LMFDB - Embedded newform 672.2.bo.a.125.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(125,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4, 4]))

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

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

chi := DirichletCharacter("672.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bo (of order $8$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$496$
Relative dimension:	$124$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			125.18
Character	$\chi$	$=$	672.125
Dual form			672.2.bo.a.629.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26371 - 0.634854i) q^{2} +(0.826142 - 1.52233i) q^{3} +(1.19392 + 1.60454i) q^{4} +(-0.561080 - 1.35457i) q^{5} +(-2.01046 + 1.39930i) q^{6} +(0.332748 - 2.62474i) q^{7} +(-0.490121 - 2.78564i) q^{8} +(-1.63498 - 2.51532i) q^{9} +O(q^{10})$	\(q+(-1.26371 - 0.634854i) q^{2} +(0.826142 - 1.52233i) q^{3} +(1.19392 + 1.60454i) q^{4} +(-0.561080 - 1.35457i) q^{5} +(-2.01046 + 1.39930i) q^{6} +(0.332748 - 2.62474i) q^{7} +(-0.490121 - 2.78564i) q^{8} +(-1.63498 - 2.51532i) q^{9} +(-0.150910 + 2.06798i) q^{10} +(-2.18090 - 5.26516i) q^{11} +(3.42899 - 0.491966i) q^{12} +(3.09075 + 1.28023i) q^{13} +(-2.08682 + 3.10567i) q^{14} +(-2.52563 - 0.264915i) q^{15} +(-1.14910 + 3.83139i) q^{16} +6.22334i q^{17} +(0.469279 + 4.21661i) q^{18} +(0.242716 + 0.100536i) q^{19} +(1.50357 - 2.51752i) q^{20} +(-3.72083 - 2.67496i) q^{21} +(-0.586582 + 8.03819i) q^{22} +(-1.40280 + 1.40280i) q^{23} +(-4.64557 - 1.55520i) q^{24} +(2.01549 - 2.01549i) q^{25} +(-3.09305 - 3.58001i) q^{26} +(-5.17987 + 0.410969i) q^{27} +(4.60878 - 2.59983i) q^{28} +(0.337636 - 0.815124i) q^{29} +(3.02348 + 1.93818i) q^{30} +1.89320i q^{31} +(3.88450 - 4.11225i) q^{32} +(-9.81705 - 1.02972i) q^{33} +(3.95091 - 7.86449i) q^{34} +(-3.74209 + 1.02196i) q^{35} +(2.08390 - 5.62649i) q^{36} +(-2.71449 - 6.55336i) q^{37} +(-0.242896 - 0.281138i) q^{38} +(4.50233 - 3.64749i) q^{39} +(-3.49833 + 2.22687i) q^{40} +(5.35450 + 5.35450i) q^{41} +(3.00384 + 5.74256i) q^{42} +(-8.40764 + 3.48256i) q^{43} +(5.84434 - 9.78553i) q^{44} +(-2.48981 + 3.62598i) q^{45} +(2.66331 - 0.882161i) q^{46} -8.60357i q^{47} +(4.88332 + 4.91458i) q^{48} +(-6.77856 - 1.74676i) q^{49} +(-3.82654 + 1.26745i) q^{50} +(9.47398 + 5.14136i) q^{51} +(1.63593 + 6.48772i) q^{52} +(0.141325 + 0.341189i) q^{53} +(6.80676 + 2.76912i) q^{54} +(-5.90835 + 5.90835i) q^{55} +(-7.47467 + 0.359527i) q^{56} +(0.353567 - 0.286437i) q^{57} +(-0.944158 + 0.815731i) q^{58} +(0.625795 + 1.51080i) q^{59} +(-2.59034 - 4.36876i) q^{60} +(0.541579 - 1.30749i) q^{61} +(1.20191 - 2.39246i) q^{62} +(-7.14611 + 3.45444i) q^{63} +(-7.51956 + 2.73060i) q^{64} -4.90493i q^{65} +(11.7522 + 7.53365i) q^{66} +(8.32493 + 3.44830i) q^{67} +(-9.98560 + 7.43018i) q^{68} +(0.976617 + 3.29445i) q^{69} +(5.37771 + 1.08422i) q^{70} +(3.39310 + 3.39310i) q^{71} +(-6.20544 + 5.78728i) q^{72} +(-8.10438 + 8.10438i) q^{73} +(-0.730098 + 10.0048i) q^{74} +(-1.40316 - 4.73333i) q^{75} +(0.128469 + 0.509480i) q^{76} +(-14.5454 + 3.97233i) q^{77} +(-8.00525 + 1.75105i) q^{78} -11.8488i q^{79} +(5.83461 - 0.593182i) q^{80} +(-3.65368 + 8.22500i) q^{81} +(-3.36721 - 10.1659i) q^{82} +(6.16492 - 14.8834i) q^{83} +(-0.150294 - 9.16392i) q^{84} +(8.42993 - 3.49179i) q^{85} +(12.8357 + 0.936680i) q^{86} +(-0.961954 - 1.18740i) q^{87} +(-13.5979 + 8.65577i) q^{88} +(-0.319265 + 0.319265i) q^{89} +(5.44837 - 3.00152i) q^{90} +(4.38871 - 7.68643i) q^{91} +(-3.92570 - 0.576018i) q^{92} +(2.88208 + 1.56405i) q^{93} +(-5.46201 + 10.8724i) q^{94} -0.385184i q^{95} +(-3.05106 - 9.31080i) q^{96} +8.63683i q^{97} +(7.45719 + 6.51078i) q^{98} +(-9.67784 + 14.0941i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

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 $

$2$	−1.26371	−	0.634854i	−0.893577	−	0.448909i
$2$	−1.26371	−	0.634854i	−0.893577	−	0.448909i
$3$	0.826142	−	1.52233i	0.476973	−	0.878918i
$3$	0.826142	−	1.52233i	0.476973	−	0.878918i
$4$	1.19392	+	1.60454i	0.596961	+	0.802270i
$5$	−0.561080	−	1.35457i	−0.250922	−	0.605780i	0.747357	−	0.664423i	$-0.231323\pi$
$5$	−0.561080	−	1.35457i	−0.250922	−	0.605780i	−0.998279	+	0.0586427i	$0.981323\pi$
$6$	−2.01046	+	1.39930i	−0.820767	+	0.571263i
$7$	0.332748	−	2.62474i	0.125767	−	0.992060i
$7$	0.332748	−	2.62474i	0.125767	−	0.992060i
$8$	−0.490121	−	2.78564i	−0.173284	−	0.984872i
$9$	−1.63498	−	2.51532i	−0.544993	−	0.838440i
$10$	−0.150910	+	2.06798i	−0.0477218	+	0.653953i
$11$	−2.18090	−	5.26516i	−0.657566	−	1.58751i	−0.801551	−	0.597926i	$-0.795992\pi$
$11$	−2.18090	−	5.26516i	−0.657566	−	1.58751i	0.143985	−	0.989580i	$-0.454008\pi$
$12$	3.42899	−	0.491966i	0.989864	−	0.142018i
$13$	3.09075	+	1.28023i	0.857219	+	0.355072i	0.767619	−	0.640906i	$-0.221441\pi$
$13$	3.09075	+	1.28023i	0.857219	+	0.355072i	0.0895998	+	0.995978i	$0.471441\pi$
$14$	−2.08682	+	3.10567i	−0.557727	+	0.830024i
$15$	−2.52563	−	0.264915i	−0.652115	−	0.0684007i
$16$	−1.14910	+	3.83139i	−0.287275	+	0.957848i
$17$			6.22334i			1.50938i	0.656080	+	0.754691i	$0.272213\pi$
$17$			6.22334i			1.50938i	−0.656080	+	0.754691i	$0.727787\pi$
$18$	0.469279	+	4.21661i	0.110610	+	0.993864i
$19$	0.242716	+	0.100536i	0.0556828	+	0.0230646i	0.410351	−	0.911928i	$-0.365406\pi$
$19$	0.242716	+	0.100536i	0.0556828	+	0.0230646i	−0.354668	+	0.934992i	$0.615406\pi$
$20$	1.50357	−	2.51752i	0.336209	−	0.562935i
$21$	−3.72083	−	2.67496i	−0.811952	−	0.583725i
$22$	−0.586582	+	8.03819i	−0.125060	+	1.71375i
$23$	−1.40280	+	1.40280i	−0.292505	+	0.292505i	−0.838069	−	0.545564i	$-0.816315\pi$
$23$	−1.40280	+	1.40280i	−0.292505	+	0.292505i	0.545564	+	0.838069i	$0.316315\pi$
$24$	−4.64557	−	1.55520i	−0.948273	−	0.317455i
$25$	2.01549	−	2.01549i	0.403099	−	0.403099i
$26$	−3.09305	−	3.58001i	−0.606597	−	0.702098i
$27$	−5.17987	+	0.410969i	−0.996867	+	0.0790910i
$28$	4.60878	−	2.59983i	0.870978	−	0.491322i
$29$	0.337636	−	0.815124i	0.0626974	−	0.151365i	−0.889426	−	0.457080i	$-0.848895\pi$
$29$	0.337636	−	0.815124i	0.0626974	−	0.151365i	0.952123	+	0.305715i	$0.0988954\pi$
$30$	3.02348	+	1.93818i	0.552009	+	0.353862i
$31$			1.89320i			0.340029i	0.985442	+	0.170015i	$0.0543815\pi$
$31$			1.89320i			0.340029i	−0.985442	+	0.170015i	$0.945619\pi$
$32$	3.88450	−	4.11225i	0.686690	−	0.726951i
$33$	−9.81705	−	1.02972i	−1.70893	−	0.179251i
$34$	3.95091	−	7.86449i	0.677576	−	1.34875i
$35$	−3.74209	+	1.02196i	−0.632528	+	0.172743i
$36$	2.08390	−	5.62649i	0.347316	−	0.937748i
$37$	−2.71449	−	6.55336i	−0.446260	−	1.07737i	−0.973712	−	0.227782i	$-0.926853\pi$
$37$	−2.71449	−	6.55336i	−0.446260	−	1.07737i	0.527453	−	0.849584i	$-0.323147\pi$
$38$	−0.242896	−	0.281138i	−0.0394030	−	0.0456065i
$39$	4.50233	−	3.64749i	0.720949	−	0.584066i
$40$	−3.49833	+	2.22687i	−0.553135	+	0.352099i
$41$	5.35450	+	5.35450i	0.836232	+	0.836232i	0.988361	−	0.152128i	$-0.0486127\pi$
$41$	5.35450	+	5.35450i	0.836232	+	0.836232i	−0.152128	+	0.988361i	$0.548613\pi$
$42$	3.00384	+	5.74256i	0.463502	+	0.886096i
$43$	−8.40764	+	3.48256i	−1.28215	+	0.531085i	−0.916637	−	0.399720i	$-0.869107\pi$
$43$	−8.40764	+	3.48256i	−1.28215	+	0.531085i	−0.365516	+	0.930805i	$0.619107\pi$
$44$	5.84434	−	9.78553i	0.881067	−	1.47522i
$45$	−2.48981	+	3.62598i	−0.371160	+	0.540530i
$46$	2.66331	−	0.882161i	0.392684	−	0.130068i
$47$		−	8.60357i		−	1.25496i	−0.778633	−	0.627480i	$-0.784086\pi$
$47$		−	8.60357i		−	1.25496i	0.778633	−	0.627480i	$-0.215914\pi$
$48$	4.88332	+	4.91458i	0.704847	+	0.709359i
$49$	−6.77856	−	1.74676i	−0.968365	−	0.249537i
$50$	−3.82654	+	1.26745i	−0.541155	+	0.179245i
$51$	9.47398	+	5.14136i	1.32662	+	0.719935i
$52$	1.63593	+	6.48772i	0.226863	+	0.899685i
$53$	0.141325	+	0.341189i	0.0194125	+	0.0468659i	0.933289	−	0.359127i	$-0.116926\pi$
$53$	0.141325	+	0.341189i	0.0194125	+	0.0468659i	−0.913876	+	0.405993i	$0.866926\pi$
$54$	6.80676	+	2.76912i	0.926283	+	0.376829i
$55$	−5.90835	+	5.90835i	−0.796682	+	0.796682i
$56$	−7.47467	+	0.359527i	−0.998845	+	0.0480438i
$57$	0.353567	−	0.286437i	0.0468311	−	0.0379395i
$58$	−0.944158	+	0.815731i	−0.123974	+	0.107111i
$59$	0.625795	+	1.51080i	0.0814716	+	0.196690i	0.959366	−	0.282164i	$-0.0910523\pi$
$59$	0.625795	+	1.51080i	0.0814716	+	0.196690i	−0.877895	+	0.478854i	$0.841052\pi$
$60$	−2.59034	−	4.36876i	−0.334411	−	0.564005i
$61$	0.541579	−	1.30749i	0.0693421	−	0.167407i	−0.885409	−	0.464813i	$-0.846122\pi$
$61$	0.541579	−	1.30749i	0.0693421	−	0.167407i	0.954751	+	0.297406i	$0.0961216\pi$
$62$	1.20191	−	2.39246i	0.152642	−	0.303842i
$63$	−7.14611	+	3.45444i	−0.900325	+	0.435218i
$64$	−7.51956	+	2.73060i	−0.939945	+	0.341325i
$65$		−	4.90493i		−	0.608382i
$66$	11.7522	+	7.53365i	1.44659	+	0.927328i
$67$	8.32493	+	3.44830i	1.01705	+	0.421277i	0.828023	−	0.560695i	$-0.189466\pi$
$67$	8.32493	+	3.44830i	1.01705	+	0.421277i	0.189030	+	0.981971i	$0.439466\pi$
$68$	−9.98560	+	7.43018i	−1.21093	+	0.901042i
$69$	0.976617	+	3.29445i	0.117571	+	0.396605i
$70$	5.37771	+	1.08422i	0.642759	+	0.129589i
$71$	3.39310	+	3.39310i	0.402687	+	0.402687i	0.879179	−	0.476492i	$-0.158092\pi$
$71$	3.39310	+	3.39310i	0.402687	+	0.402687i	−0.476492	+	0.879179i	$0.658092\pi$
$72$	−6.20544	+	5.78728i	−0.731318	+	0.682037i
$73$	−8.10438	+	8.10438i	−0.948545	+	0.948545i	−0.998739	−	0.0501940i	$-0.984016\pi$
$73$	−8.10438	+	8.10438i	−0.948545	+	0.948545i	0.0501940	+	0.998739i	$0.484016\pi$
$74$	−0.730098	+	10.0048i	−0.0848722	+	1.16304i
$75$	−1.40316	−	4.73333i	−0.162024	−	0.546558i
$76$	0.128469	+	0.509480i	0.0147364	+	0.0584413i
$77$	−14.5454	+	3.97233i	−1.65760	+	0.452689i
$78$	−8.00525	+	1.75105i	−0.906416	+	0.198267i
$79$		−	11.8488i		−	1.33310i	−0.745460	−	0.666550i	$-0.767770\pi$
$79$		−	11.8488i		−	1.33310i	0.745460	−	0.666550i	$-0.232230\pi$
$80$	5.83461	−	0.593182i	0.652330	−	0.0663198i
$81$	−3.65368	+	8.22500i	−0.405964	+	0.913889i
$82$	−3.36721	−	10.1659i	−0.371846	−	1.12263i
$83$	6.16492	−	14.8834i	0.676688	−	1.63367i	−0.0933211	−	0.995636i	$-0.529748\pi$
$83$	6.16492	−	14.8834i	0.676688	−	1.63367i	0.770009	−	0.638033i	$-0.220252\pi$
$84$	−0.150294	−	9.16392i	−0.0163984	−	0.999866i
$85$	8.42993	−	3.49179i	0.914354	−	0.378738i
$86$	12.8357	+	0.936680i	1.38411	+	0.101005i
$87$	−0.961954	−	1.18740i	−0.103132	−	0.127303i
$88$	−13.5979	+	8.65577i	−1.44954	+	0.922708i
$89$	−0.319265	+	0.319265i	−0.0338421	+	0.0338421i	−0.723825	−	0.689983i	$-0.757618\pi$
$89$	−0.319265	+	0.319265i	−0.0338421	+	0.0338421i	0.689983	+	0.723825i	$0.257618\pi$
$90$	5.44837	−	3.00152i	0.574309	−	0.316388i
$91$	4.38871	−	7.68643i	0.460062	−	0.805756i
$92$	−3.92570	−	0.576018i	−0.409282	−	0.0600540i
$93$	2.88208	+	1.56405i	0.298858	+	0.162185i
$94$	−5.46201	+	10.8724i	−0.563363	+	1.12140i
$95$		−	0.385184i		−	0.0395190i
$96$	−3.05106	−	9.31080i	−0.311397	−	0.950280i
$97$			8.63683i			0.876937i	0.898747	+	0.438468i	$0.144479\pi$
$97$			8.63683i			0.876937i	−0.898747	+	0.438468i	$0.855521\pi$
$98$	7.45719	+	6.51078i	0.753290	+	0.657689i
$99$	−9.67784	+	14.0941i	−0.972660	+	1.41651i
$100$	5.64029	+	0.827600i	0.564029	+	0.0827600i
$101$	2.19955	+	5.31018i	0.218863	+	0.528383i	0.994732	−	0.102512i	$-0.0326880\pi$
$101$	2.19955	+	5.31018i	0.218863	+	0.528383i	−0.775869	+	0.630895i	$0.782688\pi$
$102$	−8.70835	−	12.5118i	−0.862255	−	1.23885i
$103$	−10.5367	−	10.5367i	−1.03822	−	1.03822i	−0.999240	−	0.0389752i	$-0.987591\pi$
$103$	−10.5367	−	10.5367i	−1.03822	−	1.03822i	−0.0389752	−	0.999240i	$-0.512409\pi$
$104$	2.05141	−	9.23717i	0.201158	−	0.905779i
$105$	−1.53573	+	6.54098i	−0.149872	+	0.638334i
$106$	0.0380112	−	0.520884i	0.00369198	−	0.0505928i
$107$	−2.24734	−	5.42557i	−0.217259	−	0.524509i	0.777246	−	0.629196i	$-0.216616\pi$
$107$	−2.24734	−	5.42557i	−0.217259	−	0.524509i	−0.994505	+	0.104687i	$0.966616\pi$
$108$	−6.84378	−	7.82066i	−0.658543	−	0.752543i
$109$	3.25754	−	7.86439i	0.312015	−	0.753272i	−0.687615	−	0.726076i	$-0.741342\pi$
$109$	3.25754	−	7.86439i	0.312015	−	0.753272i	0.999630	−	0.0271961i	$-0.00865787\pi$
$110$	11.2174	−	3.71550i	1.06953	−	0.354259i
$111$	−12.2189	−	1.28165i	−1.15977	−	0.121649i
$112$	9.67406	+	4.29099i	0.914113	+	0.405460i
$113$	5.53371			0.520568			0.260284	−	0.965532i	$-0.416184\pi$
$113$	5.53371			0.520568			0.260284	+	0.965532i	$0.416184\pi$
$114$	−0.628651	+	0.137509i	−0.0588786	+	0.0128789i
$115$	2.68728	+	1.11311i	0.250590	+	0.103798i
$116$	1.71101	−	0.431445i	0.158863	−	0.0400586i
$117$	−1.83312	−	9.86737i	−0.169472	−	0.912239i
$118$	0.168316	−	2.30650i	0.0154947	−	0.212331i
$119$	16.3347	+	2.07081i	1.49740	+	0.189830i
$120$	0.499908	+	7.16533i	0.0456352	+	0.654102i
$121$	−15.1874	+	15.1874i	−1.38067	+	1.38067i
$122$	−1.51446	+	1.30846i	−0.137113	+	0.118462i
$123$	12.5749	−	3.72774i	1.13384	−	0.336119i
$124$	−3.03772	+	2.26034i	−0.272795	+	0.202984i
$125$	−10.6338	−	4.40467i	−0.951117	−	0.393965i
$126$	11.2237	+	0.171332i	0.999884	+	0.0152635i
$127$	19.6094			1.74005			0.870026	−	0.493006i	$-0.164102\pi$
$127$	19.6094			1.74005			0.870026	+	0.493006i	$0.164102\pi$
$128$	11.2361	+	1.32313i	0.993138	+	0.116950i
$129$	−1.64430	+	15.6763i	−0.144772	+	1.38022i
$130$	−3.11391	+	6.19841i	−0.273108	+	0.543636i
$131$	15.7466	+	6.52247i	1.37579	+	0.569871i	0.943352	−	0.331794i	$-0.107654\pi$
$131$	15.7466	+	6.52247i	1.37579	+	0.569871i	0.432437	+	0.901664i	$0.357654\pi$
$132$	−10.0686	−	16.9813i	−0.876356	−	1.47803i
$133$	0.344645	−	0.603614i	0.0298845	−	0.0523399i
$134$	−8.33113	−	9.64276i	−0.719700	−	0.833008i
$135$	3.46301	+	6.78590i	0.298048	+	0.584037i
$136$	17.3360	−	3.05019i	1.48655	−	0.261552i
$137$	−0.372185	+	0.372185i	−0.0317979	+	0.0317979i	−0.722827	−	0.691029i	$-0.757158\pi$
$137$	−0.372185	+	0.372185i	−0.0317979	+	0.0317979i	0.691029	+	0.722827i	$0.257158\pi$
$138$	0.857332	−	4.78323i	0.0729809	−	0.407176i
$139$	1.18330	+	2.85673i	0.100366	+	0.242305i	0.966084	−	0.258227i	$-0.0831381\pi$
$139$	1.18330	+	2.85673i	0.100366	+	0.242305i	−0.865719	+	0.500531i	$0.833138\pi$
$140$	−6.10754	−	4.78419i	−0.516181	−	0.404338i
$141$	−13.0975	−	7.10777i	−1.10301	−	0.598582i
$142$	−2.13377	−	6.44201i	−0.179062	−	0.540601i
$143$		−	19.0653i		−	1.59432i
$144$	11.5159	−	3.37389i	0.959662	−	0.281158i
$145$	−1.29358			−0.107426
$146$	15.3867	−	5.09648i	1.27341	−	0.421788i
$147$	−8.25919	+	8.87614i	−0.681207	+	0.732091i
$148$	7.27425	−	12.1797i	0.597939	−	1.00117i
$149$	−0.0875248	−	0.211304i	−0.00717031	−	0.0173107i	0.920254	−	0.391322i	$-0.127982\pi$
$149$	−0.0875248	−	0.211304i	−0.00717031	−	0.0173107i	−0.927424	+	0.374011i	$0.877982\pi$
$150$	−1.23178	+	6.87236i	−0.100574	+	0.561126i
$151$	−3.68429	−	3.68429i	−0.299824	−	0.299824i	0.541121	−	0.840945i	$-0.318000\pi$
$151$	−3.68429	−	3.68429i	−0.299824	−	0.299824i	−0.840945	+	0.541121i	$0.818000\pi$
$152$	0.161097	−	0.725393i	0.0130667	−	0.0588372i
$153$	15.6537	−	10.1750i	1.26553	−	0.822603i
$154$	20.9030	+	4.21432i	1.68441	+	0.339599i
$155$	2.56447	−	1.06224i	0.205983	−	0.0853210i
$156$	11.2280	+	2.86935i	0.898957	+	0.229732i
$157$	8.79848	−	21.2414i	0.702195	−	1.69525i	−0.0164427	−	0.999865i	$-0.505234\pi$
$157$	8.79848	−	21.2414i	0.702195	−	1.69525i	0.718638	−	0.695384i	$-0.244766\pi$
$158$	−7.52228	+	14.9735i	−0.598441	+	1.19123i
$159$	0.636157	+	0.0667269i	0.0504505	+	0.00529179i
$160$	−7.74984	−	2.95452i	−0.612678	−	0.233575i
$161$	3.21522	+	4.14878i	0.253395	+	0.326970i
$162$	9.83886	−	8.07446i	0.773014	−	0.634389i
$163$	−2.12144	−	0.878728i	−0.166164	−	0.0688273i	0.298051	−	0.954550i	$-0.403663\pi$
$163$	−2.12144	−	0.878728i	−0.166164	−	0.0688273i	−0.464215	+	0.885723i	$0.653663\pi$
$164$	−2.19866	+	14.9844i	−0.171686	+	1.17008i
$165$	4.11333	+	13.8756i	0.320222	+	1.08021i
$166$	−17.2395	+	14.8945i	−1.33804	+	1.15604i
$167$	2.03110	−	2.03110i	0.157171	−	0.157171i	−0.624141	−	0.781312i	$-0.714551\pi$
$167$	2.03110	−	2.03110i	0.157171	−	0.157171i	0.781312	+	0.624141i	$0.214551\pi$
$168$	−5.62782	+	11.6759i	−0.434196	+	0.900819i
$169$	−1.27866	−	1.27866i	−0.0983582	−	0.0983582i
$170$	−12.8698	−	0.939163i	−0.987065	−	0.0720305i
$171$	−0.143955	−	0.774883i	−0.0110085	−	0.0592568i
$172$	−15.6260	−	9.33250i	−1.19147	−	0.711596i
$173$	3.94540	−	9.52504i	0.299963	−	0.724175i	−0.699987	−	0.714156i	$-0.746811\pi$
$173$	3.94540	−	9.52504i	0.299963	−	0.724175i	0.999950	−	0.0100194i	$-0.00318931\pi$
$174$	0.461804	+	2.11123i	0.0350093	+	0.160052i
$175$	−4.61950	−	5.96081i	−0.349202	−	0.450595i
$176$	22.6790	−	2.30568i	1.70949	−	0.173797i
$177$	2.81694	+	0.295470i	0.211734	+	0.0222089i
$178$	0.606145	−	0.200772i	0.0454325	−	0.0150485i
$179$	16.6111	+	6.88055i	1.24157	+	0.514276i	0.904206	−	0.427097i	$-0.140464\pi$
$179$	16.6111	+	6.88055i	1.24157	+	0.514276i	0.337367	+	0.941373i	$0.390464\pi$
$180$	−8.79068	+	0.334133i	−0.655219	+	0.0249048i
$181$	−1.73005	−	4.17671i	−0.128594	−	0.310452i	0.846449	−	0.532470i	$-0.178736\pi$
$181$	−1.73005	−	4.17671i	−0.128594	−	0.310452i	−0.975043	+	0.222017i	$0.928736\pi$
$182$	−10.4258	+	6.92721i	−0.772813	+	0.513479i
$183$	−1.54301	−	1.90463i	−0.114062	−	0.140794i
$184$	4.59525	+	3.22016i	0.338766	+	0.237393i
$185$	−7.35392	+	7.35392i	−0.540671	+	0.540671i
$186$	−2.64917	−	3.80621i	−0.194246	−	0.279085i
$187$	32.7669	−	13.5725i	2.39615	−	0.992519i
$188$	13.8048	−	10.2720i	1.00682	−	0.749162i
$189$	−0.644906	+	13.7326i	−0.0469100	+	0.998899i
$190$	−0.244535	+	0.486760i	−0.0177404	+	0.0353133i
$191$			6.04027i			0.437058i	0.975830	+	0.218529i	$0.0701259\pi$
$191$			6.04027i			0.437058i	−0.975830	+	0.218529i	$0.929874\pi$
$192$	−2.05534	+	13.7031i	−0.148332	+	0.988938i
$193$	−5.78332			−0.416292			−0.208146	−	0.978098i	$-0.566743\pi$
$193$	−5.78332			−0.416292			−0.208146	+	0.978098i	$0.566743\pi$
$194$	5.48312	−	10.9144i	0.393665	−	0.783611i
$195$	−7.46693	−	4.05217i	−0.534718	−	0.290182i
$196$	−5.29032	−	12.9620i	−0.377880	−	0.925854i
$197$	19.9977	−	8.28330i	1.42477	−	0.590161i	0.468719	−	0.883347i	$-0.344716\pi$
$197$	19.9977	−	8.28330i	1.42477	−	0.590161i	0.956055	+	0.293186i	$0.0947156\pi$
$198$	21.1777	−	11.6668i	1.50503	−	0.829126i
$199$	18.4440	+	18.4440i	1.30746	+	1.30746i	0.923241	+	0.384222i	$0.125530\pi$
$199$	18.4440	+	18.4440i	1.30746	+	1.30746i	0.384222	+	0.923241i	$0.374470\pi$
$200$	−6.60228	−	4.62660i	−0.466851	−	0.327150i
$201$	12.1270	−	9.82451i	0.855374	−	0.692968i
$202$	0.591597	−	8.10691i	0.0416246	−	0.570400i
$203$	−2.02714	−	1.15744i	−0.142278	−	0.0812362i
$204$	3.06167	+	21.3398i	0.214360	+	1.49408i
$205$	4.24872	−	10.2573i	0.296744	−	0.716403i
$206$	6.62608	+	20.0047i	0.461661	+	1.39379i
$207$	5.82206	+	1.23495i	0.404661	+	0.0858347i
$208$	−8.45664	+	10.3708i	−0.586363	+	0.719082i
$209$		−	1.49720i		−	0.103563i
$210$	6.09328	−	7.29093i	0.420476	−	0.503122i
$211$	2.02529	−	4.88949i	0.139427	−	0.336607i	−0.838707	−	0.544583i	$-0.816688\pi$
$211$	2.02529	−	4.88949i	0.139427	−	0.336607i	0.978134	+	0.207977i	$0.0666878\pi$
$212$	−0.378720	+	0.634115i	−0.0260106	+	0.0435512i
$213$	7.96860	−	2.36224i	0.545999	−	0.161858i
$214$	−0.604452	+	8.28307i	−0.0413195	+	0.566219i
$215$	9.43471	+	9.43471i	0.643442	+	0.643442i
$216$	3.68358	+	14.2278i	0.250636	+	0.968081i
$217$	4.96917	+	0.629960i	0.337329	+	0.0427644i
$218$	−9.10932	+	7.87024i	−0.616961	+	0.533040i
$219$	5.64218	+	19.0329i	0.381263	+	1.28612i
$220$	−16.5343	−	2.42608i	−1.11474	−	0.163566i
$221$	−7.96731	+	19.2348i	−0.535939	+	1.29387i
$222$	14.6275	+	9.37687i	0.981735	+	0.629334i
$223$		−	6.97988i		−	0.467407i	−0.972308	−	0.233704i	$-0.924915\pi$
$223$		−	6.97988i		−	0.467407i	0.972308	−	0.233704i	$-0.0750845\pi$
$224$	−9.50105	−	11.5642i	−0.634816	−	0.772664i
$225$	−8.36491	−	1.77432i	−0.557661	−	0.118288i
$226$	−6.99300	−	3.51310i	−0.465168	−	0.233688i
$227$	−9.57112	−	3.96449i	−0.635258	−	0.263132i	0.0417275	−	0.999129i	$-0.486714\pi$
$227$	−9.57112	−	3.96449i	−0.635258	−	0.263132i	−0.676985	+	0.735997i	$0.736714\pi$
$228$	0.881730	+	0.225330i	0.0583940	+	0.0149228i
$229$	19.3420	−	8.01171i	1.27815	−	0.529428i	0.362720	−	0.931898i	$-0.381848\pi$
$229$	19.3420	−	8.01171i	1.27815	−	0.529428i	0.915433	+	0.402470i	$0.131848\pi$
$230$	−2.68928	−	3.11267i	−0.177326	−	0.205243i
$231$	−5.96935	+	25.4246i	−0.392754	+	1.67282i
$232$	−2.43612	−	0.541021i	−0.159939	−	0.0355197i
$233$	−16.8034	+	16.8034i	−1.10083	+	1.10083i	−0.106519	+	0.994311i	$0.533971\pi$
$233$	−16.8034	+	16.8034i	−1.10083	+	1.10083i	−0.994311	+	0.106519i	$0.966029\pi$
$234$	−3.94780	+	13.6333i	−0.258076	+	0.891234i
$235$	−11.6541	+	4.82729i	−0.760230	+	0.314898i
$236$	−1.67700	+	2.80790i	−0.109163	+	0.182778i
$237$	−18.0379	−	9.78883i	−1.17169	−	0.635853i
$238$	−19.3276	−	12.9870i	−1.25282	−	0.841824i
$239$	1.44849			0.0936953			0.0468477	−	0.998902i	$-0.485082\pi$
$239$	1.44849			0.0936953			0.0468477	+	0.998902i	$0.485082\pi$
$240$	3.91720	−	9.37226i	0.252854	−	0.604977i
$241$	20.9347			1.34852			0.674262	−	0.738493i	$-0.264462\pi$
$241$	20.9347			1.34852			0.674262	+	0.738493i	$0.264462\pi$
$242$	28.8343	−	9.55069i	1.85354	−	0.613942i
$243$	9.50271	+	12.3571i	0.609599	+	0.792710i
$244$	2.74452	−	0.692052i	0.175700	−	0.0443041i
$245$	1.43721	+	10.1621i	0.0918201	+	0.649231i
$246$	−18.2576	−	3.27243i	−1.16406	−	0.208643i
$247$	0.621464	+	0.621464i	0.0395428	+	0.0395428i
$248$	5.27378	−	0.927899i	0.334885	−	0.0589216i
$249$	−17.5644	−	21.6809i	−1.11310	−	1.37397i
$250$	10.6417	+	12.3171i	0.673041	+	0.779004i
$251$	−7.75772	−	18.7288i	−0.489663	−	1.18215i	−0.954890	−	0.296959i	$-0.904027\pi$
$251$	−7.75772	−	18.7288i	−0.489663	−	1.18215i	0.465227	−	0.885191i	$-0.345973\pi$
$252$	−14.0747	−	7.34190i	−0.886621	−	0.462496i
$253$	10.4454	+	4.32661i	0.656695	+	0.272012i
$254$	−24.7806	−	12.4491i	−1.55487	−	0.781125i
$255$	1.64866	−	15.7179i	0.103243	−	0.984290i
$256$	−13.3591	−	8.80532i	−0.834946	−	0.550332i
$257$	−19.1651			−1.19549			−0.597744	−	0.801687i	$-0.703936\pi$
$257$	−19.1651			−1.19549			−0.597744	+	0.801687i	$0.703936\pi$
$258$	12.0301	−	18.7664i	0.748959	−	1.16834i
$259$	−18.1041	+	4.94422i	−1.12494	+	0.307219i
$260$	7.87017	−	5.85611i	0.488087	−	0.363180i
$261$	−2.60233	+	0.483450i	−0.161080	+	0.0299248i
$262$	−15.7583	−	18.2393i	−0.973554	−	1.12683i
$263$	−15.2294	−	15.2294i	−0.939088	−	0.939088i	0.0591606	−	0.998248i	$-0.481158\pi$
$263$	−15.2294	−	15.2294i	−0.939088	−	0.939088i	−0.998248	+	0.0591606i	$0.981158\pi$
$264$	1.94313	+	27.8514i	0.119591	+	1.71414i
$265$	0.382868	−	0.382868i	0.0235194	−	0.0235194i
$266$	−0.818737	+	0.543993i	−0.0502000	+	0.0333543i
$267$	0.222269	+	0.749786i	0.0136026	+	0.0458861i
$268$	4.40638	+	17.4747i	0.269162	+	1.06744i
$269$	−11.1046	+	26.8090i	−0.677062	+	1.63457i	0.0922778	+	0.995733i	$0.470585\pi$
$269$	−11.1046	+	26.8090i	−0.677062	+	1.63457i	−0.769340	+	0.638840i	$0.779415\pi$
$270$	−0.0681826	−	10.7739i	−0.00414946	−	0.655679i
$271$	−0.872067			−0.0529743			−0.0264871	−	0.999649i	$-0.508432\pi$
$271$	−0.872067			−0.0529743			−0.0264871	+	0.999649i	$0.508432\pi$
$272$	−23.8441	−	7.15125i	−1.44576	−	0.433608i
$273$	−8.07558	−	13.0311i	−0.488756	−	0.788681i
$274$	0.706617	−	0.234051i	0.0426883	−	0.0141395i
$275$	−15.0075	−	6.21631i	−0.904986	−	0.374858i
$276$	−4.12007	+	5.50033i	−0.247999	+	0.331081i
$277$	22.6195	−	9.36932i	1.35908	−	0.562948i	0.420272	−	0.907398i	$-0.361935\pi$
$277$	22.6195	−	9.36932i	1.35908	−	0.562948i	0.938805	+	0.344450i	$0.111935\pi$
$278$	0.318263	−	4.36129i	0.0190881	−	0.261573i
$279$	4.76201	−	3.09535i	0.285094	−	0.185314i
$280$	4.68089	+	9.92322i	0.279737	+	0.593026i
$281$	−9.07870	−	9.07870i	−0.541590	−	0.541590i	0.382405	−	0.923995i	$-0.375096\pi$
$281$	−9.07870	−	9.07870i	−0.541590	−	0.541590i	−0.923995	+	0.382405i	$0.875096\pi$
$282$	12.0390	+	17.2971i	0.716913	+	1.03003i
$283$	−15.2546	+	6.31867i	−0.906794	+	0.375606i	−0.786828	−	0.617172i	$-0.788278\pi$
$283$	−15.2546	+	6.31867i	−0.906794	+	0.375606i	−0.119965	+	0.992778i	$0.538278\pi$
$284$	−1.39327	+	9.49546i	−0.0826754	+	0.563452i
$285$	−0.586377	−	0.318216i	−0.0347340	−	0.0188495i
$286$	−12.1037	+	24.0930i	−0.715707	+	1.42465i
$287$	15.8359	−	12.2725i	0.934763	−	0.724422i
$288$	−16.6947	−	3.04732i	−0.983746	−	0.179565i
$289$	−21.7300			−1.27823
$290$	1.63471	+	0.821234i	0.0959935	+	0.0482245i
$291$	13.1481	+	7.13524i	0.770756	+	0.418275i
$292$	−22.6798	−	3.32781i	−1.32723	−	0.194745i
$293$	−1.86900	−	4.51216i	−0.109188	−	0.263603i	0.859836	−	0.510571i	$-0.170566\pi$
$293$	−1.86900	−	4.51216i	−0.109188	−	0.263603i	−0.969024	+	0.246968i	$0.920566\pi$
$294$	16.0723	−	5.97348i	0.937353	−	0.348380i
$295$	1.69536	−	1.69536i	0.0987078	−	0.0987078i
$296$	−16.9249	+	10.7735i	−0.983738	+	0.626199i
$297$	13.4606	+	26.3766i	0.781064	+	1.53053i
$298$	−0.0235409	+	0.322592i	−0.00136369	+	0.0186872i
$299$	−6.13163	+	2.53980i	−0.354601	+	0.146881i
$300$	5.91956	−	7.90266i	0.341766	−	0.456260i
$301$	6.34320	+	23.2267i	0.365616	+	1.33877i
$302$	2.31689	+	6.99486i	0.133322	+	0.402509i
$303$	9.90099	+	1.03852i	0.568797	+	0.0596614i
$304$	−0.664099	+	0.814413i	−0.0380887	+	0.0467098i
$305$	−2.07495			−0.118811
$306$	−26.2414	+	2.92048i	−1.50012	+	0.166953i
$307$	20.5885	+	8.52802i	1.17505	+	0.486720i	0.882857	−	0.469641i	$-0.155617\pi$
$307$	20.5885	+	8.52802i	1.17505	+	0.486720i	0.292188	+	0.956361i	$0.405617\pi$
$308$	−23.7398	−	18.5960i	−1.35270	−	1.05961i
$309$	−24.7452	+	7.33556i	−1.40771	+	0.417305i
$310$	−3.91511	−	0.285703i	−0.222363	−	0.0162268i
$311$	4.01647	+	4.01647i	0.227753	+	0.227753i	0.811754	−	0.584000i	$-0.198513\pi$
$311$	4.01647	+	4.01647i	0.227753	+	0.227753i	−0.584000	+	0.811754i	$0.698513\pi$
$312$	−12.3673	−	10.7541i	−0.700159	−	0.608833i
$313$	7.02718	+	7.02718i	0.397200	+	0.397200i	0.877244	−	0.480044i	$-0.159379\pi$
$313$	7.02718	+	7.02718i	0.397200	+	0.397200i	−0.480044	+	0.877244i	$0.659379\pi$
$314$	−24.6039	+	21.2572i	−1.38848	+	1.19961i
$315$	8.68880	+	7.74167i	0.489558	+	0.436193i
$316$	19.0120	−	14.1466i	1.06951	−	0.795808i
$317$	6.69649	−	16.1667i	0.376112	−	0.908015i	−0.616575	−	0.787296i	$-0.711480\pi$
$317$	6.69649	−	16.1667i	0.376112	−	0.908015i	0.992687	−	0.120718i	$-0.0385198\pi$
$318$	−0.761555	−	0.488190i	−0.0427059	−	0.0273763i
$319$	−5.02811			−0.281520
$320$	7.91786	+	8.65366i	0.442622	+	0.483754i
$321$	−10.1161	−	1.06109i	−0.564627	−	0.0592241i
$322$	−1.42924	−	7.28405i	−0.0796482	−	0.405924i
$323$	−0.625671	+	1.51050i	−0.0348133	+	0.0840467i
$324$	−17.5596	+	3.95753i	−0.975531	+	0.219863i
$325$	8.80968	−	3.64909i	0.488673	−	0.202415i
$326$	2.12302	+	2.45726i	0.117583	+	0.136095i
$327$	−9.28101	−	11.4561i	−0.513241	−	0.633526i
$328$	12.2913	−	17.5401i	0.678676	−	0.968487i
$329$	−22.5822	−	2.86282i	−1.24500	−	0.157833i
$330$	3.61092	−	20.1461i	0.198775	−	1.10901i
$331$	19.8547	−	8.22407i	1.09131	−	0.452036i	0.236847	−	0.971547i	$-0.423886\pi$
$331$	19.8547	−	8.22407i	1.09131	−	0.452036i	0.854464	+	0.519511i	$0.173886\pi$
$332$	31.2415	−	7.87779i	1.71460	−	0.432350i
$333$	−12.0457	+	17.5424i	−0.660099	+	0.961320i
$334$	−3.85618	+	1.27727i	−0.211001	+	0.0698891i
$335$		−	13.2114i		−	0.721818i
$336$	14.5244	−	11.1822i	0.792373	−	0.610037i
$337$		−	0.205564i		−	0.0111978i	−0.999984	−	0.00559888i	$-0.998218\pi$
$337$		−	0.205564i		−	0.0111978i	0.999984	−	0.00559888i	$-0.00178219\pi$
$338$	0.804090	+	2.42761i	0.0437367	+	0.132045i
$339$	4.57163	−	8.42414i	0.248297	−	0.457536i
$340$	15.6674	+	9.35724i	0.849684	+	0.507468i
$341$	9.96801	−	4.12889i	0.539798	−	0.223592i
$342$	−0.310020	+	1.07062i	−0.0167640	+	0.0578923i
$343$	−6.84034	+	17.2107i	−0.369344	+	0.929293i
$344$	13.8219	+	21.7138i	0.745228	+	1.17073i
$345$	3.91459	−	3.17134i	0.210754	−	0.170739i
$346$	−11.0328	+	9.53213i	−0.593129	+	0.512450i
$347$	7.23551	−	2.99705i	0.388423	−	0.160890i	−0.179921	−	0.983681i	$-0.557584\pi$
$347$	7.23551	−	2.99705i	0.388423	−	0.160890i	0.568344	+	0.822791i	$0.307584\pi$
$348$	0.756736	−	2.96116i	0.0405653	−	0.158735i
$349$	−9.36028	+	22.5977i	−0.501045	+	1.20963i	0.447871	+	0.894098i	$0.352182\pi$
$349$	−9.36028	+	22.5977i	−0.501045	+	1.20963i	−0.948915	+	0.315530i	$0.897818\pi$
$350$	2.05347	+	10.4654i	0.109763	+	0.559401i
$351$	−16.5358	−	5.36123i	−0.882617	−	0.286161i
$352$	−30.1234	−	11.4841i	−1.60558	−	0.612105i
$353$	2.15993			0.114961			0.0574807	−	0.998347i	$-0.481693\pi$
$353$	2.15993			0.114961			0.0574807	+	0.998347i	$0.481693\pi$
$354$	−3.37221	−	2.16173i	−0.179231	−	0.114895i
$355$	2.69238	−	6.49998i	0.142897	−	0.344983i
$356$	−0.893452	−	0.131096i	−0.0473529	−	0.00694810i
$357$	16.6472	−	23.1560i	0.881063	−	1.22555i
$358$	−16.6235	−	19.2406i	−0.878578	−	1.01690i
$359$	−14.6412	−	14.6412i	−0.772733	−	0.772733i	0.205851	−	0.978583i	$-0.434004\pi$
$359$	−14.6412	−	14.6412i	−0.772733	−	0.772733i	−0.978583	+	0.205851i	$0.934004\pi$
$360$	11.3210	+	5.15855i	0.596669	+	0.271880i
$361$	−13.3862	−	13.3862i	−0.704538	−	0.704538i
$362$	−0.465319	+	6.37647i	−0.0244566	+	0.335140i
$363$	10.5733	+	35.6672i	0.554955	+	1.87204i
$364$	17.5730	−	2.13512i	0.921074	−	0.111911i
$365$	15.5251	+	6.43071i	0.812622	+	0.336599i
$366$	0.740750	+	3.38649i	0.0387196	+	0.177014i
$367$	−18.9937			−0.991464			−0.495732	−	0.868476i	$-0.665100\pi$
$367$	−18.9937			−0.991464			−0.495732	+	0.868476i	$0.665100\pi$
$368$	−3.76273	−	6.98666i	−0.196146	−	0.364205i
$369$	4.71378	−	22.2228i	0.245390	−	1.15687i
$370$	13.9619	−	4.62455i	0.725843	−	0.240419i
$371$	0.942559	−	0.257412i	0.0489352	−	0.0133642i
$372$	0.931391	+	6.49177i	0.0482903	+	0.336583i
$373$	−4.00895	+	1.66056i	−0.207576	+	0.0859807i	−0.484049	−	0.875041i	$-0.660834\pi$
$373$	−4.00895	+	1.66056i	−0.207576	+	0.0859807i	0.276473	+	0.961022i	$0.410834\pi$
$374$	−50.0244	−	3.65050i	−2.58670	−	0.188763i
$375$	−15.4904	+	12.5493i	−0.799920	+	0.648042i
$376$	−23.9664	+	4.21680i	−1.23597	+	0.217465i
$377$	2.08709	−	2.08709i	0.107491	−	0.107491i
$378$	9.53316	−	16.9446i	0.490333	−	0.871535i
$379$	7.43440	+	17.9482i	0.381879	+	0.921938i	0.991602	+	0.129324i	$0.0412807\pi$
$379$	7.43440	+	17.9482i	0.381879	+	0.921938i	−0.609723	+	0.792615i	$0.708719\pi$
$380$	0.618043	−	0.459879i	0.0317049	−	0.0235913i
$381$	16.2001	−	29.8520i	0.829958	−	1.52936i
$382$	3.83469	−	7.63314i	0.196200	−	0.390546i
$383$	−24.6979			−1.26201			−0.631003	−	0.775781i	$-0.717356\pi$
$383$	−24.6979			−1.26201			−0.631003	+	0.775781i	$0.717356\pi$
$384$	11.2968	−	16.0119i	0.576489	−	0.817105i
$385$	13.5419	+	17.4739i	0.690160	+	0.890552i
$386$	7.30843	+	3.67156i	0.371989	+	0.186877i
$387$	22.5061	+	15.4540i	1.14405	+	0.785571i
$388$	−13.8581	+	10.3117i	−0.703541	+	0.523497i
$389$	−2.45027	+	1.01493i	−0.124234	+	0.0514592i	−0.443934	−	0.896059i	$-0.646418\pi$
$389$	−2.45027	+	1.01493i	−0.124234	+	0.0514592i	0.319701	+	0.947519i	$0.396418\pi$
$390$	6.86349	+	9.86117i	0.347546	+	0.499340i
$391$	−8.73013	−	8.73013i	−0.441502	−	0.441502i
$392$	−1.54352	+	19.7387i	−0.0779594	+	0.996957i
$393$	22.9383	−	18.5831i	1.15708	−	0.937393i
$394$	−30.5299	−	2.22790i	−1.53807	−	0.112240i
$395$	−16.0501	+	6.64815i	−0.807566	+	0.334505i
$396$	−34.1691	+	1.29877i	−1.71706	+	0.0652654i
$397$	−1.99868	−	0.827882i	−0.100311	−	0.0415502i	0.331964	−	0.943292i	$-0.392289\pi$
$397$	−1.99868	−	0.827882i	−0.100311	−	0.0415502i	−0.432275	+	0.901742i	$0.642289\pi$
$398$	−11.5986	−	35.0172i	−0.581387	−	1.75525i
$399$	−0.634174	−	1.02333i	−0.0317484	−	0.0512308i
$400$	5.40614	+	10.0382i	0.270307	+	0.501908i
$401$	33.6741			1.68161			0.840803	−	0.541341i	$-0.182083\pi$
$401$	33.6741			1.68161			0.840803	+	0.541341i	$0.182083\pi$
$402$	−21.5622	+	4.71644i	−1.07542	+	0.235235i
$403$	−2.42373	+	5.85141i	−0.120735	+	0.291479i
$404$	−5.89431	+	9.86920i	−0.293253	+	0.491011i
$405$	13.1913	+	0.334270i	0.655482	+	0.0166100i
$406$	1.82692	+	2.74961i	0.0906684	+	0.136461i
$407$	−28.5845	+	28.5845i	−1.41688	+	1.41688i
$408$	9.67857	−	28.9110i	0.479161	−	1.43131i
$409$	−5.91854	−	5.91854i	−0.292653	−	0.292653i	0.545474	−	0.838127i	$-0.316349\pi$
$409$	−5.91854	−	5.91854i	−0.292653	−	0.292653i	−0.838127	+	0.545474i	$0.816349\pi$
$410$	−11.8811	+	10.2650i	−0.586763	+	0.506950i
$411$	0.259111	+	0.874067i	0.0127810	+	0.0431145i
$412$	4.32658	−	29.4867i	0.213155	−	1.45270i
$413$	4.17370	−	1.13984i	0.205375	−	0.0560876i
$414$	−6.57338	−	5.25677i	−0.323064	−	0.258356i
$415$	−23.6196			−1.15944
$416$	17.2706	−	7.73688i	0.846763	−	0.379332i
$417$	5.32645	+	0.558695i	0.260838	+	0.0273594i
$418$	−0.950501	+	1.89202i	−0.0464905	+	0.0925418i
$419$	37.5091	+	15.5368i	1.83244	+	0.759021i	0.965398	+	0.260782i	$0.0839803\pi$
$419$	37.5091	+	15.5368i	1.83244	+	0.759021i	0.867040	+	0.498239i	$0.166020\pi$
$420$	−12.3288	+	5.34527i	−0.601584	+	0.260823i
$421$	7.31641	+	17.6634i	0.356580	+	0.860861i	0.995776	+	0.0918166i	$0.0292674\pi$
$421$	7.31641	+	17.6634i	0.356580	+	0.860861i	−0.639196	+	0.769044i	$0.720733\pi$
$422$	−5.66350	+	4.89313i	−0.275695	+	0.238194i
$423$	−21.6407	+	14.0667i	−1.05221	+	0.683945i
$424$	0.881162	−	0.560905i	0.0427930	−	0.0272399i
$425$	12.5431	+	12.5431i	0.608430	+	0.608430i
$426$	−11.5697	−	2.07371i	−0.560552	−	0.100472i
$427$	−3.25161	−	1.85657i	−0.157356	−	0.0898457i
$428$	6.02239	−	10.0837i	0.291103	−	0.487412i
$429$	−29.0237	−	15.7507i	−1.40128	−	0.760449i
$430$	−5.93307	−	17.9124i	−0.286118	−	0.863812i
$431$	31.4033			1.51264			0.756321	−	0.654201i	$-0.226995\pi$
$431$	31.4033			1.51264			0.756321	+	0.654201i	$0.226995\pi$
$432$	4.37762	−	20.3184i	0.210618	−	0.977568i
$433$	−2.70854			−0.130164			−0.0650820	−	0.997880i	$-0.520731\pi$
$433$	−2.70854			−0.130164			−0.0650820	+	0.997880i	$0.520731\pi$
$434$	−5.87965	−	3.95078i	−0.282232	−	0.189644i
$435$	−1.06868	+	1.96926i	−0.0512393	+	0.0944187i
$436$	16.5080	−	4.16262i	0.790589	−	0.199353i
$437$	−0.481515	+	0.199450i	−0.0230340	+	0.00954100i
$438$	4.95304	−	27.6340i	0.236665	−	1.32040i
$439$	15.3571	−	15.3571i	0.732955	−	0.732955i	−0.238249	−	0.971204i	$-0.576574\pi$
$439$	15.3571	−	15.3571i	0.732955	−	0.732955i	0.971204	+	0.238249i	$0.0765736\pi$
$440$	19.3543	+	13.5627i	0.922682	+	0.646577i
$441$	6.68915	+	19.9062i	0.318531	+	0.947912i
$442$	22.2796	−	19.2491i	1.05973	−	0.915586i
$443$	−31.4621	+	13.0320i	−1.49481	+	0.619171i	−0.972358	−	0.233497i	$-0.924983\pi$
$443$	−31.4621	+	13.0320i	−1.49481	+	0.619171i	−0.522454	+	0.852668i	$0.674983\pi$
$444$	−12.5320	−	21.1360i	−0.594742	−	1.00307i
$445$	0.611599	+	0.253333i	0.0289926	+	0.0120091i
$446$	−4.43120	+	8.82054i	−0.209823	+	0.417665i
$447$	−0.393982	−	0.0413250i	−0.0186347	−	0.00195461i
$448$	4.66501	+	20.6455i	0.220401	+	0.975409i
$449$		−	15.0934i		−	0.712300i	−0.934429	−	0.356150i	$-0.884089\pi$
$449$		−	15.0934i		−	0.712300i	0.934429	−	0.356150i	$-0.115911\pi$
$450$	9.44438	+	7.55272i	0.445212	+	0.356039i
$451$	16.5147	−	39.8699i	0.777645	−	1.87740i
$452$	6.60682	+	8.87907i	0.310759	+	0.417636i
$453$	−8.65246	+	2.56496i	−0.406528	+	0.120513i
$454$	9.57824	+	11.0862i	0.449529	+	0.520302i
$455$	−12.8742	−	1.63211i	−0.603551	−	0.0765144i
$456$	−0.971199	−	0.844521i	−0.0454806	−	0.0395483i
$457$	18.0811	+	18.0811i	0.845796	+	0.845796i	0.989605	−	0.143809i	$-0.0459351\pi$
$457$	18.0811	+	18.0811i	0.845796	+	0.845796i	−0.143809	+	0.989605i	$0.545935\pi$
$458$	−29.5289	−	2.15485i	−1.37979	−	0.100690i
$459$	−2.55760	−	32.2361i	−0.119379	−	1.50465i
$460$	1.42237	+	5.64081i	0.0663185	+	0.263004i
$461$	−11.1742	+	26.9768i	−0.520433	+	1.25644i	0.417202	+	0.908814i	$0.363011\pi$
$461$	−11.1742	+	26.9768i	−0.520433	+	1.25644i	−0.937635	+	0.347622i	$0.886989\pi$
$462$	23.6844	−	28.3396i	1.10190	−	1.31848i
$463$			24.3744i			1.13278i	0.824139	+	0.566388i	$0.191659\pi$
$463$			24.3744i			1.13278i	−0.824139	+	0.566388i	$0.808341\pi$
$464$	2.73508	+	2.23028i	0.126973	+	0.103538i
$465$	0.501537	−	4.78153i	0.0232582	−	0.221738i
$466$	31.9024	−	10.5669i	1.47785	−	0.489504i
$467$	−1.54269	+	3.72439i	−0.0713873	+	0.172344i	−0.955546	−	0.294843i	$-0.904733\pi$
$467$	−1.54269	+	3.72439i	−0.0713873	+	0.172344i	0.884158	+	0.467187i	$0.154733\pi$
$468$	13.6440	−	14.7222i	0.630694	−	0.680533i
$469$	11.8210	−	20.7034i	0.545843	−	0.955994i
$470$	17.7920	+	1.29836i	0.820685	+	0.0598890i
$471$	−25.0677	−	30.9426i	−1.15506	−	1.42576i
$472$	3.90184	−	2.48372i	0.179597	−	0.114322i
$473$	36.6725	+	36.6725i	1.68620	+	1.68620i
$474$	16.5801	+	23.8216i	0.761551	+	1.09416i
$475$	0.691823	−	0.286562i	0.0317430	−	0.0131484i
$476$	16.1796	+	28.6820i	0.741592	+	1.31464i
$477$	0.627136	−	0.913315i	0.0287146	−	0.0418178i
$478$	−1.83048	−	0.919582i	−0.0837240	−	0.0420607i
$479$	−25.5216			−1.16611			−0.583055	−	0.812433i	$-0.698143\pi$
$479$	−25.5216			−1.16611			−0.583055	+	0.812433i	$0.698143\pi$
$480$	−10.9002	+	9.35697i	−0.497524	+	0.427085i
$481$		−	23.7300i		−	1.08199i
$482$	−26.4554	−	13.2905i	−1.20501	−	0.605365i
$483$	8.97205	−	1.46715i	0.408242	−	0.0667575i
$484$	−42.5014	−	6.23624i	−1.93188	−	0.283465i
$485$	11.6992	−	4.84595i	0.531231	−	0.220043i
$486$	−4.16370	−	21.6486i	−0.188869	−	0.982002i
$487$	7.52635	−	7.52635i	0.341052	−	0.341052i	−0.515711	−	0.856763i	$-0.672472\pi$
$487$	7.52635	−	7.52635i	0.341052	−	0.341052i	0.856763	+	0.515711i	$0.172472\pi$
$488$	−3.90763	−	0.867816i	−0.176890	−	0.0392842i
$489$	−3.09032	+	2.50357i	−0.139749	+	0.113216i
$490$	4.63521	−	13.7543i	0.209398	−	0.621357i
$491$	−10.7573	−	25.9704i	−0.485469	−	1.17203i	−0.956977	−	0.290165i	$-0.906290\pi$
$491$	−10.7573	−	25.9704i	−0.485469	−	1.17203i	0.471507	−	0.881862i	$-0.343710\pi$
$492$	20.9948	+	15.7263i	0.946517	+	0.708996i
$493$	5.07280	+	2.10122i	0.228467	+	0.0946343i
$494$	−0.390811	−	1.17989i	−0.0175834	−	0.0530857i
$495$	24.5214	+	5.20136i	1.10216	+	0.233784i
$496$	−7.25360	−	2.17548i	−0.325696	−	0.0976820i
$497$	10.0351	−	7.77697i	0.450134	−	0.348845i
$498$	8.43213	+	38.5491i	0.377853	+	1.72743i
$499$	−9.11120	+	21.9964i	−0.407873	+	0.984694i	0.577823	+	0.816162i	$0.303902\pi$
$499$	−9.11120	+	21.9964i	−0.407873	+	0.984694i	−0.985696	+	0.168531i	$0.946098\pi$
$500$	−5.62847	−	22.3212i	−0.251713	−	0.998234i
$501$	−1.41403	−	4.76999i	−0.0631743	−	0.213107i
$502$	−2.08654	+	28.5928i	−0.0931268	+	1.27616i
$503$	4.64689	+	4.64689i	0.207195	+	0.207195i	0.803074	−	0.595879i	$-0.203196\pi$
$503$	4.64689	+	4.64689i	0.207195	+	0.207195i	−0.595879	+	0.803074i	$0.703196\pi$
$504$	13.1253	+	18.2134i	0.584646	+	0.811289i
$505$	5.95887	−	5.95887i	0.265166	−	0.265166i
$506$	−10.4531	−	12.0989i	−0.464699	−	0.537860i
$507$	−3.00289	+	0.890186i	−0.133363	+	0.0395346i
$508$	23.4121	+	31.4641i	1.03874	+	1.39599i
$509$	−20.9350	−	8.67157i	−0.927928	−	0.384360i	−0.133036	−	0.991111i	$-0.542473\pi$
$509$	−20.9350	−	8.67157i	−0.927928	−	0.384360i	−0.794892	+	0.606751i	$0.792473\pi$
$510$	−12.0620	+	18.8161i	−0.534112	+	0.833193i
$511$	18.5752	+	23.9686i	0.821718	+	1.06031i
$512$	11.2920	+	19.6085i	0.499039	+	0.866579i
$513$	−1.29855	−	0.421016i	−0.0573326	−	0.0185883i
$514$	24.2191	+	12.1670i	1.06826	+	0.536665i
$515$	−8.36076	+	20.1847i	−0.368419	+	0.889442i
$516$	−27.1164	+	16.0779i	−1.19373	+	0.707791i
$517$	−45.2992	+	18.7635i	−1.99226	+	0.825220i
$518$	26.0172	+	5.24542i	1.14313	+	0.230470i
$519$	−11.2408	−	13.8752i	−0.493416	−	0.609055i
$520$	−13.6634	+	2.40401i	−0.599178	+	0.105423i
$521$	19.1214	+	19.1214i	0.837724	+	0.837724i	0.988559	−	0.150835i	$-0.0481963\pi$
$521$	19.1214	+	19.1214i	0.837724	+	0.837724i	−0.150835	+	0.988559i	$0.548196\pi$
$522$	3.59550	+	1.04116i	0.157371	+	0.0455702i
$523$	5.96245	+	14.3946i	0.260720	+	0.629433i	0.998983	−	0.0450792i	$-0.0143540\pi$
$523$	5.96245	+	14.3946i	0.260720	+	0.629433i	−0.738264	+	0.674512i	$0.764354\pi$
$524$	8.33468	+	33.0534i	0.364102	+	1.44395i
$525$	−12.8907	+	2.10794i	−0.562596	+	0.0919980i
$526$	9.57712	+	28.9141i	0.417582	+	1.26071i
$527$	−11.7820			−0.513234
$528$	15.2260	−	36.4297i	0.662628	−	1.58540i
$529$			19.0643i			0.828882i
$530$	−0.726900	+	0.240769i	−0.0315745	+	0.0104583i
$531$	2.77699	−	4.04421i	0.120511	−	0.175504i
$532$	1.38000	−	0.167671i	0.0598307	−	0.00726944i
$533$	9.69442	+	23.4044i	0.419912	+	1.01376i
$534$	0.195121	−	1.08862i	0.00844371	−	0.0471092i
$535$	−6.08835	+	6.08835i	−0.263222	+	0.263222i
$536$	5.52549	−	24.8803i	0.238665	−	1.07467i
$537$	24.1976	−	19.6033i	1.04420	−	0.845945i
$538$	31.0528	−	26.8289i	1.33878	−	1.15668i
$539$	5.58640	+	39.4997i	0.240623	+	1.70137i
$540$	−6.75369	+	13.6584i	−0.290633	+	0.587763i
$541$	16.8052	+	6.96094i	0.722512	+	0.299274i	0.713471	−	0.700685i	$-0.247122\pi$
$541$	16.8052	+	6.96094i	0.722512	+	0.299274i	0.00904101	+	0.999959i	$0.497122\pi$
$542$	1.10204	+	0.553635i	0.0473366	+	0.0237806i
$543$	−7.78760	−	0.816846i	−0.334198	−	0.0350542i
$544$	25.5920	+	24.1746i	1.09725	+	1.03648i
$545$	−12.4806			−0.534609
$546$	1.93231	+	21.5944i	0.0826953	+	0.924155i
$547$	−7.24056	−	2.99914i	−0.309584	−	0.128234i	0.222482	−	0.974937i	$-0.428584\pi$
$547$	−7.24056	−	2.99914i	−0.309584	−	0.128234i	−0.532066	+	0.846703i	$0.678584\pi$
$548$	−1.04155	−	0.152826i	−0.0444927	−	0.00652842i
$549$	−4.17422	+	0.775471i	−0.178151	+	0.0330963i
$550$	15.0187	+	17.3832i	0.640398	+	0.741221i
$551$	0.163899	−	0.163899i	0.00698233	−	0.00698233i
$552$	8.69848	−	4.33518i	0.370232	−	0.184518i
$553$	−31.1002	−	3.94268i	−1.32251	−	0.167660i
$554$	−34.5327	−	2.52000i	−1.46715	−	0.107065i
$555$	5.11972	+	17.2705i	0.217320	+	0.733091i
$556$	−3.17097	+	5.30936i	−0.134479	+	0.225167i
$557$	30.9344	+	12.8135i	1.31073	+	0.542924i	0.925098	−	0.379727i	$-0.123982\pi$
$557$	30.9344	+	12.8135i	1.31073	+	0.542924i	0.385636	+	0.922651i	$0.373982\pi$
$558$	−7.98289	+	0.888440i	−0.337943	+	0.0376106i
$559$	−30.4444			−1.28766
$560$	0.384506	−	15.5117i	0.0162483	−	0.655491i
$561$	6.40828	−	61.0948i	0.270558	−	2.57943i
$562$	5.70919	+	17.2365i	0.240828	+	0.727077i
$563$	8.93231	−	21.5645i	0.376452	−	0.908836i	−0.616173	−	0.787611i	$-0.711318\pi$
$563$	8.93231	−	21.5645i	0.376452	−	0.908836i	0.992625	−	0.121225i	$-0.0386822\pi$
$564$	−4.23266	−	29.5016i	−0.178227	−	1.24224i
$565$	−3.10485	−	7.49578i	−0.130622	−	0.315350i
$566$	23.2888	+	1.69949i	0.978903	+	0.0714349i
$567$	20.3728	+	12.3268i	0.855576	+	0.517678i
$568$	7.78891	−	11.1150i	0.326816	−	0.466374i
$569$	30.2554	+	30.2554i	1.26837	+	1.26837i	0.946928	+	0.321445i	$0.104169\pi$
$569$	30.2554	+	30.2554i	1.26837	+	1.26837i	0.321445	+	0.946928i	$0.395831\pi$
$570$	0.538989	+	0.774396i	0.0225758	+	0.0324359i
$571$	−4.99198	−	12.0517i	−0.208908	−	0.504348i	0.784344	−	0.620326i	$-0.213000\pi$
$571$	−4.99198	−	12.0517i	−0.208908	−	0.504348i	−0.993252	+	0.115978i	$0.963000\pi$
$572$	30.5911	−	22.7625i	1.27908	−	0.951749i
$573$	9.19528	+	4.99012i	0.384139	+	0.208465i
$574$	−27.8032	+	5.45538i	−1.16048	+	0.227703i
$575$			5.65469i			0.235817i
$576$	19.1627	+	14.4496i	0.798445	+	0.602068i
$577$		−	16.7014i		−	0.695290i	−0.937626	−	0.347645i	$-0.886981\pi$
$577$		−	16.7014i		−	0.695290i	0.937626	−	0.347645i	$-0.113019\pi$
$578$	27.4604	+	13.7954i	1.14220	+	0.573811i
$579$	−4.77784	+	8.80412i	−0.198560	+	0.365887i
$580$	−1.54443	−	2.07560i	−0.0641291	−	0.0861847i
$581$	−37.0138	−	21.1338i	−1.53559	−	0.876777i
$582$	−12.0855	−	17.3640i	−0.500962	−	0.719761i
$583$	1.48820	−	1.48820i	0.0616349	−	0.0616349i
$584$	26.5480	+	18.6037i	1.09856	+	0.769828i
$585$	−12.3375	+	8.01947i	−0.510092	+	0.331564i
$586$	−0.502691	+	6.88860i	−0.0207660	+	0.284565i
$587$	−36.1126	+	14.9583i	−1.49052	+	0.617395i	−0.971431	−	0.237322i	$-0.923730\pi$
$587$	−36.1126	+	14.9583i	−1.49052	+	0.617395i	−0.519094	+	0.854717i	$0.673730\pi$
$588$	−24.1029	−	2.65479i	−0.993989	−	0.109482i
$589$	−0.190335	+	0.459510i	−0.00784263	+	0.0189338i
$590$	−3.21875	+	1.06614i	−0.132514	+	0.0438922i
$591$	3.91098	−	37.2862i	0.160876	−	1.53375i
$592$	28.2277	−	2.86980i	1.16015	−	0.117948i
$593$		−	28.2856i		−	1.16155i	−0.814064	−	0.580776i	$-0.802749\pi$
$593$		−	28.2856i		−	1.16155i	0.814064	−	0.580776i	$-0.197251\pi$
$594$	−0.265024	−	41.8779i	−0.0108741	−	1.71827i
$595$	−6.36001	−	23.2883i	−0.260735	−	0.954727i
$596$	0.234548	−	0.392717i	0.00960744	−	0.0160863i
$597$	43.3153	−	12.8405i	1.77278	−	0.525528i
$598$	9.36100	+	0.683113i	0.382800	+	0.0279346i
$599$	−16.1169	+	16.1169i	−0.658519	+	0.658519i	−0.955029	−	0.296511i	$-0.904177\pi$
$599$	−16.1169	+	16.1169i	−0.658519	+	0.658519i	0.296511	+	0.955029i	$0.404177\pi$
$600$	−12.4976	+	6.22862i	−0.510214	+	0.254282i
$601$	−9.30966	−	9.30966i	−0.379749	−	0.379749i	0.491263	−	0.871011i	$-0.336536\pi$
$601$	−9.30966	−	9.30966i	−0.379749	−	0.379749i	−0.871011	+	0.491263i	$0.836536\pi$
$602$	6.72961	−	33.3788i	0.274278	−	1.36042i
$603$	−4.93752	−	26.5778i	−0.201071	−	1.08233i
$604$	1.51284	−	10.3104i	0.0615566	−	0.419523i
$605$	29.0937	+	12.0510i	1.18283	+	0.489943i
$606$	−11.8527	−	7.59806i	−0.481481	−	0.308650i
$607$			14.4107i			0.584911i	0.956279	+	0.292456i	$0.0944723\pi$
$607$			14.4107i			0.584911i	−0.956279	+	0.292456i	$0.905528\pi$
$608$	1.35626	−	0.607576i	0.0550036	−	0.0246405i
$609$	−3.43671	+	2.12978i	−0.139263	+	0.0863029i
$610$	2.62213	+	1.31729i	0.106167	+	0.0533354i
$611$	11.0145	−	26.5915i	0.445601	−	1.07578i
$612$	35.0156	+	12.9688i	1.41542	+	0.524233i
$613$	−15.1944	−	36.6824i	−0.613694	−	1.48159i	−0.858913	−	0.512121i	$-0.828860\pi$
$613$	−15.1944	−	36.6824i	−0.613694	−	1.48159i	0.245219	−	0.969468i	$-0.421140\pi$
$614$	−20.6038	−	23.8476i	−0.831501	−	0.962410i
$615$	−12.1050	−	14.9420i	−0.488120	−	0.602518i
$616$	18.1945	+	38.5713i	0.733077	+	1.55408i
$617$	−22.7938	+	22.7938i	−0.917643	+	0.917643i	−0.996858	−	0.0792144i	$-0.974759\pi$
$617$	−22.7938	+	22.7938i	−0.917643	+	0.917643i	0.0792144	+	0.996858i	$0.474759\pi$
$618$	35.9278	+	6.43959i	1.44523	+	0.259038i
$619$	−8.01952	−	19.3608i	−0.322332	−	0.778178i	−0.999118	−	0.0419981i	$-0.986628\pi$
$619$	−8.01952	−	19.3608i	−0.322332	−	0.778178i	0.676786	−	0.736180i	$-0.263372\pi$
$620$	4.76618	+	2.84656i	0.191414	+	0.114321i
$621$	6.68984	−	7.84286i	0.268454	−	0.314723i
$622$	−2.52578	−	7.62553i	−0.101275	−	0.305756i
$623$	0.731755	+	0.944225i	0.0293171	+	0.0378296i
$624$	8.80133	+	21.4415i	0.352335	+	0.858348i
$625$			2.62387i			0.104955i
$626$	−4.41908	−	13.3416i	−0.176622	−	0.533236i
$627$	−2.27923	−	1.23690i	−0.0910236	−	0.0493969i
$628$	44.5874	−	11.2431i	1.77923	−	0.448647i
$629$	40.7838	−	16.8932i	1.62616	−	0.673576i
$630$	−6.06529	−	15.2993i	−0.241647	−	0.609540i
$631$	7.43862	+	7.43862i	0.296127	+	0.296127i	0.839495	−	0.543368i	$-0.182851\pi$
$631$	7.43862	+	7.43862i	0.296127	+	0.296127i	−0.543368	+	0.839495i	$0.682851\pi$
$632$	−33.0066	+	5.80738i	−1.31293	+	0.231005i
$633$	−5.77025	−	7.12258i	−0.229347	−	0.283097i
$634$	−18.7259	+	16.1788i	−0.743702	+	0.642541i
$635$	−11.0024	−	26.5622i	−0.436618	−	1.05409i
$636$	0.652455	+	1.10041i	0.0258715	+	0.0436339i
$637$	−18.7146	−	14.0769i	−0.741498	−	0.557747i
$638$	6.35407	+	3.19211i	0.251560	+	0.126377i
$639$	2.98708	−	14.0824i	0.118167	−	0.557090i
$640$	−4.51206	−	15.9624i	−0.178355	−	0.630969i
$641$		−	6.77065i		−	0.267425i	−0.991020	−	0.133712i	$-0.957310\pi$
$641$		−	6.77065i		−	0.267425i	0.991020	−	0.133712i	$-0.0426898\pi$
$642$	12.1102	+	7.76317i	0.477952	+	0.306388i
$643$	−1.00214	+	2.41938i	−0.0395205	+	0.0954109i	−0.942407	−	0.334467i	$-0.891444\pi$
$643$	−1.00214	+	2.41938i	−0.0395205	+	0.0954109i	0.902887	+	0.429878i	$0.141444\pi$
$644$	−2.81817	+	10.1123i	−0.111051	+	0.398479i
$645$	22.1572	−	6.56834i	0.872437	−	0.258628i
$646$	1.74961	−	1.51163i	0.0688377	−	0.0594742i
$647$	16.4649	−	16.4649i	0.647302	−	0.647302i	−0.305038	−	0.952340i	$-0.598669\pi$
$647$	16.4649	−	16.4649i	0.647302	−	0.647302i	0.952340	+	0.305038i	$0.0986692\pi$
$648$	24.7026	+	6.14658i	0.970411	+	0.241461i
$649$	6.58983	−	6.58983i	0.258673	−	0.258673i
$650$	−13.4495	−	0.981470i	−0.527533	−	0.0384964i
$651$	5.06424	−	7.04428i	0.198483	−	0.276087i
$652$	−1.12287	−	4.45306i	−0.0439752	−	0.174395i
$653$	−12.5236	−	5.18743i	−0.490085	−	0.203000i	0.123935	−	0.992290i	$-0.460449\pi$
$653$	−12.5236	−	5.18743i	−0.490085	−	0.203000i	−0.614020	+	0.789291i	$0.710449\pi$
$654$	4.45553	+	20.3693i	0.174225	+	0.796504i
$655$		−	24.9895i		−	0.976420i
$656$	−26.6681	+	14.3623i	−1.04121	+	0.560754i
$657$	33.6356	+	7.13461i	1.31225	+	0.278348i
$658$	26.7198	+	17.9541i	1.04165	+	0.699926i
$659$	14.2967	+	5.92190i	0.556921	+	0.230684i	0.643348	−	0.765574i	$-0.277545\pi$
$659$	14.2967	+	5.92190i	0.556921	+	0.230684i	−0.0864268	+	0.996258i	$0.527545\pi$
$660$	−17.3530	+	23.1664i	−0.675463	+	0.901750i
$661$	1.28560	+	3.10372i	0.0500042	+	0.120721i	0.946908	−	0.321505i	$-0.104189\pi$
$661$	1.28560	+	3.10372i	0.0500042	+	0.120721i	−0.896904	+	0.442226i	$0.854189\pi$
$662$	−30.3116	−	2.21197i	−1.17809	−	0.0859707i
$663$	22.6996	+	28.0195i	0.881578	+	1.08819i
$664$	−44.4814	−	9.87855i	−1.72621	−	0.383362i
$665$	−1.01101	−	0.128169i	−0.0392052	−	0.00497019i
$666$	26.3591	−	14.5213i	1.02139	−	0.562689i
$667$	0.669823	+	1.61710i	0.0259357	+	0.0626142i
$668$	5.68397	+	0.834009i	0.219919	+	0.0322688i
$669$	−10.6257	−	5.76637i	−0.410813	−	0.222941i
$670$	−8.38733	+	16.6954i	−0.324031	+	0.645000i
$671$	−8.06526			−0.311356
$672$	−25.4537	+	4.91010i	−0.981898	+	0.189411i
$673$	−7.43946			−0.286770			−0.143385	−	0.989667i	$-0.545799\pi$
$673$	−7.43946			−0.286770			−0.143385	+	0.989667i	$0.545799\pi$
$674$	−0.130503	+	0.259773i	−0.00502678	+	0.0100061i
$675$	−9.61170	+	11.2683i	−0.369955	+	0.433718i
$676$	0.525040	−	3.57827i	0.0201939	−	0.137626i
$677$	−13.0534	−	31.5137i	−0.501683	−	1.21117i	−0.948566	−	0.316578i	$-0.897466\pi$
$677$	−13.0534	−	31.5137i	−0.501683	−	1.21117i	0.446883	−	0.894592i	$-0.352534\pi$
$678$	−11.1253	+	7.74335i	−0.427265	+	0.297381i
$679$	22.6695	+	2.87389i	0.869974	+	0.110290i
$680$	−13.8586	−	21.7713i	−0.531451	−	0.834892i
$681$	−13.9424	+	11.2952i	−0.534272	+	0.432832i
$682$	−15.2179	−	1.11052i	−0.582724	−	0.0425239i
$683$	−6.18653	−	14.9356i	−0.236721	−	0.571495i	0.760219	−	0.649667i	$-0.225092\pi$
$683$	−6.18653	−	14.9356i	−0.236721	−	0.571495i	−0.996940	+	0.0781720i	$0.975092\pi$
$684$	1.07146	−	1.15613i	0.0409683	−	0.0442058i
$685$	0.712976	+	0.295324i	0.0272414	+	0.0112838i
$686$	19.5705	−	17.4068i	0.747205	−	0.664593i
$687$	3.78274	−	36.0637i	0.144321	−	1.37591i
$688$	−3.68181	−	36.2148i	−0.140368	−	1.38068i
$689$			1.23546i			0.0470672i
$690$	−6.96024	+	1.52246i	−0.264972	+	0.0579591i
$691$	−8.44671	−	3.49874i	−0.321328	−	0.133098i	0.216189	−	0.976352i	$-0.430637\pi$
$691$	−8.44671	−	3.49874i	−0.321328	−	0.133098i	−0.537516	+	0.843253i	$0.680637\pi$
$692$	19.9938	−	5.04160i	0.760051	−	0.191653i
$693$	33.7731	+	30.0916i	1.28293	+	1.14309i
$694$	−11.0463	−	0.806095i	−0.419311	−	0.0305989i
$695$	3.20570	−	3.20570i	0.121599	−	0.121599i
$696$	−2.83620	+	3.26163i	−0.107506	+	0.123632i
$697$	−33.3229	+	33.3229i	−1.26219	+	1.26219i
$698$	26.1749	−	22.6145i	0.990736	−	0.855973i
$699$	11.6984	+	39.4624i	0.442473	+	1.49261i
$700$	4.04903	−	14.5289i	0.153039	−	0.549142i
$701$	6.24933	−	15.0872i	0.236034	−	0.569837i	−0.760832	−	0.648949i	$-0.775209\pi$
$701$	6.24933	−	15.0872i	0.236034	−	0.569837i	0.996866	+	0.0791127i	$0.0252087\pi$
$702$	17.4929	+	17.2729i	0.660226	+	0.651922i
$703$		−	1.86351i		−	0.0702836i
$704$	30.7765	+	33.6365i	1.15993	+	1.26772i
$705$	−2.27921	+	21.7294i	−0.0858401	+	0.818378i
$706$	−2.72952	−	1.37124i	−0.102727	−	0.0516072i
$707$	14.6698	−	4.00630i	0.551713	−	0.150672i
$708$	2.88911	+	4.87266i	0.108579	+	0.183126i
$709$	−2.94552	−	7.11112i	−0.110621	−	0.267064i	0.858868	−	0.512197i	$-0.171168\pi$
$709$	−2.94552	−	7.11112i	−0.110621	−	0.267064i	−0.969489	+	0.245133i	$0.921168\pi$
$710$	−7.52892	+	6.50481i	−0.282555	+	0.244121i
$711$	−29.8037	+	19.3726i	−1.11772	+	0.726531i
$712$	1.04584	+	0.732879i	0.0391944	+	0.0274658i
$713$	−2.65579	−	2.65579i	−0.0994602	−	0.0994602i
$714$	−35.7379	+	18.6939i	−1.33746	+	0.699602i
$715$	−25.8253	+	10.6972i	−0.965810	+	0.400052i
$716$	8.79225	+	34.8680i	0.328582	+	1.30308i
$717$	1.19666	−	2.20509i	0.0446901	−	0.0823505i
$718$	9.20720	+	27.7972i	0.343610	+	1.03738i
$719$			50.7016i			1.89085i	0.325839	+	0.945425i	$0.394353\pi$
$719$			50.7016i			1.89085i	−0.325839	+	0.945425i	$0.605647\pi$
$720$	−11.0315	−	13.7061i	−0.411120	−	0.510796i
$721$	−31.1623	+	24.1501i	−1.16054	+	0.899399i
$722$	8.41800	+	25.4146i	0.313286	+	0.945833i
$723$	17.2950	−	31.8695i	0.643209	−	1.18524i
$724$	4.63616	−	7.76260i	0.172301	−	0.288495i
$725$	−0.962376	−	2.32338i	−0.0357417	−	0.0862882i
$726$	9.28188	−	51.7855i	0.344483	−	1.92194i
$727$	−17.8195	+	17.8195i	−0.660888	+	0.660888i	−0.955589	−	0.294702i	$-0.904780\pi$
$727$	−17.8195	+	17.8195i	−0.660888	+	0.660888i	0.294702	+	0.955589i	$0.404780\pi$
$728$	−23.5626	−	8.45809i	−0.873288	−	0.313478i
$729$	26.6622	−	4.25754i	0.987489	−	0.157686i
$730$	−15.5367	−	17.9827i	−0.575038	−	0.665571i
$731$	−21.6732	−	52.3236i	−0.801610	−	1.93526i
$732$	1.21383	−	4.74980i	0.0448644	−	0.175558i
$733$	2.36554	−	5.71091i	0.0873731	−	0.210937i	−0.874153	−	0.485650i	$-0.838583\pi$
$733$	2.36554	−	5.71091i	0.0873731	−	0.210937i	0.961526	+	0.274713i	$0.0885828\pi$
$734$	24.0025	+	12.0582i	0.885950	+	0.445077i
$735$	16.6574	+	6.20740i	0.614417	+	0.228963i
$736$	0.319490	+	11.2179i	0.0117765	+	0.413497i
$737$		−	51.3525i		−	1.89159i
$738$	−20.0651	+	25.0906i	−0.738605	+	0.923597i
$739$	−43.8964	−	18.1825i	−1.61476	−	0.668854i	−0.621353	−	0.783530i	$-0.713417\pi$
$739$	−43.8964	−	18.1825i	−1.61476	−	0.668854i	−0.993403	+	0.114676i	$0.963417\pi$
$740$	−20.5797	−	3.01966i	−0.756523	−	0.111005i
$741$	1.45949	−	0.432656i	0.0536157	−	0.0158940i
$742$	−1.35454	−	0.273093i	−0.0497267	−	0.0100256i
$743$	−12.6476	−	12.6476i	−0.463994	−	0.463994i	0.435968	−	0.899962i	$-0.356406\pi$
$743$	−12.6476	−	12.6476i	−0.463994	−	0.463994i	−0.899962	+	0.435968i	$0.856406\pi$
$744$	2.94432	−	8.79501i	0.107944	−	0.322441i
$745$	−0.237116	+	0.237116i	−0.00868727	+	0.00868727i
$746$	6.12037	+	0.446630i	0.224083	+	0.0163523i
$747$	−47.5161	+	8.82737i	−1.73852	+	0.322976i
$748$	60.8987	+	36.3713i	2.22668	+	1.32987i
$749$	−14.9885	+	4.09335i	−0.547669	+	0.149568i
$750$	27.5423	−	6.02452i	1.00570	−	0.219984i
$751$			17.4670i			0.637379i	0.947859	+	0.318689i	$0.103243\pi$
$751$			17.4670i			0.637379i	−0.947859	+	0.318689i	$0.896757\pi$
$752$	32.9637	+	9.88638i	1.20206	+	0.360519i
$753$	−34.9204	−	3.66282i	−1.27257	−	0.133481i
$754$	−3.96248	+	1.31248i	−0.144305	+	0.0477977i
$755$	−2.92344	+	7.05780i	−0.106395	+	0.256860i
$756$	−22.8045	+	15.3609i	−0.829391	+	0.558669i
$757$	−25.4033	+	10.5224i	−0.923297	+	0.382442i	−0.793132	−	0.609050i	$-0.791551\pi$
$757$	−25.4033	+	10.5224i	−0.923297	+	0.382442i	−0.130165	+	0.991492i	$0.541551\pi$
$758$	1.99958	−	27.4011i	0.0726280	−	0.995253i
$759$	15.2159	−	12.3269i	0.552302	−	0.447438i
$760$	−1.07298	+	0.188787i	−0.0389211	+	0.00684801i
$761$	13.9226	−	13.9226i	0.504695	−	0.504695i	−0.408198	−	0.912893i	$-0.633843\pi$
$761$	13.9226	−	13.9226i	0.504695	−	0.504695i	0.912893	+	0.408198i	$0.133843\pi$
$762$	−39.4239	+	27.4395i	−1.42818	+	0.994028i
$763$	−19.5581	−	11.1671i	−0.708050	−	0.404275i
$764$	−9.69186	+	7.21161i	−0.350639	+	0.260907i
$765$	−22.5657	−	15.4950i	−0.815866	−	0.560222i
$766$	31.2110	+	15.6796i	1.12770	+	0.566526i
$767$			5.47067i			0.197535i
$768$	−24.4411	+	13.0626i	−0.881944	+	0.471355i
$769$		−	3.65791i		−	0.131908i	−0.997823	−	0.0659538i	$-0.978991\pi$
$769$		−	3.65791i		−	0.131908i	0.997823	−	0.0659538i	$-0.0210090\pi$
$770$	−6.01967	−	30.6791i	−0.216934	−	1.10560i
$771$	−15.8331	+	29.1756i	−0.570215	+	1.05074i
$772$	−6.90483	−	9.27956i	−0.248510	−	0.333979i
$773$	−6.35203	−	15.3352i	−0.228467	−	0.551567i	0.767524	−	0.641020i	$-0.221488\pi$
$773$	−6.35203	−	15.3352i	−0.228467	−	0.551567i	−0.995991	+	0.0894523i	$0.971488\pi$
$774$	−18.6301	−	33.8174i	−0.669645	−	1.21554i
$775$	3.81574	+	3.81574i	0.137065	+	0.137065i
$776$	24.0591	−	4.23309i	0.863671	−	0.151959i
$777$	−7.42984	+	31.6451i	−0.266544	+	1.13526i
$778$	3.74076	+	0.272980i	0.134113	+	0.00978681i
$779$	0.761301	+	1.83794i	0.0272764	+	0.0658511i
$780$	−2.41306	−	16.8190i	−0.0864014	−	0.602216i
$781$	10.4652	−	25.2652i	0.374474	−	0.904061i
$782$	5.48999	+	16.5747i	0.196322	+	0.592710i
$783$	−1.41392	+	4.36100i	−0.0505294	+	0.155849i
$784$	14.4818	−	23.9641i	0.517206	−	0.855861i
$785$	−33.7096			−1.20315
$786$	−40.7849	+	8.92116i	−1.45475	+	0.318207i
$787$	−32.4559	−	13.4437i	−1.15693	−	0.479215i	−0.280076	−	0.959978i	$-0.590360\pi$
$787$	−32.4559	−	13.4437i	−1.15693	−	0.479215i	−0.876851	+	0.480763i	$0.840360\pi$
$788$	37.1665	+	22.1974i	1.32400	+	0.790751i
$789$	−35.7659	+	10.6026i	−1.27330	+	0.377462i
$790$	24.5032	+	1.78811i	0.871785	+	0.0636180i
$791$	1.84133	−	14.5246i	0.0654703	−	0.516434i
$792$	44.0044	+	20.0511i	1.56363	+	0.712486i
$793$	3.34777	−	3.34777i	0.118883	−	0.118883i
$794$	2.00017	+	2.31507i	0.0709834	+	0.0821589i
$795$	−0.266549	−	0.899156i	−0.00945351	−	0.0318898i
$796$	−7.57347	+	51.6149i	−0.268434	+	1.82944i
$797$	16.0003	+	6.62752i	0.566758	+	0.234759i	0.647616	−	0.761967i	$-0.275766\pi$
$797$	16.0003	+	6.62752i	0.566758	+	0.234759i	−0.0808580	+	0.996726i	$0.525766\pi$
$798$	0.151744	+	1.69580i	0.00537168	+	0.0600308i
$799$	53.5430			1.89421
$800$	−0.459030	−	16.1174i	−0.0162292	−	0.569837i
$801$	1.32505	+	0.281062i	0.0468183	+	0.00993085i
$802$	−42.5543	−	21.3782i	−1.50265	−	0.754889i
$803$	60.3457	+	24.9960i	2.12955	+	0.882090i
$804$	30.2425	+	7.72860i	1.06657	+	0.272567i
$805$	3.81581	−	6.68303i	0.134489	−	0.235546i
$806$	6.77768	−	5.85576i	0.238734	−	0.206260i
$807$	31.6381	+	39.0530i	1.11371	+	1.37473i
$808$	13.7142	−	8.72978i	0.482464	−	0.307113i
$809$	32.4343	−	32.4343i	1.14033	−	1.14033i	0.151938	−	0.988390i	$-0.451448\pi$
$809$	32.4343	−	32.4343i	1.14033	−	1.14033i	0.988390	−	0.151938i	$-0.0485515\pi$
$810$	−16.4578	−	8.79697i	−0.578267	−	0.309094i
$811$	2.16179	+	5.21903i	0.0759108	+	0.183265i	0.957280	−	0.289164i	$-0.0933773\pi$
$811$	2.16179	+	5.21903i	0.0759108	+	0.183265i	−0.881369	+	0.472429i	$0.843377\pi$
$812$	−0.563096	−	4.63453i	−0.0197608	−	0.162640i
$813$	−0.720450	+	1.32757i	−0.0252673	+	0.0465600i
$814$	54.2694	−	17.9755i	1.90214	−	0.630041i
$815$			3.36666i			0.117929i
$816$	−30.5851	+	30.3906i	−1.07069	+	1.06388i
$817$	−2.39079			−0.0836432
$818$	3.72191	+	11.2367i	0.130133	+	0.392883i
$819$	−26.5093	+	1.52813i	−0.926310	+	0.0533971i
$820$	21.5309	−	5.42919i	0.751893	−	0.189596i
$821$	14.9620	+	36.1214i	0.522176	+	1.26064i	0.936549	+	0.350537i	$0.114001\pi$
$821$	14.9620	+	36.1214i	0.522176	+	1.26064i	−0.414373	+	0.910107i	$0.635999\pi$
$822$	0.227463	−	1.26906i	0.00793369	−	0.0442637i
$823$	11.5664	+	11.5664i	0.403180	+	0.403180i	0.879352	−	0.476172i	$-0.157976\pi$
$823$	11.5664	+	11.5664i	0.403180	+	0.403180i	−0.476172	+	0.879352i	$0.657976\pi$
$824$	−24.1873	+	34.5158i	−0.842603	+	1.20242i
$825$	−21.8616	+	17.7108i	−0.761123	+	0.616612i
$826$	−5.99798	−	1.20927i	−0.208696	−	0.0420759i
$827$	−19.5130	+	8.08255i	−0.678533	+	0.281058i	−0.695214	−	0.718803i	$-0.744690\pi$
$827$	−19.5130	+	8.08255i	−0.678533	+	0.281058i	0.0166804	+	0.999861i	$0.494690\pi$
$828$	4.96956	+	10.8162i	0.172704	+	0.375888i
$829$	−10.7307	+	25.9062i	−0.372693	+	0.899761i	0.620599	+	0.784128i	$0.286889\pi$
$829$	−10.7307	+	25.9062i	−0.372693	+	0.899761i	−0.993292	+	0.115632i	$0.963111\pi$
$830$	29.8483	+	14.9950i	1.03605	+	0.520484i
$831$	4.42374	−	42.1748i	0.153458	−	1.46303i
$832$	−26.7369	−	1.18716i	−0.926934	−	0.0411575i
$833$	10.8707	−	42.1853i	0.376646	−	1.46163i
$834$	−6.37640	−	4.08755i	−0.220797	−	0.141540i
$835$	−3.89088	−	1.61165i	−0.134649	−	0.0557736i
$836$	2.40231	−	1.78754i	0.0830858	−	0.0618232i
$837$	−0.778047	−	9.80655i	−0.0268932	−	0.338964i
$838$	−37.5370	−	43.4467i	−1.29669	−	1.50084i
$839$	−16.0894	+	16.0894i	−0.555469	+	0.555469i	−0.928014	−	0.372545i	$-0.878485\pi$
$839$	−16.0894	+	16.0894i	−0.555469	+	0.555469i	0.372545	+	0.928014i	$0.378485\pi$
$840$	18.9735	+	1.07212i	0.654648	+	0.0369916i
$841$	19.9557	+	19.9557i	0.688126	+	0.688126i
$842$	1.96784	−	26.9662i	0.0678164	−	0.929318i
$843$	−21.3211	+	6.32049i	−0.734337	+	0.217689i
$844$	10.2634	−	2.58801i	0.353282	−	0.0890828i
$845$	−1.01460	+	2.44945i	−0.0349032	+	0.0842637i
$846$	36.2779	−	4.03747i	1.24726	−	0.138811i
$847$	34.8095	+	44.9167i	1.19607	+	1.54335i
$848$	−1.46963	+	0.149411i	−0.0504671	+	0.00513080i
$849$	−2.98337	+	28.4427i	−0.102389	+	0.976151i
$850$	−7.88780	−	23.8139i	−0.270549	−	0.816809i
$851$	13.0010	+	5.38519i	0.445668	+	0.184602i
$852$	13.3042	+	9.96561i	0.455794	+	0.341416i
$853$	17.0508	+	41.1643i	0.583808	+	1.40944i	0.889336	+	0.457254i	$0.151167\pi$
$853$	17.0508	+	41.1643i	0.583808	+	1.40944i	−0.305528	+	0.952183i	$0.598833\pi$
$854$	2.93044	+	4.41046i	0.100278	+	0.150923i
$855$	−0.968860	+	0.629767i	−0.0331343	+	0.0215376i
$856$	−14.0122	+	8.91947i	−0.478927	+	0.304861i
$857$	−4.90071	+	4.90071i	−0.167405	+	0.167405i	−0.785838	−	0.618433i	$-0.787768\pi$
$857$	−4.90071	+	4.90071i	−0.167405	+	0.167405i	0.618433	+	0.785838i	$0.287768\pi$
$858$	26.6782	+	38.3301i	0.910779	+	1.30857i
$859$	−18.9512	+	7.84983i	−0.646605	+	0.267833i	−0.681790	−	0.731548i	$-0.738798\pi$
$859$	−18.9512	+	7.84983i	−0.646605	+	0.267833i	0.0351846	+	0.999381i	$0.488798\pi$
$860$	−3.87407	+	26.4027i	−0.132105	+	0.900324i
$861$	−5.60010	−	34.2463i	−0.190851	−	1.16711i
$862$	−39.6846	−	19.9365i	−1.35166	−	0.679039i
$863$			7.63410i			0.259868i	0.991523	+	0.129934i	$0.0414765\pi$
$863$			7.63410i			0.259868i	−0.991523	+	0.129934i	$0.958523\pi$
$864$	−18.4312	+	22.8974i	−0.627043	+	0.778984i
$865$	−15.1160			−0.513959
$866$	3.42281	+	1.71953i	0.116312	+	0.0584319i
$867$	−17.9520	+	33.0802i	−0.609683	+	1.12346i
$868$	4.92200	+	8.72536i	0.167064	+	0.296158i
$869$	−62.3861	+	25.8412i	−2.11630	+	0.876602i
$870$	2.60069	−	1.81011i	0.0881717	−	0.0613686i
$871$	21.3156	+	21.3156i	0.722253	+	0.722253i
$872$	−23.5039	−	5.21981i	−0.795944	−	0.176765i
$873$	21.7244	−	14.1210i	0.735259	−	0.477925i
$874$	0.735117	+	0.0536447i	0.0248657	+	0.00181456i
$875$	−15.0995	+	26.4454i	−0.510456	+	0.894017i
$876$	−23.8027	+	31.7769i	−0.804220	+	1.07364i
$877$	14.3121	−	34.5524i	0.483285	−	1.16675i	−0.474755	−	0.880118i	$-0.657463\pi$
$877$	14.3121	−	34.5524i	0.483285	−	1.16675i	0.958040	−	0.286635i	$-0.0925365\pi$
$878$	−29.1564	+	9.65740i	−0.983982	+	0.325921i
$879$	−8.41305	−	0.882450i	−0.283765	−	0.0297643i
$880$	−15.8479	−	29.4265i	−0.534233	−	0.991967i
$881$		−	2.57815i		−	0.0868600i	−0.999056	−	0.0434300i	$-0.986171\pi$
$881$		−	2.57815i		−	0.0868600i	0.999056	−	0.0434300i	$-0.0138285\pi$
$882$	4.18436	−	29.4022i	0.140895	−	0.990025i
$883$	10.9825	−	26.5140i	0.369590	−	0.892269i	−0.624228	−	0.781243i	$-0.714586\pi$
$883$	10.9825	−	26.5140i	0.369590	−	0.892269i	0.993817	−	0.111026i	$-0.0354138\pi$
$884$	−40.3753	+	10.1810i	−1.35797	+	0.342422i
$885$	−1.18029	−	3.98151i	−0.0396751	−	0.133837i
$886$	48.0324	+	3.50514i	1.61368	+	0.117757i
$887$	26.9989	+	26.9989i	0.906534	+	0.906534i	0.995991	−	0.0894564i	$-0.0285130\pi$
$887$	26.9989	+	26.9989i	0.906534	+	0.906534i	−0.0894564	+	0.995991i	$0.528513\pi$
$888$	2.41854	+	34.6657i	0.0811610	+	1.16330i
$889$	6.52499	−	51.4696i	0.218841	−	1.72624i
$890$	−0.612055	−	0.708415i	−0.0205161	−	0.0237461i
$891$	51.2743	+	1.29930i	1.71775	+	0.0435282i
$892$	11.1995	−	8.33343i	0.374987	−	0.279024i
$893$	0.864970	−	2.08822i	0.0289451	−	0.0698797i
$894$	0.471643	+	0.302344i	0.0157741	+	0.0101119i
$895$		−	26.3614i		−	0.881164i
$896$	7.21167	−	29.0515i	0.240925	−	0.970544i
$897$	−1.19917	+	11.4326i	−0.0400392	+	0.381723i
$898$	−9.58208	+	19.0736i	−0.319758	+	0.636495i
$899$	1.54320	+	0.639212i	0.0514684	+	0.0213189i
$900$	−7.14007	−	15.5402i	−0.238002	−	0.518008i
$901$	−2.12333	+	0.879514i	−0.0707385	+	0.0293009i
$902$	−46.1813	+	39.8996i	−1.53767	+	1.32851i
$903$	40.5991	+	9.53211i	1.35105	+	0.317209i
$904$	−2.71219	−	15.4149i	−0.0902061	−	0.512693i
$905$	−4.68693	+	4.68693i	−0.155799	+	0.155799i
$906$	12.5626	+	2.25168i	0.417364	+	0.0748070i
$907$	16.1959	−	6.70857i	0.537777	−	0.222754i	−0.0972287	−	0.995262i	$-0.530998\pi$
$907$	16.1959	−	6.70857i	0.537777	−	0.222754i	0.635005	+	0.772508i	$0.280998\pi$
$908$	−5.06599	−	20.0905i	−0.168121	−	0.666728i
$909$	9.76059	−	14.2146i	0.323738	−	0.471469i
$910$	15.2331	+	10.2357i	0.504972	+	0.339311i
$911$	48.7219			1.61423			0.807115	−	0.590395i	$-0.201028\pi$
$911$	48.7219			1.61423			0.807115	+	0.590395i	$0.201028\pi$
$912$	0.691167	+	1.68380i	0.0228868	+	0.0557561i
$913$	−91.8088			−3.03843
$914$	−11.3704	−	34.3280i	−0.376099	−	1.13547i
$915$	−1.71420	+	3.15876i	−0.0566697	+	0.104425i
$916$	35.9479	+	21.4696i	1.18775	+	0.709376i
$917$	22.3595	−	39.1605i	0.738375	−	1.29319i
$918$	−17.2332	+	42.3608i	−0.568779	+	1.39811i
$919$	20.3926	+	20.3926i	0.672689	+	0.672689i	0.958335	−	0.285647i	$-0.0922083\pi$
$919$	20.3926	+	20.3926i	0.672689	+	0.672689i	−0.285647	+	0.958335i	$0.592208\pi$
$920$	1.78362	−	8.03134i	0.0588042	−	0.264785i
$921$	29.9914	−	24.2971i	0.988252	−	0.800616i
$922$	31.2472	−	26.9969i	1.02907	−	0.889095i
$923$	6.14327	+	14.8312i	0.202208	+	0.488173i
$924$	−47.9217	+	20.7769i	−1.57651	+	0.683511i
$925$	−18.6793	−	7.73722i	−0.614172	−	0.254398i
$926$	15.4742	−	30.8022i	0.508513	−	1.01222i
$927$	−9.27592	+	43.7306i	−0.304661	+	1.43630i
$928$	−2.04045	−	4.55480i	−0.0669811	−	0.149519i
$929$	−24.7324			−0.811445			−0.405723	−	0.913996i	$-0.632980\pi$
$929$	−24.7324			−0.811445			−0.405723	+	0.913996i	$0.632980\pi$
$930$	−3.66937	+	5.72406i	−0.120323	+	0.187699i
$931$	−1.46965	−	1.10546i	−0.0481659	−	0.0362299i
$932$	−47.0238	−	6.89981i	−1.54032	−	0.226011i
$933$	9.43258	−	2.79622i	0.308809	−	0.0915443i
$934$	4.31395	−	3.72716i	0.141157	−	0.121956i
$935$	−36.7697	−	36.7697i	−1.20250	−	1.20250i
$936$	−26.5885	+	9.94263i	−0.869072	+	0.324985i
$937$	36.0250	−	36.0250i	1.17688	−	1.17688i	0.196351	−	0.980534i	$-0.437091\pi$
$937$	36.0250	−	36.0250i	1.17688	−	1.17688i	0.980534	−	0.196351i	$-0.0629092\pi$
$938$	−28.0819	+	18.6585i	−0.916908	+	0.609220i
$939$	16.5031	−	4.89225i	0.538560	−	0.159652i
$940$	−21.6597	−	12.9361i	−0.706461	−	0.421929i
$941$	−3.07963	+	7.43488i	−0.100393	+	0.242370i	−0.966094	−	0.258192i	$-0.916873\pi$
$941$	−3.07963	+	7.43488i	−0.100393	+	0.242370i	0.865701	+	0.500562i	$0.166873\pi$
$942$	12.0342	+	55.0168i	0.392096	+	1.79254i
$943$	−15.0226			−0.489204
$944$	−6.50758	+	0.661600i	−0.211804	+	0.0215333i
$945$	18.9636	−	6.83151i	0.616884	−	0.222229i
$946$	−23.0617	−	69.6250i	−0.749800	−	2.26370i
$947$	−3.56819	−	1.47799i	−0.115951	−	0.0480284i	0.323954	−	0.946073i	$-0.394988\pi$
$947$	−3.56819	−	1.47799i	−0.115951	−	0.0480284i	−0.439905	+	0.898045i	$0.644988\pi$
$948$	−5.82923	−	40.6296i	−0.189325	−	1.31959i
$949$	−35.4240	+	14.6731i	−1.14991	+	0.476310i
$950$	−1.05619	−	0.0770747i	−0.0342672	−	0.00250063i
$951$	−19.0789	−	23.5503i	−0.618675	−	0.763670i
$952$	−2.23746	−	46.5174i	−0.0725165	−	1.50764i
$953$	16.2966	+	16.2966i	0.527900	+	0.527900i	0.919946	−	0.392046i	$-0.128233\pi$
$953$	16.2966	+	16.2966i	0.527900	+	0.527900i	−0.392046	+	0.919946i	$0.628233\pi$
$954$	−1.37234	+	0.756025i	−0.0444311	+	0.0244772i
$955$	8.18194	−	3.38907i	0.264762	−	0.109668i
$956$	1.72939	+	2.32417i	0.0559324	+	0.0751690i
$957$	−4.15393	+	7.65445i	−0.134278	+	0.247433i
$958$	32.2518	+	16.2025i	1.04201	+	0.523478i
$959$	0.853047	+	1.10074i	0.0275463	+	0.0355446i
$960$	19.7150	−	4.90444i	0.636299	−	0.158290i
$961$	27.4158			0.884380
$962$	−15.0651	+	29.9878i	−0.485717	+	0.966844i
$963$	−9.97268	+	14.5235i	−0.321365	+	0.468013i
$964$	24.9944	+	33.5906i	0.805016	+	1.08188i
$965$	3.24490	+	7.83388i	0.104457	+	0.252182i
$966$	−12.2695	−	3.84189i	−0.394764	−	0.123611i
$967$	−23.5368	+	23.5368i	−0.756892	+	0.756892i	−0.975756	−	0.218863i	$-0.929765\pi$
$967$	−23.5368	+	23.5368i	−0.756892	+	0.756892i	0.218863	+	0.975756i	$0.429765\pi$
$968$	49.7503	+	34.8630i	1.59904	+	1.12054i
$969$	1.78259	+	2.20037i	0.0572651	+	0.0706860i
$970$	−17.8608	−	1.30338i	−0.573476	−	0.0418490i
$971$	13.6869	−	5.66931i	0.439234	−	0.181937i	−0.152097	−	0.988366i	$-0.548603\pi$
$971$	13.6869	−	5.66931i	0.439234	−	0.181937i	0.591331	+	0.806429i	$0.298603\pi$
$972$	−8.48201	+	30.0009i	−0.272061	+	0.962280i
$973$	7.89192	−	2.15528i	0.253003	−	0.0690950i
$974$	−14.2893	+	4.73299i	−0.457857	+	0.151655i
$975$	1.72292	−	16.4259i	0.0551777	−	0.526050i
$976$	4.38717	+	3.57744i	0.140430	+	0.114511i
$977$	11.0164			0.352445			0.176222	−	0.984350i	$-0.443612\pi$
$977$	11.0164			0.352445			0.176222	+	0.984350i	$0.443612\pi$
$978$	5.49467	−	1.20189i	0.175700	−	0.0384321i
$979$	2.37727	+	0.984697i	0.0759779	+	0.0314711i
$980$	−14.5895	+	14.4388i	−0.466046	+	0.461230i
$981$	−25.1075	+	4.66437i	−0.801620	+	0.148922i
$982$	−2.89331	+	39.6483i	−0.0923293	+	1.26523i
$983$	−25.5714	−	25.5714i	−0.815602	−	0.815602i	0.169865	−	0.985467i	$-0.445667\pi$
$983$	−25.5714	−	25.5714i	−0.815602	−	0.815602i	−0.985467	+	0.169865i	$0.945667\pi$
$984$	−16.5474	−	33.2021i	−0.527511	−	1.05844i
$985$	−22.4406	−	22.4406i	−0.715016	−	0.715016i
$986$	−5.07657	−	5.87582i	−0.161671	−	0.187124i
$987$	−23.0142	+	32.0124i	−0.732551	+	1.01897i
$988$	−0.255185	+	1.73914i	−0.00811851	+	0.0553295i
$989$	6.90893	−	16.6796i	0.219691	−	0.530381i
$990$	−27.6859	−	22.1405i	−0.879914	−	0.703672i
$991$	−36.3059			−1.15330			−0.576648	−	0.816993i	$-0.695640\pi$
$991$	−36.3059			−1.15330			−0.576648	+	0.816993i	$0.695640\pi$
$992$	7.78533	+	7.35415i	0.247184	+	0.233494i
$993$	3.88301	−	37.0196i	0.123224	−	1.17478i
$994$	−17.6186	+	3.45703i	−0.558829	+	0.109650i
$995$	14.6351	−	35.3322i	0.463964	−	1.12011i
$996$	13.8173	−	54.0681i	0.437818	−	1.71321i
$997$	40.8787	−	16.9325i	1.29464	−	0.536258i	0.374276	−	0.927318i	$-0.377891\pi$
$997$	40.8787	−	16.9325i	1.29464	−	0.536258i	0.920365	+	0.391060i	$0.127891\pi$
$998$	25.4784	−	22.0128i	0.806505	−	0.696802i
$999$	16.7540	+	32.8300i	0.530072	+	1.03870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bo.a.125.18	yes	496
3.2	odd	2	inner	672.2.bo.a.125.108	yes	496
7.6	odd	2	inner	672.2.bo.a.125.17	✓	496
21.20	even	2	inner	672.2.bo.a.125.107	yes	496
32.21	even	8	inner	672.2.bo.a.629.107	yes	496
96.53	odd	8	inner	672.2.bo.a.629.17	yes	496
224.181	odd	8	inner	672.2.bo.a.629.108	yes	496
672.629	even	8	inner	672.2.bo.a.629.18	yes	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bo.a.125.17	✓	496	7.6	odd	2	inner
672.2.bo.a.125.18	yes	496	1.1	even	1	trivial
672.2.bo.a.125.107	yes	496	21.20	even	2	inner
672.2.bo.a.125.108	yes	496	3.2	odd	2	inner
672.2.bo.a.629.17	yes	496	96.53	odd	8	inner
672.2.bo.a.629.18	yes	496	672.629	even	8	inner
672.2.bo.a.629.107	yes	496	32.21	even	8	inner
672.2.bo.a.629.108	yes	496	224.181	odd	8	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bo (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26371 - 0.634854i) q^{2} +(0.826142 - 1.52233i) q^{3} +(1.19392 + 1.60454i) q^{4} +(-0.561080 - 1.35457i) q^{5} +(-2.01046 + 1.39930i) q^{6} +(0.332748 - 2.62474i) q^{7} +(-0.490121 - 2.78564i) q^{8} +(-1.63498 - 2.51532i) q^{9} +O(q^{10})\)	\(q+(-1.26371 - 0.634854i) q^{2} +(0.826142 - 1.52233i) q^{3} +(1.19392 + 1.60454i) q^{4} +(-0.561080 - 1.35457i) q^{5} +(-2.01046 + 1.39930i) q^{6} +(0.332748 - 2.62474i) q^{7} +(-0.490121 - 2.78564i) q^{8} +(-1.63498 - 2.51532i) q^{9} +(-0.150910 + 2.06798i) q^{10} +(-2.18090 - 5.26516i) q^{11} +(3.42899 - 0.491966i) q^{12} +(3.09075 + 1.28023i) q^{13} +(-2.08682 + 3.10567i) q^{14} +(-2.52563 - 0.264915i) q^{15} +(-1.14910 + 3.83139i) q^{16} +6.22334i q^{17} +(0.469279 + 4.21661i) q^{18} +(0.242716 + 0.100536i) q^{19} +(1.50357 - 2.51752i) q^{20} +(-3.72083 - 2.67496i) q^{21} +(-0.586582 + 8.03819i) q^{22} +(-1.40280 + 1.40280i) q^{23} +(-4.64557 - 1.55520i) q^{24} +(2.01549 - 2.01549i) q^{25} +(-3.09305 - 3.58001i) q^{26} +(-5.17987 + 0.410969i) q^{27} +(4.60878 - 2.59983i) q^{28} +(0.337636 - 0.815124i) q^{29} +(3.02348 + 1.93818i) q^{30} +1.89320i q^{31} +(3.88450 - 4.11225i) q^{32} +(-9.81705 - 1.02972i) q^{33} +(3.95091 - 7.86449i) q^{34} +(-3.74209 + 1.02196i) q^{35} +(2.08390 - 5.62649i) q^{36} +(-2.71449 - 6.55336i) q^{37} +(-0.242896 - 0.281138i) q^{38} +(4.50233 - 3.64749i) q^{39} +(-3.49833 + 2.22687i) q^{40} +(5.35450 + 5.35450i) q^{41} +(3.00384 + 5.74256i) q^{42} +(-8.40764 + 3.48256i) q^{43} +(5.84434 - 9.78553i) q^{44} +(-2.48981 + 3.62598i) q^{45} +(2.66331 - 0.882161i) q^{46} -8.60357i q^{47} +(4.88332 + 4.91458i) q^{48} +(-6.77856 - 1.74676i) q^{49} +(-3.82654 + 1.26745i) q^{50} +(9.47398 + 5.14136i) q^{51} +(1.63593 + 6.48772i) q^{52} +(0.141325 + 0.341189i) q^{53} +(6.80676 + 2.76912i) q^{54} +(-5.90835 + 5.90835i) q^{55} +(-7.47467 + 0.359527i) q^{56} +(0.353567 - 0.286437i) q^{57} +(-0.944158 + 0.815731i) q^{58} +(0.625795 + 1.51080i) q^{59} +(-2.59034 - 4.36876i) q^{60} +(0.541579 - 1.30749i) q^{61} +(1.20191 - 2.39246i) q^{62} +(-7.14611 + 3.45444i) q^{63} +(-7.51956 + 2.73060i) q^{64} -4.90493i q^{65} +(11.7522 + 7.53365i) q^{66} +(8.32493 + 3.44830i) q^{67} +(-9.98560 + 7.43018i) q^{68} +(0.976617 + 3.29445i) q^{69} +(5.37771 + 1.08422i) q^{70} +(3.39310 + 3.39310i) q^{71} +(-6.20544 + 5.78728i) q^{72} +(-8.10438 + 8.10438i) q^{73} +(-0.730098 + 10.0048i) q^{74} +(-1.40316 - 4.73333i) q^{75} +(0.128469 + 0.509480i) q^{76} +(-14.5454 + 3.97233i) q^{77} +(-8.00525 + 1.75105i) q^{78} -11.8488i q^{79} +(5.83461 - 0.593182i) q^{80} +(-3.65368 + 8.22500i) q^{81} +(-3.36721 - 10.1659i) q^{82} +(6.16492 - 14.8834i) q^{83} +(-0.150294 - 9.16392i) q^{84} +(8.42993 - 3.49179i) q^{85} +(12.8357 + 0.936680i) q^{86} +(-0.961954 - 1.18740i) q^{87} +(-13.5979 + 8.65577i) q^{88} +(-0.319265 + 0.319265i) q^{89} +(5.44837 - 3.00152i) q^{90} +(4.38871 - 7.68643i) q^{91} +(-3.92570 - 0.576018i) q^{92} +(2.88208 + 1.56405i) q^{93} +(-5.46201 + 10.8724i) q^{94} -0.385184i q^{95} +(-3.05106 - 9.31080i) q^{96} +8.63683i q^{97} +(7.45719 + 6.51078i) q^{98} +(-9.67784 + 14.0941i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more