LMFDB - Embedded newform 585.2.bt.b.571.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			571.23
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.527033 + 0.304283i) q^{2} +(-1.60346 + 0.654926i) q^{3} +(-0.814824 + 1.41132i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.645792 - 0.833072i) q^{6} +(1.11998 - 0.646621i) q^{7} -2.20888i q^{8} +(2.14214 - 2.10029i) q^{9} +O(q^{10})$	\(q+(-0.527033 + 0.304283i) q^{2} +(-1.60346 + 0.654926i) q^{3} +(-0.814824 + 1.41132i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.645792 - 0.833072i) q^{6} +(1.11998 - 0.646621i) q^{7} -2.20888i q^{8} +(2.14214 - 2.10029i) q^{9} -0.608566 q^{10} +(2.32348 - 1.34146i) q^{11} +(0.382227 - 2.79663i) q^{12} +(2.47611 - 2.62086i) q^{13} +(-0.393511 + 0.681581i) q^{14} +(-1.71610 - 0.234546i) q^{15} +(-0.957524 - 1.65848i) q^{16} -1.63642 q^{17} +(-0.489899 + 1.75874i) q^{18} +2.80454i q^{19} +(-1.41132 + 0.814824i) q^{20} +(-1.37235 + 1.77033i) q^{21} +(-0.816367 + 1.41399i) q^{22} +(4.00047 - 6.92901i) q^{23} +(1.44665 + 3.54184i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.507508 + 2.13472i) q^{26} +(-2.05930 + 4.77067i) q^{27} +2.10753i q^{28} +(1.93551 + 3.35240i) q^{29} +(0.975808 - 0.398565i) q^{30} +(7.48207 + 4.31977i) q^{31} +(4.83518 + 2.79159i) q^{32} +(-2.84704 + 3.67268i) q^{33} +(0.862446 - 0.497933i) q^{34} +1.29324 q^{35} +(1.21870 + 4.73461i) q^{36} +10.1601i q^{37} +(-0.853374 - 1.47809i) q^{38} +(-2.25386 + 5.82410i) q^{39} +(1.10444 - 1.91295i) q^{40} +(-7.08878 - 4.09271i) q^{41} +(0.184593 - 1.35061i) q^{42} +(-6.05745 - 10.4918i) q^{43} +4.37222i q^{44} +(2.90530 - 0.747832i) q^{45} +4.86909i q^{46} +(10.5167 - 6.07183i) q^{47} +(2.62153 + 2.03219i) q^{48} +(-2.66376 + 4.61377i) q^{49} +(-0.527033 - 0.304283i) q^{50} +(2.62392 - 1.07173i) q^{51} +(1.68127 + 5.63011i) q^{52} +3.10426 q^{53} +(-0.366312 - 3.14091i) q^{54} +2.68292 q^{55} +(-1.42831 - 2.47390i) q^{56} +(-1.83677 - 4.49696i) q^{57} +(-2.04016 - 1.17789i) q^{58} +(8.90917 + 5.14371i) q^{59} +(1.72934 - 2.23084i) q^{60} +(2.42579 + 4.20160i) q^{61} -5.25773 q^{62} +(1.04107 - 3.73744i) q^{63} +0.432360 q^{64} +(3.45480 - 1.03168i) q^{65} +(0.382951 - 2.80193i) q^{66} +(-11.3875 - 6.57457i) q^{67} +(1.33339 - 2.30950i) q^{68} +(-1.87659 + 13.7304i) q^{69} +(-0.681581 + 0.393511i) q^{70} -0.938010i q^{71} +(-4.63929 - 4.73174i) q^{72} +14.6411i q^{73} +(-3.09153 - 5.35469i) q^{74} +(-1.36891 - 1.06117i) q^{75} +(-3.95810 - 2.28521i) q^{76} +(1.73483 - 3.00482i) q^{77} +(-0.584313 - 3.75530i) q^{78} +(3.27558 + 5.67348i) q^{79} -1.91505i q^{80} +(0.177565 - 8.99825i) q^{81} +4.98136 q^{82} +(9.19282 - 5.30748i) q^{83} +(-1.38028 - 3.37933i) q^{84} +(-1.41718 - 0.818208i) q^{85} +(6.38495 + 3.68635i) q^{86} +(-5.29908 - 4.10782i) q^{87} +(-2.96312 - 5.13228i) q^{88} -10.4458i q^{89} +(-1.30364 + 1.27816i) q^{90} +(1.07849 - 4.53641i) q^{91} +(6.51935 + 11.2918i) q^{92} +(-14.8263 - 2.02637i) q^{93} +(-3.69511 + 6.40011i) q^{94} +(-1.40227 + 2.42881i) q^{95} +(-9.58129 - 1.30951i) q^{96} +(9.03460 - 5.21613i) q^{97} -3.24215i q^{98} +(2.15977 - 7.75358i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.527033	+	0.304283i	−0.372669	+	0.215160i	−0.674624	−	0.738162i	$-0.735694\pi$
$2$	−0.527033	+	0.304283i	−0.372669	+	0.215160i	0.301955	+	0.953322i	$0.402361\pi$
$3$	−1.60346	+	0.654926i	−0.925756	+	0.378122i
$3$	−1.60346	+	0.654926i	−0.925756	+	0.378122i
$4$	−0.814824	+	1.41132i	−0.407412	+	0.705658i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	0.645792	−	0.833072i	0.263644	−	0.340100i
$7$	1.11998	−	0.646621i	0.423313	−	0.244400i	−0.273181	−	0.961963i	$-0.588076\pi$
$7$	1.11998	−	0.646621i	0.423313	−	0.244400i	0.696494	+	0.717563i	$0.254742\pi$
$8$		−	2.20888i		−	0.780957i
$9$	2.14214	−	2.10029i	0.714048	−	0.700097i
$10$	−0.608566			−0.192445
$11$	2.32348	−	1.34146i	0.700555	−	0.404466i	−0.106999	−	0.994259i	$-0.534124\pi$
$11$	2.32348	−	1.34146i	0.700555	−	0.404466i	0.807554	+	0.589793i	$0.200791\pi$
$12$	0.382227	−	2.79663i	0.110339	−	0.807319i
$13$	2.47611	−	2.62086i	0.686748	−	0.726895i
$13$	2.47611	−	2.62086i	0.686748	−	0.726895i
$14$	−0.393511	+	0.681581i	−0.105170	+	0.182160i
$15$	−1.71610	−	0.234546i	−0.443094	−	0.0605595i
$16$	−0.957524	−	1.65848i	−0.239381	−	0.414620i
$17$	−1.63642			−0.396889			−0.198445	−	0.980112i	$-0.563589\pi$
$17$	−1.63642			−0.396889			−0.198445	+	0.980112i	$0.563589\pi$
$18$	−0.489899	+	1.75874i	−0.115470	+	0.414539i
$19$			2.80454i			0.643406i	0.946841	+	0.321703i	$0.104255\pi$
$19$			2.80454i			0.643406i	−0.946841	+	0.321703i	$0.895745\pi$
$20$	−1.41132	+	0.814824i	−0.315580	+	0.182200i
$21$	−1.37235	+	1.77033i	−0.299472	+	0.386318i
$22$	−0.816367	+	1.41399i	−0.174050	+	0.301463i
$23$	4.00047	−	6.92901i	0.834155	−	1.44480i	−0.0605617	−	0.998164i	$-0.519289\pi$
$23$	4.00047	−	6.92901i	0.834155	−	1.44480i	0.894717	−	0.446634i	$-0.147377\pi$
$24$	1.44665	+	3.54184i	0.295297	+	0.722975i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.507508	+	2.13472i	−0.0995306	+	0.418652i
$27$	−2.05930	+	4.77067i	−0.396313	+	0.918116i
$28$			2.10753i			0.398286i
$29$	1.93551	+	3.35240i	0.359415	+	0.622526i	0.987863	−	0.155326i	$-0.0496428\pi$
$29$	1.93551	+	3.35240i	0.359415	+	0.622526i	−0.628448	+	0.777852i	$0.716309\pi$
$30$	0.975808	−	0.398565i	0.178157	−	0.0727677i
$31$	7.48207	+	4.31977i	1.34382	+	0.775854i	0.987366	−	0.158459i	$-0.0506524\pi$
$31$	7.48207	+	4.31977i	1.34382	+	0.775854i	0.356454	+	0.934313i	$0.383986\pi$
$32$	4.83518	+	2.79159i	0.854748	+	0.493489i
$33$	−2.84704	+	3.67268i	−0.495606	+	0.639331i
$34$	0.862446	−	0.497933i	0.147908	−	0.0853949i
$35$	1.29324			0.218598
$36$	1.21870	+	4.73461i	0.203117	+	0.789102i
$37$			10.1601i			1.67030i	0.550019	+	0.835152i	$0.314620\pi$
$37$			10.1601i			1.67030i	−0.550019	+	0.835152i	$0.685380\pi$
$38$	−0.853374	−	1.47809i	−0.138436	−	0.239777i
$39$	−2.25386	+	5.82410i	−0.360907	+	0.932602i
$40$	1.10444	−	1.91295i	0.174627	−	0.302463i
$41$	−7.08878	−	4.09271i	−1.10708	−	0.639174i	−0.169009	−	0.985614i	$-0.554057\pi$
$41$	−7.08878	−	4.09271i	−1.10708	−	0.639174i	−0.938072	+	0.346441i	$0.887390\pi$
$42$	0.184593	−	1.35061i	0.0284833	−	0.208403i
$43$	−6.05745	−	10.4918i	−0.923752	−	1.59999i	−0.793556	−	0.608498i	$-0.791772\pi$
$43$	−6.05745	−	10.4918i	−0.923752	−	1.59999i	−0.130197	−	0.991488i	$-0.541561\pi$
$44$			4.37222i			0.659137i
$45$	2.90530	−	0.747832i	0.433096	−	0.111480i
$46$			4.86909i			0.717908i
$47$	10.5167	−	6.07183i	1.53402	−	0.885667i	0.534850	−	0.844947i	$-0.320368\pi$
$47$	10.5167	−	6.07183i	1.53402	−	0.885667i	0.999171	−	0.0407203i	$-0.0129653\pi$
$48$	2.62153	+	2.03219i	0.378385	+	0.293322i
$49$	−2.66376	+	4.61377i	−0.380538	+	0.659110i
$50$	−0.527033	−	0.304283i	−0.0745338	−	0.0430321i
$51$	2.62392	−	1.07173i	0.367423	−	0.150072i
$52$	1.68127	+	5.63011i	0.233150	+	0.780755i
$53$	3.10426			0.426403			0.213201	−	0.977008i	$-0.431611\pi$
$53$	3.10426			0.426403			0.213201	+	0.977008i	$0.431611\pi$
$54$	−0.366312	−	3.14091i	−0.0498488	−	0.427424i
$55$	2.68292			0.361765
$56$	−1.42831	−	2.47390i	−0.190866	−	0.330589i
$57$	−1.83677	−	4.49696i	−0.243286	−	0.595637i
$58$	−2.04016	−	1.17789i	−0.267886	−	0.154664i
$59$	8.90917	+	5.14371i	1.15987	+	0.669654i	0.951274	−	0.308347i	$-0.0997757\pi$
$59$	8.90917	+	5.14371i	1.15987	+	0.669654i	0.208601	+	0.978001i	$0.433109\pi$
$60$	1.72934	−	2.23084i	0.223256	−	0.288001i
$61$	2.42579	+	4.20160i	0.310591	+	0.537960i	0.978490	−	0.206292i	$-0.0661397\pi$
$61$	2.42579	+	4.20160i	0.310591	+	0.537960i	−0.667899	+	0.744252i	$0.732806\pi$
$62$	−5.25773			−0.667733
$63$	1.04107	−	3.73744i	0.131162	−	0.470873i
$64$	0.432360			0.0540450
$65$	3.45480	−	1.03168i	0.428515	−	0.127964i
$66$	0.382951	−	2.80193i	0.0471380	−	0.344894i
$67$	−11.3875	−	6.57457i	−1.39120	−	0.803212i	−0.397755	−	0.917492i	$-0.630211\pi$
$67$	−11.3875	−	6.57457i	−1.39120	−	0.803212i	−0.993449	+	0.114280i	$0.963544\pi$
$68$	1.33339	−	2.30950i	0.161697	−	0.280068i
$69$	−1.87659	+	13.7304i	−0.225914	+	1.65294i
$70$	−0.681581	+	0.393511i	−0.0814646	+	0.0470336i
$71$		−	0.938010i		−	0.111321i	−0.998450	−	0.0556607i	$-0.982274\pi$
$71$		−	0.938010i		−	0.111321i	0.998450	−	0.0556607i	$-0.0177265\pi$
$72$	−4.63929	−	4.73174i	−0.546745	−	0.557641i
$73$			14.6411i			1.71362i	0.515636	+	0.856808i	$0.327556\pi$
$73$			14.6411i			1.71362i	−0.515636	+	0.856808i	$0.672444\pi$
$74$	−3.09153	−	5.35469i	−0.359383	−	0.622470i
$75$	−1.36891	−	1.06117i	−0.158068	−	0.122533i
$76$	−3.95810	−	2.28521i	−0.454025	−	0.262132i
$77$	1.73483	−	3.00482i	0.197703	−	0.342431i
$78$	−0.584313	−	3.75530i	−0.0661604	−	0.425204i
$79$	3.27558	+	5.67348i	0.368532	+	0.638316i	0.989336	−	0.145649i	$-0.0465271\pi$
$79$	3.27558	+	5.67348i	0.368532	+	0.638316i	−0.620804	+	0.783966i	$0.713194\pi$
$80$		−	1.91505i		−	0.214109i
$81$	0.177565	−	8.99825i	0.0197295	−	0.999805i
$82$	4.98136			0.550099
$83$	9.19282	−	5.30748i	1.00904	−	0.582571i	0.0981318	−	0.995173i	$-0.468713\pi$
$83$	9.19282	−	5.30748i	1.00904	−	0.582571i	0.910911	+	0.412602i	$0.135380\pi$
$84$	−1.38028	−	3.37933i	−0.150600	−	0.368715i
$85$	−1.41718	−	0.818208i	−0.153715	−	0.0887472i
$86$	6.38495	+	3.68635i	0.688507	+	0.397510i
$87$	−5.29908	−	4.10782i	−0.568121	−	0.440404i
$88$	−2.96312	−	5.13228i	−0.315870	−	0.547103i
$89$		−	10.4458i		−	1.10725i	−0.832766	−	0.553625i	$-0.813244\pi$
$89$		−	10.4458i		−	1.10725i	0.832766	−	0.553625i	$-0.186756\pi$
$90$	−1.30364	+	1.27816i	−0.137415	+	0.134730i
$91$	1.07849	−	4.53641i	0.113056	−	0.475545i
$92$	6.51935	+	11.2918i	0.679689	+	1.17726i
$93$	−14.8263	−	2.02637i	−1.53742	−	0.210125i
$94$	−3.69511	+	6.40011i	−0.381121	+	0.660121i
$95$	−1.40227	+	2.42881i	−0.143870	+	0.249190i
$96$	−9.58129	−	1.30951i	−0.977887	−	0.133652i
$97$	9.03460	−	5.21613i	0.917325	−	0.529618i	0.0345440	−	0.999403i	$-0.489002\pi$
$97$	9.03460	−	5.21613i	0.917325	−	0.529618i	0.882781	+	0.469786i	$0.155669\pi$
$98$		−	3.24215i		−	0.327506i
$99$	2.15977	−	7.75358i	0.217065	−	0.779264i
$100$	−1.62965			−0.162965
$101$	−0.634391	−	1.09880i	−0.0631243	−	0.109334i	0.832736	−	0.553670i	$-0.186773\pi$
$101$	−0.634391	−	1.09880i	−0.0631243	−	0.109334i	−0.895860	+	0.444336i	$0.853440\pi$
$102$	−1.05678	+	1.36325i	−0.104637	+	0.134982i
$103$	1.80837	−	3.13218i	0.178184	−	0.308623i	−0.763075	−	0.646310i	$-0.776311\pi$
$103$	1.80837	−	3.13218i	0.178184	−	0.308623i	0.941258	+	0.337687i	$0.109645\pi$
$104$	−5.78916	−	5.46942i	−0.567674	−	0.536321i
$105$	−2.07366	+	0.846978i	−0.202368	+	0.0826565i
$106$	−1.63605	+	0.944573i	−0.158907	+	0.0917450i
$107$	−20.1809			−1.95096			−0.975481	−	0.220084i	$-0.929367\pi$
$107$	−20.1809			−1.95096			−0.975481	+	0.220084i	$0.929367\pi$
$108$	−5.05496	−	6.79358i	−0.486413	−	0.653713i
$109$			9.06439i			0.868211i	0.900862	+	0.434106i	$0.142936\pi$
$109$			9.06439i			0.868211i	−0.900862	+	0.434106i	$0.857064\pi$
$110$	−1.41399	+	0.816367i	−0.134819	+	0.0778375i
$111$	−6.65409	−	16.2912i	−0.631578	−	1.54629i
$112$	−2.14482	−	1.23831i	−0.202666	−	0.117009i
$113$	3.03004	−	5.24818i	0.285042	−	0.493707i	−0.687577	−	0.726111i	$-0.741326\pi$
$113$	3.03004	−	5.24818i	0.285042	−	0.493707i	0.972619	+	0.232404i	$0.0746592\pi$
$114$	2.33639	+	1.81115i	0.218823	+	0.169630i
$115$	6.92901	−	4.00047i	0.646134	−	0.373045i
$116$	−6.30840			−0.585720
$117$	−0.200385	−	10.8148i	−0.0185256	−	0.999828i
$118$	−6.26057			−0.576332
$119$	−1.83275	+	1.05814i	−0.168008	+	0.0969997i
$120$	−0.518083	+	3.79065i	−0.0472943	+	0.346037i
$121$	−1.90097	+	3.29257i	−0.172815	+	0.299324i
$122$	−2.55695	−	1.47625i	−0.231495	−	0.133654i
$123$	14.0470	+	1.91985i	1.26657	+	0.173107i
$124$	−12.1931	+	7.03971i	−1.09498	+	0.632185i
$125$			1.00000i			0.0894427i
$126$	0.588561	+	2.28653i	0.0524332	+	0.203701i
$127$	3.95419			0.350878			0.175439	−	0.984490i	$-0.443866\pi$
$127$	3.95419			0.350878			0.175439	+	0.984490i	$0.443866\pi$
$128$	−9.89824	+	5.71475i	−0.874889	+	0.505117i
$129$	16.5842	+	12.8560i	1.46016	+	1.13191i
$130$	−1.50687	+	1.59496i	−0.132162	+	0.139888i
$131$	−1.48172	+	2.56641i	−0.129458	+	0.224228i	−0.923467	−	0.383678i	$-0.874657\pi$
$131$	−1.48172	+	2.56641i	−0.129458	+	0.224228i	0.794009	+	0.607906i	$0.207990\pi$
$132$	−2.86348	−	7.01066i	−0.249234	−	0.610200i
$133$	1.81348	+	3.14103i	0.157248	+	0.272362i
$134$	8.00212			0.691278
$135$	−4.16874	+	3.10187i	−0.358788	+	0.266966i
$136$			3.61465i			0.309953i
$137$	2.22850	−	1.28663i	0.190394	−	0.109924i	−0.401773	−	0.915739i	$-0.631606\pi$
$137$	2.22850	−	1.28663i	0.190394	−	0.109924i	0.592167	+	0.805815i	$0.298273\pi$
$138$	−3.18889	−	7.80738i	−0.271457	−	0.664608i
$139$	−1.08452	+	1.87844i	−0.0919875	+	0.159327i	−0.908347	−	0.418217i	$-0.862655\pi$
$139$	−1.08452	+	1.87844i	−0.0919875	+	0.159327i	0.816360	+	0.577544i	$0.195989\pi$
$140$	−1.05376	+	1.82517i	−0.0890594	+	0.154255i
$141$	−12.8865	+	16.6236i	−1.08524	+	1.39996i
$142$	0.285420	+	0.494362i	0.0239519	+	0.0414860i
$143$	2.23740	−	9.41111i	0.187101	−	0.786996i
$144$	−5.53445	−	1.54163i	−0.461204	−	0.128469i
$145$			3.87102i			0.321471i
$146$	−4.45505	−	7.71637i	−0.368702	−	0.638611i
$147$	1.24955	−	9.14255i	0.103061	−	0.754065i
$148$	−14.3391	−	8.27866i	−1.17866	−	0.680502i
$149$	8.74044	+	5.04629i	0.716044	+	0.413408i	0.813295	−	0.581851i	$-0.197672\pi$
$149$	8.74044	+	5.04629i	0.716044	+	0.413408i	−0.0972506	+	0.995260i	$0.531005\pi$
$150$	1.04436	+	0.142736i	0.0852714	+	0.0116544i
$151$	8.48108	−	4.89655i	0.690181	−	0.398476i	−0.113499	−	0.993538i	$-0.536206\pi$
$151$	8.48108	−	4.89655i	0.690181	−	0.398476i	0.803680	+	0.595062i	$0.202873\pi$
$152$	6.19490			0.502472
$153$	−3.50544	+	3.43695i	−0.283398	+	0.277861i
$154$			2.11152i			0.170151i
$155$	4.31977	+	7.48207i	0.346973	+	0.600974i
$156$	−6.38315	−	7.92653i	−0.511061	−	0.634630i
$157$	8.17538	−	14.1602i	0.652466	−	1.13010i	−0.330056	−	0.943961i	$-0.607068\pi$
$157$	8.17538	−	14.1602i	0.652466	−	1.13010i	0.982523	−	0.186143i	$-0.0595989\pi$
$158$	−3.45268	−	1.99341i	−0.274681	−	0.158587i
$159$	−4.97755	+	2.03306i	−0.394745	+	0.161232i
$160$	2.79159	+	4.83518i	0.220695	+	0.382255i
$161$		−	10.3471i		−	0.815469i
$162$	2.64443	+	4.79641i	0.207766	+	0.376841i
$163$			2.36973i			0.185612i	0.995684	+	0.0928058i	$0.0295836\pi$
$163$			2.36973i			0.185612i	−0.995684	+	0.0928058i	$0.970416\pi$
$164$	11.5522	−	6.66967i	0.902076	−	0.520814i
$165$	−4.30195	+	1.75711i	−0.334906	+	0.136791i
$166$	−3.22995	+	5.59443i	−0.250693	+	0.434212i
$167$	−1.09870	−	0.634337i	−0.0850203	−	0.0490865i	0.456887	−	0.889525i	$-0.348964\pi$
$167$	−1.09870	−	0.634337i	−0.0850203	−	0.0490865i	−0.541907	+	0.840438i	$0.682298\pi$
$168$	3.91045	+	3.03136i	0.301698	+	0.233874i
$169$	−0.737796	−	12.9790i	−0.0567535	−	0.998388i
$170$	0.995867			0.0763795
$171$	5.89035	+	6.00774i	0.450447	+	0.459423i
$172$	19.7430			1.50539
$173$	−4.40726	−	7.63359i	−0.335078	−	0.580371i	0.648422	−	0.761281i	$-0.275429\pi$
$173$	−4.40726	−	7.63359i	−0.335078	−	0.580371i	−0.983500	+	0.180910i	$0.942096\pi$
$174$	4.04273	+	0.552536i	0.306479	+	0.0418876i
$175$	1.11998	+	0.646621i	0.0846626	+	0.0488800i
$176$	−4.44957	−	2.56896i	−0.335399	−	0.193643i
$177$	−17.6542	−	2.41287i	−1.32697	−	0.181363i
$178$	3.17847	+	5.50527i	0.238236	+	0.412638i
$179$	16.7507			1.25200			0.626002	−	0.779822i	$-0.284690\pi$
$179$	16.7507			1.25200			0.626002	+	0.779822i	$0.284690\pi$
$180$	−1.31188	+	4.70964i	−0.0977816	+	0.351036i
$181$	−2.27780			−0.169308			−0.0846539	−	0.996410i	$-0.526978\pi$
$181$	−2.27780			−0.169308			−0.0846539	+	0.996410i	$0.526978\pi$
$182$	0.811953	+	2.71901i	0.0601859	+	0.201546i
$183$	−6.64139	−	5.14836i	−0.490946	−	0.380578i
$184$	−15.3053	−	8.83655i	−1.12833	−	0.651439i
$185$	−5.08003	+	8.79887i	−0.373491	+	0.646906i
$186$	8.43054	−	3.44342i	0.618157	−	0.252484i
$187$	−3.80218	+	2.19519i	−0.278043	+	0.160528i
$188$			19.7899i			1.44333i
$189$	0.778438	+	6.67464i	0.0566230	+	0.485509i
$190$		−	1.70675i		−	0.123821i
$191$	−2.23864	−	3.87743i	−0.161982	−	0.280561i	0.773597	−	0.633677i	$-0.218455\pi$
$191$	−2.23864	−	3.87743i	−0.161982	−	0.280561i	−0.935579	+	0.353116i	$0.885122\pi$
$192$	−0.693270	+	0.283164i	−0.0500325	+	0.0204356i
$193$	5.17752	+	2.98924i	0.372686	+	0.215170i	0.674631	−	0.738155i	$-0.264303\pi$
$193$	5.17752	+	2.98924i	0.372686	+	0.215170i	−0.301945	+	0.953325i	$0.597636\pi$
$194$	−3.17436	+	5.49815i	−0.227905	+	0.394744i
$195$	−4.86395	+	3.91689i	−0.348315	+	0.280494i
$196$	−4.34100	−	7.51882i	−0.310071	−	0.537059i
$197$			14.8976i			1.06141i	0.847556	+	0.530707i	$0.178073\pi$
$197$			14.8976i			1.06141i	−0.847556	+	0.530707i	$0.821927\pi$
$198$	1.22101	+	4.74358i	0.0867735	+	0.337111i
$199$	−12.0750			−0.855975			−0.427988	−	0.903785i	$-0.640777\pi$
$199$	−12.0750			−0.855975			−0.427988	+	0.903785i	$0.640777\pi$
$200$	1.91295	−	1.10444i	0.135266	−	0.0780957i
$201$	22.5652	+	3.08408i	1.59163	+	0.217534i
$202$	0.668691	+	0.386069i	0.0470489	+	0.0271637i
$203$	4.33547	+	2.50308i	0.304290	+	0.175682i
$204$	−0.625483	+	4.57646i	−0.0437926	+	0.320416i
$205$	−4.09271	−	7.08878i	−0.285847	−	0.495102i
$206$			2.20102i			0.153352i
$207$	−5.98335	−	23.2451i	−0.415872	−	1.61564i
$208$	−6.71757	−	1.59704i	−0.465780	−	0.110735i
$209$	3.76219	+	6.51630i	0.260236	+	0.450742i
$210$	0.835165	−	1.07736i	0.0576319	−	0.0743451i
$211$	9.04101	−	15.6595i	0.622408	−	1.07804i	−0.366627	−	0.930368i	$-0.619488\pi$
$211$	9.04101	−	15.6595i	0.622408	−	1.07804i	0.989036	−	0.147675i	$-0.0471790\pi$
$212$	−2.52943	+	4.38109i	−0.173722	+	0.300895i
$213$	0.614327	+	1.50406i	0.0420930	+	0.103056i
$214$	10.6360	−	6.14070i	0.727063	−	0.419770i
$215$		−	12.1149i		−	0.826229i
$216$	10.5378	+	4.54875i	0.717008	+	0.309503i
$217$	11.1730			0.758475
$218$	−2.75814	−	4.77723i	−0.186805	−	0.323555i
$219$	−9.58886	−	23.4764i	−0.647955	−	1.58639i
$220$	−2.18611	+	3.78645i	−0.147387	+	0.255283i
$221$	−4.05194	+	4.28882i	−0.272563	+	0.288497i
$222$	8.46406	+	6.56129i	0.568071	+	0.440365i
$223$	−7.95118	+	4.59062i	−0.532450	+	0.307410i	−0.742014	−	0.670385i	$-0.766129\pi$
$223$	−7.95118	+	4.59062i	−0.532450	+	0.307410i	0.209563	+	0.977795i	$0.432796\pi$
$224$	7.22042			0.482434
$225$	2.88998	+	0.805007i	0.192665	+	0.0536671i
$226$			3.68795i			0.245319i
$227$	1.31183	−	0.757384i	0.0870690	−	0.0502693i	−0.455833	−	0.890065i	$-0.650659\pi$
$227$	1.31183	−	0.757384i	0.0870690	−	0.0502693i	0.542902	+	0.839796i	$0.317325\pi$
$228$	7.84328	+	1.07197i	0.519434	+	0.0709931i
$229$	20.9453	+	12.0928i	1.38410	+	0.799112i	0.992642	−	0.121083i	$-0.0386367\pi$
$229$	20.9453	+	12.0928i	1.38410	+	0.799112i	0.391460	+	0.920195i	$0.371970\pi$
$230$	−2.43455	+	4.21676i	−0.160529	+	0.278045i
$231$	−0.813796	+	5.95428i	−0.0535438	+	0.391763i
$232$	7.40505	−	4.27531i	0.486165	−	0.280688i
$233$	−13.0557			−0.855308			−0.427654	−	0.903942i	$-0.640660\pi$
$233$	−13.0557			−0.855308			−0.427654	+	0.903942i	$0.640660\pi$
$234$	3.39637	+	5.63878i	0.222027	+	0.368619i
$235$	12.1437			0.792165
$236$	−14.5188	+	8.38244i	−0.945094	+	0.545650i
$237$	−8.96796	−	6.95191i	−0.582532	−	0.451575i
$238$	0.643948	−	1.11535i	0.0417410	−	0.0722975i
$239$	−17.8534	−	10.3076i	−1.15484	−	0.666746i	−0.204776	−	0.978809i	$-0.565647\pi$
$239$	−17.8534	−	10.3076i	−1.15484	−	0.666746i	−0.950061	+	0.312063i	$0.898980\pi$
$240$	1.25421	+	3.07070i	0.0809592	+	0.198213i
$241$	3.58808	−	2.07158i	0.231129	−	0.133442i	−0.379964	−	0.925001i	$-0.624064\pi$
$241$	3.58808	−	2.07158i	0.231129	−	0.133442i	0.611093	+	0.791559i	$0.290730\pi$
$242$		−	2.31372i		−	0.148732i
$243$	5.60847	+	14.5446i	0.359783	+	0.933036i
$244$	−7.90638			−0.506154
$245$	−4.61377	+	2.66376i	−0.294763	+	0.170182i
$246$	−7.98740	+	3.26242i	−0.509258	+	0.208004i
$247$	7.35031	+	6.94435i	0.467689	+	0.441858i
$248$	9.54186	−	16.5270i	0.605909	−	1.04946i
$249$	−11.2643	+	14.5309i	−0.713845	+	0.920860i
$250$	−0.304283	−	0.527033i	−0.0192445	−	0.0333325i
$251$	−6.85373			−0.432604			−0.216302	−	0.976327i	$-0.569400\pi$
$251$	−6.85373			−0.432604			−0.216302	+	0.976327i	$0.569400\pi$
$252$	4.42642	+	4.51463i	0.278838	+	0.284395i
$253$		−	21.4659i		−	1.34955i
$254$	−2.08399	+	1.20319i	−0.130761	+	0.0754950i
$255$	2.80825	+	0.383815i	0.175859	+	0.0240354i
$256$	3.04544	−	5.27486i	0.190340	−	0.329679i
$257$	−8.76209	+	15.1764i	−0.546564	+	0.946677i	0.451943	+	0.892047i	$0.350731\pi$
$257$	−8.76209	+	15.1764i	−0.546564	+	0.946677i	−0.998507	+	0.0546298i	$0.982602\pi$
$258$	−12.6523	−	1.72924i	−0.787697	−	0.107658i
$259$	6.56971	+	11.3791i	0.408222	+	0.707061i
$260$	−1.35903	+	5.71645i	−0.0842836	+	0.354519i
$261$	11.1872	+	3.11620i	0.692468	+	0.192888i
$262$		−	1.80344i		−	0.111417i
$263$	15.1431	+	26.2285i	0.933761	+	1.61732i	0.776829	+	0.629711i	$0.216827\pi$
$263$	15.1431	+	26.2285i	0.933761	+	1.61732i	0.156931	+	0.987609i	$0.449840\pi$
$264$	8.11250	+	6.28876i	0.499290	+	0.387047i
$265$	2.68837	+	1.55213i	0.165145	+	0.0953466i
$266$	−1.91152	−	1.10362i	−0.117203	−	0.0676673i
$267$	6.84121	+	16.7494i	0.418675	+	1.02504i
$268$	18.5576	−	10.7142i	1.13359	−	0.654476i
$269$	−12.9862			−0.791780			−0.395890	−	0.918298i	$-0.629564\pi$
$269$	−12.9862			−0.791780			−0.395890	+	0.918298i	$0.629564\pi$
$270$	1.25322	−	2.90326i	0.0762685	−	0.176687i
$271$		−	18.8780i		−	1.14676i	−0.819290	−	0.573380i	$-0.805632\pi$
$271$		−	18.8780i		−	1.14676i	0.819290	−	0.573380i	$-0.194368\pi$
$272$	1.56691	+	2.71397i	0.0950078	+	0.164558i
$273$	1.24170	+	7.98027i	0.0751513	+	0.482988i
$274$	−0.782996	+	1.35619i	−0.0473025	+	0.0819304i
$275$	2.32348	+	1.34146i	0.140111	+	0.0808931i
$276$	−17.8488	−	13.8363i	−1.07437	−	0.832847i
$277$	4.81803	+	8.34507i	0.289487	+	0.501407i	0.973687	−	0.227888i	$-0.0731819\pi$
$277$	4.81803	+	8.34507i	0.289487	+	0.501407i	−0.684200	+	0.729294i	$0.739849\pi$
$278$		−	1.32000i		−	0.0791683i
$279$	25.1005	−	6.46093i	1.50272	−	0.386806i
$280$		−	2.85661i		−	0.170715i
$281$	−1.84340	+	1.06429i	−0.109968	+	0.0634900i	−0.553975	−	0.832533i	$-0.686890\pi$
$281$	−1.84340	+	1.06429i	−0.109968	+	0.0634900i	0.444007	+	0.896023i	$0.353556\pi$
$282$	1.73334	−	12.6823i	0.103219	−	0.755221i
$283$	3.93032	−	6.80751i	0.233633	−	0.404664i	−0.725241	−	0.688495i	$-0.758272\pi$
$283$	3.93032	−	6.80751i	0.233633	−	0.404664i	0.958875	+	0.283830i	$0.0916052\pi$
$284$	1.32383	+	0.764313i	0.0785548	+	0.0453536i
$285$	0.657794	−	4.81287i	0.0389643	−	0.285090i
$286$	1.68445	+	5.64077i	0.0996038	+	0.333546i
$287$	−10.5857			−0.624855
$288$	16.2208	−	4.17529i	0.955821	−	0.246031i
$289$	−14.3221			−0.842479
$290$	−1.17789	−	2.04016i	−0.0691678	−	0.119802i
$291$	−11.0704	+	14.2808i	−0.648959	+	0.837157i
$292$	−20.6633	−	11.9299i	−1.20923	−	0.698147i
$293$	2.89009	+	1.66859i	0.168841	+	0.0974802i	0.582039	−	0.813161i	$-0.302255\pi$
$293$	2.89009	+	1.66859i	0.168841	+	0.0974802i	−0.413198	+	0.910641i	$0.635588\pi$
$294$	2.12337	+	5.19864i	0.123837	+	0.303191i
$295$	5.14371	+	8.90917i	0.299478	+	0.518712i
$296$	22.4423			1.30443
$297$	1.61492	+	13.8470i	0.0937074	+	0.803485i
$298$	−6.14200			−0.355797
$299$	−8.25438	−	27.6416i	−0.477363	−	1.59856i
$300$	2.61307	−	1.06730i	0.150866	−	0.0616205i
$301$	−13.5684	−	7.83375i	−0.782072	−	0.451530i
$302$	−2.97987	+	5.16129i	−0.171473	+	0.296999i
$303$	1.73685	+	1.34640i	0.0997794	+	0.0773484i
$304$	4.65128	−	2.68542i	0.266769	−	0.154019i
$305$			4.85159i			0.277801i
$306$	0.801679	−	2.87803i	0.0458290	−	0.164526i
$307$			15.8453i			0.904341i	0.891932	+	0.452171i	$0.149350\pi$
$307$			15.8453i			0.904341i	−0.891932	+	0.452171i	$0.850650\pi$
$308$	2.82717	+	4.89680i	0.161093	+	0.279021i
$309$	−0.848290	+	6.20667i	−0.0482575	+	0.353085i
$310$	−4.55333	−	2.62887i	−0.258612	−	0.149310i
$311$	7.32849	−	12.6933i	0.415560	−	0.719772i	−0.579927	−	0.814669i	$-0.696919\pi$
$311$	7.32849	−	12.6933i	0.415560	−	0.719772i	0.995487	+	0.0948969i	$0.0302521\pi$
$312$	12.8647	+	4.97850i	0.728322	+	0.281852i
$313$	−9.47920	−	16.4184i	−0.535796	−	0.928026i	−0.999124	−	0.0418390i	$-0.986678\pi$
$313$	−9.47920	−	16.4184i	−0.535796	−	0.928026i	0.463329	−	0.886187i	$-0.346655\pi$
$314$			9.95051i			0.561540i
$315$	2.77031	−	2.71618i	0.156089	−	0.153040i
$316$	−10.6761			−0.600578
$317$	−16.2497	+	9.38179i	−0.912676	+	0.526934i	−0.881291	−	0.472574i	$-0.843325\pi$
$317$	−16.2497	+	9.38179i	−0.912676	+	0.526934i	−0.0313849	+	0.999507i	$0.509992\pi$
$318$	2.00471	−	2.58607i	0.112418	−	0.145020i
$319$	8.99424	+	5.19282i	0.503580	+	0.290742i
$320$	0.374435	+	0.216180i	0.0209315	+	0.0120848i
$321$	32.3592	−	13.2170i	1.80611	−	0.737701i
$322$	3.14846	+	5.45329i	0.175457	+	0.303900i
$323$		−	4.58940i		−	0.255361i
$324$	12.5547	+	7.58259i	0.697483	+	0.421255i
$325$	3.50778	+	0.833942i	0.194577	+	0.0462588i
$326$	−0.721068	−	1.24893i	−0.0399363	−	0.0691716i
$327$	−5.93650	−	14.5344i	−0.328289	−	0.803752i
$328$	−9.04029	+	15.6582i	−0.499167	+	0.864582i
$329$	7.85234	−	13.6007i	0.432914	−	0.749829i
$330$	1.73261	−	2.23507i	0.0953770	−	0.123036i
$331$	0.926344	−	0.534825i	0.0509165	−	0.0293966i	−0.474326	−	0.880349i	$-0.657308\pi$
$331$	0.926344	−	0.534825i	0.0509165	−	0.0293966i	0.525242	+	0.850953i	$0.323975\pi$
$332$			17.2986i			0.949386i
$333$	21.3391	+	21.7643i	1.16937	+	1.19268i
$334$	0.772071			0.0422459
$335$	−6.57457	−	11.3875i	−0.359207	−	0.622165i
$336$	4.25012	+	0.580881i	0.231863	+	0.0316897i
$337$	−9.21947	+	15.9686i	−0.502217	+	0.869865i	0.497780	+	0.867303i	$0.334149\pi$
$337$	−9.21947	+	15.9686i	−0.502217	+	0.869865i	−0.999997	+	0.00256156i	$0.999185\pi$
$338$	4.33814	+	6.61589i	0.235964	+	0.359857i
$339$	−1.42136	+	10.3997i	−0.0771979	+	0.564833i
$340$	2.30950	−	1.33339i	0.125250	−	0.0723133i
$341$	23.1792			1.25523
$342$	−4.93246	−	1.37394i	−0.266717	−	0.0742944i
$343$			15.9425i			0.860813i
$344$	−23.1751	+	13.3802i	−1.24952	+	0.721410i
$345$	−8.49036	+	10.9526i	−0.457106	+	0.589666i
$346$	4.64554	+	2.68211i	0.249746	+	0.144191i
$347$	−4.71025	+	8.15839i	−0.252859	+	0.437965i	−0.964312	−	0.264769i	$-0.914704\pi$
$347$	−4.71025	+	8.15839i	−0.252859	+	0.437965i	0.711452	+	0.702734i	$0.248038\pi$
$348$	10.1152	−	4.13154i	0.542234	−	0.221474i
$349$	−0.446328	+	0.257688i	−0.0238914	+	0.0137937i	−0.511898	−	0.859046i	$-0.671057\pi$
$349$	−0.446328	+	0.257688i	−0.0238914	+	0.0137937i	0.488007	+	0.872840i	$0.337724\pi$
$350$	−0.787022			−0.0420681
$351$	7.40420	+	17.2098i	0.395207	+	0.918592i
$352$	14.9793			0.798397
$353$	−20.3083	+	11.7250i	−1.08090	+	0.624059i	−0.931139	−	0.364663i	$-0.881184\pi$
$353$	−20.3083	+	11.7250i	−1.08090	+	0.624059i	−0.149762	+	0.988722i	$0.547851\pi$
$354$	10.0386	−	4.10021i	0.533543	−	0.217924i
$355$	0.469005	−	0.812340i	0.0248922	−	0.0431146i
$356$	14.7423	+	8.51147i	0.781341	+	0.451107i
$357$	2.24574	−	2.89700i	0.118857	−	0.153326i
$358$	−8.82815	+	5.09694i	−0.466582	+	0.269381i
$359$		−	7.56895i		−	0.399474i	−0.979850	−	0.199737i	$-0.935991\pi$
$359$		−	7.56895i		−	0.399474i	0.979850	−	0.199737i	$-0.0640088\pi$
$360$	−1.65187	−	6.41745i	−0.0870612	−	0.338229i
$361$	11.1345			0.586028
$362$	1.20048	−	0.693096i	0.0630957	−	0.0364283i
$363$	0.891727	−	6.52448i	0.0468035	−	0.342446i
$364$	5.52353	+	5.21847i	0.289512	+	0.273522i
$365$	−7.32057	+	12.6796i	−0.383176	+	0.663680i
$366$	5.06679	+	0.692499i	0.264845	+	0.0361975i
$367$	−8.64699	−	14.9770i	−0.451369	−	0.781794i	0.547102	−	0.837066i	$-0.315731\pi$
$367$	−8.64699	−	14.9770i	−0.451369	−	0.781794i	−0.998471	+	0.0552716i	$0.982398\pi$
$368$	−15.3222			−0.798724
$369$	−23.7811	+	6.12132i	−1.23799	+	0.318663i
$370$		−	6.18306i		−	0.321442i
$371$	3.47671	−	2.00728i	0.180502	−	0.104213i
$372$	14.9407	−	19.2735i	0.774638	−	0.999283i
$373$	−12.5175	+	21.6809i	−0.648131	+	1.12260i	0.335438	+	0.942062i	$0.391116\pi$
$373$	−12.5175	+	21.6809i	−0.648131	+	1.12260i	−0.983569	+	0.180533i	$0.942218\pi$
$374$	1.33592	−	2.31387i	0.0690786	−	0.119648i
$375$	−0.654926	−	1.60346i	−0.0338202	−	0.0828021i
$376$	−13.4119	−	23.2302i	−0.691668	−	1.19800i
$377$	13.5787	+	3.22821i	0.699339	+	0.166261i
$378$	−2.44124	−	3.28089i	−0.125564	−	0.168751i
$379$			0.454028i			0.0233219i	0.999932	+	0.0116609i	$0.00371187\pi$
$379$			0.454028i			0.0233219i	−0.999932	+	0.0116609i	$0.996288\pi$
$380$	−2.28521	−	3.95810i	−0.117229	−	0.203046i
$381$	−6.34038	+	2.58970i	−0.324827	+	0.132675i
$382$	2.35967	+	1.36236i	0.120731	+	0.0697042i
$383$	−1.53416	−	0.885745i	−0.0783917	−	0.0452595i	0.460292	−	0.887768i	$-0.347745\pi$
$383$	−1.53416	−	0.885745i	−0.0783917	−	0.0452595i	−0.538683	+	0.842508i	$0.681078\pi$
$384$	12.1287	−	15.6460i	0.618938	−	0.798430i
$385$	3.00482	−	1.73483i	0.153140	−	0.0884153i
$386$	−3.63830			−0.185184
$387$	−35.0118	−	9.75257i	−1.77975	−	0.495751i
$388$			17.0009i			0.863090i
$389$	2.51275	+	4.35221i	0.127401	+	0.220666i	0.922669	−	0.385593i	$-0.126003\pi$
$389$	2.51275	+	4.35221i	0.127401	+	0.220666i	−0.795268	+	0.606258i	$0.792670\pi$
$390$	1.37162	−	3.54435i	0.0694548	−	0.179475i
$391$	−6.54643	+	11.3387i	−0.331067	+	0.573425i
$392$	10.1913	+	5.88393i	0.514737	+	0.297183i
$393$	0.695060	−	5.08553i	0.0350612	−	0.256531i
$394$	−4.53310	−	7.85155i	−0.228374	−	0.395556i
$395$			6.55117i			0.329625i
$396$	9.18292	+	9.36592i	0.461459	+	0.470655i
$397$		−	16.9342i		−	0.849901i	−0.905217	−	0.424951i	$-0.860291\pi$
$397$		−	16.9342i		−	0.849901i	0.905217	−	0.424951i	$-0.139709\pi$
$398$	6.36394	−	3.67422i	0.318995	−	0.184172i
$399$	−4.96497	−	3.84882i	−0.248560	−	0.192682i
$400$	0.957524	−	1.65848i	0.0478762	−	0.0829240i
$401$	−31.3441	−	18.0965i	−1.56525	−	0.903698i	−0.996711	−	0.0810430i	$-0.974175\pi$
$401$	−31.3441	−	18.0965i	−1.56525	−	0.903698i	−0.568541	−	0.822655i	$-0.692492\pi$
$402$	−12.8310	+	5.24079i	−0.639954	+	0.261387i
$403$	29.8479	−	8.91322i	1.48683	−	0.443999i
$404$	2.06767			0.102870
$405$	4.65290	−	7.70393i	0.231204	−	0.382811i
$406$	−3.04658			−0.151199
$407$	13.6293	+	23.6067i	0.675581	+	1.17014i
$408$	−2.36732	−	5.79593i	−0.117200	−	0.286941i
$409$	−29.1173	−	16.8109i	−1.43976	−	0.831246i	−0.441927	−	0.897051i	$-0.645705\pi$
$409$	−29.1173	−	16.8109i	−1.43976	−	0.831246i	−0.997832	+	0.0658052i	$0.979038\pi$
$410$	4.31399	+	2.49068i	0.213053	+	0.123006i
$411$	−2.73066	+	3.52255i	−0.134693	+	0.173755i
$412$	2.94700	+	5.10436i	0.145188	+	0.251474i
$413$	13.3041			0.654653
$414$	10.2265	+	10.4303i	0.502605	+	0.512621i
$415$	10.6150			0.521068
$416$	19.2888	−	5.76005i	0.945711	−	0.282410i
$417$	0.508738	−	3.72227i	0.0249130	−	0.182280i
$418$	−3.96559	−	2.28954i	−0.193964	−	0.111985i
$419$	17.6186	−	30.5163i	0.860725	−	1.49082i	−0.0105051	−	0.999945i	$-0.503344\pi$
$419$	17.6186	−	30.5163i	0.860725	−	1.49082i	0.871230	−	0.490875i	$-0.163323\pi$
$420$	0.494312	−	3.61672i	0.0241200	−	0.176478i
$421$	−3.25429	+	1.87887i	−0.158605	+	0.0915704i	−0.577202	−	0.816602i	$-0.695855\pi$
$421$	−3.25429	+	1.87887i	−0.158605	+	0.0915704i	0.418597	+	0.908172i	$0.362522\pi$
$422$			11.0041i			0.535671i
$423$	9.77572	−	35.0949i	0.475312	−	1.70637i
$424$		−	6.85693i		−	0.333002i
$425$	−0.818208	−	1.41718i	−0.0396889	−	0.0687432i
$426$	−0.781430	−	0.605759i	−0.0378604	−	0.0293491i
$427$	5.43368	+	3.13714i	0.262954	+	0.151817i
$428$	16.4439	−	28.4816i	0.794845	−	1.37671i
$429$	2.57600	+	16.5556i	0.124371	+	0.799313i
$430$	3.68635	+	6.38495i	0.177772	+	0.307910i
$431$			17.6971i			0.852439i	0.904620	+	0.426220i	$0.140155\pi$
$431$			17.6971i			0.852439i	−0.904620	+	0.426220i	$0.859845\pi$
$432$	9.88389	−	1.15272i	0.475539	−	0.0554603i
$433$	−4.88751			−0.234879			−0.117439	−	0.993080i	$-0.537469\pi$
$433$	−4.88751			−0.234879			−0.117439	+	0.993080i	$0.537469\pi$
$434$	−5.88856	+	3.39976i	−0.282660	+	0.163194i
$435$	−2.53523	−	6.20701i	−0.121555	−	0.297604i
$436$	−12.7927	−	7.38588i	−0.612660	−	0.353720i
$437$	19.4327	+	11.2195i	0.929593	+	0.536701i
$438$	12.1971	+	9.45513i	0.582801	+	0.451784i
$439$	−5.70710	−	9.88498i	−0.272385	−	0.471785i	0.697087	−	0.716986i	$-0.254479\pi$
$439$	−5.70710	−	9.88498i	−0.272385	−	0.471785i	−0.969472	+	0.245202i	$0.921146\pi$
$440$		−	5.92625i		−	0.282523i
$441$	3.98409	+	15.4780i	0.189719	+	0.737050i
$442$	0.830495	−	3.49328i	0.0395026	−	0.166159i
$443$	−5.83655	−	10.1092i	−0.277303	−	0.480303i	0.693411	−	0.720543i	$-0.256107\pi$
$443$	−5.83655	−	10.1092i	−0.277303	−	0.480303i	−0.970714	+	0.240240i	$0.922774\pi$
$444$	28.4140	+	3.88345i	1.34847	+	0.184300i
$445$	5.22289	−	9.04631i	0.247589	−	0.428836i
$446$	2.79369	−	4.83881i	0.132285	−	0.229124i
$447$	−17.3199	−	2.36717i	−0.819201	−	0.111963i
$448$	0.484235	−	0.279573i	0.0228779	−	0.0132086i
$449$			6.01106i			0.283679i	0.989890	+	0.141840i	$0.0453017\pi$
$449$			6.01106i			0.283679i	−0.989890	+	0.141840i	$0.954698\pi$
$450$	−1.76806	+	0.455105i	−0.0833473	+	0.0214538i
$451$	−21.9608			−1.03409
$452$	4.93789	+	8.55268i	0.232259	+	0.402284i
$453$	−10.3922	+	13.4059i	−0.488266	+	0.629864i
$454$	−0.460918	+	0.798333i	−0.0216319	+	0.0374676i
$455$	3.20220	−	3.38940i	0.150122	−	0.158898i
$456$	−9.93325	+	4.05720i	−0.465167	+	0.189996i
$457$	−23.0370	+	13.3004i	−1.07762	+	0.622167i	−0.930255	−	0.366914i	$-0.880414\pi$
$457$	−23.0370	+	13.3004i	−1.07762	+	0.622167i	−0.147370	+	0.989081i	$0.547081\pi$
$458$	−14.7185			−0.687749
$459$	3.36987	−	7.80680i	0.157292	−	0.364390i
$460$			13.0387i			0.607933i
$461$	−3.75595	+	2.16850i	−0.174932	+	0.100997i	−0.584909	−	0.811099i	$-0.698870\pi$
$461$	−3.75595	+	2.16850i	−0.174932	+	0.100997i	0.409977	+	0.912096i	$0.365537\pi$
$462$	−1.38289	−	3.38573i	−0.0643378	−	0.157518i
$463$	−30.3881	−	17.5446i	−1.41225	−	0.815365i	−0.416654	−	0.909065i	$-0.636797\pi$
$463$	−30.3881	−	17.5446i	−1.41225	−	0.815365i	−0.995600	+	0.0937000i	$0.970131\pi$
$464$	3.70660	−	6.42001i	0.172074	−	0.298042i
$465$	−11.8268	−	9.16804i	−0.548453	−	0.425158i
$466$	6.88080	−	3.97263i	0.318747	−	0.184028i
$467$	−37.7211			−1.74552			−0.872762	−	0.488146i	$-0.837674\pi$
$467$	−37.7211			−1.74552			−0.872762	+	0.488146i	$0.837674\pi$
$468$	15.4264	+	8.52935i	0.713085	+	0.394269i
$469$	−17.0050			−0.785219
$470$	−6.40011	+	3.69511i	−0.295215	+	0.170443i
$471$	−3.83500	+	28.0595i	−0.176708	+	1.29291i
$472$	11.3618	−	19.6793i	0.522971	−	0.905812i
$473$	−28.1487	−	16.2517i	−1.29428	−	0.747252i
$474$	6.84176	+	0.935091i	0.314253	+	0.0429501i
$475$	−2.42881	+	1.40227i	−0.111441	+	0.0643406i
$476$		−	3.44880i		−	0.158075i
$477$	6.64977	−	6.51985i	0.304472	−	0.298523i
$478$	12.5458			0.573829
$479$	3.88761	−	2.24452i	0.177630	−	0.102555i	−0.408549	−	0.912736i	$-0.633965\pi$
$479$	3.88761	−	2.24452i	0.177630	−	0.102555i	0.586179	+	0.810182i	$0.300632\pi$
$480$	−7.64289	−	5.92472i	−0.348848	−	0.270425i
$481$	26.6281	+	25.1574i	1.21414	+	1.14708i
$482$	−1.26069	+	2.18358i	−0.0574230	+	0.0994595i
$483$	6.77661	+	16.5912i	0.308346	+	0.754925i
$484$	−3.09790	−	5.36573i	−0.140814	−	0.243897i
$485$	10.4323			0.473704
$486$	−7.38152	−	5.95892i	−0.334832	−	0.270302i
$487$		−	20.7990i		−	0.942493i	−0.882001	−	0.471247i	$-0.843804\pi$
$487$		−	20.7990i		−	0.942493i	0.882001	−	0.471247i	$-0.156196\pi$
$488$	9.28082	−	5.35828i	0.420123	−	0.242558i
$489$	−1.55200	−	3.79976i	−0.0701838	−	0.171831i
$490$	1.62107	−	2.80778i	0.0732327	−	0.126843i
$491$	−15.3335	+	26.5583i	−0.691990	+	1.19856i	0.279195	+	0.960234i	$0.409932\pi$
$491$	−15.3335	+	26.5583i	−0.691990	+	1.19856i	−0.971185	+	0.238327i	$0.923401\pi$
$492$	−14.1553	+	18.2604i	−0.638171	+	0.823241i
$493$	−3.16730	−	5.48593i	−0.142648	−	0.247074i
$494$	−5.98690	−	1.42333i	−0.269364	−	0.0640386i
$495$	5.74721	−	5.63491i	0.258318	−	0.253271i
$496$		−	16.5452i		−	0.742899i
$497$	−0.606537	−	1.05055i	−0.0272069	−	0.0471237i
$498$	1.51514	−	11.0858i	0.0678951	−	0.496767i
$499$	−8.32775	−	4.80803i	−0.372801	−	0.215237i	0.301880	−	0.953346i	$-0.402386\pi$
$499$	−8.32775	−	4.80803i	−0.372801	−	0.215237i	−0.674682	+	0.738109i	$0.735719\pi$
$500$	−1.41132	−	0.814824i	−0.0631160	−	0.0364400i
$501$	2.17717	+	0.297562i	0.0972687	+	0.0132941i
$502$	3.61214	−	2.08547i	0.161218	−	0.0930792i
$503$	11.4885			0.512249			0.256125	−	0.966644i	$-0.417554\pi$
$503$	11.4885			0.512249			0.256125	+	0.966644i	$0.417554\pi$
$504$	−8.25555	−	2.29959i	−0.367731	−	0.102432i
$505$		−	1.26878i		−	0.0564601i
$506$	6.53170	+	11.3132i	0.290369	+	0.502934i
$507$	9.68334	+	20.3281i	0.430052	+	0.902804i
$508$	−3.22197	+	5.58062i	−0.142952	+	0.247600i
$509$	−23.5359	−	13.5885i	−1.04321	−	0.602299i	−0.122471	−	0.992472i	$-0.539082\pi$
$509$	−23.5359	−	13.5885i	−1.04321	−	0.602299i	−0.920742	+	0.390173i	$0.872415\pi$
$510$	−1.59683	+	0.652219i	−0.0707088	+	0.0288807i
$511$	9.46727	+	16.3978i	0.418807	+	0.725395i
$512$		−	19.1523i		−	0.846420i
$513$	−13.3795	−	5.77540i	−0.590722	−	0.254990i
$514$		−	10.6646i		−	0.470396i
$515$	3.13218	−	1.80837i	0.138021	−	0.0796862i
$516$	−31.6571	+	12.9302i	−1.39362	+	0.569221i
$517$	16.2902	−	28.2155i	0.716444	−	1.24092i
$518$	−6.92491	−	3.99810i	−0.304263	−	0.175666i
$519$	12.0663	+	9.35371i	0.529651	+	0.410582i
$520$	−2.27885	−	7.63123i	−0.0999341	−	0.334652i
$521$	18.6966			0.819114			0.409557	−	0.912284i	$-0.365683\pi$
$521$	18.6966			0.819114			0.409557	+	0.912284i	$0.365683\pi$
$522$	−6.84421	+	1.76172i	−0.299563	+	0.0771084i
$523$	23.4184			1.02401			0.512007	−	0.858981i	$-0.328902\pi$
$523$	23.4184			1.02401			0.512007	+	0.858981i	$0.328902\pi$
$524$	−2.41467	−	4.18234i	−0.105486	−	0.182706i
$525$	−2.21933	−	0.303324i	−0.0968594	−	0.0132382i
$526$	−15.9618	−	9.21554i	−0.695967	−	0.401817i
$527$	−12.2438	−	7.06895i	−0.533348	−	0.307928i
$528$	8.81718	+	1.20508i	0.383718	+	0.0524443i
$529$	−20.5075	−	35.5200i	−0.891629	−	1.54435i
$530$	−1.88915			−0.0820593
$531$	29.8880	−	7.69326i	1.29703	−	0.333859i
$532$	−5.91066			−0.256260
$533$	−28.2790	+	8.44470i	−1.22490	+	0.365781i
$534$	−8.70209	−	6.74580i	−0.376576	−	0.291919i
$535$	−17.4772	−	10.0905i	−0.755604	−	0.436248i
$536$	−14.5224	+	25.1536i	−0.627274	+	1.08647i
$537$	−26.8590	+	10.9704i	−1.15905	+	0.473409i
$538$	6.84413	−	3.95146i	0.295072	−	0.170360i
$539$			14.2933i			0.615657i
$540$	−0.980930	−	8.41089i	−0.0422125	−	0.361947i
$541$			26.8018i			1.15230i	0.817344	+	0.576151i	$0.195446\pi$
$541$			26.8018i			1.15230i	−0.817344	+	0.576151i	$0.804554\pi$
$542$	5.74426	+	9.94935i	0.246737	+	0.427361i
$543$	3.65236	−	1.49179i	0.156738	−	0.0640189i
$544$	−7.91238	−	4.56821i	−0.339240	−	0.195860i
$545$	−4.53219	+	7.84999i	−0.194138	+	0.336257i
$546$	−3.08268	−	3.82804i	−0.131926	−	0.163825i
$547$	17.4524	+	30.2284i	0.746209	+	1.29247i	0.949628	+	0.313380i	$0.101461\pi$
$547$	17.4524	+	30.2284i	0.746209	+	1.29247i	−0.203418	+	0.979092i	$0.565205\pi$
$548$			4.19349i			0.179137i
$549$	14.0210	+	3.90556i	0.598401	+	0.166685i
$550$	−1.63273			−0.0696200
$551$	−9.40196	+	5.42822i	−0.400537	+	0.231250i
$552$	30.3287	+	4.14515i	1.29088	+	0.176429i
$553$	7.33718	+	4.23612i	0.312009	+	0.180138i
$554$	−5.07852	−	2.93209i	−0.215766	−	0.124572i
$555$	2.38300	−	17.4356i	0.101153	−	0.740102i
$556$	−1.76738	−	3.06119i	−0.0749536	−	0.129823i
$557$		−	28.6771i		−	1.21509i	−0.794287	−	0.607543i	$-0.792155\pi$
$557$		−	28.6771i		−	1.21509i	0.794287	−	0.607543i	$-0.207845\pi$
$558$	−11.2628	+	11.0428i	−0.476793	+	0.467477i
$559$	−42.4964	−	10.1031i	−1.79741	−	0.427316i
$560$	−1.23831	−	2.14482i	−0.0523282	−	0.0906350i
$561$	4.65894	−	6.01003i	0.196701	−	0.253744i
$562$	0.647688	−	1.12183i	0.0273211	−	0.0473215i
$563$	−17.9053	+	31.0129i	−0.754618	+	1.30704i	0.190946	+	0.981600i	$0.438844\pi$
$563$	−17.9053	+	31.0129i	−0.754618	+	1.30704i	−0.945564	+	0.325436i	$0.894489\pi$
$564$	−12.9609	−	31.7322i	−0.545753	−	1.33617i
$565$	5.24818	−	3.03004i	0.220792	−	0.127475i
$566$			4.78371i			0.201074i
$567$	−5.61959	−	10.1927i	−0.236000	−	0.428052i
$568$	−2.07195			−0.0869371
$569$	−3.53605	−	6.12462i	−0.148239	−	0.256757i	0.782338	−	0.622854i	$-0.214027\pi$
$569$	−3.53605	−	6.12462i	−0.148239	−	0.256757i	−0.930577	+	0.366097i	$0.880694\pi$
$570$	1.11779	+	2.73670i	0.0468192	+	0.114628i
$571$	−2.13580	+	3.69932i	−0.0893806	+	0.154812i	−0.907249	−	0.420593i	$-0.861822\pi$
$571$	−2.13580	+	3.69932i	−0.0893806	+	0.154812i	0.817869	+	0.575405i	$0.195155\pi$
$572$	11.4590	+	10.8261i	0.479123	+	0.452661i
$573$	6.12899	+	4.75115i	0.256042	+	0.198482i
$574$	5.57903	−	3.22105i	0.232864	−	0.134444i
$575$	8.00093			0.333662
$576$	0.926177	−	0.908081i	0.0385907	−	0.0378367i
$577$		−	33.2474i		−	1.38411i	−0.721847	−	0.692053i	$-0.756707\pi$
$577$		−	33.2474i		−	1.38411i	0.721847	−	0.692053i	$-0.243293\pi$
$578$	7.54824	−	4.35798i	0.313966	−	0.181268i
$579$	−10.2597	−	1.40223i	−0.426377	−	0.0582746i
$580$	−5.46324	−	3.15420i	−0.226849	−	0.130971i
$581$	6.86385	−	11.8885i	0.284761	−	0.493220i
$582$	1.48906	−	10.8950i	0.0617237	−	0.451612i
$583$	7.21268	−	4.16424i	0.298719	−	0.172465i
$584$	32.3405			1.33826
$585$	5.23386	−	9.46608i	0.216394	−	0.391374i
$586$	−2.03089			−0.0838955
$587$	−4.96357	+	2.86572i	−0.204869	+	0.118281i	−0.598924	−	0.800806i	$-0.704405\pi$
$587$	−4.96357	+	2.86572i	−0.204869	+	0.118281i	0.394056	+	0.919087i	$0.371072\pi$
$588$	11.8849	+	9.21308i	0.490124	+	0.379941i
$589$	−12.1150	+	20.9838i	−0.499190	+	0.864622i
$590$	−5.42181	−	3.13028i	−0.223212	−	0.128872i
$591$	−9.75685	−	23.8877i	−0.401343	−	0.982610i
$592$	16.8503	−	9.72851i	0.692542	−	0.399839i
$593$		−	13.9269i		−	0.571909i	−0.958243	−	0.285954i	$-0.907689\pi$
$593$		−	13.9269i		−	0.571909i	0.958243	−	0.285954i	$-0.0923106\pi$
$594$	−5.06453	−	6.80644i	−0.207800	−	0.279272i
$595$	−2.11628			−0.0867591
$596$	−14.2438	+	8.22368i	−0.583450	+	0.336855i
$597$	19.3618	−	7.90824i	0.792424	−	0.323663i
$598$	12.7612	+	12.0564i	0.521844	+	0.493022i
$599$	8.32840	−	14.4252i	0.340289	−	0.589398i	−0.644197	−	0.764859i	$-0.722808\pi$
$599$	8.32840	−	14.4252i	0.340289	−	0.589398i	0.984486	+	0.175461i	$0.0561417\pi$
$600$	−2.34400	+	3.02376i	−0.0956933	+	0.123444i
$601$	2.26464	+	3.92248i	0.0923768	+	0.160001i	0.908511	−	0.417861i	$-0.137220\pi$
$601$	2.26464	+	3.92248i	0.0923768	+	0.160001i	−0.816134	+	0.577863i	$0.803887\pi$
$602$	9.53470			0.388605
$603$	−38.2022	+	9.83335i	−1.55571	+	0.400445i
$604$			15.9593i			0.649376i
$605$	−3.29257	+	1.90097i	−0.133862	+	0.0772852i
$606$	−1.32506	−	0.181102i	−0.0538270	−	0.00735675i
$607$	−0.994895	+	1.72321i	−0.0403815	+	0.0699429i	−0.885510	−	0.464621i	$-0.846191\pi$
$607$	−0.994895	+	1.72321i	−0.0403815	+	0.0699429i	0.845128	+	0.534564i	$0.179524\pi$
$608$	−7.82915	+	13.5605i	−0.317514	+	0.549950i
$609$	−8.59107	−	1.17418i	−0.348128	−	0.0475800i
$610$	−1.47625	−	2.55695i	−0.0597718	−	0.103528i
$611$	10.1271	−	42.5973i	0.409699	−	1.72330i
$612$	−1.99431	−	7.74780i	−0.0806150	−	0.313186i
$613$		−	10.7003i		−	0.432180i	−0.976373	−	0.216090i	$-0.930670\pi$
$613$		−	10.7003i		−	0.432180i	0.976373	−	0.216090i	$-0.0693305\pi$
$614$	−4.82146	−	8.35102i	−0.194578	−	0.337020i
$615$	11.2051	+	8.68613i	0.451833	+	0.350258i
$616$	−6.63728	−	3.83204i	−0.267424	−	0.154397i
$617$	−22.5316	−	13.0086i	−0.907087	−	0.523707i	−0.0275944	−	0.999619i	$-0.508785\pi$
$617$	−22.5316	−	13.0086i	−0.907087	−	0.523707i	−0.879493	+	0.475912i	$0.842118\pi$
$618$	−1.44151	−	3.52924i	−0.0579858	−	0.141967i
$619$	−5.02248	+	2.89973i	−0.201871	+	0.116550i	−0.597528	−	0.801848i	$-0.703850\pi$
$619$	−5.02248	+	2.89973i	−0.201871	+	0.116550i	0.395657	+	0.918398i	$0.370517\pi$
$620$	−14.0794			−0.565443
$621$	24.8179	+	33.3538i	0.995906	+	1.33844i
$622$			8.91973i			0.357649i
$623$	−6.75446	−	11.6991i	−0.270612	−	0.468713i
$624$	11.8173	−	1.83873i	0.473070	−	0.0736081i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	9.99170	+	5.76871i	0.399349	+	0.230564i
$627$	−10.3002	−	7.98464i	−0.411350	−	0.318876i
$628$	13.3230	+	23.0761i	0.531645	+	0.920836i
$629$		−	16.6261i		−	0.662926i
$630$	−0.633558	+	2.27448i	−0.0252416	+	0.0906173i
$631$		−	14.5417i		−	0.578895i	−0.957194	−	0.289447i	$-0.906529\pi$
$631$		−	14.5417i		−	0.578895i	0.957194	−	0.289447i	$-0.0934715\pi$
$632$	12.5320	−	7.23537i	0.498497	−	0.287808i
$633$	−4.24106	+	31.0305i	−0.168567	+	1.23335i
$634$	5.70943	−	9.88903i	0.226751	−	0.392744i
$635$	3.42443	+	1.97710i	0.135894	+	0.0784587i
$636$	1.18653	−	8.68148i	0.0470491	−	0.344243i
$637$	5.49628	+	18.4055i	0.217771	+	0.729254i
$638$	−6.32035			−0.250225
$639$	−1.97009	−	2.00935i	−0.0779357	−	0.0794888i
$640$	−11.4295			−0.451791
$641$	−19.9422	−	34.5410i	−0.787671	−	1.36429i	−0.927390	−	0.374095i	$-0.877953\pi$
$641$	−19.9422	−	34.5410i	−0.787671	−	1.36429i	0.139720	−	0.990191i	$-0.455380\pi$
$642$	−13.0327	+	16.8121i	−0.514359	+	0.663522i
$643$	−8.77952	−	5.06886i	−0.346231	−	0.199896i	0.316793	−	0.948495i	$-0.397394\pi$
$643$	−8.77952	−	5.06886i	−0.346231	−	0.199896i	−0.663024	+	0.748598i	$0.730727\pi$
$644$	14.6031	+	8.43110i	0.575442	+	0.332232i
$645$	7.93436	+	19.4257i	0.312415	+	0.764887i
$646$	1.39648	+	2.41877i	0.0549436	+	0.0951651i
$647$	−31.1854			−1.22602			−0.613012	−	0.790074i	$-0.710042\pi$
$647$	−31.1854			−1.22602			−0.613012	+	0.790074i	$0.710042\pi$
$648$	−19.8760	−	0.392220i	−0.780805	−	0.0154079i
$649$	27.6003			1.08341
$650$	−2.10247	+	0.627843i	−0.0824657	+	0.0246260i
$651$	−17.9155	+	7.31750i	−0.702162	+	0.286796i
$652$	−3.34444	−	1.93091i	−0.130978	−	0.0756204i
$653$	−1.81951	+	3.15149i	−0.0712031	+	0.123327i	−0.899429	−	0.437067i	$-0.856017\pi$
$653$	−1.81951	+	3.15149i	−0.0712031	+	0.123327i	0.828226	+	0.560395i	$0.189351\pi$
$654$	7.55129	+	5.85371i	0.295279	+	0.228898i
$655$	−2.56641	+	1.48172i	−0.100278	+	0.0578954i
$656$			15.6755i			0.612024i
$657$	30.7506	+	31.3634i	1.19970	+	1.22360i
$658$			9.55733i			0.372584i
$659$	−7.33832	−	12.7103i	−0.285860	−	0.495125i	0.686957	−	0.726698i	$-0.258946\pi$
$659$	−7.33832	−	12.7103i	−0.285860	−	0.495125i	−0.972817	+	0.231573i	$0.925613\pi$
$660$	1.02549	−	7.50315i	0.0399170	−	0.292060i
$661$	20.3379	+	11.7421i	0.791052	+	0.456714i	0.840333	−	0.542071i	$-0.182359\pi$
$661$	20.3379	+	11.7421i	0.791052	+	0.456714i	−0.0492805	+	0.998785i	$0.515693\pi$
$662$	−0.325476	+	0.563741i	−0.0126500	+	0.0219104i
$663$	3.68826	−	9.53065i	0.143240	−	0.370140i
$664$	−11.7236	−	20.3058i	−0.454963	−	0.788019i
$665$			3.62695i			0.140647i
$666$	−17.8689	−	4.97741i	−0.692406	−	0.192871i
$667$	30.9718			1.19923
$668$	1.79050	−	1.03375i	0.0692765	−	0.0399968i
$669$	9.74286	−	12.5683i	0.376681	−	0.485918i
$670$	6.93004	+	4.00106i	0.267731	+	0.154574i
$671$	11.2726	+	6.50822i	0.435172	+	0.251247i
$672$	−11.5776	+	4.72884i	−0.446616	+	0.182419i
$673$	5.72069	+	9.90852i	0.220516	+	0.381945i	0.954965	−	0.296719i	$-0.0958924\pi$
$673$	5.72069	+	9.90852i	0.220516	+	0.381945i	−0.734449	+	0.678664i	$0.762559\pi$
$674$		−	11.2213i		−	0.432229i
$675$	−5.16117	+	0.601927i	−0.198654	+	0.0231682i
$676$	18.9187	+	9.53438i	0.727643	+	0.366707i
$677$	14.1714	+	24.5456i	0.544652	+	0.943365i	0.998629	+	0.0523515i	$0.0166716\pi$
$677$	14.1714	+	24.5456i	0.544652	+	0.943365i	−0.453977	+	0.891014i	$0.649995\pi$
$678$	−2.41533	−	5.91347i	−0.0927604	−	0.227105i
$679$	6.74572	−	11.6839i	0.258877	−	0.448388i
$680$	−1.80732	+	3.13038i	−0.0693077	+	0.120044i
$681$	−1.60743	+	2.07358i	−0.0615968	+	0.0794598i
$682$	−12.2162	+	7.05304i	−0.467783	+	0.270075i
$683$			20.4346i			0.781907i	0.920410	+	0.390954i	$0.127855\pi$
$683$			20.4346i			0.781907i	−0.920410	+	0.390954i	$0.872145\pi$
$684$	−13.2784	+	3.41791i	−0.507713	+	0.130687i
$685$	2.57325			0.0983189
$686$	−4.85102	−	8.40221i	−0.185213	−	0.320798i
$687$	−41.5047	−	5.67261i	−1.58350	−	0.216424i
$688$	−11.6003	+	20.0923i	−0.442258	+	0.766013i
$689$	7.68648	−	8.13583i	0.292832	−	0.309950i
$690$	1.14203	−	8.35583i	0.0434762	−	0.318101i
$691$	−20.9192	+	12.0777i	−0.795805	+	0.459458i	−0.842002	−	0.539474i	$-0.818623\pi$
$691$	−20.9192	+	12.0777i	−0.795805	+	0.459458i	0.0461969	+	0.998932i	$0.485290\pi$
$692$	14.3646			0.546059
$693$	−2.59473	−	10.0804i	−0.0985656	−	0.382923i
$694$		−	5.73299i		−	0.217621i
$695$	−1.87844	+	1.08452i	−0.0712532	+	0.0411381i
$696$	−9.07367	+	11.7050i	−0.343936	+	0.443678i
$697$	11.6002	+	6.69737i	0.439389	+	0.253681i
$698$	0.156820	−	0.271620i	0.00593572	−	0.0102810i
$699$	20.9343	−	8.55052i	0.791807	−	0.323411i
$700$	−1.82517	+	1.05376i	−0.0689851	+	0.0398286i
$701$	20.0185			0.756090			0.378045	−	0.925787i	$-0.376596\pi$
$701$	20.0185			0.756090			0.378045	+	0.925787i	$0.376596\pi$
$702$	−9.13891	−	6.81718i	−0.344926	−	0.257298i
$703$	−28.4943			−1.07468
$704$	1.00458	−	0.579994i	0.0378615	−	0.0218593i
$705$	−19.4718	+	7.95319i	−0.733351	+	0.299535i
$706$	7.13543	−	12.3589i	0.268545	−	0.465134i
$707$	−1.42101	−	0.820422i	−0.0534426	−	0.0308551i
$708$	17.7904	−	22.9496i	0.668604	−	0.862499i
$709$	−22.1079	+	12.7640i	−0.830278	+	0.479361i	−0.853948	−	0.520358i	$-0.825798\pi$
$709$	−22.1079	+	12.7640i	−0.830278	+	0.479361i	0.0236696	+	0.999720i	$0.492465\pi$
$710$			0.570841i			0.0214233i
$711$	18.9327	+	5.27373i	0.710033	+	0.197780i
$712$	−23.0735			−0.864715
$713$	59.8635	−	34.5622i	2.24191	−	1.29437i
$714$	−0.302071	+	2.21016i	−0.0113047	+	0.0827130i
$715$	6.64320	−	7.03156i	0.248442	−	0.262965i
$716$	−13.6488	+	23.6405i	−0.510081	+	0.883486i
$717$	35.3778	+	4.83523i	1.32121	+	0.180575i
$718$	2.30310	+	3.98909i	0.0859510	+	0.148871i
$719$	2.74377			0.102325			0.0511627	−	0.998690i	$-0.483707\pi$
$719$	2.74377			0.102325			0.0511627	+	0.998690i	$0.483707\pi$
$720$	−4.02216	−	4.10231i	−0.149897	−	0.152884i
$721$		−	4.67731i		−	0.174192i
$722$	−5.86827	+	3.38805i	−0.218394	+	0.126090i
$723$	−4.39660	+	5.67162i	−0.163511	+	0.210930i
$724$	1.85601	−	3.21470i	0.0689780	−	0.119473i
$725$	−1.93551	+	3.35240i	−0.0718831	+	0.124505i
$726$	1.51532	+	3.70996i	0.0562387	+	0.137689i
$727$	−1.29832	−	2.24876i	−0.0481522	−	0.0834020i	0.840945	−	0.541121i	$-0.182000\pi$
$727$	−1.29832	−	2.24876i	−0.0481522	−	0.0834020i	−0.889097	+	0.457719i	$0.848667\pi$
$728$	−10.0204	−	2.38225i	−0.371380	−	0.0882921i
$729$	−18.5186	−	19.6485i	−0.685873	−	0.727722i
$730$		−	8.91009i		−	0.329777i
$731$	9.91251	+	17.1690i	0.366627	+	0.635017i
$732$	12.6775	−	5.17809i	0.468575	−	0.191388i
$733$	32.2331	+	18.6098i	1.19056	+	0.687368i	0.958433	−	0.285318i	$-0.0920992\pi$
$733$	32.2331	+	18.6098i	1.19056	+	0.687368i	0.232124	+	0.972686i	$0.425433\pi$
$734$	9.11450	+	5.26226i	0.336422	+	0.194234i
$735$	5.65342	−	7.29291i	0.208529	−	0.269003i
$736$	38.6860	−	22.3354i	1.42598	−	0.823292i
$737$	−35.2781			−1.29949
$738$	10.6708	−	10.4623i	0.392797	−	0.385123i
$739$			48.8971i			1.79871i	0.437222	+	0.899354i	$0.355962\pi$
$739$			48.8971i			1.79871i	−0.437222	+	0.899354i	$0.644038\pi$
$740$	−8.27866	−	14.3391i	−0.304330	−	0.527114i
$741$	−16.3339	−	6.32105i	−0.600042	−	0.232210i
$742$	−1.22156	+	2.11581i	−0.0448449	+	0.0776737i
$743$	32.8343	+	18.9569i	1.20457	+	0.695461i	0.961569	−	0.274564i	$-0.0885334\pi$
$743$	32.8343	+	18.9569i	1.20457	+	0.695461i	0.243005	+	0.970025i	$0.421867\pi$
$744$	−4.47601	+	32.7495i	−0.164098	+	1.20066i
$745$	5.04629	+	8.74044i	0.184882	+	0.320225i
$746$		−	15.2354i		−	0.557808i
$747$	8.54511	−	30.6770i	0.312649	−	1.12241i
$748$		−	7.15477i		−	0.261604i
$749$	−22.6022	+	13.0494i	−0.825867	+	0.476815i
$750$	0.833072	+	0.645792i	0.0304195	+	0.0235810i
$751$	−23.5341	+	40.7622i	−0.858770	+	1.48743i	0.0143334	+	0.999897i	$0.495437\pi$
$751$	−23.5341	+	40.7622i	−0.858770	+	1.48743i	−0.873103	+	0.487536i	$0.837896\pi$
$752$	−20.1400	−	11.6278i	−0.734431	−	0.424024i
$753$	10.9897	−	4.48868i	0.400485	−	0.163577i
$754$	−8.13872	+	2.43039i	−0.296395	+	0.0885097i
$755$	9.79311			0.356408
$756$	−10.0543	−	4.34004i	−0.365672	−	0.157846i
$757$	−18.0923			−0.657575			−0.328787	−	0.944404i	$-0.606640\pi$
$757$	−18.0923			−0.657575			−0.328787	+	0.944404i	$0.606640\pi$
$758$	−0.138153	−	0.239288i	−0.00501794	−	0.00869133i
$759$	14.0586	+	34.4196i	0.510293	+	1.24935i
$760$	5.36494	+	3.09745i	0.194607	+	0.112356i
$761$	11.4273	+	6.59758i	0.414241	+	0.239162i	0.692610	−	0.721312i	$-0.256461\pi$
$761$	11.4273	+	6.59758i	0.414241	+	0.239162i	−0.278369	+	0.960474i	$0.589794\pi$
$762$	2.55359	−	3.29413i	0.0925067	−	0.119334i
$763$	5.86122	+	10.1519i	0.212191	+	0.367525i
$764$	7.29638			0.263974
$765$	−4.75428	+	1.22376i	−0.171891	+	0.0442453i
$766$	1.07807			0.0389522
$767$	35.5410	−	10.6133i	1.28331	−	0.383224i
$768$	−1.42859	+	10.4525i	−0.0515498	+	0.377174i
$769$	15.3574	+	8.86659i	0.553801	+	0.319737i	0.750654	−	0.660696i	$-0.229739\pi$
$769$	15.3574	+	8.86659i	0.553801	+	0.319737i	−0.196852	+	0.980433i	$0.563072\pi$
$770$	−1.05576	+	1.82863i	−0.0380469	+	0.0658992i
$771$	4.11022	−	30.0732i	0.148026	−	1.08306i
$772$	−8.43753	+	4.87141i	−0.303673	+	0.175326i
$773$			31.2282i			1.12320i	0.827409	+	0.561600i	$0.189814\pi$
$773$			31.2282i			1.12320i	−0.827409	+	0.561600i	$0.810186\pi$
$774$	21.4199	−	5.51355i	0.769923	−	0.198180i
$775$			8.63955i			0.310342i
$776$	−11.5218	−	19.9563i	−0.413608	−	0.716391i
$777$	−17.9867	−	13.9432i	−0.645269	−	0.500208i
$778$	−2.64860	−	1.52917i	−0.0949570	−	0.0548235i
$779$	11.4782	−	19.8808i	0.411248	−	0.712303i
$780$	−1.56470	−	10.0561i	−0.0560254	−	0.360068i
$781$	−1.25830	−	2.17945i	−0.0450256	−	0.0779867i
$782$		−	7.96786i		−	0.284930i
$783$	−19.9790	+	2.33007i	−0.713991	+	0.0832700i
$784$	10.2025			0.364374
$785$	14.1602	−	8.17538i	0.505398	−	0.291792i
$786$	1.18112	+	2.89174i	0.0421292	+	0.103145i
$787$	42.4929	+	24.5333i	1.51471	+	0.874517i	0.999851	+	0.0172402i	$0.00548801\pi$
$787$	42.4929	+	24.5333i	1.51471	+	0.874517i	0.514856	+	0.857277i	$0.327845\pi$
$788$	−21.0253	−	12.1390i	−0.748995	−	0.432433i
$789$	−41.4590	−	32.1387i	−1.47598	−	1.14417i
$790$	−1.99341	−	3.45268i	−0.0709223	−	0.122841i
$791$		−	7.83714i		−	0.278657i
$792$	−17.1267	−	4.77067i	−0.608571	−	0.169518i
$793$	17.0183	+	4.04594i	0.604338	+	0.143676i
$794$	5.15277	+	8.92486i	0.182865	+	0.316732i
$795$	−5.32721	−	0.728091i	−0.188937	−	0.0258227i
$796$	9.83901	−	17.0417i	0.348735	−	0.604026i
$797$	3.16482	−	5.48164i	0.112104	−	0.194170i	−0.804515	−	0.593933i	$-0.797574\pi$
$797$	3.16482	−	5.48164i	0.112104	−	0.194170i	0.916618	+	0.399763i	$0.130908\pi$
$798$	3.78784	+	0.517699i	0.134088	+	0.0183263i
$799$	−17.2097	+	9.93604i	−0.608836	+	0.351512i
$800$			5.58319i			0.197396i
$801$	−21.9392	−	22.3764i	−0.775182	−	0.790630i
$802$	22.0259			0.777760
$803$	19.6405	+	34.0184i	0.693099	+	1.20048i
$804$	−22.7393	+	29.3337i	−0.801952	+	1.03452i
$805$	5.17357	−	8.96089i	0.182344	−	0.315830i
$806$	−13.0187	+	13.7798i	−0.458564	+	0.485372i
$807$	20.8227	−	8.50497i	0.732995	−	0.299389i
$808$	−2.42711	+	1.40129i	−0.0853855	+	0.0492973i
$809$	−18.0426			−0.634343			−0.317172	−	0.948368i	$-0.602733\pi$
$809$	−18.0426			−0.634343			−0.317172	+	0.948368i	$0.602733\pi$
$810$	−0.108060	+	5.47602i	−0.00379685	+	0.192408i
$811$			27.0401i			0.949505i	0.880119	+	0.474753i	$0.157462\pi$
$811$			27.0401i			0.949505i	−0.880119	+	0.474753i	$0.842538\pi$
$812$	−7.06529	+	4.07915i	−0.247943	+	0.143150i
$813$	12.3637	+	30.2701i	0.433614	+	1.06162i
$814$	−14.3662	−	8.29434i	−0.503536	−	0.290716i
$815$	−1.18487	+	2.05225i	−0.0415040	+	0.0718871i
$816$	−4.28992	−	3.32552i	−0.150177	−	0.116416i
$817$	29.4247	−	16.9884i	1.02944	−	0.594348i
$818$	20.4611			0.715405
$819$	−7.21750	−	11.9828i	−0.252200	−	0.418713i
$820$	13.3393			0.465830
$821$	−16.7031	+	9.64355i	−0.582943	+	0.336562i	−0.762302	−	0.647222i	$-0.775931\pi$
$821$	−16.7031	+	9.64355i	−0.582943	+	0.336562i	0.179359	+	0.983784i	$0.442598\pi$
$822$	0.367297	−	2.68739i	0.0128109	−	0.0937336i
$823$	10.0877	−	17.4724i	0.351635	−	0.609050i	−0.634901	−	0.772594i	$-0.718959\pi$
$823$	10.0877	−	17.4724i	0.351635	−	0.609050i	0.986536	+	0.163544i	$0.0522924\pi$
$824$	−6.91862	−	3.99447i	−0.241021	−	0.139154i
$825$	−4.60415	−	0.629268i	−0.160296	−	0.0219083i
$826$	−7.01172	+	4.04822i	−0.243969	+	0.140855i
$827$			27.9744i			0.972765i	0.873746	+	0.486382i	$0.161684\pi$
$827$			27.9744i			0.972765i	−0.873746	+	0.486382i	$0.838316\pi$
$828$	37.6815	+	10.4962i	1.30952	+	0.364770i
$829$	34.1583			1.18637			0.593184	−	0.805067i	$-0.297871\pi$
$829$	34.1583			1.18637			0.593184	+	0.805067i	$0.297871\pi$
$830$	−5.59443	+	3.22995i	−0.194186	+	0.112113i
$831$	−13.1909	−	10.2255i	−0.457587	−	0.354719i
$832$	1.07057	−	1.13315i	0.0371153	−	0.0392850i
$833$	4.35903	−	7.55005i	0.151031	−	0.261594i
$834$	0.864501	+	2.11656i	0.0299352	+	0.0732905i
$835$	−0.634337	−	1.09870i	−0.0219521	−	0.0380222i
$836$	−12.2621			−0.424093
$837$	−36.0160	+	26.7988i	−1.24490	+	0.926301i
$838$			21.4441i			0.740776i
$839$	5.52785	−	3.19150i	0.190843	−	0.110183i	−0.401534	−	0.915844i	$-0.631523\pi$
$839$	5.52785	−	3.19150i	0.190843	−	0.110183i	0.592377	+	0.805661i	$0.298190\pi$
$840$	1.87087	+	4.58046i	0.0645512	+	0.158041i
$841$	7.00760	−	12.1375i	0.241641	−	0.418535i
$842$	1.14341	−	1.98045i	0.0394046	−	0.0682508i
$843$	2.25878	−	2.91383i	0.0777965	−	0.100358i
$844$	14.7337	+	25.5194i	0.507153	+	0.878415i
$845$	5.85057	−	11.6091i	0.201266	−	0.399365i
$846$	5.52664	+	21.4708i	0.190010	+	0.738180i
$847$			4.91682i			0.168944i
$848$	−2.97240	−	5.14836i	−0.102073	−	0.176795i
$849$	−1.84368	+	13.4896i	−0.0632749	+	0.462962i
$850$	0.862446	+	0.497933i	0.0295817	+	0.0170790i
$851$	70.3992	+	40.6450i	2.41325	+	1.39329i
$852$	−2.62327	−	0.358533i	−0.0898718	−	0.0122831i
$853$	9.33565	−	5.38994i	0.319646	−	0.184548i	−0.331589	−	0.943424i	$-0.607585\pi$
$853$	9.33565	−	5.38994i	0.319646	−	0.184548i	0.651235	+	0.758876i	$0.274251\pi$
$854$	−3.81831			−0.130660
$855$	2.09733	+	8.14803i	0.0717271	+	0.278657i
$856$			44.5772i			1.52362i
$857$	−15.2790	−	26.4641i	−0.521922	−	0.903995i	−0.999675	−	0.0255008i	$-0.991882\pi$
$857$	−15.2790	−	26.4641i	−0.521922	−	0.903995i	0.477753	−	0.878494i	$-0.341451\pi$
$858$	−6.39523	−	7.94153i	−0.218330	−	0.271120i
$859$	24.3155	−	42.1156i	0.829633	−	1.43697i	−0.0686938	−	0.997638i	$-0.521883\pi$
$859$	24.3155	−	42.1156i	0.829633	−	1.43697i	0.898327	−	0.439328i	$-0.144784\pi$
$860$	17.0980	+	9.87151i	0.583035	+	0.336616i
$861$	16.9737	−	6.93286i	0.578464	−	0.236271i
$862$	−5.38492	−	9.32696i	−0.183411	−	0.317678i
$863$		−	23.8864i		−	0.813101i	−0.913628	−	0.406551i	$-0.866732\pi$
$863$		−	23.8864i		−	0.813101i	0.913628	−	0.406551i	$-0.133268\pi$
$864$	−23.2749	+	17.3183i	−0.791827	+	0.589181i
$865$		−	8.81452i		−	0.299703i
$866$	2.57588	−	1.48719i	0.0875320	−	0.0505367i
$867$	22.9649	−	9.37994i	0.779930	−	0.318559i
$868$	−9.10405	+	15.7687i	−0.309012	+	0.535224i
$869$	15.2215	+	8.78814i	0.516354	+	0.298117i
$870$	3.22484	+	2.49988i	0.109332	+	0.0847537i
$871$	−45.4277	+	13.5657i	−1.53926	+	0.459655i
$872$	20.0221			0.678035
$873$	8.39804	−	30.1490i	0.284230	−	1.02039i
$874$	−13.6556			−0.461907
$875$	0.646621	+	1.11998i	0.0218598	+	0.0378622i
$876$	40.9459	+	5.59624i	1.38343	+	0.189079i
$877$	−15.0998	−	8.71786i	−0.509883	−	0.294381i	0.222902	−	0.974841i	$-0.428447\pi$
$877$	−15.0998	−	8.71786i	−0.509883	−	0.294381i	−0.732786	+	0.680459i	$0.761780\pi$
$878$	6.01566	+	3.47314i	0.203019	+	0.117213i
$879$	−5.72693	−	0.782722i	−0.193165	−	0.0264006i
$880$	−2.56896	−	4.44957i	−0.0865997	−	0.149995i
$881$	−4.15954			−0.140139			−0.0700693	−	0.997542i	$-0.522322\pi$
$881$	−4.15954			−0.140139			−0.0700693	+	0.997542i	$0.522322\pi$
$882$	−6.80945	−	6.94515i	−0.229286	−	0.233855i
$883$	−38.5919			−1.29872			−0.649360	−	0.760481i	$-0.724963\pi$
$883$	−38.5919			−1.29872			−0.649360	+	0.760481i	$0.724963\pi$
$884$	−2.75126	−	9.21320i	−0.0925348	−	0.309874i
$885$	−14.0826	−	10.9167i	−0.473380	−	0.366961i
$886$	6.15211	+	3.55192i	0.206684	+	0.119329i
$887$	8.50698	−	14.7345i	0.285636	−	0.494737i	−0.687127	−	0.726537i	$-0.741128\pi$
$887$	8.50698	−	14.7345i	0.285636	−	0.494737i	0.972763	+	0.231801i	$0.0744617\pi$
$888$	−35.9853	+	14.6981i	−1.20759	+	0.493235i
$889$	4.42862	−	2.55686i	0.148531	−	0.0857545i
$890$			6.35694i			0.213085i
$891$	−11.6582	−	21.1454i	−0.390565	−	0.708399i
$892$		−	14.9622i		−	0.500971i
$893$	17.0287	+	29.4946i	0.569844	+	0.986999i
$894$	9.84843	−	4.02255i	0.329381	−	0.134534i
$895$	14.5065	+	8.37533i	0.484899	+	0.279956i
$896$	−7.39055	+	12.8008i	−0.246901	+	0.427645i
$897$	31.3387	+	38.9161i	1.04637	+	1.29937i
$898$	−1.82906	−	3.16803i	−0.0610365	−	0.105718i
$899$			33.4439i			1.11542i
$900$	−3.49094	+	3.42273i	−0.116365	+	0.114091i
$901$	−5.07986			−0.169235
$902$	11.5741	−	6.68230i	0.385375	−	0.222496i
$903$	26.8869	+	3.67474i	0.894741	+	0.122288i
$904$	−11.5926	−	6.69298i	−0.385564	−	0.222605i
$905$	−1.97264	−	1.13890i	−0.0655726	−	0.0378584i
$906$	1.39783	−	10.2275i	0.0464399	−	0.339786i
$907$	−3.58333	−	6.20652i	−0.118983	−	0.206084i	0.800382	−	0.599490i	$-0.204630\pi$
$907$	−3.58333	−	6.20652i	−0.118983	−	0.206084i	−0.919365	+	0.393406i	$0.871297\pi$
$908$			2.46854i			0.0819213i
$909$	−3.66675	−	1.02138i	−0.121618	−	0.0338770i
$910$	−0.656331	+	2.76070i	−0.0217572	+	0.0915164i
$911$	−15.9695	−	27.6599i	−0.529092	−	0.916415i	−0.999424	−	0.0339252i	$-0.989199\pi$
$911$	−15.9695	−	27.6599i	−0.529092	−	0.916415i	0.470332	−	0.882490i	$-0.344134\pi$
$912$	−5.69938	+	7.35220i	−0.188725	+	0.243456i
$913$	14.2395	−	24.6636i	0.471260	−	0.816247i
$914$	8.09417	−	14.0195i	0.267731	−	0.463724i
$915$	−3.17743	−	7.77931i	−0.105043	−	0.257176i
$916$	−34.1334	+	19.7069i	−1.12780	+	0.651136i
$917$			3.83243i			0.126558i
$918$	0.599439	+	5.13984i	0.0197844	+	0.169640i
$919$	−3.93617			−0.129842			−0.0649212	−	0.997890i	$-0.520680\pi$
$919$	−3.93617			−0.129842			−0.0649212	+	0.997890i	$0.520680\pi$
$920$	−8.83655	−	15.3053i	−0.291332	−	0.504602i
$921$	−10.3775	−	25.4073i	−0.341951	−	0.837199i
$922$	1.31967	−	2.28574i	0.0434612	−	0.0752770i
$923$	−2.45839	−	2.32261i	−0.0809189	−	0.0764497i
$924$	−7.74028	−	6.00022i	−0.254637	−	0.197393i
$925$	−8.79887	+	5.08003i	−0.289305	+	0.167030i
$926$	21.3540			0.701737
$927$	−2.70471	−	10.5077i	−0.0888344	−	0.345118i
$928$			21.6126i			0.709470i
$929$	27.6977	−	15.9913i	0.908731	−	0.524656i	0.0287082	−	0.999588i	$-0.490861\pi$
$929$	27.6977	−	15.9913i	0.908731	−	0.524656i	0.880023	+	0.474932i	$0.157527\pi$
$930$	9.02278	+	1.23318i	0.295869	+	0.0404375i
$931$	−12.9395	−	7.47064i	−0.424076	−	0.244840i
$932$	10.6381	−	18.4257i	0.348463	−	0.603555i
$933$	−3.43773	+	25.1528i	−0.112546	+	0.823465i
$934$	19.8803	−	11.4779i	0.650502	−	0.375568i
$935$	−4.39038			−0.143581
$936$	−23.8886	+	0.442625i	−0.780823	+	0.0144677i
$937$	7.16241			0.233986			0.116993	−	0.993133i	$-0.462675\pi$
$937$	7.16241			0.233986			0.116993	+	0.993133i	$0.462675\pi$
$938$	8.96221	−	5.17434i	0.292627	−	0.168948i
$939$	25.9523	+	20.1181i	0.846923	+	0.656529i
$940$	−9.89494	+	17.1385i	−0.322737	+	0.558998i
$941$	1.82640	+	1.05447i	0.0595390	+	0.0343749i	0.529474	−	0.848326i	$-0.322389\pi$
$941$	1.82640	+	1.05447i	0.0595390	+	0.0343749i	−0.469935	+	0.882701i	$0.655723\pi$
$942$	−6.51684	−	15.9552i	−0.212330	−	0.519849i
$943$	−56.7168	+	32.7455i	−1.84695	+	1.06634i
$944$		−	19.7009i		−	0.641210i
$945$	−2.66317	+	6.16963i	−0.0866331	+	0.200698i
$946$	19.7804			0.643116
$947$	26.1813	−	15.1158i	0.850778	−	0.491197i	−0.0101350	−	0.999949i	$-0.503226\pi$
$947$	26.1813	−	15.1158i	0.850778	−	0.491197i	0.860913	+	0.508751i	$0.169893\pi$
$948$	17.1187	−	6.99205i	0.555988	−	0.227091i
$949$	38.3723	+	36.2530i	1.24562	+	1.17682i
$950$	0.853374	−	1.47809i	0.0276871	−	0.0479555i
$951$	19.9114	−	25.6857i	0.645670	−	0.832915i
$952$	2.33731	+	4.04833i	0.0757525	+	0.131207i
$953$	20.7373			0.671746			0.335873	−	0.941907i	$-0.390969\pi$
$953$	20.7373			0.671746			0.335873	+	0.941907i	$0.390969\pi$
$954$	−1.52077	+	5.45959i	−0.0492369	+	0.176761i
$955$		−	4.47727i		−	0.144881i
$956$	29.0947	−	16.7978i	0.940990	−	0.543281i
$957$	−17.8228	−	2.43591i	−0.576129	−	0.0787418i
$958$	−1.36593	+	2.36587i	−0.0441313	+	0.0764377i
$959$	1.66392	−	2.88199i	0.0537307	−	0.0930643i
$960$	−0.741971	−	0.101408i	−0.0239470	−	0.00327294i
$961$	21.8209	+	37.7949i	0.703900	+	1.21919i
$962$	−21.6888	−	5.15632i	−0.699276	−	0.166246i
$963$	−43.2304	+	42.3858i	−1.39308	+	1.36586i
$964$			6.75190i			0.217464i
$965$	2.98924	+	5.17752i	0.0962271	+	0.166670i
$966$	−8.61991	−	6.68210i	−0.277341	−	0.214993i
$967$	1.36898	+	0.790382i	0.0440235	+	0.0254170i	0.521850	−	0.853037i	$-0.325242\pi$
$967$	1.36898	+	0.790382i	0.0440235	+	0.0254170i	−0.477827	+	0.878454i	$0.658575\pi$
$968$	7.27289	+	4.19900i	0.233759	+	0.134961i
$969$	3.00572	+	7.35891i	0.0965576	+	0.236402i
$970$	−5.49815	+	3.17436i	−0.176535	+	0.101922i
$971$	32.7664			1.05152			0.525762	−	0.850632i	$-0.323780\pi$
$971$	32.7664			1.05152			0.525762	+	0.850632i	$0.323780\pi$
$972$	−25.0969	−	3.93596i	−0.804985	−	0.126246i
$973$			2.80508i			0.0899269i
$974$	6.32878	+	10.9618i	0.202787	+	0.351238i
$975$	−6.17075	+	0.960148i	−0.197622	+	0.0307494i
$976$	4.64551	−	8.04627i	0.148699	−	0.257555i
$977$	20.6666	+	11.9319i	0.661184	+	0.381735i	0.792728	−	0.609576i	$-0.208660\pi$
$977$	20.6666	+	11.9319i	0.661184	+	0.381735i	−0.131544	+	0.991310i	$0.541993\pi$
$978$	1.97416	+	1.53035i	0.0631265	+	0.0489353i
$979$	−14.0126	−	24.2705i	−0.447845	−	0.775690i
$980$		−	8.68199i		−	0.277336i
$981$	19.0378	+	19.4172i	0.607832	+	0.619945i
$982$		−	18.6628i		−	0.595555i
$983$	−0.893648	+	0.515948i	−0.0285030	+	0.0164562i	−0.514184	−	0.857680i	$-0.671905\pi$
$983$	−0.893648	+	0.515948i	−0.0285030	+	0.0164562i	0.485681	+	0.874136i	$0.338572\pi$
$984$	4.24073	−	31.0280i	0.135189	−	0.989138i
$985$	−7.44882	+	12.9017i	−0.237339	+	0.411084i
$986$	3.33855	+	1.92751i	0.106321	+	0.0613845i
$987$	−3.68347	+	26.9508i	−0.117246	+	0.857852i
$988$	−15.7899	+	4.71519i	−0.502343	+	0.150010i
$989$	−96.9305			−3.08221
$990$	−1.31436	+	4.71856i	−0.0417731	+	0.149966i
$991$	14.3880			0.457051			0.228525	−	0.973538i	$-0.426610\pi$
$991$	14.3880			0.457051			0.228525	+	0.973538i	$0.426610\pi$
$992$	24.1181	+	41.7738i	0.765751	+	1.32632i
$993$	−1.13508	+	1.46425i	−0.0360207	+	0.0464667i
$994$	0.639330	+	0.369117i	0.0202783	+	0.0117077i
$995$	−10.4573	−	6.03751i	−0.331518	−	0.191402i
$996$	−11.3293	−	27.7376i	−0.358983	−	0.878900i
$997$	−16.7493	−	29.0106i	−0.530455	−	0.918775i	−0.999369	−	0.0355308i	$-0.988688\pi$
$997$	−16.7493	−	29.0106i	−0.530455	−	0.918775i	0.468914	−	0.883244i	$-0.344646\pi$
$998$	5.85200			0.185242
$999$	−48.4703	−	20.9226i	−1.53353	−	0.661963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.571.23	yes	108
9.7	even	3	inner	585.2.bt.b.376.32	yes	108
13.12	even	2	inner	585.2.bt.b.571.32	yes	108
117.25	even	6	inner	585.2.bt.b.376.23	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.23	✓	108	117.25	even	6	inner
585.2.bt.b.376.32	yes	108	9.7	even	3	inner
585.2.bt.b.571.23	yes	108	1.1	even	1	trivial
585.2.bt.b.571.32	yes	108	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.527033 + 0.304283i) q^{2} +(-1.60346 + 0.654926i) q^{3} +(-0.814824 + 1.41132i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.645792 - 0.833072i) q^{6} +(1.11998 - 0.646621i) q^{7} -2.20888i q^{8} +(2.14214 - 2.10029i) q^{9} +O(q^{10})\)	\(q+(-0.527033 + 0.304283i) q^{2} +(-1.60346 + 0.654926i) q^{3} +(-0.814824 + 1.41132i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.645792 - 0.833072i) q^{6} +(1.11998 - 0.646621i) q^{7} -2.20888i q^{8} +(2.14214 - 2.10029i) q^{9} -0.608566 q^{10} +(2.32348 - 1.34146i) q^{11} +(0.382227 - 2.79663i) q^{12} +(2.47611 - 2.62086i) q^{13} +(-0.393511 + 0.681581i) q^{14} +(-1.71610 - 0.234546i) q^{15} +(-0.957524 - 1.65848i) q^{16} -1.63642 q^{17} +(-0.489899 + 1.75874i) q^{18} +2.80454i q^{19} +(-1.41132 + 0.814824i) q^{20} +(-1.37235 + 1.77033i) q^{21} +(-0.816367 + 1.41399i) q^{22} +(4.00047 - 6.92901i) q^{23} +(1.44665 + 3.54184i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.507508 + 2.13472i) q^{26} +(-2.05930 + 4.77067i) q^{27} +2.10753i q^{28} +(1.93551 + 3.35240i) q^{29} +(0.975808 - 0.398565i) q^{30} +(7.48207 + 4.31977i) q^{31} +(4.83518 + 2.79159i) q^{32} +(-2.84704 + 3.67268i) q^{33} +(0.862446 - 0.497933i) q^{34} +1.29324 q^{35} +(1.21870 + 4.73461i) q^{36} +10.1601i q^{37} +(-0.853374 - 1.47809i) q^{38} +(-2.25386 + 5.82410i) q^{39} +(1.10444 - 1.91295i) q^{40} +(-7.08878 - 4.09271i) q^{41} +(0.184593 - 1.35061i) q^{42} +(-6.05745 - 10.4918i) q^{43} +4.37222i q^{44} +(2.90530 - 0.747832i) q^{45} +4.86909i q^{46} +(10.5167 - 6.07183i) q^{47} +(2.62153 + 2.03219i) q^{48} +(-2.66376 + 4.61377i) q^{49} +(-0.527033 - 0.304283i) q^{50} +(2.62392 - 1.07173i) q^{51} +(1.68127 + 5.63011i) q^{52} +3.10426 q^{53} +(-0.366312 - 3.14091i) q^{54} +2.68292 q^{55} +(-1.42831 - 2.47390i) q^{56} +(-1.83677 - 4.49696i) q^{57} +(-2.04016 - 1.17789i) q^{58} +(8.90917 + 5.14371i) q^{59} +(1.72934 - 2.23084i) q^{60} +(2.42579 + 4.20160i) q^{61} -5.25773 q^{62} +(1.04107 - 3.73744i) q^{63} +0.432360 q^{64} +(3.45480 - 1.03168i) q^{65} +(0.382951 - 2.80193i) q^{66} +(-11.3875 - 6.57457i) q^{67} +(1.33339 - 2.30950i) q^{68} +(-1.87659 + 13.7304i) q^{69} +(-0.681581 + 0.393511i) q^{70} -0.938010i q^{71} +(-4.63929 - 4.73174i) q^{72} +14.6411i q^{73} +(-3.09153 - 5.35469i) q^{74} +(-1.36891 - 1.06117i) q^{75} +(-3.95810 - 2.28521i) q^{76} +(1.73483 - 3.00482i) q^{77} +(-0.584313 - 3.75530i) q^{78} +(3.27558 + 5.67348i) q^{79} -1.91505i q^{80} +(0.177565 - 8.99825i) q^{81} +4.98136 q^{82} +(9.19282 - 5.30748i) q^{83} +(-1.38028 - 3.37933i) q^{84} +(-1.41718 - 0.818208i) q^{85} +(6.38495 + 3.68635i) q^{86} +(-5.29908 - 4.10782i) q^{87} +(-2.96312 - 5.13228i) q^{88} -10.4458i q^{89} +(-1.30364 + 1.27816i) q^{90} +(1.07849 - 4.53641i) q^{91} +(6.51935 + 11.2918i) q^{92} +(-14.8263 - 2.02637i) q^{93} +(-3.69511 + 6.40011i) q^{94} +(-1.40227 + 2.42881i) q^{95} +(-9.58129 - 1.30951i) q^{96} +(9.03460 - 5.21613i) q^{97} -3.24215i q^{98} +(2.15977 - 7.75358i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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