LMFDB - Embedded newform 240.2.y.e.163.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(163,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("240.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.y (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.7
Root			$-1.20803 - 0.735291i$ of defining polynomial
Character	$\chi$	$=$	240.163
Dual form			240.2.y.e.187.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11192 - 0.873858i) q^{2} +1.00000 q^{3} +(0.472743 - 1.94333i) q^{4} +(-1.61356 - 1.54804i) q^{5} +(1.11192 - 0.873858i) q^{6} +(0.143894 - 0.143894i) q^{7} +(-1.17254 - 2.57394i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.11192 - 0.873858i) q^{2} +1.00000 q^{3} +(0.472743 - 1.94333i) q^{4} +(-1.61356 - 1.54804i) q^{5} +(1.11192 - 0.873858i) q^{6} +(0.143894 - 0.143894i) q^{7} +(-1.17254 - 2.57394i) q^{8} +1.00000 q^{9} +(-3.14692 - 0.311271i) q^{10} +(0.749545 + 0.749545i) q^{11} +(0.472743 - 1.94333i) q^{12} +3.29132i q^{13} +(0.0342559 - 0.285741i) q^{14} +(-1.61356 - 1.54804i) q^{15} +(-3.55303 - 1.83739i) q^{16} +(1.35709 - 1.35709i) q^{17} +(1.11192 - 0.873858i) q^{18} +(4.25468 + 4.25468i) q^{19} +(-3.77114 + 2.40385i) q^{20} +(0.143894 - 0.143894i) q^{21} +(1.48843 + 0.178440i) q^{22} +(0.837388 + 0.837388i) q^{23} +(-1.17254 - 2.57394i) q^{24} +(0.207170 + 4.99571i) q^{25} +(2.87614 + 3.65969i) q^{26} +1.00000 q^{27} +(-0.211607 - 0.347657i) q^{28} +(-2.77462 + 2.77462i) q^{29} +(-3.14692 - 0.311271i) q^{30} -6.60915i q^{31} +(-5.55631 + 1.06181i) q^{32} +(0.749545 + 0.749545i) q^{33} +(0.323074 - 2.69488i) q^{34} +(-0.454934 + 0.00942893i) q^{35} +(0.472743 - 1.94333i) q^{36} +10.0194i q^{37} +(8.44886 + 1.01289i) q^{38} +3.29132i q^{39} +(-2.09259 + 5.96834i) q^{40} -1.72608i q^{41} +(0.0342559 - 0.285741i) q^{42} -4.17171i q^{43} +(1.81095 - 1.10227i) q^{44} +(-1.61356 - 1.54804i) q^{45} +(1.66287 + 0.199352i) q^{46} +(-8.54502 - 8.54502i) q^{47} +(-3.55303 - 1.83739i) q^{48} +6.95859i q^{49} +(4.59590 + 5.37380i) q^{50} +(1.35709 - 1.35709i) q^{51} +(6.39610 + 1.55595i) q^{52} -5.05524 q^{53} +(1.11192 - 0.873858i) q^{54} +(-0.0491155 - 2.36976i) q^{55} +(-0.539094 - 0.201653i) q^{56} +(4.25468 + 4.25468i) q^{57} +(-0.660538 + 5.50979i) q^{58} +(3.08237 - 3.08237i) q^{59} +(-3.77114 + 2.40385i) q^{60} +(-5.00346 - 5.00346i) q^{61} +(-5.77546 - 7.34887i) q^{62} +(0.143894 - 0.143894i) q^{63} +(-5.25031 + 6.03608i) q^{64} +(5.09507 - 5.31074i) q^{65} +(1.48843 + 0.178440i) q^{66} +4.26739i q^{67} +(-1.99571 - 3.27881i) q^{68} +(0.837388 + 0.837388i) q^{69} +(-0.497612 + 0.408032i) q^{70} +13.2111 q^{71} +(-1.17254 - 2.57394i) q^{72} +(-11.6889 + 11.6889i) q^{73} +(8.75550 + 11.1407i) q^{74} +(0.207170 + 4.99571i) q^{75} +(10.2796 - 6.25686i) q^{76} +0.215710 q^{77} +(2.87614 + 3.65969i) q^{78} +9.95558 q^{79} +(2.88869 + 8.46496i) q^{80} +1.00000 q^{81} +(-1.50835 - 1.91927i) q^{82} -10.0134 q^{83} +(-0.211607 - 0.347657i) q^{84} +(-4.29056 + 0.0889259i) q^{85} +(-3.64549 - 4.63862i) q^{86} +(-2.77462 + 2.77462i) q^{87} +(1.05041 - 2.80815i) q^{88} +5.76005 q^{89} +(-3.14692 - 0.311271i) q^{90} +(0.473599 + 0.473599i) q^{91} +(2.02319 - 1.23145i) q^{92} -6.60915i q^{93} +(-16.9685 - 2.03426i) q^{94} +(-0.278797 - 13.4516i) q^{95} +(-5.55631 + 1.06181i) q^{96} +(11.7668 - 11.7668i) q^{97} +(6.08082 + 7.73741i) q^{98} +(0.749545 + 0.749545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9	$ 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9} - 14 q^{10} - 8 q^{12} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} - 12 q^{20} - 4 q^{21} - 8 q^{22} - 4 q^{24} + 32 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{28} + 12 q^{29} - 14 q^{30} - 28 q^{32} - 20 q^{35} - 8 q^{36} - 16 q^{38} - 44 q^{40} - 4 q^{42} + 52 q^{44} - 4 q^{45} - 16 q^{46} - 32 q^{47} - 8 q^{48} + 22 q^{50} - 8 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} - 4 q^{55} + 20 q^{56} + 8 q^{57} - 44 q^{58} - 24 q^{59} - 12 q^{60} + 40 q^{61} + 40 q^{62} - 4 q^{63} - 8 q^{64} - 4 q^{65} - 8 q^{66} + 24 q^{68} + 56 q^{70} - 4 q^{72} + 8 q^{73} + 64 q^{74} + 32 q^{75} + 16 q^{76} - 72 q^{77} + 20 q^{78} - 48 q^{79} + 16 q^{80} + 16 q^{81} + 8 q^{82} - 8 q^{83} + 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} - 16 q^{88} - 14 q^{90} - 40 q^{91} - 20 q^{94} + 8 q^{95} - 28 q^{96} + 48 q^{97} + 30 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9 - 14 * q^10 - 8 * q^12 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 8 * q^17 + 2 * q^18 + 8 * q^19 - 12 * q^20 - 4 * q^21 - 8 * q^22 - 4 * q^24 + 32 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^28 + 12 * q^29 - 14 * q^30 - 28 * q^32 - 20 * q^35 - 8 * q^36 - 16 * q^38 - 44 * q^40 - 4 * q^42 + 52 * q^44 - 4 * q^45 - 16 * q^46 - 32 * q^47 - 8 * q^48 + 22 * q^50 - 8 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 - 4 * q^55 + 20 * q^56 + 8 * q^57 - 44 * q^58 - 24 * q^59 - 12 * q^60 + 40 * q^61 + 40 * q^62 - 4 * q^63 - 8 * q^64 - 4 * q^65 - 8 * q^66 + 24 * q^68 + 56 * q^70 - 4 * q^72 + 8 * q^73 + 64 * q^74 + 32 * q^75 + 16 * q^76 - 72 * q^77 + 20 * q^78 - 48 * q^79 + 16 * q^80 + 16 * q^81 + 8 * q^82 - 8 * q^83 + 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 - 16 * q^88 - 14 * q^90 - 40 * q^91 - 20 * q^94 + 8 * q^95 - 28 * q^96 + 48 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.11192	−	0.873858i	0.786248	−	0.617911i
$2$	1.11192	−	0.873858i	0.786248	−	0.617911i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.472743	−	1.94333i	0.236372	−	0.971663i
$5$	−1.61356	−	1.54804i	−0.721607	−	0.692303i
$5$	−1.61356	−	1.54804i	−0.721607	−	0.692303i
$6$	1.11192	−	0.873858i	0.453940	−	0.356751i
$7$	0.143894	−	0.143894i	0.0543867	−	0.0543867i	−0.679390	−	0.733777i	$-0.737756\pi$
$7$	0.143894	−	0.143894i	0.0543867	−	0.0543867i	0.733777	+	0.679390i	$0.237756\pi$
$8$	−1.17254	−	2.57394i	−0.414554	−	0.910024i
$9$	1.00000			0.333333
$10$	−3.14692	−	0.311271i	−0.995144	−	0.0984324i
$11$	0.749545	+	0.749545i	0.225996	+	0.225996i	0.811018	−	0.585021i	$-0.198914\pi$
$11$	0.749545	+	0.749545i	0.225996	+	0.225996i	−0.585021	+	0.811018i	$0.698914\pi$
$12$	0.472743	−	1.94333i	0.136469	−	0.560990i
$13$			3.29132i			0.912847i	0.889763	+	0.456423i	$0.150870\pi$
$13$			3.29132i			0.912847i	−0.889763	+	0.456423i	$0.849130\pi$
$14$	0.0342559	−	0.285741i	0.00915528	−	0.0763676i
$15$	−1.61356	−	1.54804i	−0.416620	−	0.399701i
$16$	−3.55303	−	1.83739i	−0.888257	−	0.459347i
$17$	1.35709	−	1.35709i	0.329142	−	0.329142i	−0.523118	−	0.852260i	$-0.675231\pi$
$17$	1.35709	−	1.35709i	0.329142	−	0.329142i	0.852260	+	0.523118i	$0.175231\pi$
$18$	1.11192	−	0.873858i	0.262083	−	0.205970i
$19$	4.25468	+	4.25468i	0.976091	+	0.976091i	0.999721	−	0.0236300i	$-0.00752237\pi$
$19$	4.25468	+	4.25468i	0.976091	+	0.976091i	−0.0236300	+	0.999721i	$0.507522\pi$
$20$	−3.77114	+	2.40385i	−0.843252	+	0.537518i
$21$	0.143894	−	0.143894i	0.0314002	−	0.0314002i
$22$	1.48843	+	0.178440i	0.317335	+	0.0380435i
$23$	0.837388	+	0.837388i	0.174608	+	0.174608i	0.789000	−	0.614393i	$-0.210599\pi$
$23$	0.837388	+	0.837388i	0.174608	+	0.174608i	−0.614393	+	0.789000i	$0.710599\pi$
$24$	−1.17254	−	2.57394i	−0.239343	−	0.525403i
$25$	0.207170	+	4.99571i	0.0414341	+	0.999141i
$26$	2.87614	+	3.65969i	0.564058	+	0.717724i
$27$	1.00000			0.192450
$28$	−0.211607	−	0.347657i	−0.0399900	−	0.0657010i
$29$	−2.77462	+	2.77462i	−0.515234	+	0.515234i	−0.916126	−	0.400891i	$-0.868701\pi$
$29$	−2.77462	+	2.77462i	−0.515234	+	0.515234i	0.400891	+	0.916126i	$0.368701\pi$
$30$	−3.14692	−	0.311271i	−0.574547	−	0.0568300i
$31$		−	6.60915i		−	1.18704i	−0.804820	−	0.593520i	$-0.797738\pi$
$31$		−	6.60915i		−	1.18704i	0.804820	−	0.593520i	$-0.202262\pi$
$32$	−5.55631	+	1.06181i	−0.982226	+	0.187703i
$33$	0.749545	+	0.749545i	0.130479	+	0.130479i
$34$	0.323074	−	2.69488i	0.0554067	−	0.462167i
$35$	−0.454934	+	0.00942893i	−0.0768979	+	0.00159378i
$36$	0.472743	−	1.94333i	0.0787906	−	0.323888i
$37$			10.0194i			1.64717i	0.567191	+	0.823586i	$0.308030\pi$
$37$			10.0194i			1.64717i	−0.567191	+	0.823586i	$0.691970\pi$
$38$	8.44886	+	1.01289i	1.37059	+	0.164312i
$39$			3.29132i			0.527032i
$40$	−2.09259	+	5.96834i	−0.330867	+	0.943677i
$41$		−	1.72608i		−	0.269569i	−0.990875	−	0.134784i	$-0.956966\pi$
$41$		−	1.72608i		−	0.269569i	0.990875	−	0.134784i	$-0.0430342\pi$
$42$	0.0342559	−	0.285741i	0.00528580	−	0.0440908i
$43$		−	4.17171i		−	0.636180i	−0.948061	−	0.318090i	$-0.896959\pi$
$43$		−	4.17171i		−	0.636180i	0.948061	−	0.318090i	$-0.103041\pi$
$44$	1.81095	−	1.10227i	0.273011	−	0.166173i
$45$	−1.61356	−	1.54804i	−0.240536	−	0.230768i
$46$	1.66287	+	0.199352i	0.245177	+	0.0293929i
$47$	−8.54502	−	8.54502i	−1.24642	−	1.24642i	−0.957290	−	0.289128i	$-0.906635\pi$
$47$	−8.54502	−	8.54502i	−1.24642	−	1.24642i	−0.289128	−	0.957290i	$-0.593365\pi$
$48$	−3.55303	−	1.83739i	−0.512835	−	0.265204i
$49$			6.95859i			0.994084i
$50$	4.59590	+	5.37380i	0.649958	+	0.759970i
$51$	1.35709	−	1.35709i	0.190030	−	0.190030i
$52$	6.39610	+	1.55595i	0.886979	+	0.215771i
$53$	−5.05524			−0.694391			−0.347196	−	0.937793i	$-0.612866\pi$
$53$	−5.05524			−0.694391			−0.347196	+	0.937793i	$0.612866\pi$
$54$	1.11192	−	0.873858i	0.151313	−	0.118917i
$55$	−0.0491155	−	2.36976i	−0.00662273	−	0.319538i
$56$	−0.539094	−	0.201653i	−0.0720395	−	0.0269470i
$57$	4.25468	+	4.25468i	0.563546	+	0.563546i
$58$	−0.660538	+	5.50979i	−0.0867329	+	0.723471i
$59$	3.08237	−	3.08237i	0.401290	−	0.401290i	−0.477398	−	0.878687i	$-0.658420\pi$
$59$	3.08237	−	3.08237i	0.401290	−	0.401290i	0.878687	+	0.477398i	$0.158420\pi$
$60$	−3.77114	+	2.40385i	−0.486852	+	0.310336i
$61$	−5.00346	−	5.00346i	−0.640627	−	0.640627i	0.310083	−	0.950710i	$-0.399643\pi$
$61$	−5.00346	−	5.00346i	−0.640627	−	0.640627i	−0.950710	+	0.310083i	$0.899643\pi$
$62$	−5.77546	−	7.34887i	−0.733485	−	0.933307i
$63$	0.143894	−	0.143894i	0.0181289	−	0.0181289i
$64$	−5.25031	+	6.03608i	−0.656289	+	0.754509i
$65$	5.09507	−	5.31074i	0.631966	−	0.658717i
$66$	1.48843	+	0.178440i	0.183213	+	0.0219644i
$67$			4.26739i			0.521345i	0.965427	+	0.260672i	$0.0839442\pi$
$67$			4.26739i			0.521345i	−0.965427	+	0.260672i	$0.916056\pi$
$68$	−1.99571	−	3.27881i	−0.242015	−	0.397614i
$69$	0.837388	+	0.837388i	0.100810	+	0.100810i
$70$	−0.497612	+	0.408032i	−0.0594760	+	0.0487692i
$71$	13.2111			1.56786			0.783932	−	0.620846i	$-0.213211\pi$
$71$	13.2111			1.56786			0.783932	+	0.620846i	$0.213211\pi$
$72$	−1.17254	−	2.57394i	−0.138185	−	0.303341i
$73$	−11.6889	+	11.6889i	−1.36808	+	1.36808i	−0.504904	+	0.863175i	$0.668472\pi$
$73$	−11.6889	+	11.6889i	−1.36808	+	1.36808i	−0.863175	+	0.504904i	$0.831528\pi$
$74$	8.75550	+	11.1407i	1.01781	+	1.29509i
$75$	0.207170	+	4.99571i	0.0239220	+	0.576854i
$76$	10.2796	−	6.25686i	1.17915	−	0.717711i
$77$	0.215710			0.0245824
$78$	2.87614	+	3.65969i	0.325659	+	0.414378i
$79$	9.95558			1.12009			0.560045	−	0.828462i	$-0.310784\pi$
$79$	9.95558			1.12009			0.560045	+	0.828462i	$0.310784\pi$
$80$	2.88869	+	8.46496i	0.322965	+	0.946411i
$81$	1.00000			0.111111
$82$	−1.50835	−	1.91927i	−0.166570	−	0.211948i
$83$	−10.0134			−1.09912			−0.549559	−	0.835455i	$-0.685204\pi$
$83$	−10.0134			−1.09912			−0.549559	+	0.835455i	$0.685204\pi$
$84$	−0.211607	−	0.347657i	−0.0230883	−	0.0379325i
$85$	−4.29056	+	0.0889259i	−0.465377	+	0.00964537i
$86$	−3.64549	−	4.63862i	−0.393103	−	0.500195i
$87$	−2.77462	+	2.77462i	−0.297471	+	0.297471i
$88$	1.05041	−	2.80815i	0.111974	−	0.299350i
$89$	5.76005			0.610564			0.305282	−	0.952262i	$-0.401249\pi$
$89$	5.76005			0.610564			0.305282	+	0.952262i	$0.401249\pi$
$90$	−3.14692	−	0.311271i	−0.331715	−	0.0328108i
$91$	0.473599	+	0.473599i	0.0496467	+	0.0496467i
$92$	2.02319	−	1.23145i	0.210932	−	0.128387i
$93$		−	6.60915i		−	0.685337i
$94$	−16.9685	−	2.03426i	−1.75017	−	0.209818i
$95$	−0.278797	−	13.4516i	−0.0286040	−	1.38010i
$96$	−5.55631	+	1.06181i	−0.567088	+	0.108370i
$97$	11.7668	−	11.7668i	1.19474	−	1.19474i	0.219021	−	0.975720i	$-0.429714\pi$
$97$	11.7668	−	11.7668i	1.19474	−	1.19474i	0.975720	−	0.219021i	$-0.0702865\pi$
$98$	6.08082	+	7.73741i	0.614256	+	0.781597i
$99$	0.749545	+	0.749545i	0.0753321	+	0.0753321i
$100$	9.80622	+	1.95909i	0.980622	+	0.195909i
$101$	−1.29314	+	1.29314i	−0.128672	+	0.128672i	−0.768510	−	0.639838i	$-0.779002\pi$
$101$	−1.29314	+	1.29314i	−0.128672	+	0.128672i	0.639838	+	0.768510i	$0.279002\pi$
$102$	0.323074	−	2.69488i	0.0319890	−	0.266832i
$103$	−11.2892	−	11.2892i	−1.11236	−	1.11236i	−0.992830	−	0.119532i	$-0.961861\pi$
$103$	−11.2892	−	11.2892i	−1.11236	−	1.11236i	−0.119532	−	0.992830i	$-0.538139\pi$
$104$	8.47164	−	3.85919i	0.830713	−	0.378425i
$105$	−0.454934	+	0.00942893i	−0.0443970	+	0.000920169i
$106$	−5.62104	+	4.41757i	−0.545964	+	0.429072i
$107$	1.39451			0.134812			0.0674060	−	0.997726i	$-0.478528\pi$
$107$	1.39451			0.134812			0.0674060	+	0.997726i	$0.478528\pi$
$108$	0.472743	−	1.94333i	0.0454897	−	0.186997i
$109$	−4.55325	+	4.55325i	−0.436123	+	0.436123i	−0.890705	−	0.454582i	$-0.849789\pi$
$109$	−4.55325	+	4.55325i	−0.436123	+	0.436123i	0.454582	+	0.890705i	$0.349789\pi$
$110$	−2.12545	−	2.59207i	−0.202653	−	0.247144i
$111$			10.0194i			0.950995i
$112$	−0.775647	+	0.246870i	−0.0732917	+	0.0233270i
$113$	−11.4501	−	11.4501i	−1.07714	−	1.07714i	−0.996765	−	0.0803726i	$-0.974389\pi$
$113$	−11.4501	−	11.4501i	−1.07714	−	1.07714i	−0.0803726	−	0.996765i	$-0.525611\pi$
$114$	8.44886	+	1.01289i	0.791309	+	0.0948656i
$115$	−0.0548716	−	2.64749i	−0.00511680	−	0.246879i
$116$	4.08031	+	6.70368i	0.378847	+	0.622421i
$117$			3.29132i			0.304282i
$118$	0.733801	−	6.12090i	0.0675519	−	0.563475i
$119$		−	0.390552i		−	0.0358018i
$120$	−2.09259	+	5.96834i	−0.191026	+	0.544832i
$121$		−	9.87636i		−	0.897851i
$122$	−9.93577	−	1.19114i	−0.899542	−	0.107841i
$123$		−	1.72608i		−	0.155636i
$124$	−12.8437	−	3.12443i	−1.15340	−	0.280582i
$125$	7.39925	−	8.38159i	0.661809	−	0.749672i
$126$	0.0342559	−	0.285741i	0.00305176	−	0.0254559i
$127$	−4.94562	−	4.94562i	−0.438853	−	0.438853i	0.452773	−	0.891626i	$-0.350435\pi$
$127$	−4.94562	−	4.94562i	−0.438853	−	0.438853i	−0.891626	+	0.452773i	$0.850435\pi$
$128$	−0.563267	+	11.2997i	−0.0497862	+	0.998760i
$129$		−	4.17171i		−	0.367299i
$130$	1.02449	−	10.3575i	0.0898537	−	0.908414i
$131$	−12.7313	+	12.7313i	−1.11234	+	1.11234i	−0.119509	+	0.992833i	$0.538132\pi$
$131$	−12.7313	+	12.7313i	−1.11234	+	1.11234i	−0.992833	+	0.119509i	$0.961868\pi$
$132$	1.81095	−	1.10227i	0.157623	−	0.0959401i
$133$	1.22444			0.106173
$134$	3.72909	+	4.74501i	0.322145	+	0.409906i
$135$	−1.61356	−	1.54804i	−0.138873	−	0.133234i
$136$	−5.08429	−	1.90182i	−0.435974	−	0.163080i
$137$	−6.06032	−	6.06032i	−0.517768	−	0.517768i	0.399127	−	0.916896i	$-0.369313\pi$
$137$	−6.06032	−	6.06032i	−0.517768	−	0.517768i	−0.916896	+	0.399127i	$0.869313\pi$
$138$	1.66287	+	0.199352i	0.141553	+	0.0169700i
$139$	10.3543	−	10.3543i	0.878239	−	0.878239i	−0.115114	−	0.993352i	$-0.536723\pi$
$139$	10.3543	−	10.3543i	0.878239	−	0.878239i	0.993352	+	0.115114i	$0.0367232\pi$
$140$	−0.196744	+	0.888542i	−0.0166279	+	0.0750955i
$141$	−8.54502	−	8.54502i	−0.719620	−	0.719620i
$142$	14.6897	−	11.5446i	1.23273	−	0.968801i
$143$	−2.46699	+	2.46699i	−0.206300	+	0.206300i
$144$	−3.55303	−	1.83739i	−0.296086	−	0.153116i
$145$	8.77224	−	0.181813i	0.728495	−	0.0150987i
$146$	−2.78270	+	23.2115i	−0.230298	+	1.92100i
$147$			6.95859i			0.573935i
$148$	19.4709	+	4.73658i	1.60050	+	0.389345i
$149$	0.485009	+	0.485009i	0.0397335	+	0.0397335i	0.726694	−	0.686961i	$-0.241056\pi$
$149$	0.485009	+	0.485009i	0.0397335	+	0.0397335i	−0.686961	+	0.726694i	$0.741056\pi$
$150$	4.59590	+	5.37380i	0.375253	+	0.438769i
$151$	6.47302			0.526767			0.263383	−	0.964691i	$-0.415162\pi$
$151$	6.47302			0.526767			0.263383	+	0.964691i	$0.415162\pi$
$152$	5.96251	−	15.9401i	0.483624	−	1.29291i
$153$	1.35709	−	1.35709i	0.109714	−	0.109714i
$154$	0.239852	−	0.188500i	0.0193278	−	0.0151897i
$155$	−10.2312	+	10.6643i	−0.821790	+	0.856576i
$156$	6.39610	+	1.55595i	0.512098	+	0.124575i
$157$	−11.7463			−0.937455			−0.468728	−	0.883343i	$-0.655287\pi$
$157$	−11.7463			−0.937455			−0.468728	+	0.883343i	$0.655287\pi$
$158$	11.0698	−	8.69977i	0.880669	−	0.692117i
$159$	−5.05524			−0.400907
$160$	10.6092	+	6.88807i	0.838729	+	0.544550i
$161$	0.240990			0.0189926
$162$	1.11192	−	0.873858i	0.0873609	−	0.0686568i
$163$	1.87143			0.146582			0.0732908	−	0.997311i	$-0.476650\pi$
$163$	1.87143			0.146582			0.0732908	+	0.997311i	$0.476650\pi$
$164$	−3.35434	−	0.815994i	−0.261930	−	0.0637184i
$165$	−0.0491155	−	2.36976i	−0.00382364	−	0.184486i
$166$	−11.1342	+	8.75033i	−0.864179	+	0.679157i
$167$	4.79897	−	4.79897i	0.371355	−	0.371355i	−0.496615	−	0.867971i	$-0.665424\pi$
$167$	4.79897	−	4.79897i	0.371355	−	0.371355i	0.867971	+	0.496615i	$0.165424\pi$
$168$	−0.539094	−	0.201653i	−0.0415920	−	0.0155578i
$169$	2.16724			0.166711
$170$	−4.69306	+	3.84822i	−0.359941	+	0.295145i
$171$	4.25468	+	4.25468i	0.325364	+	0.325364i
$172$	−8.10699	−	1.97215i	−0.618152	−	0.150375i
$173$			12.8446i			0.976560i	0.872687	+	0.488280i	$0.162375\pi$
$173$			12.8446i			0.976560i	−0.872687	+	0.488280i	$0.837625\pi$
$174$	−0.660538	+	5.50979i	−0.0500753	+	0.417696i
$175$	0.748661	+	0.689040i	0.0565934	+	0.0520865i
$176$	−1.28595	−	4.04036i	−0.0969320	−	0.304554i
$177$	3.08237	−	3.08237i	0.231685	−	0.231685i
$178$	6.40473	−	5.03346i	0.480054	−	0.377274i
$179$	−3.47791	−	3.47791i	−0.259951	−	0.259951i	0.565083	−	0.825034i	$-0.308844\pi$
$179$	−3.47791	−	3.47791i	−0.259951	−	0.259951i	−0.825034	+	0.565083i	$0.808844\pi$
$180$	−3.77114	+	2.40385i	−0.281084	+	0.179173i
$181$	16.3185	−	16.3185i	1.21295	−	1.21295i	0.242893	−	0.970053i	$-0.421903\pi$
$181$	16.3185	−	16.3185i	1.21295	−	1.21295i	0.970053	−	0.242893i	$-0.0780965\pi$
$182$	0.940464	+	0.112747i	0.0697119	+	0.00835737i
$183$	−5.00346	−	5.00346i	−0.369866	−	0.369866i
$184$	1.17352	−	3.13725i	0.0865128	−	0.231281i
$185$	15.5103	−	16.1669i	1.14034	−	1.18861i
$186$	−5.77546	−	7.34887i	−0.423478	−	0.538845i
$187$	2.03439			0.148770
$188$	−20.6453	+	12.5661i	−1.50572	+	0.916480i
$189$	0.143894	−	0.143894i	0.0104667	−	0.0104667i
$190$	−12.0648	−	14.7135i	−0.875272	−	1.06743i
$191$			21.5483i			1.55918i	0.626289	+	0.779591i	$0.284573\pi$
$191$			21.5483i			1.55918i	−0.626289	+	0.779591i	$0.715427\pi$
$192$	−5.25031	+	6.03608i	−0.378909	+	0.435616i
$193$	11.3161	+	11.3161i	0.814552	+	0.814552i	0.985313	−	0.170760i	$-0.0546224\pi$
$193$	11.3161	+	11.3161i	0.814552	+	0.814552i	−0.170760	+	0.985313i	$0.554622\pi$
$194$	2.80126	−	23.3664i	0.201119	−	1.67761i
$195$	5.09507	−	5.31074i	0.364866	−	0.380310i
$196$	13.5228	+	3.28963i	0.965915	+	0.234973i
$197$			23.3109i			1.66083i	0.557142	+	0.830417i	$0.311898\pi$
$197$			23.3109i			1.66083i	−0.557142	+	0.830417i	$0.688102\pi$
$198$	1.48843	+	0.178440i	0.105778	+	0.0126812i
$199$		−	2.14992i		−	0.152404i	−0.997092	−	0.0762018i	$-0.975721\pi$
$199$		−	2.14992i		−	0.152404i	0.997092	−	0.0762018i	$-0.0242793\pi$
$200$	12.6157	−	6.39089i	0.892066	−	0.451904i
$201$			4.26739i			0.300999i
$202$	−0.307850	+	2.56789i	−0.0216603	+	0.180676i
$203$			0.798501i			0.0560438i
$204$	−1.99571	−	3.27881i	−0.139727	−	0.229563i
$205$	−2.67204	+	2.78514i	−0.186623	+	0.194523i
$206$	−22.4180	−	2.68756i	−1.56193	−	0.187251i
$207$	0.837388	+	0.837388i	0.0582025	+	0.0582025i
$208$	6.04742	−	11.6941i	0.419313	−	0.810842i
$209$			6.37815i			0.441186i
$210$	−0.497612	+	0.408032i	−0.0343385	+	0.0281569i
$211$	6.27270	−	6.27270i	0.431830	−	0.431830i	−0.457420	−	0.889251i	$-0.651226\pi$
$211$	6.27270	−	6.27270i	0.431830	−	0.431830i	0.889251	+	0.457420i	$0.151226\pi$
$212$	−2.38983	+	9.82398i	−0.164134	+	0.674714i
$213$	13.2111			0.905207
$214$	1.55058	−	1.21860i	0.105996	−	0.0833019i
$215$	−6.45796	+	6.73132i	−0.440429	+	0.459072i
$216$	−1.17254	−	2.57394i	−0.0797810	−	0.175134i
$217$	−0.951015	−	0.951015i	−0.0645591	−	0.0645591i
$218$	−1.08397	+	9.04176i	−0.0734155	+	0.612385i
$219$	−11.6889	+	11.6889i	−0.789861	+	0.789861i
$220$	−4.62844	−	1.02484i	−0.312049	−	0.0690948i
$221$	4.46660	+	4.46660i	0.300456	+	0.300456i
$222$	8.75550	+	11.1407i	0.587631	+	0.747718i
$223$	−5.00009	+	5.00009i	−0.334831	+	0.334831i	−0.854418	−	0.519587i	$-0.826086\pi$
$223$	−5.00009	+	5.00009i	−0.334831	+	0.334831i	0.519587	+	0.854418i	$0.326086\pi$
$224$	−0.646730	+	0.952305i	−0.0432115	+	0.0636286i
$225$	0.207170	+	4.99571i	0.0138114	+	0.333047i
$226$	−22.7374	−	2.72587i	−1.51247	−	0.181322i
$227$			22.5630i			1.49756i	0.662821	+	0.748778i	$0.269359\pi$
$227$			22.5630i			1.49756i	−0.662821	+	0.748778i	$0.730641\pi$
$228$	10.2796	−	6.25686i	0.680783	−	0.414371i
$229$	−6.83720	−	6.83720i	−0.451815	−	0.451815i	0.444142	−	0.895957i	$-0.353509\pi$
$229$	−6.83720	−	6.83720i	−0.451815	−	0.451815i	−0.895957	+	0.444142i	$0.853509\pi$
$230$	−2.37454	−	2.89585i	−0.156573	−	0.190947i
$231$	0.215710			0.0141926
$232$	10.3951	+	3.88836i	0.682469	+	0.255283i
$233$	3.10894	−	3.10894i	0.203673	−	0.203673i	−0.597899	−	0.801572i	$-0.703997\pi$
$233$	3.10894	−	3.10894i	0.203673	−	0.203673i	0.801572	+	0.597899i	$0.203997\pi$
$234$	2.87614	+	3.65969i	0.188019	+	0.239241i
$235$	0.559930	+	27.0159i	0.0365258	+	1.76232i
$236$	−4.53287	−	7.44721i	−0.295065	−	0.484772i
$237$	9.95558			0.646685
$238$	−0.341287	−	0.434264i	−0.0221224	−	0.0281491i
$239$	11.0671			0.715873			0.357937	−	0.933746i	$-0.383480\pi$
$239$	11.0671			0.715873			0.357937	+	0.933746i	$0.383480\pi$
$240$	2.88869	+	8.46496i	0.186464	+	0.546411i
$241$	−23.4743			−1.51211			−0.756056	−	0.654507i	$-0.772876\pi$
$241$	−23.4743			−1.51211			−0.756056	+	0.654507i	$0.772876\pi$
$242$	−8.63054	−	10.9818i	−0.554792	−	0.705934i
$243$	1.00000			0.0641500
$244$	−12.0887	+	7.35799i	−0.773899	+	0.471047i
$245$	10.7721	−	11.2281i	0.688207	−	0.717338i
$246$	−1.50835	−	1.91927i	−0.0961690	−	0.122368i
$247$	−14.0035	+	14.0035i	−0.891021	+	0.891021i
$248$	−17.0116	+	7.74948i	−1.08023	+	0.492092i
$249$	−10.0134			−0.634576
$250$	0.903067	−	15.7856i	0.0571150	−	0.998368i
$251$	−1.76187	−	1.76187i	−0.111209	−	0.111209i	0.649313	−	0.760521i	$-0.275057\pi$
$251$	−1.76187	−	1.76187i	−0.111209	−	0.111209i	−0.760521	+	0.649313i	$0.775057\pi$
$252$	−0.211607	−	0.347657i	−0.0133300	−	0.0219003i
$253$			1.25532i			0.0789213i
$254$	−9.82092	−	1.17738i	−0.616219	−	0.0738751i
$255$	−4.29056	+	0.0889259i	−0.268685	+	0.00556875i
$256$	9.24801	+	13.0566i	0.578001	+	0.816036i
$257$	−4.05693	+	4.05693i	−0.253064	+	0.253064i	−0.822226	−	0.569162i	$-0.807268\pi$
$257$	−4.05693	+	4.05693i	−0.253064	+	0.253064i	0.569162	+	0.822226i	$0.307268\pi$
$258$	−3.64549	−	4.63862i	−0.226958	−	0.288788i
$259$	1.44172	+	1.44172i	0.0895842	+	0.0895842i
$260$	−7.91184	−	12.4120i	−0.490672	−	0.769760i
$261$	−2.77462	+	2.77462i	−0.171745	+	0.171745i
$262$	−3.03087	+	25.2816i	−0.187248	+	1.56190i
$263$	22.2576	+	22.2576i	1.37246	+	1.37246i	0.856784	+	0.515676i	$0.172459\pi$
$263$	22.2576	+	22.2576i	1.37246	+	1.37246i	0.515676	+	0.856784i	$0.327541\pi$
$264$	1.05041	−	2.80815i	0.0646485	−	0.172830i
$265$	8.15695	+	7.82570i	0.501078	+	0.480729i
$266$	1.36149	−	1.06999i	0.0834781	−	0.0656053i
$267$	5.76005			0.352509
$268$	8.29293	+	2.01738i	0.506571	+	0.123231i
$269$	−11.9600	+	11.9600i	−0.729217	+	0.729217i	−0.970464	−	0.241247i	$-0.922444\pi$
$269$	−11.9600	+	11.9600i	−0.729217	+	0.729217i	0.241247	+	0.970464i	$0.422444\pi$
$270$	−3.14692	−	0.311271i	−0.191516	−	0.0189433i
$271$			15.7162i			0.954691i	0.878716	+	0.477346i	$0.158401\pi$
$271$			15.7162i			0.954691i	−0.878716	+	0.477346i	$0.841599\pi$
$272$	−7.31526	+	2.32827i	−0.443553	+	0.141172i
$273$	0.473599	+	0.473599i	0.0286635	+	0.0286635i
$274$	−12.0345	−	1.44275i	−0.727029	−	0.0871595i
$275$	−3.58922	+	3.89979i	−0.216438	+	0.235166i
$276$	2.02319	−	1.23145i	0.121782	−	0.0741245i
$277$		−	4.59363i		−	0.276004i	−0.990432	−	0.138002i	$-0.955932\pi$
$277$		−	4.59363i		−	0.276004i	0.990432	−	0.138002i	$-0.0440681\pi$
$278$	2.46498	−	20.5613i	0.147840	−	1.23319i
$279$		−	6.60915i		−	0.395680i
$280$	0.557696	+	1.15992i	0.0333287	+	0.0693182i
$281$		−	20.5117i		−	1.22363i	−0.791002	−	0.611814i	$-0.790440\pi$
$281$		−	20.5117i		−	1.22363i	0.791002	−	0.611814i	$-0.209560\pi$
$282$	−16.9685	−	2.03426i	−1.01046	−	0.121139i
$283$		−	28.8990i		−	1.71787i	−0.512088	−	0.858933i	$-0.671128\pi$
$283$		−	28.8990i		−	1.71787i	0.512088	−	0.858933i	$-0.328872\pi$
$284$	6.24544	−	25.6734i	0.370599	−	1.52344i
$285$	−0.278797	−	13.4516i	−0.0165145	−	0.796804i
$286$	−0.587302	+	4.89890i	−0.0347279	+	0.289678i
$287$	−0.248372	−	0.248372i	−0.0146610	−	0.0146610i
$288$	−5.55631	+	1.06181i	−0.327409	+	0.0625677i
$289$			13.3166i			0.783332i
$290$	9.59517	−	7.86786i	0.563448	−	0.462017i
$291$	11.7668	−	11.7668i	0.689784	−	0.689784i
$292$	17.1895	+	28.2411i	1.00594	+	1.65269i
$293$	8.86723			0.518029			0.259014	−	0.965873i	$-0.416602\pi$
$293$	8.86723			0.518029			0.259014	+	0.965873i	$0.416602\pi$
$294$	6.08082	+	7.73741i	0.354641	+	0.451255i
$295$	−9.74521	+	0.201978i	−0.567388	+	0.0117596i
$296$	25.7892	−	11.7481i	1.49897	−	0.682843i
$297$	0.749545	+	0.749545i	0.0434930	+	0.0434930i
$298$	0.963122	+	0.115463i	0.0557921	+	0.00668861i
$299$	−2.75611	+	2.75611i	−0.159390	+	0.159390i
$300$	9.80622	+	1.95909i	0.566162	+	0.113108i
$301$	−0.600283	−	0.600283i	−0.0345997	−	0.0345997i
$302$	7.19749	−	5.65650i	0.414169	−	0.325495i
$303$	−1.29314	+	1.29314i	−0.0742890	+	0.0742890i
$304$	−7.29950	−	22.9345i	−0.418655	−	1.31538i
$305$	0.327862	+	15.8189i	0.0187733	+	0.905789i
$306$	0.323074	−	2.69488i	0.0184689	−	0.154056i
$307$		−	14.1518i		−	0.807684i	−0.914829	−	0.403842i	$-0.867675\pi$
$307$		−	14.1518i		−	0.807684i	0.914829	−	0.403842i	$-0.132325\pi$
$308$	0.101975	−	0.419194i	0.00581058	−	0.0238858i
$309$	−11.2892	−	11.2892i	−0.642222	−	0.642222i
$310$	−2.05723	+	20.7985i	−0.116843	+	1.18127i
$311$	7.15165			0.405533			0.202766	−	0.979227i	$-0.435007\pi$
$311$	7.15165			0.405533			0.202766	+	0.979227i	$0.435007\pi$
$312$	8.47164	−	3.85919i	0.479612	−	0.218484i
$313$	−5.98016	+	5.98016i	−0.338019	+	0.338019i	−0.855621	−	0.517602i	$-0.826825\pi$
$313$	−5.98016	+	5.98016i	−0.338019	+	0.338019i	0.517602	+	0.855621i	$0.326825\pi$
$314$	−13.0610	+	10.2646i	−0.737072	+	0.579264i
$315$	−0.454934	+	0.00942893i	−0.0256326	+	0.000531260i
$316$	4.70644	−	19.3469i	0.264758	−	1.08835i
$317$	7.76996			0.436404			0.218202	−	0.975904i	$-0.429981\pi$
$317$	7.76996			0.436404			0.218202	+	0.975904i	$0.429981\pi$
$318$	−5.62104	+	4.41757i	−0.315212	+	0.247725i
$319$	−4.15941			−0.232882
$320$	17.8158	−	1.61191i	0.995932	−	0.0901088i
$321$	1.39451			0.0778338
$322$	0.267962	−	0.210591i	0.0149329	−	0.0117358i
$323$	11.5479			0.642544
$324$	0.472743	−	1.94333i	0.0262635	−	0.107963i
$325$	−16.4424	+	0.681863i	−0.912063	+	0.0378229i
$326$	2.08088	−	1.63536i	0.115249	−	0.0905744i
$327$	−4.55325	+	4.55325i	−0.251795	+	0.251795i
$328$	−4.44283	+	2.02390i	−0.245314	+	0.111751i
$329$	−2.45915			−0.135577
$330$	−2.12545	−	2.59207i	−0.117002	−	0.142689i
$331$	−0.751395	−	0.751395i	−0.0413004	−	0.0413004i	0.686155	−	0.727455i	$-0.259297\pi$
$331$	−0.751395	−	0.751395i	−0.0413004	−	0.0413004i	−0.727455	+	0.686155i	$0.759297\pi$
$332$	−4.73379	+	19.4594i	−0.259800	+	1.06797i
$333$			10.0194i			0.549057i
$334$	1.14246	−	9.52970i	0.0625127	−	0.521442i
$335$	6.60607	−	6.88570i	0.360928	−	0.376206i
$336$	−0.775647	+	0.246870i	−0.0423150	+	0.0134678i
$337$	−0.379414	+	0.379414i	−0.0206680	+	0.0206680i	−0.717365	−	0.696697i	$-0.754652\pi$
$337$	−0.379414	+	0.379414i	−0.0206680	+	0.0206680i	0.696697	+	0.717365i	$0.254652\pi$
$338$	2.40981	−	1.89386i	0.131076	−	0.103013i
$339$	−11.4501	−	11.4501i	−0.621886	−	0.621886i
$340$	−1.85552	+	8.38000i	−0.100630	+	0.454469i
$341$	4.95386	−	4.95386i	0.268266	−	0.268266i
$342$	8.44886	+	1.01289i	0.456862	+	0.0547707i
$343$	2.00855	+	2.00855i	0.108452	+	0.108452i
$344$	−10.7377	+	4.89149i	−0.578939	+	0.263731i
$345$	−0.0548716	−	2.64749i	−0.00295419	−	0.142536i
$346$	11.2244	+	14.2822i	0.603427	+	0.767818i
$347$	16.7455			0.898947			0.449473	−	0.893294i	$-0.351612\pi$
$347$	16.7455			0.898947			0.449473	+	0.893294i	$0.351612\pi$
$348$	4.08031	+	6.70368i	0.218728	+	0.359355i
$349$	21.0019	−	21.0019i	1.12421	−	1.12421i	0.133104	−	0.991102i	$-0.457506\pi$
$349$	21.0019	−	21.0019i	1.12421	−	1.12421i	0.991102	−	0.133104i	$-0.0424944\pi$
$350$	1.43458	+	0.111935i	0.0766813	+	0.00598320i
$351$			3.29132i			0.175677i
$352$	−4.96058	−	3.36883i	−0.264400	−	0.179559i
$353$	−9.02933	−	9.02933i	−0.480583	−	0.480583i	0.424735	−	0.905318i	$-0.360367\pi$
$353$	−9.02933	−	9.02933i	−0.480583	−	0.480583i	−0.905318	+	0.424735i	$0.860367\pi$
$354$	0.733801	−	6.12090i	0.0390011	−	0.325322i
$355$	−21.3169	−	20.4512i	−1.13138	−	1.08544i
$356$	2.72302	−	11.1936i	0.144320	−	0.593262i
$357$		−	0.390552i		−	0.0206702i
$358$	−6.90636	−	0.827965i	−0.365012	−	0.0437593i
$359$		−	12.2651i		−	0.647326i	−0.946172	−	0.323663i	$-0.895086\pi$
$359$		−	12.2651i		−	0.647326i	0.946172	−	0.323663i	$-0.104914\pi$
$360$	−2.09259	+	5.96834i	−0.110289	+	0.314559i
$361$			17.2046i			0.905506i
$362$	3.88486	−	32.4050i	0.204184	−	1.70317i
$363$		−	9.87636i		−	0.518375i
$364$	1.14425	−	0.696467i	0.0599749	−	0.0365048i
$365$	36.9555	−	0.765938i	1.93434	−	0.0400910i
$366$	−9.93577	−	1.19114i	−0.519351	−	0.0622621i
$367$	−1.25485	−	1.25485i	−0.0655025	−	0.0655025i	0.673597	−	0.739099i	$-0.264749\pi$
$367$	−1.25485	−	1.25485i	−0.0655025	−	0.0655025i	−0.739099	+	0.673597i	$0.764749\pi$
$368$	−1.43666	−	4.51387i	−0.0748909	−	0.235302i
$369$		−	1.72608i		−	0.0898563i
$370$	3.11873	−	31.5301i	0.162135	−	1.63917i
$371$	−0.727417	+	0.727417i	−0.0377656	+	0.0377656i
$372$	−12.8437	−	3.12443i	−0.665917	−	0.161994i
$373$	8.25732			0.427548			0.213774	−	0.976883i	$-0.431424\pi$
$373$	8.25732			0.427548			0.213774	+	0.976883i	$0.431424\pi$
$374$	2.26209	−	1.77777i	0.116970	−	0.0919264i
$375$	7.39925	−	8.38159i	0.382096	−	0.432824i
$376$	−11.9750	+	32.0137i	−0.617563	+	1.65098i
$377$	−9.13216	−	9.13216i	−0.470330	−	0.470330i
$378$	0.0342559	−	0.285741i	0.00176193	−	0.0146969i
$379$	1.03027	−	1.03027i	0.0529214	−	0.0529214i	−0.680151	−	0.733072i	$-0.738086\pi$
$379$	1.03027	−	1.03027i	0.0529214	−	0.0529214i	0.733072	+	0.680151i	$0.238086\pi$
$380$	−26.2726	−	5.81736i	−1.34776	−	0.298424i
$381$	−4.94562	−	4.94562i	−0.253372	−	0.253372i
$382$	18.8302	+	23.9601i	0.963436	+	1.22590i
$383$	12.3374	−	12.3374i	0.630413	−	0.630413i	−0.317759	−	0.948172i	$-0.602930\pi$
$383$	12.3374	−	12.3374i	0.630413	−	0.630413i	0.948172	+	0.317759i	$0.102930\pi$
$384$	−0.563267	+	11.2997i	−0.0287441	+	0.576634i
$385$	−0.348061	−	0.333926i	−0.0177388	−	0.0170184i
$386$	22.4713	+	2.69396i	1.14376	+	0.137119i
$387$		−	4.17171i		−	0.212060i
$388$	−17.3041	−	28.4295i	−0.878483	−	1.44329i
$389$	−12.8354	−	12.8354i	−0.650781	−	0.650781i	0.302400	−	0.953181i	$-0.402212\pi$
$389$	−12.8354	−	12.8354i	−0.650781	−	0.650781i	−0.953181	+	0.302400i	$0.902212\pi$
$390$	1.02449	−	10.3575i	0.0518770	−	0.524473i
$391$	2.27282			0.114941
$392$	17.9110	−	8.15920i	0.904641	−	0.412102i
$393$	−12.7313	+	12.7313i	−0.642211	+	0.642211i
$394$	20.3704	+	25.9199i	1.02625	+	1.30583i
$395$	−16.0640	−	15.4116i	−0.808266	−	0.775442i
$396$	1.81095	−	1.10227i	0.0910038	−	0.0553910i
$397$	14.3934			0.722383			0.361191	−	0.932492i	$-0.382370\pi$
$397$	14.3934			0.722383			0.361191	+	0.932492i	$0.382370\pi$
$398$	−1.87872	−	2.39054i	−0.0941718	−	0.119827i
$399$	1.22444			0.0612988
$400$	8.44297	−	18.1305i	0.422149	−	0.906527i
$401$	−37.4272			−1.86902			−0.934512	−	0.355932i	$-0.884164\pi$
$401$	−37.4272			−1.86902			−0.934512	+	0.355932i	$0.884164\pi$
$402$	3.72909	+	4.74501i	0.185990	+	0.236659i
$403$	21.7528			1.08358
$404$	1.90167	+	3.12432i	0.0946116	+	0.155440i
$405$	−1.61356	−	1.54804i	−0.0801786	−	0.0769225i
$406$	0.697777	+	0.887871i	0.0346301	+	0.0440643i
$407$	−7.50996	+	7.50996i	−0.372255	+	0.372255i
$408$	−5.08429	−	1.90182i	−0.251710	−	0.0941542i
$409$	8.19166			0.405052			0.202526	−	0.979277i	$-0.435085\pi$
$409$	8.19166			0.405052			0.202526	+	0.979277i	$0.435085\pi$
$410$	−0.537279	+	5.43185i	−0.0265343	+	0.268260i
$411$	−6.06032	−	6.06032i	−0.298934	−	0.298934i
$412$	−27.2756	+	16.6018i	−1.34377	+	0.817910i
$413$		−	0.887066i		−	0.0436497i
$414$	1.66287	+	0.199352i	0.0817256	+	0.00979762i
$415$	16.1573	+	15.5012i	0.793131	+	0.760922i
$416$	−3.49475	−	18.2876i	−0.171344	−	0.896621i
$417$	10.3543	−	10.3543i	0.507051	−	0.507051i
$418$	5.57360	+	7.09201i	0.272614	+	0.346881i
$419$	−22.2183	−	22.2183i	−1.08544	−	1.08544i	−0.995992	−	0.0894455i	$-0.971491\pi$
$419$	−22.2183	−	22.2183i	−1.08544	−	1.08544i	−0.0894455	−	0.995992i	$-0.528509\pi$
$420$	−0.196744	+	0.888542i	−0.00960010	+	0.0433564i
$421$	−2.75098	+	2.75098i	−0.134074	+	0.134074i	−0.770959	−	0.636885i	$-0.780223\pi$
$421$	−2.75098	+	2.75098i	−0.134074	+	0.134074i	0.636885	+	0.770959i	$0.280223\pi$
$422$	1.49331	−	12.4562i	0.0726930	−	0.606359i
$423$	−8.54502	−	8.54502i	−0.415473	−	0.415473i
$424$	5.92746	+	13.0119i	0.287863	+	0.631913i
$425$	7.06075	+	6.49845i	0.342497	+	0.315221i
$426$	14.6897	−	11.5446i	0.711717	−	0.559337i
$427$	−1.43993			−0.0696832
$428$	0.659244	−	2.70998i	0.0318658	−	0.130992i
$429$	−2.46699	+	2.46699i	−0.119107	+	0.119107i
$430$	−1.29853	+	13.1280i	−0.0626207	+	0.633091i
$431$			5.32770i			0.256626i	0.991734	+	0.128313i	$0.0409563\pi$
$431$			5.32770i			0.256626i	−0.991734	+	0.128313i	$0.959044\pi$
$432$	−3.55303	−	1.83739i	−0.170945	−	0.0884014i
$433$	−3.38866	−	3.38866i	−0.162849	−	0.162849i	0.620979	−	0.783827i	$-0.286735\pi$
$433$	−3.38866	−	3.38866i	−0.162849	−	0.162849i	−0.783827	+	0.620979i	$0.786735\pi$
$434$	−1.88851	−	0.226403i	−0.0906513	−	0.0108677i
$435$	8.77224	−	0.181813i	0.420597	−	0.00871726i
$436$	6.69593	+	11.0010i	0.320677	+	0.526851i
$437$			7.12564i			0.340866i
$438$	−2.78270	+	23.2115i	−0.132963	+	1.10909i
$439$		−	5.99801i		−	0.286269i	−0.989703	−	0.143135i	$-0.954282\pi$
$439$		−	5.99801i		−	0.286269i	0.989703	−	0.143135i	$-0.0457182\pi$
$440$	−6.04203	+	2.90505i	−0.288042	+	0.138493i
$441$			6.95859i			0.331361i
$442$	8.86968	+	1.06334i	0.421888	+	0.0505778i
$443$		−	13.3394i		−	0.633773i	−0.948463	−	0.316887i	$-0.897363\pi$
$443$		−	13.3394i		−	0.633773i	0.948463	−	0.316887i	$-0.102637\pi$
$444$	19.4709	+	4.73658i	0.924047	+	0.224788i
$445$	−9.29420	−	8.91676i	−0.440587	−	0.422695i
$446$	−1.19034	+	9.92908i	−0.0563643	+	0.470156i
$447$	0.485009	+	0.485009i	0.0229401	+	0.0229401i
$448$	0.113066	+	1.62404i	0.00534188	+	0.0767287i
$449$			29.7201i			1.40258i	0.712877	+	0.701289i	$0.247392\pi$
$449$			29.7201i			1.40258i	−0.712877	+	0.701289i	$0.752608\pi$
$450$	4.59590	+	5.37380i	0.216653	+	0.253323i
$451$	1.29378	−	1.29378i	0.0609216	−	0.0609216i
$452$	−27.6643	+	16.8384i	−1.30122	+	0.792010i
$453$	6.47302			0.304129
$454$	19.7168	+	25.0883i	0.925356	+	1.17745i
$455$	−0.0310336	−	1.49733i	−0.00145488	−	0.0701960i
$456$	5.96251	−	15.9401i	0.279220	−	0.746462i
$457$	−13.8443	−	13.8443i	−0.647611	−	0.647611i	0.304804	−	0.952415i	$-0.401409\pi$
$457$	−13.8443	−	13.8443i	−0.647611	−	0.647611i	−0.952415	+	0.304804i	$0.901409\pi$
$458$	−13.5772	−	1.62769i	−0.634420	−	0.0760571i
$459$	1.35709	−	1.35709i	0.0633433	−	0.0633433i
$460$	−5.17087	−	1.14495i	−0.241093	−	0.0533835i
$461$	23.8766	+	23.8766i	1.11205	+	1.11205i	0.992874	+	0.119172i	$0.0380240\pi$
$461$	23.8766	+	23.8766i	1.11205	+	1.11205i	0.119172	+	0.992874i	$0.461976\pi$
$462$	0.239852	−	0.188500i	0.0111589	−	0.00876979i
$463$	−10.5750	+	10.5750i	−0.491463	+	0.491463i	−0.908767	−	0.417304i	$-0.862975\pi$
$463$	−10.5750	+	10.5750i	−0.491463	+	0.491463i	0.417304	+	0.908767i	$0.362975\pi$
$464$	14.9564	−	4.76025i	0.694332	−	0.220989i
$465$	−10.2312	+	10.6643i	−0.474461	+	0.494544i
$466$	0.740126	−	6.17366i	0.0342857	−	0.285989i
$467$		−	30.0161i		−	1.38898i	−0.719502	−	0.694491i	$-0.755630\pi$
$467$		−	30.0161i		−	1.38898i	0.719502	−	0.694491i	$-0.244370\pi$
$468$	6.39610	+	1.55595i	0.295660	+	0.0719237i
$469$	0.614050	+	0.614050i	0.0283542	+	0.0283542i
$470$	24.2307	+	29.5503i	1.11768	+	1.36305i
$471$	−11.7463			−0.541240
$472$	−11.5480	−	4.31963i	−0.531540	−	0.198827i
$473$	3.12689	−	3.12689i	0.143774	−	0.143774i
$474$	11.0698	−	8.69977i	0.508455	−	0.399594i
$475$	−20.3737	+	22.1366i	−0.934809	+	1.01570i
$476$	−0.758970	−	0.184631i	−0.0347873	−	0.00846254i
$477$	−5.05524			−0.231464
$478$	12.3058	−	9.67111i	0.562854	−	0.442346i
$479$	21.9152			1.00133			0.500665	−	0.865641i	$-0.333089\pi$
$479$	21.9152			1.00133			0.500665	+	0.865641i	$0.333089\pi$
$480$	10.6092	+	6.88807i	0.484240	+	0.314396i
$481$	−32.9769			−1.50362
$482$	−26.1016	+	20.5132i	−1.18890	+	0.934351i
$483$	0.240990			0.0109654
$484$	−19.1930	−	4.66899i	−0.872409	−	0.212227i
$485$	−37.2020	+	0.771047i	−1.68926	+	0.0350114i
$486$	1.11192	−	0.873858i	0.0504378	−	0.0396390i
$487$	−5.66360	+	5.66360i	−0.256642	+	0.256642i	−0.823687	−	0.567045i	$-0.808087\pi$
$487$	−5.66360	+	5.66360i	−0.256642	+	0.256642i	0.567045	+	0.823687i	$0.308087\pi$
$488$	−7.01185	+	18.7453i	−0.317411	+	0.848561i
$489$	1.87143			0.0846289
$490$	2.16600	−	21.8981i	0.0978501	−	0.989257i
$491$	−25.4744	−	25.4744i	−1.14964	−	1.14964i	−0.986623	−	0.163018i	$-0.947877\pi$
$491$	−25.4744	−	25.4744i	−1.14964	−	1.14964i	−0.163018	−	0.986623i	$-0.552123\pi$
$492$	−3.35434	−	0.815994i	−0.151225	−	0.0367879i
$493$			7.53080i			0.339170i
$494$	−3.33373	+	27.8079i	−0.149992	+	1.25114i
$495$	−0.0491155	−	2.36976i	−0.00220758	−	0.106513i
$496$	−12.1436	+	23.4825i	−0.545263	+	1.05440i
$497$	1.90099	−	1.90099i	0.0852709	−	0.0852709i
$498$	−11.1342	+	8.75033i	−0.498934	+	0.392112i
$499$	18.8209	+	18.8209i	0.842537	+	0.842537i	0.989188	−	0.146651i	$-0.0468494\pi$
$499$	18.8209	+	18.8209i	0.842537	+	0.842537i	−0.146651	+	0.989188i	$0.546849\pi$
$500$	−12.7902	−	18.3415i	−0.571996	−	0.820256i
$501$	4.79897	−	4.79897i	0.214402	−	0.214402i
$502$	−3.49870	−	0.419439i	−0.156154	−	0.0187205i
$503$	7.85721	+	7.85721i	0.350336	+	0.350336i	0.860234	−	0.509899i	$-0.170317\pi$
$503$	7.85721	+	7.85721i	0.350336	+	0.350336i	−0.509899	+	0.860234i	$0.670317\pi$
$504$	−0.539094	−	0.201653i	−0.0240132	−	0.00898232i
$505$	4.08839	−	0.0847357i	0.181931	−	0.00377069i
$506$	1.09697	+	1.39582i	0.0487664	+	0.0620517i
$507$	2.16724			0.0962507
$508$	−11.9490	+	7.27294i	−0.530149	+	0.322685i
$509$	−10.1248	+	10.1248i	−0.448776	+	0.448776i	−0.894948	−	0.446171i	$-0.852787\pi$
$509$	−10.1248	+	10.1248i	−0.448776	+	0.448776i	0.446171	+	0.894948i	$0.352787\pi$
$510$	−4.69306	+	3.84822i	−0.207812	+	0.170402i
$511$			3.36391i			0.148811i
$512$	21.6927	+	6.43646i	0.958690	+	0.284454i
$513$	4.25468	+	4.25468i	0.187849	+	0.187849i
$514$	−0.965809	+	8.05617i	−0.0426000	+	0.355342i
$515$	0.739751	+	35.6920i	0.0325973	+	1.57278i
$516$	−8.10699	−	1.97215i	−0.356891	−	0.0868190i
$517$		−	12.8097i		−	0.563372i
$518$	2.86294	+	0.343222i	0.125791	+	0.0150803i
$519$			12.8446i			0.563817i
$520$	−19.6437	−	6.88736i	−0.861433	−	0.302031i
$521$			37.3503i			1.63634i	0.574973	+	0.818172i	$0.305013\pi$
$521$			37.3503i			1.63634i	−0.574973	+	0.818172i	$0.694987\pi$
$522$	−0.660538	+	5.50979i	−0.0289110	+	0.241157i
$523$			8.27258i			0.361735i	0.983507	+	0.180867i	$0.0578905\pi$
$523$			8.27258i			0.361735i	−0.983507	+	0.180867i	$0.942110\pi$
$524$	18.7225	+	30.7598i	0.817895	+	1.34375i
$525$	0.748661	+	0.689040i	0.0326742	+	0.0300722i
$526$	44.1986	+	5.29873i	1.92715	+	0.231035i
$527$	−8.96919	−	8.96919i	−0.390704	−	0.390704i
$528$	−1.28595	−	4.04036i	−0.0559637	−	0.175834i
$529$		−	21.5976i		−	0.939024i
$530$	15.9085	+	1.57355i	0.691019	+	0.0683506i
$531$	3.08237	−	3.08237i	0.133763	−	0.133763i
$532$	0.578847	−	2.37949i	0.0250962	−	0.103164i
$533$	5.68108			0.246075
$534$	6.40473	−	5.03346i	0.277160	−	0.217819i
$535$	−2.25012	−	2.15875i	−0.0972814	−	0.0933308i
$536$	10.9840	−	5.00367i	0.474436	−	0.216126i
$537$	−3.47791	−	3.47791i	−0.150083	−	0.150083i
$538$	−2.84726	+	23.7500i	−0.122754	+	1.02394i
$539$	−5.21578	+	5.21578i	−0.224659	+	0.224659i
$540$	−3.77114	+	2.40385i	−0.162284	+	0.103445i
$541$	11.1960	+	11.1960i	0.481352	+	0.481352i	0.905563	−	0.424211i	$-0.139449\pi$
$541$	11.1960	+	11.1960i	0.481352	+	0.481352i	−0.424211	+	0.905563i	$0.639449\pi$
$542$	13.7337	+	17.4752i	0.589914	+	0.750624i
$543$	16.3185	−	16.3185i	0.700295	−	0.700295i
$544$	−6.09942	+	8.98135i	−0.261511	+	0.385072i
$545$	14.3956	−	0.298361i	0.616638	−	0.0127804i
$546$	0.940464	+	0.112747i	0.0402482	+	0.00482513i
$547$		−	26.6966i		−	1.14147i	−0.821136	−	0.570733i	$-0.806659\pi$
$547$		−	26.6966i		−	1.14147i	0.821136	−	0.570733i	$-0.193341\pi$
$548$	−14.6422	+	8.91220i	−0.625482	+	0.380710i
$549$	−5.00346	−	5.00346i	−0.213542	−	0.213542i
$550$	−0.583074	+	7.47274i	−0.0248624	+	0.318639i
$551$	−23.6103			−1.00583
$552$	1.17352	−	3.13725i	0.0499482	−	0.133530i
$553$	1.43255	−	1.43255i	0.0609180	−	0.0609180i
$554$	−4.01418	−	5.10776i	−0.170546	−	0.217008i
$555$	15.5103	−	16.1669i	0.658377	−	0.686245i
$556$	−15.2268	−	25.0167i	−0.645761	−	1.06094i
$557$	−0.715510			−0.0303171			−0.0151586	−	0.999885i	$-0.504825\pi$
$557$	−0.715510			−0.0303171			−0.0151586	+	0.999885i	$0.504825\pi$
$558$	−5.77546	−	7.34887i	−0.244495	−	0.311102i
$559$	13.7304			0.580735
$560$	1.63372	+	0.802389i	0.0690372	+	0.0339071i
$561$	2.03439			0.0858922
$562$	−17.9244	−	22.8075i	−0.756093	−	0.962075i
$563$	16.6892			0.703364			0.351682	−	0.936119i	$-0.385610\pi$
$563$	16.6892			0.703364			0.351682	+	0.936119i	$0.385610\pi$
$564$	−20.6453	+	12.5661i	−0.869326	+	0.529130i
$565$	0.750294	+	36.2007i	0.0315651	+	1.52298i
$566$	−25.2536	−	32.1334i	−1.06149	−	1.35067i
$567$	0.143894	−	0.143894i	0.00604297	−	0.00604297i
$568$	−15.4905	−	34.0044i	−0.649965	−	1.42679i
$569$	−23.0249			−0.965253			−0.482626	−	0.875826i	$-0.660317\pi$
$569$	−23.0249			−0.965253			−0.482626	+	0.875826i	$0.660317\pi$
$570$	−12.0648	−	14.7135i	−0.505338	−	0.616281i
$571$	−7.65518	−	7.65518i	−0.320359	−	0.320359i	0.528546	−	0.848905i	$-0.322738\pi$
$571$	−7.65518	−	7.65518i	−0.320359	−	0.320359i	−0.848905	+	0.528546i	$0.822738\pi$
$572$	3.62791	+	5.96041i	0.151691	+	0.249217i
$573$			21.5483i			0.900194i
$574$	−0.493213	−	0.0591286i	−0.0205863	−	0.00246798i
$575$	−4.00986	+	4.35683i	−0.167223	+	0.181692i
$576$	−5.25031	+	6.03608i	−0.218763	+	0.251503i
$577$	22.0343	−	22.0343i	0.917298	−	0.917298i	−0.0795337	−	0.996832i	$-0.525343\pi$
$577$	22.0343	−	22.0343i	0.917298	−	0.917298i	0.996832	+	0.0795337i	$0.0253431\pi$
$578$	11.6369	+	14.8071i	0.484029	+	0.615893i
$579$	11.3161	+	11.3161i	0.470282	+	0.470282i
$580$	3.79370	−	17.1333i	0.157525	−	0.711420i
$581$	−1.44087	+	1.44087i	−0.0597774	+	0.0597774i
$582$	2.80126	−	23.3664i	0.116116	−	0.968567i
$583$	−3.78913	−	3.78913i	−0.156930	−	0.156930i
$584$	43.7921	+	16.3808i	1.81213	+	0.677842i
$585$	5.09507	−	5.31074i	0.210655	−	0.219572i
$586$	9.85967	−	7.74870i	0.407299	−	0.320096i
$587$	22.5696			0.931547			0.465773	−	0.884904i	$-0.345776\pi$
$587$	22.5696			0.931547			0.465773	+	0.884904i	$0.345776\pi$
$588$	13.5228	+	3.28963i	0.557671	+	0.135662i
$589$	28.1198	−	28.1198i	1.15866	−	1.15866i
$590$	−10.6594	+	8.74051i	−0.438841	+	0.359841i
$591$			23.3109i			0.958883i
$592$	18.4094	−	35.5990i	0.756624	−	1.46311i
$593$	−26.4172	−	26.4172i	−1.08482	−	1.08482i	−0.996052	−	0.0887706i	$-0.971706\pi$
$593$	−26.4172	−	26.4172i	−1.08482	−	1.08482i	−0.0887706	−	0.996052i	$-0.528294\pi$
$594$	1.48843	+	0.178440i	0.0610711	+	0.00732148i
$595$	−0.604589	+	0.630180i	−0.0247857	+	0.0258349i
$596$	1.17182	−	0.713246i	0.0479994	−	0.0292157i
$597$		−	2.14992i		−	0.0879902i
$598$	−0.656131	+	5.47303i	−0.0268312	+	0.223809i
$599$		−	17.4693i		−	0.713775i	−0.934147	−	0.356888i	$-0.883838\pi$
$599$		−	17.4693i		−	0.713775i	0.934147	−	0.356888i	$-0.116162\pi$
$600$	12.6157	−	6.39089i	0.515035	−	0.260907i
$601$		−	25.8843i		−	1.05584i	−0.849294	−	0.527921i	$-0.822972\pi$
$601$		−	25.8843i		−	1.05584i	0.849294	−	0.527921i	$-0.177028\pi$
$602$	−1.19203	−	0.142906i	−0.0485835	−	0.00582441i
$603$			4.26739i			0.173782i
$604$	3.06008	−	12.5792i	0.124513	−	0.511839i
$605$	−15.2890	+	15.9361i	−0.621585	+	0.647896i
$606$	−0.307850	+	2.56789i	−0.0125056	+	0.104314i
$607$	−22.7204	−	22.7204i	−0.922193	−	0.922193i	0.0749912	−	0.997184i	$-0.476107\pi$
$607$	−22.7204	−	22.7204i	−0.922193	−	0.922193i	−0.997184	+	0.0749912i	$0.976107\pi$
$608$	−28.1580	−	19.1227i	−1.14196	−	0.775526i
$609$			0.798501i			0.0323569i
$610$	14.1881	+	17.3029i	0.574457	+	0.700574i
$611$	28.1243	−	28.1243i	1.13779	−	1.13779i
$612$	−1.99571	−	3.27881i	−0.0806716	−	0.132538i
$613$	−0.840532			−0.0339488			−0.0169744	−	0.999856i	$-0.505403\pi$
$613$	−0.840532			−0.0339488			−0.0169744	+	0.999856i	$0.505403\pi$
$614$	−12.3666	−	15.7357i	−0.499077	−	0.635040i
$615$	−2.67204	+	2.78514i	−0.107747	+	0.112308i
$616$	−0.252927	−	0.555223i	−0.0101907	−	0.0223706i
$617$	7.18912	+	7.18912i	0.289423	+	0.289423i	0.836852	−	0.547429i	$-0.184393\pi$
$617$	7.18912	+	7.18912i	0.289423	+	0.289423i	−0.547429	+	0.836852i	$0.684393\pi$
$618$	−22.4180	−	2.68756i	−0.901782	−	0.108110i
$619$	−31.9741	+	31.9741i	−1.28515	+	1.28515i	−0.347447	+	0.937700i	$0.612951\pi$
$619$	−31.9741	+	31.9741i	−1.28515	+	1.28515i	−0.937700	+	0.347447i	$0.887049\pi$
$620$	15.8874	+	24.9240i	0.638055	+	1.00097i
$621$	0.837388	+	0.837388i	0.0336032	+	0.0336032i
$622$	7.95208	−	6.24953i	0.318849	−	0.250583i
$623$	0.828834	−	0.828834i	0.0332065	−	0.0332065i
$624$	6.04742	−	11.6941i	0.242091	−	0.468140i
$625$	−24.9142	+	2.06992i	−0.996566	+	0.0827970i
$626$	−1.42366	+	11.8753i	−0.0569010	+	0.474632i
$627$			6.37815i			0.254719i
$628$	−5.55298	+	22.8269i	−0.221588	+	0.910891i
$629$	13.5971	+	13.5971i	0.542153	+	0.542153i
$630$	−0.497612	+	0.408032i	−0.0198253	+	0.0162564i
$631$	28.2004			1.12264			0.561320	−	0.827599i	$-0.310294\pi$
$631$	28.2004			1.12264			0.561320	+	0.827599i	$0.310294\pi$
$632$	−11.6733	−	25.6251i	−0.464339	−	1.01931i
$633$	6.27270	−	6.27270i	0.249317	−	0.249317i
$634$	8.63959	−	6.78984i	0.343122	−	0.269659i
$635$	0.324072	+	15.6361i	0.0128604	+	0.620498i
$636$	−2.38983	+	9.82398i	−0.0947630	+	0.389546i
$637$	−22.9029			−0.907446
$638$	−4.62494	+	3.63473i	−0.183103	+	0.143900i
$639$	13.2111			0.522621
$640$	18.4012	−	17.3608i	0.727370	−	0.686245i
$641$	36.6103			1.44602			0.723011	−	0.690837i	$-0.242758\pi$
$641$	36.6103			1.44602			0.723011	+	0.690837i	$0.242758\pi$
$642$	1.55058	−	1.21860i	0.0611967	−	0.0480944i
$643$	13.4647			0.530996			0.265498	−	0.964111i	$-0.414464\pi$
$643$	13.4647			0.530996			0.265498	+	0.964111i	$0.414464\pi$
$644$	0.113926	−	0.468321i	0.00448932	−	0.0184544i
$645$	−6.45796	+	6.73132i	−0.254282	+	0.265045i
$646$	12.8404	−	10.0913i	0.505199	−	0.397035i
$647$	23.4382	−	23.4382i	0.921451	−	0.921451i	−0.0756812	−	0.997132i	$-0.524113\pi$
$647$	23.4382	−	23.4382i	0.921451	−	0.921451i	0.997132	+	0.0756812i	$0.0241131\pi$
$648$	−1.17254	−	2.57394i	−0.0460616	−	0.101114i
$649$	4.62075			0.181380
$650$	−17.6869	+	15.1265i	−0.693736	+	0.593312i
$651$	−0.951015	−	0.951015i	−0.0372732	−	0.0372732i
$652$	0.884706	−	3.63680i	0.0346477	−	0.142428i
$653$			15.0338i			0.588318i	0.955756	+	0.294159i	$0.0950396\pi$
$653$			15.0338i			0.588318i	−0.955756	+	0.294159i	$0.904960\pi$
$654$	−1.08397	+	9.04176i	−0.0423865	+	0.353561i
$655$	40.2514	−	0.834247i	1.57275	−	0.0325967i
$656$	−3.17148	+	6.13282i	−0.123826	+	0.239446i
$657$	−11.6889	+	11.6889i	−0.456027	+	0.456027i
$658$	−2.73438	+	2.14895i	−0.106597	+	0.0837746i
$659$	−12.8233	−	12.8233i	−0.499524	−	0.499524i	0.411766	−	0.911290i	$-0.364912\pi$
$659$	−12.8233	−	12.8233i	−0.499524	−	0.499524i	−0.911290	+	0.411766i	$0.864912\pi$
$660$	−4.62844	−	1.02484i	−0.180162	−	0.0398919i
$661$	22.6599	−	22.6599i	0.881369	−	0.881369i	−0.112305	−	0.993674i	$-0.535823\pi$
$661$	22.6599	−	22.6599i	0.881369	−	0.881369i	0.993674	+	0.112305i	$0.0358232\pi$
$662$	−1.49211	−	0.178880i	−0.0579923	−	0.00695238i
$663$	4.46660	+	4.46660i	0.173468	+	0.173468i
$664$	11.7411	+	25.7740i	0.455644	+	1.00022i
$665$	−1.97572	−	1.89548i	−0.0766150	−	0.0735036i
$666$	8.75550	+	11.1407i	0.339269	+	0.431695i
$667$	−4.64687			−0.179928
$668$	−7.05727	−	11.5946i	−0.273054	−	0.448610i
$669$	−5.00009	+	5.00009i	−0.193315	+	0.193315i
$670$	1.32831	−	13.4291i	0.0513172	−	0.518813i
$671$		−	7.50063i		−	0.289559i
$672$	−0.646730	+	0.952305i	−0.0249481	+	0.0367360i
$673$	18.5901	+	18.5901i	0.716595	+	0.716595i	0.967906	−	0.251311i	$-0.0808617\pi$
$673$	18.5901	+	18.5901i	0.716595	+	0.716595i	−0.251311	+	0.967906i	$0.580862\pi$
$674$	−0.0903249	+	0.753433i	−0.00347918	+	0.0290211i
$675$	0.207170	+	4.99571i	0.00797399	+	0.192285i
$676$	1.02455	−	4.21166i	0.0394058	−	0.161987i
$677$		−	1.52496i		−	0.0586089i	−0.999571	−	0.0293044i	$-0.990671\pi$
$677$		−	1.52496i		−	0.0586089i	0.999571	−	0.0293044i	$-0.00932923\pi$
$678$	−22.7374	−	2.72587i	−0.873226	−	0.104686i
$679$		−	3.38635i		−	0.129956i
$680$	5.25973	+	10.9394i	0.201702	+	0.419506i
$681$			22.5630i			0.864614i
$682$	1.17934	−	9.83728i	0.0451591	−	0.376689i
$683$			3.77382i			0.144401i	0.997390	+	0.0722006i	$0.0230022\pi$
$683$			3.77382i			0.144401i	−0.997390	+	0.0722006i	$0.976998\pi$
$684$	10.2796	−	6.25686i	0.393050	−	0.239237i
$685$	0.397115	+	19.1603i	0.0151730	+	0.732078i
$686$	3.98854	+	0.478164i	0.152283	+	0.0182564i
$687$	−6.83720	−	6.83720i	−0.260856	−	0.260856i
$688$	−7.66505	+	14.8222i	−0.292227	+	0.565091i
$689$		−	16.6384i		−	0.633873i
$690$	−2.37454	−	2.89585i	−0.0903972	−	0.110243i
$691$	−15.9624	+	15.9624i	−0.607239	+	0.607239i	−0.942224	−	0.334984i	$-0.891269\pi$
$691$	−15.9624	+	15.9624i	−0.607239	+	0.607239i	0.334984	+	0.942224i	$0.391269\pi$
$692$	24.9613	+	6.07222i	0.948887	+	0.230831i
$693$	0.215710			0.00819413
$694$	18.6197	−	14.6332i	0.706795	−	0.555469i
$695$	−32.7361	+	0.678486i	−1.24175	+	0.0257364i
$696$	10.3951	+	3.88836i	0.394023	+	0.147388i
$697$	−2.34244	−	2.34244i	−0.0887263	−	0.0887263i
$698$	4.99980	−	41.7052i	0.189245	−	1.57856i
$699$	3.10894	−	3.10894i	0.117591	−	0.117591i
$700$	1.69295	−	1.12915i	0.0639876	−	0.0426780i
$701$	−20.1411	−	20.1411i	−0.760717	−	0.760717i	0.215735	−	0.976452i	$-0.430785\pi$
$701$	−20.1411	−	20.1411i	−0.760717	−	0.760717i	−0.976452	+	0.215735i	$0.930785\pi$
$702$	2.87614	+	3.65969i	0.108553	+	0.138126i
$703$	−42.6292	+	42.6292i	−1.60779	+	1.60779i
$704$	−8.45966	+	0.588964i	−0.318835	+	0.0221974i
$705$	0.559930	+	27.0159i	0.0210882	+	1.01748i
$706$	−17.9303	−	2.14956i	−0.674814	−	0.0808997i
$707$			0.372149i			0.0139961i
$708$	−4.53287	−	7.44721i	−0.170356	−	0.279883i
$709$	8.20276	+	8.20276i	0.308061	+	0.308061i	0.844157	−	0.536096i	$-0.180101\pi$
$709$	8.20276	+	8.20276i	0.308061	+	0.308061i	−0.536096	+	0.844157i	$0.680101\pi$
$710$	−41.5742	−	4.11221i	−1.56025	−	0.154329i
$711$	9.95558			0.373364
$712$	−6.75387	−	14.8260i	−0.253112	−	0.555628i
$713$	5.53443	−	5.53443i	0.207266	−	0.207266i
$714$	−0.341287	−	0.434264i	−0.0127724	−	0.0162519i
$715$	7.79963	−	0.161655i	0.291690	−	0.00604554i
$716$	−8.40286	+	5.11455i	−0.314030	+	0.191140i
$717$	11.0671			0.413310
$718$	−10.7179	−	13.6378i	−0.399990	−	0.508959i
$719$	−23.6655			−0.882576			−0.441288	−	0.897366i	$-0.645478\pi$
$719$	−23.6655			−0.882576			−0.441288	+	0.897366i	$0.645478\pi$
$720$	2.88869	+	8.46496i	0.107655	+	0.315470i
$721$	−3.24890			−0.120995
$722$	15.0344	+	19.1302i	0.559522	+	0.711952i
$723$	−23.4743			−0.873018
$724$	−23.9977	−	39.4267i	−0.891869	−	1.46528i
$725$	−14.4360	−	13.2864i	−0.536140	−	0.493444i
$726$	−8.63054	−	10.9818i	−0.320309	−	0.407571i
$727$	−1.68416	+	1.68416i	−0.0624622	+	0.0624622i	−0.737648	−	0.675186i	$-0.764064\pi$
$727$	−1.68416	+	1.68416i	−0.0624622	+	0.0624622i	0.675186	+	0.737648i	$0.264064\pi$
$728$	0.663703	−	1.77433i	0.0245985	−	0.0657610i
$729$	1.00000			0.0370370
$730$	40.4224	−	33.1456i	1.49610	−	1.22677i
$731$	−5.66137	−	5.66137i	−0.209393	−	0.209393i
$732$	−12.0887	+	7.35799i	−0.446811	+	0.271959i
$733$		−	48.4131i		−	1.78818i	−0.447889	−	0.894089i	$-0.647824\pi$
$733$		−	48.4131i		−	1.78818i	0.447889	−	0.894089i	$-0.352176\pi$
$734$	−2.49185	−	0.298734i	−0.0919759	−	0.0110265i
$735$	10.7721	−	11.2281i	0.397337	−	0.414155i
$736$	−5.54193	−	3.76364i	−0.204278	−	0.138730i
$737$	−3.19860	+	3.19860i	−0.117822	+	0.117822i
$738$	−1.50835	−	1.91927i	−0.0555232	−	0.0706493i
$739$	2.35313	+	2.35313i	0.0865612	+	0.0865612i	0.749062	−	0.662500i	$-0.230505\pi$
$739$	2.35313	+	2.35313i	0.0865612	+	0.0865612i	−0.662500	+	0.749062i	$0.730505\pi$
$740$	−24.0851	−	37.7844i	−0.885385	−	1.38898i
$741$	−14.0035	+	14.0035i	−0.514431	+	0.514431i
$742$	−0.173172	+	1.44449i	−0.00635735	+	0.0530290i
$743$	17.6788	+	17.6788i	0.648571	+	0.648571i	0.952648	−	0.304076i	$-0.0983478\pi$
$743$	17.6788	+	17.6788i	0.648571	+	0.648571i	−0.304076	+	0.952648i	$0.598348\pi$
$744$	−17.0116	+	7.74948i	−0.623674	+	0.284110i
$745$	−0.0317812	−	1.53340i	−0.00116437	−	0.0561796i
$746$	9.18150	−	7.21573i	0.336159	−	0.264187i
$747$	−10.0134			−0.366373
$748$	0.961746	−	3.95349i	0.0351649	−	0.144554i
$749$	0.200661	−	0.200661i	0.00733198	−	0.00733198i
$750$	0.903067	−	15.7856i	0.0329754	−	0.576408i
$751$		−	40.8647i		−	1.49117i	−0.666409	−	0.745587i	$-0.732169\pi$
$751$		−	40.8647i		−	1.49117i	0.666409	−	0.745587i	$-0.267831\pi$
$752$	14.6602	+	46.0612i	0.534601	+	1.67968i
$753$	−1.76187	−	1.76187i	−0.0642063	−	0.0642063i
$754$	−18.1345	−	2.17404i	−0.660418	−	0.0791738i
$755$	−10.4446	−	10.0205i	−0.380119	−	0.364682i
$756$	−0.211607	−	0.347657i	−0.00769609	−	0.0126442i
$757$			24.6892i			0.897345i	0.893696	+	0.448673i	$0.148103\pi$
$757$			24.6892i			0.897345i	−0.893696	+	0.448673i	$0.851897\pi$
$758$	0.245270	−	2.04589i	0.00890862	−	0.0743101i
$759$			1.25532i			0.0455652i
$760$	−34.2967	+	16.4901i	−1.24407	+	0.598159i
$761$			6.54343i			0.237199i	0.992942	+	0.118600i	$0.0378405\pi$
$761$			6.54343i			0.237199i	−0.992942	+	0.118600i	$0.962160\pi$
$762$	−9.82092	−	1.17738i	−0.355774	−	0.0426518i
$763$			1.31037i			0.0474385i
$764$	41.8754	+	10.1868i	1.51500	+	0.368546i
$765$	−4.29056	+	0.0889259i	−0.155126	+	0.00321512i
$766$	2.93710	−	24.4994i	0.106122	−	0.885200i
$767$	10.1450	+	10.1450i	0.366316	+	0.366316i
$768$	9.24801	+	13.0566i	0.333709	+	0.471139i
$769$			26.2710i			0.947357i	0.880698	+	0.473678i	$0.157074\pi$
$769$			26.2710i			0.947357i	−0.880698	+	0.473678i	$0.842926\pi$
$770$	−0.678821	−	0.0671440i	−0.0244630	−	0.00241970i
$771$	−4.05693	+	4.05693i	−0.146107	+	0.146107i
$772$	27.3405	−	16.6413i	0.984007	−	0.598933i
$773$	−9.19242			−0.330628			−0.165314	−	0.986241i	$-0.552864\pi$
$773$	−9.19242			−0.330628			−0.165314	+	0.986241i	$0.552864\pi$
$774$	−3.64549	−	4.63862i	−0.131034	−	0.166732i
$775$	33.0174	−	1.36922i	1.18602	−	0.0491839i
$776$	−44.0842	−	16.4901i	−1.58253	−	0.591959i
$777$	1.44172	+	1.44172i	0.0517215	+	0.0517215i
$778$	−25.4883	−	3.05565i	−0.913800	−	0.109550i
$779$	7.34393	−	7.34393i	0.263124	−	0.263124i
$780$	−7.91184	−	12.4120i	−0.283289	−	0.444421i
$781$	9.90228	+	9.90228i	0.354332	+	0.354332i
$782$	2.52719	−	1.98612i	0.0903723	−	0.0710235i
$783$	−2.77462	+	2.77462i	−0.0991569	+	0.0991569i
$784$	12.7856	−	24.7241i	0.456630	−	0.883002i
$785$	18.9534	+	18.1837i	0.676475	+	0.649003i
$786$	−3.03087	+	25.2816i	−0.108108	+	0.901766i
$787$			20.9534i			0.746908i	0.927649	+	0.373454i	$0.121827\pi$
$787$			20.9534i			0.746908i	−0.927649	+	0.373454i	$0.878173\pi$
$788$	45.3007	+	11.0201i	1.61377	+	0.392574i
$789$	22.2576	+	22.2576i	0.792390	+	0.792390i
$790$	−31.3294	−	3.09888i	−1.11465	−	0.110253i
$791$	−3.29520			−0.117164
$792$	1.05041	−	2.80815i	0.0373248	−	0.0997833i
$793$	16.4680	−	16.4680i	0.584794	−	0.584794i
$794$	16.0043	−	12.5778i	0.567972	−	0.446368i
$795$	8.15695	+	7.82570i	0.289297	+	0.277549i
$796$	−4.17799	−	1.01636i	−0.148085	−	0.0360239i
$797$	−25.5883			−0.906384			−0.453192	−	0.891413i	$-0.649715\pi$
$797$	−25.5883			−0.906384			−0.453192	+	0.891413i	$0.649715\pi$
$798$	1.36149	−	1.06999i	0.0481961	−	0.0378772i
$799$	−23.1926			−0.820497
$800$	−6.45559	−	27.5377i	−0.228240	−	0.973605i
$801$	5.76005			0.203521
$802$	−41.6161	+	32.7060i	−1.46952	+	1.15489i
$803$	−17.5227			−0.618362
$804$	8.29293	+	2.01738i	0.292469	+	0.0711475i
$805$	−0.388852	−	0.373061i	−0.0137052	−	0.0131487i
$806$	24.1874	−	19.0089i	0.851966	−	0.669559i
$807$	−11.9600	+	11.9600i	−0.421014	+	0.421014i
$808$	4.84472	+	1.81221i	0.170437	+	0.0637532i
$809$	−4.93002			−0.173330			−0.0866652	−	0.996237i	$-0.527621\pi$
$809$	−4.93002			−0.173330			−0.0866652	+	0.996237i	$0.527621\pi$
$810$	−3.14692	−	0.311271i	−0.110572	−	0.0109369i
$811$	35.3133	+	35.3133i	1.24002	+	1.24002i	0.959993	+	0.280025i	$0.0903426\pi$
$811$	35.3133	+	35.3133i	1.24002	+	1.24002i	0.280025	+	0.959993i	$0.409657\pi$
$812$	1.55175	+	0.377486i	0.0544557	+	0.0132472i
$813$			15.7162i			0.551191i
$814$	−1.78785	+	14.9131i	−0.0626642	+	0.522705i
$815$	−3.01967	−	2.89704i	−0.105774	−	0.101479i
$816$	−7.31526	+	2.32827i	−0.256085	+	0.0815057i
$817$	17.7493	−	17.7493i	0.620970	−	0.620970i
$818$	9.10849	−	7.15835i	0.318471	−	0.250286i
$819$	0.473599	+	0.473599i	0.0165489	+	0.0165489i
$820$	4.14925	+	6.50930i	0.144898	+	0.227314i
$821$	36.2490	−	36.2490i	1.26510	−	1.26510i	0.316509	−	0.948589i	$-0.397489\pi$
$821$	36.2490	−	36.2490i	1.26510	−	1.26510i	0.948589	−	0.316509i	$-0.102511\pi$
$822$	−12.0345	−	1.44275i	−0.419750	−	0.0503215i
$823$	23.0235	+	23.0235i	0.802548	+	0.802548i	0.983493	−	0.180945i	$-0.0579156\pi$
$823$	23.0235	+	23.0235i	0.802548	+	0.802548i	−0.180945	+	0.983493i	$0.557916\pi$
$824$	−15.8208	+	42.2949i	−0.551142	+	1.47341i
$825$	−3.58922	+	3.89979i	−0.124961	+	0.135773i
$826$	−0.775170	−	0.986349i	−0.0269716	−	0.0343195i
$827$	44.8863			1.56085			0.780424	−	0.625250i	$-0.215003\pi$
$827$	44.8863			1.56085			0.780424	+	0.625250i	$0.215003\pi$
$828$	2.02319	−	1.23145i	0.0703106	−	0.0427958i
$829$	7.27338	−	7.27338i	0.252615	−	0.252615i	−0.569427	−	0.822042i	$-0.692835\pi$
$829$	7.27338	−	7.27338i	0.252615	−	0.252615i	0.822042	+	0.569427i	$0.192835\pi$
$830$	31.5115	+	3.11689i	1.09378	+	0.108189i
$831$		−	4.59363i		−	0.159351i
$832$	−19.8666	−	17.2804i	−0.688751	−	0.599091i
$833$	9.44340	+	9.44340i	0.327195	+	0.327195i
$834$	2.46498	−	20.5613i	0.0853554	−	0.711981i
$835$	−15.1724	+	0.314462i	−0.525063	+	0.0108824i
$836$	12.3948	+	3.01523i	0.428684	+	0.104284i
$837$		−	6.60915i		−	0.228446i
$838$	−44.1208	−	5.28939i	−1.52413	−	0.182719i
$839$		−	6.23853i		−	0.215378i	−0.994185	−	0.107689i	$-0.965655\pi$
$839$		−	6.23853i		−	0.215378i	0.994185	−	0.107689i	$-0.0343451\pi$
$840$	0.557696	+	1.15992i	0.0192424	+	0.0400209i
$841$			13.6029i			0.469067i
$842$	−0.654909	+	5.46283i	−0.0225696	+	0.188262i
$843$		−	20.5117i		−	0.706462i
$844$	−9.22452	−	15.1553i	−0.317521	−	0.521666i
$845$	−3.49699	−	3.35497i	−0.120300	−	0.115415i
$846$	−16.9685	−	2.03426i	−0.583390	−	0.0699394i
$847$	−1.42115	−	1.42115i	−0.0488312	−	0.0488312i
$848$	17.9614	+	9.28845i	0.616798	+	0.318967i
$849$		−	28.8990i		−	0.991811i
$850$	13.5297	+	1.05568i	0.464066	+	0.0362096i
$851$	−8.39009	+	8.39009i	−0.287609	+	0.287609i
$852$	6.24544	−	25.6734i	0.213965	−	0.879556i
$853$	32.1759			1.10168			0.550841	−	0.834610i	$-0.314307\pi$
$853$	32.1759			1.10168			0.550841	+	0.834610i	$0.314307\pi$
$854$	−1.60109	+	1.25830i	−0.0547882	+	0.0430580i
$855$	−0.278797	−	13.4516i	−0.00953465	−	0.460035i
$856$	−1.63511	−	3.58937i	−0.0558869	−	0.122682i
$857$	−11.0467	−	11.0467i	−0.377348	−	0.377348i	0.492797	−	0.870145i	$-0.335975\pi$
$857$	−11.0467	−	11.0467i	−0.377348	−	0.377348i	−0.870145	+	0.492797i	$0.835975\pi$
$858$	−0.587302	+	4.89890i	−0.0200502	+	0.167246i
$859$	−1.75107	+	1.75107i	−0.0597457	+	0.0597457i	−0.736348	−	0.676603i	$-0.763452\pi$
$859$	−1.75107	+	1.75107i	−0.0597457	+	0.0597457i	0.676603	+	0.736348i	$0.263452\pi$
$860$	10.0282	+	15.7321i	0.341958	+	0.536460i
$861$	−0.248372	−	0.248372i	−0.00846451	−	0.00846451i
$862$	4.65566	+	5.92399i	0.158572	+	0.201772i
$863$	−4.70982	+	4.70982i	−0.160324	+	0.160324i	−0.782710	−	0.622386i	$-0.786163\pi$
$863$	−4.70982	+	4.70982i	−0.160324	+	0.160324i	0.622386	+	0.782710i	$0.286163\pi$
$864$	−5.55631	+	1.06181i	−0.189029	+	0.0361235i
$865$	19.8840	−	20.7256i	0.676075	−	0.704693i
$866$	−6.72913	−	0.806718i	−0.228665	−	0.0274134i
$867$			13.3166i			0.452257i
$868$	−2.29772	+	1.39855i	−0.0779896	+	0.0474697i
$869$	7.46216	+	7.46216i	0.253136	+	0.253136i
$870$	9.59517	−	7.86786i	0.325307	−	0.266745i
$871$	−14.0453			−0.475908
$872$	17.0587	+	6.38093i	0.577679	+	0.216086i
$873$	11.7668	−	11.7668i	0.398247	−	0.398247i
$874$	6.22680	+	7.92316i	0.210625	+	0.268005i
$875$	−0.141353	−	2.27076i	−0.00477860	−	0.0767658i
$876$	17.1895	+	28.2411i	0.580778	+	0.954179i
$877$	−16.7655			−0.566130			−0.283065	−	0.959101i	$-0.591351\pi$
$877$	−16.7655			−0.566130			−0.283065	+	0.959101i	$0.591351\pi$
$878$	−5.24141	−	6.66932i	−0.176889	−	0.225079i
$879$	8.86723			0.299084
$880$	−4.17966	+	8.51007i	−0.140896	+	0.286874i
$881$	50.5390			1.70270			0.851352	−	0.524595i	$-0.175783\pi$
$881$	50.5390			1.70270			0.851352	+	0.524595i	$0.175783\pi$
$882$	6.08082	+	7.73741i	0.204752	+	0.260532i
$883$	−27.3039			−0.918848			−0.459424	−	0.888217i	$-0.651944\pi$
$883$	−27.3039			−0.918848			−0.459424	+	0.888217i	$0.651944\pi$
$884$	10.7916	−	6.56850i	0.362961	−	0.220922i
$885$	−9.74521	+	0.201978i	−0.327582	+	0.00678943i
$886$	−11.6567	−	14.8324i	−0.391615	−	0.498303i
$887$	−2.95052	+	2.95052i	−0.0990688	+	0.0990688i	−0.754904	−	0.655835i	$-0.772317\pi$
$887$	−2.95052	+	2.95052i	−0.0990688	+	0.0990688i	0.655835	+	0.754904i	$0.272317\pi$
$888$	25.7892	−	11.7481i	0.865429	−	0.394239i
$889$	−1.42329			−0.0477355
$890$	−18.1264	−	1.79293i	−0.607599	−	0.0600992i
$891$	0.749545	+	0.749545i	0.0251107	+	0.0251107i
$892$	7.35304	+	12.0806i	0.246198	+	0.404487i
$893$		−	72.7126i		−	2.43324i
$894$	0.963122	+	0.115463i	0.0322116	+	0.00386167i
$895$	0.227897	+	10.9957i	0.00761776	+	0.367547i
$896$	1.54490	+	1.70700i	0.0516115	+	0.0570269i
$897$	−2.75611	+	2.75611i	−0.0920238	+	0.0920238i
$898$	25.9711	+	33.0464i	0.866668	+	1.10277i
$899$	18.3379	+	18.3379i	0.611603	+	0.611603i
$900$	9.80622	+	1.95909i	0.326874	+	0.0653029i
$901$	−6.86040	+	6.86040i	−0.228553	+	0.228553i
$902$	0.308002	−	2.56916i	0.0102553	−	0.0855436i
$903$	−0.600283	−	0.600283i	−0.0199762	−	0.0199762i
$904$	−16.0462	+	42.8976i	−0.533689	+	1.42675i
$905$	−51.5926	+	1.06931i	−1.71500	+	0.0355449i
$906$	7.19749	−	5.65650i	0.239121	−	0.187925i
$907$	−0.0410041			−0.00136152			−0.000680760	−	1.00000i	$-0.500217\pi$
$907$	−0.0410041			−0.00136152			−0.000680760		1.00000i	$0.500217\pi$
$908$	43.8472	+	10.6665i	1.45512	+	0.353980i
$909$	−1.29314	+	1.29314i	−0.0428907	+	0.0428907i
$910$	−1.34296	−	1.63780i	−0.0445188	−	0.0542924i
$911$			21.7776i			0.721525i	0.932658	+	0.360763i	$0.117484\pi$
$911$			21.7776i			0.721525i	−0.932658	+	0.360763i	$0.882516\pi$
$912$	−7.29950	−	22.9345i	−0.241711	−	0.759437i
$913$	−7.50552	−	7.50552i	−0.248397	−	0.248397i
$914$	−27.4918	−	3.29584i	−0.909349	−	0.109017i
$915$	0.327862	+	15.8189i	0.0108388	+	0.522957i
$916$	−16.5191	+	10.0547i	−0.545808	+	0.332216i
$917$			3.66392i			0.120993i
$918$	0.323074	−	2.69488i	0.0106630	−	0.0889441i
$919$			34.4842i			1.13753i	0.822500	+	0.568765i	$0.192579\pi$
$919$			34.4842i			1.13753i	−0.822500	+	0.568765i	$0.807421\pi$
$920$	−6.75012	+	3.24551i	−0.222545	+	0.107001i
$921$		−	14.1518i		−	0.466317i
$922$	47.4138	+	5.68417i	1.56149	+	0.187198i
$923$			43.4818i			1.43122i
$924$	0.101975	−	0.419194i	0.00335474	−	0.0137905i
$925$	−50.0538	+	2.07571i	−1.64576	+	0.0682490i
$926$	−2.51754	+	20.9997i	−0.0827314	+	0.690093i
$927$	−11.2892	−	11.2892i	−0.370787	−	0.370787i
$928$	12.4705	−	18.3628i	0.409365	−	0.602788i
$929$		−	19.8125i		−	0.650028i	−0.945709	−	0.325014i	$-0.894631\pi$
$929$		−	19.8125i		−	0.650028i	0.945709	−	0.325014i	$-0.105369\pi$
$930$	−2.05723	+	20.7985i	−0.0674594	+	0.682009i
$931$	−29.6066	+	29.6066i	−0.970316	+	0.970316i
$932$	−4.57194	−	7.51140i	−0.149759	−	0.246044i
$933$	7.15165			0.234134
$934$	−26.2299	−	33.3756i	−0.858267	−	1.09208i
$935$	−3.28262	−	3.14931i	−0.107353	−	0.102994i
$936$	8.47164	−	3.85919i	0.276904	−	0.126142i
$937$	20.7731	+	20.7731i	0.678628	+	0.678628i	0.959690	−	0.281062i	$-0.0906866\pi$
$937$	20.7731	+	20.7731i	0.678628	+	0.678628i	−0.281062	+	0.959690i	$0.590687\pi$
$938$	1.21937	+	0.146183i	0.0398138	+	0.00477306i
$939$	−5.98016	+	5.98016i	−0.195155	+	0.195155i
$940$	52.7654	+	11.6835i	1.72102	+	0.381073i
$941$	−24.6412	−	24.6412i	−0.803279	−	0.803279i	0.180328	−	0.983607i	$-0.442284\pi$
$941$	−24.6412	−	24.6412i	−0.803279	−	0.803279i	−0.983607	+	0.180328i	$0.942284\pi$
$942$	−13.0610	+	10.2646i	−0.425549	+	0.334438i
$943$	1.44540	−	1.44540i	0.0470687	−	0.0470687i
$944$	−16.6152	+	5.28823i	−0.540780	+	0.172117i
$945$	−0.454934	+	0.00942893i	−0.0147990	+	0.000306723i
$946$	0.744400	−	6.20931i	0.0242025	−	0.201882i
$947$			46.1706i			1.50034i	0.661244	+	0.750171i	$0.270029\pi$
$947$			46.1706i			1.50034i	−0.661244	+	0.750171i	$0.729971\pi$
$948$	4.70644	−	19.3469i	0.152858	−	0.628359i
$949$	−38.4718	−	38.4718i	−1.24885	−	1.24885i
$950$	−3.30973	+	42.4179i	−0.107382	+	1.37622i
$951$	7.76996			0.251958
$952$	−1.00526	+	0.457937i	−0.0325806	+	0.0148418i
$953$	5.45044	−	5.45044i	0.176557	−	0.176557i	−0.613296	−	0.789853i	$-0.710157\pi$
$953$	5.45044	−	5.45044i	0.176557	−	0.176557i	0.789853	+	0.613296i	$0.210157\pi$
$954$	−5.62104	+	4.41757i	−0.181988	+	0.143024i
$955$	33.3576	−	34.7696i	1.07943	−	1.12512i
$956$	5.23191	−	21.5070i	0.169212	−	0.695588i
$957$	−4.15941			−0.134455
$958$	24.3680	−	19.1508i	0.787294	−	0.618733i
$959$	−1.74408			−0.0563194
$960$	17.8158	−	1.61191i	0.575002	−	0.0520243i
$961$	−12.6809			−0.409062
$962$	−36.6677	+	28.8171i	−1.18221	+	0.929101i
$963$	1.39451			0.0449374
$964$	−11.0973	+	45.6182i	−0.357420	+	1.46926i
$965$	−0.741512	−	35.7770i	−0.0238701	−	1.15170i
$966$	0.267962	−	0.210591i	0.00862153	−	0.00677565i
$967$	−18.1852	+	18.1852i	−0.584798	+	0.584798i	−0.936218	−	0.351420i	$-0.885699\pi$
$967$	−18.1852	+	18.1852i	−0.584798	+	0.584798i	0.351420	+	0.936218i	$0.385699\pi$
$968$	−25.4211	+	11.5804i	−0.817067	+	0.372208i
$969$	11.5479			0.370973
$970$	−40.6920	+	33.3666i	−1.30654	+	1.07134i
$971$	−11.6265	−	11.6265i	−0.373112	−	0.373112i	0.495497	−	0.868609i	$-0.334986\pi$
$971$	−11.6265	−	11.6265i	−0.373112	−	0.373112i	−0.868609	+	0.495497i	$0.834986\pi$
$972$	0.472743	−	1.94333i	0.0151632	−	0.0623322i
$973$		−	2.97983i		−	0.0955290i
$974$	−1.34830	+	11.2467i	−0.0432023	+	0.360366i
$975$	−16.4424	+	0.681863i	−0.526580	+	0.0218371i
$976$	8.58413	+	26.9707i	0.274771	+	0.863311i
$977$	−8.35835	+	8.35835i	−0.267407	+	0.267407i	−0.828055	−	0.560647i	$-0.810552\pi$
$977$	−8.35835	+	8.35835i	−0.267407	+	0.267407i	0.560647	+	0.828055i	$0.310552\pi$
$978$	2.08088	−	1.63536i	0.0665393	−	0.0522932i
$979$	4.31741	+	4.31741i	0.137985	+	0.137985i
$980$	−16.7274	−	26.2418i	−0.534338	−	0.838264i
$981$	−4.55325	+	4.55325i	−0.145374	+	0.145374i
$982$	−50.5865	−	6.06453i	−1.61428	−	0.193527i
$983$	−18.1290	−	18.1290i	−0.578226	−	0.578226i	0.356188	−	0.934414i	$-0.384076\pi$
$983$	−18.1290	−	18.1290i	−0.578226	−	0.578226i	−0.934414	+	0.356188i	$0.884076\pi$
$984$	−4.44283	+	2.02390i	−0.141632	+	0.0645194i
$985$	36.0861	−	37.6136i	1.14980	−	1.19847i
$986$	6.58085	+	8.37367i	0.209577	+	0.266672i
$987$	−2.45915			−0.0782755
$988$	20.5933	+	33.8334i	0.655160	+	1.07638i
$989$	3.49334	−	3.49334i	0.111082	−	0.111082i
$990$	−2.12545	−	2.59207i	−0.0675512	−	0.0823814i
$991$		−	28.8183i		−	0.915444i	−0.889095	−	0.457722i	$-0.848666\pi$
$991$		−	28.8183i		−	0.915444i	0.889095	−	0.457722i	$-0.151334\pi$
$992$	7.01766	+	36.7225i	0.222811	+	1.16594i
$993$	−0.751395	−	0.751395i	−0.0238448	−	0.0238448i
$994$	0.452557	−	3.77494i	0.0143542	−	0.119734i
$995$	−3.32815	+	3.46903i	−0.105509	+	0.109975i
$996$	−4.73379	+	19.4594i	−0.149996	+	0.616594i
$997$			30.7058i			0.972463i	0.873830	+	0.486232i	$0.161629\pi$
$997$			30.7058i			0.972463i	−0.873830	+	0.486232i	$0.838371\pi$
$998$	37.3741	+	4.48057i	1.18306	+	0.141830i
$999$			10.0194i			0.316998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.y.e.163.7	✓	16
3.2	odd	2		720.2.z.f.163.2		16
4.3	odd	2		960.2.y.e.943.4		16
5.2	odd	4		240.2.bc.e.67.5	yes	16
8.3	odd	2		1920.2.y.j.223.5		16
8.5	even	2		1920.2.y.i.223.5		16
15.2	even	4		720.2.bd.f.307.4		16
16.3	odd	4		1920.2.bc.i.1183.1		16
16.5	even	4		960.2.bc.e.463.8		16
16.11	odd	4		240.2.bc.e.43.5	yes	16
16.13	even	4		1920.2.bc.j.1183.1		16
20.7	even	4		960.2.bc.e.367.8		16
40.27	even	4		1920.2.bc.j.607.1		16
40.37	odd	4		1920.2.bc.i.607.1		16
48.11	even	4		720.2.bd.f.523.4		16
80.27	even	4	inner	240.2.y.e.187.7	yes	16
80.37	odd	4		960.2.y.e.847.4		16
80.67	even	4		1920.2.y.i.1567.5		16
80.77	odd	4		1920.2.y.j.1567.5		16
240.107	odd	4		720.2.z.f.667.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.7	✓	16	1.1	even	1	trivial
240.2.y.e.187.7	yes	16	80.27	even	4	inner
240.2.bc.e.43.5	yes	16	16.11	odd	4
240.2.bc.e.67.5	yes	16	5.2	odd	4
720.2.z.f.163.2		16	3.2	odd	2
720.2.z.f.667.2		16	240.107	odd	4
720.2.bd.f.307.4		16	15.2	even	4
720.2.bd.f.523.4		16	48.11	even	4
960.2.y.e.847.4		16	80.37	odd	4
960.2.y.e.943.4		16	4.3	odd	2
960.2.bc.e.367.8		16	20.7	even	4
960.2.bc.e.463.8		16	16.5	even	4
1920.2.y.i.223.5		16	8.5	even	2
1920.2.y.i.1567.5		16	80.67	even	4
1920.2.y.j.223.5		16	8.3	odd	2
1920.2.y.j.1567.5		16	80.77	odd	4
1920.2.bc.i.607.1		16	40.37	odd	4
1920.2.bc.i.1183.1		16	16.3	odd	4
1920.2.bc.j.607.1		16	40.27	even	4
1920.2.bc.j.1183.1		16	16.13	even	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11192 - 0.873858i) q^{2} +1.00000 q^{3} +(0.472743 - 1.94333i) q^{4} +(-1.61356 - 1.54804i) q^{5} +(1.11192 - 0.873858i) q^{6} +(0.143894 - 0.143894i) q^{7} +(-1.17254 - 2.57394i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.11192 - 0.873858i) q^{2} +1.00000 q^{3} +(0.472743 - 1.94333i) q^{4} +(-1.61356 - 1.54804i) q^{5} +(1.11192 - 0.873858i) q^{6} +(0.143894 - 0.143894i) q^{7} +(-1.17254 - 2.57394i) q^{8} +1.00000 q^{9} +(-3.14692 - 0.311271i) q^{10} +(0.749545 + 0.749545i) q^{11} +(0.472743 - 1.94333i) q^{12} +3.29132i q^{13} +(0.0342559 - 0.285741i) q^{14} +(-1.61356 - 1.54804i) q^{15} +(-3.55303 - 1.83739i) q^{16} +(1.35709 - 1.35709i) q^{17} +(1.11192 - 0.873858i) q^{18} +(4.25468 + 4.25468i) q^{19} +(-3.77114 + 2.40385i) q^{20} +(0.143894 - 0.143894i) q^{21} +(1.48843 + 0.178440i) q^{22} +(0.837388 + 0.837388i) q^{23} +(-1.17254 - 2.57394i) q^{24} +(0.207170 + 4.99571i) q^{25} +(2.87614 + 3.65969i) q^{26} +1.00000 q^{27} +(-0.211607 - 0.347657i) q^{28} +(-2.77462 + 2.77462i) q^{29} +(-3.14692 - 0.311271i) q^{30} -6.60915i q^{31} +(-5.55631 + 1.06181i) q^{32} +(0.749545 + 0.749545i) q^{33} +(0.323074 - 2.69488i) q^{34} +(-0.454934 + 0.00942893i) q^{35} +(0.472743 - 1.94333i) q^{36} +10.0194i q^{37} +(8.44886 + 1.01289i) q^{38} +3.29132i q^{39} +(-2.09259 + 5.96834i) q^{40} -1.72608i q^{41} +(0.0342559 - 0.285741i) q^{42} -4.17171i q^{43} +(1.81095 - 1.10227i) q^{44} +(-1.61356 - 1.54804i) q^{45} +(1.66287 + 0.199352i) q^{46} +(-8.54502 - 8.54502i) q^{47} +(-3.55303 - 1.83739i) q^{48} +6.95859i q^{49} +(4.59590 + 5.37380i) q^{50} +(1.35709 - 1.35709i) q^{51} +(6.39610 + 1.55595i) q^{52} -5.05524 q^{53} +(1.11192 - 0.873858i) q^{54} +(-0.0491155 - 2.36976i) q^{55} +(-0.539094 - 0.201653i) q^{56} +(4.25468 + 4.25468i) q^{57} +(-0.660538 + 5.50979i) q^{58} +(3.08237 - 3.08237i) q^{59} +(-3.77114 + 2.40385i) q^{60} +(-5.00346 - 5.00346i) q^{61} +(-5.77546 - 7.34887i) q^{62} +(0.143894 - 0.143894i) q^{63} +(-5.25031 + 6.03608i) q^{64} +(5.09507 - 5.31074i) q^{65} +(1.48843 + 0.178440i) q^{66} +4.26739i q^{67} +(-1.99571 - 3.27881i) q^{68} +(0.837388 + 0.837388i) q^{69} +(-0.497612 + 0.408032i) q^{70} +13.2111 q^{71} +(-1.17254 - 2.57394i) q^{72} +(-11.6889 + 11.6889i) q^{73} +(8.75550 + 11.1407i) q^{74} +(0.207170 + 4.99571i) q^{75} +(10.2796 - 6.25686i) q^{76} +0.215710 q^{77} +(2.87614 + 3.65969i) q^{78} +9.95558 q^{79} +(2.88869 + 8.46496i) q^{80} +1.00000 q^{81} +(-1.50835 - 1.91927i) q^{82} -10.0134 q^{83} +(-0.211607 - 0.347657i) q^{84} +(-4.29056 + 0.0889259i) q^{85} +(-3.64549 - 4.63862i) q^{86} +(-2.77462 + 2.77462i) q^{87} +(1.05041 - 2.80815i) q^{88} +5.76005 q^{89} +(-3.14692 - 0.311271i) q^{90} +(0.473599 + 0.473599i) q^{91} +(2.02319 - 1.23145i) q^{92} -6.60915i q^{93} +(-16.9685 - 2.03426i) q^{94} +(-0.278797 - 13.4516i) q^{95} +(-5.55631 + 1.06181i) q^{96} +(11.7668 - 11.7668i) q^{97} +(6.08082 + 7.73741i) q^{98} +(0.749545 + 0.749545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9	\( 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9} - 14 q^{10} - 8 q^{12} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} - 12 q^{20} - 4 q^{21} - 8 q^{22} - 4 q^{24} + 32 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{28} + 12 q^{29} - 14 q^{30} - 28 q^{32} - 20 q^{35} - 8 q^{36} - 16 q^{38} - 44 q^{40} - 4 q^{42} + 52 q^{44} - 4 q^{45} - 16 q^{46} - 32 q^{47} - 8 q^{48} + 22 q^{50} - 8 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} - 4 q^{55} + 20 q^{56} + 8 q^{57} - 44 q^{58} - 24 q^{59} - 12 q^{60} + 40 q^{61} + 40 q^{62} - 4 q^{63} - 8 q^{64} - 4 q^{65} - 8 q^{66} + 24 q^{68} + 56 q^{70} - 4 q^{72} + 8 q^{73} + 64 q^{74} + 32 q^{75} + 16 q^{76} - 72 q^{77} + 20 q^{78} - 48 q^{79} + 16 q^{80} + 16 q^{81} + 8 q^{82} - 8 q^{83} + 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} - 16 q^{88} - 14 q^{90} - 40 q^{91} - 20 q^{94} + 8 q^{95} - 28 q^{96} + 48 q^{97} + 30 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9 - 14 * q^10 - 8 * q^12 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 8 * q^17 + 2 * q^18 + 8 * q^19 - 12 * q^20 - 4 * q^21 - 8 * q^22 - 4 * q^24 + 32 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^28 + 12 * q^29 - 14 * q^30 - 28 * q^32 - 20 * q^35 - 8 * q^36 - 16 * q^38 - 44 * q^40 - 4 * q^42 + 52 * q^44 - 4 * q^45 - 16 * q^46 - 32 * q^47 - 8 * q^48 + 22 * q^50 - 8 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 - 4 * q^55 + 20 * q^56 + 8 * q^57 - 44 * q^58 - 24 * q^59 - 12 * q^60 + 40 * q^61 + 40 * q^62 - 4 * q^63 - 8 * q^64 - 4 * q^65 - 8 * q^66 + 24 * q^68 + 56 * q^70 - 4 * q^72 + 8 * q^73 + 64 * q^74 + 32 * q^75 + 16 * q^76 - 72 * q^77 + 20 * q^78 - 48 * q^79 + 16 * q^80 + 16 * q^81 + 8 * q^82 - 8 * q^83 + 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 - 16 * q^88 - 14 * q^90 - 40 * q^91 - 20 * q^94 + 8 * q^95 - 28 * q^96 + 48 * q^97 + 30 * q^98

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