573\pi$
$264$	4.07167	+	0.850388i	0.250594	+	0.0523378i
$265$		0			0
$266$		0			0
$267$	−6.35568	−	1.32741i	−0.388961	−	0.0812365i
$268$	−0.570231			−0.0348324
$269$	−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	$0.900904\pi$
$270$	9.26178	+	0.873992i	0.563654	+	0.0531895i
$271$	−17.8672	−	10.3156i	−1.08535	−	0.626629i	−0.153017	−	0.988224i	$-0.548899\pi$
$271$	−17.8672	−	10.3156i	−1.08535	−	0.626629i	−0.932335	+	0.361595i	$0.882232\pi$
$272$	1.83233	+	3.17369i	0.111101	+	0.192433i
$273$		0			0
$274$	−2.36028	+	4.08812i	−0.142590	+	0.246973i
$275$	3.73244	−	2.15493i	0.225075	−	0.129947i
$276$	4.86340	+	4.34791i	0.292742	+	0.261713i
$277$	7.75718	−	13.4358i	0.466084	−	0.807281i	−0.533166	−	0.846011i	$-0.678998\pi$
$277$	7.75718	−	13.4358i	0.466084	−	0.807281i	0.999250	+	0.0387296i	$0.0123311\pi$
$278$	−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	−0.105783	−	0.994389i	$-0.533735\pi$
$281$	11.7759	−	6.79883i	0.702492	−	0.405584i	0.808275	+	0.588805i	$0.200401\pi$
$282$	−8.45070	+	2.77895i	−0.503232	+	0.165484i
$283$		−	5.44783i		−	0.323840i	−0.986804	−	0.161920i	$-0.948231\pi$
$283$		−	5.44783i		−	0.323840i	0.986804	−	0.161920i	$-0.0517687\pi$
$284$			5.96254i			0.353811i
$285$	8.88748	−	2.92258i	0.526449	−	0.173119i
$286$	−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
$290$	5.87327	−	10.1728i	0.344890	−	0.597368i
$291$	−7.11600	−	6.36175i	−0.417147	−	0.372932i
$292$	10.7226	−	6.19070i	0.627493	−	0.362284i
$293$	−12.2311	+	21.1849i	−0.714550	+	1.23764i	0.248583	+	0.968610i	$0.420035\pi$
$293$	−12.2311	+	21.1849i	−0.714550	+	1.23764i	−0.963133	+	0.269026i	$0.913298\pi$
$294$		0			0
$295$	13.0606	+	22.6216i	0.760418	+	1.31708i
$296$	8.10950	+	4.68202i	0.471355	+	0.272137i
$297$	−5.19642	−	11.3451i	−0.301527	−	0.658312i
$298$	8.68202	+	15.0377i	0.502936	+	0.871111i
$299$	−18.4226			−1.06541
$300$	−3.04277	−	0.635497i	−0.175674	−	0.0366904i
$301$		0			0
$302$	9.72787	+	5.61639i	0.559776	+	0.323187i
$303$	0.424416	+	0.0886415i	0.0243821	+	0.00509232i
$304$	−2.61281	−	1.50851i	−0.149855	−	0.0865187i
$305$	17.5644	−	10.1408i	1.00573	−	0.580660i
$306$	4.40035	−	10.0750i	0.251552	−	0.575947i
$307$		−	31.2223i		−	1.78195i	−0.454053	−	0.890975i	$-0.650022\pi$
$307$		−	31.2223i		−	1.78195i	0.454053	−	0.890975i	$-0.349978\pi$
$308$		0			0
$309$	0.216844	+	0.193860i	0.0123358	+	0.0110283i
$310$	4.15953	+	7.20451i	0.236245	+	0.409189i
$311$	−10.9100			−0.618651			−0.309325	−	0.950956i	$-0.600103\pi$
$311$	−10.9100			−0.618651			−0.309325	+	0.950956i	$0.600103\pi$
$312$	8.29308	+	1.73205i	0.469503	+	0.0980581i
$313$		−	3.42405i		−	0.193539i	−0.995307	−	0.0967694i	$-0.969149\pi$
$313$		−	3.42405i		−	0.193539i	0.995307	−	0.0967694i	$-0.0308509\pi$
$314$	−13.8431			−0.781210
$315$		0			0
$316$	−3.03663			−0.170824
$317$			19.0471i			1.06979i	0.844917	+	0.534897i	$0.179650\pi$
$317$			19.0471i			1.06979i	−0.844917	+	0.534897i	$0.820350\pi$
$318$		0			0
$319$	−15.7563			−0.882186
$320$	−0.895175	−	1.55049i	−0.0500418	−	0.0866749i
$321$	2.82960	−	13.5481i	0.157933	−	0.756183i
$322$		0			0
$323$		−	11.0563i		−	0.615191i
$324$	−2.65953	+	8.59808i	−0.147752	+	0.477671i
$325$	7.60215	−	4.38910i	0.421692	−	0.243464i
$326$	3.75489	+	2.16789i	0.207964	+	0.120068i
$327$	−21.8797	+	24.4738i	−1.20995	+	1.35340i
$328$	−6.99911	−	4.04094i	−0.386461	−	0.223123i
$329$		0			0
$330$	−2.32634	−	7.07432i	−0.128061	−	0.389429i
$331$	0.0732502			0.00402620			0.00201310	−	0.999998i	$-0.499359\pi$
$331$	0.0732502			0.00402620			0.00201310	+	0.999998i	$0.499359\pi$
$332$	−7.00270	−	12.1290i	−0.384323	−	0.665667i
$333$	−3.13439	−	27.9167i	−0.171764	−	1.52983i
$334$	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	−0.834016	−	0.551741i	$-0.813964\pi$
$337$	1.11639	−	1.93364i	0.0608136	−	0.105332i	0.894829	+	0.446408i	$0.147297\pi$
$338$	−9.46139	+	5.46254i	−0.514632	+	0.297123i
$339$	0.410596	−	1.96594i	0.0223005	−	0.106775i
$340$	3.28052	−	5.68202i	0.177911	−	0.308151i
$341$	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
$345$	2.38779	−	11.4328i	0.128554	−	0.615520i
$346$			17.4182i			0.936406i
$347$		−	31.8409i		−	1.70931i	−0.519195	−	0.854656i	$-0.673768\pi$
$347$		−	31.8409i		−	1.70931i	0.519195	−	0.854656i	$-0.326232\pi$
$348$	8.47203	+	7.57405i	0.454148	+	0.406012i
$349$	12.7613	−	7.36772i	0.683095	−	0.394385i	−0.117925	−	0.993022i	$-0.537624\pi$
$349$	12.7613	−	7.36772i	0.683095	−	0.394385i	0.801020	+	0.598637i	$0.204291\pi$
$350$		0			0
$351$	−10.5839	−	23.1075i	−0.564929	−	1.23339i
$352$	−1.20075	+	2.07976i	−0.0640003	+	0.110852i
$353$	1.07979	−	1.87025i	0.0574713	−	0.0995431i	−0.835858	−	0.548945i	$-0.815030\pi$
$353$	1.07979	−	1.87025i	0.0574713	−	0.0995431i	0.893330	+	0.449402i	$0.148363\pi$
$354$	−24.0060	+	7.89419i	−1.27590	+	0.419572i
$355$	9.24484	−	5.33751i	0.490665	−	0.283286i
$356$	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	−0.492139	−	0.870517i	$-0.663785\pi$
$359$	−28.2712	−	16.3224i	−1.49210	−	0.861463i	−0.999959	+	0.00905364i	$0.997118\pi$
$360$	−2.14977	+	4.92206i	−0.113303	+	0.259415i
$361$	−4.94882	−	8.57161i	−0.260464	−	0.451138i
$362$	−13.3577			−0.702067
$363$	6.04071	−	6.75690i	0.317055	−	0.354645i
$364$		0			0
$365$	−19.1972	−	11.0835i	−1.00483	−	0.580138i
$366$	6.12937	+	18.6392i	0.320388	+	0.974288i
$367$	25.7212	+	14.8501i	1.34264	+	0.775171i	0.987194	−	0.159527i	$-0.0509969\pi$
$367$	25.7212	+	14.8501i	1.34264	+	0.775171i	0.355442	+	0.934698i	$0.384330\pi$
$368$	−3.26178	+	1.88319i	−0.170032	+	0.0981682i
$369$	2.70522	+	24.0942i	0.140828	+	1.25430i
$370$		−	16.7649i		−	0.871566i
$371$		0			0
$372$	−7.64539	+	2.51413i	−0.396395	+	0.130352i
$373$	1.00836	+	1.74653i	0.0522109	+	0.0904320i	0.890950	−	0.454102i	$-0.150040\pi$
$373$	1.00836	+	1.74653i	0.0522109	+	0.0904320i	−0.838739	+	0.544534i	$0.816707\pi$
$374$	−8.80071			−0.455074
$375$	6.58198	+	20.0156i	0.339892	+	1.03360i
$376$		−	5.13604i		−	0.264871i
$377$	−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	$0.661059\pi$
$380$			5.40150i			0.277091i
$381$	0.758309	+	2.30599i	0.0388494	+	0.118140i
$382$	9.25333			0.473441
$383$	0.418256	+	0.724440i	0.0213719	+	0.0370172i	0.876514	−	0.481377i	$-0.159863\pi$
$383$	0.418256	+	0.724440i	0.0213719	+	0.0370172i	−0.855142	+	0.518394i	$0.826530\pi$
$384$	1.64537	−	0.541068i	0.0839650	−	0.0276113i
$385$		0			0
$386$		−	24.5602i		−	1.25008i
$387$	19.1415	+	8.36028i	0.973018	+	0.424977i
$388$	4.77256	−	2.75544i	0.242290	−	0.139886i
$389$	−21.4964	−	12.4109i	−1.08991	−	0.629260i	−0.156357	−	0.987701i	$-0.549975\pi$
$389$	−21.4964	−	12.4109i	−1.08991	−	0.629260i	−0.933552	+	0.358441i	$0.883308\pi$
$390$	−4.73823	−	14.4088i	−0.239930	−	0.729619i
$391$	−11.9533	−	6.90127i	−0.604507	−	0.349012i
$392$		0			0
$393$	−12.1117	+	13.5477i	−0.610954	+	0.683389i
$394$	−12.4861			−0.629041
$395$	2.71831	+	4.70825i	0.136773	+	0.236898i
$396$	7.15953	−	0.803848i	0.359780	−	0.0403949i
$397$	2.62744	+	1.51695i	0.131867	+	0.0761336i	0.564482	−	0.825445i	$-0.309076\pi$
$397$	2.62744	+	1.51695i	0.131867	+	0.0761336i	−0.432615	+	0.901579i	$0.642409\pi$
$398$	0.0895727	+	0.155144i	0.00448987	+	0.00777669i
$399$		0			0
$400$	0.897324	−	1.55421i	0.0448662	−	0.0777105i
$401$	−11.3251	+	6.53854i	−0.565548	+	0.326519i	−0.755369	−	0.655300i	$-0.772542\pi$
$401$	−11.3251	+	6.53854i	−0.565548	+	0.326519i	0.189822	+	0.981819i	$0.439209\pi$
$402$	−0.938241	+	0.308534i	−0.0467952	+	0.0153883i
$403$	11.3640	−	19.6831i	0.566083	−	0.980485i
$404$	−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
$408$	4.73205	+	4.23048i	0.234271	+	0.209440i
$409$			5.56709i			0.275275i	0.990483	+	0.137637i	$0.0439508\pi$
$409$			5.56709i			0.275275i	−0.990483	+	0.137637i	$0.956049\pi$
$410$			14.4694i			0.714592i
$411$	−1.67158	+	8.00355i	−0.0824530	+	0.394786i
$412$	−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
$416$	−2.44566	+	4.23601i	−0.119908	+	0.207688i
$417$	−0.837019	+	4.00766i	−0.0409890	+	0.196256i
$418$	6.27467	−	3.62268i	0.306904	−	0.177191i
$419$	−8.19938	+	14.2017i	−0.400566	+	0.693800i	−0.993794	−	0.111234i	$-0.964520\pi$
$419$	−8.19938	+	14.2017i	−0.400566	+	0.693800i	0.593228	+	0.805034i	$0.297853\pi$
$420$		0			0
$421$	−7.72892	−	13.3869i	−0.376684	−	0.652437i	0.613893	−	0.789389i	$-0.289603\pi$
$421$	−7.72892	−	13.3869i	−0.376684	−	0.652437i	−0.990578	+	0.136952i	$0.956269\pi$
$422$	13.0961	+	7.56103i	0.637508	+	0.368065i
$423$	−12.4009	+	9.14481i	−0.602954	+	0.444636i
$424$		0			0
$425$	6.57678			0.319021
$426$	3.22614	+	9.81058i	0.156307	+	0.475324i
$427$		0			0
$428$	6.92024	+	3.99540i	0.334502	+	0.193125i
$429$	−13.5602	+	15.1679i	−0.654692	+	0.732313i
$430$	10.7953	+	6.23269i	0.520597	+	0.300567i
$431$	−21.6737	+	12.5133i	−1.04398	+	0.602744i	−0.920959	−	0.389660i	$-0.872593\pi$
$431$	−21.6737	+	12.5133i	−1.04398	+	0.602744i	−0.123024	+	0.992404i	$0.539259\pi$
$432$	−4.23601	−	3.00935i	−0.203805	−	0.144787i
$433$		−	2.25168i		−	0.108209i	−0.998535	−	0.0541044i	$-0.982770\pi$
$433$		−	2.25168i		−	0.108209i	0.998535	−	0.0541044i	$-0.0172304\pi$
$434$		0			0
$435$	4.15953	−	19.9159i	0.199434	−	0.954893i
$436$	−9.47667	−	16.4141i	−0.453850	−	0.786091i
$437$	11.3632			0.543576
$438$	14.2931	−	15.9877i	0.682950	−	0.763920i
$439$		−	18.7400i		−	0.894412i	−0.894431	−	0.447206i	$-0.852419\pi$
$439$		−	18.7400i		−	0.894412i	0.894431	−	0.447206i	$-0.147581\pi$
$440$	4.29953			0.204972
$441$		0			0
$442$	−17.9251			−0.852609
$443$		−	1.20451i		−	0.0572281i	−0.999591	−	0.0286141i	$-0.990891\pi$
$443$		−	1.20451i		−	0.0572281i	0.999591	−	0.0286141i	$-0.00910938\pi$
$444$	15.8764	+	3.31587i	0.753462	+	0.157364i
$445$	−6.71136			−0.318149
$446$	4.19762	+	7.27049i	0.198763	+	0.344268i
$447$	22.4216	+	20.0450i	1.06050	+	0.948097i
$448$		0			0
$449$			26.8022i			1.26487i	0.774612	+	0.632436i	$0.217945\pi$
$449$			26.8022i			1.26487i	−0.774612	+	0.632436i	$0.782055\pi$
$450$	−5.35033	+	0.600717i	−0.252217	+	0.0283181i
$451$	16.8084	−	9.70433i	0.791476	−	0.456959i
$452$	1.00418	+	0.579764i	0.0472327	+	0.0272698i
$453$	19.0448	+	3.97760i	0.894803	+	0.186884i
$454$	−2.10030	−	1.21261i	−0.0985719	−	0.0569105i
$455$		0			0
$456$	−5.11524	−	1.06834i	−0.239543	−	0.0500298i
$457$	13.8488			0.647821			0.323911	−	0.946088i	$-0.395002\pi$
$457$	13.8488			0.647821			0.323911	+	0.946088i	$0.395002\pi$
$458$	1.00987	+	1.74915i	0.0471883	+	0.0817326i
$459$	1.78897	−	18.9579i	0.0835022	−	0.884881i
$460$	5.83973	+	3.37157i	0.272279	+	0.157200i
$461$	−2.40241	−	4.16110i	−0.111892	−	0.193802i	0.804641	−	0.593761i	$-0.202358\pi$
$461$	−2.40241	−	4.16110i	−0.111892	−	0.193802i	−0.916533	+	0.399959i	$0.869024\pi$
$462$		0			0
$463$	10.5194	−	18.2201i	0.488877	−	0.846760i	−0.511041	−	0.859556i	$-0.670740\pi$
$463$	10.5194	−	18.2201i	0.488877	−	0.846760i	0.999918	+	0.0127960i	$0.00407321\pi$
$464$	−5.68202	+	3.28052i	−0.263781	+	0.152294i
$465$	10.7421	+	9.60351i	0.498153	+	0.445352i
$466$	−6.36446	+	11.0236i	−0.294828	+	0.510657i
$467$	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
$471$	−22.7770	+	7.49005i	−1.04951	+	0.345123i
$472$		−	14.5900i		−	0.671560i
$473$		−	16.7206i		−	0.768812i
$474$	−4.99637	+	1.64302i	−0.229491	+	0.0754665i
$475$	−4.68907	+	2.70724i	−0.215149	+	0.124217i
$476$		0			0
$477$		0			0
$478$	−8.72474	+	15.1117i	−0.399060	+	0.691193i
$479$	−13.4781	+	23.3447i	−0.615828	+	1.06665i	0.374411	+	0.927263i	$0.377845\pi$
$479$	−13.4781	+	23.3447i	−0.615828	+	1.06665i	−0.990239	+	0.139382i	$0.955488\pi$
$480$	−2.31181	−	2.06678i	−0.105519	−	0.0943351i
$481$	−39.6662	+	22.9013i	−1.80862	+	1.04421i
$482$	−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
$486$	0.276237	+	15.5860i	0.0125304	+	0.706996i
$487$	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	$0.733425\pi$
$488$	−11.3283			−0.512807
$489$	7.35116	+	1.53533i	0.332431	+	0.0694299i
$490$		0			0
$491$	−33.7430	−	19.4815i	−1.52280	−	0.879188i	−0.999637	−	0.0269544i	$-0.991419\pi$
$491$	−33.7430	−	19.4815i	−1.52280	−	0.879188i	−0.523162	−	0.852234i	$-0.675248\pi$
$492$	−13.7026	−	2.86185i	−0.617759	−	0.129022i
$493$	−20.8227	−	12.0220i	−0.937807	−	0.541443i
$494$	12.7801	−	7.37859i	0.575004	−	0.331979i
$495$	−7.65538	−	10.3812i	−0.344084	−	0.466599i
$496$		−	4.64661i		−	0.208639i
$497$		0			0
$498$	−18.0847	−	16.1678i	−0.810393	−	0.724497i
$499$	−13.0048	−	22.5250i	−0.582176	−	1.00836i	−0.995221	−	0.0976483i	$-0.968868\pi$
$499$	−13.0048	−	22.5250i	−0.582176	−	1.00836i	0.413045	−	0.910711i	$-0.364465\pi$
$500$	−12.1648			−0.544026
$501$	21.0494	+	4.39628i	0.940419	+	0.196411i
$502$			27.3560i			1.22096i
$503$	−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
$506$		−	9.04499i		−	0.402099i
$507$	−12.6119	+	14.1072i	−0.560114	+	0.626521i
$508$	−1.40150			−0.0621817
$509$	−0.469435	−	0.813086i	−0.0208074	−	0.0360394i	0.855434	−	0.517911i	$-0.173290\pi$
$509$	−0.469435	−	0.813086i	−0.0208074	−	0.0360394i	−0.876242	+	0.481872i	$0.839957\pi$
$510$	2.32330	−	11.1240i	0.102878	−	0.492580i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	6.52826	+	14.2529i	0.288230	+	0.629281i
$514$	3.02826	−	1.74837i	0.133571	−	0.0771172i
$515$	0.260376	+	0.150328i	0.0114735	+	0.00662424i
$516$	−8.03754	+	8.99047i	−0.353833	+	0.395784i
$517$	10.6818	+	6.16711i	0.469783	+	0.271229i
$518$		0			0
$519$	9.42442	+	28.6593i	0.413686	+	1.25801i
$520$	8.75718			0.384028
$521$	−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	$-0.499591\pi$
$522$	18.0377	+	7.87817i	0.789489	+	0.344818i
$523$	21.0697	+	12.1646i	0.921315	+	0.531922i	0.884054	−	0.467384i	$-0.154803\pi$
$523$	21.0697	+	12.1646i	0.921315	+	0.531922i	0.0372609	+	0.999306i	$0.488137\pi$
$524$	−5.24589	−	9.08614i	−0.229168	−	0.396930i
$525$		0			0
$526$	−4.82174	+	8.35150i	−0.210238	+	0.364143i
$527$	14.7469	−	8.51413i	0.642385	−	0.370881i
$528$	−0.850388	+	4.07167i	−0.0370084	+	0.177197i
$529$	−4.40718	+	7.63346i	−0.191616	+	0.331889i
$530$		0			0
$531$	−35.2274	+	25.9777i	−1.52874	+	1.12734i
$532$		0			0
$533$	34.2349	−	19.7655i	1.48288	−	0.856141i
$534$	1.32741	−	6.35568i	0.0574429	−	0.275037i
$535$		−	14.3063i		−	0.618516i
$536$		−	0.570231i		−	0.0246302i
$537$	−16.9441	−	15.1481i	−0.731190	−	0.653689i
$538$	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	$0.796058\pi$
$542$	10.3156	−	17.8672i	0.443093	−	0.767460i
$543$	−21.9784	+	7.22745i	−0.943185	+	0.310160i
$544$	−3.17369	+	1.83233i	−0.136071	+	0.0785606i
$545$	−16.9665	+	29.3869i	−0.726767	+	1.25880i
$546$		0			0
$547$	−12.2477	−	21.2136i	−0.523672	−	0.907026i	−0.999620	−	0.0275530i	$-0.991229\pi$
$547$	−12.2477	−	21.2136i	−0.523672	−	0.907026i	0.475949	−	0.879473i	$-0.342105\pi$
$548$	−4.08812	−	2.36028i	−0.174636	−	0.100826i
$549$	20.1702	+	27.3520i	0.860843	+	1.16736i
$550$	2.15493	+	3.73244i	0.0918864	+	0.159152i
$551$	19.7947			0.843283
$552$	−4.34791	+	4.86340i	−0.185059	+	0.207000i
$553$		0			0
$554$	13.4358	+	7.75718i	0.570834	+	0.329571i
$555$	−9.07096	−	27.5845i	−0.385041	−	1.17090i
$556$	−2.04707	−	1.18187i	−0.0868150	−	0.0501227i
$557$	−2.20344	+	1.27216i	−0.0933627	+	0.0539030i	−0.545954	−	0.837815i	$-0.683833\pi$
$557$	−2.20344	+	1.27216i	−0.0933627	+	0.0539030i	0.452592	+	0.891718i	$0.350499\pi$
$558$	−11.2192	+	8.27336i	−0.474946	+	0.350239i
$559$		−	34.0560i		−	1.44042i
$560$		0			0
$561$	−14.4804	+	4.76178i	−0.611364	+	0.201043i
$562$	6.79883	+	11.7759i	0.286791	+	0.496737i
$563$	−15.8141			−0.666487			−0.333243	−	0.942841i	$-0.608143\pi$
$563$	−15.8141			−0.666487			−0.333243	+	0.942841i	$0.608143\pi$
$564$	−2.77895	−	8.45070i	−0.117015	−	0.355838i
$565$		−	2.07596i		−	0.0873363i
$566$	5.44783			0.228990
$567$		0			0
$568$	−5.96254			−0.250182
$569$		−	6.38311i		−	0.267594i	−0.991009	−	0.133797i	$-0.957283\pi$
$569$		−	6.38311i		−	0.267594i	0.991009	−	0.133797i	$-0.0427170\pi$
$570$	2.92258	+	8.88748i	0.122414	+	0.372255i
$571$	−7.82375			−0.327414			−0.163707	−	0.986509i	$-0.552345\pi$
$571$	−7.82375			−0.327414			−0.163707	+	0.986509i	$0.552345\pi$
$572$	−5.87327	−	10.1728i	−0.245574	−	0.425346i
$573$	15.2252	−	5.00668i	0.636040	−	0.209157i
$574$		0			0
$575$			6.75933i			0.281884i
$576$	2.41449	−	1.78052i	0.100604	−	0.0741882i
$577$	12.4012	−	7.15986i	0.516270	−	0.298069i	−0.219137	−	0.975694i	$-0.570324\pi$
$577$	12.4012	−	7.15986i	0.516270	−	0.298069i	0.735407	+	0.677625i	$0.236991\pi$
$578$	3.09191	+	1.78512i	0.128607	+	0.0742510i
$579$	−13.2887	−	40.4106i	−0.552261	−	1.67941i
$580$	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
$585$	−15.5923	−	21.1441i	−0.644662	−	0.874202i
$586$	−21.1849	−	12.2311i	−0.875141	−	0.505263i
$587$	2.37575	+	4.11492i	0.0980577	+	0.169841i	0.910881	−	0.412670i	$-0.135404\pi$
$587$	2.37575	+	4.11492i	0.0980577	+	0.169841i	−0.812823	+	0.582511i	$0.802070\pi$
$588$		0			0
$589$	−7.00943	+	12.1407i	−0.288819	+	0.500249i
$590$	−22.6216	+	13.0606i	−0.931318	+	0.537697i
$591$	−20.5443	+	6.75583i	−0.845078	+	0.277898i
$592$	−4.68202	+	8.10950i	−0.192430	+	0.333298i
$593$	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
$597$	0.231324	+	0.206805i	0.00946746	+	0.00846398i
$598$		−	18.4226i		−	0.753357i
$599$			15.0655i			0.615561i	0.951457	+	0.307780i	$0.0995862\pi$
$599$			15.0655i			0.615561i	−0.951457	+	0.307780i	$0.900414\pi$
$600$	0.635497	−	3.04277i	0.0259440	−	0.124220i
$601$	19.8704	−	11.4722i	0.810530	−	0.467960i	−0.0366096	−	0.999330i	$-0.511656\pi$
$601$	19.8704	−	11.4722i	0.810530	−	0.467960i	0.847140	+	0.531370i	$0.178322\pi$
$602$		0			0
$603$	−1.37682	+	1.01531i	−0.0560683	+	0.0413464i
$604$	−5.61639	+	9.72787i	−0.228528	+	0.395821i
$605$	4.68425	−	8.11336i	0.190442	−	0.329855i
$606$	−0.0886415	+	0.424416i	−0.00360081	+	0.0172407i
$607$	21.2030	−	12.2416i	0.860605	−	0.496870i	−0.00360990	−	0.999993i	$-0.501149\pi$
$607$	21.2030	−	12.2416i	0.860605	−	0.496870i	0.864215	+	0.503123i	$0.167816\pi$
$608$	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
$612$	10.0750	+	4.40035i	0.407256	+	0.177874i
$613$	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	$0.827676\pi$
$614$	31.2223			1.26003
$615$	7.82892	+	23.8075i	0.315693	+	0.960011i
$616$		0			0
$617$	−11.7607	−	6.79005i	−0.473468	−	0.273357i	0.244222	−	0.969719i	$-0.421467\pi$
$617$	−11.7607	−	6.79005i	−0.473468	−	0.273357i	−0.717690	+	0.696362i	$0.754801\pi$
$618$	−0.193860	+	0.216844i	−0.00779818	+	0.00872274i
$619$	−30.7325	−	17.7434i	−1.23524	−	0.713169i	−0.267126	−	0.963662i	$-0.586074\pi$
$619$	−30.7325	−	17.7434i	−1.23524	−	0.713169i	−0.968118	+	0.250493i	$0.919407\pi$
$620$	−7.20451	+	4.15953i	−0.289340	+	0.167051i
$621$	19.4841	+	1.83863i	0.781872	+	0.0737817i
$622$		−	10.9100i		−	0.437452i
$623$		0			0
$624$	−1.73205	+	8.29308i	−0.0693375	+	0.331989i
$625$	6.40300	+	11.0903i	0.256120	+	0.443613i
$626$	3.42405			0.136853
$627$	8.36404	−	9.35568i	0.334028	−	0.373630i
$628$		−	13.8431i		−	0.552399i
$629$	−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	$0.319530\pi$
$632$		−	3.03663i		−	0.120790i
$633$	25.6390	+	5.35482i	1.01906	+	0.212835i
$634$	−19.0471			−0.756458
$635$	1.25459	+	2.17302i	0.0497869	+	0.0862335i
$636$		0			0
$637$		0			0
$638$		−	15.7563i		−	0.623800i
$639$	10.6164	+	14.3965i	0.419978	+	0.569516i
$640$	1.55049	−	0.895175i	0.0612884	−	0.0353849i
$641$	−0.932777	−	0.538539i	−0.0368425	−	0.0212710i	0.481466	−	0.876465i	$-0.340105\pi$
$641$	−0.932777	−	0.538539i	−0.0368425	−	0.0212710i	−0.518308	+	0.855194i	$0.673438\pi$
$642$	13.5481	+	2.82960i	0.534702	+	0.111675i
$643$	−33.3126	−	19.2330i	−1.31372	−	0.758477i	−0.331010	−	0.943627i	$-0.607389\pi$
$643$	−33.3126	−	19.2330i	−1.31372	−	0.758477i	−0.982710	+	0.185150i	$0.940723\pi$
$644$		0			0
$645$	21.1346	+	4.41407i	0.832175	+	0.173804i
$646$	11.0563			0.435006
$647$	−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	$0.889640\pi$
$648$	−8.59808	−	2.65953i	−0.337764	−	0.104476i
$649$	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
$653$	9.85934	−	5.69229i	0.385826	−	0.222757i	−0.294524	−	0.955644i	$-0.595161\pi$
$653$	9.85934	−	5.69229i	0.385826	−	0.222757i	0.680350	+	0.732887i	$0.261828\pi$
$654$	−24.4738	−	21.8797i	−0.957000	−	0.855564i
$655$	−9.39197	+	16.2674i	−0.366975	+	0.635619i
$656$	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	0.258723	−	0.965952i	$-0.416698\pi$
$659$	31.4373	−	18.1503i	1.22462	−	0.707036i	0.965900	+	0.258915i	$0.0833650\pi$
$660$	7.07432	−	2.32634i	0.275368	−	0.0905527i
$661$		−	36.0758i		−	1.40319i	−0.712578	−	0.701593i	$-0.752473\pi$
$661$		−	36.0758i		−	1.40319i	0.712578	−	0.701593i	$-0.247527\pi$
$662$			0.0732502i			0.00284695i
$663$	−29.4934	+	9.69869i	−1.14543	+	0.376666i
$664$	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
$668$	−6.20756	+	10.7518i	−0.240178	+	0.416000i
$669$	10.8405	+	9.69145i	0.419117	+	0.374693i
$670$	−0.884136	+	0.510456i	−0.0341572	+	0.0197206i
$671$	13.6025	−	23.5602i	0.525117	−	0.909530i
$672$		0			0
$673$	4.78512	+	8.28806i	0.184453	+	0.319481i	0.943392	−	0.331680i	$-0.107615\pi$
$673$	4.78512	+	8.28806i	0.184453	+	0.319481i	−0.758939	+	0.651161i	$0.774282\pi$
$674$	1.93364	+	1.11639i	0.0744811	+	0.0430017i
$675$	−8.47824	+	3.88329i	−0.326328	+	0.149468i
$676$	−5.46254	−	9.46139i	−0.210098	−	0.363900i
$677$	15.6282			0.600639			0.300320	−	0.953839i	$-0.402907\pi$
$677$	15.6282			0.600639			0.300320	+	0.953839i	$0.402907\pi$
$678$	1.96594	+	0.410596i	0.0755015	+	0.0157689i
$679$		0			0
$680$	5.68202	+	3.28052i	0.217896	+	0.125802i
$681$	−4.11188	−	0.858785i	−0.157567	−	0.0329087i
$682$	9.66385	+	5.57943i	0.370048	+	0.213647i
$683$	9.63996	−	5.56563i	0.368863	−	0.212963i	−0.304099	−	0.952640i	$-0.598355\pi$
$683$	9.63996	−	5.56563i	0.368863	−	0.212963i	0.672961	+	0.739678i	$0.265022\pi$
$684$	−8.99452	+	1.00987i	−0.343914	+	0.0386135i
$685$			8.45145i			0.322913i
$686$		0			0
$687$	2.60803	+	2.33159i	0.0995025	+	0.0889559i
$688$	−3.48127	−	6.02973i	−0.132722	−	0.229881i
$689$		0			0
$690$	11.4328	+	2.38779i	0.435238	+	0.0909017i
$691$		−	3.02419i		−	0.115046i	−0.998344	−	0.0575228i	$-0.981680\pi$
$691$		−	3.02419i		−	0.115046i	0.998344	−	0.0575228i	$-0.0183202\pi$
$692$	−17.4182			−0.662139
$693$		0			0
$694$	31.8409			1.20867
$695$			4.23194i			0.160527i
$696$	−7.57405	+	8.47203i	−0.287094	+	0.321131i
$697$	29.6174			1.12184
$698$	7.36772	+	12.7613i	0.278872	+	0.483021i
$699$	−4.50739	+	21.5815i	−0.170485	+	0.816286i
$700$		0			0
$701$			50.1486i			1.89409i	0.321103	+	0.947044i	$0.395946\pi$
$701$			50.1486i			1.89409i	−0.321103	+	0.947044i	$0.604054\pi$
$702$	23.1075	−	10.5839i	0.872137	−	0.399465i
$703$	24.4664	−	14.1257i	0.922769	−	0.532761i
$704$	−2.07976	−	1.20075i	−0.0783840	−	0.0452550i
$705$	−10.6151	+	11.8736i	−0.399786	+	0.447185i
$706$	1.87025	+	1.07979i	0.0703876	+	0.0406383i
$707$		0			0
$708$	−7.89419	−	24.0060i	−0.296682	−	0.902200i
$709$	−3.60770			−0.135490			−0.0677449	−	0.997703i	$-0.521580\pi$
$709$	−3.60770			−0.135490			−0.0677449	+	0.997703i	$0.521580\pi$
$710$	5.33751	+	9.24484i	0.200313	+	0.346953i
$711$	−7.33190	+	5.40676i	−0.274968	+	0.202769i
$712$	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
$716$	11.3640	−	6.56103i	0.424694	−	0.245197i
$717$	−6.17898	+	29.5850i	−0.230758	+	1.10487i
$718$	16.3224	−	28.2712i	0.609146	−	1.05507i
$719$	−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
$723$	−4.04856	+	19.3846i	−0.150568	+	0.720920i
$724$		−	13.3577i		−	0.496437i
$725$			11.7747i			0.437303i
$726$	6.75690	+	6.04071i	0.250772	+	0.224192i
$727$	−19.4757	+	11.2443i	−0.722315	+	0.417029i	−0.815604	−	0.578610i	$-0.803595\pi$
$727$	−19.4757	+	11.2443i	−0.722315	+	0.417029i	0.0932892	+	0.995639i	$0.470262\pi$
$728$		0			0
$729$	8.88761	+	25.4953i	0.329171	+	0.944270i
$730$	11.0835	−	19.1972i	0.410220	−	0.710521i
$731$	12.7577	−	22.0970i	0.471860	−	0.817285i
$732$	−18.6392	+	6.12937i	−0.688926	+	0.226548i
$733$	27.0065	−	15.5922i	0.997509	−	0.575912i	0.0899987	−	0.995942i	$-0.471314\pi$
$733$	27.0065	−	15.5922i	0.997509	−	0.575912i	0.907510	+	0.420030i	$0.137980\pi$
$734$	−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
$738$	−24.0942	+	2.70522i	−0.886921	+	0.0995805i
$739$	−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	$0.857279\pi$
$740$	16.7649			0.616290
$741$	17.0357	−	19.0554i	0.625821	−	0.700018i
$742$		0			0
$743$	−1.78246	−	1.02910i	−0.0653921	−	0.0377542i	0.466947	−	0.884285i	$-0.345354\pi$
$743$	−1.78246	−	1.02910i	−0.0653921	−	0.0377542i	−0.532340	+	0.846531i	$0.678687\pi$
$744$	−2.51413	−	7.64539i	−0.0921726	−	0.280294i
$745$	26.9227	+	15.5439i	0.986373	+	0.569483i
$746$	−1.74653	+	1.00836i	−0.0639450	+	0.0369187i
$747$	−38.5039	−	16.8170i	−1.40878	−	0.615302i
$748$		−	8.80071i		−	0.321786i
$749$		0			0
$750$	−20.0156	+	6.58198i	−0.730866	+	0.240340i
$751$	−11.9053	−	20.6205i	−0.434429	−	0.752454i	0.562820	−	0.826580i	$-0.309717\pi$
$751$	−11.9053	−	20.6205i	−0.434429	−	0.752454i	−0.997249	+	0.0741262i	$0.976383\pi$
$752$	5.13604			0.187292
$753$	14.8014	+	45.0107i	0.539395	+	1.64028i
$754$		−	32.0921i		−	1.16873i
$755$	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	$0.441387\pi$
$758$		−	18.8709i		−	0.685421i
$759$	−4.89395	−	14.8824i	−0.177639	−	0.540195i
$760$	−5.40150			−0.195933
$761$	−13.9368	−	24.1392i	−0.505207	−	0.875044i	−0.999982	−	0.00602283i	$-0.998083\pi$
$761$	−13.9368	−	24.1392i	−0.505207	−	0.875044i	0.494775	−	0.869021i	$-0.335250\pi$
$762$	−2.30599	+	0.758309i	−0.0835374	+	0.0274707i
$763$		0			0
$764$			9.25333i			0.334774i
$765$	−2.19615	−	19.5602i	−0.0794021	−	0.707200i
$766$	−0.724440	+	0.418256i	−0.0261751	+	0.0151122i
$767$	61.8035	+	35.6823i	2.23159	+	1.28841i
$768$	0.541068	+	1.64537i	0.0195241	+	0.0593722i
$769$	6.21166	+	3.58631i	0.223998	+	0.129326i	0.607800	−	0.794090i	$-0.292052\pi$
$769$	6.21166	+	3.58631i	0.223998	+	0.129326i	−0.383802	+	0.923415i	$0.625385\pi$
$770$		0			0
$771$	4.03663	−	4.51521i	0.145376	−	0.162611i
$772$	24.5602			0.883941
$773$	−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	$0.845595\pi$
$774$	−8.36028	+	19.1415i	−0.300504	+	0.688028i
$775$	−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
$779$	−21.1164	+	12.1916i	−0.756573	+	0.436808i
$780$	14.4088	−	4.73823i	0.515918	−	0.169656i
$781$	7.15953	−	12.4007i	0.256188	−	0.443731i
$782$	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
$786$	−13.5477	−	12.1117i	−0.483229	−	0.432010i
$787$			18.3552i			0.654292i	0.944974	+	0.327146i	$0.106087\pi$
$787$			18.3552i			0.654292i	−0.944974	+	0.327146i	$0.893913\pi$
$788$		−	12.4861i		−	0.444799i
$789$	−3.41482	+	16.3502i	−0.121571	+	0.582083i
$790$	−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
$794$	−1.51695	+	2.62744i	−0.0538346	+	0.0932442i
$795$		0			0
$796$	−0.155144	+	0.0895727i	−0.00549895	+	0.00317482i
$797$	−12.4226	+	21.5166i	−0.440031	+	0.762156i	−0.997691	−	0.0679130i	$-0.978366\pi$
$797$	−12.4226	+	21.5166i	−0.440031	+	0.762156i	0.557660	+	0.830069i	$0.311699\pi$
$798$		0			0
$799$	9.41094	+	16.3002i	0.332935	+	0.576660i
$800$	1.55421	+	0.897324i	0.0549497	+	0.0317252i
$801$	−1.25477	−	11.1757i	−0.0443350	−	0.394873i
$802$	−6.53854	−	11.3251i	−0.230884	−	0.399903i
$803$	−29.7340			−1.04929
$804$	−0.308534	−	0.938241i	−0.0108811	−	0.0330892i
$805$		0			0
$806$	19.6831	+	11.3640i	0.693307	+	0.400281i
$807$	7.97814	−	8.92402i	0.280844	−	0.314140i
$808$	−0.216787	−	0.125162i	−0.00762654	−	0.00440319i
$809$	−32.7237	+	18.8930i	−1.15050	+	0.664244i	−0.949010	−	0.315246i	$-0.897913\pi$
$809$	−32.7237	+	18.8930i	−1.15050	+	0.664244i	−0.201494	+	0.979490i	$0.564580\pi$
$810$	3.57322	+	15.7120i	0.125550	+	0.552062i
$811$		−	36.5165i		−	1.28227i	−0.767429	−	0.641134i	$-0.778464\pi$
$811$		−	36.5165i		−	1.28227i	0.767429	−	0.641134i	$-0.221536\pi$
$812$		0			0
$813$	7.30565	−	34.9795i	0.256220	−	1.22679i
$814$	−11.2439	−	19.4750i	−0.394098	−	0.682598i
$815$	7.76255			0.271910
$816$	−4.23048	+	4.73205i	−0.148097	+	0.165655i
$817$			21.0060i			0.734909i
$818$	−5.56709			−0.194649
$819$		0			0
$820$	−14.4694			−0.505293
$821$		−	6.37558i		−	0.222509i	−0.993792	−	0.111255i	$-0.964513\pi$
$821$		−	6.37558i		−	0.222509i	0.993792	−	0.111255i	$-0.0354869\pi$
$822$	−8.00355	−	1.67158i	−0.279156	−	0.0583031i
$823$	28.0587			0.978064			0.489032	−	0.872266i	$-0.337350\pi$
$823$	28.0587			0.978064			0.489032	+	0.872266i	$0.337350\pi$
$824$	−0.0839657	−	0.145433i	−0.00292508	−	0.00506639i
$825$	5.56516	+	4.97529i	0.193754	+	0.173217i
$826$		0			0
$827$		−	0.581579i		−	0.0202235i	−0.999949	−	0.0101117i	$-0.996781\pi$
$827$		−	0.581579i		−	0.0202235i	0.999949	−	0.0101117i	$-0.00321872\pi$
$828$	−4.52249	+	10.3546i	−0.157167	+	0.359847i
$829$	−44.9680	+	25.9623i	−1.56180	+	0.901708i	−0.564729	+	0.825276i	$0.691019\pi$
$829$	−44.9680	+	25.9623i	−1.56180	+	0.901708i	−0.997075	+	0.0764314i	$0.975647\pi$
$830$	−21.7152	−	12.5373i	−0.753746	−	0.435175i
$831$	26.3041	+	5.49374i	0.912479	+	0.190576i
$832$	−4.23601	−	2.44566i	−0.146857	−	0.0847881i
$833$		0			0
$834$	−4.00766	−	0.837019i	−0.138774	−	0.0289836i
$835$	22.2274			0.769211
$836$	3.62268	+	6.27467i	0.125293	+	0.217014i
$837$	−13.9833	+	19.6831i	−0.483333	+	0.680347i
$838$	−14.2017	−	8.19938i	−0.490591	−	0.283243i
$839$	3.33038	+	5.76838i	0.114977	+	0.199147i	0.917771	−	0.397111i	$-0.129987\pi$
$839$	3.33038	+	5.76838i	0.114977	+	0.199147i	−0.802793	+	0.596257i	$0.796654\pi$
$840$		0			0
$841$	7.02357	−	12.1652i	0.242192	−	0.419489i
$842$	13.3869	−	7.72892i	0.461342	−	0.266356i
$843$	17.5582	+	15.6971i	0.604735	+	0.540637i
$844$	−7.56103	+	13.0961i	−0.260261	+	0.450786i
$845$	−9.77985	+	16.9392i	−0.336437	+	0.582726i
$846$	−9.14481	−	12.4009i	−0.314405	−	0.426353i
$847$		0			0
$848$		0			0
$849$	8.96371	−	2.94765i	0.307634	−	0.101163i
$850$			6.57678i			0.225582i
$851$		−	35.2686i		−	1.20899i
$852$	−9.81058	+	3.22614i	−0.336105	+	0.110526i
$853$	19.2287	−	11.1017i	0.658378	−	0.380115i	−0.133281	−	0.991078i	$-0.542551\pi$
$853$	19.2287	−	11.1017i	0.658378	−	0.380115i	0.791659	+	0.610964i	$0.209218\pi$
$854$		0			0
$855$	9.61746	+	13.0419i	0.328910	+	0.446023i
$856$	−3.99540	+	6.92024i	−0.136560	+	0.236529i
$857$	7.64830	−	13.2472i	0.261261	−	0.452517i	−0.705316	−	0.708893i	$-0.749195\pi$
$857$	7.64830	−	13.2472i	0.261261	−	0.452517i	0.966577	+	0.256375i	$0.0825283\pi$
$858$	−15.1679	−	13.5602i	−0.517823	−	0.462937i
$859$	3.68620	−	2.12823i	0.125772	−	0.0726143i	−0.435794	−	0.900046i	$-0.643532\pi$
$859$	3.68620	−	2.12823i	0.125772	−	0.0726143i	0.561566	+	0.827432i	$0.310199\pi$
$860$	−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	0.806439	−	0.591317i	$-0.201392\pi$
$863$	20.4922	+	11.8312i	0.697562	+	0.402738i	−0.108876	+	0.994055i	$0.534725\pi$
$864$	3.00935	−	4.23601i	0.102380	−	0.144112i
$865$	15.5923	+	27.0067i	0.530154	+	0.918254i
$866$	2.25168			0.0765151
$867$	6.05321	+	1.26424i	0.205578	+	0.0429359i
$868$		0			0
$869$	6.31546	+	3.64623i	0.214237	+	0.123690i
$870$	19.9159	+	4.15953i	0.675211	+	0.141021i
$871$	2.41551	+	1.39459i	0.0818463	+	0.0472540i
$872$	16.4141	−	9.47667i	0.555851	−	0.320920i
$873$	6.61719	−	15.1506i	0.223958	−	0.512770i
$874$			11.3632i			0.384367i
$875$		0			0
$876$	15.9877	+	14.2931i	0.540173	+	0.482918i
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	0.985226	−	0.171258i	$-0.0547831\pi$
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	−0.640927	+	0.767602i	$0.721450\pi$
$878$	18.7400			0.632445
$879$	−41.4749	−	8.66224i	−1.39891	−	0.292170i
$880$			4.29953i			0.144937i
$881$	−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	$0.637204\pi$
$884$		−	17.9251i		−	0.602885i
$885$	−30.1543	+	33.7294i	−1.01363	+	1.13380i
$886$	1.20451			0.0404664
$887$	4.86059	+	8.41879i	0.163203	+	0.282675i	0.936016	−	0.351959i	$-0.114484\pi$
$887$	4.86059	+	8.41879i	0.163203	+	0.282675i	−0.772813	+	0.634634i	$0.781151\pi$
$888$	−3.31587	+	15.8764i	−0.111273	+	0.532778i
$889$		0			0
$890$		−	6.71136i		−	0.224965i
$891$	15.8553	−	14.6885i	0.531174	−	0.492084i
$892$	−7.27049	+	4.19762i	−0.243434	+	0.140547i
$893$	−13.4195	−	7.74775i	−0.449066	−	0.259269i
$894$	−20.0450	+	22.4216i	−0.670406	+	0.749889i
$895$	−20.3456	−	11.7465i	−0.680079	−	0.392644i
$896$		0			0
$897$	−9.96789	−	30.3120i	−0.332818	−	1.01209i
$898$	−26.8022			−0.894400
$899$	15.2433	+	26.4021i	0.508392	+	0.880560i
$900$	−0.600717	−	5.35033i	−0.0200239	−	0.178344i
$901$		0			0
$902$	9.70433	+	16.8084i	0.323119	+	0.559658i
$903$		0			0
$904$	−0.579764	+	1.00418i	−0.0192827	+	0.0333985i
$905$	−20.7110	+	11.9575i	−0.688458	+	0.397481i
$906$	−3.97760	+	19.0448i	−0.132147	+	0.632721i
$907$	8.04314	−	13.9311i	0.267068	−	0.462575i	−0.701035	−	0.713127i	$-0.747278\pi$
$907$	8.04314	−	13.9311i	0.267068	−	0.462575i	0.968103	+	0.250551i	$0.0806118\pi$
$908$	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	0.0193161	−	0.999813i	$-0.493851\pi$
$911$	27.0087	−	15.5935i	0.894838	−	0.516635i	0.875522	+	0.483179i	$0.160518\pi$
$912$	1.06834	−	5.11524i	0.0353764	−	0.169383i
$913$			33.6340i			1.11312i
$914$			13.8488i			0.458079i
$915$	26.1889	+	23.4130i	0.865778	+	0.774011i
$916$	−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	$0.306385\pi$
$920$	−3.37157	+	5.83973i	−0.111157	+	0.192530i
$921$	51.3722	−	16.8934i	1.69277	−	0.556656i
$922$	4.16110	−	2.40241i	0.137039	−	0.0791193i
$923$	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
$927$	−0.201644	+	0.461680i	−0.00662286	+	0.0151636i
$928$	−3.28052	−	5.68202i	−0.107688	−	0.186521i
$929$	−54.7487			−1.79625			−0.898124	−	0.439743i	$-0.855069\pi$
$929$	−54.7487			−1.79625			−0.898124	+	0.439743i	$0.855069\pi$
$930$	−9.60351	+	10.7421i	−0.314911	+	0.352247i
$931$		0			0
$932$	−11.0236	−	6.36446i	−0.361089	−	0.208475i
$933$	−5.90307	−	17.9510i	−0.193258	−	0.587691i
$934$	5.04288	+	2.91151i	0.165008	+	0.0952675i
$935$	−13.6454	+	7.87817i	−0.446252	+	0.257644i
$936$	1.63726	+	14.5824i	0.0535154	+	0.476639i
$937$			58.2065i			1.90152i	0.309924	+	0.950761i	$0.399696\pi$
$937$			58.2065i			1.90152i	−0.309924	+	0.950761i	$0.600304\pi$
$938$		0			0
$939$	5.63384	−	1.85265i	0.183853	−	0.0604588i
$940$	−4.59766	−	7.96337i	−0.149959	−	0.259737i
$941$	33.3316			1.08658			0.543289	−	0.839545i	$-0.317179\pi$
$941$	33.3316			1.08658			0.543289	+	0.839545i	$0.317179\pi$
$942$	−7.49005	−	22.7770i	−0.244039	−	0.742114i
$943$			30.4394i			0.991245i
$944$	14.5900			0.474864
$945$		0			0
$946$	16.7206			0.543632
$947$		−	7.61522i		−	0.247461i	−0.992316	−	0.123731i	$-0.960514\pi$
$947$		−	7.61522i		−	0.247461i	0.992316	−	0.123731i	$-0.0394859\pi$
$948$	−1.64302	−	4.99637i	−0.0533629	−	0.162275i
$949$	−60.5615			−1.96591
$950$	−2.70724	−	4.68907i	−0.0878344	−	0.152134i
$951$	−31.3396	+	10.3058i	−1.01626	+	0.334188i
$952$		0			0
$953$		−	55.7861i		−	1.80709i	−0.428495	−	0.903544i	$-0.640956\pi$
$953$		−	55.7861i		−	1.80709i	0.428495	−	0.903544i	$-0.359044\pi$
$954$		0			0
$955$	14.3472	−	8.28334i	0.464264	−	0.268043i
$956$	−15.1117	−	8.72474i	−0.488747	−	0.282178i
$957$	−8.52526	−	25.9250i	−0.275582	−	0.838037i
$958$	−23.3447	−	13.4781i	−0.754232	−	0.435456i
$959$		0			0
$960$	2.06678	−	2.31181i	0.0667050	−	0.0746135i
$961$	9.40903			0.303517
$962$	−22.9013	−	39.6662i	−0.738367	−	1.27889i
$963$	23.8227	−	2.67473i	0.767676	−	0.0861921i
$964$	−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	−0.996775	−	0.0802517i	$-0.974428\pi$
$967$	−13.3369	+	23.1003i	−0.428887	+	0.742855i	0.567887	+	0.823106i	$0.307761\pi$
$968$	−4.53172	+	2.61639i	−0.145655	+	0.0840939i
$969$	18.1918	−	5.98223i	0.584404	−	0.192177i
$970$	4.93320	−	8.54455i	0.158395	−	0.274349i
$971$	−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
$975$	11.3350	+	10.1336i	0.363010	+	0.324533i
$976$		−	11.3283i		−	0.362610i
$977$			14.7771i			0.472761i	0.971661	+	0.236380i	$0.0759612\pi$
$977$			14.7771i			0.472761i	−0.971661	+	0.236380i	$0.924039\pi$
$978$	−1.53533	+	7.35116i	−0.0490943	+	0.235064i
$979$	−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
$983$	−10.2568	+	17.7652i	−0.327140	+	0.566623i	−0.981943	−	0.189176i	$-0.939418\pi$
$983$	−10.2568	+	17.7652i	−0.327140	+	0.566623i	0.654803	+	0.755800i	$0.272752\pi$
$984$	2.86185	−	13.7026i	0.0912323	−	0.436821i
$985$	−19.3596	+	11.1772i	−0.616847	+	0.356137i
$986$	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
$990$	10.3812	−	7.65538i	0.329936	−	0.243304i
$991$	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	$0.786179\pi$
$992$	4.64661			0.147530
$993$	0.0396334	+	0.120524i	0.00125773	+	0.00382471i
$994$		0			0
$995$	0.277763	+	0.160366i	0.00880567	+	0.00508396i
$996$	16.1678	−	18.0847i	0.512297	−	0.573035i
$997$	−0.0172917	−	0.00998339i	−0.000547635	−	0.000316177i	0.499726	−	0.866183i	$-0.333434\pi$
$997$	−0.0172917	−	0.00998339i	−0.000547635	−	0.000316177i	−0.500274	+	0.865867i	$0.666767\pi$
$998$	22.5250	−	13.0048i	0.713018	−	0.411661i
$999$	44.2374	−	20.2621i	1.39961	−	0.641064i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.5	✓	16	7.2	even	3
126.2.m.a.41.8	yes	16	7.5	odd	6
126.2.m.a.83.5	yes	16	63.47	even	6
126.2.m.a.83.8	yes	16	63.2	odd	6
378.2.m.a.125.1		16	21.2	odd	6
378.2.m.a.125.4		16	21.5	even	6
378.2.m.a.251.1		16	63.61	odd	6
378.2.m.a.251.4		16	63.16	even	3
882.2.l.a.227.2		16	63.11	odd	6	inner
882.2.l.a.227.3		16	63.38	even	6	inner
882.2.l.a.509.6		16	7.6	odd	2	inner
882.2.l.a.509.7		16	1.1	even	1	trivial
882.2.t.b.803.2		16	9.2	odd	6
882.2.t.b.803.3		16	63.20	even	6
882.2.t.b.815.2		16	7.3	odd	6
882.2.t.b.815.3		16	7.4	even	3
1008.2.cc.b.209.1		16	252.191	even	6
1008.2.cc.b.209.8		16	252.47	odd	6
1008.2.cc.b.545.1		16	28.19	even	6
1008.2.cc.b.545.8		16	28.23	odd	6
1134.2.d.a.1133.3		16	63.5	even	6
1134.2.d.a.1133.6		16	63.23	odd	6
1134.2.d.a.1133.11		16	63.58	even	3
1134.2.d.a.1133.14		16	63.40	odd	6
2646.2.l.b.521.5		16	63.52	odd	6
2646.2.l.b.521.8		16	63.25	even	3
2646.2.l.b.1097.1		16	3.2	odd	2
2646.2.l.b.1097.4		16	21.20	even	2
2646.2.t.a.1979.5		16	9.7	even	3
2646.2.t.a.1979.8		16	63.34	odd	6
2646.2.t.a.2285.5		16	21.17	even	6
2646.2.t.a.2285.8		16	21.11	odd	6
3024.2.cc.b.881.3		16	84.23	even	6
3024.2.cc.b.881.6		16	84.47	odd	6
3024.2.cc.b.2897.3		16	252.187	even	6
3024.2.cc.b.2897.6		16	252.79	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.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.541068 + 1.64537i) q^{3} -1.00000 q^{4} +(0.895175 + 1.55049i) q^{5} +(-1.64537 + 0.541068i) q^{6} -1.00000i q^{8} +(-2.41449 + 1.78052i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.541068 + 1.64537i) q^{3} -1.00000 q^{4} +(0.895175 + 1.55049i) q^{5} +(-1.64537 + 0.541068i) q^{6} -1.00000i q^{8} +(-2.41449 + 1.78052i) q^{9} +(-1.55049 + 0.895175i) q^{10} +(2.07976 + 1.20075i) q^{11} +(-0.541068 - 1.64537i) q^{12} +(4.23601 + 2.44566i) q^{13} +(-2.06678 + 2.31181i) q^{15} +1.00000 q^{16} +(1.83233 + 3.17369i) q^{17} +(-1.78052 - 2.41449i) q^{18} +(-2.61281 - 1.50851i) q^{19} +(-0.895175 - 1.55049i) q^{20} +(-1.20075 + 2.07976i) q^{22} +(-3.26178 + 1.88319i) q^{23} +(1.64537 - 0.541068i) q^{24} +(0.897324 - 1.55421i) q^{25} +(-2.44566 + 4.23601i) q^{26} +(-4.23601 - 3.00935i) q^{27} +(-5.68202 + 3.28052i) q^{29} +(-2.31181 - 2.06678i) q^{30} -4.64661i q^{31} +1.00000i q^{32} +(-0.850388 + 4.07167i) q^{33} +(-3.17369 + 1.83233i) q^{34} +(2.41449 - 1.78052i) q^{36} +(-4.68202 + 8.10950i) q^{37} +(1.50851 - 2.61281i) q^{38} +(-1.73205 + 8.29308i) q^{39} +(1.55049 - 0.895175i) q^{40} +(4.04094 - 6.99911i) q^{41} +(-3.48127 - 6.02973i) q^{43} +(-2.07976 - 1.20075i) q^{44} +(-4.92206 - 2.14977i) q^{45} +(-1.88319 - 3.26178i) q^{46} +5.13604 q^{47} +(0.541068 + 1.64537i) q^{48} +(1.55421 + 0.897324i) q^{50} +(-4.23048 + 4.73205i) q^{51} +(-4.23601 - 2.44566i) q^{52} +(3.00935 - 4.23601i) q^{54} +4.29953i q^{55} +(1.06834 - 5.11524i) q^{57} +(-3.28052 - 5.68202i) q^{58} +14.5900 q^{59} +(2.06678 - 2.31181i) q^{60} -11.3283i q^{61} +4.64661 q^{62} -1.00000 q^{64} +8.75718i q^{65} +(-4.07167 - 0.850388i) q^{66} +0.570231 q^{67} +(-1.83233 - 3.17369i) q^{68} +(-4.86340 - 4.34791i) q^{69} -5.96254i q^{71} +(1.78052 + 2.41449i) q^{72} +(-10.7226 + 6.19070i) q^{73} +(-8.10950 - 4.68202i) q^{74} +(3.04277 + 0.635497i) q^{75} +(2.61281 + 1.50851i) q^{76} +(-8.29308 - 1.73205i) q^{78} +3.03663 q^{79} +(0.895175 + 1.55049i) q^{80} +(2.65953 - 8.59808i) q^{81} +(6.99911 + 4.04094i) q^{82} +(7.00270 + 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} +(6.02973 - 3.48127i) q^{86} +(-8.47203 - 7.57405i) q^{87} +(1.20075 - 2.07976i) q^{88} +(-1.87432 + 3.24641i) q^{89} +(2.14977 - 4.92206i) q^{90} +(3.26178 - 1.88319i) q^{92} +(7.64539 - 2.51413i) q^{93} +5.13604i q^{94} -5.40150i q^{95} +(-1.64537 + 0.541068i) q^{96} +(-4.77256 + 2.75544i) q^{97} +(-7.15953 + 0.803848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 12 * q^9	\( 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 12 * q^9 + 12 * q^11 + 16 * q^16 + 12 * q^18 + 48 * q^23 - 8 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 + 60 * q^50 + 24 * q^51 + 48 * q^57 - 12 * q^58 - 16 * q^64 + 56 * q^67 - 12 * q^72 - 36 * q^74 - 24 * q^78 + 8 * q^79 - 12 * q^85 + 24 * q^86 - 48 * q^92 + 84 * q^93 - 72 * q^99

Introduction

L-functions

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