LMFDB - Embedded newform 825.2.n.n.676.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 9 x^{14} - 15 x^{13} + 44 x^{12} - 61 x^{11} + 208 x^{10} - 281 x^{9} + 851 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 9x^14 - 15x^13 + 44x^12 - 61x^11 + 208x^10 - 281x^9 + 851x^8 - 1252x^7 + 1929x^6 - 1320x^5 + 1261x^4 + 45x^3 + 640x^2 + 200*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			676.3
Root			$1.13858 - 0.827228i$ of defining polynomial
Character	$\chi$	$=$	825.676
Dual form			825.2.n.n.526.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.434899 + 1.33848i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.0156350 - 0.0113595i) q^{4} +(-0.434899 + 1.33848i) q^{6} +(1.75053 - 1.27183i) q^{7} +(2.29917 + 1.67044i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-2.30777 - 2.38206i) q^{11} +0.0193259 q^{12} +(0.756861 + 2.32938i) q^{13} +(2.46363 + 1.78993i) q^{14} +(-1.22401 + 3.76711i) q^{16} +(0.750133 - 2.30867i) q^{17} +(-1.13858 + 0.827228i) q^{18} +(4.03915 + 2.93461i) q^{19} +2.16377 q^{21} +(2.18469 - 4.12487i) q^{22} +2.41686 q^{23} +(0.878204 + 2.70283i) q^{24} +(-2.78868 + 2.02609i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.0129221 - 0.0397702i) q^{28} +(-4.39054 + 3.18992i) q^{29} +(0.713252 + 2.19517i) q^{31} +0.109320 q^{32} +(-0.466888 - 3.28360i) q^{33} +3.41635 q^{34} +(0.0156350 + 0.0113595i) q^{36} +(7.57149 - 5.50101i) q^{37} +(-2.17131 + 6.68259i) q^{38} +(-0.756861 + 2.32938i) q^{39} +(-4.78007 - 3.47293i) q^{41} +(0.941023 + 2.89617i) q^{42} +3.11043 q^{43} +(-0.0631409 - 0.0110283i) q^{44} +(1.05109 + 3.23493i) q^{46} +(-9.70136 - 7.04845i) q^{47} +(-3.20450 + 2.32820i) q^{48} +(-0.716330 + 2.20464i) q^{49} +(1.96387 - 1.42684i) q^{51} +(0.0382941 + 0.0278223i) q^{52} +(2.18021 + 6.71000i) q^{53} -1.40736 q^{54} +6.14928 q^{56} +(1.54282 + 4.74830i) q^{57} +(-6.17909 - 4.48937i) q^{58} +(-3.46225 + 2.51548i) q^{59} +(-1.59567 + 4.91096i) q^{61} +(-2.62800 + 1.90935i) q^{62} +(1.75053 + 1.27183i) q^{63} +(2.49556 + 7.68054i) q^{64} +(4.19199 - 2.05296i) q^{66} -14.0857 q^{67} +(-0.0144970 - 0.0446172i) q^{68} +(1.95528 + 1.42060i) q^{69} +(2.10763 - 6.48661i) q^{71} +(-0.878204 + 2.70283i) q^{72} +(2.91403 - 2.11717i) q^{73} +(10.6558 + 7.74193i) q^{74} +0.0964877 q^{76} +(-7.06940 - 1.23476i) q^{77} -3.44699 q^{78} +(-3.30738 - 10.1791i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(2.56960 - 7.90842i) q^{82} +(0.736627 - 2.26711i) q^{83} +(0.0338306 - 0.0245793i) q^{84} +(1.35272 + 4.16326i) q^{86} -5.42701 q^{87} +(-1.32686 - 9.33175i) q^{88} -10.3078 q^{89} +(4.28749 + 3.11504i) q^{91} +(0.0377877 - 0.0274543i) q^{92} +(-0.713252 + 2.19517i) q^{93} +(5.21511 - 16.0505i) q^{94} +(0.0884418 + 0.0642567i) q^{96} +(-1.63060 - 5.01848i) q^{97} -3.26240 q^{98} +(1.55233 - 2.93092i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 2 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 3 q^{11} - 14 q^{12} - 11 q^{13} + 4 q^{14} + 16 q^{16} - 17 q^{17} - 3 q^{18} + 8 q^{19} - 16 q^{21} - 23 q^{22} - 14 q^{23}+ \cdots + 8 q^{99}+O(q^{100}) $ 16 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 - 2 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 3 * q^11 - 14 * q^12 - 11 * q^13 + 4 * q^14 + 16 * q^16 - 17 * q^17 - 3 * q^18 + 8 * q^19 - 16 * q^21 - 23 * q^22 - 14 * q^23 - q^24 + 33 * q^26 + 4 * q^27 + 7 * q^28 + 4 * q^29 - 5 * q^31 + 24 * q^32 + 12 * q^33 - 16 * q^34 - 6 * q^36 + 2 * q^37 - 3 * q^38 + 11 * q^39 + 2 * q^41 - 4 * q^42 + 22 * q^43 - 40 * q^46 - 20 * q^47 + 9 * q^48 - 26 * q^49 - 18 * q^51 - 43 * q^52 + 40 * q^53 - 2 * q^54 - 8 * q^56 + 2 * q^57 + 26 * q^58 + 6 * q^59 - 2 * q^61 + 26 * q^62 - 4 * q^63 + 4 * q^64 - 7 * q^66 - 12 * q^67 - 56 * q^68 + 4 * q^69 + 11 * q^71 + q^72 - 21 * q^73 + 66 * q^74 - 10 * q^76 + 23 * q^77 + 2 * q^78 - 7 * q^79 - 4 * q^81 + 20 * q^82 + 13 * q^83 + 18 * q^84 + 37 * q^86 + 56 * q^87 + 26 * q^88 + 42 * q^89 + 2 * q^91 + 92 * q^92 + 5 * q^93 + 88 * q^94 + 11 * q^96 - 27 * q^97 - 54 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.434899	+	1.33848i	0.307520	+	0.946450i	0.978725	+	0.205178i	$0.0657773\pi$
$2$	0.434899	+	1.33848i	0.307520	+	0.946450i	−0.671204	+	0.741272i	$0.734223\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.0156350	−	0.0113595i	0.00781750	−	0.00567974i
$5$		0			0
$5$		0			0
$6$	−0.434899	+	1.33848i	−0.177547	+	0.546433i
$7$	1.75053	−	1.27183i	0.661637	−	0.480708i	−0.205578	−	0.978641i	$-0.565907\pi$
$7$	1.75053	−	1.27183i	0.661637	−	0.480708i	0.867216	+	0.497933i	$0.165907\pi$
$8$	2.29917	+	1.67044i	0.812878	+	0.590591i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−2.30777	−	2.38206i	−0.695819	−	0.718217i
$11$	−2.30777	−	2.38206i	−0.695819	−	0.718217i
$12$	0.0193259			0.00557891
$13$	0.756861	+	2.32938i	0.209915	+	0.646053i	0.999476	+	0.0323802i	$0.0103087\pi$
$13$	0.756861	+	2.32938i	0.209915	+	0.646053i	−0.789560	+	0.613673i	$0.789691\pi$
$14$	2.46363	+	1.78993i	0.658433	+	0.478380i
$15$		0			0
$16$	−1.22401	+	3.76711i	−0.306002	+	0.941778i
$17$	0.750133	−	2.30867i	0.181934	−	0.559935i	−0.817948	−	0.575292i	$-0.804888\pi$
$17$	0.750133	−	2.30867i	0.181934	−	0.559935i	0.999882	+	0.0153569i	$0.00488844\pi$
$18$	−1.13858	+	0.827228i	−0.268366	+	0.194979i
$19$	4.03915	+	2.93461i	0.926644	+	0.673246i	0.945169	−	0.326582i	$-0.105897\pi$
$19$	4.03915	+	2.93461i	0.926644	+	0.673246i	−0.0185249	+	0.999828i	$0.505897\pi$
$20$		0			0
$21$	2.16377			0.472174
$22$	2.18469	−	4.12487i	0.465778	−	0.879425i
$23$	2.41686			0.503951			0.251976	−	0.967734i	$-0.418920\pi$
$23$	2.41686			0.503951			0.251976	+	0.967734i	$0.418920\pi$
$24$	0.878204	+	2.70283i	0.179263	+	0.551714i
$25$		0			0
$26$	−2.78868	+	2.02609i	−0.546904	+	0.397349i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	0.0129221	−	0.0397702i	0.00244205	−	0.00751586i
$29$	−4.39054	+	3.18992i	−0.815303	+	0.592352i	−0.915363	−	0.402629i	$-0.868096\pi$
$29$	−4.39054	+	3.18992i	−0.815303	+	0.592352i	0.100060	+	0.994981i	$0.468096\pi$
$30$		0			0
$31$	0.713252	+	2.19517i	0.128104	+	0.394263i	0.994454	−	0.105174i	$-0.0335400\pi$
$31$	0.713252	+	2.19517i	0.128104	+	0.394263i	−0.866350	+	0.499438i	$0.833540\pi$
$32$	0.109320			0.0193252
$33$	−0.466888	−	3.28360i	−0.0812748	−	0.571601i
$34$	3.41635			0.585899
$35$		0			0
$36$	0.0156350	+	0.0113595i	0.00260583	+	0.00189325i
$37$	7.57149	−	5.50101i	1.24475	−	0.904361i	0.246841	−	0.969056i	$-0.420608\pi$
$37$	7.57149	−	5.50101i	1.24475	−	0.904361i	0.997905	+	0.0646952i	$0.0206075\pi$
$38$	−2.17131	+	6.68259i	−0.352232	+	1.08406i
$39$	−0.756861	+	2.32938i	−0.121195	+	0.372999i
$40$		0			0
$41$	−4.78007	−	3.47293i	−0.746522	−	0.542380i	0.148225	−	0.988954i	$-0.452644\pi$
$41$	−4.78007	−	3.47293i	−0.746522	−	0.542380i	−0.894747	+	0.446574i	$0.852644\pi$
$42$	0.941023	+	2.89617i	0.145203	+	0.446889i
$43$	3.11043			0.474336			0.237168	−	0.971469i	$-0.423781\pi$
$43$	3.11043			0.474336			0.237168	+	0.971469i	$0.423781\pi$
$44$	−0.0631409	−	0.0110283i	−0.00951885	−	0.00166259i
$45$		0			0
$46$	1.05109	+	3.23493i	0.154975	+	0.476965i
$47$	−9.70136	−	7.04845i	−1.41509	−	1.02812i	−0.992558	−	0.121773i	$-0.961142\pi$
$47$	−9.70136	−	7.04845i	−1.41509	−	1.02812i	−0.422531	−	0.906349i	$-0.638858\pi$
$48$	−3.20450	+	2.32820i	−0.462529	+	0.336047i
$49$	−0.716330	+	2.20464i	−0.102333	+	0.314948i
$50$		0			0
$51$	1.96387	−	1.42684i	0.274997	−	0.199797i
$52$	0.0382941	+	0.0278223i	0.00531043	+	0.00385825i
$53$	2.18021	+	6.71000i	0.299475	+	0.921690i	0.981681	+	0.190530i	$0.0610206\pi$
$53$	2.18021	+	6.71000i	0.299475	+	0.921690i	−0.682206	+	0.731160i	$0.738979\pi$
$54$	−1.40736			−0.191518
$55$		0			0
$56$	6.14928			0.821732
$57$	1.54282	+	4.74830i	0.204351	+	0.628928i
$58$	−6.17909	−	4.48937i	−0.811354	−	0.589484i
$59$	−3.46225	+	2.51548i	−0.450747	+	0.327487i	−0.789891	−	0.613248i	$-0.789863\pi$
$59$	−3.46225	+	2.51548i	−0.450747	+	0.327487i	0.339144	+	0.940735i	$0.389863\pi$
$60$		0			0
$61$	−1.59567	+	4.91096i	−0.204304	+	0.628783i	0.795437	+	0.606036i	$0.207241\pi$
$61$	−1.59567	+	4.91096i	−0.204304	+	0.628783i	−0.999741	+	0.0227473i	$0.992759\pi$
$62$	−2.62800	+	1.90935i	−0.333756	+	0.242488i
$63$	1.75053	+	1.27183i	0.220546	+	0.160236i
$64$	2.49556	+	7.68054i	0.311945	+	0.960068i
$65$		0			0
$66$	4.19199	−	2.05296i	0.515998	−	0.252701i
$67$	−14.0857			−1.72084			−0.860422	−	0.509582i	$-0.829800\pi$
$67$	−14.0857			−1.72084			−0.860422	+	0.509582i	$0.829800\pi$
$68$	−0.0144970	−	0.0446172i	−0.00175802	−	0.00541063i
$69$	1.95528	+	1.42060i	0.235389	+	0.171020i
$70$		0			0
$71$	2.10763	−	6.48661i	0.250129	−	0.769819i	−0.744621	−	0.667488i	$-0.767370\pi$
$71$	2.10763	−	6.48661i	0.250129	−	0.769819i	0.994750	−	0.102332i	$-0.0326303\pi$
$72$	−0.878204	+	2.70283i	−0.103497	+	0.318532i
$73$	2.91403	−	2.11717i	0.341062	−	0.247796i	−0.404048	−	0.914738i	$-0.632397\pi$
$73$	2.91403	−	2.11717i	0.341062	−	0.247796i	0.745110	+	0.666942i	$0.232397\pi$
$74$	10.6558	+	7.74193i	1.23872	+	0.899981i
$75$		0			0
$76$	0.0964877			0.0110679
$77$	−7.06940	−	1.23476i	−0.805632	−	0.140714i
$78$	−3.44699			−0.390295
$79$	−3.30738	−	10.1791i	−0.372110	−	1.14524i	−0.945408	−	0.325889i	$-0.894336\pi$
$79$	−3.30738	−	10.1791i	−0.372110	−	1.14524i	0.573298	−	0.819347i	$-0.305664\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	2.56960	−	7.90842i	0.283765	−	0.873339i
$83$	0.736627	−	2.26711i	0.0808553	−	0.248847i	−0.902455	−	0.430785i	$-0.858237\pi$
$83$	0.736627	−	2.26711i	0.0808553	−	0.248847i	0.983310	+	0.181937i	$0.0582369\pi$
$84$	0.0338306	−	0.0245793i	0.00369122	−	0.00268183i
$85$		0			0
$86$	1.35272	+	4.16326i	0.145868	+	0.448935i
$87$	−5.42701			−0.581836
$88$	−1.32686	−	9.33175i	−0.141444	−	0.994767i
$89$	−10.3078			−1.09262			−0.546310	−	0.837583i	$-0.683968\pi$
$89$	−10.3078			−1.09262			−0.546310	+	0.837583i	$0.683968\pi$
$90$		0			0
$91$	4.28749	+	3.11504i	0.449451	+	0.326545i
$92$	0.0377877	−	0.0274543i	0.00393964	−	0.00286231i
$93$	−0.713252	+	2.19517i	−0.0739608	+	0.227628i
$94$	5.21511	−	16.0505i	0.537898	−	1.65548i
$95$		0			0
$96$	0.0884418	+	0.0642567i	0.00902655	+	0.00655817i
$97$	−1.63060	−	5.01848i	−0.165563	−	0.509549i	0.833515	−	0.552497i	$-0.186325\pi$
$97$	−1.63060	−	5.01848i	−0.165563	−	0.509549i	−0.999077	+	0.0429481i	$0.986325\pi$
$98$	−3.26240			−0.329552
$99$	1.55233	−	2.93092i	0.156015	−	0.294568i
$100$		0			0
$101$	−4.89032	−	15.0509i	−0.486605	−	1.49762i	−0.829643	−	0.558294i	$-0.811456\pi$
$101$	−4.89032	−	15.0509i	−0.486605	−	1.49762i	0.343038	−	0.939322i	$-0.388544\pi$
$102$	2.76388	+	2.00808i	0.273665	+	0.198830i
$103$	−1.41403	+	1.02735i	−0.139329	+	0.101228i	−0.655266	−	0.755398i	$-0.727444\pi$
$103$	−1.41403	+	1.02735i	−0.139329	+	0.101228i	0.515938	+	0.856626i	$0.327444\pi$
$104$	−2.15094	+	6.61992i	−0.210917	+	0.649137i
$105$		0			0
$106$	−8.03305	+	5.83635i	−0.780239	+	0.566877i
$107$	7.22247	+	5.24743i	0.698222	+	0.507288i	0.879353	−	0.476171i	$-0.157976\pi$
$107$	7.22247	+	5.24743i	0.698222	+	0.507288i	−0.181131	+	0.983459i	$0.557976\pi$
$108$	0.00597204	+	0.0183800i	0.000574659	+	0.00176862i
$109$	−18.8496			−1.80546			−0.902730	−	0.430207i	$-0.858441\pi$
$109$	−18.8496			−1.80546			−0.902730	+	0.430207i	$0.858441\pi$
$110$		0			0
$111$	9.35888			0.888306
$112$	2.64848	+	8.15117i	0.250257	+	0.770213i
$113$	−0.568323	−	0.412911i	−0.0534633	−	0.0388434i	0.560733	−	0.827997i	$-0.310520\pi$
$113$	−0.568323	−	0.412911i	−0.0534633	−	0.0388434i	−0.614196	+	0.789154i	$0.710520\pi$
$114$	−5.68455	+	4.13007i	−0.532407	+	0.386816i
$115$		0			0
$116$	−0.0324103	+	0.0997486i	−0.00300922	+	0.00926142i
$117$	−1.98149	+	1.43964i	−0.183189	+	0.133094i
$118$	−4.87265	−	3.54019i	−0.448564	−	0.325901i
$119$	−1.62312	−	4.99544i	−0.148791	−	0.457931i
$120$		0			0
$121$	−0.348388	+	10.9945i	−0.0316716	+	0.999498i
$122$	−7.26718			−0.657940
$123$	−1.82582	−	5.61931i	−0.164629	−	0.506676i
$124$	0.0360876	+	0.0262192i	0.00324077	+	0.00235455i
$125$		0			0
$126$	−0.941023	+	2.89617i	−0.0838330	+	0.258011i
$127$	5.96078	−	18.3454i	0.528933	−	1.62789i	−0.227471	−	0.973785i	$-0.573046\pi$
$127$	5.96078	−	18.3454i	0.528933	−	1.62789i	0.756404	−	0.654104i	$-0.226954\pi$
$128$	−9.01808	+	6.55202i	−0.797093	+	0.579122i
$129$	2.51639	+	1.82826i	0.221556	+	0.160970i
$130$		0			0
$131$	−0.731549			−0.0639157			−0.0319579	−	0.999489i	$-0.510174\pi$
$131$	−0.731549			−0.0639157			−0.0319579	+	0.999489i	$0.510174\pi$
$132$	−0.0445998	−	0.0460354i	−0.00388191	−	0.00400687i
$133$	10.8030			0.936737
$134$	−6.12587	−	18.8535i	−0.529195	−	1.62869i
$135$		0			0
$136$	5.58118	−	4.05497i	0.478583	−	0.347711i
$137$	−4.17135	+	12.8381i	−0.356382	+	1.09683i	0.598821	+	0.800883i	$0.295636\pi$
$137$	−4.17135	+	12.8381i	−0.356382	+	1.09683i	−0.955204	+	0.295949i	$0.904364\pi$
$138$	−1.05109	+	3.23493i	−0.0894750	+	0.275376i
$139$	13.1809	−	9.57648i	1.11799	−	0.812266i	0.134085	−	0.990970i	$-0.457190\pi$
$139$	13.1809	−	9.57648i	1.11799	−	0.812266i	0.983903	+	0.178704i	$0.0571903\pi$
$140$		0			0
$141$	−3.70559	−	11.4046i	−0.312067	−	0.960443i
$142$	9.59883			0.805516
$143$	3.80205	−	7.17856i	0.317943	−	0.600301i
$144$	−3.96097			−0.330081
$145$		0			0
$146$	4.10111	+	2.97963i	0.339410	+	0.246596i
$147$	−1.87538	+	1.36254i	−0.154678	+	0.112380i
$148$	0.0558916	−	0.172017i	0.00459426	−	0.0141397i
$149$	0.607130	−	1.86855i	0.0497380	−	0.153078i	−0.923103	−	0.384554i	$-0.874355\pi$
$149$	0.607130	−	1.86855i	0.0497380	−	0.153078i	0.972841	+	0.231476i	$0.0743554\pi$
$150$		0			0
$151$	−5.18994	−	3.77071i	−0.422351	−	0.306856i	0.356232	−	0.934398i	$-0.384061\pi$
$151$	−5.18994	−	3.77071i	−0.422351	−	0.306856i	−0.778583	+	0.627542i	$0.784061\pi$
$152$	4.38457	+	13.4943i	0.355636	+	1.09453i
$153$	2.42748			0.196250
$154$	−1.42177	−	9.99926i	−0.114570	−	0.805763i
$155$		0			0
$156$	0.0146270	+	0.0450174i	0.00117110	+	0.00360427i
$157$	8.17196	+	5.93728i	0.652194	+	0.473846i	0.864018	−	0.503461i	$-0.167940\pi$
$157$	8.17196	+	5.93728i	0.652194	+	0.473846i	−0.211824	+	0.977308i	$0.567940\pi$
$158$	12.1862	−	8.85376i	0.969478	−	0.704367i
$159$	−2.18021	+	6.71000i	−0.172902	+	0.532138i
$160$		0			0
$161$	4.23079	−	3.07385i	0.333433	−	0.242253i
$162$	−1.13858	−	0.827228i	−0.0894554	−	0.0649932i
$163$	5.30383	+	16.3235i	0.415428	+	1.27856i	0.911868	+	0.410484i	$0.134640\pi$
$163$	5.30383	+	16.3235i	0.415428	+	1.27856i	−0.496440	+	0.868071i	$0.665360\pi$
$164$	−0.114187			−0.00891651
$165$		0			0
$166$	3.35484			0.260386
$167$	3.99777	+	12.3039i	0.309357	+	0.952102i	0.978015	+	0.208532i	$0.0668687\pi$
$167$	3.99777	+	12.3039i	0.309357	+	0.952102i	−0.668659	+	0.743569i	$0.733131\pi$
$168$	4.97487	+	3.61446i	0.383820	+	0.278861i
$169$	5.66405	−	4.11518i	0.435697	−	0.316552i
$170$		0			0
$171$	−1.54282	+	4.74830i	−0.117982	+	0.363112i
$172$	0.0486315	−	0.0353329i	0.00370812	−	0.00269411i
$173$	−0.150974	−	0.109689i	−0.0114784	−	0.00833952i	0.582031	−	0.813166i	$-0.302258\pi$
$173$	−0.150974	−	0.109689i	−0.0114784	−	0.00833952i	−0.593510	+	0.804827i	$0.702258\pi$
$174$	−2.36020	−	7.26396i	−0.178927	−	0.550679i
$175$		0			0
$176$	11.7982	−	5.77797i	0.889323	−	0.435531i
$177$	−4.27958			−0.321673
$178$	−4.48284	−	13.7968i	−0.336003	−	1.03411i
$179$	−6.42258	−	4.66627i	−0.480046	−	0.348774i	0.321298	−	0.946978i	$-0.395881\pi$
$179$	−6.42258	−	4.66627i	−0.480046	−	0.348774i	−0.801343	+	0.598205i	$0.795881\pi$
$180$		0			0
$181$	1.03612	−	3.18886i	0.0770145	−	0.237026i	−0.905136	−	0.425121i	$-0.860231\pi$
$181$	1.03612	−	3.18886i	0.0770145	−	0.237026i	0.982151	+	0.188095i	$0.0602314\pi$
$182$	−2.30480	+	7.09346i	−0.170843	+	0.525802i
$183$	−4.17751	+	3.03514i	−0.308810	+	0.224364i
$184$	5.55678	+	4.03723i	0.409651	+	0.297629i
$185$		0			0
$186$	−3.24838			−0.238183
$187$	−7.23052	+	3.54103i	−0.528748	+	0.258945i
$188$	−0.231747			−0.0169019
$189$	0.668642	+	2.05787i	0.0486366	+	0.149688i
$190$		0			0
$191$	−19.1058	+	13.8812i	−1.38245	+	1.00441i	−0.385800	+	0.922582i	$0.626074\pi$
$191$	−19.1058	+	13.8812i	−1.38245	+	1.00441i	−0.996647	+	0.0818239i	$0.973926\pi$
$192$	−2.49556	+	7.68054i	−0.180102	+	0.554296i
$193$	4.16951	−	12.8324i	0.300128	−	0.923698i	−0.681323	−	0.731983i	$-0.738595\pi$
$193$	4.16951	−	12.8324i	0.300128	−	0.923698i	0.981451	−	0.191715i	$-0.0614050\pi$
$194$	6.00800	−	4.36507i	0.431349	−	0.313393i
$195$		0			0
$196$	0.0138437	+	0.0426066i	0.000988838	+	0.00304333i
$197$	19.9986			1.42484			0.712422	−	0.701751i	$-0.247598\pi$
$197$	19.9986			1.42484			0.712422	+	0.701751i	$0.247598\pi$
$198$	4.59809	+	0.803113i	0.326772	+	0.0570748i
$199$	9.08289			0.643869			0.321934	−	0.946762i	$-0.395667\pi$
$199$	9.08289			0.643869			0.321934	+	0.946762i	$0.395667\pi$
$200$		0			0
$201$	−11.3956	−	8.27938i	−0.803783	−	0.583982i
$202$	18.0185	−	13.0912i	1.26778	−	0.921095i
$203$	−3.62873	+	11.1681i	−0.254687	+	0.783845i
$204$	0.0144970	−	0.0446172i	0.00101499	−	0.00312383i
$205$		0			0
$206$	−1.99006	−	1.44586i	−0.138654	−	0.100738i
$207$	0.746852	+	2.29858i	0.0519098	+	0.159762i
$208$	−9.70143			−0.672673
$209$	−2.33101	−	16.3939i	−0.161240	−	1.13399i
$210$		0			0
$211$	−8.29369	−	25.5254i	−0.570961	−	1.75724i	−0.649537	−	0.760330i	$-0.725037\pi$
$211$	−8.29369	−	25.5254i	−0.570961	−	1.75724i	0.0785763	−	0.996908i	$-0.474963\pi$
$212$	0.110310	+	0.0801447i	0.00757611	+	0.00550436i
$213$	5.51784	−	4.00895i	0.378076	−	0.274688i
$214$	−3.88255	+	11.9493i	−0.265405	+	0.816834i
$215$		0			0
$216$	−2.29917	+	1.67044i	−0.156439	+	0.113659i
$217$	4.04045	+	2.93556i	0.274284	+	0.199279i
$218$	−8.19766	−	25.2298i	−0.555216	−	1.70878i
$219$	3.60194			0.243397
$220$		0			0
$221$	5.94552			0.399939
$222$	4.07017	+	12.5267i	0.273172	+	0.840737i
$223$	4.71258	+	3.42389i	0.315578	+	0.229281i	0.734286	−	0.678840i	$-0.237517\pi$
$223$	4.71258	+	3.42389i	0.315578	+	0.229281i	−0.418708	+	0.908121i	$0.637517\pi$
$224$	0.191368	−	0.139037i	0.0127863	−	0.00928979i
$225$		0			0
$226$	0.305511	−	0.940265i	0.0203223	−	0.0625455i
$227$	14.7971	−	10.7507i	0.982118	−	0.713550i	0.0239368	−	0.999713i	$-0.492380\pi$
$227$	14.7971	−	10.7507i	0.982118	−	0.713550i	0.958181	+	0.286163i	$0.0923800\pi$
$228$	0.0780602	+	0.0567141i	0.00516966	+	0.00375598i
$229$	−7.26308	−	22.3535i	−0.479958	−	1.47716i	−0.839153	−	0.543896i	$-0.816949\pi$
$229$	−7.26308	−	22.3535i	−0.479958	−	1.47716i	0.359195	−	0.933263i	$-0.383051\pi$
$230$		0			0
$231$	−4.99349	−	5.15423i	−0.328547	−	0.339123i
$232$	−15.4232			−1.01258
$233$	−8.46541	−	26.0538i	−0.554587	−	1.70684i	−0.697031	−	0.717041i	$-0.745496\pi$
$233$	−8.46541	−	26.0538i	−0.554587	−	1.70684i	0.142443	−	0.989803i	$-0.454504\pi$
$234$	−2.78868	−	2.02609i	−0.182301	−	0.132450i
$235$		0			0
$236$	−0.0255578	+	0.0786589i	−0.00166367	+	0.00512026i
$237$	3.30738	−	10.1791i	0.214838	−	0.661203i
$238$	5.98042	−	4.34503i	0.387653	−	0.281646i
$239$	17.7286	+	12.8806i	1.14677	+	0.833177i	0.988048	−	0.154146i	$-0.0492627\pi$
$239$	17.7286	+	12.8806i	1.14677	+	0.833177i	0.158722	+	0.987323i	$0.449263\pi$
$240$		0			0
$241$	−22.7034			−1.46245			−0.731227	−	0.682134i	$-0.761052\pi$
$241$	−22.7034			−1.46245			−0.731227	+	0.682134i	$0.761052\pi$
$242$	−14.8674	+	4.31518i	−0.955715	+	0.277390i
$243$	−1.00000			−0.0641500
$244$	0.0308377	+	0.0949087i	0.00197418	+	0.00607591i
$245$		0			0
$246$	6.72730	−	4.88767i	0.428917	−	0.311627i
$247$	−3.77875	+	11.6298i	−0.240436	+	0.739986i
$248$	−2.02701	+	6.23850i	−0.128715	+	0.396145i
$249$	1.92852	−	1.40115i	0.122215	−	0.0887942i
$250$		0			0
$251$	0.804148	+	2.47491i	0.0507573	+	0.156215i	0.973222	−	0.229866i	$-0.0738286\pi$
$251$	0.804148	+	2.47491i	0.0507573	+	0.156215i	−0.922465	+	0.386081i	$0.873829\pi$
$252$	0.0418169			0.00263421
$253$	−5.57757	−	5.75711i	−0.350659	−	0.361946i
$254$	27.1473			1.70337
$255$		0			0
$256$	0.375205	+	0.272602i	0.0234503	+	0.0170376i
$257$	13.6890	−	9.94562i	0.853895	−	0.620391i	−0.0723224	−	0.997381i	$-0.523041\pi$
$257$	13.6890	−	9.94562i	0.853895	−	0.620391i	0.926217	+	0.376990i	$0.123041\pi$
$258$	−1.35272	+	4.16326i	−0.0842169	+	0.259193i
$259$	6.25774	−	19.2594i	0.388837	−	1.19672i
$260$		0			0
$261$	−4.39054	−	3.18992i	−0.271768	−	0.197451i
$262$	−0.318150	−	0.979166i	−0.0196554	−	0.0604931i
$263$	−17.8845			−1.10281			−0.551403	−	0.834239i	$-0.685907\pi$
$263$	−17.8845			−1.10281			−0.551403	+	0.834239i	$0.685907\pi$
$264$	4.41161	−	8.32945i	0.271516	−	0.512642i
$265$		0			0
$266$	4.69821	+	14.4596i	0.288066	+	0.886575i
$267$	−8.33915	−	6.05875i	−0.510348	−	0.370789i
$268$	−0.220230	+	0.160007i	−0.0134527	+	0.00977395i
$269$	−8.89457	+	27.3747i	−0.542312	+	1.66906i	0.184986	+	0.982741i	$0.440776\pi$
$269$	−8.89457	+	27.3747i	−0.542312	+	1.66906i	−0.727298	+	0.686322i	$0.759224\pi$
$270$		0			0
$271$	−18.1181	+	13.1636i	−1.10060	+	0.799629i	−0.981157	−	0.193212i	$-0.938109\pi$
$271$	−18.1181	+	13.1636i	−1.10060	+	0.799629i	−0.119438	+	0.992842i	$0.538109\pi$
$272$	7.77885	+	5.65167i	0.471662	+	0.342683i
$273$	1.63767	+	5.04024i	0.0991166	+	0.305049i
$274$	−18.9977			−1.14769
$275$		0			0
$276$	0.0467081			0.00281150
$277$	−0.845202	−	2.60126i	−0.0507833	−	0.156295i	0.922449	−	0.386119i	$-0.126185\pi$
$277$	−0.845202	−	2.60126i	−0.0507833	−	0.156295i	−0.973232	+	0.229825i	$0.926185\pi$
$278$	18.5503	+	13.4776i	1.11257	+	0.808332i
$279$	−1.86732	+	1.35669i	−0.111793	+	0.0812227i
$280$		0			0
$281$	1.39517	−	4.29390i	0.0832291	−	0.256153i	−0.900779	−	0.434279i	$-0.857003\pi$
$281$	1.39517	−	4.29390i	0.0832291	−	0.256153i	0.984008	+	0.178126i	$0.0570034\pi$
$282$	13.6533	−	9.91974i	0.813045	−	0.590712i
$283$	11.0266	+	8.01127i	0.655462	+	0.476221i	0.865127	−	0.501552i	$-0.167238\pi$
$283$	11.0266	+	8.01127i	0.655462	+	0.476221i	−0.209666	+	0.977773i	$0.567238\pi$
$284$	−0.0407318	−	0.125360i	−0.00241699	−	0.00743873i
$285$		0			0
$286$	11.2619	+	1.96703i	0.665929	+	0.116313i
$287$	−12.7846			−0.754653
$288$	0.0337817	+	0.103970i	0.00199061	+	0.00612646i
$289$	8.98602	+	6.52873i	0.528590	+	0.384043i
$290$		0			0
$291$	1.63060	−	5.01848i	0.0955876	−	0.294188i
$292$	0.0215109	−	0.0662039i	0.00125883	−	0.00387429i
$293$	−8.68284	+	6.30845i	−0.507257	+	0.368544i	−0.811782	−	0.583961i	$-0.801502\pi$
$293$	−8.68284	+	6.30845i	−0.507257	+	0.368544i	0.304525	+	0.952504i	$0.401502\pi$
$294$	−2.63934	−	1.91759i	−0.153929	−	0.111836i
$295$		0			0
$296$	26.5973			1.54593
$297$	2.97861	−	1.45872i	0.172837	−	0.0846438i
$298$	2.76507			0.160176
$299$	1.82923	+	5.62979i	0.105787	+	0.325579i
$300$		0			0
$301$	5.44489	−	3.95595i	0.313838	−	0.228017i
$302$	2.78993	−	8.58652i	0.160542	−	0.494099i
$303$	4.89032	−	15.0509i	0.280941	−	0.864649i
$304$	−15.9990	+	11.6239i	−0.917603	+	0.666678i
$305$		0			0
$306$	1.05571	+	3.24914i	0.0603509	+	0.185741i
$307$	5.07712			0.289766			0.144883	−	0.989449i	$-0.453719\pi$
$307$	5.07712			0.289766			0.144883	+	0.989449i	$0.453719\pi$
$308$	−0.124556	+	0.0609993i	−0.00709725	+	0.00347576i
$309$	−1.74784			−0.0994310
$310$		0			0
$311$	3.29852	+	2.39651i	0.187042	+	0.135894i	0.677366	−	0.735647i	$-0.263122\pi$
$311$	3.29852	+	2.39651i	0.187042	+	0.135894i	−0.490324	+	0.871540i	$0.663122\pi$
$312$	−5.63124	+	4.09134i	−0.318806	+	0.231626i
$313$	−9.06243	+	27.8913i	−0.512239	+	1.57651i	0.276011	+	0.961155i	$0.410987\pi$
$313$	−9.06243	+	27.8913i	−0.512239	+	1.57651i	−0.788250	+	0.615355i	$0.789013\pi$
$314$	−4.39296	+	13.5202i	−0.247909	+	0.762986i
$315$		0			0
$316$	−0.167340	−	0.121580i	−0.00941362	−	0.00683939i
$317$	−0.359088	−	1.10516i	−0.0201684	−	0.0620719i	0.940466	−	0.339888i	$-0.110389\pi$
$317$	−0.359088	−	1.10516i	−0.0201684	−	0.0620719i	−0.960634	+	0.277816i	$0.910389\pi$
$318$	−9.92940			−0.556813
$319$	17.7309	+	3.09693i	0.992741	+	0.173395i
$320$		0			0
$321$	2.75874	+	8.49052i	0.153978	+	0.473894i
$322$	5.95426	+	4.32602i	0.331818	+	0.241080i
$323$	9.80495	−	7.12372i	0.545562	−	0.396374i
$324$	−0.00597204	+	0.0183800i	−0.000331780	+	0.00102111i
$325$		0			0
$326$	−19.5421	+	14.1982i	−1.08234	+	0.786364i
$327$	−15.2496	−	11.0795i	−0.843306	−	0.612697i
$328$	−5.18886	−	15.9697i	−0.286507	−	0.881778i
$329$	−25.9470			−1.43050
$330$		0			0
$331$	14.8212			0.814644			0.407322	−	0.913285i	$-0.366463\pi$
$331$	14.8212			0.814644			0.407322	+	0.913285i	$0.366463\pi$
$332$	−0.0142360	−	0.0438139i	−0.000781302	−	0.00240460i
$333$	7.57149	+	5.50101i	0.414915	+	0.301454i
$334$	−14.7299	+	10.7019i	−0.805984	+	0.585581i
$335$		0			0
$336$	−2.64848	+	8.15117i	−0.144486	+	0.444683i
$337$	−9.18829	+	6.67568i	−0.500518	+	0.363648i	−0.809215	−	0.587513i	$-0.800107\pi$
$337$	−9.18829	+	6.67568i	−0.500518	+	0.363648i	0.308697	+	0.951161i	$0.400107\pi$
$338$	7.97139	+	5.79155i	0.433586	+	0.315019i
$339$	−0.217080	−	0.668104i	−0.0117902	−	0.0362864i
$340$		0			0
$341$	3.58298	−	6.76495i	0.194030	−	0.366342i
$342$	−7.02649			−0.379949
$343$	6.23047	+	19.1754i	0.336414	+	1.03538i
$344$	7.15140	+	5.19579i	0.385577	+	0.280138i
$345$		0			0
$346$	0.0811585	−	0.249780i	0.00436311	−	0.0134283i
$347$	−2.16848	+	6.67390i	−0.116410	+	0.358274i	−0.992239	−	0.124349i	$-0.960316\pi$
$347$	−2.16848	+	6.67390i	−0.116410	+	0.358274i	0.875828	+	0.482623i	$0.160316\pi$
$348$	−0.0848512	+	0.0616480i	−0.00454850	+	0.00330468i
$349$	−4.46308	−	3.24262i	−0.238903	−	0.173573i	0.461891	−	0.886937i	$-0.347171\pi$
$349$	−4.46308	−	3.24262i	−0.238903	−	0.173573i	−0.700795	+	0.713363i	$0.747171\pi$
$350$		0			0
$351$	−2.44925			−0.130731
$352$	−0.252286	−	0.260406i	−0.0134469	−	0.0138797i
$353$	−14.6513			−0.779810			−0.389905	−	0.920855i	$-0.627492\pi$
$353$	−14.6513			−0.779810			−0.389905	+	0.920855i	$0.627492\pi$
$354$	−1.86119	−	5.72815i	−0.0989210	−	0.304448i
$355$		0			0
$356$	−0.161162	+	0.117091i	−0.00854155	+	0.00620580i
$357$	1.62312	−	4.99544i	0.0859044	−	0.264387i
$358$	3.45255	−	10.6259i	0.182473	−	0.561595i
$359$	7.16241	−	5.20380i	0.378018	−	0.274646i	−0.382510	−	0.923951i	$-0.624940\pi$
$359$	7.16241	−	5.20380i	0.378018	−	0.274646i	0.760528	+	0.649305i	$0.224940\pi$
$360$		0			0
$361$	1.83144	+	5.63659i	0.0963915	+	0.296663i
$362$	4.71885			0.248017
$363$	−6.74425	+	8.68995i	−0.353981	+	0.456104i
$364$	0.102420			0.00536827
$365$		0			0
$366$	−5.87928	−	4.27154i	−0.307315	−	0.223277i
$367$	−17.4330	+	12.6658i	−0.909997	+	0.661152i	−0.941014	−	0.338367i	$-0.890125\pi$
$367$	−17.4330	+	12.6658i	−0.909997	+	0.661152i	0.0310170	+	0.999519i	$0.490125\pi$
$368$	−2.95826	+	9.10460i	−0.154210	+	0.474610i
$369$	1.82582	−	5.61931i	0.0950486	−	0.292530i
$370$		0			0
$371$	12.3505	+	8.97318i	0.641207	+	0.465864i
$372$	0.0137843	+	0.0424236i	0.000714680	+	0.00219956i
$373$	−4.26418			−0.220791			−0.110395	−	0.993888i	$-0.535212\pi$
$373$	−4.26418			−0.220791			−0.110395	+	0.993888i	$0.535212\pi$
$374$	−7.88415	−	8.13794i	−0.407680	−	0.420803i
$375$		0			0
$376$	−10.5310	−	32.4111i	−0.543096	−	1.67148i
$377$	−10.7536	−	7.81291i	−0.553836	−	0.402385i
$378$	−2.46363	+	1.78993i	−0.126715	+	0.0920642i
$379$	−11.4369	+	35.1991i	−0.587474	+	1.80806i	0.00162714	+	0.999999i	$0.499482\pi$
$379$	−11.4369	+	35.1991i	−0.587474	+	1.80806i	−0.589101	+	0.808060i	$0.700518\pi$
$380$		0			0
$381$	15.6055	−	11.3381i	0.799495	−	0.580867i
$382$	−26.8888	−	19.5359i	−1.37575	−	0.999542i
$383$	3.04211	+	9.36267i	0.155445	+	0.478410i	0.998206	−	0.0598782i	$-0.0190712\pi$
$383$	3.04211	+	9.36267i	0.155445	+	0.478410i	−0.842761	+	0.538288i	$0.819071\pi$
$384$	−11.1470			−0.568841
$385$		0			0
$386$	18.9893			0.966530
$387$	0.961175	+	2.95819i	0.0488593	+	0.150373i
$388$	−0.0825018	−	0.0599410i	−0.00418839	−	0.00304305i
$389$	2.37865	−	1.72819i	0.120603	−	0.0876229i	−0.525849	−	0.850578i	$-0.676252\pi$
$389$	2.37865	−	1.72819i	0.120603	−	0.0876229i	0.646451	+	0.762955i	$0.276252\pi$
$390$		0			0
$391$	1.81297	−	5.57975i	0.0916858	−	0.282180i
$392$	−5.32968	+	3.87224i	−0.269190	+	0.195578i
$393$	−0.591836	−	0.429994i	−0.0298542	−	0.0216903i
$394$	8.69740	+	26.7678i	0.438168	+	1.34854i
$395$		0			0
$396$	−0.00902304	−	0.0634585i	−0.000453425	−	0.00318891i
$397$	−34.7013			−1.74161			−0.870805	−	0.491629i	$-0.836402\pi$
$397$	−34.7013			−1.74161			−0.870805	+	0.491629i	$0.836402\pi$
$398$	3.95014	+	12.1573i	0.198003	+	0.609390i
$399$	8.73979	+	6.34983i	0.437537	+	0.317889i
$400$		0			0
$401$	−3.32315	+	10.2276i	−0.165950	+	0.510742i	−0.999105	−	0.0422978i	$-0.986532\pi$
$401$	−3.32315	+	10.2276i	−0.165950	+	0.510742i	0.833155	+	0.553040i	$0.186532\pi$
$402$	6.12587	−	18.8535i	0.305531	−	0.940327i
$403$	−4.57354	+	3.32287i	−0.227824	+	0.165524i
$404$	−0.247430	−	0.179768i	−0.0123101	−	0.00894382i
$405$		0			0
$406$	−16.5264			−0.820192
$407$	−30.5770	−	5.34065i	−1.51565	−	0.264726i
$408$	6.89872			0.341538
$409$	−6.13095	−	18.8691i	−0.303156	−	0.933018i	−0.980359	−	0.197221i	$-0.936808\pi$
$409$	−6.13095	−	18.8691i	−0.303156	−	0.933018i	0.677203	−	0.735796i	$-0.263192\pi$
$410$		0			0
$411$	−10.9207	+	7.93437i	−0.538680	+	0.391374i
$412$	−0.0104381	+	0.0321253i	−0.000514251	+	0.00158270i
$413$	−2.86151	+	8.80682i	−0.140806	+	0.433355i
$414$	−2.75180	+	1.99930i	−0.135243	+	0.0982601i
$415$		0			0
$416$	0.0827401	+	0.254648i	0.00405667	+	0.0124851i
$417$	16.2925			0.797846
$418$	20.9292	−	10.2497i	1.02368	−	0.501330i
$419$	26.5771			1.29838			0.649189	−	0.760628i	$-0.275109\pi$
$419$	26.5771			1.29838			0.649189	+	0.760628i	$0.275109\pi$
$420$		0			0
$421$	32.3790	+	23.5247i	1.57806	+	1.14652i	0.918881	+	0.394536i	$0.129095\pi$
$421$	32.3790	+	23.5247i	1.57806	+	1.14652i	0.659176	+	0.751989i	$0.270905\pi$
$422$	30.5583	−	22.2019i	1.48756	−	1.08077i
$423$	3.70559	−	11.4046i	0.180172	−	0.554512i
$424$	−6.19600	+	19.0693i	−0.300905	+	0.926089i
$425$		0			0
$426$	7.76561	+	5.64205i	0.376245	+	0.273358i
$427$	3.45266	+	10.6262i	0.167086	+	0.514237i
$428$	0.172531			0.00833961
$429$	7.29537	−	3.57279i	0.352224	−	0.172496i
$430$		0			0
$431$	6.06629	+	18.6701i	0.292203	+	0.899308i	0.984147	+	0.177357i	$0.0567546\pi$
$431$	6.06629	+	18.6701i	0.292203	+	0.899308i	−0.691944	+	0.721951i	$0.743245\pi$
$432$	−3.20450	−	2.32820i	−0.154176	−	0.112016i
$433$	−32.4200	+	23.5545i	−1.55801	+	1.13196i	−0.620385	+	0.784298i	$0.713023\pi$
$433$	−32.4200	+	23.5545i	−1.55801	+	1.13196i	−0.937621	+	0.347660i	$0.886977\pi$
$434$	−2.17201	+	6.68475i	−0.104260	+	0.320878i
$435$		0			0
$436$	−0.294713	+	0.214121i	−0.0141142	+	0.0102546i
$437$	9.76207	+	7.09256i	0.466983	+	0.339283i
$438$	1.56648	+	4.82114i	0.0748495	+	0.230363i
$439$	7.34629			0.350619			0.175310	−	0.984513i	$-0.443907\pi$
$439$	7.34629			0.350619			0.175310	+	0.984513i	$0.443907\pi$
$440$		0			0
$441$	−2.31809			−0.110385
$442$	2.58570	+	7.95797i	0.122989	+	0.378522i
$443$	−22.4169	−	16.2868i	−1.06506	−	0.773811i	−0.0900413	−	0.995938i	$-0.528700\pi$
$443$	−22.4169	−	16.2868i	−1.06506	−	0.773811i	−0.975018	+	0.222127i	$0.928700\pi$
$444$	0.146326	−	0.106312i	0.00694433	−	0.00504535i
$445$		0			0
$446$	−2.53332	+	7.79675i	−0.119956	+	0.369187i
$447$	1.58949	−	1.15483i	0.0751801	−	0.0546216i
$448$	14.1369	+	10.2711i	0.667907	+	0.485263i
$449$	−1.02732	−	3.16178i	−0.0484824	−	0.149214i	0.923884	−	0.382672i	$-0.124996\pi$
$449$	−1.02732	−	3.16178i	−0.0484824	−	0.149214i	−0.972367	+	0.233458i	$0.924996\pi$
$450$		0			0
$451$	2.75860	+	19.4011i	0.129898	+	0.913563i
$452$	−0.0135762			−0.000638570
$453$	−1.98238	−	6.10114i	−0.0931403	−	0.286656i
$454$	20.8249	+	15.1302i	0.977361	+	0.710094i
$455$		0			0
$456$	−4.38457	+	13.4943i	−0.205326	+	0.631930i
$457$	5.47865	−	16.8616i	0.256280	−	0.788750i	−0.737294	−	0.675572i	$-0.763897\pi$
$457$	5.47865	−	16.8616i	0.256280	−	0.788750i	0.993575	−	0.113178i	$-0.0361032\pi$
$458$	26.7610	−	19.4430i	1.25046	−	0.908513i
$459$	1.96387	+	1.42684i	0.0916658	+	0.0665991i
$460$		0			0
$461$	−24.4362			−1.13811			−0.569055	−	0.822300i	$-0.692691\pi$
$461$	−24.4362			−1.13811			−0.569055	+	0.822300i	$0.692691\pi$
$462$	4.72718	−	8.92527i	0.219928	−	0.415241i
$463$	23.1516			1.07594			0.537972	−	0.842963i	$-0.319191\pi$
$463$	23.1516			1.07594			0.537972	+	0.842963i	$0.319191\pi$
$464$	−6.64270	−	20.4441i	−0.308380	−	0.949095i
$465$		0			0
$466$	31.1910	−	22.6616i	1.44490	−	1.04978i
$467$	7.15067	−	22.0075i	0.330893	−	1.01839i	−0.637816	−	0.770189i	$-0.720162\pi$
$467$	7.15067	−	22.0075i	0.330893	−	1.01839i	0.968710	−	0.248197i	$-0.0798379\pi$
$468$	−0.0146270	+	0.0450174i	−0.000676135	+	0.00208093i
$469$	−24.6574	+	17.9147i	−1.13858	+	0.827223i
$470$		0			0
$471$	3.12141	+	9.60672i	0.143827	+	0.442654i
$472$	−12.1623			−0.559813
$473$	−7.17816	−	7.40922i	−0.330052	−	0.340676i
$474$	15.0629			0.691862
$475$		0			0
$476$	−0.0821230	−	0.0596659i	−0.00376410	−	0.00273478i
$477$	−5.70787	+	4.14701i	−0.261345	+	0.189879i
$478$	−9.53030	+	29.3312i	−0.435906	+	1.34158i
$479$	−3.32793	+	10.2423i	−0.152057	+	0.467984i	−0.997851	−	0.0655263i	$-0.979127\pi$
$479$	−3.32793	+	10.2423i	−0.152057	+	0.467984i	0.845794	+	0.533510i	$0.179127\pi$
$480$		0			0
$481$	18.5445	+	13.4734i	0.845557	+	0.614333i
$482$	−9.87370	−	30.3881i	−0.449735	−	1.38414i
$483$	5.22954			0.237952
$484$	0.119445	+	0.175856i	0.00542930	+	0.00799346i
$485$		0			0
$486$	−0.434899	−	1.33848i	−0.0197274	−	0.0607148i
$487$	14.9600	+	10.8691i	0.677901	+	0.492524i	0.872661	−	0.488327i	$-0.162393\pi$
$487$	14.9600	+	10.8691i	0.677901	+	0.492524i	−0.194759	+	0.980851i	$0.562393\pi$
$488$	−11.8722	+	8.62564i	−0.537428	+	0.390464i
$489$	−5.30383	+	16.3235i	−0.239847	+	0.738174i
$490$		0			0
$491$	28.6296	−	20.8006i	1.29204	−	0.938720i	0.292192	−	0.956360i	$-0.405615\pi$
$491$	28.6296	−	20.8006i	1.29204	−	0.938720i	0.999844	+	0.0176399i	$0.00561525\pi$
$492$	−0.0923792	−	0.0671174i	−0.00416478	−	0.00302589i
$493$	4.07098	+	12.5292i	0.183348	+	0.564286i
$494$	−17.2097			−0.774299
$495$		0			0
$496$	−9.14246			−0.410508
$497$	−4.56043	−	14.0355i	−0.204563	−	0.629580i
$498$	2.71412	+	1.97193i	0.121623	+	0.0883641i
$499$	3.26309	−	2.37077i	0.146076	−	0.106130i	−0.512347	−	0.858779i	$-0.671224\pi$
$499$	3.26309	−	2.37077i	0.146076	−	0.106130i	0.658423	+	0.752648i	$0.271224\pi$
$500$		0			0
$501$	−3.99777	+	12.3039i	−0.178607	+	0.549696i
$502$	−2.96290	+	2.15268i	−0.132241	+	0.0960786i
$503$	27.6841	+	20.1137i	1.23437	+	0.896825i	0.997210	−	0.0746449i	$-0.0237823\pi$
$503$	27.6841	+	20.1137i	1.23437	+	0.896825i	0.237163	+	0.971470i	$0.423782\pi$
$504$	1.90023	+	5.84831i	0.0846431	+	0.260505i
$505$		0			0
$506$	5.28011	−	9.96925i	0.234730	−	0.443187i
$507$	7.00116			0.310932
$508$	−0.115197	−	0.354541i	−0.00511106	−	0.0157302i
$509$	−19.6456	−	14.2734i	−0.870775	−	0.632655i	0.0600196	−	0.998197i	$-0.480884\pi$
$509$	−19.6456	−	14.2734i	−0.870775	−	0.632655i	−0.930795	+	0.365542i	$0.880884\pi$
$510$		0			0
$511$	2.40841	−	7.41233i	0.106542	−	0.327902i
$512$	−7.09089	+	21.8235i	−0.313376	+	0.964473i
$513$	−4.03915	+	2.93461i	−0.178333	+	0.129566i
$514$	19.2654	+	13.9971i	0.849759	+	0.617386i
$515$		0			0
$516$	0.0601119			0.00264628
$517$	5.59871	+	39.3754i	0.246231	+	1.73173i
$518$	28.4998			1.25221
$519$	−0.0576670	−	0.177481i	−0.00253130	−	0.00779055i
$520$		0			0
$521$	−34.8505	+	25.3204i	−1.52683	+	1.10931i	−0.568861	+	0.822434i	$0.692616\pi$
$521$	−34.8505	+	25.3204i	−1.52683	+	1.10931i	−0.957969	+	0.286873i	$0.907384\pi$
$522$	2.36020	−	7.26396i	0.103303	−	0.317935i
$523$	−10.4342	+	32.1131i	−0.456254	+	1.40421i	0.413402	+	0.910548i	$0.364340\pi$
$523$	−10.4342	+	32.1131i	−0.456254	+	1.40421i	−0.869656	+	0.493657i	$0.835660\pi$
$524$	−0.0114378	+	0.00831002i	−0.000499661	+	0.000363025i
$525$		0			0
$526$	−7.77796	−	23.9381i	−0.339135	−	1.04375i
$527$	5.60295			0.244068
$528$	12.9412	+	2.26033i	0.563191	+	0.0983684i
$529$	−17.1588			−0.746033
$530$		0			0
$531$	−3.46225	−	2.51548i	−0.150249	−	0.109162i
$532$	0.168904	−	0.122716i	0.00732294	−	0.00532043i
$533$	4.47191	−	13.7631i	0.193700	−	0.596147i
$534$	4.48284	−	13.7968i	0.193991	−	0.597044i
$535$		0			0
$536$	−32.3854	−	23.5294i	−1.39884	−	1.01631i
$537$	−2.45321	−	7.55019i	−0.105864	−	0.325815i
$538$	−40.5088			−1.74646
$539$	6.90469	−	3.38146i	0.297406	−	0.145650i
$540$		0			0
$541$	−1.48597	−	4.57334i	−0.0638867	−	0.196623i	0.914018	−	0.405673i	$-0.132963\pi$
$541$	−1.48597	−	4.57334i	−0.0638867	−	0.196623i	−0.977905	+	0.209050i	$0.932963\pi$
$542$	−25.4987	−	18.5259i	−1.09527	−	0.795757i
$543$	2.71261	−	1.97082i	0.116409	−	0.0845762i
$544$	0.0820045	−	0.252384i	0.00351592	−	0.0108209i
$545$		0			0
$546$	−6.03406	+	4.38400i	−0.258234	+	0.187618i
$547$	17.7494	+	12.8957i	0.758911	+	0.551381i	0.898576	−	0.438818i	$-0.144603\pi$
$547$	17.7494	+	12.8957i	0.758911	+	0.551381i	−0.139665	+	0.990199i	$0.544603\pi$
$548$	0.0806151	+	0.248108i	0.00344371	+	0.0105986i
$549$	−5.16368			−0.220381
$550$		0			0
$551$	−27.0952			−1.15429
$552$	2.12250	+	6.53238i	0.0903396	+	0.278037i
$553$	−18.7358	−	13.6123i	−0.796726	−	0.578855i
$554$	3.11417	−	2.26258i	0.132308	−	0.0961277i
$555$		0			0
$556$	0.0972992	−	0.299456i	0.00412641	−	0.0126998i
$557$	19.1426	−	13.9079i	0.811099	−	0.589298i	−0.103050	−	0.994676i	$-0.532860\pi$
$557$	19.1426	−	13.9079i	0.811099	−	0.589298i	0.914149	+	0.405379i	$0.132860\pi$
$558$	−2.62800	−	1.90935i	−0.111252	−	0.0808293i
$559$	2.35416	+	7.24537i	0.0995705	+	0.306446i
$560$		0			0
$561$	−7.93098	−	1.38524i	−0.334846	−	0.0584850i
$562$	6.35408			0.268031
$563$	−10.6290	−	32.7126i	−0.447957	−	1.37867i	−0.879208	−	0.476439i	$-0.841927\pi$
$563$	−10.6290	−	32.7126i	−0.447957	−	1.37867i	0.431250	−	0.902232i	$-0.358073\pi$
$564$	−0.187488	−	0.136218i	−0.00789465	−	0.00573580i
$565$		0			0
$566$	−5.92750	+	18.2430i	−0.249152	+	0.766810i
$567$	−0.668642	+	2.05787i	−0.0280803	+	0.0864224i
$568$	15.6813	−	11.3931i	0.657973	−	0.478045i
$569$	30.9052	+	22.4540i	1.29561	+	0.941319i	0.999903	−	0.0139586i	$-0.00444331\pi$
$569$	30.9052	+	22.4540i	1.29561	+	0.941319i	0.295711	+	0.955277i	$0.404443\pi$
$570$		0			0
$571$	18.0690			0.756165			0.378083	−	0.925772i	$-0.376584\pi$
$571$	18.0690			0.756165			0.378083	+	0.925772i	$0.376584\pi$
$572$	−0.0220997	−	0.155426i	−0.000924035	−	0.00649869i
$573$	−23.6161			−0.986575
$574$	−5.56003	−	17.1120i	−0.232071	−	0.714242i
$575$		0			0
$576$	−6.53346	+	4.74684i	−0.272228	+	0.197785i
$577$	9.53797	−	29.3548i	0.397071	−	1.22206i	−0.530266	−	0.847831i	$-0.677908\pi$
$577$	9.53797	−	29.3548i	0.397071	−	1.22206i	0.927337	−	0.374227i	$-0.122092\pi$
$578$	−4.83057	+	14.8670i	−0.200925	+	0.618385i
$579$	10.9159	−	7.93087i	0.453650	−	0.329596i
$580$		0			0
$581$	−1.59389	−	4.90550i	−0.0661258	−	0.203514i
$582$	7.42629			0.307830
$583$	10.9522	−	20.6785i	0.453593	−	0.856417i
$584$	10.2365			0.423588
$585$		0			0
$586$	−12.2199	−	8.87829i	−0.504800	−	0.366759i
$587$	−18.2683	+	13.2727i	−0.754015	+	0.547824i	−0.897069	−	0.441891i	$-0.854308\pi$
$587$	−18.2683	+	13.2727i	−0.754015	+	0.547824i	0.143054	+	0.989715i	$0.454308\pi$
$588$	−0.0138437	+	0.0426066i	−0.000570906	+	0.00175707i
$589$	−3.56103	+	10.9597i	−0.146730	+	0.451587i
$590$		0			0
$591$	16.1792	+	11.7549i	0.665525	+	0.483532i
$592$	11.4553	+	35.2559i	0.470812	+	1.44901i
$593$	20.9313			0.859544			0.429772	−	0.902937i	$-0.358594\pi$
$593$	20.9313			0.859544			0.429772	+	0.902937i	$0.358594\pi$
$594$	3.24787	+	3.35242i	0.133262	+	0.137552i
$595$		0			0
$596$	−0.0117333	−	0.0361115i	−0.000480616	−	0.00147918i
$597$	7.34821	+	5.33879i	0.300742	+	0.218502i
$598$	−6.73985	+	4.89679i	−0.275613	+	0.200245i
$599$	−0.789533	+	2.42993i	−0.0322594	+	0.0992844i	−0.965890	−	0.258954i	$-0.916622\pi$
$599$	−0.789533	+	2.42993i	−0.0322594	+	0.0992844i	0.933630	+	0.358238i	$0.116622\pi$
$600$		0			0
$601$	5.24063	−	3.80754i	0.213770	−	0.155313i	−0.475748	−	0.879582i	$-0.657823\pi$
$601$	5.24063	−	3.80754i	0.213770	−	0.155313i	0.689518	+	0.724269i	$0.257823\pi$
$602$	7.66295	+	5.56746i	0.312318	+	0.226913i
$603$	−4.35273	−	13.3963i	−0.177257	−	0.545540i
$604$	−0.123978			−0.00504459
$605$		0			0
$606$	22.2721			0.904743
$607$	10.9765	+	33.7821i	0.445522	+	1.37117i	0.881911	+	0.471416i	$0.156257\pi$
$607$	10.9765	+	33.7821i	0.445522	+	1.37117i	−0.436389	+	0.899758i	$0.643743\pi$
$608$	0.441560	+	0.320812i	0.0179076	+	0.0130106i
$609$	−9.50013	+	6.90225i	−0.384965	+	0.279693i
$610$		0			0
$611$	9.07593	−	27.9328i	0.367173	−	1.13004i
$612$	0.0379536	−	0.0275749i	0.00153418	−	0.00111465i
$613$	−10.6521	−	7.73922i	−0.430235	−	0.312584i	0.351508	−	0.936185i	$-0.385669\pi$
$613$	−10.6521	−	7.73922i	−0.430235	−	0.312584i	−0.781743	+	0.623601i	$0.785669\pi$
$614$	2.20803	+	6.79563i	0.0891090	+	0.274249i
$615$		0			0
$616$	−14.1911	−	14.6479i	−0.571777	−	0.590182i
$617$	30.6703			1.23474			0.617370	−	0.786673i	$-0.288198\pi$
$617$	30.6703			1.23474			0.617370	+	0.786673i	$0.288198\pi$
$618$	−0.760134	−	2.33945i	−0.0305771	−	0.0941065i
$619$	28.9236	+	21.0143i	1.16254	+	0.844634i	0.990097	−	0.140386i	$-0.0448342\pi$
$619$	28.9236	+	21.0143i	1.16254	+	0.844634i	0.172442	+	0.985020i	$0.444834\pi$
$620$		0			0
$621$	−0.746852	+	2.29858i	−0.0299702	+	0.0922386i
$622$	−1.77317	+	5.45725i	−0.0710976	+	0.218816i
$623$	−18.0440	+	13.1097i	−0.722918	+	0.525231i
$624$	−7.84862	−	5.70236i	−0.314196	−	0.228277i
$625$		0			0
$626$	−41.2733			−1.64961
$627$	7.75026	−	14.6331i	0.309515	−	0.584389i
$628$	0.195213			0.00778985
$629$	−7.02040	−	21.6066i	−0.279922	−	0.861511i
$630$		0			0
$631$	−3.17149	+	2.30422i	−0.126255	+	0.0917295i	−0.649121	−	0.760686i	$-0.724863\pi$
$631$	−3.17149	+	2.30422i	−0.126255	+	0.0917295i	0.522866	+	0.852415i	$0.324863\pi$
$632$	9.39935	−	28.9282i	0.373886	−	1.15070i
$633$	8.29369	−	25.5254i	0.329645	−	1.01454i
$634$	1.32307	−	0.961265i	0.0525457	−	0.0381767i
$635$		0			0
$636$	0.0421346	+	0.129677i	0.00167074	+	0.00514202i
$637$	−5.67759			−0.224954
$638$	3.56599	+	25.0794i	0.141179	+	0.992903i
$639$	6.82043			0.269812
$640$		0			0
$641$	−18.0168	−	13.0900i	−0.711622	−	0.517024i	0.172074	−	0.985084i	$-0.444953\pi$
$641$	−18.0168	−	13.0900i	−0.711622	−	0.517024i	−0.883697	+	0.468060i	$0.844953\pi$
$642$	−10.1646	+	7.38504i	−0.401166	+	0.291464i
$643$	4.55565	−	14.0209i	0.179657	−	0.552928i	−0.820158	−	0.572137i	$-0.806115\pi$
$643$	4.55565	−	14.0209i	0.179657	−	0.552928i	0.999816	+	0.0192085i	$0.00611462\pi$
$644$	0.0312310	−	0.0961192i	0.00123067	−	0.00378763i
$645$		0			0
$646$	13.7991	+	10.0257i	0.542920	+	0.394454i
$647$	−5.79882	−	17.8469i	−0.227975	−	0.701635i	−0.997976	−	0.0635925i	$-0.979744\pi$
$647$	−5.79882	−	17.8469i	−0.227975	−	0.701635i	0.770001	−	0.638043i	$-0.220256\pi$
$648$	−2.84193			−0.111641
$649$	13.9821	+	2.44215i	0.548845	+	0.0958626i
$650$		0			0
$651$	1.54332	+	4.74984i	0.0604873	+	0.186161i
$652$	0.268352	+	0.194969i	0.0105095	+	0.00763558i
$653$	−18.3120	+	13.3045i	−0.716605	+	0.520644i	−0.885298	−	0.465025i	$-0.846045\pi$
$653$	−18.3120	+	13.3045i	−0.716605	+	0.520644i	0.168693	+	0.985669i	$0.446045\pi$
$654$	8.19766	−	25.2298i	0.320554	−	0.986564i
$655$		0			0
$656$	18.9337	−	13.7562i	0.739238	−	0.537088i
$657$	2.91403	+	2.11717i	0.113687	+	0.0825987i
$658$	−11.2843	−	34.7296i	−0.439908	−	1.35390i
$659$	20.4233			0.795580			0.397790	−	0.917476i	$-0.369777\pi$
$659$	20.4233			0.795580			0.397790	+	0.917476i	$0.369777\pi$
$660$		0			0
$661$	−12.4374			−0.483758			−0.241879	−	0.970306i	$-0.577764\pi$
$661$	−12.4374			−0.483758			−0.241879	+	0.970306i	$0.577764\pi$
$662$	6.44571	+	19.8379i	0.250520	+	0.771020i
$663$	4.81002	+	3.49469i	0.186806	+	0.135722i
$664$	5.48070	−	3.98196i	0.212692	−	0.154530i
$665$		0			0
$666$	−4.07017	+	12.5267i	−0.157716	+	0.485400i
$667$	−10.6113	+	7.70959i	−0.410873	+	0.298517i
$668$	0.202271	+	0.146958i	0.00782609	+	0.00568599i
$669$	1.80005	+	5.53997i	0.0695938	+	0.214188i
$670$		0			0
$671$	15.3806	−	7.53239i	0.593762	−	0.290785i
$672$	0.236544			0.00912487
$673$	−7.13876	−	21.9708i	−0.275179	−	0.846914i	−0.989172	−	0.146761i	$-0.953115\pi$
$673$	−7.13876	−	21.9708i	−0.275179	−	0.846914i	0.713993	−	0.700153i	$-0.246885\pi$
$674$	−12.9313	−	9.39512i	−0.498094	−	0.361886i
$675$		0			0
$676$	0.0418112	−	0.128682i	0.00160812	−	0.00494929i
$677$	−9.17658	+	28.2426i	−0.352685	+	1.08545i	0.604655	+	0.796487i	$0.293311\pi$
$677$	−9.17658	+	28.2426i	−0.352685	+	1.08545i	−0.957340	+	0.288965i	$0.906689\pi$
$678$	0.799837	−	0.581116i	0.0307176	−	0.0223176i
$679$	−9.23708	−	6.71113i	−0.354487	−	0.257550i
$680$		0			0
$681$	18.2902			0.700883
$682$	10.6130	+	1.85369i	0.406393	+	0.0709816i
$683$	50.1762			1.91994			0.959969	−	0.280105i	$-0.0903694\pi$
$683$	50.1762			1.91994			0.959969	+	0.280105i	$0.0903694\pi$
$684$	0.0298163	+	0.0917653i	0.00114006	+	0.00350873i
$685$		0			0
$686$	−22.9563	+	16.6788i	−0.876477	+	0.636798i
$687$	7.26308	−	22.3535i	0.277104	−	0.852838i
$688$	−3.80719	+	11.7173i	−0.145148	+	0.446719i
$689$	−13.9800	+	10.1571i	−0.532596	+	0.386954i
$690$		0			0
$691$	−7.36152	−	22.6564i	−0.280046	−	0.861892i	−0.987840	−	0.155473i	$-0.950310\pi$
$691$	−7.36152	−	22.6564i	−0.280046	−	0.861892i	0.707795	−	0.706418i	$-0.249690\pi$
$692$	−0.00360649			−0.000137098
$693$	−1.01024	−	7.10496i	−0.0383758	−	0.269895i
$694$	−9.87597			−0.374887
$695$		0			0
$696$	−12.4776	−	9.06551i	−0.472962	−	0.343627i
$697$	−11.6035	+	8.43046i	−0.439515	+	0.319326i
$698$	2.39920	−	7.38397i	0.0908110	−	0.279488i
$699$	8.46541	−	26.0538i	0.320191	−	0.985447i
$700$		0			0
$701$	9.21689	+	6.69646i	0.348117	+	0.252922i	0.748079	−	0.663610i	$-0.230977\pi$
$701$	9.21689	+	6.69646i	0.348117	+	0.252922i	−0.399962	+	0.916532i	$0.630977\pi$
$702$	−1.06518	−	3.27828i	−0.0402026	−	0.123731i
$703$	46.7257			1.76229
$704$	12.5363	−	23.6695i	0.472480	−	0.892078i
$705$		0			0
$706$	−6.37184	−	19.6105i	−0.239808	−	0.738052i
$707$	−27.7028	−	20.1273i	−1.04187	−	0.756964i
$708$	−0.0669112	+	0.0486138i	−0.00251468	+	0.00182702i
$709$	11.9398	−	36.7470i	0.448409	−	1.38006i	−0.430293	−	0.902689i	$-0.641590\pi$
$709$	11.9398	−	36.7470i	0.448409	−	1.38006i	0.878702	−	0.477371i	$-0.158410\pi$
$710$		0			0
$711$	8.65885	−	6.29102i	0.324732	−	0.235932i
$712$	−23.6992	−	17.2185i	−0.888167	−	0.645291i
$713$	1.72383	+	5.30542i	0.0645581	+	0.198689i
$714$	7.39220			0.276646
$715$		0			0
$716$	−0.153423			−0.00573370
$717$	6.77173	+	20.8413i	0.252895	+	0.778331i
$718$	10.0801	+	7.32364i	0.376187	+	0.273316i
$719$	8.83338	−	6.41783i	0.329430	−	0.239345i	−0.410759	−	0.911744i	$-0.634736\pi$
$719$	8.83338	−	6.41783i	0.329430	−	0.239345i	0.740189	+	0.672399i	$0.234736\pi$
$720$		0			0
$721$	−1.16868	+	3.59682i	−0.0435239	+	0.133953i
$722$	−6.74799	+	4.90270i	−0.251134	+	0.182460i
$723$	−18.3674	−	13.3447i	−0.683092	−	0.496296i
$724$	−0.0200240	−	0.0616276i	−0.000744187	−	0.00229037i
$725$		0			0
$726$	−14.5644	−	5.24781i	−0.540536	−	0.194764i
$727$	9.96114			0.369438			0.184719	−	0.982791i	$-0.440862\pi$
$727$	9.96114			0.369438			0.184719	+	0.982791i	$0.440862\pi$
$728$	4.65415	+	14.3240i	0.172494	+	0.530883i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	2.33323	−	7.18096i	0.0862978	−	0.265597i
$732$	−0.0308377	+	0.0949087i	−0.00113979	+	0.00350793i
$733$	4.28172	−	3.11085i	0.158149	−	0.114902i	−0.505896	−	0.862594i	$-0.668838\pi$
$733$	4.28172	−	3.11085i	0.158149	−	0.114902i	0.664045	+	0.747692i	$0.268838\pi$
$734$	−24.5346	−	17.8255i	−0.905590	−	0.657950i
$735$		0			0
$736$	0.264212			0.00973897
$737$	32.5066	+	33.5530i	1.19740	+	1.23594i
$738$	8.31540			0.306094
$739$	−4.01822	−	12.3668i	−0.147813	−	0.454920i	0.849549	−	0.527509i	$-0.176874\pi$
$739$	−4.01822	−	12.3668i	−0.147813	−	0.454920i	−0.997362	+	0.0725887i	$0.976874\pi$
$740$		0			0
$741$	−9.89290	+	7.18761i	−0.363425	+	0.264043i
$742$	−6.63921	+	20.4334i	−0.243733	+	0.750134i
$743$	16.6940	−	51.3789i	0.612444	−	1.88491i	0.178599	−	0.983922i	$-0.442844\pi$
$743$	16.6940	−	51.3789i	0.612444	−	1.88491i	0.433845	−	0.900987i	$-0.357156\pi$
$744$	−5.30678	+	3.85560i	−0.194556	+	0.141353i
$745$		0			0
$746$	−1.85449	−	5.70753i	−0.0678977	−	0.208968i
$747$	2.38378			0.0872178
$748$	−0.0728249	+	0.137499i	−0.00266274	+	0.00502746i
$749$	19.3170			0.705827
$750$		0			0
$751$	35.5526	+	25.8305i	1.29733	+	0.942567i	0.999926	−	0.0121839i	$-0.00387834\pi$
$751$	35.5526	+	25.8305i	1.29733	+	0.942567i	0.297407	+	0.954751i	$0.403878\pi$
$752$	38.4268	−	27.9187i	1.40128	−	1.01809i
$753$	−0.804148	+	2.47491i	−0.0293048	+	0.0901908i
$754$	5.78074	−	17.7913i	0.210522	−	0.647920i
$755$		0			0
$756$	0.0338306	+	0.0245793i	0.00123041	+	0.000893942i
$757$	6.18371	+	19.0315i	0.224751	+	0.691712i	0.998317	+	0.0579961i	$0.0184711\pi$
$757$	6.18371	+	19.0315i	0.224751	+	0.691712i	−0.773566	+	0.633716i	$0.781529\pi$
$758$	−52.0873			−1.89190
$759$	−1.12841	−	7.93601i	−0.0409585	−	0.288059i
$760$		0			0
$761$	5.44929	+	16.7712i	0.197536	+	0.607955i	0.999938	+	0.0111696i	$0.00355548\pi$
$761$	5.44929	+	16.7712i	0.197536	+	0.607955i	−0.802401	+	0.596785i	$0.796445\pi$
$762$	21.9626	+	15.9568i	0.795622	+	0.578054i
$763$	−32.9967	+	23.9735i	−1.19456	+	0.867899i
$764$	−0.141036	+	0.434064i	−0.00510250	+	0.0157039i
$765$		0			0
$766$	−11.2088	+	8.14364i	−0.404989	+	0.294242i
$767$	−8.47994	−	6.16104i	−0.306193	−	0.222462i
$768$	0.143315	+	0.441080i	0.00517145	+	0.0159161i
$769$	−37.2865			−1.34458			−0.672292	−	0.740286i	$-0.734690\pi$
$769$	−37.2865			−1.34458			−0.672292	+	0.740286i	$0.734690\pi$
$770$		0			0
$771$	16.9205			0.609377
$772$	−0.0805795	−	0.247998i	−0.00290012	−	0.00892565i
$773$	16.5413	+	12.0180i	0.594949	+	0.432256i	0.844082	−	0.536213i	$-0.180146\pi$
$773$	16.5413	+	12.0180i	0.594949	+	0.432256i	−0.249134	+	0.968469i	$0.580146\pi$
$774$	−3.54148	+	2.57303i	−0.127296	+	0.0924858i
$775$		0			0
$776$	4.63405	−	14.2621i	0.166353	−	0.511981i
$777$	16.3830	−	11.9029i	0.587736	−	0.427015i
$778$	3.34763	+	2.43220i	0.120018	+	0.0871985i
$779$	−9.11572	−	28.0553i	−0.326605	−	1.00519i
$780$		0			0
$781$	−20.3154	+	9.94912i	−0.726942	+	0.356008i
$782$	8.25686			0.295265
$783$	−1.67704	−	5.16139i	−0.0599324	−	0.184453i
$784$	−7.42832	−	5.39699i	−0.265297	−	0.192750i
$785$		0			0
$786$	0.318150	−	0.979166i	0.0113480	−	0.0349257i
$787$	−1.30809	+	4.02588i	−0.0466283	+	0.143507i	−0.971660	−	0.236383i	$-0.924038\pi$
$787$	−1.30809	+	4.02588i	−0.0466283	+	0.143507i	0.925032	+	0.379890i	$0.124038\pi$
$788$	0.312678	−	0.227174i	0.0111387	−	0.00809275i
$789$	−14.4689	−	10.5122i	−0.515105	−	0.374246i
$790$		0			0
$791$	−1.52002			−0.0540457
$792$	8.46499	−	4.14559i	0.300790	−	0.147307i
$793$	−12.6472			−0.449114
$794$	−15.0916	−	46.4471i	−0.535580	−	1.64835i
$795$		0			0
$796$	0.142011	−	0.103177i	0.00503344	−	0.00365701i
$797$	−5.24688	+	16.1482i	−0.185854	+	0.572000i	−0.999962	−	0.00871342i	$-0.997226\pi$
$797$	−5.24688	+	16.1482i	−0.185854	+	0.572000i	0.814108	+	0.580714i	$0.197226\pi$
$798$	−4.69821	+	14.4596i	−0.166315	+	0.511864i
$799$	−23.5499	+	17.1100i	−0.833134	+	0.605307i
$800$		0			0
$801$	−3.18527	−	9.80326i	−0.112546	−	0.346381i
$802$	−15.1347			−0.534425
$803$	−11.7681	−	2.05545i	−0.415289	−	0.0725353i
$804$	−0.272219			−0.00960044
$805$		0			0
$806$	−6.43663	−	4.67649i	−0.226721	−	0.164722i
$807$	−23.2863	+	16.9185i	−0.819716	+	0.595559i
$808$	13.8979	−	42.7734i	0.488927	−	1.50476i
$809$	−4.32523	+	13.3117i	−0.152067	+	0.468014i	−0.997852	−	0.0655098i	$-0.979133\pi$
$809$	−4.32523	+	13.3117i	−0.152067	+	0.468014i	0.845785	+	0.533524i	$0.179133\pi$
$810$		0			0
$811$	39.4928	+	28.6932i	1.38678	+	1.00755i	0.996210	+	0.0869816i	$0.0277221\pi$
$811$	39.4928	+	28.6932i	1.38678	+	1.00755i	0.390570	+	0.920573i	$0.372278\pi$
$812$	0.0701285	+	0.215833i	0.00246103	+	0.00757426i
$813$	−22.3952			−0.785434
$814$	−6.14955	−	43.2494i	−0.215542	−	1.51589i
$815$		0			0
$816$	2.97126	+	9.14459i	0.104015	+	0.320125i
$817$	12.5635	+	9.12790i	0.439541	+	0.319345i
$818$	22.5896	−	16.4123i	0.789828	−	0.573844i
$819$	−1.63767	+	5.04024i	−0.0572250	+	0.176120i
$820$		0			0
$821$	22.8707	−	16.6165i	0.798192	−	0.579920i	−0.112191	−	0.993687i	$-0.535787\pi$
$821$	22.8707	−	16.6165i	0.798192	−	0.579920i	0.910383	+	0.413766i	$0.135787\pi$
$822$	−15.3694	−	11.1666i	−0.536071	−	0.389478i
$823$	−5.14035	−	15.8204i	−0.179181	−	0.551463i	0.820619	−	0.571476i	$-0.193629\pi$
$823$	−5.14035	−	15.8204i	−0.179181	−	0.551463i	−0.999800	+	0.0200134i	$0.993629\pi$
$824$	−4.96723			−0.173042
$825$		0			0
$826$	−13.0322			−0.453450
$827$	−9.88523	−	30.4236i	−0.343743	−	1.05793i	−0.962253	−	0.272156i	$-0.912263\pi$
$827$	−9.88523	−	30.4236i	−0.343743	−	1.05793i	0.618510	−	0.785777i	$-0.287737\pi$
$828$	0.0377877	+	0.0274543i	0.00131321	+	0.000954104i
$829$	−43.3871	+	31.5226i	−1.50690	+	1.09482i	−0.539366	+	0.842071i	$0.681336\pi$
$829$	−43.3871	+	31.5226i	−1.50690	+	1.09482i	−0.967531	+	0.252754i	$0.918664\pi$
$830$		0			0
$831$	0.845202	−	2.60126i	0.0293197	−	0.0902368i
$832$	−16.0021	+	11.6262i	−0.554773	+	0.403066i
$833$	4.55244	+	3.30754i	0.157733	+	0.114599i
$834$	7.08559	+	21.8072i	0.245354	+	0.755122i
$835$		0			0
$836$	−0.222672	−	0.229839i	−0.00770126	−	0.00794916i
$837$	−2.30813			−0.0797808
$838$	11.5584	+	35.5730i	0.399277	+	1.22885i
$839$	−30.6044	−	22.2354i	−1.05658	−	0.767652i	−0.0831294	−	0.996539i	$-0.526491\pi$
$839$	−30.6044	−	22.2354i	−1.05658	−	0.767652i	−0.973453	+	0.228887i	$0.926491\pi$
$840$		0			0
$841$	0.139804	−	0.430274i	0.00482084	−	0.0148370i
$842$	−17.4058	+	53.5696i	−0.599844	+	1.84613i
$843$	3.65261	−	2.65378i	0.125803	−	0.0914010i
$844$	−0.419627	−	0.304877i	−0.0144441	−	0.0104943i
$845$		0			0
$846$	16.8765			0.580225
$847$	13.3733	+	19.6892i	0.459511	+	0.676530i
$848$	−27.9459			−0.959667
$849$	4.21178	+	12.9625i	0.144548	+	0.444872i
$850$		0			0
$851$	18.2993	−	13.2952i	0.627291	−	0.455754i
$852$	0.0407318	−	0.125360i	0.00139545	−	0.00429475i
$853$	−6.85633	+	21.1016i	−0.234756	+	0.722505i	0.762397	+	0.647109i	$0.224022\pi$
$853$	−6.85633	+	21.1016i	−0.234756	+	0.722505i	−0.997154	+	0.0753962i	$0.975978\pi$
$854$	−12.7214	+	9.24265i	−0.435318	+	0.316277i
$855$		0			0
$856$	7.84013	+	24.1294i	0.267970	+	0.824727i
$857$	13.7471			0.469592			0.234796	−	0.972045i	$-0.424558\pi$
$857$	13.7471			0.469592			0.234796	+	0.972045i	$0.424558\pi$
$858$	7.95487	+	8.21093i	0.271575	+	0.280317i
$859$	43.9972			1.50117			0.750583	−	0.660776i	$-0.229773\pi$
$859$	43.9972			1.50117			0.750583	+	0.660776i	$0.229773\pi$
$860$		0			0
$861$	−10.3430	−	7.51462i	−0.352488	−	0.256097i
$862$	−22.3514	+	16.2393i	−0.761292	+	0.553111i
$863$	−1.62747	+	5.00883i	−0.0553996	+	0.170502i	−0.974928	−	0.222522i	$-0.928571\pi$
$863$	−1.62747	+	5.00883i	−0.0553996	+	0.170502i	0.919528	+	0.393024i	$0.128571\pi$
$864$	−0.0337817	+	0.103970i	−0.00114928	+	0.00353712i
$865$		0			0
$866$	−45.6267	−	33.1498i	−1.55046	−	1.12647i
$867$	3.43236	+	10.5637i	0.116569	+	0.358762i
$868$	0.0965189			0.00327606
$869$	−16.6145	+	31.3694i	−0.563607	+	1.06413i
$870$		0			0
$871$	−10.6609	−	32.8110i	−0.361232	−	1.11176i
$872$	−43.3383	−	31.4871i	−1.46762	−	1.06629i
$873$	4.26897	−	3.10159i	0.144483	−	0.104973i
$874$	−5.24775	+	16.1509i	−0.177508	+	0.546313i
$875$		0			0
$876$	0.0563164	−	0.0409162i	0.00190275	−	0.00138243i
$877$	−0.243619	−	0.177000i	−0.00822643	−	0.00597685i	0.583664	−	0.811995i	$-0.301618\pi$
$877$	−0.243619	−	0.177000i	−0.00822643	−	0.00597685i	−0.591891	+	0.806018i	$0.701618\pi$
$878$	3.19490	+	9.83288i	0.107823	+	0.331844i
$879$	−10.7326			−0.362001
$880$		0			0
$881$	24.5711			0.827821			0.413911	−	0.910318i	$-0.364163\pi$
$881$	24.5711			0.827821			0.413911	+	0.910318i	$0.364163\pi$
$882$	−1.00814	−	3.10273i	−0.0339457	−	0.104474i
$883$	−1.68153	−	1.22170i	−0.0565880	−	0.0411136i	0.559132	−	0.829079i	$-0.311135\pi$
$883$	−1.68153	−	1.22170i	−0.0565880	−	0.0411136i	−0.615720	+	0.787965i	$0.711135\pi$
$884$	0.0929581	−	0.0675380i	0.00312652	−	0.00227155i
$885$		0			0
$886$	12.0505	−	37.0878i	0.404846	−	1.24599i
$887$	−24.7103	+	17.9531i	−0.829689	+	0.602805i	−0.919471	−	0.393157i	$-0.871383\pi$
$887$	−24.7103	+	17.9531i	−0.829689	+	0.602805i	0.0897821	+	0.995961i	$0.471383\pi$
$888$	21.5176	+	15.6335i	0.722084	+	0.524625i
$889$	−12.8978	−	39.6952i	−0.432577	−	1.33133i
$890$		0			0
$891$	3.26716	+	0.570651i	0.109454	+	0.0191175i
$892$	0.112575			0.00376928
$893$	−18.5007	−	56.9395i	−0.619104	−	1.90541i
$894$	2.23699	+	1.62527i	0.0748160	+	0.0543570i
$895$		0			0
$896$	−7.45333	+	22.9390i	−0.248998	+	0.766337i
$897$	−1.82923	+	5.62979i	−0.0610762	+	0.187973i
$898$	3.78521	−	2.75011i	0.126314	−	0.0917725i
$899$	−10.1340	−	7.36275i	−0.337986	−	0.245561i
$900$		0			0
$901$	17.1266			0.570571
$902$	−24.7683	+	12.1299i	−0.824696	+	0.403881i
$903$	6.73026			0.223969
$904$	−0.616926	−	1.89870i	−0.0205186	−	0.0631499i
$905$		0			0
$906$	7.30413	−	5.30676i	0.242664	−	0.176305i
$907$	11.0784	−	34.0958i	0.367852	−	1.13213i	−0.580323	−	0.814386i	$-0.697074\pi$
$907$	11.0784	−	34.0958i	0.367852	−	1.13213i	0.948176	−	0.317747i	$-0.102926\pi$
$908$	0.109230	−	0.336175i	0.00362492	−	0.0111564i
$909$	12.8030	−	9.30194i	0.424649	−	0.308526i
$910$		0			0
$911$	2.90393	+	8.93737i	0.0962114	+	0.296108i	0.987568	−	0.157195i	$-0.0502453\pi$
$911$	2.90393	+	8.93737i	0.0962114	+	0.296108i	−0.891356	+	0.453304i	$0.850245\pi$
$912$	−19.7758			−0.654842
$913$	−7.10034	+	3.47727i	−0.234987	+	0.115081i
$914$	24.9516			0.825324
$915$		0			0
$916$	−0.367482	−	0.266991i	−0.0121420	−	0.00882164i
$917$	−1.28060	+	0.930408i	−0.0422890	+	0.0307248i
$918$	−1.05571	+	3.24914i	−0.0348436	+	0.107238i
$919$	−0.265339	+	0.816629i	−0.00875272	+	0.0269381i	−0.955337	−	0.295517i	$-0.904508\pi$
$919$	−0.265339	+	0.816629i	−0.00875272	+	0.0269381i	0.946585	+	0.322455i	$0.104508\pi$
$920$		0			0
$921$	4.10747	+	2.98425i	0.135346	+	0.0983345i
$922$	−10.6273	−	32.7075i	−0.349992	−	1.07716i
$923$	16.7050			0.549850
$924$	−0.136623	−	0.0238628i	−0.00449455	−	0.000785029i
$925$		0			0
$926$	10.0686	+	30.9880i	0.330875	+	1.01833i
$927$	−1.41403	−	1.02735i	−0.0464429	−	0.0337427i
$928$	−0.479974	+	0.348722i	−0.0157559	+	0.0114473i
$929$	12.4105	−	38.1955i	0.407174	−	1.25315i	−0.511892	−	0.859050i	$-0.671055\pi$
$929$	12.4105	−	38.1955i	0.407174	−	1.25315i	0.919066	−	0.394103i	$-0.128945\pi$
$930$		0			0
$931$	−9.36311	+	6.80270i	−0.306864	+	0.222950i
$932$	−0.428315	−	0.311189i	−0.0140299	−	0.0101933i
$933$	1.25992	+	3.87764i	0.0412480	+	0.126948i
$934$	32.5665			1.06561
$935$		0			0
$936$	−6.96060			−0.227514
$937$	−9.75230	−	30.0145i	−0.318594	−	0.980530i	−0.974250	−	0.225471i	$-0.927608\pi$
$937$	−9.75230	−	30.0145i	−0.318594	−	0.980530i	0.655656	−	0.755060i	$-0.272392\pi$
$938$	−34.7020	−	25.2125i	−1.13306	−	0.823217i
$939$	−23.7258	+	17.2378i	−0.774261	+	0.562534i
$940$		0			0
$941$	3.39145	−	10.4378i	0.110558	−	0.340263i	−0.880437	−	0.474164i	$-0.842750\pi$
$941$	3.39145	−	10.4378i	0.110558	−	0.340263i	0.990995	+	0.133901i	$0.0427504\pi$
$942$	−11.5009	+	8.35591i	−0.374720	+	0.272250i
$943$	−11.5528	−	8.39359i	−0.376211	−	0.273333i
$944$	−5.23824	−	16.1217i	−0.170490	−	0.524715i
$945$		0			0
$946$	6.79534	−	12.8301i	0.220935	−	0.417143i
$947$	32.3272			1.05049			0.525246	−	0.850951i	$-0.323973\pi$
$947$	32.3272			1.05049			0.525246	+	0.850951i	$0.323973\pi$
$948$	−0.0639182	−	0.196720i	−0.00207597	−	0.00638917i
$949$	7.13721	+	5.18549i	0.231684	+	0.168328i
$950$		0			0
$951$	0.359088	−	1.10516i	0.0116442	−	0.0358372i
$952$	4.61278	−	14.1967i	0.149501	−	0.460117i
$953$	−3.68704	+	2.67879i	−0.119435	+	0.0867746i	−0.645899	−	0.763423i	$-0.723517\pi$
$953$	−3.68704	+	2.67879i	−0.119435	+	0.0867746i	0.526464	+	0.850197i	$0.323517\pi$
$954$	−8.03305	−	5.83635i	−0.260080	−	0.188959i
$955$		0			0
$956$	0.423504			0.0136971
$957$	12.5243	+	12.9274i	0.404853	+	0.417885i
$958$	−15.1565			−0.489684
$959$	9.02584	+	27.7787i	0.291460	+	0.897021i
$960$		0			0
$961$	20.7695	−	15.0899i	0.669984	−	0.486772i
$962$	−9.96888	+	30.6811i	−0.321410	+	0.989197i
$963$	−2.75874	+	8.49052i	−0.0888990	+	0.273603i
$964$	−0.354968	+	0.257899i	−0.0114327	+	0.00830637i
$965$		0			0
$966$	2.27433	+	6.99966i	0.0731752	+	0.225210i
$967$	3.69371			0.118782			0.0593909	−	0.998235i	$-0.481084\pi$
$967$	3.69371			0.118782			0.0593909	+	0.998235i	$0.481084\pi$
$968$	−19.1667	+	24.6962i	−0.616040	+	0.793766i
$969$	12.1196			0.389337
$970$		0			0
$971$	43.1697	+	31.3646i	1.38538	+	1.00654i	0.996354	+	0.0853116i	$0.0271886\pi$
$971$	43.1697	+	31.3646i	1.38538	+	1.00654i	0.389027	+	0.921227i	$0.372811\pi$
$972$	−0.0156350	+	0.0113595i	−0.000501493	+	0.000364356i
$973$	10.8938	−	33.5278i	0.349240	−	1.07485i
$974$	−8.04197	+	24.7506i	−0.257681	+	0.793061i
$975$		0			0
$976$	−16.5470	−	12.0221i	−0.529657	−	0.384818i
$977$	−11.2675	−	34.6777i	−0.360479	−	1.10944i	−0.952764	−	0.303711i	$-0.901774\pi$
$977$	−11.2675	−	34.6777i	−0.360479	−	1.10944i	0.592286	−	0.805728i	$-0.298226\pi$
$978$	−24.1554			−0.772403
$979$	23.7879	+	24.5537i	0.760266	+	0.784738i
$980$		0			0
$981$	−5.82483	−	17.9270i	−0.185973	−	0.572365i
$982$	40.2923	+	29.2741i	1.28578	+	0.934173i
$983$	4.15822	−	3.02113i	0.132627	−	0.0963590i	−0.519494	−	0.854474i	$-0.673880\pi$
$983$	4.15822	−	3.02113i	0.132627	−	0.0963590i	0.652121	+	0.758115i	$0.273880\pi$
$984$	5.18886	−	15.9697i	0.165415	−	0.509095i
$985$		0			0
$986$	−14.9996	+	10.8979i	−0.477685	+	0.347059i
$987$	−20.9915	−	15.2512i	−0.668168	−	0.485452i
$988$	0.0730278	+	0.224756i	0.00232332	+	0.00715045i
$989$	7.51749			0.239042
$990$		0			0
$991$	−57.4924			−1.82631			−0.913154	−	0.407616i	$-0.866360\pi$
$991$	−57.4924			−1.82631			−0.913154	+	0.407616i	$0.866360\pi$
$992$	0.0779728	+	0.239976i	0.00247564	+	0.00761923i
$993$	11.9906	+	8.71165i	0.380509	+	0.276456i
$994$	16.8030	−	12.2081i	0.532959	−	0.387218i
$995$		0			0
$996$	0.0142360	−	0.0438139i	0.000451085	−	0.00138830i
$997$	5.40487	−	3.92687i	0.171174	−	0.124365i	−0.498900	−	0.866660i	$-0.666262\pi$
$997$	5.40487	−	3.92687i	0.171174	−	0.124365i	0.670074	+	0.742295i	$0.266262\pi$
$998$	4.59236	+	3.33654i	0.145368	+	0.105616i
$999$	2.89205	+	8.90082i	0.0915005	+	0.281610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.n.676.3	yes	16
5.2	odd	4		825.2.bx.j.49.3		32
5.3	odd	4		825.2.bx.j.49.6		32
5.4	even	2		825.2.n.m.676.2	yes	16
11.3	even	5		9075.2.a.dv.1.6		8
11.8	odd	10		9075.2.a.dt.1.3		8
11.9	even	5	inner	825.2.n.n.526.3	yes	16
55.9	even	10		825.2.n.m.526.2	✓	16
55.14	even	10		9075.2.a.du.1.3		8
55.19	odd	10		9075.2.a.dw.1.6		8
55.42	odd	20		825.2.bx.j.724.6		32
55.53	odd	20		825.2.bx.j.724.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.n.m.526.2	✓	16	55.9	even	10
825.2.n.m.676.2	yes	16	5.4	even	2
825.2.n.n.526.3	yes	16	11.9	even	5	inner
825.2.n.n.676.3	yes	16	1.1	even	1	trivial
825.2.bx.j.49.3		32	5.2	odd	4
825.2.bx.j.49.6		32	5.3	odd	4
825.2.bx.j.724.3		32	55.53	odd	20
825.2.bx.j.724.6		32	55.42	odd	20
9075.2.a.dt.1.3		8	11.8	odd	10
9075.2.a.du.1.3		8	55.14	even	10
9075.2.a.dv.1.6		8	11.3	even	5
9075.2.a.dw.1.6		8	55.19	odd	10

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.434899 + 1.33848i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.0156350 - 0.0113595i) q^{4} +(-0.434899 + 1.33848i) q^{6} +(1.75053 - 1.27183i) q^{7} +(2.29917 + 1.67044i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-2.30777 - 2.38206i) q^{11} +0.0193259 q^{12} +(0.756861 + 2.32938i) q^{13} +(2.46363 + 1.78993i) q^{14} +(-1.22401 + 3.76711i) q^{16} +(0.750133 - 2.30867i) q^{17} +(-1.13858 + 0.827228i) q^{18} +(4.03915 + 2.93461i) q^{19} +2.16377 q^{21} +(2.18469 - 4.12487i) q^{22} +2.41686 q^{23} +(0.878204 + 2.70283i) q^{24} +(-2.78868 + 2.02609i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.0129221 - 0.0397702i) q^{28} +(-4.39054 + 3.18992i) q^{29} +(0.713252 + 2.19517i) q^{31} +0.109320 q^{32} +(-0.466888 - 3.28360i) q^{33} +3.41635 q^{34} +(0.0156350 + 0.0113595i) q^{36} +(7.57149 - 5.50101i) q^{37} +(-2.17131 + 6.68259i) q^{38} +(-0.756861 + 2.32938i) q^{39} +(-4.78007 - 3.47293i) q^{41} +(0.941023 + 2.89617i) q^{42} +3.11043 q^{43} +(-0.0631409 - 0.0110283i) q^{44} +(1.05109 + 3.23493i) q^{46} +(-9.70136 - 7.04845i) q^{47} +(-3.20450 + 2.32820i) q^{48} +(-0.716330 + 2.20464i) q^{49} +(1.96387 - 1.42684i) q^{51} +(0.0382941 + 0.0278223i) q^{52} +(2.18021 + 6.71000i) q^{53} -1.40736 q^{54} +6.14928 q^{56} +(1.54282 + 4.74830i) q^{57} +(-6.17909 - 4.48937i) q^{58} +(-3.46225 + 2.51548i) q^{59} +(-1.59567 + 4.91096i) q^{61} +(-2.62800 + 1.90935i) q^{62} +(1.75053 + 1.27183i) q^{63} +(2.49556 + 7.68054i) q^{64} +(4.19199 - 2.05296i) q^{66} -14.0857 q^{67} +(-0.0144970 - 0.0446172i) q^{68} +(1.95528 + 1.42060i) q^{69} +(2.10763 - 6.48661i) q^{71} +(-0.878204 + 2.70283i) q^{72} +(2.91403 - 2.11717i) q^{73} +(10.6558 + 7.74193i) q^{74} +0.0964877 q^{76} +(-7.06940 - 1.23476i) q^{77} -3.44699 q^{78} +(-3.30738 - 10.1791i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(2.56960 - 7.90842i) q^{82} +(0.736627 - 2.26711i) q^{83} +(0.0338306 - 0.0245793i) q^{84} +(1.35272 + 4.16326i) q^{86} -5.42701 q^{87} +(-1.32686 - 9.33175i) q^{88} -10.3078 q^{89} +(4.28749 + 3.11504i) q^{91} +(0.0377877 - 0.0274543i) q^{92} +(-0.713252 + 2.19517i) q^{93} +(5.21511 - 16.0505i) q^{94} +(0.0884418 + 0.0642567i) q^{96} +(-1.63060 - 5.01848i) q^{97} -3.26240 q^{98} +(1.55233 - 2.93092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 2 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 3 q^{11} - 14 q^{12} - 11 q^{13} + 4 q^{14} + 16 q^{16} - 17 q^{17} - 3 q^{18} + 8 q^{19} - 16 q^{21} - 23 q^{22} - 14 q^{23}+ \cdots + 8 q^{99}+O(q^{100}) \) 16 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 - 2 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 3 * q^11 - 14 * q^12 - 11 * q^13 + 4 * q^14 + 16 * q^16 - 17 * q^17 - 3 * q^18 + 8 * q^19 - 16 * q^21 - 23 * q^22 - 14 * q^23 - q^24 + 33 * q^26 + 4 * q^27 + 7 * q^28 + 4 * q^29 - 5 * q^31 + 24 * q^32 + 12 * q^33 - 16 * q^34 - 6 * q^36 + 2 * q^37 - 3 * q^38 + 11 * q^39 + 2 * q^41 - 4 * q^42 + 22 * q^43 - 40 * q^46 - 20 * q^47 + 9 * q^48 - 26 * q^49 - 18 * q^51 - 43 * q^52 + 40 * q^53 - 2 * q^54 - 8 * q^56 + 2 * q^57 + 26 * q^58 + 6 * q^59 - 2 * q^61 + 26 * q^62 - 4 * q^63 + 4 * q^64 - 7 * q^66 - 12 * q^67 - 56 * q^68 + 4 * q^69 + 11 * q^71 + q^72 - 21 * q^73 + 66 * q^74 - 10 * q^76 + 23 * q^77 + 2 * q^78 - 7 * q^79 - 4 * q^81 + 20 * q^82 + 13 * q^83 + 18 * q^84 + 37 * q^86 + 56 * q^87 + 26 * q^88 + 42 * q^89 + 2 * q^91 + 92 * q^92 + 5 * q^93 + 88 * q^94 + 11 * q^96 - 27 * q^97 - 54 * q^98 + 8 * q^99

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