LMFDB - Embedded newform 357.2.p.a.16.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(16,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("357.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.p (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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			16.7
Character	$\chi$	$=$	357.16
Dual form			357.2.p.a.67.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.636934 + 1.10320i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.188631 + 0.326718i) q^{4} +(-2.74862 - 1.58692i) q^{5} -1.27387i q^{6} +(1.56475 - 2.13344i) q^{7} -3.02832 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.636934 + 1.10320i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.188631 + 0.326718i) q^{4} +(-2.74862 - 1.58692i) q^{5} -1.27387i q^{6} +(1.56475 - 2.13344i) q^{7} -3.02832 q^{8} +(0.500000 - 0.866025i) q^{9} +(3.50138 - 2.02152i) q^{10} +(4.27881 - 2.47037i) q^{11} +(-0.326718 - 0.188631i) q^{12} +0.743886 q^{13} +(1.35697 + 3.08509i) q^{14} +3.17383 q^{15} +(1.55158 - 2.68741i) q^{16} +(-1.94771 + 3.63406i) q^{17} +(0.636934 + 1.10320i) q^{18} +(3.14440 - 5.44627i) q^{19} -1.19737i q^{20} +(-0.288391 + 2.62999i) q^{21} +6.29386i q^{22} +(2.82658 + 1.63193i) q^{23} +(2.62260 - 1.51416i) q^{24} +(2.53661 + 4.39354i) q^{25} +(-0.473806 + 0.820657i) q^{26} +1.00000i q^{27} +(0.992193 + 0.108799i) q^{28} -6.08788i q^{29} +(-2.02152 + 3.50138i) q^{30} +(-4.76674 + 2.75208i) q^{31} +(-1.05181 - 1.82180i) q^{32} +(-2.47037 + 4.27881i) q^{33} +(-2.76854 - 4.46337i) q^{34} +(-7.68649 + 3.38089i) q^{35} +0.377262 q^{36} +(3.27785 + 1.89247i) q^{37} +(4.00555 + 6.93782i) q^{38} +(-0.644224 + 0.371943i) q^{39} +(8.32369 + 4.80569i) q^{40} -10.9609i q^{41} +(-2.71772 - 1.99328i) q^{42} +8.93958 q^{43} +(1.61423 + 0.931977i) q^{44} +(-2.74862 + 1.58692i) q^{45} +(-3.60069 + 2.07886i) q^{46} +(4.61618 - 7.99546i) q^{47} +3.10315i q^{48} +(-2.10313 - 6.67659i) q^{49} -6.46262 q^{50} +(-0.130267 - 4.12105i) q^{51} +(0.140320 + 0.243041i) q^{52} +(3.57891 + 6.19885i) q^{53} +(-1.10320 - 0.636934i) q^{54} -15.6811 q^{55} +(-4.73855 + 6.46073i) q^{56} +6.28881i q^{57} +(6.71616 + 3.87758i) q^{58} +(0.996006 + 1.72513i) q^{59} +(0.598683 + 1.03695i) q^{60} +(-3.35339 - 1.93608i) q^{61} -7.01157i q^{62} +(-1.06524 - 2.42183i) q^{63} +8.88605 q^{64} +(-2.04466 - 1.18049i) q^{65} +(-3.14693 - 5.45064i) q^{66} +(-5.24920 - 9.09187i) q^{67} +(-1.55471 + 0.0491446i) q^{68} -3.26385 q^{69} +(1.16598 - 10.6332i) q^{70} +8.26433i q^{71} +(-1.51416 + 2.62260i) q^{72} +(0.712022 - 0.411086i) q^{73} +(-4.17555 + 2.41076i) q^{74} +(-4.39354 - 2.53661i) q^{75} +2.37253 q^{76} +(1.42487 - 12.9941i) q^{77} -0.947613i q^{78} +(-11.4826 - 6.62947i) q^{79} +(-8.52939 + 4.92444i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(12.0921 + 6.98137i) q^{82} -14.5817 q^{83} +(-0.913664 + 0.401874i) q^{84} +(11.1205 - 6.89781i) q^{85} +(-5.69392 + 9.86216i) q^{86} +(3.04394 + 5.27226i) q^{87} +(-12.9576 + 7.48108i) q^{88} +(6.37433 - 11.0407i) q^{89} -4.04304i q^{90} +(1.16399 - 1.58704i) q^{91} +1.23133i q^{92} +(2.75208 - 4.76674i) q^{93} +(5.88040 + 10.1852i) q^{94} +(-17.2856 + 9.97982i) q^{95} +(1.82180 + 1.05181i) q^{96} +2.95888i q^{97} +(8.70518 + 1.93237i) q^{98} -4.94075i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) $ 48 * q - 24 * q^4 + 24 * q^9	$ 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.636934	+	1.10320i	−0.450380	+	0.780081i	−0.998410	−	0.0563778i	$-0.982045\pi$
$2$	−0.636934	+	1.10320i	−0.450380	+	0.780081i	0.548029	+	0.836459i	$0.315378\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.188631	+	0.326718i	0.0943154	+	0.163359i
$5$	−2.74862	−	1.58692i	−1.22922	−	0.709691i	−0.262354	−	0.964972i	$-0.584499\pi$
$5$	−2.74862	−	1.58692i	−1.22922	−	0.709691i	−0.966867	+	0.255281i	$0.917832\pi$
$6$		−	1.27387i		−	0.520054i
$7$	1.56475	−	2.13344i	0.591419	−	0.806364i
$7$	1.56475	−	2.13344i	0.591419	−	0.806364i
$8$	−3.02832			−1.07067
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	3.50138	−	2.02152i	1.10723	−	0.639261i
$11$	4.27881	−	2.47037i	1.29011	−	0.744846i	0.311437	−	0.950267i	$-0.399190\pi$
$11$	4.27881	−	2.47037i	1.29011	−	0.744846i	0.978674	+	0.205421i	$0.0658563\pi$
$12$	−0.326718	−	0.188631i	−0.0943154	−	0.0544530i
$13$	0.743886			0.206317			0.103158	−	0.994665i	$-0.467105\pi$
$13$	0.743886			0.206317			0.103158	+	0.994665i	$0.467105\pi$
$14$	1.35697	+	3.08509i	0.362666	+	0.824525i
$15$	3.17383			0.819481
$16$	1.55158	−	2.68741i	0.387894	−	0.671852i
$17$	−1.94771	+	3.63406i	−0.472389	+	0.881390i
$17$	−1.94771	+	3.63406i	−0.472389	+	0.881390i
$18$	0.636934	+	1.10320i	0.150127	+	0.260027i
$19$	3.14440	−	5.44627i	0.721376	−	1.24946i	−0.239073	−	0.971002i	$-0.576843\pi$
$19$	3.14440	−	5.44627i	0.721376	−	1.24946i	0.960448	−	0.278458i	$-0.0898233\pi$
$20$		−	1.19737i		−	0.267739i
$21$	−0.288391	+	2.62999i	−0.0629321	+	0.573910i
$22$			6.29386i			1.34186i
$23$	2.82658	+	1.63193i	0.589383	+	0.340280i	0.764853	−	0.644204i	$-0.222811\pi$
$23$	2.82658	+	1.63193i	0.589383	+	0.340280i	−0.175471	+	0.984485i	$0.556145\pi$
$24$	2.62260	−	1.51416i	0.535336	−	0.309076i
$25$	2.53661	+	4.39354i	0.507322	+	0.878708i
$26$	−0.473806	+	0.820657i	−0.0929211	+	0.160944i
$27$			1.00000i			0.192450i
$28$	0.992193	+	0.108799i	0.187507	+	0.0205611i
$29$		−	6.08788i		−	1.13049i	−0.824923	−	0.565245i	$-0.808782\pi$
$29$		−	6.08788i		−	1.13049i	0.824923	−	0.565245i	$-0.191218\pi$
$30$	−2.02152	+	3.50138i	−0.369078	+	0.639261i
$31$	−4.76674	+	2.75208i	−0.856132	+	0.494288i	−0.862715	−	0.505690i	$-0.831238\pi$
$31$	−4.76674	+	2.75208i	−0.856132	+	0.494288i	0.00658325	+	0.999978i	$0.497904\pi$
$32$	−1.05181	−	1.82180i	−0.185936	−	0.322051i
$33$	−2.47037	+	4.27881i	−0.430037	+	0.744846i
$34$	−2.76854	−	4.46337i	−0.474801	−	0.765462i
$35$	−7.68649	+	3.38089i	−1.29925	+	0.571475i
$36$	0.377262			0.0628769
$37$	3.27785	+	1.89247i	0.538876	+	0.311120i	0.744623	−	0.667485i	$-0.232629\pi$
$37$	3.27785	+	1.89247i	0.538876	+	0.311120i	−0.205747	+	0.978605i	$0.565963\pi$
$38$	4.00555	+	6.93782i	0.649787	+	1.12546i
$39$	−0.644224	+	0.371943i	−0.103158	+	0.0595586i
$40$	8.32369	+	4.80569i	1.31609	+	0.759846i
$41$		−	10.9609i		−	1.71180i	−0.517137	−	0.855902i	$-0.673002\pi$
$41$		−	10.9609i		−	1.71180i	0.517137	−	0.855902i	$-0.326998\pi$
$42$	−2.71772	−	1.99328i	−0.419353	−	0.307570i
$43$	8.93958			1.36327			0.681637	−	0.731691i	$-0.261269\pi$
$43$	8.93958			1.36327			0.681637	+	0.731691i	$0.261269\pi$
$44$	1.61423	+	0.931977i	0.243355	+	0.140501i
$45$	−2.74862	+	1.58692i	−0.409740	+	0.236564i
$46$	−3.60069	+	2.07886i	−0.530893	+	0.306511i
$47$	4.61618	−	7.99546i	0.673339	−	1.16626i	−0.303613	−	0.952796i	$-0.598193\pi$
$47$	4.61618	−	7.99546i	0.673339	−	1.16626i	0.976951	−	0.213461i	$-0.0684738\pi$
$48$			3.10315i			0.447901i
$49$	−2.10313	−	6.67659i	−0.300447	−	0.953798i
$50$	−6.46262			−0.913952
$51$	−0.130267	−	4.12105i	−0.0182410	−	0.577062i
$52$	0.140320	+	0.243041i	0.0194589	+	0.0337037i
$53$	3.57891	+	6.19885i	0.491601	+	0.851477i	0.999953	−	0.00967162i	$-0.00307862\pi$
$53$	3.57891	+	6.19885i	0.491601	+	0.851477i	−0.508352	+	0.861149i	$0.669745\pi$
$54$	−1.10320	−	0.636934i	−0.150127	−	0.0866757i
$55$	−15.6811			−2.11444
$56$	−4.73855	+	6.46073i	−0.633215	+	0.863351i
$57$			6.28881i			0.832973i
$58$	6.71616	+	3.87758i	0.881875	+	0.509151i
$59$	0.996006	+	1.72513i	0.129669	+	0.224593i	0.923548	−	0.383482i	$-0.125275\pi$
$59$	0.996006	+	1.72513i	0.129669	+	0.224593i	−0.793879	+	0.608075i	$0.791942\pi$
$60$	0.598683	+	1.03695i	0.0772896	+	0.133870i
$61$	−3.35339	−	1.93608i	−0.429358	−	0.247890i	0.269715	−	0.962940i	$-0.413071\pi$
$61$	−3.35339	−	1.93608i	−0.429358	−	0.247890i	−0.699073	+	0.715050i	$0.746404\pi$
$62$		−	7.01157i		−	0.890470i
$63$	−1.06524	−	2.42183i	−0.134208	−	0.305122i
$64$	8.88605			1.11076
$65$	−2.04466	−	1.18049i	−0.253609	−	0.146421i
$66$	−3.14693	−	5.45064i	−0.387360	−	0.670928i
$67$	−5.24920	−	9.09187i	−0.641291	−	1.11075i	−0.985145	−	0.171726i	$-0.945066\pi$
$67$	−5.24920	−	9.09187i	−0.641291	−	1.11075i	0.343853	−	0.939023i	$-0.388268\pi$
$68$	−1.55471	+	0.0491446i	−0.188537	+	0.00595966i
$69$	−3.26385			−0.392922
$70$	1.16598	−	10.6332i	0.139361	−	1.27090i
$71$			8.26433i			0.980795i	0.871499	+	0.490398i	$0.163148\pi$
$71$			8.26433i			0.980795i	−0.871499	+	0.490398i	$0.836852\pi$
$72$	−1.51416	+	2.62260i	−0.178445	+	0.309076i
$73$	0.712022	−	0.411086i	0.0833358	−	0.0481140i	−0.457753	−	0.889079i	$-0.651346\pi$
$73$	0.712022	−	0.411086i	0.0833358	−	0.0481140i	0.541089	+	0.840965i	$0.318012\pi$
$74$	−4.17555	+	2.41076i	−0.485398	+	0.280245i
$75$	−4.39354	−	2.53661i	−0.507322	−	0.292903i
$76$	2.37253			0.272147
$77$	1.42487	−	12.9941i	0.162379	−	1.48082i
$78$		−	0.947613i		−	0.107296i
$79$	−11.4826	−	6.62947i	−1.29189	−	0.745874i	−0.312902	−	0.949785i	$-0.601301\pi$
$79$	−11.4826	−	6.62947i	−1.29189	−	0.745874i	−0.978989	+	0.203911i	$0.934635\pi$
$80$	−8.52939	+	4.92444i	−0.953614	+	0.550569i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	12.0921	+	6.98137i	1.33535	+	0.770963i
$83$	−14.5817			−1.60055			−0.800277	−	0.599631i	$-0.795314\pi$
$83$	−14.5817			−1.60055			−0.800277	+	0.599631i	$0.795314\pi$
$84$	−0.913664	+	0.401874i	−0.0996889	+	0.0438480i
$85$	11.1205	−	6.89781i	1.20618	−	0.748173i
$86$	−5.69392	+	9.86216i	−0.613991	+	1.06346i
$87$	3.04394	+	5.27226i	0.326345	+	0.565245i
$88$	−12.9576	+	7.48108i	−1.38129	+	0.797485i
$89$	6.37433	−	11.0407i	0.675677	−	1.17031i	−0.300593	−	0.953753i	$-0.597185\pi$
$89$	6.37433	−	11.0407i	0.675677	−	1.17031i	0.976270	−	0.216555i	$-0.0694821\pi$
$90$		−	4.04304i		−	0.426174i
$91$	1.16399	−	1.58704i	0.122020	−	0.166367i
$92$			1.23133i			0.128375i
$93$	2.75208	−	4.76674i	0.285377	−	0.494288i
$94$	5.88040	+	10.1852i	0.606517	+	1.05052i
$95$	−17.2856	+	9.97982i	−1.77346	+	1.02391i
$96$	1.82180	+	1.05181i	0.185936	+	0.107350i
$97$			2.95888i			0.300429i	0.988653	+	0.150214i	$0.0479964\pi$
$97$			2.95888i			0.300429i	−0.988653	+	0.150214i	$0.952004\pi$
$98$	8.70518	+	1.93237i	0.879356	+	0.195199i
$99$		−	4.94075i		−	0.496564i
$100$	−0.956966	+	1.65751i	−0.0956966	+	0.165751i
$101$	3.60078	+	6.23673i	0.358291	+	0.620578i	0.987675	−	0.156516i	$-0.0500262\pi$
$101$	3.60078	+	6.23673i	0.358291	+	0.620578i	−0.629384	+	0.777094i	$0.716693\pi$
$102$	4.62932	+	2.48112i	0.458371	+	0.245668i
$103$	−3.96625	+	6.86975i	−0.390806	+	0.676896i	−0.992556	−	0.121788i	$-0.961137\pi$
$103$	−3.96625	+	6.86975i	−0.390806	+	0.676896i	0.601750	+	0.798685i	$0.294470\pi$
$104$	−2.25272			−0.220898
$105$	4.96625	−	6.77118i	0.484656	−	0.660800i
$106$	−9.11811			−0.885629
$107$	0.152347	+	0.0879576i	0.0147280	+	0.00850319i	0.507346	−	0.861743i	$-0.330627\pi$
$107$	0.152347	+	0.0879576i	0.0147280	+	0.00850319i	−0.492618	+	0.870246i	$0.663960\pi$
$108$	−0.326718	+	0.188631i	−0.0314385	+	0.0181510i
$109$	−2.83826	+	1.63867i	−0.271856	+	0.156956i	−0.629731	−	0.776813i	$-0.716835\pi$
$109$	−2.83826	+	1.63867i	−0.271856	+	0.156956i	0.357875	+	0.933770i	$0.383502\pi$
$110$	9.98783	−	17.2994i	0.952303	−	1.64944i
$111$	−3.78494			−0.359251
$112$	−3.30560	−	7.51531i	−0.312350	−	0.710130i
$113$			7.29804i			0.686541i	0.939236	+	0.343271i	$0.111535\pi$
$113$			7.29804i			0.686541i	−0.939236	+	0.343271i	$0.888465\pi$
$114$	−6.93782	−	4.00555i	−0.649787	−	0.375155i
$115$	−5.17947	−	8.97110i	−0.482988	−	0.836559i
$116$	1.98902	−	1.14836i	0.184676	−	0.106623i
$117$	0.371943	−	0.644224i	0.0343862	−	0.0595586i
$118$	−2.53756			−0.233601
$119$	4.70539	+	9.84171i	0.431342	+	0.902189i
$120$	−9.61137			−0.877394
$121$	6.70550	−	11.6143i	0.609591	−	1.05584i
$122$	4.27178	−	2.46631i	0.386749	−	0.223290i
$123$	5.48045	+	9.49242i	0.494155	+	0.855902i
$124$	−1.79831	−	1.03825i	−0.161493	−	0.0932379i
$125$		−	0.232402i		−	0.0207867i
$126$	3.35025	+	0.367372i	0.298464	+	0.0327281i
$127$	−12.9878			−1.15248			−0.576239	−	0.817281i	$-0.695480\pi$
$127$	−12.9878			−1.15248			−0.576239	+	0.817281i	$0.695480\pi$
$128$	−3.55619	+	6.15951i	−0.314326	+	0.544429i
$129$	−7.74190	+	4.46979i	−0.681637	+	0.393543i
$130$	2.60463	−	1.50378i	0.228441	−	0.131890i
$131$	16.6813	+	9.63097i	1.45745	+	0.841462i	0.998886	−	0.0471970i	$-0.0150289\pi$
$131$	16.6813	+	9.63097i	1.45745	+	0.841462i	0.458569	+	0.888659i	$0.348362\pi$
$132$	−1.86395			−0.162236
$133$	−6.69909	−	15.2304i	−0.580884	−	1.32065i
$134$	13.3736			1.15530
$135$	1.58692	−	2.74862i	0.136580	−	0.236564i
$136$	5.89828	−	11.0051i	0.505773	−	0.943679i
$137$	−2.33054	−	4.03662i	−0.199112	−	0.344872i	0.749129	−	0.662424i	$-0.230472\pi$
$137$	−2.33054	−	4.03662i	−0.199112	−	0.344872i	−0.948241	+	0.317553i	$0.897139\pi$
$138$	2.07886	−	3.60069i	0.176964	−	0.306511i
$139$			6.31083i			0.535278i	0.963519	+	0.267639i	$0.0862434\pi$
$139$			6.31083i			0.535278i	−0.963519	+	0.267639i	$0.913757\pi$
$140$	−2.55451	−	1.87358i	−0.215895	−	0.158346i
$141$			9.23236i			0.777505i
$142$	−9.11722	−	5.26383i	−0.765100	−	0.441731i
$143$	3.18295	−	1.83768i	0.266172	−	0.153674i
$144$	−1.55158	−	2.68741i	−0.129298	−	0.223951i
$145$	−9.66096	+	16.7333i	−0.802299	+	1.38962i
$146$			1.04734i			0.0866783i
$147$	5.15966	+	4.73053i	0.425561	+	0.390168i
$148$			1.42791i			0.117374i
$149$	8.71939	−	15.1024i	0.714320	−	1.23724i	−0.248901	−	0.968529i	$-0.580069\pi$
$149$	8.71939	−	15.1024i	0.714320	−	1.23724i	0.963221	−	0.268710i	$-0.0865972\pi$
$150$	5.59679	−	3.23131i	0.456976	−	0.263835i
$151$	3.67057	+	6.35761i	0.298706	+	0.517375i	0.975840	−	0.218485i	$-0.0701115\pi$
$151$	3.67057	+	6.35761i	0.298706	+	0.517375i	−0.677134	+	0.735860i	$0.736778\pi$
$152$	−9.52225	+	16.4930i	−0.772357	+	1.33776i
$153$	2.17334	+	3.50380i	0.175704	+	0.283265i
$154$	13.4276	+	9.84830i	1.08202	+	0.793599i
$155$	17.4693			1.40317
$156$	−0.243041	−	0.140320i	−0.0194589	−	0.0112346i
$157$	3.16842	+	5.48787i	0.252868	+	0.437980i	0.964314	−	0.264761i	$-0.0852929\pi$
$157$	3.16842	+	5.48787i	0.252868	+	0.437980i	−0.711447	+	0.702740i	$0.751960\pi$
$158$	14.6273	−	8.44507i	1.16368	−	0.671854i
$159$	−6.19885	−	3.57891i	−0.491601	−	0.283826i
$160$			6.67657i			0.527829i
$161$	7.90450	−	3.47679i	0.622962	−	0.274009i
$162$	1.27387			0.100084
$163$	12.1929	+	7.03957i	0.955021	+	0.551381i	0.894637	−	0.446794i	$-0.147434\pi$
$163$	12.1929	+	7.03957i	0.955021	+	0.551381i	0.0603836	+	0.998175i	$0.480768\pi$
$164$	3.58112	−	2.06756i	0.279639	−	0.161450i
$165$	13.5802	−	7.84056i	1.05722	−	0.610387i
$166$	9.28760	−	16.0866i	0.720857	−	1.24856i
$167$			2.70279i			0.209148i	0.994517	+	0.104574i	$0.0333480\pi$
$167$			2.70279i			0.209148i	−0.994517	+	0.104574i	$0.966652\pi$
$168$	0.873340	−	7.96443i	0.0673796	−	0.614469i
$169$	−12.4466			−0.957433
$170$	0.526674	+	16.6616i	0.0403940	+	1.27788i
$171$	−3.14440	−	5.44627i	−0.240459	−	0.416487i
$172$	1.68628	+	2.92072i	0.128578	+	0.222703i
$173$	7.55152	+	4.35987i	0.574131	+	0.331475i	0.758798	−	0.651326i	$-0.225787\pi$
$173$	7.55152	+	4.35987i	0.574131	+	0.331475i	−0.184666	+	0.982801i	$0.559120\pi$
$174$	−7.75515			−0.587916
$175$	13.3425	+	1.46307i	1.00860	+	0.110598i
$176$		−	15.3319i		−	1.15568i
$177$	−1.72513	−	0.996006i	−0.129669	−	0.0748644i
$178$	8.12005	+	14.0643i	0.608623	+	1.05417i
$179$	8.09919	+	14.0282i	0.605362	+	1.04852i	0.991994	+	0.126283i	$0.0403049\pi$
$179$	8.09919	+	14.0282i	0.605362	+	1.04852i	−0.386632	+	0.922234i	$0.626362\pi$
$180$	−1.03695	−	0.598683i	−0.0772896	−	0.0446232i
$181$			9.37012i			0.696475i	0.937406	+	0.348238i	$0.113220\pi$
$181$			9.37012i			0.696475i	−0.937406	+	0.348238i	$0.886780\pi$
$182$	1.00943	+	2.29496i	0.0748242	+	0.170114i
$183$	3.87217			0.286239
$184$	−8.55978	−	4.94199i	−0.631035	−	0.364328i
$185$	−6.00639	−	10.4034i	−0.441598	−	0.764871i
$186$	3.50578	+	6.07220i	0.257057	+	0.445235i
$187$	0.643615	+	20.3611i	0.0470658	+	1.48895i
$188$	3.48301			0.254025
$189$	2.13344	+	1.56475i	0.155185	+	0.113819i
$190$		−	25.4259i		−	1.84459i
$191$	−8.81419	+	15.2666i	−0.637772	+	1.10465i	0.348148	+	0.937439i	$0.386811\pi$
$191$	−8.81419	+	15.2666i	−0.637772	+	1.10465i	−0.985921	+	0.167214i	$0.946523\pi$
$192$	−7.69554	+	4.44302i	−0.555378	+	0.320648i
$193$	14.2086	−	8.20336i	1.02276	−	0.590491i	0.107858	−	0.994166i	$-0.465601\pi$
$193$	14.2086	−	8.20336i	1.02276	−	0.590491i	0.914902	+	0.403676i	$0.132268\pi$
$194$	−3.26424	−	1.88461i	−0.234359	−	0.135307i
$195$	2.36097			0.169073
$196$	1.78465	−	1.94654i	0.127475	−	0.139039i
$197$			7.77584i			0.554006i	0.960869	+	0.277003i	$0.0893411\pi$
$197$			7.77584i			0.554006i	−0.960869	+	0.277003i	$0.910659\pi$
$198$	5.45064	+	3.14693i	0.387360	+	0.223643i
$199$	−5.18201	+	2.99183i	−0.367343	+	0.212085i	−0.672297	−	0.740282i	$-0.734692\pi$
$199$	−5.18201	+	2.99183i	−0.367343	+	0.212085i	0.304954	+	0.952367i	$0.401359\pi$
$200$	−7.68166	−	13.3050i	−0.543176	−	0.940808i
$201$	9.09187	+	5.24920i	0.641291	+	0.370250i
$202$	−9.17383			−0.645469
$203$	−12.9881	−	9.52599i	−0.911587	−	0.668594i
$204$	1.32185	−	0.819917i	0.0925479	−	0.0574057i
$205$	−17.3940	+	30.1274i	−1.21485	+	2.10419i
$206$	−5.05248	−	8.75115i	−0.352023	−	0.609721i
$207$	2.82658	−	1.63193i	0.196461	−	0.113427i
$208$	1.15420	−	1.99913i	0.0800291	−	0.138614i
$209$		−	31.0714i		−	2.14926i
$210$	4.30681	+	9.79157i	0.297198	+	0.675683i
$211$		−	5.75620i		−	0.396273i	−0.980174	−	0.198136i	$-0.936511\pi$
$211$		−	5.75620i		−	0.396273i	0.980174	−	0.198136i	$-0.0634889\pi$
$212$	−1.35018	+	2.33859i	−0.0927310	+	0.160615i
$213$	−4.13216	−	7.15712i	−0.283131	−	0.490398i
$214$	−0.194070	+	0.112046i	−0.0132664	+	0.00765933i
$215$	−24.5715	−	14.1864i	−1.67576	−	0.967503i
$216$		−	3.02832i		−	0.206051i
$217$	−1.58735	+	14.4759i	−0.107756	+	0.982685i
$218$		−	4.17490i		−	0.282760i
$219$	−0.411086	+	0.712022i	−0.0277786	+	0.0481140i
$220$	−2.95794	−	5.12331i	−0.199424	−	0.345413i
$221$	−1.44887	+	2.70333i	−0.0974618	+	0.181846i
$222$	2.41076	−	4.17555i	0.161799	−	0.280245i
$223$	0.122313			0.00819066			0.00409533	−	0.999992i	$-0.498696\pi$
$223$	0.122313			0.00819066			0.00409533	+	0.999992i	$0.498696\pi$
$224$	−5.53252	−	0.606668i	−0.369657	−	0.0405347i
$225$	5.07322			0.338215
$226$	−8.05121	−	4.64837i	−0.535558	−	0.309205i
$227$	5.16768	−	2.98356i	0.342991	−	0.198026i	−0.318603	−	0.947888i	$-0.603214\pi$
$227$	5.16768	−	2.98356i	0.342991	−	0.198026i	0.661594	+	0.749862i	$0.269880\pi$
$228$	−2.05467	+	1.18626i	−0.136074	+	0.0785622i
$229$	3.69271	−	6.39596i	0.244021	−	0.422657i	−0.717835	−	0.696213i	$-0.754867\pi$
$229$	3.69271	−	6.39596i	0.244021	−	0.422657i	0.961856	+	0.273557i	$0.0882001\pi$
$230$	13.1959			0.870112
$231$	5.26308	+	11.9657i	0.346285	+	0.787283i
$232$			18.4360i			1.21038i
$233$	−9.49911	−	5.48431i	−0.622307	−	0.359289i	0.155459	−	0.987842i	$-0.450314\pi$
$233$	−9.49911	−	5.48431i	−0.622307	−	0.359289i	−0.777767	+	0.628553i	$0.783648\pi$
$234$	0.473806	+	0.820657i	0.0309737	+	0.0536480i
$235$	−25.3763	+	14.6510i	−1.65536	+	0.955725i
$236$	−0.375755	+	0.650826i	−0.0244596	+	0.0423652i
$237$	13.2589			0.861261
$238$	−13.8544	−	1.07753i	−0.898048	−	0.0698460i
$239$	−1.45939			−0.0943998			−0.0471999	−	0.998885i	$-0.515030\pi$
$239$	−1.45939			−0.0943998			−0.0471999	+	0.998885i	$0.515030\pi$
$240$	4.92444	−	8.52939i	0.317871	−	0.550569i
$241$	15.4864	−	8.94105i	0.997564	−	0.575944i	0.0900371	−	0.995938i	$-0.471301\pi$
$241$	15.4864	−	8.94105i	0.997564	−	0.575944i	0.907527	+	0.419995i	$0.137968\pi$
$242$	8.54192	+	14.7950i	0.549095	+	0.951061i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		−	1.46082i		−	0.0935194i
$245$	−4.81449	+	21.6889i	−0.307586	+	1.38565i
$246$	−13.9627			−0.890231
$247$	2.33908	−	4.05140i	0.148832	−	0.257785i
$248$	14.4352	−	8.33416i	0.916636	−	0.529220i
$249$	12.6282	−	7.29087i	0.800277	−	0.462040i
$250$	0.256386	+	0.148025i	0.0162153	+	0.00936191i
$251$	22.9570			1.44903			0.724516	−	0.689258i	$-0.242063\pi$
$251$	22.9570			1.44903			0.724516	+	0.689258i	$0.242063\pi$
$252$	0.590319	−	0.804865i	0.0371866	−	0.0507017i
$253$	16.1259			1.01383
$254$	8.27234	−	14.3281i	0.519053	−	0.899026i
$255$	−6.18171	+	11.5339i	−0.387114	+	0.722282i
$256$	4.35593	+	7.54469i	0.272245	+	0.471543i
$257$	6.98808	−	12.1037i	0.435904	−	0.755008i	−0.561465	−	0.827501i	$-0.689762\pi$
$257$	6.98808	−	12.1037i	0.435904	−	0.755008i	0.997369	+	0.0724925i	$0.0230953\pi$
$258$		−	11.3878i		−	0.708976i
$259$	9.16649	−	4.03187i	0.569578	−	0.250528i
$260$		−	0.890704i		−	0.0552391i
$261$	−5.27226	−	3.04394i	−0.326345	−	0.188415i
$262$	−21.2498	+	12.2686i	−1.31282	+	0.757955i
$263$	−1.98521	−	3.43849i	−0.122414	−	0.212026i	0.798305	−	0.602253i	$-0.205730\pi$
$263$	−1.98521	−	3.43849i	−0.122414	−	0.212026i	−0.920719	+	0.390226i	$0.872397\pi$
$264$	7.48108	−	12.9576i	0.460428	−	0.797485i
$265$		−	22.7177i		−	1.39554i
$266$	21.0691	+	2.31033i	1.29183	+	0.141656i
$267$			12.7487i			0.780205i
$268$	1.98032	−	3.43001i	0.120967	−	0.209522i
$269$	4.03364	−	2.32883i	0.245936	−	0.141991i	−0.371966	−	0.928246i	$-0.621316\pi$
$269$	4.03364	−	2.32883i	0.245936	−	0.141991i	0.617902	+	0.786255i	$0.287983\pi$
$270$	2.02152	+	3.50138i	0.123026	+	0.213087i
$271$	−7.72913	+	13.3872i	−0.469511	+	0.813217i	−0.999392	−	0.0348546i	$-0.988903\pi$
$271$	−7.72913	+	13.3872i	−0.469511	+	0.813217i	0.529881	+	0.848072i	$0.322237\pi$
$272$	6.74419	+	10.8728i	0.408927	+	0.659261i
$273$	−0.214530	+	1.95641i	−0.0129840	+	0.118407i
$274$	5.93761			0.358704
$275$	21.7074	+	12.5328i	1.30900	+	0.755754i
$276$	−0.615663	−	1.06636i	−0.0370586	−	0.0641873i
$277$	−10.5054	+	6.06532i	−0.631211	+	0.364430i	−0.781221	−	0.624255i	$-0.785403\pi$
$277$	−10.5054	+	6.06532i	−0.631211	+	0.364430i	0.150010	+	0.988684i	$0.452069\pi$
$278$	−6.96212	−	4.01958i	−0.417560	−	0.241078i
$279$			5.50416i			0.329525i
$280$	23.2771	−	10.2384i	1.39107	−	0.611862i
$281$	−22.9909			−1.37152			−0.685760	−	0.727828i	$-0.740530\pi$
$281$	−22.9909			−1.37152			−0.685760	+	0.727828i	$0.740530\pi$
$282$	−10.1852	−	5.88040i	−0.606517	−	0.350173i
$283$	−9.33765	+	5.39109i	−0.555066	+	0.320467i	−0.751163	−	0.660117i	$-0.770507\pi$
$283$	−9.33765	+	5.39109i	−0.555066	+	0.320467i	0.196097	+	0.980585i	$0.437173\pi$
$284$	−2.70011	+	1.55891i	−0.160222	+	0.0925041i
$285$	9.97982	−	17.2856i	0.591153	−	1.02391i
$286$			4.68192i			0.276847i
$287$	−23.3844	−	17.1510i	−1.38034	−	1.01239i
$288$	−2.10363			−0.123958
$289$	−9.41286	−	14.1562i	−0.553697	−	0.832718i
$290$	−12.3068	−	21.3160i	−0.722679	−	1.25172i
$291$	−1.47944	−	2.56246i	−0.0867262	−	0.150214i
$292$	0.268618	+	0.155087i	0.0157197	+	0.00907578i
$293$	−20.4193			−1.19291			−0.596453	−	0.802648i	$-0.703424\pi$
$293$	−20.4193			−1.19291			−0.596453	+	0.802648i	$0.703424\pi$
$294$	−8.50509	+	2.67911i	−0.496027	+	0.156249i
$295$		−	6.32232i		−	0.368099i
$296$	−9.92638	−	5.73100i	−0.576959	−	0.333107i
$297$	2.47037	+	4.27881i	0.143346	+	0.248282i
$298$	11.1073	+	19.2385i	0.643431	+	1.11446i
$299$	2.10265	+	1.21397i	0.121600	+	0.0702056i
$300$		−	1.91393i		−	0.110501i
$301$	13.9882	−	19.0721i	0.806266	−	1.09929i
$302$	−9.35163			−0.538126
$303$	−6.23673	−	3.60078i	−0.358291	−	0.206859i
$304$	−9.75756	−	16.9006i	−0.559635	−	0.969315i
$305$	6.14481	+	10.6431i	0.351851	+	0.609423i
$306$	−5.24967	+	0.165942i	−0.300104	+	0.00948630i
$307$	−19.0997			−1.09008			−0.545038	−	0.838412i	$-0.683485\pi$
$307$	−19.0997			−1.09008			−0.545038	+	0.838412i	$0.683485\pi$
$308$	4.51418	−	1.98556i	0.257219	−	0.113138i
$309$		−	7.93250i		−	0.451264i
$310$	−11.1268	+	19.2721i	−0.631958	+	1.09458i
$311$	−9.14670	+	5.28085i	−0.518661	+	0.299449i	−0.736387	−	0.676561i	$-0.763470\pi$
$311$	−9.14670	+	5.28085i	−0.518661	+	0.299449i	0.217725	+	0.976010i	$0.430136\pi$
$312$	1.95092	−	1.12636i	0.110449	−	0.0637677i
$313$	−3.94505	−	2.27768i	−0.222988	−	0.128742i	0.384345	−	0.923189i	$-0.374427\pi$
$313$	−3.94505	−	2.27768i	−0.222988	−	0.128742i	−0.607333	+	0.794447i	$0.707761\pi$
$314$	−8.07230			−0.455546
$315$	−0.915306	+	8.34714i	−0.0515716	+	0.470308i
$316$		−	5.00209i		−	0.281390i
$317$	10.9722	+	6.33482i	0.616262	+	0.355799i	0.775412	−	0.631455i	$-0.217542\pi$
$317$	10.9722	+	6.33482i	0.616262	+	0.355799i	−0.159150	+	0.987254i	$0.550875\pi$
$318$	7.89651	−	4.55905i	0.442814	−	0.255659i
$319$	−15.0393	−	26.0489i	−0.842041	−	1.45846i
$320$	−24.4244	−	14.1014i	−1.36536	−	0.788293i
$321$	−0.175915			−0.00981863
$322$	−1.19905	+	10.9347i	−0.0668204	+	0.609369i
$323$	13.6677	+	22.0347i	0.760492	+	1.22604i
$324$	0.188631	−	0.326718i	0.0104795	−	0.0181510i
$325$	1.88695	+	3.26829i	0.104669	+	0.181292i
$326$	−15.5321	+	8.96747i	−0.860245	+	0.496662i
$327$	1.63867	−	2.83826i	0.0906188	−	0.156956i
$328$			33.1931i			1.83278i
$329$	−9.83467	−	22.3592i	−0.542203	−	1.23270i
$330$			19.9757i			1.09962i
$331$	−6.43636	+	11.1481i	−0.353774	+	0.612755i	−0.986907	−	0.161288i	$-0.948435\pi$
$331$	−6.43636	+	11.1481i	−0.353774	+	0.612755i	0.633133	+	0.774043i	$0.281769\pi$
$332$	−2.75056	−	4.76412i	−0.150957	−	0.261465i
$333$	3.27785	−	1.89247i	0.179625	−	0.103707i
$334$	−2.98173	−	1.72150i	−0.163153	−	0.0941963i
$335$			33.3202i			1.82047i
$336$	6.62038	+	4.85565i	0.361172	+	0.264897i
$337$			9.17523i			0.499807i	0.968271	+	0.249903i	$0.0803988\pi$
$337$			9.17523i			0.499807i	−0.968271	+	0.249903i	$0.919601\pi$
$338$	7.92768	−	13.7311i	0.431209	−	0.746876i
$339$	−3.64902	−	6.32028i	−0.198187	−	0.343271i
$340$	4.35130	+	2.33212i	0.235983	+	0.126477i
$341$	−13.5973	+	23.5513i	−0.736337	+	1.27537i
$342$	8.01111			0.433191
$343$	−17.5350	−	5.96027i	−0.946799	−	0.321825i
$344$	−27.0719			−1.45962
$345$	8.97110	+	5.17947i	0.482988	+	0.278853i
$346$	−9.61963	+	5.55390i	−0.517155	+	0.298579i
$347$	16.0954	−	9.29266i	0.864044	−	0.498856i	−0.00132034	−	0.999999i	$-0.500420\pi$
$347$	16.0954	−	9.29266i	0.864044	−	0.498856i	0.865364	+	0.501143i	$0.167087\pi$
$348$	−1.14836	+	1.98902i	−0.0615586	+	0.106623i
$349$	14.4101			0.771355			0.385678	−	0.922634i	$-0.373968\pi$
$349$	14.4101			0.771355			0.385678	+	0.922634i	$0.373968\pi$
$350$	−10.1124	+	13.7876i	−0.540528	+	0.736978i
$351$			0.743886i			0.0397057i
$352$	−9.00104	−	5.19675i	−0.479757	−	0.276988i
$353$	0.00519931	+	0.00900547i	0.000276731	+	0.000479313i	0.866164	−	0.499760i	$-0.166579\pi$
$353$	0.00519931	+	0.00900547i	0.000276731	+	0.000479313i	−0.865887	+	0.500240i	$0.833245\pi$
$354$	2.19759	−	1.26878i	0.116801	−	0.0674349i
$355$	13.1148	−	22.7155i	0.696061	−	1.20561i
$356$	4.80958			0.254907
$357$	−8.99584	−	6.17048i	−0.476110	−	0.326577i
$358$	−20.6346			−1.09057
$359$	1.24405	−	2.15475i	0.0656583	−	0.113724i	−0.831328	−	0.555783i	$-0.812419\pi$
$359$	1.24405	−	2.15475i	0.0656583	−	0.113724i	0.896986	+	0.442059i	$0.145752\pi$
$360$	8.32369	−	4.80569i	0.438697	−	0.253282i
$361$	−10.2746	−	17.7961i	−0.540766	−	0.936635i
$362$	−10.3371	−	5.96814i	−0.543307	−	0.313679i
$363$			13.4110i			0.703895i
$364$	0.738079	+	0.0809340i	0.0386858	+	0.00424210i
$365$	−2.60944			−0.136584
$366$	−2.46631	+	4.27178i	−0.128916	+	0.223290i
$367$	24.0899	−	13.9083i	1.25748	−	0.726009i	0.284899	−	0.958557i	$-0.408040\pi$
$367$	24.0899	−	13.9083i	1.25748	−	0.726009i	0.972585	+	0.232549i	$0.0747066\pi$
$368$	8.77130	−	5.06412i	0.457236	−	0.263985i
$369$	−9.49242	−	5.48045i	−0.494155	−	0.285301i
$370$	15.3027			0.795549
$371$	18.8250	+	2.06425i	0.977343	+	0.107171i
$372$	2.07651			0.107662
$373$	1.84811	−	3.20102i	0.0956916	−	0.165743i	−0.814205	−	0.580577i	$-0.802827\pi$
$373$	1.84811	−	3.20102i	0.0956916	−	0.165743i	0.909897	+	0.414834i	$0.136160\pi$
$374$	−22.8723	−	12.2586i	−1.18270	−	0.633878i
$375$	0.116201	+	0.201266i	0.00600060	+	0.0103933i
$376$	−13.9792	+	24.2128i	−0.720925	+	1.24868i
$377$		−	4.52869i		−	0.233239i
$378$	−3.08509	+	1.35697i	−0.158680	+	0.0697952i
$379$		−	32.8737i		−	1.68861i	−0.535865	−	0.844304i	$-0.680014\pi$
$379$		−	32.8737i		−	1.68861i	0.535865	−	0.844304i	$-0.319986\pi$
$380$	−6.52118	−	3.76500i	−0.334529	−	0.193141i
$381$	11.2477	−	6.49388i	0.576239	−	0.332692i
$382$	−11.2281	−	19.4477i	−0.574480	−	0.995028i
$383$	−12.0737	+	20.9122i	−0.616936	+	1.06856i	0.373106	+	0.927789i	$0.378293\pi$
$383$	−12.0737	+	20.9122i	−0.616936	+	1.06856i	−0.990042	+	0.140776i	$0.955040\pi$
$384$		−	7.11239i		−	0.362952i
$385$	−24.5370	+	33.4547i	−1.25052	+	1.70501i
$386$			20.9000i			1.06378i
$387$	4.46979	−	7.74190i	0.227212	−	0.393543i
$388$	−0.966719	+	0.558135i	−0.0490777	+	0.0283350i
$389$	7.41652	+	12.8458i	0.376032	+	0.651307i	0.990481	−	0.137650i	$-0.0439548\pi$
$389$	7.41652	+	12.8458i	0.376032	+	0.651307i	−0.614449	+	0.788957i	$0.710621\pi$
$390$	−1.50378	+	2.60463i	−0.0761470	+	0.131890i
$391$	−11.4359	+	7.09346i	−0.578338	+	0.358732i
$392$	6.36894	+	20.2188i	0.321680	+	1.02120i
$393$	−19.2619			−0.971636
$394$	−8.57832	−	4.95269i	−0.432169	−	0.249513i
$395$	21.0408	+	36.4438i	1.05868	+	1.83369i
$396$	1.61423	−	0.931977i	0.0811182	−	0.0468336i
$397$	11.8542	+	6.84402i	0.594945	+	0.343491i	0.767050	−	0.641587i	$-0.221724\pi$
$397$	11.8542	+	6.84402i	0.594945	+	0.343491i	−0.172106	+	0.985079i	$0.555057\pi$
$398$		−	7.62240i		−	0.382076i
$399$	13.4168	+	9.84040i	0.671680	+	0.492636i
$400$	15.7430			0.787149
$401$	5.50126	+	3.17615i	0.274720	+	0.158609i	0.631031	−	0.775758i	$-0.282632\pi$
$401$	5.50126	+	3.17615i	0.274720	+	0.158609i	−0.356311	+	0.934367i	$0.615966\pi$
$402$	−11.5818	+	6.68678i	−0.577650	+	0.333506i
$403$	−3.54591	+	2.04723i	−0.176634	+	0.101980i
$404$	−1.35844	+	2.35288i	−0.0675847	+	0.117060i
$405$			3.17383i			0.157709i
$406$	18.7817	−	8.26109i	0.932118	−	0.409991i
$407$	18.7004			0.926946
$408$	0.394489	+	12.4798i	0.0195301	+	0.617844i
$409$	18.0044	+	31.1845i	0.890260	+	1.54198i	0.839564	+	0.543261i	$0.182811\pi$
$409$	18.0044	+	31.1845i	0.890260	+	1.54198i	0.0506961	+	0.998714i	$0.483856\pi$
$410$	−22.1577	−	38.3783i	−1.09429	−	1.89537i
$411$	4.03662	+	2.33054i	0.199112	+	0.114957i
$412$	−2.99263			−0.147436
$413$	5.23896	+	0.574479i	0.257793	+	0.0282682i
$414$			4.15772i			0.204341i
$415$	40.0797	+	23.1400i	1.96743	+	1.13590i
$416$	−0.782431	−	1.35521i	−0.0383618	−	0.0664446i
$417$	−3.15541	−	5.46534i	−0.154521	−	0.267639i
$418$	34.2781	+	19.7904i	1.67659	+	0.967982i
$419$		−	31.6659i		−	1.54698i	−0.633809	−	0.773489i	$-0.718510\pi$
$419$		−	31.6659i		−	1.54698i	0.633809	−	0.773489i	$-0.281490\pi$
$420$	3.14906	+	0.345310i	0.153658	+	0.0168494i
$421$	−0.874124			−0.0426022			−0.0213011	−	0.999773i	$-0.506781\pi$
$421$	−0.874124			−0.0426022			−0.0213011	+	0.999773i	$0.506781\pi$
$422$	6.35024	+	3.66632i	0.309125	+	0.178473i
$423$	−4.61618	−	7.99546i	−0.224446	−	0.388752i
$424$	−10.8381	−	18.7721i	−0.526343	−	0.911653i
$425$	−20.9070	+	0.660872i	−1.01414	+	0.0320570i
$426$	10.5277			0.510067
$427$	−9.37773	+	4.12478i	−0.453820	+	0.199612i
$428$			0.0663661i			0.00320793i
$429$	−1.83768	+	3.18295i	−0.0887239	+	0.153674i
$430$	31.3009	−	18.0716i	1.50946	−	0.871488i
$431$	−21.0715	+	12.1656i	−1.01498	+	0.585998i	−0.912646	−	0.408752i	$-0.865964\pi$
$431$	−21.0715	+	12.1656i	−1.01498	+	0.585998i	−0.102333	+	0.994750i	$0.532631\pi$
$432$	2.68741	+	1.55158i	0.129298	+	0.0746502i
$433$	−5.56768			−0.267566			−0.133783	−	0.991011i	$-0.542712\pi$
$433$	−5.56768			−0.267566			−0.133783	+	0.991011i	$0.542712\pi$
$434$	−14.9588	−	10.9713i	−0.718043	−	0.526641i
$435$		−	19.3219i		−	0.926415i
$436$	−1.07077	−	0.618208i	−0.0512805	−	0.0296068i
$437$	17.7758	−	10.2629i	0.850333	−	0.490940i
$438$	−0.523669	−	0.907021i	−0.0250219	−	0.0433392i
$439$	16.4158	+	9.47765i	0.783482	+	0.452344i	0.837663	−	0.546188i	$-0.183921\pi$
$439$	16.4158	+	9.47765i	0.783482	+	0.452344i	−0.0541808	+	0.998531i	$0.517255\pi$
$440$	47.4874			2.26387
$441$	−6.83366	−	1.51693i	−0.325412	−	0.0722348i
$442$	−2.05948	−	3.32024i	−0.0979596	−	0.157928i
$443$	7.12278	−	12.3370i	0.338414	−	0.586150i	−0.645721	−	0.763574i	$-0.723443\pi$
$443$	7.12278	−	12.3370i	0.338414	−	0.586150i	0.984135	+	0.177424i	$0.0567763\pi$
$444$	−0.713956	−	1.23661i	−0.0338829	−	0.0586868i
$445$	−35.0412	+	20.2311i	−1.66111	+	0.959044i
$446$	−0.0779051	+	0.134936i	−0.00368891	+	0.00638938i
$447$			17.4388i			0.824826i
$448$	13.9044	−	18.9578i	0.656922	−	0.895674i
$449$			15.0765i			0.711502i	0.934581	+	0.355751i	$0.115775\pi$
$449$			15.0765i			0.711502i	−0.934581	+	0.355751i	$0.884225\pi$
$450$	−3.23131	+	5.59679i	−0.152325	+	0.263835i
$451$	−27.0775	−	46.8997i	−1.27503	−	2.20842i
$452$	−2.38440	+	1.37663i	−0.112153	+	0.0647514i
$453$	−6.35761	−	3.67057i	−0.298706	−	0.172458i
$454$			7.60132i			0.356748i
$455$	−5.71787	+	2.51500i	−0.268058	+	0.117905i
$456$		−	19.0445i		−	0.891841i
$457$	8.10512	−	14.0385i	0.379142	−	0.656692i	−0.611796	−	0.791016i	$-0.709553\pi$
$457$	8.10512	−	14.0385i	0.379142	−	0.656692i	0.990938	+	0.134323i	$0.0428860\pi$
$458$	4.70402	+	8.14760i	0.219804	+	0.380712i
$459$	−3.63406	−	1.94771i	−0.169624	−	0.0909113i
$460$	1.95401	−	3.38445i	0.0911063	−	0.157801i
$461$	38.7111			1.80296			0.901479	−	0.432823i	$-0.142482\pi$
$461$	38.7111			1.80296			0.901479	+	0.432823i	$0.142482\pi$
$462$	−16.5528	−	1.81509i	−0.770104	−	0.0844458i
$463$	14.0578			0.653323			0.326661	−	0.945141i	$-0.394076\pi$
$463$	14.0578			0.653323			0.326661	+	0.945141i	$0.394076\pi$
$464$	−16.3606	−	9.44580i	−0.759522	−	0.438510i
$465$	−15.1288	+	8.73464i	−0.701583	+	0.405059i
$466$	12.1006	−	6.98629i	0.560550	−	0.323634i
$467$	−3.81853	+	6.61388i	−0.176700	+	0.306054i	−0.940748	−	0.339105i	$-0.889876\pi$
$467$	−3.81853	+	6.61388i	−0.176700	+	0.306054i	0.764048	+	0.645159i	$0.223209\pi$
$468$	0.280640			0.0129726
$469$	−27.6106	−	3.02764i	−1.27494	−	0.139804i
$470$		−	37.3268i		−	1.72176i
$471$	−5.48787	−	3.16842i	−0.252868	−	0.145993i
$472$	−3.01622	−	5.22425i	−0.138833	−	0.240465i
$473$	38.2508	−	22.0841i	1.75877	−	1.01543i
$474$	−8.44507	+	14.6273i	−0.387895	+	0.671854i
$475$	31.9045			1.46388
$476$	−2.32789	+	3.39379i	−0.106698	+	0.155554i
$477$	7.15781			0.327734
$478$	0.929532	−	1.61000i	0.0425158	−	0.0736395i
$479$	−12.7641	+	7.36936i	−0.583207	+	0.336715i	−0.762407	−	0.647098i	$-0.775982\pi$
$479$	−12.7641	+	7.36936i	−0.583207	+	0.336715i	0.179200	+	0.983813i	$0.442649\pi$
$480$	−3.33829	−	5.78208i	−0.152371	−	0.263915i
$481$	2.43835	+	1.40778i	0.111179	+	0.0641894i
$482$			22.7794i			1.03757i
$483$	−5.10711	+	6.96324i	−0.232381	+	0.316838i
$484$	5.05946			0.229975
$485$	4.69549	−	8.13283i	0.213211	−	0.369293i
$486$	−1.10320	+	0.636934i	−0.0500422	+	0.0288919i
$487$	−13.6590	+	7.88604i	−0.618949	+	0.357351i	−0.776460	−	0.630167i	$-0.782987\pi$
$487$	−13.6590	+	7.88604i	−0.618949	+	0.357351i	0.157510	+	0.987517i	$0.449653\pi$
$488$	10.1551	+	5.86307i	0.459702	+	0.265409i
$489$	−14.0791			−0.636680
$490$	−20.8607	−	19.1257i	−0.942392	−	0.864013i
$491$	25.6331			1.15680			0.578402	−	0.815752i	$-0.303677\pi$
$491$	25.6331			1.15680			0.578402	+	0.815752i	$0.303677\pi$
$492$	−2.06756	+	3.58112i	−0.0932129	+	0.161450i
$493$	22.1237	+	11.8574i	0.996403	+	0.534031i
$494$	2.97968	+	5.16095i	0.134062	+	0.232202i
$495$	−7.84056	+	13.5802i	−0.352407	+	0.610387i
$496$			17.0802i			0.766925i
$497$	17.6314	+	12.9316i	0.790878	+	0.580061i
$498$			18.5752i			0.832374i
$499$	28.4192	+	16.4078i	1.27222	+	0.734515i	0.975405	−	0.220421i	$-0.0707431\pi$
$499$	28.4192	+	16.4078i	1.27222	+	0.734515i	0.296812	+	0.954936i	$0.404076\pi$
$500$	0.0759300	−	0.0438382i	0.00339569	−	0.00196050i
$501$	−1.35140	−	2.34069i	−0.0603759	−	0.104574i
$502$	−14.6221	+	25.3262i	−0.652615	+	1.13036i
$503$			17.4324i			0.777271i	0.921392	+	0.388636i	$0.127053\pi$
$503$			17.4324i			0.777271i	−0.921392	+	0.388636i	$0.872947\pi$
$504$	3.22588	+	7.33407i	0.143692	+	0.326685i
$505$		−	22.8566i		−	1.01710i
$506$	−10.2711	+	17.7901i	−0.456607	+	0.790866i
$507$	10.7791	−	6.22332i	0.478717	−	0.276387i
$508$	−2.44989	−	4.24334i	−0.108696	−	0.188268i
$509$	13.6302	−	23.6083i	0.604150	−	1.04642i	−0.388035	−	0.921645i	$-0.626846\pi$
$509$	13.6302	−	23.6083i	0.604150	−	1.04642i	0.992185	−	0.124774i	$-0.0398206\pi$
$510$	−8.78690	−	14.1660i	−0.389091	−	0.627282i
$511$	0.237107	−	2.16230i	0.0104890	−	0.0956546i
$512$	−25.3225			−1.11911
$513$	5.44627	+	3.14440i	0.240459	+	0.138829i
$514$	8.90188	+	15.4185i	0.392645	+	0.680081i
$515$	21.8034	−	12.5882i	0.960774	−	0.554703i
$516$	−2.92072	−	1.68628i	−0.128578	−	0.0742343i
$517$		−	45.6148i		−	2.00613i
$518$	−1.39048	+	12.6805i	−0.0610943	+	0.557150i
$519$	−8.71974			−0.382754
$520$	6.19188	+	3.57488i	0.271532	+	0.156769i
$521$	7.22805	−	4.17312i	0.316667	−	0.182828i	−0.333239	−	0.942842i	$-0.608142\pi$
$521$	7.22805	−	4.17312i	0.316667	−	0.182828i	0.649906	+	0.760015i	$0.274808\pi$
$522$	6.71616	−	3.87758i	0.293958	−	0.169717i
$523$	−9.30683	+	16.1199i	−0.406959	+	0.704874i	−0.994547	−	0.104286i	$-0.966744\pi$
$523$	−9.30683	+	16.1199i	−0.406959	+	0.704874i	0.587588	+	0.809160i	$0.300078\pi$
$524$			7.26679i			0.317451i
$525$	−12.2865	+	5.40420i	−0.536226	+	0.235859i
$526$	5.05780			0.220530
$527$	−0.717008	−	22.6829i	−0.0312334	−	0.988082i
$528$	7.66594	+	13.2778i	0.333617	+	0.577842i
$529$	−6.17363	−	10.6930i	−0.268419	−	0.464915i
$530$	25.0622	+	14.4697i	1.08863	+	0.628523i
$531$	1.99201			0.0864459
$532$	3.71240	−	5.06164i	0.160953	−	0.219450i
$533$		−	8.15366i		−	0.353174i
$534$	−14.0643	−	8.12005i	−0.608623	−	0.351389i
$535$	−0.279163	−	0.483524i	−0.0120693	−	0.0209046i
$536$	15.8962	+	27.5331i	0.686612	+	1.18925i
$537$	−14.0282	−	8.09919i	−0.605362	−	0.349506i
$538$			5.93323i			0.255800i
$539$	−25.4926	−	23.3724i	−1.09804	−	1.00672i
$540$	1.19737			0.0515264
$541$	21.4213	+	12.3676i	0.920973	+	0.531724i	0.883945	−	0.467590i	$-0.154878\pi$
$541$	21.4213	+	12.3676i	0.920973	+	0.531724i	0.0370276	+	0.999314i	$0.488211\pi$
$542$	−9.84589	−	17.0536i	−0.422917	−	0.732514i
$543$	−4.68506	−	8.11476i	−0.201055	−	0.348238i
$544$	8.66916	−	0.274033i	0.371687	−	0.0117491i
$545$	10.4017			0.445562
$546$	−2.02167	−	1.48277i	−0.0865197	−	0.0634569i
$547$		−	30.0717i		−	1.28577i	−0.765962	−	0.642886i	$-0.777737\pi$
$547$		−	30.0717i		−	1.28577i	0.765962	−	0.642886i	$-0.222263\pi$
$548$	0.879225	−	1.52286i	0.0375586	−	0.0650534i
$549$	−3.35339	+	1.93608i	−0.143119	+	0.0826300i
$550$	−27.6523	+	15.9651i	−1.17910	+	0.680753i
$551$	−33.1562	−	19.1428i	−1.41250	−	0.815509i
$552$	9.88398			0.420690
$553$	−32.1109	+	14.1239i	−1.36550	+	0.600611i
$554$		−	15.4528i		−	0.656528i
$555$	10.4034	+	6.00639i	0.441598	+	0.254957i
$556$	−2.06186	+	1.19042i	−0.0874424	+	0.0504849i
$557$	−3.06956	−	5.31664i	−0.130062	−	0.225273i	0.793639	−	0.608390i	$-0.208184\pi$
$557$	−3.06956	−	5.31664i	−0.130062	−	0.225273i	−0.923700	+	0.383116i	$0.874851\pi$
$558$	−6.07220	−	3.50578i	−0.257057	−	0.148412i
$559$	6.65003			0.281266
$560$	−2.84033	+	25.9024i	−0.120026	+	1.09458i
$561$	−10.7379	−	17.3114i	−0.453355	−	0.730887i
$562$	14.6437	−	25.3636i	0.617705	−	1.06990i
$563$	2.93926	+	5.09095i	0.123875	+	0.214558i	0.921293	−	0.388870i	$-0.127134\pi$
$563$	2.93926	+	5.09095i	0.123875	+	0.214558i	−0.797418	+	0.603428i	$0.793801\pi$
$564$	−3.01638	+	1.74151i	−0.127012	+	0.0733307i
$565$	11.5814	−	20.0595i	0.487232	−	0.843911i
$566$		−	13.7351i		−	0.577328i
$567$	−2.62999	−	0.288391i	−0.110449	−	0.0121113i
$568$		−	25.0270i		−	1.05011i
$569$	−8.79854	+	15.2395i	−0.368854	+	0.638874i	−0.989387	−	0.145307i	$-0.953583\pi$
$569$	−8.79854	+	15.2395i	−0.368854	+	0.638874i	0.620533	+	0.784181i	$0.286916\pi$
$570$	12.7130	+	22.0195i	0.532488	+	0.922296i
$571$	32.9300	−	19.0122i	1.37808	−	0.795634i	0.386151	−	0.922436i	$-0.373805\pi$
$571$	32.9300	−	19.0122i	1.37808	−	0.795634i	0.991928	+	0.126802i	$0.0404712\pi$
$572$	1.20081	+	0.693285i	0.0502082	+	0.0289877i
$573$		−	17.6284i		−	0.736436i
$574$	33.8154	−	14.8737i	1.41143	−	0.620814i
$575$			16.5583i			0.690527i
$576$	4.44302	−	7.69554i	0.185126	−	0.320648i
$577$	12.5849	+	21.7976i	0.523914	+	0.907446i	0.999612	+	0.0278375i	$0.00886208\pi$
$577$	12.5849	+	21.7976i	0.523914	+	0.907446i	−0.475698	+	0.879609i	$0.657805\pi$
$578$	21.6125	−	1.36771i	0.898962	−	0.0568894i
$579$	−8.20336	+	14.2086i	−0.340920	+	0.590491i
$580$	−7.28942			−0.302677
$581$	−22.8167	+	31.1093i	−0.946598	+	1.29063i
$582$	3.76922			0.156239
$583$	30.6270	+	17.6825i	1.26844	+	0.732334i
$584$	−2.15623	+	1.24490i	−0.0892253	+	0.0515143i
$585$	−2.04466	+	1.18049i	−0.0845363	+	0.0488071i
$586$	13.0057	−	22.5266i	0.537261	−	0.930564i
$587$	−34.8772			−1.43954			−0.719769	−	0.694214i	$-0.755752\pi$
$587$	−34.8772			−1.43954			−0.719769	+	0.694214i	$0.755752\pi$
$588$	−0.572279	+	2.57808i	−0.0236004	+	0.106318i
$589$			34.6146i			1.42627i
$590$	6.97479	+	4.02690i	0.287148	+	0.165785i
$591$	−3.88792	−	6.73407i	−0.159928	−	0.277003i
$592$	10.1717	−	5.87262i	0.418053	−	0.241363i
$593$	−5.50597	+	9.53661i	−0.226103	+	0.391622i	−0.956650	−	0.291241i	$-0.905932\pi$
$593$	−5.50597	+	9.53661i	−0.226103	+	0.391622i	0.730547	+	0.682863i	$0.239265\pi$
$594$	−6.29386			−0.258240
$595$	2.68466	−	34.5182i	0.110061	−	1.41511i
$596$	6.57898			0.269485
$597$	2.99183	−	5.18201i	0.122448	−	0.212085i
$598$	−2.67850	+	1.54643i	−0.109532	+	0.0632384i
$599$	−17.0193	−	29.4783i	−0.695390	−	1.20445i	−0.970049	−	0.242909i	$-0.921898\pi$
$599$	−17.0193	−	29.4783i	−0.695390	−	1.20445i	0.274659	−	0.961542i	$-0.411435\pi$
$600$	13.3050	+	7.68166i	0.543176	+	0.313603i
$601$			36.5628i			1.49143i	0.666266	+	0.745714i	$0.267891\pi$
$601$			36.5628i			1.49143i	−0.666266	+	0.745714i	$0.732109\pi$
$602$	12.1308	+	27.5794i	0.494413	+	1.12405i
$603$	−10.4984			−0.427528
$604$	−1.38476	+	2.39848i	−0.0563452	+	0.0975928i
$605$	−36.8618	+	21.2822i	−1.49864	+	0.865242i
$606$	7.94477	−	4.58692i	0.322734	−	0.186331i
$607$	−39.3338	−	22.7094i	−1.59651	−	0.921746i	−0.992153	−	0.125033i	$-0.960096\pi$
$607$	−39.3338	−	22.7094i	−1.59651	−	0.921746i	−0.604358	−	0.796713i	$-0.706570\pi$
$608$	−13.2293			−0.536520
$609$	16.0110	+	1.75569i	0.648800	+	0.0711442i
$610$	−15.6553			−0.633866
$611$	3.43391	−	5.94771i	0.138921	−	0.240619i
$612$	−0.734796	+	1.37099i	−0.0297024	+	0.0554191i
$613$	−22.4762	−	38.9298i	−0.907803	−	1.57236i	−0.817110	−	0.576482i	$-0.804425\pi$
$613$	−22.4762	−	38.9298i	−0.907803	−	1.57236i	−0.0906936	−	0.995879i	$-0.528908\pi$
$614$	12.1652	−	21.0708i	0.490948	−	0.850347i
$615$		−	34.7881i		−	1.40279i
$616$	−4.31495	+	39.3503i	−0.173854	+	1.58547i
$617$			8.34165i			0.335822i	0.985802	+	0.167911i	$0.0537022\pi$
$617$			8.34165i			0.335822i	−0.985802	+	0.167911i	$0.946298\pi$
$618$	8.75115	+	5.05248i	0.352023	+	0.203240i
$619$	−18.7848	+	10.8454i	−0.755025	+	0.435914i	−0.827507	−	0.561456i	$-0.810242\pi$
$619$	−18.7848	+	10.8454i	−0.755025	+	0.435914i	0.0724814	+	0.997370i	$0.476908\pi$
$620$	3.29524	+	5.70753i	0.132340	+	0.229220i
$621$	−1.63193	+	2.82658i	−0.0654870	+	0.113427i
$622$		−	13.4542i		−	0.539464i
$623$	−13.5804	−	30.8751i	−0.544086	−	1.23698i
$624$			2.30839i			0.0924096i
$625$	12.3143	−	21.3289i	0.492570	−	0.853157i
$626$	5.02548	−	2.90146i	0.200858	−	0.115966i
$627$	15.5357	+	26.9086i	0.620437	+	1.07463i
$628$	−1.19532	+	2.07036i	−0.0476986	+	0.0826164i
$629$	−13.2617	+	8.22595i	−0.528777	+	0.327990i
$630$	−8.62559	−	6.32634i	−0.343652	−	0.252048i
$631$	31.1223			1.23896			0.619480	−	0.785012i	$-0.287343\pi$
$631$	31.1223			1.23896			0.619480	+	0.785012i	$0.287343\pi$
$632$	34.7729	+	20.0761i	1.38319	+	0.798586i
$633$	2.87810	+	4.98501i	0.114394	+	0.198136i
$634$	−13.9772	+	8.06973i	−0.555105	+	0.320490i
$635$	35.6984	+	20.6105i	1.41665	+	0.817903i
$636$		−	2.70037i		−	0.107077i
$637$	−1.56449	−	4.96662i	−0.0619873	−	0.196785i
$638$	38.3163			1.51695
$639$	7.15712	+	4.13216i	0.283131	+	0.163466i
$640$	19.5493	−	11.2868i	0.772752	−	0.446149i
$641$	21.3830	−	12.3455i	0.844579	−	0.487618i	−0.0142392	−	0.999899i	$-0.504533\pi$
$641$	21.3830	−	12.3455i	0.844579	−	0.487618i	0.858818	+	0.512281i	$0.171199\pi$
$642$	0.112046	−	0.194070i	0.00442212	−	0.00765933i
$643$			14.1538i			0.558170i	0.960266	+	0.279085i	$0.0900311\pi$
$643$			14.1538i			0.558170i	−0.960266	+	0.279085i	$0.909969\pi$
$644$	2.62696	+	1.92672i	0.103517	+	0.0759232i
$645$	28.3727			1.11718
$646$	−33.0142	+	1.04358i	−1.29892	+	0.0410591i
$647$	6.13230	+	10.6214i	0.241085	+	0.417572i	0.961024	−	0.276466i	$-0.0891633\pi$
$647$	6.13230	+	10.6214i	0.241085	+	0.417572i	−0.719938	+	0.694038i	$0.755830\pi$
$648$	1.51416	+	2.62260i	0.0594817	+	0.103025i
$649$	8.52345	+	4.92102i	0.334575	+	0.193167i
$650$	−4.80745			−0.188564
$651$	−5.86324	−	13.3301i	−0.229799	−	0.522449i
$652$			5.31152i			0.208015i
$653$	−22.1559	−	12.7917i	−0.867026	−	0.500578i	−0.000667074	−	1.00000i	$-0.500212\pi$
$653$	−22.1559	−	12.7917i	−0.867026	−	0.500578i	−0.866359	+	0.499422i	$0.833546\pi$
$654$	2.08745	+	3.61557i	0.0816258	+	0.141380i
$655$	−30.5671	−	52.9438i	−1.19436	−	2.06868i
$656$	−29.4564	−	17.0067i	−1.15008	−	0.663999i
$657$		−	0.822172i		−	0.0320760i
$658$	30.9307	+	3.39171i	1.20581	+	0.132223i
$659$	−44.6401			−1.73893			−0.869466	−	0.493992i	$-0.835537\pi$
$659$	−44.6401			−1.73893			−0.869466	+	0.493992i	$0.835537\pi$
$660$	5.12331	+	2.95794i	0.199424	+	0.115138i
$661$	14.8125	+	25.6560i	0.576140	+	0.997904i	0.995917	+	0.0902765i	$0.0287751\pi$
$661$	14.8125	+	25.6560i	0.576140	+	0.997904i	−0.419777	+	0.907627i	$0.637892\pi$
$662$	−8.19907	−	14.2012i	−0.318666	−	0.551946i
$663$	−0.0969036	−	3.06559i	−0.00376342	−	0.119058i
$664$	44.1581			1.71367
$665$	−5.75618	+	52.4936i	−0.223215	+	2.03561i
$666$			4.82151i			0.186830i
$667$	9.93497	−	17.2079i	0.384684	−	0.666292i
$668$	−0.883052	+	0.509830i	−0.0341663	+	0.0197259i
$669$	−0.105926	+	0.0611563i	−0.00409533	+	0.00236444i
$670$	−36.7589	−	21.2227i	−1.42012	−	0.819906i
$671$	−19.1314			−0.738560
$672$	5.09464	−	2.24087i	0.196530	−	0.0864434i
$673$			24.8456i			0.957726i	0.877890	+	0.478863i	$0.158951\pi$
$673$			24.8456i			0.957726i	−0.877890	+	0.478863i	$0.841049\pi$
$674$	−10.1221	−	5.84401i	−0.389890	−	0.225103i
$675$	−4.39354	+	2.53661i	−0.169107	+	0.0976342i
$676$	−2.34782	−	4.06654i	−0.0903007	−	0.156405i
$677$	19.5138	+	11.2663i	0.749976	+	0.432999i	0.825685	−	0.564131i	$-0.190789\pi$
$677$	19.5138	+	11.2663i	0.749976	+	0.432999i	−0.0757091	+	0.997130i	$0.524122\pi$
$678$	9.29673			0.357039
$679$	6.31259	+	4.62990i	0.242255	+	0.177679i
$680$	−33.6763	+	20.8888i	−1.29143	+	0.801048i
$681$	−2.98356	+	5.16768i	−0.114330	+	0.198026i
$682$	−17.3212	−	30.0012i	−0.663263	−	1.14881i
$683$	−35.7821	+	20.6588i	−1.36916	+	0.790487i	−0.990821	−	0.135179i	$-0.956839\pi$
$683$	−35.7821	+	20.6588i	−1.36916	+	0.790487i	−0.378342	+	0.925666i	$0.623506\pi$
$684$	1.18626	−	2.05467i	0.0453579	−	0.0785622i
$685$			14.7935i			0.565231i
$686$	17.7440	−	15.5483i	0.677469	−	0.593637i
$687$			7.38542i			0.281771i
$688$	13.8704	−	24.0243i	0.528805	−	0.915918i
$689$	2.66230	+	4.61124i	0.101426	+	0.175674i
$690$	−11.4280	+	6.59795i	−0.435056	+	0.251180i
$691$	7.01804	+	4.05186i	0.266979	+	0.154140i	0.627514	−	0.778605i	$-0.284073\pi$
$691$	7.01804	+	4.05186i	0.266979	+	0.154140i	−0.360535	+	0.932746i	$0.617406\pi$
$692$			3.28962i			0.125053i
$693$	−10.5408	−	7.73103i	−0.400412	−	0.293677i
$694$			23.6752i			0.898700i
$695$	10.0148	−	17.3461i	0.379882	−	0.657974i
$696$	−9.21801	−	15.9661i	−0.349408	−	0.605192i
$697$	39.8326	+	21.3486i	1.50877	+	0.808638i
$698$	−9.17829	+	15.8973i	−0.347403	+	0.601720i
$699$	10.9686			0.414872
$700$	2.03880	+	4.63522i	0.0770593	+	0.175195i
$701$	−16.1389			−0.609560			−0.304780	−	0.952423i	$-0.598583\pi$
$701$	−16.1389			−0.609560			−0.304780	+	0.952423i	$0.598583\pi$
$702$	−0.820657	−	0.473806i	−0.0309737	−	0.0178827i
$703$	20.6138	−	11.9014i	0.777464	−	0.448869i
$704$	38.0217	−	21.9519i	1.43300	−	0.827342i
$705$	14.6510	−	25.3763i	0.551788	−	0.955725i
$706$	−0.0132465			−0.000498537
$707$	18.9400	+	2.07687i	0.712312	+	0.0781086i
$708$		−	0.751510i		−	0.0282435i
$709$	−21.0400	−	12.1475i	−0.790175	−	0.456208i	0.0498493	−	0.998757i	$-0.484126\pi$
$709$	−21.0400	−	12.1475i	−0.790175	−	0.456208i	−0.840024	+	0.542549i	$0.817459\pi$
$710$	16.7065	+	28.9365i	0.626985	+	1.08597i
$711$	−11.4826	+	6.62947i	−0.430630	+	0.248625i
$712$	−19.3035	+	33.4346i	−0.723429	+	1.25302i
$713$	−17.9648			−0.672786
$714$	12.5370	−	5.99404i	0.469187	−	0.224321i
$715$	−11.6650			−0.436245
$716$	−3.05551	+	5.29230i	−0.114190	+	0.197783i
$717$	1.26386	−	0.729693i	0.0471999	−	0.0272509i
$718$	1.58475	+	2.74487i	0.0591424	+	0.102438i
$719$	−1.70478	−	0.984257i	−0.0635777	−	0.0367066i	0.467874	−	0.883795i	$-0.345020\pi$
$719$	−1.70478	−	0.984257i	−0.0635777	−	0.0367066i	−0.531452	+	0.847088i	$0.678353\pi$
$720$			9.84889i			0.367046i
$721$	8.45001	+	19.2112i	0.314695	+	0.715462i
$722$	26.1769			0.974202
$723$	−8.94105	+	15.4864i	−0.332521	+	0.575944i
$724$	−3.06139	+	1.76749i	−0.113776	+	0.0656884i
$725$	26.7473	−	15.4426i	0.993371	−	0.573523i
$726$	−14.7950	−	8.54192i	−0.549095	−	0.317020i
$727$	0.209358			0.00776466			0.00388233	−	0.999992i	$-0.498764\pi$
$727$	0.209358			0.00776466			0.00388233	+	0.999992i	$0.498764\pi$
$728$	−3.52494	+	4.80605i	−0.130643	+	0.178124i
$729$	−1.00000			−0.0370370
$730$	1.66204	−	2.87874i	0.0615148	−	0.106547i
$731$	−17.4117	+	32.4870i	−0.643995	+	1.20158i
$732$	0.730410	+	1.26511i	0.0269967	+	0.0467597i
$733$	−7.74413	+	13.4132i	−0.286036	+	0.495429i	−0.972860	−	0.231395i	$-0.925671\pi$
$733$	−7.74413	+	13.4132i	−0.286036	+	0.495429i	0.686824	+	0.726824i	$0.259004\pi$
$734$			35.4347i			1.30792i
$735$	−6.67499	−	21.1904i	−0.246211	−	0.781619i
$736$		−	6.86594i		−	0.253082i
$737$	−44.9207	−	25.9350i	−1.65467	−	0.955327i
$738$	12.0921	−	6.98137i	0.445116	−	0.256988i
$739$	12.6177	+	21.8546i	0.464151	+	0.803934i	0.999163	−	0.0409110i	$-0.0130260\pi$
$739$	12.6177	+	21.8546i	0.464151	+	0.803934i	−0.535011	+	0.844845i	$0.679693\pi$
$740$	2.26598	−	3.92479i	0.0832990	−	0.144278i
$741$			4.67816i			0.171856i
$742$	−14.2675	+	19.4529i	−0.523778	+	0.714140i
$743$			51.8623i			1.90264i	0.308200	+	0.951322i	$0.400274\pi$
$743$			51.8623i			1.90264i	−0.308200	+	0.951322i	$0.599726\pi$
$744$	−8.33416	+	14.4352i	−0.305545	+	0.529220i
$745$	−47.9326	+	27.6739i	−1.75611	+	1.01389i
$746$	2.35425	+	4.07768i	0.0861952	+	0.149295i
$747$	−7.29087	+	12.6282i	−0.266759	+	0.462040i
$748$	−6.53092	+	4.05100i	−0.238794	+	0.148119i
$749$	0.426037	−	0.187392i	0.0155671	−	0.00684715i
$750$	−0.296049			−0.0108102
$751$	21.3137	+	12.3055i	0.777749	+	0.449034i	0.835632	−	0.549290i	$-0.185102\pi$
$751$	21.3137	+	12.3055i	0.777749	+	0.449034i	−0.0578827	+	0.998323i	$0.518435\pi$
$752$	−14.3247	−	24.8111i	−0.522368	−	0.904768i
$753$	−19.8813	+	11.4785i	−0.724516	+	0.418299i
$754$	4.99606	+	2.88447i	0.181946	+	0.105046i
$755$		−	23.2995i		−	0.847957i
$756$	−0.108799	+	0.992193i	−0.00395698	+	0.0360857i
$757$	−18.5687			−0.674891			−0.337446	−	0.941345i	$-0.609563\pi$
$757$	−18.5687			−0.674891			−0.337446	+	0.941345i	$0.609563\pi$
$758$	36.2663	+	20.9384i	1.31725	+	0.760515i
$759$	−13.9654	+	8.06294i	−0.506913	+	0.292666i
$760$	52.3461	−	30.2220i	1.89879	−	1.09627i
$761$	14.6694	−	25.4081i	0.531764	−	0.921042i	−0.467549	−	0.883967i	$-0.654863\pi$
$761$	14.6694	−	25.4081i	0.531764	−	0.921042i	0.999312	−	0.0370747i	$-0.0118040\pi$
$762$			16.5447i			0.599351i
$763$	−0.945157	+	8.61937i	−0.0342170	+	0.312042i
$764$	−6.65051			−0.240607
$765$	−0.413445	−	13.0795i	−0.0149481	−	0.472891i
$766$	−15.3803	−	26.6394i	−0.555711	−	0.962520i
$767$	0.740915	+	1.28330i	0.0267529	+	0.0463374i
$768$	−7.54469	−	4.35593i	−0.272245	−	0.157181i
$769$	45.5279			1.64178			0.820889	−	0.571087i	$-0.193478\pi$
$769$	45.5279			1.64178			0.820889	+	0.571087i	$0.193478\pi$
$770$	−21.2789	−	48.3777i	−0.766837	−	1.74341i
$771$			13.9762i			0.503339i
$772$	5.36037	+	3.09481i	0.192924	+	0.111385i
$773$	−11.0200	−	19.0872i	−0.396362	−	0.686520i	0.596912	−	0.802307i	$-0.296394\pi$
$773$	−11.0200	−	19.0872i	−0.396362	−	0.686520i	−0.993274	+	0.115787i	$0.963061\pi$
$774$	5.69392	+	9.86216i	0.204664	+	0.354488i
$775$	−24.1827	−	13.9619i	−0.868670	−	0.501527i
$776$		−	8.96042i		−	0.321660i
$777$	−5.92248	+	8.07494i	−0.212468	+	0.289687i
$778$	−18.8953			−0.677430
$779$	−59.6960	−	34.4655i	−2.13883	−	1.23485i
$780$	0.445352	+	0.771372i	0.0159462	+	0.0276196i
$781$	20.4160	+	35.3615i	0.730541	+	1.26533i
$782$	−0.541612	−	17.1342i	−0.0193680	−	0.612716i
$783$	6.08788			0.217563
$784$	−21.2059	−	4.70726i	−0.757353	−	0.168117i
$785$		−	20.1121i		−	0.717832i
$786$	12.2686	−	21.2498i	0.437606	−	0.757955i
$787$	−16.8737	+	9.74205i	−0.601483	+	0.347267i	−0.769625	−	0.638496i	$-0.779557\pi$
$787$	−16.8737	+	9.74205i	−0.601483	+	0.347267i	0.168142	+	0.985763i	$0.446223\pi$
$788$	−2.54051	+	1.46676i	−0.0905018	+	0.0522512i
$789$	3.43849	+	1.98521i	0.122414	+	0.0706755i
$790$	−53.6065			−1.90723
$791$	15.5699	+	11.4196i	0.553603	+	0.406034i
$792$			14.9622i			0.531657i
$793$	−2.49454	−	1.44023i	−0.0885838	−	0.0511439i
$794$	−15.1007	+	8.71837i	−0.535903	+	0.309403i
$795$	11.3589	+	19.6741i	0.402857	+	0.697769i
$796$	−1.95497	−	1.12870i	−0.0692922	−	0.0400058i
$797$	−9.74415			−0.345155			−0.172578	−	0.984996i	$-0.555210\pi$
$797$	−9.74415			−0.345155			−0.172578	+	0.984996i	$0.555210\pi$
$798$	−19.4016	+	8.53375i	−0.686808	+	0.302091i
$799$	20.0650	+	32.3483i	0.709850	+	1.14440i
$800$	5.33609	−	9.24238i	0.188659	−	0.326768i
$801$	−6.37433	−	11.0407i	−0.225226	−	0.390103i
$802$	−7.00787	+	4.04600i	−0.247457	+	0.142869i
$803$	2.03107	−	3.51792i	0.0716750	−	0.124145i
$804$			3.96064i			0.139681i
$805$	−27.2439	−	2.98742i	−0.960220	−	0.105293i
$806$		−	5.21581i		−	0.183719i
$807$	−2.32883	+	4.03364i	−0.0819785	+	0.141991i
$808$	−10.9043	−	18.8868i	−0.383612	−	0.664435i
$809$	3.50657	−	2.02452i	0.123284	−	0.0711783i	−0.437090	−	0.899418i	$-0.643991\pi$
$809$	3.50657	−	2.02452i	0.123284	−	0.0711783i	0.560374	+	0.828240i	$0.310657\pi$
$810$	−3.50138	−	2.02152i	−0.123026	−	0.0710291i
$811$			10.5069i			0.368946i	0.982838	+	0.184473i	$0.0590578\pi$
$811$			10.5069i			0.368946i	−0.982838	+	0.184473i	$0.940942\pi$
$812$	0.662355	−	6.04035i	0.0232441	−	0.211975i
$813$		−	15.4583i		−	0.542145i
$814$	−11.9109	+	20.6304i	−0.417478	+	0.723094i
$815$	−22.3424	−	38.6982i	−0.782621	−	1.35554i
$816$	−11.2771	−	6.04404i	−0.394776	−	0.211584i
$817$	28.1097	−	48.6874i	0.983432	−	1.70335i
$818$	−45.8704			−1.60382
$819$	−0.792417	−	1.80157i	−0.0276893	−	0.0629518i
$820$	−13.1242			−0.458317
$821$	−17.1779	−	9.91769i	−0.599514	−	0.346130i	0.169336	−	0.985558i	$-0.445838\pi$
$821$	−17.1779	−	9.91769i	−0.599514	−	0.346130i	−0.768851	+	0.639429i	$0.779171\pi$
$822$	−5.14212	+	2.96880i	−0.179352	+	0.103549i
$823$	−10.4625	+	6.04055i	−0.364701	+	0.210560i	−0.671141	−	0.741330i	$-0.734196\pi$
$823$	−10.4625	+	6.04055i	−0.364701	+	0.210560i	0.306440	+	0.951890i	$0.400862\pi$
$824$	12.0111	−	20.8038i	0.418425	−	0.724734i
$825$	−25.0655			−0.872670
$826$	−3.97064	+	5.41373i	−0.138156	+	0.188368i
$827$		−	40.3180i		−	1.40199i	−0.713164	−	0.700997i	$-0.752739\pi$
$827$		−	40.3180i		−	1.40199i	0.713164	−	0.700997i	$-0.247261\pi$
$828$	1.06636	+	0.615663i	0.0370586	+	0.0213958i
$829$	20.1259	+	34.8591i	0.699002	+	1.21071i	0.968813	+	0.247794i	$0.0797055\pi$
$829$	20.1259	+	34.8591i	0.699002	+	1.21071i	−0.269811	+	0.962913i	$0.586961\pi$
$830$	−51.0562	+	29.4773i	−1.77219	+	1.02317i
$831$	6.06532	−	10.5054i	0.210404	−	0.364430i
$832$	6.61021			0.229168
$833$	28.3594	+	5.36114i	0.982597	+	0.185753i
$834$	8.03916			0.278373
$835$	4.28911	−	7.42895i	0.148431	−	0.257090i
$836$	10.1516	−	5.86103i	0.351100	−	0.202708i
$837$	−2.75208	−	4.76674i	−0.0951258	−	0.164763i
$838$	34.9338	+	20.1691i	1.20677	+	0.696729i
$839$			2.41715i			0.0834493i	0.999129	+	0.0417246i	$0.0132852\pi$
$839$			2.41715i			0.0834493i	−0.999129	+	0.0417246i	$0.986715\pi$
$840$	−15.0394	+	20.5053i	−0.518908	+	0.707500i
$841$	−8.06226			−0.278009
$842$	0.556759	−	0.964335i	0.0191872	−	0.0332332i
$843$	19.9107	−	11.4954i	0.685760	−	0.395924i
$844$	1.88065	−	1.08580i	0.0647348	−	0.0373746i
$845$	34.2111	+	19.7518i	1.17690	+	0.679482i
$846$	11.7608			0.404345
$847$	−14.2859	−	32.4792i	−0.490870	−	1.11600i
$848$	22.2118			0.762756
$849$	5.39109	−	9.33765i	0.185022	−	0.320467i
$850$	12.5873	−	23.4856i	0.431741	−	0.805548i
$851$	6.17675	+	10.6984i	0.211736	+	0.366738i
$852$	1.55891	−	2.70011i	0.0534073	−	0.0925041i
$853$		−	21.4145i		−	0.733219i	−0.930375	−	0.366610i	$-0.880518\pi$
$853$		−	21.4145i		−	0.733219i	0.930375	−	0.366610i	$-0.119482\pi$
$854$	1.42253	−	12.9727i	0.0486778	−	0.443918i
$855$			19.9596i			0.682605i
$856$	−0.461355	−	0.266364i	−0.0157688	−	0.00910412i
$857$	2.62606	−	1.51616i	0.0897045	−	0.0517909i	−0.454477	−	0.890759i	$-0.650174\pi$
$857$	2.62606	−	1.51616i	0.0897045	−	0.0517909i	0.544181	+	0.838968i	$0.316840\pi$
$858$	−2.34096	−	4.05466i	−0.0799190	−	0.138424i
$859$	−12.3577	+	21.4041i	−0.421638	+	0.730299i	−0.996100	−	0.0882326i	$-0.971878\pi$
$859$	−12.3577	+	21.4041i	−0.421638	+	0.730299i	0.574462	+	0.818531i	$0.305211\pi$
$860$		−	10.7039i		−	0.365002i
$861$	28.8270	+	3.16103i	0.982422	+	0.107728i
$862$		−	30.9948i		−	1.05569i
$863$	12.5705	−	21.7728i	0.427905	−	0.741154i	−0.568782	−	0.822489i	$-0.692585\pi$
$863$	12.5705	−	21.7728i	0.427905	−	0.741154i	0.996687	+	0.0813350i	$0.0259184\pi$
$864$	1.82180	−	1.05181i	0.0619788	−	0.0357835i
$865$	−13.8375	−	23.9673i	−0.470489	−	0.814911i
$866$	3.54624	−	6.14227i	0.120506	−	0.208723i
$867$	15.2299	+	7.55320i	0.517234	+	0.256520i
$868$	−5.02895	+	2.21198i	−0.170694	+	0.0750794i
$869$	−65.5091			−2.22224
$870$	21.3160	+	12.3068i	0.722679	+	0.417239i
$871$	−3.90480	−	6.76332i	−0.132309	−	0.229166i
$872$	8.59516	−	4.96242i	0.291069	−	0.168049i
$873$	2.56246	+	1.47944i	0.0867262	+	0.0500714i
$874$			26.1471i			0.884439i
$875$	−0.495816	−	0.363651i	−0.0167616	−	0.0122936i
$876$	−0.310174			−0.0104798
$877$	−15.5990	−	9.00610i	−0.526741	−	0.304114i	0.212947	−	0.977064i	$-0.431694\pi$
$877$	−15.5990	−	9.00610i	−0.526741	−	0.304114i	−0.739688	+	0.672949i	$0.765027\pi$
$878$	−20.9115	+	12.0733i	−0.705730	+	0.407453i
$879$	17.6836	−	10.2096i	0.596453	−	0.344362i
$880$	−24.3304	+	42.1416i	−0.820179	+	1.42059i
$881$			38.6440i			1.30195i	0.759099	+	0.650975i	$0.225640\pi$
$881$			38.6440i			1.30195i	−0.759099	+	0.650975i	$0.774360\pi$
$882$	6.02607	−	6.57272i	0.202908	−	0.221315i
$883$	56.8678			1.91375			0.956877	−	0.290492i	$-0.0938189\pi$
$883$	56.8678			1.91375			0.956877	+	0.290492i	$0.0938189\pi$
$884$	−1.15653	+	0.0365580i	−0.0388983	+	0.00122958i
$885$	3.16116	+	5.47529i	0.106261	+	0.184050i
$886$	9.07348	+	15.7157i	0.304830	+	0.527980i
$887$	0.764939	+	0.441638i	0.0256841	+	0.0148287i	0.512787	−	0.858516i	$-0.328613\pi$
$887$	0.764939	+	0.441638i	0.0256841	+	0.0148287i	−0.487103	+	0.873345i	$0.661946\pi$
$888$	11.4620			0.384639
$889$	−20.3226	+	27.7086i	−0.681597	+	0.929317i
$890$		−	51.5434i		−	1.72774i
$891$	−4.27881	−	2.47037i	−0.143346	−	0.0827607i
$892$	0.0230719	+	0.0399618i	0.000772506	+	0.00133802i
$893$	−29.0303	−	50.2819i	−0.971461	−	1.68262i
$894$	−19.2385	−	11.1073i	−0.643431	−	0.371485i
$895$		−	51.4110i		−	1.71848i
$896$	7.57639	+	17.2250i	0.253110	+	0.575447i
$897$	−2.42794			−0.0810664
$898$	−16.6324	−	9.60270i	−0.555029	−	0.320446i
$899$	16.7543	+	29.0193i	0.558788	+	0.967849i
$900$	0.956966	+	1.65751i	0.0318989	+	0.0552505i
$901$	−29.4977	+	0.932425i	−0.982711	+	0.0310636i
$902$	68.9864			2.29699
$903$	−2.57810	+	23.5110i	−0.0857937	+	0.782396i
$904$		−	22.1008i		−	0.735060i
$905$	14.8696	−	25.7549i	0.494282	−	0.856122i
$906$	8.09875	−	4.67581i	0.269063	−	0.155344i
$907$	3.07410	−	1.77483i	0.102074	−	0.0589323i	−0.448094	−	0.893986i	$-0.647897\pi$
$907$	3.07410	−	1.77483i	0.102074	−	0.0589323i	0.550168	+	0.835054i	$0.314564\pi$
$908$	1.94957	+	1.12558i	0.0646986	+	0.0373538i
$909$	7.20156			0.238861
$910$	0.867355	−	7.90986i	0.0287526	−	0.262209i
$911$			7.80002i			0.258426i	0.991617	+	0.129213i	$0.0412451\pi$
$911$			7.80002i			0.258426i	−0.991617	+	0.129213i	$0.958755\pi$
$912$	16.9006	+	9.75756i	0.559635	+	0.323105i
$913$	−62.3925	+	36.0223i	−2.06489	+	1.19217i
$914$	10.3248	+	17.8832i	0.341516	+	0.591522i
$915$	−10.6431	−	6.14481i	−0.351851	−	0.203141i
$916$	2.78623			0.0920597
$917$	46.6492	−	20.5186i	1.54049	−	0.677583i
$918$	4.46337	−	2.76854i	0.147313	−	0.0913756i
$919$	9.84771	−	17.0567i	0.324846	−	0.562650i	−0.656635	−	0.754208i	$-0.728021\pi$
$919$	9.84771	−	17.0567i	0.324846	−	0.562650i	0.981481	+	0.191559i	$0.0613542\pi$
$920$	15.6851	+	27.1673i	0.517121	+	0.895680i
$921$	16.5408	−	9.54983i	0.545038	−	0.314678i
$922$	−24.6564	+	42.7062i	−0.812016	+	1.40645i
$923$			6.14772i			0.202355i
$924$	−2.91662	+	3.97664i	−0.0959497	+	0.130822i
$925$			19.2019i			0.631353i
$926$	−8.95391	+	15.5086i	−0.294244	+	0.509645i
$927$	3.96625	+	6.86975i	0.130269	+	0.225632i
$928$	−11.0909	+	6.40332i	−0.364076	+	0.210199i
$929$	3.54644	+	2.04754i	0.116355	+	0.0671776i	0.557048	−	0.830480i	$-0.311934\pi$
$929$	3.54644	+	2.04754i	0.116355	+	0.0671776i	−0.440693	+	0.897658i	$0.645267\pi$
$930$		−	22.2536i		−	0.729723i
$931$	−42.9756	−	9.53968i	−1.40847	−	0.312651i
$932$		−	4.13804i		−	0.135546i
$933$	5.28085	−	9.14670i	0.172887	−	0.299449i
$934$	−4.86430	−	8.42521i	−0.159165	−	0.275681i
$935$	30.5423	−	56.9862i	0.998839	−	1.86365i
$936$	−1.12636	+	1.95092i	−0.0368163	+	0.0637677i
$937$	17.9607			0.586749			0.293375	−	0.955998i	$-0.405222\pi$
$937$	17.9607			0.586749			0.293375	+	0.955998i	$0.405222\pi$
$938$	20.9262	−	28.5317i	0.683266	−	0.931593i
$939$	4.55536			0.148658
$940$	−9.57348	−	5.52725i	−0.312253	−	0.180279i
$941$	27.5185	−	15.8878i	0.897078	−	0.517929i	0.0208273	−	0.999783i	$-0.493370\pi$
$941$	27.5185	−	15.8878i	0.897078	−	0.517929i	0.876251	+	0.481855i	$0.160037\pi$
$942$	6.99082	−	4.03615i	0.227773	−	0.131505i
$943$	17.8874	−	30.9819i	0.582493	−	1.00891i
$944$	6.18151			0.201191
$945$	−3.38089	−	7.68649i	−0.109980	−	0.250042i
$946$			56.2645i			1.82932i
$947$	−28.7770	−	16.6144i	−0.935128	−	0.539897i	−0.0466985	−	0.998909i	$-0.514870\pi$
$947$	−28.7770	−	16.6144i	−0.935128	−	0.539897i	−0.888430	+	0.459012i	$0.848203\pi$
$948$	2.50105	+	4.33194i	0.0812302	+	0.140695i
$949$	0.529663	−	0.305801i	0.0171936	−	0.00992673i
$950$	−20.3211	+	35.1971i	−0.659303	+	1.14195i
$951$	−12.6696			−0.410842
$952$	−14.2494	−	29.8038i	−0.461826	−	0.965948i
$953$	−28.5693			−0.925449			−0.462725	−	0.886502i	$-0.653128\pi$
$953$	−28.5693			−0.925449			−0.462725	+	0.886502i	$0.653128\pi$
$954$	−4.55905	+	7.89651i	−0.147605	+	0.255659i
$955$	48.4537	−	27.9748i	1.56793	−	0.905242i
$956$	−0.275285	−	0.476808i	−0.00890335	−	0.0154211i
$957$	26.0489	+	15.0393i	0.842041	+	0.486153i
$958$		−	18.7752i		−	0.606598i
$959$	−12.2586	−	1.34422i	−0.395851	−	0.0434070i
$960$	28.2028			0.910243
$961$	−0.352127	+	0.609902i	−0.0113589	+	0.0196742i
$962$	−3.10614	+	1.79333i	−0.100146	+	0.0578192i
$963$	0.152347	−	0.0879576i	0.00490932	−	0.00283440i
$964$	5.84241	+	3.37311i	0.188171	+	0.108641i
$965$	−52.0722			−1.67626
$966$	−4.42896	−	10.0693i	−0.142500	−	0.323974i
$967$	−17.7201			−0.569840			−0.284920	−	0.958551i	$-0.591967\pi$
$967$	−17.7201			−0.569840			−0.284920	+	0.958551i	$0.591967\pi$
$968$	−20.3064	+	35.1717i	−0.652672	+	1.13046i
$969$	−22.8539	−	12.2488i	−0.734174	−	0.393487i
$970$	5.98144	+	10.3602i	0.192052	+	0.332644i
$971$	−24.2470	+	41.9971i	−0.778124	+	1.34775i	0.154898	+	0.987930i	$0.450495\pi$
$971$	−24.2470	+	41.9971i	−0.778124	+	1.34775i	−0.933022	+	0.359820i	$0.882838\pi$
$972$			0.377262i			0.0121007i
$973$	13.4638	+	9.87485i	0.431629	+	0.316573i
$974$		−	20.0915i		−	0.643774i
$975$	−3.26829	−	1.88695i	−0.104669	−	0.0604308i
$976$	−10.4061	+	6.00796i	−0.333091	+	0.192310i
$977$	15.5309	+	26.9002i	0.496876	+	0.860614i	0.999994	−	0.00360361i	$-0.00114707\pi$
$977$	15.5309	+	26.9002i	0.496876	+	0.860614i	−0.503118	+	0.864218i	$0.667814\pi$
$978$	8.96747	−	15.5321i	0.286748	−	0.496662i
$979$		−	62.9879i		−	2.01310i
$980$	−7.99432	+	2.51822i	−0.255369	+	0.0804415i
$981$			3.27734i			0.104638i
$982$	−16.3266	+	28.2784i	−0.521001	+	0.902401i
$983$	−9.15652	+	5.28652i	−0.292047	+	0.168614i	−0.638865	−	0.769319i	$-0.720596\pi$
$983$	−9.15652	+	5.28652i	−0.292047	+	0.168614i	0.346817	+	0.937933i	$0.387262\pi$
$984$	−16.5965	−	28.7460i	−0.529078	−	0.916390i
$985$	12.3396	−	21.3728i	0.393173	−	0.680995i
$986$	−27.1725	+	16.8546i	−0.865348	+	0.536759i
$987$	19.6967	+	14.4463i	0.626952	+	0.459831i
$988$	1.76489			0.0561486
$989$	25.2684	+	14.5887i	0.803490	+	0.463895i
$990$	−9.98783	−	17.2994i	−0.317434	−	0.549812i
$991$	−49.0062	+	28.2938i	−1.55673	+	0.898781i	−0.559168	+	0.829054i	$0.688879\pi$
$991$	−49.0062	+	28.2938i	−1.55673	+	0.898781i	−0.997566	+	0.0697264i	$0.977787\pi$
$992$	10.0275	+	5.78935i	0.318372	+	0.183812i
$993$		−	12.8727i		−	0.408504i
$994$	−25.4962	+	11.2145i	−0.808691	+	0.355702i
$995$	18.9912			0.602061
$996$	4.76412	+	2.75056i	0.150957	+	0.0871550i
$997$	42.9391	−	24.7909i	1.35989	−	0.785136i	0.370285	−	0.928918i	$-0.379260\pi$
$997$	42.9391	−	24.7909i	1.35989	−	0.785136i	0.989609	+	0.143783i	$0.0459266\pi$
$998$	−36.2023	+	20.9014i	−1.14596	+	0.661622i
$999$	−1.89247	+	3.27785i	−0.0598751	+	0.103707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.p.a.16.7	✓	48
7.4	even	3	inner	357.2.p.a.67.8	yes	48
17.16	even	2	inner	357.2.p.a.16.8	yes	48
119.67	even	6	inner	357.2.p.a.67.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.p.a.16.7	✓	48	1.1	even	1	trivial
357.2.p.a.16.8	yes	48	17.16	even	2	inner
357.2.p.a.67.7	yes	48	119.67	even	6	inner
357.2.p.a.67.8	yes	48	7.4	even	3	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.636934 + 1.10320i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.188631 + 0.326718i) q^{4} +(-2.74862 - 1.58692i) q^{5} -1.27387i q^{6} +(1.56475 - 2.13344i) q^{7} -3.02832 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.636934 + 1.10320i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.188631 + 0.326718i) q^{4} +(-2.74862 - 1.58692i) q^{5} -1.27387i q^{6} +(1.56475 - 2.13344i) q^{7} -3.02832 q^{8} +(0.500000 - 0.866025i) q^{9} +(3.50138 - 2.02152i) q^{10} +(4.27881 - 2.47037i) q^{11} +(-0.326718 - 0.188631i) q^{12} +0.743886 q^{13} +(1.35697 + 3.08509i) q^{14} +3.17383 q^{15} +(1.55158 - 2.68741i) q^{16} +(-1.94771 + 3.63406i) q^{17} +(0.636934 + 1.10320i) q^{18} +(3.14440 - 5.44627i) q^{19} -1.19737i q^{20} +(-0.288391 + 2.62999i) q^{21} +6.29386i q^{22} +(2.82658 + 1.63193i) q^{23} +(2.62260 - 1.51416i) q^{24} +(2.53661 + 4.39354i) q^{25} +(-0.473806 + 0.820657i) q^{26} +1.00000i q^{27} +(0.992193 + 0.108799i) q^{28} -6.08788i q^{29} +(-2.02152 + 3.50138i) q^{30} +(-4.76674 + 2.75208i) q^{31} +(-1.05181 - 1.82180i) q^{32} +(-2.47037 + 4.27881i) q^{33} +(-2.76854 - 4.46337i) q^{34} +(-7.68649 + 3.38089i) q^{35} +0.377262 q^{36} +(3.27785 + 1.89247i) q^{37} +(4.00555 + 6.93782i) q^{38} +(-0.644224 + 0.371943i) q^{39} +(8.32369 + 4.80569i) q^{40} -10.9609i q^{41} +(-2.71772 - 1.99328i) q^{42} +8.93958 q^{43} +(1.61423 + 0.931977i) q^{44} +(-2.74862 + 1.58692i) q^{45} +(-3.60069 + 2.07886i) q^{46} +(4.61618 - 7.99546i) q^{47} +3.10315i q^{48} +(-2.10313 - 6.67659i) q^{49} -6.46262 q^{50} +(-0.130267 - 4.12105i) q^{51} +(0.140320 + 0.243041i) q^{52} +(3.57891 + 6.19885i) q^{53} +(-1.10320 - 0.636934i) q^{54} -15.6811 q^{55} +(-4.73855 + 6.46073i) q^{56} +6.28881i q^{57} +(6.71616 + 3.87758i) q^{58} +(0.996006 + 1.72513i) q^{59} +(0.598683 + 1.03695i) q^{60} +(-3.35339 - 1.93608i) q^{61} -7.01157i q^{62} +(-1.06524 - 2.42183i) q^{63} +8.88605 q^{64} +(-2.04466 - 1.18049i) q^{65} +(-3.14693 - 5.45064i) q^{66} +(-5.24920 - 9.09187i) q^{67} +(-1.55471 + 0.0491446i) q^{68} -3.26385 q^{69} +(1.16598 - 10.6332i) q^{70} +8.26433i q^{71} +(-1.51416 + 2.62260i) q^{72} +(0.712022 - 0.411086i) q^{73} +(-4.17555 + 2.41076i) q^{74} +(-4.39354 - 2.53661i) q^{75} +2.37253 q^{76} +(1.42487 - 12.9941i) q^{77} -0.947613i q^{78} +(-11.4826 - 6.62947i) q^{79} +(-8.52939 + 4.92444i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(12.0921 + 6.98137i) q^{82} -14.5817 q^{83} +(-0.913664 + 0.401874i) q^{84} +(11.1205 - 6.89781i) q^{85} +(-5.69392 + 9.86216i) q^{86} +(3.04394 + 5.27226i) q^{87} +(-12.9576 + 7.48108i) q^{88} +(6.37433 - 11.0407i) q^{89} -4.04304i q^{90} +(1.16399 - 1.58704i) q^{91} +1.23133i q^{92} +(2.75208 - 4.76674i) q^{93} +(5.88040 + 10.1852i) q^{94} +(-17.2856 + 9.97982i) q^{95} +(1.82180 + 1.05181i) q^{96} +2.95888i q^{97} +(8.70518 + 1.93237i) q^{98} -4.94075i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) \) 48 * q - 24 * q^4 + 24 * q^9	\( 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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