LMFDB - Embedded newform 462.2.u.b.349.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(13,462)]

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([0, 5, 1]))

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

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

chi := DirichletCharacter("462.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.u (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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.8
Character	$\chi$	$=$	462.349
Dual form			462.2.u.b.139.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.18694 - 3.01006i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-2.24683 - 1.39706i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.18694 - 3.01006i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-2.24683 - 1.39706i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +3.72064 q^{10} +(-2.71647 - 1.90283i) q^{11} -1.00000i q^{12} +(4.11000 - 2.98609i) q^{13} +(-0.190406 - 2.63889i) q^{14} +(-1.14974 + 3.53854i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-4.90468 - 3.56346i) q^{17} +(0.951057 + 0.309017i) q^{18} +(0.0255089 + 0.0785084i) q^{19} +(2.18694 + 3.01006i) q^{20} +(2.56857 + 0.634376i) q^{21} +(-0.0572763 - 3.31613i) q^{22} +2.24601 q^{23} +(0.809017 - 0.587785i) q^{24} +(-2.73268 - 8.41032i) q^{25} +(4.83159 + 1.56988i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.02299 - 1.70514i) q^{28} +(9.40327 + 3.05531i) q^{29} +(-3.53854 + 1.14974i) q^{30} +(1.60336 + 2.20684i) q^{31} -1.00000i q^{32} +(3.17153 + 0.970268i) q^{33} -6.06252i q^{34} +(-9.11889 + 3.70780i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-2.49736 + 7.68607i) q^{37} +(-0.0485209 + 0.0667833i) q^{38} +(-2.98609 + 4.11000i) q^{39} +(-1.14974 + 3.53854i) q^{40} +(-2.40988 - 7.41686i) q^{41} +(0.996549 + 2.45090i) q^{42} +3.56568i q^{43} +(2.64914 - 1.99551i) q^{44} -3.72064i q^{45} +(1.32017 + 1.81706i) q^{46} +(9.34367 - 3.03594i) q^{47} +(0.951057 + 0.309017i) q^{48} +(3.09645 + 6.27790i) q^{49} +(5.19786 - 7.15425i) q^{50} +(5.76580 + 1.87342i) q^{51} +(1.56988 + 4.83159i) q^{52} +(1.23123 - 0.894540i) q^{53} -1.00000 q^{54} +(-11.6684 + 4.01536i) q^{55} +(2.56857 + 0.634376i) q^{56} +(-0.0485209 - 0.0667833i) q^{57} +(3.05531 + 9.40327i) q^{58} +(3.05835 + 0.993718i) q^{59} +(-3.01006 - 2.18694i) q^{60} +(-3.40260 - 2.47213i) q^{61} +(-0.842937 + 2.59429i) q^{62} +(-2.63889 + 0.190406i) q^{63} +(0.809017 - 0.587785i) q^{64} -18.9017i q^{65} +(1.07921 + 3.13613i) q^{66} -9.56243 q^{67} +(4.90468 - 3.56346i) q^{68} +(-2.13609 + 0.694056i) q^{69} +(-8.35962 - 5.19795i) q^{70} +(5.72886 + 4.16226i) q^{71} +(-0.587785 + 0.809017i) q^{72} +(-0.831452 + 2.55895i) q^{73} +(-7.68607 + 2.49736i) q^{74} +(5.19786 + 7.15425i) q^{75} -0.0825487 q^{76} +(3.44506 + 8.07041i) q^{77} -5.08024 q^{78} +(-6.41455 - 8.82886i) q^{79} +(-3.53854 + 1.14974i) q^{80} +(0.309017 - 0.951057i) q^{81} +(4.58387 - 6.30916i) q^{82} +(-9.69963 - 7.04720i) q^{83} +(-1.39706 + 2.24683i) q^{84} +(-21.4524 + 6.97032i) q^{85} +(-2.88469 + 2.09585i) q^{86} -9.88718 q^{87} +(3.17153 + 0.970268i) q^{88} +12.4627i q^{89} +(3.01006 - 2.18694i) q^{90} +(-13.4062 + 0.967306i) q^{91} +(-0.694056 + 2.13609i) q^{92} +(-2.20684 - 1.60336i) q^{93} +(7.94820 + 5.77471i) q^{94} +(0.292101 + 0.0949095i) q^{95} +(0.309017 + 0.951057i) q^{96} +(4.43008 + 6.09749i) q^{97} +(-3.25888 + 6.19514i) q^{98} +(-3.31613 + 0.0572763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9	$ 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} - 12 q^{17} - 16 q^{19} + 10 q^{20} - 8 q^{21} - 4 q^{22} + 8 q^{23} + 8 q^{24} + 6 q^{25} + 10 q^{28} + 20 q^{29} - 50 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{36} - 16 q^{37} + 6 q^{40} + 40 q^{41} + 12 q^{44} + 52 q^{49} + 40 q^{51} - 32 q^{54} - 40 q^{55} - 8 q^{56} + 10 q^{58} + 60 q^{59} + 4 q^{60} - 4 q^{61} + 20 q^{62} - 10 q^{63} + 8 q^{64} + 8 q^{66} - 16 q^{67} + 12 q^{68} + 30 q^{69} - 28 q^{70} - 48 q^{71} - 74 q^{73} - 40 q^{74} - 24 q^{76} + 6 q^{77} - 60 q^{79} - 8 q^{81} + 20 q^{82} + 4 q^{83} - 2 q^{84} - 10 q^{85} - 36 q^{86} + 20 q^{87} - 16 q^{88} - 4 q^{90} - 20 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} - 8 q^{96} + 60 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 - 12 * q^17 - 16 * q^19 + 10 * q^20 - 8 * q^21 - 4 * q^22 + 8 * q^23 + 8 * q^24 + 6 * q^25 + 10 * q^28 + 20 * q^29 - 50 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^36 - 16 * q^37 + 6 * q^40 + 40 * q^41 + 12 * q^44 + 52 * q^49 + 40 * q^51 - 32 * q^54 - 40 * q^55 - 8 * q^56 + 10 * q^58 + 60 * q^59 + 4 * q^60 - 4 * q^61 + 20 * q^62 - 10 * q^63 + 8 * q^64 + 8 * q^66 - 16 * q^67 + 12 * q^68 + 30 * q^69 - 28 * q^70 - 48 * q^71 - 74 * q^73 - 40 * q^74 - 24 * q^76 + 6 * q^77 - 60 * q^79 - 8 * q^81 + 20 * q^82 + 4 * q^83 - 2 * q^84 - 10 * q^85 - 36 * q^86 + 20 * q^87 - 16 * q^88 - 4 * q^90 - 20 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 - 8 * q^96 + 60 * q^97 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	2.18694	−	3.01006i	0.978027	−	1.34614i	0.0401415	−	0.999194i	$-0.487219\pi$
$5$	2.18694	−	3.01006i	0.978027	−	1.34614i	0.937886	−	0.346945i	$-0.112781\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	−2.24683	−	1.39706i	−0.849220	−	0.528039i
$7$	−2.24683	−	1.39706i	−0.849220	−	0.528039i
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	3.72064			1.17657
$11$	−2.71647	−	1.90283i	−0.819047	−	0.573726i
$11$	−2.71647	−	1.90283i	−0.819047	−	0.573726i
$12$		−	1.00000i		−	0.288675i
$13$	4.11000	−	2.98609i	1.13991	−	0.828192i	0.152802	−	0.988257i	$-0.451170\pi$
$13$	4.11000	−	2.98609i	1.13991	−	0.828192i	0.987106	+	0.160065i	$0.0511705\pi$
$14$	−0.190406	−	2.63889i	−0.0508881	−	0.705273i
$15$	−1.14974	+	3.53854i	−0.296862	+	0.913646i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−4.90468	−	3.56346i	−1.18956	−	0.864266i	−0.196343	−	0.980535i	$-0.562907\pi$
$17$	−4.90468	−	3.56346i	−1.18956	−	0.864266i	−0.993218	+	0.116269i	$0.962907\pi$
$18$	0.951057	+	0.309017i	0.224166	+	0.0728360i
$19$	0.0255089	+	0.0785084i	0.00585215	+	0.0180111i	0.953940	−	0.299998i	$-0.0969859\pi$
$19$	0.0255089	+	0.0785084i	0.00585215	+	0.0180111i	−0.948088	+	0.318009i	$0.896986\pi$
$20$	2.18694	+	3.01006i	0.489014	+	0.673069i
$21$	2.56857	+	0.634376i	0.560509	+	0.138432i
$22$	−0.0572763	−	3.31613i	−0.0122113	−	0.707001i
$23$	2.24601			0.468326			0.234163	−	0.972197i	$-0.424765\pi$
$23$	2.24601			0.468326			0.234163	+	0.972197i	$0.424765\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	−2.73268	−	8.41032i	−0.546536	−	1.68206i
$26$	4.83159	+	1.56988i	0.947553	+	0.307879i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	2.02299	−	1.70514i	0.382309	−	0.322242i
$29$	9.40327	+	3.05531i	1.74614	+	0.567356i	0.995620	−	0.0934887i	$-0.0298019\pi$
$29$	9.40327	+	3.05531i	1.74614	+	0.567356i	0.750523	+	0.660845i	$0.229802\pi$
$30$	−3.53854	+	1.14974i	−0.646045	+	0.209913i
$31$	1.60336	+	2.20684i	0.287972	+	0.396360i	0.928354	−	0.371697i	$-0.121224\pi$
$31$	1.60336	+	2.20684i	0.287972	+	0.396360i	−0.640382	+	0.768057i	$0.721224\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.17153	+	0.970268i	0.552092	+	0.168902i
$34$		−	6.06252i		−	1.03971i
$35$	−9.11889	+	3.70780i	−1.54137	+	0.626732i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−2.49736	+	7.68607i	−0.410563	+	1.26358i	0.505597	+	0.862770i	$0.331272\pi$
$37$	−2.49736	+	7.68607i	−0.410563	+	1.26358i	−0.916160	+	0.400813i	$0.868728\pi$
$38$	−0.0485209	+	0.0667833i	−0.00787113	+	0.0108337i
$39$	−2.98609	+	4.11000i	−0.478157	+	0.658126i
$40$	−1.14974	+	3.53854i	−0.181790	+	0.559492i
$41$	−2.40988	−	7.41686i	−0.376361	−	1.15832i	−0.942556	−	0.334048i	$-0.891585\pi$
$41$	−2.40988	−	7.41686i	−0.376361	−	1.15832i	0.566195	−	0.824271i	$-0.308415\pi$
$42$	0.996549	+	2.45090i	0.153771	+	0.378181i
$43$			3.56568i			0.543760i	0.962331	+	0.271880i	$0.0876455\pi$
$43$			3.56568i			0.543760i	−0.962331	+	0.271880i	$0.912355\pi$
$44$	2.64914	−	1.99551i	0.399373	−	0.300834i
$45$		−	3.72064i		−	0.554640i
$46$	1.32017	+	1.81706i	0.194649	+	0.267911i
$47$	9.34367	−	3.03594i	1.36291	−	0.442838i	0.465900	−	0.884838i	$-0.345731\pi$
$47$	9.34367	−	3.03594i	1.36291	−	0.442838i	0.897015	+	0.442000i	$0.145731\pi$
$48$	0.951057	+	0.309017i	0.137273	+	0.0446028i
$49$	3.09645	+	6.27790i	0.442350	+	0.896843i
$50$	5.19786	−	7.15425i	0.735089	−	1.01176i
$51$	5.76580	+	1.87342i	0.807374	+	0.262332i
$52$	1.56988	+	4.83159i	0.217703	+	0.670021i
$53$	1.23123	−	0.894540i	0.169122	−	0.122875i	−0.500004	−	0.866023i	$-0.666668\pi$
$53$	1.23123	−	0.894540i	0.169122	−	0.122875i	0.669127	+	0.743148i	$0.266668\pi$
$54$	−1.00000			−0.136083
$55$	−11.6684	+	4.01536i	−1.57337	+	0.541431i
$56$	2.56857	+	0.634376i	0.343240	+	0.0847720i
$57$	−0.0485209	−	0.0667833i	−0.00642675	−	0.00884566i
$58$	3.05531	+	9.40327i	0.401181	+	1.23471i
$59$	3.05835	+	0.993718i	0.398163	+	0.129371i	0.501252	−	0.865301i	$-0.332873\pi$
$59$	3.05835	+	0.993718i	0.398163	+	0.129371i	−0.103089	+	0.994672i	$0.532873\pi$
$60$	−3.01006	−	2.18694i	−0.388597	−	0.282332i
$61$	−3.40260	−	2.47213i	−0.435658	−	0.316524i	0.348249	−	0.937402i	$-0.386776\pi$
$61$	−3.40260	−	2.47213i	−0.435658	−	0.316524i	−0.783907	+	0.620878i	$0.786776\pi$
$62$	−0.842937	+	2.59429i	−0.107053	+	0.329476i
$63$	−2.63889	+	0.190406i	−0.332469	+	0.0239889i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$		−	18.9017i		−	2.34447i
$66$	1.07921	+	3.13613i	0.132842	+	0.386031i
$67$	−9.56243			−1.16824			−0.584118	−	0.811669i	$-0.698560\pi$
$67$	−9.56243			−1.16824			−0.584118	+	0.811669i	$0.698560\pi$
$68$	4.90468	−	3.56346i	0.594780	−	0.432133i
$69$	−2.13609	+	0.694056i	−0.257154	+	0.0835545i
$70$	−8.35962	−	5.19795i	−0.999166	−	0.621274i
$71$	5.72886	+	4.16226i	0.679891	+	0.493969i	0.873321	−	0.487145i	$-0.161962\pi$
$71$	5.72886	+	4.16226i	0.679891	+	0.493969i	−0.193431	+	0.981114i	$0.561962\pi$
$72$	−0.587785	+	0.809017i	−0.0692712	+	0.0953436i
$73$	−0.831452	+	2.55895i	−0.0973141	+	0.299502i	−0.987850	−	0.155411i	$-0.950330\pi$
$73$	−0.831452	+	2.55895i	−0.0973141	+	0.299502i	0.890536	+	0.454913i	$0.150330\pi$
$74$	−7.68607	+	2.49736i	−0.893488	+	0.290312i
$75$	5.19786	+	7.15425i	0.600198	+	0.826101i
$76$	−0.0825487			−0.00946898
$77$	3.44506	+	8.07041i	0.392601	+	0.919709i
$78$	−5.08024			−0.575223
$79$	−6.41455	−	8.82886i	−0.721693	−	0.993325i	−0.999466	−	0.0326781i	$-0.989596\pi$
$79$	−6.41455	−	8.82886i	−0.721693	−	0.993325i	0.277773	−	0.960647i	$-0.410404\pi$
$80$	−3.53854	+	1.14974i	−0.395620	+	0.128545i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	4.58387	−	6.30916i	0.506204	−	0.696730i
$83$	−9.69963	−	7.04720i	−1.06467	−	0.773530i	−0.0897258	−	0.995967i	$-0.528599\pi$
$83$	−9.69963	−	7.04720i	−1.06467	−	0.773530i	−0.974947	+	0.222436i	$0.928599\pi$
$84$	−1.39706	+	2.24683i	−0.152432	+	0.245149i
$85$	−21.4524	+	6.97032i	−2.32684	+	0.756038i
$86$	−2.88469	+	2.09585i	−0.311064	+	0.226002i
$87$	−9.88718			−1.06002
$88$	3.17153	+	0.970268i	0.338086	+	0.103431i
$89$			12.4627i			1.32105i	0.750805	+	0.660524i	$0.229666\pi$
$89$			12.4627i			1.32105i	−0.750805	+	0.660524i	$0.770334\pi$
$90$	3.01006	−	2.18694i	0.317288	−	0.230523i
$91$	−13.4062	+	0.967306i	−1.40535	+	0.101401i
$92$	−0.694056	+	2.13609i	−0.0723604	+	0.222702i
$93$	−2.20684	−	1.60336i	−0.228838	−	0.166261i
$94$	7.94820	+	5.77471i	0.819794	+	0.595616i
$95$	0.292101	+	0.0949095i	0.0299690	+	0.00973751i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	4.43008	+	6.09749i	0.449807	+	0.619106i	0.972356	−	0.233503i	$-0.0750189\pi$
$97$	4.43008	+	6.09749i	0.449807	+	0.619106i	−0.522549	+	0.852609i	$0.675019\pi$
$98$	−3.25888	+	6.19514i	−0.329197	+	0.625803i
$99$	−3.31613	+	0.0572763i	−0.333284	+	0.00575648i
$100$	8.84313			0.884313
$101$	−2.72552	+	1.98020i	−0.271199	+	0.197038i	−0.715070	−	0.699053i	$-0.753605\pi$
$101$	−2.72552	+	1.98020i	−0.271199	+	0.197038i	0.443871	+	0.896091i	$0.353605\pi$
$102$	1.87342	+	5.76580i	0.185496	+	0.570899i
$103$	−4.90232	−	1.59286i	−0.483039	−	0.156949i	0.0573670	−	0.998353i	$-0.481729\pi$
$103$	−4.90232	−	1.59286i	−0.483039	−	0.156949i	−0.540406	+	0.841404i	$0.681729\pi$
$104$	−2.98609	+	4.11000i	−0.292810	+	0.403018i
$105$	7.52681	−	6.34422i	0.734541	−	0.619132i
$106$	1.44740	+	0.470288i	0.140584	+	0.0456784i
$107$	12.3187	−	4.00258i	1.19089	−	0.386944i	0.354489	−	0.935060i	$-0.384655\pi$
$107$	12.3187	−	4.00258i	1.19089	−	0.386944i	0.836402	+	0.548116i	$0.184655\pi$
$108$	−0.587785	−	0.809017i	−0.0565597	−	0.0778477i
$109$			6.45391i			0.618173i	0.951034	+	0.309086i	$0.100023\pi$
$109$			6.45391i			0.618173i	−0.951034	+	0.309086i	$0.899977\pi$
$110$	−10.1070	−	7.07976i	−0.963665	−	0.675028i
$111$		−	8.08162i		−	0.767073i
$112$	0.996549	+	2.45090i	0.0941650	+	0.231588i
$113$	−4.44216	−	13.6716i	−0.417883	−	1.28611i	−0.909646	−	0.415383i	$-0.863647\pi$
$113$	−4.44216	−	13.6716i	−0.417883	−	1.28611i	0.491763	−	0.870729i	$-0.336353\pi$
$114$	0.0255089	−	0.0785084i	0.00238913	−	0.00735299i
$115$	4.91188	−	6.76063i	0.458036	−	0.630432i
$116$	−5.81154	+	7.99890i	−0.539588	+	0.742679i
$117$	1.56988	−	4.83159i	0.145135	−	0.446681i
$118$	0.993718	+	3.05835i	0.0914791	+	0.281544i
$119$	6.04160	+	14.8586i	0.553832	+	1.36209i
$120$		−	3.72064i		−	0.339646i
$121$	3.75844	+	10.3380i	0.341676	+	0.939818i
$122$		−	4.20585i		−	0.380779i
$123$	4.58387	+	6.30916i	0.413314	+	0.568878i
$124$	−2.59429	+	0.842937i	−0.232974	+	0.0756980i
$125$	−13.5991	−	4.41860i	−1.21634	−	0.395212i
$126$	−1.70514	−	2.02299i	−0.151906	−	0.180222i
$127$	0.441200	−	0.607260i	0.0391502	−	0.0538856i	−0.788993	−	0.614402i	$-0.789397\pi$
$127$	0.441200	−	0.607260i	0.0391502	−	0.0538856i	0.828143	+	0.560516i	$0.189397\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−1.10185	−	3.39116i	−0.0970129	−	0.298575i
$130$	15.2918	−	11.1101i	1.34118	−	0.974424i
$131$	15.3515			1.34127			0.670634	−	0.741788i	$-0.266022\pi$
$131$	15.3515			1.34127			0.670634	+	0.741788i	$0.266022\pi$
$132$	−1.90283	+	2.71647i	−0.165621	+	0.236439i
$133$	0.0523669	−	0.212032i	0.00454078	−	0.0183855i
$134$	−5.62065	−	7.73617i	−0.485551	−	0.668303i
$135$	1.14974	+	3.53854i	0.0989538	+	0.304549i
$136$	5.76580	+	1.87342i	0.494413	+	0.160645i
$137$	15.0206	+	10.9131i	1.28330	+	0.932371i	0.999647	−	0.0265563i	$-0.00845411\pi$
$137$	15.0206	+	10.9131i	1.28330	+	0.932371i	0.283652	+	0.958927i	$0.408454\pi$
$138$	−1.81706	−	1.32017i	−0.154679	−	0.112381i
$139$	−3.35734	+	10.3328i	−0.284766	+	0.876420i	0.701702	+	0.712470i	$0.252424\pi$
$139$	−3.35734	+	10.3328i	−0.284766	+	0.876420i	−0.986469	+	0.163950i	$0.947576\pi$
$140$	−0.708431	−	9.81835i	−0.0598733	−	0.829802i
$141$	−7.94820	+	5.77471i	−0.669359	+	0.486318i
$142$			7.08126i			0.594246i
$143$	−16.8467	+	0.290977i	−1.40879	+	0.0243327i
$144$	−1.00000			−0.0833333
$145$	29.7610	−	21.6226i	2.47152	−	1.79566i
$146$	−2.55895	+	0.831452i	−0.211780	+	0.0688115i
$147$	−4.88487	−	5.01378i	−0.402898	−	0.413530i
$148$	−6.53816	−	4.75025i	−0.537434	−	0.390469i
$149$	−4.16484	+	5.73242i	−0.341197	+	0.469618i	−0.944791	−	0.327674i	$-0.893735\pi$
$149$	−4.16484	+	5.73242i	−0.341197	+	0.469618i	0.603593	+	0.797292i	$0.293735\pi$
$150$	−2.73268	+	8.41032i	−0.223122	+	0.686700i
$151$	18.1355	−	5.89258i	1.47584	−	0.479531i	0.542976	−	0.839748i	$-0.317297\pi$
$151$	18.1355	−	5.89258i	1.47584	−	0.479531i	0.932869	+	0.360217i	$0.117297\pi$
$152$	−0.0485209	−	0.0667833i	−0.00393556	−	0.00541684i
$153$	−6.06252			−0.490126
$154$	−4.50414	+	7.53078i	−0.362954	+	0.606848i
$155$	10.1492			0.815200
$156$	−2.98609	−	4.11000i	−0.239078	−	0.329063i
$157$	10.7526	−	3.49374i	0.858153	−	0.278831i	0.153296	−	0.988180i	$-0.451011\pi$
$157$	10.7526	−	3.49374i	0.858153	−	0.278831i	0.704857	+	0.709349i	$0.251011\pi$
$158$	3.37233	−	10.3790i	0.268288	−	0.825705i
$159$	−0.894540	+	1.23123i	−0.0709417	+	0.0976428i
$160$	−3.01006	−	2.18694i	−0.237966	−	0.172892i
$161$	−5.04640	−	3.13781i	−0.397712	−	0.247294i
$162$	0.951057	−	0.309017i	0.0747221	−	0.0242787i
$163$	2.20749	−	1.60383i	0.172904	−	0.125622i	−0.497968	−	0.867196i	$-0.665920\pi$
$163$	2.20749	−	1.60383i	0.172904	−	0.125622i	0.670872	+	0.741574i	$0.265920\pi$
$164$	7.79855			0.608964
$165$	9.85648	−	7.42457i	0.767326	−	0.578002i
$166$		−	11.9894i		−	0.930558i
$167$	4.00549	−	2.91016i	0.309954	−	0.225195i	−0.421922	−	0.906632i	$-0.638645\pi$
$167$	4.00549	−	2.91016i	0.309954	−	0.225195i	0.731877	+	0.681437i	$0.238645\pi$
$168$	−2.63889	+	0.190406i	−0.203595	+	0.0146901i
$169$	3.95813	−	12.1819i	0.304472	−	0.937068i
$170$	−18.2485	−	13.2583i	−1.39960	−	1.01687i
$171$	0.0667833	+	0.0485209i	0.00510704	+	0.00371049i
$172$	−3.39116	−	1.10185i	−0.258573	−	0.0840156i
$173$	−4.15780	−	12.7964i	−0.316112	−	0.972892i	−0.975294	−	0.220909i	$-0.929098\pi$
$173$	−4.15780	−	12.7964i	−0.316112	−	0.972892i	0.659182	−	0.751983i	$-0.270902\pi$
$174$	−5.81154	−	7.99890i	−0.440572	−	0.606395i
$175$	−5.60987	+	22.7142i	−0.424066	+	1.71703i
$176$	1.07921	+	3.13613i	0.0813488	+	0.236395i
$177$	−3.21574			−0.241710
$178$	−10.0826	+	7.32541i	−0.755720	+	0.549063i
$179$	−0.526789	−	1.62129i	−0.0393741	−	0.121181i	0.929437	−	0.368980i	$-0.120293\pi$
$179$	−0.526789	−	1.62129i	−0.0393741	−	0.121181i	−0.968812	+	0.247799i	$0.920293\pi$
$180$	3.53854	+	1.14974i	0.263747	+	0.0856965i
$181$	3.42750	−	4.71755i	0.254764	−	0.350652i	−0.662409	−	0.749143i	$-0.730466\pi$
$181$	3.42750	−	4.71755i	0.254764	−	0.350652i	0.917173	+	0.398490i	$0.130466\pi$
$182$	−8.66253	−	10.2773i	−0.642109	−	0.761802i
$183$	4.00000	+	1.29968i	0.295688	+	0.0960750i
$184$	−2.13609	+	0.694056i	−0.157474	+	0.0511665i
$185$	17.6740	+	24.3261i	1.29942	+	1.78849i
$186$		−	2.72780i		−	0.200012i
$187$	6.54276	+	19.0128i	0.478454	+	1.39036i
$188$			9.82452i			0.716527i
$189$	2.45090	−	0.996549i	0.178276	−	0.0724883i
$190$	0.0949095	+	0.292101i	0.00688546	+	0.0211913i
$191$	−5.21632	+	16.0542i	−0.377439	+	1.16164i	0.564379	+	0.825516i	$0.309116\pi$
$191$	−5.21632	+	16.0542i	−0.377439	+	1.16164i	−0.941818	+	0.336123i	$0.890884\pi$
$192$	−0.587785	+	0.809017i	−0.0424197	+	0.0583858i
$193$	−6.79387	+	9.35096i	−0.489033	+	0.673097i	−0.980209	−	0.197964i	$-0.936567\pi$
$193$	−6.79387	+	9.35096i	−0.489033	+	0.673097i	0.491176	+	0.871060i	$0.336567\pi$
$194$	−2.32903	+	7.16803i	−0.167215	+	0.514634i
$195$	5.84095	+	17.9766i	0.418279	+	1.28733i
$196$	−6.92749	+	1.00492i	−0.494821	+	0.0717800i
$197$		−	13.8897i		−	0.989600i	−0.869007	−	0.494800i	$-0.835241\pi$
$197$		−	13.8897i		−	0.989600i	0.869007	−	0.494800i	$-0.164759\pi$
$198$	−1.99551	−	2.64914i	−0.141815	−	0.188266i
$199$			9.42741i			0.668291i	0.942521	+	0.334146i	$0.108448\pi$
$199$			9.42741i			0.668291i	−0.942521	+	0.334146i	$0.891552\pi$
$200$	5.19786	+	7.15425i	0.367544	+	0.505882i
$201$	9.09441	−	2.95495i	0.641470	−	0.208426i
$202$	−3.20404	−	1.04105i	−0.225435	−	0.0732483i
$203$	−16.8591	−	20.0017i	−1.18327	−	1.40384i
$204$	−3.56346	+	4.90468i	−0.249492	+	0.343397i
$205$	−27.5954	−	8.96630i	−1.92735	−	0.626234i
$206$	−1.59286	−	4.90232i	−0.110980	−	0.341560i
$207$	1.81706	−	1.32017i	0.126295	−	0.0917584i
$208$	−5.08024			−0.352251
$209$	0.0800943	−	0.261805i	0.00554024	−	0.0181095i
$210$	9.55673	+	2.36028i	0.659477	+	0.162875i
$211$	11.1268	+	15.3148i	0.766003	+	1.05431i	0.996691	+	0.0812846i	$0.0259023\pi$
$211$	11.1268	+	15.3148i	0.766003	+	1.05431i	−0.230688	+	0.973028i	$0.574098\pi$
$212$	0.470288	+	1.44740i	0.0322995	+	0.0994076i
$213$	−6.73468	−	2.18823i	−0.461453	−	0.149935i
$214$	10.4789	+	7.61336i	0.716322	+	0.520439i
$215$	10.7329	+	7.79790i	0.731977	+	0.531812i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	−0.519389	−	7.19837i	−0.0352584	−	0.488657i
$218$	−5.22132	+	3.79351i	−0.353633	+	0.256929i
$219$		−	2.69064i		−	0.181816i
$220$	−0.213104	−	12.3381i	−0.0143675	−	0.831835i
$221$	−30.7990			−2.07177
$222$	6.53816	−	4.75025i	0.438813	−	0.318816i
$223$	0.947751	−	0.307943i	0.0634661	−	0.0206214i	−0.277112	−	0.960838i	$-0.589377\pi$
$223$	0.947751	−	0.307943i	0.0634661	−	0.0206214i	0.340578	+	0.940216i	$0.389377\pi$
$224$	−1.39706	+	2.24683i	−0.0933450	+	0.150122i
$225$	−7.15425	−	5.19786i	−0.476950	−	0.346524i
$226$	8.44949	−	11.6297i	0.562052	−	0.773598i
$227$	3.37257	−	10.3797i	0.223846	−	0.688926i	−0.774561	−	0.632499i	$-0.782029\pi$
$227$	3.37257	−	10.3797i	0.223846	−	0.688926i	0.998407	−	0.0564270i	$-0.0179708\pi$
$228$	0.0785084	−	0.0255089i	0.00519935	−	0.00168937i
$229$	11.5538	+	15.9024i	0.763496	+	1.05086i	0.996915	+	0.0784854i	$0.0250084\pi$
$229$	11.5538	+	15.9024i	0.763496	+	1.05086i	−0.233420	+	0.972376i	$0.574992\pi$
$230$	8.35660			0.551018
$231$	−5.77034	−	6.61083i	−0.379661	−	0.434961i
$232$	−9.88718			−0.649125
$233$	−4.07030	−	5.60228i	−0.266654	−	0.367018i	0.654603	−	0.755973i	$-0.272836\pi$
$233$	−4.07030	−	5.60228i	−0.266654	−	0.367018i	−0.921257	+	0.388955i	$0.872836\pi$
$234$	4.83159	−	1.56988i	0.315851	−	0.102626i
$235$	11.2956	−	34.7644i	0.736846	−	2.26778i
$236$	−1.89016	+	2.60159i	−0.123039	+	0.169349i
$237$	8.82886	+	6.41455i	0.573496	+	0.416669i
$238$	−8.46971	+	13.6214i	−0.549009	+	0.882946i
$239$	22.2495	−	7.22930i	1.43920	−	0.467624i	0.517552	−	0.855652i	$-0.326843\pi$
$239$	22.2495	−	7.22930i	1.43920	−	0.467624i	0.921648	+	0.388028i	$0.126843\pi$
$240$	3.01006	−	2.18694i	0.194298	−	0.141166i
$241$	0.570114			0.0367242			0.0183621	−	0.999831i	$-0.494155\pi$
$241$	0.570114			0.0367242			0.0183621	+	0.999831i	$0.494155\pi$
$242$	−6.15446	+	9.11716i	−0.395624	+	0.586073i
$243$			1.00000i			0.0641500i
$244$	3.40260	−	2.47213i	0.217829	−	0.158262i
$245$	25.6686	+	4.40887i	1.63990	+	0.281672i
$246$	−2.40988	+	7.41686i	−0.153649	+	0.472882i
$247$	0.339275	+	0.246498i	0.0215875	+	0.0156843i
$248$	−2.20684	−	1.60336i	−0.140134	−	0.101814i
$249$	11.4026	+	3.70493i	0.722611	+	0.234790i
$250$	−4.41860	−	13.5991i	−0.279457	−	0.860080i
$251$	0.663815	+	0.913663i	0.0418996	+	0.0576699i	0.829453	−	0.558577i	$-0.188652\pi$
$251$	0.663815	+	0.913663i	0.0418996	+	0.0576699i	−0.787553	+	0.616247i	$0.788652\pi$
$252$	0.634376	−	2.56857i	0.0399619	−	0.161805i
$253$	−6.10123	−	4.27379i	−0.383581	−	0.268691i
$254$	0.750615			0.0470978
$255$	18.2485	−	13.2583i	1.14277	−	0.830270i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	3.53955	+	1.15007i	0.220791	+	0.0717394i	0.417324	−	0.908758i	$-0.362968\pi$
$257$	3.53955	+	1.15007i	0.220791	+	0.0717394i	−0.196532	+	0.980497i	$0.562968\pi$
$258$	2.09585	−	2.88469i	0.130482	−	0.179593i
$259$	16.3490	−	13.7803i	1.01588	−	0.856267i
$260$	17.9766	+	5.84095i	1.11486	+	0.362240i
$261$	9.40327	−	3.05531i	0.582048	−	0.189119i
$262$	9.02340	+	12.4196i	0.557467	+	0.767288i
$263$			20.3592i			1.25540i	0.778455	+	0.627700i	$0.216004\pi$
$263$			20.3592i			1.25540i	−0.778455	+	0.627700i	$0.783996\pi$
$264$	−3.31613	+	0.0572763i	−0.204094	+	0.00352511i
$265$		−	5.66237i		−	0.347837i
$266$	0.202318	−	0.0822638i	0.0124049	−	0.00504392i
$267$	−3.85120	−	11.8528i	−0.235689	−	0.725377i
$268$	2.95495	−	9.09441i	0.180502	−	0.555530i
$269$	14.8400	−	20.4256i	0.904813	−	1.24537i	−0.0640942	−	0.997944i	$-0.520416\pi$
$269$	14.8400	−	20.4256i	0.904813	−	1.24537i	0.968907	−	0.247424i	$-0.0795842\pi$
$270$	−2.18694	+	3.01006i	−0.133093	+	0.183186i
$271$	−0.322155	+	0.991490i	−0.0195695	+	0.0602287i	−0.960364	−	0.278748i	$-0.910081\pi$
$271$	−0.322155	+	0.991490i	−0.0195695	+	0.0602287i	0.940795	+	0.338976i	$0.110081\pi$
$272$	1.87342	+	5.76580i	0.113593	+	0.349603i
$273$	12.4511	−	5.06270i	0.753577	−	0.306409i
$274$			18.5665i			1.12164i
$275$	−8.58021	+	28.0462i	−0.517406	+	1.69125i
$276$		−	2.24601i		−	0.135194i
$277$	−3.00689	−	4.13863i	−0.180666	−	0.248666i	0.709073	−	0.705135i	$-0.249114\pi$
$277$	−3.00689	−	4.13863i	−0.180666	−	0.248666i	−0.889739	+	0.456469i	$0.849114\pi$
$278$	−10.3328	+	3.35734i	−0.619723	+	0.201360i
$279$	2.59429	+	0.842937i	0.155316	+	0.0504653i
$280$	7.52681	−	6.34422i	0.449813	−	0.379139i
$281$	−10.2122	+	14.0559i	−0.609211	+	0.838507i	−0.996512	−	0.0834459i	$-0.973407\pi$
$281$	−10.2122	+	14.0559i	−0.609211	+	0.838507i	0.387301	+	0.921953i	$0.373407\pi$
$282$	−9.34367	−	3.03594i	−0.556408	−	0.180788i
$283$	−8.82546	−	27.1620i	−0.524619	−	1.61461i	−0.765067	−	0.643950i	$-0.777294\pi$
$283$	−8.82546	−	27.1620i	−0.524619	−	1.61461i	0.240448	−	0.970662i	$-0.422706\pi$
$284$	−5.72886	+	4.16226i	−0.339945	+	0.246985i
$285$	−0.307134			−0.0181930
$286$	−10.1377	−	13.4583i	−0.599452	−	0.795803i
$287$	−4.94721	+	20.0311i	−0.292025	+	1.18240i
$288$	−0.587785	−	0.809017i	−0.0346356	−	0.0476718i
$289$	6.10438	+	18.7873i	0.359081	+	1.10514i
$290$	34.9861	+	11.3677i	2.05446	+	0.667533i
$291$	−6.09749	−	4.43008i	−0.357441	−	0.259696i
$292$	−2.17677	−	1.58152i	−0.127386	−	0.0925512i
$293$	2.34433	−	7.21510i	0.136957	−	0.421511i	−0.858932	−	0.512089i	$-0.828872\pi$
$293$	2.34433	−	7.21510i	0.136957	−	0.421511i	0.995889	+	0.0905787i	$0.0288717\pi$
$294$	1.18498	−	6.89897i	0.0691092	−	0.402356i
$295$	9.67956	−	7.03261i	0.563566	−	0.409454i
$296$		−	8.08162i		−	0.469734i
$297$	3.13613	−	1.07921i	0.181977	−	0.0626223i
$298$	−7.08566			−0.410461
$299$	9.23111	−	6.70679i	0.533849	−	0.387864i
$300$	−8.41032	+	2.73268i	−0.485570	+	0.157771i
$301$	4.98146	−	8.01145i	0.287127	−	0.461772i
$302$	15.4270	+	11.2083i	0.887722	+	0.644968i
$303$	1.98020	−	2.72552i	0.113760	−	0.156577i
$304$	0.0255089	−	0.0785084i	0.00146304	−	0.00450277i
$305$	−14.8825	+	4.83563i	−0.852172	+	0.276887i
$306$	−3.56346	−	4.90468i	−0.203710	−	0.280382i
$307$	−24.8802			−1.41999			−0.709993	−	0.704209i	$-0.751302\pi$
$307$	−24.8802			−1.41999			−0.709993	+	0.704209i	$0.751302\pi$
$308$	−8.74000	+	0.782556i	−0.498008	+	0.0445903i
$309$	5.15460			0.293235
$310$	5.96552	+	8.21084i	0.338819	+	0.466344i
$311$	−14.8561	+	4.82704i	−0.842412	+	0.273716i	−0.698264	−	0.715840i	$-0.746044\pi$
$311$	−14.8561	+	4.82704i	−0.842412	+	0.273716i	−0.144148	+	0.989556i	$0.546044\pi$
$312$	1.56988	−	4.83159i	0.0888769	−	0.273535i
$313$	−13.0825	+	18.0065i	−0.739466	+	1.01779i	0.259184	+	0.965828i	$0.416547\pi$
$313$	−13.0825	+	18.0065i	−0.739466	+	1.01779i	−0.998649	+	0.0519590i	$0.983453\pi$
$314$	9.14673	+	6.64549i	0.516180	+	0.375027i
$315$	−5.19795	+	8.35962i	−0.292871	+	0.471011i
$316$	10.3790	−	3.37233i	0.583862	−	0.189708i
$317$	25.3305	−	18.4037i	1.42270	−	1.03365i	0.431385	−	0.902168i	$-0.358025\pi$
$317$	25.3305	−	18.4037i	1.42270	−	1.03365i	0.991318	−	0.131486i	$-0.0419750\pi$
$318$	−1.52188			−0.0853429
$319$	−19.7300	−	26.1925i	−1.10467	−	1.46650i
$320$		−	3.72064i		−	0.207990i
$321$	−10.4789	+	7.61336i	−0.584875	+	0.424936i
$322$	−0.427654	−	5.92698i	−0.0238322	−	0.330298i
$323$	0.154649	−	0.475959i	0.00860487	−	0.0264831i
$324$	0.809017	+	0.587785i	0.0449454	+	0.0326547i
$325$	−36.3453	−	26.4064i	−2.01607	−	1.46476i
$326$	2.59506	+	0.843185i	0.143727	+	0.0466997i
$327$	−1.99437	−	6.13803i	−0.110289	−	0.339434i
$328$	4.58387	+	6.30916i	0.253102	+	0.348365i
$329$	−25.2350	−	6.23243i	−1.39125	−	0.343605i
$330$	11.8001	+	3.61001i	0.649574	+	0.198725i
$331$	3.72310			0.204640			0.102320	−	0.994752i	$-0.467373\pi$
$331$	3.72310			0.204640			0.102320	+	0.994752i	$0.467373\pi$
$332$	9.69963	−	7.04720i	0.532337	−	0.386765i
$333$	2.49736	+	7.68607i	0.136854	+	0.421194i
$334$	4.70874	+	1.52996i	0.257651	+	0.0837158i
$335$	−20.9124	+	28.7835i	−1.14257	+	1.57261i
$336$	−1.70514	−	2.02299i	−0.0930232	−	0.110363i
$337$	−3.63068	−	1.17968i	−0.197776	−	0.0642613i	0.208454	−	0.978032i	$-0.433157\pi$
$337$	−3.63068	−	1.17968i	−0.197776	−	0.0642613i	−0.406230	+	0.913771i	$0.633157\pi$
$338$	12.1819	−	3.95813i	0.662607	−	0.215294i
$339$	8.44949	+	11.6297i	0.458913	+	0.631640i
$340$		−	22.5564i		−	1.22329i
$341$	−0.156238	−	9.04574i	−0.00846078	−	0.489854i
$342$			0.0825487i			0.00446372i
$343$	1.81342	−	18.4313i	0.0979155	−	0.995195i
$344$	−1.10185	−	3.39116i	−0.0594080	−	0.182839i
$345$	−2.58233	+	7.94760i	−0.139028	+	0.427884i
$346$	7.90861	−	10.8853i	0.425170	−	0.585196i
$347$	−18.2084	+	25.0617i	−0.977476	+	1.34538i	−0.0392982	+	0.999228i	$0.512512\pi$
$347$	−18.2084	+	25.0617i	−0.977476	+	1.34538i	−0.938178	+	0.346153i	$0.887488\pi$
$348$	3.05531	−	9.40327i	0.163782	−	0.504068i
$349$	4.32546	+	13.3124i	0.231537	+	0.712597i	0.997562	+	0.0697862i	$0.0222317\pi$
$349$	4.32546	+	13.3124i	0.231537	+	0.712597i	−0.766025	+	0.642810i	$0.777768\pi$
$350$	−21.6736	+	8.81261i	−1.15850	+	0.471054i
$351$			5.08024i			0.271163i
$352$	−1.90283	+	2.71647i	−0.101421	+	0.144788i
$353$		−	22.0253i		−	1.17229i	−0.810207	−	0.586144i	$-0.800645\pi$
$353$		−	22.0253i		−	1.17229i	0.810207	−	0.586144i	$-0.199355\pi$
$354$	−1.89016	−	2.60159i	−0.100461	−	0.138273i
$355$	25.0573	−	8.14161i	1.32990	−	0.432112i
$356$	−11.8528	−	3.85120i	−0.628195	−	0.204113i
$357$	−10.3375	−	12.2644i	−0.547117	−	0.649102i
$358$	1.00201	−	1.37915i	0.0529580	−	0.0728904i
$359$	−9.88542	−	3.21197i	−0.521733	−	0.169521i	0.0362988	−	0.999341i	$-0.488443\pi$
$359$	−9.88542	−	3.21197i	−0.521733	−	0.169521i	−0.558032	+	0.829820i	$0.688443\pi$
$360$	1.14974	+	3.53854i	0.0605966	+	0.186497i
$361$	15.3658	−	11.1639i	0.808727	−	0.587574i
$362$	5.83121			0.306481
$363$	−6.76910	−	8.67060i	−0.355286	−	0.455088i
$364$	3.22278	−	13.0490i	0.168919	−	0.683951i
$365$	5.88425	+	8.09897i	0.307996	+	0.423920i
$366$	1.29968	+	4.00000i	0.0679353	+	0.209083i
$367$	9.08139	+	2.95072i	0.474045	+	0.154026i	0.536289	−	0.844035i	$-0.319826\pi$
$367$	9.08139	+	2.95072i	0.474045	+	0.154026i	−0.0622443	+	0.998061i	$0.519826\pi$
$368$	−1.81706	−	1.32017i	−0.0947209	−	0.0688188i
$369$	−6.30916	−	4.58387i	−0.328442	−	0.238627i
$370$	−9.29176	+	28.5971i	−0.483055	+	1.48669i
$371$	−4.01608	+	0.289775i	−0.208505	+	0.0150444i
$372$	2.20684	−	1.60336i	0.114419	−	0.0831304i
$373$			14.5897i			0.755424i	0.925923	+	0.377712i	$0.123289\pi$
$373$			14.5897i			0.755424i	−0.925923	+	0.377712i	$0.876711\pi$
$374$	−11.5360	+	16.4687i	−0.596511	+	0.851575i
$375$	14.2989			0.738392
$376$	−7.94820	+	5.77471i	−0.409897	+	0.297808i
$377$	47.7708	−	15.5217i	2.46032	−	0.799407i
$378$	2.24683	+	1.39706i	0.115564	+	0.0718570i
$379$	−5.90803	−	4.29243i	−0.303475	−	0.220488i	0.425617	−	0.904904i	$-0.360057\pi$
$379$	−5.90803	−	4.29243i	−0.303475	−	0.220488i	−0.729092	+	0.684416i	$0.760057\pi$
$380$	−0.180529	+	0.248476i	−0.00926092	+	0.0127466i
$381$	−0.231953	+	0.713877i	−0.0118833	+	0.0365730i
$382$	−16.0542	+	5.21632i	−0.821403	+	0.266890i
$383$	−9.99147	−	13.7521i	−0.510540	−	0.702699i	0.473470	−	0.880810i	$-0.343001\pi$
$383$	−9.99147	−	13.7521i	−0.510540	−	0.702699i	−0.984010	+	0.178111i	$0.943001\pi$
$384$	−1.00000			−0.0510310
$385$	31.8265	+	7.27962i	1.62203	+	0.371004i
$386$	−11.5584			−0.588308
$387$	2.09585	+	2.88469i	0.106538	+	0.146637i
$388$	−7.16803	+	2.32903i	−0.363901	+	0.118239i
$389$	−5.80305	+	17.8599i	−0.294226	+	0.905535i	0.689254	+	0.724520i	$0.257938\pi$
$389$	−5.80305	+	17.8599i	−0.294226	+	0.905535i	−0.983480	+	0.181015i	$0.942062\pi$
$390$	−11.1101	+	15.2918i	−0.562584	+	0.774331i
$391$	−11.0160	−	8.00358i	−0.557102	−	0.404758i
$392$	−4.88487	−	5.01378i	−0.246723	−	0.253234i
$393$	−14.6002	+	4.74388i	−0.736481	+	0.239297i
$394$	11.2370	−	8.16416i	0.566112	−	0.411304i
$395$	−40.6036			−2.04299
$396$	0.970268	−	3.17153i	0.0487578	−	0.159375i
$397$			8.72240i			0.437765i	0.975751	+	0.218882i	$0.0702411\pi$
$397$			8.72240i			0.437765i	−0.975751	+	0.218882i	$0.929759\pi$
$398$	−7.62693	+	5.54129i	−0.382304	+	0.277760i
$399$	0.0157177	+	0.217837i	0.000786871	+	0.0109055i
$400$	−2.73268	+	8.41032i	−0.136634	+	0.420516i
$401$	15.1378	+	10.9983i	0.755947	+	0.549228i	0.897664	−	0.440680i	$-0.145262\pi$
$401$	15.1378	+	10.9983i	0.755947	+	0.549228i	−0.141718	+	0.989907i	$0.545262\pi$
$402$	7.73617	+	5.62065i	0.385845	+	0.280333i
$403$	13.1796	+	4.28232i	0.656524	+	0.213317i
$404$	−1.04105	−	3.20404i	−0.0517944	−	0.159407i
$405$	−2.18694	−	3.01006i	−0.108670	−	0.149571i
$406$	6.27219	−	25.3959i	0.311283	−	1.26038i
$407$	21.4093	−	16.1269i	1.06122	−	0.799383i
$408$	−6.06252			−0.300140
$409$	−22.0374	+	16.0111i	−1.08968	+	0.791700i	−0.979345	−	0.202194i	$-0.935193\pi$
$409$	−22.0374	+	16.0111i	−1.08968	+	0.791700i	−0.110336	+	0.993894i	$0.535193\pi$
$410$	−8.96630	−	27.5954i	−0.442814	−	1.36284i
$411$	−17.6578	−	5.73737i	−0.870995	−	0.283004i
$412$	3.02980	−	4.17016i	0.149267	−	0.205449i
$413$	−5.48329	−	6.50541i	−0.269815	−	0.320110i
$414$	2.13609	+	0.694056i	0.104983	+	0.0341110i
$415$	−42.4249	+	13.7847i	−2.08256	+	0.676664i
$416$	−2.98609	−	4.11000i	−0.146405	−	0.201509i
$417$		−	10.8646i		−	0.532041i
$418$	0.258883	−	0.0890876i	0.0126624	−	0.00435742i
$419$			2.92140i			0.142720i	0.997451	+	0.0713598i	$0.0227339\pi$
$419$			2.92140i			0.142720i	−0.997451	+	0.0713598i	$0.977266\pi$
$420$	3.70780	+	9.11889i	0.180922	+	0.444956i
$421$	2.06588	+	6.35811i	0.100685	+	0.309875i	0.988693	−	0.149951i	$-0.0479116\pi$
$421$	2.06588	+	6.35811i	0.100685	+	0.309875i	−0.888009	+	0.459826i	$0.847912\pi$
$422$	−5.84972	+	18.0036i	−0.284760	+	0.876401i
$423$	5.77471	−	7.94820i	0.280776	−	0.386455i
$424$	−0.894540	+	1.23123i	−0.0434427	+	0.0597938i
$425$	−16.5669	+	50.9877i	−0.803614	+	2.47327i
$426$	−2.18823	−	6.73468i	−0.106020	−	0.326296i
$427$	4.19133	+	10.3081i	0.202833	+	0.498844i
$428$			12.9526i			0.626089i
$429$	15.9323	−	5.48266i	0.769217	−	0.264705i
$430$			13.2666i			0.639771i
$431$	−7.56893	−	10.4177i	−0.364583	−	0.501805i	0.586836	−	0.809706i	$-0.300373\pi$
$431$	−7.56893	−	10.4177i	−0.364583	−	0.501805i	−0.951418	+	0.307901i	$0.900373\pi$
$432$	0.951057	−	0.309017i	0.0457577	−	0.0148676i
$433$	−0.475770	−	0.154587i	−0.0228640	−	0.00742897i	0.297563	−	0.954702i	$-0.403826\pi$
$433$	−0.475770	−	0.154587i	−0.0228640	−	0.00742897i	−0.320427	+	0.947273i	$0.603826\pi$
$434$	5.51831	−	4.65129i	0.264888	−	0.223269i
$435$	−21.6226	+	29.7610i	−1.03673	+	1.42693i
$436$	−6.13803	−	1.99437i	−0.293959	−	0.0955129i
$437$	0.0572934	+	0.176331i	0.00274072	+	0.00843506i
$438$	2.17677	−	1.58152i	0.104010	−	0.0755678i
$439$	3.14103			0.149913			0.0749565	−	0.997187i	$-0.476118\pi$
$439$	3.14103			0.149913			0.0749565	+	0.997187i	$0.476118\pi$
$440$	9.85648	−	7.42457i	0.469889	−	0.353952i
$441$	6.19514	+	3.25888i	0.295006	+	0.155185i
$442$	−18.1032	−	24.9169i	−0.861082	−	1.18518i
$443$	0.868563	+	2.67316i	0.0412667	+	0.127006i	0.969567	−	0.244824i	$-0.0787303\pi$
$443$	0.868563	+	2.67316i	0.0412667	+	0.127006i	−0.928301	+	0.371830i	$0.878730\pi$
$444$	7.68607	+	2.49736i	0.364765	+	0.118519i
$445$	37.5135	+	27.2552i	1.77831	+	1.29202i
$446$	0.806205	+	0.585743i	0.0381749	+	0.0277357i
$447$	2.18959	−	6.73886i	0.103564	−	0.318737i
$448$	−2.63889	+	0.190406i	−0.124676	+	0.00899583i
$449$	2.67616	−	1.94434i	0.126296	−	0.0917592i	−0.522844	−	0.852428i	$-0.675129\pi$
$449$	2.67616	−	1.94434i	0.126296	−	0.0917592i	0.649140	+	0.760669i	$0.275129\pi$
$450$		−	8.84313i		−	0.416869i
$451$	−7.56668	+	24.7333i	−0.356301	+	1.16465i
$452$	14.3751			0.676149
$453$	−15.4270	+	11.2083i	−0.724822	+	0.526614i
$454$	10.3797	−	3.37257i	0.487144	−	0.158283i
$455$	−26.4068	+	42.4688i	−1.23797	+	1.99097i
$456$	0.0667833	+	0.0485209i	0.00312741	+	0.00227220i
$457$	12.2775	−	16.8986i	0.574318	−	0.790481i	−0.418740	−	0.908106i	$-0.637528\pi$
$457$	12.2775	−	16.8986i	0.574318	−	0.790481i	0.993058	+	0.117625i	$0.0375280\pi$
$458$	−6.07418	+	18.6944i	−0.283828	+	0.873533i
$459$	5.76580	−	1.87342i	0.269125	−	0.0874439i
$460$	4.91188	+	6.76063i	0.229018	+	0.315216i
$461$	−36.1100			−1.68181			−0.840904	−	0.541184i	$-0.817976\pi$
$461$	−36.1100			−1.68181			−0.840904	+	0.541184i	$0.817976\pi$
$462$	1.95655	−	8.55406i	0.0910271	−	0.397971i
$463$	27.7418			1.28927			0.644636	−	0.764490i	$-0.277009\pi$
$463$	27.7418			1.28927			0.644636	+	0.764490i	$0.277009\pi$
$464$	−5.81154	−	7.99890i	−0.269794	−	0.371339i
$465$	−9.65242	+	3.13626i	−0.447620	+	0.145441i
$466$	2.13988	−	6.58588i	0.0991281	−	0.305085i
$467$	11.8611	−	16.3254i	0.548865	−	0.755447i	−0.440993	−	0.897511i	$-0.645374\pi$
$467$	11.8611	−	16.3254i	0.548865	−	0.755447i	0.989858	+	0.142063i	$0.0453737\pi$
$468$	4.11000	+	2.98609i	0.189985	+	0.138032i
$469$	21.4851	+	13.3593i	0.992090	+	0.616874i
$470$	34.7644	−	11.2956i	1.60356	−	0.521029i
$471$	−9.14673	+	6.64549i	−0.421459	+	0.306208i
$472$	−3.21574			−0.148016
$473$	6.78489	−	9.68606i	0.311970	−	0.445365i
$474$			10.9131i			0.501254i
$475$	0.590573	−	0.429077i	0.0270974	−	0.0196874i
$476$	−15.9983	+	1.15434i	−0.733282	+	0.0529090i
$477$	0.470288	−	1.44740i	0.0215330	−	0.0662717i
$478$	18.9265	+	13.7509i	0.865680	+	0.628953i
$479$	7.50744	+	5.45448i	0.343024	+	0.249221i	0.745937	−	0.666017i	$-0.232002\pi$
$479$	7.50744	+	5.45448i	0.343024	+	0.249221i	−0.402913	+	0.915238i	$0.632002\pi$
$480$	3.53854	+	1.14974i	0.161511	+	0.0524782i
$481$	12.6872	+	39.0471i	0.578485	+	1.78039i
$482$	0.335104	+	0.461232i	0.0152636	+	0.0210085i
$483$	5.76905	+	1.42482i	0.262501	+	0.0648314i
$484$	−10.9934	+	0.379871i	−0.499702	+	0.0172669i
$485$	28.0421			1.27333
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−2.96882	−	9.13708i	−0.134530	−	0.414041i	0.860987	−	0.508628i	$-0.169847\pi$
$487$	−2.96882	−	9.13708i	−0.134530	−	0.414041i	−0.995517	+	0.0945868i	$0.969847\pi$
$488$	4.00000	+	1.29968i	0.181071	+	0.0588337i
$489$	−1.60383	+	2.20749i	−0.0725279	+	0.0998261i
$490$	11.5208	+	23.3578i	0.520455	+	1.05520i
$491$	−10.7490	−	3.49256i	−0.485095	−	0.157617i	0.0562513	−	0.998417i	$-0.482085\pi$
$491$	−10.7490	−	3.49256i	−0.485095	−	0.157617i	−0.541346	+	0.840800i	$0.682085\pi$
$492$	−7.41686	+	2.40988i	−0.334378	+	0.108646i
$493$	−35.2326	−	48.4935i	−1.58680	−	2.18404i
$494$			0.419367i			0.0188682i
$495$	−7.07976	+	10.1070i	−0.318211	+	0.454276i
$496$		−	2.72780i		−	0.122482i
$497$	−7.05682	−	17.3554i	−0.316542	−	0.778497i
$498$	3.70493	+	11.4026i	0.166022	+	0.510963i
$499$	5.79569	−	17.8373i	0.259451	−	0.798507i	−0.733469	−	0.679723i	$-0.762100\pi$
$499$	5.79569	−	17.8373i	0.259451	−	0.798507i	0.992920	−	0.118785i	$-0.0378999\pi$
$500$	8.40468	−	11.5681i	0.375869	−	0.517339i
$501$	−2.91016	+	4.00549i	−0.130016	+	0.178952i
$502$	−0.348988	+	1.07408i	−0.0155761	+	0.0479383i
$503$	11.0410	+	33.9806i	0.492292	+	1.51512i	0.821135	+	0.570734i	$0.193341\pi$
$503$	11.0410	+	33.9806i	0.492292	+	1.51512i	−0.328843	+	0.944385i	$0.606659\pi$
$504$	2.45090	−	0.996549i	0.109172	−	0.0443898i
$505$			12.5345i			0.557779i
$506$	−0.128643	−	7.44807i	−0.00571889	−	0.331107i
$507$			12.8088i			0.568858i
$508$	0.441200	+	0.607260i	0.0195751	+	0.0269428i
$509$	−41.8316	+	13.5919i	−1.85415	+	0.602451i	−0.858124	+	0.513443i	$0.828370\pi$
$509$	−41.8316	+	13.5919i	−1.85415	+	0.602451i	−0.996031	+	0.0890087i	$0.971630\pi$
$510$	21.4524	+	6.97032i	0.949930	+	0.308651i
$511$	5.44313	−	4.58792i	0.240790	−	0.202958i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	−0.0785084	−	0.0255089i	−0.00346623	−	0.00112625i
$514$	1.15007	+	3.53955i	0.0507274	+	0.156123i
$515$	−15.5156	+	11.2728i	−0.683701	+	0.496738i
$516$	3.56568			0.156970
$517$	−31.1587	−	9.53241i	−1.37036	−	0.419235i
$518$	20.7582	+	5.12678i	0.912064	+	0.225258i
$519$	7.90861	+	10.8853i	0.347149	+	0.477810i
$520$	5.84095	+	17.9766i	0.256143	+	0.788326i
$521$	21.7808	+	7.07700i	0.954233	+	0.310049i	0.744435	−	0.667695i	$-0.232719\pi$
$521$	21.7808	+	7.07700i	0.954233	+	0.310049i	0.209799	+	0.977745i	$0.432719\pi$
$522$	7.99890	+	5.81154i	0.350102	+	0.254364i
$523$	−18.6294	−	13.5351i	−0.814608	−	0.591848i	0.100555	−	0.994932i	$-0.467938\pi$
$523$	−18.6294	−	13.5351i	−0.814608	−	0.591848i	−0.915163	+	0.403084i	$0.867938\pi$
$524$	−4.74388	+	14.6002i	−0.207237	+	0.637811i
$525$	−1.68378	−	23.3361i	−0.0734863	−	1.01847i
$526$	−16.4709	+	11.9668i	−0.718166	+	0.521778i
$527$		−	16.5374i		−	0.720378i
$528$	−1.99551	−	2.64914i	−0.0868434	−	0.115289i
$529$	−17.9554			−0.780671
$530$	4.58096	−	3.32826i	0.198984	−	0.144570i
$531$	3.05835	−	0.993718i	0.132721	−	0.0431237i
$532$	0.185472	+	0.115325i	0.00804125	+	0.00499999i
$533$	−32.0520	−	23.2872i	−1.38833	−	1.00868i
$534$	7.32541	−	10.0826i	0.317002	−	0.436315i
$535$	14.8921	−	45.8333i	0.643844	−	1.98155i
$536$	9.09441	−	2.95495i	0.392819	−	0.127635i
$537$	1.00201	+	1.37915i	0.0432400	+	0.0595148i
$538$	25.2474			1.08849
$539$	3.53439	−	22.9458i	0.152237	−	0.988344i
$540$	−3.72064			−0.160111
$541$	−20.0595	−	27.6096i	−0.862426	−	1.18703i	−0.980985	−	0.194081i	$-0.937827\pi$
$541$	−20.0595	−	27.6096i	−0.862426	−	1.18703i	0.118559	−	0.992947i	$-0.462173\pi$
$542$	−0.991490	+	0.322155i	−0.0425882	+	0.0138377i
$543$	−1.80194	+	5.54581i	−0.0773287	+	0.237993i
$544$	−3.56346	+	4.90468i	−0.152782	+	0.210287i
$545$	19.4266	+	14.1143i	0.832146	+	0.604589i
$546$	11.4144	+	7.09739i	0.488491	+	0.303740i
$547$	−3.99373	+	1.29764i	−0.170760	+	0.0554832i	−0.393149	−	0.919475i	$-0.628614\pi$
$547$	−3.99373	+	1.29764i	−0.170760	+	0.0554832i	0.222389	+	0.974958i	$0.428614\pi$
$548$	−15.0206	+	10.9131i	−0.641649	+	0.466186i
$549$	−4.20585			−0.179501
$550$	−27.7332	+	9.54363i	−1.18255	+	0.406942i
$551$			0.816174i			0.0347702i
$552$	1.81706	−	1.32017i	0.0773393	−	0.0561903i
$553$	2.07791	+	28.7984i	0.0883618	+	1.22463i
$554$	1.58081	−	4.86525i	0.0671624	−	0.206705i
$555$	−24.3261	−	17.6740i	−1.03259	−	0.750218i
$556$	−8.78964	−	6.38605i	−0.372764	−	0.270829i
$557$	13.4395	+	4.36676i	0.569450	+	0.185025i	0.579569	−	0.814923i	$-0.303221\pi$
$557$	13.4395	+	4.36676i	0.569450	+	0.185025i	−0.0101191	+	0.999949i	$0.503221\pi$
$558$	0.842937	+	2.59429i	0.0356844	+	0.109825i
$559$	10.6474	+	14.6549i	0.450338	+	0.619837i
$560$	9.55673	+	2.36028i	0.403845	+	0.0997401i
$561$	−12.0978	−	16.0605i	−0.510770	−	0.678073i
$562$	−17.3741			−0.732882
$563$	−3.97423	+	2.88745i	−0.167494	+	0.121691i	−0.668374	−	0.743825i	$-0.733010\pi$
$563$	−3.97423	+	2.88745i	−0.167494	+	0.121691i	0.500881	+	0.865516i	$0.333010\pi$
$564$	−3.03594	−	9.34367i	−0.127836	−	0.393440i
$565$	−50.8669	−	16.5277i	−2.13999	−	0.695324i
$566$	16.7870	−	23.1054i	0.705611	−	0.971191i
$567$	−2.02299	+	1.70514i	−0.0849576	+	0.0716093i
$568$	−6.73468	−	2.18823i	−0.282581	−	0.0918161i
$569$	−14.2740	+	4.63792i	−0.598399	+	0.194432i	−0.592526	−	0.805551i	$-0.701869\pi$
$569$	−14.2740	+	4.63792i	−0.598399	+	0.194432i	−0.00587275	+	0.999983i	$0.501869\pi$
$570$	−0.180529	−	0.248476i	−0.00756151	−	0.0104075i
$571$			31.6039i			1.32258i	0.750130	+	0.661290i	$0.229991\pi$
$571$			31.6039i			1.32258i	−0.750130	+	0.661290i	$0.770009\pi$
$572$	4.92919	−	16.1121i	0.206100	−	0.673681i
$573$		−	16.8804i		−	0.705187i
$574$	−19.1134	+	7.77164i	−0.797779	+	0.324382i
$575$	−6.13763	−	18.8897i	−0.255957	−	0.787754i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−13.8266	+	19.0307i	−0.575609	+	0.792258i	−0.993205	−	0.116375i	$-0.962873\pi$
$577$	−13.8266	+	19.0307i	−0.575609	+	0.792258i	0.417596	+	0.908633i	$0.362873\pi$
$578$	−11.6112	+	15.9815i	−0.482963	+	0.664741i
$579$	3.57175	−	10.9927i	0.148437	−	0.456842i
$580$	11.3677	+	34.9861i	0.472017	+	1.45272i
$581$	11.9480	+	29.3848i	0.495688	+	1.21909i
$582$		−	7.53691i		−	0.312415i
$583$	−5.04676	+	0.0871678i	−0.209015	+	0.00361012i
$584$		−	2.69064i		−	0.111339i
$585$	−11.1101	−	15.2918i	−0.459348	−	0.632238i
$586$	7.21510	−	2.34433i	0.298053	−	0.0968433i
$587$	−42.8043	−	13.9080i	−1.76672	−	0.574043i	−0.768862	−	0.639415i	$-0.779177\pi$
$587$	−42.8043	−	13.9080i	−1.76672	−	0.574043i	−0.997861	+	0.0653723i	$0.979177\pi$
$588$	6.27790	−	3.09645i	0.258896	−	0.127695i
$589$	−0.132355	+	0.182171i	−0.00545361	+	0.00750625i
$590$	11.3790	+	3.69726i	0.468466	+	0.152214i
$591$	4.29215	+	13.2099i	0.176556	+	0.543382i
$592$	6.53816	−	4.75025i	0.268717	−	0.195234i
$593$	−8.37304			−0.343840			−0.171920	−	0.985111i	$-0.554997\pi$
$593$	−8.37304			−0.343840			−0.171920	+	0.985111i	$0.554997\pi$
$594$	2.71647	+	1.90283i	0.111458	+	0.0780743i
$595$	57.9379	+	14.3093i	2.37522	+	0.586622i
$596$	−4.16484	−	5.73242i	−0.170599	−	0.234809i
$597$	−2.91323	−	8.96600i	−0.119231	−	0.366954i
$598$	10.8518	+	3.52597i	0.443764	+	0.144188i
$599$	5.63463	+	4.09380i	0.230225	+	0.167268i	0.696917	−	0.717152i	$-0.254555\pi$
$599$	5.63463	+	4.09380i	0.230225	+	0.167268i	−0.466693	+	0.884420i	$0.654555\pi$
$600$	−7.15425	−	5.19786i	−0.292071	−	0.212202i
$601$	4.14967	−	12.7714i	0.169268	−	0.520955i	−0.830057	−	0.557679i	$-0.811692\pi$
$601$	4.14967	−	12.7714i	0.169268	−	0.520955i	0.999325	+	0.0367238i	$0.0116922\pi$
$602$	9.40943	−	0.678925i	0.383500	−	0.0276709i
$603$	−7.73617	+	5.62065i	−0.315041	+	0.228891i
$604$			19.0688i			0.775898i
$605$	39.3374	+	11.2954i	1.59929	+	0.459224i
$606$	3.36892			0.136853
$607$	12.1154	−	8.80232i	0.491747	−	0.357275i	−0.314109	−	0.949387i	$-0.601706\pi$
$607$	12.1154	−	8.80232i	0.491747	−	0.357275i	0.805856	+	0.592112i	$0.201706\pi$
$608$	0.0785084	−	0.0255089i	0.00318394	−	0.00103452i
$609$	22.2148	+	13.8130i	0.900188	+	0.559730i
$610$	−12.6598	−	9.19791i	−0.512582	−	0.372413i
$611$	29.3369	−	40.3787i	1.18684	−	1.63355i
$612$	1.87342	−	5.76580i	0.0757286	−	0.233069i
$613$	−28.5958	+	9.29135i	−1.15498	+	0.375274i	−0.823015	−	0.568019i	$-0.807710\pi$
$613$	−28.5958	+	9.29135i	−1.15498	+	0.375274i	−0.331960	+	0.943293i	$0.607710\pi$
$614$	−14.6242	−	20.1285i	−0.590184	−	0.812319i
$615$	29.0156			1.17002
$616$	−5.77034	−	6.61083i	−0.232494	−	0.266358i
$617$	5.46786			0.220128			0.110064	−	0.993925i	$-0.464894\pi$
$617$	5.46786			0.220128			0.110064	+	0.993925i	$0.464894\pi$
$618$	3.02980	+	4.17016i	0.121876	+	0.167748i
$619$	1.82050	−	0.591518i	0.0731722	−	0.0237751i	−0.272202	−	0.962240i	$-0.587752\pi$
$619$	1.82050	−	0.591518i	0.0731722	−	0.0237751i	0.345374	+	0.938465i	$0.387752\pi$
$620$	−3.13626	+	9.65242i	−0.125955	+	0.387651i
$621$	−1.32017	+	1.81706i	−0.0529767	+	0.0729162i
$622$	−12.6374	−	9.18157i	−0.506712	−	0.368148i
$623$	17.4112	−	28.0016i	0.697564	−	1.12186i
$624$	4.83159	−	1.56988i	0.193418	−	0.0628455i
$625$	−7.26929	+	5.28145i	−0.290772	+	0.211258i
$626$	−22.2572			−0.889578
$627$	0.00472808	+	0.273742i	0.000188821	+	0.0109322i
$628$			11.3060i			0.451158i
$629$	39.6378	−	28.7985i	1.58046	−	1.14827i
$630$	−9.81835	+	0.708431i	−0.391173	+	0.0282245i
$631$	0.759011	−	2.33600i	0.0302157	−	0.0929945i	−0.934811	−	0.355145i	$-0.884432\pi$
$631$	0.759011	−	2.33600i	0.0302157	−	0.0929945i	0.965027	+	0.262150i	$0.0844316\pi$
$632$	8.82886	+	6.41455i	0.351193	+	0.255157i
$633$	−15.3148	−	11.1268i	−0.608708	−	0.442252i
$634$	29.7778	+	9.67539i	1.18263	+	0.384259i
$635$	−0.863012	−	2.65608i	−0.0342476	−	0.105403i
$636$	−0.894540	−	1.23123i	−0.0354708	−	0.0488214i
$637$	31.4727	+	16.5559i	1.24700	+	0.655968i
$638$	9.59321	−	31.3575i	0.379799	−	1.24145i
$639$	7.08126			0.280130
$640$	3.01006	−	2.18694i	0.118983	−	0.0864462i
$641$	5.03549	+	15.4977i	0.198890	+	0.612120i	0.999909	+	0.0134817i	$0.00429149\pi$
$641$	5.03549	+	15.4977i	0.198890	+	0.612120i	−0.801019	+	0.598639i	$0.795709\pi$
$642$	−12.3187	−	4.00258i	−0.486179	−	0.157969i
$643$	18.6191	−	25.6270i	0.734265	−	1.01063i	−0.264664	−	0.964341i	$-0.585261\pi$
$643$	18.6191	−	25.6270i	0.734265	−	1.01063i	0.998928	−	0.0462876i	$-0.0147391\pi$
$644$	4.54366	−	3.82977i	0.179045	−	0.150914i
$645$	−12.6173	−	4.09960i	−0.496805	−	0.161422i
$646$	0.475959	−	0.154649i	0.0187264	−	0.00608456i
$647$	−12.2290	−	16.8317i	−0.480771	−	0.661724i	0.497882	−	0.867245i	$-0.334111\pi$
$647$	−12.2290	−	16.8317i	−0.480771	−	0.661724i	−0.978653	+	0.205521i	$0.934111\pi$
$648$			1.00000i			0.0392837i
$649$	−6.41704	−	8.51894i	−0.251891	−	0.334398i
$650$		−	44.9252i		−	1.76211i
$651$	2.71839	+	6.68556i	0.106542	+	0.262028i
$652$	0.843185	+	2.59506i	0.0330217	+	0.101630i
$653$	5.17341	−	15.9221i	0.202451	−	0.623081i	−0.797357	−	0.603508i	$-0.793769\pi$
$653$	5.17341	−	15.9221i	0.202451	−	0.623081i	0.999808	−	0.0195733i	$-0.00623076\pi$
$654$	3.79351	−	5.22132i	0.148338	−	0.204170i
$655$	33.5728	−	46.2090i	1.31180	−	1.80553i
$656$	−2.40988	+	7.41686i	−0.0940902	+	0.289580i
$657$	0.831452	+	2.55895i	0.0324380	+	0.0998340i
$658$	−9.79061	−	24.0789i	−0.381678	−	0.938692i
$659$		−	26.7348i		−	1.04144i	−0.853727	−	0.520721i	$-0.825663\pi$
$659$		−	26.7348i		−	1.04144i	0.853727	−	0.520721i	$-0.174337\pi$
$660$	4.01536	+	11.6684i	0.156298	+	0.454191i
$661$			27.1639i			1.05655i	0.849072	+	0.528277i	$0.177162\pi$
$661$			27.1639i			1.05655i	−0.849072	+	0.528277i	$0.822838\pi$
$662$	2.18838	+	3.01205i	0.0850539	+	0.117067i
$663$	29.2916	−	9.51743i	1.13759	−	0.369626i
$664$	11.4026	+	3.70493i	0.442507	+	0.143779i
$665$	−0.523707	−	0.621328i	−0.0203085	−	0.0240941i
$666$	−4.75025	+	6.53816i	−0.184069	+	0.253349i
$667$	21.1199	+	6.86226i	0.817764	+	0.265708i
$668$	1.52996	+	4.70874i	0.0591960	+	0.182187i
$669$	−0.806205	+	0.585743i	−0.0311697	+	0.0226461i
$670$	−35.5783			−1.37451
$671$	4.53901	+	13.1901i	0.175226	+	0.509197i
$672$	0.634376	−	2.56857i	0.0244716	−	0.0990849i
$673$	6.66683	+	9.17611i	0.256988	+	0.353713i	0.917943	−	0.396712i	$-0.129849\pi$
$673$	6.66683	+	9.17611i	0.256988	+	0.353713i	−0.660956	+	0.750425i	$0.729849\pi$
$674$	−1.17968	−	3.63068i	−0.0454396	−	0.139849i
$675$	8.41032	+	2.73268i	0.323713	+	0.105181i
$676$	10.3625	+	7.52882i	0.398559	+	0.289570i
$677$	−21.3827	−	15.5354i	−0.821803	−	0.597075i	0.0954253	−	0.995437i	$-0.469579\pi$
$677$	−21.3827	−	15.5354i	−0.821803	−	0.597075i	−0.917228	+	0.398362i	$0.869579\pi$
$678$	−4.44216	+	13.6716i	−0.170600	+	0.525053i
$679$	−1.43507	−	19.8891i	−0.0550730	−	0.763273i
$680$	18.2485	−	13.2583i	0.699800	−	0.508434i
$681$			10.9139i			0.418221i
$682$	7.22633	−	5.44335i	0.276710	−	0.208437i
$683$	−35.1304			−1.34423			−0.672113	−	0.740449i	$-0.734613\pi$
$683$	−35.1304			−1.34423			−0.672113	+	0.740449i	$0.734613\pi$
$684$	−0.0667833	+	0.0485209i	−0.00255352	+	0.00185524i
$685$	65.6983	−	21.3467i	2.51020	−	0.815614i
$686$	15.9771	−	9.36654i	0.610009	−	0.357616i
$687$	−15.9024	−	11.5538i	−0.606715	−	0.440804i
$688$	2.09585	−	2.88469i	0.0799036	−	0.109978i
$689$	2.38917	−	7.35312i	0.0910202	−	0.280131i
$690$	−7.94760	+	2.58233i	−0.302560	+	0.0983076i
$691$	−21.6814	−	29.8419i	−0.824799	−	1.13524i	−0.988869	−	0.148790i	$-0.952462\pi$
$691$	−21.6814	−	29.8419i	−0.824799	−	1.13524i	0.164070	−	0.986449i	$-0.447538\pi$
$692$	13.4549			0.511480
$693$	7.53078	+	4.50414i	0.286071	+	0.171098i
$694$	−30.9779			−1.17591
$695$	23.7602	+	32.7031i	0.901274	+	1.24050i
$696$	9.40327	−	3.05531i	0.356430	−	0.115811i
$697$	−14.6100	+	44.9649i	−0.553392	+	1.70317i
$698$	−8.22752	+	11.3242i	−0.311416	+	0.428628i
$699$	5.60228	+	4.07030i	0.211898	+	0.153953i
$700$	−19.8690	−	12.3544i	−0.750977	−	0.466952i
$701$	23.4007	−	7.60336i	0.883834	−	0.287175i	0.168286	−	0.985738i	$-0.446177\pi$
$701$	23.4007	−	7.60336i	0.883834	−	0.287175i	0.715548	+	0.698563i	$0.246177\pi$
$702$	−4.11000	+	2.98609i	−0.155122	+	0.112703i
$703$	−0.667127			−0.0251612
$704$	−3.31613	+	0.0572763i	−0.124981	+	0.00215868i
$705$			36.5535i			1.37668i
$706$	17.8188	−	12.9461i	0.670621	−	0.487235i
$707$	8.89022	−	0.641462i	0.334351	−	0.0241247i
$708$	0.993718	−	3.05835i	0.0373462	−	0.114940i
$709$	0.611855	+	0.444539i	0.0229787	+	0.0166950i	0.599215	−	0.800588i	$-0.295479\pi$
$709$	0.611855	+	0.444539i	0.0229787	+	0.0166950i	−0.576237	+	0.817283i	$0.695479\pi$
$710$	21.3150	+	15.4863i	0.799938	+	0.581189i
$711$	−10.3790	−	3.37233i	−0.389241	−	0.126472i
$712$	−3.85120	−	11.8528i	−0.144330	−	0.444201i
$713$	3.60117	+	4.95659i	0.134865	+	0.185626i
$714$	3.84592	−	15.5720i	0.143930	−	0.582769i
$715$	−35.9668	+	51.3460i	−1.34508	+	1.92023i
$716$	1.70472			0.0637086
$717$	−18.9265	+	13.7509i	−0.706825	+	0.513538i
$718$	−3.21197	−	9.88542i	−0.119870	−	0.368921i
$719$	33.0005	+	10.7225i	1.23071	+	0.399883i	0.850972	−	0.525210i	$-0.176013\pi$
$719$	33.0005	+	10.7225i	1.23071	+	0.399883i	0.379740	+	0.925093i	$0.376013\pi$
$720$	−2.18694	+	3.01006i	−0.0815023	+	0.112178i
$721$	8.78933	+	10.4277i	0.327332	+	0.388348i
$722$	18.0636	+	5.86922i	0.672257	+	0.218430i
$723$	−0.542210	+	0.176175i	−0.0201650	+	0.00655201i
$724$	3.42750	+	4.71755i	0.127382	+	0.175326i
$725$		−	87.4337i		−	3.24720i
$726$	3.03588	−	10.5728i	0.112672	−	0.392392i
$727$			1.40546i			0.0521257i	0.999660	+	0.0260629i	$0.00829701\pi$
$727$			1.40546i			0.0521257i	−0.999660	+	0.0260629i	$0.991703\pi$
$728$	12.4511	−	5.06270i	0.461470	−	0.187636i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−3.09353	+	9.52091i	−0.114497	+	0.352385i
$731$	12.7061	−	17.4885i	0.469954	−	0.646836i
$732$	−2.47213	+	3.40260i	−0.0913727	+	0.125764i
$733$	−3.16179	+	9.73099i	−0.116783	+	0.359422i	−0.992315	−	0.123739i	$-0.960511\pi$
$733$	−3.16179	+	9.73099i	−0.116783	+	0.359422i	0.875531	+	0.483161i	$0.160511\pi$
$734$	2.95072	+	9.08139i	0.108913	+	0.335200i
$735$	−25.7747	+	3.73894i	−0.950713	+	0.137913i
$736$		−	2.24601i		−	0.0827891i
$737$	25.9761	+	18.1957i	0.956841	+	0.670248i
$738$		−	7.79855i		−	0.287069i
$739$	28.7530	+	39.5752i	1.05770	+	1.45580i	0.881940	+	0.471362i	$0.156238\pi$
$739$	28.7530	+	39.5752i	1.05770	+	1.45580i	0.175758	+	0.984433i	$0.443762\pi$
$740$	−28.5971	+	9.29176i	−1.05125	+	0.341572i
$741$	−0.398841	−	0.129591i	−0.0146518	−	0.00476066i
$742$	−2.59503	−	3.07875i	−0.0952664	−	0.113025i
$743$	0.0490832	−	0.0675572i	0.00180069	−	0.00247843i	−0.808116	−	0.589024i	$-0.799512\pi$
$743$	0.0490832	−	0.0675572i	0.00180069	−	0.00247843i	0.809916	+	0.586545i	$0.199512\pi$
$744$	2.59429	+	0.842937i	0.0951114	+	0.0309036i
$745$	8.14666	+	25.0728i	0.298471	+	0.918598i
$746$	−11.8033	+	8.57559i	−0.432149	+	0.313975i
$747$	−11.9894			−0.438669
$748$	−20.1041	+	0.347239i	−0.735079	+	0.0126963i
$749$	−33.2698	−	8.21683i	−1.21565	−	0.300236i
$750$	8.40468	+	11.5681i	0.306896	+	0.422406i
$751$	−11.2751	−	34.7013i	−0.411436	−	1.26627i	−0.915400	−	0.402545i	$-0.868126\pi$
$751$	−11.2751	−	34.7013i	−0.411436	−	1.26627i	0.503964	−	0.863725i	$-0.331874\pi$
$752$	−9.34367	−	3.03594i	−0.340729	−	0.110709i
$753$	−0.913663	−	0.663815i	−0.0332957	−	0.0241908i
$754$	40.6363	+	29.5240i	1.47989	+	1.07520i
$755$	21.9241	−	67.4755i	0.797901	−	2.45569i
$756$	0.190406	+	2.63889i	0.00692499	+	0.0959755i
$757$	−19.0552	+	13.8444i	−0.692575	+	0.503185i	−0.877506	−	0.479567i	$-0.840794\pi$
$757$	−19.0552	+	13.8444i	−0.692575	+	0.503185i	0.184931	+	0.982752i	$0.440794\pi$
$758$		−	7.30273i		−	0.265247i
$759$	7.12329	+	2.17923i	0.258559	+	0.0791012i
$760$	−0.307134			−0.0111409
$761$	−17.4017	+	12.6431i	−0.630810	+	0.458310i	−0.856681	−	0.515847i	$-0.827477\pi$
$761$	−17.4017	+	12.6431i	−0.630810	+	0.458310i	0.225871	+	0.974157i	$0.427477\pi$
$762$	−0.713877	+	0.231953i	−0.0258610	+	0.00840276i
$763$	9.01650	−	14.5008i	0.326419	−	0.524965i
$764$	−13.6565	−	9.92202i	−0.494075	−	0.358966i
$765$	−13.2583	+	18.2485i	−0.479356	+	0.659777i
$766$	5.25283	−	16.1665i	0.189792	−	0.584121i
$767$	15.5371	−	5.04832i	0.561013	−	0.182284i
$768$	−0.587785	−	0.809017i	−0.0212099	−	0.0291929i
$769$	46.7777			1.68685			0.843424	−	0.537248i	$-0.180536\pi$
$769$	46.7777			1.68685			0.843424	+	0.537248i	$0.180536\pi$
$770$	12.8178	+	30.0271i	0.461922	+	1.08210i
$771$	−3.72171			−0.134034
$772$	−6.79387	−	9.35096i	−0.244517	−	0.336548i
$773$	−36.1874	+	11.7580i	−1.30157	+	0.422905i	−0.876127	−	0.482080i	$-0.839881\pi$
$773$	−36.1874	+	11.7580i	−1.30157	+	0.422905i	−0.425442	+	0.904986i	$0.639881\pi$
$774$	−1.10185	+	3.39116i	−0.0396053	+	0.121893i
$775$	14.1787	−	19.5154i	0.509315	−	0.701012i
$776$	−6.09749	−	4.43008i	−0.218887	−	0.159031i
$777$	−11.2905	+	18.1580i	−0.405044	+	0.651414i
$778$	−17.8599	+	5.80305i	−0.640310	+	0.208049i
$779$	0.520813	−	0.378393i	0.0186601	−	0.0135573i
$780$	−18.9017			−0.676790
$781$	−7.64219	−	22.2077i	−0.273459	−	0.794655i
$782$		−	13.6165i		−	0.486925i
$783$	−7.99890	+	5.81154i	−0.285857	+	0.207687i
$784$	1.18498	−	6.89897i	0.0423206	−	0.246392i
$785$	12.9989	−	40.0066i	0.463952	−	1.42790i
$786$	−12.4196	−	9.02340i	−0.442994	−	0.321854i
$787$	39.6030	+	28.7733i	1.41169	+	1.02566i	0.993073	+	0.117495i	$0.0374864\pi$
$787$	39.6030	+	28.7733i	1.41169	+	1.02566i	0.418621	+	0.908161i	$0.362514\pi$
$788$	13.2099	+	4.29215i	0.470583	+	0.152902i
$789$	−6.29133	−	19.3627i	−0.223977	−	0.689331i
$790$	−23.8662	−	32.8490i	−0.849121	−	1.16871i
$791$	−9.11923	+	36.9236i	−0.324243	+	1.31285i
$792$	3.13613	−	1.07921i	0.111437	−	0.0383482i
$793$	−21.3667			−0.758753
$794$	−7.05657	+	5.12690i	−0.250428	+	0.181947i
$795$	1.74977	+	5.38524i	0.0620579	+	0.190995i
$796$	−8.96600	−	2.91323i	−0.317791	−	0.103257i
$797$	−24.3331	+	33.4917i	−0.861923	+	1.18634i	0.119184	+	0.992872i	$0.461972\pi$
$797$	−24.3331	+	33.4917i	−0.861923	+	1.18634i	−0.981107	+	0.193463i	$0.938028\pi$
$798$	−0.166995	+	0.140757i	−0.00591156	+	0.00498275i
$799$	−56.6462	−	18.4055i	−2.00400	−	0.651139i
$800$	−8.41032	+	2.73268i	−0.297350	+	0.0966148i
$801$	7.32541	+	10.0826i	0.258831	+	0.356250i
$802$			18.7114i			0.660722i
$803$	7.12787	−	5.36919i	0.251537	−	0.189475i
$804$			9.56243i			0.337241i
$805$	−20.4811	+	8.32776i	−0.721866	+	0.293515i
$806$	4.28232	+	13.1796i	0.150838	+	0.464232i
$807$	−7.80187	+	24.0117i	−0.274639	+	0.845251i
$808$	1.98020	−	2.72552i	0.0696633	−	0.0958833i
$809$	16.6558	−	22.9247i	0.585587	−	0.805991i	−0.408707	−	0.912666i	$-0.634020\pi$
$809$	16.6558	−	22.9247i	0.585587	−	0.805991i	0.994294	+	0.106675i	$0.0340203\pi$
$810$	1.14974	−	3.53854i	0.0403977	−	0.124331i
$811$	0.836142	+	2.57338i	0.0293609	+	0.0903636i	0.964663	−	0.263486i	$-0.0848724\pi$
$811$	0.836142	+	2.57338i	0.0293609	+	0.0903636i	−0.935302	+	0.353850i	$0.884872\pi$
$812$	24.2324	−	9.85306i	0.850392	−	0.345775i
$813$		−	1.04251i		−	0.0365626i
$814$	25.6311	+	7.84133i	0.898368	+	0.274838i
$815$		−	10.1521i		−	0.355614i
$816$	−3.56346	−	4.90468i	−0.124746	−	0.171698i
$817$	−0.279936	+	0.0909566i	−0.00979371	+	0.00318217i
$818$	−25.9066	−	8.41756i	−0.905802	−	0.294313i
$819$	−10.2773	+	8.66253i	−0.359117	+	0.302693i
$820$	17.0549	−	23.4741i	0.595584	−	0.819751i
$821$	−22.8675	−	7.43009i	−0.798080	−	0.259312i	−0.118539	−	0.992949i	$-0.537821\pi$
$821$	−22.8675	−	7.43009i	−0.798080	−	0.259312i	−0.679541	+	0.733638i	$0.737821\pi$
$822$	−5.73737	−	17.6578i	−0.200114	−	0.615887i
$823$	20.4451	−	14.8542i	0.712671	−	0.517786i	−0.171364	−	0.985208i	$-0.554817\pi$
$823$	20.4451	−	14.8542i	0.712671	−	0.517786i	0.884034	+	0.467422i	$0.154817\pi$
$824$	5.15460			0.179569
$825$	−0.506502	−	29.3250i	−0.0176341	−	1.02096i
$826$	2.03999	−	8.25986i	0.0709802	−	0.287397i
$827$	6.18787	+	8.51687i	0.215173	+	0.296161i	0.902936	−	0.429775i	$-0.141407\pi$
$827$	6.18787	+	8.51687i	0.215173	+	0.296161i	−0.687763	+	0.725936i	$0.741407\pi$
$828$	0.694056	+	2.13609i	0.0241201	+	0.0742341i
$829$	34.8487	+	11.3230i	1.21035	+	0.393265i	0.843557	−	0.537039i	$-0.180457\pi$
$829$	34.8487	+	11.3230i	1.21035	+	0.393265i	0.366788	+	0.930304i	$0.380457\pi$
$830$	−36.0888	−	26.2201i	−1.25266	−	0.910111i
$831$	4.13863	+	3.00689i	0.143567	+	0.104308i
$832$	1.56988	−	4.83159i	0.0544258	−	0.167505i
$833$	7.18395	−	41.8252i	0.248909	−	1.44916i
$834$	8.78964	−	6.38605i	0.304360	−	0.221131i
$835$		−	18.4211i		−	0.637489i
$836$	0.224241	+	0.157076i	0.00775554	+	0.00543260i
$837$	−2.72780			−0.0942866
$838$	−2.36346	+	1.71715i	−0.0816444	+	0.0593181i
$839$	13.2415	−	4.30242i	0.457146	−	0.148536i	−0.0713864	−	0.997449i	$-0.522742\pi$
$839$	13.2415	−	4.30242i	0.457146	−	0.148536i	0.528533	+	0.848913i	$0.322742\pi$
$840$	−5.19795	+	8.35962i	−0.179346	+	0.288434i
$841$	55.6250	+	40.4140i	1.91810	+	1.39358i
$842$	−3.92953	+	5.40853i	−0.135421	+	0.186390i
$843$	5.36889	−	16.5238i	0.184915	−	0.569108i
$844$	−18.0036	+	5.84972i	−0.619709	+	0.201356i
$845$	−28.0120	−	38.5552i	−0.963642	−	1.32634i
$846$	9.82452			0.337774
$847$	5.99824	−	28.4784i	0.206102	−	0.978531i
$848$	−1.52188			−0.0522617
$849$	16.7870	+	23.1054i	0.576129	+	0.792974i
$850$	−50.9877	+	16.5669i	−1.74887	+	0.568241i
$851$	−5.60910	+	17.2630i	−0.192277	+	0.591769i
$852$	4.16226	−	5.72886i	0.142597	−	0.196267i
$853$	9.94314	+	7.22411i	0.340447	+	0.247349i	0.744850	−	0.667232i	$-0.232521\pi$
$853$	9.94314	+	7.22411i	0.340447	+	0.247349i	−0.404404	+	0.914581i	$0.632521\pi$
$854$	−5.87582	+	9.44980i	−0.201066	+	0.323366i
$855$	0.292101	−	0.0949095i	0.00998966	−	0.00324584i
$856$	−10.4789	+	7.61336i	−0.358161	+	0.260219i
$857$	−11.1759			−0.381761			−0.190881	−	0.981613i	$-0.561134\pi$
$857$	−11.1759			−0.381761			−0.190881	+	0.981613i	$0.561134\pi$
$858$	13.8003	+	9.66685i	0.471135	+	0.330021i
$859$			45.5406i			1.55382i	0.629609	+	0.776912i	$0.283215\pi$
$859$			45.5406i			1.55382i	−0.629609	+	0.776912i	$0.716785\pi$
$860$	−10.7329	+	7.79790i	−0.365989	+	0.265906i
$861$	−1.48489	−	20.5795i	−0.0506049	−	0.701348i
$862$	3.97922	−	12.2468i	0.135533	−	0.417127i
$863$	−6.42690	−	4.66941i	−0.218774	−	0.158949i	0.473001	−	0.881062i	$-0.343171\pi$
$863$	−6.42690	−	4.66941i	−0.218774	−	0.158949i	−0.691775	+	0.722113i	$0.743171\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−47.6107	−	15.4697i	−1.61881	−	0.525985i
$866$	−0.154587	−	0.475770i	−0.00525308	−	0.0161673i
$867$	−11.6112	−	15.9815i	−0.394337	−	0.542759i
$868$	7.00656	+	1.73045i	0.237818	+	0.0587353i
$869$	0.625060	+	36.1892i	0.0212037	+	1.22763i
$870$	−36.7866			−1.24718
$871$	−39.3016	+	28.5543i	−1.33168	+	0.967524i
$872$	−1.99437	−	6.13803i	−0.0675378	−	0.207860i
$873$	7.16803	+	2.32903i	0.242601	+	0.0788258i
$874$	−0.108979	+	0.149996i	−0.00368625	+	0.00507369i
$875$	24.3817	+	28.9265i	0.824251	+	0.977895i
$876$	2.55895	+	0.831452i	0.0864588	+	0.0280922i
$877$	5.35477	−	1.73987i	0.180818	−	0.0587512i	−0.217209	−	0.976125i	$-0.569695\pi$
$877$	5.35477	−	1.73987i	0.180818	−	0.0587512i	0.398026	+	0.917374i	$0.369695\pi$
$878$	1.84625	+	2.54115i	0.0623079	+	0.0857595i
$879$			7.58641i			0.255883i
$880$	11.8001	+	3.61001i	0.397781	+	0.121694i
$881$			17.9496i			0.604737i	0.953191	+	0.302369i	$0.0977773\pi$
$881$			17.9496i			0.604737i	−0.953191	+	0.302369i	$0.902223\pi$
$882$	1.00492	+	6.92749i	0.0338374	+	0.233261i
$883$	3.19438	+	9.83128i	0.107499	+	0.330849i	0.990309	−	0.138882i	$-0.0443509\pi$
$883$	3.19438	+	9.83128i	0.107499	+	0.330849i	−0.882810	+	0.469731i	$0.844351\pi$
$884$	9.51743	−	29.2916i	0.320106	−	0.985184i
$885$	−7.03261	+	9.67956i	−0.236399	+	0.325375i
$886$	−1.65211	+	2.27393i	−0.0555036	+	0.0763941i
$887$	−12.2119	+	37.5842i	−0.410034	+	1.26195i	0.506584	+	0.862191i	$0.330908\pi$
$887$	−12.2119	+	37.5842i	−0.410034	+	1.26195i	−0.916618	+	0.399764i	$0.869092\pi$
$888$	2.49736	+	7.68607i	0.0838058	+	0.257928i
$889$	−1.83968	+	0.748025i	−0.0617009	+	0.0250879i
$890$			46.3693i			1.55430i
$891$	−2.64914	+	1.99551i	−0.0887495	+	0.0668521i
$892$			0.996525i			0.0333661i
$893$	0.476694	+	0.656114i	0.0159520	+	0.0219560i
$894$	6.73886	−	2.18959i	0.225381	−	0.0732308i
$895$	−6.03223	−	1.95999i	−0.201635	−	0.0655152i
$896$	−1.70514	−	2.02299i	−0.0569648	−	0.0675834i
$897$	−6.70679	+	9.23111i	−0.223933	+	0.308218i
$898$	3.14601	+	1.02220i	0.104984	+	0.0341113i
$899$	8.33427	+	25.6502i	0.277963	+	0.855483i
$900$	7.15425	−	5.19786i	0.238475	−	0.173262i
$901$	−9.22645			−0.307378
$902$	−24.4572	+	8.41630i	−0.814337	+	0.280232i
$903$	−2.26198	+	9.15870i	−0.0752739	+	0.304782i
$904$	8.44949	+	11.6297i	0.281026	+	0.386799i
$905$	−6.70437	−	20.6339i	−0.222861	−	0.685895i
$906$	−18.1355	−	5.89258i	−0.602511	−	0.195768i
$907$	−15.8172	−	11.4919i	−0.525201	−	0.381581i	0.293358	−	0.956003i	$-0.405227\pi$
$907$	−15.8172	−	11.4919i	−0.525201	−	0.381581i	−0.818560	+	0.574422i	$0.805227\pi$
$908$	8.82952	+	6.41502i	0.293018	+	0.212890i
$909$	−1.04105	+	3.20404i	−0.0345296	+	0.106271i
$910$	−49.8795	+	3.59899i	−1.65349	+	0.119305i
$911$	16.8438	−	12.2377i	0.558059	−	0.405454i	−0.272689	−	0.962102i	$-0.587913\pi$
$911$	16.8438	−	12.2377i	0.558059	−	0.405454i	0.830748	+	0.556648i	$0.187913\pi$
$912$			0.0825487i			0.00273346i
$913$	12.9391	+	37.6003i	0.428223	+	1.24439i
$914$	20.8878			0.690906
$915$	12.6598	−	9.19791i	0.418521	−	0.304074i
$916$	−18.6944	+	6.07418i	−0.617681	+	0.200697i
$917$	−34.4922	−	21.4470i	−1.13903	−	0.708242i
$918$	4.90468	+	3.56346i	0.161879	+	0.117612i
$919$	−0.953053	+	1.31176i	−0.0314383	+	0.0432711i	−0.824447	−	0.565939i	$-0.808514\pi$
$919$	−0.953053	+	1.31176i	−0.0314383	+	0.0432711i	0.793008	+	0.609211i	$0.208514\pi$
$920$	−2.58233	+	7.94760i	−0.0851369	+	0.262024i
$921$	23.6624	−	7.68839i	0.779704	−	0.253341i
$922$	−21.2249	−	29.2136i	−0.699005	−	0.962098i
$923$	35.9745			1.18411
$924$	8.07041	−	3.44506i	0.265497	−	0.113334i
$925$	71.4668			2.34981
$926$	16.3062	+	22.4436i	0.535856	+	0.737543i
$927$	−4.90232	+	1.59286i	−0.161013	+	0.0523163i
$928$	3.05531	−	9.40327i	0.100295	−	0.308677i
$929$	−34.5560	+	47.5623i	−1.13375	+	1.56047i	−0.352998	+	0.935624i	$0.614838\pi$
$929$	−34.5560	+	47.5623i	−1.13375	+	1.56047i	−0.780749	+	0.624845i	$0.785162\pi$
$930$	−8.21084	−	5.96552i	−0.269244	−	0.195617i
$931$	−0.413881	+	0.403240i	−0.0135644	+	0.0132157i
$932$	6.58588	−	2.13988i	0.215728	−	0.0700942i
$933$	12.6374	−	9.18157i	0.413728	−	0.300591i
$934$	20.1792			0.660285
$935$	71.5383	+	21.8858i	2.33955	+	0.715742i
$936$			5.08024i			0.166053i
$937$	0.241151	−	0.175207i	0.00787807	−	0.00572375i	−0.583839	−	0.811869i	$-0.698450\pi$
$937$	0.241151	−	0.175207i	0.00787807	−	0.00572375i	0.591717	+	0.806146i	$0.298450\pi$
$938$	1.82074	+	25.2342i	0.0594493	+	0.823926i
$939$	6.87787	−	21.1679i	0.224451	−	0.690788i
$940$	29.5724	+	21.4856i	0.964544	+	0.700782i
$941$	−29.3051	−	21.2914i	−0.955318	−	0.694079i	−0.00325935	−	0.999995i	$-0.501037\pi$
$941$	−29.3051	−	21.2914i	−0.955318	−	0.694079i	−0.952059	+	0.305916i	$0.901037\pi$
$942$	−10.7526	−	3.49374i	−0.350340	−	0.113832i
$943$	−5.41263	−	16.6584i	−0.176260	−	0.542471i
$944$	−1.89016	−	2.60159i	−0.0615196	−	0.0846744i
$945$	2.36028	−	9.55673i	0.0767799	−	0.310880i
$946$	11.8242	−	0.204229i	0.384439	−	0.00664004i
$947$	−25.4343			−0.826505			−0.413252	−	0.910617i	$-0.635607\pi$
$947$	−25.4343			−0.826505			−0.413252	+	0.910617i	$0.635607\pi$
$948$	−8.82886	+	6.41455i	−0.286748	+	0.208335i
$949$	4.22397	+	13.0001i	0.137116	+	0.422000i
$950$	0.694261	+	0.225579i	0.0225248	+	0.00731875i
$951$	−18.4037	+	25.3305i	−0.596781	+	0.821398i
$952$	−10.3375	−	12.2644i	−0.335039	−	0.397492i
$953$	42.2008	+	13.7119i	1.36702	+	0.444171i	0.898380	−	0.439220i	$-0.144745\pi$
$953$	42.2008	+	13.7119i	1.36702	+	0.444171i	0.468637	+	0.883391i	$0.344745\pi$
$954$	1.44740	−	0.470288i	0.0468612	−	0.0152261i
$955$	36.9162	+	50.8108i	1.19458	+	1.64420i
$956$			23.3945i			0.756632i
$957$	26.8582	+	18.8137i	0.868204	+	0.608160i
$958$			9.27971i			0.299814i
$959$	−18.5024	−	45.5046i	−0.597475	−	1.46942i
$960$	1.14974	+	3.53854i	0.0371077	+	0.114206i
$961$	7.28016	−	22.4060i	0.234844	−	0.722775i
$962$	−24.1324	+	33.2154i	−0.778060	+	1.07091i
$963$	7.61336	−	10.4789i	0.245337	−	0.337678i
$964$	−0.176175	+	0.542210i	−0.00567421	+	0.0174634i
$965$	13.2892	+	40.8999i	0.427794	+	1.31661i
$966$	2.23826	+	5.50474i	0.0720149	+	0.177112i
$967$			13.2341i			0.425579i	0.977098	+	0.212789i	$0.0682548\pi$
$967$			13.2341i			0.425579i	−0.977098	+	0.212789i	$0.931745\pi$
$968$	−6.76910	−	8.67060i	−0.217567	−	0.278684i
$969$			0.500453i			0.0160769i
$970$	16.4827	+	22.6865i	0.529229	+	0.728421i
$971$	−12.2999	+	3.99648i	−0.394723	+	0.128253i	−0.499651	−	0.866227i	$-0.666539\pi$
$971$	−12.2999	+	3.99648i	−0.394723	+	0.128253i	0.104929	+	0.994480i	$0.466539\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	21.9790	−	18.5257i	0.704613	−	0.593906i
$974$	5.64703	−	7.77247i	0.180942	−	0.249046i
$975$	42.7264	+	13.8827i	1.36834	+	0.444601i
$976$	1.29968	+	4.00000i	0.0416017	+	0.128037i
$977$	−33.5349	+	24.3645i	−1.07288	+	0.779490i	−0.976427	−	0.215848i	$-0.930749\pi$
$977$	−33.5349	+	24.3645i	−1.07288	+	0.779490i	−0.0964492	+	0.995338i	$0.530749\pi$
$978$	−2.72861			−0.0872512
$979$	23.7145	−	33.8547i	0.757919	−	1.08200i
$980$	−12.1251	+	23.0498i	−0.387322	+	0.736300i
$981$	3.79351	+	5.22132i	0.121118	+	0.166704i
$982$	−3.49256	−	10.7490i	−0.111452	−	0.343014i
$983$	−11.4627	−	3.72447i	−0.365604	−	0.118792i	0.120453	−	0.992719i	$-0.461565\pi$
$983$	−11.4627	−	3.72447i	−0.365604	−	0.118792i	−0.486057	+	0.873927i	$0.661565\pi$
$984$	−6.30916	−	4.58387i	−0.201129	−	0.146129i
$985$	−41.8088	−	30.3759i	−1.33214	−	0.967855i
$986$	18.5229	−	57.0075i	0.589888	−	1.81549i
$987$	25.9258	−	1.87064i	0.825228	−	0.0595433i
$988$	−0.339275	+	0.246498i	−0.0107938	+	0.00784213i
$989$			8.00855i			0.254657i
$990$	−12.3381	+	0.213104i	−0.392131	+	0.00677289i
$991$	−21.4738			−0.682137			−0.341069	−	0.940038i	$-0.610789\pi$
$991$	−21.4738			−0.682137			−0.341069	+	0.940038i	$0.610789\pi$
$992$	2.20684	−	1.60336i	0.0700672	−	0.0509068i
$993$	−3.54088	+	1.15050i	−0.112366	+	0.0365100i
$994$	9.89294	−	15.9104i	0.313785	−	0.504646i
$995$	28.3770	+	20.6171i	0.899613	+	0.653607i
$996$	−7.04720	+	9.69963i	−0.223299	+	0.307345i
$997$	3.21337	−	9.88975i	0.101769	−	0.313211i	−0.887190	−	0.461404i	$-0.847346\pi$
$997$	3.21337	−	9.88975i	0.101769	−	0.313211i	0.988958	+	0.148193i	$0.0473457\pi$
$998$	17.8373	−	5.79569i	0.564630	−	0.183459i
$999$	−4.75025	−	6.53816i	−0.150291	−	0.206858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.u.b.349.8	yes	32
7.6	odd	2		462.2.u.a.349.5	yes	32
11.7	odd	10		462.2.u.a.139.5	✓	32
77.62	even	10	inner	462.2.u.b.139.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.139.5	✓	32	11.7	odd	10
462.2.u.a.349.5	yes	32	7.6	odd	2
462.2.u.b.139.8	yes	32	77.62	even	10	inner
462.2.u.b.349.8	yes	32	1.1	even	1	trivial

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.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.18694 - 3.01006i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-2.24683 - 1.39706i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.18694 - 3.01006i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-2.24683 - 1.39706i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +3.72064 q^{10} +(-2.71647 - 1.90283i) q^{11} -1.00000i q^{12} +(4.11000 - 2.98609i) q^{13} +(-0.190406 - 2.63889i) q^{14} +(-1.14974 + 3.53854i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-4.90468 - 3.56346i) q^{17} +(0.951057 + 0.309017i) q^{18} +(0.0255089 + 0.0785084i) q^{19} +(2.18694 + 3.01006i) q^{20} +(2.56857 + 0.634376i) q^{21} +(-0.0572763 - 3.31613i) q^{22} +2.24601 q^{23} +(0.809017 - 0.587785i) q^{24} +(-2.73268 - 8.41032i) q^{25} +(4.83159 + 1.56988i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.02299 - 1.70514i) q^{28} +(9.40327 + 3.05531i) q^{29} +(-3.53854 + 1.14974i) q^{30} +(1.60336 + 2.20684i) q^{31} -1.00000i q^{32} +(3.17153 + 0.970268i) q^{33} -6.06252i q^{34} +(-9.11889 + 3.70780i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-2.49736 + 7.68607i) q^{37} +(-0.0485209 + 0.0667833i) q^{38} +(-2.98609 + 4.11000i) q^{39} +(-1.14974 + 3.53854i) q^{40} +(-2.40988 - 7.41686i) q^{41} +(0.996549 + 2.45090i) q^{42} +3.56568i q^{43} +(2.64914 - 1.99551i) q^{44} -3.72064i q^{45} +(1.32017 + 1.81706i) q^{46} +(9.34367 - 3.03594i) q^{47} +(0.951057 + 0.309017i) q^{48} +(3.09645 + 6.27790i) q^{49} +(5.19786 - 7.15425i) q^{50} +(5.76580 + 1.87342i) q^{51} +(1.56988 + 4.83159i) q^{52} +(1.23123 - 0.894540i) q^{53} -1.00000 q^{54} +(-11.6684 + 4.01536i) q^{55} +(2.56857 + 0.634376i) q^{56} +(-0.0485209 - 0.0667833i) q^{57} +(3.05531 + 9.40327i) q^{58} +(3.05835 + 0.993718i) q^{59} +(-3.01006 - 2.18694i) q^{60} +(-3.40260 - 2.47213i) q^{61} +(-0.842937 + 2.59429i) q^{62} +(-2.63889 + 0.190406i) q^{63} +(0.809017 - 0.587785i) q^{64} -18.9017i q^{65} +(1.07921 + 3.13613i) q^{66} -9.56243 q^{67} +(4.90468 - 3.56346i) q^{68} +(-2.13609 + 0.694056i) q^{69} +(-8.35962 - 5.19795i) q^{70} +(5.72886 + 4.16226i) q^{71} +(-0.587785 + 0.809017i) q^{72} +(-0.831452 + 2.55895i) q^{73} +(-7.68607 + 2.49736i) q^{74} +(5.19786 + 7.15425i) q^{75} -0.0825487 q^{76} +(3.44506 + 8.07041i) q^{77} -5.08024 q^{78} +(-6.41455 - 8.82886i) q^{79} +(-3.53854 + 1.14974i) q^{80} +(0.309017 - 0.951057i) q^{81} +(4.58387 - 6.30916i) q^{82} +(-9.69963 - 7.04720i) q^{83} +(-1.39706 + 2.24683i) q^{84} +(-21.4524 + 6.97032i) q^{85} +(-2.88469 + 2.09585i) q^{86} -9.88718 q^{87} +(3.17153 + 0.970268i) q^{88} +12.4627i q^{89} +(3.01006 - 2.18694i) q^{90} +(-13.4062 + 0.967306i) q^{91} +(-0.694056 + 2.13609i) q^{92} +(-2.20684 - 1.60336i) q^{93} +(7.94820 + 5.77471i) q^{94} +(0.292101 + 0.0949095i) q^{95} +(0.309017 + 0.951057i) q^{96} +(4.43008 + 6.09749i) q^{97} +(-3.25888 + 6.19514i) q^{98} +(-3.31613 + 0.0572763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9	\( 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} - 12 q^{17} - 16 q^{19} + 10 q^{20} - 8 q^{21} - 4 q^{22} + 8 q^{23} + 8 q^{24} + 6 q^{25} + 10 q^{28} + 20 q^{29} - 50 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{36} - 16 q^{37} + 6 q^{40} + 40 q^{41} + 12 q^{44} + 52 q^{49} + 40 q^{51} - 32 q^{54} - 40 q^{55} - 8 q^{56} + 10 q^{58} + 60 q^{59} + 4 q^{60} - 4 q^{61} + 20 q^{62} - 10 q^{63} + 8 q^{64} + 8 q^{66} - 16 q^{67} + 12 q^{68} + 30 q^{69} - 28 q^{70} - 48 q^{71} - 74 q^{73} - 40 q^{74} - 24 q^{76} + 6 q^{77} - 60 q^{79} - 8 q^{81} + 20 q^{82} + 4 q^{83} - 2 q^{84} - 10 q^{85} - 36 q^{86} + 20 q^{87} - 16 q^{88} - 4 q^{90} - 20 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} - 8 q^{96} + 60 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 - 12 * q^17 - 16 * q^19 + 10 * q^20 - 8 * q^21 - 4 * q^22 + 8 * q^23 + 8 * q^24 + 6 * q^25 + 10 * q^28 + 20 * q^29 - 50 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^36 - 16 * q^37 + 6 * q^40 + 40 * q^41 + 12 * q^44 + 52 * q^49 + 40 * q^51 - 32 * q^54 - 40 * q^55 - 8 * q^56 + 10 * q^58 + 60 * q^59 + 4 * q^60 - 4 * q^61 + 20 * q^62 - 10 * q^63 + 8 * q^64 + 8 * q^66 - 16 * q^67 + 12 * q^68 + 30 * q^69 - 28 * q^70 - 48 * q^71 - 74 * q^73 - 40 * q^74 - 24 * q^76 + 6 * q^77 - 60 * q^79 - 8 * q^81 + 20 * q^82 + 4 * q^83 - 2 * q^84 - 10 * q^85 - 36 * q^86 + 20 * q^87 - 16 * q^88 - 4 * q^90 - 20 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 - 8 * q^96 + 60 * q^97 - 40 * q^98 - 8 * q^99

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