LMFDB - Embedded newform 2070.2.j.i.323.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.j (of order $4$, degree $2$, 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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} + 28x^{14} + 290x^{12} + 1396x^{10} + 3263x^{8} + 3508x^{6} + 1442x^{4} + 128x^{2} + 1 $ x^16 + 28x^14 + 290x^12 + 1396x^10 + 3263x^8 + 3508x^6 + 1442x^4 + 128*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.6
Root			$0.0929247i$ of defining polynomial
Character	$\chi$	$=$	2070.323
Dual form			2070.2.j.i.737.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.27669 - 1.83577i) q^{5} +(-1.54563 + 1.54563i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.27669 - 1.83577i) q^{5} +(-1.54563 + 1.54563i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.395329 - 2.20084i) q^{10} -3.67154i q^{11} +(2.00000 + 2.00000i) q^{13} -2.18585 q^{14} -1.00000 q^{16} +(0.367535 + 0.367535i) q^{17} +2.79066i q^{19} +(1.83577 - 1.27669i) q^{20} +(2.59617 - 2.59617i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-1.74011 + 4.68743i) q^{25} +2.82843i q^{26} +(-1.54563 - 1.54563i) q^{28} +8.41078 q^{29} -0.519773 q^{31} +(-0.707107 - 0.707107i) q^{32} +0.519773i q^{34} +(4.81071 + 0.864129i) q^{35} +(6.14180 - 6.14180i) q^{37} +(-1.97329 + 1.97329i) q^{38} +(2.20084 + 0.395329i) q^{40} +12.1033i q^{41} +(4.14180 + 4.14180i) q^{43} +3.67154 q^{44} +1.00000 q^{46} +(-1.13917 - 1.13917i) q^{47} +2.22206i q^{49} +(-4.54496 + 2.08407i) q^{50} +(-2.00000 + 2.00000i) q^{52} +(6.41647 - 6.41647i) q^{53} +(-6.74011 + 4.68743i) q^{55} -2.18585i q^{56} +(5.94732 + 5.94732i) q^{58} +8.96086 q^{59} +1.88191 q^{61} +(-0.367535 - 0.367535i) q^{62} -1.00000i q^{64} +(1.11816 - 6.22493i) q^{65} +(2.12908 - 2.12908i) q^{67} +(-0.367535 + 0.367535i) q^{68} +(2.79066 + 4.01272i) q^{70} +13.7211i q^{71} +(-4.42754 - 4.42754i) q^{73} +8.68582 q^{74} -2.79066 q^{76} +(5.67484 + 5.67484i) q^{77} +8.23189i q^{79} +(1.27669 + 1.83577i) q^{80} +(-8.55835 + 8.55835i) q^{82} +(5.86639 - 5.86639i) q^{83} +(0.205481 - 1.14394i) q^{85} +5.85739i q^{86} +(2.59617 + 2.59617i) q^{88} +8.50327 q^{89} -6.18252 q^{91} +(0.707107 + 0.707107i) q^{92} -1.61103i q^{94} +(5.12301 - 3.56281i) q^{95} +(-4.72525 + 4.72525i) q^{97} +(-1.57124 + 1.57124i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{10} + 32 q^{13} - 16 q^{16} - 24 q^{25} - 16 q^{31} + 32 q^{37} + 4 q^{40} + 16 q^{46} - 32 q^{52} - 104 q^{55} + 8 q^{58} - 40 q^{61} + 72 q^{67} + 24 q^{70} + 24 q^{73} - 24 q^{76} - 8 q^{82} - 8 q^{85} - 72 q^{97}+O(q^{100}) $ 16 * q - 4 * q^10 + 32 * q^13 - 16 * q^16 - 24 * q^25 - 16 * q^31 + 32 * q^37 + 4 * q^40 + 16 * q^46 - 32 * q^52 - 104 * q^55 + 8 * q^58 - 40 * q^61 + 72 * q^67 + 24 * q^70 + 24 * q^73 - 24 * q^76 - 8 * q^82 - 8 * q^85 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−1.27669	−	1.83577i	−0.570954	−	0.820982i
$5$	−1.27669	−	1.83577i	−0.570954	−	0.820982i
$6$		0			0
$7$	−1.54563	+	1.54563i	−0.584193	+	0.584193i	−0.936053	−	0.351860i	$-0.885549\pi$
$7$	−1.54563	+	1.54563i	−0.584193	+	0.584193i	0.351860	+	0.936053i	$0.385549\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	0.395329	−	2.20084i	0.125014	−	0.695968i
$11$		−	3.67154i		−	1.10701i	−0.832845	−	0.553506i	$-0.813290\pi$
$11$		−	3.67154i		−	1.10701i	0.832845	−	0.553506i	$-0.186710\pi$
$12$		0			0
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	0.927794	−	0.373094i	$-0.121703\pi$
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	−0.373094	+	0.927794i	$0.621703\pi$
$14$	−2.18585			−0.584193
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.367535	+	0.367535i	0.0891404	+	0.0891404i	0.750271	−	0.661131i	$-0.229923\pi$
$17$	0.367535	+	0.367535i	0.0891404	+	0.0891404i	−0.661131	+	0.750271i	$0.729923\pi$
$18$		0			0
$19$			2.79066i			0.640221i	0.947380	+	0.320110i	$0.103720\pi$
$19$			2.79066i			0.640221i	−0.947380	+	0.320110i	$0.896280\pi$
$20$	1.83577	−	1.27669i	0.410491	−	0.285477i
$21$		0			0
$22$	2.59617	−	2.59617i	0.553506	−	0.553506i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$24$		0			0
$25$	−1.74011	+	4.68743i	−0.348023	+	0.937486i
$26$			2.82843i			0.554700i
$27$		0			0
$28$	−1.54563	−	1.54563i	−0.292096	−	0.292096i
$29$	8.41078			1.56184			0.780921	−	0.624630i	$-0.214750\pi$
$29$	8.41078			1.56184			0.780921	+	0.624630i	$0.214750\pi$
$30$		0			0
$31$	−0.519773			−0.0933541			−0.0466770	−	0.998910i	$-0.514863\pi$
$31$	−0.519773			−0.0933541			−0.0466770	+	0.998910i	$0.514863\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$			0.519773i			0.0891404i
$35$	4.81071	+	0.864129i	0.813159	+	0.146064i
$36$		0			0
$37$	6.14180	−	6.14180i	1.00971	−	1.00971i	0.00975355	−	0.999952i	$-0.496895\pi$
$37$	6.14180	−	6.14180i	1.00971	−	1.00971i	0.999952	−	0.00975355i	$-0.00310470\pi$
$38$	−1.97329	+	1.97329i	−0.320110	+	0.320110i
$39$		0			0
$40$	2.20084	+	0.395329i	0.347984	+	0.0625069i
$41$			12.1033i			1.89022i	0.326748	+	0.945112i	$0.394047\pi$
$41$			12.1033i			1.89022i	−0.326748	+	0.945112i	$0.605953\pi$
$42$		0			0
$43$	4.14180	+	4.14180i	0.631619	+	0.631619i	0.948474	−	0.316855i	$-0.102627\pi$
$43$	4.14180	+	4.14180i	0.631619	+	0.631619i	−0.316855	+	0.948474i	$0.602627\pi$
$44$	3.67154			0.553506
$45$		0			0
$46$	1.00000			0.147442
$47$	−1.13917	−	1.13917i	−0.166165	−	0.166165i	0.619126	−	0.785291i	$-0.287487\pi$
$47$	−1.13917	−	1.13917i	−0.166165	−	0.166165i	−0.785291	+	0.619126i	$0.787487\pi$
$48$		0			0
$49$			2.22206i			0.317438i
$50$	−4.54496	+	2.08407i	−0.642754	+	0.294732i
$51$		0			0
$52$	−2.00000	+	2.00000i	−0.277350	+	0.277350i
$53$	6.41647	−	6.41647i	0.881370	−	0.881370i	−0.112304	−	0.993674i	$-0.535823\pi$
$53$	6.41647	−	6.41647i	0.881370	−	0.881370i	0.993674	+	0.112304i	$0.0358230\pi$
$54$		0			0
$55$	−6.74011	+	4.68743i	−0.908837	+	0.632053i
$56$		−	2.18585i		−	0.292096i
$57$		0			0
$58$	5.94732	+	5.94732i	0.780921	+	0.780921i
$59$	8.96086			1.16660			0.583302	−	0.812255i	$-0.301760\pi$
$59$	8.96086			1.16660			0.583302	+	0.812255i	$0.301760\pi$
$60$		0			0
$61$	1.88191			0.240955			0.120477	−	0.992716i	$-0.461558\pi$
$61$	1.88191			0.240955			0.120477	+	0.992716i	$0.461558\pi$
$62$	−0.367535	−	0.367535i	−0.0466770	−	0.0466770i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	1.11816	−	6.22493i	0.138690	−	0.772107i
$66$		0			0
$67$	2.12908	−	2.12908i	0.260109	−	0.260109i	−0.564989	−	0.825098i	$-0.691120\pi$
$67$	2.12908	−	2.12908i	0.260109	−	0.260109i	0.825098	+	0.564989i	$0.191120\pi$
$68$	−0.367535	+	0.367535i	−0.0445702	+	0.0445702i
$69$		0			0
$70$	2.79066	+	4.01272i	0.333547	+	0.479612i
$71$			13.7211i			1.62840i	0.580587	+	0.814198i	$0.302823\pi$
$71$			13.7211i			1.62840i	−0.580587	+	0.814198i	$0.697177\pi$
$72$		0			0
$73$	−4.42754	−	4.42754i	−0.518205	−	0.518205i	0.398823	−	0.917028i	$-0.369419\pi$
$73$	−4.42754	−	4.42754i	−0.518205	−	0.518205i	−0.917028	+	0.398823i	$0.869419\pi$
$74$	8.68582			1.00971
$75$		0			0
$76$	−2.79066			−0.320110
$77$	5.67484	+	5.67484i	0.646708	+	0.646708i
$78$		0			0
$79$			8.23189i			0.926160i	0.886316	+	0.463080i	$0.153256\pi$
$79$			8.23189i			0.926160i	−0.886316	+	0.463080i	$0.846744\pi$
$80$	1.27669	+	1.83577i	0.142739	+	0.205245i
$81$		0			0
$82$	−8.55835	+	8.55835i	−0.945112	+	0.945112i
$83$	5.86639	−	5.86639i	0.643920	−	0.643920i	−0.307597	−	0.951517i	$-0.599525\pi$
$83$	5.86639	−	5.86639i	0.643920	−	0.643920i	0.951517	+	0.307597i	$0.0995249\pi$
$84$		0			0
$85$	0.205481	−	1.14394i	0.0222876	−	0.124078i
$86$			5.85739i			0.631619i
$87$		0			0
$88$	2.59617	+	2.59617i	0.276753	+	0.276753i
$89$	8.50327			0.901345			0.450672	−	0.892689i	$-0.351184\pi$
$89$	8.50327			0.901345			0.450672	+	0.892689i	$0.351184\pi$
$90$		0			0
$91$	−6.18252			−0.648104
$92$	0.707107	+	0.707107i	0.0737210	+	0.0737210i
$93$		0			0
$94$		−	1.61103i		−	0.166165i
$95$	5.12301	−	3.56281i	0.525610	−	0.365537i
$96$		0			0
$97$	−4.72525	+	4.72525i	−0.479777	+	0.479777i	−0.905060	−	0.425283i	$-0.860174\pi$
$97$	−4.72525	+	4.72525i	−0.479777	+	0.479777i	0.425283	+	0.905060i	$0.360174\pi$
$98$	−1.57124	+	1.57124i	−0.158719	+	0.158719i
$99$		0			0
$100$	−4.68743	−	1.74011i	−0.468743	−	0.174011i
$101$			13.3326i			1.32664i	0.748336	+	0.663320i	$0.230853\pi$
$101$			13.3326i			1.32664i	−0.748336	+	0.663320i	$0.769147\pi$
$102$		0			0
$103$	1.54563	+	1.54563i	0.152295	+	0.152295i	0.779142	−	0.626847i	$-0.215655\pi$
$103$	1.54563	+	1.54563i	0.152295	+	0.152295i	−0.626847	+	0.779142i	$0.715655\pi$
$104$	−2.82843			−0.277350
$105$		0			0
$106$	9.07426			0.881370
$107$	−8.40178	−	8.40178i	−0.812231	−	0.812231i	0.172737	−	0.984968i	$-0.444739\pi$
$107$	−8.40178	−	8.40178i	−0.812231	−	0.812231i	−0.984968	+	0.172737i	$0.944739\pi$
$108$		0			0
$109$			6.14008i			0.588113i	0.955788	+	0.294056i	$0.0950054\pi$
$109$			6.14008i			0.588113i	−0.955788	+	0.294056i	$0.904995\pi$
$110$	−8.08049	−	1.45147i	−0.770445	−	0.138392i
$111$		0			0
$112$	1.54563	−	1.54563i	0.146048	−	0.146048i
$113$	−9.75351	+	9.75351i	−0.917533	+	0.917533i	−0.996849	−	0.0793164i	$-0.974726\pi$
$113$	−9.75351	+	9.75351i	−0.917533	+	0.917533i	0.0793164	+	0.996849i	$0.474726\pi$
$114$		0			0
$115$	−2.20084	−	0.395329i	−0.205230	−	0.0368646i
$116$			8.41078i			0.780921i
$117$		0			0
$118$	6.33629	+	6.33629i	0.583302	+	0.583302i
$119$	−1.13615			−0.104150
$120$		0			0
$121$	−2.48023			−0.225475
$122$	1.33071	+	1.33071i	0.120477	+	0.120477i
$123$		0			0
$124$		−	0.519773i		−	0.0466770i
$125$	10.8266	−	2.78996i	0.968364	−	0.249541i
$126$		0			0
$127$	3.18252	−	3.18252i	0.282403	−	0.282403i	−0.551664	−	0.834067i	$-0.686007\pi$
$127$	3.18252	−	3.18252i	0.282403	−	0.282403i	0.834067	+	0.551664i	$0.186007\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	5.19235	−	3.61103i	0.455399	−	0.316708i
$131$		−	20.3105i		−	1.77454i	−0.461250	−	0.887270i	$-0.652599\pi$
$131$		−	20.3105i		−	1.77454i	0.461250	−	0.887270i	$-0.347401\pi$
$132$		0			0
$133$	−4.31332	−	4.31332i	−0.374012	−	0.374012i
$134$	3.01098			0.260109
$135$		0			0
$136$	−0.519773			−0.0445702
$137$	5.30731	+	5.30731i	0.453434	+	0.453434i	0.896493	−	0.443059i	$-0.146107\pi$
$137$	5.30731	+	5.30731i	0.453434	+	0.453434i	−0.443059	+	0.896493i	$0.646107\pi$
$138$		0			0
$139$		−	2.54949i		−	0.216245i	−0.994138	−	0.108122i	$-0.965516\pi$
$139$		−	2.54949i		−	0.216245i	0.994138	−	0.108122i	$-0.0344839\pi$
$140$	−0.864129	+	4.81071i	−0.0730322	+	0.406580i
$141$		0			0
$142$	−9.70229	+	9.70229i	−0.814198	+	0.814198i
$143$	7.34309	−	7.34309i	0.614060	−	0.614060i
$144$		0			0
$145$	−10.7380	−	15.4403i	−0.891740	−	1.28224i
$146$		−	6.26149i		−	0.518205i
$147$		0			0
$148$	6.14180	+	6.14180i	0.504853	+	0.504853i
$149$	17.2636			1.41429			0.707144	−	0.707069i	$-0.249983\pi$
$149$	17.2636			1.41429			0.707144	+	0.707069i	$0.249983\pi$
$150$		0			0
$151$	−0.0297170			−0.00241833			−0.00120917	−	0.999999i	$-0.500385\pi$
$151$	−0.0297170			−0.00241833			−0.00120917	+	0.999999i	$0.500385\pi$
$152$	−1.97329	−	1.97329i	−0.160055	−	0.160055i
$153$		0			0
$154$			8.02544i			0.646708i
$155$	0.663591	+	0.954185i	0.0533009	+	0.0766420i
$156$		0			0
$157$	−11.9056	+	11.9056i	−0.950173	+	0.950173i	−0.998816	−	0.0486434i	$-0.984510\pi$
$157$	−11.9056	+	11.9056i	−0.950173	+	0.950173i	0.0486434	+	0.998816i	$0.484510\pi$
$158$	−5.82083	+	5.82083i	−0.463080	+	0.463080i
$159$		0			0
$160$	−0.395329	+	2.20084i	−0.0312535	+	0.173992i
$161$			2.18585i			0.172269i
$162$		0			0
$163$	0.777937	+	0.777937i	0.0609328	+	0.0609328i	0.736917	−	0.675984i	$-0.236281\pi$
$163$	0.777937	+	0.777937i	0.0609328	+	0.0609328i	−0.675984	+	0.736917i	$0.736281\pi$
$164$	−12.1033			−0.945112
$165$		0			0
$166$	8.29632			0.643920
$167$	−3.10347	−	3.10347i	−0.240154	−	0.240154i	0.576760	−	0.816914i	$-0.304317\pi$
$167$	−3.10347	−	3.10347i	−0.240154	−	0.240154i	−0.816914	+	0.576760i	$0.804317\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$	0.954185	−	0.663591i	0.0731827	−	0.0508951i
$171$		0			0
$172$	−4.14180	+	4.14180i	−0.315809	+	0.315809i
$173$	−0.771636	+	0.771636i	−0.0586664	+	0.0586664i	−0.735831	−	0.677165i	$-0.763208\pi$
$173$	−0.771636	+	0.771636i	−0.0586664	+	0.0586664i	0.677165	+	0.735831i	$0.263208\pi$
$174$		0			0
$175$	−4.55546	−	9.93460i	−0.344360	−	0.750985i
$176$			3.67154i			0.276753i
$177$		0			0
$178$	6.01272	+	6.01272i	0.450672	+	0.450672i
$179$	13.3746			0.999664			0.499832	−	0.866123i	$-0.333395\pi$
$179$	13.3746			0.999664			0.499832	+	0.866123i	$0.333395\pi$
$180$		0			0
$181$	6.01272			0.446922			0.223461	−	0.974713i	$-0.428264\pi$
$181$	6.01272			0.446922			0.223461	+	0.974713i	$0.428264\pi$
$182$	−4.37170	−	4.37170i	−0.324052	−	0.324052i
$183$		0			0
$184$			1.00000i			0.0737210i
$185$	−19.1161	−	3.43375i	−1.40545	−	0.252455i
$186$		0			0
$187$	1.34942	−	1.34942i	0.0986795	−	0.0986795i
$188$	1.13917	−	1.13917i	0.0830826	−	0.0830826i
$189$		0			0
$190$	6.14180	+	1.10323i	0.445573	+	0.0800365i
$191$		−	25.8509i		−	1.87050i	−0.353983	−	0.935252i	$-0.615173\pi$
$191$		−	25.8509i		−	1.87050i	0.353983	−	0.935252i	$-0.384827\pi$
$192$		0			0
$193$	6.42852	+	6.42852i	0.462735	+	0.462735i	0.899551	−	0.436816i	$-0.143894\pi$
$193$	6.42852	+	6.42852i	0.462735	+	0.462735i	−0.436816	+	0.899551i	$0.643894\pi$
$194$	−6.68252			−0.479777
$195$		0			0
$196$	−2.22206			−0.158719
$197$	−16.6180	−	16.6180i	−1.18398	−	1.18398i	−0.978703	−	0.205279i	$-0.934190\pi$
$197$	−16.6180	−	16.6180i	−1.18398	−	1.18398i	−0.205279	−	0.978703i	$-0.565810\pi$
$198$		0			0
$199$		−	2.25816i		−	0.160077i	−0.996792	−	0.0800385i	$-0.974496\pi$
$199$		−	2.25816i		−	0.160077i	0.996792	−	0.0800385i	$-0.0255043\pi$
$200$	−2.08407	−	4.54496i	−0.147366	−	0.321377i
$201$		0			0
$202$	−9.42754	+	9.42754i	−0.663320	+	0.663320i
$203$	−12.9999	+	12.9999i	−0.912417	+	0.912417i
$204$		0			0
$205$	22.2190	−	15.4522i	1.55184	−	1.07923i
$206$			2.18585i			0.152295i
$207$		0			0
$208$	−2.00000	−	2.00000i	−0.138675	−	0.138675i
$209$	10.2460			0.708732
$210$		0			0
$211$	−22.4101			−1.54278			−0.771389	−	0.636364i	$-0.780437\pi$
$211$	−22.4101			−1.54278			−0.771389	+	0.636364i	$0.780437\pi$
$212$	6.41647	+	6.41647i	0.440685	+	0.440685i
$213$		0			0
$214$		−	11.8819i		−	0.812231i
$215$	2.31559	−	12.8912i	0.157922	−	0.879173i
$216$		0			0
$217$	0.803377	−	0.803377i	0.0545368	−	0.0545368i
$218$	−4.34169	+	4.34169i	−0.294056	+	0.294056i
$219$		0			0
$220$	−4.68743	−	6.74011i	−0.316027	−	0.454418i
$221$			1.47014i			0.0988924i
$222$		0			0
$223$	15.9035	+	15.9035i	1.06498	+	1.06498i	0.997737	+	0.0672398i	$0.0214193\pi$
$223$	15.9035	+	15.9035i	1.06498	+	1.06498i	0.0672398	+	0.997737i	$0.478581\pi$
$224$	2.18585			0.146048
$225$		0			0
$226$	−13.7935			−0.917533
$227$	−14.9593	−	14.9593i	−0.992886	−	0.992886i	0.00708922	−	0.999975i	$-0.497743\pi$
$227$	−14.9593	−	14.9593i	−0.992886	−	0.992886i	−0.999975	+	0.00708922i	$0.997743\pi$
$228$		0			0
$229$			12.1698i			0.804203i	0.915595	+	0.402101i	$0.131720\pi$
$229$			12.1698i			0.804203i	−0.915595	+	0.402101i	$0.868280\pi$
$230$	−1.27669	−	1.83577i	−0.0841826	−	0.121047i
$231$		0			0
$232$	−5.94732	+	5.94732i	−0.390461	+	0.390461i
$233$	12.5213	−	12.5213i	0.820300	−	0.820300i	−0.165851	−	0.986151i	$-0.553037\pi$
$233$	12.5213	−	12.5213i	0.820300	−	0.820300i	0.986151	+	0.165851i	$0.0530371\pi$
$234$		0			0
$235$	−0.636887	+	3.54563i	−0.0415459	+	0.231291i
$236$			8.96086i			0.583302i
$237$		0			0
$238$	−0.803377	−	0.803377i	−0.0520752	−	0.0520752i
$239$	−7.80476			−0.504848			−0.252424	−	0.967617i	$-0.581228\pi$
$239$	−7.80476			−0.504848			−0.252424	+	0.967617i	$0.581228\pi$
$240$		0			0
$241$	7.71212			0.496781			0.248391	−	0.968660i	$-0.420098\pi$
$241$	7.71212			0.496781			0.248391	+	0.968660i	$0.420098\pi$
$242$	−1.75378	−	1.75378i	−0.112738	−	0.112738i
$243$		0			0
$244$			1.88191i			0.120477i
$245$	4.07920	−	2.83689i	0.260610	−	0.181242i
$246$		0			0
$247$	−5.58131	+	5.58131i	−0.355131	+	0.355131i
$248$	0.367535	−	0.367535i	0.0233385	−	0.0233385i
$249$		0			0
$250$	9.62839	+	5.68279i	0.608953	+	0.359411i
$251$		−	16.9296i		−	1.06859i	−0.845299	−	0.534293i	$-0.820578\pi$
$251$		−	16.9296i		−	1.06859i	0.845299	−	0.534293i	$-0.179422\pi$
$252$		0			0
$253$	−2.59617	−	2.59617i	−0.163220	−	0.163220i
$254$	4.50076			0.282403
$255$		0			0
$256$	1.00000			0.0625000
$257$	0.290594	+	0.290594i	0.0181268	+	0.0181268i	0.716112	−	0.697985i	$-0.245920\pi$
$257$	0.290594	+	0.290594i	0.0181268	+	0.0181268i	−0.697985	+	0.716112i	$0.745920\pi$
$258$		0			0
$259$			18.9859i			1.17973i
$260$	6.22493	+	1.11816i	0.386054	+	0.0693452i
$261$		0			0
$262$	14.3617	−	14.3617i	0.887270	−	0.887270i
$263$	−12.7404	+	12.7404i	−0.785610	+	0.785610i	−0.980771	−	0.195161i	$-0.937477\pi$
$263$	−12.7404	+	12.7404i	−0.785610	+	0.785610i	0.195161	+	0.980771i	$0.437477\pi$
$264$		0			0
$265$	−19.9710	−	3.58731i	−1.22681	−	0.220367i
$266$		−	6.09996i		−	0.374012i
$267$		0			0
$268$	2.12908	+	2.12908i	0.130054	+	0.130054i
$269$	−17.2551			−1.05206			−0.526031	−	0.850465i	$-0.676321\pi$
$269$	−17.2551			−1.05206			−0.526031	+	0.850465i	$0.676321\pi$
$270$		0			0
$271$	−10.1231			−0.614933			−0.307467	−	0.951559i	$-0.599481\pi$
$271$	−10.1231			−0.614933			−0.307467	+	0.951559i	$0.599481\pi$
$272$	−0.367535	−	0.367535i	−0.0222851	−	0.0222851i
$273$		0			0
$274$			7.50567i			0.453434i
$275$	17.2101	+	6.38890i	1.03781	+	0.385265i
$276$		0			0
$277$	−17.5057	+	17.5057i	−1.05181	+	1.05181i	−0.0532313	+	0.998582i	$0.516952\pi$
$277$	−17.5057	+	17.5057i	−1.05181	+	1.05181i	−0.998582	+	0.0532313i	$0.983048\pi$
$278$	1.80276	−	1.80276i	0.108122	−	0.108122i
$279$		0			0
$280$	−4.01272	+	2.79066i	−0.239806	+	0.166774i
$281$			18.8238i			1.12293i	0.827499	+	0.561467i	$0.189763\pi$
$281$			18.8238i			1.12293i	−0.827499	+	0.561467i	$0.810237\pi$
$282$		0			0
$283$	7.35114	+	7.35114i	0.436980	+	0.436980i	0.890994	−	0.454014i	$-0.150008\pi$
$283$	7.35114	+	7.35114i	0.436980	+	0.436980i	−0.454014	+	0.890994i	$0.650008\pi$
$284$	−13.7211			−0.814198
$285$		0			0
$286$	10.3847			0.614060
$287$	−18.7073	−	18.7073i	−1.10425	−	1.10425i
$288$		0			0
$289$		−	16.7298i		−	0.984108i
$290$	3.32502	−	18.5108i	0.195252	−	1.08699i
$291$		0			0
$292$	4.42754	−	4.42754i	0.259102	−	0.259102i
$293$	−11.4152	+	11.4152i	−0.666883	+	0.666883i	−0.956993	−	0.290110i	$-0.906308\pi$
$293$	−11.4152	+	11.4152i	−0.666883	+	0.666883i	0.290110	+	0.956993i	$0.406308\pi$
$294$		0			0
$295$	−11.4403	−	16.4501i	−0.666078	−	0.957761i
$296$			8.68582i			0.504853i
$297$		0			0
$298$	12.2072	+	12.2072i	0.707144	+	0.707144i
$299$	2.82843			0.163572
$300$		0			0
$301$	−12.8034			−0.737974
$302$	−0.0210131	−	0.0210131i	−0.00120917	−	0.00120917i
$303$		0			0
$304$		−	2.79066i		−	0.160055i
$305$	−2.40263	−	3.45477i	−0.137574	−	0.197819i
$306$		0			0
$307$	−5.29343	+	5.29343i	−0.302112	+	0.302112i	−0.841840	−	0.539728i	$-0.818527\pi$
$307$	−5.29343	+	5.29343i	−0.302112	+	0.302112i	0.539728	+	0.841840i	$0.318527\pi$
$308$	−5.67484	+	5.67484i	−0.323354	+	0.323354i
$309$		0			0
$310$	−0.205481	+	1.14394i	−0.0116706	+	0.0649715i
$311$			30.1680i			1.71067i	0.518074	+	0.855336i	$0.326649\pi$
$311$			30.1680i			1.71067i	−0.518074	+	0.855336i	$0.673351\pi$
$312$		0			0
$313$	11.6892	+	11.6892i	0.660710	+	0.660710i	0.955547	−	0.294837i	$-0.0952655\pi$
$313$	11.6892	+	11.6892i	0.660710	+	0.660710i	−0.294837	+	0.955547i	$0.595265\pi$
$314$	−16.8371			−0.950173
$315$		0			0
$316$	−8.23189			−0.463080
$317$	4.00114	+	4.00114i	0.224726	+	0.224726i	0.810485	−	0.585759i	$-0.199203\pi$
$317$	4.00114	+	4.00114i	0.224726	+	0.224726i	−0.585759	+	0.810485i	$0.699203\pi$
$318$		0			0
$319$		−	30.8805i		−	1.72898i
$320$	−1.83577	+	1.27669i	−0.102623	+	0.0713693i
$321$		0			0
$322$	−1.54563	+	1.54563i	−0.0861345	+	0.0861345i
$323$	−1.02567	+	1.02567i	−0.0570695	+	0.0570695i
$324$		0			0
$325$	−12.8551	+	5.89463i	−0.713072	+	0.326976i
$326$			1.10017i			0.0609328i
$327$		0			0
$328$	−8.55835	−	8.55835i	−0.472556	−	0.472556i
$329$	3.52147			0.194145
$330$		0			0
$331$	12.1308			0.666769			0.333385	−	0.942791i	$-0.391809\pi$
$331$	12.1308			0.666769			0.333385	+	0.942791i	$0.391809\pi$
$332$	5.86639	+	5.86639i	0.321960	+	0.321960i
$333$		0			0
$334$		−	4.38897i		−	0.240154i
$335$	−6.62669	−	1.19033i	−0.362055	−	0.0650344i
$336$		0			0
$337$	11.4573	−	11.4573i	0.624117	−	0.624117i	−0.322465	−	0.946581i	$-0.604511\pi$
$337$	11.4573	−	11.4573i	0.624117	−	0.624117i	0.946581	+	0.322465i	$0.104511\pi$
$338$	3.53553	−	3.53553i	0.192308	−	0.192308i
$339$		0			0
$340$	1.14394	+	0.205481i	0.0620389	+	0.0111438i
$341$			1.90837i			0.103344i
$342$		0			0
$343$	−14.2539	−	14.2539i	−0.769638	−	0.769638i
$344$	−5.85739			−0.315809
$345$		0			0
$346$	−1.09126			−0.0586664
$347$	−12.6914	−	12.6914i	−0.681308	−	0.681308i	0.278987	−	0.960295i	$-0.410001\pi$
$347$	−12.6914	−	12.6914i	−0.681308	−	0.681308i	−0.960295	+	0.278987i	$0.910001\pi$
$348$		0			0
$349$			13.8946i			0.743763i	0.928280	+	0.371881i	$0.121287\pi$
$349$			13.8946i			0.743763i	−0.928280	+	0.371881i	$0.878713\pi$
$350$	3.80363	−	10.2460i	0.203312	−	0.547673i
$351$		0			0
$352$	−2.59617	+	2.59617i	−0.138376	+	0.138376i
$353$	17.4292	−	17.4292i	0.927664	−	0.927664i	−0.0698910	−	0.997555i	$-0.522265\pi$
$353$	17.4292	−	17.4292i	0.927664	−	0.927664i	0.997555	+	0.0698910i	$0.0222652\pi$
$354$		0			0
$355$	25.1888	−	17.5176i	1.33688	−	0.929740i
$356$			8.50327i			0.450672i
$357$		0			0
$358$	9.45726	+	9.45726i	0.499832	+	0.499832i
$359$	−9.98653			−0.527069			−0.263534	−	0.964650i	$-0.584888\pi$
$359$	−9.98653			−0.527069			−0.263534	+	0.964650i	$0.584888\pi$
$360$		0			0
$361$	11.2122			0.590118
$362$	4.25163	+	4.25163i	0.223461	+	0.223461i
$363$		0			0
$364$		−	6.18252i		−	0.324052i
$365$	−2.47535	+	13.7806i	−0.129566	+	0.721308i
$366$		0			0
$367$	25.4360	−	25.4360i	1.32775	−	1.32775i	0.420416	−	0.907331i	$-0.361884\pi$
$367$	25.4360	−	25.4360i	1.32775	−	1.32775i	0.907331	−	0.420416i	$-0.138116\pi$
$368$	−0.707107	+	0.707107i	−0.0368605	+	0.0368605i
$369$		0			0
$370$	−11.0891	−	15.9452i	−0.576496	−	0.828950i
$371$			19.8350i			1.02978i
$372$		0			0
$373$	−7.82420	−	7.82420i	−0.405122	−	0.405122i	0.474912	−	0.880034i	$-0.342480\pi$
$373$	−7.82420	−	7.82420i	−0.405122	−	0.405122i	−0.880034	+	0.474912i	$0.842480\pi$
$374$	1.90837			0.0986795
$375$		0			0
$376$	1.61103			0.0830826
$377$	16.8216	+	16.8216i	0.866354	+	0.866354i
$378$		0			0
$379$		−	16.0679i		−	0.825351i	−0.910878	−	0.412676i	$-0.864594\pi$
$379$		−	16.0679i		−	0.825351i	0.910878	−	0.412676i	$-0.135406\pi$
$380$	3.56281	+	5.12301i	0.182768	+	0.262805i
$381$		0			0
$382$	18.2793	−	18.2793i	0.935252	−	0.935252i
$383$	−2.58830	+	2.58830i	−0.132256	+	0.132256i	−0.770136	−	0.637880i	$-0.779812\pi$
$383$	−2.58830	+	2.58830i	−0.132256	+	0.132256i	0.637880	+	0.770136i	$0.279812\pi$
$384$		0			0
$385$	3.17269	−	17.6627i	0.161695	−	0.900177i
$386$			9.09129i			0.462735i
$387$		0			0
$388$	−4.72525	−	4.72525i	−0.239888	−	0.239888i
$389$	32.5550			1.65060			0.825302	−	0.564692i	$-0.191005\pi$
$389$	32.5550			1.65060			0.825302	+	0.564692i	$0.191005\pi$
$390$		0			0
$391$	0.519773			0.0262861
$392$	−1.57124	−	1.57124i	−0.0793594	−	0.0793594i
$393$		0			0
$394$		−	23.5014i		−	1.18398i
$395$	15.1119	−	10.5096i	0.760361	−	0.528795i
$396$		0			0
$397$	14.3847	−	14.3847i	0.721947	−	0.721947i	−0.247055	−	0.969002i	$-0.579463\pi$
$397$	14.3847	−	14.3847i	0.721947	−	0.721947i	0.969002	+	0.247055i	$0.0794627\pi$
$398$	1.59676	−	1.59676i	0.0800385	−	0.0800385i
$399$		0			0
$400$	1.74011	−	4.68743i	0.0870057	−	0.234372i
$401$		−	14.1912i		−	0.708676i	−0.935117	−	0.354338i	$-0.884706\pi$
$401$		−	14.1912i		−	0.708676i	0.935117	−	0.354338i	$-0.115294\pi$
$402$		0			0
$403$	−1.03955	−	1.03955i	−0.0517835	−	0.0517835i
$404$	−13.3326			−0.663320
$405$		0			0
$406$	−18.3847			−0.912417
$407$	−22.5499	−	22.5499i	−1.11776	−	1.11776i
$408$		0			0
$409$		−	25.2135i		−	1.24673i	−0.781932	−	0.623364i	$-0.785766\pi$
$409$		−	25.2135i		−	1.24673i	0.781932	−	0.623364i	$-0.214234\pi$
$410$	26.6375	+	4.78479i	1.31553	+	0.236304i
$411$		0			0
$412$	−1.54563	+	1.54563i	−0.0761477	+	0.0761477i
$413$	−13.8502	+	13.8502i	−0.681522	+	0.681522i
$414$		0			0
$415$	−18.2589	−	3.27977i	−0.896295	−	0.160998i
$416$		−	2.82843i		−	0.138675i
$417$		0			0
$418$	7.24503	+	7.24503i	0.354366	+	0.354366i
$419$	14.4111			0.704030			0.352015	−	0.935994i	$-0.385497\pi$
$419$	14.4111			0.704030			0.352015	+	0.935994i	$0.385497\pi$
$420$		0			0
$421$	−18.9943			−0.925727			−0.462864	−	0.886430i	$-0.653178\pi$
$421$	−18.9943			−0.925727			−0.462864	+	0.886430i	$0.653178\pi$
$422$	−15.8464	−	15.8464i	−0.771389	−	0.771389i
$423$		0			0
$424$			9.07426i			0.440685i
$425$	−2.36235	+	1.08324i	−0.114591	+	0.0525450i
$426$		0			0
$427$	−2.90874	+	2.90874i	−0.140764	+	0.140764i
$428$	8.40178	−	8.40178i	0.406115	−	0.406115i
$429$		0			0
$430$	10.7528	−	7.47809i	0.518548	−	0.360625i
$431$		−	26.8501i		−	1.29332i	−0.762777	−	0.646662i	$-0.776164\pi$
$431$		−	26.8501i		−	1.29332i	0.762777	−	0.646662i	$-0.223836\pi$
$432$		0			0
$433$	−7.24075	−	7.24075i	−0.347968	−	0.347968i	0.511384	−	0.859352i	$-0.329133\pi$
$433$	−7.24075	−	7.24075i	−0.347968	−	0.347968i	−0.859352	+	0.511384i	$0.829133\pi$
$434$	1.13615			0.0545368
$435$		0			0
$436$	−6.14008			−0.294056
$437$	1.97329	+	1.97329i	0.0943954	+	0.0943954i
$438$		0			0
$439$			35.8089i			1.70907i	0.519396	+	0.854533i	$0.326157\pi$
$439$			35.8089i			1.70907i	−0.519396	+	0.854533i	$0.673843\pi$
$440$	1.45147	−	8.08049i	0.0691959	−	0.385222i
$441$		0			0
$442$	−1.03955	+	1.03955i	−0.0494462	+	0.0494462i
$443$	−14.3582	+	14.3582i	−0.682180	+	0.682180i	−0.960491	−	0.278311i	$-0.910225\pi$
$443$	−14.3582	+	14.3582i	−0.682180	+	0.682180i	0.278311	+	0.960491i	$0.410225\pi$
$444$		0			0
$445$	−10.8561	−	15.6101i	−0.514627	−	0.739988i
$446$			22.4909i			1.06498i
$447$		0			0
$448$	1.54563	+	1.54563i	0.0730241	+	0.0730241i
$449$	−3.66008			−0.172730			−0.0863649	−	0.996264i	$-0.527525\pi$
$449$	−3.66008			−0.172730			−0.0863649	+	0.996264i	$0.527525\pi$
$450$		0			0
$451$	44.4379			2.09250
$452$	−9.75351	−	9.75351i	−0.458767	−	0.458767i
$453$		0			0
$454$		−	21.1557i		−	0.992886i
$455$	7.89317	+	11.3497i	0.370038	+	0.532081i
$456$		0			0
$457$	7.27047	−	7.27047i	0.340098	−	0.340098i	−0.516306	−	0.856404i	$-0.672693\pi$
$457$	7.27047	−	7.27047i	0.340098	−	0.340098i	0.856404	+	0.516306i	$0.172693\pi$
$458$	−8.60535	+	8.60535i	−0.402101	+	0.402101i
$459$		0			0
$460$	0.395329	−	2.20084i	0.0184323	−	0.102615i
$461$			0.0264291i			0.00123093i	1.00000		0.000615464i	$0.000195908\pi$
$461$			0.0264291i			0.00123093i	−1.00000		0.000615464i	$0.999804\pi$
$462$		0			0
$463$	−8.00983	−	8.00983i	−0.372248	−	0.372248i	0.496047	−	0.868296i	$-0.334784\pi$
$463$	−8.00983	−	8.00983i	−0.372248	−	0.372248i	−0.868296	+	0.496047i	$0.834784\pi$
$464$	−8.41078			−0.390461
$465$		0			0
$466$	17.7078			0.820300
$467$	1.97632	+	1.97632i	0.0914531	+	0.0914531i	0.751353	−	0.659900i	$-0.229401\pi$
$467$	1.97632	+	1.97632i	0.0914531	+	0.0914531i	−0.659900	+	0.751353i	$0.729401\pi$
$468$		0			0
$469$			6.58154i			0.303907i
$470$	−2.95749	+	2.05679i	−0.136419	+	0.0948727i
$471$		0			0
$472$	−6.33629	+	6.33629i	−0.291651	+	0.291651i
$473$	15.2068	−	15.2068i	0.699210	−	0.699210i
$474$		0			0
$475$	−13.0810	−	4.85606i	−0.600198	−	0.222811i
$476$		−	1.13615i		−	0.0520752i
$477$		0			0
$478$	−5.51880	−	5.51880i	−0.252424	−	0.252424i
$479$	−23.5725			−1.07706			−0.538528	−	0.842608i	$-0.681019\pi$
$479$	−23.5725			−1.07706			−0.538528	+	0.842608i	$0.681019\pi$
$480$		0			0
$481$	24.5672			1.12017
$482$	5.45329	+	5.45329i	0.248391	+	0.248391i
$483$		0			0
$484$		−	2.48023i		−	0.112738i
$485$	14.7072	+	2.64179i	0.667819	+	0.119958i
$486$		0			0
$487$	−7.72428	+	7.72428i	−0.350021	+	0.350021i	−0.860117	−	0.510097i	$-0.829610\pi$
$487$	−7.72428	+	7.72428i	−0.350021	+	0.350021i	0.510097	+	0.860117i	$0.329610\pi$
$488$	−1.33071	+	1.33071i	−0.0602386	+	0.0602386i
$489$		0			0
$490$	4.89041	+	0.878445i	0.220926	+	0.0396841i
$491$			23.5772i			1.06402i	0.846737	+	0.532012i	$0.178564\pi$
$491$			23.5772i			1.06402i	−0.846737	+	0.532012i	$0.821436\pi$
$492$		0			0
$493$	3.09126	+	3.09126i	0.139223	+	0.139223i
$494$	−7.89317			−0.355131
$495$		0			0
$496$	0.519773			0.0233385
$497$	−21.2077	−	21.2077i	−0.951297	−	0.951297i
$498$		0			0
$499$			1.64075i			0.0734500i	0.999325	+	0.0367250i	$0.0116926\pi$
$499$			1.64075i			0.0734500i	−0.999325	+	0.0367250i	$0.988307\pi$
$500$	2.78996	+	10.8266i	0.124771	+	0.484182i
$501$		0			0
$502$	11.9710	−	11.9710i	0.534293	−	0.534293i
$503$	−3.23088	+	3.23088i	−0.144058	+	0.144058i	−0.775457	−	0.631400i	$-0.782481\pi$
$503$	−3.23088	+	3.23088i	−0.144058	+	0.144058i	0.631400	+	0.775457i	$0.282481\pi$
$504$		0			0
$505$	24.4755	−	17.0216i	1.08915	−	0.757450i
$506$		−	3.67154i		−	0.163220i
$507$		0			0
$508$	3.18252	+	3.18252i	0.141201	+	0.141201i
$509$	19.4914			0.863942			0.431971	−	0.901887i	$-0.357818\pi$
$509$	19.4914			0.863942			0.431971	+	0.901887i	$0.357818\pi$
$510$		0			0
$511$	13.6867			0.605463
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$			0.410963i			0.0181268i
$515$	0.864129	−	4.81071i	0.0380781	−	0.211985i
$516$		0			0
$517$	−4.18252	+	4.18252i	−0.183947	+	0.183947i
$518$	−13.4251	+	13.4251i	−0.589863	+	0.589863i
$519$		0			0
$520$	3.61103	+	5.19235i	0.158354	+	0.227699i
$521$			34.3242i			1.50377i	0.659294	+	0.751886i	$0.270855\pi$
$521$			34.3242i			1.50377i	−0.659294	+	0.751886i	$0.729145\pi$
$522$		0			0
$523$	−18.6870	−	18.6870i	−0.817126	−	0.817126i	0.168565	−	0.985691i	$-0.446087\pi$
$523$	−18.6870	−	18.6870i	−0.817126	−	0.817126i	−0.985691	+	0.168565i	$0.946087\pi$
$524$	20.3105			0.887270
$525$		0			0
$526$	−18.0177			−0.785610
$527$	−0.191035	−	0.191035i	−0.00832162	−	0.00832162i
$528$		0			0
$529$		−	1.00000i		−	0.0434783i
$530$	−11.5850	−	16.6583i	−0.503222	−	0.723589i
$531$		0			0
$532$	4.31332	−	4.31332i	0.187006	−	0.187006i
$533$	−24.2067	+	24.2067i	−1.04851	+	1.04851i
$534$		0			0
$535$	−4.69726	+	26.1502i	−0.203080	+	1.13057i
$536$			3.01098i			0.130054i
$537$		0			0
$538$	−12.2012	−	12.2012i	−0.526031	−	0.526031i
$539$	8.15840			0.351407
$540$		0			0
$541$	22.0000			0.945854			0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000			0.945854			0.472927	+	0.881102i	$0.343197\pi$
$542$	−7.15810	−	7.15810i	−0.307467	−	0.307467i
$543$		0			0
$544$		−	0.519773i		−	0.0222851i
$545$	11.2718	−	7.83899i	0.482830	−	0.335786i
$546$		0			0
$547$	−1.21862	+	1.21862i	−0.0521043	+	0.0521043i	−0.732679	−	0.680575i	$-0.761730\pi$
$547$	−1.21862	+	1.21862i	−0.0521043	+	0.0521043i	0.680575	+	0.732679i	$0.261730\pi$
$548$	−5.30731	+	5.30731i	−0.226717	+	0.226717i
$549$		0			0
$550$	7.65175	+	16.6870i	0.326272	+	0.711537i
$551$			23.4716i			0.999924i
$552$		0			0
$553$	−12.7235	−	12.7235i	−0.541056	−	0.541056i
$554$	−24.7568			−1.05181
$555$		0			0
$556$	2.54949			0.108122
$557$	−32.2385	−	32.2385i	−1.36599	−	1.36599i	−0.866076	−	0.499912i	$-0.833366\pi$
$557$	−32.2385	−	32.2385i	−1.36599	−	1.36599i	−0.499912	−	0.866076i	$-0.666634\pi$
$558$		0			0
$559$			16.5672i			0.700718i
$560$	−4.81071	−	0.864129i	−0.203290	−	0.0365161i
$561$		0			0
$562$	−13.3104	+	13.3104i	−0.561467	+	0.561467i
$563$	2.89500	−	2.89500i	0.122010	−	0.122010i	−0.643465	−	0.765475i	$-0.722504\pi$
$563$	2.89500	−	2.89500i	0.122010	−	0.122010i	0.765475	+	0.643465i	$0.222504\pi$
$564$		0			0
$565$	30.3574	+	5.45298i	1.27715	+	0.229409i
$566$			10.3961i			0.436980i
$567$		0			0
$568$	−9.70229	−	9.70229i	−0.407099	−	0.407099i
$569$	−0.748186			−0.0313656			−0.0156828	−	0.999877i	$-0.504992\pi$
$569$	−0.748186			−0.0313656			−0.0156828	+	0.999877i	$0.504992\pi$
$570$		0			0
$571$	−41.0121			−1.71630			−0.858150	−	0.513398i	$-0.828386\pi$
$571$	−41.0121			−1.71630			−0.858150	+	0.513398i	$0.828386\pi$
$572$	7.34309	+	7.34309i	0.307030	+	0.307030i
$573$		0			0
$574$		−	26.4561i		−	1.10425i
$575$	2.08407	+	4.54496i	0.0869116	+	0.189538i
$576$		0			0
$577$	18.5803	−	18.5803i	0.773510	−	0.773510i	−0.205208	−	0.978718i	$-0.565787\pi$
$577$	18.5803	−	18.5803i	0.773510	−	0.773510i	0.978718	+	0.205208i	$0.0657872\pi$
$578$	11.8298	−	11.8298i	0.492054	−	0.492054i
$579$		0			0
$580$	15.4403	−	10.7380i	0.641122	−	0.445870i
$581$			18.1345i			0.752346i
$582$		0			0
$583$	−23.5583	−	23.5583i	−0.975687	−	0.975687i
$584$	6.26149			0.259102
$585$		0			0
$586$	−16.1435			−0.666883
$587$	−10.8561	−	10.8561i	−0.448080	−	0.448080i	0.446636	−	0.894716i	$-0.352622\pi$
$587$	−10.8561	−	10.8561i	−0.448080	−	0.448080i	−0.894716	+	0.446636i	$0.852622\pi$
$588$		0			0
$589$		−	1.45051i		−	0.0597672i
$590$	3.54248	−	19.7215i	0.145842	−	0.811920i
$591$		0			0
$592$	−6.14180	+	6.14180i	−0.252426	+	0.252426i
$593$	−15.4679	+	15.4679i	−0.635192	+	0.635192i	−0.949366	−	0.314173i	$-0.898273\pi$
$593$	−15.4679	+	15.4679i	−0.635192	+	0.635192i	0.314173	+	0.949366i	$0.398273\pi$
$594$		0			0
$595$	1.45051	+	2.08571i	0.0594651	+	0.0855056i
$596$			17.2636i			0.707144i
$597$		0			0
$598$	2.00000	+	2.00000i	0.0817861	+	0.0817861i
$599$	−6.03935			−0.246761			−0.123381	−	0.992359i	$-0.539374\pi$
$599$	−6.03935			−0.246761			−0.123381	+	0.992359i	$0.539374\pi$
$600$		0			0
$601$	3.25178			0.132643			0.0663214	−	0.997798i	$-0.478874\pi$
$601$	3.25178			0.132643			0.0663214	+	0.997798i	$0.478874\pi$
$602$	−9.05335	−	9.05335i	−0.368987	−	0.368987i
$603$		0			0
$604$		−	0.0297170i		−	0.00120917i
$605$	3.16649	+	4.55313i	0.128736	+	0.185111i
$606$		0			0
$607$	−28.8937	+	28.8937i	−1.17276	+	1.17276i	−0.191208	+	0.981550i	$0.561241\pi$
$607$	−28.8937	+	28.8937i	−1.17276	+	1.17276i	−0.981550	+	0.191208i	$0.938759\pi$
$608$	1.97329	−	1.97329i	0.0800276	−	0.0800276i
$609$		0			0
$610$	0.743975	−	4.14180i	0.0301227	−	0.167697i
$611$		−	4.55668i		−	0.184344i
$612$		0			0
$613$	30.4933	+	30.4933i	1.23161	+	1.23161i	0.963344	+	0.268268i	$0.0864511\pi$
$613$	30.4933	+	30.4933i	1.23161	+	1.23161i	0.268268	+	0.963344i	$0.413549\pi$
$614$	−7.48605			−0.302112
$615$		0			0
$616$	−8.02544			−0.323354
$617$	3.81450	+	3.81450i	0.153566	+	0.153566i	0.779709	−	0.626143i	$-0.215367\pi$
$617$	3.81450	+	3.81450i	0.153566	+	0.153566i	−0.626143	+	0.779709i	$0.715367\pi$
$618$		0			0
$619$			1.28927i			0.0518201i	0.999664	+	0.0259100i	$0.00824835\pi$
$619$			1.28927i			0.0518201i	−0.999664	+	0.0259100i	$0.991752\pi$
$620$	−0.954185	+	0.663591i	−0.0383210	+	0.0266504i
$621$		0			0
$622$	−21.3320	+	21.3320i	−0.855336	+	0.855336i
$623$	−13.1429	+	13.1429i	−0.526559	+	0.526559i
$624$		0			0
$625$	−18.9440	−	16.3133i	−0.757760	−	0.652533i
$626$			16.5310i			0.660710i
$627$		0			0
$628$	−11.9056	−	11.9056i	−0.475086	−	0.475086i
$629$	4.51466			0.180011
$630$		0			0
$631$	39.0156			1.55319			0.776593	−	0.630002i	$-0.216946\pi$
$631$	39.0156			1.55319			0.776593	+	0.630002i	$0.216946\pi$
$632$	−5.82083	−	5.82083i	−0.231540	−	0.231540i
$633$		0			0
$634$			5.65846i			0.224726i
$635$	−9.90546	−	1.77928i	−0.393086	−	0.0706085i
$636$		0			0
$637$	−4.44413	+	4.44413i	−0.176083	+	0.176083i
$638$	21.8358	−	21.8358i	0.864489	−	0.864489i
$639$		0			0
$640$	−2.20084	−	0.395329i	−0.0869960	−	0.0156267i
$641$			0.282154i			0.0111444i	0.999984	+	0.00557220i	$0.00177370\pi$
$641$			0.282154i			0.0111444i	−0.999984	+	0.00557220i	$0.998226\pi$
$642$		0			0
$643$	10.3907	+	10.3907i	0.409769	+	0.409769i	0.881658	−	0.471889i	$-0.156428\pi$
$643$	10.3907	+	10.3907i	0.409769	+	0.409769i	−0.471889	+	0.881658i	$0.656428\pi$
$644$	−2.18585			−0.0861345
$645$		0			0
$646$	−1.45051			−0.0570695
$647$	13.6046	+	13.6046i	0.534851	+	0.534851i	0.922012	−	0.387161i	$-0.126544\pi$
$647$	13.6046	+	13.6046i	0.534851	+	0.534851i	−0.387161	+	0.922012i	$0.626544\pi$
$648$		0			0
$649$		−	32.9002i		−	1.29145i
$650$	−13.2581	−	4.92178i	−0.520024	−	0.193048i
$651$		0			0
$652$	−0.777937	+	0.777937i	−0.0304664	+	0.0304664i
$653$	−18.0017	+	18.0017i	−0.704461	+	0.704461i	−0.965365	−	0.260904i	$-0.915979\pi$
$653$	−18.0017	+	18.0017i	−0.704461	+	0.704461i	0.260904	+	0.965365i	$0.415979\pi$
$654$		0			0
$655$	−37.2855	+	25.9303i	−1.45687	+	1.01318i
$656$		−	12.1033i		−	0.472556i
$657$		0			0
$658$	2.49006	+	2.49006i	0.0970725	+	0.0970725i
$659$	16.0723			0.626088			0.313044	−	0.949739i	$-0.398651\pi$
$659$	16.0723			0.626088			0.313044	+	0.949739i	$0.398651\pi$
$660$		0			0
$661$	15.9116			0.618891			0.309445	−	0.950917i	$-0.399857\pi$
$661$	15.9116			0.618891			0.309445	+	0.950917i	$0.399857\pi$
$662$	8.57777	+	8.57777i	0.333385	+	0.333385i
$663$		0			0
$664$			8.29632i			0.321960i
$665$	−2.41149	+	13.4251i	−0.0935135	+	0.520601i
$666$		0			0
$667$	5.94732	−	5.94732i	0.230281	−	0.230281i
$668$	3.10347	−	3.10347i	0.120077	−	0.120077i
$669$		0			0
$670$	−3.84409	−	5.52746i	−0.148510	−	0.213545i
$671$		−	6.90953i		−	0.266740i
$672$		0			0
$673$	−8.50319	−	8.50319i	−0.327774	−	0.327774i	0.523966	−	0.851739i	$-0.324452\pi$
$673$	−8.50319	−	8.50319i	−0.327774	−	0.327774i	−0.851739	+	0.523966i	$0.824452\pi$
$674$	16.2030			0.624117
$675$		0			0
$676$	5.00000			0.192308
$677$	−6.71555	−	6.71555i	−0.258100	−	0.258100i	0.566181	−	0.824281i	$-0.308420\pi$
$677$	−6.71555	−	6.71555i	−0.258100	−	0.258100i	−0.824281	+	0.566181i	$0.808420\pi$
$678$		0			0
$679$		−	14.6070i		−	0.560564i
$680$	0.663591	+	0.954185i	0.0254475	+	0.0365913i
$681$		0			0
$682$	−1.34942	+	1.34942i	−0.0516720	+	0.0516720i
$683$	22.6129	−	22.6129i	0.865260	−	0.865260i	−0.126684	−	0.991943i	$-0.540433\pi$
$683$	22.6129	−	22.6129i	0.865260	−	0.865260i	0.991943	+	0.126684i	$0.0404333\pi$
$684$		0			0
$685$	2.96720	−	16.5188i	0.113371	−	0.631151i
$686$		−	20.1580i		−	0.769638i
$687$		0			0
$688$	−4.14180	−	4.14180i	−0.157905	−	0.157905i
$689$	25.6659			0.977792
$690$		0			0
$691$	−4.60120			−0.175038			−0.0875190	−	0.996163i	$-0.527894\pi$
$691$	−4.60120			−0.175038			−0.0875190	+	0.996163i	$0.527894\pi$
$692$	−0.771636	−	0.771636i	−0.0293332	−	0.0293332i
$693$		0			0
$694$		−	17.9483i		−	0.681308i
$695$	−4.68028	+	3.25491i	−0.177533	+	0.123466i
$696$		0			0
$697$	−4.44840	+	4.44840i	−0.168495	+	0.168495i
$698$	−9.82499	+	9.82499i	−0.371881	+	0.371881i
$699$		0			0
$700$	9.93460	−	4.55546i	0.375492	−	0.172180i
$701$		−	40.2549i		−	1.52041i	−0.649685	−	0.760204i	$-0.725099\pi$
$701$		−	40.2549i		−	1.52041i	0.649685	−	0.760204i	$-0.274901\pi$
$702$		0			0
$703$	17.1397	+	17.1397i	0.646435	+	0.646435i
$704$	−3.67154			−0.138376
$705$		0			0
$706$	24.6486			0.927664
$707$	−20.6072	−	20.6072i	−0.775013	−	0.775013i
$708$		0			0
$709$			14.5819i			0.547634i	0.961782	+	0.273817i	$0.0882862\pi$
$709$			14.5819i			0.547634i	−0.961782	+	0.273817i	$0.911714\pi$
$710$	30.1980	+	5.42435i	1.13331	+	0.203572i
$711$		0			0
$712$	−6.01272	+	6.01272i	−0.225336	+	0.225336i
$713$	−0.367535	+	0.367535i	−0.0137643	+	0.0137643i
$714$		0			0
$715$	−22.8551	−	4.10537i	−0.854732	−	0.153532i
$716$			13.3746i			0.499832i
$717$		0			0
$718$	−7.06154	−	7.06154i	−0.263534	−	0.263534i
$719$	−36.4109			−1.35790			−0.678949	−	0.734185i	$-0.737564\pi$
$719$	−36.4109			−1.35790			−0.678949	+	0.734185i	$0.737564\pi$
$720$		0			0
$721$	−4.77794			−0.177940
$722$	7.92825	+	7.92825i	0.295059	+	0.295059i
$723$		0			0
$724$			6.01272i			0.223461i
$725$	−14.6357	+	39.4249i	−0.543556	+	1.46421i
$726$		0			0
$727$	−29.2118	+	29.2118i	−1.08341	+	1.08341i	−0.0872170	+	0.996189i	$0.527797\pi$
$727$	−29.2118	+	29.2118i	−1.08341	+	1.08341i	−0.996189	+	0.0872170i	$0.972203\pi$
$728$	4.37170	−	4.37170i	0.162026	−	0.162026i
$729$		0			0
$730$	−11.4947	+	7.99400i	−0.425437	+	0.295871i
$731$			3.04452i			0.112606i
$732$		0			0
$733$	22.4084	+	22.4084i	0.827673	+	0.827673i	0.987195	−	0.159521i	$-0.0509950\pi$
$733$	22.4084	+	22.4084i	0.827673	+	0.827673i	−0.159521	+	0.987195i	$0.550995\pi$
$734$	35.9719			1.32775
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	−7.81702	−	7.81702i	−0.287943	−	0.287943i
$738$		0			0
$739$		−	0.718504i		−	0.0264306i	−0.999913	−	0.0132153i	$-0.995793\pi$
$739$		−	0.718504i		−	0.0264306i	0.999913	−	0.0132153i	$-0.00420668\pi$
$740$	3.43375	−	19.1161i	0.126227	−	0.702723i
$741$		0			0
$742$	−14.0254	+	14.0254i	−0.514890	+	0.514890i
$743$	−29.2845	+	29.2845i	−1.07435	+	1.07435i	−0.0773402	+	0.997005i	$0.524643\pi$
$743$	−29.2845	+	29.2845i	−1.07435	+	1.07435i	−0.997005	+	0.0773402i	$0.975357\pi$
$744$		0			0
$745$	−22.0403	−	31.6920i	−0.807494	−	1.16111i
$746$		−	11.0651i		−	0.405122i
$747$		0			0
$748$	1.34942	+	1.34942i	0.0493397	+	0.0493397i
$749$	25.9721			0.948999
$750$		0			0
$751$	15.7596			0.575074			0.287537	−	0.957769i	$-0.407164\pi$
$751$	15.7596			0.575074			0.287537	+	0.957769i	$0.407164\pi$
$752$	1.13917	+	1.13917i	0.0415413	+	0.0415413i
$753$		0			0
$754$			23.7893i			0.866354i
$755$	0.0379394	+	0.0545535i	0.00138076	+	0.00198541i
$756$		0			0
$757$	8.62258	−	8.62258i	0.313393	−	0.313393i	−0.532829	−	0.846223i	$-0.678871\pi$
$757$	8.62258	−	8.62258i	0.313393	−	0.313393i	0.846223	+	0.532829i	$0.178871\pi$
$758$	11.3617	−	11.3617i	0.412676	−	0.412676i
$759$		0			0
$760$	−1.10323	+	6.14180i	−0.0400182	+	0.222787i
$761$			12.3628i			0.448152i	0.974572	+	0.224076i	$0.0719364\pi$
$761$			12.3628i			0.448152i	−0.974572	+	0.224076i	$0.928064\pi$
$762$		0			0
$763$	−9.49028	−	9.49028i	−0.343571	−	0.343571i
$764$	25.8509			0.935252
$765$		0			0
$766$	−3.66041			−0.132256
$767$	17.9217	+	17.9217i	0.647116	+	0.647116i
$768$		0			0
$769$		−	17.7384i		−	0.639663i	−0.947474	−	0.319831i	$-0.896374\pi$
$769$		−	17.7384i		−	0.639663i	0.947474	−	0.319831i	$-0.103626\pi$
$770$	14.7329	−	10.2460i	0.530936	−	0.369241i
$771$		0			0
$772$	−6.42852	+	6.42852i	−0.231367	+	0.231367i
$773$	18.2478	−	18.2478i	0.656327	−	0.656327i	−0.298182	−	0.954509i	$-0.596380\pi$
$773$	18.2478	−	18.2478i	0.656327	−	0.656327i	0.954509	+	0.298182i	$0.0963802\pi$
$774$		0			0
$775$	0.904465	−	2.43640i	0.0324893	−	0.0875181i
$776$		−	6.68252i		−	0.239888i
$777$		0			0
$778$	23.0199	+	23.0199i	0.825302	+	0.825302i
$779$	−33.7763			−1.21016
$780$		0			0
$781$	50.3776			1.80265
$782$	0.367535	+	0.367535i	0.0131430	+	0.0131430i
$783$		0			0
$784$		−	2.22206i		−	0.0793594i
$785$	37.0558	+	6.65619i	1.32258	+	0.237570i
$786$		0			0
$787$	10.3116	−	10.3116i	0.367569	−	0.367569i	−0.499021	−	0.866590i	$-0.666307\pi$
$787$	10.3116	−	10.3116i	0.367569	−	0.367569i	0.866590	+	0.499021i	$0.166307\pi$
$788$	16.6180	−	16.6180i	0.591991	−	0.591991i
$789$		0			0
$790$	18.1171	+	3.25430i	0.644578	+	0.115783i
$791$		−	30.1506i		−	1.07203i
$792$		0			0
$793$	3.76383	+	3.76383i	0.133658	+	0.133658i
$794$	20.3430			0.721947
$795$		0			0
$796$	2.25816			0.0800385
$797$	19.8355	+	19.8355i	0.702609	+	0.702609i	0.964970	−	0.262361i	$-0.0845012\pi$
$797$	19.8355	+	19.8355i	0.702609	+	0.702609i	−0.262361	+	0.964970i	$0.584501\pi$
$798$		0			0
$799$		−	0.837371i		−	0.0296241i
$800$	4.54496	−	2.08407i	0.160689	−	0.0736829i
$801$		0			0
$802$	10.0347	−	10.0347i	0.354338	−	0.354338i
$803$	−16.2559	+	16.2559i	−0.573659	+	0.573659i
$804$		0			0
$805$	4.01272	−	2.79066i	0.141430	−	0.0983577i
$806$		−	1.47014i		−	0.0517835i
$807$		0			0
$808$	−9.42754	−	9.42754i	−0.331660	−	0.331660i
$809$	−31.5588			−1.10955			−0.554774	−	0.832001i	$-0.687195\pi$
$809$	−31.5588			−1.10955			−0.554774	+	0.832001i	$0.687195\pi$
$810$		0			0
$811$	10.7702			0.378193			0.189097	−	0.981958i	$-0.439444\pi$
$811$	10.7702			0.378193			0.189097	+	0.981958i	$0.439444\pi$
$812$	−12.9999	−	12.9999i	−0.456208	−	0.456208i
$813$		0			0
$814$		−	31.8904i		−	1.11776i
$815$	0.434929	−	2.42130i	0.0152349	−	0.0848145i
$816$		0			0
$817$	−11.5583	+	11.5583i	−0.404375	+	0.404375i
$818$	17.8286	−	17.8286i	0.623364	−	0.623364i
$819$		0			0
$820$	15.4522	+	22.2190i	0.539615	+	0.775919i
$821$		−	29.6629i		−	1.03524i	−0.855610	−	0.517622i	$-0.826817\pi$
$821$		−	29.6629i		−	1.03524i	0.855610	−	0.517622i	$-0.173183\pi$
$822$		0			0
$823$	17.4671	+	17.4671i	0.608865	+	0.608865i	0.942649	−	0.333785i	$-0.108326\pi$
$823$	17.4671	+	17.4671i	0.608865	+	0.608865i	−0.333785	+	0.942649i	$0.608326\pi$
$824$	−2.18585			−0.0761477
$825$		0			0
$826$	−19.5871			−0.681522
$827$	11.0873	+	11.0873i	0.385541	+	0.385541i	0.873094	−	0.487552i	$-0.162110\pi$
$827$	11.0873	+	11.0873i	0.385541	+	0.385541i	−0.487552	+	0.873094i	$0.662110\pi$
$828$		0			0
$829$			26.0509i			0.904784i	0.891819	+	0.452392i	$0.149429\pi$
$829$			26.0509i			0.904784i	−0.891819	+	0.452392i	$0.850571\pi$
$830$	−10.5919	−	15.2302i	−0.367649	−	0.528646i
$831$		0			0
$832$	2.00000	−	2.00000i	0.0693375	−	0.0693375i
$833$	−0.816687	+	0.816687i	−0.0282965	+	0.0282965i
$834$		0			0
$835$	−1.73508	+	9.65944i	−0.0600451	+	0.334279i
$836$			10.2460i			0.354366i
$837$		0			0
$838$	10.1902	+	10.1902i	0.352015	+	0.352015i
$839$	−29.7734			−1.02789			−0.513946	−	0.857822i	$-0.671817\pi$
$839$	−29.7734			−1.02789			−0.513946	+	0.857822i	$0.671817\pi$
$840$		0			0
$841$	41.7412			1.43935
$842$	−13.4310	−	13.4310i	−0.462864	−	0.462864i
$843$		0			0
$844$		−	22.4101i		−	0.771389i
$845$	−9.17886	+	6.38346i	−0.315762	+	0.219598i
$846$		0			0
$847$	3.83351	−	3.83351i	0.131721	−	0.131721i
$848$	−6.41647	+	6.41647i	−0.220343	+	0.220343i
$849$		0			0
$850$	−2.43640	−	0.904465i	−0.0835679	−	0.0310229i
$851$		−	8.68582i		−	0.297746i
$852$		0			0
$853$	6.27933	+	6.27933i	0.215000	+	0.215000i	0.806388	−	0.591387i	$-0.201420\pi$
$853$	6.27933	+	6.27933i	0.215000	+	0.215000i	−0.591387	+	0.806388i	$0.701420\pi$
$854$	−4.11358			−0.140764
$855$		0			0
$856$	11.8819			0.406115
$857$	−34.1776	−	34.1776i	−1.16749	−	1.16749i	−0.982797	−	0.184689i	$-0.940872\pi$
$857$	−34.1776	−	34.1776i	−1.16749	−	1.16749i	−0.184689	−	0.982797i	$-0.559128\pi$
$858$		0			0
$859$			50.5764i			1.72564i	0.505508	+	0.862822i	$0.331305\pi$
$859$			50.5764i			1.72564i	−0.505508	+	0.862822i	$0.668695\pi$
$860$	12.8912	+	2.31559i	0.439587	+	0.0789611i
$861$		0			0
$862$	18.9859	−	18.9859i	0.646662	−	0.646662i
$863$	38.9845	−	38.9845i	1.32705	−	1.32705i	0.419117	−	0.907932i	$-0.362340\pi$
$863$	38.9845	−	38.9845i	1.32705	−	1.32705i	0.907932	−	0.419117i	$-0.137660\pi$
$864$		0			0
$865$	2.40169	+	0.431405i	0.0816599	+	0.0146682i
$866$		−	10.2400i		−	0.347968i
$867$		0			0
$868$	0.803377	+	0.803377i	0.0272684	+	0.0272684i
$869$	30.2237			1.02527
$870$		0			0
$871$	8.51633			0.288565
$872$	−4.34169	−	4.34169i	−0.147028	−	0.147028i
$873$		0			0
$874$			2.79066i			0.0943954i
$875$	−12.4217	+	21.0462i	−0.419931	+	0.711492i
$876$		0			0
$877$	30.3345	−	30.3345i	1.02432	−	1.02432i	0.0246260	−	0.999697i	$-0.492161\pi$
$877$	30.3345	−	30.3345i	1.02432	−	1.02432i	0.999697	−	0.0246260i	$-0.00783948\pi$
$878$	−25.3207	+	25.3207i	−0.854533	+	0.854533i
$879$		0			0
$880$	6.74011	−	4.68743i	0.227209	−	0.158013i
$881$			8.21130i			0.276646i	0.990387	+	0.138323i	$0.0441712\pi$
$881$			8.21130i			0.276646i	−0.990387	+	0.138323i	$0.955829\pi$
$882$		0			0
$883$	4.85275	+	4.85275i	0.163308	+	0.163308i	0.784030	−	0.620722i	$-0.213161\pi$
$883$	4.85275	+	4.85275i	0.163308	+	0.163308i	−0.620722	+	0.784030i	$0.713161\pi$
$884$	−1.47014			−0.0494462
$885$		0			0
$886$	−20.3056			−0.682180
$887$	−27.9893	−	27.9893i	−0.939788	−	0.939788i	0.0584995	−	0.998287i	$-0.481368\pi$
$887$	−27.9893	−	27.9893i	−0.939788	−	0.939788i	−0.998287	+	0.0584995i	$0.981368\pi$
$888$		0			0
$889$			9.83798i			0.329955i
$890$	3.36159	−	18.7144i	0.112681	−	0.627307i
$891$		0			0
$892$	−15.9035	+	15.9035i	−0.532488	+	0.532488i
$893$	3.17904	−	3.17904i	0.106382	−	0.106382i
$894$		0			0
$895$	−17.0752	−	24.5527i	−0.570762	−	0.820706i
$896$			2.18585i			0.0730241i
$897$		0			0
$898$	−2.58807	−	2.58807i	−0.0863649	−	0.0863649i
$899$	−4.37170			−0.145804
$900$		0			0
$901$	4.71656			0.157131
$902$	31.4223	+	31.4223i	1.04625	+	1.04625i
$903$		0			0
$904$		−	13.7935i		−	0.458767i
$905$	−7.67639	−	11.0380i	−0.255172	−	0.366915i
$906$		0			0
$907$	−9.78683	+	9.78683i	−0.324966	+	0.324966i	−0.850669	−	0.525702i	$-0.823803\pi$
$907$	−9.78683	+	9.78683i	−0.324966	+	0.324966i	0.525702	+	0.850669i	$0.323803\pi$
$908$	14.9593	−	14.9593i	0.496443	−	0.496443i
$909$		0			0
$910$	−2.44413	+	13.6068i	−0.0810220	+	0.451059i
$911$		−	9.22522i		−	0.305645i	−0.988254	−	0.152823i	$-0.951164\pi$
$911$		−	9.22522i		−	0.305645i	0.988254	−	0.152823i	$-0.0488363\pi$
$912$		0			0
$913$	−21.5387	−	21.5387i	−0.712827	−	0.712827i
$914$	10.2820			0.340098
$915$		0			0
$916$	−12.1698			−0.402101
$917$	31.3926	+	31.3926i	1.03667	+	1.03667i
$918$		0			0
$919$			6.50784i			0.214674i	0.994223	+	0.107337i	$0.0342323\pi$
$919$			6.50784i			0.214674i	−0.994223	+	0.107337i	$0.965768\pi$
$920$	1.83577	−	1.27669i	0.0605236	−	0.0420913i
$921$		0			0
$922$	−0.0186882	+	0.0186882i	−0.000615464	+	0.000615464i
$923$	−27.4422	+	27.4422i	−0.903272	+	0.903272i
$924$		0			0
$925$	18.1018	+	39.4767i	0.595185	+	1.29799i
$926$		−	11.3276i		−	0.372248i
$927$		0			0
$928$	−5.94732	−	5.94732i	−0.195230	−	0.195230i
$929$	47.6095			1.56202			0.781008	−	0.624521i	$-0.214706\pi$
$929$	47.6095			1.56202			0.781008	+	0.624521i	$0.214706\pi$
$930$		0			0
$931$	−6.20101			−0.203230
$932$	12.5213	+	12.5213i	0.410150	+	0.410150i
$933$		0			0
$934$			2.79493i			0.0914531i
$935$	−4.20003	−	0.754433i	−0.137356	−	0.0246726i
$936$		0			0
$937$	−0.822065	+	0.822065i	−0.0268557	+	0.0268557i	−0.720407	−	0.693551i	$-0.756045\pi$
$937$	−0.822065	+	0.822065i	−0.0268557	+	0.0268557i	0.693551	+	0.720407i	$0.256045\pi$
$938$	−4.65385	+	4.65385i	−0.151954	+	0.151954i
$939$		0			0
$940$	−3.54563	−	0.636887i	−0.115646	−	0.0207730i
$941$			45.7028i			1.48987i	0.667138	+	0.744934i	$0.267519\pi$
$941$			45.7028i			1.48987i	−0.667138	+	0.744934i	$0.732481\pi$
$942$		0			0
$943$	8.55835	+	8.55835i	0.278698	+	0.278698i
$944$	−8.96086			−0.291651
$945$		0			0
$946$	21.5057			0.699210
$947$	−3.24399	−	3.24399i	−0.105416	−	0.105416i	0.652432	−	0.757847i	$-0.273749\pi$
$947$	−3.24399	−	3.24399i	−0.105416	−	0.105416i	−0.757847	+	0.652432i	$0.773749\pi$
$948$		0			0
$949$		−	17.7102i		−	0.574897i
$950$	−5.81592	−	12.6834i	−0.188693	−	0.411505i
$951$		0			0
$952$	0.803377	−	0.803377i	0.0260376	−	0.0260376i
$953$	−3.07943	+	3.07943i	−0.0997526	+	0.0997526i	−0.755222	−	0.655469i	$-0.772471\pi$
$953$	−3.07943	+	3.07943i	−0.0997526	+	0.0997526i	0.655469	+	0.755222i	$0.272471\pi$
$954$		0			0
$955$	−47.4563	+	33.0036i	−1.53565	+	1.06797i
$956$		−	7.80476i		−	0.252424i
$957$		0			0
$958$	−16.6683	−	16.6683i	−0.538528	−	0.538528i
$959$	−16.4063			−0.529786
$960$		0			0
$961$	−30.7298			−0.991285
$962$	17.3716	+	17.3716i	0.560084	+	0.560084i
$963$		0			0
$964$			7.71212i			0.248391i
$965$	3.59405	−	20.0085i	0.115697	−	0.644097i
$966$		0			0
$967$	−40.6772	+	40.6772i	−1.30809	+	1.30809i	−0.385296	+	0.922793i	$0.625901\pi$
$967$	−40.6772	+	40.6772i	−1.30809	+	1.30809i	−0.922793	+	0.385296i	$0.874099\pi$
$968$	1.75378	−	1.75378i	0.0563688	−	0.0563688i
$969$		0			0
$970$	8.53152	+	12.2676i	0.273931	+	0.393888i
$971$			32.2259i			1.03418i	0.855932	+	0.517089i	$0.172984\pi$
$971$			32.2259i			1.03418i	−0.855932	+	0.517089i	$0.827016\pi$
$972$		0			0
$973$	3.94057	+	3.94057i	0.126329	+	0.126329i
$974$	−10.9238			−0.350021
$975$		0			0
$976$	−1.88191			−0.0602386
$977$	−30.7751	−	30.7751i	−0.984582	−	0.984582i	0.0153006	−	0.999883i	$-0.495129\pi$
$977$	−30.7751	−	30.7751i	−0.984582	−	0.984582i	−0.999883	+	0.0153006i	$0.995129\pi$
$978$		0			0
$979$		−	31.2201i		−	0.997799i
$980$	2.83689	+	4.07920i	0.0906211	+	0.130305i
$981$		0			0
$982$	−16.6716	+	16.6716i	−0.532012	+	0.532012i
$983$	3.22950	−	3.22950i	0.103005	−	0.103005i	−0.653726	−	0.756731i	$-0.726795\pi$
$983$	3.22950	−	3.22950i	0.103005	−	0.103005i	0.756731	+	0.653726i	$0.226795\pi$
$984$		0			0
$985$	−9.29077	+	51.7229i	−0.296029	+	1.64803i
$986$			4.37170i			0.139223i
$987$		0			0
$988$	−5.58131	−	5.58131i	−0.177565	−	0.177565i
$989$	5.85739			0.186254
$990$		0			0
$991$	−5.33087			−0.169341			−0.0846704	−	0.996409i	$-0.526984\pi$
$991$	−5.33087			−0.169341			−0.0846704	+	0.996409i	$0.526984\pi$
$992$	0.367535	+	0.367535i	0.0116693	+	0.0116693i
$993$		0			0
$994$		−	29.9923i		−	0.951297i
$995$	−4.14547	+	2.88298i	−0.131420	+	0.0913966i
$996$		0			0
$997$	−38.6937	+	38.6937i	−1.22544	+	1.22544i	−0.259773	+	0.965670i	$0.583648\pi$
$997$	−38.6937	+	38.6937i	−1.22544	+	1.22544i	−0.965670	+	0.259773i	$0.916352\pi$
$998$	−1.16018	+	1.16018i	−0.0367250	+	0.0367250i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.i.323.6	yes	16
3.2	odd	2	inner	2070.2.j.i.323.3	✓	16
5.2	odd	4	inner	2070.2.j.i.737.3	yes	16
15.2	even	4	inner	2070.2.j.i.737.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.i.323.3	✓	16	3.2	odd	2	inner
2070.2.j.i.323.6	yes	16	1.1	even	1	trivial
2070.2.j.i.737.3	yes	16	5.2	odd	4	inner
2070.2.j.i.737.6	yes	16	15.2	even	4	inner

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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.27669 - 1.83577i) q^{5} +(-1.54563 + 1.54563i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.27669 - 1.83577i) q^{5} +(-1.54563 + 1.54563i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.395329 - 2.20084i) q^{10} -3.67154i q^{11} +(2.00000 + 2.00000i) q^{13} -2.18585 q^{14} -1.00000 q^{16} +(0.367535 + 0.367535i) q^{17} +2.79066i q^{19} +(1.83577 - 1.27669i) q^{20} +(2.59617 - 2.59617i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-1.74011 + 4.68743i) q^{25} +2.82843i q^{26} +(-1.54563 - 1.54563i) q^{28} +8.41078 q^{29} -0.519773 q^{31} +(-0.707107 - 0.707107i) q^{32} +0.519773i q^{34} +(4.81071 + 0.864129i) q^{35} +(6.14180 - 6.14180i) q^{37} +(-1.97329 + 1.97329i) q^{38} +(2.20084 + 0.395329i) q^{40} +12.1033i q^{41} +(4.14180 + 4.14180i) q^{43} +3.67154 q^{44} +1.00000 q^{46} +(-1.13917 - 1.13917i) q^{47} +2.22206i q^{49} +(-4.54496 + 2.08407i) q^{50} +(-2.00000 + 2.00000i) q^{52} +(6.41647 - 6.41647i) q^{53} +(-6.74011 + 4.68743i) q^{55} -2.18585i q^{56} +(5.94732 + 5.94732i) q^{58} +8.96086 q^{59} +1.88191 q^{61} +(-0.367535 - 0.367535i) q^{62} -1.00000i q^{64} +(1.11816 - 6.22493i) q^{65} +(2.12908 - 2.12908i) q^{67} +(-0.367535 + 0.367535i) q^{68} +(2.79066 + 4.01272i) q^{70} +13.7211i q^{71} +(-4.42754 - 4.42754i) q^{73} +8.68582 q^{74} -2.79066 q^{76} +(5.67484 + 5.67484i) q^{77} +8.23189i q^{79} +(1.27669 + 1.83577i) q^{80} +(-8.55835 + 8.55835i) q^{82} +(5.86639 - 5.86639i) q^{83} +(0.205481 - 1.14394i) q^{85} +5.85739i q^{86} +(2.59617 + 2.59617i) q^{88} +8.50327 q^{89} -6.18252 q^{91} +(0.707107 + 0.707107i) q^{92} -1.61103i q^{94} +(5.12301 - 3.56281i) q^{95} +(-4.72525 + 4.72525i) q^{97} +(-1.57124 + 1.57124i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 4 q^{10} + 32 q^{13} - 16 q^{16} - 24 q^{25} - 16 q^{31} + 32 q^{37} + 4 q^{40} + 16 q^{46} - 32 q^{52} - 104 q^{55} + 8 q^{58} - 40 q^{61} + 72 q^{67} + 24 q^{70} + 24 q^{73} - 24 q^{76} - 8 q^{82} - 8 q^{85} - 72 q^{97}+O(q^{100}) \) 16 * q - 4 * q^10 + 32 * q^13 - 16 * q^16 - 24 * q^25 - 16 * q^31 + 32 * q^37 + 4 * q^40 + 16 * q^46 - 32 * q^52 - 104 * q^55 + 8 * q^58 - 40 * q^61 + 72 * q^67 + 24 * q^70 + 24 * q^73 - 24 * q^76 - 8 * q^82 - 8 * q^85 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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