LMFDB - Embedded newform 1890.2.j.i.1261.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(631,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 0]))

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

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

chi := DirichletCharacter("1890.631");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.j (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1261.3
Root			$-1.62241 - 0.606458i$ of defining polynomial
Character	$\chi$	$=$	1890.1261
Dual form			1890.2.j.i.631.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -1.00000 q^{10} +(1.05042 - 1.81937i) q^{11} +(1.55042 + 2.68540i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +6.81681 q^{17} +2.81681 q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.05042 - 1.81937i) q^{22} +(-2.55042 - 4.41745i) q^{23} +(-0.500000 + 0.866025i) q^{25} +3.10083 q^{26} +1.00000 q^{28} +(-0.449585 + 0.778704i) q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.40841 - 5.90353i) q^{34} +1.00000 q^{35} +0.715980 q^{37} +(1.40841 - 2.43943i) q^{38} +(0.500000 + 0.866025i) q^{40} +(-4.05042 - 7.01552i) q^{41} +(0.500000 - 0.866025i) q^{43} -2.10083 q^{44} -5.10083 q^{46} +(5.91764 - 10.2497i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(1.55042 - 2.68540i) q^{52} +4.71598 q^{53} -2.10083 q^{55} +(0.500000 - 0.866025i) q^{56} +(0.449585 + 0.778704i) q^{58} +(-5.50924 - 9.54228i) q^{59} +(3.45882 - 5.99085i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(1.55042 - 2.68540i) q^{65} +(0.307575 + 0.532735i) q^{67} +(-3.40841 - 5.90353i) q^{68} +(0.500000 - 0.866025i) q^{70} -4.71598 q^{71} -8.63362 q^{73} +(0.357990 - 0.620057i) q^{74} +(-1.40841 - 2.43943i) q^{76} +(1.05042 + 1.81937i) q^{77} +(2.81681 - 4.87886i) q^{79} +1.00000 q^{80} -8.10083 q^{82} +(2.91764 - 5.05350i) q^{83} +(-3.40841 - 5.90353i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(-1.05042 + 1.81937i) q^{88} +13.6336 q^{89} -3.10083 q^{91} +(-2.55042 + 4.41745i) q^{92} +(-5.91764 - 10.2497i) q^{94} +(-1.40841 - 2.43943i) q^{95} +(-1.60083 + 2.77272i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 6 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 3 q^{11} + 3 q^{14} - 3 q^{16} + 18 q^{17} - 6 q^{19} - 3 q^{20} + 3 q^{22} - 6 q^{23} - 3 q^{25} + 6 q^{28} - 12 q^{29} + 12 q^{31} + 3 q^{32} + 9 q^{34} + 6 q^{35} - 3 q^{38} + 3 q^{40} - 15 q^{41} + 3 q^{43} + 6 q^{44} - 12 q^{46} - 6 q^{47} - 3 q^{49} + 3 q^{50} + 24 q^{53} + 6 q^{55} + 3 q^{56} + 12 q^{58} - 3 q^{59} + 24 q^{62} + 6 q^{64} + 9 q^{67} - 9 q^{68} + 3 q^{70} - 24 q^{71} - 6 q^{73} + 3 q^{76} - 3 q^{77} - 6 q^{79} + 6 q^{80} - 30 q^{82} - 24 q^{83} - 9 q^{85} - 3 q^{86} + 3 q^{88} + 36 q^{89} - 6 q^{92} + 6 q^{94} + 3 q^{95} + 9 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 3 * q^11 + 3 * q^14 - 3 * q^16 + 18 * q^17 - 6 * q^19 - 3 * q^20 + 3 * q^22 - 6 * q^23 - 3 * q^25 + 6 * q^28 - 12 * q^29 + 12 * q^31 + 3 * q^32 + 9 * q^34 + 6 * q^35 - 3 * q^38 + 3 * q^40 - 15 * q^41 + 3 * q^43 + 6 * q^44 - 12 * q^46 - 6 * q^47 - 3 * q^49 + 3 * q^50 + 24 * q^53 + 6 * q^55 + 3 * q^56 + 12 * q^58 - 3 * q^59 + 24 * q^62 + 6 * q^64 + 9 * q^67 - 9 * q^68 + 3 * q^70 - 24 * q^71 - 6 * q^73 + 3 * q^76 - 3 * q^77 - 6 * q^79 + 6 * q^80 - 30 * q^82 - 24 * q^83 - 9 * q^85 - 3 * q^86 + 3 * q^88 + 36 * q^89 - 6 * q^92 + 6 * q^94 + 3 * q^95 + 9 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.00000			−0.316228
$11$	1.05042	−	1.81937i	0.316712	−	0.548561i	−0.663088	−	0.748542i	$-0.730754\pi$
$11$	1.05042	−	1.81937i	0.316712	−	0.548561i	0.979800	+	0.199980i	$0.0640878\pi$
$12$		0			0
$13$	1.55042	+	2.68540i	0.430008	+	0.744795i	0.996873	−	0.0790149i	$-0.0251775\pi$
$13$	1.55042	+	2.68540i	0.430008	+	0.744795i	−0.566866	+	0.823810i	$0.691844\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.81681			1.65332			0.826660	−	0.562702i	$-0.190238\pi$
$17$	6.81681			1.65332			0.826660	+	0.562702i	$0.190238\pi$
$18$		0			0
$19$	2.81681			0.646221			0.323110	−	0.946361i	$-0.395272\pi$
$19$	2.81681			0.646221			0.323110	+	0.946361i	$0.395272\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	−1.05042	−	1.81937i	−0.223949	−	0.387892i
$23$	−2.55042	−	4.41745i	−0.531798	−	0.921102i	−0.999311	−	0.0371154i	$-0.988183\pi$
$23$	−2.55042	−	4.41745i	−0.531798	−	0.921102i	0.467513	−	0.883986i	$-0.345150\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.10083			0.608123
$27$		0			0
$28$	1.00000			0.188982
$29$	−0.449585	+	0.778704i	−0.0834858	+	0.144602i	−0.904745	−	0.425954i	$-0.859939\pi$
$29$	−0.449585	+	0.778704i	−0.0834858	+	0.144602i	0.821259	+	0.570555i	$0.193272\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	3.40841	−	5.90353i	0.584537	−	1.01245i
$35$	1.00000			0.169031
$36$		0			0
$37$	0.715980			0.117706			0.0588532	−	0.998267i	$-0.481256\pi$
$37$	0.715980			0.117706			0.0588532	+	0.998267i	$0.481256\pi$
$38$	1.40841	−	2.43943i	0.228473	−	0.395728i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−4.05042	−	7.01552i	−0.632569	−	1.09564i	−0.987025	−	0.160568i	$-0.948667\pi$
$41$	−4.05042	−	7.01552i	−0.632569	−	1.09564i	0.354456	−	0.935073i	$-0.384666\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	−2.10083			−0.316712
$45$		0			0
$46$	−5.10083			−0.752076
$47$	5.91764	−	10.2497i	0.863177	−	1.49507i	−0.00566976	−	0.999984i	$-0.501805\pi$
$47$	5.91764	−	10.2497i	0.863177	−	1.49507i	0.868846	−	0.495082i	$-0.164862\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	1.55042	−	2.68540i	0.215004	−	0.372398i
$53$	4.71598			0.647790			0.323895	−	0.946093i	$-0.395008\pi$
$53$	4.71598			0.647790			0.323895	+	0.946093i	$0.395008\pi$
$54$		0			0
$55$	−2.10083			−0.283276
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	0.449585	+	0.778704i	0.0590334	+	0.102249i
$59$	−5.50924	−	9.54228i	−0.717241	−	1.24230i	−0.962089	−	0.272737i	$-0.912071\pi$
$59$	−5.50924	−	9.54228i	−0.717241	−	1.24230i	0.244847	−	0.969562i	$-0.421262\pi$
$60$		0			0
$61$	3.45882	−	5.99085i	0.442857	−	0.767050i	−0.555044	−	0.831821i	$-0.687298\pi$
$61$	3.45882	−	5.99085i	0.442857	−	0.767050i	0.997900	+	0.0647712i	$0.0206318\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	1.55042	−	2.68540i	0.192305	−	0.333083i
$66$		0			0
$67$	0.307575	+	0.532735i	0.0375762	+	0.0650839i	0.884202	−	0.467105i	$-0.154703\pi$
$67$	0.307575	+	0.532735i	0.0375762	+	0.0650839i	−0.846626	+	0.532189i	$0.821370\pi$
$68$	−3.40841	−	5.90353i	−0.413330	−	0.715908i
$69$		0			0
$70$	0.500000	−	0.866025i	0.0597614	−	0.103510i
$71$	−4.71598			−0.559684			−0.279842	−	0.960046i	$-0.590282\pi$
$71$	−4.71598			−0.559684			−0.279842	+	0.960046i	$0.590282\pi$
$72$		0			0
$73$	−8.63362			−1.01049			−0.505244	−	0.862976i	$-0.668598\pi$
$73$	−8.63362			−1.01049			−0.505244	+	0.862976i	$0.668598\pi$
$74$	0.357990	−	0.620057i	0.0416155	−	0.0720801i
$75$		0			0
$76$	−1.40841	−	2.43943i	−0.161555	−	0.279822i
$77$	1.05042	+	1.81937i	0.119706	+	0.207337i
$78$		0			0
$79$	2.81681	−	4.87886i	0.316916	−	0.548914i	−0.662927	−	0.748684i	$-0.730686\pi$
$79$	2.81681	−	4.87886i	0.316916	−	0.548914i	0.979843	+	0.199770i	$0.0640194\pi$
$80$	1.00000			0.111803
$81$		0			0
$82$	−8.10083			−0.894587
$83$	2.91764	−	5.05350i	0.320253	−	0.554694i	−0.660287	−	0.751013i	$-0.729566\pi$
$83$	2.91764	−	5.05350i	0.320253	−	0.554694i	0.980540	+	0.196319i	$0.0628989\pi$
$84$		0			0
$85$	−3.40841	−	5.90353i	−0.369693	−	0.640328i
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$		0			0
$88$	−1.05042	+	1.81937i	−0.111975	+	0.193946i
$89$	13.6336			1.44516			0.722580	−	0.691287i	$-0.242956\pi$
$89$	13.6336			1.44516			0.722580	+	0.691287i	$0.242956\pi$
$90$		0			0
$91$	−3.10083			−0.325055
$92$	−2.55042	+	4.41745i	−0.265899	+	0.460551i
$93$		0			0
$94$	−5.91764	−	10.2497i	−0.610358	−	1.05717i
$95$	−1.40841	−	2.43943i	−0.144499	−	0.250280i
$96$		0			0
$97$	−1.60083	+	2.77272i	−0.162540	+	0.281527i	−0.935779	−	0.352587i	$-0.885302\pi$
$97$	−1.60083	+	2.77272i	−0.162540	+	0.281527i	0.773239	+	0.634115i	$0.218635\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	1.00000			0.100000
$101$	−7.20166	+	12.4736i	−0.716592	+	1.24117i	0.245750	+	0.969333i	$0.420966\pi$
$101$	−7.20166	+	12.4736i	−0.716592	+	1.24117i	−0.962342	+	0.271841i	$0.912368\pi$
$102$		0			0
$103$	−5.45882	−	9.45495i	−0.537874	−	0.931624i	−0.999018	−	0.0442994i	$-0.985894\pi$
$103$	−5.45882	−	9.45495i	−0.537874	−	0.931624i	0.461145	−	0.887325i	$-0.347439\pi$
$104$	−1.55042	−	2.68540i	−0.152031	−	0.263325i
$105$		0			0
$106$	2.35799	−	4.08416i	0.229028	−	0.396689i
$107$	11.0185			1.06520			0.532598	−	0.846368i	$-0.321216\pi$
$107$	11.0185			1.06520			0.532598	+	0.846368i	$0.321216\pi$
$108$		0			0
$109$	3.66887			0.351414			0.175707	−	0.984442i	$-0.443779\pi$
$109$	3.66887			0.351414			0.175707	+	0.984442i	$0.443779\pi$
$110$	−1.05042	+	1.81937i	−0.100153	+	0.173470i
$111$		0			0
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	5.72522	+	9.91636i	0.538583	+	0.932853i	0.998981	+	0.0451403i	$0.0143735\pi$
$113$	5.72522	+	9.91636i	0.538583	+	0.932853i	−0.460398	+	0.887713i	$0.652293\pi$
$114$		0			0
$115$	−2.55042	+	4.41745i	−0.237827	+	0.411929i
$116$	0.899170			0.0834858
$117$		0			0
$118$	−11.0185			−1.01433
$119$	−3.40841	+	5.90353i	−0.312448	+	0.541176i
$120$		0			0
$121$	3.29326	+	5.70409i	0.299387	+	0.518553i
$122$	−3.45882	−	5.99085i	−0.313147	−	0.542386i
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	1.00000			0.0894427
$126$		0			0
$127$	12.9361			1.14789			0.573947	−	0.818892i	$-0.305411\pi$
$127$	12.9361			1.14789			0.573947	+	0.818892i	$0.305411\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.55042	−	2.68540i	−0.135980	−	0.235525i
$131$	5.72522	+	9.91636i	0.500214	+	0.866397i	1.00000		0.000247572i	$7.88046e-5\pi$
$131$	5.72522	+	9.91636i	0.500214	+	0.866397i	−0.499786	+	0.866149i	$0.666588\pi$
$132$		0			0
$133$	−1.40841	+	2.43943i	−0.122124	+	0.211525i
$134$	0.615149			0.0531408
$135$		0			0
$136$	−6.81681			−0.584537
$137$	−0.0411797	+	0.0713253i	−0.00351822	+	0.00609373i	−0.867779	−	0.496950i	$-0.834453\pi$
$137$	−0.0411797	+	0.0713253i	−0.00351822	+	0.00609373i	0.864261	+	0.503044i	$0.167787\pi$
$138$		0			0
$139$	3.50000	+	6.06218i	0.296866	+	0.514187i	0.975417	−	0.220366i	$-0.0707252\pi$
$139$	3.50000	+	6.06218i	0.296866	+	0.514187i	−0.678551	+	0.734553i	$0.737392\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$		0			0
$142$	−2.35799	+	4.08416i	−0.197878	+	0.342735i
$143$	6.51432			0.544755
$144$		0			0
$145$	0.899170			0.0746720
$146$	−4.31681	+	7.47693i	−0.357262	+	0.618796i
$147$		0			0
$148$	−0.357990	−	0.620057i	−0.0294266	−	0.0509683i
$149$	−7.20166	−	12.4736i	−0.589983	−	1.02188i	−0.994234	−	0.107232i	$-0.965801\pi$
$149$	−7.20166	−	12.4736i	−0.589983	−	1.02188i	0.404251	−	0.914648i	$-0.367532\pi$
$150$		0			0
$151$	−0.917641	+	1.58940i	−0.0746765	+	0.129344i	−0.900946	−	0.433932i	$-0.857126\pi$
$151$	−0.917641	+	1.58940i	−0.0746765	+	0.129344i	0.826269	+	0.563276i	$0.190459\pi$
$152$	−2.81681			−0.228473
$153$		0			0
$154$	2.10083			0.169290
$155$	2.00000	−	3.46410i	0.160644	−	0.278243i
$156$		0			0
$157$	−10.7521	−	18.6231i	−0.858109	−	1.48629i	−0.873730	−	0.486411i	$-0.838306\pi$
$157$	−10.7521	−	18.6231i	−0.858109	−	1.48629i	0.0156213	−	0.999878i	$-0.495027\pi$
$158$	−2.81681	−	4.87886i	−0.224093	−	0.388141i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	5.10083			0.402002
$162$		0			0
$163$	22.0185			1.72462			0.862310	−	0.506381i	$-0.169017\pi$
$163$	22.0185			1.72462			0.862310	+	0.506381i	$0.169017\pi$
$164$	−4.05042	+	7.01552i	−0.316284	+	0.547820i
$165$		0			0
$166$	−2.91764	−	5.05350i	−0.226453	−	0.392228i
$167$	−7.45882	−	12.9191i	−0.577181	−	0.999707i	−0.995801	−	0.0915451i	$-0.970819\pi$
$167$	−7.45882	−	12.9191i	−0.577181	−	0.999707i	0.418620	−	0.908161i	$-0.362514\pi$
$168$		0			0
$169$	1.69243	−	2.93137i	0.130187	−	0.225490i
$170$	−6.81681			−0.522825
$171$		0			0
$172$	−1.00000			−0.0762493
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	−0.998755	−	0.0498898i	$-0.984113\pi$
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	0.542583	+	0.840002i	$0.317446\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	1.05042	+	1.81937i	0.0791780	+	0.137140i
$177$		0			0
$178$	6.81681	−	11.8071i	0.510942	−	0.884977i
$179$	−12.3849			−0.925687			−0.462844	−	0.886440i	$-0.653171\pi$
$179$	−12.3849			−0.925687			−0.462844	+	0.886440i	$0.653171\pi$
$180$		0			0
$181$	−23.4689			−1.74443			−0.872215	−	0.489123i	$-0.837317\pi$
$181$	−23.4689			−1.74443			−0.872215	+	0.489123i	$0.837317\pi$
$182$	−1.55042	+	2.68540i	−0.114924	+	0.199055i
$183$		0			0
$184$	2.55042	+	4.41745i	0.188019	+	0.325659i
$185$	−0.357990	−	0.620057i	−0.0263199	−	0.0455875i
$186$		0			0
$187$	7.16048	−	12.4023i	0.523626	−	0.906947i
$188$	−11.8353			−0.863177
$189$		0			0
$190$	−2.81681			−0.204353
$191$	−10.6336	+	18.4180i	−0.769422	+	1.33268i	0.168455	+	0.985709i	$0.446122\pi$
$191$	−10.6336	+	18.4180i	−0.769422	+	1.33268i	−0.937877	+	0.346968i	$0.887211\pi$
$192$		0			0
$193$	−3.57397	−	6.19030i	−0.257260	−	0.445587i	0.708247	−	0.705965i	$-0.249486\pi$
$193$	−3.57397	−	6.19030i	−0.257260	−	0.445587i	−0.965507	+	0.260377i	$0.916153\pi$
$194$	1.60083	+	2.77272i	0.114933	+	0.199070i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	20.7529			1.47858			0.739292	−	0.673385i	$-0.235160\pi$
$197$	20.7529			1.47858			0.739292	+	0.673385i	$0.235160\pi$
$198$		0			0
$199$	−1.46721			−0.104008			−0.0520039	−	0.998647i	$-0.516561\pi$
$199$	−1.46721			−0.104008			−0.0520039	+	0.998647i	$0.516561\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	7.20166	+	12.4736i	0.506707	+	0.877642i
$203$	−0.449585	−	0.778704i	−0.0315547	−	0.0546543i
$204$		0			0
$205$	−4.05042	+	7.01552i	−0.282893	+	0.489986i
$206$	−10.9176			−0.760668
$207$		0			0
$208$	−3.10083			−0.215004
$209$	2.95882	−	5.12483i	0.204666	−	0.354492i
$210$		0			0
$211$	5.81681	+	10.0750i	0.400446	+	0.693592i	0.993780	−	0.111364i	$-0.0355220\pi$
$211$	5.81681	+	10.0750i	0.400446	+	0.693592i	−0.593334	+	0.804956i	$0.702189\pi$
$212$	−2.35799	−	4.08416i	−0.161947	−	0.280501i
$213$		0			0
$214$	5.50924	−	9.54228i	0.376604	−	0.652297i
$215$	−1.00000			−0.0681994
$216$		0			0
$217$	−4.00000			−0.271538
$218$	1.83444	−	3.17734i	0.124244	−	0.215196i
$219$		0			0
$220$	1.05042	+	1.81937i	0.0708190	+	0.122662i
$221$	10.5689	+	18.3058i	0.710940	+	1.23138i
$222$		0			0
$223$	−10.5597	+	18.2899i	−0.707127	+	1.22478i	0.258792	+	0.965933i	$0.416676\pi$
$223$	−10.5597	+	18.2899i	−0.707127	+	1.22478i	−0.965919	+	0.258846i	$0.916658\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	11.4504			0.761671
$227$	13.5924	−	23.5428i	0.902162	−	1.56259i	0.0774798	−	0.996994i	$-0.475313\pi$
$227$	13.5924	−	23.5428i	0.902162	−	1.56259i	0.824682	−	0.565596i	$-0.191354\pi$
$228$		0			0
$229$	11.9916	+	20.7701i	0.792428	+	1.37253i	0.924460	+	0.381280i	$0.124517\pi$
$229$	11.9916	+	20.7701i	0.792428	+	1.37253i	−0.132032	+	0.991245i	$0.542150\pi$
$230$	2.55042	+	4.41745i	0.168169	+	0.291278i
$231$		0			0
$232$	0.449585	−	0.778704i	0.0295167	−	0.0511244i
$233$	−15.7345			−1.03080			−0.515399	−	0.856950i	$-0.672356\pi$
$233$	−15.7345			−1.03080			−0.515399	+	0.856950i	$0.672356\pi$
$234$		0			0
$235$	−11.8353			−0.772049
$236$	−5.50924	+	9.54228i	−0.358621	+	0.621149i
$237$		0			0
$238$	3.40841	+	5.90353i	0.220934	+	0.382669i
$239$	8.01847	+	13.8884i	0.518672	+	0.898366i	0.999765	+	0.0216962i	$0.00690666\pi$
$239$	8.01847	+	13.8884i	0.518672	+	0.898366i	−0.481093	+	0.876670i	$0.659760\pi$
$240$		0			0
$241$	7.14201	−	12.3703i	0.460057	−	0.796843i	−0.538906	−	0.842366i	$-0.681162\pi$
$241$	7.14201	−	12.3703i	0.460057	−	0.796843i	0.998963	+	0.0455233i	$0.0144955\pi$
$242$	6.58651			0.423397
$243$		0			0
$244$	−6.91764			−0.442857
$245$	−0.500000	+	0.866025i	−0.0319438	+	0.0553283i
$246$		0			0
$247$	4.36723	+	7.56426i	0.277880	+	0.481302i
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	25.2017			1.59071			0.795357	−	0.606141i	$-0.207283\pi$
$251$	25.2017			1.59071			0.795357	+	0.606141i	$0.207283\pi$
$252$		0			0
$253$	−10.7160			−0.673708
$254$	6.46806	−	11.2030i	0.405842	−	0.702939i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.21598	+	10.7664i	0.387742	+	0.671589i	0.992145	−	0.125089i	$-0.0399218\pi$
$257$	6.21598	+	10.7664i	0.387742	+	0.671589i	−0.604403	+	0.796679i	$0.706588\pi$
$258$		0			0
$259$	−0.357990	+	0.620057i	−0.0222444	+	0.0385284i
$260$	−3.10083			−0.192305
$261$		0			0
$262$	11.4504			0.707410
$263$	−5.46806	+	9.47095i	−0.337175	+	0.584004i	−0.983900	−	0.178719i	$-0.942805\pi$
$263$	−5.46806	+	9.47095i	−0.337175	+	0.584004i	0.646725	+	0.762723i	$0.276138\pi$
$264$		0			0
$265$	−2.35799	−	4.08416i	−0.144850	−	0.250888i
$266$	1.40841	+	2.43943i	0.0863549	+	0.149571i
$267$		0			0
$268$	0.307575	−	0.532735i	0.0187881	−	0.0325420i
$269$	2.05372			0.125218			0.0626088	−	0.998038i	$-0.480058\pi$
$269$	2.05372			0.125218			0.0626088	+	0.998038i	$0.480058\pi$
$270$		0			0
$271$	−3.26555			−0.198368			−0.0991840	−	0.995069i	$-0.531623\pi$
$271$	−3.26555			−0.198368			−0.0991840	+	0.995069i	$0.531623\pi$
$272$	−3.40841	+	5.90353i	−0.206665	+	0.357954i
$273$		0			0
$274$	0.0411797	+	0.0713253i	0.00248775	+	0.00430892i
$275$	1.05042	+	1.81937i	0.0633424	+	0.109712i
$276$		0			0
$277$	−10.8168	+	18.7353i	−0.649919	+	1.12569i	0.333223	+	0.942848i	$0.391864\pi$
$277$	−10.8168	+	18.7353i	−0.649919	+	1.12569i	−0.983142	+	0.182845i	$0.941469\pi$
$278$	7.00000			0.419832
$279$		0			0
$280$	−1.00000			−0.0597614
$281$	−11.6429	+	20.1660i	−0.694555	+	1.20300i	0.275776	+	0.961222i	$0.411065\pi$
$281$	−11.6429	+	20.1660i	−0.694555	+	1.20300i	−0.970331	+	0.241782i	$0.922268\pi$
$282$		0			0
$283$	−3.10083	−	5.37080i	−0.184325	−	0.319261i	0.759024	−	0.651063i	$-0.225677\pi$
$283$	−3.10083	−	5.37080i	−0.184325	−	0.319261i	−0.943349	+	0.331802i	$0.892343\pi$
$284$	2.35799	+	4.08416i	0.139921	+	0.242350i
$285$		0			0
$286$	3.25716	−	5.64157i	0.192600	−	0.333593i
$287$	8.10083			0.478177
$288$		0			0
$289$	29.4689			1.73346
$290$	0.449585	−	0.778704i	0.0264005	−	0.0457271i
$291$		0			0
$292$	4.31681	+	7.47693i	0.252622	+	0.437555i
$293$	−16.1840	−	28.0316i	−0.945481	−	1.63762i	−0.754784	−	0.655973i	$-0.772259\pi$
$293$	−16.1840	−	28.0316i	−0.945481	−	1.63762i	−0.190697	−	0.981649i	$-0.561075\pi$
$294$		0			0
$295$	−5.50924	+	9.54228i	−0.320760	+	0.555573i
$296$	−0.715980			−0.0416155
$297$		0			0
$298$	−14.4033			−0.834362
$299$	7.90841	−	13.6978i	0.457355	−	0.792162i
$300$		0			0
$301$	0.500000	+	0.866025i	0.0288195	+	0.0499169i
$302$	0.917641	+	1.58940i	0.0528043	+	0.0914597i
$303$		0			0
$304$	−1.40841	+	2.43943i	−0.0807776	+	0.139911i
$305$	−6.91764			−0.396103
$306$		0			0
$307$	−7.73445			−0.441428			−0.220714	−	0.975339i	$-0.570839\pi$
$307$	−7.73445			−0.441428			−0.220714	+	0.975339i	$0.570839\pi$
$308$	1.05042	−	1.81937i	0.0598530	−	0.103668i
$309$		0			0
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	5.48568	+	9.50148i	0.311064	+	0.538779i	0.978593	−	0.205805i	$-0.0659812\pi$
$311$	5.48568	+	9.50148i	0.311064	+	0.538779i	−0.667529	+	0.744584i	$0.732648\pi$
$312$		0			0
$313$	5.79326	−	10.0342i	0.327454	−	0.567167i	−0.654552	−	0.756017i	$-0.727143\pi$
$313$	5.79326	−	10.0342i	0.327454	−	0.567167i	0.982006	+	0.188850i	$0.0604760\pi$
$314$	−21.5042			−1.21355
$315$		0			0
$316$	−5.63362			−0.316916
$317$	−1.07397	+	1.86017i	−0.0603201	+	0.104478i	−0.894609	−	0.446851i	$-0.852545\pi$
$317$	−1.07397	+	1.86017i	−0.0603201	+	0.104478i	0.834288	+	0.551328i	$0.185879\pi$
$318$		0			0
$319$	0.944501	+	1.63592i	0.0528819	+	0.0915942i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	2.55042	−	4.41745i	0.142129	−	0.246175i
$323$	19.2017			1.06841
$324$		0			0
$325$	−3.10083			−0.172003
$326$	11.0092	−	19.0686i	0.609745	−	1.05611i
$327$		0			0
$328$	4.05042	+	7.01552i	0.223647	+	0.387368i
$329$	5.91764	+	10.2497i	0.326250	+	0.565082i
$330$		0			0
$331$	−1.08236	+	1.87470i	−0.0594918	+	0.103043i	−0.894237	−	0.447593i	$-0.852281\pi$
$331$	−1.08236	+	1.87470i	−0.0594918	+	0.103043i	0.834746	+	0.550636i	$0.185615\pi$
$332$	−5.83528			−0.320253
$333$		0			0
$334$	−14.9176			−0.816257
$335$	0.307575	−	0.532735i	0.0168046	−	0.0291064i
$336$		0			0
$337$	15.5924	+	27.0069i	0.849374	+	1.47116i	0.881767	+	0.471684i	$0.156354\pi$
$337$	15.5924	+	27.0069i	0.849374	+	1.47116i	−0.0323931	+	0.999475i	$0.510313\pi$
$338$	−1.69243	−	2.93137i	−0.0920558	−	0.159445i
$339$		0			0
$340$	−3.40841	+	5.90353i	−0.184847	+	0.320164i
$341$	8.40332			0.455065
$342$		0			0
$343$	1.00000			0.0539949
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$		0			0
$346$	6.00000	+	10.3923i	0.322562	+	0.558694i
$347$	−12.7109	−	22.0159i	−0.682357	−	1.18188i	−0.974260	−	0.225429i	$-0.927622\pi$
$347$	−12.7109	−	22.0159i	−0.682357	−	1.18188i	0.291903	−	0.956448i	$-0.405712\pi$
$348$		0			0
$349$	−11.3765	+	19.7046i	−0.608968	+	1.05476i	0.382443	+	0.923979i	$0.375083\pi$
$349$	−11.3765	+	19.7046i	−0.608968	+	1.05476i	−0.991411	+	0.130784i	$0.958250\pi$
$350$	−1.00000			−0.0534522
$351$		0			0
$352$	2.10083			0.111975
$353$	−15.6008	+	27.0214i	−0.830348	+	1.43821i	0.0674137	+	0.997725i	$0.478525\pi$
$353$	−15.6008	+	27.0214i	−0.830348	+	1.43821i	−0.897762	+	0.440481i	$0.854808\pi$
$354$		0			0
$355$	2.35799	+	4.08416i	0.125149	+	0.216765i
$356$	−6.81681	−	11.8071i	−0.361290	−	0.625773i
$357$		0			0
$358$	−6.19243	+	10.7256i	−0.327280	+	0.566865i
$359$	−12.3496			−0.651787			−0.325893	−	0.945406i	$-0.605665\pi$
$359$	−12.3496			−0.651787			−0.325893	+	0.945406i	$0.605665\pi$
$360$		0			0
$361$	−11.0656			−0.582399
$362$	−11.7345	+	20.3247i	−0.616749	+	1.06824i
$363$		0			0
$364$	1.55042	+	2.68540i	0.0812638	+	0.140753i
$365$	4.31681	+	7.47693i	0.225952	+	0.391361i
$366$		0			0
$367$	11.0924	−	19.2127i	0.579021	−	1.00289i	−0.416571	−	0.909103i	$-0.636768\pi$
$367$	11.0924	−	19.2127i	0.579021	−	1.00289i	0.995592	−	0.0937902i	$-0.0298983\pi$
$368$	5.10083			0.265899
$369$		0			0
$370$	−0.715980			−0.0372220
$371$	−2.35799	+	4.08416i	−0.122421	+	0.212039i
$372$		0			0
$373$	−6.18319	−	10.7096i	−0.320153	−	0.554522i	0.660366	−	0.750944i	$-0.270401\pi$
$373$	−6.18319	−	10.7096i	−0.320153	−	0.554522i	−0.980519	+	0.196422i	$0.937068\pi$
$374$	−7.16048	−	12.4023i	−0.370260	−	0.641309i
$375$		0			0
$376$	−5.91764	+	10.2497i	−0.305179	+	0.528586i
$377$	−2.78817			−0.143598
$378$		0			0
$379$	17.1849			0.882728			0.441364	−	0.897328i	$-0.354495\pi$
$379$	17.1849			0.882728			0.441364	+	0.897328i	$0.354495\pi$
$380$	−1.40841	+	2.43943i	−0.0722497	+	0.125140i
$381$		0			0
$382$	10.6336	+	18.4180i	0.544063	+	0.942345i
$383$	−10.6336	−	18.4180i	−0.543353	−	0.941114i	−0.998709	−	0.0508049i	$-0.983821\pi$
$383$	−10.6336	−	18.4180i	−0.543353	−	0.941114i	0.455356	−	0.890309i	$-0.349512\pi$
$384$		0			0
$385$	1.05042	−	1.81937i	0.0535341	−	0.0927238i
$386$	−7.14794			−0.363821
$387$		0			0
$388$	3.20166			0.162540
$389$	−2.01847	+	3.49609i	−0.102341	+	0.177259i	−0.912649	−	0.408745i	$-0.865966\pi$
$389$	−2.01847	+	3.49609i	−0.102341	+	0.177259i	0.810308	+	0.586004i	$0.199300\pi$
$390$		0			0
$391$	−17.3857	−	30.1129i	−0.879232	−	1.52288i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		0			0
$394$	10.3765	−	17.9726i	0.522759	−	0.905444i
$395$	−5.63362			−0.283458
$396$		0			0
$397$	36.7714			1.84550			0.922752	−	0.385395i	$-0.125935\pi$
$397$	36.7714			1.84550			0.922752	+	0.385395i	$0.125935\pi$
$398$	−0.733605	+	1.27064i	−0.0367723	+	0.0636915i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	4.33528	+	7.50893i	0.216494	+	0.374978i	0.953734	−	0.300653i	$-0.0972046\pi$
$401$	4.33528	+	7.50893i	0.216494	+	0.374978i	−0.737240	+	0.675631i	$0.763871\pi$
$402$		0			0
$403$	−6.20166	+	10.7416i	−0.308927	+	0.535077i
$404$	14.4033			0.716592
$405$		0			0
$406$	−0.899170			−0.0446250
$407$	0.752076	−	1.30263i	0.0372790	−	0.0645692i
$408$		0			0
$409$	17.8857	+	30.9789i	0.884391	+	1.53181i	0.846410	+	0.532531i	$0.178759\pi$
$409$	17.8857	+	30.9789i	0.884391	+	1.53181i	0.0379804	+	0.999278i	$0.487908\pi$
$410$	4.05042	+	7.01552i	0.200036	+	0.346472i
$411$		0			0
$412$	−5.45882	+	9.45495i	−0.268937	+	0.465812i
$413$	11.0185			0.542184
$414$		0			0
$415$	−5.83528			−0.286443
$416$	−1.55042	+	2.68540i	−0.0760154	+	0.131662i
$417$		0			0
$418$	−2.95882	−	5.12483i	−0.144721	−	0.250663i
$419$	−3.92688	−	6.80155i	−0.191840	−	0.332277i	0.754020	−	0.656852i	$-0.228112\pi$
$419$	−3.92688	−	6.80155i	−0.191840	−	0.332277i	−0.945860	+	0.324574i	$0.894779\pi$
$420$		0			0
$421$	−17.1017	+	29.6210i	−0.833485	+	1.44364i	0.0617735	+	0.998090i	$0.480324\pi$
$421$	−17.1017	+	29.6210i	−0.833485	+	1.44364i	−0.895258	+	0.445548i	$0.853009\pi$
$422$	11.6336			0.566316
$423$		0			0
$424$	−4.71598			−0.229028
$425$	−3.40841	+	5.90353i	−0.165332	+	0.286363i
$426$		0			0
$427$	3.45882	+	5.99085i	0.167384	+	0.289918i
$428$	−5.50924	−	9.54228i	−0.266299	−	0.461243i
$429$		0			0
$430$	−0.500000	+	0.866025i	−0.0241121	+	0.0417635i
$431$	−25.4689			−1.22679			−0.613397	−	0.789775i	$-0.710197\pi$
$431$	−25.4689			−1.22679			−0.613397	+	0.789775i	$0.710197\pi$
$432$		0			0
$433$	29.0000			1.39365			0.696826	−	0.717241i	$-0.254595\pi$
$433$	29.0000			1.39365			0.696826	+	0.717241i	$0.254595\pi$
$434$	−2.00000	+	3.46410i	−0.0960031	+	0.166282i
$435$		0			0
$436$	−1.83444	−	3.17734i	−0.0878535	−	0.152167i
$437$	−7.18404	−	12.4431i	−0.343659	−	0.595235i
$438$		0			0
$439$	−4.36723	+	7.56426i	−0.208436	+	0.361022i	−0.951222	−	0.308507i	$-0.900171\pi$
$439$	−4.36723	+	7.56426i	−0.208436	+	0.361022i	0.742786	+	0.669529i	$0.233504\pi$
$440$	2.10083			0.100153
$441$		0			0
$442$	21.1378			1.00542
$443$	−9.08651	+	15.7383i	−0.431713	+	0.747749i	−0.997021	−	0.0771309i	$-0.975424\pi$
$443$	−9.08651	+	15.7383i	−0.431713	+	0.747749i	0.565308	+	0.824880i	$0.308757\pi$
$444$		0			0
$445$	−6.81681	−	11.8071i	−0.323148	−	0.559708i
$446$	10.5597	+	18.2899i	0.500014	+	0.866050i
$447$		0			0
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	3.22013			0.151967			0.0759837	−	0.997109i	$-0.475790\pi$
$449$	3.22013			0.151967			0.0759837	+	0.997109i	$0.475790\pi$
$450$		0			0
$451$	−17.0185			−0.801369
$452$	5.72522	−	9.91636i	0.269291	−	0.466427i
$453$		0			0
$454$	−13.5924	−	23.5428i	−0.637925	−	1.10492i
$455$	1.55042	+	2.68540i	0.0726846	+	0.125893i
$456$		0			0
$457$	−3.76640	+	6.52359i	−0.176185	+	0.305161i	−0.940571	−	0.339598i	$-0.889709\pi$
$457$	−3.76640	+	6.52359i	−0.176185	+	0.305161i	0.764386	+	0.644759i	$0.223042\pi$
$458$	23.9832			1.12066
$459$		0			0
$460$	5.10083			0.237827
$461$	−13.8437	+	23.9779i	−0.644764	+	1.11676i	0.339592	+	0.940573i	$0.389711\pi$
$461$	−13.8437	+	23.9779i	−0.644764	+	1.11676i	−0.984356	+	0.176191i	$0.943622\pi$
$462$		0			0
$463$	6.63362	+	11.4898i	0.308290	+	0.533975i	0.977989	−	0.208659i	$-0.0669098\pi$
$463$	6.63362	+	11.4898i	0.308290	+	0.533975i	−0.669698	+	0.742634i	$0.733576\pi$
$464$	−0.449585	−	0.778704i	−0.0208714	−	0.0361504i
$465$		0			0
$466$	−7.86723	+	13.6264i	−0.364442	+	0.631232i
$467$	−25.4570			−1.17801			−0.589006	−	0.808129i	$-0.700480\pi$
$467$	−25.4570			−1.17801			−0.589006	+	0.808129i	$0.700480\pi$
$468$		0			0
$469$	−0.615149			−0.0284050
$470$	−5.91764	+	10.2497i	−0.272960	+	0.472781i
$471$		0			0
$472$	5.50924	+	9.54228i	0.253583	+	0.439219i
$473$	−1.05042	−	1.81937i	−0.0482981	−	0.0836548i
$474$		0			0
$475$	−1.40841	+	2.43943i	−0.0646221	+	0.111929i
$476$	6.81681			0.312448
$477$		0			0
$478$	16.0369			0.733513
$479$	14.0361	−	24.3112i	0.641326	−	1.11081i	−0.343811	−	0.939039i	$-0.611718\pi$
$479$	14.0361	−	24.3112i	0.641326	−	1.11081i	0.985137	−	0.171770i	$-0.0549485\pi$
$480$		0			0
$481$	1.11007	+	1.92269i	0.0506147	+	0.0876671i
$482$	−7.14201	−	12.3703i	−0.325310	−	0.563453i
$483$		0			0
$484$	3.29326	−	5.70409i	0.149693	−	0.259277i
$485$	3.20166			0.145380
$486$		0			0
$487$	11.4320			0.518032			0.259016	−	0.965873i	$-0.416602\pi$
$487$	11.4320			0.518032			0.259016	+	0.965873i	$0.416602\pi$
$488$	−3.45882	+	5.99085i	−0.156573	+	0.271193i
$489$		0			0
$490$	0.500000	+	0.866025i	0.0225877	+	0.0391230i
$491$	−17.4916	−	30.2964i	−0.789385	−	1.36726i	−0.926344	−	0.376679i	$-0.877066\pi$
$491$	−17.4916	−	30.2964i	−0.789385	−	1.36726i	0.136959	−	0.990577i	$-0.456267\pi$
$492$		0			0
$493$	−3.06473	+	5.30828i	−0.138029	+	0.239073i
$494$	8.73445			0.392982
$495$		0			0
$496$	−4.00000			−0.179605
$497$	2.35799	−	4.08416i	0.105770	−	0.183200i
$498$		0			0
$499$	−8.43527	−	14.6103i	−0.377614	−	0.654047i	0.613100	−	0.790005i	$-0.289922\pi$
$499$	−8.43527	−	14.6103i	−0.377614	−	0.654047i	−0.990715	+	0.135958i	$0.956589\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	12.6008	−	21.8253i	0.562403	−	0.974110i
$503$	−5.83528			−0.260182			−0.130091	−	0.991502i	$-0.541527\pi$
$503$	−5.83528			−0.260182			−0.130091	+	0.991502i	$0.541527\pi$
$504$		0			0
$505$	14.4033			0.640939
$506$	−5.35799	+	9.28031i	−0.238192	+	0.412560i
$507$		0			0
$508$	−6.46806	−	11.2030i	−0.286974	−	0.497053i
$509$	10.7613	+	18.6391i	0.476987	+	0.826165i	0.999652	−	0.0263726i	$-0.00839563\pi$
$509$	10.7613	+	18.6391i	0.476987	+	0.826165i	−0.522665	+	0.852538i	$0.675062\pi$
$510$		0			0
$511$	4.31681	−	7.47693i	0.190964	−	0.330760i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	12.4320			0.548350
$515$	−5.45882	+	9.45495i	−0.240544	+	0.416635i
$516$		0			0
$517$	−12.4320	−	21.5328i	−0.546757	−	0.947011i
$518$	0.357990	+	0.620057i	0.0157292	+	0.0272437i
$519$		0			0
$520$	−1.55042	+	2.68540i	−0.0679902	+	0.117762i
$521$	−33.7899			−1.48036			−0.740180	−	0.672408i	$-0.765260\pi$
$521$	−33.7899			−1.48036			−0.740180	+	0.672408i	$0.765260\pi$
$522$		0			0
$523$	32.0554			1.40169			0.700843	−	0.713316i	$-0.252807\pi$
$523$	32.0554			1.40169			0.700843	+	0.713316i	$0.252807\pi$
$524$	5.72522	−	9.91636i	0.250107	−	0.433198i
$525$		0			0
$526$	5.46806	+	9.47095i	0.238419	+	0.412953i
$527$	13.6336	+	23.6141i	0.593890	+	1.02865i
$528$		0			0
$529$	−1.50924	+	2.61407i	−0.0656189	+	0.113655i
$530$	−4.71598			−0.204849
$531$		0			0
$532$	2.81681			0.122124
$533$	12.5597	−	21.7540i	0.544019	−	0.942268i
$534$		0			0
$535$	−5.50924	−	9.54228i	−0.238185	−	0.412549i
$536$	−0.307575	−	0.532735i	−0.0132852	−	0.0230106i
$537$		0			0
$538$	1.02686	−	1.77857i	0.0442711	−	0.0766798i
$539$	−2.10083			−0.0904892
$540$		0			0
$541$	16.5680			0.712316			0.356158	−	0.934426i	$-0.384087\pi$
$541$	16.5680			0.712316			0.356158	+	0.934426i	$0.384087\pi$
$542$	−1.63277	+	2.82805i	−0.0701337	+	0.121475i
$543$		0			0
$544$	3.40841	+	5.90353i	0.146134	+	0.253112i
$545$	−1.83444	−	3.17734i	−0.0785786	−	0.136102i
$546$		0			0
$547$	21.2529	−	36.8111i	0.908709	−	1.57393i	0.0928501	−	0.995680i	$-0.470402\pi$
$547$	21.2529	−	36.8111i	0.908709	−	1.57393i	0.815859	−	0.578251i	$-0.196264\pi$
$548$	0.0823593			0.00351822
$549$		0			0
$550$	2.10083			0.0895797
$551$	−1.26640	+	2.19346i	−0.0539502	+	0.0934446i
$552$		0			0
$553$	2.81681	+	4.87886i	0.119783	+	0.207470i
$554$	10.8168	+	18.7353i	0.459562	+	0.795985i
$555$		0			0
$556$	3.50000	−	6.06218i	0.148433	−	0.257094i
$557$	11.8353			0.501477			0.250738	−	0.968055i	$-0.419327\pi$
$557$	11.8353			0.501477			0.250738	+	0.968055i	$0.419327\pi$
$558$		0			0
$559$	3.10083			0.131151
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$		0			0
$562$	11.6429	+	20.1660i	0.491124	+	0.850652i
$563$	−14.2521	−	24.6853i	−0.600653	−	1.04036i	−0.992722	−	0.120426i	$-0.961574\pi$
$563$	−14.2521	−	24.6853i	−0.600653	−	1.04036i	0.392069	−	0.919936i	$-0.371759\pi$
$564$		0			0
$565$	5.72522	−	9.91636i	0.240862	−	0.417185i
$566$	−6.20166			−0.260675
$567$		0			0
$568$	4.71598			0.197878
$569$	−2.50924	+	4.34612i	−0.105193	+	0.182199i	−0.913817	−	0.406126i	$-0.866879\pi$
$569$	−2.50924	+	4.34612i	−0.105193	+	0.182199i	0.808624	+	0.588325i	$0.200213\pi$
$570$		0			0
$571$	10.1420	+	17.5665i	0.424430	+	0.735134i	0.996367	−	0.0851633i	$-0.0271412\pi$
$571$	10.1420	+	17.5665i	0.424430	+	0.735134i	−0.571937	+	0.820297i	$0.693808\pi$
$572$	−3.25716	−	5.64157i	−0.136189	−	0.235886i
$573$		0			0
$574$	4.05042	−	7.01552i	0.169061	−	0.292822i
$575$	5.10083			0.212719
$576$		0			0
$577$	10.4504			0.435057			0.217529	−	0.976054i	$-0.430200\pi$
$577$	10.4504			0.435057			0.217529	+	0.976054i	$0.430200\pi$
$578$	14.7345	−	25.5208i	0.612872	−	1.06153i
$579$		0			0
$580$	−0.449585	−	0.778704i	−0.0186680	−	0.0323339i
$581$	2.91764	+	5.05350i	0.121044	+	0.209655i
$582$		0			0
$583$	4.95374	−	8.58012i	0.205163	−	0.355352i
$584$	8.63362			0.357262
$585$		0			0
$586$	−32.3681			−1.33711
$587$	−0.315964	+	0.547266i	−0.0130412	+	0.0225881i	−0.872472	−	0.488663i	$-0.837485\pi$
$587$	−0.315964	+	0.547266i	−0.0130412	+	0.0225881i	0.859431	+	0.511252i	$0.170818\pi$
$588$		0			0
$589$	5.63362	+	9.75772i	0.232129	+	0.402060i
$590$	5.50924	+	9.54228i	0.226812	+	0.392849i
$591$		0			0
$592$	−0.357990	+	0.620057i	−0.0147133	+	0.0254842i
$593$	15.6521			0.642754			0.321377	−	0.946951i	$-0.395854\pi$
$593$	15.6521			0.642754			0.321377	+	0.946951i	$0.395854\pi$
$594$		0			0
$595$	6.81681			0.279462
$596$	−7.20166	+	12.4736i	−0.294992	+	0.510940i
$597$		0			0
$598$	−7.90841	−	13.6978i	−0.323399	−	0.560143i
$599$	21.8168	+	37.7878i	0.891411	+	1.54397i	0.838185	+	0.545386i	$0.183617\pi$
$599$	21.8168	+	37.7878i	0.891411	+	1.54397i	0.0532258	+	0.998583i	$0.483050\pi$
$600$		0			0
$601$	−17.3529	+	30.0561i	−0.707840	+	1.22601i	0.257817	+	0.966194i	$0.416997\pi$
$601$	−17.3529	+	30.0561i	−0.707840	+	1.22601i	−0.965657	+	0.259821i	$0.916337\pi$
$602$	1.00000			0.0407570
$603$		0			0
$604$	1.83528			0.0746765
$605$	3.29326	−	5.70409i	0.133890	−	0.231904i
$606$		0			0
$607$	4.56804	+	7.91208i	0.185411	+	0.321141i	0.943715	−	0.330760i	$-0.107305\pi$
$607$	4.56804	+	7.91208i	0.185411	+	0.321141i	−0.758304	+	0.651901i	$0.773972\pi$
$608$	1.40841	+	2.43943i	0.0571184	+	0.0989319i
$609$		0			0
$610$	−3.45882	+	5.99085i	−0.140044	+	0.242563i
$611$	36.6992			1.48469
$612$		0			0
$613$	1.39502			0.0563442			0.0281721	−	0.999603i	$-0.491031\pi$
$613$	1.39502			0.0563442			0.0281721	+	0.999603i	$0.491031\pi$
$614$	−3.86723	+	6.69823i	−0.156069	+	0.270319i
$615$		0			0
$616$	−1.05042	−	1.81937i	−0.0423224	−	0.0733046i
$617$	6.39078	+	11.0692i	0.257283	+	0.445627i	0.965513	−	0.260354i	$-0.0838394\pi$
$617$	6.39078	+	11.0692i	0.257283	+	0.445627i	−0.708230	+	0.705982i	$0.750506\pi$
$618$		0			0
$619$	−19.5185	+	33.8070i	−0.784514	+	1.35882i	0.144776	+	0.989465i	$0.453754\pi$
$619$	−19.5185	+	33.8070i	−0.784514	+	1.35882i	−0.929289	+	0.369353i	$0.879579\pi$
$620$	−4.00000			−0.160644
$621$		0			0
$622$	10.9714			0.439912
$623$	−6.81681	+	11.8071i	−0.273110	+	0.473040i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−5.79326	−	10.0342i	−0.231545	−	0.401048i
$627$		0			0
$628$	−10.7521	+	18.6231i	−0.429055	+	0.743144i
$629$	4.88070			0.194606
$630$		0			0
$631$	−9.32096			−0.371062			−0.185531	−	0.982638i	$-0.559400\pi$
$631$	−9.32096			−0.371062			−0.185531	+	0.982638i	$0.559400\pi$
$632$	−2.81681	+	4.87886i	−0.112047	+	0.194071i
$633$		0			0
$634$	1.07397	+	1.86017i	0.0426528	+	0.0738768i
$635$	−6.46806	−	11.2030i	−0.256677	−	0.444578i
$636$		0			0
$637$	1.55042	−	2.68540i	0.0614297	−	0.106399i
$638$	1.88900			0.0747863
$639$		0			0
$640$	−1.00000			−0.0395285
$641$	−12.3260	+	21.3493i	−0.486850	+	0.843248i	−0.999886	−	0.0151189i	$-0.995187\pi$
$641$	−12.3260	+	21.3493i	−0.486850	+	0.843248i	0.513036	+	0.858367i	$0.328521\pi$
$642$		0			0
$643$	−7.12354	−	12.3383i	−0.280925	−	0.486576i	0.690688	−	0.723153i	$-0.257308\pi$
$643$	−7.12354	−	12.3383i	−0.280925	−	0.486576i	−0.971613	+	0.236577i	$0.923975\pi$
$644$	−2.55042	−	4.41745i	−0.100500	−	0.174072i
$645$		0			0
$646$	9.60083	−	16.6291i	0.377740	−	0.654264i
$647$	−22.4570			−0.882877			−0.441439	−	0.897291i	$-0.645532\pi$
$647$	−22.4570			−0.882877			−0.441439	+	0.897291i	$0.645532\pi$
$648$		0			0
$649$	−23.1479			−0.908636
$650$	−1.55042	+	2.68540i	−0.0608123	+	0.105330i
$651$		0			0
$652$	−11.0092	−	19.0686i	−0.431155	−	0.746782i
$653$	25.0369	+	43.3653i	0.979771	+	1.69701i	0.663195	+	0.748446i	$0.269200\pi$
$653$	25.0369	+	43.3653i	0.979771	+	1.69701i	0.316576	+	0.948567i	$0.397467\pi$
$654$		0			0
$655$	5.72522	−	9.91636i	0.223703	−	0.387464i
$656$	8.10083			0.316284
$657$		0			0
$658$	11.8353			0.461387
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$	−18.3681	−	31.8144i	−0.714435	−	1.23744i	−0.963177	−	0.268868i	$-0.913350\pi$
$661$	−18.3681	−	31.8144i	−0.714435	−	1.23744i	0.248742	−	0.968570i	$-0.419983\pi$
$662$	1.08236	+	1.87470i	0.0420671	+	0.0728623i
$663$		0			0
$664$	−2.91764	+	5.05350i	−0.113226	+	0.196114i
$665$	2.81681			0.109231
$666$		0			0
$667$	4.58651			0.177590
$668$	−7.45882	+	12.9191i	−0.288590	+	0.499853i
$669$		0			0
$670$	−0.307575	−	0.532735i	−0.0118826	−	0.0205813i
$671$	−7.26640	−	12.5858i	−0.280516	−	0.485868i
$672$		0			0
$673$	−10.0824	+	17.4632i	−0.388646	+	0.673155i	−0.992268	−	0.124116i	$-0.960391\pi$
$673$	−10.0824	+	17.4632i	−0.388646	+	0.673155i	0.603621	+	0.797271i	$0.293724\pi$
$674$	31.1849			1.20120
$675$		0			0
$676$	−3.38485			−0.130187
$677$	12.2849	−	21.2780i	0.472146	−	0.817780i	−0.527346	−	0.849650i	$-0.676813\pi$
$677$	12.2849	−	21.2780i	0.472146	−	0.817780i	0.999492	+	0.0318700i	$0.0101463\pi$
$678$		0			0
$679$	−1.60083	−	2.77272i	−0.0614342	−	0.106407i
$680$	3.40841	+	5.90353i	0.130706	+	0.226390i
$681$		0			0
$682$	4.20166	−	7.27749i	0.160890	−	0.278669i
$683$	−41.7177			−1.59628			−0.798141	−	0.602470i	$-0.794183\pi$
$683$	−41.7177			−1.59628			−0.798141	+	0.602470i	$0.794183\pi$
$684$		0			0
$685$	0.0823593			0.00314679
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$		0			0
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	7.31173	+	12.6643i	0.278555	+	0.482471i
$690$		0			0
$691$	19.8353	−	34.3557i	0.754570	−	1.30695i	−0.191018	−	0.981586i	$-0.561179\pi$
$691$	19.8353	−	34.3557i	0.754570	−	1.30695i	0.945588	−	0.325367i	$-0.105488\pi$
$692$	12.0000			0.456172
$693$		0			0
$694$	−25.4218			−0.964998
$695$	3.50000	−	6.06218i	0.132763	−	0.229952i
$696$		0			0
$697$	−27.6109	−	47.8235i	−1.04584	−	1.81144i
$698$	11.3765	+	19.7046i	0.430605	+	0.745830i
$699$		0			0
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	−10.0017			−0.377759			−0.188879	−	0.982000i	$-0.560486\pi$
$701$	−10.0017			−0.377759			−0.188879	+	0.982000i	$0.560486\pi$
$702$		0			0
$703$	2.01678			0.0760643
$704$	1.05042	−	1.81937i	0.0395890	−	0.0685702i
$705$		0			0
$706$	15.6008	+	27.0214i	0.587145	+	1.01696i
$707$	−7.20166	−	12.4736i	−0.270846	−	0.469120i
$708$		0			0
$709$	−14.7336	+	25.5194i	−0.553332	+	0.958399i	0.444699	+	0.895680i	$0.353311\pi$
$709$	−14.7336	+	25.5194i	−0.553332	+	0.958399i	−0.998031	+	0.0627193i	$0.980023\pi$
$710$	4.71598			0.176988
$711$		0			0
$712$	−13.6336			−0.510942
$713$	10.2017	−	17.6698i	0.382055	−	0.661739i
$714$		0			0
$715$	−3.25716	−	5.64157i	−0.121811	−	0.210983i
$716$	6.19243	+	10.7256i	0.231422	+	0.400834i
$717$		0			0
$718$	−6.17480	+	10.6951i	−0.230441	+	0.399136i
$719$	−29.8000			−1.11135			−0.555677	−	0.831398i	$-0.687541\pi$
$719$	−29.8000			−1.11135			−0.555677	+	0.831398i	$0.687541\pi$
$720$		0			0
$721$	10.9176			0.406594
$722$	−5.53279	+	9.58307i	−0.205909	+	0.356645i
$723$		0			0
$724$	11.7345	+	20.3247i	0.436107	+	0.755360i
$725$	−0.449585	−	0.778704i	−0.0166972	−	0.0289203i
$726$		0			0
$727$	−0.357990	+	0.620057i	−0.0132771	+	0.0229966i	−0.872588	−	0.488458i	$-0.837560\pi$
$727$	−0.357990	+	0.620057i	−0.0132771	+	0.0229966i	0.859311	+	0.511454i	$0.170893\pi$
$728$	3.10083			0.114924
$729$		0			0
$730$	8.63362			0.319545
$731$	3.40841	−	5.90353i	0.126064	−	0.218350i
$732$		0			0
$733$	0.698355	+	1.20959i	0.0257943	+	0.0446771i	0.878634	−	0.477495i	$-0.158455\pi$
$733$	0.698355	+	1.20959i	0.0257943	+	0.0446771i	−0.852840	+	0.522172i	$0.825122\pi$
$734$	−11.0924	−	19.2127i	−0.409429	−	0.709153i
$735$		0			0
$736$	2.55042	−	4.41745i	0.0940096	−	0.162829i
$737$	1.29232			0.0476034
$738$		0			0
$739$	−17.0017			−0.625417			−0.312709	−	0.949849i	$-0.601236\pi$
$739$	−17.0017			−0.625417			−0.312709	+	0.949849i	$0.601236\pi$
$740$	−0.357990	+	0.620057i	−0.0131600	+	0.0227937i
$741$		0			0
$742$	2.35799	+	4.08416i	0.0865645	+	0.149934i
$743$	7.20166	+	12.4736i	0.264203	+	0.457614i	0.967355	−	0.253427i	$-0.0815577\pi$
$743$	7.20166	+	12.4736i	0.264203	+	0.457614i	−0.703151	+	0.711040i	$0.748224\pi$
$744$		0			0
$745$	−7.20166	+	12.4736i	−0.263848	+	0.456999i
$746$	−12.3664			−0.452765
$747$		0			0
$748$	−14.3210			−0.523626
$749$	−5.50924	+	9.54228i	−0.201303	+	0.348667i
$750$		0			0
$751$	−20.6790	−	35.8170i	−0.754586	−	1.30698i	−0.945580	−	0.325390i	$-0.894505\pi$
$751$	−20.6790	−	35.8170i	−0.754586	−	1.30698i	0.190994	−	0.981591i	$-0.438829\pi$
$752$	5.91764	+	10.2497i	0.215794	+	0.373766i
$753$		0			0
$754$	−1.39409	+	2.41463i	−0.0507696	+	0.0879356i
$755$	1.83528			0.0667927
$756$		0			0
$757$	8.51432			0.309458			0.154729	−	0.987957i	$-0.450550\pi$
$757$	8.51432			0.309458			0.154729	+	0.987957i	$0.450550\pi$
$758$	8.59244	−	14.8825i	0.312092	−	0.540558i
$759$		0			0
$760$	1.40841	+	2.43943i	0.0510882	+	0.0884874i
$761$	−7.58651	−	13.1402i	−0.275011	−	0.476333i	0.695127	−	0.718887i	$-0.255348\pi$
$761$	−7.58651	−	13.1402i	−0.275011	−	0.476333i	−0.970138	+	0.242554i	$0.922015\pi$
$762$		0			0
$763$	−1.83444	+	3.17734i	−0.0664110	+	0.115027i
$764$	21.2672			0.769422
$765$		0			0
$766$	−21.2672			−0.768417
$767$	17.0832	−	29.5890i	0.616839	−	1.06840i
$768$		0			0
$769$	−20.3117	−	35.1809i	−0.732460	−	1.26866i	−0.955829	−	0.293923i	$-0.905039\pi$
$769$	−20.3117	−	35.1809i	−0.732460	−	1.26866i	0.223369	−	0.974734i	$-0.428294\pi$
$770$	−1.05042	−	1.81937i	−0.0378543	−	0.0655656i
$771$		0			0
$772$	−3.57397	+	6.19030i	−0.128630	+	0.222794i
$773$	36.5697			1.31532			0.657661	−	0.753314i	$-0.271546\pi$
$773$	36.5697			1.31532			0.657661	+	0.753314i	$0.271546\pi$
$774$		0			0
$775$	−4.00000			−0.143684
$776$	1.60083	−	2.77272i	0.0574665	−	0.0995348i
$777$		0			0
$778$	2.01847	+	3.49609i	0.0723657	+	0.125341i
$779$	−11.4093	−	19.7614i	−0.408779	−	0.708026i
$780$		0			0
$781$	−4.95374	+	8.58012i	−0.177259	+	0.307021i
$782$	−34.7714			−1.24342
$783$		0			0
$784$	1.00000			0.0357143
$785$	−10.7521	+	18.6231i	−0.383758	+	0.664688i
$786$		0			0
$787$	−2.93611	−	5.08549i	−0.104661	−	0.181278i	0.808939	−	0.587893i	$-0.200042\pi$
$787$	−2.93611	−	5.08549i	−0.104661	−	0.181278i	−0.913600	+	0.406615i	$0.866709\pi$
$788$	−10.3765	−	17.9726i	−0.369646	−	0.640246i
$789$		0			0
$790$	−2.81681	+	4.87886i	−0.100218	+	0.173582i
$791$	−11.4504			−0.407130
$792$		0			0
$793$	21.4504			0.761727
$794$	18.3857	−	31.8450i	0.652484	−	1.13014i
$795$		0			0
$796$	0.733605	+	1.27064i	0.0260019	+	0.0450367i
$797$	−12.2672	−	21.2475i	−0.434528	−	0.752625i	0.562729	−	0.826641i	$-0.309751\pi$
$797$	−12.2672	−	21.2475i	−0.434528	−	0.752625i	−0.997257	+	0.0740169i	$0.976418\pi$
$798$		0			0
$799$	40.3394	−	69.8699i	1.42711	−	2.47182i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$	8.67056			0.306168
$803$	−9.06889	+	15.7078i	−0.320034	+	0.554315i
$804$		0			0
$805$	−2.55042	−	4.41745i	−0.0898903	−	0.155695i
$806$	6.20166	+	10.7416i	0.218444	+	0.378356i
$807$		0			0
$808$	7.20166	−	12.4736i	0.253354	−	0.438821i
$809$	−35.0185			−1.23118			−0.615592	−	0.788065i	$-0.711083\pi$
$809$	−35.0185			−1.23118			−0.615592	+	0.788065i	$0.711083\pi$
$810$		0			0
$811$	−21.7882			−0.765086			−0.382543	−	0.923938i	$-0.624952\pi$
$811$	−21.7882			−0.765086			−0.382543	+	0.923938i	$0.624952\pi$
$812$	−0.449585	+	0.778704i	−0.0157773	+	0.0273271i
$813$		0			0
$814$	−0.752076	−	1.30263i	−0.0263603	−	0.0456573i
$815$	−11.0092	−	19.0686i	−0.385637	−	0.667942i
$816$		0			0
$817$	1.40841	−	2.43943i	0.0492739	−	0.0853448i
$818$	35.7714			1.25072
$819$		0			0
$820$	8.10083			0.282893
$821$	9.83444	−	17.0337i	0.343224	−	0.594482i	−0.641805	−	0.766868i	$-0.721814\pi$
$821$	9.83444	−	17.0337i	0.343224	−	0.594482i	0.985029	+	0.172386i	$0.0551476\pi$
$822$		0			0
$823$	3.73360	+	6.46679i	0.130145	+	0.225418i	0.923732	−	0.383038i	$-0.125122\pi$
$823$	3.73360	+	6.46679i	0.130145	+	0.225418i	−0.793587	+	0.608457i	$0.791789\pi$
$824$	5.45882	+	9.45495i	0.190167	+	0.329379i
$825$		0			0
$826$	5.50924	−	9.54228i	0.191691	−	0.332018i
$827$	−10.7512			−0.373857			−0.186928	−	0.982374i	$-0.559853\pi$
$827$	−10.7512			−0.373857			−0.186928	+	0.982374i	$0.559853\pi$
$828$		0			0
$829$	−31.0083			−1.07696			−0.538481	−	0.842637i	$-0.681002\pi$
$829$	−31.0083			−1.07696			−0.538481	+	0.842637i	$0.681002\pi$
$830$	−2.91764	+	5.05350i	−0.101273	+	0.175410i
$831$		0			0
$832$	1.55042	+	2.68540i	0.0537510	+	0.0930994i
$833$	−3.40841	−	5.90353i	−0.118094	−	0.204545i
$834$		0			0
$835$	−7.45882	+	12.9191i	−0.258123	+	0.447082i
$836$	−5.91764			−0.204666
$837$		0			0
$838$	−7.85375			−0.271303
$839$	−2.50331	+	4.33585i	−0.0864237	+	0.149690i	−0.905997	−	0.423284i	$-0.860877\pi$
$839$	−2.50331	+	4.33585i	−0.0864237	+	0.149690i	0.819573	+	0.572974i	$0.194211\pi$
$840$		0			0
$841$	14.0957	+	24.4146i	0.486060	+	0.841881i
$842$	17.1017	+	29.6210i	0.589363	+	1.02081i
$843$		0			0
$844$	5.81681	−	10.0750i	0.200223	−	0.346796i
$845$	−3.38485			−0.116442
$846$		0			0
$847$	−6.58651			−0.226315
$848$	−2.35799	+	4.08416i	−0.0809737	+	0.140251i
$849$		0			0
$850$	3.40841	+	5.90353i	0.116907	+	0.202489i
$851$	−1.82605	−	3.16280i	−0.0625960	−	0.108420i
$852$		0			0
$853$	−15.8705	+	27.4886i	−0.543397	+	0.941191i	0.455309	+	0.890333i	$0.349529\pi$
$853$	−15.8705	+	27.4886i	−0.543397	+	0.941191i	−0.998706	+	0.0508573i	$0.983805\pi$
$854$	6.91764			0.236717
$855$		0			0
$856$	−11.0185			−0.376604
$857$	15.6244	−	27.0622i	0.533719	−	0.924428i	−0.465505	−	0.885045i	$-0.654127\pi$
$857$	15.6244	−	27.0622i	0.533719	−	0.924428i	0.999224	−	0.0393831i	$-0.0125393\pi$
$858$		0			0
$859$	7.50924	+	13.0064i	0.256212	+	0.443772i	0.965224	−	0.261424i	$-0.0841922\pi$
$859$	7.50924	+	13.0064i	0.256212	+	0.443772i	−0.709012	+	0.705196i	$0.750859\pi$
$860$	0.500000	+	0.866025i	0.0170499	+	0.0295312i
$861$		0			0
$862$	−12.7345	+	22.0567i	−0.433737	+	0.751255i
$863$	−17.8353			−0.607120			−0.303560	−	0.952812i	$-0.598175\pi$
$863$	−17.8353			−0.607120			−0.303560	+	0.952812i	$0.598175\pi$
$864$		0			0
$865$	12.0000			0.408012
$866$	14.5000	−	25.1147i	0.492730	−	0.853433i
$867$		0			0
$868$	2.00000	+	3.46410i	0.0678844	+	0.117579i
$869$	−5.91764	−	10.2497i	−0.200742	−	0.347696i
$870$		0			0
$871$	−0.953737	+	1.65192i	−0.0323161	+	0.0559732i
$872$	−3.66887			−0.124244
$873$		0			0
$874$	−14.3681			−0.486007
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$		0			0
$877$	2.94450	+	5.10003i	0.0994287	+	0.172216i	0.911448	−	0.411415i	$-0.134965\pi$
$877$	2.94450	+	5.10003i	0.0994287	+	0.172216i	−0.812020	+	0.583630i	$0.801632\pi$
$878$	4.36723	+	7.56426i	0.147387	+	0.255281i
$879$		0			0
$880$	1.05042	−	1.81937i	0.0354095	−	0.0613310i
$881$	−7.85375			−0.264600			−0.132300	−	0.991210i	$-0.542236\pi$
$881$	−7.85375			−0.264600			−0.132300	+	0.991210i	$0.542236\pi$
$882$		0			0
$883$	13.1127			0.441277			0.220639	−	0.975356i	$-0.429186\pi$
$883$	13.1127			0.441277			0.220639	+	0.975356i	$0.429186\pi$
$884$	10.5689	−	18.3058i	0.355470	−	0.615692i
$885$		0			0
$886$	9.08651	+	15.7383i	0.305267	+	0.528739i
$887$	−22.8538	−	39.5839i	−0.767354	−	1.32910i	−0.938993	−	0.343936i	$-0.888240\pi$
$887$	−22.8538	−	39.5839i	−0.767354	−	1.32910i	0.171639	−	0.985160i	$-0.445094\pi$
$888$		0			0
$889$	−6.46806	+	11.2030i	−0.216932	+	0.375737i
$890$	−13.6336			−0.457000
$891$		0			0
$892$	21.1193			0.707127
$893$	16.6689	−	28.8713i	0.557802	−	0.966142i
$894$		0			0
$895$	6.19243	+	10.7256i	0.206990	+	0.358517i
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$		0			0
$898$	1.61007	−	2.78872i	0.0537286	−	0.0930607i
$899$	−3.59668			−0.119956
$900$		0			0
$901$	32.1479			1.07100
$902$	−8.50924	+	14.7384i	−0.283327	+	0.490736i
$903$		0			0
$904$	−5.72522	−	9.91636i	−0.190418	−	0.329813i
$905$	11.7345	+	20.3247i	0.390066	+	0.675615i
$906$		0			0
$907$	23.7580	−	41.1501i	0.788872	−	1.36637i	−0.137787	−	0.990462i	$-0.543999\pi$
$907$	23.7580	−	41.1501i	0.788872	−	1.36637i	0.926659	−	0.375904i	$-0.122668\pi$
$908$	−27.1849			−0.902162
$909$		0			0
$910$	3.10083			0.102792
$911$	−15.9445	+	27.6167i	−0.528265	+	0.914982i	0.471192	+	0.882031i	$0.343824\pi$
$911$	−15.9445	+	27.6167i	−0.528265	+	0.914982i	−0.999457	+	0.0329510i	$0.989509\pi$
$912$		0			0
$913$	−6.12947	−	10.6166i	−0.202856	−	0.351357i
$914$	3.76640	+	6.52359i	0.124581	+	0.215781i
$915$		0			0
$916$	11.9916	−	20.7701i	0.396214	−	0.686263i
$917$	−11.4504			−0.378127
$918$		0			0
$919$	0.110997			0.00366146			0.00183073	−	0.999998i	$-0.499417\pi$
$919$	0.110997			0.00366146			0.00183073	+	0.999998i	$0.499417\pi$
$920$	2.55042	−	4.41745i	0.0840847	−	0.145639i
$921$		0			0
$922$	13.8437	+	23.9779i	0.455917	+	0.789671i
$923$	−7.31173	−	12.6643i	−0.240668	−	0.416850i
$924$		0			0
$925$	−0.357990	+	0.620057i	−0.0117706	+	0.0203873i
$926$	13.2672			0.435989
$927$		0			0
$928$	−0.899170			−0.0295167
$929$	12.6873	−	21.9751i	0.416258	−	0.720980i	−0.579301	−	0.815113i	$-0.696675\pi$
$929$	12.6873	−	21.9751i	0.416258	−	0.720980i	0.995560	+	0.0941331i	$0.0300079\pi$
$930$		0			0
$931$	−1.40841	−	2.43943i	−0.0461586	−	0.0799491i
$932$	7.86723	+	13.6264i	0.257700	+	0.446349i
$933$		0			0
$934$	−12.7285	+	22.0464i	−0.416490	+	0.721382i
$935$	−14.3210			−0.468346
$936$		0			0
$937$	−57.5613			−1.88044			−0.940222	−	0.340562i	$-0.889383\pi$
$937$	−57.5613			−1.88044			−0.940222	+	0.340562i	$0.889383\pi$
$938$	−0.307575	+	0.532735i	−0.0100427	+	0.0173944i
$939$		0			0
$940$	5.91764	+	10.2497i	0.193012	+	0.334307i
$941$	−7.11930	−	12.3310i	−0.232083	−	0.401979i	0.726338	−	0.687337i	$-0.241221\pi$
$941$	−7.11930	−	12.3310i	−0.232083	−	0.401979i	−0.958421	+	0.285359i	$0.907887\pi$
$942$		0			0
$943$	−20.6605	+	35.7850i	−0.672798	+	1.16532i
$944$	11.0185			0.358621
$945$		0			0
$946$	−2.10083			−0.0683039
$947$	−16.7201	+	28.9601i	−0.543331	+	0.941077i	0.455379	+	0.890298i	$0.349504\pi$
$947$	−16.7201	+	28.9601i	−0.543331	+	0.941077i	−0.998710	+	0.0507795i	$0.983829\pi$
$948$		0			0
$949$	−13.3857	−	23.1847i	−0.434518	−	0.752607i
$950$	1.40841	+	2.43943i	0.0456947	+	0.0791455i
$951$		0			0
$952$	3.40841	−	5.90353i	0.110467	−	0.191335i
$953$	25.9361			0.840153			0.420077	−	0.907489i	$-0.362003\pi$
$953$	25.9361			0.840153			0.420077	+	0.907489i	$0.362003\pi$
$954$		0			0
$955$	21.2672			0.688192
$956$	8.01847	−	13.8884i	0.259336	−	0.449183i
$957$		0			0
$958$	−14.0361	−	24.3112i	−0.453486	−	0.785460i
$959$	−0.0411797	−	0.0713253i	−0.00132976	−	0.00230321i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	2.22013			0.0715799
$963$		0			0
$964$	−14.2840			−0.460057
$965$	−3.57397	+	6.19030i	−0.115050	+	0.199273i
$966$		0			0
$967$	−25.8722	−	44.8120i	−0.831995	−	1.44106i	−0.896454	−	0.443137i	$-0.853866\pi$
$967$	−25.8722	−	44.8120i	−0.831995	−	1.44106i	0.0644595	−	0.997920i	$-0.479468\pi$
$968$	−3.29326	−	5.70409i	−0.105849	−	0.183336i
$969$		0			0
$970$	1.60083	−	2.77272i	0.0513996	−	0.0890267i
$971$	20.0739			0.644202			0.322101	−	0.946705i	$-0.395611\pi$
$971$	20.0739			0.644202			0.322101	+	0.946705i	$0.395611\pi$
$972$		0			0
$973$	−7.00000			−0.224410
$974$	5.71598	−	9.90037i	0.183152	−	0.317228i
$975$		0			0
$976$	3.45882	+	5.99085i	0.110714	+	0.191763i
$977$	1.02271	+	1.77138i	0.0327193	+	0.0566716i	0.881921	−	0.471397i	$-0.156250\pi$
$977$	1.02271	+	1.77138i	0.0327193	+	0.0566716i	−0.849202	+	0.528068i	$0.822917\pi$
$978$		0			0
$979$	14.3210	−	24.8046i	0.457700	−	0.792760i
$980$	1.00000			0.0319438
$981$		0			0
$982$	−34.9832			−1.11636
$983$	−23.8353	+	41.2839i	−0.760227	+	1.31675i	0.182506	+	0.983205i	$0.441579\pi$
$983$	−23.8353	+	41.2839i	−0.760227	+	1.31675i	−0.942733	+	0.333548i	$0.891754\pi$
$984$		0			0
$985$	−10.3765	−	17.9726i	−0.330622	−	0.572653i
$986$	3.06473	+	5.30828i	0.0976010	+	0.169050i
$987$		0			0
$988$	4.36723	−	7.56426i	0.138940	−	0.240651i
$989$	−5.10083			−0.162197
$990$		0			0
$991$	−62.0369			−1.97067			−0.985334	−	0.170636i	$-0.945418\pi$
$991$	−62.0369			−1.97067			−0.985334	+	0.170636i	$0.945418\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$		0			0
$994$	−2.35799	−	4.08416i	−0.0747909	−	0.129542i
$995$	0.733605	+	1.27064i	0.0232568	+	0.0402820i
$996$		0			0
$997$	−0.568040	+	0.983875i	−0.0179900	+	0.0311596i	−0.874880	−	0.484339i	$-0.839060\pi$
$997$	−0.568040	+	0.983875i	−0.0179900	+	0.0311596i	0.856890	+	0.515499i	$0.172393\pi$
$998$	−16.8705			−0.534027
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.j.i.1261.3		6
3.2	odd	2		630.2.j.j.421.2	yes	6
9.2	odd	6		5670.2.a.br.1.3		3
9.4	even	3	inner	1890.2.j.i.631.3		6
9.5	odd	6		630.2.j.j.211.2	✓	6
9.7	even	3		5670.2.a.bq.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.j.211.2	✓	6	9.5	odd	6
630.2.j.j.421.2	yes	6	3.2	odd	2
1890.2.j.i.631.3		6	9.4	even	3	inner
1890.2.j.i.1261.3		6	1.1	even	1	trivial
5670.2.a.bq.1.1		3	9.7	even	3
5670.2.a.br.1.3		3	9.2	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.j (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -1.00000 q^{10} +(1.05042 - 1.81937i) q^{11} +(1.55042 + 2.68540i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +6.81681 q^{17} +2.81681 q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.05042 - 1.81937i) q^{22} +(-2.55042 - 4.41745i) q^{23} +(-0.500000 + 0.866025i) q^{25} +3.10083 q^{26} +1.00000 q^{28} +(-0.449585 + 0.778704i) q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.40841 - 5.90353i) q^{34} +1.00000 q^{35} +0.715980 q^{37} +(1.40841 - 2.43943i) q^{38} +(0.500000 + 0.866025i) q^{40} +(-4.05042 - 7.01552i) q^{41} +(0.500000 - 0.866025i) q^{43} -2.10083 q^{44} -5.10083 q^{46} +(5.91764 - 10.2497i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(1.55042 - 2.68540i) q^{52} +4.71598 q^{53} -2.10083 q^{55} +(0.500000 - 0.866025i) q^{56} +(0.449585 + 0.778704i) q^{58} +(-5.50924 - 9.54228i) q^{59} +(3.45882 - 5.99085i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(1.55042 - 2.68540i) q^{65} +(0.307575 + 0.532735i) q^{67} +(-3.40841 - 5.90353i) q^{68} +(0.500000 - 0.866025i) q^{70} -4.71598 q^{71} -8.63362 q^{73} +(0.357990 - 0.620057i) q^{74} +(-1.40841 - 2.43943i) q^{76} +(1.05042 + 1.81937i) q^{77} +(2.81681 - 4.87886i) q^{79} +1.00000 q^{80} -8.10083 q^{82} +(2.91764 - 5.05350i) q^{83} +(-3.40841 - 5.90353i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(-1.05042 + 1.81937i) q^{88} +13.6336 q^{89} -3.10083 q^{91} +(-2.55042 + 4.41745i) q^{92} +(-5.91764 - 10.2497i) q^{94} +(-1.40841 - 2.43943i) q^{95} +(-1.60083 + 2.77272i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 6 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 3 q^{11} + 3 q^{14} - 3 q^{16} + 18 q^{17} - 6 q^{19} - 3 q^{20} + 3 q^{22} - 6 q^{23} - 3 q^{25} + 6 q^{28} - 12 q^{29} + 12 q^{31} + 3 q^{32} + 9 q^{34} + 6 q^{35} - 3 q^{38} + 3 q^{40} - 15 q^{41} + 3 q^{43} + 6 q^{44} - 12 q^{46} - 6 q^{47} - 3 q^{49} + 3 q^{50} + 24 q^{53} + 6 q^{55} + 3 q^{56} + 12 q^{58} - 3 q^{59} + 24 q^{62} + 6 q^{64} + 9 q^{67} - 9 q^{68} + 3 q^{70} - 24 q^{71} - 6 q^{73} + 3 q^{76} - 3 q^{77} - 6 q^{79} + 6 q^{80} - 30 q^{82} - 24 q^{83} - 9 q^{85} - 3 q^{86} + 3 q^{88} + 36 q^{89} - 6 q^{92} + 6 q^{94} + 3 q^{95} + 9 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 3 * q^11 + 3 * q^14 - 3 * q^16 + 18 * q^17 - 6 * q^19 - 3 * q^20 + 3 * q^22 - 6 * q^23 - 3 * q^25 + 6 * q^28 - 12 * q^29 + 12 * q^31 + 3 * q^32 + 9 * q^34 + 6 * q^35 - 3 * q^38 + 3 * q^40 - 15 * q^41 + 3 * q^43 + 6 * q^44 - 12 * q^46 - 6 * q^47 - 3 * q^49 + 3 * q^50 + 24 * q^53 + 6 * q^55 + 3 * q^56 + 12 * q^58 - 3 * q^59 + 24 * q^62 + 6 * q^64 + 9 * q^67 - 9 * q^68 + 3 * q^70 - 24 * q^71 - 6 * q^73 + 3 * q^76 - 3 * q^77 - 6 * q^79 + 6 * q^80 - 30 * q^82 - 24 * q^83 - 9 * q^85 - 3 * q^86 + 3 * q^88 + 36 * q^89 - 6 * q^92 + 6 * q^94 + 3 * q^95 + 9 * q^97 - 6 * q^98

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