LMFDB - Embedded newform 585.2.i.e.391.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.4
Root			$0.172467 + 1.52157i$ of defining polynomial
Character	$\chi$	$=$	585.391
Dual form			585.2.i.e.196.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327533 - 0.567303i) q^{2} +(0.997116 + 1.41625i) q^{3} +(0.785445 - 1.36043i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.476854 - 1.02954i) q^{6} +(0.388592 + 0.673061i) q^{7} -2.33917 q^{8} +(-1.01152 + 2.82433i) q^{9} +O(q^{10})$	\(q+(-0.327533 - 0.567303i) q^{2} +(0.997116 + 1.41625i) q^{3} +(0.785445 - 1.36043i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.476854 - 1.02954i) q^{6} +(0.388592 + 0.673061i) q^{7} -2.33917 q^{8} +(-1.01152 + 2.82433i) q^{9} -0.655066 q^{10} +(2.03399 + 3.52297i) q^{11} +(2.70989 - 0.244122i) q^{12} +(0.500000 - 0.866025i) q^{13} +(0.254553 - 0.440899i) q^{14} +(1.72507 - 0.155404i) q^{15} +(-0.804735 - 1.39384i) q^{16} +5.29154 q^{17} +(1.93356 - 0.351222i) q^{18} +6.65042 q^{19} +(-0.785445 - 1.36043i) q^{20} +(-0.565750 + 1.22146i) q^{21} +(1.33239 - 2.30778i) q^{22} +(-1.15283 + 1.99677i) q^{23} +(-2.33242 - 3.31284i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.655066 q^{26} +(-5.00855 + 1.38362i) q^{27} +1.22087 q^{28} +(-3.19008 - 5.52538i) q^{29} +(-0.653176 - 0.927736i) q^{30} +(4.47259 - 7.74675i) q^{31} +(-2.86632 + 4.96461i) q^{32} +(-2.96128 + 6.39344i) q^{33} +(-1.73315 - 3.00191i) q^{34} +0.777184 q^{35} +(3.04781 + 3.59445i) q^{36} -2.80592 q^{37} +(-2.17823 - 3.77280i) q^{38} +(1.72507 - 0.155404i) q^{39} +(-1.16958 + 2.02578i) q^{40} +(-3.80493 + 6.59034i) q^{41} +(0.878241 - 0.0791169i) q^{42} +(-4.42183 - 7.65883i) q^{43} +6.39034 q^{44} +(1.94018 + 2.28817i) q^{45} +1.51036 q^{46} +(2.04391 + 3.54016i) q^{47} +(1.17161 - 2.52953i) q^{48} +(3.19799 - 5.53909i) q^{49} +(-0.327533 + 0.567303i) q^{50} +(5.27628 + 7.49413i) q^{51} +(-0.785445 - 1.36043i) q^{52} -4.78025 q^{53} +(2.42540 + 2.38819i) q^{54} +4.06797 q^{55} +(-0.908981 - 1.57440i) q^{56} +(6.63124 + 9.41864i) q^{57} +(-2.08971 + 3.61949i) q^{58} +(2.37049 - 4.10581i) q^{59} +(1.14353 - 2.46889i) q^{60} +(7.18299 + 12.4413i) q^{61} -5.85967 q^{62} +(-2.29401 + 0.416697i) q^{63} +0.536314 q^{64} +(-0.500000 - 0.866025i) q^{65} +(4.59693 - 0.414118i) q^{66} +(-5.39353 + 9.34188i) q^{67} +(4.15621 - 7.19877i) q^{68} +(-3.97743 + 0.358309i) q^{69} +(-0.254553 - 0.440899i) q^{70} +0.307776 q^{71} +(2.36611 - 6.60657i) q^{72} -7.50636 q^{73} +(0.919032 + 1.59181i) q^{74} +(0.727949 - 1.57165i) q^{75} +(5.22353 - 9.04743i) q^{76} +(-1.58078 + 2.73799i) q^{77} +(-0.653176 - 0.927736i) q^{78} +(-3.80949 - 6.59822i) q^{79} -1.60947 q^{80} +(-6.95366 - 5.71372i) q^{81} +4.98496 q^{82} +(6.26484 + 10.8510i) q^{83} +(1.21735 + 1.72905i) q^{84} +(2.64577 - 4.58261i) q^{85} +(-2.89659 + 5.01704i) q^{86} +(4.64443 - 10.0274i) q^{87} +(-4.75783 - 8.24081i) q^{88} -11.7743 q^{89} +(0.662611 - 1.85012i) q^{90} +0.777184 q^{91} +(1.81098 + 3.13670i) q^{92} +(15.4310 - 1.39011i) q^{93} +(1.33889 - 2.31903i) q^{94} +(3.32521 - 5.75943i) q^{95} +(-9.88918 + 0.890873i) q^{96} +(3.04268 + 5.27007i) q^{97} -4.18979 q^{98} +(-12.0074 + 2.18109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.327533	−	0.567303i	−0.231601	−	0.401144i	0.726679	−	0.686978i	$-0.241063\pi$
$2$	−0.327533	−	0.567303i	−0.231601	−	0.401144i	−0.958279	+	0.285833i	$0.907730\pi$
$3$	0.997116	+	1.41625i	0.575685	+	0.817671i
$3$	0.997116	+	1.41625i	0.575685	+	0.817671i
$4$	0.785445	−	1.36043i	0.392722	−	0.680215i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.476854	−	1.02954i	0.194675	−	0.420306i
$7$	0.388592	+	0.673061i	0.146874	+	0.254393i	0.930071	−	0.367381i	$-0.119746\pi$
$7$	0.388592	+	0.673061i	0.146874	+	0.254393i	−0.783197	+	0.621774i	$0.786412\pi$
$8$	−2.33917			−0.827020
$9$	−1.01152	+	2.82433i	−0.337173	+	0.941443i
$10$	−0.655066			−0.207150
$11$	2.03399	+	3.52297i	0.613270	+	1.06221i	0.990685	+	0.136171i	$0.0434796\pi$
$11$	2.03399	+	3.52297i	0.613270	+	1.06221i	−0.377415	+	0.926044i	$0.623187\pi$
$12$	2.70989	−	0.244122i	0.782277	−	0.0704719i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	0.254553	−	0.440899i	0.0680322	−	0.117835i
$15$	1.72507	−	0.155404i	0.445410	−	0.0401250i
$16$	−0.804735	−	1.39384i	−0.201184	−	0.348461i
$17$	5.29154			1.28339			0.641693	−	0.766961i	$-0.278232\pi$
$17$	5.29154			1.28339			0.641693	+	0.766961i	$0.278232\pi$
$18$	1.93356	−	0.351222i	0.455744	−	0.0827837i
$19$	6.65042			1.52571			0.762855	−	0.646569i	$-0.223797\pi$
$19$	6.65042			1.52571			0.762855	+	0.646569i	$0.223797\pi$
$20$	−0.785445	−	1.36043i	−0.175631	−	0.304201i
$21$	−0.565750	+	1.22146i	−0.123457	+	0.266545i
$22$	1.33239	−	2.30778i	0.284067	−	0.492019i
$23$	−1.15283	+	1.99677i	−0.240383	+	0.416355i	−0.960823	−	0.277162i	$-0.910606\pi$
$23$	−1.15283	+	1.99677i	−0.240383	+	0.416355i	0.720441	+	0.693517i	$0.243940\pi$
$24$	−2.33242	−	3.31284i	−0.476103	−	0.676231i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.655066			−0.128469
$27$	−5.00855	+	1.38362i	−0.963896	+	0.266278i
$28$	1.22087			0.230723
$29$	−3.19008	−	5.52538i	−0.592383	−	1.02604i	−0.993910	−	0.110190i	$-0.964854\pi$
$29$	−3.19008	−	5.52538i	−0.592383	−	1.02604i	0.401527	−	0.915847i	$-0.368479\pi$
$30$	−0.653176	−	0.927736i	−0.119253	−	0.169381i
$31$	4.47259	−	7.74675i	0.803300	−	1.39136i	−0.114132	−	0.993466i	$-0.536409\pi$
$31$	4.47259	−	7.74675i	0.803300	−	1.39136i	0.917433	−	0.397891i	$-0.130258\pi$
$32$	−2.86632	+	4.96461i	−0.506699	+	0.877628i
$33$	−2.96128	+	6.39344i	−0.515492	+	1.11295i
$34$	−1.73315	−	3.00191i	−0.297233	−	0.514823i
$35$	0.777184			0.131368
$36$	3.04781	+	3.59445i	0.507968	+	0.599076i
$37$	−2.80592			−0.461291			−0.230645	−	0.973038i	$-0.574084\pi$
$37$	−2.80592			−0.461291			−0.230645	+	0.973038i	$0.574084\pi$
$38$	−2.17823	−	3.77280i	−0.353355	−	0.612030i
$39$	1.72507	−	0.155404i	0.276231	−	0.0248845i
$40$	−1.16958	+	2.02578i	−0.184927	+	0.320304i
$41$	−3.80493	+	6.59034i	−0.594231	+	1.02924i	0.399424	+	0.916766i	$0.369210\pi$
$41$	−3.80493	+	6.59034i	−0.594231	+	1.02924i	−0.993655	+	0.112471i	$0.964123\pi$
$42$	0.878241	−	0.0791169i	0.135516	−	0.0122080i
$43$	−4.42183	−	7.65883i	−0.674323	−	1.16796i	−0.976666	−	0.214762i	$-0.931102\pi$
$43$	−4.42183	−	7.65883i	−0.674323	−	1.16796i	0.302344	−	0.953199i	$-0.402231\pi$
$44$	6.39034			0.963379
$45$	1.94018	+	2.28817i	0.289225	+	0.341100i
$46$	1.51036			0.222691
$47$	2.04391	+	3.54016i	0.298135	+	0.516385i	0.975709	−	0.219070i	$-0.0703022\pi$
$47$	2.04391	+	3.54016i	0.298135	+	0.516385i	−0.677574	+	0.735454i	$0.736969\pi$
$48$	1.17161	−	2.52953i	0.169108	−	0.365106i
$49$	3.19799	−	5.53909i	0.456856	−	0.791298i
$50$	−0.327533	+	0.567303i	−0.0463201	+	0.0802288i
$51$	5.27628	+	7.49413i	0.738827	+	1.04939i
$52$	−0.785445	−	1.36043i	−0.108922	−	0.188658i
$53$	−4.78025			−0.656618			−0.328309	−	0.944570i	$-0.606479\pi$
$53$	−4.78025			−0.656618			−0.328309	+	0.944570i	$0.606479\pi$
$54$	2.42540	+	2.38819i	0.330055	+	0.324991i
$55$	4.06797			0.548525
$56$	−0.908981	−	1.57440i	−0.121468	−	0.210388i
$57$	6.63124	+	9.41864i	0.878329	+	1.24753i
$58$	−2.08971	+	3.61949i	−0.274393	+	0.475262i
$59$	2.37049	−	4.10581i	0.308612	−	0.534532i	−0.669447	−	0.742860i	$-0.733469\pi$
$59$	2.37049	−	4.10581i	0.308612	−	0.534532i	0.978059	+	0.208328i	$0.0668022\pi$
$60$	1.14353	−	2.46889i	0.147629	−	0.318732i
$61$	7.18299	+	12.4413i	0.919688	+	1.59295i	0.799889	+	0.600148i	$0.204891\pi$
$61$	7.18299	+	12.4413i	0.919688	+	1.59295i	0.119798	+	0.992798i	$0.461775\pi$
$62$	−5.85967			−0.744179
$63$	−2.29401	+	0.416697i	−0.289018	+	0.0524989i
$64$	0.536314			0.0670393
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	4.59693	−	0.414118i	0.565844	−	0.0509744i
$67$	−5.39353	+	9.34188i	−0.658925	+	1.14129i	0.321969	+	0.946750i	$0.395655\pi$
$67$	−5.39353	+	9.34188i	−0.658925	+	1.14129i	−0.980894	+	0.194542i	$0.937678\pi$
$68$	4.15621	−	7.19877i	0.504015	−	0.872979i
$69$	−3.97743	+	0.358309i	−0.478826	+	0.0431354i
$70$	−0.254553	−	0.440899i	−0.0304249	−	0.0526975i
$71$	0.307776			0.0365262			0.0182631	−	0.999833i	$-0.494186\pi$
$71$	0.307776			0.0365262			0.0182631	+	0.999833i	$0.494186\pi$
$72$	2.36611	−	6.60657i	0.278849	−	0.778592i
$73$	−7.50636			−0.878553			−0.439277	−	0.898352i	$-0.644765\pi$
$73$	−7.50636			−0.878553			−0.439277	+	0.898352i	$0.644765\pi$
$74$	0.919032	+	1.59181i	0.106835	+	0.185044i
$75$	0.727949	−	1.57165i	0.0840563	−	0.181479i
$76$	5.22353	−	9.04743i	0.599180	−	1.03781i
$77$	−1.58078	+	2.73799i	−0.180147	+	0.312023i
$78$	−0.653176	−	0.927736i	−0.0739577	−	0.105045i
$79$	−3.80949	−	6.59822i	−0.428601	−	0.742358i	0.568148	−	0.822926i	$-0.307660\pi$
$79$	−3.80949	−	6.59822i	−0.428601	−	0.742358i	−0.996749	+	0.0805679i	$0.974327\pi$
$80$	−1.60947			−0.179944
$81$	−6.95366	−	5.71372i	−0.772629	−	0.634858i
$82$	4.98496			0.550497
$83$	6.26484	+	10.8510i	0.687656	+	1.19105i	0.972594	+	0.232509i	$0.0746934\pi$
$83$	6.26484	+	10.8510i	0.687656	+	1.19105i	−0.284939	+	0.958546i	$0.591973\pi$
$84$	1.21735	+	1.72905i	0.132824	+	0.188655i
$85$	2.64577	−	4.58261i	0.286974	−	0.497054i
$86$	−2.89659	+	5.01704i	−0.312347	+	0.541001i
$87$	4.64443	−	10.0274i	0.497935	−	1.07505i
$88$	−4.75783	−	8.24081i	−0.507187	−	0.878473i
$89$	−11.7743			−1.24807			−0.624037	−	0.781394i	$-0.714509\pi$
$89$	−11.7743			−1.24807			−0.624037	+	0.781394i	$0.714509\pi$
$90$	0.662611	−	1.85012i	0.0698454	−	0.195020i
$91$	0.777184			0.0814710
$92$	1.81098	+	3.13670i	0.188807	+	0.327024i
$93$	15.4310	−	1.39011i	1.60012	−	0.144148i
$94$	1.33889	−	2.31903i	0.138096	−	0.239190i
$95$	3.32521	−	5.75943i	0.341159	−	0.590905i
$96$	−9.88918	+	0.890873i	−1.00931	+	0.0909243i
$97$	3.04268	+	5.27007i	0.308937	+	0.535095i	0.978130	−	0.207994i	$-0.0666934\pi$
$97$	3.04268	+	5.27007i	0.308937	+	0.535095i	−0.669193	+	0.743089i	$0.733360\pi$
$98$	−4.18979			−0.423233
$99$	−12.0074	+	2.18109i	−1.20679	+	0.219208i
$100$	−1.57089			−0.157089
$101$	−4.67604	−	8.09915i	−0.465284	−	0.805895i	0.533930	−	0.845528i	$-0.320714\pi$
$101$	−4.67604	−	8.09915i	−0.465284	−	0.805895i	−0.999214	+	0.0396332i	$0.987381\pi$
$102$	2.52329	−	5.44782i	0.249843	−	0.539415i
$103$	1.10733	−	1.91796i	0.109109	−	0.188982i	−0.806301	−	0.591506i	$-0.798534\pi$
$103$	1.10733	−	1.91796i	0.109109	−	0.188982i	0.915409	+	0.402524i	$0.131867\pi$
$104$	−1.16958	+	2.02578i	−0.114687	+	0.198644i
$105$	0.774942	+	1.10069i	0.0756266	+	0.107416i
$106$	1.56569	+	2.71185i	0.152073	+	0.263399i
$107$	−15.4985			−1.49830			−0.749148	−	0.662403i	$-0.769537\pi$
$107$	−15.4985			−1.49830			−0.749148	+	0.662403i	$0.769537\pi$
$108$	−2.05162	+	7.90054i	−0.197417	+	0.760230i
$109$	−5.88278			−0.563468			−0.281734	−	0.959493i	$-0.590910\pi$
$109$	−5.88278			−0.563468			−0.281734	+	0.959493i	$0.590910\pi$
$110$	−1.33239	−	2.30778i	−0.127039	−	0.220038i
$111$	−2.79783	−	3.97388i	−0.265558	−	0.377184i
$112$	0.625427	−	1.08327i	0.0590973	−	0.102360i
$113$	−5.28790	+	9.15892i	−0.497444	+	0.861599i	−0.999996	−	0.00294864i	$-0.999061\pi$
$113$	−5.28790	+	9.15892i	−0.497444	+	0.861599i	0.502551	+	0.864547i	$0.332395\pi$
$114$	3.17128	−	6.84684i	0.297018	−	0.641265i
$115$	1.15283	+	1.99677i	0.107502	+	0.186200i
$116$	−10.0225			−0.930568
$117$	1.94018	+	2.28817i	0.179370	+	0.211541i
$118$	−3.10566			−0.285899
$119$	2.05625	+	3.56153i	0.188496	+	0.326485i
$120$	−4.03521	+	0.363515i	−0.368363	+	0.0331842i
$121$	−2.77420	+	4.80506i	−0.252200	+	0.436824i
$122$	4.70533	−	8.14987i	0.426001	−	0.737855i
$123$	−13.1275	+	1.18260i	−1.18367	+	0.106631i
$124$	−7.02594	−	12.1693i	−0.630948	−	1.09283i
$125$	−1.00000			−0.0894427
$126$	0.987758	+	1.16492i	0.0879965	+	0.103779i
$127$	−11.4873			−1.01934			−0.509668	−	0.860371i	$-0.670232\pi$
$127$	−11.4873			−1.01934			−0.509668	+	0.860371i	$0.670232\pi$
$128$	5.55698	+	9.62497i	0.491172	+	0.850736i
$129$	6.43773	−	13.8992i	0.566811	−	1.22375i
$130$	−0.327533	+	0.567303i	−0.0287265	+	0.0497558i
$131$	−6.28967	+	10.8940i	−0.549531	+	0.951815i	0.448776	+	0.893644i	$0.351860\pi$
$131$	−6.28967	+	10.8940i	−0.549531	+	0.951815i	−0.998307	+	0.0581709i	$0.981473\pi$
$132$	6.37191	+	9.05030i	0.554603	+	0.787728i
$133$	2.58430	+	4.47613i	0.224087	+	0.388130i
$134$	7.06624			0.610430
$135$	−1.30603	+	5.02934i	−0.112405	+	0.432857i
$136$	−12.3778			−1.06139
$137$	0.906022	+	1.56928i	0.0774067	+	0.134072i	0.902130	−	0.431464i	$-0.142003\pi$
$137$	0.906022	+	1.56928i	0.0774067	+	0.134072i	−0.824724	+	0.565536i	$0.808669\pi$
$138$	1.50601	+	2.13905i	0.128200	+	0.182088i
$139$	10.2052	−	17.6760i	0.865597	−	1.49926i	−0.000855357	−	1.00000i	$-0.500272\pi$
$139$	10.2052	−	17.6760i	0.865597	−	1.49926i	0.866453	−	0.499259i	$-0.166394\pi$
$140$	0.610435	−	1.05730i	0.0515911	−	0.0893585i
$141$	−2.97572	+	6.42463i	−0.250601	+	0.541051i
$142$	−0.100807	−	0.174602i	−0.00845950	−	0.0146523i
$143$	4.06797			0.340181
$144$	4.75067	−	0.862938i	0.395890	−	0.0719115i
$145$	−6.38016			−0.529843
$146$	2.45858	+	4.25838i	0.203473	+	0.352426i
$147$	11.0335	−	0.993959i	0.910027	−	0.0819803i
$148$	−2.20390	+	3.81726i	−0.181159	+	0.313777i
$149$	0.232060	−	0.401939i	0.0190111	−	0.0329281i	−0.856363	−	0.516374i	$-0.827282\pi$
$149$	0.232060	−	0.401939i	0.0190111	−	0.0329281i	0.875374	+	0.483446i	$0.160615\pi$
$150$	−1.13003	+	0.101800i	−0.0922666	+	0.00831190i
$151$	4.98238	+	8.62973i	0.405460	+	0.702278i	0.994375	−	0.105917i	$-0.0337779\pi$
$151$	4.98238	+	8.62973i	0.405460	+	0.702278i	−0.588915	+	0.808195i	$0.700445\pi$
$152$	−15.5564			−1.26179
$153$	−5.35249	+	14.9450i	−0.432723	+	1.20823i
$154$	2.07103			0.166888
$155$	−4.47259	−	7.74675i	−0.359247	−	0.622234i
$156$	1.14353	−	2.46889i	0.0915555	−	0.197669i
$157$	4.65985	−	8.07110i	0.371897	−	0.644144i	−0.617961	−	0.786209i	$-0.712041\pi$
$157$	4.65985	−	8.07110i	0.371897	−	0.644144i	0.989857	+	0.142065i	$0.0453742\pi$
$158$	−2.49546	+	4.32227i	−0.198528	+	0.343861i
$159$	−4.76647	−	6.77003i	−0.378005	−	0.536898i
$160$	2.86632	+	4.96461i	0.226603	+	0.392487i
$161$	−1.79193			−0.141224
$162$	−0.963865	+	5.81627i	−0.0757284	+	0.456969i
$163$	8.93727			0.700021			0.350010	−	0.936746i	$-0.386178\pi$
$163$	8.93727			0.700021			0.350010	+	0.936746i	$0.386178\pi$
$164$	5.97713	+	10.3527i	0.466735	+	0.808409i
$165$	4.05624	+	5.76126i	0.315778	+	0.448514i
$166$	4.10388	−	7.10813i	0.318523	−	0.551698i
$167$	8.17252	−	14.1552i	0.632409	−	1.09536i	−0.354649	−	0.935000i	$-0.615400\pi$
$167$	8.17252	−	14.1552i	0.632409	−	1.09536i	0.987058	−	0.160365i	$-0.0512671\pi$
$168$	1.32338	−	2.85720i	0.102101	−	0.220438i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−3.46630			−0.265853
$171$	−6.72703	+	18.7830i	−0.514428	+	1.43637i
$172$	−13.8924			−1.05929
$173$	−5.50039	−	9.52696i	−0.418187	−	0.724321i	0.577570	−	0.816341i	$-0.304001\pi$
$173$	−5.50039	−	9.52696i	−0.418187	−	0.724321i	−0.995757	+	0.0920197i	$0.970668\pi$
$174$	−7.20978	+	0.649497i	−0.546572	+	0.0492383i
$175$	0.388592	−	0.673061i	0.0293748	−	0.0508786i
$176$	3.27364	−	5.67011i	0.246760	−	0.427401i
$177$	8.17851	−	0.736766i	0.614734	−	0.0553787i
$178$	3.85647	+	6.67961i	0.289055	+	0.500658i
$179$	−2.87227			−0.214683			−0.107342	−	0.994222i	$-0.534234\pi$
$179$	−2.87227			−0.214683			−0.107342	+	0.994222i	$0.534234\pi$
$180$	4.63679	−	0.842252i	0.345606	−	0.0627777i
$181$	−10.8459			−0.806169			−0.403084	−	0.915163i	$-0.632062\pi$
$181$	−10.8459			−0.806169			−0.403084	+	0.915163i	$0.632062\pi$
$182$	−0.254553	−	0.440899i	−0.0188687	−	0.0326816i
$183$	−10.4577	+	22.5783i	−0.773056	+	1.66904i
$184$	2.69667	−	4.67077i	0.198801	−	0.344334i
$185$	−1.40296	+	2.43000i	−0.103148	+	0.178657i
$186$	−5.84278	−	8.29875i	−0.428413	−	0.608494i
$187$	10.7629	+	18.6419i	0.787063	+	1.36323i
$188$	6.42151			0.468337
$189$	−2.87754	−	2.83340i	−0.209310	−	0.206099i
$190$	−4.35646			−0.316051
$191$	−6.94768	−	12.0337i	−0.502716	−	0.870730i	−0.999995	−	0.00313924i	$-0.999001\pi$
$191$	−6.94768	−	12.0337i	−0.502716	−	0.870730i	0.497279	−	0.867591i	$-0.334333\pi$
$192$	0.534768	+	0.759554i	0.0385935	+	0.0548161i
$193$	−10.8934	+	18.8679i	−0.784123	+	1.35814i	0.145399	+	0.989373i	$0.453553\pi$
$193$	−10.8934	+	18.8679i	−0.784123	+	1.35814i	−0.929522	+	0.368768i	$0.879780\pi$
$194$	1.99315	−	3.45224i	0.143100	−	0.247857i
$195$	0.727949	−	1.57165i	0.0521295	−	0.112548i
$196$	−5.02369	−	8.70129i	−0.358835	−	0.621521i
$197$	−3.29282			−0.234604			−0.117302	−	0.993096i	$-0.537425\pi$
$197$	−3.29282			−0.234604			−0.117302	+	0.993096i	$0.537425\pi$
$198$	5.17017	+	6.09748i	0.367428	+	0.433329i
$199$	−19.7792			−1.40211			−0.701055	−	0.713107i	$-0.747287\pi$
$199$	−19.7792			−1.40211			−0.701055	+	0.713107i	$0.747287\pi$
$200$	1.16958	+	2.02578i	0.0827020	+	0.143244i
$201$	−18.6084	+	1.67635i	−1.31254	+	0.118241i
$202$	−3.06312	+	5.30547i	−0.215520	+	0.373292i
$203$	2.47928	−	4.29424i	0.174011	−	0.301396i
$204$	14.3395	−	1.29178i	1.00396	−	0.0904427i
$205$	3.80493	+	6.59034i	0.265748	+	0.460289i
$206$	−1.45075			−0.101079
$207$	−4.47341	−	5.27575i	−0.310924	−	0.366690i
$208$	−1.60947			−0.111597
$209$	13.5269	+	23.4292i	0.935672	+	1.62063i
$210$	0.370603	−	0.800138i	0.0255741	−	0.0552148i
$211$	1.21405	−	2.10279i	0.0835783	−	0.144762i	−0.821206	−	0.570632i	$-0.806698\pi$
$211$	1.21405	−	2.10279i	0.0835783	−	0.144762i	0.904785	+	0.425870i	$0.140032\pi$
$212$	−3.75462	+	6.50320i	−0.257869	+	0.446642i
$213$	0.306888	+	0.435887i	0.0210276	+	0.0298665i
$214$	5.07626	+	8.79235i	0.347006	+	0.601033i
$215$	−8.84366			−0.603132
$216$	11.7158	−	3.23652i	0.797162	−	0.220217i
$217$	6.95204			0.471935
$218$	1.92680	+	3.33732i	0.130500	+	0.226032i
$219$	−7.48471	−	10.6309i	−0.505770	−	0.718368i
$220$	3.19517	−	5.53419i	0.215418	−	0.373115i
$221$	2.64577	−	4.58261i	0.177974	−	0.308260i
$222$	−1.33802	+	2.88880i	−0.0898018	+	0.193883i
$223$	4.72863	+	8.19022i	0.316652	+	0.548458i	0.979787	−	0.200042i	$-0.0641078\pi$
$223$	4.72863	+	8.19022i	0.316652	+	0.548458i	−0.663135	+	0.748500i	$0.730774\pi$
$224$	−4.45532			−0.297683
$225$	2.95170	−	0.536163i	0.196780	−	0.0357442i
$226$	6.92785			0.460834
$227$	−12.0411	−	20.8557i	−0.799193	−	1.38424i	−0.920142	−	0.391585i	$-0.871927\pi$
$227$	−12.0411	−	20.8557i	−0.799193	−	1.38424i	0.120949	−	0.992659i	$-0.461406\pi$
$228$	18.0219	−	1.62351i	1.19353	−	0.107520i
$229$	−4.98700	+	8.63774i	−0.329550	+	0.570798i	−0.982423	−	0.186670i	$-0.940230\pi$
$229$	−4.98700	+	8.63774i	−0.329550	+	0.570798i	0.652872	+	0.757468i	$0.273564\pi$
$230$	0.755182	−	1.30801i	0.0497953	−	0.0862479i
$231$	−5.45390	+	0.491318i	−0.358840	+	0.0323264i
$232$	7.46213	+	12.9248i	0.489913	+	0.848554i
$233$	18.2730			1.19710			0.598552	−	0.801084i	$-0.295743\pi$
$233$	18.2730			1.19710			0.598552	+	0.801084i	$0.295743\pi$
$234$	0.662611	−	1.85012i	0.0433163	−	0.120946i
$235$	4.08782			0.266660
$236$	−3.72378	−	6.44978i	−0.242398	−	0.419845i
$237$	5.54622	−	11.9744i	0.360266	−	0.777819i
$238$	1.34698	−	2.33303i	0.0873116	−	0.151228i
$239$	13.2720	−	22.9878i	0.858495	−	1.48696i	−0.0148689	−	0.999889i	$-0.504733\pi$
$239$	13.2720	−	22.9878i	0.858495	−	1.48696i	0.873364	−	0.487068i	$-0.161934\pi$
$240$	−1.60483	−	2.27941i	−0.103591	−	0.147135i
$241$	−7.20936	−	12.4870i	−0.464396	−	0.804357i	0.534778	−	0.844992i	$-0.320395\pi$
$241$	−7.20936	−	12.4870i	−0.464396	−	0.804357i	−0.999174	+	0.0406354i	$0.987062\pi$
$242$	3.63457			0.233639
$243$	1.15845	−	15.5454i	0.0743147	−	0.997235i
$244$	22.5674			1.44473
$245$	−3.19799	−	5.53909i	−0.204312	−	0.353879i
$246$	4.97058	+	7.05994i	0.316913	+	0.450125i
$247$	3.32521	−	5.75943i	0.211578	−	0.366464i
$248$	−10.4621	+	18.1209i	−0.664346	+	1.15068i
$249$	−9.12097	+	19.6923i	−0.578018	+	1.24795i
$250$	0.327533	+	0.567303i	0.0207150	+	0.0358794i
$251$	13.7541			0.868148			0.434074	−	0.900877i	$-0.357076\pi$
$251$	13.7541			0.868148			0.434074	+	0.900877i	$0.357076\pi$
$252$	−1.23493	+	3.44814i	−0.0777935	+	0.217212i
$253$	−9.37940			−0.589678
$254$	3.76248	+	6.51681i	0.236079	+	0.408901i
$255$	9.12825	−	0.822324i	0.571633	−	0.0514959i
$256$	4.17650	−	7.23391i	0.261031	−	0.452120i
$257$	2.45679	−	4.25528i	0.153250	−	0.265437i	−0.779170	−	0.626812i	$-0.784359\pi$
$257$	2.45679	−	4.25528i	0.153250	−	0.265437i	0.932421	+	0.361375i	$0.117693\pi$
$258$	−9.99361	+	0.900280i	−0.622175	+	0.0560490i
$259$	−1.09036	−	1.88856i	−0.0677516	−	0.117349i
$260$	−1.57089			−0.0974224
$261$	18.8323	−	3.42080i	1.16569	−	0.211742i
$262$	8.24029			0.509087
$263$	−13.0361	−	22.5793i	−0.803843	−	1.39230i	−0.917069	−	0.398728i	$-0.869452\pi$
$263$	−13.0361	−	22.5793i	−0.803843	−	1.39230i	0.113226	−	0.993569i	$-0.463882\pi$
$264$	6.92692	−	14.9553i	0.426323	−	0.920436i
$265$	−2.39013	+	4.13982i	−0.146824	+	0.254307i
$266$	1.69288	−	2.93216i	0.103797	−	0.179782i
$267$	−11.7404	−	16.6754i	−0.718498	−	1.02052i
$268$	8.47265	+	14.6751i	0.517549	+	0.896421i
$269$	29.7277			1.81253			0.906263	−	0.422713i	$-0.138922\pi$
$269$	29.7277			1.81253			0.906263	+	0.422713i	$0.138922\pi$
$270$	3.28093	−	0.906362i	0.199671	−	0.0551594i
$271$	14.2980			0.868540			0.434270	−	0.900783i	$-0.357006\pi$
$271$	14.2980			0.868540			0.434270	+	0.900783i	$0.357006\pi$
$272$	−4.25829	−	7.37557i	−0.258197	−	0.447210i
$273$	0.774942	+	1.10069i	0.0469016	+	0.0666165i
$274$	0.593504	−	1.02798i	0.0358549	−	0.0621025i
$275$	2.03399	−	3.52297i	0.122654	−	0.212443i
$276$	−2.63660	+	5.69245i	−0.158704	+	0.342645i
$277$	−0.939303	−	1.62692i	−0.0564373	−	0.0977522i	0.836426	−	0.548079i	$-0.184641\pi$
$277$	−0.939303	−	1.62692i	−0.0564373	−	0.0977522i	−0.892864	+	0.450327i	$0.851307\pi$
$278$	−13.3702			−0.801892
$279$	17.3552	+	20.4680i	1.03903	+	1.22539i
$280$	−1.81796			−0.108644
$281$	−1.78593	−	3.09331i	−0.106539	−	0.184532i	0.807827	−	0.589420i	$-0.200644\pi$
$281$	−1.78593	−	3.09331i	−0.106539	−	0.184532i	−0.914366	+	0.404888i	$0.867310\pi$
$282$	4.61936	−	0.416138i	0.275079	−	0.0247807i
$283$	6.87413	−	11.9063i	0.408625	−	0.707759i	−0.586111	−	0.810231i	$-0.699342\pi$
$283$	6.87413	−	11.9063i	0.408625	−	0.707759i	0.994736	+	0.102472i	$0.0326752\pi$
$284$	0.241741	−	0.418707i	0.0143447	−	0.0248457i
$285$	11.4724	−	1.03350i	0.679566	−	0.0612192i
$286$	−1.33239	−	2.30778i	−0.0787861	−	0.136462i
$287$	−5.91426			−0.349108
$288$	−11.1224	−	13.1172i	−0.655391	−	0.772940i
$289$	11.0004			0.647081
$290$	2.08971	+	3.61949i	0.122712	+	0.212544i
$291$	−4.42983	+	9.56406i	−0.259681	+	0.560655i
$292$	−5.89583	+	10.2119i	−0.345027	+	0.597605i
$293$	3.74904	−	6.49352i	0.219021	−	0.379355i	−0.735488	−	0.677538i	$-0.763047\pi$
$293$	3.74904	−	6.49352i	0.219021	−	0.379355i	0.954509	+	0.298182i	$0.0963803\pi$
$294$	−4.17771	−	5.93378i	−0.243649	−	0.346065i
$295$	−2.37049	−	4.10581i	−0.138015	−	0.239050i
$296$	6.56352			0.381497
$297$	−15.0618	−	14.8307i	−0.873973	−	0.860565i
$298$	−0.304028			−0.0176119
$299$	1.15283	+	1.99677i	0.0666702	+	0.115476i
$300$	−1.56636	−	2.22477i	−0.0904338	−	0.128447i
$301$	3.43657	−	5.95232i	0.198081	−	0.343086i
$302$	3.26379	−	5.65304i	0.187810	−	0.325296i
$303$	6.80785	−	14.6982i	0.391100	−	0.844391i
$304$	−5.35183	−	9.26963i	−0.306948	−	0.531650i
$305$	14.3660			0.822594
$306$	10.2315	−	1.85850i	0.584895	−	0.106244i
$307$	−18.4113			−1.05079			−0.525395	−	0.850858i	$-0.676082\pi$
$307$	−18.4113			−1.05079			−0.525395	+	0.850858i	$0.676082\pi$
$308$	2.48323	+	4.30108i	0.141495	+	0.245077i
$309$	3.82044	−	0.344167i	0.217337	−	0.0195790i
$310$	−2.92984	+	5.07463i	−0.166404	+	0.288219i
$311$	−8.63239	+	14.9517i	−0.489498	+	0.847835i	−0.999927	−	0.0120846i	$-0.996153\pi$
$311$	−8.63239	+	14.9517i	−0.489498	+	0.847835i	0.510429	+	0.859920i	$0.329487\pi$
$312$	−4.03521	+	0.363515i	−0.228449	+	0.0205800i
$313$	4.53031	+	7.84672i	0.256068	+	0.443523i	0.965185	−	0.261568i	$-0.0842396\pi$
$313$	4.53031	+	7.84672i	0.256068	+	0.443523i	−0.709117	+	0.705091i	$0.750906\pi$
$314$	−6.10502			−0.344526
$315$	−0.786136	+	2.19502i	−0.0442938	+	0.123675i
$316$	−11.9686			−0.673284
$317$	−4.01943	−	6.96187i	−0.225754	−	0.391017i	0.730791	−	0.682601i	$-0.239151\pi$
$317$	−4.01943	−	6.96187i	−0.225754	−	0.391017i	−0.956545	+	0.291584i	$0.905818\pi$
$318$	−2.27949	+	4.92144i	−0.127827	+	0.275981i
$319$	12.9772	−	22.4771i	0.726582	−	1.25848i
$320$	0.268157	−	0.464462i	0.0149904	−	0.0259642i
$321$	−15.4538	−	21.9497i	−0.862547	−	1.22511i
$322$	0.586916	+	1.01657i	0.0327075	+	0.0566511i
$323$	35.1909			1.95808
$324$	−13.2348	+	4.97215i	−0.735269	+	0.276230i
$325$	−1.00000			−0.0554700
$326$	−2.92725	−	5.07014i	−0.162125	−	0.280809i
$327$	−5.86581	−	8.33148i	−0.324380	−	0.460732i
$328$	8.90037	−	15.4159i	0.491441	−	0.851200i
$329$	−1.58849	+	2.75135i	−0.0875765	+	0.151687i
$330$	1.93983	−	4.18812i	0.106784	−	0.230548i
$331$	14.9332	+	25.8651i	0.820803	+	1.42167i	0.905085	+	0.425230i	$0.139807\pi$
$331$	14.9332	+	25.8651i	0.820803	+	1.42167i	−0.0842828	+	0.996442i	$0.526860\pi$
$332$	19.6827			1.08023
$333$	2.83824	−	7.92484i	0.155535	−	0.434279i
$334$	−10.7071			−0.585865
$335$	5.39353	+	9.34188i	0.294680	+	0.510401i
$336$	2.15781	−	0.194387i	0.117718	−	0.0106047i
$337$	−12.1043	+	20.9653i	−0.659366	+	1.14205i	0.321414	+	0.946939i	$0.395842\pi$
$337$	−12.1043	+	20.9653i	−0.659366	+	1.14205i	−0.980780	+	0.195116i	$0.937492\pi$
$338$	−0.327533	+	0.567303i	−0.0178154	+	0.0308572i
$339$	−18.2440	+	1.64352i	−0.990876	+	0.0892637i
$340$	−4.15621	−	7.19877i	−0.225402	−	0.390408i
$341$	36.3887			1.97056
$342$	12.8590	−	2.33577i	0.695333	−	0.126304i
$343$	10.4111			0.562149
$344$	10.3434	+	17.9153i	0.557678	+	0.965927i
$345$	−1.67841	+	3.62371i	−0.0903626	+	0.195094i
$346$	−3.60312	+	6.24078i	−0.193705	+	0.335507i
$347$	11.4572	−	19.8444i	0.615053	−	1.06530i	−0.375323	−	0.926894i	$-0.622468\pi$
$347$	11.4572	−	19.8444i	0.615053	−	1.06530i	0.990375	−	0.138408i	$-0.0441986\pi$
$348$	−9.99362	−	14.1944i	−0.535714	−	0.760899i
$349$	6.17874	+	10.7019i	0.330740	+	0.572859i	0.982657	−	0.185431i	$-0.0593682\pi$
$349$	6.17874	+	10.7019i	0.330740	+	0.572859i	−0.651917	+	0.758291i	$0.726035\pi$
$350$	−0.509106			−0.0272129
$351$	−1.30603	+	5.02934i	−0.0697105	+	0.268446i
$352$	−23.3202			−1.24297
$353$	13.5190	+	23.4156i	0.719544	+	1.24629i	0.961181	+	0.275920i	$0.0889826\pi$
$353$	13.5190	+	23.4156i	0.719544	+	1.24629i	−0.241636	+	0.970367i	$0.577684\pi$
$354$	−3.09670	−	4.39838i	−0.164588	−	0.233771i
$355$	0.153888	−	0.266541i	0.00816751	−	0.0141465i
$356$	−9.24807	+	16.0181i	−0.490147	+	0.848959i
$357$	−2.99369	+	6.46342i	−0.158443	+	0.342080i
$358$	0.940762	+	1.62945i	0.0497208	+	0.0861190i
$359$	−28.4894			−1.50361			−0.751806	−	0.659384i	$-0.770817\pi$
$359$	−28.4894			−1.50361			−0.751806	+	0.659384i	$0.770817\pi$
$360$	−4.53840	−	5.35240i	−0.239195	−	0.282096i
$361$	25.2280			1.32779
$362$	3.55238	+	6.15291i	0.186709	+	0.323390i
$363$	−9.57136	+	0.862242i	−0.502366	+	0.0452560i
$364$	0.610435	−	1.05730i	0.0319955	−	0.0554178i
$365$	−3.75318	+	6.50070i	−0.196450	+	0.340262i
$366$	16.2340	−	1.46245i	0.848565	−	0.0764435i
$367$	15.1600	+	26.2579i	0.791347	+	1.37065i	0.925133	+	0.379643i	$0.123953\pi$
$367$	15.1600	+	26.2579i	0.791347	+	1.37065i	−0.133786	+	0.991010i	$0.542713\pi$
$368$	3.71091			0.193444
$369$	−14.7645	−	17.4126i	−0.768609	−	0.906465i
$370$	1.83806			0.0955563
$371$	−1.85757	−	3.21740i	−0.0964401	−	0.167039i
$372$	10.2290	−	22.0847i	0.530352	−	1.14504i
$373$	4.66810	−	8.08538i	0.241705	−	0.418645i	−0.719495	−	0.694498i	$-0.755627\pi$
$373$	4.66810	−	8.08538i	0.241705	−	0.418645i	0.961200	+	0.275852i	$0.0889600\pi$
$374$	7.05042	−	12.2117i	0.364568	−	0.631451i
$375$	−0.997116	−	1.41625i	−0.0514908	−	0.0731348i
$376$	−4.78104	−	8.28101i	−0.246564	−	0.427061i
$377$	−6.38016			−0.328595
$378$	−0.664906	+	2.56047i	−0.0341991	+	0.131696i
$379$	−22.5156			−1.15655			−0.578274	−	0.815843i	$-0.696274\pi$
$379$	−22.5156			−1.15655			−0.578274	+	0.815843i	$0.696274\pi$
$380$	−5.22353	−	9.04743i	−0.267962	−	0.464123i
$381$	−11.4542	−	16.2689i	−0.586817	−	0.833482i
$382$	−4.55118	+	7.88288i	−0.232859	+	0.403323i
$383$	1.51690	−	2.62735i	0.0775100	−	0.134251i	−0.824665	−	0.565621i	$-0.808636\pi$
$383$	1.51690	−	2.62735i	0.0775100	−	0.134251i	0.902175	+	0.431370i	$0.141970\pi$
$384$	−8.09040	+	17.4673i	−0.412861	+	0.891373i
$385$	1.58078	+	2.73799i	0.0805641	+	0.139541i
$386$	14.2718			0.726413
$387$	26.1038	−	4.74164i	1.32693	−	0.241031i
$388$	9.55942			0.485306
$389$	9.14936	+	15.8472i	0.463891	+	0.803483i	0.999151	−	0.0412048i	$-0.0131196\pi$
$389$	9.14936	+	15.8472i	0.463891	+	0.803483i	−0.535260	+	0.844687i	$0.679786\pi$
$390$	−1.13003	+	0.101800i	−0.0572213	+	0.00515482i
$391$	−6.10027	+	10.5660i	−0.308504	+	0.534345i
$392$	−7.48064	+	12.9568i	−0.377829	+	0.654419i
$393$	−21.7002	+	1.95487i	−1.09463	+	0.0986103i
$394$	1.07851	+	1.86803i	0.0543344	+	0.0941100i
$395$	−7.61897			−0.383352
$396$	−6.46395	+	18.0484i	−0.324826	+	0.906966i
$397$	−29.4753			−1.47932			−0.739661	−	0.672980i	$-0.765014\pi$
$397$	−29.4753			−1.47932			−0.739661	+	0.672980i	$0.765014\pi$
$398$	6.47834	+	11.2208i	0.324730	+	0.562448i
$399$	−3.76247	+	8.12323i	−0.188359	+	0.406670i
$400$	−0.804735	+	1.39384i	−0.0402368	+	0.0696921i
$401$	13.8838	−	24.0474i	0.693322	−	1.20087i	−0.277421	−	0.960748i	$-0.589480\pi$
$401$	13.8838	−	24.0474i	0.693322	−	1.20087i	0.970743	−	0.240121i	$-0.0771870\pi$
$402$	7.04586	+	10.0075i	0.351415	+	0.499131i
$403$	−4.47259	−	7.74675i	−0.222795	−	0.385893i
$404$	−14.6911			−0.730909
$405$	−8.42506	+	3.16518i	−0.418645	+	0.157279i
$406$	−3.24818			−0.161204
$407$	−5.70721	−	9.88518i	−0.282896	−	0.489990i
$408$	−12.3421	−	17.5300i	−0.611025	−	0.867866i
$409$	4.90416	−	8.49426i	0.242495	−	0.420014i	−0.718929	−	0.695083i	$-0.755367\pi$
$409$	4.90416	−	8.49426i	0.242495	−	0.420014i	0.961424	+	0.275069i	$0.0887008\pi$
$410$	2.49248	−	4.31710i	0.123095	−	0.213206i
$411$	−1.31908	+	2.84790i	−0.0650652	+	0.140477i
$412$	−1.73950	−	3.01290i	−0.0856989	−	0.148435i
$413$	3.68462			0.181308
$414$	−1.52776	+	4.26577i	−0.0750855	+	0.209651i
$415$	12.5297			0.615058
$416$	2.86632	+	4.96461i	0.140533	+	0.243410i
$417$	35.2094	−	3.17186i	1.72421	−	0.155327i
$418$	8.86098	−	15.3477i	0.433405	−	0.750679i
$419$	−7.24144	+	12.5425i	−0.353768	+	0.612744i	−0.986906	−	0.161295i	$-0.948433\pi$
$419$	−7.24144	+	12.5425i	−0.353768	+	0.612744i	0.633139	+	0.774038i	$0.281766\pi$
$420$	2.10608	−	0.189727i	0.102766	−	0.00925775i
$421$	17.9112	+	31.0231i	0.872937	+	1.51197i	0.858944	+	0.512070i	$0.171121\pi$
$421$	17.9112	+	31.0231i	0.872937	+	1.51197i	0.0139933	+	0.999902i	$0.495546\pi$
$422$	−1.59056			−0.0774272
$423$	−12.0660	+	2.19174i	−0.586670	+	0.106566i
$424$	11.1818			0.543037
$425$	−2.64577	−	4.58261i	−0.128339	−	0.222289i
$426$	0.146764	−	0.316866i	0.00711074	−	0.0153522i
$427$	−5.58250	+	9.66918i	−0.270156	+	0.467924i
$428$	−12.1732	+	21.0846i	−0.588414	+	1.01916i
$429$	4.05624	+	5.76126i	0.195837	+	0.278156i
$430$	2.89659	+	5.01704i	0.139686	+	0.241943i
$431$	7.34712			0.353898			0.176949	−	0.984220i	$-0.443377\pi$
$431$	7.34712			0.353898			0.176949	+	0.984220i	$0.443377\pi$
$432$	5.95911	+	5.86769i	0.286708	+	0.282309i
$433$	−6.55302			−0.314918			−0.157459	−	0.987526i	$-0.550330\pi$
$433$	−6.55302			−0.314918			−0.157459	+	0.987526i	$0.550330\pi$
$434$	−2.27702	−	3.94392i	−0.109301	−	0.189314i
$435$	−6.36176	−	9.03589i	−0.305023	−	0.433238i
$436$	−4.62060	+	8.00311i	−0.221286	+	0.383279i
$437$	−7.66683	+	13.2793i	−0.366754	+	0.635237i
$438$	−3.57944	+	7.72806i	−0.171032	+	0.369261i
$439$	0.855543	+	1.48184i	0.0408329	+	0.0707246i	0.885720	−	0.464221i	$-0.153666\pi$
$439$	0.855543	+	1.48184i	0.0408329	+	0.0707246i	−0.844887	+	0.534945i	$0.820332\pi$
$440$	−9.51567			−0.453642
$441$	12.4094	+	14.6351i	0.590922	+	0.696908i
$442$	−3.46630			−0.164875
$443$	11.0458	+	19.1319i	0.524801	+	0.908982i	0.999583	+	0.0288783i	$0.00919352\pi$
$443$	11.0458	+	19.1319i	0.524801	+	0.908982i	−0.474782	+	0.880103i	$0.657473\pi$
$444$	−7.60373	+	0.684987i	−0.360857	+	0.0325080i
$445$	−5.88716	+	10.1969i	−0.279078	+	0.483377i
$446$	3.09756	−	5.36513i	0.146674	−	0.254046i
$447$	0.800636	−	0.0721258i	0.0378688	−	0.00341143i
$448$	0.208407	+	0.360972i	0.00984632	+	0.0170543i
$449$	35.4082			1.67102			0.835508	−	0.549479i	$-0.185174\pi$
$449$	35.4082			1.67102			0.835508	+	0.549479i	$0.185174\pi$
$450$	−1.27095	−	1.49890i	−0.0599129	−	0.0706587i
$451$	−30.9567			−1.45770
$452$	8.30671	+	14.3876i	0.390715	+	0.676738i
$453$	−7.25384	+	15.6611i	−0.340815	+	0.735824i
$454$	−7.88769	+	13.6619i	−0.370187	+	0.641183i
$455$	0.388592	−	0.673061i	0.0182175	−	0.0315536i
$456$	−15.5116	−	22.0318i	−0.726396	−	1.03173i
$457$	1.26715	+	2.19477i	0.0592748	+	0.102667i	0.894140	−	0.447787i	$-0.147788\pi$
$457$	1.26715	+	2.19477i	0.0592748	+	0.102667i	−0.834865	+	0.550454i	$0.814455\pi$
$458$	6.53363			0.305296
$459$	−26.5029	+	7.32148i	−1.23705	+	0.341737i
$460$	3.62195			0.168874
$461$	1.09872	+	1.90304i	0.0511724	+	0.0886332i	0.890477	−	0.455028i	$-0.150371\pi$
$461$	1.09872	+	1.90304i	0.0511724	+	0.0886332i	−0.839305	+	0.543662i	$0.817038\pi$
$462$	2.06506	+	2.93309i	0.0960752	+	0.136460i
$463$	12.7269	−	22.0436i	0.591468	−	1.02445i	−0.402568	−	0.915390i	$-0.631882\pi$
$463$	12.7269	−	22.0436i	0.591468	−	1.02445i	0.994035	−	0.109061i	$-0.0347845\pi$
$464$	−5.13434	+	8.89294i	−0.238356	+	0.412844i
$465$	6.51163	−	14.0587i	0.301970	−	0.651957i
$466$	−5.98501	−	10.3663i	−0.277250	−	0.480211i
$467$	−15.4769			−0.716187			−0.358093	−	0.933686i	$-0.616573\pi$
$467$	−15.4769			−0.716187			−0.358093	+	0.933686i	$0.616573\pi$
$468$	4.63679	−	0.842252i	0.214336	−	0.0389331i
$469$	−8.38353			−0.387116
$470$	−1.33889	−	2.31903i	−0.0617586	−	0.106969i
$471$	16.0771	−	1.44832i	0.740794	−	0.0667349i
$472$	−5.54498	+	9.60418i	−0.255228	+	0.442068i
$473$	17.9879	−	31.1559i	0.827084	−	1.43255i
$474$	−8.60967	+	0.775608i	−0.395455	+	0.0356248i
$475$	−3.32521	−	5.75943i	−0.152571	−	0.264261i
$476$	6.46028			0.296106
$477$	4.83532	−	13.5010i	0.221394	−	0.618169i
$478$	−17.3881			−0.795312
$479$	4.81116	+	8.33317i	0.219828	+	0.380752i	0.954755	−	0.297393i	$-0.0961172\pi$
$479$	4.81116	+	8.33317i	0.219828	+	0.380752i	−0.734928	+	0.678146i	$0.762784\pi$
$480$	−4.17307	+	9.00972i	−0.190474	+	0.411235i
$481$	−1.40296	+	2.43000i	−0.0639695	+	0.110798i
$482$	−4.72260	+	8.17979i	−0.215109	+	0.372579i
$483$	−1.78676	−	2.53782i	−0.0813004	−	0.115475i
$484$	4.35797	+	7.54822i	0.198089	+	0.343101i
$485$	6.08536			0.276322
$486$	−9.19836	+	4.43442i	−0.417246	+	0.201149i
$487$	−20.0963			−0.910649			−0.455325	−	0.890325i	$-0.650477\pi$
$487$	−20.0963			−0.910649			−0.455325	+	0.890325i	$0.650477\pi$
$488$	−16.8022	−	29.1023i	−0.760600	−	1.31740i
$489$	8.91149	+	12.6574i	0.402992	+	0.572387i
$490$	−2.09489	+	3.62846i	−0.0946377	+	0.163917i
$491$	−1.48336	+	2.56925i	−0.0669430	+	0.115949i	−0.897554	−	0.440904i	$-0.854658\pi$
$491$	−1.48336	+	2.56925i	−0.0669430	+	0.115949i	0.830611	+	0.556853i	$0.187991\pi$
$492$	−8.70209	+	18.7879i	−0.392320	+	0.847025i
$493$	−16.8804	−	29.2378i	−0.760256	−	1.31680i
$494$	−4.35646			−0.196006
$495$	−4.11483	+	11.4893i	−0.184948	+	0.516405i
$496$	−14.3970			−0.646444
$497$	0.119599	+	0.207152i	0.00536475	+	0.00929202i
$498$	14.1589	−	1.27552i	0.634477	−	0.0571572i
$499$	−6.97206	+	12.0760i	−0.312112	+	0.540594i	−0.978819	−	0.204726i	$-0.934370\pi$
$499$	−6.97206	+	12.0760i	−0.312112	+	0.540594i	0.666707	+	0.745320i	$0.267703\pi$
$500$	−0.785445	+	1.36043i	−0.0351261	+	0.0608403i
$501$	28.1963	−	2.54008i	1.25972	−	0.113482i
$502$	−4.50490	−	7.80272i	−0.201064	−	0.348253i
$503$	−25.1391			−1.12090			−0.560448	−	0.828190i	$-0.689371\pi$
$503$	−25.1391			−1.12090			−0.560448	+	0.828190i	$0.689371\pi$
$504$	5.36608	−	0.974723i	0.239024	−	0.0434176i
$505$	−9.35209			−0.416162
$506$	3.07206	+	5.32097i	0.136570	+	0.236546i
$507$	0.727949	−	1.57165i	0.0323294	−	0.0697995i
$508$	−9.02267	+	15.6277i	−0.400316	+	0.693368i
$509$	1.04078	−	1.80269i	0.0461320	−	0.0799029i	−0.842037	−	0.539419i	$-0.818644\pi$
$509$	1.04078	−	1.80269i	0.0461320	−	0.0799029i	0.888169	+	0.459516i	$0.151977\pi$
$510$	−3.45631	−	4.90915i	−0.153048	−	0.217381i
$511$	−2.91691	−	5.05224i	−0.129037	−	0.223498i
$512$	16.7562			0.740525
$513$	−33.3090	+	9.20165i	−1.47063	+	0.406263i
$514$	−3.21871			−0.141971
$515$	−1.10733	−	1.91796i	−0.0487949	−	0.0845153i
$516$	−13.8523	−	19.6751i	−0.609815	−	0.866148i
$517$	−8.31457	+	14.4013i	−0.365674	+	0.633367i
$518$	−0.714256	+	1.23713i	−0.0313826	+	0.0543563i
$519$	8.00801	−	17.2894i	0.351513	−	0.758921i
$520$	1.16958	+	2.02578i	0.0512896	+	0.0888362i
$521$	−16.7112			−0.732130			−0.366065	−	0.930589i	$-0.619295\pi$
$521$	−16.7112			−0.732130			−0.366065	+	0.930589i	$0.619295\pi$
$522$	−8.10883	−	9.56321i	−0.354914	−	0.418570i
$523$	39.1071			1.71003			0.855016	−	0.518602i	$-0.173547\pi$
$523$	39.1071			1.71003			0.855016	+	0.518602i	$0.173547\pi$
$524$	9.88037	+	17.1133i	0.431626	+	0.747598i
$525$	1.34069	−	0.120777i	0.0585126	−	0.00527115i
$526$	−8.53953	+	14.7909i	−0.372341	+	0.644914i
$527$	23.6669	−	40.9922i	1.03094	−	1.78565i
$528$	11.2945	−	1.01747i	0.491530	−	0.0442798i
$529$	8.84194	+	15.3147i	0.384432	+	0.665856i
$530$	3.13138			0.136018
$531$	9.19837	+	10.8482i	0.399175	+	0.470770i
$532$	8.11929			0.352016
$533$	3.80493	+	6.59034i	0.164810	+	0.285459i
$534$	−5.61463	+	12.1221i	−0.242969	+	0.524573i
$535$	−7.74925	+	13.4221i	−0.335029	+	0.580288i
$536$	12.6164	−	21.8522i	0.544944	−	0.943871i
$537$	−2.86399	−	4.06785i	−0.123590	−	0.175541i
$538$	−9.73678	−	16.8646i	−0.419782	−	0.727084i
$539$	26.0187			1.12070
$540$	5.81626	+	5.72703i	0.250292	+	0.246452i
$541$	4.87732			0.209692			0.104846	−	0.994488i	$-0.466565\pi$
$541$	4.87732			0.209692			0.104846	+	0.994488i	$0.466565\pi$
$542$	−4.68306	−	8.11129i	−0.201154	−	0.348410i
$543$	−10.8146	−	15.3605i	−0.464099	−	0.659181i
$544$	−15.1672	+	26.2704i	−0.650290	+	1.12634i
$545$	−2.94139	+	5.09464i	−0.125995	+	0.218230i
$546$	0.370603	−	0.800138i	0.0158604	−	0.0342427i
$547$	7.47398	+	12.9453i	0.319564	+	0.553501i	0.980397	−	0.197032i	$-0.0631302\pi$
$547$	7.47398	+	12.9453i	0.319564	+	0.553501i	−0.660833	+	0.750533i	$0.729797\pi$
$548$	2.84652			0.121597
$549$	−42.4041	+	7.70250i	−1.80976	+	0.328735i
$550$	−2.66479			−0.113627
$551$	−21.2154	−	36.7461i	−0.903805	−	1.56544i
$552$	9.30387	−	0.838145i	0.395999	−	0.0356738i
$553$	2.96067	−	5.12803i	0.125901	−	0.218066i
$554$	−0.615305	+	1.06574i	−0.0261418	+	0.0452789i
$555$	−4.84040	+	0.436050i	−0.205463	+	0.0185093i
$556$	−16.0313	−	27.7670i	−0.679879	−	1.17758i
$557$	−23.5505			−0.997866			−0.498933	−	0.866641i	$-0.666275\pi$
$557$	−23.5505			−0.997866			−0.498933	+	0.866641i	$0.666275\pi$
$558$	5.92717	−	16.5496i	0.250917	−	0.700602i
$559$	−8.84366			−0.374047
$560$	−0.625427	−	1.08327i	−0.0264291	−	0.0457766i
$561$	−15.6697	+	33.8311i	−0.661576	+	1.42835i
$562$	−1.16990	+	2.02632i	−0.0493492	+	0.0854753i
$563$	0.146577	−	0.253878i	0.00617747	−	0.0106997i	−0.862920	−	0.505340i	$-0.831367\pi$
$563$	0.146577	−	0.253878i	0.00617747	−	0.0106997i	0.869098	+	0.494641i	$0.164700\pi$
$564$	6.40299	+	9.09445i	0.269615	+	0.382946i
$565$	5.28790	+	9.15892i	0.222464	+	0.385319i
$566$	−9.00601			−0.378551
$567$	1.14355	−	6.90054i	0.0480246	−	0.289795i
$568$	−0.719938			−0.0302079
$569$	−16.9315	−	29.3263i	−0.709807	−	1.22942i	−0.964928	−	0.262513i	$-0.915449\pi$
$569$	−16.9315	−	29.3263i	−0.709807	−	1.22942i	0.255121	−	0.966909i	$-0.417885\pi$
$570$	−4.34389	−	6.16983i	−0.181946	−	0.258426i
$571$	11.0154	−	19.0793i	0.460981	−	0.798443i	−0.538029	−	0.842926i	$-0.680831\pi$
$571$	11.0154	−	19.0793i	0.460981	−	0.798443i	0.999010	+	0.0444833i	$0.0141642\pi$
$572$	3.19517	−	5.53419i	0.133597	−	0.231396i
$573$	10.1151	−	21.8387i	0.422565	−	0.912323i
$574$	1.93711	+	3.35518i	0.0808536	+	0.140043i
$575$	2.30567			0.0961531
$576$	−0.542492	+	1.51473i	−0.0226038	+	0.0631137i
$577$	23.7846			0.990165			0.495083	−	0.868846i	$-0.335138\pi$
$577$	23.7846			0.990165			0.495083	+	0.868846i	$0.335138\pi$
$578$	−3.60299	−	6.24055i	−0.149864	−	0.259573i
$579$	−37.5836	+	3.38574i	−1.56192	+	0.140707i
$580$	−5.01126	+	8.67976i	−0.208081	+	0.360407i
$581$	−4.86893	+	8.43324i	−0.201997	+	0.349870i
$582$	6.87664	−	0.619486i	0.285046	−	0.0256785i
$583$	−9.72297	−	16.8407i	−0.402684	−	0.697470i
$584$	17.5586			0.726581
$585$	2.95170	−	0.536163i	0.122038	−	0.0221676i
$586$	−4.91173			−0.202902
$587$	−5.84863	−	10.1301i	−0.241399	−	0.418115i	0.719714	−	0.694271i	$-0.244273\pi$
$587$	−5.84863	−	10.1301i	−0.241399	−	0.418115i	−0.961113	+	0.276155i	$0.910940\pi$
$588$	7.31398	−	15.7910i	0.301624	−	0.651210i
$589$	29.7446	−	51.5191i	1.22560	−	2.12281i
$590$	−1.55283	+	2.68958i	−0.0639289	+	0.110728i
$591$	−3.28333	−	4.66346i	−0.135058	−	0.191829i
$592$	2.25803	+	3.91101i	0.0928043	+	0.160742i
$593$	14.5999			0.599545			0.299773	−	0.954011i	$-0.403089\pi$
$593$	14.5999			0.599545			0.299773	+	0.954011i	$0.403089\pi$
$594$	−3.48028	+	13.4021i	−0.142798	+	0.549896i
$595$	4.11250			0.168596
$596$	−0.364540	−	0.631402i	−0.0149321	−	0.0258632i
$597$	−19.7222	−	28.0123i	−0.807174	−	1.14647i
$598$	0.755182	−	1.30801i	0.0308817	−	0.0534887i
$599$	−8.74420	+	15.1454i	−0.357278	+	0.618824i	−0.987505	−	0.157587i	$-0.949629\pi$
$599$	−8.74420	+	15.1454i	−0.357278	+	0.618824i	0.630227	+	0.776411i	$0.282962\pi$
$600$	−1.70279	+	3.67636i	−0.0695163	+	0.150087i
$601$	22.3969	+	38.7926i	0.913590	+	1.58238i	0.808952	+	0.587874i	$0.200035\pi$
$601$	22.3969	+	38.7926i	0.913590	+	1.58238i	0.104638	+	0.994510i	$0.466632\pi$
$602$	−4.50236			−0.183503
$603$	−20.9289	−	24.6826i	−0.852289	−	1.00515i
$604$	15.6535			0.636933
$605$	2.77420	+	4.80506i	0.112787	+	0.195354i
$606$	−10.5681	+	0.952038i	−0.429302	+	0.0386739i
$607$	21.1894	−	36.7011i	0.860050	−	1.48965i	−0.0118293	−	0.999930i	$-0.503765\pi$
$607$	21.1894	−	36.7011i	0.860050	−	1.48965i	0.871879	−	0.489721i	$-0.162901\pi$
$608$	−19.0622	+	33.0167i	−0.773075	+	1.33901i
$609$	8.55383	−	0.770577i	0.346619	−	0.0312254i
$610$	−4.70533	−	8.14987i	−0.190513	−	0.329979i
$611$	4.08782			0.165375
$612$	16.1276	+	19.0202i	0.651919	+	0.768846i
$613$	−6.73566			−0.272051			−0.136025	−	0.990705i	$-0.543433\pi$
$613$	−6.73566			−0.272051			−0.136025	+	0.990705i	$0.543433\pi$
$614$	6.03031	+	10.4448i	0.243364	+	0.421518i
$615$	−5.53959	+	11.9601i	−0.223378	+	0.482276i
$616$	3.69771	−	6.40462i	0.148985	−	0.258050i
$617$	−7.39237	+	12.8040i	−0.297606	+	0.515468i	−0.975588	−	0.219610i	$-0.929521\pi$
$617$	−7.39237	+	12.8040i	−0.297606	+	0.515468i	0.677982	+	0.735079i	$0.262855\pi$
$618$	−1.44657	−	2.05463i	−0.0581895	−	0.0826491i
$619$	−13.6898	−	23.7114i	−0.550239	−	0.953041i	−0.998257	−	0.0590168i	$-0.981203\pi$
$619$	−13.6898	−	23.7114i	−0.550239	−	0.953041i	0.448018	−	0.894024i	$-0.352130\pi$
$620$	−14.0519			−0.564337
$621$	3.01127	−	11.5960i	0.120838	−	0.465332i
$622$	11.3096			0.453472
$623$	−4.57540	−	7.92483i	−0.183310	−	0.317502i
$624$	−1.60483	−	2.27941i	−0.0642446	−	0.0912495i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	2.96765	−	5.14011i	0.118611	−	0.205440i
$627$	−19.6937	+	42.5190i	−0.786492	+	1.69805i
$628$	−7.32011	−	12.6788i	−0.292104	−	0.505940i
$629$	−14.8476			−0.592014
$630$	1.50273	−	0.272964i	0.0598701	−	0.0108751i
$631$	19.2458			0.766162			0.383081	−	0.923715i	$-0.374863\pi$
$631$	19.2458			0.766162			0.383081	+	0.923715i	$0.374863\pi$
$632$	8.91102	+	15.4343i	0.354461	+	0.613945i
$633$	4.18861	−	0.377334i	0.166482	−	0.0149977i
$634$	−2.63299	+	4.56048i	−0.104570	+	0.181120i
$635$	−5.74367	+	9.94833i	−0.227931	+	0.394787i
$636$	−12.9539	+	1.16696i	−0.513657	+	0.0462731i
$637$	−3.19799	−	5.53909i	−0.126709	−	0.219467i
$638$	−17.0018			−0.673107
$639$	−0.311321	+	0.869259i	−0.0123157	+	0.0343874i
$640$	11.1140			0.439318
$641$	13.9581	+	24.1761i	0.551310	+	0.954898i	0.998180	+	0.0602987i	$0.0192053\pi$
$641$	13.9581	+	24.1761i	0.551310	+	0.954898i	−0.446870	+	0.894599i	$0.647461\pi$
$642$	−7.39053	+	15.9562i	−0.291681	+	0.629743i
$643$	−1.62382	+	2.81254i	−0.0640372	+	0.110916i	−0.896266	−	0.443516i	$-0.853731\pi$
$643$	−1.62382	+	2.81254i	−0.0640372	+	0.110916i	0.832229	+	0.554432i	$0.187064\pi$
$644$	−1.40746	+	2.43779i	−0.0554617	+	0.0960625i
$645$	−8.81815	−	12.5248i	−0.347214	−	0.493164i
$646$	−11.5262	−	19.9639i	−0.453492	−	0.785471i
$647$	−1.47061			−0.0578155			−0.0289077	−	0.999582i	$-0.509203\pi$
$647$	−1.47061			−0.0578155			−0.0289077	+	0.999582i	$0.509203\pi$
$648$	16.2658	+	13.3654i	0.638979	+	0.525041i
$649$	19.2862			0.757050
$650$	0.327533	+	0.567303i	0.0128469	+	0.0222515i
$651$	6.93199	+	9.84582i	0.271686	+	0.385888i
$652$	7.01973	−	12.1585i	0.274914	−	0.476165i
$653$	1.19989	−	2.07827i	0.0469554	−	0.0813291i	−0.841592	−	0.540113i	$-0.818381\pi$
$653$	1.19989	−	2.07827i	0.0469554	−	0.0813291i	0.888548	+	0.458784i	$0.151715\pi$
$654$	−2.80523	+	6.05653i	−0.109693	+	0.236829i
$655$	6.28967	+	10.8940i	0.245758	+	0.425665i
$656$	12.2479			0.478198
$657$	7.59283	−	21.2004i	0.296224	−	0.827107i
$658$	2.08113			0.0811311
$659$	1.75372	+	3.03754i	0.0683154	+	0.118326i	0.898160	−	0.439669i	$-0.144904\pi$
$659$	1.75372	+	3.03754i	0.0683154	+	0.118326i	−0.829844	+	0.557995i	$0.811571\pi$
$660$	11.0237	−	0.993081i	0.429099	−	0.0386556i
$661$	10.1473	−	17.5757i	0.394685	−	0.683614i	−0.598376	−	0.801215i	$-0.704187\pi$
$661$	10.1473	−	17.5757i	0.394685	−	0.683614i	0.993061	+	0.117601i	$0.0375205\pi$
$662$	9.78222	−	16.9433i	0.380197	−	0.658520i
$663$	9.12825	−	0.822324i	0.354512	−	0.0319364i
$664$	−14.6545	−	25.3823i	−0.568705	−	0.985026i
$665$	5.16860			0.200430
$666$	−5.42541	+	0.985501i	−0.210230	+	0.0381874i
$667$	14.7105			0.569595
$668$	−12.8381	−	22.2363i	−0.496722	−	0.860348i
$669$	−6.88440	+	14.8635i	−0.266166	+	0.574657i
$670$	3.53312	−	6.11954i	0.136496	−	0.236419i
$671$	−29.2202	+	50.6109i	−1.12803	+	1.95381i
$672$	−4.44247	−	6.30983i	−0.171372	−	0.243407i
$673$	−4.94555	−	8.56594i	−0.190637	−	0.330193i	0.754825	−	0.655927i	$-0.227722\pi$
$673$	−4.94555	−	8.56594i	−0.190637	−	0.330193i	−0.945462	+	0.325734i	$0.894389\pi$
$674$	15.8583			0.610838
$675$	3.70253	+	3.64572i	0.142510	+	0.140324i
$676$	−1.57089			−0.0604188
$677$	−4.01710	−	6.95783i	−0.154390	−	0.267411i	0.778447	−	0.627711i	$-0.216008\pi$
$677$	−4.01710	−	6.95783i	−0.154390	−	0.267411i	−0.932837	+	0.360300i	$0.882674\pi$
$678$	6.90787	+	9.81155i	0.265295	+	0.376810i
$679$	−2.36472	+	4.09581i	−0.0907496	+	0.157183i
$680$	−6.18889	+	10.7195i	−0.237333	+	0.411073i
$681$	17.5306	−	37.8487i	0.671773	−	1.45037i
$682$	−11.9185	−	20.6434i	−0.456383	−	0.790478i
$683$	0.652224			0.0249567			0.0124783	−	0.999922i	$-0.496028\pi$
$683$	0.652224			0.0249567			0.0124783	+	0.999922i	$0.496028\pi$
$684$	20.2692	+	23.9046i	0.775012	+	0.914016i
$685$	1.81204			0.0692347
$686$	−3.40999	−	5.90628i	−0.130194	−	0.225503i
$687$	−17.2058	+	1.55000i	−0.656443	+	0.0591360i
$688$	−7.11681	+	12.3267i	−0.271326	+	0.469950i
$689$	−2.39013	+	4.13982i	−0.0910566	+	0.157715i
$690$	2.60548	−	0.234716i	0.0991888	−	0.00893549i
$691$	−20.5644	−	35.6186i	−0.782308	−	1.35500i	−0.930594	−	0.366052i	$-0.880709\pi$
$691$	−20.5644	−	35.6186i	−0.782308	−	1.35500i	0.148286	−	0.988944i	$-0.452624\pi$
$692$	−17.2810			−0.656926
$693$	−6.13400	−	7.23418i	−0.233011	−	0.274804i
$694$	−15.0104			−0.569786
$695$	−10.2052	−	17.6760i	−0.387107	−	0.670489i
$696$	−10.8641	+	23.4557i	−0.411803	+	0.889087i
$697$	−20.1339	+	34.8730i	−0.762628	+	1.32091i
$698$	4.04748	−	7.01044i	0.153199	−	0.265349i
$699$	18.2203	+	25.8791i	0.689155	+	0.978838i
$700$	−0.610435	−	1.05730i	−0.0230723	−	0.0399623i
$701$	28.9154			1.09212			0.546060	−	0.837746i	$-0.316127\pi$
$701$	28.9154			1.09212			0.546060	+	0.837746i	$0.316127\pi$
$702$	3.28093	−	0.906362i	0.123831	−	0.0342084i
$703$	−18.6606			−0.703796
$704$	1.09086	+	1.88942i	0.0411132	+	0.0712101i
$705$	4.07603	+	5.78937i	0.153512	+	0.218040i
$706$	8.85584	−	15.3388i	0.333294	−	0.577282i
$707$	3.63415	−	6.29452i	0.136676	−	0.236730i
$708$	5.42145	−	11.7050i	0.203750	−	0.439900i
$709$	19.1429	+	33.1565i	0.718927	+	1.24522i	0.961425	+	0.275066i	$0.0886998\pi$
$709$	19.1429	+	33.1565i	0.718927	+	1.24522i	−0.242498	+	0.970152i	$0.577967\pi$
$710$	−0.201613			−0.00756641
$711$	22.4889	−	4.08501i	0.843400	−	0.153200i
$712$	27.5421			1.03218
$713$	10.3123	+	17.8614i	0.386199	+	0.668916i
$714$	4.64725	−	0.418650i	0.173919	−	0.0156676i
$715$	2.03399	−	3.52297i	0.0760668	−	0.131752i
$716$	−2.25601	+	3.90752i	−0.0843110	+	0.146031i
$717$	45.7902	−	4.12504i	1.71007	−	0.154052i
$718$	9.33121	+	16.1621i	0.348238	+	0.603165i
$719$	−31.0939			−1.15961			−0.579803	−	0.814757i	$-0.696870\pi$
$719$	−31.0939			−1.15961			−0.579803	+	0.814757i	$0.696870\pi$
$720$	1.62801	−	4.54567i	0.0606724	−	0.169407i
$721$	1.72120			0.0641009
$722$	−8.26301	−	14.3120i	−0.307517	−	0.532636i
$723$	10.4961	−	22.6612i	0.390354	−	0.842779i
$724$	−8.51885	+	14.7551i	−0.316600	+	0.548368i
$725$	−3.19008	+	5.52538i	−0.118477	+	0.205207i
$726$	3.62409	+	5.14745i	0.134503	+	0.191040i
$727$	11.6752	+	20.2220i	0.433008	+	0.749992i	0.997131	−	0.0756988i	$-0.0241187\pi$
$727$	11.6752	+	20.2220i	0.433008	+	0.749992i	−0.564122	+	0.825691i	$0.690785\pi$
$728$	−1.81796			−0.0673782
$729$	23.1712	−	13.8599i	0.858192	−	0.513328i
$730$	4.91716			0.181992
$731$	−23.3983	−	40.5270i	−0.865417	−	1.49895i
$732$	22.5023	+	31.9610i	0.831708	+	1.18131i
$733$	−0.558131	+	0.966711i	−0.0206150	+	0.0357063i	−0.876149	−	0.482041i	$-0.839896\pi$
$733$	−0.558131	+	0.966711i	−0.0206150	+	0.0357063i	0.855534	+	0.517747i	$0.173229\pi$
$734$	9.93081	−	17.2007i	0.366553	−	0.634888i
$735$	4.65595	−	10.0523i	0.171737	−	0.370783i
$736$	−6.60879	−	11.4468i	−0.243603	−	0.421933i
$737$	−43.8815			−1.61640
$738$	−5.04238	+	14.0792i	−0.185613	+	0.518261i
$739$	1.73962			0.0639930			0.0319965	−	0.999488i	$-0.489813\pi$
$739$	1.73962			0.0639930			0.0319965	+	0.999488i	$0.489813\pi$
$740$	2.20390	+	3.81726i	0.0810168	+	0.140325i
$741$	11.4724	−	1.03350i	0.421449	−	0.0379665i
$742$	−1.21683	+	2.10761i	−0.0446712	+	0.0773728i
$743$	13.6377	−	23.6211i	0.500317	−	0.866575i	−0.499683	−	0.866209i	$-0.666550\pi$
$743$	13.6377	−	23.6211i	0.500317	−	0.866575i	1.00000		0.000366439i	$-0.000116641\pi$
$744$	−36.0957	+	3.25170i	−1.32333	+	0.119213i
$745$	−0.232060	−	0.401939i	−0.00850201	−	0.0147259i
$746$	−6.11582			−0.223916
$747$	−36.9839	+	6.71795i	−1.35317	+	0.245797i
$748$	33.8147			1.23639
$749$	−6.02259	−	10.4314i	−0.220061	−	0.381156i
$750$	−0.476854	+	1.02954i	−0.0174123	+	0.0375933i
$751$	−16.3324	+	28.2885i	−0.595977	+	1.03226i	0.397432	+	0.917632i	$0.369902\pi$
$751$	−16.3324	+	28.2885i	−0.595977	+	1.03226i	−0.993408	+	0.114630i	$0.963432\pi$
$752$	3.28961	−	5.69778i	0.119960	−	0.207777i
$753$	13.7144	+	19.4792i	0.499780	+	0.709860i
$754$	2.08971	+	3.61949i	0.0761028	+	0.131814i
$755$	9.96476			0.362655
$756$	−6.11479	+	1.68922i	−0.222393	+	0.0614363i
$757$	43.4319			1.57856			0.789279	−	0.614035i	$-0.210455\pi$
$757$	43.4319			1.57856			0.789279	+	0.614035i	$0.210455\pi$
$758$	7.37459	+	12.7732i	0.267857	+	0.463942i
$759$	−9.35235	−	13.2836i	−0.339469	−	0.482163i
$760$	−7.77822	+	13.4723i	−0.282146	+	0.488690i
$761$	−24.7445	+	42.8587i	−0.896987	+	1.55363i	−0.0656602	+	0.997842i	$0.520915\pi$
$761$	−24.7445	+	42.8587i	−0.896987	+	1.55363i	−0.831326	+	0.555784i	$0.812418\pi$
$762$	−5.47779	+	11.8266i	−0.198439	+	0.428433i
$763$	−2.28600	−	3.95947i	−0.0827588	−	0.143342i
$764$	−21.8281			−0.789711
$765$	10.2665	+	12.1079i	0.371187	+	0.437763i
$766$	−1.98734			−0.0718055
$767$	−2.37049	−	4.10581i	−0.0855935	−	0.148252i
$768$	14.4095	−	1.29809i	0.519957	−	0.0468407i
$769$	4.52027	−	7.82934i	0.163005	−	0.282333i	−0.772940	−	0.634479i	$-0.781215\pi$
$769$	4.52027	−	7.82934i	0.163005	−	0.282333i	0.935945	+	0.352146i	$0.114548\pi$
$770$	1.03552	−	1.79357i	0.0373174	−	0.0646356i
$771$	8.47624	−	0.763587i	0.305264	−	0.0274999i
$772$	17.1123	+	29.6394i	0.615885	+	1.06674i
$773$	−8.64817			−0.311053			−0.155527	−	0.987832i	$-0.549707\pi$
$773$	−8.64817			−0.311053			−0.155527	+	0.987832i	$0.549707\pi$
$774$	−11.2398	−	13.2557i	−0.404006	−	0.476468i
$775$	−8.94517			−0.321320
$776$	−7.11733	−	12.3276i	−0.255497	−	0.442534i
$777$	1.58745	−	3.42733i	0.0569495	−	0.122955i
$778$	5.99343	−	10.3809i	0.214875	−	0.372174i
$779$	−25.3044	+	43.8285i	−0.906624	+	1.57032i
$780$	−1.56636	−	2.22477i	−0.0560846	−	0.0796595i
$781$	0.626011	+	1.08428i	0.0224004	+	0.0387987i
$782$	7.99215			0.285799
$783$	23.6227	+	23.2603i	0.844207	+	0.831255i
$784$	−10.2942			−0.367648
$785$	−4.65985	−	8.07110i	−0.166317	−	0.288070i
$786$	8.21652	+	11.6703i	0.293074	+	0.416266i
$787$	−9.17712	+	15.8952i	−0.327129	+	0.566604i	−0.981941	−	0.189188i	$-0.939415\pi$
$787$	−9.17712	+	15.8952i	−0.327129	+	0.566604i	0.654812	+	0.755792i	$0.272748\pi$
$788$	−2.58633	+	4.47965i	−0.0921342	+	0.159581i
$789$	18.9793	−	40.9766i	0.675681	−	1.45880i
$790$	2.49546	+	4.32227i	0.0887846	+	0.153779i
$791$	−8.21935			−0.292246
$792$	28.0874	−	5.10194i	0.998042	−	0.181290i
$793$	14.3660			0.510151
$794$	9.65412	+	16.7214i	0.342612	+	0.593421i
$795$	−8.24625	+	0.742868i	−0.292464	+	0.0263468i
$796$	−15.5355	+	26.9082i	−0.550640	+	0.953737i
$797$	−7.12643	+	12.3433i	−0.252431	+	0.437223i	−0.964195	−	0.265196i	$-0.914563\pi$
$797$	−7.12643	+	12.3433i	−0.252431	+	0.437223i	0.711764	+	0.702419i	$0.247897\pi$
$798$	5.84067	−	0.526161i	0.206758	−	0.0186259i
$799$	10.8154	+	18.7329i	0.382622	+	0.662721i
$800$	5.73264			0.202679
$801$	11.9099	−	33.2545i	0.420817	−	1.17499i
$802$	−18.1896			−0.642295
$803$	−15.2678	−	26.4447i	−0.538790	−	0.933212i
$804$	−12.3353	+	26.6321i	−0.435033	+	0.939242i
$805$	−0.895965	+	1.55186i	−0.0315786	+	0.0546957i
$806$	−2.92984	+	5.07463i	−0.103199	+	0.178746i
$807$	29.6419	+	42.1017i	1.04344	+	1.48205i
$808$	10.9380	+	18.9453i	0.384799	+	0.666492i
$809$	−2.15221			−0.0756676			−0.0378338	−	0.999284i	$-0.512046\pi$
$809$	−2.15221			−0.0756676			−0.0378338	+	0.999284i	$0.512046\pi$
$810$	4.55510	+	3.74286i	0.160050	+	0.131511i
$811$	−30.3748			−1.06660			−0.533302	−	0.845925i	$-0.679049\pi$
$811$	−30.3748			−1.06660			−0.533302	+	0.845925i	$0.679049\pi$
$812$	−3.89467	−	6.74577i	−0.136676	−	0.236730i
$813$	14.2567	+	20.2495i	0.500006	+	0.710180i
$814$	−3.73860	+	6.47544i	−0.131038	+	0.226964i
$815$	4.46863	−	7.73990i	0.156529	−	0.271117i
$816$	6.19964	−	13.3851i	0.217031	−	0.468572i
$817$	−29.4070	−	50.9344i	−1.02882	−	1.78197i
$818$	−6.42510			−0.224648
$819$	−0.786136	+	2.19502i	−0.0274698	+	0.0767003i
$820$	11.9543			0.417461
$821$	5.98030	+	10.3582i	0.208714	+	0.361503i	0.951310	−	0.308237i	$-0.0997389\pi$
$821$	5.98030	+	10.3582i	0.208714	+	0.361503i	−0.742596	+	0.669740i	$0.766406\pi$
$822$	2.04767	−	0.184465i	0.0714206	−	0.00643397i
$823$	−1.94193	+	3.36352i	−0.0676914	+	0.117245i	−0.897885	−	0.440231i	$-0.854897\pi$
$823$	−1.94193	+	3.36352i	−0.0676914	+	0.117245i	0.830193	+	0.557476i	$0.188230\pi$
$824$	−2.59024	+	4.48642i	−0.0902352	+	0.156292i
$825$	7.01752	−	0.632178i	0.244319	−	0.0220096i
$826$	−1.20683	−	2.09030i	−0.0419911	−	0.0727307i
$827$	−30.4261			−1.05802			−0.529010	−	0.848615i	$-0.677437\pi$
$827$	−30.4261			−1.05802			−0.529010	+	0.848615i	$0.677437\pi$
$828$	−10.6909	+	1.94195i	−0.371535	+	0.0674876i
$829$	−23.8577			−0.828613			−0.414307	−	0.910137i	$-0.635976\pi$
$829$	−23.8577			−0.828613			−0.414307	+	0.910137i	$0.635976\pi$
$830$	−4.10388	−	7.10813i	−0.142448	−	0.246727i
$831$	1.36753	−	2.95252i	0.0474391	−	0.102422i
$832$	0.268157	−	0.464462i	0.00929668	−	0.0161023i
$833$	16.9223	−	29.3103i	0.586323	−	1.01554i
$834$	−13.3316	−	18.9355i	−0.461637	−	0.655684i
$835$	−8.17252	−	14.1552i	−0.282822	−	0.489862i
$836$	42.4984			1.46984
$837$	−11.6826	+	44.9883i	−0.403811	+	1.55502i
$838$	9.48724			0.327731
$839$	9.51666	+	16.4833i	0.328552	+	0.569068i	0.982225	−	0.187709i	$-0.0601061\pi$
$839$	9.51666	+	16.4833i	0.328552	+	0.569068i	−0.653673	+	0.756777i	$0.726773\pi$
$840$	−1.81272	−	2.57469i	−0.0625447	−	0.0888351i
$841$	−5.85322	+	10.1381i	−0.201835	+	0.349589i
$842$	11.7330	−	20.3221i	0.404346	−	0.700347i
$843$	2.60013	−	5.61371i	0.0895531	−	0.193346i
$844$	−1.90713	−	3.30325i	−0.0656461	−	0.113702i
$845$	−1.00000			−0.0344010
$846$	5.19539	+	6.12723i	0.178621	+	0.210658i
$847$	−4.31213			−0.148167
$848$	3.84684	+	6.66292i	0.132101	+	0.228806i
$849$	23.7166	−	2.13653i	0.813953	−	0.0733255i
$850$	−1.73315	+	3.00191i	−0.0594466	+	0.102965i
$851$	3.23477	−	5.60278i	0.110886	−	0.192061i
$852$	0.834037	−	0.0751347i	0.0285736	−	0.00257407i
$853$	−10.5264	−	18.2322i	−0.360416	−	0.624259i	0.627613	−	0.778525i	$-0.284032\pi$
$853$	−10.5264	−	18.2322i	−0.360416	−	0.624259i	−0.988029	+	0.154266i	$0.950699\pi$
$854$	7.31381			0.250273
$855$	12.9030	+	15.2173i	0.441273	+	0.520419i
$856$	36.2536			1.23912
$857$	4.94067	+	8.55749i	0.168770	+	0.292318i	0.937988	−	0.346669i	$-0.112687\pi$
$857$	4.94067	+	8.55749i	0.168770	+	0.292318i	−0.769218	+	0.638987i	$0.779354\pi$
$858$	1.93983	−	4.18812i	0.0662247	−	0.142980i
$859$	4.91195	−	8.50775i	0.167594	−	0.290281i	−0.769980	−	0.638068i	$-0.779734\pi$
$859$	4.91195	−	8.50775i	0.167594	−	0.290281i	0.937573	+	0.347788i	$0.113067\pi$
$860$	−6.94620	+	12.0312i	−0.236864	+	0.410260i
$861$	−5.89721	−	8.37606i	−0.200976	−	0.285456i
$862$	−2.40642	−	4.16805i	−0.0819631	−	0.141964i
$863$	46.5764			1.58548			0.792739	−	0.609561i	$-0.208654\pi$
$863$	46.5764			1.58548			0.792739	+	0.609561i	$0.208654\pi$
$864$	7.48698	−	28.8314i	0.254712	−	0.980865i
$865$	−11.0008			−0.374038
$866$	2.14633	+	3.71755i	0.0729352	+	0.126327i
$867$	10.9687	+	15.5793i	0.372515	+	0.529100i
$868$	5.46044	−	9.45777i	0.185340	−	0.321017i
$869$	15.4969	−	26.8414i	0.525696	−	0.910532i
$870$	−3.04241	+	6.56860i	−0.103147	+	0.222696i
$871$	5.39353	+	9.34188i	0.182753	+	0.316537i
$872$	13.7608			0.465999
$873$	−17.9621	+	3.26274i	−0.607926	+	0.110427i
$874$	10.0446			0.339762
$875$	−0.388592	−	0.673061i	−0.0131368	−	0.0227536i
$876$	−20.3414	+	1.83247i	−0.687272	+	0.0619133i
$877$	27.9143	−	48.3489i	0.942598	−	1.63263i	0.182106	−	0.983279i	$-0.441709\pi$
$877$	27.9143	−	48.3489i	0.942598	−	1.63263i	0.760491	−	0.649348i	$-0.224958\pi$
$878$	0.560437	−	0.970705i	0.0189138	−	0.0327597i
$879$	12.9347	−	1.16523i	0.436275	−	0.0393021i
$880$	−3.27364	−	5.67011i	−0.110354	−	0.191140i
$881$	1.22939			0.0414192			0.0207096	−	0.999786i	$-0.493407\pi$
$881$	1.22939			0.0414192			0.0207096	+	0.999786i	$0.493407\pi$
$882$	4.23805	−	11.8333i	0.142703	−	0.398449i
$883$	−5.89957			−0.198536			−0.0992681	−	0.995061i	$-0.531650\pi$
$883$	−5.89957			−0.198536			−0.0992681	+	0.995061i	$0.531650\pi$
$884$	−4.15621	−	7.19877i	−0.139788	−	0.242121i
$885$	3.45120	−	7.45118i	0.116011	−	0.250469i
$886$	7.23571	−	12.5326i	0.243088	−	0.421041i
$887$	21.2331	−	36.7769i	0.712939	−	1.23485i	−0.250810	−	0.968036i	$-0.580697\pi$
$887$	21.2331	−	36.7769i	0.712939	−	1.23485i	0.963749	−	0.266810i	$-0.0859697\pi$
$888$	6.54459	+	9.29557i	0.219622	+	0.311939i
$889$	−4.46389	−	7.73168i	−0.149714	−	0.259312i
$890$	7.71295			0.258539
$891$	5.98563	−	36.1192i	0.200526	−	1.21004i
$892$	14.8563			0.497426
$893$	13.5929	+	23.5435i	0.454867	+	0.787853i
$894$	−0.303152	−	0.430580i	−0.0101389	−	0.0144007i
$895$	−1.43613	+	2.48746i	−0.0480047	+	0.0831465i
$896$	−4.31880	+	7.48037i	−0.144281	+	0.249902i
$897$	−1.67841	+	3.62371i	−0.0560405	+	0.120992i
$898$	−11.5973	−	20.0872i	−0.387008	−	0.670318i
$899$	−57.0716			−1.90345
$900$	1.58898	−	4.43671i	0.0529662	−	0.147890i
$901$	−25.2949			−0.842695
$902$	10.1393	+	17.5619i	0.337603	+	0.584746i
$903$	11.8566	−	1.06811i	0.394564	−	0.0355445i
$904$	12.3693	−	21.4242i	0.411396	−	0.712560i
$905$	−5.42295	+	9.39282i	−0.180265	+	0.312228i
$906$	11.2605	−	1.01441i	0.374105	−	0.0337014i
$907$	5.58861	+	9.67977i	0.185567	+	0.321411i	0.943767	−	0.330610i	$-0.107255\pi$
$907$	5.58861	+	9.67977i	0.185567	+	0.321411i	−0.758200	+	0.652021i	$0.773921\pi$
$908$	−37.8304			−1.25544
$909$	27.6046	−	5.01424i	0.915585	−	0.166312i
$910$	−0.509106			−0.0168767
$911$	14.0144	+	24.2737i	0.464319	+	0.804224i	0.999171	−	0.0407218i	$-0.0129657\pi$
$911$	14.0144	+	24.2737i	0.464319	+	0.804224i	−0.534851	+	0.844946i	$0.679632\pi$
$912$	7.79171	−	16.8224i	0.258009	−	0.557046i
$913$	−25.4852	+	44.1417i	−0.843437	+	1.46088i
$914$	0.830067	−	1.43772i	0.0274562	−	0.0475555i
$915$	14.3245	+	20.3458i	0.473555	+	0.672611i
$916$	7.83403	+	13.5689i	0.258844	+	0.448330i
$917$	−9.77645			−0.322847
$918$	12.8341	+	12.6372i	0.423588	+	0.417089i
$919$	43.1860			1.42457			0.712287	−	0.701888i	$-0.247659\pi$
$919$	43.1860			1.42457			0.712287	+	0.701888i	$0.247659\pi$
$920$	−2.69667	−	4.67077i	−0.0889067	−	0.153991i
$921$	−18.3582	−	26.0750i	−0.604924	−	0.859201i
$922$	0.719732	−	1.24661i	0.0237031	−	0.0410550i
$923$	0.153888	−	0.266541i	0.00506528	−	0.00877332i
$924$	−3.61533	+	7.80555i	−0.118936	+	0.256784i
$925$	1.40296	+	2.43000i	0.0461291	+	0.0798979i
$926$	−16.6739			−0.547937
$927$	4.29685	+	5.06752i	0.141127	+	0.166439i
$928$	36.5752			1.20064
$929$	9.19180	+	15.9207i	0.301573	+	0.522340i	0.976492	−	0.215551i	$-0.0691549\pi$
$929$	9.19180	+	15.9207i	0.301573	+	0.522340i	−0.674919	+	0.737892i	$0.735822\pi$
$930$	−10.1083	+	0.910614i	−0.331465	+	0.0298602i
$931$	21.2680	−	36.8372i	0.697030	−	1.20729i
$932$	14.3524	−	24.8591i	0.470129	−	0.814288i
$933$	−29.7829	+	2.68301i	−0.975047	+	0.0878377i
$934$	5.06920	+	8.78011i	0.165869	+	0.287294i
$935$	21.5258			0.703970
$936$	−4.53840	−	5.35240i	−0.148342	−	0.174949i
$937$	−13.2414			−0.432579			−0.216289	−	0.976329i	$-0.569395\pi$
$937$	−13.2414			−0.432579			−0.216289	+	0.976329i	$0.569395\pi$
$938$	2.74588	+	4.75601i	0.0896562	+	0.155289i
$939$	−6.59566	+	14.2401i	−0.215241	+	0.464709i
$940$	3.21076	−	5.56119i	0.104723	−	0.181386i
$941$	−7.66547	+	13.2770i	−0.249887	+	0.432817i	−0.963494	−	0.267729i	$-0.913727\pi$
$941$	−7.66547	+	13.2770i	−0.249887	+	0.432817i	0.713607	+	0.700546i	$0.247060\pi$
$942$	−6.08741	−	8.64622i	−0.198339	−	0.281709i
$943$	−8.77292	−	15.1951i	−0.285685	−	0.494822i
$944$	−7.63048			−0.248351
$945$	−3.89257	+	1.07533i	−0.126625	+	0.0349804i
$946$	−23.5665			−0.766213
$947$	−22.0478	−	38.1879i	−0.716457	−	1.24094i	−0.962395	−	0.271654i	$-0.912429\pi$
$947$	−22.0478	−	38.1879i	−0.716457	−	1.24094i	0.245938	−	0.969286i	$-0.420904\pi$
$948$	−11.9340	−	16.9505i	−0.387600	−	0.550525i
$949$	−3.75318	+	6.50070i	−0.121833	+	0.211022i
$950$	−2.17823	+	3.77280i	−0.0706711	+	0.122406i
$951$	5.85189	−	12.6343i	0.189760	−	0.409695i
$952$	−4.80991	−	8.33101i	−0.155890	−	0.270009i
$953$	−23.1623			−0.750300			−0.375150	−	0.926964i	$-0.622409\pi$
$953$	−23.1623			−0.750300			−0.375150	+	0.926964i	$0.622409\pi$
$954$	−9.24289	+	1.67893i	−0.299250	+	0.0543573i
$955$	−13.8954			−0.449643
$956$	−20.8489	−	36.1113i	−0.674300	−	1.16792i
$957$	44.7729	−	4.03339i	1.44730	−	0.130381i
$958$	3.15163	−	5.45878i	0.101824	−	0.176365i
$959$	−0.704146	+	1.21962i	−0.0227381	+	0.0393835i
$960$	0.925177	−	0.0833452i	0.0298600	−	0.00268995i
$961$	−24.5081	−	42.4492i	−0.790582	−	1.36933i
$962$	1.83806			0.0592615
$963$	15.6770	−	43.7728i	0.505185	−	1.41056i
$964$	−22.6502			−0.729514
$965$	10.8934	+	18.8679i	0.350670	+	0.607379i
$966$	−0.854489	+	1.84485i	−0.0274927	+	0.0593572i
$967$	14.4178	−	24.9723i	0.463644	−	0.803056i	−0.535495	−	0.844539i	$-0.679875\pi$
$967$	14.4178	−	24.9723i	0.463644	−	0.803056i	0.999139	+	0.0414828i	$0.0132082\pi$
$968$	6.48932	−	11.2398i	0.208575	−	0.361262i
$969$	35.0894	+	49.8391i	1.12724	+	1.60106i
$970$	−1.99315	−	3.45224i	−0.0639963	−	0.110845i
$971$	−1.72410			−0.0553290			−0.0276645	−	0.999617i	$-0.508807\pi$
$971$	−1.72410			−0.0553290			−0.0276645	+	0.999617i	$0.508807\pi$
$972$	−20.2385	−	13.7860i	−0.649149	−	0.442186i
$973$	15.8627			0.508535
$974$	6.58219	+	11.4007i	0.210907	+	0.365302i
$975$	−0.997116	−	1.41625i	−0.0319333	−	0.0453563i
$976$	11.5608	−	20.0239i	0.370053	−	0.640950i
$977$	−1.59192	+	2.75729i	−0.0509301	+	0.0882135i	−0.890367	−	0.455244i	$-0.849552\pi$
$977$	−1.59192	+	2.75729i	−0.0509301	+	0.0882135i	0.839436	+	0.543458i	$0.182885\pi$
$978$	4.26178	−	9.20123i	0.136277	−	0.294223i
$979$	−23.9488	−	41.4805i	−0.765407	−	1.32572i
$980$	−10.0474			−0.320952
$981$	5.95055	−	16.6149i	0.189986	−	0.530473i
$982$	1.94339			0.0620162
$983$	−5.85946	−	10.1489i	−0.186888	−	0.323699i	0.757323	−	0.653040i	$-0.226507\pi$
$983$	−5.85946	−	10.1489i	−0.186888	−	0.323699i	−0.944211	+	0.329341i	$0.893173\pi$
$984$	30.7074	−	2.76630i	0.978917	−	0.0881864i
$985$	−1.64641	+	2.85167i	−0.0524590	+	0.0908617i
$986$	−11.0578	+	19.1527i	−0.352152	+	0.609945i
$987$	−5.48051	+	0.493715i	−0.174447	+	0.0157151i
$988$	−5.22353	−	9.04743i	−0.166183	−	0.287837i
$989$	20.3906			0.648382
$990$	7.86566	−	1.42876i	0.249987	−	0.0454090i
$991$	45.8521			1.45654			0.728271	−	0.685290i	$-0.240324\pi$
$991$	45.8521			1.45654			0.728271	+	0.685290i	$0.240324\pi$
$992$	25.6397	+	44.4093i	0.814062	+	1.41000i
$993$	−21.7412	+	46.9396i	−0.689936	+	1.48958i
$994$	0.0783452	−	0.135698i	0.00248496	−	0.00430408i
$995$	−9.88960	+	17.1293i	−0.313521	+	0.543035i
$996$	19.6260	+	27.8756i	0.621873	+	0.883274i
$997$	12.0839	+	20.9299i	0.382701	+	0.662857i	0.991447	−	0.130508i	$-0.0416607\pi$
$997$	12.0839	+	20.9299i	0.382701	+	0.662857i	−0.608747	+	0.793365i	$0.708327\pi$
$998$	9.13431			0.289141
$999$	14.0536	−	3.88233i	0.444636	−	0.122831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.e.391.4	yes	16
3.2	odd	2		1755.2.i.f.1171.5		16
9.2	odd	6		1755.2.i.f.586.5		16
9.4	even	3		5265.2.a.bf.1.5		8
9.5	odd	6		5265.2.a.ba.1.4		8
9.7	even	3	inner	585.2.i.e.196.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.4	✓	16	9.7	even	3	inner
585.2.i.e.391.4	yes	16	1.1	even	1	trivial
1755.2.i.f.586.5		16	9.2	odd	6
1755.2.i.f.1171.5		16	3.2	odd	2
5265.2.a.ba.1.4		8	9.5	odd	6
5265.2.a.bf.1.5		8	9.4	even	3

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.327533 - 0.567303i) q^{2} +(0.997116 + 1.41625i) q^{3} +(0.785445 - 1.36043i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.476854 - 1.02954i) q^{6} +(0.388592 + 0.673061i) q^{7} -2.33917 q^{8} +(-1.01152 + 2.82433i) q^{9} +O(q^{10})\)	\(q+(-0.327533 - 0.567303i) q^{2} +(0.997116 + 1.41625i) q^{3} +(0.785445 - 1.36043i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.476854 - 1.02954i) q^{6} +(0.388592 + 0.673061i) q^{7} -2.33917 q^{8} +(-1.01152 + 2.82433i) q^{9} -0.655066 q^{10} +(2.03399 + 3.52297i) q^{11} +(2.70989 - 0.244122i) q^{12} +(0.500000 - 0.866025i) q^{13} +(0.254553 - 0.440899i) q^{14} +(1.72507 - 0.155404i) q^{15} +(-0.804735 - 1.39384i) q^{16} +5.29154 q^{17} +(1.93356 - 0.351222i) q^{18} +6.65042 q^{19} +(-0.785445 - 1.36043i) q^{20} +(-0.565750 + 1.22146i) q^{21} +(1.33239 - 2.30778i) q^{22} +(-1.15283 + 1.99677i) q^{23} +(-2.33242 - 3.31284i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.655066 q^{26} +(-5.00855 + 1.38362i) q^{27} +1.22087 q^{28} +(-3.19008 - 5.52538i) q^{29} +(-0.653176 - 0.927736i) q^{30} +(4.47259 - 7.74675i) q^{31} +(-2.86632 + 4.96461i) q^{32} +(-2.96128 + 6.39344i) q^{33} +(-1.73315 - 3.00191i) q^{34} +0.777184 q^{35} +(3.04781 + 3.59445i) q^{36} -2.80592 q^{37} +(-2.17823 - 3.77280i) q^{38} +(1.72507 - 0.155404i) q^{39} +(-1.16958 + 2.02578i) q^{40} +(-3.80493 + 6.59034i) q^{41} +(0.878241 - 0.0791169i) q^{42} +(-4.42183 - 7.65883i) q^{43} +6.39034 q^{44} +(1.94018 + 2.28817i) q^{45} +1.51036 q^{46} +(2.04391 + 3.54016i) q^{47} +(1.17161 - 2.52953i) q^{48} +(3.19799 - 5.53909i) q^{49} +(-0.327533 + 0.567303i) q^{50} +(5.27628 + 7.49413i) q^{51} +(-0.785445 - 1.36043i) q^{52} -4.78025 q^{53} +(2.42540 + 2.38819i) q^{54} +4.06797 q^{55} +(-0.908981 - 1.57440i) q^{56} +(6.63124 + 9.41864i) q^{57} +(-2.08971 + 3.61949i) q^{58} +(2.37049 - 4.10581i) q^{59} +(1.14353 - 2.46889i) q^{60} +(7.18299 + 12.4413i) q^{61} -5.85967 q^{62} +(-2.29401 + 0.416697i) q^{63} +0.536314 q^{64} +(-0.500000 - 0.866025i) q^{65} +(4.59693 - 0.414118i) q^{66} +(-5.39353 + 9.34188i) q^{67} +(4.15621 - 7.19877i) q^{68} +(-3.97743 + 0.358309i) q^{69} +(-0.254553 - 0.440899i) q^{70} +0.307776 q^{71} +(2.36611 - 6.60657i) q^{72} -7.50636 q^{73} +(0.919032 + 1.59181i) q^{74} +(0.727949 - 1.57165i) q^{75} +(5.22353 - 9.04743i) q^{76} +(-1.58078 + 2.73799i) q^{77} +(-0.653176 - 0.927736i) q^{78} +(-3.80949 - 6.59822i) q^{79} -1.60947 q^{80} +(-6.95366 - 5.71372i) q^{81} +4.98496 q^{82} +(6.26484 + 10.8510i) q^{83} +(1.21735 + 1.72905i) q^{84} +(2.64577 - 4.58261i) q^{85} +(-2.89659 + 5.01704i) q^{86} +(4.64443 - 10.0274i) q^{87} +(-4.75783 - 8.24081i) q^{88} -11.7743 q^{89} +(0.662611 - 1.85012i) q^{90} +0.777184 q^{91} +(1.81098 + 3.13670i) q^{92} +(15.4310 - 1.39011i) q^{93} +(1.33889 - 2.31903i) q^{94} +(3.32521 - 5.75943i) q^{95} +(-9.88918 + 0.890873i) q^{96} +(3.04268 + 5.27007i) q^{97} -4.18979 q^{98} +(-12.0074 + 2.18109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more