LMFDB - Embedded newform 731.2.m.c.689.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			689.7
Character	$\chi$	$=$	731.689
Dual form			731.2.m.c.87.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14159 + 1.14159i) q^{2} +(-2.60557 - 1.07926i) q^{3} -0.606454i q^{4} +(0.611497 - 1.47629i) q^{5} +(4.20657 - 1.74242i) q^{6} +(-0.771748 - 1.86317i) q^{7} +(-1.59086 - 1.59086i) q^{8} +(3.50287 + 3.50287i) q^{9} +O(q^{10})$	\(q+(-1.14159 + 1.14159i) q^{2} +(-2.60557 - 1.07926i) q^{3} -0.606454i q^{4} +(0.611497 - 1.47629i) q^{5} +(4.20657 - 1.74242i) q^{6} +(-0.771748 - 1.86317i) q^{7} +(-1.59086 - 1.59086i) q^{8} +(3.50287 + 3.50287i) q^{9} +(0.987233 + 2.38339i) q^{10} +(-0.196435 + 0.0813659i) q^{11} +(-0.654523 + 1.58016i) q^{12} -3.95416i q^{13} +(3.00799 + 1.24595i) q^{14} +(-3.18660 + 3.18660i) q^{15} +4.84512 q^{16} +(3.83953 - 1.50267i) q^{17} -7.99767 q^{18} +(1.18065 - 1.18065i) q^{19} +(-0.895300 - 0.370845i) q^{20} +5.68753i q^{21} +(0.131361 - 0.317134i) q^{22} +(-3.83013 + 1.58649i) q^{23} +(2.42814 + 5.86204i) q^{24} +(1.73005 + 1.73005i) q^{25} +(4.51403 + 4.51403i) q^{26} +(-2.10866 - 5.09076i) q^{27} +(-1.12992 + 0.468030i) q^{28} +(-0.633451 + 1.52929i) q^{29} -7.27557i q^{30} +(-3.53886 - 1.46584i) q^{31} +(-2.34943 + 2.34943i) q^{32} +0.599639 q^{33} +(-2.66773 + 6.09860i) q^{34} -3.22248 q^{35} +(2.12433 - 2.12433i) q^{36} +(-8.71079 - 3.60813i) q^{37} +2.69563i q^{38} +(-4.26758 + 10.3028i) q^{39} +(-3.32136 + 1.37575i) q^{40} +(2.83976 + 6.85578i) q^{41} +(-6.49282 - 6.49282i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(0.0493447 + 0.119129i) q^{44} +(7.31322 - 3.02924i) q^{45} +(2.56131 - 6.18356i) q^{46} -9.34141i q^{47} +(-12.6243 - 5.22916i) q^{48} +(2.07396 - 2.07396i) q^{49} -3.95000 q^{50} +(-11.6259 - 0.228540i) q^{51} -2.39802 q^{52} +(-2.72753 + 2.72753i) q^{53} +(8.21879 + 3.40434i) q^{54} +0.339748i q^{55} +(-1.73629 + 4.19177i) q^{56} +(-4.35049 + 1.80203i) q^{57} +(-1.02268 - 2.46896i) q^{58} +(-2.66615 - 2.66615i) q^{59} +(1.93253 + 1.93253i) q^{60} +(-5.30405 - 12.8051i) q^{61} +(5.71331 - 2.36653i) q^{62} +(3.82309 - 9.22975i) q^{63} +4.32608i q^{64} +(-5.83747 - 2.41796i) q^{65} +(-0.684542 + 0.684542i) q^{66} -0.714752 q^{67} +(-0.911302 - 2.32850i) q^{68} +11.6919 q^{69} +(3.67876 - 3.67876i) q^{70} +(-12.4813 - 5.16992i) q^{71} -11.1451i q^{72} +(0.207677 - 0.501377i) q^{73} +(14.0631 - 5.82515i) q^{74} +(-2.64058 - 6.37493i) q^{75} +(-0.716009 - 0.716009i) q^{76} +(0.303196 + 0.303196i) q^{77} +(-6.88980 - 16.6334i) q^{78} +(-2.93176 + 1.21437i) q^{79} +(2.96278 - 7.15278i) q^{80} +0.678738i q^{81} +(-11.0683 - 4.58465i) q^{82} +(-10.8255 + 10.8255i) q^{83} +3.44922 q^{84} +(0.129488 - 6.58712i) q^{85} +1.61445 q^{86} +(3.30100 - 3.30100i) q^{87} +(0.441941 + 0.183058i) q^{88} +16.0725i q^{89} +(-4.89055 + 11.8068i) q^{90} +(-7.36725 + 3.05162i) q^{91} +(0.962134 + 2.32280i) q^{92} +(7.63871 + 7.63871i) q^{93} +(10.6641 + 10.6641i) q^{94} +(-1.02101 - 2.46494i) q^{95} +(8.65724 - 3.58595i) q^{96} +(-2.75322 + 6.64685i) q^{97} +4.73522i q^{98} +(-0.973098 - 0.403070i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.14159	+	1.14159i	−0.807226	+	0.807226i	−0.984213	−	0.176987i	$-0.943365\pi$
$2$	−1.14159	+	1.14159i	−0.807226	+	0.807226i	0.176987	+	0.984213i	$0.443365\pi$
$3$	−2.60557	−	1.07926i	−1.50433	−	0.623112i	−0.529949	−	0.848030i	$-0.677789\pi$
$3$	−2.60557	−	1.07926i	−1.50433	−	0.623112i	−0.974378	+	0.224917i	$0.927789\pi$
$4$		−	0.606454i		−	0.303227i
$5$	0.611497	−	1.47629i	0.273470	−	0.660215i	−0.726157	−	0.687529i	$-0.758695\pi$
$5$	0.611497	−	1.47629i	0.273470	−	0.660215i	0.999627	+	0.0273142i	$0.00869545\pi$
$6$	4.20657	−	1.74242i	1.71732	−	0.711339i
$7$	−0.771748	−	1.86317i	−0.291693	−	0.704210i	0.708305	−	0.705906i	$-0.249460\pi$
$7$	−0.771748	−	1.86317i	−0.291693	−	0.704210i	−0.999999	+	0.00169617i	$0.999460\pi$
$8$	−1.59086	−	1.59086i	−0.562453	−	0.562453i
$9$	3.50287	+	3.50287i	1.16762	+	1.16762i
$10$	0.987233	+	2.38339i	0.312190	+	0.753694i
$11$	−0.196435	+	0.0813659i	−0.0592273	+	0.0245327i	−0.412100	−	0.911138i	$-0.635205\pi$
$11$	−0.196435	+	0.0813659i	−0.0592273	+	0.0245327i	0.352873	+	0.935671i	$0.385205\pi$
$12$	−0.654523	+	1.58016i	−0.188945	+	0.456153i
$13$		−	3.95416i		−	1.09669i	−0.836253	−	0.548343i	$-0.815259\pi$
$13$		−	3.95416i		−	1.09669i	0.836253	−	0.548343i	$-0.184741\pi$
$14$	3.00799	+	1.24595i	0.803919	+	0.332994i
$15$	−3.18660	+	3.18660i	−0.822776	+	0.822776i
$16$	4.84512			1.21128
$17$	3.83953	−	1.50267i	0.931222	−	0.364452i
$17$	3.83953	−	1.50267i	0.931222	−	0.364452i
$18$	−7.99767			−1.88507
$19$	1.18065	−	1.18065i	0.270859	−	0.270859i	−0.558587	−	0.829446i	$-0.688656\pi$
$19$	1.18065	−	1.18065i	0.270859	−	0.270859i	0.829446	+	0.558587i	$0.188656\pi$
$20$	−0.895300	−	0.370845i	−0.200195	−	0.0829235i
$21$			5.68753i			1.24112i
$22$	0.131361	−	0.317134i	0.0280063	−	0.0676132i
$23$	−3.83013	+	1.58649i	−0.798637	+	0.330806i	−0.744410	−	0.667723i	$-0.767269\pi$
$23$	−3.83013	+	1.58649i	−0.798637	+	0.330806i	−0.0542264	+	0.998529i	$0.517269\pi$
$24$	2.42814	+	5.86204i	0.495641	+	1.19658i
$25$	1.73005	+	1.73005i	0.346009	+	0.346009i
$26$	4.51403	+	4.51403i	0.885274	+	0.885274i
$27$	−2.10866	−	5.09076i	−0.405812	−	0.979718i
$28$	−1.12992	+	0.468030i	−0.213536	+	0.0884494i
$29$	−0.633451	+	1.52929i	−0.117629	+	0.283981i	−0.971718	−	0.236146i	$-0.924116\pi$
$29$	−0.633451	+	1.52929i	−0.117629	+	0.283981i	0.854089	+	0.520127i	$0.174116\pi$
$30$		−	7.27557i		−	1.32833i
$31$	−3.53886	−	1.46584i	−0.635597	−	0.263273i	0.0415319	−	0.999137i	$-0.486776\pi$
$31$	−3.53886	−	1.46584i	−0.635597	−	0.263273i	−0.677129	+	0.735864i	$0.736776\pi$
$32$	−2.34943	+	2.34943i	−0.415324	+	0.415324i
$33$	0.599639			0.104384
$34$	−2.66773	+	6.09860i	−0.457512	+	1.04590i
$35$	−3.22248			−0.544699
$36$	2.12433	−	2.12433i	0.354055	−	0.354055i
$37$	−8.71079	−	3.60813i	−1.43204	−	0.593172i	−0.474189	−	0.880423i	$-0.657259\pi$
$37$	−8.71079	−	3.60813i	−1.43204	−	0.593172i	−0.957855	+	0.287251i	$0.907259\pi$
$38$			2.69563i			0.437289i
$39$	−4.26758	+	10.3028i	−0.683359	+	1.64977i
$40$	−3.32136	+	1.37575i	−0.525154	+	0.217526i
$41$	2.83976	+	6.85578i	0.443495	+	1.07069i	0.974714	+	0.223457i	$0.0717344\pi$
$41$	2.83976	+	6.85578i	0.443495	+	1.07069i	−0.531218	+	0.847235i	$0.678266\pi$
$42$	−6.49282	−	6.49282i	−1.00186	−	1.00186i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$44$	0.0493447	+	0.119129i	0.00743899	+	0.0179593i
$45$	7.31322	−	3.02924i	1.09019	−	0.451572i
$46$	2.56131	−	6.18356i	0.377645	−	0.911715i
$47$		−	9.34141i		−	1.36258i	−0.732011	−	0.681292i	$-0.761418\pi$
$47$		−	9.34141i		−	1.36258i	0.732011	−	0.681292i	$-0.238582\pi$
$48$	−12.6243	−	5.22916i	−1.82216	−	0.754764i
$49$	2.07396	−	2.07396i	0.296280	−	0.296280i
$50$	−3.95000			−0.558615
$51$	−11.6259	−	0.228540i	−1.62796	−	0.0320019i
$52$	−2.39802			−0.332545
$53$	−2.72753	+	2.72753i	−0.374656	+	0.374656i	−0.869170	−	0.494514i	$-0.835346\pi$
$53$	−2.72753	+	2.72753i	−0.374656	+	0.374656i	0.494514	+	0.869170i	$0.335346\pi$
$54$	8.21879	+	3.40434i	1.11844	+	0.463271i
$55$			0.339748i			0.0458117i
$56$	−1.73629	+	4.19177i	−0.232021	+	0.560149i
$57$	−4.35049	+	1.80203i	−0.576236	+	0.238685i
$58$	−1.02268	−	2.46896i	−0.134284	−	0.324190i
$59$	−2.66615	−	2.66615i	−0.347104	−	0.347104i	0.511926	−	0.859030i	$-0.328932\pi$
$59$	−2.66615	−	2.66615i	−0.347104	−	0.347104i	−0.859030	+	0.511926i	$0.828932\pi$
$60$	1.93253	+	1.93253i	0.249488	+	0.249488i
$61$	−5.30405	−	12.8051i	−0.679114	−	1.63953i	−0.765634	−	0.643276i	$-0.777575\pi$
$61$	−5.30405	−	12.8051i	−0.679114	−	1.63953i	0.0865199	−	0.996250i	$-0.472425\pi$
$62$	5.71331	−	2.36653i	0.725591	−	0.300550i
$63$	3.82309	−	9.22975i	0.481664	−	1.16284i
$64$			4.32608i			0.540760i
$65$	−5.83747	−	2.41796i	−0.724049	−	0.299911i
$66$	−0.684542	+	0.684542i	−0.0842613	+	0.0842613i
$67$	−0.714752			−0.0873209			−0.0436605	−	0.999046i	$-0.513902\pi$
$67$	−0.714752			−0.0873209			−0.0436605	+	0.999046i	$0.513902\pi$
$68$	−0.911302	−	2.32850i	−0.110512	−	0.282372i
$69$	11.6919			1.40754
$70$	3.67876	−	3.67876i	0.439695	−	0.439695i
$71$	−12.4813	−	5.16992i	−1.48126	−	0.613557i	−0.511864	−	0.859067i	$-0.671045\pi$
$71$	−12.4813	−	5.16992i	−1.48126	−	0.613557i	−0.969394	+	0.245509i	$0.921045\pi$
$72$		−	11.1451i		−	1.31347i
$73$	0.207677	−	0.501377i	0.0243068	−	0.0586817i	−0.911260	−	0.411831i	$-0.864889\pi$
$73$	0.207677	−	0.501377i	0.0243068	−	0.0586817i	0.935567	+	0.353150i	$0.114889\pi$
$74$	14.0631	−	5.82515i	1.63481	−	0.677159i
$75$	−2.64058	−	6.37493i	−0.304908	−	0.736113i
$76$	−0.716009	−	0.716009i	−0.0821319	−	0.0821319i
$77$	0.303196	+	0.303196i	0.0345524	+	0.0345524i
$78$	−6.88980	−	16.6334i	−0.780116	−	1.88337i
$79$	−2.93176	+	1.21437i	−0.329849	+	0.136628i	−0.541461	−	0.840726i	$-0.682129\pi$
$79$	−2.93176	+	1.21437i	−0.329849	+	0.136628i	0.211612	+	0.977354i	$0.432129\pi$
$80$	2.96278	−	7.15278i	0.331249	−	0.799705i
$81$			0.678738i			0.0754154i
$82$	−11.0683	−	4.58465i	−1.22229	−	0.506290i
$83$	−10.8255	+	10.8255i	−1.18825	+	1.18825i	−0.210697	+	0.977551i	$0.567573\pi$
$83$	−10.8255	+	10.8255i	−1.18825	+	1.18825i	−0.977551	+	0.210697i	$0.932427\pi$
$84$	3.44922			0.376341
$85$	0.129488	−	6.58712i	0.0140449	−	0.714473i
$86$	1.61445			0.174091
$87$	3.30100	−	3.30100i	0.353904	−	0.353904i
$88$	0.441941	+	0.183058i	0.0471111	+	0.0195140i
$89$			16.0725i			1.70368i	0.523804	+	0.851839i	$0.324513\pi$
$89$			16.0725i			1.70368i	−0.523804	+	0.851839i	$0.675487\pi$
$90$	−4.89055	+	11.8068i	−0.515510	+	1.24455i
$91$	−7.36725	+	3.05162i	−0.772298	+	0.319896i
$92$	0.962134	+	2.32280i	0.100309	+	0.242168i
$93$	7.63871	+	7.63871i	0.792097	+	0.792097i
$94$	10.6641	+	10.6641i	1.09991	+	1.09991i
$95$	−1.02101	−	2.46494i	−0.104753	−	0.252897i
$96$	8.65724	−	3.58595i	0.883576	−	0.365989i
$97$	−2.75322	+	6.64685i	−0.279547	+	0.674885i	−0.999823	−	0.0188017i	$-0.994015\pi$
$97$	−2.75322	+	6.64685i	−0.279547	+	0.674885i	0.720277	+	0.693687i	$0.244015\pi$
$98$			4.73522i			0.478329i
$99$	−0.973098	−	0.403070i	−0.0978000	−	0.0405101i
$100$	1.04919	−	1.04919i	0.104919	−	0.104919i
$101$	−4.02029			−0.400034			−0.200017	−	0.979792i	$-0.564100\pi$
$101$	−4.02029			−0.400034			−0.200017	+	0.979792i	$0.564100\pi$
$102$	13.5329	−	13.0112i	1.33996	−	1.28830i
$103$	13.1156			1.29232			0.646161	−	0.763201i	$-0.276374\pi$
$103$	13.1156			1.29232			0.646161	+	0.763201i	$0.276374\pi$
$104$	−6.29051	+	6.29051i	−0.616835	+	0.616835i
$105$	8.39641	+	3.47791i	0.819406	+	0.339409i
$106$		−	6.22745i		−	0.604863i
$107$	−7.24028	+	17.4796i	−0.699944	+	1.68981i	0.0237723	+	0.999717i	$0.492432\pi$
$107$	−7.24028	+	17.4796i	−0.699944	+	1.68981i	−0.723716	+	0.690097i	$0.757568\pi$
$108$	−3.08732	+	1.27881i	−0.297077	+	0.123053i
$109$	1.52347	+	3.67798i	0.145922	+	0.352287i	0.979894	−	0.199521i	$-0.0639385\pi$
$109$	1.52347	+	3.67798i	0.145922	+	0.352287i	−0.833972	+	0.551807i	$0.813938\pi$
$110$	−0.387853	−	0.387853i	−0.0369804	−	0.0369804i
$111$	18.8024	+	18.8024i	1.78465	+	1.78465i
$112$	−3.73921	−	9.02726i	−0.353323	−	0.852996i
$113$	−1.11413	+	0.461490i	−0.104809	+	0.0434133i	−0.434472	−	0.900685i	$-0.643065\pi$
$113$	−1.11413	+	0.461490i	−0.104809	+	0.0434133i	0.329663	+	0.944099i	$0.393065\pi$
$114$	2.90929	−	7.02366i	0.272480	−	0.657826i
$115$			6.62449i			0.617737i
$116$	0.927442	+	0.384159i	0.0861108	+	0.0356683i
$117$	13.8509	−	13.8509i	1.28052	−	1.28052i
$118$	6.08731			0.560382
$119$	−5.76288	−	5.99399i	−0.528282	−	0.549468i
$120$	10.1388			0.925546
$121$	−7.74621	+	7.74621i	−0.704201	+	0.704201i
$122$	20.6732	+	8.56313i	1.87167	+	0.775270i
$123$		−	20.9280i		−	1.88702i
$124$	−0.888966	+	2.14615i	−0.0798315	+	0.192730i
$125$	10.9934	−	4.55361i	0.983278	−	0.407287i
$126$	6.17219	+	14.9010i	0.549862	+	1.32749i
$127$	1.82125	+	1.82125i	0.161610	+	0.161610i	0.783280	−	0.621670i	$-0.213545\pi$
$127$	1.82125	+	1.82125i	0.161610	+	0.161610i	−0.621670	+	0.783280i	$0.713545\pi$
$128$	−9.63746	−	9.63746i	−0.851839	−	0.851839i
$129$	1.07926	+	2.60557i	0.0950237	+	0.229408i
$130$	9.42431	−	3.90368i	0.826567	−	0.342375i
$131$	−4.28398	+	10.3424i	−0.374293	+	0.903624i	0.618719	+	0.785612i	$0.287652\pi$
$131$	−4.28398	+	10.3424i	−0.374293	+	0.903624i	−0.993012	+	0.118011i	$0.962348\pi$
$132$		−	0.363654i		−	0.0316520i
$133$	−3.11091	−	1.28858i	−0.269750	−	0.111734i
$134$	0.815954	−	0.815954i	0.0704877	−	0.0704877i
$135$	−8.80486			−0.757802
$136$	−8.49868	−	3.71760i	−0.728756	−	0.318782i
$137$	13.1185			1.12079			0.560396	−	0.828225i	$-0.310649\pi$
$137$	13.1185			1.12079			0.560396	+	0.828225i	$0.310649\pi$
$138$	−13.3474	+	13.3474i	−1.13620	+	1.13620i
$139$	−3.39690	−	1.40704i	−0.288121	−	0.119344i	0.233942	−	0.972251i	$-0.424837\pi$
$139$	−3.39690	−	1.40704i	−0.288121	−	0.119344i	−0.522063	+	0.852907i	$0.674837\pi$
$140$			1.95429i			0.165168i
$141$	−10.0818	+	24.3397i	−0.849043	+	2.04977i
$142$	20.1505	−	8.34659i	1.69099	−	0.700431i
$143$	0.321734	+	0.776734i	0.0269047	+	0.0649537i
$144$	16.9718	+	16.9718i	1.41432	+	1.41432i
$145$	1.87031	+	1.87031i	0.155321	+	0.155321i
$146$	0.335284	+	0.809448i	0.0277483	+	0.0669904i
$147$	−7.64219	+	3.16550i	−0.630317	+	0.261086i
$148$	−2.18816	+	5.28270i	−0.179866	+	0.434235i
$149$		−	1.04562i		−	0.0856602i	−0.999082	−	0.0428301i	$-0.986363\pi$
$149$		−	1.04562i		−	0.0856602i	0.999082	−	0.0428301i	$-0.0136374\pi$
$150$	10.2920	+	4.26309i	0.840339	+	0.348080i
$151$	−0.851662	+	0.851662i	−0.0693073	+	0.0693073i	−0.740911	−	0.671603i	$-0.765606\pi$
$151$	−0.851662	+	0.851662i	−0.0693073	+	0.0693073i	0.671603	+	0.740911i	$0.265606\pi$
$152$	−3.75649			−0.304691
$153$	18.7130	+	8.18569i	1.51286	+	0.661774i
$154$	−0.692251			−0.0557832
$155$	−4.32800	+	4.32800i	−0.347633	+	0.347633i
$156$	6.24820	+	2.58809i	0.500257	+	0.207213i
$157$		−	14.0092i		−	1.11805i	−0.829150	−	0.559026i	$-0.811175\pi$
$157$		−	14.0092i		−	1.11805i	0.829150	−	0.559026i	$-0.188825\pi$
$158$	1.96055	−	4.73318i	0.155973	−	0.376552i
$159$	10.0505	−	4.16306i	0.797057	−	0.330152i
$160$	2.03176	+	4.90509i	0.160624	+	0.387782i
$161$	5.91179	+	5.91179i	0.465914	+	0.465914i
$162$	−0.774841	−	0.774841i	−0.0608772	−	0.0608772i
$163$	−7.78356	−	18.7912i	−0.609655	−	1.47184i	−0.863376	−	0.504561i	$-0.831655\pi$
$163$	−7.78356	−	18.7912i	−0.609655	−	1.47184i	0.253721	−	0.967277i	$-0.418345\pi$
$164$	4.15772	−	1.72218i	0.324663	−	0.134480i
$165$	0.366678	−	0.885238i	0.0285458	−	0.0689157i
$166$		−	24.7165i		−	1.91837i
$167$	0.0919718	+	0.0380960i	0.00711699	+	0.00294795i	0.386239	−	0.922399i	$-0.373774\pi$
$167$	0.0919718	+	0.0380960i	0.00711699	+	0.00294795i	−0.379122	+	0.925347i	$0.623774\pi$
$168$	9.04804	−	9.04804i	0.698072	−	0.698072i
$169$	−2.63539			−0.202722
$170$	7.37196	+	7.66761i	0.565404	+	0.588079i
$171$	8.27130			0.632522
$172$	−0.428828	+	0.428828i	−0.0326978	+	0.0326978i
$173$	−6.42402	−	2.66092i	−0.488409	−	0.202306i	0.124868	−	0.992173i	$-0.460149\pi$
$173$	−6.42402	−	2.66092i	−0.488409	−	0.202306i	−0.613277	+	0.789868i	$0.710149\pi$
$174$			7.53678i			0.571362i
$175$	1.88820	−	4.55852i	0.142735	−	0.344592i
$176$	−0.951749	+	0.394228i	−0.0717408	+	0.0297160i
$177$	4.06937	+	9.82433i	0.305873	+	0.738442i
$178$	−18.3482	−	18.3482i	−1.37525	−	1.37525i
$179$	11.3540	+	11.3540i	0.848637	+	0.848637i	0.989963	−	0.141326i	$-0.0451366\pi$
$179$	11.3540	+	11.3540i	0.848637	+	0.848637i	−0.141326	+	0.989963i	$0.545137\pi$
$180$	−1.83709	−	4.43514i	−0.136929	−	0.330575i
$181$	14.2832	−	5.91630i	1.06166	−	0.439755i	0.217622	−	0.976033i	$-0.430170\pi$
$181$	14.2832	−	5.91630i	1.06166	−	0.439755i	0.844042	+	0.536278i	$0.180170\pi$
$182$	4.92669	−	11.8941i	0.365190	−	0.881648i
$183$			39.0891i			2.88955i
$184$	8.61707	+	3.56931i	0.635259	+	0.263133i
$185$	−10.6532	+	10.6532i	−0.783242	+	0.783242i
$186$	−17.4405			−1.27880
$187$	−0.631950	+	0.607583i	−0.0462127	+	0.0444309i
$188$	−5.66514			−0.413173
$189$	−7.85758	+	7.85758i	−0.571555	+	0.571555i
$190$	3.97952	+	1.64837i	0.288705	+	0.119585i
$191$			6.84137i			0.495024i	0.968885	+	0.247512i	$0.0796129\pi$
$191$			6.84137i			0.495024i	−0.968885	+	0.247512i	$0.920387\pi$
$192$	4.66898	−	11.2719i	0.336954	−	0.813480i
$193$	1.90355	−	0.788478i	0.137021	−	0.0567559i	−0.313119	−	0.949714i	$-0.601374\pi$
$193$	1.90355	−	0.788478i	0.137021	−	0.0567559i	0.450140	+	0.892958i	$0.351374\pi$
$194$	−4.44493	−	10.7310i	−0.319128	−	0.770442i
$195$	12.6003	+	12.6003i	0.902328	+	0.902328i
$196$	−1.25776	−	1.25776i	−0.0898401	−	0.0898401i
$197$	−1.74946	−	4.22357i	−0.124644	−	0.300917i	0.849224	−	0.528033i	$-0.177070\pi$
$197$	−1.74946	−	4.22357i	−0.124644	−	0.300917i	−0.973868	+	0.227116i	$0.927070\pi$
$198$	1.57102	−	0.650737i	0.111647	−	0.0462459i
$199$	−0.929618	+	2.24430i	−0.0658989	+	0.159094i	−0.953398	−	0.301715i	$-0.902441\pi$
$199$	−0.929618	+	2.24430i	−0.0658989	+	0.159094i	0.887499	+	0.460809i	$0.152441\pi$
$200$		−	5.50451i		−	0.389228i
$201$	1.86234	+	0.771405i	0.131359	+	0.0544107i
$202$	4.58952	−	4.58952i	0.322918	−	0.322918i
$203$	3.33818			0.234294
$204$	−0.138599	+	7.05060i	−0.00970386	+	0.493641i
$205$	11.8576			0.828170
$206$	−14.9727	+	14.9727i	−1.04320	+	1.04320i
$207$	−18.9737	−	7.85916i	−1.31876	−	0.546249i
$208$		−	19.1584i		−	1.32840i
$209$	−0.135856	+	0.327985i	−0.00939733	+	0.0226872i
$210$	−13.5556	+	5.61491i	−0.935425	+	0.387466i
$211$	−2.63963	−	6.37262i	−0.181719	−	0.438710i	0.806602	−	0.591095i	$-0.201304\pi$
$211$	−2.63963	−	6.37262i	−0.181719	−	0.438710i	−0.988321	+	0.152386i	$0.951304\pi$
$212$	1.65413	+	1.65413i	0.113606	+	0.113606i
$213$	26.9412	+	26.9412i	1.84598	+	1.84598i
$214$	−11.6891	−	28.2199i	−0.799049	−	1.92908i
$215$	−1.47629	+	0.611497i	−0.100682	+	0.0417038i
$216$	−4.74410	+	11.4533i	−0.322795	+	0.779296i
$217$			7.72473i			0.524389i
$218$	−5.93792	−	2.45957i	−0.402167	−	0.166583i
$219$	−1.08223	+	1.08223i	−0.0731306	+	0.0731306i
$220$	0.206042			0.0138913
$221$	−5.94181	−	15.1821i	−0.399689	−	1.02126i
$222$	−42.9294			−2.88123
$223$	−11.4929	+	11.4929i	−0.769619	+	0.769619i	−0.978039	−	0.208420i	$-0.933168\pi$
$223$	−11.4929	+	11.4929i	−0.769619	+	0.769619i	0.208420	+	0.978039i	$0.433168\pi$
$224$	6.19054	+	2.56420i	0.413623	+	0.171328i
$225$			12.1202i			0.808016i
$226$	0.745053	−	1.79872i	0.0495602	−	0.119649i
$227$	−12.4827	+	5.17051i	−0.828507	+	0.343179i	−0.756311	−	0.654212i	$-0.773001\pi$
$227$	−12.4827	+	5.17051i	−0.828507	+	0.343179i	−0.0721953	+	0.997391i	$0.523001\pi$
$228$	1.09285	+	2.63837i	0.0723758	+	0.174731i
$229$	−14.9022	−	14.9022i	−0.984765	−	0.984765i	0.0151205	−	0.999886i	$-0.495187\pi$
$229$	−14.9022	−	14.9022i	−0.984765	−	0.984765i	−0.999886	+	0.0151205i	$0.995187\pi$
$230$	−7.56245	−	7.56245i	−0.498654	−	0.498654i
$231$	−0.462770	−	1.11723i	−0.0304481	−	0.0735081i
$232$	3.44061	−	1.42515i	0.225887	−	0.0935654i
$233$	−3.98404	+	9.61832i	−0.261003	+	0.630117i	−0.999001	−	0.0446856i	$-0.985771\pi$
$233$	−3.98404	+	9.61832i	−0.261003	+	0.630117i	0.737998	+	0.674803i	$0.235771\pi$
$234$			31.6241i			2.06733i
$235$	−13.7906	−	5.71225i	−0.899599	−	0.372626i
$236$	−1.61690	+	1.61690i	−0.105251	+	0.105251i
$237$	8.94953			0.581335
$238$	13.4215	+	0.263837i	0.869988	+	0.0171020i
$239$	−15.0942			−0.976365			−0.488182	−	0.872742i	$-0.662340\pi$
$239$	−15.0942			−0.976365			−0.488182	+	0.872742i	$0.662340\pi$
$240$	−15.4395	+	15.4395i	−0.996612	+	0.996612i
$241$	−8.75492	−	3.62641i	−0.563954	−	0.233597i	0.0824467	−	0.996595i	$-0.473727\pi$
$241$	−8.75492	−	3.62641i	−0.563954	−	0.233597i	−0.646401	+	0.762998i	$0.723727\pi$
$242$		−	17.6860i		−	1.13690i
$243$	−5.59345	+	13.5038i	−0.358820	+	0.866269i
$244$	−7.76572	+	3.21666i	−0.497149	+	0.205926i
$245$	−1.79353	−	4.32997i	−0.114585	−	0.276632i
$246$	23.8912	+	23.8912i	1.52325	+	1.52325i
$247$	−4.66847	−	4.66847i	−0.297048	−	0.297048i
$248$	3.29787	+	7.96176i	0.209415	+	0.505572i
$249$	39.8900	−	16.5230i	2.52793	−	1.04710i
$250$	−7.35158	+	17.7483i	−0.464955	+	1.12250i
$251$		−	5.21545i		−	0.329196i	−0.986361	−	0.164598i	$-0.947367\pi$
$251$		−	5.21545i		−	0.329196i	0.986361	−	0.164598i	$-0.0526327\pi$
$252$	−5.59742	−	2.31853i	−0.352604	−	0.146054i
$253$	0.623283	−	0.623283i	0.0391855	−	0.0391855i
$254$	−4.15825			−0.260912
$255$	−7.44662	+	17.0234i	−0.466325	+	1.06605i
$256$	13.3519			0.834494
$257$	3.01107	−	3.01107i	0.187825	−	0.187825i	−0.606930	−	0.794755i	$-0.707599\pi$
$257$	3.01107	−	3.01107i	0.187825	−	0.187825i	0.794755	+	0.606930i	$0.207599\pi$
$258$	−4.20657	−	1.74242i	−0.261889	−	0.108478i
$259$			19.0142i			1.18148i
$260$	−1.46638	+	3.54016i	−0.0909411	+	0.219551i
$261$	−7.57578	+	3.13799i	−0.468929	+	0.194237i
$262$	−6.91628	−	16.6974i	−0.427289	−	1.03157i
$263$	−0.267813	−	0.267813i	−0.0165141	−	0.0165141i	0.698802	−	0.715316i	$-0.253717\pi$
$263$	−0.267813	−	0.267813i	−0.0165141	−	0.0165141i	−0.715316	+	0.698802i	$0.753717\pi$
$264$	−0.953940	−	0.953940i	−0.0587110	−	0.0587110i
$265$	2.35874	+	5.69450i	0.144896	+	0.349810i
$266$	5.02241	−	2.08035i	0.307943	−	0.127554i
$267$	17.3464	−	41.8779i	1.06158	−	2.56289i
$268$			0.433465i			0.0264781i
$269$	12.2170	+	5.06043i	0.744881	+	0.308540i	0.722651	−	0.691213i	$-0.242923\pi$
$269$	12.2170	+	5.06043i	0.744881	+	0.308540i	0.0222298	+	0.999753i	$0.492923\pi$
$270$	10.0515	−	10.0515i	0.611717	−	0.611717i
$271$	3.06708			0.186312			0.0931558	−	0.995652i	$-0.470305\pi$
$271$	3.06708			0.186312			0.0931558	+	0.995652i	$0.470305\pi$
$272$	18.6030	−	7.28063i	1.12797	−	0.441453i
$273$	22.4894			1.36112
$274$	−14.9760	+	14.9760i	−0.904732	+	0.904732i
$275$	−0.480607	−	0.199074i	−0.0289817	−	0.0120046i
$276$		−	7.09061i		−	0.426804i
$277$	0.884252	−	2.13477i	0.0531296	−	0.128266i	−0.895086	−	0.445893i	$-0.852886\pi$
$277$	0.884252	−	2.13477i	0.0531296	−	0.128266i	0.948216	+	0.317627i	$0.102886\pi$
$278$	5.48412	−	2.27160i	0.328916	−	0.136241i
$279$	−7.26149	−	17.5308i	−0.434734	−	1.04954i
$280$	5.12651	+	5.12651i	0.306368	+	0.306368i
$281$	−13.9277	−	13.9277i	−0.830855	−	0.830855i	0.156779	−	0.987634i	$-0.449889\pi$
$281$	−13.9277	−	13.9277i	−0.830855	−	0.830855i	−0.987634	+	0.156779i	$0.949889\pi$
$282$	−16.2766	−	39.2953i	−0.969259	−	2.34000i
$283$	23.2604	−	9.63475i	1.38268	−	0.572727i	0.437487	−	0.899225i	$-0.355869\pi$
$283$	23.2604	−	9.63475i	1.38268	−	0.572727i	0.945198	+	0.326498i	$0.105869\pi$
$284$	−3.13532	+	7.56934i	−0.186047	+	0.449158i
$285$			7.52450i			0.445713i
$286$	−1.25400	−	0.519424i	−0.0741505	−	0.0307142i
$287$	10.5819	−	10.5819i	0.624628	−	0.624628i
$288$	−16.4595			−0.969883
$289$	12.4840	−	11.5391i	0.734350	−	0.678771i
$290$	−4.27025			−0.250758
$291$	14.3474	−	14.3474i	0.841059	−	0.841059i
$292$	−0.304062	−	0.125947i	−0.0177939	−	0.00737047i
$293$			16.1764i			0.945035i	0.881321	+	0.472517i	$0.156655\pi$
$293$			16.1764i			0.945035i	−0.881321	+	0.472517i	$0.843345\pi$
$294$	5.11054	−	12.3379i	0.298053	−	0.719564i
$295$	−5.56635	+	2.30566i	−0.324085	+	0.134241i
$296$	8.11761	+	19.5976i	0.471826	+	1.13909i
$297$	0.828429	+	0.828429i	0.0480703	+	0.0480703i
$298$	1.19366	+	1.19366i	0.0691471	+	0.0691471i
$299$	6.27324	+	15.1449i	0.362791	+	0.875854i
$300$	−3.86610	+	1.60139i	−0.223209	+	0.0924564i
$301$	−0.771748	+	1.86317i	−0.0444828	+	0.107391i
$302$		−	1.94450i		−	0.111893i
$303$	10.4751	+	4.33895i	0.601781	+	0.249266i
$304$	5.72038	−	5.72038i	0.328086	−	0.328086i
$305$	−22.1474			−1.26816
$306$	−30.7073	+	12.0179i	−1.75542	+	0.687017i
$307$	2.26615			0.129336			0.0646681	−	0.997907i	$-0.479401\pi$
$307$	2.26615			0.129336			0.0646681	+	0.997907i	$0.479401\pi$
$308$	0.183875	−	0.183875i	0.0104772	−	0.0104772i
$309$	−34.1737	−	14.1552i	−1.94407	−	0.805262i
$310$		−	9.88160i		−	0.561237i
$311$	1.45508	−	3.51287i	0.0825099	−	0.199197i	−0.877240	−	0.480051i	$-0.840618\pi$
$311$	1.45508	−	3.51287i	0.0825099	−	0.199197i	0.959750	+	0.280855i	$0.0906180\pi$
$312$	23.1795	−	9.60125i	1.31228	−	0.543563i
$313$	4.60995	+	11.1294i	0.260570	+	0.629071i	0.998974	−	0.0452872i	$-0.0144203\pi$
$313$	4.60995	+	11.1294i	0.260570	+	0.629071i	−0.738404	+	0.674358i	$0.764420\pi$
$314$	15.9927	+	15.9927i	0.902521	+	0.902521i
$315$	−11.2879	−	11.2879i	−0.636003	−	0.636003i
$316$	0.736463	+	1.77798i	0.0414293	+	0.100019i
$317$	−18.1951	+	7.53666i	−1.02194	+	0.423301i	−0.829796	−	0.558066i	$-0.811543\pi$
$317$	−18.1951	+	7.53666i	−1.02194	+	0.423301i	−0.192142	+	0.981367i	$0.561543\pi$
$318$	−6.72105	+	16.2261i	−0.376898	+	0.909912i
$319$		−	0.351946i		−	0.0197052i
$320$	6.38653	+	2.64539i	0.357018	+	0.147882i
$321$	37.7301	−	37.7301i	2.10589	−	2.10589i
$322$	−13.4977			−0.752196
$323$	2.75900	−	6.30726i	0.153515	−	0.350945i
$324$	0.411624			0.0228680
$325$	6.84088	−	6.84088i	0.379464	−	0.379464i
$326$	30.3374	+	12.5662i	1.68024	+	0.695976i
$327$		−	11.2275i		−	0.620880i
$328$	6.38892	−	15.4242i	0.352769	−	0.851660i
$329$	−17.4046	+	7.20922i	−0.959546	+	0.397457i
$330$	0.591983	+	1.42917i	0.0325876	+	0.0786735i
$331$	−4.69699	−	4.69699i	−0.258170	−	0.258170i	0.566139	−	0.824309i	$-0.308436\pi$
$331$	−4.69699	−	4.69699i	−0.258170	−	0.258170i	−0.824309	+	0.566139i	$0.808436\pi$
$332$	6.56515	+	6.56515i	0.360309	+	0.360309i
$333$	−17.8739	−	43.1515i	−0.979486	−	2.36469i
$334$	−0.148484	+	0.0615041i	−0.00812469	+	0.00336535i
$335$	−0.437069	+	1.05518i	−0.0238796	+	0.0576506i
$336$			27.5568i			1.50334i
$337$	7.91263	+	3.27752i	0.431028	+	0.178538i	0.587640	−	0.809122i	$-0.300057\pi$
$337$	7.91263	+	3.27752i	0.431028	+	0.178538i	−0.156612	+	0.987660i	$0.550057\pi$
$338$	3.00853	−	3.00853i	0.163642	−	0.163642i
$339$	3.40102			0.184718
$340$	−3.99479	−	0.0785285i	−0.216648	−	0.00425880i
$341$	0.814423			0.0441035
$342$	−9.44243	+	9.44243i	−0.510588	+	0.510588i
$343$	−18.5069	−	7.66579i	−0.999276	−	0.413914i
$344$			2.24981i			0.121302i
$345$	7.14957	−	17.2606i	0.384920	−	0.929278i
$346$	10.3713	−	4.29592i	0.557563	−	0.230950i
$347$	−12.3226	−	29.7493i	−0.661511	−	1.59703i	−0.795436	−	0.606037i	$-0.792758\pi$
$347$	−12.3226	−	29.7493i	−0.661511	−	1.59703i	0.133925	−	0.990991i	$-0.457242\pi$
$348$	−2.00191	−	2.00191i	−0.107313	−	0.107313i
$349$	−3.80357	−	3.80357i	−0.203600	−	0.203600i	0.597940	−	0.801541i	$-0.295986\pi$
$349$	−3.80357	−	3.80357i	−0.203600	−	0.203600i	−0.801541	+	0.597940i	$0.795986\pi$
$350$	3.04841	+	7.35951i	0.162944	+	0.393382i
$351$	−20.1297	+	8.33799i	−1.07444	+	0.445049i
$352$	0.270345	−	0.652672i	0.0144095	−	0.0347875i
$353$			6.71121i			0.357202i	0.983922	+	0.178601i	$0.0571571\pi$
$353$			6.71121i			0.357202i	−0.983922	+	0.178601i	$0.942843\pi$
$354$	−15.8609	−	6.56980i	−0.842997	−	0.349181i
$355$	−15.2646	+	15.2646i	−0.810159	+	0.810159i
$356$	9.74722			0.516602
$357$	8.54649	+	21.8374i	0.452328	+	1.15576i
$358$	−25.9232			−1.37008
$359$	18.4384	−	18.4384i	0.973139	−	0.973139i	−0.0265096	−	0.999649i	$-0.508439\pi$
$359$	18.4384	−	18.4384i	0.973139	−	0.973139i	0.999649	+	0.0265096i	$0.00843927\pi$
$360$	−16.4534	−	6.81521i	−0.867169	−	0.359193i
$361$			16.2121i			0.853271i
$362$	−9.55159	+	23.0596i	−0.502020	+	1.21198i
$363$	28.5435	−	11.8231i	1.49814	−	0.620552i
$364$	1.85067	+	4.46790i	0.0970013	+	0.234182i
$365$	−0.613181	−	0.613181i	−0.0320954	−	0.0320954i
$366$	−44.6237	−	44.6237i	−2.33252	−	2.33252i
$367$	−9.69093	−	23.3960i	−0.505862	−	1.22126i	−0.946245	−	0.323450i	$-0.895157\pi$
$367$	−9.69093	−	23.3960i	−0.505862	−	1.22126i	0.440383	−	0.897810i	$-0.354843\pi$
$368$	−18.5574	+	7.68674i	−0.967373	+	0.400699i
$369$	−14.0676	+	33.9622i	−0.732329	+	1.76800i
$370$		−	24.3233i		−	1.26451i
$371$	7.18682	+	2.97688i	0.373121	+	0.154552i
$372$	4.63253	−	4.63253i	0.240185	−	0.240185i
$373$	18.3668			0.950997			0.475499	−	0.879716i	$-0.342268\pi$
$373$	18.3668			0.950997			0.475499	+	0.879716i	$0.342268\pi$
$374$	0.0278165	−	1.41504i	0.00143835	−	0.0731699i
$375$	−33.5586			−1.73296
$376$	−14.8609	+	14.8609i	−0.766390	+	0.766390i
$377$	6.04704	+	2.50477i	0.311438	+	0.129002i
$378$		−	17.9403i		−	0.922747i
$379$	11.7095	−	28.2692i	0.601476	−	1.45209i	−0.270586	−	0.962696i	$-0.587217\pi$
$379$	11.7095	−	28.2692i	0.601476	−	1.45209i	0.872062	−	0.489396i	$-0.162783\pi$
$380$	−1.49487	+	0.619196i	−0.0766853	+	0.0317641i
$381$	−2.77979	−	6.71101i	−0.142413	−	0.343815i
$382$	−7.81003	−	7.81003i	−0.399596	−	0.399596i
$383$	−13.8692	−	13.8692i	−0.708683	−	0.708683i	0.257575	−	0.966258i	$-0.417077\pi$
$383$	−13.8692	−	13.8692i	−0.708683	−	0.708683i	−0.966258	+	0.257575i	$0.917077\pi$
$384$	14.7097	+	35.5124i	0.750653	+	1.81224i
$385$	0.633007	−	0.262200i	0.0322610	−	0.0133630i
$386$	−1.27296	+	3.07320i	−0.0647919	+	0.156422i
$387$		−	4.95380i		−	0.251816i
$388$	4.03101	+	1.66970i	0.204644	+	0.0847662i
$389$	−3.38037	+	3.38037i	−0.171391	+	0.171391i	−0.787590	−	0.616199i	$-0.788672\pi$
$389$	−3.38037	+	3.38037i	−0.171391	+	0.171391i	0.616199	+	0.787590i	$0.288672\pi$
$390$	−28.7688			−1.45676
$391$	−12.3219	+	11.8468i	−0.623145	+	0.599119i
$392$	−6.59874			−0.333287
$393$	22.3244	−	22.3244i	1.12612	−	1.12612i
$394$	6.81876	+	2.82442i	0.343524	+	0.142292i
$395$			5.07070i			0.255135i
$396$	−0.244444	+	0.590139i	−0.0122838	+	0.0296556i
$397$	−12.0134	+	4.97611i	−0.602935	+	0.249744i	−0.663204	−	0.748438i	$-0.730804\pi$
$397$	−12.0134	+	4.97611i	−0.602935	+	0.249744i	0.0602695	+	0.998182i	$0.480804\pi$
$398$	−1.50082	−	3.62331i	−0.0752295	−	0.181620i
$399$	6.71497	+	6.71497i	0.336169	+	0.336169i
$400$	8.38228	+	8.38228i	0.419114	+	0.419114i
$401$	−7.57358	−	18.2842i	−0.378206	−	0.913071i	−0.992302	−	0.123840i	$-0.960479\pi$
$401$	−7.57358	−	18.2842i	−0.378206	−	0.913071i	0.614096	−	0.789231i	$-0.289521\pi$
$402$	−3.00665	+	1.24540i	−0.149958	+	0.0621147i
$403$	−5.79617	+	13.9932i	−0.288728	+	0.697051i
$404$			2.43812i			0.121301i
$405$	1.00201	+	0.415047i	0.0497904	+	0.0206238i
$406$	−3.81083	+	3.81083i	−0.189128	+	0.189128i
$407$	2.00468			0.0993682
$408$	18.1316	+	18.8588i	0.897650	+	0.933649i
$409$	8.86899			0.438543			0.219272	−	0.975664i	$-0.429632\pi$
$409$	8.86899			0.438543			0.219272	+	0.975664i	$0.429632\pi$
$410$	−13.5365	+	13.5365i	−0.668520	+	0.668520i
$411$	−34.1812	−	14.1583i	−1.68604	−	0.698379i
$412$		−	7.95403i		−	0.391867i
$413$	−2.90988	+	7.02508i	−0.143186	+	0.345682i
$414$	30.6321	−	12.6882i	1.50549	−	0.623593i
$415$	9.36172	+	22.6012i	0.459549	+	1.10945i
$416$	9.29001	+	9.29001i	0.455480	+	0.455480i
$417$	7.33228	+	7.33228i	0.359063	+	0.359063i
$418$	−0.219332	−	0.529515i	−0.0107279	−	0.0258994i
$419$	31.8479	−	13.1918i	1.55587	−	0.644464i	0.571507	−	0.820597i	$-0.306359\pi$
$419$	31.8479	−	13.1918i	1.55587	−	0.644464i	0.984366	+	0.176133i	$0.0563589\pi$
$420$	2.10919	−	5.09204i	0.102918	−	0.248466i
$421$		−	15.8442i		−	0.772201i	−0.922457	−	0.386100i	$-0.873822\pi$
$421$		−	15.8442i		−	0.772201i	0.922457	−	0.386100i	$-0.126178\pi$
$422$	10.2883	+	4.26155i	0.500826	+	0.207449i
$423$	32.7217	−	32.7217i	1.59098	−	1.59098i
$424$	8.67824			0.421452
$425$	9.24225	+	4.04287i	0.448315	+	0.196108i
$426$	−61.5116			−2.98025
$427$	−19.7646	+	19.7646i	−0.956478	+	0.956478i
$428$	10.6006	+	4.39090i	0.512398	+	0.212242i
$429$		−	2.37107i		−	0.114476i
$430$	0.987233	−	2.38339i	0.0476086	−	0.114937i
$431$	−14.1702	+	5.86950i	−0.682556	+	0.282724i	−0.696895	−	0.717173i	$-0.745436\pi$
$431$	−14.1702	+	5.86950i	−0.682556	+	0.282724i	0.0143390	+	0.999897i	$0.495436\pi$
$432$	−10.2167	−	24.6654i	−0.491553	−	1.18671i
$433$	−16.4718	−	16.4718i	−0.791583	−	0.791583i	0.190168	−	0.981751i	$-0.439097\pi$
$433$	−16.4718	−	16.4718i	−0.791583	−	0.791583i	−0.981751	+	0.190168i	$0.939097\pi$
$434$	−8.81848	−	8.81848i	−0.423300	−	0.423300i
$435$	−2.85466	−	6.89177i	−0.136871	−	0.330435i
$436$	2.23053	−	0.923915i	0.106823	−	0.0442475i
$437$	−2.64894	+	6.39512i	−0.126716	+	0.305920i
$438$		−	2.47093i		−	0.118066i
$439$	−31.2963	−	12.9634i	−1.49369	−	0.618707i	−0.521574	−	0.853206i	$-0.674655\pi$
$439$	−31.2963	−	12.9634i	−1.49369	−	0.618707i	−0.972116	+	0.234499i	$0.924655\pi$
$440$	0.540491	−	0.540491i	0.0257669	−	0.0257669i
$441$	14.5296			0.691886
$442$	24.1148	+	10.5486i	1.14703	+	0.501747i
$443$	10.5102			0.499355			0.249678	−	0.968329i	$-0.419675\pi$
$443$	10.5102			0.499355			0.249678	+	0.968329i	$0.419675\pi$
$444$	11.4028	−	11.4028i	0.541154	−	0.541154i
$445$	23.7275	+	9.82827i	1.12479	+	0.465905i
$446$		−	26.2403i		−	1.24251i
$447$	−1.12849	+	2.72443i	−0.0533759	+	0.128861i
$448$	8.06020	−	3.33865i	0.380809	−	0.157736i
$449$	11.9390	+	28.8234i	0.563437	+	1.36026i	0.907001	+	0.421129i	$0.138366\pi$
$449$	11.9390	+	28.8234i	0.563437	+	1.36026i	−0.343564	+	0.939129i	$0.611634\pi$
$450$	−13.8363	−	13.8363i	−0.652251	−	0.652251i
$451$	−1.11565	−	1.11565i	−0.0525340	−	0.0525340i
$452$	0.279872	+	0.675672i	0.0131641	+	0.0317809i
$453$	3.13823	−	1.29990i	0.147447	−	0.0610745i
$454$	8.34754	−	20.1527i	0.391769	−	0.945815i
$455$			12.7422i			0.597365i
$456$	9.78778	+	4.05423i	0.458355	+	0.189857i
$457$	−28.8912	+	28.8912i	−1.35147	+	1.35147i	−0.467454	+	0.884017i	$0.654829\pi$
$457$	−28.8912	+	28.8912i	−1.35147	+	1.35147i	−0.884017	+	0.467454i	$0.845171\pi$
$458$	34.0244			1.58986
$459$	−15.7460	−	16.3775i	−0.734961	−	0.764436i
$460$	4.01745			0.187315
$461$	−3.18214	+	3.18214i	−0.148207	+	0.148207i	−0.777317	−	0.629110i	$-0.783420\pi$
$461$	−3.18214	+	3.18214i	−0.148207	+	0.148207i	0.629110	+	0.777317i	$0.283420\pi$
$462$	1.80371	+	0.747120i	0.0839161	+	0.0347592i
$463$		−	14.1998i		−	0.659923i	−0.943994	−	0.329961i	$-0.892964\pi$
$463$		−	14.1998i		−	0.659923i	0.943994	−	0.329961i	$-0.107036\pi$
$464$	−3.06915	+	7.40957i	−0.142482	+	0.343981i
$465$	15.9480	−	6.60586i	0.739569	−	0.306339i
$466$	−6.43204	−	15.5283i	−0.297959	−	0.719335i
$467$	7.90559	+	7.90559i	0.365827	+	0.365827i	0.865953	−	0.500126i	$-0.166713\pi$
$467$	7.90559	+	7.90559i	0.365827	+	0.365827i	−0.500126	+	0.865953i	$0.666713\pi$
$468$	−8.39994	−	8.39994i	−0.388287	−	0.388287i
$469$	0.551609	+	1.33170i	0.0254709	+	0.0614923i
$470$	22.2642	−	9.22215i	1.02697	−	0.425386i
$471$	−15.1196	+	36.5018i	−0.696672	+	1.68192i
$472$			8.48294i			0.390459i
$473$	0.196435	+	0.0813659i	0.00903207	+	0.00374121i
$474$	−10.2167	+	10.2167i	−0.469268	+	0.469268i
$475$	4.08515			0.187439
$476$	−3.63508	+	3.49492i	−0.166614	+	0.160189i
$477$	−19.1084			−0.874912
$478$	17.2314	−	17.2314i	0.788147	−	0.788147i
$479$	35.6869	+	14.7820i	1.63058	+	0.675407i	0.995296	−	0.0968761i	$-0.0308851\pi$
$479$	35.6869	+	14.7820i	1.63058	+	0.675407i	0.635279	+	0.772283i	$0.280885\pi$
$480$		−	14.9734i		−	0.683437i
$481$	−14.2671	+	34.4439i	−0.650524	+	1.57050i
$482$	14.1344	−	5.85466i	0.643804	−	0.266672i
$483$	−9.02321	−	21.7839i	−0.410570	−	0.991204i
$484$	4.69772	+	4.69772i	0.213533	+	0.213533i
$485$	8.12906	+	8.12906i	0.369122	+	0.369122i
$486$	−9.03036	−	21.8012i	−0.409625	−	0.988923i
$487$	16.8953	−	6.99824i	0.765597	−	0.317121i	0.0345095	−	0.999404i	$-0.489013\pi$
$487$	16.8953	−	6.99824i	0.765597	−	0.317121i	0.731087	+	0.682284i	$0.239013\pi$
$488$	−11.9331	+	28.8091i	−0.540187	+	1.30413i
$489$			57.3622i			2.59401i
$490$	6.99053	+	2.89557i	0.315800	+	0.130809i
$491$	22.4776	−	22.4776i	1.01440	−	1.01440i	0.0145030	−	0.999895i	$-0.495383\pi$
$491$	22.4776	−	22.4776i	1.01440	−	1.01440i	0.999895	−	0.0145030i	$-0.00461660\pi$
$492$	−12.6919			−0.572195
$493$	−0.134137	+	6.82360i	−0.00604121	+	0.307320i
$494$	10.6590			0.479569
$495$	−1.19009	+	1.19009i	−0.0534907	+	0.0534907i
$496$	−17.1462	−	7.10218i	−0.769887	−	0.318897i
$497$			27.2446i			1.22209i
$498$	−26.6755	+	64.4005i	−1.19536	+	2.88585i
$499$	7.01373	−	2.90518i	0.313978	−	0.130054i	−0.220129	−	0.975471i	$-0.570648\pi$
$499$	7.01373	−	2.90518i	0.313978	−	0.130054i	0.534107	+	0.845417i	$0.320648\pi$
$500$	−2.76156	−	6.66699i	−0.123501	−	0.298157i
$501$	−0.198523	−	0.198523i	−0.00886937	−	0.00886937i
$502$	5.95390	+	5.95390i	0.265736	+	0.265736i
$503$	4.22782	+	10.2069i	0.188509	+	0.455102i	0.989673	−	0.143344i	$-0.0457854\pi$
$503$	4.22782	+	10.2069i	0.188509	+	0.455102i	−0.801164	+	0.598445i	$0.795785\pi$
$504$	−20.7652	+	8.60123i	−0.924956	+	0.383129i
$505$	−2.45840	+	5.93509i	−0.109397	+	0.264108i
$506$			1.42307i			0.0632631i
$507$	6.86668	+	2.84427i	0.304960	+	0.126319i
$508$	1.10451	−	1.10451i	0.0490045	−	0.0490045i
$509$	−39.7947			−1.76387			−0.881935	−	0.471371i	$-0.843759\pi$
$509$	−39.7947			−1.76387			−0.881935	+	0.471371i	$0.843759\pi$
$510$	−10.9328	−	27.9348i	−0.484113	−	1.23697i
$511$	−1.09442			−0.0484144
$512$	4.03254	−	4.03254i	0.178215	−	0.178215i
$513$	−8.49999	−	3.52081i	−0.375284	−	0.155448i
$514$			6.87480i			0.303235i
$515$	8.02017	−	19.3624i	0.353411	−	0.853210i
$516$	1.58016	−	0.654523i	0.0695626	−	0.0288138i
$517$	0.760072	+	1.83498i	0.0334279	+	0.0807022i
$518$	−21.7064	−	21.7064i	−0.953725	−	0.953725i
$519$	13.8664	+	13.8664i	0.608667	+	0.608667i
$520$	5.43995	+	13.1332i	0.238558	+	0.575929i
$521$	5.62879	−	2.33152i	0.246602	−	0.102146i	−0.255959	−	0.966688i	$-0.582391\pi$
$521$	5.62879	−	2.33152i	0.246602	−	0.102146i	0.502561	+	0.864542i	$0.332391\pi$
$522$	5.06613	−	12.2307i	0.221739	−	0.535324i
$523$			4.08197i			0.178492i	0.996010	+	0.0892461i	$0.0284458\pi$
$523$			4.08197i			0.178492i	−0.996010	+	0.0892461i	$0.971554\pi$
$524$	6.27222	+	2.59804i	0.274003	+	0.113496i
$525$	−9.83968	+	9.83968i	−0.429439	+	0.429439i
$526$	0.611466			0.0266612
$527$	−15.7902	−	0.310400i	−0.687833	−	0.0135212i
$528$	2.90532			0.126438
$529$	−4.11054	+	4.11054i	−0.178719	+	0.178719i
$530$	−9.19349	−	3.80807i	−0.399340	−	0.165412i
$531$		−	18.6784i		−	0.810572i
$532$	−0.781464	+	1.88662i	−0.0338808	+	0.0817954i
$533$	27.1088	−	11.2289i	1.17421	−	0.486375i
$534$	28.0049	+	67.6099i	1.21189	+	2.92577i
$535$	21.3774	+	21.3774i	0.924227	+	0.924227i
$536$	1.13707	+	1.13707i	0.0491139	+	0.0491139i
$537$	−17.3297	−	41.8375i	−0.747831	−	1.80542i
$538$	−19.7237	+	8.16982i	−0.850348	+	0.352226i
$539$	−0.238648	+	0.576147i	−0.0102793	+	0.0248164i
$540$			5.33975i			0.229786i
$541$	−5.87812	−	2.43480i	−0.252720	−	0.104680i	0.252727	−	0.967538i	$-0.418673\pi$
$541$	−5.87812	−	2.43480i	−0.252720	−	0.104680i	−0.505447	+	0.862857i	$0.668673\pi$
$542$	−3.50134	+	3.50134i	−0.150396	+	0.150396i
$543$	−43.6012			−1.87111
$544$	−5.49027	+	12.5511i	−0.235393	+	0.538124i
$545$	6.36134			0.272490
$546$	−25.6737	+	25.6737i	−1.09873	+	1.09873i
$547$	1.78744	+	0.740382i	0.0764254	+	0.0316564i	0.420569	−	0.907261i	$-0.361831\pi$
$547$	1.78744	+	0.740382i	0.0764254	+	0.0316564i	−0.344143	+	0.938917i	$0.611831\pi$
$548$		−	7.95579i		−	0.339854i
$549$	26.2752	−	63.4340i	1.12140	−	2.70730i
$550$	0.775917	−	0.321395i	0.0330852	−	0.0137043i
$551$	1.05767	+	2.55343i	0.0450581	+	0.108780i
$552$	−18.6001	−	18.6001i	−0.791675	−	0.791675i
$553$	4.52516	+	4.52516i	0.192429	+	0.192429i
$554$	1.42758	+	3.44649i	0.0606522	+	0.146427i
$555$	39.2554	−	16.2601i	1.66630	−	0.690204i
$556$	−0.853306	+	2.06006i	−0.0361882	+	0.0873661i
$557$		−	9.26384i		−	0.392522i	−0.980552	−	0.196261i	$-0.937120\pi$
$557$		−	9.26384i		−	0.392522i	0.980552	−	0.196261i	$-0.0628799\pi$
$558$	28.3026	+	11.7233i	1.19814	+	0.496288i
$559$	−2.79601	+	2.79601i	−0.118259	+	0.118259i
$560$	−15.6133			−0.659784
$561$	2.30233	−	0.901061i	0.0972045	−	0.0380428i
$562$	31.7994			1.34138
$563$	18.5864	−	18.5864i	0.783324	−	0.783324i	−0.197066	−	0.980390i	$-0.563141\pi$
$563$	18.5864	−	18.5864i	0.783324	−	0.783324i	0.980390	+	0.197066i	$0.0631415\pi$
$564$	14.7609	+	6.11417i	0.621547	+	0.257453i
$565$			1.92698i			0.0810687i
$566$	−15.5548	+	37.5527i	−0.653819	+	1.57846i
$567$	1.26460	−	0.523815i	0.0531083	−	0.0219982i
$568$	11.6314	+	28.0806i	0.488041	+	1.17824i
$569$	−31.8690	−	31.8690i	−1.33602	−	1.33602i	−0.899880	−	0.436138i	$-0.856346\pi$
$569$	−31.8690	−	31.8690i	−1.33602	−	1.33602i	−0.436138	−	0.899880i	$-0.643654\pi$
$570$	−8.58989	−	8.58989i	−0.359791	−	0.359791i
$571$	13.0004	+	31.3857i	0.544048	+	1.31345i	0.921845	+	0.387560i	$0.126682\pi$
$571$	13.0004	+	31.3857i	0.544048	+	1.31345i	−0.377796	+	0.925889i	$0.623318\pi$
$572$	0.471054	−	0.195117i	0.0196957	−	0.00815824i
$573$	7.38363	−	17.8257i	0.308455	−	0.744677i
$574$			24.1603i			1.00843i
$575$	−9.37099	−	3.88159i	−0.390797	−	0.161874i
$576$	−15.1537	+	15.1537i	−0.631403	+	0.631403i
$577$	18.5921			0.773999			0.387000	−	0.922080i	$-0.373511\pi$
$577$	18.5921			0.773999			0.387000	+	0.922080i	$0.373511\pi$
$578$	−1.07862	+	27.4245i	−0.0448648	+	1.14071i
$579$	−5.81082			−0.241489
$580$	1.13426	−	1.13426i	0.0470974	−	0.0470974i
$581$	28.5241	+	11.8151i	1.18338	+	0.490172i
$582$			32.7577i			1.35785i
$583$	0.313854	−	0.757710i	0.0129985	−	0.0313812i
$584$	−1.12800	+	0.467234i	−0.0466771	+	0.0193343i
$585$	−11.9781	−	28.9177i	−0.495233	−	1.19560i
$586$	−18.4668	−	18.4668i	−0.762856	−	0.762856i
$587$	−19.8800	−	19.8800i	−0.820537	−	0.820537i	0.165648	−	0.986185i	$-0.447028\pi$
$587$	−19.8800	−	19.8800i	−0.820537	−	0.820537i	−0.986185	+	0.165648i	$0.947028\pi$
$588$	1.91973	+	4.63464i	0.0791683	+	0.191129i
$589$	−5.90879	+	2.44750i	−0.243467	+	0.100847i
$590$	3.72237	−	8.98660i	0.153248	−	0.369973i
$591$			12.8929i			0.530345i
$592$	−42.2048	−	17.4818i	−1.73461	−	0.718498i
$593$	−0.366821	+	0.366821i	−0.0150636	+	0.0150636i	−0.714598	−	0.699535i	$-0.753391\pi$
$593$	−0.366821	+	0.366821i	−0.0150636	+	0.0150636i	0.699535	+	0.714598i	$0.253391\pi$
$594$	−1.89145			−0.0776072
$595$	−12.3728	+	4.84234i	−0.507236	+	0.198517i
$596$	−0.634118			−0.0259745
$597$	4.84437	−	4.84437i	0.198267	−	0.198267i
$598$	−24.4508	−	10.1278i	−0.999866	−	0.414158i
$599$			15.7600i			0.643938i	0.946750	+	0.321969i	$0.104345\pi$
$599$			15.7600i			0.643938i	−0.946750	+	0.321969i	$0.895655\pi$
$600$	−5.94081	+	14.3424i	−0.242533	+	0.585525i
$601$	25.3037	−	10.4811i	1.03216	−	0.427534i	0.198668	−	0.980067i	$-0.436338\pi$
$601$	25.3037	−	10.4811i	1.03216	−	0.427534i	0.833491	+	0.552533i	$0.186338\pi$
$602$	−1.24595	−	3.00799i	−0.0507811	−	0.122597i
$603$	−2.50368	−	2.50368i	−0.101958	−	0.101958i
$604$	0.516494	+	0.516494i	0.0210159	+	0.0210159i
$605$	6.69883	+	16.1724i	0.272346	+	0.657501i
$606$	−16.9116	+	7.00502i	−0.686988	+	0.284560i
$607$	−5.13490	+	12.3967i	−0.208419	+	0.503168i	−0.993175	−	0.116637i	$-0.962789\pi$
$607$	−5.13490	+	12.3967i	−0.208419	+	0.503168i	0.784755	+	0.619806i	$0.212789\pi$
$608$			5.54769i			0.224989i
$609$	−8.69785	−	3.60277i	−0.352455	−	0.145992i
$610$	25.2833	−	25.2833i	1.02369	−	1.02369i
$611$	−36.9374			−1.49433
$612$	4.96425	−	11.3486i	0.200668	−	0.458740i
$613$	−37.3138			−1.50709			−0.753545	−	0.657397i	$-0.771658\pi$
$613$	−37.3138			−1.50709			−0.753545	+	0.657397i	$0.771658\pi$
$614$	−2.58702	+	2.58702i	−0.104404	+	0.104404i
$615$	−30.8958	−	12.7974i	−1.24584	−	0.516043i
$616$		−	0.964683i		−	0.0388682i
$617$	18.3290	−	44.2502i	0.737899	−	1.78145i	0.123664	−	0.992324i	$-0.460536\pi$
$617$	18.3290	−	44.2502i	0.737899	−	1.78145i	0.614236	−	0.789123i	$-0.289464\pi$
$618$	55.1718	−	22.8529i	2.21933	−	0.919278i
$619$	17.3746	+	41.9460i	0.698344	+	1.68595i	0.727254	+	0.686369i	$0.240796\pi$
$619$	17.3746	+	41.9460i	0.698344	+	1.68595i	−0.0289100	+	0.999582i	$0.509204\pi$
$620$	2.62474	+	2.62474i	0.105412	+	0.105412i
$621$	16.1529	+	16.1529i	0.648193	+	0.648193i
$622$	2.34915	+	5.67136i	0.0941925	+	0.227401i
$623$	29.9457	−	12.4039i	1.19975	−	0.496952i
$624$	−20.6769	+	49.9185i	−0.827740	+	1.99834i
$625$		−	6.78062i		−	0.271225i
$626$	−17.9679	−	7.44254i	−0.718141	−	0.297464i
$627$	0.707963	−	0.707963i	0.0282733	−	0.0282733i
$628$	−8.49592			−0.339024
$629$	−38.8671	−	0.764040i	−1.54973	−	0.0304643i
$630$	25.7724			1.02680
$631$	−10.2301	+	10.2301i	−0.407254	+	0.407254i	−0.880780	−	0.473526i	$-0.842981\pi$
$631$	−10.2301	+	10.2301i	−0.407254	+	0.407254i	0.473526	+	0.880780i	$0.342981\pi$
$632$	6.59591	+	2.73212i	0.262371	+	0.108678i
$633$			19.4532i			0.773194i
$634$	12.1676	−	29.3751i	0.483236	−	1.16663i
$635$	3.80238	−	1.57500i	0.150893	−	0.0625018i
$636$	−2.52470	−	6.09517i	−0.100111	−	0.241689i
$637$	−8.20077	−	8.20077i	−0.324926	−	0.324926i
$638$	0.401778	+	0.401778i	0.0159065	+	0.0159065i
$639$	−25.6108	−	61.8299i	−1.01315	−	2.44595i
$640$	−20.1209	+	8.33436i	−0.795349	+	0.329445i
$641$	8.35724	−	20.1762i	0.330091	−	0.796910i	−0.668493	−	0.743718i	$-0.733060\pi$
$641$	8.35724	−	20.1762i	0.330091	−	0.796910i	0.998584	−	0.0531922i	$-0.0169396\pi$
$642$			86.1446i			3.39986i
$643$	−33.7319	−	13.9722i	−1.33026	−	0.551011i	−0.399529	−	0.916721i	$-0.630826\pi$
$643$	−33.7319	−	13.9722i	−1.33026	−	0.551011i	−0.930729	+	0.365710i	$0.880826\pi$
$644$	3.58523	−	3.58523i	0.141278	−	0.141278i
$645$	4.50653			0.177444
$646$	4.05065	+	10.3500i	0.159371	+	0.407213i
$647$	26.2132			1.03055			0.515274	−	0.857025i	$-0.327690\pi$
$647$	26.2132			1.03055			0.515274	+	0.857025i	$0.327690\pi$
$648$	1.07978	−	1.07978i	0.0424176	−	0.0424176i
$649$	0.740659	+	0.306791i	0.0290734	+	0.0120426i
$650$			15.6189i			0.612626i
$651$	8.33701	−	20.1273i	0.326753	−	0.788852i
$652$	−11.3960	+	4.72037i	−0.446301	+	0.184864i
$653$	−7.38019	−	17.8174i	−0.288809	−	0.697247i	0.711174	−	0.703016i	$-0.248164\pi$
$653$	−7.38019	−	17.8174i	−0.288809	−	0.697247i	−0.999983	+	0.00576864i	$0.998164\pi$
$654$	12.8171	+	12.8171i	0.501190	+	0.501190i
$655$	12.6488	+	12.6488i	0.494228	+	0.494228i
$656$	13.7590	+	33.2171i	0.537197	+	1.29691i
$657$	2.48372	−	1.02879i	0.0968991	−	0.0401369i
$658$	11.6389	−	28.0989i	0.453733	−	1.09541i
$659$		−	28.4003i		−	1.10632i	−0.833076	−	0.553159i	$-0.813422\pi$
$659$		−	28.4003i		−	1.10632i	0.833076	−	0.553159i	$-0.186578\pi$
$660$	−0.536857	−	0.222373i	−0.0208971	−	0.00865587i
$661$	12.2287	−	12.2287i	0.475643	−	0.475643i	−0.428092	−	0.903735i	$-0.640814\pi$
$661$	12.2287	−	12.2287i	0.475643	−	0.475643i	0.903735	+	0.428092i	$0.140814\pi$
$662$	10.7241			0.416803
$663$	−0.903682	+	45.9708i	−0.0350961	+	1.78536i
$664$	34.4435			1.33667
$665$	−3.80462	+	3.80462i	−0.147537	+	0.147537i
$666$	69.6660	+	28.8566i	2.69950	+	1.11817i
$667$		−	6.86232i		−	0.265710i
$668$	0.0231035	−	0.0557767i	0.000893900	−	0.00215807i
$669$	42.3493	−	17.5416i	1.63732	−	0.678199i
$670$	−0.705627	−	1.70353i	−0.0272608	−	0.0658133i
$671$	2.08380	+	2.08380i	0.0804441	+	0.0804441i
$672$	−13.3624	−	13.3624i	−0.515467	−	0.515467i
$673$	0.501206	+	1.21002i	0.0193201	+	0.0466428i	0.933245	−	0.359240i	$-0.116964\pi$
$673$	0.501206	+	1.21002i	0.0193201	+	0.0466428i	−0.913925	+	0.405883i	$0.866964\pi$
$674$	−12.7746	+	5.29140i	−0.492058	+	0.203817i
$675$	5.15917	−	12.4553i	0.198576	−	0.479406i
$676$			1.59824i			0.0614708i
$677$	−39.1535	−	16.2179i	−1.50479	−	0.623305i	−0.530316	−	0.847800i	$-0.677927\pi$
$677$	−39.1535	−	16.2179i	−1.50479	−	0.623305i	−0.974475	+	0.224495i	$0.927927\pi$
$678$	−3.88257	+	3.88257i	−0.149109	+	0.149109i
$679$	14.5090			0.556803
$680$	−10.6852	+	10.2732i	−0.409757	+	0.393958i
$681$	38.1049			1.46018
$682$	−0.929737	+	0.929737i	−0.0356015	+	0.0356015i
$683$	22.8816	+	9.47789i	0.875542	+	0.362661i	0.774766	−	0.632248i	$-0.217868\pi$
$683$	22.8816	+	9.47789i	0.875542	+	0.362661i	0.100776	+	0.994909i	$0.467868\pi$
$684$		−	5.01617i		−	0.191798i
$685$	8.02194	−	19.3667i	0.306503	−	0.739963i
$686$	29.8784	−	12.3760i	1.14076	−	0.472520i
$687$	22.7453	+	54.9121i	0.867789	+	2.09503i
$688$	−3.42602	−	3.42602i	−0.130616	−	0.130616i
$689$	10.7851	+	10.7851i	0.410880	+	0.410880i
$690$	11.5426	+	27.8664i	0.439420	+	1.06085i
$691$	−22.8709	+	9.47343i	−0.870049	+	0.360386i	−0.772629	−	0.634857i	$-0.781059\pi$
$691$	−22.8709	+	9.47343i	−0.870049	+	0.360386i	−0.0974197	+	0.995243i	$0.531059\pi$
$692$	−1.61372	+	3.89587i	−0.0613446	+	0.148099i
$693$			2.12411i			0.0806883i
$694$	48.0289	+	19.8942i	1.82315	+	0.755174i
$695$	−4.15439	+	4.15439i	−0.157585	+	0.157585i
$696$	−10.5028			−0.398109
$697$	21.2053	+	22.0557i	0.803208	+	0.835420i
$698$	8.68423			0.328703
$699$	20.7614	−	20.7614i	0.785268	−	0.785268i
$700$	−2.76453	−	1.14511i	−0.104490	−	0.0432810i
$701$		−	43.5809i		−	1.64603i	−0.568021	−	0.823014i	$-0.692291\pi$
$701$		−	43.5809i		−	1.64603i	0.568021	−	0.823014i	$-0.307709\pi$
$702$	13.4613	−	32.4984i	0.508064	−	1.22657i
$703$	−14.5443	+	6.02445i	−0.548549	+	0.227216i
$704$	−0.351995	−	0.849792i	−0.0132663	−	0.0320277i
$705$	29.7673	+	29.7673i	1.12110	+	1.12110i
$706$	−7.66145	−	7.66145i	−0.288342	−	0.288342i
$707$	3.10265	+	7.49047i	0.116687	+	0.281708i
$708$	5.95801	−	2.46789i	0.223916	−	0.0927489i
$709$	−11.9512	+	28.8527i	−0.448836	+	1.08359i	0.523922	+	0.851766i	$0.324468\pi$
$709$	−11.9512	+	28.8527i	−0.448836	+	1.08359i	−0.972759	+	0.231821i	$0.925532\pi$
$710$		−	34.8517i		−	1.30796i
$711$	−14.5234	−	6.01577i	−0.544668	−	0.225609i
$712$	25.5690	−	25.5690i	0.958239	−	0.958239i
$713$	15.8798			0.594704
$714$	−34.6860	−	15.1728i	−1.29809	−	0.567827i
$715$	1.34342			0.0502411
$716$	6.88568	−	6.88568i	0.257330	−	0.257330i
$717$	39.3291	+	16.2906i	1.46877	+	0.608385i
$718$			42.0981i			1.57109i
$719$	2.70526	−	6.53106i	0.100889	−	0.243568i	−0.865373	−	0.501128i	$-0.832919\pi$
$719$	2.70526	−	6.53106i	0.100889	−	0.243568i	0.966262	+	0.257560i	$0.0829186\pi$
$720$	35.4335	−	14.6770i	1.32053	−	0.546980i
$721$	−10.1220	−	24.4366i	−0.376962	−	0.910066i
$722$	−18.5076	−	18.5076i	−0.688782	−	0.688782i
$723$	18.8977	+	18.8977i	0.702814	+	0.702814i
$724$	−3.58797	−	8.66212i	−0.133346	−	0.321925i
$725$	−3.74163	+	1.54983i	−0.138961	+	0.0575594i
$726$	−19.0878	+	46.0821i	−0.708415	+	1.71027i
$727$			23.3744i			0.866909i	0.901175	+	0.433455i	$0.142706\pi$
$727$			23.3744i			0.866909i	−0.901175	+	0.433455i	$0.857294\pi$
$728$	16.5749	+	6.86556i	0.614308	+	0.254455i
$729$	30.5881	−	30.5881i	1.13289	−	1.13289i
$730$	1.40000			0.0518164
$731$	−3.77751	−	1.65241i	−0.139716	−	0.0611165i
$732$	23.7057			0.876189
$733$	15.2333	−	15.2333i	0.562655	−	0.562655i	−0.367406	−	0.930061i	$-0.619754\pi$
$733$	15.2333	−	15.2333i	0.562655	−	0.562655i	0.930061	+	0.367406i	$0.119754\pi$
$734$	37.7717	+	15.6455i	1.39418	+	0.577487i
$735$			13.2177i			0.487544i
$736$	5.27126	−	12.7259i	0.194301	−	0.469085i
$737$	0.140402	−	0.0581564i	0.00517178	−	0.00214222i
$738$	−22.7114	−	54.8303i	−0.836019	−	2.01833i
$739$	10.2372	+	10.2372i	0.376582	+	0.376582i	0.869868	−	0.493285i	$-0.164204\pi$
$739$	10.2372	+	10.2372i	0.376582	+	0.376582i	−0.493285	+	0.869868i	$0.664204\pi$
$740$	6.46071	+	6.46071i	0.237500	+	0.237500i
$741$	7.12552	+	17.2025i	0.261763	+	0.631951i
$742$	−11.6028	+	4.80602i	−0.425951	+	0.176435i
$743$	−6.07126	+	14.6573i	−0.222733	+	0.537725i	−0.995259	−	0.0972577i	$-0.968993\pi$
$743$	−6.07126	+	14.6573i	−0.222733	+	0.537725i	0.772526	+	0.634983i	$0.218993\pi$
$744$		−	24.3042i		−	0.891035i
$745$	−1.54363	−	0.639391i	−0.0565541	−	0.0234255i
$746$	−20.9674	+	20.9674i	−0.767670	+	0.767670i
$747$	−75.8402			−2.77485
$748$	0.368472	+	0.383249i	0.0134727	+	0.0140130i
$749$	38.1550			1.39415
$750$	38.3101	−	38.3101i	1.39889	−	1.39889i
$751$	27.9493	+	11.5770i	1.01989	+	0.422450i	0.829052	−	0.559172i	$-0.188881\pi$
$751$	27.9493	+	11.5770i	1.01989	+	0.422450i	0.190834	+	0.981622i	$0.438881\pi$
$752$		−	45.2603i		−	1.65047i
$753$	−5.62883	+	13.5892i	−0.205126	+	0.495218i
$754$	−9.76266	+	4.04382i	−0.355535	+	0.147267i
$755$	0.736507	+	1.77809i	0.0268042	+	0.0647111i
$756$	4.76526	+	4.76526i	0.173311	+	0.173311i
$757$	13.0204	+	13.0204i	0.473233	+	0.473233i	0.902959	−	0.429726i	$-0.141390\pi$
$757$	13.0204	+	13.0204i	0.473233	+	0.473233i	−0.429726	+	0.902959i	$0.641390\pi$
$758$	18.9044	+	45.6393i	0.686639	+	1.65769i
$759$	−2.29669	+	0.951322i	−0.0833647	+	0.0345308i
$760$	−2.29708	+	5.54564i	−0.0833239	+	0.201162i
$761$		−	39.9240i		−	1.44724i	−0.690197	−	0.723621i	$-0.742476\pi$
$761$		−	39.9240i		−	1.44724i	0.690197	−	0.723621i	$-0.257524\pi$
$762$	10.8346	+	4.48784i	0.392496	+	0.162577i
$763$	5.67695	−	5.67695i	0.205519	−	0.205519i
$764$	4.14898			0.150105
$765$	23.5274	−	22.6202i	0.850634	−	0.817836i
$766$	31.6659			1.14413
$767$	−10.5424	+	10.5424i	−0.380664	+	0.380664i
$768$	−34.7893	−	14.4102i	−1.25535	−	0.519983i
$769$			42.9326i			1.54819i	0.633071	+	0.774094i	$0.281794\pi$
$769$			42.9326i			1.54819i	−0.633071	+	0.774094i	$0.718206\pi$
$770$	−0.423310	+	1.02196i	−0.0152550	+	0.0368289i
$771$	−11.0953	+	4.59581i	−0.399586	+	0.165514i
$772$	−0.478176	−	1.15442i	−0.0172099	−	0.0415484i
$773$	−21.9189	−	21.9189i	−0.788368	−	0.788368i	0.192858	−	0.981227i	$-0.438224\pi$
$773$	−21.9189	−	21.9189i	−0.788368	−	0.788368i	−0.981227	+	0.192858i	$0.938224\pi$
$774$	5.65521	+	5.65521i	0.203272	+	0.203272i
$775$	−3.58641	−	8.65835i	−0.128828	−	0.311017i
$776$	14.9542	−	6.19422i	0.536823	−	0.222359i
$777$	20.5213	−	49.5428i	0.736198	−	1.77734i
$778$		−	7.71798i		−	0.276703i
$779$	11.4470	+	4.74151i	0.410132	+	0.169882i
$780$	7.64152	−	7.64152i	0.273610	−	0.273610i
$781$	2.87241			0.102783
$782$	0.542372	−	27.5907i	0.0193952	−	0.986643i
$783$	9.12097			0.325957
$784$	10.0486	−	10.0486i	0.358878	−	0.358878i
$785$	−20.6815	−	8.56656i	−0.738155	−	0.305754i
$786$			50.9707i			1.81806i
$787$	15.3700	−	37.1065i	0.547882	−	1.32270i	−0.371169	−	0.928565i	$-0.621043\pi$
$787$	15.3700	−	37.1065i	0.547882	−	1.32270i	0.919051	−	0.394139i	$-0.128957\pi$
$788$	−2.56141	+	1.06097i	−0.0912463	+	0.0377954i
$789$	0.408765	+	0.986847i	0.0145524	+	0.0351327i
$790$	−5.78866	−	5.78866i	−0.205951	−	0.205951i
$791$	1.71966	+	1.71966i	0.0611442	+	0.0611442i
$792$	0.906832	+	2.18929i	0.0322229	+	0.0777929i
$793$	−50.6335	+	20.9731i	−1.79805	+	0.744776i
$794$	8.03369	−	19.3950i	0.285105	−	0.688304i
$795$		−	17.3831i		−	0.616515i
$796$	1.36106	+	0.563771i	0.0482416	+	0.0199823i
$797$	7.25943	−	7.25943i	0.257142	−	0.257142i	−0.566749	−	0.823891i	$-0.691799\pi$
$797$	7.25943	−	7.25943i	0.257142	−	0.257142i	0.823891	+	0.566749i	$0.191799\pi$
$798$	−15.3315			−0.542728
$799$	−14.0371	−	35.8666i	−0.496596	−	1.26887i
$800$	−8.12923			−0.287412
$801$	−56.2997	+	56.2997i	−1.98925	+	1.98925i
$802$	29.5190	+	12.2272i	1.04235	+	0.431757i
$803$			0.115386i			0.00407187i
$804$	0.467822	−	1.12942i	0.0164988	−	0.0398317i
$805$	12.3425	−	5.11244i	0.435017	−	0.180190i
$806$	−9.35764	−	22.5914i	−0.329609	−	0.795746i
$807$	−26.3706	−	26.3706i	−0.928289	−	0.928289i
$808$	6.39571	+	6.39571i	0.225000	+	0.225000i
$809$	−17.8443	−	43.0801i	−0.627374	−	1.51461i	−0.842874	−	0.538110i	$-0.819138\pi$
$809$	−17.8443	−	43.0801i	−0.627374	−	1.51461i	0.215501	−	0.976504i	$-0.430862\pi$
$810$	−1.61770	+	0.670073i	−0.0568402	+	0.0235440i
$811$	8.50825	−	20.5407i	0.298765	−	0.721283i	−0.701200	−	0.712964i	$-0.747352\pi$
$811$	8.50825	−	20.5407i	0.298765	−	0.721283i	0.999965	−	0.00831840i	$-0.00264786\pi$
$812$		−	2.02445i		−	0.0710443i
$813$	−7.99148	−	3.31018i	−0.280273	−	0.116093i
$814$	−2.28852	+	2.28852i	−0.0802126	+	0.0802126i
$815$	−32.5007			−1.13845
$816$	−56.3291	−	1.10730i	−1.97191	−	0.0387633i
$817$	−1.66969			−0.0584150
$818$	−10.1248	+	10.1248i	−0.354004	+	0.354004i
$819$	−36.4959	−	15.1171i	−1.27527	−	0.528234i
$820$		−	7.19108i		−	0.251124i
$821$	−3.01806	+	7.28623i	−0.105331	+	0.254291i	−0.967754	−	0.251896i	$-0.918946\pi$
$821$	−3.01806	+	7.28623i	−0.105331	+	0.254291i	0.862423	+	0.506188i	$0.168946\pi$
$822$	55.1839	−	22.8579i	1.92476	−	0.797262i
$823$	6.03125	+	14.5607i	0.210236	+	0.507555i	0.993459	−	0.114185i	$-0.0364258\pi$
$823$	6.03125	+	14.5607i	0.210236	+	0.507555i	−0.783223	+	0.621741i	$0.786426\pi$
$824$	−20.8651	−	20.8651i	−0.726870	−	0.726870i
$825$	1.03740	+	1.03740i	0.0361177	+	0.0361177i
$826$	−4.69787	−	11.3417i	−0.163460	−	0.394627i
$827$	−29.8230	+	12.3531i	−1.03705	+	0.429559i	−0.835251	−	0.549869i	$-0.814678\pi$
$827$	−29.8230	+	12.3531i	−1.03705	+	0.429559i	−0.201796	+	0.979428i	$0.564678\pi$
$828$	−4.76622	+	11.5067i	−0.165638	+	0.399885i
$829$			10.4914i			0.364380i	0.983263	+	0.182190i	$0.0583185\pi$
$829$			10.4914i			0.364380i	−0.983263	+	0.182190i	$0.941681\pi$
$830$	−36.4885	−	15.1140i	−1.26654	−	0.524616i
$831$	−4.60796	+	4.60796i	−0.159848	+	0.159848i
$832$	17.1060			0.593044
$833$	4.84654	−	11.0795i	0.167923	−	0.383882i
$834$	−16.7409			−0.579691
$835$	0.112481	−	0.112481i	0.00389257	−	0.00389257i
$836$	0.198908	+	0.0823902i	0.00687936	+	0.00284953i
$837$			21.1064i			0.729545i
$838$	−21.2976	+	51.4170i	−0.735713	+	1.77617i
$839$	−32.9010	+	13.6280i	−1.13587	+	0.470492i	−0.869772	−	0.493454i	$-0.835734\pi$
$839$	−32.9010	+	13.6280i	−1.13587	+	0.470492i	−0.266097	+	0.963946i	$0.585734\pi$
$840$	−7.82464	−	18.8903i	−0.269976	−	0.651779i
$841$	18.5686	+	18.5686i	0.640298	+	0.640298i
$842$	18.0876	+	18.0876i	0.623340	+	0.623340i
$843$	21.2579	+	51.3211i	0.732161	+	1.76759i
$844$	−3.86471	+	1.60081i	−0.133029	+	0.0551023i
$845$	−1.61153	+	3.89058i	−0.0554384	+	0.133840i
$846$			74.7095i			2.56857i
$847$	20.4106	+	8.45434i	0.701316	+	0.290495i
$848$	−13.2152	+	13.2152i	−0.453813	+	0.453813i
$849$	−71.0049			−2.43688
$850$	−15.1661	+	5.93556i	−0.520195	+	0.203588i
$851$	39.0877			1.33991
$852$	16.3386	−	16.3386i	0.559752	−	0.559752i
$853$	34.2406	+	14.1829i	1.17238	+	0.485614i	0.881977	−	0.471292i	$-0.156212\pi$
$853$	34.2406	+	14.1829i	1.17238	+	0.485614i	0.290399	+	0.956906i	$0.406212\pi$
$854$		−	45.1262i		−	1.54419i
$855$	5.05788	−	12.2108i	0.172976	−	0.417601i
$856$	39.3258	−	16.2893i	1.34413	−	0.556756i
$857$	10.0123	+	24.1719i	0.342014	+	0.825695i	0.997512	+	0.0704981i	$0.0224589\pi$
$857$	10.0123	+	24.1719i	0.342014	+	0.825695i	−0.655498	+	0.755197i	$0.727541\pi$
$858$	2.70679	+	2.70679i	0.0924082	+	0.0924082i
$859$	−11.0868	−	11.0868i	−0.378278	−	0.378278i	0.492203	−	0.870481i	$-0.336192\pi$
$859$	−11.0868	−	11.0868i	−0.378278	−	0.378278i	−0.870481	+	0.492203i	$0.836192\pi$
$860$	0.370845	+	0.895300i	0.0126457	+	0.0305295i
$861$	−38.9924	+	16.1512i	−1.32886	+	0.550431i
$862$	9.47602	−	22.8771i	0.322755	−	0.779199i
$863$			54.5731i			1.85769i	0.370467	+	0.928846i	$0.379198\pi$
$863$			54.5731i			1.85769i	−0.370467	+	0.928846i	$0.620802\pi$
$864$	16.9145	+	7.00623i	0.575444	+	0.238357i
$865$	−7.85654	+	7.85654i	−0.267130	+	0.267130i
$866$	37.6080			1.27797
$867$	−44.9815	+	16.5925i	−1.52765	+	0.563511i
$868$	4.68470			0.159009
$869$	0.477090	−	0.477090i	0.0161842	−	0.0161842i
$870$	11.1264	+	4.60872i	0.377221	+	0.156250i
$871$			2.82625i			0.0957637i
$872$	3.42752	−	8.27476i	0.116070	−	0.280219i
$873$	−32.9272	+	13.6389i	−1.11442	+	0.461606i
$874$	−4.27659	−	10.3246i	−0.144658	−	0.349235i
$875$	−16.9682	−	16.9682i	−0.573632	−	0.573632i
$876$	0.656325	+	0.656325i	0.0221752	+	0.0221752i
$877$	−13.8299	−	33.3883i	−0.467002	−	1.12744i	−0.965465	−	0.260532i	$-0.916102\pi$
$877$	−13.8299	−	33.3883i	−0.467002	−	1.12744i	0.498463	−	0.866911i	$-0.333898\pi$
$878$	50.5264	−	20.9287i	1.70518	−	0.706310i
$879$	17.4586	−	42.1487i	0.588863	−	1.42164i
$880$			1.64612i			0.0554908i
$881$	−25.8745	−	10.7176i	−0.871733	−	0.361084i	−0.0984479	−	0.995142i	$-0.531388\pi$
$881$	−25.8745	−	10.7176i	−0.871733	−	0.361084i	−0.773285	+	0.634059i	$0.781388\pi$
$882$	−16.5868	+	16.5868i	−0.558508	+	0.558508i
$883$	14.3678			0.483513			0.241757	−	0.970337i	$-0.422276\pi$
$883$	14.3678			0.483513			0.241757	+	0.970337i	$0.422276\pi$
$884$	−9.20726	+	3.60344i	−0.309674	+	0.121197i
$885$	16.9919			0.571177
$886$	−11.9983	+	11.9983i	−0.403092	+	0.403092i
$887$	25.0778	+	10.3876i	0.842030	+	0.348780i	0.761654	−	0.647984i	$-0.224388\pi$
$887$	25.0778	+	10.3876i	0.842030	+	0.348780i	0.0803763	+	0.996765i	$0.474388\pi$
$888$		−	59.8240i		−	2.00756i
$889$	1.98775	−	4.79884i	0.0666668	−	0.160948i
$890$	−38.3070	+	15.8673i	−1.28405	+	0.531872i
$891$	−0.0552261	−	0.133328i	−0.00185015	−	0.00446665i
$892$	6.96990	+	6.96990i	0.233370	+	0.233370i
$893$	−11.0289	−	11.0289i	−0.369069	−	0.369069i
$894$	−1.82190	−	4.39845i	−0.0609334	−	0.147106i
$895$	23.7047	−	9.81879i	0.792359	−	0.328206i
$896$	−10.5185	+	25.3939i	−0.351398	+	0.848350i
$897$		−	46.2317i		−	1.54363i
$898$	−46.5339	−	19.2750i	−1.55286	−	0.643214i
$899$	4.48338	−	4.48338i	0.149529	−	0.149529i
$900$	7.35037			0.245012
$901$	−6.37385	+	14.5710i	−0.212344	+	0.485432i
$902$	2.54723			0.0848136
$903$	4.02169	−	4.02169i	0.133833	−	0.133833i
$904$	2.50659	+	1.03827i	0.0833681	+	0.0345322i
$905$		−	24.7039i		−	0.821186i
$906$	−2.09862	+	5.06652i	−0.0697221	+	0.168324i
$907$	−42.2670	+	17.5076i	−1.40345	+	0.581329i	−0.950646	−	0.310279i	$-0.899578\pi$
$907$	−42.2670	+	17.5076i	−1.40345	+	0.581329i	−0.452808	+	0.891608i	$0.649578\pi$
$908$	3.13568	+	7.57020i	0.104061	+	0.251226i
$909$	−14.0825	−	14.0825i	−0.467088	−	0.467088i
$910$	−14.5464	−	14.5464i	−0.482208	−	0.482208i
$911$	−7.28943	−	17.5982i	−0.241510	−	0.583056i	0.755924	−	0.654660i	$-0.227188\pi$
$911$	−7.28943	−	17.5982i	−0.241510	−	0.583056i	−0.997433	+	0.0716043i	$0.977188\pi$
$912$	−21.0787	+	8.73106i	−0.697984	+	0.289114i
$913$	1.24567	−	3.00732i	0.0412257	−	0.0995277i
$914$		−	65.9637i		−	2.18189i
$915$	57.7066	+	23.9029i	1.90772	+	0.790204i
$916$	−9.03751	+	9.03751i	−0.298608	+	0.298608i
$917$	22.5758			0.745520
$918$	36.6719	+	0.720886i	1.21035	+	0.0237928i
$919$	−16.2695			−0.536681			−0.268341	−	0.963324i	$-0.586475\pi$
$919$	−16.2695			−0.536681			−0.268341	+	0.963324i	$0.586475\pi$
$920$	10.5386	−	10.5386i	0.347448	−	0.347448i
$921$	−5.90462	−	2.44577i	−0.194564	−	0.0805910i
$922$		−	7.26539i		−	0.239273i
$923$	−20.4427	+	49.3531i	−0.672880	+	1.62448i
$924$	−0.677547	+	0.280649i	−0.0222897	+	0.00923268i
$925$	−8.82783	−	21.3123i	−0.290257	−	0.700743i
$926$	16.2104	+	16.2104i	0.532707	+	0.532707i
$927$	45.9423	+	45.9423i	1.50894	+	1.50894i
$928$	−2.10470	−	5.08119i	−0.0690901	−	0.166798i
$929$	−38.1327	+	15.7951i	−1.25109	+	0.518219i	−0.907164	−	0.420777i	$-0.861758\pi$
$929$	−38.1327	+	15.7951i	−1.25109	+	0.518219i	−0.343928	+	0.938996i	$0.611758\pi$
$930$	−10.6648	+	25.7472i	−0.349714	+	0.844284i
$931$		−	4.89723i		−	0.160500i
$932$	5.83307	+	2.41614i	0.191069	+	0.0791433i
$933$	−7.58262	+	7.58262i	−0.248244	+	0.248244i
$934$	−18.0499			−0.590610
$935$	0.510531	+	1.30447i	0.0166961	+	0.0426608i
$936$	−44.0696			−1.44046
$937$	−33.9481	+	33.9481i	−1.10903	+	1.10903i	−0.115757	+	0.993278i	$0.536929\pi$
$937$	−33.9481	+	33.9481i	−1.10903	+	1.10903i	−0.993278	+	0.115757i	$0.963071\pi$
$938$	−2.14997	−	0.890546i	−0.0701990	−	0.0290774i
$939$		−	33.9738i		−	1.10869i
$940$	−3.46422	+	8.36336i	−0.112990	+	0.272783i
$941$	13.4249	−	5.56077i	0.437639	−	0.181276i	−0.152975	−	0.988230i	$-0.548885\pi$
$941$	13.4249	−	5.56077i	0.437639	−	0.181276i	0.590614	+	0.806954i	$0.298885\pi$
$942$	−24.4098	−	58.9305i	−0.795314	−	1.92006i
$943$	−21.7533	−	21.7533i	−0.708383	−	0.708383i
$944$	−12.9178	−	12.9178i	−0.420440	−	0.420440i
$945$	6.79514	+	16.4049i	0.221046	+	0.533652i
$946$	−0.317134	+	0.131361i	−0.0103109	+	0.00427092i
$947$	12.6077	−	30.4377i	0.409696	−	0.989093i	−0.575522	−	0.817786i	$-0.695201\pi$
$947$	12.6077	−	30.4377i	0.409696	−	0.989093i	0.985218	−	0.171307i	$-0.0547989\pi$
$948$		−	5.42748i		−	0.176276i
$949$	−1.98252	−	0.821188i	−0.0643554	−	0.0266569i
$950$	−4.66356	+	4.66356i	−0.151306	+	0.151306i
$951$	55.5426			1.80109
$952$	−0.367668	+	18.7035i	−0.0119162	+	0.606184i
$953$	29.5832			0.958293			0.479146	−	0.877735i	$-0.340946\pi$
$953$	29.5832			0.958293			0.479146	+	0.877735i	$0.340946\pi$
$954$	21.8139	−	21.8139i	0.706252	−	0.706252i
$955$	10.0998	+	4.18348i	0.326822	+	0.135374i
$956$			9.15396i			0.296060i
$957$	−0.379842	+	0.917019i	−0.0122785	+	0.0296430i
$958$	−57.6148	+	23.8648i	−1.86145	+	0.771037i
$959$	−10.1242	−	24.4420i	−0.326927	−	0.789273i
$960$	−13.7855	−	13.7855i	−0.444924	−	0.444924i
$961$	−11.5455	−	11.5455i	−0.372436	−	0.372436i
$962$	−23.0336	−	55.6079i	−0.742632	−	1.79287i
$963$	−86.5904	+	35.8669i	−2.79034	+	1.15579i
$964$	−2.19925	+	5.30946i	−0.0708331	+	0.171006i
$965$		−	3.29234i		−	0.105984i
$966$	35.1691	+	14.5675i	1.13155	+	0.468703i
$967$	−33.3191	+	33.3191i	−1.07147	+	1.07147i	−0.0742289	+	0.997241i	$0.523650\pi$
$967$	−33.3191	+	33.3191i	−1.07147	+	1.07147i	−0.997241	+	0.0742289i	$0.976350\pi$
$968$	24.6462			0.792160
$969$	−13.9960	+	13.4563i	−0.449615	+	0.432279i
$970$	−18.5601			−0.595929
$971$	26.8321	−	26.8321i	0.861082	−	0.861082i	−0.130381	−	0.991464i	$-0.541620\pi$
$971$	26.8321	−	26.8321i	0.861082	−	0.861082i	0.991464	+	0.130381i	$0.0416202\pi$
$972$	8.18943	+	3.39217i	0.262676	+	0.108804i
$973$			7.41486i			0.237709i
$974$	−11.2983	+	27.2766i	−0.362022	+	0.873998i
$975$	−25.2075	+	10.4413i	−0.807285	+	0.334389i
$976$	−25.6988	−	62.0423i	−0.822598	−	1.98593i
$977$	17.3726	+	17.3726i	0.555798	+	0.555798i	0.928108	−	0.372310i	$-0.121434\pi$
$977$	17.3726	+	17.3726i	0.555798	+	0.555798i	−0.372310	+	0.928108i	$0.621434\pi$
$978$	−65.4841	−	65.4841i	−2.09395	−	2.09395i
$979$	−1.30775	−	3.15719i	−0.0417959	−	0.100904i
$980$	−2.62593	+	1.08770i	−0.0838823	+	0.0347452i
$981$	−7.54696	+	18.2200i	−0.240956	+	0.581719i
$982$			51.3203i			1.63770i
$983$	33.5582	+	13.9003i	1.07034	+	0.443349i	0.847111	−	0.531417i	$-0.178340\pi$
$983$	33.5582	+	13.9003i	1.07034	+	0.443349i	0.223229	+	0.974766i	$0.428340\pi$
$984$	−33.2935	+	33.2935i	−1.06136	+	1.06136i
$985$	−7.30499			−0.232756
$986$	−7.63663	−	7.94289i	−0.243200	−	0.252953i
$987$	53.1295			1.69113
$988$	−2.83122	+	2.83122i	−0.0900730	+	0.0900730i
$989$	3.83013	+	1.58649i	0.121791	+	0.0504475i
$990$		−	2.71720i		−	0.0863582i
$991$	11.1105	−	26.8230i	0.352936	−	0.852062i	−0.643319	−	0.765598i	$-0.722443\pi$
$991$	11.1105	−	26.8230i	0.352936	−	0.852062i	0.996255	−	0.0864641i	$-0.0275568\pi$
$992$	11.7582	−	4.87039i	0.373322	−	0.154635i
$993$	7.16905	+	17.3076i	0.227503	+	0.549241i
$994$	−31.1022	−	31.1022i	−0.986501	−	0.986501i
$995$	2.74476	+	2.74476i	0.0870148	+	0.0870148i
$996$	−10.0204	−	24.1915i	−0.317509	−	0.766536i
$997$	−18.2115	+	7.54346i	−0.576764	+	0.238904i	−0.651945	−	0.758266i	$-0.726047\pi$
$997$	−18.2115	+	7.54346i	−0.576764	+	0.238904i	0.0751806	+	0.997170i	$0.476047\pi$
$998$	−4.69028	+	11.3233i	−0.148468	+	0.358434i
$999$			51.9529i			1.64372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.689.7	yes	128
17.2	even	8	inner	731.2.m.c.87.7	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.7	✓	128	17.2	even	8	inner
731.2.m.c.689.7	yes	128	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14159 + 1.14159i) q^{2} +(-2.60557 - 1.07926i) q^{3} -0.606454i q^{4} +(0.611497 - 1.47629i) q^{5} +(4.20657 - 1.74242i) q^{6} +(-0.771748 - 1.86317i) q^{7} +(-1.59086 - 1.59086i) q^{8} +(3.50287 + 3.50287i) q^{9} +O(q^{10})\)	\(q+(-1.14159 + 1.14159i) q^{2} +(-2.60557 - 1.07926i) q^{3} -0.606454i q^{4} +(0.611497 - 1.47629i) q^{5} +(4.20657 - 1.74242i) q^{6} +(-0.771748 - 1.86317i) q^{7} +(-1.59086 - 1.59086i) q^{8} +(3.50287 + 3.50287i) q^{9} +(0.987233 + 2.38339i) q^{10} +(-0.196435 + 0.0813659i) q^{11} +(-0.654523 + 1.58016i) q^{12} -3.95416i q^{13} +(3.00799 + 1.24595i) q^{14} +(-3.18660 + 3.18660i) q^{15} +4.84512 q^{16} +(3.83953 - 1.50267i) q^{17} -7.99767 q^{18} +(1.18065 - 1.18065i) q^{19} +(-0.895300 - 0.370845i) q^{20} +5.68753i q^{21} +(0.131361 - 0.317134i) q^{22} +(-3.83013 + 1.58649i) q^{23} +(2.42814 + 5.86204i) q^{24} +(1.73005 + 1.73005i) q^{25} +(4.51403 + 4.51403i) q^{26} +(-2.10866 - 5.09076i) q^{27} +(-1.12992 + 0.468030i) q^{28} +(-0.633451 + 1.52929i) q^{29} -7.27557i q^{30} +(-3.53886 - 1.46584i) q^{31} +(-2.34943 + 2.34943i) q^{32} +0.599639 q^{33} +(-2.66773 + 6.09860i) q^{34} -3.22248 q^{35} +(2.12433 - 2.12433i) q^{36} +(-8.71079 - 3.60813i) q^{37} +2.69563i q^{38} +(-4.26758 + 10.3028i) q^{39} +(-3.32136 + 1.37575i) q^{40} +(2.83976 + 6.85578i) q^{41} +(-6.49282 - 6.49282i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(0.0493447 + 0.119129i) q^{44} +(7.31322 - 3.02924i) q^{45} +(2.56131 - 6.18356i) q^{46} -9.34141i q^{47} +(-12.6243 - 5.22916i) q^{48} +(2.07396 - 2.07396i) q^{49} -3.95000 q^{50} +(-11.6259 - 0.228540i) q^{51} -2.39802 q^{52} +(-2.72753 + 2.72753i) q^{53} +(8.21879 + 3.40434i) q^{54} +0.339748i q^{55} +(-1.73629 + 4.19177i) q^{56} +(-4.35049 + 1.80203i) q^{57} +(-1.02268 - 2.46896i) q^{58} +(-2.66615 - 2.66615i) q^{59} +(1.93253 + 1.93253i) q^{60} +(-5.30405 - 12.8051i) q^{61} +(5.71331 - 2.36653i) q^{62} +(3.82309 - 9.22975i) q^{63} +4.32608i q^{64} +(-5.83747 - 2.41796i) q^{65} +(-0.684542 + 0.684542i) q^{66} -0.714752 q^{67} +(-0.911302 - 2.32850i) q^{68} +11.6919 q^{69} +(3.67876 - 3.67876i) q^{70} +(-12.4813 - 5.16992i) q^{71} -11.1451i q^{72} +(0.207677 - 0.501377i) q^{73} +(14.0631 - 5.82515i) q^{74} +(-2.64058 - 6.37493i) q^{75} +(-0.716009 - 0.716009i) q^{76} +(0.303196 + 0.303196i) q^{77} +(-6.88980 - 16.6334i) q^{78} +(-2.93176 + 1.21437i) q^{79} +(2.96278 - 7.15278i) q^{80} +0.678738i q^{81} +(-11.0683 - 4.58465i) q^{82} +(-10.8255 + 10.8255i) q^{83} +3.44922 q^{84} +(0.129488 - 6.58712i) q^{85} +1.61445 q^{86} +(3.30100 - 3.30100i) q^{87} +(0.441941 + 0.183058i) q^{88} +16.0725i q^{89} +(-4.89055 + 11.8068i) q^{90} +(-7.36725 + 3.05162i) q^{91} +(0.962134 + 2.32280i) q^{92} +(7.63871 + 7.63871i) q^{93} +(10.6641 + 10.6641i) q^{94} +(-1.02101 - 2.46494i) q^{95} +(8.65724 - 3.58595i) q^{96} +(-2.75322 + 6.64685i) q^{97} +4.73522i q^{98} +(-0.973098 - 0.403070i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Introduction

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