LMFDB - Embedded newform 240.2.y.e.187.7

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			187.7
Root			$-1.20803 + 0.735291i$ of defining polynomial
Character	$\chi$	$=$	240.187
Dual form			240.2.y.e.163.7

$q$-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 $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

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

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	0.733777	−	0.679390i	$-0.237756\pi$
$7$	0.143894	+	0.143894i	0.0543867	+	0.0543867i	−0.679390	+	0.733777i	$0.737756\pi$
$8$	−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	−0.585021	−	0.811018i	$-0.698914\pi$
$11$	0.749545	−	0.749545i	0.225996	−	0.225996i	0.811018	+	0.585021i	$0.198914\pi$
$12$	0.472743	+	1.94333i	0.136469	+	0.560990i
$13$		−	3.29132i		−	0.912847i	−0.889763	−	0.456423i	$-0.849130\pi$
$13$		−	3.29132i		−	0.912847i	0.889763	−	0.456423i	$-0.150870\pi$
$14$	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	0.852260	−	0.523118i	$-0.175231\pi$
$17$	1.35709	+	1.35709i	0.329142	+	0.329142i	−0.523118	+	0.852260i	$0.675231\pi$
$18$	1.11192	+	0.873858i	0.262083	+	0.205970i
$19$	4.25468	−	4.25468i	0.976091	−	0.976091i	−0.0236300	−	0.999721i	$-0.507522\pi$
$19$	4.25468	−	4.25468i	0.976091	−	0.976091i	0.999721	+	0.0236300i	$0.00752237\pi$
$20$	−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	−0.614393	−	0.789000i	$-0.710599\pi$
$23$	0.837388	−	0.837388i	0.174608	−	0.174608i	0.789000	+	0.614393i	$0.210599\pi$
$24$	−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	0.400891	−	0.916126i	$-0.368701\pi$
$29$	−2.77462	−	2.77462i	−0.515234	−	0.515234i	−0.916126	+	0.400891i	$0.868701\pi$
$30$	−3.14692	+	0.311271i	−0.574547	+	0.0568300i
$31$			6.60915i			1.18704i	0.804820	+	0.593520i	$0.202262\pi$
$31$			6.60915i			1.18704i	−0.804820	+	0.593520i	$0.797738\pi$
$32$	−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	$-0.691970\pi$
$37$		−	10.0194i		−	1.64717i	0.567191	−	0.823586i	$-0.308030\pi$
$38$	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	$0.0430342\pi$
$41$			1.72608i			0.269569i	−0.990875	+	0.134784i	$0.956966\pi$
$42$	0.0342559	+	0.285741i	0.00528580	+	0.0440908i
$43$			4.17171i			0.636180i	0.948061	+	0.318090i	$0.103041\pi$
$43$			4.17171i			0.636180i	−0.948061	+	0.318090i	$0.896959\pi$
$44$	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	−0.289128	+	0.957290i	$0.593365\pi$
$47$	−8.54502	+	8.54502i	−1.24642	+	1.24642i	−0.957290	+	0.289128i	$0.906635\pi$
$48$	−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	0.878687	−	0.477398i	$-0.158420\pi$
$59$	3.08237	+	3.08237i	0.401290	+	0.401290i	−0.477398	+	0.878687i	$0.658420\pi$
$60$	−3.77114	−	2.40385i	−0.486852	−	0.310336i
$61$	−5.00346	+	5.00346i	−0.640627	+	0.640627i	−0.950710	−	0.310083i	$-0.899643\pi$
$61$	−5.00346	+	5.00346i	−0.640627	+	0.640627i	0.310083	+	0.950710i	$0.399643\pi$
$62$	−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	$-0.916056\pi$
$67$		−	4.26739i		−	0.521345i	0.965427	−	0.260672i	$-0.0839442\pi$
$68$	−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	−0.863175	−	0.504904i	$-0.831528\pi$
$73$	−11.6889	−	11.6889i	−1.36808	−	1.36808i	−0.504904	−	0.863175i	$-0.668472\pi$
$74$	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	0.975720	+	0.219021i	$0.0702865\pi$
$97$	11.7668	+	11.7668i	1.19474	+	1.19474i	0.219021	+	0.975720i	$0.429714\pi$
$98$	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	0.639838	−	0.768510i	$-0.279002\pi$
$101$	−1.29314	−	1.29314i	−0.128672	−	0.128672i	−0.768510	+	0.639838i	$0.779002\pi$
$102$	0.323074	+	2.69488i	0.0319890	+	0.266832i
$103$	−11.2892	+	11.2892i	−1.11236	+	1.11236i	−0.119532	+	0.992830i	$0.538139\pi$
$103$	−11.2892	+	11.2892i	−1.11236	+	1.11236i	−0.992830	+	0.119532i	$0.961861\pi$
$104$	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	0.454582	−	0.890705i	$-0.349789\pi$
$109$	−4.55325	−	4.55325i	−0.436123	−	0.436123i	−0.890705	+	0.454582i	$0.849789\pi$
$110$	−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	−0.0803726	+	0.996765i	$0.525611\pi$
$113$	−11.4501	+	11.4501i	−1.07714	+	1.07714i	−0.996765	+	0.0803726i	$0.974389\pi$
$114$	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	−0.891626	−	0.452773i	$-0.850435\pi$
$127$	−4.94562	+	4.94562i	−0.438853	+	0.438853i	0.452773	+	0.891626i	$0.350435\pi$
$128$	−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	−0.992833	−	0.119509i	$-0.961868\pi$
$131$	−12.7313	−	12.7313i	−1.11234	−	1.11234i	−0.119509	−	0.992833i	$-0.538132\pi$
$132$	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	−0.916896	−	0.399127i	$-0.869313\pi$
$137$	−6.06032	+	6.06032i	−0.517768	+	0.517768i	0.399127	+	0.916896i	$0.369313\pi$
$138$	1.66287	−	0.199352i	0.141553	−	0.0169700i
$139$	10.3543	+	10.3543i	0.878239	+	0.878239i	0.993352	−	0.115114i	$-0.0367232\pi$
$139$	10.3543	+	10.3543i	0.878239	+	0.878239i	−0.115114	+	0.993352i	$0.536723\pi$
$140$	−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	−0.686961	−	0.726694i	$-0.741056\pi$
$149$	0.485009	−	0.485009i	0.0397335	−	0.0397335i	0.726694	+	0.686961i	$0.241056\pi$
$150$	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	0.867971	−	0.496615i	$-0.165424\pi$
$167$	4.79897	+	4.79897i	0.371355	+	0.371355i	−0.496615	+	0.867971i	$0.665424\pi$
$168$	−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	$-0.837625\pi$
$173$		−	12.8446i		−	0.976560i	0.872687	−	0.488280i	$-0.162375\pi$
$174$	−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	−0.825034	−	0.565083i	$-0.808844\pi$
$179$	−3.47791	+	3.47791i	−0.259951	+	0.259951i	0.565083	+	0.825034i	$0.308844\pi$
$180$	−3.77114	−	2.40385i	−0.281084	−	0.179173i
$181$	16.3185	+	16.3185i	1.21295	+	1.21295i	0.970053	+	0.242893i	$0.0780965\pi$
$181$	16.3185	+	16.3185i	1.21295	+	1.21295i	0.242893	+	0.970053i	$0.421903\pi$
$182$	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	$-0.715427\pi$
$191$		−	21.5483i		−	1.55918i	0.626289	−	0.779591i	$-0.284573\pi$
$192$	−5.25031	−	6.03608i	−0.378909	−	0.435616i
$193$	11.3161	−	11.3161i	0.814552	−	0.814552i	−0.170760	−	0.985313i	$-0.554622\pi$
$193$	11.3161	−	11.3161i	0.814552	−	0.814552i	0.985313	+	0.170760i	$0.0546224\pi$
$194$	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	$-0.688102\pi$
$197$		−	23.3109i		−	1.66083i	0.557142	−	0.830417i	$-0.311898\pi$
$198$	1.48843	−	0.178440i	0.105778	−	0.0126812i
$199$			2.14992i			0.152404i	0.997092	+	0.0762018i	$0.0242793\pi$
$199$			2.14992i			0.152404i	−0.997092	+	0.0762018i	$0.975721\pi$
$200$	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	0.889251	−	0.457420i	$-0.151226\pi$
$211$	6.27270	+	6.27270i	0.431830	+	0.431830i	−0.457420	+	0.889251i	$0.651226\pi$
$212$	−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	0.519587	−	0.854418i	$-0.326086\pi$
$223$	−5.00009	−	5.00009i	−0.334831	−	0.334831i	−0.854418	+	0.519587i	$0.826086\pi$
$224$	−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	$-0.730641\pi$
$227$		−	22.5630i		−	1.49756i	0.662821	−	0.748778i	$-0.269359\pi$
$228$	10.2796	+	6.25686i	0.680783	+	0.414371i
$229$	−6.83720	+	6.83720i	−0.451815	+	0.451815i	−0.895957	−	0.444142i	$-0.853509\pi$
$229$	−6.83720	+	6.83720i	−0.451815	+	0.451815i	0.444142	+	0.895957i	$0.353509\pi$
$230$	−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	0.801572	−	0.597899i	$-0.203997\pi$
$233$	3.10894	+	3.10894i	0.203673	+	0.203673i	−0.597899	+	0.801572i	$0.703997\pi$
$234$	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	−0.760521	−	0.649313i	$-0.775057\pi$
$251$	−1.76187	+	1.76187i	−0.111209	+	0.111209i	0.649313	+	0.760521i	$0.275057\pi$
$252$	−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	0.569162	−	0.822226i	$-0.307268\pi$
$257$	−4.05693	−	4.05693i	−0.253064	−	0.253064i	−0.822226	+	0.569162i	$0.807268\pi$
$258$	−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	0.515676	−	0.856784i	$-0.327541\pi$
$263$	22.2576	−	22.2576i	1.37246	−	1.37246i	0.856784	−	0.515676i	$-0.172459\pi$
$264$	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	0.241247	−	0.970464i	$-0.422444\pi$
$269$	−11.9600	−	11.9600i	−0.729217	−	0.729217i	−0.970464	+	0.241247i	$0.922444\pi$
$270$	−3.14692	+	0.311271i	−0.191516	+	0.0189433i
$271$		−	15.7162i		−	0.954691i	−0.878716	−	0.477346i	$-0.841599\pi$
$271$		−	15.7162i		−	0.954691i	0.878716	−	0.477346i	$-0.158401\pi$
$272$	−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	$0.0440681\pi$
$277$			4.59363i			0.276004i	−0.990432	+	0.138002i	$0.955932\pi$
$278$	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	$0.209560\pi$
$281$			20.5117i			1.22363i	−0.791002	+	0.611814i	$0.790440\pi$
$282$	−16.9685	+	2.03426i	−1.01046	+	0.121139i
$283$			28.8990i			1.71787i	0.512088	+	0.858933i	$0.328872\pi$
$283$			28.8990i			1.71787i	−0.512088	+	0.858933i	$0.671128\pi$
$284$	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	$0.132325\pi$
$307$			14.1518i			0.807684i	−0.914829	+	0.403842i	$0.867675\pi$
$308$	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	0.517602	−	0.855621i	$-0.326825\pi$
$313$	−5.98016	−	5.98016i	−0.338019	−	0.338019i	−0.855621	+	0.517602i	$0.826825\pi$
$314$	−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	−0.727455	−	0.686155i	$-0.759297\pi$
$331$	−0.751395	+	0.751395i	−0.0413004	+	0.0413004i	0.686155	+	0.727455i	$0.259297\pi$
$332$	−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	0.696697	−	0.717365i	$-0.254652\pi$
$337$	−0.379414	−	0.379414i	−0.0206680	−	0.0206680i	−0.717365	+	0.696697i	$0.754652\pi$
$338$	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	0.991102	+	0.133104i	$0.0424944\pi$
$349$	21.0019	+	21.0019i	1.12421	+	1.12421i	0.133104	+	0.991102i	$0.457506\pi$
$350$	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	−0.905318	−	0.424735i	$-0.860367\pi$
$353$	−9.02933	+	9.02933i	−0.480583	+	0.480583i	0.424735	+	0.905318i	$0.360367\pi$
$354$	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	$0.104914\pi$
$359$			12.2651i			0.647326i	−0.946172	+	0.323663i	$0.895086\pi$
$360$	−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	−0.739099	−	0.673597i	$-0.764749\pi$
$367$	−1.25485	+	1.25485i	−0.0655025	+	0.0655025i	0.673597	+	0.739099i	$0.264749\pi$
$368$	−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	0.733072	−	0.680151i	$-0.238086\pi$
$379$	1.03027	+	1.03027i	0.0529214	+	0.0529214i	−0.680151	+	0.733072i	$0.738086\pi$
$380$	−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	0.948172	−	0.317759i	$-0.102930\pi$
$383$	12.3374	+	12.3374i	0.630413	+	0.630413i	−0.317759	+	0.948172i	$0.602930\pi$
$384$	−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	−0.953181	−	0.302400i	$-0.902212\pi$
$389$	−12.8354	+	12.8354i	−0.650781	+	0.650781i	0.302400	+	0.953181i	$0.402212\pi$
$390$	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	−0.0894455	+	0.995992i	$0.528509\pi$
$419$	−22.2183	+	22.2183i	−1.08544	+	1.08544i	−0.995992	+	0.0894455i	$0.971491\pi$
$420$	−0.196744	−	0.888542i	−0.00960010	−	0.0433564i
$421$	−2.75098	−	2.75098i	−0.134074	−	0.134074i	0.636885	−	0.770959i	$-0.280223\pi$
$421$	−2.75098	−	2.75098i	−0.134074	−	0.134074i	−0.770959	+	0.636885i	$0.780223\pi$
$422$	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	$-0.959044\pi$
$431$		−	5.32770i		−	0.256626i	0.991734	−	0.128313i	$-0.0409563\pi$
$432$	−3.55303	+	1.83739i	−0.170945	+	0.0884014i
$433$	−3.38866	+	3.38866i	−0.162849	+	0.162849i	−0.783827	−	0.620979i	$-0.786735\pi$
$433$	−3.38866	+	3.38866i	−0.162849	+	0.162849i	0.620979	+	0.783827i	$0.286735\pi$
$434$	−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	$0.0457182\pi$
$439$			5.99801i			0.286269i	−0.989703	+	0.143135i	$0.954282\pi$
$440$	−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	$0.102637\pi$
$443$			13.3394i			0.633773i	−0.948463	+	0.316887i	$0.897363\pi$
$444$	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	$-0.752608\pi$
$449$		−	29.7201i		−	1.40258i	0.712877	−	0.701289i	$-0.247392\pi$
$450$	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	−0.952415	−	0.304804i	$-0.901409\pi$
$457$	−13.8443	+	13.8443i	−0.647611	+	0.647611i	0.304804	+	0.952415i	$0.401409\pi$
$458$	−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	0.119172	−	0.992874i	$-0.461976\pi$
$461$	23.8766	−	23.8766i	1.11205	−	1.11205i	0.992874	−	0.119172i	$-0.0380240\pi$
$462$	0.239852	+	0.188500i	0.0111589	+	0.00876979i
$463$	−10.5750	−	10.5750i	−0.491463	−	0.491463i	0.417304	−	0.908767i	$-0.362975\pi$
$463$	−10.5750	−	10.5750i	−0.491463	−	0.491463i	−0.908767	+	0.417304i	$0.862975\pi$
$464$	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	$0.244370\pi$
$467$			30.0161i			1.38898i	−0.719502	+	0.694491i	$0.755630\pi$
$468$	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	0.567045	−	0.823687i	$-0.308087\pi$
$487$	−5.66360	−	5.66360i	−0.256642	−	0.256642i	−0.823687	+	0.567045i	$0.808087\pi$
$488$	−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	−0.163018	+	0.986623i	$0.552123\pi$
$491$	−25.4744	+	25.4744i	−1.14964	+	1.14964i	−0.986623	+	0.163018i	$0.947877\pi$
$492$	−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	−0.146651	−	0.989188i	$-0.546849\pi$
$499$	18.8209	−	18.8209i	0.842537	−	0.842537i	0.989188	+	0.146651i	$0.0468494\pi$
$500$	−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	−0.509899	−	0.860234i	$-0.670317\pi$
$503$	7.85721	−	7.85721i	0.350336	−	0.350336i	0.860234	+	0.509899i	$0.170317\pi$
$504$	−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	0.446171	−	0.894948i	$-0.352787\pi$
$509$	−10.1248	−	10.1248i	−0.448776	−	0.448776i	−0.894948	+	0.446171i	$0.852787\pi$
$510$	−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	$-0.694987\pi$
$521$		−	37.3503i		−	1.63634i	0.574973	−	0.818172i	$-0.305013\pi$
$522$	−0.660538	−	5.50979i	−0.0289110	−	0.241157i
$523$		−	8.27258i		−	0.361735i	−0.983507	−	0.180867i	$-0.942110\pi$
$523$		−	8.27258i		−	0.361735i	0.983507	−	0.180867i	$-0.0578905\pi$
$524$	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	−0.424211	−	0.905563i	$-0.639449\pi$
$541$	11.1960	−	11.1960i	0.481352	−	0.481352i	0.905563	+	0.424211i	$0.139449\pi$
$542$	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	$0.193341\pi$
$547$			26.6966i			1.14147i	−0.821136	+	0.570733i	$0.806659\pi$
$548$	−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	−0.848905	−	0.528546i	$-0.822738\pi$
$571$	−7.65518	+	7.65518i	−0.320359	+	0.320359i	0.528546	+	0.848905i	$0.322738\pi$
$572$	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	0.996832	−	0.0795337i	$-0.0253431\pi$
$577$	22.0343	+	22.0343i	0.917298	+	0.917298i	−0.0795337	+	0.996832i	$0.525343\pi$
$578$	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	−0.0887706	+	0.996052i	$0.528294\pi$
$593$	−26.4172	+	26.4172i	−1.08482	+	1.08482i	−0.996052	+	0.0887706i	$0.971706\pi$
$594$	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	$0.116162\pi$
$599$			17.4693i			0.713775i	−0.934147	+	0.356888i	$0.883838\pi$
$600$	12.6157	+	6.39089i	0.515035	+	0.260907i
$601$			25.8843i			1.05584i	0.849294	+	0.527921i	$0.177028\pi$
$601$			25.8843i			1.05584i	−0.849294	+	0.527921i	$0.822972\pi$
$602$	−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	−0.997184	−	0.0749912i	$-0.976107\pi$
$607$	−22.7204	+	22.7204i	−0.922193	+	0.922193i	0.0749912	+	0.997184i	$0.476107\pi$
$608$	−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	−0.547429	−	0.836852i	$-0.684393\pi$
$617$	7.18912	−	7.18912i	0.289423	−	0.289423i	0.836852	+	0.547429i	$0.184393\pi$
$618$	−22.4180	+	2.68756i	−0.901782	+	0.108110i
$619$	−31.9741	−	31.9741i	−1.28515	−	1.28515i	−0.937700	−	0.347447i	$-0.887049\pi$
$619$	−31.9741	−	31.9741i	−1.28515	−	1.28515i	−0.347447	−	0.937700i	$-0.612951\pi$
$620$	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	0.997132	−	0.0756812i	$-0.0241131\pi$
$647$	23.4382	+	23.4382i	0.921451	+	0.921451i	−0.0756812	+	0.997132i	$0.524113\pi$
$648$	−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	$-0.904960\pi$
$653$		−	15.0338i		−	0.588318i	0.955756	−	0.294159i	$-0.0950396\pi$
$654$	−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	−0.911290	−	0.411766i	$-0.864912\pi$
$659$	−12.8233	+	12.8233i	−0.499524	+	0.499524i	0.411766	+	0.911290i	$0.364912\pi$
$660$	−4.62844	+	1.02484i	−0.180162	+	0.0398919i
$661$	22.6599	+	22.6599i	0.881369	+	0.881369i	0.993674	−	0.112305i	$-0.0358232\pi$
$661$	22.6599	+	22.6599i	0.881369	+	0.881369i	−0.112305	+	0.993674i	$0.535823\pi$
$662$	−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	−0.251311	−	0.967906i	$-0.580862\pi$
$673$	18.5901	−	18.5901i	0.716595	−	0.716595i	0.967906	+	0.251311i	$0.0808617\pi$
$674$	−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	$0.00932923\pi$
$677$			1.52496i			0.0586089i	−0.999571	+	0.0293044i	$0.990671\pi$
$678$	−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	$-0.976998\pi$
$683$		−	3.77382i		−	0.144401i	0.997390	−	0.0722006i	$-0.0230022\pi$
$684$	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	0.334984	−	0.942224i	$-0.391269\pi$
$691$	−15.9624	−	15.9624i	−0.607239	−	0.607239i	−0.942224	+	0.334984i	$0.891269\pi$
$692$	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	−0.976452	−	0.215735i	$-0.930785\pi$
$701$	−20.1411	+	20.1411i	−0.760717	+	0.760717i	0.215735	+	0.976452i	$0.430785\pi$
$702$	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	−0.536096	−	0.844157i	$-0.680101\pi$
$709$	8.20276	−	8.20276i	0.308061	−	0.308061i	0.844157	+	0.536096i	$0.180101\pi$
$710$	−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	0.675186	−	0.737648i	$-0.264064\pi$
$727$	−1.68416	−	1.68416i	−0.0624622	−	0.0624622i	−0.737648	+	0.675186i	$0.764064\pi$
$728$	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	$0.352176\pi$
$733$			48.4131i			1.78818i	−0.447889	+	0.894089i	$0.647824\pi$
$734$	−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	−0.662500	−	0.749062i	$-0.730505\pi$
$739$	2.35313	−	2.35313i	0.0865612	−	0.0865612i	0.749062	+	0.662500i	$0.230505\pi$
$740$	−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	−0.304076	−	0.952648i	$-0.598348\pi$
$743$	17.6788	−	17.6788i	0.648571	−	0.648571i	0.952648	+	0.304076i	$0.0983478\pi$
$744$	−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	$0.267831\pi$
$751$			40.8647i			1.49117i	−0.666409	+	0.745587i	$0.732169\pi$
$752$	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	$-0.851897\pi$
$757$		−	24.6892i		−	0.897345i	0.893696	−	0.448673i	$-0.148103\pi$
$758$	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	$-0.962160\pi$
$761$		−	6.54343i		−	0.237199i	0.992942	−	0.118600i	$-0.0378405\pi$
$762$	−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	$-0.842926\pi$
$769$		−	26.2710i		−	0.947357i	0.880698	−	0.473678i	$-0.157074\pi$
$770$	−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	$-0.878173\pi$
$787$		−	20.9534i		−	0.746908i	0.927649	−	0.373454i	$-0.121827\pi$
$788$	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	0.280025	−	0.959993i	$-0.409657\pi$
$811$	35.3133	−	35.3133i	1.24002	−	1.24002i	0.959993	−	0.280025i	$-0.0903426\pi$
$812$	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	0.948589	+	0.316509i	$0.102511\pi$
$821$	36.2490	+	36.2490i	1.26510	+	1.26510i	0.316509	+	0.948589i	$0.397489\pi$
$822$	−12.0345	+	1.44275i	−0.419750	+	0.0503215i
$823$	23.0235	−	23.0235i	0.802548	−	0.802548i	−0.180945	−	0.983493i	$-0.557916\pi$
$823$	23.0235	−	23.0235i	0.802548	−	0.802548i	0.983493	+	0.180945i	$0.0579156\pi$
$824$	−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	0.822042	−	0.569427i	$-0.192835\pi$
$829$	7.27338	+	7.27338i	0.252615	+	0.252615i	−0.569427	+	0.822042i	$0.692835\pi$
$830$	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	$0.0343451\pi$
$839$			6.23853i			0.215378i	−0.994185	+	0.107689i	$0.965655\pi$
$840$	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	−0.870145	−	0.492797i	$-0.835975\pi$
$857$	−11.0467	+	11.0467i	−0.377348	+	0.377348i	0.492797	+	0.870145i	$0.335975\pi$
$858$	−0.587302	−	4.89890i	−0.0200502	−	0.167246i
$859$	−1.75107	−	1.75107i	−0.0597457	−	0.0597457i	0.676603	−	0.736348i	$-0.263452\pi$
$859$	−1.75107	−	1.75107i	−0.0597457	−	0.0597457i	−0.736348	+	0.676603i	$0.763452\pi$
$860$	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	0.622386	−	0.782710i	$-0.286163\pi$
$863$	−4.70982	−	4.70982i	−0.160324	−	0.160324i	−0.782710	+	0.622386i	$0.786163\pi$
$864$	−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	0.655835	−	0.754904i	$-0.272317\pi$
$887$	−2.95052	−	2.95052i	−0.0990688	−	0.0990688i	−0.754904	+	0.655835i	$0.772317\pi$
$888$	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	$-0.882516\pi$
$911$		−	21.7776i		−	0.721525i	0.932658	−	0.360763i	$-0.117484\pi$
$912$	−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	$-0.807421\pi$
$919$		−	34.4842i		−	1.13753i	0.822500	−	0.568765i	$-0.192579\pi$
$920$	−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	$0.105369\pi$
$929$			19.8125i			0.650028i	−0.945709	+	0.325014i	$0.894631\pi$
$930$	−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	−0.281062	−	0.959690i	$-0.590687\pi$
$937$	20.7731	−	20.7731i	0.678628	−	0.678628i	0.959690	+	0.281062i	$0.0906866\pi$
$938$	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	−0.983607	−	0.180328i	$-0.942284\pi$
$941$	−24.6412	+	24.6412i	−0.803279	+	0.803279i	0.180328	+	0.983607i	$0.442284\pi$
$942$	−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	$-0.729971\pi$
$947$		−	46.1706i		−	1.50034i	0.661244	−	0.750171i	$-0.270029\pi$
$948$	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	0.789853	−	0.613296i	$-0.210157\pi$
$953$	5.45044	+	5.45044i	0.176557	+	0.176557i	−0.613296	+	0.789853i	$0.710157\pi$
$954$	−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	0.351420	−	0.936218i	$-0.385699\pi$
$967$	−18.1852	−	18.1852i	−0.584798	−	0.584798i	−0.936218	+	0.351420i	$0.885699\pi$
$968$	−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	−0.868609	−	0.495497i	$-0.834986\pi$
$971$	−11.6265	+	11.6265i	−0.373112	+	0.373112i	0.495497	+	0.868609i	$0.334986\pi$
$972$	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	0.560647	−	0.828055i	$-0.310552\pi$
$977$	−8.35835	−	8.35835i	−0.267407	−	0.267407i	−0.828055	+	0.560647i	$0.810552\pi$
$978$	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	−0.934414	−	0.356188i	$-0.884076\pi$
$983$	−18.1290	+	18.1290i	−0.578226	+	0.578226i	0.356188	+	0.934414i	$0.384076\pi$
$984$	−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	$0.151334\pi$
$991$			28.8183i			0.915444i	−0.889095	+	0.457722i	$0.848666\pi$
$992$	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	$-0.838371\pi$
$997$		−	30.7058i		−	0.972463i	0.873830	−	0.486232i	$-0.161629\pi$
$998$	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.187.7	yes	16
3.2	odd	2		720.2.z.f.667.2		16
4.3	odd	2		960.2.y.e.847.4		16
5.3	odd	4		240.2.bc.e.43.5	yes	16
8.3	odd	2		1920.2.y.j.1567.5		16
8.5	even	2		1920.2.y.i.1567.5		16
15.8	even	4		720.2.bd.f.523.4		16
16.3	odd	4		240.2.bc.e.67.5	yes	16
16.5	even	4		1920.2.bc.j.607.1		16
16.11	odd	4		1920.2.bc.i.607.1		16
16.13	even	4		960.2.bc.e.367.8		16
20.3	even	4		960.2.bc.e.463.8		16
40.3	even	4		1920.2.bc.j.1183.1		16
40.13	odd	4		1920.2.bc.i.1183.1		16
48.35	even	4		720.2.bd.f.307.4		16
80.3	even	4	inner	240.2.y.e.163.7	✓	16
80.13	odd	4		960.2.y.e.943.4		16
80.43	even	4		1920.2.y.i.223.5		16
80.53	odd	4		1920.2.y.j.223.5		16
240.83	odd	4		720.2.z.f.163.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.7	✓	16	80.3	even	4	inner
240.2.y.e.187.7	yes	16	1.1	even	1	trivial
240.2.bc.e.43.5	yes	16	5.3	odd	4
240.2.bc.e.67.5	yes	16	16.3	odd	4
720.2.z.f.163.2		16	240.83	odd	4
720.2.z.f.667.2		16	3.2	odd	2
720.2.bd.f.307.4		16	48.35	even	4
720.2.bd.f.523.4		16	15.8	even	4
960.2.y.e.847.4		16	4.3	odd	2
960.2.y.e.943.4		16	80.13	odd	4
960.2.bc.e.367.8		16	16.13	even	4
960.2.bc.e.463.8		16	20.3	even	4
1920.2.y.i.223.5		16	80.43	even	4
1920.2.y.i.1567.5		16	8.5	even	2
1920.2.y.j.223.5		16	80.53	odd	4
1920.2.y.j.1567.5		16	8.3	odd	2
1920.2.bc.i.607.1		16	16.11	odd	4
1920.2.bc.i.1183.1		16	40.13	odd	4
1920.2.bc.j.607.1		16	16.5	even	4
1920.2.bc.j.1183.1		16	40.3	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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