LMFDB - Embedded newform 504.2.bt.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(11,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 4]))

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

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

chi := DirichletCharacter("504.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bt (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	504.11
Dual form			504.2.bt.a.275.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38769 - 0.272632i) q^{2} +(1.73194 + 0.0199803i) q^{3} +(1.85134 + 0.756656i) q^{4} +(0.662921 - 1.14821i) q^{5} +(-2.39793 - 0.499908i) q^{6} +(0.655004 - 2.56339i) q^{7} +(-2.36279 - 1.55474i) q^{8} +(2.99920 + 0.0692093i) q^{9} +O(q^{10})$	\(q+(-1.38769 - 0.272632i) q^{2} +(1.73194 + 0.0199803i) q^{3} +(1.85134 + 0.756656i) q^{4} +(0.662921 - 1.14821i) q^{5} +(-2.39793 - 0.499908i) q^{6} +(0.655004 - 2.56339i) q^{7} +(-2.36279 - 1.55474i) q^{8} +(2.99920 + 0.0692093i) q^{9} +(-1.23297 + 1.41263i) q^{10} +(0.333297 - 0.192429i) q^{11} +(3.19129 + 1.34747i) q^{12} +(1.26167 - 0.728426i) q^{13} +(-1.60780 + 3.37860i) q^{14} +(1.17108 - 1.97539i) q^{15} +(2.85494 + 2.80166i) q^{16} +(-5.91788 - 3.41669i) q^{17} +(-4.14308 - 0.913720i) q^{18} +(-1.73667 - 3.00801i) q^{19} +(2.09610 - 1.62413i) q^{20} +(1.18564 - 4.42654i) q^{21} +(-0.514974 + 0.176164i) q^{22} +(1.23894 - 2.14590i) q^{23} +(-4.06114 - 2.73991i) q^{24} +(1.62107 + 2.80778i) q^{25} +(-1.94939 + 0.666854i) q^{26} +(5.19304 + 0.179791i) q^{27} +(3.15224 - 4.25010i) q^{28} +(-4.72947 + 8.19168i) q^{29} +(-2.16364 + 2.42194i) q^{30} +6.19835i q^{31} +(-3.19794 - 4.66617i) q^{32} +(0.581094 - 0.326615i) q^{33} +(7.28066 + 6.35470i) q^{34} +(-2.50910 - 2.45141i) q^{35} +(5.50018 + 2.39749i) q^{36} +(7.92081 - 4.57308i) q^{37} +(1.58988 + 4.64764i) q^{38} +(2.19969 - 1.23638i) q^{39} +(-3.35151 + 1.68232i) q^{40} +(2.15658 - 1.24510i) q^{41} +(-2.85212 + 5.81940i) q^{42} +(-1.64502 + 2.84926i) q^{43} +(0.762650 - 0.104061i) q^{44} +(2.06770 - 3.39784i) q^{45} +(-2.30429 + 2.64006i) q^{46} +3.96734 q^{47} +(4.88860 + 4.90934i) q^{48} +(-6.14194 - 3.35806i) q^{49} +(-1.48405 - 4.33827i) q^{50} +(-10.1811 - 6.03573i) q^{51} +(2.88695 - 0.393916i) q^{52} +(-0.114978 + 0.199147i) q^{53} +(-7.15729 - 1.66528i) q^{54} -0.510261i q^{55} +(-5.53304 + 5.03840i) q^{56} +(-2.94771 - 5.24437i) q^{57} +(8.79633 - 10.0781i) q^{58} -4.10518i q^{59} +(3.66275 - 2.77101i) q^{60} -4.29926i q^{61} +(1.68987 - 8.60137i) q^{62} +(2.14190 - 7.64279i) q^{63} +(3.16559 + 7.34704i) q^{64} -1.93156i q^{65} +(-0.895421 + 0.294815i) q^{66} +14.9698 q^{67} +(-8.37078 - 10.8033i) q^{68} +(2.18863 - 3.69180i) q^{69} +(2.81351 + 4.08585i) q^{70} +5.68595 q^{71} +(-6.97889 - 4.82649i) q^{72} +(-6.97110 + 12.0743i) q^{73} +(-12.2384 + 4.18653i) q^{74} +(2.75149 + 4.89528i) q^{75} +(-0.939154 - 6.88292i) q^{76} +(-0.274960 - 0.980412i) q^{77} +(-3.38955 + 1.11600i) q^{78} -4.78615i q^{79} +(5.10950 - 1.42081i) q^{80} +(8.99042 + 0.415145i) q^{81} +(-3.33211 + 1.13986i) q^{82} +(6.63767 + 3.83226i) q^{83} +(5.54440 - 7.29792i) q^{84} +(-7.84618 + 4.52999i) q^{85} +(3.05957 - 3.50539i) q^{86} +(-8.35481 + 14.0930i) q^{87} +(-1.08669 - 0.0635186i) q^{88} +(-5.36142 + 3.09542i) q^{89} +(-3.79568 + 4.15141i) q^{90} +(-1.04084 - 3.71128i) q^{91} +(3.91740 - 3.03535i) q^{92} +(-0.123845 + 10.7351i) q^{93} +(-5.50542 - 1.08162i) q^{94} -4.60511 q^{95} +(-5.44540 - 8.14541i) q^{96} +(-5.48708 + 9.50389i) q^{97} +(7.60756 + 6.33443i) q^{98} +(1.01294 - 0.554066i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 184 * q - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^9	$ 184 q - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{10} - 6 q^{11} - 8 q^{12} + 12 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} - 6 q^{20} + 2 q^{22} - 8 q^{24} - 74 q^{25} - 6 q^{26} - 8 q^{27} + 3 q^{30} - 14 q^{33} - 4 q^{34} + 30 q^{35} - 38 q^{36} + 39 q^{38} + 6 q^{40} - 12 q^{41} - 20 q^{42} - 4 q^{43} + 9 q^{44} - 6 q^{46} - 5 q^{48} - 2 q^{49} - 21 q^{50} - 34 q^{51} + 9 q^{52} + 47 q^{54} - 24 q^{56} + 4 q^{57} - 3 q^{58} - 11 q^{60} - 8 q^{64} - 26 q^{66} - 4 q^{67} - 42 q^{68} - 3 q^{70} + 52 q^{72} - 4 q^{73} + 27 q^{74} + 30 q^{75} + 2 q^{76} - 29 q^{78} + 87 q^{80} + 14 q^{81} - 4 q^{82} - 72 q^{83} - 59 q^{84} - 27 q^{86} - 7 q^{88} - 24 q^{89} - 49 q^{90} - 36 q^{91} - 36 q^{92} - 18 q^{94} + 23 q^{96} - 4 q^{97} + 57 q^{98} + 10 q^{99}+O(q^{100}) $ 184 * q - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^9 - 6 * q^10 - 6 * q^11 - 8 * q^12 + 12 * q^14 - 2 * q^16 + 2 * q^18 - 4 * q^19 - 6 * q^20 + 2 * q^22 - 8 * q^24 - 74 * q^25 - 6 * q^26 - 8 * q^27 + 3 * q^30 - 14 * q^33 - 4 * q^34 + 30 * q^35 - 38 * q^36 + 39 * q^38 + 6 * q^40 - 12 * q^41 - 20 * q^42 - 4 * q^43 + 9 * q^44 - 6 * q^46 - 5 * q^48 - 2 * q^49 - 21 * q^50 - 34 * q^51 + 9 * q^52 + 47 * q^54 - 24 * q^56 + 4 * q^57 - 3 * q^58 - 11 * q^60 - 8 * q^64 - 26 * q^66 - 4 * q^67 - 42 * q^68 - 3 * q^70 + 52 * q^72 - 4 * q^73 + 27 * q^74 + 30 * q^75 + 2 * q^76 - 29 * q^78 + 87 * q^80 + 14 * q^81 - 4 * q^82 - 72 * q^83 - 59 * q^84 - 27 * q^86 - 7 * q^88 - 24 * q^89 - 49 * q^90 - 36 * q^91 - 36 * q^92 - 18 * q^94 + 23 * q^96 - 4 * q^97 + 57 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.38769	−	0.272632i	−0.981242	−	0.192780i
$2$	−1.38769	−	0.272632i	−0.981242	−	0.192780i
$3$	1.73194	+	0.0199803i	0.999933	+	0.0115357i
$3$	1.73194	+	0.0199803i	0.999933	+	0.0115357i
$4$	1.85134	+	0.756656i	0.925672	+	0.378328i
$5$	0.662921	−	1.14821i	0.296467	−	0.513496i	−0.678858	−	0.734270i	$-0.737525\pi$
$5$	0.662921	−	1.14821i	0.296467	−	0.513496i	0.975325	+	0.220773i	$0.0708581\pi$
$6$	−2.39793	−	0.499908i	−0.978953	−	0.204087i
$7$	0.655004	−	2.56339i	0.247568	−	0.968870i
$7$	0.655004	−	2.56339i	0.247568	−	0.968870i
$8$	−2.36279	−	1.55474i	−0.835374	−	0.549682i
$9$	2.99920	+	0.0692093i	0.999734	+	0.0230698i
$10$	−1.23297	+	1.41263i	−0.389898	+	0.446711i
$11$	0.333297	−	0.192429i	0.100493	−	0.0580196i	−0.448911	−	0.893576i	$-0.648188\pi$
$11$	0.333297	−	0.192429i	0.100493	−	0.0580196i	0.549404	+	0.835557i	$0.314855\pi$
$12$	3.19129	+	1.34747i	0.921246	+	0.388981i
$13$	1.26167	−	0.728426i	0.349924	−	0.202029i	−0.314728	−	0.949182i	$-0.601913\pi$
$13$	1.26167	−	0.728426i	0.349924	−	0.202029i	0.664652	+	0.747153i	$0.268580\pi$
$14$	−1.60780	+	3.37860i	−0.429703	+	0.902970i
$15$	1.17108	−	1.97539i	0.302371	−	0.510042i
$16$	2.85494	+	2.80166i	0.713736	+	0.700415i
$17$	−5.91788	−	3.41669i	−1.43530	−	0.828670i	−0.437780	−	0.899082i	$-0.644235\pi$
$17$	−5.91788	−	3.41669i	−1.43530	−	0.828670i	−0.997518	+	0.0704127i	$0.977568\pi$
$18$	−4.14308	−	0.913720i	−0.976533	−	0.215366i
$19$	−1.73667	−	3.00801i	−0.398420	−	0.690084i	0.595111	−	0.803644i	$-0.297108\pi$
$19$	−1.73667	−	3.00801i	−0.398420	−	0.690084i	−0.993531	+	0.113559i	$0.963775\pi$
$20$	2.09610	−	1.62413i	0.468701	−	0.363167i
$21$	1.18564	−	4.42654i	0.258729	−	0.965950i
$22$	−0.514974	+	0.176164i	−0.109793	+	0.0375582i
$23$	1.23894	−	2.14590i	0.258336	−	0.447451i	−0.707460	−	0.706753i	$-0.750159\pi$
$23$	1.23894	−	2.14590i	0.258336	−	0.447451i	0.965796	+	0.259302i	$0.0834925\pi$
$24$	−4.06114	−	2.73991i	−0.828977	−	0.559282i
$25$	1.62107	+	2.80778i	0.324214	+	0.561556i
$26$	−1.94939	+	0.666854i	−0.382308	+	0.130781i
$27$	5.19304	+	0.179791i	0.999401	+	0.0346008i
$28$	3.15224	−	4.25010i	0.595718	−	0.803194i
$29$	−4.72947	+	8.19168i	−0.878240	+	1.52116i	−0.0249698	+	0.999688i	$0.507949\pi$
$29$	−4.72947	+	8.19168i	−0.878240	+	1.52116i	−0.853271	+	0.521469i	$0.825384\pi$
$30$	−2.16364	+	2.42194i	−0.395025	+	0.442184i
$31$			6.19835i			1.11326i	0.830761	+	0.556629i	$0.187905\pi$
$31$			6.19835i			1.11326i	−0.830761	+	0.556629i	$0.812095\pi$
$32$	−3.19794	−	4.66617i	−0.565322	−	0.824870i
$33$	0.581094	−	0.326615i	0.101155	−	0.0568564i
$34$	7.28066	+	6.35470i	1.24862	+	1.08982i
$35$	−2.50910	−	2.45141i	−0.424116	−	0.414364i
$36$	5.50018	+	2.39749i	0.916697	+	0.399582i
$37$	7.92081	−	4.57308i	1.30217	−	0.751810i	0.321396	−	0.946945i	$-0.395848\pi$
$37$	7.92081	−	4.57308i	1.30217	−	0.751810i	0.980776	+	0.195135i	$0.0625145\pi$
$38$	1.58988	+	4.64764i	0.257912	+	0.753947i
$39$	2.19969	−	1.23638i	0.352232	−	0.197979i
$40$	−3.35151	+	1.68232i	−0.529921	+	0.265999i
$41$	2.15658	−	1.24510i	0.336801	−	0.194452i	−0.322055	−	0.946721i	$-0.604374\pi$
$41$	2.15658	−	1.24510i	0.336801	−	0.194452i	0.658857	+	0.752269i	$0.271040\pi$
$42$	−2.85212	+	5.81940i	−0.440091	+	0.897953i
$43$	−1.64502	+	2.84926i	−0.250863	+	0.434508i	−0.963764	−	0.266757i	$-0.914048\pi$
$43$	−1.64502	+	2.84926i	−0.250863	+	0.434508i	0.712900	+	0.701265i	$0.247381\pi$
$44$	0.762650	−	0.104061i	0.114974	−	0.0156878i
$45$	2.06770	−	3.39784i	0.308235	−	0.506520i
$46$	−2.30429	+	2.64006i	−0.339750	+	0.389256i
$47$	3.96734			0.578696			0.289348	−	0.957224i	$-0.406562\pi$
$47$	3.96734			0.578696			0.289348	+	0.957224i	$0.406562\pi$
$48$	4.88860	+	4.90934i	0.705609	+	0.708602i
$49$	−6.14194	−	3.35806i	−0.877420	−	0.479723i
$50$	−1.48405	−	4.33827i	−0.209876	−	0.613524i
$51$	−10.1811	−	6.03573i	−1.42564	−	0.845171i
$52$	2.88695	−	0.393916i	0.400348	−	0.0546263i
$53$	−0.114978	+	0.199147i	−0.0157934	+	0.0273549i	−0.873814	−	0.486260i	$-0.838361\pi$
$53$	−0.114978	+	0.199147i	−0.0157934	+	0.0273549i	0.858021	+	0.513615i	$0.171694\pi$
$54$	−7.15729	−	1.66528i	−0.973984	−	0.226616i
$55$		−	0.510261i		−	0.0688036i
$56$	−5.53304	+	5.03840i	−0.739383	+	0.673285i
$57$	−2.94771	−	5.24437i	−0.390433	−	0.694634i
$58$	8.79633	−	10.0781i	1.15501	−	1.32332i
$59$		−	4.10518i		−	0.534449i	−0.963634	−	0.267224i	$-0.913894\pi$
$59$		−	4.10518i		−	0.534449i	0.963634	−	0.267224i	$-0.0861065\pi$
$60$	3.66275	−	2.77101i	0.472860	−	0.357736i
$61$		−	4.29926i		−	0.550463i	−0.961378	−	0.275232i	$-0.911245\pi$
$61$		−	4.29926i		−	0.550463i	0.961378	−	0.275232i	$-0.0887546\pi$
$62$	1.68987	−	8.60137i	0.214614	−	1.09237i
$63$	2.14190	−	7.64279i	0.269854	−	0.962901i
$64$	3.16559	+	7.34704i	0.395699	+	0.918380i
$65$		−	1.93156i		−	0.239580i
$66$	−0.895421	+	0.294815i	−0.110219	+	0.0362892i
$67$	14.9698			1.82885			0.914424	−	0.404758i	$-0.132644\pi$
$67$	14.9698			1.82885			0.914424	+	0.404758i	$0.132644\pi$
$68$	−8.37078	−	10.8033i	−1.01511	−	1.31009i
$69$	2.18863	−	3.69180i	0.263480	−	0.444441i
$70$	2.81351	+	4.08585i	0.336279	+	0.488352i
$71$	5.68595			0.674798			0.337399	−	0.941362i	$-0.390453\pi$
$71$	5.68595			0.674798			0.337399	+	0.941362i	$0.390453\pi$
$72$	−6.97889	−	4.82649i	−0.822470	−	0.568808i
$73$	−6.97110	+	12.0743i	−0.815906	+	1.41319i	0.0927701	+	0.995688i	$0.470428\pi$
$73$	−6.97110	+	12.0743i	−0.815906	+	1.41319i	−0.908676	+	0.417503i	$0.862905\pi$
$74$	−12.2384	+	4.18653i	−1.42268	+	0.486674i
$75$	2.75149	+	4.89528i	0.317715	+	0.565258i
$76$	−0.939154	−	6.88292i	−0.107728	−	0.789525i
$77$	−0.274960	−	0.980412i	−0.0313346	−	0.111728i
$78$	−3.38955	+	1.11600i	−0.383791	+	0.126362i
$79$		−	4.78615i		−	0.538484i	−0.963073	−	0.269242i	$-0.913227\pi$
$79$		−	4.78615i		−	0.538484i	0.963073	−	0.269242i	$-0.0867731\pi$
$80$	5.10950	−	1.42081i	0.571260	−	0.158851i
$81$	8.99042	+	0.415145i	0.998936	+	0.0461273i
$82$	−3.33211	+	1.13986i	−0.367970	+	0.125876i
$83$	6.63767	+	3.83226i	0.728579	+	0.420645i	0.817902	−	0.575357i	$-0.195137\pi$
$83$	6.63767	+	3.83226i	0.728579	+	0.420645i	−0.0893229	+	0.996003i	$0.528470\pi$
$84$	5.54440	−	7.29792i	0.604943	−	0.796268i
$85$	−7.84618	+	4.52999i	−0.851038	+	0.491347i
$86$	3.05957	−	3.50539i	0.329922	−	0.377996i
$87$	−8.35481	+	14.0930i	−0.895729	+	1.51092i
$88$	−1.08669	−	0.0635186i	−0.115841	−	0.00677110i
$89$	−5.36142	+	3.09542i	−0.568310	+	0.328114i	−0.756474	−	0.654024i	$-0.773080\pi$
$89$	−5.36142	+	3.09542i	−0.568310	+	0.328114i	0.188164	+	0.982138i	$0.439746\pi$
$90$	−3.79568	+	4.15141i	−0.400100	+	0.437598i
$91$	−1.04084	−	3.71128i	−0.109110	−	0.389047i
$92$	3.91740	−	3.03535i	0.408417	−	0.316457i
$93$	−0.123845	+	10.7351i	−0.0128422	+	1.11318i
$94$	−5.50542	−	1.08162i	−0.567840	−	0.111561i
$95$	−4.60511			−0.472474
$96$	−5.44540	−	8.14541i	−0.555769	−	0.831337i
$97$	−5.48708	+	9.50389i	−0.557128	+	0.964974i	0.440606	+	0.897700i	$0.354763\pi$
$97$	−5.48708	+	9.50389i	−0.557128	+	0.964974i	−0.997735	+	0.0672738i	$0.978570\pi$
$98$	7.60756	+	6.33443i	0.768480	+	0.639874i
$99$	1.01294	−	0.554066i	0.101805	−	0.0556858i
$100$	0.876638	+	6.42475i	0.0876638	+	0.642475i
$101$	5.38231	+	9.32243i	0.535559	+	0.927616i	0.999136	+	0.0415592i	$0.0132325\pi$
$101$	5.38231	+	9.32243i	0.535559	+	0.927616i	−0.463577	+	0.886057i	$0.653434\pi$
$102$	12.4827	+	11.1514i	1.23597	+	1.10415i
$103$	−13.2674	−	7.65993i	−1.30727	−	0.754756i	−0.325634	−	0.945496i	$-0.605578\pi$
$103$	−13.2674	−	7.65993i	−1.30727	−	0.754756i	−0.981641	+	0.190740i	$0.938911\pi$
$104$	−4.11358	−	0.240445i	−0.403369	−	0.0235775i
$105$	−4.29662	−	4.29582i	−0.419307	−	0.419229i
$106$	0.213847	−	0.245007i	0.0207706	−	0.0237972i
$107$	10.7046	−	6.18030i	1.03485	−	0.597472i	0.116481	−	0.993193i	$-0.462839\pi$
$107$	10.7046	−	6.18030i	1.03485	−	0.597472i	0.918371	+	0.395721i	$0.129505\pi$
$108$	9.47806	+	4.26220i	0.912027	+	0.410130i
$109$	1.64974	+	0.952480i	0.158017	+	0.0912310i	0.576923	−	0.816798i	$-0.304253\pi$
$109$	1.64974	+	0.952480i	0.158017	+	0.0912310i	−0.418906	+	0.908029i	$0.637586\pi$
$110$	−0.139114	+	0.708082i	−0.0132640	+	0.0675130i
$111$	13.8097	−	7.76202i	1.31076	−	0.736738i
$112$	9.05175	−	5.48324i	0.855310	−	0.518117i
$113$	−14.1944	+	8.19513i	−1.33530	+	0.770933i	−0.986106	−	0.166119i	$-0.946877\pi$
$113$	−14.1944	+	8.19513i	−1.33530	+	0.770933i	−0.349190	+	0.937052i	$0.613543\pi$
$114$	2.66070	+	8.08118i	0.249198	+	0.756872i
$115$	−1.64263	−	2.84512i	−0.153176	−	0.265309i
$116$	−14.9542	+	11.5870i	−1.38846	+	1.07583i
$117$	3.83442	−	2.09738i	0.354492	−	0.193903i
$118$	−1.11920	+	5.69670i	−0.103031	+	0.524423i
$119$	−12.6346	+	12.9319i	−1.15821	+	1.18547i
$120$	−5.83822	+	2.84671i	−0.532954	+	0.259868i
$121$	−5.42594	+	9.39801i	−0.493267	+	0.854364i
$122$	−1.17212	+	5.96602i	−0.106118	+	0.540138i
$123$	3.75994	−	2.11335i	0.339022	−	0.190554i
$124$	−4.69002	+	11.4753i	−0.421176	+	1.03051i
$125$	10.9278			0.977410
$126$	−5.05596	+	10.0218i	−0.450420	+	0.892817i
$127$			0.512322i			0.0454612i	0.999742	+	0.0227306i	$0.00723601\pi$
$127$			0.512322i			0.0454612i	−0.999742	+	0.0227306i	$0.992764\pi$
$128$	−2.38980	−	11.0584i	−0.211231	−	0.977436i
$129$	−2.90600	+	4.90187i	−0.255859	+	0.431585i
$130$	−0.526604	+	2.68039i	−0.0461862	+	0.235086i
$131$	11.2103	+	6.47227i	0.979449	+	0.565485i	0.902104	−	0.431519i	$-0.142022\pi$
$131$	11.2103	+	6.47227i	0.979449	+	0.565485i	0.0773452	+	0.997004i	$0.475356\pi$
$132$	1.32294	−	0.164989i	0.115147	−	0.0143605i
$133$	−8.84823	+	2.48151i	−0.767238	+	0.215175i
$134$	−20.7733	−	4.08124i	−1.79454	−	0.352565i
$135$	3.64901	−	5.84353i	0.314057	−	0.502931i
$136$	8.67069	+	17.2737i	0.743505	+	1.48121i
$137$	−4.19165	+	2.42005i	−0.358117	+	0.206759i	−0.668255	−	0.743933i	$-0.732958\pi$
$137$	−4.19165	+	2.42005i	−0.358117	+	0.206759i	0.310137	+	0.950692i	$0.399625\pi$
$138$	−4.04364	+	4.52637i	−0.344217	+	0.385310i
$139$	0.324362	+	0.561811i	0.0275120	+	0.0476522i	0.879454	−	0.475985i	$-0.157908\pi$
$139$	0.324362	+	0.561811i	0.0275120	+	0.0476522i	−0.851942	+	0.523637i	$0.824575\pi$
$140$	−2.79033	−	6.43693i	−0.235826	−	0.544020i
$141$	6.87117	+	0.0792688i	0.578657	+	0.00667563i
$142$	−7.89031	−	1.55017i	−0.662140	−	0.130088i
$143$	0.280341	−	0.485564i	0.0234433	−	0.0406049i
$144$	8.36865	+	8.60033i	0.697388	+	0.716694i
$145$	6.27053	+	10.8609i	0.520739	+	0.901946i
$146$	12.9655	−	14.8548i	1.07304	−	1.22939i
$147$	−10.5703	−	5.93867i	−0.871827	−	0.489813i
$148$	18.1244	−	2.47302i	1.48981	−	0.203281i
$149$	−11.5821	+	20.0608i	−0.948841	+	1.64344i	−0.200970	+	0.979597i	$0.564409\pi$
$149$	−11.5821	+	20.0608i	−0.948841	+	1.64344i	−0.747871	+	0.663844i	$0.768924\pi$
$150$	−2.48359	−	7.54326i	−0.202785	−	0.615904i
$151$	−5.68656	+	3.28313i	−0.462765	+	0.267178i	−0.713206	−	0.700954i	$-0.752758\pi$
$151$	−5.68656	+	3.28313i	−0.462765	+	0.267178i	0.250441	+	0.968132i	$0.419424\pi$
$152$	−0.573255	+	9.80737i	−0.0464972	+	0.795483i
$153$	−17.5125	−	10.6569i	−1.41580	−	0.861561i
$154$	0.114266	+	1.43547i	0.00920781	+	0.115673i
$155$	7.11703	+	4.10902i	0.571654	+	0.330044i
$156$	5.00789	−	0.624555i	0.400952	−	0.0500044i
$157$		−	6.42333i		−	0.512638i	−0.966592	−	0.256319i	$-0.917490\pi$
$157$		−	6.42333i		−	0.512638i	0.966592	−	0.256319i	$-0.0825097\pi$
$158$	−1.30486	+	6.64167i	−0.103809	+	0.528383i
$159$	−0.203113	+	0.342612i	−0.0161079	+	0.0271709i
$160$	−7.47774	+	0.578616i	−0.591167	+	0.0457436i
$161$	−4.68927	−	4.58145i	−0.369566	−	0.361069i
$162$	−12.3627	−	3.02717i	−0.971305	−	0.237837i
$163$	−4.23961	−	7.34321i	−0.332072	−	0.575165i	0.650846	−	0.759210i	$-0.274414\pi$
$163$	−4.23961	−	7.34321i	−0.332072	−	0.575165i	−0.982918	+	0.184045i	$0.941081\pi$
$164$	4.93469	−	0.673323i	0.385334	−	0.0525777i
$165$	0.0101952	−	0.883740i	0.000793695	−	0.0687990i
$166$	−8.16621	−	7.12762i	−0.633820	−	0.553211i
$167$	6.44985	+	11.1715i	0.499105	+	0.864474i	0.999999	−	0.00103366i	$-0.000329023\pi$
$167$	6.44985	+	11.1715i	0.499105	+	0.864474i	−0.500895	+	0.865508i	$0.666996\pi$
$168$	−9.68353	+	8.61564i	−0.747101	+	0.664711i
$169$	−5.43879	+	9.42026i	−0.418369	+	0.724636i
$170$	12.1231	−	4.14709i	0.929796	−	0.318067i
$171$	−5.00045	−	9.14181i	−0.382394	−	0.699092i
$172$	−5.20141	+	4.03024i	−0.396603	+	0.307303i
$173$	−5.51544			−0.419331			−0.209665	−	0.977773i	$-0.567237\pi$
$173$	−5.51544			−0.419331			−0.209665	+	0.977773i	$0.567237\pi$
$174$	15.4360	−	17.2788i	1.17020	−	1.30990i
$175$	8.25924	−	2.31633i	0.624340	−	0.175098i
$176$	1.49067	+	0.384410i	0.112363	+	0.0289760i
$177$	0.0820228	−	7.10990i	0.00616521	−	0.534413i
$178$	8.28388	−	2.83377i	0.620903	−	0.212400i
$179$	5.94365	+	3.43157i	0.444250	+	0.256488i	0.705399	−	0.708811i	$-0.250768\pi$
$179$	5.94365	+	3.43157i	0.444250	+	0.256488i	−0.261149	+	0.965298i	$0.584101\pi$
$180$	6.39902	−	4.72603i	0.476955	−	0.352258i
$181$			4.70643i			0.349826i	0.984584	+	0.174913i	$0.0559645\pi$
$181$			4.70643i			0.349826i	−0.984584	+	0.174913i	$0.944036\pi$
$182$	0.432545	+	5.43385i	0.0320624	+	0.402784i
$183$	0.0859006	−	7.44603i	0.00634996	−	0.550427i
$184$	−6.26366	+	3.14410i	−0.461763	+	0.231786i
$185$		−	12.1264i		−	0.891548i
$186$	3.09861	−	14.8632i	0.227201	−	1.08983i
$187$	−2.62988			−0.192316
$188$	7.34490	+	3.00191i	0.535682	+	0.218937i
$189$	3.86234	−	13.1940i	0.280944	−	0.959724i
$190$	6.39045	+	1.25550i	0.463612	+	0.0910837i
$191$	−8.76411			−0.634149			−0.317074	−	0.948401i	$-0.602700\pi$
$191$	−8.76411			−0.634149			−0.317074	+	0.948401i	$0.602700\pi$
$192$	5.33580	+	12.7879i	0.385078	+	0.922884i
$193$	2.38834			0.171917			0.0859583	−	0.996299i	$-0.472605\pi$
$193$	2.38834			0.171917			0.0859583	+	0.996299i	$0.472605\pi$
$194$	10.2054	−	11.6925i	0.732705	−	0.839470i
$195$	0.0385931	−	3.34533i	0.00276371	−	0.239564i
$196$	−8.82994	−	10.8643i	−0.630710	−	0.776019i
$197$	3.13757			0.223542			0.111771	−	0.993734i	$-0.464348\pi$
$197$	3.13757			0.223542			0.111771	+	0.993734i	$0.464348\pi$
$198$	−1.55670	+	0.492709i	−0.110630	+	0.0350153i
$199$	−14.1237	−	8.15431i	−1.00120	−	0.578044i	−0.0925978	−	0.995704i	$-0.529517\pi$
$199$	−14.1237	−	8.15431i	−1.00120	−	0.578044i	−0.908604	+	0.417660i	$0.862850\pi$
$200$	0.535096	−	9.15454i	0.0378370	−	0.647324i
$201$	25.9267	+	0.299101i	1.82873	+	0.0210970i
$202$	−4.92735	−	14.4040i	−0.346687	−	1.01346i
$203$	17.9006	+	17.4891i	1.25638	+	1.22749i
$204$	−14.2818	−	18.8778i	−0.999925	−	1.32171i
$205$		−	3.30162i		−	0.230595i
$206$	16.3226	+	14.2467i	1.13725	+	0.992614i
$207$	3.86433	−	6.35024i	0.268590	−	0.441372i
$208$	5.64280	+	1.45516i	0.391258	+	0.100897i
$209$	−1.15766	−	0.668373i	−0.0800768	−	0.0462323i
$210$	4.79118	+	7.13264i	0.330623	+	0.492199i
$211$	−3.53108	−	6.11602i	−0.243090	−	0.421044i	0.718503	−	0.695524i	$-0.244828\pi$
$211$	−3.53108	−	6.11602i	−0.243090	−	0.421044i	−0.961593	+	0.274480i	$0.911494\pi$
$212$	−0.363549	+	0.281691i	−0.0249686	+	0.0193466i
$213$	9.84770	+	0.113607i	0.674753	+	0.00778424i
$214$	−16.5396	+	5.65790i	−1.13062	+	0.386766i
$215$	2.18104	+	3.77767i	0.148746	+	0.257635i
$216$	−11.9906	−	8.49862i	−0.815854	−	0.578258i
$217$	15.8888	+	4.05995i	1.07860	+	0.275607i
$218$	−2.02965	−	1.77152i	−0.137465	−	0.119982i
$219$	−12.3147	+	20.7726i	−0.832153	+	1.40368i
$220$	0.386092	−	0.944669i	0.0260303	−	0.0636895i
$221$	−9.95523			−0.669661
$222$	−21.2797	+	7.00627i	−1.42820	+	0.470230i
$223$	0.571432	+	0.329917i	0.0382659	+	0.0220928i	0.519011	−	0.854768i	$-0.326300\pi$
$223$	0.571432	+	0.329917i	0.0382659	+	0.0220928i	−0.480745	+	0.876860i	$0.659634\pi$
$224$	−14.0559	+	5.14121i	−0.939148	+	0.343512i
$225$	4.66760	+	8.53329i	0.311173	+	0.568886i
$226$	21.9316	−	7.50242i	1.45887	−	0.499054i
$227$	−4.46278	+	2.57659i	−0.296205	+	0.171014i	−0.640737	−	0.767761i	$-0.721371\pi$
$227$	−4.46278	+	2.57659i	−0.296205	+	0.171014i	0.344532	+	0.938775i	$0.388038\pi$
$228$	−1.48903	−	11.9395i	−0.0986135	−	0.790715i
$229$	−19.7160	−	11.3831i	−1.30287	−	0.752213i	−0.321976	−	0.946748i	$-0.604347\pi$
$229$	−19.7160	−	11.3831i	−1.30287	−	0.752213i	−0.980896	+	0.194534i	$0.937680\pi$
$230$	1.50379	+	4.39597i	0.0991567	+	0.289862i
$231$	−0.456624	−	1.70350i	−0.0300436	−	0.112082i
$232$	23.9107	−	12.0022i	1.56981	−	0.787981i
$233$	7.77316	−	4.48784i	0.509237	−	0.294008i	−0.223283	−	0.974754i	$-0.571677\pi$
$233$	7.77316	−	4.48784i	0.509237	−	0.294008i	0.732520	+	0.680746i	$0.238344\pi$
$234$	−5.89278	+	1.86511i	−0.385223	+	0.121926i
$235$	2.63003	−	4.55535i	0.171564	−	0.297158i
$236$	3.10621	−	7.60009i	0.202197	−	0.494724i
$237$	0.0956289	−	8.28930i	0.00621176	−	0.538448i
$238$	21.0584	−	14.5008i	1.36502	−	0.939949i
$239$	3.16867	+	5.48830i	0.204964	+	0.355008i	0.950121	−	0.311881i	$-0.100959\pi$
$239$	3.16867	+	5.48830i	0.204964	+	0.355008i	−0.745157	+	0.666889i	$0.767626\pi$
$240$	8.87772	−	2.35865i	0.573054	−	0.152250i
$241$	−11.3225	−	19.6112i	−0.729349	−	1.26327i	−0.957159	−	0.289563i	$-0.906490\pi$
$241$	−11.3225	−	19.6112i	−0.729349	−	1.26327i	0.227810	−	0.973706i	$-0.426843\pi$
$242$	10.0917	−	11.5622i	0.648719	−	0.743246i
$243$	15.5625	+	0.898637i	0.998337	+	0.0576476i
$244$	3.25306	−	7.95940i	0.208256	−	0.509548i
$245$	−7.92739	+	4.82612i	−0.506463	+	0.308330i
$246$	−5.79378	+	1.90758i	−0.369398	+	0.121623i
$247$	−4.38222	−	2.53008i	−0.278834	−	0.160985i
$248$	9.63680	−	14.6454i	0.611938	−	0.929986i
$249$	11.4195	+	6.76985i	0.723678	+	0.429022i
$250$	−15.1643	−	2.97926i	−0.959076	−	0.188425i
$251$		−	15.3611i		−	0.969587i	−0.874629	−	0.484793i	$-0.838895\pi$
$251$		−	15.3611i		−	0.969587i	0.874629	−	0.484793i	$-0.161105\pi$
$252$	9.74836	−	12.5287i	0.614089	−	0.789237i
$253$		−	0.953629i		−	0.0599541i
$254$	0.139676	−	0.710942i	0.00876402	−	0.0446085i
$255$	−13.6796	+	7.68889i	−0.856649	+	0.481497i
$256$	0.301413	+	15.9972i	0.0188383	+	0.999823i
$257$	−12.9129	−	7.45524i	−0.805482	−	0.465045i	0.0399026	−	0.999204i	$-0.487295\pi$
$257$	−12.9129	−	7.45524i	−0.805482	−	0.465045i	−0.845384	+	0.534158i	$0.820629\pi$
$258$	5.36902	−	6.00998i	0.334261	−	0.374165i
$259$	−6.53442	−	23.2995i	−0.406029	−	1.44776i
$260$	1.46152	−	3.57597i	0.0906398	−	0.221772i
$261$	−14.7516	+	24.2412i	−0.913099	+	1.50049i
$262$	−13.7918	−	12.0378i	−0.852062	−	0.743696i
$263$	9.15450	+	15.8561i	0.564491	+	0.977727i	0.997097	+	0.0761438i	$0.0242608\pi$
$263$	9.15450	+	15.8561i	0.564491	+	0.977727i	−0.432606	+	0.901583i	$0.642406\pi$
$264$	−1.88081	−	0.131722i	−0.115756	−	0.00810696i
$265$	0.152442	+	0.264037i	0.00936444	+	0.0162197i
$266$	12.9551	−	1.03125i	0.794328	−	0.0632300i
$267$	−9.34749	+	5.25394i	−0.572057	+	0.321536i
$268$	27.7142	+	11.3270i	1.69291	+	0.691904i
$269$	12.4665	−	21.5926i	0.760095	−	1.31652i	−0.182706	−	0.983168i	$-0.558486\pi$
$269$	12.4665	−	21.5926i	0.760095	−	1.31652i	0.942801	−	0.333356i	$-0.108181\pi$
$270$	−6.65682	+	7.11414i	−0.405121	+	0.432953i
$271$	12.5772	−	7.26146i	0.764012	−	0.441102i	−0.0667224	−	0.997772i	$-0.521254\pi$
$271$	12.5772	−	7.26146i	0.764012	−	0.441102i	0.830734	+	0.556669i	$0.187921\pi$
$272$	−7.32282	−	26.3344i	−0.444011	−	1.59676i
$273$	−1.72851	−	6.44849i	−0.104614	−	0.390280i
$274$	6.47648	−	2.21549i	0.391259	−	0.133843i
$275$	1.08060	+	0.623883i	0.0651624	+	0.0376215i
$276$	6.84533	−	5.17876i	0.412041	−	0.311725i
$277$	−26.8457	+	15.4994i	−1.61300	+	0.931268i	−0.624334	+	0.781158i	$0.714630\pi$
$277$	−26.8457	+	15.4994i	−1.61300	+	0.931268i	−0.988669	+	0.150110i	$0.952037\pi$
$278$	−0.296944	−	0.868048i	−0.0178095	−	0.0520621i
$279$	−0.428984	+	18.5901i	−0.0256826	+	1.11296i
$280$	2.11719	+	9.69317i	0.126527	+	0.579278i
$281$	18.9063	+	10.9155i	1.12785	+	0.651166i	0.943394	−	0.331674i	$-0.107614\pi$
$281$	18.9063	+	10.9155i	1.12785	+	0.651166i	0.184459	+	0.982840i	$0.440947\pi$
$282$	−9.51342	−	1.98330i	−0.566516	−	0.118104i
$283$	25.1118			1.49274			0.746372	−	0.665529i	$-0.231794\pi$
$283$	25.1118			1.49274			0.746372	+	0.665529i	$0.231794\pi$
$284$	10.5266	+	4.30231i	0.624641	+	0.255295i
$285$	−7.97575	−	0.0920117i	−0.472443	−	0.00545030i
$286$	−0.521405	+	0.597381i	−0.0308313	+	0.0353239i
$287$	−1.77911	−	6.34371i	−0.105018	−	0.374457i
$288$	−9.26833	−	14.2161i	−0.546142	−	0.837693i
$289$	14.8476	+	25.7167i	0.873386	+	1.51275i
$290$	−5.74050	−	16.7810i	−0.337094	−	0.985416i
$291$	−9.69315	+	16.3505i	−0.568223	+	0.958483i
$292$	−22.0420	+	17.0790i	−1.28991	+	0.999470i
$293$	−12.5864	−	21.8003i	−0.735304	−	1.27358i	−0.954590	−	0.297924i	$-0.903706\pi$
$293$	−12.5864	−	21.8003i	−0.735304	−	1.27358i	0.219285	−	0.975661i	$-0.429627\pi$
$294$	13.0492	+	11.1228i	0.761047	+	0.648696i
$295$	−4.71362	−	2.72141i	−0.274437	−	0.158447i
$296$	−25.8252	−	1.50952i	−1.50106	−	0.0877390i
$297$	1.76542	−	0.939368i	0.102440	−	0.0545077i
$298$	21.5415	−	24.6804i	1.24787	−	1.42970i
$299$		−	3.60989i		−	0.208765i
$300$	1.38991	+	11.1448i	0.0802466	+	0.643444i
$301$	6.22627	+	6.08311i	0.358876	+	0.350624i
$302$	8.78624	−	3.00562i	0.505591	−	0.172954i
$303$	9.13554	+	16.2534i	0.524823	+	0.933732i
$304$	3.46930	−	13.4533i	0.198978	−	0.771597i
$305$	−4.93646	−	2.85007i	−0.282661	−	0.163194i
$306$	21.3964	+	19.5629i	1.22315	+	1.11834i
$307$	−9.51936			−0.543299			−0.271649	−	0.962396i	$-0.587569\pi$
$307$	−9.51936			−0.543299			−0.271649	+	0.962396i	$0.587569\pi$
$308$	0.232789	−	2.02313i	0.0132644	−	0.115278i
$309$	−22.8252	−	13.5316i	−1.29848	−	0.769786i
$310$	−8.75595	−	7.64236i	−0.497305	−	0.434057i
$311$	−21.7967			−1.23598			−0.617989	−	0.786187i	$-0.712052\pi$
$311$	−21.7967			−1.23598			−0.617989	+	0.786187i	$0.712052\pi$
$312$	−7.11965	−	0.498625i	−0.403071	−	0.0282291i
$313$	6.49725			0.367246			0.183623	−	0.982997i	$-0.441217\pi$
$313$	6.49725			0.367246			0.183623	+	0.982997i	$0.441217\pi$
$314$	−1.75121	+	8.91356i	−0.0988263	+	0.503021i
$315$	−7.35564	−	7.52593i	−0.414443	−	0.424038i
$316$	3.62147	−	8.86080i	0.203723	−	0.498459i
$317$	23.9888			1.34735			0.673674	−	0.739029i	$-0.264715\pi$
$317$	23.9888			1.34735			0.673674	+	0.739029i	$0.264715\pi$
$318$	0.375264	−	0.420063i	0.0210438	−	0.0235560i
$319$			3.64035i			0.203820i
$320$	10.5345	+	1.23574i	0.588897	+	0.0690798i
$321$	18.6631	−	10.4900i	1.04168	−	0.585495i
$322$	5.25818	+	7.63606i	0.293027	+	0.425541i
$323$			23.7347i			1.32064i
$324$	16.3302	+	7.57123i	0.907235	+	0.420624i
$325$	4.09052	+	2.36166i	0.226901	+	0.131001i
$326$	3.88124	+	11.3459i	0.214962	+	0.628393i
$327$	2.83822	+	1.68260i	0.156954	+	0.0930478i
$328$	−7.03136	−	0.410994i	−0.388242	−	0.0226933i
$329$	2.59862	−	10.1698i	0.143267	−	0.560681i
$330$	−0.255084	+	1.22357i	−0.0140419	+	0.0673555i
$331$	−0.456546			−0.0250941			−0.0125470	−	0.999921i	$-0.503994\pi$
$331$	−0.456546			−0.0250941			−0.0125470	+	0.999921i	$0.503994\pi$
$332$	9.38891	+	12.1173i	0.515283	+	0.665021i
$333$	24.0726	−	13.1674i	1.31917	−	0.721569i
$334$	−5.90466	−	17.2609i	−0.323089	−	0.944476i
$335$	9.92377	−	17.1885i	0.542194	−	0.939107i
$336$	15.7866	−	9.31576i	0.861230	−	0.508216i
$337$	−12.0089	−	20.8000i	−0.654165	−	1.13305i	−0.982102	−	0.188348i	$-0.939687\pi$
$337$	−12.0089	−	20.8000i	−0.654165	−	1.13305i	0.327937	−	0.944699i	$-0.393647\pi$
$338$	10.1156	−	11.5896i	0.550216	−	0.630390i
$339$	−24.7475	+	13.9098i	−1.34410	+	0.755479i
$340$	−17.9536	+	2.44972i	−0.973672	+	0.132855i
$341$	1.19274	+	2.06589i	0.0645907	+	0.111874i
$342$	4.44670	+	14.0493i	0.240450	+	0.759696i
$343$	−12.6310	+	13.5446i	−0.682011	+	0.731342i
$344$	8.31669	−	4.17464i	0.448406	−	0.225081i
$345$	−2.78809	−	4.96039i	−0.150106	−	0.267058i
$346$	7.65369	+	1.50369i	0.411465	+	0.0808386i
$347$			14.4482i			0.775618i	0.921740	+	0.387809i	$0.126768\pi$
$347$			14.4482i			0.775618i	−0.921740	+	0.387809i	$0.873232\pi$
$348$	−26.1311	+	19.7692i	−1.40078	+	1.05974i
$349$	4.81930	+	2.78242i	0.257971	+	0.148940i	0.623409	−	0.781896i	$-0.285747\pi$
$349$	4.81930	+	2.78242i	0.257971	+	0.148940i	−0.365438	+	0.930836i	$0.619081\pi$
$350$	−12.0927	+	0.962605i	−0.646384	+	0.0514534i
$351$	6.68287	−	3.55591i	0.356705	−	0.189800i
$352$	−1.96377	−	0.939844i	−0.104669	−	0.0500938i
$353$	20.2317	−	11.6808i	1.07682	−	0.621705i	0.146786	−	0.989168i	$-0.453107\pi$
$353$	20.2317	−	11.6808i	1.07682	−	0.621705i	0.930038	+	0.367464i	$0.119774\pi$
$354$	−2.05221	+	9.84395i	−0.109074	+	0.523200i
$355$	3.76933	−	6.52868i	0.200056	−	0.346506i
$356$	−12.2680	+	1.67393i	−0.650203	+	0.0887182i
$357$	−22.1406	+	22.1448i	−1.17181	+	1.17203i
$358$	−7.31237	−	6.38237i	−0.386471	−	0.337319i
$359$	−13.6790	−	23.6928i	−0.721953	−	1.25046i	−0.960216	−	0.279258i	$-0.909912\pi$
$359$	−13.6790	−	23.6928i	−0.721953	−	1.25046i	0.238264	−	0.971201i	$-0.423422\pi$
$360$	−10.1683	+	4.81367i	−0.535916	+	0.253703i
$361$	3.46793	−	6.00663i	0.182522	−	0.316138i
$362$	1.28313	−	6.53105i	0.0674396	−	0.343264i
$363$	−9.58516	+	16.1683i	−0.503090	+	0.848617i
$364$	0.881206	−	7.65840i	0.0461878	−	0.401409i
$365$	9.24258	+	16.0086i	0.483779	+	0.837929i
$366$	−2.14923	+	10.3093i	−0.112342	+	0.538878i
$367$	−21.9367	+	12.6651i	−1.14509	+	0.661115i	−0.947685	−	0.319208i	$-0.896583\pi$
$367$	−21.9367	+	12.6651i	−1.14509	+	0.661115i	−0.197400	+	0.980323i	$0.563250\pi$
$368$	9.54917	−	2.65535i	0.497785	−	0.138420i
$369$	6.55419	−	3.58506i	0.341198	−	0.186631i
$370$	−3.30604	+	16.8276i	−0.171873	+	0.874824i
$371$	0.435181	+	0.425175i	0.0225935	+	0.0220740i
$372$	−8.35209	+	19.7807i	−0.433036	+	1.02558i
$373$	18.0358	+	10.4130i	0.933858	+	0.539163i	0.888030	−	0.459786i	$-0.152074\pi$
$373$	18.0358	+	10.4130i	0.933858	+	0.539163i	0.0458283	+	0.998949i	$0.485407\pi$
$374$	3.64945	+	0.716991i	0.188709	+	0.0370747i
$375$	18.9262	+	0.218341i	0.977345	+	0.0112751i
$376$	−9.37400	−	6.16816i	−0.483427	−	0.318099i
$377$			13.7803i			0.709720i
$378$	−8.95683	+	17.2562i	−0.460690	+	0.887561i
$379$	−34.5563			−1.77504			−0.887518	−	0.460773i	$-0.847572\pi$
$379$	−34.5563			−1.77504			−0.887518	+	0.460773i	$0.847572\pi$
$380$	−8.52564	−	3.48448i	−0.437356	−	0.178750i
$381$	−0.0102364	+	0.887309i	−0.000524425	+	0.0454582i
$382$	12.1618	+	2.38938i	0.622253	+	0.122251i
$383$	6.79383	−	11.7673i	0.347148	−	0.601278i	−0.638593	−	0.769544i	$-0.720483\pi$
$383$	6.79383	−	11.7673i	0.347148	−	0.601278i	0.985742	+	0.168266i	$0.0538167\pi$
$384$	−3.91804	−	19.2002i	−0.199941	−	0.979808i
$385$	−1.30800	−	0.334223i	−0.0666618	−	0.0170336i
$386$	−3.31427	−	0.651139i	−0.168692	−	0.0331421i
$387$	−5.13094	+	8.43165i	−0.260821	+	0.428605i
$388$	−17.3496	+	13.4431i	−0.880794	+	0.682472i
$389$	−4.85170	−	8.40339i	−0.245991	−	0.426069i	0.716419	−	0.697670i	$-0.245780\pi$
$389$	−4.85170	−	8.40339i	−0.245991	−	0.426069i	−0.962410	+	0.271602i	$0.912447\pi$
$390$	−0.965600	+	4.63174i	−0.0488950	+	0.234537i
$391$	−14.6638	+	8.46612i	−0.741578	+	0.428150i
$392$	9.29123	+	17.4835i	0.469278	+	0.883050i
$393$	19.2862	+	11.4335i	0.972861	+	0.576746i
$394$	−4.35396	−	0.855402i	−0.219349	−	0.0430945i
$395$	−5.49552	−	3.17284i	−0.276509	−	0.159643i
$396$	2.29454	−	0.259318i	0.115305	−	0.0130312i
$397$	3.33701	−	1.92662i	0.167480	−	0.0966945i	−0.413917	−	0.910315i	$-0.635840\pi$
$397$	3.33701	−	1.92662i	0.167480	−	0.0966945i	0.581397	+	0.813620i	$0.302506\pi$
$398$	17.3761	+	15.1662i	0.870985	+	0.760213i
$399$	−15.3741	+	4.12103i	−0.769670	+	0.206310i
$400$	−3.23837	+	12.5577i	−0.161918	+	0.627887i
$401$	−5.12244	−	2.95744i	−0.255803	−	0.147688i	0.366616	−	0.930372i	$-0.380516\pi$
$401$	−5.12244	−	2.95744i	−0.255803	−	0.147688i	−0.622418	+	0.782685i	$0.713850\pi$
$402$	−35.8965	−	7.48350i	−1.79036	−	0.373243i
$403$	4.51504	+	7.82028i	0.224910	+	0.389556i
$404$	2.91063	+	21.3316i	0.144809	+	1.06128i
$405$	6.43661	−	10.0477i	0.319838	−	0.499275i
$406$	−20.0724	−	29.1496i	−0.996176	−	1.44667i
$407$	1.75999	−	3.04839i	0.0872393	−	0.151103i
$408$	14.6719	+	30.0902i	0.726369	+	1.48968i
$409$	14.2590			0.705062			0.352531	−	0.935800i	$-0.385321\pi$
$409$	14.2590			0.705062			0.352531	+	0.935800i	$0.385321\pi$
$410$	−0.900128	+	4.58161i	−0.0444541	+	0.226270i
$411$	−7.30803	+	4.10763i	−0.360479	+	0.202614i
$412$	−18.7666	−	24.2200i	−0.924562	−	1.19323i
$413$	−10.5232	−	2.68891i	−0.517811	−	0.132313i
$414$	−7.09376	+	7.75859i	−0.348639	+	0.381314i
$415$	8.80051	−	5.08097i	0.432000	−	0.249415i
$416$	−7.43371	−	3.55771i	−0.364468	−	0.174431i
$417$	0.550548	+	0.979501i	0.0269605	+	0.0479664i
$418$	1.42424	+	1.24311i	0.0696620	+	0.0608023i
$419$	−11.1735	+	6.45102i	−0.545861	+	0.315153i	−0.747451	−	0.664317i	$-0.768723\pi$
$419$	−11.1735	+	6.45102i	−0.545861	+	0.315153i	0.201590	+	0.979470i	$0.435389\pi$
$420$	−4.70407	−	11.2041i	−0.229535	−	0.546704i
$421$	18.7578	+	10.8298i	0.914200	+	0.527814i	0.881780	−	0.471661i	$-0.156345\pi$
$421$	18.7578	+	10.8298i	0.914200	+	0.527814i	0.0324200	+	0.999474i	$0.489679\pi$
$422$	3.23261	+	9.44980i	0.157361	+	0.460009i
$423$	11.8988	+	0.274577i	0.578542	+	0.0133504i
$424$	0.581289	−	0.291784i	0.0282299	−	0.0141703i
$425$		−	22.1548i		−	1.07467i
$426$	−13.6345	−	2.84245i	−0.660595	−	0.137717i
$427$	−11.0207	−	2.81603i	−0.533328	−	0.136277i
$428$	24.4942	−	3.34216i	1.18397	−	0.161550i
$429$	0.495234	−	0.835365i	0.0239101	−	0.0403318i
$430$	−1.99668	−	5.83684i	−0.0962885	−	0.281477i
$431$	9.75413	−	16.8946i	0.469840	−	0.813786i	−0.529565	−	0.848269i	$-0.677645\pi$
$431$	9.75413	−	16.8946i	0.469840	−	0.813786i	0.999405	+	0.0344826i	$0.0109783\pi$
$432$	14.3221	+	15.0624i	0.689074	+	0.724691i
$433$	19.4916			0.936706			0.468353	−	0.883542i	$-0.344848\pi$
$433$	19.4916			0.936706			0.468353	+	0.883542i	$0.344848\pi$
$434$	−20.9418	−	9.96573i	−1.00524	−	0.478370i
$435$	10.6431	+	18.9356i	0.510300	+	0.907894i
$436$	2.33354	+	3.01166i	0.111756	+	0.144232i
$437$	−8.60651			−0.411705
$438$	22.7523	−	25.4685i	1.08715	−	1.21693i
$439$		−	10.1238i		−	0.483182i	−0.970378	−	0.241591i	$-0.922331\pi$
$439$		−	10.1238i		−	0.483182i	0.970378	−	0.241591i	$-0.0776691\pi$
$440$	−0.793322	+	1.20564i	−0.0378201	+	0.0574767i
$441$	−18.1885	−	10.4966i	−0.866119	−	0.499838i
$442$	13.8147	+	2.71412i	0.657099	+	0.129097i
$443$			6.88730i			0.327225i	0.986525	+	0.163613i	$0.0523147\pi$
$443$			6.88730i			0.327225i	−0.986525	+	0.163613i	$0.947685\pi$
$444$	31.4397	−	3.92098i	1.49206	−	0.186081i
$445$			8.20807i			0.389100i
$446$	−0.703022	−	0.613611i	−0.0332891	−	0.0290553i
$447$	−20.4602	+	34.5125i	−0.967736	+	1.63239i
$448$	20.9068	−	3.30230i	0.987754	−	0.156019i
$449$			32.6203i			1.53945i	0.638377	+	0.769724i	$0.279606\pi$
$449$			32.6203i			1.53945i	−0.638377	+	0.769724i	$0.720394\pi$
$450$	−4.15071	−	13.1141i	−0.195666	−	0.618203i
$451$	0.479188	−	0.829978i	0.0225641	−	0.0390821i
$452$	−32.4796	+	4.43174i	−1.52771	+	0.208452i
$453$	−9.91435	+	5.57256i	−0.465817	+	0.261822i
$454$	6.89539	−	2.35879i	0.323617	−	0.110704i
$455$	−4.95133	−	1.26518i	−0.232122	−	0.0593124i
$456$	−1.18880	+	16.9743i	−0.0556705	+	0.794894i
$457$	−24.9530			−1.16725			−0.583626	−	0.812023i	$-0.698366\pi$
$457$	−24.9530			−1.16725			−0.583626	+	0.812023i	$0.698366\pi$
$458$	24.2563	+	21.1713i	1.13342	+	0.989271i
$459$	−30.1175	−	18.8070i	−1.40577	−	0.877836i
$460$	−0.888298	−	6.51021i	−0.0414171	−	0.303540i
$461$	−4.73588	+	8.20278i	−0.220572	+	0.382042i	−0.954982	−	0.296665i	$-0.904126\pi$
$461$	−4.73588	+	8.20278i	−0.220572	+	0.382042i	0.734410	+	0.678706i	$0.237459\pi$
$462$	0.169220	+	2.48842i	0.00787283	+	0.115772i
$463$	22.3090	−	12.8801i	1.03679	−	0.598588i	0.117864	−	0.993030i	$-0.462395\pi$
$463$	22.3090	−	12.8801i	1.03679	−	0.598588i	0.918921	+	0.394441i	$0.129062\pi$
$464$	−36.4527	+	10.1364i	−1.69227	+	0.470572i
$465$	12.2441	+	7.25876i	0.567808	+	0.336617i
$466$	−12.0102	+	4.10849i	−0.556363	+	0.190322i
$467$	19.5107	−	11.2645i	0.902848	−	0.521260i	0.0247252	−	0.999694i	$-0.492129\pi$
$467$	19.5107	−	11.2645i	0.902848	−	0.521260i	0.878123	+	0.478434i	$0.158796\pi$
$468$	8.68582	−	0.981630i	0.401502	−	0.0453758i
$469$	9.80526	−	38.3733i	0.452765	−	1.77192i
$470$	−4.89159	+	5.60436i	−0.225632	+	0.258510i
$471$	0.128340	−	11.1248i	0.00591361	−	0.512603i
$472$	−6.38247	+	9.69969i	−0.293777	+	0.446464i
$473$			1.26620i			0.0582199i
$474$	−2.39263	+	11.4769i	−0.109897	+	0.527150i
$475$	5.63054	−	9.75239i	0.258347	−	0.447470i
$476$	−33.1759	+	14.3814i	−1.52061	+	0.659169i
$477$	−0.358624	+	0.589324i	−0.0164203	+	0.0269833i
$478$	−2.90083	−	8.47991i	−0.132681	−	0.387862i
$479$	3.50498	+	6.07080i	0.160147	+	0.277382i	0.934921	−	0.354856i	$-0.115470\pi$
$479$	3.50498	+	6.07080i	0.160147	+	0.277382i	−0.774775	+	0.632238i	$0.782137\pi$
$480$	−12.9625	+	0.852717i	−0.591656	+	0.0389210i
$481$	6.66230	−	11.5394i	0.303775	−	0.526153i
$482$	10.3655	+	30.3011i	0.472134	+	1.38018i
$483$	−8.02997	−	8.02847i	−0.365376	−	0.365308i
$484$	−17.1563	+	13.2934i	−0.779834	+	0.604244i
$485$	7.27499	+	12.6007i	0.330341	+	0.572167i
$486$	−21.3509	−	5.48987i	−0.968497	−	0.249026i
$487$	31.1644	+	17.9928i	1.41219	+	0.815330i	0.995595	−	0.0937610i	$-0.0298890\pi$
$487$	31.1644	+	17.9928i	1.41219	+	0.815330i	0.416598	+	0.909091i	$0.363222\pi$
$488$	−6.68421	+	10.1583i	−0.302580	+	0.459843i
$489$	−7.19601	−	12.8027i	−0.325415	−	0.578957i
$490$	12.3165	−	4.53588i	0.556402	−	0.204910i
$491$	−12.6196	+	7.28595i	−0.569516	+	0.328810i	−0.756956	−	0.653466i	$-0.773314\pi$
$491$	−12.6196	+	7.28595i	−0.569516	+	0.328810i	0.187440	+	0.982276i	$0.439981\pi$
$492$	8.56001	−	1.06756i	0.385915	−	0.0481291i
$493$	55.9769	−	32.3183i	2.52107	−	1.45554i
$494$	5.39136	+	4.70568i	0.242569	+	0.211719i
$495$	0.0353148	−	1.53038i	0.00158728	−	0.0687853i
$496$	−17.3657	+	17.6960i	−0.779742	+	0.794572i
$497$	3.72432	−	14.5753i	0.167059	−	0.653792i
$498$	−14.0009	−	12.5077i	−0.627397	−	0.560485i
$499$	−9.36168	+	16.2149i	−0.419086	+	0.725879i	−0.995848	−	0.0910339i	$-0.970983\pi$
$499$	−9.36168	+	16.2149i	−0.419086	+	0.725879i	0.576762	+	0.816913i	$0.304316\pi$
$500$	20.2311	+	8.26857i	0.904761	+	0.369782i
$501$	10.9475	+	19.4771i	0.489099	+	0.870174i
$502$	−4.18794	+	21.3164i	−0.186917	+	0.951399i
$503$	26.7559			1.19299			0.596493	−	0.802619i	$-0.296560\pi$
$503$	26.7559			1.19299			0.596493	+	0.802619i	$0.296560\pi$
$504$	−16.9434	+	14.7283i	−0.754719	+	0.656048i
$505$	14.2722			0.635103
$506$	−0.259990	+	1.32334i	−0.0115580	+	0.0588295i
$507$	−9.60786	+	16.2066i	−0.426700	+	0.719761i
$508$	−0.387652	+	0.948484i	−0.0171993	+	0.0420822i
$509$	7.25450	−	12.5652i	0.321550	−	0.556941i	−0.659258	−	0.751917i	$-0.729129\pi$
$509$	7.25450	−	12.5652i	0.321550	−	0.556941i	0.980808	+	0.194976i	$0.0624628\pi$
$510$	21.0792	−	6.94026i	0.933403	−	0.307320i
$511$	26.3850	+	25.7784i	1.16721	+	1.14037i
$512$	3.94307	−	22.2812i	0.174261	−	0.984700i
$513$	−8.47781	−	15.9329i	−0.374304	−	0.703457i
$514$	15.8864	+	13.8660i	0.700721	+	0.611603i
$515$	−17.5905	+	10.1559i	−0.775128	+	0.447521i
$516$	−9.08903	+	6.87619i	−0.400122	+	0.302708i
$517$	1.32230	−	0.763431i	0.0581548	−	0.0335757i
$518$	2.71553	+	34.1139i	0.119314	+	1.49888i
$519$	−9.55238	−	0.110200i	−0.419303	−	0.00483726i
$520$	−3.00306	+	4.56387i	−0.131693	+	0.200139i
$521$	−37.8042	−	21.8262i	−1.65623	−	0.956225i	−0.974431	−	0.224685i	$-0.927865\pi$
$521$	−37.8042	−	21.8262i	−1.65623	−	0.956225i	−0.681799	−	0.731540i	$-0.738802\pi$
$522$	27.0795	−	29.6174i	1.18524	−	1.29632i
$523$	−20.7539	−	35.9468i	−0.907504	−	1.57184i	−0.817521	−	0.575899i	$-0.804652\pi$
$523$	−20.7539	−	35.9468i	−0.907504	−	1.57184i	−0.0899828	−	0.995943i	$-0.528681\pi$
$524$	15.8568	+	20.4647i	0.692709	+	0.894006i
$525$	14.3508	−	3.84671i	0.626318	−	0.167884i
$526$	−8.38070	−	24.4990i	−0.365416	−	1.06821i
$527$	21.1779	−	36.6811i	0.922522	−	1.59786i
$528$	2.57406	+	0.695558i	0.112021	+	0.0302703i
$529$	8.43008	+	14.6013i	0.366525	+	0.634840i
$530$	−0.139557	−	0.407962i	−0.00606195	−	0.0177207i
$531$	0.284117	−	12.3123i	0.0123296	−	0.534306i
$532$	−18.2588	−	2.10093i	−0.791617	−	0.0910867i
$533$	1.81393	−	3.14182i	0.0785700	−	0.136087i
$534$	14.4038	−	4.74240i	0.623312	−	0.205224i
$535$		−	16.3882i		−	0.708524i
$536$	−35.3705	−	23.2740i	−1.52777	−	1.00529i
$537$	10.2255	+	6.06201i	0.441261	+	0.261595i
$538$	−23.1864	+	26.5650i	−0.999637	+	1.14530i
$539$	−2.69328	+	0.0626550i	−0.116008	+	0.00269874i
$540$	11.1771	−	8.05733i	0.480987	−	0.346732i
$541$	−18.3156	+	10.5745i	−0.787450	+	0.454634i	−0.839064	−	0.544033i	$-0.816897\pi$
$541$	−18.3156	+	10.5745i	−0.787450	+	0.454634i	0.0516141	+	0.998667i	$0.483563\pi$
$542$	−19.4329	+	6.64767i	−0.834716	+	0.285542i
$543$	−0.0940361	+	8.15124i	−0.00403548	+	0.349803i
$544$	2.98218	+	38.5403i	0.127860	+	1.65240i
$545$	2.18730	−	1.26284i	0.0936936	−	0.0540940i
$546$	0.640570	+	9.41972i	0.0274139	+	0.403127i
$547$	9.60052	−	16.6286i	0.410489	−	0.710987i	−0.584454	−	0.811427i	$-0.698691\pi$
$547$	9.60052	−	16.6286i	0.410489	−	0.710987i	0.994943	+	0.100439i	$0.0320248\pi$
$548$	−9.59134	+	1.30871i	−0.409722	+	0.0559053i
$549$	0.297549	−	12.8943i	0.0126991	−	0.550317i
$550$	−1.32944	−	1.16036i	−0.0566874	−	0.0494779i
$551$	32.8542			1.39964
$552$	−10.9111	+	5.32023i	−0.464406	+	0.226444i
$553$	−12.2688	−	3.13495i	−0.521721	−	0.133312i
$554$	41.4791	−	14.1893i	1.76228	−	0.602844i
$555$	0.242289	−	21.0021i	0.0102846	−	0.891489i
$556$	0.175407	+	1.28554i	0.00743893	+	0.0545188i
$557$	15.4560	−	26.7705i	0.654890	−	1.13430i	−0.327031	−	0.945014i	$-0.606048\pi$
$557$	15.4560	−	26.7705i	0.654890	−	1.13430i	0.981921	−	0.189289i	$-0.0606184\pi$
$558$	5.66356	−	25.6803i	0.239758	−	1.08713i
$559$			4.79310i			0.202727i
$560$	−0.295330	−	14.0283i	−0.0124800	−	0.592803i
$561$	−4.55479	−	0.0525460i	−0.192303	−	0.00221849i
$562$	−23.2600	−	20.3018i	−0.981164	−	0.856379i
$563$			1.05933i			0.0446453i	0.999751	+	0.0223227i	$0.00710612\pi$
$563$			1.05933i			0.0446453i	−0.999751	+	0.0223227i	$0.992894\pi$
$564$	12.6609	+	5.34587i	0.533121	+	0.225102i
$565$			21.7309i			0.914226i
$566$	−34.8473	−	6.84630i	−1.46474	−	0.287771i
$567$	6.95295	−	22.7740i	0.291996	−	0.956419i
$568$	−13.4347	−	8.84015i	−0.563709	−	0.370924i
$569$		−	21.4163i		−	0.897818i	−0.893577	−	0.448909i	$-0.851813\pi$
$569$		−	21.4163i		−	0.897818i	0.893577	−	0.448909i	$-0.148187\pi$
$570$	11.0428	+	2.30213i	0.462530	+	0.0964257i
$571$	−0.592715			−0.0248044			−0.0124022	−	0.999923i	$-0.503948\pi$
$571$	−0.592715			−0.0248044			−0.0124022	+	0.999923i	$0.503948\pi$
$572$	0.886412	−	0.686825i	0.0370627	−	0.0287176i
$573$	−15.1789	−	0.175110i	−0.634106	−	0.00731532i
$574$	0.739352	+	9.28811i	0.0308599	+	0.387678i
$575$	8.03361			0.335025
$576$	8.98576	+	22.2544i	0.374407	+	0.927265i
$577$	19.9296	−	34.5191i	0.829680	−	1.43705i	−0.0686102	−	0.997644i	$-0.521856\pi$
$577$	19.9296	−	34.5191i	0.829680	−	1.43705i	0.898290	−	0.439404i	$-0.144810\pi$
$578$	−13.5925	−	39.7347i	−0.565375	−	1.65274i
$579$	4.13646	+	0.0477199i	0.171905	+	0.00198317i
$580$	3.39096	+	24.8518i	0.140802	+	1.03192i
$581$	14.1713	−	14.5048i	0.587924	−	0.601760i
$582$	17.9087	−	20.0467i	0.742340	−	0.830962i
$583$			0.0885001i			0.00366530i
$584$	35.2436	−	17.6909i	1.45839	−	0.732053i
$585$	0.133682	−	5.79312i	0.00552706	−	0.239516i
$586$	11.5225	+	33.6834i	0.475990	+	1.39145i
$587$	−25.6516	−	14.8100i	−1.05876	−	0.611273i	−0.133668	−	0.991026i	$-0.542676\pi$
$587$	−25.6516	−	14.8100i	−1.05876	−	0.611273i	−0.925088	+	0.379753i	$0.876009\pi$
$588$	−15.0758	−	18.9926i	−0.621716	−	0.783243i
$589$	18.6447	−	10.7645i	0.768241	−	0.443544i
$590$	5.79908	+	5.06154i	0.238744	+	0.208380i
$591$	5.43406	+	0.0626897i	0.223527	+	0.00257871i
$592$	35.4257	+	9.13551i	1.45599	+	0.375467i
$593$	3.55918	−	2.05489i	0.146158	−	0.0843843i	−0.425138	−	0.905129i	$-0.639774\pi$
$593$	3.55918	−	2.05489i	0.146158	−	0.0843843i	0.571296	+	0.820744i	$0.306441\pi$
$594$	−2.70595	+	0.822237i	−0.111027	+	0.0337368i
$595$	6.47286	+	23.0800i	0.265361	+	0.946187i
$596$	−36.6215	+	28.3757i	−1.50008	+	1.16231i
$597$	−24.2984	−	14.4049i	−0.994467	−	0.589555i
$598$	−0.984172	+	5.00939i	−0.0402458	+	0.204849i
$599$	−41.7143			−1.70440			−0.852200	−	0.523216i	$-0.824732\pi$
$599$	−41.7143			−1.70440			−0.852200	+	0.523216i	$0.824732\pi$
$600$	1.10966	−	15.8444i	0.0453018	−	0.646844i
$601$	−12.9180	+	22.3746i	−0.526935	+	0.912678i	0.472573	+	0.881292i	$0.343325\pi$
$601$	−12.9180	+	22.3746i	−0.526935	+	0.912678i	−0.999507	+	0.0313861i	$0.990008\pi$
$602$	−6.98165	−	10.1389i	−0.284551	−	0.413232i
$603$	44.8973	+	1.03605i	1.82836	+	0.0421911i
$604$	−13.0120	+	1.77544i	−0.529450	+	0.0722418i
$605$	7.19394	+	12.4603i	0.292475	+	0.506582i
$606$	−8.24606	−	25.0452i	−0.334973	−	1.01739i
$607$	−8.91365	−	5.14630i	−0.361794	−	0.208882i	0.308073	−	0.951363i	$-0.400316\pi$
$607$	−8.91365	−	5.14630i	−0.361794	−	0.208882i	−0.669867	+	0.742481i	$0.733649\pi$
$608$	−8.48210	+	17.7231i	−0.343994	+	0.718765i
$609$	30.6533	+	30.6476i	1.24214	+	1.24190i
$610$	6.07324	+	5.30084i	0.245898	+	0.214625i
$611$	5.00547	−	2.88991i	0.202500	−	0.116913i
$612$	−24.3580	−	32.9805i	−0.984612	−	1.33316i
$613$	−19.4452	−	11.2267i	−0.785386	−	0.453443i	0.0529497	−	0.998597i	$-0.483138\pi$
$613$	−19.4452	−	11.2267i	−0.785386	−	0.453443i	−0.838336	+	0.545154i	$0.816471\pi$
$614$	13.2099	+	2.59529i	0.533108	+	0.104737i
$615$	0.0659675	−	5.71819i	0.00266007	−	0.230580i
$616$	−0.874609	+	2.74400i	−0.0352390	+	0.110559i
$617$	−10.4323	+	6.02309i	−0.419988	+	0.242480i	−0.695072	−	0.718940i	$-0.744628\pi$
$617$	−10.4323	+	6.02309i	−0.419988	+	0.242480i	0.275084	+	0.961420i	$0.411294\pi$
$618$	27.9851	+	25.0005i	1.12573	+	1.00567i
$619$	−3.43593	−	5.95120i	−0.138102	−	0.239199i	0.788676	−	0.614809i	$-0.210767\pi$
$619$	−3.43593	−	5.95120i	−0.138102	−	0.239199i	−0.926778	+	0.375610i	$0.877433\pi$
$620$	10.0670	+	12.9923i	0.404299	+	0.521785i
$621$	6.81966	−	10.9210i	0.273663	−	0.438244i
$622$	30.2470	+	5.94248i	1.21279	+	0.238272i
$623$	4.42301	+	15.7709i	0.177204	+	0.631849i
$624$	9.74389	+	2.63298i	0.390068	+	0.105404i
$625$	−0.861102	+	1.49147i	−0.0344441	+	0.0596589i
$626$	−9.01614	−	1.77136i	−0.360357	−	0.0707978i
$627$	−1.99163	−	1.18071i	−0.0795381	−	0.0471530i
$628$	4.86025	−	11.8918i	0.193945	−	0.474534i
$629$	−62.4992			−2.49201
$630$	8.15551	+	12.4490i	0.324923	+	0.495980i
$631$			16.5719i			0.659719i	0.944030	+	0.329859i	$0.107001\pi$
$631$			16.5719i			0.659719i	−0.944030	+	0.329859i	$0.892999\pi$
$632$	−7.44120	+	11.3087i	−0.295995	+	0.449835i
$633$	−5.99341	−	10.6631i	−0.238217	−	0.423820i
$634$	−33.2890	−	6.54013i	−1.32207	−	0.259742i
$635$	0.588255	+	0.339629i	0.0233442	+	0.0134778i
$636$	−0.635271	+	0.480607i	−0.0251901	+	0.0190573i
$637$	−10.1952	+	0.237176i	−0.403949	+	0.00939725i
$638$	0.992477	−	5.05166i	0.0392925	−	0.199997i
$639$	17.0533	+	0.393521i	0.674618	+	0.0155674i
$640$	−14.2817	−	4.58686i	−0.564533	−	0.181312i
$641$	−35.9616	+	20.7624i	−1.42040	+	0.820067i	−0.996333	−	0.0855643i	$-0.972731\pi$
$641$	−35.9616	+	20.7624i	−1.42040	+	0.820067i	−0.424066	+	0.905632i	$0.639397\pi$
$642$	−28.7585	+	9.46864i	−1.13501	+	0.373698i
$643$	10.0656	+	17.4341i	0.396948	+	0.687534i	0.993348	−	0.115154i	$-0.0367361\pi$
$643$	10.0656	+	17.4341i	0.396948	+	0.687534i	−0.596400	+	0.802687i	$0.703403\pi$
$644$	−5.21487	−	12.0300i	−0.205495	−	0.474048i
$645$	3.70194	+	6.58625i	0.145764	+	0.259334i
$646$	6.47085	−	32.9363i	0.254592	−	1.29586i
$647$	−15.5081	+	26.8609i	−0.609688	+	1.05601i	0.381603	+	0.924326i	$0.375372\pi$
$647$	−15.5081	+	26.8609i	−0.609688	+	1.05601i	−0.991292	+	0.131685i	$0.957961\pi$
$648$	−20.5971	−	14.9586i	−0.809129	−	0.587631i
$649$	−0.789956	−	1.36824i	−0.0310085	−	0.0537082i
$650$	−5.03249	−	4.39245i	−0.197390	−	0.172286i
$651$	27.4373	+	7.34903i	1.07535	+	0.288031i
$652$	−2.29268	−	16.8027i	−0.0897884	−	0.658046i
$653$	−3.07344	+	5.32335i	−0.120273	+	0.208319i	−0.919875	−	0.392211i	$-0.871710\pi$
$653$	−3.07344	+	5.32335i	−0.120273	+	0.208319i	0.799602	+	0.600530i	$0.205044\pi$
$654$	−3.47983	−	3.10870i	−0.136072	−	0.121560i
$655$	14.8631	−	8.58121i	0.580749	−	0.335296i
$656$	9.64527	+	2.48731i	0.376585	+	0.0971130i
$657$	−21.7434	+	35.7308i	−0.848291	+	1.39399i
$658$	−6.37870	+	13.4041i	−0.248668	+	0.522545i
$659$	1.14968	+	0.663771i	0.0447854	+	0.0258568i	0.522226	−	0.852807i	$-0.325102\pi$
$659$	1.14968	+	0.663771i	0.0447854	+	0.0258568i	−0.477440	+	0.878664i	$0.658435\pi$
$660$	0.687561	−	1.62839i	0.0267633	−	0.0633850i
$661$			18.0089i			0.700466i	0.936663	+	0.350233i	$0.113898\pi$
$661$			18.0089i			0.700466i	−0.936663	+	0.350233i	$0.886102\pi$
$662$	0.633543	+	0.124469i	0.0246233	+	0.00483764i
$663$	−17.2418	−	0.198909i	−0.669616	−	0.00772498i
$664$	−9.72530	−	19.3747i	−0.377415	−	0.751883i
$665$	−3.01637	+	11.8047i	−0.116970	+	0.457766i
$666$	−36.9951	+	11.7092i	−1.43353	+	0.453724i
$667$	11.7190	+	20.2979i	0.453762	+	0.785939i
$668$	3.48793	+	25.5625i	0.134952	+	0.989045i
$669$	0.983092	+	0.582812i	0.0380085	+	0.0225328i
$670$	−18.4572	+	21.1467i	−0.713064	+	0.816967i
$671$	−0.827302	−	1.43293i	−0.0319376	−	0.0553176i
$672$	−24.4466	+	8.62341i	−0.943049	+	0.332655i
$673$	4.96451	−	8.59878i	0.191368	−	0.331459i	−0.754336	−	0.656489i	$-0.772041\pi$
$673$	4.96451	−	8.59878i	0.191368	−	0.331459i	0.945704	+	0.325030i	$0.105374\pi$
$674$	10.9938	+	32.1378i	0.423465	+	1.23790i
$675$	7.91348	+	14.8724i	0.304590	+	0.572437i
$676$	−17.1970	+	13.3248i	−0.661422	+	0.512494i
$677$	23.0433			0.885626			0.442813	−	0.896614i	$-0.353980\pi$
$677$	23.0433			0.885626			0.442813	+	0.896614i	$0.353980\pi$
$678$	38.1340	−	12.5555i	1.46453	−	0.482192i
$679$	20.7681	+	20.2906i	0.797008	+	0.778682i
$680$	25.5819	+	1.49530i	0.981019	+	0.0573420i
$681$	−7.78073	+	4.37331i	−0.298158	+	0.167586i
$682$	−1.09192	−	3.19199i	−0.0418119	−	0.122228i
$683$	−22.6624	−	13.0841i	−0.867152	−	0.500650i	−0.000751213	−	1.00000i	$-0.500239\pi$
$683$	−22.6624	−	13.0841i	−0.867152	−	0.500650i	−0.866401	+	0.499349i	$0.833572\pi$
$684$	−2.34035	−	20.7083i	−0.0894855	−	0.791800i
$685$			6.41722i			0.245189i
$686$	21.2206	−	15.3521i	0.810206	−	0.586145i
$687$	−33.9195	−	20.1087i	−1.29411	−	0.767193i
$688$	−12.6791	+	3.52569i	−0.483386	+	0.134416i
$689$			0.335011i			0.0127629i
$690$	2.51663	+	7.64359i	0.0958063	+	0.290986i
$691$	43.9537			1.67208			0.836038	−	0.548672i	$-0.184866\pi$
$691$	43.9537			1.67208			0.836038	+	0.548672i	$0.184866\pi$
$692$	−10.2110	−	4.17329i	−0.388163	−	0.158645i
$693$	−0.756806	−	2.95948i	−0.0287487	−	0.112421i
$694$	3.93903	−	20.0495i	0.149524	−	0.761069i
$695$	0.860105			0.0326256
$696$	41.6515	−	20.3093i	1.57880	−	0.769820i
$697$	−17.0165			−0.644547
$698$	−5.92909	−	5.17502i	−0.224419	−	0.195877i
$699$	13.5523	−	7.61733i	0.512594	−	0.288114i
$700$	17.0434	+	1.96108i	0.644178	+	0.0741217i
$701$	30.5993			1.15572			0.577860	−	0.816136i	$-0.303888\pi$
$701$	30.5993			1.15572			0.577860	+	0.816136i	$0.303888\pi$
$702$	−10.2432	+	3.11252i	−0.386604	+	0.117474i
$703$	−27.5117	−	15.8839i	−1.03762	−	0.599073i
$704$	2.46887	+	1.83960i	0.0930489	+	0.0693324i
$705$	4.64606	−	7.83702i	0.174981	−	0.295159i
$706$	−31.2598	+	10.6934i	−1.17648	+	0.402452i
$707$	27.4224	−	7.69072i	1.03133	−	0.289239i
$708$	5.53160	−	13.1008i	0.207890	−	0.492358i
$709$		−	8.98224i		−	0.337335i	−0.985673	−	0.168668i	$-0.946054\pi$
$709$		−	8.98224i		−	0.337335i	0.985673	−	0.168668i	$-0.0539464\pi$
$710$	−7.01058	+	8.03211i	−0.263102	+	0.301440i
$711$	0.331246	−	14.3546i	0.0124227	−	0.538340i
$712$	17.4805	+	1.02176i	0.655109	+	0.0382921i
$713$	13.3010	+	7.67936i	0.498128	+	0.287594i
$714$	36.7616	−	24.6937i	1.37577	−	0.924140i
$715$	−0.371687	−	0.643781i	−0.0139003	−	0.0240761i
$716$	8.40723	+	10.8503i	0.314193	+	0.405495i
$717$	5.37827	+	9.56869i	0.200855	+	0.357349i
$718$	12.5228	+	36.6075i	0.467347	+	1.36618i
$719$	−6.74553	−	11.6836i	−0.251566	−	0.435725i	0.712391	−	0.701783i	$-0.247612\pi$
$719$	−6.74553	−	11.6836i	−0.251566	−	0.435725i	−0.963957	+	0.266058i	$0.914279\pi$
$720$	15.4228	−	3.90766i	0.574772	−	0.145630i
$721$	−28.3256	+	28.9922i	−1.05490	+	1.07973i
$722$	−6.44999	+	7.38984i	−0.240044	+	0.275021i
$723$	−19.2181	−	34.1916i	−0.714727	−	1.27160i
$724$	−3.56115	+	8.71322i	−0.132349	+	0.323824i
$725$	−30.6672			−1.13895
$726$	17.7092	−	19.8233i	0.657250	−	0.735713i
$727$	8.53122	+	4.92550i	0.316405	+	0.182677i	0.649789	−	0.760114i	$-0.274857\pi$
$727$	8.53122	+	4.92550i	0.316405	+	0.182677i	−0.333384	+	0.942791i	$0.608191\pi$
$728$	−3.31077	+	10.3872i	−0.122705	+	0.384976i
$729$	26.9354	+	1.86733i	0.997606	+	0.0691602i
$730$	−8.46133	−	24.7348i	−0.313168	−	0.915474i
$731$	19.4701	−	11.2411i	0.720127	−	0.415766i
$732$	5.79312	−	13.7202i	0.214120	−	0.507112i
$733$	−2.70589	−	1.56224i	−0.0999442	−	0.0577028i	0.449195	−	0.893434i	$-0.351711\pi$
$733$	−2.70589	−	1.56224i	−0.0999442	−	0.0577028i	−0.549139	+	0.835731i	$0.685044\pi$
$734$	33.8941	−	11.5946i	1.25106	−	0.427964i
$735$	−13.8262	+	8.20014i	−0.509986	+	0.302467i
$736$	−13.9752	+	1.08138i	−0.515132	+	0.0398601i
$737$	4.98938	−	2.88062i	0.183786	−	0.106109i
$738$	−10.0726	+	3.18805i	−0.370776	+	0.117354i
$739$	10.5046	−	18.1945i	0.386419	−	0.669297i	−0.605546	−	0.795810i	$-0.707045\pi$
$739$	10.5046	−	18.1945i	0.386419	−	0.669297i	0.991965	+	0.126513i	$0.0403786\pi$
$740$	9.17548	−	22.4501i	0.337297	−	0.825281i
$741$	−7.53917	−	4.46949i	−0.276958	−	0.164191i
$742$	−0.487978	−	0.708653i	−0.0179142	−	0.0260155i
$743$	−6.56707	−	11.3745i	−0.240922	−	0.417290i	0.720055	−	0.693917i	$-0.244117\pi$
$743$	−6.56707	−	11.3745i	−0.240922	−	0.417290i	−0.960977	+	0.276627i	$0.910783\pi$
$744$	16.9829	−	25.1724i	0.622625	−	0.922865i
$745$	15.3560	+	26.5974i	0.562601	+	0.974453i
$746$	−22.1891	−	19.3671i	−0.812401	−	0.709079i
$747$	19.6425	+	11.9531i	0.718681	+	0.437342i
$748$	−4.86882	−	1.98992i	−0.178022	−	0.0727586i
$749$	−8.83096	−	31.4882i	−0.322676	−	1.15055i
$750$	−26.2041	−	5.46288i	−0.956839	−	0.199476i
$751$	30.8465	+	17.8092i	1.12561	+	0.649868i	0.942826	−	0.333286i	$-0.108157\pi$
$751$	30.8465	+	17.8092i	1.12561	+	0.649868i	0.182779	+	0.983154i	$0.441491\pi$
$752$	11.3265	+	11.1151i	0.413036	+	0.405327i
$753$	0.306921	−	26.6045i	0.0111848	−	0.969522i
$754$	3.75695	−	19.1227i	0.136820	−	0.696407i
$755$			8.70584i			0.316838i
$756$	17.1339	−	21.5042i	0.623152	−	0.782101i
$757$			31.7853i			1.15526i	0.816300	+	0.577628i	$0.196022\pi$
$757$			31.7853i			1.15526i	−0.816300	+	0.577628i	$0.803978\pi$
$758$	47.9532	+	9.42115i	1.74174	+	0.342192i
$759$	0.0190538	−	1.65162i	0.000691610	−	0.0599501i
$760$	10.8809	+	7.15973i	0.394693	+	0.259711i
$761$	14.7863	+	8.53689i	0.536004	+	0.309462i	0.743458	−	0.668783i	$-0.233184\pi$
$761$	14.7863	+	8.53689i	0.536004	+	0.309462i	−0.207454	+	0.978245i	$0.566518\pi$
$762$	0.256114	−	1.22852i	0.00927803	−	0.0445044i
$763$	3.52217	−	3.60506i	0.127511	−	0.130512i
$764$	−16.2254	−	6.63141i	−0.587013	−	0.239916i
$765$	−23.8458	+	13.0433i	−0.862146	+	0.471583i
$766$	−12.6358	+	14.4770i	−0.456551	+	0.523076i
$767$	−2.99032	−	5.17938i	−0.107974	−	0.187017i
$768$	0.202400	+	27.7121i	0.00730348	+	0.999973i
$769$	4.46328	+	7.73063i	0.160950	+	0.278774i	0.935210	−	0.354094i	$-0.115211\pi$
$769$	4.46328	+	7.73063i	0.160950	+	0.278774i	−0.774260	+	0.632868i	$0.781878\pi$
$770$	1.72397	+	0.820400i	0.0621276	+	0.0295651i
$771$	−22.2153	−	13.1700i	−0.800064	−	0.474306i
$772$	4.42164	+	1.80715i	0.159138	+	0.0650409i
$773$	−25.1937	+	43.6368i	−0.906155	+	1.56951i	−0.0867959	+	0.996226i	$0.527663\pi$
$773$	−25.1937	+	43.6368i	−0.906155	+	1.56951i	−0.819359	+	0.573281i	$0.805671\pi$
$774$	9.41888	−	10.3016i	0.338555	−	0.370284i
$775$	−17.4036	+	10.0480i	−0.625156	+	0.360934i
$776$	27.7409	−	13.9248i	0.995839	−	0.499871i
$777$	−10.8517	−	40.4838i	−0.389301	−	1.45235i
$778$	4.44160	+	12.9840i	0.159239	+	0.465499i
$779$	−7.49056	−	4.32467i	−0.268377	−	0.154948i
$780$	2.60271	−	6.16415i	0.0931920	−	0.220712i
$781$	1.89511	−	1.09414i	0.0678123	−	0.0391515i
$782$	22.6568	−	7.75050i	0.810206	−	0.277157i
$783$	−26.0331	+	41.6894i	−0.930348	+	1.48986i
$784$	−8.12674	−	26.7947i	−0.290241	−	0.956954i
$785$	−7.37535	−	4.25816i	−0.263238	−	0.151980i
$786$	−23.6460	−	21.1242i	−0.843426	−	0.753476i
$787$	−1.74835			−0.0623218			−0.0311609	−	0.999514i	$-0.509920\pi$
$787$	−1.74835			−0.0623218			−0.0311609	+	0.999514i	$0.509920\pi$
$788$	5.80871	+	2.37406i	0.206927	+	0.0845723i
$789$	15.5382	+	27.6446i	0.553175	+	0.984174i
$790$	6.76103	+	5.90116i	0.240547	+	0.209954i
$791$	11.7099	+	41.7536i	0.416357	+	1.48459i
$792$	−3.25480	−	0.265714i	−0.115654	−	0.00944173i
$793$	−3.13169	−	5.42424i	−0.111210	−	0.192621i
$794$	−5.15598	+	1.76377i	−0.182979	+	0.0625939i
$795$	0.258744	+	0.460342i	0.00917672	+	0.0163266i
$796$	−19.9778	−	25.7832i	−0.708094	−	0.913861i
$797$	−17.1209	−	29.6543i	−0.606453	−	1.05041i	−0.991820	−	0.127645i	$-0.959258\pi$
$797$	−17.1209	−	29.6543i	−0.606453	−	1.05041i	0.385367	−	0.922764i	$-0.374075\pi$
$798$	22.4580	−	1.52721i	0.795005	−	0.0540627i
$799$	−23.4782	−	13.5552i	−0.830601	−	0.479547i
$800$	7.91748	−	16.5433i	0.279925	−	0.584894i
$801$	−16.2942	+	8.91272i	−0.575728	+	0.314916i
$802$	6.30205	+	5.50055i	0.222533	+	0.194231i
$803$			5.36577i			0.189354i
$804$	47.7728	+	20.1713i	1.68482	+	0.711387i
$805$	−8.36909	+	2.34714i	−0.294972	+	0.0827258i
$806$	−4.13340	−	12.0830i	−0.145593	−	0.425607i
$807$	22.0226	−	37.1479i	0.775232	−	1.30767i
$808$	1.77663	−	30.3950i	0.0625018	−	1.06929i
$809$	25.5520	+	14.7525i	0.898361	+	0.518669i	0.876668	−	0.481096i	$-0.159761\pi$
$809$	25.5520	+	14.7525i	0.898361	+	0.518669i	0.0216930	+	0.999765i	$0.493094\pi$
$810$	−11.6713	+	12.1882i	−0.410089	+	0.428251i
$811$	−4.53371			−0.159200			−0.0796000	−	0.996827i	$-0.525364\pi$
$811$	−4.53371			−0.159200			−0.0796000	+	0.996827i	$0.525364\pi$
$812$	19.9070	+	45.9229i	0.698600	+	1.61158i
$813$	21.9280	−	12.3251i	0.769049	−	0.432260i
$814$	−3.27340	+	3.75037i	−0.114733	+	0.131451i
$815$	−11.2421			−0.393794
$816$	−12.1565	−	45.7557i	−0.425562	−	1.60177i
$817$	11.4275			0.399796
$818$	−19.7870	−	3.88746i	−0.691836	−	0.135922i
$819$	−2.86483	−	11.2029i	−0.100105	−	0.391461i
$820$	2.49819	−	6.11243i	0.0872405	−	0.213455i
$821$	11.0612			0.386038			0.193019	−	0.981195i	$-0.438172\pi$
$821$	11.0612			0.386038			0.193019	+	0.981195i	$0.438172\pi$
$822$	11.2611	−	3.70769i	0.392777	−	0.129320i
$823$		−	50.7969i		−	1.77067i	−0.464957	−	0.885333i	$-0.653930\pi$
$823$		−	50.7969i		−	1.77067i	0.464957	−	0.885333i	$-0.346070\pi$
$824$	19.4389	+	38.7261i	0.677188	+	1.34909i
$825$	1.85906	+	1.10212i	0.0647241	+	0.0383707i
$826$	13.8698	+	6.60032i	0.482591	+	0.229654i
$827$			6.10815i			0.212401i	0.994345	+	0.106201i	$0.0338685\pi$
$827$			6.10815i			0.212401i	−0.994345	+	0.106201i	$0.966131\pi$
$828$	11.9592	−	8.83250i	0.415609	−	0.306951i
$829$	2.69990	+	1.55879i	0.0937713	+	0.0541389i	0.546152	−	0.837686i	$-0.316092\pi$
$829$	2.69990	+	1.55879i	0.0937713	+	0.0541389i	−0.452381	+	0.891825i	$0.649425\pi$
$830$	−13.5976	+	4.65149i	−0.471979	+	0.161456i
$831$	−46.8047	+	26.3076i	−1.62364	+	0.912599i
$832$	9.34571	+	6.96365i	0.324004	+	0.241421i
$833$	24.8738	+	40.8577i	0.861826	+	1.41564i
$834$	−0.496945	−	1.50934i	−0.0172078	−	0.0522641i
$835$	17.1030			0.591873
$836$	−1.63749	−	2.11334i	−0.0566338	−	0.0730912i
$837$	−1.11441	+	32.1883i	−0.0385196	+	1.11259i
$838$	17.2641	−	5.90574i	0.596377	−	0.204010i
$839$	5.95493	−	10.3142i	0.205587	−	0.356087i	−0.744733	−	0.667363i	$-0.767423\pi$
$839$	5.95493	−	10.3142i	0.205587	−	0.356087i	0.950320	+	0.311276i	$0.100756\pi$
$840$	3.47317	+	16.8302i	0.119836	+	0.580699i
$841$	−30.2357	−	52.3698i	−1.04261	−	1.80586i
$842$	−23.0774	−	20.1424i	−0.795300	−	0.694153i
$843$	32.5263	+	19.2827i	1.12027	+	0.664133i
$844$	−1.90953	−	13.9947i	−0.0657287	−	0.481716i
$845$	7.21098	+	12.4898i	0.248065	+	0.429662i
$846$	−16.4370	−	3.62503i	−0.565116	−	0.124631i
$847$	20.5367	+	20.0645i	0.705651	+	0.689426i
$848$	−0.886197	+	0.246426i	−0.0304321	+	0.00846229i
$849$	43.4921	+	0.501743i	1.49264	+	0.0172198i
$850$	−6.04011	+	30.7439i	−0.207174	+	1.05451i
$851$		−	22.6630i		−	0.776878i
$852$	18.1455	+	7.66164i	0.621655	+	0.262484i
$853$	−14.7920	−	8.54017i	−0.506469	−	0.292410i	0.224912	−	0.974379i	$-0.427790\pi$
$853$	−14.7920	−	8.54017i	−0.506469	−	0.292410i	−0.731381	+	0.681969i	$0.761124\pi$
$854$	14.5255	+	6.91236i	0.497052	+	0.236536i
$855$	−13.8117	−	0.318717i	−0.472349	−	0.0108999i
$856$	−34.9015	−	2.04004i	−1.19291	−	0.0697272i
$857$	−19.6677	+	11.3552i	−0.671836	+	0.387885i	−0.796772	−	0.604280i	$-0.793461\pi$
$857$	−19.6677	+	11.3552i	−0.671836	+	0.387885i	0.124936	+	0.992165i	$0.460127\pi$
$858$	−0.914976	+	1.02421i	−0.0312368	+	0.0349658i
$859$	−20.4648	+	35.4461i	−0.698251	+	1.20941i	0.270821	+	0.962630i	$0.412705\pi$
$859$	−20.4648	+	35.4461i	−0.698251	+	1.20941i	−0.969072	+	0.246777i	$0.920629\pi$
$860$	1.17946	+	8.64405i	0.0402191	+	0.294760i
$861$	−2.95456	−	11.0224i	−0.100691	−	0.375644i
$862$	−18.1417	+	20.7852i	−0.617908	+	0.707946i
$863$	−27.4584	−	47.5594i	−0.934696	−	1.61894i	−0.775176	−	0.631746i	$-0.782339\pi$
$863$	−27.4584	−	47.5594i	−0.934696	−	1.61894i	−0.159520	−	0.987195i	$-0.550995\pi$
$864$	−15.7681	−	24.8066i	−0.536442	−	0.843937i
$865$	−3.65630	+	6.33289i	−0.124318	+	0.215325i
$866$	−27.0482	−	5.31403i	−0.919135	−	0.180578i
$867$	25.2012	+	44.8364i	0.855878	+	1.52272i
$868$	26.3436	+	19.5387i	0.894161	+	0.663187i
$869$	−0.920994	−	1.59521i	−0.0312426	−	0.0541137i
$870$	−9.60688	−	29.1784i	−0.325704	−	0.989239i
$871$	18.8869	−	10.9044i	0.639958	−	0.369480i
$872$	−2.41715	−	4.81543i	−0.0818550	−	0.163071i
$873$	−17.1146	+	28.1243i	−0.579242	+	0.951864i
$874$	11.9431	+	2.34641i	0.403982	+	0.0793685i
$875$	7.15774	−	28.0122i	0.241976	−	0.946984i
$876$	−38.5166	+	29.1392i	−1.30135	+	0.984524i
$877$	−18.9608	−	10.9470i	−0.640262	−	0.369656i	0.144453	−	0.989512i	$-0.453858\pi$
$877$	−18.9608	−	10.9470i	−0.640262	−	0.369656i	−0.784716	+	0.619856i	$0.787191\pi$
$878$	−2.76007	+	14.0486i	−0.0931478	+	0.474118i
$879$	−21.3632	−	38.0081i	−0.720564	−	1.28198i
$880$	1.42958	−	1.45677i	0.0481911	−	0.0491076i
$881$		−	50.3492i		−	1.69631i	−0.529749	−	0.848154i	$-0.677714\pi$
$881$		−	50.3492i		−	1.69631i	0.529749	−	0.848154i	$-0.322286\pi$
$882$	22.3782	+	19.5247i	0.753514	+	0.657432i
$883$	−35.3128			−1.18837			−0.594185	−	0.804329i	$-0.702525\pi$
$883$	−35.3128			−1.18837			−0.594185	+	0.804329i	$0.702525\pi$
$884$	−18.4305	−	7.53268i	−0.619886	−	0.253351i
$885$	−8.10931	−	4.80748i	−0.272591	−	0.161602i
$886$	1.87770	−	9.55741i	0.0630826	−	0.321087i
$887$	−12.5594	+	21.7534i	−0.421702	+	0.730409i	−0.996106	−	0.0881626i	$-0.971900\pi$
$887$	−12.5594	+	21.7534i	−0.421702	+	0.730409i	0.574404	+	0.818572i	$0.305234\pi$
$888$	−44.6974	−	3.13039i	−1.49995	−	0.105049i
$889$	1.31328	+	0.335573i	0.0440461	+	0.0112548i
$890$	2.23779	−	11.3902i	0.0750107	−	0.381801i
$891$	3.07637	−	1.59165i	0.103062	−	0.0533223i
$892$	0.808284	+	1.04317i	0.0270633	+	0.0349278i
$893$	−6.88997	−	11.9338i	−0.230564	−	0.399349i
$894$	37.8016	−	42.3144i	1.26428	−	1.41521i
$895$	7.88035	−	4.54972i	0.263411	−	0.152080i
$896$	−29.9124	−	1.11732i	−0.999303	−	0.0373270i
$897$	0.0721268	−	6.25210i	0.00240824	−	0.208751i
$898$	8.89334	−	45.2667i	0.296775	−	1.51057i
$899$	−50.7749	−	29.3149i	−1.69344	−	0.977707i
$900$	2.18456	+	19.3298i	0.0728187	+	0.644327i
$901$	1.36085	−	0.785686i	0.0453364	−	0.0261750i
$902$	−0.891241	+	1.02111i	−0.0296751	+	0.0339991i
$903$	10.6620	+	10.6600i	0.354808	+	0.354741i
$904$	46.2797	+	2.70512i	1.53924	+	0.0899708i
$905$	5.40399	+	3.11999i	0.179635	+	0.103712i
$906$	15.2773	−	5.02999i	0.507553	−	0.167110i
$907$	14.8971	+	25.8025i	0.494649	+	0.856757i	0.999981	−	0.00616780i	$-0.00196328\pi$
$907$	14.8971	+	25.8025i	0.494649	+	0.856757i	−0.505332	+	0.862925i	$0.668630\pi$
$908$	−10.2117	+	1.39336i	−0.338888	+	0.0462402i
$909$	15.4974	+	28.3323i	0.514017	+	0.939724i
$910$	6.52596	+	3.10556i	0.216333	+	0.102948i
$911$	−16.9787	+	29.4080i	−0.562529	+	0.974329i	0.434746	+	0.900553i	$0.356838\pi$
$911$	−16.9787	+	29.4080i	−0.562529	+	0.974329i	−0.997275	+	0.0737760i	$0.976495\pi$
$912$	6.27741	−	23.2309i	0.207866	−	0.769251i
$913$	2.94976			0.0976226
$914$	34.6269	+	6.80299i	1.14536	+	0.225023i
$915$	−8.49269	−	5.03476i	−0.280760	−	0.166444i
$916$	−27.8881	−	35.9922i	−0.921448	−	1.18922i
$917$	23.9338	−	24.4970i	0.790362	−	0.808963i
$918$	36.6663	+	34.3092i	1.21017	+	1.13237i
$919$	−41.3444	+	23.8702i	−1.36383	+	0.787405i	−0.990131	−	0.140147i	$-0.955242\pi$
$919$	−41.3444	+	23.8702i	−1.36383	+	0.787405i	−0.373694	+	0.927552i	$0.621909\pi$
$920$	−0.542214	+	9.27630i	−0.0178762	+	0.305831i
$921$	−16.4869	−	0.190200i	−0.543263	−	0.00626731i
$922$	8.80825	−	10.0917i	0.290084	−	0.332353i
$923$	7.17379	−	4.14179i	0.236128	−	0.136329i
$924$	0.443599	−	3.49928i	0.0145933	−	0.115118i
$925$	25.6804	+	14.8266i	0.844366	+	0.487495i
$926$	−34.4694	+	11.7914i	−1.13273	+	0.387488i
$927$	−39.2614	−	23.8919i	−1.28951	−	0.784713i
$928$	53.3484	−	4.12801i	1.75125	−	0.135509i
$929$		−	10.0206i		−	0.328766i	−0.986397	−	0.164383i	$-0.947437\pi$
$929$		−	10.0206i		−	0.328766i	0.986397	−	0.164383i	$-0.0525633\pi$
$930$	−15.0120	−	13.4110i	−0.492264	−	0.439765i
$931$	0.565462	+	24.3069i	0.0185323	+	0.796625i
$932$	17.7865	−	2.42692i	0.582617	−	0.0794964i
$933$	−37.7505	−	0.435505i	−1.23589	−	0.0142578i
$934$	−30.1458	+	10.3124i	−0.986401	+	0.337431i
$935$	−1.74341	+	3.01967i	−0.0570155	+	0.0987537i
$936$	−12.3208	−	1.00584i	−0.402718	−	0.0328769i
$937$	32.1321			1.04971			0.524855	−	0.851191i	$-0.324119\pi$
$937$	32.1321			1.04971			0.524855	+	0.851191i	$0.324119\pi$
$938$	−24.0684	+	50.5769i	−0.785862	+	1.65139i
$939$	11.2528	+	0.129817i	0.367222	+	0.00423643i
$940$	8.31592	−	6.44348i	0.271235	−	0.210163i
$941$	26.3889			0.860255			0.430127	−	0.902768i	$-0.358469\pi$
$941$	26.3889			0.860255			0.430127	+	0.902768i	$0.358469\pi$
$942$	−3.21107	+	15.4027i	−0.104622	+	0.501848i
$943$		−	6.17041i		−	0.200936i
$944$	11.5013	−	11.7201i	0.374336	−	0.381455i
$945$	−12.5891	−	13.1814i	−0.409524	−	0.428791i
$946$	0.345207	−	1.75709i	0.0112236	−	0.0571278i
$947$		−	0.887034i		−	0.0288247i	−0.999896	−	0.0144124i	$-0.995412\pi$
$947$		−	0.887034i		−	0.0288247i	0.999896	−	0.0144124i	$-0.00458776\pi$
$948$	6.44919	−	15.2740i	0.209460	−	0.496076i
$949$			20.3117i			0.659346i
$950$	−10.4722	+	11.9982i	−0.339764	+	0.389272i
$951$	41.5471	+	0.479305i	1.34726	+	0.0155425i
$952$	49.9585	−	10.9120i	1.61917	−	0.353660i
$953$		−	28.5646i		−	0.925297i	−0.886542	−	0.462649i	$-0.846899\pi$
$953$		−	28.5646i		−	0.925297i	0.886542	−	0.462649i	$-0.153101\pi$
$954$	0.658326	−	0.720025i	0.0213141	−	0.0233117i
$955$	−5.80991	+	10.0631i	−0.188004	+	0.325633i
$956$	1.71354	+	12.5583i	0.0554200	+	0.406165i
$957$	−0.0727354	+	6.30485i	−0.00235120	+	0.203807i
$958$	−3.20871	−	9.37993i	−0.103669	−	0.303052i
$959$	3.45799	+	12.3300i	0.111664	+	0.398156i
$960$	18.2204	+	2.35070i	0.588061	+	0.0758685i
$961$	−7.41959			−0.239342
$962$	−12.3912	+	14.1968i	−0.399508	+	0.457722i
$963$	32.5330	−	17.7951i	1.04836	−	0.573439i
$964$	−6.12297	−	44.8743i	−0.197208	−	1.44531i
$965$	1.58328	−	2.74233i	0.0509677	−	0.0882786i
$966$	8.95426	+	13.3302i	0.288099	+	0.428893i
$967$	−0.844149	+	0.487370i	−0.0271460	+	0.0156728i	−0.513512	−	0.858083i	$-0.671656\pi$
$967$	−0.844149	+	0.487370i	−0.0271460	+	0.0156728i	0.486366	+	0.873755i	$0.338322\pi$
$968$	27.4318	−	13.7696i	0.881692	−	0.442573i
$969$	−0.474228	+	41.1070i	−0.0152344	+	1.32055i
$970$	−6.66006	−	19.4692i	−0.213842	−	0.625117i
$971$	−38.1882	+	22.0479i	−1.22552	+	0.707552i	−0.966089	−	0.258211i	$-0.916867\pi$
$971$	−38.1882	+	22.0479i	−1.22552	+	0.707552i	−0.259427	+	0.965763i	$0.583534\pi$
$972$	28.1316	+	13.4392i	0.902323	+	0.431061i
$973$	1.65260	−	0.463477i	0.0529799	−	0.0148584i
$974$	−38.3410	−	33.4647i	−1.22852	−	1.07228i
$975$	7.03732	+	4.17197i	0.225375	+	0.133610i
$976$	12.0450	−	12.2741i	0.385553	−	0.392886i
$977$		−	40.9856i		−	1.31125i	−0.755088	−	0.655623i	$-0.772406\pi$
$977$		−	40.9856i		−	1.31125i	0.755088	−	0.655623i	$-0.227594\pi$
$978$	6.49537	+	19.7280i	0.207699	+	0.630831i
$979$	−1.19130	+	2.06339i	−0.0380740	+	0.0659462i
$980$	−18.3280	+	2.93650i	−0.585468	+	0.0938031i
$981$	4.88199	+	2.97086i	0.155870	+	0.0948522i
$982$	19.4985	−	6.67009i	0.622221	−	0.212851i
$983$	−15.3390	−	26.5679i	−0.489237	−	0.847383i	0.510686	−	0.859767i	$-0.329391\pi$
$983$	−15.3390	−	26.5679i	−0.489237	−	0.847383i	−0.999923	+	0.0123837i	$0.996058\pi$
$984$	−12.1697	−	0.852303i	−0.387954	−	0.0271704i
$985$	2.07996	−	3.60259i	0.0662730	−	0.114788i
$986$	−86.4893	+	29.5865i	−2.75438	+	0.942226i
$987$	4.70385	−	17.5616i	0.149725	−	0.558991i
$988$	−6.19860	−	7.99987i	−0.197204	−	0.254510i
$989$	4.07615	+	7.06010i	0.129614	+	0.224498i
$990$	−0.466236	+	2.11405i	−0.0148179	+	0.0671890i
$991$	28.3896	+	16.3907i	0.901825	+	0.520669i	0.877792	−	0.479043i	$-0.159016\pi$
$991$	28.3896	+	16.3907i	0.901825	+	0.520669i	0.0240328	+	0.999711i	$0.492349\pi$
$992$	28.9226	−	19.8220i	0.918293	−	0.629349i
$993$	−0.790709	−	0.00912195i	−0.0250924	−	0.000289476i
$994$	−9.14189	+	19.2106i	−0.289963	+	0.609322i
$995$	−18.7258	+	10.8113i	−0.593647	+	0.342742i
$996$	16.0189	+	21.1739i	0.507578	+	0.670921i
$997$	19.6351	−	11.3363i	0.621849	−	0.359025i	−0.155739	−	0.987798i	$-0.549776\pi$
$997$	19.6351	−	11.3363i	0.621849	−	0.359025i	0.777589	+	0.628773i	$0.216443\pi$
$998$	17.4118	−	19.9489i	0.551160	−	0.631471i
$999$	41.9553	−	22.3241i	1.32741	−	0.706303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bt.a.11.7	✓	184
7.2	even	3		504.2.cy.a.443.57	yes	184
8.3	odd	2	inner	504.2.bt.a.11.86	yes	184
9.5	odd	6		504.2.cy.a.347.26	yes	184
56.51	odd	6		504.2.cy.a.443.26	yes	184
63.23	odd	6	inner	504.2.bt.a.275.86	yes	184
72.59	even	6		504.2.cy.a.347.57	yes	184
504.275	even	6	inner	504.2.bt.a.275.7	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bt.a.11.7	✓	184	1.1	even	1	trivial
504.2.bt.a.11.86	yes	184	8.3	odd	2	inner
504.2.bt.a.275.7	yes	184	504.275	even	6	inner
504.2.bt.a.275.86	yes	184	63.23	odd	6	inner
504.2.cy.a.347.26	yes	184	9.5	odd	6
504.2.cy.a.347.57	yes	184	72.59	even	6
504.2.cy.a.443.26	yes	184	56.51	odd	6
504.2.cy.a.443.57	yes	184	7.2	even	3

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38769 - 0.272632i) q^{2} +(1.73194 + 0.0199803i) q^{3} +(1.85134 + 0.756656i) q^{4} +(0.662921 - 1.14821i) q^{5} +(-2.39793 - 0.499908i) q^{6} +(0.655004 - 2.56339i) q^{7} +(-2.36279 - 1.55474i) q^{8} +(2.99920 + 0.0692093i) q^{9} +O(q^{10})\)	\(q+(-1.38769 - 0.272632i) q^{2} +(1.73194 + 0.0199803i) q^{3} +(1.85134 + 0.756656i) q^{4} +(0.662921 - 1.14821i) q^{5} +(-2.39793 - 0.499908i) q^{6} +(0.655004 - 2.56339i) q^{7} +(-2.36279 - 1.55474i) q^{8} +(2.99920 + 0.0692093i) q^{9} +(-1.23297 + 1.41263i) q^{10} +(0.333297 - 0.192429i) q^{11} +(3.19129 + 1.34747i) q^{12} +(1.26167 - 0.728426i) q^{13} +(-1.60780 + 3.37860i) q^{14} +(1.17108 - 1.97539i) q^{15} +(2.85494 + 2.80166i) q^{16} +(-5.91788 - 3.41669i) q^{17} +(-4.14308 - 0.913720i) q^{18} +(-1.73667 - 3.00801i) q^{19} +(2.09610 - 1.62413i) q^{20} +(1.18564 - 4.42654i) q^{21} +(-0.514974 + 0.176164i) q^{22} +(1.23894 - 2.14590i) q^{23} +(-4.06114 - 2.73991i) q^{24} +(1.62107 + 2.80778i) q^{25} +(-1.94939 + 0.666854i) q^{26} +(5.19304 + 0.179791i) q^{27} +(3.15224 - 4.25010i) q^{28} +(-4.72947 + 8.19168i) q^{29} +(-2.16364 + 2.42194i) q^{30} +6.19835i q^{31} +(-3.19794 - 4.66617i) q^{32} +(0.581094 - 0.326615i) q^{33} +(7.28066 + 6.35470i) q^{34} +(-2.50910 - 2.45141i) q^{35} +(5.50018 + 2.39749i) q^{36} +(7.92081 - 4.57308i) q^{37} +(1.58988 + 4.64764i) q^{38} +(2.19969 - 1.23638i) q^{39} +(-3.35151 + 1.68232i) q^{40} +(2.15658 - 1.24510i) q^{41} +(-2.85212 + 5.81940i) q^{42} +(-1.64502 + 2.84926i) q^{43} +(0.762650 - 0.104061i) q^{44} +(2.06770 - 3.39784i) q^{45} +(-2.30429 + 2.64006i) q^{46} +3.96734 q^{47} +(4.88860 + 4.90934i) q^{48} +(-6.14194 - 3.35806i) q^{49} +(-1.48405 - 4.33827i) q^{50} +(-10.1811 - 6.03573i) q^{51} +(2.88695 - 0.393916i) q^{52} +(-0.114978 + 0.199147i) q^{53} +(-7.15729 - 1.66528i) q^{54} -0.510261i q^{55} +(-5.53304 + 5.03840i) q^{56} +(-2.94771 - 5.24437i) q^{57} +(8.79633 - 10.0781i) q^{58} -4.10518i q^{59} +(3.66275 - 2.77101i) q^{60} -4.29926i q^{61} +(1.68987 - 8.60137i) q^{62} +(2.14190 - 7.64279i) q^{63} +(3.16559 + 7.34704i) q^{64} -1.93156i q^{65} +(-0.895421 + 0.294815i) q^{66} +14.9698 q^{67} +(-8.37078 - 10.8033i) q^{68} +(2.18863 - 3.69180i) q^{69} +(2.81351 + 4.08585i) q^{70} +5.68595 q^{71} +(-6.97889 - 4.82649i) q^{72} +(-6.97110 + 12.0743i) q^{73} +(-12.2384 + 4.18653i) q^{74} +(2.75149 + 4.89528i) q^{75} +(-0.939154 - 6.88292i) q^{76} +(-0.274960 - 0.980412i) q^{77} +(-3.38955 + 1.11600i) q^{78} -4.78615i q^{79} +(5.10950 - 1.42081i) q^{80} +(8.99042 + 0.415145i) q^{81} +(-3.33211 + 1.13986i) q^{82} +(6.63767 + 3.83226i) q^{83} +(5.54440 - 7.29792i) q^{84} +(-7.84618 + 4.52999i) q^{85} +(3.05957 - 3.50539i) q^{86} +(-8.35481 + 14.0930i) q^{87} +(-1.08669 - 0.0635186i) q^{88} +(-5.36142 + 3.09542i) q^{89} +(-3.79568 + 4.15141i) q^{90} +(-1.04084 - 3.71128i) q^{91} +(3.91740 - 3.03535i) q^{92} +(-0.123845 + 10.7351i) q^{93} +(-5.50542 - 1.08162i) q^{94} -4.60511 q^{95} +(-5.44540 - 8.14541i) q^{96} +(-5.48708 + 9.50389i) q^{97} +(7.60756 + 6.33443i) q^{98} +(1.01294 - 0.554066i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 184 * q - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^9	\( 184 q - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{10} - 6 q^{11} - 8 q^{12} + 12 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} - 6 q^{20} + 2 q^{22} - 8 q^{24} - 74 q^{25} - 6 q^{26} - 8 q^{27} + 3 q^{30} - 14 q^{33} - 4 q^{34} + 30 q^{35} - 38 q^{36} + 39 q^{38} + 6 q^{40} - 12 q^{41} - 20 q^{42} - 4 q^{43} + 9 q^{44} - 6 q^{46} - 5 q^{48} - 2 q^{49} - 21 q^{50} - 34 q^{51} + 9 q^{52} + 47 q^{54} - 24 q^{56} + 4 q^{57} - 3 q^{58} - 11 q^{60} - 8 q^{64} - 26 q^{66} - 4 q^{67} - 42 q^{68} - 3 q^{70} + 52 q^{72} - 4 q^{73} + 27 q^{74} + 30 q^{75} + 2 q^{76} - 29 q^{78} + 87 q^{80} + 14 q^{81} - 4 q^{82} - 72 q^{83} - 59 q^{84} - 27 q^{86} - 7 q^{88} - 24 q^{89} - 49 q^{90} - 36 q^{91} - 36 q^{92} - 18 q^{94} + 23 q^{96} - 4 q^{97} + 57 q^{98} + 10 q^{99}+O(q^{100}) \) 184 * q - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^9 - 6 * q^10 - 6 * q^11 - 8 * q^12 + 12 * q^14 - 2 * q^16 + 2 * q^18 - 4 * q^19 - 6 * q^20 + 2 * q^22 - 8 * q^24 - 74 * q^25 - 6 * q^26 - 8 * q^27 + 3 * q^30 - 14 * q^33 - 4 * q^34 + 30 * q^35 - 38 * q^36 + 39 * q^38 + 6 * q^40 - 12 * q^41 - 20 * q^42 - 4 * q^43 + 9 * q^44 - 6 * q^46 - 5 * q^48 - 2 * q^49 - 21 * q^50 - 34 * q^51 + 9 * q^52 + 47 * q^54 - 24 * q^56 + 4 * q^57 - 3 * q^58 - 11 * q^60 - 8 * q^64 - 26 * q^66 - 4 * q^67 - 42 * q^68 - 3 * q^70 + 52 * q^72 - 4 * q^73 + 27 * q^74 + 30 * q^75 + 2 * q^76 - 29 * q^78 + 87 * q^80 + 14 * q^81 - 4 * q^82 - 72 * q^83 - 59 * q^84 - 27 * q^86 - 7 * q^88 - 24 * q^89 - 49 * q^90 - 36 * q^91 - 36 * q^92 - 18 * q^94 + 23 * q^96 - 4 * q^97 + 57 * q^98 + 10 * q^99

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