LMFDB - Embedded newform 504.2.cq.a.277.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(277,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4, 4]))

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

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

chi := DirichletCharacter("504.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$504 = 2^{3} \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	504.cq (of order $6$ , 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			277.4
Character	$\chi$	$=$	504.277
Dual form			504.2.cq.a.373.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40384 + 0.171013i) q^{2} +(1.37821 - 1.04907i) q^{3} +(1.94151 - 0.480149i) q^{4} +(-0.213745 - 0.123406i) q^{5} +(-1.75537 + 1.70841i) q^{6} +(-2.18219 + 1.49601i) q^{7} +(-2.64345 + 1.00607i) q^{8} +(0.798909 - 2.89167i) q^{9} +(0.321167 + 0.136688i) q^{10} +(-1.61868 + 0.934548i) q^{11} +(2.17209 - 2.69852i) q^{12} +(4.72805 - 2.72974i) q^{13} +(2.80760 - 2.47333i) q^{14} +(-0.424046 + 0.0541547i) q^{15} +(3.53891 - 1.86443i) q^{16} +(2.66475 - 4.61548i) q^{17} +(-0.627023 + 4.19605i) q^{18} +(5.13617 - 2.96537i) q^{19} +(-0.474242 - 0.136964i) q^{20} +(-1.43810 + 4.35108i) q^{21} +(2.11255 - 1.58877i) q^{22} +(0.586230 - 1.01538i) q^{23} +(-2.58778 + 4.15974i) q^{24} +(-2.46954 - 4.27737i) q^{25} +(-6.17058 + 4.64066i) q^{26} +(-1.93250 - 4.82343i) q^{27} +(-3.51844 + 3.95228i) q^{28} +(-0.0123976 - 0.00715774i) q^{29} +(0.586030 - 0.148542i) q^{30} +6.29225 q^{31} +(-4.64921 + 3.22255i) q^{32} +(-1.25048 + 2.98611i) q^{33} +(-2.95156 + 6.93509i) q^{34} +(0.651049 - 0.0504685i) q^{35} +(0.162658 - 5.99779i) q^{36} +(-9.20518 + 5.31461i) q^{37} +(-6.70322 + 5.04124i) q^{38} +(3.65254 - 8.72219i) q^{39} +(0.689180 + 0.111174i) q^{40} +(-5.17669 - 8.96629i) q^{41} +(1.27477 - 6.35413i) q^{42} +(9.20509 + 5.31456i) q^{43} +(-2.69397 + 2.59164i) q^{44} +(-0.527612 + 0.519490i) q^{45} +(-0.649327 + 1.52568i) q^{46} -9.22012 q^{47} +(2.92145 - 6.28213i) q^{48} +(2.52394 - 6.52915i) q^{49} +(4.19832 + 5.58240i) q^{50} +(-1.16938 - 9.15660i) q^{51} +(7.86886 - 7.56998i) q^{52} +(5.81764 + 3.35882i) q^{53} +(3.53778 + 6.44082i) q^{54} +0.461315 q^{55} +(4.26342 - 6.15006i) q^{56} +(3.96783 - 9.47509i) q^{57} +(0.0186282 + 0.00792814i) q^{58} +12.4017i q^{59} +(-0.797288 + 0.308747i) q^{60} +2.78872i q^{61} +(-8.83328 + 1.07606i) q^{62} +(2.58258 + 7.50535i) q^{63} +(5.97563 - 5.31900i) q^{64} -1.34746 q^{65} +(1.24480 - 4.40586i) q^{66} -1.96871i q^{67} +(2.95752 - 10.2405i) q^{68} +(-0.257257 - 2.01440i) q^{69} +(-0.905335 + 0.182188i) q^{70} +8.78800 q^{71} +(0.797356 + 8.44773i) q^{72} +(0.891446 - 1.54403i) q^{73} +(12.0137 - 9.03505i) q^{74} +(-7.89080 - 3.30438i) q^{75} +(8.54810 - 8.22342i) q^{76} +(2.13419 - 4.46093i) q^{77} +(-3.63596 + 12.8692i) q^{78} -4.65221 q^{79} +(-0.986507 - 0.0382108i) q^{80} +(-7.72349 - 4.62036i) q^{81} +(8.80058 + 11.7019i) q^{82} +(-3.89087 - 2.24639i) q^{83} +(-0.702924 + 9.13816i) q^{84} +(-1.13916 + 0.657692i) q^{85} +(-13.8313 - 5.88658i) q^{86} +(-0.0245954 + 0.00314106i) q^{87} +(3.33868 - 4.09894i) q^{88} +(6.71334 + 11.6278i) q^{89} +(0.651841 - 0.819508i) q^{90} +(-6.23381 + 13.0300i) q^{91} +(0.650637 - 2.25285i) q^{92} +(8.67202 - 6.60100i) q^{93} +(12.9435 - 1.57676i) q^{94} -1.46378 q^{95} +(-3.02690 + 9.31868i) q^{96} +(-2.06206 + 3.57159i) q^{97} +(-2.42662 + 9.59747i) q^{98} +(1.40922 + 5.42732i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$184 q - 2 q^{2} - 2 q^{4} - 2 q^{6} - 2 q^{7} - 8 q^{8} - 2 q^{9} + 2 q^{10} + 16 q^{12} - 4 q^{14} - 2 q^{15} - 2 q^{16} - 4 q^{17} - 14 q^{18} + 6 q^{20} + 2 q^{22} + 2 q^{23} + 12 q^{24} + 78 q^{25}+ \cdots - 83 q^{98}+O(q^{100})$ 184 * q - 2 * q^2 - 2 * q^4 - 2 * q^6 - 2 * q^7 - 8 * q^8 - 2 * q^9 + 2 * q^10 + 16 * q^12 - 4 * q^14 - 2 * q^15 - 2 * q^16 - 4 * q^17 - 14 * q^18 + 6 * q^20 + 2 * q^22 + 2 * q^23 + 12 * q^24 + 78 * q^25 - 4 * q^26 - 8 * q^28 - 9 * q^30 - 4 * q^31 - 2 * q^32 - 14 * q^33 - 18 * q^36 - 5 * q^38 + 4 * q^39 - 4 * q^40 - 4 * q^41 - 12 * q^42 + 17 * q^44 - 6 * q^46 - 84 * q^47 - 3 * q^48 - 2 * q^49 - 31 * q^50 + 9 * q^52 - q^54 + 4 * q^55 - 16 * q^56 - 20 * q^57 + 5 * q^58 + 17 * q^60 + 32 * q^62 + 8 * q^63 - 8 * q^64 - 44 * q^65 - 56 * q^66 - 12 * q^68 + 5 * q^70 - 16 * q^71 + 36 * q^72 - 4 * q^73 + 19 * q^74 - 6 * q^76 - 47 * q^78 - 4 * q^79 - 11 * q^80 - 18 * q^81 - 65 * q^84 - 23 * q^86 - 14 * q^87 - 7 * q^88 + 4 * q^89 - 35 * q^90 - 48 * q^92 - 18 * q^94 - 44 * q^95 + 95 * q^96 - 4 * q^97 - 83 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$ .

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.40384	+	0.171013i	−0.992662	+	0.120925i
$2$	−1.40384	+	0.171013i	−0.992662	+	0.120925i
$3$	1.37821	−	1.04907i	0.795708	−	0.605680i
$3$	1.37821	−	1.04907i	0.795708	−	0.605680i
$4$	1.94151	−	0.480149i	0.970755	−	0.240074i
$5$	−0.213745	−	0.123406i	−0.0955898	−	0.0551888i	0.451443	−	0.892300i	$-0.350909\pi$
$5$	−0.213745	−	0.123406i	−0.0955898	−	0.0551888i	−0.547033	+	0.837111i	$0.684243\pi$
$6$	−1.75537	+	1.70841i	−0.716627	+	0.697456i
$7$	−2.18219	+	1.49601i	−0.824792	+	0.565437i
$7$	−2.18219	+	1.49601i	−0.824792	+	0.565437i
$8$	−2.64345	+	1.00607i	−0.934600	+	0.355701i
$9$	0.798909	−	2.89167i	0.266303	−	0.963889i
$10$	0.321167	+	0.136688i	0.101562	+	0.0432246i
$11$	−1.61868	+	0.934548i	−0.488052	+	0.281777i	−0.723766	−	0.690046i	$-0.757590\pi$
$11$	−1.61868	+	0.934548i	−0.488052	+	0.281777i	0.235714	+	0.971822i	$0.424257\pi$
$12$	2.17209	−	2.69852i	0.627029	−	0.778996i
$13$	4.72805	−	2.72974i	1.31132	−	0.757093i	0.329009	−	0.944327i	$-0.393285\pi$
$13$	4.72805	−	2.72974i	1.31132	−	0.757093i	0.982315	+	0.187234i	$0.0599521\pi$
$14$	2.80760	−	2.47333i	0.750364	−	0.661025i
$15$	−0.424046	+	0.0541547i	−0.109488	+	0.0139827i
$16$	3.53891	−	1.86443i	0.884729	−	0.466106i
$17$	2.66475	−	4.61548i	0.646297	−	1.11942i	−0.337704	−	0.941253i	$-0.609650\pi$
$17$	2.66475	−	4.61548i	0.646297	−	1.11942i	0.984000	−	0.178166i	$-0.0570165\pi$
$18$	−0.627023	+	4.19605i	−0.147791	+	0.989019i
$19$	5.13617	−	2.96537i	1.17832	−	0.680302i	0.222693	−	0.974889i	$-0.428515\pi$
$19$	5.13617	−	2.96537i	1.17832	−	0.680302i	0.955625	+	0.294586i	$0.0951818\pi$
$20$	−0.474242	−	0.136964i	−0.106044	−	0.0306261i
$21$	−1.43810	+	4.35108i	−0.313819	+	0.949483i
$22$	2.11255	−	1.58877i	0.450397	−	0.338726i
$23$	0.586230	−	1.01538i	0.122237	−	0.211721i	−0.798412	−	0.602111i	$-0.794326\pi$
$23$	0.586230	−	1.01538i	0.122237	−	0.211721i	0.920650	+	0.390390i	$0.127660\pi$
$24$	−2.58778	+	4.15974i	−0.528228	+	0.849103i
$25$	−2.46954	−	4.27737i	−0.493908	−	0.855474i
$26$	−6.17058	+	4.64066i	−1.21015	+	0.910109i
$27$	−1.93250	−	4.82343i	−0.371909	−	0.928269i
$28$	−3.51844	+	3.95228i	−0.664923	+	0.746912i
$29$	−0.0123976	−	0.00715774i	−0.00230217	−	0.00132916i	0.498848	−	0.866689i	$-0.333756\pi$
$29$	−0.0123976	−	0.00715774i	−0.00230217	−	0.00132916i	−0.501151	+	0.865360i	$0.667090\pi$
$30$	0.586030	−	0.148542i	0.106994	−	0.0271199i
$31$	6.29225			1.13012			0.565060	−	0.825050i	$-0.308853\pi$
$31$	6.29225			1.13012			0.565060	+	0.825050i	$0.308853\pi$
$32$	−4.64921	+	3.22255i	−0.821873	+	0.569671i
$33$	−1.25048	+	2.98611i	−0.217680	+	0.519815i
$34$	−2.95156	+	6.93509i	−0.506189	+	1.18936i
$35$	0.651049	−	0.0504685i	0.110047	−	0.00853074i
$36$	0.162658	−	5.99779i	0.0271097	−	0.999632i
$37$	−9.20518	+	5.31461i	−1.51332	+	0.873717i	−0.513443	+	0.858124i	$0.671630\pi$
$37$	−9.20518	+	5.31461i	−1.51332	+	0.873717i	−0.999878	+	0.0155929i	$0.995036\pi$
$38$	−6.70322	+	5.04124i	−1.08741	+	0.817798i
$39$	3.65254	−	8.72219i	0.584875	−	1.39667i
$40$	0.689180	+	0.111174i	0.108969	+	0.0175781i
$41$	−5.17669	−	8.96629i	−0.808463	−	1.40030i	−0.913928	−	0.405877i	$-0.866966\pi$
$41$	−5.17669	−	8.96629i	−0.808463	−	1.40030i	0.105464	−	0.994423i	$-0.466367\pi$
$42$	1.27477	−	6.35413i	0.196701	−	0.980464i
$43$	9.20509	+	5.31456i	1.40376	+	0.810463i	0.994777	−	0.102077i	$-0.0325487\pi$
$43$	9.20509	+	5.31456i	1.40376	+	0.810463i	0.408987	+	0.912540i	$0.365882\pi$
$44$	−2.69397	+	2.59164i	−0.406131	+	0.390705i
$45$	−0.527612	+	0.519490i	−0.0786517	+	0.0774410i
$46$	−0.649327	+	1.52568i	−0.0957380	+	0.224949i
$47$	−9.22012			−1.34489			−0.672446	−	0.740146i	$-0.734756\pi$
$47$	−9.22012			−1.34489			−0.672446	+	0.740146i	$0.734756\pi$
$48$	2.92145	−	6.28213i	0.421674	−	0.906747i
$49$	2.52394	−	6.52915i	0.360562	−	0.932735i
$50$	4.19832	+	5.58240i	0.593732	+	0.789471i
$51$	−1.16938	−	9.15660i	−0.163746	−	1.28218i
$52$	7.86886	−	7.56998i	1.09122	−	1.04977i
$53$	5.81764	+	3.35882i	0.799114	+	0.461369i	0.843161	−	0.537661i	$-0.180692\pi$
$53$	5.81764	+	3.35882i	0.799114	+	0.461369i	−0.0440470	+	0.999029i	$0.514025\pi$
$54$	3.53778	+	6.44082i	0.481431	+	0.876484i
$55$	0.461315			0.0622037
$56$	4.26342	−	6.15006i	0.569724	−	0.821836i
$57$	3.96783	−	9.47509i	0.525552	−	1.25501i
$58$	0.0186282	+	0.00792814i	0.00244600	+	0.00104102i
$59$			12.4017i			1.61457i	0.590165	+	0.807283i	$0.299063\pi$
$59$			12.4017i			1.61457i	−0.590165	+	0.807283i	$0.700937\pi$
$60$	−0.797288	+	0.308747i	−0.102929	+	0.0398591i
$61$			2.78872i			0.357059i	0.983935	+	0.178530i	$0.0571340\pi$
$61$			2.78872i			0.357059i	−0.983935	+	0.178530i	$0.942866\pi$
$62$	−8.83328	+	1.07606i	−1.12183	+	0.136659i
$63$	2.58258	+	7.50535i	0.325374	+	0.945585i
$64$	5.97563	−	5.31900i	0.746954	−	0.664875i
$65$	−1.34746			−0.167132
$66$	1.24480	−	4.40586i	0.153224	−	0.542324i
$67$		−	1.96871i		−	0.240517i	−0.992743	−	0.120258i	$-0.961628\pi$
$67$		−	1.96871i		−	0.240517i	0.992743	−	0.120258i	$-0.0383723\pi$
$68$	2.95752	−	10.2405i	0.358652	−	1.24184i
$69$	−0.257257	−	2.01440i	−0.0309702	−	0.242505i
$70$	−0.905335	+	0.182188i	−0.108208	+	0.0217756i
$71$	8.78800			1.04294			0.521472	−	0.853268i	$-0.325383\pi$
$71$	8.78800			1.04294			0.521472	+	0.853268i	$0.325383\pi$
$72$	0.797356	+	8.44773i	0.0939693	+	0.995575i
$73$	0.891446	−	1.54403i	0.104336	−	0.180715i	−0.809131	−	0.587629i	$-0.800062\pi$
$73$	0.891446	−	1.54403i	0.104336	−	0.180715i	0.913467	+	0.406914i	$0.133395\pi$
$74$	12.0137	−	9.03505i	1.39656	−	1.05030i
$75$	−7.89080	−	3.30438i	−0.911151	−	0.381557i
$76$	8.54810	−	8.22342i	0.980535	−	0.943290i
$77$	2.13419	−	4.46093i	0.243214	−	0.508370i
$78$	−3.63596	+	12.8692i	−0.411691	+	1.45714i
$79$	−4.65221			−0.523414			−0.261707	−	0.965147i	$-0.584285\pi$
$79$	−4.65221			−0.523414			−0.261707	+	0.965147i	$0.584285\pi$
$80$	−0.986507	−	0.0382108i	−0.110295	−	0.00427209i
$81$	−7.72349	−	4.62036i	−0.858166	−	0.513373i
$82$	8.80058	+	11.7019i	0.971861	+	1.29226i
$83$	−3.89087	−	2.24639i	−0.427078	−	0.246574i	0.271023	−	0.962573i	$-0.412638\pi$
$83$	−3.89087	−	2.24639i	−0.427078	−	0.246574i	−0.698101	+	0.715999i	$0.745971\pi$
$84$	−0.702924	+	9.13816i	−0.0766953	+	0.997055i
$85$	−1.13916	+	0.657692i	−0.123559	+	0.0713367i
$86$	−13.8313	−	5.88658i	−1.49147	−	0.634767i
$87$	−0.0245954	+	0.00314106i	−0.00263690	+	0.000336757i
$88$	3.33868	−	4.09894i	0.355905	−	0.436949i
$89$	6.71334	+	11.6278i	0.711612	+	1.23255i	0.964252	+	0.264988i	$0.0853680\pi$
$89$	6.71334	+	11.6278i	0.711612	+	1.23255i	−0.252639	+	0.967561i	$0.581299\pi$
$90$	0.651841	−	0.819508i	0.0687100	−	0.0863837i
$91$	−6.23381	+	13.0300i	−0.653481	+	1.36592i
$92$	0.650637	−	2.25285i	0.0678336	−	0.234875i
$93$	8.67202	−	6.60100i	0.899246	−	0.684492i
$94$	12.9435	−	1.57676i	1.33502	−	0.162630i
$95$	−1.46378			−0.150180
$96$	−3.02690	+	9.31868i	−0.308932	+	0.951084i
$97$	−2.06206	+	3.57159i	−0.209370	+	0.362640i	−0.951516	−	0.307598i	$-0.900475\pi$
$97$	−2.06206	+	3.57159i	−0.209370	+	0.362640i	0.742146	+	0.670238i	$0.233808\pi$
$98$	−2.42662	+	9.59747i	−0.245126	+	0.969491i
$99$	1.40922	+	5.42732i	0.141632	+	0.545466i
$100$	−6.84841	−	7.11881i	−0.684841	−	0.711881i
$101$	10.1142	−	5.83941i	1.00640	−	0.581043i	0.0962618	−	0.995356i	$-0.469311\pi$
$101$	10.1142	−	5.83941i	1.00640	−	0.581043i	0.910135	+	0.414313i	$0.135978\pi$
$102$	3.20752	+	12.6544i	0.317592	+	1.25297i
$103$	−5.87774	+	10.1805i	−0.579150	+	1.00312i	0.416427	+	0.909169i	$0.363282\pi$
$103$	−5.87774	+	10.1805i	−0.579150	+	1.00312i	−0.995577	+	0.0939487i	$0.970051\pi$
$104$	−9.75203	+	11.9727i	−0.956265	+	1.17402i
$105$	0.844336	−	0.752552i	0.0823987	−	0.0734415i
$106$	−8.74141	−	3.72033i	−0.849041	−	0.361351i
$107$	−1.77646	+	1.02564i	−0.171737	+	0.0991525i	−0.583405	−	0.812182i	$-0.698280\pi$
$107$	−1.77646	+	1.02564i	−0.171737	+	0.0991525i	0.411668	+	0.911334i	$0.364947\pi$
$108$	−6.06792	−	8.43684i	−0.583886	−	0.811835i
$109$	−8.66752	−	5.00420i	−0.830198	−	0.479315i	0.0237225	−	0.999719i	$-0.492448\pi$
$109$	−8.66752	−	5.00420i	−0.830198	−	0.479315i	−0.853920	+	0.520404i	$0.825782\pi$
$110$	−0.647610	+	0.0788909i	−0.0617472	+	0.00752195i
$111$	−7.11124	+	16.9815i	−0.674969	+	1.61181i
$112$	−4.93341	+	9.36277i	−0.466163	+	0.884699i
$113$	−0.759378	−	1.31528i	−0.0714363	−	0.123731i	0.828095	−	0.560588i	$-0.189425\pi$
$113$	−0.759378	−	1.31528i	−0.0714363	−	0.123731i	−0.899531	+	0.436857i	$0.856092\pi$
$114$	−3.94981	+	13.9800i	−0.369934	+	1.30935i
$115$	−0.250608	+	0.144688i	−0.0233693	+	0.0134923i
$116$	−0.0275068	−	0.00794414i	−0.00255394	−	0.000737595i
$117$	−4.11622	−	15.8528i	−0.380545	−	1.46559i
$118$	−2.12086	−	17.4100i	−0.195241	−	1.60272i
$119$	1.08979	+	14.0584i	0.0999006	+	1.28873i
$120$	1.06646	−	0.569777i	0.0973541	−	0.0520133i
$121$	−3.75324	+	6.50080i	−0.341204	+	0.590982i
$122$	−0.476908	−	3.91491i	−0.0431772	−	0.354439i
$123$	−16.5408	−	6.92670i	−1.49143	−	0.624560i
$124$	12.2165	−	3.02121i	1.09707	−	0.271313i
$125$			2.45308i			0.219410i
$126$	−4.90903	−	10.0946i	−0.437331	−	0.899301i
$127$	−6.26076			−0.555553			−0.277777	−	0.960646i	$-0.589597\pi$
$127$	−6.26076			−0.555553			−0.277777	+	0.960646i	$0.589597\pi$
$128$	−7.47919	+	8.48892i	−0.661073	+	0.750322i
$129$	18.2619	−	2.33221i	1.60787	−	0.205340i
$130$	1.89162	−	0.230434i	0.165906	−	0.0202104i
$131$	11.6467	+	6.72424i	1.01758	+	0.587499i	0.913402	−	0.407059i	$-0.133446\pi$
$131$	11.6467	+	6.72424i	1.01758	+	0.587499i	0.104177	+	0.994559i	$0.466779\pi$
$132$	−0.994035	+	6.39798i	−0.0865196	+	0.556873i
$133$	−6.77191	+	14.1547i	−0.587199	+	1.22737i
$134$	0.336676	+	2.76375i	0.0290844	+	0.238752i
$135$	−0.182177	+	1.26947i	−0.0156793	+	0.109258i
$136$	−2.40062	+	14.8817i	−0.205851	+	1.27610i
$137$	−0.385507	−	0.667718i	−0.0329361	−	0.0570470i	0.849088	−	0.528252i	$-0.177152\pi$
$137$	−0.385507	−	0.667718i	−0.0329361	−	0.0570470i	−0.882024	+	0.471205i	$0.843819\pi$
$138$	0.705636	+	2.78389i	0.0600677	+	0.236981i
$139$	−0.0270629	+	0.0156248i	−0.00229544	+	0.00132528i	−0.501147	−	0.865362i	$-0.667089\pi$
$139$	−0.0270629	+	0.0156248i	−0.00229544	+	0.00132528i	0.498852	+	0.866687i	$0.333755\pi$
$140$	1.23979	−	0.410586i	0.104781	−	0.0347008i
$141$	−12.7072	+	9.67254i	−1.07014	+	0.814575i
$142$	−12.3369	+	1.50286i	−1.03529	+	0.126118i
$143$	−5.10214	+	8.83717i	−0.426663	+	0.739001i
$144$	−2.56403	−	11.7229i	−0.213669	−	0.976906i
$145$	0.00176661	+	0.00305986i	0.000146709	+	0.000254108i
$146$	−0.987395	+	2.32001i	−0.0817174	+	0.192006i
$147$	−3.37102	−	11.6463i	−0.278037	−	0.960570i
$148$	−15.3201	+	14.7382i	−1.25931	+	1.21147i
$149$	13.3931	+	7.73249i	1.09720	+	0.633470i	0.935485	−	0.353367i	$-0.114963\pi$
$149$	13.3931	+	7.73249i	1.09720	+	0.633470i	0.161718	+	0.986837i	$0.448297\pi$
$150$	11.6425	+	3.28938i	0.950604	+	0.268577i
$151$	−2.83010	−	4.90188i	−0.230310	−	0.398909i	0.727589	−	0.686013i	$-0.240641\pi$
$151$	−2.83010	−	4.90188i	−0.230310	−	0.398909i	−0.957899	+	0.287104i	$0.907307\pi$
$152$	−10.5938	+	13.0062i	−0.859272	+	1.05494i
$153$	−11.2176	−	11.3929i	−0.906885	−	0.921063i
$154$	−2.23318	+	6.62738i	−0.179955	+	0.534050i
$155$	−1.34494	−	0.776500i	−0.108028	−	0.0623700i
$156$	2.90350	−	18.6880i	0.232466	−	1.49624i
$157$			9.24156i			0.737557i	0.929517	+	0.368778i	$0.120224\pi$
$157$			9.24156i			0.737557i	−0.929517	+	0.368778i	$0.879776\pi$
$158$	6.53094	−	0.795589i	0.519573	−	0.0632936i
$159$	11.5415	−	1.47396i	0.915304	−	0.116893i
$160$	1.39143	−	0.115064i	0.110002	−	0.00909661i
$161$	0.239747	+	3.09276i	0.0188947	+	0.243743i
$162$	11.6327	+	5.16540i	0.913947	+	0.405832i
$163$	−2.08108	+	1.20151i	−0.163002	+	0.0941095i	−0.579282	−	0.815127i	$-0.696667\pi$
$163$	−2.08108	+	1.20151i	−0.163002	+	0.0941095i	0.416280	+	0.909237i	$0.363334\pi$
$164$	−14.3557	−	14.9226i	−1.12100	−	1.16526i
$165$	0.635787	−	0.483951i	0.0494960	−	0.0376755i
$166$	5.84630	+	2.48818i	0.453761	+	0.193120i
$167$	1.95626	+	3.38835i	0.151380	+	0.262198i	0.931735	−	0.363139i	$-0.118295\pi$
$167$	1.95626	+	3.38835i	0.151380	+	0.262198i	−0.780355	+	0.625337i	$0.784962\pi$
$168$	−0.575955	−	12.9487i	−0.0444359	−	0.999012i
$169$	8.40295	−	14.5543i	0.646381	−	1.11956i
$170$	1.48671	−	1.11810i	0.114026	−	0.0857545i
$171$	−4.47153	−	17.2212i	−0.341947	−	1.31693i
$172$	20.4236	+	5.89846i	1.55728	+	0.449753i
$173$		−	9.73992i		−	0.740513i	−0.928930	−	0.370256i	$-0.879270\pi$
$173$		−	9.73992i		−	0.740513i	0.928930	−	0.370256i	$-0.120730\pi$
$174$	0.0339907	−	0.00861566i	0.00257683	−	0.000653151i
$175$	11.7880	+	5.63961i	0.891088	+	0.426314i
$176$	−3.98599	+	6.32520i	−0.300455	+	0.476780i
$177$	13.0103	+	17.0921i	0.977910	+	1.28472i
$178$	−11.4129	−	15.1755i	−0.855436	−	1.13745i
$179$	16.5335	+	9.54562i	1.23577	+	0.713473i	0.968227	−	0.250073i	$-0.0804545\pi$
$179$	16.5335	+	9.54562i	1.23577	+	0.713473i	0.267544	+	0.963546i	$0.413788\pi$
$180$	−0.774931	+	1.26193i	−0.0577599	+	0.0940585i
$181$		−	11.0363i		−	0.820324i	−0.912013	−	0.410162i	$-0.865472\pi$
$181$		−	11.0363i		−	0.820324i	0.912013	−	0.410162i	$-0.134528\pi$
$182$	6.52294	−	19.3580i	0.483513	−	1.43491i
$183$	2.92556	+	3.84344i	0.216264	+	0.284115i
$184$	−0.528122	+	3.27389i	−0.0389336	+	0.241355i
$185$	2.62342			0.192877
$186$	−11.0452	+	10.7497i	−0.809875	+	0.788210i
$187$			9.96135i			0.728446i
$188$	−17.9009	+	4.42703i	−1.30556	+	0.322874i
$189$	11.4330	+	7.63462i	0.831625	+	0.555337i
$190$	2.05490	−	0.250325i	0.149078	−	0.0181605i
$191$	−2.64762			−0.191575			−0.0957874	−	0.995402i	$-0.530537\pi$
$191$	−2.64762			−0.191575			−0.0957874	+	0.995402i	$0.530537\pi$
$192$	2.65566	−	13.5995i	0.191656	−	0.981462i
$193$	−1.35109			−0.0972533			−0.0486266	−	0.998817i	$-0.515484\pi$
$193$	−1.35109			−0.0972533			−0.0486266	+	0.998817i	$0.515484\pi$
$194$	2.28400	−	5.36656i	0.163982	−	0.385296i
$195$	−1.85708	+	1.41358i	−0.132988	+	0.101229i
$196$	1.76528	−	13.8883i	0.126092	−	0.992019i
$197$		−	15.4647i		−	1.10181i	−0.834567	−	0.550907i	$-0.814282\pi$
$197$		−	15.4647i		−	1.10181i	0.834567	−	0.550907i	$-0.185718\pi$
$198$	−2.90646	−	7.37807i	−0.206553	−	0.524336i
$199$	−8.95285	+	15.5068i	−0.634651	+	1.09925i	0.351938	+	0.936023i	$0.385523\pi$
$199$	−8.95285	+	15.5068i	−0.634651	+	1.09925i	−0.986589	+	0.163224i	$0.947811\pi$
$200$	10.8315	+	8.82247i	0.765900	+	0.623843i
$201$	−2.06532	−	2.71329i	−0.145676	−	0.191381i
$202$	−13.2000	+	9.92723i	−0.928749	+	0.698477i
$203$	0.0377619	−	0.00292726i	0.00265037	−	0.000205453i
$204$	−6.66689	−	17.2161i	−0.466776	−	1.20537i
$205$			2.55534i			0.178472i
$206$	6.51037	−	15.2970i	0.453599	−	1.06579i
$207$	−2.46780	−	2.50638i	−0.171524	−	0.174205i
$208$	11.6428	−	18.4754i	0.807280	−	1.28104i
$209$	−5.54256	+	9.59999i	−0.383387	+	0.664046i
$210$	−1.05661	+	1.20085i	−0.0729132	+	0.0828666i
$211$	3.27095	−	1.88848i	0.225181	−	0.130008i	−0.383166	−	0.923680i	$-0.625166\pi$
$211$	3.27095	−	1.88848i	0.225181	−	0.130008i	0.608347	+	0.793671i	$0.291833\pi$
$212$	12.9077	+	3.72784i	0.886507	+	0.256029i
$213$	12.1117	−	9.21922i	0.829879	−	0.631691i
$214$	2.31846	−	1.74363i	0.158487	−	0.119192i
$215$	−1.31170	−	2.27193i	−0.0894570	−	0.154944i
$216$	9.96118	+	10.8062i	0.677772	+	0.735272i
$217$	−13.7309	+	9.41323i	−0.932114	+	0.639012i
$218$	13.0236	+	5.54281i	0.882067	+	0.375406i
$219$	−0.391197	−	3.06318i	−0.0264346	−	0.206991i
$220$	0.895647	−	0.221500i	0.0603845	−	0.0149335i
$221$		−	29.0963i		−	1.95723i
$222$	7.07896	−	25.0553i	0.475109	−	1.68160i
$223$	−2.01131	+	3.48369i	−0.134687	+	0.233285i	−0.925478	−	0.378802i	$-0.876336\pi$
$223$	−2.01131	+	3.48369i	−0.134687	+	0.233285i	0.790791	+	0.612087i	$0.209670\pi$
$224$	5.32453	−	13.9875i	0.355760	−	0.934577i
$225$	−14.3417	+	3.72387i	−0.956112	+	0.248258i
$226$	1.29097	+	1.71658i	0.0858742	+	0.114185i
$227$	−17.2327	+	9.94930i	−1.14377	+	0.660358i	−0.947362	−	0.320163i	$-0.896262\pi$
$227$	−17.2327	+	9.94930i	−1.14377	+	0.660358i	−0.196412	+	0.980522i	$0.562929\pi$
$228$	3.15412	−	20.3011i	0.208887	−	1.34447i
$229$	12.2271	+	7.05931i	0.807988	+	0.466492i	0.846257	−	0.532775i	$-0.178851\pi$
$229$	12.2271	+	7.05931i	0.807988	+	0.466492i	−0.0382684	+	0.999267i	$0.512184\pi$
$230$	0.327068	−	0.245976i	0.0215662	−	0.0162192i
$231$	−1.73846	−	8.38699i	−0.114382	−	0.551824i
$232$	0.0399735	+	0.00644825i	0.00262439	+	0.000423348i
$233$	−1.07535	−	1.86256i	−0.0704484	−	0.122020i	0.828650	−	0.559768i	$-0.189110\pi$
$233$	−1.07535	−	1.86256i	−0.0704484	−	0.122020i	−0.899098	+	0.437748i	$0.855776\pi$
$234$	8.48953	+	21.5507i	0.554978	+	1.40882i
$235$	1.97076	+	1.13782i	0.128558	+	0.0742230i
$236$	5.95466	+	24.0780i	0.387616	+	1.56735i
$237$	−6.41171	+	4.88049i	−0.416485	+	0.317022i
$238$	−3.93404	−	19.5493i	−0.255006	−	1.26719i
$239$	−10.4593	−	18.1161i	−0.676559	−	1.17183i	−0.976011	−	0.217722i	$-0.930137\pi$
$239$	−10.4593	−	18.1161i	−0.676559	−	1.17183i	0.299452	−	0.954111i	$-0.403196\pi$
$240$	−1.39970	+	0.982252i	−0.0903500	+	0.0634041i
$241$	1.97108	+	3.41401i	0.126968	+	0.219915i	0.922501	−	0.385996i	$-0.126142\pi$
$241$	1.97108	+	3.41401i	0.126968	+	0.219915i	−0.795532	+	0.605911i	$0.792809\pi$
$242$	4.15721	−	9.76791i	0.267236	−	0.627905i
$243$	−15.4916	+	1.73467i	−0.993789	+	0.111279i
$244$	1.33900	+	5.41433i	0.0857207	+	0.346617i
$245$	−1.34521	+	1.08411i	−0.0859426	+	0.0692610i
$246$	24.4051	+	6.89525i	1.55601	+	0.439625i
$247$	16.1894	−	28.0408i	1.03010	−	1.78419i
$248$	−16.6332	+	6.33046i	−1.05621	+	0.401985i
$249$	−7.71904	+	0.985794i	−0.489175	+	0.0624721i
$250$	−0.419509	−	3.44373i	−0.0265321	−	0.217800i
$251$		−	1.53948i		−	0.0971712i	−0.998819	−	0.0485856i	$-0.984529\pi$
$251$		−	1.53948i		−	0.0971712i	0.998819	−	0.0485856i	$-0.0154714\pi$
$252$	8.61778	+	13.3317i	0.542869	+	0.839817i
$253$			2.19144i			0.137775i
$254$	8.78908	−	1.07067i	0.551476	−	0.0671800i
$255$	−0.880028	+	2.10149i	−0.0551095	+	0.131600i
$256$	9.04783	−	13.1961i	0.565490	−	0.824755i
$257$	1.30685	−	2.26352i	0.0815188	−	0.141195i	−0.822384	−	0.568933i	$-0.807356\pi$
$257$	1.30685	−	2.26352i	0.0815188	−	0.141195i	0.903902	+	0.427739i	$0.140690\pi$
$258$	−25.2378	+	6.39706i	−1.57124	+	0.398263i
$259$	12.1368	−	25.3685i	0.754143	−	1.57632i
$260$	−2.61611	+	0.646983i	−0.162244	+	0.0401242i
$261$	−0.0306023	+	0.0301313i	−0.00189424	+	0.00186508i
$262$	−17.5000	−	7.44798i	−1.08115	−	0.460138i
$263$	2.39181	+	4.14273i	0.147485	+	0.255452i	0.930297	−	0.366806i	$-0.119549\pi$
$263$	2.39181	+	4.14273i	0.147485	+	0.255452i	−0.782812	+	0.622258i	$0.786215\pi$
$264$	0.301324	−	9.15170i	0.0185452	−	0.563248i
$265$	−0.828995	−	1.43586i	−0.0509248	−	0.0882043i
$266$	7.08600	−	21.0290i	0.434470	−	1.28937i
$267$	21.4508	+	8.98282i	1.31277	+	0.549739i
$268$	−0.945275	−	3.82228i	−0.0577419	−	0.233483i
$269$	8.92577	+	5.15329i	0.544214	+	0.314202i	0.746785	−	0.665066i	$-0.231596\pi$
$269$	8.92577	+	5.15329i	0.544214	+	0.314202i	−0.202571	+	0.979268i	$0.564930\pi$
$270$	0.0386512	−	1.81328i	0.00235224	−	0.110353i
$271$	3.85789	+	6.68207i	0.234350	+	0.405907i	0.959084	−	0.283123i	$-0.0913704\pi$
$271$	3.85789	+	6.68207i	0.234350	+	0.405907i	−0.724733	+	0.689029i	$0.758037\pi$
$272$	0.825100	−	21.3020i	0.0500290	−	1.29163i
$273$	5.07789	+	24.4977i	0.307328	+	1.48267i
$274$	0.655377	+	0.871440i	0.0395928	+	0.0526456i
$275$	7.99482	+	4.61581i	0.482106	+	0.278344i
$276$	−1.46668	−	3.78745i	−0.0882837	−	0.227978i
$277$	−18.7619	+	10.8322i	−1.12729	+	0.650842i	−0.943252	−	0.332077i	$-0.892250\pi$
$277$	−18.7619	+	10.8322i	−1.12729	+	0.650842i	−0.184039	+	0.982919i	$0.558917\pi$
$278$	0.0353198	−	0.0265627i	0.00211834	−	0.00159313i
$279$	5.02693	−	18.1951i	0.300954	−	1.08931i
$280$	−1.67024	+	0.788414i	−0.0998159	+	0.0471168i
$281$	1.09787	−	1.90157i	0.0654936	−	0.113438i	−0.831419	−	0.555646i	$-0.812471\pi$
$281$	1.09787	−	1.90157i	0.0654936	−	0.113438i	0.896913	+	0.442207i	$0.145804\pi$
$282$	16.1847	−	15.7518i	0.963787	−	0.938003i
$283$			20.9306i			1.24419i	0.782940	+	0.622097i	$0.213719\pi$
$283$			20.9306i			1.24419i	−0.782940	+	0.622097i	$0.786281\pi$
$284$	17.0620	−	4.21955i	1.01244	−	0.250384i
$285$	−2.01739	+	1.53560i	−0.119500	+	0.0909612i
$286$	5.65130	−	13.2785i	0.334168	−	0.785172i
$287$	24.7102	+	11.8218i	1.45859	+	0.697820i
$288$	5.60424	+	16.0185i	0.330233	+	0.943899i
$289$	−5.70179	−	9.87578i	−0.335399	−	0.580929i
$290$	−0.00300331	−	0.00399343i	−0.000176361	−	0.000234502i
$291$	0.904900	+	7.08562i	0.0530462	+	0.415367i
$292$	0.989387	−	3.42578i	0.0578995	−	0.200478i
$293$	−0.725056	+	0.418611i	−0.0423582	+	0.0244555i	−0.521030	−	0.853539i	$-0.674452\pi$
$293$	−0.725056	+	0.418611i	−0.0423582	+	0.0244555i	0.478671	+	0.877994i	$0.341119\pi$
$294$	6.72402	+	15.7730i	0.392153	+	0.919900i
$295$	1.53044	−	2.65081i	0.0891059	−	0.154336i
$296$	18.9865	−	23.3100i	1.10357	−	1.35486i
$297$	7.63583	+	6.00160i	0.443076	+	0.348248i
$298$	−20.1240	−	8.56475i	−1.16575	−	0.496143i
$299$		−	6.40102i		−	0.370180i
$300$	−16.9067	−	2.62674i	−0.976106	−	0.151655i
$301$	−28.0379	+	2.17346i	−1.61608	+	0.125276i
$302$	4.81128	+	6.39745i	0.276858	+	0.368132i
$303$	7.81346	−	18.6584i	0.448871	−	1.07190i
$304$	12.6478	−	20.0702i	0.725399	−	1.15110i
$305$	0.344145	−	0.596076i	0.0197057	−	0.0341312i
$306$	17.6959	+	14.0754i	1.01161	+	0.804639i
$307$			2.44381i			0.139475i	0.997565	+	0.0697377i	$0.0222162\pi$
$307$			2.44381i			0.139475i	−0.997565	+	0.0697377i	$0.977784\pi$
$308$	2.00165	−	9.68566i	0.114055	−	0.551892i
$309$	2.57935	+	20.1970i	0.146734	+	1.14897i
$310$	2.02086	+	0.860077i	0.114777	+	0.0488491i
$311$	−8.76072			−0.496775			−0.248387	−	0.968661i	$-0.579901\pi$
$311$	−8.76072			−0.496775			−0.248387	+	0.968661i	$0.579901\pi$
$312$	−0.880142	+	26.7314i	−0.0498282	+	1.51337i
$313$	−8.63775			−0.488235			−0.244117	−	0.969746i	$-0.578498\pi$
$313$	−8.63775			−0.488235			−0.244117	+	0.969746i	$0.578498\pi$
$314$	−1.58043	−	12.9736i	−0.0891887	−	0.732144i
$315$	0.374191	−	1.92294i	0.0210833	−	0.108345i
$316$	−9.03231	+	2.23375i	−0.508107	+	0.125658i
$317$			14.1456i			0.794498i	0.917711	+	0.397249i	$0.130035\pi$
$317$			14.1456i			0.794498i	−0.917711	+	0.397249i	$0.869965\pi$
$318$	−15.9504	+	4.04296i	−0.894452	+	0.226718i
$319$	0.0267570			0.00149810
$320$	−1.93366	+	0.399483i	−0.108095	+	0.0223318i
$321$	−1.37237	+	3.27718i	−0.0765980	+	0.182914i
$322$	−0.865467	−	4.30072i	−0.0482306	−	0.239670i
$323$		−	31.6079i		−	1.75871i
$324$	−17.2137	−	5.26204i	−0.956316	−	0.292336i
$325$	−23.3522	−	13.4824i	−1.29535	−	0.747870i
$326$	2.71601	−	2.04261i	0.150426	−	0.113130i
$327$	−17.1954	+	2.19601i	−0.950907	+	0.121440i
$328$	22.7051	+	18.4938i	1.25368	+	1.02115i
$329$	20.1201	−	13.7933i	1.10926	−	0.760452i
$330$	−0.809779	+	0.788116i	−0.0445769	+	0.0433843i
$331$		−	11.3562i		−	0.624195i	−0.950050	−	0.312097i	$-0.898969\pi$
$331$		−	11.3562i		−	0.624195i	0.950050	−	0.312097i	$-0.101031\pi$
$332$	−8.63276	−	2.49320i	−0.473784	−	0.136832i
$333$	8.01400	+	30.8642i	0.439164	+	1.69135i
$334$	−3.32572	−	4.42213i	−0.181975	−	0.241968i
$335$	−0.242951	+	0.420803i	−0.0132738	+	0.0229909i
$336$	3.02294	+	18.0793i	0.164915	+	0.986308i
$337$	7.01019	+	12.1420i	0.381869	+	0.661417i	0.991329	−	0.131400i	$-0.0419472\pi$
$337$	7.01019	+	12.1420i	0.381869	+	0.661417i	−0.609460	+	0.792817i	$0.708614\pi$
$338$	−9.30738	+	21.8689i	−0.506255	+	1.18951i
$339$	−2.42640	−	1.01609i	−0.131784	−	0.0551864i
$340$	−1.89589	+	1.82388i	−0.102819	+	0.0989137i
$341$	−10.1852	+	5.88041i	−0.551557	+	0.318442i
$342$	9.22234	+	23.4110i	0.498687	+	1.26592i
$343$	4.25992	+	18.0237i	0.230014	+	0.973187i
$344$	−29.6800	−	4.78777i	−1.60024	−	0.258139i
$345$	−0.193601	+	0.462315i	−0.0104231	+	0.0248902i
$346$	1.66565	+	13.6733i	0.0895461	+	0.735079i
$347$			6.36234i			0.341549i	0.985310	+	0.170774i	$0.0546269\pi$
$347$			6.36234i			0.341549i	−0.985310	+	0.170774i	$0.945373\pi$
$348$	−0.0462440	+	0.0179078i	−0.00247894	+	0.000959960i
$349$	−4.42346	−	2.55388i	−0.236782	−	0.136706i	0.376915	−	0.926248i	$-0.376985\pi$
$349$	−4.42346	−	2.55388i	−0.236782	−	0.136706i	−0.613697	+	0.789542i	$0.710318\pi$
$350$	−17.5128	−	5.90118i	−0.936101	−	0.315431i
$351$	−22.3036	−	17.5302i	−1.19048	−	0.935691i
$352$	4.51398	−	9.56120i	0.240596	−	0.509614i
$353$	10.6838	+	18.5050i	0.568644	+	0.984920i	0.996700	+	0.0811679i	$0.0258650\pi$
$353$	10.6838	+	18.5050i	0.568644	+	0.984920i	−0.428057	+	0.903752i	$0.640802\pi$
$354$	−21.1872	−	21.7696i	−1.12609	−	1.15704i
$355$	−1.87839	−	1.08449i	−0.0996948	−	0.0575588i
$356$	18.6171	+	19.3522i	0.986704	+	1.02566i
$357$	16.2501	+	18.2321i	0.860048	+	0.964943i
$358$	−24.8427	−	10.5730i	−1.31298	−	0.558802i
$359$	−7.57368	−	13.1180i	−0.399723	−	0.692341i	0.593968	−	0.804489i	$-0.297561\pi$
$359$	−7.57368	−	13.1180i	−0.399723	−	0.692341i	−0.993692	+	0.112147i	$0.964227\pi$
$360$	0.872069	−	1.90406i	0.0459621	−	0.100353i
$361$	8.08683	−	14.0068i	0.425623	−	0.737200i
$362$	1.88736	+	15.4932i	0.0991973	+	0.814304i
$363$	1.64705	+	12.8969i	0.0864476	+	0.676910i
$364$	−5.84666	+	28.2910i	−0.306448	+	1.48285i
$365$	−0.381085	+	0.220019i	−0.0199469	+	0.0115163i
$366$	−4.76429	−	4.89524i	−0.249033	−	0.255878i
$367$	−12.2203	−	21.1662i	−0.637895	−	1.10487i	−0.985894	−	0.167372i	$-0.946472\pi$
$367$	−12.2203	−	21.1662i	−0.637895	−	1.10487i	0.347999	−	0.937495i	$-0.386861\pi$
$368$	0.181517	−	4.68632i	0.00946224	−	0.244292i
$369$	−30.0632	+	7.80603i	−1.56503	+	0.406365i
$370$	−3.68285	+	0.448639i	−0.191462	+	0.0233236i
$371$	−17.7200	+	1.37363i	−0.919978	+	0.0713155i
$372$	13.6673	−	16.9798i	0.708618	−	0.880359i
$373$	−26.8004	−	15.4732i	−1.38767	−	0.801173i	−0.394620	−	0.918844i	$-0.629124\pi$
$373$	−26.8004	−	15.4732i	−1.38767	−	0.801173i	−0.993053	+	0.117671i	$0.962457\pi$
$374$	−1.70352	−	13.9841i	−0.0880870	−	0.723100i
$375$	2.57345	+	3.38086i	0.132893	+	0.174587i
$376$	24.3729	−	9.27611i	1.25694	−	0.478379i
$377$	−0.0781550			−0.00402519
$378$	−17.3556	−	8.76257i	−0.892676	−	0.450698i
$379$			7.96954i			0.409368i	0.978828	+	0.204684i	$0.0656167\pi$
$379$			7.96954i			0.409368i	−0.978828	+	0.204684i	$0.934383\pi$
$380$	−2.84193	+	0.702830i	−0.145788	+	0.0360544i
$381$	−8.62863	+	6.56797i	−0.442058	+	0.336488i
$382$	3.71682	−	0.452777i	0.190169	−	0.0231661i
$383$	−3.45503	+	5.98428i	−0.176544	+	0.305782i	−0.940694	−	0.339255i	$-0.889825\pi$
$383$	−3.45503	+	5.98428i	−0.176544	+	0.305782i	0.764151	+	0.645038i	$0.223158\pi$
$384$	−1.40241	+	19.5457i	−0.0715663	+	0.997436i
$385$	−1.00668	+	0.690130i	−0.0513051	+	0.0351723i
$386$	1.89670	−	0.231053i	0.0965396	−	0.0117603i
$387$	22.7220	−	22.3722i	1.15502	−	1.13724i
$388$	−2.28861	+	7.92436i	−0.116186	+	0.402298i
$389$	32.6202	−	18.8333i	1.65391	−	0.954886i	0.678470	−	0.734628i	$-0.262643\pi$
$389$	32.6202	−	18.8333i	1.65391	−	0.954886i	0.975442	−	0.220258i	$-0.0706899\pi$
$390$	2.36530	−	2.30202i	0.119772	−	0.116567i
$391$	−3.12431	−	5.41147i	−0.158003	−	0.273670i
$392$	−0.103095	+	19.7987i	−0.00520708	+	0.999986i
$393$	23.1058	−	2.95082i	1.16553	−	0.148849i
$394$	2.64467	+	21.7099i	0.133236	+	1.09373i
$395$	0.994388	+	0.574110i	0.0500331	+	0.0288866i
$396$	5.34194	+	9.86055i	0.268442	+	0.495511i
$397$	−2.08436	+	1.20340i	−0.104611	+	0.0603971i	−0.551393	−	0.834246i	$-0.685903\pi$
$397$	−2.08436	+	1.20340i	−0.104611	+	0.0603971i	0.446782	+	0.894643i	$0.352570\pi$
$398$	9.91647	−	23.3000i	0.497068	−	1.16793i
$399$	5.51621	+	26.6124i	0.276156	+	1.33228i
$400$	−16.7143	−	10.5330i	−0.835717	−	0.526649i
$401$	−17.6721	+	30.6089i	−0.882501	+	1.52854i	−0.0339488	+	0.999424i	$0.510808\pi$
$401$	−17.6721	+	30.6089i	−0.882501	+	1.52854i	−0.848552	+	0.529112i	$0.822525\pi$
$402$	3.36337	+	3.45582i	0.167750	+	0.172361i
$403$	29.7500	−	17.1762i	1.48195	−	0.855607i
$404$	16.8329	−	16.1936i	0.837470	−	0.805660i
$405$	1.08068	+	1.94070i	0.0536994	+	0.0964343i
$406$	−0.0525109	+	0.0105672i	−0.00260607	+	0.000524440i
$407$	9.93352	−	17.2054i	0.492386	−	0.852838i
$408$	12.3034	+	23.0285i	0.609109	+	1.14008i
$409$	24.5036			1.21162			0.605812	−	0.795608i	$-0.292849\pi$
$409$	24.5036			1.21162			0.605812	+	0.795608i	$0.292849\pi$
$410$	−0.436996	−	3.58727i	−0.0215817	−	0.177163i
$411$	−1.23179	−	0.515830i	−0.0607598	−	0.0254440i
$412$	−6.52351	+	22.5878i	−0.321390	+	1.11282i
$413$	−18.5530	−	27.0629i	−0.912935	−	1.33168i
$414$	3.89301	+	3.09652i	0.191331	+	0.152185i
$415$	0.554436	+	0.960312i	0.0272162	+	0.0471399i
$416$	−13.1850	+	27.9275i	−0.646447	+	1.36926i
$417$	−0.0209068	+	0.0499250i	−0.00102381	+	0.00244484i
$418$	6.13912	−	14.4247i	0.300274	−	0.705533i
$419$	−7.56849	+	4.36967i	−0.369745	+	0.213472i	−0.673347	−	0.739327i	$-0.735144\pi$
$419$	−7.56849	+	4.36967i	−0.369745	+	0.213472i	0.303602	+	0.952799i	$0.401811\pi$
$420$	1.27795	−	1.86649i	0.0623575	−	0.0910755i
$421$	−0.976041	−	0.563517i	−0.0475693	−	0.0274642i	0.476027	−	0.879431i	$-0.342077\pi$
$421$	−0.976041	−	0.563517i	−0.0475693	−	0.0274642i	−0.523596	+	0.851967i	$0.675410\pi$
$422$	−4.26892	+	3.21049i	−0.207808	+	0.156284i
$423$	−7.36603	+	26.6615i	−0.358149	+	1.29633i
$424$	−18.7578	−	3.02588i	−0.910961	−	0.146950i
$425$	−26.3228			−1.27685
$426$	−15.4262	+	15.0135i	−0.747402	+	0.727408i
$427$	−4.17194	−	6.08553i	−0.201894	−	0.294499i
$428$	−2.95656	+	2.84426i	−0.142911	+	0.137482i
$429$	2.23899	+	17.5320i	0.108100	+	0.846451i
$430$	2.22994	+	2.96509i	0.107537	+	0.142989i
$431$	13.1417	−	22.7620i	0.633011	−	1.09641i	−0.353922	−	0.935275i	$-0.615152\pi$
$431$	13.1417	−	22.7620i	0.633011	−	1.09641i	0.986933	−	0.161132i	$-0.0515146\pi$
$432$	−15.8319	−	13.4667i	−0.761711	−	0.647917i
$433$	−17.8216			−0.856451			−0.428225	−	0.903672i	$-0.640861\pi$
$433$	−17.8216			−0.856451			−0.428225	+	0.903672i	$0.640861\pi$
$434$	17.6661	−	15.5628i	0.848002	−	0.747038i
$435$	0.00564477	+	0.00236383i	0.000270646	+	0.000113337i
$436$	−19.2308	−	5.55399i	−0.920990	−	0.265988i
$437$		−	6.95355i		−	0.332633i
$438$	1.07302	+	4.23330i	0.0512709	+	0.202275i
$439$	−9.08234			−0.433476			−0.216738	−	0.976230i	$-0.569542\pi$
$439$	−9.08234			−0.433476			−0.216738	+	0.976230i	$0.569542\pi$
$440$	−1.21946	+	0.464116i	−0.0581356	+	0.0221259i
$441$	−16.8637	−	12.5146i	−0.803035	−	0.595932i
$442$	4.97585	+	40.8464i	0.236677	+	1.94287i
$443$			32.1592i			1.52793i	0.645259	+	0.763964i	$0.276749\pi$
$443$			32.1592i			1.52793i	−0.645259	+	0.763964i	$0.723251\pi$
$444$	−5.65290	+	36.3842i	−0.268275	+	1.72672i
$445$		−	3.31386i		−	0.157092i
$446$	2.22779	−	5.23448i	0.105489	−	0.247860i
$447$	26.5703	−	3.39328i	1.25673	−	0.160496i
$448$	−5.08273	+	20.5467i	−0.240136	+	0.970739i
$449$	31.5353			1.48824			0.744122	−	0.668044i	$-0.232868\pi$
$449$	31.5353			1.48824			0.744122	+	0.668044i	$0.232868\pi$
$450$	19.4965	−	7.68031i	0.919075	−	0.362053i
$451$	16.7589	+	9.67573i	0.789144	+	0.455613i
$452$	−2.10587	−	2.18902i	−0.0990518	−	0.102963i
$453$	−9.04287	−	3.78683i	−0.424871	−	0.177921i
$454$	22.4904	−	16.9142i	1.05553	−	0.793823i
$455$	2.94043	−	2.01581i	0.137849	−	0.0945027i
$456$	−0.956115	+	29.0388i	−0.0447742	+	1.35987i
$457$	31.1086			1.45520			0.727600	−	0.686001i	$-0.240636\pi$
$457$	31.1086			1.45520			0.727600	+	0.686001i	$0.240636\pi$
$458$	−18.3721	−	7.81912i	−0.858470	−	0.365363i
$459$	−27.4121	−	3.93382i	−1.27949	−	0.183615i
$460$	−0.417085	+	0.401243i	−0.0194467	+	0.0187080i
$461$	19.2187	+	11.0959i	0.895103	+	0.516788i	0.875608	−	0.483022i	$-0.160461\pi$
$461$	19.2187	+	11.0959i	0.895103	+	0.516788i	0.0194945	+	0.999810i	$0.493794\pi$
$462$	3.87479	+	11.4767i	0.180272	+	0.533943i
$463$	−18.6891	−	32.3704i	−0.868555	−	1.50438i	−0.863473	−	0.504395i	$-0.831716\pi$
$463$	−18.6891	−	32.3704i	−0.868555	−	1.50438i	−0.00508254	−	0.999987i	$-0.501618\pi$
$464$	−0.0572190	−	0.00221629i	−0.00265632	−	0.000102888i
$465$	−2.66820	+	0.340755i	−0.123735	+	0.0158021i
$466$	1.82813	+	2.43083i	0.0846866	+	0.112606i
$467$	−18.5047	+	10.6837i	−0.856296	+	0.494383i	−0.862770	−	0.505596i	$-0.831273\pi$
$467$	−18.5047	+	10.6837i	−0.856296	+	0.494383i	0.00647422	+	0.999979i	$0.497939\pi$
$468$	−15.6034	−	28.8019i	−0.721266	−	1.33137i
$469$	2.94521	+	4.29611i	0.135997	+	0.198376i
$470$	−2.96120	−	1.26028i	−0.136590	−	0.0581325i
$471$	9.69503	+	12.7368i	0.446724	+	0.586880i
$472$	−12.4770	−	32.7833i	−0.574302	−	1.50897i
$473$	−19.8669			−0.913479
$474$	8.16636	−	7.94789i	0.375093	−	0.365059i
$475$	−25.3680	−	14.6462i	−1.16396	−	0.672014i
$476$	8.86593	+	26.7712i	0.406369	+	1.22705i
$477$	14.3603	−	14.1393i	0.657515	−	0.647394i
$478$	17.7813	+	23.6434i	0.813297	+	1.08142i
$479$	−1.16842	−	2.02377i	−0.0533866	−	0.0924683i	0.838097	−	0.545521i	$-0.183668\pi$
$479$	−1.16842	−	2.02377i	−0.0533866	−	0.0924683i	−0.891484	+	0.453053i	$0.850335\pi$
$480$	1.79697	−	1.61829i	0.0820199	−	0.0738643i
$481$	−29.0150	+	50.2554i	−1.32297	+	2.29145i
$482$	−3.35091	−	4.45562i	−0.152630	−	0.202948i
$483$	3.57494	+	4.01095i	0.162665	+	0.182505i
$484$	−4.16560	+	14.4235i	−0.189345	+	0.655613i
$485$	0.881509	−	0.508940i	0.0400273	−	0.0231098i
$486$	21.4511	−	5.08446i	0.973040	−	0.230636i
$487$	3.39056	−	5.87262i	0.153641	−	0.266114i	−0.778922	−	0.627120i	$-0.784233\pi$
$487$	3.39056	−	5.87262i	0.153641	−	0.266114i	0.932563	+	0.361006i	$0.117567\pi$
$488$	−2.80566	−	7.37184i	−0.127006	−	0.333708i
$489$	−1.60769	+	3.83912i	−0.0727021	+	0.173611i
$490$	1.70306	−	1.75196i	0.0769366	−	0.0791453i
$491$	−6.61633	+	3.81994i	−0.298591	+	0.172391i	−0.641810	−	0.766864i	$-0.721816\pi$
$491$	−6.61633	+	3.81994i	−0.298591	+	0.172391i	0.343219	+	0.939255i	$0.388483\pi$
$492$	−35.4400	−	5.50620i	−1.59776	−	0.248239i
$493$	−0.0660728	+	0.0381472i	−0.00297577	+	0.00171806i
$494$	−17.9319	+	42.1333i	−0.806793	+	1.89567i
$495$	0.368548	−	1.33397i	0.0165650	−	0.0599575i
$496$	22.2677	−	11.7314i	0.999850	−	0.526756i
$497$	−19.1771	+	13.1469i	−0.860212	+	0.589719i
$498$	10.6677	−	2.70395i	0.478030	−	0.121167i
$499$	6.32647	+	3.65259i	0.283212	+	0.163512i	0.634876	−	0.772614i	$-0.281051\pi$
$499$	6.32647	+	3.65259i	0.283212	+	0.163512i	−0.351665	+	0.936126i	$0.614384\pi$
$500$	1.17784	+	4.76268i	0.0526748	+	0.212994i
$501$	6.25074	+	2.61759i	0.279263	+	0.116945i
$502$	0.263271	+	2.16118i	0.0117504	+	0.0964581i
$503$	2.20140			0.0981554			0.0490777	−	0.998795i	$-0.484372\pi$
$503$	2.20140			0.0981554			0.0490777	+	0.998795i	$0.484372\pi$
$504$	−14.3778	−	17.2417i	−0.640440	−	0.768008i
$505$	−2.88247			−0.128268
$506$	−0.374765	−	3.07642i	−0.0166603	−	0.136764i
$507$	−3.68750	−	28.8742i	−0.163768	−	1.28235i
$508$	−12.1553	+	3.00610i	−0.539306	+	0.133374i
$509$	−17.8227	−	10.2899i	−0.789978	−	0.456094i	0.0499769	−	0.998750i	$-0.484085\pi$
$509$	−17.8227	−	10.2899i	−0.789978	−	0.456094i	−0.839955	+	0.542656i	$0.817419\pi$
$510$	0.876033	−	3.10064i	0.0387914	−	0.137299i
$511$	0.364569	+	4.70298i	0.0161276	+	0.208048i
$512$	−10.4450	+	20.0724i	−0.461607	+	0.887085i
$513$	−24.2289	−	19.0434i	−1.06973	−	0.840785i
$514$	−1.44750	+	3.40110i	−0.0638467	+	0.150016i
$515$	2.51268	−	1.45069i	0.110722	−	0.0639252i
$516$	34.3358	−	13.2964i	1.51155	−	0.585342i
$517$	14.9245	−	8.61664i	0.656377	−	0.378959i
$518$	−12.6997	+	37.6888i	−0.557993	+	1.65595i
$519$	−10.2179	−	13.4236i	−0.448514	−	0.589232i
$520$	3.56195	−	1.35565i	0.156202	−	0.0594490i
$521$	9.03080	−	15.6418i	0.395647	−	0.685280i	−0.597537	−	0.801841i	$-0.703854\pi$
$521$	9.03080	−	15.6418i	0.395647	−	0.685280i	0.993183	+	0.116562i	$0.0371872\pi$
$522$	0.0378078	−	0.0475327i	0.00165480	−	0.00208045i
$523$	35.0286	−	20.2238i	1.53169	−	0.884323i	0.532409	−	0.846487i	$-0.321287\pi$
$523$	35.0286	−	20.2238i	1.53169	−	0.884323i	0.999284	−	0.0378360i	$-0.0120464\pi$
$524$	25.8408	+	7.46301i	1.12886	+	0.326023i
$525$	22.1626	−	4.59387i	0.967256	−	0.200493i
$526$	−4.06616	−	5.40668i	−0.177293	−	0.235743i
$527$	16.7673	−	29.0418i	0.730393	−	1.26508i
$528$	1.14205	+	12.8990i	0.0497015	+	0.561358i
$529$	10.8127	+	18.7281i	0.470116	+	0.814265i
$530$	1.40932	+	1.87395i	0.0612171	+	0.0813990i
$531$	35.8616	+	9.90783i	1.55626	+	0.429963i
$532$	−6.35134	+	30.7331i	−0.275366	+	1.33245i
$533$	−48.9513	−	28.2620i	−2.12032	−	1.22416i
$534$	−31.6495	−	8.94204i	−1.36961	−	0.386960i
$535$	0.506281			0.0218884
$536$	1.98067	+	5.20419i	0.0855519	+	0.224787i
$537$	32.8006	−	4.18894i	1.41545	−	0.180766i
$538$	−13.4116	−	5.70796i	−0.578215	−	0.246087i
$539$	2.01634	+	12.9274i	0.0868501	+	0.556821i
$540$	0.255834	+	2.55215i	0.0110093	+	0.109827i
$541$	28.5785	−	16.4998i	1.22869	−	0.709383i	0.261932	−	0.965086i	$-0.415640\pi$
$541$	28.5785	−	16.4998i	1.22869	−	0.709383i	0.966755	+	0.255703i	$0.0823069\pi$
$542$	−6.55857	−	8.72078i	−0.281715	−	0.374589i
$543$	−11.5779	−	15.2103i	−0.496854	−	0.652739i
$544$	2.48462	+	30.0456i	0.106527	+	1.28820i
$545$	1.23509	+	2.13925i	0.0529056	+	0.0916352i
$546$	−11.3180	−	33.5224i	−0.484364	−	1.43463i
$547$	26.3987	+	15.2413i	1.12873	+	0.651672i	0.943615	−	0.331045i	$-0.107401\pi$
$547$	26.3987	+	15.2413i	1.12873	+	0.651672i	0.185114	+	0.982717i	$0.440735\pi$
$548$	−1.06907	−	1.11128i	−0.0456684	−	0.0474715i
$549$	8.06406	+	2.22793i	0.344166	+	0.0950859i
$550$	−12.0128	−	5.11262i	−0.512227	−	0.218003i
$551$	−0.0849013			−0.00361692
$552$	2.70668	+	5.06614i	0.115204	+	0.215629i
$553$	10.1520	−	6.95973i	0.431708	−	0.295958i
$554$	24.4861	−	18.4151i	1.04032	−	0.782383i
$555$	3.61561	−	2.75215i	0.153474	−	0.116822i
$556$	−0.0450406	+	0.0433298i	−0.00191015	+	0.00183759i
$557$	10.3874	+	5.99718i	0.440129	+	0.254108i	0.703652	−	0.710544i	$-0.251551\pi$
$557$	10.3874	+	5.99718i	0.440129	+	0.254108i	−0.263523	+	0.964653i	$0.584885\pi$
$558$	−3.94538	+	26.4026i	−0.167021	+	1.11771i
$559$	58.0295			2.45439
$560$	2.20991	−	1.39244i	0.0933859	−	0.0588412i
$561$	10.4501	+	13.7288i	0.441205	+	0.579630i
$562$	−1.21604	+	2.85724i	−0.0512955	+	0.120526i
$563$		−	35.8607i		−	1.51135i	−0.654947	−	0.755675i	$-0.727309\pi$
$563$		−	35.8607i		−	1.51135i	0.654947	−	0.755675i	$-0.272691\pi$
$564$	−20.0269	+	24.8807i	−0.843286	+	1.04767i
$565$			0.374847i			0.0157699i
$566$	−3.57941	−	29.3831i	−0.150454	−	1.23506i
$567$	23.7662	−	1.47187i	0.998088	−	0.0618127i
$568$	−23.2306	+	8.84137i	−0.974736	+	0.370976i
$569$	23.3603			0.979315			0.489658	−	0.871915i	$-0.337122\pi$
$569$	23.3603			0.979315			0.489658	+	0.871915i	$0.337122\pi$
$570$	2.56947	−	2.50073i	0.107623	−	0.104744i
$571$		−	10.8742i		−	0.455070i	−0.973770	−	0.227535i	$-0.926933\pi$
$571$		−	10.8742i		−	0.455070i	0.973770	−	0.227535i	$-0.0730666\pi$
$572$	−5.66270	+	19.6072i	−0.236770	+	0.819820i
$573$	−3.64896	+	2.77753i	−0.152438	+	0.116033i
$574$	−36.7107	−	12.3701i	−1.53227	−	0.516320i
$575$	−5.79088			−0.241496
$576$	−10.6068	−	21.5289i	−0.441950	−	0.897039i
$577$	12.7926	−	22.1575i	0.532564	−	0.922429i	−0.466713	−	0.884409i	$-0.654562\pi$
$577$	12.7926	−	22.1575i	0.532564	−	0.922429i	0.999277	−	0.0380196i	$-0.0121049\pi$
$578$	9.69326	+	12.8889i	0.403186	+	0.536107i
$579$	−1.86208	+	1.41738i	−0.0773852	+	0.0589044i
$580$	0.00489909	+	0.00509252i	0.000203423	+	0.000211455i
$581$	11.8512	−	0.918694i	0.491673	−	0.0381139i
$582$	−2.48206	−	9.79230i	−0.102885	−	0.405904i
$583$	−12.5559			−0.520012
$584$	−0.803084	+	4.97842i	−0.0332319	+	0.206009i
$585$	−1.07650	+	3.89642i	−0.0445078	+	0.161097i
$586$	0.946271	−	0.711655i	0.0390901	−	0.0293982i
$587$	14.1601	+	8.17531i	0.584448	+	0.337431i	0.762899	−	0.646518i	$-0.223775\pi$
$587$	14.1601	+	8.17531i	0.584448	+	0.337431i	−0.178451	+	0.983949i	$0.557109\pi$
$588$	−12.1368	−	20.9928i	−0.500514	−	0.865729i
$589$	32.3180	−	18.6588i	1.33164	−	0.768824i
$590$	−1.69517	+	3.98302i	−0.0697890	+	0.163978i
$591$	−16.2235	−	21.3136i	−0.667347	−	0.876722i
$592$	−22.6676	+	35.9703i	−0.931634	+	1.47837i
$593$	−15.7408	−	27.2639i	−0.646398	−	1.11959i	−0.983977	−	0.178297i	$-0.942941\pi$
$593$	−15.7408	−	27.2639i	−0.646398	−	1.11959i	0.337578	−	0.941297i	$-0.390392\pi$
$594$	−11.7458	−	7.11943i	−0.481936	−	0.292114i
$595$	1.50195	−	3.13939i	0.0615738	−	0.128703i
$596$	29.7155	+	8.58204i	1.21719	+	0.351534i
$597$	3.92881	+	30.7637i	0.160796	+	1.25908i
$598$	1.09466	+	8.98598i	0.0447639	+	0.367464i
$599$	−33.3343			−1.36200			−0.681001	−	0.732283i	$-0.738455\pi$
$599$	−33.3343			−1.36200			−0.681001	+	0.732283i	$0.738455\pi$
$600$	24.1834	+	0.796247i	0.987282	+	0.0325067i
$601$	19.5850	−	33.9222i	0.798888	−	1.38371i	−0.121454	−	0.992597i	$-0.538756\pi$
$601$	19.5850	−	33.9222i	0.798888	−	1.38371i	0.920341	−	0.391117i	$-0.127911\pi$
$602$	38.9889	−	7.84604i	1.58907	−	0.319781i
$603$	−5.69287	−	1.57282i	−0.231831	−	0.0640503i
$604$	−7.84830	−	8.15817i	−0.319343	−	0.331951i
$605$	1.60447	−	0.926344i	0.0652312	−	0.0376612i
$606$	−7.77798	+	27.5295i	−0.315959	+	1.11831i
$607$	10.3616	−	17.9468i	0.420563	−	0.728437i	−0.575432	−	0.817850i	$-0.695166\pi$
$607$	10.3616	−	17.9468i	0.420563	−	0.728437i	0.995995	+	0.0894134i	$0.0284992\pi$
$608$	−14.3231	+	30.3382i	−0.580879	+	1.23038i
$609$	0.0489728	−	0.0436492i	0.00198448	−	0.00176875i
$610$	−0.381186	+	0.895646i	−0.0154338	+	0.0362636i
$611$	−43.5931	+	25.1685i	−1.76359	+	1.01821i
$612$	−27.2493	−	16.7334i	−1.10149	−	0.676406i
$613$	8.53195	+	4.92592i	0.344602	+	0.198956i	0.662305	−	0.749234i	$-0.269578\pi$
$613$	8.53195	+	4.92592i	0.344602	+	0.198956i	−0.317703	+	0.948190i	$0.602912\pi$
$614$	−0.417923	−	3.43070i	−0.0168660	−	0.138452i
$615$	2.68072	+	3.52178i	0.108097	+	0.142012i
$616$	−1.15361	+	13.9394i	−0.0464804	+	0.561634i
$617$	−15.8841	−	27.5121i	−0.639471	−	1.10760i	−0.985549	−	0.169391i	$-0.945820\pi$
$617$	−15.8841	−	27.5121i	−0.639471	−	1.10760i	0.346078	−	0.938206i	$-0.387513\pi$
$618$	−7.07494	−	27.9122i	−0.284596	−	1.12279i
$619$	−34.1177	+	19.6979i	−1.37131	+	0.791724i	−0.991092	−	0.133175i	$-0.957483\pi$
$619$	−34.1177	+	19.6979i	−1.37131	+	0.791724i	−0.380213	+	0.924899i	$0.624149\pi$
$620$	−2.98404	−	0.861812i	−0.119842	−	0.0346112i
$621$	−6.03050	−	0.865417i	−0.241996	−	0.0347280i
$622$	12.2986	−	1.49820i	0.493129	−	0.0600723i
$623$	−32.0451	−	15.3310i	−1.28386	−	0.614224i
$624$	−3.33584	−	37.6770i	−0.133541	−	1.50829i
$625$	−12.0450	+	20.8625i	−0.481799	+	0.834501i
$626$	12.1260	−	1.47717i	0.484652	−	0.0590395i
$627$	2.43226	+	19.0453i	0.0971352	+	0.760596i
$628$	4.43732	+	17.9426i	0.177068	+	0.715986i
$629$			56.6484i			2.25872i
$630$	−0.196455	+	2.76348i	−0.00782693	+	0.110100i
$631$	24.5273			0.976416			0.488208	−	0.872727i	$-0.337651\pi$
$631$	24.5273			0.976416			0.488208	+	0.872727i	$0.337651\pi$
$632$	12.2979	−	4.68046i	0.489183	−	0.186179i
$633$	2.52689	−	6.03417i	0.100435	−	0.239837i
$634$	−2.41909	−	19.8581i	−0.0960743	−	0.788668i
$635$	1.33821	+	0.772615i	0.0531052	+	0.0306603i
$636$	21.7003	−	8.40337i	0.860472	−	0.333215i
$637$	−5.88958	−	37.7598i	−0.233354	−	1.49610i
$638$	−0.0375624	+	0.00457580i	−0.00148711	+	0.000181158i
$639$	7.02081	−	25.4120i	0.277739	−	1.00528i
$640$	2.64622	−	0.891490i	0.104601	−	0.0352392i
$641$	15.8286	+	27.4159i	0.625192	+	1.08286i	0.988504	+	0.151197i	$0.0483127\pi$
$641$	15.8286	+	27.4159i	0.625192	+	1.08286i	−0.363311	+	0.931668i	$0.618354\pi$
$642$	1.36613	−	4.83531i	0.0539170	−	0.190835i
$643$	−1.66533	+	0.961476i	−0.0656740	+	0.0379169i	−0.532477	−	0.846444i	$-0.678739\pi$
$643$	−1.66533	+	0.961476i	−0.0656740	+	0.0379169i	0.466803	+	0.884361i	$0.345406\pi$
$644$	1.95045	+	5.88950i	0.0768586	+	0.232079i
$645$	−4.19120	−	1.75512i	−0.165028	−	0.0691079i
$646$	5.40536	+	44.3723i	0.212671	+	1.74580i
$647$	−5.35164	+	9.26931i	−0.210395	+	0.364414i	−0.951838	−	0.306601i	$-0.900808\pi$
$647$	−5.35164	+	9.26931i	−0.210395	+	0.364414i	0.741443	+	0.671015i	$0.234142\pi$
$648$	25.0651	+	4.44328i	0.984649	+	0.174548i
$649$	−11.5900	−	20.0745i	−0.454947	−	0.787991i
$650$	35.0883	+	14.9336i	1.37628	+	0.585742i
$651$	−9.04889	+	27.3780i	−0.354654	+	1.07303i
$652$	−3.46352	+	3.33197i	−0.135642	+	0.130490i
$653$	−24.5277	−	14.1611i	−0.959844	−	0.554166i	−0.0637191	−	0.997968i	$-0.520296\pi$
$653$	−24.5277	−	14.1611i	−0.959844	−	0.554166i	−0.896125	+	0.443802i	$0.853630\pi$
$654$	23.7639	−	6.02347i	0.929244	−	0.235536i
$655$	−1.65962	−	2.87455i	−0.0648468	−	0.112318i
$656$	−35.0369	−	22.0794i	−1.36796	−	0.862055i
$657$	−3.75264	−	3.81131i	−0.146404	−	0.148693i
$658$	−25.8864	+	22.8044i	−1.00916	+	0.889008i
$659$	−39.6810	−	22.9098i	−1.54575	−	0.892440i	−0.998459	−	0.0554980i	$-0.982325\pi$
$659$	−39.6810	−	22.9098i	−1.54575	−	0.892440i	−0.547292	−	0.836942i	$-0.684341\pi$
$660$	1.00202	−	1.24487i	0.0390035	−	0.0484564i
$661$			36.3355i			1.41329i	0.707570	+	0.706643i	$0.249791\pi$
$661$			36.3355i			1.41329i	−0.707570	+	0.706643i	$0.750209\pi$
$662$	1.94206	+	15.9423i	0.0754804	+	0.619614i
$663$	−30.5240	−	40.1007i	−1.18545	−	1.55738i
$664$	12.5453	+	2.02373i	0.486854	+	0.0785358i
$665$	3.19424	−	2.18982i	0.123867	−	0.0849174i
$666$	−16.5285	−	41.9578i	−0.640467	−	1.62583i
$667$	−0.0145356	+	0.00839216i	−0.000562822	+	0.000324946i
$668$	5.42501	+	5.63921i	0.209900	+	0.218188i
$669$	0.882630	+	6.91124i	0.0341244	+	0.267204i
$670$	0.269100	−	0.632286i	0.0103962	−	0.0244274i
$671$	−2.60619	−	4.51406i	−0.100611	−	0.174263i
$672$	−7.33551	−	24.8634i	−0.282974	−	0.959128i
$673$	−22.5166	+	38.9999i	−0.867952	+	1.50334i	−0.00386641	+	0.999993i	$0.501231\pi$
$673$	−22.5166	+	38.9999i	−0.867952	+	1.50334i	−0.864086	+	0.503345i	$0.832103\pi$
$674$	−11.9176	−	15.8465i	−0.459048	−	0.610386i
$675$	−15.8592	+	20.1777i	−0.610421	+	0.776639i
$676$	9.32616	−	32.2920i	0.358698	−	1.24200i
$677$			14.3514i			0.551569i	0.961220	+	0.275784i	$0.0889375\pi$
$677$			14.3514i			0.551569i	−0.961220	+	0.275784i	$0.911062\pi$
$678$	3.58003	+	1.01148i	0.137490	+	0.0388455i
$679$	−0.843306	−	10.8787i	−0.0323631	−	0.417488i
$680$	2.34961	−	2.88465i	0.0901035	−	0.110621i
$681$	−13.3127	+	31.7905i	−0.510144	+	1.21821i
$682$	13.2927	−	9.99692i	0.509002	−	0.382802i
$683$	32.4429	+	18.7309i	1.24139	+	0.716718i	0.969377	−	0.245576i	$-0.0789770\pi$
$683$	32.4429	+	18.7309i	1.24139	+	0.716718i	0.272014	+	0.962293i	$0.412310\pi$
$684$	−16.9502	−	31.2880i	−0.648108	−	1.19633i
$685$			0.190295i			0.00727081i
$686$	−9.06251	−	24.5738i	−0.346008	−	0.938231i
$687$	24.2572	−	3.09786i	0.925468	−	0.118191i
$688$	42.4847	+	1.64557i	1.61971	+	0.0627370i
$689$	36.6748			1.39720
$690$	0.192722	−	0.682123i	0.00733681	−	0.0259680i
$691$		−	6.44426i		−	0.245151i	−0.992459	−	0.122576i	$-0.960885\pi$
$691$		−	6.44426i		−	0.245151i	0.992459	−	0.122576i	$-0.0391154\pi$
$692$	−4.67661	−	18.9101i	−0.177778	−	0.718856i
$693$	−11.1945	−	9.73525i	−0.425244	−	0.369812i
$694$	−1.08804	−	8.93168i	−0.0413016	−	0.339042i
$695$	0.00771275			0.000292561
$696$	0.0618564	−	0.0330480i	0.00234466	−	0.00125268i
$697$	−55.1784			−2.09003
$698$	6.64655	+	2.82876i	0.251576	+	0.107070i
$699$	−3.43600	−	1.43887i	−0.129962	−	0.0544232i
$700$	25.5943	+	5.28936i	0.967375	+	0.199919i
$701$			9.34965i			0.353131i	0.984289	+	0.176566i	$0.0564988\pi$
$701$			9.34965i			0.353131i	−0.984289	+	0.176566i	$0.943501\pi$
$702$	34.3085	+	20.7953i	1.29489	+	0.784867i
$703$	−31.5196	+	54.5935i	−1.18878	+	2.05903i
$704$	−4.70180	+	14.1943i	−0.177206	+	0.534968i
$705$	3.90976	−	0.499312i	0.147250	−	0.0188052i
$706$	−18.1630	−	24.1508i	−0.683572	−	0.908929i
$707$	−13.3353	+	27.8736i	−0.501524	+	1.04829i
$708$	33.4663	+	26.9377i	1.25774	+	1.01238i
$709$		−	39.7884i		−	1.49428i	−0.664664	−	0.747142i	$-0.731425\pi$
$709$		−	39.7884i		−	1.49428i	0.664664	−	0.747142i	$-0.268575\pi$
$710$	2.82242	+	1.20122i	0.105923	+	0.0450809i
$711$	−3.71669	+	13.4526i	−0.139387	+	0.504514i
$712$	−29.4448	−	23.9835i	−1.10349	−	0.898819i
$713$	3.68870	−	6.38902i	0.138143	−	0.239271i
$714$	−25.9304	−	22.8158i	−0.970422	−	0.853861i
$715$	2.18112	−	1.25927i	0.0815692	−	0.0470940i
$716$	36.6832	+	10.5944i	1.37092	+	0.395930i
$717$	−33.4202	−	13.9952i	−1.24810	−	0.522660i
$718$	12.8755	+	17.1203i	0.480511	+	0.638924i
$719$	6.14870	+	10.6499i	0.229308	+	0.397173i	0.957603	−	0.288090i	$-0.0930204\pi$
$719$	6.14870	+	10.6499i	0.229308	+	0.397173i	−0.728295	+	0.685264i	$0.759687\pi$
$720$	−0.898622	+	2.82212i	−0.0334897	+	0.105174i
$721$	−2.40378	−	31.0090i	−0.0895215	−	1.15484i
$722$	−8.95723	+	21.0462i	−0.333354	+	0.783258i
$723$	6.29808	+	2.63741i	0.234228	+	0.0980864i
$724$	−5.29908	−	21.4271i	−0.196939	−	0.796333i
$725$			0.0707053i			0.00262593i
$726$	−4.51772	−	17.8234i	−0.167668	−	0.661489i
$727$	−9.42711	+	16.3282i	−0.349632	+	0.605581i	−0.986184	−	0.165653i	$-0.947027\pi$
$727$	−9.42711	+	16.3282i	−0.349632	+	0.605581i	0.636552	+	0.771234i	$0.280360\pi$
$728$	3.36961	−	40.7158i	0.124886	−	1.50903i
$729$	−19.5309	+	18.6425i	−0.723367	+	0.690464i
$730$	0.497354	−	0.374042i	0.0184079	−	0.0138439i
$731$	49.0586	−	28.3240i	1.81450	−	1.04760i
$732$	7.52542	+	6.05736i	0.278148	+	0.223887i
$733$	30.8654	+	17.8201i	1.14004	+	0.658201i	0.946440	−	0.322880i	$-0.104651\pi$
$733$	30.8654	+	17.8201i	1.14004	+	0.658201i	0.193598	+	0.981081i	$0.437984\pi$
$734$	20.7750	+	27.6240i	0.766819	+	1.01962i
$735$	−0.716682	+	2.90534i	−0.0264352	+	0.107165i
$736$	0.546602	+	6.60987i	0.0201480	+	0.243643i
$737$	1.83986	+	3.18673i	0.0677720	+	0.117385i
$738$	40.8689	−	16.0996i	1.50441	−	0.592634i
$739$	−23.5817	−	13.6149i	−0.867465	−	0.500831i	−0.000960259	−	1.00000i	$-0.500306\pi$
$739$	−23.5817	−	13.6149i	−0.867465	−	0.500831i	−0.866505	+	0.499168i	$0.833639\pi$
$740$	5.09339	−	1.25963i	0.187237	−	0.0463049i
$741$	−7.10444	−	55.6298i	−0.260988	−	2.04361i
$742$	24.6411	−	4.95871i	0.904603	−	0.182040i
$743$	4.04913	+	7.01330i	0.148548	+	0.257293i	0.930691	−	0.365806i	$-0.119207\pi$
$743$	4.04913	+	7.01330i	0.148548	+	0.257293i	−0.782143	+	0.623099i	$0.785873\pi$
$744$	−16.2829	+	26.1741i	−0.596961	+	0.959588i
$745$	−1.90847	−	3.30557i	−0.0699209	−	0.121107i
$746$	40.2695	+	17.1386i	1.47437	+	0.627490i
$747$	−9.60427	+	9.45644i	−0.351402	+	0.345993i
$748$	4.78293	+	19.3400i	0.174881	+	0.707142i
$749$	2.34222	−	4.89575i	0.0855829	−	0.178887i
$750$	−4.19088	−	4.30607i	−0.153029	−	0.157236i
$751$	1.03002	−	1.78404i	0.0375858	−	0.0651005i	−0.846621	−	0.532197i	$-0.821367\pi$
$751$	1.03002	−	1.78404i	0.0375858	−	0.0651005i	0.884206	+	0.467096i	$0.154700\pi$
$752$	−32.6292	+	17.1902i	−1.18986	+	0.626863i
$753$	−1.61502	−	2.12172i	−0.0588547	−	0.0773199i
$754$	0.109717	−	0.0133655i	0.00399565	−	0.000486744i
$755$			1.39700i			0.0508422i
$756$	25.8629	+	9.33317i	0.940626	+	0.339444i
$757$			19.6209i			0.713134i	0.934270	+	0.356567i	$0.116053\pi$
$757$			19.6209i			0.713134i	−0.934270	+	0.356567i	$0.883947\pi$
$758$	−1.36290	−	11.1879i	−0.0495026	−	0.406364i
$759$	2.29897	+	3.02026i	0.0834474	+	0.109628i
$760$	3.86942	−	1.47267i	0.140358	−	0.0534192i
$761$	1.12973	−	1.95675i	0.0409527	−	0.0709322i	−0.844823	−	0.535047i	$-0.820294\pi$
$761$	1.12973	−	1.95675i	0.0409527	−	0.0709322i	0.885775	+	0.464114i	$0.153627\pi$
$762$	10.9900	−	10.6960i	0.398125	−	0.387474i
$763$	26.4005	−	2.04654i	0.955763	−	0.0740896i
$764$	−5.14037	+	1.27125i	−0.185972	+	0.0459922i
$765$	0.991745	+	3.81950i	0.0358566	+	0.138094i
$766$	3.82690	−	8.99180i	0.138271	−	0.324887i
$767$	33.8534	+	58.6359i	1.22238	+	2.11722i
$768$	−1.37382	−	27.6787i	−0.0495733	−	0.998770i
$769$	5.98749	+	10.3706i	0.215914	+	0.373974i	0.953555	−	0.301219i	$-0.0973935\pi$
$769$	5.98749	+	10.3706i	0.215914	+	0.373974i	−0.737641	+	0.675193i	$0.764060\pi$
$770$	1.29519	−	1.14098i	0.0466754	−	0.0411182i
$771$	−0.573488	−	4.49057i	−0.0206537	−	0.161724i
$772$	−2.62315	+	0.648722i	−0.0944091	+	0.0233480i
$773$	7.73185	+	4.46398i	0.278095	+	0.160558i	0.632561	−	0.774511i	$-0.282004\pi$
$773$	7.73185	+	4.46398i	0.278095	+	0.160558i	−0.354466	+	0.935069i	$0.615337\pi$
$774$	−28.0720	+	35.2927i	−1.00903	+	1.26857i
$775$	−15.5390	−	26.9143i	−0.558176	−	0.966789i
$776$	1.85766	−	11.5159i	0.0666861	−	0.413396i
$777$	−9.88630	−	47.6954i	−0.354669	−	1.71106i
$778$	−42.5727	+	32.0173i	−1.52631	+	1.14788i
$779$	−53.1767	−	30.7016i	−1.90525	−	1.10000i
$780$	−2.92681	+	3.63616i	−0.104797	+	0.130195i
$781$	−14.2250	+	8.21281i	−0.509011	+	0.293877i
$782$	5.31145	+	7.06251i	0.189937	+	0.252555i
$783$	−0.0105666	+	0.0736311i	−0.000377618	+	0.00263136i
$784$	−3.24111	−	27.8118i	−0.115754	−	0.993278i
$785$	1.14046	−	1.97534i	0.0407049	−	0.0705029i
$786$	−31.9321	+	8.09386i	−1.13898	+	0.288698i
$787$		−	3.54971i		−	0.126534i	−0.997997	−	0.0632668i	$-0.979848\pi$
$787$		−	3.54971i		−	0.126534i	0.997997	−	0.0632668i	$-0.0201519\pi$
$788$	−7.42535	−	30.0249i	−0.264517	−	1.06959i
$789$	7.64241	+	3.20037i	0.272077	+	0.113936i
$790$	−1.49414	−	0.635903i	−0.0531590	−	0.0226244i
$791$	3.62478	+	1.73417i	0.128882	+	0.0616598i
$792$	−9.18548	−	12.9291i	−0.326392	−	0.459414i
$793$	7.61248	+	13.1852i	0.270327	+	0.468220i
$794$	2.72029	−	2.04583i	0.0965396	−	0.0726039i
$795$	−2.64885	−	1.10924i	−0.0939449	−	0.0393407i
$796$	−9.93648	+	34.4053i	−0.352189	+	1.21946i
$797$	−14.0042	+	8.08535i	−0.496056	+	0.286398i	−0.727083	−	0.686549i	$-0.759125\pi$
$797$	−14.0042	+	8.08535i	−0.496056	+	0.286398i	0.231028	+	0.972947i	$0.425791\pi$
$798$	−12.2949	−	36.4160i	−0.435236	−	1.28911i
$799$	−24.5693	+	42.5553i	−0.869200	+	1.50550i
$800$	25.2655	+	11.9282i	0.893269	+	0.421726i
$801$	38.9872	−	10.1232i	1.37754	−	0.357684i
$802$	19.5741	−	45.9920i	0.691187	−	1.62404i
$803$			3.33240i			0.117598i
$804$	−5.31262	−	4.27623i	−0.187361	−	0.150811i
$805$	0.330420	−	0.690648i	0.0116458	−	0.0243422i
$806$	−38.8268	+	29.2002i	−1.36762	+	1.02853i
$807$	17.7077	−	2.26144i	0.623341	−	0.0796065i
$808$	−20.8614	+	25.6118i	−0.733901	+	0.901019i
$809$	−7.73189	+	13.3920i	−0.271839	+	0.470838i	−0.969333	−	0.245752i	$-0.920965\pi$
$809$	−7.73189	+	13.3920i	−0.271839	+	0.470838i	0.697494	+	0.716591i	$0.254298\pi$
$810$	−1.84898	−	2.53962i	−0.0649666	−	0.0892331i
$811$			6.24515i			0.219297i	0.993970	+	0.109648i	$0.0349725\pi$
$811$			6.24515i			0.219297i	−0.993970	+	0.109648i	$0.965028\pi$
$812$	0.0719095	−	0.0238146i	0.00252353	−	0.000835729i
$813$	12.3269	+	5.16208i	0.432324	+	0.181042i
$814$	−11.0027	+	25.8523i	−0.385644	+	0.906121i
$815$	0.593093			0.0207752
$816$	−21.2101	−	30.2242i	−0.742503	−	1.05806i
$817$	63.0386			2.20544
$818$	−34.3990	+	4.19043i	−1.20273	+	0.146515i
$819$	32.6982	+	28.4359i	1.14257	+	0.993630i
$820$	1.22694	+	4.96121i	0.0428467	+	0.173253i
$821$			17.2711i			0.602766i	0.953503	+	0.301383i	$0.0974483\pi$
$821$			17.2711i			0.602766i	−0.953503	+	0.301383i	$0.902552\pi$
$822$	1.81745	+	0.513488i	0.0633907	+	0.0179100i
$823$	40.8571			1.42419			0.712094	−	0.702084i	$-0.247747\pi$
$823$	40.8571			1.42419			0.712094	+	0.702084i	$0.247747\pi$
$824$	5.29512	−	32.8251i	0.184464	−	1.14352i
$825$	15.8608	−	2.02557i	0.552203	−	0.0705214i
$826$	30.6735	+	34.8191i	1.06727	+	1.21151i
$827$		−	5.65493i		−	0.196641i	−0.995155	−	0.0983206i	$-0.968653\pi$
$827$		−	5.65493i		−	0.196641i	0.995155	−	0.0983206i	$-0.0313471\pi$
$828$	−5.99468	−	3.68125i	−0.208330	−	0.127932i
$829$	13.1244	+	7.57740i	0.455830	+	0.263174i	0.710289	−	0.703910i	$-0.248564\pi$
$829$	13.1244	+	7.57740i	0.455830	+	0.263174i	−0.254459	+	0.967084i	$0.581897\pi$
$830$	−0.942564	−	1.25330i	−0.0327169	−	0.0435028i
$831$	−14.4940	+	34.6114i	−0.502792	+	1.20066i
$832$	13.7336	−	41.4604i	0.476126	−	1.43738i
$833$	−23.4095	−	29.0477i	−0.811091	−	1.00644i
$834$	0.0208119	−	0.0736618i	0.000720657	−	0.00255070i
$835$		−	0.965657i		−	0.0334179i
$836$	−6.15151	+	21.2997i	−0.212754	+	0.736667i
$837$	−12.1598	−	30.3502i	−0.420303	−	1.04906i
$838$	9.87764	−	7.42861i	0.341218	−	0.256617i
$839$	−1.40726	+	2.43745i	−0.0485842	+	0.0841503i	−0.889295	−	0.457334i	$-0.848804\pi$
$839$	−1.40726	+	2.43745i	−0.0485842	+	0.0841503i	0.840711	+	0.541485i	$0.182138\pi$
$840$	−1.47484	+	2.83879i	−0.0508867	+	0.0979477i
$841$	−14.4999	−	25.1146i	−0.499996	−	0.866019i
$842$	1.46657	+	0.624170i	0.0505413	+	0.0215103i
$843$	−0.481784	−	3.77250i	−0.0165935	−	0.129932i
$844$	5.44382	−	5.23705i	0.187384	−	0.180267i
$845$	−3.59218	+	2.07395i	−0.123575	+	0.0713459i
$846$	5.78123	−	38.6881i	0.198763	−	1.33012i
$847$	−1.53494	−	19.8009i	−0.0527411	−	0.680366i
$848$	26.8504	+	1.04001i	0.922046	+	0.0357140i
$849$	21.9576	+	28.8467i	0.753584	+	0.990016i
$850$	36.9530	−	4.50155i	1.26748	−	0.154402i
$851$			12.4623i			0.427203i
$852$	19.0884	−	23.7146i	0.653956	−	0.812449i
$853$	28.8215	+	16.6401i	0.986830	+	0.569747i	0.904325	−	0.426844i	$-0.140375\pi$
$853$	28.8215	+	16.6401i	0.986830	+	0.569747i	0.0825050	+	0.996591i	$0.473708\pi$
$854$	6.89743	+	7.82963i	0.236025	+	0.267924i
$855$	−1.16942	+	4.23275i	−0.0399934	+	0.144757i
$856$	3.66412	−	4.49848i	0.125237	−	0.153755i
$857$	−11.4582	−	19.8462i	−0.391406	−	0.677935i	0.601229	−	0.799077i	$-0.294678\pi$
$857$	−11.4582	−	19.8462i	−0.391406	−	0.677935i	−0.992635	+	0.121142i	$0.961344\pi$
$858$	−6.14137	−	24.2291i	−0.209663	−	0.827167i
$859$	−0.518408	−	0.299303i	−0.0176879	−	0.0102121i	0.491130	−	0.871086i	$-0.336584\pi$
$859$	−0.518408	−	0.299303i	−0.0176879	−	0.0102121i	−0.508818	+	0.860874i	$0.669917\pi$
$860$	−3.63753	−	3.78115i	−0.124039	−	0.128936i
$861$	46.4576	−	9.62974i	1.58327	−	0.328181i
$862$	−14.5561	+	34.2015i	−0.495783	+	1.16491i
$863$	−12.0455	−	20.8635i	−0.410035	−	0.710201i	0.584858	−	0.811135i	$-0.301150\pi$
$863$	−12.0455	−	20.8635i	−0.410035	−	0.710201i	−0.994893	+	0.100935i	$0.967817\pi$
$864$	24.5283	+	16.1976i	0.834470	+	0.551053i
$865$	−1.20196	+	2.08186i	−0.0408680	+	0.0707854i
$866$	25.0186	−	3.04772i	0.850166	−	0.103566i
$867$	−18.2186	−	7.62931i	−0.618737	−	0.259105i
$868$	−22.1389	+	24.8687i	−0.751444	+	0.844100i
$869$	7.53046	−	4.34771i	0.255453	−	0.147486i
$870$	−0.00832857	−	0.00235310i	−0.000282365	−	7.97774e-5i
$871$	−5.37407	−	9.30817i	−0.182094	−	0.315395i
$872$	27.9467	+	4.50817i	0.946396	+	0.152666i
$873$	8.68045	+	8.81615i	0.293789	+	0.298382i
$874$	1.18915	+	9.76164i	0.0402235	+	0.330192i
$875$	−3.66983	−	5.35310i	−0.124063	−	0.180968i
$876$	−2.23029	−	5.75936i	−0.0753547	−	0.194591i
$877$	−42.8125	−	24.7178i	−1.44568	−	0.834662i	−0.447457	−	0.894306i	$-0.647670\pi$
$877$	−42.8125	−	24.7178i	−1.44568	−	0.834662i	−0.998220	+	0.0596437i	$0.981004\pi$
$878$	12.7501	−	1.55320i	0.430295	−	0.0524179i
$879$	−0.560125	+	1.33757i	−0.0188925	+	0.0451150i
$880$	1.63255	−	0.860087i	0.0550334	−	0.0289935i
$881$	−18.6267			−0.627550			−0.313775	−	0.949497i	$-0.601594\pi$
$881$	−18.6267			−0.627550			−0.313775	+	0.949497i	$0.601594\pi$
$882$	25.8141	+	14.6845i	0.869205	+	0.494452i
$883$		−	7.79292i		−	0.262253i	−0.991366	−	0.131126i	$-0.958141\pi$
$883$		−	7.79292i		−	0.262253i	0.991366	−	0.131126i	$-0.0418594\pi$
$884$	−13.9705	−	56.4907i	−0.469880	−	1.89999i
$885$	−0.671611	−	5.25890i	−0.0225759	−	0.176776i
$886$	−5.49964	−	45.1462i	−0.184764	−	1.51671i
$887$	13.9914	−	24.2339i	0.469786	−	0.813694i	−0.529617	−	0.848237i	$-0.677664\pi$
$887$	13.9914	−	24.2339i	0.469786	−	0.813694i	0.999403	+	0.0345431i	$0.0109976\pi$
$888$	1.71357	−	52.0441i	0.0575038	−	1.74649i
$889$	13.6622	−	9.36614i	0.458215	−	0.314130i
$890$	0.566714	+	4.65212i	0.0189963	+	0.155939i
$891$	16.8198	+	0.260929i	0.563486	+	0.00874146i
$892$	−2.23228	+	7.72934i	−0.0747424	+	0.258797i
$893$	−47.3561	+	27.3411i	−1.58471	+	0.914933i
$894$	−36.7201	+	9.30748i	−1.22810	+	0.311289i
$895$	−2.35597	−	4.08066i	−0.0787514	−	0.136401i
$896$	3.62157	−	29.7134i	0.120988	−	0.992654i
$897$	−6.71511	−	8.82193i	−0.224211	−	0.294556i
$898$	−44.2704	+	5.39295i	−1.47732	+	0.179965i
$899$	−0.0780085	−	0.0450382i	−0.00260173	−	0.00150211i
$900$	−26.0565	+	14.1161i	−0.868550	+	0.470535i
$901$	31.0051	−	17.9008i	1.03293	−	0.596362i
$902$	−25.1814	−	10.7172i	−0.838448	−	0.356842i
$903$	−36.3619	+	32.4092i	−1.21005	+	1.07851i
$904$	3.33065	+	2.71289i	0.110776	+	0.0902293i
$905$	−1.36195	+	2.35896i	−0.0452727	+	0.0784146i
$906$	13.3423	+	3.76964i	0.443268	+	0.125238i
$907$	−29.4750	+	17.0174i	−0.978701	+	0.565053i	−0.901878	−	0.431991i	$-0.857811\pi$
$907$	−29.4750	+	17.0174i	−0.978701	+	0.565053i	−0.0768232	+	0.997045i	$0.524478\pi$
$908$	−28.6803	+	27.5909i	−0.951789	+	0.915636i
$909$	−8.80535	−	33.9119i	−0.292055	−	1.12479i
$910$	−3.78314	+	3.33272i	−0.125410	+	0.110479i
$911$	−16.3116	+	28.2525i	−0.540427	+	0.936047i	0.458452	+	0.888719i	$0.348404\pi$
$911$	−16.3116	+	28.2525i	−0.540427	+	0.936047i	−0.998879	+	0.0473280i	$0.984929\pi$
$912$	−3.62379	−	40.9293i	−0.119996	−	1.35530i
$913$	8.39745			0.277915
$914$	−43.6714	+	5.31998i	−1.44452	+	0.175969i
$915$	−0.151022	−	1.18255i	−0.00499264	−	0.0390938i
$916$	27.1285	+	7.83490i	0.896351	+	0.258872i
$917$	−35.4749	+	2.74997i	−1.17148	+	0.0908120i
$918$	39.1548	+	0.834611i	1.29230	+	0.0275463i
$919$	20.2462	+	35.0675i	0.667861	+	1.15677i	0.978501	+	0.206242i	$0.0661234\pi$
$919$	20.2462	+	35.0675i	0.667861	+	1.15677i	−0.310640	+	0.950528i	$0.600543\pi$
$920$	0.516901	−	0.634606i	0.0170417	−	0.0209223i
$921$	2.56372	+	3.36807i	0.0844775	+	0.110982i
$922$	−28.8774	−	12.2902i	−0.951026	−	0.404756i
$923$	41.5501	−	23.9890i	1.36764	−	0.789606i
$924$	−7.40223	−	15.4487i	−0.243516	−	0.508225i
$925$	45.4651	+	26.2493i	1.49488	+	0.863072i
$926$	31.7722	+	42.2467i	1.04410	+	1.38831i
$927$	24.7430	+	25.1298i	0.812665	+	0.825370i
$928$	0.0807051	−	0.00667390i	0.00264927	−	0.000219081i
$929$	−11.2111			−0.367824			−0.183912	−	0.982943i	$-0.558876\pi$
$929$	−11.2111			−0.367824			−0.183912	+	0.982943i	$0.558876\pi$
$930$	3.68745	−	0.934661i	0.120916	−	0.0306487i
$931$	−6.39796	−	41.0192i	−0.209685	−	1.34435i
$932$	−2.98210	−	3.09984i	−0.0976820	−	0.101539i
$933$	−12.0741	+	9.19060i	−0.395288	+	0.300887i
$934$	24.1505	−	18.1627i	0.790229	−	0.594302i
$935$	1.22929	−	2.12919i	0.0402020	−	0.0696320i
$936$	26.8300	+	37.7647i	0.876968	+	1.23438i
$937$	−17.4506			−0.570085			−0.285042	−	0.958515i	$-0.592008\pi$
$937$	−17.4506			−0.570085			−0.285042	+	0.958515i	$0.592008\pi$
$938$	−4.86928	−	5.52737i	−0.158988	−	0.180475i
$939$	−11.9046	+	9.06160i	−0.388492	+	0.295714i
$940$	4.37256	+	1.26283i	0.142617	+	0.0411888i
$941$			52.9672i			1.72668i	0.504622	+	0.863341i	$0.331632\pi$
$941$			52.9672i			1.72668i	−0.504622	+	0.863341i	$0.668368\pi$
$942$	−15.7884	−	16.2224i	−0.514414	−	0.528553i
$943$	−12.1389			−0.395298
$944$	23.1221	+	43.8886i	0.752559	+	1.42845i
$945$	−1.50158	−	3.04276i	−0.0488465	−	0.0989810i
$946$	27.8898	−	3.39749i	0.906776	−	0.110462i
$947$			16.3803i			0.532287i	0.963933	+	0.266143i	$0.0857495\pi$
$947$			16.3803i			0.532287i	−0.963933	+	0.266143i	$0.914251\pi$
$948$	−10.1050	+	12.5541i	−0.328196	+	0.407738i
$949$		−	9.73366i		−	0.315968i
$950$	38.1172	+	16.2226i	1.23668	+	0.526331i
$951$	14.8397	+	19.4956i	0.481212	+	0.632189i
$952$	−17.0245	−	36.0661i	−0.551768	−	1.16891i
$953$	13.8276			0.447919			0.223960	−	0.974598i	$-0.428102\pi$
$953$	13.8276			0.447919			0.223960	+	0.974598i	$0.428102\pi$
$954$	−17.7416	+	22.3051i	−0.574404	+	0.722153i
$955$	0.565915	+	0.326731i	0.0183126	+	0.0105728i
$956$	−29.0053	−	30.1506i	−0.938099	−	0.975139i
$957$	0.0368767	−	0.0280699i	0.00119205	−	0.000907372i
$958$	1.98636	+	2.64122i	0.0641765	+	0.0853340i
$959$	1.84016	+	0.880369i	0.0594219	+	0.0284286i
$960$	−2.24590	+	2.57911i	−0.0724860	+	0.0832405i
$961$	8.59235			0.277173
$962$	32.1379	−	75.5123i	1.03617	−	2.43462i
$963$	1.54658	+	5.95634i	0.0498379	+	0.191940i
$964$	5.46609	+	5.68191i	0.176051	+	0.183002i
$965$	0.288788	+	0.166732i	0.00929642	+	0.00536729i
$966$	−5.70455	−	5.01935i	−0.183541	−	0.161495i
$967$	6.91834	+	11.9829i	0.222479	+	0.385345i	0.955560	−	0.294796i	$-0.0952518\pi$
$967$	6.91834	+	11.9829i	0.222479	+	0.385345i	−0.733081	+	0.680141i	$0.761919\pi$
$968$	3.38121	−	20.9606i	0.108676	−	0.673698i
$969$	−33.1588	−	43.5622i	−1.06522	−	1.39942i
$970$	−1.15046	+	0.865217i	−0.0369390	+	0.0277804i
$971$	30.5544	−	17.6406i	0.980538	−	0.566114i	0.0781058	−	0.996945i	$-0.475113\pi$
$971$	30.5544	−	17.6406i	0.980538	−	0.566114i	0.902433	+	0.430831i	$0.141779\pi$
$972$	−29.2443	+	10.8062i	−0.938010	+	0.346608i
$973$	0.0356817	−	0.0745825i	0.00114390	−	0.00239100i
$974$	−3.75550	+	8.82403i	−0.120334	+	0.282740i
$975$	−46.3282	+	5.91654i	−1.48369	+	0.189481i
$976$	5.19936	+	9.86905i	0.166428	+	0.315901i
$977$	−13.0646			−0.417975			−0.208988	−	0.977918i	$-0.567017\pi$
$977$	−13.0646			−0.417975			−0.208988	+	0.977918i	$0.567017\pi$
$978$	1.60039	−	5.66443i	0.0511747	−	0.181128i
$979$	−21.7335	−	12.5479i	−0.694607	−	0.401032i
$980$	−2.09121	+	2.75070i	−0.0668014	+	0.0878680i
$981$	−21.3950	+	21.0657i	−0.683091	+	0.672576i
$982$	8.63498	−	6.49405i	0.275553	−	0.207233i
$983$	0.366240	+	0.634345i	0.0116812	+	0.0202325i	0.871807	−	0.489850i	$-0.162948\pi$
$983$	0.366240	+	0.634345i	0.0116812	+	0.0202325i	−0.860126	+	0.510082i	$0.829615\pi$
$984$	50.6935	+	1.66911i	1.61605	+	0.0532091i
$985$	−1.90843	+	3.30551i	−0.0608078	+	0.105322i
$986$	0.0862317	−	0.0648517i	0.00274618	−	0.00206530i
$987$	13.2595	−	40.1174i	0.422053	−	1.27695i
$988$	17.9680	−	62.2148i	0.571640	−	1.97932i
$989$	10.7926	−	6.23111i	0.343185	−	0.198138i
$990$	−0.289255	+	1.93570i	−0.00919313	+	0.0615206i
$991$	−9.51755	+	16.4849i	−0.302335	+	0.523659i	−0.976664	−	0.214771i	$-0.931099\pi$
$991$	−9.51755	+	16.4849i	−0.302335	+	0.523659i	0.674329	+	0.738431i	$0.264433\pi$
$992$	−29.2540	+	20.2771i	−0.928815	+	0.643797i
$993$	−11.9135	−	15.6512i	−0.378062	−	0.496677i
$994$	24.6732	−	21.7356i	0.782588	−	0.689412i
$995$	3.82726	−	2.20967i	0.121332	−	0.0700512i
$996$	−14.5133	+	5.62022i	−0.459870	+	0.178083i
$997$	17.0655	−	9.85278i	0.540470	−	0.312041i	−0.204799	−	0.978804i	$-0.565654\pi$
$997$	17.0655	−	9.85278i	0.540470	−	0.312041i	0.745269	+	0.666763i	$0.232321\pi$
$998$	−9.50596	−	4.04573i	−0.300906	−	0.128065i
$999$	43.4236	+	34.1300i	1.37386	+	1.07983i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cq.a.277.4	yes	184
7.2	even	3		504.2.w.a.205.65	yes	184
8.5	even	2	inner	504.2.cq.a.277.3	yes	184
9.4	even	3		504.2.w.a.445.58	yes	184
56.37	even	6		504.2.w.a.205.58	✓	184
63.58	even	3	inner	504.2.cq.a.373.4	yes	184
72.13	even	6		504.2.w.a.445.65	yes	184
504.373	even	6	inner	504.2.cq.a.373.3	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.w.a.205.58	✓	184	56.37	even	6
504.2.w.a.205.65	yes	184	7.2	even	3
504.2.w.a.445.58	yes	184	9.4	even	3
504.2.w.a.445.65	yes	184	72.13	even	6
504.2.cq.a.277.3	yes	184	8.5	even	2	inner
504.2.cq.a.277.4	yes	184	1.1	even	1	trivial
504.2.cq.a.373.3	yes	184	504.373	even	6	inner
504.2.cq.a.373.4	yes	184	63.58	even	3	inner

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	504.2.cq.a.277.4

Level	$504$
Weight	$2$
Character	504.277
Analytic conductor	$4.024$
Analytic rank	$0$
Dimension	$184$
Inner twists	$4$