LMFDB - Embedded newform 456.2.u.d.11.65

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(11,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("456.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.u (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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.65
Character	$\chi$	$=$	456.11
Dual form			456.2.u.d.83.65

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39823 + 0.212052i) q^{2} +(-1.43570 + 0.968901i) q^{3} +(1.91007 + 0.592994i) q^{4} +(1.07875 - 1.86846i) q^{5} +(-2.21289 + 1.05030i) q^{6} -3.66890i q^{7} +(2.54496 + 1.23417i) q^{8} +(1.12246 - 2.78210i) q^{9} +O(q^{10})$	\(q+(1.39823 + 0.212052i) q^{2} +(-1.43570 + 0.968901i) q^{3} +(1.91007 + 0.592994i) q^{4} +(1.07875 - 1.86846i) q^{5} +(-2.21289 + 1.05030i) q^{6} -3.66890i q^{7} +(2.54496 + 1.23417i) q^{8} +(1.12246 - 2.78210i) q^{9} +(1.90455 - 2.38377i) q^{10} -3.82357i q^{11} +(-3.31683 + 0.999307i) q^{12} +(-1.79332 + 1.03537i) q^{13} +(0.777998 - 5.12994i) q^{14} +(0.261585 + 3.72775i) q^{15} +(3.29672 + 2.26532i) q^{16} +(3.42951 + 1.98003i) q^{17} +(2.15940 - 3.65198i) q^{18} +(-4.15094 + 1.33029i) q^{19} +(3.16848 - 2.92919i) q^{20} +(3.55480 + 5.26743i) q^{21} +(0.810797 - 5.34621i) q^{22} +(0.581950 + 1.00797i) q^{23} +(-4.84959 + 0.693913i) q^{24} +(0.172576 + 0.298910i) q^{25} +(-2.72701 + 1.06741i) q^{26} +(1.08407 + 5.08181i) q^{27} +(2.17563 - 7.00784i) q^{28} +(3.45292 + 5.98063i) q^{29} +(-0.424723 + 5.26770i) q^{30} -1.31165i q^{31} +(4.12919 + 3.86650i) q^{32} +(3.70466 + 5.48949i) q^{33} +(4.37536 + 3.49576i) q^{34} +(-6.85518 - 3.95784i) q^{35} +(3.79374 - 4.64839i) q^{36} -8.74114i q^{37} +(-6.08604 + 0.979832i) q^{38} +(1.57149 - 3.22403i) q^{39} +(5.05139 - 3.42378i) q^{40} +(1.80920 + 1.04454i) q^{41} +(3.85344 + 8.11885i) q^{42} +(-5.31807 + 9.21118i) q^{43} +(2.26735 - 7.30328i) q^{44} +(-3.98738 - 5.09847i) q^{45} +(0.599956 + 1.53277i) q^{46} +(-3.09399 - 5.35895i) q^{47} +(-6.92796 - 0.0581197i) q^{48} -6.46079 q^{49} +(0.177915 + 0.454539i) q^{50} +(-6.84219 + 0.480133i) q^{51} +(-4.03932 + 0.914204i) q^{52} +(3.84474 + 6.65929i) q^{53} +(0.438160 + 7.33539i) q^{54} +(-7.14418 - 4.12470i) q^{55} +(4.52805 - 9.33719i) q^{56} +(4.67058 - 5.93175i) q^{57} +(3.55975 + 9.09447i) q^{58} +(-0.250420 - 0.144580i) q^{59} +(-1.71089 + 7.27537i) q^{60} +(-9.24783 + 5.33924i) q^{61} +(0.278139 - 1.83399i) q^{62} +(-10.2072 - 4.11819i) q^{63} +(4.95363 + 6.28184i) q^{64} +4.46765i q^{65} +(4.01589 + 8.46113i) q^{66} +(2.31946 + 4.01743i) q^{67} +(5.37645 + 5.81567i) q^{68} +(-1.81213 - 0.883285i) q^{69} +(-8.74581 - 6.98761i) q^{70} +(4.99046 - 8.64374i) q^{71} +(6.29021 - 5.69502i) q^{72} +(5.73429 - 9.93208i) q^{73} +(1.85358 - 12.2221i) q^{74} +(-0.537382 - 0.261936i) q^{75} +(-8.71744 + 0.0794659i) q^{76} -14.0283 q^{77} +(2.88096 - 4.17468i) q^{78} +(2.33161 + 1.34616i) q^{79} +(7.78900 - 3.71605i) q^{80} +(-6.48017 - 6.24559i) q^{81} +(2.30817 + 1.84415i) q^{82} +12.7910i q^{83} +(3.66635 + 12.1691i) q^{84} +(7.39920 - 4.27193i) q^{85} +(-9.38912 + 11.7516i) q^{86} +(-10.7520 - 5.24085i) q^{87} +(4.71895 - 9.73083i) q^{88} +(2.48876 - 1.43689i) q^{89} +(-4.49411 - 7.97435i) q^{90} +(3.79867 + 6.57949i) q^{91} +(0.513846 + 2.27038i) q^{92} +(1.27086 + 1.88314i) q^{93} +(-3.18972 - 8.14911i) q^{94} +(-1.99225 + 9.19092i) q^{95} +(-9.67452 - 1.55035i) q^{96} +(-8.13940 + 14.0979i) q^{97} +(-9.03364 - 1.37003i) q^{98} +(-10.6376 - 4.29180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9}+O(q^{10}) $ 136 * q - 2 * q^3 - 4 * q^4 - 9 * q^6 - 10 * q^9	$ 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9} + 18 q^{12} + 28 q^{16} - 10 q^{18} + 16 q^{19} + 10 q^{22} + 11 q^{24} - 96 q^{25} - 80 q^{27} + 6 q^{28} - 4 q^{30} - 40 q^{33} + 40 q^{34} + q^{36} - 56 q^{40} + 26 q^{42} - 20 q^{43} - 64 q^{46} - 19 q^{48} - 72 q^{49} - 42 q^{51} - 26 q^{52} + 6 q^{54} + 10 q^{57} + 144 q^{58} - 18 q^{60} - 112 q^{64} + 49 q^{66} - 12 q^{67} + 72 q^{70} - 45 q^{72} + 4 q^{73} + 144 q^{75} + 32 q^{76} - 50 q^{78} + 22 q^{81} - 22 q^{82} + 36 q^{84} + 100 q^{88} - 2 q^{90} + 24 q^{91} - 88 q^{94} - 66 q^{96} - 28 q^{97} + 80 q^{99}+O(q^{100}) $ 136 * q - 2 * q^3 - 4 * q^4 - 9 * q^6 - 10 * q^9 + 18 * q^12 + 28 * q^16 - 10 * q^18 + 16 * q^19 + 10 * q^22 + 11 * q^24 - 96 * q^25 - 80 * q^27 + 6 * q^28 - 4 * q^30 - 40 * q^33 + 40 * q^34 + q^36 - 56 * q^40 + 26 * q^42 - 20 * q^43 - 64 * q^46 - 19 * q^48 - 72 * q^49 - 42 * q^51 - 26 * q^52 + 6 * q^54 + 10 * q^57 + 144 * q^58 - 18 * q^60 - 112 * q^64 + 49 * q^66 - 12 * q^67 + 72 * q^70 - 45 * q^72 + 4 * q^73 + 144 * q^75 + 32 * q^76 - 50 * q^78 + 22 * q^81 - 22 * q^82 + 36 * q^84 + 100 * q^88 - 2 * q^90 + 24 * q^91 - 88 * q^94 - 66 * q^96 - 28 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	1.39823	+	0.212052i	0.988695	+	0.149944i
$2$	1.39823	+	0.212052i	0.988695	+	0.149944i
$3$	−1.43570	+	0.968901i	−0.828901	+	0.559396i
$3$	−1.43570	+	0.968901i	−0.828901	+	0.559396i
$4$	1.91007	+	0.592994i	0.955034	+	0.296497i
$5$	1.07875	−	1.86846i	0.482434	−	0.835600i	−0.517363	−	0.855766i	$-0.673086\pi$
$5$	1.07875	−	1.86846i	0.482434	−	0.835600i	0.999797	+	0.0201663i	$0.00641955\pi$
$6$	−2.21289	+	1.05030i	−0.903408	+	0.428783i
$7$		−	3.66890i		−	1.38671i	−0.720595	−	0.693356i	$-0.756131\pi$
$7$		−	3.66890i		−	1.38671i	0.720595	−	0.693356i	$-0.243869\pi$
$8$	2.54496	+	1.23417i	0.899779	+	0.436346i
$9$	1.12246	−	2.78210i	0.374153	−	0.927367i
$10$	1.90455	−	2.38377i	0.602273	−	0.753815i
$11$		−	3.82357i		−	1.15285i	−0.817150	−	0.576425i	$-0.804447\pi$
$11$		−	3.82357i		−	1.15285i	0.817150	−	0.576425i	$-0.195553\pi$
$12$	−3.31683	+	0.999307i	−0.957487	+	0.288475i
$13$	−1.79332	+	1.03537i	−0.497376	+	0.287160i	−0.727629	−	0.685970i	$-0.759378\pi$
$13$	−1.79332	+	1.03537i	−0.497376	+	0.287160i	0.230253	+	0.973131i	$0.426045\pi$
$14$	0.777998	−	5.12994i	0.207929	−	1.37103i
$15$	0.261585	+	3.72775i	0.0675410	+	0.962501i
$16$	3.29672	+	2.26532i	0.824179	+	0.566329i
$17$	3.42951	+	1.98003i	0.831778	+	0.480227i	0.854461	−	0.519515i	$-0.173887\pi$
$17$	3.42951	+	1.98003i	0.831778	+	0.480227i	−0.0226828	+	0.999743i	$0.507221\pi$
$18$	2.15940	−	3.65198i	0.508976	−	0.860781i
$19$	−4.15094	+	1.33029i	−0.952291	+	0.305190i
$19$	−4.15094	+	1.33029i	−0.952291	+	0.305190i
$20$	3.16848	−	2.92919i	0.708494	−	0.654986i
$21$	3.55480	+	5.26743i	0.775720	+	1.14945i
$22$	0.810797	−	5.34621i	0.172863	−	1.13982i
$23$	0.581950	+	1.00797i	0.121345	+	0.210176i	0.920298	−	0.391217i	$-0.127946\pi$
$23$	0.581950	+	1.00797i	0.121345	+	0.210176i	−0.798953	+	0.601393i	$0.794613\pi$
$24$	−4.84959	+	0.693913i	−0.989918	+	0.141644i
$25$	0.172576	+	0.298910i	0.0345152	+	0.0597821i
$26$	−2.72701	+	1.06741i	−0.534811	+	0.209335i
$27$	1.08407	+	5.08181i	0.208629	+	0.977995i
$28$	2.17563	−	7.00784i	0.411156	−	1.32436i
$29$	3.45292	+	5.98063i	0.641191	+	1.11058i	0.985167	+	0.171597i	$0.0548927\pi$
$29$	3.45292	+	5.98063i	0.641191	+	1.11058i	−0.343976	+	0.938978i	$0.611774\pi$
$30$	−0.424723	+	5.26770i	−0.0775435	+	0.961747i
$31$		−	1.31165i		−	0.235580i	−0.993039	−	0.117790i	$-0.962419\pi$
$31$		−	1.31165i		−	0.235580i	0.993039	−	0.117790i	$-0.0375809\pi$
$32$	4.12919	+	3.86650i	0.729944	+	0.683507i
$33$	3.70466	+	5.48949i	0.644899	+	0.955598i
$34$	4.37536	+	3.49576i	0.750368	+	0.599518i
$35$	−6.85518	−	3.95784i	−1.15874	−	0.668997i
$36$	3.79374	−	4.64839i	0.632291	−	0.774731i
$37$		−	8.74114i		−	1.43704i	−0.695509	−	0.718518i	$-0.744821\pi$
$37$		−	8.74114i		−	1.43704i	0.695509	−	0.718518i	$-0.255179\pi$
$38$	−6.08604	+	0.979832i	−0.987287	+	0.158950i
$39$	1.57149	−	3.22403i	0.251639	−	0.516258i
$40$	5.05139	−	3.42378i	0.798695	−	0.541347i
$41$	1.80920	+	1.04454i	0.282550	+	0.163130i	0.634577	−	0.772860i	$-0.281174\pi$
$41$	1.80920	+	1.04454i	0.282550	+	0.163130i	−0.352027	+	0.935990i	$0.614508\pi$
$42$	3.85344	+	8.11885i	0.594598	+	1.25277i
$43$	−5.31807	+	9.21118i	−0.810999	+	1.40469i	0.101167	+	0.994869i	$0.467742\pi$
$43$	−5.31807	+	9.21118i	−0.810999	+	1.40469i	−0.912166	+	0.409822i	$0.865591\pi$
$44$	2.26735	−	7.30328i	0.341817	−	1.10101i
$45$	−3.98738	−	5.09847i	−0.594403	−	0.760036i
$46$	0.599956	+	1.53277i	0.0884586	+	0.225995i
$47$	−3.09399	−	5.35895i	−0.451305	−	0.781684i	0.547162	−	0.837027i	$-0.315708\pi$
$47$	−3.09399	−	5.35895i	−0.451305	−	0.781684i	−0.998467	+	0.0553431i	$0.982375\pi$
$48$	−6.92796	−	0.0581197i	−0.999965	−	0.00838886i
$49$	−6.46079			−0.922970
$50$	0.177915	+	0.454539i	0.0251610	+	0.0642815i
$51$	−6.84219	+	0.480133i	−0.958099	+	0.0672321i
$52$	−4.03932	+	0.914204i	−0.560153	+	0.126777i
$53$	3.84474	+	6.65929i	0.528116	+	0.914724i	0.999463	+	0.0327756i	$0.0104347\pi$
$53$	3.84474	+	6.65929i	0.528116	+	0.914724i	−0.471347	+	0.881948i	$0.656232\pi$
$54$	0.438160	+	7.33539i	0.0596261	+	0.998221i
$55$	−7.14418	−	4.12470i	−0.963321	−	0.556174i
$56$	4.52805	−	9.33719i	0.605087	−	1.24773i
$57$	4.67058	−	5.93175i	0.618633	−	0.785680i
$58$	3.55975	+	9.09447i	0.467418	+	1.19416i
$59$	−0.250420	−	0.144580i	−0.0326019	−	0.0188227i	0.483610	−	0.875283i	$-0.339325\pi$
$59$	−0.250420	−	0.144580i	−0.0326019	−	0.0188227i	−0.516212	+	0.856461i	$0.672658\pi$
$60$	−1.71089	+	7.27537i	−0.220875	+	0.939247i
$61$	−9.24783	+	5.33924i	−1.18406	+	0.683619i	−0.956951	−	0.290249i	$-0.906262\pi$
$61$	−9.24783	+	5.33924i	−1.18406	+	0.683619i	−0.227112	+	0.973869i	$0.572928\pi$
$62$	0.278139	−	1.83399i	0.0353237	−	0.232917i
$63$	−10.2072	−	4.11819i	−1.28599	−	0.518843i
$64$	4.95363	+	6.28184i	0.619204	+	0.785230i
$65$			4.46765i			0.554143i
$66$	4.01589	+	8.46113i	0.494322	+	1.04149i
$67$	2.31946	+	4.01743i	0.283368	+	0.490807i	0.972212	−	0.234102i	$-0.0752150\pi$
$67$	2.31946	+	4.01743i	0.283368	+	0.490807i	−0.688844	+	0.724909i	$0.741882\pi$
$68$	5.37645	+	5.81567i	0.651990	+	0.705253i
$69$	−1.81213	−	0.883285i	−0.218154	−	0.106335i
$70$	−8.74581	−	6.98761i	−1.04532	−	0.835179i
$71$	4.99046	−	8.64374i	0.592259	−	1.02582i	−0.401668	−	0.915785i	$-0.631570\pi$
$71$	4.99046	−	8.64374i	0.592259	−	1.02582i	0.993927	−	0.110038i	$-0.0350971\pi$
$72$	6.29021	−	5.69502i	0.741308	−	0.671165i
$73$	5.73429	−	9.93208i	0.671148	−	1.16246i	−0.306431	−	0.951893i	$-0.599135\pi$
$73$	5.73429	−	9.93208i	0.671148	−	1.16246i	0.977579	−	0.210569i	$-0.0675317\pi$
$74$	1.85358	−	12.2221i	0.215474	−	1.42079i
$75$	−0.537382	−	0.261936i	−0.0620515	−	0.0302458i
$76$	−8.71744	+	0.0794659i	−0.999958	+	0.00911536i
$77$	−14.0283			−1.59867
$78$	2.88096	−	4.17468i	0.326204	−	0.472689i
$79$	2.33161	+	1.34616i	0.262327	+	0.151454i	0.625396	−	0.780308i	$-0.284938\pi$
$79$	2.33161	+	1.34616i	0.262327	+	0.151454i	−0.363069	+	0.931762i	$0.618271\pi$
$80$	7.78900	−	3.71605i	0.870837	−	0.415467i
$81$	−6.48017	−	6.24559i	−0.720019	−	0.693955i
$82$	2.30817	+	1.84415i	0.254895	+	0.203652i
$83$			12.7910i			1.40400i	0.712179	+	0.701998i	$0.247709\pi$
$83$			12.7910i			1.40400i	−0.712179	+	0.701998i	$0.752291\pi$
$84$	3.66635	+	12.1691i	0.400032	+	1.32776i
$85$	7.39920	−	4.27193i	0.802556	−	0.463356i
$86$	−9.38912	+	11.7516i	−1.01245	+	1.26721i
$87$	−10.7520	−	5.24085i	−1.15273	−	0.561878i
$88$	4.71895	−	9.73083i	0.503042	−	1.03731i
$89$	2.48876	−	1.43689i	0.263808	−	0.152310i	−0.362262	−	0.932076i	$-0.617996\pi$
$89$	2.48876	−	1.43689i	0.263808	−	0.152310i	0.626070	+	0.779767i	$0.284662\pi$
$90$	−4.49411	−	7.97435i	−0.473721	−	0.840570i
$91$	3.79867	+	6.57949i	0.398209	+	0.689718i
$92$	0.513846	+	2.27038i	0.0535721	+	0.236703i
$93$	1.27086	+	1.88314i	0.131782	+	0.195272i
$94$	−3.18972	−	8.14911i	−0.328994	−	0.840517i
$95$	−1.99225	+	9.19092i	−0.204401	+	0.942969i
$96$	−9.67452	−	1.55035i	−0.987402	−	0.158232i
$97$	−8.13940	+	14.0979i	−0.826431	+	1.43142i	0.0743902	+	0.997229i	$0.476299\pi$
$97$	−8.13940	+	14.0979i	−0.826431	+	1.43142i	−0.900821	+	0.434191i	$0.857034\pi$
$98$	−9.03364	−	1.37003i	−0.912536	−	0.138394i
$99$	−10.6376	−	4.29180i	−1.06911	−	0.431343i
$100$	0.152380	+	0.673275i	0.0152380	+	0.0673275i
$101$	−7.82563	−	13.5544i	−0.778679	−	1.34871i	−0.932703	−	0.360645i	$-0.882557\pi$
$101$	−7.82563	−	13.5544i	−0.778679	−	1.34871i	0.154024	−	0.988067i	$-0.450777\pi$
$102$	−9.66874	−	0.779569i	−0.957348	−	0.0771889i
$103$			14.7988i			1.45817i	0.684424	+	0.729085i	$0.260054\pi$
$103$			14.7988i			1.45817i	−0.684424	+	0.729085i	$0.739946\pi$
$104$	−5.84174	+	0.421714i	−0.572830	+	0.0413525i
$105$	13.6767	−	0.959729i	1.33471	−	0.0936600i
$106$	3.96370	+	10.1265i	0.384988	+	0.983570i
$107$		−	11.4735i		−	1.10919i	−0.832121	−	0.554594i	$-0.812873\pi$
$107$		−	11.4735i		−	1.10919i	0.832121	−	0.554594i	$-0.187127\pi$
$108$	−0.942841	+	10.3494i	−0.0907250	+	0.995876i
$109$	−10.4677	−	6.04350i	−1.00262	−	0.578862i	−0.0935969	−	0.995610i	$-0.529837\pi$
$109$	−10.4677	−	6.04350i	−1.00262	−	0.578862i	−0.909022	+	0.416748i	$0.863170\pi$
$110$	−9.11452	−	7.28219i	−0.869036	−	0.694330i
$111$	8.46931	+	12.5496i	0.803871	+	1.19116i
$112$	8.31121	−	12.0953i	0.785336	−	1.14290i
$113$			7.10514i			0.668395i	0.942503	+	0.334197i	$0.108465\pi$
$113$			7.10514i			0.668395i	−0.942503	+	0.334197i	$0.891535\pi$
$114$	7.78836	−	7.30352i	0.729447	−	0.684037i
$115$	2.51113			0.234164
$116$	3.04883	+	13.4710i	0.283077	+	1.25075i
$117$	0.867582	+	6.15135i	0.0802080	+	0.568692i
$118$	−0.319485	−	0.255258i	−0.0294110	−	0.0234984i
$119$	7.26452	−	12.5825i	0.665937	−	1.15344i
$120$	−3.93497	+	9.80981i	−0.359212	+	0.895509i
$121$	−3.61969			−0.329063
$122$	−14.0627	+	5.50443i	−1.27318	+	0.498348i
$123$	−3.60953	+	0.253289i	−0.325460	+	0.0228383i
$124$	0.777803	−	2.50535i	0.0698487	−	0.224987i
$125$	11.5322			1.03147
$126$	−13.3987	−	7.92262i	−1.19365	−	0.705803i
$127$	−0.263796	+	0.152302i	−0.0234081	+	0.0135147i	−0.511658	−	0.859189i	$-0.670969\pi$
$127$	−0.263796	+	0.152302i	−0.0234081	+	0.0135147i	0.488250	+	0.872704i	$0.337635\pi$
$128$	5.59421	+	9.83386i	0.494463	+	0.869199i
$129$	−1.28957	−	18.3772i	−0.113540	−	1.61802i
$130$	−0.947375	+	6.24678i	−0.0830903	+	0.547879i
$131$	−6.75670	−	3.90098i	−0.590336	−	0.340830i	0.174895	−	0.984587i	$-0.444042\pi$
$131$	−6.75670	−	3.90098i	−0.590336	−	0.340830i	−0.765230	+	0.643757i	$0.777375\pi$
$132$	3.82092	+	12.6821i	0.332568	+	1.10384i
$133$	4.88071	+	15.2294i	0.423211	+	1.32055i
$134$	2.39123	+	6.10912i	0.206571	+	0.527748i
$135$	10.6646	+	3.45649i	0.917862	+	0.297488i
$136$	6.28426	+	9.27170i	0.538871	+	0.795042i
$137$	0.996806	−	0.575506i	0.0851629	−	0.0491688i	−0.456814	−	0.889562i	$-0.651009\pi$
$137$	0.996806	−	0.575506i	0.0851629	−	0.0491688i	0.541977	+	0.840394i	$0.317676\pi$
$138$	−2.34646	−	1.61930i	−0.199744	−	0.137844i
$139$	4.12458	+	7.14399i	0.349843	+	0.605945i	0.986221	−	0.165432i	$-0.0529017\pi$
$139$	4.12458	+	7.14399i	0.349843	+	0.605945i	−0.636379	+	0.771377i	$0.719568\pi$
$140$	−10.7469	−	11.6248i	−0.908277	−	0.982476i
$141$	9.63434	+	4.69607i	0.811358	+	0.395480i
$142$	8.81072	−	11.0277i	0.739379	−	0.925420i
$143$	3.95882	+	6.85687i	0.331053	+	0.573400i
$144$	10.0028	−	6.62907i	0.833564	−	0.552422i
$145$	14.8994			1.23733
$146$	10.1239	−	12.6713i	0.837864	−	1.04869i
$147$	9.27575	−	6.25987i	0.765051	−	0.516305i
$148$	5.18345	−	16.6962i	0.426077	−	1.37242i
$149$	10.2433	−	17.7419i	0.839161	−	1.45347i	−0.0514365	−	0.998676i	$-0.516380\pi$
$149$	10.2433	−	17.7419i	0.839161	−	1.45347i	0.890597	−	0.454793i	$-0.150287\pi$
$150$	−0.695836	−	0.480199i	−0.0568148	−	0.0392081i
$151$			3.41159i			0.277631i	0.990318	+	0.138816i	$0.0443296\pi$
$151$			3.41159i			0.277631i	−0.990318	+	0.138816i	$0.955670\pi$
$152$	−12.2058	−	1.73744i	−0.990020	−	0.140925i
$153$	9.35813	−	7.31874i	0.756560	−	0.591685i
$154$	−19.6147	−	2.97473i	−1.58060	−	0.239711i
$155$	−2.45077	−	1.41495i	−0.196851	−	0.113652i
$156$	4.91348	−	5.22623i	0.393393	−	0.418433i
$157$	6.21293	+	3.58703i	0.495846	+	0.286277i	0.726996	−	0.686641i	$-0.240916\pi$
$157$	6.21293	+	3.58703i	0.495846	+	0.286277i	−0.231151	+	0.972918i	$0.574249\pi$
$158$	2.97466	+	2.37665i	0.236651	+	0.189076i
$159$	−11.9721	−	5.83555i	−0.949448	−	0.462789i
$160$	11.6788	−	3.54420i	0.923288	−	0.280194i
$161$	3.69813	−	2.13511i	0.291453	−	0.168271i
$162$	−7.73634	−	10.1069i	−0.607824	−	0.794072i
$163$	14.0278			1.09874			0.549370	−	0.835579i	$-0.314868\pi$
$163$	14.0278			1.09874			0.549370	+	0.835579i	$0.314868\pi$
$164$	2.83629	+	3.06799i	0.221477	+	0.239570i
$165$	14.2533	−	1.00019i	1.10962	−	0.0778647i
$166$	−2.71237	+	17.8847i	−0.210520	+	1.38812i
$167$	4.19536	+	7.26657i	0.324646	+	0.562304i	0.981441	−	0.191766i	$-0.0614213\pi$
$167$	4.19536	+	7.26657i	0.324646	+	0.562304i	−0.656794	+	0.754070i	$0.728088\pi$
$168$	2.54589	+	17.7926i	0.196420	+	1.37273i
$169$	−4.35601	+	7.54483i	−0.335078	+	0.580372i
$170$	11.2516	−	4.40410i	0.862960	−	0.337779i
$171$	−0.958256	+	13.0415i	−0.0732797	+	0.997311i
$172$	−15.6201	+	14.4404i	−1.19102	+	1.10107i
$173$	−6.57164	+	11.3824i	−0.499633	+	0.865389i	−1.00000		0.000424180i	$-0.999865\pi$
$173$	−6.57164	+	11.3824i	−0.499633	+	0.865389i	0.500367	+	0.865813i	$0.333198\pi$
$174$	−13.9224	−	9.60787i	−1.05545	−	0.728371i
$175$	1.09667	−	0.633163i	0.0829005	−	0.0478626i
$176$	8.66160	−	12.6052i	0.652893	−	0.950155i
$177$	0.499612	−	0.0350590i	0.0375531	−	0.00263519i
$178$	3.78454	−	1.48134i	0.283663	−	0.111031i
$179$			2.99121i			0.223574i	0.993732	+	0.111787i	$0.0356574\pi$
$179$			2.99121i			0.223574i	−0.993732	+	0.111787i	$0.964343\pi$
$180$	−4.59280	−	12.1029i	−0.342327	−	0.902099i
$181$	−13.9848	+	8.07413i	−1.03948	+	0.600146i	−0.919687	−	0.392653i	$-0.871557\pi$
$181$	−13.9848	+	8.07413i	−1.03948	+	0.600146i	−0.119796	+	0.992799i	$0.538224\pi$
$182$	3.91620	+	10.0051i	0.290288	+	0.741629i
$183$	8.10390	−	16.6258i	0.599057	−	1.22901i
$184$	0.237033	+	3.28346i	0.0174743	+	0.242060i
$185$	−16.3325	−	9.42955i	−1.20079	−	0.693274i
$186$	1.37763	+	2.90254i	0.101013	+	0.212825i
$187$	7.57078	−	13.1130i	0.553630	−	0.958916i
$188$	−2.73191	−	12.0707i	−0.199245	−	0.880345i
$189$	18.6446	−	3.97733i	1.35620	−	0.289308i
$190$	−4.73457	+	12.4285i	−0.343482	+	0.901659i
$191$	9.57522			0.692839			0.346419	−	0.938080i	$-0.387397\pi$
$191$	9.57522			0.692839			0.346419	+	0.938080i	$0.387397\pi$
$192$	−13.1984	−	4.21925i	−0.952513	−	0.304498i
$193$	3.03673	−	5.25977i	0.218588	−	0.378606i	−0.735788	−	0.677212i	$-0.763188\pi$
$193$	3.03673	−	5.25977i	0.218588	−	0.378606i	0.954377	+	0.298605i	$0.0965215\pi$
$194$	−14.3702	+	17.9860i	−1.03172	+	1.29132i
$195$	−4.32871	−	6.41419i	−0.309985	−	0.459330i
$196$	−12.3405	−	3.83121i	−0.881468	−	0.273658i
$197$	−2.32538			−0.165676			−0.0828382	−	0.996563i	$-0.526398\pi$
$197$	−2.32538			−0.165676			−0.0828382	+	0.996563i	$0.526398\pi$
$198$	−13.9636	−	8.25663i	−0.992351	−	0.586773i
$199$	−18.2282	+	10.5241i	−1.29216	+	0.746031i	−0.979037	−	0.203680i	$-0.934710\pi$
$199$	−18.2282	+	10.5241i	−1.29216	+	0.746031i	−0.313126	+	0.949711i	$0.601376\pi$
$200$	0.0702914	+	0.973703i	0.00497035	+	0.0688512i
$201$	−7.22255	−	3.52049i	−0.509439	−	0.248316i
$202$	−8.06775	−	20.6115i	−0.567645	−	1.45022i
$203$	21.9423	−	12.6684i	1.54005	−	0.889147i
$204$	−13.3538	−	3.14029i	−0.934951	−	0.219865i
$205$	3.90337	−	2.25361i	0.272623	−	0.157399i
$206$	−3.13812	+	20.6921i	−0.218643	+	1.44168i
$207$	3.45748	−	0.487641i	0.240312	−	0.0338934i
$208$	−8.25750	−	0.649104i	−0.572554	−	0.0450073i
$209$	5.08647	+	15.8714i	0.351839	+	1.09785i
$210$	19.3267	+	1.55826i	1.33367	+	0.107530i
$211$	11.7997	−	20.4376i	0.812322	−	1.40698i	−0.0989128	−	0.995096i	$-0.531536\pi$
$211$	11.7997	−	20.4376i	0.812322	−	1.40698i	0.911235	−	0.411887i	$-0.135130\pi$
$212$	3.39480	+	14.9996i	0.233156	+	1.03018i
$213$	1.21013	+	17.2451i	0.0829166	+	1.18161i
$214$	2.43299	−	16.0426i	0.166316	−	1.09665i
$215$	11.4738	+	19.8732i	0.782507	+	1.35534i
$216$	−3.51293	+	14.2709i	−0.239025	+	0.971014i
$217$	−4.81232			−0.326681
$218$	−13.3546	−	10.6699i	−0.904487	−	0.722655i
$219$	1.39050	+	19.8154i	0.0939611	+	1.33900i
$220$	−11.2000	−	12.1149i	−0.755101	−	0.816787i
$221$	−8.20026			−0.551609
$222$	9.18082	+	19.3432i	0.616176	+	1.29823i
$223$	−22.6912	−	13.1008i	−1.51952	−	0.877293i	−0.999736	−	0.0229927i	$-0.992681\pi$
$223$	−22.6912	−	13.1008i	−1.51952	−	0.877293i	−0.519780	−	0.854300i	$-0.673986\pi$
$224$	14.1858	−	15.1495i	0.947828	−	1.01222i
$225$	1.02531	−	0.144609i	0.0683539	−	0.00964059i
$226$	−1.50666	+	9.93458i	−0.100222	+	0.660838i
$227$		−	10.4797i		−	0.695563i	−0.937576	−	0.347781i	$-0.886935\pi$
$227$		−	10.4797i		−	0.695563i	0.937576	−	0.347781i	$-0.113065\pi$
$228$	12.4386	−	8.56043i	0.823767	−	0.566928i
$229$			6.23491i			0.412015i	0.978550	+	0.206007i	$0.0660471\pi$
$229$			6.23491i			0.412015i	−0.978550	+	0.206007i	$0.933953\pi$
$230$	3.51112	+	0.532490i	0.231516	+	0.0351114i
$231$	20.1404	−	13.5920i	1.32514	−	0.894289i
$232$	1.40640	+	19.4820i	0.0923346	+	1.27905i
$233$	−5.68815	−	3.28405i	−0.372643	−	0.215146i	0.301969	−	0.953318i	$-0.402356\pi$
$233$	−5.68815	−	3.28405i	−0.372643	−	0.215146i	−0.674613	+	0.738172i	$0.735689\pi$
$234$	−0.0913328	+	8.78494i	−0.00597061	+	0.574290i
$235$	−13.3506			−0.870900
$236$	−0.392584	−	0.424655i	−0.0255551	−	0.0276427i
$237$	−4.65178	+	0.326427i	−0.302166	+	0.0212037i
$238$	12.8256	−	16.0527i	0.831359	−	1.04054i
$239$	−26.5569			−1.71782			−0.858910	−	0.512126i	$-0.828858\pi$
$239$	−26.5569			−1.71782			−0.858910	+	0.512126i	$0.828858\pi$
$240$	−7.58216	+	12.8819i	−0.489427	+	0.831523i
$241$	−0.822295	−	1.42426i	−0.0529687	−	0.0917445i	0.838325	−	0.545170i	$-0.183535\pi$
$241$	−0.822295	−	1.42426i	−0.0529687	−	0.0917445i	−0.891294	+	0.453426i	$0.850202\pi$
$242$	−5.06115	−	0.767565i	−0.325343	−	0.0493409i
$243$	15.3549	+	2.68814i	0.985019	+	0.172444i
$244$	−20.8301	+	4.71439i	−1.33351	+	0.301808i
$245$	−6.96961	+	12.0717i	−0.445272	+	0.771234i
$246$	−5.10064	−	0.411253i	−0.325205	−	0.0262206i
$247$	6.06660	−	6.68340i	0.386009	−	0.425255i
$248$	1.61881	−	3.33810i	0.102794	−	0.211970i
$249$	−12.3932	−	18.3640i	−0.785389	−	1.16377i
$250$	16.1246	+	2.44543i	1.01981	+	0.154663i
$251$	11.6818	−	6.74449i	0.737349	−	0.425709i	−0.0837557	−	0.996486i	$-0.526692\pi$
$251$	11.6818	−	6.74449i	0.737349	−	0.425709i	0.821105	+	0.570778i	$0.193358\pi$
$252$	−17.0544	−	13.9188i	−1.07433	−	0.876805i
$253$	3.85404	−	2.22513i	0.242301	−	0.139893i
$254$	−0.401142	+	0.157015i	−0.0251699	+	0.00985198i
$255$	−6.48394	+	13.3023i	−0.406040	+	0.833022i
$256$	5.73667	+	14.9362i	0.358542	+	0.933514i
$257$	9.76432	−	5.63743i	0.609082	−	0.351653i	−0.163524	−	0.986539i	$-0.552286\pi$
$257$	9.76432	−	5.63743i	0.609082	−	0.351653i	0.772606	+	0.634886i	$0.218953\pi$
$258$	2.09381	−	25.9689i	0.130355	−	1.61675i
$259$	−32.0703			−1.99275
$260$	−2.64929	+	8.53351i	−0.164302	+	0.529226i
$261$	20.5145	−	2.89335i	1.26981	−	0.179094i
$262$	−8.62017	−	6.88723i	−0.532556	−	0.425494i
$263$	3.18409	−	5.51500i	0.196339	−	0.340070i	−0.750999	−	0.660303i	$-0.770428\pi$
$263$	3.18409	−	5.51500i	0.196339	−	0.340070i	0.947339	+	0.320233i	$0.103761\pi$
$264$	2.65323	+	18.5427i	0.163295	+	1.14123i
$265$	16.5901			1.01912
$266$	3.59490	+	22.3291i	0.220418	+	1.36908i
$267$	−2.18091	+	4.47430i	−0.133469	+	0.273823i
$268$	2.04802	+	9.04899i	0.125103	+	0.552755i
$269$	5.56240	−	9.63436i	0.339145	−	0.587417i	−0.645127	−	0.764076i	$-0.723195\pi$
$269$	5.56240	−	9.63436i	0.339145	−	0.587417i	0.984272	+	0.176658i	$0.0565288\pi$
$270$	14.1785	+	7.09441i	0.862879	+	0.431752i
$271$	9.42512	+	5.44160i	0.572535	+	0.330553i	0.758161	−	0.652067i	$-0.226098\pi$
$271$	9.42512	+	5.44160i	0.572535	+	0.330553i	−0.185626	+	0.982620i	$0.559431\pi$
$272$	6.82073	+	14.2965i	0.413567	+	0.866854i
$273$	−11.8286	−	5.76562i	−0.715901	−	0.348951i
$274$	1.51580	−	0.593312i	0.0915726	−	0.0358433i
$275$	1.14290	−	0.659856i	0.0689198	−	0.0397908i
$276$	−2.93750	−	2.76171i	−0.176817	−	0.166236i
$277$		−	15.7567i		−	0.946731i	−0.880866	−	0.473365i	$-0.843039\pi$
$277$		−	15.7567i		−	0.946731i	0.880866	−	0.473365i	$-0.156961\pi$
$278$	4.25220	+	10.8635i	0.255030	+	0.651551i
$279$	−3.64915	−	1.47228i	−0.218469	−	0.0881430i
$280$	−12.5615	−	18.5330i	−0.750692	−	1.10756i
$281$	−19.2977	+	11.1415i	−1.15120	+	0.664648i	−0.949180	−	0.314732i	$-0.898085\pi$
$281$	−19.2977	+	11.1415i	−1.15120	+	0.664648i	−0.202024	+	0.979381i	$0.564752\pi$
$282$	12.4752	+	8.60914i	0.742885	+	0.512667i
$283$	−10.9335	+	18.9375i	−0.649932	+	1.12572i	0.333207	+	0.942854i	$0.391869\pi$
$283$	−10.9335	+	18.9375i	−0.649932	+	1.12572i	−0.983139	+	0.182861i	$0.941464\pi$
$284$	14.6578	−	13.5508i	0.869781	−	0.804092i
$285$	−6.04483	−	15.1257i	−0.358065	−	0.895968i
$286$	4.08130	+	10.4269i	0.241332	+	0.616557i
$287$	3.83232	−	6.63777i	0.226215	−	0.391815i
$288$	15.3918	−	7.14782i	0.906973	−	0.421189i
$289$	−0.658974	−	1.14138i	−0.0387632	−	0.0671398i
$290$	20.8327	+	3.15946i	1.22334	+	0.185530i
$291$	−1.97371	−	28.1265i	−0.115701	−	1.64881i
$292$	16.8425	−	15.5705i	0.985635	−	0.911197i
$293$	−20.0779			−1.17297			−0.586483	−	0.809961i	$-0.699488\pi$
$293$	−20.0779			−1.17297			−0.586483	+	0.809961i	$0.699488\pi$
$294$	14.2970	−	6.78576i	0.833818	−	0.395754i
$295$	−0.540284	+	0.311933i	−0.0314565	+	0.0181614i
$296$	10.7881	−	22.2458i	0.627045	−	1.29301i
$297$	19.4307	−	4.14501i	1.12748	−	0.240518i
$298$	18.0846	−	22.6350i	1.04761	−	1.31121i
$299$	−2.08724	−	1.20507i	−0.120708	−	0.0696910i
$300$	−0.871109	−	0.818980i	−0.0502935	−	0.0472838i
$301$	33.7948	+	19.5115i	1.94790	+	1.12462i
$302$	−0.723436	+	4.77017i	−0.0416291	+	0.274493i
$303$	24.3681	+	11.8778i	1.39991	+	0.682359i
$304$	−16.6980	−	5.01760i	−0.957697	−	0.287779i
$305$			23.0389i			1.31920i
$306$	14.6367	−	8.24883i	0.836726	−	0.471554i
$307$	4.36650	−	7.56301i	0.249210	−	0.431644i	−0.714097	−	0.700047i	$-0.753163\pi$
$307$	4.36650	−	7.56301i	0.249210	−	0.431644i	0.963307	+	0.268403i	$0.0864959\pi$
$308$	−26.7950	−	8.31869i	−1.52678	−	0.474001i
$309$	−14.3386	−	21.2466i	−0.815693	−	1.20868i
$310$	−3.12668	−	2.49811i	−0.177584	−	0.141883i
$311$	−10.0096			−0.567591			−0.283796	−	0.958885i	$-0.591594\pi$
$311$	−10.0096			−0.567591			−0.283796	+	0.958885i	$0.591594\pi$
$312$	7.97838	−	6.26553i	0.451687	−	0.354716i
$313$	5.97192	+	10.3437i	0.337553	+	0.584659i	0.983972	−	0.178324i	$-0.0570675\pi$
$313$	5.97192	+	10.3437i	0.337553	+	0.584659i	−0.646419	+	0.762983i	$0.723734\pi$
$314$	7.92643	+	6.33295i	0.447314	+	0.357389i
$315$	−18.7058	+	14.6293i	−1.05395	+	0.824266i
$316$	3.65527	+	3.95388i	0.205625	+	0.222423i
$317$	16.2744	+	28.1880i	0.914059	+	1.58320i	0.808273	+	0.588807i	$0.200402\pi$
$317$	16.2744	+	28.1880i	0.914059	+	1.58320i	0.105785	+	0.994389i	$0.466264\pi$
$318$	−15.5022	−	10.6981i	−0.869322	−	0.599921i
$319$	22.8674	−	13.2025i	1.28033	−	0.739197i
$320$	17.0811	−	2.47908i	0.954863	−	0.138585i
$321$	11.1167	+	16.4725i	0.620475	+	0.919407i
$322$	5.62357	−	2.20117i	0.313389	−	0.122667i
$323$	−16.8697	−	3.65673i	−0.938656	−	0.203466i
$324$	−8.67396	−	15.7722i	−0.481887	−	0.876234i
$325$	−0.618966	−	0.357360i	−0.0343341	−	0.0198228i
$326$	19.6140	+	2.97462i	1.08632	+	0.164749i
$327$	20.8839	−	1.46548i	1.15488	−	0.0810411i
$328$	3.31520	+	4.89119i	0.183051	+	0.270071i
$329$	−19.6614	+	11.3515i	−1.08397	+	0.625830i
$330$	20.1414	+	1.62396i	1.10875	+	0.0893960i
$331$	7.87195			0.432682			0.216341	−	0.976318i	$-0.430588\pi$
$331$	7.87195			0.432682			0.216341	+	0.976318i	$0.430588\pi$
$332$	−7.58500	+	24.4317i	−0.416281	+	1.34086i
$333$	−24.3187	−	9.81158i	−1.33266	−	0.537671i
$334$	4.32516	+	11.0499i	0.236662	+	0.604626i
$335$	10.0085			0.546825
$336$	−0.213235	+	25.4180i	−0.0116329	+	1.38666i
$337$	1.89375	−	3.28007i	0.103159	−	0.178677i	−0.809825	−	0.586671i	$-0.800438\pi$
$337$	1.89375	−	3.28007i	0.103159	−	0.178677i	0.912985	+	0.407994i	$0.133772\pi$
$338$	−7.69059	+	9.62568i	−0.418313	+	0.523568i
$339$	−6.88418	−	10.2008i	−0.373897	−	0.554033i
$340$	16.6662	−	3.77199i	0.903852	−	0.204565i
$341$	−5.01520			−0.271588
$342$	−4.10535	+	18.0318i	−0.221992	+	0.975049i
$343$		−	1.97830i		−	0.106818i
$344$	−24.9025	+	16.8786i	−1.34265	+	0.910035i
$345$	−3.60522	+	2.43303i	−0.194099	+	0.130990i
$346$	−11.6023	+	14.5216i	−0.623744	+	0.780689i
$347$	25.7677	+	14.8770i	1.38328	+	0.798640i	0.992547	−	0.121863i	$-0.0388867\pi$
$347$	25.7677	+	14.8770i	1.38328	+	0.798640i	0.390737	+	0.920502i	$0.372220\pi$
$348$	−17.4292	−	16.3862i	−0.934306	−	0.878395i
$349$		−	24.6630i		−	1.32018i	−0.751185	−	0.660091i	$-0.770518\pi$
$349$		−	24.6630i		−	1.32018i	0.751185	−	0.660091i	$-0.229482\pi$
$350$	1.66766	−	0.652753i	0.0891400	−	0.0348911i
$351$	−7.20564	−	7.99088i	−0.384608	−	0.426522i
$352$	14.7838	−	15.7882i	0.787981	−	0.841516i
$353$			10.3443i			0.550571i	0.961363	+	0.275285i	$0.0887724\pi$
$353$			10.3443i			0.550571i	−0.961363	+	0.275285i	$0.911228\pi$
$354$	0.706004	+	0.0569235i	0.0375237	+	0.00302545i
$355$	−10.7670	−	18.6489i	−0.571452	−	0.989783i
$356$	5.60577	−	1.26873i	0.297105	−	0.0672426i
$357$	1.76156	+	25.1033i	0.0932316	+	1.32861i
$358$	−0.634293	+	4.18239i	−0.0335234	+	0.221046i
$359$	−11.6893	+	20.2465i	−0.616940	+	1.06857i	0.373101	+	0.927791i	$0.378294\pi$
$359$	−11.6893	+	20.2465i	−0.616940	+	1.06857i	−0.990041	+	0.140780i	$0.955039\pi$
$360$	−3.85531	−	17.8965i	−0.203193	−	0.943230i
$361$	15.4606	−	11.0439i	0.813718	−	0.581260i
$362$	−21.2661	+	8.32395i	−1.11772	+	0.437497i
$363$	5.19679	−	3.50713i	0.272761	−	0.184076i
$364$	3.35412	+	14.8199i	0.175803	+	0.776771i
$365$	−12.3718	−	21.4286i	−0.647569	−	1.12162i
$366$	14.8566	−	21.5281i	0.776568	−	1.12529i
$367$	16.3571	−	9.44380i	0.853836	−	0.492962i	−0.00810748	−	0.999967i	$-0.502581\pi$
$367$	16.3571	−	9.44380i	0.853836	−	0.492962i	0.861943	+	0.507005i	$0.169247\pi$
$368$	−0.364841	+	4.64128i	−0.0190187	+	0.241944i
$369$	4.93678	−	3.86092i	0.256998	−	0.200992i
$370$	−20.8369	−	16.6480i	−1.08326	−	0.865487i
$371$	24.4322	−	14.1060i	1.26846	−	0.732345i
$372$	1.31074	+	4.35054i	0.0679589	+	0.225565i
$373$			3.34044i			0.172961i	0.996254	+	0.0864807i	$0.0275621\pi$
$373$			3.34044i			0.172961i	−0.996254	+	0.0864807i	$0.972438\pi$
$374$	13.3663	−	16.7295i	0.691155	−	0.865061i
$375$	−16.5568	+	11.1736i	−0.854989	+	0.577001i
$376$	−1.26021	−	17.4568i	−0.0649901	−	0.900268i
$377$	−12.3844	−	7.15011i	−0.637826	−	0.368249i
$378$	26.9128	−	1.60756i	1.38424	−	0.0826842i
$379$	−6.56097			−0.337014			−0.168507	−	0.985700i	$-0.553895\pi$
$379$	−6.56097			−0.337014			−0.168507	+	0.985700i	$0.553895\pi$
$380$	−9.25550	+	16.3739i	−0.474797	+	0.839963i
$381$	0.231165	−	0.474252i	0.0118429	−	0.0242967i
$382$	13.3883	+	2.03045i	0.685006	+	0.103887i
$383$	2.26391	−	3.92121i	0.115681	−	0.200365i	−0.802371	−	0.596825i	$-0.796428\pi$
$383$	2.26391	−	3.92121i	0.115681	−	0.200365i	0.918052	+	0.396461i	$0.129762\pi$
$384$	−17.5596	−	8.69822i	−0.896087	−	0.443879i
$385$	−15.1331	+	26.2113i	−0.771253	+	1.33585i
$386$	5.36137	−	6.71039i	0.272887	−	0.341550i
$387$	19.6571	+	25.1346i	0.999226	+	1.27766i
$388$	−23.9067	+	22.1012i	−1.21368	+	1.12202i
$389$	−11.6768	−	20.2248i	−0.592036	−	1.02544i	−0.993958	−	0.109762i	$-0.964991\pi$
$389$	−11.6768	−	20.2248i	−0.592036	−	1.02544i	0.401922	−	0.915674i	$-0.368342\pi$
$390$	−4.69237	−	9.88640i	−0.237607	−	0.500617i
$391$			4.60911i			0.233093i
$392$	−16.4424	−	7.97374i	−0.830469	−	0.402735i
$393$	13.4802	−	0.945942i	0.679989	−	0.0477165i
$394$	−3.25141	−	0.493103i	−0.163803	−	0.0248421i
$395$	5.03047	−	2.90435i	0.253111	−	0.146134i
$396$	−17.7734	−	14.5056i	−0.893149	−	0.728936i
$397$	−14.4976	−	8.37022i	−0.727616	−	0.420089i	0.0899335	−	0.995948i	$-0.471335\pi$
$397$	−14.4976	−	8.37022i	−0.727616	−	0.420089i	−0.817549	+	0.575859i	$0.804668\pi$
$398$	−27.7188	+	10.8497i	−1.38942	+	0.543845i
$399$	−21.7630	−	17.1359i	−1.08951	−	0.857866i
$400$	−0.108193	+	1.37636i	−0.00540964	+	0.0688181i
$401$	−22.1136	−	12.7673i	−1.10430	−	0.637570i	−0.166955	−	0.985965i	$-0.553393\pi$
$401$	−22.1136	−	12.7673i	−1.10430	−	0.637570i	−0.937348	+	0.348395i	$0.886727\pi$
$402$	−9.35222	−	6.45399i	−0.466446	−	0.321896i
$403$	1.35805	+	2.35221i	0.0676492	+	0.117172i
$404$	−6.90981	−	30.5304i	−0.343776	−	1.51894i
$405$	−18.6601	+	5.37046i	−0.927230	+	0.266860i
$406$	33.3667	−	13.0604i	1.65596	−	0.648175i
$407$	−33.4224			−1.65669
$408$	−18.0057	−	7.22254i	−0.891414	−	0.357569i
$409$	−10.1002	−	17.4941i	−0.499424	−	0.865029i	0.500575	−	0.865693i	$-0.333122\pi$
$409$	−10.1002	−	17.4941i	−0.499424	−	0.865029i	−1.00000		0.000664432i	$0.999789\pi$
$410$	5.93567	−	2.32334i	0.293142	−	0.114741i
$411$	−0.873504	+	1.79206i	−0.0430868	+	0.0883958i
$412$	−8.77560	+	28.2667i	−0.432343	+	1.39260i
$413$	−0.530449	+	0.918765i	−0.0261017	+	0.0452095i
$414$	4.93775	+	0.0513353i	0.242677	+	0.00252299i
$415$	23.8995	+	13.7984i	1.17318	+	0.677335i
$416$	−11.4082	−	2.65862i	−0.559333	−	0.130349i
$417$	−12.8435	−	6.26030i	−0.628948	−	0.306568i
$418$	3.74646	+	23.2704i	0.183245	+	1.13819i
$419$		−	20.2872i		−	0.991093i	−0.868581	−	0.495547i	$-0.834968\pi$
$419$		−	20.2872i		−	0.991093i	0.868581	−	0.495547i	$-0.165032\pi$
$420$	26.6926	+	6.27707i	1.30246	+	0.306290i
$421$	−28.6568	−	16.5450i	−1.39665	−	0.806353i	−0.402606	−	0.915374i	$-0.631895\pi$
$421$	−28.6568	−	16.5450i	−1.39665	−	0.806353i	−0.994040	+	0.109020i	$0.965229\pi$
$422$	20.8324	−	26.0742i	1.01411	−	1.26927i
$423$	−18.3820	+	2.59259i	−0.893765	+	0.126056i
$424$	1.56599	+	21.6927i	0.0760512	+	1.05349i
$425$			1.36682i			0.0663006i
$426$	−1.96483	+	24.3691i	−0.0951961	+	1.18069i
$427$	19.5891	+	33.9293i	0.947983	+	1.64195i
$428$	6.80374	−	21.9152i	0.328871	−	1.05931i
$429$	−12.3273	−	6.00869i	−0.595167	−	0.290103i
$430$	11.8288	+	30.2203i	0.570435	+	1.45735i
$431$	15.0587	+	26.0823i	0.725350	+	1.25634i	0.958830	+	0.283981i	$0.0916552\pi$
$431$	15.0587	+	26.0823i	0.725350	+	1.25634i	−0.233480	+	0.972362i	$0.575011\pi$
$432$	−7.93805	+	19.2090i	−0.381920	+	0.924196i
$433$	8.35752	+	14.4757i	0.401637	+	0.695655i	0.993924	−	0.110072i	$-0.0351081\pi$
$433$	8.35752	+	14.4757i	0.401637	+	0.695655i	−0.592287	+	0.805727i	$0.701775\pi$
$434$	−6.72870	−	1.02046i	−0.322988	−	0.0489838i
$435$	−21.3911	+	14.4361i	−1.02562	+	0.692156i
$436$	−16.4102	−	17.7507i	−0.785904	−	0.850107i
$437$	−3.75653	−	3.40985i	−0.179699	−	0.163115i
$438$	−2.25768	+	28.0013i	−0.107876	+	1.33795i
$439$	−6.06557	−	3.50196i	−0.289494	−	0.167139i	0.348220	−	0.937413i	$-0.386786\pi$
$439$	−6.06557	−	3.50196i	−0.289494	−	0.167139i	−0.637714	+	0.770274i	$0.720120\pi$
$440$	−13.0911	−	19.3143i	−0.624092	−	0.920775i
$441$	−7.25198	+	17.9746i	−0.345332	+	0.855932i
$442$	−11.4658	−	1.73888i	−0.545373	−	0.0827103i
$443$	−2.63682	+	1.52237i	−0.125279	+	0.0723299i	−0.561330	−	0.827592i	$-0.689710\pi$
$443$	−2.63682	+	1.52237i	−0.125279	+	0.0723299i	0.436051	+	0.899922i	$0.356377\pi$
$444$	8.73508	+	28.9929i	0.414549	+	1.37594i
$445$		−	6.20019i		−	0.293917i
$446$	−28.9494	−	23.1296i	−1.37079	−	1.09522i
$447$	2.48387	+	35.3967i	0.117483	+	1.67420i
$448$	23.0474	−	18.1744i	1.08889	−	0.858657i
$449$			23.6457i			1.11591i	0.829871	+	0.557955i	$0.188414\pi$
$449$			23.6457i			1.11591i	−0.829871	+	0.557955i	$0.811586\pi$
$450$	1.46428	+	0.0152234i	0.0690267	+	0.000717637i
$451$	3.99388	−	6.91761i	0.188065	−	0.325738i
$452$	−4.21330	+	13.5713i	−0.198177	+	0.638340i
$453$	−3.30550	−	4.89802i	−0.155306	−	0.230129i
$454$	2.22225	−	14.6530i	0.104295	−	0.687699i
$455$	16.3913			0.768437
$456$	19.2072	−	9.33176i	0.899462	−	0.437000i
$457$	−27.6827			−1.29494			−0.647471	−	0.762090i	$-0.724173\pi$
$457$	−27.6827			−1.29494			−0.647471	+	0.762090i	$0.724173\pi$
$458$	−1.32213	+	8.71781i	−0.0617790	+	0.407357i
$459$	−6.34431	+	19.5746i	−0.296127	+	0.913664i
$460$	4.79642	+	1.48908i	0.223634	+	0.0694289i
$461$	5.78701	−	10.0234i	0.269528	−	0.466836i	−0.699212	−	0.714914i	$-0.746466\pi$
$461$	5.78701	−	10.0234i	0.269528	−	0.466836i	0.968740	+	0.248078i	$0.0797989\pi$
$462$	31.0430	−	14.7339i	1.44425	−	0.685483i
$463$		−	6.91939i		−	0.321571i	−0.986989	−	0.160786i	$-0.948597\pi$
$463$		−	6.91939i		−	0.321571i	0.986989	−	0.160786i	$-0.0514028\pi$
$464$	−2.16474	+	27.5384i	−0.100495	+	1.27844i
$465$	4.88951	−	0.343109i	0.226746	−	0.0159113i
$466$	−7.25692	−	5.79803i	−0.336170	−	0.268589i
$467$			13.6977i			0.633854i	0.948450	+	0.316927i	$0.102651\pi$
$467$			13.6977i			0.633854i	−0.948450	+	0.316927i	$0.897349\pi$
$468$	−1.99057	+	12.2640i	−0.0920142	+	0.566902i
$469$	14.7395	−	8.50987i	0.680608	−	0.392949i
$470$	−18.6672	−	2.83103i	−0.861054	−	0.130586i
$471$	−12.3954	+	0.869813i	−0.571149	+	0.0400789i
$472$	−0.458872	−	0.677012i	−0.0211213	−	0.0311620i
$473$	35.2196	+	20.3340i	1.61940	+	0.934960i
$474$	−6.57346	−	0.530004i	−0.301929	−	0.0243439i
$475$	−1.11399	−	1.01118i	−0.0511134	−	0.0463963i
$476$	21.3371	−	19.7256i	0.977983	−	0.904123i
$477$	22.8424	−	3.22167i	1.04588	−	0.147510i
$478$	−37.1325	−	5.63145i	−1.69840	−	0.257576i
$479$	−8.26883	−	14.3220i	−0.377813	−	0.654391i	0.612931	−	0.790136i	$-0.289990\pi$
$479$	−8.26883	−	14.3220i	−0.377813	−	0.654391i	−0.990744	+	0.135746i	$0.956657\pi$
$480$	−13.3332	+	16.4040i	−0.608575	+	0.748736i
$481$	9.05033	+	15.6756i	0.412659	+	0.714747i
$482$	−0.847737	−	2.16580i	−0.0386133	−	0.0986496i
$483$	−3.24068	+	6.64850i	−0.147456	+	0.302517i
$484$	−6.91386	−	2.14646i	−0.314266	−	0.0975662i
$485$	17.5608	+	30.4163i	0.797396	+	1.38113i
$486$	20.8996	+	7.01468i	0.948026	+	0.318192i
$487$			38.5354i			1.74620i	0.487537	+	0.873102i	$0.337895\pi$
$487$			38.5354i			1.74620i	−0.487537	+	0.873102i	$0.662105\pi$
$488$	−30.1249	+	2.17471i	−1.36369	+	0.0984445i
$489$	−20.1397	+	13.5915i	−0.910746	+	0.614630i
$490$	−12.3049	+	15.4011i	−0.555880	+	0.695749i
$491$	20.6674	+	11.9323i	0.932708	+	0.538499i	0.887667	−	0.460486i	$-0.152325\pi$
$491$	20.6674	+	11.9323i	0.932708	+	0.538499i	0.0450410	+	0.998985i	$0.485658\pi$
$492$	−7.04464	−	1.65663i	−0.317597	−	0.0746866i
$493$			27.3475i			1.23167i
$494$	9.89971	−	8.05846i	0.445409	−	0.362567i
$495$	−19.4944	+	15.2460i	−0.876207	+	0.685258i
$496$	2.97131	−	4.32415i	0.133416	−	0.194160i
$497$	−31.7130	−	18.3095i	−1.42252	−	0.821293i
$498$	−13.4344	−	28.3051i	−0.602009	−	1.26838i
$499$	19.5218	−	33.8128i	0.873917	−	1.51367i	0.0160052	−	0.999872i	$-0.494905\pi$
$499$	19.5218	−	33.8128i	0.873917	−	1.51367i	0.857912	−	0.513797i	$-0.171761\pi$
$500$	22.0273	+	6.83854i	0.985091	+	0.305829i
$501$	−13.0639	−	6.36772i	−0.583650	−	0.284489i
$502$	17.7640	−	6.95316i	0.792845	−	0.310335i
$503$	−4.50052	−	7.79513i	−0.200668	−	0.347568i	0.748076	−	0.663613i	$-0.230978\pi$
$503$	−4.50052	−	7.79513i	−0.200668	−	0.347568i	−0.948744	+	0.316046i	$0.897645\pi$
$504$	−20.8944	−	23.0781i	−0.930712	−	1.02798i
$505$	−33.7678			−1.50265
$506$	5.86065	−	2.29397i	0.260538	−	0.101980i
$507$	−1.05628	−	15.0527i	−0.0469111	−	0.668512i
$508$	−0.594182	+	0.134479i	−0.0263626	+	0.00596653i
$509$	−15.0299	−	26.0326i	−0.666189	−	1.15387i	−0.978961	−	0.204046i	$-0.934591\pi$
$509$	−15.0299	−	26.0326i	−0.666189	−	1.15387i	0.312772	−	0.949828i	$-0.398742\pi$
$510$	−11.8868	+	17.2247i	−0.526356	+	0.762722i
$511$	−36.4398	−	21.0385i	−1.61200	−	0.930689i
$512$	4.85390	+	22.1007i	0.214514	+	0.976721i
$513$	−11.2602	−	19.6522i	−0.497150	−	0.867665i
$514$	14.8481	−	5.81185i	0.654924	−	0.256350i
$515$	27.6509	+	15.9643i	1.21845	+	0.703470i
$516$	8.43438	−	35.8663i	0.371303	−	1.57893i
$517$	−20.4903	+	11.8301i	−0.901164	+	0.520287i
$518$	−44.8416	−	6.80059i	−1.97022	−	0.298801i
$519$	−1.59355	−	22.7090i	−0.0699489	−	0.996814i
$520$	−5.51385	+	11.3700i	−0.241798	+	0.498607i
$521$		−	1.48162i		−	0.0649111i	−0.999473	−	0.0324556i	$-0.989667\pi$
$521$		−	1.48162i		−	0.0649111i	0.999473	−	0.0324556i	$-0.0103327\pi$
$522$	29.2974	+	0.304591i	1.28231	+	0.0133316i
$523$	10.2283	+	17.7160i	0.447254	+	0.774666i	0.998206	−	0.0598706i	$-0.0190688\pi$
$523$	10.2283	+	17.7160i	0.447254	+	0.774666i	−0.550953	+	0.834537i	$0.685735\pi$
$524$	−10.5925	−	11.4578i	−0.462735	−	0.500537i
$525$	−0.961016	+	1.97160i	−0.0419422	+	0.0860476i
$526$	5.62154	−	7.03602i	0.245111	−	0.306785i
$527$	2.59711	−	4.49833i	0.113132	−	0.195950i
$528$	−0.222225	+	26.4895i	−0.00967109	+	1.15281i
$529$	10.8227	−	18.7454i	0.470551	−	0.815018i
$530$	23.1967	+	3.51798i	1.00760	+	0.152811i
$531$	−0.683323	+	0.534409i	−0.0296537	+	0.0231914i
$532$	0.291552	+	31.9834i	0.0126404	+	1.38665i
$533$	−4.32596			−0.187378
$534$	−3.99819	+	5.79361i	−0.173018	+	0.250714i
$535$	−21.4378	−	12.3771i	−0.926838	−	0.535110i
$536$	0.944735	+	13.0868i	0.0408063	+	0.565264i
$537$	−2.89819	−	4.29448i	−0.125066	−	0.185320i
$538$	9.82048	−	12.2915i	0.423391	−	0.529923i
$539$			24.7033i			1.06405i
$540$	18.3204	+	12.9262i	0.788385	+	0.556254i
$541$	−2.00336	+	1.15664i	−0.0861310	+	0.0497278i	−0.542447	−	0.840090i	$-0.682502\pi$
$541$	−2.00336	+	1.15664i	−0.0861310	+	0.0497278i	0.456316	+	0.889818i	$0.349169\pi$
$542$	12.0245	+	9.60719i	0.516498	+	0.412664i
$543$	12.2549	−	25.1419i	0.525909	−	1.07894i
$544$	6.50530	+	21.4361i	0.278912	+	0.919066i
$545$	−22.5841	+	13.0389i	−0.967395	+	0.558526i
$546$	−15.3165	−	10.5699i	−0.655484	−	0.452351i
$547$	−15.3088	−	26.5156i	−0.654556	−	1.13372i	−0.982005	−	0.188855i	$-0.939522\pi$
$547$	−15.3088	−	26.5156i	−0.654556	−	1.13372i	0.327450	−	0.944869i	$-0.393811\pi$
$548$	2.24524	−	0.508156i	0.0959119	−	0.0217073i
$549$	4.47398	+	31.7215i	0.190945	+	1.35384i
$550$	1.73796	−	0.680272i	0.0741070	−	0.0290069i
$551$	−22.2889	−	20.2319i	−0.949538	−	0.861906i
$552$	−3.52166	−	4.48440i	−0.149892	−	0.190869i
$553$	4.93891	−	8.55444i	0.210024	−	0.363772i
$554$	3.34125	−	22.0315i	0.141956	−	0.936027i
$555$	32.5848	−	2.28655i	1.38315	−	0.0970588i
$556$	3.64189	+	16.0914i	0.154451	+	0.682425i
$557$	12.2916	+	21.2896i	0.520810	+	0.902069i	0.999707	+	0.0241983i	$0.00770331\pi$
$557$	12.2916	+	21.2896i	0.520810	+	0.902069i	−0.478897	+	0.877871i	$0.658963\pi$
$558$	−4.79014	−	2.83239i	−0.202783	−	0.119905i
$559$		−	22.0247i		−	0.931547i
$560$	−13.6338	−	28.5770i	−0.576134	−	1.20760i
$561$	1.83582	+	26.1616i	0.0775086	+	1.10454i
$562$	−29.3451	+	11.4862i	−1.23785	+	0.484518i
$563$		−	36.4287i		−	1.53529i	−0.640877	−	0.767644i	$-0.721429\pi$
$563$		−	36.4287i		−	1.53529i	0.640877	−	0.767644i	$-0.278571\pi$
$564$	15.6175	+	14.6829i	0.657615	+	0.618262i
$565$	13.2756	+	7.66470i	0.558511	+	0.322456i
$566$	−19.3033	+	24.1604i	−0.811378	+	1.01554i
$567$	−22.9144	+	23.7751i	−0.962315	+	0.998458i
$568$	23.3684	−	15.8389i	0.980516	−	0.664584i
$569$		−	18.5763i		−	0.778758i	−0.921078	−	0.389379i	$-0.872690\pi$
$569$		−	18.5763i		−	0.778758i	0.921078	−	0.389379i	$-0.127310\pi$
$570$	−5.24459	−	22.4309i	−0.219672	−	0.939529i
$571$	−33.1840			−1.38871			−0.694353	−	0.719634i	$-0.744309\pi$
$571$	−33.1840			−1.38871			−0.694353	+	0.719634i	$0.744309\pi$
$572$	3.49552	+	15.4446i	0.146155	+	0.645773i
$573$	−13.7471	+	9.27745i	−0.574295	+	0.387571i
$574$	6.76600	−	8.46845i	0.282407	−	0.353466i
$575$	−0.200861	+	0.347902i	−0.00837649	+	0.0145085i
$576$	23.0370	−	6.73038i	0.959874	−	0.280433i
$577$	−36.6594			−1.52615			−0.763076	−	0.646309i	$-0.776312\pi$
$577$	−36.6594			−1.52615			−0.763076	+	0.646309i	$0.776312\pi$
$578$	−0.679362	−	1.73564i	−0.0282578	−	0.0721930i
$579$	0.736370	+	10.4937i	0.0306025	+	0.436104i
$580$	28.4589	+	8.83526i	1.18169	+	0.366864i
$581$	46.9289			1.94694
$582$	3.20461	−	39.7458i	0.132835	−	1.64752i
$583$	25.4623	−	14.7006i	1.05454	−	0.608838i
$584$	26.8514	−	18.1996i	1.11112	−	0.753106i
$585$	12.4294	+	5.01475i	0.513894	+	0.207335i
$586$	−28.0735	−	4.25758i	−1.15971	−	0.175879i
$587$	4.77404	+	2.75629i	0.197046	+	0.113764i	0.595277	−	0.803521i	$-0.297042\pi$
$587$	4.77404	+	2.75629i	0.197046	+	0.113764i	−0.398231	+	0.917285i	$0.630376\pi$
$588$	21.4294	−	6.45631i	0.883732	−	0.266254i
$589$	1.74488	+	5.44460i	0.0718967	+	0.224341i
$590$	−0.821585	+	0.321584i	−0.0338241	+	0.0132394i
$591$	3.33854	−	2.25306i	0.137329	−	0.0926787i
$592$	19.8015	−	28.8171i	0.813835	−	1.18437i
$593$	28.7331	−	16.5891i	1.17993	−	0.681232i	0.223930	−	0.974605i	$-0.428111\pi$
$593$	28.7331	−	16.5891i	1.17993	−	0.681232i	0.955998	+	0.293373i	$0.0947778\pi$
$594$	28.0474	−	1.67534i	1.15080	−	0.0687399i
$595$	−15.6733	−	27.1469i	−0.642541	−	1.11291i
$596$	30.0861	−	27.8139i	1.23238	−	1.13930i
$597$	15.9734	−	32.7707i	0.653749	−	1.34122i
$598$	−2.66290	−	2.12756i	−0.108894	−	0.0870025i
$599$	6.59062	+	11.4153i	0.269285	+	0.466416i	0.968677	−	0.248322i	$-0.0798792\pi$
$599$	6.59062	+	11.4153i	0.269285	+	0.466416i	−0.699392	+	0.714738i	$0.746546\pi$
$600$	−1.04434	−	1.32984i	−0.0426350	−	0.0542904i
$601$	−7.67982			−0.313266			−0.156633	−	0.987657i	$-0.550064\pi$
$601$	−7.67982			−0.313266			−0.156633	+	0.987657i	$0.550064\pi$
$602$	43.1153	+	34.4477i	1.75725	+	1.40398i
$603$	13.7804	−	1.94358i	0.561181	−	0.0791487i
$604$	−2.02305	+	6.51637i	−0.0823169	+	0.265147i
$605$	−3.90476	+	6.76325i	−0.158751	+	0.274965i
$606$	31.5534	+	21.7751i	1.28177	+	0.884553i
$607$			16.8530i			0.684041i	0.939692	+	0.342021i	$0.111111\pi$
$607$			16.8530i			0.684041i	−0.939692	+	0.342021i	$0.888889\pi$
$608$	−22.2836	−	10.5566i	−0.903719	−	0.428126i
$609$	−19.2281	+	39.4479i	−0.779162	+	1.59851i
$610$	−4.88546	+	32.2136i	−0.197806	+	1.30429i
$611$	11.0970	+	6.40686i	0.448937	+	0.259194i
$612$	22.2146	−	8.42997i	0.897973	−	0.340761i
$613$	−17.4163	−	10.0553i	−0.703437	−	0.406130i	0.105189	−	0.994452i	$-0.466455\pi$
$613$	−17.4163	−	10.0553i	−0.703437	−	0.406130i	−0.808626	+	0.588323i	$0.799789\pi$
$614$	7.70911	−	9.64886i	0.311114	−	0.389396i
$615$	−3.42053	+	7.01749i	−0.137929	+	0.282972i
$616$	−35.7014	−	17.3133i	−1.43845	−	0.697574i
$617$	7.33082	−	4.23245i	0.295128	−	0.170392i	−0.345124	−	0.938557i	$-0.612163\pi$
$617$	7.33082	−	4.23245i	0.295128	−	0.170392i	0.640252	+	0.768165i	$0.278830\pi$
$618$	−15.5432	−	32.7481i	−0.625238	−	1.31732i
$619$	31.4150			1.26267			0.631337	−	0.775508i	$-0.282506\pi$
$619$	31.4150			1.26267			0.631337	+	0.775508i	$0.282506\pi$
$620$	−3.84208	−	4.15595i	−0.154302	−	0.166907i
$621$	−4.49143	+	4.05007i	−0.180235	+	0.162524i
$622$	−13.9956	−	2.12256i	−0.561174	−	0.0851067i
$623$	−5.27179	−	9.13100i	−0.211210	−	0.365826i
$624$	12.4842	−	7.06878i	0.499768	−	0.282978i
$625$	11.5776	−	20.0529i	0.463102	−	0.802117i
$626$	6.15669	+	15.7291i	0.246071	+	0.628663i
$627$	−22.6805	−	17.8583i	−0.905771	−	0.713191i
$628$	9.74002	+	10.5357i	0.388669	+	0.420420i
$629$	17.3077	−	29.9778i	0.690104	−	1.19529i
$630$	−29.2570	+	16.4884i	−1.16563	+	0.656914i
$631$	37.3805	−	21.5817i	1.48810	−	0.859152i	0.488188	−	0.872739i	$-0.337658\pi$
$631$	37.3805	−	21.5817i	1.48810	−	0.859152i	0.999908	+	0.0135861i	$0.00432472\pi$
$632$	4.27246	+	6.30353i	0.169950	+	0.250741i
$633$	2.86128	+	40.7750i	0.113726	+	1.62066i
$634$	16.7779	+	42.8642i	0.666335	+	1.70235i
$635$			0.657188i			0.0260797i
$636$	−19.4070	−	18.2457i	−0.769539	−	0.723488i
$637$	11.5862	−	6.68932i	0.459064	−	0.265040i
$638$	34.7734	−	13.6110i	1.37669	−	0.538863i
$639$	−18.4461	−	23.5862i	−0.729718	−	0.933056i
$640$	24.4089	+	0.155774i	0.964848	+	0.00615752i
$641$	−19.9228	−	11.5024i	−0.786904	−	0.454319i	0.0519675	−	0.998649i	$-0.483451\pi$
$641$	−19.9228	−	11.5024i	−0.786904	−	0.454319i	−0.838871	+	0.544330i	$0.816784\pi$
$642$	12.0506	+	25.3896i	0.475601	+	1.00205i
$643$	13.9687	−	24.1946i	0.550874	−	0.954141i	−0.447338	−	0.894365i	$-0.647628\pi$
$643$	13.9687	−	24.1946i	0.550874	−	0.954141i	0.998212	−	0.0597762i	$-0.0190387\pi$
$644$	8.32978	−	1.88525i	0.328239	−	0.0742891i
$645$	−35.7281	−	17.4149i	−1.40679	−	0.685713i
$646$	−22.8122	−	8.69020i	−0.897536	−	0.341911i
$647$	23.9772			0.942641			0.471321	−	0.881962i	$-0.343777\pi$
$647$	23.9772			0.942641			0.471321	+	0.881962i	$0.343777\pi$
$648$	−8.78361	−	23.8924i	−0.345053	−	0.938583i
$649$	−0.552812	+	0.957499i	−0.0216998	+	0.0375851i
$650$	−0.789675	−	0.630924i	−0.0309736	−	0.0247469i
$651$	6.90904	−	4.66266i	0.270787	−	0.182744i
$652$	26.7940	+	8.31839i	1.04933	+	0.325773i
$653$	1.35039			0.0528449			0.0264224	−	0.999651i	$-0.491588\pi$
$653$	1.35039			0.0528449			0.0264224	+	0.999651i	$0.491588\pi$
$654$	29.5112	+	2.37942i	1.15398	+	0.0930428i
$655$	−14.5776	+	8.41641i	−0.569596	+	0.328856i
$656$	3.59820	+	7.54198i	0.140486	+	0.294465i
$657$	−21.1955	−	27.1017i	−0.826917	−	1.05734i
$658$	−29.8982	+	11.7027i	−1.16555	+	0.456221i
$659$	−34.2317	+	19.7637i	−1.33348	+	0.769884i	−0.985831	−	0.167741i	$-0.946353\pi$
$659$	−34.2317	+	19.7637i	−1.33348	+	0.769884i	−0.347648	+	0.937625i	$0.613019\pi$
$660$	27.8179	+	6.54170i	1.08281	+	0.254635i
$661$	15.4440	−	8.91660i	0.600702	−	0.346816i	−0.168615	−	0.985682i	$-0.553930\pi$
$661$	15.4440	−	8.91660i	0.600702	−	0.346816i	0.769318	+	0.638866i	$0.220596\pi$
$662$	11.0068	+	1.66927i	0.427790	+	0.0648779i
$663$	11.7731	−	7.94524i	0.457229	−	0.308568i
$664$	−15.7863	+	32.5526i	−0.612629	+	1.26329i
$665$	33.7205	+	7.30936i	1.30763	+	0.283445i
$666$	−31.9225	−	18.8756i	−1.23697	−	0.731417i
$667$	−4.01886	+	6.96086i	−0.155611	+	0.269526i
$668$	3.70438	+	16.3675i	0.143327	+	0.633276i
$669$	45.2711	−	3.17678i	1.75028	−	0.122822i
$670$	13.9942	+	2.12233i	0.540642	+	0.0819929i
$671$	20.4149	+	35.3597i	0.788110	+	1.36505i
$672$	−5.68809	+	35.4948i	−0.219423	+	1.36924i
$673$	6.81327			0.262632			0.131316	−	0.991341i	$-0.458080\pi$
$673$	6.81327			0.262632			0.131316	+	0.991341i	$0.458080\pi$
$674$	3.34344	−	4.18471i	0.128784	−	0.161189i
$675$	−1.33192	+	1.20104i	−0.0512657	+	0.0462279i
$676$	−12.7943	+	11.8281i	−0.492089	+	0.454925i
$677$	−9.78930			−0.376233			−0.188117	−	0.982147i	$-0.560238\pi$
$677$	−9.78930			−0.376233			−0.188117	+	0.982147i	$0.560238\pi$
$678$	−7.46252	−	15.7229i	−0.286596	−	0.603833i
$679$	51.7235	+	29.8626i	1.98497	+	1.14602i
$680$	24.1030	−	1.73999i	0.924307	−	0.0667255i
$681$	10.1538	+	15.0457i	0.389095	+	0.576553i
$682$	−7.01238	−	1.06349i	−0.268518	−	0.0407229i
$683$		−	44.1301i		−	1.68859i	−0.535878	−	0.844295i	$-0.680019\pi$
$683$		−	44.1301i		−	1.68859i	0.535878	−	0.844295i	$-0.319981\pi$
$684$	−9.56389	+	24.3420i	−0.365684	+	0.930739i
$685$		−	2.48332i		−	0.0948828i
$686$	0.419503	−	2.76611i	0.0160167	−	0.105611i
$687$	−6.04102	−	8.95145i	−0.230479	−	0.341519i
$688$	−38.3984	+	18.3195i	−1.46393	+	0.698425i
$689$	−13.7897	−	7.96147i	−0.525345	−	0.303308i
$690$	−5.55684	+	2.63743i	−0.211545	+	0.100405i
$691$	−12.9044			−0.490906			−0.245453	−	0.969409i	$-0.578937\pi$
$691$	−12.9044			−0.490906			−0.245453	+	0.969409i	$0.578937\pi$
$692$	−19.3020	+	17.8442i	−0.733751	+	0.678336i
$693$	−15.7462	+	39.0281i	−0.598148	+	1.48255i
$694$	32.8744	+	26.2655i	1.24789	+	0.997025i
$695$	17.7977			0.675104
$696$	−20.8953	−	26.6076i	−0.792033	−	1.00856i
$697$	4.13645	+	7.16454i	0.156679	+	0.271376i
$698$	5.22986	−	34.4845i	0.197953	−	1.30526i
$699$	11.3484	−	0.796344i	0.429236	−	0.0301205i
$700$	2.47018	−	0.559065i	0.0933639	−	0.0211307i
$701$	−3.83813	+	6.64783i	−0.144964	+	0.251085i	−0.929360	−	0.369176i	$-0.879640\pi$
$701$	−3.83813	+	6.64783i	−0.144964	+	0.251085i	0.784395	+	0.620261i	$0.212973\pi$
$702$	−8.38062	−	12.7010i	−0.316306	−	0.479369i
$703$	11.6283	+	36.2840i	0.438569	+	1.36848i
$704$	24.0191	−	18.9406i	0.905253	−	0.713849i
$705$	19.1675	−	12.9355i	0.721889	−	0.487177i
$706$	−2.19353	+	14.4636i	−0.0825547	+	0.544347i
$707$	−49.7296	+	28.7114i	−1.87028	+	1.07980i
$708$	0.975082	+	0.229302i	0.0366458	+	0.00861769i
$709$	1.71210	−	0.988479i	0.0642991	−	0.0371231i	−0.467506	−	0.883990i	$-0.654847\pi$
$709$	1.71210	−	0.988479i	0.0642991	−	0.0371231i	0.531805	+	0.846867i	$0.321514\pi$
$710$	−11.1001	−	28.3586i	−0.416579	−	1.06428i
$711$	6.36228	−	4.97577i	0.238604	−	0.186606i
$712$	8.10716	−	0.585254i	0.303829	−	0.0219333i
$713$	1.32210	−	0.763317i	0.0495132	−	0.0285864i
$714$	−2.86016	+	35.4736i	−0.107039	+	1.32757i
$715$	17.0824			0.638844
$716$	−1.77377	+	5.71341i	−0.0662889	+	0.213520i
$717$	38.1277	−	25.7310i	1.42390	−	0.960941i
$718$	−20.6377	+	25.8305i	−0.770191	+	0.963984i
$719$	16.5506	−	28.6665i	0.617234	−	1.06908i	−0.372754	−	0.927930i	$-0.621586\pi$
$719$	16.5506	−	28.6665i	0.617234	−	1.06908i	0.989988	−	0.141151i	$-0.0450803\pi$
$720$	−1.59560	−	25.8409i	−0.0594644	−	0.963034i
$721$	54.2952			2.02206
$722$	23.9594	−	12.1634i	0.891675	−	0.452677i
$723$	2.56053	+	1.24808i	0.0952272	+	0.0464166i
$724$	−31.4998	+	7.12923i	−1.17068	+	0.264956i
$725$	−1.19178	+	2.06423i	−0.0442617	+	0.0766635i
$726$	8.00998	−	3.80176i	0.297278	−	0.141097i
$727$	−8.79853	−	5.07983i	−0.326319	−	0.188401i	0.327886	−	0.944717i	$-0.393664\pi$
$727$	−8.79853	−	5.07983i	−0.326319	−	0.188401i	−0.654206	+	0.756317i	$0.726997\pi$
$728$	1.54723	+	21.4327i	0.0573440	+	0.794350i
$729$	−24.6496	+	11.0181i	−0.912948	+	0.408076i
$730$	−12.7546	−	32.5854i	−0.472068	−	1.20604i
$731$	−36.4768	+	21.0599i	−1.34914	+	0.778928i
$732$	25.3380	−	26.9508i	0.936519	−	0.996129i
$733$			5.79678i			0.214109i	0.994253	+	0.107054i	$0.0341419\pi$
$733$			5.79678i			0.214109i	−0.994253	+	0.107054i	$0.965858\pi$
$734$	24.8735	−	9.73599i	0.918099	−	0.359362i
$735$	−1.69005	−	24.0842i	−0.0623384	−	0.888360i
$736$	−1.49433	+	6.41220i	−0.0550816	+	0.236357i
$737$	15.3609	−	8.86864i	0.565827	−	0.326680i
$738$	7.72145	−	4.35158i	0.284230	−	0.160184i
$739$	−7.22865	+	12.5204i	−0.265910	+	0.460570i	−0.967802	−	0.251714i	$-0.919006\pi$
$739$	−7.22865	+	12.5204i	−0.265910	+	0.460570i	0.701892	+	0.712284i	$0.252339\pi$
$740$	−25.6044	−	27.6961i	−0.941238	−	1.01813i
$741$	−2.23425	+	15.4733i	−0.0820773	+	0.568425i
$742$	37.1530	−	14.5424i	1.36393	−	0.533868i
$743$	−9.96482	+	17.2596i	−0.365574	+	0.633192i	−0.988868	−	0.148795i	$-0.952460\pi$
$743$	−9.96482	+	17.2596i	−0.365574	+	0.633192i	0.623294	+	0.781987i	$0.285794\pi$
$744$	0.910173	+	6.36098i	0.0333686	+	0.233205i
$745$	−22.0999	−	38.2782i	−0.809679	−	1.40241i
$746$	−0.708349	+	4.67069i	−0.0259345	+	0.171006i
$747$	35.5859	+	14.3574i	1.30202	+	0.525310i
$748$	22.2366	−	20.5572i	0.813051	−	0.751647i
$749$	−42.0952			−1.53813
$750$	−25.5195	+	12.1123i	−0.931840	+	0.442278i
$751$	3.22798	−	1.86367i	0.117791	−	0.0680064i	−0.439947	−	0.898024i	$-0.645003\pi$
$751$	3.22798	−	1.86367i	0.117791	−	0.0680064i	0.557738	+	0.830017i	$0.311669\pi$
$752$	1.93971	−	24.6758i	0.0707341	−	0.899835i
$753$	−10.2368	+	21.0016i	−0.373050	+	0.765340i
$754$	−15.7999	−	12.6236i	−0.575399	−	0.459724i
$755$	6.37442	+	3.68027i	0.231989	+	0.133939i
$756$	37.9710	+	3.45919i	1.38099	+	0.125809i
$757$	35.6354	+	20.5741i	1.29519	+	0.747779i	0.979569	−	0.201106i	$-0.0644537\pi$
$757$	35.6354	+	20.5741i	1.29519	+	0.747779i	0.315622	+	0.948885i	$0.397787\pi$
$758$	−9.17371	−	1.39127i	−0.333204	−	0.0505332i
$759$	−3.37730	+	6.92879i	−0.122588	+	0.251499i
$760$	−16.4134	+	20.9317i	−0.595376	+	0.759274i
$761$		−	6.62679i		−	0.240221i	−0.992761	−	0.120110i	$-0.961675\pi$
$761$		−	6.62679i		−	0.240221i	0.992761	−	0.120110i	$-0.0383249\pi$
$762$	0.423787	−	0.614093i	0.0153522	−	0.0222462i
$763$	−22.1730	+	38.4047i	−0.802715	+	1.39034i
$764$	18.2893	+	5.67805i	0.661684	+	0.205425i
$765$	−3.57963	−	25.3804i	−0.129422	−	0.917630i
$766$	3.99696	−	5.00267i	0.144416	−	0.180754i
$767$	0.598777			0.0216206
$768$	−22.7079	−	15.8856i	−0.819399	−	0.573223i
$769$	3.50222	+	6.06602i	0.126293	+	0.218746i	0.922238	−	0.386623i	$-0.126359\pi$
$769$	3.50222	+	6.06602i	0.126293	+	0.218746i	−0.795944	+	0.605370i	$0.793025\pi$
$770$	−26.7176	+	33.4402i	−0.962836	+	1.20510i
$771$	−8.55650	+	17.5543i	−0.308155	+	0.632203i
$772$	8.91936	−	8.24575i	0.321015	−	0.296771i
$773$	−17.5574	−	30.4103i	−0.631495	−	1.09378i	−0.987246	−	0.159201i	$-0.949108\pi$
$773$	−17.5574	−	30.4103i	−0.631495	−	1.09378i	0.355751	−	0.934581i	$-0.384225\pi$
$774$	22.1552	+	39.3122i	0.796352	+	1.41305i
$775$	0.392067	−	0.226360i	0.0140835	−	0.00813108i
$776$	−38.1136	+	25.8330i	−1.36820	+	0.927351i
$777$	46.0433	−	31.0730i	1.65180	−	1.11474i
$778$	−12.0380	−	30.7549i	−0.431585	−	1.10262i
$779$	−8.89944	−	1.92907i	−0.318855	−	0.0691161i
$780$	−4.46455	−	14.8184i	−0.159857	−	0.530585i
$781$	−33.0499	−	19.0814i	−1.18262	−	0.682786i
$782$	−0.977373	+	6.44458i	−0.0349508	+	0.230458i
$783$	−26.6492	+	24.0305i	−0.952366	+	0.858780i
$784$	−21.2994	−	14.6357i	−0.760693	−	0.522705i
$785$	13.4044	−	7.73906i	0.478425	−	0.276219i
$786$	19.0490	+	1.53588i	0.679456	+	0.0547830i
$787$	−1.50478			−0.0536397			−0.0268199	−	0.999640i	$-0.508538\pi$
$787$	−1.50478			−0.0536397			−0.0268199	+	0.999640i	$0.508538\pi$
$788$	−4.44163	−	1.37894i	−0.158227	−	0.0491226i
$789$	0.772104	+	11.0029i	0.0274876	+	0.391715i
$790$	7.64961	−	2.99421i	0.272161	−	0.106529i
$791$	26.0680			0.926871
$792$	−21.7753	−	24.0511i	−0.773752	−	0.854617i
$793$	11.0562	−	19.1499i	0.392617	−	0.680032i
$794$	−18.4960	−	14.7777i	−0.656400	−	0.524441i
$795$	−23.8184	+	16.0742i	−0.844753	+	0.570093i
$796$	−41.0578	+	9.29245i	−1.45526	+	0.329362i
$797$	31.3167			1.10929			0.554647	−	0.832086i	$-0.312853\pi$
$797$	31.3167			1.10929			0.554647	+	0.832086i	$0.312853\pi$
$798$	−26.7959	−	28.5747i	−0.948563	−	1.01153i
$799$		−	24.5048i		−	0.866917i
$800$	−0.443139	+	1.90152i	−0.0156673	+	0.0672289i
$801$	−1.20403	−	8.53683i	−0.0425423	−	0.301634i
$802$	−28.2125	−	22.5408i	−0.996219	−	0.795945i
$803$	−37.9760	−	21.9255i	−1.34014	−	0.773733i
$804$	−11.7079	−	11.0073i	−0.412907	−	0.388197i
$805$		−	9.21306i		−	0.324718i
$806$	1.40007	+	3.57689i	0.0493152	+	0.125991i
$807$	1.34882	+	19.2215i	0.0474806	+	0.676627i
$808$	−3.18744	−	44.1536i	−0.112134	−	1.55332i
$809$		−	51.0216i		−	1.79382i	−0.442209	−	0.896912i	$-0.645805\pi$
$809$		−	51.0216i		−	1.79382i	0.442209	−	0.896912i	$-0.354195\pi$
$810$	−27.2299	+	3.55218i	−0.956761	+	0.124811i
$811$	1.29675	+	2.24603i	0.0455349	+	0.0788688i	0.887895	−	0.460047i	$-0.152167\pi$
$811$	1.29675	+	2.24603i	0.0455349	+	0.0788688i	−0.842360	+	0.538916i	$0.818834\pi$
$812$	49.4236	−	11.1858i	1.73443	−	0.392546i
$813$	−18.8040	+	1.31952i	−0.659485	+	0.0462777i
$814$	−46.7320	−	7.08730i	−1.63796	−	0.248410i
$815$	15.1325	−	26.2103i	0.530069	−	0.918107i
$816$	−23.6444	−	13.9169i	−0.827721	−	0.487188i
$817$	9.82146	−	45.3097i	0.343609	−	1.58518i
$818$	−10.4127	−	26.6025i	−0.364073	−	0.930135i
$819$	22.5686	−	3.18307i	0.788612	−	0.111225i
$820$	8.79208	−	1.98988i	0.307033	−	0.0694895i
$821$	4.40977	+	7.63795i	0.153902	+	0.266566i	0.932659	−	0.360760i	$-0.117483\pi$
$821$	4.40977	+	7.63795i	0.153902	+	0.266566i	−0.778757	+	0.627326i	$0.784149\pi$
$822$	−1.60137	+	2.32048i	−0.0558541	+	0.0809359i
$823$	−20.9044	+	12.0692i	−0.728683	+	0.420705i	−0.817940	−	0.575303i	$-0.804884\pi$
$823$	−20.9044	+	12.0692i	−0.728683	+	0.420705i	0.0892572	+	0.996009i	$0.471551\pi$
$824$	−18.2643	+	37.6623i	−0.636267	+	1.31203i
$825$	−1.00153	+	2.05472i	−0.0348688	+	0.0715361i
$826$	−0.936514	+	1.17216i	−0.0325855	+	0.0407846i
$827$	−7.55632	+	4.36264i	−0.262759	+	0.151704i	−0.625592	−	0.780150i	$-0.715143\pi$
$827$	−7.55632	+	4.36264i	−0.262759	+	0.151704i	0.362834	+	0.931854i	$0.381809\pi$
$828$	6.89319	+	1.11884i	0.239555	+	0.0388823i
$829$			0.905028i			0.0314329i	0.999876	+	0.0157165i	$0.00500291\pi$
$829$			0.905028i			0.0314329i	−0.999876	+	0.0157165i	$0.994997\pi$
$830$	30.4909	+	24.3612i	1.05835	+	0.845589i
$831$	15.2667	+	22.6219i	0.529597	+	0.784746i
$832$	−15.3875	−	6.13648i	−0.533464	−	0.212744i
$833$	−22.1573	−	12.7926i	−0.767707	−	0.443236i
$834$	−16.6306	−	11.4768i	−0.575869	−	0.397409i
$835$	18.1030			0.626482
$836$	0.303843	+	33.3317i	0.0105086	+	1.15280i
$837$	6.66557	−	1.42192i	0.230396	−	0.0491488i
$838$	4.30194	−	28.3660i	0.148608	−	0.979889i
$839$	−19.2720	+	33.3800i	−0.665342	+	1.15241i	0.313851	+	0.949472i	$0.398381\pi$
$839$	−19.2720	+	33.3800i	−0.665342	+	1.15241i	−0.979193	+	0.202934i	$0.934952\pi$
$840$	35.9912	+	14.4370i	1.24181	+	0.498123i
$841$	−9.34531	+	16.1865i	−0.322252	+	0.558157i
$842$	−36.5602	−	29.2104i	−1.25995	−	1.00666i
$843$	16.9106	−	34.6935i	0.582433	−	1.19491i
$844$	34.6575	−	32.0401i	1.19296	−	1.10287i
$845$	9.39814	+	16.2781i	0.323306	+	0.559982i
$846$	−26.2520	−	0.272929i	−0.902562	−	0.00938349i
$847$			13.2803i			0.456316i
$848$	−2.41038	+	30.6633i	−0.0827728	+	1.05298i
$849$	−2.65126	−	37.7820i	−0.0909909	−	1.29668i
$850$	−0.289838	+	1.91112i	−0.00994135	+	0.0655510i
$851$	8.81079	−	5.08691i	0.302030	−	0.174377i
$852$	−7.91480	+	33.6568i	−0.271156	+	1.15306i
$853$	19.6528	+	11.3465i	0.672899	+	0.388498i	0.797174	−	0.603749i	$-0.206327\pi$
$853$	19.6528	+	11.3465i	0.672899	+	0.388498i	−0.124275	+	0.992248i	$0.539661\pi$
$854$	20.1952	+	51.5947i	0.691065	+	1.76554i
$855$	23.3338	+	15.8591i	0.798001	+	0.542369i
$856$	14.1603	−	29.1997i	0.483990	−	0.998024i
$857$	35.9084	+	20.7317i	1.22661	+	0.708181i	0.966318	−	0.257350i	$-0.0828492\pi$
$857$	35.9084	+	20.7317i	1.22661	+	0.708181i	0.260288	+	0.965531i	$0.416183\pi$
$858$	−15.9622	−	11.0155i	−0.544940	−	0.376064i
$859$	−0.0883436	−	0.153016i	−0.00301425	−	0.00522083i	0.864514	−	0.502608i	$-0.167626\pi$
$859$	−0.0883436	−	0.153016i	−0.00301425	−	0.00522083i	−0.867529	+	0.497387i	$0.834293\pi$
$860$	10.1310	+	44.7631i	0.345466	+	1.52641i
$861$	0.929292	+	13.2430i	0.0316702	+	0.451319i
$862$	15.5246	+	39.6622i	0.528769	+	1.35090i
$863$	18.7559			0.638458			0.319229	−	0.947678i	$-0.396576\pi$
$863$	18.7559			0.638458			0.319229	+	0.947678i	$0.396576\pi$
$864$	−15.1725	+	25.1753i	−0.516179	+	0.856481i
$865$	14.1784	+	24.5577i	0.482079	+	0.834986i
$866$	8.61610	+	22.0125i	0.292787	+	0.748014i
$867$	2.05197	+	1.00019i	0.0696885	+	0.0339683i
$868$	−9.19185	−	2.85368i	−0.311992	−	0.0968601i
$869$	5.14713	−	8.91508i	0.174604	−	0.302423i
$870$	−32.9707	+	15.6488i	−1.11781	+	0.530545i
$871$	−8.31906	−	4.80301i	−0.281881	−	0.162744i
$872$	−19.1810	−	28.2994i	−0.649551	−	0.958337i
$873$	30.0855	+	38.4689i	1.01824	+	1.30197i
$874$	−4.52941	−	5.56432i	−0.153210	−	0.188216i
$875$		−	42.3105i		−	1.43036i
$876$	−9.09449	+	38.6734i	−0.307274	+	1.30665i
$877$	16.6266	+	9.59936i	0.561440	+	0.324147i	0.753723	−	0.657192i	$-0.228256\pi$
$877$	16.6266	+	9.59936i	0.561440	+	0.324147i	−0.192284	+	0.981339i	$0.561589\pi$
$878$	−7.73844	−	6.18275i	−0.261160	−	0.208658i
$879$	28.8259	−	19.4536i	0.972273	−	0.656152i
$880$	−14.2086	−	29.7818i	−0.478972	−	1.00394i
$881$		−	49.0878i		−	1.65381i	−0.562341	−	0.826905i	$-0.690099\pi$
$881$		−	49.0878i		−	1.65381i	0.562341	−	0.826905i	$-0.309901\pi$
$882$	−13.9515	+	23.5947i	−0.469770	+	0.794475i
$883$	7.13570	+	12.3594i	0.240135	+	0.415927i	0.960753	−	0.277406i	$-0.0894749\pi$
$883$	7.13570	+	12.3594i	0.240135	+	0.415927i	−0.720617	+	0.693333i	$0.756142\pi$
$884$	−15.6630	−	4.86271i	−0.526805	−	0.163550i
$885$	0.473452	−	0.971324i	0.0159149	−	0.0326507i
$886$	−4.00969	+	1.56947i	−0.134708	+	0.0527274i
$887$	−14.1794	−	24.5595i	−0.476099	−	0.824628i	0.523526	−	0.852010i	$-0.324616\pi$
$887$	−14.1794	−	24.5595i	−0.476099	−	0.824628i	−0.999625	+	0.0273820i	$0.991283\pi$
$888$	6.06559	+	42.3909i	0.203548	+	1.42255i
$889$	0.558782	+	0.967839i	0.0187409	+	0.0324603i
$890$	1.31477	−	8.66927i	0.0440710	−	0.290594i
$891$	−23.8805	+	24.7774i	−0.800026	+	0.830073i
$892$	−35.5731	−	38.4791i	−1.19107	−	1.28838i
$893$	19.9720	+	18.1288i	0.668336	+	0.606657i
$894$	−4.03294	+	50.0192i	−0.134882	+	1.67289i
$895$	5.58895	+	3.22678i	0.186818	+	0.107859i
$896$	36.0794	−	20.5246i	1.20533	−	0.685678i
$897$	4.16424	−	0.292215i	0.139040	−	0.00975678i
$898$	−5.01413	+	33.0620i	−0.167324	+	1.10329i
$899$	7.84452	−	4.52903i	0.261629	−	0.151052i
$900$	2.04416	+	0.331789i	0.0681387	+	0.0110596i
$901$			30.4508i			1.01446i
$902$	7.05124	−	8.82546i	0.234781	−	0.293856i
$903$	−67.4239	+	4.73130i	−2.24373	+	0.157448i
$904$	−8.76897	+	18.0823i	−0.291652	+	0.601408i
$905$			34.8400i			1.15812i
$906$	−3.58319	−	7.54947i	−0.119044	−	0.250814i
$907$	−14.9504	+	25.8948i	−0.496419	+	0.859823i	−0.999991	−	0.00412985i	$-0.998685\pi$
$907$	−14.9504	+	25.8948i	−0.496419	+	0.859823i	0.503572	+	0.863953i	$0.332019\pi$
$908$	6.21441	−	20.0170i	0.206232	−	0.664286i
$909$	−46.4936	+	6.55743i	−1.54210	+	0.217496i
$910$	22.9188	+	3.47582i	0.759750	+	0.115222i
$911$	−13.1690			−0.436309			−0.218155	−	0.975914i	$-0.570004\pi$
$911$	−13.1690			−0.436309			−0.218155	+	0.975914i	$0.570004\pi$
$912$	28.8349	−	8.97497i	0.954818	−	0.297191i
$913$	48.9074			1.61860
$914$	−38.7066	−	5.87018i	−1.28030	−	0.194168i
$915$	−22.3224	−	33.0769i	−0.737957	−	1.09349i
$916$	−3.69727	+	11.9091i	−0.122161	+	0.393488i
$917$	−14.3123	+	24.7896i	−0.472634	+	0.818625i
$918$	−13.0216	+	26.0244i	−0.429777	+	0.858933i
$919$			42.2052i			1.39222i	0.717935	+	0.696110i	$0.245088\pi$
$919$			42.2052i			1.39222i	−0.717935	+	0.696110i	$0.754912\pi$
$920$	6.39071	+	3.09917i	0.210696	+	0.102176i
$921$	1.05883	+	15.0889i	0.0348895	+	0.497196i
$922$	10.2170	−	12.7878i	0.336480	−	0.421145i
$923$			20.6679i			0.680293i
$924$	46.5295	−	14.0186i	1.53071	−	0.461177i
$925$	2.61282	−	1.50851i	0.0859089	−	0.0495995i
$926$	1.46727	−	9.67486i	0.0482176	−	0.317936i
$927$	41.1718	+	16.6111i	1.35226	+	0.545579i
$928$	−8.86637	+	38.0459i	−0.291053	+	1.24892i
$929$	37.9958	+	21.9369i	1.24660	+	0.719726i	0.970430	−	0.241382i	$-0.0776006\pi$
$929$	37.9958	+	21.9369i	1.24660	+	0.719726i	0.276172	+	0.961108i	$0.410934\pi$
$930$	6.90940	+	0.557090i	0.226568	+	0.0182677i
$931$	26.8184	−	8.59475i	0.878937	−	0.281681i
$932$	−8.91732	−	9.64580i	−0.292097	−	0.315959i
$933$	14.3707	−	9.69830i	0.470477	−	0.317508i
$934$	−2.90463	+	19.1525i	−0.0950424	+	0.626688i
$935$	−16.3340	−	28.2914i	−0.534180	−	0.925227i
$936$	−5.38387	+	16.7257i	−0.175977	+	0.546696i
$937$	−7.34455	−	12.7211i	−0.239936	−	0.415581i	0.720760	−	0.693185i	$-0.243793\pi$
$937$	−7.34455	−	12.7211i	−0.239936	−	0.415581i	−0.960696	+	0.277604i	$0.910460\pi$
$938$	22.4137	−	8.77316i	0.731834	−	0.286454i
$939$	−18.5959	−	9.06419i	−0.606853	−	0.295799i
$940$	−25.5006	−	7.91685i	−0.831738	−	0.258219i
$941$	19.3027	+	33.4333i	0.629251	+	1.08989i	0.987702	+	0.156346i	$0.0499714\pi$
$941$	19.3027	+	33.4333i	0.629251	+	1.08989i	−0.358452	+	0.933548i	$0.616695\pi$
$942$	−17.5160	−	1.41227i	−0.570701	−	0.0460144i
$943$			2.43149i			0.0791801i
$944$	−0.498044	−	1.04392i	−0.0162100	−	0.0339767i
$945$	12.6815	−	39.1273i	0.412530	−	1.27281i
$946$	44.9330	+	35.9000i	1.46090	+	1.16721i
$947$	3.08166	+	1.77920i	0.100140	+	0.0578161i	0.549234	−	0.835669i	$-0.314920\pi$
$947$	3.08166	+	1.77920i	0.100140	+	0.0578161i	−0.449093	+	0.893485i	$0.648253\pi$
$948$	−9.07879	−	2.13498i	−0.294865	−	0.0693410i
$949$			23.7485i			0.770908i
$950$	−1.34319	−	1.65009i	−0.0435787	−	0.0535359i
$951$	−50.6765	−	24.7012i	−1.64330	−	0.800992i
$952$	34.0169	−	23.0563i	1.10249	−	0.747259i
$953$	47.1324	+	27.2119i	1.52677	+	0.881479i	0.999495	+	0.0317825i	$0.0101184\pi$
$953$	47.1324	+	27.2119i	1.52677	+	0.881479i	0.527272	+	0.849697i	$0.323215\pi$
$954$	32.6220	+	0.339155i	1.05617	+	0.0109805i
$955$	10.3293	−	17.8909i	0.334249	−	0.578936i
$956$	−50.7254	−	15.7481i	−1.64058	−	0.509329i
$957$	−20.0387	+	41.1110i	−0.647761	+	1.32893i
$958$	−8.52467	−	21.7789i	−0.275419	−	0.703643i
$959$	−2.11147	−	3.65718i	−0.0681830	−	0.118096i
$960$	−22.1213	+	20.1091i	−0.713963	+	0.649019i
$961$	29.2796			0.944502
$962$	9.33034	+	23.8372i	0.300822	+	0.768542i
$963$	−31.9205	−	12.8786i	−1.02862	−	0.415007i
$964$	−0.726063	−	3.20804i	−0.0233849	−	0.103324i
$965$	−6.55177	−	11.3480i	−0.210909	−	0.365305i
$966$	−5.94103	+	8.60891i	−0.191150	+	0.276987i
$967$	−37.3798	−	21.5813i	−1.20205	−	0.694006i	−0.241043	−	0.970515i	$-0.577489\pi$
$967$	−37.3798	−	21.5813i	−1.20205	−	0.694006i	−0.961012	+	0.276508i	$0.910823\pi$
$968$	−9.21197	−	4.46733i	−0.296084	−	0.143585i
$969$	27.7628	−	11.0951i	0.891871	−	0.356427i
$970$	18.1042	+	46.2526i	0.581289	+	1.48508i
$971$	−34.2153	−	19.7542i	−1.09802	−	0.633942i	−0.162320	−	0.986738i	$-0.551898\pi$
$971$	−34.2153	−	19.7542i	−1.09802	−	0.633942i	−0.935700	+	0.352796i	$0.885231\pi$
$972$	27.7349	+	14.2399i	0.889597	+	0.456746i
$973$	26.2105	−	15.1327i	0.840271	−	0.485131i
$974$	−8.17152	+	53.8811i	−0.261832	+	1.72646i
$975$	1.23490	−	0.0866557i	0.0395483	−	0.00277520i
$976$	−42.5825	−	3.34732i	−1.36303	−	0.107145i
$977$		−	16.8458i		−	0.538945i	−0.963008	−	0.269472i	$-0.913151\pi$
$977$		−	16.8458i		−	0.538945i	0.963008	−	0.269472i	$-0.0868493\pi$
$978$	−31.0419	+	14.7334i	−0.992610	+	0.471121i
$979$	−5.49404	−	9.51595i	−0.175590	−	0.304131i
$980$	−20.4709	+	18.9249i	−0.653918	+	0.604533i
$981$	−28.5631	+	22.3385i	−0.911951	+	0.713212i
$982$	26.3674	+	21.0667i	0.841419	+	0.672265i
$983$	6.99149	−	12.1096i	0.222994	−	0.386237i	−0.732722	−	0.680528i	$-0.761750\pi$
$983$	6.99149	−	12.1096i	0.222994	−	0.386237i	0.955716	+	0.294292i	$0.0950837\pi$
$984$	−9.49870	−	3.81017i	−0.302807	−	0.121464i
$985$	−2.50852	+	4.34488i	−0.0799279	+	0.138439i
$986$	−5.79911	+	38.2380i	−0.184681	+	1.21775i
$987$	17.2294	−	35.3474i	0.548417	−	1.12512i
$988$	15.5508	−	9.16829i	0.494738	−	0.291682i
$989$	−12.3794			−0.393643
$990$	−30.4905	+	17.1836i	−0.969051	+	0.546129i
$991$	−2.69020	−	1.55319i	−0.0854570	−	0.0493386i	0.456663	−	0.889640i	$-0.349045\pi$
$991$	−2.69020	−	1.55319i	−0.0854570	−	0.0493386i	−0.542120	+	0.840301i	$0.682378\pi$
$992$	5.07151	−	5.41606i	0.161021	−	0.171960i
$993$	−11.3018	+	7.62715i	−0.358650	+	0.242040i
$994$	−40.4593	−	32.3256i	−1.28329	−	1.02531i
$995$			45.4115i			1.43964i
$996$	−12.7821	−	42.4257i	−0.405018	−	1.34431i
$997$	−8.81747	+	5.09077i	−0.279252	+	0.161226i	−0.633085	−	0.774082i	$-0.718212\pi$
$997$	−8.81747	+	5.09077i	−0.279252	+	0.161226i	0.353833	+	0.935309i	$0.384878\pi$
$998$	34.4660	−	43.1383i	1.09100	−	1.36552i
$999$	44.4208	−	9.47599i	1.40541	−	0.299807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.u.d.11.65	yes	136
3.2	odd	2	inner	456.2.u.d.11.4	✓	136
8.3	odd	2	inner	456.2.u.d.11.48	yes	136
19.7	even	3	inner	456.2.u.d.83.21	yes	136
24.11	even	2	inner	456.2.u.d.11.21	yes	136
57.26	odd	6	inner	456.2.u.d.83.48	yes	136
152.83	odd	6	inner	456.2.u.d.83.4	yes	136
456.83	even	6	inner	456.2.u.d.83.65	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.u.d.11.4	✓	136	3.2	odd	2	inner
456.2.u.d.11.21	yes	136	24.11	even	2	inner
456.2.u.d.11.48	yes	136	8.3	odd	2	inner
456.2.u.d.11.65	yes	136	1.1	even	1	trivial
456.2.u.d.83.4	yes	136	152.83	odd	6	inner
456.2.u.d.83.21	yes	136	19.7	even	3	inner
456.2.u.d.83.48	yes	136	57.26	odd	6	inner
456.2.u.d.83.65	yes	136	456.83	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39823 + 0.212052i) q^{2} +(-1.43570 + 0.968901i) q^{3} +(1.91007 + 0.592994i) q^{4} +(1.07875 - 1.86846i) q^{5} +(-2.21289 + 1.05030i) q^{6} -3.66890i q^{7} +(2.54496 + 1.23417i) q^{8} +(1.12246 - 2.78210i) q^{9} +O(q^{10})\)	\(q+(1.39823 + 0.212052i) q^{2} +(-1.43570 + 0.968901i) q^{3} +(1.91007 + 0.592994i) q^{4} +(1.07875 - 1.86846i) q^{5} +(-2.21289 + 1.05030i) q^{6} -3.66890i q^{7} +(2.54496 + 1.23417i) q^{8} +(1.12246 - 2.78210i) q^{9} +(1.90455 - 2.38377i) q^{10} -3.82357i q^{11} +(-3.31683 + 0.999307i) q^{12} +(-1.79332 + 1.03537i) q^{13} +(0.777998 - 5.12994i) q^{14} +(0.261585 + 3.72775i) q^{15} +(3.29672 + 2.26532i) q^{16} +(3.42951 + 1.98003i) q^{17} +(2.15940 - 3.65198i) q^{18} +(-4.15094 + 1.33029i) q^{19} +(3.16848 - 2.92919i) q^{20} +(3.55480 + 5.26743i) q^{21} +(0.810797 - 5.34621i) q^{22} +(0.581950 + 1.00797i) q^{23} +(-4.84959 + 0.693913i) q^{24} +(0.172576 + 0.298910i) q^{25} +(-2.72701 + 1.06741i) q^{26} +(1.08407 + 5.08181i) q^{27} +(2.17563 - 7.00784i) q^{28} +(3.45292 + 5.98063i) q^{29} +(-0.424723 + 5.26770i) q^{30} -1.31165i q^{31} +(4.12919 + 3.86650i) q^{32} +(3.70466 + 5.48949i) q^{33} +(4.37536 + 3.49576i) q^{34} +(-6.85518 - 3.95784i) q^{35} +(3.79374 - 4.64839i) q^{36} -8.74114i q^{37} +(-6.08604 + 0.979832i) q^{38} +(1.57149 - 3.22403i) q^{39} +(5.05139 - 3.42378i) q^{40} +(1.80920 + 1.04454i) q^{41} +(3.85344 + 8.11885i) q^{42} +(-5.31807 + 9.21118i) q^{43} +(2.26735 - 7.30328i) q^{44} +(-3.98738 - 5.09847i) q^{45} +(0.599956 + 1.53277i) q^{46} +(-3.09399 - 5.35895i) q^{47} +(-6.92796 - 0.0581197i) q^{48} -6.46079 q^{49} +(0.177915 + 0.454539i) q^{50} +(-6.84219 + 0.480133i) q^{51} +(-4.03932 + 0.914204i) q^{52} +(3.84474 + 6.65929i) q^{53} +(0.438160 + 7.33539i) q^{54} +(-7.14418 - 4.12470i) q^{55} +(4.52805 - 9.33719i) q^{56} +(4.67058 - 5.93175i) q^{57} +(3.55975 + 9.09447i) q^{58} +(-0.250420 - 0.144580i) q^{59} +(-1.71089 + 7.27537i) q^{60} +(-9.24783 + 5.33924i) q^{61} +(0.278139 - 1.83399i) q^{62} +(-10.2072 - 4.11819i) q^{63} +(4.95363 + 6.28184i) q^{64} +4.46765i q^{65} +(4.01589 + 8.46113i) q^{66} +(2.31946 + 4.01743i) q^{67} +(5.37645 + 5.81567i) q^{68} +(-1.81213 - 0.883285i) q^{69} +(-8.74581 - 6.98761i) q^{70} +(4.99046 - 8.64374i) q^{71} +(6.29021 - 5.69502i) q^{72} +(5.73429 - 9.93208i) q^{73} +(1.85358 - 12.2221i) q^{74} +(-0.537382 - 0.261936i) q^{75} +(-8.71744 + 0.0794659i) q^{76} -14.0283 q^{77} +(2.88096 - 4.17468i) q^{78} +(2.33161 + 1.34616i) q^{79} +(7.78900 - 3.71605i) q^{80} +(-6.48017 - 6.24559i) q^{81} +(2.30817 + 1.84415i) q^{82} +12.7910i q^{83} +(3.66635 + 12.1691i) q^{84} +(7.39920 - 4.27193i) q^{85} +(-9.38912 + 11.7516i) q^{86} +(-10.7520 - 5.24085i) q^{87} +(4.71895 - 9.73083i) q^{88} +(2.48876 - 1.43689i) q^{89} +(-4.49411 - 7.97435i) q^{90} +(3.79867 + 6.57949i) q^{91} +(0.513846 + 2.27038i) q^{92} +(1.27086 + 1.88314i) q^{93} +(-3.18972 - 8.14911i) q^{94} +(-1.99225 + 9.19092i) q^{95} +(-9.67452 - 1.55035i) q^{96} +(-8.13940 + 14.0979i) q^{97} +(-9.03364 - 1.37003i) q^{98} +(-10.6376 - 4.29180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9}+O(q^{10}) \) 136 * q - 2 * q^3 - 4 * q^4 - 9 * q^6 - 10 * q^9	\( 136 q - 2 q^{3} - 4 q^{4} - 9 q^{6} - 10 q^{9} + 18 q^{12} + 28 q^{16} - 10 q^{18} + 16 q^{19} + 10 q^{22} + 11 q^{24} - 96 q^{25} - 80 q^{27} + 6 q^{28} - 4 q^{30} - 40 q^{33} + 40 q^{34} + q^{36} - 56 q^{40} + 26 q^{42} - 20 q^{43} - 64 q^{46} - 19 q^{48} - 72 q^{49} - 42 q^{51} - 26 q^{52} + 6 q^{54} + 10 q^{57} + 144 q^{58} - 18 q^{60} - 112 q^{64} + 49 q^{66} - 12 q^{67} + 72 q^{70} - 45 q^{72} + 4 q^{73} + 144 q^{75} + 32 q^{76} - 50 q^{78} + 22 q^{81} - 22 q^{82} + 36 q^{84} + 100 q^{88} - 2 q^{90} + 24 q^{91} - 88 q^{94} - 66 q^{96} - 28 q^{97} + 80 q^{99}+O(q^{100}) \) 136 * q - 2 * q^3 - 4 * q^4 - 9 * q^6 - 10 * q^9 + 18 * q^12 + 28 * q^16 - 10 * q^18 + 16 * q^19 + 10 * q^22 + 11 * q^24 - 96 * q^25 - 80 * q^27 + 6 * q^28 - 4 * q^30 - 40 * q^33 + 40 * q^34 + q^36 - 56 * q^40 + 26 * q^42 - 20 * q^43 - 64 * q^46 - 19 * q^48 - 72 * q^49 - 42 * q^51 - 26 * q^52 + 6 * q^54 + 10 * q^57 + 144 * q^58 - 18 * q^60 - 112 * q^64 + 49 * q^66 - 12 * q^67 + 72 * q^70 - 45 * q^72 + 4 * q^73 + 144 * q^75 + 32 * q^76 - 50 * q^78 + 22 * q^81 - 22 * q^82 + 36 * q^84 + 100 * q^88 - 2 * q^90 + 24 * q^91 - 88 * q^94 - 66 * q^96 - 28 * q^97 + 80 * q^99

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