LMFDB - Embedded newform 966.2.k.a.229.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(229,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("966.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.13
Character	$\chi$	$=$	966.229
Dual form			966.2.k.a.367.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.242904 - 0.420722i) q^{5} +1.00000i q^{6} +(2.51079 + 0.834227i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.242904 - 0.420722i) q^{5} +1.00000i q^{6} +(2.51079 + 0.834227i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.242904 + 0.420722i) q^{10} +(-2.65306 + 1.53174i) q^{11} +(-0.866025 - 0.500000i) q^{12} +5.07423i q^{13} +(-1.97786 + 1.75729i) q^{14} -0.485808i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.418779 - 0.725347i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.41446 + 5.91401i) q^{19} -0.485808 q^{20} +(2.59152 - 0.532933i) q^{21} -3.06349i q^{22} +(4.78706 - 0.289912i) q^{23} +(0.866025 - 0.500000i) q^{24} +(2.38200 + 4.12574i) q^{25} +(-4.39441 - 2.53711i) q^{26} -1.00000i q^{27} +(-0.532933 - 2.59152i) q^{28} +4.62895 q^{29} +(0.420722 + 0.242904i) q^{30} +(7.97469 - 4.60419i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.53174 + 2.65306i) q^{33} +0.837558 q^{34} +(0.960858 - 0.853707i) q^{35} -1.00000 q^{36} +(-4.82160 - 2.78375i) q^{37} +(-3.41446 - 5.91401i) q^{38} +(2.53711 + 4.39441i) q^{39} +(0.242904 - 0.420722i) q^{40} -8.68814i q^{41} +(-0.834227 + 2.51079i) q^{42} +5.27242i q^{43} +(2.65306 + 1.53174i) q^{44} +(-0.242904 - 0.420722i) q^{45} +(-2.14246 + 4.29067i) q^{46} +(3.68699 + 2.12869i) q^{47} +1.00000i q^{48} +(5.60813 + 4.18914i) q^{49} -4.76399 q^{50} +(-0.725347 - 0.418779i) q^{51} +(4.39441 - 2.53711i) q^{52} +(7.31519 - 4.22343i) q^{53} +(0.866025 + 0.500000i) q^{54} +1.48827i q^{55} +(2.51079 + 0.834227i) q^{56} +6.82891i q^{57} +(-2.31447 + 4.00878i) q^{58} +(-3.15927 + 1.82401i) q^{59} +(-0.420722 + 0.242904i) q^{60} +(-4.90732 + 8.49972i) q^{61} +9.20838i q^{62} +(1.97786 - 1.75729i) q^{63} +1.00000 q^{64} +(2.13484 + 1.23255i) q^{65} +(-1.53174 - 2.65306i) q^{66} +(-3.54252 + 2.04527i) q^{67} +(-0.418779 + 0.725347i) q^{68} +(4.00076 - 2.64460i) q^{69} +(0.258903 + 1.25898i) q^{70} -1.32082 q^{71} +(0.500000 - 0.866025i) q^{72} +(3.26928 - 1.88752i) q^{73} +(4.82160 - 2.78375i) q^{74} +(4.12574 + 2.38200i) q^{75} +6.82891 q^{76} +(-7.93909 + 1.63263i) q^{77} -5.07423 q^{78} +(-9.12312 - 5.26723i) q^{79} +(0.242904 + 0.420722i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.52415 + 4.34407i) q^{82} +6.95787 q^{83} +(-1.75729 - 1.97786i) q^{84} -0.406892 q^{85} +(-4.56605 - 2.63621i) q^{86} +(4.00878 - 2.31447i) q^{87} +(-2.65306 + 1.53174i) q^{88} +(-5.22221 + 9.04513i) q^{89} +0.485808 q^{90} +(-4.23305 + 12.7403i) q^{91} +(-2.64460 - 4.00076i) q^{92} +(4.60419 - 7.97469i) q^{93} +(-3.68699 + 2.12869i) q^{94} +(1.65877 + 2.87307i) q^{95} +(-0.866025 - 0.500000i) q^{96} +9.53965 q^{97} +(-6.43196 + 2.76222i) q^{98} +3.06349i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9} - 16 q^{16} + 16 q^{18} + 8 q^{23} - 24 q^{25} - 12 q^{26} - 8 q^{29} + 48 q^{31} - 16 q^{32} - 20 q^{35} - 32 q^{36} - 8 q^{39} + 8 q^{46} + 12 q^{47} + 24 q^{49} + 48 q^{50} + 12 q^{52} + 4 q^{58} - 12 q^{59} + 32 q^{64} + 64 q^{70} + 48 q^{71} + 16 q^{72} + 12 q^{73} + 36 q^{75} + 64 q^{77} + 16 q^{78} - 16 q^{81} - 12 q^{82} + 32 q^{85} - 24 q^{87} - 16 q^{92} - 12 q^{94} + 40 q^{95} - 24 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9 - 16 * q^16 + 16 * q^18 + 8 * q^23 - 24 * q^25 - 12 * q^26 - 8 * q^29 + 48 * q^31 - 16 * q^32 - 20 * q^35 - 32 * q^36 - 8 * q^39 + 8 * q^46 + 12 * q^47 + 24 * q^49 + 48 * q^50 + 12 * q^52 + 4 * q^58 - 12 * q^59 + 32 * q^64 + 64 * q^70 + 48 * q^71 + 16 * q^72 + 12 * q^73 + 36 * q^75 + 64 * q^77 + 16 * q^78 - 16 * q^81 - 12 * q^82 + 32 * q^85 - 24 * q^87 - 16 * q^92 - 12 * q^94 + 40 * q^95 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.242904	−	0.420722i	0.108630	−	0.188153i	−0.806586	−	0.591117i	$-0.798687\pi$
$5$	0.242904	−	0.420722i	0.108630	−	0.188153i	0.915215	+	0.402965i	$0.132020\pi$
$6$			1.00000i			0.408248i
$7$	2.51079	+	0.834227i	0.948989	+	0.315308i
$7$	2.51079	+	0.834227i	0.948989	+	0.315308i
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.242904	+	0.420722i	0.0768130	+	0.133044i
$11$	−2.65306	+	1.53174i	−0.799927	+	0.461838i	−0.843446	−	0.537215i	$-0.819476\pi$
$11$	−2.65306	+	1.53174i	−0.799927	+	0.461838i	0.0435188	+	0.999053i	$0.486143\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$			5.07423i			1.40734i	0.710528	+	0.703668i	$0.248456\pi$
$13$			5.07423i			1.40734i	−0.710528	+	0.703668i	$0.751544\pi$
$14$	−1.97786	+	1.75729i	−0.528604	+	0.469657i
$15$		−	0.485808i		−	0.125435i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.418779	−	0.725347i	−0.101569	−	0.175922i	0.810762	−	0.585375i	$-0.199053\pi$
$17$	−0.418779	−	0.725347i	−0.101569	−	0.175922i	−0.912331	+	0.409453i	$0.865720\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−3.41446	+	5.91401i	−0.783330	+	1.35677i	0.146662	+	0.989187i	$0.453147\pi$
$19$	−3.41446	+	5.91401i	−0.783330	+	1.35677i	−0.929992	+	0.367580i	$0.880186\pi$
$20$	−0.485808			−0.108630
$21$	2.59152	−	0.532933i	0.565516	−	0.116296i
$22$		−	3.06349i		−	0.653137i
$23$	4.78706	−	0.289912i	0.998171	−	0.0604509i
$23$	4.78706	−	0.289912i	0.998171	−	0.0604509i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	2.38200	+	4.12574i	0.476399	+	0.825147i
$26$	−4.39441	−	2.53711i	−0.861814	−	0.497569i
$27$		−	1.00000i		−	0.192450i
$28$	−0.532933	−	2.59152i	−0.100715	−	0.489751i
$29$	4.62895			0.859574			0.429787	−	0.902930i	$-0.358589\pi$
$29$	4.62895			0.859574			0.429787	+	0.902930i	$0.358589\pi$
$30$	0.420722	+	0.242904i	0.0768130	+	0.0443480i
$31$	7.97469	−	4.60419i	1.43230	−	0.826937i	0.435002	−	0.900430i	$-0.356748\pi$
$31$	7.97469	−	4.60419i	1.43230	−	0.826937i	0.997296	+	0.0734924i	$0.0234145\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.53174	+	2.65306i	−0.266642	+	0.461838i
$34$	0.837558			0.143640
$35$	0.960858	−	0.853707i	0.162415	−	0.144303i
$36$	−1.00000			−0.166667
$37$	−4.82160	−	2.78375i	−0.792665	−	0.457646i	0.0482347	−	0.998836i	$-0.484640\pi$
$37$	−4.82160	−	2.78375i	−0.792665	−	0.457646i	−0.840900	+	0.541190i	$0.817974\pi$
$38$	−3.41446	−	5.91401i	−0.553898	−	0.959379i
$39$	2.53711	+	4.39441i	0.406263	+	0.703668i
$40$	0.242904	−	0.420722i	0.0384065	−	0.0665220i
$41$		−	8.68814i		−	1.35686i	−0.734665	−	0.678430i	$-0.762661\pi$
$41$		−	8.68814i		−	1.35686i	0.734665	−	0.678430i	$-0.237339\pi$
$42$	−0.834227	+	2.51079i	−0.128724	+	0.387423i
$43$			5.27242i			0.804036i	0.915632	+	0.402018i	$0.131691\pi$
$43$			5.27242i			0.804036i	−0.915632	+	0.402018i	$0.868309\pi$
$44$	2.65306	+	1.53174i	0.399963	+	0.230919i
$45$	−0.242904	−	0.420722i	−0.0362100	−	0.0627175i
$46$	−2.14246	+	4.29067i	−0.315888	+	0.632625i
$47$	3.68699	+	2.12869i	0.537803	+	0.310501i	0.744188	−	0.667970i	$-0.232837\pi$
$47$	3.68699	+	2.12869i	0.537803	+	0.310501i	−0.206385	+	0.978471i	$0.566170\pi$
$48$			1.00000i			0.144338i
$49$	5.60813	+	4.18914i	0.801162	+	0.598448i
$50$	−4.76399			−0.673730
$51$	−0.725347	−	0.418779i	−0.101569	−	0.0586408i
$52$	4.39441	−	2.53711i	0.609395	−	0.351834i
$53$	7.31519	−	4.22343i	1.00482	−	0.580132i	0.0951481	−	0.995463i	$-0.469668\pi$
$53$	7.31519	−	4.22343i	1.00482	−	0.580132i	0.909670	+	0.415331i	$0.136334\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$			1.48827i			0.200678i
$56$	2.51079	+	0.834227i	0.335518	+	0.111478i
$57$			6.82891i			0.904511i
$58$	−2.31447	+	4.00878i	−0.303905	+	0.526379i
$59$	−3.15927	+	1.82401i	−0.411302	+	0.237465i	−0.691349	−	0.722521i	$-0.742983\pi$
$59$	−3.15927	+	1.82401i	−0.411302	+	0.237465i	0.280047	+	0.959986i	$0.409650\pi$
$60$	−0.420722	+	0.242904i	−0.0543150	+	0.0313588i
$61$	−4.90732	+	8.49972i	−0.628318	+	1.08828i	0.359571	+	0.933118i	$0.382923\pi$
$61$	−4.90732	+	8.49972i	−0.628318	+	1.08828i	−0.987889	+	0.155161i	$0.950410\pi$
$62$			9.20838i			1.16947i
$63$	1.97786	−	1.75729i	0.249186	−	0.221398i
$64$	1.00000			0.125000
$65$	2.13484	+	1.23255i	0.264794	+	0.152879i
$66$	−1.53174	−	2.65306i	−0.188545	−	0.326569i
$67$	−3.54252	+	2.04527i	−0.432788	+	0.249870i	−0.700533	−	0.713620i	$-0.747055\pi$
$67$	−3.54252	+	2.04527i	−0.432788	+	0.249870i	0.267746	+	0.963490i	$0.413721\pi$
$68$	−0.418779	+	0.725347i	−0.0507844	+	0.0879612i
$69$	4.00076	−	2.64460i	0.481635	−	0.318373i
$70$	0.258903	+	1.25898i	0.0309449	+	0.150477i
$71$	−1.32082			−0.156752			−0.0783760	−	0.996924i	$-0.524973\pi$
$71$	−1.32082			−0.156752			−0.0783760	+	0.996924i	$0.524973\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	3.26928	−	1.88752i	0.382640	−	0.220917i	−0.296326	−	0.955087i	$-0.595762\pi$
$73$	3.26928	−	1.88752i	0.382640	−	0.220917i	0.678966	+	0.734169i	$0.262428\pi$
$74$	4.82160	−	2.78375i	0.560499	−	0.323604i
$75$	4.12574	+	2.38200i	0.476399	+	0.275049i
$76$	6.82891			0.783330
$77$	−7.93909	+	1.63263i	−0.904743	+	0.186056i
$78$	−5.07423			−0.574543
$79$	−9.12312	−	5.26723i	−1.02643	−	0.592610i	−0.110471	−	0.993879i	$-0.535236\pi$
$79$	−9.12312	−	5.26723i	−1.02643	−	0.592610i	−0.915960	+	0.401269i	$0.868569\pi$
$80$	0.242904	+	0.420722i	0.0271575	+	0.0470381i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.52415	+	4.34407i	0.830904	+	0.479723i
$83$	6.95787			0.763725			0.381863	−	0.924219i	$-0.375283\pi$
$83$	6.95787			0.763725			0.381863	+	0.924219i	$0.375283\pi$
$84$	−1.75729	−	1.97786i	−0.191737	−	0.215802i
$85$	−0.406892			−0.0441337
$86$	−4.56605	−	2.63621i	−0.492369	−	0.284270i
$87$	4.00878	−	2.31447i	0.429787	−	0.248138i
$88$	−2.65306	+	1.53174i	−0.282817	+	0.163284i
$89$	−5.22221	+	9.04513i	−0.553553	+	0.958782i	0.444462	+	0.895798i	$0.353395\pi$
$89$	−5.22221	+	9.04513i	−0.553553	+	0.958782i	−0.998015	+	0.0629838i	$0.979938\pi$
$90$	0.485808			0.0512086
$91$	−4.23305	+	12.7403i	−0.443745	+	1.33555i
$92$	−2.64460	−	4.00076i	−0.275719	−	0.417108i
$93$	4.60419	−	7.97469i	0.477432	−	0.826937i
$94$	−3.68699	+	2.12869i	−0.380284	+	0.219557i
$95$	1.65877	+	2.87307i	0.170186	+	0.294771i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	9.53965			0.968604			0.484302	−	0.874901i	$-0.339074\pi$
$97$	9.53965			0.968604			0.484302	+	0.874901i	$0.339074\pi$
$98$	−6.43196	+	2.76222i	−0.649726	+	0.279026i
$99$			3.06349i			0.307892i
$100$	2.38200	−	4.12574i	0.238200	−	0.412574i
$101$	−2.59731	+	1.49955i	−0.258442	+	0.149211i	−0.623623	−	0.781725i	$-0.714340\pi$
$101$	−2.59731	+	1.49955i	−0.258442	+	0.149211i	0.365182	+	0.930936i	$0.381007\pi$
$102$	0.725347	−	0.418779i	0.0718200	−	0.0414653i
$103$	7.49493	−	12.9816i	0.738497	−	1.27911i	−0.214675	−	0.976686i	$-0.568869\pi$
$103$	7.49493	−	12.9816i	0.738497	−	1.27911i	0.953172	−	0.302429i	$-0.0977975\pi$
$104$			5.07423i			0.497569i
$105$	0.405274	−	1.21976i	0.0395507	−	0.119037i
$106$			8.44685i			0.820431i
$107$	−6.39367	−	3.69139i	−0.618099	−	0.356860i	0.158029	−	0.987434i	$-0.449486\pi$
$107$	−6.39367	−	3.69139i	−0.618099	−	0.356860i	−0.776129	+	0.630575i	$0.782819\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	1.05921	−	0.611537i	0.101454	−	0.0585746i	−0.448414	−	0.893826i	$-0.648011\pi$
$109$	1.05921	−	0.611537i	0.101454	−	0.0585746i	0.549869	+	0.835251i	$0.314678\pi$
$110$	−1.28888	−	0.744133i	−0.122889	−	0.0709503i
$111$	−5.56750			−0.528444
$112$	−1.97786	+	1.75729i	−0.186890	+	0.166049i
$113$		−	8.65289i		−	0.813995i	−0.913429	−	0.406998i	$-0.866576\pi$
$113$		−	8.65289i		−	0.813995i	0.913429	−	0.406998i	$-0.133424\pi$
$114$	−5.91401	−	3.41446i	−0.553898	−	0.319793i
$115$	1.04082	−	2.08444i	0.0970573	−	0.194375i
$116$	−2.31447	−	4.00878i	−0.214893	−	0.372206i
$117$	4.39441	+	2.53711i	0.406263	+	0.234556i
$118$		−	3.64801i		−	0.335827i
$119$	−0.446363	−	2.17055i	−0.0409180	−	0.198974i
$120$		−	0.485808i		−	0.0443480i
$121$	−0.807526	+	1.39868i	−0.0734115	+	0.127152i
$122$	−4.90732	−	8.49972i	−0.444288	−	0.769529i
$123$	−4.34407	−	7.52415i	−0.391692	−	0.678430i
$124$	−7.97469	−	4.60419i	−0.716149	−	0.413469i
$125$	4.74342			0.424265
$126$	0.532933	+	2.59152i	0.0474775	+	0.230871i
$127$	7.27976			0.645974			0.322987	−	0.946403i	$-0.395313\pi$
$127$	7.27976			0.645974			0.322987	+	0.946403i	$0.395313\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	2.63621	+	4.56605i	0.232105	+	0.402018i
$130$	−2.13484	+	1.23255i	−0.187238	+	0.108102i
$131$	−15.3287	−	8.85000i	−1.33927	−	0.773228i	−0.352571	−	0.935785i	$-0.614693\pi$
$131$	−15.3287	−	8.85000i	−1.33927	−	0.773228i	−0.986699	+	0.162557i	$0.948026\pi$
$132$	3.06349			0.266642
$133$	−13.5066	+	12.0004i	−1.17117	+	1.04057i
$134$		−	4.09055i		−	0.353370i
$135$	−0.420722	−	0.242904i	−0.0362100	−	0.0209058i
$136$	−0.418779	−	0.725347i	−0.0359100	−	0.0621980i
$137$	−3.86939	+	2.23400i	−0.330585	+	0.190863i	−0.656101	−	0.754673i	$-0.727795\pi$
$137$	−3.86939	+	2.23400i	−0.330585	+	0.190863i	0.325516	+	0.945537i	$0.394462\pi$
$138$	0.289912	+	4.78706i	0.0246790	+	0.407502i
$139$			19.9740i			1.69417i	0.531454	+	0.847087i	$0.321646\pi$
$139$			19.9740i			1.69417i	−0.531454	+	0.847087i	$0.678354\pi$
$140$	−1.21976	−	0.405274i	−0.103089	−	0.0342519i
$141$	4.25737			0.358536
$142$	0.660408	−	1.14386i	0.0554202	−	0.0959906i
$143$	−7.77241	−	13.4622i	−0.649962	−	1.12577i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	1.12439	−	1.94750i	0.0933754	−	0.161731i
$146$			3.77504i			0.312424i
$147$	6.95135	+	0.823832i	0.573338	+	0.0679485i
$148$			5.56750i			0.457646i
$149$	−16.9732	−	9.79947i	−1.39050	−	0.802804i	−0.397127	−	0.917764i	$-0.629993\pi$
$149$	−16.9732	−	9.79947i	−1.39050	−	0.802804i	−0.993370	+	0.114960i	$0.963326\pi$
$150$	−4.12574	+	2.38200i	−0.336865	+	0.194489i
$151$	4.34232	+	7.52112i	0.353373	+	0.612060i	0.986838	−	0.161711i	$-0.0517014\pi$
$151$	4.34232	+	7.52112i	0.353373	+	0.612060i	−0.633465	+	0.773771i	$0.718368\pi$
$152$	−3.41446	+	5.91401i	−0.276949	+	0.479690i
$153$	−0.837558			−0.0677126
$154$	2.55564	−	7.69177i	0.205939	−	0.619820i
$155$		−	4.47351i		−	0.359321i
$156$	2.53711	−	4.39441i	0.203132	−	0.351834i
$157$	−3.73996	−	6.47780i	−0.298481	−	0.516984i	0.677308	−	0.735700i	$-0.263147\pi$
$157$	−3.73996	−	6.47780i	−0.298481	−	0.516984i	−0.975789	+	0.218716i	$0.929813\pi$
$158$	9.12312	−	5.26723i	0.725796	−	0.419039i
$159$	4.22343	−	7.31519i	0.334939	−	0.580132i
$160$	−0.485808			−0.0384065
$161$	12.2612	+	3.26558i	0.966314	+	0.257364i
$162$	1.00000			0.0785674
$163$	8.60562	−	14.9054i	0.674044	−	1.16748i	−0.302704	−	0.953085i	$-0.597889\pi$
$163$	8.60562	−	14.9054i	0.674044	−	1.16748i	0.976747	−	0.214393i	$-0.0687775\pi$
$164$	−7.52415	+	4.34407i	−0.587538	+	0.339215i
$165$	0.744133	+	1.28888i	0.0579307	+	0.100339i
$166$	−3.47893	+	6.02569i	−0.270018	+	0.467684i
$167$			19.5560i			1.51329i	0.653826	+	0.756645i	$0.273163\pi$
$167$			19.5560i			1.51329i	−0.653826	+	0.756645i	$0.726837\pi$
$168$	2.59152	−	0.532933i	0.199940	−	0.0411167i
$169$	−12.7478			−0.980597
$170$	0.203446	−	0.352379i	0.0156036	−	0.0270262i
$171$	3.41446	+	5.91401i	0.261110	+	0.452256i
$172$	4.56605	−	2.63621i	0.348158	−	0.201009i
$173$	−18.2657	−	10.5457i	−1.38871	−	0.801775i	−0.395544	−	0.918447i	$-0.629444\pi$
$173$	−18.2657	−	10.5457i	−1.38871	−	0.801775i	−0.993170	+	0.116673i	$0.962777\pi$
$174$			4.62895i			0.350919i
$175$	2.53889	+	12.3460i	0.191922	+	0.933269i
$176$		−	3.06349i		−	0.230919i
$177$	−1.82401	+	3.15927i	−0.137101	+	0.237465i
$178$	−5.22221	−	9.04513i	−0.391421	−	0.677961i
$179$	−8.98104	−	15.5556i	−0.671275	−	1.16268i	−0.977543	−	0.210737i	$-0.932414\pi$
$179$	−8.98104	−	15.5556i	−0.671275	−	1.16268i	0.306268	−	0.951945i	$-0.400920\pi$
$180$	−0.242904	+	0.420722i	−0.0181050	+	0.0313588i
$181$	6.32867			0.470406			0.235203	−	0.971946i	$-0.424424\pi$
$181$	6.32867			0.470406			0.235203	+	0.971946i	$0.424424\pi$
$182$	−8.91691	−	10.0361i	−0.660965	−	0.743924i
$183$			9.81464i			0.725519i
$184$	4.78706	−	0.289912i	0.352907	−	0.0213726i
$185$	−2.34237	+	1.35237i	−0.172214	+	0.0994280i
$186$	4.60419	+	7.97469i	0.337596	+	0.584733i
$187$	2.22209	+	1.28292i	0.162495	+	0.0938167i
$188$		−	4.25737i		−	0.310501i
$189$	0.834227	−	2.51079i	0.0606811	−	0.182633i
$190$	−3.31754			−0.240680
$191$	15.6759	+	9.05046i	1.13426	+	0.654868i	0.945004	−	0.327059i	$-0.106058\pi$
$191$	15.6759	+	9.05046i	1.13426	+	0.654868i	0.189261	+	0.981927i	$0.439391\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−7.59857	−	13.1611i	−0.546957	−	0.947357i	−0.998481	−	0.0550982i	$-0.982453\pi$
$193$	−7.59857	−	13.1611i	−0.546957	−	0.947357i	0.451524	−	0.892259i	$-0.350881\pi$
$194$	−4.76982	+	8.26158i	−0.342453	+	0.593147i
$195$	2.46510			0.176529
$196$	0.823832	−	6.95135i	0.0588451	−	0.496525i
$197$	−4.52116			−0.322119			−0.161060	−	0.986945i	$-0.551491\pi$
$197$	−4.52116			−0.322119			−0.161060	+	0.986945i	$0.551491\pi$
$198$	−2.65306	−	1.53174i	−0.188545	−	0.108856i
$199$	1.40852	+	2.43964i	0.0998476	+	0.172941i	0.911621	−	0.411031i	$-0.134831\pi$
$199$	1.40852	+	2.43964i	0.0998476	+	0.172941i	−0.811774	+	0.583972i	$0.801498\pi$
$200$	2.38200	+	4.12574i	0.168433	+	0.291734i
$201$	−2.04527	+	3.54252i	−0.144263	+	0.249870i
$202$		−	2.99911i		−	0.211017i
$203$	11.6223	+	3.86159i	0.815726	+	0.271030i
$204$			0.837558i			0.0586408i
$205$	−3.65529	−	2.11038i	−0.255297	−	0.147396i
$206$	7.49493	+	12.9816i	0.522196	+	0.904470i
$207$	2.14246	−	4.29067i	0.148911	−	0.298222i
$208$	−4.39441	−	2.53711i	−0.304697	−	0.175917i
$209$		−	20.9203i		−	1.44709i
$210$	0.853707	+	0.960858i	0.0589114	+	0.0663055i
$211$	7.17107			0.493677			0.246838	−	0.969057i	$-0.420608\pi$
$211$	7.17107			0.493677			0.246838	+	0.969057i	$0.420608\pi$
$212$	−7.31519	−	4.22343i	−0.502409	−	0.290066i
$213$	−1.14386	+	0.660408i	−0.0783760	+	0.0452504i
$214$	6.39367	−	3.69139i	0.437062	−	0.252338i
$215$	2.21822	+	1.28069i	0.151281	+	0.0873424i
$216$		−	1.00000i		−	0.0680414i
$217$	23.8637	−	4.90746i	1.61997	−	0.333140i
$218$			1.22307i			0.0828370i
$219$	1.88752	−	3.26928i	0.127547	−	0.220917i
$220$	1.28888	−	0.744133i	0.0868960	−	0.0501694i
$221$	3.68057	−	2.12498i	0.247582	−	0.142942i
$222$	2.78375	−	4.82160i	0.186833	−	0.323604i
$223$		−	7.50608i		−	0.502645i	−0.967903	−	0.251322i	$-0.919135\pi$
$223$		−	7.50608i		−	0.502645i	0.967903	−	0.251322i	$-0.0808654\pi$
$224$	−0.532933	−	2.59152i	−0.0356081	−	0.173153i
$225$	4.76399			0.317599
$226$	7.49362	+	4.32644i	0.498468	+	0.287791i
$227$	8.87766	+	15.3766i	0.589231	+	1.02058i	0.994333	+	0.106306i	$0.0339024\pi$
$227$	8.87766	+	15.3766i	0.589231	+	1.02058i	−0.405103	+	0.914271i	$0.632764\pi$
$228$	5.91401	−	3.41446i	0.391665	−	0.226128i
$229$	10.2713	−	17.7904i	0.678747	−	1.17562i	−0.296612	−	0.954998i	$-0.595857\pi$
$229$	10.2713	−	17.7904i	0.678747	−	1.17562i	0.975359	−	0.220626i	$-0.0708100\pi$
$230$	1.28477	+	1.94360i	0.0847151	+	0.128157i
$231$	−6.05914	+	5.38345i	−0.398662	+	0.354205i
$232$	4.62895			0.303905
$233$	7.83721	−	13.5744i	0.513433	−	0.889291i	−0.486446	−	0.873711i	$-0.661707\pi$
$233$	7.83721	−	13.5744i	0.513433	−	0.889291i	0.999879	−	0.0155807i	$-0.00495969\pi$
$234$	−4.39441	+	2.53711i	−0.287271	+	0.165856i
$235$	1.79117	−	1.03413i	0.116843	−	0.0674594i
$236$	3.15927	+	1.82401i	0.205651	+	0.118733i
$237$	−10.5345			−0.684287
$238$	2.10293	+	0.698713i	0.136313	+	0.0452909i
$239$	−11.4132			−0.738255			−0.369128	−	0.929379i	$-0.620343\pi$
$239$	−11.4132			−0.738255			−0.369128	+	0.929379i	$0.620343\pi$
$240$	0.420722	+	0.242904i	0.0271575	+	0.0156794i
$241$	−8.55783	−	14.8226i	−0.551258	−	0.954808i	−0.998184	−	0.0602365i	$-0.980815\pi$
$241$	−8.55783	−	14.8226i	−0.551258	−	0.954808i	0.446926	−	0.894571i	$-0.352519\pi$
$242$	−0.807526	−	1.39868i	−0.0519098	−	0.0899103i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	9.81464			0.628318
$245$	3.12470	−	1.34191i	0.199630	−	0.0857313i
$246$	8.68814			0.553936
$247$	−30.0090	−	17.3257i	−1.90943	−	1.10241i
$248$	7.97469	−	4.60419i	0.506394	−	0.292366i
$249$	6.02569	−	3.47893i	0.381863	−	0.220468i
$250$	−2.37171	+	4.10793i	−0.150000	+	0.259808i
$251$	26.4084			1.66688			0.833441	−	0.552608i	$-0.186368\pi$
$251$	26.4084			1.66688			0.833441	+	0.552608i	$0.186368\pi$
$252$	−2.51079	−	0.834227i	−0.158165	−	0.0525513i
$253$	−12.2563	+	8.10170i	−0.770545	+	0.509350i
$254$	−3.63988	+	6.30446i	−0.228386	+	0.395577i
$255$	−0.352379	+	0.203446i	−0.0220668	+	0.0127403i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−21.6943	−	12.5252i	−1.35325	−	0.781300i	−0.364548	−	0.931184i	$-0.618777\pi$
$257$	−21.6943	−	12.5252i	−1.35325	−	0.781300i	−0.988704	+	0.149884i	$0.952110\pi$
$258$	−5.27242			−0.328246
$259$	−9.78373	−	11.0117i	−0.607932	−	0.684235i
$260$		−	2.46510i		−	0.152879i
$261$	2.31447	−	4.00878i	0.143262	−	0.248138i
$262$	15.3287	−	8.85000i	0.947007	−	0.546755i
$263$	−13.7220	+	7.92239i	−0.846134	+	0.488515i	−0.859344	−	0.511397i	$-0.829128\pi$
$263$	−13.7220	+	7.92239i	−0.846134	+	0.488515i	0.0132108	+	0.999913i	$0.495795\pi$
$264$	−1.53174	+	2.65306i	−0.0942723	+	0.163284i
$265$		−	4.10355i		−	0.252079i
$266$	−3.63936	−	17.6973i	−0.223143	−	1.08509i
$267$			10.4444i			0.639188i
$268$	3.54252	+	2.04527i	0.216394	+	0.124935i
$269$	15.9218	−	9.19246i	0.970770	−	0.560474i	0.0712992	−	0.997455i	$-0.477285\pi$
$269$	15.9218	−	9.19246i	0.970770	−	0.560474i	0.899471	+	0.436981i	$0.143952\pi$
$270$	0.420722	−	0.242904i	0.0256043	−	0.0147827i
$271$	−1.82200	−	1.05194i	−0.110679	−	0.0639005i	0.443639	−	0.896206i	$-0.353687\pi$
$271$	−1.82200	−	1.05194i	−0.110679	−	0.0639005i	−0.554318	+	0.832305i	$0.687021\pi$
$272$	0.837558			0.0507844
$273$	2.70422	+	13.1500i	0.163667	+	0.795872i
$274$		−	4.46799i		−	0.269921i
$275$	−12.6391	−	7.29721i	−0.762169	−	0.440038i
$276$	−4.29067	−	2.14246i	−0.258268	−	0.128961i
$277$	−6.61062	−	11.4499i	−0.397194	−	0.687960i	0.596185	−	0.802847i	$-0.296683\pi$
$277$	−6.61062	−	11.4499i	−0.397194	−	0.687960i	−0.993378	+	0.114888i	$0.963349\pi$
$278$	−17.2980	−	9.98701i	−1.03747	−	0.598981i
$279$		−	9.20838i		−	0.551292i
$280$	0.960858	−	0.853707i	0.0574223	−	0.0510188i
$281$		−	23.3817i		−	1.39483i	−0.716665	−	0.697417i	$-0.754332\pi$
$281$		−	23.3817i		−	1.39483i	0.716665	−	0.697417i	$-0.245668\pi$
$282$	−2.12869	+	3.68699i	−0.126761	+	0.219557i
$283$	−0.520276	−	0.901145i	−0.0309272	−	0.0535675i	0.850148	−	0.526545i	$-0.176513\pi$
$283$	−0.520276	−	0.901145i	−0.0309272	−	0.0535675i	−0.881075	+	0.472977i	$0.843179\pi$
$284$	0.660408	+	1.14386i	0.0391880	+	0.0678756i
$285$	2.87307	+	1.65877i	0.170186	+	0.0982570i
$286$	15.5448			0.919184
$287$	7.24788	−	21.8141i	0.427829	−	1.28765i
$288$	−1.00000			−0.0589256
$289$	8.14925	−	14.1149i	0.479368	−	0.830289i
$290$	1.12439	+	1.94750i	0.0660264	+	0.114361i
$291$	8.26158	−	4.76982i	0.484302	−	0.279612i
$292$	−3.26928	−	1.88752i	−0.191320	−	0.110459i
$293$	−9.81859			−0.573608			−0.286804	−	0.957989i	$-0.592593\pi$
$293$	−9.81859			−0.573608			−0.286804	+	0.957989i	$0.592593\pi$
$294$	−4.18914	+	5.60813i	−0.244315	+	0.327073i
$295$			1.77223i			0.103183i
$296$	−4.82160	−	2.78375i	−0.280250	−	0.161802i
$297$	1.53174	+	2.65306i	0.0888807	+	0.153946i
$298$	16.9732	−	9.79947i	0.983230	−	0.567668i
$299$	1.47108	+	24.2906i	0.0850748	+	1.40476i
$300$		−	4.76399i		−	0.275049i
$301$	−4.39839	+	13.2379i	−0.253519	+	0.763021i
$302$	−8.68464			−0.499745
$303$	−1.49955	+	2.59731i	−0.0861472	+	0.149211i
$304$	−3.41446	−	5.91401i	−0.195832	−	0.339192i
$305$	2.38401	+	4.12923i	0.136508	+	0.236439i
$306$	0.418779	−	0.725347i	0.0239400	−	0.0414653i
$307$			8.35548i			0.476872i	0.971158	+	0.238436i	$0.0766348\pi$
$307$			8.35548i			0.476872i	−0.971158	+	0.238436i	$0.923365\pi$
$308$	5.38345	+	6.05914i	0.306750	+	0.345251i
$309$		−	14.9899i		−	0.852743i
$310$	3.87417	+	2.23675i	0.220038	+	0.127039i
$311$	−10.6677	+	6.15900i	−0.604910	+	0.349245i	−0.770971	−	0.636871i	$-0.780229\pi$
$311$	−10.6677	+	6.15900i	−0.604910	+	0.349245i	0.166061	+	0.986116i	$0.446895\pi$
$312$	2.53711	+	4.39441i	0.143636	+	0.248784i
$313$	−13.3301	+	23.0884i	−0.753461	+	1.30503i	0.192674	+	0.981263i	$0.438284\pi$
$313$	−13.3301	+	23.0884i	−0.753461	+	1.30503i	−0.946136	+	0.323770i	$0.895049\pi$
$314$	7.47992			0.422116
$315$	−0.258903	−	1.25898i	−0.0145875	−	0.0709356i
$316$			10.5345i			0.592610i
$317$	−9.18736	+	15.9130i	−0.516014	+	0.893762i	0.483814	+	0.875171i	$0.339251\pi$
$317$	−9.18736	+	15.9130i	−0.516014	+	0.893762i	−0.999827	+	0.0185906i	$0.994082\pi$
$318$	4.22343	+	7.31519i	0.236838	+	0.410215i
$319$	−12.2809	+	7.09036i	−0.687596	+	0.396984i
$320$	0.242904	−	0.420722i	0.0135787	−	0.0235191i
$321$	−7.38277			−0.412066
$322$	−8.95866	+	8.98568i	−0.499246	+	0.500752i
$323$	5.71961			0.318248
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−20.9349	+	12.0868i	−1.16126	+	0.670454i
$326$	8.60562	+	14.9054i	0.476621	+	0.825532i
$327$	0.611537	−	1.05921i	0.0338181	−	0.0585746i
$328$		−	8.68814i		−	0.479723i
$329$	7.48146	+	8.42048i	0.412466	+	0.464236i
$330$	−1.48827			−0.0819263
$331$	−0.155874	+	0.269982i	−0.00856763	+	0.0148396i	−0.870277	−	0.492562i	$-0.836061\pi$
$331$	−0.155874	+	0.269982i	−0.00856763	+	0.0148396i	0.861710	+	0.507401i	$0.169394\pi$
$332$	−3.47893	−	6.02569i	−0.190931	−	0.330703i
$333$	−4.82160	+	2.78375i	−0.264222	+	0.152549i
$334$	−16.9360	−	9.77800i	−0.926696	−	0.535028i
$335$			1.98722i			0.108573i
$336$	−0.834227	+	2.51079i	−0.0455108	+	0.136975i
$337$		−	32.9634i		−	1.79563i	−0.440373	−	0.897815i	$-0.645154\pi$
$337$		−	32.9634i		−	1.79563i	0.440373	−	0.897815i	$-0.354846\pi$
$338$	6.37388	−	11.0399i	0.346693	−	0.600491i
$339$	−4.32644	−	7.49362i	−0.234980	−	0.406998i
$340$	0.203446	+	0.352379i	0.0110334	+	0.0191104i
$341$	−14.1049	+	24.4304i	−0.763822	+	1.32298i
$342$	−6.82891			−0.369265
$343$	10.5862	+	15.1965i	0.571598	+	0.820533i
$344$			5.27242i			0.284270i
$345$	−0.140842	−	2.32559i	−0.00758266	−	0.125206i
$346$	18.2657	−	10.5457i	0.981969	−	0.566940i
$347$	13.0936	+	22.6787i	0.702900	+	1.21746i	0.967444	+	0.253085i	$0.0814452\pi$
$347$	13.0936	+	22.6787i	0.702900	+	1.21746i	−0.264544	+	0.964374i	$0.585221\pi$
$348$	−4.00878	−	2.31447i	−0.214893	−	0.124069i
$349$			2.84126i			0.152089i	0.997104	+	0.0760446i	$0.0242291\pi$
$349$			2.84126i			0.152089i	−0.997104	+	0.0760446i	$0.975771\pi$
$350$	−11.9614	−	3.97425i	−0.639363	−	0.212432i
$351$	5.07423			0.270842
$352$	2.65306	+	1.53174i	0.141408	+	0.0816422i
$353$	3.92196	−	2.26435i	0.208745	−	0.120519i	−0.391983	−	0.919972i	$-0.628211\pi$
$353$	3.92196	−	2.26435i	0.208745	−	0.120519i	0.600728	+	0.799453i	$0.294877\pi$
$354$	−1.82401	−	3.15927i	−0.0969448	−	0.167913i
$355$	−0.320831	+	0.555696i	−0.0170280	+	0.0294933i
$356$	10.4444			0.553553
$357$	−1.47184	−	1.65657i	−0.0778979	−	0.0876750i
$358$	17.9621			0.949326
$359$	−15.4334	−	8.91049i	−0.814545	−	0.470278i	0.0339868	−	0.999422i	$-0.489180\pi$
$359$	−15.4334	−	8.91049i	−0.814545	−	0.470278i	−0.848532	+	0.529145i	$0.822513\pi$
$360$	−0.242904	−	0.420722i	−0.0128022	−	0.0221740i
$361$	−13.8170	−	23.9318i	−0.727211	−	1.25957i
$362$	−3.16433	+	5.48079i	−0.166314	+	0.288064i
$363$			1.61505i			0.0847683i
$364$	13.1500	−	2.70422i	0.689245	−	0.141740i
$365$		−	1.83394i		−	0.0959929i
$366$	−8.49972	−	4.90732i	−0.444288	−	0.256510i
$367$	11.7504	+	20.3523i	0.613365	+	1.06238i	0.990669	+	0.136290i	$0.0435179\pi$
$367$	11.7504	+	20.3523i	0.613365	+	1.06238i	−0.377304	+	0.926090i	$0.623149\pi$
$368$	−2.14246	+	4.29067i	−0.111683	+	0.223667i
$369$	−7.52415	−	4.34407i	−0.391692	−	0.226143i
$370$		−	2.70473i		−	0.140612i
$371$	21.8902	−	4.50161i	1.13648	−	0.233712i
$372$	−9.20838			−0.477432
$373$	4.55066	+	2.62732i	0.235624	+	0.136038i	0.613164	−	0.789956i	$-0.289897\pi$
$373$	4.55066	+	2.62732i	0.235624	+	0.136038i	−0.377540	+	0.925993i	$0.623230\pi$
$374$	−2.22209	+	1.28292i	−0.114902	+	0.0663384i
$375$	4.10793	−	2.37171i	0.212132	−	0.122475i
$376$	3.68699	+	2.12869i	0.190142	+	0.109779i
$377$			23.4883i			1.20971i
$378$	1.75729	+	1.97786i	0.0903855	+	0.101730i
$379$		−	32.0689i		−	1.64727i	−0.567121	−	0.823635i	$-0.691943\pi$
$379$		−	32.0689i		−	1.64727i	0.567121	−	0.823635i	$-0.308057\pi$
$380$	1.65877	−	2.87307i	0.0850931	−	0.147386i
$381$	6.30446	−	3.63988i	0.322987	−	0.186477i
$382$	−15.6759	+	9.05046i	−0.802046	+	0.463062i
$383$	9.14917	−	15.8468i	0.467501	−	0.809735i	−0.531810	−	0.846864i	$-0.678488\pi$
$383$	9.14917	−	15.8468i	0.467501	−	0.809735i	0.999310	+	0.0371291i	$0.0118213\pi$
$384$			1.00000i			0.0510310i
$385$	−1.24155	+	3.73672i	−0.0632753	+	0.190441i
$386$	15.1971			0.773514
$387$	4.56605	+	2.63621i	0.232105	+	0.134006i
$388$	−4.76982	−	8.26158i	−0.242151	−	0.419418i
$389$	27.2229	−	15.7172i	1.38026	−	0.796892i	0.388068	−	0.921631i	$-0.373142\pi$
$389$	27.2229	−	15.7172i	1.38026	−	0.796892i	0.992190	+	0.124738i	$0.0398091\pi$
$390$	−1.23255	+	2.13484i	−0.0624126	+	0.108102i
$391$	−2.21501	−	3.35087i	−0.112018	−	0.169461i
$392$	5.60813	+	4.18914i	0.283253	+	0.211583i
$393$	−17.7000			−0.892847
$394$	2.26058	−	3.91544i	0.113886	−	0.197257i
$395$	−4.43208	+	2.55886i	−0.223002	+	0.128750i
$396$	2.65306	−	1.53174i	0.133321	−	0.0769730i
$397$	−9.69103	−	5.59512i	−0.486379	−	0.280811i	0.236692	−	0.971585i	$-0.423937\pi$
$397$	−9.69103	−	5.59512i	−0.486379	−	0.280811i	−0.723071	+	0.690774i	$0.757270\pi$
$398$	−2.81705			−0.141206
$399$	−5.69686	+	17.1460i	−0.285200	+	0.858372i
$400$	−4.76399			−0.238200
$401$	11.5257	+	6.65435i	0.575565	+	0.332303i	0.759369	−	0.650660i	$-0.225508\pi$
$401$	11.5257	+	6.65435i	0.575565	+	0.332303i	−0.183804	+	0.982963i	$0.558841\pi$
$402$	−2.04527	−	3.54252i	−0.102009	−	0.176685i
$403$	23.3627	+	40.4654i	1.16378	+	2.01572i
$404$	2.59731	+	1.49955i	0.129221	+	0.0746056i
$405$	−0.485808			−0.0241400
$406$	−9.15539	+	8.13442i	−0.454374	+	0.403705i
$407$	17.0560			0.845432
$408$	−0.725347	−	0.418779i	−0.0359100	−	0.0207327i
$409$	−22.0680	+	12.7409i	−1.09119	+	0.629999i	−0.933893	−	0.357552i	$-0.883611\pi$
$409$	−22.0680	+	12.7409i	−1.09119	+	0.629999i	−0.157297	+	0.987551i	$0.550278\pi$
$410$	3.65529	−	2.11038i	0.180522	−	0.104224i
$411$	−2.23400	+	3.86939i	−0.110195	+	0.190863i
$412$	−14.9899			−0.738497
$413$	−9.45390	+	1.94415i	−0.465196	+	0.0956652i
$414$	2.64460	+	4.00076i	0.129975	+	0.196627i
$415$	1.69009	−	2.92733i	0.0829634	−	0.143697i
$416$	4.39441	−	2.53711i	0.215454	−	0.124392i
$417$	9.98701	+	17.2980i	0.489066	+	0.847087i
$418$	18.1175	+	10.4601i	0.886155	+	0.511622i
$419$	13.3786			0.653589			0.326794	−	0.945095i	$-0.394032\pi$
$419$	13.3786			0.653589			0.326794	+	0.945095i	$0.394032\pi$
$420$	−1.25898	+	0.258903i	−0.0614320	+	0.0126332i
$421$		−	5.07456i		−	0.247319i	−0.992325	−	0.123659i	$-0.960537\pi$
$421$		−	5.07456i		−	0.247319i	0.992325	−	0.123659i	$-0.0394630\pi$
$422$	−3.58553	+	6.21033i	−0.174541	+	0.302314i
$423$	3.68699	−	2.12869i	0.179268	−	0.103500i
$424$	7.31519	−	4.22343i	0.355257	−	0.205108i
$425$	1.99506	−	3.45555i	0.0967746	−	0.167619i
$426$		−	1.32082i		−	0.0639937i
$427$	−19.4119	+	17.2472i	−0.939410	+	0.834651i
$428$			7.38277i			0.356860i
$429$	−13.4622	−	7.77241i	−0.649962	−	0.375255i
$430$	−2.21822	+	1.28069i	−0.106972	+	0.0617604i
$431$	−18.8706	+	10.8949i	−0.908965	+	0.524791i	−0.880098	−	0.474792i	$-0.842523\pi$
$431$	−18.8706	+	10.8949i	−0.908965	+	0.524791i	−0.0288669	+	0.999583i	$0.509190\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−0.143761			−0.00690873			−0.00345437	−	0.999994i	$-0.501100\pi$
$433$	−0.143761			−0.00690873			−0.00345437	+	0.999994i	$0.501100\pi$
$434$	−7.68188	+	23.1203i	−0.368742	+	1.10981i
$435$		−	2.24878i		−	0.107821i
$436$	−1.05921	−	0.611537i	−0.0507271	−	0.0292873i
$437$	−14.6307	+	29.3006i	−0.699879	+	1.40164i
$438$	1.88752	+	3.26928i	0.0901891	+	0.156212i
$439$	24.8389	+	14.3408i	1.18550	+	0.684448i	0.957280	−	0.289162i	$-0.0933767\pi$
$439$	24.8389	+	14.3408i	1.18550	+	0.684448i	0.228218	+	0.973610i	$0.426710\pi$
$440$			1.48827i			0.0709503i
$441$	6.43196	−	2.76222i	0.306284	−	0.131534i
$442$			4.24996i			0.202150i
$443$	13.9610	−	24.1811i	0.663305	−	1.14888i	−0.316437	−	0.948613i	$-0.602487\pi$
$443$	13.9610	−	24.1811i	0.663305	−	1.14888i	0.979742	−	0.200264i	$-0.0641800\pi$
$444$	2.78375	+	4.82160i	0.132111	+	0.228823i
$445$	2.53699	+	4.39419i	0.120265	+	0.208305i
$446$	6.50046	+	3.75304i	0.307806	+	0.177712i
$447$	−19.5989			−0.926998
$448$	2.51079	+	0.834227i	0.118624	+	0.0394135i
$449$	19.7589			0.932482			0.466241	−	0.884658i	$-0.345608\pi$
$449$	19.7589			0.932482			0.466241	+	0.884658i	$0.345608\pi$
$450$	−2.38200	+	4.12574i	−0.112288	+	0.194489i
$451$	13.3080	+	23.0501i	0.626650	+	1.08539i
$452$	−7.49362	+	4.32644i	−0.352470	+	0.203499i
$453$	7.52112	+	4.34232i	0.353373	+	0.204020i
$454$	−17.7553			−0.833298
$455$	4.33190	+	4.87561i	0.203083	+	0.228572i
$456$			6.82891i			0.319793i
$457$	−28.7619	−	16.6057i	−1.34542	−	0.776781i	−0.357826	−	0.933788i	$-0.616482\pi$
$457$	−28.7619	−	16.6057i	−1.34542	−	0.776781i	−0.987597	+	0.157007i	$0.949815\pi$
$458$	10.2713	+	17.7904i	0.479947	+	0.831292i
$459$	−0.725347	+	0.418779i	−0.0338563	+	0.0195469i
$460$	−2.32559	+	0.140842i	−0.108431	+	0.00656678i
$461$			18.0808i			0.842105i	0.907036	+	0.421053i	$0.138339\pi$
$461$			18.0808i			0.842105i	−0.907036	+	0.421053i	$0.861661\pi$
$462$	−1.63263	−	7.93909i	−0.0759570	−	0.369360i
$463$	−14.4807			−0.672975			−0.336488	−	0.941688i	$-0.609239\pi$
$463$	−14.4807			−0.672975			−0.336488	+	0.941688i	$0.609239\pi$
$464$	−2.31447	+	4.00878i	−0.107447	+	0.186103i
$465$	−2.23675	−	3.87417i	−0.103727	−	0.179660i
$466$	7.83721	+	13.5744i	0.363052	+	0.628824i
$467$	−15.4907	+	26.8307i	−0.716825	+	1.24158i	0.245427	+	0.969415i	$0.421072\pi$
$467$	−15.4907	+	26.8307i	−0.716825	+	1.24158i	−0.962252	+	0.272161i	$0.912262\pi$
$468$		−	5.07423i		−	0.234556i
$469$	−10.6007	+	2.17999i	−0.489497	+	0.100663i
$470$			2.06827i			0.0954020i
$471$	−6.47780	−	3.73996i	−0.298481	−	0.172328i
$472$	−3.15927	+	1.82401i	−0.145417	+	0.0839567i
$473$	−8.07599	−	13.9880i	−0.371334	−	0.643170i
$474$	5.26723	−	9.12312i	0.241932	−	0.419039i
$475$	−32.5329			−1.49271
$476$	−1.65657	+	1.47184i	−0.0759288	+	0.0674615i
$477$		−	8.44685i		−	0.386755i
$478$	5.70658	−	9.88408i	0.261013	−	0.452087i
$479$	8.04393	+	13.9325i	0.367537	+	0.636592i	0.989180	−	0.146709i	$-0.0468680\pi$
$479$	8.04393	+	13.9325i	0.367537	+	0.636592i	−0.621643	+	0.783301i	$0.713535\pi$
$480$	−0.420722	+	0.242904i	−0.0192032	+	0.0110870i
$481$	14.1254	−	24.4659i	0.644061	−	1.11555i
$482$	17.1157			0.779597
$483$	12.2513	−	3.30250i	0.557452	−	0.150269i
$484$	1.61505			0.0734115
$485$	2.31722	−	4.01354i	0.105219	−	0.182245i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	4.71230	+	8.16194i	0.213535	+	0.369853i	0.952818	−	0.303541i	$-0.0981690\pi$
$487$	4.71230	+	8.16194i	0.213535	+	0.369853i	−0.739284	+	0.673394i	$0.764836\pi$
$488$	−4.90732	+	8.49972i	−0.222144	+	0.384764i
$489$		−	17.2112i		−	0.778319i
$490$	−0.400224	+	3.37702i	−0.0180803	+	0.152558i
$491$	26.3527			1.18928			0.594641	−	0.803991i	$-0.297294\pi$
$491$	26.3527			1.18928			0.594641	+	0.803991i	$0.297294\pi$
$492$	−4.34407	+	7.52415i	−0.195846	+	0.339215i
$493$	−1.93851	−	3.35759i	−0.0873059	−	0.151218i
$494$	30.0090	−	17.3257i	1.35017	−	0.779521i
$495$	1.28888	+	0.744133i	0.0579307	+	0.0334463i
$496$			9.20838i			0.413469i
$497$	−3.31629	−	1.10186i	−0.148756	−	0.0494252i
$498$			6.95787i			0.311789i
$499$	−14.3554	+	24.8642i	−0.642634	+	1.11307i	0.342209	+	0.939624i	$0.388825\pi$
$499$	−14.3554	+	24.8642i	−0.642634	+	1.11307i	−0.984843	+	0.173451i	$0.944508\pi$
$500$	−2.37171	−	4.10793i	−0.106066	−	0.183712i
$501$	9.77800	+	16.9360i	0.436849	+	0.756645i
$502$	−13.2042	+	22.8703i	−0.589332	+	1.02075i
$503$	−35.8498			−1.59846			−0.799232	−	0.601023i	$-0.794760\pi$
$503$	−35.8498			−1.59846			−0.799232	+	0.601023i	$0.794760\pi$
$504$	1.97786	−	1.75729i	0.0881007	−	0.0782761i
$505$			1.45699i			0.0648353i
$506$	−0.888142	−	14.6651i	−0.0394827	−	0.651943i
$507$	−11.0399	+	6.37388i	−0.490299	+	0.283074i
$508$	−3.63988	−	6.30446i	−0.161494	−	0.279715i
$509$	7.57359	+	4.37262i	0.335694	+	0.193813i	0.658366	−	0.752698i	$-0.271248\pi$
$509$	7.57359	+	4.37262i	0.335694	+	0.193813i	−0.322672	+	0.946511i	$0.604581\pi$
$510$		−	0.406892i		−	0.0180175i
$511$	9.78309	−	2.01184i	0.432778	−	0.0889987i
$512$	1.00000			0.0441942
$513$	5.91401	+	3.41446i	0.261110	+	0.150752i
$514$	21.6943	−	12.5252i	0.956894	−	0.552463i
$515$	−3.64109	−	6.30656i	−0.160446	−	0.277900i
$516$	2.63621	−	4.56605i	0.116053	−	0.201009i
$517$	−13.0424			−0.573604
$518$	14.4283	−	2.96711i	0.633943	−	0.130367i
$519$	−21.0914			−0.925810
$520$	2.13484	+	1.23255i	0.0936188	+	0.0540509i
$521$	9.90828	+	17.1616i	0.434090	+	0.751865i	0.997221	−	0.0745023i	$-0.0237368\pi$
$521$	9.90828	+	17.1616i	0.434090	+	0.751865i	−0.563131	+	0.826367i	$0.690403\pi$
$522$	2.31447	+	4.00878i	0.101302	+	0.175460i
$523$	4.75142	−	8.22970i	0.207765	−	0.359860i	−0.743245	−	0.669019i	$-0.766714\pi$
$523$	4.75142	−	8.22970i	0.207765	−	0.359860i	0.951010	+	0.309159i	$0.100048\pi$
$524$			17.7000i			0.773228i
$525$	8.37173	+	9.42249i	0.365372	+	0.411231i
$526$		−	15.8448i		−	0.690865i
$527$	−6.67927	−	3.85628i	−0.290954	−	0.167982i
$528$	−1.53174	−	2.65306i	−0.0666606	−	0.115459i
$529$	22.8319	−	2.77566i	0.992691	−	0.120681i
$530$	3.55378	+	2.05177i	0.154366	+	0.0891234i
$531$			3.64801i			0.158310i
$532$	17.1460	+	5.69686i	0.743372	+	0.246990i
$533$	44.0856			1.90956
$534$	−9.04513	−	5.22221i	−0.391421	−	0.225987i
$535$	−3.10609	+	1.79330i	−0.134288	+	0.0775313i
$536$	−3.54252	+	2.04527i	−0.153014	+	0.0883424i
$537$	−15.5556	−	8.98104i	−0.671275	−	0.387561i
$538$			18.3849i			0.792631i
$539$	−21.2954	−	2.52380i	−0.917257	−	0.108708i
$540$			0.485808i			0.0209058i
$541$	18.8075	−	32.5755i	0.808596	−	1.40053i	−0.105241	−	0.994447i	$-0.533561\pi$
$541$	18.8075	−	32.5755i	0.808596	−	1.40053i	0.913837	−	0.406082i	$-0.133105\pi$
$542$	1.82200	−	1.05194i	0.0782618	−	0.0451845i
$543$	5.48079	−	3.16433i	0.235203	−	0.135795i
$544$	−0.418779	+	0.725347i	−0.0179550	+	0.0310990i
$545$		−	0.594179i		−	0.0254518i
$546$	−12.7403	−	4.23305i	−0.545235	−	0.181158i
$547$	30.5698			1.30707			0.653536	−	0.756895i	$-0.273285\pi$
$547$	30.5698			1.30707			0.653536	+	0.756895i	$0.273285\pi$
$548$	3.86939	+	2.23400i	0.165292	+	0.0954316i
$549$	4.90732	+	8.49972i	0.209439	+	0.362759i
$550$	12.6391	−	7.29721i	0.538935	−	0.311154i
$551$	−15.8053	+	27.3756i	−0.673330	+	1.16624i
$552$	4.00076	−	2.64460i	0.170284	−	0.112562i
$553$	−18.5122	−	20.8357i	−0.787217	−	0.886023i
$554$	13.2212			0.561717
$555$	−1.35237	+	2.34237i	−0.0574048	+	0.0994280i
$556$	17.2980	−	9.98701i	0.733599	−	0.423544i
$557$	−5.73818	+	3.31294i	−0.243134	+	0.140374i	−0.616616	−	0.787264i	$-0.711497\pi$
$557$	−5.73818	+	3.31294i	−0.243134	+	0.140374i	0.373482	+	0.927637i	$0.378164\pi$
$558$	7.97469	+	4.60419i	0.337596	+	0.194911i
$559$	−26.7534			−1.13155
$560$	0.258903	+	1.25898i	0.0109407	+	0.0532017i
$561$	2.56585			0.108330
$562$	20.2491	+	11.6908i	0.854158	+	0.493149i
$563$	−9.16761	−	15.8788i	−0.386369	−	0.669210i	0.605589	−	0.795777i	$-0.292937\pi$
$563$	−9.16761	−	15.8788i	−0.386369	−	0.669210i	−0.991958	+	0.126567i	$0.959604\pi$
$564$	−2.12869	−	3.68699i	−0.0896339	−	0.155250i
$565$	−3.64046	−	2.10182i	−0.153155	−	0.0884243i
$566$	1.04055			0.0437377
$567$	−0.532933	−	2.59152i	−0.0223811	−	0.108834i
$568$	−1.32082			−0.0554202
$569$	−10.7157	−	6.18673i	−0.449227	−	0.259361i	0.258277	−	0.966071i	$-0.416845\pi$
$569$	−10.7157	−	6.18673i	−0.449227	−	0.259361i	−0.707504	+	0.706710i	$0.750179\pi$
$570$	−2.87307	+	1.65877i	−0.120340	+	0.0694782i
$571$	−31.4999	+	18.1865i	−1.31823	+	0.761081i	−0.983444	−	0.181213i	$-0.941998\pi$
$571$	−31.4999	+	18.1865i	−1.31823	+	0.761081i	−0.334787	+	0.942294i	$0.608664\pi$
$572$	−7.77241	+	13.4622i	−0.324981	+	0.562883i
$573$	18.1009			0.756177
$574$	15.2676	+	17.1839i	0.637259	+	0.717242i
$575$	12.5989	+	19.0596i	0.525409	+	0.794840i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−17.6816	+	10.2085i	−0.736095	+	0.424984i	−0.820648	−	0.571435i	$-0.806387\pi$
$577$	−17.6816	+	10.2085i	−0.736095	+	0.424984i	0.0845530	+	0.996419i	$0.473054\pi$
$578$	8.14925	+	14.1149i	0.338964	+	0.587103i
$579$	−13.1611	−	7.59857i	−0.546957	−	0.315786i
$580$	−2.24878			−0.0933754
$581$	17.4697	+	5.80444i	0.724767	+	0.240809i
$582$			9.53965i			0.395431i
$583$	−12.9384	+	22.4100i	−0.535854	+	0.928127i
$584$	3.26928	−	1.88752i	0.135284	−	0.0781061i
$585$	2.13484	−	1.23255i	0.0882647	−	0.0509596i
$586$	4.90929	−	8.50315i	0.202801	−	0.351262i
$587$			7.38638i			0.304869i	0.988314	+	0.152434i	$0.0487112\pi$
$587$			7.38638i			0.304869i	−0.988314	+	0.152434i	$0.951289\pi$
$588$	−2.76222	−	6.43196i	−0.113912	−	0.265250i
$589$			62.8832i			2.59106i
$590$	−1.53480	−	0.886116i	−0.0631866	−	0.0364808i
$591$	−3.91544	+	2.26058i	−0.161060	+	0.0929878i
$592$	4.82160	−	2.78375i	0.198166	−	0.114411i
$593$	4.87777	+	2.81618i	0.200306	+	0.115647i	0.596798	−	0.802391i	$-0.296439\pi$
$593$	4.87777	+	2.81618i	0.200306	+	0.115647i	−0.396492	+	0.918038i	$0.629773\pi$
$594$	−3.06349			−0.125696
$595$	−1.02162	−	0.339441i	−0.0418824	−	0.0139157i
$596$			19.5989i			0.802804i
$597$	2.43964	+	1.40852i	0.0998476	+	0.0576471i
$598$	−21.7718	−	10.8713i	−0.890317	−	0.444561i
$599$	−4.26837	−	7.39303i	−0.174401	−	0.302071i	0.765553	−	0.643373i	$-0.222465\pi$
$599$	−4.26837	−	7.39303i	−0.174401	−	0.302071i	−0.939954	+	0.341302i	$0.889132\pi$
$600$	4.12574	+	2.38200i	0.168433	+	0.0972446i
$601$		−	29.9904i		−	1.22333i	−0.791116	−	0.611667i	$-0.790499\pi$
$601$		−	29.9904i		−	1.22333i	0.791116	−	0.611667i	$-0.209501\pi$
$602$	−9.26519	−	10.4281i	−0.377621	−	0.425017i
$603$			4.09055i			0.166580i
$604$	4.34232	−	7.52112i	0.176686	−	0.306030i
$605$	0.392303	+	0.679488i	0.0159494	+	0.0276251i
$606$	−1.49955	−	2.59731i	−0.0609153	−	0.105508i
$607$	11.3972	+	6.58018i	0.462598	+	0.267081i	0.713136	−	0.701026i	$-0.247274\pi$
$607$	11.3972	+	6.58018i	0.462598	+	0.267081i	−0.250538	+	0.968107i	$0.580607\pi$
$608$	6.82891			0.276949
$609$	11.9960	−	2.46692i	0.486103	−	0.0999647i
$610$	−4.76803			−0.193052
$611$	−10.8014	+	18.7086i	−0.436979	+	0.756871i
$612$	0.418779	+	0.725347i	0.0169281	+	0.0293204i
$613$	22.2084	−	12.8220i	0.896989	−	0.517877i	0.0207667	−	0.999784i	$-0.493389\pi$
$613$	22.2084	−	12.8220i	0.896989	−	0.517877i	0.876222	+	0.481908i	$0.160056\pi$
$614$	−7.23605	−	4.17774i	−0.292023	−	0.168600i
$615$	−4.22077			−0.170198
$616$	−7.93909	+	1.63263i	−0.319875	+	0.0657807i
$617$		−	8.14544i		−	0.327923i	−0.986467	−	0.163962i	$-0.947573\pi$
$617$		−	8.14544i		−	0.327923i	0.986467	−	0.163962i	$-0.0524273\pi$
$618$	12.9816	+	7.49493i	0.522196	+	0.301490i
$619$	−11.4902	−	19.9016i	−0.461830	−	0.799914i	0.537222	−	0.843441i	$-0.319474\pi$
$619$	−11.4902	−	19.9016i	−0.461830	−	0.799914i	−0.999052	+	0.0435272i	$0.986140\pi$
$620$	−3.87417	+	2.23675i	−0.155590	+	0.0898301i
$621$	−0.289912	−	4.78706i	−0.0116338	−	0.192098i
$622$		−	12.3180i		−	0.493907i
$623$	−20.6576	+	18.3539i	−0.827627	+	0.735334i
$624$	−5.07423			−0.203132
$625$	−10.7578	+	18.6330i	−0.430311	+	0.745321i
$626$	−13.3301	−	23.0884i	−0.532778	−	0.922798i
$627$	−10.4601	−	18.1175i	−0.417738	−	0.723543i
$628$	−3.73996	+	6.47780i	−0.149241	+	0.258492i
$629$			4.66310i			0.185930i
$630$	1.21976	+	0.405274i	0.0485965	+	0.0161465i
$631$			30.8839i			1.22947i	0.788735	+	0.614734i	$0.210736\pi$
$631$			30.8839i			1.22947i	−0.788735	+	0.614734i	$0.789264\pi$
$632$	−9.12312	−	5.26723i	−0.362898	−	0.209519i
$633$	6.21033	−	3.58553i	0.246838	−	0.142512i
$634$	−9.18736	−	15.9130i	−0.364877	−	0.631985i
$635$	1.76828	−	3.06276i	0.0701722	−	0.121542i
$636$	−8.44685			−0.334939
$637$	−21.2566	+	28.4569i	−0.842218	+	1.12750i
$638$		−	14.1807i		−	0.561420i
$639$	−0.660408	+	1.14386i	−0.0261253	+	0.0452504i
$640$	0.242904	+	0.420722i	0.00960162	+	0.0166305i
$641$	19.6895	−	11.3677i	0.777687	−	0.448998i	−0.0579231	−	0.998321i	$-0.518448\pi$
$641$	19.6895	−	11.3677i	0.777687	−	0.448998i	0.835610	+	0.549323i	$0.185114\pi$
$642$	3.69139	−	6.39367i	0.145687	−	0.252338i
$643$	30.1236			1.18796			0.593979	−	0.804480i	$-0.297556\pi$
$643$	30.1236			1.18796			0.593979	+	0.804480i	$0.297556\pi$
$644$	−3.30250	−	12.2513i	−0.130137	−	0.482767i
$645$	2.56138			0.100854
$646$	−2.85981	+	4.95333i	−0.112518	+	0.194886i
$647$	−9.96335	+	5.75234i	−0.391700	+	0.226148i	−0.682896	−	0.730515i	$-0.739280\pi$
$647$	−9.96335	+	5.75234i	−0.391700	+	0.226148i	0.291197	+	0.956663i	$0.405947\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	5.58782	−	9.67838i	0.219341	−	0.379910i
$650$		−	24.1736i		−	0.948165i
$651$	18.2129	−	16.1818i	0.713818	−	0.634216i
$652$	−17.2112			−0.674044
$653$	4.31398	−	7.47204i	0.168819	−	0.292404i	−0.769186	−	0.639025i	$-0.779338\pi$
$653$	4.31398	−	7.47204i	0.168819	−	0.292404i	0.938005	+	0.346622i	$0.112671\pi$
$654$	0.611537	+	1.05921i	0.0239130	+	0.0414185i
$655$	−7.44678	+	4.29940i	−0.290970	+	0.167991i
$656$	7.52415	+	4.34407i	0.293769	+	0.169608i
$657$		−	3.77504i		−	0.147278i
$658$	−11.0331	+	2.26890i	−0.430114	+	0.0884508i
$659$		−	45.4300i		−	1.76970i	−0.465875	−	0.884851i	$-0.654260\pi$
$659$		−	45.4300i		−	1.76970i	0.465875	−	0.884851i	$-0.345740\pi$
$660$	0.744133	−	1.28888i	0.0289653	−	0.0501694i
$661$	−16.4006	−	28.4066i	−0.637909	−	1.10489i	−0.985891	−	0.167389i	$-0.946466\pi$
$661$	−16.4006	−	28.4066i	−0.637909	−	1.10489i	0.347982	−	0.937501i	$-0.386867\pi$
$662$	−0.155874	−	0.269982i	−0.00605823	−	0.0104932i
$663$	2.12498	−	3.68057i	0.0825274	−	0.142942i
$664$	6.95787			0.270018
$665$	1.76803	+	8.59747i	0.0685612	+	0.333396i
$666$		−	5.56750i		−	0.215736i
$667$	22.1590	−	1.34199i	0.858002	−	0.0519620i
$668$	16.9360	−	9.77800i	0.655273	−	0.378322i
$669$	−3.75304	−	6.50046i	−0.145101	−	0.251322i
$670$	−1.72098	−	0.993610i	−0.0664874	−	0.0383865i
$671$		−	30.0670i		−	1.16072i
$672$	−1.75729	−	1.97786i	−0.0677891	−	0.0762975i
$673$	−23.7788			−0.916606			−0.458303	−	0.888796i	$-0.651543\pi$
$673$	−23.7788			−0.916606			−0.458303	+	0.888796i	$0.651543\pi$
$674$	28.5471	+	16.4817i	1.09959	+	0.634851i
$675$	4.12574	−	2.38200i	0.158800	−	0.0916830i
$676$	6.37388	+	11.0399i	0.245149	+	0.424611i
$677$	−21.7479	+	37.6685i	−0.835841	+	1.44772i	0.0575029	+	0.998345i	$0.481686\pi$
$677$	−21.7479	+	37.6685i	−0.835841	+	1.44772i	−0.893344	+	0.449374i	$0.851647\pi$
$678$	8.65289			0.332312
$679$	23.9520	+	7.95823i	0.919195	+	0.305409i
$680$	−0.406892			−0.0156036
$681$	15.3766	+	8.87766i	0.589231	+	0.340192i
$682$	−14.1049	−	24.4304i	−0.540104	−	0.935487i
$683$	2.58058	+	4.46970i	0.0987431	+	0.171028i	0.911165	−	0.412042i	$-0.135184\pi$
$683$	2.58058	+	4.46970i	0.0987431	+	0.171028i	−0.812422	+	0.583071i	$0.801851\pi$
$684$	3.41446	−	5.91401i	0.130555	−	0.226128i
$685$			2.17059i			0.0829338i
$686$	−18.4536	+	1.56963i	−0.704563	+	0.0599288i
$687$		−	20.5426i		−	0.783749i
$688$	−4.56605	−	2.63621i	−0.174079	−	0.100504i
$689$	21.4306	+	37.1189i	0.816441	+	1.41412i
$690$	2.08444	+	1.04082i	0.0793534	+	0.0396235i
$691$	5.29687	+	3.05815i	0.201502	+	0.116337i	0.597356	−	0.801976i	$-0.296218\pi$
$691$	5.29687	+	3.05815i	0.201502	+	0.116337i	−0.395854	+	0.918314i	$0.629551\pi$
$692$			21.0914i			0.801775i
$693$	−2.55564	+	7.69177i	−0.0970808	+	0.292186i
$694$	−26.1871			−0.994051
$695$	8.40351	+	4.85177i	0.318763	+	0.184038i
$696$	4.00878	−	2.31447i	0.151953	−	0.0877299i
$697$	−6.30192	+	3.63841i	−0.238702	+	0.137815i
$698$	−2.46060	−	1.42063i	−0.0931352	−	0.0537716i
$699$		−	15.6744i		−	0.592861i
$700$	9.42249	−	8.37173i	0.356137	−	0.316422i
$701$		−	40.5366i		−	1.53104i	−0.643409	−	0.765522i	$-0.722481\pi$
$701$		−	40.5366i		−	1.53104i	0.643409	−	0.765522i	$-0.277519\pi$
$702$	−2.53711	+	4.39441i	−0.0957571	+	0.165856i
$703$	32.9262	−	19.0100i	1.24184	−	0.716975i
$704$	−2.65306	+	1.53174i	−0.0999908	+	0.0577297i
$705$	1.03413	−	1.79117i	0.0389477	−	0.0674594i
$706$			4.52869i			0.170440i
$707$	−7.77226	+	1.59833i	−0.292306	+	0.0601112i
$708$	3.64801			0.137101
$709$	−3.22290	−	1.86074i	−0.121038	−	0.0698816i	0.438258	−	0.898849i	$-0.355595\pi$
$709$	−3.22290	−	1.86074i	−0.121038	−	0.0698816i	−0.559297	+	0.828967i	$0.688929\pi$
$710$	−0.320831	−	0.555696i	−0.0120406	−	0.0208549i
$711$	−9.12312	+	5.26723i	−0.342144	+	0.197537i
$712$	−5.22221	+	9.04513i	−0.195710	+	0.338981i
$713$	36.8405	−	24.3525i	1.37969	−	0.912009i
$714$	2.17055	−	0.446363i	0.0812308	−	0.0167047i
$715$	−7.55180			−0.282421
$716$	−8.98104	+	15.5556i	−0.335637	+	0.581341i
$717$	−9.88408	+	5.70658i	−0.369128	+	0.213116i
$718$	15.4334	−	8.91049i	0.575970	−	0.332537i
$719$	−16.9903	−	9.80936i	−0.633632	−	0.365827i	0.148525	−	0.988909i	$-0.452547\pi$
$719$	−16.9903	−	9.80936i	−0.633632	−	0.365827i	−0.782157	+	0.623081i	$0.785881\pi$
$720$	0.485808			0.0181050
$721$	29.6478	−	26.3416i	1.10414	−	0.981012i
$722$	27.6340			1.02843
$723$	−14.8226	−	8.55783i	−0.551258	−	0.318269i
$724$	−3.16433	−	5.48079i	−0.117602	−	0.203692i
$725$	11.0261	+	19.0978i	0.409500	+	0.709275i
$726$	−1.39868	−	0.807526i	−0.0519098	−	0.0299701i
$727$	43.3463			1.60762			0.803812	−	0.594883i	$-0.202802\pi$
$727$	43.3463			1.60762			0.803812	+	0.594883i	$0.202802\pi$
$728$	−4.23305	+	12.7403i	−0.156887	+	0.472187i
$729$	−1.00000			−0.0370370
$730$	1.58824	+	0.916971i	0.0587834	+	0.0339386i
$731$	3.82433	−	2.20798i	0.141448	−	0.0816650i
$732$	8.49972	−	4.90732i	0.314159	−	0.181380i
$733$	18.1992	−	31.5219i	0.672203	−	1.16429i	−0.305075	−	0.952328i	$-0.598682\pi$
$733$	18.1992	−	31.5219i	0.672203	−	1.16429i	0.977278	−	0.211961i	$-0.0679851\pi$
$734$	−23.5008			−0.867429
$735$	2.03512	−	2.72447i	0.0750663	−	0.100494i
$736$	−2.64460	−	4.00076i	−0.0974813	−	0.147470i
$737$	6.26567	−	10.8525i	0.230799	−	0.399755i
$738$	7.52415	−	4.34407i	0.276968	−	0.159908i
$739$	−17.7137	−	30.6811i	−0.651610	−	1.12862i	−0.982732	−	0.185033i	$-0.940761\pi$
$739$	−17.7137	−	30.6811i	−0.651610	−	1.12862i	0.331122	−	0.943588i	$-0.392573\pi$
$740$	2.34237	+	1.35237i	0.0861072	+	0.0497140i
$741$	−34.6514			−1.27295
$742$	−7.04659	+	21.2083i	−0.258688	+	0.778580i
$743$		−	39.9225i		−	1.46461i	−0.680975	−	0.732307i	$-0.738444\pi$
$743$		−	39.9225i		−	1.46461i	0.680975	−	0.732307i	$-0.261556\pi$
$744$	4.60419	−	7.97469i	0.168798	−	0.292366i
$745$	−8.24570	+	4.76066i	−0.302099	+	0.174417i
$746$	−4.55066	+	2.62732i	−0.166611	+	0.0961931i
$747$	3.47893	−	6.02569i	0.127288	−	0.220468i
$748$		−	2.56585i		−	0.0938167i
$749$	−12.9737	−	14.6021i	−0.474049	−	0.533548i
$750$			4.74342i			0.173205i
$751$	17.1730	+	9.91482i	0.626651	+	0.361797i	0.779454	−	0.626460i	$-0.215497\pi$
$751$	17.1730	+	9.91482i	0.626651	+	0.361797i	−0.152803	+	0.988257i	$0.548830\pi$
$752$	−3.68699	+	2.12869i	−0.134451	+	0.0776252i
$753$	22.8703	−	13.2042i	0.833441	−	0.481187i
$754$	−20.3415	−	11.7442i	−0.740793	−	0.427697i
$755$	4.21906			0.153547
$756$	−2.59152	+	0.532933i	−0.0942527	+	0.0193826i
$757$		−	29.3384i		−	1.06632i	−0.846013	−	0.533162i	$-0.821004\pi$
$757$		−	29.3384i		−	1.06632i	0.846013	−	0.533162i	$-0.178996\pi$
$758$	27.7725	+	16.0345i	1.00874	+	0.582398i
$759$	−6.56339	+	13.1444i	−0.238236	+	0.477112i
$760$	1.65877	+	2.87307i	0.0601699	+	0.104217i
$761$	−40.7579	−	23.5316i	−1.47747	−	0.853020i	−0.477798	−	0.878470i	$-0.658565\pi$
$761$	−40.7579	−	23.5316i	−1.47747	−	0.853020i	−0.999676	+	0.0254494i	$0.991898\pi$
$762$			7.27976i			0.263718i
$763$	3.16962	−	0.651817i	0.114748	−	0.0235974i
$764$		−	18.1009i		−	0.654868i
$765$	−0.203446	+	0.352379i	−0.00735561	+	0.0127403i
$766$	9.14917	+	15.8468i	0.330573	+	0.572569i
$767$	−9.25541	−	16.0308i	−0.334194	−	0.578840i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−17.8827			−0.644867			−0.322433	−	0.946592i	$-0.604501\pi$
$769$	−17.8827			−0.644867			−0.322433	+	0.946592i	$0.604501\pi$
$770$	−2.61532	−	2.94358i	−0.0942496	−	0.106079i
$771$	−25.0504			−0.902168
$772$	−7.59857	+	13.1611i	−0.273478	+	0.473679i
$773$	23.0130	+	39.8596i	0.827719	+	1.43365i	0.899824	+	0.436254i	$0.143695\pi$
$773$	23.0130	+	39.8596i	0.827719	+	1.43365i	−0.0721051	+	0.997397i	$0.522972\pi$
$774$	−4.56605	+	2.63621i	−0.164123	+	0.0947565i
$775$	37.9914	+	21.9343i	1.36469	+	0.787904i
$776$	9.53965			0.342453
$777$	−13.9788	−	4.64456i	−0.501487	−	0.166623i
$778$			31.4343i			1.12698i
$779$	51.3818	+	29.6653i	1.84094	+	1.06287i
$780$	−1.23255	−	2.13484i	−0.0441323	−	0.0764395i
$781$	3.50420	−	2.02315i	0.125390	−	0.0723940i
$782$	4.00944	−	0.242819i	0.143377	−	0.00868317i
$783$		−	4.62895i		−	0.165425i
$784$	−6.43196	+	2.76222i	−0.229713	+	0.0986506i
$785$	−3.63380			−0.129696
$786$	8.85000	−	15.3287i	0.315669	−	0.546755i
$787$	12.0189	+	20.8173i	0.428427	+	0.742057i	0.996734	−	0.0807596i	$-0.0257346\pi$
$787$	12.0189	+	20.8173i	0.428427	+	0.742057i	−0.568307	+	0.822817i	$0.692401\pi$
$788$	2.26058	+	3.91544i	0.0805298	+	0.139482i
$789$	−7.92239	+	13.7220i	−0.282045	+	0.488515i
$790$		−	5.11773i		−	0.182081i
$791$	7.21847	−	21.7256i	0.256659	−	0.772473i
$792$			3.06349i			0.108856i
$793$	−43.1295	−	24.9008i	−1.53157	−	0.884255i
$794$	9.69103	−	5.59512i	0.343922	−	0.198563i
$795$	−2.05177	−	3.55378i	−0.0727689	−	0.126039i
$796$	1.40852	−	2.43964i	0.0499238	−	0.0864706i
$797$	−25.2324			−0.893777			−0.446888	−	0.894590i	$-0.647468\pi$
$797$	−25.2324			−0.893777			−0.446888	+	0.894590i	$0.647468\pi$
$798$	−12.0004	−	13.5066i	−0.424810	−	0.478129i
$799$		−	3.56580i		−	0.126149i
$800$	2.38200	−	4.12574i	0.0842163	−	0.145867i
$801$	5.22221	+	9.04513i	0.184518	+	0.319594i
$802$	−11.5257	+	6.65435i	−0.406986	+	0.234973i
$803$	−5.78239	+	10.0154i	−0.204056	+	0.353435i
$804$	4.09055			0.144263
$805$	4.35219	−	4.36531i	0.153394	−	0.153857i
$806$	−46.7254			−1.64583
$807$	9.19246	−	15.9218i	0.323590	−	0.560474i
$808$	−2.59731	+	1.49955i	−0.0913729	+	0.0527542i
$809$	14.9227	+	25.8468i	0.524653	+	0.908725i	0.999588	+	0.0287045i	$0.00913818\pi$
$809$	14.9227	+	25.8468i	0.524653	+	0.908725i	−0.474935	+	0.880021i	$0.657528\pi$
$810$	0.242904	−	0.420722i	0.00853477	−	0.0147827i
$811$		−	9.88754i		−	0.347198i	−0.984816	−	0.173599i	$-0.944460\pi$
$811$		−	9.88754i		−	0.347198i	0.984816	−	0.173599i	$-0.0555397\pi$
$812$	−2.46692	−	11.9960i	−0.0865719	−	0.420977i
$813$	−2.10387			−0.0737859
$814$	−8.52798	+	14.7709i	−0.298905	+	0.517719i
$815$	−4.18068	−	7.24114i	−0.146443	−	0.253646i
$816$	0.725347	−	0.418779i	0.0253922	−	0.0146602i
$817$	−31.1811	−	18.0024i	−1.09089	−	0.629825i
$818$		−	25.4819i		−	0.890953i
$819$	8.91691	+	10.0361i	0.311582	+	0.350689i
$820$			4.22077i			0.147396i
$821$	4.91451	−	8.51218i	0.171518	−	0.297077i	−0.767433	−	0.641129i	$-0.778466\pi$
$821$	4.91451	−	8.51218i	0.171518	−	0.297077i	0.938951	+	0.344052i	$0.111800\pi$
$822$	−2.23400	−	3.86939i	−0.0779195	−	0.134961i
$823$	−14.2192	−	24.6284i	−0.495651	−	0.858492i	0.504337	−	0.863507i	$-0.331737\pi$
$823$	−14.2192	−	24.6284i	−0.495651	−	0.858492i	−0.999987	+	0.00501499i	$0.998404\pi$
$824$	7.49493	−	12.9816i	0.261098	−	0.452235i
$825$	−14.5944			−0.508112
$826$	3.04327	−	9.15939i	0.105889	−	0.318696i
$827$		−	11.0980i		−	0.385914i	−0.981207	−	0.192957i	$-0.938192\pi$
$827$		−	11.0980i		−	0.385914i	0.981207	−	0.192957i	$-0.0618077\pi$
$828$	−4.78706	+	0.289912i	−0.166362	+	0.0100752i
$829$	41.0940	−	23.7257i	1.42726	−	0.824026i	0.430352	−	0.902661i	$-0.358390\pi$
$829$	41.0940	−	23.7257i	1.42726	−	0.824026i	0.996903	+	0.0786350i	$0.0250562\pi$
$830$	1.69009	+	2.92733i	0.0586640	+	0.101609i
$831$	−11.4499	−	6.61062i	−0.397194	−	0.229320i
$832$			5.07423i			0.175917i
$833$	0.690007	−	5.82216i	0.0239073	−	0.201726i
$834$	−19.9740			−0.691644
$835$	8.22764	+	4.75023i	0.284729	+	0.164388i
$836$	−18.1175	+	10.4601i	−0.626606	+	0.361771i
$837$	−4.60419	−	7.97469i	−0.159144	−	0.275646i
$838$	−6.68932	+	11.5862i	−0.231079	+	0.400240i
$839$	2.13043			0.0735506			0.0367753	−	0.999324i	$-0.488291\pi$
$839$	2.13043			0.0735506			0.0367753	+	0.999324i	$0.488291\pi$
$840$	0.405274	−	1.21976i	0.0139833	−	0.0420858i
$841$	−7.57286			−0.261133
$842$	4.39470	+	2.53728i	0.151451	+	0.0874404i
$843$	−11.6908	−	20.2491i	−0.402654	−	0.697417i
$844$	−3.58553	−	6.21033i	−0.123419	−	0.213768i
$845$	−3.09648	+	5.36326i	−0.106522	+	0.184502i
$846$			4.25737i			0.146372i
$847$	−3.19434	+	2.83812i	−0.109759	+	0.0975191i
$848$			8.44685i			0.290066i
$849$	−0.901145	−	0.520276i	−0.0309272	−	0.0178558i
$850$	1.99506	+	3.45555i	0.0684300	+	0.118524i
$851$	−23.8883	−	11.9281i	−0.818881	−	0.408891i
$852$	1.14386	+	0.660408i	0.0391880	+	0.0226252i
$853$			6.39947i			0.219114i	0.993981	+	0.109557i	$0.0349432\pi$
$853$			6.39947i			0.219114i	−0.993981	+	0.109557i	$0.965057\pi$
$854$	−5.23055	−	25.4348i	−0.178986	−	0.870362i
$855$	3.31754			0.113457
$856$	−6.39367	−	3.69139i	−0.218531	−	0.126169i
$857$	−12.9055	+	7.45097i	−0.440842	+	0.254520i	−0.703955	−	0.710245i	$-0.748584\pi$
$857$	−12.9055	+	7.45097i	−0.440842	+	0.254520i	0.263113	+	0.964765i	$0.415251\pi$
$858$	13.4622	−	7.77241i	0.459592	−	0.265346i
$859$	24.1115	+	13.9208i	0.822674	+	0.474971i	0.851338	−	0.524618i	$-0.175792\pi$
$859$	24.1115	+	13.9208i	0.822674	+	0.474971i	−0.0286636	+	0.999589i	$0.509125\pi$
$860$		−	2.56138i		−	0.0873424i
$861$	−4.63020	−	22.5155i	−0.157797	−	0.767327i
$862$		−	21.7899i		−	0.742167i
$863$	−15.0719	+	26.1053i	−0.513053	+	0.888635i	0.486832	+	0.873496i	$0.338152\pi$
$863$	−15.0719	+	26.1053i	−0.513053	+	0.888635i	−0.999885	+	0.0151390i	$0.995181\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−8.87361	+	5.12318i	−0.301712	+	0.174193i
$866$	0.0718807	−	0.124501i	0.00244261	−	0.00423072i
$867$		−	16.2985i		−	0.553526i
$868$	−16.1818	−	18.2129i	−0.549248	−	0.618185i
$869$	32.2722			1.09476
$870$	1.94750	+	1.12439i	0.0660264	+	0.0381204i
$871$	−10.3782	−	17.9755i	−0.351651	−	0.609078i
$872$	1.05921	−	0.611537i	0.0358695	−	0.0207092i
$873$	4.76982	−	8.26158i	0.161434	−	0.279612i
$874$	−18.0598	−	27.3208i	−0.610880	−	0.924141i
$875$	11.9097	+	3.95709i	0.402623	+	0.133774i
$876$	−3.77504			−0.127547
$877$	−18.2441	+	31.5997i	−0.616059	+	1.06705i	0.374139	+	0.927373i	$0.377938\pi$
$877$	−18.2441	+	31.5997i	−0.616059	+	1.06705i	−0.990198	+	0.139672i	$0.955395\pi$
$878$	−24.8389	+	14.3408i	−0.838274	+	0.483978i
$879$	−8.50315	+	4.90929i	−0.286804	+	0.165586i
$880$	−1.28888	−	0.744133i	−0.0434480	−	0.0250847i
$881$	52.0502			1.75362			0.876808	−	0.480840i	$-0.159668\pi$
$881$	52.0502			1.75362			0.876808	+	0.480840i	$0.159668\pi$
$882$	−0.823832	+	6.95135i	−0.0277399	+	0.234064i
$883$	31.9734			1.07599			0.537995	−	0.842948i	$-0.319182\pi$
$883$	31.9734			1.07599			0.537995	+	0.842948i	$0.319182\pi$
$884$	−3.68057	−	2.12498i	−0.123791	−	0.0714708i
$885$	0.886116	+	1.53480i	0.0297865	+	0.0515917i
$886$	13.9610	+	24.1811i	0.469027	+	0.812379i
$887$	32.0287	+	18.4918i	1.07542	+	0.620893i	0.929657	−	0.368427i	$-0.120104\pi$
$887$	32.0287	+	18.4918i	1.07542	+	0.620893i	0.145761	+	0.989320i	$0.453437\pi$
$888$	−5.56750			−0.186833
$889$	18.2780	+	6.07297i	0.613023	+	0.203681i
$890$	−5.07398			−0.170080
$891$	2.65306	+	1.53174i	0.0888807	+	0.0513153i
$892$	−6.50046	+	3.75304i	−0.217651	+	0.125661i
$893$	−25.1782	+	14.5366i	−0.842555	+	0.486449i
$894$	9.79947	−	16.9732i	0.327743	−	0.567668i
$895$	−8.72612			−0.291682
$896$	−1.97786	+	1.75729i	−0.0660755	+	0.0587071i
$897$	13.4193	+	20.3008i	0.448058	+	0.677823i
$898$	−9.87947	+	17.1117i	−0.329682	+	0.571026i
$899$	36.9144	−	21.3126i	1.23117	−	0.710814i
$900$	−2.38200	−	4.12574i	−0.0793998	−	0.137525i
$901$	−6.12690	−	3.53737i	−0.204117	−	0.117847i
$902$	−26.6160			−0.886216
$903$	2.80985	+	13.6636i	0.0935058	+	0.454695i
$904$		−	8.65289i		−	0.287791i
$905$	1.53726	−	2.66261i	0.0511002	−	0.0885081i
$906$	−7.52112	+	4.34232i	−0.249872	+	0.144264i
$907$	−10.2414	+	5.91288i	−0.340061	+	0.196334i	−0.660299	−	0.751003i	$-0.729570\pi$
$907$	−10.2414	+	5.91288i	−0.340061	+	0.196334i	0.320238	+	0.947337i	$0.396237\pi$
$908$	8.87766	−	15.3766i	0.294615	−	0.510289i
$909$			2.99911i			0.0994742i
$910$	−6.38835	+	1.31373i	−0.211772	+	0.0435498i
$911$		−	16.1989i		−	0.536694i	−0.963322	−	0.268347i	$-0.913523\pi$
$911$		−	16.1989i		−	0.536694i	0.963322	−	0.268347i	$-0.0864774\pi$
$912$	−5.91401	−	3.41446i	−0.195832	−	0.113064i
$913$	−18.4596	+	10.6577i	−0.610924	+	0.352717i
$914$	28.7619	−	16.6057i	0.951358	−	0.549267i
$915$	4.12923	+	2.38401i	0.136508	+	0.0788131i
$916$	−20.5426			−0.678747
$917$	−31.1041	−	35.0081i	−1.02715	−	1.15607i
$918$		−	0.837558i		−	0.0276435i
$919$	51.1444	+	29.5282i	1.68710	+	0.974046i	0.956723	+	0.291000i	$0.0939879\pi$
$919$	51.1444	+	29.5282i	1.68710	+	0.974046i	0.730375	+	0.683047i	$0.239345\pi$
$920$	1.04082	−	2.08444i	0.0343149	−	0.0687220i
$921$	4.17774	+	7.23605i	0.137661	+	0.238436i
$922$	−15.6584	−	9.04038i	−0.515682	−	0.297729i
$923$		−	6.70212i		−	0.220603i
$924$	7.69177	+	2.55564i	0.253041	+	0.0840744i
$925$		−	26.5235i		−	0.872088i
$926$	7.24035	−	12.5407i	0.237933	−	0.412111i
$927$	−7.49493	−	12.9816i	−0.246166	−	0.426371i
$928$	−2.31447	−	4.00878i	−0.0759763	−	0.131595i
$929$	28.8442	+	16.6532i	0.946349	+	0.546375i	0.891945	−	0.452144i	$-0.149341\pi$
$929$	28.8442	+	16.6532i	0.946349	+	0.546375i	0.0544041	+	0.998519i	$0.482674\pi$
$930$	4.47351			0.146692
$931$	−43.9233	+	18.8629i	−1.43953	+	0.618208i
$932$	−15.6744			−0.513433
$933$	−6.15900	+	10.6677i	−0.201637	+	0.349245i
$934$	−15.4907	−	26.8307i	−0.506871	−	0.877927i
$935$	1.07951	−	0.623255i	0.0353037	−	0.0203826i
$936$	4.39441	+	2.53711i	0.143636	+	0.0829281i
$937$	11.8010			0.385520			0.192760	−	0.981246i	$-0.438256\pi$
$937$	11.8010			0.385520			0.192760	+	0.981246i	$0.438256\pi$
$938$	3.41244	−	10.2705i	0.111420	−	0.335344i
$939$			26.6602i			0.870022i
$940$	−1.79117	−	1.03413i	−0.0584216	−	0.0337297i
$941$	4.11457	+	7.12665i	0.134131	+	0.232322i	0.925265	−	0.379321i	$-0.123842\pi$
$941$	4.11457	+	7.12665i	0.134131	+	0.232322i	−0.791134	+	0.611643i	$0.790509\pi$
$942$	6.47780	−	3.73996i	0.211058	−	0.121854i
$943$	−2.51880	−	41.5907i	−0.0820234	−	1.35438i
$944$		−	3.64801i		−	0.118733i
$945$	−0.853707	−	0.960858i	−0.0277711	−	0.0312567i
$946$	16.1520			0.525146
$947$	−9.99078	+	17.3045i	−0.324657	+	0.562322i	−0.981443	−	0.191755i	$-0.938582\pi$
$947$	−9.99078	+	17.3045i	−0.324657	+	0.562322i	0.656786	+	0.754077i	$0.271915\pi$
$948$	5.26723	+	9.12312i	0.171072	+	0.296305i
$949$	9.57769	+	16.5891i	0.310905	+	0.538503i
$950$	16.2664	−	28.1743i	0.527753	−	0.914095i
$951$			18.3747i			0.595841i
$952$	−0.446363	−	2.17055i	−0.0144667	−	0.0703479i
$953$		−	11.3231i		−	0.366791i	−0.983039	−	0.183395i	$-0.941291\pi$
$953$		−	11.3231i		−	0.366791i	0.983039	−	0.183395i	$-0.0587088\pi$
$954$	7.31519	+	4.22343i	0.236838	+	0.136738i
$955$	7.61545	−	4.39678i	0.246430	−	0.142277i
$956$	5.70658	+	9.88408i	0.184564	+	0.319674i
$957$	−7.09036	+	12.2809i	−0.229199	+	0.396984i
$958$	−16.0879			−0.519775
$959$	−11.5789	+	2.38114i	−0.373902	+	0.0768911i
$960$		−	0.485808i		−	0.0156794i
$961$	26.8972	−	46.5873i	0.867651	−	1.50281i
$962$	14.1254	+	24.4659i	0.455420	+	0.788811i
$963$	−6.39367	+	3.69139i	−0.206033	+	0.118953i
$964$	−8.55783	+	14.8226i	−0.275629	+	0.477404i
$965$	−7.38289			−0.237664
$966$	−3.26558	+	12.2612i	−0.105068	+	0.394496i
$967$	−38.2537			−1.23016			−0.615078	−	0.788466i	$-0.710876\pi$
$967$	−38.2537			−1.23016			−0.615078	+	0.788466i	$0.710876\pi$
$968$	−0.807526	+	1.39868i	−0.0259549	+	0.0449552i
$969$	4.95333	−	2.85981i	0.159124	−	0.0918702i
$970$	2.31722	+	4.01354i	0.0744014	+	0.128867i
$971$	18.3139	−	31.7205i	0.587720	−	1.01796i	−0.406811	−	0.913512i	$-0.633359\pi$
$971$	18.3139	−	31.7205i	0.587720	−	1.01796i	0.994530	−	0.104448i	$-0.0333075\pi$
$972$			1.00000i			0.0320750i
$973$	−16.6629	+	50.1506i	−0.534187	+	1.60775i
$974$	−9.42460			−0.301984
$975$	−12.0868	+	20.9349i	−0.387087	+	0.670454i
$976$	−4.90732	−	8.49972i	−0.157079	−	0.272070i
$977$	−18.6175	+	10.7488i	−0.595625	+	0.343884i	−0.767319	−	0.641266i	$-0.778409\pi$
$977$	−18.6175	+	10.7488i	−0.595625	+	0.343884i	0.171693	+	0.985150i	$0.445076\pi$
$978$	14.9054	+	8.60562i	0.476621	+	0.275177i
$979$		−	31.9963i		−	1.02261i
$980$	−2.72447	−	2.03512i	−0.0870301	−	0.0650094i
$981$		−	1.22307i		−	0.0390497i
$982$	−13.1764	+	22.8221i	−0.420475	+	0.728283i
$983$	9.84579	+	17.0534i	0.314032	+	0.543919i	0.979231	−	0.202747i	$-0.0649868\pi$
$983$	9.84579	+	17.0534i	0.314032	+	0.543919i	−0.665199	+	0.746666i	$0.731653\pi$
$984$	−4.34407	−	7.52415i	−0.138484	−	0.239861i
$985$	−1.09821	+	1.90215i	−0.0349918	+	0.0606075i
$986$	3.87701			0.123469
$987$	10.6894	+	3.55162i	0.340247	+	0.113049i
$988$			34.6514i			1.10241i
$989$	1.52854	+	25.2394i	0.0486047	+	0.802565i
$990$	−1.28888	+	0.744133i	−0.0409632	+	0.0236501i
$991$	−16.1075	−	27.8991i	−0.511673	−	0.886243i	−0.999908	−	0.0135315i	$-0.995693\pi$
$991$	−16.1075	−	27.8991i	−0.511673	−	0.886243i	0.488236	−	0.872712i	$-0.337641\pi$
$992$	−7.97469	−	4.60419i	−0.253197	−	0.146183i
$993$			0.311749i			0.00989305i
$994$	2.61238	−	2.32106i	0.0828598	−	0.0736196i
$995$	1.36854			0.0433858
$996$	−6.02569	−	3.47893i	−0.190931	−	0.110234i
$997$	−27.9939	+	16.1623i	−0.886574	+	0.511864i	−0.872820	−	0.488042i	$-0.837711\pi$
$997$	−27.9939	+	16.1623i	−0.886574	+	0.511864i	−0.0137538	+	0.999905i	$0.504378\pi$
$998$	−14.3554	−	24.8642i	−0.454411	−	0.787063i
$999$	−2.78375	+	4.82160i	−0.0880739	+	0.152549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.a.229.13	yes	32
7.3	odd	6	inner	966.2.k.a.367.12	yes	32
23.22	odd	2	inner	966.2.k.a.229.12	✓	32
161.45	even	6	inner	966.2.k.a.367.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.a.229.12	✓	32	23.22	odd	2	inner
966.2.k.a.229.13	yes	32	1.1	even	1	trivial
966.2.k.a.367.12	yes	32	7.3	odd	6	inner
966.2.k.a.367.13	yes	32	161.45	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.242904 - 0.420722i) q^{5} +1.00000i q^{6} +(2.51079 + 0.834227i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.242904 - 0.420722i) q^{5} +1.00000i q^{6} +(2.51079 + 0.834227i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.242904 + 0.420722i) q^{10} +(-2.65306 + 1.53174i) q^{11} +(-0.866025 - 0.500000i) q^{12} +5.07423i q^{13} +(-1.97786 + 1.75729i) q^{14} -0.485808i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.418779 - 0.725347i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.41446 + 5.91401i) q^{19} -0.485808 q^{20} +(2.59152 - 0.532933i) q^{21} -3.06349i q^{22} +(4.78706 - 0.289912i) q^{23} +(0.866025 - 0.500000i) q^{24} +(2.38200 + 4.12574i) q^{25} +(-4.39441 - 2.53711i) q^{26} -1.00000i q^{27} +(-0.532933 - 2.59152i) q^{28} +4.62895 q^{29} +(0.420722 + 0.242904i) q^{30} +(7.97469 - 4.60419i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.53174 + 2.65306i) q^{33} +0.837558 q^{34} +(0.960858 - 0.853707i) q^{35} -1.00000 q^{36} +(-4.82160 - 2.78375i) q^{37} +(-3.41446 - 5.91401i) q^{38} +(2.53711 + 4.39441i) q^{39} +(0.242904 - 0.420722i) q^{40} -8.68814i q^{41} +(-0.834227 + 2.51079i) q^{42} +5.27242i q^{43} +(2.65306 + 1.53174i) q^{44} +(-0.242904 - 0.420722i) q^{45} +(-2.14246 + 4.29067i) q^{46} +(3.68699 + 2.12869i) q^{47} +1.00000i q^{48} +(5.60813 + 4.18914i) q^{49} -4.76399 q^{50} +(-0.725347 - 0.418779i) q^{51} +(4.39441 - 2.53711i) q^{52} +(7.31519 - 4.22343i) q^{53} +(0.866025 + 0.500000i) q^{54} +1.48827i q^{55} +(2.51079 + 0.834227i) q^{56} +6.82891i q^{57} +(-2.31447 + 4.00878i) q^{58} +(-3.15927 + 1.82401i) q^{59} +(-0.420722 + 0.242904i) q^{60} +(-4.90732 + 8.49972i) q^{61} +9.20838i q^{62} +(1.97786 - 1.75729i) q^{63} +1.00000 q^{64} +(2.13484 + 1.23255i) q^{65} +(-1.53174 - 2.65306i) q^{66} +(-3.54252 + 2.04527i) q^{67} +(-0.418779 + 0.725347i) q^{68} +(4.00076 - 2.64460i) q^{69} +(0.258903 + 1.25898i) q^{70} -1.32082 q^{71} +(0.500000 - 0.866025i) q^{72} +(3.26928 - 1.88752i) q^{73} +(4.82160 - 2.78375i) q^{74} +(4.12574 + 2.38200i) q^{75} +6.82891 q^{76} +(-7.93909 + 1.63263i) q^{77} -5.07423 q^{78} +(-9.12312 - 5.26723i) q^{79} +(0.242904 + 0.420722i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.52415 + 4.34407i) q^{82} +6.95787 q^{83} +(-1.75729 - 1.97786i) q^{84} -0.406892 q^{85} +(-4.56605 - 2.63621i) q^{86} +(4.00878 - 2.31447i) q^{87} +(-2.65306 + 1.53174i) q^{88} +(-5.22221 + 9.04513i) q^{89} +0.485808 q^{90} +(-4.23305 + 12.7403i) q^{91} +(-2.64460 - 4.00076i) q^{92} +(4.60419 - 7.97469i) q^{93} +(-3.68699 + 2.12869i) q^{94} +(1.65877 + 2.87307i) q^{95} +(-0.866025 - 0.500000i) q^{96} +9.53965 q^{97} +(-6.43196 + 2.76222i) q^{98} +3.06349i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9} - 16 q^{16} + 16 q^{18} + 8 q^{23} - 24 q^{25} - 12 q^{26} - 8 q^{29} + 48 q^{31} - 16 q^{32} - 20 q^{35} - 32 q^{36} - 8 q^{39} + 8 q^{46} + 12 q^{47} + 24 q^{49} + 48 q^{50} + 12 q^{52} + 4 q^{58} - 12 q^{59} + 32 q^{64} + 64 q^{70} + 48 q^{71} + 16 q^{72} + 12 q^{73} + 36 q^{75} + 64 q^{77} + 16 q^{78} - 16 q^{81} - 12 q^{82} + 32 q^{85} - 24 q^{87} - 16 q^{92} - 12 q^{94} + 40 q^{95} - 24 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9 - 16 * q^16 + 16 * q^18 + 8 * q^23 - 24 * q^25 - 12 * q^26 - 8 * q^29 + 48 * q^31 - 16 * q^32 - 20 * q^35 - 32 * q^36 - 8 * q^39 + 8 * q^46 + 12 * q^47 + 24 * q^49 + 48 * q^50 + 12 * q^52 + 4 * q^58 - 12 * q^59 + 32 * q^64 + 64 * q^70 + 48 * q^71 + 16 * q^72 + 12 * q^73 + 36 * q^75 + 64 * q^77 + 16 * q^78 - 16 * q^81 - 12 * q^82 + 32 * q^85 - 24 * q^87 - 16 * q^92 - 12 * q^94 + 40 * q^95 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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