LMFDB - Embedded newform 462.2.w.a.29.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(29,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

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

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

chi := DirichletCharacter("462.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.w (of order $10$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.9
Character	$\chi$	$=$	462.29
Dual form			462.2.w.a.239.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.856700 + 1.50535i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.72358 + 2.37230i) q^{5} +(0.191735 - 1.72141i) q^{6} +(0.951057 - 0.309017i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.53213 + 2.57926i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.856700 + 1.50535i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.72358 + 2.37230i) q^{5} +(0.191735 - 1.72141i) q^{6} +(0.951057 - 0.309017i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.53213 + 2.57926i) q^{9} -2.93233i q^{10} +(3.22005 - 0.794517i) q^{11} +(-1.16693 + 1.27995i) q^{12} +(3.69192 - 5.08149i) q^{13} +(-0.951057 - 0.309017i) q^{14} +(-2.09455 + 4.62694i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.68167 + 3.40143i) q^{17} +(2.75557 - 1.18610i) q^{18} +(0.848781 + 0.275786i) q^{19} +(-1.72358 + 2.37230i) q^{20} +(1.27995 + 1.16693i) q^{21} +(-3.07208 - 1.24992i) q^{22} +5.08427i q^{23} +(1.69640 - 0.349593i) q^{24} +(-1.11202 + 3.42243i) q^{25} +(-5.97365 + 1.94096i) q^{26} +(-5.19525 - 0.0967366i) q^{27} +(0.587785 + 0.809017i) q^{28} +(-1.40310 - 4.31831i) q^{29} +(4.41417 - 2.51213i) q^{30} +(-5.16322 - 3.75130i) q^{31} +1.00000 q^{32} +(3.95464 + 4.16663i) q^{33} +5.78686 q^{34} +(2.37230 + 1.72358i) q^{35} +(-2.92648 - 0.660108i) q^{36} +(0.894385 + 2.75263i) q^{37} +(-0.524576 - 0.722016i) q^{38} +(10.8123 + 1.20430i) q^{39} +(2.78881 - 0.906140i) q^{40} +(-3.18548 + 9.80390i) q^{41} +(-0.349593 - 1.69640i) q^{42} -2.94834i q^{43} +(1.75068 + 2.81693i) q^{44} +(-8.75954 + 0.810877i) q^{45} +(2.98846 - 4.11326i) q^{46} +(-3.42626 - 1.11326i) q^{47} +(-1.57790 - 0.714295i) q^{48} +(0.809017 - 0.587785i) q^{49} +(2.91130 - 2.11518i) q^{50} +(-9.13112 - 4.13352i) q^{51} +(5.97365 + 1.94096i) q^{52} +(4.17305 - 5.74371i) q^{53} +(4.14619 + 3.13195i) q^{54} +(7.43486 + 6.26953i) q^{55} -1.00000i q^{56} +(0.311998 + 1.51397i) q^{57} +(-1.40310 + 4.31831i) q^{58} +(10.4716 - 3.40244i) q^{59} +(-5.04773 - 0.562231i) q^{60} +(-2.22985 - 3.06912i) q^{61} +(1.97217 + 6.06973i) q^{62} +(-0.660108 + 2.92648i) q^{63} +(-0.809017 - 0.587785i) q^{64} +18.4182 q^{65} +(-0.750289 - 5.69535i) q^{66} +4.70333 q^{67} +(-4.68167 - 3.40143i) q^{68} +(-7.65359 + 4.35570i) q^{69} +(-0.906140 - 2.78881i) q^{70} +(-0.962724 - 1.32508i) q^{71} +(1.97957 + 2.25418i) q^{72} +(-8.25571 + 2.68244i) q^{73} +(0.894385 - 2.75263i) q^{74} +(-6.10461 + 1.25803i) q^{75} +0.892461i q^{76} +(2.81693 - 1.75068i) q^{77} +(-8.03944 - 7.32959i) q^{78} +(7.37157 - 10.1461i) q^{79} +(-2.78881 - 0.906140i) q^{80} +(-4.30515 - 7.90352i) q^{81} +(8.33969 - 6.05914i) q^{82} +(2.82854 - 2.05506i) q^{83} +(-0.714295 + 1.57790i) q^{84} +(-16.1385 - 5.24371i) q^{85} +(-1.73299 + 2.38526i) q^{86} +(5.29851 - 5.81165i) q^{87} +(0.239420 - 3.30797i) q^{88} +1.62773i q^{89} +(7.56324 + 4.49271i) q^{90} +(1.94096 - 5.97365i) q^{91} +(-4.83543 + 1.57113i) q^{92} +(1.22367 - 10.9862i) q^{93} +(2.11755 + 2.91455i) q^{94} +(0.808695 + 2.48891i) q^{95} +(0.856700 + 1.50535i) q^{96} +(-15.5678 - 11.3107i) q^{97} -1.00000 q^{98} +(-2.88428 + 9.52265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) $ 48 * q - 12 * q^2 - 4 * q^3 - 12 * q^4 + 6 * q^6 - 12 * q^8 + 10 * q^9	$ 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9} - 8 q^{11} + 6 q^{12} + 36 q^{15} - 12 q^{16} - 24 q^{17} + 30 q^{19} - 8 q^{22} - 4 q^{24} + 18 q^{25} - 20 q^{26} - 22 q^{27} + 8 q^{29} - 24 q^{30} - 32 q^{31} + 48 q^{32} - 14 q^{33} - 4 q^{34} + 6 q^{35} - 10 q^{36} - 20 q^{37} + 20 q^{38} - 6 q^{39} + 22 q^{44} + 12 q^{45} + 20 q^{46} + 20 q^{47} - 4 q^{48} + 12 q^{49} + 28 q^{50} + 8 q^{51} + 20 q^{52} + 20 q^{53} + 18 q^{54} + 16 q^{55} - 2 q^{57} + 8 q^{58} + 30 q^{59} - 4 q^{60} - 20 q^{61} + 8 q^{62} + 4 q^{63} - 12 q^{64} - 14 q^{66} + 36 q^{67} - 24 q^{68} - 70 q^{69} - 4 q^{70} + 10 q^{72} - 20 q^{73} - 20 q^{74} - 30 q^{75} - 16 q^{77} - 16 q^{78} - 20 q^{79} + 26 q^{81} - 10 q^{82} - 46 q^{83} - 10 q^{84} + 10 q^{85} - 30 q^{86} + 8 q^{87} - 8 q^{88} - 38 q^{90} - 36 q^{91} + 10 q^{92} - 36 q^{93} + 50 q^{95} - 4 q^{96} - 2 q^{97} - 48 q^{98} + 70 q^{99}+O(q^{100}) $ 48 * q - 12 * q^2 - 4 * q^3 - 12 * q^4 + 6 * q^6 - 12 * q^8 + 10 * q^9 - 8 * q^11 + 6 * q^12 + 36 * q^15 - 12 * q^16 - 24 * q^17 + 30 * q^19 - 8 * q^22 - 4 * q^24 + 18 * q^25 - 20 * q^26 - 22 * q^27 + 8 * q^29 - 24 * q^30 - 32 * q^31 + 48 * q^32 - 14 * q^33 - 4 * q^34 + 6 * q^35 - 10 * q^36 - 20 * q^37 + 20 * q^38 - 6 * q^39 + 22 * q^44 + 12 * q^45 + 20 * q^46 + 20 * q^47 - 4 * q^48 + 12 * q^49 + 28 * q^50 + 8 * q^51 + 20 * q^52 + 20 * q^53 + 18 * q^54 + 16 * q^55 - 2 * q^57 + 8 * q^58 + 30 * q^59 - 4 * q^60 - 20 * q^61 + 8 * q^62 + 4 * q^63 - 12 * q^64 - 14 * q^66 + 36 * q^67 - 24 * q^68 - 70 * q^69 - 4 * q^70 + 10 * q^72 - 20 * q^73 - 20 * q^74 - 30 * q^75 - 16 * q^77 - 16 * q^78 - 20 * q^79 + 26 * q^81 - 10 * q^82 - 46 * q^83 - 10 * q^84 + 10 * q^85 - 30 * q^86 + 8 * q^87 - 8 * q^88 - 38 * q^90 - 36 * q^91 + 10 * q^92 - 36 * q^93 + 50 * q^95 - 4 * q^96 - 2 * q^97 - 48 * q^98 + 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	0.856700	+	1.50535i	0.494616	+	0.869112i
$3$	0.856700	+	1.50535i	0.494616	+	0.869112i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.72358	+	2.37230i	0.770809	+	1.06093i	0.996237	+	0.0866673i	$0.0276217\pi$
$5$	1.72358	+	2.37230i	0.770809	+	1.06093i	−0.225429	+	0.974260i	$0.572378\pi$
$6$	0.191735	−	1.72141i	0.0782756	−	0.702761i
$7$	0.951057	−	0.309017i	0.359466	−	0.116797i
$7$	0.951057	−	0.309017i	0.359466	−	0.116797i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−1.53213	+	2.57926i	−0.510710	+	0.859753i
$10$		−	2.93233i		−	0.927284i
$11$	3.22005	−	0.794517i	0.970883	−	0.239556i
$11$	3.22005	−	0.794517i	0.970883	−	0.239556i
$12$	−1.16693	+	1.27995i	−0.336865	+	0.369489i
$13$	3.69192	−	5.08149i	1.02395	−	1.40935i	0.114560	−	0.993416i	$-0.463454\pi$
$13$	3.69192	−	5.08149i	1.02395	−	1.40935i	0.909394	−	0.415936i	$-0.136546\pi$
$14$	−0.951057	−	0.309017i	−0.254181	−	0.0825883i
$15$	−2.09455	+	4.62694i	−0.540810	+	1.19467i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−4.68167	+	3.40143i	−1.13547	+	0.824968i	−0.986482	−	0.163870i	$-0.947602\pi$
$17$	−4.68167	+	3.40143i	−1.13547	+	0.824968i	−0.148990	+	0.988839i	$0.547602\pi$
$18$	2.75557	−	1.18610i	0.649494	−	0.279566i
$19$	0.848781	+	0.275786i	0.194724	+	0.0632696i	0.404755	−	0.914425i	$-0.367357\pi$
$19$	0.848781	+	0.275786i	0.194724	+	0.0632696i	−0.210032	+	0.977695i	$0.567357\pi$
$20$	−1.72358	+	2.37230i	−0.385404	+	0.530463i
$21$	1.27995	+	1.16693i	0.279307	+	0.254646i
$22$	−3.07208	−	1.24992i	−0.654970	−	0.266484i
$23$			5.08427i			1.06014i	0.847953	+	0.530072i	$0.177835\pi$
$23$			5.08427i			1.06014i	−0.847953	+	0.530072i	$0.822165\pi$
$24$	1.69640	−	0.349593i	0.346277	−	0.0713603i
$25$	−1.11202	+	3.42243i	−0.222403	+	0.684487i
$26$	−5.97365	+	1.94096i	−1.17153	+	0.380653i
$27$	−5.19525	−	0.0967366i	−0.999827	−	0.0186170i
$28$	0.587785	+	0.809017i	0.111081	+	0.152890i
$29$	−1.40310	−	4.31831i	−0.260550	−	0.801890i	−0.992685	−	0.120731i	$-0.961476\pi$
$29$	−1.40310	−	4.31831i	−0.260550	−	0.801890i	0.732135	−	0.681159i	$-0.238524\pi$
$30$	4.41417	−	2.51213i	0.805914	−	0.458649i
$31$	−5.16322	−	3.75130i	−0.927341	−	0.673753i	0.0179990	−	0.999838i	$-0.494270\pi$
$31$	−5.16322	−	3.75130i	−0.927341	−	0.673753i	−0.945340	+	0.326085i	$0.894270\pi$
$32$	1.00000			0.176777
$33$	3.95464	+	4.16663i	0.688415	+	0.725317i
$34$	5.78686			0.992439
$35$	2.37230	+	1.72358i	0.400993	+	0.291338i
$36$	−2.92648	−	0.660108i	−0.487746	−	0.110018i
$37$	0.894385	+	2.75263i	0.147036	+	0.452530i	0.997267	−	0.0738793i	$-0.0235379\pi$
$37$	0.894385	+	2.75263i	0.147036	+	0.452530i	−0.850231	+	0.526409i	$0.823538\pi$
$38$	−0.524576	−	0.722016i	−0.0850974	−	0.117127i
$39$	10.8123	+	1.20430i	1.73135	+	0.192843i
$40$	2.78881	−	0.906140i	0.440950	−	0.143273i
$41$	−3.18548	+	9.80390i	−0.497488	+	1.53111i	0.315554	+	0.948908i	$0.397810\pi$
$41$	−3.18548	+	9.80390i	−0.497488	+	1.53111i	−0.813043	+	0.582204i	$0.802190\pi$
$42$	−0.349593	−	1.69640i	−0.0539433	−	0.261761i
$43$		−	2.94834i		−	0.449618i	−0.974403	−	0.224809i	$-0.927824\pi$
$43$		−	2.94834i		−	0.449618i	0.974403	−	0.224809i	$-0.0721759\pi$
$44$	1.75068	+	2.81693i	0.263925	+	0.424669i
$45$	−8.75954	+	0.810877i	−1.30579	+	0.120878i
$46$	2.98846	−	4.11326i	0.440625	−	0.606468i
$47$	−3.42626	−	1.11326i	−0.499771	−	0.162386i	0.0482740	−	0.998834i	$-0.484628\pi$
$47$	−3.42626	−	1.11326i	−0.499771	−	0.162386i	−0.548045	+	0.836449i	$0.684628\pi$
$48$	−1.57790	−	0.714295i	−0.227751	−	0.103100i
$49$	0.809017	−	0.587785i	0.115574	−	0.0839693i
$50$	2.91130	−	2.11518i	0.411719	−	0.299132i
$51$	−9.13112	−	4.13352i	−1.27861	−	0.578809i
$52$	5.97365	+	1.94096i	0.828396	+	0.269162i
$53$	4.17305	−	5.74371i	0.573212	−	0.788959i	−0.419719	−	0.907654i	$-0.637871\pi$
$53$	4.17305	−	5.74371i	0.573212	−	0.788959i	0.992931	+	0.118696i	$0.0378712\pi$
$54$	4.14619	+	3.13195i	0.564225	+	0.426205i
$55$	7.43486	+	6.26953i	1.00252	+	0.845384i
$56$		−	1.00000i		−	0.133631i
$57$	0.311998	+	1.51397i	0.0413251	+	0.200531i
$58$	−1.40310	+	4.31831i	−0.184237	+	0.567022i
$59$	10.4716	−	3.40244i	1.36329	−	0.442960i	0.466150	−	0.884706i	$-0.345641\pi$
$59$	10.4716	−	3.40244i	1.36329	−	0.442960i	0.897140	+	0.441746i	$0.145641\pi$
$60$	−5.04773	−	0.562231i	−0.651659	−	0.0725837i
$61$	−2.22985	−	3.06912i	−0.285503	−	0.392961i	0.642044	−	0.766668i	$-0.278087\pi$
$61$	−2.22985	−	3.06912i	−0.285503	−	0.392961i	−0.927547	+	0.373707i	$0.878087\pi$
$62$	1.97217	+	6.06973i	0.250466	+	0.770856i
$63$	−0.660108	+	2.92648i	−0.0831659	+	0.368701i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	18.4182			2.28449
$66$	−0.750289	−	5.69535i	−0.0923542	−	0.701050i
$67$	4.70333			0.574604			0.287302	−	0.957840i	$-0.407242\pi$
$67$	4.70333			0.574604			0.287302	+	0.957840i	$0.407242\pi$
$68$	−4.68167	−	3.40143i	−0.567736	−	0.412484i
$69$	−7.65359	+	4.35570i	−0.921384	+	0.524364i
$70$	−0.906140	−	2.78881i	−0.108304	−	0.333327i
$71$	−0.962724	−	1.32508i	−0.114254	−	0.157258i	0.748060	−	0.663631i	$-0.230986\pi$
$71$	−0.962724	−	1.32508i	−0.114254	−	0.157258i	−0.862314	+	0.506374i	$0.830986\pi$
$72$	1.97957	+	2.25418i	0.233294	+	0.265657i
$73$	−8.25571	+	2.68244i	−0.966258	+	0.313956i	−0.749304	−	0.662226i	$-0.769612\pi$
$73$	−8.25571	+	2.68244i	−0.966258	+	0.313956i	−0.216953	+	0.976182i	$0.569612\pi$
$74$	0.894385	−	2.75263i	0.103970	−	0.319987i
$75$	−6.10461	+	1.25803i	−0.704899	+	0.145265i
$76$			0.892461i			0.102372i
$77$	2.81693	−	1.75068i	0.321019	−	0.199509i
$78$	−8.03944	−	7.32959i	−0.910287	−	0.829913i
$79$	7.37157	−	10.1461i	0.829367	−	1.14153i	−0.158674	−	0.987331i	$-0.550722\pi$
$79$	7.37157	−	10.1461i	0.829367	−	1.14153i	0.988041	−	0.154194i	$-0.0492781\pi$
$80$	−2.78881	−	0.906140i	−0.311799	−	0.101310i
$81$	−4.30515	−	7.90352i	−0.478350	−	0.878169i
$82$	8.33969	−	6.05914i	0.920965	−	0.669120i
$83$	2.82854	−	2.05506i	0.310473	−	0.225572i	−0.421626	−	0.906770i	$-0.638541\pi$
$83$	2.82854	−	2.05506i	0.310473	−	0.225572i	0.732099	+	0.681198i	$0.238541\pi$
$84$	−0.714295	+	1.57790i	−0.0779359	+	0.172164i
$85$	−16.1385	−	5.24371i	−1.75046	−	0.568760i
$86$	−1.73299	+	2.38526i	−0.186873	+	0.257209i
$87$	5.29851	−	5.81165i	0.568060	−	0.623074i
$88$	0.239420	−	3.30797i	0.0255223	−	0.352631i
$89$			1.62773i			0.172539i	0.996272	+	0.0862695i	$0.0274946\pi$
$89$			1.62773i			0.172539i	−0.996272	+	0.0862695i	$0.972505\pi$
$90$	7.56324	+	4.49271i	0.797235	+	0.473574i
$91$	1.94096	−	5.97365i	0.203468	−	0.626209i
$92$	−4.83543	+	1.57113i	−0.504129	+	0.163801i
$93$	1.22367	−	10.9862i	0.126889	−	1.13921i
$94$	2.11755	+	2.91455i	0.218408	+	0.300613i
$95$	0.808695	+	2.48891i	0.0829703	+	0.255356i
$96$	0.856700	+	1.50535i	0.0874366	+	0.153639i
$97$	−15.5678	−	11.3107i	−1.58067	−	1.14843i	−0.915920	−	0.401361i	$-0.868537\pi$
$97$	−15.5678	−	11.3107i	−1.58067	−	1.14843i	−0.664751	−	0.747065i	$-0.731463\pi$
$98$	−1.00000			−0.101015
$99$	−2.88428	+	9.52265i	−0.289881	+	0.957063i
$100$	−3.59856			−0.359856
$101$	−11.8029	−	8.57532i	−1.17443	−	0.853276i	−0.182901	−	0.983131i	$-0.558549\pi$
$101$	−11.8029	−	8.57532i	−1.17443	−	0.853276i	−0.991533	+	0.129855i	$0.958549\pi$
$102$	4.95760	+	8.71123i	0.490876	+	0.862540i
$103$	5.65259	+	17.3969i	0.556967	+	1.71417i	0.690693	+	0.723148i	$0.257306\pi$
$103$	5.65259	+	17.3969i	0.556967	+	1.71417i	−0.133726	+	0.991018i	$0.542694\pi$
$104$	−3.69192	−	5.08149i	−0.362023	−	0.498281i
$105$	−0.562231	+	5.04773i	−0.0548681	+	0.492608i
$106$	−6.75213	+	2.19390i	−0.655825	+	0.213090i
$107$	0.939693	−	2.89208i	0.0908435	−	0.279588i	−0.895305	−	0.445454i	$-0.853042\pi$
$107$	0.939693	−	2.89208i	0.0908435	−	0.279588i	0.986148	+	0.165867i	$0.0530421\pi$
$108$	−1.51342	−	4.97087i	−0.145629	−	0.478322i
$109$			3.76390i			0.360516i	0.983619	+	0.180258i	$0.0576933\pi$
$109$			3.76390i			0.360516i	−0.983619	+	0.180258i	$0.942307\pi$
$110$	−2.32979	−	9.44226i	−0.222136	−	0.900284i
$111$	−3.37745	+	3.70454i	−0.320573	+	0.351619i
$112$	−0.587785	+	0.809017i	−0.0555405	+	0.0764449i
$113$	−8.34635	−	2.71189i	−0.785158	−	0.255113i	−0.111117	−	0.993807i	$-0.535443\pi$
$113$	−8.34635	−	2.71189i	−0.785158	−	0.255113i	−0.674041	+	0.738694i	$0.735443\pi$
$114$	0.637480	−	1.40822i	0.0597055	−	0.131892i
$115$	−12.0614	+	8.76315i	−1.12474	+	0.817168i
$116$	3.67337	−	2.66886i	0.341064	−	0.247798i
$117$	7.44998	+	17.3079i	0.688751	+	1.60012i
$118$	−10.4716	−	3.40244i	−0.963992	−	0.313220i
$119$	−3.40143	+	4.68167i	−0.311809	+	0.429168i
$120$	3.75323	+	3.42184i	0.342621	+	0.312369i
$121$	9.73748	−	5.11678i	0.885226	−	0.465161i
$122$			3.79364i			0.343460i
$123$	−17.4873	+	3.60375i	−1.57677	+	0.324939i
$124$	1.97217	−	6.06973i	0.177106	−	0.545078i
$125$	3.90835	−	1.26990i	0.349574	−	0.113583i
$126$	2.25418	−	1.97957i	0.200818	−	0.176354i
$127$	0.158201	+	0.217745i	0.0140381	+	0.0193217i	0.815978	−	0.578082i	$-0.196199\pi$
$127$	0.158201	+	0.217745i	0.0140381	+	0.0193217i	−0.801940	+	0.597404i	$0.796199\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	4.43828	−	2.52585i	0.390769	−	0.222388i
$130$	−14.9006	−	10.8259i	−1.30687	−	0.949497i
$131$	2.61078			0.228105			0.114052	−	0.993475i	$-0.463617\pi$
$131$	2.61078			0.228105			0.114052	+	0.993475i	$0.463617\pi$
$132$	−2.74065	+	5.04865i	−0.238543	+	0.439428i
$133$	0.892461			0.0773862
$134$	−3.80508	−	2.76455i	−0.328709	−	0.238821i
$135$	−8.72494	−	12.4915i	−0.750924	−	1.07509i
$136$	1.78824	+	5.50363i	0.153340	+	0.471933i
$137$	−8.17926	−	11.2578i	−0.698801	−	0.961818i	−0.999966	−	0.00824544i	$-0.997375\pi$
$137$	−8.17926	−	11.2578i	−0.698801	−	0.961818i	0.301165	−	0.953572i	$-0.402625\pi$
$138$	8.75210	+	0.974835i	0.745028	+	0.0829834i
$139$	13.8943	−	4.51453i	1.17850	−	0.382918i	0.346690	−	0.937980i	$-0.387305\pi$
$139$	13.8943	−	4.51453i	1.17850	−	0.382918i	0.831809	+	0.555062i	$0.187305\pi$
$140$	−0.906140	+	2.78881i	−0.0765828	+	0.235698i
$141$	−1.25944	−	6.11144i	−0.106064	−	0.514676i
$142$			1.63788i			0.137448i
$143$	7.85085	−	19.2960i	0.656521	−	1.61361i
$144$	−0.276530	−	2.98723i	−0.0230442	−	0.248936i
$145$	7.82599	−	10.7715i	0.649913	−	0.894528i
$146$	8.25571	+	2.68244i	0.683247	+	0.222001i
$147$	1.57790	+	0.714295i	0.130143	+	0.0589140i
$148$	−2.34153	+	1.70122i	−0.192473	+	0.139839i
$149$	−15.1893	+	11.0357i	−1.24436	+	0.904079i	−0.997881	−	0.0650693i	$-0.979273\pi$
$149$	−15.1893	+	11.0357i	−1.24436	+	0.904079i	−0.246478	+	0.969149i	$0.579273\pi$
$150$	5.67818	+	2.57043i	0.463622	+	0.209875i
$151$	11.5726	+	3.76018i	0.941767	+	0.305999i	0.739366	−	0.673304i	$-0.235125\pi$
$151$	11.5726	+	3.76018i	0.941767	+	0.305999i	0.202401	+	0.979303i	$0.435125\pi$
$152$	0.524576	−	0.722016i	0.0425487	−	0.0585633i
$153$	−1.60024	−	17.2867i	−0.129372	−	1.39754i
$154$	−3.30797	−	0.239420i	−0.266564	−	0.0192930i
$155$		−	18.7144i		−	1.50318i
$156$	2.19581	+	10.6552i	0.175806	+	0.853101i
$157$	−3.21317	+	9.88912i	−0.256439	+	0.789237i	0.737104	+	0.675779i	$0.236193\pi$
$157$	−3.21317	+	9.88912i	−0.256439	+	0.789237i	−0.993543	+	0.113458i	$0.963807\pi$
$158$	−11.9275	+	3.87546i	−0.948897	+	0.308315i
$159$	12.2213	+	1.36125i	0.969213	+	0.107954i
$160$	1.72358	+	2.37230i	0.136261	+	0.187547i
$161$	1.57113	+	4.83543i	0.123822	+	0.381085i
$162$	−1.16264	+	8.92459i	−0.0913453	+	0.701182i
$163$	6.21893	+	4.51832i	0.487104	+	0.353902i	0.804070	−	0.594535i	$-0.202664\pi$
$163$	6.21893	+	4.51832i	0.487104	+	0.353902i	−0.316965	+	0.948437i	$0.602664\pi$
$164$	−10.3084			−0.804953
$165$	−3.06837	+	16.5631i	−0.238873	+	1.28944i
$166$	−3.49627			−0.271363
$167$	−4.98742	−	3.62357i	−0.385938	−	0.280400i	0.377851	−	0.925866i	$-0.376663\pi$
$167$	−4.98742	−	3.62357i	−0.385938	−	0.280400i	−0.763789	+	0.645466i	$0.776663\pi$
$168$	1.50535	−	0.856700i	0.116140	−	0.0660958i
$169$	−8.17407	−	25.1572i	−0.628774	−	1.93517i
$170$	9.97412	+	13.7282i	0.764980	+	1.05290i
$171$	−2.01177	+	1.76669i	−0.153844	+	0.135102i
$172$	2.80404	−	0.911089i	0.213806	−	0.0694698i
$173$	5.72196	−	17.6104i	0.435032	−	1.33889i	−0.458021	−	0.888941i	$-0.651442\pi$
$173$	5.72196	−	17.6104i	0.435032	−	1.33889i	0.893053	−	0.449951i	$-0.148558\pi$
$174$	−7.70259	+	1.58734i	−0.583932	+	0.120336i
$175$			3.59856i			0.272025i
$176$	−2.13807	+	2.53548i	−0.161163	+	0.191119i
$177$	14.0929	+	12.8486i	1.05929	+	0.965756i
$178$	0.956756	−	1.31686i	0.0717119	−	0.0987029i
$179$	4.24691	+	1.37990i	0.317429	+	0.103139i	0.463398	−	0.886150i	$-0.346630\pi$
$179$	4.24691	+	1.37990i	0.317429	+	0.103139i	−0.145969	+	0.989289i	$0.546630\pi$
$180$	−3.47804	−	8.08024i	−0.259238	−	0.602266i
$181$	8.05685	−	5.85364i	0.598861	−	0.435098i	−0.246614	−	0.969114i	$-0.579318\pi$
$181$	8.05685	−	5.85364i	0.598861	−	0.435098i	0.845474	+	0.534016i	$0.179318\pi$
$182$	−5.08149	+	3.69192i	−0.376665	+	0.273663i
$183$	2.70978	−	5.98601i	0.200313	−	0.442498i
$184$	4.83543	+	1.57113i	0.356473	+	0.115825i
$185$	−4.98854	+	6.86614i	−0.366765	+	0.504808i
$186$	−7.44748	+	8.16874i	−0.546075	+	0.598961i
$187$	−12.3727	+	14.6725i	−0.904783	+	1.07296i
$188$		−	3.60258i		−	0.262745i
$189$	−4.97087	+	1.51342i	−0.361578	+	0.110085i
$190$	0.808695	−	2.48891i	0.0586689	−	0.180564i
$191$	7.11163	−	2.31071i	0.514579	−	0.167197i	−0.0402046	−	0.999191i	$-0.512801\pi$
$191$	7.11163	−	2.31071i	0.514579	−	0.167197i	0.554784	+	0.831995i	$0.312801\pi$
$192$	0.191735	−	1.72141i	0.0138373	−	0.124232i
$193$	3.03835	+	4.18193i	0.218705	+	0.301022i	0.904246	−	0.427013i	$-0.140434\pi$
$193$	3.03835	+	4.18193i	0.218705	+	0.301022i	−0.685540	+	0.728035i	$0.740434\pi$
$194$	5.94637	+	18.3011i	0.426925	+	1.31394i
$195$	15.7788	+	27.7257i	1.12995	+	1.98548i
$196$	0.809017	+	0.587785i	0.0577869	+	0.0419847i
$197$	8.30051			0.591387			0.295693	−	0.955283i	$-0.404449\pi$
$197$	8.30051			0.591387			0.295693	+	0.955283i	$0.404449\pi$
$198$	7.93071	−	6.00865i	0.563611	−	0.427016i
$199$	19.8708			1.40860			0.704301	−	0.709902i	$-0.251261\pi$
$199$	19.8708			1.40860			0.704301	+	0.709902i	$0.251261\pi$
$200$	2.91130	+	2.11518i	0.205860	+	0.149566i
$201$	4.02935	+	7.08014i	0.284208	+	0.499395i
$202$	4.50831	+	13.8752i	0.317204	+	0.976253i
$203$	−2.66886	−	3.67337i	−0.187317	−	0.257820i
$204$	1.10955	−	9.96154i	0.0776837	−	0.697447i
$205$	−28.7483	+	9.34088i	−2.00787	+	0.652395i
$206$	5.65259	−	17.3969i	0.393835	−	1.21210i
$207$	−13.1137	−	7.78977i	−0.911462	−	0.541427i
$208$			6.28107i			0.435514i
$209$	2.95224	+	0.213673i	0.204211	+	0.0147801i
$210$	3.42184	−	3.75323i	0.236129	−	0.258997i
$211$	3.53506	−	4.86559i	0.243364	−	0.334961i	−0.669810	−	0.742533i	$-0.733624\pi$
$211$	3.53506	−	4.86559i	0.243364	−	0.334961i	0.913173	+	0.407572i	$0.133624\pi$
$212$	6.75213	+	2.19390i	0.463738	+	0.150678i
$213$	1.16993	−	2.58443i	0.0801624	−	0.177082i
$214$	−2.46015	+	1.78740i	−0.168172	+	0.122184i
$215$	6.99437	−	5.08171i	0.477012	−	0.346570i
$216$	−1.69742	+	4.91108i	−0.115495	+	0.334157i
$217$	−6.06973	−	1.97217i	−0.412040	−	0.133880i
$218$	2.21236	−	3.04506i	0.149840	−	0.206237i
$219$	−11.1107	−	10.1296i	−0.750789	−	0.684498i
$220$	−3.66518	+	9.00836i	−0.247107	+	0.607344i
$221$			36.3477i			2.44501i
$222$	4.90988	−	1.01182i	0.329530	−	0.0679090i
$223$	−1.86417	+	5.73732i	−0.124834	+	0.384199i	−0.993871	−	0.110548i	$-0.964739\pi$
$223$	−1.86417	+	5.73732i	−0.124834	+	0.384199i	0.869037	+	0.494747i	$0.164739\pi$
$224$	0.951057	−	0.309017i	0.0635451	−	0.0206471i
$225$	−7.12359	−	8.11179i	−0.474906	−	0.540786i
$226$	5.15833	+	7.09983i	0.343127	+	0.472274i
$227$	4.16647	+	12.8231i	0.276538	+	0.851097i	0.988808	+	0.149192i	$0.0476671\pi$
$227$	4.16647	+	12.8231i	0.276538	+	0.851097i	−0.712270	+	0.701905i	$0.752333\pi$
$228$	−1.34346	+	0.764571i	−0.0889730	+	0.0506350i
$229$	8.17891	+	5.94233i	0.540478	+	0.392680i	0.824262	−	0.566208i	$-0.191590\pi$
$229$	8.17891	+	5.94233i	0.540478	+	0.392680i	−0.283785	+	0.958888i	$0.591590\pi$
$230$	14.9088			0.983055
$231$	5.04865	+	2.74065i	0.332177	+	0.180321i
$232$	−4.54054			−0.298101
$233$	−14.9097	−	10.8325i	−0.976766	−	0.709662i	−0.0197823	−	0.999804i	$-0.506297\pi$
$233$	−14.9097	−	10.8325i	−0.976766	−	0.709662i	−0.956983	+	0.290142i	$0.906297\pi$
$234$	4.14619	−	18.3814i	0.271045	−	1.20163i
$235$	−3.26444	−	10.0469i	−0.212949	−	0.655389i
$236$	6.47182	+	8.90770i	0.421280	+	0.579842i
$237$	21.5886	+	2.40460i	1.40233	+	0.156196i
$238$	5.50363	−	1.78824i	0.356748	−	0.115914i
$239$	5.16500	−	15.8962i	0.334096	−	1.02824i	−0.633069	−	0.774095i	$-0.718205\pi$
$239$	5.16500	−	15.8962i	0.334096	−	1.02824i	0.967165	−	0.254148i	$-0.0817949\pi$
$240$	−1.02512	−	4.97442i	−0.0661712	−	0.321097i
$241$			21.5516i			1.38826i	0.719849	+	0.694130i	$0.244211\pi$
$241$			21.5516i			1.38826i	−0.719849	+	0.694130i	$0.755789\pi$
$242$	−10.8854	−	1.58399i	−0.699737	−	0.101823i
$243$	8.20932	−	13.2517i	0.526628	−	0.850096i
$244$	2.22985	−	3.06912i	0.142751	−	0.196480i
$245$	2.78881	+	0.906140i	0.178171	+	0.0578911i
$246$	16.2657	+	7.36326i	1.03706	+	0.469464i
$247$	4.53503	−	3.29490i	0.288557	−	0.209649i
$248$	−5.16322	+	3.75130i	−0.327865	+	0.238208i
$249$	5.51679	+	2.49737i	0.349612	+	0.158264i
$250$	−3.90835	−	1.26990i	−0.247186	−	0.0803156i
$251$	−15.6333	+	21.5174i	−0.986768	+	1.35817i	−0.0536650	+	0.998559i	$0.517090\pi$
$251$	−15.6333	+	21.5174i	−0.986768	+	1.35817i	−0.933103	+	0.359610i	$0.882910\pi$
$252$	−2.98723	+	0.276530i	−0.188178	+	0.0174198i
$253$	4.03954	+	16.3716i	0.253964	+	1.02928i
$254$		−	0.269148i		−	0.0168878i
$255$	−5.93223	−	28.7863i	−0.371491	−	1.80267i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−5.41875	+	1.76066i	−0.338012	+	0.109827i	−0.473105	−	0.881006i	$-0.656867\pi$
$257$	−5.41875	+	1.76066i	−0.338012	+	0.109827i	0.135093	+	0.990833i	$0.456867\pi$
$258$	−5.07530	−	0.565302i	−0.315974	−	0.0351941i
$259$	1.70122	+	2.34153i	0.105709	+	0.145496i
$260$	5.69153	+	17.5167i	0.352974	+	1.08634i
$261$	13.2878	+	2.99725i	0.822493	+	0.185525i
$262$	−2.11216	−	1.53458i	−0.130490	−	0.0948065i
$263$	−2.37574			−0.146494			−0.0732472	−	0.997314i	$-0.523336\pi$
$263$	−2.37574			−0.146494			−0.0732472	+	0.997314i	$0.523336\pi$
$264$	5.18475	−	2.47353i	0.319099	−	0.152235i
$265$	20.8184			1.27886
$266$	−0.722016	−	0.524576i	−0.0442697	−	0.0321638i
$267$	−2.45030	+	1.39448i	−0.149956	+	0.0853406i
$268$	1.45341	+	4.47314i	0.0887812	+	0.273240i
$269$	11.4696	+	15.7866i	0.699316	+	0.962525i	0.999961	+	0.00878943i	$0.00279780\pi$
$269$	11.4696	+	15.7866i	0.699316	+	0.962525i	−0.300646	+	0.953736i	$0.597202\pi$
$270$	−0.283664	+	15.2342i	−0.0172632	+	0.927123i
$271$	−3.06774	+	0.996770i	−0.186352	+	0.0605495i	−0.400706	−	0.916207i	$-0.631235\pi$
$271$	−3.06774	+	0.996770i	−0.186352	+	0.0605495i	0.214354	+	0.976756i	$0.431235\pi$
$272$	1.78824	−	5.50363i	0.108428	−	0.333707i
$273$	10.6552	−	2.19581i	0.644884	−	0.132897i
$274$			13.9154i			0.840659i
$275$	−0.861568	+	11.9039i	−0.0519545	+	0.717834i
$276$	−6.50760	−	5.93301i	−0.391712	−	0.357125i
$277$	0.412767	−	0.568125i	0.0248008	−	0.0341354i	−0.796437	−	0.604722i	$-0.793284\pi$
$277$	0.412767	−	0.568125i	0.0248008	−	0.0341354i	0.821237	+	0.570587i	$0.193284\pi$
$278$	−13.8943	−	4.51453i	−0.833325	−	0.270764i
$279$	17.5863	−	7.56980i	1.05286	−	0.453192i
$280$	2.37230	−	1.72358i	0.141772	−	0.103004i
$281$	17.9401	−	13.0342i	1.07021	−	0.777557i	0.0942640	−	0.995547i	$-0.469950\pi$
$281$	17.9401	−	13.0342i	1.07021	−	0.777557i	0.975951	+	0.217991i	$0.0699502\pi$
$282$	−2.57331	+	5.68453i	−0.153238	+	0.338509i
$283$	−26.4422	−	8.59159i	−1.57182	−	0.510717i	−0.611891	−	0.790942i	$-0.709591\pi$
$283$	−26.4422	−	8.59159i	−1.57182	−	0.510717i	−0.959934	+	0.280226i	$0.909591\pi$
$284$	0.962724	−	1.32508i	0.0571272	−	0.0786288i
$285$	−3.05386	+	3.34961i	−0.180895	+	0.198414i
$286$	−17.6934	+	10.9962i	−1.04623	+	0.650216i
$287$			10.3084i			0.608487i
$288$	−1.53213	+	2.57926i	−0.0902817	+	0.151984i
$289$	5.09500	−	15.6808i	0.299706	−	0.922400i
$290$	−12.6627	+	4.11436i	−0.743580	+	0.241604i
$291$	3.68954	−	33.1248i	0.216285	−	1.94181i
$292$	−5.10231	−	7.02273i	−0.298590	−	0.410974i
$293$	−2.41345	−	7.42784i	−0.140995	−	0.433939i	0.855479	−	0.517838i	$-0.173263\pi$
$293$	−2.41345	−	7.42784i	−0.140995	−	0.433939i	−0.996474	+	0.0838985i	$0.973263\pi$
$294$	−0.856700	−	1.50535i	−0.0499637	−	0.0877935i
$295$	26.1203	+	18.9775i	1.52078	+	1.10491i
$296$	2.89429			0.168227
$297$	−16.8058	+	3.81622i	−0.975174	+	0.221440i
$298$	18.7750			1.08761
$299$	25.8357	+	18.7707i	1.49412	+	1.08554i
$300$	−3.08288	−	5.41708i	−0.177990	−	0.312755i
$301$	−0.911089	−	2.80404i	−0.0525143	−	0.161622i
$302$	−7.15228	−	9.84427i	−0.411567	−	0.566474i
$303$	2.79727	−	25.1139i	0.160699	−	1.44276i
$304$	−0.848781	+	0.275786i	−0.0486809	+	0.0158174i
$305$	3.43757	−	10.5798i	0.196835	−	0.605795i
$306$	−8.86623	+	14.9258i	−0.506849	+	0.853252i
$307$		−	26.4631i		−	1.51033i	−0.655534	−	0.755166i	$-0.727556\pi$
$307$		−	26.4631i		−	1.51033i	0.655534	−	0.755166i	$-0.272444\pi$
$308$	2.53548	+	2.13807i	0.144472	+	0.121828i
$309$	−21.3458	+	23.4130i	−1.21432	+	1.33192i
$310$	−11.0000	+	15.1403i	−0.624760	+	0.859909i
$311$	−0.149341	−	0.0485239i	−0.00846836	−	0.00275154i	0.304780	−	0.952423i	$-0.401417\pi$
$311$	−0.149341	−	0.0485239i	−0.00846836	−	0.00275154i	−0.313248	+	0.949671i	$0.601417\pi$
$312$	4.48653	−	9.91093i	0.254000	−	0.561096i
$313$	8.00797	−	5.81813i	0.452637	−	0.328860i	−0.337999	−	0.941146i	$-0.609750\pi$
$313$	8.00797	−	5.81813i	0.452637	−	0.328860i	0.790636	+	0.612286i	$0.209750\pi$
$314$	8.41218	−	6.11181i	0.474727	−	0.344909i
$315$	−8.08024	+	3.47804i	−0.455270	+	0.195965i
$316$	11.9275	+	3.87546i	0.670972	+	0.218012i
$317$	−12.0569	+	16.5949i	−0.677184	+	0.932064i	−0.999896	−	0.0144332i	$-0.995406\pi$
$317$	−12.0569	+	16.5949i	−0.677184	+	0.932064i	0.322712	+	0.946497i	$0.395406\pi$
$318$	−9.08713	−	8.28478i	−0.509581	−	0.464587i
$319$	−7.94904	−	12.7904i	−0.445061	−	0.716125i
$320$		−	2.93233i		−	0.163922i
$321$	5.15861	−	1.06308i	0.287926	−	0.0593353i
$322$	1.57113	−	4.83543i	0.0875555	−	0.269468i
$323$	−4.91178	+	1.59593i	−0.273299	+	0.0888001i
$324$	6.18633	−	6.53676i	0.343685	−	0.363154i
$325$	13.2856	+	18.2860i	0.736952	+	1.01433i
$326$	−2.37542	−	7.31079i	−0.131562	−	0.404907i
$327$	−5.66597	+	3.22453i	−0.313329	+	0.178317i
$328$	8.33969	+	6.05914i	0.460483	+	0.334560i
$329$	−3.60258			−0.198617
$330$	12.2179	−	11.5963i	0.672575	−	0.638356i
$331$	−16.2021			−0.890549			−0.445275	−	0.895394i	$-0.646894\pi$
$331$	−16.2021			−0.890549			−0.445275	+	0.895394i	$0.646894\pi$
$332$	2.82854	+	2.05506i	0.155237	+	0.112786i
$333$	−8.47007	−	1.91055i	−0.464157	−	0.104697i
$334$	1.90502	+	5.86306i	0.104238	+	0.320812i
$335$	8.10657	+	11.1577i	0.442909	+	0.609613i
$336$	−1.72141	−	0.191735i	−0.0939104	−	0.0104600i
$337$	−31.2287	+	10.1468i	−1.70114	+	0.552733i	−0.988819	−	0.149124i	$-0.952355\pi$
$337$	−31.2287	+	10.1468i	−1.70114	+	0.552733i	−0.712318	+	0.701857i	$0.752355\pi$
$338$	−8.17407	+	25.1572i	−0.444611	+	1.36837i
$339$	−3.06798	−	14.8874i	−0.166630	−	0.808573i
$340$		−	16.9690i		−	0.920273i
$341$	−19.6063	−	7.97711i	−1.06174	−	0.431985i
$342$	2.66599	−	0.246792i	0.144160	−	0.0133450i
$343$	0.587785	−	0.809017i	0.0317374	−	0.0436828i
$344$	−2.80404	−	0.911089i	−0.151184	−	0.0491226i
$345$	−23.5246	−	10.6493i	−1.26652	−	0.573337i
$346$	−14.9803	+	10.8838i	−0.805345	+	0.585117i
$347$	−16.2005	+	11.7703i	−0.869686	+	0.631864i	−0.930503	−	0.366285i	$-0.880630\pi$
$347$	−16.2005	+	11.7703i	−0.869686	+	0.631864i	0.0608164	+	0.998149i	$0.480630\pi$
$348$	7.16454	+	3.24328i	0.384060	+	0.173858i
$349$	0.565146	+	0.183627i	0.0302516	+	0.00982934i	0.324104	−	0.946022i	$-0.394937\pi$
$349$	0.565146	+	0.183627i	0.0302516	+	0.00982934i	−0.293852	+	0.955851i	$0.594937\pi$
$350$	2.11518	−	2.91130i	0.113061	−	0.155615i
$351$	−19.6720	+	26.0425i	−1.05001	+	1.39005i
$352$	3.22005	−	0.794517i	0.171629	−	0.0423479i
$353$			20.5048i			1.09136i	0.837993	+	0.545681i	$0.183729\pi$
$353$			20.5048i			1.09136i	−0.837993	+	0.545681i	$0.816271\pi$
$354$	−3.84920	−	18.6783i	−0.204582	−	0.992740i
$355$	1.48415	−	4.56775i	0.0787706	−	0.242431i
$356$	−1.54806	+	0.502996i	−0.0820472	+	0.0266588i
$357$	−9.96154	−	1.10955i	−0.527220	−	0.0587234i
$358$	−2.62473	−	3.61264i	−0.138721	−	0.190934i
$359$	−6.23382	−	19.1857i	−0.329008	−	1.01258i	−0.969599	−	0.244701i	$-0.921310\pi$
$359$	−6.23382	−	19.1857i	−0.329008	−	1.01258i	0.640590	−	0.767883i	$-0.278690\pi$
$360$	−1.93566	+	8.58139i	−0.102018	+	0.452279i
$361$	−14.7270	−	10.6998i	−0.775103	−	0.563145i
$362$	−9.95881			−0.523424
$363$	16.0446	+	10.2747i	0.842124	+	0.539284i
$364$	6.28107			0.329217
$365$	−20.5930	−	14.9617i	−1.07788	−	0.783129i
$366$	−5.71074	+	3.25001i	−0.298505	+	0.169881i
$367$	0.487440	+	1.50019i	0.0254442	+	0.0783091i	0.962972	−	0.269600i	$-0.0868916\pi$
$367$	0.487440	+	1.50019i	0.0254442	+	0.0783091i	−0.937528	+	0.347910i	$0.886892\pi$
$368$	−2.98846	−	4.11326i	−0.155784	−	0.214419i
$369$	−20.4062	−	23.2370i	−1.06231	−	1.20967i
$370$	8.07163	−	2.62263i	0.419624	−	0.136344i
$371$	2.19390	−	6.75213i	0.113902	−	0.350553i
$372$	10.8266	−	2.23113i	0.561333	−	0.115679i
$373$			33.8341i			1.75186i	0.482434	+	0.875932i	$0.339753\pi$
$373$			33.8341i			1.75186i	−0.482434	+	0.875932i	$0.660247\pi$
$374$	18.6340	−	4.59776i	0.963541	−	0.237745i
$375$	5.25993	+	4.79550i	0.271621	+	0.247639i
$376$	−2.11755	+	2.91455i	−0.109204	+	0.150307i
$377$	−27.1236	−	8.81299i	−1.39694	−	0.453892i
$378$	4.91108	+	1.69742i	0.252599	+	0.0873060i
$379$	21.4059	−	15.5523i	1.09955	−	0.798869i	0.118562	−	0.992947i	$-0.462171\pi$
$379$	21.4059	−	15.5523i	1.09955	−	0.798869i	0.980986	+	0.194078i	$0.0621715\pi$
$380$	−2.11719	+	1.53823i	−0.108610	+	0.0789095i
$381$	−0.192251	+	0.424689i	−0.00984930	+	0.0217575i
$382$	−7.11163	−	2.31071i	−0.363862	−	0.118226i
$383$	−9.01245	+	12.4046i	−0.460515	+	0.633844i	−0.974615	−	0.223886i	$-0.928126\pi$
$383$	−9.01245	+	12.4046i	−0.460515	+	0.633844i	0.514101	+	0.857730i	$0.328126\pi$
$384$	−1.16693	+	1.27995i	−0.0595499	+	0.0653170i
$385$	9.00836	+	3.66518i	0.459109	+	0.186795i
$386$		−	5.16915i		−	0.263103i
$387$	7.60454	+	4.51725i	0.386561	+	0.229625i
$388$	5.94637	−	18.3011i	0.301881	−	0.929095i
$389$	10.3503	−	3.36302i	0.524782	−	0.170512i	−0.0346324	−	0.999400i	$-0.511026\pi$
$389$	10.3503	−	3.36302i	0.524782	−	0.170512i	0.559414	+	0.828888i	$0.311026\pi$
$390$	3.53141	−	31.7051i	0.178820	−	1.60545i
$391$	−17.2938	−	23.8029i	−0.874586	−	1.20376i
$392$	−0.309017	−	0.951057i	−0.0156077	−	0.0480356i
$393$	2.23665	+	3.93012i	0.112824	+	0.198248i
$394$	−6.71525	−	4.87891i	−0.338309	−	0.245796i
$395$	36.7751			1.85036
$396$	−9.94787	+	0.199551i	−0.499899	+	0.0100278i
$397$	−33.1242			−1.66246			−0.831228	−	0.555932i	$-0.812361\pi$
$397$	−33.1242			−1.66246			−0.831228	+	0.555932i	$0.812361\pi$
$398$	−16.0758	−	11.6797i	−0.805807	−	0.585453i
$399$	0.764571	+	1.34346i	0.0382764	+	0.0672573i
$400$	−1.11202	−	3.42243i	−0.0556008	−	0.171122i
$401$	−20.3498	−	28.0091i	−1.01622	−	1.39871i	−0.914820	−	0.403862i	$-0.867668\pi$
$401$	−20.3498	−	28.0091i	−1.01622	−	1.39871i	−0.101401	−	0.994846i	$-0.532332\pi$
$402$	0.901795	−	8.09635i	0.0449775	−	0.403809i
$403$	−38.1244	+	12.3874i	−1.89911	+	0.617058i
$404$	4.50831	−	13.8752i	0.224297	−	0.690315i
$405$	11.3293	−	23.8355i	0.562957	−	1.18439i
$406$			4.54054i			0.225343i
$407$	5.06698	+	8.15302i	0.251161	+	0.404130i
$408$	−6.75289	+	7.40688i	−0.334318	+	0.366695i
$409$	−9.93337	+	13.6721i	−0.491173	+	0.676042i	−0.980604	−	0.196000i	$-0.937205\pi$
$409$	−9.93337	+	13.6721i	−0.491173	+	0.676042i	0.489431	+	0.872042i	$0.337205\pi$
$410$	28.7483	+	9.34088i	1.41978	+	0.461313i
$411$	9.93969	−	21.9572i	0.490289	−	1.08307i
$412$	−14.7987	+	10.7519i	−0.729079	+	0.529707i
$413$	8.90770	−	6.47182i	0.438319	−	0.318458i
$414$	6.03046	+	14.0101i	0.296381	+	0.688557i
$415$	9.75045	+	3.16811i	0.478631	+	0.155517i
$416$	3.69192	−	5.08149i	0.181011	−	0.249141i
$417$	18.6992	+	17.0481i	0.915703	+	0.834850i
$418$	−2.26282	−	1.90815i	−0.110678	−	0.0933305i
$419$		−	22.8332i		−	1.11548i	−0.830017	−	0.557738i	$-0.811669\pi$
$419$		−	22.8332i		−	1.11548i	0.830017	−	0.557738i	$-0.188331\pi$
$420$	−4.97442	+	1.02512i	−0.242727	+	0.0500208i
$421$	7.42563	−	22.8537i	0.361903	−	1.11382i	−0.589995	−	0.807407i	$-0.700870\pi$
$421$	7.42563	−	22.8537i	0.361903	−	1.11382i	0.951898	−	0.306416i	$-0.0991297\pi$
$422$	−5.71985	+	1.85849i	−0.278438	+	0.0904699i
$423$	8.12086	−	7.13155i	0.394850	−	0.346748i
$424$	−4.17305	−	5.74371i	−0.202661	−	0.278939i
$425$	−6.43508	−	19.8051i	−0.312147	−	0.960691i
$426$	−2.46558	+	1.40318i	−0.119458	+	0.0679841i
$427$	−3.06912	−	2.22985i	−0.148525	−	0.107910i
$428$	3.04091			0.146988
$429$	35.7729	−	4.71262i	1.72713	−	0.227527i
$430$	−8.64552			−0.416924
$431$	25.3340	+	18.4063i	1.22030	+	0.886598i	0.996125	−	0.0879510i	$-0.0280319\pi$
$431$	25.3340	+	18.4063i	1.22030	+	0.886598i	0.224173	+	0.974549i	$0.428032\pi$
$432$	4.25991	−	2.97543i	0.204955	−	0.143155i
$433$	10.6852	+	32.8858i	0.513500	+	1.58039i	0.785995	+	0.618233i	$0.212151\pi$
$433$	10.6852	+	32.8858i	0.513500	+	1.58039i	−0.272495	+	0.962157i	$0.587849\pi$
$434$	3.75130	+	5.16322i	0.180068	+	0.247842i
$435$	22.9194	+	2.55283i	1.09890	+	0.122399i
$436$	−3.57968	+	1.16311i	−0.171436	+	0.0557028i
$437$	−1.40217	+	4.31544i	−0.0670749	+	0.206435i
$438$	3.03466	+	14.7257i	0.145002	+	0.703623i
$439$			37.8023i			1.80421i	0.431519	+	0.902104i	$0.357978\pi$
$439$			37.8023i			1.80421i	−0.431519	+	0.902104i	$0.642022\pi$
$440$	8.26018	−	5.13358i	0.393789	−	0.244734i
$441$	0.276530	+	2.98723i	0.0131681	+	0.142249i
$442$	21.3646	−	29.4059i	1.01621	−	1.39870i
$443$	−3.08583	−	1.00265i	−0.146612	−	0.0476372i	0.234792	−	0.972046i	$-0.424559\pi$
$443$	−3.08583	−	1.00265i	−0.146612	−	0.0476372i	−0.381404	+	0.924409i	$0.624559\pi$
$444$	−4.56691	−	2.06738i	−0.216736	−	0.0981133i
$445$	−3.86147	+	2.80552i	−0.183051	+	0.132995i
$446$	4.88046	−	3.54586i	0.231096	−	0.167901i
$447$	−29.6252	−	13.4109i	−1.40123	−	0.634314i
$448$	−0.951057	−	0.309017i	−0.0449332	−	0.0145997i
$449$	−5.40446	+	7.43860i	−0.255052	+	0.351049i	−0.917273	−	0.398260i	$-0.869614\pi$
$449$	−5.40446	+	7.43860i	−0.255052	+	0.351049i	0.662220	+	0.749309i	$0.269614\pi$
$450$	0.995110	+	10.7497i	0.0469099	+	0.506746i
$451$	−2.46805	+	34.1000i	−0.116216	+	1.60571i
$452$		−	8.77587i		−	0.412782i
$453$	4.25391	+	20.6421i	0.199866	+	0.969853i
$454$	4.16647	−	12.8231i	0.195542	−	0.601816i
$455$	17.5167	−	5.69153i	0.821196	−	0.266823i
$456$	1.53629	+	0.171116i	0.0719433	+	0.00801326i
$457$	6.95412	+	9.57152i	0.325300	+	0.447737i	0.940076	−	0.340965i	$-0.110754\pi$
$457$	6.95412	+	9.57152i	0.325300	+	0.447737i	−0.614776	+	0.788702i	$0.710754\pi$
$458$	−3.12407	−	9.61488i	−0.145978	−	0.449274i
$459$	24.6515	−	17.2184i	1.15063	−	0.803686i
$460$	−12.0614	−	8.76315i	−0.562368	−	0.408584i
$461$	6.00472			0.279668			0.139834	−	0.990175i	$-0.455343\pi$
$461$	6.00472			0.279668			0.139834	+	0.990175i	$0.455343\pi$
$462$	−2.47353	−	5.18475i	−0.115079	−	0.241217i
$463$	−23.4280			−1.08879			−0.544396	−	0.838828i	$-0.683241\pi$
$463$	−23.4280			−1.08879			−0.544396	+	0.838828i	$0.683241\pi$
$464$	3.67337	+	2.66886i	0.170532	+	0.123899i
$465$	28.1716	−	16.0326i	1.30643	−	0.743495i
$466$	5.69499	+	17.5274i	0.263815	+	0.811940i
$467$	7.87655	+	10.8411i	0.364483	+	0.501668i	0.951391	−	0.307986i	$-0.0996549\pi$
$467$	7.87655	+	10.8411i	0.364483	+	0.501668i	−0.586908	+	0.809654i	$0.699655\pi$
$468$	−14.1586	+	12.4338i	−0.654484	+	0.574752i
$469$	4.47314	−	1.45341i	0.206550	−	0.0671122i
$470$	−3.26444	+	10.0469i	−0.150578	+	0.463430i
$471$	−17.6393	+	3.63507i	−0.812774	+	0.167495i
$472$		−	11.0105i		−	0.506800i
$473$	−2.34251	−	9.49383i	−0.107709	−	0.436527i
$474$	−16.0522	−	14.6348i	−0.737300	−	0.672200i
$475$	−1.88772	+	2.59822i	−0.0866144	+	0.119214i
$476$	−5.50363	−	1.78824i	−0.252259	−	0.0819638i
$477$	8.42085	+	19.5635i	0.385564	+	0.895750i
$478$	−13.5222	+	9.82442i	−0.618489	+	0.449359i
$479$	−10.6320	+	7.72462i	−0.485790	+	0.352947i	−0.803563	−	0.595220i	$-0.797065\pi$
$479$	−10.6320	+	7.72462i	−0.485790	+	0.352947i	0.317773	+	0.948167i	$0.397065\pi$
$480$	−2.09455	+	4.62694i	−0.0956026	+	0.211190i
$481$	17.2895	+	5.61769i	0.788332	+	0.256145i
$482$	12.6677	−	17.4356i	0.576999	−	0.794170i
$483$	−5.93301	+	6.50760i	−0.269961	+	0.296106i
$484$	7.87539	+	7.67973i	0.357972	+	0.349079i
$485$		−	56.4264i		−	2.56219i
$486$	−14.4306	+	5.89552i	−0.654586	+	0.267426i
$487$	−1.69581	+	5.21917i	−0.0768446	+	0.236503i	−0.982099	−	0.188367i	$-0.939680\pi$
$487$	−1.69581	+	5.21917i	−0.0768446	+	0.236503i	0.905254	+	0.424871i	$0.139680\pi$
$488$	−3.60797	+	1.17230i	−0.163325	+	0.0530675i
$489$	−1.47387	+	13.2325i	−0.0666508	+	0.598393i
$490$	−1.72358	−	2.37230i	−0.0778634	−	0.107170i
$491$	−3.31710	−	10.2090i	−0.149698	−	0.460724i	0.847887	−	0.530177i	$-0.177875\pi$
$491$	−3.31710	−	10.2090i	−0.149698	−	0.460724i	−0.997585	+	0.0694529i	$0.977875\pi$
$492$	−8.83123	−	15.5177i	−0.398143	−	0.699594i
$493$	21.2573	+	15.4443i	0.957381	+	0.695578i
$494$	−5.60561			−0.252208
$495$	−27.5619	+	9.57067i	−1.23882	+	0.430170i
$496$	6.38209			0.286564
$497$	−1.32508	−	0.962724i	−0.0594378	−	0.0431841i
$498$	−2.99526	−	5.26310i	−0.134221	−	0.235845i
$499$	0.246511	+	0.758684i	0.0110354	+	0.0339634i	0.956423	−	0.291986i	$-0.0943161\pi$
$499$	0.246511	+	0.758684i	0.0110354	+	0.0339634i	−0.945387	+	0.325949i	$0.894316\pi$
$500$	2.41550	+	3.32465i	0.108024	+	0.148683i
$501$	1.18201	−	10.6121i	0.0528082	−	0.474113i
$502$	25.2953	−	8.21893i	1.12898	−	0.366829i
$503$	−3.32833	+	10.2435i	−0.148403	+	0.456737i	−0.997433	−	0.0716076i	$-0.977187\pi$
$503$	−3.32833	+	10.2435i	−0.148403	+	0.456737i	0.849030	+	0.528345i	$0.177187\pi$
$504$	2.57926	+	1.53213i	0.114889	+	0.0682465i
$505$		−	42.7804i		−	1.90370i
$506$	6.35494	−	15.6193i	0.282512	−	0.694363i
$507$	30.8675	−	33.8569i	1.37088	−	1.50364i
$508$	−0.158201	+	0.217745i	−0.00701903	+	0.00966087i
$509$	19.7363	+	6.41272i	0.874797	+	0.284239i	0.711795	−	0.702387i	$-0.247882\pi$
$509$	19.7363	+	6.41272i	0.874797	+	0.284239i	0.163002	+	0.986626i	$0.447882\pi$
$510$	−12.1209	+	26.7754i	−0.536721	+	1.18564i
$511$	−7.02273	+	5.10231i	−0.310667	+	0.225713i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−4.38295	−	1.51488i	−0.193512	−	0.0668838i
$514$	5.41875	+	1.76066i	0.239011	+	0.0776593i
$515$	−31.5280	+	43.3946i	−1.38929	+	1.91220i
$516$	3.77373	+	3.44052i	0.166129	+	0.151461i
$517$	−11.9172	−	0.862532i	−0.524120	−	0.0379341i
$518$		−	2.89429i		−	0.127168i
$519$	31.4117	−	6.47328i	1.37882	−	0.284146i
$520$	5.69153	−	17.5167i	0.249590	−	0.768159i
$521$	−3.87734	+	1.25982i	−0.169869	+	0.0551939i	−0.392717	−	0.919659i	$-0.628465\pi$
$521$	−3.87734	+	1.25982i	−0.169869	+	0.0551939i	0.222848	+	0.974853i	$0.428465\pi$
$522$	−8.98830	−	10.2352i	−0.393407	−	0.447982i
$523$	−8.45649	−	11.6394i	−0.369777	−	0.508954i	0.583064	−	0.812427i	$-0.301854\pi$
$523$	−8.45649	−	11.6394i	−0.369777	−	0.508954i	−0.952840	+	0.303473i	$0.901854\pi$
$524$	0.806775	+	2.48300i	0.0352441	+	0.108470i
$525$	−5.41708	+	3.08288i	−0.236421	+	0.134548i
$526$	1.92201	+	1.39643i	0.0838038	+	0.0608870i
$527$	36.9323			1.60879
$528$	−5.64846	−	1.04639i	−0.245818	−	0.0455385i
$529$	−2.84984			−0.123906
$530$	−16.8424	−	12.2368i	−0.731589	−	0.531530i
$531$	−7.26814	+	32.2220i	−0.315410	+	1.39832i
$532$	0.275786	+	0.848781i	0.0119568	+	0.0367993i
$533$	38.0579	+	52.3822i	1.64847	+	2.26892i
$534$	2.80198	+	0.312093i	0.121254	+	0.0135056i
$535$	8.48053	−	2.75549i	0.366645	−	0.119130i
$536$	1.45341	−	4.47314i	0.0627778	−	0.193210i
$537$	1.56109	+	7.57523i	0.0673661	+	0.326895i
$538$		−	19.5133i		−	0.841278i
$539$	2.13807	−	2.53548i	0.0920933	−	0.109211i
$540$	9.18392	−	12.1580i	0.395213	−	0.523196i
$541$	3.60094	−	4.95627i	0.154816	−	0.213087i	−0.724562	−	0.689209i	$-0.757958\pi$
$541$	3.60094	−	4.95627i	0.154816	−	0.213087i	0.879379	+	0.476123i	$0.157958\pi$
$542$	3.06774	+	0.996770i	0.131771	+	0.0428149i
$543$	15.7141	+	7.11353i	0.674355	+	0.305271i
$544$	−4.68167	+	3.40143i	−0.200725	+	0.145835i
$545$	−8.92912	+	6.48738i	−0.382481	+	0.277889i
$546$	−9.91093	−	4.48653i	−0.424149	−	0.192006i
$547$	6.19049	+	2.01141i	0.264686	+	0.0860018i	0.438354	−	0.898803i	$-0.355562\pi$
$547$	6.19049	+	2.01141i	0.264686	+	0.0860018i	−0.173667	+	0.984804i	$0.555562\pi$
$548$	8.17926	−	11.2578i	0.349401	−	0.480909i
$549$	11.3325	−	1.04906i	0.483658	−	0.0447726i
$550$	7.69398	−	9.12407i	0.328072	−	0.389051i
$551$		−	4.05226i		−	0.172632i
$552$	1.77742	+	8.62498i	0.0756522	+	0.367104i
$553$	3.87546	−	11.9275i	0.164802	−	0.507207i
$554$	−0.667872	+	0.217005i	−0.0283751	+	0.00921964i
$555$	−14.6096	−	1.62726i	−0.620143	−	0.0690733i
$556$	8.58715	+	11.8192i	0.364176	+	0.501246i
$557$	−3.70834	−	11.4131i	−0.157127	−	0.483588i	0.841243	−	0.540657i	$-0.181824\pi$
$557$	−3.70834	−	11.4131i	−0.157127	−	0.483588i	−0.998370	+	0.0570690i	$0.981824\pi$
$558$	−18.6770	−	4.21287i	−0.790662	−	0.178345i
$559$	−14.9820	−	10.8851i	−0.633671	−	0.460389i
$560$	−2.93233			−0.123914
$561$	−32.6868	−	6.05534i	−1.38004	−	0.255657i
$562$	−22.1751			−0.935402
$563$	−21.9263	−	15.9304i	−0.924082	−	0.671385i	0.0204547	−	0.999791i	$-0.493489\pi$
$563$	−21.9263	−	15.9304i	−0.924082	−	0.671385i	−0.944537	+	0.328406i	$0.893489\pi$
$564$	5.42313	−	3.08633i	0.228355	−	0.129958i
$565$	−7.95216	−	24.4742i	−0.334550	−	1.02964i
$566$	16.3422	+	22.4931i	0.686913	+	0.945454i
$567$	−6.53676	−	6.18633i	−0.274518	−	0.259802i
$568$	−1.55772	+	0.506134i	−0.0653605	+	0.0212369i
$569$	−0.878508	+	2.70377i	−0.0368290	+	0.113348i	−0.967781	−	0.251794i	$-0.918980\pi$
$569$	−0.878508	+	2.70377i	−0.0368290	+	0.113348i	0.930952	+	0.365142i	$0.118980\pi$
$570$	4.43947	−	0.914880i	0.185949	−	0.0383201i
$571$		−	39.7083i		−	1.66174i	−0.556466	−	0.830870i	$-0.687843\pi$
$571$		−	39.7083i		−	1.66174i	0.556466	−	0.830870i	$-0.312157\pi$
$572$	20.7776	+	1.50382i	0.868755	+	0.0628777i
$573$	9.57094	+	8.72587i	0.399832	+	0.364529i
$574$	6.05914	−	8.33969i	0.252904	−	0.348092i
$575$	−17.4006	−	5.65379i	−0.725655	−	0.235779i
$576$	2.75557	−	1.18610i	0.114815	−	0.0494208i
$577$	17.9883	−	13.0692i	0.748862	−	0.544080i	−0.146612	−	0.989194i	$-0.546837\pi$
$577$	17.9883	−	13.0692i	0.748862	−	0.544080i	0.895474	+	0.445114i	$0.146837\pi$
$578$	−13.3389	+	9.69127i	−0.554824	+	0.403104i
$579$	−3.69230	+	8.15643i	−0.153447	+	0.338970i
$580$	12.6627	+	4.11436i	0.525790	+	0.170840i
$581$	2.05506	−	2.82854i	0.0852582	−	0.117348i
$582$	−22.4552	+	24.6299i	−0.930796	+	1.02094i
$583$	8.87396	−	21.8106i	0.367522	−	0.903303i
$584$			8.68057i			0.359204i
$585$	−28.2190	+	47.5052i	−1.16671	+	1.96410i
$586$	−2.41345	+	7.42784i	−0.0996988	+	0.306841i
$587$	−35.9307	+	11.6746i	−1.48302	+	0.481862i	−0.935013	−	0.354613i	$-0.884613\pi$
$587$	−35.9307	+	11.6746i	−1.48302	+	0.481862i	−0.548005	+	0.836475i	$0.684613\pi$
$588$	−0.191735	+	1.72141i	−0.00790703	+	0.0709896i
$589$	−3.34789	−	4.60797i	−0.137947	−	0.189868i
$590$	−9.97707	−	30.7063i	−0.410750	−	1.26416i
$591$	7.11104	+	12.4951i	0.292509	+	0.513981i
$592$	−2.34153	−	1.70122i	−0.0962363	−	0.0699197i
$593$	−13.0558			−0.536137			−0.268069	−	0.963400i	$-0.586385\pi$
$593$	−13.0558			−0.536137			−0.268069	+	0.963400i	$0.586385\pi$
$594$	15.8393	+	6.79084i	0.649896	+	0.278632i
$595$	−16.9690			−0.695661
$596$	−15.1893	−	11.0357i	−0.622179	−	0.452040i
$597$	17.0233	+	29.9124i	0.696717	+	1.22423i
$598$	−9.86836	−	30.3717i	−0.403547	−	1.24199i
$599$	17.4157	+	23.9707i	0.711587	+	0.979415i	0.999762	+	0.0218372i	$0.00695156\pi$
$599$	17.4157	+	23.9707i	0.711587	+	0.979415i	−0.288175	+	0.957578i	$0.593048\pi$
$600$	−0.689971	+	6.19458i	−0.0281679	+	0.252893i
$601$	−18.6479	+	6.05908i	−0.760665	+	0.247155i	−0.663564	−	0.748119i	$-0.730957\pi$
$601$	−18.6479	+	6.05908i	−0.760665	+	0.247155i	−0.0971012	+	0.995275i	$0.530957\pi$
$602$	−0.911089	+	2.80404i	−0.0371332	+	0.114284i
$603$	−7.20612	+	12.1311i	−0.293456	+	0.494017i
$604$			12.1682i			0.495116i
$605$	28.9219	+	14.2811i	1.17584	+	0.580610i
$606$	−17.0246	+	18.6734i	−0.691579	+	0.758556i
$607$	−25.9185	+	35.6737i	−1.05200	+	1.44795i	−0.164936	+	0.986304i	$0.552742\pi$
$607$	−25.9185	+	35.6737i	−1.05200	+	1.44795i	−0.887063	+	0.461648i	$0.847258\pi$
$608$	0.848781	+	0.275786i	0.0344226	+	0.0111846i
$609$	3.24328	−	7.16454i	0.131424	−	0.290322i
$610$	−8.99968	+	6.53865i	−0.364386	+	0.264742i
$611$	−18.3065	+	13.3005i	−0.740602	+	0.538079i
$612$	15.9461	−	6.86380i	0.644583	−	0.277453i
$613$	46.0477	+	14.9618i	1.85985	+	0.604301i	0.994704	+	0.102778i	$0.0327733\pi$
$613$	46.0477	+	14.9618i	1.85985	+	0.604301i	0.865144	+	0.501523i	$0.167227\pi$
$614$	−15.5546	+	21.4091i	−0.627734	+	0.864002i
$615$	−38.6899	−	35.2737i	−1.56013	−	1.42237i
$616$	−0.794517	−	3.22005i	−0.0320120	−	0.129740i
$617$			27.3415i			1.10073i	0.834926	+	0.550363i	$0.185511\pi$
$617$			27.3415i			1.10073i	−0.834926	+	0.550363i	$0.814489\pi$
$618$	31.0309	−	6.39481i	1.24825	−	0.257237i
$619$	−11.1718	+	34.3831i	−0.449031	+	1.38197i	0.428972	+	0.903318i	$0.358876\pi$
$619$	−11.1718	+	34.3831i	−0.449031	+	1.38197i	−0.878002	+	0.478656i	$0.841124\pi$
$620$	17.7984	−	5.78306i	0.714803	−	0.232253i
$621$	0.491836	−	26.4141i	0.0197367	−	1.05996i
$622$	0.0922979	+	0.127037i	0.00370081	+	0.00509373i
$623$	0.502996	+	1.54806i	0.0201521	+	0.0620219i
$624$	−9.45518	+	5.38099i	−0.378510	+	0.215412i
$625$	24.3054	+	17.6589i	0.972217	+	0.706357i
$626$	−9.89839			−0.395619
$627$	2.20753	+	4.62719i	0.0881602	+	0.184792i
$628$	−10.3980			−0.414927
$629$	−13.5501	−	9.84473i	−0.540278	−	0.392535i
$630$	8.58139	+	1.93566i	0.341891	+	0.0771184i
$631$	2.93086	+	9.02027i	0.116676	+	0.359091i	0.992293	−	0.123915i	$-0.0395449\pi$
$631$	2.93086	+	9.02027i	0.116676	+	0.359091i	−0.875617	+	0.483006i	$0.839545\pi$
$632$	−7.37157	−	10.1461i	−0.293225	−	0.403590i
$633$	10.3529	+	1.15314i	0.411490	+	0.0458330i
$634$	19.5085	−	6.33870i	0.774782	−	0.251742i
$635$	−0.243885	+	0.750602i	−0.00967829	+	0.0297867i
$636$	2.48197	+	12.0438i	0.0984166	+	0.477568i
$637$		−	6.28107i		−	0.248865i
$638$	−1.08710	+	15.0200i	−0.0430386	+	0.594647i
$639$	4.89273	−	0.452924i	0.193554	−	0.0179174i
$640$	−1.72358	+	2.37230i	−0.0681305	+	0.0937736i
$641$	−12.8987	−	4.19105i	−0.509469	−	0.165536i	0.0429920	−	0.999075i	$-0.486311\pi$
$641$	−12.8987	−	4.19105i	−0.509469	−	0.165536i	−0.552461	+	0.833539i	$0.686311\pi$
$642$	−4.79827	−	2.17211i	−0.189372	−	0.0857262i
$643$	−30.8965	+	22.4476i	−1.21844	+	0.885248i	−0.995970	−	0.0896911i	$-0.971412\pi$
$643$	−30.8965	+	22.4476i	−1.21844	+	0.885248i	−0.222470	+	0.974939i	$0.571412\pi$
$644$	−4.11326	+	2.98846i	−0.162085	+	0.117762i
$645$	13.6418	+	6.17545i	0.537146	+	0.243158i
$646$	4.91178	+	1.59593i	0.193251	+	0.0627912i
$647$	−9.83552	+	13.5374i	−0.386674	+	0.532211i	−0.957337	−	0.288973i	$-0.906686\pi$
$647$	−9.83552	+	13.5374i	−0.386674	+	0.532211i	0.570663	+	0.821184i	$0.306686\pi$
$648$	−8.84706	+	1.65212i	−0.347545	+	0.0649013i
$649$	31.0159	−	19.2759i	1.21748	−	0.756646i
$650$		−	22.6028i		−	0.886555i
$651$	−2.23113	−	10.8266i	−0.0874449	−	0.424328i
$652$	−2.37542	+	7.31079i	−0.0930286	+	0.286313i
$653$	−7.22221	+	2.34664i	−0.282627	+	0.0918311i	−0.446900	−	0.894584i	$-0.647472\pi$
$653$	−7.22221	+	2.34664i	−0.282627	+	0.0918311i	0.164273	+	0.986415i	$0.447472\pi$
$654$	6.47920	+	0.721672i	0.253357	+	0.0282196i
$655$	4.49989	+	6.19356i	0.175825	+	0.242002i
$656$	−3.18548	−	9.80390i	−0.124372	−	0.382778i
$657$	5.73012	−	25.4035i	0.223553	−	0.991084i
$658$	2.91455	+	2.11755i	0.113621	+	0.0825505i
$659$	−4.10505			−0.159910			−0.0799551	−	0.996798i	$-0.525478\pi$
$659$	−4.10505			−0.159910			−0.0799551	+	0.996798i	$0.525478\pi$
$660$	−16.7007	+	2.20009i	−0.650072	+	0.0856385i
$661$	37.7970			1.47013			0.735066	−	0.677995i	$-0.237151\pi$
$661$	37.7970			1.47013			0.735066	+	0.677995i	$0.237151\pi$
$662$	13.1078	+	9.52337i	0.509449	+	0.370136i
$663$	−54.7158	+	31.1390i	−2.12499	+	1.20934i
$664$	−1.08041	−	3.32515i	−0.0419280	−	0.129041i
$665$	1.53823	+	2.11719i	0.0596500	+	0.0821011i
$666$	5.72944	+	6.52424i	0.222011	+	0.252809i
$667$	21.9555	−	7.13376i	0.850119	−	0.276220i
$668$	1.90502	−	5.86306i	0.0737076	−	0.226849i
$669$	−10.2337	+	2.10894i	−0.395657	+	0.0815364i
$670$		−	13.7917i		−	0.532821i
$671$	−9.61870	−	8.11108i	−0.371326	−	0.313125i
$672$	1.27995	+	1.16693i	0.0493750	+	0.0450155i
$673$	3.72400	−	5.12565i	0.143550	−	0.197579i	−0.731188	−	0.682176i	$-0.761034\pi$
$673$	3.72400	−	5.12565i	0.143550	−	0.197579i	0.874738	+	0.484597i	$0.161034\pi$
$674$	31.2287	+	10.1468i	1.20289	+	0.390841i
$675$	6.10828	−	17.6728i	0.235108	−	0.680227i
$676$	21.4000	−	15.5480i	0.823076	−	0.598000i
$677$	9.96416	−	7.23938i	0.382954	−	0.278232i	−0.379608	−	0.925147i	$-0.623941\pi$
$677$	9.96416	−	7.23938i	0.382954	−	0.278232i	0.762562	+	0.646915i	$0.223941\pi$
$678$	−6.26856	+	13.8475i	−0.240742	+	0.531809i
$679$	−18.3011	−	5.94637i	−0.702330	−	0.228201i
$680$	−9.97412	+	13.7282i	−0.382490	+	0.526452i
$681$	−15.7337	+	17.2575i	−0.602918	+	0.661309i
$682$	11.1730	+	17.9779i	0.427837	+	0.688410i
$683$		−	28.6993i		−	1.09815i	−0.835773	−	0.549075i	$-0.814980\pi$
$683$		−	28.6993i		−	1.09815i	0.835773	−	0.549075i	$-0.185020\pi$
$684$	−2.30189	−	1.36737i	−0.0880149	−	0.0522826i
$685$	12.6093	−	38.8074i	0.481776	−	1.48275i
$686$	−0.951057	+	0.309017i	−0.0363115	+	0.0117983i
$687$	−1.93838	+	17.4029i	−0.0739540	+	0.663961i
$688$	1.73299	+	2.38526i	0.0660698	+	0.0909372i
$689$	−13.7800	−	42.4106i	−0.524978	−	1.61572i
$690$	12.7723	+	22.4428i	0.486235	+	0.854385i
$691$	−6.64503	−	4.82790i	−0.252789	−	0.183662i	0.454173	−	0.890914i	$-0.349935\pi$
$691$	−6.64503	−	4.82790i	−0.252789	−	0.183662i	−0.706962	+	0.707252i	$0.749935\pi$
$692$	18.5166			0.703897
$693$	0.199551	+	9.94787i	0.00758030	+	0.377888i
$694$	20.0249			0.760134
$695$	34.6578	+	25.1804i	1.31465	+	0.955146i
$696$	−3.88988	−	6.83508i	−0.147446	−	0.259083i
$697$	−18.4339	−	56.7338i	−0.698235	−	2.14895i
$698$	−0.349280	−	0.480742i	−0.0132204	−	0.0181964i
$699$	3.53356	−	31.7244i	0.133652	−	1.19993i
$700$	−3.42243	+	1.11202i	−0.129356	+	0.0420302i
$701$	−12.5628	+	38.6644i	−0.474491	+	1.46033i	0.372152	+	0.928172i	$0.378620\pi$
$701$	−12.5628	+	38.6644i	−0.474491	+	1.46033i	−0.846643	+	0.532162i	$0.821380\pi$
$702$	31.2224	−	9.50589i	1.17841	−	0.358777i
$703$			2.58304i			0.0974213i
$704$	−3.07208	−	1.24992i	−0.115783	−	0.0471082i
$705$	12.3274	−	13.5213i	0.464279	−	0.509242i
$706$	12.0524	−	16.5888i	0.453600	−	0.624326i
$707$	−13.8752	−	4.50831i	−0.521829	−	0.169553i
$708$	−7.86476	+	17.3736i	−0.295576	+	0.652938i
$709$	−7.48142	+	5.43557i	−0.280971	+	0.204137i	−0.719341	−	0.694657i	$-0.755556\pi$
$709$	−7.48142	+	5.43557i	−0.280971	+	0.204137i	0.438370	+	0.898795i	$0.355556\pi$
$710$	−3.88556	+	2.82303i	−0.145823	+	0.105946i
$711$	14.8752	+	34.5583i	0.557863	+	1.29604i
$712$	1.54806	+	0.502996i	0.0580161	+	0.0188506i
$713$	19.0726	−	26.2512i	0.714275	−	0.983116i
$714$	7.40688	+	6.75289i	0.277195	+	0.252720i
$715$	59.3075	−	14.6336i	2.21797	−	0.547264i
$716$			4.46546i			0.166882i
$717$	28.3542	−	5.84320i	1.05891	−	0.218218i
$718$	−6.23382	+	19.1857i	−0.232644	+	0.716005i
$719$	−22.3023	+	7.24647i	−0.831737	+	0.270248i	−0.693777	−	0.720190i	$-0.744055\pi$
$719$	−22.3023	+	7.24647i	−0.831737	+	0.270248i	−0.137960	+	0.990438i	$0.544055\pi$
$720$	6.60999	−	5.80474i	0.246340	−	0.216330i
$721$	10.7519	+	14.7987i	0.400421	+	0.551132i
$722$	5.62519	+	17.3126i	0.209348	+	0.644307i
$723$	−32.4426	+	18.4633i	−1.20655	+	0.686656i
$724$	8.05685	+	5.85364i	0.299430	+	0.217549i
$725$	16.3394			0.606830
$726$	−6.94103	−	17.7432i	−0.257606	−	0.658513i
$727$	−5.54260			−0.205564			−0.102782	−	0.994704i	$-0.532774\pi$
$727$	−5.54260			−0.205564			−0.102782	+	0.994704i	$0.532774\pi$
$728$	−5.08149	−	3.69192i	−0.188333	−	0.136832i
$729$	26.9813	+	1.00514i	0.999307	+	0.0372275i
$730$	7.86581	+	24.2085i	0.291127	+	0.895996i
$731$	10.0286	+	13.8032i	0.370921	+	0.510529i
$732$	6.53040	+	0.727375i	0.241370	+	0.0268846i
$733$	18.5783	−	6.03646i	0.686205	−	0.222962i	0.0548952	−	0.998492i	$-0.482518\pi$
$733$	18.5783	−	6.03646i	0.686205	−	0.222962i	0.631310	+	0.775531i	$0.282518\pi$
$734$	0.487440	−	1.50019i	0.0179917	−	0.0553729i
$735$	1.02512	+	4.97442i	0.0378121	+	0.183484i
$736$			5.08427i			0.187409i
$737$	15.1450	−	3.73688i	0.557873	−	0.137650i
$738$	2.85059	+	30.7936i	0.104932	+	1.13353i
$739$	10.2910	−	14.1643i	0.378560	−	0.521042i	−0.576643	−	0.816996i	$-0.695638\pi$
$739$	10.2910	−	14.1643i	0.378560	−	0.521042i	0.955202	+	0.295954i	$0.0956375\pi$
$740$	−8.07163	−	2.62263i	−0.296719	−	0.0964098i
$741$	8.84512	+	4.00406i	0.324934	+	0.147093i
$742$	−5.74371	+	4.17305i	−0.210858	+	0.153197i
$743$	−7.12450	+	5.17625i	−0.261372	+	0.189898i	−0.710752	−	0.703443i	$-0.751645\pi$
$743$	−7.12450	+	5.17625i	−0.261372	+	0.189898i	0.449379	+	0.893341i	$0.351645\pi$
$744$	−10.0703	−	4.55869i	−0.369196	−	0.167130i
$745$	−52.3601	−	17.0128i	−1.91832	−	0.623301i
$746$	19.8872	−	27.3724i	0.728122	−	1.00217i
$747$	0.966825	+	10.4442i	0.0353743	+	0.382132i
$748$	−17.7777	−	7.23312i	−0.650018	−	0.264469i
$749$		−	3.04091i		−	0.111112i
$750$	−1.43665	−	6.97135i	−0.0524589	−	0.254558i
$751$	4.43807	−	13.6590i	0.161948	−	0.498423i	−0.836851	−	0.547431i	$-0.815606\pi$
$751$	4.43807	−	13.6590i	0.161948	−	0.498423i	0.998798	+	0.0490077i	$0.0156059\pi$
$752$	3.42626	−	1.11326i	0.124943	−	0.0405964i
$753$	−45.7843	−	5.09959i	−1.66847	−	0.185839i
$754$	16.7633	+	23.0727i	0.610484	+	0.840259i
$755$	11.0261	+	33.9348i	0.401280	+	1.23501i
$756$	−2.97543	−	4.25991i	−0.108215	−	0.154931i
$757$	30.5920	+	22.2264i	1.11189	+	0.807833i	0.982960	−	0.183821i	$-0.0588468\pi$
$757$	30.5920	+	22.2264i	1.11189	+	0.807833i	0.128927	+	0.991654i	$0.458847\pi$
$758$	−26.4592			−0.961041
$759$	−21.1843	+	20.1065i	−0.768941	+	0.729819i
$760$	2.61699			0.0949282
$761$	−20.7715	−	15.0914i	−0.752967	−	0.547063i	0.143778	−	0.989610i	$-0.454075\pi$
$761$	−20.7715	−	15.0914i	−0.752967	−	0.547063i	−0.896745	+	0.442547i	$0.854075\pi$
$762$	0.405160	−	0.230579i	0.0146774	−	0.00835298i
$763$	1.16311	+	3.57968i	0.0421074	+	0.129593i
$764$	4.39523	+	6.04951i	0.159014	+	0.218864i
$765$	38.2511	−	33.5912i	1.38297	−	1.21449i
$766$	14.5825	−	4.73813i	0.526886	−	0.171195i
$767$	21.3710	−	65.7730i	0.771660	−	2.37493i
$768$	1.69640	−	0.349593i	0.0612137	−	0.0126148i
$769$			4.75026i			0.171299i	0.996325	+	0.0856494i	$0.0272965\pi$
$769$			4.75026i			0.171299i	−0.996325	+	0.0856494i	$0.972704\pi$
$770$	−5.13358	−	8.26018i	−0.185001	−	0.297676i
$771$	−7.29264	−	6.64874i	−0.262638	−	0.239448i
$772$	−3.03835	+	4.18193i	−0.109353	+	0.150511i
$773$	−21.6854	−	7.04601i	−0.779969	−	0.253427i	−0.108142	−	0.994135i	$-0.534490\pi$
$773$	−21.6854	−	7.04601i	−0.779969	−	0.253427i	−0.671827	+	0.740708i	$0.734490\pi$
$774$	−3.49703	−	8.12437i	−0.125698	−	0.292024i
$775$	18.5801	−	13.4993i	0.667419	−	0.484908i
$776$	−15.5678	+	11.3107i	−0.558852	+	0.406030i
$777$	−2.06738	+	4.56691i	−0.0741667	+	0.163837i
$778$	−10.3503	−	3.36302i	−0.371077	−	0.120570i
$779$	−5.40755	+	7.44285i	−0.193746	+	0.266668i
$780$	−21.4928	+	23.5743i	−0.769565	+	0.844095i
$781$	−4.15282	−	3.50192i	−0.148600	−	0.125308i
$782$			29.4220i			1.05213i
$783$	6.87174	+	22.5704i	0.245576	+	0.806602i
$784$	−0.309017	+	0.951057i	−0.0110363	+	0.0339663i
$785$	−28.9981	+	9.42207i	−1.03499	+	0.336288i
$786$	0.500578	−	4.49421i	0.0178550	−	0.160303i
$787$	−4.76822	−	6.56290i	−0.169969	−	0.233942i	0.715532	−	0.698580i	$-0.246184\pi$
$787$	−4.76822	−	6.56290i	−0.169969	−	0.233942i	−0.885501	+	0.464638i	$0.846184\pi$
$788$	2.56500	+	7.89425i	0.0913742	+	0.281221i
$789$	−2.03530	−	3.57631i	−0.0724585	−	0.127320i
$790$	−29.7517	−	21.6159i	−1.05852	−	0.769059i
$791$	−8.77587			−0.312034
$792$	8.16529	+	5.68577i	0.290141	+	0.202035i
$793$	−23.8281			−0.846162
$794$	26.7980	+	19.4699i	0.951026	+	0.690961i
$795$	17.8351	+	31.3389i	0.632547	+	1.11148i
$796$	6.14041	+	18.8982i	0.217641	+	0.669830i
$797$	−4.80203	−	6.60943i	−0.170097	−	0.234118i	0.715455	−	0.698659i	$-0.246219\pi$
$797$	−4.80203	−	6.60943i	−0.170097	−	0.234118i	−0.885552	+	0.464541i	$0.846219\pi$
$798$	0.171116	−	1.53629i	0.00605745	−	0.0543840i
$799$	19.8273	−	6.44228i	0.701439	−	0.227911i
$800$	−1.11202	+	3.42243i	−0.0393157	+	0.121001i
$801$	−4.19834	−	2.49390i	−0.148341	−	0.0881175i
$802$			34.6212i			1.22252i
$803$	−24.4526	+	15.1969i	−0.862913	+	0.536287i
$804$	−5.48848	+	6.02002i	−0.193564	+	0.212310i
$805$	−8.76315	+	12.0614i	−0.308861	+	0.425110i
$806$	38.1244	+	12.3874i	1.34287	+	0.436326i
$807$	−13.9382	+	30.7901i	−0.490649	+	1.08386i
$808$	−11.8029	+	8.57532i	−0.415225	+	0.301679i
$809$	−14.6019	+	10.6089i	−0.513377	+	0.372990i	−0.814103	−	0.580720i	$-0.802771\pi$
$809$	−14.6019	+	10.6089i	−0.513377	+	0.372990i	0.300726	+	0.953710i	$0.402771\pi$
$810$	−23.1757	+	12.6241i	−0.814313	+	0.443566i
$811$	−18.2298	−	5.92322i	−0.640135	−	0.207992i	−0.0290754	−	0.999577i	$-0.509256\pi$
$811$	−18.2298	−	5.92322i	−0.640135	−	0.207992i	−0.611059	+	0.791585i	$0.709256\pi$
$812$	2.66886	−	3.67337i	0.0936587	−	0.128910i
$813$	−4.12862	−	3.76408i	−0.144797	−	0.132012i
$814$	0.692952	−	9.57423i	0.0242879	−	0.335577i
$815$			22.5409i			0.789572i
$816$	9.81685	−	2.02304i	0.343659	−	0.0708207i
$817$	0.813111	−	2.50250i	0.0284472	−	0.0875514i
$818$	16.0725	−	5.22228i	0.561963	−	0.182593i
$819$	12.4338	+	14.1586i	0.434472	+	0.494743i
$820$	−17.7674	−	24.4547i	−0.620465	−	0.853996i
$821$	−4.20725	−	12.9486i	−0.146834	−	0.451909i	0.850408	−	0.526124i	$-0.176355\pi$
$821$	−4.20725	−	12.9486i	−0.146834	−	0.451909i	−0.997242	+	0.0742144i	$0.976355\pi$
$822$	−20.9475	+	11.9213i	−0.730627	+	0.415803i
$823$	27.7764	+	20.1808i	0.968225	+	0.703457i	0.955046	−	0.296456i	$-0.0958049\pi$
$823$	27.7764	+	20.1808i	0.968225	+	0.703457i	0.0131788	+	0.999913i	$0.495805\pi$
$824$	18.2922			0.637238
$825$	−18.6576	+	8.90114i	−0.649576	+	0.309898i
$826$	−11.0105			−0.383105
$827$	17.7739	+	12.9135i	0.618060	+	0.449047i	0.852243	−	0.523146i	$-0.175242\pi$
$827$	17.7739	+	12.9135i	0.618060	+	0.449047i	−0.234184	+	0.972192i	$0.575242\pi$
$828$	3.35617	−	14.8790i	0.116635	−	0.517081i
$829$	−4.10265	−	12.6267i	−0.142491	−	0.438542i	0.854189	−	0.519963i	$-0.174054\pi$
$829$	−4.10265	−	12.6267i	−0.142491	−	0.438542i	−0.996680	+	0.0814207i	$0.974054\pi$
$830$	−6.02611	−	8.29422i	−0.209169	−	0.287897i
$831$	1.20884	+	0.134645i	0.0419343	+	0.00467077i
$832$	−5.97365	+	1.94096i	−0.207099	+	0.0672906i
$833$	−1.78824	+	5.50363i	−0.0619588	+	0.190690i
$834$	−5.10731	−	24.7833i	−0.176852	−	0.858176i
$835$		−	18.0772i		−	0.625587i
$836$	0.709076	+	2.87377i	0.0245239	+	0.0993915i
$837$	26.4613	+	19.9884i	0.914637	+	0.690901i
$838$	−13.4210	+	18.4725i	−0.463622	+	0.638121i
$839$	−11.6730	−	3.79279i	−0.402997	−	0.130942i	0.100503	−	0.994937i	$-0.467955\pi$
$839$	−11.6730	−	3.79279i	−0.402997	−	0.130942i	−0.503500	+	0.863995i	$0.667955\pi$
$840$	4.62694	+	2.09455i	0.159644	+	0.0722688i
$841$	6.78239	−	4.92770i	0.233876	−	0.169921i
$842$	−19.4405	+	14.1244i	−0.669965	+	0.486758i
$843$	34.9903	+	15.8396i	1.20513	+	0.545544i
$844$	5.71985	+	1.85849i	0.196885	+	0.0639719i
$845$	45.5919	−	62.7518i	1.56841	−	2.15873i
$846$	−10.7617	+	0.996223i	−0.369996	+	0.0342508i
$847$	7.67973	−	7.87539i	0.263879	−	0.270602i
$848$			7.09961i			0.243802i
$849$	−9.71971	−	47.1650i	−0.333579	−	1.61870i
$850$	−6.43508	+	19.8051i	−0.220721	+	0.679311i
$851$	−13.9951	+	4.54730i	−0.479747	+	0.155879i
$852$	2.81946	+	0.314040i	0.0965932	+	0.0107588i
$853$	3.07286	+	4.22943i	0.105213	+	0.144813i	0.858377	−	0.513020i	$-0.171473\pi$
$853$	3.07286	+	4.22943i	0.105213	+	0.144813i	−0.753164	+	0.657833i	$0.771473\pi$
$854$	1.17230	+	3.60797i	0.0401153	+	0.123462i
$855$	−7.65856	−	1.72750i	−0.261917	−	0.0590792i
$856$	−2.46015	−	1.78740i	−0.0840861	−	0.0610922i
$857$	−42.1277			−1.43905			−0.719527	−	0.694465i	$-0.755641\pi$
$857$	−42.1277			−1.43905			−0.719527	+	0.694465i	$0.755641\pi$
$858$	−31.7109	−	17.2142i	−1.08259	−	0.587683i
$859$	−13.6752			−0.466593			−0.233297	−	0.972406i	$-0.574951\pi$
$859$	−13.6752			−0.466593			−0.233297	+	0.972406i	$0.574951\pi$
$860$	6.99437	+	5.08171i	0.238506	+	0.173285i
$861$	−15.5177	+	8.83123i	−0.528843	+	0.300967i
$862$	−9.67674	−	29.7820i	−0.329591	−	1.01438i
$863$	−6.45872	−	8.88966i	−0.219857	−	0.302608i	0.684814	−	0.728718i	$-0.259883\pi$
$863$	−6.45872	−	8.88966i	−0.219857	−	0.302608i	−0.904671	+	0.426110i	$0.859883\pi$
$864$	−5.19525	−	0.0967366i	−0.176746	−	0.00329105i
$865$	51.6394	−	16.7787i	1.75579	−	0.570492i
$866$	10.6852	−	32.8858i	0.363099	−	1.11750i
$867$	27.9699	−	5.76400i	0.949908	−	0.195756i
$868$		−	6.38209i		−	0.216622i
$869$	15.6756	−	38.5278i	0.531758	−	1.30697i
$870$	−17.0417	−	15.5370i	−0.577767	−	0.526753i
$871$	17.3643	−	23.9000i	0.588368	−	0.809819i
$872$	3.57968	+	1.16311i	0.121223	+	0.0393878i
$873$	53.0251	−	22.8240i	1.79463	−	0.772474i
$874$	3.67093	−	2.66709i	0.124171	−	0.0902155i
$875$	3.32465	−	2.41550i	0.112394	−	0.0816587i
$876$	6.20048	−	13.6971i	0.209495	−	0.462782i
$877$	−39.0476	−	12.6873i	−1.31854	−	0.428421i	−0.436549	−	0.899681i	$-0.643799\pi$
$877$	−39.0476	−	12.6873i	−1.31854	−	0.428421i	−0.881994	+	0.471260i	$0.843799\pi$
$878$	22.2197	−	30.5827i	0.749877	−	1.03212i
$879$	9.11386	−	9.99651i	0.307403	−	0.337174i
$880$	−9.70007	−	0.702059i	−0.326989	−	0.0236664i
$881$			8.49510i			0.286207i	0.989708	+	0.143104i	$0.0457082\pi$
$881$			8.49510i			0.286207i	−0.989708	+	0.143104i	$0.954292\pi$
$882$	1.53213	−	2.57926i	0.0515895	−	0.0868482i
$883$	−1.52037	+	4.67922i	−0.0511646	+	0.157468i	−0.973374	−	0.229222i	$-0.926382\pi$
$883$	−1.52037	+	4.67922i	−0.0511646	+	0.157468i	0.922210	+	0.386690i	$0.126382\pi$
$884$	−34.5687	+	11.2321i	−1.16267	+	0.377775i
$885$	−6.19046	+	55.5781i	−0.208090	+	1.86824i
$886$	1.90715	+	2.62496i	0.0640719	+	0.0881874i
$887$	−10.3725	−	31.9232i	−0.348273	−	1.07188i	−0.959808	−	0.280658i	$-0.909447\pi$
$887$	−10.3725	−	31.9232i	−0.348273	−	1.07188i	0.611535	−	0.791218i	$-0.290553\pi$
$888$	2.47954	+	4.35691i	0.0832078	+	0.146208i
$889$	0.217745	+	0.158201i	0.00730293	+	0.00530589i
$890$	4.77304			0.159993
$891$	−20.1423	−	22.0293i	−0.674792	−	0.738008i
$892$	−6.03257			−0.201986
$893$	−2.60112	−	1.88983i	−0.0870433	−	0.0632407i
$894$	16.0846	+	28.2629i	0.537949	+	0.945254i
$895$	4.04633	+	12.4533i	0.135254	+	0.416269i
$896$	0.587785	+	0.809017i	0.0196365	+	0.0270274i
$897$	−6.12300	+	54.9725i	−0.204441	+	1.83548i
$898$	8.74460	−	2.84129i	0.291811	−	0.0948152i
$899$	−8.95474	+	27.5598i	−0.298657	+	0.919172i
$900$	5.51346	−	9.28161i	0.183782	−	0.309387i
$901$			41.0845i			1.36872i
$902$	22.0402	−	26.1368i	0.733857	−	0.870260i
$903$	3.44052	−	3.77373i	0.114493	−	0.125582i
$904$	−5.15833	+	7.09983i	−0.171563	+	0.236137i
$905$	27.7732	+	9.02408i	0.923214	+	0.299970i
$906$	8.69167	−	19.2002i	0.288761	−	0.637885i
$907$	43.7054	−	31.7539i	1.45122	−	1.05437i	0.465670	−	0.884958i	$-0.345813\pi$
$907$	43.7054	−	31.7539i	1.45122	−	1.05437i	0.985545	−	0.169411i	$-0.0541867\pi$
$908$	−10.9080	+	7.92509i	−0.361993	+	0.263003i
$909$	40.2016	−	17.3043i	1.33340	−	0.573946i
$910$	−17.5167	−	5.69153i	−0.580674	−	0.188672i
$911$	25.4009	−	34.9613i	0.841568	−	1.15832i	−0.144090	−	0.989565i	$-0.546026\pi$
$911$	25.4009	−	34.9613i	0.841568	−	1.15832i	0.985658	−	0.168754i	$-0.0539745\pi$
$912$	−1.14230	−	1.04144i	−0.0378254	−	0.0344856i
$913$	7.47528	−	8.86472i	0.247396	−	0.293379i
$914$		−	11.8311i		−	0.391336i
$915$	18.8712	−	3.88894i	0.623861	−	0.128564i
$916$	−3.12407	+	9.61488i	−0.103222	+	0.317685i
$917$	2.48300	−	0.806775i	0.0819958	−	0.0266420i
$918$	−30.0642	−	0.559802i	−0.992267	−	0.0184762i
$919$	3.24301	+	4.46362i	0.106977	+	0.147241i	0.859149	−	0.511726i	$-0.170994\pi$
$919$	3.24301	+	4.46362i	0.106977	+	0.147241i	−0.752172	+	0.658967i	$0.770994\pi$
$920$	4.60706	+	14.1791i	0.151890	+	0.467470i
$921$	39.8362	−	22.6710i	1.31265	−	0.747034i
$922$	−4.85792	−	3.52949i	−0.159987	−	0.116238i
$923$	−10.2877			−0.338623
$924$	−1.04639	+	5.64846i	−0.0344239	+	0.185821i
$925$	−10.4153			−0.342452
$926$	18.9537	+	13.7706i	0.622856	+	0.452532i
$927$	−53.5316	−	12.0748i	−1.75821	−	0.396589i
$928$	−1.40310	−	4.31831i	−0.0460591	−	0.141755i
$929$	12.3458	+	16.9926i	0.405054	+	0.557509i	0.962003	−	0.273038i	$-0.0880283\pi$
$929$	12.3458	+	16.9926i	0.405054	+	0.557509i	−0.556950	+	0.830546i	$0.688028\pi$
$930$	−32.2151	−	3.58821i	−1.05637	−	0.117662i
$931$	0.848781	−	0.275786i	0.0278177	−	0.00903851i
$932$	5.69499	−	17.5274i	0.186546	−	0.574128i
$933$	−0.0548953	−	0.266380i	−0.00179719	−	0.00872091i
$934$		−	13.4004i		−	0.438474i
$935$	−56.1329	−	4.06272i	−1.83574	−	0.132865i
$936$	18.7630	−	1.73690i	0.613287	−	0.0567725i
$937$	26.1332	−	35.9693i	0.853734	−	1.17506i	−0.129293	−	0.991606i	$-0.541271\pi$
$937$	26.1332	−	35.9693i	0.853734	−	1.17506i	0.983028	−	0.183458i	$-0.0587291\pi$
$938$	−4.47314	−	1.45341i	−0.146053	−	0.0474555i
$939$	15.6187	+	7.07037i	0.509698	+	0.230733i
$940$	8.54643	−	6.20934i	0.278754	−	0.202526i
$941$	−16.7278	+	12.1535i	−0.545312	+	0.396192i	−0.826054	−	0.563591i	$-0.809419\pi$
$941$	−16.7278	+	12.1535i	−0.545312	+	0.396192i	0.280742	+	0.959783i	$0.409419\pi$
$942$	16.4071	+	7.42726i	0.534572	+	0.241993i
$943$	−49.8457	−	16.1958i	−1.62320	−	0.527409i
$944$	−6.47182	+	8.90770i	−0.210640	+	0.289921i
$945$	−12.1580	−	9.18392i	−0.395499	−	0.298753i
$946$	−3.68520	+	9.05756i	−0.119816	+	0.294487i
$947$		−	3.09353i		−	0.100526i	−0.998736	−	0.0502632i	$-0.983994\pi$
$947$		−	3.09353i		−	0.100526i	0.998736	−	0.0502632i	$-0.0160060\pi$
$948$	4.38433	+	21.2751i	0.142397	+	0.690982i
$949$	−16.8486	+	51.8547i	−0.546929	+	1.68327i
$950$	3.05439	−	0.992431i	0.0990975	−	0.0321987i
$951$	−35.3103	−	3.93296i	−1.14501	−	0.127535i
$952$	3.40143	+	4.68167i	0.110241	+	0.151734i
$953$	−0.707461	−	2.17734i	−0.0229169	−	0.0705310i	0.938944	−	0.344070i	$-0.111806\pi$
$953$	−0.707461	−	2.17734i	−0.0229169	−	0.0705310i	−0.961861	+	0.273539i	$0.911806\pi$
$954$	4.68651	−	20.7768i	0.151731	−	0.672675i
$955$	17.7392	+	12.8883i	0.574026	+	0.417054i
$956$	16.7143			0.540579
$957$	12.4440	−	22.9236i	0.402258	−	0.741014i
$958$	13.1419			0.424596
$959$	−11.2578	−	8.17926i	−0.363533	−	0.264122i
$960$	4.41417	−	2.51213i	0.142467	−	0.0810785i
$961$	3.00706	+	9.25479i	0.0970021	+	0.298542i
$962$	−10.6855	−	14.7073i	−0.344514	−	0.474183i
$963$	6.01968	+	6.85475i	0.193982	+	0.220891i
$964$	−20.4968	+	6.65981i	−0.660157	+	0.214498i
$965$	−4.68397	+	14.4158i	−0.150782	+	0.464061i
$966$	8.62498	−	1.77742i	0.277504	−	0.0571877i
$967$		−	17.0631i		−	0.548712i	−0.961628	−	0.274356i	$-0.911535\pi$
$967$		−	17.0631i		−	0.548712i	0.961628	−	0.274356i	$-0.0884647\pi$
$968$	−1.85729	−	10.8421i	−0.0596957	−	0.348477i
$969$	−6.61035	−	6.02669i	−0.212355	−	0.193605i
$970$	−33.1666	+	45.6500i	−1.06492	+	1.46573i
$971$	51.3218	+	16.6755i	1.64700	+	0.535141i	0.978086	−	0.208202i	$-0.0667613\pi$
$971$	51.3218	+	16.6755i	1.64700	+	0.535141i	0.668910	+	0.743344i	$0.266761\pi$
$972$	15.1399	+	3.71253i	0.485613	+	0.119079i
$973$	11.8192	−	8.58715i	0.378906	−	0.275291i
$974$	4.43969	−	3.22563i	0.142257	−	0.103356i
$975$	−16.1451	+	35.6651i	−0.517056	+	1.14220i
$976$	3.60797	+	1.17230i	0.115488	+	0.0375244i
$977$	−10.4844	+	14.4305i	−0.335425	+	0.461673i	−0.943098	−	0.332514i	$-0.892103\pi$
$977$	−10.4844	+	14.4305i	−0.335425	+	0.461673i	0.607673	+	0.794187i	$0.292103\pi$
$978$	8.97024	−	9.83898i	0.286837	−	0.314616i
$979$	1.29326	+	5.24138i	0.0413328	+	0.167515i
$980$			2.93233i			0.0936698i
$981$	−9.70807	−	5.76679i	−0.309955	−	0.184119i
$982$	−3.31710	+	10.2090i	−0.105853	+	0.325781i
$983$	35.6569	−	11.5856i	1.13728	−	0.369524i	0.320941	−	0.947099i	$-0.396001\pi$
$983$	35.6569	−	11.5856i	1.13728	−	0.369524i	0.816338	+	0.577575i	$0.196001\pi$
$984$	−1.97649	+	17.7450i	−0.0630082	+	0.565690i
$985$	14.3066	+	19.6913i	0.455846	+	0.627418i
$986$	−8.11957	−	24.9895i	−0.258580	−	0.795827i
$987$	−3.08633	−	5.42313i	−0.0982390	−	0.172620i
$988$	4.53503	+	3.29490i	0.144279	+	0.104825i
$989$	14.9902			0.476660
$990$	27.9236	+	8.45765i	0.887469	+	0.268802i
$991$	−32.0859			−1.01924			−0.509621	−	0.860399i	$-0.670214\pi$
$991$	−32.0859			−1.01924			−0.509621	+	0.860399i	$0.670214\pi$
$992$	−5.16322	−	3.75130i	−0.163932	−	0.119104i
$993$	−13.8804	−	24.3898i	−0.440480	−	0.773987i
$994$	0.506134	+	1.55772i	0.0160536	+	0.0494079i
$995$	34.2489	+	47.1395i	1.08576	+	1.49442i
$996$	−0.670359	+	6.01850i	−0.0212411	+	0.190704i
$997$	−44.3124	+	14.3980i	−1.40339	+	0.455988i	−0.910284	−	0.413983i	$-0.864137\pi$
$997$	−44.3124	+	14.3980i	−1.40339	+	0.455988i	−0.493102	+	0.869971i	$0.664137\pi$
$998$	0.246511	−	0.758684i	0.00780318	−	0.0240157i
$999$	−4.38027	−	14.3871i	−0.138586	−	0.455189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.w.a.29.9	✓	48
3.2	odd	2		462.2.w.b.29.2	yes	48
11.8	odd	10		462.2.w.b.239.2	yes	48
33.8	even	10	inner	462.2.w.a.239.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.w.a.29.9	✓	48	1.1	even	1	trivial
462.2.w.a.239.9	yes	48	33.8	even	10	inner
462.2.w.b.29.2	yes	48	3.2	odd	2
462.2.w.b.239.2	yes	48	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.856700 + 1.50535i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.72358 + 2.37230i) q^{5} +(0.191735 - 1.72141i) q^{6} +(0.951057 - 0.309017i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.53213 + 2.57926i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.856700 + 1.50535i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.72358 + 2.37230i) q^{5} +(0.191735 - 1.72141i) q^{6} +(0.951057 - 0.309017i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.53213 + 2.57926i) q^{9} -2.93233i q^{10} +(3.22005 - 0.794517i) q^{11} +(-1.16693 + 1.27995i) q^{12} +(3.69192 - 5.08149i) q^{13} +(-0.951057 - 0.309017i) q^{14} +(-2.09455 + 4.62694i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.68167 + 3.40143i) q^{17} +(2.75557 - 1.18610i) q^{18} +(0.848781 + 0.275786i) q^{19} +(-1.72358 + 2.37230i) q^{20} +(1.27995 + 1.16693i) q^{21} +(-3.07208 - 1.24992i) q^{22} +5.08427i q^{23} +(1.69640 - 0.349593i) q^{24} +(-1.11202 + 3.42243i) q^{25} +(-5.97365 + 1.94096i) q^{26} +(-5.19525 - 0.0967366i) q^{27} +(0.587785 + 0.809017i) q^{28} +(-1.40310 - 4.31831i) q^{29} +(4.41417 - 2.51213i) q^{30} +(-5.16322 - 3.75130i) q^{31} +1.00000 q^{32} +(3.95464 + 4.16663i) q^{33} +5.78686 q^{34} +(2.37230 + 1.72358i) q^{35} +(-2.92648 - 0.660108i) q^{36} +(0.894385 + 2.75263i) q^{37} +(-0.524576 - 0.722016i) q^{38} +(10.8123 + 1.20430i) q^{39} +(2.78881 - 0.906140i) q^{40} +(-3.18548 + 9.80390i) q^{41} +(-0.349593 - 1.69640i) q^{42} -2.94834i q^{43} +(1.75068 + 2.81693i) q^{44} +(-8.75954 + 0.810877i) q^{45} +(2.98846 - 4.11326i) q^{46} +(-3.42626 - 1.11326i) q^{47} +(-1.57790 - 0.714295i) q^{48} +(0.809017 - 0.587785i) q^{49} +(2.91130 - 2.11518i) q^{50} +(-9.13112 - 4.13352i) q^{51} +(5.97365 + 1.94096i) q^{52} +(4.17305 - 5.74371i) q^{53} +(4.14619 + 3.13195i) q^{54} +(7.43486 + 6.26953i) q^{55} -1.00000i q^{56} +(0.311998 + 1.51397i) q^{57} +(-1.40310 + 4.31831i) q^{58} +(10.4716 - 3.40244i) q^{59} +(-5.04773 - 0.562231i) q^{60} +(-2.22985 - 3.06912i) q^{61} +(1.97217 + 6.06973i) q^{62} +(-0.660108 + 2.92648i) q^{63} +(-0.809017 - 0.587785i) q^{64} +18.4182 q^{65} +(-0.750289 - 5.69535i) q^{66} +4.70333 q^{67} +(-4.68167 - 3.40143i) q^{68} +(-7.65359 + 4.35570i) q^{69} +(-0.906140 - 2.78881i) q^{70} +(-0.962724 - 1.32508i) q^{71} +(1.97957 + 2.25418i) q^{72} +(-8.25571 + 2.68244i) q^{73} +(0.894385 - 2.75263i) q^{74} +(-6.10461 + 1.25803i) q^{75} +0.892461i q^{76} +(2.81693 - 1.75068i) q^{77} +(-8.03944 - 7.32959i) q^{78} +(7.37157 - 10.1461i) q^{79} +(-2.78881 - 0.906140i) q^{80} +(-4.30515 - 7.90352i) q^{81} +(8.33969 - 6.05914i) q^{82} +(2.82854 - 2.05506i) q^{83} +(-0.714295 + 1.57790i) q^{84} +(-16.1385 - 5.24371i) q^{85} +(-1.73299 + 2.38526i) q^{86} +(5.29851 - 5.81165i) q^{87} +(0.239420 - 3.30797i) q^{88} +1.62773i q^{89} +(7.56324 + 4.49271i) q^{90} +(1.94096 - 5.97365i) q^{91} +(-4.83543 + 1.57113i) q^{92} +(1.22367 - 10.9862i) q^{93} +(2.11755 + 2.91455i) q^{94} +(0.808695 + 2.48891i) q^{95} +(0.856700 + 1.50535i) q^{96} +(-15.5678 - 11.3107i) q^{97} -1.00000 q^{98} +(-2.88428 + 9.52265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 48 * q - 12 * q^2 - 4 * q^3 - 12 * q^4 + 6 * q^6 - 12 * q^8 + 10 * q^9	\( 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9} - 8 q^{11} + 6 q^{12} + 36 q^{15} - 12 q^{16} - 24 q^{17} + 30 q^{19} - 8 q^{22} - 4 q^{24} + 18 q^{25} - 20 q^{26} - 22 q^{27} + 8 q^{29} - 24 q^{30} - 32 q^{31} + 48 q^{32} - 14 q^{33} - 4 q^{34} + 6 q^{35} - 10 q^{36} - 20 q^{37} + 20 q^{38} - 6 q^{39} + 22 q^{44} + 12 q^{45} + 20 q^{46} + 20 q^{47} - 4 q^{48} + 12 q^{49} + 28 q^{50} + 8 q^{51} + 20 q^{52} + 20 q^{53} + 18 q^{54} + 16 q^{55} - 2 q^{57} + 8 q^{58} + 30 q^{59} - 4 q^{60} - 20 q^{61} + 8 q^{62} + 4 q^{63} - 12 q^{64} - 14 q^{66} + 36 q^{67} - 24 q^{68} - 70 q^{69} - 4 q^{70} + 10 q^{72} - 20 q^{73} - 20 q^{74} - 30 q^{75} - 16 q^{77} - 16 q^{78} - 20 q^{79} + 26 q^{81} - 10 q^{82} - 46 q^{83} - 10 q^{84} + 10 q^{85} - 30 q^{86} + 8 q^{87} - 8 q^{88} - 38 q^{90} - 36 q^{91} + 10 q^{92} - 36 q^{93} + 50 q^{95} - 4 q^{96} - 2 q^{97} - 48 q^{98} + 70 q^{99}+O(q^{100}) \) 48 * q - 12 * q^2 - 4 * q^3 - 12 * q^4 + 6 * q^6 - 12 * q^8 + 10 * q^9 - 8 * q^11 + 6 * q^12 + 36 * q^15 - 12 * q^16 - 24 * q^17 + 30 * q^19 - 8 * q^22 - 4 * q^24 + 18 * q^25 - 20 * q^26 - 22 * q^27 + 8 * q^29 - 24 * q^30 - 32 * q^31 + 48 * q^32 - 14 * q^33 - 4 * q^34 + 6 * q^35 - 10 * q^36 - 20 * q^37 + 20 * q^38 - 6 * q^39 + 22 * q^44 + 12 * q^45 + 20 * q^46 + 20 * q^47 - 4 * q^48 + 12 * q^49 + 28 * q^50 + 8 * q^51 + 20 * q^52 + 20 * q^53 + 18 * q^54 + 16 * q^55 - 2 * q^57 + 8 * q^58 + 30 * q^59 - 4 * q^60 - 20 * q^61 + 8 * q^62 + 4 * q^63 - 12 * q^64 - 14 * q^66 + 36 * q^67 - 24 * q^68 - 70 * q^69 - 4 * q^70 + 10 * q^72 - 20 * q^73 - 20 * q^74 - 30 * q^75 - 16 * q^77 - 16 * q^78 - 20 * q^79 + 26 * q^81 - 10 * q^82 - 46 * q^83 - 10 * q^84 + 10 * q^85 - 30 * q^86 + 8 * q^87 - 8 * q^88 - 38 * q^90 - 36 * q^91 + 10 * q^92 - 36 * q^93 + 50 * q^95 - 4 * q^96 - 2 * q^97 - 48 * q^98 + 70 * q^99

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