LMFDB - Embedded newform 414.2.e.c.139.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(139,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("414.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.1481180578947.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 6x^{8} - 11x^{7} + 22x^{6} - 45x^{5} + 66x^{4} - 99x^{3} + 162x^{2} - 162x + 243 $ x^10 - 2x^9 + 6x^8 - 11x^7 + 22x^6 - 45x^5 + 66x^4 - 99x^3 + 162x^2 - 162*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			139.5
Root			$0.452211 + 1.67198i$ of defining polynomial
Character	$\chi$	$=$	414.139
Dual form			414.2.e.c.277.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.67408 - 0.444362i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.21893 - 2.11124i) q^{5} +(-1.22187 - 1.22761i) q^{6} +(-1.79058 - 3.10138i) q^{7} +1.00000 q^{8} +(2.60509 - 1.48779i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.67408 - 0.444362i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.21893 - 2.11124i) q^{5} +(-1.22187 - 1.22761i) q^{6} +(-1.79058 - 3.10138i) q^{7} +1.00000 q^{8} +(2.60509 - 1.48779i) q^{9} -2.43785 q^{10} +(1.40736 + 2.43763i) q^{11} +(-0.452211 + 1.67198i) q^{12} +(-0.171139 + 0.296421i) q^{13} +(-1.79058 + 3.10138i) q^{14} +(1.10243 - 4.07603i) q^{15} +(-0.500000 - 0.866025i) q^{16} -5.21017 q^{17} +(-2.59101 - 1.51217i) q^{18} -1.19429 q^{19} +(1.21893 + 2.11124i) q^{20} +(-4.37571 - 4.39629i) q^{21} +(1.40736 - 2.43763i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(1.67408 - 0.444362i) q^{24} +(-0.471567 - 0.816778i) q^{25} +0.342277 q^{26} +(3.70000 - 3.64828i) q^{27} +3.58116 q^{28} +(4.34522 + 7.52614i) q^{29} +(-4.08116 + 1.08329i) q^{30} +(5.35316 - 9.27194i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.43923 + 3.45540i) q^{33} +(2.60509 + 4.51214i) q^{34} -8.73035 q^{35} +(-0.0140759 + 2.99997i) q^{36} +4.39001 q^{37} +(0.597146 + 1.03429i) q^{38} +(-0.154782 + 0.572279i) q^{39} +(1.21893 - 2.11124i) q^{40} +(0.939481 - 1.62723i) q^{41} +(-1.61944 + 5.98762i) q^{42} +(-3.85245 - 6.67263i) q^{43} -2.81473 q^{44} +(0.0343151 - 7.31348i) q^{45} +1.00000 q^{46} +(1.40442 + 2.43253i) q^{47} +(-1.22187 - 1.22761i) q^{48} +(-2.91236 + 5.04436i) q^{49} +(-0.471567 + 0.816778i) q^{50} +(-8.72224 + 2.31520i) q^{51} +(-0.171139 - 0.296421i) q^{52} -5.79515 q^{53} +(-5.00951 - 1.38015i) q^{54} +6.86190 q^{55} +(-1.79058 - 3.10138i) q^{56} +(-1.99934 + 0.530697i) q^{57} +(4.34522 - 7.52614i) q^{58} +(-4.14080 + 7.17207i) q^{59} +(2.97874 + 2.99275i) q^{60} +(5.02496 + 8.70348i) q^{61} -10.7063 q^{62} +(-9.27883 - 5.41534i) q^{63} +1.00000 q^{64} +(0.417211 + 0.722631i) q^{65} +(1.27285 - 4.70616i) q^{66} +(-3.85744 + 6.68129i) q^{67} +(2.60509 - 4.51214i) q^{68} +(-0.452211 + 1.67198i) q^{69} +(4.36518 + 7.56071i) q^{70} +13.8809 q^{71} +(2.60509 - 1.48779i) q^{72} -1.48027 q^{73} +(-2.19500 - 3.80186i) q^{74} +(-1.15239 - 1.15781i) q^{75} +(0.597146 - 1.03429i) q^{76} +(5.04000 - 8.72953i) q^{77} +(0.572999 - 0.152095i) q^{78} +(0.781073 + 1.35286i) q^{79} -2.43785 q^{80} +(4.57294 - 7.75166i) q^{81} -1.87896 q^{82} +(5.35929 + 9.28257i) q^{83} +(5.99515 - 1.59133i) q^{84} +(-6.35082 + 10.9999i) q^{85} +(-3.85245 + 6.67263i) q^{86} +(10.6186 + 10.6685i) q^{87} +(1.40736 + 2.43763i) q^{88} +1.61576 q^{89} +(-6.35082 + 3.62702i) q^{90} +1.22575 q^{91} +(-0.500000 - 0.866025i) q^{92} +(4.84152 - 17.9007i) q^{93} +(1.40442 - 2.43253i) q^{94} +(-1.45575 + 2.52144i) q^{95} +(-0.452211 + 1.67198i) q^{96} +(3.92638 + 6.80069i) q^{97} +5.82472 q^{98} +(7.29299 + 4.25636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9} - 10 q^{10} + 3 q^{11} - 2 q^{12} + 8 q^{13} + 5 q^{14} + 11 q^{15} - 5 q^{16} - 2 q^{17} - 8 q^{18} - 2 q^{19} + 5 q^{20} - 15 q^{21} + 3 q^{22} - 5 q^{23} + q^{24} - 16 q^{26} - 5 q^{27} - 10 q^{28} + 18 q^{29} + 5 q^{30} + 8 q^{31} - 5 q^{32} + 24 q^{33} + q^{34} + 2 q^{35} + 7 q^{36} - 12 q^{37} + q^{38} - 27 q^{39} + 5 q^{40} + 24 q^{41} - 3 q^{42} - 11 q^{43} - 6 q^{44} - 7 q^{45} + 10 q^{46} + 9 q^{47} + q^{48} - 4 q^{49} + 2 q^{51} + 8 q^{52} - 58 q^{53} - 20 q^{54} - 28 q^{55} + 5 q^{56} + 2 q^{57} + 18 q^{58} + 21 q^{59} - 16 q^{60} + 17 q^{61} - 16 q^{62} + 6 q^{63} + 10 q^{64} + 21 q^{65} + 21 q^{66} + 3 q^{67} + q^{68} - 2 q^{69} - q^{70} - 18 q^{71} + q^{72} - 14 q^{73} + 6 q^{74} + 13 q^{75} + q^{76} + 17 q^{77} + 15 q^{79} - 10 q^{80} + q^{81} - 48 q^{82} + 21 q^{83} + 18 q^{84} - 7 q^{85} - 11 q^{86} - 9 q^{87} + 3 q^{88} - 18 q^{89} - 7 q^{90} + 34 q^{91} - 5 q^{92} + 5 q^{93} + 9 q^{94} + 11 q^{95} - 2 q^{96} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9 - 10 * q^10 + 3 * q^11 - 2 * q^12 + 8 * q^13 + 5 * q^14 + 11 * q^15 - 5 * q^16 - 2 * q^17 - 8 * q^18 - 2 * q^19 + 5 * q^20 - 15 * q^21 + 3 * q^22 - 5 * q^23 + q^24 - 16 * q^26 - 5 * q^27 - 10 * q^28 + 18 * q^29 + 5 * q^30 + 8 * q^31 - 5 * q^32 + 24 * q^33 + q^34 + 2 * q^35 + 7 * q^36 - 12 * q^37 + q^38 - 27 * q^39 + 5 * q^40 + 24 * q^41 - 3 * q^42 - 11 * q^43 - 6 * q^44 - 7 * q^45 + 10 * q^46 + 9 * q^47 + q^48 - 4 * q^49 + 2 * q^51 + 8 * q^52 - 58 * q^53 - 20 * q^54 - 28 * q^55 + 5 * q^56 + 2 * q^57 + 18 * q^58 + 21 * q^59 - 16 * q^60 + 17 * q^61 - 16 * q^62 + 6 * q^63 + 10 * q^64 + 21 * q^65 + 21 * q^66 + 3 * q^67 + q^68 - 2 * q^69 - q^70 - 18 * q^71 + q^72 - 14 * q^73 + 6 * q^74 + 13 * q^75 + q^76 + 17 * q^77 + 15 * q^79 - 10 * q^80 + q^81 - 48 * q^82 + 21 * q^83 + 18 * q^84 - 7 * q^85 - 11 * q^86 - 9 * q^87 + 3 * q^88 - 18 * q^89 - 7 * q^90 + 34 * q^91 - 5 * q^92 + 5 * q^93 + 9 * q^94 + 11 * q^95 - 2 * q^96 - 32 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.67408	−	0.444362i	0.966530	−	0.256552i
$3$	1.67408	−	0.444362i	0.966530	−	0.256552i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.21893	−	2.11124i	0.545121	−	0.944177i	−0.453478	−	0.891267i	$-0.649817\pi$
$5$	1.21893	−	2.11124i	0.545121	−	0.944177i	0.998599	−	0.0529097i	$-0.0168496\pi$
$6$	−1.22187	−	1.22761i	−0.498826	−	0.501172i
$7$	−1.79058	−	3.10138i	−0.676776	−	1.17221i	−0.975946	−	0.218011i	$-0.930043\pi$
$7$	−1.79058	−	3.10138i	−0.676776	−	1.17221i	0.299170	−	0.954200i	$-0.403290\pi$
$8$	1.00000			0.353553
$9$	2.60509	−	1.48779i	0.868362	−	0.495931i
$10$	−2.43785			−0.770917
$11$	1.40736	+	2.43763i	0.424336	+	0.734972i	0.996358	−	0.0852664i	$-0.0271741\pi$
$11$	1.40736	+	2.43763i	0.424336	+	0.734972i	−0.572022	+	0.820238i	$0.693841\pi$
$12$	−0.452211	+	1.67198i	−0.130542	+	0.482658i
$13$	−0.171139	+	0.296421i	−0.0474653	+	0.0822123i	−0.888782	−	0.458330i	$-0.848448\pi$
$13$	−0.171139	+	0.296421i	−0.0474653	+	0.0822123i	0.841317	+	0.540543i	$0.181781\pi$
$14$	−1.79058	+	3.10138i	−0.478553	+	0.828878i
$15$	1.10243	−	4.07603i	0.284645	−	1.05243i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.21017			−1.26365			−0.631826	−	0.775110i	$-0.717694\pi$
$17$	−5.21017			−1.26365			−0.631826	+	0.775110i	$0.717694\pi$
$18$	−2.59101	−	1.51217i	−0.610707	−	0.356423i
$19$	−1.19429			−0.273989			−0.136995	−	0.990572i	$-0.543744\pi$
$19$	−1.19429			−0.273989			−0.136995	+	0.990572i	$0.543744\pi$
$20$	1.21893	+	2.11124i	0.272560	+	0.472088i
$21$	−4.37571	−	4.39629i	−0.954858	−	0.959349i
$22$	1.40736	−	2.43763i	0.300051	−	0.519704i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	1.67408	−	0.444362i	0.341720	−	0.0907049i
$25$	−0.471567	−	0.816778i	−0.0943134	−	0.163356i
$26$	0.342277			0.0671261
$27$	3.70000	−	3.64828i	0.712066	−	0.702113i
$28$	3.58116			0.676776
$29$	4.34522	+	7.52614i	0.806887	+	1.39757i	0.915010	+	0.403431i	$0.132183\pi$
$29$	4.34522	+	7.52614i	0.806887	+	1.39757i	−0.108123	+	0.994138i	$0.534484\pi$
$30$	−4.08116	+	1.08329i	−0.745115	+	0.197781i
$31$	5.35316	−	9.27194i	0.961456	−	1.66529i	0.242605	−	0.970125i	$-0.421998\pi$
$31$	5.35316	−	9.27194i	0.961456	−	1.66529i	0.718850	−	0.695165i	$-0.244669\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.43923	+	3.45540i	0.598693	+	0.601508i
$34$	2.60509	+	4.51214i	0.446768	+	0.773826i
$35$	−8.73035			−1.47570
$36$	−0.0140759	+	2.99997i	−0.00234599	+	0.499994i
$37$	4.39001			0.721713			0.360856	−	0.932621i	$-0.382484\pi$
$37$	4.39001			0.721713			0.360856	+	0.932621i	$0.382484\pi$
$38$	0.597146	+	1.03429i	0.0968699	+	0.167784i
$39$	−0.154782	+	0.572279i	−0.0247849	+	0.0916381i
$40$	1.21893	−	2.11124i	0.192729	−	0.333817i
$41$	0.939481	−	1.62723i	0.146722	−	0.254130i	−0.783292	−	0.621654i	$-0.786461\pi$
$41$	0.939481	−	1.62723i	0.146722	−	0.254130i	0.930014	+	0.367524i	$0.119794\pi$
$42$	−1.61944	+	5.98762i	−0.249885	+	0.923910i
$43$	−3.85245	−	6.67263i	−0.587492	−	1.01757i	−0.994560	−	0.104169i	$-0.966782\pi$
$43$	−3.85245	−	6.67263i	−0.587492	−	1.01757i	0.407067	−	0.913398i	$-0.366551\pi$
$44$	−2.81473			−0.424336
$45$	0.0343151	−	7.31348i	0.00511539	−	1.09023i
$46$	1.00000			0.147442
$47$	1.40442	+	2.43253i	0.204856	+	0.354821i	0.950087	−	0.311985i	$-0.100994\pi$
$47$	1.40442	+	2.43253i	0.204856	+	0.354821i	−0.745231	+	0.666807i	$0.767661\pi$
$48$	−1.22187	−	1.22761i	−0.176361	−	0.177191i
$49$	−2.91236	+	5.04436i	−0.416052	+	0.720623i
$50$	−0.471567	+	0.816778i	−0.0666896	+	0.115510i
$51$	−8.72224	+	2.31520i	−1.22136	+	0.324193i
$52$	−0.171139	−	0.296421i	−0.0237327	−	0.0411062i
$53$	−5.79515			−0.796025			−0.398012	−	0.917380i	$-0.630300\pi$
$53$	−5.79515			−0.796025			−0.398012	+	0.917380i	$0.630300\pi$
$54$	−5.00951	−	1.38015i	−0.681708	−	0.187815i
$55$	6.86190			0.925258
$56$	−1.79058	−	3.10138i	−0.239276	−	0.414439i
$57$	−1.99934	+	0.530697i	−0.264819	+	0.0702926i
$58$	4.34522	−	7.52614i	0.570555	−	0.988230i
$59$	−4.14080	+	7.17207i	−0.539086	+	0.933724i	0.459868	+	0.887988i	$0.347897\pi$
$59$	−4.14080	+	7.17207i	−0.539086	+	0.933724i	−0.998954	+	0.0457368i	$0.985436\pi$
$60$	2.97874	+	2.99275i	0.384553	+	0.386362i
$61$	5.02496	+	8.70348i	0.643380	+	1.11437i	0.984673	+	0.174410i	$0.0558017\pi$
$61$	5.02496	+	8.70348i	0.643380	+	1.11437i	−0.341293	+	0.939957i	$0.610865\pi$
$62$	−10.7063			−1.35970
$63$	−9.27883	−	5.41534i	−1.16902	−	0.682269i
$64$	1.00000			0.125000
$65$	0.417211	+	0.722631i	0.0517487	+	0.0896313i
$66$	1.27285	−	4.70616i	0.156677	−	0.579288i
$67$	−3.85744	+	6.68129i	−0.471262	+	0.816249i	−0.999460	−	0.0328720i	$-0.989535\pi$
$67$	−3.85744	+	6.68129i	−0.471262	+	0.816249i	0.528198	+	0.849121i	$0.322868\pi$
$68$	2.60509	−	4.51214i	0.315913	−	0.547177i
$69$	−0.452211	+	1.67198i	−0.0544399	+	0.201282i
$70$	4.36518	+	7.56071i	0.521738	+	0.903677i
$71$	13.8809			1.64736			0.823681	−	0.567054i	$-0.191917\pi$
$71$	13.8809			1.64736			0.823681	+	0.567054i	$0.191917\pi$
$72$	2.60509	−	1.48779i	0.307012	−	0.175338i
$73$	−1.48027			−0.173252			−0.0866260	−	0.996241i	$-0.527609\pi$
$73$	−1.48027			−0.173252			−0.0866260	+	0.996241i	$0.527609\pi$
$74$	−2.19500	−	3.80186i	−0.255164	−	0.441957i
$75$	−1.15239	−	1.15781i	−0.133066	−	0.133692i
$76$	0.597146	−	1.03429i	0.0684973	−	0.118641i
$77$	5.04000	−	8.72953i	0.574361	−	0.994823i
$78$	0.572999	−	0.152095i	0.0648794	−	0.0172214i
$79$	0.781073	+	1.35286i	0.0878776	+	0.152208i	0.906614	−	0.421961i	$-0.138658\pi$
$79$	0.781073	+	1.35286i	0.0878776	+	0.152208i	−0.818736	+	0.574170i	$0.805325\pi$
$80$	−2.43785			−0.272560
$81$	4.57294	−	7.75166i	0.508105	−	0.861295i
$82$	−1.87896			−0.207497
$83$	5.35929	+	9.28257i	0.588259	+	1.01889i	0.994461	+	0.105111i	$0.0335198\pi$
$83$	5.35929	+	9.28257i	0.588259	+	1.01889i	−0.406202	+	0.913784i	$0.633147\pi$
$84$	5.99515	−	1.59133i	0.654125	−	0.173628i
$85$	−6.35082	+	10.9999i	−0.688843	+	1.19311i
$86$	−3.85245	+	6.67263i	−0.415420	+	0.719528i
$87$	10.6186	+	10.6685i	1.13843	+	1.14378i
$88$	1.40736	+	2.43763i	0.150025	+	0.259852i
$89$	1.61576			0.171270			0.0856350	−	0.996327i	$-0.472708\pi$
$89$	1.61576			0.171270			0.0856350	+	0.996327i	$0.472708\pi$
$90$	−6.35082	+	3.62702i	−0.669435	+	0.382322i
$91$	1.22575			0.128494
$92$	−0.500000	−	0.866025i	−0.0521286	−	0.0902894i
$93$	4.84152	−	17.9007i	0.502042	−	1.85622i
$94$	1.40442	−	2.43253i	0.144855	−	0.250896i
$95$	−1.45575	+	2.52144i	−0.149357	+	0.258694i
$96$	−0.452211	+	1.67198i	−0.0461536	+	0.170645i
$97$	3.92638	+	6.80069i	0.398664	+	0.690506i	0.993561	−	0.113296i	$-0.0361408\pi$
$97$	3.92638	+	6.80069i	0.398664	+	0.690506i	−0.594898	+	0.803801i	$0.702807\pi$
$98$	5.82472			0.588386
$99$	7.29299	+	4.25636i	0.732973	+	0.427780i
$100$	0.943134			0.0943134
$101$	5.22002	+	9.04134i	0.519411	+	0.899647i	0.999745	+	0.0225611i	$0.00718204\pi$
$101$	5.22002	+	9.04134i	0.519411	+	0.899647i	−0.480334	+	0.877086i	$0.659485\pi$
$102$	6.36614	+	6.39608i	0.630342	+	0.633307i
$103$	7.39833	−	12.8143i	0.728979	−	1.26263i	−0.228336	−	0.973582i	$-0.573329\pi$
$103$	7.39833	−	12.8143i	0.728979	−	1.26263i	0.957315	−	0.289046i	$-0.0933381\pi$
$104$	−0.171139	+	0.296421i	−0.0167815	+	0.0290665i
$105$	−14.6153	+	3.87943i	−1.42631	+	0.378594i
$106$	2.89757	+	5.01875i	0.281437	+	0.487464i
$107$	−12.0642			−1.16629			−0.583144	−	0.812369i	$-0.698178\pi$
$107$	−12.0642			−1.16629			−0.583144	+	0.812369i	$0.698178\pi$
$108$	1.30951	+	5.02844i	0.126007	+	0.483862i
$109$	2.51111			0.240521			0.120260	−	0.992742i	$-0.461627\pi$
$109$	2.51111			0.240521			0.120260	+	0.992742i	$0.461627\pi$
$110$	−3.43095	−	5.94258i	−0.327128	−	0.566602i
$111$	7.34922	−	1.95075i	0.697557	−	0.185157i
$112$	−1.79058	+	3.10138i	−0.169194	+	0.293053i
$113$	−6.04131	+	10.4639i	−0.568319	+	0.984357i	0.428413	+	0.903583i	$0.359073\pi$
$113$	−6.04131	+	10.4639i	−0.568319	+	0.984357i	−0.996732	+	0.0807745i	$0.974261\pi$
$114$	1.45927	+	1.46613i	0.136673	+	0.137316i
$115$	1.21893	+	2.11124i	0.113666	+	0.196875i
$116$	−8.69044			−0.806887
$117$	−0.00481788	+	1.02682i	−0.000445413	+	0.0949296i
$118$	8.28160			0.762383
$119$	9.32923	+	16.1587i	0.855210	+	1.48127i
$120$	1.10243	−	4.07603i	0.100637	−	0.372089i
$121$	1.53865	−	2.66503i	0.139878	−	0.242275i
$122$	5.02496	−	8.70348i	0.454938	−	0.787976i
$123$	0.849688	−	3.14158i	0.0766138	−	0.283267i
$124$	5.35316	+	9.27194i	0.480728	+	0.832645i
$125$	9.89005			0.884593
$126$	−0.0504082	+	10.7434i	−0.00449072	+	0.957095i
$127$	−16.6617			−1.47849			−0.739244	−	0.673437i	$-0.764817\pi$
$127$	−16.6617			−1.47849			−0.739244	+	0.673437i	$0.764817\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−9.41436	−	9.45864i	−0.828888	−	0.832787i
$130$	0.417211	−	0.722631i	0.0365918	−	0.0633789i
$131$	8.57688	−	14.8556i	0.749365	−	1.29794i	−0.198762	−	0.980048i	$-0.563692\pi$
$131$	8.57688	−	14.8556i	0.749365	−	1.29794i	0.948127	−	0.317891i	$-0.102975\pi$
$132$	−4.71208	+	1.25076i	−0.410134	+	0.108864i
$133$	2.13848	+	3.70395i	0.185429	+	0.321173i
$134$	7.71489			0.666465
$135$	−3.19238	−	12.2586i	−0.274757	−	1.05505i
$136$	−5.21017			−0.446768
$137$	4.05702	+	7.02696i	0.346614	+	0.600354i	0.985646	−	0.168827i	$-0.0539980\pi$
$137$	4.05702	+	7.02696i	0.346614	+	0.600354i	−0.639031	+	0.769181i	$0.720665\pi$
$138$	1.67408	−	0.444362i	0.142507	−	0.0378266i
$139$	−3.45196	+	5.97897i	−0.292791	+	0.507129i	−0.974469	−	0.224524i	$-0.927917\pi$
$139$	−3.45196	+	5.97897i	−0.292791	+	0.507129i	0.681677	+	0.731653i	$0.261251\pi$
$140$	4.36518	−	7.56071i	0.368925	−	0.638996i
$141$	3.43204	+	3.44818i	0.289030	+	0.290389i
$142$	−6.94046	−	12.0212i	−0.582430	−	1.00880i
$143$	−0.963417			−0.0805650
$144$	−2.59101	−	1.51217i	−0.215917	−	0.126014i
$145$	21.1860			1.75940
$146$	0.740133	+	1.28195i	0.0612538	+	0.106095i
$147$	−2.63401	+	9.73880i	−0.217249	+	0.803243i
$148$	−2.19500	+	3.80186i	−0.180428	+	0.312511i
$149$	−3.68202	+	6.37744i	−0.301643	+	0.522461i	−0.976508	−	0.215480i	$-0.930868\pi$
$149$	−3.68202	+	6.37744i	−0.301643	+	0.522461i	0.674865	+	0.737941i	$0.264202\pi$
$150$	−0.426496	+	1.57690i	−0.0348233	+	0.128753i
$151$	−5.93651	−	10.2823i	−0.483106	−	0.836765i	0.516706	−	0.856163i	$-0.327158\pi$
$151$	−5.93651	−	10.2823i	−0.483106	−	0.836765i	−0.999812	+	0.0193986i	$0.993825\pi$
$152$	−1.19429			−0.0968699
$153$	−13.5729	+	7.75166i	−1.09731	+	0.626684i
$154$	−10.0800			−0.812269
$155$	−13.0502	−	22.6036i	−1.04822	−	1.81557i
$156$	−0.418218	−	0.420185i	−0.0334842	−	0.0336417i
$157$	2.46601	−	4.27125i	0.196809	−	0.340883i	−0.750683	−	0.660662i	$-0.770276\pi$
$157$	2.46601	−	4.27125i	0.196809	−	0.340883i	0.947492	+	0.319780i	$0.103609\pi$
$158$	0.781073	−	1.35286i	0.0621388	−	0.107628i
$159$	−9.70154	+	2.57514i	−0.769382	+	0.204222i
$160$	1.21893	+	2.11124i	0.0963647	+	0.166908i
$161$	3.58116			0.282235
$162$	−8.99960	−	0.0844547i	−0.707076	−	0.00663539i
$163$	−24.0295			−1.88214			−0.941069	−	0.338213i	$-0.890177\pi$
$163$	−24.0295			−1.88214			−0.941069	+	0.338213i	$0.890177\pi$
$164$	0.939481	+	1.62723i	0.0733611	+	0.127065i
$165$	11.4874	−	3.04916i	0.894290	−	0.237377i
$166$	5.35929	−	9.28257i	0.415962	−	0.720467i
$167$	−8.21146	+	14.2227i	−0.635422	+	1.10058i	0.351004	+	0.936374i	$0.385840\pi$
$167$	−8.21146	+	14.2227i	−0.635422	+	1.10058i	−0.986426	+	0.164209i	$0.947493\pi$
$168$	−4.37571	−	4.39629i	−0.337593	−	0.339181i
$169$	6.44142	+	11.1569i	0.495494	+	0.858221i
$170$	12.7016			0.974171
$171$	−3.11123	+	1.77686i	−0.237922	+	0.135880i
$172$	7.70489			0.587492
$173$	5.78073	+	10.0125i	0.439501	+	0.761238i	0.997651	−	0.0685019i	$-0.0218219\pi$
$173$	5.78073	+	10.0125i	0.439501	+	0.761238i	−0.558150	+	0.829740i	$0.688489\pi$
$174$	3.92991	−	14.5302i	0.297926	−	1.10153i
$175$	−1.68876	+	2.92501i	−0.127658	+	0.221110i
$176$	1.40736	−	2.43763i	0.106084	−	0.183743i
$177$	−3.74503	+	13.8466i	−0.281494	+	1.04078i
$178$	−0.807879	−	1.39929i	−0.0605531	−	0.104881i
$179$	9.63696			0.720300			0.360150	−	0.932894i	$-0.382726\pi$
$179$	9.63696			0.720300			0.360150	+	0.932894i	$0.382726\pi$
$180$	6.31650	+	3.68646i	0.470804	+	0.274772i
$181$	−25.3924			−1.88740			−0.943700	−	0.330802i	$-0.892681\pi$
$181$	−25.3924			−1.88740			−0.943700	+	0.330802i	$0.892681\pi$
$182$	−0.612875	−	1.06153i	−0.0454293	−	0.0786859i
$183$	12.2797	+	12.3374i	0.907739	+	0.912008i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	5.35110	−	9.26838i	0.393421	−	0.681425i
$186$	−17.9232	+	4.75748i	−1.31419	+	0.348835i
$187$	−7.33261	−	12.7004i	−0.536213	−	0.928749i
$188$	−2.80885			−0.204856
$189$	−17.9399	−	4.94256i	−1.30493	−	0.359518i
$190$	2.91151			0.211223
$191$	−10.1081	−	17.5078i	−0.731398	−	1.26682i	−0.956286	−	0.292434i	$-0.905535\pi$
$191$	−10.1081	−	17.5078i	−0.731398	−	1.26682i	0.224888	−	0.974385i	$-0.427798\pi$
$192$	1.67408	−	0.444362i	0.120816	−	0.0320690i
$193$	−0.624234	+	1.08120i	−0.0449333	+	0.0778268i	−0.887617	−	0.460582i	$-0.847641\pi$
$193$	−0.624234	+	1.08120i	−0.0449333	+	0.0778268i	0.842684	+	0.538408i	$0.180974\pi$
$194$	3.92638	−	6.80069i	0.281898	−	0.488261i
$195$	1.01955	+	1.02435i	0.0730118	+	0.0733551i
$196$	−2.91236	−	5.04436i	−0.208026	−	0.360311i
$197$	4.00274			0.285184			0.142592	−	0.989782i	$-0.454456\pi$
$197$	4.00274			0.285184			0.142592	+	0.989782i	$0.454456\pi$
$198$	0.0396200	−	8.44409i	0.00281567	−	0.600095i
$199$	17.2073			1.21979			0.609897	−	0.792481i	$-0.291211\pi$
$199$	17.2073			1.21979			0.609897	+	0.792481i	$0.291211\pi$
$200$	−0.471567	−	0.816778i	−0.0333448	−	0.0577549i
$201$	−3.48876	+	12.8991i	−0.246078	+	0.909833i
$202$	5.22002	−	9.04134i	0.367279	−	0.636146i
$203$	15.5609	−	26.9523i	1.09216	−	1.89168i
$204$	2.35610	−	8.71128i	0.164960	−	0.609912i
$205$	−2.29032	−	3.96695i	−0.159963	−	0.277064i
$206$	−14.7967			−1.03093
$207$	−0.0140759	+	2.99997i	−0.000978346	+	0.208512i
$208$	0.342277			0.0237327
$209$	−1.68080	−	2.91124i	−0.116264	−	0.201374i
$210$	10.6673	+	10.7175i	0.736116	+	0.739578i
$211$	0.652189	−	1.12962i	0.0448985	−	0.0777665i	−0.842703	−	0.538379i	$-0.819037\pi$
$211$	0.652189	−	1.12962i	0.0448985	−	0.0777665i	0.887601	+	0.460613i	$0.152370\pi$
$212$	2.89757	−	5.01875i	0.199006	−	0.344689i
$213$	23.2378	−	6.16814i	1.59222	−	0.422634i
$214$	6.03209	+	10.4479i	0.412345	+	0.714202i
$215$	−18.7834			−1.28102
$216$	3.70000	−	3.64828i	0.251753	−	0.248234i
$217$	−38.3411			−2.60276
$218$	−1.25555	−	2.17468i	−0.0850368	−	0.147288i
$219$	−2.47808	+	0.657773i	−0.167453	+	0.0444482i
$220$	−3.43095	+	5.94258i	−0.231314	+	0.400648i
$221$	0.891662	−	1.54440i	0.0599796	−	0.103888i
$222$	−5.36401	−	5.38924i	−0.360009	−	0.361702i
$223$	−7.46207	−	12.9247i	−0.499697	−	0.865501i	0.500303	−	0.865850i	$-0.333222\pi$
$223$	−7.46207	−	12.9247i	−0.499697	−	0.865501i	−1.00000		0.000349791i	$0.999889\pi$
$224$	3.58116			0.239276
$225$	−2.44367	−	1.42618i	−0.162911	−	0.0950788i
$226$	12.0826			0.803724
$227$	−12.3534	−	21.3968i	−0.819925	−	1.42015i	−0.905737	−	0.423841i	$-0.860682\pi$
$227$	−12.3534	−	21.3968i	−0.819925	−	1.42015i	0.0858112	−	0.996311i	$-0.472652\pi$
$228$	0.540072	−	1.99683i	0.0357672	−	0.132243i
$229$	−1.44136	+	2.49650i	−0.0952476	+	0.164974i	−0.909712	−	0.415240i	$-0.863698\pi$
$229$	−1.44136	+	2.49650i	−0.0952476	+	0.164974i	0.814464	+	0.580214i	$0.197031\pi$
$230$	1.21893	−	2.11124i	0.0803737	−	0.139211i
$231$	4.55829	−	16.8535i	0.299913	−	1.10888i
$232$	4.34522	+	7.52614i	0.285278	+	0.494115i
$233$	−8.03702			−0.526523			−0.263261	−	0.964725i	$-0.584798\pi$
$233$	−8.03702			−0.526523			−0.263261	+	0.964725i	$0.584798\pi$
$234$	0.891662	−	0.509238i	0.0582897	−	0.0332899i
$235$	6.84756			0.446685
$236$	−4.14080	−	7.17207i	−0.269543	−	0.466862i
$237$	1.90874	+	1.91771i	0.123986	+	0.124569i
$238$	9.32923	−	16.1587i	0.604724	−	1.04741i
$239$	0.917309	−	1.58883i	0.0593358	−	0.102773i	−0.834832	−	0.550505i	$-0.814435\pi$
$239$	0.917309	−	1.58883i	0.0593358	−	0.102773i	0.894167	+	0.447733i	$0.147768\pi$
$240$	−4.08116	+	1.08329i	−0.263438	+	0.0699260i
$241$	−7.88247	−	13.6528i	−0.507755	−	0.879457i	−0.999960	−	0.00897776i	$-0.997142\pi$
$241$	−7.88247	−	13.6528i	−0.507755	−	0.879457i	0.492205	−	0.870479i	$-0.336191\pi$
$242$	−3.07731			−0.197817
$243$	4.21093	−	15.0089i	0.270131	−	0.962823i
$244$	−10.0499			−0.643380
$245$	7.09992	+	12.2974i	0.453597	+	0.785653i
$246$	−3.14553	+	0.834938i	−0.200552	+	0.0532337i
$247$	0.204389	−	0.354013i	0.0130050	−	0.0225253i
$248$	5.35316	−	9.27194i	0.339926	−	0.588769i
$249$	13.0967	+	13.1583i	0.829970	+	0.833873i
$250$	−4.94502	−	8.56503i	−0.312751	−	0.541700i
$251$	−13.7419			−0.867380			−0.433690	−	0.901062i	$-0.642789\pi$
$251$	−13.7419			−0.867380			−0.433690	+	0.901062i	$0.642789\pi$
$252$	9.32923	−	5.32803i	0.587687	−	0.335634i
$253$	−2.81473			−0.176960
$254$	8.33086	+	14.4295i	0.522725	+	0.905386i
$255$	−5.74383	+	21.2368i	−0.359692	+	1.32990i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.61659	−	16.6564i	0.599867	−	1.03900i	−0.392974	−	0.919550i	$-0.628554\pi$
$257$	9.61659	−	16.6564i	0.599867	−	1.03900i	0.992840	−	0.119450i	$-0.0381130\pi$
$258$	−3.48424	+	12.8824i	−0.216919	+	0.802023i
$259$	−7.86067	−	13.6151i	−0.488438	−	0.846000i
$260$	−0.834422			−0.0517487
$261$	22.5170	+	13.1414i	1.39377	+	0.813435i
$262$	−17.1538			−1.05976
$263$	−5.15425	−	8.92742i	−0.317824	−	0.550488i	0.662209	−	0.749319i	$-0.269619\pi$
$263$	−5.15425	−	8.92742i	−0.317824	−	0.550488i	−0.980034	+	0.198831i	$0.936286\pi$
$264$	3.43923	+	3.45540i	0.211670	+	0.212665i
$265$	−7.06386	+	12.2350i	−0.433930	+	0.751588i
$266$	2.13848	−	3.70395i	0.131118	−	0.227104i
$267$	2.70491	−	0.717981i	0.165538	−	0.0439397i
$268$	−3.85744	−	6.68129i	−0.235631	−	0.408125i
$269$	−21.7951			−1.32887			−0.664437	−	0.747344i	$-0.731329\pi$
$269$	−21.7951			−1.32887			−0.664437	+	0.747344i	$0.731329\pi$
$270$	−9.02007	+	8.89399i	−0.548944	+	0.541271i
$271$	28.8728			1.75390			0.876950	−	0.480582i	$-0.159574\pi$
$271$	28.8728			1.75390			0.876950	+	0.480582i	$0.159574\pi$
$272$	2.60509	+	4.51214i	0.157957	+	0.273589i
$273$	2.05200	−	0.544676i	0.124193	−	0.0329653i
$274$	4.05702	−	7.02696i	0.245093	−	0.424514i
$275$	1.32733	−	2.29901i	0.0800412	−	0.138635i
$276$	−1.22187	−	1.22761i	−0.0735478	−	0.0738937i
$277$	13.5779	+	23.5175i	0.815814	+	1.41303i	0.908742	+	0.417359i	$0.137044\pi$
$277$	13.5779	+	23.5175i	0.815814	+	1.41303i	−0.0929278	+	0.995673i	$0.529623\pi$
$278$	6.90391			0.414069
$279$	0.150702	−	32.1186i	0.00902226	−	1.92289i
$280$	−8.73035			−0.521738
$281$	3.62210	+	6.27367i	0.216077	+	0.374256i	0.953605	−	0.301060i	$-0.0973406\pi$
$281$	3.62210	+	6.27367i	0.216077	+	0.374256i	−0.737529	+	0.675316i	$0.764007\pi$
$282$	1.27019	−	4.69632i	0.0756388	−	0.279662i
$283$	−5.75915	+	9.97514i	−0.342346	+	0.592961i	−0.984868	−	0.173307i	$-0.944555\pi$
$283$	−5.75915	+	9.97514i	−0.342346	+	0.592961i	0.642522	+	0.766267i	$0.277888\pi$
$284$	−6.94046	+	12.0212i	−0.411840	+	0.713328i
$285$	−1.31662	+	4.86798i	−0.0779897	+	0.288354i
$286$	0.481709	+	0.834344i	0.0284840	+	0.0493358i
$287$	−6.72887			−0.397192
$288$	−0.0140759	+	2.99997i	−0.000829433	+	0.176775i
$289$	10.1459			0.596817
$290$	−10.5930	−	18.3476i	−0.622043	−	1.07741i
$291$	9.59504	+	9.64017i	0.562471	+	0.565117i
$292$	0.740133	−	1.28195i	0.0433130	−	0.0750203i
$293$	4.34278	−	7.52192i	0.253708	−	0.439435i	−0.710836	−	0.703358i	$-0.751683\pi$
$293$	4.34278	−	7.52192i	0.253708	−	0.439435i	0.964544	+	0.263923i	$0.0850164\pi$
$294$	9.75105	−	2.58828i	0.568693	−	0.150952i
$295$	10.0947	+	17.4845i	0.587734	+	1.01799i
$296$	4.39001			0.255164
$297$	14.1004	+	3.88476i	0.818188	+	0.225417i
$298$	7.36404			0.426587
$299$	−0.171139	−	0.296421i	−0.00989720	−	0.0171425i
$300$	1.57888	−	0.419093i	0.0911568	−	0.0241963i
$301$	−13.7962	+	23.8958i	−0.795202	+	1.37733i
$302$	−5.93651	+	10.2823i	−0.341608	+	0.591682i
$303$	12.7563	+	12.8163i	0.732833	+	0.736280i
$304$	0.597146	+	1.03429i	0.0342487	+	0.0593204i
$305$	24.5002			1.40288
$306$	13.4996	+	7.87868i	0.771721	+	0.450394i
$307$	−12.4364			−0.709784			−0.354892	−	0.934907i	$-0.615482\pi$
$307$	−12.4364			−0.709784			−0.354892	+	0.934907i	$0.615482\pi$
$308$	5.04000	+	8.72953i	0.287181	+	0.497411i
$309$	6.69122	−	24.7397i	0.380650	−	1.40739i
$310$	−13.0502	+	22.6036i	−0.741203	+	1.28380i
$311$	−13.5253	+	23.4265i	−0.766948	+	1.32839i	0.172263	+	0.985051i	$0.444892\pi$
$311$	−13.5253	+	23.4265i	−0.766948	+	1.32839i	−0.939211	+	0.343342i	$0.888441\pi$
$312$	−0.154782	+	0.572279i	−0.00876279	+	0.0323989i
$313$	−1.02070	−	1.76791i	−0.0576934	−	0.0999279i	0.835736	−	0.549131i	$-0.185041\pi$
$313$	−1.02070	−	1.76791i	−0.0576934	−	0.0999279i	−0.893430	+	0.449203i	$0.851708\pi$
$314$	−4.93201			−0.278330
$315$	−22.7433	+	12.9890i	−1.28144	+	0.731845i
$316$	−1.56215			−0.0878776
$317$	4.01316	+	6.95100i	0.225402	+	0.390407i	0.956440	−	0.291929i	$-0.0942972\pi$
$317$	4.01316	+	6.95100i	0.225402	+	0.390407i	−0.731038	+	0.682336i	$0.760964\pi$
$318$	7.08091	+	7.11421i	0.397078	+	0.398945i
$319$	−12.2306	+	21.1840i	−0.684783	+	1.18608i
$320$	1.21893	−	2.11124i	0.0681401	−	0.118022i
$321$	−20.1964	+	5.36085i	−1.12725	+	0.299214i
$322$	−1.79058	−	3.10138i	−0.0997852	−	0.172833i
$323$	6.22247			0.346227
$324$	4.42666	+	7.83611i	0.245926	+	0.435340i
$325$	0.322813			0.0179065
$326$	12.0148	+	20.8102i	0.665437	+	1.15257i
$327$	4.20379	−	1.11584i	0.232470	−	0.0617061i
$328$	0.939481	−	1.62723i	0.0518742	−	0.0898487i
$329$	5.02947	−	8.71129i	0.277283	−	0.480269i
$330$	−8.38433	−	8.42377i	−0.461542	−	0.463713i
$331$	4.14468	+	7.17880i	0.227812	+	0.394582i	0.957159	−	0.289561i	$-0.0935094\pi$
$331$	4.14468	+	7.17880i	0.227812	+	0.394582i	−0.729347	+	0.684144i	$0.760176\pi$
$332$	−10.7186			−0.588259
$333$	11.4363	−	6.53143i	0.626708	−	0.357920i
$334$	16.4229			0.898622
$335$	9.40389	+	16.2880i	0.513789	+	0.889909i
$336$	−1.61944	+	5.98762i	−0.0883478	+	0.326651i
$337$	−8.30309	+	14.3814i	−0.452298	+	0.783403i	−0.998528	−	0.0542318i	$-0.982729\pi$
$337$	−8.30309	+	14.3814i	−0.452298	+	0.783403i	0.546230	+	0.837635i	$0.316062\pi$
$338$	6.44142	−	11.1569i	0.350367	−	0.606854i
$339$	−5.46390	+	20.2019i	−0.296758	+	1.09721i
$340$	−6.35082	−	10.9999i	−0.344422	−	0.596556i
$341$	30.1354			1.63192
$342$	3.09442	+	1.80598i	0.167327	+	0.0976560i
$343$	−4.20885			−0.227257
$344$	−3.85245	−	6.67263i	−0.207710	−	0.359764i
$345$	2.97874	+	2.99275i	0.160370	+	0.161124i
$346$	5.78073	−	10.0125i	0.310774	−	0.538277i
$347$	4.65626	−	8.06488i	0.249961	−	0.432946i	−0.713554	−	0.700601i	$-0.752915\pi$
$347$	4.65626	−	8.06488i	0.249961	−	0.432946i	0.963515	+	0.267655i	$0.0862488\pi$
$348$	−14.5485	+	3.86170i	−0.779881	+	0.207009i
$349$	−15.6367	−	27.0836i	−0.837014	−	1.44975i	−0.892380	−	0.451285i	$-0.850966\pi$
$349$	−15.6367	−	27.0836i	−0.837014	−	1.44975i	0.0553655	−	0.998466i	$-0.482368\pi$
$350$	3.37752			0.180536
$351$	0.448214	+	1.72112i	0.0239239	+	0.0918666i
$352$	−2.81473			−0.150025
$353$	1.88829	+	3.27061i	0.100504	+	0.174077i	0.911892	−	0.410430i	$-0.134621\pi$
$353$	1.88829	+	3.27061i	0.100504	+	0.174077i	−0.811389	+	0.584507i	$0.801288\pi$
$354$	13.8641	−	3.68002i	0.736866	−	0.195591i
$355$	16.9198	−	29.3060i	0.898011	−	1.55540i
$356$	−0.807879	+	1.39929i	−0.0428175	+	0.0741621i
$357$	22.7982	+	22.9054i	1.20661	+	1.21228i
$358$	−4.81848	−	8.34585i	−0.254665	−	0.441092i
$359$	−29.0029			−1.53072			−0.765359	−	0.643604i	$-0.777438\pi$
$359$	−29.0029			−1.53072			−0.765359	+	0.643604i	$0.777438\pi$
$360$	0.0343151	−	7.31348i	0.00180856	−	0.385454i
$361$	−17.5737			−0.924930
$362$	12.6962	+	21.9904i	0.667297	+	1.15579i
$363$	1.39159	−	5.14518i	0.0730397	−	0.270052i
$364$	−0.612875	+	1.06153i	−0.0321234	+	0.0556393i
$365$	−1.80434	+	3.12520i	−0.0944433	+	0.163581i
$366$	4.54469	−	16.8032i	0.237555	−	0.878318i
$367$	−14.5952	−	25.2796i	−0.761862	−	1.31958i	−0.941890	−	0.335923i	$-0.890952\pi$
$367$	−14.5952	−	25.2796i	−0.761862	−	1.31958i	0.180027	−	0.983662i	$-0.442381\pi$
$368$	1.00000			0.0521286
$369$	0.0264482	−	5.63682i	0.00137684	−	0.293441i
$370$	−10.7022			−0.556381
$371$	10.3767	+	17.9729i	0.538731	+	0.933109i
$372$	13.0817	+	13.1432i	0.678255	+	0.681445i
$373$	4.90589	−	8.49725i	0.254017	−	0.439971i	−0.710611	−	0.703585i	$-0.751581\pi$
$373$	4.90589	−	8.49725i	0.254017	−	0.439971i	0.964628	+	0.263614i	$0.0849147\pi$
$374$	−7.33261	+	12.7004i	−0.379160	+	0.656725i
$375$	16.5567	−	4.39476i	0.854986	−	0.226944i
$376$	1.40442	+	2.43253i	0.0724276	+	0.125448i
$377$	−2.97454			−0.153197
$378$	4.68955	+	18.0077i	0.241205	+	0.926214i
$379$	26.1542			1.34345			0.671725	−	0.740801i	$-0.265554\pi$
$379$	26.1542			1.34345			0.671725	+	0.740801i	$0.265554\pi$
$380$	−1.45575	−	2.52144i	−0.0746787	−	0.129347i
$381$	−27.8931	+	7.40383i	−1.42900	+	0.379310i
$382$	−10.1081	+	17.5078i	−0.517176	+	0.895776i
$383$	2.84048	−	4.91986i	0.145142	−	0.251393i	−0.784284	−	0.620402i	$-0.786969\pi$
$383$	2.84048	−	4.91986i	0.145142	−	0.251393i	0.929426	+	0.369009i	$0.120303\pi$
$384$	−1.22187	−	1.22761i	−0.0623532	−	0.0626465i
$385$	−12.2868	−	21.2813i	−0.626192	−	1.08460i
$386$	1.24847			0.0635453
$387$	−19.9634	−	11.6511i	−1.01480	−	0.592260i
$388$	−7.85276			−0.398664
$389$	−13.5080	−	23.3965i	−0.684883	−	1.18625i	−0.973474	−	0.228799i	$-0.926520\pi$
$389$	−13.5080	−	23.3965i	−0.684883	−	1.18625i	0.288591	−	0.957453i	$-0.406813\pi$
$390$	0.377335	−	1.39513i	0.0191071	−	0.0706454i
$391$	2.60509	−	4.51214i	0.131745	−	0.228189i
$392$	−2.91236	+	5.04436i	−0.147097	+	0.254779i
$393$	7.75712	−	28.6807i	0.391295	−	1.44675i
$394$	−2.00137	−	3.46648i	−0.100828	−	0.174639i
$395$	3.80828			0.191616
$396$	−7.33261	+	4.18773i	−0.368477	+	0.210442i
$397$	4.23930			0.212764			0.106382	−	0.994325i	$-0.466073\pi$
$397$	4.23930			0.212764			0.106382	+	0.994325i	$0.466073\pi$
$398$	−8.60366	−	14.9020i	−0.431262	−	0.746968i
$399$	5.22587	+	5.25045i	0.261621	+	0.262851i
$400$	−0.471567	+	0.816778i	−0.0235784	+	0.0408389i
$401$	−11.2111	+	19.4183i	−0.559858	+	0.969702i	0.437650	+	0.899146i	$0.355811\pi$
$401$	−11.2111	+	19.4183i	−0.559858	+	0.969702i	−0.997508	+	0.0705569i	$0.977522\pi$
$402$	12.9153	−	3.42820i	0.644159	−	0.170983i
$403$	1.83226	+	3.17357i	0.0912716	+	0.158087i
$404$	−10.4400			−0.519411
$405$	−10.7916	−	19.1033i	−0.536237	−	0.949251i
$406$	−31.1219			−1.54455
$407$	6.17834	+	10.7012i	0.306249	+	0.530439i
$408$	−8.72224	+	2.31520i	−0.431815	+	0.114619i
$409$	−13.2655	+	22.9765i	−0.655936	+	1.13611i	0.325722	+	0.945466i	$0.394393\pi$
$409$	−13.2655	+	22.9765i	−0.655936	+	1.13611i	−0.981658	+	0.190649i	$0.938941\pi$
$410$	−2.29032	+	3.96695i	−0.113111	+	0.195914i
$411$	9.91428	+	9.96091i	0.489035	+	0.491335i
$412$	7.39833	+	12.8143i	0.364489	+	0.631314i
$413$	29.6577			1.45936
$414$	2.60509	−	1.48779i	0.128033	−	0.0731211i
$415$	26.1304			1.28269
$416$	−0.171139	−	0.296421i	−0.00839076	−	0.0145332i
$417$	−3.12203	+	11.5432i	−0.152886	+	0.565272i
$418$	−1.68080	+	2.91124i	−0.0822108	+	0.142393i
$419$	14.1333	−	24.4796i	0.690458	−	1.19591i	−0.281230	−	0.959640i	$-0.590743\pi$
$419$	14.1333	−	24.4796i	0.690458	−	1.19591i	0.971688	−	0.236268i	$-0.0759242\pi$
$420$	3.94797	−	14.5969i	0.192641	−	0.712258i
$421$	−2.50954	−	4.34665i	−0.122307	−	0.211843i	0.798370	−	0.602167i	$-0.205696\pi$
$421$	−2.50954	−	4.34665i	−0.122307	−	0.211843i	−0.920677	+	0.390325i	$0.872363\pi$
$422$	−1.30438			−0.0634961
$423$	7.27775	+	4.24746i	0.353856	+	0.206519i
$424$	−5.79515			−0.281437
$425$	2.45694	+	4.25555i	0.119179	+	0.206425i
$426$	−16.9606	−	17.0404i	−0.821746	−	0.825611i
$427$	17.9952	−	31.1686i	0.870848	−	1.50835i
$428$	6.03209	−	10.4479i	0.291572	−	0.505017i
$429$	−1.61284	+	0.428106i	−0.0778685	+	0.0206691i
$430$	9.39170	+	16.2669i	0.452908	+	0.784460i
$431$	−2.16751			−0.104405			−0.0522027	−	0.998637i	$-0.516624\pi$
$431$	−2.16751			−0.104405			−0.0522027	+	0.998637i	$0.516624\pi$
$432$	−5.00951	−	1.38015i	−0.241020	−	0.0664027i
$433$	22.8924			1.10014			0.550069	−	0.835119i	$-0.314602\pi$
$433$	22.8924			1.10014			0.550069	+	0.835119i	$0.314602\pi$
$434$	19.1705	+	33.2043i	0.920215	+	1.59386i
$435$	35.4671	−	9.41425i	1.70052	−	0.451379i
$436$	−1.25555	+	2.17468i	−0.0601301	+	0.104148i
$437$	0.597146	−	1.03429i	0.0285654	−	0.0494767i
$438$	1.80869	+	1.81720i	0.0864225	+	0.0868290i
$439$	11.2809	+	19.5391i	0.538409	+	0.932551i	0.998990	+	0.0449335i	$0.0143076\pi$
$439$	11.2809	+	19.5391i	0.538409	+	0.932551i	−0.460581	+	0.887617i	$0.652359\pi$
$440$	6.86190			0.327128
$441$	−0.0819885	+	17.4740i	−0.00390421	+	0.832094i
$442$	−1.78332			−0.0848240
$443$	0.889869	+	1.54130i	0.0422790	+	0.0732293i	0.886391	−	0.462938i	$-0.153205\pi$
$443$	0.889869	+	1.54130i	0.0422790	+	0.0732293i	−0.844112	+	0.536168i	$0.819872\pi$
$444$	−1.98521	+	7.33999i	−0.0942140	+	0.348341i
$445$	1.96949	−	3.41126i	0.0933629	−	0.161709i
$446$	−7.46207	+	12.9247i	−0.353339	+	0.612001i
$447$	−3.33010	+	12.3125i	−0.157508	+	0.582361i
$448$	−1.79058	−	3.10138i	−0.0845970	−	0.146526i
$449$	−24.8340			−1.17199			−0.585994	−	0.810315i	$-0.699296\pi$
$449$	−24.8340			−1.17199			−0.585994	+	0.810315i	$0.699296\pi$
$450$	−0.0132755	+	2.82937i	−0.000625813	+	0.133378i
$451$	5.28877			0.249038
$452$	−6.04131	−	10.4639i	−0.284159	−	0.492179i
$453$	−14.5073	−	14.5755i	−0.681611	−	0.684816i
$454$	−12.3534	+	21.3968i	−0.579775	+	1.00420i
$455$	1.49410	−	2.58786i	0.0700445	−	0.121321i
$456$	−1.99934	+	0.530697i	−0.0936277	+	0.0248522i
$457$	−5.87051	−	10.1680i	−0.274611	−	0.475640i	0.695426	−	0.718598i	$-0.255216\pi$
$457$	−5.87051	−	10.1680i	−0.274611	−	0.475640i	−0.970037	+	0.242958i	$0.921882\pi$
$458$	2.88272			0.134700
$459$	−19.2776	+	19.0082i	−0.899804	+	0.887226i
$460$	−2.43785			−0.113666
$461$	12.2554	+	21.2270i	0.570792	+	0.988640i	0.996485	+	0.0837727i	$0.0266970\pi$
$461$	12.2554	+	21.2270i	0.570792	+	0.988640i	−0.425693	+	0.904868i	$0.639970\pi$
$462$	−16.8747	+	4.47916i	−0.785083	+	0.208390i
$463$	1.67416	−	2.89974i	0.0778050	−	0.134762i	−0.824498	−	0.565865i	$-0.808542\pi$
$463$	1.67416	−	2.89974i	0.0778050	−	0.134762i	0.902303	+	0.431103i	$0.141876\pi$
$464$	4.34522	−	7.52614i	0.201722	−	0.349392i
$465$	−31.8913	−	32.0413i	−1.47892	−	1.48588i
$466$	4.01851	+	6.96027i	0.186154	+	0.322428i
$467$	23.3879			1.08226			0.541132	−	0.840938i	$-0.317996\pi$
$467$	23.3879			1.08226			0.541132	+	0.840938i	$0.317996\pi$
$468$	−0.886844	−	0.517583i	−0.0409944	−	0.0239253i
$469$	27.6283			1.27575
$470$	−3.42378	−	5.93016i	−0.157927	−	0.273538i
$471$	2.23031	−	8.24621i	0.102767	−	0.379965i
$472$	−4.14080	+	7.17207i	−0.190596	+	0.330121i
$473$	10.8436	−	18.7816i	0.498589	−	0.863581i
$474$	0.706420	−	2.61187i	0.0324469	−	0.119967i
$475$	0.563189	+	0.975471i	0.0258409	+	0.0447577i
$476$	−18.6585			−0.855210
$477$	−15.0969	+	8.62198i	−0.691238	+	0.394774i
$478$	−1.83462			−0.0839135
$479$	−17.8685	−	30.9491i	−0.816432	−	1.41410i	−0.908295	−	0.418330i	$-0.862615\pi$
$479$	−17.8685	−	30.9491i	−0.816432	−	1.41410i	0.0918628	−	0.995772i	$-0.470718\pi$
$480$	2.97874	+	2.99275i	0.135960	+	0.136600i
$481$	−0.751300	+	1.30129i	−0.0342563	+	0.0593337i
$482$	−7.88247	+	13.6528i	−0.359037	+	0.621870i
$483$	5.99515	−	1.59133i	0.272789	−	0.0724081i
$484$	1.53865	+	2.66503i	0.0699388	+	0.121138i
$485$	19.1439			0.869279
$486$	−15.1036	+	3.85769i	−0.685112	+	0.174989i
$487$	5.42429			0.245798			0.122899	−	0.992419i	$-0.460781\pi$
$487$	5.42429			0.245798			0.122899	+	0.992419i	$0.460781\pi$
$488$	5.02496	+	8.70348i	0.227469	+	0.393988i
$489$	−40.2274	+	10.6778i	−1.81914	+	0.482867i
$490$	7.09992	−	12.2974i	0.320741	−	0.555541i
$491$	−13.2937	+	23.0253i	−0.599935	+	1.03912i	0.392895	+	0.919583i	$0.371474\pi$
$491$	−13.2937	+	23.0253i	−0.599935	+	1.03912i	−0.992830	+	0.119535i	$0.961860\pi$
$492$	2.29584	+	2.30664i	0.103505	+	0.103991i
$493$	−22.6393	−	39.2125i	−1.01962	−	1.76604i
$494$	−0.408779			−0.0183918
$495$	17.8758	−	10.2091i	0.803459	−	0.458864i
$496$	−10.7063			−0.480728
$497$	−24.8549	−	43.0500i	−1.11489	−	1.93105i
$498$	4.84707	−	17.9212i	0.217202	−	0.803069i
$499$	−4.45000	+	7.70762i	−0.199209	+	0.345041i	−0.948272	−	0.317458i	$-0.897171\pi$
$499$	−4.45000	+	7.70762i	−0.199209	+	0.345041i	0.749063	+	0.662499i	$0.230504\pi$
$500$	−4.94502	+	8.56503i	−0.221148	+	0.383040i
$501$	−7.42663	+	27.4587i	−0.331797	+	1.22677i
$502$	6.87094	+	11.9008i	0.306665	+	0.531160i
$503$	21.5150			0.959306			0.479653	−	0.877458i	$-0.340763\pi$
$503$	21.5150			0.959306			0.479653	+	0.877458i	$0.340763\pi$
$504$	−9.27883	−	5.41534i	−0.413312	−	0.241218i
$505$	25.4513			1.13257
$506$	1.40736	+	2.43763i	0.0625650	+	0.108366i
$507$	15.7411	+	15.8152i	0.699089	+	0.702376i
$508$	8.33086	−	14.4295i	0.369622	−	0.640204i
$509$	−6.55789	+	11.3586i	−0.290674	+	0.503461i	−0.973969	−	0.226680i	$-0.927213\pi$
$509$	−6.55789	+	11.3586i	−0.290674	+	0.503461i	0.683296	+	0.730142i	$0.260546\pi$
$510$	21.2636	−	5.64412i	0.941566	−	0.249926i
$511$	2.65054	+	4.59086i	0.117253	+	0.203088i
$512$	1.00000			0.0441942
$513$	−4.41888	+	4.35712i	−0.195098	+	0.192371i
$514$	−19.2332			−0.848340
$515$	−18.0360	−	31.2393i	−0.794763	−	1.37657i
$516$	12.8986	−	3.42376i	0.567829	−	0.150723i
$517$	−3.95307	+	6.84691i	−0.173856	+	0.301127i
$518$	−7.86067	+	13.6151i	−0.345378	+	0.598212i
$519$	14.1266	+	14.1930i	0.620089	+	0.623005i
$520$	0.417211	+	0.722631i	0.0182959	+	0.0316895i
$521$	−18.1276			−0.794185			−0.397093	−	0.917779i	$-0.629981\pi$
$521$	−18.1276			−0.794185			−0.397093	+	0.917779i	$0.629981\pi$
$522$	0.122326	−	26.0710i	0.00535407	−	1.14110i
$523$	−10.5671			−0.462066			−0.231033	−	0.972946i	$-0.574210\pi$
$523$	−10.5671			−0.462066			−0.231033	+	0.972946i	$0.574210\pi$
$524$	8.57688	+	14.8556i	0.374683	+	0.648969i
$525$	−1.52735	+	5.64713i	−0.0666591	+	0.246461i
$526$	−5.15425	+	8.92742i	−0.224736	+	0.389254i
$527$	−27.8909	+	48.3084i	−1.21495	+	2.10435i
$528$	1.27285	−	4.70616i	0.0553938	−	0.204809i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	14.1277			0.613669
$531$	−0.116571	+	24.8445i	−0.00505876	+	1.07816i
$532$	−4.27695			−0.185429
$533$	0.321563	+	0.556963i	0.0139284	+	0.0241248i
$534$	−1.97424	−	1.98353i	−0.0854339	−	0.0858357i
$535$	−14.7053	+	25.4704i	−0.635768	+	1.10118i
$536$	−3.85744	+	6.68129i	−0.166616	+	0.288588i
$537$	16.1330	−	4.28229i	0.696192	−	0.184795i
$538$	10.8976	+	18.8752i	0.469828	+	0.813766i
$539$	−16.3950			−0.706183
$540$	12.2125	+	3.36461i	0.525540	+	0.144790i
$541$	23.8443			1.02515			0.512574	−	0.858643i	$-0.328692\pi$
$541$	23.8443			1.02515			0.512574	+	0.858643i	$0.328692\pi$
$542$	−14.4364	−	25.0046i	−0.620097	−	1.07404i
$543$	−42.5089	+	11.2834i	−1.82423	+	0.484217i
$544$	2.60509	−	4.51214i	0.111692	−	0.193456i
$545$	3.06086	−	5.30156i	0.131113	−	0.227094i
$546$	−1.49771	−	1.50475i	−0.0640959	−	0.0643973i
$547$	18.2144	+	31.5482i	0.778790	+	1.34890i	0.932639	+	0.360810i	$0.117500\pi$
$547$	18.2144	+	31.5482i	0.778790	+	1.34890i	−0.153849	+	0.988094i	$0.549167\pi$
$548$	−8.11403			−0.346614
$549$	26.0394	+	15.1972i	1.11134	+	0.648601i
$550$	−2.65467			−0.113195
$551$	−5.18946	−	8.98841i	−0.221078	−	0.382919i
$552$	−0.452211	+	1.67198i	−0.0192474	+	0.0711640i
$553$	2.79715	−	4.84480i	0.118947	−	0.206022i
$554$	13.5779	−	23.5175i	0.576868	−	0.999164i
$555$	4.83966	−	17.8938i	0.205432	−	0.759551i
$556$	−3.45196	−	5.97897i	−0.146396	−	0.253565i
$557$	−11.9451			−0.506132			−0.253066	−	0.967449i	$-0.581439\pi$
$557$	−11.9451			−0.506132			−0.253066	+	0.967449i	$0.581439\pi$
$558$	−27.8909	+	15.9288i	−1.18071	+	0.674319i
$559$	2.63721			0.111542
$560$	4.36518	+	7.56071i	0.184462	+	0.319498i
$561$	−17.9190	−	18.0032i	−0.756539	−	0.760097i
$562$	3.62210	−	6.27367i	0.152789	−	0.264639i
$563$	−14.3334	+	24.8261i	−0.604079	+	1.04630i	0.388117	+	0.921610i	$0.373126\pi$
$563$	−14.3334	+	24.8261i	−0.604079	+	1.04630i	−0.992196	+	0.124686i	$0.960208\pi$
$564$	−4.70223	+	1.24814i	−0.198000	+	0.0525563i
$565$	14.7278	+	25.5094i	0.619605	+	1.07319i
$566$	11.5183			0.484150
$567$	−32.2290	−	0.302446i	−1.35349	−	0.0127015i
$568$	13.8809			0.582430
$569$	−12.1243	−	20.9999i	−0.508278	−	0.880364i	−0.999954	−	0.00958535i	$-0.996949\pi$
$569$	−12.1243	−	20.9999i	−0.508278	−	0.880364i	0.491676	−	0.870778i	$-0.336384\pi$
$570$	4.87410	−	1.29376i	0.204154	−	0.0541898i
$571$	0.325796	−	0.564294i	0.0136341	−	0.0236150i	−0.859128	−	0.511761i	$-0.828993\pi$
$571$	0.325796	−	0.564294i	0.0136341	−	0.0236150i	0.872762	+	0.488146i	$0.162327\pi$
$572$	0.481709	−	0.834344i	0.0201413	−	0.0348857i
$573$	−24.7016	−	24.8178i	−1.03192	−	1.03678i
$574$	3.36443	+	5.82737i	0.140429	+	0.243230i
$575$	0.943134			0.0393314
$576$	2.60509	−	1.48779i	0.108545	−	0.0619914i
$577$	42.8951			1.78575			0.892874	−	0.450307i	$-0.148685\pi$
$577$	42.8951			1.78575			0.892874	+	0.450307i	$0.148685\pi$
$578$	−5.07294	−	8.78659i	−0.211007	−	0.365474i
$579$	−0.564571	+	2.08741i	−0.0234628	+	0.0867497i
$580$	−10.5930	+	18.3476i	−0.439851	+	0.761844i
$581$	19.1925	−	33.2424i	0.796239	−	1.37913i
$582$	3.55111	−	13.1296i	0.147198	−	0.544241i
$583$	−8.15588	−	14.1264i	−0.337782	−	0.585056i
$584$	−1.48027			−0.0612538
$585$	2.16200	+	1.26179i	0.0893875	+	0.0521686i
$586$	−8.68556			−0.358797
$587$	0.322491	+	0.558570i	0.0133106	+	0.0230547i	0.872604	−	0.488428i	$-0.162430\pi$
$587$	0.322491	+	0.558570i	0.0133106	+	0.0230547i	−0.859293	+	0.511483i	$0.829096\pi$
$588$	−7.11705	−	7.15052i	−0.293502	−	0.294882i
$589$	−6.39323	+	11.0734i	−0.263429	+	0.456272i
$590$	10.0947	−	17.4845i	0.415591	−	0.719824i
$591$	6.70091	−	1.77867i	0.275639	−	0.0731645i
$592$	−2.19500	−	3.80186i	−0.0902141	−	0.156255i
$593$	11.2556			0.462213			0.231107	−	0.972928i	$-0.425765\pi$
$593$	11.2556			0.462213			0.231107	+	0.972928i	$0.425765\pi$
$594$	−3.68590	−	14.1537i	−0.151234	−	0.580733i
$595$	45.4866			1.86477
$596$	−3.68202	−	6.37744i	−0.150821	−	0.261230i
$597$	28.8064	−	7.64627i	1.17897	−	0.312941i
$598$	−0.171139	+	0.296421i	−0.00699838	+	0.0121215i
$599$	−0.251830	+	0.436182i	−0.0102895	+	0.0178219i	−0.871124	−	0.491063i	$-0.836609\pi$
$599$	−0.251830	+	0.436182i	−0.0102895	+	0.0178219i	0.860835	+	0.508884i	$0.169942\pi$
$600$	−1.15239	−	1.15781i	−0.0470459	−	0.0472672i
$601$	−8.80211	−	15.2457i	−0.359046	−	0.621885i	0.628756	−	0.777603i	$-0.283564\pi$
$601$	−8.80211	−	15.2457i	−0.359046	−	0.621885i	−0.987802	+	0.155717i	$0.950231\pi$
$602$	27.5925			1.12459
$603$	−0.108594	+	23.1444i	−0.00442230	+	0.942513i
$604$	11.8730			0.483106
$605$	−3.75101	−	6.49695i	−0.152500	−	0.264138i
$606$	4.72110	−	17.4555i	0.191782	−	0.709081i
$607$	21.9001	−	37.9320i	0.888896	−	1.53961i	0.0477141	−	0.998861i	$-0.484806\pi$
$607$	21.9001	−	37.9320i	0.888896	−	1.53961i	0.841182	−	0.540752i	$-0.181860\pi$
$608$	0.597146	−	1.03429i	0.0242175	−	0.0419459i
$609$	14.0737	−	52.0350i	0.570294	−	2.10857i
$610$	−12.2501	−	21.2178i	−0.495993	−	0.859084i
$611$	−0.961404			−0.0388942
$612$	0.0733381	−	15.6303i	0.00296452	−	0.631819i
$613$	26.8136			1.08299			0.541496	−	0.840703i	$-0.317858\pi$
$613$	26.8136			1.08299			0.541496	+	0.840703i	$0.317858\pi$
$614$	6.21821	+	10.7703i	0.250947	+	0.434652i
$615$	−5.59693	−	5.62325i	−0.225690	−	0.226752i
$616$	5.04000	−	8.72953i	0.203067	−	0.351723i
$617$	−1.72826	+	2.99343i	−0.0695771	+	0.120511i	−0.898715	−	0.438533i	$-0.855498\pi$
$617$	−1.72826	+	2.99343i	−0.0695771	+	0.120511i	0.829138	+	0.559044i	$0.188832\pi$
$618$	−24.7708	+	6.57506i	−0.996427	+	0.264488i
$619$	24.3726	+	42.2145i	0.979617	+	1.69675i	0.663773	+	0.747934i	$0.268954\pi$
$619$	24.3726	+	42.2145i	0.979617	+	1.69675i	0.315844	+	0.948811i	$0.397712\pi$
$620$	26.1004			1.04822
$621$	1.30951	+	5.02844i	0.0525487	+	0.201784i
$622$	27.0505			1.08463
$623$	−2.89315	−	5.01108i	−0.115911	−	0.200765i
$624$	0.572999	−	0.152095i	0.0229383	−	0.00608867i
$625$	14.4131	−	24.9642i	0.576523	−	0.998568i
$626$	−1.02070	+	1.76791i	−0.0407954	+	0.0706597i
$627$	−4.10744	−	4.12676i	−0.164035	−	0.164807i
$628$	2.46601	+	4.27125i	0.0984044	+	0.170441i
$629$	−22.8727			−0.911994
$630$	22.6204	+	13.2018i	0.901219	+	0.525973i
$631$	−17.2156			−0.685341			−0.342671	−	0.939456i	$-0.611331\pi$
$631$	−17.2156			−0.685341			−0.342671	+	0.939456i	$0.611331\pi$
$632$	0.781073	+	1.35286i	0.0310694	+	0.0538138i
$633$	0.589855	−	2.18089i	0.0234446	−	0.0866825i
$634$	4.01316	−	6.95100i	0.159383	−	0.276059i
$635$	−20.3094	+	35.1770i	−0.805955	+	1.39596i
$636$	2.62063	−	9.68935i	0.103915	−	0.384208i
$637$	−0.996835	−	1.72657i	−0.0394961	−	0.0684092i
$638$	24.4612			0.968429
$639$	36.1610	−	20.6519i	1.43051	−	0.816978i
$640$	−2.43785			−0.0963647
$641$	−14.0450	−	24.3267i	−0.554745	−	0.960847i	−0.997923	−	0.0644132i	$-0.979482\pi$
$641$	−14.0450	−	24.3267i	−0.554745	−	0.960847i	0.443178	−	0.896434i	$-0.353851\pi$
$642$	14.7408	+	14.8102i	0.581774	+	0.584510i
$643$	1.97257	−	3.41660i	0.0777907	−	0.134737i	−0.824506	−	0.565854i	$-0.808547\pi$
$643$	1.97257	−	3.41660i	0.0777907	−	0.134737i	0.902296	+	0.431116i	$0.141880\pi$
$644$	−1.79058	+	3.10138i	−0.0705588	+	0.122211i
$645$	−31.4449	+	8.34662i	−1.23814	+	0.328648i
$646$	−3.11123	−	5.38881i	−0.122410	−	0.212020i
$647$	−7.31843			−0.287717			−0.143859	−	0.989598i	$-0.545951\pi$
$647$	−7.31843			−0.287717			−0.143859	+	0.989598i	$0.545951\pi$
$648$	4.57294	−	7.75166i	0.179642	−	0.304514i
$649$	−23.3104			−0.915015
$650$	−0.161407	−	0.279565i	−0.00633089	−	0.0109654i
$651$	−64.1860	+	17.0373i	−2.51565	+	0.667744i
$652$	12.0148	−	20.8102i	0.470535	−	0.814990i
$653$	16.5343	−	28.6382i	0.647036	−	1.12070i	−0.336791	−	0.941579i	$-0.609342\pi$
$653$	16.5343	−	28.6382i	0.647036	−	1.12070i	0.983827	−	0.179120i	$-0.0573251\pi$
$654$	−3.06824	−	3.08267i	−0.119978	−	0.120542i
$655$	−20.9092	−	36.2158i	−0.816989	−	1.41507i
$656$	−1.87896			−0.0733611
$657$	−3.85622	+	2.20233i	−0.150445	+	0.0859210i
$658$	−10.0589			−0.392138
$659$	−3.66692	−	6.35129i	−0.142843	−	0.247411i	0.785723	−	0.618578i	$-0.212291\pi$
$659$	−3.66692	−	6.35129i	−0.142843	−	0.247411i	−0.928566	+	0.371167i	$0.878958\pi$
$660$	−3.10303	+	11.4729i	−0.120785	+	0.446583i
$661$	−8.01168	+	13.8766i	−0.311618	+	0.539739i	−0.978713	−	0.205234i	$-0.934204\pi$
$661$	−8.01168	+	13.8766i	−0.311618	+	0.539739i	0.667095	+	0.744973i	$0.267538\pi$
$662$	4.14468	−	7.17880i	0.161088	−	0.279012i
$663$	0.806439	−	2.98167i	0.0313195	−	0.115799i
$664$	5.35929	+	9.28257i	0.207981	+	0.360234i
$665$	10.4266			0.404326
$666$	−11.3746	−	6.63845i	−0.440755	−	0.257235i
$667$	−8.69044			−0.336495
$668$	−8.21146	−	14.2227i	−0.317711	−	0.550291i
$669$	−18.2353	−	18.3211i	−0.705019	−	0.708334i
$670$	9.40389	−	16.2880i	0.363304	−	0.629261i
$671$	−14.1439	+	24.4979i	−0.546019	+	0.945732i
$672$	5.99515	−	1.59133i	0.231268	−	0.0613869i
$673$	−12.5193	−	21.6840i	−0.482582	−	0.835857i	0.517218	−	0.855854i	$-0.326968\pi$
$673$	−12.5193	−	21.6840i	−0.482582	−	0.835857i	−0.999800	+	0.0199969i	$0.993634\pi$
$674$	16.6062			0.639646
$675$	−4.72464	−	1.30167i	−0.181851	−	0.0501013i
$676$	−12.8828			−0.495494
$677$	18.5367	+	32.1065i	0.712423	+	1.23395i	0.963945	+	0.266101i	$0.0857355\pi$
$677$	18.5367	+	32.1065i	0.712423	+	1.23395i	−0.251522	+	0.967851i	$0.580931\pi$
$678$	20.2273	−	5.36906i	0.776824	−	0.206197i
$679$	14.0610	−	24.3544i	0.539612	−	0.934635i
$680$	−6.35082	+	10.9999i	−0.243543	+	0.421829i
$681$	−30.1885	−	30.3305i	−1.15683	−	1.16227i
$682$	−15.0677	−	26.0980i	−0.576971	−	0.999344i
$683$	−20.6221			−0.789083			−0.394541	−	0.918878i	$-0.629097\pi$
$683$	−20.6221			−0.789083			−0.394541	+	0.918878i	$0.629097\pi$
$684$	0.0168108	−	3.58284i	0.000642777	−	0.136993i
$685$	19.7808			0.755787
$686$	2.10443	+	3.64497i	0.0803473	+	0.139166i
$687$	−1.30360	+	4.81983i	−0.0497353	+	0.183888i
$688$	−3.85245	+	6.67263i	−0.146873	+	0.254392i
$689$	0.991774	−	1.71780i	0.0377836	−	0.0654431i
$690$	1.10243	−	4.07603i	0.0419686	−	0.155172i
$691$	15.0288	+	26.0307i	0.571724	+	0.990255i	0.996389	+	0.0849042i	$0.0270584\pi$
$691$	15.0288	+	26.0307i	0.571724	+	0.990255i	−0.424665	+	0.905350i	$0.639608\pi$
$692$	−11.5615			−0.439501
$693$	0.141885	−	30.2397i	0.00538978	−	1.14871i
$694$	−9.31252			−0.353499
$695$	8.41537	+	14.5758i	0.319213	+	0.552893i
$696$	10.6186	+	10.6685i	0.402496	+	0.404389i
$697$	−4.89486	+	8.47814i	−0.185406	+	0.321132i
$698$	−15.6367	+	27.0836i	−0.591859	+	1.02513i
$699$	−13.4546	+	3.57134i	−0.508900	+	0.135081i
$700$	−1.68876	−	2.92501i	−0.0638291	−	0.110555i
$701$	41.4430			1.56528			0.782640	−	0.622474i	$-0.213873\pi$
$701$	41.4430			1.56528			0.782640	+	0.622474i	$0.213873\pi$
$702$	1.26643	−	1.24872i	0.0477982	−	0.0471301i
$703$	−5.24295			−0.197742
$704$	1.40736	+	2.43763i	0.0530420	+	0.0918715i
$705$	11.4634	−	3.04279i	0.431735	−	0.114598i
$706$	1.88829	−	3.27061i	0.0710667	−	0.123091i
$707$	18.6937	−	32.3785i	0.703050	−	1.21772i
$708$	−10.1190	−	10.1666i	−0.380296	−	0.382085i
$709$	24.1182	+	41.7739i	0.905777	+	1.56885i	0.819871	+	0.572548i	$0.194045\pi$
$709$	24.1182	+	41.7739i	0.905777	+	1.56885i	0.0859058	+	0.996303i	$0.472622\pi$
$710$	−33.8396			−1.26998
$711$	4.04753	+	2.36224i	0.151794	+	0.0885907i
$712$	1.61576			0.0605531
$713$	5.35316	+	9.27194i	0.200477	+	0.347237i
$714$	8.43757	−	31.1965i	0.315768	−	1.16750i
$715$	−1.17434	+	2.03401i	−0.0439177	+	0.0760676i
$716$	−4.81848	+	8.34585i	−0.180075	+	0.311899i
$717$	0.829635	−	3.06744i	0.0309833	−	0.114556i
$718$	14.5015	+	25.1173i	0.541190	+	0.937369i
$719$	−52.1791			−1.94595			−0.972976	−	0.230908i	$-0.925831\pi$
$719$	−52.1791			−1.94595			−0.972976	+	0.230908i	$0.925831\pi$
$720$	−6.35082	+	3.62702i	−0.236681	+	0.135171i
$721$	−52.9892			−1.97342
$722$	8.78683	+	15.2192i	0.327012	+	0.566402i
$723$	−19.2627	−	19.3533i	−0.716387	−	0.719756i
$724$	12.6962	−	21.9904i	0.471850	−	0.817268i
$725$	4.09812	−	7.09816i	0.152200	−	0.263619i
$726$	−5.15166	+	1.36744i	−0.191196	+	0.0507503i
$727$	10.3059	+	17.8504i	0.382225	+	0.662034i	0.991380	−	0.131018i	$-0.0418245\pi$
$727$	10.3059	+	17.8504i	0.382225	+	0.662034i	−0.609155	+	0.793051i	$0.708491\pi$
$728$	1.22575			0.0454293
$729$	0.380039	−	26.9973i	0.0140755	−	0.999901i
$730$	3.60867			0.133563
$731$	20.0719	+	34.7656i	0.742386	+	1.28585i
$732$	−16.8244	+	4.46580i	−0.621846	+	0.165061i
$733$	3.28852	−	5.69589i	0.121464	−	0.210383i	−0.798881	−	0.601489i	$-0.794574\pi$
$733$	3.28852	−	5.69589i	0.121464	−	0.210383i	0.920345	+	0.391107i	$0.127908\pi$
$734$	−14.5952	+	25.2796i	−0.538718	+	0.933087i
$735$	17.3503	+	17.4319i	0.639976	+	0.642986i
$736$	−0.500000	−	0.866025i	−0.0184302	−	0.0319221i
$737$	−21.7153			−0.799894
$738$	−4.89486	+	2.79551i	−0.180182	+	0.102904i
$739$	−42.0014			−1.54504			−0.772522	−	0.634987i	$-0.781005\pi$
$739$	−42.0014			−1.54504			−0.772522	+	0.634987i	$0.781005\pi$
$740$	5.35110	+	9.26838i	0.196710	+	0.340712i
$741$	0.184855	−	0.683469i	0.00679080	−	0.0251079i
$742$	10.3767	−	17.9729i	0.380940	−	0.659808i
$743$	−9.46578	+	16.3952i	−0.347266	+	0.601482i	−0.985763	−	0.168142i	$-0.946223\pi$
$743$	−9.46578	+	16.3952i	−0.347266	+	0.601482i	0.638497	+	0.769624i	$0.279556\pi$
$744$	4.84152	−	17.9007i	0.177499	−	0.656272i
$745$	8.97623	+	15.5473i	0.328864	+	0.569608i
$746$	−9.81177			−0.359235
$747$	27.7720	+	16.2084i	1.01612	+	0.593033i
$748$	14.6652			0.536213
$749$	21.6019	+	37.4156i	0.789316	+	1.36713i
$750$	−12.0843	−	12.1412i	−0.441258	−	0.443333i
$751$	10.5103	−	18.2044i	0.383527	−	0.664288i	−0.608037	−	0.793909i	$-0.708043\pi$
$751$	10.5103	−	18.2044i	0.383527	−	0.664288i	0.991564	+	0.129621i	$0.0413761\pi$
$752$	1.40442	−	2.43253i	0.0512140	−	0.0887053i
$753$	−23.0050	+	6.10637i	−0.838349	+	0.222528i
$754$	1.48727	+	2.57603i	0.0541632	+	0.0938133i
$755$	−28.9447			−1.05341
$756$	13.2503	−	13.0651i	0.481909	−	0.475173i
$757$	2.32626			0.0845495			0.0422747	−	0.999106i	$-0.486540\pi$
$757$	2.32626			0.0845495			0.0422747	+	0.999106i	$0.486540\pi$
$758$	−13.0771	−	22.6502i	−0.474981	−	0.822691i
$759$	−4.71208	+	1.25076i	−0.171038	+	0.0453996i
$760$	−1.45575	+	2.52144i	−0.0528058	+	0.0914623i
$761$	−4.19290	+	7.26232i	−0.151993	+	0.263259i	−0.931960	−	0.362561i	$-0.881902\pi$
$761$	−4.19290	+	7.26232i	−0.151993	+	0.263259i	0.779967	+	0.625820i	$0.215236\pi$
$762$	20.3584	+	20.4542i	0.737508	+	0.740977i
$763$	−4.49634	−	7.78789i	−0.162779	−	0.281941i
$764$	20.2162			0.731398
$765$	−0.178788	+	38.1045i	−0.00646408	+	1.37767i
$766$	−5.68097			−0.205262
$767$	−1.41730	−	2.45484i	−0.0511758	−	0.0886390i
$768$	−0.452211	+	1.67198i	−0.0163178	+	0.0603322i
$769$	5.88971	−	10.2013i	0.212389	−	0.367868i	−0.740073	−	0.672526i	$-0.765209\pi$
$769$	5.88971	−	10.2013i	0.212389	−	0.367868i	0.952462	+	0.304659i	$0.0985424\pi$
$770$	−12.2868	+	21.2813i	−0.442785	+	0.766926i
$771$	8.69747	−	32.1574i	0.313232	−	1.15812i
$772$	−0.624234	−	1.08120i	−0.0224667	−	0.0389134i
$773$	23.2177			0.835082			0.417541	−	0.908658i	$-0.362892\pi$
$773$	23.2177			0.835082			0.417541	+	0.908658i	$0.362892\pi$
$774$	−0.108454	+	23.1144i	−0.00389829	+	0.830831i
$775$	−10.0975			−0.362713
$776$	3.92638	+	6.80069i	0.140949	+	0.244131i
$777$	−19.2094	−	19.2997i	−0.689133	−	0.692374i
$778$	−13.5080	+	23.3965i	−0.484285	+	0.838807i
$779$	−1.12201	+	1.94339i	−0.0402003	+	0.0696290i
$780$	−1.39689	+	0.370785i	−0.0500167	+	0.0132762i
$781$	19.5355	+	33.8365i	0.699035	+	1.21076i
$782$	−5.21017			−0.186315
$783$	43.5348	+	11.9941i	1.55581	+	0.428636i
$784$	5.82472			0.208026
$785$	−6.01176	−	10.4127i	−0.214569	−	0.371645i
$786$	−28.7167	+	7.62247i	−1.02429	+	0.271884i
$787$	16.3101	−	28.2499i	0.581391	−	1.00700i	−0.413923	−	0.910312i	$-0.635842\pi$
$787$	16.3101	−	28.2499i	0.581391	−	1.00700i	0.995315	−	0.0966877i	$-0.0308248\pi$
$788$	−2.00137	+	3.46648i	−0.0712959	+	0.123488i
$789$	−12.5956	−	12.6549i	−0.448416	−	0.450525i
$790$	−1.90414	−	3.29807i	−0.0677463	−	0.117340i
$791$	43.2699			1.53850
$792$	7.29299	+	4.25636i	0.259145	+	0.151243i
$793$	−3.43986			−0.122153
$794$	−2.11965	−	3.67134i	−0.0752236	−	0.130291i
$795$	−6.38872	+	23.6212i	−0.226585	+	0.837759i
$796$	−8.60366	+	14.9020i	−0.304948	+	0.528186i
$797$	−9.58082	+	16.5945i	−0.339370	+	0.587806i	−0.984314	−	0.176423i	$-0.943547\pi$
$797$	−9.58082	+	16.5945i	−0.339370	+	0.587806i	0.644944	+	0.764230i	$0.276881\pi$
$798$	1.93409	−	7.15097i	0.0684659	−	0.253141i
$799$	−7.31728	−	12.6739i	−0.258867	−	0.448371i
$800$	0.943134			0.0333448
$801$	4.20919	−	2.40392i	0.148724	−	0.0849382i
$802$	22.4223			0.791759
$803$	−2.08327	−	3.60833i	−0.0735171	−	0.127335i
$804$	−9.42658	−	9.47091i	−0.332450	−	0.334013i
$805$	4.36518	−	7.56071i	0.153852	−	0.266480i
$806$	1.83226	−	3.17357i	0.0645388	−	0.111784i
$807$	−36.4868	+	9.68493i	−1.28440	+	0.340926i
$808$	5.22002	+	9.04134i	0.183640	+	0.318073i
$809$	−45.4318			−1.59730			−0.798648	−	0.601798i	$-0.794451\pi$
$809$	−45.4318			−1.59730			−0.798648	+	0.601798i	$0.794451\pi$
$810$	−11.1482	+	18.8974i	−0.391707	+	0.663987i
$811$	−6.84424			−0.240334			−0.120167	−	0.992754i	$-0.538343\pi$
$811$	−6.84424			−0.240334			−0.120167	+	0.992754i	$0.538343\pi$
$812$	15.5609	+	26.9523i	0.546082	+	0.945841i
$813$	48.3354	−	12.8300i	1.69520	−	0.449967i
$814$	6.17834	−	10.7012i	0.216551	−	0.375077i
$815$	−29.2903	+	50.7322i	−1.02599	+	1.77707i
$816$	6.36614	+	6.39608i	0.222860	+	0.223908i
$817$	4.60095	+	7.96907i	0.160967	+	0.278802i
$818$	26.5310			0.927634
$819$	3.19318	−	1.82366i	0.111579	−	0.0637240i
$820$	4.58063			0.159963
$821$	−10.6076	−	18.3730i	−0.370209	−	0.641221i	0.619389	−	0.785085i	$-0.287381\pi$
$821$	−10.6076	−	18.3730i	−0.370209	−	0.641221i	−0.989597	+	0.143864i	$0.954047\pi$
$822$	3.66926	−	13.5665i	0.127980	−	0.473185i
$823$	−22.1274	+	38.3259i	−0.771314	+	1.33596i	0.165528	+	0.986205i	$0.447067\pi$
$823$	−22.1274	+	38.3259i	−0.771314	+	1.33596i	−0.936843	+	0.349751i	$0.886266\pi$
$824$	7.39833	−	12.8143i	0.257733	−	0.446407i
$825$	1.20047	−	4.43854i	0.0417950	−	0.154530i
$826$	−14.8289	−	25.6844i	−0.515962	−	0.893673i
$827$	6.23594			0.216845			0.108422	−	0.994105i	$-0.465420\pi$
$827$	6.23594			0.216845			0.108422	+	0.994105i	$0.465420\pi$
$828$	−2.59101	−	1.51217i	−0.0900438	−	0.0525517i
$829$	−50.5674			−1.75628			−0.878139	−	0.478406i	$-0.841215\pi$
$829$	−50.5674			−1.75628			−0.878139	+	0.478406i	$0.841215\pi$
$830$	−13.0652	−	22.6296i	−0.453499	−	0.785483i
$831$	33.1807	+	33.3367i	1.15103	+	1.15644i
$832$	−0.171139	+	0.296421i	−0.00593316	+	0.0102765i
$833$	15.1739	−	26.2820i	0.525745	−	0.910617i
$834$	11.5577	−	3.06783i	0.400211	−	0.106230i
$835$	20.0183	+	34.6728i	0.692763	+	1.19990i
$836$	3.36161			0.116264
$837$	−14.0200	−	53.8361i	−0.484601	−	1.86085i
$838$	−28.2666			−0.976455
$839$	18.7833	+	32.5336i	0.648471	+	1.12319i	0.983488	+	0.180973i	$0.0579246\pi$
$839$	18.7833	+	32.5336i	0.648471	+	1.12319i	−0.335017	+	0.942212i	$0.608742\pi$
$840$	−14.6153	+	3.87943i	−0.504276	+	0.133853i
$841$	−23.2618	+	40.2907i	−0.802133	+	1.38933i
$842$	−2.50954	+	4.34665i	−0.0864844	+	0.149795i
$843$	8.85146	+	8.89309i	0.304861	+	0.306294i
$844$	0.652189	+	1.12962i	0.0224493	+	0.0388833i
$845$	31.4065			1.08042
$846$	0.0395372	−	8.42644i	0.00135932	−	0.289707i
$847$	−11.0203			−0.378663
$848$	2.89757	+	5.01875i	0.0995031	+	0.172344i
$849$	−5.20871	+	19.2583i	−0.178762	+	0.660944i
$850$	2.45694	−	4.25555i	0.0842725	−	0.145964i
$851$	−2.19500	+	3.80186i	−0.0752438	+	0.130326i
$852$	−6.27711	+	23.2086i	−0.215050	+	0.795112i
$853$	−16.7475	−	29.0075i	−0.573422	−	0.993197i	−0.996211	−	0.0869684i	$-0.972282\pi$
$853$	−16.7475	−	29.0075i	−0.573422	−	0.993197i	0.422789	−	0.906228i	$-0.361051\pi$
$854$	−35.9904			−1.23157
$855$	−0.0409823	+	8.73443i	−0.00140156	+	0.298711i
$856$	−12.0642			−0.412345
$857$	−10.6741	−	18.4881i	−0.364620	−	0.631541i	0.624095	−	0.781349i	$-0.285468\pi$
$857$	−10.6741	−	18.4881i	−0.364620	−	0.631541i	−0.988715	+	0.149808i	$0.952135\pi$
$858$	1.17717	+	1.18271i	0.0401879	+	0.0403769i
$859$	−6.81025	+	11.7957i	−0.232363	+	0.402464i	−0.958503	−	0.285082i	$-0.907979\pi$
$859$	−6.81025	+	11.7957i	−0.232363	+	0.402464i	0.726140	+	0.687547i	$0.241312\pi$
$860$	9.39170	−	16.2669i	0.320254	−	0.554697i
$861$	−11.2647	+	2.99005i	−0.383899	+	0.101901i
$862$	1.08376	+	1.87712i	0.0369129	+	0.0639349i
$863$	24.5727			0.836465			0.418233	−	0.908340i	$-0.362650\pi$
$863$	24.5727			0.836465			0.418233	+	0.908340i	$0.362650\pi$
$864$	1.30951	+	5.02844i	0.0445503	+	0.171071i
$865$	28.1852			0.958325
$866$	−11.4462	−	19.8254i	−0.388957	−	0.673694i
$867$	16.9850	−	4.50844i	0.576841	−	0.153115i
$868$	19.1705	−	33.2043i	0.650690	−	1.12703i
$869$	−2.19851	+	3.80793i	−0.0745793	+	0.129175i
$870$	−25.8865	−	26.0083i	−0.877635	−	0.881763i
$871$	−1.32032	−	2.28685i	−0.0447372	−	0.0774871i
$872$	2.51111			0.0850368
$873$	20.3466	+	11.8747i	0.688627	+	0.401899i
$874$	−1.19429			−0.0403975
$875$	−17.7089	−	30.6728i	−0.598671	−	1.03693i
$876$	0.669393	−	2.47497i	0.0226167	−	0.0836214i
$877$	−0.778916	+	1.34912i	−0.0263021	+	0.0455566i	−0.878877	−	0.477049i	$-0.841707\pi$
$877$	−0.778916	+	1.34912i	−0.0263021	+	0.0455566i	0.852575	+	0.522605i	$0.175040\pi$
$878$	11.2809	−	19.5391i	0.380712	−	0.659413i
$879$	3.92771	−	14.5221i	0.132478	−	0.489817i
$880$	−3.43095	−	5.94258i	−0.115657	−	0.200324i
$881$	18.8307			0.634422			0.317211	−	0.948355i	$-0.397254\pi$
$881$	18.8307			0.634422			0.317211	+	0.948355i	$0.397254\pi$
$882$	15.1739	−	8.66599i	0.510932	−	0.291799i
$883$	−20.3862			−0.686051			−0.343026	−	0.939326i	$-0.611452\pi$
$883$	−20.3862			−0.686051			−0.343026	+	0.939326i	$0.611452\pi$
$884$	0.891662	+	1.54440i	0.0299898	+	0.0519439i
$885$	24.6687	+	24.7847i	0.829229	+	0.833129i
$886$	0.889869	−	1.54130i	0.0298957	−	0.0517809i
$887$	1.82425	−	3.15969i	0.0612523	−	0.106092i	−0.833773	−	0.552107i	$-0.813824\pi$
$887$	1.82425	−	3.15969i	0.0612523	−	0.106092i	0.895025	+	0.446015i	$0.147157\pi$
$888$	7.34922	−	1.95075i	0.246624	−	0.0654629i
$889$	29.8342	+	51.6743i	1.00061	+	1.73310i
$890$	−3.93898			−0.132035
$891$	25.3314	+	0.237717i	0.848635	+	0.00796382i
$892$	14.9241			0.499697
$893$	−1.67729	−	2.90515i	−0.0561284	−	0.0972172i
$894$	12.3280	−	3.27230i	0.412310	−	0.109442i
$895$	11.7467	−	20.3460i	0.392651	−	0.680091i
$896$	−1.79058	+	3.10138i	−0.0598191	+	0.103610i
$897$	−0.418218	−	0.420185i	−0.0139639	−	0.0140296i
$898$	12.4170	+	21.5069i	0.414361	+	0.717694i
$899$	93.0426			3.10314
$900$	2.45694	−	1.40319i	0.0818982	−	0.0467730i
$901$	30.1937			1.00590
$902$	−2.64438	−	4.58021i	−0.0880483	−	0.152504i
$903$	−12.4776	+	46.1340i	−0.415230	+	1.53524i
$904$	−6.04131	+	10.4639i	−0.200931	+	0.348023i
$905$	−30.9515	+	53.6095i	−1.02886	+	1.78204i
$906$	−5.36911	+	19.8514i	−0.178377	+	0.659519i
$907$	17.7509	+	30.7455i	0.589410	+	1.02089i	0.994310	+	0.106527i	$0.0339729\pi$
$907$	17.7509	+	30.7455i	0.589410	+	1.02089i	−0.404900	+	0.914361i	$0.632694\pi$
$908$	24.7068			0.819925
$909$	27.0502	+	15.7871i	0.897200	+	0.523627i
$910$	−2.98820			−0.0990579
$911$	−18.0396	−	31.2455i	−0.597679	−	1.03521i	−0.993163	−	0.116737i	$-0.962757\pi$
$911$	−18.0396	−	31.2455i	−0.597679	−	1.03521i	0.395484	−	0.918473i	$-0.370577\pi$
$912$	1.45927	+	1.46613i	0.0483212	+	0.0485484i
$913$	−15.0850	+	26.1279i	−0.499239	+	0.864708i
$914$	−5.87051	+	10.1680i	−0.194179	+	0.336328i
$915$	41.0153	−	10.8870i	1.35592	−	0.359912i
$916$	−1.44136	−	2.49650i	−0.0476238	−	0.0824868i
$917$	−61.4304			−2.02861
$918$	26.1004	+	7.19084i	0.861441	+	0.237333i
$919$	10.8021			0.356327			0.178164	−	0.984001i	$-0.442984\pi$
$919$	10.8021			0.356327			0.178164	+	0.984001i	$0.442984\pi$
$920$	1.21893	+	2.11124i	0.0401868	+	0.0696056i
$921$	−20.8196	+	5.52627i	−0.686028	+	0.182097i
$922$	12.2554	−	21.2270i	0.403611	−	0.699074i
$923$	−2.37556	+	4.11459i	−0.0781925	+	0.135433i
$924$	12.3164	+	12.3744i	0.405181	+	0.407086i
$925$	−2.07018	−	3.58566i	−0.0680672	−	0.117896i
$926$	−3.34833			−0.110033
$927$	0.208277	−	44.3895i	0.00684071	−	1.45794i
$928$	−8.69044			−0.285278
$929$	−3.32419	−	5.75767i	−0.109063	−	0.188903i	0.806328	−	0.591469i	$-0.201452\pi$
$929$	−3.32419	−	5.75767i	−0.109063	−	0.188903i	−0.915391	+	0.402566i	$0.868118\pi$
$930$	−11.8029	+	43.6393i	−0.387033	+	1.43099i
$931$	3.47821	−	6.02444i	0.113994	−	0.197443i
$932$	4.01851	−	6.96027i	0.131631	−	0.227991i
$933$	−12.2326	+	45.2279i	−0.400476	+	1.48069i
$934$	−11.6940	−	20.2545i	−0.382638	−	0.662749i
$935$	−35.7517			−1.16920
$936$	−0.00481788	+	1.02682i	−0.000157477	+	0.0335627i
$937$	−19.6052			−0.640474			−0.320237	−	0.947337i	$-0.603763\pi$
$937$	−19.6052			−0.640474			−0.320237	+	0.947337i	$0.603763\pi$
$938$	−13.8141	−	23.9268i	−0.451047	−	0.781237i
$939$	−2.49432	−	2.50606i	−0.0813992	−	0.0817820i
$940$	−3.42378	+	5.93016i	−0.111671	+	0.193420i
$941$	15.4385	−	26.7403i	0.503282	−	0.871710i	−0.496711	−	0.867916i	$-0.665459\pi$
$941$	15.4385	−	26.7403i	0.503282	−	0.871710i	0.999993	−	0.00379360i	$-0.00120754\pi$
$942$	−8.25658	+	2.19160i	−0.269014	+	0.0714061i
$943$	0.939481	+	1.62723i	0.0305937	+	0.0529899i
$944$	8.28160			0.269543
$945$	−32.3023	+	31.8508i	−1.05079	+	1.03611i
$946$	−21.6872			−0.705111
$947$	0.948672	+	1.64315i	0.0308277	+	0.0533951i	0.881028	−	0.473065i	$-0.156852\pi$
$947$	0.948672	+	1.64315i	0.0308277	+	0.0533951i	−0.850200	+	0.526460i	$0.823519\pi$
$948$	−2.61516	+	0.694157i	−0.0849363	+	0.0225452i
$949$	0.253331	−	0.438781i	0.00822346	−	0.0142434i
$950$	0.563189	−	0.975471i	0.0182723	−	0.0316485i
$951$	9.80711	+	9.85323i	0.318017	+	0.319513i
$952$	9.32923	+	16.1587i	0.302362	+	0.523707i
$953$	9.33083			0.302255			0.151128	−	0.988514i	$-0.451710\pi$
$953$	9.33083			0.302255			0.151128	+	0.988514i	$0.451710\pi$
$954$	15.0153	+	8.76327i	0.486138	+	0.283721i
$955$	−49.2842			−1.59480
$956$	0.917309	+	1.58883i	0.0296679	+	0.0513863i
$957$	−11.0616	+	40.8986i	−0.357572	+	1.32206i
$958$	−17.8685	+	30.9491i	−0.577305	+	0.999921i
$959$	14.5288	−	25.1647i	0.469160	−	0.812610i
$960$	1.10243	−	4.07603i	0.0355806	−	0.131553i
$961$	−41.8126	−	72.4215i	−1.34879	−	2.33618i
$962$	1.50260			0.0484458
$963$	−31.4282	+	17.9490i	−1.01276	+	0.578398i
$964$	15.7649			0.507755
$965$	1.52179	+	2.63582i	0.0489882	+	0.0848500i
$966$	−4.37571	−	4.39629i	−0.140786	−	0.141448i
$967$	4.74263	−	8.21447i	0.152513	−	0.264160i	−0.779638	−	0.626231i	$-0.784597\pi$
$967$	4.74263	−	8.21447i	0.152513	−	0.264160i	0.932151	+	0.362071i	$0.117930\pi$
$968$	1.53865	−	2.66503i	0.0494542	−	0.0856572i
$969$	10.4169	−	2.76502i	0.334639	−	0.0888254i
$970$	−9.57194	−	16.5791i	−0.307337	−	0.532323i
$971$	−15.3120			−0.491385			−0.245693	−	0.969348i	$-0.579015\pi$
$971$	−15.3120			−0.491385			−0.245693	+	0.969348i	$0.579015\pi$
$972$	10.8927	+	11.1512i	0.349382	+	0.357676i
$973$	24.7240			0.792616
$974$	−2.71215	−	4.69757i	−0.0869028	−	0.150520i
$975$	0.540415	−	0.143446i	0.0173071	−	0.00459394i
$976$	5.02496	−	8.70348i	0.160845	−	0.278592i
$977$	−30.2471	+	52.3896i	−0.967692	+	1.67609i	−0.265491	+	0.964113i	$0.585534\pi$
$977$	−30.2471	+	52.3896i	−0.967692	+	1.67609i	−0.702201	+	0.711978i	$0.747799\pi$
$978$	29.3609	+	29.4990i	0.938859	+	0.943275i
$979$	2.27396	+	3.93862i	0.0726761	+	0.125879i
$980$	−14.1998			−0.453597
$981$	6.54165	−	3.73601i	0.208859	−	0.119282i
$982$	26.5873			0.848436
$983$	22.3138	+	38.6486i	0.711699	+	1.23270i	0.964219	+	0.265108i	$0.0854075\pi$
$983$	22.3138	+	38.6486i	0.711699	+	1.23270i	−0.252519	+	0.967592i	$0.581259\pi$
$984$	0.849688	−	3.14158i	0.0270871	−	0.100150i
$985$	4.87905	−	8.45077i	0.155460	−	0.269264i
$986$	−22.6393	+	39.2125i	−0.720983	+	1.24878i
$987$	4.54876	−	16.8183i	0.144789	−	0.535332i
$988$	0.204389	+	0.354013i	0.00650250	+	0.0112627i
$989$	7.70489			0.245001
$990$	−17.7792	−	10.3764i	−0.565061	−	0.329783i
$991$	26.2826			0.834894			0.417447	−	0.908701i	$-0.362925\pi$
$991$	26.2826			0.834894			0.417447	+	0.908701i	$0.362925\pi$
$992$	5.35316	+	9.27194i	0.169963	+	0.294384i
$993$	10.1285	+	10.1761i	0.321418	+	0.322930i
$994$	−24.8549	+	43.0500i	−0.788350	+	1.36546i
$995$	20.9745	−	36.3288i	0.664935	−	1.15170i
$996$	−17.9438	+	4.76293i	−0.568570	+	0.150919i
$997$	−8.34303	−	14.4505i	−0.264226	−	0.457653i	0.703134	−	0.711057i	$-0.251783\pi$
$997$	−8.34303	−	14.4505i	−0.264226	−	0.457653i	−0.967361	+	0.253404i	$0.918450\pi$
$998$	8.90000			0.281724
$999$	16.2430	−	16.0160i	0.513907	−	0.506724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.c.139.5	✓	10
3.2	odd	2		1242.2.e.c.415.2		10
9.2	odd	6		1242.2.e.c.829.2		10
9.4	even	3		3726.2.a.t.1.2		5
9.5	odd	6		3726.2.a.s.1.4		5
9.7	even	3	inner	414.2.e.c.277.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.c.139.5	✓	10	1.1	even	1	trivial
414.2.e.c.277.5	yes	10	9.7	even	3	inner
1242.2.e.c.415.2		10	3.2	odd	2
1242.2.e.c.829.2		10	9.2	odd	6
3726.2.a.s.1.4		5	9.5	odd	6
3726.2.a.t.1.2		5	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.67408 - 0.444362i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.21893 - 2.11124i) q^{5} +(-1.22187 - 1.22761i) q^{6} +(-1.79058 - 3.10138i) q^{7} +1.00000 q^{8} +(2.60509 - 1.48779i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.67408 - 0.444362i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.21893 - 2.11124i) q^{5} +(-1.22187 - 1.22761i) q^{6} +(-1.79058 - 3.10138i) q^{7} +1.00000 q^{8} +(2.60509 - 1.48779i) q^{9} -2.43785 q^{10} +(1.40736 + 2.43763i) q^{11} +(-0.452211 + 1.67198i) q^{12} +(-0.171139 + 0.296421i) q^{13} +(-1.79058 + 3.10138i) q^{14} +(1.10243 - 4.07603i) q^{15} +(-0.500000 - 0.866025i) q^{16} -5.21017 q^{17} +(-2.59101 - 1.51217i) q^{18} -1.19429 q^{19} +(1.21893 + 2.11124i) q^{20} +(-4.37571 - 4.39629i) q^{21} +(1.40736 - 2.43763i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(1.67408 - 0.444362i) q^{24} +(-0.471567 - 0.816778i) q^{25} +0.342277 q^{26} +(3.70000 - 3.64828i) q^{27} +3.58116 q^{28} +(4.34522 + 7.52614i) q^{29} +(-4.08116 + 1.08329i) q^{30} +(5.35316 - 9.27194i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.43923 + 3.45540i) q^{33} +(2.60509 + 4.51214i) q^{34} -8.73035 q^{35} +(-0.0140759 + 2.99997i) q^{36} +4.39001 q^{37} +(0.597146 + 1.03429i) q^{38} +(-0.154782 + 0.572279i) q^{39} +(1.21893 - 2.11124i) q^{40} +(0.939481 - 1.62723i) q^{41} +(-1.61944 + 5.98762i) q^{42} +(-3.85245 - 6.67263i) q^{43} -2.81473 q^{44} +(0.0343151 - 7.31348i) q^{45} +1.00000 q^{46} +(1.40442 + 2.43253i) q^{47} +(-1.22187 - 1.22761i) q^{48} +(-2.91236 + 5.04436i) q^{49} +(-0.471567 + 0.816778i) q^{50} +(-8.72224 + 2.31520i) q^{51} +(-0.171139 - 0.296421i) q^{52} -5.79515 q^{53} +(-5.00951 - 1.38015i) q^{54} +6.86190 q^{55} +(-1.79058 - 3.10138i) q^{56} +(-1.99934 + 0.530697i) q^{57} +(4.34522 - 7.52614i) q^{58} +(-4.14080 + 7.17207i) q^{59} +(2.97874 + 2.99275i) q^{60} +(5.02496 + 8.70348i) q^{61} -10.7063 q^{62} +(-9.27883 - 5.41534i) q^{63} +1.00000 q^{64} +(0.417211 + 0.722631i) q^{65} +(1.27285 - 4.70616i) q^{66} +(-3.85744 + 6.68129i) q^{67} +(2.60509 - 4.51214i) q^{68} +(-0.452211 + 1.67198i) q^{69} +(4.36518 + 7.56071i) q^{70} +13.8809 q^{71} +(2.60509 - 1.48779i) q^{72} -1.48027 q^{73} +(-2.19500 - 3.80186i) q^{74} +(-1.15239 - 1.15781i) q^{75} +(0.597146 - 1.03429i) q^{76} +(5.04000 - 8.72953i) q^{77} +(0.572999 - 0.152095i) q^{78} +(0.781073 + 1.35286i) q^{79} -2.43785 q^{80} +(4.57294 - 7.75166i) q^{81} -1.87896 q^{82} +(5.35929 + 9.28257i) q^{83} +(5.99515 - 1.59133i) q^{84} +(-6.35082 + 10.9999i) q^{85} +(-3.85245 + 6.67263i) q^{86} +(10.6186 + 10.6685i) q^{87} +(1.40736 + 2.43763i) q^{88} +1.61576 q^{89} +(-6.35082 + 3.62702i) q^{90} +1.22575 q^{91} +(-0.500000 - 0.866025i) q^{92} +(4.84152 - 17.9007i) q^{93} +(1.40442 - 2.43253i) q^{94} +(-1.45575 + 2.52144i) q^{95} +(-0.452211 + 1.67198i) q^{96} +(3.92638 + 6.80069i) q^{97} +5.82472 q^{98} +(7.29299 + 4.25636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9} - 10 q^{10} + 3 q^{11} - 2 q^{12} + 8 q^{13} + 5 q^{14} + 11 q^{15} - 5 q^{16} - 2 q^{17} - 8 q^{18} - 2 q^{19} + 5 q^{20} - 15 q^{21} + 3 q^{22} - 5 q^{23} + q^{24} - 16 q^{26} - 5 q^{27} - 10 q^{28} + 18 q^{29} + 5 q^{30} + 8 q^{31} - 5 q^{32} + 24 q^{33} + q^{34} + 2 q^{35} + 7 q^{36} - 12 q^{37} + q^{38} - 27 q^{39} + 5 q^{40} + 24 q^{41} - 3 q^{42} - 11 q^{43} - 6 q^{44} - 7 q^{45} + 10 q^{46} + 9 q^{47} + q^{48} - 4 q^{49} + 2 q^{51} + 8 q^{52} - 58 q^{53} - 20 q^{54} - 28 q^{55} + 5 q^{56} + 2 q^{57} + 18 q^{58} + 21 q^{59} - 16 q^{60} + 17 q^{61} - 16 q^{62} + 6 q^{63} + 10 q^{64} + 21 q^{65} + 21 q^{66} + 3 q^{67} + q^{68} - 2 q^{69} - q^{70} - 18 q^{71} + q^{72} - 14 q^{73} + 6 q^{74} + 13 q^{75} + q^{76} + 17 q^{77} + 15 q^{79} - 10 q^{80} + q^{81} - 48 q^{82} + 21 q^{83} + 18 q^{84} - 7 q^{85} - 11 q^{86} - 9 q^{87} + 3 q^{88} - 18 q^{89} - 7 q^{90} + 34 q^{91} - 5 q^{92} + 5 q^{93} + 9 q^{94} + 11 q^{95} - 2 q^{96} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9 - 10 * q^10 + 3 * q^11 - 2 * q^12 + 8 * q^13 + 5 * q^14 + 11 * q^15 - 5 * q^16 - 2 * q^17 - 8 * q^18 - 2 * q^19 + 5 * q^20 - 15 * q^21 + 3 * q^22 - 5 * q^23 + q^24 - 16 * q^26 - 5 * q^27 - 10 * q^28 + 18 * q^29 + 5 * q^30 + 8 * q^31 - 5 * q^32 + 24 * q^33 + q^34 + 2 * q^35 + 7 * q^36 - 12 * q^37 + q^38 - 27 * q^39 + 5 * q^40 + 24 * q^41 - 3 * q^42 - 11 * q^43 - 6 * q^44 - 7 * q^45 + 10 * q^46 + 9 * q^47 + q^48 - 4 * q^49 + 2 * q^51 + 8 * q^52 - 58 * q^53 - 20 * q^54 - 28 * q^55 + 5 * q^56 + 2 * q^57 + 18 * q^58 + 21 * q^59 - 16 * q^60 + 17 * q^61 - 16 * q^62 + 6 * q^63 + 10 * q^64 + 21 * q^65 + 21 * q^66 + 3 * q^67 + q^68 - 2 * q^69 - q^70 - 18 * q^71 + q^72 - 14 * q^73 + 6 * q^74 + 13 * q^75 + q^76 + 17 * q^77 + 15 * q^79 - 10 * q^80 + q^81 - 48 * q^82 + 21 * q^83 + 18 * q^84 - 7 * q^85 - 11 * q^86 - 9 * q^87 + 3 * q^88 - 18 * q^89 - 7 * q^90 + 34 * q^91 - 5 * q^92 + 5 * q^93 + 9 * q^94 + 11 * q^95 - 2 * q^96 - 32 * q^97 + 8 * q^98

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