LMFDB - Embedded newform 185.2.f.c.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [185,2,Mod(43,185)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(185, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("185.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.f (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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	185.43
Dual form			185.2.f.c.142.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.17009i q^{2} +(0.315449 - 0.315449i) q^{3} -2.70928 q^{4} +(2.17009 - 0.539189i) q^{5} +(0.684551 + 0.684551i) q^{6} +(-1.31545 + 1.31545i) q^{7} -1.53919i q^{8} +2.80098i q^{9} +O(q^{10})$	\(q+2.17009i q^{2} +(0.315449 - 0.315449i) q^{3} -2.70928 q^{4} +(2.17009 - 0.539189i) q^{5} +(0.684551 + 0.684551i) q^{6} +(-1.31545 + 1.31545i) q^{7} -1.53919i q^{8} +2.80098i q^{9} +(1.17009 + 4.70928i) q^{10} +4.04945i q^{11} +(-0.854638 + 0.854638i) q^{12} -5.80098i q^{13} +(-2.85464 - 2.85464i) q^{14} +(0.514465 - 0.854638i) q^{15} -2.07838 q^{16} +2.87936 q^{17} -6.07838 q^{18} +(1.68455 - 1.68455i) q^{19} +(-5.87936 + 1.46081i) q^{20} +0.829914i q^{21} -8.78765 q^{22} -8.04945i q^{23} +(-0.485535 - 0.485535i) q^{24} +(4.41855 - 2.34017i) q^{25} +12.5886 q^{26} +(1.82991 + 1.82991i) q^{27} +(3.56391 - 3.56391i) q^{28} +(0.0783777 + 0.0783777i) q^{29} +(1.85464 + 1.11643i) q^{30} +(-4.10310 + 4.10310i) q^{31} -7.58864i q^{32} +(1.27739 + 1.27739i) q^{33} +6.24846i q^{34} +(-2.14536 + 3.56391i) q^{35} -7.58864i q^{36} +(-1.00000 - 6.00000i) q^{37} +(3.65562 + 3.65562i) q^{38} +(-1.82991 - 1.82991i) q^{39} +(-0.829914 - 3.34017i) q^{40} -5.46800i q^{41} -1.80098 q^{42} +8.38962i q^{43} -10.9711i q^{44} +(1.51026 + 6.07838i) q^{45} +17.4680 q^{46} +(0.933015 - 0.933015i) q^{47} +(-0.655622 + 0.655622i) q^{48} +3.53919i q^{49} +(5.07838 + 9.58864i) q^{50} +(0.908291 - 0.908291i) q^{51} +15.7165i q^{52} +(-4.17009 - 4.17009i) q^{53} +(-3.97107 + 3.97107i) q^{54} +(2.18342 + 8.78765i) q^{55} +(2.02472 + 2.02472i) q^{56} -1.06278i q^{57} +(-0.170086 + 0.170086i) q^{58} +(8.10310 - 8.10310i) q^{59} +(-1.39383 + 2.31545i) q^{60} +(6.70928 - 6.70928i) q^{61} +(-8.90409 - 8.90409i) q^{62} +(-3.68455 - 3.68455i) q^{63} +12.3112 q^{64} +(-3.12783 - 12.5886i) q^{65} +(-2.77205 + 2.77205i) q^{66} +(-0.116433 - 0.116433i) q^{67} -7.80098 q^{68} +(-2.53919 - 2.53919i) q^{69} +(-7.73400 - 4.65562i) q^{70} -7.75872 q^{71} +4.31124 q^{72} +(-7.09171 + 7.09171i) q^{73} +(13.0205 - 2.17009i) q^{74} +(0.655622 - 2.13203i) q^{75} +(-4.56391 + 4.56391i) q^{76} +(-5.32684 - 5.32684i) q^{77} +(3.97107 - 3.97107i) q^{78} +(-1.51446 + 1.51446i) q^{79} +(-4.51026 + 1.12064i) q^{80} -7.24846 q^{81} +11.8660 q^{82} +(5.48554 + 5.48554i) q^{83} -2.24846i q^{84} +(6.24846 - 1.55252i) q^{85} -18.2062 q^{86} +0.0494483 q^{87} +6.23287 q^{88} +(-2.61757 - 2.61757i) q^{89} +(-13.1906 + 3.27739i) q^{90} +(7.63090 + 7.63090i) q^{91} +21.8082i q^{92} +2.58864i q^{93} +(2.02472 + 2.02472i) q^{94} +(2.74733 - 4.56391i) q^{95} +(-2.39383 - 2.39383i) q^{96} +0.630898 q^{97} -7.68035 q^{98} -11.3424 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{3} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 4 q^{7}+O(q^{10}) $ 6 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 4 * q^7	$ 6 q - 2 q^{3} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 4 q^{7} - 4 q^{10} + 2 q^{12} - 10 q^{14} + 18 q^{15} - 6 q^{16} - 8 q^{17} - 30 q^{18} + 14 q^{19} - 10 q^{20} - 32 q^{22} + 12 q^{24} - 2 q^{25} + 36 q^{26} + 22 q^{27} - 6 q^{29} + 4 q^{30} + 20 q^{33} - 20 q^{35} - 6 q^{37} - 4 q^{38} - 22 q^{39} - 16 q^{40} + 8 q^{42} - 24 q^{45} + 40 q^{46} - 8 q^{47} + 22 q^{48} + 24 q^{50} + 10 q^{51} - 14 q^{53} + 6 q^{54} + 4 q^{55} - 6 q^{56} + 10 q^{58} + 24 q^{59} + 2 q^{60} + 26 q^{61} - 10 q^{62} - 26 q^{63} + 22 q^{64} + 24 q^{65} + 32 q^{66} + 22 q^{67} - 28 q^{68} - 12 q^{69} - 14 q^{70} + 4 q^{71} - 26 q^{72} - 38 q^{73} + 12 q^{74} - 22 q^{75} - 6 q^{76} - 8 q^{77} - 6 q^{78} - 24 q^{79} + 6 q^{80} - 26 q^{81} + 44 q^{82} + 18 q^{83} + 20 q^{85} - 60 q^{86} - 36 q^{87} - 8 q^{88} - 6 q^{89} - 2 q^{90} + 38 q^{91} - 6 q^{94} - 14 q^{95} - 4 q^{96} - 4 q^{97} - 2 q^{98} - 72 q^{99}+O(q^{100}) $ 6 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 4 * q^7 - 4 * q^10 + 2 * q^12 - 10 * q^14 + 18 * q^15 - 6 * q^16 - 8 * q^17 - 30 * q^18 + 14 * q^19 - 10 * q^20 - 32 * q^22 + 12 * q^24 - 2 * q^25 + 36 * q^26 + 22 * q^27 - 6 * q^29 + 4 * q^30 + 20 * q^33 - 20 * q^35 - 6 * q^37 - 4 * q^38 - 22 * q^39 - 16 * q^40 + 8 * q^42 - 24 * q^45 + 40 * q^46 - 8 * q^47 + 22 * q^48 + 24 * q^50 + 10 * q^51 - 14 * q^53 + 6 * q^54 + 4 * q^55 - 6 * q^56 + 10 * q^58 + 24 * q^59 + 2 * q^60 + 26 * q^61 - 10 * q^62 - 26 * q^63 + 22 * q^64 + 24 * q^65 + 32 * q^66 + 22 * q^67 - 28 * q^68 - 12 * q^69 - 14 * q^70 + 4 * q^71 - 26 * q^72 - 38 * q^73 + 12 * q^74 - 22 * q^75 - 6 * q^76 - 8 * q^77 - 6 * q^78 - 24 * q^79 + 6 * q^80 - 26 * q^81 + 44 * q^82 + 18 * q^83 + 20 * q^85 - 60 * q^86 - 36 * q^87 - 8 * q^88 - 6 * q^89 - 2 * q^90 + 38 * q^91 - 6 * q^94 - 14 * q^95 - 4 * q^96 - 4 * q^97 - 2 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$			2.17009i			1.53448i	0.641358	+	0.767241i	$0.278371\pi$
$2$			2.17009i			1.53448i	−0.641358	+	0.767241i	$0.721629\pi$
$3$	0.315449	−	0.315449i	0.182124	−	0.182124i	−0.610156	−	0.792281i	$-0.708893\pi$
$3$	0.315449	−	0.315449i	0.182124	−	0.182124i	0.792281	+	0.610156i	$0.208893\pi$
$4$	−2.70928			−1.35464
$5$	2.17009	−	0.539189i	0.970492	−	0.241133i
$5$	2.17009	−	0.539189i	0.970492	−	0.241133i
$6$	0.684551	+	0.684551i	0.279467	+	0.279467i
$7$	−1.31545	+	1.31545i	−0.497193	+	0.497193i	−0.910563	−	0.413370i	$-0.864352\pi$
$7$	−1.31545	+	1.31545i	−0.497193	+	0.497193i	0.413370	+	0.910563i	$0.364352\pi$
$8$		−	1.53919i		−	0.544185i
$9$			2.80098i			0.933661i
$10$	1.17009	+	4.70928i	0.370014	+	1.48920i
$11$			4.04945i			1.22095i	0.792034	+	0.610477i	$0.209022\pi$
$11$			4.04945i			1.22095i	−0.792034	+	0.610477i	$0.790978\pi$
$12$	−0.854638	+	0.854638i	−0.246713	+	0.246713i
$13$		−	5.80098i		−	1.60890i	−0.594018	−	0.804452i	$-0.702459\pi$
$13$		−	5.80098i		−	1.60890i	0.594018	−	0.804452i	$-0.297541\pi$
$14$	−2.85464	−	2.85464i	−0.762934	−	0.762934i
$15$	0.514465	−	0.854638i	0.132834	−	0.220667i
$16$	−2.07838			−0.519594
$17$	2.87936			0.698348			0.349174	−	0.937058i	$-0.386462\pi$
$17$	2.87936			0.698348			0.349174	+	0.937058i	$0.386462\pi$
$18$	−6.07838			−1.43269
$19$	1.68455	−	1.68455i	0.386463	−	0.386463i	−0.486961	−	0.873424i	$-0.661895\pi$
$19$	1.68455	−	1.68455i	0.386463	−	0.386463i	0.873424	+	0.486961i	$0.161895\pi$
$20$	−5.87936	+	1.46081i	−1.31467	+	0.326647i
$21$			0.829914i			0.181102i
$22$	−8.78765			−1.87353
$23$		−	8.04945i		−	1.67843i	−0.543803	−	0.839213i	$-0.683016\pi$
$23$		−	8.04945i		−	1.67843i	0.543803	−	0.839213i	$-0.316984\pi$
$24$	−0.485535	−	0.485535i	−0.0991095	−	0.0991095i
$25$	4.41855	−	2.34017i	0.883710	−	0.468035i
$26$	12.5886			2.46883
$27$	1.82991	+	1.82991i	0.352167	+	0.352167i
$28$	3.56391	−	3.56391i	0.673516	−	0.673516i
$29$	0.0783777	+	0.0783777i	0.0145544	+	0.0145544i	0.714347	−	0.699792i	$-0.246724\pi$
$29$	0.0783777	+	0.0783777i	0.0145544	+	0.0145544i	−0.699792	+	0.714347i	$0.746724\pi$
$30$	1.85464	+	1.11643i	0.338609	+	0.203832i
$31$	−4.10310	+	4.10310i	−0.736939	+	0.736939i	−0.971984	−	0.235046i	$-0.924476\pi$
$31$	−4.10310	+	4.10310i	−0.736939	+	0.736939i	0.235046	+	0.971984i	$0.424476\pi$
$32$		−	7.58864i		−	1.34149i
$33$	1.27739	+	1.27739i	0.222366	+	0.222366i
$34$			6.24846i			1.07160i
$35$	−2.14536	+	3.56391i	−0.362632	+	0.602411i
$36$		−	7.58864i		−	1.26477i
$37$	−1.00000	−	6.00000i	−0.164399	−	0.986394i
$37$	−1.00000	−	6.00000i	−0.164399	−	0.986394i
$38$	3.65562	+	3.65562i	0.593020	+	0.593020i
$39$	−1.82991	−	1.82991i	−0.293021	−	0.293021i
$40$	−0.829914	−	3.34017i	−0.131221	−	0.528128i
$41$		−	5.46800i		−	0.853958i	−0.904262	−	0.426979i	$-0.859578\pi$
$41$		−	5.46800i		−	0.853958i	0.904262	−	0.426979i	$-0.140422\pi$
$42$	−1.80098			−0.277898
$43$			8.38962i			1.27941i	0.768623	+	0.639703i	$0.220942\pi$
$43$			8.38962i			1.27941i	−0.768623	+	0.639703i	$0.779058\pi$
$44$		−	10.9711i		−	1.65395i
$45$	1.51026	+	6.07838i	0.225136	+	0.906111i
$46$	17.4680			2.57552
$47$	0.933015	−	0.933015i	0.136094	−	0.136094i	−0.635778	−	0.771872i	$-0.719321\pi$
$47$	0.933015	−	0.933015i	0.136094	−	0.136094i	0.771872	+	0.635778i	$0.219321\pi$
$48$	−0.655622	+	0.655622i	−0.0946309	+	0.0946309i
$49$			3.53919i			0.505598i
$50$	5.07838	+	9.58864i	0.718191	+	1.35604i
$51$	0.908291	−	0.908291i	0.127186	−	0.127186i
$52$			15.7165i			2.17948i
$53$	−4.17009	−	4.17009i	−0.572805	−	0.572805i	0.360106	−	0.932911i	$-0.382741\pi$
$53$	−4.17009	−	4.17009i	−0.572805	−	0.572805i	−0.932911	+	0.360106i	$0.882741\pi$
$54$	−3.97107	+	3.97107i	−0.540394	+	0.540394i
$55$	2.18342	+	8.78765i	0.294412	+	1.18493i
$56$	2.02472	+	2.02472i	0.270565	+	0.270565i
$57$		−	1.06278i		−	0.140769i
$58$	−0.170086	+	0.170086i	−0.0223334	+	0.0223334i
$59$	8.10310	−	8.10310i	1.05493	−	1.05493i	0.0565333	−	0.998401i	$-0.481995\pi$
$59$	8.10310	−	8.10310i	1.05493	−	1.05493i	0.998401	−	0.0565333i	$-0.0180047\pi$
$60$	−1.39383	+	2.31545i	−0.179942	+	0.298923i
$61$	6.70928	−	6.70928i	0.859035	−	0.859035i	−0.132190	−	0.991224i	$-0.542201\pi$
$61$	6.70928	−	6.70928i	0.859035	−	0.859035i	0.991224	+	0.132190i	$0.0422008\pi$
$62$	−8.90409	−	8.90409i	−1.13082	−	1.13082i
$63$	−3.68455	−	3.68455i	−0.464210	−	0.464210i
$64$	12.3112			1.53891
$65$	−3.12783	−	12.5886i	−0.387959	−	1.56143i
$66$	−2.77205	+	2.77205i	−0.341216	+	0.341216i
$67$	−0.116433	−	0.116433i	−0.0142245	−	0.0142245i	0.699959	−	0.714183i	$-0.253202\pi$
$67$	−0.116433	−	0.116433i	−0.0142245	−	0.0142245i	−0.714183	+	0.699959i	$0.753202\pi$
$68$	−7.80098			−0.946008
$69$	−2.53919	−	2.53919i	−0.305682	−	0.305682i
$70$	−7.73400	−	4.65562i	−0.924390	−	0.556453i
$71$	−7.75872			−0.920791			−0.460396	−	0.887714i	$-0.652292\pi$
$71$	−7.75872			−0.920791			−0.460396	+	0.887714i	$0.652292\pi$
$72$	4.31124			0.508085
$73$	−7.09171	+	7.09171i	−0.830022	+	0.830022i	−0.987519	−	0.157498i	$-0.949657\pi$
$73$	−7.09171	+	7.09171i	−0.830022	+	0.830022i	0.157498	+	0.987519i	$0.449657\pi$
$74$	13.0205	−	2.17009i	1.51360	−	0.252267i
$75$	0.655622	−	2.13203i	0.0757047	−	0.246186i
$76$	−4.56391	+	4.56391i	−0.523517	+	0.523517i
$77$	−5.32684	−	5.32684i	−0.607050	−	0.607050i
$78$	3.97107	−	3.97107i	0.449635	−	0.449635i
$79$	−1.51446	+	1.51446i	−0.170391	+	0.170391i	−0.787151	−	0.616760i	$-0.788445\pi$
$79$	−1.51446	+	1.51446i	−0.170391	+	0.170391i	0.616760	+	0.787151i	$0.288445\pi$
$80$	−4.51026	+	1.12064i	−0.504262	+	0.125291i
$81$	−7.24846			−0.805385
$82$	11.8660			1.31038
$83$	5.48554	+	5.48554i	0.602116	+	0.602116i	0.940874	−	0.338758i	$-0.110007\pi$
$83$	5.48554	+	5.48554i	0.602116	+	0.602116i	−0.338758	+	0.940874i	$0.610007\pi$
$84$		−	2.24846i		−	0.245328i
$85$	6.24846	−	1.55252i	0.677741	−	0.168394i
$86$	−18.2062			−1.96323
$87$	0.0494483			0.00530142
$88$	6.23287			0.664426
$89$	−2.61757	−	2.61757i	−0.277462	−	0.277462i	0.554633	−	0.832095i	$-0.312859\pi$
$89$	−2.61757	−	2.61757i	−0.277462	−	0.277462i	−0.832095	+	0.554633i	$0.812859\pi$
$90$	−13.1906	+	3.27739i	−1.39041	+	0.345468i
$91$	7.63090	+	7.63090i	0.799935	+	0.799935i
$92$			21.8082i			2.27366i
$93$			2.58864i			0.268429i
$94$	2.02472	+	2.02472i	0.208834	+	0.208834i
$95$	2.74733	−	4.56391i	0.281870	−	0.468248i
$96$	−2.39383	−	2.39383i	−0.244319	−	0.244319i
$97$	0.630898			0.0640579			0.0320290	−	0.999487i	$-0.489803\pi$
$97$	0.630898			0.0640579			0.0320290	+	0.999487i	$0.489803\pi$
$98$	−7.68035			−0.775832
$99$	−11.3424			−1.13996
$100$	−11.9711	+	6.34017i	−1.19711	+	0.634017i
$101$			12.4547i			1.23929i	0.784884	+	0.619643i	$0.212723\pi$
$101$			12.4547i			1.23929i	−0.784884	+	0.619643i	$0.787277\pi$
$102$	1.97107	+	1.97107i	0.195165	+	0.195165i
$103$	−12.4391			−1.22566			−0.612829	−	0.790216i	$-0.709969\pi$
$103$	−12.4391			−1.22566			−0.612829	+	0.790216i	$0.709969\pi$
$104$	−8.92881			−0.875542
$105$	0.447480	+	1.80098i	0.0436696	+	0.175758i
$106$	9.04945	−	9.04945i	0.878960	−	0.878960i
$107$	1.31545	−	1.31545i	0.127169	−	0.127169i	−0.640658	−	0.767827i	$-0.721338\pi$
$107$	1.31545	−	1.31545i	0.127169	−	0.127169i	0.767827	+	0.640658i	$0.221338\pi$
$108$	−4.95774	−	4.95774i	−0.477059	−	0.477059i
$109$	−5.72261	+	5.72261i	−0.548126	+	0.548126i	−0.925899	−	0.377772i	$-0.876690\pi$
$109$	−5.72261	+	5.72261i	−0.548126	+	0.548126i	0.377772	+	0.925899i	$0.376690\pi$
$110$	−19.0700	+	4.73820i	−1.81825	+	0.451770i
$111$	−2.20814	−	1.57724i	−0.209588	−	0.149705i
$112$	2.73400	−	2.73400i	0.258339	−	0.258339i
$113$	0.780465			0.0734200			0.0367100	−	0.999326i	$-0.488312\pi$
$113$	0.780465			0.0734200			0.0367100	+	0.999326i	$0.488312\pi$
$114$	2.30632			0.216007
$115$	−4.34017	−	17.4680i	−0.404723	−	1.62890i
$116$	−0.212347	−	0.212347i	−0.0197159	−	0.0197159i
$117$	16.2485			1.50217
$118$	17.5844	+	17.5844i	1.61878	+	1.61878i
$119$	−3.78765	+	3.78765i	−0.347214	+	0.347214i
$120$	−1.31545	−	0.791858i	−0.120083	−	0.0722864i
$121$	−5.39803			−0.490730
$122$	14.5597	+	14.5597i	1.31817	+	1.31817i
$123$	−1.72487	−	1.72487i	−0.155527	−	0.155527i
$124$	11.1164	−	11.1164i	0.998285	−	0.998285i
$125$	8.32684	−	7.46081i	0.744775	−	0.667315i
$126$	7.99579	−	7.99579i	0.712322	−	0.712322i
$127$	−12.3721	+	12.3721i	−1.09785	+	1.09785i	−0.103183	+	0.994662i	$0.532903\pi$
$127$	−12.3721	+	12.3721i	−1.09785	+	1.09785i	−0.994662	+	0.103183i	$0.967097\pi$
$128$			11.5392i			1.01993i
$129$	2.64650	+	2.64650i	0.233011	+	0.233011i
$130$	27.3184	−	6.78765i	2.39598	−	0.595317i
$131$	−10.4566	+	10.4566i	−0.913598	+	0.913598i	−0.996553	−	0.0829554i	$-0.973564\pi$
$131$	−10.4566	+	10.4566i	−0.913598	+	0.913598i	0.0829554	+	0.996553i	$0.473564\pi$
$132$	−3.46081	−	3.46081i	−0.301225	−	0.301225i
$133$			4.43188i			0.384293i
$134$	0.252669	−	0.252669i	0.0218273	−	0.0218273i
$135$	4.95774	+	2.98440i	0.426694	+	0.256856i
$136$		−	4.43188i		−	0.380031i
$137$	11.2979	−	11.2979i	0.965246	−	0.965246i	−0.0341702	−	0.999416i	$-0.510879\pi$
$137$	11.2979	−	11.2979i	0.965246	−	0.965246i	0.999416	+	0.0341702i	$0.0108788\pi$
$138$	5.51026	−	5.51026i	0.469064	−	0.469064i
$139$	3.60197			0.305515			0.152757	−	0.988264i	$-0.451185\pi$
$139$	3.60197			0.305515			0.152757	+	0.988264i	$0.451185\pi$
$140$	5.81238	−	9.65562i	0.491236	−	0.816049i
$141$		−	0.588637i		−	0.0495722i
$142$		−	16.8371i		−	1.41294i
$143$	23.4908			1.96440
$144$		−	5.82150i		−	0.485125i
$145$	0.212347	+	0.127826i	0.0176344	+	0.0106154i
$146$	−15.3896	−	15.3896i	−1.27365	−	1.27365i
$147$	1.11643	+	1.11643i	0.0920818	+	0.0920818i
$148$	2.70928	+	16.2557i	0.222701	+	1.33621i
$149$			13.3763i			1.09583i	0.836535	+	0.547914i	$0.184578\pi$
$149$			13.3763i			1.09583i	−0.836535	+	0.547914i	$0.815422\pi$
$150$	4.62669	+	1.42276i	0.377768	+	0.116168i
$151$		−	8.54638i		−	0.695494i	−0.937588	−	0.347747i	$-0.886947\pi$
$151$		−	8.54638i		−	0.695494i	0.937588	−	0.347747i	$-0.113053\pi$
$152$	−2.59284	−	2.59284i	−0.210307	−	0.210307i
$153$			8.06505i			0.652020i
$154$	11.5597	−	11.5597i	0.931508	−	0.931508i
$155$	−6.69174	+	11.1164i	−0.537493	+	0.892893i
$156$	4.95774	+	4.95774i	0.396937	+	0.396937i
$157$	0.120638	−	0.120638i	0.00962797	−	0.00962797i	−0.702276	−	0.711904i	$-0.747833\pi$
$157$	0.120638	−	0.120638i	0.00962797	−	0.00962797i	0.711904	+	0.702276i	$0.247833\pi$
$158$	−3.28652	−	3.28652i	−0.261461	−	0.261461i
$159$	−2.63090			−0.208644
$160$	−4.09171	−	16.4680i	−0.323478	−	1.30191i
$161$	10.5886	+	10.5886i	0.834502	+	0.834502i
$162$		−	15.7298i		−	1.23585i
$163$	−5.75872			−0.451058			−0.225529	−	0.974236i	$-0.572411\pi$
$163$	−5.75872			−0.451058			−0.225529	+	0.974236i	$0.572411\pi$
$164$			14.8143i			1.15680i
$165$	3.46081	+	2.08330i	0.269424	+	0.162185i
$166$	−11.9041	+	11.9041i	−0.923936	+	0.923936i
$167$	−2.00000			−0.154765			−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000			−0.154765			−0.0773823	+	0.997001i	$0.524656\pi$
$168$	1.27739			0.0985531
$169$	−20.6514			−1.58857
$170$	3.36910	+	13.5597i	0.258398	+	1.03998i
$171$	4.71840	+	4.71840i	0.360825	+	0.360825i
$172$		−	22.7298i		−	1.73313i
$173$	11.8371	−	11.8371i	0.899958	−	0.899958i	−0.0954738	−	0.995432i	$-0.530437\pi$
$173$	11.8371	−	11.8371i	0.899958	−	0.899958i	0.995432	+	0.0954738i	$0.0304366\pi$
$174$			0.107307i			0.00813493i
$175$	−2.73400	+	8.89076i	−0.206671	+	0.672078i
$176$		−	8.41628i		−	0.634401i
$177$		−	5.11223i		−	0.384259i
$178$	5.68035	−	5.68035i	0.425760	−	0.425760i
$179$	−3.86797	−	3.86797i	−0.289106	−	0.289106i	0.547621	−	0.836727i	$-0.315534\pi$
$179$	−3.86797	−	3.86797i	−0.289106	−	0.289106i	−0.836727	+	0.547621i	$0.815534\pi$
$180$	−4.09171	−	16.4680i	−0.304978	−	1.22745i
$181$	−8.90602			−0.661980			−0.330990	−	0.943634i	$-0.607383\pi$
$181$	−8.90602			−0.661980			−0.330990	+	0.943634i	$0.607383\pi$
$182$	−16.5597	+	16.5597i	−1.22749	+	1.22749i
$183$		−	4.23287i		−	0.312902i
$184$	−12.3896			−0.913375
$185$	−5.40522	−	12.4813i	−0.397400	−	0.917646i
$186$	−5.61757			−0.411900
$187$			11.6598i			0.852651i
$188$	−2.52780	+	2.52780i	−0.184358	+	0.184358i
$189$	−4.81432			−0.350190
$190$	9.90409	+	5.96194i	0.718518	+	0.432525i
$191$	8.35157	+	8.35157i	0.604298	+	0.604298i	0.941450	−	0.337152i	$-0.109464\pi$
$191$	8.35157	+	8.35157i	0.604298	+	0.604298i	−0.337152	+	0.941450i	$0.609464\pi$
$192$	3.88357	−	3.88357i	0.280272	−	0.280272i
$193$		−	0.398032i		−	0.0286510i	−0.999897	−	0.0143255i	$-0.995440\pi$
$193$		−	0.398032i		−	0.0286510i	0.999897	−	0.0143255i	$-0.00456010\pi$
$194$			1.36910i			0.0982958i
$195$	−4.95774	−	2.98440i	−0.355031	−	0.213717i
$196$		−	9.58864i		−	0.684903i
$197$	−8.52586	+	8.52586i	−0.607442	+	0.607442i	−0.942277	−	0.334835i	$-0.891320\pi$
$197$	−8.52586	+	8.52586i	−0.607442	+	0.607442i	0.334835	+	0.942277i	$0.391320\pi$
$198$		−	24.6141i		−	1.74925i
$199$	17.2443	+	17.2443i	1.22241	+	1.22241i	0.966772	+	0.255641i	$0.0822867\pi$
$199$	17.2443	+	17.2443i	1.22241	+	1.22241i	0.255641	+	0.966772i	$0.417713\pi$
$200$	−3.60197	−	6.80098i	−0.254698	−	0.480902i
$201$	−0.0734572			−0.00518127
$202$	−27.0277			−1.90166
$203$	−0.206204			−0.0144727
$204$	−2.46081	+	2.46081i	−0.172291	+	0.172291i
$205$	−2.94828	−	11.8660i	−0.205917	−	0.828760i
$206$		−	26.9939i		−	1.88075i
$207$	22.5464			1.56708
$208$			12.0566i			0.835977i
$209$	6.82150	+	6.82150i	0.471853	+	0.471853i
$210$	−3.90829	+	0.971071i	−0.269698	+	0.0670102i
$211$	−3.63317			−0.250117			−0.125059	−	0.992149i	$-0.539912\pi$
$211$	−3.63317			−0.250117			−0.125059	+	0.992149i	$0.539912\pi$
$212$	11.2979	+	11.2979i	0.775944	+	0.775944i
$213$	−2.44748	+	2.44748i	−0.167699	+	0.167699i
$214$	2.85464	+	2.85464i	0.195139	+	0.195139i
$215$	4.52359	+	18.2062i	0.308506	+	1.24165i
$216$	2.81658	−	2.81658i	0.191644	−	0.191644i
$217$		−	10.7948i		−	0.732802i
$218$	−12.4186	−	12.4186i	−0.841090	−	0.841090i
$219$			4.47414i			0.302335i
$220$	−5.91548	−	23.8082i	−0.398822	−	1.60515i
$221$		−	16.7031i		−	1.12357i
$222$	3.42276	−	4.79186i	0.229720	−	0.321608i
$223$	−17.5578	−	17.5578i	−1.17576	−	1.17576i	−0.980815	−	0.194940i	$-0.937549\pi$
$223$	−17.5578	−	17.5578i	−1.17576	−	1.17576i	−0.194940	−	0.980815i	$-0.562451\pi$
$224$	9.98246	+	9.98246i	0.666981	+	0.666981i
$225$	6.55479	+	12.3763i	0.436986	+	0.825086i
$226$			1.69368i			0.112662i
$227$	−5.97334			−0.396464			−0.198232	−	0.980155i	$-0.563520\pi$
$227$	−5.97334			−0.396464			−0.198232	+	0.980155i	$0.563520\pi$
$228$			2.87936i			0.190690i
$229$		−	26.2472i		−	1.73447i	−0.497902	−	0.867233i	$-0.665896\pi$
$229$		−	26.2472i		−	1.73447i	0.497902	−	0.867233i	$-0.334104\pi$
$230$	37.9071	−	9.41855i	2.49952	−	0.621041i
$231$	−3.36069			−0.221117
$232$	0.120638	−	0.120638i	0.00792028	−	0.00792028i
$233$	9.14116	−	9.14116i	0.598857	−	0.598857i	−0.341151	−	0.940008i	$-0.610817\pi$
$233$	9.14116	−	9.14116i	0.598857	−	0.598857i	0.940008	+	0.341151i	$0.110817\pi$
$234$			35.2606i			2.30506i
$235$	1.52165	−	2.52780i	0.0992617	−	0.164895i
$236$	−21.9535	+	21.9535i	−1.42905	+	1.42905i
$237$			0.955472i			0.0620646i
$238$	−8.21953	−	8.21953i	−0.532793	−	0.532793i
$239$	8.67122	−	8.67122i	0.560895	−	0.560895i	−0.368667	−	0.929562i	$-0.620186\pi$
$239$	8.67122	−	8.67122i	0.560895	−	0.560895i	0.929562	+	0.368667i	$0.120186\pi$
$240$	−1.06925	+	1.77626i	−0.0690199	+	0.114657i
$241$	10.8238	+	10.8238i	0.697220	+	0.697220i	0.963810	−	0.266590i	$-0.0858969\pi$
$241$	10.8238	+	10.8238i	0.697220	+	0.697220i	−0.266590	+	0.963810i	$0.585897\pi$
$242$		−	11.7142i		−	0.753017i
$243$	−7.77626	+	7.77626i	−0.498847	+	0.498847i
$244$	−18.1773	+	18.1773i	−1.16368	+	1.16368i
$245$	1.90829	+	7.68035i	0.121916	+	0.490679i
$246$	3.74313	−	3.74313i	0.238653	−	0.238653i
$247$	−9.77205	−	9.77205i	−0.621781	−	0.621781i
$248$	6.31545	+	6.31545i	0.401031	+	0.401031i
$249$	3.46081			0.219320
$250$	16.1906	+	18.0700i	1.02398	+	1.14285i
$251$	−7.61950	+	7.61950i	−0.480939	+	0.480939i	−0.905431	−	0.424493i	$-0.860453\pi$
$251$	−7.61950	+	7.61950i	−0.480939	+	0.480939i	0.424493	+	0.905431i	$0.360453\pi$
$252$	9.98246	+	9.98246i	0.628836	+	0.628836i
$253$	32.5958			2.04928
$254$	−26.8485	−	26.8485i	−1.68462	−	1.68462i
$255$	1.48133	−	2.46081i	0.0927645	−	0.154102i
$256$	−0.418551			−0.0261594
$257$	−16.1145			−1.00519			−0.502597	−	0.864521i	$-0.667622\pi$
$257$	−16.1145			−1.00519			−0.502597	+	0.864521i	$0.667622\pi$
$258$	−5.74313	+	5.74313i	−0.357551	+	0.357551i
$259$	9.20814	+	6.57724i	0.572166	+	0.408690i
$260$	8.47414	+	34.1061i	0.525544	+	2.11517i
$261$	−0.219535	+	0.219535i	−0.0135889	+	0.0135889i
$262$	−22.6917	−	22.6917i	−1.40190	−	1.40190i
$263$	−11.3093	+	11.3093i	−0.697362	+	0.697362i	−0.963841	−	0.266479i	$-0.914140\pi$
$263$	−11.3093	+	11.3093i	−0.697362	+	0.697362i	0.266479	+	0.963841i	$0.414140\pi$
$264$	1.96615	−	1.96615i	0.121008	−	0.121008i
$265$	−11.2979	−	6.80098i	−0.694025	−	0.417781i
$266$	−9.61757			−0.589691
$267$	−1.65142			−0.101065
$268$	0.315449	+	0.315449i	0.0192691	+	0.0192691i
$269$			3.09398i			0.188643i	0.995542	+	0.0943215i	$0.0300682\pi$
$269$			3.09398i			0.188643i	−0.995542	+	0.0943215i	$0.969932\pi$
$270$	−6.47641	+	10.7587i	−0.394142	+	0.654755i
$271$	27.9155			1.69574			0.847872	−	0.530200i	$-0.177883\pi$
$271$	27.9155			1.69574			0.847872	+	0.530200i	$0.177883\pi$
$272$	−5.98440			−0.362858
$273$	4.81432			0.291376
$274$	24.5174	+	24.5174i	1.48115	+	1.48115i
$275$	9.47641	+	17.8927i	0.571449	+	1.07897i
$276$	6.87936	+	6.87936i	0.414089	+	0.414089i
$277$			20.9783i			1.26046i	0.776408	+	0.630231i	$0.217040\pi$
$277$			20.9783i			1.26046i	−0.776408	+	0.630231i	$0.782960\pi$
$278$			7.81658i			0.468807i
$279$	−11.4927	−	11.4927i	−0.688051	−	0.688051i
$280$	5.48554	+	3.30212i	0.327823	+	0.197339i
$281$	−10.8010	−	10.8010i	−0.644333	−	0.644333i	0.307285	−	0.951618i	$-0.400580\pi$
$281$	−10.8010	−	10.8010i	−0.644333	−	0.644333i	−0.951618	+	0.307285i	$0.900580\pi$
$282$	1.27739			0.0760677
$283$	−19.6020			−1.16522			−0.582608	−	0.812753i	$-0.697968\pi$
$283$	−19.6020			−1.16522			−0.582608	+	0.812753i	$0.697968\pi$
$284$	21.0205			1.24734
$285$	−0.573039	−	2.30632i	−0.0339439	−	0.136615i
$286$			50.9770i			3.01434i
$287$	7.19287	+	7.19287i	0.424582	+	0.424582i
$288$	21.2557			1.25250
$289$	−8.70928			−0.512310
$290$	−0.277394	+	0.460811i	−0.0162891	+	0.0270598i
$291$	0.199016	−	0.199016i	0.0116665	−	0.0116665i
$292$	19.2134	−	19.2134i	1.12438	−	1.12438i
$293$	20.0205	+	20.0205i	1.16961	+	1.16961i	0.982301	+	0.187310i	$0.0599770\pi$
$293$	20.0205	+	20.0205i	1.16961	+	1.16961i	0.187310	+	0.982301i	$0.440023\pi$
$294$	−2.42276	+	2.42276i	−0.141298	+	0.141298i
$295$	13.2153	−	21.9535i	0.769426	−	1.27818i
$296$	−9.23513	+	1.53919i	−0.536781	+	0.0894635i
$297$	−7.41014	+	7.41014i	−0.429980	+	0.429980i
$298$	−29.0277			−1.68153
$299$	−46.6947			−2.70043
$300$	−1.77626	+	5.77626i	−0.102552	+	0.333493i
$301$	−11.0361	−	11.0361i	−0.636111	−	0.636111i
$302$	18.5464			1.06722
$303$	3.92881	+	3.92881i	0.225704	+	0.225704i
$304$	−3.50113	+	3.50113i	−0.200804	+	0.200804i
$305$	10.9421	−	18.1773i	0.626545	−	1.04083i
$306$	−17.5018			−1.00051
$307$	−3.90409	−	3.90409i	−0.222818	−	0.222818i	0.586866	−	0.809684i	$-0.300362\pi$
$307$	−3.90409	−	3.90409i	−0.222818	−	0.222818i	−0.809684	+	0.586866i	$0.800362\pi$
$308$	14.4319	+	14.4319i	0.822333	+	0.822333i
$309$	−3.92389	+	3.92389i	−0.223222	+	0.223222i
$310$	−24.1236	−	14.5217i	−1.37013	−	0.824774i
$311$	−9.67122	+	9.67122i	−0.548405	+	0.548405i	−0.925979	−	0.377575i	$-0.876758\pi$
$311$	−9.67122	+	9.67122i	−0.548405	+	0.548405i	0.377575	+	0.925979i	$0.376758\pi$
$312$	−2.81658	+	2.81658i	−0.159458	+	0.159458i
$313$		−	18.4619i		−	1.04353i	−0.853091	−	0.521763i	$-0.825275\pi$
$313$		−	18.4619i		−	1.04353i	0.853091	−	0.521763i	$-0.174725\pi$
$314$	0.261795	+	0.261795i	0.0147740	+	0.0147740i
$315$	−9.98246	−	6.00913i	−0.562448	−	0.338576i
$316$	4.10310	−	4.10310i	0.230818	−	0.230818i
$317$	21.4813	+	21.4813i	1.20651	+	1.20651i	0.972149	+	0.234362i	$0.0753002\pi$
$317$	21.4813	+	21.4813i	1.20651	+	1.20651i	0.234362	+	0.972149i	$0.424700\pi$
$318$		−	5.70928i		−	0.320160i
$319$	−0.317387	+	0.317387i	−0.0177702	+	0.0177702i
$320$	26.7165	−	6.63809i	1.49350	−	0.371080i
$321$		−	0.829914i		−	0.0463213i
$322$	−22.9783	+	22.9783i	−1.28053	+	1.28053i
$323$	4.85043	−	4.85043i	0.269885	−	0.269885i
$324$	19.6381			1.09100
$325$	−13.5753	−	25.6319i	−0.753023	−	1.42180i
$326$		−	12.4969i		−	0.692141i
$327$			3.61038i			0.199654i
$328$	−8.41628			−0.464712
$329$			2.45467i			0.135330i
$330$	−4.52094	+	7.51026i	−0.248869	+	0.413426i
$331$	−0.904086	−	0.904086i	−0.0496931	−	0.0496931i	0.681824	−	0.731517i	$-0.261187\pi$
$331$	−0.904086	−	0.904086i	−0.0496931	−	0.0496931i	−0.731517	+	0.681824i	$0.761187\pi$
$332$	−14.8618	−	14.8618i	−0.815649	−	0.815649i
$333$	16.8059	−	2.80098i	0.920958	−	0.153493i
$334$		−	4.34017i		−	0.237484i
$335$	−0.315449	−	0.189890i	−0.0172348	−	0.0103748i
$336$		−	1.72487i		−	0.0940996i
$337$	22.1350	+	22.1350i	1.20577	+	1.20577i	0.972384	+	0.233387i	$0.0749809\pi$
$337$	22.1350	+	22.1350i	1.20577	+	1.20577i	0.233387	+	0.972384i	$0.425019\pi$
$338$		−	44.8154i		−	2.43763i
$339$	0.246197	−	0.246197i	0.0133716	−	0.0133716i
$340$	−16.9288	+	4.20620i	−0.918094	+	0.228113i
$341$	−16.6153	−	16.6153i	−0.899769	−	0.899769i
$342$	−10.2393	+	10.2393i	−0.553680	+	0.553680i
$343$	−13.8638	−	13.8638i	−0.748573	−	0.748573i
$344$	12.9132			0.696234
$345$	−6.87936	−	4.14116i	−0.370372	−	0.222952i
$346$	25.6875	+	25.6875i	1.38097	+	1.38097i
$347$		−	13.7359i		−	0.737384i	−0.929552	−	0.368692i	$-0.879806\pi$
$347$		−	13.7359i		−	0.737384i	0.929552	−	0.368692i	$-0.120194\pi$
$348$	−0.133969			−0.00718150
$349$		−	25.1350i		−	1.34545i	−0.739894	−	0.672723i	$-0.765124\pi$
$349$		−	25.1350i		−	1.34545i	0.739894	−	0.672723i	$-0.234876\pi$
$350$	−19.2937	−	5.93302i	−1.03129	−	0.317133i
$351$	10.6153	−	10.6153i	0.566603	−	0.566603i
$352$	30.7298			1.63790
$353$	0.921622			0.0490530			0.0245265	−	0.999699i	$-0.492192\pi$
$353$	0.921622			0.0490530			0.0245265	+	0.999699i	$0.492192\pi$
$354$	11.0940			0.589638
$355$	−16.8371	+	4.18342i	−0.893621	+	0.222033i
$356$	7.09171	+	7.09171i	0.375860	+	0.375860i
$357$			2.38962i			0.126472i
$358$	8.39383	−	8.39383i	0.443628	−	0.443628i
$359$		−	29.8082i		−	1.57322i	−0.617453	−	0.786608i	$-0.711836\pi$
$359$		−	29.8082i		−	1.57322i	0.617453	−	0.786608i	$-0.288164\pi$
$360$	9.35577	−	2.32457i	0.493092	−	0.122516i
$361$			13.3246i			0.701293i
$362$		−	19.3268i		−	1.01580i
$363$	−1.70280	+	1.70280i	−0.0893740	+	0.0893740i
$364$	−20.6742	−	20.6742i	−1.08362	−	1.08362i
$365$	−11.5659	+	19.2134i	−0.605384	+	1.00567i
$366$	9.18568			0.480143
$367$	−1.81852	+	1.81852i	−0.0949260	+	0.0949260i	−0.752975	−	0.658049i	$-0.771382\pi$
$367$	−1.81852	+	1.81852i	−0.0949260	+	0.0949260i	0.658049	+	0.752975i	$0.271382\pi$
$368$			16.7298i			0.872101i
$369$	15.3158			0.797308
$370$	27.0856	−	11.7298i	1.40811	−	0.609803i
$371$	10.9711			0.569590
$372$		−	7.01333i		−	0.363624i
$373$	−10.6937	+	10.6937i	−0.553698	+	0.553698i	−0.927506	−	0.373808i	$-0.878052\pi$
$373$	−10.6937	+	10.6937i	−0.553698	+	0.553698i	0.373808	+	0.927506i	$0.378052\pi$
$374$	−25.3028			−1.30838
$375$	0.273188	−	4.98020i	0.0141074	−	0.257176i
$376$	−1.43609	−	1.43609i	−0.0740605	−	0.0740605i
$377$	0.454668	−	0.454668i	0.0234166	−	0.0234166i
$378$		−	10.4475i		−	0.537360i
$379$			8.98545i			0.461551i	0.973007	+	0.230776i	$0.0741264\pi$
$379$			8.98545i			0.461551i	−0.973007	+	0.230776i	$0.925874\pi$
$380$	−7.44327	+	12.3649i	−0.381832	+	0.634306i
$381$			7.80552i			0.399889i
$382$	−18.1236	+	18.1236i	−0.927285	+	0.927285i
$383$		−	27.1545i		−	1.38753i	−0.720202	−	0.693765i	$-0.755951\pi$
$383$		−	27.1545i		−	1.38753i	0.720202	−	0.693765i	$-0.244049\pi$
$384$	3.64002	+	3.64002i	0.185754	+	0.185754i
$385$	−14.4319	−	8.68753i	−0.735517	−	0.442758i
$386$	0.863763			0.0439644
$387$	−23.4992			−1.19453
$388$	−1.70928			−0.0867753
$389$	1.19902	−	1.19902i	0.0607925	−	0.0607925i	−0.676057	−	0.736849i	$-0.736313\pi$
$389$	1.19902	−	1.19902i	0.0607925	−	0.0607925i	0.736849	+	0.676057i	$0.236313\pi$
$390$	6.47641	−	10.7587i	0.327946	−	0.544789i
$391$		−	23.1773i		−	1.17213i
$392$	5.44748			0.275139
$393$			6.59705i			0.332777i
$394$	−18.5018	−	18.5018i	−0.932110	−	0.932110i
$395$	−2.46994	+	4.10310i	−0.124276	+	0.206449i
$396$	30.7298			1.54423
$397$	−19.6959	−	19.6959i	−0.988511	−	0.988511i	0.0114236	−	0.999935i	$-0.496364\pi$
$397$	−19.6959	−	19.6959i	−0.988511	−	0.988511i	−0.999935	+	0.0114236i	$0.996364\pi$
$398$	−37.4215	+	37.4215i	−1.87577	+	1.87577i
$399$	1.39803	+	1.39803i	0.0699891	+	0.0699891i
$400$	−9.18342	+	4.86376i	−0.459171	+	0.243188i
$401$	24.1194	−	24.1194i	1.20447	−	1.20447i	0.231672	−	0.972794i	$-0.425580\pi$
$401$	24.1194	−	24.1194i	1.20447	−	1.20447i	0.972794	−	0.231672i	$-0.0744197\pi$
$402$		−	0.159409i		−	0.00795058i
$403$	23.8020	+	23.8020i	1.18566	+	1.18566i
$404$		−	33.7431i		−	1.67878i
$405$	−15.7298	+	3.90829i	−0.781620	+	0.194205i
$406$		−	0.447480i		−	0.0222081i
$407$	24.2967	−	4.04945i	1.20434	−	0.200724i
$408$	−1.39803	−	1.39803i	−0.0692129	−	0.0692129i
$409$	14.8927	+	14.8927i	0.736396	+	0.736396i	0.971879	−	0.235482i	$-0.0756670\pi$
$409$	14.8927	+	14.8927i	0.736396	+	0.736396i	−0.235482	+	0.971879i	$0.575667\pi$
$410$	25.7503	−	6.39803i	1.27172	−	0.315976i
$411$		−	7.12783i		−	0.351590i
$412$	33.7009			1.66032
$413$			21.3184i			1.04901i
$414$			48.9276i			2.40466i
$415$	14.8618	+	8.94635i	0.729538	+	0.439159i
$416$	−44.0216			−2.15833
$417$	1.13624	−	1.13624i	0.0556417	−	0.0556417i
$418$	−14.8033	+	14.8033i	−0.724051	+	0.724051i
$419$		−	2.19183i		−	0.107078i	−0.998566	−	0.0535389i	$-0.982950\pi$
$419$		−	2.19183i		−	0.107078i	0.998566	−	0.0535389i	$-0.0170501\pi$
$420$	−1.21235	−	4.87936i	−0.0591565	−	0.238088i
$421$	−16.7165	+	16.7165i	−0.814711	+	0.814711i	−0.985336	−	0.170625i	$-0.945421\pi$
$421$	−16.7165	+	16.7165i	−0.814711	+	0.814711i	0.170625	+	0.985336i	$0.445421\pi$
$422$		−	7.88428i		−	0.383801i
$423$	2.61336	+	2.61336i	0.127066	+	0.127066i
$424$	−6.41855	+	6.41855i	−0.311712	+	0.311712i
$425$	12.7226	−	6.73820i	0.617137	−	0.326851i
$426$	−5.31124	−	5.31124i	−0.257331	−	0.257331i
$427$			17.6514i			0.854212i
$428$	−3.56391	+	3.56391i	−0.172268	+	0.172268i
$429$	7.41014	−	7.41014i	0.357765	−	0.357765i
$430$	−39.5090	+	9.81658i	−1.90529	+	0.473398i
$431$	16.3093	−	16.3093i	0.785592	−	0.785592i	−0.195177	−	0.980768i	$-0.562528\pi$
$431$	16.3093	−	16.3093i	0.785592	−	0.785592i	0.980768	+	0.195177i	$0.0625280\pi$
$432$	−3.80325	−	3.80325i	−0.182984	−	0.182984i
$433$	1.60424	+	1.60424i	0.0770946	+	0.0770946i	0.744603	−	0.667508i	$-0.232639\pi$
$433$	1.60424	+	1.60424i	0.0770946	+	0.0770946i	−0.667508	+	0.744603i	$0.732639\pi$
$434$	23.4257			1.12447
$435$	0.107307	−	0.0266620i	0.00514498	−	0.00127834i
$436$	15.5041	−	15.5041i	0.742513	−	0.742513i
$437$	−13.5597	−	13.5597i	−0.648649	−	0.648649i
$438$	−9.70928			−0.463927
$439$	−10.4722	−	10.4722i	−0.499811	−	0.499811i	0.411568	−	0.911379i	$-0.364981\pi$
$439$	−10.4722	−	10.4722i	−0.499811	−	0.499811i	−0.911379	+	0.411568i	$0.864981\pi$
$440$	13.5259	−	3.36069i	0.644820	−	0.160215i
$441$	−9.91321			−0.472058
$442$	36.2472			1.72411
$443$	15.9041	−	15.9041i	0.755626	−	0.755626i	−0.219897	−	0.975523i	$-0.570572\pi$
$443$	15.9041	−	15.9041i	0.755626	−	0.755626i	0.975523	+	0.219897i	$0.0705722\pi$
$444$	5.98246	+	4.27319i	0.283915	+	0.202797i
$445$	−7.09171	−	4.26898i	−0.336179	−	0.202369i
$446$	38.1019	−	38.1019i	1.80418	−	1.80418i
$447$	4.21953	+	4.21953i	0.199577	+	0.199577i
$448$	−16.1948	+	16.1948i	−0.765133	+	0.765133i
$449$	8.46800	−	8.46800i	0.399630	−	0.399630i	−0.478473	−	0.878102i	$-0.658809\pi$
$449$	8.46800	−	8.46800i	0.399630	−	0.399630i	0.878102	+	0.478473i	$0.158809\pi$
$450$	−26.8576	+	14.2245i	−1.26608	+	0.670547i
$451$	22.1424			1.04264
$452$	−2.11450			−0.0994575
$453$	−2.69594	−	2.69594i	−0.126667	−	0.126667i
$454$		−	12.9627i		−	0.608368i
$455$	20.6742	+	12.4452i	0.969222	+	0.583441i
$456$	−1.63582			−0.0766042
$457$	13.7093			0.641293			0.320646	−	0.947199i	$-0.396100\pi$
$457$	13.7093			0.641293			0.320646	+	0.947199i	$0.396100\pi$
$458$	56.9588			2.66151
$459$	5.26898	+	5.26898i	0.245935	+	0.245935i
$460$	11.7587	+	47.3256i	0.548253	+	2.20657i
$461$	11.9060	+	11.9060i	0.554519	+	0.554519i	0.927742	−	0.373223i	$-0.121747\pi$
$461$	11.9060	+	11.9060i	0.554519	+	0.554519i	−0.373223	+	0.927742i	$0.621747\pi$
$462$		−	7.29299i		−	0.339301i
$463$		−	20.6453i		−	0.959467i	−0.877414	−	0.479734i	$-0.840733\pi$
$463$		−	20.6453i		−	0.959467i	0.877414	−	0.479734i	$-0.159267\pi$
$464$	−0.162899	−	0.162899i	−0.00756238	−	0.00756238i
$465$	1.39576	+	5.61757i	0.0647270	+	0.260508i
$466$	19.8371	+	19.8371i	0.918936	+	0.918936i
$467$	15.4452			0.714719			0.357360	−	0.933967i	$-0.383677\pi$
$467$	15.4452			0.714719			0.357360	+	0.933967i	$0.383677\pi$
$468$	−44.0216			−2.03490
$469$	0.306323			0.0141447
$470$	5.48554	+	3.30212i	0.253029	+	0.152315i
$471$		−	0.0761103i		−	0.00350698i
$472$	−12.4722	−	12.4722i	−0.574080	−	0.574080i
$473$	−33.9733			−1.56210
$474$	−2.07346			−0.0952370
$475$	3.50113	−	11.3854i	0.160643	−	0.522399i
$476$	10.2618	−	10.2618i	0.470349	−	0.470349i
$477$	11.6803	−	11.6803i	0.534806	−	0.534806i
$478$	18.8173	+	18.8173i	0.860683	+	0.860683i
$479$	23.9330	−	23.9330i	1.09353	−	1.09353i	0.0983783	−	0.995149i	$-0.468634\pi$
$479$	23.9330	−	23.9330i	1.09353	−	1.09353i	0.995149	−	0.0983783i	$-0.0313655\pi$
$480$	−6.48554	−	3.90409i	−0.296023	−	0.178196i
$481$	−34.8059	+	5.80098i	−1.58701	+	0.264502i
$482$	−23.4885	+	23.4885i	−1.06987	+	1.06987i
$483$	6.68035			0.303966
$484$	14.6248			0.664762
$485$	1.36910	−	0.340173i	0.0621677	−	0.0154465i
$486$	−16.8752	−	16.8752i	−0.765473	−	0.765473i
$487$	−24.9893			−1.13237			−0.566187	−	0.824277i	$-0.691582\pi$
$487$	−24.9893			−1.13237			−0.566187	+	0.824277i	$0.691582\pi$
$488$	−10.3268	−	10.3268i	−0.467474	−	0.467474i
$489$	−1.81658	+	1.81658i	−0.0821487	+	0.0821487i
$490$	−16.6670	+	4.14116i	−0.752939	+	0.187078i
$491$	18.6803			0.843032			0.421516	−	0.906821i	$-0.361498\pi$
$491$	18.6803			0.843032			0.421516	+	0.906821i	$0.361498\pi$
$492$	4.67316	+	4.67316i	0.210682	+	0.210682i
$493$	0.225678	+	0.225678i	0.0101640	+	0.0101640i
$494$	21.2062	−	21.2062i	0.954112	−	0.954112i
$495$	−24.6141	+	6.11572i	−1.10632	+	0.274881i
$496$	8.52780	−	8.52780i	0.382909	−	0.382909i
$497$	10.2062	−	10.2062i	0.457811	−	0.457811i
$498$			7.51026i			0.336543i
$499$	19.8196	+	19.8196i	0.887246	+	0.887246i	0.994258	−	0.107012i	$-0.0341284\pi$
$499$	19.8196	+	19.8196i	0.887246	+	0.887246i	−0.107012	+	0.994258i	$0.534128\pi$
$500$	−22.5597	+	20.2134i	−1.00890	+	0.903970i
$501$	−0.630898	+	0.630898i	−0.0281864	+	0.0281864i
$502$	−16.5350	−	16.5350i	−0.737992	−	0.737992i
$503$			3.65142i			0.162809i	0.996681	+	0.0814043i	$0.0259405\pi$
$503$			3.65142i			0.162809i	−0.996681	+	0.0814043i	$0.974060\pi$
$504$	−5.67122	+	5.67122i	−0.252616	+	0.252616i
$505$	6.71542	+	27.0277i	0.298832	+	1.20272i
$506$			70.7358i			3.14459i
$507$	−6.51446	+	6.51446i	−0.289318	+	0.289318i
$508$	33.5194	−	33.5194i	1.48718	−	1.48718i
$509$	−5.91548			−0.262199			−0.131100	−	0.991369i	$-0.541851\pi$
$509$	−5.91548			−0.262199			−0.131100	+	0.991369i	$0.541851\pi$
$510$	5.34017	+	3.21461i	0.236467	+	0.142346i
$511$		−	18.6576i		−	0.825362i
$512$			22.1701i			0.979789i
$513$	6.16517			0.272199
$514$		−	34.9698i		−	1.54245i
$515$	−26.9939	+	6.70701i	−1.18949	+	0.295546i
$516$	−7.17009	−	7.17009i	−0.315645	−	0.315645i
$517$	3.77820	+	3.77820i	0.166165	+	0.166165i
$518$	−14.2732	+	19.9825i	−0.627128	+	0.877979i
$519$		−	7.46800i		−	0.327809i
$520$	−19.3763	+	4.81432i	−0.849707	+	0.211122i
$521$			18.8527i			0.825952i	0.910742	+	0.412976i	$0.135511\pi$
$521$			18.8527i			0.825952i	−0.910742	+	0.412976i	$0.864489\pi$
$522$	−0.476410	−	0.476410i	−0.0208519	−	0.0208519i
$523$			17.3835i			0.760126i	0.924961	+	0.380063i	$0.124098\pi$
$523$			17.3835i			0.760126i	−0.924961	+	0.380063i	$0.875902\pi$
$524$	28.3298	−	28.3298i	1.23759	−	1.23759i
$525$	1.94214	+	3.66701i	0.0847620	+	0.160042i
$526$	−24.5422	−	24.5422i	−1.07009	−	1.07009i
$527$	−11.8143	+	11.8143i	−0.514640	+	0.514640i
$528$	−2.65491	−	2.65491i	−0.115540	−	0.115540i
$529$	−41.7936			−1.81711
$530$	14.7587	−	24.5174i	0.641078	−	1.06497i
$531$	22.6967	+	22.6967i	0.984951	+	0.984951i
$532$		−	12.0072i		−	0.520578i
$533$	−31.7198			−1.37394
$534$		−	3.58372i		−	0.155083i
$535$	2.14536	−	3.56391i	0.0927521	−	0.154081i
$536$	−0.179212	+	0.179212i	−0.00774079	+	0.00774079i
$537$	−2.44029			−0.105306
$538$	−6.71420			−0.289470
$539$	−14.3318			−0.617313
$540$	−13.4319	−	8.08557i	−0.578016	−	0.347947i
$541$	−19.4885	−	19.4885i	−0.837877	−	0.837877i	0.150702	−	0.988579i	$-0.451846\pi$
$541$	−19.4885	−	19.4885i	−0.837877	−	0.837877i	−0.988579	+	0.150702i	$0.951846\pi$
$542$			60.5790i			2.60209i
$543$	−2.80939	+	2.80939i	−0.120563	+	0.120563i
$544$		−	21.8504i		−	0.936830i
$545$	−9.33299	+	15.5041i	−0.399781	+	0.664123i
$546$			10.4475i			0.447111i
$547$		−	6.29072i		−	0.268972i	−0.990915	−	0.134486i	$-0.957062\pi$
$547$		−	6.29072i		−	0.268972i	0.990915	−	0.134486i	$-0.0429383\pi$
$548$	−30.6092	+	30.6092i	−1.30756	+	1.30756i
$549$	18.7926	+	18.7926i	0.802047	+	0.802047i
$550$	−38.8287	+	20.5646i	−1.65566	+	0.876879i
$551$	0.264063			0.0112494
$552$	−3.90829	+	3.90829i	−0.166348	+	0.166348i
$553$		−	3.98440i		−	0.169434i
$554$	−45.5246			−1.93416
$555$	−5.64229	−	2.23215i	−0.239502	−	0.0947495i
$556$	−9.75872			−0.413862
$557$			38.6837i			1.63908i	0.573023	+	0.819540i	$0.305771\pi$
$557$			38.6837i			1.63908i	−0.573023	+	0.819540i	$0.694229\pi$
$558$	24.9402	−	24.9402i	1.05580	−	1.05580i
$559$	48.6681			2.05844
$560$	4.45887	−	7.40716i	0.188422	−	0.313010i
$561$	3.67808	+	3.67808i	0.155289	+	0.155289i
$562$	23.4391	−	23.4391i	0.988717	−	0.988717i
$563$		−	1.65142i		−	0.0695989i	−0.999394	−	0.0347995i	$-0.988921\pi$
$563$		−	1.65142i		−	0.0695989i	0.999394	−	0.0347995i	$-0.0110792\pi$
$564$			1.59478i			0.0671524i
$565$	1.69368	−	0.420818i	0.0712535	−	0.0177040i
$566$		−	42.5380i		−	1.78800i
$567$	9.53498	−	9.53498i	0.400432	−	0.400432i
$568$			11.9421i			0.501081i
$569$	23.8976	+	23.8976i	1.00184	+	1.00184i	0.999998	+	0.00184176i	$0.000586252\pi$
$569$	23.8976	+	23.8976i	1.00184	+	1.00184i	0.00184176	+	0.999998i	$0.499414\pi$
$570$	5.00492	−	1.24354i	0.209633	−	0.0520863i
$571$	28.9627			1.21205			0.606025	−	0.795446i	$-0.292763\pi$
$571$	28.9627			1.21205			0.606025	+	0.795446i	$0.292763\pi$
$572$	−63.6430			−2.66105
$573$	5.26898			0.220115
$574$	−15.6092	+	15.6092i	−0.651514	+	0.651514i
$575$	−18.8371	−	35.5669i	−0.785561	−	1.48324i
$576$			34.4836i			1.43682i
$577$	−35.1494			−1.46329			−0.731644	−	0.681687i	$-0.761247\pi$
$577$	−35.1494			−1.46329			−0.731644	+	0.681687i	$0.761247\pi$
$578$		−	18.8999i		−	0.786131i
$579$	−0.125559	−	0.125559i	−0.00521804	−	0.00521804i
$580$	−0.575306	−	0.346316i	−0.0238883	−	0.0143800i
$581$	−14.4319			−0.598735
$582$	0.431882	+	0.431882i	0.0179021	+	0.0179021i
$583$	16.8865	−	16.8865i	0.699369	−	0.699369i
$584$	10.9155	+	10.9155i	0.451686	+	0.451686i
$585$	35.2606	−	8.76099i	1.45785	−	0.362222i
$586$	−43.4463	+	43.4463i	−1.79475	+	1.79475i
$587$			22.5730i			0.931689i	0.884867	+	0.465845i	$0.154249\pi$
$587$			22.5730i			0.931689i	−0.884867	+	0.465845i	$0.845751\pi$
$588$	−3.02472	−	3.02472i	−0.124738	−	0.124738i
$589$			13.8238i			0.569599i
$590$	47.6411	+	28.6784i	1.96135	+	1.18067i
$591$			5.37894i			0.221260i
$592$	2.07838	+	12.4703i	0.0854208	+	0.512525i
$593$	4.09398	+	4.09398i	0.168119	+	0.168119i	0.786152	−	0.618033i	$-0.212070\pi$
$593$	4.09398	+	4.09398i	0.168119	+	0.168119i	−0.618033	+	0.786152i	$0.712070\pi$
$594$	−16.0806	−	16.0806i	−0.659797	−	0.659797i
$595$	−6.17727	+	10.2618i	−0.253244	+	0.420693i
$596$		−	36.2401i		−	1.48445i
$597$	10.8794			0.445263
$598$		−	101.332i		−	4.14376i
$599$		−	2.23287i		−	0.0912324i	−0.998959	−	0.0456162i	$-0.985475\pi$
$599$		−	2.23287i		−	0.0912324i	0.998959	−	0.0456162i	$-0.0145251\pi$
$600$	−3.28160	−	1.00913i	−0.133971	−	0.0411974i
$601$	−4.25687			−0.173642			−0.0868208	−	0.996224i	$-0.527671\pi$
$601$	−4.25687			−0.173642			−0.0868208	+	0.996224i	$0.527671\pi$
$602$	23.9493	−	23.9493i	0.976102	−	0.976102i
$603$	0.326127	−	0.326127i	0.0132809	−	0.0132809i
$604$			23.1545i			0.942143i
$605$	−11.7142	+	2.91056i	−0.476250	+	0.118331i
$606$	−8.52586	+	8.52586i	−0.346339	+	0.346339i
$607$			22.0494i			0.894960i	0.894294	+	0.447480i	$0.147678\pi$
$607$			22.0494i			0.894960i	−0.894294	+	0.447480i	$0.852322\pi$
$608$	−12.7834	−	12.7834i	−0.518437	−	0.518437i
$609$	−0.0650468	+	0.0650468i	−0.00263583	+	0.00263583i
$610$	39.4463	+	23.7454i	1.59713	+	0.961423i
$611$	−5.41241	−	5.41241i	−0.218963	−	0.218963i
$612$		−	21.8504i		−	0.883251i
$613$	−27.1217	+	27.1217i	−1.09543	+	1.09543i	−0.100497	+	0.994937i	$0.532043\pi$
$613$	−27.1217	+	27.1217i	−1.09543	+	1.09543i	−0.994937	+	0.100497i	$0.967957\pi$
$614$	8.47220	−	8.47220i	0.341910	−	0.341910i
$615$	−4.67316	−	2.81309i	−0.188440	−	0.113435i
$616$	−8.19902	+	8.19902i	−0.330348	+	0.330348i
$617$	−1.08452	−	1.08452i	−0.0436612	−	0.0436612i	0.684939	−	0.728600i	$-0.259829\pi$
$617$	−1.08452	−	1.08452i	−0.0436612	−	0.0436612i	−0.728600	+	0.684939i	$0.759829\pi$
$618$	−8.51518	−	8.51518i	−0.342531	−	0.342531i
$619$	−29.8888			−1.20133			−0.600666	−	0.799500i	$-0.705098\pi$
$619$	−29.8888			−1.20133			−0.600666	+	0.799500i	$0.705098\pi$
$620$	18.1298	−	30.1175i	0.728109	−	1.20955i
$621$	14.7298	−	14.7298i	0.591086	−	0.591086i
$622$	−20.9874	−	20.9874i	−0.841517	−	0.841517i
$623$	6.88655			0.275904
$624$	3.80325	+	3.80325i	0.152252	+	0.152252i
$625$	14.0472	−	20.6803i	0.561887	−	0.827214i
$626$	40.0638			1.60127
$627$	4.30367			0.171872
$628$	−0.326842	+	0.326842i	−0.0130424	+	0.0130424i
$629$	−2.87936	−	17.2762i	−0.114808	−	0.688846i
$630$	13.0403	−	21.6628i	0.519539	−	0.863067i
$631$	23.7750	−	23.7750i	0.946469	−	0.946469i	−0.0521690	−	0.998638i	$-0.516613\pi$
$631$	23.7750	−	23.7750i	0.946469	−	0.946469i	0.998638	+	0.0521690i	$0.0166134\pi$
$632$	2.33105	+	2.33105i	0.0927241	+	0.0927241i
$633$	−1.14608	+	1.14608i	−0.0455525	+	0.0455525i
$634$	−46.6163	+	46.6163i	−1.85137	+	1.85137i
$635$	−20.1776	+	33.5194i	−0.800724	+	1.33018i
$636$	7.12783			0.282637
$637$	20.5308			0.813459
$638$	−0.688756	−	0.688756i	−0.0272681	−	0.0272681i
$639$		−	21.7321i		−	0.859707i
$640$	6.22180	+	25.0410i	0.245938	+	0.989834i
$641$	−44.2278			−1.74689			−0.873446	−	0.486921i	$-0.838120\pi$
$641$	−44.2278			−1.74689			−0.873446	+	0.486921i	$0.838120\pi$
$642$	1.80098			0.0710792
$643$	−6.72383			−0.265162			−0.132581	−	0.991172i	$-0.542326\pi$
$643$	−6.72383			−0.265162			−0.132581	+	0.991172i	$0.542326\pi$
$644$	−28.6875	−	28.6875i	−1.13045	−	1.13045i
$645$	7.17009	+	4.31616i	0.282322	+	0.169949i
$646$	10.5259	+	10.5259i	0.414134	+	0.414134i
$647$		−	22.9711i		−	0.903086i	−0.892249	−	0.451543i	$-0.850874\pi$
$647$		−	22.9711i		−	0.903086i	0.892249	−	0.451543i	$-0.149126\pi$
$648$			11.1568i			0.438279i
$649$	32.8131	+	32.8131i	1.28803	+	1.28803i
$650$	55.6235	−	29.4596i	2.18173	−	1.15550i
$651$	−3.40522	−	3.40522i	−0.133461	−	0.133461i
$652$	15.6020			0.611020
$653$	−10.6491			−0.416733			−0.208367	−	0.978051i	$-0.566815\pi$
$653$	−10.6491			−0.416733			−0.208367	+	0.978051i	$0.566815\pi$
$654$	−7.83483			−0.306366
$655$	−17.0537	+	28.3298i	−0.666341	+	1.10694i
$656$			11.3646i			0.443712i
$657$	−19.8638	−	19.8638i	−0.774959	−	0.774959i
$658$	−5.32684			−0.207662
$659$	7.16290			0.279027			0.139513	−	0.990220i	$-0.455446\pi$
$659$	7.16290			0.279027			0.139513	+	0.990220i	$0.455446\pi$
$660$	−9.37629	−	5.64423i	−0.364972	−	0.219701i
$661$	−24.7503	+	24.7503i	−0.962676	+	0.962676i	−0.999328	−	0.0366525i	$-0.988331\pi$
$661$	−24.7503	+	24.7503i	−0.962676	+	0.962676i	0.0366525	+	0.999328i	$0.488331\pi$
$662$	1.96194	−	1.96194i	0.0762532	−	0.0762532i
$663$	−5.26898	−	5.26898i	−0.204630	−	0.204630i
$664$	8.44327	−	8.44327i	0.327663	−	0.327663i
$665$	2.38962	+	9.61757i	0.0926655	+	0.372953i
$666$	6.07838	+	36.4703i	0.235532	+	1.41319i
$667$	0.630898	−	0.630898i	0.0244285	−	0.0244285i
$668$	5.41855			0.209650
$669$	−11.0772			−0.428268
$670$	0.412078	−	0.684551i	0.0159200	−	0.0264465i
$671$	27.1689	+	27.1689i	1.04884	+	1.04884i
$672$	6.29791			0.242947
$673$	12.8166	+	12.8166i	0.494043	+	0.494043i	0.909577	−	0.415534i	$-0.136405\pi$
$673$	12.8166	+	12.8166i	0.494043	+	0.494043i	−0.415534	+	0.909577i	$0.636405\pi$
$674$	−48.0349	+	48.0349i	−1.85024	+	1.85024i
$675$	12.3679	+	3.80325i	0.476040	+	0.146387i
$676$	55.9504			2.15194
$677$	4.72487	+	4.72487i	0.181592	+	0.181592i	0.792049	−	0.610457i	$-0.209014\pi$
$677$	4.72487	+	4.72487i	0.181592	+	0.181592i	−0.610457	+	0.792049i	$0.709014\pi$
$678$	0.534268	+	0.534268i	0.0205185	+	0.0205185i
$679$	−0.829914	+	0.829914i	−0.0318492	+	0.0318492i
$680$	−2.38962	−	9.61757i	−0.0916378	−	0.368817i
$681$	−1.88428	+	1.88428i	−0.0722059	+	0.0722059i
$682$	36.0566	−	36.0566i	1.38068	−	1.38068i
$683$		−	25.2534i		−	0.966294i	−0.875539	−	0.483147i	$-0.839494\pi$
$683$		−	25.2534i		−	0.966294i	0.875539	−	0.483147i	$-0.160506\pi$
$684$	−12.7834	−	12.7834i	−0.488787	−	0.488787i
$685$	18.4257	−	30.6092i	0.704011	−	1.16952i
$686$	30.0856	−	30.0856i	1.14867	−	1.14867i
$687$	−8.27966	−	8.27966i	−0.315889	−	0.315889i
$688$		−	17.4368i		−	0.664772i
$689$	−24.1906	+	24.1906i	−0.921589	+	0.921589i
$690$	8.98667	−	14.9288i	0.342117	−	0.568330i
$691$			1.86603i			0.0709872i	0.999370	+	0.0354936i	$0.0113003\pi$
$691$			1.86603i			0.0709872i	−0.999370	+	0.0354936i	$0.988700\pi$
$692$	−32.0700	+	32.0700i	−1.21912	+	1.21912i
$693$	14.9204	−	14.9204i	0.566779	−	0.566779i
$694$	29.8082			1.13150
$695$	7.81658	−	1.94214i	0.296500	−	0.0736696i
$696$		−	0.0761103i		−	0.00288495i
$697$		−	15.7443i		−	0.596360i
$698$	54.5452			2.06456
$699$		−	5.76713i		−	0.218133i
$700$	7.40716	−	24.0875i	0.279964	−	0.910422i
$701$	16.8154	+	16.8154i	0.635107	+	0.635107i	0.949345	−	0.314237i	$-0.101749\pi$
$701$	16.8154	+	16.8154i	0.635107	+	0.635107i	−0.314237	+	0.949345i	$0.601749\pi$
$702$	23.0361	+	23.0361i	0.869442	+	0.869442i
$703$	−11.7919	−	8.42276i	−0.444738	−	0.317670i
$704$			49.8537i			1.87893i
$705$	−0.317387	−	1.27739i	−0.0119535	−	0.0481094i
$706$			2.00000i			0.0752710i
$707$	−16.3835	−	16.3835i	−0.616164	−	0.616164i
$708$			13.8504i			0.520531i
$709$	−18.1122	+	18.1122i	−0.680219	+	0.680219i	−0.960049	−	0.279830i	$-0.909722\pi$
$709$	−18.1122	+	18.1122i	−0.680219	+	0.680219i	0.279830	+	0.960049i	$0.409722\pi$
$710$	−9.07838	−	36.5380i	−0.340705	−	1.37125i
$711$	−4.24199	−	4.24199i	−0.159087	−	0.159087i
$712$	−4.02893	+	4.02893i	−0.150991	+	0.150991i
$713$	33.0277	+	33.0277i	1.23690	+	1.23690i
$714$	−5.18568			−0.194069
$715$	50.9770	−	12.6660i	1.90643	−	0.473680i
$716$	10.4794	+	10.4794i	0.391633	+	0.391633i
$717$		−	5.47065i		−	0.204305i
$718$	64.6863			2.41407
$719$		−	0.160631i		−	0.00599053i	−0.999996	−	0.00299527i	$-0.999047\pi$
$719$		−	0.160631i		−	0.00599053i	0.999996	−	0.00299527i	$-0.000953424\pi$
$720$	−3.13889	−	12.6332i	−0.116980	−	0.470810i
$721$	16.3630	−	16.3630i	0.609388	−	0.609388i
$722$	−28.9155			−1.07612
$723$	6.82869			0.253962
$724$	24.1289			0.896742
$725$	0.529734	+	0.162899i	0.0196738	+	0.00604990i
$726$	−3.69523	−	3.69523i	−0.137143	−	0.137143i
$727$		−	17.3379i		−	0.643027i	−0.946905	−	0.321514i	$-0.895808\pi$
$727$		−	17.3379i		−	0.643027i	0.946905	−	0.321514i	$-0.104192\pi$
$728$	11.7454	−	11.7454i	0.435313	−	0.435313i
$729$		−	16.8394i		−	0.623680i
$730$	−41.6947	−	25.0989i	−1.54319	−	0.928952i
$731$			24.1568i			0.893470i
$732$			11.4680i			0.423869i
$733$	−1.07611	+	1.07611i	−0.0397470	+	0.0397470i	−0.726701	−	0.686954i	$-0.758947\pi$
$733$	−1.07611	+	1.07611i	−0.0397470	+	0.0397470i	0.686954	+	0.726701i	$0.258947\pi$
$734$	−3.94635	−	3.94635i	−0.145662	−	0.145662i
$735$	3.02472	+	1.82079i	0.111569	+	0.0671608i
$736$	−61.0843			−2.25160
$737$	0.471489	−	0.471489i	0.0173675	−	0.0173675i
$738$			33.2366i			1.22345i
$739$	−45.1727			−1.66171			−0.830853	−	0.556492i	$-0.812147\pi$
$739$	−45.1727			−1.66171			−0.830853	+	0.556492i	$0.812147\pi$
$740$	14.6442	+	33.8154i	0.538333	+	1.24308i
$741$	−6.16517			−0.226483
$742$			23.8082i			0.874025i
$743$	−16.4855	+	16.4855i	−0.604796	+	0.604796i	−0.941581	−	0.336786i	$-0.890660\pi$
$743$	−16.4855	+	16.4855i	−0.604796	+	0.604796i	0.336786	+	0.941581i	$0.390660\pi$
$744$	3.98440			0.146075
$745$	7.21235	+	29.0277i	0.264240	+	1.06349i
$746$	−23.2062	−	23.2062i	−0.849639	−	0.849639i
$747$	−15.3649	+	15.3649i	−0.562172	+	0.562172i
$748$		−	31.5897i		−	1.15503i
$749$			3.46081i			0.126455i
$750$	10.8075	+	0.592842i	0.394633	+	0.0216475i
$751$		−	42.9132i		−	1.56593i	−0.622069	−	0.782963i	$-0.713708\pi$
$751$		−	42.9132i		−	1.56593i	0.622069	−	0.782963i	$-0.286292\pi$
$752$	−1.93916	+	1.93916i	−0.0707138	+	0.0707138i
$753$			4.80713i			0.175181i
$754$	0.986669	+	0.986669i	0.0359324	+	0.0359324i
$755$	−4.60811	−	18.5464i	−0.167706	−	0.674972i
$756$	13.0433			0.474380
$757$	−1.58759			−0.0577020			−0.0288510	−	0.999584i	$-0.509185\pi$
$757$	−1.58759			−0.0577020			−0.0288510	+	0.999584i	$0.509185\pi$
$758$	−19.4992			−0.708243
$759$	10.2823	−	10.2823i	0.373224	−	0.373224i
$760$	−7.02472	−	4.22866i	−0.254814	−	0.153390i
$761$			45.0616i			1.63348i	0.577006	+	0.816740i	$0.304221\pi$
$761$			45.0616i			1.63348i	−0.577006	+	0.816740i	$0.695779\pi$
$762$	−16.9387			−0.613623
$763$		−	15.0556i		−	0.545049i
$764$	−22.6267	−	22.6267i	−0.818605	−	0.818605i
$765$	4.34858	+	17.5018i	0.157223	+	0.632781i
$766$	58.9276			2.12914
$767$	−47.0060	−	47.0060i	−1.69729	−	1.69729i
$768$	−0.132031	+	0.132031i	−0.00476427	+	0.00476427i
$769$	−7.94441	−	7.94441i	−0.286483	−	0.286483i	0.549205	−	0.835688i	$-0.314931\pi$
$769$	−7.94441	−	7.94441i	−0.286483	−	0.286483i	−0.835688	+	0.549205i	$0.814931\pi$
$770$	18.8527	−	31.3184i	0.679404	−	1.12864i
$771$	−5.08330	+	5.08330i	−0.183071	+	0.183071i
$772$			1.07838i			0.0388117i
$773$	10.9506	+	10.9506i	0.393864	+	0.393864i	0.876062	−	0.482198i	$-0.160161\pi$
$773$	10.9506	+	10.9506i	0.393864	+	0.393864i	−0.482198	+	0.876062i	$0.660161\pi$
$774$		−	50.9953i		−	1.83299i
$775$	−8.52780	+	27.7317i	−0.306327	+	0.996153i
$776$		−	0.971071i		−	0.0348594i
$777$	4.97948	−	0.829914i	0.178638	−	0.0297730i
$778$	2.60197	+	2.60197i	0.0932851	+	0.0932851i
$779$	−9.21112	−	9.21112i	−0.330023	−	0.330023i
$780$	13.4319	+	8.08557i	0.480939	+	0.289510i
$781$		−	31.4186i		−	1.12424i
$782$	50.2967			1.79861
$783$			0.286849i			0.0102511i
$784$		−	7.35577i		−	0.262706i
$785$	0.196748	−	0.326842i	0.00702225	−	0.0116655i
$786$	−14.3162			−0.510641
$787$	4.32878	−	4.32878i	0.154304	−	0.154304i	−0.625733	−	0.780037i	$-0.715200\pi$
$787$	4.32878	−	4.32878i	0.154304	−	0.154304i	0.780037	+	0.625733i	$0.215200\pi$
$788$	23.0989	−	23.0989i	0.822864	−	0.822864i
$789$			7.13501i			0.254013i
$790$	−8.90409	−	5.35998i	−0.316793	−	0.190699i
$791$	−1.02666	+	1.02666i	−0.0365039	+	0.0365039i
$792$			17.4582i			0.620349i
$793$	−38.9204	−	38.9204i	−1.38210	−	1.38210i
$794$	42.7419	−	42.7419i	1.51685	−	1.51685i
$795$	−5.70928	+	1.41855i	−0.202487	+	0.0503108i
$796$	−46.7194	−	46.7194i	−1.65593	−	1.65593i
$797$		−	26.7682i		−	0.948178i	−0.880477	−	0.474089i	$-0.842778\pi$
$797$		−	26.7682i		−	0.948178i	0.880477	−	0.474089i	$-0.157222\pi$
$798$	−3.03385	+	3.03385i	−0.107397	+	0.107397i
$799$	2.68649	−	2.68649i	0.0950411	−	0.0950411i
$800$	−17.7587	−	33.5308i	−0.627866	−	1.18549i
$801$	7.33176	−	7.33176i	0.259055	−	0.259055i
$802$	52.3412	+	52.3412i	1.84823	+	1.84823i
$803$	−28.7175	−	28.7175i	−1.01342	−	1.01342i
$804$	0.199016			0.00701875
$805$	28.6875	+	17.2690i	1.01110	+	0.608652i
$806$	−51.6525	+	51.6525i	−1.81938	+	1.81938i
$807$	0.975991	+	0.975991i	0.0343565	+	0.0343565i
$808$	19.1701			0.674401
$809$	22.2618	+	22.2618i	0.782683	+	0.782683i	0.980283	−	0.197600i	$-0.0633146\pi$
$809$	22.2618	+	22.2618i	0.782683	+	0.782683i	−0.197600	+	0.980283i	$0.563315\pi$
$810$	−8.48133	−	34.1350i	−0.298004	−	1.19938i
$811$	12.5236			0.439763			0.219881	−	0.975527i	$-0.429433\pi$
$811$	12.5236			0.439763			0.219881	+	0.975527i	$0.429433\pi$
$812$	0.558663			0.0196052
$813$	8.80590	−	8.80590i	0.308837	−	0.308837i
$814$	8.78765	+	52.7259i	0.308007	+	1.84804i
$815$	−12.4969	+	3.10504i	−0.437748	+	0.108765i
$816$	−1.88777	+	1.88777i	−0.0660853	+	0.0660853i
$817$	14.1327	+	14.1327i	0.494442	+	0.494442i
$818$	−32.3184	+	32.3184i	−1.12999	+	1.12999i
$819$	−21.3740	+	21.3740i	−0.746869	+	0.746869i
$820$	7.98771	+	32.1483i	0.278943	+	1.12267i
$821$	−51.3607			−1.79250			−0.896250	−	0.443549i	$-0.853719\pi$
$821$	−51.3607			−1.79250			−0.896250	+	0.443549i	$0.853719\pi$
$822$	15.4680			0.539508
$823$	29.0670	+	29.0670i	1.01321	+	1.01321i	0.999912	+	0.0132998i	$0.00423359\pi$
$823$	29.0670	+	29.0670i	1.01321	+	1.01321i	0.0132998	+	0.999912i	$0.495766\pi$
$824$			19.1461i			0.666985i
$825$	8.63355	+	2.65491i	0.300582	+	0.0924320i
$826$	−46.2628			−1.60969
$827$	−25.4908			−0.886401			−0.443201	−	0.896422i	$-0.646157\pi$
$827$	−25.4908			−0.886401			−0.443201	+	0.896422i	$0.646157\pi$
$828$	−61.0843			−2.12283
$829$	16.2762	+	16.2762i	0.565295	+	0.565295i	0.930807	−	0.365512i	$-0.119106\pi$
$829$	16.2762	+	16.2762i	0.565295	+	0.565295i	−0.365512	+	0.930807i	$0.619106\pi$
$830$	−19.4143	+	32.2514i	−0.673882	+	1.11946i
$831$	6.61757	+	6.61757i	0.229561	+	0.229561i
$832$		−	71.4173i		−	2.47595i
$833$			10.1906i			0.353084i
$834$	2.46573	+	2.46573i	0.0853813	+	0.0853813i
$835$	−4.34017	+	1.07838i	−0.150198	+	0.0373188i
$836$	−18.4813	−	18.4813i	−0.639190	−	0.639190i
$837$	−15.0166			−0.519051
$838$	4.75646			0.164309
$839$	36.0677			1.24520			0.622598	−	0.782542i	$-0.286077\pi$
$839$	36.0677			1.24520			0.622598	+	0.782542i	$0.286077\pi$
$840$	2.77205	−	0.688756i	0.0956450	−	0.0237644i
$841$		−	28.9877i		−	0.999576i
$842$	−36.2762	−	36.2762i	−1.25016	−	1.25016i
$843$	−6.81432			−0.234697
$844$	9.84324			0.338818
$845$	−44.8154	+	11.1350i	−1.54170	+	0.383056i
$846$	−5.67122	+	5.67122i	−0.194981	+	0.194981i
$847$	7.10083	−	7.10083i	0.243988	−	0.243988i
$848$	8.66701	+	8.66701i	0.297627	+	0.297627i
$849$	−6.18342	+	6.18342i	−0.212214	+	0.212214i
$850$	14.6225	+	27.6092i	0.501547	+	0.946986i
$851$	−48.2967	+	8.04945i	−1.65559	+	0.275932i
$852$	6.63090	−	6.63090i	0.227171	−	0.227171i
$853$	−21.2267			−0.726789			−0.363395	−	0.931635i	$-0.618382\pi$
$853$	−21.2267			−0.726789			−0.363395	+	0.931635i	$0.618382\pi$
$854$	−38.3051			−1.31077
$855$	12.7834	+	7.69523i	0.437185	+	0.263171i
$856$	−2.02472	−	2.02472i	−0.0692036	−	0.0692036i
$857$	−20.6765			−0.706295			−0.353147	−	0.935568i	$-0.614889\pi$
$857$	−20.6765			−0.706295			−0.353147	+	0.935568i	$0.614889\pi$
$858$	16.0806	+	16.0806i	0.548984	+	0.548984i
$859$	10.1103	−	10.1103i	0.344959	−	0.344959i	−0.513269	−	0.858228i	$-0.671566\pi$
$859$	10.1103	−	10.1103i	0.344959	−	0.344959i	0.858228	+	0.513269i	$0.171566\pi$
$860$	−12.2557	−	49.3256i	−0.417914	−	1.68199i
$861$	4.53797			0.154653
$862$	35.3926	+	35.3926i	1.20548	+	1.20548i
$863$	20.0475	+	20.0475i	0.682425	+	0.682425i	0.960546	−	0.278121i	$-0.0897116\pi$
$863$	20.0475	+	20.0475i	0.682425	+	0.682425i	−0.278121	+	0.960546i	$0.589712\pi$
$864$	13.8865	−	13.8865i	0.472430	−	0.472430i
$865$	19.3051	−	32.0700i	0.656393	−	1.09041i
$866$	−3.48133	+	3.48133i	−0.118300	+	0.118300i
$867$	−2.74733	+	2.74733i	−0.0933042	+	0.0933042i
$868$			29.2462i			0.992681i
$869$	−6.13275	−	6.13275i	−0.208039	−	0.208039i
$870$	0.0578588	+	0.232866i	0.00196160	+	0.00789489i
$871$	−0.675425	+	0.675425i	−0.0228859	+	0.0228859i
$872$	8.80817	+	8.80817i	0.298282	+	0.298282i
$873$			1.76713i			0.0598084i
$874$	29.4257	−	29.4257i	0.995340	−	0.995340i
$875$	−1.13922	+	20.7678i	−0.0385126	+	0.702081i
$876$		−	12.1217i		−	0.409554i
$877$	17.7370	−	17.7370i	0.598935	−	0.598935i	−0.341094	−	0.940029i	$-0.610797\pi$
$877$	17.7370	−	17.7370i	0.598935	−	0.598935i	0.940029	+	0.341094i	$0.110797\pi$
$878$	22.7256	−	22.7256i	0.766951	−	0.766951i
$879$	12.6309			0.426030
$880$	−4.53797	−	18.2641i	−0.152975	−	0.615681i
$881$		−	18.5224i		−	0.624034i	−0.950076	−	0.312017i	$-0.898995\pi$
$881$		−	18.5224i		−	0.624034i	0.950076	−	0.312017i	$-0.101005\pi$
$882$		−	21.5125i		−	0.724364i
$883$	−9.33856			−0.314268			−0.157134	−	0.987577i	$-0.550225\pi$
$883$	−9.33856			−0.314268			−0.157134	+	0.987577i	$0.550225\pi$
$884$			45.2534i			1.52204i
$885$	−2.75646	−	11.0940i	−0.0926573	−	0.372920i
$886$	34.5132	+	34.5132i	1.15950	+	1.15950i
$887$	7.26212	+	7.26212i	0.243838	+	0.243838i	0.818436	−	0.574598i	$-0.194841\pi$
$887$	7.26212	+	7.26212i	0.243838	+	0.243838i	−0.574598	+	0.818436i	$0.694841\pi$
$888$	−2.42768	+	3.39875i	−0.0814675	+	0.114054i
$889$		−	32.5497i		−	1.09168i
$890$	9.26406	−	15.3896i	0.310532	−	0.515861i
$891$		−	29.3523i		−	0.983338i
$892$	47.5688	+	47.5688i	1.59272	+	1.59272i
$893$		−	3.14342i		−	0.105191i
$894$	−9.15676	+	9.15676i	−0.306248	+	0.306248i
$895$	−10.4794	−	6.30826i	−0.350287	−	0.210862i
$896$	−15.1792	−	15.1792i	−0.507102	−	0.507102i
$897$	−14.7298	+	14.7298i	−0.491814	+	0.491814i
$898$	18.3763	+	18.3763i	0.613225	+	0.613225i
$899$	−0.643184			−0.0214514
$900$	−17.7587	−	33.5308i	−0.591957	−	1.11769i
$901$	−12.0072	−	12.0072i	−0.400017	−	0.400017i
$902$			48.0509i			1.59992i
$903$	−6.96266			−0.231703
$904$		−	1.20128i		−	0.0399541i
$905$	−19.3268	+	4.80203i	−0.642446	+	0.159625i
$906$	5.85043	−	5.85043i	0.194368	−	0.194368i
$907$	−14.0312			−0.465898			−0.232949	−	0.972489i	$-0.574838\pi$
$907$	−14.0312			−0.465898			−0.232949	+	0.972489i	$0.574838\pi$
$908$	16.1834			0.537066
$909$	−34.8853			−1.15707
$910$	−27.0072	+	44.8648i	−0.895280	+	1.48725i
$911$	−9.92356	−	9.92356i	−0.328782	−	0.328782i	0.523341	−	0.852123i	$-0.324685\pi$
$911$	−9.92356	−	9.92356i	−0.328782	−	0.328782i	−0.852123	+	0.523341i	$0.824685\pi$
$912$			2.20886i			0.0731426i
$913$	−22.2134	+	22.2134i	−0.735156	+	0.735156i
$914$			29.7503i			0.984053i
$915$	−2.28231	−	9.18568i	−0.0754510	−	0.303669i
$916$			71.1110i			2.34957i
$917$		−	27.5103i		−	0.908469i
$918$	−11.4341	+	11.4341i	−0.377383	+	0.377383i
$919$	31.9919	+	31.9919i	1.05532	+	1.05532i	0.998378	+	0.0569383i	$0.0181338\pi$
$919$	31.9919	+	31.9919i	1.05532	+	1.05532i	0.0569383	+	0.998378i	$0.481866\pi$
$920$	−26.8865	+	6.68035i	−0.886423	+	0.220244i
$921$	−2.46308			−0.0811612
$922$	−25.8371	+	25.8371i	−0.850900	+	0.850900i
$923$			45.0082i			1.48146i
$924$	9.10504			0.299534
$925$	−18.4596	−	24.1711i	−0.606948	−	0.794742i
$926$	44.8020			1.47229
$927$		−	34.8416i		−	1.14435i
$928$	0.594780	−	0.594780i	0.0195246	−	0.0195246i
$929$	2.51971			0.0826692			0.0413346	−	0.999145i	$-0.486839\pi$
$929$	2.51971			0.0826692			0.0413346	+	0.999145i	$0.486839\pi$
$930$	−12.1906	+	3.02893i	−0.399746	+	0.0993225i
$931$	5.96194	+	5.96194i	0.195395	+	0.195395i
$932$	−24.7659	+	24.7659i	−0.811234	+	0.811234i
$933$			6.10155i			0.199756i
$934$			33.5174i			1.09672i
$935$	6.28685	+	25.3028i	0.205602	+	0.827491i
$936$		−	25.0095i		−	0.817460i
$937$	−7.10731	+	7.10731i	−0.232186	+	0.232186i	−0.813604	−	0.581419i	$-0.802498\pi$
$937$	−7.10731	+	7.10731i	−0.232186	+	0.232186i	0.581419	+	0.813604i	$0.302498\pi$
$938$			0.664748i			0.0217048i
$939$	−5.82377	−	5.82377i	−0.190052	−	0.190052i
$940$	−4.12258	+	6.84849i	−0.134464	+	0.223373i
$941$	25.5018			0.831337			0.415668	−	0.909516i	$-0.363548\pi$
$941$	25.5018			0.831337			0.415668	+	0.909516i	$0.363548\pi$
$942$	0.165166			0.00538140
$943$	−44.0144			−1.43331
$944$	−16.8413	+	16.8413i	−0.548138	+	0.548138i
$945$	−10.4475	+	2.59583i	−0.339857	+	0.0844422i
$946$		−	73.7251i		−	2.39701i
$947$	37.5585			1.22049			0.610243	−	0.792214i	$-0.291072\pi$
$947$	37.5585			1.22049			0.610243	+	0.792214i	$0.291072\pi$
$948$		−	2.58864i		−	0.0840750i
$949$	41.1389	+	41.1389i	1.33542	+	1.33542i
$950$	24.7073	+	7.59776i	0.801612	+	0.246504i
$951$	13.5525			0.439471
$952$	5.82991	+	5.82991i	0.188949	+	0.188949i
$953$	22.7321	−	22.7321i	0.736364	−	0.736364i	−0.235509	−	0.971872i	$-0.575676\pi$
$953$	22.7321	−	22.7321i	0.736364	−	0.736364i	0.971872	+	0.235509i	$0.0756756\pi$
$954$	25.3474	+	25.3474i	0.820651	+	0.820651i
$955$	22.6267	+	13.6205i	0.732183	+	0.440751i
$956$	−23.4927	+	23.4927i	−0.759809	+	0.759809i
$957$			0.200238i			0.00647279i
$958$	51.9367	+	51.9367i	1.67800	+	1.67800i
$959$			29.7237i			0.959827i
$960$	6.33370	−	10.5217i	0.204419	−	0.339585i
$961$		−	2.67089i		−	0.0861578i
$962$	−12.5886	−	75.5318i	−0.405874	−	2.43524i
$963$	3.68455	+	3.68455i	0.118733	+	0.118733i
$964$	−29.3246	−	29.3246i	−0.944481	−	0.944481i
$965$	−0.214614	−	0.863763i	−0.00690868	−	0.0278055i
$966$			14.4969i			0.466431i
$967$	50.4657			1.62287			0.811434	−	0.584444i	$-0.198687\pi$
$967$	50.4657			1.62287			0.811434	+	0.584444i	$0.198687\pi$
$968$			8.30859i			0.267048i
$969$		−	3.06013i		−	0.0983054i
$970$	0.738205	+	2.97107i	0.0237023	+	0.0953953i
$971$	0.470266			0.0150916			0.00754578	−	0.999972i	$-0.497598\pi$
$971$	0.470266			0.0150916			0.00754578	+	0.999972i	$0.497598\pi$
$972$	21.0680	−	21.0680i	0.675757	−	0.675757i
$973$	−4.73820	+	4.73820i	−0.151900	+	0.151900i
$974$		−	54.2290i		−	1.73761i
$975$	−12.3679	−	3.80325i	−0.396089	−	0.121802i
$976$	−13.9444	+	13.9444i	−0.446350	+	0.446350i
$977$		−	8.40400i		−	0.268868i	−0.990923	−	0.134434i	$-0.957078\pi$
$977$		−	8.40400i		−	0.268868i	0.990923	−	0.134434i	$-0.0429216\pi$
$978$	−3.94214	−	3.94214i	−0.126056	−	0.126056i
$979$	10.5997	−	10.5997i	0.338768	−	0.338768i
$980$	−5.17009	−	20.8082i	−0.165152	−	0.664693i
$981$	−16.0289	−	16.0289i	−0.511764	−	0.511764i
$982$			40.5380i			1.29362i
$983$	−32.8801	+	32.8801i	−1.04871	+	1.04871i	−0.0499604	+	0.998751i	$0.515910\pi$
$983$	−32.8801	+	32.8801i	−1.04871	+	1.04871i	−0.998751	+	0.0499604i	$0.984090\pi$
$984$	−2.65491	+	2.65491i	−0.0846353	+	0.0846353i
$985$	−13.9048	+	23.0989i	−0.443044	+	0.735992i
$986$	−0.489741	+	0.489741i	−0.0155965	+	0.0155965i
$987$	0.774322	+	0.774322i	0.0246469	+	0.0246469i
$988$	26.4752	+	26.4752i	0.842288	+	0.842288i
$989$	67.5318			2.14739
$990$	−13.2716	−	53.4147i	−0.421800	−	1.69763i
$991$	−26.3370	+	26.3370i	−0.836623	+	0.836623i	−0.988413	−	0.151790i	$-0.951496\pi$
$991$	−26.3370	+	26.3370i	−0.836623	+	0.836623i	0.151790	+	0.988413i	$0.451496\pi$
$992$	31.1370	+	31.1370i	0.988599	+	0.988599i
$993$	−0.570386			−0.0181006
$994$	22.1483	+	22.1483i	0.702503	+	0.702503i
$995$	46.7194	+	28.1236i	1.48111	+	0.891579i
$996$	−9.37629			−0.297099
$997$	55.2228			1.74893			0.874463	−	0.485093i	$-0.161214\pi$
$997$	55.2228			1.74893			0.874463	+	0.485093i	$0.161214\pi$
$998$	−43.0102	+	43.0102i	−1.36146	+	1.36146i
$999$	9.14957	−	12.8094i	0.289480	−	0.405271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.f.c.43.3	✓	6
5.2	odd	4		185.2.k.c.117.1	yes	6
5.3	odd	4		925.2.k.c.857.3		6
5.4	even	2		925.2.f.c.43.1		6
37.31	odd	4		185.2.k.c.68.1	yes	6
185.68	even	4		925.2.f.c.882.3		6
185.142	even	4	inner	185.2.f.c.142.1	yes	6
185.179	odd	4		925.2.k.c.68.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.f.c.43.3	✓	6	1.1	even	1	trivial
185.2.f.c.142.1	yes	6	185.142	even	4	inner
185.2.k.c.68.1	yes	6	37.31	odd	4
185.2.k.c.117.1	yes	6	5.2	odd	4
925.2.f.c.43.1		6	5.4	even	2
925.2.f.c.882.3		6	185.68	even	4
925.2.k.c.68.3		6	185.179	odd	4
925.2.k.c.857.3		6	5.3	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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.17009i q^{2} +(0.315449 - 0.315449i) q^{3} -2.70928 q^{4} +(2.17009 - 0.539189i) q^{5} +(0.684551 + 0.684551i) q^{6} +(-1.31545 + 1.31545i) q^{7} -1.53919i q^{8} +2.80098i q^{9} +O(q^{10})\)	\(q+2.17009i q^{2} +(0.315449 - 0.315449i) q^{3} -2.70928 q^{4} +(2.17009 - 0.539189i) q^{5} +(0.684551 + 0.684551i) q^{6} +(-1.31545 + 1.31545i) q^{7} -1.53919i q^{8} +2.80098i q^{9} +(1.17009 + 4.70928i) q^{10} +4.04945i q^{11} +(-0.854638 + 0.854638i) q^{12} -5.80098i q^{13} +(-2.85464 - 2.85464i) q^{14} +(0.514465 - 0.854638i) q^{15} -2.07838 q^{16} +2.87936 q^{17} -6.07838 q^{18} +(1.68455 - 1.68455i) q^{19} +(-5.87936 + 1.46081i) q^{20} +0.829914i q^{21} -8.78765 q^{22} -8.04945i q^{23} +(-0.485535 - 0.485535i) q^{24} +(4.41855 - 2.34017i) q^{25} +12.5886 q^{26} +(1.82991 + 1.82991i) q^{27} +(3.56391 - 3.56391i) q^{28} +(0.0783777 + 0.0783777i) q^{29} +(1.85464 + 1.11643i) q^{30} +(-4.10310 + 4.10310i) q^{31} -7.58864i q^{32} +(1.27739 + 1.27739i) q^{33} +6.24846i q^{34} +(-2.14536 + 3.56391i) q^{35} -7.58864i q^{36} +(-1.00000 - 6.00000i) q^{37} +(3.65562 + 3.65562i) q^{38} +(-1.82991 - 1.82991i) q^{39} +(-0.829914 - 3.34017i) q^{40} -5.46800i q^{41} -1.80098 q^{42} +8.38962i q^{43} -10.9711i q^{44} +(1.51026 + 6.07838i) q^{45} +17.4680 q^{46} +(0.933015 - 0.933015i) q^{47} +(-0.655622 + 0.655622i) q^{48} +3.53919i q^{49} +(5.07838 + 9.58864i) q^{50} +(0.908291 - 0.908291i) q^{51} +15.7165i q^{52} +(-4.17009 - 4.17009i) q^{53} +(-3.97107 + 3.97107i) q^{54} +(2.18342 + 8.78765i) q^{55} +(2.02472 + 2.02472i) q^{56} -1.06278i q^{57} +(-0.170086 + 0.170086i) q^{58} +(8.10310 - 8.10310i) q^{59} +(-1.39383 + 2.31545i) q^{60} +(6.70928 - 6.70928i) q^{61} +(-8.90409 - 8.90409i) q^{62} +(-3.68455 - 3.68455i) q^{63} +12.3112 q^{64} +(-3.12783 - 12.5886i) q^{65} +(-2.77205 + 2.77205i) q^{66} +(-0.116433 - 0.116433i) q^{67} -7.80098 q^{68} +(-2.53919 - 2.53919i) q^{69} +(-7.73400 - 4.65562i) q^{70} -7.75872 q^{71} +4.31124 q^{72} +(-7.09171 + 7.09171i) q^{73} +(13.0205 - 2.17009i) q^{74} +(0.655622 - 2.13203i) q^{75} +(-4.56391 + 4.56391i) q^{76} +(-5.32684 - 5.32684i) q^{77} +(3.97107 - 3.97107i) q^{78} +(-1.51446 + 1.51446i) q^{79} +(-4.51026 + 1.12064i) q^{80} -7.24846 q^{81} +11.8660 q^{82} +(5.48554 + 5.48554i) q^{83} -2.24846i q^{84} +(6.24846 - 1.55252i) q^{85} -18.2062 q^{86} +0.0494483 q^{87} +6.23287 q^{88} +(-2.61757 - 2.61757i) q^{89} +(-13.1906 + 3.27739i) q^{90} +(7.63090 + 7.63090i) q^{91} +21.8082i q^{92} +2.58864i q^{93} +(2.02472 + 2.02472i) q^{94} +(2.74733 - 4.56391i) q^{95} +(-2.39383 - 2.39383i) q^{96} +0.630898 q^{97} -7.68035 q^{98} -11.3424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{3} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 4 q^{7}+O(q^{10}) \) 6 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 4 * q^7	\( 6 q - 2 q^{3} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 4 q^{7} - 4 q^{10} + 2 q^{12} - 10 q^{14} + 18 q^{15} - 6 q^{16} - 8 q^{17} - 30 q^{18} + 14 q^{19} - 10 q^{20} - 32 q^{22} + 12 q^{24} - 2 q^{25} + 36 q^{26} + 22 q^{27} - 6 q^{29} + 4 q^{30} + 20 q^{33} - 20 q^{35} - 6 q^{37} - 4 q^{38} - 22 q^{39} - 16 q^{40} + 8 q^{42} - 24 q^{45} + 40 q^{46} - 8 q^{47} + 22 q^{48} + 24 q^{50} + 10 q^{51} - 14 q^{53} + 6 q^{54} + 4 q^{55} - 6 q^{56} + 10 q^{58} + 24 q^{59} + 2 q^{60} + 26 q^{61} - 10 q^{62} - 26 q^{63} + 22 q^{64} + 24 q^{65} + 32 q^{66} + 22 q^{67} - 28 q^{68} - 12 q^{69} - 14 q^{70} + 4 q^{71} - 26 q^{72} - 38 q^{73} + 12 q^{74} - 22 q^{75} - 6 q^{76} - 8 q^{77} - 6 q^{78} - 24 q^{79} + 6 q^{80} - 26 q^{81} + 44 q^{82} + 18 q^{83} + 20 q^{85} - 60 q^{86} - 36 q^{87} - 8 q^{88} - 6 q^{89} - 2 q^{90} + 38 q^{91} - 6 q^{94} - 14 q^{95} - 4 q^{96} - 4 q^{97} - 2 q^{98} - 72 q^{99}+O(q^{100}) \) 6 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 4 * q^7 - 4 * q^10 + 2 * q^12 - 10 * q^14 + 18 * q^15 - 6 * q^16 - 8 * q^17 - 30 * q^18 + 14 * q^19 - 10 * q^20 - 32 * q^22 + 12 * q^24 - 2 * q^25 + 36 * q^26 + 22 * q^27 - 6 * q^29 + 4 * q^30 + 20 * q^33 - 20 * q^35 - 6 * q^37 - 4 * q^38 - 22 * q^39 - 16 * q^40 + 8 * q^42 - 24 * q^45 + 40 * q^46 - 8 * q^47 + 22 * q^48 + 24 * q^50 + 10 * q^51 - 14 * q^53 + 6 * q^54 + 4 * q^55 - 6 * q^56 + 10 * q^58 + 24 * q^59 + 2 * q^60 + 26 * q^61 - 10 * q^62 - 26 * q^63 + 22 * q^64 + 24 * q^65 + 32 * q^66 + 22 * q^67 - 28 * q^68 - 12 * q^69 - 14 * q^70 + 4 * q^71 - 26 * q^72 - 38 * q^73 + 12 * q^74 - 22 * q^75 - 6 * q^76 - 8 * q^77 - 6 * q^78 - 24 * q^79 + 6 * q^80 - 26 * q^81 + 44 * q^82 + 18 * q^83 + 20 * q^85 - 60 * q^86 - 36 * q^87 - 8 * q^88 - 6 * q^89 - 2 * q^90 + 38 * q^91 - 6 * q^94 - 14 * q^95 - 4 * q^96 - 4 * q^97 - 2 * q^98 - 72 * q^99

Introduction

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