LMFDB - Embedded newform 273.2.cg.a.124.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			124.8
Character	$\chi$	$=$	273.124
Dual form			273.2.cg.a.262.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.569735 - 2.12628i) q^{2} +1.00000i q^{3} +(-2.46442 - 1.42283i) q^{4} +(0.837395 + 3.12520i) q^{5} +(2.12628 + 0.569735i) q^{6} +(0.780325 + 2.52806i) q^{7} +(-1.31631 + 1.31631i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.569735 - 2.12628i) q^{2} +1.00000i q^{3} +(-2.46442 - 1.42283i) q^{4} +(0.837395 + 3.12520i) q^{5} +(2.12628 + 0.569735i) q^{6} +(0.780325 + 2.52806i) q^{7} +(-1.31631 + 1.31631i) q^{8} -1.00000 q^{9} +7.12215 q^{10} +(2.85107 - 2.85107i) q^{11} +(1.42283 - 2.46442i) q^{12} +(2.61925 - 2.47781i) q^{13} +(5.81994 - 0.218864i) q^{14} +(-3.12520 + 0.837395i) q^{15} +(-0.796765 - 1.38004i) q^{16} +(-3.80501 + 6.59048i) q^{17} +(-0.569735 + 2.12628i) q^{18} +(1.95154 - 1.95154i) q^{19} +(2.38294 - 8.89327i) q^{20} +(-2.52806 + 0.780325i) q^{21} +(-4.43782 - 7.68652i) q^{22} +(-3.89447 + 2.24848i) q^{23} +(-1.31631 - 1.31631i) q^{24} +(-4.73553 + 2.73406i) q^{25} +(-3.77625 - 6.98094i) q^{26} -1.00000i q^{27} +(1.67396 - 7.34047i) q^{28} +(1.49169 - 2.58368i) q^{29} +7.12215i q^{30} +(2.58181 + 0.691794i) q^{31} +(-6.98452 + 1.87150i) q^{32} +(2.85107 + 2.85107i) q^{33} +(11.8454 + 11.8454i) q^{34} +(-7.24726 + 4.55566i) q^{35} +(2.46442 + 1.42283i) q^{36} +(-1.64078 - 0.439645i) q^{37} +(-3.03766 - 5.26138i) q^{38} +(2.47781 + 2.61925i) q^{39} +(-5.21601 - 3.01147i) q^{40} +(-2.95120 - 11.0140i) q^{41} +(0.218864 + 5.81994i) q^{42} +(6.30996 - 3.64306i) q^{43} +(-11.0828 + 2.96963i) q^{44} +(-0.837395 - 3.12520i) q^{45} +(2.56207 + 9.56178i) q^{46} +(-2.48667 + 0.666302i) q^{47} +(1.38004 - 0.796765i) q^{48} +(-5.78219 + 3.94542i) q^{49} +(3.11538 + 11.6267i) q^{50} +(-6.59048 - 3.80501i) q^{51} +(-9.98042 + 2.37961i) q^{52} +(-3.91287 - 6.77729i) q^{53} +(-2.12628 - 0.569735i) q^{54} +(11.2976 + 6.52269i) q^{55} +(-4.35487 - 2.30057i) q^{56} +(1.95154 + 1.95154i) q^{57} +(-4.64375 - 4.64375i) q^{58} +(-7.90374 + 2.11780i) q^{59} +(8.89327 + 2.38294i) q^{60} -9.20877i q^{61} +(2.94189 - 5.09551i) q^{62} +(-0.780325 - 2.52806i) q^{63} +12.7302i q^{64} +(9.93701 + 6.11076i) q^{65} +(7.68652 - 4.43782i) q^{66} +(5.52580 + 5.52580i) q^{67} +(18.7543 - 10.8278i) q^{68} +(-2.24848 - 3.89447i) q^{69} +(5.55759 + 18.0052i) q^{70} +(-0.721147 + 2.69136i) q^{71} +(1.31631 - 1.31631i) q^{72} +(0.453517 - 1.69255i) q^{73} +(-1.86962 + 3.23827i) q^{74} +(-2.73406 - 4.73553i) q^{75} +(-7.58612 + 2.03270i) q^{76} +(9.43244 + 4.98292i) q^{77} +(6.98094 - 3.77625i) q^{78} +(4.31023 - 7.46554i) q^{79} +(3.64569 - 3.64569i) q^{80} +1.00000 q^{81} -25.1003 q^{82} +(-1.63865 + 1.63865i) q^{83} +(7.34047 + 1.67396i) q^{84} +(-23.7829 - 6.37260i) q^{85} +(-4.15115 - 15.4923i) q^{86} +(2.58368 + 1.49169i) q^{87} +7.50579i q^{88} +(-4.66770 + 17.4201i) q^{89} -7.12215 q^{90} +(8.30792 + 4.68812i) q^{91} +12.7968 q^{92} +(-0.691794 + 2.58181i) q^{93} +5.66697i q^{94} +(7.73317 + 4.46475i) q^{95} +(-1.87150 - 6.98452i) q^{96} +(-12.7508 - 3.41658i) q^{97} +(5.09475 + 14.5424i) q^{98} +(-2.85107 + 2.85107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 - 36 * q^9	$ 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.569735	−	2.12628i	0.402863	−	1.50351i	−0.405099	−	0.914273i	$-0.632763\pi$
$2$	0.569735	−	2.12628i	0.402863	−	1.50351i	0.807962	−	0.589234i	$-0.200570\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−2.46442	−	1.42283i	−1.23221	−	0.711416i
$5$	0.837395	+	3.12520i	0.374495	+	1.39763i	0.854082	+	0.520139i	$0.174120\pi$
$5$	0.837395	+	3.12520i	0.374495	+	1.39763i	−0.479587	+	0.877494i	$0.659214\pi$
$6$	2.12628	+	0.569735i	0.868050	+	0.232593i
$7$	0.780325	+	2.52806i	0.294935	+	0.955517i
$7$	0.780325	+	2.52806i	0.294935	+	0.955517i
$8$	−1.31631	+	1.31631i	−0.465386	+	0.465386i
$9$	−1.00000			−0.333333
$10$	7.12215			2.25222
$11$	2.85107	−	2.85107i	0.859630	−	0.859630i	−0.131665	−	0.991294i	$-0.542032\pi$
$11$	2.85107	−	2.85107i	0.859630	−	0.859630i	0.991294	+	0.131665i	$0.0420322\pi$
$12$	1.42283	−	2.46442i	0.410736	−	0.711416i
$13$	2.61925	−	2.47781i	0.726448	−	0.687221i
$13$	2.61925	−	2.47781i	0.726448	−	0.687221i
$14$	5.81994	−	0.218864i	1.55545	−	0.0584939i
$15$	−3.12520	+	0.837395i	−0.806924	+	0.216215i
$16$	−0.796765	−	1.38004i	−0.199191	−	0.345009i
$17$	−3.80501	+	6.59048i	−0.922852	+	1.59843i	−0.127871	+	0.991791i	$0.540814\pi$
$17$	−3.80501	+	6.59048i	−0.922852	+	1.59843i	−0.794980	+	0.606635i	$0.792519\pi$
$18$	−0.569735	+	2.12628i	−0.134288	+	0.501169i
$19$	1.95154	−	1.95154i	0.447714	−	0.447714i	−0.446880	−	0.894594i	$-0.647465\pi$
$19$	1.95154	−	1.95154i	0.447714	−	0.447714i	0.894594	+	0.446880i	$0.147465\pi$
$20$	2.38294	−	8.89327i	0.532843	−	1.98860i
$21$	−2.52806	+	0.780325i	−0.551668	+	0.170281i
$22$	−4.43782	−	7.68652i	−0.946146	−	1.63877i
$23$	−3.89447	+	2.24848i	−0.812054	+	0.468840i	−0.847669	−	0.530526i	$-0.821994\pi$
$23$	−3.89447	+	2.24848i	−0.812054	+	0.468840i	0.0356146	+	0.999366i	$0.488661\pi$
$24$	−1.31631	−	1.31631i	−0.268691	−	0.268691i
$25$	−4.73553	+	2.73406i	−0.947106	+	0.546812i
$26$	−3.77625	−	6.98094i	−0.740583	−	1.36908i
$27$		−	1.00000i		−	0.192450i
$28$	1.67396	−	7.34047i	0.316349	−	1.38722i
$29$	1.49169	−	2.58368i	0.276999	−	0.479777i	−0.693638	−	0.720323i	$-0.743993\pi$
$29$	1.49169	−	2.58368i	0.276999	−	0.479777i	0.970638	+	0.240547i	$0.0773267\pi$
$30$			7.12215i			1.30032i
$31$	2.58181	+	0.691794i	0.463707	+	0.124250i	0.483106	−	0.875562i	$-0.339509\pi$
$31$	2.58181	+	0.691794i	0.463707	+	0.124250i	−0.0193991	+	0.999812i	$0.506175\pi$
$32$	−6.98452	+	1.87150i	−1.23470	+	0.330837i
$33$	2.85107	+	2.85107i	0.496307	+	0.496307i
$34$	11.8454	+	11.8454i	2.03146	+	2.03146i
$35$	−7.24726	+	4.55566i	−1.22501	+	0.770047i
$36$	2.46442	+	1.42283i	0.410736	+	0.237139i
$37$	−1.64078	−	0.439645i	−0.269742	−	0.0722772i	0.121412	−	0.992602i	$-0.461258\pi$
$37$	−1.64078	−	0.439645i	−0.269742	−	0.0722772i	−0.391155	+	0.920325i	$0.627924\pi$
$38$	−3.03766	−	5.26138i	−0.492774	−	0.853509i
$39$	2.47781	+	2.61925i	0.396767	+	0.419415i
$40$	−5.21601	−	3.01147i	−0.824724	−	0.476155i
$41$	−2.95120	−	11.0140i	−0.460900	−	1.72010i	−0.670138	−	0.742236i	$-0.733765\pi$
$41$	−2.95120	−	11.0140i	−0.460900	−	1.72010i	0.209239	−	0.977865i	$-0.432901\pi$
$42$	0.218864	+	5.81994i	0.0337715	+	0.898037i
$43$	6.30996	−	3.64306i	0.962260	−	0.555561i	0.0653923	−	0.997860i	$-0.479170\pi$
$43$	6.30996	−	3.64306i	0.962260	−	0.555561i	0.896868	+	0.442298i	$0.145837\pi$
$44$	−11.0828	+	2.96963i	−1.67080	+	0.447689i
$45$	−0.837395	−	3.12520i	−0.124832	−	0.465878i
$46$	2.56207	+	9.56178i	0.377757	+	1.40981i
$47$	−2.48667	+	0.666302i	−0.362718	+	0.0971901i	−0.435575	−	0.900152i	$-0.643455\pi$
$47$	−2.48667	+	0.666302i	−0.362718	+	0.0971901i	0.0728569	+	0.997342i	$0.476788\pi$
$48$	1.38004	−	0.796765i	0.199191	−	0.115003i
$49$	−5.78219	+	3.94542i	−0.826027	+	0.563631i
$50$	3.11538	+	11.6267i	0.440581	+	1.64427i
$51$	−6.59048	−	3.80501i	−0.922852	−	0.532809i
$52$	−9.98042	+	2.37961i	−1.38404	+	0.329993i
$53$	−3.91287	−	6.77729i	−0.537474	−	0.930933i	−0.999039	−	0.0438262i	$-0.986045\pi$
$53$	−3.91287	−	6.77729i	−0.537474	−	0.930933i	0.461565	−	0.887106i	$-0.347288\pi$
$54$	−2.12628	−	0.569735i	−0.289350	−	0.0775311i
$55$	11.2976	+	6.52269i	1.52337	+	0.879520i
$56$	−4.35487	−	2.30057i	−0.581944	−	0.307426i
$57$	1.95154	+	1.95154i	0.258488	+	0.258488i
$58$	−4.64375	−	4.64375i	−0.609755	−	0.609755i
$59$	−7.90374	+	2.11780i	−1.02898	+	0.275714i	−0.733539	−	0.679647i	$-0.762133\pi$
$59$	−7.90374	+	2.11780i	−1.02898	+	0.275714i	−0.295440	+	0.955361i	$0.595466\pi$
$60$	8.89327	+	2.38294i	1.14812	+	0.307637i
$61$		−	9.20877i		−	1.17906i	−0.807746	−	0.589531i	$-0.799312\pi$
$61$		−	9.20877i		−	1.17906i	0.807746	−	0.589531i	$-0.200688\pi$
$62$	2.94189	−	5.09551i	0.373621	−	0.647130i
$63$	−0.780325	−	2.52806i	−0.0983117	−	0.318506i
$64$			12.7302i			1.59128i
$65$	9.93701	+	6.11076i	1.23253	+	0.757947i
$66$	7.68652	−	4.43782i	0.946146	−	0.546257i
$67$	5.52580	+	5.52580i	0.675084	+	0.675084i	0.958884	−	0.283799i	$-0.0915950\pi$
$67$	5.52580	+	5.52580i	0.675084	+	0.675084i	−0.283799	+	0.958884i	$0.591595\pi$
$68$	18.7543	−	10.8278i	2.27429	−	1.31306i
$69$	−2.24848	−	3.89447i	−0.270685	−	0.468840i
$70$	5.55759	+	18.0052i	0.664259	+	2.15204i
$71$	−0.721147	+	2.69136i	−0.0855844	+	0.319405i	−0.995424	−	0.0955544i	$-0.969538\pi$
$71$	−0.721147	+	2.69136i	−0.0855844	+	0.319405i	0.909840	+	0.414960i	$0.136204\pi$
$72$	1.31631	−	1.31631i	0.155129	−	0.155129i
$73$	0.453517	−	1.69255i	0.0530802	−	0.198098i	−0.934294	−	0.356504i	$-0.883969\pi$
$73$	0.453517	−	1.69255i	0.0530802	−	0.198098i	0.987374	+	0.158406i	$0.0506354\pi$
$74$	−1.86962	+	3.23827i	−0.217339	+	0.376441i
$75$	−2.73406	−	4.73553i	−0.315702	−	0.546812i
$76$	−7.58612	+	2.03270i	−0.870188	+	0.233166i
$77$	9.43244	+	4.98292i	1.07493	+	0.567856i
$78$	6.98094	−	3.77625i	0.790436	−	0.427576i
$79$	4.31023	−	7.46554i	0.484939	−	0.839939i	−0.514911	−	0.857244i	$-0.672175\pi$
$79$	4.31023	−	7.46554i	0.484939	−	0.839939i	0.999850	+	0.0173043i	$0.00550840\pi$
$80$	3.64569	−	3.64569i	0.407600	−	0.407600i
$81$	1.00000			0.111111
$82$	−25.1003			−2.77186
$83$	−1.63865	+	1.63865i	−0.179865	+	0.179865i	−0.791297	−	0.611432i	$-0.790594\pi$
$83$	−1.63865	+	1.63865i	−0.179865	+	0.179865i	0.611432	+	0.791297i	$0.290594\pi$
$84$	7.34047	+	1.67396i	0.800910	+	0.182644i
$85$	−23.7829	−	6.37260i	−2.57962	−	0.691206i
$86$	−4.15115	−	15.4923i	−0.447631	−	1.67058i
$87$	2.58368	+	1.49169i	0.276999	+	0.159926i
$88$			7.50579i			0.800120i
$89$	−4.66770	+	17.4201i	−0.494775	+	1.84653i	0.0365089	+	0.999333i	$0.488376\pi$
$89$	−4.66770	+	17.4201i	−0.494775	+	1.84653i	−0.531284	+	0.847194i	$0.678290\pi$
$90$	−7.12215			−0.750740
$91$	8.30792	+	4.68812i	0.870907	+	0.491448i
$92$	12.7968			1.33416
$93$	−0.691794	+	2.58181i	−0.0717357	+	0.267721i
$94$			5.66697i			0.584504i
$95$	7.73317	+	4.46475i	0.793407	+	0.458074i
$96$	−1.87150	−	6.98452i	−0.191009	−	0.712855i
$97$	−12.7508	−	3.41658i	−1.29465	−	0.346901i	−0.455226	−	0.890376i	$-0.650441\pi$
$97$	−12.7508	−	3.41658i	−1.29465	−	0.346901i	−0.839425	+	0.543475i	$0.817108\pi$
$98$	5.09475	+	14.5424i	0.514647	+	1.46900i
$99$	−2.85107	+	2.85107i	−0.286543	+	0.286543i
$100$	15.5604			1.55604
$101$	3.97164			0.395193			0.197597	−	0.980283i	$-0.436686\pi$
$101$	3.97164			0.395193			0.197597	+	0.980283i	$0.436686\pi$
$102$	−11.8454	+	11.8454i	−1.17286	+	1.17286i
$103$	1.90417	−	3.29812i	0.187623	−	0.324973i	−0.756834	−	0.653607i	$-0.773255\pi$
$103$	1.90417	−	3.29812i	0.187623	−	0.324973i	0.944457	+	0.328634i	$0.106588\pi$
$104$	−0.186171	+	6.70932i	−0.0182556	+	0.657903i
$105$	−4.55566	−	7.24726i	−0.444587	−	0.707260i
$106$	−16.6397	+	4.45860i	−1.61619	+	0.433057i
$107$	3.43298	+	5.94610i	0.331879	+	0.574832i	0.982880	−	0.184245i	$-0.0589840\pi$
$107$	3.43298	+	5.94610i	0.331879	+	0.574832i	−0.651001	+	0.759077i	$0.725651\pi$
$108$	−1.42283	+	2.46442i	−0.136912	+	0.237139i
$109$	1.26210	−	4.71023i	0.120887	−	0.451158i	−0.878772	−	0.477241i	$-0.841637\pi$
$109$	1.26210	−	4.71023i	0.120887	−	0.451158i	0.999660	+	0.0260833i	$0.00830352\pi$
$110$	20.3057	−	20.3057i	1.93608	−	1.93608i
$111$	0.439645	−	1.64078i	0.0417293	−	0.155736i
$112$	2.86708	−	3.09115i	0.270914	−	0.292086i
$113$	−4.45378	−	7.71418i	−0.418977	−	0.725689i	0.576860	−	0.816843i	$-0.304278\pi$
$113$	−4.45378	−	7.71418i	−0.418977	−	0.725689i	−0.995837	+	0.0911542i	$0.970944\pi$
$114$	5.26138	−	3.03766i	0.492774	−	0.284503i
$115$	−10.2882	−	10.2882i	−0.959376	−	0.959376i
$116$	−7.35227	+	4.24484i	−0.682642	+	0.394123i
$117$	−2.61925	+	2.47781i	−0.242149	+	0.229074i
$118$			18.0122i			1.65815i
$119$	−19.6303	−	4.47660i	−1.79950	−	0.410369i
$120$	3.01147	−	5.21601i	0.274908	−	0.476155i
$121$		−	5.25719i		−	0.477926i
$122$	−19.5804	−	5.24656i	−1.77273	−	0.475001i
$123$	11.0140	−	2.95120i	0.993101	−	0.266101i
$124$	−5.37835	−	5.37835i	−0.482990	−	0.482990i
$125$	−1.07096	−	1.07096i	−0.0957897	−	0.0957897i
$126$	−5.81994	+	0.218864i	−0.518482	+	0.0194980i
$127$	5.06664	+	2.92523i	0.449592	+	0.259572i	0.707658	−	0.706555i	$-0.249752\pi$
$127$	5.06664	+	2.92523i	0.449592	+	0.259572i	−0.258066	+	0.966127i	$0.583085\pi$
$128$	13.0990	+	3.50987i	1.15780	+	0.310231i
$129$	3.64306	+	6.30996i	0.320753	+	0.555561i
$130$	18.6547	−	17.6473i	1.63612	−	1.54777i
$131$	2.26616	+	1.30837i	0.197995	+	0.114313i	0.595720	−	0.803192i	$-0.296867\pi$
$131$	2.26616	+	1.30837i	0.197995	+	0.114313i	−0.397725	+	0.917505i	$0.630200\pi$
$132$	−2.96963	−	11.0828i	−0.258473	−	0.964635i
$133$	6.45645	+	3.41078i	0.559845	+	0.295752i
$134$	14.8976	−	8.60116i	1.28696	−	0.743027i
$135$	3.12520	−	0.837395i	0.268975	−	0.0720715i
$136$	−3.66654	−	13.6837i	−0.314403	−	1.17337i
$137$	−2.91890	−	10.8935i	−0.249379	−	0.930695i	−0.971132	−	0.238544i	$-0.923330\pi$
$137$	−2.91890	−	10.8935i	−0.249379	−	0.930695i	0.721753	−	0.692151i	$-0.243337\pi$
$138$	−9.56178	+	2.56207i	−0.813953	+	0.218098i
$139$	2.50525	−	1.44641i	0.212493	−	0.122683i	−0.389977	−	0.920825i	$-0.627517\pi$
$139$	2.50525	−	1.44641i	0.212493	−	0.122683i	0.602469	+	0.798142i	$0.294184\pi$
$140$	24.3422	−	0.915410i	2.05729	−	0.0773663i
$141$	−0.666302	−	2.48667i	−0.0561127	−	0.209416i
$142$	5.31171	+	3.06672i	0.445749	+	0.257353i
$143$	0.403238	−	14.5321i	0.0337204	−	1.21523i
$144$	0.796765	+	1.38004i	0.0663971	+	0.115003i
$145$	9.32365	+	2.49826i	0.774287	+	0.207469i
$146$	−3.34045	−	1.92861i	−0.276458	−	0.159613i
$147$	−3.94542	−	5.78219i	−0.325413	−	0.476907i
$148$	3.41802	+	3.41802i	0.280959	+	0.280959i
$149$	−1.01600	−	1.01600i	−0.0832337	−	0.0832337i	0.664264	−	0.747498i	$-0.268745\pi$
$149$	−1.01600	−	1.01600i	−0.0832337	−	0.0832337i	−0.747498	+	0.664264i	$0.768745\pi$
$150$	−11.6267	+	3.11538i	−0.949320	+	0.254369i
$151$	−7.75599	−	2.07821i	−0.631174	−	0.169122i	−0.0709714	−	0.997478i	$-0.522610\pi$
$151$	−7.75599	−	2.07821i	−0.631174	−	0.169122i	−0.560202	+	0.828356i	$0.689277\pi$
$152$			5.13767i			0.416720i
$153$	3.80501	−	6.59048i	0.307617	−	0.532809i
$154$	15.9691	−	17.2171i	1.28682	−	1.38739i
$155$			8.64798i			0.694623i
$156$	−2.37961	−	9.98042i	−0.190522	−	0.799073i
$157$	−1.71529	+	0.990321i	−0.136895	+	0.0790362i	−0.566883	−	0.823798i	$-0.691851\pi$
$157$	−1.71529	+	0.990321i	−0.136895	+	0.0790362i	0.429989	+	0.902834i	$0.358518\pi$
$158$	−13.4181	−	13.4181i	−1.06749	−	1.06749i
$159$	6.77729	−	3.91287i	0.537474	−	0.310311i
$160$	−11.6976	−	20.2609i	−0.924777	−	1.60176i
$161$	−8.72324	−	8.09093i	−0.687488	−	0.637654i
$162$	0.569735	−	2.12628i	0.0447626	−	0.167056i
$163$	−0.0789174	+	0.0789174i	−0.00618129	+	0.00618129i	−0.710191	−	0.704009i	$-0.751391\pi$
$163$	−0.0789174	+	0.0789174i	−0.00618129	+	0.00618129i	0.704009	+	0.710191i	$0.251391\pi$
$164$	−8.39811	+	31.3422i	−0.655782	+	2.44741i
$165$	−6.52269	+	11.2976i	−0.507791	+	0.879520i
$166$	2.55063	+	4.41781i	0.197967	+	0.342889i
$167$	21.7275	−	5.82186i	1.68132	−	0.450509i	0.713195	−	0.700965i	$-0.247247\pi$
$167$	21.7275	−	5.82186i	1.68132	−	0.450509i	0.968128	+	0.250456i	$0.0805805\pi$
$168$	2.30057	−	4.35487i	0.177492	−	0.335985i
$169$	0.720896	−	12.9800i	0.0554536	−	0.998461i
$170$	−27.0999	+	46.9384i	−2.07847	+	3.60001i
$171$	−1.95154	+	1.95154i	−0.149238	+	0.149238i
$172$	−20.7338			−1.58094
$173$	4.72817			0.359476			0.179738	−	0.983714i	$-0.442475\pi$
$173$	4.72817			0.359476			0.179738	+	0.983714i	$0.442475\pi$
$174$	4.64375	−	4.64375i	0.352042	−	0.352042i
$175$	−10.6071	−	9.83825i	−0.801823	−	0.743702i
$176$	−6.20621	−	1.66295i	−0.467811	−	0.125350i
$177$	−2.11780	−	7.90374i	−0.159184	−	0.594082i
$178$	34.3807	+	19.8497i	2.57694	+	1.48780i
$179$			22.9111i			1.71246i	0.516598	+	0.856228i	$0.327198\pi$
$179$			22.9111i			1.71246i	−0.516598	+	0.856228i	$0.672802\pi$
$180$	−2.38294	+	8.89327i	−0.177614	+	0.662865i
$181$	−4.84056			−0.359796			−0.179898	−	0.983685i	$-0.557577\pi$
$181$	−4.84056			−0.359796			−0.179898	+	0.983685i	$0.557577\pi$
$182$	14.7016	−	14.9940i	1.08975	−	1.11143i
$183$	9.20877			0.680732
$184$	2.16665	−	8.08604i	0.159727	−	0.596111i
$185$		−	5.49592i		−	0.404068i
$186$	5.09551	+	2.94189i	0.373621	+	0.215710i
$187$	7.94155	+	29.6383i	0.580744	+	2.16737i
$188$	7.07623	+	1.89607i	0.516087	+	0.138285i
$189$	2.52806	−	0.780325i	0.183889	−	0.0567603i
$190$	13.8992	−	13.8992i	1.00835	−	1.00835i
$191$	14.8270			1.07284			0.536422	−	0.843950i	$-0.319775\pi$
$191$	14.8270			1.07284			0.536422	+	0.843950i	$0.319775\pi$
$192$	−12.7302			−0.918726
$193$	−11.1217	+	11.1217i	−0.800557	+	0.800557i	−0.983182	−	0.182626i	$-0.941540\pi$
$193$	−11.1217	+	11.1217i	−0.800557	+	0.800557i	0.182626	+	0.983182i	$0.441540\pi$
$194$	−14.5292	+	25.1653i	−1.04313	+	1.80676i
$195$	−6.11076	+	9.93701i	−0.437601	+	0.711604i
$196$	19.8634	−	1.49608i	1.41881	−	0.106863i
$197$	−8.62996	+	2.31239i	−0.614859	+	0.164751i	−0.552790	−	0.833321i	$-0.686437\pi$
$197$	−8.62996	+	2.31239i	−0.614859	+	0.164751i	−0.0620697	+	0.998072i	$0.519770\pi$
$198$	4.43782	+	7.68652i	0.315382	+	0.546257i
$199$	3.40589	−	5.89918i	0.241437	−	0.418181i	−0.719687	−	0.694299i	$-0.755715\pi$
$199$	3.40589	−	5.89918i	0.241437	−	0.418181i	0.961124	+	0.276117i	$0.0890479\pi$
$200$	2.63456	−	9.83230i	0.186291	−	0.695249i
$201$	−5.52580	+	5.52580i	−0.389760	+	0.389760i
$202$	2.26278	−	8.44483i	0.159209	−	0.594176i
$203$	7.69569	+	1.75497i	0.540132	+	0.123175i
$204$	10.8278	+	18.7543i	0.758097	+	1.31306i
$205$	31.9497	−	18.4462i	2.23146	−	1.28834i
$206$	−5.92785	−	5.92785i	−0.413013	−	0.413013i
$207$	3.89447	−	2.24848i	0.270685	−	0.156280i
$208$	−5.50639	−	1.64042i	−0.381800	−	0.113743i
$209$		−	11.1280i		−	0.769737i
$210$	−18.0052	+	5.55759i	−1.24248	+	0.383510i
$211$	−1.65897	+	2.87342i	−0.114208	+	0.197814i	−0.917463	−	0.397821i	$-0.869766\pi$
$211$	−1.65897	+	2.87342i	−0.114208	+	0.197814i	0.803255	+	0.595636i	$0.203100\pi$
$212$			22.2694i			1.52947i
$213$	−2.69136	−	0.721147i	−0.184409	−	0.0494122i
$214$	14.5990	−	3.91178i	0.997965	−	0.267404i
$215$	16.6692	+	16.6692i	1.13683	+	1.13683i
$216$	1.31631	+	1.31631i	0.0895637	+	0.0895637i
$217$	0.265753	+	7.06680i	0.0180405	+	0.479725i
$218$	−9.29619	−	5.36716i	−0.629618	−	0.363510i
$219$	1.69255	+	0.453517i	0.114372	+	0.0306459i
$220$	−18.5614	−	32.1493i	−1.25141	−	2.16750i
$221$	6.36370	+	26.6902i	0.428069	+	1.79538i
$222$	−3.23827	−	1.86962i	−0.217339	−	0.125480i
$223$	5.97866	+	22.3127i	0.400361	+	1.49417i	0.812455	+	0.583024i	$0.198131\pi$
$223$	5.97866	+	22.3127i	0.400361	+	1.49417i	−0.412094	+	0.911141i	$0.635202\pi$
$224$	−10.1815	−	16.1969i	−0.680277	−	1.08220i
$225$	4.73553	−	2.73406i	0.315702	−	0.182271i
$226$	−18.9400	+	5.07495i	−1.25987	+	0.337581i
$227$	4.46674	+	16.6701i	0.296468	+	1.10643i	0.940045	+	0.341052i	$0.110783\pi$
$227$	4.46674	+	16.6701i	0.296468	+	1.10643i	−0.643577	+	0.765382i	$0.722550\pi$
$228$	−2.03270	−	7.58612i	−0.134619	−	0.502403i
$229$	7.29710	−	1.95525i	0.482206	−	0.129207i	−0.00952370	−	0.999955i	$-0.503032\pi$
$229$	7.29710	−	1.95525i	0.482206	−	0.129207i	0.491730	+	0.870748i	$0.336365\pi$
$230$	−27.7370	+	16.0140i	−1.82892	+	1.05593i
$231$	−4.98292	+	9.43244i	−0.327852	+	0.620609i
$232$	1.43740	+	5.36445i	0.0943699	+	0.352193i
$233$	18.4325	+	10.6420i	1.20755	+	0.697181i	0.962224	−	0.272258i	$-0.0877705\pi$
$233$	18.4325	+	10.6420i	1.20755	+	0.697181i	0.245330	+	0.969440i	$0.421104\pi$
$234$	3.77625	+	6.98094i	0.246861	+	0.456359i
$235$	−4.16465	−	7.21339i	−0.271672	−	0.470550i
$236$	22.4914	+	6.02655i	1.46406	+	0.392295i
$237$	7.46554	+	4.31023i	0.484939	+	0.279980i
$238$	−20.7026	+	39.1890i	−1.34195	+	2.54025i
$239$	−14.8128	−	14.8128i	−0.958161	−	0.958161i	0.0409982	−	0.999159i	$-0.486946\pi$
$239$	−14.8128	−	14.8128i	−0.958161	−	0.958161i	−0.999159	+	0.0409982i	$0.986946\pi$
$240$	3.64569	+	3.64569i	0.235328	+	0.235328i
$241$	−4.45546	+	1.19384i	−0.287001	+	0.0769018i	−0.399448	−	0.916756i	$-0.630798\pi$
$241$	−4.45546	+	1.19384i	−0.287001	+	0.0769018i	0.112446	+	0.993658i	$0.464131\pi$
$242$	−11.1783	−	2.99521i	−0.718566	−	0.192539i
$243$			1.00000i			0.0641500i
$244$	−13.1025	+	22.6942i	−0.838804	+	1.45285i
$245$	−17.1722	−	14.7666i	−1.09709	−	0.943405i
$246$		−	25.1003i		−	1.60034i
$247$	0.276014	−	9.94712i	0.0175623	−	0.632920i
$248$	−4.30908	+	2.48785i	−0.273627	+	0.157979i
$249$	−1.63865	−	1.63865i	−0.103845	−	0.103845i
$250$	−2.88733	+	1.66700i	−0.182611	+	0.105430i
$251$	−7.81358	−	13.5335i	−0.493189	−	0.854228i	0.506780	−	0.862075i	$-0.330835\pi$
$251$	−7.81358	−	13.5335i	−0.493189	−	0.854228i	−0.999969	+	0.00784717i	$0.997502\pi$
$252$	−1.67396	+	7.34047i	−0.105450	+	0.462406i
$253$	−4.69286	+	17.5140i	−0.295037	+	1.10109i
$254$	9.10649	−	9.10649i	0.571392	−	0.571392i
$255$	6.37260	−	23.7829i	0.399068	−	1.48934i
$256$	2.19568	−	3.80304i	0.137230	−	0.237690i
$257$	−1.95456	−	3.38540i	−0.121922	−	0.211175i	0.798604	−	0.601857i	$-0.205572\pi$
$257$	−1.95456	−	3.38540i	−0.121922	−	0.211175i	−0.920526	+	0.390682i	$0.872239\pi$
$258$	15.4923	−	4.15115i	0.964510	−	0.258440i
$259$	−0.168890	−	4.49105i	−0.0104943	−	0.279060i
$260$	−15.7943	−	29.1981i	−0.979523	−	1.81079i
$261$	−1.49169	+	2.58368i	−0.0923331	+	0.159926i
$262$	4.07306	−	4.07306i	0.251635	−	0.251635i
$263$	1.84465			0.113746			0.0568729	−	0.998381i	$-0.481887\pi$
$263$	1.84465			0.113746			0.0568729	+	0.998381i	$0.481887\pi$
$264$	−7.50579			−0.461950
$265$	17.9038	−	17.9038i	1.09982	−	1.09982i
$266$	10.9307	−	11.7850i	0.670206	−	0.722584i
$267$	−17.4201	−	4.66770i	−1.06609	−	0.285659i
$268$	−5.75559	−	21.4802i	−0.351579	−	1.31211i
$269$	0.703253	+	0.406023i	0.0428781	+	0.0247557i	0.521286	−	0.853382i	$-0.325453\pi$
$269$	0.703253	+	0.406023i	0.0428781	+	0.0247557i	−0.478408	+	0.878138i	$0.658786\pi$
$270$		−	7.12215i		−	0.433440i
$271$	−1.77909	+	6.63966i	−0.108072	+	0.403330i	−0.998676	−	0.0514502i	$-0.983616\pi$
$271$	−1.77909	+	6.63966i	−0.108072	+	0.403330i	0.890604	+	0.454781i	$0.150282\pi$
$272$	12.1268			0.735296
$273$	−4.68812	+	8.30792i	−0.283738	+	0.502818i
$274$	−24.8256			−1.49977
$275$	−5.70633	+	21.2963i	−0.344105	+	1.28422i
$276$			12.7968i			0.770277i
$277$	−16.4623	−	9.50450i	−0.989122	−	0.571070i	−0.0841102	−	0.996456i	$-0.526805\pi$
$277$	−16.4623	−	9.50450i	−0.989122	−	0.571070i	−0.905012	+	0.425387i	$0.860138\pi$
$278$	−1.64814	−	6.15093i	−0.0988487	−	0.368908i
$279$	−2.58181	−	0.691794i	−0.154569	−	0.0414166i
$280$	3.54299	−	15.5363i	0.211734	−	0.928473i
$281$	3.58709	−	3.58709i	0.213988	−	0.213988i	−0.591971	−	0.805959i	$-0.701650\pi$
$281$	3.58709	−	3.58709i	0.213988	−	0.213988i	0.805959	+	0.591971i	$0.201650\pi$
$282$	−5.66697			−0.337463
$283$	−14.0844			−0.837233			−0.418616	−	0.908163i	$-0.637485\pi$
$283$	−14.0844			−0.837233			−0.418616	+	0.908163i	$0.637485\pi$
$284$	5.60655	−	5.60655i	0.332688	−	0.332688i
$285$	−4.46475	+	7.73317i	−0.264469	+	0.458074i
$286$	−30.6695	−	9.13682i	−1.81353	−	0.540271i
$287$	25.5412	−	16.0553i	1.50765	−	0.947716i
$288$	6.98452	−	1.87150i	0.411567	−	0.110279i
$289$	−20.4563	−	35.4313i	−1.20331	−	2.08419i
$290$	10.6240	−	18.4013i	0.623863	−	1.08056i
$291$	3.41658	−	12.7508i	0.200283	−	0.747467i
$292$	−3.52587	+	3.52587i	−0.206336	+	0.206336i
$293$	−7.18612	+	26.8190i	−0.419818	+	1.56678i	0.355168	+	0.934803i	$0.384424\pi$
$293$	−7.18612	+	26.8190i	−0.419818	+	1.56678i	−0.774985	+	0.631979i	$0.782243\pi$
$294$	−14.5424	+	5.09475i	−0.848129	+	0.297132i
$295$	−13.2371	−	22.9274i	−0.770695	−	1.33488i
$296$	2.73849	−	1.58107i	0.159171	−	0.0918976i
$297$	−2.85107	−	2.85107i	−0.165436	−	0.165436i
$298$	−2.73914	+	1.58145i	−0.158674	+	0.0916107i
$299$	−4.62929	+	15.5391i	−0.267718	+	0.898649i
$300$			15.5604i			0.898381i
$301$	14.1337	+	13.1092i	0.814653	+	0.755602i
$302$	−8.83772	+	15.3074i	−0.508553	+	0.880840i
$303$			3.97164i			0.228165i
$304$	−4.24812	−	1.13828i	−0.243646	−	0.0652848i
$305$	28.7793	−	7.71138i	1.64790	−	0.441553i
$306$	−11.8454	−	11.8454i	−0.677154	−	0.677154i
$307$	20.3066	+	20.3066i	1.15896	+	1.15896i	0.984700	+	0.174260i	$0.0557532\pi$
$307$	20.3066	+	20.3066i	1.15896	+	1.15896i	0.174260	+	0.984700i	$0.444247\pi$
$308$	−16.1556	−	25.7007i	−0.920551	−	1.46444i
$309$	3.29812	+	1.90417i	0.187623	+	0.108324i
$310$	18.3880	+	4.92706i	1.04437	+	0.279838i
$311$	3.76230	+	6.51650i	0.213341	+	0.369517i	0.952758	−	0.303731i	$-0.0982323\pi$
$311$	3.76230	+	6.51650i	0.213341	+	0.369517i	−0.739417	+	0.673247i	$0.764899\pi$
$312$	−6.70932	−	0.186171i	−0.379840	−	0.0105399i
$313$	21.8314	+	12.6043i	1.23398	+	0.712439i	0.967857	−	0.251500i	$-0.0809237\pi$
$313$	21.8314	+	12.6043i	1.23398	+	0.712439i	0.266124	+	0.963939i	$0.414257\pi$
$314$	1.12844	+	4.21140i	0.0636816	+	0.237663i
$315$	7.24726	−	4.55566i	0.408337	−	0.256682i
$316$	−21.2444	+	12.2655i	−1.19509	+	0.689987i
$317$	−7.23738	+	1.93925i	−0.406492	+	0.108919i	−0.456270	−	0.889841i	$-0.650815\pi$
$317$	−7.23738	+	1.93925i	−0.406492	+	0.108919i	0.0497787	+	0.998760i	$0.484148\pi$
$318$	−4.45860	−	16.6397i	−0.250026	−	0.933109i
$319$	−3.11334	−	11.6191i	−0.174314	−	0.650547i
$320$	−39.7846	+	10.6602i	−2.22402	+	0.595926i
$321$	−5.94610	+	3.43298i	−0.331879	+	0.191611i
$322$	−22.1735	+	13.9384i	−1.23568	+	0.776755i
$323$	5.43595	+	20.2872i	0.302464	+	1.12881i
$324$	−2.46442	−	1.42283i	−0.136912	−	0.0790462i
$325$	−5.62903	+	18.8949i	−0.312242	+	1.04810i
$326$	0.122838	+	0.212762i	0.00680339	+	0.0117838i
$327$	4.71023	+	1.26210i	0.260476	+	0.0697943i
$328$	18.3826	+	10.6132i	1.01501	+	0.586015i
$329$	−3.62486	−	5.76653i	−0.199845	−	0.317919i
$330$	20.3057	+	20.3057i	1.11779	+	1.11779i
$331$	19.5567	+	19.5567i	1.07493	+	1.07493i	0.996955	+	0.0779768i	$0.0248460\pi$
$331$	19.5567	+	19.5567i	1.07493	+	1.07493i	0.0779768	+	0.996955i	$0.475154\pi$
$332$	6.36982	−	1.70679i	0.349589	−	0.0936722i
$333$	1.64078	+	0.439645i	0.0899141	+	0.0240924i
$334$		−	49.5156i		−	2.70937i
$335$	−12.6420	+	21.8965i	−0.690704	+	1.19634i
$336$	3.09115	+	2.86708i	0.168636	+	0.156412i
$337$			15.1198i			0.823630i	0.911267	+	0.411815i	$0.135105\pi$
$337$			15.1198i			0.823630i	−0.911267	+	0.411815i	$0.864895\pi$
$338$	−27.1884	−	8.92798i	−1.47885	−	0.485618i
$339$	7.71418	−	4.45378i	0.418977	−	0.241896i
$340$	49.5438	+	49.5438i	2.68689	+	2.68689i
$341$	9.33327	−	5.38857i	0.505425	−	0.291807i
$342$	3.03766	+	5.26138i	0.164258	+	0.284503i
$343$	−14.4862	−	11.5390i	−0.782184	−	0.623048i
$344$	−3.51048	+	13.1013i	−0.189272	+	0.706373i
$345$	10.2882	−	10.2882i	0.553896	−	0.553896i
$346$	2.69381	−	10.0534i	0.144820	−	0.540475i
$347$	−0.127576	+	0.220968i	−0.00684864	+	0.0118622i	−0.869429	−	0.494057i	$-0.835513\pi$
$347$	−0.127576	+	0.220968i	−0.00684864	+	0.0118622i	0.862581	+	0.505919i	$0.168847\pi$
$348$	−4.24484	−	7.35227i	−0.227547	−	0.394123i
$349$	−23.4871	+	6.29335i	−1.25723	+	0.336875i	−0.825127	−	0.564947i	$-0.808897\pi$
$349$	−23.4871	+	6.29335i	−1.25723	+	0.336875i	−0.432108	+	0.901822i	$0.642230\pi$
$350$	−26.9621	+	16.9485i	−1.44119	+	0.905936i
$351$	−2.47781	−	2.61925i	−0.132256	−	0.139805i
$352$	−14.5776	+	25.2491i	−0.776988	+	1.34578i
$353$	6.83333	−	6.83333i	0.363701	−	0.363701i	−0.501472	−	0.865174i	$-0.667208\pi$
$353$	6.83333	−	6.83333i	0.363701	−	0.363701i	0.865174	+	0.501472i	$0.167208\pi$
$354$	−18.0122			−0.957335
$355$	−9.01492			−0.478462
$356$	36.2890	−	36.2890i	1.92331	−	1.92331i
$357$	4.47660	−	19.6303i	0.236927	−	1.03894i
$358$	48.7154	+	13.0533i	2.57469	+	0.689886i
$359$	−5.25807	−	19.6234i	−0.277510	−	1.03568i	−0.954140	−	0.299360i	$-0.903227\pi$
$359$	−5.25807	−	19.6234i	−0.277510	−	1.03568i	0.676630	−	0.736323i	$-0.263440\pi$
$360$	5.21601	+	3.01147i	0.274908	+	0.158718i
$361$			11.3830i			0.599104i
$362$	−2.75783	+	10.2924i	−0.144949	+	0.540955i
$363$	5.25719			0.275931
$364$	−13.8038	−	23.3742i	−0.723515	−	1.22514i
$365$	5.66933			0.296746
$366$	5.24656	−	19.5804i	0.274242	−	1.02349i
$367$			21.7644i			1.13609i	0.822996	+	0.568047i	$0.192301\pi$
$367$			21.7644i			1.13609i	−0.822996	+	0.568047i	$0.807699\pi$
$368$	6.20596	+	3.58301i	0.323508	+	0.186777i
$369$	2.95120	+	11.0140i	0.153633	+	0.573367i
$370$	−11.6859	−	3.13122i	−0.607519	−	0.162784i
$371$	14.0801	−	15.1805i	0.731002	−	0.788131i
$372$	5.37835	−	5.37835i	0.278854	−	0.278854i
$373$	15.5277			0.803994			0.401997	−	0.915641i	$-0.368316\pi$
$373$	15.5277			0.803994			0.401997	+	0.915641i	$0.368316\pi$
$374$	67.5438			3.49261
$375$	1.07096	−	1.07096i	0.0553042	−	0.0553042i
$376$	2.39617	−	4.15030i	0.123573	−	0.214035i
$377$	−2.49477	−	10.4634i	−0.128487	−	0.538893i
$378$	−0.218864	−	5.81994i	−0.0112572	−	0.299346i
$379$	22.4101	−	6.00477i	1.15113	−	0.308444i	0.367712	−	0.929940i	$-0.380141\pi$
$379$	22.4101	−	6.00477i	1.15113	−	0.308444i	0.783418	+	0.621495i	$0.213474\pi$
$380$	−12.7052	−	22.0060i	−0.651761	−	1.12888i
$381$	−2.92523	+	5.06664i	−0.149864	+	0.259572i
$382$	8.44746	−	31.5264i	0.432210	−	1.61303i
$383$	1.14154	−	1.14154i	0.0583300	−	0.0583300i	−0.677340	−	0.735670i	$-0.736867\pi$
$383$	1.14154	−	1.14154i	0.0583300	−	0.0583300i	0.735670	+	0.677340i	$0.236867\pi$
$384$	−3.50987	+	13.0990i	−0.179112	+	0.668456i
$385$	−7.67394	+	33.6509i	−0.391100	+	1.71501i
$386$	17.3114	+	29.9842i	0.881127	+	1.52616i
$387$	−6.30996	+	3.64306i	−0.320753	+	0.185187i
$388$	26.5621	+	26.5621i	1.34849	+	1.34849i
$389$	−14.1958	+	8.19595i	−0.719756	+	0.415551i	−0.814663	−	0.579935i	$-0.803078\pi$
$389$	−14.1958	+	8.19595i	−0.719756	+	0.415551i	0.0949069	+	0.995486i	$0.469745\pi$
$390$	17.6473	+	18.6547i	0.893608	+	0.944615i
$391$		−	34.2219i		−	1.73068i
$392$	2.41776	−	12.8046i	0.122115	−	0.646728i
$393$	−1.30837	+	2.26616i	−0.0659984	+	0.114313i
$394$			19.6672i			0.990818i
$395$	26.9407	+	7.21874i	1.35553	+	0.363214i
$396$	11.0828	−	2.96963i	0.556932	−	0.149230i
$397$	−24.4888	−	24.4888i	−1.22906	−	1.22906i	−0.964321	−	0.264735i	$-0.914716\pi$
$397$	−24.4888	−	24.4888i	−1.22906	−	1.22906i	−0.264735	−	0.964321i	$-0.585284\pi$
$398$	−10.6028	−	10.6028i	−0.531472	−	0.531472i
$399$	−3.41078	+	6.45645i	−0.170753	+	0.323227i
$400$	7.54620	+	4.35680i	0.377310	+	0.217840i
$401$	−34.9887	−	9.37520i	−1.74725	−	0.468175i	−0.763218	−	0.646142i	$-0.776382\pi$
$401$	−34.9887	−	9.37520i	−1.74725	−	0.468175i	−0.984037	+	0.177966i	$0.943048\pi$
$402$	8.60116	+	14.8976i	0.428987	+	0.743027i
$403$	8.47653	−	4.58526i	0.422246	−	0.228408i
$404$	−9.78778	−	5.65098i	−0.486960	−	0.281147i
$405$	0.837395	+	3.12520i	0.0416105	+	0.155293i
$406$	8.11606	−	15.3633i	0.402793	−	0.762469i
$407$	−5.93143	+	3.42451i	−0.294010	+	0.169747i
$408$	13.6837	−	3.66654i	0.677445	−	0.181521i
$409$	5.72054	+	21.3494i	0.282863	+	1.05566i	0.950387	+	0.311070i	$0.100687\pi$
$409$	5.72054	+	21.3494i	0.282863	+	1.05566i	−0.667525	+	0.744588i	$0.732646\pi$
$410$	−21.0189	−	78.4435i	−1.03805	−	3.87405i
$411$	10.8935	−	2.91890i	0.537337	−	0.143979i
$412$	−9.38533	+	5.41862i	−0.462382	+	0.266956i
$413$	−11.5214	−	18.3286i	−0.566932	−	0.901890i
$414$	−2.56207	−	9.56178i	−0.125919	−	0.469936i
$415$	−6.49329	−	3.74890i	−0.318743	−	0.184026i
$416$	−13.6570	+	22.2082i	−0.669587	+	1.08885i
$417$	1.44641	+	2.50525i	0.0708309	+	0.122683i
$418$	−23.6611	−	6.33999i	−1.15730	−	0.310099i
$419$	−6.99593	−	4.03910i	−0.341774	−	0.197323i	0.319282	−	0.947660i	$-0.396558\pi$
$419$	−6.99593	−	4.03910i	−0.341774	−	0.197323i	−0.661056	+	0.750336i	$0.729891\pi$
$420$	0.915410	+	24.3422i	0.0446674	+	1.18778i
$421$	5.31808	+	5.31808i	0.259187	+	0.259187i	0.824724	−	0.565536i	$-0.191331\pi$
$421$	5.31808	+	5.31808i	0.259187	+	0.259187i	−0.565536	+	0.824724i	$0.691331\pi$
$422$	5.16452	+	5.16452i	0.251405	+	0.251405i
$423$	2.48667	−	0.666302i	0.120906	−	0.0323967i
$424$	14.0716	+	3.77047i	0.683377	+	0.183110i
$425$		−	41.6125i		−	2.01850i
$426$	−3.06672	+	5.31171i	−0.148583	+	0.257353i
$427$	23.2803	−	7.18583i	1.12661	−	0.347747i
$428$		−	19.5382i		−	0.944416i
$429$	14.5321	+	0.403238i	0.701615	+	0.0194685i
$430$	44.9405	−	25.9464i	2.16722	−	1.25125i
$431$	−7.41610	−	7.41610i	−0.357221	−	0.357221i	0.505567	−	0.862787i	$-0.331283\pi$
$431$	−7.41610	−	7.41610i	−0.357221	−	0.357221i	−0.862787	+	0.505567i	$0.831283\pi$
$432$	−1.38004	+	0.796765i	−0.0663971	+	0.0383344i
$433$	−2.59289	−	4.49102i	−0.124607	−	0.215825i	0.796973	−	0.604016i	$-0.206434\pi$
$433$	−2.59289	−	4.49102i	−0.124607	−	0.215825i	−0.921579	+	0.388191i	$0.873100\pi$
$434$	15.1774	+	3.46114i	0.728538	+	0.166140i
$435$	−2.49826	+	9.32365i	−0.119783	+	0.447035i
$436$	−9.81220	+	9.81220i	−0.469919	+	0.469919i
$437$	−3.21223	+	11.9882i	−0.153662	+	0.573474i
$438$	1.92861	−	3.34045i	0.0921525	−	0.159613i
$439$	4.33909	+	7.51552i	0.207093	+	0.358696i	0.950798	−	0.309812i	$-0.100266\pi$
$439$	4.33909	+	7.51552i	0.207093	+	0.358696i	−0.743704	+	0.668509i	$0.766933\pi$
$440$	−23.4571	+	6.28531i	−1.11827	+	0.299641i
$441$	5.78219	−	3.94542i	0.275342	−	0.187877i
$442$	60.3764	+	1.67533i	2.87181	+	0.0796875i
$443$	5.13279	−	8.89025i	0.243866	−	0.422388i	−0.717946	−	0.696099i	$-0.754918\pi$
$443$	5.13279	−	8.89025i	0.243866	−	0.422388i	0.961812	+	0.273710i	$0.0882509\pi$
$444$	−3.41802	+	3.41802i	−0.162212	+	0.162212i
$445$	−58.3500			−2.76606
$446$	50.8492			2.40778
$447$	1.01600	−	1.01600i	0.0480550	−	0.0480550i
$448$	−32.1828	+	9.93372i	−1.52050	+	0.469324i
$449$	7.73538	+	2.07269i	0.365055	+	0.0978162i	0.436684	−	0.899615i	$-0.356153\pi$
$449$	7.73538	+	2.07269i	0.365055	+	0.0978162i	−0.0716285	+	0.997431i	$0.522820\pi$
$450$	−3.11538	−	11.6267i	−0.146860	−	0.548090i
$451$	−39.8158	−	22.9877i	−1.87485	−	1.08245i
$452$			25.3479i			1.19227i
$453$	2.07821	−	7.75599i	0.0976429	−	0.364408i
$454$	37.9901			1.78297
$455$	−7.69429	+	29.8897i	−0.360714	+	1.40125i
$456$	−5.13767			−0.240594
$457$	−6.71765	+	25.0706i	−0.314238	+	1.17275i	0.610458	+	0.792049i	$0.290985\pi$
$457$	−6.71765	+	25.0706i	−0.314238	+	1.17275i	−0.924696	+	0.380705i	$0.875681\pi$
$458$		−	16.6296i		−	0.777052i
$459$	6.59048	+	3.80501i	0.307617	+	0.177603i
$460$	10.7160	+	39.9926i	0.499635	+	1.86466i
$461$	−14.2955	−	3.83046i	−0.665807	−	0.178402i	−0.0899418	−	0.995947i	$-0.528668\pi$
$461$	−14.2955	−	3.83046i	−0.665807	−	0.178402i	−0.575865	+	0.817545i	$0.695335\pi$
$462$	17.2171	+	15.9691i	0.801010	+	0.742948i
$463$	6.69179	−	6.69179i	0.310994	−	0.310994i	−0.534301	−	0.845294i	$-0.679425\pi$
$463$	6.69179	−	6.69179i	0.310994	−	0.310994i	0.845294	+	0.534301i	$0.179425\pi$
$464$	−4.75409			−0.220703
$465$	−8.64798			−0.401041
$466$	33.1295	−	33.1295i	1.53470	−	1.53470i
$467$	15.6442	−	27.0965i	0.723925	−	1.25388i	−0.235490	−	0.971877i	$-0.575669\pi$
$467$	15.6442	−	27.0965i	0.723925	−	1.25388i	0.959415	−	0.281998i	$-0.0909973\pi$
$468$	9.98042	−	2.37961i	0.461345	−	0.109998i
$469$	−9.65765	+	18.2815i	−0.445949	+	0.844161i
$470$	−17.7104	+	4.74550i	−0.816922	+	0.218894i
$471$	−0.990321	−	1.71529i	−0.0456316	−	0.0790362i
$472$	7.61610	−	13.1915i	0.350559	−	0.607187i
$473$	7.60353	−	28.3767i	0.349611	−	1.30476i
$474$	13.4181	−	13.4181i	0.616316	−	0.616316i
$475$	−3.90595	+	14.5772i	−0.179217	+	0.668848i
$476$	42.0077	+	38.9628i	1.92542	+	1.78586i
$477$	3.91287	+	6.77729i	0.179158	+	0.310311i
$478$	−39.9355	+	23.0568i	−1.82661	+	1.05459i
$479$	−23.0874	−	23.0874i	−1.05489	−	1.05489i	−0.998403	−	0.0564893i	$-0.982009\pi$
$479$	−23.0874	−	23.0874i	−1.05489	−	1.05489i	−0.0564893	−	0.998403i	$-0.517991\pi$
$480$	20.2609	−	11.6976i	0.924777	−	0.533920i
$481$	−5.38696	+	2.91400i	−0.245624	+	0.132867i
$482$			10.1537i			0.462489i
$483$	8.09093	−	8.72324i	0.368150	−	0.396921i
$484$	−7.48010	+	12.9559i	−0.340004	+	0.588905i
$485$		−	42.7099i		−	1.93936i
$486$	2.12628	+	0.569735i	0.0964500	+	0.0258437i
$487$	−0.530719	+	0.142206i	−0.0240492	+	0.00644395i	−0.270824	−	0.962629i	$-0.587296\pi$
$487$	−0.530719	+	0.142206i	−0.0240492	+	0.00644395i	0.246774	+	0.969073i	$0.420629\pi$
$488$	12.1216	+	12.1216i	0.548720	+	0.548720i
$489$	−0.0789174	−	0.0789174i	−0.00356877	−	0.00356877i
$490$	−41.1816	+	28.0998i	−1.86039	+	1.26942i
$491$	−11.1482	−	6.43644i	−0.503113	−	0.290472i	0.226885	−	0.973921i	$-0.427146\pi$
$491$	−11.1482	−	6.43644i	−0.503113	−	0.290472i	−0.729998	+	0.683449i	$0.760479\pi$
$492$	−31.3422	−	8.39811i	−1.41301	−	0.378616i
$493$	11.3518	+	19.6619i	0.511259	+	0.885526i
$494$	−20.9931	−	6.25410i	−0.944524	−	0.281385i
$495$	−11.2976	−	6.52269i	−0.507791	−	0.293173i
$496$	−1.10239	−	4.11419i	−0.0494989	−	0.184733i
$497$	−7.36664	+	0.277029i	−0.330439	+	0.0124265i
$498$	−4.41781	+	2.55063i	−0.197967	+	0.114296i
$499$	−3.59890	+	0.964321i	−0.161109	+	0.0431689i	−0.338472	−	0.940977i	$-0.609910\pi$
$499$	−3.59890	+	0.964321i	−0.161109	+	0.0431689i	0.177363	+	0.984145i	$0.443243\pi$
$500$	1.11550	+	4.16309i	0.0498866	+	0.186179i
$501$	5.82186	+	21.7275i	0.260102	+	0.970713i
$502$	−33.2277	+	8.90334i	−1.48303	+	0.397375i
$503$	−12.0422	+	6.95256i	−0.536935	+	0.309999i	−0.743836	−	0.668362i	$-0.766996\pi$
$503$	−12.0422	+	6.95256i	−0.536935	+	0.309999i	0.206901	+	0.978362i	$0.433662\pi$
$504$	4.35487	+	2.30057i	0.193981	+	0.102475i
$505$	3.32584	+	12.4122i	0.147998	+	0.552335i
$506$	34.5659	+	19.9566i	1.53664	+	0.887181i
$507$	12.9800	+	0.720896i	0.576462	+	0.0320161i
$508$	−8.32421	−	14.4179i	−0.369327	−	0.639693i
$509$	17.7870	+	4.76601i	0.788394	+	0.211249i	0.630482	−	0.776204i	$-0.282857\pi$
$509$	17.7870	+	4.76601i	0.788394	+	0.211249i	0.157912	+	0.987453i	$0.449524\pi$
$510$	−46.9384	−	27.0999i	−2.07847	−	1.20000i
$511$	4.63276	−	0.174219i	0.204941	−	0.00770700i
$512$	12.3429	+	12.3429i	0.545485	+	0.545485i
$513$	−1.95154	−	1.95154i	−0.0861626	−	0.0861626i
$514$	−8.31188	+	2.22716i	−0.366621	+	0.0982359i
$515$	11.9018	+	3.18908i	0.524457	+	0.140528i
$516$		−	20.7338i		−	0.912756i
$517$	−5.19000	+	8.98935i	−0.228256	+	0.395351i
$518$	−9.64546	−	2.19960i	−0.423797	−	0.0966450i
$519$			4.72817i			0.207544i
$520$	−21.1239	+	5.03653i	−0.926343	+	0.220866i
$521$	2.00007	−	1.15474i	0.0876246	−	0.0505901i	−0.455547	−	0.890211i	$-0.650556\pi$
$521$	2.00007	−	1.15474i	0.0876246	−	0.0505901i	0.543172	+	0.839621i	$0.317223\pi$
$522$	4.64375	+	4.64375i	0.203252	+	0.203252i
$523$	0.471611	−	0.272285i	0.0206221	−	0.0119062i	−0.489654	−	0.871917i	$-0.662877\pi$
$523$	0.471611	−	0.272285i	0.0206221	−	0.0119062i	0.510276	+	0.860011i	$0.329543\pi$
$524$	−3.72317	−	6.44872i	−0.162647	−	0.281714i
$525$	9.83825	−	10.6071i	0.429376	−	0.462933i
$526$	1.05096	−	3.92223i	0.0458240	−	0.171017i
$527$	−14.3831	+	14.3831i	−0.626537	+	0.626537i
$528$	1.66295	−	6.20621i	0.0723706	−	0.270091i
$529$	−1.38871	+	2.40532i	−0.0603787	+	0.104579i
$530$	−27.8680	−	48.2689i	−1.21051	−	2.09667i
$531$	7.90374	−	2.11780i	0.342993	−	0.0919048i
$532$	−11.0584	−	17.5920i	−0.479443	−	0.762711i
$533$	−35.0206	−	21.5359i	−1.51691	−	0.932824i
$534$	−19.8497	+	34.3807i	−0.858980	+	1.48780i
$535$	−15.7080	+	15.7080i	−0.679116	+	0.679116i
$536$	−14.5474			−0.628350
$537$	−22.9111			−0.988687
$538$	1.26399	−	1.26399i	0.0544943	−	0.0544943i
$539$	−5.23675	+	27.7341i	−0.225563	+	1.19459i
$540$	−8.89327	−	2.38294i	−0.382705	−	0.102546i
$541$	−9.59647	−	35.8145i	−0.412584	−	1.53979i	−0.789626	−	0.613589i	$-0.789725\pi$
$541$	−9.59647	−	35.8145i	−0.412584	−	1.53979i	0.377041	−	0.926196i	$-0.376941\pi$
$542$	13.1042	+	7.56569i	0.562872	+	0.324974i
$543$		−	4.84056i		−	0.207728i
$544$	14.2421	−	53.1524i	0.610627	−	2.27889i
$545$	15.7773			0.675825
$546$	14.9940	+	14.7016i	0.641683	+	0.629169i
$547$	−11.4043			−0.487613			−0.243806	−	0.969824i	$-0.578396\pi$
$547$	−11.4043			−0.487613			−0.243806	+	0.969824i	$0.578396\pi$
$548$	−8.30622	+	30.9992i	−0.354824	+	1.32422i
$549$			9.20877i			0.393021i
$550$	42.0308	+	24.2665i	1.79220	+	1.03473i
$551$	−2.13106	−	7.95324i	−0.0907864	−	0.338819i
$552$	8.08604	+	2.16665i	0.344165	+	0.0922186i
$553$	22.2367	+	5.07098i	0.945602	+	0.215640i
$554$	−29.5883	+	29.5883i	−1.25709	+	1.25709i
$555$	5.49592			0.233289
$556$	−8.23198			−0.349114
$557$	1.79124	−	1.79124i	0.0758971	−	0.0758971i	−0.668139	−	0.744036i	$-0.732909\pi$
$557$	1.79124	−	1.79124i	0.0758971	−	0.0758971i	0.744036	+	0.668139i	$0.232909\pi$
$558$	−2.94189	+	5.09551i	−0.124540	+	0.215710i
$559$	7.50053	−	25.1770i	0.317239	−	1.06487i
$560$	12.0613	+	6.37170i	0.509685	+	0.269253i
$561$	−29.6383	+	7.94155i	−1.25133	+	0.335293i
$562$	−5.58346	−	9.67084i	−0.235524	−	0.407940i
$563$	−7.30294	+	12.6491i	−0.307782	+	0.533094i	−0.977877	−	0.209181i	$-0.932920\pi$
$563$	−7.30294	+	12.6491i	−0.307782	+	0.533094i	0.670095	+	0.742276i	$0.266253\pi$
$564$	−1.89607	+	7.07623i	−0.0798389	+	0.297963i
$565$	20.3788	−	20.3788i	0.857342	−	0.857342i
$566$	−8.02439	+	29.9474i	−0.337290	+	1.25879i
$567$	0.780325	+	2.52806i	0.0327706	+	0.106169i
$568$	−2.59341	−	4.49192i	−0.108817	−	0.188477i
$569$	15.1038	−	8.72017i	0.633183	−	0.365568i	−0.148801	−	0.988867i	$-0.547541\pi$
$569$	15.1038	−	8.72017i	0.633183	−	0.365568i	0.781984	+	0.623299i	$0.214208\pi$
$570$	13.8992	+	13.8992i	0.582172	+	0.582172i
$571$	30.0741	−	17.3633i	1.25856	−	0.726630i	0.285766	−	0.958299i	$-0.407752\pi$
$571$	30.0741	−	17.3633i	1.25856	−	0.726630i	0.972795	+	0.231669i	$0.0744187\pi$
$572$	−21.6704	+	35.2393i	−0.906086	+	1.47343i
$573$			14.8270i			0.619407i
$574$	−19.5864	−	63.4551i	−0.817520	−	2.64856i
$575$	12.2949	−	21.2954i	0.512734	−	0.888081i
$576$		−	12.7302i		−	0.530427i
$577$	18.0494	+	4.83633i	0.751407	+	0.201339i	0.614142	−	0.789196i	$-0.289502\pi$
$577$	18.0494	+	4.83633i	0.751407	+	0.201339i	0.137265	+	0.990534i	$0.456169\pi$
$578$	−86.9915	+	23.3093i	−3.61837	+	0.969539i
$579$	−11.1217	−	11.1217i	−0.462202	−	0.462202i
$580$	−19.4227	−	19.4227i	−0.806485	−	0.806485i
$581$	−5.42127	−	2.86392i	−0.224912	−	0.118815i
$582$	−25.1653	−	14.5292i	−1.04313	−	0.602254i
$583$	−30.4784	−	8.16666i	−1.26229	−	0.338229i
$584$	1.63095	+	2.82489i	0.0674893	+	0.116895i
$585$	−9.93701	−	6.11076i	−0.410845	−	0.252649i
$586$	52.9305	+	30.5594i	2.18654	+	1.26240i
$587$	8.61022	+	32.1338i	0.355382	+	1.32630i	0.880004	+	0.474967i	$0.157540\pi$
$587$	8.61022	+	32.1338i	0.355382	+	1.32630i	−0.524622	+	0.851335i	$0.675793\pi$
$588$	1.49608	+	19.8634i	0.0616971	+	0.819152i
$589$	6.38857	−	3.68844i	0.263237	−	0.151980i
$590$	−56.2916	+	15.0833i	−2.31749	+	0.620969i
$591$	−2.31239	−	8.62996i	−0.0951191	−	0.354989i
$592$	0.700588	+	2.61463i	0.0287940	+	0.107461i
$593$	4.42742	−	1.18632i	0.181812	−	0.0487164i	−0.166764	−	0.985997i	$-0.553332\pi$
$593$	4.42742	−	1.18632i	0.181812	−	0.0487164i	0.348576	+	0.937280i	$0.386665\pi$
$594$	−7.68652	+	4.43782i	−0.315382	+	0.182086i
$595$	−2.44804	−	65.0973i	−0.100360	−	2.66873i
$596$	1.05825	+	3.94943i	0.0433475	+	0.161775i
$597$	5.89918	+	3.40589i	0.241437	+	0.139394i
$598$	30.4030	+	18.6963i	1.24327	+	0.764549i
$599$	−9.84386	−	17.0501i	−0.402209	−	0.696646i	0.591783	−	0.806097i	$-0.298424\pi$
$599$	−9.84386	−	17.0501i	−0.402209	−	0.696646i	−0.993992	+	0.109451i	$0.965091\pi$
$600$	9.83230	+	2.63456i	0.401402	+	0.107555i
$601$	10.6224	+	6.13284i	0.433296	+	0.250164i	0.700750	−	0.713407i	$-0.252849\pi$
$601$	10.6224	+	6.13284i	0.433296	+	0.250164i	−0.267454	+	0.963571i	$0.586182\pi$
$602$	35.9263	−	22.5834i	1.46425	−	0.920431i
$603$	−5.52580	−	5.52580i	−0.225028	−	0.225028i
$604$	16.1570	+	16.1570i	0.657421	+	0.657421i
$605$	16.4298	−	4.40235i	0.667966	−	0.178981i
$606$	8.44483	+	2.26278i	0.343048	+	0.0919193i
$607$			24.0707i			0.976998i	0.872564	+	0.488499i	$0.162455\pi$
$607$			24.0707i			0.976998i	−0.872564	+	0.488499i	$0.837545\pi$
$608$	−9.97828	+	17.2829i	−0.404672	+	0.700913i
$609$	−1.75497	+	7.69569i	−0.0711149	+	0.311845i
$610$		−	65.5862i		−	2.65551i
$611$	−4.86223	+	7.90671i	−0.196705	+	0.319871i
$612$	−18.7543	+	10.8278i	−0.758097	+	0.437687i
$613$	−34.2309	−	34.2309i	−1.38257	−	1.38257i	−0.840023	−	0.542551i	$-0.817459\pi$
$613$	−34.2309	−	34.2309i	−1.38257	−	1.38257i	−0.542551	−	0.840023i	$-0.682541\pi$
$614$	54.7469	−	31.6081i	2.20941	−	1.27560i
$615$	18.4462	+	31.9497i	0.743822	+	1.28834i
$616$	−18.9751	+	5.85696i	−0.764529	+	0.235983i
$617$	4.83334	−	18.0383i	0.194583	−	0.726194i	−0.797791	−	0.602934i	$-0.793998\pi$
$617$	4.83334	−	18.0383i	0.194583	−	0.726194i	0.992374	−	0.123260i	$-0.0393350\pi$
$618$	5.92785	−	5.92785i	0.238453	−	0.238453i
$619$	2.60140	−	9.70855i	0.104559	−	0.390219i	−0.893736	−	0.448594i	$-0.851925\pi$
$619$	2.60140	−	9.70855i	0.104559	−	0.390219i	0.998295	+	0.0583743i	$0.0185917\pi$
$620$	12.3046	−	21.3122i	0.494165	−	0.855920i
$621$	2.24848	+	3.89447i	0.0902282	+	0.156280i
$622$	15.9994	−	4.28703i	0.641518	−	0.171894i
$623$	−47.6814	+	1.79310i	−1.91032	+	0.0718391i
$624$	1.64042	−	5.50639i	0.0656695	−	0.220432i
$625$	−11.2201	+	19.4339i	−0.448806	+	0.777354i
$626$	39.2384	−	39.2384i	1.56828	−	1.56828i
$627$	11.1280			0.444408
$628$	5.63624			0.224910
$629$	9.14066	−	9.14066i	0.364462	−	0.364462i
$630$	−5.55759	−	18.0052i	−0.221420	−	0.717345i
$631$	8.95627	+	2.39983i	0.356543	+	0.0955355i	0.432645	−	0.901565i	$-0.357581\pi$
$631$	8.95627	+	2.39983i	0.356543	+	0.0955355i	−0.0761011	+	0.997100i	$0.524247\pi$
$632$	4.15337	+	15.5006i	0.165212	+	0.616580i
$633$	−2.87342	−	1.65897i	−0.114208	−	0.0659381i
$634$			16.4936i			0.655043i
$635$	−4.89914	+	18.2838i	−0.194416	+	0.725572i
$636$	−22.2694			−0.883040
$637$	−5.36896	+	24.6612i	−0.212726	+	0.977112i
$638$	−26.4793			−1.04833
$639$	0.721147	−	2.69136i	0.0285281	−	0.106468i
$640$			43.8762i			1.73436i
$641$	27.8044	+	16.0529i	1.09821	+	0.634052i	0.935750	−	0.352664i	$-0.114724\pi$
$641$	27.8044	+	16.0529i	1.09821	+	0.634052i	0.162459	+	0.986715i	$0.448057\pi$
$642$	3.91178	+	14.5990i	0.154386	+	0.576175i
$643$	−7.89631	−	2.11581i	−0.311400	−	0.0834393i	0.0997345	−	0.995014i	$-0.468201\pi$
$643$	−7.89631	−	2.11581i	−0.311400	−	0.0834393i	−0.411134	+	0.911575i	$0.634867\pi$
$644$	9.98567	+	32.3511i	0.393490	+	1.27481i
$645$	−16.6692	+	16.6692i	−0.656350	+	0.656350i
$646$	46.2334			1.81903
$647$	8.00103			0.314553			0.157276	−	0.987555i	$-0.449729\pi$
$647$	8.00103			0.314553			0.157276	+	0.987555i	$0.449729\pi$
$648$	−1.31631	+	1.31631i	−0.0517096	+	0.0517096i
$649$	−16.4961	+	28.5721i	−0.647529	+	1.12155i
$650$	36.9688	+	22.7340i	1.45004	+	0.891700i
$651$	−7.06680	+	0.265753i	−0.276970	+	0.0104157i
$652$	0.306771	−	0.0821991i	0.0120141	−	0.00321917i
$653$	22.5078	+	38.9846i	0.880797	+	1.52558i	0.850457	+	0.526045i	$0.176326\pi$
$653$	22.5078	+	38.9846i	0.880797	+	1.52558i	0.0303396	+	0.999540i	$0.490341\pi$
$654$	5.36716	−	9.29619i	0.209873	−	0.363510i
$655$	−2.19124	+	8.17782i	−0.0856189	+	0.319534i
$656$	−12.8483	+	12.8483i	−0.501644	+	0.501644i
$657$	−0.453517	+	1.69255i	−0.0176934	+	0.0660326i
$658$	−14.3265	+	4.42208i	−0.558504	+	0.172391i
$659$	15.9656	+	27.6532i	0.621930	+	1.07721i	0.989126	+	0.147071i	$0.0469845\pi$
$659$	15.9656	+	27.6532i	0.621930	+	1.07721i	−0.367196	+	0.930144i	$0.619682\pi$
$660$	32.1493	−	18.5614i	1.25141	−	0.722501i
$661$	−11.2018	−	11.2018i	−0.435699	−	0.435699i	0.454863	−	0.890561i	$-0.349688\pi$
$661$	−11.2018	−	11.2018i	−0.435699	−	0.435699i	−0.890561	+	0.454863i	$0.849688\pi$
$662$	52.7251	−	30.4408i	2.04922	−	1.18312i
$663$	−26.6902	+	6.36370i	−1.03656	+	0.247146i
$664$		−	4.31394i		−	0.167413i
$665$	−5.25277	+	23.0339i	−0.203694	+	0.893216i
$666$	1.86962	−	3.23827i	0.0724462	−	0.125480i
$667$			13.4161i			0.519473i
$668$	−61.8291	−	16.5671i	−2.39224	−	0.640999i
$669$	−22.3127	+	5.97866i	−0.862657	+	0.231148i
$670$	39.3556	+	39.3556i	1.52044	+	1.52044i
$671$	−26.2548	−	26.2548i	−1.01356	−	1.01356i
$672$	16.1969	−	10.1815i	0.624810	−	0.392758i
$673$	−2.46102	−	1.42087i	−0.0948654	−	0.0547706i	0.451817	−	0.892111i	$-0.350776\pi$
$673$	−2.46102	−	1.42087i	−0.0948654	−	0.0547706i	−0.546682	+	0.837340i	$0.684109\pi$
$674$	32.1490	+	8.61430i	1.23833	+	0.331811i
$675$	2.73406	+	4.73553i	0.105234	+	0.182271i
$676$	−20.2449	+	30.9624i	−0.778651	+	1.19086i
$677$	5.65487	+	3.26484i	0.217334	+	0.125478i	0.604715	−	0.796442i	$-0.293287\pi$
$677$	5.65487	+	3.26484i	0.217334	+	0.125478i	−0.387381	+	0.921920i	$0.626620\pi$
$678$	−5.07495	−	18.9400i	−0.194902	−	0.727385i
$679$	−1.31248	−	34.9009i	−0.0503684	−	1.33937i
$680$	39.6940	−	22.9173i	1.52220	−	0.878840i
$681$	−16.6701	+	4.46674i	−0.638800	+	0.171166i
$682$	−6.14011	−	22.9152i	−0.235117	−	0.877468i
$683$	−8.43502	−	31.4799i	−0.322757	−	1.20455i	−0.916547	−	0.399926i	$-0.869036\pi$
$683$	−8.43502	−	31.4799i	−0.322757	−	1.20455i	0.593790	−	0.804620i	$-0.297631\pi$
$684$	7.58612	−	2.03270i	0.290063	−	0.0777221i
$685$	31.6001	−	18.2443i	1.20738	−	0.697080i
$686$	−32.7885	+	24.2276i	−1.25187	+	0.925015i
$687$	1.95525	+	7.29710i	0.0745975	+	0.278402i
$688$	−10.0551	−	5.80532i	−0.383347	−	0.221326i
$689$	−27.0416	−	8.05603i	−1.03020	−	0.306910i
$690$	−16.0140	−	27.7370i	−0.609642	−	1.05593i
$691$	−25.2233	−	6.75857i	−0.959541	−	0.257108i	−0.255135	−	0.966905i	$-0.582120\pi$
$691$	−25.2233	−	6.75857i	−0.959541	−	0.257108i	−0.704406	+	0.709797i	$0.748787\pi$
$692$	−11.6522	−	6.72739i	−0.442950	−	0.255737i
$693$	−9.43244	−	4.98292i	−0.358309	−	0.189285i
$694$	0.397155	+	0.397155i	0.0150758	+	0.0150758i
$695$	6.61820	+	6.61820i	0.251043	+	0.251043i
$696$	−5.36445	+	1.43740i	−0.203339	+	0.0544845i
$697$	83.8170	+	22.4587i	3.17480	+	0.850684i
$698$			53.5257i			2.02598i
$699$	−10.6420	+	18.4325i	−0.402518	+	0.697181i
$700$	12.1422	+	39.3377i	0.458931	+	1.48682i
$701$			41.5208i			1.56822i	0.620623	+	0.784109i	$0.286880\pi$
$701$			41.5208i			1.56822i	−0.620623	+	0.784109i	$0.713120\pi$
$702$	−6.98094	+	3.77625i	−0.263479	+	0.142525i
$703$	−4.06003	+	2.34406i	−0.153127	+	0.0884079i
$704$	36.2948	+	36.2948i	1.36791	+	1.36791i
$705$	7.21339	−	4.16465i	0.271672	−	0.156850i
$706$	−10.6364	−	18.4227i	−0.400305	−	0.693349i
$707$	3.09917	+	10.0406i	0.116556	+	0.377614i
$708$	−6.02655	+	22.4914i	−0.226492	+	0.845278i
$709$	−32.3620	+	32.3620i	−1.21538	+	1.21538i	−0.246149	+	0.969232i	$0.579165\pi$
$709$	−32.3620	+	32.3620i	−1.21538	+	1.21538i	−0.969232	+	0.246149i	$0.920835\pi$
$710$	−5.13611	+	19.1682i	−0.192755	+	0.719371i
$711$	−4.31023	+	7.46554i	−0.161646	+	0.279980i
$712$	−16.7861	−	29.0744i	−0.629087	−	1.08961i
$713$	−11.6103	+	3.11096i	−0.434808	+	0.116507i
$714$	−39.1890	−	20.7026i	−1.46661	−	0.774773i
$715$	45.7533	−	10.9089i	1.71108	−	0.407969i
$716$	32.5986	−	56.4625i	1.21827	−	2.11010i
$717$	14.8128	−	14.8128i	0.553195	−	0.553195i
$718$	−44.7205			−1.66896
$719$	−42.5082			−1.58529			−0.792645	−	0.609684i	$-0.791296\pi$
$719$	−42.5082			−1.58529			−0.792645	+	0.609684i	$0.791296\pi$
$720$	−3.64569	+	3.64569i	−0.135867	+	0.135867i
$721$	9.82371	+	2.24025i	0.365854	+	0.0834313i
$722$	24.2034	+	6.48528i	0.900757	+	0.241357i
$723$	−1.19384	−	4.45546i	−0.0443992	−	0.165700i
$724$	11.9291	+	6.88729i	0.443343	+	0.255964i
$725$			16.3134i			0.605866i
$726$	2.99521	−	11.1783i	0.111162	−	0.414864i
$727$	−44.5147			−1.65096			−0.825479	−	0.564433i	$-0.809095\pi$
$727$	−44.5147			−1.65096			−0.825479	+	0.564433i	$0.809095\pi$
$728$	−17.1068	+	4.76479i	−0.634022	+	0.176595i
$729$	−1.00000			−0.0370370
$730$	3.23002	−	12.0546i	0.119548	−	0.446160i
$731$			55.4476i			2.05080i
$732$	−22.6942	−	13.1025i	−0.838804	−	0.484283i
$733$	0.0203237	+	0.0758491i	0.000750673	+	0.00280155i	0.966300	−	0.257418i	$-0.0828717\pi$
$733$	0.0203237	+	0.0758491i	0.000750673	+	0.00280155i	−0.965549	+	0.260220i	$0.916205\pi$
$734$	46.2772	+	12.3999i	1.70812	+	0.457691i
$735$	14.7666	−	17.1722i	0.544675	−	0.633406i
$736$	22.9930	−	22.9930i	0.847534	−	0.847534i
$737$	31.5089			1.16064
$738$	25.1003			0.923954
$739$	−29.2407	+	29.2407i	−1.07564	+	1.07564i	−0.0787424	+	0.996895i	$0.525090\pi$
$739$	−29.2407	+	29.2407i	−1.07564	+	1.07564i	−0.996895	+	0.0787424i	$0.974910\pi$
$740$	−7.81977	+	13.5442i	−0.287460	+	0.497896i
$741$	9.94712	+	0.276014i	0.365417	+	0.0101396i
$742$	−24.2560	−	38.5871i	−0.890466	−	1.41658i
$743$	28.0978	−	7.52879i	1.03081	−	0.276205i	0.296510	−	0.955030i	$-0.404177\pi$
$743$	28.0978	−	7.52879i	1.03081	−	0.276205i	0.734300	+	0.678825i	$0.237511\pi$
$744$	−2.48785	−	4.30908i	−0.0912090	−	0.157979i
$745$	2.32441	−	4.02599i	0.0851596	−	0.147501i
$746$	8.84667	−	33.0162i	0.323900	−	1.20881i
$747$	1.63865	−	1.63865i	0.0599549	−	0.0599549i
$748$	22.5990	−	84.3405i	0.826300	−	3.08380i
$749$	−12.3533	+	13.3187i	−0.451379	+	0.486654i
$750$	−1.66700	−	2.88733i	−0.0608702	−	0.105430i
$751$	1.12001	−	0.646638i	0.0408697	−	0.0235961i	−0.479426	−	0.877582i	$-0.659155\pi$
$751$	1.12001	−	0.646638i	0.0408697	−	0.0235961i	0.520296	+	0.853986i	$0.325822\pi$
$752$	2.90081	+	2.90081i	0.105782	+	0.105782i
$753$	13.5335	−	7.81358i	0.493189	−	0.284743i
$754$	−23.6695	−	0.656784i	−0.861992	−	0.0239187i
$755$		−	25.9793i		−	0.945484i
$756$	−7.34047	−	1.67396i	−0.266970	−	0.0608813i
$757$	23.6428	−	40.9506i	0.859313	−	1.48837i	−0.0132729	−	0.999912i	$-0.504225\pi$
$757$	23.6428	−	40.9506i	0.859313	−	1.48837i	0.872586	−	0.488461i	$-0.162442\pi$
$758$		−	51.0713i		−	1.85499i
$759$	−17.5140	−	4.69286i	−0.635717	−	0.170340i
$760$	−16.0563	+	4.30226i	−0.582422	+	0.156059i
$761$	15.0892	+	15.0892i	0.546983	+	0.546983i	0.925567	−	0.378584i	$-0.123589\pi$
$761$	15.0892	+	15.0892i	0.546983	+	0.546983i	−0.378584	+	0.925567i	$0.623589\pi$
$762$	9.10649	+	9.10649i	0.329893	+	0.329893i
$763$	12.8926	−	0.484837i	0.466743	−	0.0175523i
$764$	−36.5399	−	21.0963i	−1.32197	−	0.763238i
$765$	23.7829	+	6.37260i	0.859872	+	0.230402i
$766$	−1.77686	−	3.07761i	−0.0642005	−	0.111199i
$767$	−15.4543	+	25.1310i	−0.558024	+	0.907429i
$768$	3.80304	+	2.19568i	0.137230	+	0.0792299i
$769$	6.12447	+	22.8568i	0.220854	+	0.824238i	0.984023	+	0.178040i	$0.0569755\pi$
$769$	6.12447	+	22.8568i	0.220854	+	0.824238i	−0.763169	+	0.646198i	$0.776358\pi$
$770$	67.1792	+	35.4891i	2.42097	+	1.27894i
$771$	3.38540	−	1.95456i	0.121922	−	0.0703918i
$772$	43.2327	−	11.5842i	1.55598	−	0.416924i
$773$	−13.0876	−	48.8435i	−0.470728	−	1.75678i	−0.637165	−	0.770728i	$-0.719893\pi$
$773$	−13.0876	−	48.8435i	−0.470728	−	1.75678i	0.166437	−	0.986052i	$-0.446774\pi$
$774$	4.15115	+	15.4923i	0.149210	+	0.556860i
$775$	−14.1176	+	3.78281i	−0.507121	+	0.135883i
$776$	21.2813	−	12.2868i	0.763956	−	0.441070i
$777$	4.49105	−	0.168890i	0.161116	−	0.00605890i
$778$	9.33904	+	34.8538i	0.334821	+	1.24957i
$779$	−27.2537	−	15.7349i	−0.976465	−	0.563762i
$780$	29.1981	−	15.7943i	1.04546	−	0.565528i
$781$	5.61720	+	9.72928i	0.200999	+	0.348141i
$782$	−72.7654	−	19.4974i	−2.60209	−	0.697227i
$783$	−2.58368	−	1.49169i	−0.0923331	−	0.0533085i
$784$	10.0519	+	4.83606i	0.358995	+	0.172716i
$785$	−4.53132	−	4.53132i	−0.161730	−	0.161730i
$786$	4.07306	+	4.07306i	0.145281	+	0.145281i
$787$	−42.0555	+	11.2687i	−1.49912	+	0.401687i	−0.912804	−	0.408398i	$-0.866088\pi$
$787$	−42.0555	+	11.2687i	−1.49912	+	0.401687i	−0.586312	+	0.810085i	$0.699421\pi$
$788$	24.5580	+	6.58029i	0.874841	+	0.234413i
$789$			1.84465i			0.0656711i
$790$	30.6981	−	53.1707i	1.09219	−	1.89173i
$791$	16.0265	−	17.2790i	0.569837	−	0.614370i
$792$		−	7.50579i		−	0.266707i
$793$	−22.8176	−	24.1200i	−0.810277	−	0.856528i
$794$	−66.0221	+	38.1179i	−2.34304	+	1.35275i
$795$	17.9038	+	17.9038i	0.634982	+	0.634982i
$796$	−16.7871	+	9.69202i	−0.595002	+	0.343524i
$797$	4.66397	+	8.07823i	0.165206	+	0.286146i	0.936728	−	0.350057i	$-0.113838\pi$
$797$	4.66397	+	8.07823i	0.165206	+	0.286146i	−0.771522	+	0.636202i	$0.780504\pi$
$798$	11.7850	+	10.9307i	0.417184	+	0.386944i
$799$	5.07058	−	18.9236i	0.179384	−	0.669471i
$800$	27.9586	−	27.9586i	0.988486	−	0.988486i
$801$	4.66770	−	17.4201i	0.164925	−	0.615509i
$802$	−39.8686	+	69.0545i	−1.40781	+	2.43840i
$803$	−3.53257	−	6.11858i	−0.124662	−	0.215920i
$804$	21.4802	−	5.75559i	0.757547	−	0.202984i
$805$	17.9810	−	34.0372i	0.633746	−	1.19965i
$806$	−4.92017	−	20.6359i	−0.173306	−	0.726867i
$807$	−0.406023	+	0.703253i	−0.0142927	+	0.0247557i
$808$	−5.22792	+	5.22792i	−0.183918	+	0.183918i
$809$	47.1436			1.65748			0.828740	−	0.559634i	$-0.189058\pi$
$809$	47.1436			1.65748			0.828740	+	0.559634i	$0.189058\pi$
$810$	7.12215			0.250247
$811$	1.45328	−	1.45328i	0.0510314	−	0.0510314i	−0.681131	−	0.732162i	$-0.738511\pi$
$811$	1.45328	−	1.45328i	0.0510314	−	0.0510314i	0.732162	+	0.681131i	$0.238511\pi$
$812$	−16.4684	−	15.2746i	−0.577927	−	0.536035i
$813$	−6.63966	−	1.77909i	−0.232863	−	0.0623954i
$814$	3.90213	+	14.5629i	0.136770	+	0.510431i
$815$	−0.312718	−	0.180548i	−0.0109540	−	0.00632431i
$816$			12.1268i			0.424523i
$817$	5.20457	−	19.4237i	0.182085	−	0.679550i
$818$	48.6539			1.70114
$819$	−8.30792	−	4.68812i	−0.290302	−	0.163816i
$820$	−104.983			−3.66617
$821$	−3.24217	+	12.0999i	−0.113153	+	0.422291i	−0.999142	−	0.0414143i	$-0.986814\pi$
$821$	−3.24217	+	12.0999i	−0.113153	+	0.422291i	0.885990	+	0.463705i	$0.153480\pi$
$822$		−	24.8256i		−	0.865893i
$823$	−10.6995	−	6.17737i	−0.372962	−	0.215330i	0.301790	−	0.953374i	$-0.402416\pi$
$823$	−10.6995	−	6.17737i	−0.372962	−	0.215330i	−0.674752	+	0.738045i	$0.735749\pi$
$824$	1.83487	+	6.84783i	0.0639207	+	0.238555i
$825$	−21.2963	−	5.70633i	−0.741442	−	0.198669i
$826$	−45.5358	+	14.0553i	−1.58439	+	0.489047i
$827$	39.0342	−	39.0342i	1.35735	−	1.35735i	0.480185	−	0.877167i	$-0.340570\pi$
$827$	39.0342	−	39.0342i	1.35735	−	1.35735i	0.877167	−	0.480185i	$-0.159430\pi$
$828$	−12.7968			−0.444720
$829$	43.7929			1.52099			0.760495	−	0.649344i	$-0.224956\pi$
$829$	43.7929			1.52099			0.760495	+	0.649344i	$0.224956\pi$
$830$	−11.6707	+	11.6707i	−0.405095	+	0.405095i
$831$	9.50450	−	16.4623i	0.329707	−	0.571070i
$832$	31.5431	+	33.3436i	1.09356	+	1.15598i
$833$	−4.00089	−	53.1198i	−0.138623	−	1.84049i
$834$	6.15093	−	1.64814i	0.212989	−	0.0570703i
$835$	36.3890	+	63.0276i	1.25929	+	2.18116i
$836$	−15.8332	+	27.4239i	−0.547603	+	0.948476i
$837$	0.691794	−	2.58181i	0.0239119	−	0.0892404i
$838$	−12.5741	+	12.5741i	−0.434365	+	0.434365i
$839$	−13.1086	+	48.9218i	−0.452558	+	1.68897i	0.242612	+	0.970123i	$0.421996\pi$
$839$	−13.1086	+	48.9218i	−0.452558	+	1.68897i	−0.695170	+	0.718846i	$0.744671\pi$
$840$	15.5363	+	3.54299i	0.536054	+	0.122245i
$841$	10.0497	+	17.4067i	0.346543	+	0.600230i
$842$	14.3376	−	8.27783i	0.494107	−	0.285273i
$843$	3.58709	+	3.58709i	0.123546	+	0.123546i
$844$	8.17678	−	4.72087i	0.281456	−	0.162499i
$845$	41.1688	−	8.61644i	1.41625	−	0.296415i
$846$		−	5.66697i		−	0.194835i
$847$	13.2905	−	4.10232i	0.456667	−	0.140957i
$848$	−6.23528	+	10.7998i	−0.214120	+	0.370867i
$849$		−	14.0844i		−	0.483377i
$850$	−88.4799	−	23.7081i	−3.03483	−	0.813182i
$851$	7.37850	−	1.97706i	0.252932	−	0.0677729i
$852$	5.60655	+	5.60655i	0.192077	+	0.192077i
$853$	12.0121	+	12.0121i	0.411288	+	0.411288i	0.882187	−	0.470899i	$-0.156070\pi$
$853$	12.0121	+	12.0121i	0.411288	+	0.411288i	−0.470899	+	0.882187i	$0.656070\pi$
$854$	−2.01547	−	53.5945i	−0.0689680	−	1.83397i
$855$	−7.73317	−	4.46475i	−0.264469	−	0.152691i
$856$	−12.3458	−	3.30805i	−0.421971	−	0.113067i
$857$	−25.7042	−	44.5209i	−0.878038	−	1.52081i	−0.853491	−	0.521107i	$-0.825519\pi$
$857$	−25.7042	−	44.5209i	−0.878038	−	1.52081i	−0.0245462	−	0.999699i	$-0.507814\pi$
$858$	9.13682	−	30.6695i	0.311926	−	1.04704i
$859$	−31.2553	−	18.0452i	−1.06642	−	0.615695i	−0.139216	−	0.990262i	$-0.544458\pi$
$859$	−31.2553	−	18.0452i	−1.06642	−	0.615695i	−0.927200	+	0.374567i	$0.877791\pi$
$860$	−17.3624	−	64.7974i	−0.592053	−	2.20957i
$861$	16.0553	+	25.5412i	0.547164	+	0.870443i
$862$	−19.9939	+	11.5435i	−0.680995	+	0.393173i
$863$	11.9022	−	3.18919i	0.405156	−	0.108561i	−0.0504853	−	0.998725i	$-0.516077\pi$
$863$	11.9022	−	3.18919i	0.405156	−	0.108561i	0.455641	+	0.890164i	$0.349410\pi$
$864$	1.87150	+	6.98452i	0.0636696	+	0.237618i
$865$	3.95935	+	14.7765i	0.134622	+	0.502416i
$866$	−11.0264	+	2.95452i	−0.374694	+	0.100399i
$867$	35.4313	−	20.4563i	1.20331	−	0.694732i
$868$	9.39993	−	17.7936i	0.319055	−	0.603956i
$869$	−8.99601	−	33.5736i	−0.305169	−	1.13890i
$870$	18.4013	+	10.6240i	0.623863	+	0.360188i
$871$	28.1653	+	0.781535i	0.954346	+	0.0264813i
$872$	4.53881	+	7.86144i	0.153703	+	0.266222i
$873$	12.7508	+	3.41658i	0.431550	+	0.115634i
$874$	23.6602	+	13.6602i	0.800318	+	0.462064i
$875$	1.87176	−	3.54315i	0.0632770	−	0.119780i
$876$	−3.52587	−	3.52587i	−0.119128	−	0.119128i
$877$	22.3841	+	22.3841i	0.755857	+	0.755857i	0.975566	−	0.219709i	$-0.0705107\pi$
$877$	22.3841	+	22.3841i	0.755857	+	0.755857i	−0.219709	+	0.975566i	$0.570511\pi$
$878$	18.4522	−	4.94426i	0.622732	−	0.166861i
$879$	−26.8190	−	7.18612i	−0.904582	−	0.242382i
$880$		−	20.7882i		−	0.700770i
$881$	14.4314	−	24.9959i	0.486206	−	0.842133i	−0.513668	−	0.857989i	$-0.671714\pi$
$881$	14.4314	−	24.9959i	0.486206	−	0.842133i	0.999874	+	0.0158554i	$0.00504713\pi$
$882$	−5.09475	−	14.5424i	−0.171549	−	0.489668i
$883$			35.8803i			1.20747i	0.797185	+	0.603735i	$0.206321\pi$
$883$			35.8803i			1.20747i	−0.797185	+	0.603735i	$0.793679\pi$
$884$	22.2928	−	74.8302i	0.749790	−	2.51681i
$885$	22.9274	−	13.2371i	0.770695	−	0.444961i
$886$	−15.9788	−	15.9788i	−0.536819	−	0.536819i
$887$	−40.8742	+	23.5987i	−1.37242	+	0.792368i	−0.991233	−	0.132129i	$-0.957819\pi$
$887$	−40.8742	+	23.5987i	−1.37242	+	0.792368i	−0.381190	+	0.924497i	$0.624486\pi$
$888$	1.58107	+	2.73849i	0.0530571	+	0.0918976i
$889$	−3.44152	+	15.0914i	−0.115425	+	0.506149i
$890$	−33.2441	+	124.068i	−1.11434	+	4.15879i
$891$	2.85107	−	2.85107i	0.0955144	−	0.0955144i
$892$	17.0132	−	63.4943i	0.569645	−	2.12595i
$893$	−3.55253	+	6.15316i	−0.118881	+	0.205908i
$894$	−1.58145	−	2.73914i	−0.0528914	−	0.0916107i
$895$	−71.6018	+	19.1857i	−2.39339	+	0.641306i
$896$	1.34832	+	35.8539i	0.0450442	+	1.19780i
$897$	−15.5391	−	4.62929i	−0.518835	−	0.154567i
$898$	8.81423	−	15.2667i	0.294135	−	0.509456i
$899$	5.63862	−	5.63862i	0.188059	−	0.188059i
$900$	−15.5604			−0.518681
$901$	59.5541			1.98404
$902$	−71.5627	+	71.5627i	−2.38278	+	2.38278i
$903$	−13.1092	+	14.1337i	−0.436247	+	0.470340i
$904$	16.0168	+	4.29170i	0.532712	+	0.142740i
$905$	−4.05346	−	15.1277i	−0.134742	−	0.502862i
$906$	−15.3074	−	8.83772i	−0.508553	−	0.293613i
$907$		−	46.3410i		−	1.53873i	−0.638810	−	0.769364i	$-0.720573\pi$
$907$		−	46.3410i		−	1.53873i	0.638810	−	0.769364i	$-0.279427\pi$
$908$	12.7108	−	47.4375i	0.421824	−	1.57427i
$909$	−3.97164			−0.131731
$910$	59.1702	+	33.3894i	1.96147	+	1.10685i
$911$	8.52972			0.282602			0.141301	−	0.989967i	$-0.454871\pi$
$911$	8.52972			0.282602			0.141301	+	0.989967i	$0.454871\pi$
$912$	1.13828	−	4.24812i	0.0376922	−	0.140669i
$913$			9.34378i			0.309234i
$914$	49.4798	+	28.5672i	1.63665	+	0.944919i
$915$	7.71138	+	28.7793i	0.254930	+	0.951413i
$916$	−20.7651	−	5.56399i	−0.686098	−	0.183839i
$917$	−1.53929	+	6.74994i	−0.0508319	+	0.222903i
$918$	11.8454	−	11.8454i	0.390955	−	0.390955i
$919$	23.5080			0.775457			0.387729	−	0.921774i	$-0.373260\pi$
$919$	23.5080			0.775457			0.387729	+	0.921774i	$0.373260\pi$
$920$	27.0848			0.892961
$921$	−20.3066	+	20.3066i	−0.669125	+	0.669125i
$922$	−16.2893	+	28.2138i	−0.536459	+	0.929174i
$923$	4.77981	+	8.83619i	0.157329	+	0.290847i
$924$	25.7007	−	16.1556i	0.845493	−	0.531480i
$925$	8.97197	−	2.40403i	0.294996	−	0.0790441i
$926$	−10.4161	−	18.0412i	−0.342293	−	0.592869i
$927$	−1.90417	+	3.29812i	−0.0625411	+	0.108324i
$928$	−5.58337	+	20.8374i	−0.183283	+	0.684022i
$929$	−5.03502	+	5.03502i	−0.165194	+	0.165194i	−0.784863	−	0.619669i	$-0.787267\pi$
$929$	−5.03502	+	5.03502i	−0.165194	+	0.165194i	0.619669	+	0.784863i	$0.287267\pi$
$930$	−4.92706	+	18.3880i	−0.161565	+	0.602967i
$931$	−3.58453	+	18.9838i	−0.117478	+	0.622170i
$932$	−30.2836	−	52.4527i	−0.991972	−	1.71815i
$933$	−6.51650	+	3.76230i	−0.213341	+	0.123172i
$934$	−48.7017	−	48.7017i	−1.59357	−	1.59357i
$935$	−85.9754	+	49.6379i	−2.81170	+	1.62333i
$936$	0.186171	−	6.70932i	0.00608519	−	0.219301i
$937$		−	16.2205i		−	0.529900i	−0.964262	−	0.264950i	$-0.914645\pi$
$937$		−	16.2205i		−	0.529900i	0.964262	−	0.264950i	$-0.0853554\pi$
$938$	33.3693	+	30.9505i	1.08954	+	1.01057i
$939$	−12.6043	+	21.8314i	−0.411327	+	0.712439i
$940$			23.7024i			0.773087i
$941$	−55.5707	−	14.8901i	−1.81155	−	0.485405i	−0.815872	−	0.578232i	$-0.803743\pi$
$941$	−55.5707	−	14.8901i	−1.81155	−	0.485405i	−0.995682	+	0.0928277i	$0.970409\pi$
$942$	−4.21140	+	1.12844i	−0.137215	+	0.0367666i
$943$	36.2581	+	36.2581i	1.18073	+	1.18073i
$944$	9.22007	+	9.22007i	0.300088	+	0.300088i
$945$	4.55566	+	7.24726i	0.148196	+	0.235753i
$946$	−56.0049	−	32.3344i	−1.82088	−	1.05128i
$947$	38.8518	+	10.4103i	1.26251	+	0.338290i	0.827158	−	0.561969i	$-0.189956\pi$
$947$	38.8518	+	10.4103i	1.26251	+	0.338290i	0.435356	+	0.900259i	$0.356623\pi$
$948$	−12.2655	−	21.2444i	−0.398364	−	0.689987i
$949$	−3.00595	−	5.55693i	−0.0975771	−	0.180386i
$950$	28.7699	+	16.6103i	0.933418	+	0.538909i
$951$	−1.93925	−	7.23738i	−0.0628845	−	0.234688i
$952$	31.7322	−	19.9470i	1.02845	−	0.646485i
$953$	21.9464	−	12.6708i	0.710915	−	0.410447i	−0.100485	−	0.994939i	$-0.532039\pi$
$953$	21.9464	−	12.6708i	0.710915	−	0.410447i	0.811400	+	0.584492i	$0.198706\pi$
$954$	16.6397	−	4.45860i	0.538731	−	0.144352i
$955$	12.4161	+	46.3374i	0.401774	+	1.49944i
$956$	15.4288	+	57.5811i	0.499003	+	1.86230i
$957$	11.6191	−	3.11334i	0.375594	−	0.100640i
$958$	−62.2441	+	35.9366i	−2.01102	+	1.16106i
$959$	25.2617	−	15.8796i	0.815744	−	0.512780i
$960$	−10.6602	−	39.7846i	−0.344058	−	1.28404i
$961$	−20.6596	−	11.9278i	−0.666440	−	0.384769i
$962$	3.12684	+	13.1144i	0.100813	+	0.422825i
$963$	−3.43298	−	5.94610i	−0.110626	−	0.191611i
$964$	12.6787	+	3.39726i	0.408354	+	0.109418i
$965$	−44.0708	−	25.4443i	−1.41869	−	0.819080i
$966$	−13.9384	−	22.1735i	−0.448459	−	0.713421i
$967$	1.97447	+	1.97447i	0.0634945	+	0.0634945i	0.738141	−	0.674646i	$-0.235704\pi$
$967$	1.97447	+	1.97447i	0.0634945	+	0.0634945i	−0.674646	+	0.738141i	$0.735704\pi$
$968$	6.92010	+	6.92010i	0.222420	+	0.222420i
$969$	−20.2872	+	5.43595i	−0.651720	+	0.174628i
$970$	−90.8133	−	24.3333i	−2.91584	−	0.781297i
$971$		−	37.1765i		−	1.19305i	−0.802595	−	0.596525i	$-0.796548\pi$
$971$		−	37.1765i		−	1.19305i	0.802595	−	0.596525i	$-0.203452\pi$
$972$	1.42283	−	2.46442i	0.0456373	−	0.0790462i
$973$	5.61152	+	5.20476i	0.179897	+	0.166857i
$974$			1.20948i			0.0387541i
$975$	−18.8949	−	5.62903i	−0.605122	−	0.180273i
$976$	−12.7084	+	7.33723i	−0.406788	+	0.234859i
$977$	−8.38970	−	8.38970i	−0.268410	−	0.268410i	0.560049	−	0.828459i	$-0.310782\pi$
$977$	−8.38970	−	8.38970i	−0.268410	−	0.268410i	−0.828459	+	0.560049i	$0.810782\pi$
$978$	−0.212762	+	0.122838i	−0.00680339	+	0.00392794i
$979$	36.3580	+	62.9739i	1.16201	+	2.01265i
$980$	21.3090	+	60.8243i	0.680692	+	1.94296i
$981$	−1.26210	+	4.71023i	−0.0402958	+	0.150386i
$982$	−20.0372	+	20.0372i	−0.639413	+	0.639413i
$983$	−0.0857508	+	0.320026i	−0.00273503	+	0.0102073i	−0.967280	−	0.253712i	$-0.918349\pi$
$983$	−0.0857508	+	0.320026i	−0.00273503	+	0.0102073i	0.964545	+	0.263919i	$0.0850152\pi$
$984$	−10.6132	+	18.3826i	−0.338336	+	0.586015i
$985$	−14.4534	−	25.0340i	−0.460523	−	0.797649i
$986$	48.2741	−	12.9350i	1.53736	−	0.411935i
$987$	5.76653	−	3.62486i	0.183551	−	0.115381i
$988$	−14.8333	+	24.1211i	−0.471910	+	0.767395i
$989$	−16.3827	+	28.3756i	−0.520938	+	0.902291i
$990$	−20.3057	+	20.3057i	−0.645358	+	0.645358i
$991$	42.2269			1.34138			0.670691	−	0.741737i	$-0.265998\pi$
$991$	42.2269			1.34138			0.670691	+	0.741737i	$0.265998\pi$
$992$	−19.3274			−0.613645
$993$	−19.5567	+	19.5567i	−0.620612	+	0.620612i
$994$	−3.60799	+	15.8214i	−0.114439	+	0.501823i
$995$	21.2882	+	5.70415i	0.674881	+	0.180834i
$996$	1.70679	+	6.36982i	0.0540817	+	0.201836i
$997$	−1.01451	−	0.585728i	−0.0321299	−	0.0185502i	0.483849	−	0.875151i	$-0.339238\pi$
$997$	−1.01451	−	0.585728i	−0.0321299	−	0.0185502i	−0.515979	+	0.856601i	$0.672572\pi$
$998$			8.20167i			0.259619i
$999$	−0.439645	+	1.64078i	−0.0139098	+	0.0519119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.a.124.8	yes	36
3.2	odd	2		819.2.gh.c.397.2		36
7.3	odd	6		273.2.bt.a.241.8	yes	36
13.2	odd	12		273.2.bt.a.145.8	✓	36
21.17	even	6		819.2.et.c.514.2		36
39.2	even	12		819.2.et.c.145.2		36
91.80	even	12	inner	273.2.cg.a.262.8	yes	36
273.80	odd	12		819.2.gh.c.262.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.8	✓	36	13.2	odd	12
273.2.bt.a.241.8	yes	36	7.3	odd	6
273.2.cg.a.124.8	yes	36	1.1	even	1	trivial
273.2.cg.a.262.8	yes	36	91.80	even	12	inner
819.2.et.c.145.2		36	39.2	even	12
819.2.et.c.514.2		36	21.17	even	6
819.2.gh.c.262.2		36	273.80	odd	12
819.2.gh.c.397.2		36	3.2	odd	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.569735 - 2.12628i) q^{2} +1.00000i q^{3} +(-2.46442 - 1.42283i) q^{4} +(0.837395 + 3.12520i) q^{5} +(2.12628 + 0.569735i) q^{6} +(0.780325 + 2.52806i) q^{7} +(-1.31631 + 1.31631i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.569735 - 2.12628i) q^{2} +1.00000i q^{3} +(-2.46442 - 1.42283i) q^{4} +(0.837395 + 3.12520i) q^{5} +(2.12628 + 0.569735i) q^{6} +(0.780325 + 2.52806i) q^{7} +(-1.31631 + 1.31631i) q^{8} -1.00000 q^{9} +7.12215 q^{10} +(2.85107 - 2.85107i) q^{11} +(1.42283 - 2.46442i) q^{12} +(2.61925 - 2.47781i) q^{13} +(5.81994 - 0.218864i) q^{14} +(-3.12520 + 0.837395i) q^{15} +(-0.796765 - 1.38004i) q^{16} +(-3.80501 + 6.59048i) q^{17} +(-0.569735 + 2.12628i) q^{18} +(1.95154 - 1.95154i) q^{19} +(2.38294 - 8.89327i) q^{20} +(-2.52806 + 0.780325i) q^{21} +(-4.43782 - 7.68652i) q^{22} +(-3.89447 + 2.24848i) q^{23} +(-1.31631 - 1.31631i) q^{24} +(-4.73553 + 2.73406i) q^{25} +(-3.77625 - 6.98094i) q^{26} -1.00000i q^{27} +(1.67396 - 7.34047i) q^{28} +(1.49169 - 2.58368i) q^{29} +7.12215i q^{30} +(2.58181 + 0.691794i) q^{31} +(-6.98452 + 1.87150i) q^{32} +(2.85107 + 2.85107i) q^{33} +(11.8454 + 11.8454i) q^{34} +(-7.24726 + 4.55566i) q^{35} +(2.46442 + 1.42283i) q^{36} +(-1.64078 - 0.439645i) q^{37} +(-3.03766 - 5.26138i) q^{38} +(2.47781 + 2.61925i) q^{39} +(-5.21601 - 3.01147i) q^{40} +(-2.95120 - 11.0140i) q^{41} +(0.218864 + 5.81994i) q^{42} +(6.30996 - 3.64306i) q^{43} +(-11.0828 + 2.96963i) q^{44} +(-0.837395 - 3.12520i) q^{45} +(2.56207 + 9.56178i) q^{46} +(-2.48667 + 0.666302i) q^{47} +(1.38004 - 0.796765i) q^{48} +(-5.78219 + 3.94542i) q^{49} +(3.11538 + 11.6267i) q^{50} +(-6.59048 - 3.80501i) q^{51} +(-9.98042 + 2.37961i) q^{52} +(-3.91287 - 6.77729i) q^{53} +(-2.12628 - 0.569735i) q^{54} +(11.2976 + 6.52269i) q^{55} +(-4.35487 - 2.30057i) q^{56} +(1.95154 + 1.95154i) q^{57} +(-4.64375 - 4.64375i) q^{58} +(-7.90374 + 2.11780i) q^{59} +(8.89327 + 2.38294i) q^{60} -9.20877i q^{61} +(2.94189 - 5.09551i) q^{62} +(-0.780325 - 2.52806i) q^{63} +12.7302i q^{64} +(9.93701 + 6.11076i) q^{65} +(7.68652 - 4.43782i) q^{66} +(5.52580 + 5.52580i) q^{67} +(18.7543 - 10.8278i) q^{68} +(-2.24848 - 3.89447i) q^{69} +(5.55759 + 18.0052i) q^{70} +(-0.721147 + 2.69136i) q^{71} +(1.31631 - 1.31631i) q^{72} +(0.453517 - 1.69255i) q^{73} +(-1.86962 + 3.23827i) q^{74} +(-2.73406 - 4.73553i) q^{75} +(-7.58612 + 2.03270i) q^{76} +(9.43244 + 4.98292i) q^{77} +(6.98094 - 3.77625i) q^{78} +(4.31023 - 7.46554i) q^{79} +(3.64569 - 3.64569i) q^{80} +1.00000 q^{81} -25.1003 q^{82} +(-1.63865 + 1.63865i) q^{83} +(7.34047 + 1.67396i) q^{84} +(-23.7829 - 6.37260i) q^{85} +(-4.15115 - 15.4923i) q^{86} +(2.58368 + 1.49169i) q^{87} +7.50579i q^{88} +(-4.66770 + 17.4201i) q^{89} -7.12215 q^{90} +(8.30792 + 4.68812i) q^{91} +12.7968 q^{92} +(-0.691794 + 2.58181i) q^{93} +5.66697i q^{94} +(7.73317 + 4.46475i) q^{95} +(-1.87150 - 6.98452i) q^{96} +(-12.7508 - 3.41658i) q^{97} +(5.09475 + 14.5424i) q^{98} +(-2.85107 + 2.85107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 - 36 * q^9	\( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

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