LMFDB - Embedded newform 731.2.e.a.681.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.e (of order $3$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			681.10
Character	$\chi$	$=$	731.681
Dual form			731.2.e.a.307.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.31896 q^{2} +(1.65592 + 2.86814i) q^{3} -0.260346 q^{4} +(-0.0483968 - 0.0838257i) q^{5} +(-2.18409 - 3.78296i) q^{6} +(-1.22618 + 2.12381i) q^{7} +2.98130 q^{8} +(-3.98416 + 6.90077i) q^{9} +O(q^{10})$	\(q-1.31896 q^{2} +(1.65592 + 2.86814i) q^{3} -0.260346 q^{4} +(-0.0483968 - 0.0838257i) q^{5} +(-2.18409 - 3.78296i) q^{6} +(-1.22618 + 2.12381i) q^{7} +2.98130 q^{8} +(-3.98416 + 6.90077i) q^{9} +(0.0638334 + 0.110563i) q^{10} +3.41685 q^{11} +(-0.431114 - 0.746711i) q^{12} +(-2.27375 + 3.93826i) q^{13} +(1.61728 - 2.80122i) q^{14} +(0.160283 - 0.277618i) q^{15} -3.41153 q^{16} +(0.500000 - 0.866025i) q^{17} +(5.25494 - 9.10183i) q^{18} +(-1.05890 - 1.83407i) q^{19} +(0.0125999 + 0.0218237i) q^{20} -8.12185 q^{21} -4.50669 q^{22} +(0.736015 + 1.27482i) q^{23} +(4.93681 + 8.55081i) q^{24} +(2.49532 - 4.32201i) q^{25} +(2.99899 - 5.19440i) q^{26} -16.4543 q^{27} +(0.319232 - 0.552926i) q^{28} +(-1.64169 + 2.84350i) q^{29} +(-0.211406 + 0.366166i) q^{30} +(1.52309 + 2.63808i) q^{31} -1.46294 q^{32} +(5.65804 + 9.80002i) q^{33} +(-0.659480 + 1.14225i) q^{34} +0.237373 q^{35} +(1.03726 - 1.79659i) q^{36} +(-0.131041 - 0.226970i) q^{37} +(1.39664 + 2.41906i) q^{38} -15.0606 q^{39} +(-0.144286 - 0.249910i) q^{40} +5.03275 q^{41} +10.7124 q^{42} +(-6.18746 + 2.17148i) q^{43} -0.889565 q^{44} +0.771282 q^{45} +(-0.970774 - 1.68143i) q^{46} +4.06549 q^{47} +(-5.64922 - 9.78474i) q^{48} +(0.492957 + 0.853827i) q^{49} +(-3.29122 + 5.70056i) q^{50} +3.31185 q^{51} +(0.591964 - 1.02531i) q^{52} +(-5.21765 - 9.03723i) q^{53} +21.7025 q^{54} +(-0.165365 - 0.286420i) q^{55} +(-3.65562 + 6.33172i) q^{56} +(3.50691 - 6.07414i) q^{57} +(2.16533 - 3.75045i) q^{58} -9.17786 q^{59} +(-0.0417290 + 0.0722768i) q^{60} +(4.01453 - 6.95338i) q^{61} +(-2.00890 - 3.47952i) q^{62} +(-9.77061 - 16.9232i) q^{63} +8.75262 q^{64} +0.440170 q^{65} +(-7.46273 - 12.9258i) q^{66} +(-4.99393 - 8.64974i) q^{67} +(-0.130173 + 0.225467i) q^{68} +(-2.43757 + 4.22199i) q^{69} -0.313085 q^{70} +(-2.11209 + 3.65824i) q^{71} +(-11.8780 + 20.5733i) q^{72} +(4.87124 - 8.43723i) q^{73} +(0.172838 + 0.299364i) q^{74} +16.5282 q^{75} +(0.275680 + 0.477492i) q^{76} +(-4.18968 + 7.25674i) q^{77} +19.8644 q^{78} +(-0.716526 + 1.24106i) q^{79} +(0.165107 + 0.285974i) q^{80} +(-15.2946 - 26.4910i) q^{81} -6.63800 q^{82} +(-2.19963 - 3.80987i) q^{83} +2.11449 q^{84} -0.0967936 q^{85} +(8.16101 - 2.86410i) q^{86} -10.8741 q^{87} +10.1867 q^{88} +(9.13187 + 15.8169i) q^{89} -1.01729 q^{90} +(-5.57607 - 9.65804i) q^{91} +(-0.191619 - 0.331894i) q^{92} +(-5.04425 + 8.73690i) q^{93} -5.36222 q^{94} +(-0.102495 + 0.177526i) q^{95} +(-2.42252 - 4.19593i) q^{96} +13.9407 q^{97} +(-0.650190 - 1.12616i) q^{98} +(-13.6133 + 23.5789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) $ 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.31896			−0.932645			−0.466323	−	0.884615i	$-0.654421\pi$
$2$	−1.31896			−0.932645			−0.466323	+	0.884615i	$0.654421\pi$
$3$	1.65592	+	2.86814i	0.956047	+	1.65592i	0.731953	+	0.681355i	$0.238609\pi$
$3$	1.65592	+	2.86814i	0.956047	+	1.65592i	0.224094	+	0.974567i	$0.428058\pi$
$4$	−0.260346			−0.130173
$5$	−0.0483968	−	0.0838257i	−0.0216437	−	0.0374880i	0.855001	−	0.518627i	$-0.173557\pi$
$5$	−0.0483968	−	0.0838257i	−0.0216437	−	0.0374880i	−0.876644	+	0.481139i	$0.840223\pi$
$6$	−2.18409	−	3.78296i	−0.891653	−	1.54439i
$7$	−1.22618	+	2.12381i	−0.463453	+	0.802724i	−0.999130	−	0.0416986i	$-0.986723\pi$
$7$	−1.22618	+	2.12381i	−0.463453	+	0.802724i	0.535677	+	0.844423i	$0.320056\pi$
$8$	2.98130			1.05405
$9$	−3.98416	+	6.90077i	−1.32805	+	2.30026i
$10$	0.0638334	+	0.110563i	0.0201859	+	0.0349630i
$11$	3.41685			1.03022			0.515110	−	0.857124i	$-0.327751\pi$
$11$	3.41685			1.03022			0.515110	+	0.857124i	$0.327751\pi$
$12$	−0.431114	−	0.746711i	−0.124452	−	0.215557i
$13$	−2.27375	+	3.93826i	−0.630626	+	1.09228i	0.356798	+	0.934182i	$0.383868\pi$
$13$	−2.27375	+	3.93826i	−0.630626	+	1.09228i	−0.987424	+	0.158095i	$0.949465\pi$
$14$	1.61728	−	2.80122i	0.432237	−	0.748657i
$15$	0.160283	−	0.277618i	0.0413848	−	0.0716806i
$16$	−3.41153			−0.852882
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$	5.25494	−	9.10183i	1.23860	−	2.14532i
$19$	−1.05890	−	1.83407i	−0.242928	−	0.420763i	0.718619	−	0.695404i	$-0.244775\pi$
$19$	−1.05890	−	1.83407i	−0.242928	−	0.420763i	−0.961547	+	0.274640i	$0.911441\pi$
$20$	0.0125999	+	0.0218237i	0.00281743	+	0.00487993i
$21$	−8.12185			−1.77233
$22$	−4.50669			−0.960829
$23$	0.736015	+	1.27482i	0.153470	+	0.265817i	0.932501	−	0.361168i	$-0.117622\pi$
$23$	0.736015	+	1.27482i	0.153470	+	0.265817i	−0.779031	+	0.626985i	$0.784289\pi$
$24$	4.93681	+	8.55081i	1.00772	+	1.74543i
$25$	2.49532	−	4.32201i	0.499063	−	0.864403i
$26$	2.99899	−	5.19440i	0.588150	−	1.01871i
$27$	−16.4543			−3.16663
$28$	0.319232	−	0.552926i	0.0603292	−	0.104493i
$29$	−1.64169	+	2.84350i	−0.304855	+	0.528024i	−0.977229	−	0.212188i	$-0.931941\pi$
$29$	−1.64169	+	2.84350i	−0.304855	+	0.528024i	0.672374	+	0.740211i	$0.265275\pi$
$30$	−0.211406	+	0.366166i	−0.0385973	+	0.0668525i
$31$	1.52309	+	2.63808i	0.273556	+	0.473813i	0.969770	−	0.244022i	$-0.0784668\pi$
$31$	1.52309	+	2.63808i	0.273556	+	0.473813i	−0.696214	+	0.717834i	$0.745133\pi$
$32$	−1.46294			−0.258615
$33$	5.65804	+	9.80002i	0.984939	+	1.70596i
$34$	−0.659480	+	1.14225i	−0.113100	+	0.195895i
$35$	0.237373			0.0401234
$36$	1.03726	−	1.79659i	0.172877	−	0.299432i
$37$	−0.131041	−	0.226970i	−0.0215430	−	0.0373136i	0.855053	−	0.518541i	$-0.173525\pi$
$37$	−0.131041	−	0.226970i	−0.0215430	−	0.0373136i	−0.876596	+	0.481227i	$0.840191\pi$
$38$	1.39664	+	2.41906i	0.226565	+	0.392423i
$39$	−15.0606			−2.41163
$40$	−0.144286	−	0.249910i	−0.0228136	−	0.0395142i
$41$	5.03275			0.785984			0.392992	−	0.919542i	$-0.371440\pi$
$41$	5.03275			0.785984			0.392992	+	0.919542i	$0.371440\pi$
$42$	10.7124			1.65296
$43$	−6.18746	+	2.17148i	−0.943579	+	0.331148i
$43$	−6.18746	+	2.17148i	−0.943579	+	0.331148i
$44$	−0.889565			−0.134107
$45$	0.771282			0.114976
$46$	−0.970774	−	1.68143i	−0.143133	−	0.247913i
$47$	4.06549			0.593013			0.296507	−	0.955031i	$-0.404178\pi$
$47$	4.06549			0.593013			0.296507	+	0.955031i	$0.404178\pi$
$48$	−5.64922	−	9.78474i	−0.815395	−	1.41231i
$49$	0.492957	+	0.853827i	0.0704224	+	0.121975i
$50$	−3.29122	+	5.70056i	−0.465449	+	0.806181i
$51$	3.31185			0.463751
$52$	0.591964	−	1.02531i	0.0820906	−	0.142185i
$53$	−5.21765	−	9.03723i	−0.716699	−	1.24136i	−0.962301	−	0.271988i	$-0.912319\pi$
$53$	−5.21765	−	9.03723i	−0.716699	−	1.24136i	0.245602	−	0.969371i	$-0.421014\pi$
$54$	21.7025			2.95334
$55$	−0.165365	−	0.286420i	−0.0222978	−	0.0386209i
$56$	−3.65562	+	6.33172i	−0.488503	+	0.846112i
$57$	3.50691	−	6.07414i	0.464501	−	0.804539i
$58$	2.16533	−	3.75045i	0.284321	−	0.492459i
$59$	−9.17786			−1.19486			−0.597428	−	0.801922i	$-0.703811\pi$
$59$	−9.17786			−1.19486			−0.597428	+	0.801922i	$0.703811\pi$
$60$	−0.0417290	+	0.0722768i	−0.00538719	+	0.00933089i
$61$	4.01453	−	6.95338i	0.514008	−	0.890289i	−0.485860	−	0.874037i	$-0.661493\pi$
$61$	4.01453	−	6.95338i	0.514008	−	0.890289i	0.999868	−	0.0162518i	$-0.00517332\pi$
$62$	−2.00890	−	3.47952i	−0.255131	−	0.441899i
$63$	−9.77061	−	16.9232i	−1.23098	−	2.13212i
$64$	8.75262			1.09408
$65$	0.440170			0.0545963
$66$	−7.46273	−	12.9258i	−0.918598	−	1.59106i
$67$	−4.99393	−	8.64974i	−0.610105	−	1.05673i	−0.991222	−	0.132207i	$-0.957794\pi$
$67$	−4.99393	−	8.64974i	−0.610105	−	1.05673i	0.381117	−	0.924527i	$-0.375540\pi$
$68$	−0.130173	+	0.225467i	−0.0157858	+	0.0273418i
$69$	−2.43757	+	4.22199i	−0.293449	+	0.508268i
$70$	−0.313085			−0.0374209
$71$	−2.11209	+	3.65824i	−0.250659	+	0.434154i	−0.963707	−	0.266961i	$-0.913981\pi$
$71$	−2.11209	+	3.65824i	−0.250659	+	0.434154i	0.713049	+	0.701115i	$0.247314\pi$
$72$	−11.8780	+	20.5733i	−1.39983	+	2.42459i
$73$	4.87124	−	8.43723i	0.570135	−	0.987503i	−0.426416	−	0.904527i	$-0.640224\pi$
$73$	4.87124	−	8.43723i	0.570135	−	0.987503i	0.996552	−	0.0829764i	$-0.0264426\pi$
$74$	0.172838	+	0.299364i	0.0200920	+	0.0348003i
$75$	16.5282			1.90851
$76$	0.275680	+	0.477492i	0.0316227	+	0.0547721i
$77$	−4.18968	+	7.25674i	−0.477459	+	0.826982i
$78$	19.8644			2.24920
$79$	−0.716526	+	1.24106i	−0.0806154	+	0.139630i	−0.903514	−	0.428558i	$-0.859022\pi$
$79$	−0.716526	+	1.24106i	−0.0806154	+	0.139630i	0.822899	+	0.568188i	$0.192355\pi$
$80$	0.165107	+	0.285974i	0.0184595	+	0.0319728i
$81$	−15.2946	−	26.4910i	−1.69940	−	2.94344i
$82$	−6.63800			−0.733044
$83$	−2.19963	−	3.80987i	−0.241440	−	0.418187i	0.719684	−	0.694301i	$-0.244287\pi$
$83$	−2.19963	−	3.80987i	−0.241440	−	0.418187i	−0.961125	+	0.276114i	$0.910953\pi$
$84$	2.11449			0.230710
$85$	−0.0967936			−0.0104987
$86$	8.16101	−	2.86410i	0.880024	−	0.308843i
$87$	−10.8741			−1.16582
$88$	10.1867			1.08590
$89$	9.13187	+	15.8169i	0.967977	+	1.67658i	0.701396	+	0.712772i	$0.252560\pi$
$89$	9.13187	+	15.8169i	0.967977	+	1.67658i	0.266581	+	0.963813i	$0.414106\pi$
$90$	−1.01729			−0.107232
$91$	−5.57607	−	9.65804i	−0.584531	−	1.01244i
$92$	−0.191619	−	0.331894i	−0.0199777	−	0.0346023i
$93$	−5.04425	+	8.73690i	−0.523065	+	0.905975i
$94$	−5.36222			−0.553071
$95$	−0.102495	+	0.177526i	−0.0105157	+	0.0182138i
$96$	−2.42252	−	4.19593i	−0.247248	−	0.428246i
$97$	13.9407			1.41546			0.707730	−	0.706483i	$-0.249719\pi$
$97$	13.9407			1.41546			0.707730	+	0.706483i	$0.249719\pi$
$98$	−0.650190	−	1.12616i	−0.0656791	−	0.113760i
$99$	−13.6133	+	23.5789i	−1.36819	+	2.36977i
$100$	−0.649647	+	1.12522i	−0.0649647	+	0.112522i
$101$	−5.52837	+	9.57542i	−0.550093	+	0.952790i	0.448174	+	0.893946i	$0.352075\pi$
$101$	−5.52837	+	9.57542i	−0.550093	+	0.952790i	−0.998267	+	0.0588432i	$0.981259\pi$
$102$	−4.36819			−0.432515
$103$	−5.81736	+	10.0760i	−0.573202	+	0.992814i	0.423033	+	0.906114i	$0.360965\pi$
$103$	−5.81736	+	10.0760i	−0.573202	+	0.992814i	−0.996234	+	0.0866999i	$0.972368\pi$
$104$	−6.77875	+	11.7411i	−0.664712	+	1.15131i
$105$	0.393071	+	0.680820i	0.0383598	+	0.0664412i
$106$	6.88186	+	11.9197i	0.668425	+	1.15775i
$107$	−8.64547			−0.835789			−0.417894	−	0.908496i	$-0.637232\pi$
$107$	−8.64547			−0.835789			−0.417894	+	0.908496i	$0.637232\pi$
$108$	4.28382			0.412211
$109$	4.44444	+	7.69800i	0.425700	+	0.737335i	0.996486	−	0.0837648i	$-0.0266944\pi$
$109$	4.44444	+	7.69800i	0.425700	+	0.737335i	−0.570785	+	0.821099i	$0.693361\pi$
$110$	0.218109	+	0.377776i	0.0207959	+	0.0360196i
$111$	0.433988	−	0.751689i	0.0411923	−	0.0713471i
$112$	4.18315	−	7.24543i	0.395271	−	0.684629i
$113$	7.83955			0.737483			0.368741	−	0.929532i	$-0.379789\pi$
$113$	7.83955			0.737483			0.368741	+	0.929532i	$0.379789\pi$
$114$	−4.62547	+	8.01154i	−0.433215	+	0.750350i
$115$	0.0712415	−	0.123394i	0.00664331	−	0.0115065i
$116$	0.427409	−	0.740294i	0.0396839	−	0.0687346i
$117$	−18.1180	−	31.3813i	−1.67501	−	2.90120i
$118$	12.1052			1.11438
$119$	1.22618	+	2.12381i	0.112404	+	0.194689i
$120$	0.477852	−	0.827663i	0.0436217	−	0.0755550i
$121$	0.674881			0.0613528
$122$	−5.29501	+	9.17122i	−0.479387	+	0.830323i
$123$	8.33385	+	14.4347i	0.751438	+	1.30153i
$124$	−0.396532	−	0.686814i	−0.0356097	−	0.0616777i
$125$	−0.967029			−0.0864937
$126$	12.8870	+	22.3210i	1.14807	+	1.98851i
$127$	6.42588			0.570205			0.285102	−	0.958497i	$-0.407972\pi$
$127$	6.42588			0.570205			0.285102	+	0.958497i	$0.407972\pi$
$128$	−8.61846			−0.761771
$129$	−16.4741	−	14.1507i	−1.45046	−	1.24590i
$130$	−0.580566			−0.0509190
$131$	5.57342			0.486952			0.243476	−	0.969907i	$-0.421712\pi$
$131$	5.57342			0.486952			0.243476	+	0.969907i	$0.421712\pi$
$132$	−1.47305	−	2.55140i	−0.128213	−	0.222071i
$133$	5.19361			0.450343
$134$	6.58679	+	11.4086i	0.569012	+	0.985557i
$135$	0.796335	+	1.37929i	0.0685376	+	0.118711i
$136$	1.49065	−	2.58189i	0.127822	−	0.221395i
$137$	−20.5649			−1.75698			−0.878489	−	0.477762i	$-0.841448\pi$
$137$	−20.5649			−1.75698			−0.878489	+	0.477762i	$0.841448\pi$
$138$	3.21505	−	5.56863i	0.273683	−	0.474034i
$139$	10.3572	+	17.9392i	0.878487	+	1.52158i	0.853001	+	0.521909i	$0.174780\pi$
$139$	10.3572	+	17.9392i	0.878487	+	1.52158i	0.0254862	+	0.999675i	$0.491887\pi$
$140$	−0.0617992			−0.00522299
$141$	6.73214	+	11.6604i	0.566949	+	0.981984i
$142$	2.78576	−	4.82507i	0.233776	−	0.404911i
$143$	−7.76908	+	13.4564i	−0.649683	+	1.12528i
$144$	13.5921	−	23.5421i	1.13267	−	1.96185i
$145$	0.317811			0.0263927
$146$	−6.42497	+	11.1284i	−0.531734	+	0.920990i
$147$	−1.63260	+	2.82774i	−0.134654	+	0.233228i
$148$	0.0341161	+	0.0590908i	0.00280432	+	0.00485723i
$149$	10.7483	+	18.6166i	0.880533	+	1.52513i	0.850749	+	0.525572i	$0.176149\pi$
$149$	10.7483	+	18.6166i	0.880533	+	1.52513i	0.0297844	+	0.999556i	$0.490518\pi$
$150$	−21.8000			−1.77996
$151$	12.2700			0.998518			0.499259	−	0.866453i	$-0.333606\pi$
$151$	12.2700			0.998518			0.499259	+	0.866453i	$0.333606\pi$
$152$	−3.15690	−	5.46791i	−0.256058	−	0.443506i
$153$	3.98416	+	6.90077i	0.322100	+	0.557894i
$154$	5.52602	−	9.57135i	0.445299	−	0.771281i
$155$	0.147426	−	0.255349i	0.0118415	−	0.0205101i
$156$	3.92099			0.313930
$157$	8.77438	−	15.1977i	0.700271	−	1.21291i	−0.268100	−	0.963391i	$-0.586396\pi$
$157$	8.77438	−	15.1977i	0.700271	−	1.21291i	0.968371	−	0.249515i	$-0.0802710\pi$
$158$	0.945068	−	1.63691i	0.0751856	−	0.130225i
$159$	17.2800	−	29.9299i	1.37040	−	2.37359i
$160$	0.0708018	+	0.122632i	0.00559738	+	0.00969494i
$161$	−3.60995			−0.284504
$162$	20.1729	+	34.9405i	1.58493	+	2.74519i
$163$	3.95361	−	6.84785i	0.309670	−	0.536365i	−0.668620	−	0.743604i	$-0.733115\pi$
$163$	3.95361	−	6.84785i	0.309670	−	0.536365i	0.978290	+	0.207240i	$0.0664480\pi$
$164$	−1.31026			−0.102314
$165$	0.547662	−	0.948579i	0.0426354	−	0.0738468i
$166$	2.90122	+	5.02506i	0.225178	+	0.390020i
$167$	9.90428	+	17.1547i	0.766416	+	1.32747i	0.939495	+	0.342563i	$0.111295\pi$
$167$	9.90428	+	17.1547i	0.766416	+	1.32747i	−0.173079	+	0.984908i	$0.555372\pi$
$168$	−24.2137			−1.86813
$169$	−3.83992	−	6.65093i	−0.295378	−	0.511610i
$170$	0.127667			0.00979160
$171$	16.8753			1.29048
$172$	1.61088	−	0.565338i	0.122829	−	0.0431066i
$173$	−8.69063			−0.660736			−0.330368	−	0.943852i	$-0.607173\pi$
$173$	−8.69063			−0.660736			−0.330368	+	0.943852i	$0.607173\pi$
$174$	14.3424			1.08730
$175$	6.11942	+	10.5991i	0.462585	+	0.801220i
$176$	−11.6567			−0.878656
$177$	−15.1978	−	26.3234i	−1.14234	−	1.97859i
$178$	−12.0446	−	20.8618i	−0.902778	−	1.56366i
$179$	6.62568	−	11.4760i	0.495226	−	0.857757i	−0.504759	−	0.863261i	$-0.668419\pi$
$179$	6.62568	−	11.4760i	0.495226	−	0.857757i	0.999985	+	0.00550353i	$0.00175184\pi$
$180$	−0.200801			−0.0149668
$181$	−2.52685	+	4.37663i	−0.187819	+	0.325312i	−0.944523	−	0.328446i	$-0.893475\pi$
$181$	−2.52685	+	4.37663i	−0.187819	+	0.325312i	0.756704	+	0.653758i	$0.226809\pi$
$182$	7.35461	+	12.7386i	0.545160	+	0.944245i
$183$	26.5910			1.96567
$184$	2.19429	+	3.80061i	0.161765	+	0.280185i
$185$	−0.0126839	+	0.0219692i	−0.000932541	+	0.00161521i
$186$	6.65317	−	11.5236i	0.487834	−	0.844953i
$187$	1.70843	−	2.95908i	0.124933	−	0.216389i
$188$	−1.05844			−0.0771945
$189$	20.1760	−	34.9458i	1.46759	−	2.54193i
$190$	0.135186	−	0.234149i	0.00980743	−	0.0169870i
$191$	8.30880	+	14.3913i	0.601204	+	1.04132i	0.992639	+	0.121110i	$0.0386453\pi$
$191$	8.30880	+	14.3913i	0.601204	+	1.04132i	−0.391435	+	0.920206i	$0.628021\pi$
$192$	14.4937	+	25.1038i	1.04599	+	1.81171i
$193$	−5.50637			−0.396357			−0.198179	−	0.980166i	$-0.563503\pi$
$193$	−5.50637			−0.396357			−0.198179	+	0.980166i	$0.563503\pi$
$194$	−18.3872			−1.32012
$195$	0.728887	+	1.26247i	0.0521967	+	0.0904073i
$196$	−0.128340	−	0.222291i	−0.00916712	−	0.0158779i
$197$	8.07567	−	13.9875i	0.575368	−	0.996566i	−0.420634	−	0.907230i	$-0.638192\pi$
$197$	8.07567	−	13.9875i	0.575368	−	0.996566i	0.996002	−	0.0893355i	$-0.0284743\pi$
$198$	17.9554	−	31.0996i	1.27603	−	2.21015i
$199$	−2.41995			−0.171546			−0.0857728	−	0.996315i	$-0.527336\pi$
$199$	−2.41995			−0.171546			−0.0857728	+	0.996315i	$0.527336\pi$
$200$	7.43930	−	12.8852i	0.526038	−	0.911124i
$201$	16.5391	−	28.6466i	1.16658	−	2.02057i
$202$	7.29169	−	12.6296i	0.513042	−	0.888614i
$203$	−4.02603	−	6.97328i	−0.282572	−	0.489429i
$204$	−0.862227			−0.0603680
$205$	−0.243569	−	0.421874i	−0.0170116	−	0.0294650i
$206$	7.67286	−	13.2898i	0.534594	−	0.925943i
$207$	−11.7296			−0.815264
$208$	7.75697	−	13.4355i	0.537849	−	0.931582i
$209$	−3.61810	−	6.26673i	−0.250269	−	0.433479i
$210$	−0.518445	−	0.897973i	−0.0357761	−	0.0619660i
$211$	11.4955			0.791382			0.395691	−	0.918384i	$-0.370505\pi$
$211$	11.4955			0.791382			0.395691	+	0.918384i	$0.370505\pi$
$212$	1.35840	+	2.35281i	0.0932950	+	0.161592i
$213$	−13.9898			−0.958567
$214$	11.4030			0.779494
$215$	0.481479	+	0.413575i	0.0328366	+	0.0282056i
$216$	−49.0553			−3.33779
$217$	−7.47036			−0.507121
$218$	−5.86204	−	10.1533i	−0.397027	−	0.687671i
$219$	32.2656			2.18031
$220$	0.0430521	+	0.0745685i	0.00290257	+	0.00502740i
$221$	2.27375	+	3.93826i	0.152949	+	0.264916i
$222$	−0.572412	+	0.991447i	−0.0384178	+	0.0665415i
$223$	−5.84069			−0.391122			−0.195561	−	0.980692i	$-0.562653\pi$
$223$	−5.84069			−0.391122			−0.195561	+	0.980692i	$0.562653\pi$
$224$	1.79384	−	3.10702i	0.119856	−	0.207596i
$225$	19.8835	+	34.4392i	1.32556	+	2.29594i
$226$	−10.3400			−0.687810
$227$	7.71357	+	13.3603i	0.511968	+	0.886754i	0.999904	+	0.0138746i	$0.00441655\pi$
$227$	7.71357	+	13.3603i	0.511968	+	0.886754i	−0.487936	+	0.872879i	$0.662250\pi$
$228$	−0.913011	+	1.58138i	−0.0604656	+	0.104730i
$229$	−9.66002	+	16.7317i	−0.638352	+	1.10566i	0.347442	+	0.937702i	$0.387050\pi$
$229$	−9.66002	+	16.7317i	−0.638352	+	1.10566i	−0.985794	+	0.167957i	$0.946283\pi$
$230$	−0.0939647	+	0.162752i	−0.00619585	+	0.0107315i
$231$	−27.7512			−1.82589
$232$	−4.89439	+	8.47733i	−0.321332	+	0.556564i
$233$	−8.93539	+	15.4766i	−0.585377	+	1.01390i	0.409451	+	0.912332i	$0.365720\pi$
$233$	−8.93539	+	15.4766i	−0.585377	+	1.01390i	−0.994828	+	0.101571i	$0.967613\pi$
$234$	23.8969	+	41.3906i	1.56219	+	2.70579i
$235$	−0.196757	−	0.340793i	−0.0128350	−	0.0222309i
$236$	2.38942			0.155538
$237$	−4.74604			−0.308289
$238$	−1.61728	−	2.80122i	−0.104833	−	0.181576i
$239$	4.07631	+	7.06038i	0.263675	+	0.456698i	0.967216	−	0.253957i	$-0.0817322\pi$
$239$	4.07631	+	7.06038i	0.263675	+	0.456698i	−0.703541	+	0.710655i	$0.748399\pi$
$240$	−0.546809	+	0.947100i	−0.0352963	+	0.0611351i
$241$	−3.11039	+	5.38735i	−0.200358	+	0.347030i	−0.948644	−	0.316347i	$-0.897544\pi$
$241$	−3.11039	+	5.38735i	−0.200358	+	0.347030i	0.748286	+	0.663376i	$0.230877\pi$
$242$	−0.890141			−0.0572204
$243$	25.9718	−	44.9845i	1.66609	−	2.88575i
$244$	−1.04517	+	1.81029i	−0.0669101	+	0.115892i
$245$	0.0477151	−	0.0826449i	0.00304840	−	0.00527999i
$246$	−10.9920	−	19.0387i	−0.700825	−	1.21386i
$247$	9.63070			0.612786
$248$	4.54081	+	7.86491i	0.288342	+	0.499423i
$249$	7.28483	−	12.6177i	0.461657	−	0.799613i
$250$	1.27547			0.0806679
$251$	−0.206976	+	0.358494i	−0.0130642	+	0.0226279i	−0.872484	−	0.488643i	$-0.837492\pi$
$251$	−0.206976	+	0.358494i	−0.0130642	+	0.0226279i	0.859419	+	0.511271i	$0.170825\pi$
$252$	2.54374	+	4.40589i	0.160241	+	0.277545i
$253$	2.51485	+	4.35586i	0.158108	+	0.273850i
$254$	−8.47548			−0.531799
$255$	−0.160283	−	0.277618i	−0.0100373	−	0.0173851i
$256$	−6.13784			−0.383615
$257$	20.2345			1.26219			0.631097	−	0.775704i	$-0.282605\pi$
$257$	20.2345			1.26219			0.631097	+	0.775704i	$0.282605\pi$
$258$	21.7286	+	18.6642i	1.35277	+	1.16198i
$259$	0.642721			0.0399367
$260$	−0.114597			−0.00710698
$261$	−13.0815	−	22.6579i	−0.809726	−	1.40249i
$262$	−7.35111			−0.454153
$263$	5.03992	+	8.72940i	0.310775	+	0.538278i	0.978530	−	0.206103i	$-0.0660781\pi$
$263$	5.03992	+	8.72940i	0.310775	+	0.538278i	−0.667755	+	0.744381i	$0.732745\pi$
$264$	16.8684	+	29.2168i	1.03818	+	1.79817i
$265$	−0.505035	+	0.874746i	−0.0310240	+	0.0537352i
$266$	−6.85015			−0.420010
$267$	−30.2433	+	52.3830i	−1.85086	+	3.20579i
$268$	1.30015	+	2.25193i	0.0794194	+	0.137558i
$269$	21.7737			1.32757			0.663783	−	0.747925i	$-0.268950\pi$
$269$	21.7737			1.32757			0.663783	+	0.747925i	$0.268950\pi$
$270$	−1.05033	−	1.81923i	−0.0639213	−	0.110715i
$271$	−11.8610	+	20.5439i	−0.720505	+	1.24795i	0.240293	+	0.970700i	$0.422756\pi$
$271$	−11.8610	+	20.5439i	−0.720505	+	1.24795i	−0.960798	+	0.277250i	$0.910577\pi$
$272$	−1.70576	+	2.95447i	−0.103427	+	0.179141i
$273$	18.4671	−	31.9859i	1.11768	−	1.93588i
$274$	27.1243			1.63864
$275$	8.52613	−	14.7677i	0.514145	−	0.890525i
$276$	0.634612	−	1.09918i	0.0381992	−	0.0661629i
$277$	−14.1004	−	24.4227i	−0.847213	−	1.46742i	−0.883685	−	0.468082i	$-0.844945\pi$
$277$	−14.1004	−	24.4227i	−0.847213	−	1.46742i	0.0364721	−	0.999335i	$-0.488388\pi$
$278$	−13.6607	−	23.6611i	−0.819317	−	1.41910i
$279$	−24.2730			−1.45319
$280$	0.707681			0.0422921
$281$	9.97674	+	17.2802i	0.595162	+	1.03085i	0.993524	+	0.113623i	$0.0362456\pi$
$281$	9.97674	+	17.2802i	0.595162	+	1.03085i	−0.398361	+	0.917229i	$0.630421\pi$
$282$	−8.87942	−	15.3796i	−0.528762	−	0.915843i
$283$	2.23591	−	3.87271i	0.132911	−	0.230209i	−0.791886	−	0.610668i	$-0.790901\pi$
$283$	2.23591	−	3.87271i	0.132911	−	0.230209i	0.924798	+	0.380460i	$0.124234\pi$
$284$	0.549875	−	0.952411i	0.0326291	−	0.0565152i
$285$	−0.678892			−0.0402141
$286$	10.2471	−	17.7485i	0.605924	−	1.04949i
$287$	−6.17107	+	10.6886i	−0.364267	+	0.630929i
$288$	5.82861	−	10.0954i	0.343454	−	0.594880i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−0.419179			−0.0246151
$291$	23.0847	+	39.9838i	1.35325	+	2.34389i
$292$	−1.26821	+	2.19660i	−0.0742164	+	0.128547i
$293$	−27.9730			−1.63420			−0.817099	−	0.576498i	$-0.804419\pi$
$293$	−27.9730			−1.63420			−0.817099	+	0.576498i	$0.804419\pi$
$294$	2.15333	−	3.72968i	0.125585	−	0.217519i
$295$	0.444179	+	0.769341i	0.0258611	+	0.0447928i
$296$	−0.390673	−	0.676666i	−0.0227074	−	0.0393304i
$297$	−56.2219			−3.26233
$298$	−14.1765	−	24.5545i	−0.821225	−	1.42240i
$299$	−6.69407			−0.387128
$300$	−4.30306			−0.248437
$301$	2.97514	−	15.8036i	0.171484	−	0.910905i
$302$	−16.1836			−0.931263
$303$	−36.6182			−2.10366
$304$	3.61246	+	6.25696i	0.207189	+	0.358861i
$305$	−0.777162			−0.0445002
$306$	−5.25494	−	9.10183i	−0.300405	−	0.520317i
$307$	−2.10155	−	3.64000i	−0.119942	−	0.207746i	0.799802	−	0.600263i	$-0.204938\pi$
$307$	−2.10155	−	3.64000i	−0.119942	−	0.207746i	−0.919744	+	0.392518i	$0.871604\pi$
$308$	1.09077	−	1.88927i	0.0621523	−	0.107651i
$309$	−38.5324			−2.19203
$310$	−0.194449	+	0.336795i	−0.0110439	+	0.0191287i
$311$	−7.80077	−	13.5113i	−0.442341	−	0.766157i	0.555522	−	0.831502i	$-0.312519\pi$
$311$	−7.80077	−	13.5113i	−0.442341	−	0.766157i	−0.997863	+	0.0653450i	$0.979185\pi$
$312$	−44.9004			−2.54198
$313$	−12.0401	−	20.8540i	−0.680545	−	1.17874i	−0.974815	−	0.223016i	$-0.928410\pi$
$313$	−12.0401	−	20.8540i	−0.680545	−	1.17874i	0.294270	−	0.955722i	$-0.404923\pi$
$314$	−11.5730	+	20.0451i	−0.653105	+	1.13121i
$315$	−0.945732	+	1.63806i	−0.0532860	+	0.0922940i
$316$	0.186545	−	0.323105i	0.0104940	−	0.0181761i
$317$	26.5547			1.49146			0.745731	−	0.666248i	$-0.232101\pi$
$317$	26.5547			1.49146			0.745731	+	0.666248i	$0.232101\pi$
$318$	−22.7917	+	39.4763i	−1.27809	+	2.21372i
$319$	−5.60942	+	9.71580i	−0.314067	+	0.543981i
$320$	−0.423599	−	0.733694i	−0.0236799	−	0.0410148i
$321$	−14.3162	−	24.7964i	−0.799054	−	1.38400i
$322$	4.76138			0.265341
$323$	−2.11780			−0.117837
$324$	3.98189	+	6.89683i	0.221216	+	0.383157i
$325$	11.3475	+	19.6544i	0.629444	+	1.09023i
$326$	−5.21465	+	9.03203i	−0.288812	+	0.500238i
$327$	−14.7193	+	25.4946i	−0.813979	+	1.40985i
$328$	15.0042			0.828467
$329$	−4.98503	+	8.63433i	−0.274834	+	0.476026i
$330$	−0.722344	+	1.25114i	−0.0397637	+	0.0688728i
$331$	14.1428	−	24.4960i	0.777357	−	1.34642i	−0.156103	−	0.987741i	$-0.549893\pi$
$331$	14.1428	−	24.4960i	0.777357	−	1.34642i	0.933460	−	0.358681i	$-0.116773\pi$
$332$	0.572665	+	0.991885i	0.0314291	+	0.0544368i
$333$	2.08835			0.114441
$334$	−13.0633	−	22.6264i	−0.714794	−	1.23806i
$335$	−0.483380	+	0.837239i	−0.0264099	+	0.0457433i
$336$	27.7079			1.51159
$337$	8.58519	−	14.8700i	0.467665	−	0.810020i	−0.531652	−	0.846963i	$-0.678429\pi$
$337$	8.58519	−	14.8700i	0.467665	−	0.810020i	0.999317	+	0.0369428i	$0.0117619\pi$
$338$	5.06469	+	8.77230i	0.275483	+	0.477150i
$339$	12.9817	+	22.4849i	0.705069	+	1.22121i
$340$	0.0251999			0.00136665
$341$	5.20419	+	9.01392i	0.281823	+	0.488131i
$342$	−22.2578			−1.20356
$343$	−19.5844			−1.05746
$344$	−18.4467	+	6.47385i	−0.994580	+	0.349047i
$345$	0.471882			0.0254053
$346$	11.4626			0.616232
$347$	8.56320	+	14.8319i	0.459697	+	0.796218i	0.998945	−	0.0459290i	$-0.0146248\pi$
$347$	8.56320	+	14.8319i	0.459697	+	0.796218i	−0.539248	+	0.842147i	$0.681291\pi$
$348$	2.83102			0.151759
$349$	8.08138	+	13.9974i	0.432587	+	0.749262i	0.997095	−	0.0761652i	$-0.0242677\pi$
$349$	8.08138	+	13.9974i	0.432587	+	0.749262i	−0.564509	+	0.825427i	$0.690934\pi$
$350$	−8.07127	−	13.9798i	−0.431427	−	0.747254i
$351$	37.4130	−	64.8013i	1.99696	−	3.45884i
$352$	−4.99867			−0.266430
$353$	7.15534	−	12.3934i	0.380840	−	0.659635i	−0.610342	−	0.792138i	$-0.708968\pi$
$353$	7.15534	−	12.3934i	0.380840	−	0.659635i	0.991183	+	0.132503i	$0.0423014\pi$
$354$	20.0453	+	34.7195i	1.06540	+	1.84532i
$355$	0.408873			0.0217007
$356$	−2.37745	−	4.11787i	−0.126005	−	0.218246i
$357$	−4.06092	+	7.03373i	−0.214927	+	0.372264i
$358$	−8.73900	+	15.1364i	−0.461870	+	0.799983i
$359$	6.63765	−	11.4968i	0.350322	−	0.606775i	−0.635984	−	0.771702i	$-0.719406\pi$
$359$	6.63765	−	11.4968i	0.350322	−	0.606775i	0.986306	+	0.164927i	$0.0527388\pi$
$360$	2.29943			0.121190
$361$	7.25747	−	12.5703i	0.381972	−	0.661595i
$362$	3.33281	−	5.77259i	0.175168	−	0.303401i
$363$	1.11755	+	1.93565i	0.0586562	+	0.101596i
$364$	1.45171	+	2.51444i	0.0760903	+	0.131792i
$365$	−0.943009			−0.0493594
$366$	−35.0725			−1.83327
$367$	5.06693	+	8.77618i	0.264492	+	0.458113i	0.967430	−	0.253138i	$-0.0814626\pi$
$367$	5.06693	+	8.77618i	0.264492	+	0.458113i	−0.702939	+	0.711250i	$0.748129\pi$
$368$	−2.51093	−	4.34907i	−0.130892	−	0.226711i
$369$	−20.0513	+	34.7299i	−1.04383	+	1.80796i
$370$	0.0167296	−	0.0289765i	0.000869730	−	0.00150642i
$371$	25.5911			1.32862
$372$	1.31325	−	2.27462i	0.0680890	−	0.117934i
$373$	7.61694	−	13.1929i	0.394390	−	0.683103i	−0.598633	−	0.801023i	$-0.704289\pi$
$373$	7.61694	−	13.1929i	0.394390	−	0.683103i	0.993023	+	0.117920i	$0.0376226\pi$
$374$	−2.25334	+	3.90291i	−0.116518	+	0.201815i
$375$	−1.60133	−	2.77358i	−0.0826921	−	0.143227i
$376$	12.1205			0.625066
$377$	−7.46561	−	12.9308i	−0.384499	−	0.665971i
$378$	−26.6113	+	46.0921i	−1.36874	+	2.37072i
$379$	−14.1932			−0.729058			−0.364529	−	0.931192i	$-0.618770\pi$
$379$	−14.1932			−0.729058			−0.364529	+	0.931192i	$0.618770\pi$
$380$	0.0266841	−	0.0462182i	0.00136886	−	0.00237094i
$381$	10.6408	+	18.4303i	0.545143	+	0.944215i
$382$	−10.9590	−	18.9815i	−0.560710	−	0.971177i
$383$	−30.7860			−1.57309			−0.786545	−	0.617533i	$-0.788132\pi$
$383$	−30.7860			−1.57309			−0.786545	+	0.617533i	$0.788132\pi$
$384$	−14.2715	−	24.7190i	−0.728289	−	1.26143i
$385$	0.811069			0.0413359
$386$	7.26267			0.369660
$387$	9.66694	−	51.3497i	0.491398	−	2.61025i
$388$	−3.62941			−0.184255
$389$	−5.73485			−0.290768			−0.145384	−	0.989375i	$-0.546442\pi$
$389$	−5.73485			−0.290768			−0.145384	+	0.989375i	$0.546442\pi$
$390$	−0.961372	−	1.66515i	−0.0486810	−	0.0843179i
$391$	1.47203			0.0744438
$392$	1.46966	+	2.54552i	0.0742288	+	0.128568i
$393$	9.22915	+	15.9854i	0.465549	+	0.806355i
$394$	−10.6515	+	18.4489i	−0.536614	+	0.929442i
$395$	0.138710			0.00697927
$396$	3.54417	−	6.13868i	0.178101	−	0.308480i
$397$	9.60460	+	16.6356i	0.482041	+	0.834919i	0.999787	−	0.0206147i	$-0.00656234\pi$
$397$	9.60460	+	16.6356i	0.482041	+	0.834919i	−0.517747	+	0.855534i	$0.673229\pi$
$398$	3.19181			0.159991
$399$	8.60021	+	14.8960i	0.430549	+	0.745733i
$400$	−8.51284	+	14.7447i	−0.425642	+	0.737233i
$401$	−1.60764	+	2.78452i	−0.0802819	+	0.139052i	−0.903371	−	0.428860i	$-0.858915\pi$
$401$	−1.60764	+	2.78452i	−0.0802819	+	0.139052i	0.823089	+	0.567912i	$0.192249\pi$
$402$	−21.8144	+	37.7837i	−1.08800	+	1.88448i
$403$	−13.8526			−0.690046
$404$	1.43929	−	2.49293i	0.0716074	−	0.124028i
$405$	−1.48042	+	2.56416i	−0.0735625	+	0.127414i
$406$	5.31017	+	9.19748i	0.263539	+	0.456463i
$407$	−0.447748	−	0.775522i	−0.0221940	−	0.0384412i
$408$	9.87362			0.488817
$409$	−14.0216			−0.693324			−0.346662	−	0.937990i	$-0.612685\pi$
$409$	−14.0216			−0.693324			−0.346662	+	0.937990i	$0.612685\pi$
$410$	0.321258	+	0.556435i	0.0158658	+	0.0274804i
$411$	−34.0539	−	58.9831i	−1.67975	−	2.90942i
$412$	1.51453	−	2.62324i	0.0746155	−	0.129238i
$413$	11.2537	−	19.4920i	0.553760	−	0.959140i
$414$	15.4709			0.760352
$415$	−0.212910	+	0.368771i	−0.0104513	+	0.0181022i
$416$	3.32638	−	5.76145i	0.163089	−	0.282479i
$417$	−34.3015	+	59.4119i	−1.67975	+	2.90941i
$418$	4.77212	+	8.26556i	0.233412	+	0.404282i
$419$	11.4938			0.561508			0.280754	−	0.959780i	$-0.409415\pi$
$419$	11.4938			0.561508			0.280754	+	0.959780i	$0.409415\pi$
$420$	−0.102335	−	0.177249i	−0.00499342	−	0.00864886i
$421$	14.1557	−	24.5184i	0.689907	−	1.19495i	−0.281961	−	0.959426i	$-0.590985\pi$
$421$	14.1557	−	24.5184i	0.689907	−	1.19495i	0.971868	−	0.235528i	$-0.0756818\pi$
$422$	−15.1621			−0.738078
$423$	−16.1976	+	28.0550i	−0.787553	+	1.36408i
$424$	−15.5554	−	26.9427i	−0.755437	−	1.30845i
$425$	−2.49532	−	4.32201i	−0.121041	−	0.209648i
$426$	18.4520			0.894002
$427$	9.84510	+	17.0522i	0.476438	+	0.825214i
$428$	2.25082			0.108797
$429$	−51.4600			−2.48451
$430$	−0.635051	−	0.545489i	−0.0306249	−	0.0263058i
$431$	−34.9649			−1.68420			−0.842099	−	0.539323i	$-0.818680\pi$
$431$	−34.9649			−1.68420			−0.842099	+	0.539323i	$0.818680\pi$
$432$	56.1343			2.70076
$433$	−3.82604	−	6.62690i	−0.183868	−	0.318468i	0.759327	−	0.650710i	$-0.225528\pi$
$433$	−3.82604	−	6.62690i	−0.183868	−	0.318468i	−0.943194	+	0.332241i	$0.892195\pi$
$434$	9.85311			0.472964
$435$	0.526270	+	0.911526i	0.0252327	+	0.0437043i
$436$	−1.15709	−	2.00415i	−0.0554148	−	0.0959812i
$437$	1.55873	−	2.69980i	0.0745642	−	0.129149i
$438$	−42.5570			−2.03345
$439$	−9.98969	+	17.3027i	−0.476782	+	0.825811i	−0.999646	−	0.0266054i	$-0.991530\pi$
$439$	−9.98969	+	17.3027i	−0.476782	+	0.825811i	0.522864	+	0.852416i	$0.324864\pi$
$440$	−0.493003	−	0.853906i	−0.0235030	−	0.0407083i
$441$	−7.85608			−0.374099
$442$	−2.99899	−	5.19440i	−0.142647	−	0.247072i
$443$	3.65243	−	6.32619i	0.173532	−	0.300566i	−0.766120	−	0.642697i	$-0.777815\pi$
$443$	3.65243	−	6.32619i	0.173532	−	0.300566i	0.939652	+	0.342131i	$0.111149\pi$
$444$	−0.112987	+	0.195699i	−0.00536213	+	0.00928749i
$445$	0.883907	−	1.53097i	0.0419012	−	0.0725750i
$446$	7.70363			0.364778
$447$	−35.5966	+	61.6552i	−1.68366	+	2.91619i
$448$	−10.7323	+	18.5889i	−0.507054	+	0.878242i
$449$	−10.9954	−	19.0446i	−0.518905	−	0.898769i	−0.999759	−	0.0219685i	$-0.993007\pi$
$449$	−10.9954	−	19.0446i	−0.518905	−	0.898769i	0.480854	−	0.876801i	$-0.340327\pi$
$450$	−26.2255	−	45.4239i	−1.23628	−	2.14130i
$451$	17.1962			0.809736
$452$	−2.04100			−0.0960005
$453$	20.3182	+	35.1921i	0.954631	+	1.65347i
$454$	−10.1739	−	17.6217i	−0.477484	−	0.827027i
$455$	−0.539728	+	0.934836i	−0.0253028	+	0.0438258i
$456$	10.4552	−	18.1089i	0.489608	−	0.848025i
$457$	2.49152			0.116548			0.0582741	−	0.998301i	$-0.481440\pi$
$457$	2.49152			0.116548			0.0582741	+	0.998301i	$0.481440\pi$
$458$	12.7412	−	22.0684i	0.595356	−	1.03119i
$459$	−8.22715	+	14.2498i	−0.384010	+	0.665126i
$460$	−0.0185475	+	0.0321252i	−0.000864781	+	0.00149784i
$461$	−4.08105	−	7.06859i	−0.190074	−	0.329217i	0.755201	−	0.655493i	$-0.227539\pi$
$461$	−4.08105	−	7.06859i	−0.190074	−	0.329217i	−0.945274	+	0.326276i	$0.894206\pi$
$462$	36.6026			1.70291
$463$	5.84972	+	10.1320i	0.271860	+	0.470875i	0.969338	−	0.245731i	$-0.0790280\pi$
$463$	5.84972	+	10.1320i	0.271860	+	0.470875i	−0.697478	+	0.716606i	$0.745695\pi$
$464$	5.60068	−	9.70066i	0.260005	−	0.450342i
$465$	0.976503			0.0452842
$466$	11.7854	−	20.4129i	0.545949	−	0.945612i
$467$	19.0133	+	32.9320i	0.879829	+	1.52391i	0.851528	+	0.524309i	$0.175676\pi$
$467$	19.0133	+	32.9320i	0.879829	+	1.52391i	0.0283014	+	0.999599i	$0.490990\pi$
$468$	4.71696	+	8.17001i	0.218041	+	0.377659i
$469$	24.4939			1.13102
$470$	0.259514	+	0.449492i	0.0119705	+	0.0207335i
$471$	58.1187			2.67797
$472$	−27.3620			−1.25944
$473$	−21.1416	+	7.41963i	−0.972094	+	0.341155i
$474$	6.25984			0.287524
$475$	−10.5691			−0.484945
$476$	−0.319232	−	0.552926i	−0.0146320	−	0.0253433i
$477$	83.1517			3.80726
$478$	−5.37649	−	9.31235i	−0.245915	−	0.425937i
$479$	−19.4996	−	33.7743i	−0.890960	−	1.54319i	−0.838726	−	0.544553i	$-0.816699\pi$
$479$	−19.4996	−	33.7743i	−0.890960	−	1.54319i	−0.0522341	−	0.998635i	$-0.516634\pi$
$480$	−0.234485	+	0.406139i	−0.0107027	+	0.0185376i
$481$	1.19182			0.0543423
$482$	4.10247	−	7.10569i	0.186863	−	0.323656i
$483$	−5.97780	−	10.3539i	−0.271999	−	0.471117i
$484$	−0.175703			−0.00798650
$485$	−0.674684	−	1.16859i	−0.0306358	−	0.0530628i
$486$	−34.2557	+	59.3327i	−1.55387	+	2.69138i
$487$	9.86328	−	17.0837i	0.446948	−	0.774136i	−0.551238	−	0.834348i	$-0.685844\pi$
$487$	9.86328	−	17.0837i	0.446948	−	0.774136i	0.998186	+	0.0602120i	$0.0191777\pi$
$488$	11.9685	−	20.7301i	0.541791	−	0.938409i
$489$	26.1875			1.18424
$490$	−0.0629342	+	0.109005i	−0.00284308	+	0.00492436i
$491$	7.21017	−	12.4884i	0.325390	−	0.563593i	−0.656201	−	0.754586i	$-0.727838\pi$
$491$	7.21017	−	12.4884i	0.325390	−	0.563593i	0.981591	+	0.190993i	$0.0611709\pi$
$492$	−2.16969	−	3.75801i	−0.0978171	−	0.169424i
$493$	1.64169	+	2.84350i	0.0739381	+	0.128065i
$494$	−12.7025			−0.571512
$495$	2.63536			0.118450
$496$	−5.19608	−	8.99987i	−0.233311	−	0.404106i
$497$	−5.17961	−	8.97134i	−0.232337	−	0.402420i
$498$	−9.60839	+	16.6422i	−0.430562	+	0.745756i
$499$	15.2988	−	26.4982i	0.684866	−	1.18622i	−0.288613	−	0.957446i	$-0.593194\pi$
$499$	15.2988	−	26.4982i	0.684866	−	1.18622i	0.973479	−	0.228777i	$-0.0734727\pi$
$500$	0.251763			0.0112592
$501$	−32.8014	+	56.8137i	−1.46546	+	2.53825i
$502$	0.272993	−	0.472839i	0.0121843	−	0.0211038i
$503$	5.28450	−	9.15302i	0.235624	−	0.408113i	−0.723830	−	0.689979i	$-0.757620\pi$
$503$	5.28450	−	9.15302i	0.235624	−	0.408113i	0.959454	+	0.281866i	$0.0909532\pi$
$504$	−29.1292	−	50.4532i	−1.29752	−	2.24736i
$505$	1.07022			0.0476242
$506$	−3.31699	−	5.74520i	−0.147458	−	0.255405i
$507$	12.7172	−	22.0268i	0.564791	−	0.978247i
$508$	−1.67296			−0.0742254
$509$	−4.43785	+	7.68659i	−0.196704	+	0.340702i	−0.947458	−	0.319880i	$-0.896357\pi$
$509$	−4.43785	+	7.68659i	−0.196704	+	0.340702i	0.750754	+	0.660582i	$0.229691\pi$
$510$	0.211406	+	0.366166i	0.00936123	+	0.0162141i
$511$	11.9460	+	20.6912i	0.528462	+	0.915323i
$512$	25.3325			1.11955
$513$	17.4234	+	30.1783i	0.769263	+	1.33240i
$514$	−26.6885			−1.17718
$515$	1.12617			0.0496248
$516$	4.28897	+	3.68409i	0.188811	+	0.162183i
$517$	13.8912			0.610934
$518$	−0.847722			−0.0372468
$519$	−14.3910	−	24.9260i	−0.631695	−	1.09413i
$520$	1.31228			0.0575473
$521$	−20.9386	−	36.2666i	−0.917335	−	1.58887i	−0.803447	−	0.595376i	$-0.797003\pi$
$521$	−20.9386	−	36.2666i	−0.917335	−	1.58887i	−0.113888	−	0.993494i	$-0.536330\pi$
$522$	17.2540	+	29.8848i	0.755187	+	1.30802i
$523$	17.5005	−	30.3117i	0.765243	−	1.32544i	−0.174875	−	0.984591i	$-0.555952\pi$
$523$	17.5005	−	30.3117i	0.765243	−	1.32544i	0.940118	−	0.340849i	$-0.110715\pi$
$524$	−1.45102			−0.0633881
$525$	−20.2666	+	35.1027i	−0.884506	+	1.53201i
$526$	−6.64745	−	11.5137i	−0.289843	−	0.502022i
$527$	3.04619			0.132694
$528$	−19.3026	−	33.4330i	−0.840036	−	1.45499i
$529$	10.4166	−	18.0420i	0.452894	−	0.784436i
$530$	0.666120	−	1.15375i	0.0289344	−	0.0501159i
$531$	36.5661	−	63.3343i	1.58683	−	2.74847i
$532$	−1.35214			−0.0586226
$533$	−11.4432	+	19.8203i	−0.495662	+	0.858512i
$534$	39.8897	−	69.0911i	1.72620	−	2.98986i
$535$	0.418413	+	0.724712i	0.0180896	+	0.0313320i
$536$	−14.8884	−	25.7875i	−0.643082	−	1.11385i
$537$	43.8864			1.89384
$538$	−28.7186			−1.23815
$539$	1.68436	+	2.91740i	0.0725506	+	0.125661i
$540$	−0.207323	−	0.359094i	−0.00892176	−	0.0154529i
$541$	−12.1266	+	21.0039i	−0.521364	+	0.903030i	0.478327	+	0.878182i	$0.341243\pi$
$541$	−12.1266	+	21.0039i	−0.521364	+	0.903030i	−0.999691	+	0.0248478i	$0.992090\pi$
$542$	15.6442	−	27.0965i	0.671975	−	1.16389i
$543$	−16.7371			−0.718256
$544$	−0.731472	+	1.26695i	−0.0313616	+	0.0543199i
$545$	0.430193	−	0.745117i	0.0184275	−	0.0319173i
$546$	−24.3573	+	42.1881i	−1.04240	+	1.80549i
$547$	8.88087	+	15.3821i	0.379719	+	0.657692i	0.991021	−	0.133705i	$-0.0426875\pi$
$547$	8.88087	+	15.3821i	0.379719	+	0.657692i	−0.611303	+	0.791397i	$0.709354\pi$
$548$	5.35400			0.228712
$549$	31.9891	+	55.4067i	1.36526	+	2.36470i
$550$	−11.2456	+	19.4780i	−0.479514	+	0.830543i
$551$	6.95354			0.296231
$552$	−7.26713	+	12.5870i	−0.309310	+	0.535740i
$553$	−1.75718	−	3.04353i	−0.0747229	−	0.129424i
$554$	18.5979	+	32.2125i	0.790149	+	1.36858i
$555$	−0.0840144			−0.00356621
$556$	−2.69646	−	4.67041i	−0.114356	−	0.198070i
$557$	−41.4501			−1.75630			−0.878148	−	0.478390i	$-0.841221\pi$
$557$	−41.4501			−1.75630			−0.878148	+	0.478390i	$0.841221\pi$
$558$	32.0151			1.35531
$559$	5.51691	−	29.3052i	0.233340	−	1.23948i
$560$	−0.809804			−0.0342205
$561$	11.3161			0.477766
$562$	−13.1589	−	22.7919i	−0.555075	−	0.961419i
$563$	20.3733			0.858632			0.429316	−	0.903154i	$-0.358755\pi$
$563$	20.3733			0.858632			0.429316	+	0.903154i	$0.358755\pi$
$564$	−1.75269	−	3.03575i	−0.0738016	−	0.127828i
$565$	−0.379409	−	0.657156i	−0.0159619	−	0.0276468i
$566$	−2.94908	+	5.10795i	−0.123959	+	0.214703i
$567$	75.0157			3.15036
$568$	−6.29678	+	10.9063i	−0.264207	+	0.457620i
$569$	−7.37103	−	12.7670i	−0.309010	−	0.535220i	0.669136	−	0.743140i	$-0.266664\pi$
$569$	−7.37103	−	12.7670i	−0.309010	−	0.535220i	−0.978146	+	0.207919i	$0.933331\pi$
$570$	0.895431			0.0375055
$571$	13.0130	+	22.5391i	0.544575	+	0.943232i	0.998634	+	0.0522602i	$0.0166425\pi$
$571$	13.0130	+	22.5391i	0.544575	+	0.943232i	−0.454058	+	0.890972i	$0.650024\pi$
$572$	2.02265	−	3.50334i	0.0845714	−	0.146482i
$573$	−27.5175	+	47.6616i	−1.14956	+	1.99109i
$574$	8.13939	−	14.0978i	0.339732	−	0.588432i
$575$	7.34636			0.306364
$576$	−34.8718	+	60.3998i	−1.45299	+	2.51666i
$577$	17.5694	−	30.4310i	0.731423	−	1.26686i	−0.224853	−	0.974393i	$-0.572190\pi$
$577$	17.5694	−	30.4310i	0.731423	−	1.26686i	0.956275	−	0.292468i	$-0.0944766\pi$
$578$	0.659480	+	1.14225i	0.0274307	+	0.0475114i
$579$	−9.11812	−	15.7930i	−0.378936	−	0.656337i
$580$	−0.0827409			−0.00343563
$581$	10.7886			0.447585
$582$	−30.4477	−	52.7370i	−1.26210	−	2.18602i
$583$	−17.8279	−	30.8789i	−0.738357	−	1.27887i
$584$	14.5226	−	25.1540i	0.600951	−	1.04088i
$585$	−1.75371	+	3.03751i	−0.0725068	+	0.125585i
$586$	36.8952			1.52413
$587$	17.6977	−	30.6534i	0.730464	−	1.26520i	−0.226221	−	0.974076i	$-0.572637\pi$
$587$	17.6977	−	30.6534i	0.730464	−	1.26520i	0.956685	−	0.291125i	$-0.0940294\pi$
$588$	0.425041	−	0.736193i	0.0175284	−	0.0303601i
$589$	3.22560	−	5.58691i	0.132909	−	0.230205i
$590$	−0.585854	−	1.01473i	−0.0241192	−	0.0417757i
$591$	53.4907			2.20031
$592$	0.447050	+	0.774313i	0.0183736	+	0.0318241i
$593$	−7.87978	+	13.6482i	−0.323584	+	0.560464i	−0.981225	−	0.192868i	$-0.938221\pi$
$593$	−7.87978	+	13.6482i	−0.323584	+	0.560464i	0.657641	+	0.753332i	$0.271554\pi$
$594$	74.1544			3.04259
$595$	0.118687	−	0.205571i	0.00486567	−	0.00842759i
$596$	−2.79828	−	4.84676i	−0.114622	−	0.198531i
$597$	−4.00725	−	6.94076i	−0.164006	−	0.284066i
$598$	8.82920			0.361053
$599$	20.3184	+	35.1924i	0.830185	+	1.43792i	0.897891	+	0.440218i	$0.145099\pi$
$599$	20.3184	+	35.1924i	0.830185	+	1.43792i	−0.0677056	+	0.997705i	$0.521568\pi$
$600$	49.2756			2.01167
$601$	−12.6482			−0.515929			−0.257965	−	0.966154i	$-0.583052\pi$
$601$	−12.6482			−0.515929			−0.257965	+	0.966154i	$0.583052\pi$
$602$	−3.92409	+	20.8443i	−0.159934	+	0.849551i
$603$	79.5864			3.24101
$604$	−3.19445			−0.129980
$605$	−0.0326621	−	0.0565724i	−0.00132790	−	0.00229999i
$606$	48.2979			1.96197
$607$	17.0298	+	29.4965i	0.691219	+	1.19723i	0.971439	+	0.237291i	$0.0762595\pi$
$607$	17.0298	+	29.4965i	0.691219	+	1.19723i	−0.280219	+	0.959936i	$0.590407\pi$
$608$	1.54911	+	2.68314i	0.0628247	+	0.108816i
$609$	13.3336	−	23.0944i	0.540304	−	0.935834i
$610$	1.02505			0.0415029
$611$	−9.24393	+	16.0110i	−0.373970	+	0.647734i
$612$	−1.03726	−	1.79659i	−0.0419288	−	0.0726228i
$613$	−19.5136			−0.788149			−0.394074	−	0.919079i	$-0.628935\pi$
$613$	−19.5136			−0.788149			−0.394074	+	0.919079i	$0.628935\pi$
$614$	2.77186	+	4.80101i	0.111863	+	0.193753i
$615$	0.806663	−	1.39718i	0.0325278	−	0.0563398i
$616$	−12.4907	+	21.6346i	−0.503265	+	0.871681i
$617$	−10.0889	+	17.4745i	−0.406164	+	0.703497i	−0.994456	−	0.105151i	$-0.966467\pi$
$617$	−10.0889	+	17.4745i	−0.406164	+	0.703497i	0.588292	+	0.808649i	$0.299801\pi$
$618$	50.8227			2.04439
$619$	12.4435	−	21.5527i	0.500145	−	0.866276i	−0.499855	−	0.866109i	$-0.666614\pi$
$619$	12.4435	−	21.5527i	0.500145	−	0.866276i	1.00000		0.000166979i	$-5.31510e-5\pi$
$620$	−0.0383818	+	0.0664792i	−0.00154145	+	0.00266987i
$621$	−12.1106	−	20.9762i	−0.485982	−	0.841746i
$622$	10.2889	+	17.8209i	0.412547	+	0.714553i
$623$	−44.7893			−1.79445
$624$	51.3798			2.05684
$625$	−12.4298	−	21.5290i	−0.497191	−	0.861160i
$626$	15.8804	+	27.5056i	0.634706	+	1.09934i
$627$	11.9826	−	20.7544i	0.478538	−	0.828853i
$628$	−2.28438	+	3.95666i	−0.0911566	+	0.157888i
$629$	−0.262082			−0.0104499
$630$	1.24738	−	2.16053i	0.0496969	−	0.0860775i
$631$	−20.4465	+	35.4144i	−0.813963	+	1.40983i	0.0961069	+	0.995371i	$0.469361\pi$
$631$	−20.4465	+	35.4144i	−0.813963	+	1.40983i	−0.910070	+	0.414454i	$0.863972\pi$
$632$	−2.13618	+	3.69997i	−0.0849727	+	0.147177i
$633$	19.0356	+	32.9707i	0.756599	+	1.31047i
$634$	−35.0246			−1.39100
$635$	−0.310992	−	0.538654i	−0.0123413	−	0.0213758i
$636$	−4.49880	+	7.79214i	−0.178389	+	0.308979i
$637$	−4.48345			−0.177641
$638$	7.39860	−	12.8148i	0.292913	−	0.507341i
$639$	−16.8298	−	29.1501i	−0.665776	−	1.15316i
$640$	0.417106	+	0.722448i	0.0164875	+	0.0285573i
$641$	28.8665			1.14016			0.570079	−	0.821590i	$-0.306912\pi$
$641$	28.8665			1.14016			0.570079	+	0.821590i	$0.306912\pi$
$642$	18.8825	+	32.7055i	0.745233	+	1.29078i
$643$	−7.90891			−0.311897			−0.155949	−	0.987765i	$-0.549843\pi$
$643$	−7.90891			−0.311897			−0.155949	+	0.987765i	$0.549843\pi$
$644$	0.939838			0.0370348
$645$	−0.388901	+	2.06580i	−0.0153130	+	0.0813408i
$646$	2.79329			0.109900
$647$	15.4830			0.608701			0.304350	−	0.952560i	$-0.401561\pi$
$647$	15.4830			0.608701			0.304350	+	0.952560i	$0.401561\pi$
$648$	−45.5978	−	78.9777i	−1.79125	−	3.10254i
$649$	−31.3594			−1.23096
$650$	−14.9668	−	25.9233i	−0.587048	−	1.01680i
$651$	−12.3703	−	21.4261i	−0.484832	−	0.839754i
$652$	−1.02931	+	1.78281i	−0.0403108	+	0.0698203i
$653$	−22.8766			−0.895229			−0.447614	−	0.894227i	$-0.647726\pi$
$653$	−22.8766			−0.895229			−0.447614	+	0.894227i	$0.647726\pi$
$654$	19.4142	−	33.6263i	0.759154	−	1.31489i
$655$	−0.269736	−	0.467196i	−0.0105394	−	0.0182549i
$656$	−17.1694			−0.670351
$657$	38.8156	+	67.2306i	1.51434	+	2.62291i
$658$	6.57506	−	11.3883i	0.256322	−	0.443963i
$659$	−19.5644	+	33.8865i	−0.762121	+	1.32003i	0.179635	+	0.983733i	$0.442508\pi$
$659$	−19.5644	+	33.8865i	−0.762121	+	1.32003i	−0.941756	+	0.336298i	$0.890825\pi$
$660$	−0.142582	+	0.246959i	−0.00554999	+	0.00961287i
$661$	−4.94941			−0.192510			−0.0962549	−	0.995357i	$-0.530686\pi$
$661$	−4.94941			−0.192510			−0.0962549	+	0.995357i	$0.530686\pi$
$662$	−18.6537	+	32.3092i	−0.724998	+	1.25573i
$663$	−7.53032	+	13.0429i	−0.292453	+	0.506544i
$664$	−6.55776	−	11.3584i	−0.254490	−	0.440790i
$665$	−0.251354	−	0.435358i	−0.00974708	−	0.0168824i
$666$	−2.75445			−0.106733
$667$	−4.83324			−0.187144
$668$	−2.57854	−	4.46617i	−0.0997668	−	0.172801i
$669$	−9.67173	−	16.7519i	−0.373931	−	0.647667i
$670$	0.637559	−	1.10428i	0.0246310	−	0.0426622i
$671$	13.7171	−	23.7587i	0.529542	−	0.917193i
$672$	11.8818			0.458351
$673$	1.76622	−	3.05919i	0.0680829	−	0.117923i	−0.829975	−	0.557801i	$-0.811645\pi$
$673$	1.76622	−	3.05919i	0.0680829	−	0.117923i	0.898057	+	0.439878i	$0.144978\pi$
$674$	−11.3235	+	19.6129i	−0.436166	+	0.755461i
$675$	−41.0587	+	71.1157i	−1.58035	+	2.73724i
$676$	0.999708	+	1.73155i	0.0384503	+	0.0665979i
$677$	−13.3754			−0.514057			−0.257029	−	0.966404i	$-0.582743\pi$
$677$	−13.3754			−0.514057			−0.257029	+	0.966404i	$0.582743\pi$
$678$	−17.1223	−	29.6567i	−0.657579	−	1.13896i
$679$	−17.0938	+	29.6073i	−0.656000	+	1.13622i
$680$	−0.288571			−0.0110662
$681$	−25.5461	+	44.2472i	−0.978930	+	1.69556i
$682$	−6.86412	−	11.8890i	−0.262841	−	0.455253i
$683$	−13.1975	−	22.8588i	−0.504989	−	0.874667i	−0.999983	−	0.00577068i	$-0.998163\pi$
$683$	−13.1975	−	22.8588i	−0.504989	−	0.874667i	0.494994	−	0.868896i	$-0.335170\pi$
$684$	−4.39342			−0.167987
$685$	0.995276	+	1.72387i	0.0380275	+	0.0658656i
$686$	25.8310			0.986231
$687$	−63.9850			−2.44118
$688$	21.1087	−	7.40807i	0.804761	−	0.282430i
$689$	47.4546			1.80788
$690$	−0.622393			−0.0236941
$691$	−22.1400	−	38.3476i	−0.842246	−	1.45881i	−0.887992	−	0.459860i	$-0.847900\pi$
$691$	−22.1400	−	38.3476i	−0.842246	−	1.45881i	0.0457458	−	0.998953i	$-0.485434\pi$
$692$	2.26257			0.0860102
$693$	−33.3847	−	57.8240i	−1.26818	−	2.19655i
$694$	−11.2945	−	19.5627i	−0.428734	−	0.742589i
$695$	1.00251	−	1.73640i	0.0380274	−	0.0658654i
$696$	−32.4189			−1.22884
$697$	2.51638	−	4.35849i	0.0953146	−	0.165090i
$698$	−10.6590	−	18.4620i	−0.403450	−	0.698795i
$699$	−59.1853			−2.23859
$700$	−1.59317	−	2.75945i	−0.0602161	−	0.104297i
$701$	4.38290	−	7.59141i	0.165540	−	0.286723i	−0.771307	−	0.636463i	$-0.780397\pi$
$701$	4.38290	−	7.59141i	0.165540	−	0.286723i	0.936847	+	0.349740i	$0.113730\pi$
$702$	−49.3463	+	85.4702i	−1.86245	+	3.22587i
$703$	−0.277518	+	0.480676i	−0.0104668	+	0.0181290i
$704$	29.9064			1.12714
$705$	0.651628	−	1.12865i	0.0245417	−	0.0425075i
$706$	−9.43760	+	16.3464i	−0.355189	+	0.615205i
$707$	−13.5576	−	23.4824i	−0.509885	−	0.883147i
$708$	3.95670	+	6.85321i	0.148702	+	0.257559i
$709$	−27.3996			−1.02901			−0.514506	−	0.857487i	$-0.672025\pi$
$709$	−27.3996			−1.02901			−0.514506	+	0.857487i	$0.672025\pi$
$710$	−0.539287			−0.0202391
$711$	−5.70950	−	9.88915i	−0.214123	−	0.370872i
$712$	27.2249	+	47.1549i	1.02030	+	1.76720i
$713$	−2.24204	+	3.88333i	−0.0839651	+	0.145432i
$714$	5.35619	−	9.27720i	0.200450	−	0.347190i
$715$	1.50399			0.0562462
$716$	−1.72497	+	2.98774i	−0.0644652	+	0.111657i
$717$	−13.5001	+	23.3829i	−0.504171	+	0.873249i
$718$	−8.75479	+	15.1637i	−0.326726	+	0.565906i
$719$	4.41778	+	7.65182i	0.164755	+	0.285365i	0.936568	−	0.350485i	$-0.113983\pi$
$719$	4.41778	+	7.65182i	0.164755	+	0.285365i	−0.771813	+	0.635850i	$0.780650\pi$
$720$	−2.63125			−0.0980609
$721$	−14.2663	−	24.7099i	−0.531304	−	0.920246i
$722$	−9.57231	+	16.5797i	−0.356244	+	0.617033i
$723$	−20.6022			−0.766206
$724$	0.657856	−	1.13944i	0.0244490	−	0.0423469i
$725$	8.19308	+	14.1908i	0.304283	+	0.527034i
$726$	−1.47400	−	2.55305i	−0.0547054	−	0.0947526i
$727$	−16.5783			−0.614854			−0.307427	−	0.951572i	$-0.599468\pi$
$727$	−16.5783			−0.614854			−0.307427	+	0.951572i	$0.599468\pi$
$728$	−16.6240	−	28.7936i	−0.616125	−	1.06716i
$729$	80.2617			2.97265
$730$	1.24379			0.0460348
$731$	−1.21317	+	6.44424i	−0.0448708	+	0.238349i
$732$	−6.92288			−0.255877
$733$	51.4987			1.90215			0.951074	−	0.308964i	$-0.0999822\pi$
$733$	51.4987			1.90215			0.951074	+	0.308964i	$0.0999822\pi$
$734$	−6.68307	−	11.5754i	−0.246677	−	0.427257i
$735$	0.316050			0.0116577
$736$	−1.07675	−	1.86498i	−0.0396895	−	0.0687442i
$737$	−17.0635	−	29.5549i	−0.628543	−	1.08867i
$738$	26.4468	−	45.8073i	0.973522	−	1.68619i
$739$	4.68825			0.172460			0.0862301	−	0.996275i	$-0.472518\pi$
$739$	4.68825			0.172460			0.0862301	+	0.996275i	$0.472518\pi$
$740$	0.00330222	−	0.00571961i	0.000121392	−	0.000210257i
$741$	15.9477	+	27.6222i	0.585853	+	1.01473i
$742$	−33.7536			−1.23914
$743$	9.12276	+	15.8011i	0.334682	+	0.579686i	0.983424	−	0.181323i	$-0.0580379\pi$
$743$	9.12276	+	15.8011i	0.334682	+	0.579686i	−0.648742	+	0.761008i	$0.724705\pi$
$744$	−15.0385	+	26.0474i	−0.551337	+	0.954943i
$745$	1.04036	−	1.80196i	0.0381160	−	0.0660189i
$746$	−10.0464	+	17.4009i	−0.367826	+	0.637093i
$747$	35.0547			1.28258
$748$	−0.444783	+	0.770386i	−0.0162629	+	0.0281681i
$749$	10.6009	−	18.3613i	0.387349	−	0.670908i
$750$	2.11208	+	3.65823i	0.0771223	+	0.133580i
$751$	25.5279	+	44.2157i	0.931527	+	1.61345i	0.780712	+	0.624891i	$0.214857\pi$
$751$	25.5279	+	44.2157i	0.931527	+	1.61345i	0.150815	+	0.988562i	$0.451810\pi$
$752$	−13.8695			−0.505770
$753$	−1.37095			−0.0499601
$754$	9.84684	+	17.0552i	0.358601	+	0.621115i
$755$	−0.593829	−	1.02854i	−0.0216116	−	0.0374324i
$756$	−5.25274	+	9.09801i	−0.191040	+	0.330892i
$757$	−8.71232	+	15.0902i	−0.316655	+	0.548462i	−0.979788	−	0.200040i	$-0.935893\pi$
$757$	−8.71232	+	15.0902i	−0.316655	+	0.548462i	0.663133	+	0.748501i	$0.269226\pi$
$758$	18.7203			0.679952
$759$	−8.32881	+	14.4259i	−0.302317	+	0.523628i
$760$	−0.305567	+	0.529258i	−0.0110841	+	0.0191982i
$761$	0.592427	−	1.02611i	0.0214755	−	0.0371966i	−0.855088	−	0.518483i	$-0.826497\pi$
$761$	0.592427	−	1.02611i	0.0214755	−	0.0371966i	0.876563	+	0.481286i	$0.159830\pi$
$762$	−14.0347	−	24.3089i	−0.508425	−	0.880618i
$763$	−21.7988			−0.789169
$764$	−2.16317	−	3.74671i	−0.0782606	−	0.135551i
$765$	0.385641	−	0.667950i	0.0139429	−	0.0241498i
$766$	40.6055			1.46714
$767$	20.8682	−	36.1448i	0.753507	−	1.30511i
$768$	−10.1638	−	17.6042i	−0.366754	−	0.635237i
$769$	−8.37811	−	14.5113i	−0.302122	−	0.523291i	0.674494	−	0.738280i	$-0.264362\pi$
$769$	−8.37811	−	14.5113i	−0.302122	−	0.523291i	−0.976616	+	0.214989i	$0.931028\pi$
$770$	−1.06977			−0.0385517
$771$	33.5068	+	58.0355i	1.20672	+	2.09010i
$772$	1.43356			0.0515951
$773$	29.5042			1.06119			0.530596	−	0.847625i	$-0.321968\pi$
$773$	29.5042			1.06119			0.530596	+	0.847625i	$0.321968\pi$
$774$	−12.7503	+	67.7282i	−0.458300	+	2.43444i
$775$	15.2024			0.546087
$776$	41.5614			1.49197
$777$	1.06430	+	1.84341i	0.0381814	+	0.0661321i
$778$	7.56403			0.271184
$779$	−5.32917	−	9.23040i	−0.190937	−	0.330713i
$780$	−0.189763	−	0.328679i	−0.00679461	−	0.0117686i
$781$	−7.21669	+	12.4997i	−0.258234	+	0.447274i
$782$	−1.94155			−0.0694296
$783$	27.0129	−	46.7877i	0.965362	−	1.67206i
$784$	−1.68174	−	2.91285i	−0.0600620	−	0.104030i
$785$	−1.69861			−0.0606259
$786$	−12.1729	−	21.0840i	−0.434192	−	0.752043i
$787$	0.340992	−	0.590615i	0.0121550	−	0.0210531i	−0.859884	−	0.510490i	$-0.829464\pi$
$787$	0.340992	−	0.590615i	0.0121550	−	0.0210531i	0.872039	+	0.489436i	$0.162798\pi$
$788$	−2.10247	+	3.64159i	−0.0748975	+	0.129726i
$789$	−16.6914	+	28.9104i	−0.594231	+	1.02924i
$790$	−0.182953			−0.00650918
$791$	−9.61271	+	16.6497i	−0.341789	+	0.591996i
$792$	−40.5853	+	70.2959i	−1.44214	+	2.49786i
$793$	18.2561	+	31.6205i	0.648294	+	1.12288i
$794$	−12.6681	−	21.9417i	−0.449573	−	0.778683i
$795$	−3.34519			−0.118642
$796$	0.630025			0.0223307
$797$	−0.202022	−	0.349913i	−0.00715600	−	0.0123946i	0.862425	−	0.506184i	$-0.168945\pi$
$797$	−0.202022	−	0.349913i	−0.00715600	−	0.0123946i	−0.869581	+	0.493790i	$0.835611\pi$
$798$	−11.3433	−	19.6472i	−0.401549	−	0.695504i
$799$	2.03275	−	3.52082i	0.0719134	−	0.124558i
$800$	−3.65051	+	6.32287i	−0.129065	+	0.223547i
$801$	−145.531			−5.14210
$802$	2.12042	−	3.67267i	0.0748745	−	0.129686i
$803$	16.6443	−	28.8288i	0.587365	−	1.01735i
$804$	−4.30590	+	7.45804i	−0.151857	+	0.263025i
$805$	0.174710	+	0.302607i	0.00615772	+	0.0106655i
$806$	18.2710			0.643568
$807$	36.0556	+	62.4501i	1.26922	+	2.19835i
$808$	−16.4818	+	28.5472i	−0.579826	+	1.00429i
$809$	36.1889			1.27233			0.636167	−	0.771551i	$-0.280519\pi$
$809$	36.1889			1.27233			0.636167	+	0.771551i	$0.280519\pi$
$810$	1.95261	−	3.38202i	0.0686077	−	0.118832i
$811$	−6.81467	−	11.8033i	−0.239295	−	0.414472i	0.721217	−	0.692709i	$-0.243583\pi$
$811$	−6.81467	−	11.8033i	−0.239295	−	0.414472i	−0.960512	+	0.278238i	$0.910250\pi$
$812$	1.04816	+	1.81547i	0.0367833	+	0.0637105i
$813$	−78.5636			−2.75535
$814$	0.590561	+	1.02288i	0.0206992	+	0.0358520i
$815$	−0.765367			−0.0268096
$816$	−11.2984			−0.395525
$817$	10.5345	+	9.04883i	0.368557	+	0.316578i
$818$	18.4939			0.646625
$819$	88.8638			3.10515
$820$	0.0634124	+	0.109833i	0.00221446	+	0.00383555i
$821$	−20.4444			−0.713513			−0.356757	−	0.934197i	$-0.616117\pi$
$821$	−20.4444			−0.713513			−0.356757	+	0.934197i	$0.616117\pi$
$822$	44.9157	+	77.7963i	1.56662	+	2.71346i
$823$	6.40455	+	11.0930i	0.223249	+	0.386678i	0.955793	−	0.294042i	$-0.0950005\pi$
$823$	6.40455	+	11.0930i	0.223249	+	0.386678i	−0.732544	+	0.680720i	$0.761667\pi$
$824$	−17.3433	+	30.0395i	−0.604183	+	1.04648i
$825$	56.4744			1.96619
$826$	−14.8432	+	25.7092i	−0.516461	+	0.894537i
$827$	4.72819	+	8.18947i	0.164415	+	0.284776i	0.936448	−	0.350808i	$-0.114093\pi$
$827$	4.72819	+	8.18947i	0.164415	+	0.284776i	−0.772032	+	0.635584i	$0.780760\pi$
$828$	3.05376			0.106126
$829$	−15.2391	−	26.3949i	−0.529275	−	0.916732i	−0.999417	−	0.0341408i	$-0.989131\pi$
$829$	−15.2391	−	26.3949i	−0.529275	−	0.916732i	0.470142	−	0.882591i	$-0.344203\pi$
$830$	0.280819	−	0.486393i	0.00974738	−	0.0168830i
$831$	46.6985	−	80.8841i	1.61995	−	2.80584i
$832$	−19.9013	+	34.4701i	−0.689954	+	1.19503i
$833$	0.985914			0.0341599
$834$	45.2423	−	78.3619i	1.56661	−	2.71345i
$835$	0.958670	−	1.66047i	0.0331762	−	0.0574628i
$836$	0.941959	+	1.63152i	0.0325783	+	0.0564273i
$837$	−25.0615	−	43.4077i	−0.866251	−	1.50039i
$838$	−15.1598			−0.523688
$839$	12.3929			0.427852			0.213926	−	0.976850i	$-0.431375\pi$
$839$	12.3929			0.427852			0.213926	+	0.976850i	$0.431375\pi$
$840$	1.17187	+	2.02973i	0.0404332	+	0.0700324i
$841$	9.10969	+	15.7784i	0.314127	+	0.544084i
$842$	−18.6708	+	32.3388i	−0.643438	+	1.11447i
$843$	−33.0414	+	57.2294i	−1.13801	+	1.97109i
$844$	−2.99281			−0.103017
$845$	−0.371679	+	0.643767i	−0.0127862	+	0.0221463i
$846$	21.3639	−	37.0034i	0.734507	−	1.27220i
$847$	−0.827527	+	1.43332i	−0.0284342	+	0.0492494i
$848$	17.8001	+	30.8307i	0.611259	+	1.05873i
$849$	14.8100			0.508277
$850$	3.29122	+	5.70056i	0.112888	+	0.195528i
$851$	0.192896	−	0.334106i	0.00661240	−	0.0114530i
$852$	3.64220			0.124780
$853$	26.1031	−	45.2120i	0.893755	−	1.54803i	0.0584165	−	0.998292i	$-0.481395\pi$
$853$	26.1031	−	45.2120i	0.893755	−	1.54803i	0.835338	−	0.549736i	$-0.185272\pi$
$854$	−12.9853	−	22.4912i	−0.444347	−	0.769632i
$855$	−0.816709	−	1.41458i	−0.0279309	−	0.0483777i
$856$	−25.7748			−0.880964
$857$	17.1329	+	29.6751i	0.585249	+	1.01368i	0.994844	+	0.101414i	$0.0323366\pi$
$857$	17.1329	+	29.6751i	0.585249	+	1.01368i	−0.409595	+	0.912267i	$0.634330\pi$
$858$	67.8736			2.31717
$859$	−12.3980			−0.423015			−0.211507	−	0.977376i	$-0.567837\pi$
$859$	−12.3980			−0.423015			−0.211507	+	0.977376i	$0.567837\pi$
$860$	−0.125351	−	0.107673i	−0.00427445	−	0.00367162i
$861$	−40.8753			−1.39303
$862$	46.1172			1.57076
$863$	0.335988	+	0.581949i	0.0114372	+	0.0198098i	0.871687	−	0.490062i	$-0.163026\pi$
$863$	0.335988	+	0.581949i	0.0114372	+	0.0198098i	−0.860250	+	0.509872i	$0.829693\pi$
$864$	24.0717			0.818937
$865$	0.420598	+	0.728498i	0.0143008	+	0.0247697i
$866$	5.04639	+	8.74061i	0.171483	+	0.297018i
$867$	1.65592	−	2.86814i	0.0562381	−	0.0974072i
$868$	1.94488			0.0660136
$869$	−2.44826	+	4.24051i	−0.0830516	+	0.143850i
$870$	−0.694128	−	1.20227i	−0.0235332	−	0.0407606i
$871$	45.4199			1.53899
$872$	13.2502	+	22.9501i	0.448710	+	0.777188i
$873$	−55.5419	+	96.2013i	−1.87981	+	3.25592i
$874$	−2.05590	+	3.56092i	−0.0695419	+	0.120450i
$875$	1.18575	−	2.05378i	0.0400858	−	0.0694306i
$876$	−8.40023			−0.283817
$877$	15.4271	−	26.7206i	0.520937	−	0.902289i	−0.478767	−	0.877942i	$-0.658916\pi$
$877$	15.4271	−	26.7206i	0.520937	−	0.902289i	0.999704	−	0.0243469i	$-0.00775063\pi$
$878$	13.1760	−	22.8215i	0.444668	−	0.770188i
$879$	−46.3210	−	80.2304i	−1.56237	−	2.70610i
$880$	0.564146	+	0.977130i	0.0190174	+	0.0329390i
$881$	−12.6499			−0.426188			−0.213094	−	0.977032i	$-0.568354\pi$
$881$	−12.6499			−0.426188			−0.213094	+	0.977032i	$0.568354\pi$
$882$	10.3618			0.348901
$883$	1.75309	+	3.03644i	0.0589961	+	0.102184i	0.894015	−	0.448037i	$-0.147877\pi$
$883$	1.75309	+	3.03644i	0.0589961	+	0.102184i	−0.835019	+	0.550221i	$0.814543\pi$
$884$	−0.591964	−	1.02531i	−0.0199099	−	0.0344850i
$885$	−1.47105	+	2.54794i	−0.0494489	+	0.0856480i
$886$	−4.81740	+	8.34398i	−0.161844	+	0.280322i
$887$	−19.0927			−0.641070			−0.320535	−	0.947237i	$-0.603863\pi$
$887$	−19.0927			−0.641070			−0.320535	+	0.947237i	$0.603863\pi$
$888$	1.29385	−	2.24101i	0.0434187	−	0.0752035i
$889$	−7.87930	+	13.6473i	−0.264263	+	0.457717i
$890$	−1.16584	+	2.01929i	−0.0390789	+	0.0676867i
$891$	−52.2593	−	90.5157i	−1.75075	−	3.03239i
$892$	1.52060			0.0509136
$893$	−4.30494	−	7.45638i	−0.144059	−	0.249518i
$894$	46.9505	−	81.3207i	1.57026	−	2.71977i
$895$	−1.28265			−0.0428741
$896$	10.5678	−	18.3040i	0.353045	−	0.611492i
$897$	−11.0849	−	19.1995i	−0.370113	−	0.641054i
$898$	14.5025	+	25.1190i	0.483954	+	0.838233i
$899$	−10.0018			−0.333579
$900$	−5.17659	−	8.96612i	−0.172553	−	0.298871i
$901$	−10.4353			−0.347650
$902$	−22.6811			−0.755197
$903$	50.2536	−	17.6364i	1.67234	−	0.586904i
$904$	23.3721			0.777344
$905$	0.489165			0.0162604
$906$	−26.7988	−	46.4169i	−0.890332	−	1.54210i
$907$	−55.7300			−1.85049			−0.925243	−	0.379375i	$-0.876139\pi$
$907$	−55.7300			−1.85049			−0.925243	+	0.379375i	$0.876139\pi$
$908$	−2.00820	−	3.47831i	−0.0666445	−	0.115432i
$909$	−44.0518	−	76.3000i	−1.46111	−	2.53071i
$910$	0.711879	−	1.23301i	0.0235986	−	0.0408739i
$911$	7.28119			0.241236			0.120618	−	0.992699i	$-0.461512\pi$
$911$	7.28119			0.241236			0.120618	+	0.992699i	$0.461512\pi$
$912$	−11.9639	+	20.7221i	−0.396164	+	0.686177i
$913$	−7.51580	−	13.0178i	−0.248737	−	0.430825i
$914$	−3.28621			−0.108698
$915$	−1.28692	−	2.22901i	−0.0425443	−	0.0736889i
$916$	2.51495	−	4.35603i	0.0830964	−	0.143927i
$917$	−6.83403	+	11.8369i	−0.225679	+	0.390888i
$918$	10.8513	−	18.7950i	0.358145	−	0.620326i
$919$	27.2880			0.900147			0.450073	−	0.892992i	$-0.351398\pi$
$919$	27.2880			0.900147			0.450073	+	0.892992i	$0.351398\pi$
$920$	0.212393	−	0.367875i	0.00700238	−	0.0121285i
$921$	6.96002	−	12.0551i	0.229340	−	0.397229i
$922$	5.38274	+	9.32318i	0.177271	+	0.307043i
$923$	−9.60474	−	16.6359i	−0.316144	−	0.547577i
$924$	7.22492			0.237682
$925$	−1.30796			−0.0430053
$926$	−7.71555	−	13.3637i	−0.253549	−	0.439159i
$927$	−46.3546	−	80.2885i	−1.52248	−	2.63702i
$928$	2.40171	−	4.15988i	0.0788399	−	0.136555i
$929$	0.360367	−	0.624175i	0.0118233	−	0.0204785i	−0.860053	−	0.510204i	$-0.829570\pi$
$929$	0.360367	−	0.624175i	0.0118233	−	0.0204785i	0.871877	+	0.489726i	$0.162903\pi$
$930$	−1.28797			−0.0422341
$931$	1.04398	−	1.80823i	0.0342151	−	0.0592624i
$932$	2.32630	−	4.02927i	0.0762004	−	0.131983i
$933$	25.8349	−	44.7474i	0.845798	−	1.46496i
$934$	−25.0777	−	43.4359i	−0.820568	−	1.42127i
$935$	−0.330729			−0.0108160
$936$	−54.0153	−	93.5572i	−1.76554	−	3.05801i
$937$	5.13720	−	8.89788i	0.167825	−	0.290681i	−0.769830	−	0.638249i	$-0.779659\pi$
$937$	5.13720	−	8.89788i	0.167825	−	0.290681i	0.937655	+	0.347568i	$0.112992\pi$
$938$	−32.3064			−1.05484
$939$	39.8748	−	69.0652i	1.30127	−	2.25386i
$940$	0.0512250	+	0.0887242i	0.00167077	+	0.00289387i
$941$	−12.0315	−	20.8391i	−0.392214	−	0.679335i	0.600527	−	0.799605i	$-0.294958\pi$
$941$	−12.0315	−	20.8391i	−0.392214	−	0.679335i	−0.992741	+	0.120269i	$0.961624\pi$
$942$	−76.6563			−2.49760
$943$	3.70418	+	6.41583i	0.120625	+	0.208928i
$944$	31.3105			1.01907
$945$	−3.90581			−0.127056
$946$	27.8850	−	9.78619i	0.906618	−	0.318177i
$947$	26.8815			0.873531			0.436766	−	0.899575i	$-0.356124\pi$
$947$	26.8815			0.873531			0.436766	+	0.899575i	$0.356124\pi$
$948$	1.23562			0.0401309
$949$	22.1520	+	38.3684i	0.719084	+	1.24549i
$950$	13.9403			0.452282
$951$	43.9725	+	76.1627i	1.42591	+	2.46974i
$952$	3.65562	+	6.33172i	0.118479	+	0.205212i
$953$	2.85436	−	4.94390i	0.0924619	−	0.160149i	−0.816085	−	0.577932i	$-0.803860\pi$
$953$	2.85436	−	4.94390i	0.0924619	−	0.160149i	0.908547	+	0.417784i	$0.137193\pi$
$954$	−109.674			−3.55082
$955$	0.804238	−	1.39298i	0.0260245	−	0.0450758i
$956$	−1.06125	−	1.83814i	−0.0343234	−	0.0594498i
$957$	−37.1551			−1.20105
$958$	25.7192	+	44.5470i	0.830950	+	1.43925i
$959$	25.2163	−	43.6759i	0.814277	−	1.41037i
$960$	1.40289	−	2.42988i	0.0452782	−	0.0784241i
$961$	10.8604	−	18.8107i	0.350334	−	0.606797i
$962$	−1.57196			−0.0506821
$963$	34.4449	−	59.6603i	1.10997	−	1.92253i
$964$	0.809778	−	1.40258i	0.0260812	−	0.0451740i
$965$	0.266491	+	0.461575i	0.00857863	+	0.0148586i
$966$	7.88448	+	13.6563i	0.253679	+	0.439385i
$967$	−2.21162			−0.0711209			−0.0355604	−	0.999368i	$-0.511322\pi$
$967$	−2.21162			−0.0711209			−0.0355604	+	0.999368i	$0.511322\pi$
$968$	2.01203			0.0646690
$969$	−3.50691	−	6.07414i	−0.112658	−	0.195129i
$970$	0.889881	+	1.54132i	0.0285723	+	0.0494887i
$971$	29.6628	−	51.3774i	0.951923	−	1.64878i	0.210666	−	0.977558i	$-0.432437\pi$
$971$	29.6628	−	51.3774i	0.951923	−	1.64878i	0.741257	−	0.671221i	$-0.234230\pi$
$972$	−6.76166	+	11.7115i	−0.216880	+	0.375648i
$973$	−50.7993			−1.62855
$974$	−13.0093	+	22.5327i	−0.416844	+	0.721994i
$975$	−37.5811	+	65.0923i	−1.20356	+	2.08462i
$976$	−13.6957	+	23.7216i	−0.438388	+	0.759311i
$977$	9.26709	+	16.0511i	0.296481	+	0.513519i	0.975328	−	0.220760i	$-0.0708537\pi$
$977$	9.26709	+	16.0511i	0.296481	+	0.513519i	−0.678848	+	0.734279i	$0.737520\pi$
$978$	−34.5402			−1.10447
$979$	31.2023	+	54.0439i	0.997229	+	1.72725i
$980$	−0.0124225	+	0.0215163i	−0.000396821	+	0.000687314i
$981$	−70.8294			−2.26141
$982$	−9.50992	+	16.4717i	−0.303474	+	0.525632i
$983$	20.6364	+	35.7434i	0.658200	+	1.14004i	0.981081	+	0.193596i	$0.0620152\pi$
$983$	20.6364	+	35.7434i	0.658200	+	1.14004i	−0.322881	+	0.946439i	$0.604651\pi$
$984$	24.8458	+	43.0341i	0.792054	+	1.37188i
$985$	−1.56335			−0.0498123
$986$	−2.16533	−	3.75045i	−0.0689580	−	0.119439i
$987$	−33.0193			−1.05102
$988$	−2.50732			−0.0797684
$989$	−7.32230	−	6.28963i	−0.232836	−	0.199998i
$990$	−3.47593			−0.110472
$991$	19.5300			0.620390			0.310195	−	0.950673i	$-0.399606\pi$
$991$	19.5300			0.620390			0.310195	+	0.950673i	$0.399606\pi$
$992$	−2.22820	−	3.85936i	−0.0707455	−	0.122535i
$993$	93.6773			2.97276
$994$	6.83169	+	11.8328i	0.216688	+	0.375315i
$995$	0.117118	+	0.202854i	0.00371288	+	0.00643090i
$996$	−1.89658	+	3.28497i	−0.0600954	+	0.104088i
$997$	48.5881			1.53880			0.769401	−	0.638767i	$-0.220555\pi$
$997$	48.5881			1.53880			0.769401	+	0.638767i	$0.220555\pi$
$998$	−20.1784	+	34.9501i	−0.638737	+	1.10633i
$999$	2.15619	+	3.73463i	0.0682188	+	0.118158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.a.681.10	yes	58
43.6	even	3	inner	731.2.e.a.307.10	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.a.307.10	✓	58	43.6	even	3	inner
731.2.e.a.681.10	yes	58	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.31896 q^{2} +(1.65592 + 2.86814i) q^{3} -0.260346 q^{4} +(-0.0483968 - 0.0838257i) q^{5} +(-2.18409 - 3.78296i) q^{6} +(-1.22618 + 2.12381i) q^{7} +2.98130 q^{8} +(-3.98416 + 6.90077i) q^{9} +O(q^{10})\)	\(q-1.31896 q^{2} +(1.65592 + 2.86814i) q^{3} -0.260346 q^{4} +(-0.0483968 - 0.0838257i) q^{5} +(-2.18409 - 3.78296i) q^{6} +(-1.22618 + 2.12381i) q^{7} +2.98130 q^{8} +(-3.98416 + 6.90077i) q^{9} +(0.0638334 + 0.110563i) q^{10} +3.41685 q^{11} +(-0.431114 - 0.746711i) q^{12} +(-2.27375 + 3.93826i) q^{13} +(1.61728 - 2.80122i) q^{14} +(0.160283 - 0.277618i) q^{15} -3.41153 q^{16} +(0.500000 - 0.866025i) q^{17} +(5.25494 - 9.10183i) q^{18} +(-1.05890 - 1.83407i) q^{19} +(0.0125999 + 0.0218237i) q^{20} -8.12185 q^{21} -4.50669 q^{22} +(0.736015 + 1.27482i) q^{23} +(4.93681 + 8.55081i) q^{24} +(2.49532 - 4.32201i) q^{25} +(2.99899 - 5.19440i) q^{26} -16.4543 q^{27} +(0.319232 - 0.552926i) q^{28} +(-1.64169 + 2.84350i) q^{29} +(-0.211406 + 0.366166i) q^{30} +(1.52309 + 2.63808i) q^{31} -1.46294 q^{32} +(5.65804 + 9.80002i) q^{33} +(-0.659480 + 1.14225i) q^{34} +0.237373 q^{35} +(1.03726 - 1.79659i) q^{36} +(-0.131041 - 0.226970i) q^{37} +(1.39664 + 2.41906i) q^{38} -15.0606 q^{39} +(-0.144286 - 0.249910i) q^{40} +5.03275 q^{41} +10.7124 q^{42} +(-6.18746 + 2.17148i) q^{43} -0.889565 q^{44} +0.771282 q^{45} +(-0.970774 - 1.68143i) q^{46} +4.06549 q^{47} +(-5.64922 - 9.78474i) q^{48} +(0.492957 + 0.853827i) q^{49} +(-3.29122 + 5.70056i) q^{50} +3.31185 q^{51} +(0.591964 - 1.02531i) q^{52} +(-5.21765 - 9.03723i) q^{53} +21.7025 q^{54} +(-0.165365 - 0.286420i) q^{55} +(-3.65562 + 6.33172i) q^{56} +(3.50691 - 6.07414i) q^{57} +(2.16533 - 3.75045i) q^{58} -9.17786 q^{59} +(-0.0417290 + 0.0722768i) q^{60} +(4.01453 - 6.95338i) q^{61} +(-2.00890 - 3.47952i) q^{62} +(-9.77061 - 16.9232i) q^{63} +8.75262 q^{64} +0.440170 q^{65} +(-7.46273 - 12.9258i) q^{66} +(-4.99393 - 8.64974i) q^{67} +(-0.130173 + 0.225467i) q^{68} +(-2.43757 + 4.22199i) q^{69} -0.313085 q^{70} +(-2.11209 + 3.65824i) q^{71} +(-11.8780 + 20.5733i) q^{72} +(4.87124 - 8.43723i) q^{73} +(0.172838 + 0.299364i) q^{74} +16.5282 q^{75} +(0.275680 + 0.477492i) q^{76} +(-4.18968 + 7.25674i) q^{77} +19.8644 q^{78} +(-0.716526 + 1.24106i) q^{79} +(0.165107 + 0.285974i) q^{80} +(-15.2946 - 26.4910i) q^{81} -6.63800 q^{82} +(-2.19963 - 3.80987i) q^{83} +2.11449 q^{84} -0.0967936 q^{85} +(8.16101 - 2.86410i) q^{86} -10.8741 q^{87} +10.1867 q^{88} +(9.13187 + 15.8169i) q^{89} -1.01729 q^{90} +(-5.57607 - 9.65804i) q^{91} +(-0.191619 - 0.331894i) q^{92} +(-5.04425 + 8.73690i) q^{93} -5.36222 q^{94} +(-0.102495 + 0.177526i) q^{95} +(-2.42252 - 4.19593i) q^{96} +13.9407 q^{97} +(-0.650190 - 1.12616i) q^{98} +(-13.6133 + 23.5789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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