LMFDB - Embedded newform 429.2.i.d.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3118758597603.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 $ x^10 - 4x^8 - 16x^6 - 34x^5 + 43x^4 + 155x^3 + 199x^2 + 124*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.3
Root			$-1.80582 - 0.194943i$ of defining polynomial
Character	$\chi$	$=$	429.100
Dual form			429.2.i.d.133.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.149489 - 0.258923i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.955306 + 1.65464i) q^{4} -3.44245 q^{5} +(-0.149489 - 0.258923i) q^{6} +(-2.46991 - 4.27802i) q^{7} +1.16919 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.149489 - 0.258923i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.955306 + 1.65464i) q^{4} -3.44245 q^{5} +(-0.149489 - 0.258923i) q^{6} +(-2.46991 - 4.27802i) q^{7} +1.16919 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.514608 + 0.891327i) q^{10} +(-0.500000 + 0.866025i) q^{11} +1.91061 q^{12} +(1.73845 - 3.15876i) q^{13} -1.47690 q^{14} +(-1.72122 + 2.98125i) q^{15} +(-1.73583 + 3.00655i) q^{16} +(-2.78859 - 4.82998i) q^{17} -0.298978 q^{18} +(-2.61940 - 4.53694i) q^{19} +(-3.28859 - 5.69601i) q^{20} -4.93983 q^{21} +(0.149489 + 0.258923i) q^{22} +(-1.56999 + 2.71929i) q^{23} +(0.584594 - 1.01255i) q^{24} +6.85044 q^{25} +(-0.557996 - 0.922325i) q^{26} -1.00000 q^{27} +(4.71905 - 8.17363i) q^{28} +(-1.54252 + 2.67172i) q^{29} +(0.514608 + 0.891327i) q^{30} +8.42691 q^{31} +(1.68816 + 2.92398i) q^{32} +(0.500000 + 0.866025i) q^{33} -1.66745 q^{34} +(8.50255 + 14.7268i) q^{35} +(0.955306 - 1.65464i) q^{36} +(0.853486 - 1.47828i) q^{37} -1.56629 q^{38} +(-1.86634 - 3.08492i) q^{39} -4.02486 q^{40} +(-0.234083 + 0.405443i) q^{41} +(-0.738450 + 1.27903i) q^{42} +(-3.77835 - 6.54429i) q^{43} -1.91061 q^{44} +(1.72122 + 2.98125i) q^{45} +(0.469391 + 0.813009i) q^{46} -2.55670 q^{47} +(1.73583 + 3.00655i) q^{48} +(-8.70095 + 15.0705i) q^{49} +(1.02407 - 1.77373i) q^{50} -5.57718 q^{51} +(6.88737 - 0.141080i) q^{52} +6.18142 q^{53} +(-0.149489 + 0.258923i) q^{54} +(1.72122 - 2.98125i) q^{55} +(-2.88779 - 5.00180i) q^{56} -5.23881 q^{57} +(0.461179 + 0.798786i) q^{58} +(-5.17313 - 8.96012i) q^{59} -6.57718 q^{60} +(6.79593 + 11.7709i) q^{61} +(1.25973 - 2.18192i) q^{62} +(-2.46991 + 4.27802i) q^{63} -5.93388 q^{64} +(-5.98452 + 10.8739i) q^{65} +0.298978 q^{66} +(0.847892 - 1.46859i) q^{67} +(5.32791 - 9.22822i) q^{68} +(1.56999 + 2.71929i) q^{69} +5.08415 q^{70} +(3.42399 + 5.93053i) q^{71} +(-0.584594 - 1.01255i) q^{72} +1.86177 q^{73} +(-0.255174 - 0.441973i) q^{74} +(3.42522 - 5.93266i) q^{75} +(5.00466 - 8.66833i) q^{76} +4.93983 q^{77} +(-1.07775 + 0.0220766i) q^{78} +2.12106 q^{79} +(5.97551 - 10.3499i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.0699856 + 0.121219i) q^{82} -3.77309 q^{83} +(-4.71905 - 8.17363i) q^{84} +(9.59957 + 16.6269i) q^{85} -2.25929 q^{86} +(1.54252 + 2.67172i) q^{87} +(-0.584594 + 1.01255i) q^{88} +(1.55066 - 2.68583i) q^{89} +1.02922 q^{90} +(-17.8071 + 0.364758i) q^{91} -5.99927 q^{92} +(4.21345 - 7.29792i) q^{93} +(-0.382199 + 0.661987i) q^{94} +(9.01716 + 15.6182i) q^{95} +3.37633 q^{96} +(-4.65494 - 8.06258i) q^{97} +(2.60139 + 4.50575i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} - 5 q^{11} - 20 q^{12} + 9 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} - 8 q^{20} - 14 q^{21} - 11 q^{23} + 3 q^{24} - 6 q^{25} - 4 q^{26} - 10 q^{27} - 5 q^{28} + 2 q^{29} + 7 q^{30} + 20 q^{31} + 9 q^{32} + 5 q^{33} + 58 q^{34} + 14 q^{35} - 10 q^{36} - 15 q^{37} - 38 q^{38} - 6 q^{39} + 30 q^{40} + 2 q^{41} + q^{42} - 7 q^{43} + 20 q^{44} + 2 q^{45} - 20 q^{46} + 36 q^{47} + 4 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} - 3 q^{52} + 30 q^{53} + 2 q^{55} - 3 q^{56} - 14 q^{57} - 5 q^{58} + 4 q^{59} - 16 q^{60} + 14 q^{61} - 46 q^{62} - 7 q^{63} - 74 q^{64} - 44 q^{65} + 5 q^{67} + 24 q^{68} + 11 q^{69} + 80 q^{70} + 13 q^{71} - 3 q^{72} + 56 q^{73} - 15 q^{74} - 3 q^{75} - 2 q^{76} + 14 q^{77} - 23 q^{78} + 32 q^{79} + 22 q^{80} - 5 q^{81} - 4 q^{82} + 24 q^{83} + 5 q^{84} - 13 q^{85} + 4 q^{86} - 2 q^{87} - 3 q^{88} + 6 q^{89} + 14 q^{90} - 29 q^{91} - 4 q^{92} + 10 q^{93} + 2 q^{94} + 21 q^{95} + 18 q^{96} - 9 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 - 5 * q^11 - 20 * q^12 + 9 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 - 8 * q^20 - 14 * q^21 - 11 * q^23 + 3 * q^24 - 6 * q^25 - 4 * q^26 - 10 * q^27 - 5 * q^28 + 2 * q^29 + 7 * q^30 + 20 * q^31 + 9 * q^32 + 5 * q^33 + 58 * q^34 + 14 * q^35 - 10 * q^36 - 15 * q^37 - 38 * q^38 - 6 * q^39 + 30 * q^40 + 2 * q^41 + q^42 - 7 * q^43 + 20 * q^44 + 2 * q^45 - 20 * q^46 + 36 * q^47 + 4 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 - 3 * q^52 + 30 * q^53 + 2 * q^55 - 3 * q^56 - 14 * q^57 - 5 * q^58 + 4 * q^59 - 16 * q^60 + 14 * q^61 - 46 * q^62 - 7 * q^63 - 74 * q^64 - 44 * q^65 + 5 * q^67 + 24 * q^68 + 11 * q^69 + 80 * q^70 + 13 * q^71 - 3 * q^72 + 56 * q^73 - 15 * q^74 - 3 * q^75 - 2 * q^76 + 14 * q^77 - 23 * q^78 + 32 * q^79 + 22 * q^80 - 5 * q^81 - 4 * q^82 + 24 * q^83 + 5 * q^84 - 13 * q^85 + 4 * q^86 - 2 * q^87 - 3 * q^88 + 6 * q^89 + 14 * q^90 - 29 * q^91 - 4 * q^92 + 10 * q^93 + 2 * q^94 + 21 * q^95 + 18 * q^96 - 9 * q^97 - 16 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.149489	−	0.258923i	0.105705	−	0.183086i	−0.808321	−	0.588742i	$-0.799624\pi$
$2$	0.149489	−	0.258923i	0.105705	−	0.183086i	0.914026	+	0.405656i	$0.132957\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.955306	+	1.65464i	0.477653	+	0.827319i
$5$	−3.44245			−1.53951			−0.769755	−	0.638340i	$-0.779621\pi$
$5$	−3.44245			−1.53951			−0.769755	+	0.638340i	$0.779621\pi$
$6$	−0.149489	−	0.258923i	−0.0610286	−	0.105705i
$7$	−2.46991	−	4.27802i	−0.933540	−	1.61694i	−0.777217	−	0.629232i	$-0.783369\pi$
$7$	−2.46991	−	4.27802i	−0.933540	−	1.61694i	−0.156322	−	0.987706i	$-0.549964\pi$
$8$	1.16919			0.413370
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.514608	+	0.891327i	−0.162733	+	0.281862i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	1.91061			0.551546
$13$	1.73845	−	3.15876i	0.482159	−	0.876084i
$13$	1.73845	−	3.15876i	0.482159	−	0.876084i
$14$	−1.47690			−0.394718
$15$	−1.72122	+	2.98125i	−0.444418	+	0.769755i
$16$	−1.73583	+	3.00655i	−0.433958	+	0.751637i
$17$	−2.78859	−	4.82998i	−0.676333	−	1.17144i	−0.976077	−	0.217423i	$-0.930235\pi$
$17$	−2.78859	−	4.82998i	−0.676333	−	1.17144i	0.299745	−	0.954019i	$-0.403098\pi$
$18$	−0.298978			−0.0704698
$19$	−2.61940	−	4.53694i	−0.600932	−	1.04085i	−0.992680	−	0.120773i	$-0.961463\pi$
$19$	−2.61940	−	4.53694i	−0.600932	−	1.04085i	0.391748	−	0.920073i	$-0.371871\pi$
$20$	−3.28859	−	5.69601i	−0.735351	−	1.27367i
$21$	−4.93983			−1.07796
$22$	0.149489	+	0.258923i	0.0318712	+	0.0552025i
$23$	−1.56999	+	2.71929i	−0.327365	+	0.567012i	−0.981988	−	0.188943i	$-0.939494\pi$
$23$	−1.56999	+	2.71929i	−0.327365	+	0.567012i	0.654623	+	0.755955i	$0.272827\pi$
$24$	0.584594	−	1.01255i	0.119330	−	0.206685i
$25$	6.85044			1.37009
$26$	−0.557996	−	0.922325i	−0.109432	−	0.180883i
$27$	−1.00000			−0.192450
$28$	4.71905	−	8.17363i	0.891816	−	1.54467i
$29$	−1.54252	+	2.67172i	−0.286438	+	0.496126i	−0.972957	−	0.230986i	$-0.925805\pi$
$29$	−1.54252	+	2.67172i	−0.286438	+	0.496126i	0.686519	+	0.727112i	$0.259138\pi$
$30$	0.514608	+	0.891327i	0.0939541	+	0.162733i
$31$	8.42691			1.51352			0.756759	−	0.653694i	$-0.226782\pi$
$31$	8.42691			1.51352			0.756759	+	0.653694i	$0.226782\pi$
$32$	1.68816	+	2.92398i	0.298428	+	0.516892i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	−1.66745			−0.285966
$35$	8.50255	+	14.7268i	1.43719	+	2.48929i
$36$	0.955306	−	1.65464i	0.159218	−	0.275773i
$37$	0.853486	−	1.47828i	0.140312	−	0.243028i	−0.787302	−	0.616568i	$-0.788523\pi$
$37$	0.853486	−	1.47828i	0.140312	−	0.243028i	0.927614	+	0.373540i	$0.121856\pi$
$38$	−1.56629			−0.254085
$39$	−1.86634	−	3.08492i	−0.298854	−	0.493983i
$40$	−4.02486			−0.636387
$41$	−0.234083	+	0.405443i	−0.0365576	+	0.0633196i	−0.883725	−	0.468006i	$-0.844973\pi$
$41$	−0.234083	+	0.405443i	−0.0365576	+	0.0633196i	0.847168	+	0.531326i	$0.178306\pi$
$42$	−0.738450	+	1.27903i	−0.113945	+	0.197359i
$43$	−3.77835	−	6.54429i	−0.576193	−	0.997995i	−0.995911	−	0.0903409i	$-0.971204\pi$
$43$	−3.77835	−	6.54429i	−0.576193	−	0.997995i	0.419718	−	0.907655i	$-0.362129\pi$
$44$	−1.91061			−0.288036
$45$	1.72122	+	2.98125i	0.256585	+	0.444418i
$46$	0.469391	+	0.813009i	0.0692080	+	0.119872i
$47$	−2.55670			−0.372933			−0.186466	−	0.982461i	$-0.559704\pi$
$47$	−2.55670			−0.372933			−0.186466	+	0.982461i	$0.559704\pi$
$48$	1.73583	+	3.00655i	0.250546	+	0.433958i
$49$	−8.70095	+	15.0705i	−1.24299	+	2.15293i
$50$	1.02407	−	1.77373i	0.144825	−	0.250844i
$51$	−5.57718			−0.780962
$52$	6.88737	−	0.141080i	0.955106	−	0.0195643i
$53$	6.18142			0.849083			0.424542	−	0.905408i	$-0.360435\pi$
$53$	6.18142			0.849083			0.424542	+	0.905408i	$0.360435\pi$
$54$	−0.149489	+	0.258923i	−0.0203429	+	0.0352349i
$55$	1.72122	−	2.98125i	0.232090	−	0.401991i
$56$	−2.88779	−	5.00180i	−0.385897	−	0.668394i
$57$	−5.23881			−0.693897
$58$	0.461179	+	0.798786i	0.0605558	+	0.104886i
$59$	−5.17313	−	8.96012i	−0.673484	−	1.16651i	−0.976910	−	0.213653i	$-0.931464\pi$
$59$	−5.17313	−	8.96012i	−0.673484	−	1.16651i	0.303426	−	0.952855i	$-0.401870\pi$
$60$	−6.57718			−0.849110
$61$	6.79593	+	11.7709i	0.870130	+	1.50711i	0.861862	+	0.507144i	$0.169299\pi$
$61$	6.79593	+	11.7709i	0.870130	+	1.50711i	0.00826842	+	0.999966i	$0.497368\pi$
$62$	1.25973	−	2.18192i	0.159986	−	0.277104i
$63$	−2.46991	+	4.27802i	−0.311180	+	0.538979i
$64$	−5.93388			−0.741735
$65$	−5.98452	+	10.8739i	−0.742289	+	1.34874i
$66$	0.298978			0.0368017
$67$	0.847892	−	1.46859i	0.103587	−	0.179417i	−0.809573	−	0.587019i	$-0.800301\pi$
$67$	0.847892	−	1.46859i	0.103587	−	0.179417i	0.913160	+	0.407602i	$0.133635\pi$
$68$	5.32791	−	9.22822i	0.646105	−	1.11909i
$69$	1.56999	+	2.71929i	0.189004	+	0.327365i
$70$	5.08415			0.607672
$71$	3.42399	+	5.93053i	0.406353	+	0.703825i	0.994478	−	0.104946i	$-0.0334669\pi$
$71$	3.42399	+	5.93053i	0.406353	+	0.703825i	−0.588125	+	0.808770i	$0.700134\pi$
$72$	−0.584594	−	1.01255i	−0.0688950	−	0.119330i
$73$	1.86177			0.217904			0.108952	−	0.994047i	$-0.465251\pi$
$73$	1.86177			0.217904			0.108952	+	0.994047i	$0.465251\pi$
$74$	−0.255174	−	0.441973i	−0.0296633	−	0.0513784i
$75$	3.42522	−	5.93266i	0.395510	−	0.685044i
$76$	5.00466	−	8.66833i	0.574074	−	0.994326i
$77$	4.93983			0.562946
$78$	−1.07775	+	0.0220766i	−0.122032	+	0.00249968i
$79$	2.12106			0.238637			0.119319	−	0.992856i	$-0.461929\pi$
$79$	2.12106			0.238637			0.119319	+	0.992856i	$0.461929\pi$
$80$	5.97551	−	10.3499i	0.668082	−	1.15715i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.0699856	+	0.121219i	0.00772861	+	0.0133864i
$83$	−3.77309			−0.414151			−0.207075	−	0.978325i	$-0.566395\pi$
$83$	−3.77309			−0.414151			−0.207075	+	0.978325i	$0.566395\pi$
$84$	−4.71905	−	8.17363i	−0.514890	−	0.891816i
$85$	9.59957	+	16.6269i	1.04122	+	1.80345i
$86$	−2.25929			−0.243625
$87$	1.54252	+	2.67172i	0.165375	+	0.286438i
$88$	−0.584594	+	1.01255i	−0.0623179	+	0.107938i
$89$	1.55066	−	2.68583i	0.164370	−	0.284697i	−0.772061	−	0.635548i	$-0.780774\pi$
$89$	1.55066	−	2.68583i	0.164370	−	0.284697i	0.936431	+	0.350851i	$0.114108\pi$
$90$	1.02922			0.108489
$91$	−17.8071	+	0.364758i	−1.86669	+	0.0382370i
$92$	−5.99927			−0.625467
$93$	4.21345	−	7.29792i	0.436915	−	0.756759i
$94$	−0.382199	+	0.661987i	−0.0394208	+	0.0682788i
$95$	9.01716	+	15.6182i	0.925141	+	1.60239i
$96$	3.37633			0.344595
$97$	−4.65494	−	8.06258i	−0.472637	−	0.818631i	0.526873	−	0.849944i	$-0.323365\pi$
$97$	−4.65494	−	8.06258i	−0.472637	−	0.818631i	−0.999510	+	0.0313129i	$0.990031\pi$
$98$	2.60139	+	4.50575i	0.262780	+	0.455149i
$99$	1.00000			0.100504
$100$	6.54427	+	11.3350i	0.654427	+	1.13350i
$101$	5.64129	−	9.77101i	0.561330	−	0.972251i	−0.436051	−	0.899922i	$-0.643623\pi$
$101$	5.64129	−	9.77101i	0.561330	−	0.972251i	0.997381	−	0.0723296i	$-0.0230433\pi$
$102$	−0.833727	+	1.44406i	−0.0825513	+	0.142983i
$103$	11.0969			1.09341			0.546707	−	0.837324i	$-0.315881\pi$
$103$	11.0969			1.09341			0.546707	+	0.837324i	$0.315881\pi$
$104$	2.03257	−	3.69319i	0.199310	−	0.362147i
$105$	17.0051			1.65953
$106$	0.924054	−	1.60051i	0.0897521	−	0.155455i
$107$	9.02609	−	15.6336i	0.872585	−	1.51136i	0.0132720	−	0.999912i	$-0.495775\pi$
$107$	9.02609	−	15.6336i	0.872585	−	1.51136i	0.859313	−	0.511450i	$-0.170891\pi$
$108$	−0.955306	−	1.65464i	−0.0919244	−	0.159218i
$109$	−4.86248			−0.465741			−0.232871	−	0.972508i	$-0.574812\pi$
$109$	−4.86248			−0.465741			−0.232871	+	0.972508i	$0.574812\pi$
$110$	−0.514608	−	0.891327i	−0.0490660	−	0.0849847i
$111$	−0.853486	−	1.47828i	−0.0810093	−	0.140312i
$112$	17.1494			1.62047
$113$	7.25333	+	12.5631i	0.682336	+	1.18184i	0.974266	+	0.225401i	$0.0723693\pi$
$113$	7.25333	+	12.5631i	0.682336	+	1.18184i	−0.291930	+	0.956440i	$0.594297\pi$
$114$	−0.783144	+	1.35645i	−0.0733482	+	0.127043i
$115$	5.40459	−	9.36103i	0.503981	−	0.872920i
$116$	−5.89431			−0.547273
$117$	−3.60480	+	0.0738401i	−0.333263	+	0.00682652i
$118$	−3.09330			−0.284762
$119$	−13.7752	+	23.8593i	−1.26277	+	2.18718i
$120$	−2.01243	+	3.48564i	−0.183709	+	0.318194i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	4.06367			0.367907
$123$	0.234083	+	0.405443i	0.0211065	+	0.0365576i
$124$	8.05028	+	13.9435i	0.722936	+	1.25216i
$125$	−6.37004			−0.569754
$126$	0.738450	+	1.27903i	0.0657864	+	0.113945i
$127$	1.02449	−	1.77447i	0.0909090	−	0.157459i	−0.816985	−	0.576659i	$-0.804356\pi$
$127$	1.02449	−	1.77447i	0.0909090	−	0.157459i	0.907894	+	0.419200i	$0.137689\pi$
$128$	−4.26338	+	7.38438i	−0.376833	+	0.652693i
$129$	−7.55670			−0.665330
$130$	1.92087	+	3.17505i	0.168472	+	0.278471i
$131$	−4.31366			−0.376886			−0.188443	−	0.982084i	$-0.560344\pi$
$131$	−4.31366			−0.376886			−0.188443	+	0.982084i	$0.560344\pi$
$132$	−0.955306	+	1.65464i	−0.0831487	+	0.144018i
$133$	−12.9394	+	22.4117i	−1.12199	+	1.94334i
$134$	−0.253501	−	0.439077i	−0.0218992	−	0.0379305i
$135$	3.44245			0.296279
$136$	−3.26038	−	5.64715i	−0.279576	−	0.484239i
$137$	−8.98619	−	15.5645i	−0.767742	−	1.32977i	−0.938785	−	0.344505i	$-0.888047\pi$
$137$	−8.98619	−	15.5645i	−0.767742	−	1.32977i	0.171042	−	0.985264i	$-0.445286\pi$
$138$	0.938782			0.0799145
$139$	−2.62799	−	4.55181i	−0.222903	−	0.386080i	0.732785	−	0.680460i	$-0.238220\pi$
$139$	−2.62799	−	4.55181i	−0.222903	−	0.386080i	−0.955688	+	0.294380i	$0.904887\pi$
$140$	−16.2451	+	28.1373i	−1.37296	+	2.37803i
$141$	−1.27835	+	2.21417i	−0.107656	+	0.186466i
$142$	2.04740			0.171814
$143$	1.86634	+	3.08492i	0.156072	+	0.257974i
$144$	3.47166			0.289305
$145$	5.31004	−	9.19725i	0.440975	−	0.763790i
$146$	0.278314	−	0.482054i	0.0230334	−	0.0398951i
$147$	8.70095	+	15.0705i	0.717642	+	1.24299i
$148$	3.26136			0.268082
$149$	−1.89740	−	3.28639i	−0.155441	−	0.269231i	0.777779	−	0.628538i	$-0.216346\pi$
$149$	−1.89740	−	3.28639i	−0.155441	−	0.269231i	−0.933219	+	0.359307i	$0.883013\pi$
$150$	−1.02407	−	1.77373i	−0.0836146	−	0.144825i
$151$	6.43966			0.524052			0.262026	−	0.965061i	$-0.415609\pi$
$151$	6.43966			0.524052			0.262026	+	0.965061i	$0.415609\pi$
$152$	−3.06257	−	5.30453i	−0.248407	−	0.430254i
$153$	−2.78859	+	4.82998i	−0.225444	+	0.390481i
$154$	0.738450	−	1.27903i	0.0595060	−	0.103067i
$155$	−29.0092			−2.33007
$156$	3.32150	−	6.03517i	0.265933	−	0.483201i
$157$	15.7673			1.25837			0.629185	−	0.777255i	$-0.283389\pi$
$157$	15.7673			1.25837			0.629185	+	0.777255i	$0.283389\pi$
$158$	0.317075	−	0.549189i	0.0252251	−	0.0436912i
$159$	3.09071	−	5.35327i	0.245109	−	0.424542i
$160$	−5.81141	−	10.0657i	−0.459432	−	0.795760i
$161$	15.5109			1.22243
$162$	0.149489	+	0.258923i	0.0117450	+	0.0203429i
$163$	−1.84629	−	3.19787i	−0.144613	−	0.250476i	0.784616	−	0.619982i	$-0.212860\pi$
$163$	−1.84629	−	3.19787i	−0.144613	−	0.250476i	−0.929228	+	0.369506i	$0.879527\pi$
$164$	−0.894482			−0.0698473
$165$	−1.72122	−	2.98125i	−0.133997	−	0.232090i
$166$	−0.564036	+	0.976939i	−0.0437777	+	0.0758252i
$167$	3.45670	−	5.98718i	0.267487	−	0.463302i	−0.700725	−	0.713432i	$-0.747140\pi$
$167$	3.45670	−	5.98718i	0.267487	−	0.463302i	0.968212	+	0.250130i	$0.0804733\pi$
$168$	−5.77558			−0.445596
$169$	−6.95558	−	10.9827i	−0.535045	−	0.844824i
$170$	5.74012			0.440247
$171$	−2.61940	+	4.53694i	−0.200311	+	0.346948i
$172$	7.21896	−	12.5036i	0.550441	−	0.953391i
$173$	−3.56569	−	6.17596i	−0.271095	−	0.469550i	0.698048	−	0.716051i	$-0.254052\pi$
$173$	−3.56569	−	6.17596i	−0.271095	−	0.469550i	−0.969142	+	0.246501i	$0.920719\pi$
$174$	0.922358			0.0699238
$175$	−16.9200	−	29.3063i	−1.27903	−	2.21535i
$176$	−1.73583	−	3.00655i	−0.130843	−	0.226627i
$177$	−10.3463			−0.777672
$178$	−0.463614	−	0.803003i	−0.0347494	−	0.0601877i
$179$	12.7023	−	22.0010i	0.949412	−	1.64443i	0.202747	−	0.979231i	$-0.435013\pi$
$179$	12.7023	−	22.0010i	0.949412	−	1.64443i	0.746666	−	0.665199i	$-0.231653\pi$
$180$	−3.28859	+	5.69601i	−0.245117	+	0.424555i
$181$	−15.0513			−1.11875			−0.559377	−	0.828913i	$-0.688960\pi$
$181$	−15.0513			−1.11875			−0.559377	+	0.828913i	$0.688960\pi$
$182$	−2.56752	+	4.66518i	−0.190317	+	0.345806i
$183$	13.5919			1.00474
$184$	−1.83561	+	3.17936i	−0.135323	+	0.234386i
$185$	−2.93808	+	5.08890i	−0.216012	+	0.374144i
$186$	−1.25973	−	2.18192i	−0.0923679	−	0.159986i
$187$	5.57718			0.407844
$188$	−2.44243	−	4.23041i	−0.178133	−	0.308535i
$189$	2.46991	+	4.27802i	0.179660	+	0.311180i
$190$	5.39186			0.391167
$191$	−7.26456	−	12.5826i	−0.525645	−	0.910444i	−0.999554	−	0.0298701i	$-0.990491\pi$
$191$	−7.26456	−	12.5826i	−0.525645	−	0.910444i	0.473909	−	0.880574i	$-0.342843\pi$
$192$	−2.96694	+	5.13889i	−0.214120	+	0.370867i
$193$	−7.83163	+	13.5648i	−0.563733	+	0.976414i	0.433433	+	0.901186i	$0.357302\pi$
$193$	−7.83163	+	13.5648i	−0.563733	+	0.976414i	−0.997166	+	0.0752288i	$0.976031\pi$
$194$	−2.78345			−0.199840
$195$	6.42479	+	10.6197i	0.460089	+	0.760492i
$196$	−33.2483			−2.37488
$197$	−5.04479	+	8.73783i	−0.359426	+	0.622545i	−0.987865	−	0.155314i	$-0.950361\pi$
$197$	−5.04479	+	8.73783i	−0.359426	+	0.622545i	0.628439	+	0.777859i	$0.283694\pi$
$198$	0.149489	−	0.258923i	0.0106237	−	0.0184008i
$199$	−1.02274	−	1.77144i	−0.0725004	−	0.125574i	0.827496	−	0.561471i	$-0.189765\pi$
$199$	−1.02274	−	1.77144i	−0.0725004	−	0.125574i	−0.899997	+	0.435897i	$0.856431\pi$
$200$	8.00945			0.566353
$201$	−0.847892	−	1.46859i	−0.0598057	−	0.103587i
$202$	−1.68662	−	2.92132i	−0.118670	−	0.205543i
$203$	15.2396			1.06961
$204$	−5.32791	−	9.22822i	−0.373029	−	0.646105i
$205$	0.805817	−	1.39572i	0.0562807	−	0.0974810i
$206$	1.65887	−	2.87325i	0.115579	−	0.200189i
$207$	3.13997			0.218243
$208$	6.47932	+	10.7098i	0.449260	+	0.742592i
$209$	5.23881			0.362376
$210$	2.54208	−	4.40300i	0.175420	−	0.303836i
$211$	1.52745	−	2.64562i	0.105154	−	0.182132i	−0.808647	−	0.588294i	$-0.799800\pi$
$211$	1.52745	−	2.64562i	0.105154	−	0.182132i	0.913801	+	0.406162i	$0.133133\pi$
$212$	5.90515	+	10.2280i	0.405567	+	0.702463i
$213$	6.84799			0.469216
$214$	−2.69860	−	4.67412i	−0.184473	−	0.319516i
$215$	13.0068	+	22.5284i	0.887054	+	1.53642i
$216$	−1.16919			−0.0795531
$217$	−20.8137	−	36.0505i	−1.41293	−	2.44726i
$218$	−0.726888	+	1.25901i	−0.0492310	+	0.0852707i
$219$	0.930884	−	1.61234i	0.0629033	−	0.108952i
$220$	6.57718			0.443433
$221$	−20.1046	+	0.411820i	−1.35238	+	0.0277020i
$222$	−0.510347			−0.0342522
$223$	−7.14860	+	12.3817i	−0.478706	+	0.829142i	−0.999702	−	0.0244165i	$-0.992227\pi$
$223$	−7.14860	+	12.3817i	−0.478706	+	0.829142i	0.520996	+	0.853559i	$0.325561\pi$
$224$	8.33923	−	14.4440i	0.557188	−	0.965079i
$225$	−3.42522	−	5.93266i	−0.228348	−	0.395510i
$226$	4.33718			0.288505
$227$	13.6085	+	23.5706i	0.903229	+	1.56444i	0.823277	+	0.567640i	$0.192143\pi$
$227$	13.6085	+	23.5706i	0.903229	+	1.56444i	0.0799521	+	0.996799i	$0.474523\pi$
$228$	−5.00466	−	8.66833i	−0.331442	−	0.574074i
$229$	−5.42720			−0.358640			−0.179320	−	0.983791i	$-0.557390\pi$
$229$	−5.42720			−0.358640			−0.179320	+	0.983791i	$0.557390\pi$
$230$	−1.61585	−	2.79874i	−0.106546	−	0.184544i
$231$	2.46991	−	4.27802i	0.162508	−	0.281473i
$232$	−1.80349	+	3.12374i	−0.118405	+	0.205084i
$233$	−22.5644			−1.47824			−0.739122	−	0.673572i	$-0.764759\pi$
$233$	−22.5644			−1.47824			−0.739122	+	0.673572i	$0.764759\pi$
$234$	−0.519758	+	0.944401i	−0.0339777	+	0.0617374i
$235$	8.80130			0.574134
$236$	9.88384	−	17.1193i	0.643383	−	1.11437i
$237$	1.06053	−	1.83689i	0.0688887	−	0.119319i
$238$	4.11847	+	7.13340i	0.266961	+	0.462390i
$239$	13.6503			0.882964			0.441482	−	0.897270i	$-0.354453\pi$
$239$	13.6503			0.882964			0.441482	+	0.897270i	$0.354453\pi$
$240$	−5.97551	−	10.3499i	−0.385717	−	0.668082i
$241$	4.44842	+	7.70488i	0.286548	+	0.496315i	0.972983	−	0.230875i	$-0.0741590\pi$
$241$	4.44842	+	7.70488i	0.286548	+	0.496315i	−0.686436	+	0.727191i	$0.740826\pi$
$242$	−0.298978			−0.0192190
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−12.9844	+	22.4896i	−0.831240	+	1.43975i
$245$	29.9526	−	51.8794i	1.91360	−	3.31445i
$246$	0.139971			0.00892423
$247$	−18.8848	+	0.386834i	−1.20161	+	0.0246137i
$248$	9.85263			0.625643
$249$	−1.88655	+	3.26759i	−0.119555	+	0.207075i
$250$	−0.952251	+	1.64935i	−0.0602257	+	0.104314i
$251$	−3.45655	−	5.98692i	−0.218176	−	0.377891i	0.736075	−	0.676900i	$-0.236677\pi$
$251$	−3.45655	−	5.98692i	−0.218176	−	0.377891i	−0.954250	+	0.299009i	$0.903344\pi$
$252$	−9.43810			−0.594544
$253$	−1.56999	−	2.71929i	−0.0987041	−	0.170961i
$254$	−0.306301	−	0.530528i	−0.0192190	−	0.0332883i
$255$	19.1991			1.20230
$256$	−4.65922	−	8.07001i	−0.291201	−	0.504376i
$257$	−5.05624	+	8.75766i	−0.315399	+	0.546288i	−0.979522	−	0.201336i	$-0.935472\pi$
$257$	−5.05624	+	8.75766i	−0.315399	+	0.546288i	0.664123	+	0.747623i	$0.268805\pi$
$258$	−1.12964	+	1.95660i	−0.0703285	+	0.121813i
$259$	−8.43215			−0.523948
$260$	−23.7094	+	0.485660i	−1.47039	+	0.0301193i
$261$	3.08504			0.190959
$262$	−0.644845	+	1.11690i	−0.0398387	+	0.0690026i
$263$	12.7328	−	22.0538i	0.785137	−	1.35990i	−0.143780	−	0.989610i	$-0.545926\pi$
$263$	12.7328	−	22.0538i	0.785137	−	1.35990i	0.928917	−	0.370288i	$-0.120741\pi$
$264$	0.584594	+	1.01255i	0.0359792	+	0.0623179i
$265$	−21.2792			−1.30717
$266$	3.86860	+	6.70061i	0.237199	+	0.410841i
$267$	−1.55066	−	2.68583i	−0.0948990	−	0.164370i
$268$	3.23999			0.197914
$269$	5.10232	+	8.83748i	0.311094	+	0.538831i	0.978600	−	0.205774i	$-0.0659712\pi$
$269$	5.10232	+	8.83748i	0.311094	+	0.538831i	−0.667505	+	0.744605i	$0.732638\pi$
$270$	0.514608	−	0.891327i	0.0313180	−	0.0542444i
$271$	−8.77271	+	15.1948i	−0.532904	+	0.923017i	0.466358	+	0.884596i	$0.345566\pi$
$271$	−8.77271	+	15.1948i	−0.532904	+	0.923017i	−0.999262	+	0.0384204i	$0.987767\pi$
$272$	19.3621			1.17400
$273$	−8.58764	+	15.6038i	−0.519748	+	0.944382i
$274$	−5.37335			−0.324616
$275$	−3.42522	+	5.93266i	−0.206549	+	0.357753i
$276$	−2.99963	+	5.19552i	−0.180557	+	0.312733i
$277$	−7.45100	−	12.9055i	−0.447687	−	0.775417i	0.550548	−	0.834804i	$-0.314419\pi$
$277$	−7.45100	−	12.9055i	−0.447687	−	0.775417i	−0.998235	+	0.0593867i	$0.981085\pi$
$278$	−1.57142			−0.0942477
$279$	−4.21345	−	7.29792i	−0.252253	−	0.436915i
$280$	9.94107	+	17.2184i	0.594093	+	1.02900i
$281$	21.3906			1.27605			0.638027	−	0.770014i	$-0.279751\pi$
$281$	21.3906			1.27605			0.638027	+	0.770014i	$0.279751\pi$
$282$	0.382199	+	0.661987i	0.0227596	+	0.0394208i
$283$	1.34148	−	2.32351i	0.0797427	−	0.138118i	−0.823396	−	0.567467i	$-0.807923\pi$
$283$	1.34148	−	2.32351i	0.0797427	−	0.138118i	0.903139	+	0.429349i	$0.141257\pi$
$284$	−6.54192	+	11.3309i	−0.388192	+	0.672368i
$285$	18.0343			1.06826
$286$	1.07775	−	0.0220766i	0.0637290	−	0.00130542i
$287$	2.31266			0.136512
$288$	1.68816	−	2.92398i	0.0994759	−	0.172297i
$289$	−7.05247	+	12.2152i	−0.414851	+	0.718544i
$290$	−1.58758	−	2.74978i	−0.0932262	−	0.161472i
$291$	−9.30987			−0.545754
$292$	1.77856	+	3.08055i	0.104082	+	0.180276i
$293$	−9.39040	−	16.2647i	−0.548593	−	0.950191i	−0.998371	−	0.0570508i	$-0.981830\pi$
$293$	−9.39040	−	16.2647i	−0.548593	−	0.950191i	0.449778	−	0.893140i	$-0.351503\pi$
$294$	5.20279			0.303433
$295$	17.8082	+	30.8447i	1.03683	+	1.79585i
$296$	0.997885	−	1.72839i	0.0580009	−	0.100460i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	−1.13456			−0.0657233
$299$	5.86027	+	9.68657i	0.338908	+	0.560189i
$300$	13.0885			0.755667
$301$	−18.6644	+	32.3277i	−1.07580	+	1.86334i
$302$	0.962659	−	1.66737i	0.0553948	−	0.0959466i
$303$	−5.64129	−	9.77101i	−0.324084	−	0.561330i
$304$	18.1874			1.04312
$305$	−23.3946	−	40.5207i	−1.33957	−	2.32021i
$306$	0.833727	+	1.44406i	0.0476610	+	0.0825513i
$307$	−13.9915			−0.798535			−0.399267	−	0.916835i	$-0.630735\pi$
$307$	−13.9915			−0.798535			−0.399267	+	0.916835i	$0.630735\pi$
$308$	4.71905	+	8.17363i	0.268893	+	0.465736i
$309$	5.54847	−	9.61023i	0.315641	−	0.546707i
$310$	−4.33655	+	7.51113i	−0.246300	+	0.426604i
$311$	7.25887			0.411613			0.205806	−	0.978593i	$-0.434018\pi$
$311$	7.25887			0.411613			0.205806	+	0.978593i	$0.434018\pi$
$312$	−2.18211	−	3.60685i	−0.123537	−	0.204198i
$313$	−5.75599			−0.325348			−0.162674	−	0.986680i	$-0.552012\pi$
$313$	−5.75599			−0.325348			−0.162674	+	0.986680i	$0.552012\pi$
$314$	2.35704	−	4.08252i	0.133016	−	0.230390i
$315$	8.50255	−	14.7268i	0.479064	−	0.829764i
$316$	2.02626	+	3.50958i	0.113986	+	0.197429i
$317$	−23.1631			−1.30097			−0.650484	−	0.759520i	$-0.725434\pi$
$317$	−23.1631			−1.30097			−0.650484	+	0.759520i	$0.725434\pi$
$318$	−0.924054	−	1.60051i	−0.0518184	−	0.0897521i
$319$	−1.54252	−	2.67172i	−0.0863644	−	0.149588i
$320$	20.4271			1.14191
$321$	−9.02609	−	15.6336i	−0.503787	−	0.872585i
$322$	2.31871	−	4.01613i	0.129217	−	0.223810i
$323$	−14.6089	+	25.3033i	−0.812860	+	1.40791i
$324$	−1.91061			−0.106145
$325$	11.9091	−	21.6389i	0.660601	−	1.20031i
$326$	−1.10400			−0.0611449
$327$	−2.43124	+	4.21103i	−0.134448	+	0.232871i
$328$	−0.273686	+	0.474039i	−0.0151118	+	0.0261744i
$329$	6.31483	+	10.9376i	0.348148	+	0.603010i
$330$	−1.02922			−0.0566565
$331$	−4.02848	−	6.97754i	−0.221426	−	0.383520i	0.733816	−	0.679349i	$-0.237738\pi$
$331$	−4.02848	−	6.97754i	−0.221426	−	0.383520i	−0.955241	+	0.295829i	$0.904404\pi$
$332$	−3.60446	−	6.24311i	−0.197820	−	0.342635i
$333$	−1.70697			−0.0935415
$334$	−1.03348	−	1.79003i	−0.0565493	−	0.0979463i
$335$	−2.91882	+	5.05555i	−0.159472	+	0.276214i
$336$	8.57471	−	14.8518i	0.467789	−	0.810234i
$337$	−11.3146			−0.616344			−0.308172	−	0.951331i	$-0.599717\pi$
$337$	−11.3146			−0.616344			−0.308172	+	0.951331i	$0.599717\pi$
$338$	−3.88345	+	0.159163i	−0.211232	+	0.00865733i
$339$	14.5067			0.787894
$340$	−18.3411	+	31.7677i	−0.994684	+	1.72284i
$341$	−4.21345	+	7.29792i	−0.228171	+	0.395204i
$342$	0.783144	+	1.35645i	0.0423476	+	0.0733482i
$343$	51.3836			2.77445
$344$	−4.41760	−	7.65150i	−0.238181	−	0.412541i
$345$	−5.40459	−	9.36103i	−0.290973	−	0.503981i
$346$	−2.13213			−0.114624
$347$	9.89556	+	17.1396i	0.531222	+	0.920103i	0.999336	+	0.0364349i	$0.0116002\pi$
$347$	9.89556	+	17.1396i	0.531222	+	0.920103i	−0.468114	+	0.883668i	$0.655067\pi$
$348$	−2.94715	+	5.10462i	−0.157984	+	0.273636i
$349$	−4.05073	+	7.01607i	−0.216831	+	0.375562i	−0.953837	−	0.300324i	$-0.902905\pi$
$349$	−4.05073	+	7.01607i	−0.216831	+	0.375562i	0.737007	+	0.675885i	$0.236239\pi$
$350$	−10.1174			−0.540799
$351$	−1.73845	+	3.15876i	−0.0927916	+	0.168602i
$352$	−3.37633			−0.179959
$353$	0.436757	−	0.756486i	0.0232462	−	0.0402637i	−0.854168	−	0.519997i	$-0.825933\pi$
$353$	0.436757	−	0.756486i	0.0232462	−	0.0402637i	0.877415	+	0.479733i	$0.159266\pi$
$354$	−1.54665	+	2.67888i	−0.0822036	+	0.142381i
$355$	−11.7869	−	20.4155i	−0.625585	−	1.08354i
$356$	5.92543			0.314047
$357$	13.7752	+	23.8593i	0.729059	+	1.26277i
$358$	−3.79770	−	6.57781i	−0.200715	−	0.347648i
$359$	13.0320			0.687803			0.343901	−	0.939006i	$-0.388251\pi$
$359$	13.0320			0.687803			0.343901	+	0.939006i	$0.388251\pi$
$360$	2.01243	+	3.48564i	0.106065	+	0.183709i
$361$	−4.22255	+	7.31366i	−0.222239	+	0.384930i
$362$	−2.25000	+	3.89712i	−0.118258	+	0.204828i
$363$	−1.00000			−0.0524864
$364$	−17.6147	−	29.1158i	−0.923263	−	1.52608i
$365$	−6.40904			−0.335464
$366$	2.03183	−	3.51924i	0.106206	−	0.183954i
$367$	11.3721	−	19.6971i	0.593620	−	1.02818i	−0.400120	−	0.916463i	$-0.631031\pi$
$367$	11.3721	−	19.6971i	0.593620	−	1.02818i	0.993740	−	0.111718i	$-0.0356352\pi$
$368$	−5.45046	−	9.44047i	−0.284125	−	0.492119i
$369$	0.468165			0.0243717
$370$	0.878421	+	1.52147i	0.0456669	+	0.0790975i
$371$	−15.2676	−	26.4442i	−0.792653	−	1.37292i
$372$	16.1006			0.834775
$373$	5.69078	+	9.85672i	0.294657	+	0.510362i	0.974905	−	0.222621i	$-0.0714611\pi$
$373$	5.69078	+	9.85672i	0.294657	+	0.510362i	−0.680248	+	0.732982i	$0.738128\pi$
$374$	0.833727	−	1.44406i	0.0431110	−	0.0746705i
$375$	−3.18502	+	5.51662i	−0.164474	+	0.284877i
$376$	−2.98926			−0.154159
$377$	5.75774	+	9.51710i	0.296539	+	0.490156i
$378$	1.47690			0.0759636
$379$	2.40197	−	4.16034i	0.123381	−	0.213702i	−0.797718	−	0.603031i	$-0.793960\pi$
$379$	2.40197	−	4.16034i	0.123381	−	0.213702i	0.921099	+	0.389329i	$0.127293\pi$
$380$	−17.2283	+	29.8403i	−0.883793	+	1.53077i
$381$	−1.02449	−	1.77447i	−0.0524863	−	0.0909090i
$382$	−4.34389			−0.222253
$383$	5.70145	+	9.87519i	0.291330	+	0.504599i	0.974125	−	0.226012i	$-0.0725688\pi$
$383$	5.70145	+	9.87519i	0.291330	+	0.504599i	−0.682794	+	0.730611i	$0.739235\pi$
$384$	4.26338	+	7.38438i	0.217564	+	0.376833i
$385$	−17.0051			−0.866660
$386$	2.34149	+	4.05557i	0.119178	+	0.206423i
$387$	−3.77835	+	6.54429i	−0.192064	+	0.332665i
$388$	8.89378	−	15.4045i	0.451513	−	0.782044i
$389$	35.5503			1.80247			0.901236	−	0.433329i	$-0.142661\pi$
$389$	35.5503			1.80247			0.901236	+	0.433329i	$0.142661\pi$
$390$	3.71011	−	0.0759974i	0.187869	−	0.00384828i
$391$	17.5122			0.885629
$392$	−10.1730	+	17.6202i	−0.513816	+	0.889956i
$393$	−2.15683	+	3.73574i	−0.108798	+	0.188443i
$394$	1.50828	+	2.61242i	0.0759861	+	0.131612i
$395$	−7.30162			−0.367384
$396$	0.955306	+	1.65464i	0.0480059	+	0.0831487i
$397$	−10.8198	−	18.7405i	−0.543031	−	0.940557i	−0.998728	−	0.0504221i	$-0.983943\pi$
$397$	−10.8198	−	18.7405i	−0.543031	−	0.940557i	0.455697	−	0.890135i	$-0.349390\pi$
$398$	−0.611556			−0.0306545
$399$	12.9394	+	22.4117i	0.647780	+	1.12199i
$400$	−11.8912	+	20.5962i	−0.594560	+	1.02981i
$401$	−17.0399	+	29.5140i	−0.850933	+	1.47386i	0.0294339	+	0.999567i	$0.490630\pi$
$401$	−17.0399	+	29.5140i	−0.850933	+	1.47386i	−0.880367	+	0.474293i	$0.842704\pi$
$402$	−0.507002			−0.0252870
$403$	14.6498	−	26.6186i	0.729757	−	1.32597i
$404$	21.5566			1.07248
$405$	1.72122	−	2.98125i	0.0855283	−	0.148139i
$406$	2.27815	−	3.94586i	0.113062	−	0.195830i
$407$	0.853486	+	1.47828i	0.0423057	+	0.0732757i
$408$	−6.52077			−0.322826
$409$	7.23235	+	12.5268i	0.357617	+	0.619410i	0.987562	−	0.157229i	$-0.0502561\pi$
$409$	7.23235	+	12.5268i	0.357617	+	0.619410i	−0.629945	+	0.776639i	$0.716923\pi$
$410$	−0.240922	−	0.417288i	−0.0118983	−	0.0206084i
$411$	−17.9724			−0.886512
$412$	10.6010	+	18.3614i	0.522272	+	0.904602i
$413$	−25.5544	+	44.2615i	−1.25745	+	2.17796i
$414$	0.469391	−	0.813009i	0.0230693	−	0.0399572i
$415$	12.9887			0.637589
$416$	12.1710	−	0.249308i	0.596730	−	0.0122233i
$417$	−5.25598			−0.257387
$418$	0.783144	−	1.35645i	0.0383048	−	0.0663459i
$419$	8.58999	−	14.8783i	0.419648	−	0.726852i	−0.576256	−	0.817270i	$-0.695487\pi$
$419$	8.58999	−	14.8783i	0.419648	−	0.726852i	0.995904	+	0.0904172i	$0.0288200\pi$
$420$	16.2451	+	28.1373i	0.792678	+	1.37296i
$421$	7.73984			0.377217			0.188608	−	0.982052i	$-0.439602\pi$
$421$	7.73984			0.377217			0.188608	+	0.982052i	$0.439602\pi$
$422$	−0.456673	−	0.790981i	−0.0222305	−	0.0385044i
$423$	1.27835	+	2.21417i	0.0621555	+	0.107656i
$424$	7.22724			0.350986
$425$	−19.1031	−	33.0875i	−0.926635	−	1.60498i
$426$	1.02370	−	1.77310i	0.0495984	−	0.0859069i
$427$	33.5707	−	58.1462i	1.62460	−	2.81389i
$428$	34.4907			1.66717
$429$	3.60480	−	0.0738401i	0.174041	−	0.00356503i
$430$	7.77748			0.375063
$431$	0.534896	−	0.926468i	0.0257651	−	0.0446264i	−0.852855	−	0.522147i	$-0.825131\pi$
$431$	0.534896	−	0.926468i	0.0257651	−	0.0446264i	0.878620	+	0.477521i	$0.158464\pi$
$432$	1.73583	−	3.00655i	0.0835152	−	0.144653i
$433$	16.2563	+	28.1568i	0.781229	+	1.35313i	0.931226	+	0.364442i	$0.118740\pi$
$433$	16.2563	+	28.1568i	0.781229	+	1.35313i	−0.149997	+	0.988686i	$0.547927\pi$
$434$	−12.4457			−0.597413
$435$	−5.31004	−	9.19725i	−0.254597	−	0.440975i
$436$	−4.64516	−	8.04565i	−0.222463	−	0.385317i
$437$	16.4497			0.786896
$438$	−0.278314	−	0.482054i	−0.0132984	−	0.0230334i
$439$	0.885747	−	1.53416i	0.0422744	−	0.0732214i	−0.844114	−	0.536164i	$-0.819873\pi$
$439$	0.885747	−	1.53416i	0.0422744	−	0.0732214i	0.886388	+	0.462942i	$0.153206\pi$
$440$	2.01243	−	3.48564i	0.0959390	−	0.166171i
$441$	17.4019			0.828662
$442$	−2.89879	+	5.26710i	−0.137881	+	0.250530i
$443$	24.8844			1.18230			0.591148	−	0.806563i	$-0.298675\pi$
$443$	24.8844			1.18230			0.591148	+	0.806563i	$0.298675\pi$
$444$	1.63068	−	2.82442i	0.0773887	−	0.134041i
$445$	−5.33808	+	9.24582i	−0.253049	+	0.438294i
$446$	2.13727	+	3.70187i	0.101203	+	0.175289i
$447$	−3.79479			−0.179488
$448$	14.6562	+	25.3852i	0.692439	+	1.19934i
$449$	17.3470	+	30.0459i	0.818655	+	1.41795i	0.906673	+	0.421833i	$0.138613\pi$
$449$	17.3470	+	30.0459i	0.818655	+	1.41795i	−0.0880185	+	0.996119i	$0.528053\pi$
$450$	−2.04813			−0.0965498
$451$	−0.234083	−	0.405443i	−0.0110225	−	0.0190916i
$452$	−13.8583	+	24.0033i	−0.651840	+	1.12902i
$453$	3.21983	−	5.57691i	0.151281	−	0.262026i
$454$	8.13730			0.381902
$455$	61.2999	−	1.25566i	2.87378	−	0.0588662i
$456$	−6.12515			−0.286836
$457$	8.25684	−	14.3013i	0.386239	−	0.668985i	−0.605701	−	0.795692i	$-0.707107\pi$
$457$	8.25684	−	14.3013i	0.386239	−	0.668985i	0.991940	+	0.126707i	$0.0404408\pi$
$458$	−0.811307	+	1.40523i	−0.0379099	+	0.0656619i
$459$	2.78859	+	4.82998i	0.130160	+	0.225444i
$460$	20.6522			0.962912
$461$	−18.8636	−	32.6727i	−0.878565	−	1.52172i	−0.852915	−	0.522049i	$-0.825168\pi$
$461$	−18.8636	−	32.6727i	−0.878565	−	1.52172i	−0.0256501	−	0.999671i	$-0.508166\pi$
$462$	−0.738450	−	1.27903i	−0.0343558	−	0.0595060i
$463$	−2.63547			−0.122481			−0.0612404	−	0.998123i	$-0.519506\pi$
$463$	−2.63547			−0.122481			−0.0612404	+	0.998123i	$0.519506\pi$
$464$	−5.35510	−	9.27531i	−0.248604	−	0.430596i
$465$	−14.5046	+	25.1227i	−0.672634	+	1.16504i
$466$	−3.37313	+	5.84243i	−0.156257	+	0.270646i
$467$	−34.6374			−1.60283			−0.801415	−	0.598109i	$-0.795919\pi$
$467$	−34.6374			−1.60283			−0.801415	+	0.598109i	$0.795919\pi$
$468$	−3.56586	−	5.89409i	−0.164832	−	0.272455i
$469$	−8.37688			−0.386809
$470$	1.31570	−	2.27886i	0.0606886	−	0.105116i
$471$	7.88367	−	13.6549i	0.363260	−	0.629185i
$472$	−6.04836	−	10.4761i	−0.278398	−	0.482200i
$473$	7.55670			0.347457
$474$	−0.317075	−	0.549189i	−0.0145637	−	0.0252251i
$475$	−17.9441	−	31.0800i	−0.823330	−	1.42605i
$476$	−52.6380			−2.41266
$477$	−3.09071	−	5.35327i	−0.141514	−	0.245109i
$478$	2.04057	−	3.53437i	0.0933335	−	0.161658i
$479$	7.85316	−	13.6021i	0.358820	−	0.621494i	−0.628944	−	0.777450i	$-0.716513\pi$
$479$	7.85316	−	13.6021i	0.358820	−	0.621494i	0.987764	+	0.155956i	$0.0498459\pi$
$480$	−11.6228			−0.530507
$481$	−3.18580	−	5.26588i	−0.145260	−	0.240103i
$482$	2.65996			0.121158
$483$	7.75546	−	13.4328i	0.352886	−	0.611216i
$484$	0.955306	−	1.65464i	0.0434230	−	0.0752108i
$485$	16.0244	+	27.7550i	0.727629	+	1.26029i
$486$	0.298978			0.0135619
$487$	21.4208	+	37.1019i	0.970669	+	1.68125i	0.693546	+	0.720413i	$0.256048\pi$
$487$	21.4208	+	37.1019i	0.970669	+	1.68125i	0.277123	+	0.960834i	$0.410619\pi$
$488$	7.94572	+	13.7624i	0.359686	+	0.622994i
$489$	−3.69258			−0.166984
$490$	−8.95516	−	15.5108i	−0.404553	−	0.700706i
$491$	−0.226781	+	0.392796i	−0.0102345	+	0.0177266i	−0.871097	−	0.491110i	$-0.836591\pi$
$491$	−0.226781	+	0.392796i	−0.0102345	+	0.0177266i	0.860863	+	0.508837i	$0.169924\pi$
$492$	−0.447241	+	0.774644i	−0.0201632	+	0.0349237i
$493$	17.2058			0.774911
$494$	−2.72291	+	4.94753i	−0.122510	+	0.222600i
$495$	−3.44245			−0.154726
$496$	−14.6277	+	25.3359i	−0.656803	+	1.13762i
$497$	16.9139	−	29.2958i	0.758694	−	1.31410i
$498$	0.564036	+	0.976939i	0.0252751	+	0.0437777i
$499$	28.9465			1.29582			0.647911	−	0.761716i	$-0.275643\pi$
$499$	28.9465			1.29582			0.647911	+	0.761716i	$0.275643\pi$
$500$	−6.08534	−	10.5401i	−0.272145	−	0.471368i
$501$	−3.45670	−	5.98718i	−0.154434	−	0.267487i
$502$	−2.06687			−0.0922488
$503$	4.91649	+	8.51560i	0.219215	+	0.379692i	0.954568	−	0.297992i	$-0.0963170\pi$
$503$	4.91649	+	8.51560i	0.219215	+	0.379692i	−0.735353	+	0.677684i	$0.762984\pi$
$504$	−2.88779	+	5.00180i	−0.128632	+	0.222798i
$505$	−19.4199	+	33.6362i	−0.864172	+	1.49679i
$506$	−0.938782			−0.0417340
$507$	−12.9891	+	0.532357i	−0.576866	+	0.0236428i
$508$	3.91482			0.173692
$509$	7.27107	−	12.5939i	0.322284	−	0.558213i	−0.658675	−	0.752428i	$-0.728883\pi$
$509$	7.27107	−	12.5939i	0.322284	−	0.558213i	0.980959	+	0.194215i	$0.0622159\pi$
$510$	2.87006	−	4.97109i	0.127088	−	0.220124i
$511$	−4.59841	−	7.96468i	−0.203422	−	0.352337i
$512$	−19.8395			−0.876791
$513$	2.61940	+	4.53694i	0.115649	+	0.200311i
$514$	1.51170	+	2.61835i	0.0666784	+	0.115490i
$515$	−38.2006			−1.68332
$516$	−7.21896	−	12.5036i	−0.317797	−	0.550441i
$517$	1.27835	−	2.21417i	0.0562218	−	0.0973789i
$518$	−1.26051	+	2.18327i	−0.0553838	+	0.0959275i
$519$	−7.13139			−0.313033
$520$	−6.99703	+	12.7136i	−0.306840	+	0.557528i
$521$	10.8892			0.477066			0.238533	−	0.971134i	$-0.423333\pi$
$521$	10.8892			0.477066			0.238533	+	0.971134i	$0.423333\pi$
$522$	0.461179	−	0.798786i	0.0201853	−	0.0349619i
$523$	−7.18124	+	12.4383i	−0.314014	+	0.543888i	−0.979227	−	0.202765i	$-0.935007\pi$
$523$	−7.18124	+	12.4383i	−0.314014	+	0.543888i	0.665214	+	0.746653i	$0.268341\pi$
$524$	−4.12087	−	7.13755i	−0.180021	−	0.311805i
$525$	−33.8400			−1.47690
$526$	−3.80682	−	6.59361i	−0.165985	−	0.287495i
$527$	−23.4992	−	40.7018i	−1.02364	−	1.77300i
$528$	−3.47166			−0.151085
$529$	6.57029	+	11.3801i	0.285665	+	0.494786i
$530$	−3.18101	+	5.50967i	−0.138174	+	0.239325i
$531$	−5.17313	+	8.96012i	−0.224495	+	0.388836i
$532$	−49.4444			−2.14368
$533$	0.873758	+	1.44425i	0.0378467	+	0.0625576i
$534$	−0.927228			−0.0401251
$535$	−31.0718	+	53.8180i	−1.34335	+	2.32676i
$536$	0.991345	−	1.71706i	0.0428196	−	0.0741657i
$537$	−12.7023	−	22.0010i	−0.548144	−	0.949412i
$538$	3.05097			0.131536
$539$	−8.70095	−	15.0705i	−0.374777	−	0.649132i
$540$	3.28859	+	5.69601i	0.141518	+	0.245117i
$541$	1.24396			0.0534821			0.0267411	−	0.999642i	$-0.491487\pi$
$541$	1.24396			0.0534821			0.0267411	+	0.999642i	$0.491487\pi$
$542$	2.62285	+	4.54290i	0.112661	+	0.195134i
$543$	−7.52565	+	13.0348i	−0.322956	+	0.559377i
$544$	9.41519	−	16.3076i	0.403673	−	0.699182i
$545$	16.7388			0.717013
$546$	2.75641	+	4.55613i	0.117963	+	0.194984i
$547$	−24.0562			−1.02857			−0.514285	−	0.857620i	$-0.671942\pi$
$547$	−24.0562			−1.02857			−0.514285	+	0.857620i	$0.671942\pi$
$548$	17.1691	−	29.7378i	0.733429	−	1.27034i
$549$	6.79593	−	11.7709i	0.290043	−	0.502370i
$550$	1.02407	+	1.77373i	0.0436663	+	0.0756323i
$551$	16.1619			0.688520
$552$	1.83561	+	3.17936i	0.0781286	+	0.135323i
$553$	−5.23883	−	9.07391i	−0.222778	−	0.385862i
$554$	−4.45537			−0.189291
$555$	2.93808	+	5.08890i	0.124715	+	0.216012i
$556$	5.02107	−	8.69675i	0.212941	−	0.368824i
$557$	−16.7249	+	28.9683i	−0.708655	+	1.22743i	0.256701	+	0.966491i	$0.417364\pi$
$557$	−16.7249	+	28.9683i	−0.708655	+	1.22743i	−0.965356	+	0.260936i	$0.915969\pi$
$558$	−2.51946			−0.106657
$559$	−27.2404	+	0.557988i	−1.15214	+	0.0236004i
$560$	−59.0360			−2.49472
$561$	2.78859	−	4.82998i	0.117734	−	0.203922i
$562$	3.19766	−	5.53850i	0.134885	−	0.233628i
$563$	1.91284	+	3.31314i	0.0806167	+	0.139632i	0.903515	−	0.428556i	$-0.140978\pi$
$563$	1.91284	+	3.31314i	0.0806167	+	0.139632i	−0.822898	+	0.568189i	$0.807644\pi$
$564$	−4.88486			−0.205690
$565$	−24.9692	−	43.2480i	−1.05046	−	1.81946i
$566$	−0.401073	−	0.694679i	−0.0168584	−	0.0291995i
$567$	4.93983			0.207453
$568$	4.00329	+	6.93390i	0.167974	+	0.290940i
$569$	−1.11738	+	1.93537i	−0.0468432	+	0.0811347i	−0.888496	−	0.458884i	$-0.848249\pi$
$569$	−1.11738	+	1.93537i	−0.0468432	+	0.0811347i	0.841653	+	0.540019i	$0.181583\pi$
$570$	2.69593	−	4.66949i	0.112920	−	0.195583i
$571$	29.8859			1.25068			0.625342	−	0.780351i	$-0.284959\pi$
$571$	29.8859			1.25068			0.625342	+	0.780351i	$0.284959\pi$
$572$	−3.32150	+	6.03517i	−0.138879	+	0.252343i
$573$	−14.5291			−0.606963
$574$	0.345717	−	0.598799i	0.0144299	−	0.0249934i
$575$	−10.7551	+	18.6284i	−0.448518	+	0.776857i
$576$	2.96694	+	5.13889i	0.123622	+	0.214120i
$577$	25.5675			1.06439			0.532195	−	0.846622i	$-0.321367\pi$
$577$	25.5675			1.06439			0.532195	+	0.846622i	$0.321367\pi$
$578$	2.10853	+	3.65209i	0.0877035	+	0.151907i
$579$	7.83163	+	13.5648i	0.325471	+	0.563733i
$580$	20.2908			0.842531
$581$	9.31922	+	16.1414i	0.386626	+	0.669656i
$582$	−1.39172	+	2.41054i	−0.0576888	+	0.0999199i
$583$	−3.09071	+	5.35327i	−0.128004	+	0.221710i
$584$	2.17676			0.0900748
$585$	12.4093	−	0.254191i	0.513062	−	0.0105095i
$586$	−5.61505			−0.231955
$587$	15.8340	−	27.4253i	0.653539	−	1.13196i	−0.328719	−	0.944428i	$-0.606617\pi$
$587$	15.8340	−	27.4253i	0.653539	−	1.13196i	0.982258	−	0.187535i	$-0.0600497\pi$
$588$	−16.6241	+	28.7939i	−0.685568	+	1.18744i
$589$	−22.0735	−	38.2324i	−0.909522	−	1.57534i
$590$	10.6485			0.438393
$591$	5.04479	+	8.73783i	0.207515	+	0.359426i
$592$	2.96301	+	5.13209i	0.121779	+	0.210928i
$593$	10.3336			0.424349			0.212175	−	0.977232i	$-0.431945\pi$
$593$	10.3336			0.424349			0.212175	+	0.977232i	$0.431945\pi$
$594$	−0.149489	−	0.258923i	−0.00613361	−	0.0106237i
$595$	47.4202	−	82.1343i	1.94404	−	3.36718i
$596$	3.62519	−	6.27901i	0.148494	−	0.257198i
$597$	−2.04549			−0.0837162
$598$	3.38412	−	0.0693198i	0.138387	−	0.00283470i
$599$	14.5906			0.596157			0.298079	−	0.954541i	$-0.403654\pi$
$599$	14.5906			0.596157			0.298079	+	0.954541i	$0.403654\pi$
$600$	4.00472	−	6.93638i	0.163492	−	0.283177i
$601$	10.1755	−	17.6246i	0.415069	−	0.718920i	−0.580367	−	0.814355i	$-0.697091\pi$
$601$	10.1755	−	17.6246i	0.415069	−	0.718920i	0.995436	+	0.0954348i	$0.0304241\pi$
$602$	5.58025	+	9.66527i	0.227434	+	0.393927i
$603$	−1.69578			−0.0690577
$604$	6.15185	+	10.6553i	0.250315	+	0.433559i
$605$	1.72122	+	2.98125i	0.0699777	+	0.121205i
$606$	−3.37325			−0.137029
$607$	9.30102	+	16.1098i	0.377517	+	0.653878i	0.990700	−	0.136062i	$-0.0434447\pi$
$607$	9.30102	+	16.1098i	0.377517	+	0.653878i	−0.613183	+	0.789941i	$0.710111\pi$
$608$	8.84396	−	15.3182i	0.358670	−	0.621234i
$609$	7.61978	−	13.1978i	0.308769	−	0.534803i
$610$	−13.9890			−0.566397
$611$	−4.44469	+	8.07601i	−0.179813	+	0.326720i
$612$	−10.6558			−0.430736
$613$	−11.6788	+	20.2282i	−0.471701	+	0.817010i	−0.999476	−	0.0323745i	$-0.989693\pi$
$613$	−11.6788	+	20.2282i	−0.471701	+	0.817010i	0.527775	+	0.849384i	$0.323026\pi$
$614$	−2.09157	+	3.62270i	−0.0844089	+	0.146200i
$615$	−0.805817	−	1.39572i	−0.0324937	−	0.0562807i
$616$	5.77558			0.232705
$617$	4.75083	+	8.22868i	0.191261	+	0.331274i	0.945668	−	0.325132i	$-0.105409\pi$
$617$	4.75083	+	8.22868i	0.191261	+	0.331274i	−0.754407	+	0.656407i	$0.772076\pi$
$618$	−1.65887	−	2.87325i	−0.0667295	−	0.115579i
$619$	−45.3682			−1.82350			−0.911750	−	0.410745i	$-0.865269\pi$
$619$	−45.3682			−1.82350			−0.911750	+	0.410745i	$0.865269\pi$
$620$	−27.7127	−	47.9997i	−1.11297	−	1.92772i
$621$	1.56999	−	2.71929i	0.0630014	−	0.109122i
$622$	1.08512	−	1.87949i	0.0435094	−	0.0753605i
$623$	−15.3200			−0.613784
$624$	12.5146	−	0.256348i	0.500986	−	0.0102621i
$625$	−12.3237			−0.492947
$626$	−0.860457	+	1.49036i	−0.0343908	+	0.0595666i
$627$	2.61940	−	4.53694i	0.104609	−	0.181188i
$628$	15.0626	+	26.0892i	0.601064	+	1.04107i
$629$	−9.52009			−0.379591
$630$	−2.54208	−	4.40300i	−0.101279	−	0.175420i
$631$	7.16599	+	12.4119i	0.285274	+	0.494109i	0.972676	−	0.232169i	$-0.0745822\pi$
$631$	7.16599	+	12.4119i	0.285274	+	0.494109i	−0.687402	+	0.726277i	$0.741249\pi$
$632$	2.47991			0.0986456
$633$	−1.52745	−	2.64562i	−0.0607106	−	0.105154i
$634$	−3.46263	+	5.99744i	−0.137518	+	0.238189i
$635$	−3.52676	+	6.10853i	−0.139955	+	0.242410i
$636$	11.8103			0.468309
$637$	32.4780	+	53.6835i	1.28682	+	2.12702i
$638$	−0.922358			−0.0365165
$639$	3.42399	−	5.93053i	0.135451	−	0.234608i
$640$	14.6764	−	25.4203i	0.580137	−	1.00483i
$641$	−12.4043	−	21.4848i	−0.489939	−	0.848599i	0.509994	−	0.860178i	$-0.329648\pi$
$641$	−12.4043	−	21.4848i	−0.489939	−	0.848599i	−0.999933	+	0.0115791i	$0.996314\pi$
$642$	−5.39721			−0.213011
$643$	−4.79370	−	8.30293i	−0.189045	−	0.327435i	0.755887	−	0.654702i	$-0.227206\pi$
$643$	−4.79370	−	8.30293i	−0.189045	−	0.327435i	−0.944932	+	0.327266i	$0.893873\pi$
$644$	14.8177	+	25.6650i	0.583898	+	1.01134i
$645$	26.0135			1.02428
$646$	4.36774	+	7.56514i	0.171846	+	0.297646i
$647$	9.81662	−	17.0029i	0.385931	−	0.668452i	−0.605967	−	0.795490i	$-0.707214\pi$
$647$	9.81662	−	17.0029i	0.385931	−	0.668452i	0.991898	+	0.127038i	$0.0405469\pi$
$648$	−0.584594	+	1.01255i	−0.0229650	+	0.0397766i
$649$	10.3463			0.406126
$650$	−3.82252	−	6.31833i	−0.149932	−	0.247825i
$651$	−41.6275			−1.63151
$652$	3.52755	−	6.10989i	0.138149	−	0.239282i
$653$	−13.2856	+	23.0113i	−0.519906	+	0.900503i	0.479826	+	0.877363i	$0.340700\pi$
$653$	−13.2856	+	23.0113i	−0.519906	+	0.900503i	−0.999732	+	0.0231400i	$0.992634\pi$
$654$	0.726888	+	1.25901i	0.0284236	+	0.0492310i
$655$	14.8496			0.580220
$656$	−0.812656	−	1.40756i	−0.0317289	−	0.0549560i
$657$	−0.930884	−	1.61234i	−0.0363173	−	0.0629033i
$658$	3.77599			0.147203
$659$	13.9721	+	24.2004i	0.544277	+	0.942715i	0.998652	+	0.0519049i	$0.0165293\pi$
$659$	13.9721	+	24.2004i	0.544277	+	0.942715i	−0.454375	+	0.890810i	$0.650137\pi$
$660$	3.28859	−	5.69601i	0.128008	−	0.221717i
$661$	−0.541856	+	0.938522i	−0.0210758	+	0.0365043i	−0.876371	−	0.481637i	$-0.840042\pi$
$661$	−0.541856	+	0.938522i	−0.0210758	+	0.0365043i	0.855295	+	0.518141i	$0.173376\pi$
$662$	−2.40886			−0.0936229
$663$	−9.69565	+	17.6170i	−0.376548	+	0.684188i
$664$	−4.41145			−0.171198
$665$	44.5432	−	77.1511i	1.72731	−	2.99179i
$666$	−0.255174	+	0.441973i	−0.00988777	+	0.0171261i
$667$	−4.84346	−	8.38912i	−0.187540	−	0.324828i
$668$	13.2088			0.511065
$669$	7.14860	+	12.3817i	0.276381	+	0.478706i
$670$	0.872664	+	1.51150i	0.0337140	+	0.0583943i
$671$	−13.5919			−0.524708
$672$	−8.33923	−	14.4440i	−0.321693	−	0.557188i
$673$	21.5347	−	37.2992i	0.830101	−	1.43778i	−0.0678562	−	0.997695i	$-0.521616\pi$
$673$	21.5347	−	37.2992i	0.830101	−	1.43778i	0.897957	−	0.440082i	$-0.145051\pi$
$674$	−1.69140	+	2.92960i	−0.0651504	+	0.112844i
$675$	−6.85044			−0.263674
$676$	11.5277	−	22.0008i	0.443373	−	0.846185i
$677$	−27.2704			−1.04808			−0.524042	−	0.851692i	$-0.675577\pi$
$677$	−27.2704			−1.04808			−0.524042	+	0.851692i	$0.675577\pi$
$678$	2.16859	−	3.75610i	0.0832841	−	0.144252i
$679$	−22.9946	+	39.8278i	−0.882451	+	1.52845i
$680$	11.2237	+	19.4400i	0.430409	+	0.745491i
$681$	27.2170			1.04296
$682$	1.25973	+	2.18192i	0.0482376	+	0.0835499i
$683$	−10.1262	−	17.5391i	−0.387468	−	0.671115i	0.604640	−	0.796499i	$-0.293317\pi$
$683$	−10.1262	−	17.5391i	−0.387468	−	0.671115i	−0.992108	+	0.125384i	$0.959984\pi$
$684$	−10.0093			−0.382716
$685$	30.9345	+	53.5801i	1.18195	+	2.04719i
$686$	7.68129	−	13.3044i	0.293273	−	0.507964i
$687$	−2.71360	+	4.70010i	−0.103530	+	0.179320i
$688$	26.2343			1.00017
$689$	10.7461	−	19.5256i	0.409393	−	0.743868i
$690$	−3.23171			−0.123029
$691$	24.8315	−	43.0094i	0.944634	−	1.63615i	0.188153	−	0.982140i	$-0.439750\pi$
$691$	24.8315	−	43.0094i	0.944634	−	1.63615i	0.756482	−	0.654015i	$-0.226917\pi$
$692$	6.81266	−	11.7999i	0.258978	−	0.448564i
$693$	−2.46991	−	4.27802i	−0.0938243	−	0.162508i
$694$	5.91711			0.224610
$695$	9.04672	+	15.6694i	0.343162	+	0.594373i
$696$	1.80349	+	3.12374i	0.0683612	+	0.118405i
$697$	2.61104			0.0989003
$698$	1.21108	+	2.09765i	0.0458400	+	0.0793973i
$699$	−11.2822	+	19.5413i	−0.426732	+	0.739122i
$700$	32.3276	−	55.9930i	1.22187	−	2.11634i
$701$	−49.8338			−1.88219			−0.941097	−	0.338135i	$-0.890204\pi$
$701$	−49.8338			−1.88219			−0.941097	+	0.338135i	$0.890204\pi$
$702$	0.557996	+	0.922325i	0.0210602	+	0.0348109i
$703$	−8.94249			−0.337273
$704$	2.96694	−	5.13889i	0.111821	−	0.193679i
$705$	4.40065	−	7.62215i	0.165738	−	0.287067i
$706$	−0.130581	−	0.226173i	−0.00491448	−	0.00851212i
$707$	−55.7340			−2.09609
$708$	−9.88384	−	17.1193i	−0.371457	−	0.643383i
$709$	−12.5828	−	21.7941i	−0.472558	−	0.818495i	0.526949	−	0.849897i	$-0.323336\pi$
$709$	−12.5828	−	21.7941i	−0.472558	−	0.818495i	−0.999507	+	0.0314023i	$0.990003\pi$
$710$	−7.04806			−0.264509
$711$	−1.06053	−	1.83689i	−0.0397729	−	0.0688887i
$712$	1.81302	−	3.14023i	0.0679456	−	0.117685i
$713$	−13.2301	+	22.9152i	−0.495472	+	0.858183i
$714$	8.23694			0.308260
$715$	−6.42479	−	10.6197i	−0.240274	−	0.397154i
$716$	48.5382			1.81396
$717$	6.82515	−	11.8215i	0.254890	−	0.441482i
$718$	1.94814	−	3.37428i	0.0727040	−	0.125927i
$719$	6.02908	+	10.4427i	0.224847	+	0.389446i	0.956273	−	0.292474i	$-0.0944786\pi$
$719$	6.02908	+	10.4427i	0.224847	+	0.389446i	−0.731427	+	0.681920i	$0.761145\pi$
$720$	−11.9510			−0.445388
$721$	−27.4085	−	47.4729i	−1.02075	−	1.76798i
$722$	1.26245	+	2.18662i	0.0469835	+	0.0813777i
$723$	8.89683			0.330877
$724$	−14.3786	−	24.9045i	−0.534376	−	0.925567i
$725$	−10.5669	+	18.3025i	−0.392446	+	0.679736i
$726$	−0.149489	+	0.258923i	−0.00554806	+	0.00960952i
$727$	−12.6614			−0.469587			−0.234793	−	0.972045i	$-0.575441\pi$
$727$	−12.6614			−0.469587			−0.234793	+	0.972045i	$0.575441\pi$
$728$	−20.8198	+	0.426470i	−0.771633	+	0.0158060i
$729$	1.00000			0.0370370
$730$	−0.958081	+	1.65945i	−0.0354602	+	0.0614188i
$731$	−21.0725	+	36.4987i	−0.779396	+	1.34995i
$732$	12.9844	+	22.4896i	0.479917	+	0.831240i
$733$	5.66939			0.209404			0.104702	−	0.994504i	$-0.466611\pi$
$733$	5.66939			0.209404			0.104702	+	0.994504i	$0.466611\pi$
$734$	−3.40002	−	5.88900i	−0.125497	−	0.217367i
$735$	−29.9526	−	51.8794i	−1.10482	−	1.91360i
$736$	−10.6016			−0.390779
$737$	0.847892	+	1.46859i	0.0312325	+	0.0540963i
$738$	0.0699856	−	0.121219i	0.00257620	−	0.00446212i
$739$	−21.8199	+	37.7933i	−0.802660	+	1.39025i	0.115200	+	0.993342i	$0.463249\pi$
$739$	−21.8199	+	37.7933i	−0.802660	+	1.39025i	−0.917860	+	0.396905i	$0.870084\pi$
$740$	−11.2271			−0.412715
$741$	−9.10740	+	16.5482i	−0.334569	+	0.607912i
$742$	−9.12934			−0.335149
$743$	−5.00136	+	8.66260i	−0.183482	+	0.317800i	−0.943064	−	0.332611i	$-0.892070\pi$
$743$	−5.00136	+	8.66260i	−0.183482	+	0.317800i	0.759582	+	0.650412i	$0.225404\pi$
$744$	4.92632	−	8.53263i	0.180608	−	0.312821i
$745$	6.53169	+	11.3132i	0.239303	+	0.414484i
$746$	3.40284			0.124587
$747$	1.88655	+	3.26759i	0.0690251	+	0.119555i
$748$	5.32791	+	9.22822i	0.194808	+	0.337417i
$749$	−89.1747			−3.25837
$750$	0.952251	+	1.64935i	0.0347713	+	0.0602257i
$751$	10.8252	−	18.7498i	0.395017	−	0.684189i	−0.598087	−	0.801431i	$-0.704072\pi$
$751$	10.8252	−	18.7498i	0.395017	−	0.684189i	0.993103	+	0.117243i	$0.0374055\pi$
$752$	4.43800	−	7.68684i	0.161837	−	0.280310i
$753$	−6.91310			−0.251927
$754$	3.32491	−	0.0681071i	0.121086	−	0.00248031i
$755$	−22.1682			−0.806783
$756$	−4.71905	+	8.17363i	−0.171630	+	0.297272i
$757$	−12.4573	+	21.5767i	−0.452769	+	0.784218i	−0.998557	−	0.0537048i	$-0.982897\pi$
$757$	−12.4573	+	21.5767i	−0.452769	+	0.784218i	0.545788	+	0.837923i	$0.316230\pi$
$758$	−0.718137	−	1.24385i	−0.0260839	−	0.0451787i
$759$	−3.13997			−0.113974
$760$	10.5427	+	18.2606i	0.382426	+	0.662380i
$761$	4.46193	+	7.72828i	0.161745	+	0.280150i	0.935494	−	0.353341i	$-0.114955\pi$
$761$	4.46193	+	7.72828i	0.161745	+	0.280150i	−0.773750	+	0.633491i	$0.781621\pi$
$762$	−0.612602			−0.0221922
$763$	12.0099	+	20.8018i	0.434788	+	0.753075i
$764$	13.8798	−	24.0404i	0.502152	−	0.869753i
$765$	9.59957	−	16.6269i	0.347073	−	0.601149i
$766$	3.40921			0.123180
$767$	−37.2961	+	0.763969i	−1.34669	+	0.0275853i
$768$	−9.31845			−0.336250
$769$	3.20555	−	5.55217i	0.115595	−	0.200216i	−0.802422	−	0.596756i	$-0.796456\pi$
$769$	3.20555	−	5.55217i	0.115595	−	0.200216i	0.918017	+	0.396540i	$0.129789\pi$
$770$	−2.54208	+	4.40300i	−0.0916100	+	0.158673i
$771$	5.05624	+	8.75766i	0.182096	+	0.315399i
$772$	−29.9264			−1.07708
$773$	−4.59372	−	7.95656i	−0.165225	−	0.286177i	0.771510	−	0.636217i	$-0.219502\pi$
$773$	−4.59372	−	7.95656i	−0.165225	−	0.286177i	−0.936735	+	0.350039i	$0.886168\pi$
$774$	1.12964	+	1.95660i	0.0406042	+	0.0703285i
$775$	57.7280			2.07365
$776$	−5.44249	−	9.42667i	−0.195374	−	0.338398i
$777$	−4.21607	+	7.30245i	−0.151251	+	0.261974i
$778$	5.31438	−	9.20477i	0.190530	−	0.330007i
$779$	2.45263			0.0878745
$780$	−11.4341	+	20.7758i	−0.409406	+	0.743892i
$781$	−6.84799			−0.245040
$782$	2.61788	−	4.53430i	0.0936152	−	0.162146i
$783$	1.54252	−	2.67172i	0.0551251	−	0.0954795i
$784$	−30.2068	−	52.3197i	−1.07881	−	1.86856i
$785$	−54.2782			−1.93727
$786$	0.644845	+	1.11690i	0.0230009	+	0.0398387i
$787$	16.2306	+	28.1122i	0.578558	+	1.00209i	0.995645	+	0.0932254i	$0.0297177\pi$
$787$	16.2306	+	28.1122i	0.578558	+	1.00209i	−0.417087	+	0.908867i	$0.636949\pi$
$788$	−19.2773			−0.686724
$789$	−12.7328	−	22.0538i	−0.453299	−	0.785137i
$790$	−1.09151	+	1.89055i	−0.0388343	+	0.0672629i
$791$	35.8302	−	62.0598i	1.27398	−	2.20659i
$792$	1.16919			0.0415453
$793$	48.9959	−	1.00363i	1.73990	−	0.0356398i
$794$	−6.46977			−0.229604
$795$	−10.6396	+	18.4283i	−0.377348	+	0.653586i
$796$	1.95407	−	3.38454i	0.0692600	−	0.119962i
$797$	−1.82915	−	3.16818i	−0.0647918	−	0.112223i	0.831810	−	0.555061i	$-0.187305\pi$
$797$	−1.82915	−	3.16818i	−0.0647918	−	0.112223i	−0.896602	+	0.442838i	$0.853972\pi$
$798$	7.73719			0.273894
$799$	7.12959	+	12.3488i	0.252227	+	0.436869i
$800$	11.5647	+	20.0306i	0.408872	+	0.708188i
$801$	−3.10133			−0.109580
$802$	5.09456	+	8.82404i	0.179895	+	0.311588i
$803$	−0.930884	+	1.61234i	−0.0328502	+	0.0568982i
$804$	1.61999	−	2.80591i	0.0571328	−	0.0989568i
$805$	−53.3955			−1.88194
$806$	−4.70218	−	7.77235i	−0.165627	−	0.273769i
$807$	10.2046			0.359221
$808$	6.59573	−	11.4241i	0.232037	−	0.401900i
$809$	−4.55094	+	7.88246i	−0.160003	+	0.277132i	−0.934869	−	0.354992i	$-0.884484\pi$
$809$	−4.55094	+	7.88246i	−0.160003	+	0.277132i	0.774867	+	0.632125i	$0.217817\pi$
$810$	−0.514608	−	0.891327i	−0.0180815	−	0.0313180i
$811$	6.73229			0.236403			0.118201	−	0.992990i	$-0.462287\pi$
$811$	6.73229			0.236403			0.118201	+	0.992990i	$0.462287\pi$
$812$	14.5584	+	25.2159i	0.510901	+	0.884906i
$813$	8.77271	+	15.1948i	0.307672	+	0.532904i
$814$	0.510347			0.0178877
$815$	6.35576	+	11.0085i	0.222632	+	0.385611i
$816$	9.68105	−	16.7681i	0.338904	−	0.587000i
$817$	−19.7940	+	34.2843i	−0.692506	+	1.19946i
$818$	4.32463			0.151207
$819$	9.21942	+	15.2390i	0.322153	+	0.532494i
$820$	3.07921			0.107531
$821$	8.79034	−	15.2253i	0.306785	−	0.531367i	−0.670872	−	0.741573i	$-0.734080\pi$
$821$	8.79034	−	15.2253i	0.306785	−	0.531367i	0.977657	+	0.210206i	$0.0674134\pi$
$822$	−2.68667	+	4.65346i	−0.0937085	+	0.162308i
$823$	−12.1191	−	20.9908i	−0.422444	−	0.731695i	0.573734	−	0.819042i	$-0.305494\pi$
$823$	−12.1191	−	20.9908i	−0.422444	−	0.731695i	−0.996178	+	0.0873469i	$0.972161\pi$
$824$	12.9744			0.451984
$825$	3.42522	+	5.93266i	0.119251	+	0.206549i
$826$	7.64019	+	13.2332i	0.265836	+	0.460442i
$827$	−8.63617			−0.300309			−0.150154	−	0.988663i	$-0.547977\pi$
$827$	−8.63617			−0.300309			−0.150154	+	0.988663i	$0.547977\pi$
$828$	2.99963	+	5.19552i	0.104244	+	0.180557i
$829$	−4.78638	+	8.29025i	−0.166238	+	0.287932i	−0.937094	−	0.349077i	$-0.886495\pi$
$829$	−4.78638	+	8.29025i	−0.166238	+	0.287932i	0.770856	+	0.637009i	$0.219829\pi$
$830$	1.94166	−	3.36306i	0.0673961	−	0.116734i
$831$	−14.9020			−0.516945
$832$	−10.3158	+	18.7437i	−0.357634	+	0.649822i
$833$	97.0536			3.36271
$834$	−0.785712	+	1.36089i	−0.0272070	+	0.0471239i
$835$	−11.8995	+	20.6105i	−0.411799	+	0.713257i
$836$	5.00466	+	8.66833i	0.173090	+	0.299801i
$837$	−8.42691			−0.291277
$838$	−2.56822	−	4.44828i	−0.0887176	−	0.153663i
$839$	18.9960	+	32.9020i	0.655814	+	1.13590i	0.981689	+	0.190490i	$0.0610077\pi$
$839$	18.9960	+	32.9020i	0.655814	+	1.13590i	−0.325875	+	0.945413i	$0.605659\pi$
$840$	19.8821			0.685999
$841$	9.74127	+	16.8724i	0.335906	+	0.581806i
$842$	1.15702	−	2.00402i	0.0398736	−	0.0690631i
$843$	10.6953	−	18.5248i	0.368365	−	0.638027i
$844$	5.83672			0.200908
$845$	23.9442	+	37.8074i	0.823706	+	1.30061i
$846$	0.764397			0.0262805
$847$	−2.46991	+	4.27802i	−0.0848673	+	0.146994i
$848$	−10.7299	+	18.5847i	−0.368466	+	0.638202i
$849$	−1.34148	−	2.32351i	−0.0460395	−	0.0797427i
$850$	−11.4228			−0.391799
$851$	2.67992	+	4.64176i	0.0918665	+	0.159117i
$852$	6.54192	+	11.3309i	0.224123	+	0.388192i
$853$	2.75690			0.0943945			0.0471972	−	0.998886i	$-0.484971\pi$
$853$	2.75690			0.0943945			0.0471972	+	0.998886i	$0.484971\pi$
$854$	−10.0369	−	17.3844i	−0.343456	−	0.594883i
$855$	9.01716	−	15.6182i	0.308380	−	0.534130i
$856$	10.5532	−	18.2787i	0.360701	−	0.624752i
$857$	31.7546			1.08472			0.542359	−	0.840147i	$-0.317531\pi$
$857$	31.7546			1.08472			0.542359	+	0.840147i	$0.317531\pi$
$858$	0.519758	−	0.944401i	0.0177443	−	0.0322413i
$859$	37.6069			1.28313			0.641566	−	0.767068i	$-0.278285\pi$
$859$	37.6069			1.28313			0.641566	+	0.767068i	$0.278285\pi$
$860$	−24.8509	+	43.0430i	−0.847408	+	1.46775i
$861$	1.15633	−	2.00282i	0.0394076	−	0.0682559i
$862$	−0.159922	−	0.276994i	−0.00544697	−	0.00943444i
$863$	33.6440			1.14525			0.572627	−	0.819816i	$-0.305924\pi$
$863$	33.6440			1.14525			0.572627	+	0.819816i	$0.305924\pi$
$864$	−1.68816	−	2.92398i	−0.0574325	−	0.0994759i
$865$	12.2747	+	21.2604i	0.417353	+	0.722876i
$866$	9.72056			0.330318
$867$	7.05247	+	12.2152i	0.239515	+	0.414851i
$868$	39.7670	−	68.8784i	1.34978	−	2.33789i
$869$	−1.06053	+	1.83689i	−0.0359759	+	0.0623122i
$870$	−3.17517			−0.107648
$871$	−3.16492	−	5.23137i	−0.107239	−	0.177258i
$872$	−5.68515			−0.192523
$873$	−4.65494	+	8.06258i	−0.157546	+	0.272877i
$874$	2.45905	−	4.25920i	0.0831786	−	0.144070i
$875$	15.7335	+	27.2511i	0.531888	+	0.921257i
$876$	3.55712			0.120184
$877$	19.5396	+	33.8435i	0.659804	+	1.14281i	0.980666	+	0.195689i	$0.0626942\pi$
$877$	19.5396	+	33.8435i	0.659804	+	1.14281i	−0.320862	+	0.947126i	$0.603972\pi$
$878$	−0.264819	−	0.458680i	−0.00893721	−	0.0154797i
$879$	−18.7808			−0.633461
$880$	5.97551	+	10.3499i	0.201434	+	0.348894i
$881$	−3.92975	+	6.80652i	−0.132396	+	0.229317i	−0.924600	−	0.380940i	$-0.875601\pi$
$881$	−3.92975	+	6.80652i	−0.132396	+	0.229317i	0.792203	+	0.610257i	$0.208934\pi$
$882$	2.60139	−	4.50575i	0.0875935	−	0.151716i
$883$	6.36927			0.214343			0.107171	−	0.994241i	$-0.465821\pi$
$883$	6.36927			0.214343			0.107171	+	0.994241i	$0.465821\pi$
$884$	−19.8875	−	32.8724i	−0.668887	−	1.10562i
$885$	35.6164			1.19723
$886$	3.71995	−	6.44314i	0.124974	−	0.216462i
$887$	1.37929	−	2.38900i	0.0463120	−	0.0802148i	−0.841940	−	0.539571i	$-0.818586\pi$
$887$	1.37929	−	2.38900i	0.0463120	−	0.0802148i	0.888252	+	0.459356i	$0.151920\pi$
$888$	−0.997885	−	1.72839i	−0.0334868	−	0.0580009i
$889$	−10.1216			−0.339469
$890$	1.59597	+	2.76430i	0.0534969	+	0.0926594i
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	−27.3164			−0.914621
$893$	6.69703	+	11.5996i	0.224107	+	0.388166i
$894$	−0.567280	+	0.982558i	−0.0189727	+	0.0328616i
$895$	−43.7269	+	75.7372i	−1.46163	+	2.53162i
$896$	42.1207			1.40715
$897$	11.3190	−	0.231856i	0.377929	−	0.00774144i
$898$	10.3727			0.346143
$899$	−12.9987	+	22.5143i	−0.433530	+	0.750895i
$900$	6.54427	−	11.3350i	0.218142	−	0.377833i
$901$	−17.2374	−	29.8561i	−0.574263	−	0.994652i
$902$	−0.139971			−0.00466053
$903$	18.6644	+	32.3277i	0.621112	+	1.07580i
$904$	8.48051	+	14.6887i	0.282057	+	0.488538i
$905$	51.8133			1.72233
$906$	−0.962659	−	1.66737i	−0.0319822	−	0.0553948i
$907$	−23.5142	+	40.7278i	−0.780777	+	1.35235i	0.150713	+	0.988578i	$0.451843\pi$
$907$	−23.5142	+	40.7278i	−0.780777	+	1.35235i	−0.931490	+	0.363768i	$0.881490\pi$
$908$	−26.0006	+	45.0344i	−0.862860	+	1.49452i
$909$	−11.2826			−0.374220
$910$	8.83854	−	16.0596i	0.292995	−	0.532372i
$911$	−21.5111			−0.712693			−0.356346	−	0.934354i	$-0.615978\pi$
$911$	−21.5111			−0.712693			−0.356346	+	0.934354i	$0.615978\pi$
$912$	9.09368	−	15.7507i	0.301122	−	0.521559i
$913$	1.88655	−	3.26759i	0.0624356	−	0.108142i
$914$	−2.46861	−	4.27577i	−0.0816545	−	0.141430i
$915$	−46.7893			−1.54681
$916$	−5.18464	−	8.98006i	−0.171305	−	0.296710i
$917$	10.6544	+	18.4539i	0.351838	+	0.609402i
$918$	1.66745			0.0550342
$919$	−10.2867	−	17.8171i	−0.339328	−	0.587733i	0.644979	−	0.764201i	$-0.276866\pi$
$919$	−10.2867	−	17.8171i	−0.339328	−	0.587733i	−0.984306	+	0.176467i	$0.943533\pi$
$920$	6.31898	−	10.9448i	0.208331	−	0.360839i
$921$	−6.99573	+	12.1170i	−0.230517	+	0.399267i
$922$	−11.2796			−0.371474
$923$	24.6856	−	0.505656i	0.812536	−	0.0166439i
$924$	9.43810			0.310491
$925$	5.84675	−	10.1269i	0.192240	−	0.332970i
$926$	−0.393974	+	0.682383i	−0.0129468	+	0.0224245i
$927$	−5.54847	−	9.61023i	−0.182236	−	0.315641i
$928$	−10.4161			−0.341925
$929$	−8.79355	−	15.2309i	−0.288507	−	0.499709i	0.684947	−	0.728593i	$-0.259825\pi$
$929$	−8.79355	−	15.2309i	−0.288507	−	0.499709i	−0.973454	+	0.228885i	$0.926492\pi$
$930$	4.33655	+	7.51113i	0.142201	+	0.246300i
$931$	91.1652			2.98782
$932$	−21.5559	−	37.3359i	−0.706087	−	1.22298i
$933$	3.62943	−	6.28637i	0.118822	−	0.205806i
$934$	−5.17792	+	8.96842i	−0.169427	+	0.293456i
$935$	−19.1991			−0.627879
$936$	−4.21468	+	0.0863329i	−0.137761	+	0.00282188i
$937$	−26.7279			−0.873161			−0.436580	−	0.899665i	$-0.643811\pi$
$937$	−26.7279			−0.873161			−0.436580	+	0.899665i	$0.643811\pi$
$938$	−1.25225	+	2.16896i	−0.0408875	+	0.0708192i
$939$	−2.87799	+	4.98483i	−0.0939198	+	0.162674i
$940$	8.40794	+	14.5630i	0.274237	+	0.474992i
$941$	−48.0352			−1.56590			−0.782952	−	0.622082i	$-0.786287\pi$
$941$	−48.0352			−1.56590			−0.782952	+	0.622082i	$0.786287\pi$
$942$	−2.35704	−	4.08252i	−0.0767966	−	0.133016i
$943$	−0.735013	−	1.27308i	−0.0239353	−	0.0414572i
$944$	35.9187			1.16905
$945$	−8.50255	−	14.7268i	−0.276588	−	0.479064i
$946$	1.12964	−	1.95660i	0.0367279	−	0.0636146i
$947$	26.8330	−	46.4761i	0.871955	−	1.51027i	0.0119844	−	0.999928i	$-0.496185\pi$
$947$	26.8330	−	46.4761i	0.871955	−	1.51027i	0.859971	−	0.510343i	$-0.170481\pi$
$948$	4.05252			0.131620
$949$	3.23659	−	5.88089i	0.105064	−	0.190902i
$950$	−10.7298			−0.348119
$951$	−11.5815	+	20.0598i	−0.375557	+	0.650484i
$952$	−16.1057	+	27.8960i	−0.521990	+	0.904113i
$953$	3.11176	+	5.38974i	0.100800	+	0.174591i	0.912014	−	0.410158i	$-0.134526\pi$
$953$	3.11176	+	5.38974i	0.100800	+	0.174591i	−0.811215	+	0.584749i	$0.801193\pi$
$954$	−1.84811			−0.0598347
$955$	25.0079	+	43.3149i	0.809235	+	1.40164i
$956$	13.0402	+	22.5863i	0.421751	+	0.730493i
$957$	−3.08504			−0.0997251
$958$	−2.34792	−	4.06672i	−0.0758579	−	0.131390i
$959$	−44.3902	+	76.8862i	−1.43344	+	2.48278i
$960$	10.2135	−	17.6904i	0.329640	−	0.570954i
$961$	40.0128			1.29074
$962$	−1.83970	+	0.0376841i	−0.0593142	+	0.00121498i
$963$	−18.0522			−0.581723
$964$	−8.49920	+	14.7210i	−0.273741	+	0.474133i
$965$	26.9600	−	46.6960i	0.867872	−	1.50320i
$966$	−2.31871	−	4.01613i	−0.0746033	−	0.129217i
$967$	22.8853			0.735943			0.367971	−	0.929837i	$-0.380052\pi$
$967$	22.8853			0.735943			0.367971	+	0.929837i	$0.380052\pi$
$968$	−0.584594	−	1.01255i	−0.0187896	−	0.0325445i
$969$	14.6089	+	25.3033i	0.469305	+	0.812860i
$970$	9.58187			0.307655
$971$	−12.8177	−	22.2009i	−0.411339	−	0.712460i	0.583698	−	0.811971i	$-0.301605\pi$
$971$	−12.8177	−	22.2009i	−0.411339	−	0.712460i	−0.995036	+	0.0995114i	$0.968272\pi$
$972$	−0.955306	+	1.65464i	−0.0306415	+	0.0530726i
$973$	−12.9818	+	22.4852i	−0.416178	+	0.720842i
$974$	12.8087			0.410417
$975$	−12.7853	−	21.1331i	−0.409457	−	0.676800i
$976$	−47.1864			−1.51040
$977$	−1.64436	+	2.84811i	−0.0526077	+	0.0911192i	−0.891130	−	0.453748i	$-0.850087\pi$
$977$	−1.64436	+	2.84811i	−0.0526077	+	0.0911192i	0.838522	+	0.544867i	$0.183420\pi$
$978$	−0.552000	+	0.956093i	−0.0176510	+	0.0305725i
$979$	1.55066	+	2.68583i	0.0495594	+	0.0858394i
$980$	114.455			3.65615
$981$	2.43124	+	4.21103i	0.0776235	+	0.134448i
$982$	0.0678026	+	0.117437i	0.00216367	+	0.00374758i
$983$	−35.2780			−1.12519			−0.562596	−	0.826732i	$-0.690197\pi$
$983$	−35.2780			−1.12519			−0.562596	+	0.826732i	$0.690197\pi$
$984$	0.273686	+	0.474039i	0.00872480	+	0.0151118i
$985$	17.3664	−	30.0795i	0.553340	−	0.958413i
$986$	2.57208	−	4.45497i	0.0819117	−	0.141875i
$987$	12.6297			0.402006
$988$	−18.6809	−	30.8780i	−0.594317	−	0.982360i
$989$	23.7278			0.754501
$990$	−0.514608	+	0.891327i	−0.0163553	+	0.0283282i
$991$	−12.2850	+	21.2782i	−0.390245	+	0.675925i	−0.992482	−	0.122393i	$-0.960943\pi$
$991$	−12.2850	+	21.2782i	−0.390245	+	0.675925i	0.602236	+	0.798318i	$0.294277\pi$
$992$	14.2260	+	24.6401i	0.451676	+	0.782325i
$993$	−8.05697			−0.255680
$994$	−5.05690	−	8.75880i	−0.160395	−	0.277812i
$995$	3.52074	+	6.09810i	0.111615	+	0.193323i
$996$	−7.20892			−0.228423
$997$	−21.7925	−	37.7457i	−0.690175	−	1.19542i	−0.971780	−	0.235888i	$-0.924200\pi$
$997$	−21.7925	−	37.7457i	−0.690175	−	1.19542i	0.281605	−	0.959530i	$-0.409133\pi$
$998$	4.32718	−	7.49490i	0.136975	−	0.237247i
$999$	−0.853486	+	1.47828i	−0.0270031	+	0.0467707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.d.100.3	✓	10
13.3	even	3	inner	429.2.i.d.133.3	yes	10
13.4	even	6		5577.2.a.s.1.3		5
13.9	even	3		5577.2.a.r.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.d.100.3	✓	10	1.1	even	1	trivial
429.2.i.d.133.3	yes	10	13.3	even	3	inner
5577.2.a.r.1.3		5	13.9	even	3
5577.2.a.s.1.3		5	13.4	even	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.149489 - 0.258923i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.955306 + 1.65464i) q^{4} -3.44245 q^{5} +(-0.149489 - 0.258923i) q^{6} +(-2.46991 - 4.27802i) q^{7} +1.16919 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.149489 - 0.258923i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.955306 + 1.65464i) q^{4} -3.44245 q^{5} +(-0.149489 - 0.258923i) q^{6} +(-2.46991 - 4.27802i) q^{7} +1.16919 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.514608 + 0.891327i) q^{10} +(-0.500000 + 0.866025i) q^{11} +1.91061 q^{12} +(1.73845 - 3.15876i) q^{13} -1.47690 q^{14} +(-1.72122 + 2.98125i) q^{15} +(-1.73583 + 3.00655i) q^{16} +(-2.78859 - 4.82998i) q^{17} -0.298978 q^{18} +(-2.61940 - 4.53694i) q^{19} +(-3.28859 - 5.69601i) q^{20} -4.93983 q^{21} +(0.149489 + 0.258923i) q^{22} +(-1.56999 + 2.71929i) q^{23} +(0.584594 - 1.01255i) q^{24} +6.85044 q^{25} +(-0.557996 - 0.922325i) q^{26} -1.00000 q^{27} +(4.71905 - 8.17363i) q^{28} +(-1.54252 + 2.67172i) q^{29} +(0.514608 + 0.891327i) q^{30} +8.42691 q^{31} +(1.68816 + 2.92398i) q^{32} +(0.500000 + 0.866025i) q^{33} -1.66745 q^{34} +(8.50255 + 14.7268i) q^{35} +(0.955306 - 1.65464i) q^{36} +(0.853486 - 1.47828i) q^{37} -1.56629 q^{38} +(-1.86634 - 3.08492i) q^{39} -4.02486 q^{40} +(-0.234083 + 0.405443i) q^{41} +(-0.738450 + 1.27903i) q^{42} +(-3.77835 - 6.54429i) q^{43} -1.91061 q^{44} +(1.72122 + 2.98125i) q^{45} +(0.469391 + 0.813009i) q^{46} -2.55670 q^{47} +(1.73583 + 3.00655i) q^{48} +(-8.70095 + 15.0705i) q^{49} +(1.02407 - 1.77373i) q^{50} -5.57718 q^{51} +(6.88737 - 0.141080i) q^{52} +6.18142 q^{53} +(-0.149489 + 0.258923i) q^{54} +(1.72122 - 2.98125i) q^{55} +(-2.88779 - 5.00180i) q^{56} -5.23881 q^{57} +(0.461179 + 0.798786i) q^{58} +(-5.17313 - 8.96012i) q^{59} -6.57718 q^{60} +(6.79593 + 11.7709i) q^{61} +(1.25973 - 2.18192i) q^{62} +(-2.46991 + 4.27802i) q^{63} -5.93388 q^{64} +(-5.98452 + 10.8739i) q^{65} +0.298978 q^{66} +(0.847892 - 1.46859i) q^{67} +(5.32791 - 9.22822i) q^{68} +(1.56999 + 2.71929i) q^{69} +5.08415 q^{70} +(3.42399 + 5.93053i) q^{71} +(-0.584594 - 1.01255i) q^{72} +1.86177 q^{73} +(-0.255174 - 0.441973i) q^{74} +(3.42522 - 5.93266i) q^{75} +(5.00466 - 8.66833i) q^{76} +4.93983 q^{77} +(-1.07775 + 0.0220766i) q^{78} +2.12106 q^{79} +(5.97551 - 10.3499i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.0699856 + 0.121219i) q^{82} -3.77309 q^{83} +(-4.71905 - 8.17363i) q^{84} +(9.59957 + 16.6269i) q^{85} -2.25929 q^{86} +(1.54252 + 2.67172i) q^{87} +(-0.584594 + 1.01255i) q^{88} +(1.55066 - 2.68583i) q^{89} +1.02922 q^{90} +(-17.8071 + 0.364758i) q^{91} -5.99927 q^{92} +(4.21345 - 7.29792i) q^{93} +(-0.382199 + 0.661987i) q^{94} +(9.01716 + 15.6182i) q^{95} +3.37633 q^{96} +(-4.65494 - 8.06258i) q^{97} +(2.60139 + 4.50575i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} - 5 q^{11} - 20 q^{12} + 9 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} - 8 q^{20} - 14 q^{21} - 11 q^{23} + 3 q^{24} - 6 q^{25} - 4 q^{26} - 10 q^{27} - 5 q^{28} + 2 q^{29} + 7 q^{30} + 20 q^{31} + 9 q^{32} + 5 q^{33} + 58 q^{34} + 14 q^{35} - 10 q^{36} - 15 q^{37} - 38 q^{38} - 6 q^{39} + 30 q^{40} + 2 q^{41} + q^{42} - 7 q^{43} + 20 q^{44} + 2 q^{45} - 20 q^{46} + 36 q^{47} + 4 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} - 3 q^{52} + 30 q^{53} + 2 q^{55} - 3 q^{56} - 14 q^{57} - 5 q^{58} + 4 q^{59} - 16 q^{60} + 14 q^{61} - 46 q^{62} - 7 q^{63} - 74 q^{64} - 44 q^{65} + 5 q^{67} + 24 q^{68} + 11 q^{69} + 80 q^{70} + 13 q^{71} - 3 q^{72} + 56 q^{73} - 15 q^{74} - 3 q^{75} - 2 q^{76} + 14 q^{77} - 23 q^{78} + 32 q^{79} + 22 q^{80} - 5 q^{81} - 4 q^{82} + 24 q^{83} + 5 q^{84} - 13 q^{85} + 4 q^{86} - 2 q^{87} - 3 q^{88} + 6 q^{89} + 14 q^{90} - 29 q^{91} - 4 q^{92} + 10 q^{93} + 2 q^{94} + 21 q^{95} + 18 q^{96} - 9 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 - 5 * q^11 - 20 * q^12 + 9 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 - 8 * q^20 - 14 * q^21 - 11 * q^23 + 3 * q^24 - 6 * q^25 - 4 * q^26 - 10 * q^27 - 5 * q^28 + 2 * q^29 + 7 * q^30 + 20 * q^31 + 9 * q^32 + 5 * q^33 + 58 * q^34 + 14 * q^35 - 10 * q^36 - 15 * q^37 - 38 * q^38 - 6 * q^39 + 30 * q^40 + 2 * q^41 + q^42 - 7 * q^43 + 20 * q^44 + 2 * q^45 - 20 * q^46 + 36 * q^47 + 4 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 - 3 * q^52 + 30 * q^53 + 2 * q^55 - 3 * q^56 - 14 * q^57 - 5 * q^58 + 4 * q^59 - 16 * q^60 + 14 * q^61 - 46 * q^62 - 7 * q^63 - 74 * q^64 - 44 * q^65 + 5 * q^67 + 24 * q^68 + 11 * q^69 + 80 * q^70 + 13 * q^71 - 3 * q^72 + 56 * q^73 - 15 * q^74 - 3 * q^75 - 2 * q^76 + 14 * q^77 - 23 * q^78 + 32 * q^79 + 22 * q^80 - 5 * q^81 - 4 * q^82 + 24 * q^83 + 5 * q^84 - 13 * q^85 + 4 * q^86 - 2 * q^87 - 3 * q^88 + 6 * q^89 + 14 * q^90 - 29 * q^91 - 4 * q^92 + 10 * q^93 + 2 * q^94 + 21 * q^95 + 18 * q^96 - 9 * q^97 - 16 * q^98 + 10 * q^99

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