LMFDB - Embedded newform 240.2.bc.e.67.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(43,240)]

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, 1, 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("240.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bc (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			67.5
Root			$-1.20803 + 0.735291i$ of defining polynomial
Character	$\chi$	$=$	240.67
Dual form			240.2.bc.e.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.873858 + 1.11192i) q^{2} -1.00000i q^{3} +(-0.472743 + 1.94333i) q^{4} +(1.54804 + 1.61356i) q^{5} +(1.11192 - 0.873858i) q^{6} +(0.143894 + 0.143894i) q^{7} +(-2.57394 + 1.17254i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.873858 + 1.11192i) q^{2} -1.00000i q^{3} +(-0.472743 + 1.94333i) q^{4} +(1.54804 + 1.61356i) q^{5} +(1.11192 - 0.873858i) q^{6} +(0.143894 + 0.143894i) q^{7} +(-2.57394 + 1.17254i) q^{8} -1.00000 q^{9} +(-0.441393 + 3.13132i) q^{10} +(0.749545 + 0.749545i) q^{11} +(1.94333 + 0.472743i) q^{12} +3.29132 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} +(-0.873858 - 1.11192i) q^{18} +(-4.25468 - 4.25468i) q^{19} +(-3.86750 + 2.24554i) q^{20} +(0.143894 - 0.143894i) q^{21} +(-0.178440 + 1.48843i) 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} +1.00000i q^{27} +(-0.347657 + 0.211607i) q^{28} +(2.77462 - 2.77462i) q^{29} +(3.13132 + 0.441393i) q^{30} -6.60915i q^{31} +(-1.06181 - 5.55631i) q^{32} +(0.749545 - 0.749545i) q^{33} +(-0.323074 + 2.69488i) q^{34} +(-0.00942893 + 0.454934i) q^{35} +(0.472743 - 1.94333i) q^{36} -10.0194 q^{37} +(1.01289 - 8.44886i) q^{38} -3.29132i q^{39} +(-5.87651 - 2.33808i) q^{40} -1.72608i q^{41} +(0.285741 + 0.0342559i) q^{42} -4.17171 q^{43} +(-1.81095 + 1.10227i) q^{44} +(-1.54804 - 1.61356i) q^{45} +(1.66287 + 0.199352i) q^{46} +(8.54502 - 8.54502i) q^{47} +(-1.83739 + 3.55303i) q^{48} -6.95859i q^{49} +(-5.73588 + 4.13518i) q^{50} +(1.35709 - 1.35709i) q^{51} +(-1.55595 + 6.39610i) q^{52} +5.05524i 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} +(5.50979 + 0.660538i) q^{58} +(-3.08237 + 3.08237i) q^{59} +(2.24554 + 3.86750i) q^{60} +(-5.00346 - 5.00346i) q^{61} +(7.34887 - 5.77546i) 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} -4.26739 q^{67} +(-3.27881 + 1.99571i) q^{68} +(-0.837388 - 0.837388i) q^{69} +(-0.514091 + 0.387064i) q^{70} +13.2111 q^{71} +(2.57394 - 1.17254i) q^{72} +(11.6889 + 11.6889i) q^{73} +(-8.75550 - 11.1407i) q^{74} +(4.99571 + 0.207170i) q^{75} +(10.2796 - 6.25686i) q^{76} +0.215710i q^{77} +(3.65969 - 2.87614i) q^{78} -9.95558 q^{79} +(-2.53547 - 8.57738i) q^{80} +1.00000 q^{81} +(1.91927 - 1.50835i) q^{82} +10.0134i q^{83} +(0.211607 + 0.347657i) q^{84} +(-0.0889259 + 4.29056i) q^{85} +(-3.64549 - 4.63862i) q^{86} +(-2.77462 - 2.77462i) q^{87} +(-2.80815 - 1.05041i) q^{88} -5.76005 q^{89} +(0.441393 - 3.13132i) q^{90} +(0.473599 + 0.473599i) q^{91} +(1.23145 + 2.02319i) q^{92} -6.60915 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} +(7.73741 - 6.08082i) q^{98} +(-0.749545 - 0.749545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9	$ 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 4 q^{24} - 32 q^{25} + 20 q^{26} + 12 q^{28} - 12 q^{29} + 2 q^{30} - 28 q^{32} + 12 q^{35} - 8 q^{36} - 24 q^{37} + 16 q^{38} + 16 q^{40} + 24 q^{42} + 24 q^{43} - 52 q^{44} + 8 q^{45} - 16 q^{46} + 32 q^{47} - 16 q^{48} + 6 q^{50} - 8 q^{51} + 24 q^{52} - 2 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 12 q^{58} + 24 q^{59} + 24 q^{60} + 40 q^{61} + 28 q^{62} + 4 q^{63} + 8 q^{64} - 4 q^{65} - 8 q^{66} + 16 q^{67} - 8 q^{68} + 12 q^{70} - 8 q^{72} - 8 q^{73} - 64 q^{74} + 24 q^{75} + 16 q^{76} + 12 q^{78} + 48 q^{79} + 16 q^{81} - 32 q^{82} - 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{88} + 2 q^{90} - 40 q^{91} - 16 q^{92} - 32 q^{93} + 20 q^{94} - 8 q^{95} - 28 q^{96} + 48 q^{97} + 62 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 4 * q^24 - 32 * q^25 + 20 * q^26 + 12 * q^28 - 12 * q^29 + 2 * q^30 - 28 * q^32 + 12 * q^35 - 8 * q^36 - 24 * q^37 + 16 * q^38 + 16 * q^40 + 24 * q^42 + 24 * q^43 - 52 * q^44 + 8 * q^45 - 16 * q^46 + 32 * q^47 - 16 * q^48 + 6 * q^50 - 8 * q^51 + 24 * q^52 - 2 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 12 * q^58 + 24 * q^59 + 24 * q^60 + 40 * q^61 + 28 * q^62 + 4 * q^63 + 8 * q^64 - 4 * q^65 - 8 * q^66 + 16 * q^67 - 8 * q^68 + 12 * q^70 - 8 * q^72 - 8 * q^73 - 64 * q^74 + 24 * q^75 + 16 * q^76 + 12 * q^78 + 48 * q^79 + 16 * q^81 - 32 * q^82 - 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^88 + 2 * q^90 - 40 * q^91 - 16 * q^92 - 32 * q^93 + 20 * q^94 - 8 * q^95 - 28 * q^96 + 48 * q^97 + 62 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.873858	+	1.11192i	0.617911	+	0.786248i
$2$	0.873858	+	1.11192i	0.617911	+	0.786248i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−0.472743	+	1.94333i	−0.236372	+	0.971663i
$5$	1.54804	+	1.61356i	0.692303	+	0.721607i
$5$	1.54804	+	1.61356i	0.692303	+	0.721607i
$6$	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	$0.737756\pi$
$8$	−2.57394	+	1.17254i	−0.910024	+	0.414554i
$9$	−1.00000			−0.333333
$10$	−0.441393	+	3.13132i	−0.139581	+	0.990211i
$11$	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	$0.698914\pi$
$12$	1.94333	+	0.472743i	0.560990	+	0.136469i
$13$	3.29132			0.912847			0.456423	−	0.889763i	$-0.349130\pi$
$13$	3.29132			0.912847			0.456423	+	0.889763i	$0.349130\pi$
$14$	−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	$0.675231\pi$
$18$	−0.873858	−	1.11192i	−0.205970	−	0.262083i
$19$	−4.25468	−	4.25468i	−0.976091	−	0.976091i	0.0236300	−	0.999721i	$-0.492478\pi$
$19$	−4.25468	−	4.25468i	−0.976091	−	0.976091i	−0.999721	+	0.0236300i	$0.992478\pi$
$20$	−3.86750	+	2.24554i	−0.864800	+	0.502117i
$21$	0.143894	−	0.143894i	0.0314002	−	0.0314002i
$22$	−0.178440	+	1.48843i	−0.0380435	+	0.317335i
$23$	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
$27$			1.00000i			0.192450i
$28$	−0.347657	+	0.211607i	−0.0657010	+	0.0399900i
$29$	2.77462	−	2.77462i	0.515234	−	0.515234i	−0.400891	−	0.916126i	$-0.631299\pi$
$29$	2.77462	−	2.77462i	0.515234	−	0.515234i	0.916126	+	0.400891i	$0.131299\pi$
$30$	3.13132	+	0.441393i	0.571698	+	0.0805870i
$31$		−	6.60915i		−	1.18704i	−0.804820	−	0.593520i	$-0.797738\pi$
$31$		−	6.60915i		−	1.18704i	0.804820	−	0.593520i	$-0.202262\pi$
$32$	−1.06181	−	5.55631i	−0.187703	−	0.982226i
$33$	0.749545	−	0.749545i	0.130479	−	0.130479i
$34$	−0.323074	+	2.69488i	−0.0554067	+	0.462167i
$35$	−0.00942893	+	0.454934i	−0.00159378	+	0.0768979i
$36$	0.472743	−	1.94333i	0.0787906	−	0.323888i
$37$	−10.0194			−1.64717			−0.823586	−	0.567191i	$-0.808030\pi$
$37$	−10.0194			−1.64717			−0.823586	+	0.567191i	$0.808030\pi$
$38$	1.01289	−	8.44886i	0.164312	−	1.37059i
$39$		−	3.29132i		−	0.527032i
$40$	−5.87651	−	2.33808i	−0.929158	−	0.369683i
$41$		−	1.72608i		−	0.269569i	−0.990875	−	0.134784i	$-0.956966\pi$
$41$		−	1.72608i		−	0.269569i	0.990875	−	0.134784i	$-0.0430342\pi$
$42$	0.285741	+	0.0342559i	0.0440908	+	0.00528580i
$43$	−4.17171			−0.636180			−0.318090	−	0.948061i	$-0.603041\pi$
$43$	−4.17171			−0.636180			−0.318090	+	0.948061i	$0.603041\pi$
$44$	−1.81095	+	1.10227i	−0.273011	+	0.166173i
$45$	−1.54804	−	1.61356i	−0.230768	−	0.240536i
$46$	1.66287	+	0.199352i	0.245177	+	0.0293929i
$47$	8.54502	−	8.54502i	1.24642	−	1.24642i	0.289128	−	0.957290i	$-0.406635\pi$
$47$	8.54502	−	8.54502i	1.24642	−	1.24642i	0.957290	−	0.289128i	$-0.0933654\pi$
$48$	−1.83739	+	3.55303i	−0.265204	+	0.512835i
$49$		−	6.95859i		−	0.994084i
$50$	−5.73588	+	4.13518i	−0.811175	+	0.584803i
$51$	1.35709	−	1.35709i	0.190030	−	0.190030i
$52$	−1.55595	+	6.39610i	−0.215771	+	0.886979i
$53$			5.05524i			0.694391i	0.937793	+	0.347196i	$0.112866\pi$
$53$			5.05524i			0.694391i	−0.937793	+	0.347196i	$0.887134\pi$
$54$	−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
$58$	5.50979	+	0.660538i	0.723471	+	0.0867329i
$59$	−3.08237	+	3.08237i	−0.401290	+	0.401290i	−0.878687	−	0.477398i	$-0.841580\pi$
$59$	−3.08237	+	3.08237i	−0.401290	+	0.401290i	0.477398	+	0.878687i	$0.341580\pi$
$60$	2.24554	+	3.86750i	0.289897	+	0.499292i
$61$	−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	$0.899643\pi$
$62$	7.34887	−	5.77546i	0.933307	−	0.733485i
$63$	−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
$67$	−4.26739			−0.521345			−0.260672	−	0.965427i	$-0.583944\pi$
$67$	−4.26739			−0.521345			−0.260672	+	0.965427i	$0.583944\pi$
$68$	−3.27881	+	1.99571i	−0.397614	+	0.242015i
$69$	−0.837388	−	0.837388i	−0.100810	−	0.100810i
$70$	−0.514091	+	0.387064i	−0.0614456	+	0.0462629i
$71$	13.2111			1.56786			0.783932	−	0.620846i	$-0.213211\pi$
$71$	13.2111			1.56786			0.783932	+	0.620846i	$0.213211\pi$
$72$	2.57394	−	1.17254i	0.303341	−	0.138185i
$73$	11.6889	+	11.6889i	1.36808	+	1.36808i	0.863175	+	0.504904i	$0.168472\pi$
$73$	11.6889	+	11.6889i	1.36808	+	1.36808i	0.504904	+	0.863175i	$0.331528\pi$
$74$	−8.75550	−	11.1407i	−1.01781	−	1.29509i
$75$	4.99571	+	0.207170i	0.576854	+	0.0239220i
$76$	10.2796	−	6.25686i	1.17915	−	0.717711i
$77$			0.215710i			0.0245824i
$78$	3.65969	−	2.87614i	0.414378	−	0.325659i
$79$	−9.95558			−1.12009			−0.560045	−	0.828462i	$-0.689216\pi$
$79$	−9.95558			−1.12009			−0.560045	+	0.828462i	$0.689216\pi$
$80$	−2.53547	−	8.57738i	−0.283474	−	0.958980i
$81$	1.00000			0.111111
$82$	1.91927	−	1.50835i	0.211948	−	0.166570i
$83$			10.0134i			1.09912i	0.835455	+	0.549559i	$0.185204\pi$
$83$			10.0134i			1.09912i	−0.835455	+	0.549559i	$0.814796\pi$
$84$	0.211607	+	0.347657i	0.0230883	+	0.0379325i
$85$	−0.0889259	+	4.29056i	−0.00964537	+	0.465377i
$86$	−3.64549	−	4.63862i	−0.393103	−	0.500195i
$87$	−2.77462	−	2.77462i	−0.297471	−	0.297471i
$88$	−2.80815	−	1.05041i	−0.299350	−	0.111974i
$89$	−5.76005			−0.610564			−0.305282	−	0.952262i	$-0.598751\pi$
$89$	−5.76005			−0.610564			−0.305282	+	0.952262i	$0.598751\pi$
$90$	0.441393	−	3.13132i	0.0465269	−	0.330070i
$91$	0.473599	+	0.473599i	0.0496467	+	0.0496467i
$92$	1.23145	+	2.02319i	0.128387	+	0.210932i
$93$	−6.60915			−0.685337
$94$	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	$0.429714\pi$
$98$	7.73741	−	6.08082i	0.781597	−	0.614256i
$99$	−0.749545	−	0.749545i	−0.0753321	−	0.0753321i
$100$	−9.61034	−	2.76429i	−0.961034	−	0.276429i
$101$	−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	$0.279002\pi$
$102$	2.69488	+	0.323074i	0.266832	+	0.0319890i
$103$	−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
$107$			1.39451i			0.134812i	0.997726	+	0.0674060i	$0.0214723\pi$
$107$			1.39451i			0.134812i	−0.997726	+	0.0674060i	$0.978528\pi$
$108$	−1.94333	−	0.472743i	−0.186997	−	0.0454897i
$109$	4.55325	−	4.55325i	0.436123	−	0.436123i	−0.454582	−	0.890705i	$-0.650211\pi$
$109$	4.55325	−	4.55325i	0.436123	−	0.436123i	0.890705	+	0.454582i	$0.150211\pi$
$110$	−2.67791	+	2.01622i	−0.255329	+	0.192239i
$111$			10.0194i			0.950995i
$112$	−0.246870	−	0.775647i	−0.0233270	−	0.0732917i
$113$	−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
$115$	2.64749	+	0.0548716i	0.246879	+	0.00511680i
$116$	4.08031	+	6.70368i	0.378847	+	0.622421i
$117$	−3.29132			−0.304282
$118$	−6.12090	−	0.733801i	−0.563475	−	0.0675519i
$119$			0.390552i			0.0358018i
$120$	−2.33808	+	5.87651i	−0.213437	+	0.536450i
$121$		−	9.87636i		−	0.897851i
$122$	1.19114	−	9.93577i	0.107841	−	0.899542i
$123$	−1.72608			−0.155636
$124$	12.8437	+	3.12443i	1.15340	+	0.280582i
$125$	−8.38159	+	7.39925i	−0.749672	+	0.661809i
$126$	0.0342559	−	0.285741i	0.00305176	−	0.0254559i
$127$	4.94562	−	4.94562i	0.438853	−	0.438853i	−0.452773	−	0.891626i	$-0.649565\pi$
$127$	4.94562	−	4.94562i	0.438853	−	0.438853i	0.891626	+	0.452773i	$0.149565\pi$
$128$	11.2997	+	0.563267i	0.998760	+	0.0497862i
$129$			4.17171i			0.367299i
$130$	−1.45276	+	10.3062i	−0.127416	+	0.903910i
$131$	−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	$0.961868\pi$
$132$	1.10227	+	1.81095i	0.0959401	+	0.157623i
$133$		−	1.22444i		−	0.106173i
$134$	−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	$-0.630687\pi$
$137$	6.06032	−	6.06032i	0.517768	−	0.517768i	0.916896	+	0.399127i	$0.130687\pi$
$138$	0.199352	−	1.66287i	0.0169700	−	0.141553i
$139$	−10.3543	+	10.3543i	−0.878239	+	0.878239i	−0.993352	−	0.115114i	$-0.963277\pi$
$139$	−10.3543	+	10.3543i	−0.878239	+	0.878239i	0.115114	+	0.993352i	$0.463277\pi$
$140$	−0.879627	−	0.233390i	−0.0743421	−	0.0197251i
$141$	−8.54502	−	8.54502i	−0.719620	−	0.719620i
$142$	11.5446	+	14.6897i	0.968801	+	1.23273i
$143$	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
$147$	−6.95859			−0.573935
$148$	4.73658	−	19.4709i	0.389345	−	1.60050i
$149$	−0.485009	−	0.485009i	−0.0397335	−	0.0397335i	0.686961	−	0.726694i	$-0.258944\pi$
$149$	−0.485009	−	0.485009i	−0.0397335	−	0.0397335i	−0.726694	+	0.686961i	$0.758944\pi$
$150$	4.13518	+	5.73588i	0.337636	+	0.468332i
$151$	6.47302			0.526767			0.263383	−	0.964691i	$-0.415162\pi$
$151$	6.47302			0.526767			0.263383	+	0.964691i	$0.415162\pi$
$152$	15.9401	+	5.96251i	1.29291	+	0.483624i
$153$	−1.35709	−	1.35709i	−0.109714	−	0.109714i
$154$	−0.239852	+	0.188500i	−0.0193278	+	0.0151897i
$155$	10.6643	−	10.2312i	0.856576	−	0.821790i
$156$	6.39610	+	1.55595i	0.512098	+	0.124575i
$157$		−	11.7463i		−	0.937455i	−0.883343	−	0.468728i	$-0.844713\pi$
$157$		−	11.7463i		−	0.937455i	0.883343	−	0.468728i	$-0.155287\pi$
$158$	−8.69977	−	11.0698i	−0.692117	−	0.880669i
$159$	5.05524			0.400907
$160$	7.32173	−	10.3147i	0.578834	−	0.815445i
$161$	0.240990			0.0189926
$162$	0.873858	+	1.11192i	0.0686568	+	0.0873609i
$163$		−	1.87143i		−	0.146582i	−0.997311	−	0.0732908i	$-0.976650\pi$
$163$		−	1.87143i		−	0.146582i	0.997311	−	0.0732908i	$-0.0233501\pi$
$164$	3.35434	+	0.815994i	0.261930	+	0.0637184i
$165$	2.36976	+	0.0491155i	0.184486	+	0.00382364i
$166$	−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	$0.665424\pi$
$168$	−0.201653	+	0.539094i	−0.0155578	+	0.0415920i
$169$	−2.16724			−0.166711
$170$	−4.84848	+	3.65046i	−0.371861	+	0.279978i
$171$	4.25468	+	4.25468i	0.325364	+	0.325364i
$172$	1.97215	−	8.10699i	0.150375	−	0.618152i
$173$	12.8446			0.976560			0.488280	−	0.872687i	$-0.337625\pi$
$173$	12.8446			0.976560			0.488280	+	0.872687i	$0.337625\pi$
$174$	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
$178$	−5.03346	−	6.40473i	−0.377274	−	0.480054i
$179$	3.47791	+	3.47791i	0.259951	+	0.259951i	0.825034	−	0.565083i	$-0.191156\pi$
$179$	3.47791	+	3.47791i	0.259951	+	0.259951i	−0.565083	+	0.825034i	$0.691156\pi$
$180$	3.86750	−	2.24554i	0.288267	−	0.167372i
$181$	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	$-0.0780965\pi$
$182$	−0.112747	+	0.940464i	−0.00835737	+	0.0697119i
$183$	−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
$187$			2.03439i			0.148770i
$188$	12.5661	+	20.6453i	0.916480	+	1.50572i
$189$	−0.143894	+	0.143894i	−0.0104667	+	0.0104667i
$190$	15.2008	−	11.4448i	1.10278	−	0.830292i
$191$			21.5483i			1.55918i	0.626289	+	0.779591i	$0.284573\pi$
$191$			21.5483i			1.55918i	−0.626289	+	0.779591i	$0.715427\pi$
$192$	−6.03608	−	5.25031i	−0.435616	−	0.378909i
$193$	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
$195$	5.31074	−	5.09507i	0.380310	−	0.364866i
$196$	13.5228	+	3.28963i	0.965915	+	0.234973i
$197$	−23.3109			−1.66083			−0.830417	−	0.557142i	$-0.811898\pi$
$197$	−23.3109			−1.66083			−0.830417	+	0.557142i	$0.811898\pi$
$198$	0.178440	−	1.48843i	0.0126812	−	0.105778i
$199$			2.14992i			0.152404i	0.997092	+	0.0762018i	$0.0242793\pi$
$199$			2.14992i			0.152404i	−0.997092	+	0.0762018i	$0.975721\pi$
$200$	−5.32441	−	13.1016i	−0.376492	−	0.926420i
$201$			4.26739i			0.300999i
$202$	−2.56789	−	0.307850i	−0.180676	−	0.0216603i
$203$	0.798501			0.0560438
$204$	1.99571	+	3.27881i	0.139727	+	0.229563i
$205$	2.78514	−	2.67204i	0.194523	−	0.186623i
$206$	−22.4180	−	2.68756i	−1.56193	−	0.187251i
$207$	−0.837388	+	0.837388i	−0.0582025	+	0.0582025i
$208$	−11.6941	−	6.04742i	−0.810842	−	0.419313i
$209$		−	6.37815i		−	0.441186i
$210$	0.387064	+	0.514091i	0.0267099	+	0.0354756i
$211$	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	$0.151226\pi$
$212$	−9.82398	−	2.38983i	−0.674714	−	0.164134i
$213$		−	13.2111i		−	0.905207i
$214$	−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
$218$	9.04176	+	1.08397i	0.612385	+	0.0734155i
$219$	11.6889	−	11.6889i	0.789861	−	0.789861i
$220$	−4.58200	−	1.21574i	−0.308918	−	0.0819649i
$221$	4.46660	+	4.46660i	0.300456	+	0.300456i
$222$	−11.1407	+	8.75550i	−0.747718	+	0.587631i
$223$	5.00009	+	5.00009i	0.334831	+	0.334831i	0.854418	−	0.519587i	$-0.173914\pi$
$223$	5.00009	+	5.00009i	0.334831	+	0.334831i	−0.519587	+	0.854418i	$0.673914\pi$
$224$	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
$227$	−22.5630			−1.49756			−0.748778	−	0.662821i	$-0.769359\pi$
$227$	−22.5630			−1.49756			−0.748778	+	0.662821i	$0.769359\pi$
$228$	−6.25686	−	10.2796i	−0.414371	−	0.680783i
$229$	6.83720	+	6.83720i	0.451815	+	0.451815i	0.895957	−	0.444142i	$-0.146491\pi$
$229$	6.83720	+	6.83720i	0.451815	+	0.451815i	−0.444142	+	0.895957i	$0.646491\pi$
$230$	2.25251	+	2.99175i	0.148526	+	0.197270i
$231$	0.215710			0.0141926
$232$	−3.88836	+	10.3951i	−0.255283	+	0.682469i
$233$	−3.10894	−	3.10894i	−0.203673	−	0.203673i	0.597899	−	0.801572i	$-0.296003\pi$
$233$	−3.10894	−	3.10894i	−0.203673	−	0.203673i	−0.801572	+	0.597899i	$0.796003\pi$
$234$	−2.87614	−	3.65969i	−0.188019	−	0.239241i
$235$	27.0159	+	0.559930i	1.76232	+	0.0365258i
$236$	−4.53287	−	7.44721i	−0.295065	−	0.484772i
$237$			9.95558i			0.646685i
$238$	−0.434264	+	0.341287i	−0.0281491	+	0.0221224i
$239$	−11.0671			−0.715873			−0.357937	−	0.933746i	$-0.616520\pi$
$239$	−11.0671			−0.715873			−0.357937	+	0.933746i	$0.616520\pi$
$240$	−8.57738	+	2.53547i	−0.553667	+	0.163664i
$241$	−23.4743			−1.51211			−0.756056	−	0.654507i	$-0.772876\pi$
$241$	−23.4743			−1.51211			−0.756056	+	0.654507i	$0.772876\pi$
$242$	10.9818	−	8.63054i	0.705934	−	0.554792i
$243$		−	1.00000i		−	0.0641500i
$244$	12.0887	−	7.35799i	0.773899	−	0.471047i
$245$	11.2281	−	10.7721i	0.717338	−	0.688207i
$246$	−1.50835	−	1.91927i	−0.0961690	−	0.122368i
$247$	−14.0035	−	14.0035i	−0.891021	−	0.891021i
$248$	7.74948	+	17.0116i	0.492092	+	1.08023i
$249$	10.0134			0.634576
$250$	−15.5517	−	2.85379i	−0.983577	−	0.180489i
$251$	−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	$0.775057\pi$
$252$	0.347657	−	0.211607i	0.0219003	−	0.0133300i
$253$	1.25532			0.0789213
$254$	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	$0.807268\pi$
$258$	−4.63862	+	3.64549i	−0.288788	+	0.226958i
$259$	−1.44172	−	1.44172i	−0.0895842	−	0.0895842i
$260$	−12.7292	+	7.39077i	−0.789429	+	0.458356i
$261$	−2.77462	+	2.77462i	−0.171745	+	0.171745i
$262$	−25.2816	−	3.03087i	−1.56190	−	0.187248i
$263$	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
$267$			5.76005i			0.352509i
$268$	2.01738	−	8.29293i	0.123231	−	0.506571i
$269$	11.9600	−	11.9600i	0.729217	−	0.729217i	−0.241247	−	0.970464i	$-0.577556\pi$
$269$	11.9600	−	11.9600i	0.729217	−	0.729217i	0.970464	+	0.241247i	$0.0775564\pi$
$270$	−3.13132	−	0.441393i	−0.190566	−	0.0268623i
$271$			15.7162i			0.954691i	0.878716	+	0.477346i	$0.158401\pi$
$271$			15.7162i			0.954691i	−0.878716	+	0.477346i	$0.841599\pi$
$272$	−2.32827	−	7.31526i	−0.141172	−	0.443553i
$273$	0.473599	−	0.473599i	0.0286635	−	0.0286635i
$274$	12.0345	+	1.44275i	0.727029	+	0.0871595i
$275$	−3.89979	+	3.58922i	−0.235166	+	0.216438i
$276$	2.02319	−	1.23145i	0.121782	−	0.0741245i
$277$	4.59363			0.276004			0.138002	−	0.990432i	$-0.455932\pi$
$277$	4.59363			0.276004			0.138002	+	0.990432i	$0.455932\pi$
$278$	−20.5613	−	2.46498i	−1.23319	−	0.147840i
$279$			6.60915i			0.395680i
$280$	−0.509157	−	1.18203i	−0.0304280	−	0.0706397i
$281$		−	20.5117i		−	1.22363i	−0.791002	−	0.611814i	$-0.790440\pi$
$281$		−	20.5117i		−	1.22363i	0.791002	−	0.611814i	$-0.209560\pi$
$282$	2.03426	−	16.9685i	0.121139	−	1.01046i
$283$	−28.8990			−1.71787			−0.858933	−	0.512088i	$-0.828872\pi$
$283$	−28.8990			−1.71787			−0.858933	+	0.512088i	$0.828872\pi$
$284$	−6.24544	+	25.6734i	−0.370599	+	1.52344i
$285$	−13.4516	−	0.278797i	−0.796804	−	0.0165145i
$286$	−0.587302	+	4.89890i	−0.0347279	+	0.289678i
$287$	0.248372	−	0.248372i	0.0146610	−	0.0146610i
$288$	1.06181	+	5.55631i	0.0625677	+	0.327409i
$289$		−	13.3166i		−	0.783332i
$290$	7.46353	+	9.91293i	0.438274	+	0.582107i
$291$	11.7668	−	11.7668i	0.689784	−	0.689784i
$292$	−28.2411	+	17.1895i	−1.65269	+	1.00594i
$293$		−	8.86723i		−	0.518029i	−0.965873	−	0.259014i	$-0.916602\pi$
$293$		−	8.86723i		−	0.518029i	0.965873	−	0.259014i	$-0.0833977\pi$
$294$	−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
$298$	0.115463	−	0.963122i	0.00668861	−	0.0557921i
$299$	2.75611	−	2.75611i	0.159390	−	0.159390i
$300$	−2.76429	+	9.61034i	−0.159596	+	0.554854i
$301$	−0.600283	−	0.600283i	−0.0345997	−	0.0345997i
$302$	5.65650	+	7.19749i	0.325495	+	0.414169i
$303$	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
$307$	14.1518			0.807684			0.403842	−	0.914829i	$-0.367675\pi$
$307$	14.1518			0.807684			0.403842	+	0.914829i	$0.367675\pi$
$308$	−0.419194	−	0.101975i	−0.0238858	−	0.00581058i
$309$	11.2892	+	11.2892i	0.642222	+	0.642222i
$310$	20.6954	+	2.91723i	1.17542	+	0.165688i
$311$	7.15165			0.405533			0.202766	−	0.979227i	$-0.435007\pi$
$311$	7.15165			0.405533			0.202766	+	0.979227i	$0.435007\pi$
$312$	3.85919	+	8.47164i	0.218484	+	0.479612i
$313$	5.98016	+	5.98016i	0.338019	+	0.338019i	0.855621	−	0.517602i	$-0.173175\pi$
$313$	5.98016	+	5.98016i	0.338019	+	0.338019i	−0.517602	+	0.855621i	$0.673175\pi$
$314$	13.0610	−	10.2646i	0.737072	−	0.579264i
$315$	0.00942893	−	0.454934i	0.000531260	−	0.0256326i
$316$	4.70644	−	19.3469i	0.264758	−	1.08835i
$317$			7.76996i			0.436404i	0.975904	+	0.218202i	$0.0700192\pi$
$317$			7.76996i			0.436404i	−0.975904	+	0.218202i	$0.929981\pi$
$318$	4.41757	+	5.62104i	0.247725	+	0.315212i
$319$	4.15941			0.232882
$320$	17.8673	−	0.872350i	0.998810	−	0.0487659i
$321$	1.39451			0.0778338
$322$	0.210591	+	0.267962i	0.0117358	+	0.0149329i
$323$		−	11.5479i		−	0.642544i
$324$	−0.472743	+	1.94333i	−0.0262635	+	0.107963i
$325$	−0.681863	+	16.4424i	−0.0378229	+	0.912063i
$326$	2.08088	−	1.63536i	0.115249	−	0.0905744i
$327$	−4.55325	−	4.55325i	−0.251795	−	0.251795i
$328$	2.02390	+	4.44283i	0.111751	+	0.245314i
$329$	2.45915			0.135577
$330$	2.01622	+	2.67791i	0.110989	+	0.147414i
$331$	−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	$0.759297\pi$
$332$	−19.4594	−	4.73379i	−1.06797	−	0.259800i
$333$	10.0194			0.549057
$334$	−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	$0.754652\pi$
$338$	−1.89386	−	2.40981i	−0.103013	−	0.131076i
$339$	11.4501	+	11.4501i	0.621886	+	0.621886i
$340$	−8.29592	−	2.20115i	−0.449909	−	0.119374i
$341$	4.95386	−	4.95386i	0.268266	−	0.268266i
$342$	−1.01289	+	8.44886i	−0.0547707	+	0.456862i
$343$	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
$347$			16.7455i			0.898947i	0.893294	+	0.449473i	$0.148388\pi$
$347$			16.7455i			0.898947i	−0.893294	+	0.449473i	$0.851612\pi$
$348$	6.70368	−	4.08031i	0.359355	−	0.218728i
$349$	−21.0019	+	21.0019i	−1.12421	+	1.12421i	−0.133104	+	0.991102i	$0.542494\pi$
$349$	−21.0019	+	21.0019i	−1.12421	+	1.12421i	−0.991102	+	0.133104i	$0.957506\pi$
$350$	−1.42038	−	0.230330i	−0.0759226	−	0.0123116i
$351$			3.29132i			0.175677i
$352$	3.36883	−	4.96058i	0.179559	−	0.264400i
$353$	−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
$355$	20.4512	+	21.3169i	1.08544	+	1.13138i
$356$	2.72302	−	11.1936i	0.144320	−	0.593262i
$357$	0.390552			0.0206702
$358$	−0.827965	+	6.90636i	−0.0437593	+	0.365012i
$359$			12.2651i			0.647326i	0.946172	+	0.323663i	$0.104914\pi$
$359$			12.2651i			0.647326i	−0.946172	+	0.323663i	$0.895086\pi$
$360$	5.87651	+	2.33808i	0.309719	+	0.123228i
$361$			17.2046i			0.905506i
$362$	32.4050	+	3.88486i	1.70317	+	0.204184i
$363$	−9.87636			−0.518375
$364$	−1.14425	+	0.696467i	−0.0599749	+	0.0365048i
$365$	−0.765938	+	36.9555i	−0.0400910	+	1.93434i
$366$	−9.93577	−	1.19114i	−0.519351	−	0.0622621i
$367$	1.25485	−	1.25485i	0.0655025	−	0.0655025i	−0.673597	−	0.739099i	$-0.735251\pi$
$367$	1.25485	−	1.25485i	0.0655025	−	0.0655025i	0.739099	+	0.673597i	$0.235251\pi$
$368$	−4.51387	+	1.43666i	−0.235302	+	0.0748909i
$369$			1.72608i			0.0898563i
$370$	4.42247	−	31.3738i	0.229913	−	1.63105i
$371$	−0.727417	+	0.727417i	−0.0377656	+	0.0377656i
$372$	3.12443	−	12.8437i	0.161994	−	0.665917i
$373$		−	8.25732i		−	0.427548i	−0.976883	−	0.213774i	$-0.931424\pi$
$373$		−	8.25732i		−	0.427548i	0.976883	−	0.213774i	$-0.0685756\pi$
$374$	−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
$378$	−0.285741	−	0.0342559i	−0.0146969	−	0.00176193i
$379$	−1.03027	+	1.03027i	−0.0529214	+	0.0529214i	−0.733072	−	0.680151i	$-0.761914\pi$
$379$	−1.03027	+	1.03027i	−0.0529214	+	0.0529214i	0.680151	+	0.733072i	$0.261914\pi$
$380$	26.0090	+	6.90094i	1.33423	+	0.354011i
$381$	−4.94562	−	4.94562i	−0.253372	−	0.253372i
$382$	−23.9601	+	18.8302i	−1.22590	+	0.963436i
$383$	−12.3374	−	12.3374i	−0.630413	−	0.630413i	0.317759	−	0.948172i	$-0.397070\pi$
$383$	−12.3374	−	12.3374i	−0.630413	−	0.630413i	−0.948172	+	0.317759i	$0.897070\pi$
$384$	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
$387$	4.17171			0.212060
$388$	−28.4295	+	17.3041i	−1.44329	+	0.878483i
$389$	12.8354	+	12.8354i	0.650781	+	0.650781i	0.953181	−	0.302400i	$-0.0977880\pi$
$389$	12.8354	+	12.8354i	0.650781	+	0.650781i	−0.302400	+	0.953181i	$0.597788\pi$
$390$	10.3062	+	1.45276i	0.521873	+	0.0735635i
$391$	2.27282			0.114941
$392$	8.15920	+	17.9110i	0.412102	+	0.904641i
$393$	12.7313	+	12.7313i	0.642211	+	0.642211i
$394$	−20.3704	−	25.9199i	−1.02625	−	1.30583i
$395$	−15.4116	−	16.0640i	−0.775442	−	0.808266i
$396$	1.81095	−	1.10227i	0.0910038	−	0.0553910i
$397$			14.3934i			0.722383i	0.932492	+	0.361191i	$0.117630\pi$
$397$			14.3934i			0.722383i	−0.932492	+	0.361191i	$0.882370\pi$
$398$	−2.39054	+	1.87872i	−0.119827	+	0.0941718i
$399$	−1.22444			−0.0612988
$400$	9.91513	−	17.3692i	0.495757	−	0.868461i
$401$	−37.4272			−1.86902			−0.934512	−	0.355932i	$-0.884164\pi$
$401$	−37.4272			−1.86902			−0.934512	+	0.355932i	$0.884164\pi$
$402$	−4.74501	+	3.72909i	−0.236659	+	0.185990i
$403$		−	21.7528i		−	1.08358i
$404$	−1.90167	−	3.12432i	−0.0946116	−	0.155440i
$405$	1.54804	+	1.61356i	0.0769225	+	0.0801786i
$406$	0.697777	+	0.887871i	0.0346301	+	0.0440643i
$407$	−7.50996	−	7.50996i	−0.372255	−	0.372255i
$408$	−1.90182	+	5.08429i	−0.0941542	+	0.251710i
$409$	−8.19166			−0.405052			−0.202526	−	0.979277i	$-0.564915\pi$
$409$	−8.19166			−0.405052			−0.202526	+	0.979277i	$0.564915\pi$
$410$	5.40492	+	0.761881i	0.266930	+	0.0376266i
$411$	−6.06032	−	6.06032i	−0.298934	−	0.298934i
$412$	−16.6018	−	27.2756i	−0.817910	−	1.34377i
$413$	−0.887066			−0.0436497
$414$	−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
$418$	7.09201	−	5.57360i	0.346881	−	0.272614i
$419$	22.2183	+	22.2183i	1.08544	+	1.08544i	0.995992	+	0.0894455i	$0.0285095\pi$
$419$	22.2183	+	22.2183i	1.08544	+	1.08544i	0.0894455	+	0.995992i	$0.471491\pi$
$420$	−0.233390	+	0.879627i	−0.0113883	+	0.0429214i
$421$	−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	$0.280223\pi$
$422$	12.4562	+	1.49331i	0.606359	+	0.0726930i
$423$	−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
$427$		−	1.43993i		−	0.0696832i
$428$	−2.70998	−	0.659244i	−0.130992	−	0.0318658i
$429$	2.46699	−	2.46699i	0.119107	−	0.119107i
$430$	1.84136	−	13.0630i	0.0887985	−	0.629952i
$431$			5.32770i			0.256626i	0.991734	+	0.128313i	$0.0409563\pi$
$431$			5.32770i			0.256626i	−0.991734	+	0.128313i	$0.959044\pi$
$432$	1.83739	−	3.55303i	0.0884014	−	0.170945i
$433$	−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
$435$	0.181813	−	8.77224i	0.00871726	−	0.420597i
$436$	6.69593	+	11.0010i	0.320677	+	0.526851i
$437$	−7.12564			−0.340866
$438$	23.2115	+	2.78270i	1.10909	+	0.132963i
$439$			5.99801i			0.286269i	0.989703	+	0.143135i	$0.0457182\pi$
$439$			5.99801i			0.286269i	−0.989703	+	0.143135i	$0.954282\pi$
$440$	−2.65221	−	6.15721i	−0.126439	−	0.293533i
$441$			6.95859i			0.331361i
$442$	−1.06334	+	8.86968i	−0.0505778	+	0.421888i
$443$	−13.3394			−0.633773			−0.316887	−	0.948463i	$-0.602637\pi$
$443$	−13.3394			−0.633773			−0.316887	+	0.948463i	$0.602637\pi$
$444$	−19.4709	−	4.73658i	−0.924047	−	0.224788i
$445$	−8.91676	−	9.29420i	−0.422695	−	0.440587i
$446$	−1.19034	+	9.92908i	−0.0563643	+	0.470156i
$447$	−0.485009	+	0.485009i	−0.0229401	+	0.0229401i
$448$	1.62404	−	0.113066i	0.0767287	−	0.00534188i
$449$		−	29.7201i		−	1.40258i	−0.712877	−	0.701289i	$-0.752608\pi$
$449$		−	29.7201i		−	1.40258i	0.712877	−	0.701289i	$-0.247392\pi$
$450$	5.73588	−	4.13518i	0.270392	−	0.194934i
$451$	1.29378	−	1.29378i	0.0609216	−	0.0609216i
$452$	−16.8384	−	27.6643i	−0.792010	−	1.30122i
$453$		−	6.47302i		−	0.304129i
$454$	−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	$-0.598591\pi$
$457$	13.8443	−	13.8443i	0.647611	−	0.647611i	0.952415	+	0.304804i	$0.0985910\pi$
$458$	−1.62769	+	13.5772i	−0.0760571	+	0.634420i
$459$	−1.35709	+	1.35709i	−0.0633433	+	0.0633433i
$460$	−1.35821	+	5.11899i	−0.0633271	+	0.238674i
$461$	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	$0.461976\pi$
$462$	0.188500	+	0.239852i	0.00876979	+	0.0111589i
$463$	10.5750	+	10.5750i	0.491463	+	0.491463i	0.908767	−	0.417304i	$-0.137025\pi$
$463$	10.5750	+	10.5750i	0.491463	+	0.491463i	−0.417304	+	0.908767i	$0.637025\pi$
$464$	−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
$467$	30.0161			1.38898			0.694491	−	0.719502i	$-0.255630\pi$
$467$	30.0161			1.38898			0.694491	+	0.719502i	$0.255630\pi$
$468$	1.55595	−	6.39610i	0.0719237	−	0.295660i
$469$	−0.614050	−	0.614050i	−0.0283542	−	0.0283542i
$470$	22.9855	+	30.5289i	1.06024	+	1.40819i
$471$	−11.7463			−0.541240
$472$	4.31963	−	11.5480i	0.198827	−	0.531540i
$473$	−3.12689	−	3.12689i	−0.143774	−	0.143774i
$474$	−11.0698	+	8.69977i	−0.508455	+	0.399594i
$475$	22.1366	−	20.3737i	1.01570	−	0.934809i
$476$	−0.758970	−	0.184631i	−0.0347873	−	0.00846254i
$477$		−	5.05524i		−	0.231464i
$478$	−9.67111	−	12.3058i	−0.442346	−	0.562854i
$479$	−21.9152			−1.00133			−0.500665	−	0.865641i	$-0.666911\pi$
$479$	−21.9152			−1.00133			−0.500665	+	0.865641i	$0.666911\pi$
$480$	−10.3147	−	7.32173i	−0.470798	−	0.334190i
$481$	−32.9769			−1.50362
$482$	−20.5132	−	26.1016i	−0.934351	−	1.18890i
$483$		−	0.240990i		−	0.0109654i
$484$	19.1930	+	4.66899i	0.872409	+	0.212227i
$485$	−0.771047	+	37.2020i	−0.0350114	+	1.68926i
$486$	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	$0.808087\pi$
$488$	18.7453	+	7.01185i	0.848561	+	0.317411i
$489$	−1.87143			−0.0846289
$490$	21.7896	+	3.07147i	0.984353	+	0.138755i
$491$	−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	$-0.552123\pi$
$492$	0.815994	−	3.35434i	0.0367879	−	0.151225i
$493$	7.53080			0.339170
$494$	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
$498$	8.75033	+	11.1342i	0.392112	+	0.498934i
$499$	−18.8209	−	18.8209i	−0.842537	−	0.842537i	0.146651	−	0.989188i	$-0.453151\pi$
$499$	−18.8209	−	18.8209i	−0.842537	−	0.842537i	−0.989188	+	0.146651i	$0.953151\pi$
$500$	−10.4168	−	19.7861i	−0.465854	−	0.884862i
$501$	4.79897	−	4.79897i	0.214402	−	0.214402i
$502$	0.419439	−	3.49870i	0.0187205	−	0.156154i
$503$	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
$507$			2.16724i			0.0962507i
$508$	7.27294	+	11.9490i	0.322685	+	0.530149i
$509$	10.1248	−	10.1248i	0.448776	−	0.448776i	−0.446171	−	0.894948i	$-0.647213\pi$
$509$	10.1248	−	10.1248i	0.448776	−	0.448776i	0.894948	+	0.446171i	$0.147213\pi$
$510$	3.65046	+	4.84848i	0.161645	+	0.214694i
$511$			3.36391i			0.148811i
$512$	−6.43646	+	21.6927i	−0.284454	+	0.958690i
$513$	4.25468	−	4.25468i	0.187849	−	0.187849i
$514$	0.965809	−	8.05617i	0.0426000	−	0.355342i
$515$	−35.6920	−	0.739751i	−1.57278	−	0.0325973i
$516$	−8.10699	−	1.97215i	−0.356891	−	0.0868190i
$517$	12.8097			0.563372
$518$	0.343222	−	2.86294i	0.0150803	−	0.125791i
$519$		−	12.8446i		−	0.563817i
$520$	−19.3414	−	7.69536i	−0.848179	−	0.337464i
$521$			37.3503i			1.63634i	0.574973	+	0.818172i	$0.305013\pi$
$521$			37.3503i			1.63634i	−0.574973	+	0.818172i	$0.694987\pi$
$522$	−5.50979	−	0.660538i	−0.241157	−	0.0289110i
$523$	8.27258			0.361735			0.180867	−	0.983507i	$-0.442110\pi$
$523$	8.27258			0.361735			0.180867	+	0.983507i	$0.442110\pi$
$524$	−18.7225	−	30.7598i	−0.817895	−	1.34375i
$525$	0.689040	+	0.748661i	0.0300722	+	0.0326742i
$526$	44.1986	+	5.29873i	1.92715	+	0.231035i
$527$	8.96919	−	8.96919i	0.390704	−	0.390704i
$528$	−4.04036	+	1.28595i	−0.175834	+	0.0559637i
$529$			21.5976i			0.939024i
$530$	−15.8296	−	2.23135i	−0.687594	−	0.0969236i
$531$	3.08237	−	3.08237i	0.133763	−	0.133763i
$532$	2.37949	+	0.578847i	0.103164	+	0.0250962i
$533$		−	5.68108i		−	0.246075i
$534$	−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
$538$	23.7500	+	2.84726i	1.02394	+	0.122754i
$539$	5.21578	−	5.21578i	0.224659	−	0.224659i
$540$	−2.24554	−	3.86750i	−0.0966325	−	0.166431i
$541$	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	$0.639449\pi$
$542$	−17.4752	+	13.7337i	−0.750624	+	0.589914i
$543$	−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
$547$	26.6966			1.14147			0.570733	−	0.821136i	$-0.306659\pi$
$547$	26.6966			1.14147			0.570733	+	0.821136i	$0.306659\pi$
$548$	8.91220	+	14.6422i	0.380710	+	0.625482i
$549$	5.00346	+	5.00346i	0.213542	+	0.213542i
$550$	−7.39880	−	1.19979i	−0.315486	−	0.0511593i
$551$	−23.6103			−1.00583
$552$	3.13725	+	1.17352i	0.133530	+	0.0499482i
$553$	−1.43255	−	1.43255i	−0.0609180	−	0.0609180i
$554$	4.01418	+	5.10776i	0.170546	+	0.217008i
$555$	−16.1669	+	15.5103i	−0.686245	+	0.658377i
$556$	−15.2268	−	25.0167i	−0.645761	−	1.06094i
$557$		−	0.715510i		−	0.0303171i	−0.999885	−	0.0151586i	$-0.995175\pi$
$557$		−	0.715510i		−	0.0303171i	0.999885	−	0.0151586i	$-0.00482531\pi$
$558$	−7.34887	+	5.77546i	−0.311102	+	0.244495i
$559$	−13.7304			−0.580735
$560$	0.869392	−	1.59907i	0.0367385	−	0.0675730i
$561$	2.03439			0.0858922
$562$	22.8075	−	17.9244i	0.962075	−	0.756093i
$563$		−	16.6892i		−	0.703364i	−0.936119	−	0.351682i	$-0.885610\pi$
$563$		−	16.6892i		−	0.703364i	0.936119	−	0.351682i	$-0.114390\pi$
$564$	20.6453	−	12.5661i	0.869326	−	0.529130i
$565$	−36.2007	−	0.750294i	−1.52298	−	0.0315651i
$566$	−25.2536	−	32.1334i	−1.06149	−	1.35067i
$567$	0.143894	+	0.143894i	0.00604297	+	0.00604297i
$568$	−34.0044	+	15.4905i	−1.42679	+	0.649965i
$569$	23.0249			0.965253			0.482626	−	0.875826i	$-0.339683\pi$
$569$	23.0249			0.965253			0.482626	+	0.875826i	$0.339683\pi$
$570$	−11.4448	−	15.2008i	−0.479369	−	0.636690i
$571$	−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	$0.822738\pi$
$572$	−5.96041	+	3.62791i	−0.249217	+	0.151691i
$573$	21.5483			0.900194
$574$	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	$0.525343\pi$
$578$	14.8071	−	11.6369i	0.615893	−	0.484029i
$579$	−11.3161	−	11.3161i	−0.470282	−	0.470282i
$580$	−4.50034	+	16.9614i	−0.186866	+	0.704283i
$581$	−1.44087	+	1.44087i	−0.0597774	+	0.0597774i
$582$	23.3664	+	2.80126i	0.968567	+	0.116116i
$583$	−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
$587$			22.5696i			0.931547i	0.884904	+	0.465773i	$0.154224\pi$
$587$			22.5696i			0.931547i	−0.884904	+	0.465773i	$0.845776\pi$
$588$	3.28963	−	13.5228i	0.135662	−	0.557671i
$589$	−28.1198	+	28.1198i	−1.15866	+	1.15866i
$590$	−8.29134	−	11.0124i	−0.341349	−	0.453374i
$591$			23.3109i			0.958883i
$592$	35.5990	+	18.4094i	1.46311	+	0.756624i
$593$	−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
$595$	−0.630180	+	0.604589i	−0.0258349	+	0.0247857i
$596$	1.17182	−	0.713246i	0.0479994	−	0.0292157i
$597$	2.14992			0.0879902
$598$	5.47303	+	0.656131i	0.223809	+	0.0268312i
$599$			17.4693i			0.713775i	0.934147	+	0.356888i	$0.116162\pi$
$599$			17.4693i			0.713775i	−0.934147	+	0.356888i	$0.883838\pi$
$600$	−13.1016	+	5.32441i	−0.534869	+	0.217368i
$601$		−	25.8843i		−	1.05584i	−0.849294	−	0.527921i	$-0.822972\pi$
$601$		−	25.8843i		−	1.05584i	0.849294	−	0.527921i	$-0.177028\pi$
$602$	0.142906	−	1.19203i	0.00582441	−	0.0485835i
$603$	4.26739			0.173782
$604$	−3.06008	+	12.5792i	−0.124513	+	0.511839i
$605$	15.9361	−	15.2890i	0.647896	−	0.621585i
$606$	−0.307850	+	2.56789i	−0.0125056	+	0.104314i
$607$	22.7204	−	22.7204i	0.922193	−	0.922193i	−0.0749912	−	0.997184i	$-0.523893\pi$
$607$	22.7204	−	22.7204i	0.922193	−	0.922193i	0.997184	+	0.0749912i	$0.0238929\pi$
$608$	−19.1227	+	28.1580i	−0.775526	+	1.14196i
$609$		−	0.798501i		−	0.0323569i
$610$	17.8759	−	13.4589i	0.723775	−	0.544937i
$611$	28.1243	−	28.1243i	1.13779	−	1.13779i
$612$	3.27881	−	1.99571i	0.132538	−	0.0806716i
$613$			0.840532i			0.0339488i	0.999856	+	0.0169744i	$0.00540337\pi$
$613$			0.840532i			0.0339488i	−0.999856	+	0.0169744i	$0.994597\pi$
$614$	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	$-0.815607\pi$
$617$	−7.18912	+	7.18912i	−0.289423	+	0.289423i	0.547429	+	0.836852i	$0.315607\pi$
$618$	−2.68756	+	22.4180i	−0.108110	+	0.901782i
$619$	31.9741	−	31.9741i	1.28515	−	1.28515i	0.347447	−	0.937700i	$-0.387049\pi$
$619$	31.9741	−	31.9741i	1.28515	−	1.28515i	0.937700	−	0.347447i	$-0.112951\pi$
$620$	14.8411	+	25.5609i	0.596033	+	1.02655i
$621$	0.837388	+	0.837388i	0.0336032	+	0.0336032i
$622$	6.24953	+	7.95208i	0.250583	+	0.318849i
$623$	−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
$627$	−6.37815			−0.254719
$628$	22.8269	+	5.55298i	0.910891	+	0.221588i
$629$	−13.5971	−	13.5971i	−0.542153	−	0.542153i
$630$	0.514091	−	0.387064i	0.0204819	−	0.0154210i
$631$	28.2004			1.12264			0.561320	−	0.827599i	$-0.310294\pi$
$631$	28.2004			1.12264			0.561320	+	0.827599i	$0.310294\pi$
$632$	25.6251	−	11.6733i	1.01931	−	0.464339i
$633$	−6.27270	−	6.27270i	−0.249317	−	0.249317i
$634$	−8.63959	+	6.78984i	−0.343122	+	0.269659i
$635$	15.6361	+	0.324072i	0.620498	+	0.0128604i
$636$	−2.38983	+	9.82398i	−0.0947630	+	0.389546i
$637$		−	22.9029i		−	0.907446i
$638$	3.63473	+	4.62494i	0.143900	+	0.183103i
$639$	−13.2111			−0.522621
$640$	16.5834	+	19.1047i	0.655518	+	0.755180i
$641$	36.6103			1.44602			0.723011	−	0.690837i	$-0.242758\pi$
$641$	36.6103			1.44602			0.723011	+	0.690837i	$0.242758\pi$
$642$	1.21860	+	1.55058i	0.0480944	+	0.0611967i
$643$		−	13.4647i		−	0.530996i	−0.964111	−	0.265498i	$-0.914464\pi$
$643$		−	13.4647i		−	0.530996i	0.964111	−	0.265498i	$-0.0855364\pi$
$644$	−0.113926	+	0.468321i	−0.00448932	+	0.0184544i
$645$	−6.73132	+	6.45796i	−0.265045	+	0.254282i
$646$	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	$0.524113\pi$
$648$	−2.57394	+	1.17254i	−0.101114	+	0.0460616i
$649$	−4.62075			−0.181380
$650$	−18.8786	+	13.6102i	−0.740479	+	0.533835i
$651$	−0.951015	−	0.951015i	−0.0372732	−	0.0372732i
$652$	3.63680	+	0.884706i	0.142428	+	0.0346477i
$653$	15.0338			0.588318			0.294159	−	0.955756i	$-0.404960\pi$
$653$	15.0338			0.588318			0.294159	+	0.955756i	$0.404960\pi$
$654$	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
$658$	2.14895	+	2.73438i	0.0837746	+	0.106597i
$659$	12.8233	+	12.8233i	0.499524	+	0.499524i	0.911290	−	0.411766i	$-0.135088\pi$
$659$	12.8233	+	12.8233i	0.499524	+	0.499524i	−0.411766	+	0.911290i	$0.635088\pi$
$660$	−1.21574	+	4.58200i	−0.0473225	+	0.178354i
$661$	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	$0.0358232\pi$
$662$	0.178880	−	1.49211i	0.00695238	−	0.0579923i
$663$	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
$667$		−	4.64687i		−	0.179928i
$668$	−11.5946	+	7.05727i	−0.448610	+	0.273054i
$669$	5.00009	−	5.00009i	0.193315	−	0.193315i
$670$	1.88360	−	13.3626i	0.0727697	−	0.516241i
$671$		−	7.50063i		−	0.289559i
$672$	−0.952305	−	0.646730i	−0.0367360	−	0.0249481i
$673$	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
$675$	−4.99571	−	0.207170i	−0.192285	−	0.00797399i
$676$	1.02455	−	4.21166i	0.0394058	−	0.161987i
$677$	1.52496			0.0586089			0.0293044	−	0.999571i	$-0.490671\pi$
$677$	1.52496			0.0586089			0.0293044	+	0.999571i	$0.490671\pi$
$678$	−2.72587	+	22.7374i	−0.104686	+	0.873226i
$679$			3.38635i			0.129956i
$680$	−4.80195	−	11.1479i	−0.184146	−	0.427503i
$681$			22.5630i			0.864614i
$682$	9.83728	+	1.17934i	0.376689	+	0.0451591i
$683$	3.77382			0.144401			0.0722006	−	0.997390i	$-0.476998\pi$
$683$	3.77382			0.144401			0.0722006	+	0.997390i	$0.476998\pi$
$684$	−10.2796	+	6.25686i	−0.393050	+	0.239237i
$685$	19.1603	+	0.397115i	0.732078	+	0.0151730i
$686$	3.98854	+	0.478164i	0.152283	+	0.0182564i
$687$	6.83720	−	6.83720i	0.260856	−	0.260856i
$688$	14.8222	+	7.66505i	0.565091	+	0.292227i
$689$			16.6384i			0.633873i
$690$	2.99175	−	2.25251i	0.113894	−	0.0857518i
$691$	−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	$0.391269\pi$
$692$	−6.07222	+	24.9613i	−0.230831	+	0.948887i
$693$		−	0.215710i		−	0.00819413i
$694$	−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
$698$	−41.7052	−	4.99980i	−1.57856	−	0.189245i
$699$	−3.10894	+	3.10894i	−0.117591	+	0.117591i
$700$	−0.985104	−	1.78063i	−0.0372334	−	0.0673015i
$701$	−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	$0.930785\pi$
$702$	−3.65969	+	2.87614i	−0.138126	+	0.108553i
$703$	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
$707$	−0.372149			−0.0139961
$708$	−7.44721	+	4.53287i	−0.279883	+	0.170356i
$709$	−8.20276	−	8.20276i	−0.308061	−	0.308061i	0.536096	−	0.844157i	$-0.319899\pi$
$709$	−8.20276	−	8.20276i	−0.308061	−	0.308061i	−0.844157	+	0.536096i	$0.819899\pi$
$710$	−5.83127	+	41.3681i	−0.218844	+	1.55252i
$711$	9.95558			0.373364
$712$	14.8260	−	6.75387i	0.555628	−	0.253112i
$713$	−5.53443	−	5.53443i	−0.207266	−	0.207266i
$714$	0.341287	+	0.434264i	0.0127724	+	0.0162519i
$715$	−0.161655	+	7.79963i	−0.00604554	+	0.291690i
$716$	−8.40286	+	5.11455i	−0.314030	+	0.191140i
$717$			11.0671i			0.413310i
$718$	−13.6378	+	10.7179i	−0.508959	+	0.399990i
$719$	23.6655			0.882576			0.441288	−	0.897366i	$-0.354522\pi$
$719$	23.6655			0.882576			0.441288	+	0.897366i	$0.354522\pi$
$720$	2.53547	+	8.57738i	0.0944915	+	0.319660i
$721$	−3.24890			−0.120995
$722$	−19.1302	+	15.0344i	−0.711952	+	0.559522i
$723$			23.4743i			0.873018i
$724$	23.9977	+	39.4267i	0.891869	+	1.46528i
$725$	13.2864	+	14.4360i	0.493444	+	0.536140i
$726$	−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	$0.764064\pi$
$728$	−1.77433	−	0.663703i	−0.0657610	−	0.0245985i
$729$	−1.00000			−0.0370370
$730$	−41.7610	+	31.4422i	−1.54564	+	1.16373i
$731$	−5.66137	−	5.66137i	−0.209393	−	0.209393i
$732$	−7.35799	−	12.0887i	−0.271959	−	0.446811i
$733$	−48.4131			−1.78818			−0.894089	−	0.447889i	$-0.852176\pi$
$733$	−48.4131			−1.78818			−0.894089	+	0.447889i	$0.852176\pi$
$734$	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
$738$	−1.91927	+	1.50835i	−0.0706493	+	0.0555232i
$739$	−2.35313	−	2.35313i	−0.0865612	−	0.0865612i	0.662500	−	0.749062i	$-0.269495\pi$
$739$	−2.35313	−	2.35313i	−0.0865612	−	0.0865612i	−0.749062	+	0.662500i	$0.769495\pi$
$740$	38.7499	−	22.4988i	1.42447	−	0.827073i
$741$	−14.0035	+	14.0035i	−0.514431	+	0.514431i
$742$	−1.44449	−	0.173172i	−0.0530290	−	0.00635735i
$743$	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
$747$		−	10.0134i		−	0.366373i
$748$	−3.95349	−	0.961746i	−0.144554	−	0.0351649i
$749$	−0.200661	+	0.200661i	−0.00733198	+	0.00733198i
$750$	−2.85379	+	15.5517i	−0.104206	+	0.567868i
$751$		−	40.8647i		−	1.49117i	−0.666409	−	0.745587i	$-0.732169\pi$
$751$		−	40.8647i		−	1.49117i	0.666409	−	0.745587i	$-0.267831\pi$
$752$	−46.0612	+	14.6602i	−1.67968	+	0.534601i
$753$	−1.76187	+	1.76187i	−0.0642063	+	0.0642063i
$754$	18.1345	+	2.17404i	0.660418	+	0.0791738i
$755$	10.0205	+	10.4446i	0.364682	+	0.380119i
$756$	−0.211607	−	0.347657i	−0.00769609	−	0.0126442i
$757$	−24.6892			−0.897345			−0.448673	−	0.893696i	$-0.648103\pi$
$757$	−24.6892			−0.897345			−0.448673	+	0.893696i	$0.648103\pi$
$758$	−2.04589	−	0.245270i	−0.0743101	−	0.00890862i
$759$		−	1.25532i		−	0.0455652i
$760$	15.0549	+	34.9505i	0.546098	+	1.26779i
$761$			6.54343i			0.237199i	0.992942	+	0.118600i	$0.0378405\pi$
$761$			6.54343i			0.237199i	−0.992942	+	0.118600i	$0.962160\pi$
$762$	1.17738	−	9.82092i	0.0426518	−	0.355774i
$763$	1.31037			0.0474385
$764$	−41.8754	−	10.1868i	−1.51500	−	0.368546i
$765$	0.0889259	−	4.29056i	0.00321512	−	0.155126i
$766$	2.93710	−	24.4994i	0.106122	−	0.885200i
$767$	−10.1450	+	10.1450i	−0.366316	+	0.366316i
$768$	13.0566	−	9.24801i	0.471139	−	0.333709i
$769$		−	26.2710i		−	0.947357i	−0.880698	−	0.473678i	$-0.842926\pi$
$769$		−	26.2710i		−	0.947357i	0.880698	−	0.473678i	$-0.157074\pi$
$770$	−0.675456	−	0.0952127i	−0.0243417	−	0.00343123i
$771$	−4.05693	+	4.05693i	−0.146107	+	0.146107i
$772$	16.6413	+	27.3405i	0.598933	+	0.984007i
$773$			9.19242i			0.330628i	0.986241	+	0.165314i	$0.0528638\pi$
$773$			9.19242i			0.330628i	−0.986241	+	0.165314i	$0.947136\pi$
$774$	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
$778$	−3.05565	+	25.4883i	−0.109550	+	0.913800i
$779$	−7.34393	+	7.34393i	−0.263124	+	0.263124i
$780$	7.39077	+	12.7292i	0.264632	+	0.455777i
$781$	9.90228	+	9.90228i	0.354332	+	0.354332i
$782$	1.98612	+	2.52719i	0.0710235	+	0.0903723i
$783$	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
$787$	−20.9534			−0.746908			−0.373454	−	0.927649i	$-0.621827\pi$
$787$	−20.9534			−0.746908			−0.373454	+	0.927649i	$0.621827\pi$
$788$	11.0201	−	45.3007i	0.392574	−	1.61377i
$789$	−22.2576	−	22.2576i	−0.792390	−	0.792390i
$790$	4.39432	−	31.1741i	0.156343	−	1.10913i
$791$	−3.29520			−0.117164
$792$	2.80815	+	1.05041i	0.0997833	+	0.0373248i
$793$	−16.4680	−	16.4680i	−0.584794	−	0.584794i
$794$	−16.0043	+	12.5778i	−0.567972	+	0.446368i
$795$	7.82570	+	8.15695i	0.277549	+	0.289297i
$796$	−4.17799	−	1.01636i	−0.148085	−	0.0360239i
$797$		−	25.5883i		−	0.906384i	−0.891413	−	0.453192i	$-0.850285\pi$
$797$		−	25.5883i		−	0.906384i	0.891413	−	0.453192i	$-0.149715\pi$
$798$	−1.06999	−	1.36149i	−0.0378772	−	0.0481961i
$799$	23.1926			0.820497
$800$	27.9777	−	4.15338i	0.989160	−	0.146844i
$801$	5.76005			0.203521
$802$	−32.7060	−	41.6161i	−1.15489	−	1.46952i
$803$			17.5227i			0.618362i
$804$	−8.29293	−	2.01738i	−0.292469	−	0.0711475i
$805$	0.373061	+	0.388852i	0.0131487	+	0.0137052i
$806$	24.1874	−	19.0089i	0.851966	−	0.669559i
$807$	−11.9600	−	11.9600i	−0.421014	−	0.421014i
$808$	1.81221	−	4.84472i	0.0637532	−	0.170437i
$809$	4.93002			0.173330			0.0866652	−	0.996237i	$-0.472379\pi$
$809$	4.93002			0.173330			0.0866652	+	0.996237i	$0.472379\pi$
$810$	−0.441393	+	3.13132i	−0.0155090	+	0.110023i
$811$	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	$0.409657\pi$
$812$	−0.377486	+	1.55175i	−0.0132472	+	0.0544557i
$813$	15.7162			0.551191
$814$	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
$818$	−7.15835	−	9.10849i	−0.250286	−	0.318471i
$819$	−0.473599	−	0.473599i	−0.0165489	−	0.0165489i
$820$	3.87598	+	6.67563i	0.135355	+	0.233123i
$821$	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	$-0.102511\pi$
$822$	1.44275	−	12.0345i	0.0503215	−	0.419750i
$823$	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
$827$			44.8863i			1.56085i	0.625250	+	0.780424i	$0.284997\pi$
$827$			44.8863i			1.56085i	−0.625250	+	0.780424i	$0.715003\pi$
$828$	−1.23145	−	2.02319i	−0.0427958	−	0.0703106i
$829$	−7.27338	+	7.27338i	−0.252615	+	0.252615i	−0.822042	−	0.569427i	$-0.807165\pi$
$829$	−7.27338	+	7.27338i	−0.252615	+	0.252615i	0.569427	+	0.822042i	$0.307165\pi$
$830$	−31.3553	−	4.41986i	−1.08836	−	0.153416i
$831$		−	4.59363i		−	0.159351i
$832$	17.2804	−	19.8666i	0.599091	−	0.688751i
$833$	9.44340	−	9.44340i	0.327195	−	0.327195i
$834$	−2.46498	+	20.5613i	−0.0853554	+	0.711981i
$835$	−0.314462	+	15.1724i	−0.0108824	+	0.525063i
$836$	12.3948	+	3.01523i	0.428684	+	0.104284i
$837$	6.60915			0.228446
$838$	−5.28939	+	44.1208i	−0.182719	+	1.52413i
$839$			6.23853i			0.215378i	0.994185	+	0.107689i	$0.0343451\pi$
$839$			6.23853i			0.215378i	−0.994185	+	0.107689i	$0.965655\pi$
$840$	−1.18203	+	0.509157i	−0.0407838	+	0.0175676i
$841$			13.6029i			0.469067i
$842$	−5.46283	−	0.654909i	−0.188262	−	0.0225696i
$843$	−20.5117			−0.706462
$844$	9.22452	+	15.1553i	0.317521	+	0.521666i
$845$	−3.35497	−	3.49699i	−0.115415	−	0.120300i
$846$	−16.9685	−	2.03426i	−0.583390	−	0.0699394i
$847$	1.42115	−	1.42115i	0.0488312	−	0.0488312i
$848$	9.28845	−	17.9614i	0.318967	−	0.616798i
$849$			28.8990i			0.991811i
$850$	−13.3959	−	2.17228i	−0.459475	−	0.0745085i
$851$	−8.39009	+	8.39009i	−0.287609	+	0.287609i
$852$	25.6734	+	6.24544i	0.879556	+	0.213965i
$853$		−	32.1759i		−	1.10168i	−0.834610	−	0.550841i	$-0.814307\pi$
$853$		−	32.1759i		−	1.10168i	0.834610	−	0.550841i	$-0.185693\pi$
$854$	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	$-0.664025\pi$
$857$	11.0467	−	11.0467i	0.377348	−	0.377348i	0.870145	+	0.492797i	$0.164025\pi$
$858$	4.89890	+	0.587302i	0.167246	+	0.0200502i
$859$	1.75107	−	1.75107i	0.0597457	−	0.0597457i	−0.676603	−	0.736348i	$-0.736548\pi$
$859$	1.75107	−	1.75107i	0.0597457	−	0.0597457i	0.736348	+	0.676603i	$0.236548\pi$
$860$	16.1341	−	9.36773i	0.550168	−	0.319437i
$861$	−0.248372	−	0.248372i	−0.00846451	−	0.00846451i
$862$	−5.92399	+	4.65566i	−0.201772	+	0.158572i
$863$	4.70982	+	4.70982i	0.160324	+	0.160324i	0.782710	−	0.622386i	$-0.213837\pi$
$863$	4.70982	+	4.70982i	0.160324	+	0.160324i	−0.622386	+	0.782710i	$0.713837\pi$
$864$	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
$867$	−13.3166			−0.452257
$868$	1.39855	+	2.29772i	0.0474697	+	0.0779896i
$869$	−7.46216	−	7.46216i	−0.253136	−	0.253136i
$870$	9.91293	−	7.46353i	0.336080	−	0.253038i
$871$	−14.0453			−0.475908
$872$	−6.38093	+	17.0587i	−0.216086	+	0.577679i
$873$	−11.7668	−	11.7668i	−0.398247	−	0.398247i
$874$	−6.22680	−	7.92316i	−0.210625	−	0.268005i
$875$	−2.27076	−	0.141353i	−0.0767658	−	0.00477860i
$876$	17.1895	+	28.2411i	0.580778	+	0.954179i
$877$		−	16.7655i		−	0.566130i	−0.959101	−	0.283065i	$-0.908649\pi$
$877$		−	16.7655i		−	0.566130i	0.959101	−	0.283065i	$-0.0913512\pi$
$878$	−6.66932	+	5.24141i	−0.225079	+	0.176889i
$879$	−8.86723			−0.299084
$880$	4.52868	−	8.32958i	0.152662	−	0.280790i
$881$	50.5390			1.70270			0.851352	−	0.524595i	$-0.175783\pi$
$881$	50.5390			1.70270			0.851352	+	0.524595i	$0.175783\pi$
$882$	−7.73741	+	6.08082i	−0.260532	+	0.204752i
$883$			27.3039i			0.918848i	0.888217	+	0.459424i	$0.151944\pi$
$883$			27.3039i			0.918848i	−0.888217	+	0.459424i	$0.848056\pi$
$884$	−10.7916	+	6.56850i	−0.362961	+	0.220922i
$885$	−0.201978	+	9.74521i	−0.00678943	+	0.327582i
$886$	−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	$0.772317\pi$
$888$	−11.7481	−	25.7892i	−0.394239	−	0.865429i
$889$	1.42329			0.0477355
$890$	2.54244	−	18.0366i	0.0852229	−	0.604587i
$891$	0.749545	+	0.749545i	0.0251107	+	0.0251107i
$892$	−12.0806	+	7.35304i	−0.404487	+	0.246198i
$893$	−72.7126			−2.43324
$894$	−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
$898$	33.0464	−	25.9711i	1.10277	−	0.866668i
$899$	−18.3379	−	18.3379i	−0.611603	−	0.611603i
$900$	9.61034	+	2.76429i	0.320345	+	0.0921429i
$901$	−6.86040	+	6.86040i	−0.228553	+	0.228553i
$902$	2.56916	+	0.308002i	0.0855436	+	0.0102553i
$903$	−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
$907$		−	0.0410041i		−	0.00136152i	−1.00000		0.000680760i	$-0.999783\pi$
$907$		−	0.0410041i		−	0.00136152i	1.00000		0.000680760i	$-0.000216693\pi$
$908$	10.6665	−	43.8472i	0.353980	−	1.45512i
$909$	1.29314	−	1.29314i	0.0428907	−	0.0428907i
$910$	−1.69204	+	1.27395i	−0.0560904	+	0.0422310i
$911$			21.7776i			0.721525i	0.932658	+	0.360763i	$0.117484\pi$
$911$			21.7776i			0.721525i	−0.932658	+	0.360763i	$0.882516\pi$
$912$	22.9345	−	7.29950i	0.759437	−	0.241711i
$913$	−7.50552	+	7.50552i	−0.248397	+	0.248397i
$914$	27.4918	+	3.29584i	0.909349	+	0.109017i
$915$	−15.8189	−	0.327862i	−0.522957	−	0.0108388i
$916$	−16.5191	+	10.0547i	−0.545808	+	0.332216i
$917$	−3.66392			−0.120993
$918$	−2.69488	−	0.323074i	−0.0889441	−	0.0106630i
$919$		−	34.4842i		−	1.13753i	−0.822500	−	0.568765i	$-0.807421\pi$
$919$		−	34.4842i		−	1.13753i	0.822500	−	0.568765i	$-0.192579\pi$
$920$	−6.87880	+	2.96304i	−0.226787	+	0.0976885i
$921$		−	14.1518i		−	0.466317i
$922$	−5.68417	+	47.4138i	−0.187198	+	1.56149i
$923$	43.4818			1.43122
$924$	−0.101975	+	0.419194i	−0.00335474	+	0.0137905i
$925$	2.07571	−	50.0538i	0.0682490	−	1.64576i
$926$	−2.51754	+	20.9997i	−0.0827314	+	0.690093i
$927$	11.2892	−	11.2892i	0.370787	−	0.370787i
$928$	−18.3628	−	12.4705i	−0.602788	−	0.409365i
$929$			19.8125i			0.650028i	0.945709	+	0.325014i	$0.105369\pi$
$929$			19.8125i			0.650028i	−0.945709	+	0.325014i	$0.894631\pi$
$930$	2.91723	−	20.6954i	0.0956599	−	0.678628i
$931$	−29.6066	+	29.6066i	−0.970316	+	0.970316i
$932$	7.51140	−	4.57194i	0.246044	−	0.149759i
$933$		−	7.15165i		−	0.234134i
$934$	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	$-0.909313\pi$
$937$	−20.7731	+	20.7731i	−0.678628	+	0.678628i	0.281062	+	0.959690i	$0.409313\pi$
$938$	0.146183	−	1.21937i	0.00477306	−	0.0398138i
$939$	5.98016	−	5.98016i	0.195155	−	0.195155i
$940$	−13.8597	+	52.2360i	−0.452054	+	1.70375i
$941$	−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	$0.942284\pi$
$942$	−10.2646	−	13.0610i	−0.334438	−	0.425549i
$943$	−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
$947$	−46.1706			−1.50034			−0.750171	−	0.661244i	$-0.770029\pi$
$947$	−46.1706			−1.50034			−0.750171	+	0.661244i	$0.770029\pi$
$948$	−19.3469	−	4.70644i	−0.628359	−	0.152858i
$949$	38.4718	+	38.4718i	1.24885	+	1.24885i
$950$	41.9982	+	6.81044i	1.36260	+	0.220960i
$951$	7.76996			0.251958
$952$	−0.457937	−	1.00526i	−0.0148418	−	0.0325806i
$953$	−5.45044	−	5.45044i	−0.176557	−	0.176557i	0.613296	−	0.789853i	$-0.289843\pi$
$953$	−5.45044	−	5.45044i	−0.176557	−	0.176557i	−0.789853	+	0.613296i	$0.789843\pi$
$954$	5.62104	−	4.41757i	0.181988	−	0.143024i
$955$	−34.7696	+	33.3576i	−1.12512	+	1.07943i
$956$	5.23191	−	21.5070i	0.169212	−	0.695588i
$957$		−	4.15941i		−	0.134455i
$958$	−19.1508	−	24.3680i	−0.618733	−	0.787294i
$959$	1.74408			0.0563194
$960$	−0.872350	−	17.8673i	−0.0281550	−	0.576663i
$961$	−12.6809			−0.409062
$962$	−28.8171	−	36.6677i	−0.929101	−	1.18221i
$963$		−	1.39451i		−	0.0449374i
$964$	11.0973	−	45.6182i	0.357420	−	1.46926i
$965$	35.7770	+	0.741512i	1.15170	+	0.0238701i
$966$	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	$0.885699\pi$
$968$	11.5804	+	25.4211i	0.372208	+	0.817067i
$969$	−11.5479			−0.370973
$970$	−42.0396	+	31.6520i	−1.34981	+	1.01628i
$971$	−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	$0.834986\pi$
$972$	1.94333	+	0.472743i	0.0623322	+	0.0151632i
$973$	−2.97983			−0.0955290
$974$	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	$0.810552\pi$
$978$	−1.63536	−	2.08088i	−0.0522932	−	0.0665393i
$979$	−4.31741	−	4.31741i	−0.137985	−	0.137985i
$980$	15.6258	+	26.9124i	0.499147	+	0.859684i
$981$	−4.55325	+	4.55325i	−0.145374	+	0.145374i
$982$	6.06453	−	50.5865i	0.193527	−	1.61428i
$983$	−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
$987$		−	2.45915i		−	0.0782755i
$988$	33.8334	−	20.5933i	1.07638	−	0.655160i
$989$	−3.49334	+	3.49334i	−0.111082	+	0.111082i
$990$	2.67791	−	2.01622i	0.0851096	−	0.0640798i
$991$		−	28.8183i		−	0.915444i	−0.889095	−	0.457722i	$-0.848666\pi$
$991$		−	28.8183i		−	0.915444i	0.889095	−	0.457722i	$-0.151334\pi$
$992$	−36.7225	+	7.01766i	−1.16594	+	0.222811i
$993$	−0.751395	+	0.751395i	−0.0238448	+	0.0238448i
$994$	−0.452557	+	3.77494i	−0.0143542	+	0.119734i
$995$	−3.46903	+	3.32815i	−0.109975	+	0.105509i
$996$	−4.73379	+	19.4594i	−0.149996	+	0.616594i
$997$	−30.7058			−0.972463			−0.486232	−	0.873830i	$-0.661629\pi$
$997$	−30.7058			−0.972463			−0.486232	+	0.873830i	$0.661629\pi$
$998$	4.48057	−	37.3741i	0.141830	−	1.18306i
$999$		−	10.0194i		−	0.316998i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.7	✓	16	5.3	odd	4
240.2.y.e.187.7	yes	16	16.11	odd	4
240.2.bc.e.43.5	yes	16	80.43	even	4	inner
240.2.bc.e.67.5	yes	16	1.1	even	1	trivial
720.2.z.f.163.2		16	15.8	even	4
720.2.z.f.667.2		16	48.11	even	4
720.2.bd.f.307.4		16	3.2	odd	2
720.2.bd.f.523.4		16	240.203	odd	4
960.2.y.e.847.4		16	16.5	even	4
960.2.y.e.943.4		16	20.3	even	4
960.2.bc.e.367.8		16	4.3	odd	2
960.2.bc.e.463.8		16	80.53	odd	4
1920.2.y.i.223.5		16	40.13	odd	4
1920.2.y.i.1567.5		16	16.3	odd	4
1920.2.y.j.223.5		16	40.3	even	4
1920.2.y.j.1567.5		16	16.13	even	4
1920.2.bc.i.607.1		16	8.5	even	2
1920.2.bc.i.1183.1		16	80.3	even	4
1920.2.bc.j.607.1		16	8.3	odd	2
1920.2.bc.j.1183.1		16	80.13	odd	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.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.873858 + 1.11192i) q^{2} -1.00000i q^{3} +(-0.472743 + 1.94333i) q^{4} +(1.54804 + 1.61356i) q^{5} +(1.11192 - 0.873858i) q^{6} +(0.143894 + 0.143894i) q^{7} +(-2.57394 + 1.17254i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.873858 + 1.11192i) q^{2} -1.00000i q^{3} +(-0.472743 + 1.94333i) q^{4} +(1.54804 + 1.61356i) q^{5} +(1.11192 - 0.873858i) q^{6} +(0.143894 + 0.143894i) q^{7} +(-2.57394 + 1.17254i) q^{8} -1.00000 q^{9} +(-0.441393 + 3.13132i) q^{10} +(0.749545 + 0.749545i) q^{11} +(1.94333 + 0.472743i) q^{12} +3.29132 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} +(-0.873858 - 1.11192i) q^{18} +(-4.25468 - 4.25468i) q^{19} +(-3.86750 + 2.24554i) q^{20} +(0.143894 - 0.143894i) q^{21} +(-0.178440 + 1.48843i) 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} +1.00000i q^{27} +(-0.347657 + 0.211607i) q^{28} +(2.77462 - 2.77462i) q^{29} +(3.13132 + 0.441393i) q^{30} -6.60915i q^{31} +(-1.06181 - 5.55631i) q^{32} +(0.749545 - 0.749545i) q^{33} +(-0.323074 + 2.69488i) q^{34} +(-0.00942893 + 0.454934i) q^{35} +(0.472743 - 1.94333i) q^{36} -10.0194 q^{37} +(1.01289 - 8.44886i) q^{38} -3.29132i q^{39} +(-5.87651 - 2.33808i) q^{40} -1.72608i q^{41} +(0.285741 + 0.0342559i) q^{42} -4.17171 q^{43} +(-1.81095 + 1.10227i) q^{44} +(-1.54804 - 1.61356i) q^{45} +(1.66287 + 0.199352i) q^{46} +(8.54502 - 8.54502i) q^{47} +(-1.83739 + 3.55303i) q^{48} -6.95859i q^{49} +(-5.73588 + 4.13518i) q^{50} +(1.35709 - 1.35709i) q^{51} +(-1.55595 + 6.39610i) q^{52} +5.05524i 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} +(5.50979 + 0.660538i) q^{58} +(-3.08237 + 3.08237i) q^{59} +(2.24554 + 3.86750i) q^{60} +(-5.00346 - 5.00346i) q^{61} +(7.34887 - 5.77546i) 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} -4.26739 q^{67} +(-3.27881 + 1.99571i) q^{68} +(-0.837388 - 0.837388i) q^{69} +(-0.514091 + 0.387064i) q^{70} +13.2111 q^{71} +(2.57394 - 1.17254i) q^{72} +(11.6889 + 11.6889i) q^{73} +(-8.75550 - 11.1407i) q^{74} +(4.99571 + 0.207170i) q^{75} +(10.2796 - 6.25686i) q^{76} +0.215710i q^{77} +(3.65969 - 2.87614i) q^{78} -9.95558 q^{79} +(-2.53547 - 8.57738i) q^{80} +1.00000 q^{81} +(1.91927 - 1.50835i) q^{82} +10.0134i q^{83} +(0.211607 + 0.347657i) q^{84} +(-0.0889259 + 4.29056i) q^{85} +(-3.64549 - 4.63862i) q^{86} +(-2.77462 - 2.77462i) q^{87} +(-2.80815 - 1.05041i) q^{88} -5.76005 q^{89} +(0.441393 - 3.13132i) q^{90} +(0.473599 + 0.473599i) q^{91} +(1.23145 + 2.02319i) q^{92} -6.60915 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} +(7.73741 - 6.08082i) q^{98} +(-0.749545 - 0.749545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9	\( 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 4 q^{24} - 32 q^{25} + 20 q^{26} + 12 q^{28} - 12 q^{29} + 2 q^{30} - 28 q^{32} + 12 q^{35} - 8 q^{36} - 24 q^{37} + 16 q^{38} + 16 q^{40} + 24 q^{42} + 24 q^{43} - 52 q^{44} + 8 q^{45} - 16 q^{46} + 32 q^{47} - 16 q^{48} + 6 q^{50} - 8 q^{51} + 24 q^{52} - 2 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 12 q^{58} + 24 q^{59} + 24 q^{60} + 40 q^{61} + 28 q^{62} + 4 q^{63} + 8 q^{64} - 4 q^{65} - 8 q^{66} + 16 q^{67} - 8 q^{68} + 12 q^{70} - 8 q^{72} - 8 q^{73} - 64 q^{74} + 24 q^{75} + 16 q^{76} + 12 q^{78} + 48 q^{79} + 16 q^{81} - 32 q^{82} - 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{88} + 2 q^{90} - 40 q^{91} - 16 q^{92} - 32 q^{93} + 20 q^{94} - 8 q^{95} - 28 q^{96} + 48 q^{97} + 62 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 4 * q^24 - 32 * q^25 + 20 * q^26 + 12 * q^28 - 12 * q^29 + 2 * q^30 - 28 * q^32 + 12 * q^35 - 8 * q^36 - 24 * q^37 + 16 * q^38 + 16 * q^40 + 24 * q^42 + 24 * q^43 - 52 * q^44 + 8 * q^45 - 16 * q^46 + 32 * q^47 - 16 * q^48 + 6 * q^50 - 8 * q^51 + 24 * q^52 - 2 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 12 * q^58 + 24 * q^59 + 24 * q^60 + 40 * q^61 + 28 * q^62 + 4 * q^63 + 8 * q^64 - 4 * q^65 - 8 * q^66 + 16 * q^67 - 8 * q^68 + 12 * q^70 - 8 * q^72 - 8 * q^73 - 64 * q^74 + 24 * q^75 + 16 * q^76 + 12 * q^78 + 48 * q^79 + 16 * q^81 - 32 * q^82 - 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^88 + 2 * q^90 - 40 * q^91 - 16 * q^92 - 32 * q^93 + 20 * q^94 - 8 * q^95 - 28 * q^96 + 48 * q^97 + 62 * q^98

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