LMFDB - Embedded newform 504.2.br.a.155.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(155,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("504.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.br (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.14
Character	$\chi$	$=$	504.155
Dual form			504.2.br.a.491.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16781 - 0.797628i) q^{2} +(-1.30518 + 1.13865i) q^{3} +(0.727580 + 1.86296i) q^{4} +(1.17058 + 2.02750i) q^{5} +(2.43242 - 0.288684i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(0.636271 - 2.75593i) q^{8} +(0.406968 - 2.97227i) q^{9} +O(q^{10})$	\(q+(-1.16781 - 0.797628i) q^{2} +(-1.30518 + 1.13865i) q^{3} +(0.727580 + 1.86296i) q^{4} +(1.17058 + 2.02750i) q^{5} +(2.43242 - 0.288684i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(0.636271 - 2.75593i) q^{8} +(0.406968 - 2.97227i) q^{9} +(0.250172 - 3.30142i) q^{10} +(3.74998 + 2.16505i) q^{11} +(-3.07088 - 1.60304i) q^{12} +(4.95064 - 2.85826i) q^{13} +(0.612543 + 1.27467i) q^{14} +(-3.83641 - 1.31337i) q^{15} +(-2.94125 + 2.71091i) q^{16} -0.835037i q^{17} +(-2.84603 + 3.14645i) q^{18} -2.79658 q^{19} +(-2.92546 + 3.65591i) q^{20} +(1.69964 - 0.333509i) q^{21} +(-2.65238 - 5.51947i) q^{22} +(4.32248 + 7.48676i) q^{23} +(2.30759 + 4.32146i) q^{24} +(-0.240497 + 0.416553i) q^{25} +(-8.06126 - 0.610858i) q^{26} +(2.85320 + 4.34272i) q^{27} +(0.301378 - 1.97716i) q^{28} +(-3.19193 + 5.52858i) q^{29} +(3.43264 + 4.59380i) q^{30} +(-7.02846 + 4.05788i) q^{31} +(5.59713 - 0.819814i) q^{32} +(-7.35962 + 1.44413i) q^{33} +(-0.666049 + 0.975168i) q^{34} -2.34115i q^{35} +(5.83332 - 1.40440i) q^{36} +2.91840i q^{37} +(3.26589 + 2.23063i) q^{38} +(-3.20692 + 9.36756i) q^{39} +(6.33245 - 1.93599i) q^{40} +(0.387918 - 0.223964i) q^{41} +(-2.25088 - 0.966202i) q^{42} +(6.48309 - 11.2290i) q^{43} +(-1.30500 + 8.56133i) q^{44} +(6.50265 - 2.65414i) q^{45} +(0.923789 - 12.1909i) q^{46} +(-4.13514 + 7.16227i) q^{47} +(0.752085 - 6.88726i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.613110 - 0.294630i) q^{50} +(0.950812 + 1.08987i) q^{51} +(8.92681 + 7.14325i) q^{52} +9.10223 q^{53} +(0.131871 - 7.34729i) q^{54} +10.1374i q^{55} +(-1.92899 + 2.06857i) q^{56} +(3.65003 - 3.18432i) q^{57} +(8.13732 - 3.91038i) q^{58} +(-8.38108 + 4.83882i) q^{59} +(-0.344543 - 8.10267i) q^{60} +(3.82374 + 2.20764i) q^{61} +(11.4446 + 0.867240i) q^{62} +(-1.83858 + 2.37058i) q^{63} +(-7.19032 - 3.50704i) q^{64} +(11.5902 + 6.69161i) q^{65} +(9.74655 + 4.18376i) q^{66} +(1.10041 + 1.90597i) q^{67} +(1.55564 - 0.607557i) q^{68} +(-14.1664 - 4.84976i) q^{69} +(-1.86737 + 2.73403i) q^{70} +4.50393 q^{71} +(-7.93243 - 3.01274i) q^{72} +2.85366 q^{73} +(2.32779 - 3.40814i) q^{74} +(-0.160416 - 0.817516i) q^{75} +(-2.03474 - 5.20993i) q^{76} +(-2.16505 - 3.74998i) q^{77} +(11.2169 - 8.38164i) q^{78} +(-6.46798 - 3.73429i) q^{79} +(-8.93932 - 2.79006i) q^{80} +(-8.66875 - 2.41923i) q^{81} +(-0.631656 - 0.0478650i) q^{82} +(-4.89442 - 2.82579i) q^{83} +(1.85794 + 2.92371i) q^{84} +(1.69304 - 0.977475i) q^{85} +(-16.5276 + 7.94235i) q^{86} +(-2.12907 - 10.8502i) q^{87} +(8.35275 - 8.95714i) q^{88} -8.68661i q^{89} +(-9.71091 - 2.08715i) q^{90} -5.71651 q^{91} +(-10.8026 + 13.4998i) q^{92} +(4.55288 - 13.2992i) q^{93} +(10.5419 - 5.06590i) q^{94} +(-3.27361 - 5.67006i) q^{95} +(-6.37177 + 7.44316i) q^{96} +(-3.64813 + 6.31875i) q^{97} +(0.106859 - 1.41017i) q^{98} +(7.96124 - 10.2649i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{6}+O(q^{10}) $ 144 * q + 6 * q^6	$ 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) $ 144 * q + 6 * q^6 - 12 * q^12 + 34 * q^18 - 42 * q^20 - 30 * q^24 - 72 * q^25 + 24 * q^27 - 36 * q^30 - 30 * q^32 - 16 * q^33 + 12 * q^34 - 12 * q^36 + 12 * q^40 + 24 * q^41 - 20 * q^42 - 24 * q^46 - 24 * q^48 + 72 * q^49 - 78 * q^50 + 18 * q^52 + 10 * q^54 + 8 * q^57 - 18 * q^58 - 72 * q^59 + 88 * q^60 - 12 * q^64 + 2 * q^66 + 78 * q^68 + 42 * q^72 + 84 * q^74 - 112 * q^75 + 12 * q^76 + 112 * q^78 - 8 * q^81 - 36 * q^82 - 14 * q^84 + 30 * q^86 + 24 * q^88 + 104 * q^90 - 114 * q^92 - 42 * q^94 - 80 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.16781	−	0.797628i	−0.825769	−	0.564008i
$2$	−1.16781	−	0.797628i	−0.825769	−	0.564008i
$3$	−1.30518	+	1.13865i	−0.753544	+	0.657398i
$3$	−1.30518	+	1.13865i	−0.753544	+	0.657398i
$4$	0.727580	+	1.86296i	0.363790	+	0.931481i
$5$	1.17058	+	2.02750i	0.523498	+	0.906724i	0.999626	+	0.0273486i	$0.00870642\pi$
$5$	1.17058	+	2.02750i	0.523498	+	0.906724i	−0.476128	+	0.879376i	$0.657960\pi$
$6$	2.43242	−	0.288684i	0.993031	−	0.117855i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	0.636271	−	2.75593i	0.224956	−	0.974369i
$9$	0.406968	−	2.97227i	0.135656	−	0.990756i
$10$	0.250172	−	3.30142i	0.0791114	−	1.04400i
$11$	3.74998	+	2.16505i	1.13066	+	0.652788i	0.944102	−	0.329655i	$-0.106932\pi$
$11$	3.74998	+	2.16505i	1.13066	+	0.652788i	0.186561	+	0.982443i	$0.440266\pi$
$12$	−3.07088	−	1.60304i	−0.886485	−	0.462757i
$13$	4.95064	−	2.85826i	1.37306	−	0.792737i	0.381749	−	0.924266i	$-0.375322\pi$
$13$	4.95064	−	2.85826i	1.37306	−	0.792737i	0.991312	+	0.131529i	$0.0419885\pi$
$14$	0.612543	+	1.27467i	0.163709	+	0.340671i
$15$	−3.83641	−	1.31337i	−0.990557	−	0.339110i
$16$	−2.94125	+	2.71091i	−0.735313	+	0.677727i
$17$		−	0.835037i		−	0.202526i	−0.994860	−	0.101263i	$-0.967712\pi$
$17$		−	0.835037i		−	0.202526i	0.994860	−	0.101263i	$-0.0322884\pi$
$18$	−2.84603	+	3.14645i	−0.670815	+	0.741625i
$19$	−2.79658			−0.641580			−0.320790	−	0.947150i	$-0.603948\pi$
$19$	−2.79658			−0.641580			−0.320790	+	0.947150i	$0.603948\pi$
$20$	−2.92546	+	3.65591i	−0.654153	+	0.817485i
$21$	1.69964	−	0.333509i	0.370892	−	0.0727776i
$22$	−2.65238	−	5.51947i	−0.565489	−	1.17676i
$23$	4.32248	+	7.48676i	0.901300	+	1.56110i	0.825808	+	0.563951i	$0.190719\pi$
$23$	4.32248	+	7.48676i	0.901300	+	1.56110i	0.0754919	+	0.997146i	$0.475947\pi$
$24$	2.30759	+	4.32146i	0.471034	+	0.882115i
$25$	−0.240497	+	0.416553i	−0.0480994	+	0.0833106i
$26$	−8.06126	−	0.610858i	−1.58094	−	0.119799i
$27$	2.85320	+	4.34272i	0.549098	+	0.835758i
$28$	0.301378	−	1.97716i	0.0569550	−	0.373649i
$29$	−3.19193	+	5.52858i	−0.592726	+	1.02663i	0.401138	+	0.916018i	$0.368615\pi$
$29$	−3.19193	+	5.52858i	−0.592726	+	1.02663i	−0.993864	+	0.110613i	$0.964718\pi$
$30$	3.43264	+	4.59380i	0.626711	+	0.838709i
$31$	−7.02846	+	4.05788i	−1.26235	+	0.728818i	−0.973529	−	0.228566i	$-0.926596\pi$
$31$	−7.02846	+	4.05788i	−1.26235	+	0.728818i	−0.288821	+	0.957383i	$0.593263\pi$
$32$	5.59713	−	0.819814i	0.989443	−	0.144924i
$33$	−7.35962	+	1.44413i	−1.28115	+	0.251391i
$34$	−0.666049	+	0.975168i	−0.114226	+	0.167240i
$35$		−	2.34115i		−	0.395727i
$36$	5.83332	−	1.40440i	0.972221	−	0.234066i
$37$			2.91840i			0.479781i	0.970800	+	0.239891i	$0.0771116\pi$
$37$			2.91840i			0.479781i	−0.970800	+	0.239891i	$0.922888\pi$
$38$	3.26589	+	2.23063i	0.529797	+	0.361856i
$39$	−3.20692	+	9.36756i	−0.513518	+	1.50001i
$40$	6.33245	−	1.93599i	1.00125	−	0.306107i
$41$	0.387918	−	0.223964i	0.0605825	−	0.0349773i	−0.469403	−	0.882984i	$-0.655531\pi$
$41$	0.387918	−	0.223964i	0.0605825	−	0.0349773i	0.529985	+	0.848007i	$0.322197\pi$
$42$	−2.25088	−	0.966202i	−0.347318	−	0.149088i
$43$	6.48309	−	11.2290i	0.988662	−	1.71241i	0.364292	−	0.931285i	$-0.381311\pi$
$43$	6.48309	−	11.2290i	0.988662	−	1.71241i	0.624371	−	0.781128i	$-0.285355\pi$
$44$	−1.30500	+	8.56133i	−0.196736	+	1.29067i
$45$	6.50265	−	2.65414i	0.969358	−	0.395656i
$46$	0.923789	−	12.1909i	0.136205	−	1.79745i
$47$	−4.13514	+	7.16227i	−0.603172	+	1.04472i	0.389166	+	0.921168i	$0.372763\pi$
$47$	−4.13514	+	7.16227i	−0.603172	+	1.04472i	−0.992338	+	0.123556i	$0.960570\pi$
$48$	0.752085	−	6.88726i	0.108554	−	0.994091i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	0.613110	−	0.294630i	0.0867069	−	0.0416669i
$51$	0.950812	+	1.08987i	0.133140	+	0.152612i
$52$	8.92681	+	7.14325i	1.23793	+	0.990590i
$53$	9.10223			1.25029			0.625144	−	0.780510i	$-0.285040\pi$
$53$	9.10223			1.25029			0.625144	+	0.780510i	$0.285040\pi$
$54$	0.131871	−	7.34729i	0.0179454	−	0.999839i
$55$			10.1374i			1.36693i
$56$	−1.92899	+	2.06857i	−0.257772	+	0.276424i
$57$	3.65003	−	3.18432i	0.483459	−	0.421773i
$58$	8.13732	−	3.91038i	1.06848	−	0.513459i
$59$	−8.38108	+	4.83882i	−1.09112	+	0.629961i	−0.933876	−	0.357598i	$-0.883596\pi$
$59$	−8.38108	+	4.83882i	−1.09112	+	0.629961i	−0.157249	+	0.987559i	$0.550262\pi$
$60$	−0.344543	−	8.10267i	−0.0444803	−	1.04605i
$61$	3.82374	+	2.20764i	0.489580	+	0.282659i	0.724400	−	0.689380i	$-0.242117\pi$
$61$	3.82374	+	2.20764i	0.489580	+	0.282659i	−0.234820	+	0.972039i	$0.575450\pi$
$62$	11.4446	+	0.867240i	1.45347	+	0.110140i
$63$	−1.83858	+	2.37058i	−0.231639	+	0.298664i
$64$	−7.19032	−	3.50704i	−0.898790	−	0.438380i
$65$	11.5902	+	6.69161i	1.43759	+	0.829992i
$66$	9.74655	+	4.18376i	1.19972	+	0.514985i
$67$	1.10041	+	1.90597i	0.134437	+	0.232851i	0.925382	−	0.379036i	$-0.123744\pi$
$67$	1.10041	+	1.90597i	0.134437	+	0.232851i	−0.790945	+	0.611887i	$0.790411\pi$
$68$	1.55564	−	0.607557i	0.188649	−	0.0736771i
$69$	−14.1664	−	4.84976i	−1.70543	−	0.583842i
$70$	−1.86737	+	2.73403i	−0.223193	+	0.326779i
$71$	4.50393			0.534518			0.267259	−	0.963625i	$-0.413882\pi$
$71$	4.50393			0.534518			0.267259	+	0.963625i	$0.413882\pi$
$72$	−7.93243	−	3.01274i	−0.934845	−	0.355055i
$73$	2.85366			0.333995			0.166998	−	0.985957i	$-0.446593\pi$
$73$	2.85366			0.333995			0.166998	+	0.985957i	$0.446593\pi$
$74$	2.32779	−	3.40814i	0.270600	−	0.396189i
$75$	−0.160416	−	0.817516i	−0.0185232	−	0.0943986i
$76$	−2.03474	−	5.20993i	−0.233401	−	0.597620i
$77$	−2.16505	−	3.74998i	−0.246731	−	0.427350i
$78$	11.2169	−	8.38164i	1.27006	−	0.949034i
$79$	−6.46798	−	3.73429i	−0.727704	−	0.420140i	0.0898776	−	0.995953i	$-0.471352\pi$
$79$	−6.46798	−	3.73429i	−0.727704	−	0.420140i	−0.817582	+	0.575813i	$0.804686\pi$
$80$	−8.93932	−	2.79006i	−0.999447	−	0.311938i
$81$	−8.66875	−	2.41923i	−0.963195	−	0.268804i
$82$	−0.631656	−	0.0478650i	−0.0697547	−	0.00528581i
$83$	−4.89442	−	2.82579i	−0.537232	−	0.310171i	0.206724	−	0.978399i	$-0.433720\pi$
$83$	−4.89442	−	2.82579i	−0.537232	−	0.310171i	−0.743957	+	0.668228i	$0.767053\pi$
$84$	1.85794	+	2.92371i	0.202718	+	0.319003i
$85$	1.69304	−	0.977475i	0.183636	−	0.106022i
$86$	−16.5276	+	7.94235i	−1.78222	+	0.856445i
$87$	−2.12907	−	10.8502i	−0.228260	−	1.16327i
$88$	8.35275	−	8.95714i	0.890406	−	0.954834i
$89$		−	8.68661i		−	0.920779i	−0.887717	−	0.460389i	$-0.847710\pi$
$89$		−	8.68661i		−	0.920779i	0.887717	−	0.460389i	$-0.152290\pi$
$90$	−9.71091	−	2.08715i	−1.02362	−	0.220005i
$91$	−5.71651			−0.599253
$92$	−10.8026	+	13.4998i	−1.12625	+	1.40746i
$93$	4.55288	−	13.2992i	0.472112	−	1.37906i
$94$	10.5419	−	5.06590i	1.08731	−	0.522508i
$95$	−3.27361	−	5.67006i	−0.335866	−	0.581736i
$96$	−6.37177	+	7.44316i	−0.650316	+	0.759664i
$97$	−3.64813	+	6.31875i	−0.370411	+	0.641571i	−0.989629	−	0.143648i	$-0.954117\pi$
$97$	−3.64813	+	6.31875i	−0.370411	+	0.641571i	0.619217	+	0.785220i	$0.287450\pi$
$98$	0.106859	−	1.41017i	0.0107943	−	0.142449i
$99$	7.96124	−	10.2649i	0.800135	−	1.03166i
$100$	−0.951003	−	0.144961i	−0.0951003	−	0.0144961i
$101$	−3.40502	+	5.89767i	−0.338812	+	0.586840i	−0.984210	−	0.177007i	$-0.943358\pi$
$101$	−3.40502	+	5.89767i	−0.338812	+	0.586840i	0.645397	+	0.763847i	$0.276692\pi$
$102$	−0.241062	−	2.03116i	−0.0238686	−	0.201115i
$103$	−2.86229	+	1.65255i	−0.282030	+	0.162830i	−0.634342	−	0.773052i	$-0.718729\pi$
$103$	−2.86229	+	1.65255i	−0.282030	+	0.162830i	0.352312	+	0.935883i	$0.385396\pi$
$104$	−4.72721	−	15.4623i	−0.463541	−	1.51620i
$105$	2.66575	+	3.05562i	0.260150	+	0.298198i
$106$	−10.6297	−	7.26019i	−1.03245	−	0.705172i
$107$			2.36937i			0.229055i	0.993420	+	0.114528i	$0.0365354\pi$
$107$			2.36937i			0.229055i	−0.993420	+	0.114528i	$0.963465\pi$
$108$	−6.01440	+	8.47508i	−0.578736	+	0.815515i
$109$			15.8120i			1.51452i	0.653115	+	0.757258i	$0.273462\pi$
$109$			15.8120i			1.51452i	−0.653115	+	0.757258i	$0.726538\pi$
$110$	8.08590	−	11.8387i	0.770961	−	1.12877i
$111$	−3.32302	−	3.80902i	−0.315407	−	0.361536i
$112$	3.90265	−	0.877090i	0.368766	−	0.0828772i
$113$	−2.41824	+	1.39617i	−0.227489	+	0.131341i	−0.609413	−	0.792853i	$-0.708595\pi$
$113$	−2.41824	+	1.39617i	−0.227489	+	0.131341i	0.381924	+	0.924194i	$0.375262\pi$
$114$	−6.80246	+	0.807328i	−0.637109	+	0.0756131i
$115$	−10.1196	+	17.5276i	−0.943657	+	1.63446i
$116$	−12.6219	−	1.92395i	−1.17192	−	0.178634i
$117$	−6.48075	−	15.8779i	−0.599145	−	1.46791i
$118$	13.6471	+	1.03414i	1.25632	+	0.0952002i
$119$	−0.417519	+	0.723163i	−0.0382739	+	0.0662923i
$120$	−6.06055	+	9.73723i	−0.553250	+	0.888883i
$121$	3.87492	+	6.71156i	0.352266	+	0.610142i
$122$	−2.70455	−	5.62803i	−0.244858	−	0.509538i
$123$	−0.251284	+	0.734014i	−0.0226576	+	0.0661838i
$124$	−12.6735	−	10.1413i	−1.13811	−	0.910717i
$125$	10.5797			0.946275
$126$	4.03795	−	1.30189i	0.359730	−	0.115982i
$127$		−	13.0937i		−	1.16188i	−0.813947	−	0.580939i	$-0.802686\pi$
$127$		−	13.0937i		−	1.16188i	0.813947	−	0.580939i	$-0.197314\pi$
$128$	5.59965	+	9.83077i	0.494944	+	0.868925i
$129$	4.32434	+	22.0378i	0.380737	+	1.94032i
$130$	−8.19780	−	17.0592i	−0.718995	−	1.49619i
$131$	19.3616	−	11.1784i	1.69163	−	0.976665i	0.738431	−	0.674329i	$-0.235567\pi$
$131$	19.3616	−	11.1784i	1.69163	−	0.976665i	0.953201	−	0.302336i	$-0.0977665\pi$
$132$	−8.04508	−	12.6600i	−0.700234	−	1.10191i
$133$	2.42191	+	1.39829i	0.210006	+	0.121247i
$134$	0.235177	−	3.10354i	0.0203162	−	0.268105i
$135$	−5.46498	+	10.8683i	−0.470350	+	0.935398i
$136$	−2.30131	−	0.531310i	−0.197335	−	0.0455594i
$137$	−3.02705	−	1.74767i	−0.258618	−	0.149313i	0.365086	−	0.930974i	$-0.381040\pi$
$137$	−3.02705	−	1.74767i	−0.258618	−	0.149313i	−0.623704	+	0.781661i	$0.714373\pi$
$138$	12.6754	+	16.9631i	1.07900	+	1.44400i
$139$	0.250284	+	0.433505i	0.0212288	+	0.0367694i	0.876445	−	0.481503i	$-0.159909\pi$
$139$	0.250284	+	0.433505i	0.0212288	+	0.0367694i	−0.855216	+	0.518272i	$0.826575\pi$
$140$	4.36148	−	1.70338i	0.368612	−	0.143962i
$141$	−2.75821	−	14.0565i	−0.232283	−	1.18377i
$142$	−5.25975	−	3.59246i	−0.441388	−	0.301472i
$143$	24.7531			2.06996
$144$	6.86055	+	9.84545i	0.571713	+	0.820454i
$145$	−14.9456			−1.24116
$146$	−3.33254	−	2.27615i	−0.275803	−	0.188376i
$147$	−1.63868	−	0.560992i	−0.135156	−	0.0462698i
$148$	−5.43686	+	2.12337i	−0.446907	+	0.174540i
$149$	−5.56925	−	9.64622i	−0.456251	−	0.790249i	0.542509	−	0.840050i	$-0.317475\pi$
$149$	−5.56925	−	9.64622i	−0.456251	−	0.790249i	−0.998759	+	0.0498011i	$0.984141\pi$
$150$	−0.464737	+	1.08266i	−0.0379457	+	0.0883987i
$151$	−0.0993683	−	0.0573703i	−0.00808648	−	0.00466873i	0.495951	−	0.868350i	$-0.334819\pi$
$151$	−0.0993683	−	0.0573703i	−0.00808648	−	0.00466873i	−0.504038	+	0.863682i	$0.668153\pi$
$152$	−1.77938	+	7.70719i	−0.144327	+	0.625136i
$153$	−2.48195	−	0.339833i	−0.200654	−	0.0274739i
$154$	−0.462709	+	6.10619i	−0.0372862	+	0.492051i
$155$	−16.4547	−	9.50013i	−1.32167	−	0.763069i
$156$	−19.7847	+	0.841289i	−1.58404	+	0.0673570i
$157$	8.04897	−	4.64707i	0.642378	−	0.370877i	−0.143152	−	0.989701i	$-0.545724\pi$
$157$	8.04897	−	4.64707i	0.642378	−	0.370877i	0.785530	+	0.618824i	$0.212391\pi$
$158$	4.57482	+	9.51999i	0.363953	+	0.757370i
$159$	−11.8800	+	10.3642i	−0.942146	+	0.821937i
$160$	8.21404	+	10.3885i	0.649377	+	0.821285i
$161$		−	8.64497i		−	0.681319i
$162$	8.19385	+	9.73965i	0.643769	+	0.765220i
$163$	23.1230			1.81113			0.905566	−	0.424205i	$-0.139446\pi$
$163$	23.1230			1.81113			0.905566	+	0.424205i	$0.139446\pi$
$164$	0.699478	+	0.559724i	0.0546201	+	0.0437071i
$165$	−11.5430	−	13.2311i	−0.898619	−	1.03004i
$166$	3.46184	+	7.20393i	0.268691	+	0.559133i
$167$	−3.29049	−	5.69930i	−0.254626	−	0.441025i	0.710168	−	0.704032i	$-0.248619\pi$
$167$	−3.29049	−	5.69930i	−0.254626	−	0.441025i	−0.964794	+	0.263007i	$0.915286\pi$
$168$	0.162303	−	4.89629i	0.0125219	−	0.377757i
$169$	9.83925	−	17.0421i	0.756865	−	1.31093i
$170$	−2.75681	−	0.208903i	−0.211438	−	0.0160221i
$171$	−1.13812	+	8.31219i	−0.0870341	+	0.635649i
$172$	25.6363	+	3.90772i	1.95475	+	0.297961i
$173$	−0.420646	+	0.728581i	−0.0319811	+	0.0553930i	−0.881573	−	0.472048i	$-0.843515\pi$
$173$	−0.420646	+	0.728581i	−0.0319811	+	0.0553930i	0.849592	+	0.527441i	$0.176848\pi$
$174$	−6.16809	+	14.3693i	−0.467602	+	1.08933i
$175$	0.416553	−	0.240497i	0.0314885	−	0.0181799i
$176$	−16.8989	+	3.79789i	−1.27380	+	0.286277i
$177$	5.42908	−	15.8586i	0.408075	−	1.19201i
$178$	−6.92868	+	10.1443i	−0.519327	+	0.760351i
$179$			14.3811i			1.07489i	0.843298	+	0.537446i	$0.180611\pi$
$179$			14.3811i			1.07489i	−0.843298	+	0.537446i	$0.819389\pi$
$180$	9.67576	+	10.1831i	0.721189	+	0.759003i
$181$		−	0.791999i		−	0.0588688i	−0.999567	−	0.0294344i	$-0.990629\pi$
$181$		−	0.791999i		−	0.0588688i	0.999567	−	0.0294344i	$-0.00937062\pi$
$182$	6.67582	+	4.55965i	0.494845	+	0.337984i
$183$	−7.50437	+	1.47253i	−0.554739	+	0.108853i
$184$	23.3833	−	7.14886i	1.72384	−	0.527021i
$185$	−5.91704	+	3.41621i	−0.435029	+	0.251164i
$186$	−15.9247	+	11.8995i	−1.16766	+	0.872512i
$187$	1.80790	−	3.13138i	0.132207	−	0.228989i
$188$	−16.3517	−	2.49248i	−1.19257	−	0.181782i
$189$	−0.299580	−	5.18751i	−0.0217912	−	0.377336i
$190$	−0.699627	+	9.23271i	−0.0507563	+	0.669811i
$191$	11.7531	−	20.3569i	0.850423	−	1.47298i	−0.0304034	−	0.999538i	$-0.509679\pi$
$191$	11.7531	−	20.3569i	0.850423	−	1.47298i	0.880827	−	0.473439i	$-0.156987\pi$
$192$	13.3779	−	3.60993i	0.965467	−	0.260524i
$193$	−9.00647	−	15.5997i	−0.648300	−	1.12289i	−0.983529	−	0.180752i	$-0.942147\pi$
$193$	−9.00647	−	15.5997i	−0.648300	−	1.12289i	0.335228	−	0.942137i	$-0.391186\pi$
$194$	9.30034	−	4.46927i	0.667726	−	0.320875i
$195$	−22.7466	+	4.46343i	−1.62892	+	0.319633i
$196$	−1.24958	+	1.56158i	−0.0892559	+	0.111542i
$197$	4.47512			0.318839			0.159419	−	0.987211i	$-0.449038\pi$
$197$	4.47512			0.318839			0.159419	+	0.987211i	$0.449038\pi$
$198$	−17.4848	+	5.63733i	−1.24259	+	0.400628i
$199$			13.7687i			0.976037i	0.872833	+	0.488019i	$0.162280\pi$
$199$			13.7687i			0.976037i	−0.872833	+	0.488019i	$0.837720\pi$
$200$	0.994971	+	0.927834i	0.0703550	+	0.0656078i
$201$	−3.60645	−	1.23464i	−0.254380	−	0.0870851i
$202$	8.68057	−	4.17144i	0.610763	−	0.293502i
$203$	5.52858	−	3.19193i	0.388030	−	0.224029i
$204$	−1.33859	+	2.56430i	−0.0937204	+	0.179537i
$205$	0.908174	+	0.524335i	0.0634296	+	0.0366211i
$206$	4.66074	+	0.353178i	0.324729	+	0.0246070i
$207$	24.0118	−	9.80071i	1.66893	−	0.681196i
$208$	−6.81263	+	21.8276i	−0.472371	+	1.51347i
$209$	−10.4871	−	6.05475i	−0.725411	−	0.418816i
$210$	−0.675852	−	5.69466i	−0.0466382	−	0.392969i
$211$	3.78741	+	6.55998i	0.260736	+	0.451608i	0.966438	−	0.256901i	$-0.0827015\pi$
$211$	3.78741	+	6.55998i	0.260736	+	0.451608i	−0.705702	+	0.708509i	$0.749368\pi$
$212$	6.62261	+	16.9571i	0.454842	+	1.16462i
$213$	−5.87842	+	5.12838i	−0.402782	+	0.351391i
$214$	1.88987	−	2.76698i	0.129189	−	0.189147i
$215$	30.3558			2.07025
$216$	13.7837	−	5.10007i	0.937859	−	0.347016i
$217$	8.11577			0.550934
$218$	12.6121	−	18.4655i	0.854199	−	1.25064i
$219$	−3.72452	+	3.24931i	−0.251680	+	0.219568i
$220$	−18.8857	+	7.37581i	−1.27327	+	0.497277i
$221$	−2.38675	−	4.13397i	−0.160550	−	0.278081i
$222$	0.842493	+	7.09876i	0.0565444	+	0.476438i
$223$	−6.65936	−	3.84478i	−0.445944	−	0.257466i	0.260172	−	0.965562i	$-0.416221\pi$
$223$	−6.65936	−	3.84478i	−0.445944	−	0.257466i	−0.706116	+	0.708097i	$0.749554\pi$
$224$	−5.25717	−	2.08859i	−0.351259	−	0.139550i
$225$	1.14023	+	0.884345i	0.0760155	+	0.0589564i
$226$	3.93768	+	0.298386i	0.261931	+	0.0198483i
$227$	−9.72042	−	5.61209i	−0.645167	−	0.372487i	0.141435	−	0.989948i	$-0.454828\pi$
$227$	−9.72042	−	5.61209i	−0.645167	−	0.372487i	−0.786602	+	0.617460i	$0.788162\pi$
$228$	8.58796	+	4.48302i	0.568751	+	0.296895i
$229$	14.8980	−	8.60134i	0.984484	−	0.568392i	0.0808633	−	0.996725i	$-0.474232\pi$
$229$	14.8980	−	8.60134i	0.984484	−	0.568392i	0.903621	+	0.428333i	$0.140899\pi$
$230$	25.7983	−	12.3974i	1.70109	−	0.817458i
$231$	7.09568	+	2.42916i	0.466862	+	0.159827i
$232$	13.2055	+	12.3144i	0.866980	+	0.808480i
$233$		−	0.825385i		−	0.0540728i	−0.999634	−	0.0270364i	$-0.991393\pi$
$233$		−	0.825385i		−	0.0540728i	0.999634	−	0.0270364i	$-0.00860700\pi$
$234$	−5.09631	+	23.7116i	−0.333156	+	1.55008i
$235$	−19.3620			−1.26304
$236$	−15.1125	−	12.0930i	−0.983737	−	0.787188i
$237$	12.6939	−	2.49084i	0.824556	−	0.161797i
$238$	1.06440	−	0.511496i	0.0689948	−	0.0331554i
$239$	1.11213	+	1.92626i	0.0719375	+	0.124599i	0.899750	−	0.436405i	$-0.143748\pi$
$239$	1.11213	+	1.92626i	0.0719375	+	0.124599i	−0.827813	+	0.561004i	$0.810415\pi$
$240$	14.8443	−	6.53721i	0.958194	−	0.421975i
$241$	0.657377	−	1.13861i	0.0423454	−	0.0733443i	−0.844076	−	0.536224i	$-0.819850\pi$
$241$	0.657377	−	1.13861i	0.0423454	−	0.0733443i	0.886421	+	0.462879i	$0.153184\pi$
$242$	0.828137	−	10.9286i	0.0532347	−	0.702517i
$243$	14.0689	−	6.71312i	0.902520	−	0.430647i
$244$	−1.33067	+	8.72972i	−0.0851871	+	0.558863i
$245$	−1.17058	+	2.02750i	−0.0747854	+	0.129532i
$246$	0.878923	−	0.656760i	0.0560381	−	0.0418735i
$247$	−13.8449	+	7.99335i	−0.880929	+	0.508605i
$248$	6.71125	+	21.9519i	0.426165	+	1.39395i
$249$	9.60566	−	1.88486i	0.608734	−	0.119448i
$250$	−12.3551	−	8.43865i	−0.781405	−	0.533707i
$251$		−	5.45242i		−	0.344153i	−0.985084	−	0.172077i	$-0.944952\pi$
$251$		−	5.45242i		−	0.344153i	0.985084	−	0.172077i	$-0.0550477\pi$
$252$	−5.75401	−	1.70042i	−0.362468	−	0.107116i
$253$			37.4336i			2.35343i
$254$	−10.4439	+	15.2910i	−0.655308	+	0.959443i
$255$	−1.09671	+	3.20355i	−0.0686787	+	0.200614i
$256$	1.30194	−	15.9469i	0.0813714	−	0.996684i
$257$	−14.7701	+	8.52754i	−0.921336	+	0.531933i	−0.884061	−	0.467372i	$-0.845201\pi$
$257$	−14.7701	+	8.52754i	−0.921336	+	0.531933i	−0.0372747	+	0.999305i	$0.511868\pi$
$258$	12.5280	−	29.1853i	0.779956	−	1.81700i
$259$	1.45920	−	2.52741i	0.0906702	−	0.157045i
$260$	−4.03341	+	26.4608i	−0.250141	+	1.64103i
$261$	15.1334	+	11.7372i	0.936734	+	0.726515i
$262$	−31.5270	−	2.38902i	−1.94775	−	0.147594i
$263$	7.72261	−	13.3760i	0.476197	−	0.824797i	−0.523431	−	0.852068i	$-0.675348\pi$
$263$	7.72261	−	13.3760i	0.476197	−	0.824797i	0.999628	+	0.0272708i	$0.00868164\pi$
$264$	−0.702788	+	21.2015i	−0.0432536	+	1.30486i
$265$	10.6549	+	18.4548i	0.654523	+	1.13367i
$266$	−1.71303	−	3.56473i	−0.105032	−	0.218568i
$267$	9.89098	+	11.3376i	0.605318	+	0.693847i
$268$	−2.75011	+	3.43677i	−0.167990	+	0.209934i
$269$	−13.0114			−0.793319			−0.396659	−	0.917966i	$-0.629831\pi$
$269$	−13.0114			−0.793319			−0.396659	+	0.917966i	$0.629831\pi$
$270$	15.0510	−	8.33319i	0.915973	−	0.507142i
$271$		−	12.0923i		−	0.734553i	−0.930112	−	0.367276i	$-0.880290\pi$
$271$		−	12.0923i		−	0.734553i	0.930112	−	0.367276i	$-0.119710\pi$
$272$	2.26371	+	2.45606i	0.137258	+	0.148920i
$273$	7.46105	−	6.50909i	0.451563	−	0.393948i
$274$	2.14104	+	4.45540i	0.129345	+	0.269161i
$275$	−1.80372	+	1.04138i	−0.108768	+	0.0627975i
$276$	−1.27226	−	29.9200i	−0.0765813	−	1.80097i
$277$	−15.5250	−	8.96334i	−0.932805	−	0.538555i	−0.0451071	−	0.998982i	$-0.514363\pi$
$277$	−15.5250	−	8.96334i	−0.932805	−	0.538555i	−0.887697	+	0.460427i	$0.847696\pi$
$278$	0.0534901	−	0.705887i	0.00320812	−	0.0423363i
$279$	9.20076	+	22.5419i	0.550835	+	1.34955i
$280$	−6.45206	−	1.48961i	−0.385584	−	0.0890210i
$281$	6.64341	+	3.83557i	0.396312	+	0.228811i	0.684892	−	0.728645i	$-0.259850\pi$
$281$	6.64341	+	3.83557i	0.396312	+	0.228811i	−0.288579	+	0.957456i	$0.593183\pi$
$282$	−7.99076	+	18.6154i	−0.475843	+	1.10853i
$283$	−10.0205	−	17.3559i	−0.595654	−	1.03170i	−0.993454	−	0.114231i	$-0.963559\pi$
$283$	−10.0205	−	17.3559i	−0.595654	−	1.03170i	0.397800	−	0.917472i	$-0.369774\pi$
$284$	3.27697	+	8.39064i	0.194452	+	0.497893i
$285$	10.7288	+	3.67294i	0.635522	+	0.217566i
$286$	−28.9070	−	19.7438i	−1.70931	−	1.16747i
$287$	−0.447929			−0.0264404
$288$	−0.158854	−	16.9698i	−0.00936054	−	0.999956i
$289$	16.3027			0.958983
$290$	17.4536	+	11.9210i	1.02491	+	0.700025i
$291$	−2.43337	−	12.4010i	−0.142647	−	0.726960i
$292$	2.07626	+	5.31625i	0.121504	+	0.311110i
$293$	2.38032	+	4.12283i	0.139060	+	0.240858i	0.927141	−	0.374713i	$-0.122259\pi$
$293$	2.38032	+	4.12283i	0.139060	+	0.240858i	−0.788081	+	0.615571i	$0.788925\pi$
$294$	1.46622	+	1.96219i	0.0855115	+	0.114438i
$295$	−19.6214	−	11.3284i	−1.14240	−	0.659566i
$296$	8.04290	+	1.85689i	0.467484	+	0.107930i
$297$	1.29721	+	22.4625i	0.0752720	+	1.30341i
$298$	−1.19024	+	15.7072i	−0.0689490	+	0.909892i
$299$	42.7982	+	24.7095i	2.47508	+	1.42899i
$300$	1.40629	−	0.893657i	0.0811919	−	0.0515953i
$301$	−11.2290	+	6.48309i	−0.647231	+	0.373679i
$302$	0.0702836	+	0.146257i	0.00404437	+	0.00841614i
$303$	−2.27121	−	11.5746i	−0.130478	−	0.664944i
$304$	8.22546	−	7.58128i	0.471762	−	0.434816i
$305$			10.3368i			0.591885i
$306$	2.62740	+	2.37654i	0.150199	+	0.135858i
$307$	9.22752			0.526642			0.263321	−	0.964708i	$-0.415182\pi$
$307$	9.22752			0.526642			0.263321	+	0.964708i	$0.415182\pi$
$308$	5.41083	−	6.76183i	0.308310	−	0.385291i
$309$	1.85413	−	5.41600i	0.105478	−	0.308106i
$310$	11.6385	+	24.2191i	0.661021	+	1.37555i
$311$	−8.65935	−	14.9984i	−0.491027	−	0.850483i	0.508920	−	0.860814i	$-0.330045\pi$
$311$	−8.65935	−	14.9984i	−0.491027	−	0.850483i	−0.999947	+	0.0103307i	$0.996712\pi$
$312$	23.7759	+	14.7984i	1.34604	+	0.837792i
$313$	−9.21315	+	15.9576i	−0.520758	+	0.901979i	0.478951	+	0.877842i	$0.341017\pi$
$313$	−9.21315	+	15.9576i	−0.520758	+	0.901979i	−0.999709	+	0.0241373i	$0.992316\pi$
$314$	−13.1063	−	0.993160i	−0.739633	−	0.0560472i
$315$	−6.95853	−	0.952774i	−0.392069	−	0.0536827i
$316$	2.25086	−	14.7666i	0.126621	−	0.830685i
$317$	−4.47969	+	7.75904i	−0.251604	+	0.435791i	−0.963968	−	0.266019i	$-0.914291\pi$
$317$	−4.47969	+	7.75904i	−0.251604	+	0.435791i	0.712363	+	0.701811i	$0.247625\pi$
$318$	22.1404	−	2.62766i	1.24157	−	0.147352i
$319$	−23.9393	+	13.8214i	−1.34035	+	0.773849i
$320$	−1.30631	−	18.6836i	−0.0730247	−	1.04445i
$321$	−2.69787	−	3.09244i	−0.150580	−	0.172603i
$322$	−6.89546	+	10.0957i	−0.384269	+	0.562612i
$323$			2.33525i			0.129937i
$324$	−1.80027	−	17.9097i	−0.100015	−	0.994986i
$325$			2.74961i			0.152521i
$326$	−27.0034	−	18.4435i	−1.49558	−	1.02149i
$327$	−18.0043	−	20.6375i	−0.995640	−	1.14125i
$328$	−0.370410	−	1.21158i	−0.0204525	−	0.0668981i
$329$	7.16227	−	4.13514i	0.394869	−	0.227977i
$330$	2.92651	+	24.6585i	0.161099	+	1.35741i
$331$	−1.08539	+	1.87995i	−0.0596585	+	0.103332i	−0.894312	−	0.447444i	$-0.852335\pi$
$331$	−1.08539	+	1.87995i	−0.0596585	+	0.103332i	0.834654	+	0.550775i	$0.185668\pi$
$332$	1.70326	−	11.1741i	0.0934787	−	0.613259i
$333$	8.67426	+	1.18769i	0.475346	+	0.0650852i
$334$	−0.703235	+	9.28031i	−0.0384793	+	0.507796i
$335$	−2.57623	+	4.46216i	−0.140755	+	0.243794i
$336$	−4.09496	+	5.58850i	−0.223398	+	0.304878i
$337$	−10.6654	−	18.4730i	−0.580982	−	1.00629i	−0.995363	−	0.0961865i	$-0.969335\pi$
$337$	−10.6654	−	18.4730i	−0.580982	−	1.00629i	0.414382	−	0.910103i	$-0.363998\pi$
$338$	−25.0836	+	12.0539i	−1.36437	+	0.655647i
$339$	1.56648	−	4.57577i	0.0850796	−	0.248522i
$340$	3.05282	+	2.44287i	0.165562	+	0.132483i
$341$	−35.1422			−1.90305
$342$	7.95915	−	8.79930i	0.430381	−	0.475812i
$343$		−	1.00000i		−	0.0539949i
$344$	−26.8215	−	25.0117i	−1.44612	−	1.34854i
$345$	−6.74995	−	34.3993i	−0.363405	−	1.85200i
$346$	1.07237	−	0.515328i	0.0576511	−	0.0277042i
$347$	7.66832	−	4.42730i	0.411657	−	0.237670i	−0.279845	−	0.960045i	$-0.590283\pi$
$347$	7.66832	−	4.42730i	0.411657	−	0.237670i	0.691501	+	0.722375i	$0.256950\pi$
$348$	18.6645	−	11.8608i	1.00052	−	0.635806i
$349$	11.4473	+	6.60908i	0.612757	+	0.353776i	0.774044	−	0.633132i	$-0.218231\pi$
$349$	11.4473	+	6.60908i	0.612757	+	0.353776i	−0.161286	+	0.986908i	$0.551564\pi$
$350$	−0.678284	−	0.0513983i	−0.0362558	−	0.00274736i
$351$	26.5378	+	13.3441i	1.41648	+	0.712256i
$352$	22.7641	+	9.04381i	1.21333	+	0.482037i
$353$	6.35201	+	3.66734i	0.338083	+	0.195193i	0.659424	−	0.751771i	$-0.270800\pi$
$353$	6.35201	+	3.66734i	0.338083	+	0.195193i	−0.321341	+	0.946964i	$0.604133\pi$
$354$	−18.9894	+	14.1895i	−1.00928	+	0.754165i
$355$	5.27219	+	9.13170i	0.279819	+	0.484660i
$356$	16.1828	−	6.32021i	0.857688	−	0.334970i
$357$	−0.278492	−	1.41926i	−0.0147394	−	0.0751153i
$358$	11.4707	−	16.7944i	0.606247	−	0.887612i
$359$	7.37152			0.389054			0.194527	−	0.980897i	$-0.437683\pi$
$359$	7.37152			0.389054			0.194527	+	0.980897i	$0.437683\pi$
$360$	−3.17718	−	19.6096i	−0.167452	−	1.03352i
$361$	−11.1791			−0.588375
$362$	−0.631720	+	0.924908i	−0.0332025	+	0.0486121i
$363$	−12.6995	−	4.34760i	−0.666553	−	0.228190i
$364$	−4.15922	−	10.6496i	−0.218002	−	0.558193i
$365$	3.34042	+	5.78578i	0.174846	+	0.302842i
$366$	9.93825	+	4.26605i	0.519480	+	0.222990i
$367$	−12.2740	−	7.08642i	−0.640700	−	0.369908i	0.144184	−	0.989551i	$-0.453944\pi$
$367$	−12.2740	−	7.08642i	−0.640700	−	0.369908i	−0.784884	+	0.619643i	$0.787277\pi$
$368$	−33.0094	−	10.3026i	−1.72074	−	0.537060i
$369$	−0.507812	−	1.24414i	−0.0264356	−	0.0647674i
$370$	9.63486	+	0.730102i	0.500893	+	0.0379562i
$371$	−7.88276	−	4.55112i	−0.409253	−	0.236282i
$372$	28.0885	−	1.19438i	1.45632	−	0.0619259i
$373$	16.2925	−	9.40645i	0.843591	−	0.487048i	−0.0148920	−	0.999889i	$-0.504740\pi$
$373$	16.2925	−	9.40645i	0.843591	−	0.487048i	0.858483	+	0.512841i	$0.171407\pi$
$374$	−4.60896	+	2.21483i	−0.238324	+	0.114526i
$375$	−13.8083	+	12.0465i	−0.713060	+	0.622080i
$376$	17.1077	+	15.9533i	0.882260	+	0.822728i
$377$			36.4934i			1.87950i
$378$	−3.78785	+	6.29700i	−0.194826	+	0.323883i
$379$	17.7706			0.912816			0.456408	−	0.889771i	$-0.349136\pi$
$379$	17.7706			0.912816			0.456408	+	0.889771i	$0.349136\pi$
$380$	8.18130	−	10.2240i	0.419692	−	0.524482i
$381$	14.9091	+	17.0896i	0.763816	+	0.875525i
$382$	−29.9627	+	14.3985i	−1.53302	+	0.736693i
$383$	−11.7247	−	20.3078i	−0.599106	−	1.03768i	−0.992953	−	0.118506i	$-0.962190\pi$
$383$	−11.7247	−	20.3078i	−0.599106	−	1.03768i	0.393848	−	0.919176i	$-0.371144\pi$
$384$	−18.5023	−	6.45486i	−0.944191	−	0.329398i
$385$	5.06872	−	8.77928i	0.258326	−	0.447434i
$386$	−1.92484	+	25.4013i	−0.0979717	+	1.29289i
$387$	−30.7373	−	23.8393i	−1.56247	−	1.21182i
$388$	−14.4259	−	2.19893i	−0.732364	−	0.111634i
$389$	−4.35082	+	7.53584i	−0.220595	+	0.382082i	−0.954989	−	0.296642i	$-0.904133\pi$
$389$	−4.35082	+	7.53584i	−0.220595	+	0.382082i	0.734394	+	0.678724i	$0.237467\pi$
$390$	30.1240	+	12.9309i	1.52539	+	0.654781i
$391$	6.25172	−	3.60943i	0.316163	−	0.182537i
$392$	2.70484	−	0.826939i	0.136615	−	0.0417667i
$393$	−12.5420	+	36.6359i	−0.632662	+	1.84804i
$394$	−5.22611	−	3.56948i	−0.263287	−	0.179828i
$395$		−	17.4851i		−	0.879769i
$396$	24.9155	+	7.36299i	1.25205	+	0.370004i
$397$			19.7436i			0.990904i	0.868635	+	0.495452i	$0.164998\pi$
$397$			19.7436i			0.990904i	−0.868635	+	0.495452i	$0.835002\pi$
$398$	10.9823	−	16.0793i	0.550493	−	0.805982i
$399$	−4.75318	+	0.932685i	−0.237957	+	0.0466927i
$400$	−0.421875	−	1.87715i	−0.0210937	−	0.0938577i
$401$	−11.0421	+	6.37514i	−0.551415	+	0.318359i	−0.749692	−	0.661787i	$-0.769799\pi$
$401$	−11.0421	+	6.37514i	−0.551415	+	0.318359i	0.198278	+	0.980146i	$0.436465\pi$
$402$	3.22688	+	4.31844i	0.160942	+	0.215384i
$403$	−23.1969	+	40.1783i	−1.15552	+	2.00142i
$404$	−13.4646	−	2.05239i	−0.669887	−	0.102110i
$405$	−5.24245	−	20.4078i	−0.260499	−	1.01407i
$406$	−9.00232	−	0.682169i	−0.446778	−	0.0338555i
$407$	−6.31849	+	10.9439i	−0.313196	+	0.542471i
$408$	3.60858	−	1.92692i	0.178651	−	0.0953968i
$409$	−11.1934	−	19.3875i	−0.553478	−	0.958652i	−0.998020	−	0.0628939i	$-0.979967\pi$
$409$	−11.1934	−	19.3875i	−0.553478	−	0.958652i	0.444542	−	0.895758i	$-0.353366\pi$
$410$	−0.642355	−	1.33671i	−0.0317237	−	0.0660154i
$411$	5.94080	−	1.16572i	0.293038	−	0.0575009i
$412$	−5.16118	−	4.12998i	−0.254273	−	0.203470i
$413$	9.67764			0.476206
$414$	−35.8586	−	7.70704i	−1.76235	−	0.378781i
$415$		−	13.2312i		−	0.649496i
$416$	25.3662	−	20.0566i	1.24368	−	0.983358i
$417$	−0.820274	−	0.280815i	−0.0401690	−	0.0137516i
$418$	7.41759	+	15.4357i	0.362806	+	0.754983i
$419$	−30.3014	+	17.4945i	−1.48032	+	0.854664i	−0.999751	−	0.0222925i	$-0.992903\pi$
$419$	−30.3014	+	17.4945i	−1.48032	+	0.854664i	−0.480570	+	0.876956i	$0.659570\pi$
$420$	−3.75295	+	7.18939i	−0.183125	+	0.350806i
$421$	−21.2669	−	12.2785i	−1.03649	−	0.598415i	−0.117650	−	0.993055i	$-0.537536\pi$
$421$	−21.2669	−	12.2785i	−1.03649	−	0.598415i	−0.918836	+	0.394640i	$0.870869\pi$
$422$	0.809434	−	10.6818i	0.0394026	−	0.519981i
$423$	19.6053	+	15.2055i	0.953243	+	0.739319i
$424$	5.79148	−	25.0851i	0.281259	−	1.21824i
$425$	0.347837	+	0.200824i	0.0168726	+	0.00974139i
$426$	10.9554	−	1.30021i	0.530793	−	0.0629954i
$427$	−2.20764	−	3.82374i	−0.106835	−	0.185044i
$428$	−4.41404	+	1.72390i	−0.213361	+	0.0833280i
$429$	−32.3072	+	28.1850i	−1.55980	+	1.36079i
$430$	−35.4499	−	24.2126i	−1.70955	−	1.16764i
$431$	−0.195268			−0.00940573			−0.00470286	−	0.999989i	$-0.501497\pi$
$431$	−0.195268			−0.00940573			−0.00470286	+	0.999989i	$0.501497\pi$
$432$	−20.1647	−	5.03829i	−0.970175	−	0.242405i
$433$	22.6156			1.08684			0.543419	−	0.839462i	$-0.317130\pi$
$433$	22.6156			1.08684			0.543419	+	0.839462i	$0.317130\pi$
$434$	−9.47771	−	6.47336i	−0.454945	−	0.310731i
$435$	19.5066	−	17.0177i	0.935270	−	0.815937i
$436$	−29.4572	+	11.5045i	−1.41074	+	0.550966i
$437$	−12.0882	−	20.9373i	−0.578256	−	1.00157i
$438$	6.94129	−	0.823804i	0.331668	−	0.0393629i
$439$	13.0274	+	7.52139i	0.621765	+	0.358976i	0.777556	−	0.628814i	$-0.216459\pi$
$439$	13.0274	+	7.52139i	0.621765	+	0.358976i	−0.155791	+	0.987790i	$0.549793\pi$
$440$	27.9381	+	6.45016i	1.33190	+	0.307499i
$441$	2.77754	−	1.13369i	0.132264	−	0.0539852i
$442$	−0.510089	+	6.73145i	−0.0242625	+	0.320182i
$443$	−11.8077	−	6.81716i	−0.561000	−	0.323893i	0.192547	−	0.981288i	$-0.438325\pi$
$443$	−11.8077	−	6.81716i	−0.561000	−	0.323893i	−0.753547	+	0.657395i	$0.771659\pi$
$444$	4.67829	−	8.96203i	0.222022	−	0.425319i
$445$	17.6121	−	10.1683i	0.834893	−	0.482025i
$446$	4.71019	+	9.80168i	0.223034	+	0.464123i
$447$	18.2525	+	6.24861i	0.863313	+	0.295549i
$448$	4.47348	+	6.63234i	0.211352	+	0.313349i
$449$		−	14.8982i		−	0.703092i	−0.936171	−	0.351546i	$-0.885656\pi$
$449$		−	14.8982i		−	0.703092i	0.936171	−	0.351546i	$-0.114344\pi$
$450$	−0.626202	−	1.94223i	−0.0295194	−	0.0915577i
$451$	1.93958			0.0913312
$452$	−4.36048	−	3.48926i	−0.205100	−	0.164121i
$453$	0.195018	−	0.0382670i	0.00916273	−	0.00179794i
$454$	6.87529	+	14.3072i	0.322673	+	0.671468i
$455$	−6.69161	−	11.5902i	−0.313708	−	0.543357i
$456$	−6.45336	−	12.0853i	−0.302206	−	0.565947i
$457$	9.68726	−	16.7788i	0.453151	−	0.784880i	−0.545429	−	0.838157i	$-0.683633\pi$
$457$	9.68726	−	16.7788i	0.453151	−	0.784880i	0.998580	+	0.0532768i	$0.0169666\pi$
$458$	−24.2587	−	1.83825i	−1.13353	−	0.0858959i
$459$	3.62634	−	2.38253i	0.169263	−	0.111207i
$460$	−40.0162	−	6.09964i	−1.86576	−	0.284397i
$461$	−19.4767	+	33.7346i	−0.907119	+	1.57118i	−0.0890717	+	0.996025i	$0.528390\pi$
$461$	−19.4767	+	33.7346i	−0.907119	+	1.57118i	−0.818047	+	0.575151i	$0.804943\pi$
$462$	−6.34888	−	8.49652i	−0.295377	−	0.395294i
$463$	27.0116	−	15.5951i	1.25533	−	0.724767i	0.283170	−	0.959070i	$-0.408614\pi$
$463$	27.0116	−	15.5951i	1.25533	−	0.724767i	0.972164	+	0.234303i	$0.0752807\pi$
$464$	−5.59921	−	24.9140i	−0.259937	−	1.15660i
$465$	32.2936	−	6.33676i	1.49758	−	0.293860i
$466$	−0.658350	+	0.963896i	−0.0304975	+	0.0446516i
$467$		−	36.3880i		−	1.68384i	−0.539605	−	0.841918i	$-0.681426\pi$
$467$		−	36.3880i		−	1.68384i	0.539605	−	0.841918i	$-0.318574\pi$
$468$	24.8646	−	23.6258i	1.14937	−	1.09210i
$469$		−	2.20082i		−	0.101625i
$470$	22.6112	+	15.4436i	1.04298	+	0.712362i
$471$	−5.21394	+	15.2302i	−0.240246	+	0.701770i
$472$	8.00282	+	26.1765i	0.368360	+	1.20487i
$473$	48.6230	−	28.0725i	2.23569	−	1.29077i
$474$	−16.8109	−	7.21615i	−0.772148	−	0.331449i
$475$	0.672570	−	1.16493i	0.0308596	−	0.0534504i
$476$	−1.65100	−	0.251662i	−0.0756737	−	0.0115349i
$477$	3.70432	−	27.0543i	0.169609	−	1.23873i
$478$	0.237681	−	3.13658i	0.0108713	−	0.143464i
$479$	−2.78534	+	4.82435i	−0.127265	+	0.220430i	−0.922616	−	0.385719i	$-0.873953\pi$
$479$	−2.78534	+	4.82435i	−0.127265	+	0.220430i	0.795351	+	0.606149i	$0.207287\pi$
$480$	−22.5496	−	4.20595i	−1.02924	−	0.191975i
$481$	8.34152	+	14.4479i	0.380341	+	0.658769i
$482$	−1.67588	+	0.805343i	−0.0763343	+	0.0366824i
$483$	9.84356	+	11.2832i	0.447898	+	0.513403i
$484$	−9.68406	+	12.1020i	−0.440185	+	0.550092i
$485$	−17.0817			−0.775638
$486$	−21.7844	−	3.38207i	−0.988162	−	0.153414i
$487$		−	39.2739i		−	1.77967i	−0.456283	−	0.889835i	$-0.650819\pi$
$487$		−	39.2739i		−	1.77967i	0.456283	−	0.889835i	$-0.349181\pi$
$488$	8.51703	−	9.13331i	0.385548	−	0.413446i
$489$	−30.1796	+	26.3289i	−1.36477	+	1.19063i
$490$	2.98420	−	1.43406i	0.134813	−	0.0647841i
$491$	−7.69485	+	4.44263i	−0.347264	+	0.200493i	−0.663479	−	0.748194i	$-0.730921\pi$
$491$	−7.69485	+	4.44263i	−0.347264	+	0.200493i	0.316216	+	0.948687i	$0.397588\pi$
$492$	−1.55027	+	0.0659209i	−0.0698915	+	0.00297194i
$493$	4.61657	+	2.66538i	0.207920	+	0.120043i
$494$	22.5440	+	1.70832i	1.01430	+	0.0768608i
$495$	30.1312	+	4.12561i	1.35430	+	0.185433i
$496$	9.67193	−	30.9888i	0.434283	−	1.39144i
$497$	−3.90051	−	2.25196i	−0.174962	−	0.101014i
$498$	−12.7210	−	5.46058i	−0.570043	−	0.244694i
$499$	−4.10241	−	7.10559i	−0.183649	−	0.318090i	0.759471	−	0.650541i	$-0.225458\pi$
$499$	−4.10241	−	7.10559i	−0.183649	−	0.318090i	−0.943121	+	0.332451i	$0.892124\pi$
$500$	7.69757	+	19.7095i	0.344246	+	0.881438i
$501$	10.7842	+	3.69188i	0.481801	+	0.164941i
$502$	−4.34900	+	6.36741i	−0.194105	+	0.284191i
$503$	7.90162			0.352316			0.176158	−	0.984362i	$-0.443633\pi$
$503$	7.90162			0.352316			0.176158	+	0.984362i	$0.443633\pi$
$504$	5.36331	+	6.57532i	0.238901	+	0.292888i
$505$	−15.9433			−0.709469
$506$	29.8581	−	43.7155i	1.32735	−	1.94339i
$507$	6.56296	+	33.4463i	0.291471	+	1.48540i
$508$	24.3930	−	9.52671i	1.08227	−	0.422680i
$509$	7.27823	+	12.6063i	0.322602	+	0.558763i	0.981024	−	0.193886i	$-0.0621092\pi$
$509$	7.27823	+	12.6063i	0.322602	+	0.558763i	−0.658422	+	0.752649i	$0.728776\pi$
$510$	3.83599	−	2.86638i	0.169861	−	0.126925i
$511$	−2.47134	−	1.42683i	−0.109326	−	0.0631192i
$512$	−14.2401	+	17.5846i	−0.629332	+	0.777137i
$513$	−7.97921	−	12.1448i	−0.352291	−	0.536206i
$514$	24.0506	+	1.82248i	1.06083	+	0.0803862i
$515$	−6.70107	−	3.86886i	−0.295284	−	0.170482i
$516$	−37.9093	+	24.0904i	−1.66886	+	1.06052i
$517$	−31.0134	+	17.9056i	−1.36397	+	0.787487i
$518$	−3.72000	+	1.78764i	−0.163447	+	0.0785445i
$519$	−0.280579	−	1.42989i	−0.0123160	−	0.0627654i
$520$	25.8161	−	27.6842i	1.13211	−	1.21403i
$521$		−	29.0795i		−	1.27400i	−0.770865	−	0.636999i	$-0.780176\pi$
$521$		−	29.0795i		−	1.27400i	0.770865	−	0.636999i	$-0.219824\pi$
$522$	−8.31108	−	25.7777i	−0.363766	−	1.12826i
$523$	−4.73922			−0.207231			−0.103616	−	0.994617i	$-0.533041\pi$
$523$	−4.73922			−0.207231			−0.103616	+	0.994617i	$0.533041\pi$
$524$	34.9121	+	27.9367i	1.52514	+	1.22042i
$525$	−0.269834	+	0.788198i	−0.0117765	+	0.0343998i
$526$	−19.6876	+	9.46087i	−0.858421	+	0.412513i
$527$	3.38848	+	5.86903i	0.147605	+	0.255659i
$528$	17.7316	−	24.1988i	0.771669	−	1.05312i
$529$	−25.8677	+	44.8042i	−1.12468	+	1.94801i
$530$	2.27713	−	30.0503i	0.0989120	−	1.30530i
$531$	10.9714	+	26.8801i	0.476120	+	1.16650i
$532$	−0.842828	+	5.52930i	−0.0365412	+	0.239725i
$533$	1.28029	−	2.21753i	0.0554557	−	0.0960521i
$534$	−2.50768	−	21.1295i	−0.108518	−	0.914362i
$535$	−4.80388	+	2.77352i	−0.207690	+	0.119910i
$536$	5.95288	−	1.81995i	0.257125	−	0.0786097i
$537$	−16.3749	−	18.7698i	−0.706631	−	0.809977i
$538$	15.1949	+	10.3782i	0.655098	+	0.447438i
$539$			4.33011i			0.186511i
$540$	−24.2235	−	2.27345i	−1.04241	−	0.0978337i
$541$		−	1.32007i		−	0.0567541i	−0.999597	−	0.0283771i	$-0.990966\pi$
$541$		−	1.32007i		−	0.0567541i	0.999597	−	0.0283771i	$-0.00903391\pi$
$542$	−9.64512	+	14.1215i	−0.414294	+	0.606571i
$543$	0.901807	+	1.03370i	0.0387002	+	0.0443602i
$544$	−0.684575	−	4.67381i	−0.0293509	−	0.200388i
$545$	−32.0588	+	18.5092i	−1.37325	+	0.792846i
$546$	−13.9049	+	1.65026i	−0.595077	+	0.0706247i
$547$	12.7108	−	22.0157i	0.543473	−	0.941322i	−0.455229	−	0.890375i	$-0.650443\pi$
$547$	12.7108	−	22.0157i	0.543473	−	0.941322i	0.998701	−	0.0509476i	$-0.0162242\pi$
$548$	1.05341	−	6.91084i	0.0449997	−	0.295216i
$549$	8.11783	−	10.4667i	0.346461	−	0.446710i
$550$	2.93704	+	0.222560i	0.125236	+	0.00949001i
$551$	8.92648	−	15.4611i	0.380281	−	0.658666i
$552$	−22.3793	+	35.9558i	−0.952524	+	1.53038i
$553$	3.73429	+	6.46798i	0.158798	+	0.275046i
$554$	10.9809	+	22.8507i	0.466532	+	0.970831i
$555$	3.83293	−	11.1962i	0.162699	−	0.475251i
$556$	−0.625502	+	0.781680i	−0.0265272	+	0.0331506i
$557$	−20.8986			−0.885501			−0.442750	−	0.896645i	$-0.645997\pi$
$557$	−20.8986			−0.885501			−0.442750	+	0.896645i	$0.645997\pi$
$558$	7.23526	−	33.6635i	0.306293	−	1.42509i
$559$		−	74.1213i		−	3.13500i
$560$	6.34665	+	6.88592i	0.268195	+	0.290983i
$561$	1.20590	+	6.14556i	0.0509132	+	0.259466i
$562$	−4.69891	−	9.77820i	−0.198211	−	0.412469i
$563$	−17.8861	+	10.3265i	−0.753809	+	0.435212i	−0.827069	−	0.562101i	$-0.809993\pi$
$563$	−17.8861	+	10.3265i	−0.753809	+	0.435212i	0.0732593	+	0.997313i	$0.476660\pi$
$564$	24.1799	−	15.3657i	1.01816	−	0.647011i
$565$	−5.66147	−	3.26865i	−0.238180	−	0.137513i
$566$	−2.14154	+	28.2611i	−0.0900158	+	1.18790i
$567$	6.29774	+	6.42950i	0.264480	+	0.270013i
$568$	2.86572	−	12.4125i	0.120243	−	0.520817i
$569$	−3.99918	−	2.30893i	−0.167654	−	0.0967954i	0.413825	−	0.910356i	$-0.364193\pi$
$569$	−3.99918	−	2.30893i	−0.167654	−	0.0967954i	−0.581479	+	0.813561i	$0.697526\pi$
$570$	−9.59965	−	12.8469i	−0.402085	−	0.538099i
$571$	−1.93031	−	3.34340i	−0.0807810	−	0.139917i	0.822805	−	0.568324i	$-0.192408\pi$
$571$	−1.93031	−	3.34340i	−0.0807810	−	0.139917i	−0.903586	+	0.428408i	$0.859075\pi$
$572$	18.0099	+	46.1141i	0.753031	+	1.92813i
$573$	7.83952	+	39.9520i	0.327501	+	1.66902i
$574$	0.523097	+	0.357280i	0.0218337	+	0.0149126i
$575$	−4.15818			−0.173408
$576$	−13.3501	+	19.9443i	−0.556254	+	0.831013i
$577$	22.4523			0.934700			0.467350	−	0.884073i	$-0.345209\pi$
$577$	22.4523			0.934700			0.467350	+	0.884073i	$0.345209\pi$
$578$	−19.0385	−	13.0035i	−0.791899	−	0.540874i
$579$	29.5175	+	10.1051i	1.22671	+	0.419955i
$580$	−10.8741	−	27.8430i	−0.451523	−	1.15612i
$581$	2.82579	+	4.89442i	0.117234	+	0.203055i
$582$	−7.04966	+	16.4230i	−0.292218	+	0.680755i
$583$	34.1332	+	19.7068i	1.41365	+	0.816173i
$584$	1.81570	−	7.86448i	0.0751341	−	0.325435i
$585$	24.6061	−	31.7259i	1.01734	−	1.31171i
$586$	0.508714	−	6.71330i	0.0210148	−	0.277324i
$587$	25.9071	+	14.9575i	1.06930	+	0.617362i	0.927991	−	0.372603i	$-0.121535\pi$
$587$	25.9071	+	14.9575i	1.06930	+	0.617362i	0.141311	+	0.989965i	$0.454868\pi$
$588$	−0.147168	−	3.46097i	−0.00606912	−	0.142728i
$589$	19.6557	−	11.3482i	0.809898	−	0.467595i
$590$	13.8783	+	28.8801i	0.571360	+	1.18897i
$591$	−5.84082	+	5.09558i	−0.240259	+	0.209604i
$592$	−7.91151	−	8.58374i	−0.325161	−	0.352790i
$593$		−	5.47387i		−	0.224785i	−0.993664	−	0.112392i	$-0.964149\pi$
$593$		−	5.47387i		−	0.224785i	0.993664	−	0.112392i	$-0.0358514\pi$
$594$	16.4018	−	27.2667i	0.672974	−	1.11877i
$595$	−1.95495			−0.0801451
$596$	13.9185	−	17.3937i	0.570122	−	0.712474i
$597$	−15.6777	−	17.9706i	−0.641645	−	0.735487i
$598$	−30.2713	−	62.9931i	−1.23789	−	2.57598i
$599$	6.54755	+	11.3407i	0.267526	+	0.463368i	0.968222	−	0.250091i	$-0.0804606\pi$
$599$	6.54755	+	11.3407i	0.267526	+	0.463368i	−0.700696	+	0.713460i	$0.747127\pi$
$600$	−2.35509	−	0.0780665i	−0.0961460	−	0.00318705i
$601$	−5.72592	+	9.91758i	−0.233565	+	0.404546i	−0.958855	−	0.283897i	$-0.908372\pi$
$601$	−5.72592	+	9.91758i	−0.233565	+	0.404546i	0.725290	+	0.688444i	$0.241706\pi$
$602$	18.2845	+	1.38555i	0.745222	+	0.0564707i
$603$	6.11288	−	2.49505i	0.248936	−	0.101606i
$604$	0.0345803	−	0.226861i	0.00140705	−	0.00923084i
$605$	−9.07178	+	15.7128i	−0.368820	+	0.638816i
$606$	−6.57988	+	15.3286i	−0.267289	+	0.622681i
$607$	−21.9000	+	12.6440i	−0.888894	+	0.513203i	−0.873581	−	0.486679i	$-0.838208\pi$
$607$	−21.9000	+	12.6440i	−0.888894	+	0.513203i	−0.0153137	+	0.999883i	$0.504875\pi$
$608$	−15.6528	+	2.29268i	−0.634807	+	0.0929803i
$609$	−3.58129	+	10.4611i	−0.145121	+	0.423906i
$610$	8.24494	−	12.0715i	0.333828	−	0.488761i
$611$			47.2771i			1.91263i
$612$	−1.17273	−	4.87104i	−0.0474046	−	0.196900i
$613$			38.0928i			1.53855i	0.638917	+	0.769276i	$0.279383\pi$
$613$			38.0928i			1.53855i	−0.638917	+	0.769276i	$0.720617\pi$
$614$	−10.7760	−	7.36012i	−0.434885	−	0.297030i
$615$	−1.78236	+	0.349741i	−0.0718716	+	0.0141029i
$616$	−11.7123	+	3.58074i	−0.471900	+	0.144272i
$617$	−5.31999	+	3.07150i	−0.214175	+	0.123654i	−0.603250	−	0.797552i	$-0.706128\pi$
$617$	−5.31999	+	3.07150i	−0.214175	+	0.123654i	0.389075	+	0.921206i	$0.372795\pi$
$618$	−6.48524	+	4.84598i	−0.260874	+	0.194934i
$619$	10.5904	−	18.3431i	0.425663	−	0.737270i	−0.570819	−	0.821076i	$-0.693374\pi$
$619$	10.5904	−	18.3431i	0.425663	−	0.737270i	0.996482	+	0.0838060i	$0.0267076\pi$
$620$	5.72625	−	37.5666i	0.229972	−	1.50871i
$621$	−20.1800	+	40.1326i	−0.809797	+	1.61046i
$622$	−1.85065	+	24.4223i	−0.0742044	+	0.979246i
$623$	−4.34331	+	7.52283i	−0.174011	+	0.301396i
$624$	−15.9622	−	36.2460i	−0.639001	−	1.45100i
$625$	13.5868	+	23.5330i	0.543472	+	0.941322i
$626$	23.4875	−	11.2869i	0.938749	−	0.451115i
$627$	20.5818	−	4.03863i	0.821957	−	0.161287i
$628$	14.5136	+	11.6138i	0.579155	+	0.463441i
$629$	2.43697			0.0971683
$630$	7.36631	+	6.66298i	0.293481	+	0.265459i
$631$			40.4632i			1.61082i	0.592721	+	0.805408i	$0.298054\pi$
$631$			40.4632i			1.61082i	−0.592721	+	0.805408i	$0.701946\pi$
$632$	−14.4068	+	15.4493i	−0.573073	+	0.614539i
$633$	−12.4127	−	4.24941i	−0.493362	−	0.168899i
$634$	11.4203	−	5.48800i	0.453557	−	0.217956i
$635$	26.5474	−	15.3272i	1.05350	−	0.608240i
$636$	−27.9518	−	14.5912i	−1.10836	−	0.578579i
$637$	4.95064	+	2.85826i	0.196152	+	0.113248i
$638$	38.9810	+	2.95387i	1.54327	+	0.116945i
$639$	1.83295	−	13.3869i	0.0725105	−	0.529577i
$640$	−13.3770	+	22.8609i	−0.528774	+	0.903658i
$641$	32.4846	+	18.7550i	1.28306	+	0.740777i	0.977407	−	0.211365i	$-0.0677908\pi$
$641$	32.4846	+	18.7550i	1.28306	+	0.740777i	0.305656	+	0.952142i	$0.401124\pi$
$642$	0.683997	+	5.76329i	0.0269952	+	0.227459i
$643$	−9.91973	−	17.1815i	−0.391196	−	0.677571i	0.601412	−	0.798939i	$-0.294605\pi$
$643$	−9.91973	−	17.1815i	−0.391196	−	0.677571i	−0.992608	+	0.121368i	$0.961272\pi$
$644$	16.1052	−	6.28991i	0.634635	−	0.247857i
$645$	−39.6197	+	34.5645i	−1.56002	+	1.36098i
$646$	1.86266	−	2.72714i	0.0732854	−	0.107298i
$647$	0.939565			0.0369381			0.0184691	−	0.999829i	$-0.494121\pi$
$647$	0.939565			0.0369381			0.0184691	+	0.999829i	$0.494121\pi$
$648$	−12.1829	+	22.3512i	−0.478590	+	0.878038i
$649$	−41.9052			−1.64492
$650$	2.19316	−	3.21103i	0.0860229	−	0.125947i
$651$	−10.5925	+	9.24099i	−0.415153	+	0.362183i
$652$	16.8238	+	43.0772i	0.658872	+	1.68704i
$653$	2.47055	+	4.27911i	0.0966799	+	0.167454i	0.910308	−	0.413931i	$-0.135844\pi$
$653$	2.47055	+	4.27911i	0.0966799	+	0.167454i	−0.813629	+	0.581385i	$0.802511\pi$
$654$	4.56467	+	38.4615i	0.178493	+	1.50396i
$655$	45.3285	+	26.1704i	1.77113	+	1.02256i
$656$	−0.533817	+	1.71035i	−0.0208420	+	0.0667778i
$657$	1.16135	−	8.48183i	0.0453084	−	0.330908i
$658$	−11.6625	−	0.883750i	−0.454651	−	0.0344522i
$659$	−17.3320	−	10.0066i	−0.675157	−	0.389802i	0.122871	−	0.992423i	$-0.460790\pi$
$659$	−17.3320	−	10.0066i	−0.675157	−	0.389802i	−0.798028	+	0.602621i	$0.794123\pi$
$660$	16.2507	−	31.1308i	0.632557	−	1.21177i
$661$	13.2404	−	7.64434i	0.514991	−	0.297330i	−0.219892	−	0.975524i	$-0.570570\pi$
$661$	13.2404	−	7.64434i	0.514991	−	0.297330i	0.734883	+	0.678194i	$0.237237\pi$
$662$	2.76704	−	1.32970i	0.107544	−	0.0516802i
$663$	7.82226	+	2.67790i	0.303791	+	0.104001i
$664$	−10.9019	+	11.6907i	−0.423075	+	0.453688i
$665$			6.54723i			0.253891i
$666$	−9.18258	−	8.30583i	−0.355818	−	0.321844i
$667$	−55.1882			−2.13689
$668$	8.22348	−	10.2768i	0.318176	−	0.397620i
$669$	13.0695	−	2.56454i	0.505296	−	0.0991509i
$670$	6.56770	−	3.15610i	0.253733	−	0.121931i
$671$	9.55931	+	16.5572i	0.369033	+	0.639184i
$672$	9.23969	−	3.26008i	0.356429	−	0.125760i
$673$	7.32206	−	12.6822i	0.282245	−	0.488862i	−0.689693	−	0.724102i	$-0.742254\pi$
$673$	7.32206	−	12.6822i	0.282245	−	0.488862i	0.971937	+	0.235240i	$0.0755877\pi$
$674$	−2.27938	+	30.0801i	−0.0877984	+	1.15864i
$675$	−2.49516	+	0.144096i	−0.0960388	+	0.00554626i
$676$	38.9076	+	5.93066i	1.49645	+	0.228102i
$677$	2.01058	−	3.48243i	0.0772730	−	0.133841i	−0.824799	−	0.565425i	$-0.808712\pi$
$677$	2.01058	−	3.48243i	0.0772730	−	0.133841i	0.902072	+	0.431585i	$0.142045\pi$
$678$	−5.47912	+	4.09418i	−0.210424	+	0.157236i
$679$	6.31875	−	3.64813i	0.242491	−	0.140002i
$680$	−1.61662	−	5.28783i	−0.0619947	−	0.202779i
$681$	19.0770	−	3.74336i	0.731034	−	0.143446i
$682$	41.0395	+	28.0304i	1.57148	+	1.07334i
$683$			12.0520i			0.461157i	0.973054	+	0.230578i	$0.0740618\pi$
$683$			12.0520i			0.461157i	−0.973054	+	0.230578i	$0.925938\pi$
$684$	−16.3134	+	3.92752i	−0.623757	+	0.150172i
$685$		−	8.18310i		−	0.312660i
$686$	−0.797628	+	1.16781i	−0.0304536	+	0.0445874i
$687$	−9.65056	+	28.1898i	−0.368192	+	1.07551i
$688$	11.3725	+	50.6025i	0.433573	+	1.92920i
$689$	45.0619	−	26.0165i	1.71672	−	0.991150i
$690$	−19.5551	+	45.5559i	−0.744452	+	1.73429i
$691$	22.5281	−	39.0198i	0.857009	−	1.48438i	−0.0177593	−	0.999842i	$-0.505653\pi$
$691$	22.5281	−	39.0198i	0.857009	−	1.48438i	0.874768	−	0.484541i	$-0.161013\pi$
$692$	−1.66337	−	0.253547i	−0.0632319	−	0.00963840i
$693$	−12.0271	+	4.90900i	−0.456870	+	0.186477i
$694$	−12.4865	−	0.946191i	−0.473981	−	0.0359169i
$695$	−0.585954	+	1.01490i	−0.0222265	+	0.0384974i
$696$	−31.2572	−	1.03612i	−1.18480	−	0.0392738i
$697$	−0.187019	−	0.323926i	−0.00708383	−	0.0122696i
$698$	−8.09669	−	16.8488i	−0.306464	−	0.637737i
$699$	0.939822	+	1.07727i	0.0355473	+	0.0407462i
$700$	0.751113	+	0.601041i	0.0283894	+	0.0227172i
$701$	19.9659			0.754100			0.377050	−	0.926193i	$-0.376939\pi$
$701$	19.9659			0.754100			0.377050	+	0.926193i	$0.376939\pi$
$702$	−20.3476	−	36.7507i	−0.767970	−	1.38707i
$703$		−	8.16154i		−	0.307818i
$704$	−19.3707	−	28.7188i	−0.730059	−	1.08238i
$705$	25.2708	−	22.0464i	0.951752	−	0.830317i
$706$	−4.49280	−	9.34931i	−0.169089	−	0.351866i
$707$	5.89767	−	3.40502i	0.221805	−	0.128059i
$708$	33.4941	−	1.42424i	1.25878	−	0.0535263i
$709$	−12.6541	−	7.30585i	−0.475235	−	0.274377i	0.243194	−	0.969978i	$-0.421805\pi$
$709$	−12.6541	−	7.30585i	−0.475235	−	0.274377i	−0.718429	+	0.695601i	$0.755138\pi$
$710$	1.12676	−	14.8694i	0.0422865	−	0.558038i
$711$	−13.7316	+	17.7048i	−0.514974	+	0.663983i
$712$	−23.9397	−	5.52704i	−0.897178	−	0.207134i
$713$	−60.7608	−	35.0803i	−2.27551	−	1.31377i
$714$	−0.806815	+	1.87957i	−0.0301943	+	0.0703410i
$715$	28.9754	+	50.1869i	1.08362	+	1.87688i
$716$	−26.7914	+	10.4634i	−1.00124	+	0.391035i
$717$	−3.64485	−	1.24779i	−0.136120	−	0.0465995i
$718$	−8.60857	−	5.87973i	−0.321269	−	0.219430i
$719$	−44.7348			−1.66833			−0.834163	−	0.551518i	$-0.814049\pi$
$719$	−44.7348			−1.66833			−0.834163	+	0.551518i	$0.814049\pi$
$720$	−11.9308	+	25.4346i	−0.444635	+	0.947892i
$721$	3.30509			0.123088
$722$	13.0551	+	8.91678i	0.485862	+	0.331848i
$723$	0.438482	+	2.23461i	0.0163073	+	0.0831059i
$724$	1.47546	−	0.576243i	0.0548352	−	0.0214159i
$725$	−1.53530	−	2.65921i	−0.0570195	−	0.0987607i
$726$	11.3629	+	15.2067i	0.421719	+	0.564374i
$727$	18.1033	+	10.4520i	0.671415	+	0.387642i	0.796613	−	0.604490i	$-0.206623\pi$
$727$	18.1033	+	10.4520i	0.671415	+	0.387642i	−0.125198	+	0.992132i	$0.539957\pi$
$728$	−3.63725	+	15.7543i	−0.134805	+	0.583894i
$729$	−10.7185	+	24.7813i	−0.396982	+	0.917826i
$730$	0.713906	−	9.42113i	0.0264228	−	0.348692i
$731$	−9.37667	−	5.41362i	−0.346809	−	0.200230i
$732$	−8.20331	−	12.9090i	−0.303203	−	0.477129i
$733$	9.70754	−	5.60465i	0.358556	−	0.207012i	−0.309891	−	0.950772i	$-0.600293\pi$
$733$	9.70754	−	5.60465i	0.358556	−	0.207012i	0.668447	+	0.743760i	$0.266959\pi$
$734$	8.68147	+	18.0657i	0.320439	+	0.666818i
$735$	−0.780795	−	3.97911i	−0.0288001	−	0.146772i
$736$	30.3313	+	38.3608i	1.11803	+	1.41400i
$737$			9.52980i			0.351035i
$738$	−0.399331	+	1.85797i	−0.0146996	+	0.0683928i
$739$	−47.2936			−1.73972			−0.869862	−	0.493295i	$-0.835792\pi$
$739$	−47.2936			−1.73972			−0.869862	+	0.493295i	$0.835792\pi$
$740$	−10.6694	−	8.53766i	−0.392214	−	0.313851i
$741$	8.96841	−	26.1972i	0.329463	−	0.962377i
$742$	5.57551	+	11.6024i	0.204683	+	0.425936i
$743$	−22.1430	−	38.3527i	−0.812346	−	1.40703i	−0.911218	−	0.411925i	$-0.864857\pi$
$743$	−22.1430	−	38.3527i	−0.812346	−	1.40703i	0.0988715	−	0.995100i	$-0.468477\pi$
$744$	−33.7548	−	21.0093i	−1.23751	−	0.770239i
$745$	13.0385	−	22.5833i	0.477692	−	0.827387i
$746$	−26.5294	−	2.01032i	−0.971311	−	0.0736031i
$747$	−10.3909	+	13.3975i	−0.380183	+	0.490190i
$748$	7.14903	+	1.08972i	0.261394	+	0.0398442i
$749$	1.18468	−	2.05193i	0.0432874	−	0.0749759i
$750$	25.7342	−	3.05418i	0.939681	−	0.111523i
$751$	−14.6361	+	8.45016i	−0.534079	+	0.308351i	−0.742676	−	0.669651i	$-0.766444\pi$
$751$	−14.6361	+	8.45016i	−0.534079	+	0.308351i	0.208597	+	0.978002i	$0.433110\pi$
$752$	−7.25377	−	32.2760i	−0.264518	−	1.17699i
$753$	6.20838	+	7.11636i	0.226246	+	0.259335i
$754$	29.1081	−	42.6175i	1.06005	−	1.55204i
$755$		−	0.268625i		−	0.00977628i
$756$	9.44616	−	4.33244i	0.343554	−	0.157569i
$757$		−	50.5884i		−	1.83867i	−0.393478	−	0.919334i	$-0.628728\pi$
$757$		−	50.5884i		−	1.83867i	0.393478	−	0.919334i	$-0.371272\pi$
$758$	−20.7528	−	14.1743i	−0.753775	−	0.514835i
$759$	−42.6237	−	48.8575i	−1.54714	−	1.77341i
$760$	−17.7092	+	5.41416i	−0.642381	+	0.196392i
$761$	−23.8383	+	13.7630i	−0.864137	+	0.498910i	−0.865396	−	0.501089i	$-0.832933\pi$
$761$	−23.8383	+	13.7630i	−0.864137	+	0.498910i	0.00125832	+	0.999999i	$0.499599\pi$
$762$	−3.77993	−	31.8493i	−0.136933	−	1.15378i
$763$	7.90601	−	13.6936i	0.286217	−	0.495742i
$764$	46.4755	+	7.08424i	1.68143	+	0.256299i
$765$	−2.21631	−	5.42996i	−0.0801307	−	0.196320i
$766$	−2.50578	+	33.0677i	−0.0905374	+	1.19479i
$767$	−27.6612	+	47.9106i	−0.998787	+	1.72995i
$768$	16.4587	+	22.2960i	0.593901	+	0.804538i
$769$	−15.1192	−	26.1872i	−0.545212	−	0.944334i	−0.998594	−	0.0530180i	$-0.983116\pi$
$769$	−15.1192	−	26.1872i	−0.545212	−	0.944334i	0.453382	−	0.891316i	$-0.350217\pi$
$770$	−12.9219	+	6.20962i	−0.465674	+	0.223779i
$771$	9.56777	−	27.9479i	0.344575	−	1.00652i
$772$	22.5087	−	28.1287i	0.810104	−	1.01238i
$773$	−37.6667			−1.35478			−0.677389	−	0.735625i	$-0.736889\pi$
$773$	−37.6667			−1.35478			−0.677389	+	0.735625i	$0.736889\pi$
$774$	16.8806	+	52.3569i	0.606759	+	1.88193i
$775$		−	3.90364i		−	0.140223i
$776$	15.0928	+	14.0744i	0.541801	+	0.505243i
$777$	0.973311	+	4.96022i	0.0349174	+	0.177947i
$778$	11.0917	−	5.33013i	0.397658	−	0.191094i
$779$	−1.08484	+	0.626335i	−0.0388686	+	0.0224408i
$780$	−24.8652	−	39.1286i	−0.890317	−	1.40103i
$781$	16.8897	+	9.75125i	0.604359	+	0.348927i
$782$	−10.1798	−	0.771398i	−0.364030	−	0.0275851i
$783$	−33.1163	+	1.91247i	−1.18348	+	0.0683462i
$784$	−3.81834	−	1.19175i	−0.136369	−	0.0425623i
$785$	18.8439	+	10.8795i	0.672566	+	0.388306i
$786$	43.8685	−	32.7800i	1.56474	−	1.16922i
$787$	11.8139	+	20.4623i	0.421121	+	0.729403i	0.996049	−	0.0888005i	$-0.0283034\pi$
$787$	11.8139	+	20.4623i	0.421121	+	0.729403i	−0.574928	+	0.818204i	$0.694970\pi$
$788$	3.25601	+	8.33697i	0.115991	+	0.296992i
$789$	5.15112	+	26.2513i	0.183385	+	0.934571i
$790$	−13.9466	+	20.4193i	−0.496197	+	0.726487i
$791$	2.79234			0.0992843
$792$	−23.2237	−	28.4719i	−0.825219	−	1.01170i
$793$	25.2400			0.896298
$794$	15.7481	−	23.0569i	0.558878	−	0.818258i
$795$	−34.9199	−	11.9546i	−1.23848	−	0.423985i
$796$	−25.6506	+	10.0178i	−0.909160	+	0.355073i
$797$	−24.4454	−	42.3407i	−0.865900	−	1.49978i	−0.866150	−	0.499784i	$-0.833413\pi$
$797$	−24.4454	−	42.3407i	−0.865900	−	1.49978i	0.000249782	−	1.00000i	$-0.499920\pi$
$798$	6.29477	+	2.70206i	0.222832	+	0.0956520i
$799$	5.98076	+	3.45299i	0.211584	+	0.122158i
$800$	−1.00460	+	2.52867i	−0.0355179	+	0.0894018i
$801$	−25.8189	−	3.53517i	−0.912267	−	0.124909i
$802$	17.9801	+	1.36248i	0.634898	+	0.0481107i
$803$	10.7012	+	6.17832i	0.377636	+	0.218028i
$804$	−0.323891	−	7.61699i	−0.0114228	−	0.268631i
$805$	17.5276	−	10.1196i	0.617768	−	0.356669i
$806$	59.1370	−	28.4183i	2.08301	−	1.00099i
$807$	16.9822	−	14.8154i	0.597800	−	0.521526i
$808$	14.0871	+	13.1365i	0.495581	+	0.462141i
$809$			42.2224i			1.48446i	0.670144	+	0.742231i	$0.266232\pi$
$809$			42.2224i			1.48446i	−0.670144	+	0.742231i	$0.733768\pi$
$810$	−10.1556	+	28.0140i	−0.356831	+	0.984312i
$811$	27.8380			0.977525			0.488763	−	0.872417i	$-0.337448\pi$
$811$	27.8380			0.977525			0.488763	+	0.872417i	$0.337448\pi$
$812$	9.96892	+	7.97715i	0.349841	+	0.279943i
$813$	13.7688	+	15.7825i	0.482893	+	0.553518i
$814$	16.1080	−	7.74069i	0.564585	−	0.271311i
$815$	27.0672	+	46.8818i	0.948123	+	1.64220i
$816$	−5.75112	−	0.628019i	−0.201329	−	0.0219851i
$817$	−18.1305	+	31.4030i	−0.634306	+	1.09865i
$818$	−2.39222	+	31.5692i	−0.0836421	+	1.10379i
$819$	−2.32644	+	16.9910i	−0.0812922	+	0.593714i
$820$	−0.316045	+	2.07339i	−0.0110368	+	0.0724059i
$821$	−22.0371	+	38.1693i	−0.769099	+	1.33212i	0.168954	+	0.985624i	$0.445961\pi$
$821$	−22.0371	+	38.1693i	−0.769099	+	1.33212i	−0.938052	+	0.346494i	$0.887372\pi$
$822$	−7.86757	−	3.37720i	−0.274413	−	0.117793i
$823$	33.1369	−	19.1316i	1.15508	−	0.666886i	0.204960	−	0.978770i	$-0.434293\pi$
$823$	33.1369	−	19.1316i	1.15508	−	0.666886i	0.950120	+	0.311884i	$0.100960\pi$
$824$	2.73311	+	8.93975i	0.0952124	+	0.311431i
$825$	1.16841	−	3.41298i	0.0406788	−	0.118825i
$826$	−11.3017	−	7.71916i	−0.393236	−	0.268584i
$827$			2.31948i			0.0806562i	0.999186	+	0.0403281i	$0.0128403\pi$
$827$			2.31948i			0.0806562i	−0.999186	+	0.0403281i	$0.987160\pi$
$828$	35.7288	+	37.6022i	1.24166	+	1.30677i
$829$		−	42.7497i		−	1.48476i	−0.669979	−	0.742380i	$-0.733697\pi$
$829$		−	42.7497i		−	1.48476i	0.669979	−	0.742380i	$-0.266303\pi$
$830$	−10.5536	+	15.4516i	−0.366321	+	0.536334i
$831$	30.4689	−	5.97871i	1.05695	−	0.207399i
$832$	−45.6207	+	3.18967i	−1.58161	+	0.110582i
$833$	0.723163	−	0.417519i	0.0250561	−	0.0144662i
$834$	0.733942	+	0.982213i	0.0254143	+	0.0340113i
$835$	7.70355	−	13.3429i	0.266592	−	0.461751i
$836$	3.64954	−	23.9425i	0.126222	−	0.828067i
$837$	−37.6759	−	18.9447i	−1.30227	−	0.654826i
$838$	49.3406	+	3.73888i	1.70444	+	0.129158i
$839$	8.06418	−	13.9676i	0.278406	−	0.482214i	−0.692582	−	0.721339i	$-0.743527\pi$
$839$	8.06418	−	13.9676i	0.278406	−	0.482214i	0.970989	+	0.239125i	$0.0768605\pi$
$840$	10.1172	−	5.40241i	0.349077	−	0.186401i
$841$	−5.87678	−	10.1789i	−0.202648	−	0.350996i
$842$	15.0422	+	31.3020i	0.518387	+	1.07874i
$843$	−13.0382	+	2.55840i	−0.449059	+	0.0881158i
$844$	−9.46535	+	11.8287i	−0.325811	+	0.407161i
$845$	46.0704			1.58487
$846$	−10.7670	−	33.3950i	−0.370177	−	1.14814i
$847$		−	7.74984i		−	0.266288i
$848$	−26.7720	+	24.6753i	−0.919353	+	0.847354i
$849$	32.8407	+	11.2428i	1.12709	+	0.385852i
$850$	−0.246027	−	0.511970i	−0.00843864	−	0.0175604i
$851$	−21.8493	+	12.6147i	−0.748986	+	0.432427i
$852$	−13.8310	−	7.21995i	−0.473842	−	0.247352i
$853$	19.0349	+	10.9898i	0.651744	+	0.376284i	0.789124	−	0.614234i	$-0.210535\pi$
$853$	19.0349	+	10.9898i	0.651744	+	0.376284i	−0.137380	+	0.990518i	$0.543868\pi$
$854$	−0.471810	+	6.22629i	−0.0161450	+	0.213059i
$855$	−18.1852	+	7.42252i	−0.621921	+	0.253845i
$856$	6.52981	+	1.50756i	0.223184	+	0.0515273i
$857$	12.1589	+	7.01997i	0.415342	+	0.239798i	0.693082	−	0.720859i	$-0.256252\pi$
$857$	12.1589	+	7.01997i	0.415342	+	0.239798i	−0.277741	+	0.960656i	$0.589586\pi$
$858$	60.2099	−	7.14582i	2.05553	−	0.243954i
$859$	−17.3533	−	30.0567i	−0.592085	−	1.02552i	−0.993951	−	0.109823i	$-0.964972\pi$
$859$	−17.3533	−	30.0567i	−0.592085	−	1.02552i	0.401866	−	0.915699i	$-0.368362\pi$
$860$	22.0863	+	56.5517i	0.753136	+	1.92840i
$861$	0.584626	−	0.510032i	0.0199240	−	0.0173819i
$862$	0.228037	+	0.155751i	0.00776696	+	0.00530491i
$863$	−25.5333			−0.869163			−0.434581	−	0.900633i	$-0.643104\pi$
$863$	−25.5333			−0.869163			−0.434581	+	0.900633i	$0.643104\pi$
$864$	19.5300	+	21.9677i	0.664423	+	0.747357i
$865$	−1.96959			−0.0669682
$866$	−26.4109	−	18.0389i	−0.897477	−	0.612985i
$867$	−21.2779	+	18.5630i	−0.722636	+	0.630434i
$868$	5.90488	+	15.1194i	0.200425	+	0.513185i
$869$	−16.1699	−	28.0070i	−0.548525	−	0.950074i
$870$	−36.3539	+	4.31454i	−1.23251	+	0.146277i
$871$	10.8955	+	6.29051i	0.369180	+	0.213146i
$872$	43.5769	+	10.0607i	1.47570	+	0.340699i
$873$	17.2963	+	13.4147i	0.585392	+	0.454020i
$874$	−2.58345	+	34.0928i	−0.0873866	+	1.15321i
$875$	−9.16227	−	5.28984i	−0.309741	−	0.178829i
$876$	−8.76322	−	4.57451i	−0.296082	−	0.154558i
$877$	15.5078	−	8.95342i	0.523661	−	0.302336i	−0.214770	−	0.976665i	$-0.568900\pi$
$877$	15.5078	−	8.95342i	0.523661	−	0.302336i	0.738431	+	0.674329i	$0.235567\pi$
$878$	−9.21435	−	19.1746i	−0.310969	−	0.647112i
$879$	−7.80118	−	2.67068i	−0.263127	−	0.0900797i
$880$	−27.4817	−	29.8168i	−0.926408	−	1.00512i
$881$		−	30.2200i		−	1.01814i	−0.860726	−	0.509069i	$-0.829990\pi$
$881$		−	30.2200i		−	1.01814i	0.860726	−	0.509069i	$-0.170010\pi$
$882$	−4.14792	−	0.891506i	−0.139668	−	0.0300186i
$883$	30.6286			1.03073			0.515367	−	0.856970i	$-0.327656\pi$
$883$	30.6286			1.03073			0.515367	+	0.856970i	$0.327656\pi$
$884$	5.96488	−	7.45422i	0.200621	−	0.250713i
$885$	38.5084	−	7.55626i	1.29445	−	0.254001i
$886$	8.35161	+	17.3793i	0.280578	+	0.583869i
$887$	0.740240	+	1.28213i	0.0248548	+	0.0430498i	0.878185	−	0.478321i	$-0.158754\pi$
$887$	0.740240	+	1.28213i	0.0248548	+	0.0430498i	−0.853330	+	0.521370i	$0.825421\pi$
$888$	−12.6117	+	6.73445i	−0.423222	+	0.225993i
$889$	−6.54684	+	11.3395i	−0.219574	+	0.380314i
$890$	−28.6782	−	2.17315i	−0.961295	−	0.0728441i
$891$	−27.2699	−	27.8404i	−0.913577	−	0.932689i
$892$	2.31746	−	15.2035i	0.0775945	−	0.509052i
$893$	11.5643	−	20.0299i	0.386983	−	0.670274i
$894$	−16.3314	−	21.8559i	−0.546205	−	0.730971i
$895$	−29.1576	+	16.8341i	−0.974630	+	0.562703i
$896$	0.0659460	−	11.3135i	0.00220310	−	0.377958i
$897$	−83.9945	+	16.4817i	−2.80450	+	0.550308i
$898$	−11.8833	+	17.3984i	−0.396549	+	0.580592i
$899$		−	51.8099i		−	1.72796i
$900$	−0.817890	+	2.76764i	−0.0272630	+	0.0922547i
$901$		−	7.60070i		−	0.253216i
$902$	−2.26507	−	1.54706i	−0.0754185	−	0.0515115i
$903$	7.27393	−	21.2475i	0.242061	−	0.707072i
$904$	2.30910	+	7.55285i	0.0767994	+	0.251204i
$905$	1.60578	−	0.927095i	0.0533778	−	0.0308177i
$906$	−0.258267	−	0.110863i	−0.00858036	−	0.00368317i
$907$	−14.2045	+	24.6029i	−0.471653	+	0.816927i	−0.999474	−	0.0324289i	$-0.989676\pi$
$907$	−14.2045	+	24.6029i	−0.471653	+	0.816927i	0.527821	+	0.849355i	$0.323009\pi$
$908$	3.38272	−	22.1920i	0.112259	−	0.736468i
$909$	16.1437	+	12.5208i	0.535453	+	0.415288i
$910$	−1.43011	+	18.8726i	−0.0474078	+	0.625622i
$911$	−5.37955	+	9.31766i	−0.178233	+	0.308708i	−0.941275	−	0.337640i	$-0.890371\pi$
$911$	−5.37955	+	9.31766i	−0.178233	+	0.308708i	0.763043	+	0.646348i	$0.223705\pi$
$912$	−2.10327	+	19.2608i	−0.0696462	+	0.637789i
$913$	−12.2360	−	21.1934i	−0.404952	−	0.701398i
$914$	−24.6962	+	11.8677i	−0.816877	+	0.392549i
$915$	−11.7700	−	13.4914i	−0.389104	−	0.446011i
$916$	26.8634	+	21.4961i	0.887592	+	0.710253i
$917$	−22.3569			−0.738289
$918$	−6.13526	−	0.110117i	−0.202494	−	0.00363441i
$919$		−	27.2186i		−	0.897860i	−0.893567	−	0.448930i	$-0.851805\pi$
$919$		−	27.2186i		−	0.897860i	0.893567	−	0.448930i	$-0.148195\pi$
$920$	41.8662	+	39.0412i	1.38029	+	1.28715i
$921$	−12.0435	+	10.5069i	−0.396848	+	0.346213i
$922$	49.6528	−	23.8606i	1.63523	−	0.785807i
$923$	22.2973	−	12.8734i	0.733926	−	0.423732i
$924$	0.637254	+	14.9864i	0.0209641	+	0.493016i
$925$	−1.21567	−	0.701866i	−0.0399709	−	0.0230772i
$926$	−43.9836	−	3.33295i	−1.44539	−	0.109527i
$927$	3.74695	+	9.18004i	0.123066	+	0.301512i
$928$	−13.3332	+	33.5610i	−0.437685	+	1.10169i
$929$	4.70377	+	2.71572i	0.154326	+	0.0891000i	0.575174	−	0.818031i	$-0.304934\pi$
$929$	4.70377	+	2.71572i	0.154326	+	0.0891000i	−0.420848	+	0.907131i	$0.638268\pi$
$930$	−42.7673	−	18.3581i	−1.40239	−	0.601985i
$931$	−1.39829	−	2.42191i	−0.0458271	−	0.0793750i
$932$	1.53766	−	0.600534i	0.0503678	−	0.0196711i
$933$	28.3799	+	9.71565i	0.929116	+	0.318076i
$934$	−29.0241	+	42.4944i	−0.949697	+	1.39046i
$935$	8.46514			0.276840
$936$	−47.8818	+	7.75788i	−1.56507	+	0.253574i
$937$	39.5722			1.29277			0.646383	−	0.763013i	$-0.276281\pi$
$937$	39.5722			1.29277			0.646383	+	0.763013i	$0.276281\pi$
$938$	−1.75544	+	2.57015i	−0.0573170	+	0.0839185i
$939$	−6.14533	−	31.3180i	−0.200545	−	1.02203i
$940$	−14.0874	−	36.0706i	−0.459480	−	1.17649i
$941$	18.9698	+	32.8567i	0.618399	+	1.07110i	0.989778	+	0.142618i	$0.0455519\pi$
$941$	18.9698	+	32.8567i	0.618399	+	1.07110i	−0.371378	+	0.928482i	$0.621115\pi$
$942$	18.2369	−	13.6272i	0.594191	−	0.443999i
$943$	3.35353	+	1.93616i	0.109206	+	0.0630502i
$944$	11.5333	−	36.9526i	0.375377	−	1.20270i
$945$	10.1670	−	6.67977i	0.330732	−	0.217293i
$946$	−79.1740	−	5.99957i	−2.57417	−	0.195063i
$947$	37.8999	+	21.8815i	1.23158	+	0.711054i	0.967359	−	0.253408i	$-0.0815516\pi$
$947$	37.8999	+	21.8815i	1.23158	+	0.711054i	0.264222	+	0.964462i	$0.414885\pi$
$948$	13.8762	+	21.8359i	0.450676	+	0.709198i
$949$	14.1274	−	8.15648i	0.458596	−	0.264770i
$950$	−1.71461	+	0.823956i	−0.0556294	+	0.0267327i
$951$	−2.98803	−	15.2277i	−0.0968935	−	0.493792i
$952$	1.72733	+	1.61078i	0.0559832	+	0.0522057i
$953$			31.3940i			1.01695i	0.861077	+	0.508475i	$0.169791\pi$
$953$			31.3940i			1.01695i	−0.861077	+	0.508475i	$0.830209\pi$
$954$	−25.9052	+	28.6397i	−0.838711	+	0.927245i
$955$	55.0315			1.78078
$956$	−2.77939	+	3.47336i	−0.0898919	+	0.112337i
$957$	15.5074	−	45.2978i	0.501282	−	1.46427i
$958$	7.10079	−	3.41228i	0.229416	−	0.110246i
$959$	1.74767	+	3.02705i	0.0564351	+	0.0977484i
$960$	22.9790	+	22.8980i	0.741644	+	0.739029i
$961$	17.4329	−	30.1946i	0.562350	−	0.974019i
$962$	1.78273	−	23.5259i	0.0574774	−	0.758507i
$963$	7.04239	+	0.964255i	0.226938	+	0.0310727i
$964$	2.59948	+	0.396238i	0.0837237	+	0.0127620i
$965$	21.0855	−	36.5212i	0.678767	−	1.17566i
$966$	−2.49566	−	21.0282i	−0.0802965	−	0.676571i
$967$	−11.4126	+	6.58908i	−0.367005	+	0.211891i	−0.672149	−	0.740416i	$-0.734629\pi$
$967$	−11.4126	+	6.58908i	−0.367005	+	0.211891i	0.305144	+	0.952306i	$0.401295\pi$
$968$	20.9621	−	6.40865i	0.673747	−	0.205982i
$969$	−2.65903	−	3.04791i	−0.0854202	−	0.0979131i
$970$	19.9482	+	13.6248i	0.640498	+	0.437466i
$971$			1.71689i			0.0550975i	0.999620	+	0.0275488i	$0.00877015\pi$
$971$			1.71689i			0.0550975i	−0.999620	+	0.0275488i	$0.991230\pi$
$972$	22.7425	+	21.3255i	0.729468	+	0.684015i
$973$		−	0.500569i		−	0.0160475i
$974$	−31.3259	+	45.8646i	−1.00375	+	1.46960i
$975$	−3.13083	−	3.58872i	−0.100267	−	0.114931i
$976$	−17.2313	+	3.87259i	−0.551560	+	0.123959i
$977$	41.3893	−	23.8961i	1.32416	−	0.764505i	0.339772	−	0.940508i	$-0.389650\pi$
$977$	41.3893	−	23.8961i	1.32416	−	0.764505i	0.984390	+	0.176003i	$0.0563167\pi$
$978$	56.2448	−	6.67523i	1.79851	−	0.213450i
$979$	18.8070	−	32.5747i	0.601074	−	1.04109i
$980$	−4.62884	−	0.705571i	−0.147863	−	0.0225386i
$981$	46.9976	+	6.43498i	1.50052	+	0.205453i
$982$	12.5297	+	0.949465i	0.399839	+	0.0302987i
$983$	−1.26090	+	2.18395i	−0.0402166	+	0.0696572i	−0.885433	−	0.464767i	$-0.846138\pi$
$983$	−1.26090	+	2.18395i	−0.0402166	+	0.0696572i	0.845216	+	0.534424i	$0.179471\pi$
$984$	1.86301	+	1.15955i	0.0593905	+	0.0369652i
$985$	5.23847	+	9.07329i	0.166911	+	0.289099i
$986$	−3.26532	−	6.79497i	−0.103989	−	0.216396i
$987$	−4.63956	+	13.5524i	−0.147679	+	0.431377i
$988$	−24.9646	−	19.9767i	−0.794229	−	0.635543i
$989$	112.092			3.56433
$990$	−31.8969	−	28.8514i	−1.01375	−	0.916959i
$991$		−	6.56996i		−	0.208702i	−0.994541	−	0.104351i	$-0.966724\pi$
$991$		−	6.56996i		−	0.208702i	0.994541	−	0.104351i	$-0.0332765\pi$
$992$	−36.0125	+	28.4746i	−1.14340	+	0.904068i
$993$	−0.723976	−	3.68955i	−0.0229747	−	0.117084i
$994$	2.75885	+	5.74103i	0.0875054	+	0.182095i
$995$	−27.9160	+	16.1173i	−0.884997	+	0.510953i
$996$	10.5003	+	16.5236i	0.332715	+	0.523570i
$997$	−36.4440	−	21.0410i	−1.15419	−	0.666374i	−0.204288	−	0.978911i	$-0.565488\pi$
$997$	−36.4440	−	21.0410i	−1.15419	−	0.666374i	−0.949906	+	0.312537i	$0.898821\pi$
$998$	−0.876757	+	11.5702i	−0.0277532	+	0.366249i
$999$	−12.6738	+	8.32676i	−0.400981	+	0.263447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.br.a.155.14	yes	144
8.3	odd	2	inner	504.2.br.a.155.11	✓	144
9.5	odd	6	inner	504.2.br.a.491.11	yes	144
72.59	even	6	inner	504.2.br.a.491.14	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.br.a.155.11	✓	144	8.3	odd	2	inner
504.2.br.a.155.14	yes	144	1.1	even	1	trivial
504.2.br.a.491.11	yes	144	9.5	odd	6	inner
504.2.br.a.491.14	yes	144	72.59	even	6	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.br (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16781 - 0.797628i) q^{2} +(-1.30518 + 1.13865i) q^{3} +(0.727580 + 1.86296i) q^{4} +(1.17058 + 2.02750i) q^{5} +(2.43242 - 0.288684i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(0.636271 - 2.75593i) q^{8} +(0.406968 - 2.97227i) q^{9} +O(q^{10})\)	\(q+(-1.16781 - 0.797628i) q^{2} +(-1.30518 + 1.13865i) q^{3} +(0.727580 + 1.86296i) q^{4} +(1.17058 + 2.02750i) q^{5} +(2.43242 - 0.288684i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(0.636271 - 2.75593i) q^{8} +(0.406968 - 2.97227i) q^{9} +(0.250172 - 3.30142i) q^{10} +(3.74998 + 2.16505i) q^{11} +(-3.07088 - 1.60304i) q^{12} +(4.95064 - 2.85826i) q^{13} +(0.612543 + 1.27467i) q^{14} +(-3.83641 - 1.31337i) q^{15} +(-2.94125 + 2.71091i) q^{16} -0.835037i q^{17} +(-2.84603 + 3.14645i) q^{18} -2.79658 q^{19} +(-2.92546 + 3.65591i) q^{20} +(1.69964 - 0.333509i) q^{21} +(-2.65238 - 5.51947i) q^{22} +(4.32248 + 7.48676i) q^{23} +(2.30759 + 4.32146i) q^{24} +(-0.240497 + 0.416553i) q^{25} +(-8.06126 - 0.610858i) q^{26} +(2.85320 + 4.34272i) q^{27} +(0.301378 - 1.97716i) q^{28} +(-3.19193 + 5.52858i) q^{29} +(3.43264 + 4.59380i) q^{30} +(-7.02846 + 4.05788i) q^{31} +(5.59713 - 0.819814i) q^{32} +(-7.35962 + 1.44413i) q^{33} +(-0.666049 + 0.975168i) q^{34} -2.34115i q^{35} +(5.83332 - 1.40440i) q^{36} +2.91840i q^{37} +(3.26589 + 2.23063i) q^{38} +(-3.20692 + 9.36756i) q^{39} +(6.33245 - 1.93599i) q^{40} +(0.387918 - 0.223964i) q^{41} +(-2.25088 - 0.966202i) q^{42} +(6.48309 - 11.2290i) q^{43} +(-1.30500 + 8.56133i) q^{44} +(6.50265 - 2.65414i) q^{45} +(0.923789 - 12.1909i) q^{46} +(-4.13514 + 7.16227i) q^{47} +(0.752085 - 6.88726i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.613110 - 0.294630i) q^{50} +(0.950812 + 1.08987i) q^{51} +(8.92681 + 7.14325i) q^{52} +9.10223 q^{53} +(0.131871 - 7.34729i) q^{54} +10.1374i q^{55} +(-1.92899 + 2.06857i) q^{56} +(3.65003 - 3.18432i) q^{57} +(8.13732 - 3.91038i) q^{58} +(-8.38108 + 4.83882i) q^{59} +(-0.344543 - 8.10267i) q^{60} +(3.82374 + 2.20764i) q^{61} +(11.4446 + 0.867240i) q^{62} +(-1.83858 + 2.37058i) q^{63} +(-7.19032 - 3.50704i) q^{64} +(11.5902 + 6.69161i) q^{65} +(9.74655 + 4.18376i) q^{66} +(1.10041 + 1.90597i) q^{67} +(1.55564 - 0.607557i) q^{68} +(-14.1664 - 4.84976i) q^{69} +(-1.86737 + 2.73403i) q^{70} +4.50393 q^{71} +(-7.93243 - 3.01274i) q^{72} +2.85366 q^{73} +(2.32779 - 3.40814i) q^{74} +(-0.160416 - 0.817516i) q^{75} +(-2.03474 - 5.20993i) q^{76} +(-2.16505 - 3.74998i) q^{77} +(11.2169 - 8.38164i) q^{78} +(-6.46798 - 3.73429i) q^{79} +(-8.93932 - 2.79006i) q^{80} +(-8.66875 - 2.41923i) q^{81} +(-0.631656 - 0.0478650i) q^{82} +(-4.89442 - 2.82579i) q^{83} +(1.85794 + 2.92371i) q^{84} +(1.69304 - 0.977475i) q^{85} +(-16.5276 + 7.94235i) q^{86} +(-2.12907 - 10.8502i) q^{87} +(8.35275 - 8.95714i) q^{88} -8.68661i q^{89} +(-9.71091 - 2.08715i) q^{90} -5.71651 q^{91} +(-10.8026 + 13.4998i) q^{92} +(4.55288 - 13.2992i) q^{93} +(10.5419 - 5.06590i) q^{94} +(-3.27361 - 5.67006i) q^{95} +(-6.37177 + 7.44316i) q^{96} +(-3.64813 + 6.31875i) q^{97} +(0.106859 - 1.41017i) q^{98} +(7.96124 - 10.2649i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{6}+O(q^{10}) \) 144 * q + 6 * q^6	\( 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) \) 144 * q + 6 * q^6 - 12 * q^12 + 34 * q^18 - 42 * q^20 - 30 * q^24 - 72 * q^25 + 24 * q^27 - 36 * q^30 - 30 * q^32 - 16 * q^33 + 12 * q^34 - 12 * q^36 + 12 * q^40 + 24 * q^41 - 20 * q^42 - 24 * q^46 - 24 * q^48 + 72 * q^49 - 78 * q^50 + 18 * q^52 + 10 * q^54 + 8 * q^57 - 18 * q^58 - 72 * q^59 + 88 * q^60 - 12 * q^64 + 2 * q^66 + 78 * q^68 + 42 * q^72 + 84 * q^74 - 112 * q^75 + 12 * q^76 + 112 * q^78 - 8 * q^81 - 36 * q^82 - 14 * q^84 + 30 * q^86 + 24 * q^88 + 104 * q^90 - 114 * q^92 - 42 * q^94 - 80 * q^96 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more