LMFDB - Embedded newform 585.2.i.e.391.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.1
Root			$-0.724143 + 0.165319i$ of defining polynomial
Character	$\chi$	$=$	585.391
Dual form			585.2.i.e.196.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22414 - 2.12028i) q^{2} +(-1.71693 + 0.228383i) q^{3} +(-1.99705 + 3.45900i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.58600 + 3.36079i) q^{6} +(1.96726 + 3.40740i) q^{7} +4.88214 q^{8} +(2.89568 - 0.784233i) q^{9} +O(q^{10})$	\(q+(-1.22414 - 2.12028i) q^{2} +(-1.71693 + 0.228383i) q^{3} +(-1.99705 + 3.45900i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.58600 + 3.36079i) q^{6} +(1.96726 + 3.40740i) q^{7} +4.88214 q^{8} +(2.89568 - 0.784233i) q^{9} -2.44829 q^{10} +(-2.33643 - 4.04682i) q^{11} +(2.63882 - 6.39494i) q^{12} +(0.500000 - 0.866025i) q^{13} +(4.81642 - 8.34228i) q^{14} +(-0.660679 + 1.60109i) q^{15} +(-1.98233 - 3.43350i) q^{16} -7.96946 q^{17} +(-5.20752 - 5.17964i) q^{18} -0.120966 q^{19} +(1.99705 + 3.45900i) q^{20} +(-4.15583 - 5.40096i) q^{21} +(-5.72025 + 9.90777i) q^{22} +(-0.164078 + 0.284192i) q^{23} +(-8.38229 + 1.11500i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.44829 q^{26} +(-4.79257 + 2.00779i) q^{27} -15.7149 q^{28} +(0.136463 + 0.236360i) q^{29} +(4.20353 - 0.559146i) q^{30} +(3.28806 - 5.69509i) q^{31} +(0.0288185 - 0.0499151i) q^{32} +(4.93571 + 6.41450i) q^{33} +(9.75576 + 16.8975i) q^{34} +3.93452 q^{35} +(-3.07017 + 11.5823i) q^{36} -7.43198 q^{37} +(0.148079 + 0.256481i) q^{38} +(-0.660679 + 1.60109i) q^{39} +(2.44107 - 4.22806i) q^{40} +(-0.0455066 + 0.0788197i) q^{41} +(-6.36421 + 15.4231i) q^{42} +(-3.89835 - 6.75213i) q^{43} +18.6639 q^{44} +(0.768676 - 2.89985i) q^{45} +0.803421 q^{46} +(5.78798 + 10.0251i) q^{47} +(4.18768 + 5.44235i) q^{48} +(-4.24023 + 7.34429i) q^{49} +(-1.22414 + 2.12028i) q^{50} +(13.6830 - 1.82009i) q^{51} +(1.99705 + 3.45900i) q^{52} -11.1782 q^{53} +(10.1239 + 7.70376i) q^{54} -4.67286 q^{55} +(9.60445 + 16.6354i) q^{56} +(0.207690 - 0.0276265i) q^{57} +(0.334099 - 0.578677i) q^{58} +(-2.77780 + 4.81129i) q^{59} +(-4.21877 - 5.48276i) q^{60} +(-6.63270 - 11.4882i) q^{61} -16.1002 q^{62} +(8.36875 + 8.32395i) q^{63} -8.07045 q^{64} +(-0.500000 - 0.866025i) q^{65} +(7.55850 - 18.3173i) q^{66} +(-3.41069 + 5.90749i) q^{67} +(15.9154 - 27.5663i) q^{68} +(0.216806 - 0.525410i) q^{69} +(-4.81642 - 8.34228i) q^{70} -6.32442 q^{71} +(14.1371 - 3.82874i) q^{72} -7.37048 q^{73} +(9.09780 + 15.7579i) q^{74} +(1.05625 + 1.37271i) q^{75} +(0.241575 - 0.418420i) q^{76} +(9.19274 - 15.9223i) q^{77} +(4.20353 - 0.559146i) q^{78} +(5.95876 + 10.3209i) q^{79} -3.96467 q^{80} +(7.76996 - 4.54178i) q^{81} +0.222826 q^{82} +(-0.774276 - 1.34108i) q^{83} +(26.9813 - 3.58901i) q^{84} +(-3.98473 + 6.90175i) q^{85} +(-9.54427 + 16.5312i) q^{86} +(-0.288277 - 0.374648i) q^{87} +(-11.4068 - 19.7571i) q^{88} -3.59499 q^{89} +(-7.08946 + 1.92003i) q^{90} +3.93452 q^{91} +(-0.655346 - 1.13509i) q^{92} +(-4.34470 + 10.5290i) q^{93} +(14.1706 - 24.5442i) q^{94} +(-0.0604829 + 0.104759i) q^{95} +(-0.0380796 + 0.0922823i) q^{96} +(-2.63979 - 4.57224i) q^{97} +20.7626 q^{98} +(-9.93921 - 9.88600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−1.22414	−	2.12028i	−0.865600	−	1.49926i	−0.866450	−	0.499263i	$-0.833604\pi$
$2$	−1.22414	−	2.12028i	−0.865600	−	1.49926i	0.000850327	−	1.00000i	$-0.499729\pi$
$3$	−1.71693	+	0.228383i	−0.991269	+	0.131857i
$3$	−1.71693	+	0.228383i	−0.991269	+	0.131857i
$4$	−1.99705	+	3.45900i	−0.998526	+	1.72950i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	2.58600	+	3.36079i	1.05573	+	1.37204i
$7$	1.96726	+	3.40740i	0.743555	+	1.28787i	0.950867	+	0.309600i	$0.100195\pi$
$7$	1.96726	+	3.40740i	0.743555	+	1.28787i	−0.207312	+	0.978275i	$0.566472\pi$
$8$	4.88214			1.72610
$9$	2.89568	−	0.784233i	0.965228	−	0.261411i
$10$	−2.44829			−0.774216
$11$	−2.33643	−	4.04682i	−0.704461	−	1.22016i	−0.966886	−	0.255209i	$-0.917856\pi$
$11$	−2.33643	−	4.04682i	−0.704461	−	1.22016i	0.262425	−	0.964952i	$-0.415478\pi$
$12$	2.63882	−	6.39494i	0.761762	−	1.84606i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	4.81642	−	8.34228i	1.28724	−	2.22957i
$15$	−0.660679	+	1.60109i	−0.170587	+	0.413401i
$16$	−1.98233	−	3.43350i	−0.495584	−	0.858376i
$17$	−7.96946			−1.93288			−0.966439	−	0.256897i	$-0.917300\pi$
$17$	−7.96946			−1.93288			−0.966439	+	0.256897i	$0.917300\pi$
$18$	−5.20752	−	5.17964i	−1.22742	−	1.22085i
$19$	−0.120966			−0.0277515			−0.0138757	−	0.999904i	$-0.504417\pi$
$19$	−0.120966			−0.0277515			−0.0138757	+	0.999904i	$0.504417\pi$
$20$	1.99705	+	3.45900i	0.446555	+	0.773455i
$21$	−4.15583	−	5.40096i	−0.906877	−	1.17859i
$22$	−5.72025	+	9.90777i	−1.21956	+	2.11234i
$23$	−0.164078	+	0.284192i	−0.0342127	+	0.0592581i	−0.882625	−	0.470078i	$-0.844226\pi$
$23$	−0.164078	+	0.284192i	−0.0342127	+	0.0592581i	0.848412	+	0.529336i	$0.177559\pi$
$24$	−8.38229	+	1.11500i	−1.71103	+	0.227598i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.44829			−0.480148
$27$	−4.79257	+	2.00779i	−0.922331	+	0.386400i
$28$	−15.7149			−2.96984
$29$	0.136463	+	0.236360i	0.0253405	+	0.0438910i	0.878418	−	0.477894i	$-0.158600\pi$
$29$	0.136463	+	0.236360i	0.0253405	+	0.0438910i	−0.853077	+	0.521785i	$0.825266\pi$
$30$	4.20353	−	0.559146i	0.767456	−	0.102086i
$31$	3.28806	−	5.69509i	0.590553	−	1.02287i	−0.403605	−	0.914933i	$-0.632243\pi$
$31$	3.28806	−	5.69509i	0.590553	−	1.02287i	0.994158	−	0.107934i	$-0.0344237\pi$
$32$	0.0288185	−	0.0499151i	0.00509444	−	0.00882383i
$33$	4.93571	+	6.41450i	0.859197	+	1.11662i
$34$	9.75576	+	16.8975i	1.67310	+	2.89789i
$35$	3.93452			0.665055
$36$	−3.07017	+	11.5823i	−0.511695	+	1.93039i
$37$	−7.43198			−1.22181			−0.610905	−	0.791704i	$-0.709194\pi$
$37$	−7.43198			−1.22181			−0.610905	+	0.791704i	$0.709194\pi$
$38$	0.148079	+	0.256481i	0.0240217	+	0.0416067i
$39$	−0.660679	+	1.60109i	−0.105793	+	0.256380i
$40$	2.44107	−	4.22806i	0.385967	−	0.668515i
$41$	−0.0455066	+	0.0788197i	−0.00710694	+	0.0123096i	−0.869557	−	0.493833i	$-0.835596\pi$
$41$	−0.0455066	+	0.0788197i	−0.00710694	+	0.0123096i	0.862450	+	0.506142i	$0.168929\pi$
$42$	−6.36421	+	15.4231i	−0.982019	+	2.37983i
$43$	−3.89835	−	6.75213i	−0.594492	−	1.02969i	−0.993618	−	0.112795i	$-0.964020\pi$
$43$	−3.89835	−	6.75213i	−0.594492	−	1.02969i	0.399126	−	0.916896i	$-0.369314\pi$
$44$	18.6639			2.81369
$45$	0.768676	−	2.89985i	0.114587	−	0.432284i
$46$	0.803421			0.118458
$47$	5.78798	+	10.0251i	0.844263	+	1.46231i	0.886260	+	0.463189i	$0.153295\pi$
$47$	5.78798	+	10.0251i	0.844263	+	1.46231i	−0.0419967	+	0.999118i	$0.513372\pi$
$48$	4.18768	+	5.44235i	0.604439	+	0.785536i
$49$	−4.24023	+	7.34429i	−0.605747	+	1.04918i
$50$	−1.22414	+	2.12028i	−0.173120	+	0.299853i
$51$	13.6830	−	1.82009i	1.91600	−	0.254863i
$52$	1.99705	+	3.45900i	0.276941	+	0.479677i
$53$	−11.1782			−1.53544			−0.767721	−	0.640784i	$-0.778609\pi$
$53$	−11.1782			−1.53544			−0.767721	+	0.640784i	$0.778609\pi$
$54$	10.1239	+	7.70376i	1.37769	+	1.04835i
$55$	−4.67286			−0.630089
$56$	9.60445	+	16.6354i	1.28345	+	2.22300i
$57$	0.207690	−	0.0276265i	0.0275092	−	0.00365922i
$58$	0.334099	−	0.578677i	0.0438694	−	0.0759840i
$59$	−2.77780	+	4.81129i	−0.361639	+	0.626376i	−0.988231	−	0.152971i	$-0.951116\pi$
$59$	−2.77780	+	4.81129i	−0.361639	+	0.626376i	0.626592	+	0.779347i	$0.284449\pi$
$60$	−4.21877	−	5.48276i	−0.544641	−	0.707821i
$61$	−6.63270	−	11.4882i	−0.849230	−	1.47091i	−0.881897	−	0.471443i	$-0.843733\pi$
$61$	−6.63270	−	11.4882i	−0.849230	−	1.47091i	0.0326669	−	0.999466i	$-0.489600\pi$
$62$	−16.1002			−2.04473
$63$	8.36875	+	8.32395i	1.05436	+	1.04872i
$64$	−8.07045			−1.00881
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	7.55850	−	18.3173i	0.930387	−	2.25471i
$67$	−3.41069	+	5.90749i	−0.416682	+	0.721715i	−0.995603	−	0.0936686i	$-0.970141\pi$
$67$	−3.41069	+	5.90749i	−0.416682	+	0.721715i	0.578921	+	0.815384i	$0.303474\pi$
$68$	15.9154	−	27.5663i	1.93003	−	3.34291i
$69$	0.216806	−	0.525410i	0.0261004	−	0.0632519i
$70$	−4.81642	−	8.34228i	−0.575672	−	0.997093i
$71$	−6.32442			−0.750570			−0.375285	−	0.926909i	$-0.622455\pi$
$71$	−6.32442			−0.750570			−0.375285	+	0.926909i	$0.622455\pi$
$72$	14.1371	−	3.82874i	1.66608	−	0.451221i
$73$	−7.37048			−0.862649			−0.431324	−	0.902197i	$-0.641954\pi$
$73$	−7.37048			−0.862649			−0.431324	+	0.902197i	$0.641954\pi$
$74$	9.09780	+	15.7579i	1.05760	+	1.83181i
$75$	1.05625	+	1.37271i	0.121965	+	0.158507i
$76$	0.241575	−	0.418420i	0.0277106	−	0.0479961i
$77$	9.19274	−	15.9223i	1.04761	−	1.81451i
$78$	4.20353	−	0.559146i	0.475956	−	0.0633108i
$79$	5.95876	+	10.3209i	0.670413	+	1.16119i	0.977787	+	0.209601i	$0.0672166\pi$
$79$	5.95876	+	10.3209i	0.670413	+	1.16119i	−0.307374	+	0.951589i	$0.599450\pi$
$80$	−3.96467			−0.443264
$81$	7.76996	−	4.54178i	0.863329	−	0.504642i
$82$	0.222826			0.0246071
$83$	−0.774276	−	1.34108i	−0.0849878	−	0.147203i	0.820398	−	0.571793i	$-0.193752\pi$
$83$	−0.774276	−	1.34108i	−0.0849878	−	0.147203i	−0.905386	+	0.424589i	$0.860418\pi$
$84$	26.9813	−	3.58901i	2.94391	−	0.391593i
$85$	−3.98473	+	6.90175i	−0.432205	+	0.748600i
$86$	−9.54427	+	16.5312i	−1.02918	+	1.78260i
$87$	−0.288277	−	0.374648i	−0.0309065	−	0.0401664i
$88$	−11.4068	−	19.7571i	−1.21597	−	2.10612i
$89$	−3.59499			−0.381068			−0.190534	−	0.981681i	$-0.561022\pi$
$89$	−3.59499			−0.381068			−0.190534	+	0.981681i	$0.561022\pi$
$90$	−7.08946	+	1.92003i	−0.747295	+	0.202389i
$91$	3.93452			0.412450
$92$	−0.655346	−	1.13509i	−0.0683245	−	0.118342i
$93$	−4.34470	+	10.5290i	−0.450525	+	1.09181i
$94$	14.1706	−	24.5442i	1.46159	−	2.53154i
$95$	−0.0604829	+	0.104759i	−0.00620542	+	0.0107481i
$96$	−0.0380796	+	0.0922823i	−0.00388648	+	0.00941852i
$97$	−2.63979	−	4.57224i	−0.268030	−	0.464241i	0.700323	−	0.713826i	$-0.253039\pi$
$97$	−2.63979	−	4.57224i	−0.268030	−	0.464241i	−0.968353	+	0.249585i	$0.919706\pi$
$98$	20.7626			2.09734
$99$	−9.93921	−	9.88600i	−0.998929	−	0.993580i
$100$	3.99411			0.399411
$101$	0.178545	+	0.309250i	0.0177659	+	0.0307715i	0.874772	−	0.484535i	$-0.161011\pi$
$101$	0.178545	+	0.309250i	0.0177659	+	0.0307715i	−0.857006	+	0.515307i	$0.827678\pi$
$102$	−20.6090	−	26.7837i	−2.04060	−	2.65198i
$103$	2.30623	−	3.99450i	0.227239	−	0.393590i	−0.729750	−	0.683714i	$-0.760363\pi$
$103$	2.30623	−	3.99450i	0.227239	−	0.393590i	0.956989	+	0.290125i	$0.0936968\pi$
$104$	2.44107	−	4.22806i	0.239367	−	0.414595i
$105$	−6.75529	+	0.898576i	−0.659249	+	0.0876920i
$106$	13.6837	+	23.7009i	1.32908	+	2.30203i
$107$	1.48003			0.143080			0.0715399	−	0.997438i	$-0.477209\pi$
$107$	1.48003			0.143080			0.0715399	+	0.997438i	$0.477209\pi$
$108$	2.62607	−	20.5872i	0.252693	−	1.98100i
$109$	−14.6820			−1.40628			−0.703140	−	0.711051i	$-0.748219\pi$
$109$	−14.6820			−1.40628			−0.703140	+	0.711051i	$0.748219\pi$
$110$	5.72025	+	9.90777i	0.545405	+	0.944669i
$111$	12.7602	−	1.69733i	1.21114	−	0.161104i
$112$	7.79954	−	13.5092i	0.736987	−	1.27650i
$113$	−3.53690	+	6.12609i	−0.332724	+	0.576294i	−0.983045	−	0.183365i	$-0.941301\pi$
$113$	−3.53690	+	6.12609i	−0.332724	+	0.576294i	0.650321	+	0.759659i	$0.274634\pi$
$114$	−0.312818	−	0.406541i	−0.0292981	−	0.0380760i
$115$	0.164078	+	0.284192i	0.0153004	+	0.0265010i
$116$	−1.09009			−0.101212
$117$	0.768676	−	2.89985i	0.0710641	−	0.268091i
$118$	13.6017			1.25214
$119$	−15.6780	−	27.1551i	−1.43720	−	2.48930i
$120$	−3.22553	+	7.81677i	−0.294449	+	0.713570i
$121$	−5.41783	+	9.38396i	−0.492530	+	0.853087i
$122$	−16.2387	+	28.1263i	−1.47019	+	2.54644i
$123$	0.0601305	−	0.145721i	0.00542178	−	0.0131392i
$124$	13.1329	+	22.7468i	1.17937	+	2.04272i
$125$	−1.00000			−0.0894427
$126$	7.40453	−	27.9338i	0.659648	−	2.48854i
$127$	1.23715			0.109779			0.0548896	−	0.998492i	$-0.482519\pi$
$127$	1.23715			0.109779			0.0548896	+	0.998492i	$0.482519\pi$
$128$	9.82175	+	17.0118i	0.868128	+	1.50364i
$129$	8.23525	+	10.7026i	0.725073	+	0.942312i
$130$	−1.22414	+	2.12028i	−0.107364	+	0.185961i
$131$	−6.37638	+	11.0442i	−0.557107	+	0.964938i	0.440629	+	0.897689i	$0.354755\pi$
$131$	−6.37638	+	11.0442i	−0.557107	+	0.964938i	−0.997736	+	0.0672484i	$0.978578\pi$
$132$	−32.0446	+	4.26251i	−2.78912	+	0.371004i
$133$	−0.237971	−	0.412178i	−0.0206347	−	0.0357404i
$134$	16.7007			1.44272
$135$	−0.657486	+	5.15439i	−0.0565874	+	0.443619i
$136$	−38.9080			−3.33634
$137$	−3.66450	−	6.34709i	−0.313079	−	0.542269i	0.665948	−	0.745998i	$-0.268027\pi$
$137$	−3.66450	−	6.34709i	−0.313079	−	0.542269i	−0.979027	+	0.203729i	$0.934694\pi$
$138$	−1.37942	+	0.183487i	−0.117424	+	0.0156195i
$139$	8.42736	−	14.5966i	0.714799	−	1.23807i	−0.248237	−	0.968699i	$-0.579851\pi$
$139$	8.42736	−	14.5966i	0.714799	−	1.23807i	0.963037	−	0.269370i	$-0.0868154\pi$
$140$	−7.85745	+	13.6095i	−0.664075	+	1.15021i
$141$	−12.2271	−	15.8904i	−1.02971	−	1.33822i
$142$	7.74199	+	13.4095i	0.649694	+	1.12530i
$143$	−4.67286			−0.390765
$144$	−8.43288	−	8.38773i	−0.702740	−	0.698977i
$145$	0.272925			0.0226652
$146$	9.02252	+	15.6275i	0.746709	+	1.29334i
$147$	5.60286	−	13.5780i	0.462116	−	1.11990i
$148$	14.8421	−	25.7072i	1.22001	−	2.11312i
$149$	4.11039	−	7.11941i	0.336737	−	0.583245i	−0.647080	−	0.762422i	$-0.724010\pi$
$149$	4.11039	−	7.11941i	0.336737	−	0.583245i	0.983817	+	0.179177i	$0.0573435\pi$
$150$	1.61753	−	3.91994i	0.132071	−	0.320062i
$151$	−7.70059	−	13.3378i	−0.626665	−	1.08542i	−0.988216	−	0.153063i	$-0.951086\pi$
$151$	−7.70059	−	13.3378i	−0.626665	−	1.08542i	0.361551	−	0.932352i	$-0.382247\pi$
$152$	−0.590572			−0.0479017
$153$	−23.0770	+	6.24991i	−1.86567	+	0.505275i
$154$	−45.0129			−3.62725
$155$	−3.28806	−	5.69509i	−0.264103	−	0.457440i
$156$	−4.21877	−	5.48276i	−0.337772	−	0.438972i
$157$	10.0899	−	17.4763i	0.805264	−	1.39476i	−0.110848	−	0.993837i	$-0.535357\pi$
$157$	10.0899	−	17.4763i	0.805264	−	1.39476i	0.916112	−	0.400921i	$-0.131310\pi$
$158$	14.5888	−	25.2685i	1.16062	−	2.01025i
$159$	19.1921	−	2.55290i	1.52204	−	0.202458i
$160$	−0.0288185	−	0.0499151i	−0.00227830	−	0.00394614i
$161$	−1.29114			−0.101756
$162$	−19.1414	−	10.9147i	−1.50389	−	0.857539i
$163$	8.27259			0.647959			0.323980	−	0.946064i	$-0.394979\pi$
$163$	8.27259			0.647959			0.323980	+	0.946064i	$0.394979\pi$
$164$	−0.181758	−	0.314814i	−0.0141929	−	0.0245829i
$165$	8.02297	−	1.06720i	0.624587	−	0.0830815i
$166$	−1.89565	+	3.28336i	−0.147131	+	0.254838i
$167$	6.81626	−	11.8061i	0.527458	−	0.913584i	−0.472030	−	0.881583i	$-0.656479\pi$
$167$	6.81626	−	11.8061i	0.527458	−	0.913584i	0.999488	−	0.0320015i	$-0.0101881\pi$
$168$	−20.2894	−	26.3683i	−1.56536	−	2.03436i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	19.5115			1.49646
$171$	−0.350279	+	0.0948654i	−0.0267865	+	0.00725454i
$172$	31.1408			2.37446
$173$	−1.73239	−	3.00059i	−0.131711	−	0.228130i	0.792625	−	0.609709i	$-0.208714\pi$
$173$	−1.73239	−	3.00059i	−0.131711	−	0.228130i	−0.924336	+	0.381579i	$0.875380\pi$
$174$	−0.441465	+	1.06985i	−0.0334674	+	0.0811051i
$175$	1.96726	−	3.40740i	0.148711	−	0.257575i
$176$	−9.26318	+	16.0443i	−0.698239	+	1.20938i
$177$	3.67047	−	8.89504i	0.275889	−	0.668592i
$178$	4.40078	+	7.62237i	0.329852	+	0.571321i
$179$	−6.80739			−0.508808			−0.254404	−	0.967098i	$-0.581879\pi$
$179$	−6.80739			−0.508808			−0.254404	+	0.967098i	$0.581879\pi$
$180$	8.49549	+	8.45000i	0.633216	+	0.629826i
$181$	−8.23721			−0.612267			−0.306133	−	0.951989i	$-0.599035\pi$
$181$	−8.23721			−0.612267			−0.306133	+	0.951989i	$0.599035\pi$
$182$	−4.81642	−	8.34228i	−0.357017	−	0.618371i
$183$	14.0116	+	18.2096i	1.03576	+	1.34609i
$184$	−0.801054	+	1.38747i	−0.0590544	+	0.102285i
$185$	−3.71599	+	6.43628i	−0.273205	+	0.473205i
$186$	27.6429	−	3.67701i	2.02688	−	0.269611i
$187$	18.6201	+	32.2510i	1.36164	+	2.35842i
$188$	−46.2356			−3.37208
$189$	−16.2696	−	12.3803i	−1.18344	−	0.900537i
$190$	0.296159			0.0214856
$191$	−8.86345	−	15.3519i	−0.641337	−	1.11083i	−0.985135	−	0.171784i	$-0.945047\pi$
$191$	−8.86345	−	15.3519i	−0.641337	−	1.11083i	0.343798	−	0.939044i	$-0.388286\pi$
$192$	13.8564	−	1.84315i	0.999998	−	0.133018i
$193$	−5.80167	+	10.0488i	−0.417613	+	0.723328i	−0.995699	−	0.0926485i	$-0.970467\pi$
$193$	−5.80167	+	10.0488i	−0.417613	+	0.723328i	0.578085	+	0.815976i	$0.303800\pi$
$194$	−6.46295	+	11.1942i	−0.464013	+	0.803694i
$195$	1.05625	+	1.37271i	0.0756396	+	0.0983019i
$196$	−16.9359	−	29.3339i	−1.20971	−	2.09528i
$197$	2.00369			0.142757			0.0713783	−	0.997449i	$-0.477260\pi$
$197$	2.00369			0.142757			0.0713783	+	0.997449i	$0.477260\pi$
$198$	−8.79404	+	33.1758i	−0.624965	+	2.35770i
$199$	11.2572			0.798004			0.399002	−	0.916950i	$-0.369357\pi$
$199$	11.2572			0.798004			0.399002	+	0.916950i	$0.369357\pi$
$200$	−2.44107	−	4.22806i	−0.172610	−	0.298969i
$201$	4.50674	−	10.9217i	0.317881	−	0.770356i
$202$	0.437130	−	0.757132i	0.0307564	−	0.0532716i
$203$	−0.536915	+	0.929964i	−0.0376840	+	0.0652707i
$204$	−21.0300	+	50.9642i	−1.47239	+	3.56821i
$205$	0.0455066	+	0.0788197i	0.00317832	+	0.00550501i
$206$	−11.2926			−0.786793
$207$	−0.252246	+	0.951605i	−0.0175323	+	0.0661411i
$208$	−3.96467			−0.274900
$209$	0.282628	+	0.489527i	0.0195498	+	0.0338613i
$210$	10.1747	+	13.2231i	0.702119	+	0.912481i
$211$	2.43205	−	4.21244i	0.167429	−	0.289996i	−0.770086	−	0.637940i	$-0.779787\pi$
$211$	2.43205	−	4.21244i	0.167429	−	0.289996i	0.937515	+	0.347944i	$0.113120\pi$
$212$	22.3234	−	38.6653i	1.53318	−	2.65555i
$213$	10.8586	−	1.44439i	0.744017	−	0.0989678i
$214$	−1.81177	−	3.13807i	−0.123850	−	0.214514i
$215$	−7.79669			−0.531730
$216$	−23.3980	+	9.80234i	−1.59203	+	0.666965i
$217$	25.8739			1.75643
$218$	17.9729	+	31.1299i	1.21728	+	2.10838i
$219$	12.6546	−	1.68329i	0.855117	−	0.113746i
$220$	9.33196	−	16.1634i	0.629160	−	1.08974i
$221$	−3.98473	+	6.90175i	−0.268042	+	0.464262i
$222$	−19.2191	−	24.9773i	−1.28990	−	1.67637i
$223$	7.04118	+	12.1957i	0.471513	+	0.816684i	0.999469	−	0.0325878i	$-0.0103749\pi$
$223$	7.04118	+	12.1957i	0.471513	+	0.816684i	−0.527956	+	0.849272i	$0.677042\pi$
$224$	0.226774			0.0151520
$225$	−2.12701	−	2.11562i	−0.141800	−	0.141041i
$226$	17.3187			1.15202
$227$	3.98166	+	6.89644i	0.264272	+	0.457733i	0.967373	−	0.253358i	$-0.0815350\pi$
$227$	3.98166	+	6.89644i	0.264272	+	0.457733i	−0.703101	+	0.711090i	$0.748202\pi$
$228$	−0.319207	+	0.773569i	−0.0211400	+	0.0512309i
$229$	−6.81425	+	11.8026i	−0.450298	+	0.779940i	−0.998404	−	0.0564691i	$-0.982016\pi$
$229$	−6.81425	+	11.8026i	−0.450298	+	0.779940i	0.548106	+	0.836409i	$0.315349\pi$
$230$	0.401711	−	0.695783i	0.0264880	−	0.0458786i
$231$	−12.1469	+	29.4369i	−0.799207	+	1.93681i
$232$	0.666230	+	1.15394i	0.0437401	+	0.0757601i
$233$	6.76769			0.443366			0.221683	−	0.975119i	$-0.428845\pi$
$233$	6.76769			0.443366			0.221683	+	0.975119i	$0.428845\pi$
$234$	−7.08946	+	1.92003i	−0.463453	+	0.125516i
$235$	11.5760			0.755132
$236$	−11.0948	−	19.2168i	−0.722211	−	1.25091i
$237$	−12.5879	−	16.3593i	−0.817671	−	1.06265i
$238$	−38.3842	+	66.4834i	−2.48808	+	4.30948i
$239$	−12.7338	+	22.0556i	−0.823681	+	1.42666i	0.0792425	+	0.996855i	$0.474750\pi$
$239$	−12.7338	+	22.0556i	−0.823681	+	1.42666i	−0.902923	+	0.429802i	$0.858583\pi$
$240$	6.80705	−	0.905461i	0.439393	−	0.0584473i
$241$	10.0813	+	17.4613i	0.649392	+	1.12478i	0.983268	+	0.182163i	$0.0583098\pi$
$241$	10.0813	+	17.4613i	0.649392	+	1.12478i	−0.333877	+	0.942617i	$0.608357\pi$
$242$	26.5288			1.70534
$243$	−12.3032	+	9.57243i	−0.789250	+	0.614072i
$244$	52.9834			3.39191
$245$	4.24023	+	7.34429i	0.270898	+	0.469210i
$246$	−0.382577	+	0.0508897i	−0.0243922	+	0.00324461i
$247$	−0.0604829	+	0.104759i	−0.00384844	+	0.00666569i
$248$	16.0528	−	27.8042i	1.01935	−	1.76557i
$249$	1.63566	+	2.12571i	0.103655	+	0.134712i
$250$	1.22414	+	2.12028i	0.0774216	+	0.134098i
$251$	22.3167			1.40862			0.704308	−	0.709894i	$-0.251257\pi$
$251$	22.3167			1.40862			0.704308	+	0.709894i	$0.251257\pi$
$252$	−45.5053	+	12.3241i	−2.86657	+	0.776348i
$253$	1.53343			0.0964060
$254$	−1.51445	−	2.62310i	−0.0950249	−	0.164588i
$255$	5.26525	−	12.7599i	0.329723	−	0.799053i
$256$	15.9760	−	27.6713i	0.998500	−	1.72945i
$257$	1.72736	−	2.99187i	0.107750	−	0.186628i	−0.807109	−	0.590403i	$-0.798969\pi$
$257$	1.72736	−	2.99187i	0.107750	−	0.186628i	0.914858	+	0.403775i	$0.132302\pi$
$258$	12.6114	−	30.5625i	0.785151	−	1.90274i
$259$	−14.6206	−	25.3237i	−0.908482	−	1.57354i
$260$	3.99411			0.247704
$261$	0.580514	+	0.577405i	0.0359329	+	0.0357405i
$262$	31.2224			1.92893
$263$	−7.48718	−	12.9682i	−0.461680	−	0.799652i	0.537365	−	0.843350i	$-0.319420\pi$
$263$	−7.48718	−	12.9682i	−0.461680	−	0.799652i	−0.999045	+	0.0436971i	$0.986086\pi$
$264$	24.0968	+	31.3165i	1.48306	+	1.92740i
$265$	−5.58909	+	9.68059i	−0.343335	+	0.594674i
$266$	−0.582622	+	1.00913i	−0.0357228	+	0.0618738i
$267$	6.17233	−	0.821032i	0.377741	−	0.0502464i
$268$	−13.6227	−	23.5951i	−0.832137	−	1.44130i
$269$	10.5996			0.646269			0.323135	−	0.946353i	$-0.395263\pi$
$269$	10.5996			0.646269			0.323135	+	0.946353i	$0.395263\pi$
$270$	11.7336	−	4.91566i	0.714084	−	0.299157i
$271$	−9.73751			−0.591512			−0.295756	−	0.955264i	$-0.595571\pi$
$271$	−9.73751			−0.591512			−0.295756	+	0.955264i	$0.595571\pi$
$272$	15.7981	+	27.3632i	0.957903	+	1.65914i
$273$	−6.75529	+	0.898576i	−0.408849	+	0.0543843i
$274$	−8.97173	+	15.5395i	−0.542002	+	0.938776i
$275$	−2.33643	+	4.04682i	−0.140892	+	0.244032i
$276$	1.38442	+	1.79920i	0.0833321	+	0.108299i
$277$	5.52080	+	9.56230i	0.331713	+	0.574543i	0.982848	−	0.184419i	$-0.0590403\pi$
$277$	5.52080	+	9.56230i	0.331713	+	0.574543i	−0.651135	+	0.758962i	$0.725707\pi$
$278$	−41.2652			−2.47492
$279$	5.05490	−	19.0698i	0.302629	−	1.14168i
$280$	19.2089			1.14795
$281$	10.6532	+	18.4519i	0.635519	+	1.10075i	0.986405	+	0.164333i	$0.0525471\pi$
$281$	10.6532	+	18.4519i	0.635519	+	1.10075i	−0.350886	+	0.936418i	$0.614120\pi$
$282$	−18.7245	+	45.3770i	−1.11503	+	2.70216i
$283$	1.63526	−	2.83235i	0.0972060	−	0.168366i	−0.813321	−	0.581815i	$-0.802343\pi$
$283$	1.63526	−	2.83235i	0.0972060	−	0.168366i	0.910527	+	0.413449i	$0.135676\pi$
$284$	12.6302	−	21.8761i	0.749464	−	1.29811i
$285$	0.0799196	−	0.193678i	0.00473403	−	0.0114725i
$286$	5.72025	+	9.90777i	0.338246	+	0.585859i
$287$	−0.358093			−0.0211376
$288$	0.0443042	−	0.167139i	0.00261065	−	0.00984875i
$289$	46.5123			2.73602
$290$	−0.334099	−	0.578677i	−0.0196190	−	0.0339811i
$291$	5.57654	+	7.24733i	0.326903	+	0.424846i
$292$	14.7192	−	25.4945i	0.861378	−	1.49195i
$293$	14.4984	−	25.1119i	0.847004	−	1.46705i	−0.0368649	−	0.999320i	$-0.511737\pi$
$293$	14.4984	−	25.1119i	0.847004	−	1.46705i	0.883869	−	0.467734i	$-0.154930\pi$
$294$	−35.6479	+	4.74181i	−2.07903	+	0.276548i
$295$	2.77780	+	4.81129i	0.161730	+	0.280124i
$296$	−36.2840			−2.10896
$297$	19.3227	+	14.7036i	1.12122	+	0.853190i
$298$	−20.1268			−1.16592
$299$	0.164078	+	0.284192i	0.00948889	+	0.0164352i
$300$	−6.85759	+	0.912184i	−0.395923	+	0.0526650i
$301$	15.3381	−	26.5664i	0.884075	−	1.53126i
$302$	−18.8532	+	32.6548i	−1.08488	+	1.87907i
$303$	−0.377177	−	0.490183i	−0.0216682	−	0.0281603i
$304$	0.239795	+	0.415337i	0.0137532	+	0.0238212i
$305$	−13.2654			−0.759574
$306$	41.5011	+	41.2789i	2.37246	+	2.35976i
$307$	7.67485			0.438027			0.219013	−	0.975722i	$-0.429716\pi$
$307$	7.67485			0.438027			0.219013	+	0.975722i	$0.429716\pi$
$308$	36.7168	+	63.5953i	2.09213	+	3.62368i
$309$	−3.04735	+	7.38497i	−0.173358	+	0.420116i
$310$	−8.05011	+	13.9432i	−0.457216	+	0.791921i
$311$	3.29475	−	5.70667i	0.186828	−	0.323596i	−0.757363	−	0.652994i	$-0.773513\pi$
$311$	3.29475	−	5.70667i	0.186828	−	0.323596i	0.944191	+	0.329399i	$0.106846\pi$
$312$	−3.22553	+	7.81677i	−0.182610	+	0.442537i
$313$	4.06651	+	7.04341i	0.229853	+	0.398117i	0.957764	−	0.287554i	$-0.0928422\pi$
$313$	4.06651	+	7.04341i	0.229853	+	0.398117i	−0.727911	+	0.685671i	$0.759509\pi$
$314$	−49.4061			−2.78815
$315$	11.3931	−	3.08558i	0.641930	−	0.173853i
$316$	−47.5999			−2.67770
$317$	−11.6731	−	20.2183i	−0.655624	−	1.13557i	−0.981737	−	0.190243i	$-0.939072\pi$
$317$	−11.6731	−	20.2183i	−0.655624	−	1.13557i	0.326113	−	0.945331i	$-0.394261\pi$
$318$	−28.9068	−	37.5676i	−1.62101	−	2.10668i
$319$	0.637671	−	1.10448i	0.0357027	−	0.0618389i
$320$	−4.03523	+	6.98922i	−0.225576	+	0.390709i
$321$	−2.54110	+	0.338013i	−0.141831	+	0.0188660i
$322$	1.58054	+	2.73757i	0.0880800	+	0.152559i
$323$	0.964032			0.0536402
$324$	0.192982	+	35.9464i	0.0107212	+	1.99702i
$325$	−1.00000			−0.0554700
$326$	−10.1268	−	17.5402i	−0.560874	−	0.971462i
$327$	25.2079	−	3.35311i	1.39400	−	0.185428i
$328$	−0.222170	+	0.384809i	−0.0122673	+	0.0212475i
$329$	−22.7729	+	39.4438i	−1.25551	+	2.17461i
$330$	−12.0840	−	15.7045i	−0.665204	−	0.864506i
$331$	2.24022	+	3.88018i	0.123134	+	0.213274i	0.921002	−	0.389558i	$-0.127372\pi$
$331$	2.24022	+	3.88018i	0.123134	+	0.213274i	−0.797868	+	0.602832i	$0.794039\pi$
$332$	6.18508			0.339450
$333$	−21.5206	+	5.82840i	−1.17932	+	0.319394i
$334$	−33.3763			−1.82627
$335$	3.41069	+	5.90749i	0.186346	+	0.322761i
$336$	−10.3060	+	24.9756i	−0.562237	+	1.36253i
$337$	2.32337	−	4.02420i	0.126562	−	0.219212i	−0.795780	−	0.605585i	$-0.792939\pi$
$337$	2.32337	−	4.02420i	0.126562	−	0.219212i	0.922342	+	0.386373i	$0.126272\pi$
$338$	−1.22414	+	2.12028i	−0.0665846	+	0.115328i
$339$	4.67351	−	11.3258i	0.253830	−	0.615134i
$340$	−15.9154	−	27.5663i	−0.863135	−	1.49499i
$341$	−30.7293			−1.66409
$342$	0.629932	+	0.626559i	0.0340628	+	0.0338805i
$343$	−5.82489			−0.314514
$344$	−19.0323	−	32.9649i	−1.02615	−	1.77735i
$345$	−0.346615	−	0.450464i	−0.0186611	−	0.0242522i
$346$	−4.24139	+	7.34630i	−0.228018	+	0.394939i
$347$	2.21262	−	3.83236i	0.118779	−	0.205732i	−0.800505	−	0.599326i	$-0.795435\pi$
$347$	2.21262	−	3.83236i	0.118779	−	0.205732i	0.919284	+	0.393594i	$0.128769\pi$
$348$	1.87161	−	0.248958i	0.100329	−	0.0133455i
$349$	0.00675754	+	0.0117044i	0.000361723	+	0.000626522i	0.866206	−	0.499687i	$-0.166552\pi$
$349$	0.00675754	+	0.0117044i	0.000361723	+	0.000626522i	−0.865844	+	0.500313i	$0.833218\pi$
$350$	−9.63283			−0.514897
$351$	−0.657486	+	5.15439i	−0.0350940	+	0.275121i
$352$	−0.269330			−0.0143553
$353$	−14.8536	−	25.7272i	−0.790578	−	1.36932i	−0.925609	−	0.378481i	$-0.876447\pi$
$353$	−14.8536	−	25.7272i	−0.790578	−	1.36932i	0.135031	−	0.990841i	$-0.456887\pi$
$354$	−23.3531	+	3.10639i	−1.24120	+	0.165103i
$355$	−3.16221	+	5.47711i	−0.167833	+	0.290695i
$356$	7.17938	−	12.4351i	0.380506	−	0.659056i
$357$	33.1197	+	43.0428i	1.75288	+	2.27806i
$358$	8.33322	+	14.4336i	0.440425	+	0.762838i
$359$	35.9145			1.89550			0.947748	−	0.319020i	$-0.103354\pi$
$359$	35.9145			1.89550			0.947748	+	0.319020i	$0.103354\pi$
$360$	3.75279	−	14.1575i	0.197789	−	0.746165i
$361$	−18.9854			−0.999230
$362$	10.0835	+	17.4652i	0.529978	+	0.917949i
$363$	7.15889	−	17.3489i	0.375744	−	0.910582i
$364$	−7.85745	+	13.6095i	−0.411842	+	0.713331i
$365$	−3.68524	+	6.38302i	−0.192894	+	0.334103i
$366$	21.4572	−	51.9995i	1.12158	−	2.71806i
$367$	−1.47986	−	2.56319i	−0.0772481	−	0.133798i	0.824814	−	0.565405i	$-0.191280\pi$
$367$	−1.47986	−	2.56319i	−0.0772481	−	0.133798i	−0.902062	+	0.431607i	$0.857947\pi$
$368$	1.30103			0.0678210
$369$	−0.0699597	+	0.263925i	−0.00364195	+	0.0137394i
$370$	18.1956			0.945945
$371$	−21.9904	−	38.0885i	−1.14169	−	1.97746i
$372$	−27.7431	−	36.0553i	−1.43841	−	1.86938i
$373$	−2.28220	+	3.95289i	−0.118168	+	0.204673i	−0.919042	−	0.394160i	$-0.871035\pi$
$373$	−2.28220	+	3.95289i	−0.118168	+	0.204673i	0.800874	+	0.598833i	$0.204369\pi$
$374$	45.5873	−	78.9596i	2.35726	−	4.08290i
$375$	1.71693	−	0.228383i	0.0886618	−	0.0117936i
$376$	28.2577	+	48.9438i	1.45728	+	2.52408i
$377$	0.272925			0.0140564
$378$	−6.33345	+	49.6514i	−0.325758	+	2.55379i
$379$	−22.9852			−1.18067			−0.590336	−	0.807158i	$-0.701005\pi$
$379$	−22.9852			−1.18067			−0.590336	+	0.807158i	$0.701005\pi$
$380$	−0.241575	−	0.418420i	−0.0123925	−	0.0214645i
$381$	−2.12410	+	0.282543i	−0.108821	+	0.0144751i
$382$	−21.7003	+	37.5860i	−1.11028	+	1.92306i
$383$	−4.60271	+	7.97213i	−0.235187	+	0.407357i	−0.959327	−	0.282297i	$-0.908904\pi$
$383$	−4.60271	+	7.97213i	−0.235187	+	0.407357i	0.724140	+	0.689653i	$0.242237\pi$
$384$	−20.7484	−	26.9649i	−1.05881	−	1.37605i
$385$	−9.19274	−	15.9223i	−0.468505	−	0.811475i
$386$	28.4083			1.44594
$387$	−16.5836	−	16.4948i	−0.842993	−	0.838479i
$388$	21.0872			1.07054
$389$	13.0121	+	22.5376i	0.659738	+	1.14270i	0.980683	+	0.195603i	$0.0626662\pi$
$389$	13.0121	+	22.5376i	0.659738	+	1.14270i	−0.320945	+	0.947098i	$0.604000\pi$
$390$	1.61753	−	3.91994i	0.0819069	−	0.198494i
$391$	1.30762	−	2.26486i	0.0661289	−	0.114539i
$392$	−20.7014	+	35.8559i	−1.04558	+	1.81100i
$393$	8.42548	−	20.4184i	0.425009	−	1.02997i
$394$	−2.45280	−	4.24837i	−0.123570	−	0.214030i
$395$	11.9175			0.599636
$396$	54.0448	−	14.6369i	2.71585	−	0.735530i
$397$	−32.0420			−1.60814			−0.804071	−	0.594533i	$-0.797337\pi$
$397$	−32.0420			−1.60814			−0.804071	+	0.594533i	$0.797337\pi$
$398$	−13.7805	−	23.8685i	−0.690752	−	1.19642i
$399$	0.502714	+	0.653332i	0.0251672	+	0.0327075i
$400$	−1.98233	+	3.43350i	−0.0991167	+	0.171675i
$401$	−0.412295	+	0.714116i	−0.0205890	+	0.0356612i	−0.876136	−	0.482063i	$-0.839887\pi$
$401$	−0.412295	+	0.714116i	−0.0205890	+	0.0356612i	0.855547	+	0.517725i	$0.173221\pi$
$402$	−28.6739	+	3.81415i	−1.43012	+	0.190232i
$403$	−3.28806	−	5.69509i	−0.163790	−	0.283692i
$404$	−1.42626			−0.0709590
$405$	−0.0483167	−	8.99987i	−0.00240088	−	0.447207i
$406$	2.62904			0.130477
$407$	17.3643	+	30.0759i	0.860717	+	1.49081i
$408$	66.8023	−	8.88592i	3.30721	−	0.439918i
$409$	−14.1096	+	24.4385i	−0.697675	+	1.20841i	0.271596	+	0.962411i	$0.412449\pi$
$409$	−14.1096	+	24.4385i	−0.697675	+	1.20841i	−0.969271	+	0.245997i	$0.920885\pi$
$410$	0.111413	−	0.192973i	0.00550231	−	0.00953027i
$411$	7.74124	+	10.0606i	0.381847	+	0.496252i
$412$	9.21131	+	15.9545i	0.453809	+	0.786019i
$413$	−21.8586			−1.07559
$414$	2.32645	−	0.630069i	0.114339	−	0.0309662i
$415$	−1.54855			−0.0760154
$416$	−0.0288185	−	0.0499151i	−0.00141294	−	0.00244729i
$417$	−11.1356	+	26.9860i	−0.545311	+	1.32151i
$418$	0.691955	−	1.19850i	0.0338446	−	0.0586206i
$419$	−12.4112	+	21.4968i	−0.606327	+	1.05019i	0.385514	+	0.922702i	$0.374024\pi$
$419$	−12.4112	+	21.4968i	−0.606327	+	1.05019i	−0.991840	+	0.127486i	$0.959309\pi$
$420$	10.3825	−	25.1610i	0.506614	−	1.22773i
$421$	−16.4032	−	28.4112i	−0.799444	−	1.38468i	−0.919978	−	0.391969i	$-0.871794\pi$
$421$	−16.4032	−	28.4112i	−0.799444	−	1.38468i	0.120534	−	0.992709i	$-0.461539\pi$
$422$	−11.9087			−0.579707
$423$	24.6221	+	24.4903i	1.19717	+	1.19076i
$424$	−54.5735			−2.65032
$425$	3.98473	+	6.90175i	0.193288	+	0.334784i
$426$	−16.3549	−	21.2551i	−0.792400	−	1.02981i
$427$	26.0965	−	45.2004i	1.26290	−	2.18740i
$428$	−2.95570	+	5.11942i	−0.142869	+	0.247456i
$429$	8.02297	−	1.06720i	0.387353	−	0.0515249i
$430$	9.54427	+	16.5312i	0.460265	+	0.797203i
$431$	4.17377			0.201043			0.100522	−	0.994935i	$-0.467949\pi$
$431$	4.17377			0.201043			0.100522	+	0.994935i	$0.467949\pi$
$432$	16.3943	+	12.4752i	0.788769	+	0.600214i
$433$	20.3832			0.979555			0.489777	−	0.871848i	$-0.337078\pi$
$433$	20.3832			0.979555			0.489777	+	0.871848i	$0.337078\pi$
$434$	−31.6733	−	54.8598i	−1.52037	−	2.63336i
$435$	−0.468593	+	0.0623313i	−0.0224673	+	0.00298856i
$436$	29.3207	−	50.7850i	1.40421	−	2.43216i
$437$	0.0198479	−	0.0343775i	0.000949452	−	0.00164450i
$438$	−19.0601	−	24.7706i	−0.910724	−	1.18359i
$439$	−9.11140	−	15.7814i	−0.434864	−	0.753206i	0.562421	−	0.826851i	$-0.309870\pi$
$439$	−9.11140	−	15.7814i	−0.434864	−	0.753206i	−0.997284	+	0.0736453i	$0.976537\pi$
$440$	−22.8136			−1.08760
$441$	−6.51872	+	24.5921i	−0.310415	+	1.17105i
$442$	19.5115			0.928068
$443$	−3.47615	−	6.02087i	−0.165157	−	0.286060i	0.771554	−	0.636164i	$-0.219480\pi$
$443$	−3.47615	−	6.02087i	−0.165157	−	0.286060i	−0.936711	+	0.350104i	$0.886146\pi$
$444$	−19.6117	+	47.5271i	−0.930728	+	2.25553i
$445$	−1.79749	+	3.11335i	−0.0852094	+	0.147587i
$446$	17.2388	−	29.8585i	0.816282	−	1.41384i
$447$	−5.43130	+	13.1623i	−0.256892	+	0.622554i
$448$	−15.8767	−	27.4992i	−0.750103	−	1.29922i
$449$	13.6819			0.645687			0.322843	−	0.946452i	$-0.395361\pi$
$449$	13.6819			0.645687			0.322843	+	0.946452i	$0.395361\pi$
$450$	−1.88194	+	7.09967i	−0.0887154	+	0.334681i
$451$	0.425292			0.0200262
$452$	−14.1268	−	24.4683i	−0.664466	−	1.15089i
$453$	16.2675	+	21.1414i	0.764313	+	0.993308i
$454$	9.74825	−	16.8845i	0.457508	−	0.792427i
$455$	1.96726	−	3.40740i	0.0922266	−	0.159741i
$456$	1.01397	−	0.134876i	0.0474835	−	0.00631617i
$457$	−8.41934	−	14.5827i	−0.393840	−	0.682151i	0.599112	−	0.800665i	$-0.295520\pi$
$457$	−8.41934	−	14.5827i	−0.393840	−	0.682151i	−0.992952	+	0.118514i	$0.962187\pi$
$458$	33.3665			1.55911
$459$	38.1942	−	16.0010i	1.78275	−	0.746864i
$460$	−1.31069			−0.0611113
$461$	19.6855	+	34.0962i	0.916844	+	1.58802i	0.804180	+	0.594386i	$0.202605\pi$
$461$	19.6855	+	34.0962i	0.916844	+	1.58802i	0.112664	+	0.993633i	$0.464062\pi$
$462$	77.2839	−	10.2802i	3.59557	−	0.478277i
$463$	1.44170	−	2.49710i	0.0670016	−	0.116050i	−0.830579	−	0.556902i	$-0.811990\pi$
$463$	1.44170	−	2.49710i	0.0670016	−	0.116050i	0.897580	+	0.440851i	$0.145323\pi$
$464$	0.541029	−	0.937090i	0.0251166	−	0.0435033i
$465$	6.94602	+	9.02712i	0.322114	+	0.418623i
$466$	−8.28462	−	14.3494i	−0.383778	−	0.664723i
$467$	25.1278			1.16278			0.581388	−	0.813626i	$-0.302510\pi$
$467$	25.1278			1.16278			0.581388	+	0.813626i	$0.302510\pi$
$468$	8.49549	+	8.45000i	0.392704	+	0.390602i
$469$	−26.8389			−1.23930
$470$	−14.1706	−	24.5442i	−0.653642	−	1.13214i
$471$	−13.3324	+	32.3099i	−0.614325	+	1.48876i
$472$	−13.5616	+	23.4894i	−0.624224	+	1.08119i
$473$	−18.2164	+	31.5518i	−0.837593	+	1.45075i
$474$	−19.2770	+	46.7160i	−0.885421	+	2.14574i
$475$	0.0604829	+	0.104759i	0.00277515	+	0.00480669i
$476$	125.239			5.74033
$477$	−32.3685	+	8.76630i	−1.48205	+	0.401381i
$478$	62.3520			2.85191
$479$	−10.7329	−	18.5899i	−0.490399	−	0.849396i	0.509540	−	0.860447i	$-0.329816\pi$
$479$	−10.7329	−	18.5899i	−0.490399	−	0.849396i	−0.999939	+	0.0110508i	$0.996482\pi$
$480$	0.0608790	+	0.0791190i	0.00277874	+	0.00361127i
$481$	−3.71599	+	6.43628i	−0.169434	+	0.293469i
$482$	24.6818	−	42.7502i	1.12423	−	1.94722i
$483$	2.21679	−	0.294874i	0.100868	−	0.0134172i
$484$	−21.6394	−	37.4805i	−0.983608	−	1.70366i
$485$	−5.27957			−0.239733
$486$	35.3571	+	14.3682i	1.60383	+	0.651753i
$487$	−32.0627			−1.45290			−0.726450	−	0.687220i	$-0.758831\pi$
$487$	−32.0627			−1.45290			−0.726450	+	0.687220i	$0.758831\pi$
$488$	−32.3818	−	56.0869i	−1.46585	−	2.53893i
$489$	−14.2034	+	1.88932i	−0.642302	+	0.0854378i
$490$	10.3813	−	17.9809i	0.468979	−	0.812295i
$491$	4.87000	−	8.43508i	0.219780	−	0.380670i	−0.734961	−	0.678110i	$-0.762799\pi$
$491$	4.87000	−	8.43508i	0.219780	−	0.380670i	0.954741	+	0.297440i	$0.0961328\pi$
$492$	0.383964	+	0.499003i	0.0173104	+	0.0224968i
$493$	−1.08753	−	1.88366i	−0.0489800	−	0.0848359i
$494$	0.296159			0.0133248
$495$	−13.5311	+	3.66461i	−0.608179	+	0.164712i
$496$	−26.0721			−1.17067
$497$	−12.4418	−	21.5498i	−0.558090	−	0.966640i
$498$	2.50483	−	6.07022i	0.112244	−	0.272013i
$499$	−15.8859	+	27.5151i	−0.711149	+	1.23175i	0.253277	+	0.967394i	$0.418491\pi$
$499$	−15.8859	+	27.5151i	−0.711149	+	1.23175i	−0.964426	+	0.264352i	$0.914842\pi$
$500$	1.99705	−	3.45900i	0.0893109	−	0.154691i
$501$	−9.00672	+	21.8270i	−0.402390	+	0.975156i
$502$	−27.3188	−	47.3176i	−1.21930	−	2.11189i
$503$	−7.30099			−0.325535			−0.162768	−	0.986664i	$-0.552042\pi$
$503$	−7.30099			−0.325535			−0.162768	+	0.986664i	$0.552042\pi$
$504$	40.8574	+	40.6387i	1.81994	+	1.81019i
$505$	0.357091			0.0158903
$506$	−1.87714	−	3.25130i	−0.0834490	−	0.144538i
$507$	1.05625	+	1.37271i	0.0469097	+	0.0609643i
$508$	−2.47065	+	4.27930i	−0.109617	+	0.189863i
$509$	5.39561	−	9.34547i	0.239156	−	0.414231i	−0.721316	−	0.692606i	$-0.756463\pi$
$509$	5.39561	−	9.34547i	0.239156	−	0.414231i	0.960472	+	0.278375i	$0.0897959\pi$
$510$	−33.4999	+	4.45609i	−1.48340	+	0.197319i
$511$	−14.4996	−	25.1141i	−0.641427	−	1.11098i
$512$	−38.9407			−1.72095
$513$	0.579738	−	0.242875i	0.0255960	−	0.0107232i
$514$	−8.45813			−0.373072
$515$	−2.30623	−	3.99450i	−0.101624	−	0.176019i
$516$	−53.4665	+	7.11202i	−2.35373	+	0.313089i
$517$	27.0464	−	46.8458i	1.18950	−	2.06027i
$518$	−35.7955	+	61.9996i	−1.57276	+	2.72411i
$519$	3.65967	+	4.75614i	0.160642	+	0.208772i
$520$	−2.44107	−	4.22806i	−0.107048	−	0.185413i
$521$	−3.58465			−0.157046			−0.0785231	−	0.996912i	$-0.525020\pi$
$521$	−3.58465			−0.157046			−0.0785231	+	0.996912i	$0.525020\pi$
$522$	0.513628	−	1.93768i	0.0224809	−	0.0848098i
$523$	4.70071			0.205548			0.102774	−	0.994705i	$-0.467228\pi$
$523$	4.70071			0.205548			0.102774	+	0.994705i	$0.467228\pi$
$524$	−25.4679	−	44.1118i	−1.11257	−	1.92703i
$525$	−2.59945	+	6.29954i	−0.113450	+	0.274934i
$526$	−18.3308	+	31.7498i	−0.799260	+	1.38436i
$527$	−26.2041	+	45.3868i	−1.14147	+	1.97708i
$528$	12.2400	−	29.6625i	0.532677	−	1.29089i
$529$	11.4462	+	19.8253i	0.497659	+	0.861971i
$530$	27.3674			1.18876
$531$	−4.27045	+	16.1104i	−0.185322	+	0.699132i
$532$	1.90097			0.0824173
$533$	0.0455066	+	0.0788197i	0.00197111	+	0.00341406i
$534$	−9.29664	−	12.0820i	−0.402305	−	0.522839i
$535$	0.740014	−	1.28174i	0.0319936	−	0.0554146i
$536$	−16.6515	+	28.8412i	−0.719235	+	1.24575i
$537$	11.6878	−	1.55469i	0.504366	−	0.0670898i
$538$	−12.9754	−	22.4741i	−0.559410	−	0.968927i
$539$	39.6280			1.70690
$540$	−16.5160	−	12.5678i	−0.710735	−	0.540833i
$541$	31.2736			1.34456			0.672278	−	0.740299i	$-0.265316\pi$
$541$	31.2736			1.34456			0.672278	+	0.740299i	$0.265316\pi$
$542$	11.9201	+	20.6462i	0.512013	+	0.886832i
$543$	14.1427	−	1.88123i	0.606921	−	0.0807315i
$544$	−0.229668	+	0.397796i	−0.00984693	+	0.0170554i
$545$	−7.34100	+	12.7150i	−0.314454	+	0.544650i
$546$	10.1747	+	13.2231i	0.435436	+	0.565897i
$547$	1.72662	+	2.99059i	0.0738249	+	0.127868i	0.900575	−	0.434701i	$-0.143146\pi$
$547$	1.72662	+	2.99059i	0.0738249	+	0.127868i	−0.826750	+	0.562570i	$0.809813\pi$
$548$	29.2728			1.25047
$549$	−28.2156	−	28.0645i	−1.20421	−	1.19776i
$550$	11.4405			0.487825
$551$	−0.0165073	−	0.0285915i	−0.000703235	−	0.00121804i
$552$	1.05848	−	2.56512i	0.0450518	−	0.109179i
$553$	−23.4449	+	40.6077i	−0.996978	+	1.72682i
$554$	13.5165	−	23.4113i	0.574261	−	0.994649i
$555$	4.91015	−	11.8993i	0.208424	−	0.505097i
$556$	33.6598	+	58.3004i	1.42749	+	2.47249i
$557$	12.5254			0.530720			0.265360	−	0.964149i	$-0.414509\pi$
$557$	12.5254			0.530720			0.265360	+	0.964149i	$0.414509\pi$
$558$	−46.6211	+	12.6263i	−1.97363	+	0.534515i
$559$	−7.79669			−0.329765
$560$	−7.79954	−	13.5092i	−0.329591	−	0.570868i
$561$	−39.3349	−	51.1201i	−1.66072	−	2.15829i
$562$	26.0822	−	45.1756i	1.10021	−	1.90562i
$563$	13.2158	−	22.8905i	0.556981	−	0.964719i	−0.440766	−	0.897622i	$-0.645293\pi$
$563$	13.2158	−	22.8905i	0.556981	−	0.964719i	0.997746	−	0.0670966i	$-0.0213736\pi$
$564$	79.3831	−	10.5594i	3.34263	−	0.444631i
$565$	3.53690	+	6.12609i	0.148798	+	0.257727i
$566$	−8.00716			−0.336566
$567$	30.7612	+	17.5405i	1.29185	+	0.736630i
$568$	−30.8767			−1.29556
$569$	−11.1862	−	19.3750i	−0.468949	−	0.812244i	0.530421	−	0.847735i	$-0.322034\pi$
$569$	−11.1862	−	19.3750i	−0.468949	−	0.812244i	−0.999370	+	0.0354904i	$0.988701\pi$
$570$	−0.508484	+	0.0676375i	−0.0212980	+	0.00283302i
$571$	7.47062	−	12.9395i	0.312636	−	0.541501i	−0.666297	−	0.745687i	$-0.732121\pi$
$571$	7.47062	−	12.9395i	0.312636	−	0.541501i	0.978932	+	0.204186i	$0.0654548\pi$
$572$	9.33196	−	16.1634i	0.390189	−	0.675827i
$573$	18.7240	+	24.3339i	0.782207	+	1.01656i
$574$	0.438358	+	0.759258i	0.0182967	+	0.0316908i
$575$	0.328157			0.0136851
$576$	−23.3695	+	6.32911i	−0.973728	+	0.263713i
$577$	−2.65841			−0.110671			−0.0553355	−	0.998468i	$-0.517623\pi$
$577$	−2.65841			−0.110671			−0.0553355	+	0.998468i	$0.517623\pi$
$578$	−56.9377	−	98.6190i	−2.36830	−	4.10201i
$579$	7.66608	−	18.5780i	0.318592	−	0.772077i
$580$	−0.545046	+	0.944047i	−0.0226318	+	0.0391994i
$581$	3.04640	−	5.27653i	0.126386	−	0.218907i
$582$	8.53987	−	20.6956i	0.353989	−	0.857860i
$583$	26.1171	+	45.2361i	1.08166	+	1.87349i
$584$	−35.9837			−1.48902
$585$	−2.12701	−	2.11562i	−0.0879409	−	0.0874701i
$586$	−70.9924			−2.93267
$587$	5.74909	+	9.95772i	0.237291	+	0.410999i	0.959936	−	0.280220i	$-0.0904073\pi$
$587$	5.74909	+	9.95772i	0.237291	+	0.410999i	−0.722645	+	0.691219i	$0.757074\pi$
$588$	35.7771	+	46.4963i	1.47542	+	1.91747i
$589$	−0.397743	+	0.688911i	−0.0163887	+	0.0283861i
$590$	6.80085	−	11.7794i	0.279986	−	0.484951i
$591$	−3.44018	+	0.457607i	−0.141510	+	0.0188234i
$592$	14.7327	+	25.5177i	0.605509	+	1.04877i
$593$	−22.0373			−0.904964			−0.452482	−	0.891774i	$-0.649461\pi$
$593$	−22.0373			−0.904964			−0.452482	+	0.891774i	$0.649461\pi$
$594$	7.52197	−	58.9688i	0.308630	−	2.41952i
$595$	−31.3560			−1.28547
$596$	16.4174	+	28.4357i	0.672481	+	1.16477i
$597$	−19.3279	+	2.57096i	−0.791036	+	0.105222i
$598$	0.401711	−	0.695783i	0.0164272	−	0.0284527i
$599$	−12.0613	+	20.8909i	−0.492813	+	0.853577i	−0.999966	−	0.00827908i	$-0.997365\pi$
$599$	−12.0613	+	20.8909i	−0.492813	+	0.853577i	0.507153	+	0.861856i	$0.330698\pi$
$600$	5.15676	+	6.70177i	0.210524	+	0.273599i
$601$	−0.171419	−	0.296906i	−0.00699232	−	0.0121111i	0.862508	−	0.506043i	$-0.168892\pi$
$601$	−0.171419	−	0.296906i	−0.00699232	−	0.0121111i	−0.869500	+	0.493932i	$0.835559\pi$
$602$	−75.1042			−3.06102
$603$	−5.24343	+	19.7810i	−0.213529	+	0.805545i
$604$	61.5139			2.50297
$605$	5.41783	+	9.38396i	0.220266	+	0.381512i
$606$	−0.577605	+	1.39977i	−0.0234636	+	0.0568619i
$607$	18.5443	−	32.1196i	0.752688	−	1.30369i	−0.193827	−	0.981036i	$-0.562090\pi$
$607$	18.5443	−	32.1196i	0.752688	−	1.30369i	0.946515	−	0.322659i	$-0.104577\pi$
$608$	−0.00348605	+	0.00603802i	−0.000141378	+	0.000244874i
$609$	0.709456	−	1.71930i	0.0287486	−	0.0696697i
$610$	16.2387	+	28.1263i	0.657487	+	1.13880i
$611$	11.5760			0.468313
$612$	24.4676	−	92.3048i	0.989045	−	3.73120i
$613$	38.1878			1.54239			0.771194	−	0.636600i	$-0.219660\pi$
$613$	38.1878			1.54239			0.771194	+	0.636600i	$0.219660\pi$
$614$	−9.39511	−	16.2728i	−0.379156	−	0.656717i
$615$	−0.0961326	−	0.124935i	−0.00387644	−	0.00503786i
$616$	44.8803	−	77.7349i	1.80828	−	3.13203i
$617$	6.45863	−	11.1867i	0.260015	−	0.450359i	−0.706231	−	0.707982i	$-0.749606\pi$
$617$	6.45863	−	11.1867i	0.260015	−	0.450359i	0.966246	+	0.257623i	$0.0829392\pi$
$618$	19.3886	−	2.57903i	0.779923	−	0.103744i
$619$	3.24865	+	5.62683i	0.130574	+	0.226161i	0.923898	−	0.382639i	$-0.124985\pi$
$619$	3.24865	+	5.62683i	0.130574	+	0.226161i	−0.793324	+	0.608800i	$0.791651\pi$
$620$	26.2657			1.05486
$621$	0.215758	−	1.69145i	0.00865808	−	0.0678754i
$622$	−16.1330			−0.646873
$623$	−7.07228	−	12.2495i	−0.283345	−	0.490768i
$624$	6.80705	−	0.905461i	0.272500	−	0.0362475i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	9.95599	−	17.2443i	0.397921	−	0.689220i
$627$	−0.597052	−	0.775935i	−0.0238440	−	0.0309879i
$628$	40.3003	+	69.8021i	1.60816	+	2.78541i
$629$	59.2288			2.36161
$630$	−20.4891	−	20.3794i	−0.816305	−	0.811935i
$631$	−37.1832			−1.48024			−0.740119	−	0.672476i	$-0.765231\pi$
$631$	−37.1832			−1.48024			−0.740119	+	0.672476i	$0.765231\pi$
$632$	29.0915	+	50.3880i	1.15720	+	2.00433i
$633$	−3.21361	+	7.78789i	−0.127729	+	0.309541i
$634$	−28.5790	+	49.5002i	−1.13502	+	1.96591i
$635$	0.618575	−	1.07140i	0.0245474	−	0.0425173i
$636$	−29.4972	+	71.4839i	−1.16964	+	2.83452i
$637$	4.24023	+	7.34429i	0.168004	+	0.290991i
$638$	−3.12240			−0.123617
$639$	−18.3135	+	4.95982i	−0.724471	+	0.196207i
$640$	19.6435			0.776478
$641$	−20.7912	−	36.0114i	−0.821203	−	1.42237i	−0.904787	−	0.425865i	$-0.859970\pi$
$641$	−20.7912	−	36.0114i	−0.821203	−	1.42237i	0.0835833	−	0.996501i	$-0.473364\pi$
$642$	3.82735	+	4.97407i	0.151054	+	0.196311i
$643$	7.24965	−	12.5568i	0.285898	−	0.495190i	−0.686928	−	0.726725i	$-0.741041\pi$
$643$	7.24965	−	12.5568i	0.285898	−	0.495190i	0.972827	+	0.231535i	$0.0743748\pi$
$644$	2.57847	−	4.46605i	0.101606	−	0.175987i
$645$	13.3864	−	1.78063i	0.527087	−	0.0701122i
$646$	−1.18011	−	2.04402i	−0.0464309	−	0.0804207i
$647$	−4.64226			−0.182506			−0.0912531	−	0.995828i	$-0.529087\pi$
$647$	−4.64226			−0.182506			−0.0912531	+	0.995828i	$0.529087\pi$
$648$	37.9340	−	22.1736i	1.49019	−	0.871062i
$649$	25.9606			1.01904
$650$	1.22414	+	2.12028i	0.0480148	+	0.0831642i
$651$	−44.4236	+	5.90914i	−1.74110	+	0.231598i
$652$	−16.5208	+	28.6149i	−0.647005	+	1.12065i
$653$	−5.28711	+	9.15755i	−0.206901	+	0.358362i	−0.950737	−	0.310000i	$-0.899671\pi$
$653$	−5.28711	+	9.15755i	−0.206901	+	0.358362i	0.743836	+	0.668362i	$0.233004\pi$
$654$	−37.9677	−	49.3432i	−1.48465	−	1.92947i
$655$	6.37638	+	11.0442i	0.249146	+	0.431533i
$656$	0.360837			0.0140883
$657$	−21.3426	+	5.78017i	−0.832653	+	0.225506i
$658$	111.509			4.34708
$659$	15.6513	+	27.1089i	0.609690	+	1.05601i	0.991291	+	0.131687i	$0.0420393\pi$
$659$	15.6513	+	27.1089i	0.609690	+	1.05601i	−0.381602	+	0.924327i	$0.624627\pi$
$660$	−12.3309	+	29.8827i	−0.479978	+	1.16318i
$661$	6.52034	−	11.2936i	0.253612	−	0.439269i	−0.710906	−	0.703287i	$-0.751715\pi$
$661$	6.52034	−	11.2936i	0.253612	−	0.439269i	0.964518	+	0.264019i	$0.0850480\pi$
$662$	5.48471	−	9.49979i	0.213169	−	0.369220i
$663$	5.26525	−	12.7599i	0.204485	−	0.495552i
$664$	−3.78012	−	6.54737i	−0.146697	−	0.254087i
$665$	−0.475943			−0.0184563
$666$	38.7022	+	38.4950i	1.49968	+	1.49165i
$667$	−0.0895622			−0.00346786
$668$	27.2249	+	47.1548i	1.05336	+	1.82448i
$669$	−14.8745	−	19.3310i	−0.575081	−	0.747381i
$670$	8.35035	−	14.4632i	0.322602	−	0.558763i
$671$	−30.9937	+	53.6826i	−1.19650	+	2.07240i
$672$	−0.389355	+	0.0517912i	−0.0150197	+	0.00199789i
$673$	6.13953	+	10.6340i	0.236661	+	0.409910i	0.959754	−	0.280841i	$-0.0906134\pi$
$673$	6.13953	+	10.6340i	0.236661	+	0.409910i	−0.723093	+	0.690751i	$0.757280\pi$
$674$	−11.3766			−0.438209
$675$	4.13509	+	3.14659i	0.159160	+	0.121112i
$676$	3.99411			0.153619
$677$	−18.1421	−	31.4231i	−0.697258	−	1.20769i	−0.969413	−	0.245434i	$-0.921070\pi$
$677$	−18.1421	−	31.4231i	−0.697258	−	1.20769i	0.272155	−	0.962253i	$-0.412264\pi$
$678$	−29.7349	+	3.95529i	−1.14196	+	0.151902i
$679$	10.3863	−	17.9896i	0.398589	−	0.690377i
$680$	−19.4540	+	33.6953i	−0.746027	+	1.29216i
$681$	−8.41125	−	10.9313i	−0.322320	−	0.418890i
$682$	37.6171	+	65.1547i	1.44043	+	2.49490i
$683$	−25.2755			−0.967141			−0.483571	−	0.875305i	$-0.660660\pi$
$683$	−25.2755			−0.967141			−0.483571	+	0.875305i	$0.660660\pi$
$684$	0.371386	−	1.40106i	0.0142003	−	0.0535710i
$685$	−7.32899			−0.280026
$686$	7.13050	+	12.3504i	0.272244	+	0.471540i
$687$	9.00406	−	21.8205i	0.343527	−	0.832505i
$688$	−15.4557	+	26.7700i	−0.589241	+	1.02060i
$689$	−5.58909	+	9.68059i	−0.212928	+	0.368801i
$690$	−0.530803	+	1.28635i	−0.0202073	+	0.0489706i
$691$	24.3378	+	42.1543i	0.925854	+	1.60363i	0.790181	+	0.612873i	$0.209986\pi$
$691$	24.3378	+	42.1543i	0.925854	+	1.60363i	0.135673	+	0.990754i	$0.456680\pi$
$692$	13.8387			0.526068
$693$	14.1325	−	53.3152i	0.536848	−	2.02528i
$694$	−10.8342			−0.411262
$695$	−8.42736	−	14.5966i	−0.319668	−	0.553681i
$696$	−1.40741	−	1.82908i	−0.0533477	−	0.0693312i
$697$	0.362663	−	0.628151i	0.0137368	−	0.0237929i
$698$	0.0165444	−	0.0286557i	0.000626215	−	0.00108464i
$699$	−11.6196	+	1.54562i	−0.439495	+	0.0584608i
$700$	7.85745	+	13.6095i	0.296984	+	0.514391i
$701$	22.9449			0.866615			0.433308	−	0.901246i	$-0.357346\pi$
$701$	22.9449			0.866615			0.433308	+	0.901246i	$0.357346\pi$
$702$	11.7336	−	4.91566i	0.442856	−	0.185529i
$703$	0.899015			0.0339070
$704$	18.8561	+	32.6597i	0.710665	+	1.23091i
$705$	−19.8751	+	2.64375i	−0.748539	+	0.0995692i
$706$	−36.3659	+	62.9876i	−1.36865	+	2.37057i
$707$	−0.702490	+	1.21675i	−0.0264199	+	0.0457606i
$708$	23.4378	+	30.4600i	0.880846	+	1.14476i
$709$	11.0072	+	19.0649i	0.413382	+	0.715999i	0.995257	−	0.0972792i	$-0.0310140\pi$
$709$	11.0072	+	19.0649i	0.413382	+	0.715999i	−0.581875	+	0.813278i	$0.697681\pi$
$710$	15.4840			0.581104
$711$	25.3487	+	25.2129i	0.950649	+	0.945559i
$712$	−17.5512			−0.657761
$713$	1.07900	+	1.86888i	0.0404088	+	0.0699901i
$714$	50.7193	−	122.914i	1.89812	−	4.59993i
$715$	−2.33643	+	4.04682i	−0.0873776	+	0.151342i
$716$	13.5947	−	23.5468i	0.508059	−	0.879984i
$717$	16.8259	−	40.7760i	0.628375	−	1.52281i
$718$	−43.9645	−	76.1488i	−1.64074	−	2.84185i
$719$	35.7966			1.33499			0.667494	−	0.744615i	$-0.267367\pi$
$719$	35.7966			1.33499			0.667494	+	0.744615i	$0.267367\pi$
$720$	−11.4804	+	3.10922i	−0.427850	+	0.115874i
$721$	18.1478			0.675859
$722$	23.2408	+	40.2543i	0.864933	+	1.49811i
$723$	−21.2967	−	27.6774i	−0.792031	−	1.02933i
$724$	16.4501	−	28.4925i	0.611364	−	1.05891i
$725$	0.136463	−	0.236360i	0.00506809	−	0.00877819i
$726$	−45.5480	+	6.05871i	−1.69045	+	0.224860i
$727$	15.5687	+	26.9657i	0.577410	+	1.00010i	0.995775	+	0.0918250i	$0.0292700\pi$
$727$	15.5687	+	26.9657i	0.577410	+	1.00010i	−0.418365	+	0.908279i	$0.637397\pi$
$728$	19.2089			0.711929
$729$	18.9375	−	19.2450i	0.701390	−	0.712778i
$730$	18.0450			0.667877
$731$	31.0677	+	53.8108i	1.14908	+	1.99027i
$732$	−90.9687	+	12.1005i	−3.36230	+	0.447247i
$733$	11.6605	−	20.1967i	0.430692	−	0.745980i	−0.566241	−	0.824240i	$-0.691603\pi$
$733$	11.6605	−	20.1967i	0.430692	−	0.745980i	0.996933	+	0.0782593i	$0.0249362\pi$
$734$	−3.62312	+	6.27543i	−0.133732	+	0.231630i
$735$	−8.95747	−	11.6412i	−0.330401	−	0.429393i
$736$	0.00945698	+	0.0163800i	0.000348589	+	0.000603774i
$737$	31.8754			1.17415
$738$	0.645235	−	0.174748i	0.0237514	−	0.00643255i
$739$	−23.4244			−0.861682			−0.430841	−	0.902428i	$-0.641783\pi$
$739$	−23.4244			−0.861682			−0.430841	+	0.902428i	$0.641783\pi$
$740$	−14.8421	−	25.7072i	−0.545605	−	0.945015i
$741$	0.0799196	−	0.193678i	0.00293592	−	0.00711493i
$742$	−53.8388	+	93.2516i	−1.97649	+	3.42337i
$743$	−19.8360	+	34.3570i	−0.727713	+	1.26044i	0.230135	+	0.973159i	$0.426083\pi$
$743$	−19.8360	+	34.3570i	−0.727713	+	1.26044i	−0.957848	+	0.287276i	$0.907250\pi$
$744$	−21.2115	+	51.4040i	−0.777650	+	1.88456i
$745$	−4.11039	−	7.11941i	−0.150593	−	0.260835i
$746$	11.1750			0.409145
$747$	−3.29378	−	3.27614i	−0.120513	−	0.119868i
$748$	−148.741			−5.43852
$749$	2.91160	+	5.04304i	0.106388	+	0.184269i
$750$	−2.58600	−	3.36079i	−0.0944274	−	0.122719i
$751$	10.5836	−	18.3314i	0.386203	−	0.668922i	−0.605733	−	0.795668i	$-0.707120\pi$
$751$	10.5836	−	18.3314i	0.386203	−	0.668922i	0.991935	+	0.126746i	$0.0404533\pi$
$752$	22.9474	−	39.7461i	0.836806	−	1.44939i
$753$	−38.3161	+	5.09674i	−1.39632	+	0.185736i
$754$	−0.334099	−	0.578677i	−0.0121672	−	0.0210742i
$755$	−15.4012			−0.560506
$756$	75.3148	−	31.5523i	2.73917	−	1.14755i
$757$	−6.75801			−0.245624			−0.122812	−	0.992430i	$-0.539191\pi$
$757$	−6.75801			−0.245624			−0.122812	+	0.992430i	$0.539191\pi$
$758$	28.1372	+	48.7351i	1.02199	+	1.77014i
$759$	−2.63279	+	0.350209i	−0.0955642	+	0.0127118i
$760$	−0.295286	+	0.511451i	−0.0107112	+	0.0185523i
$761$	19.1813	−	33.2229i	0.695320	−	1.20433i	−0.274752	−	0.961515i	$-0.588596\pi$
$761$	19.1813	−	33.2229i	0.695320	−	1.20433i	0.970073	−	0.242815i	$-0.0780708\pi$
$762$	3.19927	+	4.15780i	0.115897	+	0.150621i
$763$	−28.8833	−	50.0274i	−1.04565	−	1.81111i
$764$	70.8031			2.56157
$765$	−6.12593	+	23.1102i	−0.221483	+	0.835553i
$766$	22.5375			0.814313
$767$	2.77780	+	4.81129i	0.100301	+	0.173726i
$768$	−21.1100	+	51.1582i	−0.761742	+	1.84601i
$769$	8.50812	−	14.7365i	0.306811	−	0.531412i	−0.670852	−	0.741591i	$-0.734072\pi$
$769$	8.50812	−	14.7365i	0.306811	−	0.531412i	0.977663	+	0.210180i	$0.0674049\pi$
$770$	−22.5065	+	38.9823i	−0.811077	+	1.40483i
$771$	−2.28246	+	5.53132i	−0.0822007	+	0.199206i
$772$	−23.1725	−	40.1359i	−0.833996	−	1.44452i
$773$	21.8081			0.784382			0.392191	−	0.919884i	$-0.371717\pi$
$773$	21.8081			0.784382			0.392191	+	0.919884i	$0.371717\pi$
$774$	−14.6729	+	55.3539i	−0.527406	+	1.98965i
$775$	−6.57612			−0.236221
$776$	−12.8878	−	22.3223i	−0.462645	−	0.801325i
$777$	30.8861	+	40.1398i	1.10803	+	1.44001i
$778$	31.8573	−	55.1784i	1.14214	−	1.97824i
$779$	0.00550474	−	0.00953450i	0.000197228	−	0.000341609i
$780$	−6.85759	+	0.912184i	−0.245541	+	0.0326614i
$781$	14.7766	+	25.5938i	0.528747	+	0.915817i
$782$	−6.40283			−0.228965
$783$	−1.12857	−	0.858784i	−0.0403318	−	0.0306904i
$784$	33.6222			1.20079
$785$	−10.0899	−	17.4763i	−0.360125	−	0.623755i
$786$	−53.6066	+	7.13065i	−1.91209	+	0.254342i
$787$	2.41300	−	4.17944i	0.0860141	−	0.148981i	−0.819809	−	0.572637i	$-0.805920\pi$
$787$	2.41300	−	4.17944i	0.0860141	−	0.148981i	0.905823	+	0.423657i	$0.139254\pi$
$788$	−4.00147	+	6.93074i	−0.142546	+	0.246897i
$789$	15.8167	+	20.5555i	0.563088	+	0.731795i
$790$	−14.5888	−	25.2685i	−0.519045	−	0.899012i
$791$	−27.8320			−0.989592
$792$	−48.5247	−	48.2648i	−1.72425	−	1.71502i
$793$	−13.2654			−0.471068
$794$	39.2240	+	67.9380i	1.39201	+	2.41103i
$795$	7.38519	−	17.8973i	0.261926	−	0.634753i
$796$	−22.4813	+	38.9387i	−0.796828	+	1.38015i
$797$	−12.5729	+	21.7770i	−0.445357	+	0.771380i	−0.998077	−	0.0619864i	$-0.980256\pi$
$797$	−12.5729	+	21.7770i	−0.445357	+	0.771380i	0.552720	+	0.833367i	$0.313590\pi$
$798$	0.769852	−	1.86567i	0.0272525	−	0.0660438i
$799$	−46.1270	−	79.8944i	−1.63186	−	2.82646i
$800$	−0.0576370			−0.00203778
$801$	−10.4099	+	2.81931i	−0.367817	+	0.0996153i
$802$	2.01883			0.0712874
$803$	17.2206	+	29.8270i	0.607702	+	1.05257i
$804$	28.7779	+	37.4000i	1.01492	+	1.31900i
$805$	−0.645569	+	1.11816i	−0.0227533	+	0.0394099i
$806$	−8.05011	+	13.9432i	−0.283553	+	0.491128i
$807$	−18.1988	+	2.42076i	−0.640626	+	0.0852149i
$808$	0.871684	+	1.50980i	0.0306657	+	0.0531146i
$809$	−51.2155			−1.80064			−0.900320	−	0.435228i	$-0.856668\pi$
$809$	−51.2155			−1.80064			−0.900320	+	0.435228i	$0.856668\pi$
$810$	−19.0231	+	11.1196i	−0.668403	+	0.390702i
$811$	25.7297			0.903491			0.451745	−	0.892147i	$-0.350802\pi$
$811$	25.7297			0.903491			0.451745	+	0.892147i	$0.350802\pi$
$812$	−2.14449	−	3.71437i	−0.0752570	−	0.130349i
$813$	16.7186	−	2.22388i	0.586347	−	0.0779948i
$814$	42.5128	−	73.6343i	1.49007	−	2.58088i
$815$	4.13630	−	7.16428i	0.144888	−	0.250954i
$816$	−33.3735	−	43.3726i	−1.16831	−	1.51834i
$817$	0.471567	+	0.816777i	0.0164980	+	0.0285754i
$818$	69.0887			2.41563
$819$	11.3931	−	3.08558i	0.398108	−	0.107819i
$820$	−0.363516			−0.0126945
$821$	−10.6298	−	18.4114i	−0.370983	−	0.642561i	0.618734	−	0.785600i	$-0.287646\pi$
$821$	−10.6298	−	18.4114i	−0.370983	−	0.642561i	−0.989717	+	0.143039i	$0.954312\pi$
$822$	11.8549	−	28.7292i	0.413486	−	1.00205i
$823$	6.19775	−	10.7348i	0.216040	−	0.374192i	−0.737554	−	0.675288i	$-0.764019\pi$
$823$	6.19775	−	10.7348i	0.216040	−	0.374192i	0.953594	+	0.301096i	$0.0973525\pi$
$824$	11.2593	−	19.5017i	0.392237	−	0.679374i
$825$	3.08726	−	7.48170i	0.107485	−	0.260479i
$826$	26.7581	+	46.3463i	0.931033	+	1.61260i
$827$	−41.1108			−1.42956			−0.714781	−	0.699349i	$-0.753473\pi$
$827$	−41.1108			−1.42956			−0.714781	+	0.699349i	$0.753473\pi$
$828$	−2.78785	−	2.77292i	−0.0968845	−	0.0963658i
$829$	−28.6599			−0.995400			−0.497700	−	0.867349i	$-0.665822\pi$
$829$	−28.6599			−0.995400			−0.497700	+	0.867349i	$0.665822\pi$
$830$	1.89565	+	3.28336i	0.0657989	+	0.113967i
$831$	−11.6627	−	15.1569i	−0.404574	−	0.525788i
$832$	−4.03523	+	6.98922i	−0.139896	+	0.242307i
$833$	33.7923	−	58.5300i	1.17083	−	2.02795i
$834$	70.8493	−	9.42425i	2.45331	−	0.326335i
$835$	−6.81626	−	11.8061i	−0.235886	−	0.408567i
$836$	−2.25770			−0.0780840
$837$	−4.32370	+	33.8959i	−0.149449	+	1.17161i
$838$	60.7723			2.09934
$839$	17.2695	+	29.9116i	0.596209	+	1.03266i	0.993375	+	0.114917i	$0.0366603\pi$
$839$	17.2695	+	29.9116i	0.596209	+	1.03266i	−0.397166	+	0.917747i	$0.630006\pi$
$840$	−32.9803	+	4.38698i	−1.13793	+	0.151365i
$841$	14.4628	−	25.0502i	0.498716	−	0.863801i
$842$	−40.1598	+	69.5588i	−1.38400	+	2.39716i
$843$	−22.5049	−	29.2476i	−0.775111	−	1.00734i
$844$	9.71387	+	16.8249i	0.334365	+	0.579137i
$845$	−1.00000			−0.0344010
$846$	21.7852	−	82.1854i	0.748992	−	2.82559i
$847$	−42.6331			−1.46489
$848$	22.1589	+	38.3804i	0.760940	+	1.31799i
$849$	−2.16076	+	5.23640i	−0.0741571	+	0.179713i
$850$	9.75576	−	16.8975i	0.334620	−	0.579578i
$851$	1.21943	−	2.11211i	0.0418014	−	0.0724021i
$852$	−16.6890	+	40.4443i	−0.571756	+	1.38560i
$853$	14.2168	+	24.6243i	0.486775	+	0.843119i	0.999884	−	0.0152040i	$-0.00483976\pi$
$853$	14.2168	+	24.6243i	0.486775	+	0.843119i	−0.513109	+	0.858323i	$0.671506\pi$
$854$	−127.783			−4.37266
$855$	−0.0929835	+	0.350783i	−0.00317997	+	0.0119965i
$856$	7.22571			0.246970
$857$	−10.8757	−	18.8373i	−0.371507	−	0.643468i	0.618291	−	0.785949i	$-0.287825\pi$
$857$	−10.8757	−	18.8373i	−0.371507	−	0.643468i	−0.989798	+	0.142481i	$0.954492\pi$
$858$	−12.0840	−	15.7045i	−0.412542	−	0.536144i
$859$	1.93271	−	3.34755i	0.0659431	−	0.114217i	−0.831169	−	0.556020i	$-0.812328\pi$
$859$	1.93271	−	3.34755i	0.0659431	−	0.114217i	0.897112	+	0.441803i	$0.145661\pi$
$860$	15.5704	−	26.9687i	0.530946	−	0.919626i
$861$	0.614821	−	0.0817823i	0.0209530	−	0.00278713i
$862$	−5.10929	−	8.84956i	−0.174023	−	0.301417i
$863$	10.1359			0.345030			0.172515	−	0.985007i	$-0.444811\pi$
$863$	10.1359			0.345030			0.172515	+	0.985007i	$0.444811\pi$
$864$	−0.0378955	+	0.297083i	−0.00128923	+	0.0101070i
$865$	−3.46478			−0.117806
$866$	−24.9520	−	43.2181i	−0.847902	−	1.46861i
$867$	−79.8582	+	10.6226i	−2.71213	+	0.360762i
$868$	−51.6715	+	89.4977i	−1.75385	+	3.03775i
$869$	27.8445	−	48.2281i	0.944560	−	1.63603i
$870$	0.705784	+	0.917244i	0.0239283	+	0.0310975i
$871$	3.41069	+	5.90749i	0.115567	+	0.200168i
$872$	−71.6796			−2.42738
$873$	−11.2297	−	11.1696i	−0.380067	−	0.378032i
$874$	−0.0971865			−0.00328738
$875$	−1.96726	−	3.40740i	−0.0665055	−	0.115191i
$876$	−19.4494	+	47.1338i	−0.657133	+	1.59250i
$877$	−9.94057	+	17.2176i	−0.335669	+	0.581396i	−0.983613	−	0.180292i	$-0.942296\pi$
$877$	−9.94057	+	17.2176i	−0.335669	+	0.581396i	0.647944	+	0.761688i	$0.275629\pi$
$878$	−22.3073	+	38.6374i	−0.752836	+	1.30395i
$879$	−19.1575	+	46.4265i	−0.646168	+	1.56593i
$880$	9.26318	+	16.0443i	0.312262	+	0.540853i
$881$	−21.4750			−0.723511			−0.361755	−	0.932273i	$-0.617822\pi$
$881$	−21.4750			−0.723511			−0.361755	+	0.932273i	$0.617822\pi$
$882$	60.1219	−	16.2827i	2.02441	−	0.548267i
$883$	−32.0639			−1.07904			−0.539519	−	0.841974i	$-0.681394\pi$
$883$	−32.0639			−1.07904			−0.539519	+	0.841974i	$0.681394\pi$
$884$	−15.9154	−	27.5663i	−0.535294	−	0.927156i
$885$	−5.86809	−	7.62623i	−0.197254	−	0.256353i
$886$	−8.51061	+	14.7408i	−0.285920	+	0.495227i
$887$	3.77758	−	6.54296i	0.126839	−	0.219691i	−0.795611	−	0.605807i	$-0.792850\pi$
$887$	3.77758	−	6.54296i	0.126839	−	0.219691i	0.922450	+	0.386116i	$0.126184\pi$
$888$	62.2970	−	8.28663i	2.09055	−	0.278081i
$889$	2.43379	+	4.21546i	0.0816269	+	0.141382i
$890$	8.80156			0.295029
$891$	−36.5337	−	20.8321i	−1.22393	−	0.697900i
$892$	−56.2465			−1.88327
$893$	−0.700147	−	1.21269i	−0.0234295	−	0.0405811i
$894$	34.5563	−	4.59662i	1.15574	−	0.153734i
$895$	−3.40370	+	5.89538i	−0.113773	+	0.197061i
$896$	−38.6439	+	66.9332i	−1.29100	+	2.23608i
$897$	−0.346615	−	0.450464i	−0.0115731	−	0.0150406i
$898$	−16.7485	−	29.0093i	−0.558906	−	0.968054i
$899$	1.79479			0.0598595
$900$	11.5657	−	3.13231i	0.385522	−	0.104410i
$901$	89.0841			2.96782
$902$	−0.520619	−	0.901738i	−0.0173347	−	0.0300246i
$903$	−20.2671	+	49.1156i	−0.674448	+	1.63446i
$904$	−17.2676	+	29.9084i	−0.574313	+	0.994740i
$905$	−4.11860	+	7.13363i	−0.136907	+	0.237130i
$906$	24.9119	−	60.3716i	0.827642	−	2.00571i
$907$	−19.5449	−	33.8527i	−0.648977	−	1.12406i	−0.983368	−	0.181627i	$-0.941864\pi$
$907$	−19.5449	−	33.8527i	−0.648977	−	1.12406i	0.334391	−	0.942435i	$-0.391470\pi$
$908$	−31.8064			−1.05553
$909$	0.759534	+	0.755468i	0.0251922	+	0.0250573i
$910$	−9.63283			−0.319325
$911$	17.9251	+	31.0473i	0.593887	+	1.02864i	0.993703	+	0.112046i	$0.0357405\pi$
$911$	17.9251	+	31.0473i	0.593887	+	1.02864i	−0.399816	+	0.916595i	$0.630926\pi$
$912$	−0.506566	−	0.658338i	−0.0167741	−	0.0217998i
$913$	−3.61809	+	6.26671i	−0.119741	+	0.207398i
$914$	−20.6130	+	35.7027i	−0.681816	+	1.18094i
$915$	22.7757	−	3.02958i	0.752942	−	0.100155i
$916$	−27.2168	−	47.1410i	−0.899270	−	1.55758i
$917$	−50.1760			−1.65696
$918$	−80.6818	−	61.3948i	−2.66290	−	2.02633i
$919$	−20.3071			−0.669869			−0.334934	−	0.942241i	$-0.608714\pi$
$919$	−20.3071			−0.669869			−0.334934	+	0.942241i	$0.608714\pi$
$920$	0.801054	+	1.38747i	0.0264100	+	0.0457434i
$921$	−13.1772	+	1.75280i	−0.434202	+	0.0577568i
$922$	48.1957	−	83.4773i	1.58724	−	2.74918i
$923$	−3.16221	+	5.47711i	−0.104085	+	0.180281i
$924$	−77.5641	−	100.803i	−2.55167	−	3.31618i
$925$	3.71599	+	6.43628i	0.122181	+	0.211624i
$926$	−7.05940			−0.231986
$927$	3.54548	−	13.3754i	0.116449	−	0.439306i
$928$	0.0157306			0.000516382
$929$	1.90606	+	3.30140i	0.0625359	+	0.108315i	0.895598	−	0.444864i	$-0.146748\pi$
$929$	1.90606	+	3.30140i	0.0625359	+	0.108315i	−0.833062	+	0.553179i	$0.813415\pi$
$930$	10.6371	−	25.7780i	0.348804	−	0.845293i
$931$	0.512923	−	0.888408i	0.0168104	−	0.0291164i
$932$	−13.5154	+	23.4094i	−0.442713	+	0.766801i
$933$	−4.35354	+	10.5504i	−0.142528	+	0.345405i
$934$	−30.7600	−	53.2779i	−1.00650	−	1.74331i
$935$	37.2402			1.21788
$936$	3.75279	−	14.1575i	0.122664	−	0.462752i
$937$	−0.408946			−0.0133597			−0.00667983	−	0.999978i	$-0.502126\pi$
$937$	−0.408946			−0.0133597			−0.00667983	+	0.999978i	$0.502126\pi$
$938$	32.8546	+	56.9059i	1.07274	+	1.85804i
$939$	−8.59050	−	11.1643i	−0.280340	−	0.364333i
$940$	−23.1178	+	40.0412i	−0.754019	+	1.30600i
$941$	6.29373	−	10.9011i	0.205170	−	0.355365i	−0.745017	−	0.667045i	$-0.767559\pi$
$941$	6.29373	−	10.9011i	0.205170	−	0.355365i	0.950187	+	0.311681i	$0.100892\pi$
$942$	84.8267	−	11.2835i	2.76380	−	0.367636i
$943$	−0.0149333	−	0.0258652i	−0.000486295	−	0.000842287i
$944$	22.0261			0.716889
$945$	−18.8565	+	7.89971i	−0.613401	+	0.256978i
$946$	89.1981			2.90008
$947$	17.9147	+	31.0292i	0.582149	+	1.00831i	0.995224	+	0.0976150i	$0.0311214\pi$
$947$	17.9147	+	31.0292i	0.582149	+	1.00831i	−0.413075	+	0.910697i	$0.635545\pi$
$948$	81.7256	−	10.8710i	2.65432	−	0.353073i
$949$	−3.68524	+	6.38302i	−0.119628	+	0.207202i
$950$	0.148079	−	0.256481i	0.00480433	−	0.00832135i
$951$	24.6593	+	32.0475i	0.799633	+	1.03921i
$952$	−76.5422	−	132.575i	−2.48075	−	4.29678i
$953$	6.87652			0.222752			0.111376	−	0.993778i	$-0.464474\pi$
$953$	6.87652			0.222752			0.111376	+	0.993778i	$0.464474\pi$
$954$	58.2107	+	57.8990i	1.88464	+	1.87455i
$955$	−17.7269			−0.573629
$956$	−50.8601	−	88.0923i	−1.64493	−	2.84911i
$957$	−0.842591	+	2.04194i	−0.0272371	+	0.0660066i
$958$	−26.2772	+	45.5135i	−0.848979	+	1.47047i
$959$	14.4180	−	24.9728i	0.465583	−	0.806413i
$960$	5.33198	−	12.9216i	0.172089	−	0.417041i
$961$	−6.12267	−	10.6048i	−0.197506	−	0.342090i
$962$	18.1956			0.586650
$963$	4.28569	−	1.16069i	0.138105	−	0.0374026i
$964$	−80.5313			−2.59374
$965$	5.80167	+	10.0488i	0.186762	+	0.323482i
$966$	−3.33889	−	4.33925i	−0.107427	−	0.139613i
$967$	8.02651	−	13.9023i	0.258115	−	0.447068i	−0.707622	−	0.706591i	$-0.750232\pi$
$967$	8.02651	−	13.9023i	0.258115	−	0.447068i	0.965737	+	0.259523i	$0.0835653\pi$
$968$	−26.4506	+	45.8138i	−0.850155	+	1.47251i
$969$	−1.65517	+	0.220168i	−0.0531718	+	0.00707282i
$970$	6.46295	+	11.1942i	0.207513	+	0.359423i
$971$	−29.7306			−0.954100			−0.477050	−	0.878876i	$-0.658294\pi$
$971$	−29.7306			−0.954100			−0.477050	+	0.878876i	$0.658294\pi$
$972$	−8.54088	−	61.6734i	−0.273949	−	1.97817i
$973$	66.3153			2.12597
$974$	39.2493	+	67.9818i	1.25763	+	2.17828i
$975$	1.71693	−	0.228383i	0.0549857	−	0.00731410i
$976$	−26.2965	+	45.5468i	−0.841729	+	1.45792i
$977$	−12.6498	+	21.9102i	−0.404704	+	0.700968i	−0.994287	−	0.106740i	$-0.965959\pi$
$977$	−12.6498	+	21.9102i	−0.404704	+	0.700968i	0.589583	+	0.807708i	$0.299292\pi$
$978$	21.3929	+	27.8025i	0.684070	+	0.889025i
$979$	8.39944	+	14.5483i	0.268447	+	0.464965i
$980$	−33.8718			−1.08200
$981$	−42.5144	+	11.5141i	−1.35738	+	0.367617i
$982$	−23.8463			−0.760966
$983$	13.1804	+	22.8291i	0.420389	+	0.728135i	0.995977	−	0.0896044i	$-0.0285603\pi$
$983$	13.1804	+	22.8291i	0.420389	+	0.728135i	−0.575588	+	0.817740i	$0.695227\pi$
$984$	0.293566	−	0.711429i	0.00935853	−	0.0226795i
$985$	1.00184	−	1.73524i	0.0319214	−	0.0552894i
$986$	−2.66259	+	4.61174i	−0.0847942	+	0.146868i
$987$	30.0912	−	72.9232i	0.957812	−	2.32117i
$988$	−0.241575	−	0.418420i	−0.00768553	−	0.0133117i
$989$	2.55854			0.0813567
$990$	24.3340	+	24.2038i	0.773387	+	0.769246i
$991$	−47.5111			−1.50924			−0.754621	−	0.656161i	$-0.772179\pi$
$991$	−47.5111			−1.50924			−0.754621	+	0.656161i	$0.772179\pi$
$992$	−0.189514	−	0.328248i	−0.00601707	−	0.0104219i
$993$	−4.73247	−	6.15036i	−0.150180	−	0.195176i
$994$	−30.4610	+	52.7601i	−0.966165	+	1.67345i
$995$	5.62862	−	9.74905i	0.178439	−	0.309066i
$996$	−10.6193	+	1.41256i	−0.336486	+	0.0447588i
$997$	19.3542	+	33.5224i	0.612953	+	1.06167i	0.990740	+	0.135773i	$0.0433518\pi$
$997$	19.3542	+	33.5224i	0.612953	+	1.06167i	−0.377787	+	0.925892i	$0.623315\pi$
$998$	77.7863			2.46228
$999$	35.6183	−	14.9219i	1.12691	−	0.472107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.e.391.1	yes	16
3.2	odd	2		1755.2.i.f.1171.8		16
9.2	odd	6		1755.2.i.f.586.8		16
9.4	even	3		5265.2.a.bf.1.8		8
9.5	odd	6		5265.2.a.ba.1.1		8
9.7	even	3	inner	585.2.i.e.196.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.1	✓	16	9.7	even	3	inner
585.2.i.e.391.1	yes	16	1.1	even	1	trivial
1755.2.i.f.586.8		16	9.2	odd	6
1755.2.i.f.1171.8		16	3.2	odd	2
5265.2.a.ba.1.1		8	9.5	odd	6
5265.2.a.bf.1.8		8	9.4	even	3

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22414 - 2.12028i) q^{2} +(-1.71693 + 0.228383i) q^{3} +(-1.99705 + 3.45900i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.58600 + 3.36079i) q^{6} +(1.96726 + 3.40740i) q^{7} +4.88214 q^{8} +(2.89568 - 0.784233i) q^{9} +O(q^{10})\)	\(q+(-1.22414 - 2.12028i) q^{2} +(-1.71693 + 0.228383i) q^{3} +(-1.99705 + 3.45900i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.58600 + 3.36079i) q^{6} +(1.96726 + 3.40740i) q^{7} +4.88214 q^{8} +(2.89568 - 0.784233i) q^{9} -2.44829 q^{10} +(-2.33643 - 4.04682i) q^{11} +(2.63882 - 6.39494i) q^{12} +(0.500000 - 0.866025i) q^{13} +(4.81642 - 8.34228i) q^{14} +(-0.660679 + 1.60109i) q^{15} +(-1.98233 - 3.43350i) q^{16} -7.96946 q^{17} +(-5.20752 - 5.17964i) q^{18} -0.120966 q^{19} +(1.99705 + 3.45900i) q^{20} +(-4.15583 - 5.40096i) q^{21} +(-5.72025 + 9.90777i) q^{22} +(-0.164078 + 0.284192i) q^{23} +(-8.38229 + 1.11500i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.44829 q^{26} +(-4.79257 + 2.00779i) q^{27} -15.7149 q^{28} +(0.136463 + 0.236360i) q^{29} +(4.20353 - 0.559146i) q^{30} +(3.28806 - 5.69509i) q^{31} +(0.0288185 - 0.0499151i) q^{32} +(4.93571 + 6.41450i) q^{33} +(9.75576 + 16.8975i) q^{34} +3.93452 q^{35} +(-3.07017 + 11.5823i) q^{36} -7.43198 q^{37} +(0.148079 + 0.256481i) q^{38} +(-0.660679 + 1.60109i) q^{39} +(2.44107 - 4.22806i) q^{40} +(-0.0455066 + 0.0788197i) q^{41} +(-6.36421 + 15.4231i) q^{42} +(-3.89835 - 6.75213i) q^{43} +18.6639 q^{44} +(0.768676 - 2.89985i) q^{45} +0.803421 q^{46} +(5.78798 + 10.0251i) q^{47} +(4.18768 + 5.44235i) q^{48} +(-4.24023 + 7.34429i) q^{49} +(-1.22414 + 2.12028i) q^{50} +(13.6830 - 1.82009i) q^{51} +(1.99705 + 3.45900i) q^{52} -11.1782 q^{53} +(10.1239 + 7.70376i) q^{54} -4.67286 q^{55} +(9.60445 + 16.6354i) q^{56} +(0.207690 - 0.0276265i) q^{57} +(0.334099 - 0.578677i) q^{58} +(-2.77780 + 4.81129i) q^{59} +(-4.21877 - 5.48276i) q^{60} +(-6.63270 - 11.4882i) q^{61} -16.1002 q^{62} +(8.36875 + 8.32395i) q^{63} -8.07045 q^{64} +(-0.500000 - 0.866025i) q^{65} +(7.55850 - 18.3173i) q^{66} +(-3.41069 + 5.90749i) q^{67} +(15.9154 - 27.5663i) q^{68} +(0.216806 - 0.525410i) q^{69} +(-4.81642 - 8.34228i) q^{70} -6.32442 q^{71} +(14.1371 - 3.82874i) q^{72} -7.37048 q^{73} +(9.09780 + 15.7579i) q^{74} +(1.05625 + 1.37271i) q^{75} +(0.241575 - 0.418420i) q^{76} +(9.19274 - 15.9223i) q^{77} +(4.20353 - 0.559146i) q^{78} +(5.95876 + 10.3209i) q^{79} -3.96467 q^{80} +(7.76996 - 4.54178i) q^{81} +0.222826 q^{82} +(-0.774276 - 1.34108i) q^{83} +(26.9813 - 3.58901i) q^{84} +(-3.98473 + 6.90175i) q^{85} +(-9.54427 + 16.5312i) q^{86} +(-0.288277 - 0.374648i) q^{87} +(-11.4068 - 19.7571i) q^{88} -3.59499 q^{89} +(-7.08946 + 1.92003i) q^{90} +3.93452 q^{91} +(-0.655346 - 1.13509i) q^{92} +(-4.34470 + 10.5290i) q^{93} +(14.1706 - 24.5442i) q^{94} +(-0.0604829 + 0.104759i) q^{95} +(-0.0380796 + 0.0922823i) q^{96} +(-2.63979 - 4.57224i) q^{97} +20.7626 q^{98} +(-9.93921 - 9.88600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

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