LMFDB - Embedded newform 418.2.f.e.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	418.191
Dual form			418.2.f.e.267.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.690983 - 2.12663i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.30902 - 0.951057i) q^{5} +(-1.80902 + 1.31433i) q^{6} +(-1.19098 - 3.66547i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.61803 - 1.17557i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.690983 - 2.12663i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.30902 - 0.951057i) q^{5} +(-1.80902 + 1.31433i) q^{6} +(-1.19098 - 3.66547i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.61803 - 1.17557i) q^{9} -1.61803 q^{10} +(-3.04508 + 1.31433i) q^{11} +2.23607 q^{12} +(0.500000 + 0.363271i) q^{13} +(-1.19098 + 3.66547i) q^{14} +(-1.11803 - 3.44095i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.42705 - 1.03681i) q^{17} +(0.618034 + 1.90211i) q^{18} +(0.309017 - 0.951057i) q^{19} +(1.30902 + 0.951057i) q^{20} -8.61803 q^{21} +(3.23607 + 0.726543i) q^{22} +4.23607 q^{23} +(-1.80902 - 1.31433i) q^{24} +(-0.736068 + 2.26538i) q^{25} +(-0.190983 - 0.587785i) q^{26} +(1.80902 - 1.31433i) q^{27} +(3.11803 - 2.26538i) q^{28} +(-0.472136 - 1.45309i) q^{29} +(-1.11803 + 3.44095i) q^{30} +(-2.19098 - 1.59184i) q^{31} +1.00000 q^{32} +(0.690983 + 7.38394i) q^{33} -1.76393 q^{34} +(-5.04508 - 3.66547i) q^{35} +(0.618034 - 1.90211i) q^{36} +(-0.354102 - 1.08981i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(1.11803 - 0.812299i) q^{39} +(-0.500000 - 1.53884i) q^{40} +(-2.19098 + 6.74315i) q^{41} +(6.97214 + 5.06555i) q^{42} -9.70820 q^{43} +(-2.19098 - 2.48990i) q^{44} -3.23607 q^{45} +(-3.42705 - 2.48990i) q^{46} +(0.781153 - 2.40414i) q^{47} +(0.690983 + 2.12663i) q^{48} +(-6.35410 + 4.61653i) q^{49} +(1.92705 - 1.40008i) q^{50} +(-1.21885 - 3.75123i) q^{51} +(-0.190983 + 0.587785i) q^{52} +(9.66312 + 7.02067i) q^{53} -2.23607 q^{54} +(-2.73607 + 4.61653i) q^{55} -3.85410 q^{56} +(-1.80902 - 1.31433i) q^{57} +(-0.472136 + 1.45309i) q^{58} +(-0.590170 - 1.81636i) q^{59} +(2.92705 - 2.12663i) q^{60} +(5.35410 - 3.88998i) q^{61} +(0.836881 + 2.57565i) q^{62} +(-2.38197 + 7.33094i) q^{63} +(-0.809017 - 0.587785i) q^{64} +1.00000 q^{65} +(3.78115 - 6.37988i) q^{66} +5.09017 q^{67} +(1.42705 + 1.03681i) q^{68} +(2.92705 - 9.00854i) q^{69} +(1.92705 + 5.93085i) q^{70} +(6.66312 - 4.84104i) q^{71} +(-1.61803 + 1.17557i) q^{72} +(-4.42705 - 13.6251i) q^{73} +(-0.354102 + 1.08981i) q^{74} +(4.30902 + 3.13068i) q^{75} +1.00000 q^{76} +(8.44427 + 9.59632i) q^{77} -1.38197 q^{78} +(-2.42705 - 1.76336i) q^{79} +(-0.500000 + 1.53884i) q^{80} +(-3.39919 - 10.4616i) q^{81} +(5.73607 - 4.16750i) q^{82} +(8.16312 - 5.93085i) q^{83} +(-2.66312 - 8.19624i) q^{84} +(0.881966 - 2.71441i) q^{85} +(7.85410 + 5.70634i) q^{86} -3.41641 q^{87} +(0.309017 + 3.30220i) q^{88} +13.1803 q^{89} +(2.61803 + 1.90211i) q^{90} +(0.736068 - 2.26538i) q^{91} +(1.30902 + 4.02874i) q^{92} +(-4.89919 + 3.55947i) q^{93} +(-2.04508 + 1.48584i) q^{94} +(-0.500000 - 1.53884i) q^{95} +(0.690983 - 2.12663i) q^{96} +(8.42705 + 6.12261i) q^{97} +7.85410 q^{98} +(6.47214 + 1.45309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 5 q^{3} - q^{4} + 3 q^{5} - 5 q^{6} - 7 q^{7} - q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - q^2 + 5 * q^3 - q^4 + 3 * q^5 - 5 * q^6 - 7 * q^7 - q^8 - 2 * q^9	\( 4 q - q^{2} + 5 q^{3} - q^{4} + 3 q^{5} - 5 q^{6} - 7 q^{7} - q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + 2 q^{13} - 7 q^{14} - q^{16} - q^{17} - 2 q^{18} - q^{19} + 3 q^{20} - 30 q^{21} + 4 q^{22} + 8 q^{23} - 5 q^{24} + 6 q^{25} - 3 q^{26} + 5 q^{27} + 8 q^{28} + 16 q^{29} - 11 q^{31} + 4 q^{32} + 5 q^{33} - 16 q^{34} - 9 q^{35} - 2 q^{36} + 12 q^{37} - q^{38} - 2 q^{40} - 11 q^{41} + 10 q^{42} - 12 q^{43} - 11 q^{44} - 4 q^{45} - 7 q^{46} - 17 q^{47} + 5 q^{48} - 12 q^{49} + q^{50} - 25 q^{51} - 3 q^{52} + 23 q^{53} - 2 q^{55} - 2 q^{56} - 5 q^{57} + 16 q^{58} + 20 q^{59} + 5 q^{60} + 8 q^{61} + 19 q^{62} - 14 q^{63} - q^{64} + 4 q^{65} - 5 q^{66} - 2 q^{67} - q^{68} + 5 q^{69} + q^{70} + 11 q^{71} - 2 q^{72} - 11 q^{73} + 12 q^{74} + 15 q^{75} + 4 q^{76} - 2 q^{77} - 10 q^{78} - 3 q^{79} - 2 q^{80} + 11 q^{81} + 14 q^{82} + 17 q^{83} + 5 q^{84} + 8 q^{85} + 18 q^{86} + 40 q^{87} - q^{88} + 8 q^{89} + 6 q^{90} - 6 q^{91} + 3 q^{92} + 5 q^{93} + 3 q^{94} - 2 q^{95} + 5 q^{96} + 27 q^{97} + 18 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q - q^2 + 5 * q^3 - q^4 + 3 * q^5 - 5 * q^6 - 7 * q^7 - q^8 - 2 * q^9 - 2 * q^10 - q^11 + 2 * q^13 - 7 * q^14 - q^16 - q^17 - 2 * q^18 - q^19 + 3 * q^20 - 30 * q^21 + 4 * q^22 + 8 * q^23 - 5 * q^24 + 6 * q^25 - 3 * q^26 + 5 * q^27 + 8 * q^28 + 16 * q^29 - 11 * q^31 + 4 * q^32 + 5 * q^33 - 16 * q^34 - 9 * q^35 - 2 * q^36 + 12 * q^37 - q^38 - 2 * q^40 - 11 * q^41 + 10 * q^42 - 12 * q^43 - 11 * q^44 - 4 * q^45 - 7 * q^46 - 17 * q^47 + 5 * q^48 - 12 * q^49 + q^50 - 25 * q^51 - 3 * q^52 + 23 * q^53 - 2 * q^55 - 2 * q^56 - 5 * q^57 + 16 * q^58 + 20 * q^59 + 5 * q^60 + 8 * q^61 + 19 * q^62 - 14 * q^63 - q^64 + 4 * q^65 - 5 * q^66 - 2 * q^67 - q^68 + 5 * q^69 + q^70 + 11 * q^71 - 2 * q^72 - 11 * q^73 + 12 * q^74 + 15 * q^75 + 4 * q^76 - 2 * q^77 - 10 * q^78 - 3 * q^79 - 2 * q^80 + 11 * q^81 + 14 * q^82 + 17 * q^83 + 5 * q^84 + 8 * q^85 + 18 * q^86 + 40 * q^87 - q^88 + 8 * q^89 + 6 * q^90 - 6 * q^91 + 3 * q^92 + 5 * q^93 + 3 * q^94 - 2 * q^95 + 5 * q^96 + 27 * q^97 + 18 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	0.690983	−	2.12663i	0.398939	−	1.22781i	−0.526912	−	0.849920i	$-0.676650\pi$
$3$	0.690983	−	2.12663i	0.398939	−	1.22781i	0.925851	−	0.377889i	$-0.123350\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.30902	−	0.951057i	0.585410	−	0.425325i	−0.255260	−	0.966872i	$-0.582161\pi$
$5$	1.30902	−	0.951057i	0.585410	−	0.425325i	0.840670	+	0.541547i	$0.182161\pi$
$6$	−1.80902	+	1.31433i	−0.738528	+	0.536572i
$7$	−1.19098	−	3.66547i	−0.450149	−	1.38542i	−0.876737	−	0.480971i	$-0.840284\pi$
$7$	−1.19098	−	3.66547i	−0.450149	−	1.38542i	0.426587	−	0.904446i	$-0.359716\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−1.61803	−	1.17557i	−0.539345	−	0.391857i
$10$	−1.61803			−0.511667
$11$	−3.04508	+	1.31433i	−0.918128	+	0.396285i
$11$	−3.04508	+	1.31433i	−0.918128	+	0.396285i
$12$	2.23607			0.645497
$13$	0.500000	+	0.363271i	0.138675	+	0.100753i	0.654960	−	0.755664i	$-0.272685\pi$
$13$	0.500000	+	0.363271i	0.138675	+	0.100753i	−0.516285	+	0.856417i	$0.672685\pi$
$14$	−1.19098	+	3.66547i	−0.318304	+	0.979638i
$15$	−1.11803	−	3.44095i	−0.288675	−	0.888451i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.42705	−	1.03681i	0.346111	−	0.251464i	−0.401125	−	0.916023i	$-0.631381\pi$
$17$	1.42705	−	1.03681i	0.346111	−	0.251464i	0.747236	+	0.664559i	$0.231381\pi$
$18$	0.618034	+	1.90211i	0.145672	+	0.448332i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	1.30902	+	0.951057i	0.292705	+	0.212663i
$21$	−8.61803			−1.88061
$22$	3.23607	+	0.726543i	0.689932	+	0.154899i
$23$	4.23607			0.883281			0.441641	−	0.897192i	$-0.354397\pi$
$23$	4.23607			0.883281			0.441641	+	0.897192i	$0.354397\pi$
$24$	−1.80902	−	1.31433i	−0.369264	−	0.268286i
$25$	−0.736068	+	2.26538i	−0.147214	+	0.453077i
$26$	−0.190983	−	0.587785i	−0.0374548	−	0.115274i
$27$	1.80902	−	1.31433i	0.348145	−	0.252942i
$28$	3.11803	−	2.26538i	0.589253	−	0.428117i
$29$	−0.472136	−	1.45309i	−0.0876734	−	0.269831i	0.897602	−	0.440807i	$-0.145308\pi$
$29$	−0.472136	−	1.45309i	−0.0876734	−	0.269831i	−0.985275	+	0.170976i	$0.945308\pi$
$30$	−1.11803	+	3.44095i	−0.204124	+	0.628230i
$31$	−2.19098	−	1.59184i	−0.393512	−	0.285903i	0.373381	−	0.927678i	$-0.378198\pi$
$31$	−2.19098	−	1.59184i	−0.393512	−	0.285903i	−0.766893	+	0.641775i	$0.778198\pi$
$32$	1.00000			0.176777
$33$	0.690983	+	7.38394i	0.120285	+	1.28538i
$34$	−1.76393			−0.302512
$35$	−5.04508	−	3.66547i	−0.852775	−	0.619577i
$36$	0.618034	−	1.90211i	0.103006	−	0.317019i
$37$	−0.354102	−	1.08981i	−0.0582140	−	0.179164i	0.917721	−	0.397225i	$-0.130027\pi$
$37$	−0.354102	−	1.08981i	−0.0582140	−	0.179164i	−0.975935	+	0.218061i	$0.930027\pi$
$38$	−0.809017	+	0.587785i	−0.131240	+	0.0953514i
$39$	1.11803	−	0.812299i	0.179029	−	0.130072i
$40$	−0.500000	−	1.53884i	−0.0790569	−	0.243312i
$41$	−2.19098	+	6.74315i	−0.342174	+	1.05310i	0.620905	+	0.783886i	$0.286765\pi$
$41$	−2.19098	+	6.74315i	−0.342174	+	1.05310i	−0.963079	+	0.269218i	$0.913235\pi$
$42$	6.97214	+	5.06555i	1.07582	+	0.781632i
$43$	−9.70820			−1.48049			−0.740244	−	0.672339i	$-0.765290\pi$
$43$	−9.70820			−1.48049			−0.740244	+	0.672339i	$0.765290\pi$
$44$	−2.19098	−	2.48990i	−0.330303	−	0.375366i
$45$	−3.23607			−0.482405
$46$	−3.42705	−	2.48990i	−0.505291	−	0.367115i
$47$	0.781153	−	2.40414i	0.113943	−	0.350680i	−0.877782	−	0.479060i	$-0.840978\pi$
$47$	0.781153	−	2.40414i	0.113943	−	0.350680i	0.991725	+	0.128380i	$0.0409777\pi$
$48$	0.690983	+	2.12663i	0.0997348	+	0.306952i
$49$	−6.35410	+	4.61653i	−0.907729	+	0.659504i
$50$	1.92705	−	1.40008i	0.272526	−	0.198002i
$51$	−1.21885	−	3.75123i	−0.170673	−	0.525277i
$52$	−0.190983	+	0.587785i	−0.0264846	+	0.0815111i
$53$	9.66312	+	7.02067i	1.32733	+	0.964363i	0.999809	+	0.0195192i	$0.00621355\pi$
$53$	9.66312	+	7.02067i	1.32733	+	0.964363i	0.327522	+	0.944844i	$0.393786\pi$
$54$	−2.23607			−0.304290
$55$	−2.73607	+	4.61653i	−0.368931	+	0.622492i
$56$	−3.85410			−0.515026
$57$	−1.80902	−	1.31433i	−0.239610	−	0.174087i
$58$	−0.472136	+	1.45309i	−0.0619945	+	0.190799i
$59$	−0.590170	−	1.81636i	−0.0768336	−	0.236469i	0.905262	−	0.424854i	$-0.139675\pi$
$59$	−0.590170	−	1.81636i	−0.0768336	−	0.236469i	−0.982095	+	0.188385i	$0.939675\pi$
$60$	2.92705	−	2.12663i	0.377881	−	0.274546i
$61$	5.35410	−	3.88998i	0.685523	−	0.498061i	−0.189663	−	0.981849i	$-0.560739\pi$
$61$	5.35410	−	3.88998i	0.685523	−	0.498061i	0.875185	+	0.483788i	$0.160739\pi$
$62$	0.836881	+	2.57565i	0.106284	+	0.327109i
$63$	−2.38197	+	7.33094i	−0.300100	+	0.923611i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.00000			0.124035
$66$	3.78115	−	6.37988i	0.465428	−	0.785309i
$67$	5.09017			0.621863			0.310932	−	0.950432i	$-0.399359\pi$
$67$	5.09017			0.621863			0.310932	+	0.950432i	$0.399359\pi$
$68$	1.42705	+	1.03681i	0.173055	+	0.125732i
$69$	2.92705	−	9.00854i	0.352376	−	1.08450i
$70$	1.92705	+	5.93085i	0.230327	+	0.708873i
$71$	6.66312	−	4.84104i	0.790767	−	0.574526i	−0.117424	−	0.993082i	$-0.537464\pi$
$71$	6.66312	−	4.84104i	0.790767	−	0.574526i	0.908191	+	0.418556i	$0.137464\pi$
$72$	−1.61803	+	1.17557i	−0.190687	+	0.138542i
$73$	−4.42705	−	13.6251i	−0.518147	−	1.59469i	−0.777482	−	0.628905i	$-0.783503\pi$
$73$	−4.42705	−	13.6251i	−0.518147	−	1.59469i	0.259335	−	0.965788i	$-0.416497\pi$
$74$	−0.354102	+	1.08981i	−0.0411635	+	0.126688i
$75$	4.30902	+	3.13068i	0.497562	+	0.361500i
$76$	1.00000			0.114708
$77$	8.44427	+	9.59632i	0.962314	+	1.09360i
$78$	−1.38197			−0.156477
$79$	−2.42705	−	1.76336i	−0.273065	−	0.198393i	0.442822	−	0.896609i	$-0.353977\pi$
$79$	−2.42705	−	1.76336i	−0.273065	−	0.198393i	−0.715887	+	0.698216i	$0.753977\pi$
$80$	−0.500000	+	1.53884i	−0.0559017	+	0.172048i
$81$	−3.39919	−	10.4616i	−0.377687	−	1.16240i
$82$	5.73607	−	4.16750i	0.633443	−	0.460223i
$83$	8.16312	−	5.93085i	0.896019	−	0.650996i	−0.0414216	−	0.999142i	$-0.513189\pi$
$83$	8.16312	−	5.93085i	0.896019	−	0.650996i	0.937440	+	0.348146i	$0.113189\pi$
$84$	−2.66312	−	8.19624i	−0.290570	−	0.894283i
$85$	0.881966	−	2.71441i	0.0956626	−	0.294419i
$86$	7.85410	+	5.70634i	0.846930	+	0.615330i
$87$	−3.41641			−0.366277
$88$	0.309017	+	3.30220i	0.0329413	+	0.352015i
$89$	13.1803			1.39711			0.698557	−	0.715555i	$-0.253826\pi$
$89$	13.1803			1.39711			0.698557	+	0.715555i	$0.253826\pi$
$90$	2.61803	+	1.90211i	0.275965	+	0.200500i
$91$	0.736068	−	2.26538i	0.0771609	−	0.237477i
$92$	1.30902	+	4.02874i	0.136474	+	0.420025i
$93$	−4.89919	+	3.55947i	−0.508022	+	0.369100i
$94$	−2.04508	+	1.48584i	−0.210934	+	0.153253i
$95$	−0.500000	−	1.53884i	−0.0512989	−	0.157882i
$96$	0.690983	−	2.12663i	0.0705232	−	0.217048i
$97$	8.42705	+	6.12261i	0.855637	+	0.621657i	0.926695	−	0.375815i	$-0.122637\pi$
$97$	8.42705	+	6.12261i	0.855637	+	0.621657i	−0.0710572	+	0.997472i	$0.522637\pi$
$98$	7.85410			0.793384
$99$	6.47214	+	1.45309i	0.650474	+	0.146041i
$100$	−2.38197			−0.238197
$101$	7.66312	+	5.56758i	0.762509	+	0.553995i	0.899679	−	0.436552i	$-0.143801\pi$
$101$	7.66312	+	5.56758i	0.762509	+	0.553995i	−0.137170	+	0.990548i	$0.543801\pi$
$102$	−1.21885	+	3.75123i	−0.120684	+	0.371427i
$103$	3.57295	+	10.9964i	0.352053	+	1.08351i	0.957699	+	0.287773i	$0.0929150\pi$
$103$	3.57295	+	10.9964i	0.352053	+	1.08351i	−0.605645	+	0.795735i	$0.707085\pi$
$104$	0.500000	−	0.363271i	0.0490290	−	0.0356217i
$105$	−11.2812	+	8.19624i	−1.10093	+	0.799871i
$106$	−3.69098	−	11.3597i	−0.358500	−	1.10335i
$107$	0.927051	−	2.85317i	0.0896214	−	0.275826i	−0.896193	−	0.443664i	$-0.853678\pi$
$107$	0.927051	−	2.85317i	0.0896214	−	0.275826i	0.985815	+	0.167838i	$0.0536784\pi$
$108$	1.80902	+	1.31433i	0.174073	+	0.126471i
$109$	−5.32624			−0.510161			−0.255081	−	0.966920i	$-0.582102\pi$
$109$	−5.32624			−0.510161			−0.255081	+	0.966920i	$0.582102\pi$
$110$	4.92705	−	2.12663i	0.469776	−	0.202766i
$111$	−2.56231			−0.243203
$112$	3.11803	+	2.26538i	0.294627	+	0.214059i
$113$	−3.21885	+	9.90659i	−0.302804	+	0.931934i	0.677684	+	0.735353i	$0.262984\pi$
$113$	−3.21885	+	9.90659i	−0.302804	+	0.931934i	−0.980488	+	0.196581i	$0.937016\pi$
$114$	0.690983	+	2.12663i	0.0647165	+	0.199177i
$115$	5.54508	−	4.02874i	0.517082	−	0.375682i
$116$	1.23607	−	0.898056i	0.114766	−	0.0833824i
$117$	−0.381966	−	1.17557i	−0.0353128	−	0.108682i
$118$	−0.590170	+	1.81636i	−0.0543295	+	0.167209i
$119$	−5.50000	−	3.99598i	−0.504184	−	0.366311i
$120$	−3.61803			−0.330280
$121$	7.54508	−	8.00448i	0.685917	−	0.727680i
$122$	−6.61803			−0.599169
$123$	12.8262	+	9.31881i	1.15650	+	0.840249i
$124$	0.836881	−	2.57565i	0.0751541	−	0.231301i
$125$	3.69098	+	11.3597i	0.330132	+	1.01604i
$126$	6.23607	−	4.53077i	0.555553	−	0.403633i
$127$	−2.57295	+	1.86936i	−0.228312	+	0.165879i	−0.696060	−	0.717983i	$-0.745065\pi$
$127$	−2.57295	+	1.86936i	−0.228312	+	0.165879i	0.467748	+	0.883862i	$0.345065\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−6.70820	+	20.6457i	−0.590624	+	1.81776i
$130$	−0.809017	−	0.587785i	−0.0709555	−	0.0515522i
$131$	14.6525			1.28019			0.640096	−	0.768295i	$-0.278894\pi$
$131$	14.6525			1.28019			0.640096	+	0.768295i	$0.278894\pi$
$132$	−6.80902	+	2.93893i	−0.592649	+	0.255801i
$133$	−3.85410			−0.334193
$134$	−4.11803	−	2.99193i	−0.355744	−	0.258463i
$135$	1.11803	−	3.44095i	0.0962250	−	0.296150i
$136$	−0.545085	−	1.67760i	−0.0467407	−	0.143853i
$137$	6.04508	−	4.39201i	0.516466	−	0.375235i	−0.298805	−	0.954314i	$-0.596588\pi$
$137$	6.04508	−	4.39201i	0.516466	−	0.375235i	0.815271	+	0.579079i	$0.196588\pi$
$138$	−7.66312	+	5.56758i	−0.652328	+	0.473944i
$139$	0.572949	+	1.76336i	0.0485969	+	0.149566i	0.972410	−	0.233277i	$-0.0749450\pi$
$139$	0.572949	+	1.76336i	0.0485969	+	0.149566i	−0.923813	+	0.382843i	$0.874945\pi$
$140$	1.92705	−	5.93085i	0.162866	−	0.501249i
$141$	−4.57295	−	3.32244i	−0.385112	−	0.279800i
$142$	−8.23607			−0.691155
$143$	−2.00000	−	0.449028i	−0.167248	−	0.0375496i
$144$	2.00000			0.166667
$145$	−2.00000	−	1.45309i	−0.166091	−	0.120672i
$146$	−4.42705	+	13.6251i	−0.366385	+	1.12762i
$147$	5.42705	+	16.7027i	0.447616	+	1.37762i
$148$	0.927051	−	0.673542i	0.0762031	−	0.0553648i
$149$	−17.9894	+	13.0700i	−1.47375	+	1.07074i	−0.494239	+	0.869326i	$0.664553\pi$
$149$	−17.9894	+	13.0700i	−1.47375	+	1.07074i	−0.979506	+	0.201413i	$0.935447\pi$
$150$	−1.64590	−	5.06555i	−0.134387	−	0.413601i
$151$	4.23607	−	13.0373i	0.344726	−	1.06096i	−0.617004	−	0.786960i	$-0.711654\pi$
$151$	4.23607	−	13.0373i	0.344726	−	1.06096i	0.961730	−	0.273998i	$-0.0883463\pi$
$152$	−0.809017	−	0.587785i	−0.0656199	−	0.0476757i
$153$	−3.52786			−0.285211
$154$	−1.19098	−	12.7270i	−0.0959721	−	1.02557i
$155$	−4.38197			−0.351968
$156$	1.11803	+	0.812299i	0.0895144	+	0.0650360i
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	−0.757077	−	0.653325i	$-0.773373\pi$
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	0.996503	−	0.0835524i	$-0.0266266\pi$
$158$	0.927051	+	2.85317i	0.0737522	+	0.226986i
$159$	21.6074	−	15.6987i	1.71358	−	1.24499i
$160$	1.30902	−	0.951057i	0.103487	−	0.0751876i
$161$	−5.04508	−	15.5272i	−0.397608	−	1.22371i
$162$	−3.39919	+	10.4616i	−0.267065	+	0.821943i
$163$	−19.4443	−	14.1271i	−1.52299	−	1.10652i	−0.959979	−	0.280072i	$-0.909642\pi$
$163$	−19.4443	−	14.1271i	−1.52299	−	1.10652i	−0.563014	−	0.826447i	$-0.690358\pi$
$164$	−7.09017			−0.553649
$165$	7.92705	+	9.00854i	0.617120	+	0.701314i
$166$	−10.0902			−0.783149
$167$	8.59017	+	6.24112i	0.664727	+	0.482953i	0.868256	−	0.496116i	$-0.165241\pi$
$167$	8.59017	+	6.24112i	0.664727	+	0.482953i	−0.203529	+	0.979069i	$0.565241\pi$
$168$	−2.66312	+	8.19624i	−0.205464	+	0.632353i
$169$	−3.89919	−	12.0005i	−0.299937	−	0.923113i
$170$	−2.30902	+	1.67760i	−0.177094	+	0.128666i
$171$	−1.61803	+	1.17557i	−0.123734	+	0.0898981i
$172$	−3.00000	−	9.23305i	−0.228748	−	0.704014i
$173$	−4.88197	+	15.0251i	−0.371169	+	1.14234i	0.574858	+	0.818253i	$0.305057\pi$
$173$	−4.88197	+	15.0251i	−0.371169	+	1.14234i	−0.946027	+	0.324088i	$0.894943\pi$
$174$	2.76393	+	2.00811i	0.209533	+	0.152235i
$175$	9.18034			0.693968
$176$	1.69098	−	2.85317i	0.127463	−	0.215066i
$177$	−4.27051			−0.320991
$178$	−10.6631	−	7.74721i	−0.799235	−	0.580678i
$179$	−3.94427	+	12.1392i	−0.294809	+	0.907328i	0.688477	+	0.725258i	$0.258280\pi$
$179$	−3.94427	+	12.1392i	−0.294809	+	0.907328i	−0.983286	+	0.182070i	$0.941720\pi$
$180$	−1.00000	−	3.07768i	−0.0745356	−	0.229397i
$181$	−17.7533	+	12.8985i	−1.31959	+	0.958739i	−0.319654	+	0.947534i	$0.603567\pi$
$181$	−17.7533	+	12.8985i	−1.31959	+	0.958739i	−0.999937	+	0.0112052i	$0.996433\pi$
$182$	−1.92705	+	1.40008i	−0.142843	+	0.103781i
$183$	−4.57295	−	14.0741i	−0.338042	−	1.04039i
$184$	1.30902	−	4.02874i	0.0965020	−	0.297003i
$185$	−1.50000	−	1.08981i	−0.110282	−	0.0801247i
$186$	6.05573			0.444028
$187$	−2.98278	+	5.03280i	−0.218122	+	0.368035i
$188$	2.52786			0.184363
$189$	−6.97214	−	5.06555i	−0.507148	−	0.368465i
$190$	−0.500000	+	1.53884i	−0.0362738	+	0.111639i
$191$	−0.600813	−	1.84911i	−0.0434733	−	0.133797i	0.926964	−	0.375150i	$-0.122409\pi$
$191$	−0.600813	−	1.84911i	−0.0434733	−	0.133797i	−0.970437	+	0.241353i	$0.922409\pi$
$192$	−1.80902	+	1.31433i	−0.130555	+	0.0948534i
$193$	4.39919	−	3.19620i	0.316660	−	0.230067i	−0.418089	−	0.908406i	$-0.637300\pi$
$193$	4.39919	−	3.19620i	0.316660	−	0.230067i	0.734749	+	0.678339i	$0.237300\pi$
$194$	−3.21885	−	9.90659i	−0.231100	−	0.711252i
$195$	0.690983	−	2.12663i	0.0494823	−	0.152291i
$196$	−6.35410	−	4.61653i	−0.453864	−	0.329752i
$197$	23.1803			1.65153			0.825765	−	0.564014i	$-0.190744\pi$
$197$	23.1803			1.65153			0.825765	+	0.564014i	$0.190744\pi$
$198$	−4.38197	−	4.97980i	−0.311413	−	0.353899i
$199$	13.8885			0.984533			0.492266	−	0.870445i	$-0.336169\pi$
$199$	13.8885			0.984533			0.492266	+	0.870445i	$0.336169\pi$
$200$	1.92705	+	1.40008i	0.136263	+	0.0990009i
$201$	3.51722	−	10.8249i	0.248086	−	0.763529i
$202$	−2.92705	−	9.00854i	−0.205947	−	0.633838i
$203$	−4.76393	+	3.46120i	−0.334362	+	0.242929i
$204$	3.19098	−	2.31838i	0.223413	−	0.162319i
$205$	3.54508	+	10.9106i	0.247599	+	0.762033i
$206$	3.57295	−	10.9964i	0.248939	−	0.766156i
$207$	−6.85410	−	4.97980i	−0.476393	−	0.346120i
$208$	−0.618034			−0.0428529
$209$	0.309017	+	3.30220i	0.0213752	+	0.228418i
$210$	13.9443			0.962246
$211$	20.9894	+	15.2497i	1.44497	+	1.04983i	0.986975	+	0.160874i	$0.0514311\pi$
$211$	20.9894	+	15.2497i	1.44497	+	1.04983i	0.457992	+	0.888956i	$0.348569\pi$
$212$	−3.69098	+	11.3597i	−0.253498	+	0.780186i
$213$	−5.69098	−	17.5150i	−0.389940	−	1.20011i
$214$	−2.42705	+	1.76336i	−0.165910	+	0.120541i
$215$	−12.7082	+	9.23305i	−0.866692	+	0.629689i
$216$	−0.690983	−	2.12663i	−0.0470154	−	0.144699i
$217$	−3.22542	+	9.92684i	−0.218956	+	0.673878i
$218$	4.30902	+	3.13068i	0.291843	+	0.212037i
$219$	−32.0344			−2.16469
$220$	−5.23607	−	1.17557i	−0.353016	−	0.0792569i
$221$	1.09017			0.0733328
$222$	2.07295	+	1.50609i	0.139127	+	0.101082i
$223$	−6.18034	+	19.0211i	−0.413866	+	1.27375i	0.499395	+	0.866374i	$0.333556\pi$
$223$	−6.18034	+	19.0211i	−0.413866	+	1.27375i	−0.913261	+	0.407375i	$0.866444\pi$
$224$	−1.19098	−	3.66547i	−0.0795759	−	0.244909i
$225$	3.85410	−	2.80017i	0.256940	−	0.186678i
$226$	8.42705	−	6.12261i	0.560559	−	0.407270i
$227$	−4.95492	−	15.2497i	−0.328869	−	1.01216i	−0.969664	−	0.244443i	$-0.921395\pi$
$227$	−4.95492	−	15.2497i	−0.328869	−	1.01216i	0.640794	−	0.767713i	$-0.278605\pi$
$228$	0.690983	−	2.12663i	0.0457615	−	0.140839i
$229$	−19.8713	−	14.4374i	−1.31313	−	0.954048i	−0.999991	−	0.00434183i	$-0.998618\pi$
$229$	−19.8713	−	14.4374i	−1.31313	−	0.954048i	−0.313143	−	0.949706i	$-0.601382\pi$
$230$	−6.85410			−0.451946
$231$	26.2426	−	11.3269i	1.72664	−	0.745257i
$232$	−1.52786			−0.100309
$233$	−19.1353	−	13.9026i	−1.25359	−	0.910788i	−0.255168	−	0.966897i	$-0.582131\pi$
$233$	−19.1353	−	13.9026i	−1.25359	−	0.910788i	−0.998425	+	0.0561088i	$0.982131\pi$
$234$	−0.381966	+	1.17557i	−0.0249699	+	0.0768494i
$235$	−1.26393	−	3.88998i	−0.0824498	−	0.253754i
$236$	1.54508	−	1.12257i	0.100576	−	0.0730731i
$237$	−5.42705	+	3.94298i	−0.352525	+	0.256124i
$238$	2.10081	+	6.46564i	0.136175	+	0.419105i
$239$	−7.71885	+	23.7562i	−0.499291	+	1.53666i	0.310871	+	0.950452i	$0.399379\pi$
$239$	−7.71885	+	23.7562i	−0.499291	+	1.53666i	−0.810162	+	0.586207i	$0.800621\pi$
$240$	2.92705	+	2.12663i	0.188940	+	0.137273i
$241$	8.32624			0.536340			0.268170	−	0.963372i	$-0.413581\pi$
$241$	8.32624			0.536340			0.268170	+	0.963372i	$0.413581\pi$
$242$	−10.8090	+	2.04087i	−0.694830	+	0.131192i
$243$	−17.8885			−1.14755
$244$	5.35410	+	3.88998i	0.342761	+	0.249031i
$245$	−3.92705	+	12.0862i	−0.250890	+	0.772160i
$246$	−4.89919	−	15.0781i	−0.312361	−	0.961348i
$247$	0.500000	−	0.363271i	0.0318142	−	0.0231144i
$248$	−2.19098	+	1.59184i	−0.139128	+	0.101082i
$249$	−6.97214	−	21.4580i	−0.441841	−	1.35985i
$250$	3.69098	−	11.3597i	0.233438	−	0.718449i
$251$	−16.9443	−	12.3107i	−1.06951	−	0.777047i	−0.0936883	−	0.995602i	$-0.529866\pi$
$251$	−16.9443	−	12.3107i	−1.06951	−	0.777047i	−0.975825	+	0.218555i	$0.929866\pi$
$252$	−7.70820			−0.485571
$253$	−12.8992	+	5.56758i	−0.810965	+	0.350031i
$254$	3.18034			0.199552
$255$	−5.16312	−	3.75123i	−0.323327	−	0.234911i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.88197	−	8.86978i	−0.179772	−	0.553282i	0.820047	−	0.572296i	$-0.193947\pi$
$257$	−2.88197	−	8.86978i	−0.179772	−	0.553282i	−0.999819	+	0.0190144i	$0.993947\pi$
$258$	17.5623	−	12.7598i	1.09338	−	0.794388i
$259$	−3.57295	+	2.59590i	−0.222012	+	0.161301i
$260$	0.309017	+	0.951057i	0.0191644	+	0.0589820i
$261$	−0.944272	+	2.90617i	−0.0584490	+	0.179887i
$262$	−11.8541	−	8.61251i	−0.732349	−	0.532083i
$263$	16.0344			0.988726			0.494363	−	0.869256i	$-0.335401\pi$
$263$	16.0344			0.988726			0.494363	+	0.869256i	$0.335401\pi$
$264$	7.23607	+	1.62460i	0.445349	+	0.0999871i
$265$	19.3262			1.18720
$266$	3.11803	+	2.26538i	0.191179	+	0.138900i
$267$	9.10739	−	28.0297i	0.557363	−	1.71539i
$268$	1.57295	+	4.84104i	0.0960832	+	0.295714i
$269$	−8.13525	+	5.91061i	−0.496015	+	0.360376i	−0.807493	−	0.589877i	$-0.799176\pi$
$269$	−8.13525	+	5.91061i	−0.496015	+	0.360376i	0.311478	+	0.950253i	$0.399176\pi$
$270$	−2.92705	+	2.12663i	−0.178135	+	0.129422i
$271$	1.76393	+	5.42882i	0.107151	+	0.329778i	0.990229	−	0.139448i	$-0.0445329\pi$
$271$	1.76393	+	5.42882i	0.107151	+	0.329778i	−0.883078	+	0.469226i	$0.844533\pi$
$272$	−0.545085	+	1.67760i	−0.0330506	+	0.101719i
$273$	−4.30902	−	3.13068i	−0.260794	−	0.189478i
$274$	−7.47214			−0.451408
$275$	−0.736068	−	7.86572i	−0.0443866	−	0.474321i
$276$	9.47214			0.570156
$277$	4.97214	+	3.61247i	0.298747	+	0.217052i	0.727053	−	0.686582i	$-0.240890\pi$
$277$	4.97214	+	3.61247i	0.298747	+	0.217052i	−0.428306	+	0.903634i	$0.640890\pi$
$278$	0.572949	−	1.76336i	0.0343632	−	0.105759i
$279$	1.67376	+	5.15131i	0.100206	+	0.308401i
$280$	−5.04508	+	3.66547i	−0.301501	+	0.219054i
$281$	−22.6803	+	16.4782i	−1.35300	+	0.983009i	−0.354139	+	0.935193i	$0.615226\pi$
$281$	−22.6803	+	16.4782i	−1.35300	+	0.983009i	−0.998856	+	0.0478163i	$0.984774\pi$
$282$	1.74671	+	5.37582i	0.104015	+	0.320126i
$283$	−5.78115	+	17.7926i	−0.343654	+	1.05766i	0.618647	+	0.785669i	$0.287681\pi$
$283$	−5.78115	+	17.7926i	−0.343654	+	1.05766i	−0.962301	+	0.271989i	$0.912319\pi$
$284$	6.66312	+	4.84104i	0.395383	+	0.287263i
$285$	−3.61803			−0.214314
$286$	1.35410	+	1.53884i	0.0800697	+	0.0909936i
$287$	27.3262			1.61302
$288$	−1.61803	−	1.17557i	−0.0953436	−	0.0692712i
$289$	−4.29180	+	13.2088i	−0.252459	+	0.776988i
$290$	0.763932	+	2.35114i	0.0448596	+	0.138064i
$291$	18.8435	−	13.6906i	1.10462	−	0.802556i
$292$	11.5902	−	8.42075i	0.678263	−	0.492787i
$293$	6.01722	+	18.5191i	0.351530	+	1.08190i	0.957994	+	0.286787i	$0.0925872\pi$
$293$	6.01722	+	18.5191i	0.351530	+	1.08190i	−0.606465	+	0.795111i	$0.707413\pi$
$294$	5.42705	−	16.7027i	0.316512	−	0.974124i
$295$	−2.50000	−	1.81636i	−0.145556	−	0.105752i
$296$	−1.14590			−0.0666040
$297$	−3.78115	+	6.37988i	−0.219405	+	0.370198i
$298$	22.2361			1.28810
$299$	2.11803	+	1.53884i	0.122489	+	0.0889935i
$300$	−1.64590	+	5.06555i	−0.0950260	+	0.292460i
$301$	11.5623	+	35.5851i	0.666440	+	2.05109i
$302$	−11.0902	+	8.05748i	−0.638168	+	0.463656i
$303$	17.1353	−	12.4495i	0.984395	−	0.715205i
$304$	0.309017	+	0.951057i	0.0177233	+	0.0545468i
$305$	3.30902	−	10.1841i	0.189474	−	0.583140i
$306$	2.85410	+	2.07363i	0.163158	+	0.118541i
$307$	−13.7639			−0.785549			−0.392775	−	0.919635i	$-0.628485\pi$
$307$	−13.7639			−0.785549			−0.392775	+	0.919635i	$0.628485\pi$
$308$	−6.51722	+	10.9964i	−0.371353	+	0.626578i
$309$	25.8541			1.47079
$310$	3.54508	+	2.57565i	0.201347	+	0.146287i
$311$	2.32624	−	7.15942i	0.131909	−	0.405974i	−0.863188	−	0.504883i	$-0.831535\pi$
$311$	2.32624	−	7.15942i	0.131909	−	0.405974i	0.995096	+	0.0989097i	$0.0315355\pi$
$312$	−0.427051	−	1.31433i	−0.0241770	−	0.0744092i
$313$	6.42705	−	4.66953i	0.363278	−	0.263937i	−0.391140	−	0.920331i	$-0.627919\pi$
$313$	6.42705	−	4.66953i	0.363278	−	0.263937i	0.754418	+	0.656394i	$0.227919\pi$
$314$	−7.85410	+	5.70634i	−0.443233	+	0.322027i
$315$	3.85410	+	11.8617i	0.217154	+	0.668331i
$316$	0.927051	−	2.85317i	0.0521507	−	0.160503i
$317$	2.42705	+	1.76336i	0.136317	+	0.0990399i	0.653854	−	0.756621i	$-0.273151\pi$
$317$	2.42705	+	1.76336i	0.136317	+	0.0990399i	−0.517537	+	0.855661i	$0.673151\pi$
$318$	−26.7082			−1.49772
$319$	3.34752	+	3.80423i	0.187425	+	0.212996i
$320$	−1.61803			−0.0904508
$321$	−5.42705	−	3.94298i	−0.302908	−	0.220076i
$322$	−5.04508	+	15.5272i	−0.281152	+	0.865296i
$323$	−0.545085	−	1.67760i	−0.0303293	−	0.0933441i
$324$	8.89919	−	6.46564i	0.494399	−	0.359202i
$325$	−1.19098	+	0.865300i	−0.0660639	+	0.0479982i
$326$	7.42705	+	22.8581i	0.411346	+	1.26599i
$327$	−3.68034	+	11.3269i	−0.203523	+	0.626380i
$328$	5.73607	+	4.16750i	0.316721	+	0.230112i
$329$	−9.74265			−0.537129
$330$	−1.11803	−	11.9475i	−0.0615457	−	0.657686i
$331$	−3.70820			−0.203821			−0.101911	−	0.994794i	$-0.532496\pi$
$331$	−3.70820			−0.203821			−0.101911	+	0.994794i	$0.532496\pi$
$332$	8.16312	+	5.93085i	0.448009	+	0.325498i
$333$	−0.708204	+	2.17963i	−0.0388093	+	0.119443i
$334$	−3.28115	−	10.0984i	−0.179537	−	0.552557i
$335$	6.66312	−	4.84104i	0.364045	−	0.264494i
$336$	6.97214	−	5.06555i	0.380361	−	0.276349i
$337$	2.21885	+	6.82891i	0.120868	+	0.371994i	0.993126	−	0.117053i	$-0.0373446\pi$
$337$	2.21885	+	6.82891i	0.120868	+	0.371994i	−0.872257	+	0.489047i	$0.837345\pi$
$338$	−3.89919	+	12.0005i	−0.212088	+	0.652739i
$339$	18.8435	+	13.6906i	1.02344	+	0.743570i
$340$	2.85410			0.154785
$341$	8.76393	+	1.96763i	0.474594	+	0.106553i
$342$	2.00000			0.108148
$343$	2.66312	+	1.93487i	0.143795	+	0.104473i
$344$	−3.00000	+	9.23305i	−0.161749	+	0.497813i
$345$	−4.73607	−	14.5761i	−0.254981	−	0.784752i
$346$	12.7812	−	9.28605i	0.687119	−	0.499221i
$347$	−19.0902	+	13.8698i	−1.02481	+	0.744571i	−0.967264	−	0.253772i	$-0.918329\pi$
$347$	−19.0902	+	13.8698i	−1.02481	+	0.744571i	−0.0575499	+	0.998343i	$0.518329\pi$
$348$	−1.05573	−	3.24920i	−0.0565930	−	0.174175i
$349$	−8.75329	+	26.9399i	−0.468553	+	1.44206i	0.385906	+	0.922538i	$0.373889\pi$
$349$	−8.75329	+	26.9399i	−0.468553	+	1.44206i	−0.854459	+	0.519519i	$0.826111\pi$
$350$	−7.42705	−	5.39607i	−0.396993	−	0.288432i
$351$	1.38197			0.0737639
$352$	−3.04508	+	1.31433i	−0.162304	+	0.0700539i
$353$	9.05573			0.481988			0.240994	−	0.970527i	$-0.422527\pi$
$353$	9.05573			0.481988			0.240994	+	0.970527i	$0.422527\pi$
$354$	3.45492	+	2.51014i	0.183627	+	0.133413i
$355$	4.11803	−	12.6740i	0.218563	−	0.672666i
$356$	4.07295	+	12.5352i	0.215866	+	0.664367i
$357$	−12.2984	+	8.93529i	−0.650899	+	0.472906i
$358$	10.3262	−	7.50245i	0.545759	−	0.396517i
$359$	−4.06231	−	12.5025i	−0.214400	−	0.659856i	−0.999196	−	0.0401012i	$-0.987232\pi$
$359$	−4.06231	−	12.5025i	−0.214400	−	0.659856i	0.784795	−	0.619755i	$-0.212768\pi$
$360$	−1.00000	+	3.07768i	−0.0527046	+	0.162208i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	21.9443			1.15337
$363$	−11.8090	−	21.5765i	−0.619813	−	1.13247i
$364$	2.38197			0.124849
$365$	−18.7533	−	13.6251i	−0.981592	−	0.713168i
$366$	−4.57295	+	14.0741i	−0.239032	+	0.735664i
$367$	10.3713	+	31.9196i	0.541379	+	1.66619i	0.729448	+	0.684036i	$0.239777\pi$
$367$	10.3713	+	31.9196i	0.541379	+	1.66619i	−0.188069	+	0.982156i	$0.560223\pi$
$368$	−3.42705	+	2.48990i	−0.178647	+	0.129795i
$369$	11.4721	−	8.33499i	0.597216	−	0.433902i
$370$	0.572949	+	1.76336i	0.0297862	+	0.0916725i
$371$	14.2254	−	43.7814i	0.738547	−	2.27301i
$372$	−4.89919	−	3.55947i	−0.254011	−	0.184550i
$373$	21.1246			1.09379			0.546895	−	0.837201i	$-0.315810\pi$
$373$	21.1246			1.09379			0.546895	+	0.837201i	$0.315810\pi$
$374$	5.37132	−	2.31838i	0.277744	−	0.119881i
$375$	26.7082			1.37921
$376$	−2.04508	−	1.48584i	−0.105467	−	0.0766264i
$377$	0.291796	−	0.898056i	0.0150283	−	0.0462522i
$378$	2.66312	+	8.19624i	0.136976	+	0.421569i
$379$	−12.2533	+	8.90254i	−0.629409	+	0.457293i	−0.856195	−	0.516652i	$-0.827178\pi$
$379$	−12.2533	+	8.90254i	−0.629409	+	0.457293i	0.226786	+	0.973945i	$0.427178\pi$
$380$	1.30902	−	0.951057i	0.0671512	−	0.0487882i
$381$	2.19756	+	6.76340i	0.112584	+	0.346499i
$382$	−0.600813	+	1.84911i	−0.0307403	+	0.0946088i
$383$	10.0172	+	7.27794i	0.511856	+	0.371885i	0.813527	−	0.581527i	$-0.197544\pi$
$383$	10.0172	+	7.27794i	0.511856	+	0.371885i	−0.301671	+	0.953412i	$0.597544\pi$
$384$	2.23607			0.114109
$385$	20.1803	+	4.53077i	1.02849	+	0.230909i
$386$	−5.43769			−0.276771
$387$	15.7082	+	11.4127i	0.798493	+	0.580139i
$388$	−3.21885	+	9.90659i	−0.163412	+	0.502931i
$389$	−9.29180	−	28.5972i	−0.471113	−	1.44994i	−0.851129	−	0.524956i	$-0.824082\pi$
$389$	−9.29180	−	28.5972i	−0.471113	−	1.44994i	0.380016	−	0.924980i	$-0.375918\pi$
$390$	−1.80902	+	1.31433i	−0.0916031	+	0.0665536i
$391$	6.04508	−	4.39201i	0.305713	−	0.222114i
$392$	2.42705	+	7.46969i	0.122585	+	0.377277i
$393$	10.1246	−	31.1604i	0.510719	−	1.57183i
$394$	−18.7533	−	13.6251i	−0.944777	−	0.686421i
$395$	−4.85410			−0.244236
$396$	0.618034	+	6.60440i	0.0310574	+	0.331883i
$397$	−23.8328			−1.19613			−0.598067	−	0.801446i	$-0.704064\pi$
$397$	−23.8328			−1.19613			−0.598067	+	0.801446i	$0.704064\pi$
$398$	−11.2361	−	8.16348i	−0.563213	−	0.409198i
$399$	−2.66312	+	8.19624i	−0.133323	+	0.410325i
$400$	−0.736068	−	2.26538i	−0.0368034	−	0.113269i
$401$	16.6074	−	12.0660i	0.829334	−	0.602546i	−0.0900372	−	0.995938i	$-0.528699\pi$
$401$	16.6074	−	12.0660i	0.829334	−	0.602546i	0.919371	+	0.393392i	$0.128699\pi$
$402$	−9.20820	+	6.69015i	−0.459263	+	0.333674i
$403$	−0.517221	−	1.59184i	−0.0257646	−	0.0792953i
$404$	−2.92705	+	9.00854i	−0.145626	+	0.448191i
$405$	−14.3992	−	10.4616i	−0.715501	−	0.519842i
$406$	5.88854			0.292244
$407$	2.51064	+	2.85317i	0.124448	+	0.141426i
$408$	−3.94427			−0.195271
$409$	2.42705	+	1.76336i	0.120010	+	0.0871923i	0.646171	−	0.763192i	$-0.276369\pi$
$409$	2.42705	+	1.76336i	0.120010	+	0.0871923i	−0.526161	+	0.850385i	$0.676369\pi$
$410$	3.54508	−	10.9106i	0.175079	−	0.538839i
$411$	−5.16312	−	15.8904i	−0.254678	−	0.783818i
$412$	−9.35410	+	6.79615i	−0.460844	+	0.334822i
$413$	−5.95492	+	4.32650i	−0.293022	+	0.212893i
$414$	2.61803	+	8.05748i	0.128669	+	0.396004i
$415$	5.04508	−	15.5272i	0.247653	−	0.762199i
$416$	0.500000	+	0.363271i	0.0245145	+	0.0178108i
$417$	4.14590			0.203026
$418$	1.69098	−	2.85317i	0.0827087	−	0.139553i
$419$	4.58359			0.223923			0.111962	−	0.993713i	$-0.464287\pi$
$419$	4.58359			0.223923			0.111962	+	0.993713i	$0.464287\pi$
$420$	−11.2812	−	8.19624i	−0.550464	−	0.399935i
$421$	5.07295	−	15.6129i	0.247240	−	0.760928i	−0.748019	−	0.663677i	$-0.768995\pi$
$421$	5.07295	−	15.6129i	0.247240	−	0.760928i	0.995260	−	0.0972510i	$-0.0310049\pi$
$422$	−8.01722	−	24.6745i	−0.390272	−	1.20113i
$423$	−4.09017	+	2.97168i	−0.198871	+	0.144488i
$424$	9.66312	−	7.02067i	0.469283	−	0.340954i
$425$	1.29837	+	3.99598i	0.0629804	+	0.193834i
$426$	−5.69098	+	17.5150i	−0.275729	+	0.848607i
$427$	−20.6353	−	14.9924i	−0.998610	−	0.725533i
$428$	3.00000			0.145010
$429$	−2.33688	+	3.94298i	−0.112826	+	0.190369i
$430$	15.7082			0.757517
$431$	−1.64590	−	1.19581i	−0.0792801	−	0.0576004i	0.547439	−	0.836845i	$-0.315603\pi$
$431$	−1.64590	−	1.19581i	−0.0792801	−	0.0576004i	−0.626719	+	0.779245i	$0.715603\pi$
$432$	−0.690983	+	2.12663i	−0.0332449	+	0.102317i
$433$	−7.27051	−	22.3763i	−0.349398	−	1.07534i	−0.959187	−	0.282773i	$-0.908746\pi$
$433$	−7.27051	−	22.3763i	−0.349398	−	1.07534i	0.609788	−	0.792564i	$-0.291254\pi$
$434$	8.44427	−	6.13512i	0.405338	−	0.294495i
$435$	−4.47214	+	3.24920i	−0.214423	+	0.155787i
$436$	−1.64590	−	5.06555i	−0.0788242	−	0.242596i
$437$	1.30902	−	4.02874i	0.0626188	−	0.192721i
$438$	25.9164	+	18.8294i	1.23833	+	0.899702i
$439$	20.1459			0.961511			0.480756	−	0.876855i	$-0.340362\pi$
$439$	20.1459			0.961511			0.480756	+	0.876855i	$0.340362\pi$
$440$	3.54508	+	4.02874i	0.169005	+	0.192063i
$441$	15.7082			0.748010
$442$	−0.881966	−	0.640786i	−0.0419508	−	0.0304791i
$443$	−1.50000	+	4.61653i	−0.0712672	+	0.219338i	−0.980346	−	0.197287i	$-0.936787\pi$
$443$	−1.50000	+	4.61653i	−0.0712672	+	0.219338i	0.909079	+	0.416624i	$0.136787\pi$
$444$	−0.791796	−	2.43690i	−0.0375770	−	0.115650i
$445$	17.2533	−	12.5352i	0.817884	−	0.594228i
$446$	16.1803	−	11.7557i	0.766161	−	0.556649i
$447$	15.3647	+	47.2878i	0.726728	+	2.23664i
$448$	−1.19098	+	3.66547i	−0.0562687	+	0.173177i
$449$	0.572949	+	0.416272i	0.0270391	+	0.0196451i	0.601223	−	0.799081i	$-0.294680\pi$
$449$	0.572949	+	0.416272i	0.0270391	+	0.0196451i	−0.574184	+	0.818727i	$0.694680\pi$
$450$	−4.76393			−0.224574
$451$	−2.19098	−	23.4131i	−0.103169	−	1.10248i
$452$	−10.4164			−0.489947
$453$	−24.7984	−	18.0171i	−1.16513	−	0.846516i
$454$	−4.95492	+	15.2497i	−0.232546	+	0.715702i
$455$	−1.19098	−	3.66547i	−0.0558341	−	0.171840i
$456$	−1.80902	+	1.31433i	−0.0847150	+	0.0615490i
$457$	−7.28115	+	5.29007i	−0.340598	+	0.247459i	−0.744914	−	0.667160i	$-0.767510\pi$
$457$	−7.28115	+	5.29007i	−0.340598	+	0.247459i	0.404316	+	0.914619i	$0.367510\pi$
$458$	7.59017	+	23.3601i	0.354665	+	1.09155i
$459$	1.21885	−	3.75123i	0.0568909	−	0.175092i
$460$	5.54508	+	4.02874i	0.258541	+	0.187841i
$461$	30.3050			1.41144			0.705721	−	0.708490i	$-0.250623\pi$
$461$	30.3050			1.41144			0.705721	+	0.708490i	$0.250623\pi$
$462$	−27.8885	−	6.26137i	−1.29749	−	0.291305i
$463$	−22.8541			−1.06212			−0.531060	−	0.847334i	$-0.678206\pi$
$463$	−22.8541			−1.06212			−0.531060	+	0.847334i	$0.678206\pi$
$464$	1.23607	+	0.898056i	0.0573830	+	0.0416912i
$465$	−3.02786	+	9.31881i	−0.140414	+	0.432149i
$466$	7.30902	+	22.4948i	0.338584	+	1.04205i
$467$	−17.3992	+	12.6412i	−0.805138	+	0.584967i	−0.912417	−	0.409262i	$-0.865786\pi$
$467$	−17.3992	+	12.6412i	−0.805138	+	0.584967i	0.107279	+	0.994229i	$0.465786\pi$
$468$	1.00000	−	0.726543i	0.0462250	−	0.0335844i
$469$	−6.06231	−	18.6579i	−0.279931	−	0.861540i
$470$	−1.26393	+	3.88998i	−0.0583008	+	0.179432i
$471$	−17.5623	−	12.7598i	−0.809228	−	0.587939i
$472$	−1.90983			−0.0879071
$473$	29.5623	−	12.7598i	1.35928	−	0.586694i
$474$	6.70820			0.308118
$475$	1.92705	+	1.40008i	0.0884192	+	0.0642403i
$476$	2.10081	−	6.46564i	0.0962906	−	0.296352i
$477$	−7.38197	−	22.7194i	−0.337997	−	1.04025i
$478$	20.2082	−	14.6821i	0.924302	−	0.671545i
$479$	3.04508	−	2.21238i	0.139133	−	0.101086i	−0.516041	−	0.856564i	$-0.672595\pi$
$479$	3.04508	−	2.21238i	0.139133	−	0.101086i	0.655175	+	0.755477i	$0.272595\pi$
$480$	−1.11803	−	3.44095i	−0.0510310	−	0.157057i
$481$	0.218847	−	0.673542i	0.00997857	−	0.0307109i
$482$	−6.73607	−	4.89404i	−0.306819	−	0.222917i
$483$	−36.5066			−1.66111
$484$	9.94427	+	4.70228i	0.452012	+	0.213740i
$485$	16.8541			0.765305
$486$	14.4721	+	10.5146i	0.656469	+	0.476953i
$487$	4.92705	−	15.1639i	0.223266	−	0.687142i	−0.775197	−	0.631720i	$-0.782349\pi$
$487$	4.92705	−	15.1639i	0.223266	−	0.687142i	0.998463	−	0.0554225i	$-0.0176506\pi$
$488$	−2.04508	−	6.29412i	−0.0925766	−	0.284922i
$489$	−43.4787	+	31.5891i	−1.96618	+	1.42851i
$490$	10.2812	−	7.46969i	0.464455	−	0.337446i
$491$	−6.84346	−	21.0620i	−0.308841	−	0.950515i	−0.978216	−	0.207590i	$-0.933438\pi$
$491$	−6.84346	−	21.0620i	−0.308841	−	0.950515i	0.669375	−	0.742925i	$-0.266562\pi$
$492$	−4.89919	+	15.0781i	−0.220872	+	0.679775i
$493$	−2.18034	−	1.58411i	−0.0981976	−	0.0713447i
$494$	−0.618034			−0.0278067
$495$	9.85410	−	4.25325i	0.442909	−	0.191170i
$496$	2.70820			0.121602
$497$	−25.6803	−	18.6579i	−1.15192	−	0.836919i
$498$	−6.97214	+	21.4580i	−0.312429	+	0.961557i
$499$	9.57953	+	29.4828i	0.428839	+	1.31983i	0.899270	+	0.437393i	$0.144098\pi$
$499$	9.57953	+	29.4828i	0.428839	+	1.31983i	−0.470432	+	0.882436i	$0.655902\pi$
$500$	−9.66312	+	7.02067i	−0.432148	+	0.313974i
$501$	19.2082	−	13.9556i	0.858159	−	0.623489i
$502$	6.47214	+	19.9192i	0.288866	+	0.889037i
$503$	−1.79180	+	5.51458i	−0.0798922	+	0.245883i	−0.983023	−	0.183483i	$-0.941263\pi$
$503$	−1.79180	+	5.51458i	−0.0798922	+	0.245883i	0.903131	+	0.429366i	$0.141263\pi$
$504$	6.23607	+	4.53077i	0.277777	+	0.201816i
$505$	15.3262			0.682009
$506$	13.7082	+	3.07768i	0.609404	+	0.136820i
$507$	−28.2148			−1.25306
$508$	−2.57295	−	1.86936i	−0.114156	−	0.0829393i
$509$	−12.2188	+	37.6057i	−0.541591	+	1.66685i	0.187370	+	0.982289i	$0.440004\pi$
$509$	−12.2188	+	37.6057i	−0.541591	+	1.66685i	−0.728960	+	0.684556i	$0.759996\pi$
$510$	1.97214	+	6.06961i	0.0873276	+	0.268767i
$511$	−44.6697	+	32.4544i	−1.97607	+	1.43570i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−0.690983	−	2.12663i	−0.0305076	−	0.0938929i
$514$	−2.88197	+	8.86978i	−0.127118	+	0.391229i
$515$	15.1353	+	10.9964i	0.666939	+	0.484560i
$516$	−21.7082			−0.955650
$517$	0.781153	+	8.34751i	0.0343551	+	0.367123i
$518$	4.41641			0.194046
$519$	28.5795	+	20.7642i	1.25450	+	0.911449i
$520$	0.309017	−	0.951057i	0.0135513	−	0.0417066i
$521$	2.01722	+	6.20837i	0.0883761	+	0.271994i	0.985471	−	0.169845i	$-0.0543266\pi$
$521$	2.01722	+	6.20837i	0.0883761	+	0.271994i	−0.897095	+	0.441838i	$0.854327\pi$
$522$	2.47214	−	1.79611i	0.108202	−	0.0786137i
$523$	−29.7254	+	21.5968i	−1.29980	+	0.944361i	−0.999954	−	0.00962538i	$-0.996936\pi$
$523$	−29.7254	+	21.5968i	−1.29980	+	0.944361i	−0.299848	+	0.953987i	$0.596936\pi$
$524$	4.52786	+	13.9353i	0.197801	+	0.608768i
$525$	6.34346	−	19.5232i	0.276851	−	0.852061i
$526$	−12.9721	−	9.42481i	−0.565612	−	0.410941i
$527$	−4.77709			−0.208093
$528$	−4.89919	−	5.56758i	−0.213210	−	0.242298i
$529$	−5.05573			−0.219814
$530$	−15.6353	−	11.3597i	−0.679152	−	0.493433i
$531$	−1.18034	+	3.63271i	−0.0512224	+	0.157646i
$532$	−1.19098	−	3.66547i	−0.0516357	−	0.158918i
$533$	−3.54508	+	2.57565i	−0.153555	+	0.111564i
$534$	−23.8435	+	17.3233i	−1.03181	+	0.749652i
$535$	−1.50000	−	4.61653i	−0.0648507	−	0.199590i
$536$	1.57295	−	4.84104i	0.0679410	−	0.209101i
$537$	23.0902	+	16.7760i	0.996414	+	0.723937i
$538$	10.0557			0.433533
$539$	13.2812	−	22.4091i	0.572060	−	0.965228i
$540$	3.61803			0.155695
$541$	28.8713	+	20.9762i	1.24128	+	0.901839i	0.997683	−	0.0680385i	$-0.0216741\pi$
$541$	28.8713	+	20.9762i	1.24128	+	0.901839i	0.243592	+	0.969878i	$0.421674\pi$
$542$	1.76393	−	5.42882i	0.0757674	−	0.233188i
$543$	15.1631	+	46.6673i	0.650712	+	2.00268i
$544$	1.42705	−	1.03681i	0.0611843	−	0.0444530i
$545$	−6.97214	+	5.06555i	−0.298653	+	0.216984i
$546$	1.64590	+	5.06555i	0.0704379	+	0.216786i
$547$	−1.79180	+	5.51458i	−0.0766117	+	0.235786i	−0.982027	−	0.188740i	$-0.939560\pi$
$547$	−1.79180	+	5.51458i	−0.0766117	+	0.235786i	0.905415	+	0.424527i	$0.139560\pi$
$548$	6.04508	+	4.39201i	0.258233	+	0.187617i
$549$	−13.2361			−0.564902
$550$	−4.02786	+	6.79615i	−0.171749	+	0.289789i
$551$	−1.52786			−0.0650892
$552$	−7.66312	−	5.56758i	−0.326164	−	0.236972i
$553$	−3.57295	+	10.9964i	−0.151937	+	0.467615i
$554$	−1.89919	−	5.84510i	−0.0806887	−	0.248334i
$555$	−3.35410	+	2.43690i	−0.142374	+	0.103441i
$556$	−1.50000	+	1.08981i	−0.0636142	+	0.0462184i
$557$	−2.79837	−	8.61251i	−0.118571	−	0.364924i	0.874104	−	0.485739i	$-0.161449\pi$
$557$	−2.79837	−	8.61251i	−0.118571	−	0.364924i	−0.992675	+	0.120815i	$0.961449\pi$
$558$	1.67376	−	5.15131i	0.0708560	−	0.218072i
$559$	−4.85410	−	3.52671i	−0.205307	−	0.149164i
$560$	6.23607			0.263522
$561$	8.64183	+	9.82084i	0.364858	+	0.414636i
$562$	28.0344			1.18256
$563$	29.6074	+	21.5110i	1.24780	+	0.906582i	0.998092	−	0.0617388i	$-0.0196646\pi$
$563$	29.6074	+	21.5110i	1.24780	+	0.906582i	0.249710	+	0.968321i	$0.419665\pi$
$564$	1.74671	−	5.37582i	0.0735498	−	0.226363i
$565$	5.20820	+	16.0292i	0.219111	+	0.674354i
$566$	15.1353	−	10.9964i	0.636182	−	0.462213i
$567$	−34.2984	+	24.9192i	−1.44040	+	1.04651i
$568$	−2.54508	−	7.83297i	−0.106789	−	0.328664i
$569$	−4.47214	+	13.7638i	−0.187482	+	0.577009i	−0.999982	−	0.00595104i	$-0.998106\pi$
$569$	−4.47214	+	13.7638i	−0.187482	+	0.577009i	0.812501	+	0.582960i	$0.198106\pi$
$570$	2.92705	+	2.12663i	0.122601	+	0.0890746i
$571$	−24.8885			−1.04155			−0.520777	−	0.853693i	$-0.674358\pi$
$571$	−24.8885			−1.04155			−0.520777	+	0.853693i	$0.674358\pi$
$572$	−0.190983	−	2.04087i	−0.00798540	−	0.0853331i
$573$	−4.34752			−0.181620
$574$	−22.1074	−	16.0620i	−0.922745	−	0.670413i
$575$	−3.11803	+	9.59632i	−0.130031	+	0.400194i
$576$	0.618034	+	1.90211i	0.0257514	+	0.0792547i
$577$	28.4894	−	20.6987i	1.18603	−	0.861699i	0.193189	−	0.981162i	$-0.438117\pi$
$577$	28.4894	−	20.6987i	1.18603	−	0.861699i	0.992839	+	0.119462i	$0.0381170\pi$
$578$	11.2361	−	8.16348i	0.467359	−	0.339556i
$579$	−3.75735	−	11.5639i	−0.156150	−	0.480581i
$580$	0.763932	−	2.35114i	0.0317206	−	0.0976258i
$581$	−31.4615	−	22.8581i	−1.30524	−	0.948314i
$582$	−23.2918			−0.965476
$583$	−38.6525	−	8.67802i	−1.60082	−	0.359407i
$584$	−14.3262			−0.592824
$585$	−1.61803	−	1.17557i	−0.0668975	−	0.0486039i
$586$	6.01722	−	18.5191i	0.248569	−	0.765017i
$587$	−10.6353	−	32.7319i	−0.438964	−	1.35099i	−0.888970	−	0.457966i	$-0.848578\pi$
$587$	−10.6353	−	32.7319i	−0.438964	−	1.35099i	0.450006	−	0.893026i	$-0.351422\pi$
$588$	−14.2082	+	10.3229i	−0.585936	+	0.425708i
$589$	−2.19098	+	1.59184i	−0.0902779	+	0.0655907i
$590$	0.954915	+	2.93893i	0.0393132	+	0.120994i
$591$	16.0172	−	49.2959i	0.658860	−	2.02776i
$592$	0.927051	+	0.673542i	0.0381016	+	0.0276824i
$593$	1.58359			0.0650303			0.0325152	−	0.999471i	$-0.489648\pi$
$593$	1.58359			0.0650303			0.0325152	+	0.999471i	$0.489648\pi$
$594$	6.80902	−	2.93893i	0.279377	−	0.120586i
$595$	−11.0000			−0.450956
$596$	−17.9894	−	13.0700i	−0.736873	−	0.535369i
$597$	9.59675	−	29.5358i	0.392769	−	1.20882i
$598$	−0.809017	−	2.48990i	−0.0330832	−	0.101820i
$599$	−3.35410	+	2.43690i	−0.137045	+	0.0995689i	−0.654196	−	0.756325i	$-0.726993\pi$
$599$	−3.35410	+	2.43690i	−0.137045	+	0.0995689i	0.517151	+	0.855894i	$0.326993\pi$
$600$	4.30902	−	3.13068i	0.175915	−	0.127810i
$601$	1.15248	+	3.54696i	0.0470105	+	0.144683i	0.971806	−	0.235780i	$-0.0757645\pi$
$601$	1.15248	+	3.54696i	0.0470105	+	0.144683i	−0.924796	+	0.380463i	$0.875764\pi$
$602$	11.5623	−	35.5851i	0.471244	−	1.45034i
$603$	−8.23607	−	5.98385i	−0.335399	−	0.243681i
$604$	13.7082			0.557779
$605$	2.26393	−	17.6538i	0.0920419	−	0.717729i
$606$	−21.1803			−0.860392
$607$	−2.42705	−	1.76336i	−0.0985110	−	0.0715724i	0.537439	−	0.843302i	$-0.319392\pi$
$607$	−2.42705	−	1.76336i	−0.0985110	−	0.0715724i	−0.635950	+	0.771730i	$0.719392\pi$
$608$	0.309017	−	0.951057i	0.0125323	−	0.0385704i
$609$	4.06888	+	12.5227i	0.164879	+	0.507447i
$610$	−8.66312	+	6.29412i	−0.350759	+	0.254842i
$611$	1.26393	−	0.918300i	0.0511332	−	0.0371505i
$612$	−1.09017	−	3.35520i	−0.0440675	−	0.135626i
$613$	5.90983	−	18.1886i	0.238696	−	0.734630i	−0.757914	−	0.652355i	$-0.773781\pi$
$613$	5.90983	−	18.1886i	0.238696	−	0.734630i	0.996610	−	0.0822754i	$-0.0262187\pi$
$614$	11.1353	+	8.09024i	0.449382	+	0.326495i
$615$	25.6525			1.03441
$616$	11.7361	−	5.06555i	0.472860	−	0.204097i
$617$	−9.38197			−0.377704			−0.188852	−	0.982006i	$-0.560477\pi$
$617$	−9.38197			−0.377704			−0.188852	+	0.982006i	$0.560477\pi$
$618$	−20.9164	−	15.1967i	−0.841381	−	0.611299i
$619$	−3.73607	+	11.4984i	−0.150165	+	0.462161i	−0.997639	−	0.0686762i	$-0.978122\pi$
$619$	−3.73607	+	11.4984i	−0.150165	+	0.462161i	0.847474	+	0.530837i	$0.178122\pi$
$620$	−1.35410	−	4.16750i	−0.0543820	−	0.167371i
$621$	7.66312	−	5.56758i	0.307510	−	0.223419i
$622$	−6.09017	+	4.42477i	−0.244194	+	0.177417i
$623$	−15.6976	−	48.3121i	−0.628909	−	1.93558i
$624$	−0.427051	+	1.31433i	−0.0170957	+	0.0526152i
$625$	6.00000	+	4.35926i	0.240000	+	0.174370i
$626$	−7.94427			−0.317517
$627$	7.23607	+	1.62460i	0.288981	+	0.0648802i
$628$	9.70820			0.387400
$629$	−1.63525	−	1.18808i	−0.0652019	−	0.0473719i
$630$	3.85410	−	11.8617i	0.153551	−	0.472582i
$631$	−2.73607	−	8.42075i	−0.108921	−	0.335225i	0.881710	−	0.471793i	$-0.156393\pi$
$631$	−2.73607	−	8.42075i	−0.108921	−	0.335225i	−0.990631	+	0.136568i	$0.956393\pi$
$632$	−2.42705	+	1.76336i	−0.0965429	+	0.0701425i
$633$	46.9336	−	34.0993i	1.86544	−	1.35532i
$634$	−0.927051	−	2.85317i	−0.0368179	−	0.113314i
$635$	−1.59017	+	4.89404i	−0.0631040	+	0.194214i
$636$	21.6074	+	15.6987i	0.856789	+	0.622493i
$637$	−4.85410			−0.192327
$638$	−0.472136	−	5.04531i	−0.0186920	−	0.199746i
$639$	−16.4721			−0.651628
$640$	1.30902	+	0.951057i	0.0517434	+	0.0375938i
$641$	14.6738	−	45.1612i	0.579579	−	1.78376i	−0.0404508	−	0.999182i	$-0.512879\pi$
$641$	14.6738	−	45.1612i	0.579579	−	1.78376i	0.620030	−	0.784578i	$-0.287121\pi$
$642$	2.07295	+	6.37988i	0.0818128	+	0.251794i
$643$	1.14590	−	0.832544i	0.0451898	−	0.0328323i	−0.564961	−	0.825118i	$-0.691109\pi$
$643$	1.14590	−	0.832544i	0.0451898	−	0.0328323i	0.610151	+	0.792285i	$0.291109\pi$
$644$	13.2082	−	9.59632i	0.520476	−	0.378148i
$645$	10.8541	+	33.4055i	0.427380	+	1.31534i
$646$	−0.545085	+	1.67760i	−0.0214461	+	0.0660043i
$647$	−1.30902	−	0.951057i	−0.0514628	−	0.0373899i	0.561756	−	0.827303i	$-0.310126\pi$
$647$	−1.30902	−	0.951057i	−0.0514628	−	0.0373899i	−0.613219	+	0.789913i	$0.710126\pi$
$648$	−11.0000			−0.432121
$649$	4.18441	+	4.75528i	0.164252	+	0.186661i
$650$	1.47214			0.0577419
$651$	18.8820	+	13.7186i	0.740043	+	0.537672i
$652$	7.42705	−	22.8581i	0.290866	−	0.895193i
$653$	5.15248	+	15.8577i	0.201632	+	0.620559i	0.999835	+	0.0181707i	$0.00578424\pi$
$653$	5.15248	+	15.8577i	0.201632	+	0.620559i	−0.798203	+	0.602389i	$0.794216\pi$
$654$	9.63525	−	7.00042i	0.376768	−	0.273738i
$655$	19.1803	−	13.9353i	0.749438	−	0.544499i
$656$	−2.19098	−	6.74315i	−0.0855435	−	0.263276i
$657$	−8.85410	+	27.2501i	−0.345431	+	1.06313i
$658$	7.88197	+	5.72658i	0.307271	+	0.223245i
$659$	−49.4721			−1.92716			−0.963580	−	0.267419i	$-0.913829\pi$
$659$	−49.4721			−1.92716			−0.963580	+	0.267419i	$0.913829\pi$
$660$	−6.11803	+	10.3229i	−0.238144	+	0.401817i
$661$	−44.3820			−1.72626			−0.863129	−	0.504983i	$-0.831499\pi$
$661$	−44.3820			−1.72626			−0.863129	+	0.504983i	$0.831499\pi$
$662$	3.00000	+	2.17963i	0.116598	+	0.0847136i
$663$	0.753289	−	2.31838i	0.0292553	−	0.0900386i
$664$	−3.11803	−	9.59632i	−0.121003	−	0.372410i
$665$	−5.04508	+	3.66547i	−0.195640	+	0.142141i
$666$	1.85410	−	1.34708i	0.0718450	−	0.0521984i
$667$	−2.00000	−	6.15537i	−0.0774403	−	0.238337i
$668$	−3.28115	+	10.0984i	−0.126952	+	0.390717i
$669$	36.1803	+	26.2866i	1.39881	+	1.01630i
$670$	−8.23607			−0.318187
$671$	−11.1910	+	18.8824i	−0.432023	+	0.728946i
$672$	−8.61803			−0.332448
$673$	32.5795	+	23.6704i	1.25585	+	0.912427i	0.998546	−	0.0539036i	$-0.0171664\pi$
$673$	32.5795	+	23.6704i	1.25585	+	0.912427i	0.257302	+	0.966331i	$0.417166\pi$
$674$	2.21885	−	6.82891i	0.0854668	−	0.263040i
$675$	1.64590	+	5.06555i	0.0633506	+	0.194973i
$676$	10.2082	−	7.41669i	0.392623	−	0.285257i
$677$	38.3156	−	27.8379i	1.47259	−	1.06990i	0.492735	−	0.870180i	$-0.335997\pi$
$677$	38.3156	−	27.8379i	1.47259	−	1.06990i	0.979853	−	0.199718i	$-0.0640026\pi$
$678$	−7.19756	−	22.1518i	−0.276421	−	0.850735i
$679$	12.4058	−	38.1810i	0.476090	−	1.46525i
$680$	−2.30902	−	1.67760i	−0.0885468	−	0.0643330i
$681$	−35.8541			−1.37393
$682$	−5.93363	−	6.74315i	−0.227210	−	0.258209i
$683$	−28.2148			−1.07961			−0.539804	−	0.841791i	$-0.681502\pi$
$683$	−28.2148			−1.07961			−0.539804	+	0.841791i	$0.681502\pi$
$684$	−1.61803	−	1.17557i	−0.0618671	−	0.0449491i
$685$	3.73607	−	11.4984i	0.142748	−	0.439333i
$686$	−1.01722	−	3.13068i	−0.0388377	−	0.119530i
$687$	−44.4336	+	32.2829i	−1.69525	+	1.23167i
$688$	7.85410	−	5.70634i	0.299435	−	0.217552i
$689$	2.28115	+	7.02067i	0.0869050	+	0.267466i
$690$	−4.73607	+	14.5761i	−0.180299	+	0.554903i
$691$	−18.4164	−	13.3803i	−0.700593	−	0.509011i	0.179532	−	0.983752i	$-0.442542\pi$
$691$	−18.4164	−	13.3803i	−0.700593	−	0.509011i	−0.880125	+	0.474741i	$0.842542\pi$
$692$	−15.7984			−0.600564
$693$	−2.38197	−	25.4540i	−0.0904834	−	0.966918i
$694$	23.5967			0.895720
$695$	2.42705	+	1.76336i	0.0920633	+	0.0668879i
$696$	−1.05573	+	3.24920i	−0.0400173	+	0.123160i
$697$	3.86475	+	11.8945i	0.146388	+	0.450535i
$698$	22.9164	−	16.6497i	0.867399	−	0.630202i
$699$	−42.7877	+	31.0871i	−1.61838	+	1.17582i
$700$	2.83688	+	8.73102i	0.107224	+	0.330002i
$701$	−7.98936	+	24.5887i	−0.301754	+	0.928703i	0.679115	+	0.734032i	$0.262364\pi$
$701$	−7.98936	+	24.5887i	−0.301754	+	0.928703i	−0.980869	+	0.194671i	$0.937636\pi$
$702$	−1.11803	−	0.812299i	−0.0421975	−	0.0306583i
$703$	−1.14590			−0.0432184
$704$	3.23607	+	0.726543i	0.121964	+	0.0273826i
$705$	−9.14590			−0.344454
$706$	−7.32624	−	5.32282i	−0.275727	−	0.200327i
$707$	11.2812	−	34.7198i	0.424271	−	1.30577i
$708$	−1.31966	−	4.06150i	−0.0495959	−	0.152640i
$709$	29.3156	−	21.2990i	1.10097	−	0.799902i	0.119752	−	0.992804i	$-0.461790\pi$
$709$	29.3156	−	21.2990i	1.10097	−	0.799902i	0.981218	+	0.192902i	$0.0617900\pi$
$710$	−10.7812	+	7.83297i	−0.404609	+	0.293966i
$711$	1.85410	+	5.70634i	0.0695343	+	0.214004i
$712$	4.07295	−	12.5352i	0.152640	−	0.469778i
$713$	−9.28115	−	6.74315i	−0.347582	−	0.252533i
$714$	15.2016			0.568907
$715$	−3.04508	+	1.31433i	−0.113880	+	0.0491531i
$716$	−12.7639			−0.477011
$717$	45.1869	+	32.8302i	1.68754	+	1.22607i
$718$	−4.06231	+	12.5025i	−0.151604	+	0.466589i
$719$	9.84346	+	30.2951i	0.367099	+	1.12981i	0.948656	+	0.316309i	$0.102444\pi$
$719$	9.84346	+	30.2951i	0.367099	+	1.12981i	−0.581557	+	0.813506i	$0.697556\pi$
$720$	2.61803	−	1.90211i	0.0975684	−	0.0708876i
$721$	36.0517	−	26.1931i	1.34263	−	0.975481i
$722$	0.309017	+	0.951057i	0.0115004	+	0.0353947i
$723$	5.75329	−	17.7068i	0.213967	−	0.658523i
$724$	−17.7533	−	12.8985i	−0.659796	−	0.479370i
$725$	3.63932			0.135161
$726$	−3.12868	+	24.3970i	−0.116116	+	0.905456i
$727$	−45.8328			−1.69985			−0.849923	−	0.526908i	$-0.823351\pi$
$727$	−45.8328			−1.69985			−0.849923	+	0.526908i	$0.823351\pi$
$728$	−1.92705	−	1.40008i	−0.0714213	−	0.0518906i
$729$	−2.16312	+	6.65740i	−0.0801155	+	0.246570i
$730$	7.16312	+	22.0458i	0.265119	+	0.815952i
$731$	−13.8541	+	10.0656i	−0.512412	+	0.372289i
$732$	11.9721	−	8.69827i	0.442503	−	0.321497i
$733$	−7.89919	−	24.3112i	−0.291763	−	0.897955i	−0.984290	−	0.176562i	$-0.943502\pi$
$733$	−7.89919	−	24.3112i	−0.291763	−	0.897955i	0.692526	−	0.721393i	$-0.256498\pi$
$734$	10.3713	−	31.9196i	0.382813	−	1.17818i
$735$	22.9894	+	16.7027i	0.847975	+	0.616090i
$736$	4.23607			0.156144
$737$	−15.5000	+	6.69015i	−0.570950	+	0.246435i
$738$	−14.1803			−0.521986
$739$	20.3262	+	14.7679i	0.747713	+	0.543245i	0.895117	−	0.445831i	$-0.147092\pi$
$739$	20.3262	+	14.7679i	0.747713	+	0.543245i	−0.147404	+	0.989076i	$0.547092\pi$
$740$	0.572949	−	1.76336i	0.0210620	−	0.0648222i
$741$	−0.427051	−	1.31433i	−0.0156881	−	0.0482830i
$742$	−37.2426	+	27.0584i	−1.36722	+	0.993344i
$743$	−1.47214	+	1.06957i	−0.0540074	+	0.0392387i	−0.614461	−	0.788947i	$-0.710627\pi$
$743$	−1.47214	+	1.06957i	−0.0540074	+	0.0392387i	0.560454	+	0.828186i	$0.310627\pi$
$744$	1.87132	+	5.75934i	0.0686060	+	0.211148i
$745$	−11.1180	+	34.2178i	−0.407333	+	1.25364i
$746$	−17.0902	−	12.4167i	−0.625716	−	0.454609i
$747$	−20.1803			−0.738360
$748$	−5.70820	−	1.28157i	−0.208713	−	0.0468589i
$749$	−11.5623			−0.422477
$750$	−21.6074	−	15.6987i	−0.788990	−	0.573235i
$751$	−4.05166	+	12.4697i	−0.147847	+	0.455027i	−0.997366	−	0.0725311i	$-0.976892\pi$
$751$	−4.05166	+	12.4697i	−0.147847	+	0.455027i	0.849519	+	0.527558i	$0.176892\pi$
$752$	0.781153	+	2.40414i	0.0284857	+	0.0876700i
$753$	−37.8885	+	27.5276i	−1.38074	+	1.00316i
$754$	−0.763932	+	0.555029i	−0.0278208	+	0.0202130i
$755$	−6.85410	−	21.0948i	−0.249446	−	0.767717i
$756$	2.66312	−	8.19624i	0.0968567	−	0.298094i
$757$	41.1976	+	29.9318i	1.49735	+	1.08789i	0.971422	+	0.237361i	$0.0762823\pi$
$757$	41.1976	+	29.9318i	1.49735	+	1.08789i	0.525929	+	0.850528i	$0.323718\pi$
$758$	15.1459			0.550124
$759$	2.92705	+	31.2789i	0.106245	+	1.13535i
$760$	−1.61803			−0.0586923
$761$	12.2254	+	8.88229i	0.443171	+	0.321983i	0.786894	−	0.617088i	$-0.211688\pi$
$761$	12.2254	+	8.88229i	0.443171	+	0.321983i	−0.343722	+	0.939071i	$0.611688\pi$
$762$	2.19756	−	6.76340i	0.0796092	−	0.245012i
$763$	6.34346	+	19.5232i	0.229649	+	0.706786i
$764$	1.57295	−	1.14281i	0.0569073	−	0.0413456i
$765$	−4.61803	+	3.35520i	−0.166965	+	0.121307i
$766$	−3.82624	−	11.7759i	−0.138248	−	0.425482i
$767$	0.364745	−	1.12257i	0.0131702	−	0.0405337i
$768$	−1.80902	−	1.31433i	−0.0652773	−	0.0474267i
$769$	48.7082			1.75646			0.878231	−	0.478236i	$-0.158724\pi$
$769$	48.7082			1.75646			0.878231	+	0.478236i	$0.158724\pi$
$770$	−13.6631	−	15.5272i	−0.492385	−	0.559561i
$771$	−20.8541			−0.751042
$772$	4.39919	+	3.19620i	0.158330	+	0.115034i
$773$	13.4443	−	41.3772i	0.483557	−	1.48823i	−0.350503	−	0.936561i	$-0.613989\pi$
$773$	13.4443	−	41.3772i	0.483557	−	1.48823i	0.834060	−	0.551673i	$-0.186011\pi$
$774$	−6.00000	−	18.4661i	−0.215666	−	0.663750i
$775$	5.21885	−	3.79171i	0.187467	−	0.136202i
$776$	8.42705	−	6.12261i	0.302514	−	0.219789i
$777$	3.05166	+	9.39205i	0.109478	+	0.336938i
$778$	−9.29180	+	28.5972i	−0.333127	+	1.02526i
$779$	5.73607	+	4.16750i	0.205516	+	0.149316i
$780$	2.23607			0.0800641
$781$	−13.9271	+	23.4989i	−0.498349	+	0.840857i
$782$	−7.47214			−0.267203
$783$	−2.76393	−	2.00811i	−0.0987749	−	0.0717641i
$784$	2.42705	−	7.46969i	0.0866804	−	0.266775i
$785$	−4.85410	−	14.9394i	−0.173250	−	0.533210i
$786$	−26.5066	+	19.2582i	−0.945458	+	0.686916i
$787$	15.8541	−	11.5187i	0.565138	−	0.410597i	−0.268198	−	0.963364i	$-0.586428\pi$
$787$	15.8541	−	11.5187i	0.565138	−	0.410597i	0.833336	+	0.552767i	$0.186428\pi$
$788$	7.16312	+	22.0458i	0.255176	+	0.785350i
$789$	11.0795	−	34.0993i	0.394442	−	1.21397i
$790$	3.92705	+	2.85317i	0.139718	+	0.101511i
$791$	40.1459			1.42742
$792$	3.38197	−	5.70634i	0.120173	−	0.202766i
$793$	4.09017			0.145246
$794$	19.2812	+	14.0086i	0.684263	+	0.497146i
$795$	13.3541	−	41.0997i	0.473621	−	1.45766i
$796$	4.29180	+	13.2088i	0.152119	+	0.468173i
$797$	−28.1525	+	20.4540i	−0.997212	+	0.724517i	−0.961489	−	0.274845i	$-0.911373\pi$
$797$	−28.1525	+	20.4540i	−0.997212	+	0.724517i	−0.0357233	+	0.999362i	$0.511373\pi$
$798$	6.97214	−	5.06555i	0.246811	−	0.179319i
$799$	−1.37790	−	4.24074i	−0.0487466	−	0.150027i
$800$	−0.736068	+	2.26538i	−0.0260239	+	0.0800934i
$801$	−21.3262	−	15.4944i	−0.753526	−	0.547468i
$802$	−20.5279			−0.724864
$803$	31.3885	+	35.6709i	1.10768	+	1.25880i
$804$	11.3820			0.401411
$805$	−21.3713	−	15.5272i	−0.753240	−	0.547261i
$806$	−0.517221	+	1.59184i	−0.0182183	+	0.0560703i
$807$	6.94834	+	21.3848i	0.244593	+	0.752780i
$808$	7.66312	−	5.56758i	0.269588	−	0.195867i
$809$	−2.47214	+	1.79611i	−0.0869157	+	0.0631479i	−0.630394	−	0.776275i	$-0.717107\pi$
$809$	−2.47214	+	1.79611i	−0.0869157	+	0.0631479i	0.543479	+	0.839423i	$0.317107\pi$
$810$	5.50000	+	16.9273i	0.193250	+	0.594763i
$811$	14.0689	−	43.2996i	0.494025	−	1.52045i	−0.324445	−	0.945905i	$-0.605177\pi$
$811$	14.0689	−	43.2996i	0.494025	−	1.52045i	0.818470	−	0.574549i	$-0.194823\pi$
$812$	−4.76393	−	3.46120i	−0.167181	−	0.121464i
$813$	12.7639			0.447651
$814$	−0.354102	−	3.78398i	−0.0124113	−	0.132628i
$815$	−38.8885			−1.36221
$816$	3.19098	+	2.31838i	0.111707	+	0.0811597i
$817$	−3.00000	+	9.23305i	−0.104957	+	0.323024i
$818$	−0.927051	−	2.85317i	−0.0324136	−	0.0997587i
$819$	−3.85410	+	2.80017i	−0.134673	+	0.0978458i
$820$	−9.28115	+	6.74315i	−0.324112	+	0.235481i
$821$	6.35410	+	19.5559i	0.221760	+	0.682506i	0.998604	+	0.0528139i	$0.0168190\pi$
$821$	6.35410	+	19.5559i	0.221760	+	0.682506i	−0.776845	+	0.629692i	$0.783181\pi$
$822$	−5.16312	+	15.8904i	−0.180084	+	0.554243i
$823$	17.1803	+	12.4822i	0.598869	+	0.435104i	0.845477	−	0.534011i	$-0.179316\pi$
$823$	17.1803	+	12.4822i	0.598869	+	0.435104i	−0.246608	+	0.969115i	$0.579316\pi$
$824$	11.5623			0.402792
$825$	−17.2361	−	3.86974i	−0.600083	−	0.134727i
$826$	7.36068			0.256111
$827$	−42.7148	−	31.0341i	−1.48534	−	1.07916i	−0.975787	−	0.218721i	$-0.929811\pi$
$827$	−42.7148	−	31.0341i	−1.48534	−	1.07916i	−0.509551	−	0.860440i	$-0.670189\pi$
$828$	2.61803	−	8.05748i	0.0909830	−	0.280017i
$829$	−3.81966	−	11.7557i	−0.132662	−	0.408293i	0.862557	−	0.505960i	$-0.168862\pi$
$829$	−3.81966	−	11.7557i	−0.132662	−	0.408293i	−0.995219	+	0.0976677i	$0.968862\pi$
$830$	−13.2082	+	9.59632i	−0.458463	+	0.333093i
$831$	11.1180	−	8.07772i	0.385680	−	0.280213i
$832$	−0.190983	−	0.587785i	−0.00662114	−	0.0203778i
$833$	−4.28115	+	13.1760i	−0.148333	+	0.456523i
$834$	−3.35410	−	2.43690i	−0.116143	−	0.0843829i
$835$	17.1803			0.594550
$836$	−3.04508	+	1.31433i	−0.105316	+	0.0454570i
$837$	−6.05573			−0.209317
$838$	−3.70820	−	2.69417i	−0.128098	−	0.0930685i
$839$	−13.0279	+	40.0956i	−0.449772	+	1.38426i	0.427393	+	0.904066i	$0.359432\pi$
$839$	−13.0279	+	40.0956i	−0.449772	+	1.38426i	−0.877165	+	0.480189i	$0.840568\pi$
$840$	4.30902	+	13.2618i	0.148675	+	0.457575i
$841$	21.5729	−	15.6737i	0.743895	−	0.540471i
$842$	−13.2812	+	9.64932i	−0.457699	+	0.332538i
$843$	19.3713	+	59.6188i	0.667184	+	2.05338i
$844$	−8.01722	+	24.6745i	−0.275964	+	0.849330i
$845$	−16.5172	−	12.0005i	−0.568210	−	0.412828i
$846$	5.05573			0.173820
$847$	−38.3262	−	18.1231i	−1.31691	−	0.622716i
$848$	−11.9443			−0.410168
$849$	33.8435	+	24.5887i	1.16150	+	0.843882i
$850$	1.29837	−	3.99598i	0.0445339	−	0.137061i
$851$	−1.50000	−	4.61653i	−0.0514193	−	0.158252i
$852$	14.8992	−	10.8249i	0.510438	−	0.370855i
$853$	−1.11803	+	0.812299i	−0.0382808	+	0.0278126i	−0.606761	−	0.794884i	$-0.707532\pi$
$853$	−1.11803	+	0.812299i	−0.0382808	+	0.0278126i	0.568480	+	0.822697i	$0.307532\pi$
$854$	7.88197	+	24.2582i	0.269715	+	0.830098i
$855$	−1.00000	+	3.07768i	−0.0341993	+	0.105255i
$856$	−2.42705	−	1.76336i	−0.0829549	−	0.0602703i
$857$	34.0902			1.16450			0.582249	−	0.813011i	$-0.302173\pi$
$857$	34.0902			1.16450			0.582249	+	0.813011i	$0.302173\pi$
$858$	4.20820	−	1.81636i	0.143666	−	0.0620094i
$859$	−11.4721			−0.391424			−0.195712	−	0.980661i	$-0.562702\pi$
$859$	−11.4721			−0.391424			−0.195712	+	0.980661i	$0.562702\pi$
$860$	−12.7082	−	9.23305i	−0.433346	−	0.314844i
$861$	18.8820	−	58.1127i	0.643496	−	1.98048i
$862$	0.628677	+	1.93487i	0.0214128	+	0.0659019i
$863$	6.32624	−	4.59628i	0.215348	−	0.156459i	−0.474882	−	0.880049i	$-0.657509\pi$
$863$	6.32624	−	4.59628i	0.215348	−	0.156459i	0.690230	+	0.723590i	$0.257509\pi$
$864$	1.80902	−	1.31433i	0.0615440	−	0.0447143i
$865$	7.89919	+	24.3112i	0.268580	+	0.826606i
$866$	−7.27051	+	22.3763i	−0.247062	+	0.760379i
$867$	25.1246	+	18.2541i	0.853277	+	0.619942i
$868$	−10.4377			−0.354278
$869$	9.70820	+	2.17963i	0.329328	+	0.0739388i
$870$	5.52786			0.187412
$871$	2.54508	+	1.84911i	0.0862369	+	0.0626548i
$872$	−1.64590	+	5.06555i	−0.0557371	+	0.171541i
$873$	−6.43769	−	19.8132i	−0.217883	−	0.670575i
$874$	−3.42705	+	2.48990i	−0.115922	+	0.0842221i
$875$	37.2426	−	27.0584i	1.25903	−	0.914740i
$876$	−9.89919	−	30.4666i	−0.334463	−	1.02937i
$877$	1.08359	−	3.33495i	0.0365903	−	0.112613i	−0.931093	−	0.364782i	$-0.881144\pi$
$877$	1.08359	−	3.33495i	0.0365903	−	0.112613i	0.967683	+	0.252168i	$0.0811436\pi$
$878$	−16.2984	−	11.8415i	−0.550043	−	0.399630i
$879$	43.5410			1.46860
$880$	−0.500000	−	5.34307i	−0.0168550	−	0.180115i
$881$	−40.9443			−1.37945			−0.689724	−	0.724073i	$-0.742268\pi$
$881$	−40.9443			−1.37945			−0.689724	+	0.724073i	$0.742268\pi$
$882$	−12.7082	−	9.23305i	−0.427907	−	0.310893i
$883$	−16.8541	+	51.8716i	−0.567186	+	1.74562i	0.0941808	+	0.995555i	$0.469977\pi$
$883$	−16.8541	+	51.8716i	−0.567186	+	1.74562i	−0.661366	+	0.750063i	$0.730023\pi$
$884$	0.336881	+	1.03681i	0.0113305	+	0.0348718i
$885$	−5.59017	+	4.06150i	−0.187912	+	0.136526i
$886$	3.92705	−	2.85317i	0.131932	−	0.0958541i
$887$	1.42047	+	4.37177i	0.0476948	+	0.146790i	0.972068	−	0.234701i	$-0.0754110\pi$
$887$	1.42047	+	4.37177i	0.0476948	+	0.146790i	−0.924373	+	0.381490i	$0.875411\pi$
$888$	−0.791796	+	2.43690i	−0.0265709	+	0.0817769i
$889$	9.91641	+	7.20469i	0.332586	+	0.241638i
$890$	−21.3262			−0.714857
$891$	24.1008	+	27.3889i	0.807408	+	0.917562i
$892$	−20.0000			−0.669650
$893$	−2.04508	−	1.48584i	−0.0684362	−	0.0497218i
$894$	15.3647	−	47.2878i	0.513874	−	1.58154i
$895$	6.38197	+	19.6417i	0.213326	+	0.656549i
$896$	3.11803	−	2.26538i	0.104166	−	0.0756812i
$897$	4.73607	−	3.44095i	0.158133	−	0.114890i
$898$	−0.218847	−	0.673542i	−0.00730302	−	0.0224764i
$899$	−1.27864	+	3.93525i	−0.0426450	+	0.131248i
$900$	3.85410	+	2.80017i	0.128470	+	0.0933390i
$901$	21.0689			0.701906
$902$	−11.9894	+	20.2295i	−0.399202	+	0.673567i
$903$	83.6656			2.78422
$904$	8.42705	+	6.12261i	0.280280	+	0.203635i
$905$	−10.9721	+	33.7688i	−0.364726	+	1.12251i
$906$	9.47214	+	29.1522i	0.314691	+	0.968518i
$907$	46.8050	−	34.0058i	1.55413	−	1.12914i	0.613512	−	0.789686i	$-0.289756\pi$
$907$	46.8050	−	34.0058i	1.55413	−	1.12914i	0.940621	−	0.339458i	$-0.110244\pi$
$908$	12.9721	−	9.42481i	0.430495	−	0.312773i
$909$	−5.85410	−	18.0171i	−0.194168	−	0.597589i
$910$	−1.19098	+	3.66547i	−0.0394807	+	0.121509i
$911$	19.7082	+	14.3188i	0.652962	+	0.474405i	0.864279	−	0.503013i	$-0.167775\pi$
$911$	19.7082	+	14.3188i	0.652962	+	0.474405i	−0.211317	+	0.977418i	$0.567775\pi$
$912$	2.23607			0.0740436
$913$	−17.0623	+	28.7890i	−0.564680	+	0.952776i
$914$	9.00000			0.297694
$915$	−19.3713	−	14.0741i	−0.640396	−	0.465275i
$916$	7.59017	−	23.3601i	0.250786	−	0.771841i
$917$	−17.4508	−	53.7082i	−0.576278	−	1.77360i
$918$	−3.19098	+	2.31838i	−0.105318	+	0.0765181i
$919$	8.42705	−	6.12261i	0.277983	−	0.201966i	−0.440054	−	0.897971i	$-0.645041\pi$
$919$	8.42705	−	6.12261i	0.277983	−	0.201966i	0.718037	+	0.696005i	$0.245041\pi$
$920$	−2.11803	−	6.51864i	−0.0698295	−	0.214913i
$921$	−9.51064	+	29.2707i	−0.313386	+	0.964504i
$922$	−24.5172	−	17.8128i	−0.807432	−	0.586633i
$923$	5.09017			0.167545
$924$	18.8820	+	21.4580i	0.621171	+	0.705917i
$925$	2.72949			0.0897451
$926$	18.4894	+	13.4333i	0.607598	+	0.441446i
$927$	7.14590	−	21.9928i	0.234702	−	0.722339i
$928$	−0.472136	−	1.45309i	−0.0154986	−	0.0476999i
$929$	−9.75329	+	7.08618i	−0.319995	+	0.232490i	−0.736173	−	0.676793i	$-0.763369\pi$
$929$	−9.75329	+	7.08618i	−0.319995	+	0.232490i	0.416178	+	0.909283i	$0.363369\pi$
$930$	7.92705	−	5.75934i	0.259938	−	0.188856i
$931$	2.42705	+	7.46969i	0.0795434	+	0.244809i
$932$	7.30902	−	22.4948i	0.239415	−	0.736843i
$933$	−13.6180	−	9.89408i	−0.445834	−	0.323918i
$934$	21.5066			0.703717
$935$	0.881966	+	9.42481i	0.0288434	+	0.308224i
$936$	−1.23607			−0.0404021
$937$	−7.85410	−	5.70634i	−0.256582	−	0.186418i	0.452057	−	0.891989i	$-0.350690\pi$
$937$	−7.85410	−	5.70634i	−0.256582	−	0.186418i	−0.708639	+	0.705571i	$0.750690\pi$
$938$	−6.06231	+	18.6579i	−0.197941	+	0.609201i
$939$	−5.48936	−	16.8945i	−0.179138	−	0.551331i
$940$	3.30902	−	2.40414i	0.107928	−	0.0784145i
$941$	−17.8435	+	12.9640i	−0.581680	+	0.422615i	−0.839329	−	0.543623i	$-0.817052\pi$
$941$	−17.8435	+	12.9640i	−0.581680	+	0.422615i	0.257649	+	0.966239i	$0.417052\pi$
$942$	6.70820	+	20.6457i	0.218565	+	0.672674i
$943$	−9.28115	+	28.5645i	−0.302236	+	0.930187i
$944$	1.54508	+	1.12257i	0.0502882	+	0.0365365i
$945$	−13.9443			−0.453607
$946$	−31.4164	−	7.05342i	−1.02144	−	0.229327i
$947$	−11.9443			−0.388137			−0.194068	−	0.980988i	$-0.562168\pi$
$947$	−11.9443			−0.388137			−0.194068	+	0.980988i	$0.562168\pi$
$948$	−5.42705	−	3.94298i	−0.176262	−	0.128062i
$949$	2.73607	−	8.42075i	0.0888165	−	0.273349i
$950$	−0.736068	−	2.26538i	−0.0238812	−	0.0734988i
$951$	5.42705	−	3.94298i	0.175984	−	0.127860i
$952$	−5.50000	+	3.99598i	−0.178256	+	0.129511i
$953$	3.72949	+	11.4782i	0.120810	+	0.371815i	0.993114	−	0.117148i	$-0.0373752\pi$
$953$	3.72949	+	11.4782i	0.120810	+	0.371815i	−0.872304	+	0.488963i	$0.837375\pi$
$954$	−7.38197	+	22.7194i	−0.239000	+	0.735566i
$955$	−2.54508	−	1.84911i	−0.0823570	−	0.0598359i
$956$	−24.9787			−0.807869
$957$	10.4033	−	4.49028i	0.336289	−	0.145150i
$958$	−3.76393			−0.121607
$959$	−23.2984	−	16.9273i	−0.752344	−	0.546610i
$960$	−1.11803	+	3.44095i	−0.0360844	+	0.111056i
$961$	−7.31308	−	22.5074i	−0.235906	−	0.726044i
$962$	−0.572949	+	0.416272i	−0.0184726	+	0.0134211i
$963$	−4.85410	+	3.52671i	−0.156421	+	0.113647i
$964$	2.57295	+	7.91872i	0.0828691	+	0.255045i
$965$	2.71885	−	8.36775i	0.0875228	−	0.269367i
$966$	29.5344	+	21.4580i	0.950255	+	0.690401i
$967$	19.3951			0.623705			0.311853	−	0.950131i	$-0.399051\pi$
$967$	19.3951			0.623705			0.311853	+	0.950131i	$0.399051\pi$
$968$	−5.28115	−	9.64932i	−0.169743	−	0.310141i
$969$	−3.94427			−0.126708
$970$	−13.6353	−	9.90659i	−0.437802	−	0.318082i
$971$	−2.77051	+	8.52675i	−0.0889099	+	0.273637i	−0.985619	−	0.168984i	$-0.945951\pi$
$971$	−2.77051	+	8.52675i	−0.0889099	+	0.273637i	0.896709	+	0.442621i	$0.145951\pi$
$972$	−5.52786	−	17.0130i	−0.177306	−	0.545693i
$973$	5.78115	−	4.20025i	0.185335	−	0.134654i
$974$	−12.8992	+	9.37181i	−0.413317	+	0.300292i
$975$	1.01722	+	3.13068i	0.0325771	+	0.100262i
$976$	−2.04508	+	6.29412i	−0.0654616	+	0.201470i
$977$	22.3262	+	16.2210i	0.714280	+	0.518955i	0.884551	−	0.466443i	$-0.154465\pi$
$977$	22.3262	+	16.2210i	0.714280	+	0.518955i	−0.170272	+	0.985397i	$0.554465\pi$
$978$	53.7426			1.71850
$979$	−40.1353	+	17.3233i	−1.28273	+	0.553655i
$980$	−12.7082			−0.405949
$981$	8.61803	+	6.26137i	0.275153	+	0.199910i
$982$	−6.84346	+	21.0620i	−0.218384	+	0.672115i
$983$	15.0000	+	46.1653i	0.478426	+	1.47244i	0.841281	+	0.540598i	$0.181802\pi$
$983$	15.0000	+	46.1653i	0.478426	+	1.47244i	−0.362856	+	0.931845i	$0.618198\pi$
$984$	12.8262	−	9.31881i	0.408886	−	0.297073i
$985$	30.3435	−	22.0458i	0.966823	−	0.702438i
$986$	0.832816	+	2.56314i	0.0265223	+	0.0816271i
$987$	−6.73200	+	20.7190i	−0.214282	+	0.659492i
$988$	0.500000	+	0.363271i	0.0159071	+	0.0115572i
$989$	−41.1246			−1.30769
$990$	−10.4721	−	2.35114i	−0.332826	−	0.0747242i
$991$	53.8328			1.71006			0.855028	−	0.518582i	$-0.173540\pi$
$991$	53.8328			1.71006			0.855028	+	0.518582i	$0.173540\pi$
$992$	−2.19098	−	1.59184i	−0.0695638	−	0.0505410i
$993$	−2.56231	+	7.88597i	−0.0813123	+	0.250254i
$994$	9.80902	+	30.1891i	0.311123	+	0.957539i
$995$	18.1803	−	13.2088i	0.576356	−	0.418747i
$996$	18.2533	−	13.2618i	0.578378	−	0.420216i
$997$	5.72542	+	17.6210i	0.181326	+	0.558064i	0.999866	−	0.0163858i	$-0.00521600\pi$
$997$	5.72542	+	17.6210i	0.181326	+	0.558064i	−0.818540	+	0.574450i	$0.805216\pi$
$998$	9.57953	−	29.4828i	0.303235	−	0.933260i
$999$	−2.07295	−	1.50609i	−0.0655852	−	0.0476504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.e.191.1	✓	4
11.3	even	5	inner	418.2.f.e.267.1	yes	4
11.5	even	5		4598.2.a.bi.1.2		2
11.6	odd	10		4598.2.a.ba.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.e.191.1	✓	4	1.1	even	1	trivial
418.2.f.e.267.1	yes	4	11.3	even	5	inner
4598.2.a.ba.1.2		2	11.6	odd	10
4598.2.a.bi.1.2		2	11.5	even	5

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.690983 - 2.12663i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.30902 - 0.951057i) q^{5} +(-1.80902 + 1.31433i) q^{6} +(-1.19098 - 3.66547i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.61803 - 1.17557i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.690983 - 2.12663i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.30902 - 0.951057i) q^{5} +(-1.80902 + 1.31433i) q^{6} +(-1.19098 - 3.66547i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.61803 - 1.17557i) q^{9} -1.61803 q^{10} +(-3.04508 + 1.31433i) q^{11} +2.23607 q^{12} +(0.500000 + 0.363271i) q^{13} +(-1.19098 + 3.66547i) q^{14} +(-1.11803 - 3.44095i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.42705 - 1.03681i) q^{17} +(0.618034 + 1.90211i) q^{18} +(0.309017 - 0.951057i) q^{19} +(1.30902 + 0.951057i) q^{20} -8.61803 q^{21} +(3.23607 + 0.726543i) q^{22} +4.23607 q^{23} +(-1.80902 - 1.31433i) q^{24} +(-0.736068 + 2.26538i) q^{25} +(-0.190983 - 0.587785i) q^{26} +(1.80902 - 1.31433i) q^{27} +(3.11803 - 2.26538i) q^{28} +(-0.472136 - 1.45309i) q^{29} +(-1.11803 + 3.44095i) q^{30} +(-2.19098 - 1.59184i) q^{31} +1.00000 q^{32} +(0.690983 + 7.38394i) q^{33} -1.76393 q^{34} +(-5.04508 - 3.66547i) q^{35} +(0.618034 - 1.90211i) q^{36} +(-0.354102 - 1.08981i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(1.11803 - 0.812299i) q^{39} +(-0.500000 - 1.53884i) q^{40} +(-2.19098 + 6.74315i) q^{41} +(6.97214 + 5.06555i) q^{42} -9.70820 q^{43} +(-2.19098 - 2.48990i) q^{44} -3.23607 q^{45} +(-3.42705 - 2.48990i) q^{46} +(0.781153 - 2.40414i) q^{47} +(0.690983 + 2.12663i) q^{48} +(-6.35410 + 4.61653i) q^{49} +(1.92705 - 1.40008i) q^{50} +(-1.21885 - 3.75123i) q^{51} +(-0.190983 + 0.587785i) q^{52} +(9.66312 + 7.02067i) q^{53} -2.23607 q^{54} +(-2.73607 + 4.61653i) q^{55} -3.85410 q^{56} +(-1.80902 - 1.31433i) q^{57} +(-0.472136 + 1.45309i) q^{58} +(-0.590170 - 1.81636i) q^{59} +(2.92705 - 2.12663i) q^{60} +(5.35410 - 3.88998i) q^{61} +(0.836881 + 2.57565i) q^{62} +(-2.38197 + 7.33094i) q^{63} +(-0.809017 - 0.587785i) q^{64} +1.00000 q^{65} +(3.78115 - 6.37988i) q^{66} +5.09017 q^{67} +(1.42705 + 1.03681i) q^{68} +(2.92705 - 9.00854i) q^{69} +(1.92705 + 5.93085i) q^{70} +(6.66312 - 4.84104i) q^{71} +(-1.61803 + 1.17557i) q^{72} +(-4.42705 - 13.6251i) q^{73} +(-0.354102 + 1.08981i) q^{74} +(4.30902 + 3.13068i) q^{75} +1.00000 q^{76} +(8.44427 + 9.59632i) q^{77} -1.38197 q^{78} +(-2.42705 - 1.76336i) q^{79} +(-0.500000 + 1.53884i) q^{80} +(-3.39919 - 10.4616i) q^{81} +(5.73607 - 4.16750i) q^{82} +(8.16312 - 5.93085i) q^{83} +(-2.66312 - 8.19624i) q^{84} +(0.881966 - 2.71441i) q^{85} +(7.85410 + 5.70634i) q^{86} -3.41641 q^{87} +(0.309017 + 3.30220i) q^{88} +13.1803 q^{89} +(2.61803 + 1.90211i) q^{90} +(0.736068 - 2.26538i) q^{91} +(1.30902 + 4.02874i) q^{92} +(-4.89919 + 3.55947i) q^{93} +(-2.04508 + 1.48584i) q^{94} +(-0.500000 - 1.53884i) q^{95} +(0.690983 - 2.12663i) q^{96} +(8.42705 + 6.12261i) q^{97} +7.85410 q^{98} +(6.47214 + 1.45309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 5 q^{3} - q^{4} + 3 q^{5} - 5 q^{6} - 7 q^{7} - q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - q^2 + 5 * q^3 - q^4 + 3 * q^5 - 5 * q^6 - 7 * q^7 - q^8 - 2 * q^9	\( 4 q - q^{2} + 5 q^{3} - q^{4} + 3 q^{5} - 5 q^{6} - 7 q^{7} - q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + 2 q^{13} - 7 q^{14} - q^{16} - q^{17} - 2 q^{18} - q^{19} + 3 q^{20} - 30 q^{21} + 4 q^{22} + 8 q^{23} - 5 q^{24} + 6 q^{25} - 3 q^{26} + 5 q^{27} + 8 q^{28} + 16 q^{29} - 11 q^{31} + 4 q^{32} + 5 q^{33} - 16 q^{34} - 9 q^{35} - 2 q^{36} + 12 q^{37} - q^{38} - 2 q^{40} - 11 q^{41} + 10 q^{42} - 12 q^{43} - 11 q^{44} - 4 q^{45} - 7 q^{46} - 17 q^{47} + 5 q^{48} - 12 q^{49} + q^{50} - 25 q^{51} - 3 q^{52} + 23 q^{53} - 2 q^{55} - 2 q^{56} - 5 q^{57} + 16 q^{58} + 20 q^{59} + 5 q^{60} + 8 q^{61} + 19 q^{62} - 14 q^{63} - q^{64} + 4 q^{65} - 5 q^{66} - 2 q^{67} - q^{68} + 5 q^{69} + q^{70} + 11 q^{71} - 2 q^{72} - 11 q^{73} + 12 q^{74} + 15 q^{75} + 4 q^{76} - 2 q^{77} - 10 q^{78} - 3 q^{79} - 2 q^{80} + 11 q^{81} + 14 q^{82} + 17 q^{83} + 5 q^{84} + 8 q^{85} + 18 q^{86} + 40 q^{87} - q^{88} + 8 q^{89} + 6 q^{90} - 6 q^{91} + 3 q^{92} + 5 q^{93} + 3 q^{94} - 2 q^{95} + 5 q^{96} + 27 q^{97} + 18 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q - q^2 + 5 * q^3 - q^4 + 3 * q^5 - 5 * q^6 - 7 * q^7 - q^8 - 2 * q^9 - 2 * q^10 - q^11 + 2 * q^13 - 7 * q^14 - q^16 - q^17 - 2 * q^18 - q^19 + 3 * q^20 - 30 * q^21 + 4 * q^22 + 8 * q^23 - 5 * q^24 + 6 * q^25 - 3 * q^26 + 5 * q^27 + 8 * q^28 + 16 * q^29 - 11 * q^31 + 4 * q^32 + 5 * q^33 - 16 * q^34 - 9 * q^35 - 2 * q^36 + 12 * q^37 - q^38 - 2 * q^40 - 11 * q^41 + 10 * q^42 - 12 * q^43 - 11 * q^44 - 4 * q^45 - 7 * q^46 - 17 * q^47 + 5 * q^48 - 12 * q^49 + q^50 - 25 * q^51 - 3 * q^52 + 23 * q^53 - 2 * q^55 - 2 * q^56 - 5 * q^57 + 16 * q^58 + 20 * q^59 + 5 * q^60 + 8 * q^61 + 19 * q^62 - 14 * q^63 - q^64 + 4 * q^65 - 5 * q^66 - 2 * q^67 - q^68 + 5 * q^69 + q^70 + 11 * q^71 - 2 * q^72 - 11 * q^73 + 12 * q^74 + 15 * q^75 + 4 * q^76 - 2 * q^77 - 10 * q^78 - 3 * q^79 - 2 * q^80 + 11 * q^81 + 14 * q^82 + 17 * q^83 + 5 * q^84 + 8 * q^85 + 18 * q^86 + 40 * q^87 - q^88 + 8 * q^89 + 6 * q^90 - 6 * q^91 + 3 * q^92 + 5 * q^93 + 3 * q^94 - 2 * q^95 + 5 * q^96 + 27 * q^97 + 18 * q^98 + 8 * q^99

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