LMFDB - Embedded newform 429.2.n.c.157.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, degree $4$, 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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.6
Character	$\chi$	$=$	429.157
Dual form			429.2.n.c.235.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18037 - 0.857589i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.0397803 - 0.122431i) q^{4} +(-0.326657 - 0.237330i) q^{5} +(-1.18037 - 0.857589i) q^{6} +(1.48593 - 4.57323i) q^{7} +(0.843682 + 2.59659i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.18037 - 0.857589i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.0397803 - 0.122431i) q^{4} +(-0.326657 - 0.237330i) q^{5} +(-1.18037 - 0.857589i) q^{6} +(1.48593 - 4.57323i) q^{7} +(0.843682 + 2.59659i) q^{8} +(-0.809017 + 0.587785i) q^{9} -0.589108 q^{10} +(0.851691 - 3.20541i) q^{11} -0.128732 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-2.16800 - 6.67242i) q^{14} +(-0.124772 + 0.384008i) q^{15} +(3.43095 + 2.49273i) q^{16} +(-2.90776 - 2.11261i) q^{17} +(-0.450861 + 1.38761i) q^{18} +(0.212342 + 0.653522i) q^{19} +(-0.0420512 + 0.0305520i) q^{20} -4.80858 q^{21} +(-1.74361 - 4.51396i) q^{22} +3.65382 q^{23} +(2.20879 - 1.60478i) q^{24} +(-1.49471 - 4.60023i) q^{25} +(-0.450861 + 1.38761i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.500795 - 0.363849i) q^{28} +(-0.367111 + 1.12985i) q^{29} +(0.182044 + 0.560275i) q^{30} +(-1.30215 + 0.946071i) q^{31} +0.727109 q^{32} +(-3.31171 + 0.180518i) q^{33} -5.24399 q^{34} +(-1.57076 + 1.14122i) q^{35} +(0.0397803 + 0.122431i) q^{36} +(1.26905 - 3.90574i) q^{37} +(0.811095 + 0.589295i) q^{38} +(0.809017 + 0.587785i) q^{39} +(0.340654 - 1.04842i) q^{40} +(3.78262 + 11.6417i) q^{41} +(-5.67590 + 4.12378i) q^{42} +10.6099 q^{43} +(-0.358561 - 0.231786i) q^{44} +0.403770 q^{45} +(4.31286 - 3.13347i) q^{46} +(4.06790 + 12.5197i) q^{47} +(1.31051 - 4.03333i) q^{48} +(-13.0433 - 9.47651i) q^{49} +(-5.70941 - 4.14813i) q^{50} +(-1.11067 + 3.41828i) q^{51} +(0.0397803 + 0.122431i) q^{52} +(-1.90226 + 1.38207i) q^{53} +1.45902 q^{54} +(-1.03895 + 0.844936i) q^{55} +13.1284 q^{56} +(0.555919 - 0.403899i) q^{57} +(0.535621 + 1.64847i) q^{58} +(-2.83687 + 8.73098i) q^{59} +(0.0420512 + 0.0305520i) q^{60} +(9.32073 + 6.77191i) q^{61} +(-0.725684 + 2.23343i) q^{62} +(1.48593 + 4.57323i) q^{63} +(-6.00365 + 4.36191i) q^{64} +0.403770 q^{65} +(-3.75423 + 3.05316i) q^{66} -2.47381 q^{67} +(-0.374321 + 0.271960i) q^{68} +(-1.12909 - 3.47499i) q^{69} +(-0.875374 + 2.69412i) q^{70} +(-3.86231 - 2.80614i) q^{71} +(-2.20879 - 1.60478i) q^{72} +(-2.21583 + 6.81964i) q^{73} +(-1.85157 - 5.69855i) q^{74} +(-3.91319 + 2.84310i) q^{75} +0.0884585 q^{76} +(-13.3935 - 8.65799i) q^{77} +1.45902 q^{78} +(5.00447 - 3.63596i) q^{79} +(-0.529144 - 1.62854i) q^{80} +(0.309017 - 0.951057i) q^{81} +(14.4487 + 10.4976i) q^{82} +(-2.44208 - 1.77428i) q^{83} +(-0.191287 + 0.588720i) q^{84} +(0.448454 + 1.38020i) q^{85} +(12.5236 - 9.09890i) q^{86} +1.18800 q^{87} +(9.04167 - 0.492854i) q^{88} +3.70447 q^{89} +(0.476598 - 0.346269i) q^{90} +(1.48593 + 4.57323i) q^{91} +(0.145350 - 0.447341i) q^{92} +(1.30215 + 0.946071i) q^{93} +(15.5384 + 11.2893i) q^{94} +(0.0857374 - 0.263873i) q^{95} +(-0.224689 - 0.691522i) q^{96} +(14.5850 - 10.5967i) q^{97} -23.5229 q^{98} +(1.19506 + 3.09384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) $ 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	1.18037	−	0.857589i	0.834648	−	0.606407i	−0.0862228	−	0.996276i	$-0.527480\pi$
$2$	1.18037	−	0.857589i	0.834648	−	0.606407i	0.920870	+	0.389869i	$0.127480\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.0397803	−	0.122431i	0.0198902	−	0.0612156i
$5$	−0.326657	−	0.237330i	−0.146085	−	0.106137i	0.512342	−	0.858782i	$-0.328778\pi$
$5$	−0.326657	−	0.237330i	−0.146085	−	0.106137i	−0.658427	+	0.752644i	$0.728778\pi$
$6$	−1.18037	−	0.857589i	−0.481884	−	0.350109i
$7$	1.48593	−	4.57323i	0.561629	−	1.72852i	−0.116130	−	0.993234i	$-0.537049\pi$
$7$	1.48593	−	4.57323i	0.561629	−	1.72852i	0.677760	−	0.735283i	$-0.262951\pi$
$8$	0.843682	+	2.59659i	0.298287	+	0.918032i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.589108			−0.186292
$11$	0.851691	−	3.20541i	0.256794	−	0.966466i
$11$	0.851691	−	3.20541i	0.256794	−	0.966466i
$12$	−0.128732			−0.0371617
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$	−2.16800	−	6.67242i	−0.579422	−	1.78328i
$15$	−0.124772	+	0.384008i	−0.0322160	+	0.0991505i
$16$	3.43095	+	2.49273i	0.857738	+	0.623183i
$17$	−2.90776	−	2.11261i	−0.705236	−	0.512384i	0.176398	−	0.984319i	$-0.443556\pi$
$17$	−2.90776	−	2.11261i	−0.705236	−	0.512384i	−0.881633	+	0.471935i	$0.843556\pi$
$18$	−0.450861	+	1.38761i	−0.106269	+	0.327062i
$19$	0.212342	+	0.653522i	0.0487146	+	0.149928i	0.972455	−	0.233091i	$-0.0748842\pi$
$19$	0.212342	+	0.653522i	0.0487146	+	0.149928i	−0.923740	+	0.383020i	$0.874884\pi$
$20$	−0.0420512	+	0.0305520i	−0.00940293	+	0.00683163i
$21$	−4.80858			−1.04932
$22$	−1.74361	−	4.51396i	−0.371739	−	0.962380i
$23$	3.65382			0.761874			0.380937	−	0.924601i	$-0.375602\pi$
$23$	3.65382			0.761874			0.380937	+	0.924601i	$0.375602\pi$
$24$	2.20879	−	1.60478i	0.450867	−	0.327574i
$25$	−1.49471	−	4.60023i	−0.298941	−	0.920046i
$26$	−0.450861	+	1.38761i	−0.0884212	+	0.272132i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−0.500795	−	0.363849i	−0.0946414	−	0.0687610i
$29$	−0.367111	+	1.12985i	−0.0681708	+	0.209808i	−0.979339	−	0.202227i	$-0.935182\pi$
$29$	−0.367111	+	1.12985i	−0.0681708	+	0.209808i	0.911168	+	0.412035i	$0.135182\pi$
$30$	0.182044	+	0.560275i	0.0332366	+	0.102292i
$31$	−1.30215	+	0.946071i	−0.233874	+	0.169919i	−0.698550	−	0.715562i	$-0.746171\pi$
$31$	−1.30215	+	0.946071i	−0.233874	+	0.169919i	0.464676	+	0.885481i	$0.346171\pi$
$32$	0.727109			0.128536
$33$	−3.31171	+	0.180518i	−0.576494	+	0.0314242i
$34$	−5.24399			−0.899336
$35$	−1.57076	+	1.14122i	−0.265506	+	0.192901i
$36$	0.0397803	+	0.122431i	0.00663006	+	0.0204052i
$37$	1.26905	−	3.90574i	0.208631	−	0.642100i	−0.790914	−	0.611928i	$-0.790394\pi$
$37$	1.26905	−	3.90574i	0.208631	−	0.642100i	0.999545	−	0.0301724i	$-0.00960563\pi$
$38$	0.811095	+	0.589295i	0.131577	+	0.0955963i
$39$	0.809017	+	0.587785i	0.129546	+	0.0941210i
$40$	0.340654	−	1.04842i	0.0538621	−	0.165770i
$41$	3.78262	+	11.6417i	0.590746	+	1.81813i	0.574855	+	0.818255i	$0.305058\pi$
$41$	3.78262	+	11.6417i	0.590746	+	1.81813i	0.0158904	+	0.999874i	$0.494942\pi$
$42$	−5.67590	+	4.12378i	−0.875810	+	0.636313i
$43$	10.6099			1.61799			0.808995	−	0.587816i	$-0.200012\pi$
$43$	10.6099			1.61799			0.808995	+	0.587816i	$0.200012\pi$
$44$	−0.358561	−	0.231786i	−0.0540551	−	0.0349430i
$45$	0.403770			0.0601905
$46$	4.31286	−	3.13347i	0.635896	−	0.462005i
$47$	4.06790	+	12.5197i	0.593364	+	1.82619i	0.562708	+	0.826655i	$0.309759\pi$
$47$	4.06790	+	12.5197i	0.593364	+	1.82619i	0.0306553	+	0.999530i	$0.490241\pi$
$48$	1.31051	−	4.03333i	0.189155	−	0.582161i
$49$	−13.0433	−	9.47651i	−1.86333	−	1.35379i
$50$	−5.70941	−	4.14813i	−0.807433	−	0.586634i
$51$	−1.11067	+	3.41828i	−0.155524	+	0.478655i
$52$	0.0397803	+	0.122431i	0.00551654	+	0.0169782i
$53$	−1.90226	+	1.38207i	−0.261296	+	0.189842i	−0.710718	−	0.703477i	$-0.751630\pi$
$53$	−1.90226	+	1.38207i	−0.261296	+	0.189842i	0.449422	+	0.893319i	$0.351630\pi$
$54$	1.45902			0.198547
$55$	−1.03895	+	0.844936i	−0.140092	+	0.113931i
$56$	13.1284			1.75436
$57$	0.555919	−	0.403899i	0.0736332	−	0.0534977i
$58$	0.535621	+	1.64847i	0.0703305	+	0.216455i
$59$	−2.83687	+	8.73098i	−0.369329	+	1.13668i	0.577897	+	0.816110i	$0.303874\pi$
$59$	−2.83687	+	8.73098i	−0.369329	+	1.13668i	−0.947226	+	0.320567i	$0.896126\pi$
$60$	0.0420512	+	0.0305520i	0.00542878	+	0.00394424i
$61$	9.32073	+	6.77191i	1.19340	+	0.867054i	0.993619	−	0.112787i	$-0.0359779\pi$
$61$	9.32073	+	6.77191i	1.19340	+	0.867054i	0.199778	+	0.979841i	$0.435978\pi$
$62$	−0.725684	+	2.23343i	−0.0921620	+	0.283645i
$63$	1.48593	+	4.57323i	0.187210	+	0.576172i
$64$	−6.00365	+	4.36191i	−0.750456	+	0.545238i
$65$	0.403770			0.0500815
$66$	−3.75423	+	3.05316i	−0.462114	+	0.375818i
$67$	−2.47381			−0.302225			−0.151112	−	0.988517i	$-0.548286\pi$
$67$	−2.47381			−0.302225			−0.151112	+	0.988517i	$0.548286\pi$
$68$	−0.374321	+	0.271960i	−0.0453931	+	0.0329800i
$69$	−1.12909	−	3.47499i	−0.135927	−	0.418339i
$70$	−0.875374	+	2.69412i	−0.104627	+	0.322009i
$71$	−3.86231	−	2.80614i	−0.458372	−	0.333027i	0.334520	−	0.942389i	$-0.391426\pi$
$71$	−3.86231	−	2.80614i	−0.458372	−	0.333027i	−0.792892	+	0.609362i	$0.791426\pi$
$72$	−2.20879	−	1.60478i	−0.260308	−	0.189125i
$73$	−2.21583	+	6.81964i	−0.259344	+	0.798178i	0.733599	+	0.679583i	$0.237839\pi$
$73$	−2.21583	+	6.81964i	−0.259344	+	0.798178i	−0.992943	+	0.118595i	$0.962161\pi$
$74$	−1.85157	−	5.69855i	−0.215241	−	0.662442i
$75$	−3.91319	+	2.84310i	−0.451856	+	0.328293i
$76$	0.0884585			0.0101469
$77$	−13.3935	−	8.65799i	−1.52633	−	0.986669i
$78$	1.45902			0.165201
$79$	5.00447	−	3.63596i	0.563047	−	0.409077i	−0.269526	−	0.962993i	$-0.586867\pi$
$79$	5.00447	−	3.63596i	0.563047	−	0.409077i	0.832573	+	0.553916i	$0.186867\pi$
$80$	−0.529144	−	1.62854i	−0.0591601	−	0.182076i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	14.4487	+	10.4976i	1.59559	+	1.15926i
$83$	−2.44208	−	1.77428i	−0.268054	−	0.194752i	0.445636	−	0.895214i	$-0.352977\pi$
$83$	−2.44208	−	1.77428i	−0.268054	−	0.194752i	−0.713690	+	0.700462i	$0.752977\pi$
$84$	−0.191287	+	0.588720i	−0.0208711	+	0.0642346i
$85$	0.448454	+	1.38020i	0.0486417	+	0.149704i
$86$	12.5236	−	9.09890i	1.35045	−	0.981160i
$87$	1.18800			0.127367
$88$	9.04167	−	0.492854i	0.963845	−	0.0525384i
$89$	3.70447			0.392673			0.196337	−	0.980537i	$-0.437095\pi$
$89$	3.70447			0.392673			0.196337	+	0.980537i	$0.437095\pi$
$90$	0.476598	−	0.346269i	0.0502379	−	0.0365000i
$91$	1.48593	+	4.57323i	0.155768	+	0.479404i
$92$	0.145350	−	0.447341i	0.0151538	−	0.0466386i
$93$	1.30215	+	0.946071i	0.135027	+	0.0981030i
$94$	15.5384	+	11.2893i	1.60266	+	1.16440i
$95$	0.0857374	−	0.263873i	0.00879647	−	0.0270728i
$96$	−0.224689	−	0.691522i	−0.0229322	−	0.0705782i
$97$	14.5850	−	10.5967i	1.48089	−	1.07593i	0.503617	−	0.863927i	$-0.332002\pi$
$97$	14.5850	−	10.5967i	1.48089	−	1.07593i	0.977270	−	0.212000i	$-0.0679978\pi$
$98$	−23.5229			−2.37617
$99$	1.19506	+	3.09384i	0.120108	+	0.310942i
$100$	−0.622672			−0.0622672
$101$	7.89518	−	5.73618i	0.785600	−	0.570772i	−0.121055	−	0.992646i	$-0.538628\pi$
$101$	7.89518	−	5.73618i	0.785600	−	0.570772i	0.906654	+	0.421874i	$0.138628\pi$
$102$	1.62048	+	4.98733i	0.160452	+	0.493819i
$103$	3.03237	−	9.33267i	0.298788	−	0.919575i	−0.683135	−	0.730292i	$-0.739384\pi$
$103$	3.03237	−	9.33267i	0.298788	−	0.919575i	0.981923	−	0.189283i	$-0.0606162\pi$
$104$	−2.20879	−	1.60478i	−0.216590	−	0.157362i
$105$	1.57076	+	1.14122i	0.153290	+	0.111372i
$106$	−1.06012	+	3.26272i	−0.102968	+	0.316903i
$107$	3.49293	+	10.7501i	0.337674	+	1.03925i	0.965390	+	0.260811i	$0.0839899\pi$
$107$	3.49293	+	10.7501i	0.337674	+	1.03925i	−0.627716	+	0.778442i	$0.716010\pi$
$108$	0.104146	−	0.0756667i	0.0100215	−	0.00728103i
$109$	−15.6688			−1.50080			−0.750398	−	0.660986i	$-0.770138\pi$
$109$	−15.6688			−1.50080			−0.750398	+	0.660986i	$0.770138\pi$
$110$	−0.501738	+	1.88833i	−0.0478388	+	0.180045i
$111$	−4.10674			−0.389795
$112$	16.4980	−	11.9865i	1.55891	−	1.13262i
$113$	0.372451	+	1.14629i	0.0350372	+	0.107833i	0.967046	−	0.254603i	$-0.0819449\pi$
$113$	0.372451	+	1.14629i	0.0350372	+	0.107833i	−0.932008	+	0.362437i	$0.881945\pi$
$114$	0.309811	−	0.953499i	0.0290164	−	0.0893034i
$115$	−1.19355	−	0.867161i	−0.111299	−	0.0808632i
$116$	0.123725	+	0.0898917i	0.0114876	+	0.00834623i
$117$	0.309017	−	0.951057i	0.0285686	−	0.0879252i
$118$	4.13904	+	12.7387i	0.381029	+	1.17269i
$119$	−13.9822	+	10.1587i	−1.28175	+	0.931242i
$120$	−1.10238			−0.100633
$121$	−9.54925	−	5.46003i	−0.868113	−	0.496366i
$122$	16.8094			1.52185
$123$	9.90302	−	7.19497i	0.892926	−	0.648748i
$124$	0.0640285	+	0.197059i	0.00574993	+	0.0176965i
$125$	−1.22738	+	3.77748i	−0.109780	+	0.337868i
$126$	5.67590	+	4.12378i	0.505649	+	0.367376i
$127$	−7.78069	−	5.65300i	−0.690425	−	0.501623i	0.186375	−	0.982479i	$-0.440326\pi$
$127$	−7.78069	−	5.65300i	−0.690425	−	0.501623i	−0.876800	+	0.480856i	$0.840326\pi$
$128$	−3.79518	+	11.6804i	−0.335450	+	1.03241i
$129$	−3.27863	−	10.0906i	−0.288667	−	0.888426i
$130$	0.476598	−	0.346269i	0.0418004	−	0.0303698i
$131$	−17.8134			−1.55636			−0.778182	−	0.628038i	$-0.783858\pi$
$131$	−17.8134			−1.55636			−0.778182	+	0.628038i	$0.783858\pi$
$132$	−0.109640	+	0.412638i	−0.00954292	+	0.0359155i
$133$	3.30423			0.286513
$134$	−2.92002	+	2.12152i	−0.252251	+	0.183271i
$135$	−0.124772	−	0.384008i	−0.0107387	−	0.0330502i
$136$	3.03235	−	9.33263i	0.260022	−	0.800266i
$137$	−10.2735	−	7.46415i	−0.877727	−	0.637706i	0.0549225	−	0.998491i	$-0.482509\pi$
$137$	−10.2735	−	7.46415i	−0.877727	−	0.637706i	−0.932649	+	0.360785i	$0.882509\pi$
$138$	−4.31286	−	3.13347i	−0.367135	−	0.266739i
$139$	−1.00836	+	3.10340i	−0.0855277	+	0.263227i	−0.984670	−	0.174430i	$-0.944192\pi$
$139$	−1.00836	+	3.10340i	−0.0855277	+	0.263227i	0.899142	+	0.437657i	$0.144192\pi$
$140$	0.0772359	+	0.237708i	0.00652762	+	0.0200900i
$141$	10.6499	−	7.73760i	0.896883	−	0.651623i
$142$	−6.96547			−0.584529
$143$	1.19506	+	3.09384i	0.0999357	+	0.258720i
$144$	−4.24089			−0.353408
$145$	0.388067	−	0.281947i	0.0322272	−	0.0234144i
$146$	3.23294	+	9.94997i	0.267560	+	0.823465i
$147$	−4.98209	+	15.3333i	−0.410916	+	1.26467i
$148$	−0.427702	−	0.310743i	−0.0351569	−	0.0255430i
$149$	3.02277	+	2.19617i	0.247635	+	0.179917i	0.704678	−	0.709527i	$-0.251091\pi$
$149$	3.02277	+	2.19617i	0.247635	+	0.179917i	−0.457043	+	0.889445i	$0.651091\pi$
$150$	−2.18080	+	6.71182i	−0.178062	+	0.548018i
$151$	−3.32997	−	10.2486i	−0.270989	−	0.834018i	−0.990253	−	0.139281i	$-0.955521\pi$
$151$	−3.32997	−	10.2486i	−0.270989	−	0.834018i	0.719264	−	0.694737i	$-0.244479\pi$
$152$	−1.51778	+	1.10273i	−0.123108	+	0.0894431i
$153$	3.59419			0.290573
$154$	−23.2343	+	1.26648i	−1.87227	+	0.102056i
$155$	0.649889			0.0522004
$156$	0.104146	−	0.0756667i	0.00833837	−	0.00605818i
$157$	6.42953	+	19.7881i	0.513133	+	1.57926i	0.786654	+	0.617394i	$0.211811\pi$
$157$	6.42953	+	19.7881i	0.513133	+	1.57926i	−0.273522	+	0.961866i	$0.588189\pi$
$158$	2.78897	−	8.58356i	0.221878	−	0.682871i
$159$	1.90226	+	1.38207i	0.150859	+	0.109606i
$160$	−0.237515	−	0.172565i	−0.0187772	−	0.0136425i
$161$	5.42932	−	16.7097i	0.427891	−	1.31691i
$162$	−0.450861	−	1.38761i	−0.0354230	−	0.109021i
$163$	11.0751	−	8.04652i	0.867468	−	0.630252i	−0.0624385	−	0.998049i	$-0.519888\pi$
$163$	11.0751	−	8.04652i	0.867468	−	0.630252i	0.929906	+	0.367797i	$0.119888\pi$
$164$	1.57578			0.123048
$165$	1.12464	+	0.727001i	0.0875527	+	0.0565969i
$166$	−4.40416			−0.341829
$167$	−10.5448	+	7.66127i	−0.815983	+	0.592847i	−0.915559	−	0.402183i	$-0.868251\pi$
$167$	−10.5448	+	7.66127i	−0.815983	+	0.592847i	0.0995757	+	0.995030i	$0.468251\pi$
$168$	−4.05691	−	12.4859i	−0.312997	−	0.963307i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	1.71299	+	1.24456i	0.131380	+	0.0954531i
$171$	−0.555919	−	0.403899i	−0.0425122	−	0.0308869i
$172$	0.422064	−	1.29898i	0.0321821	−	0.0990463i
$173$	2.54604	+	7.83590i	0.193572	+	0.595752i	0.999990	+	0.00440714i	$0.00140284\pi$
$173$	2.54604	+	7.83590i	0.193572	+	0.595752i	−0.806419	+	0.591345i	$0.798597\pi$
$174$	1.40227	−	1.01881i	0.106306	−	0.0772359i
$175$	−23.2589			−1.75821
$176$	10.9123	−	8.87456i	0.822548	−	0.668945i
$177$	9.18030			0.690033
$178$	4.37265	−	3.17691i	0.327744	−	0.238120i
$179$	−3.21898	−	9.90700i	−0.240598	−	0.740484i	−0.996329	−	0.0856022i	$-0.972719\pi$
$179$	−3.21898	−	9.90700i	−0.240598	−	0.740484i	0.755732	−	0.654881i	$-0.227281\pi$
$180$	0.0160621	−	0.0494341i	0.00119720	−	0.00368460i
$181$	−10.6770	−	7.75729i	−0.793615	−	0.576595i	0.115419	−	0.993317i	$-0.463179\pi$
$181$	−10.6770	−	7.75729i	−0.793615	−	0.576595i	−0.909034	+	0.416722i	$0.863179\pi$
$182$	5.67590	+	4.12378i	0.420726	+	0.305675i
$183$	3.56020	−	10.9572i	0.263178	−	0.809978i
$184$	3.08266	+	9.48745i	0.227257	+	0.699424i
$185$	−1.34150	+	0.974654i	−0.0986287	+	0.0716580i
$186$	2.34836			0.172190
$187$	−9.24829	+	7.52126i	−0.676302	+	0.550009i
$188$	1.69462			0.123593
$189$	3.89022	−	2.82641i	0.282972	−	0.205591i
$190$	−0.125092	−	0.384995i	−0.00907516	−	0.0279305i
$191$	−3.20612	+	9.86743i	−0.231987	+	0.713983i	0.765520	+	0.643412i	$0.222482\pi$
$191$	−3.20612	+	9.86743i	−0.231987	+	0.713983i	−0.997507	+	0.0705702i	$0.977518\pi$
$192$	6.00365	+	4.36191i	0.433276	+	0.314793i
$193$	6.16222	+	4.47711i	0.443566	+	0.322270i	0.787050	−	0.616889i	$-0.211607\pi$
$193$	6.16222	+	4.47711i	0.443566	+	0.322270i	−0.343484	+	0.939158i	$0.611607\pi$
$194$	8.12817	−	25.0159i	0.583569	−	1.79604i
$195$	−0.124772	−	0.384008i	−0.00893510	−	0.0274994i
$196$	−1.67909	+	1.21993i	−0.119935	+	0.0871377i
$197$	2.63142			0.187481			0.0937404	−	0.995597i	$-0.470118\pi$
$197$	2.63142			0.187481			0.0937404	+	0.995597i	$0.470118\pi$
$198$	4.06385	+	2.62701i	0.288805	+	0.186693i
$199$	−11.9393			−0.846353			−0.423177	−	0.906047i	$-0.639085\pi$
$199$	−11.9393			−0.846353			−0.423177	+	0.906047i	$0.639085\pi$
$200$	10.6838	−	7.76227i	0.755462	−	0.548875i
$201$	0.764451	+	2.35274i	0.0539202	+	0.165949i
$202$	4.39995	−	13.5416i	0.309579	−	0.952786i
$203$	4.62156	+	3.35776i	0.324370	+	0.235669i
$204$	0.374321	+	0.271960i	0.0262077	+	0.0190410i
$205$	1.52731	−	4.70057i	0.106672	−	0.328302i
$206$	−4.42428	−	13.6165i	−0.308254	−	0.948708i
$207$	−2.95600	+	2.14766i	−0.205456	+	0.149273i
$208$	−4.24089			−0.294053
$209$	2.27565	−	0.124044i	0.157410	−	0.00858029i
$210$	2.83277			0.195480
$211$	3.53112	−	2.56551i	0.243092	−	0.176617i	−0.459568	−	0.888143i	$-0.651996\pi$
$211$	3.53112	−	2.56551i	0.243092	−	0.176617i	0.702660	+	0.711526i	$0.251996\pi$
$212$	0.0935365	+	0.287876i	0.00642411	+	0.0197714i
$213$	−1.47527	+	4.54042i	−0.101084	+	0.311105i
$214$	13.3421	+	9.69362i	0.912049	+	0.662643i
$215$	−3.46579	−	2.51804i	−0.236365	−	0.171729i
$216$	−0.843682	+	2.59659i	−0.0574053	+	0.176675i
$217$	2.39168	+	7.36085i	0.162358	+	0.499687i
$218$	−18.4949	+	13.4374i	−1.25264	+	0.910093i
$219$	7.17059			0.484544
$220$	0.0621168	+	0.160812i	0.00418792	+	0.0108419i
$221$	3.59419			0.241771
$222$	−4.84747	+	3.52189i	−0.325341	+	0.236374i
$223$	−0.383475	−	1.18022i	−0.0256794	−	0.0790330i	0.937396	−	0.348267i	$-0.113230\pi$
$223$	−0.383475	−	1.18022i	−0.0256794	−	0.0790330i	−0.963075	+	0.269234i	$0.913230\pi$
$224$	1.08043	−	3.32524i	0.0721896	−	0.222177i
$225$	3.91319	+	2.84310i	0.260879	+	0.189540i
$226$	1.42267	+	1.03363i	0.0946347	+	0.0687561i
$227$	−4.46395	+	13.7386i	−0.296283	+	0.911864i	0.686505	+	0.727125i	$0.259144\pi$
$227$	−4.46395	+	13.7386i	−0.296283	+	0.911864i	−0.982788	+	0.184739i	$0.940856\pi$
$228$	−0.0273352	−	0.0841291i	−0.00181032	−	0.00557158i
$229$	3.53794	−	2.57047i	0.233794	−	0.169861i	−0.464720	−	0.885458i	$-0.653845\pi$
$229$	3.53794	−	2.57047i	0.233794	−	0.169861i	0.698514	+	0.715596i	$0.253845\pi$
$230$	−2.15249			−0.141931
$231$	−4.09542	+	15.4134i	−0.269459	+	1.01413i
$232$	−3.24348			−0.212945
$233$	−1.78198	+	1.29468i	−0.116741	+	0.0848174i	−0.644624	−	0.764500i	$-0.722986\pi$
$233$	−1.78198	+	1.29468i	−0.116741	+	0.0848174i	0.527883	+	0.849317i	$0.322986\pi$
$234$	−0.450861	−	1.38761i	−0.0294737	−	0.0907108i
$235$	1.64250	−	5.05508i	0.107145	−	0.329757i
$236$	0.956094	+	0.694643i	0.0622364	+	0.0452174i
$237$	−5.00447	−	3.63596i	−0.325075	−	0.236181i
$238$	−7.79220	+	23.9819i	−0.505094	+	1.55452i
$239$	−3.49304	−	10.7505i	−0.225946	−	0.695391i	−0.998194	−	0.0600696i	$-0.980868\pi$
$239$	−3.49304	−	10.7505i	−0.225946	−	0.695391i	0.772248	−	0.635321i	$-0.219132\pi$
$240$	−1.38532	+	1.00649i	−0.0894218	+	0.0649688i
$241$	−7.16866			−0.461774			−0.230887	−	0.972981i	$-0.574163\pi$
$241$	−7.16866			−0.461774			−0.230887	+	0.972981i	$0.574163\pi$
$242$	−15.9541	+	1.74447i	−1.02557	+	0.112139i
$243$	−1.00000			−0.0641500
$244$	1.19987	−	0.871760i	0.0768141	−	0.0558087i
$245$	2.01162	+	6.19114i	0.128518	+	0.395537i
$246$	5.51891	−	16.9854i	0.351873	−	1.08295i
$247$	−0.555919	−	0.403899i	−0.0353723	−	0.0256995i
$248$	−3.55516	−	2.58297i	−0.225753	−	0.164019i
$249$	−0.932793	+	2.87084i	−0.0591134	+	0.181932i
$250$	1.79076	+	5.51141i	0.113258	+	0.348572i
$251$	13.5672	−	9.85714i	0.856353	−	0.622177i	−0.0705372	−	0.997509i	$-0.522471\pi$
$251$	13.5672	−	9.85714i	0.856353	−	0.622177i	0.926890	+	0.375332i	$0.122471\pi$
$252$	0.619017			0.0389944
$253$	3.11192	−	11.7120i	0.195645	−	0.736325i
$254$	−14.0320			−0.880449
$255$	1.17407	−	0.853010i	0.0735230	−	0.0534176i
$256$	0.950857	+	2.92644i	0.0594286	+	0.182902i
$257$	8.16792	−	25.1383i	0.509501	−	1.56808i	−0.283569	−	0.958952i	$-0.591518\pi$
$257$	8.16792	−	25.1383i	0.509501	−	1.56808i	0.793070	−	0.609131i	$-0.208482\pi$
$258$	−12.5236	−	9.09890i	−0.779683	−	0.566473i
$259$	−15.9761	−	11.6073i	−0.992708	−	0.721244i
$260$	0.0160621	−	0.0494341i	0.000996130	−	0.00306577i
$261$	−0.367111	−	1.12985i	−0.0227236	−	0.0699360i
$262$	−21.0264	+	15.2766i	−1.29902	+	0.943790i
$263$	15.9258			0.982030			0.491015	−	0.871151i	$-0.336626\pi$
$263$	15.9258			0.982030			0.491015	+	0.871151i	$0.336626\pi$
$264$	−3.26276	−	8.44684i	−0.200809	−	0.519867i
$265$	0.949395			0.0583209
$266$	3.90021	−	2.83367i	0.239137	−	0.173743i
$267$	−1.14474	−	3.52316i	−0.0700573	−	0.215614i
$268$	−0.0984092	+	0.302872i	−0.00601130	+	0.0185009i
$269$	7.40966	+	5.38343i	0.451775	+	0.328234i	0.790296	−	0.612725i	$-0.209927\pi$
$269$	7.40966	+	5.38343i	0.451775	+	0.328234i	−0.338521	+	0.940959i	$0.609927\pi$
$270$	−0.476598	−	0.346269i	−0.0290049	−	0.0210733i
$271$	−5.93537	+	18.2672i	−0.360548	+	1.10965i	0.592175	+	0.805810i	$0.298270\pi$
$271$	−5.93537	+	18.2672i	−0.360548	+	1.10965i	−0.952722	+	0.303842i	$0.901730\pi$
$272$	−4.71021	−	14.4965i	−0.285599	−	0.878982i
$273$	3.89022	−	2.82641i	0.235447	−	0.171062i
$274$	−18.5277			−1.11930
$275$	−16.0186	+	0.873162i	−0.965960	+	0.0526537i
$276$	−0.470363			−0.0283125
$277$	2.75324	−	2.00035i	0.165426	−	0.120189i	−0.501992	−	0.864872i	$-0.667399\pi$
$277$	2.75324	−	2.00035i	0.165426	−	0.120189i	0.667418	+	0.744683i	$0.267399\pi$
$278$	1.47121	+	4.52792i	0.0882374	+	0.271567i
$279$	0.497379	−	1.53077i	0.0297773	−	0.0916451i
$280$	−4.28850	−	3.11577i	−0.256287	−	0.186203i
$281$	−25.9782	−	18.8742i	−1.54973	−	1.12594i	−0.943845	−	0.330389i	$-0.892820\pi$
$281$	−25.9782	−	18.8742i	−1.54973	−	1.12594i	−0.605882	−	0.795554i	$-0.707180\pi$
$282$	5.93513	−	18.2665i	0.353432	−	1.08775i
$283$	8.72796	+	26.8619i	0.518823	+	1.59677i	0.776216	+	0.630467i	$0.217136\pi$
$283$	8.72796	+	26.8619i	0.518823	+	1.59677i	−0.257393	+	0.966307i	$0.582864\pi$
$284$	−0.497203	+	0.361239i	−0.0295036	+	0.0214356i
$285$	−0.277452			−0.0164348
$286$	4.06385	+	2.62701i	0.240301	+	0.155338i
$287$	58.8609			3.47445
$288$	−0.588244	+	0.427384i	−0.0346626	+	0.0251839i
$289$	−1.26134	−	3.88202i	−0.0741967	−	0.228354i
$290$	0.216268	−	0.665604i	0.0126997	−	0.0390856i
$291$	−14.5850	−	10.5967i	−0.854990	−	0.621187i
$292$	0.746790	+	0.542575i	0.0437026	+	0.0317518i
$293$	2.14703	−	6.60789i	0.125431	−	0.386037i	−0.868548	−	0.495604i	$-0.834947\pi$
$293$	2.14703	−	6.60789i	0.125431	−	0.386037i	0.993979	+	0.109567i	$0.0349466\pi$
$294$	7.26896	+	22.3716i	0.423935	+	1.30474i
$295$	2.99881	−	2.17876i	0.174597	−	0.126852i
$296$	11.2123			0.651700
$297$	2.57312	−	2.09262i	0.149308	−	0.121426i
$298$	5.45140			0.315791
$299$	−2.95600	+	2.14766i	−0.170950	+	0.124202i
$300$	0.192416	+	0.592196i	0.0111092	+	0.0341905i
$301$	15.7655	−	48.5213i	0.908710	−	2.79672i
$302$	−12.7197	−	9.24138i	−0.731934	−	0.531781i
$303$	−7.89518	−	5.73618i	−0.453566	−	0.329535i
$304$	−0.900520	+	2.77151i	−0.0516483	+	0.158957i
$305$	−1.43750	−	4.42418i	−0.0823112	−	0.253328i
$306$	4.24247	−	3.08234i	0.242526	−	0.176206i
$307$	10.7394			0.612930			0.306465	−	0.951882i	$-0.400854\pi$
$307$	10.7394			0.612930			0.306465	+	0.951882i	$0.400854\pi$
$308$	−1.59281	+	1.29536i	−0.0907585	+	0.0738102i
$309$	−9.81295			−0.558239
$310$	0.767110	−	0.557338i	0.0435689	−	0.0316547i
$311$	−1.32439	−	4.07604i	−0.0750991	−	0.231131i	0.906460	−	0.422293i	$-0.138775\pi$
$311$	−1.32439	−	4.07604i	−0.0750991	−	0.231131i	−0.981559	+	0.191162i	$0.938775\pi$
$312$	−0.843682	+	2.59659i	−0.0477641	+	0.147003i
$313$	−19.0216	−	13.8200i	−1.07516	−	0.781152i	−0.0983298	−	0.995154i	$-0.531350\pi$
$313$	−19.0216	−	13.8200i	−1.07516	−	0.781152i	−0.976833	+	0.214002i	$0.931350\pi$
$314$	24.5593	+	17.8433i	1.38596	+	1.00696i
$315$	0.599975	−	1.84653i	0.0338048	−	0.104040i
$316$	−0.246076	−	0.757343i	−0.0138428	−	0.0426039i
$317$	6.86086	−	4.98471i	0.385345	−	0.279969i	−0.378201	−	0.925724i	$-0.623457\pi$
$317$	6.86086	−	4.98471i	0.385345	−	0.279969i	0.763545	+	0.645754i	$0.223457\pi$
$318$	3.43062			0.192380
$319$	3.30897	+	2.13902i	0.185266	+	0.119762i
$320$	2.99635			0.167501
$321$	9.14460	−	6.64394i	0.510402	−	0.370829i
$322$	−7.92148	−	24.3798i	−0.441447	−	1.35863i
$323$	0.763198	−	2.34888i	0.0424655	−	0.130695i
$324$	−0.104146	−	0.0756667i	−0.00578590	−	0.00420370i
$325$	3.91319	+	2.84310i	0.217065	+	0.157707i
$326$	6.17209	−	18.9957i	0.341841	−	1.05208i
$327$	4.84192	+	14.9019i	0.267759	+	0.824076i
$328$	−27.0374	+	19.6438i	−1.49289	+	1.08465i
$329$	63.3000			3.48984
$330$	1.95095	−	0.106345i	0.107396	−	0.00585409i
$331$	32.5901			1.79132			0.895658	−	0.444743i	$-0.146705\pi$
$331$	32.5901			1.79132			0.895658	+	0.444743i	$0.146705\pi$
$332$	−0.314374	+	0.228406i	−0.0172535	+	0.0125354i
$333$	1.26905	+	3.90574i	0.0695436	+	0.214033i
$334$	−5.87658	+	18.0863i	−0.321552	+	0.989636i
$335$	0.808089	+	0.587111i	0.0441506	+	0.0320773i
$336$	−16.4980	−	11.9865i	−0.900040	−	0.653917i
$337$	−9.61056	+	29.5783i	−0.523521	+	1.61123i	0.243702	+	0.969850i	$0.421638\pi$
$337$	−9.61056	+	29.5783i	−0.523521	+	1.61123i	−0.767223	+	0.641381i	$0.778362\pi$
$338$	−0.450861	−	1.38761i	−0.0245236	−	0.0754759i
$339$	0.975089	−	0.708443i	0.0529595	−	0.0384774i
$340$	0.186819			0.0101317
$341$	1.92351	+	4.97969i	0.104164	+	0.269666i
$342$	−1.00257			−0.0542127
$343$	−35.4881	+	25.7836i	−1.91618	+	1.39219i
$344$	8.95136	+	27.5494i	0.482625	+	1.48537i
$345$	−0.455894	+	1.40310i	−0.0245445	+	0.0755402i
$346$	9.72524	+	7.06580i	0.522832	+	0.379860i
$347$	−4.07105	−	2.95779i	−0.218545	−	0.158783i	0.473126	−	0.880995i	$-0.343125\pi$
$347$	−4.07105	−	2.95779i	−0.218545	−	0.158783i	−0.691672	+	0.722212i	$0.743125\pi$
$348$	0.0472589	−	0.145448i	0.00253334	−	0.00779682i
$349$	−9.29087	−	28.5944i	−0.497329	−	1.53062i	−0.813295	−	0.581851i	$-0.802329\pi$
$349$	−9.29087	−	28.5944i	−0.497329	−	1.53062i	0.315966	−	0.948770i	$-0.397671\pi$
$350$	−27.4541	+	19.9466i	−1.46749	+	1.06619i
$351$	−1.00000			−0.0533761
$352$	0.619272	−	2.33068i	0.0330073	−	0.124226i
$353$	−7.51069			−0.399754			−0.199877	−	0.979821i	$-0.564054\pi$
$353$	−7.51069			−0.399754			−0.199877	+	0.979821i	$0.564054\pi$
$354$	10.8361	−	7.87292i	0.575935	−	0.418441i
$355$	0.595671	+	1.83329i	0.0316149	+	0.0973008i
$356$	0.147365	−	0.453543i	0.00781034	−	0.0240377i
$357$	13.9822	+	10.1587i	0.740016	+	0.537653i
$358$	−12.2957	−	8.93336i	−0.649849	−	0.472143i
$359$	−7.64921	+	23.5419i	−0.403710	+	1.24249i	0.518258	+	0.855225i	$0.326581\pi$
$359$	−7.64921	+	23.5419i	−0.403710	+	1.24249i	−0.921968	+	0.387267i	$0.873419\pi$
$360$	0.340654	+	1.04842i	0.0179540	+	0.0552568i
$361$	14.9893	−	10.8904i	0.788912	−	0.573178i
$362$	−19.2554			−1.01204
$363$	−2.24192	+	10.7691i	−0.117670	+	0.565232i
$364$	0.619017			0.0324453
$365$	2.34232	−	1.70180i	0.122603	−	0.0890762i
$366$	−5.19440	−	15.9867i	−0.271515	−	0.835639i
$367$	4.38220	−	13.4870i	0.228749	−	0.704016i	−0.769141	−	0.639080i	$-0.779315\pi$
$367$	4.38220	−	13.4870i	0.228749	−	0.704016i	0.997889	−	0.0649368i	$-0.0206846\pi$
$368$	12.5361	+	9.10799i	0.653488	+	0.474787i
$369$	−9.90302	−	7.19497i	−0.515531	−	0.374555i
$370$	−0.747609	+	2.30090i	−0.0388663	+	0.119618i
$371$	3.49391	+	10.7531i	0.181395	+	0.558275i
$372$	0.167629	−	0.121789i	0.00869115	−	0.00631449i
$373$	−14.5256			−0.752105			−0.376052	−	0.926598i	$-0.622719\pi$
$373$	−14.5256			−0.752105			−0.376052	+	0.926598i	$0.622719\pi$
$374$	−4.46626	+	16.8091i	−0.230945	+	0.869178i
$375$	3.97188			0.205107
$376$	−29.0765	+	21.1253i	−1.49950	+	1.08945i
$377$	−0.367111	−	1.12985i	−0.0189072	−	0.0581903i
$378$	2.16800	−	6.67242i	0.111510	−	0.343192i
$379$	14.2804	+	10.3753i	0.733535	+	0.532944i	0.890680	−	0.454631i	$-0.150229\pi$
$379$	14.2804	+	10.3753i	0.733535	+	0.532944i	−0.157145	+	0.987576i	$0.550229\pi$
$380$	−0.0288956	−	0.0209939i	−0.00148231	−	0.00107696i
$381$	−2.97196	+	9.14675i	−0.152258	+	0.468602i
$382$	4.67779	+	14.3968i	0.239337	+	0.736602i
$383$	−4.97199	+	3.61236i	−0.254057	+	0.184583i	−0.707523	−	0.706690i	$-0.750187\pi$
$383$	−4.97199	+	3.61236i	−0.254057	+	0.184583i	0.453466	+	0.891274i	$0.350187\pi$
$384$	12.2815			0.626736
$385$	2.32028	+	6.00687i	0.118252	+	0.306139i
$386$	11.1132			0.565648
$387$	−8.58356	+	6.23632i	−0.436327	+	0.317010i
$388$	−0.717164	−	2.20720i	−0.0364085	−	0.112054i
$389$	−0.853317	+	2.62624i	−0.0432649	+	0.133156i	−0.970356	−	0.241681i	$-0.922301\pi$
$389$	−0.853317	+	2.62624i	−0.0432649	+	0.133156i	0.927091	+	0.374837i	$0.122301\pi$
$390$	−0.476598	−	0.346269i	−0.0241335	−	0.0175340i
$391$	−10.6244	−	7.71910i	−0.537300	−	0.390372i
$392$	13.6022	−	41.8632i	0.687014	−	2.11441i
$393$	5.50465	+	16.9416i	0.277673	+	0.854589i
$394$	3.10605	−	2.25668i	0.156480	−	0.113690i
$395$	−2.49767			−0.125671
$396$	0.426322	−	0.0232385i	0.0214235	−	0.00116778i
$397$	−30.0458			−1.50796			−0.753978	−	0.656899i	$-0.771868\pi$
$397$	−30.0458			−1.50796			−0.753978	+	0.656899i	$0.771868\pi$
$398$	−14.0928	+	10.2390i	−0.706406	+	0.513234i
$399$	−1.02106	−	3.14251i	−0.0511171	−	0.157322i
$400$	6.33889	−	19.5091i	0.316944	−	0.975454i
$401$	16.6224	+	12.0768i	0.830081	+	0.603089i	0.919582	−	0.392898i	$-0.128527\pi$
$401$	16.6224	+	12.0768i	0.830081	+	0.603089i	−0.0895014	+	0.995987i	$0.528527\pi$
$402$	2.92002	+	2.12152i	0.145637	+	0.105812i
$403$	0.497379	−	1.53077i	0.0247762	−	0.0762533i
$404$	−0.388215	−	1.19480i	−0.0193144	−	0.0594437i
$405$	−0.326657	+	0.237330i	−0.0162317	+	0.0117930i
$406$	8.33473			0.413646
$407$	−11.4386	−	7.39431i	−0.566993	−	0.366522i
$408$	−9.81290			−0.485811
$409$	−19.1984	+	13.9485i	−0.949301	+	0.689707i	−0.950641	−	0.310292i	$-0.899573\pi$
$409$	−19.1984	+	13.9485i	−0.949301	+	0.689707i	0.00134071	+	0.999999i	$0.499573\pi$
$410$	−2.22837	−	6.85822i	−0.110051	−	0.338703i
$411$	−3.92414	+	12.0773i	−0.193563	+	0.595727i
$412$	−1.02198	−	0.742513i	−0.0503494	−	0.0365810i
$413$	35.7134	+	25.9473i	1.75734	+	1.27678i
$414$	−1.64736	+	5.07007i	−0.0809635	+	0.249180i
$415$	0.376634	+	1.15916i	0.0184883	+	0.0569010i
$416$	−0.588244	+	0.427384i	−0.0288410	+	0.0209542i
$417$	3.26311			0.159795
$418$	2.57973	−	2.09799i	0.126179	−	0.102616i
$419$	30.0526			1.46817			0.734083	−	0.679060i	$-0.237612\pi$
$419$	30.0526			1.46817			0.734083	+	0.679060i	$0.237612\pi$
$420$	0.202206	−	0.146911i	0.00986665	−	0.00716854i
$421$	3.48435	+	10.7237i	0.169817	+	0.522642i	0.999359	−	0.0358021i	$-0.0113986\pi$
$421$	3.48435	+	10.7237i	0.169817	+	0.522642i	−0.829542	+	0.558444i	$0.811399\pi$
$422$	1.96787	−	6.05649i	0.0957946	−	0.294825i
$423$	−10.6499	−	7.73760i	−0.517815	−	0.376215i
$424$	−5.19358	−	3.77336i	−0.252223	−	0.183250i
$425$	−5.37226	+	16.5341i	−0.260593	+	0.802022i
$426$	2.15245	+	6.62456i	0.104286	+	0.320961i
$427$	44.8194	−	32.5632i	2.16896	−	1.57585i
$428$	1.45510			0.0703349
$429$	2.57312	−	2.09262i	0.124232	−	0.101032i
$430$	−6.25036			−0.301419
$431$	−7.10862	+	5.16471i	−0.342410	+	0.248775i	−0.745678	−	0.666307i	$-0.767874\pi$
$431$	−7.10862	+	5.16471i	−0.342410	+	0.248775i	0.403268	+	0.915082i	$0.367874\pi$
$432$	1.31051	+	4.03333i	0.0630518	+	0.194054i
$433$	−3.70326	+	11.3975i	−0.177967	+	0.547727i	−0.999757	−	0.0220643i	$-0.992976\pi$
$433$	−3.70326	+	11.3975i	−0.177967	+	0.547727i	0.821789	+	0.569792i	$0.192976\pi$
$434$	9.13565	+	6.63744i	0.438525	+	0.318607i
$435$	−0.388067	−	0.281947i	−0.0186064	−	0.0135183i
$436$	−0.623309	+	1.91835i	−0.0298511	+	0.0918722i
$437$	0.775859	+	2.38785i	0.0371144	+	0.114226i
$438$	8.46395	−	6.14942i	0.404423	−	0.293831i
$439$	13.2274			0.631312			0.315656	−	0.948874i	$-0.397775\pi$
$439$	13.2274			0.631312			0.315656	+	0.948874i	$0.397775\pi$
$440$	−3.07049	−	1.98487i	−0.146380	−	0.0946248i
$441$	16.1224			0.767733
$442$	4.24247	−	3.08234i	0.201794	−	0.146612i
$443$	6.42783	+	19.7828i	0.305395	+	0.939910i	0.979529	+	0.201301i	$0.0645170\pi$
$443$	6.42783	+	19.7828i	0.305395	+	0.939910i	−0.674134	+	0.738609i	$0.735483\pi$
$444$	−0.163367	+	0.502793i	−0.00775308	+	0.0238615i
$445$	−1.21009	−	0.879183i	−0.0573639	−	0.0416773i
$446$	−1.46478	−	1.06423i	−0.0693594	−	0.0503926i
$447$	1.15459	−	3.55348i	0.0546105	−	0.168074i
$448$	11.0270	+	33.9375i	0.520976	+	1.60340i
$449$	−14.0158	+	10.1831i	−0.661446	+	0.480569i	−0.867151	−	0.498045i	$-0.834051\pi$
$449$	−14.0158	+	10.1831i	−0.661446	+	0.480569i	0.205705	+	0.978614i	$0.434051\pi$
$450$	7.05722			0.332681
$451$	40.5380	−	2.20969i	1.90886	−	0.104050i
$452$	0.155157			0.00729799
$453$	−8.71796	+	6.33397i	−0.409606	+	0.297596i
$454$	6.51298	+	20.0449i	0.305669	+	0.940753i
$455$	0.599975	−	1.84653i	0.0281273	−	0.0865668i
$456$	1.51778	+	1.10273i	0.0710764	+	0.0516400i
$457$	3.18200	+	2.31186i	0.148848	+	0.108144i	0.659717	−	0.751514i	$-0.270676\pi$
$457$	3.18200	+	2.31186i	0.148848	+	0.108144i	−0.510869	+	0.859659i	$0.670676\pi$
$458$	1.97168	−	6.06820i	0.0921305	−	0.283548i
$459$	−1.11067	−	3.41828i	−0.0518414	−	0.159552i
$460$	−0.153647	+	0.111631i	−0.00716384	+	0.00520484i
$461$	−9.60472			−0.447336			−0.223668	−	0.974665i	$-0.571803\pi$
$461$	−9.60472			−0.447336			−0.223668	+	0.974665i	$0.571803\pi$
$462$	8.38428	+	21.7057i	0.390072	+	1.00984i
$463$	−26.5099			−1.23202			−0.616009	−	0.787739i	$-0.711251\pi$
$463$	−26.5099			−1.23202			−0.616009	+	0.787739i	$0.711251\pi$
$464$	−4.07596	+	2.96136i	−0.189222	+	0.137478i
$465$	−0.200827	−	0.618081i	−0.00931312	−	0.0286628i
$466$	−0.993086	+	3.05640i	−0.0460038	+	0.141585i
$467$	10.6180	+	7.71440i	0.491340	+	0.356980i	0.805700	−	0.592324i	$-0.201790\pi$
$467$	10.6180	+	7.71440i	0.491340	+	0.356980i	−0.314359	+	0.949304i	$0.601790\pi$
$468$	−0.104146	−	0.0756667i	−0.00481416	−	0.00349769i
$469$	−3.67592	+	11.3133i	−0.169738	+	0.522400i
$470$	−2.39643	−	7.37545i	−0.110539	−	0.340204i
$471$	16.8327	−	12.2297i	0.775612	−	0.563515i
$472$	−25.0642			−1.15367
$473$	9.03633	−	34.0089i	0.415491	−	1.56373i
$474$	−9.02528			−0.414545
$475$	2.68896	−	1.95365i	0.123378	−	0.0896394i
$476$	0.687521	+	2.11597i	0.0315125	+	0.0969854i
$477$	0.726599	−	2.23624i	0.0332687	−	0.102391i
$478$	−13.3426	−	9.69395i	−0.610275	−	0.443391i
$479$	−24.9416	−	18.1212i	−1.13961	−	0.827977i	−0.152547	−	0.988296i	$-0.548748\pi$
$479$	−24.9416	−	18.1212i	−1.13961	−	0.827977i	−0.987065	+	0.160319i	$0.948748\pi$
$480$	−0.0907228	+	0.279216i	−0.00414091	+	0.0127444i
$481$	1.26905	+	3.90574i	0.0578638	+	0.178087i
$482$	−8.46167	+	6.14776i	−0.385418	+	0.280023i
$483$	−17.5697			−0.799447
$484$	−1.04835	+	0.951924i	−0.0476523	+	0.0432693i
$485$	−7.27921			−0.330532
$486$	−1.18037	+	0.857589i	−0.0535427	+	0.0389010i
$487$	7.80933	+	24.0346i	0.353874	+	1.08911i	0.956659	+	0.291210i	$0.0940578\pi$
$487$	7.80933	+	24.0346i	0.353874	+	1.08911i	−0.602785	+	0.797904i	$0.705942\pi$
$488$	−9.72011	+	29.9154i	−0.440009	+	1.35421i
$489$	−11.0751	−	8.04652i	−0.500833	−	0.363876i
$490$	7.68391	+	5.58269i	0.347124	+	0.252200i
$491$	−1.90662	+	5.86797i	−0.0860444	+	0.264818i	−0.984816	−	0.173599i	$-0.944460\pi$
$491$	−1.90662	+	5.86797i	−0.0860444	+	0.264818i	0.898772	+	0.438416i	$0.144460\pi$
$492$	−0.486944	−	1.49866i	−0.0219531	−	0.0675647i
$493$	3.45441	−	2.50977i	0.155579	−	0.113035i
$494$	−1.00257			−0.0451077
$495$	0.343888	−	1.29425i	0.0154566	−	0.0581721i
$496$	−6.82593			−0.306494
$497$	−18.5722	+	13.4935i	−0.833078	+	0.605267i
$498$	1.36096	+	4.18861i	0.0609862	+	0.187696i
$499$	−3.46316	+	10.6585i	−0.155032	+	0.477141i	−0.998164	−	0.0605663i	$-0.980709\pi$
$499$	−3.46316	+	10.6585i	−0.155032	+	0.477141i	0.843132	+	0.537707i	$0.180709\pi$
$500$	0.413656	+	0.300539i	0.0184993	+	0.0134405i
$501$	10.5448	+	7.66127i	0.471108	+	0.342280i
$502$	7.56093	−	23.2701i	0.337461	−	1.03860i
$503$	−8.01988	−	24.6826i	−0.357589	−	1.10054i	−0.954493	−	0.298233i	$-0.903603\pi$
$503$	−8.01988	−	24.6826i	−0.357589	−	1.10054i	0.596905	−	0.802312i	$-0.296397\pi$
$504$	−10.6211	+	7.71670i	−0.473103	+	0.343729i
$505$	−3.94039			−0.175345
$506$	−6.37083	−	16.4932i	−0.283218	−	0.733212i
$507$	−1.00000			−0.0444116
$508$	−1.00162	+	0.727722i	−0.0444398	+	0.0322874i
$509$	5.56979	+	17.1420i	0.246876	+	0.759807i	0.995322	+	0.0966114i	$0.0308004\pi$
$509$	5.56979	+	17.1420i	0.246876	+	0.759807i	−0.748446	+	0.663196i	$0.769200\pi$
$510$	0.654302	−	2.01373i	0.0289730	−	0.0891697i
$511$	27.8952	+	20.2670i	1.23401	+	0.896560i
$512$	−16.2398	−	11.7989i	−0.717704	−	0.521442i
$513$	−0.212342	+	0.653522i	−0.00937513	+	0.0288537i
$514$	−11.9171	−	36.6772i	−0.525643	−	1.61776i
$515$	−3.20547	+	2.32891i	−0.141250	+	0.102624i
$516$	−1.36583			−0.0601272
$517$	43.5953	−	2.37634i	1.91732	−	0.104511i
$518$	−28.8120			−1.26593
$519$	6.66561	−	4.84285i	0.292588	−	0.212578i
$520$	0.340654	+	1.04842i	0.0149387	+	0.0459765i
$521$	11.0329	−	33.9556i	0.483358	−	1.48762i	−0.350986	−	0.936381i	$-0.614154\pi$
$521$	11.0329	−	33.9556i	0.483358	−	1.48762i	0.834345	−	0.551243i	$-0.185846\pi$
$522$	−1.40227	−	1.01881i	−0.0613759	−	0.0445922i
$523$	18.1423	+	13.1812i	0.793309	+	0.576373i	0.908944	−	0.416919i	$-0.136890\pi$
$523$	18.1423	+	13.1812i	0.793309	+	0.576373i	−0.115634	+	0.993292i	$0.536890\pi$
$524$	−0.708623	+	2.18092i	−0.0309564	+	0.0952739i
$525$	7.18741	+	22.1206i	0.313684	+	0.965420i
$526$	18.7984	−	13.6578i	0.819649	−	0.595510i
$527$	5.78503			0.252000
$528$	−11.8123	−	7.63586i	−0.514064	−	0.332308i
$529$	−9.64962			−0.419549
$530$	1.12064	−	0.814191i	0.0486774	−	0.0353662i
$531$	−2.83687	−	8.73098i	−0.123110	−	0.378892i
$532$	0.131443	−	0.404541i	0.00569879	−	0.0175391i
$533$	−9.90302	−	7.19497i	−0.428948	−	0.311649i
$534$	−4.37265	−	3.17691i	−0.189223	−	0.137479i
$535$	1.41034	−	4.34058i	0.0609743	−	0.187660i
$536$	−2.08711	−	6.42347i	−0.0901496	−	0.277452i
$537$	−8.42739	+	6.12286i	−0.363669	+	0.264221i
$538$	13.3629			0.576116
$539$	−41.4849	+	33.7380i	−1.78688	+	1.45320i
$540$	−0.0519781			−0.00223678
$541$	−8.58965	+	6.24074i	−0.369298	+	0.268311i	−0.756920	−	0.653508i	$-0.773297\pi$
$541$	−8.58965	+	6.24074i	−0.369298	+	0.268311i	0.387622	+	0.921818i	$0.373297\pi$
$542$	8.65980	+	26.6521i	0.371970	+	1.14481i
$543$	−4.07825	+	12.5516i	−0.175014	+	0.538639i
$544$	−2.11426	−	1.53610i	−0.0906482	−	0.0658597i
$545$	5.11831	+	3.71867i	0.219244	+	0.159290i
$546$	2.16800	−	6.67242i	0.0927818	−	0.285553i
$547$	12.8380	+	39.5112i	0.548912	+	1.68938i	0.711501	+	0.702685i	$0.248016\pi$
$547$	12.8380	+	39.5112i	0.548912	+	1.68938i	−0.162589	+	0.986694i	$0.551984\pi$
$548$	−1.32253	+	0.960874i	−0.0564957	+	0.0410465i
$549$	−11.5211			−0.491707
$550$	−18.1591	+	14.7681i	−0.774307	+	0.629712i
$551$	−0.816335			−0.0347770
$552$	8.07051	−	5.86357i	0.343504	−	0.249570i
$553$	−9.19177	−	28.2894i	−0.390874	−	1.20299i
$554$	1.53437	−	4.72230i	0.0651890	−	0.200631i
$555$	1.34150	+	0.974654i	0.0569433	+	0.0413717i
$556$	0.339841	+	0.246909i	0.0144125	+	0.0104713i
$557$	12.4931	−	38.4497i	0.529348	−	1.62917i	−0.226205	−	0.974080i	$-0.572632\pi$
$557$	12.4931	−	38.4497i	0.529348	−	1.62917i	0.755553	−	0.655087i	$-0.227368\pi$
$558$	−0.725684	−	2.23343i	−0.0307207	−	0.0945485i
$559$	−8.58356	+	6.23632i	−0.363046	+	0.263768i
$560$	−8.23395			−0.347948
$561$	10.0110	+	6.47145i	0.422666	+	0.273225i
$562$	−46.8502			−1.97626
$563$	−14.6039	+	10.6104i	−0.615481	+	0.447173i	−0.851340	−	0.524614i	$-0.824210\pi$
$563$	−14.6039	+	10.6104i	−0.615481	+	0.447173i	0.235859	+	0.971787i	$0.424210\pi$
$564$	−0.523668	−	1.61168i	−0.0220504	−	0.0678641i
$565$	0.150385	−	0.462836i	0.00632673	−	0.0194717i
$566$	33.3387	+	24.2220i	1.40133	+	1.01813i
$567$	−3.89022	−	2.82641i	−0.163374	−	0.118698i
$568$	4.02781	−	12.3963i	0.169003	−	0.520138i
$569$	−4.37526	−	13.4657i	−0.183420	−	0.564510i	0.816497	−	0.577349i	$-0.195913\pi$
$569$	−4.37526	−	13.4657i	−0.183420	−	0.564510i	−0.999918	+	0.0128395i	$0.995913\pi$
$570$	−0.327496	+	0.237940i	−0.0137173	+	0.00996620i
$571$	26.7585			1.11981			0.559903	−	0.828558i	$-0.310838\pi$
$571$	26.7585			1.11981			0.559903	+	0.828558i	$0.310838\pi$
$572$	0.426322	−	0.0232385i	0.0178254	−	0.000971650i
$573$	10.3752			0.433432
$574$	69.4776	−	50.4784i	2.89994	−	2.10693i
$575$	−5.46138	−	16.8084i	−0.227755	−	0.700959i
$576$	2.29319	−	7.05771i	0.0955496	−	0.294071i
$577$	10.1084	+	7.34415i	0.420816	+	0.305741i	0.777966	−	0.628306i	$-0.216251\pi$
$577$	10.1084	+	7.34415i	0.420816	+	0.305741i	−0.357150	+	0.934047i	$0.616251\pi$
$578$	−4.81803	−	3.50050i	−0.200404	−	0.145602i
$579$	2.35376	−	7.24412i	0.0978189	−	0.301056i
$580$	−0.0190817	−	0.0587275i	−0.000792326	−	0.00243853i
$581$	−11.7429	+	8.53175i	−0.487180	+	0.353957i
$582$	−26.3033			−1.09031
$583$	2.80997	+	7.27462i	0.116377	+	0.301284i
$584$	−19.5772			−0.810112
$585$	−0.326657	+	0.237330i	−0.0135056	+	0.00981240i
$586$	−3.13256	−	9.64103i	−0.129405	−	0.398267i
$587$	−1.87270	+	5.76359i	−0.0772947	+	0.237889i	−0.982237	−	0.187646i	$-0.939914\pi$
$587$	−1.87270	+	5.76359i	−0.0772947	+	0.237889i	0.904942	+	0.425535i	$0.139914\pi$
$588$	1.67909	+	1.21993i	0.0692444	+	0.0503090i
$589$	−0.894780	−	0.650096i	−0.0368688	−	0.0267867i
$590$	1.67122	−	5.14349i	0.0688031	−	0.211754i
$591$	−0.813153	−	2.50263i	−0.0334487	−	0.102944i
$592$	14.0900	−	10.2370i	0.579097	−	0.420738i
$593$	−40.4407			−1.66070			−0.830350	−	0.557242i	$-0.811859\pi$
$593$	−40.4407			−1.66070			−0.830350	+	0.557242i	$0.811859\pi$
$594$	1.24263	−	4.67674i	0.0509858	−	0.191889i
$595$	6.97834			0.286084
$596$	0.389127	−	0.282717i	0.0159392	−	0.0115805i
$597$	3.68944	+	11.3549i	0.150999	+	0.464726i
$598$	−1.64736	+	5.07007i	−0.0673657	+	0.207330i
$599$	−14.0963	−	10.2416i	−0.575959	−	0.418459i	0.261306	−	0.965256i	$-0.415847\pi$
$599$	−14.0963	−	10.2416i	−0.575959	−	0.418459i	−0.837265	+	0.546797i	$0.815847\pi$
$600$	−10.6838	−	7.76227i	−0.436166	−	0.316893i
$601$	1.75035	−	5.38702i	0.0713982	−	0.219741i	−0.908990	−	0.416819i	$-0.863145\pi$
$601$	1.75035	−	5.38702i	0.0713982	−	0.219741i	0.980388	+	0.197077i	$0.0631451\pi$
$602$	−23.0022	−	70.7935i	−0.937499	−	2.88533i
$603$	2.00136	−	1.45407i	0.0815016	−	0.0592144i
$604$	−1.38721			−0.0564449
$605$	1.82350	+	4.04988i	0.0741357	+	0.164651i
$606$	−14.2385			−0.578400
$607$	−14.2692	+	10.3672i	−0.579167	+	0.420790i	−0.838424	−	0.545019i	$-0.816523\pi$
$607$	−14.2692	+	10.3672i	−0.579167	+	0.420790i	0.259256	+	0.965809i	$0.416523\pi$
$608$	0.154396	+	0.475182i	0.00626158	+	0.0192712i
$609$	1.76528	−	5.43297i	0.0715328	−	0.220155i
$610$	−5.49092	−	3.98938i	−0.222321	−	0.161525i
$611$	−10.6499	−	7.73760i	−0.430848	−	0.313030i
$612$	0.142978	−	0.440041i	0.00577955	−	0.0177876i
$613$	−13.2037	−	40.6370i	−0.533294	−	1.64131i	−0.747306	−	0.664480i	$-0.768653\pi$
$613$	−13.2037	−	40.6370i	−0.533294	−	1.64131i	0.214011	−	0.976831i	$-0.431347\pi$
$614$	12.6765	−	9.20999i	0.511580	−	0.371685i
$615$	−4.94248			−0.199300
$616$	11.1814	−	42.0820i	0.450510	−	1.69553i
$617$	27.5212			1.10796			0.553982	−	0.832529i	$-0.313108\pi$
$617$	27.5212			1.10796			0.553982	+	0.832529i	$0.313108\pi$
$618$	−11.5829	+	8.41547i	−0.465933	+	0.338520i
$619$	−11.4646	−	35.2844i	−0.460800	−	1.41820i	−0.864188	−	0.503169i	$-0.832167\pi$
$619$	−11.4646	−	35.2844i	−0.460800	−	1.41820i	0.403388	−	0.915029i	$-0.367833\pi$
$620$	0.0258528	−	0.0795668i	0.00103827	−	0.00319548i
$621$	2.95600	+	2.14766i	0.118620	+	0.0861826i
$622$	−5.05884	−	3.67546i	−0.202841	−	0.147372i
$623$	5.50459	−	16.9414i	0.220537	−	0.678743i
$624$	1.31051	+	4.03333i	0.0524623	+	0.161462i
$625$	−18.2685	+	13.2729i	−0.730740	+	0.530914i
$626$	−34.3044			−1.37108
$627$	−0.821188	−	2.12594i	−0.0327951	−	0.0849019i
$628$	2.67845			0.106882
$629$	−11.9414	+	8.67595i	−0.476136	+	0.345933i
$630$	−0.875374	−	2.69412i	−0.0348757	−	0.107336i
$631$	0.0232317	−	0.0714998i	0.000924839	−	0.00284636i	−0.950593	−	0.310440i	$-0.899524\pi$
$631$	0.0232317	−	0.0714998i	0.000924839	−	0.00284636i	0.951518	+	0.307593i	$0.0995237\pi$
$632$	13.6633	+	9.92694i	0.543496	+	0.394873i
$633$	−3.53112	−	2.56551i	−0.140349	−	0.101970i
$634$	3.82353	−	11.7676i	0.151852	−	0.467351i
$635$	1.19999	+	3.69319i	0.0476201	+	0.146560i
$636$	0.244882	−	0.177917i	0.00971019	−	0.00705487i
$637$	16.1224			0.638793
$638$	5.74021	−	0.312894i	0.227257	−	0.0123876i
$639$	4.77408			0.188860
$640$	4.01183	−	2.91476i	0.158581	−	0.115216i
$641$	11.2671	+	34.6765i	0.445023	+	1.36964i	0.882459	+	0.470390i	$0.155887\pi$
$641$	11.2671	+	34.6765i	0.445023	+	1.36964i	−0.437436	+	0.899250i	$0.644113\pi$
$642$	5.09624	−	15.6846i	0.201133	−	0.619022i
$643$	−8.91202	−	6.47496i	−0.351456	−	0.255348i	0.398024	−	0.917375i	$-0.369696\pi$
$643$	−8.91202	−	6.47496i	−0.351456	−	0.255348i	−0.749479	+	0.662028i	$0.769696\pi$
$644$	−1.82981	−	1.32944i	−0.0721048	−	0.0523872i
$645$	−1.32381	+	4.07428i	−0.0521251	+	0.160425i
$646$	−1.11352	−	3.42706i	−0.0438108	−	0.134836i
$647$	−3.55787	+	2.58494i	−0.139874	+	0.101625i	−0.655522	−	0.755176i	$-0.727551\pi$
$647$	−3.55787	+	2.58494i	−0.139874	+	0.101625i	0.515648	+	0.856801i	$0.327551\pi$
$648$	2.73021			0.107253
$649$	25.5702	+	16.5294i	1.00372	+	0.648836i
$650$	7.05722			0.276807
$651$	6.26151	−	4.54925i	0.245408	−	0.178299i
$652$	−0.544575	−	1.67603i	−0.0213272	−	0.0656384i
$653$	12.8100	−	39.4250i	0.501293	−	1.54282i	−0.305622	−	0.952153i	$-0.598864\pi$
$653$	12.8100	−	39.4250i	0.501293	−	1.54282i	0.806915	−	0.590668i	$-0.201136\pi$
$654$	18.4949	+	13.4374i	0.723209	+	0.525442i
$655$	5.81888	+	4.22766i	0.227362	+	0.165188i
$656$	−16.0417	+	49.3712i	−0.626322	+	1.92762i
$657$	−2.21583	−	6.81964i	−0.0864479	−	0.266059i
$658$	74.7175	−	54.2854i	2.91279	−	2.11627i
$659$	−0.460087			−0.0179224			−0.00896121	−	0.999960i	$-0.502852\pi$
$659$	−0.460087			−0.0179224			−0.00896121	+	0.999960i	$0.502852\pi$
$660$	0.133746	−	0.108770i	0.00520606	−	0.00423387i
$661$	18.5250			0.720537			0.360269	−	0.932849i	$-0.382685\pi$
$661$	18.5250			0.720537			0.360269	+	0.932849i	$0.382685\pi$
$662$	38.4684	−	27.9489i	1.49512	−	1.08627i
$663$	−1.11067	−	3.41828i	−0.0431347	−	0.132755i
$664$	2.54672	−	7.83801i	0.0988321	−	0.304174i
$665$	−1.07935	−	0.784193i	−0.0418554	−	0.0304097i
$666$	4.84747	+	3.52189i	0.187836	+	0.136471i
$667$	−1.34136	+	4.12827i	−0.0519375	+	0.159847i
$668$	0.518502	+	1.59578i	0.0200614	+	0.0617428i
$669$	−1.00395	+	0.729413i	−0.0388150	+	0.0282007i
$670$	1.45734			0.0563021
$671$	29.6451	−	24.1091i	1.14444	−	0.930723i
$672$	−3.49636			−0.134875
$673$	0.623408	−	0.452932i	0.0240306	−	0.0174593i	−0.575705	−	0.817657i	$-0.695272\pi$
$673$	0.623408	−	0.452932i	0.0240306	−	0.0174593i	0.599736	+	0.800198i	$0.295272\pi$
$674$	14.0220	+	43.1552i	0.540106	+	1.66228i
$675$	1.49471	−	4.60023i	0.0575313	−	0.177063i
$676$	−0.104146	−	0.0756667i	−0.00400563	−	0.00291026i
$677$	9.64587	+	7.00813i	0.370721	+	0.269344i	0.757510	−	0.652824i	$-0.226416\pi$
$677$	9.64587	+	7.00813i	0.370721	+	0.269344i	−0.386789	+	0.922168i	$0.626416\pi$
$678$	0.543412	−	1.67245i	0.0208696	−	0.0642301i
$679$	−26.7885	−	82.4466i	−1.02805	−	3.16401i
$680$	−3.20545	+	2.32890i	−0.122924	+	0.0893092i
$681$	14.4456			0.553558
$682$	6.54098	+	4.22830i	0.250467	+	0.161910i
$683$	−1.22385			−0.0468294			−0.0234147	−	0.999726i	$-0.507454\pi$
$683$	−1.22385			−0.0468294			−0.0234147	+	0.999726i	$0.507454\pi$
$684$	−0.0715644	+	0.0519946i	−0.00273634	+	0.00198806i
$685$	1.58445	+	4.87644i	0.0605387	+	0.186319i
$686$	−19.7774	+	60.8684i	−0.755103	+	2.32397i
$687$	−3.53794	−	2.57047i	−0.134981	−	0.0980694i
$688$	36.4020	+	26.4476i	1.38781	+	1.00830i
$689$	0.726599	−	2.23624i	0.0276812	−	0.0851941i
$690$	0.665157	+	2.04714i	0.0253221	+	0.0779334i
$691$	−24.6558	+	17.9135i	−0.937950	+	0.681461i	−0.947926	−	0.318490i	$-0.896824\pi$
$691$	−24.6558	+	17.9135i	−0.937950	+	0.681461i	0.00997618	+	0.999950i	$0.496824\pi$
$692$	1.06064			0.0403195
$693$	15.9246	−	0.868037i	0.604926	−	0.0329740i
$694$	−7.34191			−0.278695
$695$	1.06592	−	0.774435i	0.0404326	−	0.0293760i
$696$	1.00229	+	3.08473i	0.0379917	+	0.116927i
$697$	13.5955	−	41.8425i	0.514964	−	1.58490i
$698$	−35.4889	−	25.7842i	−1.34327	−	0.975946i
$699$	1.78198	+	1.29468i	0.0674005	+	0.0489693i
$700$	−0.925248	+	2.84762i	−0.0349711	+	0.107630i
$701$	−6.31001	−	19.4202i	−0.238326	−	0.733492i	−0.996663	−	0.0816289i	$-0.973988\pi$
$701$	−6.31001	−	19.4202i	−0.238326	−	0.733492i	0.758337	−	0.651863i	$-0.226012\pi$
$702$	−1.18037	+	0.857589i	−0.0445502	+	0.0323676i
$703$	2.82196			0.106432
$704$	8.86842	+	22.9591i	0.334241	+	0.865305i
$705$	−5.31523			−0.200183
$706$	−8.86539	+	6.44108i	−0.333653	+	0.242413i
$707$	−14.5012	−	44.6300i	−0.545373	−	1.67848i
$708$	0.365195	−	1.12396i	0.0137249	−	0.0422408i
$709$	−37.2775	−	27.0837i	−1.39999	−	1.01715i	−0.994685	−	0.102967i	$-0.967166\pi$
$709$	−37.2775	−	27.0837i	−1.39999	−	1.01715i	−0.405302	−	0.914183i	$-0.632834\pi$
$710$	2.27532	+	1.65312i	0.0853912	+	0.0620404i
$711$	−1.91154	+	5.88311i	−0.0716883	+	0.220634i
$712$	3.12540	+	9.61898i	0.117129	+	0.360487i
$713$	−4.75784	+	3.45677i	−0.178182	+	0.129457i
$714$	25.2161			0.943689
$715$	0.343888	−	1.29425i	0.0128607	−	0.0484021i
$716$	−1.34098			−0.0501147
$717$	−9.14491	+	6.64416i	−0.341523	+	0.248131i
$718$	11.1603	+	34.3480i	0.416500	+	1.28186i
$719$	1.50587	−	4.63458i	0.0561594	−	0.172841i	−0.919042	−	0.394159i	$-0.871036\pi$
$719$	1.50587	−	4.63458i	0.0561594	−	0.172841i	0.975202	+	0.221318i	$0.0710359\pi$
$720$	1.38532	+	1.00649i	0.0516277	+	0.0375097i
$721$	−38.1745	−	27.7354i	−1.42169	−	1.03292i
$722$	8.35347	−	25.7094i	0.310884	−	0.956803i
$723$	2.21524	+	6.81780i	0.0823856	+	0.253557i
$724$	−1.37447	+	0.998610i	−0.0510817	+	0.0371131i
$725$	5.74630			0.213412
$726$	6.58918	+	14.6342i	0.244547	+	0.543125i
$727$	−28.8112			−1.06855			−0.534274	−	0.845311i	$-0.679415\pi$
$727$	−28.8112			−1.06855			−0.534274	+	0.845311i	$0.679415\pi$
$728$	−10.6211	+	7.71670i	−0.393645	+	0.286000i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	1.30537	−	4.01750i	0.0483137	−	0.148694i
$731$	−30.8510	−	22.4145i	−1.14106	−	0.829031i
$732$	−1.19987	−	0.871760i	−0.0443487	−	0.0322212i
$733$	−6.21975	+	19.1424i	−0.229732	+	0.707042i	0.768045	+	0.640396i	$0.221230\pi$
$733$	−6.21975	+	19.1424i	−0.229732	+	0.707042i	−0.997777	+	0.0666457i	$0.978770\pi$
$734$	−6.39370	−	19.6778i	−0.235996	−	0.726320i
$735$	5.26649	−	3.82633i	0.194258	−	0.141136i
$736$	2.65672			0.0979282
$737$	−2.10693	+	7.92958i	−0.0776096	+	0.292090i
$738$	−17.8596			−0.657419
$739$	4.66310	−	3.38794i	0.171535	−	0.124628i	−0.498705	−	0.866772i	$-0.666191\pi$
$739$	4.66310	−	3.38794i	0.171535	−	0.124628i	0.670240	+	0.742144i	$0.266191\pi$
$740$	0.0659629	+	0.203013i	0.00242485	+	0.00746291i
$741$	−0.212342	+	0.653522i	−0.00780058	+	0.0240077i
$742$	13.3459	+	9.69635i	0.489943	+	0.355964i
$743$	−30.2933	−	22.0094i	−1.11135	−	0.807446i	−0.128478	−	0.991712i	$-0.541009\pi$
$743$	−30.2933	−	22.0094i	−1.11135	−	0.807446i	−0.982876	+	0.184266i	$0.941009\pi$
$744$	−1.35795	+	4.17934i	−0.0497849	+	0.153222i
$745$	−0.466191	−	1.43479i	−0.0170799	−	0.0525666i
$746$	−17.1455	+	12.4570i	−0.627742	+	0.456082i
$747$	3.01858			0.110444
$748$	0.552937	+	1.43148i	0.0202174	+	0.0523400i
$749$	54.3530			1.98602
$750$	4.68828	−	3.40624i	0.171192	−	0.124378i
$751$	1.16180	+	3.57564i	0.0423945	+	0.130477i	0.970014	−	0.243051i	$-0.0781481\pi$
$751$	1.16180	+	3.57564i	0.0423945	+	0.130477i	−0.927619	+	0.373528i	$0.878148\pi$
$752$	−17.2515	+	53.0947i	−0.629098	+	1.93616i
$753$	−13.5672	−	9.85714i	−0.494416	−	0.359214i
$754$	−1.40227	−	1.01881i	−0.0510678	−	0.0371029i
$755$	−1.34454	+	4.13807i	−0.0489329	+	0.150600i
$756$	−0.191287	−	0.588720i	−0.00695703	−	0.0214115i
$757$	0.984033	−	0.714942i	0.0357653	−	0.0259850i	−0.569759	−	0.821812i	$-0.692963\pi$
$757$	0.984033	−	0.714942i	0.0357653	−	0.0259850i	0.605524	+	0.795827i	$0.292963\pi$
$758$	25.7539			0.935424
$759$	−12.1004	+	0.659582i	−0.439216	+	0.0239413i
$760$	0.757503			0.0274775
$761$	−27.7301	+	20.1471i	−1.00522	+	0.730333i	−0.963200	−	0.268784i	$-0.913378\pi$
$761$	−27.7301	+	20.1471i	−1.00522	+	0.730333i	−0.0420162	+	0.999117i	$0.513378\pi$
$762$	4.33614	+	13.3453i	0.157082	+	0.483448i
$763$	−23.2827	+	71.6568i	−0.842891	+	2.59415i
$764$	1.08054	+	0.785060i	0.0390926	+	0.0284025i
$765$	−1.17407	−	0.853010i	−0.0424485	−	0.0308406i
$766$	−2.77087	+	8.52785i	−0.100115	+	0.308124i
$767$	−2.83687	−	8.73098i	−0.102433	−	0.315257i
$768$	2.48938	−	1.80864i	0.0898277	−	0.0652636i
$769$	−22.7421			−0.820101			−0.410050	−	0.912063i	$-0.634489\pi$
$769$	−22.7421			−0.820101			−0.410050	+	0.912063i	$0.634489\pi$
$770$	7.89021	+	5.10049i	0.284344	+	0.183809i
$771$	−26.4320			−0.951923
$772$	0.793274	−	0.576347i	0.0285506	−	0.0207432i
$773$	−4.00653	−	12.3308i	−0.144105	−	0.443509i	0.852790	−	0.522254i	$-0.174909\pi$
$773$	−4.00653	−	12.3308i	−0.144105	−	0.443509i	−0.996895	+	0.0787448i	$0.974909\pi$
$774$	−4.78358	+	14.7223i	−0.171942	+	0.529183i
$775$	6.29848	+	4.57612i	0.226248	+	0.164379i
$776$	39.8203	+	28.9311i	1.42946	+	1.03857i
$777$	−6.10233	+	18.7811i	−0.218920	+	0.673767i
$778$	1.24500	+	3.83173i	0.0446355	+	0.137374i
$779$	−6.80490	+	4.94405i	−0.243811	+	0.177139i
$780$	−0.0519781			−0.00186111
$781$	−12.2843	+	9.99032i	−0.439567	+	0.357482i
$782$	−19.1606			−0.685180
$783$	−0.961109	+	0.698286i	−0.0343472	+	0.0249547i
$784$	−21.1285	−	65.0269i	−0.754590	−	2.32239i
$785$	2.59605	−	7.98983i	0.0926572	−	0.285169i
$786$	21.0264	+	15.2766i	0.749987	+	0.544898i
$787$	34.1558	+	24.8156i	1.21752	+	0.884582i	0.995892	−	0.0905492i	$-0.0288622\pi$
$787$	34.1558	+	24.8156i	1.21752	+	0.884582i	0.221630	+	0.975131i	$0.428862\pi$
$788$	0.104679	−	0.322168i	0.00372903	−	0.0114768i
$789$	−4.92136	−	15.1464i	−0.175205	−	0.539225i
$790$	−2.94817	+	2.14197i	−0.104891	+	0.0762080i
$791$	5.79566			0.206070
$792$	−7.02517	+	5.71329i	−0.249629	+	0.203013i
$793$	−11.5211			−0.409125
$794$	−35.4652	+	25.7670i	−1.25861	+	0.914436i
$795$	−0.293379	−	0.902929i	−0.0104051	−	0.0320236i
$796$	−0.474948	+	1.46174i	−0.0168341	+	0.0518100i
$797$	−36.5842	−	26.5800i	−1.29588	−	0.941511i	−0.295972	−	0.955197i	$-0.595644\pi$
$797$	−36.5842	−	26.5800i	−1.29588	−	0.941511i	−0.999906	+	0.0136857i	$0.995644\pi$
$798$	−3.90021	−	2.83367i	−0.138066	−	0.100311i
$799$	14.6208	−	44.9982i	0.517246	−	1.59192i
$800$	−1.08681	−	3.34487i	−0.0384247	−	0.118259i
$801$	−2.99698	+	2.17743i	−0.105893	+	0.0769359i
$802$	29.9775			1.05854
$803$	19.9725	+	12.9109i	0.704814	+	0.455615i
$804$	0.318459			0.0112312
$805$	−5.73925	+	4.16981i	−0.202282	+	0.146967i
$806$	−0.725684	−	2.23343i	−0.0255611	−	0.0786691i
$807$	2.83024	−	8.71058i	0.0996291	−	0.306627i
$808$	21.5555	+	15.6610i	0.758321	+	0.550952i
$809$	27.2757	+	19.8170i	0.958963	+	0.696728i	0.952910	−	0.303254i	$-0.0980731\pi$
$809$	27.2757	+	19.8170i	0.958963	+	0.696728i	0.00605350	+	0.999982i	$0.498073\pi$
$810$	−0.182044	+	0.560275i	−0.00639639	+	0.0196861i
$811$	7.60022	+	23.3911i	0.266880	+	0.821372i	0.991254	+	0.131965i	$0.0421287\pi$
$811$	7.60022	+	23.3911i	0.266880	+	0.821372i	−0.724374	+	0.689407i	$0.757871\pi$
$812$	0.594942	−	0.432251i	0.0208784	−	0.0151690i
$813$	19.2072			0.673628
$814$	−19.8431	+	1.08163i	−0.695501	+	0.0379112i
$815$	−5.52744			−0.193618
$816$	−12.3315	+	8.95936i	−0.431689	+	0.313640i
$817$	2.25292	+	6.93378i	0.0788197	+	0.242582i
$818$	−10.6992	+	32.9287i	−0.374088	+	1.15133i
$819$	−3.89022	−	2.82641i	−0.135935	−	0.0987627i
$820$	−0.514740	−	0.373981i	−0.0179755	−	0.0130600i
$821$	6.36699	−	19.5956i	0.222210	−	0.683891i	−0.776353	−	0.630298i	$-0.782933\pi$
$821$	6.36699	−	19.5956i	0.222210	−	0.683891i	0.998563	−	0.0535929i	$-0.0170673\pi$
$822$	5.72539	+	17.6209i	0.199696	+	0.614600i
$823$	19.5953	−	14.2369i	0.683051	−	0.496265i	−0.191318	−	0.981528i	$-0.561276\pi$
$823$	19.5953	−	14.2369i	0.683051	−	0.496265i	0.874368	+	0.485263i	$0.161276\pi$
$824$	26.7914			0.933324
$825$	5.78046	+	14.9648i	0.201250	+	0.521008i
$826$	64.4071			2.24101
$827$	0.910993	−	0.661875i	0.0316783	−	0.0230157i	−0.571833	−	0.820370i	$-0.693768\pi$
$827$	0.910993	−	0.661875i	0.0316783	−	0.0230157i	0.603512	+	0.797354i	$0.293768\pi$
$828$	0.145350	+	0.447341i	0.00505126	+	0.0155462i
$829$	3.20601	−	9.86708i	0.111349	−	0.342698i	−0.879819	−	0.475309i	$-0.842336\pi$
$829$	3.20601	−	9.86708i	0.111349	−	0.342698i	0.991168	+	0.132611i	$0.0423362\pi$
$830$	1.43865	+	1.04524i	0.0499363	+	0.0362809i
$831$	−2.75324	−	2.00035i	−0.0955088	−	0.0693912i
$832$	2.29319	−	7.05771i	0.0795021	−	0.244682i
$833$	17.9066	+	55.1108i	0.620427	+	1.90948i
$834$	3.85168	−	2.79841i	0.133373	−	0.0969010i
$835$	5.26279			0.182126
$836$	0.0753393	−	0.283545i	0.00260566	−	0.00980662i
$837$	−1.60955			−0.0556342
$838$	35.4732	−	25.7728i	1.22540	−	0.890306i
$839$	−4.95645	−	15.2544i	−0.171116	−	0.526640i	0.828319	−	0.560257i	$-0.189297\pi$
$839$	−4.95645	−	15.2544i	−0.171116	−	0.526640i	−0.999435	+	0.0336167i	$0.989297\pi$
$840$	−1.63806	+	5.04143i	−0.0565184	+	0.173946i
$841$	22.3197	+	16.2162i	0.769645	+	0.559180i
$842$	13.3094	+	9.66981i	0.458671	+	0.333244i
$843$	−9.92278	+	30.5392i	−0.341759	+	1.05182i
$844$	−0.173629	−	0.534376i	−0.00597656	−	0.0183940i
$845$	−0.326657	+	0.237330i	−0.0112373	+	0.00816441i
$846$	−19.2065			−0.660333
$847$	−39.1595	+	35.5576i	−1.34554	+	1.22177i
$848$	−9.97172			−0.342430
$849$	22.8501	−	16.6016i	0.784213	−	0.569764i
$850$	7.83822	+	24.1235i	0.268849	+	0.827431i
$851$	4.63689	−	14.2709i	0.158950	−	0.489199i
$852$	0.497203	+	0.361239i	0.0170339	+	0.0123758i
$853$	−25.8294	−	18.7662i	−0.884382	−	0.642541i	0.0500251	−	0.998748i	$-0.484070\pi$
$853$	−25.8294	−	18.7662i	−0.884382	−	0.642541i	−0.934407	+	0.356207i	$0.884070\pi$
$854$	24.9777	−	76.8733i	0.854718	−	2.63055i
$855$	0.0857374	+	0.263873i	0.00293216	+	0.00902425i
$856$	−24.9667	+	18.1394i	−0.853344	+	0.619991i
$857$	−35.3804			−1.20857			−0.604285	−	0.796768i	$-0.706541\pi$
$857$	−35.3804			−1.20857			−0.604285	+	0.796768i	$0.706541\pi$
$858$	1.24263	−	4.67674i	0.0424228	−	0.159661i
$859$	−8.95220			−0.305445			−0.152723	−	0.988269i	$-0.548804\pi$
$859$	−8.95220			−0.305445			−0.152723	+	0.988269i	$0.548804\pi$
$860$	−0.446157	+	0.324152i	−0.0152138	+	0.0110535i
$861$	−18.1890	−	55.9800i	−0.619880	−	1.90779i
$862$	−3.96160	+	12.1925i	−0.134933	+	0.415280i
$863$	23.6101	+	17.1537i	0.803697	+	0.583920i	0.911996	−	0.410198i	$-0.134540\pi$
$863$	23.6101	+	17.1537i	0.803697	+	0.583920i	−0.108299	+	0.994118i	$0.534540\pi$
$864$	0.588244	+	0.427384i	0.0200125	+	0.0145399i
$865$	1.02801	−	3.16390i	0.0349535	−	0.107576i
$866$	5.40312	+	16.6291i	0.183606	+	0.565080i
$867$	−3.30224	+	2.39922i	−0.112150	+	0.0814818i
$868$	0.996340			0.0338180
$869$	−7.39246	−	19.1381i	−0.250772	−	0.649214i
$870$	−0.699858			−0.0237274
$871$	2.00136	−	1.45407i	0.0678134	−	0.0492693i
$872$	−13.2195	−	40.6853i	−0.447667	−	1.37778i
$873$	−5.57099	+	17.1457i	−0.188549	+	0.580296i
$874$	2.96359	+	2.15318i	0.100245	+	0.0728323i
$875$	15.4515	+	11.2261i	0.522355	+	0.379513i
$876$	0.285248	−	0.877904i	0.00963765	−	0.0296616i
$877$	13.8717	+	42.6928i	0.468416	+	1.44163i	0.854636	+	0.519228i	$0.173781\pi$
$877$	13.8717	+	42.6928i	0.468416	+	1.44163i	−0.386220	+	0.922407i	$0.626219\pi$
$878$	15.6133	−	11.3437i	0.526923	−	0.382832i
$879$	−6.94795			−0.234348
$880$	−5.67079	+	0.309110i	−0.191162	+	0.0104201i
$881$	−15.2732			−0.514568			−0.257284	−	0.966336i	$-0.582828\pi$
$881$	−15.2732			−0.514568			−0.257284	+	0.966336i	$0.582828\pi$
$882$	19.0304	−	13.8264i	0.640787	−	0.465559i
$883$	1.05049	+	3.23309i	0.0353520	+	0.108802i	0.967175	−	0.254110i	$-0.0817825\pi$
$883$	1.05049	+	3.23309i	0.0353520	+	0.108802i	−0.931823	+	0.362912i	$0.881783\pi$
$884$	0.142978	−	0.440041i	0.00480887	−	0.0148002i
$885$	−2.99881	−	2.17876i	−0.100804	−	0.0732383i
$886$	24.5527	+	17.8386i	0.824865	+	0.599300i
$887$	−6.49395	+	19.9863i	−0.218045	+	0.671075i	0.780878	+	0.624684i	$0.214772\pi$
$887$	−6.49395	+	19.9863i	−0.218045	+	0.671075i	−0.998923	+	0.0463912i	$0.985228\pi$
$888$	−3.46478	−	10.6635i	−0.116271	−	0.357844i
$889$	−37.4140	+	27.1829i	−1.25483	+	0.911685i
$890$	−2.18233			−0.0731520
$891$	−2.78533	−	1.80053i	−0.0933122	−	0.0603201i
$892$	−0.159750			−0.00534883
$893$	−7.31811	+	5.31692i	−0.244891	+	0.177924i
$894$	−1.68457	−	5.18459i	−0.0563406	−	0.173399i
$895$	−1.29973	+	4.00015i	−0.0434451	+	0.133710i
$896$	47.7776	+	34.7125i	1.59614	+	1.15966i
$897$	2.95600	+	2.14766i	0.0986980	+	0.0717083i
$898$	−7.81093	+	24.0396i	−0.260654	+	0.802211i
$899$	−0.590884	−	1.81855i	−0.0197071	−	0.0606522i
$900$	0.503752	−	0.365997i	0.0167917	−	0.0121999i
$901$	8.45111			0.281547
$902$	45.9548	−	37.3732i	1.53013	−	1.24439i
$903$	−51.0183			−1.69778
$904$	−2.66220	+	1.93420i	−0.0885434	+	0.0643306i
$905$	1.64668	+	5.06795i	0.0547373	+	0.168464i
$906$	−4.85848	+	14.9529i	−0.161412	+	0.496775i
$907$	9.69570	+	7.04434i	0.321940	+	0.233903i	0.737003	−	0.675889i	$-0.236240\pi$
$907$	9.69570	+	7.04434i	0.321940	+	0.233903i	−0.415063	+	0.909793i	$0.636240\pi$
$908$	1.50446	+	1.09305i	0.0499272	+	0.0362743i
$909$	−3.01569	+	9.28134i	−0.100024	+	0.307843i
$910$	−0.875374	−	2.69412i	−0.0290184	−	0.0893094i
$911$	9.13361	−	6.63596i	0.302610	−	0.219859i	−0.426109	−	0.904672i	$-0.640116\pi$
$911$	9.13361	−	6.63596i	0.302610	−	0.219859i	0.728719	+	0.684813i	$0.240116\pi$
$912$	2.91414			0.0964969
$913$	−7.76718	+	6.31673i	−0.257056	+	0.209053i
$914$	5.73856			0.189815
$915$	−3.76343	+	2.73430i	−0.124415	+	0.0903930i
$916$	−0.173965	−	0.535409i	−0.00574796	−	0.0176904i
$917$	−26.4695	+	81.4648i	−0.874100	+	2.69020i
$918$	−4.24247	−	3.08234i	−0.140023	−	0.101732i
$919$	−32.8982	−	23.9019i	−1.08521	−	0.788452i	−0.106627	−	0.994299i	$-0.534005\pi$
$919$	−32.8982	−	23.9019i	−1.08521	−	0.788452i	−0.978584	+	0.205847i	$0.934005\pi$
$920$	1.24469	−	3.83075i	0.0410361	−	0.126296i
$921$	−3.31866	−	10.2138i	−0.109353	−	0.336555i
$922$	−11.3371	+	8.23690i	−0.373368	+	0.271268i
$923$	4.77408			0.157141
$924$	1.72417	+	1.11456i	0.0567210	+	0.0366663i
$925$	−19.8642			−0.653130
$926$	−31.2914	+	22.7346i	−1.02830	+	0.747104i
$927$	3.03237	+	9.33267i	0.0995960	+	0.306525i
$928$	−0.266930	+	0.821525i	−0.00876240	+	0.0269679i
$929$	−5.93082	−	4.30899i	−0.194584	−	0.141373i	0.486227	−	0.873832i	$-0.338373\pi$
$929$	−5.93082	−	4.30899i	−0.194584	−	0.141373i	−0.680811	+	0.732459i	$0.738373\pi$
$930$	−0.767110	−	0.557338i	−0.0251545	−	0.0182758i
$931$	3.42346	−	10.5363i	0.112199	−	0.345314i
$932$	0.0876218	+	0.269672i	0.00287015	+	0.00883341i
$933$	−3.46729	+	2.51913i	−0.113514	+	0.0824727i
$934$	19.1489			0.626571
$935$	4.80604	−	0.261973i	0.157174	−	0.00856745i
$936$	2.73021			0.0892398
$937$	5.11320	−	3.71496i	0.167041	−	0.121362i	−0.501124	−	0.865375i	$-0.667080\pi$
$937$	5.11320	−	3.71496i	0.167041	−	0.121362i	0.668165	+	0.744013i	$0.267080\pi$
$938$	5.36323	+	16.5063i	0.175116	+	0.538951i
$939$	−7.26559	+	22.3612i	−0.237104	+	0.729730i
$940$	−0.553561	−	0.402186i	−0.0180552	−	0.0131179i
$941$	21.9859	+	15.9737i	0.716720	+	0.520728i	0.885335	−	0.464954i	$-0.153929\pi$
$941$	21.9859	+	15.9737i	0.716720	+	0.520728i	−0.168615	+	0.985682i	$0.553929\pi$
$942$	9.38080	−	28.8711i	0.305643	−	0.940672i
$943$	13.8210	+	42.5367i	0.450074	+	1.38518i
$944$	−31.4972	+	22.8840i	−1.02515	+	0.744812i
$945$	−1.94156			−0.0631590
$946$	−18.4995	−	47.8926i	−0.601470	−	1.55712i
$947$	10.0638			0.327029			0.163515	−	0.986541i	$-0.447717\pi$
$947$	10.0638			0.327029			0.163515	+	0.986541i	$0.447717\pi$
$948$	−0.644235	+	0.468064i	−0.0209238	+	0.0152020i
$949$	−2.21583	−	6.81964i	−0.0719290	−	0.221375i
$950$	1.49855	−	4.61205i	0.0486192	−	0.149635i
$951$	−6.86086	−	4.98471i	−0.222479	−	0.161640i
$952$	−38.1743	−	27.7353i	−1.23724	−	0.898906i
$953$	−6.71291	+	20.6602i	−0.217452	+	0.669250i	0.781518	+	0.623883i	$0.214446\pi$
$953$	−6.71291	+	20.6602i	−0.217452	+	0.669250i	−0.998970	+	0.0453670i	$0.985554\pi$
$954$	−1.06012	−	3.26272i	−0.0343227	−	0.105634i
$955$	3.38914	−	2.46236i	0.109670	−	0.0796800i
$956$	−1.45515			−0.0470629
$957$	1.01181	−	3.80801i	0.0327070	−	0.123095i
$958$	−44.9809			−1.45327
$959$	−49.4010	+	35.8919i	−1.59524	+	1.15901i
$960$	−0.925922	−	2.84969i	−0.0298840	−	0.0919735i
$961$	−8.77897	+	27.0189i	−0.283193	+	0.871577i
$962$	4.84747	+	3.52189i	0.156289	+	0.113550i
$963$	−9.14460	−	6.64394i	−0.294681	−	0.214098i
$964$	−0.285172	+	0.877668i	−0.00918476	+	0.0282678i
$965$	−0.950378	−	2.92496i	−0.0305937	−	0.0941579i
$966$	−20.7387	+	15.0675i	−0.667257	+	0.484790i
$967$	34.3030			1.10311			0.551555	−	0.834139i	$-0.314035\pi$
$967$	34.3030			1.10311			0.551555	+	0.834139i	$0.314035\pi$
$968$	6.12091	−	29.4020i	0.196734	−	0.945015i
$969$	−2.46976			−0.0793401
$970$	−8.59217	+	6.24257i	−0.275878	+	0.200437i
$971$	−3.46576	−	10.6665i	−0.111221	−	0.342304i	0.879919	−	0.475124i	$-0.157597\pi$
$971$	−3.46576	−	10.6665i	−0.111221	−	0.342304i	−0.991140	+	0.132820i	$0.957597\pi$
$972$	−0.0397803	+	0.122431i	−0.00127595	+	0.00392698i
$973$	12.6942	+	9.22289i	0.406958	+	0.295672i
$974$	29.8297	+	21.6726i	0.955806	+	0.694434i
$975$	1.49471	−	4.60023i	0.0478689	−	0.147325i
$976$	15.0984	+	46.4682i	0.483289	+	1.48741i
$977$	3.59858	−	2.61452i	0.115129	−	0.0836460i	−0.528731	−	0.848789i	$-0.677332\pi$
$977$	3.59858	−	2.61452i	0.115129	−	0.0836460i	0.643860	+	0.765143i	$0.277332\pi$
$978$	−19.9733			−0.638676
$979$	3.15507	−	11.8743i	0.100836	−	0.379505i
$980$	0.838012			0.0267693
$981$	12.6763	−	9.20987i	0.404723	−	0.294049i
$982$	2.78179	+	8.56146i	0.0887704	+	0.273207i
$983$	−6.95946	+	21.4190i	−0.221972	+	0.683161i	0.776612	+	0.629979i	$0.216936\pi$
$983$	−6.95946	+	21.4190i	−0.221972	+	0.683161i	−0.998585	+	0.0531820i	$0.983064\pi$
$984$	27.0374	+	19.6438i	0.861920	+	0.626221i
$985$	−0.859572	−	0.624515i	−0.0273882	−	0.0198987i
$986$	1.92512	−	5.92492i	0.0613084	−	0.188688i
$987$	−19.5608	−	60.2019i	−0.622627	−	1.91625i
$988$	−0.0715644	+	0.0519946i	−0.00227677	+	0.00165417i
$989$	38.7665			1.23270
$990$	−0.704018	−	1.82260i	−0.0223752	−	0.0579262i
$991$	34.9481			1.11016			0.555081	−	0.831796i	$-0.312687\pi$
$991$	34.9481			1.11016			0.555081	+	0.831796i	$0.312687\pi$
$992$	−0.946809	+	0.687897i	−0.0300612	+	0.0218407i
$993$	−10.0709	−	30.9951i	−0.319591	−	0.983599i
$994$	−10.3502	+	31.8547i	−0.328289	+	1.01037i
$995$	3.90005	+	2.83355i	0.123640	+	0.0898296i
$996$	0.314374	+	0.228406i	0.00996132	+	0.00723733i
$997$	−3.97682	+	12.2394i	−0.125947	+	0.387625i	−0.994072	−	0.108720i	$-0.965325\pi$
$997$	−3.97682	+	12.2394i	−0.125947	+	0.387625i	0.868125	+	0.496345i	$0.165325\pi$
$998$	5.05281	+	15.5510i	0.159944	+	0.492257i
$999$	3.32242	−	2.41388i	0.105117	−	0.0763718i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.c.157.6	✓	28
11.2	odd	10		4719.2.a.bo.1.11		14
11.4	even	5	inner	429.2.n.c.235.6	yes	28
11.9	even	5		4719.2.a.bp.1.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.c.157.6	✓	28	1.1	even	1	trivial
429.2.n.c.235.6	yes	28	11.4	even	5	inner
4719.2.a.bo.1.11		14	11.2	odd	10
4719.2.a.bp.1.4		14	11.9	even	5

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18037 - 0.857589i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.0397803 - 0.122431i) q^{4} +(-0.326657 - 0.237330i) q^{5} +(-1.18037 - 0.857589i) q^{6} +(1.48593 - 4.57323i) q^{7} +(0.843682 + 2.59659i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.18037 - 0.857589i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.0397803 - 0.122431i) q^{4} +(-0.326657 - 0.237330i) q^{5} +(-1.18037 - 0.857589i) q^{6} +(1.48593 - 4.57323i) q^{7} +(0.843682 + 2.59659i) q^{8} +(-0.809017 + 0.587785i) q^{9} -0.589108 q^{10} +(0.851691 - 3.20541i) q^{11} -0.128732 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-2.16800 - 6.67242i) q^{14} +(-0.124772 + 0.384008i) q^{15} +(3.43095 + 2.49273i) q^{16} +(-2.90776 - 2.11261i) q^{17} +(-0.450861 + 1.38761i) q^{18} +(0.212342 + 0.653522i) q^{19} +(-0.0420512 + 0.0305520i) q^{20} -4.80858 q^{21} +(-1.74361 - 4.51396i) q^{22} +3.65382 q^{23} +(2.20879 - 1.60478i) q^{24} +(-1.49471 - 4.60023i) q^{25} +(-0.450861 + 1.38761i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.500795 - 0.363849i) q^{28} +(-0.367111 + 1.12985i) q^{29} +(0.182044 + 0.560275i) q^{30} +(-1.30215 + 0.946071i) q^{31} +0.727109 q^{32} +(-3.31171 + 0.180518i) q^{33} -5.24399 q^{34} +(-1.57076 + 1.14122i) q^{35} +(0.0397803 + 0.122431i) q^{36} +(1.26905 - 3.90574i) q^{37} +(0.811095 + 0.589295i) q^{38} +(0.809017 + 0.587785i) q^{39} +(0.340654 - 1.04842i) q^{40} +(3.78262 + 11.6417i) q^{41} +(-5.67590 + 4.12378i) q^{42} +10.6099 q^{43} +(-0.358561 - 0.231786i) q^{44} +0.403770 q^{45} +(4.31286 - 3.13347i) q^{46} +(4.06790 + 12.5197i) q^{47} +(1.31051 - 4.03333i) q^{48} +(-13.0433 - 9.47651i) q^{49} +(-5.70941 - 4.14813i) q^{50} +(-1.11067 + 3.41828i) q^{51} +(0.0397803 + 0.122431i) q^{52} +(-1.90226 + 1.38207i) q^{53} +1.45902 q^{54} +(-1.03895 + 0.844936i) q^{55} +13.1284 q^{56} +(0.555919 - 0.403899i) q^{57} +(0.535621 + 1.64847i) q^{58} +(-2.83687 + 8.73098i) q^{59} +(0.0420512 + 0.0305520i) q^{60} +(9.32073 + 6.77191i) q^{61} +(-0.725684 + 2.23343i) q^{62} +(1.48593 + 4.57323i) q^{63} +(-6.00365 + 4.36191i) q^{64} +0.403770 q^{65} +(-3.75423 + 3.05316i) q^{66} -2.47381 q^{67} +(-0.374321 + 0.271960i) q^{68} +(-1.12909 - 3.47499i) q^{69} +(-0.875374 + 2.69412i) q^{70} +(-3.86231 - 2.80614i) q^{71} +(-2.20879 - 1.60478i) q^{72} +(-2.21583 + 6.81964i) q^{73} +(-1.85157 - 5.69855i) q^{74} +(-3.91319 + 2.84310i) q^{75} +0.0884585 q^{76} +(-13.3935 - 8.65799i) q^{77} +1.45902 q^{78} +(5.00447 - 3.63596i) q^{79} +(-0.529144 - 1.62854i) q^{80} +(0.309017 - 0.951057i) q^{81} +(14.4487 + 10.4976i) q^{82} +(-2.44208 - 1.77428i) q^{83} +(-0.191287 + 0.588720i) q^{84} +(0.448454 + 1.38020i) q^{85} +(12.5236 - 9.09890i) q^{86} +1.18800 q^{87} +(9.04167 - 0.492854i) q^{88} +3.70447 q^{89} +(0.476598 - 0.346269i) q^{90} +(1.48593 + 4.57323i) q^{91} +(0.145350 - 0.447341i) q^{92} +(1.30215 + 0.946071i) q^{93} +(15.5384 + 11.2893i) q^{94} +(0.0857374 - 0.263873i) q^{95} +(-0.224689 - 0.691522i) q^{96} +(14.5850 - 10.5967i) q^{97} -23.5229 q^{98} +(1.19506 + 3.09384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

Introduction

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