LMFDB - Embedded newform 273.2.cd.e.44.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(44,273)]

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([6, 4, 9]))

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

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

chi := DirichletCharacter("273.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cd (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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			44.6
Character	$\chi$	$=$	273.44
Dual form			273.2.cd.e.242.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00566 + 0.537415i) q^{2} +(-0.123517 + 1.72764i) q^{3} +(2.00181 - 1.15574i) q^{4} +(0.878767 - 0.235465i) q^{5} +(-0.680727 - 3.53144i) q^{6} +(-1.67646 - 2.04682i) q^{7} +(-0.457340 + 0.457340i) q^{8} +(-2.96949 - 0.426786i) q^{9} +O(q^{10})$	\(q+(-2.00566 + 0.537415i) q^{2} +(-0.123517 + 1.72764i) q^{3} +(2.00181 - 1.15574i) q^{4} +(0.878767 - 0.235465i) q^{5} +(-0.680727 - 3.53144i) q^{6} +(-1.67646 - 2.04682i) q^{7} +(-0.457340 + 0.457340i) q^{8} +(-2.96949 - 0.426786i) q^{9} +(-1.63596 + 0.944525i) q^{10} +(-3.17403 - 0.850480i) q^{11} +(1.74945 + 3.60116i) q^{12} +(-2.59867 - 2.49938i) q^{13} +(4.46240 + 3.20427i) q^{14} +(0.298256 + 1.54728i) q^{15} +(-1.64000 + 2.84056i) q^{16} +(0.340290 + 0.589400i) q^{17} +(6.18514 - 0.739860i) q^{18} +(-1.05752 - 3.94670i) q^{19} +(1.48698 - 1.48698i) q^{20} +(3.74324 - 2.64350i) q^{21} +6.82309 q^{22} +(3.79107 - 6.56633i) q^{23} +(-0.733630 - 0.846608i) q^{24} +(-3.61334 + 2.08616i) q^{25} +(6.55525 + 3.61635i) q^{26} +(1.10411 - 5.07749i) q^{27} +(-5.72155 - 2.15978i) q^{28} +4.42254i q^{29} +(-1.42973 - 2.94302i) q^{30} +(-3.11158 - 0.833747i) q^{31} +(2.09752 - 7.82804i) q^{32} +(1.86137 - 5.37854i) q^{33} +(-0.999259 - 0.999259i) q^{34} +(-1.95517 - 1.40393i) q^{35} +(-6.43759 + 2.57762i) q^{36} +(8.41103 - 2.25373i) q^{37} +(4.24203 + 7.34742i) q^{38} +(4.63902 - 4.18085i) q^{39} +(-0.294207 + 0.509582i) q^{40} +(-2.65335 - 2.65335i) q^{41} +(-6.08702 + 7.31365i) q^{42} -7.55705i q^{43} +(-7.33674 + 1.96587i) q^{44} +(-2.70998 + 0.324165i) q^{45} +(-4.07476 + 15.2072i) q^{46} +(1.92787 + 7.19489i) q^{47} +(-4.70491 - 3.18419i) q^{48} +(-1.37896 + 6.86283i) q^{49} +(6.12600 - 6.12600i) q^{50} +(-1.06030 + 0.515099i) q^{51} +(-8.09068 - 1.99988i) q^{52} +(-8.39899 + 4.84916i) q^{53} +(0.514242 + 10.7771i) q^{54} -2.98949 q^{55} +(1.70280 + 0.169381i) q^{56} +(6.94911 - 1.33952i) q^{57} +(-2.37674 - 8.87010i) q^{58} +(-5.15217 - 1.38052i) q^{59} +(2.38531 + 2.75264i) q^{60} +(-4.47892 + 7.75771i) q^{61} +6.68885 q^{62} +(4.10467 + 6.79350i) q^{63} +10.2676i q^{64} +(-2.87214 - 1.58448i) q^{65} +(-0.842767 + 11.7879i) q^{66} +(8.41297 + 2.25425i) q^{67} +(1.36239 + 0.786577i) q^{68} +(10.8760 + 7.36067i) q^{69} +(4.67590 + 1.76507i) q^{70} +(-5.49494 - 5.49494i) q^{71} +(1.55325 - 1.16288i) q^{72} +(1.20005 - 4.47865i) q^{73} +(-15.6585 + 9.04042i) q^{74} +(-3.15783 - 6.50023i) q^{75} +(-6.67832 - 6.67832i) q^{76} +(3.58036 + 7.92248i) q^{77} +(-7.05744 + 10.8784i) q^{78} +(-0.898260 + 1.55583i) q^{79} +(-0.772325 + 2.88236i) q^{80} +(8.63571 + 2.53467i) q^{81} +(6.74767 + 3.89577i) q^{82} +(-7.56791 - 7.56791i) q^{83} +(4.43804 - 9.61802i) q^{84} +(0.437819 + 0.437819i) q^{85} +(4.06127 + 15.1569i) q^{86} +(-7.64056 - 0.546258i) q^{87} +(1.84057 - 1.06265i) q^{88} +(-0.240113 - 0.896114i) q^{89} +(5.26109 - 2.10655i) q^{90} +(-0.759223 + 9.50913i) q^{91} -17.5260i q^{92} +(1.82475 - 5.27272i) q^{93} +(-7.73329 - 13.3944i) q^{94} +(-1.85862 - 3.21922i) q^{95} +(13.2650 + 4.59065i) q^{96} +(-3.00938 + 3.00938i) q^{97} +(-0.922464 - 14.5056i) q^{98} +(9.06228 + 3.88012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.00566	+	0.537415i	−1.41822	+	0.380010i	−0.884850	−	0.465875i	$-0.845740\pi$
$2$	−2.00566	+	0.537415i	−1.41822	+	0.380010i	−0.533365	+	0.845885i	$0.679073\pi$
$3$	−0.123517	+	1.72764i	−0.0713125	+	0.997454i
$3$	−0.123517	+	1.72764i	−0.0713125	+	0.997454i
$4$	2.00181	−	1.15574i	1.00090	−	0.577872i
$5$	0.878767	−	0.235465i	0.392996	−	0.105303i	−0.0569088	−	0.998379i	$-0.518124\pi$
$5$	0.878767	−	0.235465i	0.392996	−	0.105303i	0.449905	+	0.893076i	$0.351458\pi$
$6$	−0.680727	−	3.53144i	−0.277906	−	1.44170i
$7$	−1.67646	−	2.04682i	−0.633643	−	0.773626i
$7$	−1.67646	−	2.04682i	−0.633643	−	0.773626i
$8$	−0.457340	+	0.457340i	−0.161694	+	0.161694i
$9$	−2.96949	−	0.426786i	−0.989829	−	0.142262i
$10$	−1.63596	+	0.944525i	−0.517337	+	0.298685i
$11$	−3.17403	−	0.850480i	−0.957007	−	0.256429i	−0.253674	−	0.967290i	$-0.581639\pi$
$11$	−3.17403	−	0.850480i	−0.957007	−	0.256429i	−0.703333	+	0.710861i	$0.748306\pi$
$12$	1.74945	+	3.60116i	0.505024	+	1.03956i
$13$	−2.59867	−	2.49938i	−0.720741	−	0.693204i
$13$	−2.59867	−	2.49938i	−0.720741	−	0.693204i
$14$	4.46240	+	3.20427i	1.19263	+	0.856378i
$15$	0.298256	+	1.54728i	0.0770094	+	0.399505i
$16$	−1.64000	+	2.84056i	−0.410000	+	0.710141i
$17$	0.340290	+	0.589400i	0.0825325	+	0.142951i	0.904337	−	0.426819i	$-0.140366\pi$
$17$	0.340290	+	0.589400i	0.0825325	+	0.142951i	−0.821805	+	0.569769i	$0.807033\pi$
$18$	6.18514	−	0.739860i	1.45785	−	0.174387i
$19$	−1.05752	−	3.94670i	−0.242611	−	0.905436i	−0.974569	−	0.224087i	$-0.928060\pi$
$19$	−1.05752	−	3.94670i	−0.242611	−	0.905436i	0.731958	−	0.681349i	$-0.238606\pi$
$20$	1.48698	−	1.48698i	0.332500	−	0.332500i
$21$	3.74324	−	2.64350i	0.816843	−	0.576860i
$22$	6.82309			1.45469
$23$	3.79107	−	6.56633i	0.790493	−	1.36917i	−0.135168	−	0.990823i	$-0.543158\pi$
$23$	3.79107	−	6.56633i	0.790493	−	1.36917i	0.925662	−	0.378352i	$-0.123509\pi$
$24$	−0.733630	−	0.846608i	−0.149752	−	0.172813i
$25$	−3.61334	+	2.08616i	−0.722668	+	0.417233i
$26$	6.55525	+	3.61635i	1.28559	+	0.709224i
$27$	1.10411	−	5.07749i	0.212487	−	0.977164i
$28$	−5.72155	−	2.15978i	−1.08127	−	0.408161i
$29$			4.42254i			0.821244i	0.911806	+	0.410622i	$0.134688\pi$
$29$			4.42254i			0.821244i	−0.911806	+	0.410622i	$0.865312\pi$
$30$	−1.42973	−	2.94302i	−0.261032	−	0.537320i
$31$	−3.11158	−	0.833747i	−0.558857	−	0.149745i	−0.0316759	−	0.999498i	$-0.510084\pi$
$31$	−3.11158	−	0.833747i	−0.558857	−	0.149745i	−0.527181	+	0.849753i	$0.676751\pi$
$32$	2.09752	−	7.82804i	0.370792	−	1.38382i
$33$	1.86137	−	5.37854i	0.324023	−	0.936284i
$34$	−0.999259	−	0.999259i	−0.171372	−	0.171372i
$35$	−1.95517	−	1.40393i	−0.330484	−	0.237308i
$36$	−6.43759	+	2.57762i	−1.07293	+	0.429604i
$37$	8.41103	−	2.25373i	1.38276	−	0.370511i	0.510640	−	0.859795i	$-0.329409\pi$
$37$	8.41103	−	2.25373i	1.38276	−	0.370511i	0.872124	+	0.489284i	$0.162742\pi$
$38$	4.24203	+	7.34742i	0.688149	+	1.19191i
$39$	4.63902	−	4.18085i	0.742837	−	0.669472i
$40$	−0.294207	+	0.509582i	−0.0465183	+	0.0805720i
$41$	−2.65335	−	2.65335i	−0.414384	−	0.414384i	0.468879	−	0.883263i	$-0.344658\pi$
$41$	−2.65335	−	2.65335i	−0.414384	−	0.414384i	−0.883263	+	0.468879i	$0.844658\pi$
$42$	−6.08702	+	7.31365i	−0.939247	+	1.12852i
$43$		−	7.55705i		−	1.15244i	−0.817295	−	0.576220i	$-0.804527\pi$
$43$		−	7.55705i		−	1.15244i	0.817295	−	0.576220i	$-0.195473\pi$
$44$	−7.33674	+	1.96587i	−1.10605	+	0.296366i
$45$	−2.70998	+	0.324165i	−0.403980	+	0.0483236i
$46$	−4.07476	+	15.2072i	−0.600790	+	2.24218i
$47$	1.92787	+	7.19489i	0.281208	+	1.04948i	0.951566	+	0.307445i	$0.0994740\pi$
$47$	1.92787	+	7.19489i	0.281208	+	1.04948i	−0.670358	+	0.742038i	$0.733859\pi$
$48$	−4.70491	−	3.18419i	−0.679095	−	0.459598i
$49$	−1.37896	+	6.86283i	−0.196994	+	0.980405i
$50$	6.12600	−	6.12600i	0.866347	−	0.866347i
$51$	−1.06030	+	0.515099i	−0.148472	+	0.0721282i
$52$	−8.09068	−	1.99988i	−1.12198	−	0.277334i
$53$	−8.39899	+	4.84916i	−1.15369	+	0.666083i	−0.949784	−	0.312907i	$-0.898697\pi$
$53$	−8.39899	+	4.84916i	−1.15369	+	0.666083i	−0.203906	+	0.978990i	$0.565364\pi$
$54$	0.514242	+	10.7771i	0.0699795	+	1.46658i
$55$	−2.98949			−0.403103
$56$	1.70280	+	0.169381i	0.227547	+	0.0226345i
$57$	6.94911	−	1.33952i	0.920432	−	0.177424i
$58$	−2.37674	−	8.87010i	−0.312081	−	1.16470i
$59$	−5.15217	−	1.38052i	−0.670756	−	0.179728i	−0.0926605	−	0.995698i	$-0.529537\pi$
$59$	−5.15217	−	1.38052i	−0.670756	−	0.179728i	−0.578095	+	0.815969i	$0.696204\pi$
$60$	2.38531	+	2.75264i	0.307942	+	0.355365i
$61$	−4.47892	+	7.75771i	−0.573466	+	0.993273i	0.422740	+	0.906251i	$0.361068\pi$
$61$	−4.47892	+	7.75771i	−0.573466	+	0.993273i	−0.996206	+	0.0870219i	$0.972265\pi$
$62$	6.68885			0.849485
$63$	4.10467	+	6.79350i	0.517140	+	0.855901i
$64$			10.2676i			1.28345i
$65$	−2.87214	−	1.58448i	−0.356245	−	0.196530i
$66$	−0.842767	+	11.7879i	−0.103737	+	1.45098i
$67$	8.41297	+	2.25425i	1.02781	+	0.275400i	0.733052	−	0.680172i	$-0.238095\pi$
$67$	8.41297	+	2.25425i	1.02781	+	0.275400i	0.294756	+	0.955573i	$0.404762\pi$
$68$	1.36239	+	0.786577i	0.165214	+	0.0953864i
$69$	10.8760	+	7.36067i	1.30932	+	0.886120i
$70$	4.67590	+	1.76507i	0.558877	+	0.210966i
$71$	−5.49494	−	5.49494i	−0.652130	−	0.652130i	0.301376	−	0.953505i	$-0.402554\pi$
$71$	−5.49494	−	5.49494i	−0.652130	−	0.652130i	−0.953505	+	0.301376i	$0.902554\pi$
$72$	1.55325	−	1.16288i	0.183052	−	0.137047i
$73$	1.20005	−	4.47865i	0.140455	−	0.524186i	−0.859460	−	0.511202i	$-0.829200\pi$
$73$	1.20005	−	4.47865i	0.140455	−	0.524186i	0.999916	−	0.0129840i	$-0.00413305\pi$
$74$	−15.6585	+	9.04042i	−1.82026	+	1.05093i
$75$	−3.15783	−	6.50023i	−0.364635	−	0.750582i
$76$	−6.67832	−	6.67832i	−0.766056	−	0.766056i
$77$	3.58036	+	7.92248i	0.408020	+	0.902850i
$78$	−7.05744	+	10.8784i	−0.799097	+	1.23174i
$79$	−0.898260	+	1.55583i	−0.101062	+	0.175045i	−0.912123	−	0.409918i	$-0.865557\pi$
$79$	−0.898260	+	1.55583i	−0.101062	+	0.175045i	0.811060	+	0.584962i	$0.198891\pi$
$80$	−0.772325	+	2.88236i	−0.0863485	+	0.322257i
$81$	8.63571	+	2.53467i	0.959523	+	0.281630i
$82$	6.74767	+	3.89577i	0.745156	+	0.430216i
$83$	−7.56791	−	7.56791i	−0.830686	−	0.830686i	0.156924	−	0.987611i	$-0.449842\pi$
$83$	−7.56791	−	7.56791i	−0.830686	−	0.830686i	−0.987611	+	0.156924i	$0.949842\pi$
$84$	4.43804	−	9.61802i	0.484230	−	1.04941i
$85$	0.437819	+	0.437819i	0.0474881	+	0.0474881i
$86$	4.06127	+	15.1569i	0.437938	+	1.63441i
$87$	−7.64056	−	0.546258i	−0.819154	−	0.0585650i
$88$	1.84057	−	1.06265i	0.196205	−	0.113279i
$89$	−0.240113	−	0.896114i	−0.0254519	−	0.0949879i	0.952032	−	0.306000i	$-0.0989907\pi$
$89$	−0.240113	−	0.896114i	−0.0254519	−	0.0949879i	−0.977483	+	0.211012i	$0.932324\pi$
$90$	5.26109	−	2.10655i	0.554567	−	0.222050i
$91$	−0.759223	+	9.50913i	−0.0795882	+	0.996828i
$92$		−	17.5260i		−	1.82722i
$93$	1.82475	−	5.27272i	0.189218	−	0.546756i
$94$	−7.73329	−	13.3944i	−0.797628	−	1.38153i
$95$	−1.85862	−	3.21922i	−0.190690	−	0.330285i
$96$	13.2650	+	4.59065i	1.35385	+	0.468532i
$97$	−3.00938	+	3.00938i	−0.305556	+	0.305556i	−0.843183	−	0.537627i	$-0.819321\pi$
$97$	−3.00938	+	3.00938i	−0.305556	+	0.305556i	0.537627	+	0.843183i	$0.319321\pi$
$98$	−0.922464	−	14.5056i	−0.0931829	−	1.46529i
$99$	9.06228	+	3.88012i	0.910793	+	0.389967i
$100$	−4.82214	+	8.35219i	−0.482214	+	0.835219i
$101$	−2.52077	−	4.36610i	−0.250826	−	0.434444i	0.712927	−	0.701238i	$-0.247369\pi$
$101$	−2.52077	−	4.36610i	−0.250826	−	0.434444i	−0.963754	+	0.266794i	$0.914036\pi$
$102$	1.84979	−	1.60294i	0.183156	−	0.158714i
$103$	−3.39027	−	1.95737i	−0.334053	−	0.192866i	0.323586	−	0.946199i	$-0.395112\pi$
$103$	−3.39027	−	1.95737i	−0.334053	−	0.192866i	−0.657639	+	0.753333i	$0.728445\pi$
$104$	2.33154	−	0.0454082i	0.228627	−	0.00445264i
$105$	2.66699	−	3.20443i	0.260271	−	0.312720i
$106$	14.2395	−	14.2395i	1.38306	−	1.38306i
$107$	−6.48441	−	3.74378i	−0.626872	−	0.361925i	0.152668	−	0.988278i	$-0.451214\pi$
$107$	−6.48441	−	3.74378i	−0.626872	−	0.361925i	−0.779540	+	0.626353i	$0.784547\pi$
$108$	−3.65806	−	11.4402i	−0.351997	−	1.10084i
$109$	−11.6028	−	3.10895i	−1.11134	−	0.297784i	−0.343968	−	0.938981i	$-0.611771\pi$
$109$	−11.6028	−	3.10895i	−1.11134	−	0.297784i	−0.767376	+	0.641197i	$0.778438\pi$
$110$	5.99591	−	1.60660i	0.571687	−	0.153183i
$111$	2.85473	+	14.8096i	0.270959	+	1.40567i
$112$	8.56353	−	1.40530i	0.809177	−	0.132789i
$113$		−	6.02323i		−	0.566618i	−0.959029	−	0.283309i	$-0.908568\pi$
$113$		−	6.02323i		−	0.566618i	0.959029	−	0.283309i	$-0.0914321\pi$
$114$	−13.2177	+	6.42118i	−1.23795	+	0.601399i
$115$	1.78533	−	6.66294i	0.166483	−	0.621322i
$116$	5.11132	+	8.85306i	0.474574	+	0.821986i
$117$	6.65002	+	8.53096i	0.614794	+	0.788688i
$118$	11.0754			1.01958
$119$	0.635914	−	1.68462i	0.0582941	−	0.154429i
$120$	−0.844036	−	0.571227i	−0.0770496	−	0.0521456i
$121$	−0.175108	−	0.101099i	−0.0159189	−	0.00919081i
$122$	4.81407	−	17.9664i	0.435846	−	1.62660i
$123$	4.91177	−	4.25631i	0.442880	−	0.383778i
$124$	−7.19239	+	1.92719i	−0.645896	+	0.173067i
$125$	−5.90057	+	5.90057i	−0.527763	+	0.527763i
$126$	−11.8835	−	11.4195i	−1.05867	−	1.01733i
$127$		−	17.4134i		−	1.54519i	−0.634899	−	0.772595i	$-0.718958\pi$
$127$		−	17.4134i		−	1.54519i	0.634899	−	0.772595i	$-0.281042\pi$
$128$	−1.32294	−	4.93729i	−0.116933	−	0.436399i
$129$	13.0559	+	0.933424i	1.14951	+	0.0821834i
$130$	6.61206	+	1.63439i	0.579916	+	0.143346i
$131$	17.6817	+	10.2085i	1.54486	+	0.891923i	0.998522	+	0.0543568i	$0.0173109\pi$
$131$	17.6817	+	10.2085i	1.54486	+	0.891923i	0.546335	+	0.837567i	$0.316022\pi$
$132$	−2.49011	−	12.9181i	−0.216736	−	1.12437i
$133$	−6.30531	+	8.78104i	−0.546740	+	0.761413i
$134$	−18.0850			−1.56231
$135$	−0.225312	−	4.72191i	−0.0193918	−	0.406397i
$136$	−0.425184	−	0.113928i	−0.0364593	−	0.00976923i
$137$	2.24707	+	0.602100i	0.191980	+	0.0514409i	0.353528	−	0.935424i	$-0.384982\pi$
$137$	2.24707	+	0.602100i	0.191980	+	0.0514409i	−0.161548	+	0.986865i	$0.551649\pi$
$138$	−25.7693	−	8.91807i	−2.19363	−	0.759156i
$139$	3.75347			0.318365			0.159183	−	0.987249i	$-0.449114\pi$
$139$	3.75347			0.318365			0.159183	+	0.987249i	$0.449114\pi$
$140$	−5.53646	−	0.550721i	−0.467916	−	0.0465445i
$141$	−12.6683	+	2.44197i	−1.06686	+	0.205651i
$142$	13.9740	+	8.06792i	1.17268	+	0.677045i
$143$	6.12259	+	10.1432i	0.511997	+	0.848220i
$144$	6.08227	−	7.73509i	0.506856	−	0.644591i
$145$	1.04135	+	3.88638i	0.0864795	+	0.322746i
$146$			9.62757i			0.796784i
$147$	−11.6862	−	3.23002i	−0.963860	−	0.266408i
$148$	14.2325	−	14.2325i	1.16991	−	1.16991i
$149$	18.5526	−	4.97114i	1.51989	−	0.407252i	0.600181	−	0.799864i	$-0.295095\pi$
$149$	18.5526	−	4.97114i	1.51989	−	0.407252i	0.919704	+	0.392612i	$0.128428\pi$
$150$	9.82686	+	11.3402i	0.802360	+	0.925922i
$151$	3.32204	−	12.3980i	0.270344	−	1.00894i	−0.688554	−	0.725185i	$-0.741754\pi$
$151$	3.32204	−	12.3980i	0.270344	−	1.00894i	0.958898	−	0.283752i	$-0.0915791\pi$
$152$	2.28863	+	1.32134i	0.185632	+	0.107175i
$153$	−0.758940	−	1.89545i	−0.0613567	−	0.153238i
$154$	−11.4386	−	13.9657i	−0.921752	−	1.12538i
$155$	−2.93067			−0.235397
$156$	4.45442	−	13.7308i	0.356639	−	1.09934i
$157$	6.39525	+	11.0769i	0.510397	+	0.884033i	0.999927	+	0.0120470i	$0.00383477\pi$
$157$	6.39525	+	11.0769i	0.510397	+	0.884033i	−0.489531	+	0.871986i	$0.662832\pi$
$158$	0.965477	−	3.60321i	0.0768092	−	0.286656i
$159$	−7.34019	−	15.1094i	−0.582115	−	1.19825i
$160$		−	7.37291i		−	0.582880i
$161$	−19.7957	+	3.24854i	−1.56012	+	0.256021i
$162$	−18.6825	−	0.442727i	−1.46783	−	0.0347839i
$163$	−9.32315	+	2.49813i	−0.730246	+	0.195669i	−0.604739	−	0.796424i	$-0.706722\pi$
$163$	−9.32315	+	2.49813i	−0.730246	+	0.195669i	−0.125507	+	0.992093i	$0.540056\pi$
$164$	−8.37809	−	2.24490i	−0.654219	−	0.175298i
$165$	0.369253	−	5.16477i	0.0287463	−	0.402077i
$166$	19.2458	+	11.1115i	1.49376	+	0.862423i
$167$	−11.7274	+	11.7274i	−0.907490	+	0.907490i	−0.996069	−	0.0885791i	$-0.971767\pi$
$167$	−11.7274	+	11.7274i	−0.907490	+	0.907490i	0.0885791	+	0.996069i	$0.471767\pi$
$168$	−0.502955	+	2.92091i	−0.0388038	+	0.225353i
$169$	0.506174	+	12.9901i	0.0389365	+	0.999242i
$170$	−1.11341	−	0.642825i	−0.0853943	−	0.0493024i
$171$	1.45588	+	12.1710i	0.111334	+	0.930741i
$172$	−8.73402	−	15.1278i	−0.665962	−	1.15348i
$173$	−1.19647	+	2.07234i	−0.0909656	+	0.157557i	−0.907918	−	0.419149i	$-0.862329\pi$
$173$	−1.19647	+	2.07234i	−0.0909656	+	0.157557i	0.816952	+	0.576705i	$0.195662\pi$
$174$	15.6179	−	3.01054i	1.18399	−	0.228229i
$175$	10.3276	+	3.89849i	0.780695	+	0.294698i
$176$	7.62126	−	7.62126i	0.574474	−	0.574474i
$177$	3.02142	−	8.73059i	0.227104	−	0.656231i
$178$	0.963170	+	1.66826i	0.0721926	+	0.125041i
$179$	−0.596011	−	1.03232i	−0.0445480	−	0.0771593i	0.842892	−	0.538083i	$-0.180851\pi$
$179$	−0.596011	−	1.03232i	−0.0445480	−	0.0771593i	−0.887440	+	0.460924i	$0.847518\pi$
$180$	−5.05020	+	3.78096i	−0.376420	+	0.281816i
$181$			18.7073i			1.39050i	0.718768	+	0.695250i	$0.244706\pi$
$181$			18.7073i			1.39050i	−0.718768	+	0.695250i	$0.755294\pi$
$182$	−3.58761	−	19.4801i	−0.265931	−	1.44396i
$183$	−12.8493	−	8.69617i	−0.949849	−	0.642839i
$184$	1.26924	+	4.73685i	0.0935693	+	0.349205i
$185$	6.86066	−	3.96100i	0.504405	−	0.291219i
$186$	−0.826186	+	11.5559i	−0.0605789	+	0.847322i
$187$	−0.578820	−	2.16019i	−0.0423275	−	0.157968i
$188$	12.1747	+	12.1747i	0.887929	+	0.887929i
$189$	−12.2437	+	6.25229i	−0.890600	+	0.454787i
$190$	5.45782	+	5.45782i	0.395952	+	0.395952i
$191$	3.67594	+	2.12230i	0.265981	+	0.153564i	0.627060	−	0.778971i	$-0.284258\pi$
$191$	3.67594	+	2.12230i	0.265981	+	0.153564i	−0.361079	+	0.932535i	$0.617591\pi$
$192$	−17.7388	−	1.26823i	−1.28019	−	0.0915263i
$193$	2.97736	−	11.1117i	0.214315	−	0.799835i	−0.772091	−	0.635512i	$-0.780789\pi$
$193$	2.97736	−	11.1117i	0.214315	−	0.799835i	0.986406	−	0.164324i	$-0.0525442\pi$
$194$	4.41851	−	7.65308i	0.317230	−	0.549459i
$195$	3.09217	−	4.76632i	0.221435	−	0.341323i
$196$	5.17126	+	15.3318i	0.369376	+	1.09513i
$197$	12.9650	+	12.9650i	0.923718	+	0.923718i	0.997290	−	0.0735715i	$-0.0234397\pi$
$197$	12.9650	+	12.9650i	0.923718	+	0.923718i	−0.0735715	+	0.997290i	$0.523440\pi$
$198$	−20.2611	−	2.91200i	−1.43989	−	0.206947i
$199$	6.17909	−	3.56750i	0.438024	−	0.252893i	−0.264735	−	0.964321i	$-0.585285\pi$
$199$	6.17909	−	3.56750i	0.438024	−	0.252893i	0.702759	+	0.711428i	$0.251951\pi$
$200$	0.698439	−	2.60661i	0.0493871	−	0.184315i
$201$	−4.93368	+	14.2562i	−0.347995	+	1.00555i
$202$	7.40222	+	7.40222i	0.520819	+	0.520819i
$203$	9.05214	−	7.41421i	0.635336	−	0.520375i
$204$	−1.52720	+	2.25657i	−0.106925	+	0.157991i
$205$	−2.95645	−	1.70691i	−0.206487	−	0.119216i
$206$	7.85166	+	2.10385i	0.547051	+	0.146582i
$207$	−14.0600	+	17.8807i	−0.977235	+	1.24279i
$208$	11.3615	−	3.28270i	0.787777	−	0.227614i
$209$			13.4264i			0.928721i
$210$	−3.62696	+	7.86027i	−0.250284	+	0.542410i
$211$	14.0342			0.966152			0.483076	−	0.875579i	$-0.339520\pi$
$211$	14.0342			0.966152			0.483076	+	0.875579i	$0.339520\pi$
$212$	−11.2088	+	19.4142i	−0.769821	+	1.33337i
$213$	10.1720	−	8.81457i	0.696974	−	0.603964i
$214$	15.0175	+	4.02392i	1.02657	+	0.275070i
$215$	−1.77942	−	6.64089i	−0.121355	−	0.452905i
$216$	1.81718	+	2.82709i	0.123644	+	0.192359i
$217$	3.50992	+	7.76660i	0.238269	+	0.527231i
$218$	24.9420			1.68929
$219$	7.58927	+	2.62645i	0.512836	+	0.177479i
$220$	−5.98439	+	3.45509i	−0.403467	+	0.232942i
$221$	0.588834	−	2.38217i	0.0396093	−	0.160242i
$222$	−13.6845	−	28.1689i	−0.918445	−	1.89057i
$223$	7.57202	−	7.57202i	0.507060	−	0.507060i	−0.406563	−	0.913623i	$-0.633273\pi$
$223$	7.57202	−	7.57202i	0.507060	−	0.507060i	0.913623	+	0.406563i	$0.133273\pi$
$224$	−19.5390	+	8.83016i	−1.30551	+	0.589990i
$225$	11.6201	−	4.65271i	0.774674	−	0.310181i
$226$	3.23697	+	12.0805i	0.215320	+	0.803586i
$227$	−6.87881	+	25.6721i	−0.456563	+	1.70392i	0.226889	+	0.973921i	$0.427145\pi$
$227$	−6.87881	+	25.6721i	−0.456563	+	1.70392i	−0.683452	+	0.729996i	$0.739522\pi$
$228$	12.3626	−	10.7129i	0.818735	−	0.709476i
$229$	−22.1062	+	5.92334i	−1.46082	+	0.391425i	−0.899773	−	0.436359i	$-0.856268\pi$
$229$	−22.1062	+	5.92334i	−1.46082	+	0.391425i	−0.561047	+	0.827784i	$0.689601\pi$
$230$			14.3230i			0.944434i
$231$	−14.1294	+	5.20702i	−0.929648	+	0.342597i
$232$	−2.02260	−	2.02260i	−0.132790	−	0.132790i
$233$	12.6461	−	21.9038i	0.828476	−	1.43496i	−0.0707572	−	0.997494i	$-0.522542\pi$
$233$	12.6461	−	21.9038i	0.828476	−	1.43496i	0.899233	−	0.437469i	$-0.144125\pi$
$234$	−17.9223	−	13.5364i	−1.17162	−	0.884901i
$235$	3.38829	+	5.86869i	0.221028	+	0.382831i
$236$	−11.9092	+	3.19106i	−0.775222	+	0.207720i
$237$	−2.57697	−	1.74404i	−0.167392	−	0.113288i
$238$	−0.370087	+	3.72052i	−0.0239892	+	0.241166i
$239$	−5.85270	−	5.85270i	−0.378580	−	0.378580i	0.492010	−	0.870590i	$-0.336262\pi$
$239$	−5.85270	−	5.85270i	−0.378580	−	0.378580i	−0.870590	+	0.492010i	$0.836262\pi$
$240$	−4.88428	−	1.69032i	−0.315279	−	0.109110i
$241$	0.211580	−	0.789629i	0.0136291	−	0.0508645i	−0.958776	−	0.284162i	$-0.908285\pi$
$241$	0.211580	−	0.789629i	0.0136291	−	0.0508645i	0.972406	+	0.233297i	$0.0749515\pi$
$242$	0.405540	+	0.108664i	0.0260691	+	0.00698519i
$243$	−5.44566	+	14.6063i	−0.349339	+	0.936996i
$244$			20.7059i			1.32556i
$245$	0.404171	+	6.35552i	0.0258216	+	0.406040i
$246$	−7.56395	+	11.1764i	−0.482260	+	0.712579i
$247$	−7.11619	+	12.8993i	−0.452792	+	0.820764i
$248$	1.80436	−	1.04175i	0.114577	−	0.0661509i
$249$	14.0094	−	12.1399i	0.887810	−	0.769333i
$250$	8.66349	−	15.0056i	0.547927	−	0.949038i
$251$	−6.75839			−0.426586			−0.213293	−	0.976988i	$-0.568419\pi$
$251$	−6.75839			−0.426586			−0.213293	+	0.976988i	$0.568419\pi$
$252$	16.0683	+	8.85533i	1.01221	+	0.557833i
$253$	−17.6175	+	17.6175i	−1.10760	+	1.10760i
$254$	9.35823	+	34.9254i	0.587187	+	2.19141i
$255$	−0.810471	+	0.702315i	−0.0507537	+	0.0439807i
$256$	−4.96088	−	8.59250i	−0.310055	−	0.537031i
$257$	5.96220	−	10.3268i	0.371912	−	0.644170i	−0.617948	−	0.786219i	$-0.712036\pi$
$257$	5.96220	−	10.3268i	0.371912	−	0.644170i	0.989860	+	0.142049i	$0.0453691\pi$
$258$	−26.6873	+	5.14429i	−1.66148	+	0.320270i
$259$	−18.7137	−	13.4376i	−1.16281	−	0.834971i
$260$	−7.58072	+	0.147639i	−0.470136	+	0.00915620i
$261$	1.88748	−	13.1327i	0.116832	−	0.812892i
$262$	−40.9497	−	10.9724i	−2.52988	−	0.677879i
$263$	10.4572	−	6.03749i	0.644821	−	0.372288i	−0.141648	−	0.989917i	$-0.545240\pi$
$263$	10.4572	−	6.03749i	0.644821	−	0.372288i	0.786469	+	0.617629i	$0.211907\pi$
$264$	1.60854	+	3.31110i	0.0989989	+	0.203784i
$265$	−6.23894	+	6.23894i	−0.383255	+	0.383255i
$266$	7.92726	−	21.0003i	0.486051	−	1.28761i
$267$	1.57782	−	0.304144i	0.0965611	−	0.0186133i
$268$	19.4465	−	5.21067i	1.18788	−	0.318292i
$269$	21.2433	−	12.2648i	1.29523	−	0.747801i	0.315653	−	0.948875i	$-0.397776\pi$
$269$	21.2433	−	12.2648i	1.29523	−	0.747801i	0.979576	+	0.201074i	$0.0644431\pi$
$270$	2.98952	+	9.34946i	0.181937	+	0.568990i
$271$	−27.5042	+	7.36973i	−1.67076	+	0.447679i	−0.965316	−	0.261085i	$-0.915920\pi$
$271$	−27.5042	+	7.36973i	−1.67076	+	0.447679i	−0.705445	+	0.708765i	$0.749253\pi$
$272$	−2.23230			−0.135353
$273$	−16.3346	−	2.48620i	−0.988614	−	0.150472i
$274$	−4.83043			−0.291817
$275$	13.2431	−	3.54848i	0.798589	−	0.213981i
$276$	30.2787	+	2.16476i	1.82256	+	0.130303i
$277$	13.5397	−	7.81714i	0.813521	−	0.469686i	−0.0346563	−	0.999399i	$-0.511034\pi$
$277$	13.5397	−	7.81714i	0.813521	−	0.469686i	0.848177	+	0.529713i	$0.177700\pi$
$278$	−7.52819	+	2.01717i	−0.451511	+	0.120982i
$279$	8.88398	+	3.80378i	0.531870	+	0.227726i
$280$	1.53625	−	0.252104i	0.0918086	−	0.0150661i
$281$	9.25798	−	9.25798i	0.552285	−	0.552285i	−0.374815	−	0.927100i	$-0.622294\pi$
$281$	9.25798	−	9.25798i	0.552285	−	0.552285i	0.927100	+	0.374815i	$0.122294\pi$
$282$	24.0960	−	11.7059i	1.43489	−	0.697076i
$283$	−10.9844	+	6.34183i	−0.652954	+	0.376983i	−0.789587	−	0.613639i	$-0.789705\pi$
$283$	−10.9844	+	6.34183i	−0.652954	+	0.376983i	0.136633	+	0.990622i	$0.456372\pi$
$284$	−17.3506	−	4.64907i	−1.02957	−	0.275871i
$285$	5.79123	−	2.81340i	0.343043	−	0.166651i
$286$	−17.7310	−	17.0535i	−1.04845	−	1.00840i
$287$	−0.982699	+	9.87918i	−0.0580069	+	0.583150i
$288$	−9.56945	+	22.3501i	−0.563885	+	1.31699i
$289$	8.26841	−	14.3213i	0.486377	−	0.842429i
$290$	−4.17719	−	7.23511i	−0.245293	−	0.424860i
$291$	−4.82742	−	5.57084i	−0.282988	−	0.326568i
$292$	−2.77390	−	10.3523i	−0.162330	−	0.605825i
$293$	18.2773	−	18.2773i	1.06777	−	1.06777i	0.0702426	−	0.997530i	$-0.477623\pi$
$293$	18.2773	−	18.2773i	1.06777	−	1.06777i	0.997530	−	0.0702426i	$-0.0223773\pi$
$294$	25.1744	+	0.197998i	1.46820	+	0.0115475i
$295$	−4.85262			−0.282531
$296$	−2.81598	+	4.87742i	−0.163675	+	0.283494i
$297$	−7.82280	+	15.1771i	−0.453925	+	0.880665i
$298$	−34.5386	+	19.9409i	−2.00077	+	1.15514i
$299$	−26.2635	+	7.58839i	−1.51886	+	0.438848i
$300$	−13.8340	−	9.36256i	−0.798705	−	0.540548i
$301$	−15.4679	+	12.6691i	−0.891557	+	0.730235i
$302$			26.6515i			1.53362i
$303$	7.85442	−	3.81570i	0.451225	−	0.219206i
$304$	12.9452	+	3.46865i	0.742458	+	0.198941i
$305$	−2.10925	+	7.87184i	−0.120776	+	0.450740i
$306$	2.54082	+	3.39376i	0.145249	+	0.194008i
$307$	−7.49447	−	7.49447i	−0.427732	−	0.427732i	0.460123	−	0.887855i	$-0.347805\pi$
$307$	−7.49447	−	7.49447i	−0.427732	−	0.427732i	−0.887855	+	0.460123i	$0.847805\pi$
$308$	16.3235	+	11.7213i	0.930120	+	0.667882i
$309$	3.80040	−	5.61540i	0.216197	−	0.319449i
$310$	5.87794	−	1.57499i	0.333844	−	0.0894533i
$311$	9.06775	+	15.7058i	0.514185	+	0.890594i	0.999865	+	0.0164574i	$0.00523878\pi$
$311$	9.06775	+	15.7058i	0.514185	+	0.890594i	−0.485680	+	0.874137i	$0.661428\pi$
$312$	−0.209536	+	4.03368i	−0.0118626	+	0.228362i
$313$	10.6933	−	18.5213i	0.604419	−	1.04688i	−0.387724	−	0.921776i	$-0.626739\pi$
$313$	10.6933	−	18.5213i	0.604419	−	1.04688i	0.992143	−	0.125109i	$-0.0399282\pi$
$314$	−18.7796	−	18.7796i	−1.05979	−	1.05979i
$315$	5.20668	+	5.00340i	0.293363	+	0.281909i
$316$			4.15263i			0.233604i
$317$	−14.6229	+	3.91818i	−0.821302	+	0.220067i	−0.644915	−	0.764254i	$-0.723107\pi$
$317$	−14.6229	+	3.91818i	−0.821302	+	0.220067i	−0.176386	+	0.984321i	$0.556441\pi$
$318$	22.8419	+	26.3596i	1.28091	+	1.47817i
$319$	3.76128	−	14.0373i	0.210591	−	0.785937i
$320$	2.41766	+	9.02285i	0.135152	+	0.504393i
$321$	7.26884	−	10.7403i	0.405707	−	0.599466i
$322$	37.9576	−	17.1540i	2.11530	−	0.955954i
$323$	1.96632	−	1.96632i	0.109409	−	0.109409i
$324$	20.2164	−	4.90675i	1.12314	−	0.272597i
$325$	14.6040	+	3.60987i	0.810084	+	0.200240i
$326$	17.3565	−	10.0208i	0.961290	−	0.555001i
$327$	6.80430	−	19.6614i	0.376278	−	1.08728i
$328$	2.42697			0.134007
$329$	11.4947	−	16.0080i	0.633722	−	0.882547i
$330$	2.03503	+	10.5572i	0.112025	+	0.581156i
$331$	−4.78001	−	17.8392i	−0.262733	−	0.980533i	−0.963623	−	0.267264i	$-0.913880\pi$
$331$	−4.78001	−	17.8392i	−0.262733	−	0.980533i	0.700890	−	0.713269i	$-0.252786\pi$
$332$	−23.8961	−	6.40293i	−1.31147	−	0.351406i
$333$	−25.9383	+	3.10271i	−1.42141	+	0.170027i
$334$	17.2186	−	29.8235i	0.942162	−	1.63187i
$335$	7.92384			0.432925
$336$	1.37012	+	14.9683i	0.0747463	+	0.816586i
$337$		−	5.58361i		−	0.304159i	−0.988368	−	0.152079i	$-0.951403\pi$
$337$		−	5.58361i		−	0.304159i	0.988368	−	0.152079i	$-0.0485969\pi$
$338$	−7.99631	−	25.7818i	−0.434942	−	1.40234i
$339$	10.4060	+	0.743971i	0.565175	+	0.0404069i
$340$	1.38243	+	0.370422i	0.0749730	+	0.0200890i
$341$	9.16719	+	5.29268i	0.496431	+	0.286615i
$342$	−9.46089	−	23.6285i	−0.511587	−	1.27768i
$343$	16.3588	−	8.68278i	0.883290	−	0.468826i
$344$	3.45614	+	3.45614i	0.186343	+	0.186343i
$345$	11.2906	+	3.90739i	0.607868	+	0.210367i
$346$	1.28600	−	4.79940i	0.0691356	−	0.258018i
$347$	0.567305	−	0.327534i	0.0304545	−	0.0175829i	−0.484695	−	0.874683i	$-0.661070\pi$
$347$	0.567305	−	0.327534i	0.0304545	−	0.0175829i	0.515150	+	0.857100i	$0.327736\pi$
$348$	−15.9262	+	7.73702i	−0.853737	+	0.414748i
$349$	15.6699	+	15.6699i	0.838793	+	0.838793i	0.988700	−	0.149907i	$-0.0478976\pi$
$349$	15.6699	+	15.6699i	0.838793	+	0.838793i	−0.149907	+	0.988700i	$0.547898\pi$
$350$	−22.8088	−	2.26883i	−1.21918	−	0.121274i
$351$	−15.5598	+	10.4351i	−0.830522	+	0.556986i
$352$	−13.3152	+	23.0626i	−0.709702	+	1.22924i
$353$	4.10916	−	15.3356i	0.218709	−	0.816232i	−0.766119	−	0.642699i	$-0.777815\pi$
$353$	4.10916	−	15.3356i	0.218709	−	0.816232i	0.984828	−	0.173534i	$-0.0555185\pi$
$354$	−1.36800	+	19.1343i	−0.0727085	+	1.01698i
$355$	−6.12264	−	3.53491i	−0.324956	−	0.187613i
$356$	−1.51634	−	1.51634i	−0.0803657	−	0.0803657i
$357$	2.83187	+	1.30671i	0.149879	+	0.0691584i
$358$	1.75018	+	1.75018i	0.0924999	+	0.0924999i
$359$	−3.28654	−	12.2655i	−0.173457	−	0.647350i	−0.996809	−	0.0798194i	$-0.974566\pi$
$359$	−3.28654	−	12.2655i	−0.173457	−	0.647350i	0.823352	−	0.567530i	$-0.192101\pi$
$360$	1.09113	−	1.38763i	0.0575075	−	0.0731348i
$361$	1.99636	−	1.15260i	0.105071	−	0.0606630i
$362$	−10.0536	−	37.5204i	−0.528403	−	1.97203i
$363$	0.196291	−	0.290037i	0.0103026	−	0.0152230i
$364$	9.47030	+	19.9129i	0.496379	+	1.04372i
$365$		−	4.21826i		−	0.220794i
$366$	30.4448	+	10.5361i	1.59138	+	0.550733i
$367$	−11.5525	−	20.0095i	−0.603036	−	1.04449i	−0.992359	−	0.123387i	$-0.960624\pi$
$367$	−11.5525	−	20.0095i	−0.603036	−	1.04449i	0.389323	−	0.921101i	$-0.372709\pi$
$368$	12.4347	+	21.5376i	0.648205	+	1.12272i
$369$	6.74668	+	9.01151i	0.351218	+	0.469120i
$370$	−11.6314	+	11.6314i	−0.604690	+	0.604690i
$371$	24.0059	+	9.06181i	1.24633	+	0.470466i
$372$	−2.44112	−	12.6639i	−0.126566	−	0.656593i
$373$	−18.0926	+	31.3373i	−0.936799	+	1.62258i	−0.165406	+	0.986226i	$0.552893\pi$
$373$	−18.0926	+	31.3373i	−0.936799	+	1.62258i	−0.771393	+	0.636359i	$0.780440\pi$
$374$	2.32183	+	4.02153i	0.120059	+	0.207948i
$375$	−9.46525	−	10.9229i	−0.488784	−	0.564056i
$376$	−4.17220	−	2.40882i	−0.215165	−	0.124225i
$377$	11.0536	−	11.4927i	0.569290	−	0.591905i
$378$	21.1967	−	19.1199i	1.09024	−	0.983423i
$379$	−1.09448	+	1.09448i	−0.0562199	+	0.0562199i	−0.734658	−	0.678438i	$-0.762657\pi$
$379$	−1.09448	+	1.09448i	−0.0562199	+	0.0562199i	0.678438	+	0.734658i	$0.262657\pi$
$380$	−7.44119	−	4.29617i	−0.381725	−	0.220389i
$381$	30.0841	+	2.15085i	1.54126	+	0.110191i
$382$	−8.51323	−	2.28111i	−0.435575	−	0.116712i
$383$	−29.7332	+	7.96700i	−1.51930	+	0.407095i	−0.919511	−	0.393065i	$-0.871415\pi$
$383$	−29.7332	+	7.96700i	−1.51930	+	0.407095i	−0.599787	+	0.800160i	$0.704748\pi$
$384$	8.69326	−	1.67573i	0.443626	−	0.0855143i
$385$	5.01177	+	6.11896i	0.255423	+	0.311851i
$386$			23.8863i			1.21578i
$387$	−3.22524	+	22.4406i	−0.163948	+	1.14072i
$388$	−2.54612	+	9.50227i	−0.129260	+	0.482404i
$389$	−8.71387	−	15.0929i	−0.441810	−	0.765238i	0.556013	−	0.831173i	$-0.312330\pi$
$389$	−8.71387	−	15.0929i	−0.441810	−	0.765238i	−0.997824	+	0.0659351i	$0.978997\pi$
$390$	−3.64035	+	11.2214i	−0.184336	+	0.568217i
$391$	5.16026			0.260966
$392$	−2.50799	−	3.76930i	−0.126673	−	0.190378i
$393$	−19.8207	+	29.2867i	−0.999820	+	1.47732i
$394$	−32.9710	−	19.0358i	−1.66105	−	0.959010i
$395$	−0.423017	+	1.57872i	−0.0212843	+	0.0794341i
$396$	22.6254	−	2.70642i	1.13697	−	0.136003i
$397$	9.62854	−	2.57996i	0.483242	−	0.129484i	−0.00896955	−	0.999960i	$-0.502855\pi$
$397$	9.62854	−	2.57996i	0.483242	−	0.129484i	0.492212	+	0.870475i	$0.336188\pi$
$398$	−10.4759	+	10.4759i	−0.525111	+	0.525111i
$399$	−14.3917	−	11.9779i	−0.720485	−	0.599646i
$400$		−	13.6852i		−	0.684262i
$401$	1.03957	+	3.87974i	0.0519139	+	0.193745i	0.987013	−	0.160642i	$-0.0513563\pi$
$401$	1.03957	+	3.87974i	0.0519139	+	0.193745i	−0.935099	+	0.354387i	$0.884690\pi$
$402$	2.23381	−	31.2444i	0.111412	−	1.55833i
$403$	6.00213	+	9.94367i	0.298987	+	0.495330i
$404$	−10.0922	−	5.82673i	−0.502106	−	0.289891i
$405$	8.18560	+	0.193978i	0.406746	+	0.00963883i
$406$	−14.1710	+	19.7351i	−0.703296	+	0.979438i
$407$	−28.6136			−1.41832
$408$	0.249344	−	0.720494i	0.0123444	−	0.0356698i
$409$	9.69713	+	2.59834i	0.479492	+	0.128480i	0.490466	−	0.871460i	$-0.336826\pi$
$409$	9.69713	+	2.59834i	0.479492	+	0.128480i	−0.0109739	+	0.999940i	$0.503493\pi$
$410$	6.84695	+	1.83463i	0.338147	+	0.0906061i
$411$	−1.31776	+	3.80776i	−0.0650005	+	0.187823i
$412$	−9.04889			−0.445807
$413$	5.81173	+	12.8600i	0.285977	+	0.632798i
$414$	18.5902	−	43.4186i	0.913657	−	2.13391i
$415$	−8.43240	−	4.86845i	−0.413930	−	0.238983i
$416$	−25.0160	+	15.1000i	−1.22651	+	0.740339i
$417$	−0.463617	+	6.48465i	−0.0227034	+	0.317555i
$418$	−7.21553	−	26.9287i	−0.352923	−	1.31713i
$419$		−	36.2129i		−	1.76912i	−0.466429	−	0.884559i	$-0.654460\pi$
$419$		−	36.2129i		−	1.76912i	0.466429	−	0.884559i	$-0.345540\pi$
$420$	1.63530	−	9.49699i	0.0797942	−	0.463406i
$421$	9.51902	−	9.51902i	0.463929	−	0.463929i	−0.436012	−	0.899941i	$-0.643609\pi$
$421$	9.51902	−	9.51902i	0.463929	−	0.463929i	0.899941	+	0.436012i	$0.143609\pi$
$422$	−28.1478	+	7.54217i	−1.37021	+	0.367147i
$423$	−2.65409	−	22.1879i	−0.129046	−	1.07881i
$424$	1.62348	−	6.05890i	0.0788431	−	0.294246i
$425$	−2.45917	−	1.41980i	−0.119287	−	0.0688705i
$426$	−15.6645	+	23.1456i	−0.758948	+	1.12141i
$427$	23.3874	−	3.83795i	1.13179	−	0.185731i
$428$	−17.3074			−0.836584
$429$	−18.2801	+	9.32478i	−0.882573	+	0.450205i
$430$	7.13782	+	12.3631i	0.344216	+	0.596200i
$431$	−1.73246	+	6.46564i	−0.0834498	+	0.311439i	−0.995016	−	0.0997141i	$-0.968207\pi$
$431$	−1.73246	+	6.46564i	−0.0834498	+	0.311439i	0.911566	+	0.411153i	$0.134874\pi$
$432$	12.6122	+	11.4634i	0.606805	+	0.551533i
$433$			23.9119i			1.14913i	0.818459	+	0.574565i	$0.194829\pi$
$433$			23.9119i			1.14913i	−0.818459	+	0.574565i	$0.805171\pi$
$434$	−11.2136	−	13.6909i	−0.538270	−	0.657183i
$435$	−6.84289	+	1.31905i	−0.328091	+	0.0632435i
$436$	−26.8197	+	7.18631i	−1.28443	+	0.344162i
$437$	−29.9245	−	8.01824i	−1.43148	−	0.383564i
$438$	−16.6330	−	1.18917i	−0.794755	−	0.0568207i
$439$	25.4558	+	14.6969i	1.21494	+	0.701445i	0.963831	−	0.266514i	$-0.0858717\pi$
$439$	25.4558	+	14.6969i	1.21494	+	0.701445i	0.251108	+	0.967959i	$0.419205\pi$
$440$	1.36721	−	1.36721i	0.0651793	−	0.0651793i
$441$	7.02376	−	19.7906i	0.334465	−	0.942408i
$442$	0.0992141	+	5.09428i	0.00471914	+	0.242310i
$443$	29.5574	+	17.0649i	1.40431	+	0.810780i	0.994832	−	0.101539i	$-0.0323765\pi$
$443$	29.5574	+	17.0649i	1.40431	+	0.810780i	0.409481	+	0.912319i	$0.365710\pi$
$444$	22.8307	+	26.3466i	1.08350	+	1.25036i
$445$	−0.422007	−	0.730937i	−0.0200050	−	0.0346497i
$446$	−11.1176	+	19.2562i	−0.526432	+	0.911808i
$447$	6.29680	+	32.6662i	0.297828	+	1.54506i
$448$	21.0160	−	17.2133i	0.992913	−	0.813251i
$449$	−11.6015	+	11.6015i	−0.547507	+	0.547507i	−0.925719	−	0.378212i	$-0.876539\pi$
$449$	−11.6015	+	11.6015i	−0.547507	+	0.547507i	0.378212	+	0.925719i	$0.376539\pi$
$450$	−20.8056	+	15.5766i	−0.980783	+	0.734287i
$451$	6.16521	+	10.6785i	0.290308	+	0.502829i
$452$	−6.96131	−	12.0573i	−0.327432	−	0.567130i
$453$	21.0090	+	7.27066i	0.987089	+	0.341605i
$454$		−	55.1863i		−	2.59002i
$455$	1.57189	+	8.53508i	0.0736911	+	0.400131i
$456$	−2.56549	+	3.79072i	−0.120140	+	0.177517i
$457$	−0.339203	−	1.26592i	−0.0158672	−	0.0592173i	0.957538	−	0.288306i	$-0.0930921\pi$
$457$	−0.339203	−	1.26592i	−0.0158672	−	0.0592173i	−0.973406	+	0.229089i	$0.926425\pi$
$458$	41.1542	−	23.7604i	1.92301	−	1.11025i
$459$	3.36839	−	1.07706i	0.157223	−	0.0502727i
$460$	−4.12676	−	15.4013i	−0.192411	−	0.718089i
$461$	−7.48286	−	7.48286i	−0.348512	−	0.348512i	0.511043	−	0.859555i	$-0.329259\pi$
$461$	−7.48286	−	7.48286i	−0.348512	−	0.348512i	−0.859555	+	0.511043i	$0.829259\pi$
$462$	25.5405	−	18.0369i	1.18825	−	0.839152i
$463$	6.73640	+	6.73640i	0.313067	+	0.313067i	0.846097	−	0.533030i	$-0.178947\pi$
$463$	6.73640	+	6.73640i	0.313067	+	0.313067i	−0.533030	+	0.846097i	$0.678947\pi$
$464$	−12.5625	−	7.25296i	−0.583199	−	0.336710i
$465$	0.361988	−	5.06315i	0.0167868	−	0.234798i
$466$	−13.5925	+	50.7277i	−0.629658	+	2.34992i
$467$	−6.35406	+	11.0056i	−0.294031	+	0.509276i	−0.974759	−	0.223260i	$-0.928330\pi$
$467$	−6.35406	+	11.0056i	−0.294031	+	0.509276i	0.680728	+	0.732536i	$0.261663\pi$
$468$	23.1717	+	9.39162i	1.07111	+	0.434128i
$469$	−9.48997	−	20.9990i	−0.438206	−	0.969645i
$470$	−9.94967	−	9.94967i	−0.458944	−	0.458944i
$471$	−19.9268	+	9.68052i	−0.918180	+	0.446055i
$472$	2.98766	−	1.72493i	0.137518	−	0.0793962i
$473$	−6.42712	+	23.9863i	−0.295519	+	1.10289i
$474$	6.10580	+	2.11305i	0.280449	+	0.0970558i
$475$	12.0546	+	12.0546i	0.553104	+	0.553104i
$476$	−0.674012	−	4.10724i	−0.0308933	−	0.188255i
$477$	27.0102	−	10.8149i	1.23671	−	0.495182i
$478$	14.8839	+	8.59321i	0.680772	+	0.393044i
$479$	−33.7084	−	9.03215i	−1.54018	−	0.412689i	−0.613854	−	0.789419i	$-0.710382\pi$
$479$	−33.7084	−	9.03215i	−1.54018	−	0.412689i	−0.926323	+	0.376730i	$0.877048\pi$
$480$	12.7377	+	0.910679i	0.581396	+	0.0415666i
$481$	−27.4904	−	15.1657i	−1.25345	−	0.691495i
$482$			1.69743i			0.0773160i
$483$	−3.16721	−	34.6011i	−0.144113	−	1.57440i
$484$	−0.467378			−0.0212444
$485$	−1.93594	+	3.35314i	−0.0879065	+	0.152258i
$486$	3.07247	−	32.2219i	0.139370	−	1.46162i
$487$	−0.307401	−	0.0823680i	−0.0139297	−	0.00373245i	0.251847	−	0.967767i	$-0.418962\pi$
$487$	−0.307401	−	0.0823680i	−0.0139297	−	0.00373245i	−0.265777	+	0.964034i	$0.585629\pi$
$488$	−1.49952	−	5.59629i	−0.0678802	−	0.253332i
$489$	−3.16431	−	16.4156i	−0.143095	−	0.742340i
$490$	−4.22618	−	12.5298i	−0.190920	−	0.566039i
$491$	35.3105			1.59354			0.796771	−	0.604281i	$-0.206540\pi$
$491$	35.3105			1.59354			0.796771	+	0.604281i	$0.206540\pi$
$492$	4.91322	−	14.1971i	0.221505	−	0.640053i
$493$	−2.60664	+	1.50495i	−0.117397	+	0.0677794i
$494$	7.34036	−	29.6960i	0.330259	−	1.33609i
$495$	8.87726	+	1.27587i	0.399003	+	0.0573462i
$496$	7.47131	−	7.47131i	0.335472	−	0.335472i
$497$	−2.03511	+	20.4592i	−0.0912874	+	0.917721i
$498$	−21.5739	+	31.8773i	−0.966752	+	1.42846i
$499$	4.43716	+	16.5597i	0.198635	+	0.741315i	0.991296	+	0.131653i	$0.0420283\pi$
$499$	4.43716	+	16.5597i	0.198635	+	0.741315i	−0.792661	+	0.609662i	$0.791305\pi$
$500$	−4.99226	+	18.6314i	−0.223261	+	0.833220i
$501$	−18.8121	−	21.7092i	−0.840464	−	0.969895i
$502$	13.5550	−	3.63206i	0.604991	−	0.162107i
$503$		−	10.3659i		−	0.462194i	−0.972931	−	0.231097i	$-0.925769\pi$
$503$		−	10.3659i		−	0.462194i	0.972931	−	0.231097i	$-0.0742314\pi$
$504$	−4.98417	−	1.22971i	−0.222012	−	0.0547755i
$505$	−3.24323	−	3.24323i	−0.144322	−	0.144322i
$506$	25.8668	−	44.8027i	1.14992	−	1.99172i
$507$	−22.5048	−	0.730015i	−0.999474	−	0.0324211i
$508$	−20.1254	−	34.8583i	−0.892922	−	1.54659i
$509$	−0.550395	+	0.147478i	−0.0243958	+	0.00653684i	−0.270996	−	0.962580i	$-0.587353\pi$
$509$	−0.550395	+	0.147478i	−0.0243958	+	0.00653684i	0.246601	+	0.969117i	$0.420686\pi$
$510$	1.24810	−	1.84417i	0.0552666	−	0.0816610i
$511$	−11.1788	+	5.05199i	−0.494523	+	0.223487i
$512$	21.7963	+	21.7963i	0.963268	+	0.963268i
$513$	−21.2070	+	1.01192i	−0.936311	+	0.0446772i
$514$	−6.40835	+	23.9163i	−0.282660	+	1.05490i
$515$	−3.44015	−	0.921786i	−0.151591	−	0.0406187i
$516$	27.2141	−	13.2207i	1.19804	−	0.582009i
$517$		−	24.4764i		−	1.07647i
$518$	44.7550	+	16.8942i	1.96642	+	0.742288i
$519$	−3.43247	−	2.32303i	−0.150669	−	0.101970i
$520$	2.03819	−	0.588899i	0.0893805	−	0.0258249i
$521$	1.85185	−	1.06917i	0.0811311	−	0.0468411i	−0.458886	−	0.888495i	$-0.651751\pi$
$521$	1.85185	−	1.06917i	0.0811311	−	0.0468411i	0.540017	+	0.841654i	$0.318418\pi$
$522$	3.27206	+	27.3540i	0.143214	+	1.19725i
$523$	19.6304	−	34.0009i	0.858379	−	1.48676i	−0.0150960	−	0.999886i	$-0.504805\pi$
$523$	19.6304	−	34.0009i	0.858379	−	1.48676i	0.873475	−	0.486869i	$-0.161861\pi$
$524$	47.1938			2.06167
$525$	−8.01083	+	17.3609i	−0.349621	+	0.757692i
$526$	−17.7290	+	17.7290i	−0.773022	+	0.773022i
$527$	−0.567432	−	2.11768i	−0.0247177	−	0.0922478i
$528$	12.2254	+	14.1082i	0.532044	+	0.613979i
$529$	−17.2445	−	29.8683i	−0.749760	−	1.29862i
$530$	9.16030	−	15.8661i	0.397898	−	0.689180i
$531$	14.7101	+	6.29831i	0.638365	+	0.273323i
$532$	−2.47339	+	24.8653i	−0.107235	+	1.07805i
$533$	0.263445	+	13.5269i	0.0114111	+	0.585916i
$534$	−3.00112	+	1.45795i	−0.129871	+	0.0630918i
$535$	−6.57981	−	1.76306i	−0.284470	−	0.0762235i
$536$	−4.87855	+	2.81663i	−0.210721	+	0.121660i
$537$	1.85710	−	0.902184i	0.0801397	−	0.0389321i
$538$	−36.0156	+	36.0156i	−1.55274	+	1.55274i
$539$	10.2136	−	20.6101i	0.439929	−	0.887739i
$540$	−5.90835	−	9.19195i	−0.254255	−	0.395559i
$541$	−1.26084	+	0.337841i	−0.0542078	+	0.0145249i	−0.285821	−	0.958283i	$-0.592266\pi$
$541$	−1.26084	+	0.337841i	−0.0542078	+	0.0145249i	0.231613	+	0.972808i	$0.425600\pi$
$542$	51.2035	−	29.5623i	2.19938	−	1.26981i
$543$	−32.3194	−	2.31066i	−1.38696	−	0.0991600i
$544$	5.32761	−	1.42753i	0.228420	−	0.0612048i
$545$	−10.9282			−0.468112
$546$	34.0978	−	3.79197i	1.45925	−	0.162282i
$547$	13.9302			0.595611			0.297805	−	0.954627i	$-0.403745\pi$
$547$	13.9302			0.595611			0.297805	+	0.954627i	$0.403745\pi$
$548$	5.19407	−	1.39175i	0.221880	−	0.0594525i
$549$	16.6110	−	21.1249i	0.708939	−	0.901588i
$550$	−24.6542	+	14.2341i	−1.05126	+	0.606943i
$551$	17.4544	−	4.67690i	0.743584	−	0.199243i
$552$	−8.34035	+	1.60770i	−0.354989	+	0.0684284i
$553$	4.69041	−	0.769713i	0.199456	−	0.0327315i
$554$	−22.9550	+	22.9550i	−0.975263	+	0.975263i
$555$	5.99578	+	12.3420i	0.254507	+	0.523889i
$556$	7.51373	−	4.33805i	0.318653	−	0.183974i
$557$	28.1486	+	7.54240i	1.19269	+	0.319582i	0.799950	−	0.600066i	$-0.204859\pi$
$557$	28.1486	+	7.54240i	1.19269	+	0.319582i	0.392744	+	0.919648i	$0.371526\pi$
$558$	−19.8625	−	2.85471i	−0.840845	−	0.120849i
$559$	−18.8880	+	19.6383i	−0.798876	+	0.830611i
$560$	7.19444	−	3.25134i	0.304021	−	0.137394i
$561$	3.80352	−	0.733174i	0.160585	−	0.0309546i
$562$	−13.5930	+	23.5437i	−0.573386	+	0.993133i
$563$	−10.8956	−	18.8718i	−0.459196	−	0.795352i	0.539722	−	0.841843i	$-0.318529\pi$
$563$	−10.8956	−	18.8718i	−0.459196	−	0.795352i	−0.998919	+	0.0464916i	$0.985196\pi$
$564$	−22.5372	+	19.5297i	−0.948988	+	0.822348i
$565$	−1.41826	−	5.29301i	−0.0596666	−	0.222679i
$566$	18.6227	−	18.6227i	0.782772	−	0.782772i
$567$	−9.28941	−	21.9250i	−0.390118	−	0.920765i
$568$	5.02611			0.210891
$569$	−15.5147	+	26.8723i	−0.650411	+	1.12654i	0.332613	+	0.943063i	$0.392070\pi$
$569$	−15.5147	+	26.8723i	−0.650411	+	1.12654i	−0.983023	+	0.183481i	$0.941264\pi$
$570$	−10.1033	+	8.75502i	−0.423180	+	0.366707i
$571$	17.0300	−	9.83228i	0.712684	−	0.411468i	−0.0993701	−	0.995051i	$-0.531683\pi$
$571$	17.0300	−	9.83228i	0.712684	−	0.411468i	0.812054	+	0.583582i	$0.198349\pi$
$572$	23.9792	+	13.2287i	1.00262	+	0.553118i
$573$	−4.12062	+	6.08856i	−0.172141	+	0.254353i
$574$	−3.33826	−	20.3424i	−0.139336	−	0.849075i
$575$			31.6352i			1.31928i
$576$	4.38208	−	30.4896i	0.182587	−	1.27040i
$577$	−26.4164	−	7.07826i	−1.09973	−	0.294672i	−0.337075	−	0.941478i	$-0.609438\pi$
$577$	−26.4164	−	7.07826i	−1.09973	−	0.294672i	−0.762655	+	0.646806i	$0.776104\pi$
$578$	−8.88713	+	33.1672i	−0.369656	+	1.37957i
$579$	18.8292	+	6.51629i	0.782516	+	0.270808i
$580$	6.57624	+	6.57624i	0.273064	+	0.273064i
$581$	−2.80286	+	28.1775i	−0.116282	+	1.16900i
$582$	12.6760	+	8.57888i	0.525437	+	0.355606i
$583$	30.7828	−	8.24822i	1.27489	−	0.341606i
$584$	1.49943	+	2.59710i	0.0620470	+	0.107469i
$585$	7.85255	+	5.93088i	0.324663	+	0.245212i
$586$	−26.8356	+	46.4806i	−1.10857	+	1.92010i
$587$	18.3467	+	18.3467i	0.757250	+	0.757250i	0.975821	−	0.218571i	$-0.0701395\pi$
$587$	18.3467	+	18.3467i	0.757250	+	0.757250i	−0.218571	+	0.975821i	$0.570139\pi$
$588$	−27.1266	+	7.04035i	−1.11868	+	0.290339i
$589$			13.1622i			0.542339i
$590$	9.73271	−	2.60787i	0.400689	−	0.107364i
$591$	−24.0003	+	20.7975i	−0.987239	+	0.855494i
$592$	−7.39223	+	27.5882i	−0.303819	+	1.13387i
$593$	4.88293	+	18.2233i	0.200518	+	0.748343i	0.990769	+	0.135560i	$0.0432834\pi$
$593$	4.88293	+	18.2233i	0.200518	+	0.748343i	−0.790251	+	0.612783i	$0.790050\pi$
$594$	7.53347	−	34.6442i	0.309102	−	1.42147i
$595$	0.162151	−	1.63012i	0.00664755	−	0.0668285i
$596$	31.3933	−	31.3933i	1.28592	−	1.28592i
$597$	5.40013	+	11.1159i	0.221013	+	0.454943i
$598$	48.5976	−	29.3341i	1.98730	−	1.19956i
$599$	−34.2888	+	19.7966i	−1.40100	+	0.808869i	−0.994496	−	0.104779i	$-0.966586\pi$
$599$	−34.2888	+	19.7966i	−1.40100	+	0.808869i	−0.406506	+	0.913648i	$0.633253\pi$
$600$	4.41702	+	1.52861i	0.180324	+	0.0624053i
$601$	−23.9442			−0.976706			−0.488353	−	0.872646i	$-0.662402\pi$
$601$	−23.9442			−0.976706			−0.488353	+	0.872646i	$0.662402\pi$
$602$	24.2149	−	33.7226i	0.986924	−	1.37443i
$603$	−24.0201	−	10.2845i	−0.978176	−	0.418817i
$604$	−7.67885	−	28.6579i	−0.312448	−	1.16607i
$605$	−0.177685	−	0.0476105i	−0.00722391	−	0.00193564i
$606$	−13.7027	+	11.8741i	−0.556633	+	0.482352i
$607$	−8.64136	+	14.9673i	−0.350742	+	0.607503i	−0.986380	−	0.164484i	$-0.947404\pi$
$607$	−8.64136	+	14.9673i	−0.350742	+	0.607503i	0.635638	+	0.771988i	$0.280737\pi$
$608$	−33.1131			−1.34291
$609$	11.6910	+	16.5546i	0.473743	+	0.670828i
$610$		−	16.9218i		−	0.685143i
$611$	12.9729	−	23.5156i	0.524827	−	0.951340i
$612$	−3.70990	−	2.91718i	−0.149964	−	0.117920i
$613$	−13.2477	−	3.54970i	−0.535068	−	0.143371i	−0.0188402	−	0.999823i	$-0.505997\pi$
$613$	−13.2477	−	3.54970i	−0.535068	−	0.143371i	−0.516227	+	0.856452i	$0.672664\pi$
$614$	19.0590	+	11.0037i	0.769159	+	0.444074i
$615$	3.31409	−	4.89685i	0.133637	−	0.197460i
$616$	−5.26070	−	1.98582i	−0.211960	−	0.0800110i
$617$	−15.5706	−	15.5706i	−0.626851	−	0.626851i	0.320424	−	0.947274i	$-0.396175\pi$
$617$	−15.5706	−	15.5706i	−0.626851	−	0.626851i	−0.947274	+	0.320424i	$0.896175\pi$
$618$	−4.60450	+	13.3050i	−0.185220	+	0.535205i
$619$	−2.23915	+	8.35661i	−0.0899989	+	0.335881i	−0.996214	−	0.0869368i	$-0.972292\pi$
$619$	−2.23915	+	8.35661i	−0.0899989	+	0.335881i	0.906215	+	0.422817i	$0.138959\pi$
$620$	−5.86664	+	3.38711i	−0.235610	+	0.136030i
$621$	−29.1547	−	26.4991i	−1.16994	−	1.06337i
$622$	−26.6274	−	26.6274i	−1.06766	−	1.06766i
$623$	−1.43165	+	1.99377i	−0.0573577	+	0.0798786i
$624$	4.26799	+	20.0340i	0.170857	+	0.802003i
$625$	6.63496	−	11.4921i	0.265399	−	0.459684i
$626$	−11.4934	+	42.8941i	−0.459371	+	1.71439i
$627$	−23.1959	−	1.65838i	−0.926356	−	0.0662294i
$628$	25.6041	+	14.7825i	1.02172	+	0.589888i
$629$	4.19054	+	4.19054i	0.167088	+	0.167088i
$630$	−13.1317	−	7.23696i	−0.523181	−	0.288327i
$631$	−13.9374	−	13.9374i	−0.554839	−	0.554839i	0.372995	−	0.927833i	$-0.378331\pi$
$631$	−13.9374	−	13.9374i	−0.554839	−	0.554839i	−0.927833	+	0.372995i	$0.878331\pi$
$632$	−0.300734	−	1.12235i	−0.0119625	−	0.0446448i
$633$	−1.73346	+	24.2460i	−0.0688987	+	0.963692i
$634$	27.2228	−	15.7171i	1.08116	−	0.624205i
$635$	−4.10024	−	15.3023i	−0.162713	−	0.607254i
$636$	−32.1562	−	21.7627i	−1.27508	−	0.862947i
$637$	20.7363	−	14.3877i	0.821602	−	0.570061i
$638$			30.1754i			1.19465i
$639$	13.9720	+	18.6623i	0.552724	+	0.738270i
$640$	−2.32511	−	4.02722i	−0.0919082	−	0.159190i
$641$	4.39021	+	7.60407i	0.173403	+	0.300343i	0.939607	−	0.342254i	$-0.111190\pi$
$641$	4.39021	+	7.60407i	0.173403	+	0.300343i	−0.766204	+	0.642597i	$0.777857\pi$
$642$	−8.80681	+	25.4478i	−0.347577	+	1.00435i
$643$	12.7014	−	12.7014i	0.500895	−	0.500895i	−0.410821	−	0.911716i	$-0.634758\pi$
$643$	12.7014	−	12.7014i	0.500895	−	0.500895i	0.911716	+	0.410821i	$0.134758\pi$
$644$	−35.8727	+	29.3817i	−1.41358	+	1.15780i
$645$	11.6929	−	2.25394i	0.460406	−	0.0887487i
$646$	−2.88705	+	5.00051i	−0.113589	+	0.196742i
$647$	−7.00302	−	12.1296i	−0.275317	−	0.476863i	0.694898	−	0.719108i	$-0.255450\pi$
$647$	−7.00302	−	12.1296i	−0.275317	−	0.476863i	−0.970215	+	0.242245i	$0.922116\pi$
$648$	−5.10866	+	2.79025i	−0.200687	+	0.109611i
$649$	15.1791	+	8.76364i	0.595830	+	0.344003i
$650$	−31.2307	+	0.608236i	−1.22497	+	0.0238570i
$651$	−13.8514	+	5.10457i	−0.542881	+	0.200064i
$652$	−15.7760	+	15.7760i	−0.617834	+	0.617834i
$653$	−21.7170	−	12.5383i	−0.849852	−	0.490662i	0.0107487	−	0.999942i	$-0.496579\pi$
$653$	−21.7170	−	12.5383i	−0.849852	−	0.490662i	−0.860601	+	0.509280i	$0.829912\pi$
$654$	−3.08076	+	43.0909i	−0.120467	+	1.68499i
$655$	17.9418	+	4.80750i	0.701045	+	0.187845i
$656$	11.8885	−	3.18552i	0.464169	−	0.124374i
$657$	−5.47496	+	12.7871i	−0.213598	+	0.498873i
$658$	−14.4515	+	38.2839i	−0.563378	+	1.49246i
$659$		−	20.2823i		−	0.790086i	−0.918663	−	0.395043i	$-0.870730\pi$
$659$		−	20.2823i		−	0.790086i	0.918663	−	0.395043i	$-0.129270\pi$
$660$	−5.22998	−	10.7656i	−0.203577	−	0.419052i
$661$	−5.76113	+	21.5008i	−0.224082	+	0.836285i	0.758688	+	0.651454i	$0.225841\pi$
$661$	−5.76113	+	21.5008i	−0.224082	+	0.836285i	−0.982770	+	0.184831i	$0.940826\pi$
$662$	19.1741	+	33.2106i	0.745224	+	1.29077i
$663$	4.04281	+	1.31153i	0.157010	+	0.0509357i
$664$	6.92221			0.268634
$665$	−3.47327	+	9.20116i	−0.134688	+	0.356806i
$666$	50.3560	−	20.1626i	1.95125	−	0.781285i
$667$	29.0398	+	16.7662i	1.12443	+	0.649188i
$668$	−9.92208	+	37.0297i	−0.383897	+	1.43272i
$669$	12.1465	+	14.0170i	0.469609	+	0.541928i
$670$	−15.8925	+	4.25839i	−0.613982	+	0.164516i
$671$	20.8140	−	20.8140i	0.803516	−	0.803516i
$672$	−12.8419	−	34.8471i	−0.495389	−	1.34426i
$673$			3.25786i			0.125581i	0.998027	+	0.0627907i	$0.0200001\pi$
$673$			3.25786i			0.125581i	−0.998027	+	0.0627907i	$0.980000\pi$
$674$	3.00072	+	11.1988i	0.115583	+	0.431363i
$675$	6.60294	+	20.6501i	0.254147	+	0.794822i
$676$	16.0265	+	25.4187i	0.616405	+	0.977644i
$677$	−13.1798	−	7.60938i	−0.506542	−	0.292452i	0.224869	−	0.974389i	$-0.427805\pi$
$677$	−13.1798	−	7.60938i	−0.506542	−	0.292452i	−0.731411	+	0.681937i	$0.761138\pi$
$678$	−21.2707	+	4.10018i	−0.816895	+	0.157466i
$679$	11.2048	+	1.11456i	0.430000	+	0.0427728i
$680$	−0.400464			−0.0153571
$681$	−43.5025	−	15.0551i	−1.66702	−	0.576911i
$682$	−21.2306	−	5.68873i	−0.812963	−	0.217833i
$683$	3.99516	+	1.07050i	0.152870	+	0.0409615i	0.334443	−	0.942416i	$-0.391452\pi$
$683$	3.99516	+	1.07050i	0.152870	+	0.0409615i	−0.181572	+	0.983378i	$0.558119\pi$
$684$	16.9810	+	22.6814i	0.649284	+	0.867245i
$685$	2.11642			0.0808643
$686$	−28.1439	+	26.2062i	−1.07454	+	1.00056i
$687$	−7.50292	−	38.9232i	−0.286254	−	1.48501i
$688$	21.4663	+	12.3936i	0.818395	+	0.472500i
$689$	33.9461	+	8.39092i	1.29324	+	0.319669i
$690$	−24.7451	−	1.76914i	−0.942029	−	0.0673500i
$691$	2.80836	+	10.4809i	0.106835	+	0.398714i	0.998547	−	0.0538898i	$-0.0171620\pi$
$691$	2.80836	+	10.4809i	0.106835	+	0.398714i	−0.891712	+	0.452604i	$0.850495\pi$
$692$			5.53123i			0.210266i
$693$	−7.25064	−	25.0537i	−0.275429	−	0.951713i
$694$	−0.961800	+	0.961800i	−0.0365094	+	0.0365094i
$695$	3.29843	−	0.883811i	0.125116	−	0.0335249i
$696$	3.74415	−	3.24450i	0.141922	−	0.122983i
$697$	0.660976	−	2.46680i	0.0250363	−	0.0934366i
$698$	−39.8498	−	23.0073i	−1.50834	−	0.870840i
$699$	36.2798	+	24.5535i	1.37223	+	0.928698i
$700$	25.1796	−	4.13206i	0.951698	−	0.156177i
$701$	−18.6877			−0.705826			−0.352913	−	0.935656i	$-0.614809\pi$
$701$	−18.6877			−0.705826			−0.352913	+	0.935656i	$0.614809\pi$
$702$	25.5997	−	29.2914i	0.966200	−	1.10553i
$703$	−17.7896	−	30.8125i	−0.670947	−	1.16211i
$704$	8.73241	−	32.5898i	0.329115	−	1.22827i
$705$	−10.5575	+	5.12886i	−0.397618	+	0.193164i
$706$			32.9663i			1.24070i
$707$	−4.71066	+	12.4792i	−0.177163	+	0.469328i
$708$	−4.04201	−	20.9689i	−0.151908	−	0.788061i
$709$	20.7836	−	5.56894i	0.780544	−	0.209146i	0.153519	−	0.988146i	$-0.450939\pi$
$709$	20.7836	−	5.56894i	0.780544	−	0.209146i	0.627024	+	0.779000i	$0.284273\pi$
$710$	14.1796	+	3.79942i	0.532152	+	0.142590i
$711$	3.33138	−	4.23666i	0.124936	−	0.158887i
$712$	0.519642	+	0.300015i	0.0194744	+	0.0112435i
$713$	−17.2709	+	17.2709i	−0.646800	+	0.646800i
$714$	−6.38202	−	1.09893i	−0.238841	−	0.0411262i
$715$	7.76870	+	7.47188i	0.290533	+	0.279433i
$716$	−2.38620	−	1.37767i	−0.0891764	−	0.0514860i
$717$	10.8343	−	9.38847i	0.404614	−	0.350619i
$718$	13.1834	+	22.8342i	0.491998	+	0.852166i
$719$	13.2859	−	23.0119i	0.495481	−	0.858198i	−0.504506	−	0.863408i	$-0.668325\pi$
$719$	13.2859	−	23.0119i	0.495481	−	0.858198i	0.999986	+	0.00521062i	$0.00165860\pi$
$720$	3.52356	−	8.22950i	0.131315	−	0.306695i
$721$	1.67726	+	10.2207i	0.0624644	+	0.380640i
$722$	−3.38459	+	3.38459i	−0.125961	+	0.125961i
$723$	1.33806	+	0.463067i	0.0497630	+	0.0172217i
$724$	21.6208	+	37.4483i	0.803530	+	1.39176i
$725$	−9.22613	−	15.9801i	−0.342650	−	0.593487i
$726$	−0.237824	+	0.687206i	−0.00882646	+	0.0255046i
$727$		−	34.4681i		−	1.27835i	−0.769061	−	0.639176i	$-0.779276\pi$
$727$		−	34.4681i		−	1.27835i	0.769061	−	0.639176i	$-0.220724\pi$
$728$	−4.00168	−	4.69613i	−0.148312	−	0.174050i
$729$	−24.5619	−	11.2123i	−0.909699	−	0.415269i
$730$	2.26695	+	8.46039i	0.0839038	+	0.313133i
$731$	4.45413	−	2.57159i	0.164742	−	0.0951138i
$732$	−35.7724	−	2.55753i	−1.32219	−	0.0945290i
$733$	−12.5822	−	46.9574i	−0.464734	−	1.73441i	−0.657770	−	0.753218i	$-0.728500\pi$
$733$	−12.5822	−	46.9574i	−0.464734	−	1.73441i	0.193037	−	0.981192i	$-0.438166\pi$
$734$	33.9238	+	33.9238i	1.25215	+	1.25215i
$735$	−11.0300	−	0.0867517i	−0.406847	−	0.00319988i
$736$	−43.4497	−	43.4497i	−1.60158	−	1.60158i
$737$	−24.7859	−	14.3101i	−0.912999	−	0.527120i
$738$	−18.3745	−	14.4483i	−0.676374	−	0.531848i
$739$	0.723243	−	2.69918i	0.0266049	−	0.0992910i	−0.951347	−	0.308122i	$-0.900299\pi$
$739$	0.723243	−	2.69918i	0.0266049	−	0.0992910i	0.977952	+	0.208831i	$0.0669660\pi$
$740$	9.15580	−	15.8583i	0.336574	−	0.582963i
$741$	−21.4064	−	13.8875i	−0.786384	−	0.510170i
$742$	−53.0177	−	5.27376i	−1.94634	−	0.193606i
$743$	0.540468	+	0.540468i	0.0198279	+	0.0198279i	0.716951	−	0.697123i	$-0.245537\pi$
$743$	0.540468	+	0.540468i	0.0198279	+	0.0198279i	−0.697123	+	0.716951i	$0.745537\pi$
$744$	1.57689	+	3.24595i	0.0578118	+	0.119002i
$745$	15.1328	−	8.73695i	0.554425	−	0.320097i
$746$	19.4465	−	72.5752i	0.711986	−	2.65717i
$747$	19.2429	+	25.7027i	0.704062	+	0.940412i
$748$	−3.65531	−	3.65531i	−0.133651	−	0.133651i
$749$	3.20802	+	19.5487i	0.117218	+	0.714295i
$750$	24.8542	+	16.8208i	0.907547	+	0.614210i
$751$	0.425319	+	0.245558i	0.0155201	+	0.00896053i	0.507740	−	0.861510i	$-0.330481\pi$
$751$	0.425319	+	0.245558i	0.0155201	+	0.00896053i	−0.492220	+	0.870471i	$0.663814\pi$
$752$	−23.5993	−	6.32340i	−0.860576	−	0.230591i
$753$	0.834776	−	11.6761i	0.0304209	−	0.425500i
$754$	−15.9934	+	28.9909i	−0.582446	+	1.05578i
$755$		−	11.6772i		−	0.424976i
$756$	−17.2835	+	26.6665i	−0.628596	+	0.969851i
$757$	46.8738			1.70366			0.851829	−	0.523820i	$-0.175494\pi$
$757$	46.8738			1.70366			0.851829	+	0.523820i	$0.175494\pi$
$758$	1.60697	−	2.78336i	0.0583679	−	0.101096i
$759$	−28.2607	−	32.6128i	−1.02580	−	1.18377i
$760$	2.32230	+	0.622258i	0.0842386	+	0.0225717i
$761$	−10.5870	−	39.5114i	−0.383780	−	1.43229i	−0.840081	−	0.542461i	$-0.817493\pi$
$761$	−10.5870	−	39.5114i	−0.383780	−	1.43229i	0.456301	−	0.889825i	$-0.349174\pi$
$762$	−61.4944	+	11.8538i	−2.22771	+	0.429417i
$763$	13.0881	+	28.9609i	0.473822	+	1.04845i
$764$	9.81135			0.354962
$765$	−1.11324	−	1.48695i	−0.0402494	−	0.0537609i
$766$	55.3532	−	31.9582i	1.99999	−	1.15470i
$767$	9.93835	+	16.4648i	0.358853	+	0.594508i
$768$	15.4575	−	7.50931i	0.557775	−	0.270969i
$769$	0.240384	−	0.240384i	0.00866848	−	0.00866848i	−0.702759	−	0.711428i	$-0.748049\pi$
$769$	0.240384	−	0.240384i	0.00866848	−	0.00866848i	0.711428	+	0.702759i	$0.248049\pi$
$770$	−13.3403	−	9.57915i	−0.480752	−	0.345209i
$771$	17.1046	+	11.5761i	0.616008	+	0.416902i
$772$	−6.88214	−	25.6845i	−0.247694	−	0.924405i
$773$	12.1033	−	45.1700i	0.435325	−	1.62465i	−0.304964	−	0.952364i	$-0.598644\pi$
$773$	12.1033	−	45.1700i	0.435325	−	1.62465i	0.740288	−	0.672289i	$-0.234689\pi$
$774$	−5.59116	−	46.7415i	−0.200970	−	1.68009i
$775$	12.9825	−	3.47866i	0.466347	−	0.124957i
$776$		−	2.75262i		−	0.0988132i
$777$	25.5268	−	30.6708i	0.915769	−	1.10031i
$778$	25.5882	+	25.5882i	0.917381	+	0.917381i
$779$	−7.66603	+	13.2780i	−0.274664	+	0.475732i
$780$	0.681280	−	13.1150i	0.0243937	−	0.469592i
$781$	12.7678	+	22.1145i	0.456867	+	0.791318i
$782$	−10.3497	+	2.77320i	−0.370106	+	0.0991695i
$783$	22.4554	+	4.88299i	0.802490	+	0.174504i
$784$	−17.2328	−	15.1721i	−0.615458	−	0.541860i
$785$	8.22815	+	8.22815i	0.293675	+	0.293675i
$786$	24.0144	−	69.3911i	0.856566	−	2.47510i
$787$	−4.78840	+	17.8706i	−0.170688	+	0.637017i	0.826558	+	0.562852i	$0.190296\pi$
$787$	−4.78840	+	17.8706i	−0.170688	+	0.637017i	−0.997246	+	0.0741650i	$0.976371\pi$
$788$	40.9377	+	10.9692i	1.45834	+	0.390762i
$789$	9.13897	+	18.8121i	0.325356	+	0.669728i
$790$		−	3.39371i		−	0.120743i
$791$	−12.3285	+	10.0977i	−0.438350	+	0.359033i
$792$	−5.91907	+	2.37001i	−0.210325	+	0.0842145i
$793$	31.0287	−	8.96521i	1.10186	−	0.318364i
$794$	−17.9251	+	10.3490i	−0.636137	+	0.367274i
$795$	−10.0080	−	11.5493i	−0.354949	−	0.409610i
$796$	8.24623	−	14.2829i	0.292280	−	0.506243i
$797$	14.9177			0.528413			0.264206	−	0.964466i	$-0.414890\pi$
$797$	14.9177			0.528413			0.264206	+	0.964466i	$0.414890\pi$
$798$	35.3019	+	16.2894i	1.24967	+	0.576637i
$799$	−3.58464	+	3.58464i	−0.126815	+	0.126815i
$800$	8.75153	+	32.6611i	0.309413	+	1.15475i
$801$	0.330564	+	2.76348i	0.0116799	+	0.0976426i
$802$	−4.17006	−	7.22276i	−0.147250	−	0.255045i
$803$	−7.61800	+	13.1948i	−0.268833	+	0.465633i
$804$	6.60020	+	34.2401i	0.232771	+	1.20756i
$805$	−16.6309	+	7.51590i	−0.586161	+	0.264901i
$806$	−17.3821	−	16.7180i	−0.612259	−	0.588866i
$807$	18.5653	+	38.2158i	0.653531	+	1.34526i
$808$	3.14964	+	0.843944i	0.110804	+	0.0296899i
$809$	16.9527	−	9.78762i	0.596024	−	0.344114i	−0.171452	−	0.985192i	$-0.554846\pi$
$809$	16.9527	−	9.78762i	0.596024	−	0.344114i	0.767476	+	0.641078i	$0.221513\pi$
$810$	−16.5218	+	4.01001i	−0.580516	+	0.140897i
$811$	30.4392	−	30.4392i	1.06887	−	1.06887i	0.0714196	−	0.997446i	$-0.477247\pi$
$811$	30.4392	−	30.4392i	1.06887	−	1.06887i	0.997446	−	0.0714196i	$-0.0227529\pi$
$812$	9.55172	−	25.3038i	0.335200	−	0.887988i
$813$	−9.33501	−	48.4277i	−0.327393	−	1.69843i
$814$	57.3892	−	15.3774i	2.01149	−	0.538977i
$815$	−7.60465	+	4.39055i	−0.266379	+	0.153794i
$816$	0.275727	−	3.85662i	0.00965239	−	0.135009i
$817$	−29.8254	+	7.99170i	−1.04346	+	0.279594i
$818$	−20.8455			−0.728847
$819$	6.31286	−	27.9132i	0.220589	−	0.975367i
$820$	−7.89098			−0.275565
$821$	0.112336	−	0.0301003i	0.00392054	−	0.00105051i	−0.256858	−	0.966449i	$-0.582687\pi$
$821$	0.112336	−	0.0301003i	0.00392054	−	0.00105051i	0.260779	+	0.965399i	$0.416021\pi$
$822$	0.596640	−	8.34525i	0.0208102	−	0.291074i
$823$	36.8952	−	21.3015i	1.28609	−	0.742523i	0.308133	−	0.951343i	$-0.400296\pi$
$823$	36.8952	−	21.3015i	1.28609	−	0.742523i	0.977954	+	0.208821i	$0.0669625\pi$
$824$	2.44569	−	0.655321i	0.0851997	−	0.0228292i
$825$	4.49475	+	23.3176i	0.156487	+	0.811815i
$826$	−18.5675	−	22.6694i	−0.646046	−	0.788770i
$827$	1.48128	−	1.48128i	0.0515093	−	0.0515093i	−0.680883	−	0.732392i	$-0.738404\pi$
$827$	1.48128	−	1.48128i	0.0515093	−	0.0515093i	0.732392	+	0.680883i	$0.238404\pi$
$828$	−7.47986	+	52.0433i	−0.259943	+	1.80863i
$829$	−33.1399	+	19.1333i	−1.15099	+	0.664527i	−0.949129	−	0.314886i	$-0.898034\pi$
$829$	−33.1399	+	19.1333i	−1.15099	+	0.664527i	−0.201865	+	0.979413i	$0.564700\pi$
$830$	19.5289	+	5.23276i	0.677859	+	0.181632i
$831$	11.8328	+	24.3573i	0.410476	+	0.844944i
$832$	25.6627	−	26.6822i	0.889695	−	0.925038i
$833$	−4.51420	+	1.52260i	−0.156408	+	0.0527548i
$834$	−2.55509	−	13.2552i	−0.0884756	−	0.458989i
$835$	−7.54423	+	13.0670i	−0.261079	+	0.452202i
$836$	15.5174	+	26.8770i	0.536682	+	0.929560i
$837$	−7.66889	+	14.8785i	−0.265076	+	0.514276i
$838$	19.4614	+	72.6308i	0.672282	+	2.50899i
$839$	−13.8185	+	13.8185i	−0.477068	+	0.477068i	−0.904193	−	0.427125i	$-0.859527\pi$
$839$	−13.8185	+	13.8185i	−0.477068	+	0.477068i	0.427125	+	0.904193i	$0.359527\pi$
$840$	0.245793	+	2.68523i	0.00848065	+	0.0926492i
$841$	9.44117			0.325558
$842$	−13.9763	+	24.2076i	−0.481654	+	0.834249i
$843$	14.8510	+	17.1380i	0.511494	+	0.590264i
$844$	28.0937	−	16.2199i	0.967024	−	0.558312i
$845$	3.50353	+	11.2961i	0.120525	+	0.388598i
$846$	17.2473	+	43.0751i	0.592976	+	1.48095i
$847$	0.0866309	+	0.527904i	0.00297667	+	0.0181390i
$848$		−	31.8105i		−	1.09238i
$849$	−9.59966	−	19.7604i	−0.329459	−	0.678175i
$850$	5.69528	+	1.52605i	0.195346	+	0.0523429i
$851$	17.0881	−	63.7736i	0.585772	−	2.18613i
$852$	10.1750	−	29.4013i	0.348590	−	1.00727i
$853$	−12.7940	−	12.7940i	−0.438057	−	0.438057i	0.453300	−	0.891358i	$-0.350246\pi$
$853$	−12.7940	−	12.7940i	−0.438057	−	0.438057i	−0.891358	+	0.453300i	$0.850246\pi$
$854$	−44.8446	+	20.2664i	−1.53455	+	0.693500i
$855$	4.14523	+	10.3527i	0.141764	+	0.354054i
$856$	4.67776	−	1.25340i	0.159882	−	0.0428404i
$857$	−8.41293	−	14.5716i	−0.287380	−	0.497757i	0.685803	−	0.727787i	$-0.259451\pi$
$857$	−8.41293	−	14.5716i	−0.287380	−	0.497757i	−0.973184	+	0.230030i	$0.926118\pi$
$858$	31.6524	−	28.5263i	1.08060	−	0.973873i
$859$	−28.1846	+	48.8172i	−0.961647	+	1.66562i	−0.243283	+	0.969955i	$0.578224\pi$
$859$	−28.1846	+	48.8172i	−0.961647	+	1.66562i	−0.718365	+	0.695667i	$0.755109\pi$
$860$	−11.2372	−	11.2372i	−0.383186	−	0.383186i
$861$	−16.9463	−	2.91800i	−0.577528	−	0.0994451i
$862$		−	13.8989i		−	0.473399i
$863$	31.5799	−	8.46182i	1.07499	−	0.288044i	0.322450	−	0.946586i	$-0.395494\pi$
$863$	31.5799	−	8.46182i	1.07499	−	0.288044i	0.752543	+	0.658543i	$0.228827\pi$
$864$	−37.4309	−	19.2932i	−1.27343	−	0.656367i
$865$	−0.563451	+	2.10283i	−0.0191579	+	0.0714983i
$866$	−12.8506	−	47.9591i	−0.436681	−	1.62972i
$867$	23.7208	+	16.0538i	0.805600	+	0.545214i
$868$	16.0024	+	11.4907i	0.543156	+	0.390019i
$869$	4.17431	−	4.17431i	0.141604	−	0.141604i
$870$	13.0156	−	6.32303i	0.441271	−	0.214371i
$871$	−16.2283	−	26.8853i	−0.549875	−	0.910973i
$872$	6.72826	−	3.88456i	0.227848	−	0.131548i
$873$	10.2207	−	7.65195i	0.345917	−	0.258979i
$874$	64.3275			2.17591
$875$	21.9695	+	2.18534i	0.742705	+	0.0738781i
$876$	18.2278	−	3.51362i	0.615859	−	0.118714i
$877$	−9.39774	−	35.0729i	−0.317339	−	1.18433i	−0.921792	−	0.387685i	$-0.873275\pi$
$877$	−9.39774	−	35.0729i	−0.317339	−	1.18433i	0.604453	−	0.796641i	$-0.293392\pi$
$878$	−58.9540	−	15.7967i	−1.98960	−	0.533112i
$879$	29.3191	+	33.8342i	0.988908	+	1.14120i
$880$	4.90277	−	8.49184i	0.165272	−	0.286260i
$881$	−33.0535			−1.11360			−0.556800	−	0.830646i	$-0.687971\pi$
$881$	−33.0535			−1.11360			−0.556800	+	0.830646i	$0.687971\pi$
$882$	−3.45153	+	43.4678i	−0.116219	+	1.46364i
$883$		−	11.1463i		−	0.375104i	−0.982255	−	0.187552i	$-0.939945\pi$
$883$		−	11.1463i		−	0.375104i	0.982255	−	0.187552i	$-0.0600553\pi$
$884$	−1.57445	−	5.44919i	−0.0529544	−	0.183276i
$885$	0.599381	−	8.38359i	0.0201480	−	0.281811i
$886$	−68.4530	−	18.3419i	−2.29972	−	0.616209i
$887$	−23.4101	−	13.5159i	−0.786036	−	0.453818i	0.0525294	−	0.998619i	$-0.483272\pi$
$887$	−23.4101	−	13.5159i	−0.786036	−	0.453818i	−0.838565	+	0.544801i	$0.816605\pi$
$888$	−8.07860	−	5.46744i	−0.271100	−	0.183475i
$889$	−35.6421	+	29.1929i	−1.19540	+	0.979098i
$890$	1.23922	+	1.23922i	0.0415387	+	0.0415387i
$891$	−25.2543	−	15.3896i	−0.846052	−	0.515572i
$892$	6.40640	−	23.9090i	0.214502	−	0.800533i
$893$	26.3574	−	15.2174i	0.882015	−	0.509232i
$894$	−30.1845	−	62.1333i	−1.00952	−	2.07805i
$895$	−0.766830	−	0.766830i	−0.0256323	−	0.0256323i
$896$	−7.88789	+	10.9850i	−0.263516	+	0.366983i
$897$	−9.86602	−	46.3112i	−0.329417	−	1.54629i
$898$	17.0338	−	29.5034i	0.568425	−	0.984541i
$899$	3.68727	−	13.7611i	0.122977	−	0.458958i
$900$	17.8839	−	22.7437i	0.596129	−	0.758123i
$901$	−5.71619	−	3.30024i	−0.190434	−	0.109947i
$902$	−18.1041	−	18.1041i	−0.602800	−	0.602800i
$903$	−19.9771	−	28.2879i	−0.664796	−	0.941362i
$904$	2.75466	+	2.75466i	0.0916187	+	0.0916187i
$905$	4.40490	+	16.4393i	0.146424	+	0.546461i
$906$	−46.0443	−	3.29191i	−1.52972	−	0.109367i
$907$	16.8278	−	9.71555i	0.558759	−	0.322599i	−0.193889	−	0.981024i	$-0.562110\pi$
$907$	16.8278	−	9.71555i	0.558759	−	0.322599i	0.752647	+	0.658424i	$0.228777\pi$
$908$	15.9003	+	59.3407i	0.527670	+	1.96929i
$909$	5.62201	+	14.0409i	0.186470	+	0.465708i
$910$	−7.73955	−	16.2737i	−0.256563	−	0.539468i
$911$		−	2.34832i		−	0.0778032i	−0.999243	−	0.0389016i	$-0.987614\pi$
$911$		−	2.34832i		−	0.0778032i	0.999243	−	0.0389016i	$-0.0123859\pi$
$912$	−7.59154	+	21.9362i	−0.251381	+	0.726380i
$913$	17.5844	+	30.4572i	0.581960	+	1.00798i
$914$	1.36065	+	2.35672i	0.0450063	+	0.0779533i
$915$	−13.3392	−	4.61634i	−0.440980	−	0.152611i
$916$	−37.4065	+	37.4065i	−1.23595	+	1.23595i
$917$	−8.74762	−	53.3055i	−0.288872	−	1.76030i
$918$	−6.17703	+	3.97043i	−0.203872	+	0.131044i
$919$	−11.1770	+	19.3592i	−0.368697	+	0.638601i	−0.989362	−	0.145474i	$-0.953529\pi$
$919$	−11.1770	+	19.3592i	−0.368697	+	0.638601i	0.620665	+	0.784076i	$0.286863\pi$
$920$	2.23072	+	3.86373i	0.0735448	+	0.127383i
$921$	13.8735	−	12.0221i	0.457146	−	0.396140i
$922$	19.0295	+	10.9867i	0.626703	+	0.361827i
$923$	0.545580	+	28.0135i	0.0179580	+	0.922076i
$924$	−22.2664	+	26.7534i	−0.732511	+	0.880124i
$925$	−25.6903	+	25.6903i	−0.844690	+	0.844690i
$926$	−17.1312	−	9.89069i	−0.562965	−	0.325028i
$927$	9.23199	+	7.25932i	0.303218	+	0.238427i
$928$	34.6198	+	9.27635i	1.13645	+	0.304511i
$929$	−8.25438	+	2.21175i	−0.270817	+	0.0725653i	−0.391672	−	0.920105i	$-0.628103\pi$
$929$	−8.25438	+	2.21175i	−0.270817	+	0.0725653i	0.120855	+	0.992670i	$0.461437\pi$
$930$	1.99499	+	10.3495i	0.0654183	+	0.339374i
$931$	28.5438	−	1.81521i	0.935486	−	0.0594910i
$932$		−	58.4628i		−	1.91501i
$933$	−28.2540	+	13.7259i	−0.924995	+	0.449365i
$934$	6.82953	−	25.4882i	0.223469	−	0.833998i
$935$	−1.01730	−	1.76201i	−0.0332691	−	0.0576238i
$936$	−6.94286	−	0.860230i	−0.226935	−	0.0281175i
$937$	35.6642			1.16510			0.582549	−	0.812795i	$-0.302055\pi$
$937$	35.6642			1.16510			0.582549	+	0.812795i	$0.302055\pi$
$938$	30.3188	+	37.0168i	0.989945	+	1.20864i
$939$	30.6773	+	20.7618i	1.00112	+	0.677537i
$940$	13.5654	+	7.83198i	0.442454	+	0.255451i
$941$	−11.9575	+	44.6261i	−0.389805	+	1.45477i	0.440648	+	0.897680i	$0.354749\pi$
$941$	−11.9575	+	44.6261i	−0.389805	+	1.45477i	−0.830452	+	0.557090i	$0.811918\pi$
$942$	34.7640	−	30.1248i	1.13267	−	0.981519i
$943$	−27.4818	+	7.36374i	−0.894932	+	0.239796i
$944$	12.3710	−	12.3710i	0.402643	−	0.402643i
$945$	−9.28718	+	8.37727i	−0.302112	+	0.272513i
$946$		−	51.5625i		−	1.67644i
$947$	5.31277	+	19.8275i	0.172642	+	0.644309i	0.996941	+	0.0781544i	$0.0249027\pi$
$947$	5.31277	+	19.8275i	0.172642	+	0.644309i	−0.824299	+	0.566154i	$0.808431\pi$
$948$	−7.17426	−	0.512920i	−0.233009	−	0.0166589i
$949$	−14.3124	+	8.63915i	−0.464600	+	0.280439i
$950$	−30.6558	−	17.6992i	−0.994606	−	0.574236i
$951$	−4.96304	−	25.7470i	−0.160938	−	0.834904i
$952$	0.479615	+	1.06127i	0.0155444	+	0.0343960i
$953$	−47.8825			−1.55107			−0.775533	−	0.631307i	$-0.782519\pi$
$953$	−47.8825			−1.55107			−0.775533	+	0.631307i	$0.782519\pi$
$954$	−48.3613	+	36.2068i	−1.56575	+	1.17224i
$955$	3.73002	+	0.999455i	0.120700	+	0.0323416i
$956$	−18.4802	−	4.95176i	−0.597693	−	0.160151i
$957$	23.7868	+	8.23198i	0.768918	+	0.266102i
$958$	72.4617			2.34113
$959$	−2.53473	−	5.60874i	−0.0818507	−	0.181116i
$960$	−15.8869	+	3.06238i	−0.512746	+	0.0988380i
$961$	−17.8600	−	10.3115i	−0.576128	−	0.332628i
$962$	63.2867	+	15.6434i	2.04044	+	0.504365i
$963$	17.6576	+	13.8846i	0.569008	+	0.447424i
$964$	−0.489065	−	1.82522i	−0.0157517	−	0.0587863i
$965$		−	10.4656i		−	0.336900i
$966$	24.9475	+	67.6959i	0.802673	+	2.17808i
$967$	−26.7141	+	26.7141i	−0.859067	+	0.859067i	−0.991228	−	0.132161i	$-0.957808\pi$
$967$	−26.7141	+	26.7141i	−0.859067	+	0.859067i	0.132161	+	0.991228i	$0.457808\pi$
$968$	0.126321	−	0.0338475i	0.00406010	−	0.00108790i
$969$	3.15423	+	3.63998i	0.101328	+	0.116933i
$970$	2.08081	−	7.76567i	0.0668106	−	0.249341i
$971$	−5.73054	−	3.30853i	−0.183902	−	0.106176i	0.405223	−	0.914218i	$-0.367194\pi$
$971$	−5.73054	−	3.30853i	−0.183902	−	0.106176i	−0.589125	+	0.808042i	$0.700527\pi$
$972$	5.98002	+	35.5328i	0.191809	+	1.13972i
$973$	−6.29255	−	7.68269i	−0.201730	−	0.246296i
$974$	0.660809			0.0211737
$975$	−8.04040	+	24.7846i	−0.257499	+	0.793742i
$976$	−14.6908	−	25.4453i	−0.470243	−	0.814484i
$977$	−8.87641	+	33.1272i	−0.283982	+	1.05983i	0.665599	+	0.746310i	$0.268176\pi$
$977$	−8.87641	+	33.1272i	−0.283982	+	1.05983i	−0.949580	+	0.313524i	$0.898490\pi$
$978$	15.1685	+	31.2236i	0.485036	+	0.998421i
$979$			3.04851i			0.0974307i
$980$	8.15443	+	12.2554i	0.260484	+	0.391485i
$981$	33.1274	+	14.1839i	1.05768	+	0.452857i
$982$	−70.8210	+	18.9764i	−2.25999	+	0.605562i
$983$	−40.0758	−	10.7383i	−1.27822	−	0.342498i	−0.445046	−	0.895508i	$-0.646813\pi$
$983$	−40.0758	−	10.7383i	−1.27822	−	0.342498i	−0.833175	+	0.553010i	$0.813479\pi$
$984$	−0.299771	+	4.19293i	−0.00955636	+	0.133666i
$985$	14.4460	+	8.34041i	0.460288	+	0.265748i
$986$	4.41926	−	4.41926i	0.140738	−	0.140738i
$987$	26.2362	+	21.8359i	0.835108	+	0.695045i
$988$	0.663075	+	34.0464i	0.0210952	+	1.08316i
$989$	−49.6221	−	28.6493i	−1.57789	−	0.910996i
$990$	−18.4904	+	2.21181i	−0.587665	+	0.0702958i
$991$	−21.2216	−	36.7569i	−0.674126	−	1.16762i	−0.976724	−	0.214502i	$-0.931187\pi$
$991$	−21.2216	−	36.7569i	−0.674126	−	1.16762i	0.302598	−	0.953118i	$-0.402146\pi$
$992$	−13.0532	+	22.6088i	−0.414440	+	0.717831i
$993$	31.4102	−	6.05469i	0.996773	−	0.192140i
$994$	−6.91334	−	42.1279i	−0.219278	−	1.33622i
$995$	4.58996	−	4.58996i	0.145511	−	0.145511i
$996$	14.0135	−	40.4929i	0.444036	−	1.28307i
$997$	10.0971	+	17.4886i	0.319778	+	0.553871i	0.980441	−	0.196811i	$-0.0630585\pi$
$997$	10.0971	+	17.4886i	0.319778	+	0.553871i	−0.660664	+	0.750682i	$0.729725\pi$
$998$	−17.7989	−	30.8286i	−0.563414	−	0.975862i
$999$	−2.15655	−	45.1953i	−0.0682302	−	1.42992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cd.e.44.6	✓	112
3.2	odd	2	inner	273.2.cd.e.44.23	yes	112
7.4	even	3	inner	273.2.cd.e.200.23	yes	112
13.8	odd	4	inner	273.2.cd.e.86.6	yes	112
21.11	odd	6	inner	273.2.cd.e.200.6	yes	112
39.8	even	4	inner	273.2.cd.e.86.23	yes	112
91.60	odd	12	inner	273.2.cd.e.242.23	yes	112
273.242	even	12	inner	273.2.cd.e.242.6	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.e.44.6	✓	112	1.1	even	1	trivial
273.2.cd.e.44.23	yes	112	3.2	odd	2	inner
273.2.cd.e.86.6	yes	112	13.8	odd	4	inner
273.2.cd.e.86.23	yes	112	39.8	even	4	inner
273.2.cd.e.200.6	yes	112	21.11	odd	6	inner
273.2.cd.e.200.23	yes	112	7.4	even	3	inner
273.2.cd.e.242.6	yes	112	273.242	even	12	inner
273.2.cd.e.242.23	yes	112	91.60	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.00566 + 0.537415i) q^{2} +(-0.123517 + 1.72764i) q^{3} +(2.00181 - 1.15574i) q^{4} +(0.878767 - 0.235465i) q^{5} +(-0.680727 - 3.53144i) q^{6} +(-1.67646 - 2.04682i) q^{7} +(-0.457340 + 0.457340i) q^{8} +(-2.96949 - 0.426786i) q^{9} +O(q^{10})\)	\(q+(-2.00566 + 0.537415i) q^{2} +(-0.123517 + 1.72764i) q^{3} +(2.00181 - 1.15574i) q^{4} +(0.878767 - 0.235465i) q^{5} +(-0.680727 - 3.53144i) q^{6} +(-1.67646 - 2.04682i) q^{7} +(-0.457340 + 0.457340i) q^{8} +(-2.96949 - 0.426786i) q^{9} +(-1.63596 + 0.944525i) q^{10} +(-3.17403 - 0.850480i) q^{11} +(1.74945 + 3.60116i) q^{12} +(-2.59867 - 2.49938i) q^{13} +(4.46240 + 3.20427i) q^{14} +(0.298256 + 1.54728i) q^{15} +(-1.64000 + 2.84056i) q^{16} +(0.340290 + 0.589400i) q^{17} +(6.18514 - 0.739860i) q^{18} +(-1.05752 - 3.94670i) q^{19} +(1.48698 - 1.48698i) q^{20} +(3.74324 - 2.64350i) q^{21} +6.82309 q^{22} +(3.79107 - 6.56633i) q^{23} +(-0.733630 - 0.846608i) q^{24} +(-3.61334 + 2.08616i) q^{25} +(6.55525 + 3.61635i) q^{26} +(1.10411 - 5.07749i) q^{27} +(-5.72155 - 2.15978i) q^{28} +4.42254i q^{29} +(-1.42973 - 2.94302i) q^{30} +(-3.11158 - 0.833747i) q^{31} +(2.09752 - 7.82804i) q^{32} +(1.86137 - 5.37854i) q^{33} +(-0.999259 - 0.999259i) q^{34} +(-1.95517 - 1.40393i) q^{35} +(-6.43759 + 2.57762i) q^{36} +(8.41103 - 2.25373i) q^{37} +(4.24203 + 7.34742i) q^{38} +(4.63902 - 4.18085i) q^{39} +(-0.294207 + 0.509582i) q^{40} +(-2.65335 - 2.65335i) q^{41} +(-6.08702 + 7.31365i) q^{42} -7.55705i q^{43} +(-7.33674 + 1.96587i) q^{44} +(-2.70998 + 0.324165i) q^{45} +(-4.07476 + 15.2072i) q^{46} +(1.92787 + 7.19489i) q^{47} +(-4.70491 - 3.18419i) q^{48} +(-1.37896 + 6.86283i) q^{49} +(6.12600 - 6.12600i) q^{50} +(-1.06030 + 0.515099i) q^{51} +(-8.09068 - 1.99988i) q^{52} +(-8.39899 + 4.84916i) q^{53} +(0.514242 + 10.7771i) q^{54} -2.98949 q^{55} +(1.70280 + 0.169381i) q^{56} +(6.94911 - 1.33952i) q^{57} +(-2.37674 - 8.87010i) q^{58} +(-5.15217 - 1.38052i) q^{59} +(2.38531 + 2.75264i) q^{60} +(-4.47892 + 7.75771i) q^{61} +6.68885 q^{62} +(4.10467 + 6.79350i) q^{63} +10.2676i q^{64} +(-2.87214 - 1.58448i) q^{65} +(-0.842767 + 11.7879i) q^{66} +(8.41297 + 2.25425i) q^{67} +(1.36239 + 0.786577i) q^{68} +(10.8760 + 7.36067i) q^{69} +(4.67590 + 1.76507i) q^{70} +(-5.49494 - 5.49494i) q^{71} +(1.55325 - 1.16288i) q^{72} +(1.20005 - 4.47865i) q^{73} +(-15.6585 + 9.04042i) q^{74} +(-3.15783 - 6.50023i) q^{75} +(-6.67832 - 6.67832i) q^{76} +(3.58036 + 7.92248i) q^{77} +(-7.05744 + 10.8784i) q^{78} +(-0.898260 + 1.55583i) q^{79} +(-0.772325 + 2.88236i) q^{80} +(8.63571 + 2.53467i) q^{81} +(6.74767 + 3.89577i) q^{82} +(-7.56791 - 7.56791i) q^{83} +(4.43804 - 9.61802i) q^{84} +(0.437819 + 0.437819i) q^{85} +(4.06127 + 15.1569i) q^{86} +(-7.64056 - 0.546258i) q^{87} +(1.84057 - 1.06265i) q^{88} +(-0.240113 - 0.896114i) q^{89} +(5.26109 - 2.10655i) q^{90} +(-0.759223 + 9.50913i) q^{91} -17.5260i q^{92} +(1.82475 - 5.27272i) q^{93} +(-7.73329 - 13.3944i) q^{94} +(-1.85862 - 3.21922i) q^{95} +(13.2650 + 4.59065i) q^{96} +(-3.00938 + 3.00938i) q^{97} +(-0.922464 - 14.5056i) q^{98} +(9.06228 + 3.88012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Introduction

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