LMFDB - Embedded newform 585.2.bt.b.376.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.4
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24228 - 1.29458i) q^{2} +(-0.927160 + 1.46300i) q^{3} +(2.35187 + 4.07355i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(3.97292 - 2.08017i) q^{6} +(-1.32705 - 0.766174i) q^{7} -7.00039i q^{8} +(-1.28075 - 2.71287i) q^{9} +O(q^{10})$	\(q+(-2.24228 - 1.29458i) q^{2} +(-0.927160 + 1.46300i) q^{3} +(2.35187 + 4.07355i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(3.97292 - 2.08017i) q^{6} +(-1.32705 - 0.766174i) q^{7} -7.00039i q^{8} +(-1.28075 - 2.71287i) q^{9} +2.58916 q^{10} +(0.217487 + 0.125566i) q^{11} +(-8.14017 - 0.336050i) q^{12} +(0.215952 + 3.59908i) q^{13} +(1.98374 + 3.43595i) q^{14} +(0.0714432 - 1.73058i) q^{15} +(-4.35882 + 7.54970i) q^{16} -5.82409 q^{17} +(-0.640236 + 7.74104i) q^{18} +4.62116i q^{19} +(-4.07355 - 2.35187i) q^{20} +(2.35130 - 1.23111i) q^{21} +(-0.325111 - 0.563109i) q^{22} +(-1.46375 - 2.53529i) q^{23} +(10.2416 + 6.49048i) q^{24} +(0.500000 - 0.866025i) q^{25} +(4.17507 - 8.34969i) q^{26} +(5.15640 + 0.641531i) q^{27} -7.20776i q^{28} +(2.12701 - 3.68409i) q^{29} +(-2.40056 + 3.78794i) q^{30} +(0.0701012 - 0.0404730i) q^{31} +(7.42234 - 4.28529i) q^{32} +(-0.385350 + 0.201764i) q^{33} +(13.0592 + 7.53974i) q^{34} +1.53235 q^{35} +(8.03889 - 11.5975i) q^{36} -3.43139i q^{37} +(5.98246 - 10.3619i) q^{38} +(-5.46568 - 3.02098i) q^{39} +(3.50020 + 6.06252i) q^{40} +(7.46133 - 4.30780i) q^{41} +(-6.86605 - 0.283450i) q^{42} +(2.97325 - 5.14982i) q^{43} +1.18126i q^{44} +(2.46560 + 1.70904i) q^{45} +7.57977i q^{46} +(-3.97219 - 2.29334i) q^{47} +(-7.00390 - 13.3768i) q^{48} +(-2.32595 - 4.02867i) q^{49} +(-2.24228 + 1.29458i) q^{50} +(5.39986 - 8.52066i) q^{51} +(-14.1531 + 9.34425i) q^{52} +5.86094 q^{53} +(-10.7316 - 8.11385i) q^{54} -0.251133 q^{55} +(-5.36352 + 9.28989i) q^{56} +(-6.76077 - 4.28456i) q^{57} +(-9.53869 + 5.50717i) q^{58} +(-7.40522 + 4.27541i) q^{59} +(7.21762 - 3.77906i) q^{60} +(-0.243390 + 0.421564i) q^{61} -0.209582 q^{62} +(-0.378913 + 4.58140i) q^{63} -4.75527 q^{64} +(-1.98656 - 3.00892i) q^{65} +(1.12526 + 0.0464540i) q^{66} +(3.56745 - 2.05967i) q^{67} +(-13.6975 - 23.7247i) q^{68} +(5.06627 + 0.209150i) q^{69} +(-3.43595 - 1.98374i) q^{70} -7.73670i q^{71} +(-18.9912 + 8.96574i) q^{72} -14.7204i q^{73} +(-4.44221 + 7.69413i) q^{74} +(0.803417 + 1.53445i) q^{75} +(-18.8246 + 10.8684i) q^{76} +(-0.192411 - 0.333266i) q^{77} +(8.34466 + 13.8496i) q^{78} +(6.91417 - 11.9757i) q^{79} -8.71765i q^{80} +(-5.71937 + 6.94902i) q^{81} -22.3072 q^{82} +(11.8235 + 6.82628i) q^{83} +(10.5450 + 6.68274i) q^{84} +(5.04381 - 2.91205i) q^{85} +(-13.3337 + 7.69821i) q^{86} +(3.41775 + 6.52756i) q^{87} +(0.879014 - 1.52250i) q^{88} +5.99700i q^{89} +(-3.31606 - 7.02406i) q^{90} +(2.47094 - 4.94162i) q^{91} +(6.88510 - 11.9254i) q^{92} +(-0.00578304 + 0.140083i) q^{93} +(5.93783 + 10.2846i) q^{94} +(-2.31058 - 4.00205i) q^{95} +(-0.612310 + 14.8320i) q^{96} +(-7.77220 - 4.48728i) q^{97} +12.0445i q^{98} +(0.0620991 - 0.750835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−2.24228	−	1.29458i	−1.58553	−	0.915405i	−0.994031	−	0.109098i	$-0.965204\pi$
$2$	−2.24228	−	1.29458i	−1.58553	−	0.915405i	−0.591497	−	0.806307i	$-0.701463\pi$
$3$	−0.927160	+	1.46300i	−0.535296	+	0.844664i
$3$	−0.927160	+	1.46300i	−0.535296	+	0.844664i
$4$	2.35187	+	4.07355i	1.17593	+	2.03678i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	3.97292	−	2.08017i	1.62194	−	0.849227i
$7$	−1.32705	−	0.766174i	−0.501579	−	0.289587i	0.227787	−	0.973711i	$-0.426851\pi$
$7$	−1.32705	−	0.766174i	−0.501579	−	0.289587i	−0.729365	+	0.684125i	$0.760184\pi$
$8$		−	7.00039i		−	2.47501i
$9$	−1.28075	−	2.71287i	−0.426916	−	0.904291i
$10$	2.58916			0.818763
$11$	0.217487	+	0.125566i	0.0655749	+	0.0378597i	0.532429	−	0.846475i	$-0.321279\pi$
$11$	0.217487	+	0.125566i	0.0655749	+	0.0378597i	−0.466854	+	0.884334i	$0.654613\pi$
$12$	−8.14017	−	0.336050i	−2.34987	−	0.0970093i
$13$	0.215952	+	3.59908i	0.0598943	+	0.998205i
$13$	0.215952	+	3.59908i	0.0598943	+	0.998205i
$14$	1.98374	+	3.43595i	0.530178	+	0.918295i
$15$	0.0714432	−	1.73058i	0.0184466	−	0.446833i
$16$	−4.35882	+	7.54970i	−1.08971	+	1.88743i
$17$	−5.82409			−1.41255			−0.706275	−	0.707938i	$-0.749626\pi$
$17$	−5.82409			−1.41255			−0.706275	+	0.707938i	$0.749626\pi$
$18$	−0.640236	+	7.74104i	−0.150905	+	1.82458i
$19$			4.62116i			1.06017i	0.847945	+	0.530084i	$0.177840\pi$
$19$			4.62116i			1.06017i	−0.847945	+	0.530084i	$0.822160\pi$
$20$	−4.07355	−	2.35187i	−0.910874	−	0.525893i
$21$	2.35130	−	1.23111i	0.513097	−	0.268651i
$22$	−0.325111	−	0.563109i	−0.0693139	−	0.120055i
$23$	−1.46375	−	2.53529i	−0.305214	−	0.528645i	0.672095	−	0.740465i	$-0.265395\pi$
$23$	−1.46375	−	2.53529i	−0.305214	−	0.528645i	−0.977309	+	0.211819i	$0.932061\pi$
$24$	10.2416	+	6.49048i	2.09056	+	1.32486i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	4.17507	−	8.34969i	0.818798	−	1.63751i
$27$	5.15640	+	0.641531i	0.992349	+	0.123463i
$28$		−	7.20776i		−	1.36214i
$29$	2.12701	−	3.68409i	0.394976	−	0.684119i	−0.598122	−	0.801405i	$-0.704086\pi$
$29$	2.12701	−	3.68409i	0.394976	−	0.684119i	0.993098	+	0.117286i	$0.0374196\pi$
$30$	−2.40056	+	3.78794i	−0.438281	+	0.691580i
$31$	0.0701012	−	0.0404730i	0.0125906	−	0.00726916i	−0.493692	−	0.869637i	$-0.664353\pi$
$31$	0.0701012	−	0.0404730i	0.0125906	−	0.00726916i	0.506282	+	0.862368i	$0.331019\pi$
$32$	7.42234	−	4.28529i	1.31210	−	0.757539i
$33$	−0.385350	+	0.201764i	−0.0670808	+	0.0351227i
$34$	13.0592	+	7.53974i	2.23964	+	1.29306i
$35$	1.53235			0.259014
$36$	8.03889	−	11.5975i	1.33981	−	1.93292i
$37$		−	3.43139i		−	0.564117i	−0.959397	−	0.282059i	$-0.908983\pi$
$37$		−	3.43139i		−	0.564117i	0.959397	−	0.282059i	$-0.0910173\pi$
$38$	5.98246	−	10.3619i	0.970483	−	1.68093i
$39$	−5.46568	−	3.02098i	−0.875209	−	0.483744i
$40$	3.50020	+	6.06252i	0.553430	+	0.958568i
$41$	7.46133	−	4.30780i	1.16526	−	0.672766i	0.212704	−	0.977117i	$-0.431773\pi$
$41$	7.46133	−	4.30780i	1.16526	−	0.672766i	0.952560	+	0.304351i	$0.0984395\pi$
$42$	−6.86605	−	0.283450i	−1.05945	−	0.0437373i
$43$	2.97325	−	5.14982i	0.453417	−	0.785340i	−0.545179	−	0.838320i	$-0.683538\pi$
$43$	2.97325	−	5.14982i	0.453417	−	0.785340i	0.998596	+	0.0529792i	$0.0168717\pi$
$44$			1.18126i			0.178082i
$45$	2.46560	+	1.70904i	0.367550	+	0.254769i
$46$			7.57977i			1.11758i
$47$	−3.97219	−	2.29334i	−0.579403	−	0.334518i	0.181493	−	0.983392i	$-0.441907\pi$
$47$	−3.97219	−	2.29334i	−0.579403	−	0.334518i	−0.760896	+	0.648874i	$0.775240\pi$
$48$	−7.00390	−	13.3768i	−1.01093	−	1.93077i
$49$	−2.32595	−	4.02867i	−0.332279	−	0.575525i
$50$	−2.24228	+	1.29458i	−0.317106	+	0.183081i
$51$	5.39986	−	8.52066i	0.756132	−	1.19313i
$52$	−14.1531	+	9.34425i	−1.96269	+	1.29581i
$53$	5.86094			0.805063			0.402531	−	0.915406i	$-0.368130\pi$
$53$	5.86094			0.805063			0.402531	+	0.915406i	$0.368130\pi$
$54$	−10.7316	−	8.11385i	−1.46038	−	1.10416i
$55$	−0.251133			−0.0338627
$56$	−5.36352	+	9.28989i	−0.716730	+	1.24141i
$57$	−6.76077	−	4.28456i	−0.895486	−	0.567504i
$58$	−9.53869	+	5.50717i	−1.25249	+	0.723126i
$59$	−7.40522	+	4.27541i	−0.964077	+	0.556610i	−0.897426	−	0.441166i	$-0.854565\pi$
$59$	−7.40522	+	4.27541i	−0.964077	+	0.556610i	−0.0666519	+	0.997776i	$0.521232\pi$
$60$	7.21762	−	3.77906i	0.931791	−	0.487874i
$61$	−0.243390	+	0.421564i	−0.0311629	+	0.0539758i	−0.881186	−	0.472769i	$-0.843254\pi$
$61$	−0.243390	+	0.421564i	−0.0311629	+	0.0539758i	0.850023	+	0.526745i	$0.176588\pi$
$62$	−0.209582			−0.0266169
$63$	−0.378913	+	4.58140i	−0.0477385	+	0.577202i
$64$	−4.75527			−0.594408
$65$	−1.98656	−	3.00892i	−0.246402	−	0.373210i
$66$	1.12526	+	0.0464540i	0.138510	+	0.00571809i
$67$	3.56745	−	2.05967i	0.435833	−	0.251628i	−0.265995	−	0.963974i	$-0.585701\pi$
$67$	3.56745	−	2.05967i	0.435833	−	0.251628i	0.701829	+	0.712346i	$0.252367\pi$
$68$	−13.6975	−	23.7247i	−1.66106	−	2.87705i
$69$	5.06627	+	0.209150i	0.609908	+	0.0251788i
$70$	−3.43595	−	1.98374i	−0.410674	−	0.237103i
$71$		−	7.73670i		−	0.918177i	−0.888391	−	0.459088i	$-0.848176\pi$
$71$		−	7.73670i		−	0.918177i	0.888391	−	0.459088i	$-0.151824\pi$
$72$	−18.9912	+	8.96574i	−2.23813	+	1.05662i
$73$		−	14.7204i		−	1.72289i	−0.507853	−	0.861443i	$-0.669561\pi$
$73$		−	14.7204i		−	1.72289i	0.507853	−	0.861443i	$-0.330439\pi$
$74$	−4.44221	+	7.69413i	−0.516396	+	0.894424i
$75$	0.803417	+	1.53445i	0.0927706	+	0.177182i
$76$	−18.8246	+	10.8684i	−2.15933	+	1.24669i
$77$	−0.192411	−	0.333266i	−0.0219273	−	0.0379792i
$78$	8.34466	+	13.8496i	0.944847	+	1.56816i
$79$	6.91417	−	11.9757i	0.777905	−	1.34737i	−0.155243	−	0.987876i	$-0.549616\pi$
$79$	6.91417	−	11.9757i	0.777905	−	1.34737i	0.933147	−	0.359494i	$-0.117051\pi$
$80$		−	8.71765i		−	0.974663i
$81$	−5.71937	+	6.94902i	−0.635485	+	0.772113i
$82$	−22.3072			−2.46341
$83$	11.8235	+	6.82628i	1.29779	+	0.749281i	0.980023	−	0.198886i	$-0.0637325\pi$
$83$	11.8235	+	6.82628i	1.29779	+	0.749281i	0.317771	+	0.948168i	$0.397066\pi$
$84$	10.5450	+	6.68274i	1.15055	+	0.729147i
$85$	5.04381	−	2.91205i	0.547078	−	0.315856i
$86$	−13.3337	+	7.69821i	−1.43781	+	0.830120i
$87$	3.41775	+	6.52756i	0.366422	+	0.699828i
$88$	0.879014	−	1.52250i	0.0937032	−	0.162299i
$89$			5.99700i			0.635681i	0.948144	+	0.317840i	$0.102958\pi$
$89$			5.99700i			0.635681i	−0.948144	+	0.317840i	$0.897042\pi$
$90$	−3.31606	−	7.02406i	−0.349543	−	0.740401i
$91$	2.47094	−	4.94162i	0.259025	−	0.518023i
$92$	6.88510	−	11.9254i	0.717822	−	1.24330i
$93$	−0.00578304	+	0.140083i	−0.000599673	+	0.0145259i
$94$	5.93783	+	10.2846i	0.612440	+	1.06078i
$95$	−2.31058	−	4.00205i	−0.237061	−	0.410601i
$96$	−0.612310	+	14.8320i	−0.0624936	+	1.51379i
$97$	−7.77220	−	4.48728i	−0.789147	−	0.455615i	0.0505148	−	0.998723i	$-0.483914\pi$
$97$	−7.77220	−	4.48728i	−0.789147	−	0.455615i	−0.839662	+	0.543109i	$0.817247\pi$
$98$			12.0445i			1.21668i
$99$	0.0620991	−	0.750835i	0.00624120	−	0.0754618i
$100$	4.70373			0.470373
$101$	−7.62086	+	13.1997i	−0.758304	+	1.31342i	0.185411	+	0.982661i	$0.440638\pi$
$101$	−7.62086	+	13.1997i	−0.758304	+	1.31342i	−0.943715	+	0.330760i	$0.892695\pi$
$102$	−23.1386	+	12.1151i	−2.29107	+	1.19957i
$103$	6.31314	+	10.9347i	0.622052	+	1.07743i	0.989103	+	0.147225i	$0.0470341\pi$
$103$	6.31314	+	10.9347i	0.622052	+	1.07743i	−0.367051	+	0.930201i	$0.619633\pi$
$104$	25.1950	−	1.51175i	2.47057	−	0.148239i
$105$	−1.42073	+	2.24183i	−0.138649	+	0.218780i
$106$	−13.1419	−	7.58745i	−1.27645	−	0.736958i
$107$	10.0878			0.975228			0.487614	−	0.873059i	$-0.337867\pi$
$107$	10.0878			0.975228			0.487614	+	0.873059i	$0.337867\pi$
$108$	9.51385	+	22.5137i	0.915471	+	2.16638i
$109$		−	17.0654i		−	1.63457i	−0.576237	−	0.817283i	$-0.695479\pi$
$109$		−	17.0654i		−	1.63457i	0.576237	−	0.817283i	$-0.304521\pi$
$110$	0.563109	+	0.325111i	0.0536904	+	0.0309981i
$111$	5.02013	+	3.18145i	0.476490	+	0.301970i
$112$	11.5688	−	6.67924i	1.09315	−	0.631128i
$113$	−9.18733	−	15.9129i	−0.864271	−	1.49696i	−0.867769	−	0.496968i	$-0.834447\pi$
$113$	−9.18733	−	15.9129i	−0.864271	−	1.49696i	0.00349768	−	0.999994i	$-0.498887\pi$
$114$	9.61282	+	18.3595i	0.900323	+	1.71953i
$115$	2.53529	+	1.46375i	0.236417	+	0.136496i
$116$	20.0098			1.85786
$117$	9.48726	−	5.19537i	0.877098	−	0.480312i
$118$	22.1394			2.03810
$119$	7.72887	+	4.46227i	0.708505	+	0.409055i
$120$	−12.1147	−	0.500131i	−1.10592	−	0.0456555i
$121$	−5.46847	−	9.47166i	−0.497133	−	0.861060i
$122$	1.09150	−	0.630176i	0.0988194	−	0.0570534i
$123$	−0.615527	+	14.9100i	−0.0555002	+	1.34439i
$124$	0.329738	+	0.190374i	0.0296113	+	0.0170961i
$125$			1.00000i			0.0894427i
$126$	6.78061	−	9.78223i	0.604065	−	0.871471i
$127$	12.2344			1.08563			0.542814	−	0.839853i	$-0.317359\pi$
$127$	12.2344			1.08563			0.542814	+	0.839853i	$0.317359\pi$
$128$	−4.18205	−	2.41451i	−0.369644	−	0.213414i
$129$	4.77752	+	9.12458i	0.420637	+	0.803374i
$130$	0.559134	+	9.31858i	0.0490393	+	0.817293i
$131$	−9.34357	−	16.1835i	−0.816352	−	1.41396i	−0.908353	−	0.418204i	$-0.862660\pi$
$131$	−9.34357	−	16.1835i	−0.816352	−	1.41396i	0.0920018	−	0.995759i	$-0.470673\pi$
$132$	−1.72819	−	1.09522i	−0.150420	−	0.0953266i
$133$	3.54062	−	6.13253i	0.307010	−	0.531758i
$134$	−10.6656			−0.921368
$135$	−4.78634	+	2.02262i	−0.411942	+	0.174079i
$136$			40.7709i			3.49608i
$137$	15.5124	+	8.95606i	1.32531	+	0.765168i	0.984570	−	0.174990i	$-0.0559892\pi$
$137$	15.5124	+	8.95606i	1.32531	+	0.765168i	0.340740	+	0.940158i	$0.389323\pi$
$138$	−11.0892	−	7.02766i	−0.943977	−	0.598234i
$139$	−3.43047	−	5.94174i	−0.290968	−	0.503972i	0.683071	−	0.730352i	$-0.260644\pi$
$139$	−3.43047	−	5.94174i	−0.290968	−	0.503972i	−0.974039	+	0.226380i	$0.927311\pi$
$140$	3.60388	+	6.24210i	0.304583	+	0.527554i
$141$	7.03802	−	3.68502i	0.592708	−	0.310335i
$142$	−10.0158	+	17.3478i	−0.840504	+	1.45580i
$143$	−0.404957	+	0.809871i	−0.0338642	+	0.0677248i
$144$	26.0640	+	2.15567i	2.17200	+	0.179639i
$145$			4.25402i			0.353277i
$146$	−19.0567	+	33.0071i	−1.57714	+	2.73169i
$147$	8.05049	+	0.332348i	0.663993	+	0.0274116i
$148$	13.9780	−	8.07018i	1.14898	−	0.663365i
$149$	3.46820	−	2.00237i	0.284126	−	0.164040i	−0.351164	−	0.936314i	$-0.614214\pi$
$149$	3.46820	−	2.00237i	0.284126	−	0.164040i	0.635290	+	0.772274i	$0.280881\pi$
$150$	0.184978	−	4.48074i	0.0151034	−	0.365850i
$151$	9.72850	+	5.61675i	0.791694	+	0.457085i	0.840559	−	0.541721i	$-0.182227\pi$
$151$	9.72850	+	5.61675i	0.791694	+	0.457085i	−0.0488647	+	0.998805i	$0.515560\pi$
$152$	32.3500			2.62393
$153$	7.45920	+	15.8000i	0.603040	+	1.27736i
$154$			0.996367i			0.0802895i
$155$	−0.0404730	+	0.0701012i	−0.00325087	+	0.00563067i
$156$	−0.548417	−	29.3697i	−0.0439085	−	2.35146i
$157$	−7.82349	−	13.5507i	−0.624382	−	1.08146i	−0.988660	−	0.150171i	$-0.952017\pi$
$157$	−7.82349	−	13.5507i	−0.624382	−	1.08146i	0.364278	−	0.931290i	$-0.381316\pi$
$158$	−31.0069	+	17.9019i	−2.46678	+	1.42420i
$159$	−5.43403	+	8.57457i	−0.430947	+	0.680008i
$160$	−4.28529	+	7.42234i	−0.338782	+	0.586787i
$161$			4.48596i			0.353543i
$162$	21.8204	−	8.17745i	1.71438	−	0.642481i
$163$			18.8259i			1.47455i	0.675590	+	0.737277i	$0.263889\pi$
$163$			18.8259i			1.47455i	−0.675590	+	0.737277i	$0.736111\pi$
$164$	35.0961	+	20.2628i	2.74055	+	1.58226i
$165$	0.232840	−	0.367408i	0.0181266	−	0.0286027i
$166$	−17.6743	−	30.6128i	−1.37179	−	2.37601i
$167$	−1.24872	+	0.720951i	−0.0966291	+	0.0557889i	−0.547536	−	0.836782i	$-0.684434\pi$
$167$	−1.24872	+	0.720951i	−0.0966291	+	0.0557889i	0.450907	+	0.892571i	$0.351101\pi$
$168$	−8.61828	−	16.4601i	−0.664915	−	1.26992i
$169$	−12.9067	+	1.55446i	−0.992825	+	0.119574i
$170$	−15.0795			−1.15654
$171$	12.5366	−	5.91855i	0.958701	−	0.452603i
$172$	27.9708			2.13275
$173$	−8.90952	+	15.4317i	−0.677378	+	1.17325i	0.298390	+	0.954444i	$0.403550\pi$
$173$	−8.90952	+	15.4317i	−0.677378	+	1.17325i	−0.975768	+	0.218809i	$0.929783\pi$
$174$	0.786900	−	19.0611i	0.0596547	−	1.44502i
$175$	−1.32705	+	0.766174i	−0.100316	+	0.0579173i
$176$	−1.89598	+	1.09464i	−0.142915	+	0.0825119i
$177$	0.610898	−	14.7978i	0.0459179	−	1.11227i
$178$	7.76359	−	13.4469i	0.581905	−	1.00789i
$179$	−7.74708			−0.579044			−0.289522	−	0.957171i	$-0.593496\pi$
$179$	−7.74708			−0.579044			−0.289522	+	0.957171i	$0.593496\pi$
$180$	−1.16312	+	14.0632i	−0.0866939	+	1.04821i
$181$	−11.0098			−0.818352			−0.409176	−	0.912456i	$-0.634184\pi$
$181$	−11.0098			−0.818352			−0.409176	+	0.912456i	$0.634184\pi$
$182$	−11.9378	+	7.88165i	−0.884892	+	0.584227i
$183$	−0.391088	−	0.746938i	−0.0289100	−	0.0552153i
$184$	−17.7481	+	10.2468i	−1.30840	+	0.755407i
$185$	1.71570	+	2.97167i	0.126140	+	0.218482i
$186$	0.194316	−	0.306618i	0.0142479	−	0.0224824i
$187$	−1.26667	−	0.731310i	−0.0926278	−	0.0534787i
$188$		−	21.5746i		−	1.57349i
$189$	−6.35129	−	4.80204i	−0.461988	−	0.349297i
$190$			11.9649i			0.868027i
$191$	−3.67246	+	6.36090i	−0.265730	+	0.460258i	−0.967755	−	0.251895i	$-0.918946\pi$
$191$	−3.67246	+	6.36090i	−0.265730	+	0.460258i	0.702024	+	0.712153i	$0.252280\pi$
$192$	4.40889	−	6.95696i	0.318185	−	0.502076i
$193$	−20.0363	+	11.5680i	−1.44225	+	0.832682i	−0.997999	−	0.0632223i	$-0.979862\pi$
$193$	−20.0363	+	11.5680i	−1.44225	+	0.832682i	−0.444248	+	0.895904i	$0.646529\pi$
$194$	11.6183	+	20.1235i	0.834144	+	1.44478i
$195$	6.24391	−	0.116592i	0.447136	−	0.00834932i
$196$	10.9407	−	18.9498i	0.781477	−	1.35356i
$197$		−	18.5639i		−	1.32263i	−0.750110	−	0.661313i	$-0.770000\pi$
$197$		−	18.5639i		−	1.32263i	0.750110	−	0.661313i	$-0.230000\pi$
$198$	−1.11126	+	1.60319i	−0.0789737	+	0.113934i
$199$	−18.1284			−1.28509			−0.642545	−	0.766248i	$-0.722122\pi$
$199$	−18.1284			−1.28509			−0.642545	+	0.766248i	$0.722122\pi$
$200$	−6.06252	−	3.50020i	−0.428685	−	0.247501i
$201$	−0.294299	+	7.12883i	−0.0207582	+	0.502829i
$202$	34.1761	−	19.7316i	2.40462	−	1.38831i
$203$	−5.64531	+	3.25932i	−0.396223	+	0.228760i
$204$	47.4091	+	1.95719i	3.31930	+	0.137030i
$205$	−4.30780	+	7.46133i	−0.300870	+	0.521122i
$206$		−	32.6914i		−	2.27772i
$207$	−5.00323	+	7.21805i	−0.347749	+	0.501689i
$208$	−28.1133	−	14.0574i	−1.94930	−	0.974704i
$209$	−0.580263	+	1.00505i	−0.0401376	+	0.0695204i
$210$	6.08789	−	3.18755i	0.420105	−	0.219962i
$211$	8.05803	+	13.9569i	0.554738	+	0.960834i	0.997924	+	0.0644041i	$0.0205147\pi$
$211$	8.05803	+	13.9569i	0.554738	+	0.960834i	−0.443186	+	0.896429i	$0.646152\pi$
$212$	13.7842	+	23.8749i	0.946700	+	1.63973i
$213$	11.3188	+	7.17315i	0.775551	+	0.491496i
$214$	−22.6197	−	13.0595i	−1.54625	−	0.892729i
$215$			5.94650i			0.405548i
$216$	4.49097	−	36.0968i	0.305572	−	2.45608i
$217$	−0.124037			−0.00842020
$218$	−22.0925	+	38.2653i	−1.49629	+	2.59165i
$219$	21.5359	+	13.6481i	1.45526	+	0.922255i
$220$	−0.590631	−	1.02300i	−0.0398203	−	0.0689709i
$221$	−1.25772	−	20.9614i	−0.0846037	−	1.41001i
$222$	−7.13789	−	13.6326i	−0.479064	−	0.914963i
$223$	−2.02651	−	1.17001i	−0.135705	−	0.0783496i	0.430610	−	0.902538i	$-0.358298\pi$
$223$	−2.02651	−	1.17001i	−0.135705	−	0.0783496i	−0.566316	+	0.824188i	$0.691632\pi$
$224$	−13.1331			−0.877492
$225$	−2.98979	−	0.247276i	−0.199319	−	0.0164851i
$226$			47.5749i			3.16463i
$227$	19.7498	+	11.4025i	1.31084	+	0.756813i	0.982235	−	0.187655i	$-0.0600888\pi$
$227$	19.7498	+	11.4025i	1.31084	+	0.756813i	0.328603	+	0.944468i	$0.393422\pi$
$228$	1.55294	−	37.6171i	0.102846	−	2.49125i
$229$	17.8529	−	10.3074i	1.17975	−	0.681131i	0.223796	−	0.974636i	$-0.428155\pi$
$229$	17.8529	−	10.3074i	1.17975	−	0.681131i	0.955957	+	0.293505i	$0.0948218\pi$
$230$	−3.78989	−	6.56427i	−0.249898	−	0.432835i
$231$	0.665966	+	0.0274930i	0.0438173	+	0.00180891i
$232$	−25.7901	−	14.8899i	−1.69320	−	0.977571i
$233$	4.36066			0.285676			0.142838	−	0.989746i	$-0.454377\pi$
$233$	4.36066			0.285676			0.142838	+	0.989746i	$0.454377\pi$
$234$	−27.9989	−	0.632567i	−1.83034	−	0.0413522i
$235$	4.58669			0.299202
$236$	−34.8322	−	20.1104i	−2.26738	−	1.30907i
$237$	11.1099	+	21.2188i	0.721667	+	1.37831i
$238$	−11.5535	−	20.0113i	−0.748903	−	1.29714i
$239$	−1.72247	+	0.994466i	−0.111417	+	0.0643267i	−0.554673	−	0.832068i	$-0.687157\pi$
$239$	−1.72247	+	0.994466i	−0.111417	+	0.0643267i	0.443256	+	0.896395i	$0.353823\pi$
$240$	12.7539	+	8.08265i	0.823263	+	0.521733i
$241$	−13.5119	−	7.80107i	−0.870375	−	0.502511i	−0.00290222	−	0.999996i	$-0.500924\pi$
$241$	−13.5119	−	7.80107i	−0.870375	−	0.502511i	−0.867473	+	0.497484i	$0.834257\pi$
$242$			28.3174i			1.82031i
$243$	−4.86366	−	14.8103i	−0.312004	−	0.950081i
$244$	−2.28969			−0.146582
$245$	4.02867	+	2.32595i	0.257382	+	0.148600i
$246$	20.6823	−	32.6354i	1.31866	−	2.08076i
$247$	−16.6319	+	0.997950i	−1.05826	+	0.0634981i
$248$	−0.283327	−	0.490736i	−0.0179913	−	0.0311618i
$249$	−20.9491	+	10.9687i	−1.32759	+	0.695112i
$250$	1.29458	−	2.24228i	0.0818763	−	0.141814i
$251$	−23.8791			−1.50723			−0.753616	−	0.657314i	$-0.771692\pi$
$251$	−23.8791			−1.50723			−0.753616	+	0.657314i	$0.771692\pi$
$252$	−19.5537	+	9.23133i	−1.23177	+	0.581519i
$253$		−	0.735193i		−	0.0462212i
$254$	−27.4329	−	15.8384i	−1.72130	−	0.993790i
$255$	−0.416092	+	10.0790i	−0.0260567	+	0.631174i
$256$	11.0068	+	19.0643i	0.687925	+	1.19152i
$257$	−12.8565	−	22.2681i	−0.801966	−	1.38905i	−0.918321	−	0.395837i	$-0.870454\pi$
$257$	−12.8565	−	22.2681i	−0.801966	−	1.38905i	0.116355	−	0.993208i	$-0.462879\pi$
$258$	1.09997	−	26.6447i	0.0684812	−	1.65883i
$259$	−2.62904	+	4.55364i	−0.163361	+	0.282949i
$260$	7.58486	−	15.1689i	0.470393	−	0.940737i
$261$	−12.7186	−	1.05192i	−0.787264	−	0.0651121i
$262$			48.3839i			2.98917i
$263$	1.96643	−	3.40595i	0.121255	−	0.210020i	−0.799008	−	0.601321i	$-0.794641\pi$
$263$	1.96643	−	3.40595i	0.121255	−	0.210020i	0.920263	+	0.391301i	$0.127975\pi$
$264$	1.41243	+	2.69760i	0.0869290	+	0.166026i
$265$	−5.07573	+	2.93047i	−0.311799	+	0.180017i
$266$	−15.8781	+	9.16721i	−0.973547	+	0.562078i
$267$	−8.77362	−	5.56018i	−0.536937	−	0.340277i
$268$	16.7803	+	9.68813i	1.02502	+	0.591797i
$269$	1.82163			0.111067			0.0555335	−	0.998457i	$-0.482314\pi$
$269$	1.82163			0.111067			0.0555335	+	0.998457i	$0.482314\pi$
$270$	13.3507	+	1.66102i	0.812499	+	0.101087i
$271$		−	6.93268i		−	0.421130i	−0.977580	−	0.210565i	$-0.932470\pi$
$271$		−	6.93268i		−	0.421130i	0.977580	−	0.210565i	$-0.0675304\pi$
$272$	25.3862	−	43.9702i	1.53926	−	2.66608i
$273$	4.93864	+	8.19666i	0.298900	+	0.496085i
$274$	−23.1887	−	40.1639i	−1.40088	−	2.42639i
$275$	0.217487	−	0.125566i	0.0131150	−	0.00757194i
$276$	11.0632	+	21.1296i	0.665927	+	1.27185i
$277$	3.31544	−	5.74252i	0.199206	−	0.345035i	−0.749065	−	0.662496i	$-0.769497\pi$
$277$	3.31544	−	5.74252i	0.199206	−	0.345035i	0.948271	+	0.317462i	$0.102830\pi$
$278$			17.7640i			1.06542i
$279$	−0.199580	−	0.138340i	−0.0119485	−	0.00828220i
$280$		−	10.7270i		−	0.641063i
$281$	−2.96123	−	1.70967i	−0.176652	−	0.101990i	0.409067	−	0.912505i	$-0.365854\pi$
$281$	−2.96123	−	1.70967i	−0.176652	−	0.101990i	−0.585719	+	0.810514i	$0.699188\pi$
$282$	−20.5517	−	0.848435i	−1.22384	−	0.0505236i
$283$	6.29682	+	10.9064i	0.374307	+	0.648319i	0.990223	−	0.139493i	$-0.0445472\pi$
$283$	6.29682	+	10.9064i	0.374307	+	0.648319i	−0.615916	+	0.787812i	$0.711214\pi$
$284$	31.5158	−	18.1957i	1.87012	−	1.07971i
$285$	7.99728	+	0.330151i	0.473718	+	0.0195565i
$286$	1.95647	−	1.29171i	0.115688	−	0.0763801i
$287$	−13.2021			−0.779296
$288$	−21.1316	−	14.6475i	−1.24519	−	0.863111i
$289$	16.9200			0.995297
$290$	5.50717	−	9.53869i	0.323392	−	0.560131i
$291$	13.7710	−	7.21032i	0.807269	−	0.422676i
$292$	59.9641	−	34.6203i	3.50914	−	2.02600i
$293$	−9.58722	+	5.53518i	−0.560091	+	0.323369i	−0.753182	−	0.657812i	$-0.771482\pi$
$293$	−9.58722	+	5.53518i	−0.560091	+	0.323369i	0.193091	+	0.981181i	$0.438149\pi$
$294$	−17.6212	−	11.1672i	−1.02769	−	0.651284i
$295$	4.27541	−	7.40522i	0.248924	−	0.431149i
$296$	−24.0211			−1.39620
$297$	1.04090	+	0.786995i	0.0603990	+	0.0456661i
$298$	−10.3689			−0.600654
$299$	8.80862	−	5.81566i	0.509416	−	0.336328i
$300$	−4.36111	+	6.88157i	−0.251789	+	0.397308i
$301$	−7.89132	+	4.55605i	−0.454848	+	0.262607i
$302$	−14.5426	−	25.1886i	−0.836835	−	1.44944i
$303$	−12.2455	−	23.3876i	−0.703483	−	1.34358i
$304$	−34.8884	−	20.1428i	−2.00099	−	1.15527i
$305$		−	0.486781i		−	0.0278730i
$306$	3.72880	−	45.0845i	0.213161	−	2.57731i
$307$		−	19.6349i		−	1.12062i	−0.828282	−	0.560311i	$-0.810682\pi$
$307$		−	19.6349i		−	1.12062i	0.828282	−	0.560311i	$-0.189318\pi$
$308$	0.905052	−	1.56760i	0.0515701	−	0.0893221i
$309$	−21.8507	−	0.902062i	−1.24305	−	0.0513165i
$310$	0.181503	−	0.104791i	0.0103087	−	0.00595172i
$311$	12.4266	+	21.5234i	0.704646	+	1.22048i	0.966819	+	0.255462i	$0.0822275\pi$
$311$	12.4266	+	21.5234i	0.704646	+	1.22048i	−0.262173	+	0.965021i	$0.584439\pi$
$312$	−21.1481	+	38.2619i	−1.19727	+	2.16615i
$313$	−3.52811	+	6.11086i	−0.199420	+	0.345406i	−0.948341	−	0.317254i	$-0.897239\pi$
$313$	−3.52811	+	6.11086i	−0.199420	+	0.345406i	0.748920	+	0.662660i	$0.230573\pi$
$314$			40.5125i			2.28625i
$315$	−1.96255	−	4.15707i	−0.110577	−	0.234224i
$316$	65.0448			3.65906
$317$	−14.5944	−	8.42610i	−0.819705	−	0.473257i	0.0306094	−	0.999531i	$-0.490255\pi$
$317$	−14.5944	−	8.42610i	−0.819705	−	0.473257i	−0.850315	+	0.526274i	$0.823589\pi$
$318$	23.2851	−	12.1918i	1.30576	−	0.683681i
$319$	0.925196	−	0.534162i	0.0518011	−	0.0299074i
$320$	4.11818	−	2.37763i	0.230213	−	0.132914i
$321$	−9.35304	+	14.7585i	−0.522036	+	0.823740i
$322$	5.80742	−	10.0588i	0.323635	−	0.560552i
$323$		−	26.9141i		−	1.49754i
$324$	−41.7584	−	6.95498i	−2.31991	−	0.386388i
$325$	3.22487	+	1.61252i	0.178884	+	0.0894465i
$326$	24.3715	−	42.2128i	1.34982	−	2.33795i
$327$	24.9667	+	15.8223i	1.38066	+	0.874977i
$328$	−30.1563	−	52.2323i	−1.66510	−	2.88404i
$329$	3.51420	+	6.08677i	0.193744	+	0.335575i
$330$	−0.997731	+	0.522400i	−0.0549233	+	0.0287572i
$331$	−0.449163	−	0.259324i	−0.0246882	−	0.0142538i	0.487605	−	0.873064i	$-0.337871\pi$
$331$	−0.449163	−	0.259324i	−0.0246882	−	0.0142538i	−0.512293	+	0.858811i	$0.671204\pi$
$332$			64.2180i			3.52442i
$333$	−9.30893	+	4.39475i	−0.510126	+	0.240831i
$334$	3.73331			0.204278
$335$	−2.05967	+	3.56745i	−0.112532	+	0.194911i
$336$	−0.954372	+	23.1179i	−0.0520653	+	1.26118i
$337$	5.46348	+	9.46302i	0.297615	+	0.515484i	0.975590	−	0.219601i	$-0.0704756\pi$
$337$	5.46348	+	9.46302i	0.297615	+	0.515484i	−0.677975	+	0.735085i	$0.737142\pi$
$338$	30.9528	+	13.2233i	1.68361	+	0.719250i
$339$	31.7988	+	1.31275i	1.72707	+	0.0712985i
$340$	23.7247	+	13.6975i	1.28666	+	0.742851i
$341$	0.0203282			0.00110083
$342$	−35.7726	−	2.95864i	−1.93436	−	0.159985i
$343$			17.8548i			0.964068i
$344$	−36.0508	−	20.8139i	−1.94373	−	1.12221i
$345$	−4.49210	+	2.35201i	−0.241846	+	0.126628i
$346$	39.9552	−	23.0681i	2.14800	−	1.24015i
$347$	−5.49528	−	9.51811i	−0.295002	−	0.510959i	0.679983	−	0.733228i	$-0.261987\pi$
$347$	−5.49528	−	9.51811i	−0.295002	−	0.510959i	−0.974985	+	0.222269i	$0.928654\pi$
$348$	−18.5523	+	29.2744i	−0.994507	+	1.56927i
$349$	15.1753	+	8.76145i	0.812314	+	0.468990i	0.847759	−	0.530382i	$-0.177951\pi$
$349$	15.1753	+	8.76145i	0.812314	+	0.468990i	−0.0354448	+	0.999372i	$0.511285\pi$
$350$	3.96749			0.212071
$351$	−1.19538	+	18.6968i	−0.0638049	+	0.997962i
$352$	2.15235			0.114721
$353$	−1.03596	−	0.598114i	−0.0551388	−	0.0318344i	0.472177	−	0.881504i	$-0.343468\pi$
$353$	−1.03596	−	0.598114i	−0.0551388	−	0.0318344i	−0.527316	+	0.849669i	$0.676802\pi$
$354$	−20.5268	+	32.3900i	−1.09098	+	1.72151i
$355$	3.86835	+	6.70017i	0.205311	+	0.355608i
$356$	−24.4291	+	14.1041i	−1.29474	+	0.747518i
$357$	−13.6942	+	7.17012i	−0.724774	+	0.379483i
$358$	17.3711	+	10.0292i	0.918091	+	0.530060i
$359$			25.1795i			1.32892i	0.747323	+	0.664461i	$0.231339\pi$
$359$			25.1795i			1.32892i	−0.747323	+	0.664461i	$0.768661\pi$
$360$	11.9640	−	17.2602i	0.630557	−	0.909690i
$361$	−2.35517			−0.123956
$362$	24.6870	+	14.2530i	1.29752	+	0.749123i
$363$	18.9272	+	0.781370i	0.993420	+	0.0410113i
$364$	25.9413	−	1.55653i	1.35969	−	0.0815844i
$365$	7.36018	+	12.7482i	0.385249	+	0.667271i
$366$	−0.0900436	+	2.18114i	−0.00470665	+	0.114010i
$367$	3.12159	−	5.40676i	0.162946	−	0.282231i	−0.772978	−	0.634433i	$-0.781234\pi$
$367$	3.12159	−	5.40676i	0.162946	−	0.282231i	0.935924	+	0.352202i	$0.114567\pi$
$368$	25.5210			1.33037
$369$	−21.2426	−	14.7244i	−1.10585	−	0.766524i
$370$		−	8.88441i		−	0.461879i
$371$	−7.77778	−	4.49050i	−0.403802	−	0.233135i
$372$	−0.584237	+	0.305899i	−0.0302913	+	0.0158601i
$373$	2.01976	+	3.49832i	0.104579	+	0.181136i	0.913566	−	0.406690i	$-0.133317\pi$
$373$	2.01976	+	3.49832i	0.104579	+	0.181136i	−0.808987	+	0.587826i	$0.799984\pi$
$374$	1.89348	+	3.27960i	0.0979094	+	0.169584i
$375$	−1.46300	−	0.927160i	−0.0755491	−	0.0478783i
$376$	−16.0543	+	27.8069i	−0.827937	+	1.43403i
$377$	13.7187	+	6.85969i	0.706547	+	0.353292i
$378$	8.02471	+	18.9897i	0.412747	+	0.976727i
$379$		−	17.1896i		−	0.882968i	−0.897269	−	0.441484i	$-0.854452\pi$
$379$		−	17.1896i		−	0.882968i	0.897269	−	0.441484i	$-0.145548\pi$
$380$	10.8684	−	18.8246i	0.557535	−	0.965680i
$381$	−11.3433	+	17.8990i	−0.581133	+	0.916992i
$382$	16.4694	−	9.50859i	0.842646	−	0.486502i
$383$	14.0860	−	8.13254i	0.719760	−	0.415554i	−0.0949045	−	0.995486i	$-0.530255\pi$
$383$	14.0860	−	8.13254i	0.719760	−	0.415554i	0.814664	+	0.579933i	$0.196921\pi$
$384$	7.40986	−	3.87971i	0.378133	−	0.197986i
$385$	0.333266	+	0.192411i	0.0169848	+	0.00980620i
$386$	59.9027			3.04896
$387$	−17.7788	−	1.47043i	−0.903747	−	0.0747460i
$388$		−	42.2140i		−	2.14309i
$389$	−0.558513	+	0.967373i	−0.0283178	+	0.0490478i	−0.879837	−	0.475276i	$-0.842348\pi$
$389$	−0.558513	+	0.967373i	−0.0283178	+	0.0490478i	0.851519	+	0.524323i	$0.175682\pi$
$390$	−14.1515	−	7.82180i	−0.716589	−	0.396072i
$391$	8.52503	+	14.7658i	0.431129	+	0.746738i
$392$	−28.2023	+	16.2826i	−1.42443	+	0.822395i
$393$	32.3395	+	1.33507i	1.63131	+	0.0673454i
$394$	−24.0325	+	41.6255i	−1.21074	+	2.09706i
$395$			13.8283i			0.695779i
$396$	3.20462	−	1.51290i	0.161038	−	0.0760261i
$397$		−	32.1786i		−	1.61500i	−0.589870	−	0.807498i	$-0.700821\pi$
$397$		−	32.1786i		−	1.61500i	0.589870	−	0.807498i	$-0.299179\pi$
$398$	40.6490	+	23.4687i	2.03755	+	1.17638i
$399$	5.68918	+	10.8658i	0.284815	+	0.543969i
$400$	4.35882	+	7.54970i	0.217941	+	0.377485i
$401$	5.36232	−	3.09594i	0.267781	−	0.154604i	−0.360098	−	0.932915i	$-0.617257\pi$
$401$	5.36232	−	3.09594i	0.267781	−	0.154604i	0.627879	+	0.778311i	$0.283923\pi$
$402$	9.88872	−	15.6038i	0.493205	−	0.778247i
$403$	0.160804	+	0.243560i	0.00801021	+	0.0121326i
$404$	−71.6930			−3.56686
$405$	1.47861	−	8.87771i	0.0734726	−	0.441137i
$406$	16.8778			0.837631
$407$	0.430868	−	0.746285i	0.0213573	−	0.0369920i
$408$	−59.6479	−	37.8012i	−2.95301	−	1.87144i
$409$	−0.385766	+	0.222722i	−0.0190749	+	0.0110129i	−0.509507	−	0.860466i	$-0.670172\pi$
$409$	−0.385766	+	0.222722i	−0.0190749	+	0.0110129i	0.490432	+	0.871479i	$0.336839\pi$
$410$	19.3186	−	11.1536i	0.954076	−	0.550836i
$411$	−27.4852	+	14.3909i	−1.35574	+	0.709851i
$412$	−29.6953	+	51.4338i	−1.46298	+	2.53396i
$413$	13.1028			0.644747
$414$	20.5630	−	9.70778i	1.01061	−	0.477111i
$415$	−13.6526			−0.670177
$416$	17.0260	+	25.7881i	0.834766	+	1.26437i
$417$	11.8734	+	0.490167i	0.581441	+	0.0240036i
$418$	2.60222	−	1.50239i	0.127279	−	0.0734844i
$419$	−6.21374	−	10.7625i	−0.303561	−	0.525783i	0.673379	−	0.739298i	$-0.264842\pi$
$419$	−6.21374	−	10.7625i	−0.303561	−	0.525783i	−0.976940	+	0.213514i	$0.931509\pi$
$420$	−12.4736	−	0.514946i	−0.608648	−	0.0251268i
$421$	−32.6433	−	18.8466i	−1.59094	−	0.918527i	−0.993147	−	0.116873i	$-0.962713\pi$
$421$	−32.6433	−	18.8466i	−1.59094	−	0.918527i	−0.597788	−	0.801654i	$-0.703954\pi$
$422$		−	41.7270i		−	2.03124i
$423$	−1.13418	+	13.7132i	−0.0551456	+	0.666760i
$424$		−	41.0289i		−	1.99254i
$425$	−2.91205	+	5.04381i	−0.141255	+	0.244661i
$426$	−16.0937	−	30.7373i	−0.779740	−	1.48923i
$427$	0.645983	−	0.372959i	0.0312613	−	0.0180487i
$428$	23.7252	+	41.0933i	1.14680	+	1.98632i
$429$	−0.809383	−	1.34333i	−0.0390774	−	0.0648567i
$430$	7.69821	−	13.3337i	0.371241	−	0.643008i
$431$		−	15.3244i		−	0.738151i	−0.929399	−	0.369075i	$-0.879674\pi$
$431$		−	15.3244i		−	0.738151i	0.929399	−	0.369075i	$-0.120326\pi$
$432$	−27.3192	+	36.1330i	−1.31440	+	1.73845i
$433$	−26.4169			−1.26951			−0.634757	−	0.772712i	$-0.718900\pi$
$433$	−26.4169			−1.26951			−0.634757	+	0.772712i	$0.718900\pi$
$434$	0.278126	+	0.160576i	0.0133505	+	0.00770790i
$435$	−6.22364	−	3.94416i	−0.298401	−	0.189108i
$436$	69.5167	−	40.1355i	3.32925	−	1.92214i
$437$	11.7160	−	6.76424i	0.560453	−	0.323578i
$438$	−30.6209	−	58.4828i	−1.46312	−	2.79441i
$439$	2.01559	−	3.49110i	0.0961987	−	0.166621i	−0.813910	−	0.580992i	$-0.802665\pi$
$439$	2.01559	−	3.49110i	0.0961987	−	0.166621i	0.910108	+	0.414371i	$0.135998\pi$
$440$			1.75803i			0.0838107i
$441$	−7.95031	+	11.4697i	−0.378586	+	0.546178i
$442$	−24.3160	+	48.6294i	−1.15659	+	2.31306i
$443$	−1.84594	+	3.19726i	−0.0877033	+	0.151907i	−0.906540	−	0.422120i	$-0.861286\pi$
$443$	−1.84594	+	3.19726i	−0.0877033	+	0.151907i	0.818837	+	0.574027i	$0.194619\pi$
$444$	−1.15312	+	27.9321i	−0.0547246	+	1.32560i
$445$	−2.99850	−	5.19355i	−0.142143	−	0.246198i
$446$	3.02934	+	5.24696i	0.143443	+	0.248451i
$447$	−0.286111	+	6.93050i	−0.0135326	+	0.327802i
$448$	6.31049	+	3.64336i	0.298143	+	0.172133i
$449$		−	12.2525i		−	0.578233i	−0.957294	−	0.289116i	$-0.906639\pi$
$449$		−	12.2525i		−	0.578233i	0.957294	−	0.289116i	$-0.0933614\pi$
$450$	6.38382	+	4.42498i	0.300936	+	0.208596i
$451$	2.16366			0.101883
$452$	43.2148	−	74.8502i	2.03265	−	3.52066i
$453$	−17.2372	+	9.02518i	−0.809874	+	0.424040i
$454$	−29.5229	−	51.1352i	−1.38558	−	2.39990i
$455$	0.330914	+	5.51504i	0.0155135	+	0.258549i
$456$	−29.9936	+	47.3281i	−1.40458	+	2.21634i
$457$	10.8822	+	6.28285i	0.509049	+	0.293899i	0.732443	−	0.680829i	$-0.238380\pi$
$457$	10.8822	+	6.28285i	0.509049	+	0.293899i	−0.223394	+	0.974728i	$0.571714\pi$
$458$	−53.3748			−2.49404
$459$	−30.0313	−	3.73633i	−1.40174	−	0.174397i
$460$			13.7702i			0.642039i
$461$	−2.95803	−	1.70782i	−0.137769	−	0.0795411i	0.429531	−	0.903052i	$-0.358679\pi$
$461$	−2.95803	−	1.70782i	−0.137769	−	0.0795411i	−0.567300	+	0.823511i	$0.692012\pi$
$462$	−1.45769	−	0.923792i	−0.0678177	−	0.0429787i
$463$	−31.1460	+	17.9821i	−1.44748	+	0.835700i	−0.998331	−	0.0577589i	$-0.981605\pi$
$463$	−31.1460	+	17.9821i	−1.44748	+	0.835700i	−0.449145	+	0.893459i	$0.648271\pi$
$464$	18.5425	+	32.1166i	0.860816	+	1.49098i
$465$	−0.0650333	−	0.124207i	−0.00301585	−	0.00575997i
$466$	−9.77780	−	5.64521i	−0.452948	−	0.261510i
$467$	31.3646			1.45138			0.725690	−	0.688021i	$-0.241521\pi$
$467$	31.3646			1.45138			0.725690	+	0.688021i	$0.241521\pi$
$468$	43.4764	+	26.4281i	2.00970	+	1.22164i
$469$	−6.31225			−0.291473
$470$	−10.2846	−	5.93783i	−0.474394	−	0.273891i
$471$	27.0783	+	1.11787i	1.24770	+	0.0515088i
$472$	29.9295	+	51.8394i	1.37762	+	2.38610i
$473$	1.29329	−	0.746681i	0.0594655	−	0.0343324i
$474$	2.55794	−	61.9611i	0.117490	−	2.84597i
$475$	4.00205	+	2.31058i	0.183626	+	0.106017i
$476$			41.9786i			1.92409i
$477$	−7.50639	−	15.9000i	−0.343694	−	0.728011i
$478$	5.14966			0.235540
$479$	−12.6025	−	7.27608i	−0.575825	−	0.332453i	0.183647	−	0.982992i	$-0.441210\pi$
$479$	−12.6025	−	7.27608i	−0.575825	−	0.332453i	−0.759472	+	0.650539i	$0.774543\pi$
$480$	−6.88574	−	13.1511i	−0.314290	−	0.600262i
$481$	12.3498	−	0.741016i	0.563105	−	0.0337874i
$482$	20.1982	+	34.9843i	0.920003	+	1.59349i
$483$	−6.56296	−	4.15920i	−0.298625	−	0.189250i
$484$	25.7222	−	44.5522i	1.16919	−	2.02510i
$485$	8.97457			0.407514
$486$	−8.26743	+	39.5052i	−0.375018	+	1.79199i
$487$			2.00734i			0.0909611i	0.998965	+	0.0454806i	$0.0144819\pi$
$487$			2.00734i			0.0909611i	−0.998965	+	0.0454806i	$0.985518\pi$
$488$	2.95112	+	1.70383i	0.133591	+	0.0771287i
$489$	−27.5423	−	17.4546i	−1.24550	−	0.789323i
$490$	−6.02226	−	10.4309i	−0.272058	−	0.471218i
$491$	−7.46424	−	12.9284i	−0.336856	−	0.583452i	0.646983	−	0.762504i	$-0.276030\pi$
$491$	−7.46424	−	12.9284i	−0.336856	−	0.583452i	−0.983840	+	0.179052i	$0.942697\pi$
$492$	−62.1842	+	32.5589i	−2.80348	+	1.46787i
$493$	−12.3879	+	21.4565i	−0.557923	+	0.966351i
$494$	38.5853	+	19.2937i	1.73604	+	0.868063i
$495$	0.321638	+	0.681292i	0.0144566	+	0.0306218i
$496$			0.705658i			0.0316850i
$497$	−5.92765	+	10.2670i	−0.265892	+	0.460538i
$498$	61.1735	+	2.52542i	2.74125	+	0.113167i
$499$	24.9042	−	14.3784i	1.11486	−	0.643667i	0.174779	−	0.984608i	$-0.444079\pi$
$499$	24.9042	−	14.3784i	1.11486	−	0.643667i	0.940085	+	0.340940i	$0.110745\pi$
$500$	−4.07355	+	2.35187i	−0.182175	+	0.105179i
$501$	0.103014	−	2.49532i	0.00460233	−	0.111483i
$502$	53.5434	+	30.9133i	2.38976	+	1.37973i
$503$	42.5805			1.89857			0.949285	−	0.314416i	$-0.101809\pi$
$503$	42.5805			1.89857			0.949285	+	0.314416i	$0.101809\pi$
$504$	32.0716	+	2.65254i	1.42858	+	0.118153i
$505$		−	15.2417i		−	0.678248i
$506$	−0.951765	+	1.64851i	−0.0423111	+	0.0732850i
$507$	9.69243	−	20.3238i	0.430456	−	0.902612i
$508$	28.7737	+	49.8375i	1.27663	+	2.21118i
$509$	−20.7332	+	11.9703i	−0.918984	+	0.530576i	−0.883311	−	0.468788i	$-0.844691\pi$
$509$	−20.7332	+	11.9703i	−0.918984	+	0.530576i	−0.0356735	+	0.999363i	$0.511358\pi$
$510$	13.9811	−	22.0613i	0.619093	−	0.976892i
$511$	−11.2784	+	19.5347i	−0.498925	+	0.864163i
$512$		−	47.3387i		−	2.09209i
$513$	−2.96462	+	23.8286i	−0.130891	+	1.05206i
$514$			66.5749i			2.93649i
$515$	−10.9347	−	6.31314i	−0.481839	−	0.278190i
$516$	−25.9334	+	40.9213i	−1.14165	+	1.80146i
$517$	−0.575934	−	0.997547i	−0.0253295	−	0.0438721i
$518$	11.7901	−	6.80701i	0.518026	−	0.299083i
$519$	−14.3161	−	27.3423i	−0.628407	−	1.20019i
$520$	−21.0636	+	13.9067i	−0.923700	+	0.609849i
$521$	−15.4433			−0.676583			−0.338292	−	0.941041i	$-0.609849\pi$
$521$	−15.4433			−0.676583			−0.338292	+	0.941041i	$0.609849\pi$
$522$	27.1569	+	18.8240i	1.18863	+	0.823903i
$523$	−7.64335			−0.334220			−0.167110	−	0.985938i	$-0.553444\pi$
$523$	−7.64335			−0.334220			−0.167110	+	0.985938i	$0.553444\pi$
$524$	43.9497	−	76.1231i	1.91995	−	3.32545i
$525$	0.109476	−	2.65185i	0.00477792	−	0.115736i
$526$	−8.81855	+	5.09139i	−0.384507	+	0.221995i
$527$	−0.408276	+	0.235718i	−0.0177848	+	0.0102680i
$528$	0.156410	−	3.78873i	0.00680686	−	0.164883i
$529$	7.21486	−	12.4965i	0.313689	−	0.543326i
$530$	15.1749			0.659156
$531$	21.0829	+	14.6137i	0.914918	+	0.634181i
$532$	33.3082			1.44410
$533$	17.1154	+	25.9236i	0.741351	+	1.12288i
$534$	12.4748	+	23.8256i	0.539837	+	1.03103i
$535$	−8.73632	+	5.04392i	−0.377704	+	0.218068i
$536$	−14.4185	−	24.9735i	−0.622784	−	1.07869i
$537$	7.18278	−	11.3340i	0.309960	−	0.489098i
$538$	−4.08461	−	2.35825i	−0.176100	−	0.101671i
$539$		−	1.16825i		−	0.0503200i
$540$	−19.4961	−	14.7405i	−0.838977	−	0.634329i
$541$			14.2204i			0.611384i	0.952130	+	0.305692i	$0.0988879\pi$
$541$			14.2204i			0.611384i	−0.952130	+	0.305692i	$0.901112\pi$
$542$	−8.97489	+	15.5450i	−0.385505	+	0.667714i
$543$	10.2078	−	16.1073i	0.438060	−	0.691232i
$544$	−43.2284	+	24.9579i	−1.85340	+	1.07006i
$545$	8.53268	+	14.7790i	0.365500	+	0.633065i
$546$	−0.462577	−	24.7726i	−0.0197965	−	1.06017i
$547$	−7.46291	+	12.9261i	−0.319091	+	0.552682i	−0.980299	−	0.197521i	$-0.936711\pi$
$547$	−7.46291	+	12.9261i	−0.319091	+	0.552682i	0.661208	+	0.750203i	$0.270044\pi$
$548$			84.2539i			3.59915i
$549$	1.45537	+	0.120369i	0.0621138	+	0.00513723i
$550$	−0.650222			−0.0277256
$551$	17.0248	+	9.82927i	0.725281	+	0.418741i
$552$	1.46414	−	35.4659i	0.0623178	−	1.50953i
$553$	−18.3509	+	10.5949i	−0.780361	+	0.450542i
$554$	−14.8683	+	8.58421i	−0.631693	+	0.364708i
$555$	−5.93829	−	0.245150i	−0.252066	−	0.0104060i
$556$	16.1360	−	27.9484i	0.684319	−	1.18527i
$557$			12.4593i			0.527919i	0.964534	+	0.263959i	$0.0850285\pi$
$557$			12.4593i			0.527919i	−0.964534	+	0.263959i	$0.914972\pi$
$558$	0.268421	+	0.568569i	0.0113632	+	0.0240694i
$559$	19.1767	+	9.58885i	0.811088	+	0.405565i
$560$	−6.67924	+	11.5688i	−0.282249	+	0.488870i
$561$	2.24431	−	1.17509i	0.0947549	−	0.0496125i
$562$	4.42660	+	7.66710i	0.186725	+	0.323417i
$563$	−3.69857	−	6.40611i	−0.155876	−	0.269985i	0.777502	−	0.628881i	$-0.216487\pi$
$563$	−3.69857	−	6.40611i	−0.155876	−	0.269985i	−0.933378	+	0.358896i	$0.883153\pi$
$564$	31.5636	+	20.0031i	1.32907	+	0.842281i
$565$	15.9129	+	9.18733i	0.669462	+	0.386514i
$566$		−	32.6069i		−	1.37057i
$567$	12.9141	−	4.83968i	0.542339	−	0.203247i
$568$	−54.1599			−2.27250
$569$	15.2090	−	26.3427i	0.637593	−	1.10434i	−0.348367	−	0.937358i	$-0.613264\pi$
$569$	15.2090	−	26.3427i	0.637593	−	1.10434i	0.985959	−	0.166985i	$-0.0534031\pi$
$570$	−17.5047	−	11.0934i	−0.733191	−	0.464651i
$571$	−7.37664	−	12.7767i	−0.308703	−	0.534689i	0.669376	−	0.742924i	$-0.266561\pi$
$571$	−7.37664	−	12.7767i	−0.308703	−	0.534689i	−0.978079	+	0.208235i	$0.933228\pi$
$572$	−4.25146	+	0.255096i	−0.177762	+	0.0106661i
$573$	−5.90104	−	11.2704i	−0.246519	−	0.470827i
$574$	29.6028	+	17.0912i	1.23560	+	0.713371i
$575$	−2.92751			−0.122085
$576$	6.09030	+	12.9004i	0.253763	+	0.537518i
$577$		−	27.6196i		−	1.14982i	−0.818218	−	0.574909i	$-0.805038\pi$
$577$		−	27.6196i		−	1.14982i	0.818218	−	0.574909i	$-0.194962\pi$
$578$	−37.9394	−	21.9043i	−1.57807	−	0.911100i
$579$	1.65291	−	40.0386i	0.0686925	−	1.66395i
$580$	−17.3290	+	10.0049i	−0.719547	+	0.415431i
$581$	−10.4602	−	18.1177i	−0.433963	−	0.751647i
$582$	−40.2126	−	1.66010i	−1.66687	−	0.0688132i
$583$	1.27468	+	0.735938i	0.0527919	+	0.0304794i
$584$	−103.048			−4.26417
$585$	−5.61853	+	9.24295i	−0.232298	+	0.382149i
$586$	28.6629			1.18405
$587$	−29.4387	−	16.9965i	−1.21507	−	0.701519i	−0.251207	−	0.967933i	$-0.580828\pi$
$587$	−29.4387	−	16.9965i	−1.21507	−	0.701519i	−0.963859	+	0.266415i	$0.914161\pi$
$588$	17.5798	+	33.5757i	0.724980	+	1.38464i
$589$	0.187032	+	0.323949i	0.00770653	+	0.0133481i
$590$	−19.1733	+	11.0697i	−0.789351	+	0.455732i
$591$	27.1591	+	17.2117i	1.11718	+	0.707996i
$592$	25.9060	+	14.9568i	1.06473	+	0.614722i
$593$		−	35.6087i		−	1.46228i	−0.682230	−	0.731138i	$-0.738990\pi$
$593$		−	35.6087i		−	1.46228i	0.682230	−	0.731138i	$-0.261010\pi$
$594$	−1.31515	−	3.11218i	−0.0539613	−	0.127694i
$595$	−8.92453			−0.365870
$596$	16.3135	+	9.41861i	0.668227	+	0.385801i
$597$	16.8080	−	26.5219i	0.687904	−	1.08547i
$598$	−27.2802	+	1.63687i	−1.11557	+	0.0669365i
$599$	2.52548	+	4.37425i	0.103188	+	0.178727i	0.912996	−	0.407967i	$-0.133762\pi$
$599$	2.52548	+	4.37425i	0.103188	+	0.178727i	−0.809808	+	0.586694i	$0.800429\pi$
$600$	10.7417	−	5.62423i	0.438529	−	0.229608i
$601$	11.5025	−	19.9230i	0.469198	−	0.812674i	−0.530182	−	0.847884i	$-0.677877\pi$
$601$	11.5025	−	19.9230i	0.469198	−	0.812674i	0.999380	+	0.0352095i	$0.0112098\pi$
$602$	23.5927			0.961566
$603$	−10.1566	−	7.04012i	−0.413610	−	0.286696i
$604$			52.8394i			2.15000i
$605$	9.47166	+	5.46847i	0.385078	+	0.222325i
$606$	−2.81938	+	68.2941i	−0.114529	+	2.77426i
$607$	13.8611	+	24.0081i	0.562604	+	0.974459i	0.997268	+	0.0738660i	$0.0235337\pi$
$607$	13.8611	+	24.0081i	0.562604	+	0.974459i	−0.434664	+	0.900593i	$0.643133\pi$
$608$	19.8030	+	34.2998i	0.803118	+	1.39104i
$609$	0.465713	−	11.2810i	0.0188716	−	0.457130i
$610$	−0.630176	+	1.09150i	−0.0255151	+	0.0441934i
$611$	7.39612	−	14.7915i	0.299215	−	0.598399i
$612$	−46.8192	+	67.5450i	−1.89255	+	2.73034i
$613$		−	17.8934i		−	0.722707i	−0.932429	−	0.361354i	$-0.882315\pi$
$613$		−	17.8934i		−	0.722707i	0.932429	−	0.361354i	$-0.117685\pi$
$614$	−25.4189	+	44.0268i	−1.02582	+	1.77678i
$615$	−6.92192	−	13.2202i	−0.279119	−	0.533089i
$616$	−2.33300	+	1.34696i	−0.0939991	+	0.0542704i
$617$	−1.94317	+	1.12189i	−0.0782290	+	0.0451655i	−0.538604	−	0.842559i	$-0.681048\pi$
$617$	−1.94317	+	1.12189i	−0.0782290	+	0.0451655i	0.460375	+	0.887724i	$0.347715\pi$
$618$	47.8276	+	30.3102i	1.92391	+	1.21925i
$619$	−9.25481	−	5.34327i	−0.371982	−	0.214764i	0.302342	−	0.953200i	$-0.402232\pi$
$619$	−9.25481	−	5.34327i	−0.371982	−	0.214764i	−0.674324	+	0.738436i	$0.735565\pi$
$620$	−0.380748			−0.0152912
$621$	−5.92122	−	14.0120i	−0.237610	−	0.562283i
$622$		−	64.3487i		−	2.58015i
$623$	4.59474	−	7.95833i	0.184085	−	0.318844i
$624$	46.6315	−	28.0963i	1.86675	−	1.12475i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	15.8220	−	9.13482i	0.632373	−	0.365101i
$627$	−0.932386	−	1.78076i	−0.0372359	−	0.0711169i
$628$	36.7996	−	63.7388i	1.46846	−	2.54345i
$629$			19.9847i			0.796844i
$630$	−0.981065	+	11.8620i	−0.0390866	+	0.472592i
$631$			4.80562i			0.191309i	0.995415	+	0.0956543i	$0.0304943\pi$
$631$			4.80562i			0.191309i	−0.995415	+	0.0956543i	$0.969506\pi$
$632$	−83.8345	−	48.4019i	−3.33476	−	1.92532i
$633$	−27.8901	−	1.15138i	−1.10853	−	0.0457634i
$634$	21.8165	+	37.7873i	0.866444	+	1.50073i
$635$	−10.5953	+	6.11721i	−0.420462	+	0.242754i
$636$	−47.7091	−	1.96957i	−1.89179	−	0.0780985i
$637$	13.9972	−	9.24129i	0.554590	−	0.366153i
$638$	−2.76606			−0.109509
$639$	−20.9887	+	9.90876i	−0.830299	+	0.391985i
$640$	4.82901			0.190884
$641$	6.39364	−	11.0741i	0.252534	−	0.437401i	−0.711689	−	0.702495i	$-0.752070\pi$
$641$	6.39364	−	11.0741i	0.252534	−	0.437401i	0.964223	+	0.265094i	$0.0854029\pi$
$642$	40.0782	−	20.9844i	1.58176	−	0.828190i
$643$	−20.8908	+	12.0613i	−0.823855	+	0.475653i	−0.851744	−	0.523958i	$-0.824455\pi$
$643$	−20.8908	+	12.0613i	−0.823855	+	0.475653i	0.0278893	+	0.999611i	$0.491121\pi$
$644$	−18.2738	+	10.5504i	−0.720088	+	0.415743i
$645$	−8.69974	−	5.51336i	−0.342552	−	0.217088i
$646$	−34.8424	+	60.3488i	−1.37086	+	2.37439i
$647$	−20.0819			−0.789500			−0.394750	−	0.918788i	$-0.629169\pi$
$647$	−20.0819			−0.789500			−0.394750	+	0.918788i	$0.629169\pi$
$648$	48.6459	+	40.0378i	1.91099	+	1.57283i
$649$	−2.14739			−0.0842924
$650$	−5.14351	−	7.79056i	−0.201745	−	0.305571i
$651$	0.115002	−	0.181467i	0.00450730	−	0.00711225i
$652$	−76.6881	+	44.2759i	−3.00334	+	1.73398i
$653$	−4.42877	−	7.67086i	−0.173311	−	0.300184i	0.766264	−	0.642525i	$-0.222113\pi$
$653$	−4.42877	−	7.67086i	−0.173311	−	0.300184i	−0.939576	+	0.342342i	$0.888780\pi$
$654$	−35.4989	−	67.7993i	−1.38812	−	2.65116i
$655$	16.1835	+	9.34357i	0.632343	+	0.365084i
$656$			75.1078i			2.93247i
$657$	−39.9345	+	18.8531i	−1.55799	+	0.735528i
$658$		−	18.1976i		−	0.709417i
$659$	−3.88106	+	6.72219i	−0.151185	+	0.261859i	−0.931663	−	0.363323i	$-0.881642\pi$
$659$	−3.88106	+	6.72219i	−0.151185	+	0.261859i	0.780479	+	0.625183i	$0.214975\pi$
$660$	2.04427	+	0.0843932i	0.0795729	+	0.00328500i
$661$	−26.0838	+	15.0595i	−1.01454	+	0.585746i	−0.912518	−	0.409036i	$-0.865865\pi$
$661$	−26.0838	+	15.0595i	−1.01454	+	0.585746i	−0.102024	+	0.994782i	$0.532532\pi$
$662$	0.671431	+	1.16295i	0.0260959	+	0.0451995i
$663$	31.8326	+	17.5945i	1.23628	+	0.683313i
$664$	47.7866	−	82.7688i	1.85448	−	3.21205i
$665$			7.08123i			0.274598i
$666$	26.5625	+	2.19690i	1.02928	+	0.0851282i
$667$	−12.4537			−0.482208
$668$	−5.87366	−	3.39116i	−0.227259	−	0.131208i
$669$	3.59063	−	1.88001i	0.138822	−	0.0726853i
$670$	9.23669	−	5.33280i	0.356844	−	0.206024i
$671$	−0.105869	+	0.0611233i	−0.00408701	+	0.00235964i
$672$	12.1765	−	19.2138i	0.469718	−	0.741187i
$673$	−21.0206	+	36.4087i	−0.810284	+	1.40345i	0.102382	+	0.994745i	$0.467354\pi$
$673$	−21.0206	+	36.4087i	−0.810284	+	1.40345i	−0.912666	+	0.408707i	$0.865980\pi$
$674$		−	28.2916i		−	1.08975i
$675$	3.13378	−	4.14481i	0.120619	−	0.159534i
$676$	−36.6871	−	48.9204i	−1.41104	−	1.88155i
$677$	4.68838	−	8.12051i	0.180189	−	0.312096i	−0.761756	−	0.647864i	$-0.775662\pi$
$677$	4.68838	−	8.12051i	0.180189	−	0.312096i	0.941945	+	0.335768i	$0.108996\pi$
$678$	−69.6021	−	44.1095i	−2.67305	−	1.69402i
$679$	6.87608	+	11.9097i	0.263880	+	0.457053i
$680$	−20.3855	−	35.3087i	−0.781747	−	1.35403i
$681$	−34.9931	+	18.3220i	−1.34094	+	0.702099i
$682$	−0.0455814	−	0.0263164i	−0.00174540	−	0.00100771i
$683$		−	44.3711i		−	1.69781i	−0.528543	−	0.848907i	$-0.677261\pi$
$683$		−	44.3711i		−	1.69781i	0.528543	−	0.848907i	$-0.322739\pi$
$684$	53.5940	+	37.1490i	2.04922	+	1.42043i
$685$	−17.9121			−0.684387
$686$	23.1144	−	40.0353i	0.882512	−	1.52856i
$687$	−1.47279	+	35.6754i	−0.0561903	+	1.36110i
$688$	25.9198	+	44.8943i	0.988181	+	1.71158i
$689$	1.26568	+	21.0940i	0.0482187	+	0.803617i
$690$	13.1174	+	0.541523i	0.499370	+	0.0206154i
$691$	−10.9831	−	6.34108i	−0.417816	−	0.241226i	0.276326	−	0.961064i	$-0.410883\pi$
$691$	−10.9831	−	6.34108i	−0.417816	−	0.241226i	−0.694142	+	0.719838i	$0.744216\pi$
$692$	−83.8160			−3.18621
$693$	−0.657679	+	0.948819i	−0.0249832	+	0.0360426i
$694$			28.4563i			1.08019i
$695$	5.94174	+	3.43047i	0.225383	+	0.130125i
$696$	45.6955	−	23.9256i	1.73208	−	0.906898i
$697$	−43.4555	+	25.0890i	−1.64599	+	0.950315i
$698$	−22.6848	−	39.2912i	−0.858631	−	1.48719i
$699$	−4.04303	+	6.37965i	−0.152921	+	0.241301i
$700$	−6.24210	−	3.60388i	−0.235929	−	0.136214i
$701$	12.8109			0.483863			0.241931	−	0.970293i	$-0.422219\pi$
$701$	12.8109			0.483863			0.241931	+	0.970293i	$0.422219\pi$
$702$	26.8849	−	40.3759i	1.01470	−	1.52389i
$703$	15.8570			0.598059
$704$	−1.03421	−	0.597102i	−0.0389783	−	0.0225041i
$705$	−4.25259	+	6.71033i	−0.160162	+	0.252726i
$706$	1.54861	+	2.68227i	0.0582828	+	0.100949i
$707$	20.2266	−	11.6778i	0.760698	−	0.439189i
$708$	61.7165	−	32.3140i	2.31945	−	1.21444i
$709$	27.3071	+	15.7657i	1.02554	+	0.592095i	0.915703	−	0.401855i	$-0.131634\pi$
$709$	27.3071	+	15.7657i	1.02554	+	0.592095i	0.109835	+	0.993950i	$0.464968\pi$
$710$		−	20.0315i		−	0.751770i
$711$	−41.3438	−	3.41942i	−1.55052	−	0.128238i
$712$	41.9814			1.57332
$713$	−0.205222	−	0.118485i	−0.00768561	−	0.00443729i
$714$	39.9885	+	1.65084i	1.49653	+	0.0617812i
$715$	−0.0542327	−	0.903847i	−0.00202819	−	0.0338020i
$716$	−18.2201	−	31.5581i	−0.680917	−	1.17938i
$717$	0.142096	−	3.44200i	0.00530667	−	0.128544i
$718$	32.5968	−	56.4593i	1.21650	−	2.10704i
$719$	38.0117			1.41760			0.708798	−	0.705412i	$-0.249238\pi$
$719$	38.0117			1.41760			0.708798	+	0.705412i	$0.249238\pi$
$720$	−23.6499	+	11.1651i	−0.881379	+	0.416099i
$721$		−	19.3478i		−	0.720552i
$722$	5.28093	+	3.04895i	0.196536	+	0.113470i
$723$	23.9406	−	12.5350i	0.890362	−	0.466183i
$724$	−25.8936	−	44.8490i	−0.962327	−	1.66680i
$725$	−2.12701	−	3.68409i	−0.0789952	−	0.136824i
$726$	−41.4285	−	26.2548i	−1.53755	−	0.974407i
$727$	21.1813	−	36.6871i	0.785571	−	1.36065i	−0.143087	−	0.989710i	$-0.545703\pi$
$727$	21.1813	−	36.6871i	0.785571	−	1.36065i	0.928658	−	0.370938i	$-0.120964\pi$
$728$	−34.5933	−	17.2976i	−1.28211	−	0.641090i
$729$	26.1769	+	6.61597i	0.969514	+	0.245036i
$730$		−	38.1133i		−	1.41064i
$731$	−17.3165	+	29.9930i	−0.640473	+	1.10933i
$732$	2.12291	−	3.34982i	0.0784649	−	0.123813i
$733$	31.9043	−	18.4200i	1.17841	−	0.680358i	0.222767	−	0.974872i	$-0.428491\pi$
$733$	31.9043	−	18.4200i	1.17841	−	0.680358i	0.955647	+	0.294514i	$0.0951578\pi$
$734$	−13.9989	+	8.08230i	−0.516711	+	0.298323i
$735$	−7.13810	+	3.73742i	−0.263293	+	0.137857i
$736$	−21.7289	−	12.5452i	−0.800939	−	0.462422i
$737$	1.03450			0.0381063
$738$	28.5699	+	60.5165i	1.05167	+	2.22764i
$739$			32.9682i			1.21275i	0.795178	+	0.606377i	$0.207378\pi$
$739$			32.9682i			1.21275i	−0.795178	+	0.606377i	$0.792622\pi$
$740$	−8.07018	+	13.9780i	−0.296666	+	0.513840i
$741$	13.9605	−	25.2578i	0.512850	−	0.927869i
$742$	11.6266	+	20.1379i	0.426827	+	0.739285i
$743$	36.8114	−	21.2531i	1.35048	−	0.779699i	0.362162	−	0.932115i	$-0.382039\pi$
$743$	36.8114	−	21.2531i	1.35048	−	0.779699i	0.988316	+	0.152416i	$0.0487055\pi$
$744$	0.980637	+	0.0404835i	0.0359519	+	0.00148420i
$745$	−2.00237	+	3.46820i	−0.0733611	+	0.127065i
$746$		−	10.4589i		−	0.382929i
$747$	3.37595	−	40.8183i	0.123520	−	1.49346i
$748$		−	6.87978i		−	0.251550i
$749$	−13.3871	−	7.72904i	−0.489153	−	0.282413i
$750$	2.08017	+	3.97292i	0.0759571	+	0.145070i
$751$	2.26265	+	3.91903i	0.0825653	+	0.143007i	0.904351	−	0.426789i	$-0.140355\pi$
$751$	2.26265	+	3.91903i	0.0825653	+	0.143007i	−0.821786	+	0.569796i	$0.807022\pi$
$752$	34.6281	−	19.9926i	1.26276	−	0.729054i
$753$	22.1397	−	34.9351i	0.806816	−	1.27311i
$754$	−21.8806	−	33.1412i	−0.796845	−	1.20693i
$755$	−11.2335			−0.408829
$756$	4.62400	−	37.1661i	0.168173	−	1.35172i
$757$	14.1973			0.516008			0.258004	−	0.966144i	$-0.416935\pi$
$757$	14.1973			0.516008			0.258004	+	0.966144i	$0.416935\pi$
$758$	−22.2532	+	38.5437i	−0.808274	+	1.39997i
$759$	1.07559	+	0.681641i	0.0390414	+	0.0247420i
$760$	−28.0159	+	16.1750i	−1.01624	+	0.586728i
$761$	−28.0332	+	16.1849i	−1.01620	+	0.586704i	−0.913001	−	0.407957i	$-0.866241\pi$
$761$	−28.0332	+	16.1849i	−1.01620	+	0.586704i	−0.103200	+	0.994661i	$0.532908\pi$
$762$	48.6063	−	25.4497i	1.76082	−	0.921945i
$763$	−13.0750	+	22.6466i	−0.473348	+	0.819863i
$764$	−34.5486			−1.24992
$765$	−14.3599	−	9.95362i	−0.519182	−	0.359874i
$766$	−42.1129			−1.52160
$767$	−16.9867	−	25.7287i	−0.613354	−	0.929009i
$768$	−38.0962	−	1.57272i	−1.37468	−	0.0567508i
$769$	6.48735	−	3.74548i	0.233940	−	0.135065i	−0.378448	−	0.925622i	$-0.623542\pi$
$769$	6.48735	−	3.74548i	0.233940	−	0.135065i	0.612388	+	0.790557i	$0.290209\pi$
$770$	−0.498184	−	0.862879i	−0.0179533	−	0.0310960i
$771$	44.4983	+	1.83702i	1.60257	+	0.0661586i
$772$	−94.2456	−	54.4127i	−3.39197	−	1.95836i
$773$			9.00636i			0.323936i	0.986796	+	0.161968i	$0.0517842\pi$
$773$			9.00636i			0.323936i	−0.986796	+	0.161968i	$0.948216\pi$
$774$	37.9614	+	26.3132i	1.36449	+	0.945807i
$775$		−	0.0809459i		−	0.00290766i
$776$	−31.4127	+	54.4085i	−1.12765	+	1.95315i
$777$	−4.22444	−	8.06825i	−0.151551	−	0.289447i
$778$	2.50468	−	1.44608i	0.0897972	−	0.0518444i
$779$	19.9071	+	34.4800i	0.713245	+	1.23538i
$780$	15.1598	+	25.1607i	0.542808	+	0.900897i
$781$	0.971469	−	1.68263i	0.0347619	−	0.0602094i
$782$		−	44.1453i		−	1.57863i
$783$	13.3312	−	17.6321i	0.476417	−	0.630120i
$784$	40.5537			1.44835
$785$	13.5507	+	7.82349i	0.483644	+	0.279232i
$786$	−70.7858	−	44.8597i	−2.52485	−	1.60009i
$787$	−33.9198	+	19.5836i	−1.20911	+	0.698080i	−0.962565	−	0.271052i	$-0.912628\pi$
$787$	−33.9198	+	19.5836i	−1.20911	+	0.698080i	−0.246544	+	0.969131i	$0.579295\pi$
$788$	75.6212	−	43.6599i	2.69389	−	1.55532i
$789$	3.15972	+	6.03475i	0.112489	+	0.214843i
$790$	17.9019	−	31.0069i	0.636920	−	1.10318i
$791$			28.1564i			1.00113i
$792$	−5.25614	−	0.434718i	−0.186769	−	0.0154470i
$793$	−1.56980	−	0.784943i	−0.0557454	−	0.0278741i
$794$	−41.6577	+	72.1532i	−1.47838	+	2.56062i
$795$	0.418725	−	10.1428i	0.0148506	−	0.359728i
$796$	−42.6357	−	73.8471i	−1.51118	−	2.61744i
$797$	0.174764	+	0.302700i	0.00619046	+	0.0107222i	0.869104	−	0.494629i	$-0.164696\pi$
$797$	0.174764	+	0.302700i	0.00619046	+	0.0107222i	−0.862914	+	0.505352i	$0.831363\pi$
$798$	1.30987	−	31.7291i	0.0463689	−	1.12320i
$799$	23.1344	+	13.3566i	0.818435	+	0.472524i
$800$		−	8.57057i		−	0.303016i
$801$	16.2691	−	7.68065i	0.574840	−	0.271382i
$802$	−16.0317			−0.566100
$803$	1.84838	−	3.20149i	0.0652280	−	0.112978i
$804$	−29.7318	+	15.5672i	−1.04856	+	0.549013i
$805$	−2.24298	−	3.88495i	−0.0790546	−	0.136927i
$806$	−0.0452596	−	0.754301i	−0.00159420	−	0.0265691i
$807$	−1.68895	+	2.66505i	−0.0594537	+	0.0938144i
$808$	92.4032	+	53.3490i	3.25073	+	1.87681i
$809$	53.9374			1.89634			0.948169	−	0.317766i	$-0.102933\pi$
$809$	53.9374			1.89634			0.948169	+	0.317766i	$0.102933\pi$
$810$	−14.8083	+	17.9921i	−0.520312	+	0.632178i
$811$			24.9538i			0.876246i	0.898915	+	0.438123i	$0.144357\pi$
$811$			24.9538i			0.876246i	−0.898915	+	0.438123i	$0.855643\pi$
$812$	−26.5540	−	15.3310i	−0.931864	−	0.538012i
$813$	10.1425	+	6.42770i	0.355714	+	0.225429i
$814$	−1.93225	+	1.11558i	−0.0677253	+	0.0391012i
$815$	−9.41293	−	16.3037i	−0.329720	−	0.571093i
$816$	40.7914	+	77.9074i	1.42798	+	2.72731i
$817$	23.7982	+	13.7399i	0.832593	+	0.480698i
$818$	1.15333			0.0403251
$819$	−16.5706	−	0.374374i	−0.579025	−	0.0130817i
$820$	−40.5255			−1.41521
$821$	45.7631	+	26.4213i	1.59714	+	0.922110i	0.992035	+	0.125966i	$0.0402031\pi$
$821$	45.7631	+	26.4213i	1.59714	+	0.922110i	0.605107	+	0.796144i	$0.293130\pi$
$822$	80.2595	+	3.31335i	2.79937	+	0.115566i
$823$	−18.0076	−	31.1901i	−0.627706	−	1.08722i	−0.988011	−	0.154384i	$-0.950661\pi$
$823$	−18.0076	−	31.1901i	−0.627706	−	1.08722i	0.360305	−	0.932835i	$-0.382673\pi$
$824$	76.5470	−	44.1944i	2.66664	−	1.53959i
$825$	−0.0179417	+	0.434605i	−0.000624651	+	0.0151310i
$826$	−29.3801	−	16.9626i	−1.02227	−	0.590205i
$827$		−	37.7986i		−	1.31439i	−0.753722	−	0.657193i	$-0.771744\pi$
$827$		−	37.7986i		−	1.31439i	0.753722	−	0.657193i	$-0.228256\pi$
$828$	−41.1701	−	3.40504i	−1.43076	−	0.118333i
$829$	5.36374			0.186290			0.0931452	−	0.995653i	$-0.470308\pi$
$829$	5.36374			0.186290			0.0931452	+	0.995653i	$0.470308\pi$
$830$	30.6128	+	17.6743i	1.06259	+	0.613484i
$831$	5.32737	+	10.1747i	0.184804	+	0.352958i
$832$	−1.02691	−	17.1146i	−0.0356017	−	0.593341i
$833$	13.5466	+	23.4634i	0.469361	+	0.812957i
$834$	−25.9888	−	16.4701i	−0.899919	−	0.570313i
$835$	0.720951	−	1.24872i	0.0249495	−	0.0432139i
$836$	−5.45881			−0.188797
$837$	0.387434	−	0.163723i	0.0133917	−	0.00565908i
$838$			32.1767i			1.11153i
$839$	23.8149	+	13.7495i	0.822182	+	0.474687i	0.851168	−	0.524893i	$-0.175895\pi$
$839$	23.8149	+	13.7495i	0.822182	+	0.474687i	−0.0289862	+	0.999580i	$0.509228\pi$
$840$	15.6937	+	9.94568i	0.541483	+	0.343159i
$841$	5.45165	+	9.44253i	0.187988	+	0.325604i
$842$	48.7968	+	84.5185i	1.68165	+	2.91270i
$843$	5.24679	−	2.74715i	0.180709	−	0.0946170i
$844$	−37.9028	+	65.6496i	−1.30467	+	2.25975i
$845$	10.4003	−	7.79956i	0.357782	−	0.268313i
$846$	20.2960	−	29.2806i	0.697791	−	1.00669i
$847$			16.7592i			0.575852i
$848$	−25.5468	+	44.2484i	−0.877281	+	1.51950i
$849$	−21.7943	−	0.899731i	−0.747977	−	0.0308787i
$850$	13.0592	−	7.53974i	0.447928	−	0.258611i
$851$	−8.69959	+	5.02271i	−0.298218	+	0.172176i
$852$	−2.59992	+	62.9780i	−0.0890717	+	2.15759i
$853$	1.96422	+	1.13405i	0.0672537	+	0.0388290i	0.533250	−	0.845958i	$-0.320971\pi$
$853$	1.96422	+	1.13405i	0.0672537	+	0.0388290i	−0.465996	+	0.884787i	$0.654304\pi$
$854$	−1.93130			−0.0660876
$855$	−7.89777	+	11.3939i	−0.270098	+	0.389664i
$856$		−	70.6188i		−	2.41370i
$857$	−18.1803	+	31.4892i	−0.621028	+	1.07565i	0.368267	+	0.929720i	$0.379951\pi$
$857$	−18.1803	+	31.4892i	−0.621028	+	1.07565i	−0.989295	+	0.145931i	$0.953382\pi$
$858$	0.0758107	+	4.05993i	0.00258813	+	0.138604i
$859$	−21.3591	−	36.9951i	−0.728764	−	1.26226i	−0.957406	−	0.288746i	$-0.906762\pi$
$859$	−21.3591	−	36.9951i	−0.728764	−	1.26226i	0.228641	−	0.973511i	$-0.426572\pi$
$860$	−24.2234	+	13.9854i	−0.826011	+	0.476898i
$861$	12.2405	−	19.3147i	0.417154	−	0.658243i
$862$	−19.8386	+	34.3615i	−0.675707	+	1.17036i
$863$		−	11.9420i		−	0.406510i	−0.979126	−	0.203255i	$-0.934848\pi$
$863$		−	11.9420i		−	0.406510i	0.979126	−	0.203255i	$-0.0651520\pi$
$864$	41.0217	−	17.3350i	1.39559	−	0.589748i
$865$		−	17.8190i		−	0.605865i
$866$	59.2339	+	34.1987i	2.01285	+	1.16212i
$867$	−15.6876	+	24.7541i	−0.532778	+	0.840692i
$868$	−0.291719	−	0.505273i	−0.00990160	−	0.0171501i
$869$	3.00749	−	1.73638i	0.102022	−	0.0589025i
$870$	8.84910	+	16.9009i	0.300013	+	0.572994i
$871$	8.18330	+	12.3947i	0.277281	+	0.419980i
$872$	−119.464			−4.04557
$873$	−2.21919	+	26.8321i	−0.0751084	+	0.908128i
$874$	−35.0274			−1.18482
$875$	0.766174	−	1.32705i	0.0259014	−	0.0448626i
$876$	−4.94678	+	119.826i	−0.167136	+	4.04855i
$877$	4.90269	−	2.83057i	0.165552	−	0.0955816i	−0.414935	−	0.909851i	$-0.636196\pi$
$877$	4.90269	−	2.83057i	0.165552	−	0.0955816i	0.580487	+	0.814270i	$0.302862\pi$
$878$	−9.03900	+	5.21867i	−0.305052	+	0.176122i
$879$	0.790903	−	19.1581i	0.0266765	−	0.646187i
$880$	1.09464	−	1.89598i	0.0369004	−	0.0639134i
$881$	−17.9922			−0.606171			−0.303086	−	0.952963i	$-0.598017\pi$
$881$	−17.9922			−0.606171			−0.303086	+	0.952963i	$0.598017\pi$
$882$	32.6753	−	15.4260i	1.10023	−	0.519421i
$883$	−19.6145			−0.660080			−0.330040	−	0.943967i	$-0.607062\pi$
$883$	−19.6145			−0.660080			−0.330040	+	0.943967i	$0.607062\pi$
$884$	82.4292	−	54.4217i	2.77239	−	1.83040i
$885$	6.86986	+	13.1207i	0.230928	+	0.441049i
$886$	8.27822	−	4.77943i	0.278112	−	0.160568i
$887$	8.49316	+	14.7106i	0.285172	+	0.493933i	0.972651	−	0.232272i	$-0.0746158\pi$
$887$	8.49316	+	14.7106i	0.285172	+	0.493933i	−0.687479	+	0.726205i	$0.741283\pi$
$888$	22.2714	−	35.1429i	0.747379	−	1.17932i
$889$	−16.2357	−	9.37369i	−0.544528	−	0.314383i
$890$			15.5272i			0.520472i
$891$	−2.11645	+	0.793164i	−0.0709039	+	0.0265720i
$892$		−	11.0068i		−	0.368536i
$893$	10.5979	−	18.3561i	0.354646	−	0.614264i
$894$	9.61362	−	15.1697i	0.321528	−	0.507351i
$895$	6.70917	−	3.87354i	0.224263	−	0.129478i
$896$	3.69987	+	6.40836i	0.123604	+	0.214088i
$897$	0.341323	+	18.2791i	0.0113965	+	0.610321i
$898$	−15.8619	+	27.4735i	−0.529317	+	0.916804i
$899$		−	0.344346i		−	0.0114846i
$900$	−6.02430	−	12.7606i	−0.200810	−	0.425355i
$901$	−34.1347			−1.13719
$902$	−4.85153	−	2.80103i	−0.161538	−	0.0932641i
$903$	0.650999	−	15.7692i	0.0216639	−	0.524766i
$904$	−111.397	+	64.3149i	−3.70500	+	2.13908i
$905$	9.53476	−	5.50490i	0.316946	−	0.182989i
$906$	50.3343	+	2.07795i	1.67225	+	0.0690352i
$907$	0.585772	−	1.01459i	0.0194502	−	0.0336888i	−0.856136	−	0.516750i	$-0.827142\pi$
$907$	0.585772	−	1.01459i	0.0194502	−	0.0336888i	0.875587	+	0.483061i	$0.160475\pi$
$908$			107.269i			3.55985i
$909$	45.5696	+	3.76891i	1.51145	+	0.125007i
$910$	6.39765	−	12.7946i	0.212080	−	0.424138i
$911$	−8.73068	+	15.1220i	−0.289260	+	0.501014i	−0.973633	−	0.228118i	$-0.926743\pi$
$911$	−8.73068	+	15.1220i	−0.289260	+	0.501014i	0.684373	+	0.729132i	$0.260076\pi$
$912$	61.8162	−	32.3662i	2.04694	−	1.07175i
$913$	1.71430	+	2.96926i	0.0567351	+	0.0982681i
$914$	−16.2673	−	28.1758i	−0.538074	−	0.931972i
$915$	0.712161	+	0.451324i	0.0235433	+	0.0149203i
$916$	83.9753	+	48.4832i	2.77462	+	1.60193i
$917$			28.6352i			0.945618i
$918$	62.5016	+	47.2558i	2.06286	+	1.55967i
$919$	−18.2213			−0.601067			−0.300533	−	0.953771i	$-0.597165\pi$
$919$	−18.2213			−0.601067			−0.300533	+	0.953771i	$0.597165\pi$
$920$	10.2468	−	17.7481i	0.337828	−	0.585136i
$921$	28.7259	+	18.2047i	0.946550	+	0.599865i
$922$	4.42182	+	7.65881i	0.145625	+	0.252229i
$923$	27.8450	−	1.67076i	0.916528	−	0.0549936i
$924$	1.45427	+	2.77751i	0.0478419	+	0.0913733i
$925$	−2.97167	−	1.71570i	−0.0977080	−	0.0564117i
$926$	93.1171			3.06002
$927$	21.5789	−	31.1313i	0.708742	−	1.02249i
$928$		−	36.4594i		−	1.19684i
$929$	27.3867	+	15.8117i	0.898530	+	0.518767i	0.876723	−	0.480996i	$-0.159725\pi$
$929$	27.3867	+	15.8117i	0.898530	+	0.518767i	0.0218070	+	0.999762i	$0.493058\pi$
$930$	−0.0149732	+	0.362697i	−0.000490990	+	0.0118933i
$931$	18.6172	−	10.7486i	0.610153	−	0.352272i
$932$	10.2557	+	17.7634i	0.335936	+	0.581859i
$933$	−43.0102	−	1.77559i	−1.40809	−	0.0581302i
$934$	−70.3281	−	40.6039i	−2.30121	−	1.32860i
$935$	1.46262			0.0478328
$936$	−36.3696	−	66.4146i	−1.18878	−	2.17083i
$937$	−39.3498			−1.28550			−0.642751	−	0.766075i	$-0.722207\pi$
$937$	−39.3498			−1.28550			−0.642751	+	0.766075i	$0.722207\pi$
$938$	14.1538	+	8.17171i	0.462138	+	0.266816i
$939$	−5.66908	−	10.8274i	−0.185003	−	0.353338i
$940$	10.7873	+	18.6841i	0.351842	+	0.609409i
$941$	6.49145	−	3.74784i	0.211615	−	0.122176i	−0.390447	−	0.920626i	$-0.627679\pi$
$941$	6.49145	−	3.74784i	0.211615	−	0.122176i	0.602062	+	0.798450i	$0.294346\pi$
$942$	−59.2698	−	37.5615i	−1.93111	−	1.22382i
$943$	−21.8431	−	12.6111i	−0.711309	−	0.410674i
$944$		−	74.5430i		−	2.42617i
$945$	7.90140	+	0.983048i	0.257032	+	0.0319786i
$946$	−3.86655			−0.125712
$947$	5.54331	+	3.20043i	0.180133	+	0.104000i	0.587355	−	0.809329i	$-0.300169\pi$
$947$	5.54331	+	3.20043i	0.180133	+	0.104000i	−0.407222	+	0.913329i	$0.633502\pi$
$948$	−60.3070	+	95.1607i	−1.95868	+	3.09068i
$949$	52.9797	−	3.17889i	1.71979	−	0.103191i
$950$	−5.98246	−	10.3619i	−0.194097	−	0.336185i
$951$	25.8588	−	13.5393i	0.838529	−	0.439043i
$952$	31.2376	−	54.1052i	1.01242	−	1.75356i
$953$	−3.81114			−0.123455			−0.0617274	−	0.998093i	$-0.519661\pi$
$953$	−3.81114			−0.123455			−0.0617274	+	0.998093i	$0.519661\pi$
$954$	−3.75239	+	45.3698i	−0.121488	+	1.46890i
$955$		−	7.34493i		−	0.237676i
$956$	−8.10202	−	4.67771i	−0.262038	−	0.151288i
$957$	−0.0763246	+	1.84882i	−0.00246722	+	0.0597638i
$958$	18.8389	+	32.6300i	0.608658	+	1.05423i
$959$	−13.7238	−	23.7703i	−0.443165	−	0.767584i
$960$	−0.339732	+	8.22936i	−0.0109648	+	0.265601i
$961$	−15.4967	+	26.8411i	−0.499894	+	0.865842i
$962$	−28.6511	−	14.3263i	−0.923748	−	0.461898i
$963$	−12.9200	−	27.3670i	−0.416341	−	0.881890i
$964$		−	73.3884i		−	2.36368i
$965$	11.5680	−	20.0363i	0.372387	−	0.644992i
$966$	9.33156	+	17.8223i	0.300238	+	0.573425i
$967$	−1.24008	+	0.715960i	−0.0398783	+	0.0230237i	−0.519807	−	0.854284i	$-0.673996\pi$
$967$	−1.24008	+	0.715960i	−0.0398783	+	0.0230237i	0.479928	+	0.877308i	$0.340663\pi$
$968$	−66.3054	+	38.2814i	−2.13113	+	1.23041i
$969$	39.3754	+	24.9537i	1.26492	+	0.801627i
$970$	−20.1235	−	11.6183i	−0.646125	−	0.373040i
$971$	−8.89250			−0.285374			−0.142687	−	0.989768i	$-0.545574\pi$
$971$	−8.89250			−0.285374			−0.142687	+	0.989768i	$0.545574\pi$
$972$	48.8919	−	54.6442i	1.56821	−	1.75271i
$973$			10.5133i			0.337042i
$974$	2.59866	−	4.50100i	0.0832663	−	0.144221i
$975$	−5.34909	+	3.22293i	−0.171308	+	0.103216i
$976$	−2.12179	−	3.67505i	−0.0679169	−	0.117635i
$977$	−26.7155	+	15.4242i	−0.854704	+	0.493463i	−0.862235	−	0.506508i	$-0.830936\pi$
$977$	−26.7155	+	15.4242i	−0.854704	+	0.493463i	0.00753136	+	0.999972i	$0.497603\pi$
$978$	39.1610	+	74.7936i	1.25223	+	2.39164i
$979$	−0.753022	+	1.30427i	−0.0240667	+	0.0416847i
$980$			21.8813i			0.698974i
$981$	−46.2962	+	21.8564i	−1.47812	+	0.697823i
$982$			38.6522i			1.23344i
$983$	−47.2004	−	27.2512i	−1.50546	−	0.869178i	−0.999980	−	0.00633959i	$-0.997982\pi$
$983$	−47.2004	−	27.2512i	−1.50546	−	0.869178i	−0.505480	−	0.862838i	$-0.668685\pi$
$984$	104.376	+	4.30893i	3.32737	+	0.137364i
$985$	9.28197	+	16.0768i	0.295748	+	0.512251i
$986$	55.5542	−	32.0742i	1.76921	−	1.02145i
$987$	−12.1632	−	0.502132i	−0.387158	−	0.0159830i
$988$	−43.1813	−	65.4040i	−1.37378	−	2.08078i
$989$	−17.4084			−0.553555
$990$	0.160784	−	1.94403i	0.00511006	−	0.0617853i
$991$	38.1517			1.21193			0.605964	−	0.795492i	$-0.292788\pi$
$991$	38.1517			1.21193			0.605964	+	0.795492i	$0.292788\pi$
$992$	0.346877	−	0.600808i	0.0110133	−	0.0190757i
$993$	0.795838	−	0.416691i	0.0252551	−	0.0132233i
$994$	26.5829	−	15.3476i	0.843158	−	0.486797i
$995$	15.6997	−	9.06422i	0.497713	−	0.287355i
$996$	−93.9510	−	59.5403i	−2.97695	−	1.88661i
$997$	−4.54387	+	7.87021i	−0.143906	+	0.249252i	−0.928964	−	0.370170i	$-0.879300\pi$
$997$	−4.54387	+	7.87021i	−0.143906	+	0.249252i	0.785058	+	0.619422i	$0.212633\pi$
$998$	−74.4561			−2.35687
$999$	2.20134	−	17.6936i	0.0696474	−	0.559801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.4	✓	108
9.4	even	3	inner	585.2.bt.b.571.51	yes	108
13.12	even	2	inner	585.2.bt.b.376.51	yes	108
117.103	even	6	inner	585.2.bt.b.571.4	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.4	✓	108	1.1	even	1	trivial
585.2.bt.b.376.51	yes	108	13.12	even	2	inner
585.2.bt.b.571.4	yes	108	117.103	even	6	inner
585.2.bt.b.571.51	yes	108	9.4	even	3	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.24228 - 1.29458i) q^{2} +(-0.927160 + 1.46300i) q^{3} +(2.35187 + 4.07355i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(3.97292 - 2.08017i) q^{6} +(-1.32705 - 0.766174i) q^{7} -7.00039i q^{8} +(-1.28075 - 2.71287i) q^{9} +O(q^{10})\)	\(q+(-2.24228 - 1.29458i) q^{2} +(-0.927160 + 1.46300i) q^{3} +(2.35187 + 4.07355i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(3.97292 - 2.08017i) q^{6} +(-1.32705 - 0.766174i) q^{7} -7.00039i q^{8} +(-1.28075 - 2.71287i) q^{9} +2.58916 q^{10} +(0.217487 + 0.125566i) q^{11} +(-8.14017 - 0.336050i) q^{12} +(0.215952 + 3.59908i) q^{13} +(1.98374 + 3.43595i) q^{14} +(0.0714432 - 1.73058i) q^{15} +(-4.35882 + 7.54970i) q^{16} -5.82409 q^{17} +(-0.640236 + 7.74104i) q^{18} +4.62116i q^{19} +(-4.07355 - 2.35187i) q^{20} +(2.35130 - 1.23111i) q^{21} +(-0.325111 - 0.563109i) q^{22} +(-1.46375 - 2.53529i) q^{23} +(10.2416 + 6.49048i) q^{24} +(0.500000 - 0.866025i) q^{25} +(4.17507 - 8.34969i) q^{26} +(5.15640 + 0.641531i) q^{27} -7.20776i q^{28} +(2.12701 - 3.68409i) q^{29} +(-2.40056 + 3.78794i) q^{30} +(0.0701012 - 0.0404730i) q^{31} +(7.42234 - 4.28529i) q^{32} +(-0.385350 + 0.201764i) q^{33} +(13.0592 + 7.53974i) q^{34} +1.53235 q^{35} +(8.03889 - 11.5975i) q^{36} -3.43139i q^{37} +(5.98246 - 10.3619i) q^{38} +(-5.46568 - 3.02098i) q^{39} +(3.50020 + 6.06252i) q^{40} +(7.46133 - 4.30780i) q^{41} +(-6.86605 - 0.283450i) q^{42} +(2.97325 - 5.14982i) q^{43} +1.18126i q^{44} +(2.46560 + 1.70904i) q^{45} +7.57977i q^{46} +(-3.97219 - 2.29334i) q^{47} +(-7.00390 - 13.3768i) q^{48} +(-2.32595 - 4.02867i) q^{49} +(-2.24228 + 1.29458i) q^{50} +(5.39986 - 8.52066i) q^{51} +(-14.1531 + 9.34425i) q^{52} +5.86094 q^{53} +(-10.7316 - 8.11385i) q^{54} -0.251133 q^{55} +(-5.36352 + 9.28989i) q^{56} +(-6.76077 - 4.28456i) q^{57} +(-9.53869 + 5.50717i) q^{58} +(-7.40522 + 4.27541i) q^{59} +(7.21762 - 3.77906i) q^{60} +(-0.243390 + 0.421564i) q^{61} -0.209582 q^{62} +(-0.378913 + 4.58140i) q^{63} -4.75527 q^{64} +(-1.98656 - 3.00892i) q^{65} +(1.12526 + 0.0464540i) q^{66} +(3.56745 - 2.05967i) q^{67} +(-13.6975 - 23.7247i) q^{68} +(5.06627 + 0.209150i) q^{69} +(-3.43595 - 1.98374i) q^{70} -7.73670i q^{71} +(-18.9912 + 8.96574i) q^{72} -14.7204i q^{73} +(-4.44221 + 7.69413i) q^{74} +(0.803417 + 1.53445i) q^{75} +(-18.8246 + 10.8684i) q^{76} +(-0.192411 - 0.333266i) q^{77} +(8.34466 + 13.8496i) q^{78} +(6.91417 - 11.9757i) q^{79} -8.71765i q^{80} +(-5.71937 + 6.94902i) q^{81} -22.3072 q^{82} +(11.8235 + 6.82628i) q^{83} +(10.5450 + 6.68274i) q^{84} +(5.04381 - 2.91205i) q^{85} +(-13.3337 + 7.69821i) q^{86} +(3.41775 + 6.52756i) q^{87} +(0.879014 - 1.52250i) q^{88} +5.99700i q^{89} +(-3.31606 - 7.02406i) q^{90} +(2.47094 - 4.94162i) q^{91} +(6.88510 - 11.9254i) q^{92} +(-0.00578304 + 0.140083i) q^{93} +(5.93783 + 10.2846i) q^{94} +(-2.31058 - 4.00205i) q^{95} +(-0.612310 + 14.8320i) q^{96} +(-7.77220 - 4.48728i) q^{97} +12.0445i q^{98} +(0.0620991 - 0.750835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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