LMFDB - Embedded newform 806.2.k.b.729.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [806,2,Mod(157,806)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(806, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("806.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 806 = 2 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	806.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.43594240292$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 9 x^{18} - 13 x^{17} + 68 x^{16} - 21 x^{15} + 395 x^{14} - 48 x^{13} + 1897 x^{12} + \cdots + 1 $ x^20 - x^19 + 9x^18 - 13x^17 + 68x^16 - 21x^15 + 395x^14 - 48x^13 + 1897x^12 - 355x^11 + 6380x^10 - 503x^9 + 16359x^8 + 12969x^7 + 28891x^6 + 20987x^5 + 54362x^4 + 4170x^3 + 240x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.3
Root			$0.0189075 + 0.0581914i$ of defining polynomial
Character	$\chi$	$=$	806.729
Dual form			806.2.k.b.157.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.0495006 + 0.0359643i) q^{3} +(0.309017 - 0.951057i) q^{4} +2.93507 q^{5} -0.0611861 q^{6} +(0.366057 - 1.12661i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.925894 - 2.84961i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.0495006 + 0.0359643i) q^{3} +(0.309017 - 0.951057i) q^{4} +2.93507 q^{5} -0.0611861 q^{6} +(0.366057 - 1.12661i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.925894 - 2.84961i) q^{9} +(-2.37452 + 1.72519i) q^{10} +(0.491996 - 1.51421i) q^{11} +(0.0495006 - 0.0359643i) q^{12} +(-0.809017 - 0.587785i) q^{13} +(0.366057 + 1.12661i) q^{14} +(0.145288 + 0.105558i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.39665 - 4.29845i) q^{17} +(2.42402 + 1.76116i) q^{18} +(3.89650 - 2.83097i) q^{19} +(0.906987 - 2.79142i) q^{20} +(0.0586376 - 0.0426027i) q^{21} +(0.491996 + 1.51421i) q^{22} +(-0.236966 - 0.729307i) q^{23} +(-0.0189075 + 0.0581914i) q^{24} +3.61464 q^{25} +1.00000 q^{26} +(0.113374 - 0.348931i) q^{27} +(-0.958349 - 0.696281i) q^{28} +(-6.68139 + 4.85431i) q^{29} -0.179585 q^{30} +(-5.43885 - 1.19118i) q^{31} +1.00000 q^{32} +(0.0788116 - 0.0572600i) q^{33} +(3.65648 + 2.65659i) q^{34} +(1.07440 - 3.30667i) q^{35} -2.99626 q^{36} -10.2984 q^{37} +(-1.48833 + 4.58061i) q^{38} +(-0.0189075 - 0.0581914i) q^{39} +(0.906987 + 2.79142i) q^{40} +(6.77007 - 4.91875i) q^{41} +(-0.0223976 + 0.0689327i) q^{42} +(-2.64357 + 1.92067i) q^{43} +(-1.28806 - 0.935833i) q^{44} +(-2.71756 - 8.36380i) q^{45} +(0.620386 + 0.450737i) q^{46} +(7.70333 + 5.59679i) q^{47} +(-0.0189075 - 0.0581914i) q^{48} +(4.52787 + 3.28969i) q^{49} +(-2.92430 + 2.12463i) q^{50} +(0.0854556 - 0.263005i) q^{51} +(-0.809017 + 0.587785i) q^{52} +(-3.45693 - 10.6393i) q^{53} +(0.113374 + 0.348931i) q^{54} +(1.44404 - 4.44431i) q^{55} +1.18458 q^{56} +0.294693 q^{57} +(2.55206 - 7.85445i) q^{58} +(9.02117 + 6.55426i) q^{59} +(0.145288 - 0.105558i) q^{60} +11.1196 q^{61} +(5.10028 - 2.23319i) q^{62} -3.54932 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-2.37452 - 1.72519i) q^{65} +(-0.0301033 + 0.0926486i) q^{66} +7.99205 q^{67} -4.51965 q^{68} +(0.0144990 - 0.0446235i) q^{69} +(1.07440 + 3.30667i) q^{70} +(-0.235274 - 0.724098i) q^{71} +(2.42402 - 1.76116i) q^{72} +(0.0851332 - 0.262013i) q^{73} +(8.33160 - 6.05326i) q^{74} +(0.178927 + 0.129998i) q^{75} +(-1.48833 - 4.58061i) q^{76} +(-1.52582 - 1.10857i) q^{77} +(0.0495006 + 0.0359643i) q^{78} +(3.26842 + 10.0592i) q^{79} +(-2.37452 - 1.72519i) q^{80} +(-7.25391 + 5.27027i) q^{81} +(-2.58594 + 7.95870i) q^{82} +(10.7299 - 7.79576i) q^{83} +(-0.0223976 - 0.0689327i) q^{84} +(-4.09927 - 12.6162i) q^{85} +(1.00975 - 3.10770i) q^{86} -0.505315 q^{87} +1.59213 q^{88} +(1.99038 - 6.12576i) q^{89} +(7.11468 + 5.16911i) q^{90} +(-0.958349 + 0.696281i) q^{91} -0.766839 q^{92} +(-0.226386 - 0.254569i) q^{93} -9.52184 q^{94} +(11.4365 - 8.30910i) q^{95} +(0.0495006 + 0.0359643i) q^{96} +(-3.79293 + 11.6734i) q^{97} -5.59676 q^{98} -4.77044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{2} - q^{3} - 5 q^{4} - 4 q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 5 * q^2 - q^3 - 5 * q^4 - 4 * q^5 + 4 * q^6 - 5 * q^7 - 5 * q^8 - 2 * q^9	\( 20 q - 5 q^{2} - q^{3} - 5 q^{4} - 4 q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{8} - 2 q^{9} + q^{10} + 5 q^{11} - q^{12} - 5 q^{13} - 5 q^{14} - 7 q^{15} - 5 q^{16} - 13 q^{17} - 2 q^{18} + 12 q^{19} + q^{20} - 2 q^{21} + 5 q^{22} + 9 q^{23} - q^{24} - 8 q^{25} + 20 q^{26} - 7 q^{27} + 10 q^{28} - 8 q^{29} + 28 q^{30} - 38 q^{31} + 20 q^{32} - 4 q^{33} + 17 q^{34} + 28 q^{35} + 8 q^{36} - 44 q^{37} + 12 q^{38} - q^{39} + q^{40} - 2 q^{41} + 23 q^{42} + 18 q^{43} + 26 q^{45} - 6 q^{46} + 15 q^{47} - q^{48} + 6 q^{49} + 12 q^{50} + 7 q^{51} - 5 q^{52} + 2 q^{53} - 7 q^{54} + 15 q^{55} - 10 q^{56} - 46 q^{57} + 2 q^{58} - 6 q^{59} - 7 q^{60} + 22 q^{61} + 27 q^{62} - 30 q^{63} - 5 q^{64} + q^{65} + 16 q^{66} - 44 q^{67} - 8 q^{68} - 19 q^{69} + 28 q^{70} + 55 q^{71} - 2 q^{72} - q^{73} + 26 q^{74} + 19 q^{75} + 12 q^{76} - 12 q^{77} - q^{78} + 26 q^{79} + q^{80} + 35 q^{81} + 3 q^{82} - 29 q^{83} + 23 q^{84} - 10 q^{85} - 12 q^{86} - 94 q^{87} - 10 q^{88} + 26 q^{89} + 6 q^{90} + 10 q^{91} - 6 q^{92} - 7 q^{93} + 20 q^{94} + 27 q^{95} - q^{96} - 2 q^{97} - 14 q^{98} + 6 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - q^3 - 5 * q^4 - 4 * q^5 + 4 * q^6 - 5 * q^7 - 5 * q^8 - 2 * q^9 + q^10 + 5 * q^11 - q^12 - 5 * q^13 - 5 * q^14 - 7 * q^15 - 5 * q^16 - 13 * q^17 - 2 * q^18 + 12 * q^19 + q^20 - 2 * q^21 + 5 * q^22 + 9 * q^23 - q^24 - 8 * q^25 + 20 * q^26 - 7 * q^27 + 10 * q^28 - 8 * q^29 + 28 * q^30 - 38 * q^31 + 20 * q^32 - 4 * q^33 + 17 * q^34 + 28 * q^35 + 8 * q^36 - 44 * q^37 + 12 * q^38 - q^39 + q^40 - 2 * q^41 + 23 * q^42 + 18 * q^43 + 26 * q^45 - 6 * q^46 + 15 * q^47 - q^48 + 6 * q^49 + 12 * q^50 + 7 * q^51 - 5 * q^52 + 2 * q^53 - 7 * q^54 + 15 * q^55 - 10 * q^56 - 46 * q^57 + 2 * q^58 - 6 * q^59 - 7 * q^60 + 22 * q^61 + 27 * q^62 - 30 * q^63 - 5 * q^64 + q^65 + 16 * q^66 - 44 * q^67 - 8 * q^68 - 19 * q^69 + 28 * q^70 + 55 * q^71 - 2 * q^72 - q^73 + 26 * q^74 + 19 * q^75 + 12 * q^76 - 12 * q^77 - q^78 + 26 * q^79 + q^80 + 35 * q^81 + 3 * q^82 - 29 * q^83 + 23 * q^84 - 10 * q^85 - 12 * q^86 - 94 * q^87 - 10 * q^88 + 26 * q^89 + 6 * q^90 + 10 * q^91 - 6 * q^92 - 7 * q^93 + 20 * q^94 + 27 * q^95 - q^96 - 2 * q^97 - 14 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/806\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.0495006	+	0.0359643i	0.0285792	+	0.0207640i	0.601983	−	0.798509i	$-0.294377\pi$
$3$	0.0495006	+	0.0359643i	0.0285792	+	0.0207640i	−0.573404	+	0.819273i	$0.694377\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.93507			1.31260			0.656302	−	0.754499i	$-0.272120\pi$
$5$	2.93507			1.31260			0.656302	+	0.754499i	$0.272120\pi$
$6$	−0.0611861			−0.0249791
$7$	0.366057	−	1.12661i	0.138356	−	0.425817i	−0.857741	−	0.514083i	$-0.828132\pi$
$7$	0.366057	−	1.12661i	0.138356	−	0.425817i	0.996097	+	0.0882654i	$0.0281324\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.925894	−	2.84961i	−0.308631	−	0.949870i
$10$	−2.37452	+	1.72519i	−0.750890	+	0.545553i
$11$	0.491996	−	1.51421i	0.148343	−	0.456551i	−0.849083	−	0.528259i	$-0.822845\pi$
$11$	0.491996	−	1.51421i	0.148343	−	0.456551i	0.997426	+	0.0717079i	$0.0228449\pi$
$12$	0.0495006	−	0.0359643i	0.0142896	−	0.0103820i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$	0.366057	+	1.12661i	0.0978328	+	0.301098i
$15$	0.145288	+	0.105558i	0.0375131	+	0.0272549i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.39665	−	4.29845i	−0.338737	−	1.04253i	−0.964852	−	0.262795i	$-0.915356\pi$
$17$	−1.39665	−	4.29845i	−0.338737	−	1.04253i	0.626114	−	0.779731i	$-0.284644\pi$
$18$	2.42402	+	1.76116i	0.571348	+	0.415108i
$19$	3.89650	−	2.83097i	0.893918	−	0.649470i	−0.0429785	−	0.999076i	$-0.513685\pi$
$19$	3.89650	−	2.83097i	0.893918	−	0.649470i	0.936897	+	0.349606i	$0.113685\pi$
$20$	0.906987	−	2.79142i	0.202808	−	0.624180i
$21$	0.0586376	−	0.0426027i	0.0127958	−	0.00929668i
$22$	0.491996	+	1.51421i	0.104894	+	0.322831i
$23$	−0.236966	−	0.729307i	−0.0494109	−	0.152071i	0.923307	−	0.384063i	$-0.125476\pi$
$23$	−0.236966	−	0.729307i	−0.0494109	−	0.152071i	−0.972718	+	0.231992i	$0.925476\pi$
$24$	−0.0189075	+	0.0581914i	−0.00385949	+	0.0118783i
$25$	3.61464			0.722927
$26$	1.00000			0.196116
$27$	0.113374	−	0.348931i	0.0218189	−	0.0671518i
$28$	−0.958349	−	0.696281i	−0.181111	−	0.131585i
$29$	−6.68139	+	4.85431i	−1.24070	+	0.901424i	−0.997645	−	0.0685882i	$-0.978151\pi$
$29$	−6.68139	+	4.85431i	−1.24070	+	0.901424i	−0.243058	+	0.970012i	$0.578151\pi$
$30$	−0.179585			−0.0327877
$31$	−5.43885	−	1.19118i	−0.976846	−	0.213943i
$31$	−5.43885	−	1.19118i	−0.976846	−	0.213943i
$32$	1.00000			0.176777
$33$	0.0788116	−	0.0572600i	0.0137193	−	0.00996768i
$34$	3.65648	+	2.65659i	0.627081	+	0.455601i
$35$	1.07440	−	3.30667i	0.181607	−	0.558929i
$36$	−2.99626			−0.499376
$37$	−10.2984			−1.69305			−0.846525	−	0.532349i	$-0.821310\pi$
$37$	−10.2984			−1.69305			−0.846525	+	0.532349i	$0.821310\pi$
$38$	−1.48833	+	4.58061i	−0.241439	+	0.743073i
$39$	−0.0189075	−	0.0581914i	−0.00302763	−	0.00931809i
$40$	0.906987	+	2.79142i	0.143407	+	0.441362i
$41$	6.77007	−	4.91875i	1.05731	−	0.768179i	0.0837196	−	0.996489i	$-0.473320\pi$
$41$	6.77007	−	4.91875i	1.05731	−	0.768179i	0.973588	+	0.228310i	$0.0733200\pi$
$42$	−0.0223976	+	0.0689327i	−0.00345602	+	0.0106365i
$43$	−2.64357	+	1.92067i	−0.403141	+	0.292899i	−0.770819	−	0.637054i	$-0.780153\pi$
$43$	−2.64357	+	1.92067i	−0.403141	+	0.292899i	0.367678	+	0.929953i	$0.380153\pi$
$44$	−1.28806	−	0.935833i	−0.194183	−	0.141082i
$45$	−2.71756	−	8.36380i	−0.405111	−	1.24680i
$46$	0.620386	+	0.450737i	0.0914709	+	0.0664575i
$47$	7.70333	+	5.59679i	1.12365	+	0.816376i	0.984758	−	0.173932i	$-0.0556472\pi$
$47$	7.70333	+	5.59679i	1.12365	+	0.816376i	0.138888	+	0.990308i	$0.455647\pi$
$48$	−0.0189075	−	0.0581914i	−0.00272907	−	0.00839921i
$49$	4.52787	+	3.28969i	0.646839	+	0.469956i
$50$	−2.92430	+	2.12463i	−0.413559	+	0.300468i
$51$	0.0854556	−	0.263005i	0.0119662	−	0.0368281i
$52$	−0.809017	+	0.587785i	−0.112190	+	0.0815111i
$53$	−3.45693	−	10.6393i	−0.474846	−	1.46143i	−0.846166	−	0.532920i	$-0.821095\pi$
$53$	−3.45693	−	10.6393i	−0.474846	−	1.46143i	0.371320	−	0.928505i	$-0.378905\pi$
$54$	0.113374	+	0.348931i	0.0154283	+	0.0474835i
$55$	1.44404	−	4.44431i	0.194715	−	0.599271i
$56$	1.18458			0.158297
$57$	0.294693			0.0390330
$58$	2.55206	−	7.85445i	0.335102	−	1.03134i
$59$	9.02117	+	6.55426i	1.17446	+	0.853293i	0.991536	−	0.129835i	$-0.0414448\pi$
$59$	9.02117	+	6.55426i	1.17446	+	0.853293i	0.182921	+	0.983128i	$0.441445\pi$
$60$	0.145288	−	0.105558i	0.0187566	−	0.0136274i
$61$	11.1196			1.42372			0.711862	−	0.702319i	$-0.247852\pi$
$61$	11.1196			1.42372			0.711862	+	0.702319i	$0.247852\pi$
$62$	5.10028	−	2.23319i	0.647736	−	0.283615i
$63$	−3.54932			−0.447172
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−2.37452	−	1.72519i	−0.294523	−	0.213984i
$66$	−0.0301033	+	0.0926486i	−0.00370547	+	0.0114043i
$67$	7.99205			0.976384			0.488192	−	0.872736i	$-0.337657\pi$
$67$	7.99205			0.976384			0.488192	+	0.872736i	$0.337657\pi$
$68$	−4.51965			−0.548089
$69$	0.0144990	−	0.0446235i	0.00174548	−	0.00537203i
$70$	1.07440	+	3.30667i	0.128416	+	0.395223i
$71$	−0.235274	−	0.724098i	−0.0279219	−	0.0859346i	0.936124	−	0.351669i	$-0.114386\pi$
$71$	−0.235274	−	0.724098i	−0.0279219	−	0.0859346i	−0.964046	+	0.265734i	$0.914386\pi$
$72$	2.42402	−	1.76116i	0.285674	−	0.207554i
$73$	0.0851332	−	0.262013i	0.00996409	−	0.0306663i	−0.945951	−	0.324310i	$-0.894868\pi$
$73$	0.0851332	−	0.262013i	0.00996409	−	0.0306663i	0.955915	+	0.293644i	$0.0948679\pi$
$74$	8.33160	−	6.05326i	0.968529	−	0.703677i
$75$	0.178927	+	0.129998i	0.0206607	+	0.0150109i
$76$	−1.48833	−	4.58061i	−0.170723	−	0.525432i
$77$	−1.52582	−	1.10857i	−0.173883	−	0.126334i
$78$	0.0495006	+	0.0359643i	0.00560484	+	0.00407215i
$79$	3.26842	+	10.0592i	0.367726	+	1.13175i	0.948256	+	0.317506i	$0.102845\pi$
$79$	3.26842	+	10.0592i	0.367726	+	1.13175i	−0.580530	+	0.814239i	$0.697155\pi$
$80$	−2.37452	−	1.72519i	−0.265480	−	0.192882i
$81$	−7.25391	+	5.27027i	−0.805990	+	0.585586i
$82$	−2.58594	+	7.95870i	−0.285569	+	0.878891i
$83$	10.7299	−	7.79576i	1.17776	−	0.855696i	0.185847	−	0.982579i	$-0.440497\pi$
$83$	10.7299	−	7.79576i	1.17776	−	0.855696i	0.991918	+	0.126883i	$0.0404972\pi$
$84$	−0.0223976	−	0.0689327i	−0.00244378	−	0.00752117i
$85$	−4.09927	−	12.6162i	−0.444628	−	1.36842i
$86$	1.00975	−	3.10770i	0.108885	−	0.335112i
$87$	−0.505315			−0.0541754
$88$	1.59213			0.169722
$89$	1.99038	−	6.12576i	0.210980	−	0.649329i	−0.788435	−	0.615118i	$-0.789108\pi$
$89$	1.99038	−	6.12576i	0.210980	−	0.649329i	0.999415	−	0.0342109i	$-0.0108918\pi$
$90$	7.11468	+	5.16911i	0.749953	+	0.544872i
$91$	−0.958349	+	0.696281i	−0.100462	+	0.0729901i
$92$	−0.766839			−0.0799485
$93$	−0.226386	−	0.254569i	−0.0234752	−	0.0263975i
$94$	−9.52184			−0.982102
$95$	11.4365	−	8.30910i	1.17336	−	0.852496i
$96$	0.0495006	+	0.0359643i	0.00505213	+	0.00367059i
$97$	−3.79293	+	11.6734i	−0.385113	+	1.18526i	0.551285	+	0.834317i	$0.314138\pi$
$97$	−3.79293	+	11.6734i	−0.385113	+	1.18526i	−0.936398	+	0.350940i	$0.885862\pi$
$98$	−5.59676			−0.565358
$99$	−4.77044			−0.479447
$100$	1.11698	−	3.43772i	0.111698	−	0.343772i
$101$	0.304308	+	0.936565i	0.0302798	+	0.0931917i	0.965054	−	0.262050i	$-0.0843986\pi$
$101$	0.304308	+	0.936565i	0.0302798	+	0.0931917i	−0.934774	+	0.355242i	$0.884399\pi$
$102$	0.0854556	+	0.263005i	0.00846136	+	0.0260414i
$103$	10.6219	−	7.71728i	1.04661	−	0.760406i	0.0750442	−	0.997180i	$-0.476090\pi$
$103$	10.6219	−	7.71728i	1.04661	−	0.760406i	0.971565	+	0.236774i	$0.0760902\pi$
$104$	0.309017	−	0.951057i	0.0303016	−	0.0932588i
$105$	0.172106	−	0.125042i	0.0167958	−	0.0122029i
$106$	9.05036	+	6.57547i	0.879049	+	0.638666i
$107$	−0.140720	−	0.433093i	−0.0136040	−	0.0418687i	0.944024	−	0.329876i	$-0.107007\pi$
$107$	−0.140720	−	0.433093i	−0.0136040	−	0.0418687i	−0.957628	+	0.288008i	$0.907007\pi$
$108$	−0.296818	−	0.215651i	−0.0285613	−	0.0207510i
$109$	−1.96488	−	1.42757i	−0.188201	−	0.136736i	0.489695	−	0.871894i	$-0.337108\pi$
$109$	−1.96488	−	1.42757i	−0.188201	−	0.136736i	−0.677896	+	0.735158i	$0.737108\pi$
$110$	1.44404	+	4.44431i	0.137684	+	0.423748i
$111$	−0.509778	−	0.370375i	−0.0483860	−	0.0351545i
$112$	−0.958349	+	0.696281i	−0.0905555	+	0.0657924i
$113$	−1.51855	+	4.67363i	−0.142854	+	0.439658i	−0.996729	−	0.0808199i	$-0.974246\pi$
$113$	−1.51855	+	4.67363i	−0.142854	+	0.439658i	0.853875	+	0.520478i	$0.174246\pi$
$114$	−0.238412	+	0.173216i	−0.0223293	+	0.0162232i
$115$	−0.695513	−	2.14057i	−0.0648569	−	0.199609i
$116$	2.55206	+	7.85445i	0.236953	+	0.729267i
$117$	−0.925894	+	2.84961i	−0.0855989	+	0.263446i
$118$	−11.1508			−1.02651
$119$	−5.35391			−0.490792
$120$	−0.0554950	+	0.170796i	−0.00506597	+	0.0155915i
$121$	6.84842	+	4.97567i	0.622583	+	0.452333i
$122$	−8.99598	+	6.53596i	−0.814458	+	0.591738i
$123$	0.512022			0.0461675
$124$	−2.81358	+	4.80456i	−0.252667	+	0.431462i
$125$	−4.06614			−0.363686
$126$	2.87146	−	2.08624i	0.255810	−	0.185857i
$127$	6.12095	+	4.44713i	0.543146	+	0.394619i	0.825252	−	0.564764i	$-0.191033\pi$
$127$	6.12095	+	4.44713i	0.543146	+	0.394619i	−0.282106	+	0.959383i	$0.591033\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−0.199934			−0.0176032
$130$	2.93507			0.257423
$131$	−1.61105	+	4.95831i	−0.140758	+	0.433209i	−0.996441	−	0.0842911i	$-0.973137\pi$
$131$	−1.61105	+	4.95831i	−0.140758	+	0.433209i	0.855683	+	0.517500i	$0.173137\pi$
$132$	−0.0301033	−	0.0926486i	−0.00262016	−	0.00806402i
$133$	−1.76305	−	5.42612i	−0.152876	−	0.470504i
$134$	−6.46570	+	4.69761i	−0.558552	+	0.405812i
$135$	0.332762	−	1.02414i	0.0286396	−	0.0881436i
$136$	3.65648	−	2.65659i	0.313540	−	0.227800i
$137$	−3.99168	−	2.90013i	−0.341032	−	0.247774i	0.404065	−	0.914730i	$-0.367597\pi$
$137$	−3.99168	−	2.90013i	−0.341032	−	0.247774i	−0.745097	+	0.666956i	$0.767597\pi$
$138$	0.0144990	+	0.0446235i	0.00123424	+	0.00379860i
$139$	12.8934	+	9.36758i	1.09360	+	0.794548i	0.980004	−	0.198979i	$-0.0637627\pi$
$139$	12.8934	+	9.36758i	1.09360	+	0.794548i	0.113597	+	0.993527i	$0.463763\pi$
$140$	−2.81282	−	2.04364i	−0.237727	−	0.172719i
$141$	0.180035	+	0.554089i	0.0151616	+	0.0466627i
$142$	0.615955	+	0.447517i	0.0516898	+	0.0375548i
$143$	−1.28806	+	0.935833i	−0.107713	+	0.0782583i
$144$	−0.925894	+	2.84961i	−0.0771578	+	0.237467i
$145$	−19.6104	+	14.2478i	−1.62855	+	1.18321i
$146$	0.0851332	+	0.262013i	0.00704568	+	0.0216844i
$147$	0.105821	+	0.325683i	0.00872797	+	0.0268619i
$148$	−3.18239	+	9.79438i	−0.261591	+	0.805093i
$149$	−5.84454			−0.478804			−0.239402	−	0.970921i	$-0.576951\pi$
$149$	−5.84454			−0.478804			−0.239402	+	0.970921i	$0.576951\pi$
$150$	−0.221166			−0.0180581
$151$	−0.939371	+	2.89109i	−0.0764449	+	0.235273i	−0.981976	−	0.189007i	$-0.939473\pi$
$151$	−0.939371	+	2.89109i	−0.0764449	+	0.235273i	0.905531	+	0.424281i	$0.139473\pi$
$152$	3.89650	+	2.83097i	0.316048	+	0.229622i
$153$	−10.9557	+	7.95981i	−0.885719	+	0.643513i
$154$	1.88602			0.151980
$155$	−15.9634	−	3.49621i	−1.28221	−	0.280822i
$156$	−0.0611861			−0.00489881
$157$	8.29876	−	6.02941i	0.662314	−	0.481199i	−0.205130	−	0.978735i	$-0.565762\pi$
$157$	8.29876	−	6.02941i	0.662314	−	0.481199i	0.867443	+	0.497536i	$0.165762\pi$
$158$	−8.55684	−	6.21691i	−0.680746	−	0.494591i
$159$	0.211516	−	0.650979i	0.0167743	−	0.0516260i
$160$	2.93507			0.232038
$161$	−0.908386			−0.0715908
$162$	2.77075	−	8.52748i	0.217690	−	0.669982i
$163$	5.58602	+	17.1920i	0.437531	+	1.34658i	0.890471	+	0.455041i	$0.150375\pi$
$163$	5.58602	+	17.1920i	0.437531	+	1.34658i	−0.452939	+	0.891541i	$0.649625\pi$
$164$	−2.58594	−	7.95870i	−0.201928	−	0.621470i
$165$	0.231318	−	0.168062i	0.0180080	−	0.0130836i
$166$	−4.09847	+	12.6138i	−0.318103	+	0.979021i
$167$	−17.7289	+	12.8808i	−1.37191	+	0.996748i	−0.374320	+	0.927300i	$0.622124\pi$
$167$	−17.7289	+	12.8808i	−1.37191	+	0.996748i	−0.997586	+	0.0694479i	$0.977876\pi$
$168$	0.0586376	+	0.0426027i	0.00452399	+	0.00328687i
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$	10.7320	+	7.79727i	0.823108	+	0.598023i
$171$	−11.6749	−	8.48232i	−0.892803	−	0.648659i
$172$	1.00975	+	3.10770i	0.0769930	+	0.236960i
$173$	−19.4323	−	14.1184i	−1.47741	−	1.07340i	−0.978381	−	0.206812i	$-0.933691\pi$
$173$	−19.4323	−	14.1184i	−1.47741	−	1.07340i	−0.499026	−	0.866587i	$-0.666309\pi$
$174$	0.408808	−	0.297017i	0.0309917	−	0.0225168i
$175$	1.32316	−	4.07228i	0.100022	−	0.307835i
$176$	−1.28806	+	0.935833i	−0.0970914	+	0.0705411i
$177$	0.210834	+	0.648880i	0.0158472	+	0.0487728i
$178$	1.99038	+	6.12576i	0.149185	+	0.459145i
$179$	6.53200	−	20.1034i	0.488225	−	1.50260i	−0.339031	−	0.940775i	$-0.610099\pi$
$179$	6.53200	−	20.1034i	0.488225	−	1.50260i	0.827256	−	0.561825i	$-0.189901\pi$
$180$	−8.79422			−0.655483
$181$	16.8411			1.25179			0.625895	−	0.779907i	$-0.284734\pi$
$181$	16.8411			1.25179			0.625895	+	0.779907i	$0.284734\pi$
$182$	0.366057	−	1.12661i	0.0271339	−	0.0835097i
$183$	0.550429	+	0.399910i	0.0406889	+	0.0295622i
$184$	0.620386	−	0.450737i	0.0457354	−	0.0332287i
$185$	−30.2266			−2.22230
$186$	0.332782	+	0.0728839i	0.0244008	+	0.00534411i
$187$	−7.19590			−0.526216
$188$	7.70333	−	5.59679i	0.561823	−	0.408188i
$189$	−0.351606	−	0.255457i	−0.0255756	−	0.0185818i
$190$	−4.36835	+	13.4444i	−0.316914	+	0.975360i
$191$	−4.31402			−0.312152			−0.156076	−	0.987745i	$-0.549884\pi$
$191$	−4.31402			−0.312152			−0.156076	+	0.987745i	$0.549884\pi$
$192$	−0.0611861			−0.00441573
$193$	−2.09956	+	6.46178i	−0.151130	+	0.465129i	−0.997748	−	0.0670710i	$-0.978635\pi$
$193$	−2.09956	+	6.46178i	−0.151130	+	0.465129i	0.846619	+	0.532200i	$0.178635\pi$
$194$	−3.79293	−	11.6734i	−0.272316	−	0.838103i
$195$	−0.0554950	−	0.170796i	−0.00397408	−	0.0122310i
$196$	4.52787	−	3.28969i	0.323419	−	0.234978i
$197$	−1.16939	+	3.59902i	−0.0833158	+	0.256420i	−0.984033	−	0.177986i	$-0.943042\pi$
$197$	−1.16939	+	3.59902i	−0.0833158	+	0.256420i	0.900717	+	0.434406i	$0.143042\pi$
$198$	3.85937	−	2.80400i	0.274273	−	0.199271i
$199$	21.3386	+	15.5034i	1.51266	+	1.09901i	0.964981	+	0.262318i	$0.0844870\pi$
$199$	21.3386	+	15.5034i	1.51266	+	1.09901i	0.547675	+	0.836691i	$0.315513\pi$
$200$	1.11698	+	3.43772i	0.0789827	+	0.243084i
$201$	0.395611	+	0.287428i	0.0279043	+	0.0202736i
$202$	−0.796689	−	0.578829i	−0.0560549	−	0.0407263i
$203$	3.02314	+	9.30426i	0.212183	+	0.653031i
$204$	−0.223726	−	0.162546i	−0.0156639	−	0.0113805i
$205$	19.8706	−	14.4369i	1.38783	−	1.00831i
$206$	−4.05721	+	12.4868i	−0.282679	+	0.869998i
$207$	−1.85883	+	1.35052i	−0.129198	+	0.0938678i
$208$	0.309017	+	0.951057i	0.0214265	+	0.0659439i
$209$	−2.36962	−	7.29294i	−0.163910	−	0.504464i
$210$	−0.0657385	+	0.202322i	−0.00453639	+	0.0139616i
$211$	−24.3135			−1.67381			−0.836905	−	0.547348i	$-0.815637\pi$
$211$	−24.3135			−1.67381			−0.836905	+	0.547348i	$0.815637\pi$
$212$	−11.1869			−0.768317
$213$	0.0143955	−	0.0443047i	0.000986362	−	0.00303571i
$214$	0.368411	+	0.267666i	0.0251841	+	0.0182973i
$215$	−7.75906	+	5.63729i	−0.529164	+	0.384460i
$216$	0.366888			0.0249635
$217$	−3.33292	+	5.69141i	−0.226254	+	0.386358i
$218$	2.42872			0.164494
$219$	0.0136373	−	0.00990805i	0.000921521	−	0.000669524i
$220$	−3.78056	−	2.74674i	−0.254885	−	0.185185i
$221$	−1.39665	+	4.29845i	−0.0939488	+	0.289145i
$222$	0.630120			0.0422909
$223$	−11.2819			−0.755492			−0.377746	−	0.925909i	$-0.623301\pi$
$223$	−11.2819			−0.755492			−0.377746	+	0.925909i	$0.623301\pi$
$224$	0.366057	−	1.12661i	0.0244582	−	0.0752746i
$225$	−3.34677	−	10.3003i	−0.223118	−	0.686687i
$226$	−1.51855	−	4.67363i	−0.101013	−	0.310885i
$227$	−15.2158	+	11.0549i	−1.00991	+	0.733740i	−0.964190	−	0.265214i	$-0.914557\pi$
$227$	−15.2158	+	11.0549i	−1.00991	+	0.733740i	−0.0457174	+	0.998954i	$0.514557\pi$
$228$	0.0910651	−	0.280270i	0.00603093	−	0.0185613i
$229$	7.11464	−	5.16909i	0.470149	−	0.341583i	−0.327351	−	0.944903i	$-0.606156\pi$
$229$	7.11464	−	5.16909i	0.470149	−	0.341583i	0.797499	+	0.603320i	$0.206156\pi$
$230$	1.82088	+	1.32294i	0.120065	+	0.0872323i
$231$	−0.0356600	−	0.109750i	−0.00234625	−	0.00722103i
$232$	−6.68139	−	4.85431i	−0.438655	−	0.318701i
$233$	11.0498	+	8.02817i	0.723898	+	0.525943i	0.887627	−	0.460562i	$-0.152352\pi$
$233$	11.0498	+	8.02817i	0.723898	+	0.525943i	−0.163729	+	0.986505i	$0.552352\pi$
$234$	−0.925894	−	2.84961i	−0.0605276	−	0.186285i
$235$	22.6098	+	16.4270i	1.47490	+	1.07158i
$236$	9.02117	−	6.55426i	0.587228	−	0.426646i
$237$	−0.199982	+	0.615481i	−0.0129902	+	0.0399798i
$238$	4.33141	−	3.14695i	0.280763	−	0.203987i
$239$	−6.94578	−	21.3769i	−0.449285	−	1.38276i	−0.877715	−	0.479182i	$-0.840933\pi$
$239$	−6.94578	−	21.3769i	−0.449285	−	1.38276i	0.428430	−	0.903575i	$-0.359067\pi$
$240$	−0.0554950	−	0.170796i	−0.00358218	−	0.0110248i
$241$	3.55476	−	10.9404i	0.228982	−	0.704735i	−0.768881	−	0.639392i	$-0.779186\pi$
$241$	3.55476	−	10.9404i	0.228982	−	0.704735i	0.997863	−	0.0653427i	$-0.0208141\pi$
$242$	−8.46511			−0.544158
$243$	−1.64928			−0.105801
$244$	3.43616	−	10.5754i	0.219978	−	0.677021i
$245$	13.2896	+	9.65548i	0.849043	+	0.616866i
$246$	−0.414234	+	0.300959i	−0.0264106	+	0.0191884i
$247$	−4.81634			−0.306456
$248$	−0.547814	−	5.54075i	−0.0347862	−	0.351838i
$249$	0.811508			0.0514272
$250$	3.28957	−	2.39002i	0.208051	−	0.151158i
$251$	8.15569	+	5.92546i	0.514783	+	0.374012i	0.814635	−	0.579974i	$-0.196937\pi$
$251$	8.15569	+	5.92546i	0.514783	+	0.374012i	−0.299852	+	0.953986i	$0.596937\pi$
$252$	−1.09680	+	3.37560i	−0.0690919	+	0.212643i
$253$	−1.22091			−0.0767580
$254$	−7.56591			−0.474727
$255$	0.250818	−	0.771939i	0.0157068	−	0.0483407i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	6.28021	+	19.3285i	0.391749	+	1.20568i	0.931465	+	0.363832i	$0.118532\pi$
$257$	6.28021	+	19.3285i	0.391749	+	1.20568i	−0.539716	+	0.841847i	$0.681468\pi$
$258$	0.161750	−	0.117518i	0.0100701	−	0.00731635i
$259$	−3.76981	+	11.6023i	−0.234244	+	0.720930i
$260$	−2.37452	+	1.72519i	−0.147262	+	0.106992i
$261$	20.0192	+	14.5448i	1.23915	+	0.900299i
$262$	−1.61105	−	4.95831i	−0.0995311	−	0.306325i
$263$	4.38617	+	3.18674i	0.270463	+	0.196503i	0.714747	−	0.699383i	$-0.246542\pi$
$263$	4.38617	+	3.18674i	0.270463	+	0.196503i	−0.444284	+	0.895886i	$0.646542\pi$
$264$	0.0788116	+	0.0572600i	0.00485052	+	0.00352411i
$265$	−10.1463	−	31.2272i	−0.623284	−	1.91827i
$266$	4.61573	+	3.35353i	0.283009	+	0.205618i
$267$	0.318834	−	0.231646i	0.0195123	−	0.0141765i
$268$	2.46968	−	7.60089i	0.150860	−	0.464298i
$269$	−16.6291	+	12.0818i	−1.01389	+	0.736638i	−0.965022	−	0.262167i	$-0.915563\pi$
$269$	−16.6291	+	12.0818i	−1.01389	+	0.736638i	−0.0488723	+	0.998805i	$0.515563\pi$
$270$	0.332762	+	1.02414i	0.0202513	+	0.0623269i
$271$	−0.162380	−	0.499754i	−0.00986388	−	0.0303579i	0.946003	−	0.324157i	$-0.105080\pi$
$271$	−0.162380	−	0.499754i	−0.00986388	−	0.0303579i	−0.955867	+	0.293799i	$0.905080\pi$
$272$	−1.39665	+	4.29845i	−0.0846843	+	0.260632i
$273$	−0.0724801			−0.00438670
$274$	4.93399			0.298073
$275$	1.77839	−	5.47332i	0.107241	−	0.330053i
$276$	−0.0379590	−	0.0275788i	−0.00228486	−	0.00166005i
$277$	−24.8361	+	18.0445i	−1.49226	+	1.08419i	−0.518918	+	0.854824i	$0.673665\pi$
$277$	−24.8361	+	18.0445i	−1.49226	+	1.08419i	−0.973341	+	0.229365i	$0.926335\pi$
$278$	−15.9371			−0.955842
$279$	1.64139	+	16.6015i	0.0982675	+	0.993906i
$280$	3.47684			0.207781
$281$	−16.0104	+	11.6323i	−0.955103	+	0.693923i	−0.952008	−	0.306072i	$-0.900985\pi$
$281$	−16.0104	+	11.6323i	−0.955103	+	0.693923i	−0.00309475	+	0.999995i	$0.500985\pi$
$282$	−0.471337	−	0.342446i	−0.0280677	−	0.0203924i
$283$	6.55457	−	20.1729i	0.389629	−	1.19915i	−0.543437	−	0.839450i	$-0.682877\pi$
$283$	6.55457	−	20.1729i	0.389629	−	1.19915i	0.933066	−	0.359705i	$-0.117123\pi$
$284$	−0.761362			−0.0451785
$285$	0.864944			0.0512349
$286$	0.491996	−	1.51421i	0.0290924	−	0.0895371i
$287$	−3.06326	−	9.42776i	−0.180819	−	0.556503i
$288$	−0.925894	−	2.84961i	−0.0545588	−	0.167915i
$289$	−2.77272	+	2.01450i	−0.163101	+	0.118500i
$290$	7.49049	−	23.0533i	0.439857	−	1.35374i
$291$	−0.607579	+	0.441432i	−0.0356169	+	0.0258772i
$292$	−0.222882	−	0.161933i	−0.0130432	−	0.00947641i
$293$	−6.42359	−	19.7698i	−0.375270	−	1.15496i	−0.943296	−	0.331952i	$-0.892293\pi$
$293$	−6.42359	−	19.7698i	−0.375270	−	1.15496i	0.568027	−	0.823010i	$-0.307707\pi$
$294$	−0.277043	−	0.201283i	−0.0161575	−	0.0117391i
$295$	26.4778	+	19.2372i	1.54160	+	1.12003i
$296$	−3.18239	−	9.79438i	−0.184973	−	0.569287i
$297$	−0.472574	−	0.343345i	−0.0274215	−	0.0199229i
$298$	4.72833	−	3.43534i	0.273905	−	0.199004i
$299$	−0.236966	+	0.729307i	−0.0137041	+	0.0421769i
$300$	0.178927	−	0.129998i	0.0103303	−	0.00750543i
$301$	1.19614	+	3.68134i	0.0689443	+	0.212189i
$302$	−0.939371	−	2.89109i	−0.0540547	−	0.166363i
$303$	−0.0186194	+	0.0573047i	−0.00106966	+	0.00329207i
$304$	−4.81634			−0.276236
$305$	32.6369			1.86879
$306$	4.18472	−	12.8792i	0.239225	−	0.736258i
$307$	−5.71360	−	4.15117i	−0.326092	−	0.236920i	0.412678	−	0.910877i	$-0.364593\pi$
$307$	−5.71360	−	4.15117i	−0.326092	−	0.236920i	−0.738771	+	0.673957i	$0.764593\pi$
$308$	−1.52582	+	1.10857i	−0.0869417	+	0.0631668i
$309$	0.803338			0.0457003
$310$	14.9697	−	6.55456i	0.850221	−	0.372274i
$311$	33.4321			1.89576			0.947881	−	0.318624i	$-0.103221\pi$
$311$	33.4321			1.89576			0.947881	+	0.318624i	$0.103221\pi$
$312$	0.0495006	−	0.0359643i	0.00280242	−	0.00203608i
$313$	4.86775	+	3.53662i	0.275141	+	0.199902i	0.716795	−	0.697284i	$-0.245608\pi$
$313$	4.86775	+	3.53662i	0.275141	+	0.199902i	−0.441654	+	0.897185i	$0.645608\pi$
$314$	−3.16985	+	9.75578i	−0.178885	+	0.550551i
$315$	−10.4175			−0.586960
$316$	10.5768			0.594994
$317$	−4.11415	+	12.6621i	−0.231074	+	0.711173i	0.766544	+	0.642192i	$0.221975\pi$
$317$	−4.11415	+	12.6621i	−0.231074	+	0.711173i	−0.997618	+	0.0689808i	$0.978025\pi$
$318$	0.211516	+	0.650979i	0.0118612	+	0.0365051i
$319$	4.06323	+	12.5053i	0.227497	+	0.700164i
$320$	−2.37452	+	1.72519i	−0.132740	+	0.0964411i
$321$	0.00861014	−	0.0264993i	0.000480571	−	0.00147905i
$322$	0.734900	−	0.533936i	0.0409544	−	0.0297551i
$323$	−17.6108	−	12.7950i	−0.979893	−	0.711934i
$324$	2.77075	+	8.52748i	0.153930	+	0.473749i
$325$	−2.92430	−	2.12463i	−0.162211	−	0.117853i
$326$	−14.6244	−	10.6252i	−0.809970	−	0.588478i
$327$	−0.0459212	−	0.141331i	−0.00253945	−	0.00781561i
$328$	6.77007	+	4.91875i	0.373815	+	0.271592i
$329$	9.12524	−	6.62988i	0.503091	−	0.365517i
$330$	−0.0883554	+	0.271930i	−0.00486381	+	0.0149693i
$331$	4.35120	−	3.16133i	0.239163	−	0.173762i	−0.461747	−	0.887012i	$-0.652777\pi$
$331$	4.35120	−	3.16133i	0.239163	−	0.173762i	0.700910	+	0.713249i	$0.252777\pi$
$332$	−4.09847	−	12.6138i	−0.224933	−	0.692273i
$333$	9.53525	+	29.3465i	0.522528	+	1.60818i
$334$	6.77185	−	20.8416i	0.370539	−	1.14040i
$335$	23.4572			1.28161
$336$	−0.0724801			−0.00395411
$337$	1.75113	−	5.38942i	0.0953901	−	0.293581i	−0.891965	−	0.452104i	$-0.850673\pi$
$337$	1.75113	−	5.38942i	0.0953901	−	0.293581i	0.987355	+	0.158524i	$0.0506735\pi$
$338$	−0.809017	−	0.587785i	−0.0440047	−	0.0319713i
$339$	−0.243253	+	0.176734i	−0.0132117	+	0.00959885i
$340$	−13.2655			−0.719423
$341$	−4.47960	+	7.64950i	−0.242584	+	0.414244i
$342$	14.4310			0.780338
$343$	12.0721	−	8.77089i	0.651832	−	0.473584i
$344$	−2.64357	−	1.92067i	−0.142532	−	0.103555i
$345$	0.0425557	−	0.130973i	0.00229112	−	0.00705135i
$346$	24.0196			1.29130
$347$	13.1977			0.708487			0.354244	−	0.935153i	$-0.384738\pi$
$347$	13.1977			0.708487			0.354244	+	0.935153i	$0.384738\pi$
$348$	−0.156151	+	0.480583i	−0.00837056	+	0.0257619i
$349$	4.17661	+	12.8543i	0.223569	+	0.688075i	0.998434	+	0.0559476i	$0.0178180\pi$
$349$	4.17661	+	12.8543i	0.223569	+	0.688075i	−0.774865	+	0.632127i	$0.782182\pi$
$350$	1.32316	+	4.07228i	0.0707260	+	0.217672i
$351$	−0.296818	+	0.215651i	−0.0158430	+	0.0115106i
$352$	0.491996	−	1.51421i	0.0262235	−	0.0807076i
$353$	16.8258	−	12.2247i	0.895548	−	0.650654i	−0.0417705	−	0.999127i	$-0.513300\pi$
$353$	16.8258	−	12.2247i	0.895548	−	0.650654i	0.937319	+	0.348473i	$0.113300\pi$
$354$	−0.551970	−	0.401030i	−0.0293369	−	0.0213145i
$355$	−0.690545	−	2.12528i	−0.0366503	−	0.112798i
$356$	−5.21088	−	3.78593i	−0.276176	−	0.200654i
$357$	−0.265022	−	0.192550i	−0.0140264	−	0.0101908i
$358$	6.53200	+	20.1034i	0.345227	+	1.06250i
$359$	−15.5693	−	11.3118i	−0.821716	−	0.597012i	0.0954876	−	0.995431i	$-0.469559\pi$
$359$	−15.5693	−	11.3118i	−0.821716	−	0.597012i	−0.917203	+	0.398419i	$0.869559\pi$
$360$	7.11468	−	5.16911i	0.374976	−	0.272436i
$361$	1.29698	−	3.99169i	0.0682620	−	0.210089i
$362$	−13.6248	+	9.89896i	−0.716101	+	0.520278i
$363$	0.160054	+	0.492597i	0.00840068	+	0.0258546i
$364$	0.366057	+	1.12661i	0.0191866	+	0.0590503i
$365$	0.249872	−	0.769027i	0.0130789	−	0.0402527i
$366$	−0.680368			−0.0355634
$367$	−22.0647			−1.15177			−0.575885	−	0.817531i	$-0.695342\pi$
$367$	−22.0647			−1.15177			−0.575885	+	0.817531i	$0.695342\pi$
$368$	−0.236966	+	0.729307i	−0.0123527	+	0.0380178i
$369$	−20.2849	−	14.7378i	−1.05599	−	0.767221i
$370$	24.4538	−	17.7667i	1.27129	−	0.923649i
$371$	−13.2518			−0.687998
$372$	−0.312066	+	0.136640i	−0.0161799	+	0.00708446i
$373$	−27.4587			−1.42176			−0.710880	−	0.703314i	$-0.751703\pi$
$373$	−27.4587			−1.42176			−0.710880	+	0.703314i	$0.751703\pi$
$374$	5.82160	−	4.22964i	0.301028	−	0.218710i
$375$	−0.201276	−	0.146236i	−0.0103939	−	0.00755158i
$376$	−2.94241	+	9.05580i	−0.151743	+	0.467017i
$377$	8.25865			0.425342
$378$	0.434609			0.0223539
$379$	−10.9135	+	33.5884i	−0.560591	+	1.72532i	0.120111	+	0.992760i	$0.461675\pi$
$379$	−10.9135	+	33.5884i	−0.560591	+	1.72532i	−0.680702	+	0.732561i	$0.738325\pi$
$380$	−4.36835	−	13.4444i	−0.224092	−	0.689684i
$381$	0.143053	+	0.440271i	0.00732881	+	0.0225558i
$382$	3.49012	−	2.53572i	0.178570	−	0.129739i
$383$	4.01032	−	12.3425i	0.204918	−	0.630672i	−0.794799	−	0.606873i	$-0.792424\pi$
$383$	4.01032	−	12.3425i	0.204918	−	0.630672i	0.999717	−	0.0237992i	$-0.00757623\pi$
$384$	0.0495006	−	0.0359643i	0.00252607	−	0.00183529i
$385$	−4.47839	−	3.25374i	−0.228240	−	0.165826i
$386$	−2.09956	−	6.46178i	−0.106865	−	0.328896i
$387$	7.92081	+	5.75481i	0.402637	+	0.292533i
$388$	9.93001	+	7.21458i	0.504120	+	0.366265i
$389$	−7.63953	−	23.5121i	−0.387340	−	1.19211i	−0.934769	−	0.355257i	$-0.884393\pi$
$389$	−7.63953	−	23.5121i	−0.387340	−	1.19211i	0.547429	−	0.836852i	$-0.315607\pi$
$390$	0.145288	+	0.105558i	0.00735693	+	0.00534512i
$391$	−2.80393	+	2.03717i	−0.141801	+	0.103024i
$392$	−1.72949	+	5.32283i	−0.0873526	+	0.268844i
$393$	−0.258070	+	0.187499i	−0.0130179	+	0.00945806i
$394$	−1.16939	−	3.59902i	−0.0589132	−	0.181316i
$395$	9.59305	+	29.5244i	0.482679	+	1.48553i
$396$	−1.47415	+	4.53696i	−0.0740787	+	0.227991i
$397$	−6.27839			−0.315103			−0.157552	−	0.987511i	$-0.550360\pi$
$397$	−6.27839			−0.315103			−0.157552	+	0.987511i	$0.550360\pi$
$398$	−26.3760			−1.32211
$399$	0.107874	−	0.332003i	0.00540047	−	0.0166209i
$400$	−2.92430	−	2.12463i	−0.146215	−	0.106232i
$401$	12.9544	−	9.41193i	0.646912	−	0.470009i	−0.215306	−	0.976547i	$-0.569075\pi$
$401$	12.9544	−	9.41193i	0.646912	−	0.470009i	0.862218	+	0.506537i	$0.169075\pi$
$402$	−0.489002			−0.0243892
$403$	3.69996	+	4.16056i	0.184308	+	0.207252i
$404$	0.984762			0.0489938
$405$	−21.2907	+	15.4686i	−1.05794	+	0.768642i
$406$	−7.91467	−	5.75035i	−0.392799	−	0.285385i
$407$	−5.06679	+	15.5940i	−0.251151	+	0.772964i
$408$	0.276540			0.0136908
$409$	12.4927			0.617725			0.308862	−	0.951107i	$-0.400052\pi$
$409$	12.4927			0.617725			0.308862	+	0.951107i	$0.400052\pi$
$410$	−7.58991	+	23.3593i	−0.374839	+	1.15364i
$411$	−0.0932896	−	0.287116i	−0.00460164	−	0.0141624i
$412$	−4.05721	−	12.4868i	−0.199885	−	0.615181i
$413$	10.6863	−	7.76408i	0.525841	−	0.382046i
$414$	0.710012	−	2.18519i	0.0348952	−	0.107396i
$415$	31.4931	−	22.8811i	1.54594	−	1.12319i
$416$	−0.809017	−	0.587785i	−0.0396653	−	0.0288185i
$417$	0.301331	+	0.927401i	0.0147562	+	0.0454150i
$418$	6.20375	+	4.50729i	0.303435	+	0.220459i
$419$	29.1556	+	21.1828i	1.42434	+	1.03485i	0.991035	+	0.133600i	$0.0426537\pi$
$419$	29.1556	+	21.1828i	1.42434	+	1.03485i	0.433308	+	0.901246i	$0.357346\pi$
$420$	−0.0657385	−	0.202322i	−0.00320771	−	0.00987232i
$421$	19.9763	+	14.5136i	0.973586	+	0.707352i	0.956266	−	0.292498i	$-0.0944865\pi$
$421$	19.9763	+	14.5136i	0.973586	+	0.707352i	0.0173203	+	0.999850i	$0.494487\pi$
$422$	19.6700	−	14.2911i	0.957522	−	0.695681i
$423$	8.81621	−	27.1335i	0.428659	−	1.31928i
$424$	9.05036	−	6.57547i	0.439524	−	0.319333i
$425$	−5.04838	−	15.5373i	−0.244883	−	0.753671i
$426$	0.0143955	+	0.0443047i	0.000697463	+	0.00214657i
$427$	4.07042	−	12.5275i	0.196982	−	0.606247i
$428$	−0.455381			−0.0220117
$429$	−0.0974165			−0.00470331
$430$	2.96370	−	9.12132i	0.142922	−	0.439869i
$431$	−10.9014	−	7.92035i	−0.525103	−	0.381510i	0.293420	−	0.955984i	$-0.405207\pi$
$431$	−10.9014	−	7.92035i	−0.525103	−	0.381510i	−0.818523	+	0.574474i	$0.805207\pi$
$432$	−0.296818	+	0.215651i	−0.0142807	+	0.0103755i
$433$	14.1335			0.679214			0.339607	−	0.940567i	$-0.389706\pi$
$433$	14.1335			0.679214			0.339607	+	0.940567i	$0.389706\pi$
$434$	−0.648932	−	6.56349i	−0.0311497	−	0.315057i
$435$	−1.48313			−0.0711108
$436$	−1.96488	+	1.42757i	−0.0941006	+	0.0683681i
$437$	−2.98799	−	2.17090i	−0.142935	−	0.103848i
$438$	−0.00520897	+	0.0160316i	−0.000248894	+	0.000766018i
$439$	15.0724			0.719367			0.359683	−	0.933074i	$-0.382885\pi$
$439$	15.0724			0.719367			0.359683	+	0.933074i	$0.382885\pi$
$440$	4.67303			0.222778
$441$	5.18201	−	15.9486i	0.246762	−	0.759456i
$442$	−1.39665	−	4.29845i	−0.0664319	−	0.204456i
$443$	−4.70035	−	14.4662i	−0.223320	−	0.687309i	−0.998458	−	0.0555165i	$-0.982319\pi$
$443$	−4.70035	−	14.4662i	−0.223320	−	0.687309i	0.775138	−	0.631793i	$-0.217681\pi$
$444$	−0.509778	+	0.370375i	−0.0241930	+	0.0175772i
$445$	5.84191	−	17.9795i	0.276933	−	0.852312i
$446$	9.12725	−	6.63134i	0.432188	−	0.314003i
$447$	−0.289308	−	0.210195i	−0.0136838	−	0.00994187i
$448$	0.366057	+	1.12661i	0.0172946	+	0.0532272i
$449$	−9.32352	−	6.77393i	−0.440004	−	0.319682i	0.345633	−	0.938370i	$-0.387664\pi$
$449$	−9.32352	−	6.77393i	−0.440004	−	0.319682i	−0.785636	+	0.618688i	$0.787664\pi$
$450$	8.76196	+	6.36594i	0.413043	+	0.300093i
$451$	−4.11716	−	12.6713i	−0.193870	−	0.596669i
$452$	3.97563	+	2.88846i	0.186998	+	0.135862i
$453$	−0.150475	+	0.109327i	−0.00706995	+	0.00513662i
$454$	5.81191	−	17.8872i	0.272767	−	0.839489i
$455$	−2.81282	+	2.04364i	−0.131867	+	0.0958071i
$456$	0.0910651	+	0.280270i	0.00426451	+	0.0131248i
$457$	−5.87914	−	18.0941i	−0.275015	−	0.846408i	−0.989216	−	0.146467i	$-0.953210\pi$
$457$	−5.87914	−	18.0941i	−0.275015	−	0.846408i	0.714201	−	0.699941i	$-0.246790\pi$
$458$	−2.71755	+	8.36376i	−0.126983	+	0.390813i
$459$	−1.65820			−0.0773984
$460$	−2.25073			−0.104941
$461$	12.0999	−	37.2395i	0.563547	−	1.73442i	−0.108684	−	0.994076i	$-0.534664\pi$
$461$	12.0999	−	37.2395i	0.563547	−	1.73442i	0.672231	−	0.740342i	$-0.265336\pi$
$462$	0.0933590	+	0.0678293i	0.00434345	+	0.00315570i
$463$	−16.9520	+	12.3164i	−0.787828	+	0.572390i	−0.907318	−	0.420445i	$-0.861874\pi$
$463$	−16.9520	+	12.3164i	−0.787828	+	0.572390i	0.119490	+	0.992835i	$0.461874\pi$
$464$	8.25865			0.383398
$465$	−0.664459	−	0.747177i	−0.0308136	−	0.0346495i
$466$	−13.6583			−0.632710
$467$	25.7738	−	18.7258i	1.19267	−	0.866526i	0.199127	−	0.979974i	$-0.436189\pi$
$467$	25.7738	−	18.7258i	1.19267	−	0.866526i	0.993544	+	0.113448i	$0.0361894\pi$
$468$	2.42402	+	1.76116i	0.112050	+	0.0814094i
$469$	2.92554	−	9.00390i	0.135089	−	0.415761i
$470$	−27.9473			−1.28911
$471$	0.627637			0.0289200
$472$	−3.44578	+	10.6050i	−0.158605	+	0.488136i
$473$	1.60766	+	4.94788i	0.0739204	+	0.227504i
$474$	−0.199982	−	0.615481i	−0.00918548	−	0.0282700i
$475$	14.0844	−	10.2329i	0.646238	−	0.469519i
$476$	−1.65445	+	5.09187i	−0.0758316	+	0.233386i
$477$	−27.1172	+	19.7018i	−1.24161	+	0.902083i
$478$	18.1843	+	13.2117i	0.831730	+	0.604287i
$479$	−6.13650	−	18.8862i	−0.280384	−	0.862933i	−0.987744	−	0.156080i	$-0.950114\pi$
$479$	−6.13650	−	18.8862i	−0.280384	−	0.862933i	0.707360	−	0.706853i	$-0.249886\pi$
$480$	0.145288	+	0.105558i	0.00663145	+	0.00481803i
$481$	8.33160	+	6.05326i	0.379888	+	0.276005i
$482$	3.55476	+	10.9404i	0.161915	+	0.498323i
$483$	−0.0449656	−	0.0326694i	−0.00204601	−	0.00148651i
$484$	6.84842	−	4.97567i	0.311292	−	0.226167i
$485$	−11.1325	+	34.2623i	−0.505501	+	1.55577i
$486$	1.33429	−	0.969420i	0.0605248	−	0.0439738i
$487$	9.16592	+	28.2098i	0.415347	+	1.27831i	0.911940	+	0.410324i	$0.134584\pi$
$487$	9.16592	+	28.2098i	0.415347	+	1.27831i	−0.496592	+	0.867984i	$0.665416\pi$
$488$	3.43616	+	10.5754i	0.155548	+	0.478726i
$489$	−0.341787	+	1.05191i	−0.0154561	+	0.0475691i
$490$	−16.4269			−0.742091
$491$	4.21140			0.190058			0.0950290	−	0.995475i	$-0.469706\pi$
$491$	4.21140			0.190058			0.0950290	+	0.995475i	$0.469706\pi$
$492$	0.158223	−	0.486962i	0.00713327	−	0.0219539i
$493$	30.1976	+	21.9398i	1.36003	+	0.988120i
$494$	3.89650	−	2.83097i	0.175312	−	0.127371i
$495$	−14.0016			−0.629324
$496$	3.69996	+	4.16056i	0.166133	+	0.186815i
$497$	−0.901898			−0.0404556
$498$	−0.656523	+	0.476992i	−0.0294195	+	0.0213745i
$499$	−15.1049	−	10.9744i	−0.676190	−	0.491281i	0.195902	−	0.980624i	$-0.437237\pi$
$499$	−15.1049	−	10.9744i	−0.676190	−	0.491281i	−0.872092	+	0.489343i	$0.837237\pi$
$500$	−1.25651	+	3.86713i	−0.0561926	+	0.172943i
$501$	−1.34084			−0.0599044
$502$	−10.0810			−0.449937
$503$	−5.87745	+	18.0889i	−0.262063	+	0.806546i	0.730293	+	0.683134i	$0.239384\pi$
$503$	−5.87745	+	18.0889i	−0.262063	+	0.806546i	−0.992356	+	0.123412i	$0.960616\pi$
$504$	−1.09680	−	3.37560i	−0.0488554	−	0.150361i
$505$	0.893166	+	2.74888i	0.0397454	+	0.122324i
$506$	0.987737	−	0.717633i	0.0439103	−	0.0319027i
$507$	−0.0189075	+	0.0581914i	−0.000839713	+	0.00258437i
$508$	6.12095	−	4.44713i	0.271573	−	0.197309i
$509$	−24.2075	−	17.5878i	−1.07298	−	0.779564i	−0.0965330	−	0.995330i	$-0.530775\pi$
$509$	−24.2075	−	17.5878i	−1.07298	−	0.779564i	−0.976445	+	0.215765i	$0.930775\pi$
$510$	0.250818	+	0.771939i	0.0111064	+	0.0341820i
$511$	−0.264022	−	0.191823i	−0.0116797	−	0.00848577i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−0.546050	−	1.68057i	−0.0241087	−	0.0741989i
$514$	−16.4418	−	11.9457i	−0.725217	−	0.526901i
$515$	31.1761	−	22.6507i	1.37378	−	0.998111i
$516$	−0.0617829	+	0.190148i	−0.00271984	+	0.00837081i
$517$	12.2647	−	8.91085i	0.539402	−	0.391899i
$518$	−3.76981	−	11.6023i	−0.165636	−	0.509775i
$519$	−0.454151	−	1.39773i	−0.0199350	−	0.0613537i
$520$	0.906987	−	2.79142i	0.0397740	−	0.122412i
$521$	4.40692			0.193071			0.0965354	−	0.995330i	$-0.469224\pi$
$521$	4.40692			0.193071			0.0965354	+	0.995330i	$0.469224\pi$
$522$	−24.7450			−1.08306
$523$	0.942969	−	2.90216i	0.0412331	−	0.126903i	−0.928321	−	0.371780i	$-0.878748\pi$
$523$	0.942969	−	2.90216i	0.0412331	−	0.126903i	0.969554	+	0.244877i	$0.0787477\pi$
$524$	4.21779	+	3.06440i	0.184255	+	0.133869i
$525$	0.211954	−	0.153993i	0.00925042	−	0.00672083i
$526$	−5.42160			−0.236393
$527$	2.47593	+	25.0423i	0.107853	+	1.09086i
$528$	−0.0974165			−0.00423951
$529$	18.1317	−	13.1734i	0.788333	−	0.572757i
$530$	26.5634	+	19.2995i	1.15384	+	0.838315i
$531$	10.3244	−	31.7754i	0.448043	−	1.37893i
$532$	−5.70536			−0.247359
$533$	−8.36827			−0.362470
$534$	−0.121784	+	0.374811i	−0.00527009	+	0.0162197i
$535$	−0.413024	−	1.27116i	−0.0178566	−	0.0549570i
$536$	2.46968	+	7.60089i	0.106674	+	0.328309i
$537$	1.04634	−	0.760213i	0.0451530	−	0.0328056i
$538$	6.35175	−	19.5487i	0.273844	−	0.842804i
$539$	7.20898	−	5.23763i	0.310513	−	0.225601i
$540$	−0.871182	−	0.632951i	−0.0374897	−	0.0272379i
$541$	−4.69768	−	14.4580i	−0.201969	−	0.621597i	−0.999824	−	0.0187477i	$-0.994032\pi$
$541$	−4.69768	−	14.4580i	−0.201969	−	0.621597i	0.797855	−	0.602849i	$-0.205968\pi$
$542$	0.425116	+	0.308865i	0.0182603	+	0.0132669i
$543$	0.833646	+	0.605679i	0.0357752	+	0.0259922i
$544$	−1.39665	−	4.29845i	−0.0598809	−	0.184294i
$545$	−5.76705	−	4.19001i	−0.247033	−	0.179480i
$546$	0.0586376	−	0.0426027i	0.00250946	−	0.00182323i
$547$	−1.43452	+	4.41501i	−0.0613358	+	0.188772i	−0.977029	−	0.213105i	$-0.931642\pi$
$547$	−1.43452	+	4.41501i	−0.0613358	+	0.188772i	0.915693	+	0.401878i	$0.131642\pi$
$548$	−3.99168	+	2.90013i	−0.170516	+	0.123887i
$549$	−10.2956	−	31.6866i	−0.439406	−	1.35235i
$550$	1.77839	+	5.47332i	0.0758307	+	0.233383i
$551$	−12.2916	+	37.8297i	−0.523640	+	1.61160i
$552$	0.0469199			0.00199704
$553$	12.5292			0.532794
$554$	9.48656	−	29.1966i	0.403045	−	1.24045i
$555$	−1.49623	−	1.08708i	−0.0635116	−	0.0461439i
$556$	12.8934	−	9.36758i	0.546800	−	0.397274i
$557$	−6.27510			−0.265884			−0.132942	−	0.991124i	$-0.542442\pi$
$557$	−6.27510			−0.265884			−0.132942	+	0.991124i	$0.542442\pi$
$558$	−11.0860	−	12.4661i	−0.469309	−	0.527733i
$559$	3.26763			0.138206
$560$	−2.81282	+	2.04364i	−0.118863	+	0.0863593i
$561$	−0.356201	−	0.258795i	−0.0150388	−	0.0109263i
$562$	6.11545	−	18.8214i	0.257965	−	0.793933i
$563$	3.51524			0.148150			0.0740749	−	0.997253i	$-0.476400\pi$
$563$	3.51524			0.148150			0.0740749	+	0.997253i	$0.476400\pi$
$564$	0.582604			0.0245321
$565$	−4.45706	+	13.7174i	−0.187510	+	0.577096i
$566$	6.55457	+	20.1729i	0.275509	+	0.847930i
$567$	3.28218	+	10.1015i	0.137839	+	0.424224i
$568$	0.615955	−	0.447517i	0.0258449	−	0.0187774i
$569$	−8.11018	+	24.9606i	−0.339996	+	1.04640i	0.624212	+	0.781255i	$0.285420\pi$
$569$	−8.11018	+	24.9606i	−0.339996	+	1.04640i	−0.964208	+	0.265146i	$0.914580\pi$
$570$	−0.699755	+	0.508402i	−0.0293095	+	0.0212946i
$571$	23.8662	+	17.3398i	0.998771	+	0.725649i	0.961824	−	0.273668i	$-0.0882369\pi$
$571$	23.8662	+	17.3398i	0.998771	+	0.725649i	0.0369465	+	0.999317i	$0.488237\pi$
$572$	0.491996	+	1.51421i	0.0205714	+	0.0633123i
$573$	−0.213547	−	0.155151i	−0.00892104	−	0.00648152i
$574$	8.01973	+	5.82667i	0.334737	+	0.243201i
$575$	−0.856547	−	2.63618i	−0.0357205	−	0.109936i
$576$	2.42402	+	1.76116i	0.101001	+	0.0733815i
$577$	−28.6551	+	20.8191i	−1.19293	+	0.866712i	−0.993570	−	0.113216i	$-0.963885\pi$
$577$	−28.6551	+	20.8191i	−1.19293	+	0.866712i	−0.199356	+	0.979927i	$0.563885\pi$
$578$	1.05909	−	3.25953i	0.0440521	−	0.135579i
$579$	−0.336323	+	0.244353i	−0.0139771	+	0.0101550i
$580$	7.49049	+	23.0533i	0.311026	+	0.957238i
$581$	−4.85499	−	14.9421i	−0.201419	−	0.619904i
$582$	0.232074	−	0.714252i	0.00961979	−	0.0296067i
$583$	−17.8110			−0.737655
$584$	0.275497			0.0114001
$585$	−2.71756	+	8.36380i	−0.112357	+	0.345801i
$586$	16.8172	+	12.2184i	0.694711	+	0.504737i
$587$	−31.6877	+	23.0225i	−1.30789	+	0.950238i	−0.999999	−	0.00118308i	$-0.999623\pi$
$587$	−31.6877	+	23.0225i	−1.30789	+	0.950238i	−0.307892	+	0.951421i	$0.599623\pi$
$588$	0.342444			0.0141221
$589$	−24.5647	+	10.7558i	−1.01217	+	0.443184i
$590$	−32.7283			−1.34740
$591$	−0.187322	+	0.136097i	−0.00770539	+	0.00559829i
$592$	8.33160	+	6.05326i	0.342427	+	0.248788i
$593$	5.41987	−	16.6806i	0.222567	−	0.684992i	−0.775962	−	0.630780i	$-0.782735\pi$
$593$	5.41987	−	16.6806i	0.222567	−	0.684992i	0.998529	−	0.0542125i	$-0.0172648\pi$
$594$	0.584134			0.0239673
$595$	−15.7141			−0.644216
$596$	−1.80606	+	5.55849i	−0.0739792	+	0.227685i
$597$	0.498706	+	1.53486i	0.0204107	+	0.0628176i
$598$	−0.236966	−	0.729307i	−0.00969027	−	0.0298236i
$599$	17.3988	−	12.6410i	0.710897	−	0.516497i	−0.172566	−	0.984998i	$-0.555206\pi$
$599$	17.3988	−	12.6410i	0.710897	−	0.516497i	0.883463	+	0.468501i	$0.155206\pi$
$600$	−0.0683439	+	0.210341i	−0.00279013	+	0.00858713i
$601$	−19.2419	+	13.9801i	−0.784894	+	0.570259i	−0.906444	−	0.422326i	$-0.861214\pi$
$601$	−19.2419	+	13.9801i	−0.784894	+	0.570259i	0.121550	+	0.992585i	$0.461214\pi$
$602$	−3.13153	−	2.27519i	−0.127632	−	0.0927299i
$603$	−7.39979	−	22.7742i	−0.301343	−	0.927438i
$604$	2.45931	+	1.78679i	0.100068	+	0.0727035i
$605$	20.1006	+	14.6039i	0.817205	+	0.593734i
$606$	−0.0186194	−	0.0573047i	−0.000756363	−	0.00232785i
$607$	−24.8167	−	18.0304i	−1.00728	−	0.731832i	−0.0436437	−	0.999047i	$-0.513897\pi$
$607$	−24.8167	−	18.0304i	−1.00728	−	0.731832i	−0.963637	+	0.267215i	$0.913897\pi$
$608$	3.89650	−	2.83097i	0.158024	−	0.114811i
$609$	−0.184974	+	0.569291i	−0.00749552	+	0.0230688i
$610$	−26.4038	+	19.1835i	−1.06906	+	0.776718i
$611$	−2.94241	−	9.05580i	−0.119037	−	0.366359i
$612$	4.18472	+	12.8792i	0.169157	+	0.520613i
$613$	−7.60558	+	23.4076i	−0.307186	+	0.945422i	0.671666	+	0.740854i	$0.265579\pi$
$613$	−7.60558	+	23.4076i	−0.307186	+	0.945422i	−0.978852	+	0.204568i	$0.934421\pi$
$614$	7.06239			0.285015
$615$	1.50282			0.0605996
$616$	0.582812	−	1.79371i	0.0234821	−	0.0722706i
$617$	8.75556	+	6.36129i	0.352486	+	0.256096i	0.749911	−	0.661539i	$-0.230096\pi$
$617$	8.75556	+	6.36129i	0.352486	+	0.256096i	−0.397425	+	0.917634i	$0.630096\pi$
$618$	−0.649914	+	0.472190i	−0.0261434	+	0.0189943i
$619$	−29.9817			−1.20507			−0.602533	−	0.798094i	$-0.705842\pi$
$619$	−29.9817			−1.20507			−0.602533	+	0.798094i	$0.705842\pi$
$620$	−8.25805	+	14.1017i	−0.331651	+	0.566338i
$621$	−0.281344			−0.0112899
$622$	−27.0472	+	19.6509i	−1.08449	+	0.787930i
$623$	−6.17273	−	4.48475i	−0.247305	−	0.179678i
$624$	−0.0189075	+	0.0581914i	−0.000756907	+	0.00232952i
$625$	−30.0076			−1.20030
$626$	−6.01687			−0.240482
$627$	0.144988	−	0.446227i	0.00579026	−	0.0178206i
$628$	−3.16985	−	9.75578i	−0.126491	−	0.389298i
$629$	14.3833	+	44.2672i	0.573499	+	1.76505i
$630$	8.42794	−	6.12325i	0.335777	−	0.243956i
$631$	0.916778	−	2.82155i	0.0364963	−	0.112324i	−0.931149	−	0.364640i	$-0.881192\pi$
$631$	0.916778	−	2.82155i	0.0364963	−	0.112324i	0.967645	+	0.252316i	$0.0811921\pi$
$632$	−8.55684	+	6.21691i	−0.340373	+	0.247295i
$633$	−1.20353	−	0.874417i	−0.0478361	−	0.0347550i
$634$	−4.11415	−	12.6621i	−0.163394	−	0.502875i
$635$	17.9654	+	13.0526i	0.712936	+	0.517978i
$636$	−0.553756	−	0.402327i	−0.0219579	−	0.0159533i
$637$	−1.72949	−	5.32283i	−0.0685250	−	0.210898i
$638$	−10.6377	−	7.72872i	−0.421149	−	0.305983i
$639$	−1.84556	+	1.34088i	−0.0730092	+	0.0530443i
$640$	0.906987	−	2.79142i	0.0358518	−	0.110340i
$641$	9.39008	−	6.82229i	0.370886	−	0.269464i	−0.386692	−	0.922209i	$-0.626382\pi$
$641$	9.39008	−	6.82229i	0.370886	−	0.269464i	0.757578	+	0.652744i	$0.226382\pi$
$642$	0.00861014	+	0.0264993i	0.000339815	+	0.00104584i
$643$	9.14819	+	28.1552i	0.360769	+	1.11033i	0.952588	+	0.304263i	$0.0984101\pi$
$643$	9.14819	+	28.1552i	0.360769	+	1.11033i	−0.591819	+	0.806071i	$0.701590\pi$
$644$	−0.280707	+	0.863926i	−0.0110614	+	0.0340435i
$645$	−0.586819			−0.0231060
$646$	21.7682			0.856458
$647$	−0.509652	+	1.56855i	−0.0200365	+	0.0616659i	−0.960575	−	0.278022i	$-0.910321\pi$
$647$	−0.509652	+	1.56855i	−0.0200365	+	0.0616659i	0.940538	+	0.339688i	$0.110321\pi$
$648$	−7.25391	−	5.27027i	−0.284960	−	0.207036i
$649$	14.3629	−	10.4353i	0.563794	−	0.409620i
$650$	3.61464			0.141778
$651$	−0.369669	+	0.161862i	−0.0144885	+	0.00634386i
$652$	18.0767			0.707940
$653$	−24.8165	+	18.0302i	−0.971145	+	0.705578i	−0.955712	−	0.294303i	$-0.904913\pi$
$653$	−24.8165	+	18.0302i	−0.971145	+	0.705578i	−0.0154328	+	0.999881i	$0.504913\pi$
$654$	0.120223	+	0.0873473i	0.00470110	+	0.00341555i
$655$	−4.72855	+	14.5530i	−0.184760	+	0.568632i
$656$	−8.36827			−0.326726
$657$	−0.825459			−0.0322042
$658$	−3.48553	+	10.7274i	−0.135880	+	0.418196i
$659$	−0.945591	−	2.91023i	−0.0368350	−	0.113366i	0.930948	−	0.365151i	$-0.118983\pi$
$659$	−0.945591	−	2.91023i	−0.0368350	−	0.113366i	−0.967783	+	0.251784i	$0.918983\pi$
$660$	−0.0883554	−	0.271930i	−0.00343923	−	0.0105849i
$661$	16.1164	−	11.7093i	0.626857	−	0.455438i	−0.228453	−	0.973555i	$-0.573367\pi$
$661$	16.1164	−	11.7093i	0.626857	−	0.455438i	0.855310	+	0.518117i	$0.173367\pi$
$662$	−1.66201	+	5.11514i	−0.0645958	+	0.198806i
$663$	−0.223726	+	0.162546i	−0.00868878	+	0.00631277i
$664$	10.7299	+	7.79576i	0.416403	+	0.302534i
$665$	−5.17469	−	15.9260i	−0.200666	−	0.617585i
$666$	−24.9636	−	18.1371i	−0.967320	−	0.702799i
$667$	5.12355	+	3.72248i	0.198385	+	0.144135i
$668$	6.77185	+	20.8416i	0.262011	+	0.806386i
$669$	−0.558461	−	0.405746i	−0.0215914	−	0.0156870i
$670$	−18.9773	+	13.7878i	−0.733157	+	0.532670i
$671$	5.47083	−	16.8375i	0.211199	−	0.650003i
$672$	0.0586376	−	0.0426027i	0.00226200	−	0.00164344i
$673$	−0.743201	−	2.28734i	−0.0286483	−	0.0881703i	0.935710	−	0.352770i	$-0.114760\pi$
$673$	−0.743201	−	2.28734i	−0.0286483	−	0.0881703i	−0.964358	+	0.264600i	$0.914760\pi$
$674$	1.75113	+	5.38942i	0.0674510	+	0.207593i
$675$	0.409808	−	1.26126i	0.0157735	−	0.0485458i
$676$	1.00000			0.0384615
$677$	−26.5664			−1.02103			−0.510515	−	0.859869i	$-0.670545\pi$
$677$	−26.5664			−1.02103			−0.510515	+	0.859869i	$0.670545\pi$
$678$	0.0929144	−	0.285961i	0.00356836	−	0.0109823i
$679$	11.7629	+	8.54628i	0.451420	+	0.327976i
$680$	10.7320	−	7.79727i	0.411554	−	0.299012i
$681$	−1.15077			−0.0440977
$682$	−0.872193	−	8.82162i	−0.0333980	−	0.337797i
$683$	22.2994			0.853262			0.426631	−	0.904426i	$-0.359700\pi$
$683$	22.2994			0.853262			0.426631	+	0.904426i	$0.359700\pi$
$684$	−11.6749	+	8.48232i	−0.446401	+	0.324330i
$685$	−11.7159	−	8.51207i	−0.447640	−	0.325230i
$686$	−4.61113	+	14.1916i	−0.176054	+	0.541838i
$687$	0.538081			0.0205291
$688$	3.26763			0.124577
$689$	−3.45693	+	10.6393i	−0.131699	+	0.405326i
$690$	0.0425557	+	0.130973i	0.00162007	+	0.00498606i
$691$	9.26862	+	28.5259i	0.352595	+	1.08518i	0.957391	+	0.288795i	$0.0932546\pi$
$691$	9.26862	+	28.5259i	0.352595	+	1.08518i	−0.604796	+	0.796380i	$0.706745\pi$
$692$	−19.4323	+	14.1184i	−0.738704	+	0.536700i
$693$	−1.74625	+	5.37441i	−0.0663347	+	0.204157i
$694$	−10.6771	+	7.75738i	−0.405298	+	0.294466i
$695$	37.8429	+	27.4945i	1.43546	+	1.04293i
$696$	−0.156151	−	0.480583i	−0.00591888	−	0.0182164i
$697$	−30.5984	−	22.2310i	−1.15900	−	0.842061i
$698$	−10.9345	−	7.94439i	−0.413878	−	0.300700i
$699$	0.258246	+	0.794798i	0.00976775	+	0.0300620i
$700$	−3.46408	−	2.51680i	−0.130930	−	0.0951263i
$701$	3.06539	−	2.22713i	0.115778	−	0.0841177i	−0.528390	−	0.849002i	$-0.677204\pi$
$701$	3.06539	−	2.22713i	0.115778	−	0.0841177i	0.644168	+	0.764884i	$0.277204\pi$
$702$	0.113374	−	0.348931i	0.00427904	−	0.0131695i
$703$	−40.1278	+	29.1546i	−1.51345	+	1.09958i
$704$	0.491996	+	1.51421i	0.0185428	+	0.0570689i
$705$	0.528414	+	1.62629i	0.0199012	+	0.0612497i
$706$	−6.42689	+	19.7799i	−0.241879	+	0.744428i
$707$	1.16653			0.0438720
$708$	0.682273			0.0256414
$709$	−7.00845	+	21.5698i	−0.263208	+	0.810070i	0.728893	+	0.684628i	$0.240035\pi$
$709$	−7.00845	+	21.5698i	−0.263208	+	0.810070i	−0.992101	+	0.125443i	$0.959965\pi$
$710$	1.80787	+	1.31349i	0.0678482	+	0.0492946i
$711$	25.6385	−	18.6275i	0.961518	−	0.698584i
$712$	6.44101			0.241387
$713$	0.420085	+	4.24886i	0.0157323	+	0.159121i
$714$	0.327585			0.0122596
$715$	−3.78056	+	2.74674i	−0.141385	+	0.102722i
$716$	−17.1010	−	12.4246i	−0.639094	−	0.464329i
$717$	0.424985	−	1.30797i	0.0158714	−	0.0488470i
$718$	19.2447			0.718206
$719$	−17.6246			−0.657286			−0.328643	−	0.944454i	$-0.606591\pi$
$719$	−17.6246			−0.657286			−0.328643	+	0.944454i	$0.606591\pi$
$720$	−2.71756	+	8.36380i	−0.101278	+	0.311701i
$721$	−4.80611	−	14.7917i	−0.178989	−	0.550871i
$722$	1.29698	+	3.99169i	0.0482685	+	0.148555i
$723$	0.569428	−	0.413713i	0.0211772	−	0.0153862i
$724$	5.20419	−	16.0169i	0.193412	−	0.595262i
$725$	−24.1508	+	17.5466i	−0.896938	+	0.651664i
$726$	−0.419028	−	0.304442i	−0.0155516	−	0.0112989i
$727$	7.38176	+	22.7187i	0.273774	+	0.842591i	0.989541	+	0.144252i	$0.0460774\pi$
$727$	7.38176	+	22.7187i	0.273774	+	0.842591i	−0.715767	+	0.698340i	$0.753923\pi$
$728$	−0.958349	−	0.696281i	−0.0355188	−	0.0258059i
$729$	21.6801	+	15.7515i	0.802966	+	0.583389i
$730$	0.249872	+	0.769027i	0.00924818	+	0.0284630i
$731$	11.9480	+	8.68074i	0.441913	+	0.321069i
$732$	0.550429	−	0.399910i	0.0203444	−	0.0147811i
$733$	12.5303	−	38.5644i	0.462818	−	1.42441i	−0.398888	−	0.916999i	$-0.630604\pi$
$733$	12.5303	−	38.5644i	0.462818	−	1.42441i	0.861706	−	0.507407i	$-0.169396\pi$
$734$	17.8507	−	12.9693i	0.658883	−	0.478706i
$735$	0.310592	+	0.955904i	0.0114564	+	0.0352590i
$736$	−0.236966	−	0.729307i	−0.00873469	−	0.0268826i
$737$	3.93206	−	12.1016i	0.144839	−	0.445770i
$738$	25.0735			0.922968
$739$	−7.36563			−0.270949			−0.135475	−	0.990781i	$-0.543256\pi$
$739$	−7.36563			−0.270949			−0.135475	+	0.990781i	$0.543256\pi$
$740$	−9.34053	+	28.7472i	−0.343365	+	1.05677i
$741$	−0.238412	−	0.173216i	−0.00875827	−	0.00636325i
$742$	10.7209	−	7.78920i	0.393577	−	0.285951i
$743$	10.8580			0.398341			0.199171	−	0.979965i	$-0.436175\pi$
$743$	10.8580			0.398341			0.199171	+	0.979965i	$0.436175\pi$
$744$	0.172152	−	0.293972i	0.00631140	−	0.0107775i
$745$	−17.1541			−0.628479
$746$	22.2146	−	16.1398i	0.813334	−	0.590921i
$747$	−32.1497	−	23.3581i	−1.17629	−	0.854628i
$748$	−2.22365	+	6.84370i	−0.0813048	+	0.250231i
$749$	−0.539437			−0.0197106
$750$	0.248791			0.00908457
$751$	12.4386	−	38.2820i	0.453891	−	1.39693i	−0.418542	−	0.908197i	$-0.637459\pi$
$751$	12.4386	−	38.2820i	0.453891	−	1.39693i	0.872433	−	0.488734i	$-0.162541\pi$
$752$	−2.94241	−	9.05580i	−0.107299	−	0.330231i
$753$	0.190607	+	0.586627i	0.00694610	+	0.0213779i
$754$	−6.68139	+	4.85431i	−0.243322	+	0.176784i
$755$	−2.75712	+	8.48554i	−0.100342	+	0.308821i
$756$	−0.351606	+	0.255457i	−0.0127878	+	0.00929088i
$757$	−7.94671	−	5.77362i	−0.288828	−	0.209846i	0.433931	−	0.900946i	$-0.357126\pi$
$757$	−7.94671	−	5.77362i	−0.288828	−	0.209846i	−0.722759	+	0.691100i	$0.757126\pi$
$758$	−10.9135	−	33.5884i	−0.396398	−	1.21999i
$759$	−0.0604358	−	0.0439092i	−0.00219368	−	0.00159380i
$760$	11.4365	+	8.30910i	0.414845	+	0.301403i
$761$	−15.3503	−	47.2434i	−0.556448	−	1.71257i	−0.692087	−	0.721814i	$-0.743309\pi$
$761$	−15.3503	−	47.2434i	−0.556448	−	1.71257i	0.135639	−	0.990758i	$-0.456691\pi$
$762$	−0.374517	−	0.272102i	−0.0135673	−	0.00985723i
$763$	−2.32756	+	1.69107i	−0.0842635	+	0.0612210i
$764$	−1.33311	+	4.10288i	−0.0482301	+	0.148437i
$765$	−32.1559	+	23.3626i	−1.16260	+	0.844677i
$766$	4.01032	+	12.3425i	0.144899	+	0.445952i
$767$	−3.44578	−	10.6050i	−0.124420	−	0.382925i
$768$	−0.0189075	+	0.0581914i	−0.000682267	+	0.00209980i
$769$	0.137815			0.00496973			0.00248486	−	0.999997i	$-0.499209\pi$
$769$	0.137815			0.00496973			0.00248486	+	0.999997i	$0.499209\pi$
$770$	5.53559			0.199489
$771$	−0.384262	+	1.18264i	−0.0138388	+	0.0425916i
$772$	5.49672	+	3.99360i	0.197831	+	0.143733i
$773$	18.2578	−	13.2651i	0.656687	−	0.477111i	−0.208855	−	0.977947i	$-0.566974\pi$
$773$	18.2578	−	13.2651i	0.656687	−	0.477111i	0.865543	+	0.500835i	$0.166974\pi$
$774$	−9.79066			−0.351918
$775$	−19.6595	−	4.30570i	−0.706189	−	0.154665i
$776$	−12.2742			−0.440617
$777$	−0.603875	+	0.438741i	−0.0216639	+	0.0157397i
$778$	20.0006	+	14.5313i	0.717055	+	0.520971i
$779$	12.4548	−	38.3318i	0.446238	−	1.37338i
$780$	−0.179585			−0.00643019
$781$	−1.21219			−0.0433756
$782$	1.07101	−	3.29622i	0.0382991	−	0.117872i
$783$	0.936320	+	2.88170i	0.0334614	+	0.102983i
$784$	−1.72949	−	5.32283i	−0.0617676	−	0.190101i
$785$	24.3575	−	17.6967i	0.869355	−	0.631623i
$786$	0.0985740	−	0.303379i	0.00351602	−	0.0108212i
$787$	5.25468	−	3.81775i	0.187309	−	0.136088i	−0.490179	−	0.871622i	$-0.663069\pi$
$787$	5.25468	−	3.81775i	0.187309	−	0.136088i	0.677488	+	0.735534i	$0.263069\pi$
$788$	3.06151	+	2.22432i	0.109062	+	0.0792380i
$789$	0.102509	+	0.315491i	0.00364942	+	0.0112318i
$790$	−25.1149	−	18.2471i	−0.893549	−	0.649201i
$791$	4.70947	+	3.42163i	0.167449	+	0.121659i
$792$	−1.47415	−	4.53696i	−0.0523816	−	0.161214i
$793$	−8.99598	−	6.53596i	−0.319457	−	0.232099i
$794$	5.07932	−	3.69034i	0.180258	−	0.130965i
$795$	0.620814	−	1.91067i	0.0220180	−	0.0677645i
$796$	21.3386	−	15.5034i	0.756328	−	0.549505i
$797$	4.60748	+	14.1804i	0.163205	+	0.502295i	0.998900	−	0.0469005i	$-0.0149344\pi$
$797$	4.60748	+	14.1804i	0.163205	+	0.502295i	−0.835694	+	0.549195i	$0.814934\pi$
$798$	0.107874	+	0.332003i	0.00381871	+	0.0117528i
$799$	13.2987	−	40.9291i	0.470473	−	1.44797i
$800$	3.61464			0.127797
$801$	−19.2989			−0.681893
$802$	−4.94814	+	15.2288i	−0.174725	+	0.537748i
$803$	−0.354858	−	0.257819i	−0.0125226	−	0.00909824i
$804$	0.395611	−	0.287428i	0.0139521	−	0.0101368i
$805$	−2.66618			−0.0939704
$806$	−5.43885	−	1.19118i	−0.191575	−	0.0419577i
$807$	−1.25766			−0.0442718
$808$	−0.796689	+	0.578829i	−0.0280274	+	0.0203631i
$809$	20.8519	+	15.1498i	0.733114	+	0.532639i	0.890547	−	0.454891i	$-0.150322\pi$
$809$	20.8519	+	15.1498i	0.733114	+	0.532639i	−0.157433	+	0.987530i	$0.550322\pi$
$810$	8.13233	−	25.0287i	0.285741	−	0.879420i
$811$	24.2532			0.851646			0.425823	−	0.904806i	$-0.359985\pi$
$811$	24.2532			0.851646			0.425823	+	0.904806i	$0.359985\pi$
$812$	9.78308			0.343319
$813$	0.00993540	−	0.0305780i	0.000348450	−	0.00107242i
$814$	−5.06679	−	15.5940i	−0.177591	−	0.546568i
$815$	16.3954	+	50.4598i	0.574305	+	1.76753i
$816$	−0.223726	+	0.162546i	−0.00783196	+	0.00569025i
$817$	−4.86331	+	14.9677i	−0.170146	+	0.523655i
$818$	−10.1068	+	7.34303i	−0.353376	+	0.256743i
$819$	2.87146	+	2.08624i	0.100337	+	0.0728990i
$820$	−7.58991	−	23.3593i	−0.265051	−	0.815744i
$821$	−11.3672	−	8.25875i	−0.396718	−	0.288232i	0.371485	−	0.928439i	$-0.378849\pi$
$821$	−11.3672	−	8.25875i	−0.396718	−	0.288232i	−0.768203	+	0.640207i	$0.778849\pi$
$822$	0.244235	+	0.177447i	0.00851868	+	0.00618919i
$823$	−3.46416	−	10.6616i	−0.120753	−	0.371639i	0.872350	−	0.488881i	$-0.162595\pi$
$823$	−3.46416	−	10.6616i	−0.120753	−	0.371639i	−0.993103	+	0.117242i	$0.962595\pi$
$824$	10.6219	+	7.71728i	0.370032	+	0.268844i
$825$	0.284875	−	0.206974i	0.00991808	−	0.00720591i
$826$	−4.08182	+	12.5625i	−0.142025	+	0.437107i
$827$	−41.3290	+	30.0273i	−1.43715	+	1.04415i	−0.448521	+	0.893772i	$0.648049\pi$
$827$	−41.3290	+	30.0273i	−1.43715	+	1.04415i	−0.988629	+	0.150378i	$0.951951\pi$
$828$	0.710012	+	2.18519i	0.0246746	+	0.0759406i
$829$	15.8937	+	48.9159i	0.552013	+	1.69892i	0.703705	+	0.710493i	$0.251528\pi$
$829$	15.8937	+	48.9159i	0.552013	+	1.69892i	−0.151692	+	0.988428i	$0.548472\pi$
$830$	−12.0293	+	37.0224i	−0.417543	+	1.28507i
$831$	−1.87836			−0.0651596
$832$	1.00000			0.0346688
$833$	7.81671	−	24.0574i	0.270833	−	0.833538i
$834$	−0.788895	−	0.573166i	−0.0273172	−	0.0198471i
$835$	−52.0356	+	37.8061i	−1.80077	+	1.30833i
$836$	−7.66826			−0.265212
$837$	−1.03227	+	1.76273i	−0.0356804	+	0.0609289i
$838$	−36.0383			−1.24492
$839$	34.2554	−	24.8880i	1.18263	−	0.859229i	0.190162	−	0.981753i	$-0.439099\pi$
$839$	34.2554	−	24.8880i	1.18263	−	0.859229i	0.992466	+	0.122524i	$0.0390987\pi$
$840$	0.172106	+	0.125042i	0.00593821	+	0.00431436i
$841$	12.1151	−	37.2865i	0.417763	−	1.28574i
$842$	−24.6921			−0.850946
$843$	−1.21087			−0.0417047
$844$	−7.51328	+	23.1235i	−0.258618	+	0.795944i
$845$	0.906987	+	2.79142i	0.0312013	+	0.0960277i
$846$	8.81621	+	27.1335i	0.303108	+	0.932869i
$847$	8.11253	−	5.89410i	0.278750	−	0.202524i
$848$	−3.45693	+	10.6393i	−0.118711	+	0.365356i
$849$	1.04996	−	0.762840i	0.0360345	−	0.0261806i
$850$	13.2168	+	9.60259i	0.453334	+	0.329366i
$851$	2.44038	+	7.51071i	0.0836551	+	0.257464i
$852$	−0.0376879	−	0.0273818i	−0.00129116	−	0.000938086i
$853$	−8.53515	−	6.20115i	−0.292238	−	0.212323i	0.432000	−	0.901874i	$-0.357808\pi$
$853$	−8.53515	−	6.20115i	−0.292238	−	0.212323i	−0.724238	+	0.689550i	$0.757808\pi$
$854$	4.07042	+	12.5275i	0.139287	+	0.428681i
$855$	−34.2667	−	24.8962i	−1.17190	−	0.851432i
$856$	0.368411	−	0.267666i	0.0125920	−	0.00914864i
$857$	7.00648	−	21.5637i	0.239337	−	0.736603i	−0.757180	−	0.653207i	$-0.773423\pi$
$857$	7.00648	−	21.5637i	0.239337	−	0.736603i	0.996516	−	0.0833963i	$-0.0265767\pi$
$858$	0.0788116	−	0.0572600i	0.00269058	−	0.00195482i
$859$	−4.29245	−	13.2108i	−0.146457	−	0.450747i	0.850739	−	0.525589i	$-0.176155\pi$
$859$	−4.29245	−	13.2108i	−0.146457	−	0.450747i	−0.997195	+	0.0748417i	$0.976155\pi$
$860$	2.96370	+	9.12132i	0.101061	+	0.311035i
$861$	0.187429	−	0.576848i	0.00638757	−	0.0196589i
$862$	13.4749			0.458957
$863$	3.31372			0.112800			0.0564001	−	0.998408i	$-0.482038\pi$
$863$	3.31372			0.112800			0.0564001	+	0.998408i	$0.482038\pi$
$864$	0.113374	−	0.348931i	0.00385708	−	0.0118709i
$865$	−57.0350	−	41.4384i	−1.93925	−	1.40895i
$866$	−11.4343	+	8.30748i	−0.388552	+	0.282300i
$867$	−0.209701			−0.00712183
$868$	4.38292	+	4.92854i	0.148766	+	0.167286i
$869$	16.8397			0.571249
$870$	1.19988	−	0.871764i	0.0406798	−	0.0295556i
$871$	−6.46570	−	4.69761i	−0.219082	−	0.159172i
$872$	0.750517	−	2.30985i	0.0254157	−	0.0782215i
$873$	36.7766			1.24470
$874$	3.69336			0.124930
$875$	−1.48844	+	4.58094i	−0.0503184	+	0.154864i
$876$	−0.00520897	−	0.0160316i	−0.000175995	−	0.000541656i
$877$	14.4743	+	44.5472i	0.488762	+	1.50425i	0.826458	+	0.562998i	$0.190352\pi$
$877$	14.4743	+	44.5472i	0.488762	+	1.50425i	−0.337696	+	0.941255i	$0.609648\pi$
$878$	−12.1938	+	8.85934i	−0.411522	+	0.298988i
$879$	0.393034	−	1.20963i	0.0132567	−	0.0408000i
$880$	−3.78056	+	2.74674i	−0.127443	+	0.0925924i
$881$	26.6104	+	19.3336i	0.896528	+	0.651366i	0.937572	−	0.347792i	$-0.113068\pi$
$881$	26.6104	+	19.3336i	0.896528	+	0.651366i	−0.0410441	+	0.999157i	$0.513068\pi$
$882$	5.18201	+	15.9486i	0.174487	+	0.537016i
$883$	4.56117	+	3.31388i	0.153495	+	0.111521i	0.661882	−	0.749608i	$-0.269758\pi$
$883$	4.56117	+	3.31388i	0.153495	+	0.111521i	−0.508387	+	0.861129i	$0.669758\pi$
$884$	3.65648	+	2.65659i	0.122981	+	0.0893507i
$885$	0.618812	+	1.90451i	0.0208011	+	0.0640193i
$886$	12.3057	+	8.94059i	0.413417	+	0.300365i
$887$	−23.8188	+	17.3054i	−0.799757	+	0.581058i	−0.910843	−	0.412753i	$-0.864567\pi$
$887$	−23.8188	+	17.3054i	−0.799757	+	0.581058i	0.111086	+	0.993811i	$0.464567\pi$
$888$	0.194718	−	0.599280i	0.00653430	−	0.0201105i
$889$	7.25078	−	5.26800i	0.243183	−	0.176683i
$890$	5.84191	+	17.9795i	0.195821	+	0.602675i
$891$	4.41140	+	13.5769i	0.147787	+	0.454843i
$892$	−3.48630	+	10.7297i	−0.116730	+	0.359258i
$893$	45.8604			1.53466
$894$	0.357605			0.0119601
$895$	19.1719	−	59.0050i	0.640845	−	1.97232i
$896$	−0.958349	−	0.696281i	−0.0320162	−	0.0232611i
$897$	−0.0379590	+	0.0275788i	−0.00126741	+	0.000920830i
$898$	11.5245			0.384578
$899$	42.1215	−	18.4431i	1.40483	−	0.615113i
$900$	−10.8304			−0.361013
$901$	−40.9045	+	29.7189i	−1.36273	+	0.990079i
$902$	10.7789	+	7.83131i	0.358897	+	0.260754i
$903$	−0.0731871	+	0.225247i	−0.00243551	+	0.00749574i
$904$	−4.91414			−0.163442
$905$	49.4299			1.64310
$906$	0.0574764	−	0.176894i	0.00190953	−	0.00587692i
$907$	−5.91789	−	18.2134i	−0.196500	−	0.604766i	−0.999956	−	0.00940118i	$-0.997007\pi$
$907$	−5.91789	−	18.2134i	−0.196500	−	0.604766i	0.803455	−	0.595365i	$-0.202993\pi$
$908$	5.81191	+	17.8872i	0.192875	+	0.593608i
$909$	2.38709	−	1.73432i	0.0791746	−	0.0575237i
$910$	1.07440	−	3.30667i	0.0356161	−	0.109615i
$911$	18.3443	−	13.3279i	0.607774	−	0.441573i	−0.240856	−	0.970561i	$-0.577428\pi$
$911$	18.3443	−	13.3279i	0.607774	−	0.441573i	0.848630	+	0.528987i	$0.177428\pi$
$912$	−0.238412	−	0.173216i	−0.00789460	−	0.00573576i
$913$	−6.52532	−	20.0829i	−0.215957	−	0.664646i
$914$	15.3918	+	11.1828i	0.509115	+	0.369894i
$915$	1.61555	+	1.17376i	0.0534084	+	0.0388034i
$916$	−2.71755	−	8.36376i	−0.0897904	−	0.276346i
$917$	4.99633	+	3.63004i	0.164993	+	0.119875i
$918$	1.34152	−	0.974668i	0.0442766	−	0.0321688i
$919$	0.305070	−	0.938909i	0.0100633	−	0.0309718i	−0.945899	−	0.324462i	$-0.894817\pi$
$919$	0.305070	−	0.938909i	0.0100633	−	0.0309718i	0.955962	+	0.293490i	$0.0948168\pi$
$920$	1.82088	−	1.32294i	0.0600325	−	0.0436162i
$921$	−0.133533	−	0.410971i	−0.00440005	−	0.0135419i
$922$	12.0999	+	37.2395i	0.398488	+	1.22642i
$923$	−0.235274	+	0.724098i	−0.00774413	+	0.0238340i
$924$	−0.115398			−0.00379632
$925$	−37.2251			−1.22395
$926$	6.47510	−	19.9283i	0.212785	−	0.654885i
$927$	−31.8260	−	23.1229i	−1.04530	−	0.759457i
$928$	−6.68139	+	4.85431i	−0.219327	+	0.159351i
$929$	26.0372			0.854251			0.427126	−	0.904192i	$-0.359526\pi$
$929$	26.0372			0.854251			0.427126	+	0.904192i	$0.359526\pi$
$930$	0.976738	+	0.213919i	0.0320285	+	0.00701469i
$931$	26.9559			0.883443
$932$	11.0498	−	8.02817i	0.361949	−	0.262971i
$933$	1.65491	+	1.20236i	0.0541793	+	0.0393636i
$934$	−9.84473	+	30.2990i	−0.322129	+	0.991412i
$935$	−21.1205			−0.690713
$936$	−2.99626			−0.0979357
$937$	−5.31523	+	16.3586i	−0.173641	+	0.534412i	−0.999569	−	0.0293637i	$-0.990652\pi$
$937$	−5.31523	+	16.3586i	−0.173641	+	0.534412i	0.825928	+	0.563776i	$0.190652\pi$
$938$	2.92554	+	9.00390i	0.0955224	+	0.293988i
$939$	0.113764	+	0.350130i	0.00371255	+	0.0114261i
$940$	22.6098	−	16.4270i	0.737451	−	0.535789i
$941$	−10.2572	+	31.5683i	−0.334374	+	1.02910i	0.632655	+	0.774434i	$0.281965\pi$
$941$	−10.2572	+	31.5683i	−0.334374	+	1.02910i	−0.967029	+	0.254665i	$0.918035\pi$
$942$	−0.507769	+	0.368916i	−0.0165440	+	0.0120199i
$943$	−5.19156	−	3.77189i	−0.169060	−	0.122830i
$944$	−3.44578	−	10.6050i	−0.112151	−	0.345164i
$945$	−1.03199	−	0.749784i	−0.0335706	−	0.0243905i
$946$	−4.20892	−	3.05796i	−0.136844	−	0.0994228i
$947$	2.35802	+	7.25723i	0.0766253	+	0.235828i	0.982031	−	0.188719i	$-0.0604334\pi$
$947$	2.35802	+	7.25723i	0.0766253	+	0.235828i	−0.905406	+	0.424547i	$0.860433\pi$
$948$	0.523560	+	0.380388i	0.0170044	+	0.0123544i
$949$	−0.222882	+	0.161933i	−0.00723505	+	0.00525657i
$950$	−5.37977	+	16.5572i	−0.174543	+	0.537188i
$951$	−0.659035	+	0.478817i	−0.0213707	+	0.0155267i
$952$	−1.65445	−	5.09187i	−0.0536210	−	0.165029i
$953$	−1.23253	−	3.79334i	−0.0399256	−	0.122878i	0.929107	−	0.369811i	$-0.120577\pi$
$953$	−1.23253	−	3.79334i	−0.0399256	−	0.122878i	−0.969033	+	0.246932i	$0.920577\pi$
$954$	10.3578	−	31.8782i	0.335348	−	1.03209i
$955$	−12.6620			−0.409731
$956$	−22.4770			−0.726958
$957$	−0.248613	+	0.765152i	−0.00803652	+	0.0247339i
$958$	16.0656	+	11.6723i	0.519055	+	0.377116i
$959$	−4.72848	+	3.43544i	−0.152691	+	0.110936i
$960$	−0.179585			−0.00579610
$961$	28.1622	+	12.9573i	0.908457	+	0.417979i
$962$	−10.2984			−0.332034
$963$	−1.10385	+	0.801997i	−0.0355712	+	0.0258440i
$964$	−9.30649	−	6.76156i	−0.299742	−	0.217775i
$965$	−6.16235	+	18.9658i	−0.198373	+	0.610530i
$966$	0.0555806			0.00178828
$967$	15.2505			0.490422			0.245211	−	0.969470i	$-0.421143\pi$
$967$	15.2505			0.490422			0.245211	+	0.969470i	$0.421143\pi$
$968$	−2.61586	+	8.05080i	−0.0840770	+	0.258762i
$969$	−0.411583	−	1.26672i	−0.0132219	−	0.0406930i
$970$	−11.1325	−	34.2623i	−0.357443	−	1.10010i
$971$	−33.6458	+	24.4451i	−1.07975	+	0.784481i	−0.977639	−	0.210292i	$-0.932558\pi$
$971$	−33.6458	+	24.4451i	−1.07975	+	0.784481i	−0.102107	+	0.994773i	$0.532558\pi$
$972$	−0.509655	+	1.56856i	−0.0163472	+	0.0503114i
$973$	15.2733	−	11.0967i	0.489639	−	0.355744i
$974$	−23.9967	−	17.4346i	−0.768903	−	0.558641i
$975$	−0.0683439	−	0.210341i	−0.00218876	−	0.00673630i
$976$	−8.99598	−	6.53596i	−0.287954	−	0.209211i
$977$	18.0722	+	13.1302i	0.578181	+	0.420073i	0.838068	−	0.545566i	$-0.183685\pi$
$977$	18.0722	+	13.1302i	0.578181	+	0.420073i	−0.259887	+	0.965639i	$0.583685\pi$
$978$	−0.341787	−	1.05191i	−0.0109291	−	0.0336364i
$979$	−8.29642	−	6.02770i	−0.265155	−	0.192646i
$980$	13.2896	−	9.65548i	0.424521	−	0.308433i
$981$	−2.24874	+	6.92091i	−0.0717967	+	0.220968i
$982$	−3.40710	+	2.47540i	−0.108725	+	0.0789932i
$983$	2.70096	+	8.31271i	0.0861474	+	0.265134i	0.984846	−	0.173433i	$-0.0554860\pi$
$983$	2.70096	+	8.31271i	0.0861474	+	0.265134i	−0.898698	+	0.438567i	$0.855486\pi$
$984$	0.158223	+	0.486962i	0.00504398	+	0.0155238i
$985$	−3.43225	+	10.5634i	−0.109361	+	0.336577i
$986$	−37.3263			−1.18871
$987$	0.690144			0.0219675
$988$	−1.48833	+	4.58061i	−0.0473501	+	0.145729i
$989$	2.02719	+	1.47284i	0.0644610	+	0.0468336i
$990$	11.3275	−	8.22992i	0.360012	−	0.261564i
$991$	−21.8666			−0.694614			−0.347307	−	0.937751i	$-0.612904\pi$
$991$	−21.8666			−0.694614			−0.347307	+	0.937751i	$0.612904\pi$
$992$	−5.43885	−	1.19118i	−0.172684	−	0.0378201i
$993$	0.329082			0.0104431
$994$	0.729651	−	0.530122i	0.0231431	−	0.0168145i
$995$	62.6304	+	45.5037i	1.98552	+	1.44256i
$996$	0.250770	−	0.771790i	0.00794594	−	0.0244551i
$997$	27.2290			0.862351			0.431175	−	0.902268i	$-0.358099\pi$
$997$	27.2290			0.862351			0.431175	+	0.902268i	$0.358099\pi$
$998$	18.6707			0.591012
$999$	−1.16758	+	3.59344i	−0.0369405	+	0.113691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	806.2.k.b.729.3	yes	20
31.2	even	5	inner	806.2.k.b.157.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
806.2.k.b.157.3	✓	20	31.2	even	5	inner
806.2.k.b.729.3	yes	20	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:	\( N \)	\(=\)	\( 806 = 2 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	806.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.0495006 + 0.0359643i) q^{3} +(0.309017 - 0.951057i) q^{4} +2.93507 q^{5} -0.0611861 q^{6} +(0.366057 - 1.12661i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.925894 - 2.84961i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.0495006 + 0.0359643i) q^{3} +(0.309017 - 0.951057i) q^{4} +2.93507 q^{5} -0.0611861 q^{6} +(0.366057 - 1.12661i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.925894 - 2.84961i) q^{9} +(-2.37452 + 1.72519i) q^{10} +(0.491996 - 1.51421i) q^{11} +(0.0495006 - 0.0359643i) q^{12} +(-0.809017 - 0.587785i) q^{13} +(0.366057 + 1.12661i) q^{14} +(0.145288 + 0.105558i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.39665 - 4.29845i) q^{17} +(2.42402 + 1.76116i) q^{18} +(3.89650 - 2.83097i) q^{19} +(0.906987 - 2.79142i) q^{20} +(0.0586376 - 0.0426027i) q^{21} +(0.491996 + 1.51421i) q^{22} +(-0.236966 - 0.729307i) q^{23} +(-0.0189075 + 0.0581914i) q^{24} +3.61464 q^{25} +1.00000 q^{26} +(0.113374 - 0.348931i) q^{27} +(-0.958349 - 0.696281i) q^{28} +(-6.68139 + 4.85431i) q^{29} -0.179585 q^{30} +(-5.43885 - 1.19118i) q^{31} +1.00000 q^{32} +(0.0788116 - 0.0572600i) q^{33} +(3.65648 + 2.65659i) q^{34} +(1.07440 - 3.30667i) q^{35} -2.99626 q^{36} -10.2984 q^{37} +(-1.48833 + 4.58061i) q^{38} +(-0.0189075 - 0.0581914i) q^{39} +(0.906987 + 2.79142i) q^{40} +(6.77007 - 4.91875i) q^{41} +(-0.0223976 + 0.0689327i) q^{42} +(-2.64357 + 1.92067i) q^{43} +(-1.28806 - 0.935833i) q^{44} +(-2.71756 - 8.36380i) q^{45} +(0.620386 + 0.450737i) q^{46} +(7.70333 + 5.59679i) q^{47} +(-0.0189075 - 0.0581914i) q^{48} +(4.52787 + 3.28969i) q^{49} +(-2.92430 + 2.12463i) q^{50} +(0.0854556 - 0.263005i) q^{51} +(-0.809017 + 0.587785i) q^{52} +(-3.45693 - 10.6393i) q^{53} +(0.113374 + 0.348931i) q^{54} +(1.44404 - 4.44431i) q^{55} +1.18458 q^{56} +0.294693 q^{57} +(2.55206 - 7.85445i) q^{58} +(9.02117 + 6.55426i) q^{59} +(0.145288 - 0.105558i) q^{60} +11.1196 q^{61} +(5.10028 - 2.23319i) q^{62} -3.54932 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-2.37452 - 1.72519i) q^{65} +(-0.0301033 + 0.0926486i) q^{66} +7.99205 q^{67} -4.51965 q^{68} +(0.0144990 - 0.0446235i) q^{69} +(1.07440 + 3.30667i) q^{70} +(-0.235274 - 0.724098i) q^{71} +(2.42402 - 1.76116i) q^{72} +(0.0851332 - 0.262013i) q^{73} +(8.33160 - 6.05326i) q^{74} +(0.178927 + 0.129998i) q^{75} +(-1.48833 - 4.58061i) q^{76} +(-1.52582 - 1.10857i) q^{77} +(0.0495006 + 0.0359643i) q^{78} +(3.26842 + 10.0592i) q^{79} +(-2.37452 - 1.72519i) q^{80} +(-7.25391 + 5.27027i) q^{81} +(-2.58594 + 7.95870i) q^{82} +(10.7299 - 7.79576i) q^{83} +(-0.0223976 - 0.0689327i) q^{84} +(-4.09927 - 12.6162i) q^{85} +(1.00975 - 3.10770i) q^{86} -0.505315 q^{87} +1.59213 q^{88} +(1.99038 - 6.12576i) q^{89} +(7.11468 + 5.16911i) q^{90} +(-0.958349 + 0.696281i) q^{91} -0.766839 q^{92} +(-0.226386 - 0.254569i) q^{93} -9.52184 q^{94} +(11.4365 - 8.30910i) q^{95} +(0.0495006 + 0.0359643i) q^{96} +(-3.79293 + 11.6734i) q^{97} -5.59676 q^{98} -4.77044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{2} - q^{3} - 5 q^{4} - 4 q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 5 * q^2 - q^3 - 5 * q^4 - 4 * q^5 + 4 * q^6 - 5 * q^7 - 5 * q^8 - 2 * q^9	\( 20 q - 5 q^{2} - q^{3} - 5 q^{4} - 4 q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{8} - 2 q^{9} + q^{10} + 5 q^{11} - q^{12} - 5 q^{13} - 5 q^{14} - 7 q^{15} - 5 q^{16} - 13 q^{17} - 2 q^{18} + 12 q^{19} + q^{20} - 2 q^{21} + 5 q^{22} + 9 q^{23} - q^{24} - 8 q^{25} + 20 q^{26} - 7 q^{27} + 10 q^{28} - 8 q^{29} + 28 q^{30} - 38 q^{31} + 20 q^{32} - 4 q^{33} + 17 q^{34} + 28 q^{35} + 8 q^{36} - 44 q^{37} + 12 q^{38} - q^{39} + q^{40} - 2 q^{41} + 23 q^{42} + 18 q^{43} + 26 q^{45} - 6 q^{46} + 15 q^{47} - q^{48} + 6 q^{49} + 12 q^{50} + 7 q^{51} - 5 q^{52} + 2 q^{53} - 7 q^{54} + 15 q^{55} - 10 q^{56} - 46 q^{57} + 2 q^{58} - 6 q^{59} - 7 q^{60} + 22 q^{61} + 27 q^{62} - 30 q^{63} - 5 q^{64} + q^{65} + 16 q^{66} - 44 q^{67} - 8 q^{68} - 19 q^{69} + 28 q^{70} + 55 q^{71} - 2 q^{72} - q^{73} + 26 q^{74} + 19 q^{75} + 12 q^{76} - 12 q^{77} - q^{78} + 26 q^{79} + q^{80} + 35 q^{81} + 3 q^{82} - 29 q^{83} + 23 q^{84} - 10 q^{85} - 12 q^{86} - 94 q^{87} - 10 q^{88} + 26 q^{89} + 6 q^{90} + 10 q^{91} - 6 q^{92} - 7 q^{93} + 20 q^{94} + 27 q^{95} - q^{96} - 2 q^{97} - 14 q^{98} + 6 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - q^3 - 5 * q^4 - 4 * q^5 + 4 * q^6 - 5 * q^7 - 5 * q^8 - 2 * q^9 + q^10 + 5 * q^11 - q^12 - 5 * q^13 - 5 * q^14 - 7 * q^15 - 5 * q^16 - 13 * q^17 - 2 * q^18 + 12 * q^19 + q^20 - 2 * q^21 + 5 * q^22 + 9 * q^23 - q^24 - 8 * q^25 + 20 * q^26 - 7 * q^27 + 10 * q^28 - 8 * q^29 + 28 * q^30 - 38 * q^31 + 20 * q^32 - 4 * q^33 + 17 * q^34 + 28 * q^35 + 8 * q^36 - 44 * q^37 + 12 * q^38 - q^39 + q^40 - 2 * q^41 + 23 * q^42 + 18 * q^43 + 26 * q^45 - 6 * q^46 + 15 * q^47 - q^48 + 6 * q^49 + 12 * q^50 + 7 * q^51 - 5 * q^52 + 2 * q^53 - 7 * q^54 + 15 * q^55 - 10 * q^56 - 46 * q^57 + 2 * q^58 - 6 * q^59 - 7 * q^60 + 22 * q^61 + 27 * q^62 - 30 * q^63 - 5 * q^64 + q^65 + 16 * q^66 - 44 * q^67 - 8 * q^68 - 19 * q^69 + 28 * q^70 + 55 * q^71 - 2 * q^72 - q^73 + 26 * q^74 + 19 * q^75 + 12 * q^76 - 12 * q^77 - q^78 + 26 * q^79 + q^80 + 35 * q^81 + 3 * q^82 - 29 * q^83 + 23 * q^84 - 10 * q^85 - 12 * q^86 - 94 * q^87 - 10 * q^88 + 26 * q^89 + 6 * q^90 + 10 * q^91 - 6 * q^92 - 7 * q^93 + 20 * q^94 + 27 * q^95 - q^96 - 2 * q^97 - 14 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more