LMFDB - Embedded newform 625.2.e.a.124.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(124,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("625.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.e (of order $10$, degree $4$, not 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.2
Root			$-0.357358 + 1.86824i$ of defining polynomial
Character	$\chi$	$=$	625.124
Dual form			625.2.e.a.499.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.19625 + 0.713605i) q^{2} +(-0.279141 + 0.384204i) q^{3} +(2.69625 + 1.95894i) q^{4} +(-0.887234 + 0.644613i) q^{6} +3.03582i q^{7} +(1.80902 + 2.48990i) q^{8} +(0.857358 + 2.63868i) q^{9} +O(q^{10})$	\(q+(2.19625 + 0.713605i) q^{2} +(-0.279141 + 0.384204i) q^{3} +(2.69625 + 1.95894i) q^{4} +(-0.887234 + 0.644613i) q^{6} +3.03582i q^{7} +(1.80902 + 2.48990i) q^{8} +(0.857358 + 2.63868i) q^{9} +(0.618034 - 1.90211i) q^{11} +(-1.50527 + 0.489091i) q^{12} +(-1.35736 + 0.441032i) q^{13} +(-2.16637 + 6.66742i) q^{14} +(0.136498 + 0.420099i) q^{16} +(-1.09343 - 1.50497i) q^{17} +6.40701i q^{18} +(0.730800 - 0.530958i) q^{19} +(-1.16637 - 0.847421i) q^{21} +(2.71472 - 3.73648i) q^{22} +(3.16637 + 1.02882i) q^{23} -1.46160 q^{24} -3.29582 q^{26} +(-2.60809 - 0.847421i) q^{27} +(-5.94699 + 8.18532i) q^{28} +(3.20619 + 2.32943i) q^{29} +(5.21004 - 3.78532i) q^{31} -5.13532i q^{32} +(0.558282 + 0.768409i) q^{33} +(-1.32748 - 4.08557i) q^{34} +(-2.85736 + 8.79404i) q^{36} +(-3.63324 + 1.18051i) q^{37} +(1.98391 - 0.644613i) q^{38} +(0.209447 - 0.644613i) q^{39} +(-0.566805 - 1.74445i) q^{41} +(-1.95693 - 2.69348i) q^{42} +3.59445i q^{43} +(5.39250 - 3.91788i) q^{44} +(6.21998 + 4.51908i) q^{46} +(-2.82134 + 3.88324i) q^{47} +(-0.199506 - 0.0648235i) q^{48} -2.21619 q^{49} +0.883436 q^{51} +(-4.52373 - 1.46985i) q^{52} +(5.58674 - 7.68949i) q^{53} +(-5.12330 - 3.72230i) q^{54} +(-7.55888 + 5.49184i) q^{56} +0.428989i q^{57} +(5.37930 + 7.40398i) q^{58} +(-3.28968 - 10.1246i) q^{59} +(4.41097 - 13.5756i) q^{61} +(14.1438 - 4.59559i) q^{62} +(-8.01054 + 2.60278i) q^{63} +(3.93759 - 12.1186i) q^{64} +(0.677786 + 2.08601i) q^{66} +(6.28353 + 8.64854i) q^{67} -6.19974i q^{68} +(-1.27914 + 0.929350i) q^{69} +(-10.0802 - 7.32371i) q^{71} +(-5.01906 + 6.90814i) q^{72} +(-0.254532 - 0.0827026i) q^{73} -8.82193 q^{74} +3.01054 q^{76} +(5.77447 + 1.87624i) q^{77} +(0.919998 - 1.26627i) q^{78} +(-6.93470 - 5.03835i) q^{79} +(-5.68017 + 4.12688i) q^{81} -4.23572i q^{82} +(-7.41677 - 10.2083i) q^{83} +(-1.48479 - 4.56972i) q^{84} +(-2.56502 + 7.89432i) q^{86} +(-1.78996 + 0.581593i) q^{87} +(5.85410 - 1.90211i) q^{88} +(1.47338 - 4.53460i) q^{89} +(-1.33889 - 4.12069i) q^{91} +(6.52195 + 8.97669i) q^{92} +3.05836i q^{93} +(-8.96746 + 6.51524i) q^{94} +(1.97301 + 1.43348i) q^{96} +(-5.85319 + 8.05623i) q^{97} +(-4.86730 - 1.58148i) q^{98} +5.54893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9	$ 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9 - 4 * q^11 + 10 * q^12 - 5 * q^13 - 7 * q^14 - 2 * q^16 + 15 * q^17 + 10 * q^19 + q^21 + 10 * q^22 + 15 * q^23 - 20 * q^24 + 6 * q^26 - 5 * q^27 - 20 * q^28 + 15 * q^29 + q^31 + 10 * q^33 - 12 * q^34 - 17 * q^36 - 5 * q^37 + 12 * q^39 - 9 * q^41 + 5 * q^42 + 8 * q^44 + 16 * q^46 - 15 * q^47 - 5 * q^48 + 14 * q^49 - 4 * q^51 - 20 * q^52 + 35 * q^53 - 10 * q^54 - 15 * q^56 - 20 * q^58 + 15 * q^59 + 6 * q^61 + 45 * q^62 - 20 * q^63 - 26 * q^64 - 18 * q^66 - 13 * q^69 - 29 * q^71 + 5 * q^72 + 10 * q^73 - 12 * q^74 - 20 * q^76 + 20 * q^77 - 25 * q^78 - 10 * q^79 - 12 * q^81 + 15 * q^83 - 27 * q^84 + 16 * q^86 - 55 * q^87 + 20 * q^88 + 40 * q^89 + q^91 - 5 * q^92 - 7 * q^94 + 11 * q^96 - 10 * q^97 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	2.19625	+	0.713605i	1.55298	+	0.504595i	0.954922	−	0.296855i	$-0.0959379\pi$
$2$	2.19625	+	0.713605i	1.55298	+	0.504595i	0.598061	+	0.801450i	$0.295938\pi$
$3$	−0.279141	+	0.384204i	−0.161162	+	0.221821i	−0.881959	−	0.471325i	$-0.843776\pi$
$3$	−0.279141	+	0.384204i	−0.161162	+	0.221821i	0.720797	+	0.693146i	$0.243776\pi$
$4$	2.69625	+	1.95894i	1.34813	+	0.979470i
$5$		0			0
$5$		0			0
$6$	−0.887234	+	0.644613i	−0.362212	+	0.263162i
$7$			3.03582i			1.14743i	0.819055	+	0.573716i	$0.194498\pi$
$7$			3.03582i			1.14743i	−0.819055	+	0.573716i	$0.805502\pi$
$8$	1.80902	+	2.48990i	0.639584	+	0.880312i
$9$	0.857358	+	2.63868i	0.285786	+	0.879558i
$10$		0			0
$11$	0.618034	−	1.90211i	0.186344	−	0.573509i	−0.813625	−	0.581390i	$-0.802509\pi$
$11$	0.618034	−	1.90211i	0.186344	−	0.573509i	0.999969	+	0.00788181i	$0.00250889\pi$
$12$	−1.50527	+	0.489091i	−0.434533	+	0.141188i
$13$	−1.35736	+	0.441032i	−0.376463	+	0.122320i	−0.491136	−	0.871083i	$-0.663418\pi$
$13$	−1.35736	+	0.441032i	−0.376463	+	0.122320i	0.114673	+	0.993403i	$0.463418\pi$
$14$	−2.16637	+	6.66742i	−0.578988	+	1.78194i
$15$		0			0
$16$	0.136498	+	0.420099i	0.0341246	+	0.105025i
$17$	−1.09343	−	1.50497i	−0.265195	−	0.365009i	0.655565	−	0.755138i	$-0.272430\pi$
$17$	−1.09343	−	1.50497i	−0.265195	−	0.365009i	−0.920760	+	0.390129i	$0.872430\pi$
$18$			6.40701i			1.51015i
$19$	0.730800	−	0.530958i	0.167657	−	0.121810i	−0.500793	−	0.865567i	$-0.666958\pi$
$19$	0.730800	−	0.530958i	0.167657	−	0.121810i	0.668450	+	0.743757i	$0.266958\pi$
$20$		0			0
$21$	−1.16637	−	0.847421i	−0.254524	−	0.184922i
$22$	2.71472	−	3.73648i	0.578779	−	0.796621i
$23$	3.16637	+	1.02882i	0.660235	+	0.214523i	0.619922	−	0.784664i	$-0.287164\pi$
$23$	3.16637	+	1.02882i	0.660235	+	0.214523i	0.0403132	+	0.999187i	$0.487164\pi$
$24$	−1.46160			−0.298348
$25$		0			0
$26$	−3.29582			−0.646364
$27$	−2.60809	−	0.847421i	−0.501928	−	0.163086i
$28$	−5.94699	+	8.18532i	−1.12387	+	1.54688i
$29$	3.20619	+	2.32943i	0.595375	+	0.432565i	0.844234	−	0.535974i	$-0.180056\pi$
$29$	3.20619	+	2.32943i	0.595375	+	0.432565i	−0.248859	+	0.968540i	$0.580056\pi$
$30$		0			0
$31$	5.21004	−	3.78532i	0.935751	−	0.679863i	−0.0116431	−	0.999932i	$-0.503706\pi$
$31$	5.21004	−	3.78532i	0.935751	−	0.679863i	0.947394	+	0.320069i	$0.103706\pi$
$32$		−	5.13532i		−	0.907805i
$33$	0.558282	+	0.768409i	0.0971844	+	0.133763i
$34$	−1.32748	−	4.08557i	−0.227661	−	0.700669i
$35$		0			0
$36$	−2.85736	+	8.79404i	−0.476226	+	1.46567i
$37$	−3.63324	+	1.18051i	−0.597301	+	0.194075i	−0.592037	−	0.805911i	$-0.701676\pi$
$37$	−3.63324	+	1.18051i	−0.597301	+	0.194075i	−0.00526493	+	0.999986i	$0.501676\pi$
$38$	1.98391	−	0.644613i	0.321833	−	0.104570i
$39$	0.209447	−	0.644613i	0.0335384	−	0.103221i
$40$		0			0
$41$	−0.566805	−	1.74445i	−0.0885201	−	0.272437i	0.896991	−	0.442049i	$-0.145748\pi$
$41$	−0.566805	−	1.74445i	−0.0885201	−	0.272437i	−0.985511	+	0.169613i	$0.945748\pi$
$42$	−1.95693	−	2.69348i	−0.301960	−	0.415613i
$43$			3.59445i			0.548149i	0.961708	+	0.274074i	$0.0883715\pi$
$43$			3.59445i			0.548149i	−0.961708	+	0.274074i	$0.911629\pi$
$44$	5.39250	−	3.91788i	0.812950	−	0.590643i
$45$		0			0
$46$	6.21998	+	4.51908i	0.917086	+	0.666302i
$47$	−2.82134	+	3.88324i	−0.411534	+	0.566428i	−0.963592	−	0.267378i	$-0.913843\pi$
$47$	−2.82134	+	3.88324i	−0.411534	+	0.566428i	0.552057	+	0.833806i	$0.313843\pi$
$48$	−0.199506	−	0.0648235i	−0.0287962	−	0.00935647i
$49$	−2.21619			−0.316598
$50$		0			0
$51$	0.883436			0.123706
$52$	−4.52373	−	1.46985i	−0.627329	−	0.203831i
$53$	5.58674	−	7.68949i	0.767398	−	1.05623i	−0.229165	−	0.973388i	$-0.573599\pi$
$53$	5.58674	−	7.68949i	0.767398	−	1.05623i	0.996562	−	0.0828447i	$-0.0264005\pi$
$54$	−5.12330	−	3.72230i	−0.697193	−	0.506540i
$55$		0			0
$56$	−7.55888	+	5.49184i	−1.01010	+	0.733879i
$57$			0.428989i			0.0568209i
$58$	5.37930	+	7.40398i	0.706337	+	0.972190i
$59$	−3.28968	−	10.1246i	−0.428279	−	1.31811i	−0.899819	−	0.436263i	$-0.856302\pi$
$59$	−3.28968	−	10.1246i	−0.428279	−	1.31811i	0.471540	−	0.881845i	$-0.343698\pi$
$60$		0			0
$61$	4.41097	−	13.5756i	0.564766	−	1.73817i	−0.103879	−	0.994590i	$-0.533125\pi$
$61$	4.41097	−	13.5756i	0.564766	−	1.73817i	0.668645	−	0.743582i	$-0.266875\pi$
$62$	14.1438	−	4.59559i	1.79626	−	0.583641i
$63$	−8.01054	+	2.60278i	−1.00923	+	0.327920i
$64$	3.93759	−	12.1186i	0.492198	−	1.51483i
$65$		0			0
$66$	0.677786	+	2.08601i	0.0834297	+	0.256770i
$67$	6.28353	+	8.64854i	0.767656	+	1.05659i	0.996538	+	0.0831333i	$0.0264927\pi$
$67$	6.28353	+	8.64854i	0.767656	+	1.05659i	−0.228883	+	0.973454i	$0.573507\pi$
$68$		−	6.19974i		−	0.751828i
$69$	−1.27914	+	0.929350i	−0.153990	+	0.111881i
$70$		0			0
$71$	−10.0802	−	7.32371i	−1.19630	−	0.869165i	−0.202387	−	0.979306i	$-0.564870\pi$
$71$	−10.0802	−	7.32371i	−1.19630	−	0.869165i	−0.993916	+	0.110141i	$0.964870\pi$
$72$	−5.01906	+	6.90814i	−0.591502	+	0.814132i
$73$	−0.254532	−	0.0827026i	−0.0297908	−	0.00967961i	0.294084	−	0.955780i	$-0.404986\pi$
$73$	−0.254532	−	0.0827026i	−0.0297908	−	0.00967961i	−0.323874	+	0.946100i	$0.604986\pi$
$74$	−8.82193			−1.02553
$75$		0			0
$76$	3.01054			0.345332
$77$	5.77447	+	1.87624i	0.658062	+	0.213817i
$78$	0.919998	−	1.26627i	0.104169	−	0.143377i
$79$	−6.93470	−	5.03835i	−0.780214	−	0.566859i	0.124829	−	0.992178i	$-0.460162\pi$
$79$	−6.93470	−	5.03835i	−0.780214	−	0.566859i	−0.905043	+	0.425319i	$0.860162\pi$
$80$		0			0
$81$	−5.68017	+	4.12688i	−0.631129	+	0.458542i
$82$		−	4.23572i		−	0.467757i
$83$	−7.41677	−	10.2083i	−0.814097	−	1.12051i	−0.990678	−	0.136222i	$-0.956504\pi$
$83$	−7.41677	−	10.2083i	−0.814097	−	1.12051i	0.176582	−	0.984286i	$-0.443496\pi$
$84$	−1.48479	−	4.56972i	−0.162004	−	0.498597i
$85$		0			0
$86$	−2.56502	+	7.89432i	−0.276593	+	0.851266i
$87$	−1.78996	+	0.581593i	−0.191904	+	0.0623533i
$88$	5.85410	−	1.90211i	0.624049	−	0.202766i
$89$	1.47338	−	4.53460i	0.156178	−	0.480666i	−0.842100	−	0.539321i	$-0.818681\pi$
$89$	1.47338	−	4.53460i	0.156178	−	0.480666i	0.998278	+	0.0586546i	$0.0186810\pi$
$90$		0			0
$91$	−1.33889	−	4.12069i	−0.140354	−	0.431966i
$92$	6.52195	+	8.97669i	0.679960	+	0.935885i
$93$			3.05836i			0.317137i
$94$	−8.96746	+	6.51524i	−0.924923	+	0.671996i
$95$		0			0
$96$	1.97301	+	1.43348i	0.201370	+	0.146304i
$97$	−5.85319	+	8.05623i	−0.594302	+	0.817986i	−0.995172	−	0.0981488i	$-0.968708\pi$
$97$	−5.85319	+	8.05623i	−0.594302	+	0.817986i	0.400870	+	0.916135i	$0.368708\pi$
$98$	−4.86730	−	1.58148i	−0.491671	−	0.159754i
$99$	5.54893			0.557689
$100$		0			0
$101$	9.34612			0.929974			0.464987	−	0.885318i	$-0.346059\pi$
$101$	9.34612			0.929974			0.464987	+	0.885318i	$0.346059\pi$
$102$	1.94025	+	0.630425i	0.192113	+	0.0624213i
$103$	−5.33949	+	7.34917i	−0.526115	+	0.724136i	−0.986532	−	0.163567i	$-0.947700\pi$
$103$	−5.33949	+	7.34917i	−0.526115	+	0.724136i	0.460417	+	0.887703i	$0.347700\pi$
$104$	−3.55361	−	2.58185i	−0.348460	−	0.253171i
$105$		0			0
$106$	17.7571	−	12.9013i	1.72473	−	1.25309i
$107$			5.62871i			0.544148i	0.962276	+	0.272074i	$0.0877096\pi$
$107$			5.62871i			0.544148i	−0.962276	+	0.272074i	$0.912290\pi$
$108$	−5.37202	−	7.39396i	−0.516923	−	0.711484i
$109$	3.12509	+	9.61803i	0.299329	+	0.921240i	0.981733	+	0.190265i	$0.0609346\pi$
$109$	3.12509	+	9.61803i	0.299329	+	0.921240i	−0.682404	+	0.730975i	$0.739065\pi$
$110$		0			0
$111$	0.560629	−	1.72544i	0.0532125	−	0.163771i
$112$	−1.27534	+	0.414384i	−0.120509	+	0.0391556i
$113$	10.1877	−	3.31019i	0.958381	−	0.311397i	0.212264	−	0.977212i	$-0.431916\pi$
$113$	10.1877	−	3.31019i	0.958381	−	0.311397i	0.746116	+	0.665815i	$0.231916\pi$
$114$	−0.306129	+	0.942167i	−0.0286716	+	0.0882420i
$115$		0			0
$116$	4.08147	+	12.5615i	0.378955	+	1.16630i
$117$	−2.32748	−	3.20350i	−0.215176	−	0.296164i
$118$		−	24.5836i		−	2.26311i
$119$	4.56882	−	3.31944i	0.418823	−	0.304293i
$120$		0			0
$121$	5.66312	+	4.11450i	0.514829	+	0.374045i
$122$	19.3752	−	26.6676i	1.75415	−	2.41437i
$123$	0.828443	+	0.269177i	0.0746982	+	0.0242709i
$124$	21.4628			1.92742
$125$		0			0
$126$	−19.4505			−1.73279
$127$	−10.8049	−	3.51072i	−0.958779	−	0.311526i	−0.212501	−	0.977161i	$-0.568161\pi$
$127$	−10.8049	−	3.51072i	−0.958779	−	0.311526i	−0.746278	+	0.665635i	$0.768161\pi$
$128$	11.2589	−	15.4966i	0.995158	−	1.36972i
$129$	−1.38100	−	1.00336i	−0.121591	−	0.0883408i
$130$		0			0
$131$	−6.46219	+	4.69506i	−0.564605	+	0.410209i	−0.833141	−	0.553060i	$-0.813460\pi$
$131$	−6.46219	+	4.69506i	−0.564605	+	0.410209i	0.268537	+	0.963269i	$0.413460\pi$
$132$			3.16546i			0.275518i
$133$	1.61189	+	2.21858i	0.139769	+	0.192375i
$134$	7.62857	+	23.4783i	0.659008	+	2.02822i
$135$		0			0
$136$	1.76920	−	5.44504i	0.151708	−	0.466908i
$137$	−8.88027	+	2.88537i	−0.758692	+	0.246514i	−0.662717	−	0.748870i	$-0.730597\pi$
$137$	−8.88027	+	2.88537i	−0.758692	+	0.246514i	−0.0959750	+	0.995384i	$0.530597\pi$
$138$	−3.47250	+	1.12828i	−0.295599	+	0.0960460i
$139$	−5.53605	+	17.0382i	−0.469562	+	1.44516i	0.383592	+	0.923503i	$0.374687\pi$
$139$	−5.53605	+	17.0382i	−0.469562	+	1.44516i	−0.853154	+	0.521660i	$0.825313\pi$
$140$		0			0
$141$	−0.704407	−	2.16794i	−0.0593217	−	0.182574i
$142$	−16.9125	−	23.2780i	−1.41926	−	1.95345i
$143$			2.85442i			0.238699i
$144$	−0.991477	+	0.720350i	−0.0826231	+	0.0600292i
$145$		0			0
$146$	−0.500000	−	0.363271i	−0.0413803	−	0.0300645i
$147$	0.618628	−	0.851468i	0.0510236	−	0.0702279i
$148$	−12.1087	−	3.93435i	−0.995328	−	0.323402i
$149$	6.31395			0.517259			0.258629	−	0.965977i	$-0.416729\pi$
$149$	6.31395			0.517259			0.258629	+	0.965977i	$0.416729\pi$
$150$		0			0
$151$	4.71947			0.384065			0.192033	−	0.981389i	$-0.438492\pi$
$151$	4.71947			0.384065			0.192033	+	0.981389i	$0.438492\pi$
$152$	2.64406	+	0.859107i	0.214462	+	0.0696828i
$153$	3.03367	−	4.17549i	0.245258	−	0.337569i
$154$	11.3433	+	8.24138i	0.914068	+	0.664109i
$155$		0			0
$156$	1.82748	−	1.32774i	0.146316	−	0.106305i
$157$			1.46908i			0.117245i	0.998280	+	0.0586225i	$0.0186708\pi$
$157$			1.46908i			0.117245i	−0.998280	+	0.0586225i	$0.981329\pi$
$158$	−11.6349	−	16.0141i	−0.925626	−	1.27402i
$159$	1.39485	+	4.29290i	0.110619	+	0.340449i
$160$		0			0
$161$	−3.12330	+	9.61253i	−0.246151	+	0.757574i
$162$	−15.4200	+	5.01027i	−1.21151	+	0.393644i
$163$	4.24142	−	1.37812i	0.332214	−	0.107943i	−0.138160	−	0.990410i	$-0.544119\pi$
$163$	4.24142	−	1.37812i	0.332214	−	0.107943i	0.470374	+	0.882467i	$0.344119\pi$
$164$	1.88902	−	5.81380i	0.147508	−	0.453982i
$165$		0			0
$166$	−9.00439	−	27.7127i	−0.698876	−	2.15092i
$167$	−6.13275	−	8.44101i	−0.474567	−	0.653185i	0.502883	−	0.864355i	$-0.332273\pi$
$167$	−6.13275	−	8.44101i	−0.474567	−	0.653185i	−0.977449	+	0.211170i	$0.932273\pi$
$168$		−	4.43715i		−	0.342334i
$169$	−8.86931	+	6.44393i	−0.682255	+	0.495687i
$170$		0			0
$171$	2.02758	+	1.47312i	0.155053	+	0.112653i
$172$	−7.04132	+	9.69155i	−0.536896	+	0.738973i
$173$	7.30049	+	2.37207i	0.555046	+	0.180345i	0.573091	−	0.819492i	$-0.305744\pi$
$173$	7.30049	+	2.37207i	0.555046	+	0.180345i	−0.0180448	+	0.999837i	$0.505744\pi$
$174$	−4.34623			−0.329486
$175$		0			0
$176$	0.883436			0.0665915
$177$	4.80819	+	1.56228i	0.361406	+	0.117428i
$178$	6.47182	−	8.90770i	0.485084	−	0.667660i
$179$	12.5533	+	9.12053i	0.938280	+	0.681700i	0.948006	−	0.318253i	$-0.103096\pi$
$179$	12.5533	+	9.12053i	0.938280	+	0.681700i	−0.00972631	+	0.999953i	$0.503096\pi$
$180$		0			0
$181$	1.28679	−	0.934906i	0.0956462	−	0.0694910i	−0.538934	−	0.842348i	$-0.681173\pi$
$181$	1.28679	−	0.934906i	0.0956462	−	0.0694910i	0.634580	+	0.772857i	$0.281173\pi$
$182$		−	10.0055i		−	0.741658i
$183$	3.98451	+	5.48421i	0.294543	+	0.405404i
$184$	3.16637	+	9.74510i	0.233428	+	0.718418i
$185$		0			0
$186$	−2.18246	+	6.71692i	−0.160026	+	0.492509i
$187$	−3.53840	+	1.14970i	−0.258753	+	0.0840741i
$188$	−15.2141	+	4.94335i	−1.10960	+	0.360531i
$189$	2.57261	−	7.91769i	0.187130	−	0.575927i
$190$		0			0
$191$	6.07788	+	18.7058i	0.439780	+	1.35350i	0.888108	+	0.459635i	$0.152020\pi$
$191$	6.07788	+	18.7058i	0.439780	+	1.35350i	−0.448328	+	0.893869i	$0.647980\pi$
$192$	3.55690	+	4.89565i	0.256697	+	0.353313i
$193$		−	13.1100i		−	0.943680i	−0.881684	−	0.471840i	$-0.843590\pi$
$193$		−	13.1100i		−	0.943680i	0.881684	−	0.471840i	$-0.156410\pi$
$194$	−18.6040	+	13.5166i	−1.33569	+	0.970437i
$195$		0			0
$196$	−5.97539	−	4.34138i	−0.426814	−	0.310098i
$197$	−2.01580	+	2.77451i	−0.143620	+	0.197676i	−0.874767	−	0.484544i	$-0.838985\pi$
$197$	−2.01580	+	2.77451i	−0.143620	+	0.197676i	0.731147	+	0.682220i	$0.238985\pi$
$198$	12.1869	+	3.95975i	0.866082	+	0.281407i
$199$	−17.6959			−1.25443			−0.627215	−	0.778846i	$-0.715805\pi$
$199$	−17.6959			−1.25443			−0.627215	+	0.778846i	$0.715805\pi$
$200$		0			0
$201$	−5.07680			−0.358090
$202$	20.5264	+	6.66944i	1.44423	+	0.469260i
$203$	−7.07174	+	9.73341i	−0.496339	+	0.683152i
$204$	2.38197	+	1.73060i	0.166771	+	0.121166i
$205$		0			0
$206$	−16.9713	+	12.3303i	−1.18244	+	0.859096i
$207$			9.23710i			0.642023i
$208$	−0.370554	−	0.510024i	−0.0256933	−	0.0353638i
$209$	−0.558282	−	1.71821i	−0.0386172	−	0.118851i
$210$		0			0
$211$	−1.00235	+	3.08491i	−0.0690044	+	0.212374i	−0.979612	−	0.200898i	$-0.935614\pi$
$211$	−1.00235	+	3.08491i	−0.0690044	+	0.212374i	0.910608	+	0.413272i	$0.135614\pi$
$212$	30.1265	−	9.78869i	2.06910	−	0.672290i
$213$	5.62761	−	1.82852i	0.385597	−	0.125288i
$214$	−4.01668	+	12.3621i	−0.274575	+	0.845054i
$215$		0			0
$216$	−2.60809	−	8.02688i	−0.177458	−	0.546160i
$217$	11.4915	+	15.8167i	0.780096	+	1.07371i
$218$			23.3537i			1.58171i
$219$	0.102825	−	0.0747068i	0.00694828	−	0.00504822i
$220$		0			0
$221$	2.14791	+	1.56055i	0.144484	+	0.104974i
$222$	2.46256	−	3.38943i	0.165276	−	0.227483i
$223$	−27.3094	−	8.87335i	−1.82877	−	0.594203i	−0.999368	−	0.0355515i	$-0.988681\pi$
$223$	−27.3094	−	8.87335i	−1.82877	−	0.594203i	−0.829402	−	0.558652i	$-0.811319\pi$
$224$	15.5899			1.04164
$225$		0			0
$226$	24.7370			1.64548
$227$	11.1470	+	3.62187i	0.739851	+	0.240392i	0.654609	−	0.755968i	$-0.272833\pi$
$227$	11.1470	+	3.62187i	0.739851	+	0.240392i	0.0852426	+	0.996360i	$0.472833\pi$
$228$	−0.840364	+	1.15666i	−0.0556544	+	0.0766018i
$229$	−13.2689	−	9.64043i	−0.876835	−	0.637058i	0.0555774	−	0.998454i	$-0.482300\pi$
$229$	−13.2689	−	9.64043i	−0.876835	−	0.637058i	−0.932412	+	0.361397i	$0.882300\pi$
$230$		0			0
$231$	−2.33275	+	1.69484i	−0.153484	+	0.111512i
$232$			12.1971i			0.800777i
$233$	13.2337	+	18.2147i	0.866971	+	1.19328i	0.979862	+	0.199676i	$0.0639890\pi$
$233$	13.2337	+	18.2147i	0.866971	+	1.19328i	−0.112891	+	0.993607i	$0.536011\pi$
$234$	−2.82570	−	8.69660i	−0.184722	−	0.568514i
$235$		0			0
$236$	10.9637	−	33.7427i	0.713674	−	2.19646i
$237$	3.87152	−	1.25793i	0.251482	−	0.0817114i
$238$	12.4030	−	4.02999i	0.803969	−	0.261226i
$239$	2.04981	−	6.30867i	0.132591	−	0.408074i	−0.862616	−	0.505859i	$-0.831176\pi$
$239$	2.04981	−	6.30867i	0.132591	−	0.408074i	0.995208	+	0.0977848i	$0.0311757\pi$
$240$		0			0
$241$	8.10430	+	24.9425i	0.522044	+	1.60668i	0.770089	+	0.637936i	$0.220212\pi$
$241$	8.10430	+	24.9425i	0.522044	+	1.60668i	−0.248045	+	0.968748i	$0.579788\pi$
$242$	9.50150	+	13.0777i	0.610780	+	0.840666i
$243$		−	11.5613i		−	0.741655i
$244$	38.4868	−	27.9623i	2.46386	−	1.79010i
$245$		0			0
$246$	1.62738	+	1.18236i	0.103758	+	0.0753846i
$247$	−0.757788	+	1.04301i	−0.0482169	+	0.0663649i
$248$	18.8501	+	6.12477i	1.19698	+	0.388923i
$249$	5.99241			0.379753
$250$		0			0
$251$	−10.9121			−0.688766			−0.344383	−	0.938829i	$-0.611912\pi$
$251$	−10.9121			−0.688766			−0.344383	+	0.938829i	$0.611912\pi$
$252$	−26.6971	−	8.67441i	−1.68176	−	0.546437i
$253$	3.91385	−	5.38696i	0.246062	−	0.338675i
$254$	−21.2250	−	15.4208i	−1.33177	−	0.967590i
$255$		0			0
$256$	15.1684	−	11.0205i	0.948024	−	0.688780i
$257$			6.58051i			0.410481i	0.978712	+	0.205240i	$0.0657976\pi$
$257$			6.58051i			0.410481i	−0.978712	+	0.205240i	$0.934202\pi$
$258$	−2.31703	−	3.18912i	−0.144252	−	0.198546i
$259$	−3.58382	−	11.0299i	−0.222688	−	0.685362i
$260$		0			0
$261$	−3.39777	+	10.4573i	−0.210317	+	0.647288i
$262$	−17.5430	+	5.70007i	−1.08381	+	0.352152i
$263$	−25.7805	+	8.37660i	−1.58970	+	0.516524i	−0.964531	−	0.263969i	$-0.914968\pi$
$263$	−25.7805	+	8.37660i	−1.58970	+	0.516524i	−0.625165	+	0.780493i	$0.714968\pi$
$264$	−0.903319	+	2.78013i	−0.0555954	+	0.171105i
$265$		0			0
$266$	1.95693	+	6.02280i	0.119987	+	0.369282i
$267$	1.33093	+	1.83187i	0.0814517	+	0.112109i
$268$			35.6277i			2.17631i
$269$	0.816664	−	0.593341i	0.0497929	−	0.0361766i	−0.562610	−	0.826722i	$-0.690203\pi$
$269$	0.816664	−	0.593341i	0.0497929	−	0.0361766i	0.612403	+	0.790546i	$0.290203\pi$
$270$		0			0
$271$	−5.05800	−	3.67485i	−0.307252	−	0.223231i	0.423465	−	0.905913i	$-0.360814\pi$
$271$	−5.05800	−	3.67485i	−0.307252	−	0.223231i	−0.730716	+	0.682681i	$0.760814\pi$
$272$	0.482986	−	0.664773i	0.0292853	−	0.0403078i
$273$	1.95693	+	0.635844i	0.118439	+	0.0384830i
$274$	−21.5623			−1.30263
$275$		0			0
$276$	−5.26943			−0.317182
$277$	−23.4629	−	7.62355i	−1.40975	−	0.458055i	−0.497418	−	0.867511i	$-0.665718\pi$
$277$	−23.4629	−	7.62355i	−1.40975	−	0.458055i	−0.912330	+	0.409456i	$0.865718\pi$
$278$	−24.3171	+	33.4696i	−1.45844	+	2.00738i
$279$	14.4551	+	10.5022i	0.865404	+	0.628753i
$280$		0			0
$281$	−1.48771	+	1.08089i	−0.0887495	+	0.0644803i	−0.631275	−	0.775559i	$-0.717468\pi$
$281$	−1.48771	+	1.08089i	−0.0887495	+	0.0644803i	0.542526	+	0.840039i	$0.317468\pi$
$282$		−	5.26401i		−	0.313467i
$283$	−5.07915	−	6.99084i	−0.301924	−	0.415563i	0.630918	−	0.775850i	$-0.282679\pi$
$283$	−5.07915	−	6.99084i	−0.301924	−	0.415563i	−0.932841	+	0.360287i	$0.882679\pi$
$284$	−12.8321	−	39.4931i	−0.761445	−	2.34349i
$285$		0			0
$286$	−2.03693	+	6.26902i	−0.120446	+	0.370695i
$287$	5.29582	−	1.72072i	0.312602	−	0.101571i
$288$	13.5504	−	4.40280i	0.798467	−	0.259438i
$289$	4.18393	−	12.8768i	0.246114	−	0.757460i
$290$		0			0
$291$	−1.46137	−	4.49765i	−0.0856672	−	0.263657i
$292$	−0.524274	−	0.721601i	−0.0306808	−	0.0422285i
$293$		−	6.29156i		−	0.367557i	−0.982968	−	0.183779i	$-0.941167\pi$
$293$		−	6.29156i		−	0.367557i	0.982968	−	0.183779i	$-0.0588329\pi$
$294$	1.96627	−	1.42858i	0.114675	−	0.0833166i
$295$		0			0
$296$	−9.51195	−	6.91084i	−0.552871	−	0.401684i
$297$	−3.22378	+	4.43715i	−0.187063	+	0.257470i
$298$	13.8670	+	4.50567i	0.803295	+	0.261006i
$299$	−4.75164			−0.274795
$300$		0			0
$301$	−10.9121			−0.628963
$302$	10.3651	+	3.36784i	0.596447	+	0.193797i
$303$	−2.60888	+	3.59082i	−0.149876	+	0.206287i
$304$	0.322808	+	0.234534i	0.0185143	+	0.0134514i
$305$		0			0
$306$	9.64236	−	7.00558i	0.551217	−	0.400483i
$307$		−	28.6661i		−	1.63606i	−0.575175	−	0.818030i	$-0.695066\pi$
$307$		−	28.6661i		−	1.63606i	0.575175	−	0.818030i	$-0.304934\pi$
$308$	11.8940	+	16.3706i	0.677722	+	0.932804i
$309$	−1.33312	−	4.10291i	−0.0758383	−	0.233406i
$310$		0			0
$311$	−2.42161	+	7.45295i	−0.137317	+	0.422618i	−0.995943	−	0.0899842i	$-0.971318\pi$
$311$	−2.42161	+	7.45295i	−0.137317	+	0.422618i	0.858626	+	0.512602i	$0.171318\pi$
$312$	1.98391	−	0.644613i	0.112317	−	0.0364940i
$313$	20.3614	−	6.61582i	1.15090	−	0.373949i	0.329415	−	0.944185i	$-0.393149\pi$
$313$	20.3614	−	6.61582i	1.15090	−	0.373949i	0.821480	+	0.570237i	$0.193149\pi$
$314$	−1.04834	+	3.22646i	−0.0591613	+	0.182080i
$315$		0			0
$316$	−8.82785	−	27.1693i	−0.496605	−	1.52839i
$317$	−2.36280	−	3.25211i	−0.132708	−	0.182657i	0.737491	−	0.675356i	$-0.236010\pi$
$317$	−2.36280	−	3.25211i	−0.132708	−	0.182657i	−0.870200	+	0.492699i	$0.836010\pi$
$318$			10.4237i			0.584530i
$319$	6.41238	−	4.65887i	0.359025	−	0.260847i
$320$		0			0
$321$	−2.16258	−	1.57120i	−0.120703	−	0.0876961i
$322$	−13.7191	+	18.8827i	−0.764536	+	1.05229i
$323$	−1.59815	−	0.519271i	−0.0889235	−	0.0288930i
$324$	−23.3995			−1.29997
$325$		0			0
$326$	10.2987			0.570390
$327$	−4.56763	−	1.48411i	−0.252590	−	0.0820716i
$328$	3.31813	−	4.56702i	0.183213	−	0.252171i
$329$	−11.7888	−	8.56506i	−0.649938	−	0.472207i
$330$		0			0
$331$	−9.42008	+	6.84409i	−0.517775	+	0.376185i	−0.815765	−	0.578384i	$-0.803684\pi$
$331$	−9.42008	+	6.84409i	−0.517775	+	0.376185i	0.297990	+	0.954569i	$0.403684\pi$
$332$		−	42.0532i		−	2.30797i
$333$	−6.22998	−	8.57483i	−0.341401	−	0.469898i
$334$	−7.44552	−	22.9149i	−0.407400	−	1.25385i
$335$		0			0
$336$	0.196792	−	0.605664i	0.0107359	−	0.0330417i
$337$	20.4808	−	6.65461i	1.11566	−	0.362500i	0.307550	−	0.951532i	$-0.400491\pi$
$337$	20.4808	−	6.65461i	1.11566	−	0.362500i	0.808110	+	0.589032i	$0.200491\pi$
$338$	−24.0777	+	7.82330i	−1.30965	+	0.425532i
$339$	−1.57202	+	4.83818i	−0.0853804	+	0.262774i
$340$		0			0
$341$	−3.98012	−	12.2495i	−0.215535	−	0.663350i
$342$	3.40185	+	4.68224i	0.183951	+	0.253187i
$343$			14.5228i			0.784157i
$344$	−8.94982	+	6.50243i	−0.482542	+	0.350587i
$345$		0			0
$346$	14.3410	+	10.4193i	0.770976	+	0.560147i
$347$	9.16782	−	12.6184i	0.492155	−	0.677393i	−0.488629	−	0.872492i	$-0.662503\pi$
$347$	9.16782	−	12.6184i	0.492155	−	0.677393i	0.980784	+	0.195099i	$0.0625028\pi$
$348$	−5.96548	−	1.93830i	−0.319783	−	0.103904i
$349$	−5.56598			−0.297940			−0.148970	−	0.988842i	$-0.547596\pi$
$349$	−5.56598			−0.297940			−0.148970	+	0.988842i	$0.547596\pi$
$350$		0			0
$351$	3.91385			0.208906
$352$	−9.76796	−	3.17380i	−0.520634	−	0.169164i
$353$	−4.71531	+	6.49007i	−0.250971	+	0.345431i	−0.915851	−	0.401519i	$-0.868483\pi$
$353$	−4.71531	+	6.49007i	−0.250971	+	0.345431i	0.664880	+	0.746950i	$0.268483\pi$
$354$	9.44515	+	6.86230i	0.502004	+	0.364727i
$355$		0			0
$356$	12.8556	−	9.34014i	0.681346	−	0.495027i
$357$			2.68195i			0.141944i
$358$	21.0618	+	28.9891i	1.11315	+	1.53212i
$359$	3.81411	+	11.7386i	0.201301	+	0.619541i	0.999845	+	0.0176044i	$0.00560395\pi$
$359$	3.81411	+	11.7386i	0.201301	+	0.619541i	−0.798544	+	0.601936i	$0.794396\pi$
$360$		0			0
$361$	−5.61917	+	17.2940i	−0.295746	+	0.910212i
$362$	3.49326	−	1.13503i	0.183602	−	0.0596558i
$363$	−3.16162	+	1.02727i	−0.165942	+	0.0539178i
$364$	4.46219	−	13.7332i	0.233883	−	0.719816i
$365$		0			0
$366$	4.83742	+	14.8881i	0.252856	+	0.778211i
$367$	−15.7967	−	21.7423i	−0.824581	−	1.13494i	−0.988908	−	0.148532i	$-0.952545\pi$
$367$	−15.7967	−	21.7423i	−0.824581	−	1.13494i	0.164327	−	0.986406i	$-0.447455\pi$
$368$			1.47062i			0.0766615i
$369$	4.11707	−	2.99123i	0.214326	−	0.155717i
$370$		0			0
$371$	23.3439	+	16.9603i	1.21195	+	0.880536i
$372$	−5.99114	+	8.24610i	−0.310626	+	0.427540i
$373$	26.2862	+	8.54089i	1.36105	+	0.442231i	0.896392	−	0.443262i	$-0.146179\pi$
$373$	26.2862	+	8.54089i	1.36105	+	0.442231i	0.464654	+	0.885492i	$0.346179\pi$
$374$	−8.59164			−0.444263
$375$		0			0
$376$	−14.7727			−0.761845
$377$	−5.37930	−	1.74784i	−0.277048	−	0.0900184i
$378$	11.3002	−	15.5534i	0.581220	−	0.799981i
$379$	−2.81103	−	2.04233i	−0.144393	−	0.104908i	0.513244	−	0.858243i	$-0.328444\pi$
$379$	−2.81103	−	2.04233i	−0.144393	−	0.104908i	−0.657637	+	0.753335i	$0.728444\pi$
$380$		0			0
$381$	4.36492	−	3.17130i	0.223622	−	0.162471i
$382$			45.4198i			2.32388i
$383$	16.0888	+	22.1443i	0.822098	+	1.13152i	0.989343	+	0.145606i	$0.0465132\pi$
$383$	16.0888	+	22.1443i	0.822098	+	1.13152i	−0.167244	+	0.985916i	$0.553487\pi$
$384$	2.81103	+	8.65146i	0.143450	+	0.441493i
$385$		0			0
$386$	9.35538	−	28.7929i	0.476176	−	1.46552i
$387$	−9.48459	+	3.08173i	−0.482129	+	0.156653i
$388$	−31.5634	+	10.2556i	−1.60239	+	0.520647i
$389$	−3.36350	+	10.3518i	−0.170536	+	0.524857i	−0.999402	−	0.0345916i	$-0.988987\pi$
$389$	−3.36350	+	10.3518i	−0.170536	+	0.524857i	0.828865	+	0.559448i	$0.188987\pi$
$390$		0			0
$391$	−1.91385	−	5.89024i	−0.0967878	−	0.297882i
$392$	−4.00912	−	5.51808i	−0.202491	−	0.278705i
$393$		−	3.79339i		−	0.191351i
$394$	−6.40712	+	4.65504i	−0.322786	+	0.234518i
$395$		0			0
$396$	14.9613	+	10.8700i	0.751835	+	0.546240i
$397$	9.53460	−	13.1233i	0.478528	−	0.658637i	−0.499693	−	0.866202i	$-0.666554\pi$
$397$	9.53460	−	13.1233i	0.478528	−	0.658637i	0.978221	+	0.207565i	$0.0665539\pi$
$398$	−38.8647	−	12.6279i	−1.94811	−	0.632979i
$399$	−1.30233			−0.0651981
$400$		0			0
$401$	3.78686			0.189107			0.0945534	−	0.995520i	$-0.469858\pi$
$401$	3.78686			0.189107			0.0945534	+	0.995520i	$0.469858\pi$
$402$	−11.1499	−	3.62283i	−0.556108	−	0.180690i
$403$	−5.40244	+	7.43582i	−0.269115	+	0.370405i
$404$	25.1995	+	18.3085i	1.25372	+	0.910882i
$405$		0			0
$406$	−22.4771	+	16.3306i	−1.11552	+	0.810473i
$407$			7.64044i			0.378722i
$408$	1.59815	+	2.19967i	0.0791203	+	0.108900i
$409$	−0.573491	−	1.76502i	−0.0283573	−	0.0872748i	0.935876	−	0.352329i	$-0.114610\pi$
$409$	−0.573491	−	1.76502i	−0.0283573	−	0.0872748i	−0.964234	+	0.265054i	$0.914610\pi$
$410$		0			0
$411$	1.37027	−	4.21726i	0.0675905	−	0.208022i
$412$	−28.7932	+	9.35547i	−1.41854	+	0.460911i
$413$	30.7364	−	9.98686i	1.51244	−	0.491421i
$414$	−6.59164	+	20.2870i	−0.323961	+	0.997051i
$415$		0			0
$416$	2.26484	+	6.97046i	0.111043	+	0.341755i
$417$	−5.00082	−	6.88304i	−0.244891	−	0.337064i
$418$		−	4.17202i		−	0.204060i
$419$	11.6071	−	8.43307i	0.567045	−	0.411983i	−0.266985	−	0.963701i	$-0.586028\pi$
$419$	11.6071	−	8.43307i	0.567045	−	0.411983i	0.834031	+	0.551718i	$0.186028\pi$
$420$		0			0
$421$	−12.5030	−	9.08394i	−0.609358	−	0.442724i	0.239830	−	0.970815i	$-0.422908\pi$
$421$	−12.5030	−	9.08394i	−0.609358	−	0.442724i	−0.849188	+	0.528091i	$0.822908\pi$
$422$	−4.40281	+	6.05995i	−0.214325	+	0.294994i
$423$	−12.6655	−	4.11527i	−0.615818	−	0.200091i
$424$	29.2525			1.42063
$425$		0			0
$426$	13.6645			0.662046
$427$	41.2129	+	13.3909i	1.99443	+	0.648030i
$428$	−11.0263	+	15.1764i	−0.532977	+	0.733580i
$429$	−1.09668	−	0.796785i	−0.0529483	−	0.0384692i
$430$		0			0
$431$	−10.1162	+	7.34985i	−0.487280	+	0.354030i	−0.804137	−	0.594444i	$-0.797372\pi$
$431$	−10.1162	+	7.34985i	−0.487280	+	0.354030i	0.316857	+	0.948473i	$0.397372\pi$
$432$		−	1.21133i		−	0.0582801i
$433$	−13.2223	−	18.1989i	−0.635424	−	0.874586i	0.362937	−	0.931813i	$-0.381774\pi$
$433$	−13.2223	−	18.1989i	−0.635424	−	0.874586i	−0.998361	+	0.0572279i	$0.981774\pi$
$434$	13.9514	+	42.9379i	0.669688	+	2.06109i
$435$		0			0
$436$	−10.4151	+	32.0545i	−0.498794	+	1.53513i
$437$	2.86025	−	0.929350i	0.136824	−	0.0444569i
$438$	0.279141	−	0.0906984i	0.0133379	−	0.00433374i
$439$	−3.76308	+	11.5816i	−0.179602	+	0.552758i	−0.999814	−	0.0193023i	$-0.993855\pi$
$439$	−3.76308	+	11.5816i	−0.179602	+	0.552758i	0.820212	+	0.572060i	$0.193855\pi$
$440$		0			0
$441$	−1.90006	−	5.84779i	−0.0904792	−	0.278466i
$442$	3.60373	+	4.96011i	0.171412	+	0.235929i
$443$			20.7101i			0.983968i	0.870604	+	0.491984i	$0.163728\pi$
$443$			20.7101i			0.983968i	−0.870604	+	0.491984i	$0.836272\pi$
$444$	4.89162	−	3.55397i	0.232146	−	0.168664i
$445$		0			0
$446$	−53.6461	−	38.9762i	−2.54022	−	1.84558i
$447$	−1.76248	+	2.42585i	−0.0833625	+	0.114739i
$448$	36.7900	+	11.9538i	1.73816	+	0.564764i
$449$	25.9539			1.22484			0.612420	−	0.790533i	$-0.290196\pi$
$449$	25.9539			1.22484			0.612420	+	0.790533i	$0.290196\pi$
$450$		0			0
$451$	−3.66844			−0.172740
$452$	33.9531	+	11.0320i	1.59702	+	0.518904i
$453$	−1.31740	+	1.81324i	−0.0618968	+	0.0851936i
$454$	21.8970	+	15.9091i	1.02768	+	0.746650i
$455$		0			0
$456$	−1.06814	+	0.776048i	−0.0500202	+	0.0363418i
$457$		−	8.50150i		−	0.397684i	−0.980032	−	0.198842i	$-0.936282\pi$
$457$		−	8.50150i		−	0.397684i	0.980032	−	0.198842i	$-0.0637180\pi$
$458$	−22.2624	−	30.6416i	−1.04025	−	1.43179i
$459$	1.57641	+	4.85170i	0.0735806	+	0.226458i
$460$		0			0
$461$	4.56884	−	14.0614i	0.212792	−	0.654906i	−0.786511	−	0.617576i	$-0.788115\pi$
$461$	4.56884	−	14.0614i	0.212792	−	0.654906i	0.999303	−	0.0373301i	$-0.0118853\pi$
$462$	−6.33275	+	2.05763i	−0.294626	+	0.0957298i
$463$	−21.1060	+	6.85774i	−0.980877	+	0.318706i	−0.755199	−	0.655496i	$-0.772460\pi$
$463$	−21.1060	+	6.85774i	−0.980877	+	0.318706i	−0.225678	+	0.974202i	$0.572460\pi$
$464$	−0.540953	+	1.66488i	−0.0251131	+	0.0772902i
$465$		0			0
$466$	16.0665	+	49.4477i	0.744267	+	2.29062i
$467$	16.7527	+	23.0581i	0.775222	+	1.06700i	0.995793	+	0.0916308i	$0.0292080\pi$
$467$	16.7527	+	23.0581i	0.775222	+	1.06700i	−0.220571	+	0.975371i	$0.570792\pi$
$468$		−	13.1968i		−	0.610024i
$469$	−26.2554	+	19.0757i	−1.21236	+	0.880832i
$470$		0			0
$471$	−0.564426	−	0.410079i	−0.0260074	−	0.0188955i
$472$	19.2581	−	26.5065i	0.886426	−	1.22006i
$473$	6.83706	+	2.22149i	0.314368	+	0.102144i
$474$	9.40048			0.431779
$475$		0			0
$476$	18.8213			0.862671
$477$	25.0799	+	8.14895i	1.14833	+	0.373115i
$478$	9.00380	−	12.3927i	0.411824	−	0.566827i
$479$	20.2715	+	14.7281i	0.926227	+	0.672943i	0.945066	−	0.326879i	$-0.105997\pi$
$479$	20.2715	+	14.7281i	0.926227	+	0.672943i	−0.0188390	+	0.999823i	$0.505997\pi$
$480$		0			0
$481$	4.41097	−	3.20475i	0.201123	−	0.146124i
$482$			60.5632i			2.75858i
$483$	−2.82134	−	3.88324i	−0.128375	−	0.176693i
$484$	7.20913	+	22.1874i	0.327688	+	1.00852i
$485$		0			0
$486$	8.25017	−	25.3914i	0.374235	−	1.15178i
$487$	1.39310	−	0.452644i	0.0631272	−	0.0205113i	−0.277283	−	0.960788i	$-0.589434\pi$
$487$	1.39310	−	0.452644i	0.0631272	−	0.0205113i	0.340410	+	0.940277i	$0.389434\pi$
$488$	41.7813	−	13.5756i	1.89135	−	0.614537i
$489$	−0.654474	+	2.01426i	−0.0295963	+	0.0910881i
$490$		0			0
$491$	−6.20155	−	19.0864i	−0.279872	−	0.861358i	−0.987889	−	0.155162i	$-0.950410\pi$
$491$	−6.20155	−	19.0864i	−0.279872	−	0.861358i	0.708017	−	0.706195i	$-0.249590\pi$
$492$	1.70639	+	2.34864i	0.0769298	+	0.105885i
$493$		−	7.37229i		−	0.332031i
$494$	−2.40859	+	1.74994i	−0.108367	+	0.0787335i
$495$		0			0
$496$	2.30137	+	1.67204i	0.103335	+	0.0750770i
$497$	22.2335	−	30.6017i	0.997307	−	1.37268i
$498$	13.1608	+	4.27621i	0.589751	+	0.191622i
$499$	−0.624999			−0.0279788			−0.0139894	−	0.999902i	$-0.504453\pi$
$499$	−0.624999			−0.0279788			−0.0139894	+	0.999902i	$0.504453\pi$
$500$		0			0
$501$	4.95498			0.221372
$502$	−23.9657	−	7.78693i	−1.06964	−	0.347548i
$503$	11.3473	−	15.6182i	0.505951	−	0.696382i	−0.477279	−	0.878752i	$-0.658377\pi$
$503$	11.3473	−	15.6182i	0.505951	−	0.696382i	0.983230	+	0.182370i	$0.0583767\pi$
$504$	−20.9719	−	15.2369i	−0.934161	−	0.678707i
$505$		0			0
$506$	12.4400	−	9.03816i	0.553024	−	0.401795i
$507$		−	5.20639i		−	0.231224i
$508$	−22.2554	−	30.6319i	−0.987423	−	1.35907i
$509$	3.25091	+	10.0053i	0.144094	+	0.443476i	0.996893	−	0.0787629i	$-0.0250970\pi$
$509$	3.25091	+	10.0053i	0.144094	+	0.443476i	−0.852799	+	0.522239i	$0.825097\pi$
$510$		0			0
$511$	0.251070	−	0.772714i	0.0111067	−	0.0341828i
$512$	4.74321	−	1.54116i	0.209622	−	0.0681103i
$513$	−2.35594	+	0.765491i	−0.104017	+	0.0337973i
$514$	−4.69588	+	14.4524i	−0.207127	+	0.637470i
$515$		0			0
$516$	−1.75801	−	5.41061i	−0.0773923	−	0.238189i
$517$	5.64267	+	7.76648i	0.248165	+	0.341569i
$518$		−	26.7818i		−	1.17672i
$519$	−2.94923	+	2.14274i	−0.129457	+	0.0940558i
$520$		0			0
$521$	8.09580	+	5.88195i	0.354684	+	0.257693i	0.750831	−	0.660494i	$-0.229653\pi$
$521$	8.09580	+	5.88195i	0.354684	+	0.257693i	−0.396148	+	0.918187i	$0.629653\pi$
$522$	−14.9247	+	20.5421i	−0.653237	+	0.899103i
$523$	−21.6680	−	7.04035i	−0.947474	−	0.307853i	−0.205785	−	0.978597i	$-0.565975\pi$
$523$	−21.6680	−	7.04035i	−0.947474	−	0.307853i	−0.741689	+	0.670744i	$0.765975\pi$
$524$	−26.6210			−1.16295
$525$		0			0
$526$	−62.5981			−2.72941
$527$	−11.3936	−	3.70200i	−0.496312	−	0.161262i
$528$	−0.246603	+	0.339420i	−0.0107320	+	0.0147714i
$529$	−9.63993	−	7.00382i	−0.419127	−	0.304514i
$530$		0			0
$531$	23.8951	−	17.3608i	1.03696	−	0.753393i
$532$			9.13943i			0.396245i
$533$	1.53871	+	2.11786i	0.0666491	+	0.0917346i
$534$	1.61583	+	4.97301i	0.0699237	+	0.215203i
$535$		0			0
$536$	−10.1670	+	31.2907i	−0.439146	+	1.35155i
$537$	−7.00829	+	2.27713i	−0.302430	+	0.0982655i
$538$	2.21701	−	0.720350i	0.0955821	−	0.0310565i
$539$	−1.36968	+	4.21544i	−0.0589962	+	0.181572i
$540$		0			0
$541$	1.00709	+	3.09949i	0.0432980	+	0.133257i	0.970369	−	0.241629i	$-0.0776817\pi$
$541$	1.00709	+	3.09949i	0.0432980	+	0.133257i	−0.927071	+	0.374886i	$0.877682\pi$
$542$	−8.48624	−	11.6803i	−0.364515	−	0.501712i
$543$			0.755360i			0.0324156i
$544$	−7.72851	+	5.61509i	−0.331357	+	0.240745i
$545$		0			0
$546$	3.84416	+	2.79295i	0.164515	+	0.119527i
$547$	−7.98700	+	10.9932i	−0.341499	+	0.470033i	−0.944879	−	0.327421i	$-0.893821\pi$
$547$	−7.98700	+	10.9932i	−0.341499	+	0.470033i	0.603379	+	0.797454i	$0.293821\pi$
$548$	−29.5957	−	9.61622i	−1.26427	−	0.410785i
$549$	39.6033			1.69023
$550$		0			0
$551$	3.57992			0.152510
$552$	−4.62798	−	1.50372i	−0.196980	−	0.0640026i
$553$	15.2955	−	21.0525i	0.650432	−	0.895242i
$554$	−46.0901	−	33.4865i	−1.95818	−	1.42270i
$555$		0			0
$556$	−48.3034	+	35.0945i	−2.04852	+	1.48834i
$557$		−	27.6399i		−	1.17114i	−0.810621	−	0.585571i	$-0.800870\pi$
$557$		−	27.6399i		−	1.17114i	0.810621	−	0.585571i	$-0.199130\pi$
$558$	24.2525	+	33.3808i	1.02669	+	1.41312i
$559$	−1.58527	−	4.87896i	−0.0670498	−	0.206358i
$560$		0			0
$561$	0.545994	−	1.68040i	0.0230519	−	0.0709464i
$562$	−4.03871	+	1.31226i	−0.170363	+	0.0553543i
$563$	−1.57804	+	0.512737i	−0.0665065	+	0.0216093i	−0.342081	−	0.939670i	$-0.611132\pi$
$563$	−1.57804	+	0.512737i	−0.0665065	+	0.0216093i	0.275575	+	0.961280i	$0.411132\pi$
$564$	2.34761	−	7.22520i	0.0988522	−	0.304236i
$565$		0			0
$566$	−6.16637	−	18.9781i	−0.259192	−	0.797711i
$567$	−12.5285	−	17.2439i	−0.526146	−	0.724178i
$568$		−	38.3475i		−	1.60902i
$569$	14.4675	−	10.5113i	0.606509	−	0.440655i	−0.241674	−	0.970357i	$-0.577697\pi$
$569$	14.4675	−	10.5113i	0.606509	−	0.440655i	0.848183	+	0.529703i	$0.177697\pi$
$570$		0			0
$571$	29.8303	+	21.6730i	1.24836	+	0.906987i	0.998126	−	0.0611975i	$-0.0194920\pi$
$571$	29.8303	+	21.6730i	1.24836	+	0.906987i	0.250235	+	0.968185i	$0.419492\pi$
$572$	−5.59164	+	7.69623i	−0.233798	+	0.321796i
$573$	−8.88344	−	2.88640i	−0.371111	−	0.120581i
$574$	12.8589			0.536718
$575$		0			0
$576$	35.3531			1.47305
$577$	−21.6971	−	7.04982i	−0.903262	−	0.293488i	−0.179679	−	0.983725i	$-0.557506\pi$
$577$	−21.6971	−	7.04982i	−0.903262	−	0.293488i	−0.723583	+	0.690238i	$0.757506\pi$
$578$	18.3779	−	25.2950i	0.764421	−	1.05213i
$579$	5.03693	+	3.65954i	0.209328	+	0.152085i
$580$		0			0
$581$	30.9906	−	22.5160i	1.28571	−	0.934120i
$582$		−	10.9208i		−	0.452682i
$583$	−11.1735	−	15.3790i	−0.462758	−	0.636932i
$584$	−0.254532	−	0.783370i	−0.0105326	−	0.0324161i
$585$		0			0
$586$	4.48969	−	13.8179i	0.185467	−	0.570810i
$587$	10.5429	−	3.42560i	0.435153	−	0.141390i	−0.0832455	−	0.996529i	$-0.526529\pi$
$587$	10.5429	−	3.42560i	0.435153	−	0.141390i	0.518398	+	0.855139i	$0.326529\pi$
$588$	3.33595	−	1.08392i	0.137572	−	0.0447000i
$589$	1.79766	−	5.53262i	0.0740712	−	0.227968i
$590$		0			0
$591$	−0.503288	−	1.54896i	−0.0207025	−	0.0637157i
$592$	−0.991864	−	1.36518i	−0.0407654	−	0.0561087i
$593$		−	11.1321i		−	0.457139i	−0.973528	−	0.228570i	$-0.926595\pi$
$593$		−	11.1321i		−	0.457139i	0.973528	−	0.228570i	$-0.0734049\pi$
$594$	−10.2466	+	7.44459i	−0.420423	+	0.305455i
$595$		0			0
$596$	17.0240	+	12.3687i	0.697330	+	0.506640i
$597$	4.93965	−	6.79885i	0.202167	−	0.278258i
$598$	−10.4358	−	3.39080i	−0.426752	−	0.138660i
$599$	−36.2736			−1.48210			−0.741049	−	0.671451i	$-0.765671\pi$
$599$	−36.2736			−1.48210			−0.741049	+	0.671451i	$0.765671\pi$
$600$		0			0
$601$	−15.1051			−0.616150			−0.308075	−	0.951362i	$-0.599685\pi$
$601$	−15.1051			−0.616150			−0.308075	+	0.951362i	$0.599685\pi$
$602$	−23.9657	−	7.78693i	−0.976769	−	0.317372i
$603$	−17.4335	+	23.9951i	−0.709945	+	0.977156i
$604$	12.7249	+	9.24517i	0.517768	+	0.376181i
$605$		0			0
$606$	−8.29219	+	6.02463i	−0.336847	+	0.244734i
$607$		−	33.5066i		−	1.35999i	−0.733216	−	0.679996i	$-0.761982\pi$
$607$		−	33.5066i		−	1.35999i	0.733216	−	0.679996i	$-0.238018\pi$
$608$	−2.72664	−	3.75289i	−0.110580	−	0.152200i
$609$	−1.76561	−	5.43399i	−0.0715461	−	0.220196i
$610$		0			0
$611$	2.11693	−	6.51524i	0.0856418	−	0.263579i
$612$	16.3591	−	5.31539i	0.661277	−	0.214862i
$613$	−26.6571	+	8.66140i	−1.07667	+	0.349831i	−0.793081	−	0.609116i	$-0.791524\pi$
$613$	−26.6571	+	8.66140i	−1.07667	+	0.349831i	−0.283587	+	0.958947i	$0.591524\pi$
$614$	20.4563	−	62.9579i	0.825548	−	2.54078i
$615$		0			0
$616$	5.77447	+	17.7720i	0.232660	+	0.716054i
$617$	−17.9406	−	24.6931i	−0.722260	−	0.994105i	−0.999446	−	0.0332890i	$-0.989402\pi$
$617$	−17.9406	−	24.6931i	−0.722260	−	0.994105i	0.277186	−	0.960816i	$-0.410598\pi$
$618$		−	9.96234i		−	0.400744i
$619$	−17.5533	+	12.7532i	−0.705528	+	0.512596i	−0.881728	−	0.471758i	$-0.843619\pi$
$619$	−17.5533	+	12.7532i	−0.705528	+	0.512596i	0.176200	+	0.984354i	$0.443619\pi$
$620$		0			0
$621$	−7.38636	−	5.36650i	−0.296404	−	0.215350i
$622$	−10.6369	+	14.6405i	−0.426502	+	0.587029i
$623$	13.7662	+	4.47291i	0.551531	+	0.179203i
$624$	0.299391			0.0119852
$625$		0			0
$626$	49.4399			1.97601
$627$	0.815985	+	0.265130i	0.0325873	+	0.0105883i
$628$	−2.87783	+	3.96100i	−0.114838	+	0.158061i
$629$	5.74932	+	4.17712i	0.229240	+	0.166553i
$630$		0			0
$631$	13.1285	−	9.53840i	0.522637	−	0.379718i	−0.294960	−	0.955510i	$-0.595306\pi$
$631$	13.1285	−	9.53840i	0.522637	−	0.379718i	0.817596	+	0.575792i	$0.195306\pi$
$632$		−	26.3812i		−	1.04939i
$633$	−0.905439	−	1.24623i	−0.0359880	−	0.0495332i
$634$	−2.86857	−	8.82857i	−0.113926	−	0.350627i
$635$		0			0
$636$	−4.64868	+	14.3072i	−0.184332	+	0.567316i
$637$	3.00816	−	0.977409i	0.119187	−	0.0387264i
$638$	17.4078	−	5.65614i	0.689181	−	0.223929i
$639$	10.6825	−	32.8775i	0.422595	−	1.30061i
$640$		0			0
$641$	−6.85321	−	21.0920i	−0.270685	−	0.833084i	−0.990329	−	0.138740i	$-0.955695\pi$
$641$	−6.85321	−	21.0920i	−0.270685	−	0.833084i	0.719643	−	0.694344i	$-0.244305\pi$
$642$	−3.62834	−	4.99398i	−0.143199	−	0.197097i
$643$			13.2767i			0.523583i	0.965124	+	0.261792i	$0.0843133\pi$
$643$			13.2767i			0.523583i	−0.965124	+	0.261792i	$0.915687\pi$
$644$	−27.2516	+	19.7994i	−1.07386	+	0.780207i
$645$		0			0
$646$	−3.13939	−	2.28090i	−0.123518	−	0.0897407i
$647$	−6.63333	+	9.12999i	−0.260783	+	0.358937i	−0.919251	−	0.393672i	$-0.871205\pi$
$647$	−6.63333	+	9.12999i	−0.260783	+	0.358937i	0.658468	+	0.752609i	$0.271205\pi$
$648$	−20.5510	−	6.67743i	−0.807321	−	0.262314i
$649$	−21.2912			−0.835754
$650$		0			0
$651$	−9.28462			−0.363893
$652$	14.1356	+	4.59293i	0.553592	+	0.179873i
$653$	21.0506	−	28.9736i	0.823773	−	1.13383i	−0.165277	−	0.986247i	$-0.552852\pi$
$653$	21.0506	−	28.9736i	0.823773	−	1.13383i	0.989050	−	0.147579i	$-0.0471480\pi$
$654$	−8.97259	−	6.51897i	−0.350856	−	0.254912i
$655$		0			0
$656$	0.655472	−	0.476228i	0.0255919	−	0.0185936i
$657$		−	0.742534i		−	0.0289690i
$658$	−19.7791	−	27.2236i	−0.771069	−	1.06129i
$659$	−12.2882	−	37.8193i	−0.478681	−	1.47323i	−0.840928	−	0.541147i	$-0.817990\pi$
$659$	−12.2882	−	37.8193i	−0.478681	−	1.47323i	0.362247	−	0.932082i	$-0.382010\pi$
$660$		0			0
$661$	−1.93053	+	5.94157i	−0.0750890	+	0.231100i	−0.981555	−	0.191178i	$-0.938769\pi$
$661$	−1.93053	+	5.94157i	−0.0750890	+	0.231100i	0.906466	+	0.422278i	$0.138769\pi$
$662$	−25.5728	+	8.30912i	−0.993917	+	0.322943i
$663$	−1.19914	+	0.389624i	−0.0465707	+	0.0151317i
$664$	12.0006	−	36.9340i	0.465713	−	1.43332i
$665$		0			0
$666$	−7.56355	−	23.2782i	−0.293082	−	0.902012i
$667$	7.75544	+	10.6744i	0.300292	+	0.413316i
$668$		−	34.7728i		−	1.34540i
$669$	11.0323	−	8.01546i	0.426535	−	0.309896i
$670$		0			0
$671$	−23.0961	−	16.7803i	−0.891616	−	0.647797i
$672$	−4.35178	+	5.98970i	−0.167873	+	0.231058i
$673$	39.4334	+	12.8127i	1.52005	+	0.493893i	0.945789	−	0.324782i	$-0.105291\pi$
$673$	39.4334	+	12.8127i	1.52005	+	0.493893i	0.574257	+	0.818675i	$0.305291\pi$
$674$	49.7297			1.91552
$675$		0			0
$676$	−36.5372			−1.40528
$677$	−1.36872	−	0.444723i	−0.0526041	−	0.0170921i	0.282597	−	0.959239i	$-0.408804\pi$
$677$	−1.36872	−	0.444723i	−0.0526041	−	0.0170921i	−0.335201	+	0.942147i	$0.608804\pi$
$678$	−6.90510	+	9.50406i	−0.265189	+	0.365001i
$679$	−24.4572	−	17.7692i	−0.938583	−	0.681920i
$680$		0			0
$681$	−4.50312	+	3.27171i	−0.172560	+	0.125372i
$682$		−	29.7433i		−	1.13893i
$683$	−4.98808	−	6.86550i	−0.190864	−	0.262701i	0.702851	−	0.711337i	$-0.251910\pi$
$683$	−4.98808	−	6.86550i	−0.190864	−	0.262701i	−0.893715	+	0.448636i	$0.851910\pi$
$684$	2.58111	+	7.94382i	0.0986910	+	0.303740i
$685$		0			0
$686$	−10.3635	+	31.8957i	−0.395682	+	1.21778i
$687$	7.40779	−	2.40694i	0.282625	−	0.0918304i
$688$	−1.51003	+	0.490637i	−0.0575692	+	0.0187054i
$689$	−4.19189	+	12.9013i	−0.159698	+	0.491501i
$690$		0			0
$691$	−13.5287	−	41.6370i	−0.514655	−	1.58395i	−0.783908	−	0.620877i	$-0.786777\pi$
$691$	−13.5287	−	41.6370i	−0.514655	−	1.58395i	0.269253	−	0.963070i	$-0.413223\pi$
$692$	15.0372	+	20.6969i	0.571629	+	0.786780i
$693$			16.8456i			0.639910i
$694$	29.1394	−	21.1710i	1.10612	−	0.803641i
$695$		0			0
$696$	−4.68617	−	3.40470i	−0.177629	−	0.129055i
$697$	−2.00558	+	2.76045i	−0.0759668	+	0.104559i
$698$	−12.2243	−	3.97191i	−0.462696	−	0.150339i
$699$	−10.6922			−0.404418
$700$		0			0
$701$	0.840795			0.0317564			0.0158782	−	0.999874i	$-0.494946\pi$
$701$	0.840795			0.0317564			0.0158782	+	0.999874i	$0.494946\pi$
$702$	8.59580	+	2.79295i	0.324428	+	0.105413i
$703$	−2.02837	+	2.79182i	−0.0765015	+	0.105295i
$704$	−20.6175	−	14.9795i	−0.777050	−	0.564560i
$705$		0			0
$706$	−14.9873	+	10.8889i	−0.564056	+	0.409811i
$707$			28.3731i			1.06708i
$708$	9.90369	+	13.6313i	0.372203	+	0.512294i
$709$	4.13503	+	12.7263i	0.155294	+	0.477947i	0.998191	−	0.0601294i	$-0.0191513\pi$
$709$	4.13503	+	12.7263i	0.155294	+	0.477947i	−0.842896	+	0.538076i	$0.819151\pi$
$710$		0			0
$711$	7.34906	−	22.6181i	0.275611	−	0.848244i
$712$	13.9561	−	4.53460i	0.523025	−	0.169941i
$713$	20.3913	−	6.62555i	0.763662	−	0.248129i
$714$	−1.91385	+	5.89024i	−0.0716242	+	0.220437i
$715$		0			0
$716$	15.9803	+	49.1824i	0.597214	+	1.83803i
$717$	1.85163	+	2.54855i	0.0691505	+	0.0951775i
$718$			28.5027i			1.06371i
$719$	35.1233	−	25.5186i	1.30988	−	0.951683i	0.309880	−	0.950776i	$-0.399711\pi$
$719$	35.1233	−	25.5186i	1.30988	−	0.951683i	1.00000		0.000907154i	$-0.000288756\pi$
$720$		0			0
$721$	−22.3107	−	16.2097i	−0.830896	−	0.603681i
$722$	−24.6822	+	33.9721i	−0.918577	+	1.26431i
$723$	−11.8452	−	3.84875i	−0.440529	−	0.143137i
$724$	5.30093			0.197007
$725$		0			0
$726$	−7.67677			−0.284912
$727$	−30.4795	−	9.90338i	−1.13042	−	0.367296i	−0.316685	−	0.948531i	$-0.602570\pi$
$727$	−30.4795	−	9.90338i	−1.13042	−	0.367296i	−0.813736	+	0.581235i	$0.802570\pi$
$728$	7.83802	−	10.7881i	0.290496	−	0.399834i
$729$	−12.5986	−	9.15342i	−0.466615	−	0.339016i
$730$		0			0
$731$	5.40955	−	3.93027i	0.200079	−	0.145366i
$732$			22.5922i			0.835032i
$733$	4.78415	+	6.58481i	0.176706	+	0.243216i	0.888178	−	0.459499i	$-0.151971\pi$
$733$	4.78415	+	6.58481i	0.176706	+	0.243216i	−0.711472	+	0.702715i	$0.751971\pi$
$734$	−19.1781	−	59.0241i	−0.707877	−	2.17862i
$735$		0			0
$736$	5.28331	−	16.2603i	0.194745	−	0.599364i
$737$	20.3339	−	6.60690i	0.749010	−	0.243368i
$738$	11.1767	−	3.63152i	0.411419	−	0.133678i
$739$	2.20241	−	6.77831i	0.0810169	−	0.249344i	−0.902341	−	0.431023i	$-0.858153\pi$
$739$	2.20241	−	6.77831i	0.0810169	−	0.249344i	0.983358	+	0.181678i	$0.0581529\pi$
$740$		0			0
$741$	−0.189198	−	0.582291i	−0.00695036	−	0.0213910i
$742$	39.1660	+	53.9074i	1.43783	+	1.97900i
$743$		−	21.9040i		−	0.803578i	−0.915732	−	0.401789i	$-0.868388\pi$
$743$		−	21.9040i		−	0.803578i	0.915732	−	0.401789i	$-0.131612\pi$
$744$	−7.61500	+	5.53262i	−0.279179	+	0.202836i
$745$		0			0
$746$	51.6362	+	37.5159i	1.89054	+	1.37355i
$747$	20.5776	−	28.3226i	0.752895	−	1.03627i
$748$	−11.7926	−	3.83165i	−0.431180	−	0.140099i
$749$	−17.0877			−0.624373
$750$		0			0
$751$	9.21909			0.336409			0.168205	−	0.985752i	$-0.446203\pi$
$751$	9.21909			0.336409			0.168205	+	0.985752i	$0.446203\pi$
$752$	−2.01645	−	0.655185i	−0.0735325	−	0.0238921i
$753$	3.04601	−	4.19248i	0.111003	−	0.152782i
$754$	−10.5670	−	7.67740i	−0.384829	−	0.279594i
$755$		0			0
$756$	22.4467	−	16.3085i	0.816379	−	0.593134i
$757$			45.6524i			1.65926i	0.558311	+	0.829632i	$0.311450\pi$
$757$			45.6524i			1.65926i	−0.558311	+	0.829632i	$0.688550\pi$
$758$	−4.71631	−	6.49144i	−0.171304	−	0.235780i
$759$	0.977177	+	3.00744i	0.0354693	+	0.109163i
$760$		0			0
$761$	12.3316	−	37.9526i	0.447019	−	1.37578i	−0.433236	−	0.901280i	$-0.642628\pi$
$761$	12.3316	−	37.9526i	0.447019	−	1.37578i	0.880255	−	0.474501i	$-0.157372\pi$
$762$	11.8495	−	3.85014i	0.429263	−	0.139476i
$763$	−29.1986	+	9.48719i	−1.05706	+	0.343459i
$764$	−20.2561	+	62.3417i	−0.732838	+	2.25544i
$765$		0			0
$766$	19.5327	+	60.1155i	0.705745	+	2.17206i
$767$	8.93053	+	12.2918i	0.322463	+	0.443832i
$768$			8.90403i			0.321296i
$769$	−35.8734	+	26.0636i	−1.29363	+	0.939876i	−0.999872	−	0.0160040i	$-0.994906\pi$
$769$	−35.8734	+	26.0636i	−1.29363	+	0.939876i	−0.293757	+	0.955880i	$0.594906\pi$
$770$		0			0
$771$	−2.52826	−	1.83689i	−0.0910531	−	0.0661539i
$772$	25.6818	−	35.3479i	0.924307	−	1.27220i
$773$	36.6103	+	11.8954i	1.31678	+	0.427848i	0.881389	−	0.472392i	$-0.156609\pi$
$773$	36.6103	+	11.8954i	1.31678	+	0.427848i	0.435393	+	0.900240i	$0.356609\pi$
$774$	−23.0297			−0.827785
$775$		0			0
$776$	−30.6477			−1.10019
$777$	5.23811	+	1.70197i	0.187916	+	0.0610577i
$778$	−14.7742	+	20.3349i	−0.529680	+	0.729042i
$779$	−1.34045	−	0.973893i	−0.0480265	−	0.0348933i
$780$		0			0
$781$	−20.1605	+	14.6474i	−0.721398	+	0.524126i
$782$		−	14.3022i		−	0.511445i
$783$	−6.38803	−	8.79238i	−0.228290	−	0.314214i
$784$	−0.302506	−	0.931017i	−0.0108038	−	0.0332506i
$785$		0			0
$786$	2.70698	−	8.33123i	0.0965548	−	0.297165i
$787$	50.4252	−	16.3841i	1.79746	−	0.584031i	0.797646	−	0.603126i	$-0.206078\pi$
$787$	50.4252	−	16.3841i	1.79746	−	0.584031i	0.999818	+	0.0190942i	$0.00607824\pi$
$788$	−10.8702	+	3.53195i	−0.387236	+	0.125820i
$789$	3.97807	−	12.2433i	0.141623	−	0.435871i
$790$		0			0
$791$	10.0491	+	30.9281i	0.357306	+	1.09968i
$792$	10.0381	+	13.8163i	0.356689	+	0.490940i
$793$			20.3723i			0.723440i
$794$	30.3052	−	22.0180i	1.07549	−	0.781390i
$795$		0			0
$796$	−47.7126	−	34.6653i	−1.69113	−	1.22868i
$797$	−7.45127	+	10.2558i	−0.263938	+	0.363279i	−0.920331	−	0.391139i	$-0.872081\pi$
$797$	−7.45127	+	10.2558i	−0.263938	+	0.363279i	0.656394	+	0.754418i	$0.272081\pi$
$798$	−2.86025	−	0.929350i	−0.101252	−	0.0328986i
$799$	8.92908			0.315888
$800$		0			0
$801$	13.2285			0.467407
$802$	8.31689	+	2.70232i	0.293680	+	0.0954223i
$803$	−0.314619	+	0.433036i	−0.0111027	+	0.0152815i
$804$	−13.6883	−	9.94515i	−0.482750	−	0.350738i
$805$		0			0
$806$	−17.1714	+	12.4757i	−0.604835	+	0.439439i
$807$			0.479392i			0.0168754i
$808$	16.9073	+	23.2709i	0.594796	+	0.818667i
$809$	12.9458	+	39.8431i	0.455150	+	1.40081i	0.870959	+	0.491356i	$0.163499\pi$
$809$	12.9458	+	39.8431i	0.455150	+	1.40081i	−0.415808	+	0.909452i	$0.636501\pi$
$810$		0			0
$811$	−10.6761	+	32.8577i	−0.374889	+	1.15379i	0.568665	+	0.822569i	$0.307460\pi$
$811$	−10.6761	+	32.8577i	−0.374889	+	1.15379i	−0.943554	+	0.331220i	$0.892540\pi$
$812$	−38.1344	+	12.3906i	−1.33825	+	0.434825i
$813$	2.82379	−	0.917505i	0.0990346	−	0.0321783i
$814$	−5.45225	+	16.7803i	−0.191101	+	0.588150i
$815$		0			0
$816$	0.120588	+	0.371131i	0.00422141	+	0.0129922i
$817$	1.90850	+	2.62683i	0.0667700	+	0.0919011i
$818$		−	4.28568i		−	0.149845i
$819$	9.72525	−	7.06581i	0.339828	−	0.246899i
$820$		0			0
$821$	17.0985	+	12.4228i	0.596740	+	0.433557i	0.844720	−	0.535208i	$-0.179767\pi$
$821$	17.0985	+	12.4228i	0.596740	+	0.433557i	−0.247980	+	0.968765i	$0.579767\pi$
$822$	6.01892	−	8.28433i	0.209934	−	0.288949i
$823$	−3.02164	−	0.981789i	−0.105328	−	0.0342230i	0.255879	−	0.966709i	$-0.417635\pi$
$823$	−3.02164	−	0.981789i	−0.105328	−	0.0342230i	−0.361207	+	0.932486i	$0.617635\pi$
$824$	−27.9579			−0.973960
$825$		0			0
$826$	74.6315			2.59676
$827$	9.26787	+	3.01131i	0.322275	+	0.104714i	0.465687	−	0.884949i	$-0.345807\pi$
$827$	9.26787	+	3.01131i	0.322275	+	0.104714i	−0.143412	+	0.989663i	$0.545807\pi$
$828$	−18.0949	+	24.9055i	−0.628842	+	0.865527i
$829$	18.9595	+	13.7749i	0.658490	+	0.478421i	0.866153	−	0.499780i	$-0.166586\pi$
$829$	18.9595	+	13.7749i	0.658490	+	0.478421i	−0.207663	+	0.978200i	$0.566586\pi$
$830$		0			0
$831$	9.47845	−	6.88650i	0.328804	−	0.238890i
$832$			18.1859i			0.630484i
$833$	2.42323	+	3.33530i	0.0839601	+	0.115561i
$834$	−6.07128	−	18.6855i	−0.210231	−	0.647026i
$835$		0			0
$836$	1.86061	−	5.72638i	0.0643507	−	0.198051i
$837$	−16.7960	+	5.45736i	−0.580556	+	0.188634i
$838$	31.5101	−	10.2382i	1.08850	−	0.353674i
$839$	−13.1894	+	40.5929i	−0.455350	+	1.40142i	0.415375	+	0.909650i	$0.363650\pi$
$839$	−13.1894	+	40.5929i	−0.455350	+	1.40142i	−0.870724	+	0.491771i	$0.836350\pi$
$840$		0			0
$841$	−4.10809	−	12.6434i	−0.141658	−	0.435980i
$842$	−20.9773	−	28.8728i	−0.722926	−	0.995022i
$843$		−	0.873305i		−	0.0300782i
$844$	−8.74573	+	6.35414i	−0.301040	+	0.218719i
$845$		0			0
$846$	−24.8799	−	18.0763i	−0.855390	−	0.621477i
$847$	−12.4909	+	17.1922i	−0.429191	+	0.590731i
$848$	3.99293	+	1.29738i	0.137118	+	0.0445522i
$849$	4.10371			0.140839
$850$		0			0
$851$	−12.7187			−0.435993
$852$	18.7554	+	6.09400i	0.642550	+	0.208777i
$853$	−9.96942	+	13.7217i	−0.341347	+	0.469823i	−0.944834	−	0.327549i	$-0.893777\pi$
$853$	−9.96942	+	13.7217i	−0.341347	+	0.469823i	0.603488	+	0.797372i	$0.293777\pi$
$854$	80.9581	+	58.8195i	2.77033	+	2.01276i
$855$		0			0
$856$	−14.0149	+	10.1824i	−0.479020	+	0.348029i
$857$		−	39.3176i		−	1.34306i	−0.740976	−	0.671531i	$-0.765637\pi$
$857$		−	39.3176i		−	1.34306i	0.740976	−	0.671531i	$-0.234363\pi$
$858$	−1.84000	−	2.53254i	−0.0628164	−	0.0864594i
$859$	−0.218492	−	0.672450i	−0.00745486	−	0.0229437i	0.947260	−	0.320466i	$-0.103840\pi$
$859$	−0.218492	−	0.672450i	−0.00745486	−	0.0229437i	−0.954715	+	0.297523i	$0.903840\pi$
$860$		0			0
$861$	−0.817173	+	2.51500i	−0.0278492	+	0.0857110i
$862$	−27.4626	+	8.92314i	−0.935380	+	0.303923i
$863$	0.864900	−	0.281023i	0.0294415	−	0.00956613i	−0.294259	−	0.955726i	$-0.595073\pi$
$863$	0.864900	−	0.281023i	0.0294415	−	0.00956613i	0.323701	+	0.946160i	$0.395073\pi$
$864$	−4.35178	+	13.3934i	−0.148050	+	0.455652i
$865$		0			0
$866$	−16.0526	−	49.4050i	−0.545491	−	1.67885i
$867$	3.77942	+	5.20193i	0.128356	+	0.176667i
$868$			65.1571i			2.21158i
$869$	−13.8694	+	10.0767i	−0.470487	+	0.341829i
$870$		0			0
$871$	−12.3433	−	8.96792i	−0.418236	−	0.303866i
$872$	−18.2946	+	25.1803i	−0.619533	+	0.852713i
$873$	−26.2761	−	8.53761i	−0.889310	−	0.288954i
$874$	6.94501			0.234918
$875$		0			0
$876$	0.423589			0.0143117
$877$	32.0138	+	10.4019i	1.08103	+	0.351248i	0.794774	−	0.606906i	$-0.207589\pi$
$877$	32.0138	+	10.4019i	1.08103	+	0.351248i	0.286255	+	0.958153i	$0.407589\pi$
$878$	−16.5293	+	22.7506i	−0.557837	+	0.767797i
$879$	2.41725	+	1.75623i	0.0815317	+	0.0592363i
$880$		0			0
$881$	16.1223	−	11.7136i	0.543175	−	0.394640i	−0.282088	−	0.959389i	$-0.591027\pi$
$881$	16.1223	−	11.7136i	0.543175	−	0.394640i	0.825263	+	0.564749i	$0.191027\pi$
$882$		−	14.1991i		−	0.478109i
$883$	9.17421	+	12.6272i	0.308737	+	0.424940i	0.934987	−	0.354683i	$-0.115411\pi$
$883$	9.17421	+	12.6272i	0.308737	+	0.424940i	−0.626250	+	0.779622i	$0.715411\pi$
$884$	2.73428	+	8.41526i	0.0919639	+	0.283036i
$885$		0			0
$886$	−14.7789	+	45.4846i	−0.496505	+	1.52809i
$887$	−44.6015	+	14.4919i	−1.49757	+	0.486591i	−0.939309	−	0.343073i	$-0.888532\pi$
$887$	−44.6015	+	14.4919i	−1.49757	+	0.486591i	−0.558263	+	0.829664i	$0.688532\pi$
$888$	5.31035	−	1.72544i	0.178204	−	0.0579019i
$889$	10.6579	−	32.8017i	0.357455	−	1.10013i
$890$		0			0
$891$	4.33926	+	13.3549i	0.145371	+	0.447405i
$892$	−56.2505	−	77.4222i	−1.88341	−	2.59229i
$893$			4.33588i			0.145095i
$894$	−5.60195	+	4.07005i	−0.187357	+	0.136123i
$895$		0			0
$896$	47.0448	+	34.1800i	1.57166	+	1.14187i
$897$	1.32638	−	1.82560i	0.0442865	−	0.0609551i
$898$	57.0013	+	18.5208i	1.90216	+	0.618048i
$899$	25.5220			0.851208
$900$		0			0
$901$	−17.6811			−0.589044
$902$	−8.05681	−	2.61782i	−0.268262	−	0.0871638i
$903$	3.04601	−	4.19248i	0.101365	−	0.139517i
$904$	26.6718	+	19.3782i	0.887091	+	0.644510i
$905$		0			0
$906$	−4.18728	+	3.04223i	−0.139113	+	0.101071i
$907$			1.43447i			0.0476308i	0.999716	+	0.0238154i	$0.00758139\pi$
$907$			1.43447i			0.0476308i	−0.999716	+	0.0238154i	$0.992419\pi$
$908$	22.9600	+	31.6018i	0.761955	+	1.04874i
$909$	8.01297	+	24.6614i	0.265773	+	0.817966i
$910$		0			0
$911$	−0.868737	+	2.67370i	−0.0287825	+	0.0885835i	−0.964416	−	0.264390i	$-0.914829\pi$
$911$	−0.868737	+	2.67370i	−0.0287825	+	0.0885835i	0.935633	+	0.352973i	$0.114829\pi$
$912$	−0.180218	+	0.0585563i	−0.00596761	+	0.00193899i
$913$	−24.0012	+	7.79846i	−0.794323	+	0.258091i
$914$	6.06672	−	18.6714i	0.200669	−	0.617596i
$915$		0			0
$916$	−16.8913	−	51.9860i	−0.558104	−	1.71767i
$917$	−14.2533	−	19.6180i	−0.470687	−	0.647845i
$918$			11.7805i			0.388814i
$919$	0.802736	−	0.583222i	0.0264798	−	0.0192387i	−0.574467	−	0.818528i	$-0.694790\pi$
$919$	0.802736	−	0.583222i	0.0264798	−	0.0192387i	0.600946	+	0.799289i	$0.294790\pi$
$920$		0			0
$921$	11.0136	+	8.00188i	0.362912	+	0.263671i
$922$	20.0686	−	27.6221i	0.660925	−	0.909685i
$923$	16.9125	+	5.49519i	0.556681	+	0.180877i
$924$	−9.60977			−0.316138
$925$		0			0
$926$	−51.2477			−1.68410
$927$	−23.9699	−	7.78830i	−0.787276	−	0.255801i
$928$	11.9624	−	16.4648i	0.392685	−	0.540484i
$929$	26.9587	+	19.5866i	0.884485	+	0.642616i	0.934434	−	0.356136i	$-0.115906\pi$
$929$	26.9587	+	19.5866i	0.884485	+	0.642616i	−0.0499493	+	0.998752i	$0.515906\pi$
$930$		0			0
$931$	−1.61959	+	1.17670i	−0.0530799	+	0.0385648i
$932$			75.0355i			2.45787i
$933$	−2.18749	−	3.01081i	−0.0716150	−	0.0985697i
$934$	20.3387	+	62.5962i	0.665504	+	2.04821i
$935$		0			0
$936$	3.76594	−	11.5904i	0.123094	−	0.378844i
$937$	−12.7133	+	4.13079i	−0.415325	+	0.134947i	−0.509223	−	0.860635i	$-0.670067\pi$
$937$	−12.7133	+	4.13079i	−0.415325	+	0.134947i	0.0938984	+	0.995582i	$0.470067\pi$
$938$	−71.2759	+	23.1589i	−2.32724	+	0.756166i
$939$	−3.14187	+	9.66969i	−0.102531	+	0.315559i
$940$		0			0
$941$	−0.664330	−	2.04460i	−0.0216565	−	0.0666520i	0.939644	−	0.342153i	$-0.111156\pi$
$941$	−0.664330	−	2.04460i	−0.0216565	−	0.0666520i	−0.961301	+	0.275501i	$0.911156\pi$
$942$	−0.946986	−	1.30341i	−0.0308545	−	0.0424675i
$943$		−	6.10671i		−	0.198862i
$944$	3.80429	−	2.76398i	0.123819	−	0.0899599i
$945$		0			0
$946$	13.4306	+	9.75792i	0.436667	+	0.317257i
$947$	20.5245	−	28.2495i	0.666955	−	0.917985i	−0.332731	−	0.943022i	$-0.607970\pi$
$947$	20.5245	−	28.2495i	0.666955	−	0.917985i	0.999687	+	0.0250363i	$0.00797015\pi$
$948$	12.9028	+	4.19237i	0.419063	+	0.136162i
$949$	0.381966			0.0123991
$950$		0			0
$951$	1.90903			0.0619046
$952$	16.5301	+	5.37097i	0.535745	+	0.174074i
$953$	4.86618	−	6.69772i	0.157631	−	0.216960i	−0.722896	−	0.690957i	$-0.757189\pi$
$953$	4.86618	−	6.69772i	0.157631	−	0.216960i	0.880526	+	0.473997i	$0.157189\pi$
$954$	49.2666	+	35.7943i	1.59507	+	1.15888i
$955$		0			0
$956$	17.8851	−	12.9943i	0.578446	−	0.420266i
$957$			3.76415i			0.121678i
$958$	34.0112	+	46.8124i	1.09885	+	1.51244i
$959$	−8.75947	−	26.9589i	−0.282858	−	0.870547i
$960$		0			0
$961$	3.23638	−	9.96056i	0.104399	−	0.321308i
$962$	11.9745	−	3.89076i	0.386074	−	0.125443i
$963$	−14.8523	+	4.82582i	−0.478610	+	0.155510i
$964$	−27.0096	+	83.1270i	−0.869920	+	2.67734i
$965$		0			0
$966$	−3.42527	−	10.5419i	−0.110206	−	0.339180i
$967$	−17.3321	−	23.8556i	−0.557362	−	0.767143i	0.433626	−	0.901093i	$-0.357234\pi$
$967$	−17.3321	−	23.8556i	−0.557362	−	0.767143i	−0.990988	+	0.133950i	$0.957234\pi$
$968$			21.5438i			0.692443i
$969$	0.645616	−	0.469067i	0.0207402	−	0.0150686i
$970$		0			0
$971$	−17.6905	−	12.8529i	−0.567714	−	0.412469i	0.266560	−	0.963818i	$-0.414113\pi$
$971$	−17.6905	−	12.8529i	−0.567714	−	0.412469i	−0.834274	+	0.551350i	$0.814113\pi$
$972$	22.6478	−	31.1721i	0.726429	−	0.999844i
$973$	−51.7249	−	16.8064i	−1.65822	−	0.538790i
$974$	3.38260			0.108385
$975$		0			0
$976$	6.30517			0.201823
$977$	13.1704	+	4.27933i	0.421359	+	0.136908i	0.512019	−	0.858974i	$-0.328898\pi$
$977$	13.1704	+	4.27933i	0.421359	+	0.136908i	−0.0906602	+	0.995882i	$0.528898\pi$
$978$	−2.87478	+	3.95679i	−0.0919252	+	0.126524i
$979$	−7.71472	−	5.60507i	−0.246563	−	0.179139i
$980$		0			0
$981$	−22.6995	+	16.4922i	−0.724740	+	0.526555i
$982$		−	46.3440i		−	1.47890i
$983$	1.72537	+	2.37477i	0.0550308	+	0.0757434i	0.835646	−	0.549269i	$-0.185094\pi$
$983$	1.72537	+	2.37477i	0.0550308	+	0.0757434i	−0.780615	+	0.625013i	$0.785094\pi$
$984$	0.828443	+	2.54968i	0.0264098	+	0.0812810i
$985$		0			0
$986$	5.26090	−	16.1914i	0.167541	−	0.515639i
$987$	6.58147	−	2.13845i	0.209491	−	0.0680676i
$988$	−4.08637	+	1.32774i	−0.130005	+	0.0422411i
$989$	−3.69804	+	11.3814i	−0.117591	+	0.361907i
$990$		0			0
$991$	9.76918	+	30.0664i	0.310328	+	0.955092i	0.977635	+	0.210309i	$0.0674470\pi$
$991$	9.76918	+	30.0664i	0.310328	+	0.955092i	−0.667307	+	0.744783i	$0.732553\pi$
$992$	−19.4388	−	26.7552i	−0.617183	−	0.849479i
$993$		−	5.52970i		−	0.175480i
$994$	70.6678	−	51.3432i	2.24145	−	1.62851i
$995$		0			0
$996$	16.1570	+	11.7388i	0.511955	+	0.371957i
$997$	−7.10542	+	9.77977i	−0.225031	+	0.309728i	−0.906572	−	0.422052i	$-0.861310\pi$
$997$	−7.10542	+	9.77977i	−0.225031	+	0.309728i	0.681541	+	0.731780i	$0.261310\pi$
$998$	−1.37265	−	0.446002i	−0.0434506	−	0.0141180i
$999$	10.4762			0.331453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.e.a.124.2		8
5.2	odd	4		625.2.d.o.501.1		16
5.3	odd	4		625.2.d.o.501.4		16
5.4	even	2		625.2.e.i.124.1		8
25.2	odd	20		125.2.d.b.76.4		16
25.3	odd	20		125.2.d.b.51.1		16
25.4	even	10		125.2.e.b.74.2		8
25.6	even	5		625.2.e.i.499.1		8
25.8	odd	20		625.2.d.o.126.4		16
25.9	even	10		625.2.b.c.624.1		8
25.11	even	5		125.2.e.b.49.2		8
25.12	odd	20		625.2.a.f.1.1		8
25.13	odd	20		625.2.a.f.1.8		8
25.14	even	10		25.2.e.a.9.1	✓	8
25.16	even	5		625.2.b.c.624.8		8
25.17	odd	20		625.2.d.o.126.1		16
25.19	even	10	inner	625.2.e.a.499.2		8
25.21	even	5		25.2.e.a.14.1	yes	8
25.22	odd	20		125.2.d.b.51.4		16
25.23	odd	20		125.2.d.b.76.1		16
75.14	odd	10		225.2.m.a.109.2		8
75.38	even	20		5625.2.a.x.1.1		8
75.62	even	20		5625.2.a.x.1.8		8
75.71	odd	10		225.2.m.a.64.2		8
100.39	odd	10		400.2.y.c.209.1		8
100.63	even	20		10000.2.a.bj.1.4		8
100.71	odd	10		400.2.y.c.289.1		8
100.87	even	20		10000.2.a.bj.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.9.1	✓	8	25.14	even	10
25.2.e.a.14.1	yes	8	25.21	even	5
125.2.d.b.51.1		16	25.3	odd	20
125.2.d.b.51.4		16	25.22	odd	20
125.2.d.b.76.1		16	25.23	odd	20
125.2.d.b.76.4		16	25.2	odd	20
125.2.e.b.49.2		8	25.11	even	5
125.2.e.b.74.2		8	25.4	even	10
225.2.m.a.64.2		8	75.71	odd	10
225.2.m.a.109.2		8	75.14	odd	10
400.2.y.c.209.1		8	100.39	odd	10
400.2.y.c.289.1		8	100.71	odd	10
625.2.a.f.1.1		8	25.12	odd	20
625.2.a.f.1.8		8	25.13	odd	20
625.2.b.c.624.1		8	25.9	even	10
625.2.b.c.624.8		8	25.16	even	5
625.2.d.o.126.1		16	25.17	odd	20
625.2.d.o.126.4		16	25.8	odd	20
625.2.d.o.501.1		16	5.2	odd	4
625.2.d.o.501.4		16	5.3	odd	4
625.2.e.a.124.2		8	1.1	even	1	trivial
625.2.e.a.499.2		8	25.19	even	10	inner
625.2.e.i.124.1		8	5.4	even	2
625.2.e.i.499.1		8	25.6	even	5
5625.2.a.x.1.1		8	75.38	even	20
5625.2.a.x.1.8		8	75.62	even	20
10000.2.a.bj.1.4		8	100.63	even	20
10000.2.a.bj.1.5		8	100.87	even	20

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.19625 + 0.713605i) q^{2} +(-0.279141 + 0.384204i) q^{3} +(2.69625 + 1.95894i) q^{4} +(-0.887234 + 0.644613i) q^{6} +3.03582i q^{7} +(1.80902 + 2.48990i) q^{8} +(0.857358 + 2.63868i) q^{9} +O(q^{10})\)	\(q+(2.19625 + 0.713605i) q^{2} +(-0.279141 + 0.384204i) q^{3} +(2.69625 + 1.95894i) q^{4} +(-0.887234 + 0.644613i) q^{6} +3.03582i q^{7} +(1.80902 + 2.48990i) q^{8} +(0.857358 + 2.63868i) q^{9} +(0.618034 - 1.90211i) q^{11} +(-1.50527 + 0.489091i) q^{12} +(-1.35736 + 0.441032i) q^{13} +(-2.16637 + 6.66742i) q^{14} +(0.136498 + 0.420099i) q^{16} +(-1.09343 - 1.50497i) q^{17} +6.40701i q^{18} +(0.730800 - 0.530958i) q^{19} +(-1.16637 - 0.847421i) q^{21} +(2.71472 - 3.73648i) q^{22} +(3.16637 + 1.02882i) q^{23} -1.46160 q^{24} -3.29582 q^{26} +(-2.60809 - 0.847421i) q^{27} +(-5.94699 + 8.18532i) q^{28} +(3.20619 + 2.32943i) q^{29} +(5.21004 - 3.78532i) q^{31} -5.13532i q^{32} +(0.558282 + 0.768409i) q^{33} +(-1.32748 - 4.08557i) q^{34} +(-2.85736 + 8.79404i) q^{36} +(-3.63324 + 1.18051i) q^{37} +(1.98391 - 0.644613i) q^{38} +(0.209447 - 0.644613i) q^{39} +(-0.566805 - 1.74445i) q^{41} +(-1.95693 - 2.69348i) q^{42} +3.59445i q^{43} +(5.39250 - 3.91788i) q^{44} +(6.21998 + 4.51908i) q^{46} +(-2.82134 + 3.88324i) q^{47} +(-0.199506 - 0.0648235i) q^{48} -2.21619 q^{49} +0.883436 q^{51} +(-4.52373 - 1.46985i) q^{52} +(5.58674 - 7.68949i) q^{53} +(-5.12330 - 3.72230i) q^{54} +(-7.55888 + 5.49184i) q^{56} +0.428989i q^{57} +(5.37930 + 7.40398i) q^{58} +(-3.28968 - 10.1246i) q^{59} +(4.41097 - 13.5756i) q^{61} +(14.1438 - 4.59559i) q^{62} +(-8.01054 + 2.60278i) q^{63} +(3.93759 - 12.1186i) q^{64} +(0.677786 + 2.08601i) q^{66} +(6.28353 + 8.64854i) q^{67} -6.19974i q^{68} +(-1.27914 + 0.929350i) q^{69} +(-10.0802 - 7.32371i) q^{71} +(-5.01906 + 6.90814i) q^{72} +(-0.254532 - 0.0827026i) q^{73} -8.82193 q^{74} +3.01054 q^{76} +(5.77447 + 1.87624i) q^{77} +(0.919998 - 1.26627i) q^{78} +(-6.93470 - 5.03835i) q^{79} +(-5.68017 + 4.12688i) q^{81} -4.23572i q^{82} +(-7.41677 - 10.2083i) q^{83} +(-1.48479 - 4.56972i) q^{84} +(-2.56502 + 7.89432i) q^{86} +(-1.78996 + 0.581593i) q^{87} +(5.85410 - 1.90211i) q^{88} +(1.47338 - 4.53460i) q^{89} +(-1.33889 - 4.12069i) q^{91} +(6.52195 + 8.97669i) q^{92} +3.05836i q^{93} +(-8.96746 + 6.51524i) q^{94} +(1.97301 + 1.43348i) q^{96} +(-5.85319 + 8.05623i) q^{97} +(-4.86730 - 1.58148i) q^{98} +5.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9	\( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9 - 4 * q^11 + 10 * q^12 - 5 * q^13 - 7 * q^14 - 2 * q^16 + 15 * q^17 + 10 * q^19 + q^21 + 10 * q^22 + 15 * q^23 - 20 * q^24 + 6 * q^26 - 5 * q^27 - 20 * q^28 + 15 * q^29 + q^31 + 10 * q^33 - 12 * q^34 - 17 * q^36 - 5 * q^37 + 12 * q^39 - 9 * q^41 + 5 * q^42 + 8 * q^44 + 16 * q^46 - 15 * q^47 - 5 * q^48 + 14 * q^49 - 4 * q^51 - 20 * q^52 + 35 * q^53 - 10 * q^54 - 15 * q^56 - 20 * q^58 + 15 * q^59 + 6 * q^61 + 45 * q^62 - 20 * q^63 - 26 * q^64 - 18 * q^66 - 13 * q^69 - 29 * q^71 + 5 * q^72 + 10 * q^73 - 12 * q^74 - 20 * q^76 + 20 * q^77 - 25 * q^78 - 10 * q^79 - 12 * q^81 + 15 * q^83 - 27 * q^84 + 16 * q^86 - 55 * q^87 + 20 * q^88 + 40 * q^89 + q^91 - 5 * q^92 - 7 * q^94 + 11 * q^96 - 10 * q^97 - 40 * q^98 - 8 * q^99

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