LMFDB - Embedded newform 440.2.y.d.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [440,2,Mod(81,440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(440, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("440.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.y (of order $5$, degree $4$, 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:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 141 x^{12} - 220 x^{11} + 1105 x^{10} - 1935 x^{9} + \cdots + 10000 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 141x^12 - 220x^11 + 1105x^10 - 1935x^9 + 9865x^8 - 18475x^7 + 34075x^6 - 18400x^5 + 23025x^4 + 26000x^3 + 41000x^2 + 25000*x + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.3
Root			$-0.460979 + 0.334921i$ of defining polynomial
Character	$\chi$	$=$	440.361
Dual form			440.2.y.d.401.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.460979 - 0.334921i) q^{3} +(0.309017 + 0.951057i) q^{5} +(1.47331 + 1.07042i) q^{7} +(-0.826721 + 2.54439i) q^{9} +(-1.20724 + 3.08910i) q^{11} +(-1.21340 + 3.73445i) q^{13} +(0.460979 + 0.334921i) q^{15} +(-0.983630 - 3.02730i) q^{17} +(6.64420 - 4.82729i) q^{19} +1.03767 q^{21} +0.734122 q^{23} +(-0.809017 + 0.587785i) q^{25} +(0.999301 + 3.07553i) q^{27} +(3.58354 + 2.60360i) q^{29} +(-0.122675 + 0.377554i) q^{31} +(0.478092 + 1.82834i) q^{33} +(-0.562754 + 1.73198i) q^{35} +(-2.42201 - 1.75969i) q^{37} +(0.691395 + 2.12789i) q^{39} +(-9.74982 + 7.08366i) q^{41} +8.72957 q^{43} -2.67533 q^{45} +(8.50332 - 6.17803i) q^{47} +(-1.13828 - 3.50328i) q^{49} +(-1.46734 - 1.06608i) q^{51} +(3.04271 - 9.36451i) q^{53} +(-3.31097 - 0.193570i) q^{55} +(1.44607 - 4.45056i) q^{57} +(-8.09998 - 5.88498i) q^{59} +(2.62936 + 8.09234i) q^{61} +(-3.94158 + 2.86373i) q^{63} -3.92663 q^{65} +1.11105 q^{67} +(0.338415 - 0.245873i) q^{69} +(1.81446 + 5.58434i) q^{71} +(-3.26510 - 2.37223i) q^{73} +(-0.176078 + 0.541913i) q^{75} +(-5.08528 + 3.25894i) q^{77} +(1.00977 - 3.10775i) q^{79} +(-5.00244 - 3.63448i) q^{81} +(-3.66402 - 11.2767i) q^{83} +(2.57518 - 1.87098i) q^{85} +2.52394 q^{87} -6.56220 q^{89} +(-5.78514 + 4.20315i) q^{91} +(0.0699002 + 0.215131i) q^{93} +(6.64420 + 4.82729i) q^{95} +(4.49404 - 13.8312i) q^{97} +(-6.86182 - 5.62552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{3} - 4 q^{5} + 8 q^{7} - 7 q^{9} - 7 q^{11} - 11 q^{13} - 3 q^{15} + 9 q^{17} - 2 q^{19} + 12 q^{21} + 20 q^{23} - 4 q^{25} - 9 q^{27} + q^{29} - 2 q^{31} - 32 q^{33} - 2 q^{35} - 16 q^{37}+ \cdots - 10 q^{99}+O(q^{100}) $ 16 * q - 3 * q^3 - 4 * q^5 + 8 * q^7 - 7 * q^9 - 7 * q^11 - 11 * q^13 - 3 * q^15 + 9 * q^17 - 2 * q^19 + 12 * q^21 + 20 * q^23 - 4 * q^25 - 9 * q^27 + q^29 - 2 * q^31 - 32 * q^33 - 2 * q^35 - 16 * q^37 + 3 * q^39 - 11 * q^41 - 16 * q^43 + 38 * q^45 - 10 * q^47 + 4 * q^49 + 26 * q^51 - 9 * q^53 + 3 * q^55 - 50 * q^57 - 60 * q^59 + 30 * q^61 + 52 * q^63 + 24 * q^65 - 4 * q^67 + 41 * q^69 - 10 * q^71 + q^73 + 2 * q^75 - 4 * q^77 + 19 * q^79 - 31 * q^81 + 64 * q^83 - 11 * q^85 + 30 * q^87 + 24 * q^89 - 9 * q^91 + 45 * q^93 - 2 * q^95 - 3 * q^97 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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			0
$2$		0			0
$3$	0.460979	−	0.334921i	0.266146	−	0.193367i	−0.446706	−	0.894681i	$-0.647403\pi$
$3$	0.460979	−	0.334921i	0.266146	−	0.193367i	0.712852	+	0.701314i	$0.247403\pi$
$4$		0			0
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$		0			0
$7$	1.47331	+	1.07042i	0.556858	+	0.404581i	0.830308	−	0.557305i	$-0.188165\pi$
$7$	1.47331	+	1.07042i	0.556858	+	0.404581i	−0.273450	+	0.961886i	$0.588165\pi$
$8$		0			0
$9$	−0.826721	+	2.54439i	−0.275574	+	0.848129i
$10$		0			0
$11$	−1.20724	+	3.08910i	−0.363997	+	0.931400i
$11$	−1.20724	+	3.08910i	−0.363997	+	0.931400i
$12$		0			0
$13$	−1.21340	+	3.73445i	−0.336536	+	1.03575i	0.629425	+	0.777061i	$0.283291\pi$
$13$	−1.21340	+	3.73445i	−0.336536	+	1.03575i	−0.965961	+	0.258689i	$0.916709\pi$
$14$		0			0
$15$	0.460979	+	0.334921i	0.119024	+	0.0864761i
$16$		0			0
$17$	−0.983630	−	3.02730i	−0.238565	−	0.734229i	−0.996628	−	0.0820473i	$-0.973854\pi$
$17$	−0.983630	−	3.02730i	−0.238565	−	0.734229i	0.758063	−	0.652181i	$-0.226146\pi$
$18$		0			0
$19$	6.64420	−	4.82729i	1.52428	−	1.10746i	0.564971	−	0.825111i	$-0.308887\pi$
$19$	6.64420	−	4.82729i	1.52428	−	1.10746i	0.959313	−	0.282346i	$-0.0911127\pi$
$20$		0			0
$21$	1.03767			0.226438
$22$		0			0
$23$	0.734122			0.153075			0.0765376	−	0.997067i	$-0.475613\pi$
$23$	0.734122			0.153075			0.0765376	+	0.997067i	$0.475613\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	0.999301	+	3.07553i	0.192316	+	0.591887i
$28$		0			0
$29$	3.58354	+	2.60360i	0.665447	+	0.483476i	0.868498	−	0.495693i	$-0.165086\pi$
$29$	3.58354	+	2.60360i	0.665447	+	0.483476i	−0.203051	+	0.979168i	$0.565086\pi$
$30$		0			0
$31$	−0.122675	+	0.377554i	−0.0220330	+	0.0678107i	−0.961468	−	0.274915i	$-0.911350\pi$
$31$	−0.122675	+	0.377554i	−0.0220330	+	0.0678107i	0.939435	+	0.342726i	$0.111350\pi$
$32$		0			0
$33$	0.478092	+	1.82834i	0.0832251	+	0.318273i
$34$		0			0
$35$	−0.562754	+	1.73198i	−0.0951227	+	0.292758i
$36$		0			0
$37$	−2.42201	−	1.75969i	−0.398175	−	0.289291i	0.370622	−	0.928784i	$-0.379145\pi$
$37$	−2.42201	−	1.75969i	−0.398175	−	0.289291i	−0.768797	+	0.639492i	$0.779145\pi$
$38$		0			0
$39$	0.691395	+	2.12789i	0.110712	+	0.340736i
$40$		0			0
$41$	−9.74982	+	7.08366i	−1.52267	+	1.10628i	−0.562521	+	0.826783i	$0.690168\pi$
$41$	−9.74982	+	7.08366i	−1.52267	+	1.10628i	−0.960146	+	0.279499i	$0.909832\pi$
$42$		0			0
$43$	8.72957			1.33125			0.665624	−	0.746288i	$-0.268166\pi$
$43$	8.72957			1.33125			0.665624	+	0.746288i	$0.268166\pi$
$44$		0			0
$45$	−2.67533			−0.398814
$46$		0			0
$47$	8.50332	−	6.17803i	1.24034	−	0.901158i	0.242716	−	0.970097i	$-0.421962\pi$
$47$	8.50332	−	6.17803i	1.24034	−	0.901158i	0.997621	+	0.0689397i	$0.0219616\pi$
$48$		0			0
$49$	−1.13828	−	3.50328i	−0.162612	−	0.500468i
$50$		0			0
$51$	−1.46734	−	1.06608i	−0.205468	−	0.149282i
$52$		0			0
$53$	3.04271	−	9.36451i	0.417949	−	1.28631i	−0.491638	−	0.870800i	$-0.663602\pi$
$53$	3.04271	−	9.36451i	0.417949	−	1.28631i	0.909587	−	0.415515i	$-0.136398\pi$
$54$		0			0
$55$	−3.31097	−	0.193570i	−0.446451	−	0.0261009i
$56$		0			0
$57$	1.44607	−	4.45056i	0.191537	−	0.589491i
$58$		0			0
$59$	−8.09998	−	5.88498i	−1.05453	−	0.766159i	−0.0814595	−	0.996677i	$-0.525958\pi$
$59$	−8.09998	−	5.88498i	−1.05453	−	0.766159i	−0.973068	+	0.230517i	$0.925958\pi$
$60$		0			0
$61$	2.62936	+	8.09234i	0.336655	+	1.03612i	0.965901	+	0.258911i	$0.0833637\pi$
$61$	2.62936	+	8.09234i	0.336655	+	1.03612i	−0.629246	+	0.777206i	$0.716636\pi$
$62$		0			0
$63$	−3.94158	+	2.86373i	−0.496592	+	0.360796i
$64$		0			0
$65$	−3.92663			−0.487039
$66$		0			0
$67$	1.11105			0.135737			0.0678684	−	0.997694i	$-0.478380\pi$
$67$	1.11105			0.135737			0.0678684	+	0.997694i	$0.478380\pi$
$68$		0			0
$69$	0.338415	−	0.245873i	0.0407404	−	0.0295996i
$70$		0			0
$71$	1.81446	+	5.58434i	0.215337	+	0.662739i	0.999130	+	0.0417161i	$0.0132825\pi$
$71$	1.81446	+	5.58434i	0.215337	+	0.662739i	−0.783793	+	0.621023i	$0.786717\pi$
$72$		0			0
$73$	−3.26510	−	2.37223i	−0.382151	−	0.277649i	0.380081	−	0.924953i	$-0.375896\pi$
$73$	−3.26510	−	2.37223i	−0.382151	−	0.277649i	−0.762232	+	0.647304i	$0.775896\pi$
$74$		0			0
$75$	−0.176078	+	0.541913i	−0.0203318	+	0.0625747i
$76$		0			0
$77$	−5.08528	+	3.25894i	−0.579522	+	0.371391i
$78$		0			0
$79$	1.00977	−	3.10775i	0.113608	−	0.349649i	−0.878046	−	0.478576i	$-0.841153\pi$
$79$	1.00977	−	3.10775i	0.113608	−	0.349649i	0.991654	+	0.128927i	$0.0411532\pi$
$80$		0			0
$81$	−5.00244	−	3.63448i	−0.555826	−	0.403832i
$82$		0			0
$83$	−3.66402	−	11.2767i	−0.402179	−	1.23778i	−0.923228	−	0.384252i	$-0.874459\pi$
$83$	−3.66402	−	11.2767i	−0.402179	−	1.23778i	0.521050	−	0.853526i	$-0.325541\pi$
$84$		0			0
$85$	2.57518	−	1.87098i	0.279317	−	0.202936i
$86$		0			0
$87$	2.52394			0.270594
$88$		0			0
$89$	−6.56220			−0.695592			−0.347796	−	0.937570i	$-0.613070\pi$
$89$	−6.56220			−0.695592			−0.347796	+	0.937570i	$0.613070\pi$
$90$		0			0
$91$	−5.78514	+	4.20315i	−0.606448	+	0.440610i
$92$		0			0
$93$	0.0699002	+	0.215131i	0.00724832	+	0.0223080i
$94$		0			0
$95$	6.64420	+	4.82729i	0.681680	+	0.495270i
$96$		0			0
$97$	4.49404	−	13.8312i	0.456300	−	1.40435i	−0.413301	−	0.910594i	$-0.635624\pi$
$97$	4.49404	−	13.8312i	0.456300	−	1.40435i	0.869602	−	0.493754i	$-0.164376\pi$
$98$		0			0
$99$	−6.86182	−	5.62552i	−0.689639	−	0.565386i
$100$		0			0
$101$	−3.05818	+	9.41212i	−0.304301	+	0.936541i	0.675637	+	0.737235i	$0.263869\pi$
$101$	−3.05818	+	9.41212i	−0.304301	+	0.936541i	−0.979937	+	0.199306i	$0.936131\pi$
$102$		0			0
$103$	−5.83397	−	4.23863i	−0.574838	−	0.417645i	0.262021	−	0.965062i	$-0.415611\pi$
$103$	−5.83397	−	4.23863i	−0.574838	−	0.417645i	−0.836860	+	0.547418i	$0.815611\pi$
$104$		0			0
$105$	0.320658	+	0.986882i	0.0312930	+	0.0963099i
$106$		0			0
$107$	7.91005	−	5.74699i	0.764693	−	0.555582i	−0.135653	−	0.990756i	$-0.543313\pi$
$107$	7.91005	−	5.74699i	0.764693	−	0.555582i	0.900346	+	0.435174i	$0.143313\pi$
$108$		0			0
$109$	18.7329			1.79429			0.897143	−	0.441741i	$-0.145639\pi$
$109$	18.7329			1.79429			0.897143	+	0.441741i	$0.145639\pi$
$110$		0			0
$111$	−1.70585			−0.161912
$112$		0			0
$113$	−10.4051	+	7.55973i	−0.978827	+	0.711159i	−0.957446	−	0.288612i	$-0.906806\pi$
$113$	−10.4051	+	7.55973i	−0.978827	+	0.711159i	−0.0213805	+	0.999771i	$0.506806\pi$
$114$		0			0
$115$	0.226856	+	0.698192i	0.0211545	+	0.0651067i
$116$		0			0
$117$	−8.49875	−	6.17470i	−0.785710	−	0.570851i
$118$		0			0
$119$	1.79130	−	5.51305i	0.164208	−	0.505380i
$120$		0			0
$121$	−8.08513	−	7.45859i	−0.735012	−	0.678054i
$122$		0			0
$123$	−2.12200	+	6.53083i	−0.191334	+	0.588866i
$124$		0			0
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$		0			0
$127$	−0.880017	−	2.70841i	−0.0780889	−	0.240333i	0.904390	−	0.426707i	$-0.140326\pi$
$127$	−0.880017	−	2.70841i	−0.0780889	−	0.240333i	−0.982479	+	0.186374i	$0.940326\pi$
$128$		0			0
$129$	4.02415	−	2.92371i	0.354306	−	0.257419i
$130$		0			0
$131$	−9.49411			−0.829504			−0.414752	−	0.909934i	$-0.636132\pi$
$131$	−9.49411			−0.829504			−0.414752	+	0.909934i	$0.636132\pi$
$132$		0			0
$133$	14.9562			1.29687
$134$		0			0
$135$	−2.61620	+	1.90078i	−0.225167	+	0.163593i
$136$		0			0
$137$	−2.17497	−	6.69388i	−0.185821	−	0.571897i	0.814141	−	0.580667i	$-0.197208\pi$
$137$	−2.17497	−	6.69388i	−0.185821	−	0.571897i	−0.999962	+	0.00877048i	$0.997208\pi$
$138$		0			0
$139$	−3.01913	−	2.19352i	−0.256079	−	0.186052i	0.452338	−	0.891847i	$-0.350590\pi$
$139$	−3.01913	−	2.19352i	−0.256079	−	0.186052i	−0.708417	+	0.705795i	$0.750590\pi$
$140$		0			0
$141$	1.85070	−	5.69588i	0.155857	−	0.479679i
$142$		0			0
$143$	−10.0712	−	8.25670i	−0.842200	−	0.690460i
$144$		0			0
$145$	−1.36879	+	4.21271i	−0.113672	+	0.349846i
$146$		0			0
$147$	−1.69804	−	1.23370i	−0.140052	−	0.101754i
$148$		0			0
$149$	3.79320	+	11.6743i	0.310751	+	0.956394i	0.977468	+	0.211083i	$0.0676991\pi$
$149$	3.79320	+	11.6743i	0.310751	+	0.956394i	−0.666717	+	0.745311i	$0.732301\pi$
$150$		0			0
$151$	4.69436	−	3.41065i	0.382022	−	0.277555i	−0.380157	−	0.924922i	$-0.624130\pi$
$151$	4.69436	−	3.41065i	0.382022	−	0.277555i	0.762178	+	0.647367i	$0.224130\pi$
$152$		0			0
$153$	8.51581			0.688463
$154$		0			0
$155$	−0.396984			−0.0318865
$156$		0			0
$157$	16.7755	−	12.1881i	1.33883	−	0.972715i	0.339341	−	0.940664i	$-0.389796\pi$
$157$	16.7755	−	12.1881i	1.33883	−	0.972715i	0.999486	−	0.0320511i	$-0.0102039\pi$
$158$		0			0
$159$	−1.73374	−	5.33591i	−0.137495	−	0.423165i
$160$		0			0
$161$	1.08159	+	0.785820i	0.0852411	+	0.0619313i
$162$		0			0
$163$	−3.65638	+	11.2532i	−0.286390	+	0.881418i	0.699588	+	0.714546i	$0.253367\pi$
$163$	−3.65638	+	11.2532i	−0.286390	+	0.881418i	−0.985979	+	0.166872i	$0.946633\pi$
$164$		0			0
$165$	−1.59112	+	1.01968i	−0.123868	+	0.0793821i
$166$		0			0
$167$	−5.61942	+	17.2948i	−0.434844	+	1.33831i	0.458402	+	0.888745i	$0.348422\pi$
$167$	−5.61942	+	17.2948i	−0.434844	+	1.33831i	−0.893246	+	0.449568i	$0.851578\pi$
$168$		0			0
$169$	−1.95657	−	1.42153i	−0.150506	−	0.109349i
$170$		0			0
$171$	6.78960	+	20.8962i	0.519214	+	1.59798i
$172$		0			0
$173$	8.26429	−	6.00436i	0.628322	−	0.456503i	−0.227496	−	0.973779i	$-0.573054\pi$
$173$	8.26429	−	6.00436i	0.628322	−	0.456503i	0.855819	+	0.517276i	$0.173054\pi$
$174$		0			0
$175$	−1.82111			−0.137663
$176$		0			0
$177$	−5.70492			−0.428808
$178$		0			0
$179$	−1.39437	+	1.01307i	−0.104220	+	0.0757202i	−0.638675	−	0.769477i	$-0.720517\pi$
$179$	−1.39437	+	1.01307i	−0.104220	+	0.0757202i	0.534455	+	0.845197i	$0.320517\pi$
$180$		0			0
$181$	4.31143	+	13.2692i	0.320466	+	0.986294i	0.973446	+	0.228918i	$0.0735188\pi$
$181$	4.31143	+	13.2692i	0.320466	+	0.986294i	−0.652979	+	0.757376i	$0.726481\pi$
$182$		0			0
$183$	3.92237	+	2.84977i	0.289950	+	0.210661i
$184$		0			0
$185$	0.925124	−	2.84724i	0.0680165	−	0.209333i
$186$		0			0
$187$	10.5391	+	0.616151i	0.770698	+	0.0450574i
$188$		0			0
$189$	−1.81984	+	5.60088i	−0.132374	+	0.407404i
$190$		0			0
$191$	−19.9770	−	14.5141i	−1.44548	−	1.05021i	−0.986860	−	0.161576i	$-0.948342\pi$
$191$	−19.9770	−	14.5141i	−1.44548	−	1.05021i	−0.458625	−	0.888630i	$-0.651658\pi$
$192$		0			0
$193$	0.824000	+	2.53601i	0.0593128	+	0.182546i	0.976323	−	0.216318i	$-0.0694047\pi$
$193$	0.824000	+	2.53601i	0.0593128	+	0.182546i	−0.917010	+	0.398864i	$0.869405\pi$
$194$		0			0
$195$	−1.81009	+	1.31511i	−0.129624	+	0.0941771i
$196$		0			0
$197$	21.4277			1.52666			0.763330	−	0.646009i	$-0.223563\pi$
$197$	21.4277			1.52666			0.763330	+	0.646009i	$0.223563\pi$
$198$		0			0
$199$	−5.78067			−0.409781			−0.204891	−	0.978785i	$-0.565684\pi$
$199$	−5.78067			−0.409781			−0.204891	+	0.978785i	$0.565684\pi$
$200$		0			0
$201$	0.512172	−	0.372115i	0.0361258	−	0.0262469i
$202$		0			0
$203$	2.49272	+	7.67180i	0.174955	+	0.538455i
$204$		0			0
$205$	−9.74982	−	7.08366i	−0.680957	−	0.494744i
$206$		0			0
$207$	−0.606915	+	1.86789i	−0.0421835	+	0.129827i
$208$		0			0
$209$	6.89085	+	26.3523i	0.476650	+	1.82283i
$210$		0			0
$211$	−3.57755	+	11.0106i	−0.246288	+	0.757998i	0.749134	+	0.662419i	$0.230470\pi$
$211$	−3.57755	+	11.0106i	−0.246288	+	0.757998i	−0.995422	+	0.0955786i	$0.969530\pi$
$212$		0			0
$213$	2.70674	+	1.96656i	0.185463	+	0.134746i
$214$		0			0
$215$	2.69759	+	8.30232i	0.183974	+	0.566213i
$216$		0			0
$217$	−0.584880	+	0.424940i	−0.0397042	+	0.0288468i
$218$		0			0
$219$	−2.29965			−0.155396
$220$		0			0
$221$	12.4988			0.840763
$222$		0			0
$223$	9.57136	−	6.95400i	0.640945	−	0.465674i	−0.219229	−	0.975673i	$-0.570354\pi$
$223$	9.57136	−	6.95400i	0.640945	−	0.465674i	0.860175	+	0.509999i	$0.170354\pi$
$224$		0			0
$225$	−0.826721	−	2.54439i	−0.0551148	−	0.169626i
$226$		0			0
$227$	5.00770	+	3.63831i	0.332373	+	0.241483i	0.741437	−	0.671023i	$-0.234145\pi$
$227$	5.00770	+	3.63831i	0.332373	+	0.241483i	−0.409064	+	0.912506i	$0.634145\pi$
$228$		0			0
$229$	5.49119	−	16.9001i	0.362868	−	1.11679i	−0.588437	−	0.808543i	$-0.700257\pi$
$229$	5.49119	−	16.9001i	0.362868	−	1.11679i	0.951305	−	0.308250i	$-0.0997434\pi$
$230$		0			0
$231$	−1.25272	+	3.20547i	−0.0824228	+	0.210904i
$232$		0			0
$233$	−5.26159	+	16.1935i	−0.344698	+	1.06087i	0.617047	+	0.786926i	$0.288329\pi$
$233$	−5.26159	+	16.1935i	−0.344698	+	1.06087i	−0.961745	+	0.273946i	$0.911671\pi$
$234$		0			0
$235$	8.50332	+	6.17803i	0.554696	+	0.403010i
$236$		0			0
$237$	−0.575368	−	1.77080i	−0.0373741	−	0.115026i
$238$		0			0
$239$	−0.959686	+	0.697253i	−0.0620769	+	0.0451015i	−0.618391	−	0.785871i	$-0.712215\pi$
$239$	−0.959686	+	0.697253i	−0.0620769	+	0.0451015i	0.556314	+	0.830972i	$0.312215\pi$
$240$		0			0
$241$	10.3606			0.667388			0.333694	−	0.942682i	$-0.391705\pi$
$241$	10.3606			0.667388			0.333694	+	0.942682i	$0.391705\pi$
$242$		0			0
$243$	−13.2247			−0.848365
$244$		0			0
$245$	2.98007	−	2.16514i	0.190389	−	0.138326i
$246$		0			0
$247$	9.96524	+	30.6699i	0.634073	+	1.95148i
$248$		0			0
$249$	−5.46583	−	3.97116i	−0.346383	−	0.251662i
$250$		0			0
$251$	6.08188	−	18.7181i	0.383885	−	1.18148i	−0.553401	−	0.832915i	$-0.686670\pi$
$251$	6.08188	−	18.7181i	0.383885	−	1.18148i	0.937286	−	0.348561i	$-0.113330\pi$
$252$		0			0
$253$	−0.886264	+	2.26778i	−0.0557189	+	0.142574i
$254$		0			0
$255$	0.560473	−	1.72496i	0.0350982	−	0.108021i
$256$		0			0
$257$	−10.8749	−	7.90107i	−0.678357	−	0.492855i	0.194455	−	0.980911i	$-0.437706\pi$
$257$	−10.8749	−	7.90107i	−0.678357	−	0.492855i	−0.872812	+	0.488056i	$0.837706\pi$
$258$		0			0
$259$	−1.68475	−	5.18513i	−0.104685	−	0.322188i
$260$		0			0
$261$	−9.58715	+	6.96547i	−0.593430	+	0.431152i
$262$		0			0
$263$	−1.60780			−0.0991410			−0.0495705	−	0.998771i	$-0.515785\pi$
$263$	−1.60780			−0.0991410			−0.0495705	+	0.998771i	$0.515785\pi$
$264$		0			0
$265$	9.84643			0.604861
$266$		0			0
$267$	−3.02503	+	2.19782i	−0.185129	+	0.134504i
$268$		0			0
$269$	2.78636	+	8.57554i	0.169887	+	0.522860i	0.999363	−	0.0356829i	$-0.0113606\pi$
$269$	2.78636	+	8.57554i	0.169887	+	0.522860i	−0.829476	+	0.558543i	$0.811361\pi$
$270$		0			0
$271$	15.6833	+	11.3946i	0.952694	+	0.692173i	0.951443	−	0.307826i	$-0.0996016\pi$
$271$	15.6833	+	11.3946i	0.952694	+	0.692173i	0.00125153	+	0.999999i	$0.499602\pi$
$272$		0			0
$273$	−1.25911	+	3.87513i	−0.0762045	+	0.234533i
$274$		0			0
$275$	−0.839051	−	3.20874i	−0.0505967	−	0.193494i
$276$		0			0
$277$	0.595467	−	1.83266i	0.0357782	−	0.110114i	−0.931572	−	0.363556i	$-0.881563\pi$
$277$	0.595467	−	1.83266i	0.0357782	−	0.110114i	0.967351	+	0.253442i	$0.0815626\pi$
$278$		0			0
$279$	−0.859226	−	0.624264i	−0.0514405	−	0.0373737i
$280$		0			0
$281$	−0.677631	−	2.08553i	−0.0404241	−	0.124413i	0.928808	−	0.370562i	$-0.120835\pi$
$281$	−0.677631	−	2.08553i	−0.0404241	−	0.124413i	−0.969232	+	0.246149i	$0.920835\pi$
$282$		0			0
$283$	23.4544	−	17.0407i	1.39422	−	1.01296i	0.398835	−	0.917023i	$-0.369415\pi$
$283$	23.4544	−	17.0407i	1.39422	−	1.01296i	0.995387	−	0.0959389i	$-0.0305853\pi$
$284$		0			0
$285$	4.67959			0.277195
$286$		0			0
$287$	−21.9470			−1.29549
$288$		0			0
$289$	5.55626	−	4.03686i	0.326839	−	0.237462i
$290$		0			0
$291$	−2.56071	−	7.88105i	−0.150111	−	0.461995i
$292$		0			0
$293$	−4.93411	−	3.58484i	−0.288254	−	0.209429i	0.434256	−	0.900790i	$-0.357011\pi$
$293$	−4.93411	−	3.58484i	−0.288254	−	0.209429i	−0.722510	+	0.691361i	$0.757011\pi$
$294$		0			0
$295$	3.09392	−	9.52210i	0.180135	−	0.554398i
$296$		0			0
$297$	−10.7070	−	0.625967i	−0.621286	−	0.0363223i
$298$		0			0
$299$	−0.890782	+	2.74154i	−0.0515152	+	0.158548i
$300$		0			0
$301$	12.8613	+	9.34432i	0.741316	+	0.538597i
$302$		0			0
$303$	1.74256	+	5.36304i	0.100107	+	0.308098i
$304$		0			0
$305$	−6.88375	+	5.00134i	−0.394162	+	0.286376i
$306$		0			0
$307$	15.2560			0.870706			0.435353	−	0.900260i	$-0.356624\pi$
$307$	15.2560			0.870706			0.435353	+	0.900260i	$0.356624\pi$
$308$		0			0
$309$	−4.10894			−0.233750
$310$		0			0
$311$	2.80386	−	2.03712i	0.158992	−	0.115515i	−0.505444	−	0.862859i	$-0.668671\pi$
$311$	2.80386	−	2.03712i	0.158992	−	0.115515i	0.664437	+	0.747344i	$0.268671\pi$
$312$		0			0
$313$	4.03157	+	12.4079i	0.227878	+	0.701336i	0.997987	+	0.0634232i	$0.0202018\pi$
$313$	4.03157	+	12.4079i	0.227878	+	0.701336i	−0.770109	+	0.637912i	$0.779798\pi$
$314$		0			0
$315$	−3.94158	−	2.86373i	−0.222083	−	0.161353i
$316$		0			0
$317$	−9.35890	+	28.8037i	−0.525648	+	1.61778i	0.237382	+	0.971416i	$0.423711\pi$
$317$	−9.35890	+	28.8037i	−0.525648	+	1.61778i	−0.763030	+	0.646363i	$0.776289\pi$
$318$		0			0
$319$	−12.3690	+	7.92677i	−0.692530	+	0.443814i
$320$		0			0
$321$	1.72158	−	5.29848i	0.0960892	−	0.295732i
$322$		0			0
$323$	−21.1491	−	15.3657i	−1.17677	−	0.854972i
$324$		0			0
$325$	−1.21340	−	3.73445i	−0.0673071	−	0.207150i
$326$		0			0
$327$	8.63546	−	6.27403i	0.477542	−	0.346955i
$328$		0			0
$329$	19.1411			1.05528
$330$		0			0
$331$	4.19183			0.230404			0.115202	−	0.993342i	$-0.463248\pi$
$331$	4.19183			0.230404			0.115202	+	0.993342i	$0.463248\pi$
$332$		0			0
$333$	6.47966	−	4.70775i	0.355083	−	0.257983i
$334$		0			0
$335$	0.343334	+	1.05667i	0.0187584	+	0.0577323i
$336$		0			0
$337$	−21.4674	−	15.5970i	−1.16940	−	0.849621i	−0.178466	−	0.983946i	$-0.557113\pi$
$337$	−21.4674	−	15.5970i	−1.16940	−	0.849621i	−0.990937	+	0.134325i	$0.957113\pi$
$338$		0			0
$339$	−2.26461	+	6.96975i	−0.122997	+	0.378545i
$340$		0			0
$341$	−1.01821	−	0.834755i	−0.0551389	−	0.0452045i
$342$		0			0
$343$	6.01221	−	18.5037i	0.324629	−	0.999105i
$344$		0			0
$345$	0.338415	+	0.245873i	0.0182196	+	0.0132373i
$346$		0			0
$347$	0.352069	+	1.08356i	0.0189001	+	0.0581684i	0.960062	−	0.279788i	$-0.0902643\pi$
$347$	0.352069	+	1.08356i	0.0189001	+	0.0581684i	−0.941162	+	0.337957i	$0.890264\pi$
$348$		0			0
$349$	−13.1401	+	9.54687i	−0.703375	+	0.511032i	−0.881030	−	0.473061i	$-0.843149\pi$
$349$	−13.1401	+	9.54687i	−0.703375	+	0.511032i	0.177654	+	0.984093i	$0.443149\pi$
$350$		0			0
$351$	−12.6980			−0.677768
$352$		0			0
$353$	−0.432655			−0.0230279			−0.0115140	−	0.999934i	$-0.503665\pi$
$353$	−0.432655			−0.0230279			−0.0115140	+	0.999934i	$0.503665\pi$
$354$		0			0
$355$	−4.75032	+	3.45131i	−0.252121	+	0.183176i
$356$		0			0
$357$	−1.02068	−	3.14134i	−0.0540203	−	0.166257i
$358$		0			0
$359$	−0.0790542	−	0.0574363i	−0.00417232	−	0.00303137i	0.585697	−	0.810530i	$-0.300821\pi$
$359$	−0.0790542	−	0.0574363i	−0.00417232	−	0.00303137i	−0.589869	+	0.807499i	$0.700821\pi$
$360$		0			0
$361$	14.9713	−	46.0769i	0.787963	−	2.42510i
$362$		0			0
$363$	−6.22511	−	0.730376i	−0.326734	−	0.0383348i
$364$		0			0
$365$	1.24716	−	3.83835i	0.0652792	−	0.200909i
$366$		0			0
$367$	−11.6423	−	8.45860i	−0.607721	−	0.441535i	0.240890	−	0.970552i	$-0.422561\pi$
$367$	−11.6423	−	8.45860i	−0.607721	−	0.441535i	−0.848611	+	0.529017i	$0.822561\pi$
$368$		0			0
$369$	−9.96319	−	30.6635i	−0.518663	−	1.59628i
$370$		0			0
$371$	14.5068	−	10.5398i	0.753157	−	0.547200i
$372$		0			0
$373$	−13.8834			−0.718855			−0.359428	−	0.933173i	$-0.617028\pi$
$373$	−13.8834			−0.718855			−0.359428	+	0.933173i	$0.617028\pi$
$374$		0			0
$375$	−0.569801			−0.0294244
$376$		0			0
$377$	−14.0713	+	10.2234i	−0.724707	+	0.526530i
$378$		0			0
$379$	5.50989	+	16.9577i	0.283024	+	0.871059i	0.986984	+	0.160819i	$0.0514135\pi$
$379$	5.50989	+	16.9577i	0.283024	+	0.871059i	−0.703960	+	0.710240i	$0.748586\pi$
$380$		0			0
$381$	−1.31277	−	0.953785i	−0.0672554	−	0.0488639i
$382$		0			0
$383$	2.59468	−	7.98559i	0.132582	−	0.408045i	−0.862624	−	0.505845i	$-0.831181\pi$
$383$	2.59468	−	7.98559i	0.132582	−	0.408045i	0.995206	+	0.0978004i	$0.0311807\pi$
$384$		0			0
$385$	−4.67088	−	3.82932i	−0.238050	−	0.195160i
$386$		0			0
$387$	−7.21693	+	22.2114i	−0.366857	+	1.12907i
$388$		0			0
$389$	6.38833	+	4.64140i	0.323901	+	0.235328i	0.737838	−	0.674977i	$-0.235847\pi$
$389$	6.38833	+	4.64140i	0.323901	+	0.235328i	−0.413937	+	0.910306i	$0.635847\pi$
$390$		0			0
$391$	−0.722105	−	2.22241i	−0.0365184	−	0.112392i
$392$		0			0
$393$	−4.37658	+	3.17977i	−0.220769	+	0.160398i
$394$		0			0
$395$	3.26768			0.164415
$396$		0			0
$397$	−36.2170			−1.81768			−0.908840	−	0.417146i	$-0.863030\pi$
$397$	−36.2170			−1.81768			−0.908840	+	0.417146i	$0.863030\pi$
$398$		0			0
$399$	6.89448	−	5.00914i	0.345156	−	0.250770i
$400$		0			0
$401$	−3.85877	−	11.8761i	−0.192698	−	0.593062i	−0.999996	−	0.00291831i	$-0.999071\pi$
$401$	−3.85877	−	11.8761i	−0.192698	−	0.593062i	0.807298	−	0.590144i	$-0.200929\pi$
$402$		0			0
$403$	−1.26110	−	0.916246i	−0.0628201	−	0.0456415i
$404$		0			0
$405$	1.91076	−	5.88072i	0.0949465	−	0.292215i
$406$		0			0
$407$	8.35982	−	5.35746i	0.414381	−	0.265559i
$408$		0			0
$409$	−2.85780	+	8.79540i	−0.141309	+	0.434905i	−0.996518	−	0.0833789i	$-0.973429\pi$
$409$	−2.85780	+	8.79540i	−0.141309	+	0.434905i	0.855209	+	0.518284i	$0.173429\pi$
$410$		0			0
$411$	−3.24453	−	2.35729i	−0.160041	−	0.116277i
$412$		0			0
$413$	−5.63436	−	17.3408i	−0.277249	−	0.853284i
$414$		0			0
$415$	9.59253	−	6.96938i	0.470879	−	0.342114i
$416$		0			0
$417$	−2.12641			−0.104131
$418$		0			0
$419$	28.9794			1.41574			0.707869	−	0.706344i	$-0.249657\pi$
$419$	28.9794			1.41574			0.707869	+	0.706344i	$0.249657\pi$
$420$		0			0
$421$	−18.4605	+	13.4124i	−0.899711	+	0.653678i	−0.938392	−	0.345574i	$-0.887684\pi$
$421$	−18.4605	+	13.4124i	−0.899711	+	0.653678i	0.0386810	+	0.999252i	$0.487684\pi$
$422$		0			0
$423$	8.68941	+	26.7432i	0.422494	+	1.30030i
$424$		0			0
$425$	2.57518	+	1.87098i	0.124914	+	0.0907556i
$426$		0			0
$427$	−4.78835	+	14.7370i	−0.231724	+	0.713174i
$428$		0			0
$429$	−7.40797	−	0.433093i	−0.357660	−	0.0209099i
$430$		0			0
$431$	7.91413	−	24.3572i	0.381210	−	1.17324i	−0.557982	−	0.829853i	$-0.688424\pi$
$431$	7.91413	−	24.3572i	0.381210	−	1.17324i	0.939192	−	0.343391i	$-0.111576\pi$
$432$		0			0
$433$	−2.13108	−	1.54832i	−0.102413	−	0.0744075i	0.535400	−	0.844599i	$-0.320161\pi$
$433$	−2.13108	−	1.54832i	−0.102413	−	0.0744075i	−0.637813	+	0.770191i	$0.720161\pi$
$434$		0			0
$435$	0.779939	+	2.40040i	0.0373952	+	0.115091i
$436$		0			0
$437$	4.87766	−	3.54382i	0.233330	−	0.169524i
$438$		0			0
$439$	−7.16551			−0.341991			−0.170996	−	0.985272i	$-0.554698\pi$
$439$	−7.16551			−0.341991			−0.170996	+	0.985272i	$0.554698\pi$
$440$		0			0
$441$	9.85473			0.469273
$442$		0			0
$443$	−12.4489	+	9.04467i	−0.591466	+	0.429725i	−0.842839	−	0.538165i	$-0.819118\pi$
$443$	−12.4489	+	9.04467i	−0.591466	+	0.429725i	0.251374	+	0.967890i	$0.419118\pi$
$444$		0			0
$445$	−2.02783	−	6.24102i	−0.0961284	−	0.295853i
$446$		0			0
$447$	5.65854	+	4.11117i	0.267640	+	0.194452i
$448$		0			0
$449$	−1.43363	+	4.41226i	−0.0676572	+	0.208228i	−0.979169	−	0.203046i	$-0.934916\pi$
$449$	−1.43363	+	4.41226i	−0.0676572	+	0.208228i	0.911512	+	0.411274i	$0.134916\pi$
$450$		0			0
$451$	−10.1118	−	38.6699i	−0.476145	−	1.82090i
$452$		0			0
$453$	1.02170	−	3.14448i	0.0480038	−	0.147740i
$454$		0			0
$455$	−5.78514	−	4.20315i	−0.271212	−	0.197047i
$456$		0			0
$457$	3.97445	+	12.2321i	0.185917	+	0.572193i	0.999963	−	0.00860706i	$-0.00273975\pi$
$457$	3.97445	+	12.2321i	0.185917	+	0.572193i	−0.814046	+	0.580800i	$0.802740\pi$
$458$		0			0
$459$	8.32762	−	6.05037i	0.388700	−	0.282407i
$460$		0			0
$461$	−19.6157			−0.913594			−0.456797	−	0.889571i	$-0.651003\pi$
$461$	−19.6157			−0.913594			−0.456797	+	0.889571i	$0.651003\pi$
$462$		0			0
$463$	−3.15807			−0.146768			−0.0733839	−	0.997304i	$-0.523380\pi$
$463$	−3.15807			−0.146768			−0.0733839	+	0.997304i	$0.523380\pi$
$464$		0			0
$465$	−0.183001	+	0.132958i	−0.00848648	+	0.00616579i
$466$		0			0
$467$	−8.94891	−	27.5419i	−0.414106	−	1.27449i	−0.913048	−	0.407852i	$-0.866278\pi$
$467$	−8.94891	−	27.5419i	−0.414106	−	1.27449i	0.498942	−	0.866635i	$-0.333722\pi$
$468$		0			0
$469$	1.63692	+	1.18929i	0.0755861	+	0.0549165i
$470$		0			0
$471$	3.65109	−	11.2369i	0.168233	−	0.517769i
$472$		0			0
$473$	−10.5387	+	26.9666i	−0.484570	+	1.23992i
$474$		0			0
$475$	−2.53786	+	7.81072i	−0.116445	+	0.358381i
$476$		0			0
$477$	21.3115	+	15.4837i	0.975785	+	0.708949i
$478$		0			0
$479$	−6.56042	−	20.1909i	−0.299753	−	0.922545i	−0.981583	−	0.191035i	$-0.938816\pi$
$479$	−6.56042	−	20.1909i	−0.299753	−	0.922545i	0.681830	−	0.731510i	$-0.261184\pi$
$480$		0			0
$481$	9.51034	−	6.90966i	0.433634	−	0.315054i
$482$		0			0
$483$	0.761777			0.0346620
$484$		0			0
$485$	14.5430			0.660364
$486$		0			0
$487$	11.3077	−	8.21556i	0.512403	−	0.372283i	−0.301331	−	0.953519i	$-0.597431\pi$
$487$	11.3077	−	8.21556i	0.512403	−	0.372283i	0.813734	+	0.581237i	$0.197431\pi$
$488$		0			0
$489$	2.08341	+	6.41208i	0.0942151	+	0.289964i
$490$		0			0
$491$	13.8304	+	10.0484i	0.624158	+	0.453477i	0.854371	−	0.519663i	$-0.173943\pi$
$491$	13.8304	+	10.0484i	0.624158	+	0.453477i	−0.230214	+	0.973140i	$0.573943\pi$
$492$		0			0
$493$	4.35699	−	13.4094i	0.196229	−	0.603931i
$494$		0			0
$495$	3.22977	−	8.26436i	0.145167	−	0.371456i
$496$		0			0
$497$	−3.30433	+	10.1697i	−0.148219	+	0.456173i
$498$		0			0
$499$	−33.1294	−	24.0699i	−1.48307	−	1.07752i	−0.976550	−	0.215291i	$-0.930930\pi$
$499$	−33.1294	−	24.0699i	−1.48307	−	1.07752i	−0.506524	−	0.862226i	$-0.669070\pi$
$500$		0			0
$501$	3.20195	+	9.85460i	0.143053	+	0.440271i
$502$		0			0
$503$	−10.8723	+	7.89920i	−0.484772	+	0.352208i	−0.803170	−	0.595749i	$-0.796855\pi$
$503$	−10.8723	+	7.89920i	−0.484772	+	0.352208i	0.318398	+	0.947957i	$0.396855\pi$
$504$		0			0
$505$	−9.89649			−0.440388
$506$		0			0
$507$	−1.37804			−0.0612009
$508$		0			0
$509$	−14.8408	+	10.7825i	−0.657807	+	0.477925i	−0.865922	−	0.500180i	$-0.833267\pi$
$509$	−14.8408	+	10.7825i	−0.657807	+	0.477925i	0.208115	+	0.978104i	$0.433267\pi$
$510$		0			0
$511$	−2.27121	−	6.99006i	−0.100472	−	0.309222i
$512$		0			0
$513$	21.4861	+	15.6105i	0.948633	+	0.689222i
$514$		0			0
$515$	2.22838	−	6.85825i	0.0981941	−	0.302210i
$516$		0			0
$517$	8.81900	+	33.7260i	0.387859	+	1.48327i
$518$		0			0
$519$	1.79868	−	5.53576i	0.0789532	−	0.242993i
$520$		0			0
$521$	−2.32521	−	1.68937i	−0.101870	−	0.0740125i	0.535684	−	0.844418i	$-0.320054\pi$
$521$	−2.32521	−	1.68937i	−0.101870	−	0.0740125i	−0.637554	+	0.770406i	$0.720054\pi$
$522$		0			0
$523$	11.6495	+	35.8535i	0.509398	+	1.56776i	0.793250	+	0.608896i	$0.208387\pi$
$523$	11.6495	+	35.8535i	0.509398	+	1.56776i	−0.283852	+	0.958868i	$0.591613\pi$
$524$		0			0
$525$	−0.839492	+	0.609927i	−0.0366385	+	0.0266194i
$526$		0			0
$527$	1.26364			0.0550449
$528$		0			0
$529$	−22.4611			−0.976568
$530$		0			0
$531$	21.6701	−	15.7442i	0.940402	−	0.683242i
$532$		0			0
$533$	−14.6232	−	45.0055i	−0.633400	−	1.94941i
$534$		0			0
$535$	7.91005	+	5.74699i	0.341981	+	0.248464i
$536$		0			0
$537$	−0.303476	+	0.934005i	−0.0130960	+	0.0403053i
$538$		0			0
$539$	12.1962	+	0.713027i	0.525326	+	0.0307122i
$540$		0			0
$541$	3.87844	−	11.9366i	0.166747	−	0.513195i	−0.832414	−	0.554155i	$-0.813042\pi$
$541$	3.87844	−	11.9366i	0.166747	−	0.513195i	0.999161	+	0.0409599i	$0.0130416\pi$
$542$		0			0
$543$	6.43162	+	4.67284i	0.276007	+	0.200531i
$544$		0			0
$545$	5.78878	+	17.8160i	0.247964	+	0.763155i
$546$		0			0
$547$	−28.7450	+	20.8844i	−1.22905	+	0.892954i	−0.996818	−	0.0797073i	$-0.974601\pi$
$547$	−28.7450	+	20.8844i	−1.22905	+	0.892954i	−0.232228	+	0.972661i	$0.574601\pi$
$548$		0			0
$549$	−22.7638			−0.971534
$550$		0			0
$551$	36.3781			1.54976
$552$		0			0
$553$	4.81430	−	3.49779i	0.204725	−	0.148741i
$554$		0			0
$555$	−0.527137	−	1.62236i	−0.0223757	−	0.0688654i
$556$		0			0
$557$	−32.2328	−	23.4185i	−1.36575	−	0.992272i	−0.998056	−	0.0623235i	$-0.980149\pi$
$557$	−32.2328	−	23.4185i	−1.36575	−	0.992272i	−0.367689	−	0.929949i	$-0.619851\pi$
$558$		0			0
$559$	−10.5924	+	32.6002i	−0.448012	+	1.37884i
$560$		0			0
$561$	5.06468	−	3.24574i	0.213831	−	0.137035i
$562$		0			0
$563$	9.96989	−	30.6842i	0.420181	−	1.29318i	−0.487354	−	0.873205i	$-0.662038\pi$
$563$	9.96989	−	30.6842i	0.420181	−	1.29318i	0.907534	−	0.419978i	$-0.137962\pi$
$564$		0			0
$565$	−10.4051	−	7.55973i	−0.437745	−	0.318040i
$566$		0			0
$567$	−3.47970	−	10.7094i	−0.146134	−	0.449754i
$568$		0			0
$569$	−14.4777	+	10.5187i	−0.606938	+	0.440966i	−0.848335	−	0.529460i	$-0.822394\pi$
$569$	−14.4777	+	10.5187i	−0.606938	+	0.440966i	0.241397	+	0.970426i	$0.422394\pi$
$570$		0			0
$571$	−11.9435			−0.499819			−0.249910	−	0.968269i	$-0.580401\pi$
$571$	−11.9435			−0.499819			−0.249910	+	0.968269i	$0.580401\pi$
$572$		0			0
$573$	−14.0701			−0.587785
$574$		0			0
$575$	−0.593918	+	0.431506i	−0.0247681	+	0.0179951i
$576$		0			0
$577$	3.69125	+	11.3605i	0.153669	+	0.472944i	0.998024	−	0.0628407i	$-0.0200160\pi$
$577$	3.69125	+	11.3605i	0.153669	+	0.472944i	−0.844355	+	0.535784i	$0.820016\pi$
$578$		0			0
$579$	1.22921	+	0.893073i	0.0510842	+	0.0371148i
$580$		0			0
$581$	6.67258	−	20.5361i	0.276825	−	0.851981i
$582$		0			0
$583$	25.2547	+	20.7045i	1.04594	+	0.857493i
$584$		0			0
$585$	3.24623	−	9.99088i	0.134215	−	0.413072i
$586$		0			0
$587$	−12.8231	−	9.31652i	−0.529265	−	0.384534i	0.290817	−	0.956779i	$-0.406073\pi$
$587$	−12.8231	−	9.31652i	−0.529265	−	0.384534i	−0.820083	+	0.572245i	$0.806073\pi$
$588$		0			0
$589$	1.00749	+	3.10073i	0.0415129	+	0.127763i
$590$		0			0
$591$	9.87771	−	7.17658i	0.406315	−	0.295205i
$592$		0			0
$593$	40.0924			1.64640			0.823198	−	0.567754i	$-0.192188\pi$
$593$	40.0924			1.64640			0.823198	+	0.567754i	$0.192188\pi$
$594$		0			0
$595$	5.79676			0.237644
$596$		0			0
$597$	−2.66477	+	1.93607i	−0.109062	+	0.0792380i
$598$		0			0
$599$	10.0619	+	30.9674i	0.411119	+	1.26529i	0.915677	+	0.401915i	$0.131655\pi$
$599$	10.0619	+	30.9674i	0.411119	+	1.26529i	−0.504558	+	0.863378i	$0.668345\pi$
$600$		0			0
$601$	−4.69376	−	3.41021i	−0.191462	−	0.139106i	0.487924	−	0.872886i	$-0.337754\pi$
$601$	−4.69376	−	3.41021i	−0.191462	−	0.139106i	−0.679387	+	0.733780i	$0.737754\pi$
$602$		0			0
$603$	−0.918532	+	2.82695i	−0.0374055	+	0.115122i
$604$		0			0
$605$	4.59510	−	9.99425i	0.186817	−	0.406324i
$606$		0			0
$607$	−4.34442	+	13.3707i	−0.176334	+	0.542702i	−0.999692	−	0.0248215i	$-0.992098\pi$
$607$	−4.34442	+	13.3707i	−0.176334	+	0.542702i	0.823357	+	0.567523i	$0.192098\pi$
$608$		0			0
$609$	3.71853	+	2.70167i	0.150683	+	0.109477i
$610$		0			0
$611$	12.7536	+	39.2516i	0.515957	+	1.58795i
$612$		0			0
$613$	−24.9748	+	18.1453i	−1.00872	+	0.732881i	−0.963941	−	0.266115i	$-0.914260\pi$
$613$	−24.9748	+	18.1453i	−1.00872	+	0.732881i	−0.0447834	+	0.998997i	$0.514260\pi$
$614$		0			0
$615$	−6.86693			−0.276901
$616$		0			0
$617$	35.9658			1.44793			0.723963	−	0.689838i	$-0.242318\pi$
$617$	35.9658			1.44793			0.723963	+	0.689838i	$0.242318\pi$
$618$		0			0
$619$	−7.16135	+	5.20303i	−0.287839	+	0.209127i	−0.722329	−	0.691549i	$-0.756929\pi$
$619$	−7.16135	+	5.20303i	−0.287839	+	0.209127i	0.434490	+	0.900676i	$0.356929\pi$
$620$		0			0
$621$	0.733610	+	2.25782i	0.0294387	+	0.0906031i
$622$		0			0
$623$	−9.66814	−	7.02432i	−0.387346	−	0.281423i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	12.0025	+	9.83998i	0.479333	+	0.392971i
$628$		0			0
$629$	−2.94476	+	9.06303i	−0.117415	+	0.361367i
$630$		0			0
$631$	36.8226	+	26.7532i	1.46588	+	1.06503i	0.981781	+	0.190017i	$0.0608543\pi$
$631$	36.8226	+	26.7532i	1.46588	+	1.06503i	0.484104	+	0.875011i	$0.339146\pi$
$632$		0			0
$633$	2.03849	+	6.27382i	0.0810227	+	0.249362i
$634$		0			0
$635$	2.30391	−	1.67389i	0.0914281	−	0.0664264i
$636$		0			0
$637$	14.4640			0.573085
$638$		0			0
$639$	−15.7088			−0.621429
$640$		0			0
$641$	−19.2290	+	13.9707i	−0.759502	+	0.551810i	−0.898757	−	0.438446i	$-0.855529\pi$
$641$	−19.2290	+	13.9707i	−0.759502	+	0.551810i	0.139256	+	0.990256i	$0.455529\pi$
$642$		0			0
$643$	−8.23777	−	25.3533i	−0.324866	−	0.999835i	−0.971501	−	0.237035i	$-0.923824\pi$
$643$	−8.23777	−	25.3533i	−0.324866	−	0.999835i	0.646635	−	0.762799i	$-0.276176\pi$
$644$		0			0
$645$	4.02415	+	2.92371i	0.158451	+	0.115121i
$646$		0			0
$647$	−11.7568	+	36.1836i	−0.462206	+	1.42252i	0.400256	+	0.916403i	$0.368921\pi$
$647$	−11.7568	+	36.1836i	−0.462206	+	1.42252i	−0.862463	+	0.506121i	$0.831079\pi$
$648$		0			0
$649$	27.9580	−	17.9171i	1.09745	−	0.703307i
$650$		0			0
$651$	−0.127296	+	0.391776i	−0.00498912	+	0.0153549i
$652$		0			0
$653$	6.35856	+	4.61977i	0.248830	+	0.180785i	0.705208	−	0.709000i	$-0.250854\pi$
$653$	6.35856	+	4.61977i	0.248830	+	0.180785i	−0.456378	+	0.889786i	$0.650854\pi$
$654$		0			0
$655$	−2.93384	−	9.02943i	−0.114635	−	0.352809i
$656$		0			0
$657$	8.73521	−	6.34650i	0.340793	−	0.247600i
$658$		0			0
$659$	27.5518			1.07327			0.536633	−	0.843816i	$-0.319696\pi$
$659$	27.5518			1.07327			0.536633	+	0.843816i	$0.319696\pi$
$660$		0			0
$661$	39.6062			1.54050			0.770251	−	0.637741i	$-0.220131\pi$
$661$	39.6062			1.54050			0.770251	+	0.637741i	$0.220131\pi$
$662$		0			0
$663$	5.76170	−	4.18612i	0.223766	−	0.162575i
$664$		0			0
$665$	4.62172	+	14.2242i	0.179222	+	0.551590i
$666$		0			0
$667$	2.63076	+	1.91136i	0.101863	+	0.0740081i
$668$		0			0
$669$	2.08315	−	6.41129i	0.0805394	−	0.247875i
$670$		0			0
$671$	−28.1723	−	1.64704i	−1.08758	−	0.0635834i
$672$		0			0
$673$	−13.3256	+	41.0120i	−0.513665	+	1.58090i	0.272033	+	0.962288i	$0.412304\pi$
$673$	−13.3256	+	41.0120i	−0.513665	+	1.58090i	−0.785698	+	0.618610i	$0.787696\pi$
$674$		0			0
$675$	−2.61620	−	1.90078i	−0.100698	−	0.0731612i
$676$		0			0
$677$	−6.68482	−	20.5738i	−0.256919	−	0.790714i	−0.993446	−	0.114306i	$-0.963536\pi$
$677$	−6.68482	−	20.5738i	−0.256919	−	0.790714i	0.736527	−	0.676408i	$-0.236464\pi$
$678$		0			0
$679$	21.4263	−	15.5671i	0.822267	−	0.597412i
$680$		0			0
$681$	3.52699			0.135154
$682$		0			0
$683$	−1.01316			−0.0387675			−0.0193838	−	0.999812i	$-0.506170\pi$
$683$	−1.01316			−0.0387675			−0.0193838	+	0.999812i	$0.506170\pi$
$684$		0			0
$685$	5.69415	−	4.13704i	0.217562	−	0.158068i
$686$		0			0
$687$	−3.12889	−	9.62972i	−0.119374	−	0.367397i
$688$		0			0
$689$	31.2793	+	22.7257i	1.19165	+	0.865782i
$690$		0			0
$691$	−5.30938	+	16.3406i	−0.201978	+	0.621625i	0.797846	+	0.602862i	$0.205973\pi$
$691$	−5.30938	+	16.3406i	−0.201978	+	0.621625i	−0.999824	+	0.0187636i	$0.994027\pi$
$692$		0			0
$693$	−4.08791	−	15.6332i	−0.155287	−	0.593855i
$694$		0			0
$695$	1.15320	−	3.54919i	0.0437435	−	0.134629i
$696$		0			0
$697$	31.0346	+	22.5480i	1.17552	+	0.854065i
$698$		0			0
$699$	2.99806	+	9.22708i	0.113397	+	0.349000i
$700$		0			0
$701$	−14.1130	+	10.2537i	−0.533041	+	0.387277i	−0.821494	−	0.570217i	$-0.806859\pi$
$701$	−14.1130	+	10.2537i	−0.533041	+	0.387277i	0.288453	+	0.957494i	$0.406859\pi$
$702$		0			0
$703$	−24.5868			−0.927310
$704$		0			0
$705$	5.98900			0.225559
$706$		0			0
$707$	−14.5806	+	10.5934i	−0.548359	+	0.398406i
$708$		0			0
$709$	−5.27585	−	16.2374i	−0.198139	−	0.609809i	−0.999926	−	0.0121985i	$-0.996117\pi$
$709$	−5.27585	−	16.2374i	−0.198139	−	0.609809i	0.801787	−	0.597610i	$-0.203883\pi$
$710$		0			0
$711$	7.07252	+	5.13849i	0.265240	+	0.192708i
$712$		0			0
$713$	−0.0900583	+	0.277171i	−0.00337271	+	0.0103801i
$714$		0			0
$715$	4.74040	−	12.1298i	0.177281	−	0.453628i
$716$		0			0
$717$	−0.208870	+	0.642837i	−0.00780041	+	0.0240072i
$718$		0			0
$719$	20.4283	+	14.8420i	0.761847	+	0.553514i	0.899476	−	0.436969i	$-0.143948\pi$
$719$	20.4283	+	14.8420i	0.761847	+	0.553514i	−0.137629	+	0.990484i	$0.543948\pi$
$720$		0			0
$721$	−4.05812	−	12.4896i	−0.151132	−	0.465138i
$722$		0			0
$723$	4.77604	−	3.46999i	0.177623	−	0.129050i
$724$		0			0
$725$	−4.42950			−0.164508
$726$		0			0
$727$	−49.9360			−1.85202			−0.926012	−	0.377493i	$-0.876786\pi$
$727$	−49.9360			−1.85202			−0.926012	+	0.377493i	$0.876786\pi$
$728$		0			0
$729$	8.91101	−	6.47423i	0.330037	−	0.239786i
$730$		0			0
$731$	−8.58667	−	26.4271i	−0.317589	−	0.977440i
$732$		0			0
$733$	−12.0960	−	8.78827i	−0.446777	−	0.324602i	0.341545	−	0.939865i	$-0.389050\pi$
$733$	−12.0960	−	8.78827i	−0.446777	−	0.324602i	−0.788322	+	0.615263i	$0.789050\pi$
$734$		0			0
$735$	0.648595	−	1.99617i	0.0239238	−	0.0736299i
$736$		0			0
$737$	−1.34131	+	3.43216i	−0.0494078	+	0.126425i
$738$		0			0
$739$	2.68449	−	8.26201i	0.0987506	−	0.303923i	−0.889462	−	0.457008i	$-0.848921\pi$
$739$	2.68449	−	8.26201i	0.0987506	−	0.303923i	0.988213	+	0.153085i	$0.0489209\pi$
$740$		0			0
$741$	14.8657	+	10.8006i	0.546106	+	0.396769i
$742$		0			0
$743$	−3.68414	−	11.3386i	−0.135158	−	0.415974i	0.860457	−	0.509524i	$-0.170178\pi$
$743$	−3.68414	−	11.3386i	−0.135158	−	0.415974i	−0.995615	+	0.0935503i	$0.970178\pi$
$744$		0			0
$745$	−9.93074	+	7.21510i	−0.363834	+	0.264341i
$746$		0			0
$747$	31.7214			1.16063
$748$		0			0
$749$	17.8056			0.650604
$750$		0			0
$751$	−42.3343	+	30.7577i	−1.54480	+	1.12236i	−0.597567	+	0.801819i	$0.703866\pi$
$751$	−42.3343	+	30.7577i	−1.54480	+	1.12236i	−0.947233	+	0.320545i	$0.896134\pi$
$752$		0			0
$753$	−3.46546	−	10.6656i	−0.126288	−	0.388676i
$754$		0			0
$755$	4.69436	+	3.41065i	0.170845	+	0.124126i
$756$		0			0
$757$	−13.9295	+	42.8707i	−0.506277	+	1.55816i	0.292335	+	0.956316i	$0.405568\pi$
$757$	−13.9295	+	42.8707i	−0.506277	+	1.55816i	−0.798612	+	0.601846i	$0.794432\pi$
$758$		0			0
$759$	0.350978	+	1.34223i	0.0127397	+	0.0487197i
$760$		0			0
$761$	7.01931	−	21.6032i	0.254450	−	0.783116i	−0.739488	−	0.673170i	$-0.764932\pi$
$761$	7.01931	−	21.6032i	0.254450	−	0.783116i	0.993938	−	0.109946i	$-0.0350678\pi$
$762$		0			0
$763$	27.5993	+	20.0521i	0.999162	+	0.725934i
$764$		0			0
$765$	2.63153	+	8.09902i	0.0951432	+	0.292821i
$766$		0			0
$767$	31.8057	−	23.1082i	1.14844	−	0.834388i
$768$		0			0
$769$	−10.5711			−0.381202			−0.190601	−	0.981668i	$-0.561044\pi$
$769$	−10.5711			−0.381202			−0.190601	+	0.981668i	$0.561044\pi$
$770$		0			0
$771$	−7.65933			−0.275844
$772$		0			0
$773$	7.04942	−	5.12171i	0.253550	−	0.184215i	−0.453749	−	0.891130i	$-0.649914\pi$
$773$	7.04942	−	5.12171i	0.253550	−	0.184215i	0.707299	+	0.706915i	$0.249914\pi$
$774$		0			0
$775$	−0.122675	−	0.377554i	−0.00440661	−	0.0135621i
$776$		0			0
$777$	−2.51324	−	1.82598i	−0.0901621	−	0.0655066i
$778$		0			0
$779$	−30.5849	+	94.1305i	−1.09582	+	3.37258i
$780$		0			0
$781$	−19.4411	−	1.13659i	−0.695657	−	0.0406703i
$782$		0			0
$783$	−4.42641	+	13.6231i	−0.158187	+	0.486849i
$784$		0			0
$785$	16.7755	+	12.1881i	0.598742	+	0.435011i
$786$		0			0
$787$	−16.0922	−	49.5266i	−0.573624	−	1.76543i	−0.640819	−	0.767692i	$-0.721405\pi$
$787$	−16.0922	−	49.5266i	−0.573624	−	1.76543i	0.0671948	−	0.997740i	$-0.478595\pi$
$788$		0			0
$789$	−0.741160	+	0.538484i	−0.0263860	+	0.0191705i
$790$		0			0
$791$	−23.4220			−0.832789
$792$		0			0
$793$	−33.4109			−1.18646
$794$		0			0
$795$	4.53899	−	3.29777i	0.160982	−	0.116960i
$796$		0			0
$797$	15.0541	+	46.3318i	0.533244	+	1.64116i	0.747414	+	0.664359i	$0.231295\pi$
$797$	15.0541	+	46.3318i	0.533244	+	1.64116i	−0.214170	+	0.976796i	$0.568705\pi$
$798$		0			0
$799$	−27.0669	−	19.6652i	−0.957557	−	0.695706i
$800$		0			0
$801$	5.42511	−	16.6968i	0.191687	−	0.589952i
$802$		0			0
$803$	11.2698	−	7.22237i	0.397704	−	0.254872i
$804$		0			0
$805$	−0.413130	+	1.27148i	−0.0145609	+	0.0448139i
$806$		0			0
$807$	4.15658	+	3.01993i	0.146319	+	0.106307i
$808$		0			0
$809$	−4.63541	−	14.2663i	−0.162972	−	0.501577i	0.835909	−	0.548868i	$-0.184941\pi$
$809$	−4.63541	−	14.2663i	−0.162972	−	0.501577i	−0.998881	+	0.0472912i	$0.984941\pi$
$810$		0			0
$811$	−30.1267	+	21.8883i	−1.05789	+	0.768604i	−0.973697	−	0.227845i	$-0.926832\pi$
$811$	−30.1267	+	21.8883i	−1.05789	+	0.768604i	−0.0841952	+	0.996449i	$0.526832\pi$
$812$		0			0
$813$	11.0460			0.387399
$814$		0			0
$815$	−11.8323			−0.414468
$816$		0			0
$817$	58.0010	−	42.1402i	2.02920	−	1.47430i
$818$		0			0
$819$	−5.91174	−	18.1945i	−0.206573	−	0.635766i
$820$		0			0
$821$	14.5410	+	10.5647i	0.507484	+	0.368709i	0.811868	−	0.583841i	$-0.198451\pi$
$821$	14.5410	+	10.5647i	0.507484	+	0.368709i	−0.304384	+	0.952549i	$0.598451\pi$
$822$		0			0
$823$	−5.67762	+	17.4739i	−0.197910	+	0.609103i	0.802021	+	0.597296i	$0.203758\pi$
$823$	−5.67762	+	17.4739i	−0.197910	+	0.609103i	−0.999930	+	0.0118068i	$0.996242\pi$
$824$		0			0
$825$	−1.46146	−	1.19814i	−0.0508814	−	0.0417140i
$826$		0			0
$827$	11.9313	−	36.7207i	0.414891	−	1.27690i	−0.497457	−	0.867489i	$-0.665733\pi$
$827$	11.9313	−	36.7207i	0.414891	−	1.27690i	0.912348	−	0.409415i	$-0.134267\pi$
$828$		0			0
$829$	−42.6490	−	30.9863i	−1.48126	−	1.07620i	−0.977148	−	0.212561i	$-0.931820\pi$
$829$	−42.6490	−	30.9863i	−1.48126	−	1.07620i	−0.504113	−	0.863638i	$-0.668180\pi$
$830$		0			0
$831$	−0.339298	−	1.04425i	−0.0117701	−	0.0362247i
$832$		0			0
$833$	−9.48583	+	6.89186i	−0.328664	+	0.238789i
$834$		0			0
$835$	−18.1848			−0.629312
$836$		0			0
$837$	−1.28377			−0.0443736
$838$		0			0
$839$	20.9129	−	15.1941i	0.721995	−	0.524560i	−0.165026	−	0.986289i	$-0.552771\pi$
$839$	20.9129	−	15.1941i	0.721995	−	0.524560i	0.887021	+	0.461729i	$0.152771\pi$
$840$		0			0
$841$	−2.89843	−	8.92044i	−0.0999458	−	0.307601i
$842$		0			0
$843$	−1.01086	−	0.734434i	−0.0348159	−	0.0252953i
$844$		0			0
$845$	0.747345	−	2.30009i	0.0257094	−	0.0791255i
$846$		0			0
$847$	−3.92805	−	19.6433i	−0.134970	−	0.674952i
$848$		0			0
$849$	5.10473	−	15.7108i	0.175194	−	0.539192i
$850$		0			0
$851$	−1.77805	−	1.29183i	−0.0609508	−	0.0442833i
$852$		0			0
$853$	−7.84633	−	24.1485i	−0.268653	−	0.826829i	−0.990829	−	0.135120i	$-0.956858\pi$
$853$	−7.84633	−	24.1485i	−0.268653	−	0.826829i	0.722176	−	0.691709i	$-0.243142\pi$
$854$		0			0
$855$	−17.7754	+	12.9146i	−0.607906	+	0.441670i
$856$		0			0
$857$	4.42328			0.151096			0.0755482	−	0.997142i	$-0.475929\pi$
$857$	4.42328			0.151096			0.0755482	+	0.997142i	$0.475929\pi$
$858$		0			0
$859$	−13.1491			−0.448643			−0.224321	−	0.974515i	$-0.572017\pi$
$859$	−13.1491			−0.448643			−0.224321	+	0.974515i	$0.572017\pi$
$860$		0			0
$861$	−10.1171	+	7.35050i	−0.344790	+	0.250504i
$862$		0			0
$863$	4.77082	+	14.6831i	0.162401	+	0.499817i	0.998835	−	0.0482490i	$-0.0153641\pi$
$863$	4.77082	+	14.6831i	0.162401	+	0.499817i	−0.836435	+	0.548066i	$0.815364\pi$
$864$		0			0
$865$	8.26429	+	6.00436i	0.280994	+	0.204154i
$866$		0			0
$867$	1.20929	−	3.72181i	0.0410697	−	0.126399i
$868$		0			0
$869$	8.38113	+	6.87109i	0.284310	+	0.233086i
$870$		0			0
$871$	−1.34815	+	4.14917i	−0.0456803	+	0.140589i
$872$		0			0
$873$	31.4767	+	22.8691i	1.06532	+	0.774003i
$874$		0			0
$875$	−0.562754	−	1.73198i	−0.0190245	−	0.0585515i
$876$		0			0
$877$	−5.68080	+	4.12734i	−0.191827	+	0.139370i	−0.679553	−	0.733626i	$-0.737826\pi$
$877$	−5.68080	+	4.12734i	−0.191827	+	0.139370i	0.487726	+	0.872997i	$0.337826\pi$
$878$		0			0
$879$	−3.47516			−0.117214
$880$		0			0
$881$	22.0522			0.742958			0.371479	−	0.928441i	$-0.378851\pi$
$881$	22.0522			0.742958			0.371479	+	0.928441i	$0.378851\pi$
$882$		0			0
$883$	−9.75332	+	7.08620i	−0.328225	+	0.238470i	−0.739677	−	0.672962i	$-0.765022\pi$
$883$	−9.75332	+	7.08620i	−0.328225	+	0.238470i	0.411452	+	0.911432i	$0.365022\pi$
$884$		0			0
$885$	−1.76292	−	5.42570i	−0.0592598	−	0.182383i
$886$		0			0
$887$	26.8102	+	19.4788i	0.900199	+	0.654033i	0.938517	−	0.345233i	$-0.112200\pi$
$887$	26.8102	+	19.4788i	0.900199	+	0.654033i	−0.0383180	+	0.999266i	$0.512200\pi$
$888$		0			0
$889$	1.60261	−	4.93232i	0.0537497	−	0.165425i
$890$		0			0
$891$	17.2665	−	11.0654i	0.578448	−	0.370703i
$892$		0			0
$893$	26.6746	−	82.0961i	0.892632	−	2.74724i
$894$		0			0
$895$	−1.39437	−	1.01307i	−0.0466085	−	0.0338631i
$896$		0			0
$897$	0.507568	+	1.56213i	0.0169472	+	0.0521582i
$898$		0			0
$899$	−1.42261	+	1.03359i	−0.0474467	+	0.0344720i
$900$		0			0
$901$	−31.3421			−1.04416
$902$		0			0
$903$	9.05841			0.301445
$904$		0			0
$905$	−11.2875	+	8.20083i	−0.375208	+	0.272605i
$906$		0			0
$907$	−6.56457	−	20.2037i	−0.217973	−	0.670852i	−0.998929	−	0.0462662i	$-0.985268\pi$
$907$	−6.56457	−	20.2037i	−0.217973	−	0.670852i	0.780956	−	0.624586i	$-0.214732\pi$
$908$		0			0
$909$	−21.4198	−	15.5624i	−0.710450	−	0.516172i
$910$		0			0
$911$	14.8255	−	45.6281i	0.491190	−	1.51173i	−0.331621	−	0.943413i	$-0.607596\pi$
$911$	14.8255	−	45.6281i	0.491190	−	1.51173i	0.822811	−	0.568315i	$-0.192404\pi$
$912$		0			0
$913$	39.2583	+	2.29516i	1.29926	+	0.0759587i
$914$		0			0
$915$	−1.49821	+	4.61102i	−0.0495293	+	0.152436i
$916$		0			0
$917$	−13.9877	−	10.1627i	−0.461916	−	0.335602i
$918$		0			0
$919$	−2.11876	−	6.52088i	−0.0698915	−	0.215104i	0.910010	−	0.414587i	$-0.136074\pi$
$919$	−2.11876	−	6.52088i	−0.0698915	−	0.215104i	−0.979901	+	0.199483i	$0.936074\pi$
$920$		0			0
$921$	7.03269	−	5.10955i	0.231735	−	0.168365i
$922$		0			0
$923$	−23.0561			−0.758901
$924$		0			0
$925$	2.99377			0.0984344
$926$		0			0
$927$	15.6078	−	11.3397i	0.512627	−	0.372445i
$928$		0			0
$929$	−12.4369	−	38.2768i	−0.408041	−	1.25582i	−0.918329	−	0.395817i	$-0.870462\pi$
$929$	−12.4369	−	38.2768i	−0.408041	−	1.25582i	0.510289	−	0.860003i	$-0.329538\pi$
$930$		0			0
$931$	−24.4743	−	17.7816i	−0.802114	−	0.582770i
$932$		0			0
$933$	0.610245	−	1.87814i	0.0199785	−	0.0614876i
$934$		0			0
$935$	2.67078	+	10.2137i	0.0873437	+	0.334024i
$936$		0			0
$937$	14.6628	−	45.1274i	0.479012	−	1.47425i	−0.361457	−	0.932389i	$-0.617721\pi$
$937$	14.6628	−	45.1274i	0.479012	−	1.47425i	0.840469	−	0.541859i	$-0.182279\pi$
$938$		0			0
$939$	6.01413	+	4.36952i	0.196264	+	0.142594i
$940$		0			0
$941$	5.72913	+	17.6324i	0.186764	+	0.574801i	0.999974	−	0.00716913i	$-0.00228202\pi$
$941$	5.72913	+	17.6324i	0.186764	+	0.574801i	−0.813210	+	0.581970i	$0.802282\pi$
$942$		0			0
$943$	−7.15756	+	5.20027i	−0.233082	+	0.169344i
$944$		0			0
$945$	−5.88911			−0.191573
$946$		0			0
$947$	−57.2726			−1.86111			−0.930555	−	0.366153i	$-0.880675\pi$
$947$	−57.2726			−1.86111			−0.930555	+	0.366153i	$0.880675\pi$
$948$		0			0
$949$	12.8208	−	9.31489i	0.416182	−	0.302374i
$950$		0			0
$951$	5.33271	+	16.4124i	0.172925	+	0.532208i
$952$		0			0
$953$	−0.914039	−	0.664088i	−0.0296086	−	0.0215119i	0.572883	−	0.819637i	$-0.305825\pi$
$953$	−0.914039	−	0.664088i	−0.0296086	−	0.0215119i	−0.602491	+	0.798126i	$0.705825\pi$
$954$		0			0
$955$	7.63053	−	23.4844i	0.246918	−	0.759936i
$956$		0			0
$957$	−3.04700	+	7.79670i	−0.0984956	+	0.252031i
$958$		0			0
$959$	3.96086	−	12.1903i	0.127903	−	0.393645i
$960$		0			0
$961$	24.9520	+	18.1287i	0.804904	+	0.584797i
$962$		0			0
$963$	8.08315	+	24.8774i	0.260476	+	0.801662i
$964$		0			0
$965$	−2.15726	+	1.56734i	−0.0694447	+	0.0504545i
$966$		0			0
$967$	−54.1275			−1.74062			−0.870311	−	0.492502i	$-0.836083\pi$
$967$	−54.1275			−1.74062			−0.870311	+	0.492502i	$0.836083\pi$
$968$		0			0
$969$	−14.8956			−0.478515
$970$		0			0
$971$	−16.3101	+	11.8500i	−0.523418	+	0.380285i	−0.817890	−	0.575375i	$-0.804856\pi$
$971$	−16.3101	+	11.8500i	−0.523418	+	0.380285i	0.294472	+	0.955660i	$0.404856\pi$
$972$		0			0
$973$	−2.10011	−	6.46347i	−0.0673264	−	0.207209i
$974$		0			0
$975$	−1.81009	−	1.31511i	−0.0579694	−	0.0421173i
$976$		0			0
$977$	−13.0910	+	40.2899i	−0.418818	+	1.28899i	0.489973	+	0.871738i	$0.337007\pi$
$977$	−13.0910	+	40.2899i	−0.418818	+	1.28899i	−0.908791	+	0.417252i	$0.862993\pi$
$978$		0			0
$979$	7.92217	−	20.2713i	0.253194	−	0.647874i
$980$		0			0
$981$	−15.4869	+	47.6637i	−0.494458	+	1.52179i
$982$		0			0
$983$	−42.6490	−	30.9863i	−1.36029	−	0.988310i	−0.998426	−	0.0560793i	$-0.982140\pi$
$983$	−42.6490	−	30.9863i	−1.36029	−	0.988310i	−0.361865	−	0.932230i	$-0.617860\pi$
$984$		0			0
$985$	6.62152	+	20.3789i	0.210979	+	0.649327i
$986$		0			0
$987$	8.82364	−	6.41075i	0.280860	−	0.204056i
$988$		0			0
$989$	6.40858			0.203781
$990$		0			0
$991$	25.8605			0.821487			0.410744	−	0.911751i	$-0.365269\pi$
$991$	25.8605			0.821487			0.410744	+	0.911751i	$0.365269\pi$
$992$		0			0
$993$	1.93234	−	1.40393i	0.0613211	−	0.0445524i
$994$		0			0
$995$	−1.78633	−	5.49775i	−0.0566304	−	0.174290i
$996$		0			0
$997$	−0.179657	−	0.130528i	−0.00568978	−	0.00413387i	0.584937	−	0.811079i	$-0.301119\pi$
$997$	−0.179657	−	0.130528i	−0.00568978	−	0.00413387i	−0.590627	+	0.806945i	$0.701119\pi$
$998$		0			0
$999$	2.99167	−	9.20742i	0.0946524	−	0.291310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.y.d.361.3	✓	16
4.3	odd	2		880.2.bo.k.801.2		16
11.4	even	5		4840.2.a.bg.1.4		8
11.5	even	5	inner	440.2.y.d.401.3	yes	16
11.7	odd	10		4840.2.a.bh.1.4		8
44.7	even	10		9680.2.a.de.1.5		8
44.15	odd	10		9680.2.a.df.1.5		8
44.27	odd	10		880.2.bo.k.401.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.d.361.3	✓	16	1.1	even	1	trivial
440.2.y.d.401.3	yes	16	11.5	even	5	inner
880.2.bo.k.401.2		16	44.27	odd	10
880.2.bo.k.801.2		16	4.3	odd	2
4840.2.a.bg.1.4		8	11.4	even	5
4840.2.a.bh.1.4		8	11.7	odd	10
9680.2.a.de.1.5		8	44.7	even	10
9680.2.a.df.1.5		8	44.15	odd	10

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:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.460979 - 0.334921i) q^{3} +(0.309017 + 0.951057i) q^{5} +(1.47331 + 1.07042i) q^{7} +(-0.826721 + 2.54439i) q^{9} +(-1.20724 + 3.08910i) q^{11} +(-1.21340 + 3.73445i) q^{13} +(0.460979 + 0.334921i) q^{15} +(-0.983630 - 3.02730i) q^{17} +(6.64420 - 4.82729i) q^{19} +1.03767 q^{21} +0.734122 q^{23} +(-0.809017 + 0.587785i) q^{25} +(0.999301 + 3.07553i) q^{27} +(3.58354 + 2.60360i) q^{29} +(-0.122675 + 0.377554i) q^{31} +(0.478092 + 1.82834i) q^{33} +(-0.562754 + 1.73198i) q^{35} +(-2.42201 - 1.75969i) q^{37} +(0.691395 + 2.12789i) q^{39} +(-9.74982 + 7.08366i) q^{41} +8.72957 q^{43} -2.67533 q^{45} +(8.50332 - 6.17803i) q^{47} +(-1.13828 - 3.50328i) q^{49} +(-1.46734 - 1.06608i) q^{51} +(3.04271 - 9.36451i) q^{53} +(-3.31097 - 0.193570i) q^{55} +(1.44607 - 4.45056i) q^{57} +(-8.09998 - 5.88498i) q^{59} +(2.62936 + 8.09234i) q^{61} +(-3.94158 + 2.86373i) q^{63} -3.92663 q^{65} +1.11105 q^{67} +(0.338415 - 0.245873i) q^{69} +(1.81446 + 5.58434i) q^{71} +(-3.26510 - 2.37223i) q^{73} +(-0.176078 + 0.541913i) q^{75} +(-5.08528 + 3.25894i) q^{77} +(1.00977 - 3.10775i) q^{79} +(-5.00244 - 3.63448i) q^{81} +(-3.66402 - 11.2767i) q^{83} +(2.57518 - 1.87098i) q^{85} +2.52394 q^{87} -6.56220 q^{89} +(-5.78514 + 4.20315i) q^{91} +(0.0699002 + 0.215131i) q^{93} +(6.64420 + 4.82729i) q^{95} +(4.49404 - 13.8312i) q^{97} +(-6.86182 - 5.62552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{3} - 4 q^{5} + 8 q^{7} - 7 q^{9} - 7 q^{11} - 11 q^{13} - 3 q^{15} + 9 q^{17} - 2 q^{19} + 12 q^{21} + 20 q^{23} - 4 q^{25} - 9 q^{27} + q^{29} - 2 q^{31} - 32 q^{33} - 2 q^{35} - 16 q^{37}+ \cdots - 10 q^{99}+O(q^{100}) \) 16 * q - 3 * q^3 - 4 * q^5 + 8 * q^7 - 7 * q^9 - 7 * q^11 - 11 * q^13 - 3 * q^15 + 9 * q^17 - 2 * q^19 + 12 * q^21 + 20 * q^23 - 4 * q^25 - 9 * q^27 + q^29 - 2 * q^31 - 32 * q^33 - 2 * q^35 - 16 * q^37 + 3 * q^39 - 11 * q^41 - 16 * q^43 + 38 * q^45 - 10 * q^47 + 4 * q^49 + 26 * q^51 - 9 * q^53 + 3 * q^55 - 50 * q^57 - 60 * q^59 + 30 * q^61 + 52 * q^63 + 24 * q^65 - 4 * q^67 + 41 * q^69 - 10 * q^71 + q^73 + 2 * q^75 - 4 * q^77 + 19 * q^79 - 31 * q^81 + 64 * q^83 - 11 * q^85 + 30 * q^87 + 24 * q^89 - 9 * q^91 + 45 * q^93 - 2 * q^95 - 3 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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