LMFDB - Embedded newform 966.2.i.n.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(277,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.i (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.173309020416.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 5x^{6} - 28x^{5} - 4x^{4} + 70x^{3} + 51x^{2} + 406x + 841 $ x^8 - 5x^6 - 28x^5 - 4x^4 + 70x^3 + 51x^2 + 406x + 841
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.1
Root			$0.435461 - 1.77894i$ of defining polynomial
Character	$\chi$	$=$	966.277
Dual form			966.2.i.n.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.94864 - 3.37514i) q^{5} +1.00000 q^{6} +(-1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.94864 - 3.37514i) q^{5} +1.00000 q^{6} +(-1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.94864 - 3.37514i) q^{10} +(-2.01318 + 3.48693i) q^{11} +(0.500000 + 0.866025i) q^{12} -0.619394 q^{13} -2.64575 q^{14} -3.89728 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.625764 - 1.08385i) q^{17} +(0.500000 - 0.866025i) q^{18} +(4.20698 + 7.28670i) q^{19} +3.89728 q^{20} +(1.32288 + 2.29129i) q^{21} -4.02636 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-5.09439 + 8.82374i) q^{25} +(-0.309697 - 0.536411i) q^{26} -1.00000 q^{27} +(-1.32288 - 2.29129i) q^{28} -9.41395 q^{29} +(-1.94864 - 3.37514i) q^{30} +(-2.59439 + 4.49362i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.01318 + 3.48693i) q^{33} +1.25153 q^{34} +10.3112 q^{35} +1.00000 q^{36} +(-0.690303 - 1.19564i) q^{37} +(-4.20698 + 7.28670i) q^{38} +(-0.309697 + 0.536411i) q^{39} +(1.94864 + 3.37514i) q^{40} -4.41395 q^{41} +(-1.32288 + 2.29129i) q^{42} +2.00000 q^{43} +(-2.01318 - 3.48693i) q^{44} +(-1.94864 + 3.37514i) q^{45} +(0.500000 - 0.866025i) q^{46} +(3.06803 + 5.31399i) q^{47} -1.00000 q^{48} +(-3.50000 - 6.06218i) q^{49} -10.1888 q^{50} +(-0.625764 - 1.08385i) q^{51} +(0.309697 - 0.536411i) q^{52} +(0.948639 - 1.64309i) q^{53} +(-0.500000 - 0.866025i) q^{54} +15.6918 q^{55} +(1.32288 - 2.29129i) q^{56} +8.41395 q^{57} +(-4.70698 - 8.15272i) q^{58} +(-5.50986 + 9.54336i) q^{59} +(1.94864 - 3.37514i) q^{60} +(0.102721 + 0.177918i) q^{61} -5.18878 q^{62} +2.64575 q^{63} +1.00000 q^{64} +(1.20698 + 2.09054i) q^{65} +(-2.01318 + 3.48693i) q^{66} +(-6.02636 + 10.4380i) q^{67} +(0.625764 + 1.08385i) q^{68} -1.00000 q^{69} +(5.15562 + 8.92979i) q^{70} +0.483327 q^{71} +(0.500000 + 0.866025i) q^{72} +(-1.57772 + 2.73269i) q^{73} +(0.690303 - 1.19564i) q^{74} +(5.09439 + 8.82374i) q^{75} -8.41395 q^{76} +(-5.32637 - 9.22554i) q^{77} -0.619394 q^{78} +(-7.73683 - 13.4006i) q^{79} +(-1.94864 + 3.37514i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.20698 - 3.82259i) q^{82} +7.13607 q^{83} -2.64575 q^{84} -4.87755 q^{85} +(1.00000 + 1.73205i) q^{86} +(-4.70698 + 8.15272i) q^{87} +(2.01318 - 3.48693i) q^{88} +(-5.10425 - 8.84083i) q^{89} -3.89728 q^{90} +(0.819381 - 1.41921i) q^{91} +1.00000 q^{92} +(2.59439 + 4.49362i) q^{93} +(-3.06803 + 5.31399i) q^{94} +(16.3958 - 28.3983i) q^{95} +(-0.500000 - 0.866025i) q^{96} +12.0531 q^{97} +(3.50000 - 6.06218i) q^{98} +4.02636 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 + 8 * q^6 - 8 * q^8 - 4 * q^9	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{15} - 4 q^{16} + 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 6 q^{25} - 2 q^{26} - 8 q^{27} - 20 q^{29} - 2 q^{30} + 14 q^{31} + 4 q^{32} + 6 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} + 16 q^{43} - 6 q^{44} - 2 q^{45} + 4 q^{46} + 10 q^{47} - 8 q^{48} - 28 q^{49} - 12 q^{50} - 2 q^{51} + 2 q^{52} - 6 q^{53} - 4 q^{54} + 44 q^{55} + 12 q^{57} - 10 q^{58} - 24 q^{59} + 2 q^{60} + 28 q^{61} + 28 q^{62} + 8 q^{64} - 18 q^{65} - 6 q^{66} - 28 q^{67} + 2 q^{68} - 8 q^{69} + 32 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 6 q^{75} - 12 q^{76} - 14 q^{77} - 4 q^{78} + 4 q^{79} - 2 q^{80} - 4 q^{81} + 10 q^{82} + 28 q^{83} - 52 q^{85} + 8 q^{86} - 10 q^{87} + 6 q^{88} + 14 q^{89} - 4 q^{90} + 14 q^{91} + 8 q^{92} - 14 q^{93} - 10 q^{94} + 34 q^{95} - 4 q^{96} + 28 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 + 8 * q^6 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^13 - 4 * q^15 - 4 * q^16 + 2 * q^17 + 4 * q^18 + 6 * q^19 + 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^24 - 6 * q^25 - 2 * q^26 - 8 * q^27 - 20 * q^29 - 2 * q^30 + 14 * q^31 + 4 * q^32 + 6 * q^33 + 4 * q^34 + 8 * q^36 - 6 * q^37 - 6 * q^38 - 2 * q^39 + 2 * q^40 + 20 * q^41 + 16 * q^43 - 6 * q^44 - 2 * q^45 + 4 * q^46 + 10 * q^47 - 8 * q^48 - 28 * q^49 - 12 * q^50 - 2 * q^51 + 2 * q^52 - 6 * q^53 - 4 * q^54 + 44 * q^55 + 12 * q^57 - 10 * q^58 - 24 * q^59 + 2 * q^60 + 28 * q^61 + 28 * q^62 + 8 * q^64 - 18 * q^65 - 6 * q^66 - 28 * q^67 + 2 * q^68 - 8 * q^69 + 32 * q^71 + 4 * q^72 - 6 * q^73 + 6 * q^74 + 6 * q^75 - 12 * q^76 - 14 * q^77 - 4 * q^78 + 4 * q^79 - 2 * q^80 - 4 * q^81 + 10 * q^82 + 28 * q^83 - 52 * q^85 + 8 * q^86 - 10 * q^87 + 6 * q^88 + 14 * q^89 - 4 * q^90 + 14 * q^91 + 8 * q^92 - 14 * q^93 - 10 * q^94 + 34 * q^95 - 4 * q^96 + 28 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.94864	−	3.37514i	−0.871458	−	1.50941i	−0.860489	−	0.509470i	$-0.829842\pi$
$5$	−1.94864	−	3.37514i	−0.871458	−	1.50941i	−0.0109694	−	0.999940i	$-0.503492\pi$
$6$	1.00000			0.408248
$7$	−1.32288	+	2.29129i	−0.500000	+	0.866025i
$7$	−1.32288	+	2.29129i	−0.500000	+	0.866025i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.94864	−	3.37514i	0.616214	−	1.06731i
$11$	−2.01318	+	3.48693i	−0.606996	+	1.05135i	0.384736	+	0.923026i	$0.374292\pi$
$11$	−2.01318	+	3.48693i	−0.606996	+	1.05135i	−0.991733	+	0.128322i	$0.959041\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−0.619394			−0.171789			−0.0858945	−	0.996304i	$-0.527375\pi$
$13$	−0.619394			−0.171789			−0.0858945	+	0.996304i	$0.527375\pi$
$14$	−2.64575			−0.707107
$15$	−3.89728			−1.00627
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.625764	−	1.08385i	0.151770	−	0.262873i	−0.780108	−	0.625645i	$-0.784836\pi$
$17$	0.625764	−	1.08385i	0.151770	−	0.262873i	0.931878	+	0.362771i	$0.118169\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	4.20698	+	7.28670i	0.965146	+	1.67168i	0.709221	+	0.704986i	$0.249047\pi$
$19$	4.20698	+	7.28670i	0.965146	+	1.67168i	0.255925	+	0.966697i	$0.417620\pi$
$20$	3.89728			0.871458
$21$	1.32288	+	2.29129i	0.288675	+	0.500000i
$22$	−4.02636			−0.858422
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−5.09439	+	8.82374i	−1.01888	+	1.76475i
$26$	−0.309697	−	0.536411i	−0.0607366	−	0.105199i
$27$	−1.00000			−0.192450
$28$	−1.32288	−	2.29129i	−0.250000	−	0.433013i
$29$	−9.41395			−1.74813			−0.874063	−	0.485812i	$-0.838524\pi$
$29$	−9.41395			−1.74813			−0.874063	+	0.485812i	$0.838524\pi$
$30$	−1.94864	−	3.37514i	−0.355771	−	0.616214i
$31$	−2.59439	+	4.49362i	−0.465966	+	0.807077i	−0.999245	−	0.0388626i	$-0.987627\pi$
$31$	−2.59439	+	4.49362i	−0.465966	+	0.807077i	0.533278	+	0.845940i	$0.320960\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.01318	+	3.48693i	0.350449	+	0.606996i
$34$	1.25153			0.214635
$35$	10.3112			1.74292
$36$	1.00000			0.166667
$37$	−0.690303	−	1.19564i	−0.113485	−	0.196562i	0.803688	−	0.595051i	$-0.202868\pi$
$37$	−0.690303	−	1.19564i	−0.113485	−	0.196562i	−0.917173	+	0.398489i	$0.869535\pi$
$38$	−4.20698	+	7.28670i	−0.682462	+	1.18206i
$39$	−0.309697	+	0.536411i	−0.0495912	+	0.0858945i
$40$	1.94864	+	3.37514i	0.308107	+	0.533657i
$41$	−4.41395			−0.689343			−0.344672	−	0.938723i	$-0.612010\pi$
$41$	−4.41395			−0.689343			−0.344672	+	0.938723i	$0.612010\pi$
$42$	−1.32288	+	2.29129i	−0.204124	+	0.353553i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−2.01318	−	3.48693i	−0.303498	−	0.525674i
$45$	−1.94864	+	3.37514i	−0.290486	+	0.503137i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	3.06803	+	5.31399i	0.447519	+	0.775125i	0.998224	−	0.0595747i	$-0.0189745\pi$
$47$	3.06803	+	5.31399i	0.447519	+	0.775125i	−0.550705	+	0.834700i	$0.685641\pi$
$48$	−1.00000			−0.144338
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$	−10.1888			−1.44091
$51$	−0.625764	−	1.08385i	−0.0876244	−	0.151770i
$52$	0.309697	−	0.536411i	0.0429473	−	0.0743868i
$53$	0.948639	−	1.64309i	0.130306	−	0.225696i	−0.793489	−	0.608585i	$-0.791737\pi$
$53$	0.948639	−	1.64309i	0.130306	−	0.225696i	0.923794	+	0.382889i	$0.125071\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	15.6918			2.11589
$56$	1.32288	−	2.29129i	0.176777	−	0.306186i
$57$	8.41395			1.11446
$58$	−4.70698	−	8.15272i	−0.618056	−	1.07050i
$59$	−5.50986	+	9.54336i	−0.717323	+	1.24244i	0.244733	+	0.969590i	$0.421300\pi$
$59$	−5.50986	+	9.54336i	−0.717323	+	1.24244i	−0.962057	+	0.272850i	$0.912034\pi$
$60$	1.94864	−	3.37514i	0.251568	−	0.435729i
$61$	0.102721	+	0.177918i	0.0131521	+	0.0227801i	0.872527	−	0.488567i	$-0.162480\pi$
$61$	0.102721	+	0.177918i	0.0131521	+	0.0227801i	−0.859374	+	0.511347i	$0.829147\pi$
$62$	−5.18878			−0.658976
$63$	2.64575			0.333333
$64$	1.00000			0.125000
$65$	1.20698	+	2.09054i	0.149707	+	0.259300i
$66$	−2.01318	+	3.48693i	−0.247805	+	0.429211i
$67$	−6.02636	+	10.4380i	−0.736237	+	1.27520i	0.217942	+	0.975962i	$0.430066\pi$
$67$	−6.02636	+	10.4380i	−0.736237	+	1.27520i	−0.954179	+	0.299238i	$0.903268\pi$
$68$	0.625764	+	1.08385i	0.0758850	+	0.131437i
$69$	−1.00000			−0.120386
$70$	5.15562	+	8.92979i	0.616214	+	1.06731i
$71$	0.483327			0.0573604			0.0286802	−	0.999589i	$-0.490870\pi$
$71$	0.483327			0.0573604			0.0286802	+	0.999589i	$0.490870\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−1.57772	+	2.73269i	−0.184658	+	0.319837i	−0.943461	−	0.331483i	$-0.892451\pi$
$73$	−1.57772	+	2.73269i	−0.184658	+	0.319837i	0.758803	+	0.651320i	$0.225784\pi$
$74$	0.690303	−	1.19564i	0.0802461	−	0.138990i
$75$	5.09439	+	8.82374i	0.588250	+	1.01888i
$76$	−8.41395			−0.965146
$77$	−5.32637	−	9.22554i	−0.606996	−	1.05135i
$78$	−0.619394			−0.0701326
$79$	−7.73683	−	13.4006i	−0.870461	−	1.50768i	−0.861521	−	0.507723i	$-0.830487\pi$
$79$	−7.73683	−	13.4006i	−0.870461	−	1.50768i	−0.00894055	−	0.999960i	$-0.502846\pi$
$80$	−1.94864	+	3.37514i	−0.217865	+	0.377352i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.20698	−	3.82259i	−0.243720	−	0.422135i
$83$	7.13607			0.783285			0.391643	−	0.920117i	$-0.371907\pi$
$83$	7.13607			0.783285			0.391643	+	0.920117i	$0.371907\pi$
$84$	−2.64575			−0.288675
$85$	−4.87755			−0.529045
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$	−4.70698	+	8.15272i	−0.504641	+	0.874063i
$88$	2.01318	−	3.48693i	0.214606	−	0.371708i
$89$	−5.10425	−	8.84083i	−0.541050	−	0.937126i	−0.998844	−	0.0480677i	$-0.984694\pi$
$89$	−5.10425	−	8.84083i	−0.541050	−	0.937126i	0.457794	−	0.889058i	$-0.348640\pi$
$90$	−3.89728			−0.410809
$91$	0.819381	−	1.41921i	0.0858945	−	0.148774i
$92$	1.00000			0.104257
$93$	2.59439	+	4.49362i	0.269026	+	0.465966i
$94$	−3.06803	+	5.31399i	−0.316443	+	0.548096i
$95$	16.3958	−	28.3983i	1.68217	−	2.91360i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	12.0531			1.22380			0.611902	−	0.790934i	$-0.290405\pi$
$97$	12.0531			1.22380			0.611902	+	0.790934i	$0.290405\pi$
$98$	3.50000	−	6.06218i	0.353553	−	0.612372i
$99$	4.02636			0.404664
$100$	−5.09439	−	8.82374i	−0.509439	−	0.882374i
$101$	5.09439	−	8.82374i	0.506911	−	0.877995i	−0.493057	−	0.869997i	$-0.664121\pi$
$101$	5.09439	−	8.82374i	0.506911	−	0.877995i	0.999968	−	0.00799839i	$-0.00254599\pi$
$102$	0.625764	−	1.08385i	0.0619598	−	0.107318i
$103$	−3.47849	−	6.02492i	−0.342746	−	0.593653i	0.642196	−	0.766541i	$-0.278024\pi$
$103$	−3.47849	−	6.02492i	−0.342746	−	0.593653i	−0.984942	+	0.172887i	$0.944690\pi$
$104$	0.619394			0.0607366
$105$	5.15562	−	8.92979i	0.503137	−	0.871458i
$106$	1.89728			0.184280
$107$	−5.56803	−	9.64412i	−0.538282	−	0.932332i	−0.998997	−	0.0447836i	$-0.985740\pi$
$107$	−5.56803	−	9.64412i	−0.538282	−	0.932332i	0.460715	−	0.887548i	$-0.347593\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−0.683933	+	1.18461i	−0.0655089	+	0.113465i	−0.896920	−	0.442194i	$-0.854200\pi$
$109$	−0.683933	+	1.18461i	−0.0655089	+	0.113465i	0.831411	+	0.555658i	$0.187534\pi$
$110$	7.84592	+	13.5895i	0.748079	+	1.29571i
$111$	−1.38061			−0.131041
$112$	2.64575			0.250000
$113$	19.7582			1.85869			0.929346	−	0.369210i	$-0.120372\pi$
$113$	19.7582			1.85869			0.929346	+	0.369210i	$0.120372\pi$
$114$	4.20698	+	7.28670i	0.394019	+	0.682462i
$115$	−1.94864	+	3.37514i	−0.181712	+	0.314734i
$116$	4.70698	−	8.15272i	0.437032	−	0.756961i
$117$	0.309697	+	0.536411i	0.0286315	+	0.0495912i
$118$	−11.0197			−1.01445
$119$	1.65562	+	2.86761i	0.151770	+	0.262873i
$120$	3.89728			0.355771
$121$	−2.60578	−	4.51334i	−0.236889	−	0.410303i
$122$	−0.102721	+	0.177918i	−0.00929995	+	0.0161080i
$123$	−2.20698	+	3.82259i	−0.198996	+	0.344672i
$124$	−2.59439	−	4.49362i	−0.232983	−	0.403539i
$125$	20.2221			1.80872
$126$	1.32288	+	2.29129i	0.117851	+	0.204124i
$127$	−15.4337			−1.36952			−0.684759	−	0.728770i	$-0.740092\pi$
$127$	−15.4337			−1.36952			−0.684759	+	0.728770i	$0.740092\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$	−1.20698	+	2.09054i	−0.105859	+	0.183353i
$131$	−10.4471	−	18.0949i	−0.912769	−	1.58096i	−0.810135	−	0.586243i	$-0.800606\pi$
$131$	−10.4471	−	18.0949i	−0.912769	−	1.58096i	−0.102634	−	0.994719i	$-0.532727\pi$
$132$	−4.02636			−0.350449
$133$	−22.2612			−1.93029
$134$	−12.0527			−1.04120
$135$	1.94864	+	3.37514i	0.167712	+	0.290486i
$136$	−0.625764	+	1.08385i	−0.0536588	+	0.0929398i
$137$	−3.18699	+	5.52003i	−0.272283	+	0.471608i	−0.969446	−	0.245305i	$-0.921112\pi$
$137$	−3.18699	+	5.52003i	−0.272283	+	0.471608i	0.697163	+	0.716912i	$0.254445\pi$
$138$	−0.500000	−	0.866025i	−0.0425628	−	0.0737210i
$139$	−2.13607			−0.181179			−0.0905894	−	0.995888i	$-0.528875\pi$
$139$	−2.13607			−0.181179			−0.0905894	+	0.995888i	$0.528875\pi$
$140$	−5.15562	+	8.92979i	−0.435729	+	0.754705i
$141$	6.13607			0.516750
$142$	0.241664	+	0.418574i	0.0202800	+	0.0351259i
$143$	1.24695	−	2.15978i	0.104275	−	0.180610i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	18.3444	+	31.7734i	1.52342	+	2.63864i
$146$	−3.15544			−0.261146
$147$	−7.00000			−0.577350
$148$	1.38061			0.113485
$149$	−5.91090	−	10.2380i	−0.484240	−	0.838727i	0.515597	−	0.856831i	$-0.327570\pi$
$149$	−5.91090	−	10.2380i	−0.484240	−	0.838727i	−0.999836	+	0.0181040i	$0.994237\pi$
$150$	−5.09439	+	8.82374i	−0.415955	+	0.720456i
$151$	−4.71684	+	8.16981i	−0.383851	+	0.664849i	−0.991609	−	0.129273i	$-0.958736\pi$
$151$	−4.71684	+	8.16981i	−0.383851	+	0.664849i	0.607758	+	0.794122i	$0.292069\pi$
$152$	−4.20698	−	7.28670i	−0.341231	−	0.591029i
$153$	−1.25153			−0.101180
$154$	5.32637	−	9.22554i	0.429211	−	0.743415i
$155$	20.2221			1.62428
$156$	−0.309697	−	0.536411i	−0.0247956	−	0.0429473i
$157$	−1.89091	+	3.27515i	−0.150911	+	0.261385i	−0.931563	−	0.363581i	$-0.881554\pi$
$157$	−1.89091	+	3.27515i	−0.150911	+	0.261385i	0.780652	+	0.624966i	$0.214887\pi$
$158$	7.73683	−	13.4006i	0.615509	−	1.06609i
$159$	−0.948639	−	1.64309i	−0.0752320	−	0.130306i
$160$	−3.89728			−0.308107
$161$	2.64575			0.208514
$162$	−1.00000			−0.0785674
$163$	−2.24166	−	3.88268i	−0.175581	−	0.304115i	0.764781	−	0.644290i	$-0.222847\pi$
$163$	−2.24166	−	3.88268i	−0.175581	−	0.304115i	−0.940362	+	0.340175i	$0.889514\pi$
$164$	2.20698	−	3.82259i	0.172336	−	0.298494i
$165$	7.84592	−	13.5895i	0.610804	−	1.05794i
$166$	3.56803	+	6.18002i	0.276933	+	0.479662i
$167$	17.1388			1.32624			0.663119	−	0.748514i	$-0.269232\pi$
$167$	17.1388			1.32624			0.663119	+	0.748514i	$0.269232\pi$
$168$	−1.32288	−	2.29129i	−0.102062	−	0.176777i
$169$	−12.6164			−0.970489
$170$	−2.43878	−	4.22408i	−0.187046	−	0.323972i
$171$	4.20698	−	7.28670i	0.321715	−	0.557228i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	1.42228	+	2.46346i	0.108134	+	0.187294i	0.915014	−	0.403421i	$-0.132179\pi$
$173$	1.42228	+	2.46346i	0.108134	+	0.187294i	−0.806880	+	0.590715i	$0.798846\pi$
$174$	−9.41395			−0.713670
$175$	−13.4785	−	23.3454i	−1.01888	−	1.76475i
$176$	4.02636			0.303498
$177$	5.50986	+	9.54336i	0.414147	+	0.717323i
$178$	5.10425	−	8.84083i	0.382580	−	0.662648i
$179$	−6.63912	+	11.4993i	−0.496231	+	0.859498i	−0.999991	−	0.00434631i	$-0.998617\pi$
$179$	−6.63912	+	11.4993i	−0.496231	+	0.859498i	0.503759	+	0.863844i	$0.331950\pi$
$180$	−1.94864	−	3.37514i	−0.145243	−	0.251568i
$181$	14.5066			1.07827			0.539135	−	0.842219i	$-0.318751\pi$
$181$	14.5066			1.07827			0.539135	+	0.842219i	$0.318751\pi$
$182$	1.63876			0.121473
$183$	0.205443			0.0151868
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	−2.69030	+	4.65974i	−0.197795	+	0.342591i
$186$	−2.59439	+	4.49362i	−0.190230	+	0.329488i
$187$	2.51955	+	4.36399i	0.184248	+	0.319126i
$188$	−6.13607			−0.447519
$189$	1.32288	−	2.29129i	0.0962250	−	0.166667i
$190$	32.7915			2.37895
$191$	7.62093	+	13.1998i	0.551431	+	0.955106i	0.998172	+	0.0604429i	$0.0192513\pi$
$191$	7.62093	+	13.1998i	0.551431	+	0.955106i	−0.446741	+	0.894663i	$0.647415\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−5.97500	+	10.3490i	−0.430090	+	0.744937i	−0.996881	−	0.0789245i	$-0.974851\pi$
$193$	−5.97500	+	10.3490i	−0.430090	+	0.744937i	0.566791	+	0.823862i	$0.308185\pi$
$194$	6.02654	+	10.4383i	0.432680	+	0.749424i
$195$	2.41395			0.172867
$196$	7.00000			0.500000
$197$	−18.5391			−1.32086			−0.660428	−	0.750889i	$-0.729625\pi$
$197$	−18.5391			−1.32086			−0.660428	+	0.750889i	$0.729625\pi$
$198$	2.01318	+	3.48693i	0.143070	+	0.247805i
$199$	4.45876	−	7.72280i	0.316073	−	0.547455i	−0.663592	−	0.748095i	$-0.730969\pi$
$199$	4.45876	−	7.72280i	0.316073	−	0.547455i	0.979665	+	0.200640i	$0.0643021\pi$
$200$	5.09439	−	8.82374i	0.360228	−	0.623933i
$201$	6.02636	+	10.4380i	0.425066	+	0.736237i
$202$	10.1888			0.716880
$203$	12.4535	−	21.5701i	0.874063	−	1.51392i
$204$	1.25153			0.0876244
$205$	8.60120	+	14.8977i	0.600734	+	1.04050i
$206$	3.47849	−	6.02492i	0.242358	−	0.419776i
$207$	−0.500000	+	0.866025i	−0.0347524	+	0.0601929i
$208$	0.309697	+	0.536411i	0.0214736	+	0.0371934i
$209$	−33.8776			−2.34336
$210$	10.3112			0.711542
$211$	17.1694			1.18199			0.590996	−	0.806675i	$-0.298735\pi$
$211$	17.1694			1.18199			0.590996	+	0.806675i	$0.298735\pi$
$212$	0.948639	+	1.64309i	0.0651528	+	0.112848i
$213$	0.241664	−	0.418574i	0.0165585	−	0.0286802i
$214$	5.56803	−	9.64412i	0.380623	−	0.659258i
$215$	−3.89728	−	6.75028i	−0.265792	−	0.460366i
$216$	1.00000			0.0680414
$217$	−6.86411	−	11.8890i	−0.465966	−	0.807077i
$218$	−1.36787			−0.0926436
$219$	1.57772	+	2.73269i	0.106612	+	0.184658i
$220$	−7.84592	+	13.5895i	−0.528972	+	0.916206i
$221$	−0.387594	+	0.671333i	−0.0260724	+	0.0451588i
$222$	−0.690303	−	1.19564i	−0.0463301	−	0.0802461i
$223$	−9.39422			−0.629084			−0.314542	−	0.949244i	$-0.601851\pi$
$223$	−9.39422			−0.629084			−0.314542	+	0.949244i	$0.601851\pi$
$224$	1.32288	+	2.29129i	0.0883883	+	0.153093i
$225$	10.1888			0.679252
$226$	9.87908	+	17.1111i	0.657147	+	1.13821i
$227$	−12.6589	+	21.9259i	−0.840203	+	1.45527i	0.0495204	+	0.998773i	$0.484231\pi$
$227$	−12.6589	+	21.9259i	−0.840203	+	1.45527i	−0.889723	+	0.456501i	$0.849103\pi$
$228$	−4.20698	+	7.28670i	−0.278614	+	0.482573i
$229$	5.98001	+	10.3577i	0.395170	+	0.684455i	0.993123	−	0.117076i	$-0.0373522\pi$
$229$	5.98001	+	10.3577i	0.395170	+	0.684455i	−0.597953	+	0.801531i	$0.704019\pi$
$230$	−3.89728			−0.256979
$231$	−10.6527			−0.700899
$232$	9.41395			0.618056
$233$	4.43215	+	7.67670i	0.290360	+	0.502917i	0.973895	−	0.227000i	$-0.0728918\pi$
$233$	4.43215	+	7.67670i	0.290360	+	0.502917i	−0.683535	+	0.729918i	$0.739558\pi$
$234$	−0.309697	+	0.536411i	−0.0202455	+	0.0350663i
$235$	11.9570	−	20.7101i	0.779987	−	1.35098i
$236$	−5.50986	−	9.54336i	−0.358662	−	0.621220i
$237$	−15.4737			−1.00512
$238$	−1.65562	+	2.86761i	−0.107318	+	0.185880i
$239$	9.93062			0.642359			0.321179	−	0.947018i	$-0.395921\pi$
$239$	9.93062			0.642359			0.321179	+	0.947018i	$0.395921\pi$
$240$	1.94864	+	3.37514i	0.125784	+	0.217865i
$241$	6.14200	−	10.6383i	0.395641	−	0.685270i	−0.597542	−	0.801838i	$-0.703856\pi$
$241$	6.14200	−	10.6383i	0.395641	−	0.685270i	0.993183	+	0.116568i	$0.0371892\pi$
$242$	2.60578	−	4.51334i	0.167506	−	0.290128i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.205443			−0.0131521
$245$	−13.6405	+	23.6260i	−0.871458	+	1.50941i
$246$	−4.41395			−0.281423
$247$	−2.60578	−	4.51334i	−0.165802	−	0.287177i
$248$	2.59439	−	4.49362i	0.164744	−	0.285345i
$249$	3.56803	−	6.18002i	0.226115	−	0.391643i
$250$	10.1111	+	17.5129i	0.639480	+	1.10761i
$251$	6.81481			0.430147			0.215073	−	0.976598i	$-0.431001\pi$
$251$	6.81481			0.430147			0.215073	+	0.976598i	$0.431001\pi$
$252$	−1.32288	+	2.29129i	−0.0833333	+	0.144338i
$253$	4.02636			0.253135
$254$	−7.71684	−	13.3660i	−0.484198	−	0.838655i
$255$	−2.43878	+	4.22408i	−0.152722	+	0.264522i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.7500	+	20.3516i	0.732945	+	1.26950i	0.955619	+	0.294605i	$0.0951882\pi$
$257$	11.7500	+	20.3516i	0.732945	+	1.26950i	−0.222674	+	0.974893i	$0.571478\pi$
$258$	2.00000			0.124515
$259$	3.65274			0.226970
$260$	−2.41395			−0.149707
$261$	4.70698	+	8.15272i	0.291354	+	0.504641i
$262$	10.4471	−	18.0949i	0.645425	−	1.11791i
$263$	−9.42669	+	16.3275i	−0.581275	+	1.00680i	0.414054	+	0.910252i	$0.364112\pi$
$263$	−9.42669	+	16.3275i	−0.581275	+	1.00680i	−0.995329	+	0.0965449i	$0.969221\pi$
$264$	−2.01318	−	3.48693i	−0.123903	−	0.214606i
$265$	−7.39422			−0.454224
$266$	−11.1306	−	19.2788i	−0.682462	−	1.18206i
$267$	−10.2085			−0.624751
$268$	−6.02636	−	10.4380i	−0.368118	−	0.637600i
$269$	13.3988	−	23.2074i	0.816940	−	1.41498i	−0.0909865	−	0.995852i	$-0.529002\pi$
$269$	13.3988	−	23.2074i	0.816940	−	1.41498i	0.907926	−	0.419129i	$-0.137665\pi$
$270$	−1.94864	+	3.37514i	−0.118590	+	0.205405i
$271$	14.2401	+	24.6646i	0.865027	+	1.49827i	0.867020	+	0.498273i	$0.166032\pi$
$271$	14.2401	+	24.6646i	0.865027	+	1.49827i	−0.00199332	+	0.999998i	$0.500634\pi$
$272$	−1.25153			−0.0758850
$273$	−0.819381	−	1.41921i	−0.0495912	−	0.0858945i
$274$	−6.37398			−0.385066
$275$	−20.5118	−	35.5275i	−1.23691	−	2.14239i
$276$	0.500000	−	0.866025i	0.0300965	−	0.0521286i
$277$	−9.69847	+	16.7982i	−0.582724	+	1.00931i	0.412431	+	0.910989i	$0.364680\pi$
$277$	−9.69847	+	16.7982i	−0.582724	+	1.00931i	−0.995155	+	0.0983191i	$0.968653\pi$
$278$	−1.06803	−	1.84989i	−0.0640564	−	0.110949i
$279$	5.18878			0.310644
$280$	−10.3112			−0.616214
$281$	22.3903			1.33569			0.667847	−	0.744299i	$-0.267216\pi$
$281$	22.3903			1.33569			0.667847	+	0.744299i	$0.267216\pi$
$282$	3.06803	+	5.31399i	0.182699	+	0.316443i
$283$	5.01973	−	8.69442i	0.298392	−	0.516830i	−0.677376	−	0.735637i	$-0.736883\pi$
$283$	5.01973	−	8.69442i	0.298392	−	0.516830i	0.975768	+	0.218807i	$0.0702165\pi$
$284$	−0.241664	+	0.418574i	−0.0143401	+	0.0248378i
$285$	−16.3958	−	28.3983i	−0.971201	−	1.68217i
$286$	2.49390			0.147468
$287$	5.83911	−	10.1136i	0.344672	−	0.596989i
$288$	−1.00000			−0.0589256
$289$	7.71684	+	13.3660i	0.453932	+	0.786233i
$290$	−18.3444	+	31.7734i	−1.07722	+	1.86580i
$291$	6.02654	−	10.4383i	0.353282	−	0.611902i
$292$	−1.57772	−	2.73269i	−0.0923290	−	0.159918i
$293$	−25.0228			−1.46185			−0.730924	−	0.682459i	$-0.760910\pi$
$293$	−25.0228			−1.46185			−0.730924	+	0.682459i	$0.760910\pi$
$294$	−3.50000	−	6.06218i	−0.204124	−	0.353553i
$295$	42.9469			2.50047
$296$	0.690303	+	1.19564i	0.0401230	+	0.0694951i
$297$	2.01318	−	3.48693i	0.116816	−	0.202332i
$298$	5.91090	−	10.2380i	0.342409	−	0.593070i
$299$	0.309697	+	0.536411i	0.0179102	+	0.0310215i
$300$	−10.1888			−0.588250
$301$	−2.64575	+	4.58258i	−0.152499	+	0.264135i
$302$	−9.43368			−0.542847
$303$	−5.09439	−	8.82374i	−0.292665	−	0.506911i
$304$	4.20698	−	7.28670i	0.241287	−	0.417921i
$305$	0.400334	−	0.693398i	0.0229230	−	0.0397039i
$306$	−0.625764	−	1.08385i	−0.0357725	−	0.0619598i
$307$	−27.6221			−1.57648			−0.788238	−	0.615370i	$-0.789007\pi$
$307$	−27.6221			−1.57648			−0.788238	+	0.615370i	$0.789007\pi$
$308$	10.6527			0.606996
$309$	−6.95698			−0.395769
$310$	10.1111	+	17.5129i	0.574270	+	0.994665i
$311$	−6.41683	+	11.1143i	−0.363865	+	0.630232i	−0.988593	−	0.150610i	$-0.951876\pi$
$311$	−6.41683	+	11.1143i	−0.363865	+	0.630232i	0.624728	+	0.780842i	$0.285210\pi$
$312$	0.309697	−	0.536411i	0.0175331	−	0.0303683i
$313$	5.66530	+	9.81259i	0.320222	+	0.554640i	0.980534	−	0.196351i	$-0.0629093\pi$
$313$	5.66530	+	9.81259i	0.320222	+	0.554640i	−0.660312	+	0.750991i	$0.729576\pi$
$314$	−3.78182			−0.213420
$315$	−5.15562	−	8.92979i	−0.290486	−	0.503137i
$316$	15.4737			0.870461
$317$	−14.5099	−	25.1318i	−0.814955	−	1.41154i	−0.909360	−	0.416010i	$-0.863428\pi$
$317$	−14.5099	−	25.1318i	−0.814955	−	1.41154i	0.0944050	−	0.995534i	$-0.469905\pi$
$318$	0.948639	−	1.64309i	0.0531971	−	0.0921400i
$319$	18.9520	−	32.8258i	1.06111	−	1.83789i
$320$	−1.94864	−	3.37514i	−0.108932	−	0.188676i
$321$	−11.1361			−0.621555
$322$	1.32288	+	2.29129i	0.0737210	+	0.127688i
$323$	10.5303			0.585921
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	3.15544	−	5.46537i	0.175032	−	0.303164i
$326$	2.24166	−	3.88268i	0.124154	−	0.215041i
$327$	0.683933	+	1.18461i	0.0378216	+	0.0655089i
$328$	4.41395			0.243720
$329$	−16.2345			−0.895037
$330$	15.6918			0.863807
$331$	−14.5512	−	25.2034i	−0.799806	−	1.38530i	−0.919742	−	0.392523i	$-0.871602\pi$
$331$	−14.5512	−	25.2034i	−0.799806	−	1.38530i	0.119936	−	0.992782i	$-0.461731\pi$
$332$	−3.56803	+	6.18002i	−0.195821	+	0.339172i
$333$	−0.690303	+	1.19564i	−0.0378284	+	0.0655207i
$334$	8.56939	+	14.8426i	0.468896	+	0.812152i
$335$	46.9728			2.56640
$336$	1.32288	−	2.29129i	0.0721688	−	0.125000i
$337$	2.54215			0.138480			0.0692399	−	0.997600i	$-0.477943\pi$
$337$	2.54215			0.138480			0.0692399	+	0.997600i	$0.477943\pi$
$338$	−6.30818	−	10.9261i	−0.343120	−	0.594300i
$339$	9.87908	−	17.1111i	0.536558	−	0.929346i
$340$	2.43878	−	4.22408i	0.132261	−	0.229083i
$341$	−10.4459	−	18.0929i	−0.565680	−	0.979786i
$342$	8.41395			0.454974
$343$	18.5203			1.00000
$344$	−2.00000			−0.107833
$345$	1.94864	+	3.37514i	0.104911	+	0.181712i
$346$	−1.42228	+	2.46346i	−0.0764624	+	0.132437i
$347$	−10.1888	+	17.6475i	−0.546962	+	0.947367i	0.451518	+	0.892262i	$0.350883\pi$
$347$	−10.1888	+	17.6475i	−0.546962	+	0.947367i	−0.998481	+	0.0551048i	$0.982451\pi$
$348$	−4.70698	−	8.15272i	−0.252320	−	0.437032i
$349$	5.63876			0.301836			0.150918	−	0.988546i	$-0.451777\pi$
$349$	5.63876			0.301836			0.150918	+	0.988546i	$0.451777\pi$
$350$	13.4785	−	23.3454i	0.720456	−	1.24787i
$351$	0.619394			0.0330608
$352$	2.01318	+	3.48693i	0.107303	+	0.185854i
$353$	2.34879	−	4.06823i	0.125014	−	0.216530i	−0.796725	−	0.604343i	$-0.793436\pi$
$353$	2.34879	−	4.06823i	0.125014	−	0.216530i	0.921738	+	0.387813i	$0.126769\pi$
$354$	−5.50986	+	9.54336i	−0.292846	+	0.507224i
$355$	−0.941830	−	1.63130i	−0.0499872	−	0.0865803i
$356$	10.2085			0.541050
$357$	3.31123			0.175249
$358$	−13.2782			−0.701777
$359$	14.2151	+	24.6213i	0.750246	+	1.29946i	0.947703	+	0.319153i	$0.103398\pi$
$359$	14.2151	+	24.6213i	0.750246	+	1.29946i	−0.197457	+	0.980312i	$0.563268\pi$
$360$	1.94864	−	3.37514i	0.102702	−	0.177886i
$361$	−25.8973	+	44.8554i	−1.36302	+	2.36081i
$362$	7.25332	+	12.5631i	0.381226	+	0.660303i
$363$	−5.21155			−0.273536
$364$	0.819381	+	1.41921i	0.0429473	+	0.0743868i
$365$	12.2976			0.643686
$366$	0.102721	+	0.177918i	0.00536933	+	0.00929995i
$367$	3.13589	−	5.43152i	0.163692	−	0.283523i	−0.772498	−	0.635017i	$-0.780993\pi$
$367$	3.13589	−	5.43152i	0.163692	−	0.283523i	0.936190	+	0.351494i	$0.114326\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	2.20698	+	3.82259i	0.114891	+	0.198996i
$370$	−5.38061			−0.279724
$371$	2.50986	+	4.34721i	0.130306	+	0.225696i
$372$	−5.18878			−0.269026
$373$	3.13698	+	5.43341i	0.162427	+	0.281331i	0.935738	−	0.352695i	$-0.114735\pi$
$373$	3.13698	+	5.43341i	0.162427	+	0.281331i	−0.773312	+	0.634026i	$0.781401\pi$
$374$	−2.51955	+	4.36399i	−0.130283	+	0.225656i
$375$	10.1111	−	17.5129i	0.522133	−	0.904361i
$376$	−3.06803	−	5.31399i	−0.158222	−	0.274048i
$377$	5.83095			0.300309
$378$	2.64575			0.136083
$379$	−28.2248			−1.44981			−0.724906	−	0.688848i	$-0.758117\pi$
$379$	−28.2248			−1.44981			−0.724906	+	0.688848i	$0.758117\pi$
$380$	16.3958	+	28.3983i	0.841085	+	1.45680i
$381$	−7.71684	+	13.3660i	−0.395346	+	0.684759i
$382$	−7.62093	+	13.1998i	−0.389921	+	0.675362i
$383$	−4.72329	−	8.18098i	−0.241349	−	0.418028i	0.719750	−	0.694233i	$-0.244256\pi$
$383$	−4.72329	−	8.18098i	−0.241349	−	0.418028i	−0.961099	+	0.276205i	$0.910923\pi$
$384$	1.00000			0.0510310
$385$	−20.7583	+	35.9545i	−1.05794	+	1.83241i
$386$	−11.9500			−0.608239
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$	−6.02654	+	10.4383i	−0.305951	+	0.529923i
$389$	−2.82091	+	4.88597i	−0.143026	+	0.247728i	−0.928635	−	0.370995i	$-0.879017\pi$
$389$	−2.82091	+	4.88597i	−0.143026	+	0.247728i	0.785609	+	0.618724i	$0.212350\pi$
$390$	1.20698	+	2.09054i	0.0611176	+	0.105859i
$391$	−1.25153			−0.0632925
$392$	3.50000	+	6.06218i	0.176777	+	0.306186i
$393$	−20.8942			−1.05397
$394$	−9.26955	−	16.0553i	−0.466993	−	0.808856i
$395$	−30.1526	+	52.2258i	−1.51714	+	2.62776i
$396$	−2.01318	+	3.48693i	−0.101166	+	0.175225i
$397$	16.3694	+	28.3526i	0.821557	+	1.42298i	0.904523	+	0.426425i	$0.140227\pi$
$397$	16.3694	+	28.3526i	0.821557	+	1.42298i	−0.0829661	+	0.996552i	$0.526439\pi$
$398$	8.91753			0.446995
$399$	−11.1306	+	19.2788i	−0.557228	+	0.965146i
$400$	10.1888			0.509439
$401$	4.94245	+	8.56057i	0.246814	+	0.427495i	0.962640	−	0.270784i	$-0.0872830\pi$
$401$	4.94245	+	8.56057i	0.246814	+	0.427495i	−0.715826	+	0.698279i	$0.753950\pi$
$402$	−6.02636	+	10.4380i	−0.300567	+	0.520598i
$403$	1.60695	−	2.78332i	0.0800479	−	0.138647i
$404$	5.09439	+	8.82374i	0.253455	+	0.438998i
$405$	3.89728			0.193657
$406$	24.9070			1.23611
$407$	5.55881			0.275540
$408$	0.625764	+	1.08385i	0.0309799	+	0.0536588i
$409$	12.5531	−	21.7426i	0.620710	−	1.07510i	−0.368644	−	0.929571i	$-0.620178\pi$
$409$	12.5531	−	21.7426i	0.620710	−	1.07510i	0.989354	−	0.145530i	$-0.0464887\pi$
$410$	−8.60120	+	14.8977i	−0.424783	+	0.735746i
$411$	3.18699	+	5.52003i	0.157203	+	0.272283i
$412$	6.95698			0.342746
$413$	−14.5777	−	25.2494i	−0.717323	−	1.24244i
$414$	−1.00000			−0.0491473
$415$	−13.9056	−	24.0852i	−0.682600	−	1.18230i
$416$	−0.309697	+	0.536411i	−0.0151841	+	0.0262997i
$417$	−1.06803	+	1.84989i	−0.0523018	+	0.0905894i
$418$	−16.9388	−	29.3388i	−0.828503	−	1.43501i
$419$	−1.66548			−0.0813640			−0.0406820	−	0.999172i	$-0.512953\pi$
$419$	−1.66548			−0.0813640			−0.0406820	+	0.999172i	$0.512953\pi$
$420$	5.15562	+	8.92979i	0.251568	+	0.435729i
$421$	4.61887			0.225110			0.112555	−	0.993645i	$-0.464097\pi$
$421$	4.61887			0.225110			0.112555	+	0.993645i	$0.464097\pi$
$422$	8.58471	+	14.8691i	0.417897	+	0.723819i
$423$	3.06803	−	5.31399i	0.149173	−	0.258375i
$424$	−0.948639	+	1.64309i	−0.0460700	+	0.0797956i
$425$	6.37577	+	11.0432i	0.309270	+	0.535672i
$426$	0.483327			0.0234173
$427$	−0.543550			−0.0263042
$428$	11.1361			0.538282
$429$	−1.24695	−	2.15978i	−0.0602034	−	0.104275i
$430$	3.89728	−	6.75028i	0.187943	−	0.325528i
$431$	16.4337	−	28.4640i	0.791582	−	1.37106i	−0.133404	−	0.991062i	$-0.542591\pi$
$431$	16.4337	−	28.4640i	0.791582	−	1.37106i	0.924987	−	0.379999i	$-0.124076\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	21.0079			1.00957			0.504787	−	0.863244i	$-0.331571\pi$
$433$	21.0079			1.00957			0.504787	+	0.863244i	$0.331571\pi$
$434$	6.86411	−	11.8890i	0.329488	−	0.570690i
$435$	36.6888			1.75909
$436$	−0.683933	−	1.18461i	−0.0327545	−	0.0567324i
$437$	4.20698	−	7.28670i	0.201247	−	0.348570i
$438$	−1.57772	+	2.73269i	−0.0753863	+	0.130573i
$439$	3.93502	+	6.81566i	0.187808	+	0.325294i	0.944519	−	0.328456i	$-0.106528\pi$
$439$	3.93502	+	6.81566i	0.187808	+	0.325294i	−0.756711	+	0.653750i	$0.773195\pi$
$440$	−15.6918			−0.748079
$441$	−3.50000	+	6.06218i	−0.166667	+	0.288675i
$442$	−0.775189			−0.0368720
$443$	−8.27806	−	14.3380i	−0.393303	−	0.681220i	0.599580	−	0.800315i	$-0.295334\pi$
$443$	−8.27806	−	14.3380i	−0.393303	−	0.681220i	−0.992883	+	0.119094i	$0.962001\pi$
$444$	0.690303	−	1.19564i	0.0327603	−	0.0567426i
$445$	−19.8927	+	34.4552i	−0.943005	+	1.63333i
$446$	−4.69711	−	8.13564i	−0.222415	−	0.385234i
$447$	−11.8218			−0.559152
$448$	−1.32288	+	2.29129i	−0.0625000	+	0.108253i
$449$	−10.4272			−0.492090			−0.246045	−	0.969258i	$-0.579131\pi$
$449$	−10.4272			−0.492090			−0.246045	+	0.969258i	$0.579131\pi$
$450$	5.09439	+	8.82374i	0.240152	+	0.415955i
$451$	8.88607	−	15.3911i	0.418429	−	0.724740i
$452$	−9.87908	+	17.1111i	−0.464673	+	0.804837i
$453$	4.71684	+	8.16981i	0.221616	+	0.383851i
$454$	−25.3179			−1.18823
$455$	−6.38672			−0.299414
$456$	−8.41395			−0.394019
$457$	−12.9041	−	22.3505i	−0.603628	−	1.04551i	−0.992267	−	0.124124i	$-0.960388\pi$
$457$	−12.9041	−	22.3505i	−0.603628	−	1.04551i	0.388639	−	0.921390i	$-0.372945\pi$
$458$	−5.98001	+	10.3577i	−0.279428	+	0.483983i
$459$	−0.625764	+	1.08385i	−0.0292081	+	0.0505900i
$460$	−1.94864	−	3.37514i	−0.0908558	−	0.157367i
$461$	−19.1660			−0.892650			−0.446325	−	0.894871i	$-0.647267\pi$
$461$	−19.1660			−0.892650			−0.446325	+	0.894871i	$0.647267\pi$
$462$	−5.32637	−	9.22554i	−0.247805	−	0.429211i
$463$	11.6891			0.543240			0.271620	−	0.962405i	$-0.412441\pi$
$463$	11.6891			0.543240			0.271620	+	0.962405i	$0.412441\pi$
$464$	4.70698	+	8.15272i	0.218516	+	0.378481i
$465$	10.1111	−	17.5129i	0.468889	−	0.812140i
$466$	−4.43215	+	7.67670i	−0.205315	+	0.355616i
$467$	−0.418788	−	0.725362i	−0.0193792	−	0.0335657i	0.856173	−	0.516689i	$-0.172836\pi$
$467$	−0.418788	−	0.725362i	−0.0193792	−	0.0335657i	−0.875552	+	0.483123i	$0.839502\pi$
$468$	−0.619394			−0.0286315
$469$	−15.9442	−	27.6162i	−0.736237	−	1.27520i
$470$	23.9140			1.10307
$471$	1.89091	+	3.27515i	0.0871285	+	0.150911i
$472$	5.50986	−	9.54336i	0.253612	−	0.439269i
$473$	−4.02636	+	6.97386i	−0.185132	+	0.320658i
$474$	−7.73683	−	13.4006i	−0.355364	−	0.615509i
$475$	−85.7279			−3.93347
$476$	−3.31123			−0.151770
$477$	−1.89728			−0.0868704
$478$	4.96531	+	8.60017i	0.227108	+	0.393363i
$479$	−1.79302	+	3.10561i	−0.0819254	+	0.141899i	−0.904077	−	0.427370i	$-0.859440\pi$
$479$	−1.79302	+	3.10561i	−0.0819254	+	0.141899i	0.822152	+	0.569269i	$0.192774\pi$
$480$	−1.94864	+	3.37514i	−0.0889428	+	0.154053i
$481$	0.427570	+	0.740572i	0.0194955	+	0.0337672i
$482$	12.2840			0.559521
$483$	1.32288	−	2.29129i	0.0601929	−	0.104257i
$484$	5.21155			0.236889
$485$	−23.4871	−	40.6808i	−1.06649	−	1.84722i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	7.51803	−	13.0216i	0.340674	−	0.590065i	−0.643884	−	0.765123i	$-0.722678\pi$
$487$	7.51803	−	13.0216i	0.340674	−	0.590065i	0.984558	+	0.175058i	$0.0560113\pi$
$488$	−0.102721	−	0.177918i	−0.00464997	−	0.00805399i
$489$	−4.48333			−0.202743
$490$	−27.2810			−1.23243
$491$	−6.13302			−0.276779			−0.138390	−	0.990378i	$-0.544193\pi$
$491$	−6.13302			−0.276779			−0.138390	+	0.990378i	$0.544193\pi$
$492$	−2.20698	−	3.82259i	−0.0994982	−	0.172336i
$493$	−5.89091	+	10.2034i	−0.265313	+	0.459536i
$494$	2.60578	−	4.51334i	0.117239	−	0.203065i
$495$	−7.84592	−	13.5895i	−0.352648	−	0.610804i
$496$	5.18878			0.232983
$497$	−0.639382	+	1.10744i	−0.0286802	+	0.0496755i
$498$	7.13607			0.319775
$499$	10.7463	+	18.6131i	0.481068	+	0.833235i	0.999764	−	0.0217242i	$-0.00691557\pi$
$499$	10.7463	+	18.6131i	0.481068	+	0.833235i	−0.518696	+	0.854959i	$0.673582\pi$
$500$	−10.1111	+	17.5129i	−0.452181	+	0.783200i
$501$	8.56939	−	14.8426i	0.382852	−	0.663119i
$502$	3.40740	+	5.90179i	0.152080	+	0.263410i
$503$	−14.0922			−0.628339			−0.314169	−	0.949367i	$-0.601726\pi$
$503$	−14.0922			−0.628339			−0.314169	+	0.949367i	$0.601726\pi$
$504$	−2.64575			−0.117851
$505$	−39.7085			−1.76701
$506$	2.01318	+	3.48693i	0.0894967	+	0.155013i
$507$	−6.30818	+	10.9261i	−0.280156	+	0.485244i
$508$	7.71684	−	13.3660i	0.342379	−	0.593019i
$509$	−5.97875	−	10.3555i	−0.265003	−	0.458999i	0.702561	−	0.711623i	$-0.252040\pi$
$509$	−5.97875	−	10.3555i	−0.265003	−	0.458999i	−0.967565	+	0.252624i	$0.918706\pi$
$510$	−4.87755			−0.215982
$511$	−4.17425	−	7.23001i	−0.184658	−	0.319837i
$512$	−1.00000			−0.0441942
$513$	−4.20698	−	7.28670i	−0.185743	−	0.321715i
$514$	−11.7500	+	20.3516i	−0.518271	+	0.897671i
$515$	−13.5566	+	23.4808i	−0.597377	+	1.03469i
$516$	1.00000	+	1.73205i	0.0440225	+	0.0762493i
$517$	−24.7060			−1.08657
$518$	1.82637	+	3.16337i	0.0802461	+	0.138990i
$519$	2.84456			0.124863
$520$	−1.20698	−	2.09054i	−0.0529294	−	0.0916764i
$521$	−11.1888	+	19.3795i	−0.490189	+	0.849033i	−0.999936	−	0.0112915i	$-0.996406\pi$
$521$	−11.1888	+	19.3795i	−0.490189	+	0.849033i	0.509747	+	0.860324i	$0.329739\pi$
$522$	−4.70698	+	8.15272i	−0.206019	+	0.356835i
$523$	−7.63301	−	13.2208i	−0.333768	−	0.578104i	0.649479	−	0.760379i	$-0.274987\pi$
$523$	−7.63301	−	13.2208i	−0.333768	−	0.578104i	−0.983247	+	0.182276i	$0.941654\pi$
$524$	20.8942			0.912769
$525$	−26.9570			−1.17650
$526$	−18.8534			−0.822046
$527$	3.24695	+	5.62388i	0.141439	+	0.244980i
$528$	2.01318	−	3.48693i	0.0876124	−	0.151749i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−3.69711	−	6.40359i	−0.160592	−	0.278154i
$531$	11.0197			0.478215
$532$	11.1306	−	19.2788i	0.482573	−	0.835841i
$533$	2.73398			0.118422
$534$	−5.10425	−	8.84083i	−0.220883	−	0.382580i
$535$	−21.7002	+	37.5858i	−0.938181	+	1.62498i
$536$	6.02636	−	10.4380i	0.260299	−	0.450851i
$537$	6.63912	+	11.4993i	0.286499	+	0.496231i
$538$	26.7976			1.15533
$539$	28.1845			1.21399
$540$	−3.89728			−0.167712
$541$	−2.39576	−	4.14957i	−0.103002	−	0.178404i	0.809918	−	0.586543i	$-0.199511\pi$
$541$	−2.39576	−	4.14957i	−0.103002	−	0.178404i	−0.912920	+	0.408139i	$0.866178\pi$
$542$	−14.2401	+	24.6646i	−0.611666	+	1.05944i
$543$	7.25332	−	12.5631i	0.311270	−	0.539135i
$544$	−0.625764	−	1.08385i	−0.0268294	−	0.0464699i
$545$	5.33096			0.228353
$546$	0.819381	−	1.41921i	0.0350663	−	0.0607366i
$547$	20.5888			0.880312			0.440156	−	0.897921i	$-0.354923\pi$
$547$	20.5888			0.880312			0.440156	+	0.897921i	$0.354923\pi$
$548$	−3.18699	−	5.52003i	−0.136141	−	0.235804i
$549$	0.102721	−	0.177918i	0.00438404	−	0.00759338i
$550$	20.5118	−	35.5275i	0.874628	−	1.51490i
$551$	−39.6043	−	68.5966i	−1.68720	−	2.92231i
$552$	1.00000			0.0425628
$553$	40.9394			1.74092
$554$	−19.3969			−0.824097
$555$	2.69030	+	4.65974i	0.114197	+	0.197795i
$556$	1.06803	−	1.84989i	0.0452947	−	0.0784527i
$557$	−13.3490	+	23.1211i	−0.565614	+	0.979672i	0.431378	+	0.902171i	$0.358027\pi$
$557$	−13.3490	+	23.1211i	−0.565614	+	0.979672i	−0.996992	+	0.0775012i	$0.975306\pi$
$558$	2.59439	+	4.49362i	0.109829	+	0.190230i
$559$	−1.23879			−0.0523952
$560$	−5.15562	−	8.92979i	−0.217865	−	0.377352i
$561$	5.03910			0.212751
$562$	11.1952	+	19.3906i	0.472239	+	0.817942i
$563$	−10.5035	+	18.1926i	−0.442670	+	0.766726i	−0.997887	−	0.0649794i	$-0.979302\pi$
$563$	−10.5035	+	18.1926i	−0.442670	+	0.766726i	0.555217	+	0.831705i	$0.312635\pi$
$564$	−3.06803	+	5.31399i	−0.129188	+	0.223759i
$565$	−38.5015	−	66.6866i	−1.61977	−	2.80553i
$566$	10.0395			0.421990
$567$	−1.32288	−	2.29129i	−0.0555556	−	0.0962250i
$568$	−0.483327			−0.0202800
$569$	8.16905	+	14.1492i	0.342465	+	0.593166i	0.984890	−	0.173182i	$-0.0554050\pi$
$569$	8.16905	+	14.1492i	0.342465	+	0.593166i	−0.642425	+	0.766348i	$0.722072\pi$
$570$	16.3958	−	28.3983i	0.686743	−	1.18947i
$571$	1.52484	−	2.64109i	0.0638124	−	0.110526i	−0.832354	−	0.554244i	$-0.813007\pi$
$571$	1.52484	−	2.64109i	0.0638124	−	0.110526i	0.896167	+	0.443718i	$0.146341\pi$
$572$	1.24695	+	2.15978i	0.0521376	+	0.0903050i
$573$	15.2419			0.636738
$574$	11.6782			0.487439
$575$	10.1888			0.424902
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−1.94694	+	3.37220i	−0.0810521	+	0.140386i	−0.903702	−	0.428162i	$-0.859161\pi$
$577$	−1.94694	+	3.37220i	−0.0810521	+	0.140386i	0.822650	+	0.568548i	$0.192495\pi$
$578$	−7.71684	+	13.3660i	−0.320978	+	0.555951i
$579$	5.97500	+	10.3490i	0.248312	+	0.430090i
$580$	−36.6888			−1.52342
$581$	−9.44013	+	16.3508i	−0.391643	+	0.678345i
$582$	12.0531			0.499616
$583$	3.81956	+	6.61567i	0.158190	+	0.273993i
$584$	1.57772	−	2.73269i	0.0652864	−	0.113079i
$585$	1.20698	−	2.09054i	0.0499023	−	0.0864333i
$586$	−12.5114	−	21.6704i	−0.516841	−	0.895195i
$587$	−36.4701			−1.50528			−0.752641	−	0.658431i	$-0.771220\pi$
$587$	−36.4701			−1.50528			−0.752641	+	0.658431i	$0.771220\pi$
$588$	3.50000	−	6.06218i	0.144338	−	0.250000i
$589$	−43.6582			−1.79890
$590$	21.4735	+	37.1931i	0.884049	+	1.53122i
$591$	−9.26955	+	16.0553i	−0.381298	+	0.660428i
$592$	−0.690303	+	1.19564i	−0.0283713	+	0.0491405i
$593$	13.4733	+	23.3364i	0.553282	+	0.958312i	0.998035	+	0.0626592i	$0.0199581\pi$
$593$	13.4733	+	23.3364i	0.553282	+	0.958312i	−0.444753	+	0.895653i	$0.646709\pi$
$594$	4.02636			0.165203
$595$	6.45239	−	11.1759i	0.264522	−	0.458166i
$596$	11.8218			0.484240
$597$	−4.45876	−	7.72280i	−0.182485	−	0.316073i
$598$	−0.309697	+	0.536411i	−0.0126645	+	0.0219355i
$599$	19.6253	−	33.9921i	0.801869	−	1.38888i	−0.116515	−	0.993189i	$-0.537172\pi$
$599$	19.6253	−	33.9921i	0.801869	−	1.38888i	0.918384	−	0.395690i	$-0.129494\pi$
$600$	−5.09439	−	8.82374i	−0.207978	−	0.360228i
$601$	−7.94999			−0.324287			−0.162143	−	0.986767i	$-0.551841\pi$
$601$	−7.94999			−0.324287			−0.162143	+	0.986767i	$0.551841\pi$
$602$	−5.29150			−0.215666
$603$	12.0527			0.490824
$604$	−4.71684	−	8.16981i	−0.191925	−	0.332425i
$605$	−10.1554	+	17.5897i	−0.412877	+	0.715124i
$606$	5.09439	−	8.82374i	0.206945	−	0.358440i
$607$	−9.06106	−	15.6942i	−0.367777	−	0.637008i	0.621441	−	0.783461i	$-0.286548\pi$
$607$	−9.06106	−	15.6942i	−0.367777	−	0.637008i	−0.989218	+	0.146453i	$0.953214\pi$
$608$	8.41395			0.341231
$609$	−12.4535	−	21.5701i	−0.504641	−	0.874063i
$610$	0.800667			0.0324181
$611$	−1.90032	−	3.29145i	−0.0768788	−	0.133158i
$612$	0.625764	−	1.08385i	0.0252950	−	0.0438122i
$613$	19.3328	−	33.4853i	0.780842	−	1.35246i	−0.150609	−	0.988593i	$-0.548123\pi$
$613$	19.3328	−	33.4853i	0.780842	−	1.35246i	0.931452	−	0.363865i	$-0.118543\pi$
$614$	−13.8111	−	23.9214i	−0.557369	−	0.965391i
$615$	17.2024			0.693668
$616$	5.32637	+	9.22554i	0.214606	+	0.371708i
$617$	11.9509			0.481124			0.240562	−	0.970634i	$-0.422668\pi$
$617$	11.9509			0.481124			0.240562	+	0.970634i	$0.422668\pi$
$618$	−3.47849	−	6.02492i	−0.139925	−	0.242358i
$619$	7.46513	−	12.9300i	0.300049	−	0.519700i	−0.676098	−	0.736812i	$-0.736330\pi$
$619$	7.46513	−	12.9300i	0.300049	−	0.519700i	0.976147	+	0.217112i	$0.0696636\pi$
$620$	−10.1111	+	17.5129i	−0.406070	+	0.703334i
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$	−12.8337			−0.514583
$623$	27.0092			1.08210
$624$	0.619394			0.0247956
$625$	−13.9337	−	24.1338i	−0.557347	−	0.965354i
$626$	−5.66530	+	9.81259i	−0.226431	+	0.392190i
$627$	−16.9388	+	29.3388i	−0.676470	+	1.17168i
$628$	−1.89091	−	3.27515i	−0.0754555	−	0.130693i
$629$	−1.72787			−0.0688945
$630$	5.15562	−	8.92979i	0.205405	−	0.355771i
$631$	27.8917			1.11035			0.555176	−	0.831733i	$-0.312651\pi$
$631$	27.8917			1.11035			0.555176	+	0.831733i	$0.312651\pi$
$632$	7.73683	+	13.4006i	0.307754	+	0.533046i
$633$	8.58471	−	14.8691i	0.341211	−	0.590996i
$634$	14.5099	−	25.1318i	0.576260	−	0.998112i
$635$	30.0747	+	52.0909i	1.19348	+	2.06716i
$636$	1.89728			0.0752320
$637$	2.16788	+	3.75488i	0.0858945	+	0.148774i
$638$	37.9039			1.50063
$639$	−0.241664	−	0.418574i	−0.00956006	−	0.0165585i
$640$	1.94864	−	3.37514i	0.0770267	−	0.133414i
$641$	−12.9770	+	22.4768i	−0.512559	+	0.887779i	0.487334	+	0.873215i	$0.337969\pi$
$641$	−12.9770	+	22.4768i	−0.512559	+	0.887779i	−0.999894	+	0.0145637i	$0.995364\pi$
$642$	−5.56803	−	9.64412i	−0.219753	−	0.380623i
$643$	49.0759			1.93536			0.967682	−	0.252175i	$-0.0811459\pi$
$643$	49.0759			1.93536			0.967682	+	0.252175i	$0.0811459\pi$
$644$	−1.32288	+	2.29129i	−0.0521286	+	0.0902894i
$645$	−7.79456			−0.306910
$646$	5.26515	+	9.11950i	0.207154	+	0.358802i
$647$	−9.15714	+	15.8606i	−0.360004	+	0.623546i	−0.987961	−	0.154703i	$-0.950558\pi$
$647$	−9.15714	+	15.8606i	−0.360004	+	0.623546i	0.627957	+	0.778248i	$0.283891\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−22.1847	−	38.4250i	−0.870825	−	1.50831i
$650$	6.31087			0.247533
$651$	−13.7282			−0.538052
$652$	4.48333			0.175581
$653$	0.584527	+	1.01243i	0.0228743	+	0.0396195i	0.877236	−	0.480059i	$-0.159385\pi$
$653$	0.584527	+	1.01243i	0.0228743	+	0.0396195i	−0.854362	+	0.519679i	$0.826052\pi$
$654$	−0.683933	+	1.18461i	−0.0267439	+	0.0463218i
$655$	−40.7153	+	70.5210i	−1.59088	+	2.75548i
$656$	2.20698	+	3.82259i	0.0861679	+	0.149247i
$657$	3.15544			0.123105
$658$	−8.11725	−	14.0595i	−0.316443	−	0.548096i
$659$	−4.40121			−0.171447			−0.0857234	−	0.996319i	$-0.527320\pi$
$659$	−4.40121			−0.171447			−0.0857234	+	0.996319i	$0.527320\pi$
$660$	7.84592	+	13.5895i	0.305402	+	0.528972i
$661$	−5.64091	+	9.77035i	−0.219406	+	0.380023i	−0.954627	−	0.297805i	$-0.903745\pi$
$661$	−5.64091	+	9.77035i	−0.219406	+	0.380023i	0.735220	+	0.677828i	$0.237079\pi$
$662$	14.5512	−	25.2034i	0.565548	−	0.979558i
$663$	0.387594	+	0.671333i	0.0150529	+	0.0260724i
$664$	−7.13607			−0.276933
$665$	43.3791	+	75.1348i	1.68217	+	2.91360i
$666$	−1.38061			−0.0534974
$667$	4.70698	+	8.15272i	0.182255	+	0.315675i
$668$	−8.56939	+	14.8426i	−0.331560	+	0.574278i
$669$	−4.69711	+	8.13564i	−0.181601	+	0.314542i
$670$	23.4864	+	40.6796i	0.907359	+	1.57159i
$671$	−0.827185			−0.0319331
$672$	2.64575			0.102062
$673$	6.54966			0.252471			0.126235	−	0.992000i	$-0.459711\pi$
$673$	6.54966			0.252471			0.126235	+	0.992000i	$0.459711\pi$
$674$	1.27108	+	2.20157i	0.0489600	+	0.0848012i
$675$	5.09439	−	8.82374i	0.196083	−	0.339626i
$676$	6.30818	−	10.9261i	0.242622	−	0.420234i
$677$	−2.37533	−	4.11419i	−0.0912913	−	0.158121i	0.816763	−	0.576973i	$-0.195766\pi$
$677$	−2.37533	−	4.11419i	−0.0912913	−	0.158121i	−0.908055	+	0.418851i	$0.862433\pi$
$678$	19.7582			0.758808
$679$	−15.9447	+	27.6171i	−0.611902	+	1.05985i
$680$	4.87755			0.187046
$681$	12.6589	+	21.9259i	0.485091	+	0.840203i
$682$	10.4459	−	18.0929i	0.399996	−	0.692813i
$683$	−9.19471	+	15.9257i	−0.351826	+	0.609380i	−0.986569	−	0.163343i	$-0.947772\pi$
$683$	−9.19471	+	15.9257i	−0.351826	+	0.609380i	0.634744	+	0.772723i	$0.281106\pi$
$684$	4.20698	+	7.28670i	0.160858	+	0.278614i
$685$	24.8412			0.949132
$686$	9.26013	+	16.0390i	0.353553	+	0.612372i
$687$	11.9600			0.456303
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$	−0.587582	+	1.01772i	−0.0223851	+	0.0387721i
$690$	−1.94864	+	3.37514i	−0.0741834	+	0.128489i
$691$	16.2250	+	28.1025i	0.617228	+	1.06907i	0.989989	+	0.141143i	$0.0450778\pi$
$691$	16.2250	+	28.1025i	0.617228	+	1.06907i	−0.372761	+	0.927927i	$0.621589\pi$
$692$	−2.84456			−0.108134
$693$	−5.32637	+	9.22554i	−0.202332	+	0.350449i
$694$	−20.3776			−0.773522
$695$	4.16242	+	7.20953i	0.157890	+	0.273473i
$696$	4.70698	−	8.15272i	0.178417	−	0.309028i
$697$	−2.76209	+	4.78408i	−0.104622	+	0.181210i
$698$	2.81938	+	4.88331i	0.106715	+	0.184836i
$699$	8.86429			0.335278
$700$	26.9570			1.01888
$701$	−33.9894			−1.28376			−0.641882	−	0.766804i	$-0.721846\pi$
$701$	−33.9894			−1.28376			−0.641882	+	0.766804i	$0.721846\pi$
$702$	0.309697	+	0.536411i	0.0116888	+	0.0202455i
$703$	5.80818	−	10.0601i	0.219059	−	0.379422i
$704$	−2.01318	+	3.48693i	−0.0758745	+	0.131419i
$705$	−11.9570	−	20.7101i	−0.450326	−	0.779987i
$706$	4.69759			0.176796
$707$	13.4785	+	23.3454i	0.506911	+	0.877995i
$708$	−11.0197			−0.414147
$709$	8.33122	+	14.4301i	0.312885	+	0.541934i	0.978986	−	0.203929i	$-0.0653711\pi$
$709$	8.33122	+	14.4301i	0.312885	+	0.541934i	−0.666100	+	0.745862i	$0.732038\pi$
$710$	0.941830	−	1.63130i	0.0353463	−	0.0612215i
$711$	−7.73683	+	13.4006i	−0.290154	+	0.502561i
$712$	5.10425	+	8.84083i	0.191290	+	0.331324i
$713$	5.18878			0.194321
$714$	1.65562	+	2.86761i	0.0619598	+	0.107318i
$715$	−9.71943			−0.363486
$716$	−6.63912	−	11.4993i	−0.248116	−	0.429749i
$717$	4.96531	−	8.60017i	0.185433	−	0.321179i
$718$	−14.2151	+	24.6213i	−0.530504	+	0.918860i
$719$	16.5966	+	28.7462i	0.618950	+	1.07205i	0.989678	+	0.143311i	$0.0457748\pi$
$719$	16.5966	+	28.7462i	0.618950	+	1.07205i	−0.370728	+	0.928741i	$0.620892\pi$
$720$	3.89728			0.145243
$721$	18.4064			0.685492
$722$	−51.7946			−1.92759
$723$	−6.14200	−	10.6383i	−0.228423	−	0.395641i
$724$	−7.25332	+	12.5631i	−0.269568	+	0.466905i
$725$	47.9583	−	83.0663i	1.78113	−	3.08500i
$726$	−2.60578	−	4.51334i	−0.0967094	−	0.167506i
$727$	27.3991			1.01618			0.508089	−	0.861305i	$-0.330352\pi$
$727$	27.3991			1.01618			0.508089	+	0.861305i	$0.330352\pi$
$728$	−0.819381	+	1.41921i	−0.0303683	+	0.0525994i
$729$	1.00000			0.0370370
$730$	6.14881	+	10.6500i	0.227578	+	0.394176i
$731$	1.25153	−	2.16771i	0.0462894	−	0.0801756i
$732$	−0.102721	+	0.177918i	−0.00379669	+	0.00657606i
$733$	0.549400	+	0.951588i	0.0202925	+	0.0351477i	0.875993	−	0.482323i	$-0.160207\pi$
$733$	0.549400	+	0.951588i	0.0202925	+	0.0351477i	−0.855701	+	0.517471i	$0.826874\pi$
$734$	6.27177			0.231495
$735$	13.6405	+	23.6260i	0.503137	+	0.871458i
$736$	−1.00000			−0.0368605
$737$	−24.2643	−	42.0269i	−0.893786	−	1.54808i
$738$	−2.20698	+	3.82259i	−0.0812399	+	0.140712i
$739$	24.7568	−	42.8801i	0.910695	−	1.57737i	0.0976092	−	0.995225i	$-0.468880\pi$
$739$	24.7568	−	42.8801i	0.910695	−	1.57737i	0.813085	−	0.582144i	$-0.197786\pi$
$740$	−2.69030	−	4.65974i	−0.0988975	−	0.171295i
$741$	−5.21155			−0.191451
$742$	−2.50986	+	4.34721i	−0.0921400	+	0.159591i
$743$	10.6054			0.389075			0.194538	−	0.980895i	$-0.437679\pi$
$743$	10.6054			0.389075			0.194538	+	0.980895i	$0.437679\pi$
$744$	−2.59439	−	4.49362i	−0.0951150	−	0.164744i
$745$	−23.0364	+	39.9002i	−0.843989	+	1.46183i
$746$	−3.13698	+	5.43341i	−0.114853	+	0.198931i
$747$	−3.56803	−	6.18002i	−0.130548	−	0.226115i
$748$	−5.03910			−0.184248
$749$	29.4633			1.07656
$750$	20.2221			0.738408
$751$	2.08928	+	3.61874i	0.0762390	+	0.132050i	0.901624	−	0.432520i	$-0.142375\pi$
$751$	2.08928	+	3.61874i	0.0762390	+	0.132050i	−0.825385	+	0.564570i	$0.809042\pi$
$752$	3.06803	−	5.31399i	0.111880	−	0.193781i
$753$	3.40740	−	5.90179i	0.124173	−	0.215073i
$754$	2.91547	+	5.04975i	0.106175	+	0.183901i
$755$	36.7657			1.33804
$756$	1.32288	+	2.29129i	0.0481125	+	0.0833333i
$757$	−18.0758			−0.656978			−0.328489	−	0.944508i	$-0.606539\pi$
$757$	−18.0758			−0.656978			−0.328489	+	0.944508i	$0.606539\pi$
$758$	−14.1124	−	24.4434i	−0.512586	−	0.887825i
$759$	2.01318	−	3.48693i	0.0730738	−	0.126567i
$760$	−16.3958	+	28.3983i	−0.594737	+	1.03011i
$761$	1.90884	+	3.30621i	0.0691955	+	0.119850i	0.898547	−	0.438876i	$-0.144623\pi$
$761$	1.90884	+	3.30621i	0.0691955	+	0.119850i	−0.829352	+	0.558727i	$0.811290\pi$
$762$	−15.4337			−0.559103
$763$	−1.80952	−	3.13418i	−0.0655089	−	0.113465i
$764$	−15.2419			−0.551431
$765$	2.43878	+	4.22408i	0.0881741	+	0.152722i
$766$	4.72329	−	8.18098i	0.170659	−	0.295591i
$767$	3.41278	−	5.91110i	0.123228	−	0.213438i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	11.4105			0.411475			0.205737	−	0.978607i	$-0.434041\pi$
$769$	11.4105			0.411475			0.205737	+	0.978607i	$0.434041\pi$
$770$	−41.5167			−1.49616
$771$	23.5000			0.846332
$772$	−5.97500	−	10.3490i	−0.215045	−	0.372469i
$773$	−12.8279	+	22.2186i	−0.461388	+	0.799147i	−0.999030	−	0.0440259i	$-0.985982\pi$
$773$	−12.8279	+	22.2186i	−0.461388	+	0.799147i	0.537643	+	0.843173i	$0.319315\pi$
$774$	1.00000	−	1.73205i	0.0359443	−	0.0622573i
$775$	−26.4337	−	45.7845i	−0.949526	−	1.64463i
$776$	−12.0531			−0.432680
$777$	1.82637	−	3.16337i	0.0655207	−	0.113485i
$778$	−5.64183			−0.202269
$779$	−18.5694	−	32.1631i	−0.665317	−	1.15236i
$780$	−1.20698	+	2.09054i	−0.0432167	+	0.0748535i
$781$	−0.973024	+	1.68533i	−0.0348175	+	0.0603057i
$782$	−0.625764	−	1.08385i	−0.0223773	−	0.0387586i
$783$	9.41395			0.336427
$784$	−3.50000	+	6.06218i	−0.125000	+	0.216506i
$785$	14.7388			0.526050
$786$	−10.4471	−	18.0949i	−0.372636	−	0.645425i
$787$	−17.8152	+	30.8568i	−0.635042	+	1.09993i	0.351464	+	0.936201i	$0.385684\pi$
$787$	−17.8152	+	30.8568i	−0.635042	+	1.09993i	−0.986506	+	0.163724i	$0.947649\pi$
$788$	9.26955	−	16.0553i	0.330214	−	0.571948i
$789$	9.42669	+	16.3275i	0.335599	+	0.581275i
$790$	−60.3051			−2.14556
$791$	−26.1376	+	45.2717i	−0.929346	+	1.60967i
$792$	−4.02636			−0.143070
$793$	−0.0636250	−	0.110202i	−0.00225939	−	0.00391338i
$794$	−16.3694	+	28.3526i	−0.580928	+	1.00620i
$795$	−3.69711	+	6.40359i	−0.131123	+	0.227112i
$796$	4.45876	+	7.72280i	0.158037	+	0.273728i
$797$	37.7840			1.33838			0.669189	−	0.743092i	$-0.266642\pi$
$797$	37.7840			1.33838			0.669189	+	0.743092i	$0.266642\pi$
$798$	−22.2612			−0.788039
$799$	7.67946			0.271680
$800$	5.09439	+	8.82374i	0.180114	+	0.311966i
$801$	−5.10425	+	8.84083i	−0.180350	+	0.312375i
$802$	−4.94245	+	8.56057i	−0.174524	+	0.302284i
$803$	−6.35246	−	11.0028i	−0.224173	−	0.388280i
$804$	−12.0527			−0.425066
$805$	−5.15562	−	8.92979i	−0.181712	−	0.314734i
$806$	3.21390			0.113205
$807$	−13.3988	−	23.2074i	−0.471661	−	0.816940i
$808$	−5.09439	+	8.82374i	−0.179220	+	0.310418i
$809$	−6.78998	+	11.7606i	−0.238723	+	0.413480i	−0.960348	−	0.278804i	$-0.910062\pi$
$809$	−6.78998	+	11.7606i	−0.238723	+	0.413480i	0.721625	+	0.692284i	$0.243395\pi$
$810$	1.94864	+	3.37514i	0.0684682	+	0.118590i
$811$	46.7245			1.64072			0.820359	−	0.571848i	$-0.193773\pi$
$811$	46.7245			1.64072			0.820359	+	0.571848i	$0.193773\pi$
$812$	12.4535	+	21.5701i	0.437032	+	0.756961i
$813$	28.4803			0.998847
$814$	2.77941	+	4.81407i	0.0974181	+	0.168733i
$815$	−8.73639	+	15.1319i	−0.306022	+	0.530046i
$816$	−0.625764	+	1.08385i	−0.0219061	+	0.0379425i
$817$	8.41395	+	14.5734i	0.294367	+	0.509858i
$818$	25.1061			0.877816
$819$	−1.63876			−0.0572630
$820$	−17.2024			−0.600734
$821$	−17.2961	−	29.9577i	−0.603638	−	1.04553i	−0.992265	−	0.124136i	$-0.960384\pi$
$821$	−17.2961	−	29.9577i	−0.603638	−	1.04553i	0.388627	−	0.921395i	$-0.372949\pi$
$822$	−3.18699	+	5.52003i	−0.111159	+	0.192533i
$823$	−20.7121	+	35.8744i	−0.721978	+	1.25050i	0.238228	+	0.971209i	$0.423433\pi$
$823$	−20.7121	+	35.8744i	−0.721978	+	1.25050i	−0.960206	+	0.279293i	$0.909900\pi$
$824$	3.47849	+	6.02492i	0.121179	+	0.209888i
$825$	−41.0237			−1.42826
$826$	14.5777	−	25.2494i	0.507224	−	0.878538i
$827$	50.4046			1.75274			0.876370	−	0.481638i	$-0.159958\pi$
$827$	50.4046			1.75274			0.876370	+	0.481638i	$0.159958\pi$
$828$	−0.500000	−	0.866025i	−0.0173762	−	0.0300965i
$829$	22.3578	−	38.7249i	0.776520	−	1.34497i	−0.157417	−	0.987532i	$-0.550317\pi$
$829$	22.3578	−	38.7249i	0.776520	−	1.34497i	0.933936	−	0.357439i	$-0.116350\pi$
$830$	13.9056	−	24.0852i	0.482671	−	0.836011i
$831$	9.69847	+	16.7982i	0.336436	+	0.582724i
$832$	−0.619394			−0.0214736
$833$	−8.76069			−0.303540
$834$	−2.13607			−0.0739659
$835$	−33.3973	−	57.8458i	−1.15576	−	2.00184i
$836$	16.9388	−	29.3388i	0.585840	−	1.01470i
$837$	2.59439	−	4.49362i	0.0896753	−	0.155322i
$838$	−0.832739	−	1.44235i	−0.0287665	−	0.0498251i
$839$	24.1691			0.834408			0.417204	−	0.908813i	$-0.363010\pi$
$839$	24.1691			0.834408			0.417204	+	0.908813i	$0.363010\pi$
$840$	−5.15562	+	8.92979i	−0.177886	+	0.308107i
$841$	59.6225			2.05595
$842$	2.30944	+	4.00006i	0.0795885	+	0.137851i
$843$	11.1952	−	19.3906i	0.385581	−	0.667847i
$844$	−8.58471	+	14.8691i	−0.295498	+	0.511817i
$845$	24.5847	+	42.5820i	0.845740	+	1.46486i
$846$	6.13607			0.210962
$847$	13.7885			0.473777
$848$	−1.89728			−0.0651528
$849$	−5.01973	−	8.69442i	−0.172277	−	0.298392i
$850$	−6.37577	+	11.0432i	−0.218687	+	0.378777i
$851$	−0.690303	+	1.19564i	−0.0236633	+	0.0409860i
$852$	0.241664	+	0.418574i	0.00827926	+	0.0143401i
$853$	−17.3969			−0.595660			−0.297830	−	0.954619i	$-0.596263\pi$
$853$	−17.3969			−0.595660			−0.297830	+	0.954619i	$0.596263\pi$
$854$	−0.271775	−	0.470728i	−0.00929995	−	0.0161080i
$855$	−32.7915			−1.12145
$856$	5.56803	+	9.64412i	0.190311	+	0.329629i
$857$	17.4918	−	30.2968i	0.597510	−	1.03492i	−0.395677	−	0.918390i	$-0.629490\pi$
$857$	17.4918	−	30.2968i	0.597510	−	1.03492i	0.993187	−	0.116528i	$-0.0371766\pi$
$858$	1.24695	−	2.15978i	0.0425702	−	0.0737338i
$859$	−13.4634	−	23.3193i	−0.459366	−	0.795646i	0.539561	−	0.841946i	$-0.318590\pi$
$859$	−13.4634	−	23.3193i	−0.459366	−	0.795646i	−0.998928	+	0.0463005i	$0.985257\pi$
$860$	7.79456			0.265792
$861$	−5.83911	−	10.1136i	−0.198996	−	0.344672i
$862$	32.8674			1.11947
$863$	−27.8580	−	48.2515i	−0.948298	−	1.64250i	−0.749010	−	0.662559i	$-0.769470\pi$
$863$	−27.8580	−	48.2515i	−0.948298	−	1.64250i	−0.199288	−	0.979941i	$-0.563863\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	5.54303	−	9.60081i	0.188469	−	0.326437i
$866$	10.5039	+	18.1933i	0.356938	+	0.618235i
$867$	15.4337			0.524155
$868$	13.7282			0.465966
$869$	62.3025			2.11347
$870$	18.3444	+	31.7734i	0.621933	+	1.07722i
$871$	3.73269	−	6.46521i	0.126477	−	0.219065i
$872$	0.683933	−	1.18461i	0.0231609	−	0.0401159i
$873$	−6.02654	−	10.4383i	−0.203967	−	0.353282i
$874$	8.41395			0.284606
$875$	−26.7514	+	46.3347i	−0.904361	+	1.56640i
$876$	−3.15544			−0.106612
$877$	11.3488	+	19.6567i	0.383222	+	0.663759i	0.991521	−	0.129949i	$-0.0414813\pi$
$877$	11.3488	+	19.6567i	0.383222	+	0.663759i	−0.608299	+	0.793708i	$0.708148\pi$
$878$	−3.93502	+	6.81566i	−0.132801	+	0.230017i
$879$	−12.5114	+	21.6704i	−0.421999	+	0.730924i
$880$	−7.84592	−	13.5895i	−0.264486	−	0.458103i
$881$	1.80423			0.0607861			0.0303930	−	0.999538i	$-0.490324\pi$
$881$	1.80423			0.0607861			0.0303930	+	0.999538i	$0.490324\pi$
$882$	−7.00000			−0.235702
$883$	−36.5861			−1.23122			−0.615610	−	0.788051i	$-0.711090\pi$
$883$	−36.5861			−1.23122			−0.615610	+	0.788051i	$0.711090\pi$
$884$	−0.387594	−	0.671333i	−0.0130362	−	0.0225794i
$885$	21.4735	−	37.1931i	0.721823	−	1.25023i
$886$	8.27806	−	14.3380i	0.278107	−	0.481695i
$887$	9.67041	+	16.7496i	0.324701	+	0.562398i	0.981452	−	0.191710i	$-0.0614032\pi$
$887$	9.67041	+	16.7496i	0.324701	+	0.562398i	−0.656751	+	0.754107i	$0.728070\pi$
$888$	1.38061			0.0463301
$889$	20.4168	−	35.3630i	0.684759	−	1.18604i
$890$	−39.7854			−1.33361
$891$	−2.01318	−	3.48693i	−0.0674440	−	0.116816i
$892$	4.69711	−	8.13564i	0.157271	−	0.272401i
$893$	−25.8143	+	44.7117i	−0.863842	+	1.49622i
$894$	−5.91090	−	10.2380i	−0.197690	−	0.342409i
$895$	51.7490			1.72978
$896$	−2.64575			−0.0883883
$897$	0.619394			0.0206810
$898$	−5.21361	−	9.03023i	−0.173980	−	0.301343i
$899$	24.4235	−	42.3027i	0.814568	−	1.41087i
$900$	−5.09439	+	8.82374i	−0.169813	+	0.294125i
$901$	−1.18725	−	2.05637i	−0.0395530	−	0.0685078i
$902$	17.7721			0.591748
$903$	2.64575	+	4.58258i	0.0880451	+	0.152499i
$904$	−19.7582			−0.657147
$905$	−28.2682	−	48.9620i	−0.939667	−	1.62755i
$906$	−4.71684	+	8.16981i	−0.156706	+	0.271424i
$907$	2.79338	−	4.83828i	0.0927528	−	0.160653i	−0.815916	−	0.578171i	$-0.803767\pi$
$907$	2.79338	−	4.83828i	0.0927528	−	0.160653i	0.908668	+	0.417518i	$0.137100\pi$
$908$	−12.6589	−	21.9259i	−0.420101	−	0.727637i
$909$	−10.1888			−0.337941
$910$	−3.19336	−	5.53106i	−0.105859	−	0.183353i
$911$	−29.3170			−0.971315			−0.485657	−	0.874149i	$-0.661420\pi$
$911$	−29.3170			−0.971315			−0.485657	+	0.874149i	$0.661420\pi$
$912$	−4.20698	−	7.28670i	−0.139307	−	0.241287i
$913$	−14.3662	+	24.8829i	−0.475451	+	0.823505i
$914$	12.9041	−	22.3505i	0.426829	−	0.739290i
$915$	−0.400334	−	0.693398i	−0.0132346	−	0.0229230i
$916$	−11.9600			−0.395170
$917$	55.2810			1.82554
$918$	−1.25153			−0.0413066
$919$	12.7567	+	22.0953i	0.420806	+	0.728857i	0.996018	−	0.0891468i	$-0.0284140\pi$
$919$	12.7567	+	22.0953i	0.420806	+	0.728857i	−0.575213	+	0.818004i	$0.695081\pi$
$920$	1.94864	−	3.37514i	0.0642447	−	0.111275i
$921$	−13.8111	+	23.9214i	−0.455090	+	0.788238i
$922$	−9.58301	−	16.5983i	−0.315599	−	0.546634i
$923$	−0.299370			−0.00985388
$924$	5.32637	−	9.22554i	0.175225	−	0.303498i
$925$	14.0667			0.462510
$926$	5.84456	+	10.1231i	0.192064	+	0.332665i
$927$	−3.47849	+	6.02492i	−0.114249	+	0.197884i
$928$	−4.70698	+	8.15272i	−0.154514	+	0.267626i
$929$	2.56087	+	4.43555i	0.0840193	+	0.145526i	0.904973	−	0.425469i	$-0.139891\pi$
$929$	2.56087	+	4.43555i	0.0840193	+	0.145526i	−0.820954	+	0.570995i	$0.806558\pi$
$930$	20.2221			0.663110
$931$	29.4488	−	51.0069i	0.965146	−	1.67168i
$932$	−8.86429			−0.290360
$933$	6.41683	+	11.1143i	0.210077	+	0.363865i
$934$	0.418788	−	0.725362i	0.0137032	−	0.0237346i
$935$	9.81938	−	17.0077i	0.321128	−	0.556210i
$936$	−0.309697	−	0.536411i	−0.0101228	−	0.0175331i
$937$	−39.6816			−1.29634			−0.648171	−	0.761494i	$-0.724466\pi$
$937$	−39.6816			−1.29634			−0.648171	+	0.761494i	$0.724466\pi$
$938$	15.9442	−	27.6162i	0.520598	−	0.901702i
$939$	11.3306			0.369760
$940$	11.9570	+	20.7101i	0.389994	+	0.675489i
$941$	5.15016	−	8.92034i	0.167890	−	0.290795i	−0.769788	−	0.638300i	$-0.779638\pi$
$941$	5.15016	−	8.92034i	0.167890	−	0.290795i	0.937678	+	0.347505i	$0.112971\pi$
$942$	−1.89091	+	3.27515i	−0.0616091	+	0.106710i
$943$	2.20698	+	3.82259i	0.0718690	+	0.124481i
$944$	11.0197			0.358662
$945$	−10.3112			−0.335424
$946$	−8.05271			−0.261816
$947$	−10.1155	−	17.5205i	−0.328708	−	0.569339i	0.653548	−	0.756885i	$-0.273280\pi$
$947$	−10.1155	−	17.5205i	−0.328708	−	0.569339i	−0.982256	+	0.187546i	$0.939947\pi$
$948$	7.73683	−	13.4006i	0.251280	−	0.435231i
$949$	0.977229	−	1.69261i	0.0317222	−	0.0549445i
$950$	−42.8640	−	74.2425i	−1.39069	−	2.40875i
$951$	−29.0197			−0.941029
$952$	−1.65562	−	2.86761i	−0.0536588	−	0.0929398i
$953$	−29.4213			−0.953049			−0.476525	−	0.879161i	$-0.658104\pi$
$953$	−29.4213			−0.953049			−0.476525	+	0.879161i	$0.658104\pi$
$954$	−0.948639	−	1.64309i	−0.0307133	−	0.0531971i
$955$	29.7009	−	51.4434i	0.961098	−	1.66467i
$956$	−4.96531	+	8.60017i	−0.160590	+	0.278149i
$957$	−18.9520	−	32.8258i	−0.612630	−	1.06111i
$958$	−3.58605			−0.115860
$959$	−8.43198	−	14.6046i	−0.272283	−	0.471608i
$960$	−3.89728			−0.125784
$961$	2.03827	+	3.53039i	0.0657508	+	0.113884i
$962$	−0.427570	+	0.740572i	−0.0137854	+	0.0238770i
$963$	−5.56803	+	9.64412i	−0.179427	+	0.310777i
$964$	6.14200	+	10.6383i	0.197820	+	0.342635i
$965$	46.5725			1.49922
$966$	2.64575			0.0851257
$967$	−8.05542			−0.259045			−0.129522	−	0.991576i	$-0.541344\pi$
$967$	−8.05542			−0.259045			−0.129522	+	0.991576i	$0.541344\pi$
$968$	2.60578	+	4.51334i	0.0837528	+	0.145064i
$969$	5.26515	−	9.11950i	0.169141	−	0.292961i
$970$	23.4871	−	40.6808i	0.754125	−	1.30618i
$971$	22.5829	+	39.1148i	0.724721	+	1.25525i	0.959089	+	0.283105i	$0.0913645\pi$
$971$	22.5829	+	39.1148i	0.724721	+	1.25525i	−0.234368	+	0.972148i	$0.575302\pi$
$972$	−1.00000			−0.0320750
$973$	2.82575	−	4.89434i	0.0905894	−	0.156905i
$974$	15.0361			0.481786
$975$	−3.15544	−	5.46537i	−0.101055	−	0.175032i
$976$	0.102721	−	0.177918i	0.00328803	−	0.00569503i
$977$	−10.1949	+	17.6581i	−0.326163	+	0.564932i	−0.981747	−	0.190191i	$-0.939089\pi$
$977$	−10.1949	+	17.6581i	−0.326163	+	0.564932i	0.655584	+	0.755123i	$0.272423\pi$
$978$	−2.24166	−	3.88268i	−0.0716805	−	0.124154i
$979$	41.1031			1.31366
$980$	−13.6405	−	23.6260i	−0.435729	−	0.754705i
$981$	1.36787			0.0436726
$982$	−3.06651	−	5.31135i	−0.0978563	−	0.169492i
$983$	24.7267	−	42.8279i	0.788660	−	1.36600i	−0.138128	−	0.990414i	$-0.544109\pi$
$983$	24.7267	−	42.8279i	0.788660	−	1.36600i	0.926788	−	0.375584i	$-0.122558\pi$
$984$	2.20698	−	3.82259i	0.0703558	−	0.121860i
$985$	36.1260	+	62.5721i	1.15107	+	1.99371i
$986$	−11.7818			−0.375210
$987$	−8.11725	+	14.0595i	−0.258375	+	0.447519i
$988$	5.21155			0.165802
$989$	−1.00000	−	1.73205i	−0.0317982	−	0.0550760i
$990$	7.84592	−	13.5895i	0.249360	−	0.431904i
$991$	29.4259	−	50.9671i	0.934744	−	1.61902i	0.159654	−	0.987173i	$-0.448962\pi$
$991$	29.4259	−	50.9671i	0.934744	−	1.61902i	0.775090	−	0.631851i	$-0.217704\pi$
$992$	2.59439	+	4.49362i	0.0823720	+	0.142672i
$993$	−29.1024			−0.923536
$994$	−1.27876			−0.0405599
$995$	−34.7541			−1.10178
$996$	3.56803	+	6.18002i	0.113057	+	0.195821i
$997$	25.1709	−	43.5974i	0.797172	−	1.38074i	−0.124279	−	0.992247i	$-0.539662\pi$
$997$	25.1709	−	43.5974i	0.797172	−	1.38074i	0.921451	−	0.388495i	$-0.127005\pi$
$998$	−10.7463	+	18.6131i	−0.340167	+	0.589186i
$999$	0.690303	+	1.19564i	0.0218402	+	0.0378284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.n.277.1	✓	8
7.2	even	3	inner	966.2.i.n.415.1	yes	8
7.3	odd	6		6762.2.a.ch.1.1		4
7.4	even	3		6762.2.a.cg.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.n.277.1	✓	8	1.1	even	1	trivial
966.2.i.n.415.1	yes	8	7.2	even	3	inner
6762.2.a.cg.1.4		4	7.4	even	3
6762.2.a.ch.1.1		4	7.3	odd	6

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.94864 - 3.37514i) q^{5} +1.00000 q^{6} +(-1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.94864 - 3.37514i) q^{5} +1.00000 q^{6} +(-1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.94864 - 3.37514i) q^{10} +(-2.01318 + 3.48693i) q^{11} +(0.500000 + 0.866025i) q^{12} -0.619394 q^{13} -2.64575 q^{14} -3.89728 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.625764 - 1.08385i) q^{17} +(0.500000 - 0.866025i) q^{18} +(4.20698 + 7.28670i) q^{19} +3.89728 q^{20} +(1.32288 + 2.29129i) q^{21} -4.02636 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-5.09439 + 8.82374i) q^{25} +(-0.309697 - 0.536411i) q^{26} -1.00000 q^{27} +(-1.32288 - 2.29129i) q^{28} -9.41395 q^{29} +(-1.94864 - 3.37514i) q^{30} +(-2.59439 + 4.49362i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.01318 + 3.48693i) q^{33} +1.25153 q^{34} +10.3112 q^{35} +1.00000 q^{36} +(-0.690303 - 1.19564i) q^{37} +(-4.20698 + 7.28670i) q^{38} +(-0.309697 + 0.536411i) q^{39} +(1.94864 + 3.37514i) q^{40} -4.41395 q^{41} +(-1.32288 + 2.29129i) q^{42} +2.00000 q^{43} +(-2.01318 - 3.48693i) q^{44} +(-1.94864 + 3.37514i) q^{45} +(0.500000 - 0.866025i) q^{46} +(3.06803 + 5.31399i) q^{47} -1.00000 q^{48} +(-3.50000 - 6.06218i) q^{49} -10.1888 q^{50} +(-0.625764 - 1.08385i) q^{51} +(0.309697 - 0.536411i) q^{52} +(0.948639 - 1.64309i) q^{53} +(-0.500000 - 0.866025i) q^{54} +15.6918 q^{55} +(1.32288 - 2.29129i) q^{56} +8.41395 q^{57} +(-4.70698 - 8.15272i) q^{58} +(-5.50986 + 9.54336i) q^{59} +(1.94864 - 3.37514i) q^{60} +(0.102721 + 0.177918i) q^{61} -5.18878 q^{62} +2.64575 q^{63} +1.00000 q^{64} +(1.20698 + 2.09054i) q^{65} +(-2.01318 + 3.48693i) q^{66} +(-6.02636 + 10.4380i) q^{67} +(0.625764 + 1.08385i) q^{68} -1.00000 q^{69} +(5.15562 + 8.92979i) q^{70} +0.483327 q^{71} +(0.500000 + 0.866025i) q^{72} +(-1.57772 + 2.73269i) q^{73} +(0.690303 - 1.19564i) q^{74} +(5.09439 + 8.82374i) q^{75} -8.41395 q^{76} +(-5.32637 - 9.22554i) q^{77} -0.619394 q^{78} +(-7.73683 - 13.4006i) q^{79} +(-1.94864 + 3.37514i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.20698 - 3.82259i) q^{82} +7.13607 q^{83} -2.64575 q^{84} -4.87755 q^{85} +(1.00000 + 1.73205i) q^{86} +(-4.70698 + 8.15272i) q^{87} +(2.01318 - 3.48693i) q^{88} +(-5.10425 - 8.84083i) q^{89} -3.89728 q^{90} +(0.819381 - 1.41921i) q^{91} +1.00000 q^{92} +(2.59439 + 4.49362i) q^{93} +(-3.06803 + 5.31399i) q^{94} +(16.3958 - 28.3983i) q^{95} +(-0.500000 - 0.866025i) q^{96} +12.0531 q^{97} +(3.50000 - 6.06218i) q^{98} +4.02636 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 + 8 * q^6 - 8 * q^8 - 4 * q^9	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{15} - 4 q^{16} + 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 6 q^{25} - 2 q^{26} - 8 q^{27} - 20 q^{29} - 2 q^{30} + 14 q^{31} + 4 q^{32} + 6 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} + 16 q^{43} - 6 q^{44} - 2 q^{45} + 4 q^{46} + 10 q^{47} - 8 q^{48} - 28 q^{49} - 12 q^{50} - 2 q^{51} + 2 q^{52} - 6 q^{53} - 4 q^{54} + 44 q^{55} + 12 q^{57} - 10 q^{58} - 24 q^{59} + 2 q^{60} + 28 q^{61} + 28 q^{62} + 8 q^{64} - 18 q^{65} - 6 q^{66} - 28 q^{67} + 2 q^{68} - 8 q^{69} + 32 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 6 q^{75} - 12 q^{76} - 14 q^{77} - 4 q^{78} + 4 q^{79} - 2 q^{80} - 4 q^{81} + 10 q^{82} + 28 q^{83} - 52 q^{85} + 8 q^{86} - 10 q^{87} + 6 q^{88} + 14 q^{89} - 4 q^{90} + 14 q^{91} + 8 q^{92} - 14 q^{93} - 10 q^{94} + 34 q^{95} - 4 q^{96} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 + 8 * q^6 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^13 - 4 * q^15 - 4 * q^16 + 2 * q^17 + 4 * q^18 + 6 * q^19 + 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^24 - 6 * q^25 - 2 * q^26 - 8 * q^27 - 20 * q^29 - 2 * q^30 + 14 * q^31 + 4 * q^32 + 6 * q^33 + 4 * q^34 + 8 * q^36 - 6 * q^37 - 6 * q^38 - 2 * q^39 + 2 * q^40 + 20 * q^41 + 16 * q^43 - 6 * q^44 - 2 * q^45 + 4 * q^46 + 10 * q^47 - 8 * q^48 - 28 * q^49 - 12 * q^50 - 2 * q^51 + 2 * q^52 - 6 * q^53 - 4 * q^54 + 44 * q^55 + 12 * q^57 - 10 * q^58 - 24 * q^59 + 2 * q^60 + 28 * q^61 + 28 * q^62 + 8 * q^64 - 18 * q^65 - 6 * q^66 - 28 * q^67 + 2 * q^68 - 8 * q^69 + 32 * q^71 + 4 * q^72 - 6 * q^73 + 6 * q^74 + 6 * q^75 - 12 * q^76 - 14 * q^77 - 4 * q^78 + 4 * q^79 - 2 * q^80 - 4 * q^81 + 10 * q^82 + 28 * q^83 - 52 * q^85 + 8 * q^86 - 10 * q^87 + 6 * q^88 + 14 * q^89 - 4 * q^90 + 14 * q^91 + 8 * q^92 - 14 * q^93 - 10 * q^94 + 34 * q^95 - 4 * q^96 + 28 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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