LMFDB - Embedded newform 720.2.cf.a.11.56

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.56
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.56

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.408461 - 1.35394i) q^{2} +(1.56018 + 0.752216i) q^{3} +(-1.66632 - 1.10607i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(1.65573 - 1.80515i) q^{6} +(-2.55094 + 4.41835i) q^{7} +(-2.17818 + 1.80431i) q^{8} +(1.86834 + 2.34719i) q^{9} +O(q^{10})$	\(q+(0.408461 - 1.35394i) q^{2} +(1.56018 + 0.752216i) q^{3} +(-1.66632 - 1.10607i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(1.65573 - 1.80515i) q^{6} +(-2.55094 + 4.41835i) q^{7} +(-2.17818 + 1.80431i) q^{8} +(1.86834 + 2.34719i) q^{9} +(-0.744969 + 1.20209i) q^{10} +(-3.01090 + 0.806767i) q^{11} +(-1.76776 - 2.97910i) q^{12} +(-2.96004 - 0.793141i) q^{13} +(4.94024 + 5.25855i) q^{14} +(-1.31233 - 1.13039i) q^{15} +(1.55324 + 3.68612i) q^{16} -4.09081i q^{17} +(3.94110 - 1.57089i) q^{18} +(5.57313 + 5.57313i) q^{19} +(1.32327 + 1.49965i) q^{20} +(-7.30348 + 4.97458i) q^{21} +(-0.137518 + 4.40611i) q^{22} +(-4.36122 + 2.51795i) q^{23} +(-4.75559 + 1.17660i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.28293 + 3.68376i) q^{26} +(1.14936 + 5.06744i) q^{27} +(9.13766 - 4.54088i) q^{28} +(-2.19675 + 0.588617i) q^{29} +(-2.06652 + 1.31510i) q^{30} +(-3.59449 + 2.07528i) q^{31} +(5.62523 - 0.597359i) q^{32} +(-5.30441 - 1.00614i) q^{33} +(-5.53872 - 1.67094i) q^{34} +(3.60757 - 3.60757i) q^{35} +(-0.517109 - 5.97767i) q^{36} +(3.51389 + 3.51389i) q^{37} +(9.82210 - 5.26929i) q^{38} +(-4.02159 - 3.46403i) q^{39} +(2.57095 - 1.17908i) q^{40} +(1.71242 + 2.96600i) q^{41} +(3.75211 + 11.9204i) q^{42} +(-2.43768 - 9.09755i) q^{43} +(5.90945 + 1.98592i) q^{44} +(-1.19718 - 2.75077i) q^{45} +(1.62777 + 6.93333i) q^{46} +(1.33117 - 2.30566i) q^{47} +(-0.349420 + 6.91939i) q^{48} +(-9.51456 - 16.4797i) q^{49} +(1.03071 - 0.968318i) q^{50} +(3.07717 - 6.38241i) q^{51} +(4.05511 + 4.59562i) q^{52} +(10.2529 - 10.2529i) q^{53} +(7.33049 + 0.513682i) q^{54} +3.11711 q^{55} +(-2.41571 - 14.2266i) q^{56} +(4.50291 + 12.8873i) q^{57} +(-0.100333 + 3.21470i) q^{58} +(-1.08447 + 4.04728i) q^{59} +(0.936481 + 3.33512i) q^{60} +(1.93367 + 7.21656i) q^{61} +(1.34160 + 5.71441i) q^{62} +(-15.1367 + 2.26746i) q^{63} +(1.48890 - 7.86023i) q^{64} +(2.65390 + 1.53223i) q^{65} +(-3.52890 + 6.77090i) q^{66} +(-3.37903 + 12.6107i) q^{67} +(-4.52470 + 6.81660i) q^{68} +(-8.69835 + 0.647886i) q^{69} +(-3.41089 - 6.35799i) q^{70} +1.42578i q^{71} +(-8.30465 - 1.74151i) q^{72} -4.54850i q^{73} +(6.19289 - 3.32232i) q^{74} +(0.975050 + 1.43153i) q^{75} +(-3.12237 - 15.4509i) q^{76} +(4.11602 - 15.3612i) q^{77} +(-6.33277 + 4.03008i) q^{78} +(3.24991 + 1.87634i) q^{79} +(-0.546276 - 3.96252i) q^{80} +(-2.01859 + 8.77071i) q^{81} +(4.71525 - 1.10702i) q^{82} +(-1.60374 - 5.98525i) q^{83} +(17.6721 - 0.211111i) q^{84} +(-1.05878 + 3.95142i) q^{85} +(-13.3133 - 0.415516i) q^{86} +(-3.87010 - 0.734080i) q^{87} +(5.10260 - 7.18988i) q^{88} +1.30008 q^{89} +(-4.21339 + 0.497332i) q^{90} +(11.0553 - 11.0553i) q^{91} +(10.0522 + 0.628085i) q^{92} +(-7.16913 + 0.533984i) q^{93} +(-2.57800 - 2.74410i) q^{94} +(-3.94080 - 6.82566i) q^{95} +(9.22572 + 3.29939i) q^{96} +(-4.60909 + 7.98319i) q^{97} +(-26.1989 + 6.15085i) q^{98} +(-7.51902 - 5.55982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.408461	−	1.35394i	0.288826	−	0.957382i
$2$	0.408461	−	1.35394i	0.288826	−	0.957382i
$3$	1.56018	+	0.752216i	0.900772	+	0.434292i
$3$	1.56018	+	0.752216i	0.900772	+	0.434292i
$4$	−1.66632	−	1.10607i	−0.833160	−	0.553033i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$6$	1.65573	−	1.80515i	0.675949	−	0.736948i
$7$	−2.55094	+	4.41835i	−0.964164	+	1.66998i	−0.252318	+	0.967644i	$0.581193\pi$
$7$	−2.55094	+	4.41835i	−0.964164	+	1.66998i	−0.711846	+	0.702336i	$0.752140\pi$
$8$	−2.17818	+	1.80431i	−0.770101	+	0.637922i
$9$	1.86834	+	2.34719i	0.622781	+	0.782396i
$10$	−0.744969	+	1.20209i	−0.235580	+	0.380134i
$11$	−3.01090	+	0.806767i	−0.907819	+	0.243249i	−0.682371	−	0.731006i	$-0.739051\pi$
$11$	−3.01090	+	0.806767i	−0.907819	+	0.243249i	−0.225448	+	0.974255i	$0.572385\pi$
$12$	−1.76776	−	2.97910i	−0.510309	−	0.859991i
$13$	−2.96004	−	0.793141i	−0.820968	−	0.219978i	−0.176198	−	0.984355i	$-0.556380\pi$
$13$	−2.96004	−	0.793141i	−0.820968	−	0.219978i	−0.644769	+	0.764377i	$0.723047\pi$
$14$	4.94024	+	5.25855i	1.32033	+	1.40541i
$15$	−1.31233	−	1.13039i	−0.338843	−	0.291865i
$16$	1.55324	+	3.68612i	0.388310	+	0.921529i
$17$		−	4.09081i		−	0.992167i	−0.868275	−	0.496084i	$-0.834771\pi$
$17$		−	4.09081i		−	0.992167i	0.868275	−	0.496084i	$-0.165229\pi$
$18$	3.94110	−	1.57089i	0.928927	−	0.370263i
$19$	5.57313	+	5.57313i	1.27856	+	1.27856i	0.941472	+	0.337092i	$0.109443\pi$
$19$	5.57313	+	5.57313i	1.27856	+	1.27856i	0.337092	+	0.941472i	$0.390557\pi$
$20$	1.32327	+	1.49965i	0.295892	+	0.335332i
$21$	−7.30348	+	4.97458i	−1.59375	+	1.08554i
$22$	−0.137518	+	4.40611i	−0.0293189	+	0.939386i
$23$	−4.36122	+	2.51795i	−0.909377	+	0.525029i	−0.880231	−	0.474546i	$-0.842612\pi$
$23$	−4.36122	+	2.51795i	−0.909377	+	0.525029i	−0.0291466	+	0.999575i	$0.509279\pi$
$24$	−4.75559	+	1.17660i	−0.970730	+	0.240173i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−2.28293	+	3.68376i	−0.447719	+	0.722444i
$27$	1.14936	+	5.06744i	0.221195	+	0.975230i
$28$	9.13766	−	4.54088i	1.72686	−	0.858146i
$29$	−2.19675	+	0.588617i	−0.407926	+	0.109304i	−0.456946	−	0.889494i	$-0.651057\pi$
$29$	−2.19675	+	0.588617i	−0.407926	+	0.109304i	0.0490200	+	0.998798i	$0.484390\pi$
$30$	−2.06652	+	1.31510i	−0.377293	+	0.240104i
$31$	−3.59449	+	2.07528i	−0.645590	+	0.372732i	−0.786765	−	0.617253i	$-0.788245\pi$
$31$	−3.59449	+	2.07528i	−0.645590	+	0.372732i	0.141175	+	0.989985i	$0.454912\pi$
$32$	5.62523	−	0.597359i	0.994409	−	0.105599i
$33$	−5.30441	−	1.00614i	−0.923379	−	0.175146i
$34$	−5.53872	−	1.67094i	−0.949883	−	0.286563i
$35$	3.60757	−	3.60757i	0.609791	−	0.609791i
$36$	−0.517109	−	5.97767i	−0.0861849	−	0.996279i
$37$	3.51389	+	3.51389i	0.577680	+	0.577680i	0.934263	−	0.356584i	$-0.116059\pi$
$37$	3.51389	+	3.51389i	0.577680	+	0.577680i	−0.356584	+	0.934263i	$0.616059\pi$
$38$	9.82210	−	5.26929i	1.59336	−	0.854792i
$39$	−4.02159	−	3.46403i	−0.643970	−	0.554689i
$40$	2.57095	−	1.17908i	0.406502	−	0.186429i
$41$	1.71242	+	2.96600i	0.267435	+	0.463211i	0.968199	−	0.250182i	$-0.0804906\pi$
$41$	1.71242	+	2.96600i	0.267435	+	0.463211i	−0.700764	+	0.713394i	$0.747157\pi$
$42$	3.75211	+	11.9204i	0.578963	+	1.83936i
$43$	−2.43768	−	9.09755i	−0.371743	−	1.38736i	−0.858046	−	0.513574i	$-0.828321\pi$
$43$	−2.43768	−	9.09755i	−0.371743	−	1.38736i	0.486303	−	0.873791i	$-0.338345\pi$
$44$	5.90945	+	1.98592i	0.890883	+	0.299388i
$45$	−1.19718	−	2.75077i	−0.178465	−	0.410061i
$46$	1.62777	+	6.93333i	0.240002	+	1.02226i
$47$	1.33117	−	2.30566i	0.194172	−	0.336315i	−0.752457	−	0.658641i	$-0.771131\pi$
$47$	1.33117	−	2.30566i	0.194172	−	0.336315i	0.946629	+	0.322326i	$0.104465\pi$
$48$	−0.349420	+	6.91939i	−0.0504344	+	0.998727i
$49$	−9.51456	−	16.4797i	−1.35922	−	2.35424i
$50$	1.03071	−	0.968318i	0.145764	−	0.136941i
$51$	3.07717	−	6.38241i	0.430890	−	0.893717i
$52$	4.05511	+	4.59562i	0.562342	+	0.637298i
$53$	10.2529	−	10.2529i	1.40834	−	1.40834i	0.639810	−	0.768533i	$-0.279013\pi$
$53$	10.2529	−	10.2529i	1.40834	−	1.40834i	0.768533	−	0.639810i	$-0.220987\pi$
$54$	7.33049	+	0.513682i	0.997554	+	0.0699033i
$55$	3.11711			0.420311
$56$	−2.41571	−	14.2266i	−0.322813	−	1.90111i
$57$	4.50291	+	12.8873i	0.596424	+	1.70696i
$58$	−0.100333	+	3.21470i	−0.0131744	+	0.422111i
$59$	−1.08447	+	4.04728i	−0.141186	+	0.526912i	0.858710	+	0.512462i	$0.171266\pi$
$59$	−1.08447	+	4.04728i	−0.141186	+	0.526912i	−0.999896	+	0.0144498i	$0.995400\pi$
$60$	0.936481	+	3.33512i	0.120899	+	0.430562i
$61$	1.93367	+	7.21656i	0.247581	+	0.923986i	0.972068	+	0.234698i	$0.0754101\pi$
$61$	1.93367	+	7.21656i	0.247581	+	0.923986i	−0.724487	+	0.689288i	$0.757923\pi$
$62$	1.34160	+	5.71441i	0.170383	+	0.725730i
$63$	−15.1367	+	2.26746i	−1.90705	+	0.285674i
$64$	1.48890	−	7.86023i	0.186112	−	0.982529i
$65$	2.65390	+	1.53223i	0.329176	+	0.190050i
$66$	−3.52890	+	6.77090i	−0.434378	+	0.833440i
$67$	−3.37903	+	12.6107i	−0.412814	+	1.54064i	0.376359	+	0.926474i	$0.377176\pi$
$67$	−3.37903	+	12.6107i	−0.412814	+	1.54064i	−0.789174	+	0.614170i	$0.789491\pi$
$68$	−4.52470	+	6.81660i	−0.548701	+	0.826634i
$69$	−8.69835	+	0.647886i	−1.04716	+	0.0779963i
$70$	−3.41089	−	6.35799i	−0.407679	−	0.759926i
$71$			1.42578i			0.169210i	0.996415	+	0.0846048i	$0.0269628\pi$
$71$			1.42578i			0.169210i	−0.996415	+	0.0846048i	$0.973037\pi$
$72$	−8.30465	−	1.74151i	−0.978712	−	0.205239i
$73$		−	4.54850i		−	0.532362i	−0.963923	−	0.266181i	$-0.914238\pi$
$73$		−	4.54850i		−	0.532362i	0.963923	−	0.266181i	$-0.0857619\pi$
$74$	6.19289	−	3.32232i	0.719909	−	0.386211i
$75$	0.975050	+	1.43153i	0.112589	+	0.165299i
$76$	−3.12237	−	15.4509i	−0.358160	−	1.77234i
$77$	4.11602	−	15.3612i	0.469064	−	1.75057i
$78$	−6.33277	+	4.03008i	−0.717045	+	0.456317i
$79$	3.24991	+	1.87634i	0.365644	+	0.211105i	0.671554	−	0.740956i	$-0.265627\pi$
$79$	3.24991	+	1.87634i	0.365644	+	0.211105i	−0.305910	+	0.952060i	$0.598961\pi$
$80$	−0.546276	−	3.96252i	−0.0610755	−	0.443023i
$81$	−2.01859	+	8.77071i	−0.224288	+	0.974523i
$82$	4.71525	−	1.10702i	0.520712	−	0.122250i
$83$	−1.60374	−	5.98525i	−0.176034	−	0.656967i	−0.996373	−	0.0850899i	$-0.972882\pi$
$83$	−1.60374	−	5.98525i	−0.176034	−	0.656967i	0.820340	−	0.571877i	$-0.193784\pi$
$84$	17.6721	−	0.211111i	1.92819	−	0.0230341i
$85$	−1.05878	+	3.95142i	−0.114841	+	0.428592i
$86$	−13.3133	−	0.415516i	−1.43561	−	0.0448063i
$87$	−3.87010	−	0.734080i	−0.414918	−	0.0787016i
$88$	5.10260	−	7.18988i	0.543939	−	0.766444i
$89$	1.30008			0.137808			0.0689039	−	0.997623i	$-0.478050\pi$
$89$	1.30008			0.137808			0.0689039	+	0.997623i	$0.478050\pi$
$90$	−4.21339	+	0.497332i	−0.444130	+	0.0524234i
$91$	11.0553	−	11.0553i	1.15891	−	1.15891i
$92$	10.0522	+	0.628085i	1.04801	+	0.0654824i
$93$	−7.16913	+	0.533984i	−0.743404	+	0.0553716i
$94$	−2.57800	−	2.74410i	−0.265900	−	0.283033i
$95$	−3.94080	−	6.82566i	−0.404317	−	0.700298i
$96$	9.22572	+	3.29939i	0.941597	+	0.336743i
$97$	−4.60909	+	7.98319i	−0.467983	+	0.810570i	−0.999331	−	0.0365840i	$-0.988352\pi$
$97$	−4.60909	+	7.98319i	−0.467983	+	0.810570i	0.531348	+	0.847154i	$0.321686\pi$
$98$	−26.1989	+	6.15085i	−2.64649	+	0.621329i
$99$	−7.51902	−	5.55982i	−0.755690	−	0.558783i
$100$	−0.890042	−	1.79104i	−0.0890042	−	0.179104i
$101$	2.04246	+	7.62255i	0.203232	+	0.758472i	0.989981	+	0.141199i	$0.0450959\pi$
$101$	2.04246	+	7.62255i	0.203232	+	0.758472i	−0.786749	+	0.617273i	$0.788237\pi$
$102$	−7.38451	−	6.77328i	−0.731176	−	0.670655i
$103$	−0.285669	−	0.494793i	−0.0281478	−	0.0487534i	0.851608	−	0.524179i	$-0.175628\pi$
$103$	−0.285669	−	0.494793i	−0.0281478	−	0.0487534i	−0.879756	+	0.475425i	$0.842294\pi$
$104$	7.87856	−	3.61325i	0.772557	−	0.354308i
$105$	8.34214	−	2.91480i	0.814110	−	0.284455i
$106$	−9.69392	−	18.0697i	−0.941556	−	1.75509i
$107$	5.59664	+	5.59664i	0.541047	+	0.541047i	0.923836	−	0.382789i	$-0.125036\pi$
$107$	5.59664	+	5.59664i	0.541047	+	0.541047i	−0.382789	+	0.923836i	$0.625036\pi$
$108$	3.68972	−	9.71524i	0.355043	−	0.934850i
$109$	−13.1697	+	13.1697i	−1.26143	+	1.26143i	−0.311026	+	0.950401i	$0.600673\pi$
$109$	−13.1697	+	13.1697i	−1.26143	+	1.26143i	−0.950401	+	0.311026i	$0.899327\pi$
$110$	1.27322	−	4.22038i	0.121397	−	0.402398i
$111$	2.83911	+	8.12551i	0.269476	+	0.771239i
$112$	−20.2488	−	2.54030i	−1.91333	−	0.240035i
$113$	10.4764	−	6.04855i	0.985536	−	0.569000i	0.0815993	−	0.996665i	$-0.473997\pi$
$113$	10.4764	−	6.04855i	0.985536	−	0.569000i	0.903937	+	0.427666i	$0.140664\pi$
$114$	19.2879	−	0.832713i	1.80648	−	0.0779907i
$115$	4.86431	−	1.30339i	0.453599	−	0.121542i
$116$	4.31154	+	1.44893i	0.400316	+	0.134529i
$117$	−3.66872	−	8.42963i	−0.339173	−	0.779320i
$118$	5.03683	+	3.12146i	0.463678	+	0.287354i
$119$	18.0746	+	10.4354i	1.65690	+	0.956612i
$120$	4.89807	+	0.0943250i	0.447131	+	0.00861066i
$121$	−1.11166	+	0.641818i	−0.101060	+	0.0583471i
$122$	10.5606	+	0.329605i	0.956115	+	0.0298410i
$123$	0.440617	+	5.91561i	0.0397291	+	0.533393i
$124$	8.28497	+	0.517664i	0.744012	+	0.0464876i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−3.11275	+	21.4204i	−0.277306	+	1.90828i
$127$		−	7.86932i		−	0.698289i	−0.937069	−	0.349144i	$-0.886472\pi$
$127$		−	7.86932i		−	0.698289i	0.937069	−	0.349144i	$-0.113528\pi$
$128$	−10.0341	−	5.22648i	−0.886901	−	0.461960i
$129$	3.04009	−	16.0275i	0.267665	−	1.41114i
$130$	3.15857	−	2.96737i	0.277025	−	0.260256i
$131$	8.61795	+	2.30917i	0.752953	+	0.201753i	0.614828	−	0.788661i	$-0.289226\pi$
$131$	8.61795	+	2.30917i	0.752953	+	0.201753i	0.138126	+	0.990415i	$0.455892\pi$
$132$	7.72598	+	7.54358i	0.672461	+	0.656584i
$133$	−38.8408	+	10.4073i	−3.36792	+	0.902432i
$134$	15.6940	+	9.72600i	1.35575	+	0.840198i
$135$	0.201351	−	5.19225i	0.0173295	−	0.446878i
$136$	7.38111	+	8.91050i	0.632925	+	0.764069i
$137$	−1.31268	+	2.27364i	−0.112150	+	0.194250i	−0.916637	−	0.399721i	$-0.869107\pi$
$137$	−1.31268	+	2.27364i	−0.112150	+	0.194250i	0.804487	+	0.593971i	$0.202440\pi$
$138$	−2.67574	+	12.0417i	−0.227774	+	1.02506i
$139$	18.8341	+	5.04657i	1.59748	+	0.428045i	0.944282	−	0.329138i	$-0.106758\pi$
$139$	18.8341	+	5.04657i	1.59748	+	0.428045i	0.653203	+	0.757183i	$0.273425\pi$
$140$	−10.0016	+	2.02115i	−0.845287	+	0.170819i
$141$	3.81123	−	2.59592i	0.320963	−	0.218616i
$142$	1.93043	+	0.582378i	0.161998	+	0.0488720i
$143$	9.55225			0.798800
$144$	−5.75003	+	10.5327i	−0.479169	+	0.877723i
$145$	2.27424			0.188866
$146$	−6.15841	−	1.85789i	−0.509674	−	0.153760i
$147$	−2.44816	−	32.8684i	−0.201921	−	2.71094i
$148$	−1.96867	−	9.74185i	−0.161824	−	0.800775i
$149$	−3.56807	−	0.956061i	−0.292307	−	0.0783235i	0.109685	−	0.993966i	$-0.465016\pi$
$149$	−3.56807	−	0.956061i	−0.292307	−	0.0783235i	−0.401993	+	0.915643i	$0.631682\pi$
$150$	2.33648	−	0.735437i	0.190773	−	0.0600482i
$151$	2.16758	−	3.75436i	0.176395	−	0.305526i	−0.764248	−	0.644923i	$-0.776890\pi$
$151$	2.16758	−	3.75436i	0.176395	−	0.305526i	0.940643	+	0.339397i	$0.110223\pi$
$152$	−22.1949	−	2.08357i	−1.80025	−	0.169000i
$153$	9.60191	−	7.64303i	0.776268	−	0.617903i
$154$	−19.1170	−	11.8473i	−1.54049	−	0.954684i
$155$	4.00914	−	1.07424i	0.322022	−	0.0862854i
$156$	2.86981	+	10.2203i	0.229768	+	0.818281i
$157$	−13.5634	−	3.63431i	−1.08248	−	0.290049i	−0.326868	−	0.945070i	$-0.605993\pi$
$157$	−13.5634	−	3.63431i	−1.08248	−	0.290049i	−0.755611	+	0.655021i	$0.772660\pi$
$158$	3.86792	−	3.63378i	0.307715	−	0.289088i
$159$	23.7088	−	8.28400i	1.88023	−	0.656964i
$160$	−5.58816	−	0.878911i	−0.441783	−	0.0694840i
$161$		−	25.6925i		−	2.02486i
$162$	11.0505	+	6.31555i	0.868210	+	0.496197i
$163$	−2.68988	−	2.68988i	−0.210687	−	0.210687i	0.593872	−	0.804560i	$-0.297599\pi$
$163$	−2.68988	−	2.68988i	−0.210687	−	0.210687i	−0.804560	+	0.593872i	$0.797599\pi$
$164$	0.427151	−	6.83635i	0.0333549	−	0.533829i
$165$	4.86326	+	2.34474i	0.378604	+	0.182538i
$166$	−8.75875	−	0.273367i	−0.679811	−	0.0212174i
$167$	6.73225	−	3.88687i	0.520957	−	0.300775i	−0.216369	−	0.976312i	$-0.569421\pi$
$167$	6.73225	−	3.88687i	0.520957	−	0.300775i	0.737326	+	0.675537i	$0.236088\pi$
$168$	6.93255	−	24.0133i	0.534858	−	1.85267i
$169$	−3.12556	−	1.80454i	−0.240428	−	0.138811i
$170$	4.91752	+	3.04753i	0.377157	+	0.233735i
$171$	−2.66868	+	23.4937i	−0.204079	+	1.79661i
$172$	−6.00053	+	17.8557i	−0.457536	+	1.36148i
$173$	6.23374	−	1.67033i	0.473942	−	0.126993i	−0.0139381	−	0.999903i	$-0.504437\pi$
$173$	6.23374	−	1.67033i	0.473942	−	0.126993i	0.487881	+	0.872910i	$0.337770\pi$
$174$	−2.57469	+	4.94005i	−0.195187	+	0.374504i
$175$	−4.41835	+	2.55094i	−0.333996	+	0.192833i
$176$	−7.65047	−	9.84541i	−0.576676	−	0.742126i
$177$	−4.73640	+	5.49875i	−0.356010	+	0.413311i
$178$	0.531031	−	1.76023i	0.0398024	−	0.131935i
$179$	−16.0170	+	16.0170i	−1.19717	+	1.19717i	−0.222159	+	0.975010i	$0.571310\pi$
$179$	−16.0170	+	16.0170i	−1.19717	+	1.19717i	−0.975010	+	0.222159i	$0.928690\pi$
$180$	−1.04765	+	5.90783i	−0.0780870	+	0.440344i
$181$	2.87003	+	2.87003i	0.213328	+	0.213328i	0.805679	−	0.592352i	$-0.201800\pi$
$181$	2.87003	+	2.87003i	0.213328	+	0.213328i	−0.592352	+	0.805679i	$0.701800\pi$
$182$	−10.4525	−	19.4838i	−0.774793	−	1.44424i
$183$	−2.41153	+	12.7137i	−0.178266	+	0.939824i
$184$	4.95633	−	13.3536i	0.365385	−	0.984437i
$185$	−2.48469	−	4.30362i	−0.182678	−	0.316408i
$186$	−2.20533	+	9.92470i	−0.161702	+	0.727714i
$187$	3.30033	+	12.3170i	0.241344	+	0.900708i
$188$	−4.76837	+	2.36960i	−0.347769	+	0.172821i
$189$	−25.3217	−	7.84843i	−1.84188	−	0.570890i
$190$	−10.8512	+	2.54759i	−0.787230	+	0.184822i
$191$	2.57130	−	4.45363i	0.186053	−	0.322253i	−0.757878	−	0.652396i	$-0.773764\pi$
$191$	2.57130	−	4.45363i	0.186053	−	0.322253i	0.943931	+	0.330143i	$0.107097\pi$
$192$	8.23554	−	11.1434i	0.594349	−	0.804207i
$193$	5.41653	+	9.38171i	0.389891	+	0.675310i	0.992434	−	0.122775i	$-0.0391795\pi$
$193$	5.41653	+	9.38171i	0.389891	+	0.675310i	−0.602544	+	0.798086i	$0.705846\pi$
$194$	8.92614	+	9.50127i	0.640859	+	0.682151i
$195$	2.98800	+	4.38687i	0.213975	+	0.314150i
$196$	−2.37334	+	37.9842i	−0.169524	+	2.71315i
$197$	0.00960139	−	0.00960139i	0.000684071	−	0.000684071i	−0.706765	−	0.707449i	$-0.749846\pi$
$197$	0.00960139	−	0.00960139i	0.000684071	−	0.000684071i	0.707449	+	0.706765i	$0.249846\pi$
$198$	−10.5989	+	7.90934i	−0.753232	+	0.562093i
$199$	−4.95666			−0.351368			−0.175684	−	0.984447i	$-0.556214\pi$
$199$	−4.95666			−0.351368			−0.175684	+	0.984447i	$0.556214\pi$
$200$	−2.78851	+	0.473495i	−0.197178	+	0.0334811i
$201$	−14.7579	+	17.1333i	−1.04094	+	1.20849i
$202$	11.1548	+	0.348148i	0.784846	+	0.0244956i
$203$	3.00305	−	11.2075i	0.210773	−	0.786615i
$204$	−12.1869	+	7.23158i	−0.853255	+	0.506312i
$205$	−0.886414	−	3.30814i	−0.0619098	−	0.231051i
$206$	−0.786606	+	0.184675i	−0.0548054	+	0.0128669i
$207$	−14.0584	−	5.53221i	−0.977124	−	0.384515i
$208$	−1.67404	−	12.1430i	−0.116074	−	0.841965i
$209$	−21.2763	−	12.2839i	−1.47171	−	0.849695i
$210$	−0.539027	−	12.4854i	−0.0371964	−	0.861572i
$211$	1.74917	−	6.52798i	0.120418	−	0.449405i	−0.879217	−	0.476421i	$-0.841934\pi$
$211$	1.74917	−	6.52798i	0.120418	−	0.449405i	0.999635	+	0.0270162i	$0.00860057\pi$
$212$	−28.4250	+	5.74422i	−1.95223	+	0.394515i
$213$	−1.07250	+	2.22448i	−0.0734863	+	0.152419i
$214$	9.86353	−	5.29152i	0.674257	−	0.361721i
$215$			9.41848i			0.642335i
$216$	−11.6468	−	8.96396i	−0.792463	−	0.609921i
$217$		−	21.1756i		−	1.43750i
$218$	12.4517	+	23.2103i	0.843335	+	1.57200i
$219$	3.42146	−	7.09650i	0.231201	−	0.479537i
$220$	−5.19410	−	3.44773i	−0.350186	−	0.232446i
$221$	−3.24459	+	12.1090i	−0.218255	+	0.814537i
$222$	12.1611	−	0.525030i	0.816202	−	0.0352377i
$223$	1.00544	+	0.580489i	0.0673290	+	0.0388724i	0.533287	−	0.845935i	$-0.320957\pi$
$223$	1.00544	+	0.580489i	0.0673290	+	0.0388724i	−0.465958	+	0.884807i	$0.654290\pi$
$224$	−11.7103	+	26.3781i	−0.782424	+	1.76246i
$225$	0.444437	+	2.96690i	0.0296292	+	0.197793i
$226$	−3.91019	−	16.6550i	−0.260102	−	1.10788i
$227$	−0.137668	−	0.513783i	−0.00913732	−	0.0341009i	0.961207	−	0.275829i	$-0.0889524\pi$
$227$	−0.137668	−	0.513783i	−0.00913732	−	0.0341009i	−0.970344	+	0.241728i	$0.922286\pi$
$228$	6.75092	−	26.4549i	0.447091	−	1.75202i
$229$	−4.28545	+	15.9935i	−0.283190	+	1.05688i	0.666961	+	0.745093i	$0.267595\pi$
$229$	−4.28545	+	15.9935i	−0.283190	+	1.05688i	−0.950152	+	0.311789i	$0.899072\pi$
$230$	0.222170	−	7.11838i	0.0146494	−	0.469372i
$231$	17.9767	−	20.8702i	1.18278	−	1.37316i
$232$	3.72286	−	5.24574i	0.244417	−	0.344400i
$233$	−9.44023			−0.618450			−0.309225	−	0.950989i	$-0.600070\pi$
$233$	−9.44023			−0.618450			−0.309225	+	0.950989i	$0.600070\pi$
$234$	−12.9118	+	1.52406i	−0.844069	+	0.0996306i
$235$	−1.88256	+	1.88256i	−0.122805	+	0.122805i
$236$	6.28363	−	5.54458i	0.409029	−	0.360921i
$237$	3.65905	+	5.37207i	0.237681	+	0.348953i
$238$	21.5117	−	20.2096i	1.39440	−	1.30999i
$239$	9.12230	+	15.8003i	0.590073	+	1.02204i	0.994222	+	0.107343i	$0.0342342\pi$
$239$	9.12230	+	15.8003i	0.590073	+	1.02204i	−0.404149	+	0.914693i	$0.632432\pi$
$240$	2.12838	−	6.59318i	0.137386	−	0.425588i
$241$	12.0582	−	20.8855i	0.776740	−	1.34535i	−0.157072	−	0.987587i	$-0.550205\pi$
$241$	12.0582	−	20.8855i	0.776740	−	1.34535i	0.933811	−	0.357766i	$-0.116461\pi$
$242$	0.414914	+	1.76728i	0.0266717	+	0.113605i
$243$	−9.74684	+	12.1655i	−0.625260	+	0.780416i
$244$	4.75988	−	14.1639i	0.304720	−	0.906749i
$245$	4.92510	+	18.3807i	0.314653	+	1.17430i
$246$	8.18937	+	1.81973i	0.522135	+	0.116022i
$247$	−12.0764	−	20.9170i	−0.768404	−	1.33091i
$248$	4.08497	−	11.0059i	0.259396	−	0.698877i
$249$	2.00007	−	10.5444i	0.126749	−	0.668227i
$250$	−1.24621	+	0.668556i	−0.0788171	+	0.0422832i
$251$	11.5922	+	11.5922i	0.731692	+	0.731692i	0.970955	−	0.239263i	$-0.0769056\pi$
$251$	11.5922	+	11.5922i	0.731692	+	0.731692i	−0.239263	+	0.970955i	$0.576906\pi$
$252$	27.7306	+	12.9639i	1.74686	+	0.816649i
$253$	11.0998	−	11.0998i	0.697837	−	0.697837i
$254$	−10.6546	−	3.21431i	−0.668529	−	0.201684i
$255$	−4.62421	+	5.36851i	−0.289579	+	0.336189i
$256$	−11.1749	+	11.4508i	−0.698431	+	0.715677i
$257$	−11.1037	+	6.41071i	−0.692628	+	0.399889i	−0.804596	−	0.593823i	$-0.797618\pi$
$257$	−11.1037	+	6.41071i	−0.692628	+	0.399889i	0.111968	+	0.993712i	$0.464285\pi$
$258$	−20.4586	−	10.6627i	−1.27369	−	0.663833i
$259$	−24.4893	+	6.56189i	−1.52169	+	0.407736i
$260$	−2.72750	−	5.48857i	−0.169152	−	0.340387i
$261$	−5.48588	−	4.05645i	−0.339567	−	0.251088i
$262$	6.64658	−	10.7250i	0.410627	−	0.662592i
$263$	−1.41865	−	0.819058i	−0.0874777	−	0.0505053i	0.455623	−	0.890173i	$-0.349417\pi$
$263$	−1.41865	−	0.819058i	−0.0874777	−	0.0505053i	−0.543101	+	0.839668i	$0.682750\pi$
$264$	13.3693	−	7.37928i	0.822825	−	0.454163i
$265$	−12.5572	+	7.24989i	−0.771381	+	0.445357i
$266$	−1.77399	+	56.8391i	−0.108770	+	3.48503i
$267$	2.02836	+	0.977938i	0.124133	+	0.0598488i
$268$	19.5788	−	17.2760i	1.19597	−	1.05530i
$269$	−1.34828	−	1.34828i	−0.0822060	−	0.0822060i	0.664808	−	0.747014i	$-0.268513\pi$
$269$	−1.34828	−	1.34828i	−0.0822060	−	0.0822060i	−0.747014	+	0.664808i	$0.768513\pi$
$270$	−6.94776	−	2.39345i	−0.422827	−	0.145661i
$271$			14.2059i			0.862944i	0.902126	+	0.431472i	$0.142006\pi$
$271$			14.2059i			0.862944i	−0.902126	+	0.431472i	$0.857994\pi$
$272$	15.0792	−	6.35400i	0.914311	−	0.385268i
$273$	25.5642	−	8.93228i	1.54721	−	0.540606i
$274$	2.54219	+	2.70599i	0.153579	+	0.163475i
$275$	−3.01090	−	0.806767i	−0.181564	−	0.0486499i
$276$	15.2108	+	8.54136i	0.915584	+	0.514129i
$277$	7.08259	−	1.89777i	0.425551	−	0.114026i	−0.0396858	−	0.999212i	$-0.512636\pi$
$277$	7.08259	−	1.89777i	0.425551	−	0.114026i	0.465237	+	0.885186i	$0.345969\pi$
$278$	14.5257	−	23.4389i	0.871197	−	1.40577i
$279$	−11.5868	−	4.55962i	−0.693685	−	0.272977i
$280$	−1.34873	+	14.3671i	−0.0806019	+	0.858599i
$281$	3.19127	−	5.52744i	0.190375	−	0.329739i	−0.755000	−	0.655725i	$-0.772363\pi$
$281$	3.19127	−	5.52744i	0.190375	−	0.329739i	0.945375	+	0.325986i	$0.105696\pi$
$282$	−1.95799	−	6.22051i	−0.116597	−	0.370426i
$283$	16.6134	+	4.45154i	0.987563	+	0.264617i	0.716227	−	0.697868i	$-0.245868\pi$
$283$	16.6134	+	4.45154i	0.987563	+	0.264617i	0.271337	+	0.962484i	$0.412534\pi$
$284$	1.57701	−	2.37581i	0.0935784	−	0.140979i
$285$	−1.01399	−	13.6136i	−0.0600638	−	0.806401i
$286$	3.90172	−	12.9332i	0.230714	−	0.764756i
$287$	−17.4731			−1.03140
$288$	11.9120	+	12.0874i	0.701919	+	0.712257i
$289$	0.265270			0.0156041
$290$	0.928940	−	3.07919i	0.0545492	−	0.180817i
$291$	−13.1961	+	8.98820i	−0.773570	+	0.526897i
$292$	−5.03094	+	7.57926i	−0.294414	+	0.443543i
$293$	10.0578	+	2.69498i	0.587583	+	0.157442i	0.540348	−	0.841441i	$-0.318292\pi$
$293$	10.0578	+	2.69498i	0.587583	+	0.157442i	0.0472347	+	0.998884i	$0.484959\pi$
$294$	−45.5018	−	10.1108i	−2.65372	−	0.589672i
$295$	2.09503	−	3.62870i	0.121977	−	0.211271i
$296$	−13.9940	−	1.31370i	−0.813386	−	0.0763575i
$297$	−7.54886	−	14.3303i	−0.438029	−	0.831526i
$298$	−2.75187	+	4.44044i	−0.159411	+	0.257228i
$299$	14.9065	−	3.99418i	0.862064	−	0.230989i
$300$	−0.0413790	−	3.46385i	−0.00238902	−	0.199986i
$301$	46.4146	+	12.4367i	2.67529	+	0.716842i
$302$	−4.19782	−	4.46829i	−0.241557	−	0.257121i
$303$	−2.54720	+	13.4289i	−0.146333	+	0.771473i
$304$	−11.8868	+	29.1996i	−0.681755	+	1.67471i
$305$		−	7.47114i		−	0.427796i
$306$	−6.42622	−	16.1223i	−0.367363	−	0.921651i
$307$	9.14432	+	9.14432i	0.521894	+	0.521894i	0.918143	−	0.396249i	$-0.129688\pi$
$307$	9.14432	+	9.14432i	0.521894	+	0.521894i	−0.396249	+	0.918143i	$0.629688\pi$
$308$	−23.8491	+	21.0441i	−1.35893	+	1.19910i
$309$	−0.0735045	−	0.986852i	−0.00418153	−	0.0561401i
$310$	0.183111	−	5.86693i	0.0104000	−	0.333219i
$311$	1.13345	−	0.654399i	0.0642722	−	0.0371076i	−0.467520	−	0.883983i	$-0.654852\pi$
$311$	1.13345	−	0.654399i	0.0642722	−	0.0371076i	0.531792	+	0.846875i	$0.321519\pi$
$312$	15.0099	+	0.289055i	0.849771	+	0.0163645i
$313$	0.754212	+	0.435445i	0.0426306	+	0.0246128i	0.521164	−	0.853457i	$-0.325498\pi$
$313$	0.754212	+	0.435445i	0.0426306	+	0.0246128i	−0.478533	+	0.878069i	$0.658831\pi$
$314$	−10.4608	+	16.8796i	−0.590336	+	0.952572i
$315$	15.2078	+	1.72747i	0.856864	+	0.0973321i
$316$	−3.34004	−	6.72119i	−0.187892	−	0.378097i
$317$	8.28523	−	2.22002i	0.465345	−	0.124689i	−0.0185257	−	0.999828i	$-0.505897\pi$
$317$	8.28523	−	2.22002i	0.465345	−	0.124689i	0.483871	+	0.875140i	$0.339231\pi$
$318$	−1.53194	−	35.4840i	−0.0859071	−	1.98984i
$319$	6.13931	−	3.54453i	0.343735	−	0.198456i
$320$	−3.47254	+	7.20704i	−0.194121	+	0.402886i
$321$	4.52190	+	12.9417i	0.252388	+	0.722333i
$322$	−34.7862	−	10.4944i	−1.93856	−	0.584830i
$323$	22.7986	−	22.7986i	1.26855	−	1.26855i
$324$	13.0646	−	12.3821i	0.725811	−	0.687894i
$325$	−2.16690	−	2.16690i	−0.120198	−	0.120198i
$326$	−4.74065	+	2.54323i	−0.262560	+	0.140856i
$327$	−30.4536	+	10.6407i	−1.68409	+	0.588431i
$328$	−9.08155	−	3.37072i	−0.501445	−	0.186117i
$329$	6.79148	+	11.7632i	0.374426	+	0.648525i
$330$	5.16109	−	5.62684i	0.284109	−	0.309747i
$331$	−1.47191	−	5.49325i	−0.0809035	−	0.301936i	0.913603	−	0.406606i	$-0.133288\pi$
$331$	−1.47191	−	5.49325i	−0.0809035	−	0.301936i	−0.994507	+	0.104670i	$0.966621\pi$
$332$	−3.94773	+	11.7472i	−0.216660	+	0.644710i
$333$	−1.68261	+	14.8129i	−0.0922067	+	0.811742i
$334$	−2.51273	−	10.7027i	−0.137490	−	0.585626i
$335$	6.52779	−	11.3065i	0.356651	−	0.617738i
$336$	−29.6809	−	19.1948i	−1.61923	−	1.04716i
$337$	4.26835	+	7.39301i	0.232512	+	0.402723i	0.958547	−	0.284935i	$-0.0919721\pi$
$337$	4.26835	+	7.39301i	0.232512	+	0.402723i	−0.726035	+	0.687658i	$0.758639\pi$
$338$	−3.71992	+	3.49474i	−0.202337	+	0.190089i
$339$	20.8949	−	1.55633i	1.13486	−	0.0845284i
$340$	6.13479	−	5.41325i	0.332706	−	0.293574i
$341$	9.14837	−	9.14837i	0.495412	−	0.495412i
$342$	30.7191	+	13.2095i	1.66110	+	0.714288i
$343$	61.3711			3.31373
$344$	21.7246	+	15.4177i	1.17131	+	0.831268i
$345$	8.56964	+	1.62549i	0.461374	+	0.0875133i
$346$	0.284716	−	9.12239i	0.0153064	−	0.490423i
$347$	−5.52917	+	20.6351i	−0.296821	+	1.10775i	0.642939	+	0.765918i	$0.277715\pi$
$347$	−5.52917	+	20.6351i	−0.296821	+	1.10775i	−0.939760	+	0.341835i	$0.888952\pi$
$348$	5.63688	+	5.50380i	0.302169	+	0.295034i
$349$	8.16186	+	30.4605i	0.436894	+	1.63051i	0.736492	+	0.676446i	$0.236481\pi$
$349$	8.16186	+	30.4605i	0.436894	+	1.63051i	−0.299597	+	0.954066i	$0.596852\pi$
$350$	1.64910	+	7.02415i	0.0881479	+	0.375457i
$351$	0.617033	−	15.9114i	0.0329348	−	0.849290i
$352$	−16.4550	+	6.33683i	−0.877056	+	0.337754i
$353$	−22.5052	−	12.9934i	−1.19783	−	0.691567i	−0.237759	−	0.971324i	$-0.576413\pi$
$353$	−22.5052	−	12.9934i	−1.19783	−	0.691567i	−0.960071	+	0.279757i	$0.909746\pi$
$354$	5.51036	+	8.65884i	0.292872	+	0.460212i
$355$	0.369020	−	1.37720i	0.0195856	−	0.0730943i
$356$	−2.16634	−	1.43797i	−0.114816	−	0.0762122i
$357$	20.3501	+	29.8772i	1.07704	+	1.58127i
$358$	15.1438	+	28.2285i	0.800375	+	1.49192i
$359$		−	14.2369i		−	0.751394i	−0.926743	−	0.375697i	$-0.877403\pi$
$359$		−	14.2369i		−	0.751394i	0.926743	−	0.375697i	$-0.122597\pi$
$360$	7.57094	+	3.83157i	0.399023	+	0.201942i
$361$			43.1196i			2.26945i
$362$	5.05815	−	2.71356i	0.265851	−	0.142622i
$363$	−2.21718	+	0.165144i	−0.116372	+	0.00866782i
$364$	−30.6494	+	6.19374i	−1.60647	+	0.324640i
$365$	−1.17724	+	4.39352i	−0.0616195	+	0.229967i
$366$	16.2286	+	8.45813i	0.848282	+	0.442113i
$367$	5.68193	+	3.28046i	0.296594	+	0.171239i	0.640912	−	0.767614i	$-0.278556\pi$
$367$	5.68193	+	3.28046i	0.296594	+	0.171239i	−0.344318	+	0.938853i	$0.611890\pi$
$368$	−16.0555	−	12.1650i	−0.836950	−	0.634144i
$369$	−3.76237	+	9.56087i	−0.195861	+	0.497719i
$370$	−6.84175	+	1.60627i	−0.355686	+	0.0835061i
$371$	19.1464	+	71.4554i	0.994032	+	3.70978i
$372$	12.5367	+	7.03974i	0.649996	+	0.364993i
$373$	2.22950	−	8.32059i	0.115439	−	0.430824i	−0.883880	−	0.467713i	$-0.845078\pi$
$373$	2.22950	−	8.32059i	0.115439	−	0.430824i	0.999319	+	0.0368890i	$0.0117448\pi$
$374$	18.0246	+	0.562560i	0.932028	+	0.0290893i
$375$	−0.571319	−	1.63511i	−0.0295028	−	0.0844369i
$376$	1.26061	+	7.42399i	0.0650108	+	0.382863i
$377$	6.96933			0.358939
$378$	−20.9693	+	31.0783i	−1.07854	+	1.59850i
$379$	13.2766	−	13.2766i	0.681975	−	0.681975i	−0.278470	−	0.960445i	$-0.589827\pi$
$379$	13.2766	−	13.2766i	0.681975	−	0.681975i	0.960445	+	0.278470i	$0.0898272\pi$
$380$	−0.983003	+	15.7325i	−0.0504270	+	0.807061i
$381$	5.91943	−	12.2776i	0.303261	−	0.628999i
$382$	−4.97968	−	5.30053i	−0.254783	−	0.271199i
$383$	−19.2133	−	33.2785i	−0.981756	−	1.70045i	−0.655549	−	0.755152i	$-0.727563\pi$
$383$	−19.2133	−	33.2785i	−0.981756	−	1.70045i	−0.326206	−	0.945299i	$-0.605770\pi$
$384$	−11.7237	−	15.7021i	−0.598270	−	0.801294i
$385$	−7.95155	+	13.7725i	−0.405248	+	0.701911i
$386$	14.9147	−	3.50161i	0.759140	−	0.178227i
$387$	16.7993	−	22.7190i	0.853954	−	1.15487i
$388$	16.5101	−	8.20457i	0.838176	−	0.416524i
$389$	7.17065	+	26.7612i	0.363566	+	1.35685i	0.869354	+	0.494190i	$0.164535\pi$
$389$	7.17065	+	26.7612i	0.363566	+	1.35685i	−0.505787	+	0.862658i	$0.668798\pi$
$390$	7.16004	−	2.25372i	0.362563	−	0.114121i
$391$	10.3005	+	17.8409i	0.520917	+	0.902254i
$392$	50.4589	+	18.7284i	2.54856	+	0.945928i
$393$	11.7086	+	10.0853i	0.590620	+	0.508735i
$394$	−0.00907793	−	0.0169215i	−0.000457340	−	0.000852494i
$395$	−2.65354	−	2.65354i	−0.133514	−	0.133514i
$396$	6.37955	+	17.5810i	0.320585	+	0.883477i
$397$	−4.31026	+	4.31026i	−0.216326	+	0.216326i	−0.806948	−	0.590622i	$-0.798882\pi$
$397$	−4.31026	+	4.31026i	−0.216326	+	0.216326i	0.590622	+	0.806948i	$0.298882\pi$
$398$	−2.02460	+	6.71103i	−0.101484	+	0.336393i
$399$	−68.4273	−	12.9793i	−3.42565	−	0.649776i
$400$	−0.497914	+	3.96889i	−0.0248957	+	0.198444i
$401$	22.3141	−	12.8831i	1.11431	−	0.643350i	0.174371	−	0.984680i	$-0.444211\pi$
$401$	22.3141	−	12.8831i	1.11431	−	0.643350i	0.939943	+	0.341330i	$0.110877\pi$
$402$	17.1694	+	26.9796i	0.856333	+	1.34562i
$403$	12.2858	−	3.29198i	0.612001	−	0.163985i
$404$	5.02766	−	14.9607i	0.250135	−	0.744322i
$405$	4.21984	−	7.94940i	0.209685	−	0.395009i
$406$	−13.9477	−	8.64381i	−0.692215	−	0.428985i
$407$	−13.4148	−	7.74506i	−0.664949	−	0.383908i
$408$	4.81326	+	19.4542i	0.238292	+	0.963127i
$409$	20.8356	−	12.0294i	1.03025	−	0.594817i	0.113196	−	0.993573i	$-0.463891\pi$
$409$	20.8356	−	12.0294i	1.03025	−	0.594817i	0.917057	+	0.398756i	$0.130558\pi$
$410$	−4.84110	−	0.151094i	−0.239085	−	0.00746201i
$411$	−3.75829	+	2.55987i	−0.185383	+	0.126269i
$412$	−0.0712580	+	1.14045i	−0.00351063	+	0.0561860i
$413$	−15.1159	−	15.1159i	−0.743806	−	0.743806i
$414$	−13.2326	+	16.7745i	−0.650346	+	0.824422i
$415$			6.19639i			0.304169i
$416$	−17.1247	−	2.69339i	−0.839607	−	0.132054i
$417$	25.5885	+	22.0409i	1.25307	+	1.07935i
$418$	−25.3222	+	23.7894i	−1.23855	+	1.16358i
$419$	2.45042	+	0.656588i	0.119711	+	0.0320764i	0.318177	−	0.948031i	$-0.396929\pi$
$419$	2.45042	+	0.656588i	0.119711	+	0.0320764i	−0.198466	+	0.980108i	$0.563596\pi$
$420$	−17.1246	−	4.36997i	−0.835596	−	0.213233i
$421$	9.55412	−	2.56002i	0.465639	−	0.124768i	−0.0183686	−	0.999831i	$-0.505847\pi$
$421$	9.55412	−	2.56002i	0.465639	−	0.124768i	0.484008	+	0.875064i	$0.339181\pi$
$422$	−8.12404	−	5.03470i	−0.395472	−	0.245085i
$423$	7.89890	−	1.18325i	0.384058	−	0.0575314i
$424$	−3.83315	+	40.8320i	−0.186154	+	1.98298i
$425$	2.04541	−	3.54275i	0.0992167	−	0.171848i
$426$	2.57375	+	2.36072i	0.124699	+	0.114377i
$427$	−36.8180	−	9.86535i	−1.78175	−	0.477418i
$428$	−3.13554	−	15.5160i	−0.151562	−	0.749996i
$429$	14.9033	+	7.18536i	0.719536	+	0.346912i
$430$	12.7521	+	3.84708i	0.614960	+	0.185523i
$431$	−23.4818			−1.13108			−0.565539	−	0.824721i	$-0.691332\pi$
$431$	−23.4818			−1.13108			−0.565539	+	0.824721i	$0.691332\pi$
$432$	−16.8939	+	12.1076i	−0.812810	+	0.582529i
$433$	−11.2687			−0.541539			−0.270769	−	0.962644i	$-0.587278\pi$
$433$	−11.2687			−0.541539			−0.270769	+	0.962644i	$0.587278\pi$
$434$	−28.6706	−	8.64943i	−1.37623	−	0.415186i
$435$	3.54824	+	1.71072i	0.170125	+	0.0820228i
$436$	36.5114	−	7.37837i	1.74858	−	0.353360i
$437$	−38.3385	−	10.2728i	−1.83398	−	0.491413i
$438$	−8.21072	−	7.53110i	−0.392323	−	0.359850i
$439$	8.59290	−	14.8833i	0.410117	−	0.710343i	−0.584785	−	0.811188i	$-0.698821\pi$
$439$	8.59290	−	14.8833i	0.410117	−	0.710343i	0.994902	+	0.100845i	$0.0321546\pi$
$440$	−6.78961	+	5.62424i	−0.323682	+	0.268125i
$441$	20.9045	−	53.1222i	0.995453	−	2.52963i
$442$	15.0696	+	9.33903i	0.716786	+	0.444212i
$443$	−35.4401	+	9.49615i	−1.68381	+	0.451176i	−0.968781	−	0.247918i	$-0.920254\pi$
$443$	−35.4401	+	9.49615i	−1.68381	+	0.451176i	−0.715030	+	0.699094i	$0.753587\pi$
$444$	4.25649	−	16.6799i	0.202004	−	0.791595i
$445$	−1.25578	−	0.336485i	−0.0595296	−	0.0159509i
$446$	1.19663	−	1.12420i	0.0566621	−	0.0532322i
$447$	−4.84767	−	4.17559i	−0.229287	−	0.197498i
$448$	30.9312	+	26.6294i	1.46136	+	1.25812i
$449$			10.5380i			0.497318i	0.968591	+	0.248659i	$0.0799899\pi$
$449$			10.5380i			0.497318i	−0.968591	+	0.248659i	$0.920010\pi$
$450$	4.19854	+	0.610120i	0.197921	+	0.0287613i
$451$	−7.54879	−	7.54879i	−0.355458	−	0.355458i
$452$	−24.1471	−	1.50877i	−1.13578	−	0.0709664i
$453$	6.20592	−	4.22700i	0.291579	−	0.198602i
$454$	−0.751864	−	0.0234662i	−0.0352867	−	0.00110132i
$455$	−13.5399	+	7.81724i	−0.634759	+	0.366478i
$456$	−33.0609	−	19.9461i	−1.54822	−	0.934064i
$457$	25.0816	+	14.4809i	1.17327	+	0.677387i	0.954448	−	0.298378i	$-0.0964455\pi$
$457$	25.0816	+	14.4809i	1.17327	+	0.677387i	0.218821	+	0.975765i	$0.429779\pi$
$458$	19.9039	+	12.3350i	0.930046	+	0.576376i
$459$	20.7299	−	4.70183i	0.967591	−	0.219462i
$460$	−9.54712	−	3.20839i	−0.445137	−	0.149592i
$461$	1.76680	−	0.473414i	0.0822883	−	0.0220491i	−0.217440	−	0.976074i	$-0.569771\pi$
$461$	1.76680	−	0.473414i	0.0822883	−	0.0220491i	0.299728	+	0.954025i	$0.403104\pi$
$462$	−20.9142	−	32.8641i	−0.973017	−	1.52897i
$463$	−9.49600	+	5.48252i	−0.441317	+	0.254794i	−0.704156	−	0.710045i	$-0.748674\pi$
$463$	−9.49600	+	5.48252i	−0.441317	+	0.254794i	0.262839	+	0.964840i	$0.415341\pi$
$464$	−5.58179	−	7.18321i	−0.259128	−	0.333472i
$465$	7.06305	+	1.33972i	0.327541	+	0.0621279i
$466$	−3.85597	+	12.7815i	−0.178624	+	0.592093i
$467$	4.60277	−	4.60277i	0.212991	−	0.212991i	−0.592546	−	0.805537i	$-0.701877\pi$
$467$	4.60277	−	4.60277i	0.212991	−	0.212991i	0.805537	+	0.592546i	$0.201877\pi$
$468$	−3.21047	+	18.1043i	−0.148404	+	0.836872i
$469$	−47.0989	−	47.0989i	−2.17482	−	2.17482i
$470$	1.77993	+	3.31784i	0.0821019	+	0.153040i
$471$	−18.4276	−	15.8728i	−0.849101	−	0.731381i
$472$	−4.94042	−	10.7724i	−0.227401	−	0.495841i
$473$	14.6792	+	25.4251i	0.674951	+	1.16905i
$474$	8.76805	−	2.75986i	0.402730	−	0.126764i
$475$	2.03991	+	7.61304i	0.0935974	+	0.349310i
$476$	−18.5759	−	37.3804i	−0.851424	−	1.71333i
$477$	43.2214	+	4.90957i	1.97897	+	0.224794i
$478$	25.1188	−	5.89726i	1.14891	−	0.269735i
$479$	6.80214	−	11.7817i	0.310798	−	0.538317i	−0.667738	−	0.744397i	$-0.732737\pi$
$479$	6.80214	−	11.7817i	0.310798	−	0.538317i	0.978535	+	0.206079i	$0.0660705\pi$
$480$	−8.05742	−	5.57476i	−0.367769	−	0.254452i
$481$	−7.61425	−	13.1883i	−0.347180	−	0.601333i
$482$	−23.3524	−	24.8571i	−1.06367	−	1.13221i
$483$	19.3263	−	40.0851i	0.879379	−	1.82393i
$484$	2.56228	+	0.160097i	0.116467	+	0.00727713i
$485$	6.51824	−	6.51824i	0.295978	−	0.295978i
$486$	12.4902	+	18.1658i	0.566565	+	0.824017i
$487$	−1.74877			−0.0792442			−0.0396221	−	0.999215i	$-0.512615\pi$
$487$	−1.74877			−0.0792442			−0.0396221	+	0.999215i	$0.512615\pi$
$488$	−17.2328	−	12.2300i	−0.780094	−	0.553626i
$489$	−2.17333	−	6.22007i	−0.0982815	−	0.281281i
$490$	26.8981	+	0.839510i	1.21513	+	0.0379252i
$491$	4.31943	−	16.1203i	0.194933	−	0.727500i	−0.797351	−	0.603516i	$-0.793766\pi$
$491$	4.31943	−	16.1203i	0.194933	−	0.727500i	0.992284	−	0.123985i	$-0.0395673\pi$
$492$	5.80884	−	10.3446i	0.261883	−	0.466373i
$493$	2.40792	+	8.98649i	0.108447	+	0.404731i
$494$	−33.2531	+	7.80700i	−1.49613	+	0.351254i
$495$	5.82383	+	7.31644i	0.261761	+	0.328850i
$496$	−13.2328	−	10.0263i	−0.594172	−	0.450195i
$497$	−6.29962	−	3.63709i	−0.282577	−	0.163146i
$498$	−13.4596	−	7.01497i	−0.603140	−	0.314349i
$499$	−1.72916	+	6.45330i	−0.0774077	+	0.288889i	−0.993768	−	0.111464i	$-0.964446\pi$
$499$	−1.72916	+	6.45330i	−0.0774077	+	0.288889i	0.916361	+	0.400354i	$0.131113\pi$
$500$	0.396159	+	1.96037i	0.0177168	+	0.0876705i
$501$	13.4273	−	1.00012i	0.599888	−	0.0446819i
$502$	20.4301	−	10.9602i	0.911840	−	0.489177i
$503$		−	6.96507i		−	0.310557i	−0.987871	−	0.155279i	$-0.950372\pi$
$503$		−	6.96507i		−	0.310557i	0.987871	−	0.155279i	$-0.0496275\pi$
$504$	28.8792	−	32.2504i	1.28638	−	1.43655i
$505$		−	7.89145i		−	0.351165i
$506$	−10.4946	−	19.5623i	−0.466543	−	0.869650i
$507$	−3.51904	−	5.16651i	−0.156286	−	0.229453i
$508$	−8.70398	+	13.1128i	−0.386177	+	0.581786i
$509$	11.1071	−	41.4523i	0.492315	−	1.83734i	−0.0522642	−	0.998633i	$-0.516644\pi$
$509$	11.1071	−	41.4523i	0.492315	−	1.83734i	0.544579	−	0.838710i	$-0.316690\pi$
$510$	5.37984	+	8.45374i	0.238223	+	0.374338i
$511$	20.0969	+	11.6029i	0.889034	+	0.513284i
$512$	10.9393	+	19.8074i	0.483451	+	0.875371i
$513$	−21.8360	+	34.6471i	−0.964081	+	1.52971i
$514$	4.14431	+	17.6523i	0.182798	+	0.778608i
$515$	0.147873	+	0.551870i	0.00651607	+	0.0243183i
$516$	−22.7932	+	23.3444i	−1.00342	+	1.02768i
$517$	−2.14789	+	8.01604i	−0.0944642	+	0.352545i
$518$	−1.11851	+	35.8374i	−0.0491445	+	1.57460i
$519$	10.9822	+	2.08311i	0.482066	+	0.0914382i
$520$	−8.54529	+	1.45101i	−0.374736	+	0.0636308i
$521$	−22.6008			−0.990160			−0.495080	−	0.868847i	$-0.664861\pi$
$521$	−22.6008			−0.990160			−0.495080	+	0.868847i	$0.664861\pi$
$522$	−7.73297	+	5.77066i	−0.338463	+	0.252575i
$523$	−12.5139	+	12.5139i	−0.547195	+	0.547195i	−0.925629	−	0.378433i	$-0.876463\pi$
$523$	−12.5139	+	12.5139i	−0.547195	+	0.547195i	0.378433	+	0.925629i	$0.376463\pi$
$524$	−11.8062	−	13.3798i	−0.515754	−	0.584501i
$525$	−8.81229	+	0.656373i	−0.384600	+	0.0286465i
$526$	−1.68842	+	1.58622i	−0.0736187	+	0.0691624i
$527$	8.48958	+	14.7044i	0.369812	+	0.640533i
$528$	−4.53027	−	21.1154i	−0.197155	−	0.918932i
$529$	1.18016	−	2.04410i	0.0513114	−	0.0888739i
$530$	4.68681	+	19.9630i	0.203582	+	0.867137i
$531$	−11.5259	+	5.01626i	−0.500181	+	0.217687i
$532$	76.2323	+	25.6185i	3.30509	+	1.11070i
$533$	−2.71638	−	10.1377i	−0.117659	−	0.439111i
$534$	2.15258	−	2.34683i	0.0931511	−	0.101557i
$535$	−3.95742	−	6.85445i	−0.171094	−	0.296344i
$536$	−15.3936	−	33.5652i	−0.664901	−	1.44980i
$537$	−37.0378	+	12.9412i	−1.59830	+	0.558456i
$538$	−2.37621	+	1.27477i	−0.102446	+	0.0549593i
$539$	41.9426	+	41.9426i	1.80660	+	1.80660i
$540$	−6.07848	+	8.42924i	−0.261576	+	0.362737i
$541$	−1.17538	+	1.17538i	−0.0505335	+	0.0505335i	−0.731922	−	0.681388i	$-0.761376\pi$
$541$	−1.17538	+	1.17538i	−0.0505335	+	0.0505335i	0.681388	+	0.731922i	$0.261376\pi$
$542$	19.2339	+	5.80254i	0.826167	+	0.249240i
$543$	2.31889	+	6.63666i	0.0995132	+	0.284806i
$544$	−2.44368	−	23.0117i	−0.104772	−	0.986620i
$545$	16.1295	−	9.31238i	0.690912	−	0.398898i
$546$	−1.65183	−	38.2609i	−0.0706917	−	1.63741i
$547$	−27.8030	+	7.44980i	−1.18877	+	0.318530i	−0.798400	−	0.602127i	$-0.794320\pi$
$547$	−27.8030	+	7.44980i	−1.18877	+	0.318530i	−0.390371	+	0.920658i	$0.627653\pi$
$548$	4.70214	−	2.33669i	0.200865	−	0.0998183i
$549$	−13.3259	+	18.0217i	−0.568735	+	0.769148i
$550$	−2.32215	+	3.74705i	−0.0990168	+	0.159775i
$551$	−15.5232	−	8.96233i	−0.661311	−	0.381808i
$552$	17.7775	−	17.1058i	0.756662	−	0.728070i
$553$	−16.5806	+	9.57284i	−0.705081	+	0.407079i
$554$	0.323486	−	10.3646i	0.0137436	−	0.440349i
$555$	−0.639329	−	8.58346i	−0.0271380	−	0.364347i
$556$	−25.8017	−	29.2409i	−1.09424	−	1.24009i
$557$	12.8462	+	12.8462i	0.544310	+	0.544310i	0.924789	−	0.380479i	$-0.124241\pi$
$557$	12.8462	+	12.8462i	0.544310	+	0.544310i	−0.380479	+	0.924789i	$0.624241\pi$
$558$	−10.9062	+	13.8255i	−0.461697	+	0.585278i
$559$			28.8626i			1.22076i
$560$	18.9013	+	7.69451i	0.798727	+	0.325152i
$561$	−4.11593	+	21.6993i	−0.173775	+	0.916147i
$562$	−6.18032	−	6.57853i	−0.260701	−	0.277499i
$563$	−33.5294	−	8.98417i	−1.41310	−	0.378638i	−0.530066	−	0.847956i	$-0.677833\pi$
$563$	−33.5294	−	8.98417i	−1.41310	−	0.378638i	−0.883029	+	0.469318i	$0.844500\pi$
$564$	−9.22198	+	0.110165i	−0.388315	+	0.00463879i
$565$	−11.6849	+	3.13096i	−0.491587	+	0.131720i
$566$	12.8131	−	20.6753i	0.538573	−	0.869047i
$567$	−33.6028	−	31.2924i	−1.41118	−	1.31416i
$568$	−2.57256	−	3.10561i	−0.107942	−	0.130308i
$569$	13.0156	−	22.5437i	0.545642	−	0.945080i	−0.452924	−	0.891549i	$-0.649619\pi$
$569$	13.0156	−	22.5437i	0.545642	−	0.945080i	0.998566	−	0.0535312i	$-0.0170476\pi$
$570$	−18.8462	−	4.18774i	−0.789381	−	0.175405i
$571$	3.71491	+	0.995406i	0.155464	+	0.0416564i	0.335712	−	0.941965i	$-0.391023\pi$
$571$	3.71491	+	0.995406i	0.155464	+	0.0416564i	−0.180248	+	0.983621i	$0.557690\pi$
$572$	−15.9171	−	10.5654i	−0.665527	−	0.441762i
$573$	7.36180	−	5.01430i	0.307543	−	0.209475i
$574$	−7.13708	+	23.6576i	−0.297896	+	0.987448i
$575$	−5.03590			−0.210012
$576$	21.2312	−	11.1909i	0.884634	−	0.466287i
$577$	6.56392			0.273259			0.136630	−	0.990622i	$-0.456373\pi$
$577$	6.56392			0.273259			0.136630	+	0.990622i	$0.456373\pi$
$578$	0.108352	−	0.359160i	0.00450686	−	0.0149391i
$579$	1.39371	+	18.7116i	0.0579207	+	0.777627i
$580$	−3.78961	−	2.51546i	−0.157355	−	0.104449i
$581$	30.5360	+	8.18210i	1.26685	+	0.339451i
$582$	6.77940	+	21.5381i	0.281015	+	0.892783i
$583$	−22.5987	+	39.1421i	−0.935942	+	1.62110i
$584$	8.20693	+	9.90744i	0.339605	+	0.409973i
$585$	1.36196	+	9.09194i	0.0563101	+	0.375905i
$586$	7.75707	−	12.5169i	0.320442	−	0.517068i
$587$	−33.9484	+	9.09645i	−1.40120	+	0.375451i	−0.878776	−	0.477234i	$-0.841639\pi$
$587$	−33.9484	+	9.09645i	−1.40120	+	0.375451i	−0.522425	+	0.852685i	$0.674973\pi$
$588$	−32.2751	+	57.4770i	−1.33100	+	2.37031i
$589$	−31.5984	−	8.46676i	−1.30199	−	0.348867i
$590$	−4.05731	−	4.31873i	−0.167037	−	0.177799i
$591$	0.0222022	−	0.00775761i	0.000913278	−	0.000319105i
$592$	−7.49470	+	18.4105i	−0.308030	+	0.756667i
$593$		−	1.51972i		−	0.0624074i	−0.999513	−	0.0312037i	$-0.990066\pi$
$593$		−	1.51972i		−	0.0624074i	0.999513	−	0.0312037i	$-0.00993406\pi$
$594$	−22.4858	+	4.36736i	−0.922602	+	0.179195i
$595$	−14.7579	−	14.7579i	−0.605014	−	0.605014i
$596$	4.88807	+	5.53962i	0.200223	+	0.226912i
$597$	−7.73329	−	3.72848i	−0.316503	−	0.152596i
$598$	0.680830	−	21.8140i	0.0278412	−	0.892040i
$599$	5.22143	−	3.01459i	0.213342	−	0.123173i	−0.389522	−	0.921017i	$-0.627360\pi$
$599$	5.22143	−	3.01459i	0.213342	−	0.123173i	0.602863	+	0.797844i	$0.294026\pi$
$600$	−4.70676	−	1.35883i	−0.192153	−	0.0554738i
$601$	−22.6270	−	13.0637i	−0.922975	−	0.532880i	−0.0383919	−	0.999263i	$-0.512224\pi$
$601$	−22.6270	−	13.0637i	−0.922975	−	0.532880i	−0.884583	+	0.466383i	$0.845557\pi$
$602$	35.7972	−	57.7627i	1.45898	−	2.35423i
$603$	−35.9129	+	15.6299i	−1.46249	+	0.636499i
$604$	−7.76446	+	3.85848i	−0.315931	+	0.156999i
$605$	1.23990	−	0.332230i	0.0504090	−	0.0135071i
$606$	17.1416	+	8.93396i	0.696329	+	0.362917i
$607$	19.9269	−	11.5048i	0.808807	−	0.466965i	−0.0377342	−	0.999288i	$-0.512014\pi$
$607$	19.9269	−	11.5048i	0.808807	−	0.466965i	0.846542	+	0.532323i	$0.178681\pi$
$608$	34.6793	+	28.0210i	1.40643	+	1.13640i
$609$	13.1158	−	15.2269i	0.531479	−	0.617024i
$610$	−10.1155	−	3.05167i	−0.409564	−	0.123558i
$611$	−5.76904	+	5.76904i	−0.233390	+	0.233390i
$612$	−24.4535	+	2.11540i	−0.988476	+	0.0855098i
$613$	−12.4071	−	12.4071i	−0.501120	−	0.501120i	0.410666	−	0.911786i	$-0.365296\pi$
$613$	−12.4071	−	12.4071i	−0.501120	−	0.501120i	−0.911786	+	0.410666i	$0.865296\pi$
$614$	16.1160	−	8.64578i	0.650388	−	0.348915i
$615$	1.10547	−	5.82808i	0.0445768	−	0.235011i
$616$	18.7510	+	40.8860i	0.755501	+	1.64734i
$617$	1.20735	+	2.09120i	0.0486063	+	0.0841885i	0.889305	−	0.457315i	$-0.151189\pi$
$617$	1.20735	+	2.09120i	0.0486063	+	0.0841885i	−0.840699	+	0.541503i	$0.817855\pi$
$618$	−1.36616	−	0.303570i	−0.0549552	−	0.0122114i
$619$	2.41761	+	9.02265i	0.0971720	+	0.362651i	0.997340	−	0.0728923i	$-0.0232229\pi$
$619$	2.41761	+	9.02265i	0.0971720	+	0.362651i	−0.900168	+	0.435543i	$0.856556\pi$
$620$	−7.86868	−	2.64433i	−0.316014	−	0.106199i
$621$	−17.7722	−	19.2062i	−0.713174	−	0.770718i
$622$	−0.423047	−	1.80193i	−0.0169627	−	0.0722506i
$623$	−3.31641	+	5.74420i	−0.132869	+	0.230136i
$624$	6.52234	−	20.2045i	0.261103	−	0.808828i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	0.897633	−	0.843298i	0.0358766	−	0.0337049i
$627$	−23.9548	−	35.1695i	−0.956664	−	1.40454i
$628$	18.5812	+	21.0580i	0.741471	+	0.840304i
$629$	14.3747	−	14.3747i	0.573155	−	0.573155i
$630$	8.55070	−	19.8849i	0.340668	−	0.792234i
$631$	44.1374			1.75708			0.878542	−	0.477665i	$-0.158517\pi$
$631$	44.1374			1.75708			0.878542	+	0.477665i	$0.158517\pi$
$632$	−10.4644	+	1.77687i	−0.416251	+	0.0706802i
$633$	7.63947	−	8.86909i	0.303642	−	0.352515i
$634$	0.378415	−	12.1245i	0.0150288	−	0.481526i
$635$	−2.03673	+	7.60118i	−0.0808251	+	0.301643i
$636$	−48.6690	−	12.4197i	−1.92985	−	0.492472i
$637$	15.0928	+	56.3270i	0.597997	+	2.23176i
$638$	−2.29142	−	9.76007i	−0.0907183	−	0.386405i
$639$	−3.34659	+	2.66385i	−0.132389	+	0.105380i
$640$	8.33952	+	7.64542i	0.329649	+	0.302212i
$641$	−6.92966	−	4.00084i	−0.273705	−	0.158024i	0.356865	−	0.934156i	$-0.383846\pi$
$641$	−6.92966	−	4.00084i	−0.273705	−	0.158024i	−0.630570	+	0.776132i	$0.717179\pi$
$642$	19.3693	−	0.836225i	0.764445	−	0.0330032i
$643$	−2.08257	+	7.77225i	−0.0821285	+	0.306508i	−0.994755	−	0.102287i	$-0.967384\pi$
$643$	−2.08257	+	7.77225i	−0.0821285	+	0.306508i	0.912626	+	0.408794i	$0.134051\pi$
$644$	−28.4176	+	42.8120i	−1.11981	+	1.68703i
$645$	−7.08473	+	14.6946i	−0.278961	+	0.578598i
$646$	−21.5557	−	40.1804i	−0.848096	−	1.58088i
$647$		−	25.4858i		−	1.00195i	−0.865462	−	0.500975i	$-0.832975\pi$
$647$		−	25.4858i		−	1.00195i	0.865462	−	0.500975i	$-0.167025\pi$
$648$	−11.4283	−	22.7463i	−0.448945	−	0.893560i
$649$		−	13.0609i		−	0.512684i
$650$	−3.81895	+	2.04876i	−0.149792	+	0.0803591i
$651$	15.9287	−	33.0379i	0.624293	−	1.29486i
$652$	1.50701	+	7.45738i	0.0590192	+	0.292053i
$653$	4.98223	−	18.5939i	0.194970	−	0.727637i	−0.797305	−	0.603577i	$-0.793742\pi$
$653$	4.98223	−	18.5939i	0.194970	−	0.727637i	0.992275	−	0.124060i	$-0.0395916\pi$
$654$	1.96776	+	45.5787i	0.0769454	+	1.78227i
$655$	−7.72664	−	4.46098i	−0.301905	−	0.174305i
$656$	−8.27322	+	10.9191i	−0.323015	+	0.426318i
$657$	10.6762	−	8.49816i	0.416518	−	0.331545i
$658$	18.7007	−	4.39046i	0.729030	−	0.171158i
$659$	8.64207	+	32.2526i	0.336647	+	1.25638i	0.902072	+	0.431585i	$0.142045\pi$
$659$	8.64207	+	32.2526i	0.336647	+	1.25638i	−0.565425	+	0.824800i	$0.691288\pi$
$660$	−5.51031	−	9.28617i	−0.214488	−	0.361464i
$661$	−4.78144	+	17.8446i	−0.185976	+	0.694073i	0.808443	+	0.588574i	$0.200311\pi$
$661$	−4.78144	+	17.8446i	−0.185976	+	0.694073i	−0.994419	+	0.105499i	$0.966356\pi$
$662$	−8.03876	−	0.250895i	−0.312435	−	0.00975132i
$663$	−14.1707	+	16.4516i	−0.550345	+	0.638926i
$664$	14.2925	+	10.1433i	0.554657	+	0.393635i
$665$	40.2109			1.55931
$666$	19.3685	+	8.32866i	0.750516	+	0.322729i
$667$	8.09840	−	8.09840i	0.313571	−	0.313571i
$668$	−15.5172	−	0.969551i	−0.600379	−	0.0375130i
$669$	1.13201	+	1.66197i	0.0437661	+	0.0642556i
$670$	−12.6419	−	13.4565i	−0.488401	−	0.519870i
$671$	−11.6442	−	20.1683i	−0.449518	−	0.778588i
$672$	−38.1121	+	32.3460i	−1.47021	+	1.24777i
$673$	11.1345	−	19.2855i	0.429202	−	0.743400i	−0.567601	−	0.823304i	$-0.692128\pi$
$673$	11.1345	−	19.2855i	0.429202	−	0.743400i	0.996803	+	0.0799044i	$0.0254615\pi$
$674$	11.7532	−	2.75935i	0.452715	−	0.106286i
$675$	−1.53834	+	4.96321i	−0.0592109	+	0.191034i
$676$	3.21224	+	6.46402i	0.123548	+	0.248616i
$677$	12.6861	+	47.3453i	0.487568	+	1.81963i	0.568209	+	0.822884i	$0.307636\pi$
$677$	12.6861	+	47.3453i	0.487568	+	1.81963i	−0.0806415	+	0.996743i	$0.525697\pi$
$678$	6.42757	−	28.9262i	0.246849	−	1.11090i
$679$	−23.5150	−	40.7292i	−0.902424	−	1.56304i
$680$	−4.82340	−	10.5173i	−0.184969	−	0.403318i
$681$	0.171689	−	0.905151i	0.00657913	−	0.0346854i
$682$	−8.64961	−	16.1231i	−0.331211	−	0.617386i
$683$	27.3057	+	27.3057i	1.04482	+	1.04482i	0.998947	+	0.0458761i	$0.0146080\pi$
$683$	27.3057	+	27.3057i	1.04482	+	1.04482i	0.0458761	+	0.998947i	$0.485392\pi$
$684$	30.4324	−	36.1963i	1.16361	−	1.38400i
$685$	1.85642	−	1.85642i	0.0709300	−	0.0709300i
$686$	25.0677	−	83.0929i	0.957089	−	3.17250i
$687$	−18.7167	+	21.7292i	−0.714085	+	0.829022i
$688$	29.7483	−	23.1162i	1.13414	−	0.881299i
$689$	−38.4810	+	22.2170i	−1.46601	+	0.846400i
$690$	5.70118	−	10.9389i	0.217040	−	0.416435i
$691$	−1.60505	+	0.430073i	−0.0610591	+	0.0163607i	−0.289219	−	0.957263i	$-0.593396\pi$
$691$	−1.60505	+	0.430073i	−0.0610591	+	0.0163607i	0.228160	+	0.973624i	$0.426729\pi$
$692$	−12.2349	−	4.11163i	−0.465101	−	0.156301i
$693$	43.7458	−	19.0389i	1.66177	−	0.723228i
$694$	25.6803	+	15.9148i	0.974813	+	0.604119i
$695$	−16.8862	−	9.74923i	−0.640528	−	0.369809i
$696$	9.75427	−	5.38393i	0.369735	−	0.204077i
$697$	12.1333	−	7.00519i	0.459583	−	0.265340i
$698$	44.5755	+	1.39123i	1.68721	+	0.0526590i
$699$	−14.7285	−	7.10109i	−0.557083	−	0.268588i
$700$	10.1839	+	0.636313i	0.384915	+	0.0240504i
$701$	10.8805	+	10.8805i	0.410953	+	0.410953i	0.882070	−	0.471118i	$-0.156149\pi$
$701$	10.8805	+	10.8805i	0.410953	+	0.410953i	−0.471118	+	0.882070i	$0.656149\pi$
$702$	−21.2911	−	7.33463i	−0.803582	−	0.276828i
$703$			39.1667i			1.47720i
$704$	1.85846	+	24.8675i	0.0700435	+	0.937230i
$705$	−4.35324	+	1.52105i	−0.163952	+	0.0572860i
$706$	−26.7848	+	25.1634i	−1.00806	+	0.947038i
$707$	−38.8893	−	10.4204i	−1.46258	−	0.391898i
$708$	13.9743	−	3.92391i	0.525188	−	0.147469i
$709$	8.45920	−	2.26664i	0.317692	−	0.0851253i	−0.0964494	−	0.995338i	$-0.530749\pi$
$709$	8.45920	−	2.26664i	0.317692	−	0.0851253i	0.414141	+	0.910213i	$0.364082\pi$
$710$	−1.71392	−	1.06217i	−0.0643223	−	0.0398624i
$711$	1.66783	+	11.1338i	0.0625485	+	0.417550i
$712$	−2.83179	+	2.34575i	−0.106126	+	0.0879106i
$713$	10.4509	−	18.1015i	0.391390	−	0.677907i
$714$	48.7642	−	15.3492i	1.82495	−	0.574428i
$715$	−9.22677	−	2.47231i	−0.345062	−	0.0924590i
$716$	44.4054	−	8.97360i	1.65951	−	0.335359i
$717$	2.34723	+	31.5133i	0.0876589	+	1.17689i
$718$	−19.2759	−	5.81521i	−0.719371	−	0.217022i
$719$	−29.6980			−1.10755			−0.553774	−	0.832667i	$-0.686813\pi$
$719$	−29.6980			−1.10755			−0.553774	+	0.832667i	$0.686813\pi$
$720$	8.28016	−	8.68556i	0.308583	−	0.323692i
$721$	2.91489			0.108556
$722$	58.3814	+	17.6127i	2.17273	+	0.655475i
$723$	34.5235	−	23.5148i	1.28394	−	0.874524i
$724$	−1.60795	−	7.95683i	−0.0597588	−	0.295713i
$725$	−2.19675	−	0.588617i	−0.0815853	−	0.0218607i
$726$	−0.682037	+	3.06939i	−0.0253128	+	0.113916i
$727$	13.1298	−	22.7414i	0.486956	−	0.843433i	−0.512931	−	0.858430i	$-0.671440\pi$
$727$	13.1298	−	22.7414i	0.486956	−	0.843433i	0.999888	+	0.0149967i	$0.00477379\pi$
$728$	−4.13312	+	44.0274i	−0.153184	+	1.63177i
$729$	−24.3579	+	11.6487i	−0.902146	+	0.431432i
$730$	5.46771	+	3.38850i	0.202369	+	0.125414i
$731$	−37.2164	+	9.97210i	−1.37650	+	0.368831i
$732$	18.0806	−	18.5178i	0.668277	−	0.684436i
$733$	9.76313	+	2.61602i	0.360610	+	0.0966250i	0.434575	−	0.900636i	$-0.356899\pi$
$733$	9.76313	+	2.61602i	0.360610	+	0.0966250i	−0.0739652	+	0.997261i	$0.523565\pi$
$734$	6.76241	−	6.35306i	0.249605	−	0.234496i
$735$	−6.14221	+	32.3820i	−0.226559	+	1.19443i
$736$	−23.0287	+	16.7693i	−0.848850	+	0.618123i
$737$		−	40.6956i		−	1.49904i
$738$	11.4081	+	8.99928i	0.419938	+	0.331268i
$739$	8.83416	+	8.83416i	0.324970	+	0.324970i	0.850670	−	0.525700i	$-0.176197\pi$
$739$	8.83416	+	8.83416i	0.324970	+	0.324970i	−0.525700	+	0.850670i	$0.676197\pi$
$740$	−0.619789	+	9.91943i	−0.0227839	+	0.364646i
$741$	−3.10734	−	41.7184i	−0.114151	−	1.53256i
$742$	104.567	+	3.26361i	3.83878	+	0.119811i
$743$	−14.5046	+	8.37424i	−0.532123	+	0.307221i	−0.741880	−	0.670532i	$-0.766066\pi$
$743$	−14.5046	+	8.37424i	−0.532123	+	0.307221i	0.209758	+	0.977753i	$0.432732\pi$
$744$	14.6521	−	14.0985i	0.537174	−	0.516875i
$745$	3.19904	+	1.84697i	0.117204	+	0.0676677i
$746$	−10.3549	−	6.41725i	−0.379121	−	0.234952i
$747$	11.0522	−	14.9468i	0.404378	−	0.546874i
$748$	8.12401	−	24.1744i	0.297043	−	0.883905i
$749$	−39.0046	+	10.4512i	−1.42520	+	0.381880i
$750$	−2.44721	+	0.105653i	−0.0893595	+	0.00385790i
$751$	43.0311	−	24.8440i	1.57023	−	0.906570i	0.574085	−	0.818795i	$-0.305358\pi$
$751$	43.0311	−	24.8440i	1.57023	−	0.906570i	0.996140	−	0.0877749i	$-0.0279756\pi$
$752$	10.5666	+	1.32562i	0.385323	+	0.0483404i
$753$	9.36611	+	26.8058i	0.341320	+	0.976856i
$754$	2.84670	−	9.43607i	0.103671	−	0.343641i
$755$	−3.06543	+	3.06543i	−0.111562	+	0.111562i
$756$	33.5131	+	41.0855i	1.21886	+	1.49426i
$757$	−8.75744	−	8.75744i	−0.318295	−	0.318295i	0.529817	−	0.848112i	$-0.322261\pi$
$757$	−8.75744	−	8.75744i	−0.318295	−	0.318295i	−0.848112	+	0.529817i	$0.822261\pi$
$758$	−12.5528	−	23.3988i	−0.455939	−	0.849883i
$759$	25.6671	−	8.96825i	0.931657	−	0.325527i
$760$	20.8994	+	7.75705i	0.758101	+	0.281378i
$761$	−9.78520	−	16.9485i	−0.354713	−	0.614381i	0.632356	−	0.774678i	$-0.282088\pi$
$761$	−9.78520	−	16.9485i	−0.354713	−	0.614381i	−0.987069	+	0.160297i	$0.948755\pi$
$762$	−14.2053	−	13.0295i	−0.514603	−	0.472008i
$763$	−24.5933	−	91.7834i	−0.890337	−	3.32278i
$764$	−9.21062	+	4.57714i	−0.333228	+	0.165595i
$765$	−11.2529	+	4.89745i	−0.406849	+	0.177068i
$766$	−52.9050	+	12.4208i	−1.91154	+	0.448781i
$767$	6.42013	−	11.1200i	0.231818	−	0.401520i
$768$	−26.0484	+	9.45945i	−0.939940	+	0.341339i
$769$	−12.2588	−	21.2328i	−0.442062	−	0.765674i	0.555780	−	0.831329i	$-0.312420\pi$
$769$	−12.2588	−	21.2328i	−0.442062	−	0.765674i	−0.997842	+	0.0656554i	$0.979086\pi$
$770$	15.3992	+	16.3915i	0.554950	+	0.590707i
$771$	−22.1460	+	1.64952i	−0.797569	+	0.0594060i
$772$	1.35111	−	21.6240i	0.0486277	−	0.778264i
$773$	9.66315	−	9.66315i	0.347559	−	0.347559i	−0.511640	−	0.859200i	$-0.670962\pi$
$773$	9.66315	−	9.66315i	0.347559	−	0.347559i	0.859200	+	0.511640i	$0.170962\pi$
$774$	−23.8984	−	32.0251i	−0.859011	−	1.15112i
$775$	−4.15056			−0.149093
$776$	−4.36476	−	25.7050i	−0.156686	−	0.922757i
$777$	−43.1438	−	8.18350i	−1.54777	−	0.293581i
$778$	39.1621	+	1.22228i	1.40403	+	0.0438207i
$779$	−6.98636	+	26.0734i	−0.250312	+	0.934178i
$780$	−0.126804	−	10.6148i	−0.00454032	−	0.380072i
$781$	−1.15028	−	4.29289i	−0.0411601	−	0.153612i
$782$	28.3629	−	6.65891i	1.01426	−	0.238122i
$783$	−5.50765	−	10.4554i	−0.196827	−	0.373644i
$784$	45.9677	−	60.6687i	1.64170	−	2.16674i
$785$	12.1606	+	7.02095i	0.434032	+	0.250588i
$786$	18.4374	−	11.7333i	0.657640	−	0.418513i
$787$	−2.20965	+	8.24651i	−0.0787654	+	0.293956i	−0.994061	−	0.108827i	$-0.965291\pi$
$787$	−2.20965	+	8.24651i	−0.0787654	+	0.293956i	0.915295	+	0.402783i	$0.131957\pi$
$788$	−0.0266187	+	0.00537921i	−0.000948253	+	0.000191626i
$789$	−1.59725	−	2.34501i	−0.0568635	−	0.0834846i
$790$	−4.67661	+	2.50887i	−0.166386	+	0.0892617i
$791$			61.7179i			2.19444i
$792$	26.4094	−	1.45640i	0.938418	−	0.0517511i
$793$		−	22.8950i		−	0.813025i
$794$	4.07527	+	7.59641i	0.144626	+	0.269586i
$795$	−25.0450	+	1.86545i	−0.888254	+	0.0661605i
$796$	8.25937	+	5.48239i	0.292746	+	0.194318i
$797$	10.1965	−	38.0540i	0.361180	−	1.34794i	−0.511345	−	0.859375i	$-0.670853\pi$
$797$	10.1965	−	38.0540i	0.361180	−	1.34794i	0.872526	−	0.488568i	$-0.162481\pi$
$798$	−45.5231	+	87.3450i	−1.61150	+	3.09198i
$799$	−9.43201	−	5.44558i	−0.333681	−	0.192651i
$800$	5.17027	+	2.29528i	0.182797	+	0.0811506i
$801$	2.42899	+	3.05153i	0.0858241	+	0.107820i
$802$	−8.32848	−	35.4743i	−0.294089	−	1.25264i
$803$	3.66958	+	13.6951i	0.129497	+	0.483288i
$804$	43.5419	−	12.2263i	1.53560	−	0.431188i
$805$	−6.64972	+	24.8171i	−0.234372	+	0.874688i
$806$	0.561136	−	17.9790i	0.0197652	−	0.633282i
$807$	−1.08936	−	3.11776i	−0.0383474	−	0.109750i
$808$	−18.2023	−	12.9180i	−0.640355	−	0.454454i
$809$	31.4385			1.10532			0.552659	−	0.833408i	$-0.313613\pi$
$809$	31.4385			1.10532			0.552659	+	0.833408i	$0.313613\pi$
$810$	−9.03939	−	8.96044i	−0.317612	−	0.314838i
$811$	−22.1011	+	22.1011i	−0.776074	+	0.776074i	−0.979161	−	0.203087i	$-0.934903\pi$
$811$	−22.1011	+	22.1011i	−0.776074	+	0.776074i	0.203087	+	0.979161i	$0.434903\pi$
$812$	−17.4003	+	15.3538i	−0.610632	+	0.538812i
$813$	−10.6859	+	22.1637i	−0.374770	+	0.777316i
$814$	−15.9658	+	14.9994i	−0.559601	+	0.525727i
$815$	1.90203	+	3.29441i	0.0666252	+	0.115398i
$816$	28.3059	+	1.42941i	0.990905	+	0.0500393i
$817$	37.1163	−	64.2874i	1.29854	−	2.24913i
$818$	−7.77663	−	33.1237i	−0.271903	−	1.15814i
$819$	46.6038	+	5.29377i	1.62847	+	0.184979i
$820$	−2.18197	+	6.49285i	−0.0761978	+	0.226740i
$821$	5.80485	+	21.6640i	0.202591	+	0.756079i	0.990170	+	0.139866i	$0.0446672\pi$
$821$	5.80485	+	21.6640i	0.202591	+	0.756079i	−0.787580	+	0.616213i	$0.788666\pi$
$822$	1.93079	+	6.13412i	0.0673442	+	0.213952i
$823$	14.1891	+	24.5763i	0.494602	+	0.856675i	0.999981	−	0.00622243i	$-0.00198067\pi$
$823$	14.1891	+	24.5763i	0.494602	+	0.856675i	−0.505379	+	0.862897i	$0.668647\pi$
$824$	1.51500	+	0.562309i	0.0527775	+	0.0195890i
$825$	−4.09068	−	3.52355i	−0.142419	−	0.122674i
$826$	−26.6404	+	14.2918i	−0.926937	+	0.497276i
$827$	−40.5748	−	40.5748i	−1.41092	−	1.41092i	−0.753664	−	0.657260i	$-0.771715\pi$
$827$	−40.5748	−	40.5748i	−1.41092	−	1.41092i	−0.657260	−	0.753664i	$-0.728285\pi$
$828$	17.3067	+	24.7679i	0.601450	+	0.860744i
$829$	0.684902	−	0.684902i	0.0237876	−	0.0237876i	−0.695113	−	0.718901i	$-0.744646\pi$
$829$	0.684902	−	0.684902i	0.0237876	−	0.0237876i	0.718901	+	0.695113i	$0.244646\pi$
$830$	8.38955	+	2.53098i	0.291206	+	0.0878517i
$831$	12.4777	+	2.36676i	0.432846	+	0.0821020i
$832$	−10.6415	+	22.0857i	−0.368926	+	0.765684i
$833$	−67.4153	+	38.9223i	−2.33580	+	1.34858i
$834$	40.2939	−	25.6425i	1.39527	−	0.887926i
$835$	−7.50885	+	2.01199i	−0.259855	+	0.0696278i
$836$	21.8664	+	44.0019i	0.756264	+	1.52184i
$837$	−14.6477	−	15.8296i	−0.506300	−	0.547152i
$838$	1.88988	−	3.04954i	0.0652850	−	0.105344i
$839$	−36.9907	−	21.3566i	−1.27706	−	0.737311i	−0.300753	−	0.953702i	$-0.597238\pi$
$839$	−36.9907	−	21.3566i	−1.27706	−	0.737311i	−0.976307	+	0.216391i	$0.930571\pi$
$840$	−12.9114	+	21.4008i	−0.445487	+	0.738397i
$841$	−20.6355	+	11.9139i	−0.711569	+	0.410824i
$842$	0.436369	−	13.9814i	0.0150383	−	0.481831i
$843$	9.13679	−	6.22329i	0.314688	−	0.214342i
$844$	−10.1350	+	8.94300i	−0.348863	+	0.307831i
$845$	2.55201	+	2.55201i	0.0877918	+	0.0877918i
$846$	1.62435	−	11.1780i	0.0558463	−	0.384307i
$847$		−	6.54895i		−	0.225025i
$848$	53.7185	+	21.8682i	1.84470	+	0.750956i
$849$	22.5714	+	19.4421i	0.774649	+	0.667250i
$850$	−3.96120	−	4.21643i	−0.135868	−	0.144623i
$851$	−24.1726	−	6.47704i	−0.828628	−	0.222030i
$852$	4.24755	−	2.52045i	0.145519	−	0.0863491i
$853$	17.6127	−	4.71930i	0.603046	−	0.161586i	0.0556372	−	0.998451i	$-0.482281\pi$
$853$	17.6127	−	4.71930i	0.603046	−	0.161586i	0.547409	+	0.836865i	$0.315614\pi$
$854$	−28.3958	+	45.8198i	−0.971686	+	1.56792i
$855$	8.65836	−	22.0025i	0.296110	−	0.752469i
$856$	−22.2886	−	2.09236i	−0.761807	−	0.0715155i
$857$	−22.9500	+	39.7506i	−0.783957	+	1.35785i	0.145663	+	0.989334i	$0.453469\pi$
$857$	−22.9500	+	39.7506i	−0.783957	+	1.35785i	−0.929620	+	0.368520i	$0.879865\pi$
$858$	15.8160	−	17.2432i	0.539948	−	0.588674i
$859$	−37.6195	−	10.0801i	−1.28356	−	0.343929i	−0.448349	−	0.893859i	$-0.647988\pi$
$859$	−37.6195	−	10.0801i	−1.28356	−	0.343929i	−0.835211	+	0.549930i	$0.814654\pi$
$860$	10.4175	−	15.6942i	0.355232	−	0.535168i
$861$	−27.2612	−	13.1435i	−0.929061	−	0.447931i
$862$	−9.59140	+	31.7930i	−0.326684	+	1.08287i
$863$	26.7465			0.910462			0.455231	−	0.890373i	$-0.349557\pi$
$863$	26.7465			0.910462			0.455231	+	0.890373i	$0.349557\pi$
$864$	9.49251	+	27.8189i	0.322942	+	0.946419i
$865$	−6.45364			−0.219430
$866$	−4.60282	+	15.2572i	−0.156410	+	0.518459i
$867$	0.413869	+	0.199540i	0.0140557	+	0.00677674i
$868$	−23.4217	+	35.2854i	−0.794983	+	1.19766i
$869$	−11.2989	−	3.02754i	−0.383289	−	0.102702i
$870$	3.76554	−	4.10534i	0.127664	−	0.139184i
$871$	20.0041	−	34.6482i	0.677814	−	1.17401i
$872$	4.92363	−	52.4482i	0.166735	−	1.77612i
$873$	−27.3494	+	4.09691i	−0.925637	+	0.138659i
$874$	−29.5685	+	47.7121i	−1.00017	+	1.61389i
$875$	4.92803	−	1.32046i	0.166598	−	0.0446398i
$876$	−13.5504	+	8.04067i	−0.457827	+	0.271669i
$877$	−22.2247	−	5.95509i	−0.750474	−	0.201089i	−0.136746	−	0.990606i	$-0.543664\pi$
$877$	−22.2247	−	5.95509i	−0.750474	−	0.201089i	−0.613728	+	0.789517i	$0.710331\pi$
$878$	−16.6413	−	17.7136i	−0.561617	−	0.597804i
$879$	13.6648	+	11.7703i	0.460902	+	0.397002i
$880$	4.84161	+	11.4900i	0.163211	+	0.387329i
$881$			22.6287i			0.762380i	0.924497	+	0.381190i	$0.124486\pi$
$881$			22.6287i			0.762380i	−0.924497	+	0.381190i	$0.875514\pi$
$882$	−63.3857	−	50.0019i	−2.13431	−	1.68365i
$883$	19.9362	+	19.9362i	0.670906	+	0.670906i	0.957925	−	0.287019i	$-0.0926644\pi$
$883$	19.9362	+	19.9362i	0.670906	+	0.670906i	−0.287019	+	0.957925i	$0.592664\pi$
$884$	18.7998	−	16.5887i	0.632307	−	0.557938i
$885$	5.99819	−	4.08552i	0.201627	−	0.137333i
$886$	−1.61867	+	51.8627i	−0.0543803	+	1.74236i
$887$	−25.1365	+	14.5126i	−0.844002	+	0.487285i	−0.858623	−	0.512608i	$-0.828679\pi$
$887$	−25.1365	+	14.5126i	−0.844002	+	0.487285i	0.0146205	+	0.999893i	$0.495346\pi$
$888$	−20.8451	−	12.5761i	−0.699514	−	0.422028i
$889$	34.7694	+	20.0741i	1.16613	+	0.673265i
$890$	−0.968517	+	1.56281i	−0.0324648	+	0.0523855i
$891$	−0.998140	−	28.0362i	−0.0334390	−	0.939248i
$892$	−1.03332	−	2.07936i	−0.0345981	−	0.0696221i
$893$	20.2685	−	5.43094i	0.678261	−	0.181739i
$894$	−7.63359	+	4.85791i	−0.255305	+	0.162473i
$895$	19.6168	−	11.3258i	0.655717	−	0.378578i
$896$	48.6889	−	31.0019i	1.62658	−	1.03570i
$897$	26.2613	+	4.98124i	0.876840	+	0.166319i
$898$	14.2678	+	4.30436i	0.476124	+	0.143638i
$899$	6.67466	−	6.67466i	0.222612	−	0.222612i
$900$	2.54101	−	5.43537i	0.0847003	−	0.181179i
$901$	−41.9426	−	41.9426i	−1.39731	−	1.39731i
$902$	−13.3040	+	7.13724i	−0.442975	+	0.237644i
$903$	63.0601	+	54.3174i	2.09851	+	1.80757i
$904$	−11.9059	+	32.0775i	−0.395986	+	1.06688i
$905$	−2.02942	−	3.51506i	−0.0674602	−	0.116844i
$906$	−3.18824	−	10.1290i	−0.105922	−	0.336514i
$907$	5.57903	+	20.8212i	0.185249	+	0.691357i	0.994577	+	0.104001i	$0.0331645\pi$
$907$	5.57903	+	20.8212i	0.185249	+	0.691357i	−0.809329	+	0.587356i	$0.800169\pi$
$908$	−0.338879	+	1.00840i	−0.0112461	+	0.0334648i
$909$	−14.0756	+	19.0356i	−0.466857	+	0.631370i
$910$	5.05359	+	21.5252i	0.167525	+	0.713555i
$911$	14.7357	−	25.5229i	0.488215	−	0.845613i	−0.511693	−	0.859168i	$-0.670982\pi$
$911$	14.7357	−	25.5229i	0.488215	−	0.845613i	0.999908	+	0.0135555i	$0.00431498\pi$
$912$	−40.5100	+	36.6153i	−1.34142	+	1.21245i
$913$	9.65741	+	16.7271i	0.319613	+	0.553587i
$914$	29.8512	−	28.0442i	0.987388	−	0.927620i
$915$	5.61991	−	11.6563i	0.185788	−	0.385347i
$916$	24.8308	−	21.9103i	0.820433	−	0.723937i
$917$	−32.1866	+	32.1866i	−1.06289	+	1.06289i
$918$	2.10138	−	29.9877i	0.0693557	−	0.989740i
$919$	−11.3807			−0.375415			−0.187707	−	0.982225i	$-0.560106\pi$
$919$	−11.3807			−0.375415			−0.187707	+	0.982225i	$0.560106\pi$
$920$	−8.24360	+	11.6158i	−0.271783	+	0.382960i
$921$	7.38831	+	21.1453i	0.243453	+	0.696762i
$922$	0.0806960	−	2.58552i	0.00265758	−	0.0851496i
$923$	1.13085	−	4.22038i	0.0372223	−	0.138916i
$924$	−53.0387	+	14.8929i	−1.74484	+	0.489942i
$925$	1.28617	+	4.80006i	0.0422891	+	0.157825i
$926$	3.54427	+	15.0964i	0.116472	+	0.496100i
$927$	0.627645	−	1.59496i	0.0206146	−	0.0523854i
$928$	−12.0056	+	4.62336i	−0.394103	+	0.151769i
$929$	2.35774	+	1.36124i	0.0773549	+	0.0446609i	0.538179	−	0.842831i	$-0.319113\pi$
$929$	2.35774	+	1.36124i	0.0773549	+	0.0446609i	−0.460824	+	0.887492i	$0.652446\pi$
$930$	4.69888	−	9.01574i	0.154082	−	0.295638i
$931$	38.8176	−	144.869i	1.27220	−	4.74790i
$932$	15.7304	+	10.4415i	0.515268	+	0.342023i
$933$	2.26064	−	0.168381i	0.0740101	−	0.00551256i
$934$	−4.35183	−	8.11193i	−0.142396	−	0.265430i
$935$		−	12.7515i		−	0.417019i
$936$	23.2008	+	11.7417i	0.758343	+	0.383789i
$937$		−	28.4748i		−	0.930231i	−0.885250	−	0.465115i	$-0.846013\pi$
$937$		−	28.4748i		−	0.930231i	0.885250	−	0.465115i	$-0.153987\pi$
$938$	−83.0072	+	44.5311i	−2.71028	+	1.45399i
$939$	0.849161	+	1.24670i	0.0277113	+	0.0406846i
$940$	5.21919	−	1.05471i	0.170231	−	0.0344009i
$941$	4.30295	−	16.0588i	0.140272	−	0.523503i	−0.859648	−	0.510886i	$-0.829317\pi$
$941$	4.30295	−	16.0588i	0.140272	−	0.523503i	0.999920	−	0.0126164i	$-0.00401604\pi$
$942$	−29.0178	+	18.4665i	−0.945453	+	0.601672i
$943$	−14.9365	−	8.62358i	−0.486399	−	0.280822i
$944$	−16.6032	+	2.28893i	−0.540388	+	0.0744982i
$945$	22.4276	+	14.1347i	0.729568	+	0.459803i
$946$	40.4201	−	9.48962i	1.31417	−	0.308534i
$947$	11.1502	+	41.6133i	0.362334	+	1.35225i	0.870999	+	0.491285i	$0.163473\pi$
$947$	11.1502	+	41.6133i	0.362334	+	1.35225i	−0.508665	+	0.860965i	$0.669861\pi$
$948$	−0.155282	−	12.9987i	−0.00504333	−	0.422179i
$949$	−3.60760	+	13.4638i	−0.117108	+	0.437052i
$950$	11.1408	+	0.347713i	0.361456	+	0.0112813i
$951$	14.5964	+	2.76864i	0.473321	+	0.0897794i
$952$	−58.1985	+	9.88222i	−1.88622	+	0.320284i
$953$	−27.2925			−0.884092			−0.442046	−	0.896992i	$-0.645747\pi$
$953$	−27.2925			−0.884092			−0.442046	+	0.896992i	$0.645747\pi$
$954$	24.3015	−	56.5139i	0.786791	−	1.82971i
$955$	−3.63637	+	3.63637i	−0.117670	+	0.117670i
$956$	2.27549	−	36.4182i	0.0735947	−	1.17785i
$957$	12.2447	−	0.912032i	0.395815	−	0.0294818i
$958$	−13.1733	−	14.0221i	−0.425609	−	0.453032i
$959$	−6.69715	−	11.5998i	−0.216262	−	0.374577i
$960$	−10.8391	+	8.63221i	−0.349829	+	0.278603i
$961$	−6.88641	+	11.9276i	−0.222142	+	0.384762i
$962$	−20.9663	+	4.92236i	−0.675980	+	0.158703i
$963$	−2.67993	+	23.5928i	−0.0863596	+	0.760268i
$964$	−43.1936	+	21.4647i	−1.39117	+	0.691331i
$965$	−2.80380	−	10.4639i	−0.0902577	−	0.336846i
$966$	−46.3788	−	42.5399i	−1.49221	−	1.36870i
$967$	−3.71347	−	6.43192i	−0.119417	−	0.206837i	0.800120	−	0.599840i	$-0.204769\pi$
$967$	−3.71347	−	6.43192i	−0.119417	−	0.206837i	−0.919537	+	0.393004i	$0.871436\pi$
$968$	1.26335	−	3.40378i	0.0406057	−	0.109402i
$969$	52.7195	−	18.4205i	1.69359	−	0.591753i
$970$	−6.16288	−	11.4878i	−0.197878	−	0.368850i
$971$	−35.7453	−	35.7453i	−1.14712	−	1.14712i	−0.987116	−	0.160004i	$-0.948849\pi$
$971$	−35.7453	−	35.7453i	−1.14712	−	1.14712i	−0.160004	−	0.987116i	$-0.551151\pi$
$972$	29.6972	−	9.49094i	0.952537	−	0.304422i
$973$	−70.3420	+	70.3420i	−2.25506	+	2.25506i
$974$	−0.714303	+	2.36773i	−0.0228878	+	0.0758669i
$975$	−1.75078	−	5.01074i	−0.0560700	−	0.160472i
$976$	−23.5976	+	18.3368i	−0.755342	+	0.586946i
$977$	−26.2812	+	15.1735i	−0.840811	+	0.485443i	−0.857540	−	0.514418i	$-0.828008\pi$
$977$	−26.2812	+	15.1735i	−0.840811	+	0.485443i	0.0167287	+	0.999860i	$0.494675\pi$
$978$	−9.30934	+	0.401910i	−0.297680	+	0.0128517i
$979$	−3.91439	+	1.04886i	−0.125105	+	0.0335217i
$980$	12.1235	−	36.0756i	0.387271	−	1.15239i
$981$	−55.5172	−	6.30627i	−1.77253	−	0.201344i
$982$	−20.0617	−	12.4328i	−0.640194	−	0.396746i
$983$	20.7117	+	11.9579i	0.660601	+	0.381398i	0.792506	−	0.609864i	$-0.208776\pi$
$983$	20.7117	+	11.9579i	0.660601	+	0.381398i	−0.131905	+	0.991262i	$0.542109\pi$
$984$	−11.6334	−	12.0902i	−0.370858	−	0.385422i
$985$	−0.0117593	+	0.00678921i	−0.000374681	+	0.000216322i
$986$	13.1507	+	0.410444i	0.418805	+	0.0130712i
$987$	1.74749	+	23.4614i	0.0556233	+	0.746784i
$988$	−3.01237	+	48.2117i	−0.0958364	+	1.53382i
$989$	33.5385	+	33.5385i	1.06646	+	1.06646i
$990$	12.2848	−	4.89664i	0.390438	−	0.155625i
$991$			14.1102i			0.448224i	0.974563	+	0.224112i	$0.0719482\pi$
$991$			14.1102i			0.448224i	−0.974563	+	0.224112i	$0.928052\pi$
$992$	−18.9801	+	13.8211i	−0.602620	+	0.438821i
$993$	1.83566	−	9.67767i	0.0582528	−	0.307111i
$994$	−7.49755	+	7.04371i	−0.237808	+	0.223413i
$995$	4.78776	+	1.28288i	0.151782	+	0.0406700i
$996$	−14.9956	+	15.3582i	−0.475154	+	0.486643i
$997$	42.4960	−	11.3868i	1.34586	−	0.360623i	0.487256	−	0.873259i	$-0.337998\pi$
$997$	42.4960	−	11.3868i	1.34586	−	0.360623i	0.858606	+	0.512637i	$0.171331\pi$
$998$	8.03110	+	4.97710i	0.254220	+	0.157547i
$999$	−13.7677	+	21.8452i	−0.435590	+	0.691150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.56	✓	384
9.5	odd	6	inner	720.2.cf.a.491.26	yes	384
16.3	odd	4	inner	720.2.cf.a.371.26	yes	384
144.131	even	12	inner	720.2.cf.a.131.56	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.56	✓	384	1.1	even	1	trivial
720.2.cf.a.131.56	yes	384	144.131	even	12	inner
720.2.cf.a.371.26	yes	384	16.3	odd	4	inner
720.2.cf.a.491.26	yes	384	9.5	odd	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.408461 - 1.35394i) q^{2} +(1.56018 + 0.752216i) q^{3} +(-1.66632 - 1.10607i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(1.65573 - 1.80515i) q^{6} +(-2.55094 + 4.41835i) q^{7} +(-2.17818 + 1.80431i) q^{8} +(1.86834 + 2.34719i) q^{9} +O(q^{10})\)	\(q+(0.408461 - 1.35394i) q^{2} +(1.56018 + 0.752216i) q^{3} +(-1.66632 - 1.10607i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(1.65573 - 1.80515i) q^{6} +(-2.55094 + 4.41835i) q^{7} +(-2.17818 + 1.80431i) q^{8} +(1.86834 + 2.34719i) q^{9} +(-0.744969 + 1.20209i) q^{10} +(-3.01090 + 0.806767i) q^{11} +(-1.76776 - 2.97910i) q^{12} +(-2.96004 - 0.793141i) q^{13} +(4.94024 + 5.25855i) q^{14} +(-1.31233 - 1.13039i) q^{15} +(1.55324 + 3.68612i) q^{16} -4.09081i q^{17} +(3.94110 - 1.57089i) q^{18} +(5.57313 + 5.57313i) q^{19} +(1.32327 + 1.49965i) q^{20} +(-7.30348 + 4.97458i) q^{21} +(-0.137518 + 4.40611i) q^{22} +(-4.36122 + 2.51795i) q^{23} +(-4.75559 + 1.17660i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.28293 + 3.68376i) q^{26} +(1.14936 + 5.06744i) q^{27} +(9.13766 - 4.54088i) q^{28} +(-2.19675 + 0.588617i) q^{29} +(-2.06652 + 1.31510i) q^{30} +(-3.59449 + 2.07528i) q^{31} +(5.62523 - 0.597359i) q^{32} +(-5.30441 - 1.00614i) q^{33} +(-5.53872 - 1.67094i) q^{34} +(3.60757 - 3.60757i) q^{35} +(-0.517109 - 5.97767i) q^{36} +(3.51389 + 3.51389i) q^{37} +(9.82210 - 5.26929i) q^{38} +(-4.02159 - 3.46403i) q^{39} +(2.57095 - 1.17908i) q^{40} +(1.71242 + 2.96600i) q^{41} +(3.75211 + 11.9204i) q^{42} +(-2.43768 - 9.09755i) q^{43} +(5.90945 + 1.98592i) q^{44} +(-1.19718 - 2.75077i) q^{45} +(1.62777 + 6.93333i) q^{46} +(1.33117 - 2.30566i) q^{47} +(-0.349420 + 6.91939i) q^{48} +(-9.51456 - 16.4797i) q^{49} +(1.03071 - 0.968318i) q^{50} +(3.07717 - 6.38241i) q^{51} +(4.05511 + 4.59562i) q^{52} +(10.2529 - 10.2529i) q^{53} +(7.33049 + 0.513682i) q^{54} +3.11711 q^{55} +(-2.41571 - 14.2266i) q^{56} +(4.50291 + 12.8873i) q^{57} +(-0.100333 + 3.21470i) q^{58} +(-1.08447 + 4.04728i) q^{59} +(0.936481 + 3.33512i) q^{60} +(1.93367 + 7.21656i) q^{61} +(1.34160 + 5.71441i) q^{62} +(-15.1367 + 2.26746i) q^{63} +(1.48890 - 7.86023i) q^{64} +(2.65390 + 1.53223i) q^{65} +(-3.52890 + 6.77090i) q^{66} +(-3.37903 + 12.6107i) q^{67} +(-4.52470 + 6.81660i) q^{68} +(-8.69835 + 0.647886i) q^{69} +(-3.41089 - 6.35799i) q^{70} +1.42578i q^{71} +(-8.30465 - 1.74151i) q^{72} -4.54850i q^{73} +(6.19289 - 3.32232i) q^{74} +(0.975050 + 1.43153i) q^{75} +(-3.12237 - 15.4509i) q^{76} +(4.11602 - 15.3612i) q^{77} +(-6.33277 + 4.03008i) q^{78} +(3.24991 + 1.87634i) q^{79} +(-0.546276 - 3.96252i) q^{80} +(-2.01859 + 8.77071i) q^{81} +(4.71525 - 1.10702i) q^{82} +(-1.60374 - 5.98525i) q^{83} +(17.6721 - 0.211111i) q^{84} +(-1.05878 + 3.95142i) q^{85} +(-13.3133 - 0.415516i) q^{86} +(-3.87010 - 0.734080i) q^{87} +(5.10260 - 7.18988i) q^{88} +1.30008 q^{89} +(-4.21339 + 0.497332i) q^{90} +(11.0553 - 11.0553i) q^{91} +(10.0522 + 0.628085i) q^{92} +(-7.16913 + 0.533984i) q^{93} +(-2.57800 - 2.74410i) q^{94} +(-3.94080 - 6.82566i) q^{95} +(9.22572 + 3.29939i) q^{96} +(-4.60909 + 7.98319i) q^{97} +(-26.1989 + 6.15085i) q^{98} +(-7.51902 - 5.55982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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