LMFDB - Embedded newform 555.2.bm.a.119.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(14,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 11]))

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

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

chi := DirichletCharacter("555.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.bm (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$72$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			119.11
Character	$\chi$	$=$	555.119
Dual form			555.2.bm.a.14.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03267 - 0.544653i) q^{2} +(1.10763 + 1.33160i) q^{3} +(2.10306 + 1.21420i) q^{4} +(2.12678 - 0.690520i) q^{5} +(-1.52619 - 3.30998i) q^{6} +(3.21898 + 1.85848i) q^{7} +(-0.637478 - 0.637478i) q^{8} +(-0.546319 + 2.94984i) q^{9} +O(q^{10})$	\(q+(-2.03267 - 0.544653i) q^{2} +(1.10763 + 1.33160i) q^{3} +(2.10306 + 1.21420i) q^{4} +(2.12678 - 0.690520i) q^{5} +(-1.52619 - 3.30998i) q^{6} +(3.21898 + 1.85848i) q^{7} +(-0.637478 - 0.637478i) q^{8} +(-0.546319 + 2.94984i) q^{9} +(-4.69914 + 0.245246i) q^{10} +0.842372 q^{11} +(0.712578 + 4.14532i) q^{12} +(1.80930 + 6.75239i) q^{13} +(-5.53090 - 5.53090i) q^{14} +(3.27518 + 2.06718i) q^{15} +(-1.47983 - 2.56313i) q^{16} +(0.861531 - 3.21528i) q^{17} +(2.71713 - 5.69850i) q^{18} +(-3.80441 + 1.01939i) q^{19} +(5.31118 + 1.13013i) q^{20} +(1.09068 + 6.34489i) q^{21} +(-1.71227 - 0.458800i) q^{22} +(-3.42164 - 3.42164i) q^{23} +(0.142777 - 1.55496i) q^{24} +(4.04636 - 2.93717i) q^{25} -14.7108i q^{26} +(-4.53312 + 2.53984i) q^{27} +(4.51314 + 7.81698i) q^{28} +(-4.61569 - 4.61569i) q^{29} +(-5.53147 - 5.98573i) q^{30} +(2.37322 - 2.37322i) q^{31} +(2.07865 + 7.75763i) q^{32} +(0.933035 + 1.12170i) q^{33} +(-3.50242 + 6.06637i) q^{34} +(8.12936 + 1.72980i) q^{35} +(-4.73064 + 5.54035i) q^{36} +(-5.69629 - 2.13360i) q^{37} +8.28833 q^{38} +(-6.98745 + 9.88839i) q^{39} +(-1.79597 - 0.915583i) q^{40} +(-2.90888 + 5.03832i) q^{41} +(1.23877 - 13.4911i) q^{42} +(1.86227 - 1.86227i) q^{43} +(1.77156 + 1.02281i) q^{44} +(0.875024 + 6.65089i) q^{45} +(5.09147 + 8.81868i) q^{46} -0.845254 q^{47} +(1.77397 - 4.80954i) q^{48} +(3.40787 + 5.90260i) q^{49} +(-9.82467 + 3.76643i) q^{50} +(5.23572 - 2.41412i) q^{51} +(-4.39371 + 16.3975i) q^{52} +(2.46608 + 4.27138i) q^{53} +(10.5977 - 2.69369i) q^{54} +(1.79154 - 0.581675i) q^{55} +(-0.867289 - 3.23677i) q^{56} +(-5.57129 - 3.93685i) q^{57} +(6.86824 + 11.8961i) q^{58} +(-0.648455 - 0.173753i) q^{59} +(4.37792 + 8.32413i) q^{60} +(-2.58029 - 9.62977i) q^{61} +(-6.11656 + 3.53140i) q^{62} +(-7.24079 + 8.48013i) q^{63} -10.9816i q^{64} +(8.51063 + 13.1115i) q^{65} +(-1.28562 - 2.78824i) q^{66} +(1.09340 - 1.89382i) q^{67} +(5.71585 - 5.71585i) q^{68} +(0.766351 - 8.34616i) q^{69} +(-15.5822 - 7.94379i) q^{70} +(8.09195 + 4.67189i) q^{71} +(2.22872 - 1.53219i) q^{72} +11.6345 q^{73} +(10.4166 + 7.43942i) q^{74} +(8.39300 + 2.13485i) q^{75} +(-9.23865 - 2.47549i) q^{76} +(2.71157 + 1.56553i) q^{77} +(19.5889 - 16.2941i) q^{78} +(15.3576 - 4.11506i) q^{79} +(-4.91716 - 4.42937i) q^{80} +(-8.40307 - 3.22310i) q^{81} +(8.65693 - 8.65693i) q^{82} +(1.51988 + 2.63251i) q^{83} +(-5.41022 + 14.6680i) q^{84} +(-0.387930 - 7.43308i) q^{85} +(-4.79969 + 2.77110i) q^{86} +(1.03378 - 11.2587i) q^{87} +(-0.536994 - 0.536994i) q^{88} +(3.08875 - 11.5274i) q^{89} +(1.84379 - 13.9957i) q^{90} +(-6.72507 + 25.0983i) q^{91} +(-3.04135 - 11.3505i) q^{92} +(5.78882 + 0.531535i) q^{93} +(1.71812 + 0.460370i) q^{94} +(-7.38722 + 4.79503i) q^{95} +(-8.02769 + 11.3605i) q^{96} +(-11.8508 + 11.8508i) q^{97} +(-3.71221 - 13.8542i) q^{98} +(-0.460204 + 2.48486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 24 q^{4} - 16 q^{6}+O(q^{10}) $ 288 * q - 24 * q^4 - 16 * q^6	$ 288 q - 24 q^{4} - 16 q^{6} - 16 q^{10} - 6 q^{15} + 112 q^{16} - 8 q^{19} - 12 q^{21} + 44 q^{24} - 12 q^{25} - 30 q^{30} - 72 q^{31} - 32 q^{34} - 4 q^{39} + 12 q^{40} + 16 q^{46} + 80 q^{49} + 12 q^{51} - 52 q^{54} - 28 q^{55} - 92 q^{60} - 8 q^{61} + 100 q^{66} - 104 q^{69} + 16 q^{70} + 52 q^{75} - 24 q^{76} + 16 q^{79} - 8 q^{81} - 192 q^{84} - 52 q^{90} - 168 q^{91} - 72 q^{94} - 112 q^{96} - 60 q^{99}+O(q^{100}) $ 288 * q - 24 * q^4 - 16 * q^6 - 16 * q^10 - 6 * q^15 + 112 * q^16 - 8 * q^19 - 12 * q^21 + 44 * q^24 - 12 * q^25 - 30 * q^30 - 72 * q^31 - 32 * q^34 - 4 * q^39 + 12 * q^40 + 16 * q^46 + 80 * q^49 + 12 * q^51 - 52 * q^54 - 28 * q^55 - 92 * q^60 - 8 * q^61 + 100 * q^66 - 104 * q^69 + 16 * q^70 + 52 * q^75 - 24 * q^76 + 16 * q^79 - 8 * q^81 - 192 * q^84 - 52 * q^90 - 168 * q^91 - 72 * q^94 - 112 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.03267	−	0.544653i	−1.43732	−	0.385128i	−0.545724	−	0.837965i	$-0.683745\pi$
$2$	−2.03267	−	0.544653i	−1.43732	−	0.385128i	−0.891593	+	0.452837i	$0.850412\pi$
$3$	1.10763	+	1.33160i	0.639490	+	0.768800i
$3$	1.10763	+	1.33160i	0.639490	+	0.768800i
$4$	2.10306	+	1.21420i	1.05153	+	0.607102i
$5$	2.12678	−	0.690520i	0.951124	−	0.308810i
$5$	2.12678	−	0.690520i	0.951124	−	0.308810i
$6$	−1.52619	−	3.30998i	−0.623063	−	1.35129i
$7$	3.21898	+	1.85848i	1.21666	+	0.702438i	0.964202	−	0.265170i	$-0.0854281\pi$
$7$	3.21898	+	1.85848i	1.21666	+	0.702438i	0.252457	+	0.967608i	$0.418761\pi$
$8$	−0.637478	−	0.637478i	−0.225383	−	0.225383i
$9$	−0.546319	+	2.94984i	−0.182106	+	0.983279i
$10$	−4.69914	+	0.245246i	−1.48600	+	0.0775537i
$11$	0.842372			0.253985			0.126992	−	0.991904i	$-0.459468\pi$
$11$	0.842372			0.253985			0.126992	+	0.991904i	$0.459468\pi$
$12$	0.712578	+	4.14532i	0.205703	+	1.19665i
$13$	1.80930	+	6.75239i	0.501809	+	1.87277i	0.487951	+	0.872871i	$0.337744\pi$
$13$	1.80930	+	6.75239i	0.501809	+	1.87277i	0.0138574	+	0.999904i	$0.495589\pi$
$14$	−5.53090	−	5.53090i	−1.47820	−	1.47820i
$15$	3.27518	+	2.06718i	0.845647	+	0.533743i
$16$	−1.47983	−	2.56313i	−0.369957	−	0.640784i
$17$	0.861531	−	3.21528i	0.208952	−	0.779819i	−0.779257	−	0.626705i	$-0.784403\pi$
$17$	0.861531	−	3.21528i	0.208952	−	0.779819i	0.988209	−	0.153114i	$-0.0489302\pi$
$18$	2.71713	−	5.69850i	0.640433	−	1.34315i
$19$	−3.80441	+	1.01939i	−0.872791	+	0.233864i	−0.667294	−	0.744794i	$-0.732548\pi$
$19$	−3.80441	+	1.01939i	−0.872791	+	0.233864i	−0.205497	+	0.978658i	$0.565881\pi$
$20$	5.31118	+	1.13013i	1.18762	+	0.252705i
$21$	1.09068	+	6.34489i	0.238006	+	1.38457i
$22$	−1.71227	−	0.458800i	−0.365056	−	0.0978166i
$23$	−3.42164	−	3.42164i	−0.713461	−	0.713461i	0.253796	−	0.967258i	$-0.418321\pi$
$23$	−3.42164	−	3.42164i	−0.713461	−	0.713461i	−0.967258	+	0.253796i	$0.918321\pi$
$24$	0.142777	−	1.55496i	0.0291443	−	0.317404i
$25$	4.04636	−	2.93717i	0.809273	−	0.587433i
$26$		−	14.7108i		−	2.88503i
$27$	−4.53312	+	2.53984i	−0.872400	+	0.488793i
$28$	4.51314	+	7.81698i	0.852903	+	1.47727i
$29$	−4.61569	−	4.61569i	−0.857112	−	0.857112i	0.133885	−	0.990997i	$-0.457255\pi$
$29$	−4.61569	−	4.61569i	−0.857112	−	0.857112i	−0.990997	+	0.133885i	$0.957255\pi$
$30$	−5.53147	−	5.98573i	−1.00990	−	1.09284i
$31$	2.37322	−	2.37322i	0.426243	−	0.426243i	−0.461104	−	0.887346i	$-0.652546\pi$
$31$	2.37322	−	2.37322i	0.426243	−	0.426243i	0.887346	+	0.461104i	$0.152546\pi$
$32$	2.07865	+	7.75763i	0.367457	+	1.37137i
$33$	0.933035	+	1.12170i	0.162421	+	0.195263i
$34$	−3.50242	+	6.06637i	−0.600660	+	1.04037i
$35$	8.12936	+	1.72980i	1.37411	+	0.292389i
$36$	−4.73064	+	5.54035i	−0.788441	+	0.923391i
$37$	−5.69629	−	2.13360i	−0.936465	−	0.350762i
$37$	−5.69629	−	2.13360i	−0.936465	−	0.350762i
$38$	8.28833			1.34454
$39$	−6.98745	+	9.88839i	−1.11889	+	1.58341i
$40$	−1.79597	−	0.915583i	−0.283967	−	0.144766i
$41$	−2.90888	+	5.03832i	−0.454290	+	0.786854i	−0.998647	−	0.0520001i	$-0.983440\pi$
$41$	−2.90888	+	5.03832i	−0.454290	+	0.786854i	0.544357	+	0.838854i	$0.316774\pi$
$42$	1.23877	−	13.4911i	0.191146	−	2.08173i
$43$	1.86227	−	1.86227i	0.283994	−	0.283994i	−0.550706	−	0.834700i	$-0.685641\pi$
$43$	1.86227	−	1.86227i	0.283994	−	0.283994i	0.834700	+	0.550706i	$0.185641\pi$
$44$	1.77156	+	1.02281i	0.267073	+	0.154195i
$45$	0.875024	+	6.65089i	0.130441	+	0.991456i
$46$	5.09147	+	8.81868i	0.750696	+	1.30024i
$47$	−0.845254			−0.123293			−0.0616465	−	0.998098i	$-0.519635\pi$
$47$	−0.845254			−0.123293			−0.0616465	+	0.998098i	$0.519635\pi$
$48$	1.77397	−	4.80954i	0.256051	−	0.694197i
$49$	3.40787	+	5.90260i	0.486839	+	0.843229i
$50$	−9.82467	+	3.76643i	−1.38942	+	0.532654i
$51$	5.23572	−	2.41412i	0.733147	−	0.338044i
$52$	−4.39371	+	16.3975i	−0.609298	+	2.27393i
$53$	2.46608	+	4.27138i	0.338743	+	0.586719i	0.984196	−	0.177080i	$-0.0566651\pi$
$53$	2.46608	+	4.27138i	0.338743	+	0.586719i	−0.645454	+	0.763799i	$0.723332\pi$
$54$	10.5977	−	2.69369i	1.44216	−	0.366565i
$55$	1.79154	−	0.581675i	0.241571	−	0.0784330i
$56$	−0.867289	−	3.23677i	−0.115896	−	0.432531i
$57$	−5.57129	−	3.93685i	−0.737935	−	0.521448i
$58$	6.86824	+	11.8961i	0.901844	+	1.56204i
$59$	−0.648455	−	0.173753i	−0.0844216	−	0.0226207i	0.216361	−	0.976313i	$-0.430581\pi$
$59$	−0.648455	−	0.173753i	−0.0844216	−	0.0226207i	−0.300783	+	0.953693i	$0.597248\pi$
$60$	4.37792	+	8.32413i	0.565188	+	1.07464i
$61$	−2.58029	−	9.62977i	−0.330372	−	1.23297i	−0.908800	−	0.417232i	$-0.863000\pi$
$61$	−2.58029	−	9.62977i	−0.330372	−	1.23297i	0.578428	−	0.815734i	$-0.303666\pi$
$62$	−6.11656	+	3.53140i	−0.776804	+	0.448488i
$63$	−7.24079	+	8.48013i	−0.912254	+	1.06840i
$64$		−	10.9816i		−	1.37270i
$65$	8.51063	+	13.1115i	1.05561	+	1.62628i
$66$	−1.28562	−	2.78824i	−0.158248	−	0.343208i
$67$	1.09340	−	1.89382i	0.133580	−	0.231367i	−0.791474	−	0.611203i	$-0.790686\pi$
$67$	1.09340	−	1.89382i	0.133580	−	0.231367i	0.925054	+	0.379835i	$0.124019\pi$
$68$	5.71585	−	5.71585i	0.693149	−	0.693149i
$69$	0.766351	−	8.34616i	0.0922579	−	1.00476i
$70$	−15.5822	−	7.94379i	−1.86243	−	0.949465i
$71$	8.09195	+	4.67189i	0.960338	+	0.554451i	0.896277	−	0.443495i	$-0.146262\pi$
$71$	8.09195	+	4.67189i	0.960338	+	0.554451i	0.0640607	+	0.997946i	$0.479595\pi$
$72$	2.22872	−	1.53219i	0.262658	−	0.180570i
$73$	11.6345			1.36172			0.680858	−	0.732415i	$-0.261607\pi$
$73$	11.6345			1.36172			0.680858	+	0.732415i	$0.261607\pi$
$74$	10.4166	+	7.43942i	1.21091	+	0.864815i
$75$	8.39300	+	2.13485i	0.969140	+	0.246511i
$76$	−9.23865	−	2.47549i	−1.05975	−	0.283958i
$77$	2.71157	+	1.56553i	0.309013	+	0.178409i
$78$	19.5889	−	16.2941i	2.21801	−	1.84495i
$79$	15.3576	−	4.11506i	1.72787	−	0.462981i	0.748178	−	0.663498i	$-0.230929\pi$
$79$	15.3576	−	4.11506i	1.72787	−	0.462981i	0.979690	+	0.200517i	$0.0642622\pi$
$80$	−4.91716	−	4.42937i	−0.549755	−	0.495218i
$81$	−8.40307	−	3.22310i	−0.933675	−	0.358123i
$82$	8.65693	−	8.65693i	0.955998	−	0.955998i
$83$	1.51988	+	2.63251i	0.166828	+	0.288955i	0.937303	−	0.348515i	$-0.113314\pi$
$83$	1.51988	+	2.63251i	0.166828	+	0.288955i	−0.770475	+	0.637471i	$0.779981\pi$
$84$	−5.41022	+	14.6680i	−0.590303	+	1.60041i
$85$	−0.387930	−	7.43308i	−0.0420769	−	0.806231i
$86$	−4.79969	+	2.77110i	−0.517563	+	0.298815i
$87$	1.03378	−	11.2587i	0.110833	−	1.20706i
$88$	−0.536994	−	0.536994i	−0.0572437	−	0.0572437i
$89$	3.08875	−	11.5274i	0.327406	−	1.22190i	−0.584464	−	0.811419i	$-0.698695\pi$
$89$	3.08875	−	11.5274i	0.327406	−	1.22190i	0.911871	−	0.410478i	$-0.134638\pi$
$90$	1.84379	−	13.9957i	0.194353	−	1.47527i
$91$	−6.72507	+	25.0983i	−0.704979	+	2.63102i
$92$	−3.04135	−	11.3505i	−0.317083	−	1.18337i
$93$	5.78882	+	0.531535i	0.600273	+	0.0551176i
$94$	1.71812	+	0.460370i	0.177211	+	0.0474836i
$95$	−7.38722	+	4.79503i	−0.757912	+	0.491960i
$96$	−8.02769	+	11.3605i	−0.819323	+	1.15948i
$97$	−11.8508	+	11.8508i	−1.20327	+	1.20327i	−0.230104	+	0.973166i	$0.573907\pi$
$97$	−11.8508	+	11.8508i	−1.20327	+	1.20327i	−0.973166	+	0.230104i	$0.926093\pi$
$98$	−3.71221	−	13.8542i	−0.374990	−	1.39948i
$99$	−0.460204	+	2.48486i	−0.0462522	+	0.249738i
$100$	12.0761	−	1.26393i	1.20761	−	0.126393i
$101$	−11.9032			−1.18441			−0.592205	−	0.805788i	$-0.701742\pi$
$101$	−11.9032			−1.18441			−0.592205	+	0.805788i	$0.701742\pi$
$102$	−11.9574	+	2.05546i	−1.18396	+	0.203521i
$103$	−2.76353	−	2.76353i	−0.272299	−	0.272299i	0.557726	−	0.830025i	$-0.311674\pi$
$103$	−2.76353	−	2.76353i	−0.272299	−	0.272299i	−0.830025	+	0.557726i	$0.811674\pi$
$104$	3.15111	−	5.45789i	0.308992	−	0.535190i
$105$	6.70091	+	12.7410i	0.653942	+	1.24340i
$106$	−2.68632	−	10.0255i	−0.260918	−	0.973761i
$107$	−1.25482	+	2.17340i	−0.121308	+	0.210111i	−0.920284	−	0.391252i	$-0.872042\pi$
$107$	−1.25482	+	2.17340i	−0.121308	+	0.210111i	0.798976	+	0.601363i	$0.205375\pi$
$108$	−12.6173	−	0.162682i	−1.21410	−	0.0156541i
$109$	0.304553	−	1.13661i	0.0291708	−	0.108867i	−0.949805	−	0.312841i	$-0.898719\pi$
$109$	0.304553	−	1.13661i	0.0291708	−	0.108867i	0.978976	+	0.203974i	$0.0653859\pi$
$110$	−3.95842	+	0.206589i	−0.377421	+	0.0196975i
$111$	−3.46827	−	9.94842i	−0.329194	−	0.944262i
$112$		−	11.0009i		−	1.03949i
$113$	11.4797	+	3.07597i	1.07992	+	0.289363i	0.754562	−	0.656229i	$-0.227850\pi$
$113$	11.4797	+	3.07597i	1.07992	+	0.289363i	0.325355	+	0.945592i	$0.394516\pi$
$114$	9.18039	+	11.0367i	0.859822	+	1.03369i
$115$	−9.63978	−	4.91435i	−0.898914	−	0.458266i
$116$	−4.10269	−	15.3115i	−0.380926	−	1.42163i
$117$	−20.9069	+	1.64817i	−1.93284	+	0.152374i
$118$	1.22346	+	0.706366i	0.112629	+	0.0650262i
$119$	8.74876	−	8.74876i	0.801998	−	0.801998i
$120$	−0.770073	−	3.40563i	−0.0702977	−	0.310891i
$121$	−10.2904			−0.935492
$122$			20.9795i			1.89940i
$123$	−9.93098	+	1.70713i	−0.895447	+	0.153926i
$124$	7.87260	−	2.10946i	0.706980	−	0.189435i
$125$	6.57754	−	9.04079i	0.588313	−	0.808633i
$126$	19.3369	−	13.2936i	1.72267	−	1.18429i
$127$	13.7274	−	7.92553i	1.21811	−	0.703277i	0.253598	−	0.967310i	$-0.418386\pi$
$127$	13.7274	−	7.92553i	1.21811	−	0.703277i	0.964514	+	0.264033i	$0.0850527\pi$
$128$	−1.82384	+	6.80667i	−0.161206	+	0.601630i
$129$	4.54251	+	0.417097i	0.399946	+	0.0367233i
$130$	−10.1581	−	31.2867i	−0.890927	−	2.74402i
$131$	1.26475	−	4.72011i	0.110502	−	0.412398i	−0.888409	−	0.459052i	$-0.848189\pi$
$131$	1.26475	−	4.72011i	0.110502	−	0.412398i	0.998911	+	0.0466540i	$0.0148558\pi$
$132$	0.600255	+	3.49190i	0.0522455	+	0.303931i
$133$	−14.1408	−	3.78902i	−1.22616	−	0.328549i
$134$	−3.25400	+	3.25400i	−0.281103	+	0.281103i
$135$	−7.88713	+	8.53190i	−0.678816	+	0.734309i
$136$	−2.59888	+	1.50046i	−0.222852	+	0.128664i
$137$	−9.06430			−0.774415			−0.387208	−	0.921993i	$-0.626560\pi$
$137$	−9.06430			−0.774415			−0.387208	+	0.921993i	$0.626560\pi$
$138$	−6.10350	+	16.5476i	−0.519565	+	1.40863i
$139$	−0.587369	+	0.339118i	−0.0498200	+	0.0287636i	−0.524703	−	0.851285i	$-0.675824\pi$
$139$	−0.587369	+	0.339118i	−0.0498200	+	0.0287636i	0.474883	+	0.880049i	$0.342490\pi$
$140$	14.9962	+	13.5086i	1.26741	+	1.14168i
$141$	−0.936227	−	1.12554i	−0.0788445	−	0.0947876i
$142$	−13.9037	−	13.9037i	−1.16677	−	1.16677i
$143$	1.52410	+	5.68802i	0.127452	+	0.475656i
$144$	8.36929	−	2.96496i	0.697440	−	0.247080i
$145$	−13.0038	−	6.62931i	−1.07990	−	0.550535i
$146$	−23.6492	−	6.33677i	−1.95722	−	0.524435i
$147$	−4.08526	+	11.0758i	−0.336946	+	0.913518i
$148$	−9.38903	−	11.4036i	−0.771773	−	0.937367i
$149$		−	11.1626i		−	0.914479i	−0.889344	−	0.457240i	$-0.848838\pi$
$149$		−	11.1626i		−	0.914479i	0.889344	−	0.457240i	$-0.151162\pi$
$150$	−15.8975	−	8.91072i	−1.29802	−	0.727558i
$151$	10.2727	+	5.93092i	0.835977	+	0.482651i	0.855895	−	0.517150i	$-0.173007\pi$
$151$	10.2727	+	5.93092i	0.835977	+	0.482651i	−0.0199178	+	0.999802i	$0.506340\pi$
$152$	3.07506	+	1.77539i	0.249421	+	0.144003i
$153$	9.01387	+	4.29794i	0.728728	+	0.347468i
$154$	−4.65908	−	4.65908i	−0.375439	−	0.375439i
$155$	3.40855	−	6.68606i	0.273781	−	0.537038i
$156$	−26.7016	+	12.3117i	−2.13784	+	0.985726i
$157$	5.76756	−	3.32990i	0.460302	−	0.265755i	−0.251869	−	0.967761i	$-0.581045\pi$
$157$	5.76756	−	3.32990i	0.460302	−	0.265755i	0.712171	+	0.702006i	$0.247712\pi$
$158$	−33.4583			−2.66180
$159$	−2.95627	+	8.01494i	−0.234447	+	0.635626i
$160$	9.77763	+	15.0634i	0.772989	+	1.19087i
$161$	−4.65514	−	17.3732i	−0.366876	−	1.36920i
$162$	15.3252	+	11.1283i	1.20406	+	0.874320i
$163$	3.98003	−	14.8537i	0.311740	−	1.16343i	−0.615246	−	0.788335i	$-0.710943\pi$
$163$	3.98003	−	14.8537i	0.311740	−	1.16343i	0.926986	−	0.375095i	$-0.122390\pi$
$164$	−12.2351	+	7.06393i	−0.955400	+	0.551601i
$165$	2.75892	+	1.74133i	0.214781	+	0.135563i
$166$	−1.65561	−	6.17884i	−0.128501	−	0.479571i
$167$	8.87381	−	2.37773i	0.686676	−	0.183994i	0.101421	−	0.994844i	$-0.467661\pi$
$167$	8.87381	−	2.37773i	0.686676	−	0.183994i	0.585255	+	0.810849i	$0.300994\pi$
$168$	3.34945	−	4.74002i	0.258415	−	0.365700i
$169$	−31.0628	+	17.9341i	−2.38945	+	1.37955i
$170$	−3.25992	+	15.3203i	−0.250024	+	1.17501i
$171$	−0.928608	−	11.7793i	−0.0710124	−	0.900785i
$172$	6.17766	−	1.65530i	0.471042	−	0.126215i
$173$	−8.72406	+	5.03684i	−0.663278	+	0.382944i	−0.793525	−	0.608538i	$-0.791756\pi$
$173$	−8.72406	+	5.03684i	−0.663278	+	0.382944i	0.130247	+	0.991482i	$0.458423\pi$
$174$	−8.23344	+	22.3222i	−0.624176	+	1.69224i
$175$	18.4838	−	1.93460i	1.39724	−	0.146242i
$176$	−1.24656	−	2.15911i	−0.0939633	−	0.162749i
$177$	−0.486877	−	1.05594i	−0.0365959	−	0.0793690i
$178$	−12.5568	+	21.7490i	−0.941173	+	1.63016i
$179$	−11.5579	−	11.5579i	−0.863881	−	0.863881i	0.127905	−	0.991786i	$-0.459175\pi$
$179$	−11.5579	−	11.5579i	−0.863881	−	0.863881i	−0.991786	+	0.127905i	$0.959175\pi$
$180$	−6.23530	+	15.0497i	−0.464752	+	1.12174i
$181$	−1.21207	+	2.09936i	−0.0900921	+	0.156044i	−0.907550	−	0.419945i	$-0.862049\pi$
$181$	−1.21207	+	2.09936i	−0.0900921	+	0.156044i	0.817458	+	0.575989i	$0.195383\pi$
$182$	27.3397	−	47.3538i	2.02656	−	3.51010i
$183$	9.96500	−	14.1021i	0.736634	−	1.04246i
$184$			4.36244i			0.321604i
$185$	−13.5880	−	0.604290i	−0.999013	−	0.0444283i
$186$	−11.4773	−	4.23334i	−0.841555	−	0.310403i
$187$	0.725729	−	2.70846i	0.0530706	−	0.198062i
$188$	−1.77762	−	1.02631i	−0.129646	−	0.0748514i
$189$	−19.3122	−	0.249003i	−1.40476	−	0.0181123i
$190$	17.6274	−	5.72326i	1.27883	−	0.415209i
$191$	−5.59320	+	5.59320i	−0.404710	+	0.404710i	−0.879889	−	0.475179i	$-0.842383\pi$
$191$	−5.59320	+	5.59320i	−0.404710	+	0.404710i	0.475179	+	0.879889i	$0.342383\pi$
$192$	14.6231	−	12.1635i	1.05533	−	0.877824i
$193$	2.40019	−	2.40019i	0.172770	−	0.172770i	−0.615426	−	0.788195i	$-0.711016\pi$
$193$	2.40019	−	2.40019i	0.172770	−	0.172770i	0.788195	+	0.615426i	$0.211016\pi$
$194$	30.5435	−	17.6343i	2.19289	−	1.26607i
$195$	−8.03262	+	25.8554i	−0.575228	+	1.85154i
$196$			16.5514i			1.18224i
$197$	3.67925	+	6.37265i	0.262136	+	0.454032i	0.966809	−	0.255499i	$-0.0822399\pi$
$197$	3.67925	+	6.37265i	0.262136	+	0.454032i	−0.704674	+	0.709532i	$0.748907\pi$
$198$	2.28883	−	4.80026i	0.162660	−	0.341139i
$199$	10.4925	−	10.4925i	0.743797	−	0.743797i	−0.229509	−	0.973306i	$-0.573712\pi$
$199$	10.4925	−	10.4925i	0.743797	−	0.743797i	0.973306	+	0.229509i	$0.0737122\pi$
$200$	−4.45185	−	0.707089i	−0.314793	−	0.0499988i
$201$	3.73289	−	0.641681i	0.263298	−	0.0452607i
$202$	24.1952	+	6.48310i	1.70237	+	0.456149i
$203$	−6.27964	−	23.4359i	−0.440744	−	1.64488i
$204$	13.9423	+	1.28019i	0.976155	+	0.0896313i
$205$	−2.70747	+	12.7240i	−0.189098	+	0.888684i
$206$	4.11219	+	7.12252i	0.286510	+	0.496250i
$207$	11.9626	−	8.22397i	0.831457	−	0.571605i
$208$	14.6298	−	14.6298i	1.01440	−	1.01440i
$209$	−3.20472	+	0.858703i	−0.221675	+	0.0593978i
$210$	−6.68132	−	29.5480i	−0.461055	−	2.03901i
$211$	21.7834			1.49963			0.749816	−	0.661647i	$-0.230142\pi$
$211$	21.7834			1.49963			0.749816	+	0.661647i	$0.230142\pi$
$212$			11.9773i			0.822605i
$213$	2.74178	+	15.9500i	0.187864	+	1.09287i
$214$	3.73438	−	3.73438i	0.255277	−	0.255277i
$215$	2.67470	−	5.24658i	0.182413	−	0.357814i
$216$	4.50886	+	1.27067i	0.306789	+	0.0864582i
$217$	12.0499	−	3.22876i	0.818001	−	0.219183i
$218$	−1.23811	+	2.14447i	−0.0838555	+	0.145242i
$219$	12.8867	+	15.4925i	0.870804	+	1.04689i
$220$	4.47399	+	0.951992i	0.301636	+	0.0641833i
$221$	23.2696			1.56528
$222$	1.63142	+	22.1109i	0.109494	+	1.48399i
$223$			13.4309i			0.899399i	0.893180	+	0.449699i	$0.148469\pi$
$223$			13.4309i			0.899399i	−0.893180	+	0.449699i	$0.851531\pi$
$224$	−7.72625	+	28.8347i	−0.516232	+	1.92660i
$225$	6.45356	+	13.5407i	0.430237	+	0.902716i
$226$	−21.6591	−	12.5049i	−1.44074	−	0.831812i
$227$	−9.58896	+	2.56936i	−0.636442	+	0.170534i	−0.562591	−	0.826735i	$-0.690195\pi$
$227$	−9.58896	+	2.56936i	−0.636442	+	0.170534i	−0.0738507	+	0.997269i	$0.523529\pi$
$228$	−6.93663	−	15.0441i	−0.459389	−	0.996320i
$229$	0.00345389	−	0.00598232i	0.000228240	−	0.000395323i	−0.865911	−	0.500198i	$-0.833261\pi$
$229$	0.00345389	−	0.00598232i	0.000228240	−	0.000395323i	0.866140	+	0.499802i	$0.166594\pi$
$230$	16.9179	+	15.2396i	1.11553	+	1.00487i
$231$	0.918759	+	5.34476i	0.0604499	+	0.351659i
$232$			5.88480i			0.386356i
$233$			26.2554i			1.72005i	0.510255	+	0.860023i	$0.329551\pi$
$233$			26.2554i			1.72005i	−0.510255	+	0.860023i	$0.670449\pi$
$234$	43.3946	+	8.03681i	2.83679	+	0.525382i
$235$	−1.79767	+	0.583665i	−0.117267	+	0.0380741i
$236$	−1.15277	−	1.15277i	−0.0750389	−	0.0750389i
$237$	22.4902	+	15.8923i	1.46089	+	1.03231i
$238$	−22.5484	+	13.0183i	−1.46160	+	0.843853i
$239$	−13.0240	−	3.48978i	−0.842454	−	0.225735i	−0.188314	−	0.982109i	$-0.560302\pi$
$239$	−13.0240	−	3.48978i	−0.842454	−	0.225735i	−0.654139	+	0.756374i	$0.726969\pi$
$240$	0.451762	−	11.4538i	0.0291611	−	0.739338i
$241$	6.20235	−	1.66191i	0.399528	−	0.107053i	−0.0534594	−	0.998570i	$-0.517025\pi$
$241$	6.20235	−	1.66191i	0.399528	−	0.107053i	0.452988	+	0.891517i	$0.350358\pi$
$242$	20.9170	+	5.60470i	1.34460	+	0.360284i
$243$	−5.01560	−	14.7595i	−0.321751	−	0.946824i
$244$	6.26599	−	23.3850i	0.401139	−	1.49707i
$245$	11.3236	+	10.2003i	0.723441	+	0.651675i
$246$	21.1162	+	1.93891i	1.34632	+	0.123620i
$247$	−13.7666	−	23.8444i	−0.875948	−	1.51719i
$248$	−3.02575			−0.192135
$249$	−1.82199	+	4.93971i	−0.115464	+	0.313042i
$250$	−18.2941	+	14.7945i	−1.15702	+	0.935686i
$251$	5.98677	+	5.98677i	0.377882	+	0.377882i	0.870337	−	0.492456i	$-0.163901\pi$
$251$	5.98677	+	5.98677i	0.377882	+	0.377882i	−0.492456	+	0.870337i	$0.663901\pi$
$252$	−25.5244	+	9.04245i	−1.60789	+	0.569621i
$253$	−2.88229	−	2.88229i	−0.181208	−	0.181208i
$254$	−32.2200	+	8.63333i	−2.02166	+	0.541703i
$255$	9.46821	−	8.74966i	0.592923	−	0.547925i
$256$	−3.56702	+	6.17825i	−0.222938	+	0.386141i
$257$	5.08054	−	18.9608i	0.316915	−	1.18274i	−0.605278	−	0.796014i	$-0.706938\pi$
$257$	5.08054	−	18.9608i	0.316915	−	1.18274i	0.922193	−	0.386729i	$-0.126395\pi$
$258$	−9.00627	−	3.32191i	−0.560706	−	0.206813i
$259$	−14.3710	−	17.4544i	−0.892969	−	1.08457i
$260$	1.97840	+	37.9079i	0.122695	+	2.35095i
$261$	16.1372	−	11.0939i	0.998865	−	0.686694i
$262$	−5.14165	+	8.90559i	−0.317652	+	0.550189i
$263$	14.2831	+	8.24633i	0.880731	+	0.508490i	0.870899	−	0.491461i	$-0.163537\pi$
$263$	14.2831	+	8.24633i	0.880731	+	0.508490i	0.00983168	+	0.999952i	$0.496870\pi$
$264$	0.120272	−	1.30985i	0.00740220	−	0.0806157i
$265$	8.19429	+	7.38140i	0.503371	+	0.453436i
$266$	26.6799	+	15.4037i	1.63585	+	0.944459i
$267$	18.7710	−	8.65505i	1.14877	−	0.529680i
$268$	4.59897	−	2.65522i	0.280927	−	0.162193i
$269$		−	4.56979i		−	0.278625i	−0.990248	−	0.139313i	$-0.955511\pi$
$269$		−	4.56979i		−	0.278625i	0.990248	−	0.139313i	$-0.0444893\pi$
$270$	20.6789	−	13.0468i	1.25848	−	0.794003i
$271$	−14.2806	−	24.7347i	−0.867484	−	1.50253i	−0.864559	−	0.502531i	$-0.832402\pi$
$271$	−14.2806	−	24.7347i	−0.867484	−	1.50253i	−0.00292538	−	0.999996i	$-0.500931\pi$
$272$	−9.51610	+	2.54983i	−0.576999	+	0.154606i
$273$	−40.8698	+	18.8445i	−2.47355	+	1.14052i
$274$	18.4248	+	4.93690i	1.11308	+	0.298249i
$275$	3.40854	−	2.47419i	0.205543	−	0.149199i
$276$	11.7456	−	16.6220i	0.707003	−	1.00053i
$277$	−21.3418	+	5.71852i	−1.28230	+	0.343592i	−0.834733	−	0.550656i	$-0.814378\pi$
$277$	−21.3418	+	5.71852i	−1.28230	+	0.343592i	−0.447572	+	0.894248i	$0.647711\pi$
$278$	1.37863	−	0.369403i	0.0826848	−	0.0221553i
$279$	5.70407	+	8.29714i	0.341494	+	0.496737i
$280$	−4.07958	−	6.28500i	−0.243802	−	0.375601i
$281$	18.4881	+	4.95388i	1.10291	+	0.295524i	0.763949	−	0.645277i	$-0.223258\pi$
$281$	18.4881	+	4.95388i	1.10291	+	0.295524i	0.338960	+	0.940801i	$0.389925\pi$
$282$	1.29001	+	2.79777i	0.0768193	+	0.166605i
$283$	4.34494	−	1.16422i	0.258280	−	0.0692060i	−0.127355	−	0.991857i	$-0.540649\pi$
$283$	4.34494	−	1.16422i	0.258280	−	0.0692060i	0.385636	+	0.922651i	$0.373982\pi$
$284$	11.3452	+	19.6505i	0.673217	+	1.16605i
$285$	−14.5674	−	4.52571i	−0.862896	−	0.268080i
$286$		−	12.3920i		−	0.732754i
$287$	−18.7272	+	10.8122i	−1.10543	+	0.638221i
$288$	−24.0193	+	1.89354i	−1.41535	+	0.111578i
$289$	5.12666	+	2.95988i	0.301568	+	0.174111i
$290$	22.8217	+	20.5578i	1.34014	+	1.20719i
$291$	−28.9069	−	2.65426i	−1.69455	−	0.155595i
$292$	24.4681	+	14.1267i	1.43189	+	0.826701i
$293$	8.17496	−	14.1594i	0.477586	−	0.827203i	−0.522084	−	0.852894i	$-0.674845\pi$
$293$	8.17496	−	14.1594i	0.477586	−	0.827203i	0.999670	+	0.0256909i	$0.00817856\pi$
$294$	14.3365	−	20.2885i	0.836120	−	1.18325i
$295$	−1.49910	+	0.0782374i	−0.0872809	+	0.00455516i
$296$	2.27114	+	4.99139i	0.132007	+	0.290119i
$297$	−3.81857	+	2.13949i	−0.221576	+	0.124146i
$298$	−6.07977	+	22.6900i	−0.352191	+	1.31440i
$299$	16.9135	−	29.2950i	0.978131	−	1.69417i
$300$	15.0589	+	14.6805i	0.869423	+	0.847581i
$301$	9.45560	−	2.53362i	0.545012	−	0.146036i
$302$	−17.6507	−	17.6507i	−1.01568	−	1.01568i
$303$	−13.1843	−	15.8503i	−0.757417	−	0.910574i
$304$	8.24269	+	8.24269i	0.472751	+	0.472751i
$305$	−12.1373	−	18.6986i	−0.694977	−	1.07068i
$306$	−15.9814	−	13.6457i	−0.913594	−	0.780075i
$307$	14.8798			0.849232			0.424616	−	0.905373i	$-0.360409\pi$
$307$	14.8798			0.849232			0.424616	+	0.905373i	$0.360409\pi$
$308$	3.80174	+	6.58481i	0.216624	+	0.375204i
$309$	0.618954	−	6.74089i	0.0352111	−	0.383476i
$310$	−10.5701	+	11.7341i	−0.600339	+	0.666452i
$311$	−7.85854	+	29.3285i	−0.445617	+	1.66307i	0.268685	+	0.963228i	$0.413411\pi$
$311$	−7.85854	+	29.3285i	−0.445617	+	1.66307i	−0.714302	+	0.699838i	$0.753256\pi$
$312$	10.7580	−	1.84929i	0.609051	−	0.104695i
$313$	−27.8776	−	7.46978i	−1.57574	−	0.422217i	−0.638133	−	0.769926i	$-0.720293\pi$
$313$	−27.8776	−	7.46978i	−1.57574	−	0.422217i	−0.937602	+	0.347709i	$0.886960\pi$
$314$	−13.5372	+	3.62728i	−0.763949	+	0.204700i
$315$	−9.54384	+	23.0353i	−0.537735	+	1.29789i
$316$	37.2946	+	9.99305i	2.09798	+	0.562153i
$317$	−22.6926	+	13.1016i	−1.27454	+	0.735857i	−0.975839	−	0.218489i	$-0.929887\pi$
$317$	−22.6926	+	13.1016i	−1.27454	+	0.735857i	−0.298703	+	0.954346i	$0.596554\pi$
$318$	10.3745	−	14.6816i	0.581773	−	0.823304i
$319$	−3.88813	−	3.88813i	−0.217693	−	0.217693i
$320$	−7.58299	−	23.3553i	−0.423902	−	1.30560i
$321$	−4.28397	+	0.736411i	−0.239108	+	0.0411025i
$322$			37.8495i			2.10927i
$323$			13.1105i			0.729485i
$324$	−13.7587	−	16.9814i	−0.764371	−	0.943413i
$325$	27.1540	+	22.0084i	1.50623	+	1.22081i
$326$	−16.1802	+	28.0249i	−0.896139	+	1.55216i
$327$	1.85084	−	0.853394i	0.102351	−	0.0471928i
$328$	5.06617	−	1.35748i	0.279732	−	0.0749540i
$329$	−2.72085	−	1.57088i	−0.150005	−	0.0866057i
$330$	−4.65955	−	5.04221i	−0.256500	−	0.277565i
$331$	−2.59343	+	9.67883i	−0.142548	+	0.531997i	0.857304	+	0.514810i	$0.172138\pi$
$331$	−2.59343	+	9.67883i	−0.142548	+	0.531997i	−0.999852	+	0.0171865i	$0.994529\pi$
$332$			7.38177i			0.405127i
$333$	9.40577	−	15.6375i	0.515433	−	0.856930i
$334$	−19.3326			−1.05783
$335$	1.01769	−	4.78275i	0.0556025	−	0.261310i
$336$	14.6488	−	12.1849i	0.799157	−	0.664741i
$337$	−1.42715	+	2.47190i	−0.0777420	+	0.134653i	−0.902275	−	0.431160i	$-0.858104\pi$
$337$	−1.42715	+	2.47190i	−0.0777420	+	0.134653i	0.824533	+	0.565813i	$0.191438\pi$
$338$	72.9085	−	19.5358i	3.96570	−	1.06261i
$339$	8.61925	+	18.6934i	0.468133	+	1.01528i
$340$	8.20943	−	16.1033i	0.445219	−	0.873322i
$341$	1.99913	−	1.99913i	0.108259	−	0.108259i
$342$	−4.52807	+	24.4492i	−0.244850	+	1.32206i
$343$		−	0.684886i		−	0.0369804i
$344$	−2.37432			−0.128015
$345$	−4.13334	−	18.2796i	−0.222531	−	0.984141i
$346$	20.4765	−	5.48666i	1.10082	−	0.294965i
$347$	−7.59820	+	7.59820i	−0.407893	+	0.407893i	−0.881003	−	0.473110i	$-0.843131\pi$
$347$	−7.59820	+	7.59820i	−0.407893	+	0.407893i	0.473110	+	0.881003i	$0.343131\pi$
$348$	15.8445	−	22.4226i	0.849354	−	1.20198i
$349$	−2.44346	−	4.23220i	−0.130796	−	0.226545i	0.793188	−	0.608977i	$-0.208420\pi$
$349$	−2.44346	−	4.23220i	−0.130796	−	0.226545i	−0.923983	+	0.382432i	$0.875086\pi$
$350$	−38.6252	−	6.13486i	−2.06460	−	0.327922i
$351$	−25.3518	−	26.0141i	−1.35318	−	1.38853i
$352$	1.75100	+	6.53481i	0.0933285	+	0.348307i
$353$	−0.387502	−	0.103831i	−0.0206247	−	0.00552636i	0.248492	−	0.968634i	$-0.420065\pi$
$353$	−0.387502	−	0.103831i	−0.0206247	−	0.00552636i	−0.269117	+	0.963108i	$0.586732\pi$
$354$	0.414544	+	2.41155i	0.0220327	+	0.128173i
$355$	20.4358	+	4.34841i	1.08462	+	0.230790i
$356$	20.4924	−	20.4924i	1.08609	−	1.08609i
$357$	21.3402	+	1.95948i	1.12945	+	0.103707i
$358$	17.1985	+	29.7886i	0.908966	+	1.57438i
$359$		−	13.7704i		−	0.726773i	−0.931639	−	0.363386i	$-0.881621\pi$
$359$		−	13.7704i		−	0.726773i	0.931639	−	0.363386i	$-0.118379\pi$
$360$	3.68199	−	4.79761i	0.194058	−	0.252856i
$361$	−3.02013	+	1.74367i	−0.158954	+	0.0917722i
$362$	3.60716	−	3.60716i	0.189588	−	0.189588i
$363$	−11.3979	−	13.7027i	−0.598237	−	0.719206i
$364$	−44.6177	+	44.6177i	−2.33860	+	2.33860i
$365$	24.7440	−	8.03387i	1.29516	−	0.420512i
$366$	−27.9364	+	23.2375i	−1.46026	+	1.21465i
$367$	−27.2648	−	15.7414i	−1.42321	−	0.821692i	−0.426640	−	0.904421i	$-0.640303\pi$
$367$	−27.2648	−	15.7414i	−1.42321	−	0.821692i	−0.996572	+	0.0827293i	$0.973636\pi$
$368$	−3.70669	+	13.8336i	−0.193225	+	0.721124i
$369$	−13.2730	−	11.3332i	−0.690967	−	0.589985i
$370$	27.2909	+	8.62909i	1.41879	+	0.448605i
$371$			18.3326i			0.951783i
$372$	11.5289	+	8.14666i	0.597744	+	0.422385i
$373$	−10.9243	+	18.9215i	−0.565641	+	0.979719i	0.431349	+	0.902185i	$0.358038\pi$
$373$	−10.9243	+	18.9215i	−0.565641	+	0.979719i	−0.996990	+	0.0775335i	$0.975296\pi$
$374$	−2.95034	+	5.11014i	−0.152559	+	0.264239i
$375$	19.3242	−	1.25519i	0.997897	−	0.0648175i
$376$	0.538831	+	0.538831i	0.0277881	+	0.0277881i
$377$	22.8158	−	39.5181i	1.17507	−	2.03528i
$378$	39.1199	+	11.0246i	2.01211	+	0.567045i
$379$	−5.35156	−	9.26918i	−0.274891	−	0.476126i	0.695216	−	0.718801i	$-0.255309\pi$
$379$	−5.35156	−	9.26918i	−0.274891	−	0.476126i	−0.970108	+	0.242675i	$0.921975\pi$
$380$	−21.3579	+	1.11466i	−1.09564	+	0.0571810i
$381$	25.7585	+	9.50090i	1.31965	+	0.486746i
$382$	14.4155	−	8.32279i	0.737561	−	0.425831i
$383$	−35.0831	+	9.40048i	−1.79266	+	0.480342i	−0.992794	−	0.119834i	$-0.961764\pi$
$383$	−35.0831	+	9.40048i	−1.79266	+	0.480342i	−0.799868	+	0.600176i	$0.795097\pi$
$384$	−11.0839	+	5.11063i	−0.565623	+	0.260801i
$385$	6.84794	+	1.45713i	0.349004	+	0.0742624i
$386$	−6.18608	+	3.57153i	−0.314863	+	0.181786i
$387$	4.47601	+	6.51080i	0.227528	+	0.330962i
$388$	−39.3124	+	10.5337i	−1.99578	+	0.534769i
$389$	1.27055	+	4.74175i	0.0644193	+	0.240416i	0.990626	−	0.136599i	$-0.0436172\pi$
$389$	1.27055	+	4.74175i	0.0644193	+	0.240416i	−0.926207	+	0.377015i	$0.876951\pi$
$390$	30.4099	−	48.1806i	1.53987	−	2.43972i
$391$	−13.9494	+	8.05367i	−0.705450	+	0.407292i
$392$	1.59034	−	5.93523i	0.0803242	−	0.299774i
$393$	7.68617	−	3.54399i	0.387716	−	0.178770i
$394$	−4.00783	−	14.9574i	−0.201912	−	0.753544i
$395$	29.8207	−	19.3566i	1.50044	−	0.973935i
$396$	−3.98496	+	4.66703i	−0.200252	+	0.234527i
$397$	−3.76056			−0.188737			−0.0943686	−	0.995537i	$-0.530083\pi$
$397$	−3.76056			−0.188737			−0.0943686	+	0.995537i	$0.530083\pi$
$398$	−27.0427	+	15.6131i	−1.35553	+	0.782615i
$399$	−10.6173	−	23.0267i	−0.531530	−	1.15278i
$400$	−13.5163	−	6.02488i	−0.675813	−	0.301244i
$401$	−16.2806	−	16.2806i	−0.813017	−	0.813017i	0.172068	−	0.985085i	$-0.444955\pi$
$401$	−16.2806	−	16.2806i	−0.813017	−	0.813017i	−0.985085	+	0.172068i	$0.944955\pi$
$402$	−7.93725	−	0.728805i	−0.395874	−	0.0363495i
$403$	20.3187	+	11.7310i	1.01215	+	0.584364i
$404$	−25.0331	−	14.4529i	−1.24544	−	0.719057i
$405$	−20.0971	−	1.05233i	−0.998632	−	0.0522907i
$406$			51.0578i			2.53396i
$407$	−4.79840	−	1.79729i	−0.237848	−	0.0890882i
$408$	−4.87661	−	1.79871i	−0.241428	−	0.0890495i
$409$	11.7232	+	3.14121i	0.579673	+	0.155323i	0.536729	−	0.843755i	$-0.319660\pi$
$409$	11.7232	+	3.14121i	0.579673	+	0.155323i	0.0429436	+	0.999077i	$0.486326\pi$
$410$	12.4336	−	24.3892i	0.614051	−	1.20449i
$411$	−10.0399	−	12.0700i	−0.495230	−	0.595370i
$412$	−2.45639	−	9.16737i	−0.121018	−	0.451644i
$413$	−1.76444	−	1.76444i	−0.0868226	−	0.0868226i
$414$	−28.7952	+	10.2012i	−1.41521	+	0.501361i
$415$	5.05024	+	4.54925i	0.247907	+	0.223314i
$416$	−48.6216	+	28.0717i	−2.38387	+	1.37633i
$417$	−1.10216	−	0.406525i	−0.0539728	−	0.0199076i
$418$	6.98185			0.341494
$419$	11.7096	−	6.76057i	0.572054	−	0.330275i	−0.185915	−	0.982566i	$-0.559525\pi$
$419$	11.7096	−	6.76057i	0.572054	−	0.330275i	0.757969	+	0.652290i	$0.226192\pi$
$420$	−1.37777	+	34.9315i	−0.0672284	+	1.70448i
$421$	−17.7870	+	17.7870i	−0.866887	+	0.866887i	−0.992127	−	0.125239i	$-0.960030\pi$
$421$	−17.7870	+	17.7870i	−0.866887	+	0.866887i	0.125239	+	0.992127i	$0.460030\pi$
$422$	−44.2785	−	11.8644i	−2.15545	−	0.577550i
$423$	0.461778	−	2.49336i	0.0224524	−	0.121231i
$424$	1.15084	−	4.29499i	0.0558897	−	0.208583i
$425$	−5.95774	−	15.5406i	−0.288993	−	0.753832i
$426$	3.11405	−	33.9144i	0.150876	−	1.64316i
$427$	9.59081	−	35.7934i	0.464132	−	1.73216i
$428$	−5.27791	+	3.04720i	−0.255117	+	0.147292i
$429$	−5.88603	+	8.32971i	−0.284180	+	0.402162i
$430$	−8.29436	+	9.20779i	−0.399990	+	0.444039i
$431$	−12.0723	+	3.23476i	−0.581502	+	0.155813i	−0.537566	−	0.843221i	$-0.680656\pi$
$431$	−12.0723	+	3.23476i	−0.581502	+	0.155813i	−0.0439355	+	0.999034i	$0.513990\pi$
$432$	13.2182	+	7.86047i	0.635961	+	0.378187i
$433$			0.168804i			0.00811219i	0.999992	+	0.00405610i	$0.00129110\pi$
$433$			0.168804i			0.00811219i	−0.999992	+	0.00405610i	$0.998709\pi$
$434$	−26.2521			−1.26014
$435$	−5.57574	−	24.6586i	−0.267337	−	1.18229i
$436$	2.02056	−	2.02056i	0.0967674	−	0.0967674i
$437$	16.5053	+	9.52933i	0.789555	+	0.455850i
$438$	−17.7564	−	38.5100i	−0.848435	−	1.84008i
$439$	5.22471	+	19.4989i	0.249362	+	0.930630i	0.971141	+	0.238507i	$0.0766580\pi$
$439$	5.22471	+	19.4989i	0.249362	+	0.930630i	−0.721779	+	0.692123i	$0.756675\pi$
$440$	−1.51287	−	0.771261i	−0.0721233	−	0.0367684i
$441$	−19.2735	+	6.82796i	−0.917786	+	0.325141i
$442$	−47.2994	−	12.6738i	−2.24980	−	0.602833i
$443$		−	29.9711i		−	1.42397i	−0.702195	−	0.711985i	$-0.747796\pi$
$443$		−	29.9711i		−	1.42397i	0.702195	−	0.711985i	$-0.252204\pi$
$444$	4.78542	−	25.1333i	0.227106	−	1.19278i
$445$	−1.39080	−	26.6490i	−0.0659302	−	1.26328i
$446$	7.31517	−	27.3006i	0.346384	−	1.29272i
$447$	14.8642	−	12.3641i	0.703051	−	0.584800i
$448$	20.4090	−	35.3494i	0.964234	−	1.67010i
$449$	−0.951429	−	3.55078i	−0.0449007	−	0.167572i	0.939835	−	0.341629i	$-0.110979\pi$
$449$	−0.951429	−	3.55078i	−0.0449007	−	0.167572i	−0.984735	+	0.174058i	$0.944312\pi$
$450$	−5.74296	−	31.0388i	−0.270726	−	1.46319i
$451$	−2.45036	+	4.24414i	−0.115383	+	0.199849i
$452$	20.4076	+	20.4076i	0.959893	+	0.959893i
$453$	3.48067	+	20.2483i	0.163536	+	0.951349i
$454$	20.8906			0.980446
$455$	3.02816	+	58.0223i	0.141963	+	2.72013i
$456$	1.04192	+	6.06123i	0.0487924	+	0.283843i
$457$	5.76350	+	21.5097i	0.269605	+	1.00618i	0.959371	+	0.282148i	$0.0910470\pi$
$457$	5.76350	+	21.5097i	0.269605	+	1.00618i	−0.689765	+	0.724033i	$0.742286\pi$
$458$	−0.0102789	+	0.0102789i	−0.000480303	+	0.000480303i
$459$	4.26088	+	16.7634i	0.198881	+	0.782448i
$460$	−14.3060	−	22.0398i	−0.667022	−	1.02761i
$461$	30.2866	+	8.11526i	1.41059	+	0.377965i	0.882134	−	0.470998i	$-0.156106\pi$
$461$	30.2866	+	8.11526i	1.41059	+	0.377965i	0.528451	+	0.848964i	$0.322773\pi$
$462$	1.04350	−	11.3645i	0.0485481	−	0.528727i
$463$	2.99509	+	11.1778i	0.139194	+	0.519477i	0.999945	+	0.0104525i	$0.00332720\pi$
$463$	2.99509	+	11.1778i	0.139194	+	0.519477i	−0.860752	+	0.509025i	$0.830006\pi$
$464$	−5.00021	+	18.6610i	−0.232129	+	0.866317i
$465$	12.6786	−	2.86685i	0.587955	−	0.132947i
$466$	14.3001	−	53.3686i	0.662438	−	2.47225i
$467$	10.3142	+	10.3142i	0.477283	+	0.477283i	0.904262	−	0.426979i	$-0.140422\pi$
$467$	10.3142	+	10.3142i	0.477283	+	0.477283i	−0.426979	+	0.904262i	$0.640422\pi$
$468$	−45.9697	−	21.9190i	−2.12495	−	1.01321i
$469$	7.03925	−	4.06411i	0.325042	−	0.187663i
$470$	3.97196	−	0.207295i	0.183213	−	0.00956183i
$471$	10.8224	+	3.99179i	0.498671	+	0.183932i
$472$	0.302612	+	0.524139i	0.0139288	+	0.0241255i
$473$	1.56873	−	1.56873i	0.0721301	−	0.0721301i
$474$	−37.0594	−	44.5531i	−1.70219	−	2.04639i
$475$	−12.3999	+	15.2990i	−0.568946	+	0.701966i
$476$	29.0220	−	7.77642i	1.33022	−	0.356431i
$477$	−13.9471	+	4.94101i	−0.638596	+	0.226233i
$478$	24.5729	+	14.1871i	1.12394	+	0.648905i
$479$	5.84249	+	1.56549i	0.266950	+	0.0715291i	0.389811	−	0.920895i	$-0.372540\pi$
$479$	5.84249	+	1.56549i	0.266950	+	0.0715291i	−0.122861	+	0.992424i	$0.539207\pi$
$480$	−9.22845	+	29.7045i	−0.421219	+	1.35582i
$481$	4.10062	−	42.3239i	0.186972	−	1.92980i
$482$	−13.5125			−0.615478
$483$	17.9780	−	25.4418i	0.818028	−	1.15764i
$484$	−21.6414	−	12.4947i	−0.983699	−	0.567939i
$485$	−17.0208	+	33.3873i	−0.772877	+	1.51604i
$486$	2.15624	+	32.7331i	0.0978090	+	1.48480i
$487$	−4.23368	+	4.23368i	−0.191846	+	0.191846i	−0.796493	−	0.604647i	$-0.793314\pi$
$487$	−4.23368	+	4.23368i	−0.191846	+	0.191846i	0.604647	+	0.796493i	$0.293314\pi$
$488$	−4.49389	+	7.78365i	−0.203429	+	0.352349i
$489$	24.1876	−	11.1525i	1.09380	−	0.504336i
$490$	−17.4616	−	26.9014i	−0.788836	−	1.21528i
$491$		−	2.27178i		−	0.102524i	−0.998685	−	0.0512619i	$-0.983676\pi$
$491$		−	2.27178i		−	0.102524i	0.998685	−	0.0512619i	$-0.0163243\pi$
$492$	−22.9583	−	8.46804i	−1.03504	−	0.381769i
$493$	−18.8173	+	10.8642i	−0.847487	+	0.489297i
$494$	14.9960	+	55.9660i	0.674704	+	2.51803i
$495$	0.737095	+	5.60252i	0.0331300	+	0.251815i
$496$	−9.59483	−	2.57093i	−0.430821	−	0.115438i
$497$	17.3652	+	30.0774i	0.778935	+	1.34916i
$498$	6.39393	−	9.04847i	0.286519	−	0.405472i
$499$	−0.910380	−	3.39758i	−0.0407542	−	0.152097i	0.942550	−	0.334064i	$-0.108420\pi$
$499$	−0.910380	−	3.39758i	−0.0407542	−	0.152097i	−0.983305	+	0.181967i	$0.941754\pi$
$500$	24.8103	−	11.0269i	1.10955	−	0.493137i
$501$	12.9951	+	9.18273i	0.580577	+	0.410254i
$502$	−8.90844	−	15.4299i	−0.397603	−	0.688669i
$503$	0.913292	−	3.40845i	0.0407217	−	0.151975i	−0.942571	−	0.334005i	$-0.891600\pi$
$503$	0.913292	−	3.40845i	0.0407217	−	0.151975i	0.983293	+	0.182029i	$0.0582666\pi$
$504$	10.0217	−	0.790054i	0.446404	−	0.0351918i
$505$	−25.3154	+	8.21938i	−1.12652	+	0.365758i
$506$	4.28891	+	7.42861i	0.190665	+	0.330242i
$507$	−58.2872	−	21.4989i	−2.58862	−	0.954801i
$508$	38.4928			1.70784
$509$	−10.2502	−	17.7539i	−0.454334	−	0.786929i	0.544316	−	0.838880i	$-0.316789\pi$
$509$	−10.2502	−	17.7539i	−0.454334	−	0.786929i	−0.998650	+	0.0519512i	$0.983456\pi$
$510$	−24.0113	+	12.6283i	−1.06324	+	0.559191i
$511$	37.4512	+	21.6225i	1.65674	+	0.956522i
$512$	20.5812	−	20.5812i	0.909571	−	0.909571i
$513$	14.6568	−	14.2836i	0.647111	−	0.630637i
$514$	−20.6541	+	35.7740i	−0.911015	+	1.57792i
$515$	−7.78569	−	3.96914i	−0.343079	−	0.174901i
$516$	9.04674	+	6.39271i	0.398261	+	0.281424i
$517$	−0.712018			−0.0313145
$518$	19.7049	+	43.3064i	0.865783	+	1.90277i
$519$	−16.3701	−	6.03802i	−0.718566	−	0.265039i
$520$	2.93293	−	13.7836i	0.128618	−	0.604452i
$521$	−17.8768	+	30.9634i	−0.783195	+	1.35653i	0.146877	+	0.989155i	$0.453078\pi$
$521$	−17.8768	+	30.9634i	−0.783195	+	1.35653i	−0.930072	+	0.367378i	$0.880255\pi$
$522$	−38.8439	+	13.7611i	−1.70015	+	0.602307i
$523$	−6.83607	−	25.5126i	−0.298921	−	1.11559i	−0.938053	−	0.346490i	$-0.887373\pi$
$523$	−6.83607	−	25.5126i	−0.298921	−	1.11559i	0.639133	−	0.769096i	$-0.279293\pi$
$524$	8.39102	−	8.39102i	0.366564	−	0.366564i
$525$	23.0493	+	22.4702i	1.00595	+	0.980681i
$526$	−24.5414	−	24.5414i	−1.07006	−	1.07006i
$527$	−5.58595	−	9.67516i	−0.243328	−	0.421456i
$528$	1.49435	−	4.05142i	0.0650330	−	0.176315i
$529$			0.415233i			0.0180536i
$530$	−12.6360	−	19.4670i	−0.548873	−	0.845593i
$531$	0.866806	−	1.81791i	0.0376162	−	0.0788906i
$532$	−25.1383	−	25.1383i	−1.08989	−	1.08989i
$533$	−39.2837	−	10.5260i	−1.70157	−	0.455933i
$534$	−42.8693	+	7.36920i	−1.85514	+	0.318896i
$535$	−1.16793	+	5.48882i	−0.0504941	+	0.237302i
$536$	−1.90429	+	0.510253i	−0.0822528	+	0.0220396i
$537$	2.58866	−	28.1925i	0.111709	−	1.21659i
$538$	−2.48895	+	9.28890i	−0.107306	+	0.400473i
$539$	2.87069	+	4.97219i	0.123650	+	0.214167i
$540$	−26.9466	+	8.36653i	−1.15960	+	0.360038i
$541$	14.1598	+	14.1598i	0.608775	+	0.608775i	0.942626	−	0.333851i	$-0.108348\pi$
$541$	14.1598	+	14.1598i	0.608775	+	0.608775i	−0.333851	+	0.942626i	$0.608348\pi$
$542$	15.5559	+	58.0556i	0.668185	+	2.49370i
$543$	−4.13803	+	0.711323i	−0.177580	+	0.0305258i
$544$	26.7338			1.14620
$545$	−0.137134	−	2.62761i	−0.00587417	−	0.112554i
$546$	93.3386	−	16.0448i	3.99452	−	0.686655i
$547$	−16.8134	−	16.8134i	−0.718890	−	0.718890i	0.249488	−	0.968378i	$-0.419738\pi$
$547$	−16.8134	−	16.8134i	−0.718890	−	0.718890i	−0.968378	+	0.249488i	$0.919738\pi$
$548$	−19.0628	−	11.0059i	−0.814322	−	0.470149i
$549$	29.8159	−	2.35051i	1.27251	−	0.100317i
$550$	−8.27603	+	3.17274i	−0.352891	+	0.135286i
$551$	22.2651	+	12.8548i	0.948526	+	0.547632i
$552$	−5.80903	+	4.83196i	−0.247249	+	0.205662i
$553$	57.0836	+	15.2955i	2.42744	+	0.650431i
$554$	46.4955			1.97540
$555$	−14.2458	−	18.7632i	−0.604702	−	0.796452i
$556$	−1.64703			−0.0698497
$557$	6.04305	+	1.61923i	0.256052	+	0.0686089i	0.384562	−	0.923099i	$-0.374353\pi$
$557$	6.04305	+	1.61923i	0.256052	+	0.0686089i	−0.128510	+	0.991708i	$0.541019\pi$
$558$	−7.07545	−	19.9721i	−0.299528	−	0.845487i
$559$	15.9442	+	9.20538i	0.674367	+	0.389346i
$560$	−7.59634	−	23.3964i	−0.321004	−	0.988680i
$561$	4.41042	−	2.03358i	0.186208	−	0.0858580i
$562$	−34.8822	−	20.1392i	−1.47142	−	0.849522i
$563$	−22.0943	−	22.0943i	−0.931165	−	0.931165i	0.0666142	−	0.997779i	$-0.478780\pi$
$563$	−22.0943	−	22.0943i	−0.931165	−	0.931165i	−0.997779	+	0.0666142i	$0.978780\pi$
$564$	−0.602309	−	3.50385i	−0.0253618	−	0.147539i
$565$	26.5387	−	1.38505i	1.11649	−	0.0582694i
$566$	−9.46595			−0.397884
$567$	−21.0592	−	25.9920i	−0.884404	−	1.09156i
$568$	−2.18021	−	8.13667i	−0.0914798	−	0.341407i
$569$	19.7201	+	19.7201i	0.826708	+	0.826708i	0.987060	−	0.160352i	$-0.0512629\pi$
$569$	19.7201	+	19.7201i	0.826708	+	0.826708i	−0.160352	+	0.987060i	$0.551263\pi$
$570$	27.1457	+	17.1334i	1.13701	+	0.717641i
$571$	1.56962	+	2.71867i	0.0656867	+	0.113773i	0.896998	−	0.442034i	$-0.145743\pi$
$571$	1.56962	+	2.71867i	0.0656867	+	0.113773i	−0.831312	+	0.555806i	$0.812410\pi$
$572$	−3.70114	+	13.8128i	−0.154752	+	0.577543i
$573$	−13.6431	−	1.25272i	−0.569948	−	0.0523331i
$574$	43.9552	−	11.7777i	1.83465	−	0.491594i
$575$	−23.8951	−	3.79527i	−0.996495	−	0.158274i
$576$	32.3938	+	5.99944i	1.34974	+	0.249977i
$577$	5.52015	+	1.47912i	0.229807	+	0.0615765i	0.371885	−	0.928279i	$-0.378712\pi$
$577$	5.52015	+	1.47912i	0.229807	+	0.0615765i	−0.142078	+	0.989855i	$0.545378\pi$
$578$	−8.80872	−	8.80872i	−0.366394	−	0.366394i
$579$	5.85462	+	0.537576i	0.243310	+	0.0223409i
$580$	−19.2984	−	29.7311i	−0.801322	−	1.23452i
$581$			11.2986i			0.468747i
$582$	57.3126	+	21.1395i	2.37568	+	0.876259i
$583$	2.07736	+	3.59809i	0.0860354	+	0.149018i
$584$	−7.41675	−	7.41675i	−0.306907	−	0.306907i
$585$	−43.3262	+	17.9419i	−1.79132	+	0.741807i
$586$	−24.3290	+	24.3290i	−1.00502	+	1.00502i
$587$	11.0780	+	41.3437i	0.457239	+	1.70644i	0.681421	+	0.731891i	$0.261362\pi$
$587$	11.0780	+	41.3437i	0.457239	+	1.70644i	−0.224183	+	0.974547i	$0.571971\pi$
$588$	−22.0398	+	18.3328i	−0.908908	+	0.756032i
$589$	−6.60946	+	11.4479i	−0.272338	+	0.471703i
$590$	3.08979	+	0.657457i	0.127205	+	0.0270671i
$591$	−4.41058	+	11.9578i	−0.181427	+	0.491879i
$592$	2.96081	+	17.7577i	0.121689	+	0.729838i
$593$	18.1194			0.744073			0.372037	−	0.928218i	$-0.378660\pi$
$593$	18.1194			0.744073			0.372037	+	0.928218i	$0.378660\pi$
$594$	8.92719	−	2.26909i	0.366287	−	0.0931020i
$595$	12.5655	−	24.6479i	0.515134	−	1.01046i
$596$	13.5537	−	23.4757i	0.555182	−	0.961603i
$597$	25.5937	+	2.35004i	1.04748	+	0.0961806i
$598$	−50.3352	+	50.3352i	−2.05836	+	2.05836i
$599$	15.1148	+	8.72652i	0.617573	+	0.356556i	0.775923	−	0.630827i	$-0.217284\pi$
$599$	15.1148	+	8.72652i	0.617573	+	0.356556i	−0.158351	+	0.987383i	$0.550618\pi$
$600$	−3.98943	−	6.71128i	−0.162868	−	0.273987i
$601$	−15.0899	−	26.1365i	−0.615531	−	1.06613i	−0.990291	−	0.139009i	$-0.955608\pi$
$601$	−15.0899	−	26.1365i	−0.615531	−	1.06613i	0.374761	−	0.927122i	$-0.377725\pi$
$602$	−20.6001			−0.839597
$603$	4.98912	+	4.25998i	0.203173	+	0.173480i
$604$	14.4027	+	24.9462i	0.586037	+	1.01505i
$605$	−21.8854	+	7.10574i	−0.889768	+	0.288889i
$606$	18.1664	+	39.3993i	0.737962	+	1.60049i
$607$	6.15250	−	22.9615i	0.249722	−	0.931977i	−0.721228	−	0.692697i	$-0.756422\pi$
$607$	6.15250	−	22.9615i	0.249722	−	0.931977i	0.970951	−	0.239279i	$-0.0769112\pi$
$608$	−15.8161	−	27.3942i	−0.641426	−	1.11098i
$609$	24.2518	−	34.3203i	0.982732	−	1.39073i
$610$	14.4868	+	44.6188i	0.586553	+	1.80656i
$611$	−1.52931	−	5.70748i	−0.0618695	−	0.230900i
$612$	13.7382	+	19.9835i	0.555332	+	0.807786i
$613$	−3.26217	−	5.65024i	−0.131758	−	0.228211i	0.792596	−	0.609747i	$-0.208729\pi$
$613$	−3.26217	−	5.65024i	−0.131758	−	0.228211i	−0.924354	+	0.381535i	$0.875395\pi$
$614$	−30.2457	−	8.10430i	−1.22062	−	0.327063i
$615$	−19.9422	+	10.4882i	−0.804146	+	0.422926i
$616$	−0.730580	−	2.72656i	−0.0294359	−	0.109856i
$617$	9.19280	−	5.30746i	0.370088	−	0.213670i	−0.303409	−	0.952860i	$-0.598125\pi$
$617$	9.19280	−	5.30746i	0.370088	−	0.213670i	0.673497	+	0.739190i	$0.264791\pi$
$618$	−4.92958	+	13.3649i	−0.198297	+	0.537615i
$619$		−	45.6214i		−	1.83368i	−0.399256	−	0.916839i	$-0.630732\pi$
$619$		−	45.6214i		−	1.83368i	0.399256	−	0.916839i	$-0.369268\pi$
$620$	15.2866	−	9.92253i	0.613926	−	0.398499i
$621$	24.2011	+	6.82028i	0.971158	+	0.273688i
$622$	31.9477	−	55.3350i	1.28099	−	2.21873i
$623$	31.3659	−	31.3659i	1.25665	−	1.25665i
$624$	35.6855	+	3.27667i	1.42856	+	0.131172i
$625$	7.74611	−	23.7697i	0.309844	−	0.950787i
$626$	52.5976	+	30.3672i	2.10222	+	1.21372i
$627$	−4.69309	−	3.31629i	−0.187424	−	0.132440i
$628$	16.1727			0.645362
$629$	−11.7677	+	16.4770i	−0.469207	+	0.656981i
$630$	31.9457	−	41.6251i	1.27275	−	1.65838i
$631$	32.0858	+	8.59738i	1.27732	+	0.342256i	0.832830	−	0.553529i	$-0.186719\pi$
$631$	32.0858	+	8.59738i	1.27732	+	0.342256i	0.444487	+	0.895785i	$0.353386\pi$
$632$	−12.4134	−	7.16689i	−0.493779	−	0.285084i
$633$	24.1279	+	29.0068i	0.958998	+	1.15292i
$634$	53.2624	−	14.2716i	2.11532	−	0.566798i
$635$	23.7224	−	26.3349i	0.941396	−	1.04507i
$636$	−15.9490	+	13.2664i	−0.632418	+	0.526047i
$637$	−33.6908	+	33.6908i	−1.33488	+	1.33488i
$638$	5.78561	+	10.0210i	0.229054	+	0.396734i
$639$	−18.2021	+	21.3176i	−0.720064	+	0.843311i
$640$	0.821239	+	15.7357i	0.0324623	+	0.622007i
$641$	−24.9030	+	14.3778i	−0.983610	+	0.567887i	−0.903358	−	0.428887i	$-0.858906\pi$
$641$	−24.9030	+	14.3778i	−0.983610	+	0.567887i	−0.0802518	+	0.996775i	$0.525572\pi$
$642$	9.10901	+	0.836397i	0.359504	+	0.0330099i
$643$	15.9374	+	15.9374i	0.628510	+	0.628510i	0.947693	−	0.319183i	$-0.103408\pi$
$643$	15.9374	+	15.9374i	0.628510	+	0.628510i	−0.319183	+	0.947693i	$0.603408\pi$
$644$	11.3046	−	42.1892i	0.445462	−	1.66249i
$645$	9.94892	−	2.24962i	0.391738	−	0.0885788i
$646$	7.14065	−	26.6493i	0.280945	−	1.04850i
$647$	−9.49956	−	35.4528i	−0.373466	−	1.39379i	−0.855573	−	0.517682i	$-0.826795\pi$
$647$	−9.49956	−	35.4528i	−0.373466	−	1.39379i	0.482107	−	0.876112i	$-0.339872\pi$
$648$	3.30212	+	7.41143i	0.129719	+	0.291149i
$649$	−0.546240	−	0.146365i	−0.0214418	−	0.00574531i
$650$	−43.2082	−	59.5254i	−1.69476	−	2.33478i
$651$	17.6462	+	12.4694i	0.691611	+	0.488714i
$652$	26.4056	−	26.4056i	1.03412	−	1.03412i
$653$	0.729608	+	2.72293i	0.0285518	+	0.106557i	0.978731	−	0.205147i	$-0.0657672\pi$
$653$	0.729608	+	2.72293i	0.0285518	+	0.106557i	−0.950179	+	0.311703i	$0.899100\pi$
$654$	−4.22695	+	0.726608i	−0.165287	+	0.0284126i
$655$	−0.569491	−	10.9120i	−0.0222519	−	0.426366i
$656$	17.2185			0.672271
$657$	−6.35616	+	34.3199i	−0.247977	+	1.33895i
$658$	4.67501	+	4.67501i	0.182251	+	0.182251i
$659$	15.8277	−	27.4143i	0.616559	−	1.06791i	−0.373550	−	0.927610i	$-0.621860\pi$
$659$	15.8277	−	27.4143i	0.616559	−	1.06791i	0.990109	−	0.140301i	$-0.0448070\pi$
$660$	3.68784	+	7.01202i	0.143549	+	0.272942i
$661$	−4.24383	−	15.8382i	−0.165066	−	0.616034i	−0.998032	−	0.0627097i	$-0.980026\pi$
$661$	−4.24383	−	15.8382i	−0.165066	−	0.616034i	0.832966	−	0.553324i	$-0.186641\pi$
$662$	10.5432	−	18.2614i	0.409773	−	0.709748i
$663$	25.7740	+	30.9858i	1.00098	+	1.20339i
$664$	0.709277	−	2.64706i	0.0275253	−	0.102726i
$665$	−32.6907	+	1.70612i	−1.26769	+	0.0661604i
$666$	−27.6359	+	26.6631i	−1.07087	+	1.03317i
$667$			31.5864i			1.22303i
$668$	21.5492	+	5.77410i	0.833765	+	0.223407i
$669$	−17.8846	+	14.8764i	−0.691458	+	0.575156i
$670$	−4.67358	+	9.16749i	−0.180556	+	0.354171i
$671$	−2.17356	−	8.11185i	−0.0839095	−	0.313154i
$672$	−46.9542	+	21.6499i	−1.81130	+	0.835163i
$673$	−5.37015	−	3.10046i	−0.207004	−	0.119514i	0.392914	−	0.919575i	$-0.371467\pi$
$673$	−5.37015	−	3.10046i	−0.207004	−	0.119514i	−0.599918	+	0.800061i	$0.704800\pi$
$674$	4.24727	−	4.24727i	0.163599	−	0.163599i
$675$	−10.8827	+	23.5917i	−0.418876	+	0.908044i
$676$	−87.1028			−3.35011
$677$			32.7413i			1.25835i	0.777263	+	0.629175i	$0.216607\pi$
$677$			32.7413i			1.25835i	−0.777263	+	0.629175i	$0.783393\pi$
$678$	−7.33872	−	42.6920i	−0.281842	−	1.63958i
$679$	−60.1720	+	16.1231i	−2.30919	+	0.618746i
$680$	−4.49113	+	4.98573i	−0.172227	+	0.191194i
$681$	−14.0424	−	9.92278i	−0.538105	−	0.380242i
$682$	−5.15242	+	2.97475i	−0.197296	+	0.113909i
$683$	8.78624	−	32.7907i	0.336196	−	1.25470i	−0.566371	−	0.824151i	$-0.691653\pi$
$683$	8.78624	−	32.7907i	0.336196	−	1.25470i	0.902567	−	0.430550i	$-0.141680\pi$
$684$	12.3495	−	25.9001i	0.472196	−	0.990315i
$685$	−19.2777	+	6.25908i	−0.736565	+	0.239147i
$686$	−0.373026	+	1.39215i	−0.0142422	+	0.0531525i
$687$	0.0117917	−	0.00202698i	0.000449881	−	7.73341e-5i
$688$	−7.52910	−	2.01742i	−0.287044	−	0.0769133i
$689$	−24.3801	+	24.3801i	−0.928809	+	0.928809i
$690$	−1.55432	+	39.4077i	−0.0591721	+	1.50023i
$691$	−39.0696	+	22.5569i	−1.48628	+	0.858104i	−0.999878	−	0.0156321i	$-0.995024\pi$
$691$	−39.0696	+	22.5569i	−1.48628	+	0.858104i	−0.486401	+	0.873736i	$0.661691\pi$
$692$	−24.4630			−0.929943
$693$	−6.09944	+	7.14342i	−0.231698	+	0.271356i
$694$	19.5830	−	11.3063i	0.743362	−	0.429180i
$695$	−1.01504	+	1.12682i	−0.0385025	+	0.0427427i
$696$	−7.83621	+	6.51817i	−0.297031	+	0.247071i
$697$	13.6935	+	13.6935i	0.518679	+	0.518679i
$698$	2.66168	+	9.93352i	0.100746	+	0.375989i
$699$	−34.9616	+	29.0812i	−1.32237	+	1.09995i
$700$	41.2216	+	18.3745i	1.55803	+	0.694492i
$701$	−20.4180	−	5.47098i	−0.771176	−	0.206636i	−0.148285	−	0.988945i	$-0.547375\pi$
$701$	−20.4180	−	5.47098i	−0.771176	−	0.206636i	−0.622891	+	0.782309i	$0.714042\pi$
$702$	37.3632	+	66.6860i	1.41018	+	2.51690i
$703$	23.8460	+	2.31036i	0.899368	+	0.0871368i
$704$		−	9.25056i		−	0.348644i
$705$	−2.76836	−	1.74729i	−0.104262	−	0.0658067i
$706$	0.731114	+	0.422109i	0.0275158	+	0.0158863i
$707$	−38.3160	−	22.1218i	−1.44102	−	0.831974i
$708$	0.258188	−	2.81187i	0.00970330	−	0.105676i
$709$	−8.73503	−	8.73503i	−0.328051	−	0.328051i	0.523794	−	0.851845i	$-0.324516\pi$
$709$	−8.73503	−	8.73503i	−0.328051	−	0.328051i	−0.851845	+	0.523794i	$0.824516\pi$
$710$	−39.1709	−	19.9693i	−1.47006	−	0.749435i
$711$	3.74860	+	47.5506i	0.140584	+	1.78329i
$712$	−9.31745	+	5.37943i	−0.349186	+	0.201603i
$713$	−16.2406			−0.608215
$714$	−42.3105	−	15.6060i	−1.58343	−	0.584040i
$715$	7.16912	+	11.0447i	0.268110	+	0.413049i
$716$	−10.2734	−	38.3408i	−0.383934	−	1.43286i
$717$	−9.77879	−	21.2082i	−0.365196	−	0.792033i
$718$	−7.50008	+	27.9907i	−0.279900	+	1.04460i
$719$	21.9194	−	12.6552i	0.817457	−	0.471959i	−0.0320820	−	0.999485i	$-0.510214\pi$
$719$	21.9194	−	12.6552i	0.817457	−	0.471959i	0.849539	+	0.527526i	$0.176880\pi$
$720$	15.7522	−	12.0850i	0.587051	−	0.450380i
$721$	−3.75978	−	14.0317i	−0.140022	−	0.522568i
$722$	7.08863	−	1.89939i	0.263811	−	0.0706880i
$723$	9.08290	+	6.41827i	0.337797	+	0.238698i
$724$	−5.09810	+	2.94339i	−0.189469	+	0.109390i
$725$	−32.2338	−	5.11971i	−1.19713	−	0.190141i
$726$	15.7051	+	34.0611i	0.582870	+	1.26412i
$727$	−6.03570	+	1.61726i	−0.223852	+	0.0599809i	−0.369001	−	0.929429i	$-0.620300\pi$
$727$	−6.03570	+	1.61726i	−0.223852	+	0.0599809i	0.145150	+	0.989410i	$0.453634\pi$
$728$	20.2867	−	11.7125i	0.751876	−	0.434096i
$729$	14.0984	−	23.0268i	0.522162	−	0.852846i
$730$	−54.6722	+	2.85332i	−2.02351	+	0.105606i
$731$	−4.38332	−	7.59213i	−0.162123	−	0.280805i
$732$	38.0799	−	17.5581i	1.40747	−	0.648966i
$733$	−18.4205	+	31.9053i	−0.680377	+	1.17845i	0.294488	+	0.955655i	$0.404851\pi$
$733$	−18.4205	+	31.9053i	−0.680377	+	1.17845i	−0.974866	+	0.222793i	$0.928483\pi$
$734$	46.8469	+	46.8469i	1.72915	+	1.72915i
$735$	−1.04036	+	26.3767i	−0.0383741	+	0.972921i
$736$	19.4314	−	33.6562i	0.716252	−	1.24058i
$737$	0.921049	−	1.59530i	0.0339273	−	0.0587637i
$738$	20.8071	+	30.2660i	0.765919	+	1.11411i
$739$		−	13.9962i		−	0.514858i	−0.966297	−	0.257429i	$-0.917125\pi$
$739$		−	13.9962i		−	0.514858i	0.966297	−	0.257429i	$-0.0828753\pi$
$740$	−27.8428	−	17.7695i	−1.02352	−	0.653220i
$741$	16.5030	−	44.7424i	0.606253	−	1.64365i
$742$	9.98492	−	37.2642i	0.366558	−	1.36801i
$743$	36.3991	+	21.0150i	1.33535	+	0.770966i	0.986114	−	0.166068i	$-0.0531073\pi$
$743$	36.3991	+	21.0150i	1.33535	+	0.770966i	0.349238	+	0.937034i	$0.386441\pi$
$744$	−3.35141	−	4.02909i	−0.122869	−	0.147714i
$745$	−7.70803	−	23.7404i	−0.282400	−	0.869783i
$746$	32.5113	−	32.5113i	1.19032	−	1.19032i
$747$	−8.59581	+	3.04521i	−0.314504	+	0.111418i
$748$	4.81487	−	4.81487i	0.176049	−	0.176049i
$749$	−8.07844	+	4.66409i	−0.295180	+	0.170422i
$750$	−39.9634	−	7.97360i	−1.45926	−	0.291155i
$751$			7.61919i			0.278028i	0.990290	+	0.139014i	$0.0443933\pi$
$751$			7.61919i			0.278028i	−0.990290	+	0.139014i	$0.955607\pi$
$752$	1.25083	+	2.16650i	0.0456130	+	0.0790041i
$753$	−1.34087	+	14.6031i	−0.0488640	+	0.532167i
$754$	−67.9006	+	67.9006i	−2.47279	+	2.47279i
$755$	25.9431	+	5.52027i	0.944165	+	0.200903i
$756$	−40.3125	−	23.9727i	−1.46615	−	0.871878i
$757$	−16.3724	−	4.38698i	−0.595066	−	0.159448i	−0.0512986	−	0.998683i	$-0.516336\pi$
$757$	−16.3724	−	4.38698i	−0.595066	−	0.159448i	−0.543768	+	0.839236i	$0.683003\pi$
$758$	5.82949	+	21.7560i	0.211737	+	0.790212i
$759$	0.645553	−	7.03057i	0.0234321	−	0.255194i
$760$	7.76592	+	1.65246i	0.281700	+	0.0599411i
$761$	−3.23631	−	5.60546i	−0.117316	−	0.203198i	0.801387	−	0.598146i	$-0.204096\pi$
$761$	−3.23631	−	5.60546i	−0.117316	−	0.203198i	−0.918703	+	0.394948i	$0.870762\pi$
$762$	−47.1840	−	33.3417i	−1.70929	−	1.20784i
$763$	3.09270	−	3.09270i	0.111963	−	0.111963i
$764$	−18.5541	+	4.97156i	−0.671265	+	0.179865i
$765$	22.1383	+	2.91650i	0.800412	+	0.105446i
$766$	76.4325			2.76162
$767$		−	4.69299i		−	0.169454i
$768$	−12.1779	+	2.09337i	−0.439432	+	0.0755379i
$769$	−5.62804	+	5.62804i	−0.202952	+	0.202952i	−0.801264	−	0.598311i	$-0.795839\pi$
$769$	−5.62804	+	5.62804i	−0.202952	+	0.202952i	0.598311	+	0.801264i	$0.295839\pi$
$770$	−13.1260	−	6.69163i	−0.473028	−	0.241150i
$771$	30.8756	−	14.2363i	1.11196	−	0.512708i
$772$	7.96207	−	2.13343i	0.286561	−	0.0767839i
$773$	2.12581	−	3.68201i	0.0764600	−	0.132433i	−0.825260	−	0.564753i	$-0.808972\pi$
$773$	2.12581	−	3.68201i	0.0764600	−	0.132433i	0.901720	+	0.432320i	$0.142305\pi$
$774$	−5.55213	−	15.6722i	−0.199567	−	0.563325i
$775$	2.63237	−	16.5734i	0.0945574	−	0.595336i
$776$	15.1093			0.542392
$777$	7.32463	−	38.4694i	0.262770	−	1.38008i
$778$		−	10.3304i		−	0.370364i
$779$	5.93054	−	22.1331i	0.212484	−	0.793000i
$780$	−48.2868	+	44.6223i	−1.72894	+	1.59773i
$781$	6.81643	+	3.93547i	0.243911	+	0.140822i
$782$	32.7410	−	8.77291i	1.17081	−	0.313719i
$783$	32.6466	+	9.20035i	1.16669	+	0.328794i
$784$	10.0861	−	17.4697i	0.360218	−	0.623916i
$785$	9.96695	−	11.0646i	0.355736	−	0.394912i
$786$	−17.5537	+	3.01747i	−0.626121	+	0.107630i
$787$		−	0.369424i		−	0.0131686i	−0.999978	−	0.00658428i	$-0.997904\pi$
$787$		−	0.369424i		−	0.0131686i	0.999978	−	0.00658428i	$-0.00209586\pi$
$788$			17.8694i			0.636572i
$789$	4.83951	+	28.1532i	0.172291	+	1.00228i
$790$	−71.1584	+	23.1037i	−2.53170	+	0.821991i
$791$	31.2362	+	31.2362i	1.11063	+	1.11063i
$792$	1.87741	−	1.29067i	0.0667110	−	0.0458621i
$793$	60.3554	−	34.8462i	2.14328	−	1.23743i
$794$	7.64399	+	2.04820i	0.271275	+	0.0726880i
$795$	−0.752846	+	19.0874i	−0.0267007	+	0.676959i
$796$	34.8066	−	9.32639i	1.23369	−	0.330565i
$797$	−6.04540	−	1.61986i	−0.214139	−	0.0573784i	0.150155	−	0.988663i	$-0.452023\pi$
$797$	−6.04540	−	1.61986i	−0.214139	−	0.0573784i	−0.364294	+	0.931284i	$0.618690\pi$
$798$	9.03992	+	52.5885i	0.320010	+	1.86161i
$799$	−0.728212	+	2.71773i	−0.0257623	+	0.0961462i
$800$	31.1964	+	25.2848i	1.10296	+	0.893954i
$801$	32.3164	+	15.4089i	1.14184	+	0.544447i
$802$	24.2259	+	41.9605i	0.855447	+	1.48168i
$803$	9.80059			0.345855
$804$	8.62964	+	3.18300i	0.304344	+	0.112256i
$805$	−21.8970	−	33.7345i	−0.771768	−	1.18898i
$806$	−34.9120	−	34.9120i	−1.22972	−	1.22972i
$807$	6.08514	−	5.06163i	0.214207	−	0.178178i
$808$	7.58801	+	7.58801i	0.266945	+	0.266945i
$809$	−41.9563	+	11.2421i	−1.47510	+	0.395253i	−0.904678	−	0.426096i	$-0.859889\pi$
$809$	−41.9563	+	11.2421i	−1.47510	+	0.395253i	−0.570426	+	0.821349i	$0.693222\pi$
$810$	40.2776	+	13.0850i	1.41521	+	0.459759i
$811$	10.7115	−	18.5528i	0.376130	−	0.651476i	−0.614366	−	0.789022i	$-0.710588\pi$
$811$	10.7115	−	18.5528i	0.376130	−	0.651476i	0.990495	+	0.137545i	$0.0439213\pi$
$812$	15.2495	−	56.9120i	0.535153	−	1.99722i
$813$	17.1192	−	46.4129i	0.600395	−	1.62777i
$814$	8.77467	+	6.26676i	0.307552	+	0.219650i
$815$	−1.79213	−	34.3388i	−0.0627755	−	1.20283i
$816$	−13.9357	−	9.84738i	−0.487846	−	0.344727i
$817$	−5.18647	+	8.98322i	−0.181451	+	0.314283i
$818$	−22.1185	−	12.7701i	−0.773354	−	0.446496i
$819$	−70.3619	−	33.5495i	−2.45864	−	1.17232i
$820$	−21.1435	+	23.4720i	−0.738364	+	0.819678i
$821$	−1.62437	−	0.937830i	−0.0566909	−	0.0327305i	0.471387	−	0.881927i	$-0.343754\pi$
$821$	−1.62437	−	0.937830i	−0.0566909	−	0.0327305i	−0.528078	+	0.849196i	$0.677087\pi$
$822$	13.8338	+	30.0027i	0.482509	+	1.04646i
$823$	−19.5427	+	11.2830i	−0.681217	+	0.393301i	−0.800313	−	0.599582i	$-0.795333\pi$
$823$	−19.5427	+	11.2830i	−0.681217	+	0.393301i	0.119097	+	0.992883i	$0.462000\pi$
$824$			3.52338i			0.122743i
$825$	7.07003	+	1.79834i	0.246147	+	0.0626101i
$826$	2.62553	+	4.54755i	0.0913538	+	0.158229i
$827$	−19.3199	+	5.17675i	−0.671818	+	0.180013i	−0.578574	−	0.815630i	$-0.696391\pi$
$827$	−19.3199	+	5.17675i	−0.671818	+	0.180013i	−0.0932445	+	0.995643i	$0.529724\pi$
$828$	35.1436	−	2.77051i	1.22133	−	0.0962819i
$829$	−37.3307	−	10.0027i	−1.29655	−	0.347409i	−0.456404	−	0.889773i	$-0.650863\pi$
$829$	−37.3307	−	10.0027i	−1.29655	−	0.347409i	−0.840144	+	0.542364i	$0.817529\pi$
$830$	−7.78773	−	11.9978i	−0.270316	−	0.416449i
$831$	−31.2536	−	22.0848i	−1.08417	−	0.766112i
$832$	74.1518	−	19.8689i	2.57075	−	0.688830i
$833$	21.9145	−	5.87197i	0.759292	−	0.203452i
$834$	2.01891	+	1.42662i	0.0699091	+	0.0494000i
$835$	17.2308	−	11.1845i	0.596295	−	0.387054i
$836$	−7.78238	−	2.08528i	−0.269159	−	0.0721210i
$837$	−4.73048	+	16.7857i	−0.163509	+	0.580199i
$838$	−27.4841	+	7.36433i	−0.949421	+	0.254397i
$839$	−1.97476	−	3.42038i	−0.0681761	−	0.118084i	0.829922	−	0.557879i	$-0.188385\pi$
$839$	−1.97476	−	3.42038i	−0.0681761	−	0.118084i	−0.898098	+	0.439794i	$0.855051\pi$
$840$	3.85045	−	12.3938i	0.132853	−	0.427627i
$841$			13.6092i			0.469281i
$842$	45.8430	−	26.4675i	1.57985	−	0.912129i
$843$	13.8814	+	30.1059i	0.478100	+	1.03690i
$844$	45.8118	+	26.4495i	1.57691	+	0.910429i
$845$	−53.6798	+	59.5914i	−1.84664	+	2.05001i
$846$	−2.29666	+	4.81668i	−0.0789608	+	0.165601i
$847$	−33.1246	−	19.1245i	−1.13817	−	0.657125i
$848$	7.29875	−	12.6418i	0.250640	−	0.434121i
$849$	6.36287	+	4.49620i	0.218373	+	0.154309i
$850$	3.64587	+	34.8339i	0.125052	+	1.19479i
$851$	12.1902	+	26.7911i	0.417876	+	0.918386i
$852$	−13.6004	+	36.8728i	−0.465940	+	1.26324i
$853$	9.56236	−	35.6872i	0.327409	−	1.22191i	−0.584459	−	0.811423i	$-0.698693\pi$
$853$	9.56236	−	35.6872i	0.327409	−	1.22191i	0.911868	−	0.410484i	$-0.134640\pi$
$854$	−38.9900	+	67.5326i	−1.33421	+	2.31092i
$855$	−10.1088	−	24.4107i	−0.345713	−	0.834828i
$856$	2.18542	−	0.585580i	0.0746960	−	0.0200147i
$857$	−15.9042	−	15.9042i	−0.543278	−	0.543278i	0.381210	−	0.924488i	$-0.375507\pi$
$857$	−15.9042	−	15.9042i	−0.543278	−	0.543278i	−0.924488	+	0.381210i	$0.875507\pi$
$858$	16.5012	−	13.7257i	0.563341	−	0.468588i
$859$	3.14774	+	3.14774i	0.107399	+	0.107399i	0.758764	−	0.651365i	$-0.225803\pi$
$859$	3.14774	+	3.14774i	0.107399	+	0.107399i	−0.651365	+	0.758764i	$0.725803\pi$
$860$	11.9955	−	7.78625i	0.409042	−	0.265509i
$861$	−35.1402	−	12.9613i	−1.19758	−	0.441720i
$862$	26.3009			0.895811
$863$	22.9542	+	39.7578i	0.781368	+	1.35337i	0.931145	+	0.364650i	$0.118811\pi$
$863$	22.9542	+	39.7578i	0.781368	+	1.35337i	−0.149776	+	0.988720i	$0.547855\pi$
$864$	−29.1260	−	29.8868i	−0.990885	−	1.01677i
$865$	−15.0761	+	16.7364i	−0.512603	+	0.569054i
$866$	0.0919395	−	0.343123i	0.00312423	−	0.0116598i
$867$	1.73706	+	10.1051i	0.0589936	+	0.343187i
$868$	29.2621	+	7.84075i	0.993220	+	0.266132i
$869$	12.9368	−	3.46641i	0.438852	−	0.117590i
$870$	−2.09674	+	53.1598i	−0.0710860	+	1.80229i
$871$	14.7661	+	3.95657i	0.500330	+	0.134063i
$872$	−0.918707	+	0.530416i	−0.0311114	+	0.0179621i
$873$	−28.4837	−	41.4324i	−0.964027	−	1.40227i
$874$	−28.3597	−	28.3597i	−0.959280	−	0.959280i
$875$	37.9750	−	16.8779i	1.28379	−	0.570577i
$876$	8.29049	+	48.2288i	0.280110	+	1.62950i
$877$			37.3219i			1.26027i	0.776485	+	0.630135i	$0.217001\pi$
$877$			37.3219i			1.26027i	−0.776485	+	0.630135i	$0.782999\pi$
$878$		−	42.4805i		−	1.43365i
$879$	27.9095	−	4.79762i	0.941365	−	0.161820i
$880$	−4.14208	−	3.73117i	−0.139629	−	0.125778i
$881$	18.4413	−	31.9412i	0.621303	−	1.07613i	−0.367941	−	0.929849i	$-0.619937\pi$
$881$	18.4413	−	31.9412i	0.621303	−	1.07613i	0.989243	−	0.146279i	$-0.0467296\pi$
$882$	42.8956	−	3.38163i	1.44437	−	0.113865i
$883$	−39.6542	+	10.6253i	−1.33447	+	0.357571i	−0.854380	−	0.519648i	$-0.826063\pi$
$883$	−39.6542	+	10.6253i	−1.33447	+	0.357571i	−0.480091	+	0.877219i	$0.659396\pi$
$884$	48.9373	+	28.2540i	1.64594	+	0.950284i
$885$	−1.76462	−	1.90954i	−0.0593172	−	0.0641885i
$886$	−16.3239	+	60.9214i	−0.548411	+	2.04670i
$887$		−	9.46558i		−	0.317823i	−0.987293	−	0.158912i	$-0.949202\pi$
$887$		−	9.46558i		−	0.317823i	0.987293	−	0.158912i	$-0.0507985\pi$
$888$	−4.13096	+	8.55285i	−0.138626	+	0.287015i
$889$	58.9176			1.97603
$890$	−11.6874	+	54.9261i	−0.391762	+	1.84113i
$891$	−7.07851	−	2.71505i	−0.237139	−	0.0909576i
$892$	−16.3078	+	28.2460i	−0.546027	+	0.945746i
$893$	3.21569	−	0.861641i	0.107609	−	0.0288337i
$894$	−36.9481	+	17.0363i	−1.23573	+	0.569778i
$895$	−32.5622	−	16.6002i	−1.08843	−	0.554883i
$896$	−18.5209	+	18.5209i	−0.618741	+	0.618741i
$897$	57.7431	−	9.92598i	1.92798	−	0.331419i
$898$			7.73578i			0.258146i
$899$	−21.9081			−0.730675
$900$	−2.86899	+	36.3129i	−0.0956328	+	1.21043i
$901$	15.8583	−	4.24921i	0.528316	−	0.141562i
$902$	7.29236	−	7.29236i	0.242809	−	0.242809i
$903$	13.8471	+	9.78477i	0.460801	+	0.325617i
$904$	−5.35718	−	9.27891i	−0.178177	−	0.308612i
$905$	−1.12814	+	5.30183i	−0.0375008	+	0.176239i
$906$	3.95325	−	43.0540i	0.131338	−	1.43037i
$907$	6.59995	+	24.6313i	0.219148	+	0.817870i	0.984665	+	0.174455i	$0.0558164\pi$
$907$	6.59995	+	24.6313i	0.219148	+	0.817870i	−0.765517	+	0.643415i	$0.777517\pi$
$908$	−23.2859	−	6.23944i	−0.772770	−	0.207063i
$909$	6.50293	−	35.1124i	0.215688	−	1.16460i
$910$	25.4468	−	119.590i	0.843552	−	3.96436i
$911$	6.80584	−	6.80584i	0.225488	−	0.225488i	−0.585317	−	0.810805i	$-0.699030\pi$
$911$	6.80584	−	6.80584i	0.225488	−	0.225488i	0.810805	+	0.585317i	$0.199030\pi$
$912$	−1.84613	+	20.1058i	−0.0611315	+	0.665770i
$913$	1.28030	+	2.21755i	0.0423719	+	0.0733902i
$914$		−	46.8613i		−	1.55003i
$915$	11.4555	−	36.8731i	0.378709	−	1.21899i
$916$	0.0145275	−	0.00838746i	0.000480002	−	0.000277129i
$917$	12.8434	−	12.8434i	0.424127	−	0.424127i
$918$	0.469263	−	36.3952i	0.0154880	−	1.20122i
$919$	−10.0880	+	10.0880i	−0.332771	+	0.332771i	−0.853638	−	0.520867i	$-0.825609\pi$
$919$	−10.0880	+	10.0880i	−0.332771	+	0.332771i	0.520867	+	0.853638i	$0.325609\pi$
$920$	3.01236	+	9.27794i	0.0993144	+	0.305885i
$921$	16.4812	+	19.8139i	0.543075	+	0.652890i
$922$	−57.1427	−	32.9913i	−1.88189	−	1.08651i
$923$	−16.9057	+	63.0928i	−0.556457	+	2.07672i
$924$	−4.55742	+	12.3559i	−0.149928	+	0.406480i
$925$	−29.3160	+	8.09763i	−0.963904	+	0.266248i
$926$		−	24.3521i		−	0.800261i
$927$	9.66174	−	6.64220i	0.317333	−	0.218158i
$928$	26.2124	−	45.4012i	0.860464	−	1.49037i
$929$	21.8196	−	37.7926i	0.715876	−	1.23993i	−0.246744	−	0.969081i	$-0.579361\pi$
$929$	21.8196	−	37.7926i	0.715876	−	1.23993i	0.962621	−	0.270854i	$-0.0873059\pi$
$930$	−27.3328	−	1.07807i	−0.896279	−	0.0353512i
$931$	−18.9820	−	18.9820i	−0.622109	−	0.622109i
$932$	−31.8794	+	55.2167i	−1.04424	+	1.80868i
$933$	−47.7582	+	22.0206i	−1.56353	+	0.720923i
$934$	−15.3477	−	26.5830i	−0.502192	−	0.869822i
$935$	−0.326781	−	6.26142i	−0.0106869	−	0.204770i
$936$	14.3784	+	12.2770i	0.469972	+	0.401287i
$937$	26.9553	−	15.5626i	0.880590	−	0.508409i	0.00973736	−	0.999953i	$-0.496900\pi$
$937$	26.9553	−	15.5626i	0.880590	−	0.508409i	0.870853	+	0.491543i	$0.163567\pi$
$938$	−16.5220	+	4.42706i	−0.539463	+	0.144549i
$939$	−20.9313	−	45.3956i	−0.683066	−	1.48143i
$940$	−4.48929	−	0.955249i	−0.146425	−	0.0311568i
$941$	−36.1912	+	20.8950i	−1.17980	+	0.681157i	−0.955968	−	0.293471i	$-0.905190\pi$
$941$	−36.1912	+	20.8950i	−1.17980	+	0.681157i	−0.223831	+	0.974628i	$0.571856\pi$
$942$	−19.8243	−	14.0085i	−0.645910	−	0.456421i
$943$	27.1924	−	7.28619i	0.885508	−	0.237271i
$944$	0.514248	+	1.91920i	0.0167374	+	0.0624647i
$945$	−41.2448	+	12.8059i	−1.34169	+	0.416577i
$946$	−4.04312	+	2.33430i	−0.131453	+	0.0758945i
$947$	9.84307	−	36.7348i	0.319857	−	1.19372i	−0.599525	−	0.800356i	$-0.704644\pi$
$947$	9.84307	−	36.7348i	0.319857	−	1.19372i	0.919382	−	0.393366i	$-0.128689\pi$
$948$	28.0018	+	60.7301i	0.909455	+	1.97242i
$949$	21.0503	+	78.5607i	0.683321	+	2.55019i
$950$	33.5376	−	24.3442i	1.08810	−	0.789830i
$951$	−42.5810	−	15.7058i	−1.38078	−	0.509295i
$952$	−11.1543			−0.361513
$953$	−9.44073	+	5.45061i	−0.305815	+	0.176562i	−0.645052	−	0.764138i	$-0.723164\pi$
$953$	−9.44073	+	5.45061i	−0.305815	+	0.176562i	0.339237	+	0.940701i	$0.389831\pi$
$954$	31.0411	−	2.44709i	1.00499	−	0.0792276i
$955$	−8.03327	+	15.7577i	−0.259951	+	0.509907i
$956$	−23.1530	−	23.1530i	−0.748822	−	0.748822i
$957$	0.870831	−	9.48403i	0.0281500	−	0.306575i
$958$	−11.0232	−	6.36427i	−0.356144	−	0.205620i
$959$	−29.1777	−	16.8458i	−0.942199	−	0.543979i
$960$	22.7008	−	35.9666i	0.732667	−	1.16082i
$961$			19.7357i			0.636634i
$962$	−31.3871	+	83.7972i	−1.01196	+	2.70173i
$963$	−5.72566	−	4.88887i	−0.184507	−	0.157542i
$964$	15.0618	+	4.03580i	0.485109	+	0.129984i
$965$	3.44729	−	6.76205i	0.110972	−	0.217678i
$966$	−50.4004	+	41.9232i	−1.62161	+	1.34886i
$967$	11.4976	+	42.9097i	0.369738	+	1.37988i	0.860882	+	0.508804i	$0.169912\pi$
$967$	11.4976	+	42.9097i	0.369738	+	1.37988i	−0.491144	+	0.871078i	$0.663421\pi$
$968$	6.55991	+	6.55991i	0.210844	+	0.210844i
$969$	−17.4579	+	14.5215i	−0.560828	+	0.466498i
$970$	52.7823	−	58.5951i	1.69474	−	1.88137i
$971$	5.05899	−	2.92081i	0.162351	−	0.0937333i	−0.416623	−	0.909079i	$-0.636787\pi$
$971$	5.05899	−	2.92081i	0.162351	−	0.0937333i	0.578974	+	0.815346i	$0.303453\pi$
$972$	7.37297	−	37.1302i	0.236488	−	1.19095i
$973$	−2.52097			−0.0808186
$974$	10.9116	−	6.29980i	0.349629	−	0.201859i
$975$	0.770089	+	60.5353i	0.0246626	+	1.93868i
$976$	−20.8640	+	20.8640i	−0.667841	+	0.667841i
$977$	29.4657	+	7.89532i	0.942692	+	0.252594i	0.697259	−	0.716820i	$-0.254403\pi$
$977$	29.4657	+	7.89532i	0.942692	+	0.252594i	0.245434	+	0.969413i	$0.421070\pi$
$978$	−55.2397	+	9.49565i	−1.76637	+	0.303637i
$979$	2.60187	−	9.71032i	0.0831562	−	0.310343i
$980$	11.4291	+	35.2011i	0.365088	+	1.12446i
$981$	3.18642	+	1.51933i	0.101734	+	0.0485085i
$982$	−1.23733	+	4.61778i	−0.0394848	+	0.147359i
$983$	12.5666	−	7.25536i	0.400814	−	0.231410i	−0.286021	−	0.958223i	$-0.592333\pi$
$983$	12.5666	−	7.25536i	0.400814	−	0.231410i	0.686835	+	0.726813i	$0.258999\pi$
$984$	7.41904	+	5.24253i	0.236510	+	0.167126i
$985$	12.2254	+	11.0126i	0.389533	+	0.350891i
$986$	44.1666	−	11.8344i	1.40655	−	0.376884i
$987$	−0.921902	−	5.36304i	−0.0293445	−	0.170708i
$988$		−	66.8618i		−	2.12716i
$989$	−12.7441			−0.405237
$990$	1.55316	−	11.7896i	0.0493626	−	0.374697i
$991$	−4.84279	+	4.84279i	−0.153836	+	0.153836i	−0.779829	−	0.625993i	$-0.784694\pi$
$991$	−4.84279	+	4.84279i	−0.153836	+	0.153836i	0.625993	+	0.779829i	$0.284694\pi$
$992$	23.3436	+	13.4775i	0.741162	+	0.427910i
$993$	−15.7609	+	7.26713i	−0.500157	+	0.230615i
$994$	−18.9160	−	70.5955i	−0.599979	−	2.23915i
$995$	15.0700	−	29.5606i	0.477751	−	0.937135i
$996$	−9.82957	+	8.17626i	−0.311462	+	0.259075i
$997$	−27.7368	−	7.43204i	−0.878432	−	0.235375i	−0.208702	−	0.977979i	$-0.566924\pi$
$997$	−27.7368	−	7.43204i	−0.878432	−	0.235375i	−0.669731	+	0.742604i	$0.733590\pi$
$998$			7.40202i			0.234307i
$999$	31.2410	−	4.79582i	0.988422	−	0.151733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bm.a.119.11	yes	288
3.2	odd	2	inner	555.2.bm.a.119.61	yes	288
5.4	even	2	inner	555.2.bm.a.119.62	yes	288
15.14	odd	2	inner	555.2.bm.a.119.12	yes	288
37.14	odd	12	inner	555.2.bm.a.14.12	yes	288
111.14	even	12	inner	555.2.bm.a.14.62	yes	288
185.14	odd	12	inner	555.2.bm.a.14.61	yes	288
555.14	even	12	inner	555.2.bm.a.14.11	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bm.a.14.11	✓	288	555.14	even	12	inner
555.2.bm.a.14.12	yes	288	37.14	odd	12	inner
555.2.bm.a.14.61	yes	288	185.14	odd	12	inner
555.2.bm.a.14.62	yes	288	111.14	even	12	inner
555.2.bm.a.119.11	yes	288	1.1	even	1	trivial
555.2.bm.a.119.12	yes	288	15.14	odd	2	inner
555.2.bm.a.119.61	yes	288	3.2	odd	2	inner
555.2.bm.a.119.62	yes	288	5.4	even	2	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:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03267 - 0.544653i) q^{2} +(1.10763 + 1.33160i) q^{3} +(2.10306 + 1.21420i) q^{4} +(2.12678 - 0.690520i) q^{5} +(-1.52619 - 3.30998i) q^{6} +(3.21898 + 1.85848i) q^{7} +(-0.637478 - 0.637478i) q^{8} +(-0.546319 + 2.94984i) q^{9} +O(q^{10})\)	\(q+(-2.03267 - 0.544653i) q^{2} +(1.10763 + 1.33160i) q^{3} +(2.10306 + 1.21420i) q^{4} +(2.12678 - 0.690520i) q^{5} +(-1.52619 - 3.30998i) q^{6} +(3.21898 + 1.85848i) q^{7} +(-0.637478 - 0.637478i) q^{8} +(-0.546319 + 2.94984i) q^{9} +(-4.69914 + 0.245246i) q^{10} +0.842372 q^{11} +(0.712578 + 4.14532i) q^{12} +(1.80930 + 6.75239i) q^{13} +(-5.53090 - 5.53090i) q^{14} +(3.27518 + 2.06718i) q^{15} +(-1.47983 - 2.56313i) q^{16} +(0.861531 - 3.21528i) q^{17} +(2.71713 - 5.69850i) q^{18} +(-3.80441 + 1.01939i) q^{19} +(5.31118 + 1.13013i) q^{20} +(1.09068 + 6.34489i) q^{21} +(-1.71227 - 0.458800i) q^{22} +(-3.42164 - 3.42164i) q^{23} +(0.142777 - 1.55496i) q^{24} +(4.04636 - 2.93717i) q^{25} -14.7108i q^{26} +(-4.53312 + 2.53984i) q^{27} +(4.51314 + 7.81698i) q^{28} +(-4.61569 - 4.61569i) q^{29} +(-5.53147 - 5.98573i) q^{30} +(2.37322 - 2.37322i) q^{31} +(2.07865 + 7.75763i) q^{32} +(0.933035 + 1.12170i) q^{33} +(-3.50242 + 6.06637i) q^{34} +(8.12936 + 1.72980i) q^{35} +(-4.73064 + 5.54035i) q^{36} +(-5.69629 - 2.13360i) q^{37} +8.28833 q^{38} +(-6.98745 + 9.88839i) q^{39} +(-1.79597 - 0.915583i) q^{40} +(-2.90888 + 5.03832i) q^{41} +(1.23877 - 13.4911i) q^{42} +(1.86227 - 1.86227i) q^{43} +(1.77156 + 1.02281i) q^{44} +(0.875024 + 6.65089i) q^{45} +(5.09147 + 8.81868i) q^{46} -0.845254 q^{47} +(1.77397 - 4.80954i) q^{48} +(3.40787 + 5.90260i) q^{49} +(-9.82467 + 3.76643i) q^{50} +(5.23572 - 2.41412i) q^{51} +(-4.39371 + 16.3975i) q^{52} +(2.46608 + 4.27138i) q^{53} +(10.5977 - 2.69369i) q^{54} +(1.79154 - 0.581675i) q^{55} +(-0.867289 - 3.23677i) q^{56} +(-5.57129 - 3.93685i) q^{57} +(6.86824 + 11.8961i) q^{58} +(-0.648455 - 0.173753i) q^{59} +(4.37792 + 8.32413i) q^{60} +(-2.58029 - 9.62977i) q^{61} +(-6.11656 + 3.53140i) q^{62} +(-7.24079 + 8.48013i) q^{63} -10.9816i q^{64} +(8.51063 + 13.1115i) q^{65} +(-1.28562 - 2.78824i) q^{66} +(1.09340 - 1.89382i) q^{67} +(5.71585 - 5.71585i) q^{68} +(0.766351 - 8.34616i) q^{69} +(-15.5822 - 7.94379i) q^{70} +(8.09195 + 4.67189i) q^{71} +(2.22872 - 1.53219i) q^{72} +11.6345 q^{73} +(10.4166 + 7.43942i) q^{74} +(8.39300 + 2.13485i) q^{75} +(-9.23865 - 2.47549i) q^{76} +(2.71157 + 1.56553i) q^{77} +(19.5889 - 16.2941i) q^{78} +(15.3576 - 4.11506i) q^{79} +(-4.91716 - 4.42937i) q^{80} +(-8.40307 - 3.22310i) q^{81} +(8.65693 - 8.65693i) q^{82} +(1.51988 + 2.63251i) q^{83} +(-5.41022 + 14.6680i) q^{84} +(-0.387930 - 7.43308i) q^{85} +(-4.79969 + 2.77110i) q^{86} +(1.03378 - 11.2587i) q^{87} +(-0.536994 - 0.536994i) q^{88} +(3.08875 - 11.5274i) q^{89} +(1.84379 - 13.9957i) q^{90} +(-6.72507 + 25.0983i) q^{91} +(-3.04135 - 11.3505i) q^{92} +(5.78882 + 0.531535i) q^{93} +(1.71812 + 0.460370i) q^{94} +(-7.38722 + 4.79503i) q^{95} +(-8.02769 + 11.3605i) q^{96} +(-11.8508 + 11.8508i) q^{97} +(-3.71221 - 13.8542i) q^{98} +(-0.460204 + 2.48486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 24 q^{4} - 16 q^{6}+O(q^{10}) \) 288 * q - 24 * q^4 - 16 * q^6	\( 288 q - 24 q^{4} - 16 q^{6} - 16 q^{10} - 6 q^{15} + 112 q^{16} - 8 q^{19} - 12 q^{21} + 44 q^{24} - 12 q^{25} - 30 q^{30} - 72 q^{31} - 32 q^{34} - 4 q^{39} + 12 q^{40} + 16 q^{46} + 80 q^{49} + 12 q^{51} - 52 q^{54} - 28 q^{55} - 92 q^{60} - 8 q^{61} + 100 q^{66} - 104 q^{69} + 16 q^{70} + 52 q^{75} - 24 q^{76} + 16 q^{79} - 8 q^{81} - 192 q^{84} - 52 q^{90} - 168 q^{91} - 72 q^{94} - 112 q^{96} - 60 q^{99}+O(q^{100}) \) 288 * q - 24 * q^4 - 16 * q^6 - 16 * q^10 - 6 * q^15 + 112 * q^16 - 8 * q^19 - 12 * q^21 + 44 * q^24 - 12 * q^25 - 30 * q^30 - 72 * q^31 - 32 * q^34 - 4 * q^39 + 12 * q^40 + 16 * q^46 + 80 * q^49 + 12 * q^51 - 52 * q^54 - 28 * q^55 - 92 * q^60 - 8 * q^61 + 100 * q^66 - 104 * q^69 + 16 * q^70 + 52 * q^75 - 24 * q^76 + 16 * q^79 - 8 * q^81 - 192 * q^84 - 52 * q^90 - 168 * q^91 - 72 * q^94 - 112 * q^96 - 60 * q^99

Introduction

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