LMFDB - Embedded newform 280.2.ba.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(19,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("280.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	280.19
Dual form			280.2.ba.b.59.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39533 + 0.230335i) q^{2} +(-0.929162 - 1.60936i) q^{3} +(1.89389 - 0.642786i) q^{4} +(2.18875 - 0.457553i) q^{5} +(1.66718 + 2.03156i) q^{6} +(1.10610 - 2.40345i) q^{7} +(-2.49455 + 1.33313i) q^{8} +(-0.226682 + 0.392626i) q^{9} +O(q^{10})$	\(q+(-1.39533 + 0.230335i) q^{2} +(-0.929162 - 1.60936i) q^{3} +(1.89389 - 0.642786i) q^{4} +(2.18875 - 0.457553i) q^{5} +(1.66718 + 2.03156i) q^{6} +(1.10610 - 2.40345i) q^{7} +(-2.49455 + 1.33313i) q^{8} +(-0.226682 + 0.392626i) q^{9} +(-2.94864 + 1.14258i) q^{10} +(1.61069 + 2.78980i) q^{11} +(-2.79420 - 2.45069i) q^{12} +0.668981i q^{13} +(-0.989775 + 3.60837i) q^{14} +(-2.77007 - 3.09734i) q^{15} +(3.17365 - 2.43473i) q^{16} +(1.62295 + 2.81103i) q^{17} +(0.225862 - 0.600055i) q^{18} +(-5.77054 - 3.33162i) q^{19} +(3.85116 - 2.27346i) q^{20} +(-4.89574 + 0.453085i) q^{21} +(-2.89004 - 3.52170i) q^{22} +(4.41240 - 7.64251i) q^{23} +(4.46331 + 2.77592i) q^{24} +(4.58129 - 2.00294i) q^{25} +(-0.154089 - 0.933449i) q^{26} -4.73247 q^{27} +(0.549930 - 5.26285i) q^{28} -3.17360i q^{29} +(4.57859 + 3.68377i) q^{30} +(-2.58684 - 4.48053i) q^{31} +(-3.86749 + 4.12826i) q^{32} +(2.99319 - 5.18435i) q^{33} +(-2.91203 - 3.54850i) q^{34} +(1.32127 - 5.76665i) q^{35} +(-0.176938 + 0.889299i) q^{36} +(-1.15890 + 2.00727i) q^{37} +(8.81919 + 3.31956i) q^{38} +(1.07663 - 0.621591i) q^{39} +(-4.84998 + 4.05928i) q^{40} +9.34903i q^{41} +(6.72681 - 1.75986i) q^{42} +6.84531i q^{43} +(4.84372 + 4.24825i) q^{44} +(-0.316505 + 0.963080i) q^{45} +(-4.39643 + 11.6802i) q^{46} +(3.12812 + 1.80602i) q^{47} +(-6.86719 - 2.84528i) q^{48} +(-4.55310 - 5.31689i) q^{49} +(-5.93106 + 3.85000i) q^{50} +(3.01597 - 5.22381i) q^{51} +(0.430011 + 1.26698i) q^{52} +(0.0130049 + 0.0225252i) q^{53} +(6.60336 - 1.09005i) q^{54} +(4.80189 + 5.36921i) q^{55} +(0.444882 + 7.47008i) q^{56} +12.3825i q^{57} +(0.730989 + 4.42822i) q^{58} +(0.0160236 - 0.00925120i) q^{59} +(-7.23714 - 4.08547i) q^{60} +(0.897835 - 1.55510i) q^{61} +(4.64151 + 5.65598i) q^{62} +(0.692921 + 0.979101i) q^{63} +(4.44555 - 6.65110i) q^{64} +(0.306094 + 1.46423i) q^{65} +(-2.98235 + 7.92332i) q^{66} +(-4.14522 + 2.39324i) q^{67} +(4.88059 + 4.28059i) q^{68} -16.3993 q^{69} +(-0.515352 + 8.35071i) q^{70} +8.13591i q^{71} +(0.0420508 - 1.28162i) q^{72} +(-6.30342 - 10.9178i) q^{73} +(1.15470 - 3.06774i) q^{74} +(-7.48021 - 5.51186i) q^{75} +(-13.0703 - 2.60051i) q^{76} +(8.48672 - 0.785418i) q^{77} +(-1.35908 + 1.11531i) q^{78} +(13.5306 + 7.81192i) q^{79} +(5.83233 - 6.78115i) q^{80} +(5.07728 + 8.79410i) q^{81} +(-2.15340 - 13.0450i) q^{82} -6.60312 q^{83} +(-8.98077 + 4.00500i) q^{84} +(4.83844 + 5.41008i) q^{85} +(-1.57671 - 9.55146i) q^{86} +(-5.10745 + 2.94879i) q^{87} +(-7.73711 - 4.81204i) q^{88} +(-1.31681 - 0.760263i) q^{89} +(0.219798 - 1.41672i) q^{90} +(1.60786 + 0.739958i) q^{91} +(3.44412 - 17.3103i) q^{92} +(-4.80718 + 8.32628i) q^{93} +(-4.78076 - 1.79948i) q^{94} +(-14.1547 - 4.65177i) q^{95} +(10.2374 + 2.38835i) q^{96} +12.1700 q^{97} +(7.57774 + 6.37008i) q^{98} -1.46046 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{4} - 52 q^{9}+O(q^{10}) $ 80 * q + 6 * q^4 - 52 * q^9	$ 80 q + 6 q^{4} - 52 q^{9} - 12 q^{10} - 6 q^{14} + 10 q^{16} - 48 q^{19} + 12 q^{24} - 22 q^{25} + 54 q^{26} - 20 q^{30} - 22 q^{35} + 28 q^{36} + 12 q^{40} + 38 q^{44} + 14 q^{46} + 16 q^{49} - 40 q^{50} + 20 q^{51} + 60 q^{54} - 104 q^{56} - 60 q^{59} - 42 q^{60} - 60 q^{64} - 12 q^{65} + 84 q^{66} - 22 q^{70} + 34 q^{74} - 6 q^{75} - 96 q^{80} - 100 q^{84} - 8 q^{86} - 36 q^{89} + 72 q^{91} - 66 q^{94} + 96 q^{96} + 104 q^{99}+O(q^{100}) $ 80 * q + 6 * q^4 - 52 * q^9 - 12 * q^10 - 6 * q^14 + 10 * q^16 - 48 * q^19 + 12 * q^24 - 22 * q^25 + 54 * q^26 - 20 * q^30 - 22 * q^35 + 28 * q^36 + 12 * q^40 + 38 * q^44 + 14 * q^46 + 16 * q^49 - 40 * q^50 + 20 * q^51 + 60 * q^54 - 104 * q^56 - 60 * q^59 - 42 * q^60 - 60 * q^64 - 12 * q^65 + 84 * q^66 - 22 * q^70 + 34 * q^74 - 6 * q^75 - 96 * q^80 - 100 * q^84 - 8 * q^86 - 36 * q^89 + 72 * q^91 - 66 * q^94 + 96 * q^96 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.39533	+	0.230335i	−0.986647	+	0.162871i
$2$	−1.39533	+	0.230335i	−0.986647	+	0.162871i
$3$	−0.929162	−	1.60936i	−0.536452	−	0.929162i	−0.999092	−	0.0426153i	$-0.986431\pi$
$3$	−0.929162	−	1.60936i	−0.536452	−	0.929162i	0.462640	−	0.886546i	$-0.346902\pi$
$4$	1.89389	−	0.642786i	0.946946	−	0.321393i
$5$	2.18875	−	0.457553i	0.978841	−	0.204624i
$5$	2.18875	−	0.457553i	0.978841	−	0.204624i
$6$	1.66718	+	2.03156i	0.680622	+	0.829382i
$7$	1.10610	−	2.40345i	0.418066	−	0.908417i
$7$	1.10610	−	2.40345i	0.418066	−	0.908417i
$8$	−2.49455	+	1.33313i	−0.881956	+	0.471331i
$9$	−0.226682	+	0.392626i	−0.0755608	+	0.130875i
$10$	−2.94864	+	1.14258i	−0.932443	+	0.361317i
$11$	1.61069	+	2.78980i	0.485642	+	0.841157i	0.999864	−	0.0165005i	$-0.00525252\pi$
$11$	1.61069	+	2.78980i	0.485642	+	0.841157i	−0.514222	+	0.857657i	$0.671919\pi$
$12$	−2.79420	−	2.45069i	−0.806617	−	0.707454i
$13$			0.668981i			0.185542i	0.995687	+	0.0927710i	$0.0295724\pi$
$13$			0.668981i			0.185542i	−0.995687	+	0.0927710i	$0.970428\pi$
$14$	−0.989775	+	3.60837i	−0.264528	+	0.964378i
$15$	−2.77007	−	3.09734i	−0.715230	−	0.799730i
$16$	3.17365	−	2.43473i	0.793413	−	0.608683i
$17$	1.62295	+	2.81103i	0.393624	+	0.681776i	0.992924	−	0.118748i	$-0.0378880\pi$
$17$	1.62295	+	2.81103i	0.393624	+	0.681776i	−0.599301	+	0.800524i	$0.704555\pi$
$18$	0.225862	−	0.600055i	0.0532361	−	0.141434i
$19$	−5.77054	−	3.33162i	−1.32385	−	0.764326i	−0.339511	−	0.940602i	$-0.610262\pi$
$19$	−5.77054	−	3.33162i	−1.32385	−	0.764326i	−0.984341	+	0.176276i	$0.943595\pi$
$20$	3.85116	−	2.27346i	0.861145	−	0.508360i
$21$	−4.89574	+	0.453085i	−1.06834	+	0.0988712i
$22$	−2.89004	−	3.52170i	−0.616158	−	0.750828i
$23$	4.41240	−	7.64251i	0.920050	−	1.59357i	0.120715	−	0.992687i	$-0.461481\pi$
$23$	4.41240	−	7.64251i	0.920050	−	1.59357i	0.799335	−	0.600886i	$-0.205185\pi$
$24$	4.46331	+	2.77592i	0.911070	+	0.566633i
$25$	4.58129	−	2.00294i	0.916258	−	0.400589i
$26$	−0.154089	−	0.933449i	−0.0302194	−	0.183064i
$27$	−4.73247			−0.910764
$28$	0.549930	−	5.26285i	0.103927	−	0.994585i
$29$		−	3.17360i		−	0.589322i	−0.955602	−	0.294661i	$-0.904793\pi$
$29$		−	3.17360i		−	0.589322i	0.955602	−	0.294661i	$-0.0952068\pi$
$30$	4.57859	+	3.68377i	0.835932	+	0.672561i
$31$	−2.58684	−	4.48053i	−0.464609	−	0.804727i	0.534574	−	0.845121i	$-0.320472\pi$
$31$	−2.58684	−	4.48053i	−0.464609	−	0.804727i	−0.999184	+	0.0403943i	$0.987139\pi$
$32$	−3.86749	+	4.12826i	−0.683682	+	0.729780i
$33$	2.99319	−	5.18435i	0.521047	−	0.902480i
$34$	−2.91203	−	3.54850i	−0.499409	−	0.608562i
$35$	1.32127	−	5.76665i	0.223336	−	0.974742i
$36$	−0.176938	+	0.889299i	−0.0294897	+	0.148216i
$37$	−1.15890	+	2.00727i	−0.190522	+	0.329994i	−0.945423	−	0.325845i	$-0.894351\pi$
$37$	−1.15890	+	2.00727i	−0.190522	+	0.329994i	0.754901	+	0.655838i	$0.227685\pi$
$38$	8.81919	+	3.31956i	1.43066	+	0.538503i
$39$	1.07663	−	0.621591i	0.172398	−	0.0995343i
$40$	−4.84998	+	4.05928i	−0.766849	+	0.641828i
$41$			9.34903i			1.46007i	0.683408	+	0.730036i	$0.260497\pi$
$41$			9.34903i			1.46007i	−0.683408	+	0.730036i	$0.739503\pi$
$42$	6.72681	−	1.75986i	1.03797	−	0.271552i
$43$			6.84531i			1.04390i	0.852976	+	0.521950i	$0.174795\pi$
$43$			6.84531i			1.04390i	−0.852976	+	0.521950i	$0.825205\pi$
$44$	4.84372	+	4.24825i	0.730218	+	0.640448i
$45$	−0.316505	+	0.963080i	−0.0471818	+	0.143568i
$46$	−4.39643	+	11.6802i	−0.648218	+	1.72214i
$47$	3.12812	+	1.80602i	0.456284	+	0.263436i	0.710480	−	0.703717i	$-0.248478\pi$
$47$	3.12812	+	1.80602i	0.456284	+	0.263436i	−0.254197	+	0.967153i	$0.581811\pi$
$48$	−6.86719	−	2.84528i	−0.991193	−	0.410680i
$49$	−4.55310	−	5.31689i	−0.650442	−	0.759556i
$50$	−5.93106	+	3.85000i	−0.838779	+	0.544472i
$51$	3.01597	−	5.22381i	0.422320	−	0.731480i
$52$	0.430011	+	1.26698i	0.0596318	+	0.175698i
$53$	0.0130049	+	0.0225252i	0.00178637	+	0.00309408i	0.866917	−	0.498452i	$-0.166098\pi$
$53$	0.0130049	+	0.0225252i	0.00178637	+	0.00309408i	−0.865131	+	0.501546i	$0.832765\pi$
$54$	6.60336	−	1.09005i	0.898603	−	0.148337i
$55$	4.80189	+	5.36921i	0.647487	+	0.723984i
$56$	0.444882	+	7.47008i	0.0594499	+	0.998231i
$57$			12.3825i			1.64010i
$58$	0.730989	+	4.42822i	0.0959836	+	0.581453i
$59$	0.0160236	−	0.00925120i	0.00208609	−	0.00120440i	−0.498957	−	0.866627i	$-0.666283\pi$
$59$	0.0160236	−	0.00925120i	0.00208609	−	0.00120440i	0.501043	+	0.865423i	$0.332950\pi$
$60$	−7.23714	−	4.08547i	−0.934311	−	0.527432i
$61$	0.897835	−	1.55510i	0.114956	−	0.199110i	−0.802806	−	0.596240i	$-0.796661\pi$
$61$	0.897835	−	1.55510i	0.114956	−	0.199110i	0.917762	+	0.397130i	$0.129994\pi$
$62$	4.64151	+	5.65598i	0.589473	+	0.718310i
$63$	0.692921	+	0.979101i	0.0872998	+	0.123355i
$64$	4.44555	−	6.65110i	0.555693	−	0.831387i
$65$	0.306094	+	1.46423i	0.0379663	+	0.181616i
$66$	−2.98235	+	7.92332i	−0.367102	+	0.975293i
$67$	−4.14522	+	2.39324i	−0.506419	+	0.292381i	−0.731360	−	0.681991i	$-0.761114\pi$
$67$	−4.14522	+	2.39324i	−0.506419	+	0.292381i	0.224942	+	0.974372i	$0.427781\pi$
$68$	4.88059	+	4.28059i	0.591858	+	0.519097i
$69$	−16.3993			−1.97425
$70$	−0.515352	+	8.35071i	−0.0615963	+	0.998101i
$71$			8.13591i			0.965555i	0.875743	+	0.482778i	$0.160372\pi$
$71$			8.13591i			0.965555i	−0.875743	+	0.482778i	$0.839628\pi$
$72$	0.0420508	−	1.28162i	0.00495574	−	0.151040i
$73$	−6.30342	−	10.9178i	−0.737760	−	1.27784i	−0.953502	−	0.301387i	$-0.902550\pi$
$73$	−6.30342	−	10.9178i	−0.737760	−	1.27784i	0.215742	−	0.976450i	$-0.430783\pi$
$74$	1.15470	−	3.06774i	0.134232	−	0.356618i
$75$	−7.48021	−	5.51186i	−0.863740	−	0.636455i
$76$	−13.0703	−	2.60051i	−1.49926	−	0.298299i
$77$	8.48672	−	0.785418i	0.967151	−	0.0895067i
$78$	−1.35908	+	1.11531i	−0.153885	+	0.126284i
$79$	13.5306	+	7.81192i	1.52232	+	0.878910i	0.999652	+	0.0263718i	$0.00839538\pi$
$79$	13.5306	+	7.81192i	1.52232	+	0.878910i	0.522665	+	0.852538i	$0.324938\pi$
$80$	5.83233	−	6.78115i	0.652074	−	0.758155i
$81$	5.07728	+	8.79410i	0.564142	+	0.977123i
$82$	−2.15340	−	13.0450i	−0.237804	−	1.44058i
$83$	−6.60312			−0.724787			−0.362393	−	0.932025i	$-0.618040\pi$
$83$	−6.60312			−0.724787			−0.362393	+	0.932025i	$0.618040\pi$
$84$	−8.98077	+	4.00500i	−0.979882	+	0.436982i
$85$	4.83844	+	5.41008i	0.524802	+	0.586805i
$86$	−1.57671	−	9.55146i	−0.170021	−	1.02996i
$87$	−5.10745	+	2.94879i	−0.547576	+	0.316143i
$88$	−7.73711	−	4.81204i	−0.824779	−	0.512965i
$89$	−1.31681	−	0.760263i	−0.139582	−	0.0805877i	0.428583	−	0.903503i	$-0.359013\pi$
$89$	−1.31681	−	0.760263i	−0.139582	−	0.0805877i	−0.568165	+	0.822915i	$0.692346\pi$
$90$	0.219798	−	1.41672i	0.0231688	−	0.149335i
$91$	1.60786	+	0.739958i	0.168549	+	0.0775687i
$92$	3.44412	−	17.3103i	0.359075	−	1.80473i
$93$	−4.80718	+	8.32628i	−0.498481	+	0.863395i
$94$	−4.78076	−	1.79948i	−0.493097	−	0.185603i
$95$	−14.1547	−	4.65177i	−1.45224	−	0.477262i
$96$	10.2374	+	2.38835i	1.04485	+	0.243760i
$97$	12.1700			1.23568			0.617839	−	0.786305i	$-0.288008\pi$
$97$	12.1700			1.23568			0.617839	+	0.786305i	$0.288008\pi$
$98$	7.57774	+	6.37008i	0.765467	+	0.643475i
$99$	−1.46046			−0.146782
$100$	7.38901	−	6.73814i	0.738901	−	0.673814i
$101$	7.06658	+	12.2397i	0.703151	+	1.21789i	0.967355	+	0.253426i	$0.0815574\pi$
$101$	7.06658	+	12.2397i	0.703151	+	1.21789i	−0.264204	+	0.964467i	$0.585109\pi$
$102$	−3.00505	+	7.98362i	−0.297544	+	0.790496i
$103$	0.433570	+	0.250322i	0.0427209	+	0.0246649i	0.521208	−	0.853429i	$-0.325481\pi$
$103$	0.433570	+	0.250322i	0.0427209	+	0.0246649i	−0.478487	+	0.878094i	$0.658815\pi$
$104$	−0.891836	−	1.66881i	−0.0874517	−	0.163640i
$105$	−10.5083	+	3.23175i	−1.02550	+	0.315387i
$106$	−0.0233345	−	0.0284346i	−0.00226645	−	0.00276181i
$107$	16.0652	+	9.27527i	1.55309	+	0.896674i	0.997888	+	0.0649558i	$0.0206907\pi$
$107$	16.0652	+	9.27527i	1.55309	+	0.896674i	0.555197	+	0.831719i	$0.312643\pi$
$108$	−8.96279	+	3.04196i	−0.862445	+	0.292713i
$109$	3.92950	−	2.26870i	0.376378	−	0.217302i	−0.299863	−	0.953982i	$-0.596941\pi$
$109$	3.92950	−	2.26870i	0.376378	−	0.217302i	0.676241	+	0.736680i	$0.263608\pi$
$110$	−7.93694	−	6.38578i	−0.756758	−	0.608860i
$111$	4.30722			0.408823
$112$	−2.34138	−	10.3208i	−0.221239	−	0.975220i
$113$			6.94668i			0.653489i	0.945113	+	0.326744i	$0.105952\pi$
$113$			6.94668i			0.653489i	−0.945113	+	0.326744i	$0.894048\pi$
$114$	−2.85211	−	17.2776i	−0.267124	−	1.61820i
$115$	6.16081	−	18.7465i	0.574499	−	1.74812i
$116$	−2.03994	−	6.01045i	−0.189404	−	0.558056i
$117$	−0.262659	−	0.151646i	−0.0242828	−	0.0140197i
$118$	−0.0202273	+	0.0165993i	−0.00186207	+	0.00152809i
$119$	8.55131	−	0.791396i	0.783897	−	0.0725471i
$120$	11.0392	+	4.03361i	1.00774	+	0.368217i
$121$	0.311339	−	0.539255i	0.0283036	−	0.0490232i
$122$	−0.894584	+	2.37667i	−0.0809918	+	0.215174i
$123$	15.0459	−	8.68675i	1.35664	−	0.783258i
$124$	−7.77921	−	6.82286i	−0.698594	−	0.612711i
$125$	9.11086	−	6.48013i	0.814901	−	0.579601i
$126$	−1.19237	−	1.20657i	−0.106225	−	0.107489i
$127$	−5.54642			−0.492166			−0.246083	−	0.969249i	$-0.579144\pi$
$127$	−5.54642			−0.492166			−0.246083	+	0.969249i	$0.579144\pi$
$128$	−4.67103	+	10.3044i	−0.412864	+	0.910793i
$129$	11.0165	−	6.36040i	0.969951	−	0.560002i
$130$	−0.764367	−	1.97259i	−0.0670394	−	0.173007i
$131$	1.39758	+	0.806895i	0.122107	+	0.0704987i	0.559810	−	0.828621i	$-0.310874\pi$
$131$	1.39758	+	0.806895i	0.122107	+	0.0704987i	−0.437702	+	0.899120i	$0.644208\pi$
$132$	2.33635	−	11.7426i	0.203353	−	1.02206i
$133$	−14.3901	+	10.1841i	−1.24778	+	0.883071i
$134$	5.23270	−	4.29415i	0.452036	−	0.370958i
$135$	−10.3582	+	2.16536i	−0.891493	+	0.186364i
$136$	−7.79600	−	4.84866i	−0.668501	−	0.415769i
$137$	−7.25548	+	4.18895i	−0.619877	+	0.357886i	−0.776821	−	0.629721i	$-0.783169\pi$
$137$	−7.25548	+	4.18895i	−0.619877	+	0.357886i	0.156944	+	0.987607i	$0.449836\pi$
$138$	22.8825	−	3.77734i	1.94789	−	0.321548i
$139$			10.1284i			0.859077i	0.903048	+	0.429539i	$0.141324\pi$
$139$			10.1284i			0.859077i	−0.903048	+	0.429539i	$0.858676\pi$
$140$	−1.20437	−	11.7707i	−0.101788	−	0.994806i
$141$		−	6.71235i		−	0.565282i
$142$	−1.87398	−	11.3523i	−0.157261	−	0.952662i
$143$	−1.86632	+	1.07752i	−0.156070	+	0.0901070i
$144$	0.236527	+	1.79797i	0.0197105	+	0.149831i
$145$	−1.45209	−	6.94623i	−0.120590	−	0.576853i
$146$	11.3101	+	13.7821i	0.936031	+	1.14061i
$147$	−4.32620	+	12.2678i	−0.356819	+	1.01183i
$148$	−0.904585	+	4.54648i	−0.0743564	+	0.373719i
$149$	−2.14985	−	1.24122i	−0.176123	−	0.101684i	0.409347	−	0.912379i	$-0.365757\pi$
$149$	−2.14985	−	1.24122i	−0.176123	−	0.101684i	−0.585470	+	0.810694i	$0.699090\pi$
$150$	11.7069	+	5.96792i	0.955867	+	0.487279i
$151$	−2.38942	+	1.37954i	−0.194449	+	0.112265i	−0.594063	−	0.804418i	$-0.702477\pi$
$151$	−2.38942	+	1.37954i	−0.194449	+	0.112265i	0.399615	+	0.916683i	$0.369144\pi$
$152$	18.8364	+	0.618034i	1.52783	+	0.0501292i
$153$	−1.47158			−0.118970
$154$	−11.6609	+	3.05070i	−0.939659	+	0.245833i
$155$	−7.71203	−	8.62317i	−0.619445	−	0.692629i
$156$	1.63947	−	1.86927i	0.131262	−	0.149661i
$157$	−4.55831	+	2.63174i	−0.363793	+	0.210036i	−0.670743	−	0.741690i	$-0.734025\pi$
$157$	−4.55831	+	2.63174i	−0.363793	+	0.210036i	0.306951	+	0.951725i	$0.400691\pi$
$158$	−20.6791	−	7.78364i	−1.64514	−	0.619233i
$159$	0.0241674	−	0.0418591i	0.00191660	−	0.00331964i
$160$	−6.57609	+	10.8053i	−0.519886	+	0.854236i
$161$	−13.4878	−	19.0583i	−1.06299	−	1.50201i
$162$	−9.11006	−	11.1012i	−0.715754	−	0.872193i
$163$	3.72563	+	2.15099i	0.291814	+	0.168479i	0.638760	−	0.769406i	$-0.279448\pi$
$163$	3.72563	+	2.15099i	0.291814	+	0.168479i	−0.346946	+	0.937885i	$0.612781\pi$
$164$	6.00942	+	17.7060i	0.469257	+	1.38261i
$165$	4.17923	−	12.7168i	0.325353	−	0.990003i
$166$	9.21353	−	1.52093i	0.715109	−	0.118047i
$167$		−	3.88102i		−	0.300322i	−0.988662	−	0.150161i	$-0.952021\pi$
$167$		−	3.88102i		−	0.300322i	0.988662	−	0.150161i	$-0.0479792\pi$
$168$	11.6086	−	7.65688i	0.895626	−	0.590741i
$169$	12.5525			0.965574
$170$	−7.99735	−	6.43438i	−0.613369	−	0.493495i
$171$	2.61616	−	1.51044i	0.200063	−	0.115506i
$172$	4.40006	+	12.9643i	0.335502	+	0.988516i
$173$	−14.3964	−	8.31178i	−1.09454	−	0.631933i	−0.159758	−	0.987156i	$-0.551071\pi$
$173$	−14.3964	−	8.31178i	−1.09454	−	0.631933i	−0.934781	+	0.355223i	$0.884405\pi$
$174$	6.44737	−	5.29095i	0.488774	−	0.401106i
$175$	0.253390	−	13.2263i	0.0191545	−	0.999817i
$176$	11.9042	+	4.93226i	0.897313	+	0.371783i
$177$	−0.0297769	−	0.0171917i	−0.00223817	−	0.00129221i
$178$	2.01250	+	0.757510i	0.150844	+	0.0567777i
$179$	7.95928	+	13.7859i	0.594905	+	1.03040i	0.993560	+	0.113304i	$0.0361435\pi$
$179$	7.95928	+	13.7859i	0.594905	+	1.03040i	−0.398656	+	0.917101i	$0.630523\pi$
$180$	0.0196275	+	2.02741i	0.00146294	+	0.151115i
$181$	7.50289			0.557685			0.278843	−	0.960337i	$-0.410049\pi$
$181$	7.50289			0.557685			0.278843	+	0.960337i	$0.410049\pi$
$182$	−2.41393	−	0.662140i	−0.178933	−	0.0490811i
$183$	−3.33693			−0.246673
$184$	−0.818525	+	24.9469i	−0.0603425	+	1.83911i
$185$	−1.61811	+	4.92369i	−0.118966	+	0.361997i
$186$	4.78977	−	12.7252i	0.351203	−	0.933054i
$187$	−5.22815	+	9.05542i	−0.382320	+	0.662198i
$188$	7.08522	+	1.40970i	0.516742	+	0.102813i
$189$	−5.23458	+	11.3742i	−0.380759	+	0.827354i
$190$	20.8219	+	3.23044i	1.51058	+	0.234361i
$191$	−12.2310	−	7.06156i	−0.885002	−	0.510956i	−0.0126977	−	0.999919i	$-0.504042\pi$
$191$	−12.2310	−	7.06156i	−0.885002	−	0.510956i	−0.872304	+	0.488963i	$0.837375\pi$
$192$	−14.8346	−	0.974517i	−1.07060	−	0.0703297i
$193$	7.10077	−	4.09963i	0.511124	−	0.295098i	−0.222171	−	0.975008i	$-0.571314\pi$
$193$	7.10077	−	4.09963i	0.511124	−	0.295098i	0.733296	+	0.679910i	$0.237981\pi$
$194$	−16.9812	+	2.80318i	−1.21918	+	0.201256i
$195$	2.07206	−	1.85313i	0.148383	−	0.132705i
$196$	−12.0407	−	7.14295i	−0.860049	−	0.510211i
$197$	6.63166			0.472486			0.236243	−	0.971694i	$-0.424084\pi$
$197$	6.63166			0.472486			0.236243	+	0.971694i	$0.424084\pi$
$198$	2.03783	−	0.336395i	0.144822	−	0.0239066i
$199$	−1.78141	−	3.08549i	−0.126281	−	0.218725i	0.795952	−	0.605360i	$-0.206971\pi$
$199$	−1.78141	−	3.08549i	−0.126281	−	0.218725i	−0.922233	+	0.386635i	$0.873637\pi$
$200$	−8.75807	+	11.1039i	−0.619289	+	0.785163i
$201$	7.70315	+	4.44742i	0.543338	+	0.313697i
$202$	−12.6794	−	15.4507i	−0.892121	−	1.08711i
$203$	−7.62757	−	3.51031i	−0.535350	−	0.246375i
$204$	2.35413	−	11.8320i	0.164822	−	0.828402i
$205$	4.27768	+	20.4627i	0.298766	+	1.42918i
$206$	−0.662631	−	0.249415i	−0.0461677	−	0.0173776i
$207$	2.00043	+	3.46485i	0.139039	+	0.240823i
$208$	1.62879	+	2.12311i	0.112936	+	0.147211i
$209$		−	21.4649i		−	1.48476i
$210$	13.9181	−	6.92978i	0.960441	−	0.478200i
$211$	−13.5590			−0.933438			−0.466719	−	0.884406i	$-0.654564\pi$
$211$	−13.5590			−0.933438			−0.466719	+	0.884406i	$0.654564\pi$
$212$	0.0391088	+	0.0343009i	0.00268601	+	0.00235580i
$213$	13.0936	−	7.55958i	0.897157	−	0.517974i
$214$	−24.5527	−	9.24169i	−1.67839	−	0.631749i
$215$	3.13209	+	14.9827i	0.213607	+	1.02181i
$216$	11.8054	−	6.30898i	0.803254	−	0.429272i
$217$	−13.6300	+	1.26141i	−0.925265	+	0.0856303i
$218$	−4.96039	+	4.07068i	−0.335960	+	0.275702i
$219$	−11.7138	+	20.2889i	−0.791545	+	1.37100i
$220$	12.5455	+	7.08212i	0.845819	+	0.477476i
$221$	−1.88053	+	1.08572i	−0.126498	+	0.0730337i
$222$	−6.01000	+	0.992102i	−0.403365	+	0.0665855i
$223$			17.5244i			1.17352i	0.809760	+	0.586761i	$0.199597\pi$
$223$			17.5244i			1.17352i	−0.809760	+	0.586761i	$0.800403\pi$
$224$	5.64422	+	13.8616i	0.377120	+	0.926164i
$225$	−0.252091	+	2.25276i	−0.0168061	+	0.150184i
$226$	−1.60006	−	9.69291i	−0.106434	−	0.644763i
$227$	−5.47563	−	9.48408i	−0.363431	−	0.629480i	0.625092	−	0.780551i	$-0.285061\pi$
$227$	−5.47563	−	9.48408i	−0.363431	−	0.629480i	−0.988523	+	0.151071i	$0.951728\pi$
$228$	7.95926	+	23.4510i	0.527115	+	1.55308i
$229$	9.35182	−	16.1978i	0.617985	−	1.07038i	−0.371867	−	0.928286i	$-0.621282\pi$
$229$	9.35182	−	16.1978i	0.617985	−	1.07038i	0.989853	−	0.142096i	$-0.0453842\pi$
$230$	−4.27841	+	27.5766i	−0.282110	+	1.81835i
$231$	−9.14955	−	12.9284i	−0.601996	−	0.850624i
$232$	4.23081	+	7.91670i	0.277766	+	0.519757i
$233$	−3.70368	−	2.13832i	−0.242636	−	0.140086i	0.373752	−	0.927529i	$-0.378071\pi$
$233$	−3.70368	−	2.13832i	−0.242636	−	0.140086i	−0.616388	+	0.787443i	$0.711405\pi$
$234$	0.401425	+	0.151097i	0.0262420	+	0.00987753i
$235$	7.67305	+	2.52166i	0.500534	+	0.164495i
$236$	0.0244003	−	0.0278205i	0.00158833	−	0.00181096i
$237$		−	29.0342i		−	1.88597i
$238$	−11.7496	+	3.07392i	−0.761614	+	0.199253i
$239$			25.1064i			1.62400i	0.583658	+	0.812000i	$0.301621\pi$
$239$			25.1064i			1.62400i	−0.583658	+	0.812000i	$0.698379\pi$
$240$	−16.3324	−	3.08551i	−1.05425	−	0.199169i
$241$	1.69808	−	0.980389i	0.109383	−	0.0631524i	−0.444310	−	0.895873i	$-0.646551\pi$
$241$	1.69808	−	0.980389i	0.109383	−	0.0631524i	0.553694	+	0.832721i	$0.313218\pi$
$242$	−0.310212	+	0.824152i	−0.0199412	+	0.0529785i
$243$	2.33652	−	4.04696i	0.149888	−	0.259613i
$244$	0.700809	−	3.52230i	0.0448647	−	0.225492i
$245$	−12.3984	−	9.55408i	−0.792103	−	0.610388i
$246$	−18.9931	+	15.5865i	−1.21096	+	0.993758i
$247$	2.22879	−	3.86038i	0.141815	−	0.245630i
$248$	12.4261	+	7.72832i	0.789058	+	0.490749i
$249$	6.13537	+	10.6268i	0.388813	+	0.673444i
$250$	−11.2201	+	11.1405i	−0.709619	+	0.704585i
$251$			10.2716i			0.648336i	0.945999	+	0.324168i	$0.105084\pi$
$251$			10.2716i			0.648336i	−0.945999	+	0.324168i	$0.894916\pi$
$252$	1.94167	+	1.40891i	0.122314	+	0.0887531i
$253$	28.4281			1.78726
$254$	7.73909	−	1.27753i	0.485594	−	0.0801596i
$255$	4.21104	−	12.8136i	0.263706	−	0.802419i
$256$	4.14415	−	15.4540i	0.259010	−	0.965875i
$257$	−4.42809	+	7.66968i	−0.276217	+	0.478422i	−0.970441	−	0.241337i	$-0.922414\pi$
$257$	−4.42809	+	7.66968i	−0.276217	+	0.478422i	0.694225	+	0.719759i	$0.255747\pi$
$258$	−13.9067	+	11.4123i	−0.865792	+	0.710501i
$259$	3.54252	+	5.00559i	0.220121	+	0.311032i
$260$	1.52090	+	2.57635i	0.0943221	+	0.159778i
$261$	1.24604	+	0.719399i	0.0771277	+	0.0445297i
$262$	−2.13595	−	0.803973i	−0.131959	−	0.0496696i
$263$	6.21178	+	10.7591i	0.383035	+	0.663436i	0.991494	−	0.130149i	$-0.0415455\pi$
$263$	6.21178	+	10.7591i	0.383035	+	0.663436i	−0.608459	+	0.793585i	$0.708212\pi$
$264$	−0.555253	+	16.9229i	−0.0341734	+	1.04153i
$265$	0.0387711	+	0.0433517i	0.00238169	+	0.00266307i
$266$	17.7333	−	17.5247i	1.08730	−	1.07451i
$267$			2.82563i			0.172926i
$268$	−6.31225	+	7.19703i	−0.385582	+	0.439628i
$269$	−13.6032	−	23.5615i	−0.829403	−	1.43657i	−0.898507	−	0.438959i	$-0.855347\pi$
$269$	−13.6032	−	23.5615i	−0.829403	−	1.43657i	0.0691035	−	0.997609i	$-0.477986\pi$
$270$	13.9544	−	5.40724i	0.849236	−	0.329074i
$271$	−5.19784	+	9.00292i	−0.315746	+	0.546889i	−0.979596	−	0.200978i	$-0.935588\pi$
$271$	−5.19784	+	9.00292i	−0.315746	+	0.546889i	0.663850	+	0.747866i	$0.268922\pi$
$272$	11.9948	+	4.96980i	0.727292	+	0.301338i
$273$	−0.303105	−	3.27516i	−0.0183448	−	0.198221i
$274$	9.15892	−	7.51616i	0.553311	−	0.454068i
$275$	12.9669	+	9.55476i	0.781931	+	0.576174i
$276$	−31.0586	+	10.5413i	−1.86951	+	0.634509i
$277$	10.2142	+	17.6915i	0.613711	+	1.06298i	0.990609	+	0.136724i	$0.0436574\pi$
$277$	10.2142	+	17.6915i	0.613711	+	1.06298i	−0.376898	+	0.926255i	$0.623009\pi$
$278$	−2.33291	−	14.1324i	−0.139919	−	0.847606i
$279$	2.34556			0.140425
$280$	4.39170	+	16.1466i	0.262454	+	0.964944i
$281$	−31.1658			−1.85919			−0.929597	−	0.368578i	$-0.879845\pi$
$281$	−31.1658			−1.85919			−0.929597	+	0.368578i	$0.879845\pi$
$282$	1.54609	+	9.36594i	0.0920681	+	0.557734i
$283$	7.09232	+	12.2843i	0.421594	+	0.730223i	0.996096	−	0.0882807i	$-0.0281373\pi$
$283$	7.09232	+	12.2843i	0.421594	+	0.730223i	−0.574501	+	0.818504i	$0.694804\pi$
$284$	5.22965	+	15.4085i	0.310322	+	0.914329i
$285$	5.66563	+	27.1021i	0.335603	+	1.60539i
$286$	2.35595	−	1.93338i	0.139310	−	0.114323i
$287$	22.4699	+	10.3409i	1.32635	+	0.610406i
$288$	−0.744167	−	2.45428i	−0.0438505	−	0.144620i
$289$	3.23206	−	5.59809i	0.190121	−	0.329299i
$290$	3.62610	+	9.35781i	0.212932	+	0.549510i
$291$	−11.3079	−	19.5859i	−0.662881	−	1.14814i
$292$	−18.9558	−	16.6255i	−1.10931	−	0.972932i
$293$		−	13.3400i		−	0.779333i	−0.920956	−	0.389666i	$-0.872590\pi$
$293$		−	13.3400i		−	0.779333i	0.920956	−	0.389666i	$-0.127410\pi$
$294$	3.21078	−	18.1141i	0.187257	−	1.05644i
$295$	0.0308387	−	0.0275802i	0.00179550	−	0.00160578i
$296$	0.214982	−	6.55220i	0.0124956	−	0.380839i
$297$	−7.62256	−	13.2027i	−0.442306	−	0.766096i
$298$	3.28565	+	1.23672i	0.190332	+	0.0716414i
$299$	5.11269	+	2.95181i	0.295675	+	0.170708i
$300$	−17.7096	−	5.63071i	−1.02247	−	0.325089i
$301$	16.4523	+	7.57158i	0.948296	+	0.436418i
$302$	3.01628	−	2.47527i	0.173568	−	0.142436i
$303$	13.1320	−	22.7453i	0.754413	−	1.30668i
$304$	−26.4253	+	3.47630i	−1.51559	+	0.199380i
$305$	1.25360	−	3.81453i	0.0717810	−	0.218419i
$306$	2.05334	−	0.338955i	0.117381	−	0.0193768i
$307$	15.5134			0.885395			0.442697	−	0.896671i	$-0.354022\pi$
$307$	15.5134			0.885395			0.442697	+	0.896671i	$0.354022\pi$
$308$	15.5681	−	6.94264i	0.887073	−	0.395593i
$309$		−	0.930357i		−	0.0529262i
$310$	12.7470	+	10.2558i	0.723983	+	0.582491i
$311$	−4.58870	−	7.94786i	−0.260201	−	0.450682i	0.706094	−	0.708118i	$-0.250456\pi$
$311$	−4.58870	−	7.94786i	−0.260201	−	0.450682i	−0.966295	+	0.257436i	$0.917122\pi$
$312$	−1.85704	+	2.98587i	−0.105134	+	0.169042i
$313$	−16.2088	+	28.0744i	−0.916175	+	1.58686i	−0.111002	+	0.993820i	$0.535406\pi$
$313$	−16.2088	+	28.0744i	−0.916175	+	1.58686i	−0.805172	+	0.593041i	$0.797927\pi$
$314$	5.75416	−	4.72208i	0.324726	−	0.266483i
$315$	1.96462	+	1.82596i	0.110694	+	0.102881i
$316$	30.6470	+	6.09763i	1.72403	+	0.343019i
$317$	−0.205982	+	0.356772i	−0.0115691	+	0.0200383i	−0.871752	−	0.489947i	$-0.837016\pi$
$317$	−0.205982	+	0.356772i	−0.0115691	+	0.0200383i	0.860183	+	0.509986i	$0.170349\pi$
$318$	−0.0240799	+	0.0639739i	−0.00135033	+	0.00358748i
$319$	8.85371	−	5.11169i	0.495713	−	0.286200i
$320$	6.68698	−	16.5917i	0.373813	−	0.927504i
$321$		−	34.4729i		−	1.92409i
$322$	23.2097	+	23.4860i	1.29343	+	1.30882i
$323$		−	21.6282i		−	1.20343i
$324$	15.2685	+	13.3915i	0.848252	+	0.743971i
$325$	1.33993	+	3.06480i	0.0743260	+	0.170004i
$326$	−5.69393	−	2.14321i	−0.315358	−	0.118701i
$327$	−7.30229	−	4.21598i	−0.403817	−	0.233144i
$328$	−12.4634	−	23.3216i	−0.688178	−	1.28772i
$329$	7.80069	−	5.52064i	0.430066	−	0.304363i
$330$	−2.90229	+	18.7068i	−0.159766	+	1.02977i
$331$	14.7269	−	25.5078i	0.809465	−	1.40203i	−0.103770	−	0.994601i	$-0.533091\pi$
$331$	14.7269	−	25.5078i	0.809465	−	1.40203i	0.913235	−	0.407433i	$-0.133576\pi$
$332$	−12.5056	+	4.24439i	−0.686334	+	0.232941i
$333$	−0.525405	−	0.910027i	−0.0287920	−	0.0498692i
$334$	0.893933	+	5.41530i	0.0489138	+	0.296312i
$335$	−7.97783	+	7.13488i	−0.435875	+	0.389820i
$336$	−14.4342	+	13.3578i	−0.787452	+	0.728725i
$337$			0.726788i			0.0395906i	0.999804	+	0.0197953i	$0.00630146\pi$
$337$			0.726788i			0.0395906i	−0.999804	+	0.0197953i	$0.993699\pi$
$338$	−17.5148	+	2.89127i	−0.952681	+	0.157264i
$339$	11.1797	−	6.45459i	0.607197	−	0.350565i
$340$	12.6410	+	7.13602i	0.685554	+	0.387005i
$341$	8.33319	−	14.4335i	0.451268	−	0.781619i
$342$	−3.30250	+	2.71015i	−0.178579	+	0.146548i
$343$	−17.8150	+	5.06212i	−0.961921	+	0.273329i
$344$	−9.12566	−	17.0759i	−0.492023	−	0.920673i
$345$	−35.8941	+	7.50357i	−1.93248	+	0.403979i
$346$	22.0023	+	8.28168i	1.18285	+	0.445226i
$347$	14.4004	−	8.31409i	0.773056	−	0.446324i	−0.0609078	−	0.998143i	$-0.519400\pi$
$347$	14.4004	−	8.31409i	0.773056	−	0.446324i	0.833964	+	0.551819i	$0.186066\pi$
$348$	−7.77752	+	8.86767i	−0.416919	+	0.475357i
$349$	−33.3428			−1.78480			−0.892401	−	0.451244i	$-0.850980\pi$
$349$	−33.3428			−1.78480			−0.892401	+	0.451244i	$0.850980\pi$
$350$	2.69292	+	18.5135i	0.143943	+	0.989586i
$351$		−	3.16593i		−	0.168985i
$352$	−17.7464	−	4.14018i	−0.945884	−	0.220672i
$353$	−4.25151	−	7.36384i	−0.226285	−	0.391938i	0.730419	−	0.682999i	$-0.239325\pi$
$353$	−4.25151	−	7.36384i	−0.226285	−	0.391938i	−0.956704	+	0.291062i	$0.905991\pi$
$354$	0.0455085	+	0.0171295i	0.00241875	+	0.000910421i
$355$	3.72261	+	17.8075i	0.197576	+	0.945125i
$356$	−2.98259	−	0.593427i	−0.158077	−	0.0314515i
$357$	−9.21918	−	13.0268i	−0.487931	−	0.689449i
$358$	−14.2812	−	17.4026i	−0.754784	−	0.919754i
$359$	−28.2304	−	16.2989i	−1.48995	−	0.860220i	−0.490012	−	0.871716i	$-0.663007\pi$
$359$	−28.2304	−	16.2989i	−1.48995	−	0.860220i	−0.999934	+	0.0114955i	$0.996341\pi$
$360$	−0.494370	−	2.82439i	−0.0260556	−	0.148859i
$361$	12.6994	+	21.9960i	0.668389	+	1.15768i
$362$	−10.4690	+	1.72817i	−0.550239	+	0.0908309i
$363$	−1.15714			−0.0607340
$364$	3.52075	+	0.367893i	0.184537	+	0.0192828i
$365$	−18.7921	−	21.0123i	−0.983625	−	1.09984i
$366$	4.65613	−	0.768611i	0.243380	−	0.0401760i
$367$	−3.02375	+	1.74576i	−0.157838	+	0.0911280i	−0.576839	−	0.816858i	$-0.695714\pi$
$367$	−3.02375	+	1.74576i	−0.157838	+	0.0911280i	0.419000	+	0.907986i	$0.362381\pi$
$368$	−4.60402	−	34.9977i	−0.240001	−	1.82438i
$369$	−3.67067	−	2.11926i	−0.191087	−	0.110324i
$370$	1.12371	−	7.24288i	0.0584187	−	0.376539i
$371$	0.0685228	−	0.00634157i	0.00355753	−	0.000329238i
$372$	−3.75227	+	18.8590i	−0.194546	+	0.977796i
$373$	12.1896	−	21.1129i	0.631151	−	1.09319i	−0.356165	−	0.934423i	$-0.615916\pi$
$373$	12.1896	−	21.1129i	0.631151	−	1.09319i	0.987317	−	0.158763i	$-0.0507507\pi$
$374$	5.20922	−	13.8395i	0.269362	−	0.715625i
$375$	−18.8943	−	8.64152i	−0.975698	−	0.446246i
$376$	−10.2109	−	0.335027i	−0.526588	−	0.0172777i
$377$	2.12308			0.109344
$378$	4.68408	−	17.0765i	0.240923	−	0.878321i
$379$	−33.6902			−1.73055			−0.865274	−	0.501299i	$-0.832856\pi$
$379$	−33.6902			−1.73055			−0.865274	+	0.501299i	$0.832856\pi$
$380$	−29.7975	+	0.288471i	−1.52858	+	0.0147982i
$381$	5.15352	+	8.92617i	0.264023	+	0.457301i
$382$	18.6928	+	7.03599i	0.956405	+	0.359992i
$383$	−12.7966	−	7.38811i	−0.653875	−	0.377515i	0.136064	−	0.990700i	$-0.456555\pi$
$383$	−12.7966	−	7.38811i	−0.653875	−	0.377515i	−0.789939	+	0.613185i	$0.789888\pi$
$384$	20.9236	−	2.05715i	1.06776	−	0.104979i
$385$	18.2160	−	5.60221i	0.928372	−	0.285515i
$386$	−8.96363	+	7.35589i	−0.456237	+	0.374405i
$387$	−2.68764	−	1.55171i	−0.136621	−	0.0788779i
$388$	23.0487	−	7.82271i	1.17012	−	0.397138i
$389$	0.178263	−	0.102920i	0.00903829	−	0.00521826i	−0.495474	−	0.868623i	$-0.665006\pi$
$389$	0.178263	−	0.102920i	0.00903829	−	0.00521826i	0.504512	+	0.863404i	$0.331672\pi$
$390$	−2.46437	+	3.06299i	−0.124788	+	0.155100i
$391$	28.6445			1.44861
$392$	18.4460	+	7.19339i	0.931664	+	0.363321i
$393$		−	2.99894i		−	0.151277i
$394$	−9.25335	+	1.52750i	−0.466177	+	0.0769544i
$395$	33.1896	+	10.9074i	1.66995	+	0.548810i
$396$	−2.76596	+	0.938764i	−0.138995	+	0.0471747i
$397$	4.39175	+	2.53558i	0.220416	+	0.127257i	0.606143	−	0.795356i	$-0.292716\pi$
$397$	4.39175	+	2.53558i	0.220416	+	0.127257i	−0.385727	+	0.922613i	$0.626049\pi$
$398$	3.19635	+	3.89496i	0.160219	+	0.195237i
$399$	29.7605	+	13.6962i	1.48989	+	0.685668i
$400$	9.66280	−	17.5109i	0.483140	−	0.875543i
$401$	−9.62688	+	16.6743i	−0.480744	+	0.832672i	−0.999756	−	0.0220944i	$-0.992967\pi$
$401$	−9.62688	+	16.6743i	−0.480744	+	0.832672i	0.519012	+	0.854767i	$0.326300\pi$
$402$	−11.7728	−	4.43131i	−0.587176	−	0.221014i
$403$	2.99739	−	1.73054i	0.149311	−	0.0862045i
$404$	21.2508	+	18.6383i	1.05727	+	0.927291i
$405$	15.1367	+	16.9250i	0.752148	+	0.841010i
$406$	11.4515	+	3.14115i	0.568329	+	0.155893i
$407$	−7.46653			−0.370102
$408$	−0.559478	+	17.0517i	−0.0276983	+	0.844186i
$409$	−18.9967	+	10.9678i	−0.939327	+	0.542321i	−0.889749	−	0.456450i	$-0.849121\pi$
$409$	−18.9967	+	10.9678i	−0.939327	+	0.542321i	−0.0495776	+	0.998770i	$0.515788\pi$
$410$	−10.6820	−	27.5669i	−0.527548	−	1.36143i
$411$	13.4830	+	7.78442i	0.665068	+	0.383977i
$412$	0.982038	+	0.195390i	0.0483815	+	0.00962617i
$413$	−0.00451114	−	0.0487445i	−0.000221979	−	0.00239856i
$414$	−3.58933	−	4.37383i	−0.176406	−	0.214962i
$415$	−14.4526	+	3.02128i	−0.709451	+	0.148309i
$416$	−2.76173	−	2.58728i	−0.135405	−	0.126852i
$417$	16.3001	−	9.41089i	0.798222	−	0.460853i
$418$	4.94410	+	29.9506i	0.241824	+	1.46493i
$419$			20.3822i			0.995734i	0.867253	+	0.497867i	$0.165883\pi$
$419$			20.3822i			0.995734i	−0.867253	+	0.497867i	$0.834117\pi$
$420$	−17.8242	+	12.8751i	−0.869731	+	0.628243i
$421$		−	21.2887i		−	1.03755i	−0.854912	−	0.518774i	$-0.826389\pi$
$421$		−	21.2887i		−	1.03755i	0.854912	−	0.518774i	$-0.173611\pi$
$422$	18.9192	−	3.12310i	0.920974	−	0.152030i
$423$	−1.41818	+	0.818788i	−0.0689544	+	0.0398108i
$424$	−0.0624704	−	0.0388530i	−0.00303383	−	0.00188687i
$425$	13.0656	+	9.62748i	0.633772	+	0.467002i
$426$	−16.5286	+	13.5640i	−0.800814	+	0.657178i
$427$	−2.74449	−	3.87798i	−0.132815	−	0.187669i
$428$	36.3878	+	7.23986i	1.75887	+	0.349952i
$429$	3.46823	+	2.00239i	0.167448	+	0.0966761i
$430$	−7.82133	−	20.1844i	−0.377178	−	0.973377i
$431$	18.7227	−	10.8096i	0.901842	−	0.520679i	0.0240450	−	0.999711i	$-0.492346\pi$
$431$	18.7227	−	10.8096i	0.901842	−	0.520679i	0.877797	+	0.479032i	$0.159012\pi$
$432$	−15.0192	+	11.5223i	−0.722613	+	0.554367i
$433$	29.8068			1.43243			0.716213	−	0.697882i	$-0.245874\pi$
$433$	29.8068			1.43243			0.716213	+	0.697882i	$0.245874\pi$
$434$	18.7278	−	4.89955i	0.898964	−	0.235186i
$435$	−9.82972	+	8.79110i	−0.471299	+	0.421501i
$436$	5.98377	−	6.82250i	0.286570	−	0.326738i
$437$	−50.9239	+	29.4009i	−2.43602	+	1.40644i
$438$	11.6714	−	31.0078i	0.557680	−	1.48161i
$439$	14.9755	−	25.9383i	0.714740	−	1.23797i	−0.248320	−	0.968678i	$-0.579878\pi$
$439$	14.9755	−	25.9383i	0.714740	−	1.23797i	0.963060	−	0.269288i	$-0.0867883\pi$
$440$	−19.1364	−	6.99223i	−0.912292	−	0.333341i
$441$	3.11965	−	0.582416i	0.148555	−	0.0277341i
$442$	2.37388	−	1.94809i	0.112914	−	0.0926613i
$443$	−32.1133	−	18.5406i	−1.52575	−	0.880893i	−0.999533	−	0.0305429i	$-0.990276\pi$
$443$	−32.1133	−	18.5406i	−1.52575	−	0.880893i	−0.526218	−	0.850350i	$-0.676390\pi$
$444$	8.15741	−	2.76862i	0.387134	−	0.131393i
$445$	−3.23004	−	1.06152i	−0.153119	−	0.0503207i
$446$	−4.03648	−	24.4524i	−0.191133	−	1.15785i
$447$			4.61317i			0.218195i
$448$	−11.0683	−	18.0414i	−0.522930	−	0.852376i
$449$	17.1980			0.811625			0.405813	−	0.913956i	$-0.366989\pi$
$449$	17.1980			0.811625			0.405813	+	0.913956i	$0.366989\pi$
$450$	−0.167139	−	3.20141i	−0.00787899	−	0.150916i
$451$	−26.0819	+	15.0584i	−1.22815	+	0.709073i
$452$	4.46523	+	13.1563i	0.210027	+	0.618819i
$453$	4.44032	+	2.56362i	0.208625	+	0.120449i
$454$	9.82483	+	11.9722i	0.461102	+	0.561883i
$455$	3.85778	+	0.883906i	0.180855	+	0.0414381i
$456$	−16.5074	−	30.8886i	−0.773029	−	1.44649i
$457$	−8.54674	−	4.93447i	−0.399800	−	0.230825i	0.286598	−	0.958051i	$-0.407476\pi$
$457$	−8.54674	−	4.93447i	−0.399800	−	0.230825i	−0.686398	+	0.727226i	$0.740809\pi$
$458$	−9.31795	+	24.7554i	−0.435399	+	1.15674i
$459$	−7.68057	−	13.3031i	−0.358498	−	0.620937i
$460$	−0.382051	−	39.4639i	−0.0178132	−	1.84001i
$461$	−19.0434			−0.886938			−0.443469	−	0.896290i	$-0.646252\pi$
$461$	−19.0434			−0.886938			−0.443469	+	0.896290i	$0.646252\pi$
$462$	15.7445	+	15.9319i	0.732500	+	0.741218i
$463$	−15.5965			−0.724831			−0.362415	−	0.932017i	$-0.618048\pi$
$463$	−15.5965			−0.724831			−0.362415	+	0.932017i	$0.618048\pi$
$464$	−7.72686	−	10.0719i	−0.358711	−	0.467576i
$465$	−6.71202	+	20.4237i	−0.311262	+	0.947127i
$466$	5.66038	+	2.13058i	0.262212	+	0.0986970i
$467$	11.3528	−	19.6636i	0.525343	−	0.909921i	−0.474221	−	0.880406i	$-0.657270\pi$
$467$	11.3528	−	19.6636i	0.525343	−	0.909921i	0.999564	−	0.0295151i	$-0.00939632\pi$
$468$	−0.594924	−	0.118368i	−0.0275004	−	0.00547157i
$469$	1.16701	+	12.6100i	0.0538876	+	0.582274i
$470$	−11.2873	−	1.75118i	−0.520642	−	0.0807758i
$471$	8.47081	+	4.89062i	0.390314	+	0.225348i
$472$	−0.0276385	+	0.0444390i	−0.00127217	+	0.00204547i
$473$	−19.0970	+	11.0257i	−0.878083	+	0.506961i
$474$	6.68757	+	40.5122i	0.307170	+	1.86079i
$475$	−33.1095	−	3.70506i	−1.51917	−	0.170000i
$476$	15.6866	−	6.99548i	0.718992	−	0.320637i
$477$	−0.0117920			−0.000539917
$478$	−5.78288	−	35.0317i	−0.264503	−	1.60231i
$479$	17.2162	+	29.8193i	0.786626	+	1.36248i	0.928023	+	0.372523i	$0.121507\pi$
$479$	17.2162	+	29.8193i	0.786626	+	1.36248i	−0.141397	+	0.989953i	$0.545159\pi$
$480$	23.4999	+	0.543371i	1.07262	+	0.0248014i
$481$	−1.34283	−	0.775282i	−0.0612277	−	0.0353498i
$482$	−2.14357	+	1.75909i	−0.0976369	+	0.0801245i
$483$	−18.1393	+	39.4149i	−0.825366	+	1.79344i
$484$	0.243017	−	1.22142i	0.0110462	−	0.0555189i
$485$	26.6372	−	5.56843i	1.20953	−	0.252849i
$486$	−2.32806	+	6.18503i	−0.105603	+	0.280559i
$487$	0.417834	+	0.723709i	0.0189338	+	0.0327944i	0.875337	−	0.483513i	$-0.160639\pi$
$487$	0.417834	+	0.723709i	0.0189338	+	0.0327944i	−0.856403	+	0.516308i	$0.827306\pi$
$488$	−0.166553	+	5.07619i	−0.00753951	+	0.229788i
$489$		−	7.99448i		−	0.361523i
$490$	19.5005	+	10.4753i	0.880941	+	0.473227i
$491$	28.3101			1.27762			0.638809	−	0.769365i	$-0.279427\pi$
$491$	28.3101			1.27762			0.638809	+	0.769365i	$0.279427\pi$
$492$	22.9116	−	26.1231i	1.03293	−	1.17772i
$493$	8.92109	−	5.15060i	0.401786	−	0.231971i
$494$	−2.22072	+	5.89987i	−0.0999149	+	0.265448i
$495$	−3.19659	+	0.668240i	−0.143676	+	0.0300351i
$496$	−19.1186	−	7.92140i	−0.858451	−	0.355681i
$497$	19.5542	+	8.99911i	0.877127	+	0.403665i
$498$	−11.0086	−	13.4147i	−0.493306	−	0.601125i
$499$	2.19914	−	3.80903i	0.0984472	−	0.170516i	−0.812595	−	0.582829i	$-0.801946\pi$
$499$	2.19914	−	3.80903i	0.0984472	−	0.170516i	0.911042	+	0.412313i	$0.135279\pi$
$500$	13.0897	−	18.1290i	0.585387	−	0.810754i
$501$	−6.24594	+	3.60609i	−0.279048	+	0.161108i
$502$	−2.36590	−	14.3322i	−0.105595	−	0.639679i
$503$			21.2435i			0.947200i	0.880740	+	0.473600i	$0.157046\pi$
$503$			21.2435i			0.947200i	−0.880740	+	0.473600i	$0.842954\pi$
$504$	−3.03379	−	1.51866i	−0.135136	−	0.0676467i
$505$	21.0673	+	23.5563i	0.937482	+	1.04824i
$506$	−39.6666	+	6.54798i	−1.76340	+	0.291093i
$507$	−11.6633	−	20.2014i	−0.517984	−	0.897174i
$508$	−10.5043	+	3.56516i	−0.466054	+	0.158178i
$509$	−4.64622	+	8.04750i	−0.205940	+	0.356699i	−0.950432	−	0.310933i	$-0.899359\pi$
$509$	−4.64622	+	8.04750i	−0.205940	+	0.356699i	0.744492	+	0.667632i	$0.232692\pi$
$510$	−2.92438	+	18.8492i	−0.129494	+	0.834654i
$511$	−33.2126	+	3.07372i	−1.46924	+	0.135973i
$512$	−2.22287	+	22.5180i	−0.0982381	+	0.995163i
$513$	27.3089	+	15.7668i	1.20572	+	0.696121i
$514$	4.41206	−	11.7217i	0.194608	−	0.517021i
$515$	1.06351	+	0.349511i	0.0468640	+	0.0154013i
$516$	16.7757	−	19.1272i	0.738511	−	0.842027i
$517$			11.6358i			0.511742i
$518$	−6.09594	−	6.16849i	−0.267840	−	0.271028i
$519$			30.8919i			1.35601i
$520$	−2.71558	−	3.24454i	−0.119086	−	0.142283i
$521$	19.2972	−	11.1412i	0.845425	−	0.488106i	−0.0136798	−	0.999906i	$-0.504355\pi$
$521$	19.2972	−	11.1412i	0.845425	−	0.488106i	0.859104	+	0.511800i	$0.171021\pi$
$522$	−1.90433	−	0.716794i	−0.0833504	−	0.0313732i
$523$	1.18906	−	2.05951i	0.0519939	−	0.0900560i	−0.838857	−	0.544352i	$-0.816776\pi$
$523$	1.18906	−	2.05951i	0.0519939	−	0.0900560i	0.890851	+	0.454296i	$0.150109\pi$
$524$	3.16553	+	0.629826i	0.138287	+	0.0275141i
$525$	−21.5213	+	11.8816i	−0.939267	+	0.518556i
$526$	−11.1457	−	13.5817i	−0.485975	−	0.592192i
$527$	8.39662	−	14.5434i	0.365762	−	0.633519i
$528$	−3.12317	−	23.7409i	−0.135919	−	1.03319i
$529$	−27.4386	−	47.5251i	−1.19298	−	2.06631i
$530$	−0.0640839	−	0.0515596i	−0.00278363	−	0.00223961i
$531$			0.00838834i			0.000364023i
$532$	−20.7072	+	28.5373i	−0.897771	+	1.23725i
$533$	−6.25432			−0.270905
$534$	−0.650840	−	3.94268i	−0.0281646	−	0.170617i
$535$	39.4068	+	12.9506i	1.70370	+	0.559903i
$536$	7.14995	−	11.4962i	0.308831	−	0.496558i
$537$	14.7909	−	25.6186i	0.638275	−	1.10552i
$538$	24.4080	+	29.7428i	1.05230	+	1.28230i
$539$	7.49943	−	21.2661i	0.323023	−	0.915996i
$540$	−18.2255	+	10.7591i	−0.784300	+	0.462996i
$541$	18.1918	+	10.5031i	0.782128	+	0.451562i	0.837184	−	0.546922i	$-0.184200\pi$
$541$	18.1918	+	10.5031i	0.782128	+	0.451562i	−0.0550562	+	0.998483i	$0.517534\pi$
$542$	5.17902	−	13.7593i	0.222458	−	0.591012i
$543$	−6.97140	−	12.0748i	−0.299171	−	0.518180i
$544$	−17.8814	−	4.17169i	−0.766660	−	0.178860i
$545$	7.56266	−	6.76358i	0.323949	−	0.289720i
$546$	1.17731	+	4.50011i	0.0503844	+	0.192587i
$547$		−	14.9270i		−	0.638234i	−0.947715	−	0.319117i	$-0.896614\pi$
$547$		−	14.9270i		−	0.638234i	0.947715	−	0.319117i	$-0.103386\pi$
$548$	−11.0485	+	12.5971i	−0.471968	+	0.538123i
$549$	0.407047	+	0.705026i	0.0173723	+	0.0300898i
$550$	−20.2938	−	10.3453i	−0.865333	−	0.441126i
$551$	−10.5732	+	18.3134i	−0.450434	+	0.780175i
$552$	40.9090	−	21.8624i	1.74120	−	0.930526i
$553$	33.7417	−	23.8794i	1.43485	−	1.01546i
$554$	−18.3271	−	22.3328i	−0.778645	−	0.948829i
$555$	9.42745	−	1.97078i	0.400173	−	0.0836551i
$556$	6.51037	+	19.1820i	0.276101	+	0.813500i
$557$	1.63827	+	2.83757i	0.0694157	+	0.120232i	0.898644	−	0.438678i	$-0.144553\pi$
$557$	1.63827	+	2.83757i	0.0694157	+	0.120232i	−0.829229	+	0.558910i	$0.811220\pi$
$558$	−3.27283	+	0.540264i	−0.138550	+	0.0228712i
$559$	−4.57938			−0.193687
$560$	−9.84699	−	21.5183i	−0.416111	−	0.909314i
$561$	19.4312			0.820385
$562$	43.4865	−	7.17855i	1.83437	−	0.302809i
$563$	4.29192	+	7.43383i	0.180883	+	0.313299i	0.942181	−	0.335103i	$-0.108771\pi$
$563$	4.29192	+	7.43383i	0.180883	+	0.313299i	−0.761298	+	0.648402i	$0.775438\pi$
$564$	−4.31460	−	12.7125i	−0.181677	−	0.535291i
$565$	3.17848	+	15.2046i	0.133720	+	0.639661i
$566$	−12.7256	−	15.5070i	−0.534897	−	0.651807i
$567$	26.7521	−	2.47582i	1.12348	−	0.103975i
$568$	−10.8462	−	20.2954i	−0.455097	−	0.851577i
$569$	−12.8908	+	22.3275i	−0.540411	+	0.936019i	0.458470	+	0.888710i	$0.348398\pi$
$569$	−12.8908	+	22.3275i	−0.540411	+	0.936019i	−0.998880	+	0.0473086i	$0.984936\pi$
$570$	−14.1480	−	36.5114i	−0.592594	−	1.52930i
$571$	−15.5532	−	26.9389i	−0.650881	−	1.12736i	−0.982909	−	0.184089i	$-0.941066\pi$
$571$	−15.5532	−	26.9389i	−0.650881	−	1.12736i	0.332029	−	0.943269i	$-0.392267\pi$
$572$	−2.84200	+	3.24036i	−0.118830	+	0.135486i
$573$			26.2453i			1.09641i
$574$	−33.7348	−	9.25343i	−1.40806	−	0.386231i
$575$	4.90699	−	43.8503i	0.204636	−	1.82869i
$576$	1.60366	+	3.25312i	0.0668193	+	0.135547i
$577$	−10.1101	−	17.5112i	−0.420889	−	0.729001i	0.575137	−	0.818057i	$-0.304949\pi$
$577$	−10.1101	−	17.5112i	−0.420889	−	0.729001i	−0.996027	+	0.0890553i	$0.971615\pi$
$578$	−3.22035	+	8.55564i	−0.133949	+	0.355868i
$579$	−13.1955	−	7.61844i	−0.548387	−	0.316611i
$580$	−7.21504	−	12.2220i	−0.299588	−	0.507492i
$581$	−7.30370	+	15.8702i	−0.303008	+	0.658409i
$582$	20.2896	+	24.7242i	0.841030	+	1.02485i
$583$	−0.0418939	+	0.0725624i	−0.00173507	+	0.00300523i
$584$	30.2791	+	18.8318i	1.25296	+	0.779267i
$585$	−0.644282	−	0.211736i	−0.0266378	−	0.00875420i
$586$	3.07267	+	18.6137i	0.126931	+	0.768927i
$587$	−21.6836			−0.894976			−0.447488	−	0.894290i	$-0.647681\pi$
$587$	−21.6836			−0.894976			−0.447488	+	0.894290i	$0.647681\pi$
$588$	−0.307797	+	26.0147i	−0.0126933	+	1.07283i
$589$			34.4734i			1.42045i
$590$	−0.0366775	+	0.0455868i	−0.00150999	+	0.00187678i
$591$	−6.16188	−	10.6727i	−0.253466	−	0.439016i
$592$	1.20923	+	9.19200i	0.0496989	+	0.377789i
$593$	−14.9180	+	25.8387i	−0.612609	+	1.06107i	0.378190	+	0.925728i	$0.376547\pi$
$593$	−14.9180	+	25.8387i	−0.612609	+	1.06107i	−0.990799	+	0.135342i	$0.956787\pi$
$594$	13.6770	+	16.6663i	0.561174	+	0.683827i
$595$	18.3546	−	5.64485i	0.752466	−	0.231416i
$596$	−4.86942	−	0.968838i	−0.199459	−	0.0396852i
$597$	−3.31044	+	5.73384i	−0.135487	+	0.234671i
$598$	−7.81380	−	2.94113i	−0.319530	−	0.120272i
$599$	−6.90813	+	3.98841i	−0.282259	+	0.162962i	−0.634445	−	0.772968i	$-0.718771\pi$
$599$	−6.90813	+	3.98841i	−0.282259	+	0.162962i	0.352187	+	0.935930i	$0.385438\pi$
$600$	26.0078	+	3.77755i	1.06176	+	0.154218i
$601$			42.8990i			1.74989i	0.484224	+	0.874944i	$0.339102\pi$
$601$			42.8990i			1.74989i	−0.484224	+	0.874944i	$0.660898\pi$
$602$	−24.7004	−	6.77531i	−1.00671	−	0.276141i
$603$		−	2.17002i		−	0.0883702i
$604$	−3.63857	+	4.14858i	−0.148051	+	0.168803i
$605$	0.434707	−	1.32275i	0.0176734	−	0.0537775i
$606$	−13.0844	+	34.7619i	−0.531519	+	1.41211i
$607$	−24.6567	−	14.2355i	−1.00078	−	0.577802i	−0.0923032	−	0.995731i	$-0.529423\pi$
$607$	−24.6567	−	14.2355i	−1.00078	−	0.577802i	−0.908480	+	0.417929i	$0.862756\pi$
$608$	36.0713	−	10.9372i	1.46288	−	0.443564i
$609$	1.43791	+	15.5371i	0.0582670	+	0.629596i
$610$	−0.870569	+	5.61128i	−0.0352483	+	0.227194i
$611$	−1.20820	+	2.09266i	−0.0488783	+	0.0846598i
$612$	−2.78701	+	0.945909i	−0.112658	+	0.0382361i
$613$	13.6922	+	23.7156i	0.553022	+	0.957863i	0.998054	+	0.0623483i	$0.0198589\pi$
$613$	13.6922	+	23.7156i	0.553022	+	0.957863i	−0.445032	+	0.895515i	$0.646808\pi$
$614$	−21.6463	+	3.57327i	−0.873572	+	0.144205i
$615$	28.9571	−	25.8975i	1.16766	−	1.04429i
$616$	−20.1235	+	13.2731i	−0.810798	+	0.534790i
$617$		−	26.4349i		−	1.06423i	−0.846673	−	0.532114i	$-0.821398\pi$
$617$		−	26.4349i		−	1.06423i	0.846673	−	0.532114i	$-0.178602\pi$
$618$	0.214293	+	1.29816i	0.00862015	+	0.0522195i
$619$	−6.44010	+	3.71819i	−0.258850	+	0.149447i	−0.623810	−	0.781576i	$-0.714416\pi$
$619$	−6.44010	+	3.71819i	−0.258850	+	0.149447i	0.364960	+	0.931023i	$0.381083\pi$
$620$	−20.1486	−	11.3742i	−0.809187	−	0.456797i
$621$	−20.8816	+	36.1679i	−0.837949	+	1.45137i
$622$	8.23341	+	10.0329i	0.330130	+	0.402285i
$623$	−3.28377	+	2.32396i	−0.131562	+	0.0931076i
$624$	1.90343	−	4.59402i	0.0761984	−	0.183908i
$625$	16.9764	−	18.3521i	0.679057	−	0.734085i
$626$	16.1501	−	42.9065i	0.645487	−	1.71489i
$627$	−34.5446	+	19.9443i	−1.37958	+	0.796500i
$628$	−6.94130	+	7.91425i	−0.276988	+	0.315813i
$629$	−7.52335			−0.299976
$630$	−3.16188	−	2.09530i	−0.125972	−	0.0834788i
$631$			23.0524i			0.917701i	0.888514	+	0.458850i	$0.151739\pi$
$631$			23.0524i			0.917701i	−0.888514	+	0.458850i	$0.848261\pi$
$632$	−44.1671	−	1.44915i	−1.75687	−	0.0576443i
$633$	12.5985	+	21.8212i	0.500744	+	0.867315i
$634$	0.205237	−	0.545260i	0.00815098	−	0.0216550i
$635$	−12.1398	+	2.53778i	−0.481752	+	0.100709i
$636$	0.0188640	−	0.0948111i	0.000748005	−	0.00375950i
$637$	3.55690	−	3.04593i	0.140929	−	0.120684i
$638$	−11.1764	+	9.17181i	−0.442480	+	0.363115i
$639$	−3.19437	−	1.84427i	−0.126367	−	0.0729581i
$640$	−5.50890	+	24.6911i	−0.217758	+	0.976003i
$641$	4.04336	+	7.00330i	0.159703	+	0.276614i	0.934762	−	0.355276i	$-0.115613\pi$
$641$	4.04336	+	7.00330i	0.159703	+	0.276614i	−0.775059	+	0.631889i	$0.782280\pi$
$642$	7.94030	+	48.1011i	0.313379	+	1.89840i
$643$	22.3144			0.879995			0.439998	−	0.897999i	$-0.354979\pi$
$643$	22.3144			0.879995			0.439998	+	0.897999i	$0.354979\pi$
$644$	−37.7949	−	27.4247i	−1.48933	−	1.08068i
$645$	21.2023	−	18.9620i	0.834838	−	0.746628i
$646$	4.98173	+	30.1785i	0.196003	+	1.18736i
$647$	1.37529	−	0.794021i	0.0540681	−	0.0312162i	−0.472722	−	0.881211i	$-0.656729\pi$
$647$	1.37529	−	0.794021i	0.0540681	−	0.0312162i	0.526790	+	0.849995i	$0.323395\pi$
$648$	−24.3892	−	15.1687i	−0.958097	−	0.595881i
$649$	0.0516180	+	0.0298017i	0.00202618	+	0.00116982i
$650$	−2.57557	−	3.96777i	−0.101022	−	0.155629i
$651$	14.6945	+	20.7635i	0.575924	+	0.813784i
$652$	8.43857	+	1.67897i	0.330480	+	0.0657535i
$653$	−22.2296	+	38.5028i	−0.869912	+	1.50673i	−0.00782554	+	0.999969i	$0.502491\pi$
$653$	−22.2296	+	38.5028i	−0.869912	+	1.50673i	−0.862086	+	0.506762i	$0.830842\pi$
$654$	11.1602	+	4.20071i	0.436398	+	0.164261i
$655$	3.42816	+	1.12663i	0.133949	+	0.0440209i
$656$	22.7624	+	29.6706i	0.888721	+	1.15844i
$657$	5.71550			0.222983
$658$	−9.61294	+	9.49988i	−0.374752	+	0.370344i
$659$	6.14200			0.239259			0.119629	−	0.992819i	$-0.461829\pi$
$659$	6.14200			0.239259			0.119629	+	0.992819i	$0.461829\pi$
$660$	−0.259167	−	26.7706i	−0.0100881	−	1.04205i
$661$	4.19173	+	7.26029i	0.163039	+	0.282393i	0.935957	−	0.352114i	$-0.114537\pi$
$661$	4.19173	+	7.26029i	0.163039	+	0.282393i	−0.772918	+	0.634506i	$0.781204\pi$
$662$	−14.6736	+	38.9839i	−0.570306	+	1.51515i
$663$	3.49463	+	2.01762i	0.135720	+	0.0783581i
$664$	16.4718	−	8.80280i	0.639230	−	0.341615i
$665$	−26.8367	+	28.8747i	−1.04068	+	1.11971i
$666$	0.942724	+	1.14877i	0.0365298	+	0.0445139i
$667$	−24.2543	−	14.0032i	−0.939128	−	0.542206i
$668$	−2.49466	−	7.35023i	−0.0965214	−	0.284389i
$669$	28.2030	−	16.2830i	1.09039	−	0.629538i
$670$	9.48829	−	11.7931i	0.366565	−	0.455606i
$671$	5.78454			0.223310
$672$	17.0638	−	21.9632i	0.658250	−	0.847248i
$673$			5.56001i			0.214323i	0.994242	+	0.107161i	$0.0341761\pi$
$673$			5.56001i			0.214323i	−0.994242	+	0.107161i	$0.965824\pi$
$674$	−0.167404	−	1.01411i	−0.00644817	−	0.0390620i
$675$	−21.6808	+	9.47887i	−0.834495	+	0.364842i
$676$	23.7730	−	8.06854i	0.914347	−	0.310329i
$677$	13.5074	+	7.79851i	0.519132	+	0.299721i	0.736579	−	0.676351i	$-0.236440\pi$
$677$	13.5074	+	7.79851i	0.519132	+	0.299721i	−0.217447	+	0.976072i	$0.569773\pi$
$678$	−14.1126	+	11.5813i	−0.541992	+	0.444779i
$679$	13.4612	−	29.2500i	0.516594	−	1.12251i
$680$	−19.2820	−	7.04545i	−0.739432	−	0.270181i
$681$	−10.1755	+	17.6245i	−0.389926	+	0.675371i
$682$	−8.30302	+	22.0589i	−0.317939	+	0.844681i
$683$	−13.9790	+	8.07076i	−0.534890	+	0.308819i	−0.743006	−	0.669285i	$-0.766600\pi$
$683$	−13.9790	+	8.07076i	−0.534890	+	0.308819i	0.208115	+	0.978104i	$0.433267\pi$
$684$	3.98383	−	4.54224i	0.152326	−	0.173677i
$685$	−13.9638	+	12.4883i	−0.533529	+	0.477155i
$686$	23.6919	−	11.1667i	0.904559	−	0.426348i
$687$	−34.7574			−1.32608
$688$	16.6665	+	21.7246i	0.635404	+	0.828244i
$689$	−0.0150689	+	0.00870005i	−0.000574081	+	0.000331446i
$690$	48.3558	−	18.7376i	1.84088	−	0.713329i
$691$	12.5750	+	7.26020i	0.478377	+	0.276191i	0.719740	−	0.694244i	$-0.244261\pi$
$691$	12.5750	+	7.26020i	0.478377	+	0.276191i	−0.241363	+	0.970435i	$0.577594\pi$
$692$	−32.6080	−	6.48780i	−1.23957	−	0.246629i
$693$	−1.61541	+	3.51014i	−0.0613645	+	0.133339i
$694$	−18.1783	+	14.9178i	−0.690040	+	0.566273i
$695$	4.63427	+	22.1685i	0.175788	+	0.840900i
$696$	8.80967	−	14.1648i	0.333930	−	0.536914i
$697$	−26.2804	+	15.1730i	−0.995442	+	0.574719i
$698$	46.5243	−	7.68001i	1.76097	−	0.290693i
$699$			7.94737i			0.300597i
$700$	−8.02180	−	25.2121i	−0.303195	−	0.952928i
$701$		−	50.0391i		−	1.88995i	−0.327140	−	0.944976i	$-0.606085\pi$
$701$		−	50.0391i		−	1.88995i	0.327140	−	0.944976i	$-0.393915\pi$
$702$	0.729224	+	4.41752i	0.0275228	+	0.166729i
$703$	13.3749	−	7.72203i	0.504446	−	0.291242i
$704$	25.7157	+	1.68932i	0.969195	+	0.0636685i
$705$	−3.07126	−	14.6917i	−0.115670	−	0.553321i
$706$	7.62841	+	9.29572i	0.287099	+	0.349849i
$707$	37.2337	−	3.44586i	1.40032	−	0.129595i
$708$	−0.0674449	−	0.0134191i	−0.00253473	−	0.000504320i
$709$	−24.6072	−	14.2069i	−0.924141	−	0.533553i	−0.0391872	−	0.999232i	$-0.512477\pi$
$709$	−24.6072	−	14.2069i	−0.924141	−	0.533553i	−0.884954	+	0.465679i	$0.845810\pi$
$710$	−9.29596	−	23.9899i	−0.348871	−	0.900325i
$711$	−6.13432	+	3.54165i	−0.230055	+	0.132822i
$712$	4.29838	+	0.141033i	0.161089	+	0.00528543i
$713$	−45.6567			−1.70986
$714$	15.8643	+	16.0531i	0.593707	+	0.600773i
$715$	−3.59190	+	3.21237i	−0.134329	+	0.120136i
$716$	23.9354	+	20.9929i	0.894507	+	0.784540i
$717$	40.4051	−	23.3279i	1.50896	−	0.871197i
$718$	43.1450	+	16.2398i	1.61016	+	0.606065i
$719$	6.99938	−	12.1233i	0.261033	−	0.452122i	−0.705484	−	0.708726i	$-0.749270\pi$
$719$	6.99938	−	12.1233i	0.261033	−	0.452122i	0.966517	+	0.256604i	$0.0826036\pi$
$720$	1.34036	+	3.82709i	0.0499525	+	0.142627i
$721$	1.08121	−	0.765181i	0.0402662	−	0.0284968i
$722$	−22.7863	−	27.7665i	−0.848017	−	1.03336i
$723$	−3.15559	−	1.82188i	−0.117358	−	0.0677564i
$724$	14.2097	−	4.82275i	0.528098	−	0.179236i
$725$	−6.35654	−	14.5392i	−0.236076	−	0.539971i
$726$	1.61459	−	0.266529i	0.0599230	−	0.00989182i
$727$		−	27.8172i		−	1.03168i	−0.856684	−	0.515842i	$-0.827479\pi$
$727$		−	27.8172i		−	1.03168i	0.856684	−	0.515842i	$-0.172521\pi$
$728$	−4.99734	+	0.297618i	−0.185214	+	0.0110304i
$729$	21.7797			0.806654
$730$	31.0611	+	24.9907i	1.14962	+	0.924946i
$731$	−19.2424	+	11.1096i	−0.711705	+	0.410903i
$732$	−6.31979	+	2.14493i	−0.233586	+	0.0792790i
$733$	−40.1317	−	23.1700i	−1.48230	−	0.855804i	−0.482498	−	0.875897i	$-0.660271\pi$
$733$	−40.1317	−	23.1700i	−1.48230	−	0.855804i	−0.999798	+	0.0200925i	$0.993604\pi$
$734$	3.81702	−	3.13239i	0.140889	−	0.115618i
$735$	−3.85582	+	28.8307i	−0.142224	+	1.06343i
$736$	14.4853	+	47.7729i	0.533936	+	1.76093i
$737$	−13.3533	−	7.70955i	−0.491877	−	0.283985i
$738$	5.60993	+	2.11159i	0.206504	+	0.0777286i
$739$	−4.81690	−	8.34311i	−0.177192	−	0.306906i	0.763725	−	0.645541i	$-0.223368\pi$
$739$	−4.81690	−	8.34311i	−0.177192	−	0.306906i	−0.940918	+	0.338635i	$0.890035\pi$
$740$	0.100344	+	10.3650i	0.00368872	+	0.381026i
$741$	−8.28362			−0.304307
$742$	−0.0941513	+	0.0246318i	−0.00345640	+	0.000904260i
$743$	32.6002			1.19599			0.597993	−	0.801501i	$-0.295965\pi$
$743$	32.6002			1.19599			0.597993	+	0.801501i	$0.295965\pi$
$744$	0.891758	−	27.1789i	0.0326934	−	0.996426i
$745$	−5.27342	−	1.73305i	−0.193203	−	0.0634940i
$746$	−12.1454	+	32.2672i	−0.444675	+	1.18139i
$747$	1.49681	−	2.59255i	0.0547655	−	0.0948566i
$748$	−4.08086	+	20.5106i	−0.149211	+	0.749941i
$749$	40.0623	−	28.3526i	1.46385	−	1.03598i
$750$	28.3542	+	7.70577i	1.03535	+	0.281375i
$751$	4.64496	+	2.68177i	0.169497	+	0.0978591i	0.582349	−	0.812939i	$-0.302134\pi$
$751$	4.64496	+	2.68177i	0.169497	+	0.0978591i	−0.412852	+	0.910798i	$0.635467\pi$
$752$	14.3248	−	1.88445i	0.522370	−	0.0687189i
$753$	16.5306	−	9.54396i	0.602409	−	0.347801i
$754$	−2.96239	+	0.489018i	−0.107884	+	0.0178090i
$755$	−4.59865	+	4.11275i	−0.167362	+	0.149678i
$756$	−2.60253	+	24.9063i	−0.0946530	+	0.905833i
$757$	−14.4301			−0.524470			−0.262235	−	0.965004i	$-0.584460\pi$
$757$	−14.4301			−0.524470			−0.262235	+	0.965004i	$0.584460\pi$
$758$	47.0089	−	7.76001i	1.70744	−	0.281856i
$759$	−26.4143	−	45.7509i	−0.958778	−	1.66065i
$760$	41.5109	−	7.26591i	1.50576	−	0.263562i
$761$	−14.5866	−	8.42159i	−0.528765	−	0.305283i	0.211748	−	0.977324i	$-0.432084\pi$
$761$	−14.5866	−	8.42159i	−0.528765	−	0.305283i	−0.740513	+	0.672042i	$0.765418\pi$
$762$	−9.24687	−	11.2679i	−0.334979	−	0.408193i
$763$	−1.10628	−	11.9537i	−0.0400500	−	0.432755i
$764$	−27.7032	−	5.51193i	−1.00227	−	0.199415i
$765$	−3.22092	+	0.673325i	−0.116453	+	0.0243441i
$766$	19.5572	+	7.36136i	0.706630	+	0.265977i
$767$	0.00618888	+	0.0107195i	0.000223467	+	0.000387057i
$768$	−28.7216	+	7.68984i	−1.03640	+	0.277483i
$769$			53.2864i			1.92156i	0.277315	+	0.960779i	$0.410555\pi$
$769$			53.2864i			1.92156i	−0.277315	+	0.960779i	$0.589445\pi$
$770$	−24.1269	+	12.0127i	−0.869473	+	0.432908i
$771$	16.4577			0.592708
$772$	10.8129	−	12.3285i	0.389165	−	0.443713i
$773$	−0.228998	+	0.132212i	−0.00823647	+	0.00475533i	−0.504113	−	0.863638i	$-0.668180\pi$
$773$	−0.228998	+	0.132212i	−0.00823647	+	0.00475533i	0.495876	+	0.868393i	$0.334847\pi$
$774$	4.10756	+	1.54609i	0.147643	+	0.0555731i
$775$	−20.8253	−	15.3453i	−0.748067	−	0.551220i
$776$	−30.3587	+	16.2242i	−1.08981	+	0.582414i
$777$	4.76421	−	10.3522i	0.170915	−	0.371382i
$778$	−0.225030	+	0.184668i	−0.00806770	+	0.00662066i
$779$	31.1474	−	53.9489i	1.11597	−	1.93292i
$780$	2.73310	−	4.84151i	0.0978607	−	0.173354i
$781$	−22.6976	+	13.1045i	−0.812183	+	0.468914i
$782$	−39.9685	+	6.59781i	−1.42927	+	0.235937i
$783$			15.0190i			0.536734i
$784$	−27.3952	−	5.78840i	−0.978398	−	0.206728i
$785$	−8.77286	+	7.84590i	−0.313117	+	0.280032i
$786$	0.690760	+	4.18452i	0.0246386	+	0.149257i
$787$	7.22171	+	12.5084i	0.257426	+	0.445875i	0.965552	−	0.260211i	$-0.0837922\pi$
$787$	7.22171	+	12.5084i	0.257426	+	0.445875i	−0.708126	+	0.706087i	$0.750459\pi$
$788$	12.5596	−	4.26273i	0.447419	−	0.151854i
$789$	11.5435	−	19.9939i	0.410960	−	0.711803i
$790$	−48.8228	−	7.57469i	−1.73704	−	0.269495i
$791$	16.6960	+	7.68371i	0.593640	+	0.273201i
$792$	3.64320	−	1.94698i	0.129455	−	0.0691830i
$793$	1.04033	+	0.600634i	0.0369432	+	0.0213292i
$794$	−6.71197	−	2.52640i	−0.238199	−	0.0896585i
$795$	0.0337437	−	0.102677i	0.00119676	−	0.00364158i
$796$	−5.35711	−	4.69853i	−0.189878	−	0.166535i
$797$		−	34.3379i		−	1.21631i	−0.793818	−	0.608156i	$-0.791909\pi$
$797$		−	34.3379i		−	1.21631i	0.793818	−	0.608156i	$-0.208091\pi$
$798$	−44.6805	−	12.2558i	−1.58167	−	0.433852i
$799$			11.7244i			0.414778i
$800$	−9.44943	+	26.6591i	−0.334088	+	0.942542i
$801$	0.596997	−	0.344676i	0.0210938	−	0.0121785i
$802$	9.59202	−	25.4835i	0.338706	−	0.899853i
$803$	20.3057	−	35.1706i	0.716574	−	1.24114i
$804$	17.4477	+	3.47145i	0.615332	+	0.122429i
$805$	−38.2417	−	35.5426i	−1.34784	−	1.25271i
$806$	−3.78374	+	3.10508i	−0.133277	+	0.109372i
$807$	−25.2792	+	43.7848i	−0.889870	+	1.54130i
$808$	−33.9449	−	21.1118i	−1.19418	−	0.742711i
$809$	8.65907	+	14.9980i	0.304437	+	0.527300i	0.977136	−	0.212616i	$-0.0681984\pi$
$809$	8.65907	+	14.9980i	0.304437	+	0.527300i	−0.672699	+	0.739916i	$0.734865\pi$
$810$	−25.0191	−	20.1295i	−0.879081	−	0.707277i
$811$		−	25.3807i		−	0.891236i	−0.895223	−	0.445618i	$-0.852984\pi$
$811$		−	25.3807i		−	0.891236i	0.895223	−	0.445618i	$-0.147016\pi$
$812$	−16.7022	−	1.74526i	−0.586131	−	0.0612465i
$813$	19.3185			0.677530
$814$	10.4183	−	1.71980i	0.365160	−	0.0602789i
$815$	9.13869	+	3.00332i	0.320114	+	0.105202i
$816$	−3.14694	−	23.9216i	−0.110165	−	0.837425i
$817$	22.8060	−	39.5011i	0.797880	−	1.38197i
$818$	23.9804	−	19.6792i	0.838456	−	0.688068i
$819$	−0.655000	+	0.463551i	−0.0228875	+	0.0161978i
$820$	21.2546	+	36.0045i	0.742243	+	1.25733i
$821$	−20.2636	−	11.6992i	−0.707206	−	0.408306i	0.102820	−	0.994700i	$-0.467214\pi$
$821$	−20.2636	−	11.6992i	−0.707206	−	0.408306i	−0.810026	+	0.586394i	$0.800547\pi$
$822$	−20.6063	−	7.75624i	−0.718727	−	0.270530i
$823$	−9.67683	−	16.7608i	−0.337313	−	0.584243i	0.646613	−	0.762818i	$-0.276185\pi$
$823$	−9.67683	−	16.7608i	−0.337313	−	0.584243i	−0.983926	+	0.178575i	$0.942851\pi$
$824$	−1.41527	−	0.0464361i	−0.0493033	−	0.00161768i
$825$	3.32870	−	29.7462i	0.115890	−	1.03563i
$826$	0.0175221	+	0.0669755i	0.000609671	+	0.00233038i
$827$		−	29.0919i		−	1.01162i	−0.862644	−	0.505812i	$-0.831193\pi$
$827$		−	29.0919i		−	1.01162i	0.862644	−	0.505812i	$-0.168807\pi$
$828$	6.01575	+	5.27620i	0.209062	+	0.183360i
$829$	−13.3551	−	23.1317i	−0.463841	−	0.803397i	0.535307	−	0.844658i	$-0.320196\pi$
$829$	−13.3551	−	23.1317i	−0.463841	−	0.803397i	−0.999148	+	0.0412606i	$0.986863\pi$
$830$	19.4703	−	7.54462i	0.675822	−	0.261878i
$831$	18.9813	−	32.8765i	0.658453	−	1.14047i
$832$	4.44946	+	2.97399i	0.154257	+	0.103104i
$833$	7.55651	−	21.4280i	0.261817	−	0.742435i
$834$	−20.5764	+	16.8858i	−0.712504	+	0.584707i
$835$	−1.77577	−	8.49459i	−0.0614531	−	0.293968i
$836$	−13.7973	−	40.6521i	−0.477190	−	1.40598i
$837$	12.2421	+	21.2040i	0.423150	+	0.732917i
$838$	−4.69472	−	28.4399i	−0.162176	−	0.982439i
$839$	−24.7914			−0.855896			−0.427948	−	0.903803i	$-0.640763\pi$
$839$	−24.7914			−0.855896			−0.427948	+	0.903803i	$0.640763\pi$
$840$	21.9050	−	22.0706i	0.755795	−	0.761508i
$841$	18.9283			0.652699
$842$	4.90352	+	29.7047i	0.168986	+	1.02369i
$843$	28.9580	+	50.1568i	0.997367	+	1.72749i
$844$	−25.6792	+	8.71551i	−0.883915	+	0.300000i
$845$	27.4743	−	5.74342i	0.945143	−	0.197580i
$846$	1.79024	−	1.46914i	0.0615496	−	0.0505099i
$847$	−0.951699	−	1.34476i	−0.0327008	−	0.0462064i
$848$	0.0961160	+	0.0398237i	0.00330064	+	0.00136755i
$849$	13.1798	−	22.8281i	0.452330	−	0.783459i
$850$	−20.4483	−	10.4241i	−0.701371	−	0.357543i
$851$	10.2271	+	17.7138i	0.350579	+	0.607221i
$852$	19.9386	−	22.7334i	0.683086	−	0.778833i
$853$		−	50.6858i		−	1.73545i	−0.497047	−	0.867724i	$-0.665582\pi$
$853$		−	50.6858i		−	1.73545i	0.497047	−	0.867724i	$-0.334418\pi$
$854$	4.72271	+	4.77892i	0.161608	+	0.163531i
$855$	5.03502	−	4.50301i	0.172194	−	0.154000i
$856$	−52.4406	−	1.72061i	−1.79238	−	0.0588094i
$857$	10.5812	+	18.3272i	0.361448	+	0.626047i	0.988199	−	0.153173i	$-0.0489491\pi$
$857$	10.5812	+	18.3272i	0.361448	+	0.626047i	−0.626751	+	0.779219i	$0.715616\pi$
$858$	−5.30055	−	1.99513i	−0.180958	−	0.0681128i
$859$	2.47660	+	1.42986i	0.0845003	+	0.0487863i	0.541655	−	0.840601i	$-0.317798\pi$
$859$	2.47660	+	1.42986i	0.0845003	+	0.0487863i	−0.457154	+	0.889387i	$0.651131\pi$
$860$	15.5625	+	26.3623i	0.530677	+	0.898948i
$861$	−4.23590	−	45.7704i	−0.144359	−	1.55985i
$862$	−23.6346	+	19.3954i	−0.804997	+	0.660611i
$863$	6.07596	−	10.5239i	0.206828	−	0.358237i	−0.743886	−	0.668307i	$-0.767019\pi$
$863$	6.07596	−	10.5239i	0.206828	−	0.358237i	0.950714	+	0.310070i	$0.100353\pi$
$864$	18.3028	−	19.5369i	0.622674	−	0.664657i
$865$	−35.3133	−	11.6053i	−1.20069	−	0.394592i
$866$	−41.5904	+	6.86555i	−1.41330	+	0.233301i
$867$	−12.0124			−0.407963
$868$	−25.0029	+	11.1501i	−0.848655	+	0.378461i
$869$			50.3304i			1.70734i
$870$	11.6908	−	14.5306i	0.396356	−	0.492634i
$871$	−1.60103	−	2.77307i	−0.0542489	−	0.0939619i
$872$	−6.77787	+	10.8979i	−0.229528	+	0.369050i
$873$	−2.75873	+	4.77826i	−0.0933688	+	0.161720i
$874$	64.2836	−	52.7535i	2.17442	−	1.78441i
$875$	−5.49714	−	29.0651i	−0.185837	−	0.982581i
$876$	−9.14326	+	45.9544i	−0.308922	+	1.55266i
$877$	16.6594	−	28.8550i	0.562549	−	0.974363i	−0.434725	−	0.900563i	$-0.643154\pi$
$877$	16.6594	−	28.8550i	0.562549	−	0.974363i	0.997273	−	0.0737992i	$-0.0235124\pi$
$878$	−14.9212	+	39.6418i	−0.503567	+	1.33785i
$879$	−21.4688	+	12.3950i	−0.724126	+	0.418074i
$880$	28.3121	+	5.34869i	0.954402	+	0.180304i
$881$		−	19.5712i		−	0.659372i	−0.944091	−	0.329686i	$-0.893057\pi$
$881$		−	19.5712i		−	0.659372i	0.944091	−	0.329686i	$-0.106943\pi$
$882$	−4.21880	+	1.53123i	−0.142054	+	0.0515591i
$883$			42.7210i			1.43768i	0.695178	+	0.718838i	$0.255325\pi$
$883$			42.7210i			1.43768i	−0.695178	+	0.718838i	$0.744675\pi$
$884$	−2.86363	+	3.26502i	−0.0963143	+	0.109814i
$885$	−0.0730405	−	0.0240039i	−0.00245523	−	0.000806883i
$886$	49.0793	+	18.4735i	1.64885	+	0.620630i
$887$	−3.02603	−	1.74708i	−0.101604	−	0.0586613i	0.448337	−	0.893865i	$-0.352017\pi$
$887$	−3.02603	−	1.74708i	−0.101604	−	0.0586613i	−0.549941	+	0.835203i	$0.685350\pi$
$888$	−10.7446	+	5.74207i	−0.360564	+	0.192691i
$889$	−6.13489	+	13.3305i	−0.205757	+	0.447091i
$890$	4.75148	+	0.737174i	0.159270	+	0.0247101i
$891$	−16.3559	+	28.3292i	−0.547942	+	0.949064i
$892$	11.2644	+	33.1894i	0.377162	+	1.11126i
$893$	−12.0340	−	20.8434i	−0.402701	−	0.697499i
$894$	−1.06257	−	6.43689i	−0.0355377	−	0.215282i
$895$	23.7287	+	26.5321i	0.793162	+	0.886870i
$896$	19.5995	+	22.6243i	0.654775	+	0.755824i
$897$		−	10.9708i		−	0.366306i
$898$	−23.9969	+	3.96130i	−0.800788	+	0.132190i
$899$	−14.2194	+	8.20958i	−0.474244	+	0.273805i
$900$	0.970610	+	4.42853i	0.0323537	+	0.147618i
$901$	−0.0422128	+	0.0731146i	−0.00140631	+	0.00243580i
$902$	32.9244	−	27.0190i	1.09626	−	0.899635i
$903$	−3.10150	−	33.5128i	−0.103212	−	1.11524i
$904$	−9.26081	−	17.3288i	−0.308010	−	0.576348i
$905$	16.4220	−	3.43297i	0.545885	−	0.114116i
$906$	−6.78621	−	2.55434i	−0.225457	−	0.0848622i
$907$	18.3487	−	10.5936i	0.609258	−	0.351755i	−0.163417	−	0.986557i	$-0.552252\pi$
$907$	18.3487	−	10.5936i	0.609258	−	0.351755i	0.772675	+	0.634802i	$0.218918\pi$
$908$	−16.4665	−	14.4422i	−0.546459	−	0.479280i
$909$	−6.40748			−0.212523
$910$	−5.58647	−	0.344760i	−0.185190	−	0.0114287i
$911$		−	14.1566i		−	0.469030i	−0.972112	−	0.234515i	$-0.924650\pi$
$911$		−	14.1566i		−	0.469030i	0.972112	−	0.234515i	$-0.0753502\pi$
$912$	30.1480	+	39.2976i	0.998299	+	1.30127i
$913$	−10.6356	−	18.4214i	−0.351987	−	0.609659i
$914$	13.0621	+	4.91660i	0.432056	+	0.162627i
$915$	−7.30373	+	1.52683i	−0.241454	+	0.0504753i
$916$	7.29960	−	36.6881i	0.241186	−	1.21221i
$917$	3.48519	−	2.46651i	0.115091	−	0.0814513i
$918$	13.7811	+	16.7932i	0.454844	+	0.554257i
$919$	−25.4716	−	14.7060i	−0.840230	−	0.485107i	0.0171122	−	0.999854i	$-0.494553\pi$
$919$	−25.4716	−	14.7060i	−0.840230	−	0.485107i	−0.857342	+	0.514746i	$0.827886\pi$
$920$	9.62299	+	54.9772i	0.317260	+	1.81254i
$921$	−14.4144	−	24.9665i	−0.474972	−	0.822675i
$922$	26.5718	−	4.38635i	0.875095	−	0.144457i
$923$	−5.44277			−0.179151
$924$	−25.6384	−	18.6037i	−0.843442	−	0.612018i
$925$	−1.28880	+	11.5171i	−0.0423755	+	0.378680i
$926$	21.7623	−	3.59241i	0.715152	−	0.118054i
$927$	−0.196565	+	0.113487i	−0.00645606	+	0.00372741i
$928$	13.1014	+	12.2739i	0.430076	+	0.402909i
$929$	16.8894	+	9.75112i	0.554125	+	0.319924i	0.750784	−	0.660548i	$-0.229676\pi$
$929$	16.8894	+	9.75112i	0.554125	+	0.319924i	−0.196659	+	0.980472i	$0.563009\pi$
$930$	4.66119	−	30.0438i	0.152846	−	0.985176i
$931$	8.55994	+	45.8505i	0.280541	+	1.50269i
$932$	−8.38884	−	1.66907i	−0.274786	−	0.0546724i
$933$	−8.52728	+	14.7697i	−0.279171	+	0.483538i
$934$	−11.3116	+	30.0521i	−0.370128	+	0.983334i
$935$	−7.29980	+	22.2123i	−0.238729	+	0.726418i
$936$	0.857379	+	0.0281312i	0.0280243	+	0.000919497i
$937$	2.05387			0.0670971			0.0335485	−	0.999437i	$-0.489319\pi$
$937$	2.05387			0.0670971			0.0335485	+	0.999437i	$0.489319\pi$
$938$	−4.53288	−	17.3263i	−0.148004	−	0.565722i
$939$	60.2423			1.96593
$940$	16.1528	−	0.156376i	0.526846	−	0.00510042i
$941$	15.1289	+	26.2040i	0.493187	+	0.854226i	0.999969	−	0.00784879i	$-0.00249837\pi$
$941$	15.1289	+	26.2040i	0.493187	+	0.854226i	−0.506782	+	0.862074i	$0.669165\pi$
$942$	−12.9461	−	4.87292i	−0.421805	−	0.158768i
$943$	71.4500	+	41.2517i	2.32673	+	1.34334i
$944$	0.0283290	−	0.0683732i	0.000922030	−	0.00222536i
$945$	−6.25288	+	27.2905i	−0.203406	+	0.887760i
$946$	24.1071	−	19.7832i	0.783789	−	0.643207i
$947$	34.8806	+	20.1383i	1.13347	+	0.654407i	0.944804	−	0.327635i	$-0.106252\pi$
$947$	34.8806	+	20.1383i	1.13347	+	0.654407i	0.188662	+	0.982042i	$0.439585\pi$
$948$	−18.6627	−	54.9876i	−0.606137	−	1.78591i
$949$	7.30383	−	4.21687i	0.237092	−	0.136885i
$950$	47.0521	−	2.45649i	1.52657	−	0.0796989i
$951$	0.765564			0.0248251
$952$	−20.2766	+	13.3742i	−0.657169	+	0.433459i
$953$		−	45.4230i		−	1.47140i	−0.677309	−	0.735698i	$-0.736854\pi$
$953$		−	45.4230i		−	1.47140i	0.677309	−	0.735698i	$-0.263146\pi$
$954$	0.0164537	−	0.00271610i	0.000532708	−	8.79369e-5i
$955$	−30.0016	−	9.85969i	−0.970830	−	0.319052i
$956$	16.1380	+	47.5488i	0.521942	+	1.53784i
$957$	−16.4531	−	9.49917i	−0.531852	−	0.307065i
$958$	−30.8906	−	37.6422i	−0.998031	−	1.21617i
$959$	2.04265	+	22.0715i	0.0659605	+	0.712727i
$960$	−32.9152	+	4.65465i	−1.06233	+	0.150228i
$961$	2.11656	−	3.66599i	0.0682761	−	0.118258i
$962$	2.05226	+	0.772475i	0.0661676	+	0.0249056i
$963$	−7.28342	+	4.20508i	−0.234705	+	0.135507i
$964$	2.58581	−	2.94825i	0.0832832	−	0.0949569i
$965$	13.6660	−	12.2221i	0.439925	−	0.393442i
$966$	16.2317	−	59.1749i	0.522245	−	1.90392i
$967$	52.7807			1.69731			0.848656	−	0.528945i	$-0.177412\pi$
$967$	52.7807			1.69731			0.848656	+	0.528945i	$0.177412\pi$
$968$	−0.0577551	+	1.76025i	−0.00185632	+	0.0565767i
$969$	−34.8075	+	20.0961i	−1.11818	+	0.645580i
$970$	−35.8850	+	13.9053i	−1.15220	+	0.446471i
$971$	−26.0287	−	15.0277i	−0.835300	−	0.482261i	0.0203639	−	0.999793i	$-0.493518\pi$
$971$	−26.0287	−	15.0277i	−0.835300	−	0.482261i	−0.855664	+	0.517532i	$0.826851\pi$
$972$	1.82378	−	9.16639i	0.0584977	−	0.294012i
$973$	24.3430	+	11.2030i	0.780400	+	0.359151i
$974$	−0.749711	−	0.913571i	−0.0240223	−	0.0292727i
$975$	3.68733	−	5.00411i	0.118089	−	0.160260i
$976$	−0.936825	−	7.12132i	−0.0299870	−	0.227948i
$977$	−36.9900	+	21.3562i	−1.18341	+	0.683245i	−0.956802	−	0.290740i	$-0.906099\pi$
$977$	−36.9900	+	21.3562i	−1.18341	+	0.683245i	−0.226613	+	0.973985i	$0.572765\pi$
$978$	1.84141	+	11.1549i	0.0588817	+	0.356696i
$979$		−	4.89820i		−	0.156547i
$980$	−29.6224	−	10.1249i	−0.946253	−	0.323428i
$981$			2.05710i			0.0656781i
$982$	−39.5020	+	6.52080i	−1.26056	+	0.208087i
$983$	−10.5472	+	6.08944i	−0.336404	+	0.194223i	−0.658681	−	0.752423i	$-0.728885\pi$
$983$	−10.5472	+	6.08944i	−0.336404	+	0.194223i	0.322277	+	0.946646i	$0.395552\pi$
$984$	−25.9522	+	41.7276i	−0.827326	+	1.33023i
$985$	14.5151	−	3.03434i	0.462489	−	0.0966820i
$986$	−11.2615	+	9.24162i	−0.358640	+	0.294313i
$987$	−16.1328	−	7.42451i	−0.513512	−	0.236325i
$988$	1.73969	−	8.74377i	0.0553470	−	0.278176i
$989$	52.3153	+	30.2043i	1.66353	+	0.960440i
$990$	4.30639	−	1.66870i	0.136866	−	0.0530348i
$991$	−16.8998	+	9.75712i	−0.536841	+	0.309945i	−0.743798	−	0.668405i	$-0.766977\pi$
$991$	−16.8998	+	9.75712i	−0.536841	+	0.309945i	0.206957	+	0.978350i	$0.433644\pi$
$992$	28.5014	+	6.64929i	0.904919	+	0.211115i
$993$	−54.7348			−1.73696
$994$	−29.3574	−	8.05272i	−0.931160	−	0.255417i
$995$	−5.31085	−	5.93830i	−0.168365	−	0.188257i
$996$	18.4505	+	16.1822i	0.584625	+	0.512753i
$997$	−25.7749	+	14.8811i	−0.816298	+	0.471290i	−0.849138	−	0.528171i	$-0.822878\pi$
$997$	−25.7749	+	14.8811i	−0.816298	+	0.471290i	0.0328401	+	0.999461i	$0.489545\pi$
$998$	−2.19118	+	5.82139i	−0.0693606	+	0.184273i
$999$	5.48446	−	9.49936i	0.173521	−	0.300547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.ba.b.19.2	✓	80
4.3	odd	2		1120.2.bq.b.719.31		80
5.4	even	2	inner	280.2.ba.b.19.39	yes	80
7.3	odd	6	inner	280.2.ba.b.59.25	yes	80
8.3	odd	2	inner	280.2.ba.b.19.16	yes	80
8.5	even	2		1120.2.bq.b.719.32		80
20.19	odd	2		1120.2.bq.b.719.9		80
28.3	even	6		1120.2.bq.b.1039.10		80
35.24	odd	6	inner	280.2.ba.b.59.16	yes	80
40.19	odd	2	inner	280.2.ba.b.19.25	yes	80
40.29	even	2		1120.2.bq.b.719.10		80
56.3	even	6	inner	280.2.ba.b.59.39	yes	80
56.45	odd	6		1120.2.bq.b.1039.9		80
140.59	even	6		1120.2.bq.b.1039.32		80
280.59	even	6	inner	280.2.ba.b.59.2	yes	80
280.269	odd	6		1120.2.bq.b.1039.31		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.2	✓	80	1.1	even	1	trivial
280.2.ba.b.19.16	yes	80	8.3	odd	2	inner
280.2.ba.b.19.25	yes	80	40.19	odd	2	inner
280.2.ba.b.19.39	yes	80	5.4	even	2	inner
280.2.ba.b.59.2	yes	80	280.59	even	6	inner
280.2.ba.b.59.16	yes	80	35.24	odd	6	inner
280.2.ba.b.59.25	yes	80	7.3	odd	6	inner
280.2.ba.b.59.39	yes	80	56.3	even	6	inner
1120.2.bq.b.719.9		80	20.19	odd	2
1120.2.bq.b.719.10		80	40.29	even	2
1120.2.bq.b.719.31		80	4.3	odd	2
1120.2.bq.b.719.32		80	8.5	even	2
1120.2.bq.b.1039.9		80	56.45	odd	6
1120.2.bq.b.1039.10		80	28.3	even	6
1120.2.bq.b.1039.31		80	280.269	odd	6
1120.2.bq.b.1039.32		80	140.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39533 + 0.230335i) q^{2} +(-0.929162 - 1.60936i) q^{3} +(1.89389 - 0.642786i) q^{4} +(2.18875 - 0.457553i) q^{5} +(1.66718 + 2.03156i) q^{6} +(1.10610 - 2.40345i) q^{7} +(-2.49455 + 1.33313i) q^{8} +(-0.226682 + 0.392626i) q^{9} +O(q^{10})\)	\(q+(-1.39533 + 0.230335i) q^{2} +(-0.929162 - 1.60936i) q^{3} +(1.89389 - 0.642786i) q^{4} +(2.18875 - 0.457553i) q^{5} +(1.66718 + 2.03156i) q^{6} +(1.10610 - 2.40345i) q^{7} +(-2.49455 + 1.33313i) q^{8} +(-0.226682 + 0.392626i) q^{9} +(-2.94864 + 1.14258i) q^{10} +(1.61069 + 2.78980i) q^{11} +(-2.79420 - 2.45069i) q^{12} +0.668981i q^{13} +(-0.989775 + 3.60837i) q^{14} +(-2.77007 - 3.09734i) q^{15} +(3.17365 - 2.43473i) q^{16} +(1.62295 + 2.81103i) q^{17} +(0.225862 - 0.600055i) q^{18} +(-5.77054 - 3.33162i) q^{19} +(3.85116 - 2.27346i) q^{20} +(-4.89574 + 0.453085i) q^{21} +(-2.89004 - 3.52170i) q^{22} +(4.41240 - 7.64251i) q^{23} +(4.46331 + 2.77592i) q^{24} +(4.58129 - 2.00294i) q^{25} +(-0.154089 - 0.933449i) q^{26} -4.73247 q^{27} +(0.549930 - 5.26285i) q^{28} -3.17360i q^{29} +(4.57859 + 3.68377i) q^{30} +(-2.58684 - 4.48053i) q^{31} +(-3.86749 + 4.12826i) q^{32} +(2.99319 - 5.18435i) q^{33} +(-2.91203 - 3.54850i) q^{34} +(1.32127 - 5.76665i) q^{35} +(-0.176938 + 0.889299i) q^{36} +(-1.15890 + 2.00727i) q^{37} +(8.81919 + 3.31956i) q^{38} +(1.07663 - 0.621591i) q^{39} +(-4.84998 + 4.05928i) q^{40} +9.34903i q^{41} +(6.72681 - 1.75986i) q^{42} +6.84531i q^{43} +(4.84372 + 4.24825i) q^{44} +(-0.316505 + 0.963080i) q^{45} +(-4.39643 + 11.6802i) q^{46} +(3.12812 + 1.80602i) q^{47} +(-6.86719 - 2.84528i) q^{48} +(-4.55310 - 5.31689i) q^{49} +(-5.93106 + 3.85000i) q^{50} +(3.01597 - 5.22381i) q^{51} +(0.430011 + 1.26698i) q^{52} +(0.0130049 + 0.0225252i) q^{53} +(6.60336 - 1.09005i) q^{54} +(4.80189 + 5.36921i) q^{55} +(0.444882 + 7.47008i) q^{56} +12.3825i q^{57} +(0.730989 + 4.42822i) q^{58} +(0.0160236 - 0.00925120i) q^{59} +(-7.23714 - 4.08547i) q^{60} +(0.897835 - 1.55510i) q^{61} +(4.64151 + 5.65598i) q^{62} +(0.692921 + 0.979101i) q^{63} +(4.44555 - 6.65110i) q^{64} +(0.306094 + 1.46423i) q^{65} +(-2.98235 + 7.92332i) q^{66} +(-4.14522 + 2.39324i) q^{67} +(4.88059 + 4.28059i) q^{68} -16.3993 q^{69} +(-0.515352 + 8.35071i) q^{70} +8.13591i q^{71} +(0.0420508 - 1.28162i) q^{72} +(-6.30342 - 10.9178i) q^{73} +(1.15470 - 3.06774i) q^{74} +(-7.48021 - 5.51186i) q^{75} +(-13.0703 - 2.60051i) q^{76} +(8.48672 - 0.785418i) q^{77} +(-1.35908 + 1.11531i) q^{78} +(13.5306 + 7.81192i) q^{79} +(5.83233 - 6.78115i) q^{80} +(5.07728 + 8.79410i) q^{81} +(-2.15340 - 13.0450i) q^{82} -6.60312 q^{83} +(-8.98077 + 4.00500i) q^{84} +(4.83844 + 5.41008i) q^{85} +(-1.57671 - 9.55146i) q^{86} +(-5.10745 + 2.94879i) q^{87} +(-7.73711 - 4.81204i) q^{88} +(-1.31681 - 0.760263i) q^{89} +(0.219798 - 1.41672i) q^{90} +(1.60786 + 0.739958i) q^{91} +(3.44412 - 17.3103i) q^{92} +(-4.80718 + 8.32628i) q^{93} +(-4.78076 - 1.79948i) q^{94} +(-14.1547 - 4.65177i) q^{95} +(10.2374 + 2.38835i) q^{96} +12.1700 q^{97} +(7.57774 + 6.37008i) q^{98} -1.46046 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{4} - 52 q^{9}+O(q^{10}) \) 80 * q + 6 * q^4 - 52 * q^9	\( 80 q + 6 q^{4} - 52 q^{9} - 12 q^{10} - 6 q^{14} + 10 q^{16} - 48 q^{19} + 12 q^{24} - 22 q^{25} + 54 q^{26} - 20 q^{30} - 22 q^{35} + 28 q^{36} + 12 q^{40} + 38 q^{44} + 14 q^{46} + 16 q^{49} - 40 q^{50} + 20 q^{51} + 60 q^{54} - 104 q^{56} - 60 q^{59} - 42 q^{60} - 60 q^{64} - 12 q^{65} + 84 q^{66} - 22 q^{70} + 34 q^{74} - 6 q^{75} - 96 q^{80} - 100 q^{84} - 8 q^{86} - 36 q^{89} + 72 q^{91} - 66 q^{94} + 96 q^{96} + 104 q^{99}+O(q^{100}) \) 80 * q + 6 * q^4 - 52 * q^9 - 12 * q^10 - 6 * q^14 + 10 * q^16 - 48 * q^19 + 12 * q^24 - 22 * q^25 + 54 * q^26 - 20 * q^30 - 22 * q^35 + 28 * q^36 + 12 * q^40 + 38 * q^44 + 14 * q^46 + 16 * q^49 - 40 * q^50 + 20 * q^51 + 60 * q^54 - 104 * q^56 - 60 * q^59 - 42 * q^60 - 60 * q^64 - 12 * q^65 + 84 * q^66 - 22 * q^70 + 34 * q^74 - 6 * q^75 - 96 * q^80 - 100 * q^84 - 8 * q^86 - 36 * q^89 + 72 * q^91 - 66 * q^94 + 96 * q^96 + 104 * q^99

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