LMFDB - Embedded newform 180.2.n.c.119.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,2,Mod(59,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 3]))

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

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

chi := DirichletCharacter("180.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.n (of order $6$, 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:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} + 7x^{4} + 36x^{2} + 81 $ x^8 + 4x^6 + 7x^4 + 36*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			119.3
Root			$-1.40294 - 1.01575i$ of defining polynomial
Character	$\chi$	$=$	180.119
Dual form			180.2.n.c.59.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(-1.40294 - 1.01575i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-1.00000 - 2.23607i) q^{6} +(1.04655 - 1.81267i) q^{7} +2.82843i q^{8} +(0.936492 + 2.85008i) q^{9} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(-1.40294 - 1.01575i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-1.00000 - 2.23607i) q^{6} +(1.04655 - 1.81267i) q^{7} +2.82843i q^{8} +(0.936492 + 2.85008i) q^{9} +3.16228 q^{10} +(0.356394 - 3.44572i) q^{12} +(2.56351 - 1.48004i) q^{14} +(-3.85243 - 0.398461i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-0.868351 + 4.15283i) q^{18} +(3.87298 + 2.23607i) q^{20} +(-3.30948 + 1.48004i) q^{21} +(-7.72750 + 4.46147i) q^{23} +(2.87298 - 3.96812i) q^{24} +(2.50000 - 4.33013i) q^{25} +(1.58114 - 4.94975i) q^{27} +4.18619 q^{28} +(-8.37298 - 4.83414i) q^{29} +(-4.43649 - 3.21209i) q^{30} +(-4.89898 + 2.82843i) q^{32} -4.68030i q^{35} +(-4.00000 + 4.47214i) q^{36} +(3.16228 + 5.47723i) q^{40} +(-10.9365 + 6.31419i) q^{41} +(-5.09981 - 0.527478i) q^{42} +(1.58114 - 2.73861i) q^{43} +(5.00000 + 4.47214i) q^{45} -12.6190 q^{46} +(11.4017 + 6.58279i) q^{47} +(6.32456 - 2.82843i) q^{48} +(1.30948 + 2.26808i) q^{49} +(6.12372 - 3.53553i) q^{50} +(5.43649 - 4.94414i) q^{54} +(5.12702 + 2.96008i) q^{56} +(-6.83651 - 11.8412i) q^{58} +(-3.16228 - 7.07107i) q^{60} +(7.80948 - 13.5264i) q^{61} +(6.14636 + 1.28520i) q^{63} -8.00000 q^{64} +(5.78996 + 10.0285i) q^{67} +(15.3730 + 1.59004i) q^{69} +(3.30948 - 5.73218i) q^{70} +(-8.06126 + 2.64880i) q^{72} +(-7.90569 + 3.53553i) q^{75} +8.94427i q^{80} +(-7.24597 + 5.33816i) q^{81} -17.8592 q^{82} +(0.379028 + 0.218832i) q^{83} +(-5.87298 - 4.25214i) q^{84} +(3.87298 - 2.23607i) q^{86} +(6.83651 + 15.2869i) q^{87} -3.74812i q^{89} +(2.96145 + 9.01276i) q^{90} +(-15.4550 - 8.92295i) q^{92} +(9.30948 + 16.1245i) q^{94} +(9.74597 + 1.00803i) q^{96} +3.70375i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 8 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^4 - 8 * q^6 - 8 * q^9	$ 8 q + 8 q^{4} - 8 q^{6} - 8 q^{9} + 36 q^{14} - 16 q^{16} + 20 q^{21} - 8 q^{24} + 20 q^{25} - 36 q^{29} - 20 q^{30} - 32 q^{36} - 72 q^{41} + 40 q^{45} - 8 q^{46} - 36 q^{49} + 28 q^{54} + 72 q^{56} + 16 q^{61} - 64 q^{64} + 92 q^{69} - 20 q^{70} + 4 q^{81} - 16 q^{84} + 28 q^{94} + 16 q^{96}+O(q^{100}) $ 8 * q + 8 * q^4 - 8 * q^6 - 8 * q^9 + 36 * q^14 - 16 * q^16 + 20 * q^21 - 8 * q^24 + 20 * q^25 - 36 * q^29 - 20 * q^30 - 32 * q^36 - 72 * q^41 + 40 * q^45 - 8 * q^46 - 36 * q^49 + 28 * q^54 + 72 * q^56 + 16 * q^61 - 64 * q^64 + 92 * q^69 - 20 * q^70 + 4 * q^81 - 16 * q^84 + 28 * q^94 + 16 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.22474	+	0.707107i	0.866025	+	0.500000i
$2$	1.22474	+	0.707107i	0.866025	+	0.500000i
$3$	−1.40294	−	1.01575i	−0.809989	−	0.586445i
$3$	−1.40294	−	1.01575i	−0.809989	−	0.586445i
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	1.93649	−	1.11803i	0.866025	−	0.500000i
$5$	1.93649	−	1.11803i	0.866025	−	0.500000i
$6$	−1.00000	−	2.23607i	−0.408248	−	0.912871i
$7$	1.04655	−	1.81267i	0.395558	−	0.685126i	−0.597614	−	0.801784i	$-0.703885\pi$
$7$	1.04655	−	1.81267i	0.395558	−	0.685126i	0.993172	+	0.116657i	$0.0372179\pi$
$8$			2.82843i			1.00000i
$9$	0.936492	+	2.85008i	0.312164	+	0.950028i
$10$	3.16228			1.00000
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	0.356394	−	3.44572i	0.102882	−	0.994694i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$	2.56351	−	1.48004i	0.685126	−	0.395558i
$15$	−3.85243	−	0.398461i	−0.994694	−	0.102882i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	−0.868351	+	4.15283i	−0.204672	+	0.978831i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	3.87298	+	2.23607i	0.866025	+	0.500000i
$21$	−3.30948	+	1.48004i	−0.722187	+	0.322972i
$22$		0			0
$23$	−7.72750	+	4.46147i	−1.61129	+	0.930281i	−0.622224	+	0.782839i	$0.713771\pi$
$23$	−7.72750	+	4.46147i	−1.61129	+	0.930281i	−0.989071	+	0.147442i	$0.952896\pi$
$24$	2.87298	−	3.96812i	0.586445	−	0.809989i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$		0			0
$27$	1.58114	−	4.94975i	0.304290	−	0.952579i
$28$	4.18619			0.791116
$29$	−8.37298	−	4.83414i	−1.55482	−	0.897678i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−8.37298	−	4.83414i	−1.55482	−	0.897678i	−0.557086	−	0.830455i	$-0.688081\pi$
$30$	−4.43649	−	3.21209i	−0.809989	−	0.586445i
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	−4.89898	+	2.82843i	−0.866025	+	0.500000i
$33$		0			0
$34$		0			0
$35$		−	4.68030i		−	0.791116i
$36$	−4.00000	+	4.47214i	−0.666667	+	0.745356i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$		0			0
$40$	3.16228	+	5.47723i	0.500000	+	0.866025i
$41$	−10.9365	+	6.31419i	−1.70799	+	0.986110i	−0.770950	+	0.636895i	$0.780218\pi$
$41$	−10.9365	+	6.31419i	−1.70799	+	0.986110i	−0.937043	+	0.349215i	$0.886448\pi$
$42$	−5.09981	−	0.527478i	−0.786918	−	0.0813916i
$43$	1.58114	−	2.73861i	0.241121	−	0.417635i	−0.719913	−	0.694065i	$-0.755818\pi$
$43$	1.58114	−	2.73861i	0.241121	−	0.417635i	0.961034	+	0.276430i	$0.0891515\pi$
$44$		0			0
$45$	5.00000	+	4.47214i	0.745356	+	0.666667i
$46$	−12.6190			−1.86056
$47$	11.4017	+	6.58279i	1.66311	+	0.960199i	0.971215	+	0.238204i	$0.0765587\pi$
$47$	11.4017	+	6.58279i	1.66311	+	0.960199i	0.691898	+	0.721995i	$0.256775\pi$
$48$	6.32456	−	2.82843i	0.912871	−	0.408248i
$49$	1.30948	+	2.26808i	0.187068	+	0.324011i
$50$	6.12372	−	3.53553i	0.866025	−	0.500000i
$51$		0			0
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	5.43649	−	4.94414i	0.739813	−	0.672813i
$55$		0			0
$56$	5.12702	+	2.96008i	0.685126	+	0.395558i
$57$		0			0
$58$	−6.83651	−	11.8412i	−0.897678	−	1.55482i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	−3.16228	−	7.07107i	−0.408248	−	0.912871i
$61$	7.80948	−	13.5264i	0.999901	−	1.73188i	0.487753	−	0.872982i	$-0.337817\pi$
$61$	7.80948	−	13.5264i	0.999901	−	1.73188i	0.512148	−	0.858898i	$-0.328850\pi$
$62$		0			0
$63$	6.14636	+	1.28520i	0.774368	+	0.161919i
$64$	−8.00000			−1.00000
$65$		0			0
$66$		0			0
$67$	5.78996	+	10.0285i	0.707357	+	1.22518i	0.965834	+	0.259161i	$0.0834459\pi$
$67$	5.78996	+	10.0285i	0.707357	+	1.22518i	−0.258478	+	0.966017i	$0.583221\pi$
$68$		0			0
$69$	15.3730	+	1.59004i	1.85069	+	0.191419i
$70$	3.30948	−	5.73218i	0.395558	−	0.685126i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	−8.06126	+	2.64880i	−0.950028	+	0.312164i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	−7.90569	+	3.53553i	−0.912871	+	0.408248i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$			8.94427i			1.00000i
$81$	−7.24597	+	5.33816i	−0.805107	+	0.593129i
$82$	−17.8592			−1.97222
$83$	0.379028	+	0.218832i	0.0416037	+	0.0240199i	0.520658	−	0.853766i	$-0.325687\pi$
$83$	0.379028	+	0.218832i	0.0416037	+	0.0240199i	−0.479054	+	0.877785i	$0.659020\pi$
$84$	−5.87298	−	4.25214i	−0.640795	−	0.463946i
$85$		0			0
$86$	3.87298	−	2.23607i	0.417635	−	0.241121i
$87$	6.83651	+	15.2869i	0.732951	+	1.63893i
$88$		0			0
$89$		−	3.74812i		−	0.397300i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$		−	3.74812i		−	0.397300i	0.980071	−	0.198650i	$-0.0636557\pi$
$90$	2.96145	+	9.01276i	0.312164	+	0.950028i
$91$		0			0
$92$	−15.4550	−	8.92295i	−1.61129	−	0.930281i
$93$		0			0
$94$	9.30948	+	16.1245i	0.960199	+	1.66311i
$95$		0			0
$96$	9.74597	+	1.00803i	0.994694	+	0.102882i
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$			3.70375i			0.374136i
$99$		0			0
$100$	10.0000			1.00000
$101$	7.74597	+	4.47214i	0.770752	+	0.444994i	0.833143	−	0.553058i	$-0.186539\pi$
$101$	7.74597	+	4.47214i	0.770752	+	0.444994i	−0.0623905	+	0.998052i	$0.519872\pi$
$102$		0			0
$103$	−7.90569	−	13.6931i	−0.778971	−	1.34922i	−0.932535	−	0.361079i	$-0.882408\pi$
$103$	−7.90569	−	13.6931i	−0.778971	−	1.34922i	0.153564	−	0.988139i	$-0.450925\pi$
$104$		0			0
$105$	−4.75403	+	6.56619i	−0.463946	+	0.640795i
$106$		0			0
$107$		−	17.4082i		−	1.68292i	−0.540322	−	0.841458i	$-0.681698\pi$
$107$		−	17.4082i		−	1.68292i	0.540322	−	0.841458i	$-0.318302\pi$
$108$	10.1544	−	2.21113i	0.977103	−	0.212767i
$109$	−3.61895			−0.346633			−0.173316	−	0.984866i	$-0.555448\pi$
$109$	−3.61895			−0.346633			−0.173316	+	0.984866i	$0.555448\pi$
$110$		0			0
$111$		0			0
$112$	4.18619	+	7.25070i	0.395558	+	0.685126i
$113$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$113$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$114$		0			0
$115$	−9.97616	+	17.2792i	−0.930281	+	1.61129i
$116$		−	19.3366i		−	1.79536i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	1.12702	−	10.8963i	0.102882	−	0.994694i
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	19.1292	−	11.0443i	1.73188	−	0.999901i
$123$	21.7569	+	2.25034i	1.96176	+	0.202906i
$124$		0			0
$125$		−	11.1803i		−	1.00000i
$126$	6.61895	+	5.92017i	0.589663	+	0.527411i
$127$	7.39374			0.656088			0.328044	−	0.944662i	$-0.393611\pi$
$127$	7.39374			0.656088			0.328044	+	0.944662i	$0.393611\pi$
$128$	−9.79796	−	5.65685i	−0.866025	−	0.500000i
$129$	−5.00000	+	2.23607i	−0.440225	+	0.196875i
$130$		0			0
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$		0			0
$134$			16.3765i			1.41471i
$135$	−2.47212	−	11.3529i	−0.212767	−	0.977103i
$136$		0			0
$137$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$137$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$138$	17.7037	+	12.8177i	1.50704	+	1.09112i
$139$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$139$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$140$	8.10653	−	4.68030i	0.685126	−	0.395558i
$141$	−9.30948	−	20.8166i	−0.783999	−	1.75308i
$142$		0			0
$143$		0			0
$144$	−11.7460	−	2.45607i	−0.978831	−	0.204672i
$145$	−21.6190			−1.79536
$146$		0			0
$147$	0.466689	−	4.51208i	0.0384919	−	0.372150i
$148$		0			0
$149$	16.0635	−	9.27427i	1.31597	−	0.759778i	0.332896	−	0.942964i	$-0.391974\pi$
$149$	16.0635	−	9.27427i	1.31597	−	0.759778i	0.983078	+	0.183186i	$0.0586410\pi$
$150$	−12.1825	−	1.26004i	−0.994694	−	0.102882i
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$		0			0
$159$		0			0
$160$	−6.32456	+	10.9545i	−0.500000	+	0.866025i
$161$			18.6766i			1.47192i
$162$	−12.6491	+	1.41421i	−0.993808	+	0.111111i
$163$	−22.1359			−1.73382			−0.866910	−	0.498464i	$-0.833898\pi$
$163$	−22.1359			−1.73382			−0.866910	+	0.498464i	$0.833898\pi$
$164$	−21.8730	−	12.6284i	−1.70799	−	0.986110i
$165$		0			0
$166$	0.309475	+	0.536026i	0.0240199	+	0.0416037i
$167$	3.29521	−	1.90249i	0.254991	−	0.147219i	−0.367057	−	0.930199i	$-0.619634\pi$
$167$	3.29521	−	1.90249i	0.254991	−	0.147219i	0.622047	+	0.782980i	$0.286301\pi$
$168$	−4.18619	−	9.36061i	−0.322972	−	0.722187i
$169$	−6.50000	+	11.2583i	−0.500000	+	0.866025i
$170$		0			0
$171$		0			0
$172$	6.32456			0.482243
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$	−2.43649	+	23.5567i	−0.184710	+	1.78583i
$175$	−5.23274	−	9.06337i	−0.395558	−	0.685126i
$176$		0			0
$177$		0			0
$178$	2.65032	−	4.59049i	0.198650	−	0.344072i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−2.74597	+	13.1324i	−0.204672	+	0.978831i
$181$	22.2379			1.65293			0.826465	−	0.562988i	$-0.190348\pi$
$181$	22.2379			1.65293			0.826465	+	0.562988i	$0.190348\pi$
$182$		0			0
$183$	−24.6957	+	11.0443i	−1.82556	+	0.816416i
$184$	−12.6190	−	21.8567i	−0.930281	−	1.61129i
$185$		0			0
$186$		0			0
$187$		0			0
$188$			26.3312i			1.92040i
$189$	−7.31754	−	8.04624i	−0.532273	−	0.585278i
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	11.2235	+	8.12602i	0.809989	+	0.586445i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$		0			0
$195$		0			0
$196$	−2.61895	+	4.53615i	−0.187068	+	0.324011i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	12.2474	+	7.07107i	0.866025	+	0.500000i
$201$	2.06351	−	19.9506i	0.145549	−	1.40721i
$202$	6.32456	+	10.9545i	0.444994	+	0.770752i
$203$	−17.5255	+	10.1183i	−1.23005	+	0.710167i
$204$		0			0
$205$	−14.1190	+	24.4547i	−0.986110	+	1.70799i
$206$		−	22.3607i		−	1.55794i
$207$	−19.9523	−	17.8459i	−1.38678	−	1.24038i
$208$		0			0
$209$		0			0
$210$	−10.4655	+	4.68030i	−0.722187	+	0.322972i
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$		0			0
$213$		0			0
$214$	12.3095	−	21.3206i	0.841458	−	1.45745i
$215$		−	7.07107i		−	0.482243i
$216$	14.0000	+	4.47214i	0.952579	+	0.304290i
$217$		0			0
$218$	−4.43229	−	2.55898i	−0.300193	−	0.173316i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	12.0693	−	20.9046i	0.808217	−	1.39987i	−0.105881	−	0.994379i	$-0.533766\pi$
$223$	12.0693	−	20.9046i	0.808217	−	1.39987i	0.914098	−	0.405494i	$-0.132900\pi$
$224$			11.8403i			0.791116i
$225$	14.6825	+	3.07008i	0.978831	+	0.204672i
$226$		0			0
$227$	−8.57321	−	4.94975i	−0.569024	−	0.328526i	0.187735	−	0.982220i	$-0.439885\pi$
$227$	−8.57321	−	4.94975i	−0.569024	−	0.328526i	−0.756760	+	0.653693i	$0.773219\pi$
$228$		0			0
$229$	−8.11895	−	14.0624i	−0.536515	−	0.929272i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−8.11895	−	14.0624i	−0.536515	−	0.929272i	0.462573	−	0.886581i	$-0.346926\pi$
$230$	−24.4365	+	14.1084i	−1.61129	+	0.930281i
$231$		0			0
$232$	13.6730	−	23.6824i	0.897678	−	1.55482i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$	29.4391			1.92040
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$	9.08517	−	12.5483i	0.586445	−	0.809989i
$241$	−1.19052	+	2.06205i	−0.0766885	+	0.132828i	−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−1.19052	+	2.06205i	−0.0766885	+	0.132828i	0.825131	+	0.564942i	$0.191101\pi$
$242$			15.5563i			1.00000i
$243$	15.5879	−	0.129018i	0.999966	−	0.00827648i
$244$	31.2379			1.99980
$245$	5.07157	+	2.92808i	0.324011	+	0.187068i
$246$	25.0554	+	18.1406i	1.59748	+	1.15660i
$247$		0			0
$248$		0			0
$249$	−0.309475	−	0.692007i	−0.0196122	−	0.0438542i
$250$	7.90569	−	13.6931i	0.500000	−	0.866025i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	3.92033	+	11.9310i	0.246958	+	0.751582i
$253$		0			0
$254$	9.05544	+	5.22816i	0.568189	+	0.328044i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$	−7.70486	−	0.796921i	−0.479684	−	0.0496141i
$259$		0			0
$260$		0			0
$261$	5.93649	−	28.3908i	0.367460	−	1.75735i
$262$		0			0
$263$	13.4722	+	7.77817i	0.830731	+	0.479623i	0.854103	−	0.520104i	$-0.174107\pi$
$263$	13.4722	+	7.77817i	0.830731	+	0.479623i	−0.0233719	+	0.999727i	$0.507440\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−3.80716	+	5.25839i	−0.232995	+	0.321808i
$268$	−11.5799	+	20.0570i	−0.707357	+	1.22518i
$269$			31.9649i			1.94894i	0.224523	+	0.974469i	$0.427917\pi$
$269$			31.9649i			1.94894i	−0.224523	+	0.974469i	$0.572083\pi$
$270$	5.00000	−	15.6525i	0.304290	−	0.952579i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	12.6190	+	28.2168i	0.759572	+	1.69845i
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$		0			0
$280$	13.2379			0.791116
$281$	22.5554	+	13.0224i	1.34554	+	0.776851i	0.987615	−	0.156898i	$-0.0501493\pi$
$281$	22.5554	+	13.0224i	1.34554	+	0.776851i	0.357930	+	0.933748i	$0.383483\pi$
$282$	3.31784	−	32.0778i	0.197575	−	1.91021i
$283$	16.8127	+	29.1204i	0.999409	+	1.73103i	0.529465	+	0.848332i	$0.322393\pi$
$283$	16.8127	+	29.1204i	0.999409	+	1.73103i	0.469945	+	0.882696i	$0.344274\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			26.4324i			1.56025i
$288$	−12.6491	−	11.3137i	−0.745356	−	0.666667i
$289$	−17.0000			−1.00000
$290$	−26.4777	−	15.2869i	−1.55482	−	0.897678i
$291$		0			0
$292$		0			0
$293$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$293$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$294$	3.76210	−	5.19615i	0.219410	−	0.303046i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	26.2316			1.51956
$299$		0			0
$300$	−14.0294	−	10.1575i	−0.809989	−	0.586445i
$301$	−3.30948	−	5.73218i	−0.190755	−	0.330397i
$302$		0			0
$303$	−6.32456	−	14.1421i	−0.363336	−	0.812444i
$304$		0			0
$305$		−	34.9250i		−	1.99980i
$306$		0			0
$307$	−21.0668			−1.20234			−0.601172	−	0.799120i	$-0.705299\pi$
$307$	−21.0668			−1.20234			−0.601172	+	0.799120i	$0.705299\pi$
$308$		0			0
$309$	−2.81754	+	27.2408i	−0.160284	+	1.54968i
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$		0			0
$315$	13.3393	−	4.38307i	0.751582	−	0.246958i
$316$		0			0
$317$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$317$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$318$		0			0
$319$		0			0
$320$	−15.4919	+	8.94427i	−0.866025	+	0.500000i
$321$	−17.6825	+	24.4227i	−0.986939	+	1.36314i
$322$	−13.2063	+	22.8740i	−0.735960	+	1.27472i
$323$		0			0
$324$	−16.4919	−	7.21222i	−0.916219	−	0.400679i
$325$		0			0
$326$	−27.1109	−	15.6525i	−1.50153	−	0.866910i
$327$	5.07718	+	3.67596i	0.280769	+	0.203281i
$328$	−17.8592	−	30.9331i	−0.986110	−	1.70799i
$329$	23.8649	−	13.7784i	1.31572	−	0.759629i
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$			0.875328i			0.0480398i
$333$		0			0
$334$	5.38105			0.294438
$335$	22.4244	+	12.9468i	1.22518	+	0.707357i
$336$	1.49193	−	14.4244i	0.0813916	−	0.786918i
$337$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$337$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$338$	−15.9217	+	9.19239i	−0.866025	+	0.500000i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	20.1334			1.08710
$344$	7.74597	+	4.47214i	0.417635	+	0.241121i
$345$	31.5474	−	14.1084i	1.69845	−	0.759572i
$346$		0			0
$347$	−20.8207	+	12.0208i	−1.11771	+	0.645311i	−0.940816	−	0.338918i	$-0.889939\pi$
$347$	−20.8207	+	12.0208i	−1.11771	+	0.645311i	−0.176896	+	0.984230i	$0.556606\pi$
$348$	−19.6412	+	27.1281i	−1.05288	+	1.45422i
$349$	−5.11895	+	8.86628i	−0.274011	+	0.474601i	−0.969885	−	0.243563i	$-0.921684\pi$
$349$	−5.11895	+	8.86628i	−0.274011	+	0.474601i	0.695874	+	0.718164i	$0.255017\pi$
$350$		−	14.8004i		−	0.791116i
$351$		0			0
$352$		0			0
$353$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$353$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$354$		0			0
$355$		0			0
$356$	6.49193	−	3.74812i	0.344072	−	0.198650i
$357$		0			0
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	−12.6491	+	14.1421i	−0.666667	+	0.745356i
$361$	19.0000			1.00000
$362$	27.2358	+	15.7246i	1.43148	+	0.826465i
$363$	1.96017	−	18.9515i	0.102882	−	0.994694i
$364$		0			0
$365$		0			0
$366$	−38.0554	−	3.93611i	−1.98919	−	0.205744i
$367$	1.58114	−	2.73861i	0.0825348	−	0.142954i	−0.821803	−	0.569771i	$-0.807032\pi$
$367$	1.58114	−	2.73861i	0.0825348	−	0.142954i	0.904338	+	0.426817i	$0.140365\pi$
$368$		−	35.6918i		−	1.86056i
$369$	−28.2379	−	25.2567i	−1.47001	−	1.31481i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	−11.3565	+	15.6854i	−0.586445	+	0.809989i
$376$	−18.6190	+	32.2490i	−0.960199	+	1.66311i
$377$		0			0
$378$	−3.27257	−	15.0289i	−0.168323	−	0.773002i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	−10.3730	−	7.51021i	−0.531424	−	0.384760i
$382$		0			0
$383$	23.2702	−	13.4350i	1.18905	−	0.686498i	0.230959	−	0.972964i	$-0.425814\pi$
$383$	23.2702	−	13.4350i	1.18905	−	0.686498i	0.958091	+	0.286466i	$0.0924804\pi$
$384$	8.00000	+	17.8885i	0.408248	+	0.912871i
$385$		0			0
$386$		0			0
$387$	9.28600	+	1.94169i	0.472034	+	0.0987017i
$388$		0			0
$389$	−4.44456	−	2.56607i	−0.225348	−	0.130105i	0.383076	−	0.923717i	$-0.374865\pi$
$389$	−4.44456	−	2.56607i	−0.225348	−	0.130105i	−0.608424	+	0.793612i	$0.708198\pi$
$390$		0			0
$391$		0			0
$392$	−6.41509	+	3.70375i	−0.324011	+	0.187068i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	10.0000	+	17.3205i	0.500000	+	0.866025i
$401$	−30.9839	+	17.8885i	−1.54726	+	0.893311i	−0.548911	+	0.835881i	$0.684957\pi$
$401$	−30.9839	+	17.8885i	−1.54726	+	0.893311i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$	16.6345	−	22.9753i	0.829652	−	1.14590i
$403$		0			0
$404$			17.8885i			0.889988i
$405$	−8.06351	+	18.4385i	−0.400679	+	0.916219i
$406$	−28.6190			−1.42033
$407$		0			0
$408$		0			0
$409$	2.00000	+	3.46410i	0.0988936	+	0.171289i	0.911227	−	0.411905i	$-0.135136\pi$
$409$	2.00000	+	3.46410i	0.0988936	+	0.171289i	−0.812333	+	0.583193i	$0.801803\pi$
$410$	−34.5842	+	19.9672i	−1.70799	+	0.986110i
$411$		0			0
$412$	15.8114	−	27.3861i	0.778971	−	1.34922i
$413$		0			0
$414$	−11.8175	−	35.9651i	−0.580800	−	1.76759i
$415$	0.978646			0.0480398
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$	−16.1270	−	1.66803i	−0.786918	−	0.0813916i
$421$	−4.00000	+	6.92820i	−0.194948	+	0.337660i	−0.946883	−	0.321577i	$-0.895787\pi$
$421$	−4.00000	+	6.92820i	−0.194948	+	0.337660i	0.751935	+	0.659237i	$0.229121\pi$
$422$		0			0
$423$	−8.08389	+	38.6606i	−0.393052	+	1.87974i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−16.3460	−	28.3121i	−0.791037	−	1.37012i
$428$	30.1519	−	17.4082i	1.45745	−	0.841458i
$429$		0			0
$430$	5.00000	−	8.66025i	0.241121	−	0.417635i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	13.9842	+	15.3767i	0.672813	+	0.739813i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$	30.3301	+	21.9595i	1.45422	+	1.05288i
$436$	−3.61895	−	6.26821i	−0.173316	−	0.300193i
$437$		0			0
$438$		0			0
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	−5.23790	+	5.85615i	−0.249424	+	0.278864i
$442$		0			0
$443$	−10.6437	−	6.14513i	−0.505696	−	0.291964i	0.225367	−	0.974274i	$-0.427642\pi$
$443$	−10.6437	−	6.14513i	−0.505696	−	0.291964i	−0.731063	+	0.682310i	$0.760975\pi$
$444$		0			0
$445$	−4.19052	−	7.25820i	−0.198650	−	0.344072i
$446$	29.5635	−	17.0685i	1.39987	−	0.808217i
$447$	−31.9565	−	3.30529i	−1.51149	−	0.156335i
$448$	−8.37238	+	14.5014i	−0.395558	+	0.685126i
$449$		−	22.3607i		−	1.05527i	−0.849473	−	0.527633i	$-0.823080\pi$
$449$		−	22.3607i		−	1.05527i	0.849473	−	0.527633i	$-0.176920\pi$
$450$	15.8114	+	14.1421i	0.745356	+	0.666667i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−7.00000	−	12.1244i	−0.328526	−	0.569024i
$455$		0			0
$456$		0			0
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$		−	22.9639i		−	1.07303i
$459$		0			0
$460$	−39.9046			−1.86056
$461$	−35.3730	−	20.4226i	−1.64748	−	0.951175i	−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−35.3730	−	20.4226i	−1.64748	−	0.951175i	−0.669417	−	0.742887i	$-0.733456\pi$
$462$		0			0
$463$	20.5548	+	35.6020i	0.955263	+	1.65456i	0.733766	+	0.679403i	$0.237761\pi$
$463$	20.5548	+	35.6020i	0.955263	+	1.65456i	0.221497	+	0.975161i	$0.428906\pi$
$464$	33.4919	−	19.3366i	1.55482	−	0.897678i
$465$		0			0
$466$		0			0
$467$		−	32.5269i		−	1.50517i	−0.658497	−	0.752583i	$-0.728808\pi$
$467$		−	32.5269i		−	1.50517i	0.658497	−	0.752583i	$-0.271192\pi$
$468$		0			0
$469$	24.2379			1.11920
$470$	36.0554	+	20.8166i	1.66311	+	0.960199i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	20.0000	−	8.94427i	0.912871	−	0.408248i
$481$		0			0
$482$	−2.91618	+	1.68366i	−0.132828	+	0.0766885i
$483$	18.9708	−	26.2022i	0.863201	−	1.19224i
$484$	−11.0000	+	19.0526i	−0.500000	+	0.866025i
$485$		0			0
$486$	19.1825	+	10.8643i	0.870134	+	0.492815i
$487$	−22.1359			−1.00308			−0.501538	−	0.865136i	$-0.667232\pi$
$487$	−22.1359			−1.00308			−0.501538	+	0.865136i	$0.667232\pi$
$488$	38.2585	+	22.0885i	1.73188	+	0.999901i
$489$	31.0554	+	22.4847i	1.40438	+	1.01679i
$490$	4.14092	+	7.17229i	0.187068	+	0.324011i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$	17.8592	+	39.9344i	0.805156	+	1.80038i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.110295	−	1.06636i	0.00494244	−	0.0477849i
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	19.3649	−	11.1803i	0.866025	−	0.500000i
$501$	−6.55544	−	0.678035i	−0.292876	−	0.0302924i
$502$		0			0
$503$		−	30.1361i		−	1.34370i	−0.740685	−	0.671852i	$-0.765499\pi$
$503$		−	30.1361i		−	1.34370i	0.740685	−	0.671852i	$-0.234501\pi$
$504$	−3.63508	+	17.3845i	−0.161919	+	0.774368i
$505$	20.0000			0.889988
$506$		0			0
$507$	20.5548	−	9.19239i	0.912871	−	0.408248i
$508$	7.39374	+	12.8063i	0.328044	+	0.568189i
$509$	−14.8649	+	8.58226i	−0.658876	+	0.380402i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	−14.8649	+	8.58226i	−0.658876	+	0.380402i	0.132973	+	0.991120i	$0.457548\pi$
$510$		0			0
$511$		0			0
$512$		−	22.6274i		−	1.00000i
$513$		0			0
$514$		0			0
$515$	−30.6186	−	17.6777i	−1.34922	−	0.778971i
$516$	−8.87298	−	6.42419i	−0.390611	−	0.282809i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$			27.4288i			1.20168i	0.799370	+	0.600839i	$0.205167\pi$
$521$			27.4288i			1.20168i	−0.799370	+	0.600839i	$0.794833\pi$
$522$	27.3460	−	30.5738i	1.19690	−	1.33818i
$523$	−43.1122			−1.88516			−0.942582	−	0.333975i	$-0.891610\pi$
$523$	−43.1122			−1.88516			−0.942582	+	0.333975i	$0.891610\pi$
$524$		0			0
$525$	−1.86492	+	18.0306i	−0.0813916	+	0.786918i
$526$	11.0000	+	19.0526i	0.479623	+	0.830731i
$527$		0			0
$528$		0			0
$529$	28.3095	−	49.0334i	1.23085	−	2.13189i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−8.38105	+	3.74812i	−0.362684	+	0.162197i
$535$	−19.4630	−	33.7109i	−0.841458	−	1.45745i
$536$	−28.3649	+	16.3765i	−1.22518	+	0.707357i
$537$		0			0
$538$	−22.6026	+	39.1489i	−0.974469	+	1.68783i
$539$		0			0
$540$	17.1917	−	15.6348i	0.739813	−	0.672813i
$541$	4.23790			0.182202			0.0911008	−	0.995842i	$-0.470961\pi$
$541$	4.23790			0.182202			0.0911008	+	0.995842i	$0.470961\pi$
$542$		0			0
$543$	−31.1985	−	22.5882i	−1.33885	−	0.969353i
$544$		0			0
$545$	−7.00807	+	4.04611i	−0.300193	+	0.173316i
$546$		0			0
$547$	−20.9989	+	36.3711i	−0.897846	+	1.55512i	−0.0676046	+	0.997712i	$0.521536\pi$
$547$	−20.9989	+	36.3711i	−0.897846	+	1.55512i	−0.830242	+	0.557403i	$0.811798\pi$
$548$		0			0
$549$	45.8649	+	9.59030i	1.95747	+	0.409304i
$550$		0			0
$551$		0			0
$552$	−4.49732	+	43.4814i	−0.191419	+	1.85069i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$	16.2131	+	9.36061i	0.685126	+	0.395558i
$561$		0			0
$562$	18.4164	+	31.8982i	0.776851	+	1.34554i
$563$	34.9633	−	20.1860i	1.47353	−	0.850740i	0.473970	−	0.880541i	$-0.342821\pi$
$563$	34.9633	−	20.1860i	1.47353	−	0.850740i	0.999556	+	0.0298010i	$0.00948736\pi$
$564$	26.7460	−	36.9411i	1.12621	−	1.55550i
$565$		0			0
$566$			47.5534i			1.99882i
$567$	2.09310	+	18.7212i	0.0879018	+	0.786217i
$568$		0			0
$569$	−27.1109	−	15.6525i	−1.13655	−	0.656186i	−0.190974	−	0.981595i	$-0.561165\pi$
$569$	−27.1109	−	15.6525i	−1.13655	−	0.656186i	−0.945573	+	0.325409i	$0.894498\pi$
$570$		0			0
$571$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$571$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$572$		0			0
$573$		0			0
$574$	−18.6905	+	32.3729i	−0.780127	+	1.35122i
$575$			44.6147i			1.86056i
$576$	−7.49193	−	22.8007i	−0.312164	−	0.950028i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−20.8207	−	12.0208i	−0.866025	−	0.500000i
$579$		0			0
$580$	−21.6190	−	37.4451i	−0.897678	−	1.55482i
$581$	0.793342	−	0.458036i	0.0329134	−	0.0190025i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−31.2890	−	18.0647i	−1.29144	−	0.745611i	−0.312527	−	0.949909i	$-0.601176\pi$
$587$	−31.2890	−	18.0647i	−1.29144	−	0.745611i	−0.978909	+	0.204298i	$0.934509\pi$
$588$	8.28185	−	3.70375i	0.341538	−	0.152740i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$	32.1270	+	18.5485i	1.31597	+	0.759778i
$597$		0			0
$598$		0			0
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$	−10.0000	−	22.3607i	−0.408248	−	0.912871i
$601$	14.0000	−	24.2487i	0.571072	−	0.989126i	−0.425384	−	0.905013i	$-0.639861\pi$
$601$	14.0000	−	24.2487i	0.571072	−	0.989126i	0.996456	−	0.0841128i	$-0.0268056\pi$
$602$		−	9.36061i		−	0.381510i
$603$	−23.1599	+	25.8935i	−0.943142	+	1.05447i
$604$		0			0
$605$	21.3014	+	12.2984i	0.866025	+	0.500000i
$606$	2.25403	−	21.7926i	0.0915638	−	0.885266i
$607$	−16.2554	−	28.1553i	−0.659788	−	1.14279i	−0.980670	−	0.195667i	$-0.937313\pi$
$607$	−16.2554	−	28.1553i	−0.659788	−	1.14279i	0.320882	−	0.947119i	$-0.396021\pi$
$608$		0			0
$609$	34.8649	+	3.60611i	1.41280	+	0.146127i
$610$	24.6957	−	42.7743i	0.999901	−	1.73188i
$611$		0			0
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	−25.8014	−	14.8965i	−1.04126	−	0.601172i
$615$	44.6480	−	19.9672i	1.80038	−	0.805156i
$616$		0			0
$617$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$617$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$618$	−22.7129	+	31.3707i	−0.913648	+	1.26192i
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	9.86492	+	45.3034i	0.395865	+	1.81796i
$622$		0			0
$623$	−6.79412	−	3.92259i	−0.272201	−	0.157155i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	19.4365	+	4.06415i	0.774368	+	0.161919i
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	14.3179	−	8.26645i	0.568189	−	0.328044i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−25.2982			−1.00000
$641$	−12.3014	−	7.10222i	−0.485876	−	0.280521i	0.236986	−	0.971513i	$-0.423841\pi$
$641$	−12.3014	−	7.10222i	−0.485876	−	0.280521i	−0.722862	+	0.690992i	$0.757174\pi$
$642$	−38.9260	+	17.4082i	−1.53629	+	0.687048i
$643$	2.58242	+	4.47288i	0.101841	+	0.176393i	0.912443	−	0.409204i	$-0.134193\pi$
$643$	2.58242	+	4.47288i	0.101841	+	0.176393i	−0.810602	+	0.585597i	$0.800860\pi$
$644$	−32.3488	+	18.6766i	−1.27472	+	0.735960i
$645$	−7.18246	+	9.92030i	−0.282809	+	0.390611i
$646$		0			0
$647$			31.8868i			1.25360i	0.779180	+	0.626800i	$0.215636\pi$
$647$			31.8868i			1.25360i	−0.779180	+	0.626800i	$0.784364\pi$
$648$	−15.0986	−	20.4947i	−0.593129	−	0.805107i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−22.1359	−	38.3406i	−0.866910	−	1.50153i
$653$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$653$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$654$	3.61895	+	8.09222i	0.141512	+	0.316431i
$655$		0			0
$656$		−	50.5135i		−	1.97222i
$657$		0			0
$658$	38.9712			1.51926
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	−0.989051	−	0.147573i	$-0.952854\pi$
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	0.366723	−	0.930330i	$-0.380480\pi$
$662$		0			0
$663$		0			0
$664$	−0.618950	+	1.07205i	−0.0240199	+	0.0416037i
$665$		0			0
$666$		0			0
$667$	86.2696			3.34037
$668$	6.59041	+	3.80498i	0.254991	+	0.147219i
$669$	−38.1663	+	17.0685i	−1.47560	+	0.659906i
$670$	18.3095	+	31.7129i	0.707357	+	1.22518i
$671$		0			0
$672$	12.0269	−	16.6113i	0.463946	−	0.640795i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	−17.4802	−	19.2209i	−0.672813	−	0.739813i
$676$	−26.0000			−1.00000
$677$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$677$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	7.00000	+	15.6525i	0.268241	+	0.599804i
$682$		0			0
$683$			43.8406i			1.67751i	0.544505	+	0.838757i	$0.316717\pi$
$683$			43.8406i			1.67751i	−0.544505	+	0.838757i	$0.683283\pi$
$684$		0			0
$685$		0			0
$686$	24.6583	+	14.2365i	0.941457	+	0.543550i
$687$	−2.89354	+	27.9756i	−0.110396	+	1.06734i
$688$	6.32456	+	10.9545i	0.241121	+	0.417635i
$689$		0			0
$690$	48.6136	+	5.02815i	1.85069	+	0.191419i
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$		0			0
$694$	−34.0000			−1.29062
$695$		0			0
$696$	−43.2379	+	19.3366i	−1.63893	+	0.732951i
$697$		0			0
$698$	−12.5388	+	7.23929i	−0.474601	+	0.274011i
$699$		0			0
$700$	10.4655	−	18.1267i	0.395558	−	0.685126i
$701$		−	30.3889i		−	1.14777i	−0.818935	−	0.573886i	$-0.805435\pi$
$701$		−	30.3889i		−	1.14777i	0.818935	−	0.573886i	$-0.194565\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−41.3014	−	29.9029i	−1.55550	−	1.12621i
$706$		0			0
$707$	16.2131	−	9.36061i	0.609755	−	0.352042i
$708$		0			0
$709$	−23.1190	+	40.0432i	−0.868250	+	1.50385i	−0.00446726	+	0.999990i	$0.501422\pi$
$709$	−23.1190	+	40.0432i	−0.868250	+	1.50385i	−0.863783	+	0.503864i	$0.831911\pi$
$710$		0			0
$711$		0			0
$712$	10.6013			0.397300
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	−25.4919	+	8.37624i	−0.950028	+	0.312164i
$721$	−33.0948			−1.23251
$722$	23.2702	+	13.4350i	0.866025	+	0.500000i
$723$	3.76477	−	1.68366i	0.140013	−	0.0626159i
$724$	22.2379	+	38.5172i	0.826465	+	1.43148i
$725$	−41.8649	+	24.1707i	−1.55482	+	0.897678i
$726$	15.8014	−	21.8247i	0.586445	−	0.809989i
$727$	15.2768	−	26.4602i	0.566585	−	0.981354i	−0.430315	−	0.902679i	$-0.641598\pi$
$727$	15.2768	−	26.4602i	0.566585	−	0.981354i	0.996900	−	0.0786754i	$-0.0250691\pi$
$728$		0			0
$729$	−22.0000	−	15.6525i	−0.814815	−	0.579721i
$730$		0			0
$731$		0			0
$732$	−43.8250	−	31.7300i	−1.61982	−	1.17277i
$733$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$733$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$734$	3.87298	−	2.23607i	0.142954	−	0.0825348i
$735$	−4.14092	−	9.25939i	−0.152740	−	0.341538i
$736$	25.2379	−	43.7133i	0.930281	−	1.61129i
$737$		0			0
$738$	−16.7250	−	50.9003i	−0.615656	−	1.87367i
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	23.9405	−	13.8221i	0.878294	−	0.507083i	0.00819813	−	0.999966i	$-0.497390\pi$
$743$	23.9405	−	13.8221i	0.878294	−	0.507083i	0.870095	+	0.492883i	$0.164057\pi$
$744$		0			0
$745$	20.7379	−	35.9191i	0.759778	−	1.31597i
$746$		0			0
$747$	−0.268733	+	1.28520i	−0.00983242	+	0.0470229i
$748$		0			0
$749$	−31.5554	−	18.2185i	−1.15301	−	0.665691i
$750$	−25.0000	+	11.1803i	−0.912871	+	0.408248i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	−45.6069	+	26.3312i	−1.66311	+	0.960199i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	6.61895	−	20.7206i	0.240729	−	0.753601i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	46.9919	−	27.1308i	1.70346	−	0.983491i	0.761249	−	0.648459i	$-0.224586\pi$
$761$	46.9919	−	27.1308i	1.70346	−	0.983491i	0.942207	−	0.335032i	$-0.108747\pi$
$762$	−7.39374	−	16.5329i	−0.267847	−	0.598924i
$763$	−3.78740	+	6.55998i	−0.137113	+	0.237487i
$764$		0			0
$765$		0			0
$766$	38.0000			1.37300
$767$		0			0
$768$	−2.85115	+	27.5658i	−0.102882	+	0.994694i
$769$	26.7379	+	46.3114i	0.964193	+	1.67003i	0.711767	+	0.702416i	$0.247895\pi$
$769$	26.7379	+	46.3114i	0.964193	+	1.67003i	0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0			−	1.00000i	$-0.5\pi$
$773$		0			0				1.00000i	$0.5\pi$
$774$	10.0000	+	8.94427i	0.359443	+	0.321495i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−3.62897	−	6.28555i	−0.130105	−	0.225348i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−37.1666	+	33.8007i	−1.32823	+	1.20794i
$784$	−10.4758			−0.374136
$785$		0			0
$786$		0			0
$787$	20.5548	+	35.6020i	0.732700	+	1.26907i	0.955725	+	0.294260i	$0.0950733\pi$
$787$	20.5548	+	35.6020i	0.732700	+	1.26907i	−0.223026	+	0.974813i	$0.571593\pi$
$788$		0			0
$789$	−11.0000	−	24.5967i	−0.391610	−	0.875667i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$797$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$798$		0			0
$799$		0			0
$800$			28.2843i			1.00000i
$801$	10.6825	−	3.51008i	0.377446	−	0.124023i
$802$	−50.5964			−1.78662
$803$		0			0
$804$	36.6190	−	16.3765i	1.29145	−	0.577554i
$805$	20.8810	+	36.1670i	0.735960	+	1.27472i
$806$		0			0
$807$	32.4685	−	44.8450i	1.14295	−	1.57862i
$808$	−12.6491	+	21.9089i	−0.444994	+	0.770752i
$809$			17.8885i			0.628928i	0.949269	+	0.314464i	$0.101825\pi$
$809$			17.8885i			0.628928i	−0.949269	+	0.314464i	$0.898175\pi$
$810$	−22.9138	+	16.8807i	−0.805107	+	0.593129i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−35.0509	−	20.2367i	−1.23005	−	0.710167i
$813$		0			0
$814$		0			0
$815$	−42.8661	+	24.7487i	−1.50153	+	0.866910i
$816$		0			0
$817$		0			0
$818$			5.65685i			0.197787i
$819$		0			0
$820$	−56.4758			−1.97222
$821$	49.5554	+	28.6108i	1.72950	+	0.998525i	0.891891	+	0.452250i	$0.149379\pi$
$821$	49.5554	+	28.6108i	1.72950	+	0.998525i	0.837606	+	0.546275i	$0.183955\pi$
$822$		0			0
$823$	27.8354	+	48.2123i	0.970280	+	1.68057i	0.694705	+	0.719295i	$0.255535\pi$
$823$	27.8354	+	48.2123i	0.970280	+	1.68057i	0.275575	+	0.961280i	$0.411132\pi$
$824$	38.7298	−	22.3607i	1.34922	−	0.778971i
$825$		0			0
$826$		0			0
$827$			57.3426i			1.99400i	0.0774065	+	0.997000i	$0.475336\pi$
$827$			57.3426i			1.99400i	−0.0774065	+	0.997000i	$0.524664\pi$
$828$	10.9577	−	52.4043i	0.380806	−	1.82118i
$829$	−39.6190			−1.37602			−0.688012	−	0.725700i	$-0.741516\pi$
$829$	−39.6190			−1.37602			−0.688012	+	0.725700i	$0.741516\pi$
$830$	1.19859	+	0.692007i	0.0416037	+	0.0240199i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	4.25409	−	7.36831i	0.147219	−	0.254991i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$	−18.5720	−	13.4464i	−0.640795	−	0.463946i
$841$	32.2379	+	55.8377i	1.11165	+	1.92544i
$842$	−9.79796	+	5.65685i	−0.337660	+	0.194948i
$843$	−18.4164	−	41.1804i	−0.634296	−	1.41833i
$844$		0			0
$845$			29.0689i			1.00000i
$846$	−37.2379	+	41.6332i	−1.28027	+	1.43138i
$847$	23.0241			0.791116
$848$		0			0
$849$	5.99193	−	57.9317i	0.205643	−	1.98821i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$853$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$854$		−	46.2334i		−	1.58207i
$855$		0			0
$856$	49.2379			1.68292
$857$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$857$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$859$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$860$	12.2474	−	7.07107i	0.417635	−	0.241121i
$861$	26.8488	−	37.0831i	0.915004	−	1.26379i
$862$		0			0
$863$			20.7755i			0.707208i	0.935395	+	0.353604i	$0.115044\pi$
$863$			20.7755i			0.707208i	−0.935395	+	0.353604i	$0.884956\pi$
$864$	6.25403	+	28.7208i	0.212767	+	0.977103i
$865$		0			0
$866$		0			0
$867$	23.8500	+	17.2678i	0.809989	+	0.586445i
$868$		0			0
$869$		0			0
$870$	21.6190	+	48.3414i	0.732951	+	1.63893i
$871$		0			0
$872$		−	10.2359i		−	0.346633i
$873$		0			0
$874$		0			0
$875$	−20.2663	−	11.7008i	−0.685126	−	0.395558i
$876$		0			0
$877$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$877$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	39.4612i		−	1.32948i	−0.747074	−	0.664741i	$-0.768542\pi$
$881$		−	39.4612i		−	1.32948i	0.747074	−	0.664741i	$-0.231458\pi$
$882$	−10.5560	+	3.46854i	−0.355440	+	0.116792i
$883$	−36.6971			−1.23496			−0.617478	−	0.786589i	$-0.711845\pi$
$883$	−36.6971			−1.23496			−0.617478	+	0.786589i	$0.711845\pi$
$884$		0			0
$885$		0			0
$886$	−8.69052	−	15.0524i	−0.291964	−	0.505696i
$887$	45.3156	−	26.1630i	1.52155	−	0.878466i	0.521871	−	0.853024i	$-0.325234\pi$
$887$	45.3156	−	26.1630i	1.52155	−	0.878466i	0.999676	−	0.0254417i	$-0.00809921\pi$
$888$		0			0
$889$	7.73790	−	13.4024i	0.259521	−	0.449503i
$890$		−	11.8526i		−	0.397300i
$891$		0			0
$892$	48.2770			1.61643
$893$		0			0
$894$	−36.8014	−	26.6448i	−1.23082	−	0.891136i
$895$		0			0
$896$	−20.5081	+	11.8403i	−0.685126	+	0.395558i
$897$		0			0
$898$	15.8114	−	27.3861i	0.527633	−	0.913887i
$899$		0			0
$900$	9.36492	+	28.5008i	0.312164	+	0.950028i
$901$		0			0
$902$		0			0
$903$	−1.17948	+	11.4035i	−0.0392505	+	0.379485i
$904$		0			0
$905$	43.0635	−	24.8627i	1.43148	−	0.826465i
$906$		0			0
$907$	−13.1837	+	22.8348i	−0.437758	+	0.758218i	−0.997516	−	0.0704373i	$-0.977561\pi$
$907$	−13.1837	+	22.8348i	−0.437758	+	0.758218i	0.559759	+	0.828656i	$0.310894\pi$
$908$		−	19.7990i		−	0.657053i
$909$	−5.49193	+	26.2648i	−0.182156	+	0.871148i
$910$		0			0
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−35.4752	+	48.9978i	−1.17277	+	1.61982i
$916$	16.2379	−	28.1249i	0.536515	−	0.929272i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$	−48.8730	−	28.2168i	−1.61129	−	0.930281i
$921$	29.5554	+	21.3986i	0.973885	+	0.705109i
$922$	−28.8819	−	50.0250i	−0.951175	−	1.64748i
$923$		0			0
$924$		0			0
$925$		0			0
$926$			58.1378i			1.91053i
$927$	31.6228	−	35.3553i	1.03863	−	1.16122i
$928$	54.6921			1.79536
$929$	42.6028	+	24.5967i	1.39775	+	0.806993i	0.994157	−	0.107944i	$-0.0344268\pi$
$929$	42.6028	+	24.5967i	1.39775	+	0.806993i	0.403596	+	0.914937i	$0.367760\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	23.0000	−	39.8372i	0.752583	−	1.30351i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	29.6852	+	17.1388i	0.969258	+	0.559601i
$939$		0			0
$940$	29.4391	+	50.9901i	0.960199	+	1.66311i
$941$	12.1351	−	7.00619i	0.395592	−	0.228395i	−0.288988	−	0.957333i	$-0.593319\pi$
$941$	12.1351	−	7.00619i	0.395592	−	0.228395i	0.684580	+	0.728937i	$0.259985\pi$
$942$		0			0
$943$	56.3411	−	97.5857i	1.83472	−	3.17783i
$944$		0			0
$945$	−23.1663	−	7.40021i	−0.753601	−	0.240729i
$946$		0			0
$947$	33.4471	+	19.3107i	1.08689	+	0.627514i	0.932746	−	0.360535i	$-0.117406\pi$
$947$	33.4471	+	19.3107i	1.08689	+	0.627514i	0.154140	+	0.988049i	$0.450739\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	30.8195	+	3.18768i	0.994694	+	0.102882i
$961$	−15.5000	+	26.8468i	−0.500000	+	0.866025i
$962$		0			0
$963$	49.6149	−	16.3027i	1.59882	−	0.525346i
$964$	−4.76210			−0.153377
$965$		0			0
$966$	41.7621	−	18.6766i	1.34367	−	0.600909i
$967$	−30.4857	−	52.8028i	−0.980354	−	1.69802i	−0.660998	−	0.750388i	$-0.729867\pi$
$967$	−30.4857	−	52.8028i	−0.980354	−	1.69802i	−0.319356	−	0.947635i	$-0.603467\pi$
$968$	−26.9444	+	15.5563i	−0.866025	+	0.500000i
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$	15.8114	+	26.8701i	0.507151	+	0.861858i
$973$		0			0
$974$	−27.1109	−	15.6525i	−0.868689	−	0.501538i
$975$		0			0
$976$	31.2379	+	54.1056i	0.999901	+	1.73188i
$977$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$977$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$978$	22.1359	+	49.4975i	0.707829	+	1.58275i
$979$		0			0
$980$			11.7123i			0.374136i
$981$	−3.38912	−	10.3143i	−0.108206	−	0.329311i
$982$		0			0
$983$	−53.3344	−	30.7926i	−1.70110	−	0.982133i	−0.944646	−	0.328090i	$-0.893595\pi$
$983$	−53.3344	−	30.7926i	−1.70110	−	0.982133i	−0.756457	−	0.654043i	$-0.773072\pi$
$984$	−6.36492	+	61.5379i	−0.202906	+	1.96176i
$985$		0			0
$986$		0			0
$987$	−47.4766	−	4.91054i	−1.51120	−	0.156304i
$988$		0			0
$989$			28.2168i			0.897243i
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.889117	−	1.22803i	0.0281727	−	0.0389117i
$997$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$997$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.n.c.119.3	yes	8
3.2	odd	2		540.2.n.c.359.1		8
4.3	odd	2	inner	180.2.n.c.119.2	yes	8
5.2	odd	4		900.2.r.a.551.1		8
5.3	odd	4		900.2.r.a.551.4		8
5.4	even	2	inner	180.2.n.c.119.2	yes	8
9.4	even	3		540.2.n.c.179.1		8
9.5	odd	6	inner	180.2.n.c.59.3	yes	8
12.11	even	2		540.2.n.c.359.3		8
15.14	odd	2		540.2.n.c.359.3		8
20.3	even	4		900.2.r.a.551.1		8
20.7	even	4		900.2.r.a.551.4		8
20.19	odd	2	CM	180.2.n.c.119.3	yes	8
36.23	even	6	inner	180.2.n.c.59.2	✓	8
36.31	odd	6		540.2.n.c.179.3		8
45.4	even	6		540.2.n.c.179.3		8
45.14	odd	6	inner	180.2.n.c.59.2	✓	8
45.23	even	12		900.2.r.a.851.1		8
45.32	even	12		900.2.r.a.851.4		8
60.59	even	2		540.2.n.c.359.1		8
180.23	odd	12		900.2.r.a.851.4		8
180.59	even	6	inner	180.2.n.c.59.3	yes	8
180.139	odd	6		540.2.n.c.179.1		8
180.167	odd	12		900.2.r.a.851.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.c.59.2	✓	8	36.23	even	6	inner
180.2.n.c.59.2	✓	8	45.14	odd	6	inner
180.2.n.c.59.3	yes	8	9.5	odd	6	inner
180.2.n.c.59.3	yes	8	180.59	even	6	inner
180.2.n.c.119.2	yes	8	4.3	odd	2	inner
180.2.n.c.119.2	yes	8	5.4	even	2	inner
180.2.n.c.119.3	yes	8	1.1	even	1	trivial
180.2.n.c.119.3	yes	8	20.19	odd	2	CM
540.2.n.c.179.1		8	9.4	even	3
540.2.n.c.179.1		8	180.139	odd	6
540.2.n.c.179.3		8	36.31	odd	6
540.2.n.c.179.3		8	45.4	even	6
540.2.n.c.359.1		8	3.2	odd	2
540.2.n.c.359.1		8	60.59	even	2
540.2.n.c.359.3		8	12.11	even	2
540.2.n.c.359.3		8	15.14	odd	2
900.2.r.a.551.1		8	5.2	odd	4
900.2.r.a.551.1		8	20.3	even	4
900.2.r.a.551.4		8	5.3	odd	4
900.2.r.a.551.4		8	20.7	even	4
900.2.r.a.851.1		8	45.23	even	12
900.2.r.a.851.1		8	180.167	odd	12
900.2.r.a.851.4		8	45.32	even	12
900.2.r.a.851.4		8	180.23	odd	12

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(-1.40294 - 1.01575i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-1.00000 - 2.23607i) q^{6} +(1.04655 - 1.81267i) q^{7} +2.82843i q^{8} +(0.936492 + 2.85008i) q^{9} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(-1.40294 - 1.01575i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-1.00000 - 2.23607i) q^{6} +(1.04655 - 1.81267i) q^{7} +2.82843i q^{8} +(0.936492 + 2.85008i) q^{9} +3.16228 q^{10} +(0.356394 - 3.44572i) q^{12} +(2.56351 - 1.48004i) q^{14} +(-3.85243 - 0.398461i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-0.868351 + 4.15283i) q^{18} +(3.87298 + 2.23607i) q^{20} +(-3.30948 + 1.48004i) q^{21} +(-7.72750 + 4.46147i) q^{23} +(2.87298 - 3.96812i) q^{24} +(2.50000 - 4.33013i) q^{25} +(1.58114 - 4.94975i) q^{27} +4.18619 q^{28} +(-8.37298 - 4.83414i) q^{29} +(-4.43649 - 3.21209i) q^{30} +(-4.89898 + 2.82843i) q^{32} -4.68030i q^{35} +(-4.00000 + 4.47214i) q^{36} +(3.16228 + 5.47723i) q^{40} +(-10.9365 + 6.31419i) q^{41} +(-5.09981 - 0.527478i) q^{42} +(1.58114 - 2.73861i) q^{43} +(5.00000 + 4.47214i) q^{45} -12.6190 q^{46} +(11.4017 + 6.58279i) q^{47} +(6.32456 - 2.82843i) q^{48} +(1.30948 + 2.26808i) q^{49} +(6.12372 - 3.53553i) q^{50} +(5.43649 - 4.94414i) q^{54} +(5.12702 + 2.96008i) q^{56} +(-6.83651 - 11.8412i) q^{58} +(-3.16228 - 7.07107i) q^{60} +(7.80948 - 13.5264i) q^{61} +(6.14636 + 1.28520i) q^{63} -8.00000 q^{64} +(5.78996 + 10.0285i) q^{67} +(15.3730 + 1.59004i) q^{69} +(3.30948 - 5.73218i) q^{70} +(-8.06126 + 2.64880i) q^{72} +(-7.90569 + 3.53553i) q^{75} +8.94427i q^{80} +(-7.24597 + 5.33816i) q^{81} -17.8592 q^{82} +(0.379028 + 0.218832i) q^{83} +(-5.87298 - 4.25214i) q^{84} +(3.87298 - 2.23607i) q^{86} +(6.83651 + 15.2869i) q^{87} -3.74812i q^{89} +(2.96145 + 9.01276i) q^{90} +(-15.4550 - 8.92295i) q^{92} +(9.30948 + 16.1245i) q^{94} +(9.74597 + 1.00803i) q^{96} +3.70375i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^4 - 8 * q^6 - 8 * q^9	\( 8 q + 8 q^{4} - 8 q^{6} - 8 q^{9} + 36 q^{14} - 16 q^{16} + 20 q^{21} - 8 q^{24} + 20 q^{25} - 36 q^{29} - 20 q^{30} - 32 q^{36} - 72 q^{41} + 40 q^{45} - 8 q^{46} - 36 q^{49} + 28 q^{54} + 72 q^{56} + 16 q^{61} - 64 q^{64} + 92 q^{69} - 20 q^{70} + 4 q^{81} - 16 q^{84} + 28 q^{94} + 16 q^{96}+O(q^{100}) \) 8 * q + 8 * q^4 - 8 * q^6 - 8 * q^9 + 36 * q^14 - 16 * q^16 + 20 * q^21 - 8 * q^24 + 20 * q^25 - 36 * q^29 - 20 * q^30 - 32 * q^36 - 72 * q^41 + 40 * q^45 - 8 * q^46 - 36 * q^49 + 28 * q^54 + 72 * q^56 + 16 * q^61 - 64 * q^64 + 92 * q^69 - 20 * q^70 + 4 * q^81 - 16 * q^84 + 28 * q^94 + 16 * q^96

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