LMFDB - Embedded newform 168.2.ba.c.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30261 - 0.550645i) q^{2} +(-1.09218 + 1.34430i) q^{3} +(1.39358 + 1.43455i) q^{4} +(-2.46958 + 1.42581i) q^{5} +(2.16291 - 1.14970i) q^{6} +(-1.02032 - 2.44110i) q^{7} +(-1.02536 - 2.63603i) q^{8} +(-0.614290 - 2.93643i) q^{9} +O(q^{10})$	\(q+(-1.30261 - 0.550645i) q^{2} +(-1.09218 + 1.34430i) q^{3} +(1.39358 + 1.43455i) q^{4} +(-2.46958 + 1.42581i) q^{5} +(2.16291 - 1.14970i) q^{6} +(-1.02032 - 2.44110i) q^{7} +(-1.02536 - 2.63603i) q^{8} +(-0.614290 - 2.93643i) q^{9} +(4.00201 - 0.497414i) q^{10} +(2.42621 - 4.20231i) q^{11} +(-3.45051 + 0.306605i) q^{12} -2.75221 q^{13} +(-0.0151045 + 3.74163i) q^{14} +(0.780502 - 4.87710i) q^{15} +(-0.115871 + 3.99832i) q^{16} +(-1.75366 + 3.03743i) q^{17} +(-0.816754 + 4.16328i) q^{18} +(-3.14493 - 5.44717i) q^{19} +(-5.48696 - 1.55575i) q^{20} +(4.39594 + 1.29450i) q^{21} +(-5.47438 + 4.13799i) q^{22} +(-3.15865 + 1.82365i) q^{23} +(4.66349 + 1.50062i) q^{24} +(1.56588 - 2.71219i) q^{25} +(3.58505 + 1.51549i) q^{26} +(4.61837 + 2.38132i) q^{27} +(2.07998 - 4.86556i) q^{28} -3.90427 q^{29} +(-3.70224 + 5.92318i) q^{30} +(-0.858051 - 0.495396i) q^{31} +(2.35259 - 5.14445i) q^{32} +(2.99932 + 7.85123i) q^{33} +(3.95689 - 2.99094i) q^{34} +(6.00030 + 4.57370i) q^{35} +(3.35640 - 4.97339i) q^{36} +(-1.06516 + 0.614970i) q^{37} +(1.09715 + 8.82727i) q^{38} +(3.00591 - 3.69980i) q^{39} +(6.29069 + 5.04791i) q^{40} +2.10659 q^{41} +(-5.01338 - 4.10683i) q^{42} +5.11768i q^{43} +(9.40954 - 2.37574i) q^{44} +(5.70384 + 6.37590i) q^{45} +(5.11867 - 0.636204i) q^{46} +(-5.61268 - 9.72145i) q^{47} +(-5.24840 - 4.52265i) q^{48} +(-4.91791 + 4.98138i) q^{49} +(-3.53319 + 2.67068i) q^{50} +(-2.16791 - 5.67487i) q^{51} +(-3.83543 - 3.94819i) q^{52} +(1.00417 - 1.73927i) q^{53} +(-4.70466 - 5.64501i) q^{54} +13.8373i q^{55} +(-5.38860 + 5.19259i) q^{56} +(10.7575 + 1.72156i) q^{57} +(5.08574 + 2.14987i) q^{58} +(0.890996 + 0.514417i) q^{59} +(8.08414 - 5.67696i) q^{60} +(-1.24347 - 2.15376i) q^{61} +(0.844918 + 1.11779i) q^{62} +(-6.54135 + 4.49563i) q^{63} +(-5.89727 + 5.40576i) q^{64} +(6.79681 - 3.92414i) q^{65} +(0.416299 - 11.8786i) q^{66} +(-5.02777 - 2.90279i) q^{67} +(-6.80122 + 1.71719i) q^{68} +(0.998281 - 6.23793i) q^{69} +(-5.29756 - 9.26178i) q^{70} +9.75277i q^{71} +(-7.11065 + 4.63019i) q^{72} +(0.291019 + 0.168020i) q^{73} +(1.72612 - 0.214540i) q^{74} +(1.93577 + 5.06722i) q^{75} +(3.43154 - 12.1026i) q^{76} +(-12.7338 - 1.63491i) q^{77} +(-5.95280 + 3.16420i) q^{78} +(-2.80082 - 4.85116i) q^{79} +(-5.41471 - 10.0394i) q^{80} +(-8.24530 + 3.60764i) q^{81} +(-2.74407 - 1.15999i) q^{82} -0.138115i q^{83} +(4.26906 + 8.11019i) q^{84} -10.0016i q^{85} +(2.81803 - 6.66634i) q^{86} +(4.26417 - 5.24852i) q^{87} +(-13.5651 - 2.08666i) q^{88} +(-0.580993 - 1.00631i) q^{89} +(-3.91902 - 11.4461i) q^{90} +(2.80813 + 6.71841i) q^{91} +(-7.01795 - 1.98985i) q^{92} +(1.60311 - 0.612418i) q^{93} +(1.95806 + 15.7538i) q^{94} +(15.5333 + 8.96815i) q^{95} +(4.34623 + 8.78124i) q^{96} +11.0953i q^{97} +(9.14908 - 3.78077i) q^{98} +(-13.8302 - 4.54296i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.30261	−	0.550645i	−0.921084	−	0.389365i
$2$	−1.30261	−	0.550645i	−0.921084	−	0.389365i
$3$	−1.09218	+	1.34430i	−0.630570	+	0.776132i
$3$	−1.09218	+	1.34430i	−0.630570	+	0.776132i
$4$	1.39358	+	1.43455i	0.696790	+	0.717275i
$5$	−2.46958	+	1.42581i	−1.10443	+	0.637643i	−0.937381	−	0.348306i	$-0.886757\pi$
$5$	−2.46958	+	1.42581i	−1.10443	+	0.637643i	−0.167049	+	0.985949i	$0.553424\pi$
$6$	2.16291	−	1.14970i	0.883006	−	0.469361i
$7$	−1.02032	−	2.44110i	−0.385643	−	0.922648i
$7$	−1.02032	−	2.44110i	−0.385643	−	0.922648i
$8$	−1.02536	−	2.63603i	−0.362520	−	0.931976i
$9$	−0.614290	−	2.93643i	−0.204763	−	0.978812i
$10$	4.00201	−	0.497414i	1.26555	−	0.157296i
$11$	2.42621	−	4.20231i	0.731529	−	1.26705i	−0.224701	−	0.974428i	$-0.572140\pi$
$11$	2.42621	−	4.20231i	0.731529	−	1.26705i	0.956230	−	0.292617i	$-0.0945262\pi$
$12$	−3.45051	+	0.306605i	−0.996075	+	0.0885091i
$13$	−2.75221			−0.763326			−0.381663	−	0.924302i	$-0.624649\pi$
$13$	−2.75221			−0.763326			−0.381663	+	0.924302i	$0.624649\pi$
$14$	−0.0151045	+	3.74163i	−0.00403685	+	0.999992i
$15$	0.780502	−	4.87710i	0.201525	−	1.25926i
$16$	−0.115871	+	3.99832i	−0.0289677	+	0.999580i
$17$	−1.75366	+	3.03743i	−0.425326	+	0.736686i	−0.996451	−	0.0841773i	$-0.973174\pi$
$17$	−1.75366	+	3.03743i	−0.425326	+	0.736686i	0.571125	+	0.820863i	$0.306507\pi$
$18$	−0.816754	+	4.16328i	−0.192511	+	0.981295i
$19$	−3.14493	−	5.44717i	−0.721496	−	1.24967i	−0.960400	−	0.278624i	$-0.910122\pi$
$19$	−3.14493	−	5.44717i	−0.721496	−	1.24967i	0.238905	−	0.971043i	$-0.423212\pi$
$20$	−5.48696	−	1.55575i	−1.22692	−	0.347877i
$21$	4.39594	+	1.29450i	0.959272	+	0.282484i
$22$	−5.47438	+	4.13799i	−1.16714	+	0.882223i
$23$	−3.15865	+	1.82365i	−0.658624	+	0.380257i	−0.791753	−	0.610842i	$-0.790831\pi$
$23$	−3.15865	+	1.82365i	−0.658624	+	0.380257i	0.133128	+	0.991099i	$0.457498\pi$
$24$	4.66349	+	1.50062i	0.951931	+	0.306313i
$25$	1.56588	−	2.71219i	0.313177	−	0.542438i
$26$	3.58505	+	1.51549i	0.703087	+	0.297212i
$27$	4.61837	+	2.38132i	0.888805	+	0.458286i
$28$	2.07998	−	4.86556i	0.393080	−	0.919504i
$29$	−3.90427			−0.725005			−0.362503	−	0.931983i	$-0.618078\pi$
$29$	−3.90427			−0.725005			−0.362503	+	0.931983i	$0.618078\pi$
$30$	−3.70224	+	5.92318i	−0.675934	+	1.08142i
$31$	−0.858051	−	0.495396i	−0.154111	−	0.0889758i	0.420962	−	0.907078i	$-0.361693\pi$
$31$	−0.858051	−	0.495396i	−0.154111	−	0.0889758i	−0.575072	+	0.818103i	$0.695026\pi$
$32$	2.35259	−	5.14445i	0.415883	−	0.909418i
$33$	2.99932	+	7.85123i	0.522115	+	1.36672i
$34$	3.95689	−	2.99094i	0.678600	−	0.512942i
$35$	6.00030	+	4.57370i	1.01424	+	0.773097i
$36$	3.35640	−	4.97339i	0.559400	−	0.828898i
$37$	−1.06516	+	0.614970i	−0.175111	+	0.101100i	−0.584994	−	0.811038i	$-0.698903\pi$
$37$	−1.06516	+	0.614970i	−0.175111	+	0.101100i	0.409883	+	0.912138i	$0.365570\pi$
$38$	1.09715	+	8.82727i	0.177981	+	1.43197i
$39$	3.00591	−	3.69980i	0.481330	−	0.592442i
$40$	6.29069	+	5.04791i	0.994646	+	0.798144i
$41$	2.10659			0.328995			0.164497	−	0.986378i	$-0.447400\pi$
$41$	2.10659			0.328995			0.164497	+	0.986378i	$0.447400\pi$
$42$	−5.01338	−	4.10683i	−0.773581	−	0.633698i
$43$			5.11768i			0.780439i	0.920722	+	0.390220i	$0.127601\pi$
$43$			5.11768i			0.780439i	−0.920722	+	0.390220i	$0.872399\pi$
$44$	9.40954	−	2.37574i	1.41854	−	0.358157i
$45$	5.70384	+	6.37590i	0.850279	+	0.950463i
$46$	5.11867	−	0.636204i	0.754706	−	0.0938032i
$47$	−5.61268	−	9.72145i	−0.818693	−	1.41802i	−0.906645	−	0.421894i	$-0.861365\pi$
$47$	−5.61268	−	9.72145i	−0.818693	−	1.41802i	0.0879518	−	0.996125i	$-0.471968\pi$
$48$	−5.24840	−	4.52265i	−0.757541	−	0.652788i
$49$	−4.91791	+	4.98138i	−0.702558	+	0.711626i
$50$	−3.53319	+	2.67068i	−0.499668	+	0.377691i
$51$	−2.16791	−	5.67487i	−0.303568	−	0.794641i
$52$	−3.83543	−	3.94819i	−0.531878	−	0.547515i
$53$	1.00417	−	1.73927i	0.137933	−	0.238907i	−0.788781	−	0.614674i	$-0.789288\pi$
$53$	1.00417	−	1.73927i	0.137933	−	0.238907i	0.926714	+	0.375767i	$0.122621\pi$
$54$	−4.70466	−	5.64501i	−0.640223	−	0.768189i
$55$			13.8373i			1.86582i
$56$	−5.38860	+	5.19259i	−0.720082	+	0.693889i
$57$	10.7575	+	1.72156i	1.42486	+	0.228026i
$58$	5.08574	+	2.14987i	0.667791	+	0.282292i
$59$	0.890996	+	0.514417i	0.115998	+	0.0669714i	0.556876	−	0.830595i	$-0.312000\pi$
$59$	0.890996	+	0.514417i	0.115998	+	0.0669714i	−0.440879	+	0.897567i	$0.645333\pi$
$60$	8.08414	−	5.67696i	1.04366	−	0.732892i
$61$	−1.24347	−	2.15376i	−0.159211	−	0.275761i	0.775374	−	0.631503i	$-0.217562\pi$
$61$	−1.24347	−	2.15376i	−0.159211	−	0.275761i	−0.934584	+	0.355742i	$0.884228\pi$
$62$	0.844918	+	1.11779i	0.107305	+	0.141959i
$63$	−6.54135	+	4.49563i	−0.824133	+	0.566397i
$64$	−5.89727	+	5.40576i	−0.737159	+	0.675720i
$65$	6.79681	−	3.92414i	0.843040	−	0.486729i
$66$	0.416299	−	11.8786i	0.0512429	−	1.46216i
$67$	−5.02777	−	2.90279i	−0.614240	−	0.354632i	0.160383	−	0.987055i	$-0.448727\pi$
$67$	−5.02777	−	2.90279i	−0.614240	−	0.354632i	−0.774623	+	0.632423i	$0.782060\pi$
$68$	−6.80122	+	1.71719i	−0.824769	+	0.208240i
$69$	0.998281	−	6.23793i	0.120179	−	0.750958i
$70$	−5.29756	−	9.26178i	−0.633179	−	1.10699i
$71$			9.75277i			1.15744i	0.815526	+	0.578720i	$0.196448\pi$
$71$			9.75277i			1.15744i	−0.815526	+	0.578720i	$0.803552\pi$
$72$	−7.11065	+	4.63019i	−0.837998	+	0.545673i
$73$	0.291019	+	0.168020i	0.0340612	+	0.0196652i	0.516934	−	0.856025i	$-0.327073\pi$
$73$	0.291019	+	0.168020i	0.0340612	+	0.0196652i	−0.482873	+	0.875691i	$0.660407\pi$
$74$	1.72612	−	0.214540i	0.200657	−	0.0249398i
$75$	1.93577	+	5.06722i	0.223524	+	0.585112i
$76$	3.43154	−	12.1026i	0.393624	−	1.38827i
$77$	−12.7338	−	1.63491i	−1.45115	−	0.186316i
$78$	−5.95280	+	3.16420i	−0.674022	+	0.358276i
$79$	−2.80082	−	4.85116i	−0.315117	−	0.545798i	0.664346	−	0.747426i	$-0.268710\pi$
$79$	−2.80082	−	4.85116i	−0.315117	−	0.545798i	−0.979462	+	0.201627i	$0.935377\pi$
$80$	−5.41471	−	10.0394i	−0.605383	−	1.12244i
$81$	−8.24530	+	3.60764i	−0.916144	+	0.400849i
$82$	−2.74407	−	1.15999i	−0.303032	−	0.128099i
$83$		−	0.138115i		−	0.0151600i	−0.999971	−	0.00758002i	$-0.997587\pi$
$83$		−	0.138115i		−	0.0151600i	0.999971	−	0.00758002i	$-0.00241282\pi$
$84$	4.26906	+	8.11019i	0.465793	+	0.884894i
$85$		−	10.0016i		−	1.08482i
$86$	2.81803	−	6.66634i	0.303876	−	0.718850i
$87$	4.26417	−	5.24852i	0.457167	−	0.562700i
$88$	−13.5651	−	2.08666i	−1.44605	−	0.222438i
$89$	−0.580993	−	1.00631i	−0.0615852	−	0.106669i	0.833589	−	0.552385i	$-0.186282\pi$
$89$	−0.580993	−	1.00631i	−0.0615852	−	0.106669i	−0.895174	+	0.445717i	$0.852949\pi$
$90$	−3.91902	−	11.4461i	−0.413101	−	1.20652i
$91$	2.80813	+	6.71841i	0.294372	+	0.704281i
$92$	−7.01795	−	1.98985i	−0.731671	−	0.207456i
$93$	1.60311	−	0.612418i	0.166234	−	0.0635048i
$94$	1.95806	+	15.7538i	0.201958	+	1.62488i
$95$	15.5333	+	8.96815i	1.59368	+	0.920113i
$96$	4.34623	+	8.78124i	0.443585	+	0.896232i
$97$			11.0953i			1.12656i	0.826266	+	0.563280i	$0.190461\pi$
$97$			11.0953i			1.12656i	−0.826266	+	0.563280i	$0.809539\pi$
$98$	9.14908	−	3.78077i	0.924197	−	0.381916i
$99$	−13.8302	−	4.54296i	−1.38999	−	0.456585i
$100$	6.07296	−	1.53331i	0.607296	−	0.153331i
$101$	6.16256	+	3.55796i	0.613198	+	0.354030i	0.774216	−	0.632922i	$-0.218144\pi$
$101$	6.16256	+	3.55796i	0.613198	+	0.354030i	−0.161018	+	0.986951i	$0.551478\pi$
$102$	−0.300901	+	8.58589i	−0.0297937	+	0.850130i
$103$	1.50519	−	0.869021i	0.148311	−	0.0856271i	−0.424008	−	0.905658i	$-0.639377\pi$
$103$	1.50519	−	0.869021i	0.148311	−	0.0856271i	0.572319	+	0.820031i	$0.306044\pi$
$104$	2.82201	+	7.25490i	0.276721	+	0.711402i
$105$	−12.7018	+	3.07091i	−1.23957	+	0.299690i
$106$	−2.26576	+	1.71265i	−0.220070	+	0.166347i
$107$	−0.532028	−	0.921500i	−0.0514331	−	0.0890847i	0.839163	−	0.543881i	$-0.183046\pi$
$107$	−0.532028	−	0.921500i	−0.0514331	−	0.0890847i	−0.890596	+	0.454796i	$0.849712\pi$
$108$	3.01993	+	9.94384i	0.290593	+	0.956847i
$109$	7.85874	+	4.53725i	0.752731	+	0.434589i	0.826680	−	0.562673i	$-0.190227\pi$
$109$	7.85874	+	4.53725i	0.752731	+	0.434589i	−0.0739489	+	0.997262i	$0.523560\pi$
$110$	7.61942	−	18.0245i	0.726484	−	1.71857i
$111$	0.336640	−	2.10355i	0.0319524	−	0.199660i
$112$	9.87851	−	3.79670i	0.933432	−	0.358755i
$113$		−	16.8126i		−	1.58159i	−0.612078	−	0.790797i	$-0.709666\pi$
$113$		−	16.8126i		−	1.58159i	0.612078	−	0.790797i	$-0.290334\pi$
$114$	−13.0648	−	8.16606i	−1.22363	−	0.764822i
$115$	5.20036	−	9.00729i	0.484936	−	0.839934i
$116$	−5.44092	−	5.60088i	−0.505176	−	0.520028i
$117$	1.69066	+	8.08169i	0.156301	+	0.747152i
$118$	−0.877358	−	1.16071i	−0.0807674	−	0.106852i
$119$	9.20396	+	1.18172i	0.843726	+	0.108328i
$120$	−13.6565	+	2.94337i	−1.24666	+	0.268691i
$121$	−6.27296	−	10.8651i	−0.570269	−	0.987735i
$122$	0.433803	+	3.49022i	0.0392747	+	0.315990i
$123$	−2.30078	+	2.83190i	−0.207454	+	0.255343i
$124$	−0.485092	−	1.92129i	−0.0435626	−	0.172537i
$125$		−	5.32750i		−	0.476506i
$126$	10.9963	−	2.25409i	0.979630	−	0.200810i
$127$	15.6371			1.38756			0.693782	−	0.720185i	$-0.255943\pi$
$127$	15.6371			1.38756			0.693782	+	0.720185i	$0.255943\pi$
$128$	10.6585	−	3.79429i	0.942086	−	0.335371i
$129$	−6.87971	−	5.58943i	−0.605724	−	0.492122i
$130$	−11.0144	+	1.36899i	−0.966026	+	0.120068i
$131$	8.73260	−	5.04177i	0.762971	−	0.440502i	−0.0673904	−	0.997727i	$-0.521467\pi$
$131$	8.73260	−	5.04177i	0.762971	−	0.440502i	0.830361	+	0.557225i	$0.188134\pi$
$132$	−7.08319	+	15.2440i	−0.616513	+	1.32682i
$133$	−10.0883	+	13.2349i	−0.874763	+	1.14761i
$134$	4.95082	+	6.54971i	0.427685	+	0.565809i
$135$	−14.8007	+	0.704060i	−1.27385	+	0.0605958i
$136$	9.80489	+	1.50824i	0.840763	+	0.129330i
$137$	−17.0704	−	9.85557i	−1.45842	−	0.842019i	−0.459485	−	0.888185i	$-0.651966\pi$
$137$	−17.0704	−	9.85557i	−1.45842	−	0.842019i	−0.998934	+	0.0461669i	$0.985299\pi$
$138$	−4.73525	+	7.57588i	−0.403091	+	0.644902i
$139$	0.111832			0.00948546			0.00474273	−	0.999989i	$-0.498490\pi$
$139$	0.111832			0.00948546			0.00474273	+	0.999989i	$0.498490\pi$
$140$	1.80069	+	14.9816i	0.152186	+	1.26617i
$141$	19.1986	+	3.07243i	1.61681	+	0.258745i
$142$	5.37032	−	12.7040i	0.450667	−	1.06610i
$143$	−6.67743	+	11.5657i	−0.558395	+	0.967169i
$144$	11.8120	−	2.11588i	0.984332	−	0.176323i
$145$	9.64192	−	5.56676i	0.800718	−	0.462295i
$146$	−0.286564	−	0.379112i	−0.0237162	−	0.0313755i
$147$	−1.32524	−	12.0517i	−0.109304	−	0.994008i
$148$	−2.36659	−	0.671015i	−0.194532	−	0.0551571i
$149$	5.49834	+	9.52340i	0.450441	+	0.780187i	0.998413	−	0.0563094i	$-0.0179333\pi$
$149$	5.49834	+	9.52340i	0.450441	+	0.780187i	−0.547972	+	0.836497i	$0.684600\pi$
$150$	0.268681	−	7.66653i	0.0219377	−	0.625969i
$151$	4.16727	−	7.21792i	0.339127	−	0.587386i	−0.645141	−	0.764063i	$-0.723202\pi$
$151$	4.16727	−	7.21792i	0.339127	−	0.587386i	0.984269	+	0.176677i	$0.0565349\pi$
$152$	−11.1342	+	13.8754i	−0.903103	+	1.12545i
$153$	9.99648	+	3.28365i	0.808168	+	0.265468i
$154$	15.6868	+	9.14143i	1.26408	+	0.736638i
$155$	2.82537			0.226939
$156$	9.49652	−	0.843840i	0.760330	−	0.0675613i
$157$	5.42198	−	9.39114i	0.432721	−	0.749495i	−0.564386	−	0.825511i	$-0.690887\pi$
$157$	5.42198	−	9.39114i	0.432721	−	0.749495i	0.997107	+	0.0760165i	$0.0242202\pi$
$158$	0.977103	+	7.86142i	0.0777342	+	0.625421i
$159$	1.24137	+	3.24949i	0.0984470	+	0.257702i
$160$	1.52510	+	16.0590i	0.120570	+	1.26957i
$161$	7.67452	+	5.84987i	0.604837	+	0.461035i
$162$	12.7269	−	0.159116i	0.999922	−	0.0125014i
$163$	−10.0621	+	5.80934i	−0.788122	+	0.455022i	−0.839301	−	0.543667i	$-0.817035\pi$
$163$	−10.0621	+	5.80934i	−0.788122	+	0.455022i	0.0511792	+	0.998689i	$0.483702\pi$
$164$	2.93571	+	3.02202i	0.229240	+	0.235980i
$165$	−18.6014	−	15.1128i	−1.44812	−	1.17653i
$166$	−0.0760521	+	0.179909i	−0.00590279	+	0.0139637i
$167$	7.75061			0.599761			0.299880	−	0.953977i	$-0.403053\pi$
$167$	7.75061			0.599761			0.299880	+	0.953977i	$0.403053\pi$
$168$	−1.09508	−	12.9151i	−0.0844874	−	0.996425i
$169$	−5.42533			−0.417333
$170$	−5.50732	+	13.0281i	−0.422392	+	0.999213i
$171$	−14.0634	+	12.5810i	−1.07545	+	0.962094i
$172$	−7.34158	+	7.13190i	−0.559790	+	0.543802i
$173$	0.880487	−	0.508349i	0.0669422	−	0.0386491i	−0.466155	−	0.884703i	$-0.654361\pi$
$173$	0.880487	−	0.508349i	0.0669422	−	0.0386491i	0.533098	+	0.846054i	$0.321028\pi$
$174$	−8.44461	+	4.48872i	−0.640184	+	0.340289i
$175$	−8.21842	−	1.05518i	−0.621254	−	0.0797642i
$176$	16.5211	+	10.1877i	1.24532	+	0.767925i
$177$	−1.66466	+	0.635932i	−0.125123	+	0.0477996i
$178$	0.202687	+	1.63075i	0.0151921	+	0.122230i
$179$	−10.8103	+	18.7240i	−0.808002	+	1.39950i	0.106244	+	0.994340i	$0.466117\pi$
$179$	−10.8103	+	18.7240i	−0.808002	+	1.39950i	−0.914246	+	0.405160i	$0.867216\pi$
$180$	−1.19779	+	17.0678i	−0.0892778	+	1.27216i
$181$	9.37049			0.696503			0.348251	−	0.937401i	$-0.386776\pi$
$181$	9.37049			0.696503			0.348251	+	0.937401i	$0.386776\pi$
$182$	0.0415708	−	10.2977i	0.00308144	−	0.763320i
$183$	4.25340	+	0.680689i	0.314420	+	0.0503180i
$184$	8.04594	+	6.45639i	0.593155	+	0.475971i
$185$	1.75366	−	3.03743i	0.128932	−	0.223317i
$186$	−2.42545	−	0.0850023i	−0.177842	−	0.00623267i
$187$	8.50950	+	14.7389i	0.622276	+	1.07781i
$188$	6.12419	−	21.5993i	0.446652	−	1.57529i
$189$	1.10084	−	13.7036i	0.0800744	−	0.996789i
$190$	−15.2955	−	20.2353i	−1.10966	−	1.46803i
$191$	−7.70657	+	4.44939i	−0.557628	+	0.321947i	−0.752193	−	0.658943i	$-0.771004\pi$
$191$	−7.70657	+	4.44939i	−0.557628	+	0.321947i	0.194565	+	0.980890i	$0.437671\pi$
$192$	−0.826091	−	13.8318i	−0.0596180	−	0.998221i
$193$	7.45779	−	12.9173i	0.536824	−	0.929806i	−0.462249	−	0.886750i	$-0.652957\pi$
$193$	7.45779	−	12.9173i	0.536824	−	0.929806i	0.999073	−	0.0430556i	$-0.0137093\pi$
$194$	6.10958	−	14.4529i	0.438643	−	1.03766i
$195$	−2.14811	+	13.4228i	−0.153829	+	0.961228i
$196$	−13.9995	−	0.113031i	−0.999967	−	0.00807364i
$197$	−2.74394			−0.195497			−0.0977487	−	0.995211i	$-0.531164\pi$
$197$	−2.74394			−0.195497			−0.0977487	+	0.995211i	$0.531164\pi$
$198$	15.5138	+	13.5332i	1.10252	+	0.961765i
$199$	−20.1826	−	11.6525i	−1.43071	−	0.826021i	−0.433535	−	0.901137i	$-0.642734\pi$
$199$	−20.1826	−	11.6525i	−1.43071	−	0.826021i	−0.997175	+	0.0751162i	$0.976067\pi$
$200$	−8.75500	−	1.34674i	−0.619072	−	0.0952287i
$201$	9.39344	−	3.58848i	0.662562	−	0.253112i
$202$	−6.06823	−	8.02801i	−0.426959	−	0.564849i
$203$	3.98360	+	9.53071i	0.279594	+	0.668925i
$204$	5.11973	−	11.0184i	0.358453	−	0.771440i
$205$	−5.20240	+	3.00361i	−0.363352	+	0.209781i
$206$	−2.43919	+	0.303170i	−0.169947	+	0.0211228i
$207$	7.29535	+	8.15492i	0.507062	+	0.566806i
$208$	0.318901	−	11.0042i	0.0221118	−	0.763006i
$209$	−30.5210			−2.11118
$210$	18.2365	+	2.99401i	1.25844	+	0.206607i
$211$		−	20.3918i		−	1.40383i	−0.712259	−	0.701916i	$-0.752328\pi$
$211$		−	20.3918i		−	1.40383i	0.712259	−	0.701916i	$-0.247672\pi$
$212$	3.89445	−	0.983280i	0.267472	−	0.0675320i
$213$	−13.1107	−	10.6518i	−0.898328	−	0.729847i
$214$	0.185605	+	1.49331i	0.0126877	+	0.102081i
$215$	−7.29686	−	12.6385i	−0.497642	−	0.861941i
$216$	1.54173	−	14.6158i	0.104902	−	0.994483i
$217$	−0.333826	+	2.60005i	−0.0226616	+	0.176503i
$218$	−7.73845	−	10.2376i	−0.524114	−	0.693380i
$219$	−0.543714	+	0.207709i	−0.0367408	+	0.0140357i
$220$	−19.8503	+	19.2833i	−1.33830	+	1.30008i
$221$	4.82645	−	8.35966i	0.324662	−	0.562332i
$222$	−1.59682	+	2.55473i	−0.107172	+	0.171463i
$223$		−	11.4666i		−	0.767860i	−0.923362	−	0.383930i	$-0.874570\pi$
$223$		−	11.4666i		−	0.767860i	0.923362	−	0.383930i	$-0.125430\pi$
$224$	−14.9585	−	0.493938i	−0.999455	−	0.0330026i
$225$	−8.92608	−	2.93204i	−0.595072	−	0.195470i
$226$	−9.25776	+	21.9002i	−0.615817	+	1.45678i
$227$	−18.3699	−	10.6059i	−1.21926	−	0.703938i	−0.254497	−	0.967073i	$-0.581910\pi$
$227$	−18.3699	−	10.6059i	−1.21926	−	0.703938i	−0.964759	+	0.263136i	$0.915243\pi$
$228$	12.5217	+	17.8313i	0.829271	+	1.18090i
$229$	−1.13465	−	1.96528i	−0.0749800	−	0.129869i	0.826098	−	0.563527i	$-0.190556\pi$
$229$	−1.13465	−	1.96528i	−0.0749800	−	0.129869i	−0.901078	+	0.433658i	$0.857223\pi$
$230$	−11.7339	+	8.86942i	−0.773707	+	0.584832i
$231$	16.1054	−	15.3324i	1.05965	−	1.00880i
$232$	4.00329	+	10.2918i	0.262829	+	0.675688i
$233$	22.5624	−	13.0264i	1.47811	−	0.853389i	0.478420	−	0.878131i	$-0.341210\pi$
$233$	22.5624	−	13.0264i	1.47811	−	0.853389i	0.999694	+	0.0247423i	$0.00787651\pi$
$234$	2.24788	−	11.4582i	0.146949	−	0.749048i
$235$	27.7219	+	16.0053i	1.80838	+	1.04407i
$236$	0.503717	+	1.99506i	0.0327892	+	0.129867i
$237$	9.58042	+	1.53319i	0.622315	+	0.0995916i
$238$	−11.3385	−	6.60743i	−0.734963	−	0.428296i
$239$			8.32874i			0.538742i	0.963037	+	0.269371i	$0.0868157\pi$
$239$			8.32874i			0.538742i	−0.963037	+	0.269371i	$0.913184\pi$
$240$	19.4098	+	3.68581i	1.25290	+	0.237918i
$241$	6.24112	+	3.60331i	0.402026	+	0.232110i	0.687358	−	0.726319i	$-0.258771\pi$
$241$	6.24112	+	3.60331i	0.402026	+	0.232110i	−0.285332	+	0.958429i	$0.592104\pi$
$242$	2.18841	+	17.6071i	0.140676	+	1.13183i
$243$	4.15558	−	15.0244i	0.266581	−	0.963813i
$244$	1.35680	−	4.78527i	0.0868601	−	0.306345i
$245$	5.04265	−	19.3139i	0.322163	−	1.23392i
$246$	4.55638	−	2.42194i	0.290504	−	0.154417i
$247$	8.65550	+	14.9918i	0.550736	+	0.953904i
$248$	−0.426065	+	2.76981i	−0.0270551	+	0.175883i
$249$	0.185668	+	0.150846i	0.0117662	+	0.00955947i
$250$	−2.93356	+	6.93965i	−0.185535	+	0.438902i
$251$		−	8.41270i		−	0.531005i	−0.964110	−	0.265502i	$-0.914462\pi$
$251$		−	8.41270i		−	0.531005i	0.964110	−	0.265502i	$-0.0855378\pi$
$252$	−15.5651	−	3.11887i	−0.980510	−	0.196471i
$253$			17.6982i			1.11268i
$254$	−20.3690	−	8.61047i	−1.27806	−	0.540269i
$255$	13.4451	+	10.9235i	0.841967	+	0.684057i
$256$	−15.9731	−	0.926576i	−0.998322	−	0.0579110i
$257$	15.1284	+	26.2032i	0.943685	+	1.63451i	0.758364	+	0.651832i	$0.225999\pi$
$257$	15.1284	+	26.2032i	0.943685	+	1.63451i	0.185321	+	0.982678i	$0.440668\pi$
$258$	5.88378	+	11.0691i	0.366308	+	0.689133i
$259$	2.58800	+	1.97269i	0.160810	+	0.122577i
$260$	15.1013	+	4.28176i	0.936541	+	0.265544i
$261$	2.39836	+	11.4646i	0.148454	+	0.709644i
$262$	−14.1514	+	1.75889i	−0.874276	+	0.108665i
$263$	−20.9078	−	12.0711i	−1.28923	−	0.744338i	−0.310714	−	0.950504i	$-0.600568\pi$
$263$	−20.9078	−	12.0711i	−1.28923	−	0.744338i	−0.978517	+	0.206166i	$0.933901\pi$
$264$	17.6207	−	15.9566i	1.08448	−	0.982063i
$265$			5.72701i			0.351808i
$266$	20.4288	−	11.6849i	1.25257	−	0.716445i
$267$	1.98733	+	0.318041i	0.121623	+	0.0194638i
$268$	−2.84241	−	11.2579i	−0.173628	−	0.687683i
$269$	−17.4083	−	10.0507i	−1.06140	−	0.612800i	−0.135581	−	0.990766i	$-0.543290\pi$
$269$	−17.4083	−	10.0507i	−1.06140	−	0.612800i	−0.925819	+	0.377966i	$0.876623\pi$
$270$	19.6673	+	7.23284i	1.19691	+	0.440177i
$271$	−1.57903	+	0.911656i	−0.0959195	+	0.0553791i	−0.547192	−	0.837007i	$-0.684303\pi$
$271$	−1.57903	+	0.911656i	−0.0959195	+	0.0553791i	0.451273	+	0.892386i	$0.350970\pi$
$272$	−11.9414	−	7.36366i	−0.724056	−	0.446487i
$273$	−12.0985	−	3.56274i	−0.732237	−	0.215627i
$274$	16.8091	+	22.2377i	1.01547	+	1.34343i
$275$	−7.59832	−	13.1607i	−0.458196	−	0.793618i
$276$	10.3398	−	7.26096i	0.622383	−	0.437059i
$277$	11.4072	+	6.58598i	0.685395	+	0.395713i	0.801885	−	0.597479i	$-0.203831\pi$
$277$	11.4072	+	6.58598i	0.685395	+	0.395713i	−0.116490	+	0.993192i	$0.537164\pi$
$278$	−0.145673	−	0.0615797i	−0.00873690	−	0.00369331i
$279$	−0.927606	+	2.82393i	−0.0555343	+	0.169064i
$280$	5.90393	−	20.5066i	0.352827	−	1.22551i
$281$			15.3821i			0.917618i	0.888535	+	0.458809i	$0.151724\pi$
$281$			15.3821i			0.917618i	−0.888535	+	0.458809i	$0.848276\pi$
$282$	−23.3164	−	14.5738i	−1.38847	−	0.867857i
$283$	4.64882	−	8.05200i	0.276344	−	0.478641i	−0.694129	−	0.719850i	$-0.744210\pi$
$283$	4.64882	−	8.05200i	0.276344	−	0.478641i	0.970473	+	0.241209i	$0.0775438\pi$
$284$	−13.9908	+	13.5913i	−0.830204	+	0.806493i
$285$	−29.0210	+	11.0866i	−1.71906	+	0.656713i
$286$	15.0667	−	11.3886i	0.890910	−	0.673424i
$287$	−2.14939	−	5.14240i	−0.126875	−	0.303546i
$288$	−16.5515	−	3.74805i	−0.975306	−	0.220856i
$289$	2.34933	+	4.06916i	0.138196	+	0.239362i
$290$	−15.6250	+	1.94204i	−0.917529	+	0.114041i
$291$	−14.9154	−	12.1181i	−0.874359	−	0.710374i
$292$	0.164525	+	0.651630i	0.00962810	+	0.0381338i
$293$			17.8462i			1.04258i	0.853378	+	0.521292i	$0.174550\pi$
$293$			17.8462i			1.04258i	−0.853378	+	0.521292i	$0.825450\pi$
$294$	−4.90994	+	16.4284i	−0.286354	+	0.958124i
$295$	−2.93385			−0.170815
$296$	2.71325	+	2.17722i	0.157704	+	0.126548i
$297$	21.2122	−	13.6302i	1.23086	−	0.790907i
$298$	−1.91817	−	15.4329i	−0.111117	−	0.894004i
$299$	8.69327	−	5.01906i	0.502745	−	0.290260i
$300$	−4.57152	+	9.83854i	−0.263937	+	0.568028i
$301$	12.4928	−	5.22166i	0.720071	−	0.300971i
$302$	−9.40283	+	7.10744i	−0.541072	+	0.408987i
$303$	−11.5136	+	4.39841i	−0.661438	+	0.252682i
$304$	22.1440	−	11.9433i	1.27004	−	0.684993i
$305$	6.14172	+	3.54592i	0.351674	+	0.203039i
$306$	−11.2134	−	9.78183i	−0.641026	−	0.559190i
$307$	−17.6654			−1.00822			−0.504110	−	0.863640i	$-0.668179\pi$
$307$	−17.6654			−1.00822			−0.504110	+	0.863640i	$0.668179\pi$
$308$	−15.4001	−	20.5456i	−0.877504	−	1.17069i
$309$	−0.475709	+	2.97255i	−0.0270622	+	0.169103i
$310$	−3.68035	−	1.55578i	−0.209030	−	0.0883621i
$311$	4.15091	−	7.18958i	0.235376	−	0.407684i	−0.724006	−	0.689794i	$-0.757701\pi$
$311$	4.15091	−	7.18958i	0.235376	−	0.407684i	0.959382	+	0.282110i	$0.0910344\pi$
$312$	−12.8349	−	4.13002i	−0.726634	−	0.233816i
$313$	−23.0954	+	13.3342i	−1.30543	+	0.753691i	−0.981330	−	0.192332i	$-0.938395\pi$
$313$	−23.0954	+	13.3342i	−1.30543	+	0.753691i	−0.324101	+	0.946023i	$0.605062\pi$
$314$	−12.2339	+	9.24740i	−0.690399	+	0.521861i
$315$	9.74446	−	20.4291i	0.549038	−	1.15105i
$316$	3.05607	−	10.7784i	0.171917	−	0.606332i
$317$	14.4097	+	24.9584i	0.809331	+	1.40180i	0.913328	+	0.407225i	$0.133504\pi$
$317$	14.4097	+	24.9584i	0.809331	+	1.40180i	−0.103996	+	0.994578i	$0.533163\pi$
$318$	0.172299	−	4.91637i	0.00966207	−	0.275696i
$319$	−9.47258	+	16.4070i	−0.530362	+	0.918615i
$320$	6.85618	−	21.7584i	0.383272	−	1.21633i
$321$	1.81984	+	0.291237i	0.101574	+	0.0162553i
$322$	−6.77570	−	11.8460i	−0.377595	−	0.660154i
$323$	22.0606			1.22748
$324$	−16.6658	−	6.80075i	−0.925879	−	0.377820i
$325$	−4.30964	+	7.46452i	−0.239056	+	0.414057i
$326$	16.3058	−	2.02666i	0.903096	−	0.112247i
$327$	−14.6826	+	5.60903i	−0.811948	+	0.310180i
$328$	−2.16002	−	5.55304i	−0.119267	−	0.306615i
$329$	−18.0043	+	23.6200i	−0.992608	+	1.30222i
$330$	15.9086	+	29.9288i	0.875742	+	1.64753i
$331$	−2.24514	+	1.29623i	−0.123404	+	0.0712472i	−0.560431	−	0.828201i	$-0.689365\pi$
$331$	−2.24514	+	1.29623i	−0.123404	+	0.0712472i	0.437027	+	0.899448i	$0.356031\pi$
$332$	0.198132	−	0.192474i	0.0108739	−	0.0105634i
$333$	2.46013	+	2.75000i	0.134815	+	0.150699i
$334$	−10.0960	−	4.26784i	−0.552430	−	0.233526i
$335$	16.5553			0.904513
$336$	−5.68520	+	17.4264i	−0.310153	+	0.950687i
$337$	11.1713			0.608541			0.304271	−	0.952586i	$-0.401587\pi$
$337$	11.1713			0.608541			0.304271	+	0.952586i	$0.401587\pi$
$338$	7.06709	+	2.98743i	0.384399	+	0.162495i
$339$	22.6012	+	18.3623i	1.22753	+	0.997306i
$340$	14.3478	−	13.9380i	0.778117	−	0.755894i
$341$	−4.16362	+	2.40387i	−0.225473	+	0.130177i
$342$	25.2467	−	8.64421i	1.36519	−	0.467426i
$343$	17.1779	+	6.92250i	0.927517	+	0.373780i
$344$	13.4903	−	5.24747i	0.727351	−	0.282925i
$345$	6.42878	+	16.8284i	0.346114	+	0.906012i
$346$	−1.42685	+	0.177345i	−0.0767079	+	0.00953410i
$347$	−7.23643	+	12.5339i	−0.388472	+	0.672853i	−0.992244	−	0.124304i	$-0.960330\pi$
$347$	−7.23643	+	12.5339i	−0.388472	+	0.672853i	0.603772	+	0.797157i	$0.293664\pi$
$348$	13.4717	−	1.19707i	0.722160	−	0.0641696i
$349$	−22.8018			−1.22055			−0.610275	−	0.792189i	$-0.708941\pi$
$349$	−22.8018			−1.22055			−0.610275	+	0.792189i	$0.708941\pi$
$350$	10.1244	+	5.89992i	0.541169	+	0.315364i
$351$	−12.7107	−	6.55390i	−0.678448	−	0.349821i
$352$	−15.9107	−	22.3678i	−0.848043	−	1.19221i
$353$	−2.06060	+	3.56907i	−0.109675	+	0.189962i	−0.915639	−	0.402003i	$-0.868314\pi$
$353$	−2.06060	+	3.56907i	−0.109675	+	0.189962i	0.805964	+	0.591965i	$0.201648\pi$
$354$	2.51857	+	0.0882660i	0.133861	+	0.00469128i
$355$	−13.9056	−	24.0852i	−0.738034	−	1.27831i
$356$	0.633942	−	2.23584i	0.0335989	−	0.118499i
$357$	−11.6410	+	11.0822i	−0.616105	+	0.586535i
$358$	24.3919	−	18.4374i	1.28915	−	0.974449i
$359$	9.83790	−	5.67992i	0.519225	−	0.299775i	−0.217393	−	0.976084i	$-0.569755\pi$
$359$	9.83790	−	5.67992i	0.519225	−	0.299775i	0.736617	+	0.676310i	$0.236422\pi$
$360$	10.9585	−	21.5731i	0.577566	−	1.13700i
$361$	−10.2811	+	17.8074i	−0.541112	+	0.937234i
$362$	−12.2061	−	5.15981i	−0.641537	−	0.271194i
$363$	21.4571	+	3.43387i	1.12621	+	0.180232i
$364$	−5.72456	+	13.3910i	−0.300048	+	0.701882i
$365$	−0.958259			−0.0501576
$366$	−5.16570	−	3.22879i	−0.270015	−	0.168771i
$367$	24.2527	+	14.0023i	1.26598	+	0.730914i	0.974225	−	0.225580i	$-0.0724275\pi$
$367$	24.2527	+	14.0023i	1.26598	+	0.730914i	0.291755	+	0.956493i	$0.405761\pi$
$368$	−6.92553	−	12.8406i	−0.361018	−	0.669363i
$369$	−1.29406	−	6.18587i	−0.0673660	−	0.322024i
$370$	−3.95689	+	2.99094i	−0.205709	+	0.155492i
$371$	−5.27029	−	0.676664i	−0.273620	−	0.0351306i
$372$	3.11260	+	1.44629i	0.161381	+	0.0749864i
$373$	27.1273	−	15.6619i	1.40460	−	0.810944i	0.409737	−	0.912204i	$-0.365621\pi$
$373$	27.1273	−	15.6619i	1.40460	−	0.810944i	0.994860	+	0.101259i	$0.0322872\pi$
$374$	−2.96865	−	23.8847i	−0.153505	−	1.23505i
$375$	7.16176	+	5.81858i	0.369832	+	0.300470i
$376$	−19.8710	+	24.7632i	−1.02477	+	1.27706i
$377$	10.7454			0.553416
$378$	−8.97978	+	17.2442i	−0.461870	+	0.886948i
$379$			28.8128i			1.48001i	0.672600	+	0.740006i	$0.265178\pi$
$379$			28.8128i			1.48001i	−0.672600	+	0.740006i	$0.734822\pi$
$380$	8.78162	+	34.7811i	0.450488	+	1.78423i
$381$	−17.0785	+	21.0209i	−0.874956	+	1.07693i
$382$	12.4887	−	1.55223i	0.638977	−	0.0794190i
$383$	−12.6701	−	21.9453i	−0.647413	−	1.12135i	−0.983738	−	0.179607i	$-0.942517\pi$
$383$	−12.6701	−	21.9453i	−0.647413	−	1.12135i	0.336325	−	0.941746i	$-0.390816\pi$
$384$	−6.54032	+	18.4723i	−0.333759	+	0.942658i
$385$	33.7781	−	14.1184i	1.72149	−	0.719540i
$386$	−16.8274	+	12.7196i	−0.856493	+	0.647409i
$387$	15.0277	−	3.14374i	0.763903	−	0.159805i
$388$	−15.9168	+	15.4622i	−0.808053	+	0.784975i
$389$	2.20886	−	3.82586i	0.111994	−	0.193979i	−0.804580	−	0.593844i	$-0.797610\pi$
$389$	2.20886	−	3.82586i	0.111994	−	0.193979i	0.916574	+	0.399865i	$0.130943\pi$
$390$	10.1894	−	16.3018i	0.515958	−	0.825475i
$391$		−	12.7923i		−	0.646932i
$392$	18.1737	+	7.85602i	0.917910	+	0.396789i
$393$	−2.75991	+	17.2458i	−0.139219	+	0.869934i
$394$	3.57427	+	1.51093i	0.180069	+	0.0761198i
$395$	13.8337	+	7.98689i	0.696049	+	0.401864i
$396$	−12.7564	−	26.1711i	−0.641033	−	1.31515i
$397$	−8.01775	−	13.8871i	−0.402399	−	0.696976i	0.591616	−	0.806220i	$-0.298490\pi$
$397$	−8.01775	−	13.8871i	−0.402399	−	0.696976i	−0.994015	+	0.109244i	$0.965157\pi$
$398$	19.8737	+	26.2921i	0.996180	+	1.31790i
$399$	−6.77352	−	28.0165i	−0.339100	−	1.40258i
$400$	10.6628	+	6.57517i	0.533139	+	0.328759i
$401$	−6.53545	+	3.77324i	−0.326365	+	0.188427i	−0.654226	−	0.756299i	$-0.727006\pi$
$401$	−6.53545	+	3.77324i	−0.326365	+	0.188427i	0.327861	+	0.944726i	$0.393672\pi$
$402$	−14.2120	−	0.498073i	−0.708828	−	0.0248416i
$403$	2.36154	+	1.36343i	0.117637	+	0.0679175i
$404$	3.48395	+	13.7988i	0.173333	+	0.686516i
$405$	15.2186	−	20.6656i	0.756218	−	1.02688i
$406$	0.0589722	−	14.6083i	0.00292674	−	0.725000i
$407$			5.96817i			0.295831i
$408$	−12.7362	+	11.5335i	−0.630537	+	0.570991i
$409$	−24.3612	−	14.0650i	−1.20458	−	0.695467i	−0.243013	−	0.970023i	$-0.578136\pi$
$409$	−24.3612	−	14.0650i	−1.20458	−	0.695467i	−0.961571	+	0.274556i	$0.911469\pi$
$410$	8.43062	−	1.04785i	0.416359	−	0.0517496i
$411$	31.8927	−	12.1836i	1.57315	−	0.600975i
$412$	3.34425	+	0.948219i	0.164760	+	0.0467154i
$413$	0.346643	−	2.69988i	0.0170572	−	0.132852i
$414$	−5.01252	−	14.6398i	−0.246352	−	0.719508i
$415$	0.196926	+	0.341085i	0.00966670	+	0.0167432i
$416$	−6.47483	+	14.1586i	−0.317454	+	0.694183i
$417$	−0.122140	+	0.150336i	−0.00598125	+	0.00736197i
$418$	39.7569	+	16.8062i	1.94457	+	0.822019i
$419$		−	19.5661i		−	0.955866i	−0.878396	−	0.477933i	$-0.841386\pi$
$419$		−	19.5661i		−	0.955866i	0.878396	−	0.477933i	$-0.158614\pi$
$420$	−22.1064	−	13.9419i	−1.07868	−	0.680294i
$421$		−	26.0983i		−	1.27195i	−0.771708	−	0.635977i	$-0.780597\pi$
$421$		−	26.0983i		−	1.27195i	0.771708	−	0.635977i	$-0.219403\pi$
$422$	−11.2287	+	26.5626i	−0.546603	+	1.29305i
$423$	−25.0986	+	22.4531i	−1.22033	+	1.09170i
$424$	−5.61439	−	0.863632i	−0.272659	−	0.0419417i
$425$	5.49207	+	9.51254i	0.266404	+	0.461426i
$426$	11.2127	+	21.0944i	0.543258	+	1.02203i
$427$	−3.98880	+	5.23296i	−0.193032	+	0.253241i
$428$	0.580514	−	2.04740i	0.0280602	−	0.0989650i
$429$	−8.25477	−	21.6082i	−0.398544	−	1.04326i
$430$	2.54561	+	20.4810i	0.122760	+	0.987683i
$431$	−10.4072	−	6.00858i	−0.501296	−	0.289423i	0.227953	−	0.973672i	$-0.426797\pi$
$431$	−10.4072	−	6.00858i	−0.501296	−	0.289423i	−0.729248	+	0.684249i	$0.760130\pi$
$432$	−10.0564	+	18.1898i	−0.483840	+	0.875157i
$433$		−	35.6343i		−	1.71247i	−0.516583	−	0.856237i	$-0.672796\pi$
$433$		−	35.6343i		−	1.71247i	0.516583	−	0.856237i	$-0.327204\pi$
$434$	1.86655	−	3.20302i	0.0895972	−	0.153750i
$435$	−3.04729	+	19.0415i	−0.146107	+	0.912972i
$436$	4.44287	+	17.5968i	0.212775	+	0.842733i
$437$	19.8674	+	11.4705i	0.950389	+	0.548707i
$438$	0.822620	+	0.0288296i	0.0393063	+	0.00137753i
$439$	−11.6950	+	6.75210i	−0.558171	+	0.322260i	−0.752411	−	0.658694i	$-0.771109\pi$
$439$	−11.6950	+	6.75210i	−0.558171	+	0.322260i	0.194240	+	0.980954i	$0.437776\pi$
$440$	36.4754	−	14.1882i	1.73890	−	0.676396i
$441$	17.6485	+	11.3811i	0.840406	+	0.541957i
$442$	−10.8902	+	8.23170i	−0.517993	+	0.391542i
$443$	−11.7659	−	20.3791i	−0.559014	−	0.968241i	−0.997579	−	0.0695416i	$-0.977846\pi$
$443$	−11.7659	−	20.3791i	−0.559014	−	0.968241i	0.438565	−	0.898700i	$-0.355487\pi$
$444$	3.48678	−	2.44854i	0.165475	−	0.116203i
$445$	2.86962	+	1.65678i	0.136033	+	0.0785387i
$446$	−6.31402	+	14.9365i	−0.298978	+	0.707263i
$447$	−18.8075	−	3.00984i	−0.889563	−	0.142360i
$448$	19.2131	+	8.88022i	0.907732	+	0.419551i
$449$		−	30.6292i		−	1.44548i	−0.691120	−	0.722740i	$-0.742883\pi$
$449$		−	30.6292i		−	1.44548i	0.691120	−	0.722740i	$-0.257117\pi$
$450$	10.0127	+	8.73441i	0.472002	+	0.411744i
$451$	5.11103	−	8.85257i	0.240669	−	0.416851i
$452$	24.1185	−	23.4297i	1.13444	−	1.10204i
$453$	5.15165	+	13.4853i	0.242046	+	0.633596i
$454$	18.0888	+	23.9307i	0.848948	+	1.12312i
$455$	−16.5141	−	12.5878i	−0.774193	−	0.590125i
$456$	−6.49221	−	30.1222i	−0.304025	−	1.41060i
$457$	5.80736	+	10.0587i	0.271657	+	0.470524i	0.969286	−	0.245935i	$-0.0790950\pi$
$457$	5.80736	+	10.0587i	0.271657	+	0.470524i	−0.697629	+	0.716459i	$0.745762\pi$
$458$	0.395839	+	3.18478i	0.0184964	+	0.148815i
$459$	−15.3322	+	9.85194i	−0.715644	+	0.459849i
$460$	20.1685	−	5.09219i	0.940362	−	0.237425i
$461$			30.8362i			1.43618i	0.695948	+	0.718092i	$0.254985\pi$
$461$			30.8362i			1.43618i	−0.695948	+	0.718092i	$0.745015\pi$
$462$	−29.4217	+	11.1038i	−1.36882	+	0.516593i
$463$	−32.3199			−1.50203			−0.751016	−	0.660284i	$-0.770436\pi$
$463$	−32.3199			−1.50203			−0.751016	+	0.660284i	$0.770436\pi$
$464$	0.452391	−	15.6105i	0.0210017	−	0.724701i
$465$	−3.08581	+	3.79815i	−0.143101	+	0.176135i
$466$	−36.5629	+	4.54444i	−1.69375	+	0.210517i
$467$	−29.3749	+	16.9596i	−1.35931	+	0.784797i	−0.989531	−	0.144323i	$-0.953900\pi$
$467$	−29.3749	+	16.9596i	−1.35931	+	0.784797i	−0.369778	+	0.929120i	$0.620566\pi$
$468$	−9.23753	+	13.6878i	−0.427005	+	0.632719i
$469$	−1.95606	+	15.2350i	−0.0903225	+	0.703489i
$470$	−27.2976	−	36.1135i	−1.25914	−	1.66579i
$471$	6.70275	+	17.5456i	0.308846	+	0.808458i
$472$	0.442424	−	2.87615i	0.0203642	−	0.132386i
$473$	21.5061	+	12.4166i	0.988852	+	0.570914i
$474$	−11.6353	−	7.27256i	−0.534427	−	0.334040i
$475$	−19.6984			−0.903823
$476$	11.1312	+	14.8504i	0.510199	+	0.680665i
$477$	−5.72409	−	1.88025i	−0.262088	−	0.0860910i
$478$	4.58618	−	10.8491i	0.209767	−	0.496226i
$479$	17.6827	−	30.6273i	0.807943	−	1.39940i	−0.106344	−	0.994329i	$-0.533914\pi$
$479$	17.6827	−	30.6273i	0.807943	−	1.39940i	0.914286	−	0.405068i	$-0.132752\pi$
$480$	−23.2538	−	15.4891i	−1.06139	−	0.706976i
$481$	2.93154	−	1.69253i	0.133667	−	0.0771726i
$482$	−6.14559	−	8.13034i	−0.279924	−	0.370327i
$483$	−16.2459	+	3.92776i	−0.739216	+	0.178719i
$484$	6.84464	−	24.1402i	0.311120	−	1.09728i
$485$	−15.8198	−	27.4008i	−0.718342	−	1.24421i
$486$	−13.6862	+	17.2826i	−0.620818	+	0.783955i
$487$	16.4191	−	28.4386i	0.744018	−	1.28868i	−0.206634	−	0.978418i	$-0.566251\pi$
$487$	16.4191	−	28.4386i	0.744018	−	1.28868i	0.950652	−	0.310259i	$-0.100416\pi$
$488$	−4.40236	+	5.48621i	−0.199286	+	0.248349i
$489$	3.18008	−	19.8713i	0.143808	−	0.898610i
$490$	−17.2037	+	22.3818i	−0.777185	+	1.01111i
$491$	−22.5295			−1.01674			−0.508371	−	0.861138i	$-0.669752\pi$
$491$	−22.5295			−1.01674			−0.508371	+	0.861138i	$0.669752\pi$
$492$	−7.26882	+	0.645891i	−0.327703	+	0.0291190i
$493$	6.84678	−	11.8590i	0.308363	−	0.534101i
$494$	−3.01959	−	24.2945i	−0.135858	−	1.09306i
$495$	40.6322	−	8.50009i	1.82628	−	0.382051i
$496$	2.08018	−	3.37336i	0.0934027	−	0.151468i
$497$	23.8075	−	9.95092i	1.06791	−	0.446360i
$498$	−0.158790	−	0.298730i	−0.00711554	−	0.0133864i
$499$	11.3117	−	6.53084i	0.506383	−	0.292361i	−0.224962	−	0.974367i	$-0.572226\pi$
$499$	11.3117	−	6.53084i	0.506383	−	0.292361i	0.731346	+	0.682007i	$0.238893\pi$
$500$	7.64256	−	7.42429i	0.341786	−	0.332024i
$501$	−8.46506	+	10.4192i	−0.378191	+	0.465494i
$502$	−4.63241	+	10.9585i	−0.206755	+	0.489100i
$503$	2.77607			0.123779			0.0618894	−	0.998083i	$-0.480287\pi$
$503$	2.77607			0.123779			0.0618894	+	0.998083i	$0.480287\pi$
$504$	18.5579	+	12.6335i	0.826633	+	0.562742i
$505$	−20.2919			−0.902978
$506$	9.74542	−	23.0538i	0.433237	−	1.02487i
$507$	5.92543	−	7.29328i	0.263158	−	0.323906i
$508$	21.7915	+	22.4321i	0.966841	+	0.995265i
$509$	27.2704	−	15.7446i	1.20874	−	0.697866i	0.246255	−	0.969205i	$-0.420800\pi$
$509$	27.2704	−	15.7446i	1.20874	−	0.697866i	0.962484	+	0.271339i	$0.0874665\pi$
$510$	−11.4988	−	21.6326i	−0.509174	−	0.957906i
$511$	0.113221	−	0.881838i	0.00500861	−	0.0390102i
$512$	20.2965	+	10.0025i	0.896989	+	0.442052i
$513$	−1.55295	−	32.6461i	−0.0685645	−	1.44136i
$514$	−5.27775	−	42.4629i	−0.232792	−	1.87296i
$515$	−2.47812	+	4.29223i	−0.109199	+	0.189138i
$516$	−1.56910	−	17.6586i	−0.0690760	−	0.777376i
$517$	−54.4701			−2.39559
$518$	−2.28490	−	3.99471i	−0.100393	−	0.175518i
$519$	−0.278275	+	1.73885i	−0.0122149	+	0.0763270i
$520$	−17.3133	−	13.8929i	−0.759239	−	0.609244i
$521$	−2.92633	+	5.06856i	−0.128205	+	0.222058i	−0.922981	−	0.384845i	$-0.874255\pi$
$521$	−2.92633	+	5.06856i	−0.128205	+	0.222058i	0.794776	+	0.606903i	$0.207588\pi$
$522$	3.18883	−	16.2546i	0.139571	−	0.711444i
$523$	−9.81038	−	16.9921i	−0.428978	−	0.743012i	0.567805	−	0.823163i	$-0.307793\pi$
$523$	−9.81038	−	16.9921i	−0.428978	−	0.743012i	−0.996783	+	0.0801516i	$0.974460\pi$
$524$	19.4023	+	5.50125i	0.847591	+	0.240323i
$525$	10.3945	−	9.89558i	0.453652	−	0.431879i
$526$	20.5878	+	27.2367i	0.897670	+	1.18758i
$527$	3.00947	−	1.73752i	0.131094	−	0.0756874i
$528$	−31.7393	+	11.0825i	−1.38127	+	0.482305i
$529$	−4.84862	+	8.39806i	−0.210810	+	0.365133i
$530$	3.15355	−	7.46006i	0.136982	−	0.324044i
$531$	0.963222	−	2.93235i	0.0418003	−	0.127253i
$532$	−33.0449	+	3.97179i	−1.43268	+	0.172199i
$533$	−5.79779			−0.251130
$534$	−2.41359	−	1.50860i	−0.104446	−	0.0652834i
$535$	2.62777	+	1.51715i	0.113609	+	0.0655919i
$536$	−2.49654	+	16.2297i	−0.107834	+	0.701018i
$537$	−13.3639	−	34.9823i	−0.576696	−	1.50960i
$538$	17.1418	+	22.6779i	0.739036	+	0.977712i
$539$	9.00148	+	32.7525i	0.387721	+	1.41075i
$540$	−21.6360	−	20.2513i	−0.931066	−	0.871475i
$541$	−35.5120	+	20.5029i	−1.52678	+	0.881488i	−0.527287	+	0.849687i	$0.676791\pi$
$541$	−35.5120	+	20.5029i	−1.52678	+	0.881488i	−0.999494	+	0.0318007i	$0.989876\pi$
$542$	2.55886	−	0.318043i	0.109913	−	0.0136611i
$543$	−10.2343	+	12.5968i	−0.439194	+	0.540579i
$544$	11.5003	+	16.1675i	0.493070	+	0.693174i
$545$	−25.8771			−1.10845
$546$	13.7979	+	11.3029i	0.590494	+	0.483718i
$547$		−	13.0813i		−	0.559315i	−0.960100	−	0.279658i	$-0.909779\pi$
$547$		−	13.0813i		−	0.559315i	0.960100	−	0.279658i	$-0.0902209\pi$
$548$	−9.65058	−	38.2228i	−0.412252	−	1.63280i
$549$	−5.56053	+	4.97442i	−0.237317	+	0.212303i
$550$	2.65078	+	21.3272i	0.113029	+	0.909394i
$551$	12.2787	+	21.2673i	0.523088	+	0.906016i
$552$	−17.4669	+	3.76463i	−0.743442	+	0.160233i
$553$	−8.98443	+	11.7868i	−0.382057	+	0.501225i
$554$	−11.2326	−	14.8603i	−0.477229	−	0.631353i
$555$	2.16791	+	5.67487i	0.0920227	+	0.240885i
$556$	0.155847	+	0.160429i	0.00660937	+	0.00680369i
$557$	19.2814	−	33.3964i	0.816980	−	1.41505i	−0.0909180	−	0.995858i	$-0.528980\pi$
$557$	19.2814	−	33.3964i	0.816980	−	1.41505i	0.907898	−	0.419192i	$-0.137687\pi$
$558$	2.76329	−	3.16769i	0.116979	−	0.134099i
$559$		−	14.0849i		−	0.595730i
$560$	−18.9824	+	23.4612i	−0.802153	+	0.991416i
$561$	−29.1074	−	4.65817i	−1.22891	−	0.196668i
$562$	8.47007	−	20.0368i	0.357288	−	0.845203i
$563$	−9.75701	−	5.63321i	−0.411209	−	0.237411i	0.280100	−	0.959971i	$-0.409632\pi$
$563$	−9.75701	−	5.63321i	−0.411209	−	0.237411i	−0.691309	+	0.722559i	$0.742966\pi$
$564$	22.3472	+	31.8230i	0.940988	+	1.33999i
$565$	23.9716	+	41.5200i	1.00849	+	1.74676i
$566$	−10.4894	+	7.92875i	−0.440902	+	0.333270i
$567$	17.2194	+	16.4466i	0.723148	+	0.690693i
$568$	25.7086	−	10.0001i	1.07871	−	0.419595i
$569$	−26.7497	+	15.4440i	−1.12141	+	0.647445i	−0.941760	−	0.336286i	$-0.890829\pi$
$569$	−26.7497	+	15.4440i	−1.12141	+	0.647445i	−0.179648	+	0.983731i	$0.557496\pi$
$570$	43.9078	+	1.53880i	1.83910	+	0.0644531i
$571$	−6.49082	−	3.74748i	−0.271633	−	0.156827i	0.357997	−	0.933723i	$-0.383460\pi$
$571$	−6.49082	−	3.74748i	−0.271633	−	0.156827i	−0.629629	+	0.776896i	$0.716793\pi$
$572$	−25.8971	+	6.53855i	−1.08281	+	0.273390i
$573$	2.43564	−	15.2195i	0.101750	−	0.635803i
$574$	−0.0318191	+	7.88209i	−0.00132810	+	0.328992i
$575$			11.4225i			0.476350i
$576$	19.4963	+	13.9962i	0.812345	+	0.583177i
$577$	18.4495	+	10.6518i	0.768064	+	0.443442i	0.832184	−	0.554500i	$-0.187091\pi$
$577$	18.4495	+	10.6518i	0.768064	+	0.443442i	−0.0641196	+	0.997942i	$0.520424\pi$
$578$	−0.819596	−	6.59418i	−0.0340907	−	0.274282i
$579$	9.21946	+	24.1335i	0.383148	+	1.00295i
$580$	21.4226	+	6.07409i	0.889524	+	0.252213i
$581$	−0.337151	+	0.140921i	−0.0139874	+	0.00584637i
$582$	12.7562	+	23.9982i	0.528763	+	0.994759i
$583$	−4.87263	−	8.43964i	−0.201804	−	0.349534i
$584$	0.144505	−	0.939414i	0.00597967	−	0.0388732i
$585$	−15.6982	−	17.5478i	−0.649040	−	0.725513i
$586$	9.82690	−	23.2466i	0.405946	−	0.960307i
$587$		−	15.2002i		−	0.627381i	−0.949525	−	0.313691i	$-0.898435\pi$
$587$		−	15.2002i		−	0.627381i	0.949525	−	0.313691i	$-0.101565\pi$
$588$	15.4420	−	18.6961i	0.636816	−	0.771016i
$589$			6.23194i			0.256783i
$590$	3.82166	+	1.61551i	0.157335	+	0.0665095i
$591$	2.99687	−	3.68868i	0.123275	−	0.151732i
$592$	−2.33543	−	4.33010i	−0.0959854	−	0.177966i
$593$	4.55071	+	7.88206i	0.186875	+	0.323678i	0.944207	−	0.329353i	$-0.106831\pi$
$593$	4.55071	+	7.88206i	0.186875	+	0.323678i	−0.757332	+	0.653031i	$0.773497\pi$
$594$	−35.1366	+	6.07449i	−1.44167	+	0.249240i
$595$	−24.4148	+	10.2048i	−1.00091	+	0.418355i
$596$	−5.99943	+	21.1593i	−0.245746	+	0.866717i
$597$	37.7075	−	14.4050i	1.54326	−	0.589557i
$598$	−14.0877	+	1.75097i	−0.576087	+	0.0716024i
$599$	37.6136	+	21.7162i	1.53685	+	0.887302i	0.999021	+	0.0442488i	$0.0140894\pi$
$599$	37.6136	+	21.7162i	1.53685	+	0.887302i	0.537831	+	0.843053i	$0.319244\pi$
$600$	11.3725	−	10.2985i	0.464278	−	0.420434i
$601$		−	15.5284i		−	0.633415i	−0.948523	−	0.316708i	$-0.897423\pi$
$601$		−	15.5284i		−	0.633415i	0.948523	−	0.316708i	$-0.102577\pi$
$602$	−19.1485	−	0.0773002i	−0.780433	−	0.00315052i
$603$	−5.43533	+	16.5469i	−0.221344	+	0.673841i
$604$	16.1619	−	4.08059i	0.657618	−	0.166037i
$605$	30.9831	+	17.8881i	1.25964	+	0.727256i
$606$	17.4197	+	0.610490i	0.707625	+	0.0247995i
$607$	1.01612	−	0.586656i	0.0412430	−	0.0238116i	−0.479237	−	0.877686i	$-0.659086\pi$
$607$	1.01612	−	0.586656i	0.0412430	−	0.0238116i	0.520480	+	0.853874i	$0.325753\pi$
$608$	−35.4214	+	3.36394i	−1.43653	+	0.136426i
$609$	−17.1629	−	5.05409i	−0.695478	−	0.204802i
$610$	−6.04771	−	8.00086i	−0.244865	−	0.323945i
$611$	15.4473	+	26.7555i	0.624930	+	1.08241i
$612$	9.22033	+	18.9165i	0.372710	+	0.764654i
$613$	−35.7276	−	20.6273i	−1.44302	−	0.833131i	−0.444974	−	0.895543i	$-0.646787\pi$
$613$	−35.7276	−	20.6273i	−1.44302	−	0.833131i	−0.998050	+	0.0624126i	$0.980121\pi$
$614$	23.0112	+	9.72739i	0.928655	+	0.392565i
$615$	1.64420	−	10.2741i	0.0663006	−	0.414291i
$616$	8.74702	+	35.2429i	0.352427	+	1.41998i
$617$		−	15.3232i		−	0.616887i	−0.951243	−	0.308444i	$-0.900192\pi$
$617$		−	15.3232i		−	0.616887i	0.951243	−	0.308444i	$-0.0998081\pi$
$618$	2.25648	−	3.61013i	0.0907691	−	0.145221i
$619$	−7.95796	+	13.7836i	−0.319857	+	0.554009i	−0.980458	−	0.196728i	$-0.936968\pi$
$619$	−7.95796	+	13.7836i	−0.319857	+	0.554009i	0.660601	+	0.750738i	$0.270302\pi$
$620$	3.93738	+	4.05313i	0.158129	+	0.162778i
$621$	−18.9305	+	0.900509i	−0.759655	+	0.0361362i
$622$	−9.36592	+	7.07954i	−0.375539	+	0.283864i
$623$	−1.86370	+	2.44502i	−0.0746677	+	0.0979575i
$624$	14.4447	+	12.4473i	0.578251	+	0.498290i
$625$	15.4254	+	26.7176i	0.617017	+	1.06871i
$626$	37.4267	−	4.65180i	1.49587	−	0.185923i
$627$	33.3344	−	41.0294i	1.33125	−	1.63856i
$628$	21.0280	−	5.30920i	0.839110	−	0.211860i
$629$		−	4.31380i		−	0.172002i
$630$	−23.9424	+	21.2454i	−0.953887	+	0.846435i
$631$	−27.9268			−1.11175			−0.555875	−	0.831266i	$-0.687617\pi$
$631$	−27.9268			−1.11175			−0.555875	+	0.831266i	$0.687617\pi$
$632$	−9.91594	+	12.3572i	−0.394435	+	0.491544i
$633$	27.4128	+	22.2715i	1.08956	+	0.885215i
$634$	−5.02703	−	40.4457i	−0.199649	−	1.60630i
$635$	−38.6170	+	22.2955i	−1.53247	+	0.884770i
$636$	−2.93162	+	6.30923i	−0.116246	+	0.250177i
$637$	13.5351	−	13.7098i	0.536281	−	0.543203i
$638$	21.3735	−	16.1559i	0.846184	−	0.639616i
$639$	28.6384	−	5.99103i	1.13292	−	0.237001i
$640$	−20.9121	+	24.5673i	−0.826622	+	0.971108i
$641$	−7.03036	−	4.05898i	−0.277683	−	0.160320i	0.354691	−	0.934984i	$-0.384586\pi$
$641$	−7.03036	−	4.05898i	−0.277683	−	0.160320i	−0.632374	+	0.774663i	$0.717919\pi$
$642$	−2.21018	−	1.38146i	−0.0872287	−	0.0545217i
$643$	21.5611			0.850285			0.425143	−	0.905126i	$-0.360224\pi$
$643$	21.5611			0.850285			0.425143	+	0.905126i	$0.360224\pi$
$644$	2.30312	+	19.1618i	0.0907558	+	0.755079i
$645$	24.9595	+	3.99436i	0.982778	+	0.157278i
$646$	−28.7363	−	12.1475i	−1.13061	−	0.477939i
$647$	−19.5173	+	33.8049i	−0.767304	+	1.32901i	0.171716	+	0.985147i	$0.445069\pi$
$647$	−19.5173	+	33.8049i	−0.767304	+	1.32901i	−0.939020	+	0.343863i	$0.888264\pi$
$648$	17.9642	+	18.0357i	0.705702	+	0.708508i
$649$	4.32348	−	2.49616i	0.169712	−	0.0979830i
$650$	9.72408	−	7.35027i	0.381410	−	0.288301i
$651$	−3.13065	−	3.28848i	−0.122700	−	0.128886i
$652$	−22.3561	−	6.33877i	−0.875531	−	0.248245i
$653$	8.53952	+	14.7909i	0.334177	+	0.578812i	0.983326	−	0.181849i	$-0.0582083\pi$
$653$	8.53952	+	14.7909i	0.334177	+	0.578812i	−0.649149	+	0.760661i	$0.724875\pi$
$654$	22.2142	+	0.778521i	0.868645	+	0.0304426i
$655$	−14.3772	+	24.9021i	−0.561765	+	0.973006i
$656$	−0.244092	+	8.42284i	−0.00953021	+	0.328857i
$657$	0.314609	−	0.957770i	0.0122741	−	0.0373662i
$658$	36.4588	−	20.8537i	1.42131	−	0.812962i
$659$	6.99022			0.272300			0.136150	−	0.990688i	$-0.456527\pi$
$659$	6.99022			0.272300			0.136150	+	0.990688i	$0.456527\pi$
$660$	−4.24257	−	47.7456i	−0.165142	−	1.85849i
$661$	23.0740	−	39.9653i	0.897474	−	1.55447i	0.0667617	−	0.997769i	$-0.478733\pi$
$661$	23.0740	−	39.9653i	0.897474	−	1.55447i	0.830712	−	0.556702i	$-0.187933\pi$
$662$	3.63830	−	0.452207i	0.141406	−	0.0175755i
$663$	5.96655	+	15.6184i	0.231722	+	0.606570i
$664$	−0.364074	+	0.141617i	−0.0141288	+	0.00549582i
$665$	6.04325	−	47.0686i	0.234347	−	1.82524i
$666$	−1.69032	−	4.93683i	−0.0654985	−	0.191298i
$667$	12.3322	−	7.12002i	0.477506	−	0.275688i
$668$	10.8011	+	11.1186i	0.417907	+	0.430193i
$669$	15.4145	+	12.5236i	0.595961	+	0.484189i
$670$	−21.5651	−	9.11610i	−0.833133	−	0.352186i
$671$	−12.0677			−0.465869
$672$	17.0013	−	19.5692i	0.655841	−	0.754899i
$673$	8.04494			0.310110			0.155055	−	0.987906i	$-0.450445\pi$
$673$	8.04494			0.310110			0.155055	+	0.987906i	$0.450445\pi$
$674$	−14.5519	−	6.15144i	−0.560517	−	0.236945i
$675$	13.6904	−	8.79702i	0.526945	−	0.338597i
$676$	−7.56063	−	7.78291i	−0.290794	−	0.299343i
$677$	8.53140	−	4.92561i	0.327888	−	0.189306i	−0.327015	−	0.945019i	$-0.606043\pi$
$677$	8.53140	−	4.92561i	0.327888	−	0.189306i	0.654903	+	0.755713i	$0.272709\pi$
$678$	−19.3293	−	36.3642i	−0.742339	−	1.39656i
$679$	27.0847	−	11.3207i	1.03942	−	0.434450i
$680$	−26.3644	+	10.2552i	−1.01103	+	0.393270i
$681$	34.3208	−	13.1112i	1.31518	−	0.502422i
$682$	6.74725	−	0.838621i	0.258365	−	0.0321125i
$683$	20.1018	−	34.8173i	0.769173	−	1.33225i	−0.168839	−	0.985644i	$-0.554002\pi$
$683$	20.1018	−	34.8173i	0.769173	−	1.33225i	0.938012	−	0.346603i	$-0.112665\pi$
$684$	−37.6465	−	2.64197i	−1.43945	−	0.101018i
$685$	56.2088			2.14763
$686$	−18.5642	−	18.4762i	−0.708784	−	0.705425i
$687$	3.88117	+	0.621119i	0.148076	+	0.0236972i
$688$	−20.4621	−	0.592989i	−0.780112	−	0.0226075i
$689$	−2.76368	+	4.78683i	−0.105288	+	0.182364i
$690$	0.892301	−	25.4608i	0.0339693	−	0.969277i
$691$	17.2791	+	29.9282i	0.657326	+	1.13852i	0.981305	+	0.192458i	$0.0616460\pi$
$691$	17.2791	+	29.9282i	0.657326	+	1.13852i	−0.323979	+	0.946064i	$0.605021\pi$
$692$	1.95628	+	0.554678i	0.0743667	+	0.0210857i
$693$	3.02139	+	38.3961i	0.114773	+	1.45855i
$694$	16.3280	−	12.3420i	0.619801	−	0.468497i
$695$	−0.276178	+	0.159451i	−0.0104760	+	0.00604834i
$696$	−18.2075	−	5.85883i	−0.690155	−	0.222078i
$697$	−3.69426	+	6.39864i	−0.139930	+	0.242366i
$698$	29.7018	+	12.5557i	1.12423	+	0.475240i
$699$	−7.13078	+	44.5579i	−0.269711	+	1.68533i
$700$	−9.93931	−	13.2602i	−0.375671	−	0.501189i
$701$	−29.6534			−1.11999			−0.559997	−	0.828495i	$-0.689198\pi$
$701$	−29.6534			−1.11999			−0.559997	+	0.828495i	$0.689198\pi$
$702$	12.9482	+	15.5363i	0.488699	+	0.586379i
$703$	6.69969	+	3.86807i	0.252684	+	0.145887i
$704$	8.40869	+	37.8977i	0.316915	+	1.42832i
$705$	−51.7932	+	19.7860i	−1.95064	+	0.745184i
$706$	4.64945	−	3.51444i	0.174984	−	0.132268i
$707$	2.39755	−	18.6736i	0.0901692	−	0.702295i
$708$	−3.23211	−	1.50182i	−0.121470	−	0.0564417i
$709$	−9.81381	+	5.66601i	−0.368565	+	0.212791i	−0.672832	−	0.739796i	$-0.734922\pi$
$709$	−9.81381	+	5.66601i	−0.368565	+	0.212791i	0.304266	+	0.952587i	$0.401589\pi$
$710$	4.85116	+	39.0307i	0.182061	+	1.46480i
$711$	−12.5246	+	11.2044i	−0.469709	+	0.420199i
$712$	−2.05693	+	2.56335i	−0.0770868	+	0.0960654i
$713$	3.61371			0.135335
$714$	21.2660	−	8.02580i	0.795860	−	0.300358i
$715$		−	38.0831i		−	1.42423i
$716$	−41.9256	+	10.5855i	−1.56683	+	0.395598i
$717$	−11.1963	−	9.09648i	−0.418135	−	0.339714i
$718$	−15.9426	+	1.98152i	−0.594971	+	0.0739495i
$719$	8.51080	+	14.7411i	0.317399	+	0.549752i	0.979945	−	0.199270i	$-0.0638572\pi$
$719$	8.51080	+	14.7411i	0.317399	+	0.549752i	−0.662545	+	0.749022i	$0.730524\pi$
$720$	−26.1538	+	22.0670i	−0.974695	+	0.822389i
$721$	−3.65713	−	2.78763i	−0.136199	−	0.103817i
$722$	23.1979	−	17.5349i	0.863335	−	0.652580i
$723$	−11.6604	+	4.45448i	−0.433653	+	0.165664i
$724$	13.0585	+	13.4424i	0.485316	+	0.499584i
$725$	−6.11364	+	10.5891i	−0.227055	+	0.393271i
$726$	−26.0594	−	16.2883i	−0.967155	−	0.604514i
$727$			42.1153i			1.56197i	0.624550	+	0.780985i	$0.285282\pi$
$727$			42.1153i			1.56197i	−0.624550	+	0.780985i	$0.714718\pi$
$728$	14.8306	−	14.2911i	0.549658	−	0.529663i
$729$	15.6586	+	21.9956i	0.579949	+	0.814653i
$730$	1.24824	+	0.527661i	0.0461993	+	0.0195296i
$731$	−15.5446	−	8.97469i	−0.574939	−	0.331941i
$732$	4.95097	+	7.05031i	0.182993	+	0.260587i
$733$	−20.3500	−	35.2472i	−0.751644	−	1.30189i	−0.947026	−	0.321158i	$-0.895928\pi$
$733$	−20.3500	−	35.2472i	−0.751644	−	1.30189i	0.195382	−	0.980727i	$-0.437405\pi$
$734$	−23.8815	−	31.5941i	−0.881481	−	1.16616i
$735$	20.4563	+	27.8731i	0.754541	+	1.02812i
$736$	1.95064	+	20.5398i	0.0719017	+	0.757107i
$737$	−24.3968	+	14.0855i	−0.898669	+	0.518847i
$738$	−1.72057	+	8.77034i	−0.0633350	+	0.322841i
$739$	7.63741	+	4.40946i	0.280947	+	0.162205i	0.633852	−	0.773454i	$-0.281473\pi$
$739$	7.63741	+	4.40946i	0.280947	+	0.162205i	−0.352905	+	0.935659i	$0.614806\pi$
$740$	6.80122	−	1.71719i	0.250018	−	0.0631251i
$741$	−29.6068	−	4.73810i	−1.08763	−	0.174058i
$742$	6.49252	+	3.78349i	0.238348	+	0.138896i
$743$		−	16.3412i		−	0.599502i	−0.954017	−	0.299751i	$-0.903096\pi$
$743$		−	16.3412i		−	0.599502i	0.954017	−	0.299751i	$-0.0969036\pi$
$744$	−3.25811	−	3.59788i	−0.119448	−	0.131905i
$745$	−27.1572	−	15.6792i	−0.994962	−	0.574441i
$746$	−43.9604	+	5.46388i	−1.60950	+	0.200047i
$747$	−0.405564	+	0.0848424i	−0.0148388	+	0.00310422i
$748$	−9.28501	+	32.7471i	−0.339494	+	1.19735i
$749$	−1.70663	+	2.23895i	−0.0623590	+	0.0818096i
$750$	−6.12500	−	11.5229i	−0.223653	−	0.420758i
$751$	6.17492	+	10.6953i	0.225326	+	0.390276i	0.956417	−	0.292004i	$-0.0943219\pi$
$751$	6.17492	+	10.6953i	0.225326	+	0.390276i	−0.731091	+	0.682280i	$0.760989\pi$
$752$	39.5198	−	21.3149i	1.44114	−	0.777273i
$753$	11.3092	+	9.18817i	0.412130	+	0.334836i
$754$	−13.9970	−	5.91690i	−0.509742	−	0.215481i
$755$			23.7670i			0.864969i
$756$	21.1926	−	17.5178i	0.770767	−	0.637117i
$757$			29.0246i			1.05492i	0.849581	+	0.527459i	$0.176855\pi$
$757$			29.0246i			1.05492i	−0.849581	+	0.527459i	$0.823145\pi$
$758$	15.8656	−	37.5318i	0.576265	−	1.36322i
$759$	−23.7917	−	19.3296i	−0.863583	−	0.701620i
$760$	7.71305	−	50.1418i	0.279782	−	1.81883i
$761$	−15.5050	−	26.8554i	−0.562055	−	0.973507i	−0.997317	−	0.0732037i	$-0.976678\pi$
$761$	−15.5050	−	26.8554i	−0.562055	−	0.973507i	0.435262	−	0.900304i	$-0.356656\pi$
$762$	33.8216	−	17.9778i	1.22523	−	0.651269i
$763$	3.05745	−	23.8134i	0.110687	−	0.862102i
$764$	−17.1226	−	4.85489i	−0.619474	−	0.175644i
$765$	−29.3690	+	6.14387i	−1.06184	+	0.222132i
$766$	4.42015	+	35.5629i	0.159706	+	1.28494i
$767$	−2.45221	−	1.41578i	−0.0885442	−	0.0511210i
$768$	18.6911	−	20.4607i	0.674458	−	0.738313i
$769$			42.3916i			1.52868i	0.644813	+	0.764340i	$0.276935\pi$
$769$			42.3916i			1.52868i	−0.644813	+	0.764340i	$0.723065\pi$
$770$	−51.7739	−	0.209005i	−1.86580	−	0.00753203i
$771$	−51.7479	−	8.28143i	−1.86366	−	0.298248i
$772$	28.9235	−	7.30267i	1.04098	−	0.262829i
$773$	−2.88336	−	1.66471i	−0.103707	−	0.0598754i	0.447249	−	0.894409i	$-0.352404\pi$
$773$	−2.88336	−	1.66471i	−0.103707	−	0.0598754i	−0.550957	+	0.834534i	$0.685737\pi$
$774$	−21.3064	−	4.17989i	−0.765841	−	0.150243i
$775$	−2.68722	+	1.55147i	−0.0965277	+	0.0557303i
$776$	29.2476	−	11.3767i	1.04993	−	0.408400i
$777$	−5.47845	+	1.32452i	−0.196538	+	0.0475168i
$778$	−4.98397	+	3.76730i	−0.178684	+	0.135064i
$779$	−6.62508	−	11.4750i	−0.237368	−	0.411134i
$780$	−22.2493	+	15.6242i	−0.796651	+	0.559436i
$781$	40.9842	+	23.6622i	1.46653	+	0.846701i
$782$	−7.04399	+	16.6633i	−0.251893	+	0.595878i
$783$	−18.0314	−	9.29733i	−0.644388	−	0.332260i
$784$	−19.3473	−	20.2406i	−0.690976	−	0.722878i
$785$			30.9229i			1.10369i
$786$	13.0914	−	20.9448i	0.466954	−	0.747075i
$787$	−11.2617	+	19.5059i	−0.401437	+	0.695309i	−0.993900	−	0.110289i	$-0.964822\pi$
$787$	−11.2617	+	19.5059i	−0.401437	+	0.695309i	0.592463	+	0.805598i	$0.298156\pi$
$788$	−3.82389	−	3.93631i	−0.136221	−	0.140225i
$789$	39.0623	−	14.9226i	1.39065	−	0.531257i
$790$	−13.6220	−	18.0212i	−0.484647	−	0.641167i
$791$	−41.0411	+	17.1542i	−1.45925	+	0.609932i
$792$	2.20560	+	41.1150i	0.0783727	+	1.46096i
$793$	3.42230	+	5.92761i	0.121530	+	0.210495i
$794$	2.79710	+	22.5045i	0.0992654	+	0.798653i
$795$	−7.69883	−	6.25492i	−0.273049	−	0.221839i
$796$	−11.4101	−	45.1916i	−0.404420	−	1.60178i
$797$		−	20.3781i		−	0.721831i	−0.932599	−	0.360915i	$-0.882464\pi$
$797$		−	20.3781i		−	0.721831i	0.932599	−	0.360915i	$-0.117536\pi$
$798$	−6.60392	+	40.2244i	−0.233776	+	1.42393i
$799$	39.3710			1.39285
$800$	−10.2688	−	14.4363i	−0.363058	−	0.510400i
$801$	−2.59807	+	2.32422i	−0.0917981	+	0.0821221i
$802$	10.5909	−	1.31635i	0.373976	−	0.0464818i
$803$	1.41214	−	0.815301i	0.0498335	−	0.0287714i
$804$	18.2384	+	8.47454i	0.643218	+	0.298874i
$805$	−27.2937	−	3.50430i	−0.961976	−	0.123510i
$806$	−2.32539	−	3.07639i	−0.0819084	−	0.108361i
$807$	32.5241	−	12.4248i	1.14490	−	0.437374i
$808$	3.06002	−	19.8929i	0.107651	−	0.699828i
$809$	5.45505	+	3.14948i	0.191789	+	0.110730i	0.592820	−	0.805335i	$-0.298015\pi$
$809$	5.45505	+	3.14948i	0.191789	+	0.110730i	−0.401031	+	0.916065i	$0.631348\pi$
$810$	−31.2033	+	18.5392i	−1.09637	+	0.651400i
$811$	9.32889			0.327582			0.163791	−	0.986495i	$-0.447628\pi$
$811$	9.32889			0.327582			0.163791	+	0.986495i	$0.447628\pi$
$812$	−8.12083	+	18.9965i	−0.284985	+	0.666646i
$813$	0.499048	−	3.11839i	0.0175024	−	0.109367i
$814$	3.28635	−	7.77420i	0.115186	−	0.272485i
$815$	16.5660	−	28.6932i	0.580283	−	1.00508i
$816$	22.9412	−	8.01045i	0.803101	−	0.280422i
$817$	27.8769	−	16.0947i	0.975290	−	0.563084i
$818$	23.9883	+	31.7355i	0.838732	+	1.10961i
$819$	18.0032	−	12.3729i	0.629082	−	0.432345i
$820$	−11.5588	−	3.27734i	−0.403650	−	0.114450i
$821$	−21.8378	−	37.8241i	−0.762143	−	1.32007i	−0.941744	−	0.336331i	$-0.890814\pi$
$821$	−21.8378	−	37.8241i	−0.762143	−	1.32007i	0.179600	−	0.983740i	$-0.442520\pi$
$822$	−48.2526	−	1.69106i	−1.68300	−	0.0589826i
$823$	12.0388	−	20.8519i	0.419647	−	0.726850i	−0.576257	−	0.817269i	$-0.695487\pi$
$823$	12.0388	−	20.8519i	0.419647	−	0.726850i	0.995904	+	0.0904188i	$0.0288205\pi$
$824$	−3.83412	−	3.07665i	−0.133568	−	0.107180i
$825$	25.9906	+	4.15938i	0.904877	+	0.144811i
$826$	−1.93821	+	3.32601i	−0.0674391	+	0.115727i
$827$	40.9864			1.42524			0.712618	−	0.701553i	$-0.247510\pi$
$827$	40.9864			1.42524			0.712618	+	0.701553i	$0.247510\pi$
$828$	−1.53200	+	21.8301i	−0.0532406	+	0.758648i
$829$	−8.07095	+	13.9793i	−0.280316	+	0.485521i	−0.971462	−	0.237194i	$-0.923772\pi$
$829$	−8.07095	+	13.9793i	−0.280316	+	0.485521i	0.691147	+	0.722714i	$0.257106\pi$
$830$	−0.0687001	−	0.552737i	−0.00238462	−	0.0191858i
$831$	−21.3123	+	8.14170i	−0.739315	+	0.282433i
$832$	16.2305	−	14.8778i	0.562692	−	0.515794i
$833$	−6.50627	−	23.6735i	−0.225429	−	0.820238i
$834$	0.241883	−	0.128573i	0.00837572	−	0.00445211i
$835$	−19.1408	+	11.0509i	−0.662393	+	0.382433i
$836$	−42.5334	−	43.7839i	−1.47105	−	1.51430i
$837$	−2.78310	−	4.33122i	−0.0961979	−	0.149709i
$838$	−10.7740	+	25.4870i	−0.372181	+	0.880432i
$839$	40.8898			1.41167			0.705836	−	0.708375i	$-0.250571\pi$
$839$	40.8898			1.41167			0.705836	+	0.708375i	$0.250571\pi$
$840$	21.1190	+	30.3336i	0.728673	+	1.04661i
$841$	−13.7566			−0.474367
$842$	−14.3709	+	33.9959i	−0.495255	+	1.17158i
$843$	−20.6781	−	16.8000i	−0.712193	−	0.578622i
$844$	29.2531	−	28.4177i	1.00693	−	0.978176i
$845$	13.3983	−	7.73551i	0.460915	−	0.266110i
$846$	45.0573	−	15.4271i	1.54910	−	0.530396i
$847$	−20.1223	+	26.3987i	−0.691411	+	0.907071i
$848$	6.83780	+	4.21651i	0.234811	+	0.144796i
$849$	5.74696	+	15.0436i	0.197235	+	0.516296i
$850$	−1.91598	−	15.4153i	−0.0657176	−	0.528740i
$851$	2.24298	−	3.88495i	0.0768882	−	0.133174i
$852$	−2.99024	−	33.6520i	−0.102444	−	1.15290i
$853$	23.3041			0.797917			0.398958	−	0.916969i	$-0.369372\pi$
$853$	23.3041			0.797917			0.398958	+	0.916969i	$0.369372\pi$
$854$	8.07735	−	4.62009i	0.276401	−	0.158096i
$855$	16.7924	−	51.1216i	0.574290	−	1.74832i
$856$	−1.88358	+	2.34731i	−0.0643793	+	0.0802294i
$857$	−3.23327	+	5.60019i	−0.110447	+	0.191299i	−0.915950	−	0.401292i	$-0.868561\pi$
$857$	−3.23327	+	5.60019i	−0.110447	+	0.191299i	0.805504	+	0.592591i	$0.201895\pi$
$858$	−1.14574	+	32.6925i	−0.0391151	+	1.11610i
$859$	1.10393	+	1.91207i	0.0376657	+	0.0652390i	0.884244	−	0.467026i	$-0.154674\pi$
$859$	1.10393	+	1.91207i	0.0376657	+	0.0652390i	−0.846578	+	0.532265i	$0.821341\pi$
$860$	7.96186	−	28.0805i	0.271497	−	0.957538i
$861$	9.26045	+	2.72699i	0.315595	+	0.0929356i
$862$	10.2479	+	13.5575i	0.349044	+	0.461770i
$863$	−21.2034	+	12.2418i	−0.721771	+	0.416715i	−0.815404	−	0.578892i	$-0.803485\pi$
$863$	−21.2034	+	12.2418i	−0.721771	+	0.416715i	0.0936330	+	0.995607i	$0.470152\pi$
$864$	23.1157	−	18.1567i	0.786412	−	0.617702i
$865$	−1.44962	+	2.51082i	−0.0492886	+	0.0853704i
$866$	−19.6218	+	46.4175i	−0.666778	+	1.57733i
$867$	−8.03607	−	1.28604i	−0.272919	−	0.0436764i
$868$	−4.19511	+	3.14448i	−0.142391	+	0.106731i
$869$	−27.1815			−0.922068
$870$	14.4546	−	23.1257i	0.490056	−	0.784035i
$871$	13.8375	+	7.98908i	0.468866	+	0.270700i
$872$	3.90225	−	25.3682i	0.132147	−	0.859074i
$873$	32.5807	−	6.81574i	1.10269	−	0.230678i
$874$	−19.5634	−	25.8815i	−0.661740	−	0.875453i
$875$	−13.0049	+	5.43574i	−0.439647	+	0.183761i
$876$	−1.05568	−	0.490526i	−0.0356680	−	0.0165733i
$877$	−15.3248	+	8.84776i	−0.517481	+	0.298768i	−0.735903	−	0.677087i	$-0.763242\pi$
$877$	−15.3248	+	8.84776i	−0.517481	+	0.298768i	0.218422	+	0.975854i	$0.429909\pi$
$878$	18.9520	−	2.35556i	0.639599	−	0.0794964i
$879$	−23.9906	−	19.4912i	−0.809183	−	0.657422i
$880$	−55.3258	−	1.60333i	−1.86503	−	0.0540484i
$881$	55.0445			1.85450			0.927249	−	0.374446i	$-0.122167\pi$
$881$	55.0445			1.85450			0.927249	+	0.374446i	$0.122167\pi$
$882$	−16.7222	−	24.5432i	−0.563065	−	0.826412i
$883$			49.3732i			1.66154i	0.556616	+	0.830770i	$0.312100\pi$
$883$			49.3732i			1.66154i	−0.556616	+	0.830770i	$0.687900\pi$
$884$	18.7184	−	4.72606i	0.629568	−	0.158955i
$885$	3.20429	−	3.94398i	0.107711	−	0.132575i
$886$	4.10469	+	33.0249i	0.137900	+	1.10949i
$887$	−12.2514	−	21.2201i	−0.411363	−	0.712502i	0.583676	−	0.811987i	$-0.301614\pi$
$887$	−12.2514	−	21.2201i	−0.411363	−	0.712502i	−0.995039	+	0.0994850i	$0.968280\pi$
$888$	−5.89019	+	1.26951i	−0.197662	+	0.0426019i
$889$	−15.9547	−	38.1716i	−0.535105	−	1.28023i
$890$	−2.82570	−	3.73827i	−0.0947176	−	0.125307i
$891$	−4.84434	+	43.4022i	−0.162292	+	1.45403i
$892$	16.4494	−	15.9796i	0.550767	−	0.535037i
$893$	−35.3029	+	61.1465i	−1.18137	+	2.04619i
$894$	22.8414	+	14.2769i	0.763932	+	0.477491i
$895$		−	61.6540i		−	2.06087i
$896$	−20.1373	−	22.1470i	−0.672738	−	0.739880i
$897$	−2.74748	+	17.1681i	−0.0917357	+	0.573226i
$898$	−16.8658	+	39.8978i	−0.562819	+	1.33141i
$899$	3.35007	+	1.93416i	0.111731	+	0.0645079i
$900$	−8.23303	−	16.8909i	−0.274434	−	0.563032i
$901$	3.52194	+	6.10018i	0.117333	+	0.203226i
$902$	−11.5323	+	8.71707i	−0.383984	+	0.290247i
$903$	−6.62485	+	22.4970i	−0.220461	+	0.748654i
$904$	−44.3184	+	17.2390i	−1.47401	+	0.573359i
$905$	−23.1412	+	13.3606i	−0.769239	+	0.444120i
$906$	0.715038	−	20.4028i	0.0237556	−	0.677839i
$907$	−6.23747	−	3.60121i	−0.207112	−	0.119576i	0.392857	−	0.919600i	$-0.371487\pi$
$907$	−6.23747	−	3.60121i	−0.207112	−	0.119576i	−0.599968	+	0.800024i	$0.704820\pi$
$908$	−10.3853	−	41.1328i	−0.344648	−	1.36504i
$909$	6.66211	−	20.2816i	0.220968	−	0.672697i
$910$	14.5800	+	25.4904i	0.483322	+	0.844998i
$911$			13.3025i			0.440730i	0.975417	+	0.220365i	$0.0707248\pi$
$911$			13.3025i			0.440730i	−0.975417	+	0.220365i	$0.929275\pi$
$912$	−8.12983	+	42.8123i	−0.269205	+	1.41766i
$913$	−0.580401	−	0.335095i	−0.0192085	−	0.0110900i
$914$	−2.02598	−	16.3003i	−0.0670134	−	0.539166i
$915$	−11.4746	+	4.38354i	−0.379340	+	0.144915i
$916$	1.23806	−	4.36649i	0.0409066	−	0.144273i
$917$	−21.2175	−	16.1729i	−0.700663	−	0.534077i
$918$	25.3967	−	4.39065i	0.838217	−	0.144913i
$919$	−3.29521	−	5.70747i	−0.108699	−	0.188272i	0.806544	−	0.591173i	$-0.201335\pi$
$919$	−3.29521	−	5.70747i	−0.108699	−	0.188272i	−0.915243	+	0.402901i	$0.868002\pi$
$920$	−29.0757	−	4.47256i	−0.958597	−	0.147456i
$921$	19.2938	−	23.7477i	0.635753	−	0.782512i
$922$	16.9798	−	40.1675i	0.559200	−	1.32285i
$923$		−	26.8417i		−	0.883505i
$924$	44.4392	+	1.73706i	1.46194	+	0.0571450i
$925$			3.85188i			0.126649i
$926$	42.1002	+	17.7968i	1.38350	+	0.584839i
$927$	−3.47644	−	3.88606i	−0.114181	−	0.127635i
$928$	−9.18516	+	20.0853i	−0.301518	+	0.659333i
$929$	−6.17532	−	10.6960i	−0.202606	−	0.350923i	0.746762	−	0.665092i	$-0.231608\pi$
$929$	−6.17532	−	10.6960i	−0.202606	−	0.350923i	−0.949367	+	0.314169i	$0.898274\pi$
$930$	6.11103	−	3.24831i	0.200389	−	0.106516i
$931$	42.6009	+	11.1226i	1.39619	+	0.364529i
$932$	50.1296	+	14.2136i	1.64205	+	0.465581i
$933$	5.13143	+	13.4324i	0.167995	+	0.439756i
$934$	47.6027	−	5.91659i	1.55761	−	0.193597i
$935$	−42.0298	−	24.2659i	−1.37452	−	0.793580i
$936$	19.5700	−	12.7433i	0.639666	−	0.416527i
$937$		−	11.2161i		−	0.366413i	−0.983074	−	0.183206i	$-0.941352\pi$
$937$		−	11.2161i		−	0.366413i	0.983074	−	0.183206i	$-0.0586476\pi$
$938$	10.9371	−	18.7682i	0.357108	−	0.612804i
$939$	7.29923	−	45.6105i	0.238201	−	1.48844i
$940$	15.6724	+	62.0731i	0.511176	+	2.02460i
$941$	8.10816	+	4.68125i	0.264318	+	0.152604i	0.626303	−	0.779580i	$-0.284567\pi$
$941$	8.10816	+	4.68125i	0.264318	+	0.152604i	−0.361985	+	0.932184i	$0.617901\pi$
$942$	0.930327	−	26.5459i	0.0303117	−	0.864911i
$943$	−6.65399	+	3.84168i	−0.216684	+	0.125102i
$944$	−2.16004	+	3.50288i	−0.0703035	+	0.114009i
$945$	16.8201	+	35.4117i	0.547159	+	1.15194i
$946$	−21.1769	−	28.0162i	−0.688521	−	0.910884i
$947$	19.4899	+	33.7574i	0.633335	+	1.09697i	0.986865	+	0.161546i	$0.0516480\pi$
$947$	19.4899	+	33.7574i	0.633335	+	1.09697i	−0.353530	+	0.935423i	$0.615019\pi$
$948$	11.1516	+	15.8802i	0.362188	+	0.515765i
$949$	−0.800945	−	0.462426i	−0.0259998	−	0.0150110i
$950$	25.6593	+	10.8468i	0.832496	+	0.351917i
$951$	−49.2896	−	7.88801i	−1.59832	−	0.255786i
$952$	−6.32235	−	25.4736i	−0.204908	−	0.825603i
$953$			0.425521i			0.0137840i	0.999976	+	0.00689198i	$0.00219380\pi$
$953$			0.425521i			0.0137840i	−0.999976	+	0.00689198i	$0.997806\pi$
$954$	6.42090	+	5.60118i	0.207884	+	0.181345i
$955$	12.6880	−	21.9763i	0.410574	−	0.711135i
$956$	−11.9480	+	11.6068i	−0.386426	+	0.375390i
$957$	−11.7102	−	30.6534i	−0.378536	−	0.990882i
$958$	−39.8984	+	30.1585i	−1.28906	+	0.974378i
$959$	−6.64124	+	51.7262i	−0.214457	+	1.67033i
$960$	21.7616	+	32.9808i	0.702353	+	1.06445i
$961$	−15.0092	−	25.9966i	−0.484167	−	0.838601i
$962$	−4.75063	+	0.590461i	−0.153167	+	0.0190372i
$963$	−2.37910	+	2.12833i	−0.0766656	+	0.0685846i
$964$	3.52836	+	13.9747i	0.113641	+	0.450095i
$965$			42.5337i			1.36921i
$966$	23.3249	+	3.82941i	0.750467	+	0.123209i
$967$	−25.1685			−0.809365			−0.404682	−	0.914457i	$-0.632618\pi$
$967$	−25.1685			−0.809365			−0.404682	+	0.914457i	$0.632618\pi$
$968$	−22.2086	+	27.6763i	−0.713811	+	0.889551i
$969$	−24.0941	+	29.6560i	−0.774014	+	0.952689i
$970$	5.51897	+	44.4036i	0.177203	+	1.42571i
$971$	−11.2476	+	6.49383i	−0.360954	+	0.208397i	−0.669499	−	0.742813i	$-0.733491\pi$
$971$	−11.2476	+	6.49383i	−0.360954	+	0.208397i	0.308545	+	0.951210i	$0.400158\pi$
$972$	27.3443	−	14.9762i	0.877070	−	0.480363i
$973$	−0.114104	−	0.272993i	−0.00365801	−	0.00875174i
$974$	−37.0472	+	28.0033i	−1.18707	+	0.897285i
$975$	−5.32766	−	13.9461i	−0.170622	−	0.446631i
$976$	8.75551	−	4.72225i	0.280257	−	0.151156i
$977$	33.4781	+	19.3286i	1.07106	+	0.618377i	0.928471	−	0.371405i	$-0.121124\pi$
$977$	33.4781	+	19.3286i	1.07106	+	0.618377i	0.142589	+	0.989782i	$0.454457\pi$
$978$	−15.0844	+	24.1334i	−0.482347	+	0.771701i
$979$	−5.63844			−0.180205
$980$	34.7342	−	19.6816i	1.10954	−	0.628705i
$981$	8.49578	−	25.8639i	0.271249	−	0.825770i
$982$	29.3471	+	12.4058i	0.936504	+	0.395884i
$983$	24.2049	−	41.9241i	0.772017	−	1.33717i	−0.164439	−	0.986387i	$-0.552581\pi$
$983$	24.2049	−	41.9241i	0.772017	−	1.33717i	0.936456	−	0.350785i	$-0.114085\pi$
$984$	9.82408	+	3.16119i	0.313180	+	0.100775i
$985$	6.77637	−	3.91234i	0.215913	−	0.124657i
$986$	−15.4488	+	11.6775i	−0.491989	+	0.371886i
$987$	−12.0886	−	50.0005i	−0.384783	−	1.59153i
$988$	−9.44432	+	33.3090i	−0.300464	+	1.05970i
$989$	−9.33285	−	16.1650i	−0.296767	−	0.514016i
$990$	−57.6084	−	11.3016i	−1.83092	−	0.359190i
$991$	8.16959	−	14.1502i	0.259516	−	0.449494i	−0.706597	−	0.707617i	$-0.749770\pi$
$991$	8.16959	−	14.1502i	0.259516	−	0.449494i	0.966112	+	0.258122i	$0.0831037\pi$
$992$	−4.56718	+	3.24873i	−0.145008	+	0.103147i
$993$	0.709567	−	4.43385i	0.0225174	−	0.140704i
$994$	−36.4912	−	0.147311i	−1.15743	−	0.00467242i
$995$	66.4569			2.10682
$996$	0.0423466	+	0.476565i	0.00134180	+	0.0151005i
$997$	−4.94566	+	8.56614i	−0.156631	+	0.271292i	−0.933652	−	0.358182i	$-0.883397\pi$
$997$	−4.94566	+	8.56614i	−0.156631	+	0.271292i	0.777021	+	0.629475i	$0.216730\pi$
$998$	−18.3310	+	2.27837i	−0.580256	+	0.0721206i
$999$	−6.38373	+	0.303669i	−0.201972	+	0.00960767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.101.4	yes	48
3.2	odd	2	inner	168.2.ba.c.101.21	yes	48
4.3	odd	2		672.2.bi.c.17.18		48
7.5	odd	6	inner	168.2.ba.c.5.14	yes	48
8.3	odd	2		672.2.bi.c.17.7		48
8.5	even	2	inner	168.2.ba.c.101.11	yes	48
12.11	even	2		672.2.bi.c.17.17		48
21.5	even	6	inner	168.2.ba.c.5.11	yes	48
24.5	odd	2	inner	168.2.ba.c.101.14	yes	48
24.11	even	2		672.2.bi.c.17.8		48
28.19	even	6		672.2.bi.c.593.8		48
56.5	odd	6	inner	168.2.ba.c.5.21	yes	48
56.19	even	6		672.2.bi.c.593.17		48
84.47	odd	6		672.2.bi.c.593.7		48
168.5	even	6	inner	168.2.ba.c.5.4	✓	48
168.131	odd	6		672.2.bi.c.593.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.4	✓	48	168.5	even	6	inner
168.2.ba.c.5.11	yes	48	21.5	even	6	inner
168.2.ba.c.5.14	yes	48	7.5	odd	6	inner
168.2.ba.c.5.21	yes	48	56.5	odd	6	inner
168.2.ba.c.101.4	yes	48	1.1	even	1	trivial
168.2.ba.c.101.11	yes	48	8.5	even	2	inner
168.2.ba.c.101.14	yes	48	24.5	odd	2	inner
168.2.ba.c.101.21	yes	48	3.2	odd	2	inner
672.2.bi.c.17.7		48	8.3	odd	2
672.2.bi.c.17.8		48	24.11	even	2
672.2.bi.c.17.17		48	12.11	even	2
672.2.bi.c.17.18		48	4.3	odd	2
672.2.bi.c.593.7		48	84.47	odd	6
672.2.bi.c.593.8		48	28.19	even	6
672.2.bi.c.593.17		48	56.19	even	6
672.2.bi.c.593.18		48	168.131	odd	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30261 - 0.550645i) q^{2} +(-1.09218 + 1.34430i) q^{3} +(1.39358 + 1.43455i) q^{4} +(-2.46958 + 1.42581i) q^{5} +(2.16291 - 1.14970i) q^{6} +(-1.02032 - 2.44110i) q^{7} +(-1.02536 - 2.63603i) q^{8} +(-0.614290 - 2.93643i) q^{9} +O(q^{10})\)	\(q+(-1.30261 - 0.550645i) q^{2} +(-1.09218 + 1.34430i) q^{3} +(1.39358 + 1.43455i) q^{4} +(-2.46958 + 1.42581i) q^{5} +(2.16291 - 1.14970i) q^{6} +(-1.02032 - 2.44110i) q^{7} +(-1.02536 - 2.63603i) q^{8} +(-0.614290 - 2.93643i) q^{9} +(4.00201 - 0.497414i) q^{10} +(2.42621 - 4.20231i) q^{11} +(-3.45051 + 0.306605i) q^{12} -2.75221 q^{13} +(-0.0151045 + 3.74163i) q^{14} +(0.780502 - 4.87710i) q^{15} +(-0.115871 + 3.99832i) q^{16} +(-1.75366 + 3.03743i) q^{17} +(-0.816754 + 4.16328i) q^{18} +(-3.14493 - 5.44717i) q^{19} +(-5.48696 - 1.55575i) q^{20} +(4.39594 + 1.29450i) q^{21} +(-5.47438 + 4.13799i) q^{22} +(-3.15865 + 1.82365i) q^{23} +(4.66349 + 1.50062i) q^{24} +(1.56588 - 2.71219i) q^{25} +(3.58505 + 1.51549i) q^{26} +(4.61837 + 2.38132i) q^{27} +(2.07998 - 4.86556i) q^{28} -3.90427 q^{29} +(-3.70224 + 5.92318i) q^{30} +(-0.858051 - 0.495396i) q^{31} +(2.35259 - 5.14445i) q^{32} +(2.99932 + 7.85123i) q^{33} +(3.95689 - 2.99094i) q^{34} +(6.00030 + 4.57370i) q^{35} +(3.35640 - 4.97339i) q^{36} +(-1.06516 + 0.614970i) q^{37} +(1.09715 + 8.82727i) q^{38} +(3.00591 - 3.69980i) q^{39} +(6.29069 + 5.04791i) q^{40} +2.10659 q^{41} +(-5.01338 - 4.10683i) q^{42} +5.11768i q^{43} +(9.40954 - 2.37574i) q^{44} +(5.70384 + 6.37590i) q^{45} +(5.11867 - 0.636204i) q^{46} +(-5.61268 - 9.72145i) q^{47} +(-5.24840 - 4.52265i) q^{48} +(-4.91791 + 4.98138i) q^{49} +(-3.53319 + 2.67068i) q^{50} +(-2.16791 - 5.67487i) q^{51} +(-3.83543 - 3.94819i) q^{52} +(1.00417 - 1.73927i) q^{53} +(-4.70466 - 5.64501i) q^{54} +13.8373i q^{55} +(-5.38860 + 5.19259i) q^{56} +(10.7575 + 1.72156i) q^{57} +(5.08574 + 2.14987i) q^{58} +(0.890996 + 0.514417i) q^{59} +(8.08414 - 5.67696i) q^{60} +(-1.24347 - 2.15376i) q^{61} +(0.844918 + 1.11779i) q^{62} +(-6.54135 + 4.49563i) q^{63} +(-5.89727 + 5.40576i) q^{64} +(6.79681 - 3.92414i) q^{65} +(0.416299 - 11.8786i) q^{66} +(-5.02777 - 2.90279i) q^{67} +(-6.80122 + 1.71719i) q^{68} +(0.998281 - 6.23793i) q^{69} +(-5.29756 - 9.26178i) q^{70} +9.75277i q^{71} +(-7.11065 + 4.63019i) q^{72} +(0.291019 + 0.168020i) q^{73} +(1.72612 - 0.214540i) q^{74} +(1.93577 + 5.06722i) q^{75} +(3.43154 - 12.1026i) q^{76} +(-12.7338 - 1.63491i) q^{77} +(-5.95280 + 3.16420i) q^{78} +(-2.80082 - 4.85116i) q^{79} +(-5.41471 - 10.0394i) q^{80} +(-8.24530 + 3.60764i) q^{81} +(-2.74407 - 1.15999i) q^{82} -0.138115i q^{83} +(4.26906 + 8.11019i) q^{84} -10.0016i q^{85} +(2.81803 - 6.66634i) q^{86} +(4.26417 - 5.24852i) q^{87} +(-13.5651 - 2.08666i) q^{88} +(-0.580993 - 1.00631i) q^{89} +(-3.91902 - 11.4461i) q^{90} +(2.80813 + 6.71841i) q^{91} +(-7.01795 - 1.98985i) q^{92} +(1.60311 - 0.612418i) q^{93} +(1.95806 + 15.7538i) q^{94} +(15.5333 + 8.96815i) q^{95} +(4.34623 + 8.78124i) q^{96} +11.0953i q^{97} +(9.14908 - 3.78077i) q^{98} +(-13.8302 - 4.54296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

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