LMFDB - Embedded newform 585.2.i.e.196.1

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			196.1
Root			$-0.724143 - 0.165319i$ of defining polynomial
Character	$\chi$	$=$	585.196
Dual form			585.2.i.e.391.1

$q$-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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	0.000850327		1.00000i	$0.499729\pi$
$2$	−1.22414	+	2.12028i	−0.865600	+	1.49926i	−0.866450	+	0.499263i	$0.833604\pi$
$3$	−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	−0.207312	−	0.978275i	$-0.566472\pi$
$7$	1.96726	−	3.40740i	0.743555	−	1.28787i	0.950867	−	0.309600i	$-0.100195\pi$
$8$	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	0.262425	+	0.964952i	$0.415478\pi$
$11$	−2.33643	+	4.04682i	−0.704461	+	1.22016i	−0.966886	+	0.255209i	$0.917856\pi$
$12$	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	0.848412	−	0.529336i	$-0.177559\pi$
$23$	−0.164078	−	0.284192i	−0.0342127	−	0.0592581i	−0.882625	+	0.470078i	$0.844226\pi$
$24$	−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	−0.853077	−	0.521785i	$-0.825266\pi$
$29$	0.136463	−	0.236360i	0.0253405	−	0.0438910i	0.878418	+	0.477894i	$0.158600\pi$
$30$	4.20353	+	0.559146i	0.767456	+	0.102086i
$31$	3.28806	+	5.69509i	0.590553	+	1.02287i	0.994158	+	0.107934i	$0.0344237\pi$
$31$	3.28806	+	5.69509i	0.590553	+	1.02287i	−0.403605	+	0.914933i	$0.632243\pi$
$32$	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	0.862450	−	0.506142i	$-0.168929\pi$
$41$	−0.0455066	−	0.0788197i	−0.00710694	−	0.0123096i	−0.869557	+	0.493833i	$0.835596\pi$
$42$	−6.36421	−	15.4231i	−0.982019	−	2.37983i
$43$	−3.89835	+	6.75213i	−0.594492	+	1.02969i	0.399126	+	0.916896i	$0.369314\pi$
$43$	−3.89835	+	6.75213i	−0.594492	+	1.02969i	−0.993618	+	0.112795i	$0.964020\pi$
$44$	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	−0.0419967	−	0.999118i	$-0.513372\pi$
$47$	5.78798	−	10.0251i	0.844263	−	1.46231i	0.886260	−	0.463189i	$-0.153295\pi$
$48$	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	0.626592	−	0.779347i	$-0.284449\pi$
$59$	−2.77780	−	4.81129i	−0.361639	−	0.626376i	−0.988231	+	0.152971i	$0.951116\pi$
$60$	−4.21877	+	5.48276i	−0.544641	+	0.707821i
$61$	−6.63270	+	11.4882i	−0.849230	+	1.47091i	0.0326669	+	0.999466i	$0.489600\pi$
$61$	−6.63270	+	11.4882i	−0.849230	+	1.47091i	−0.881897	+	0.471443i	$0.843733\pi$
$62$	−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	0.578921	−	0.815384i	$-0.303474\pi$
$67$	−3.41069	−	5.90749i	−0.416682	−	0.721715i	−0.995603	+	0.0936686i	$0.970141\pi$
$68$	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	−0.307374	−	0.951589i	$-0.599450\pi$
$79$	5.95876	−	10.3209i	0.670413	−	1.16119i	0.977787	−	0.209601i	$-0.0672166\pi$
$80$	−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	−0.905386	−	0.424589i	$-0.860418\pi$
$83$	−0.774276	+	1.34108i	−0.0849878	+	0.147203i	0.820398	+	0.571793i	$0.193752\pi$
$84$	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	−0.968353	−	0.249585i	$-0.919706\pi$
$97$	−2.63979	+	4.57224i	−0.268030	+	0.464241i	0.700323	+	0.713826i	$0.253039\pi$
$98$	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	−0.857006	−	0.515307i	$-0.827678\pi$
$101$	0.178545	−	0.309250i	0.0177659	−	0.0307715i	0.874772	+	0.484535i	$0.161011\pi$
$102$	−20.6090	+	26.7837i	−2.04060	+	2.65198i
$103$	2.30623	+	3.99450i	0.227239	+	0.393590i	0.956989	−	0.290125i	$-0.0936968\pi$
$103$	2.30623	+	3.99450i	0.227239	+	0.393590i	−0.729750	+	0.683714i	$0.760363\pi$
$104$	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	0.650321	−	0.759659i	$-0.274634\pi$
$113$	−3.53690	−	6.12609i	−0.332724	−	0.576294i	−0.983045	+	0.183365i	$0.941301\pi$
$114$	−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	−0.997736	−	0.0672484i	$-0.978578\pi$
$131$	−6.37638	−	11.0442i	−0.557107	−	0.964938i	0.440629	−	0.897689i	$-0.354755\pi$
$132$	−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	−0.979027	−	0.203729i	$-0.934694\pi$
$137$	−3.66450	+	6.34709i	−0.313079	+	0.542269i	0.665948	+	0.745998i	$0.268027\pi$
$138$	−1.37942	−	0.183487i	−0.117424	−	0.0156195i
$139$	8.42736	+	14.5966i	0.714799	+	1.23807i	0.963037	+	0.269370i	$0.0868154\pi$
$139$	8.42736	+	14.5966i	0.714799	+	1.23807i	−0.248237	+	0.968699i	$0.579851\pi$
$140$	−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	0.983817	−	0.179177i	$-0.0573435\pi$
$149$	4.11039	+	7.11941i	0.336737	+	0.583245i	−0.647080	+	0.762422i	$0.724010\pi$
$150$	1.61753	+	3.91994i	0.132071	+	0.320062i
$151$	−7.70059	+	13.3378i	−0.626665	+	1.08542i	0.361551	+	0.932352i	$0.382247\pi$
$151$	−7.70059	+	13.3378i	−0.626665	+	1.08542i	−0.988216	+	0.153063i	$0.951086\pi$
$152$	−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	0.916112	+	0.400921i	$0.131310\pi$
$157$	10.0899	+	17.4763i	0.805264	+	1.39476i	−0.110848	+	0.993837i	$0.535357\pi$
$158$	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	0.999488	+	0.0320015i	$0.0101881\pi$
$167$	6.81626	+	11.8061i	0.527458	+	0.913584i	−0.472030	+	0.881583i	$0.656479\pi$
$168$	−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	−0.924336	−	0.381579i	$-0.875380\pi$
$173$	−1.73239	+	3.00059i	−0.131711	+	0.228130i	0.792625	+	0.609709i	$0.208714\pi$
$174$	−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	0.343798	+	0.939044i	$0.388286\pi$
$191$	−8.86345	+	15.3519i	−0.641337	+	1.11083i	−0.985135	+	0.171784i	$0.945047\pi$
$192$	13.8564	+	1.84315i	0.999998	+	0.133018i
$193$	−5.80167	−	10.0488i	−0.417613	−	0.723328i	0.578085	−	0.815976i	$-0.303800\pi$
$193$	−5.80167	−	10.0488i	−0.417613	−	0.723328i	−0.995699	+	0.0926485i	$0.970467\pi$
$194$	−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	0.937515	−	0.347944i	$-0.113120\pi$
$211$	2.43205	+	4.21244i	0.167429	+	0.289996i	−0.770086	+	0.637940i	$0.779787\pi$
$212$	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	−0.527956	−	0.849272i	$-0.677042\pi$
$223$	7.04118	−	12.1957i	0.471513	−	0.816684i	0.999469	+	0.0325878i	$0.0103749\pi$
$224$	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	−0.703101	−	0.711090i	$-0.748202\pi$
$227$	3.98166	−	6.89644i	0.264272	−	0.457733i	0.967373	+	0.253358i	$0.0815350\pi$
$228$	−0.319207	−	0.773569i	−0.0211400	−	0.0512309i
$229$	−6.81425	−	11.8026i	−0.450298	−	0.779940i	0.548106	−	0.836409i	$-0.315349\pi$
$229$	−6.81425	−	11.8026i	−0.450298	−	0.779940i	−0.998404	+	0.0564691i	$0.982016\pi$
$230$	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	−0.902923	−	0.429802i	$-0.858583\pi$
$239$	−12.7338	−	22.0556i	−0.823681	−	1.42666i	0.0792425	−	0.996855i	$-0.474750\pi$
$240$	6.80705	+	0.905461i	0.439393	+	0.0584473i
$241$	10.0813	−	17.4613i	0.649392	−	1.12478i	−0.333877	−	0.942617i	$-0.608357\pi$
$241$	10.0813	−	17.4613i	0.649392	−	1.12478i	0.983268	−	0.182163i	$-0.0583098\pi$
$242$	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	0.914858	−	0.403775i	$-0.132302\pi$
$257$	1.72736	+	2.99187i	0.107750	+	0.186628i	−0.807109	+	0.590403i	$0.798969\pi$
$258$	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	−0.999045	−	0.0436971i	$-0.986086\pi$
$263$	−7.48718	+	12.9682i	−0.461680	+	0.799652i	0.537365	+	0.843350i	$0.319420\pi$
$264$	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	−0.651135	−	0.758962i	$-0.725707\pi$
$277$	5.52080	−	9.56230i	0.331713	−	0.574543i	0.982848	+	0.184419i	$0.0590403\pi$
$278$	−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	−0.350886	−	0.936418i	$-0.614120\pi$
$281$	10.6532	−	18.4519i	0.635519	−	1.10075i	0.986405	−	0.164333i	$-0.0525471\pi$
$282$	−18.7245	−	45.3770i	−1.11503	−	2.70216i
$283$	1.63526	+	2.83235i	0.0972060	+	0.168366i	0.910527	−	0.413449i	$-0.135676\pi$
$283$	1.63526	+	2.83235i	0.0972060	+	0.168366i	−0.813321	+	0.581815i	$0.802343\pi$
$284$	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	0.883869	+	0.467734i	$0.154930\pi$
$293$	14.4984	+	25.1119i	0.847004	+	1.46705i	−0.0368649	+	0.999320i	$0.511737\pi$
$294$	−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	0.944191	−	0.329399i	$-0.106846\pi$
$311$	3.29475	+	5.70667i	0.186828	+	0.323596i	−0.757363	+	0.652994i	$0.773513\pi$
$312$	−3.22553	−	7.81677i	−0.182610	−	0.442537i
$313$	4.06651	−	7.04341i	0.229853	−	0.398117i	−0.727911	−	0.685671i	$-0.759509\pi$
$313$	4.06651	−	7.04341i	0.229853	−	0.398117i	0.957764	+	0.287554i	$0.0928422\pi$
$314$	−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	0.326113	+	0.945331i	$0.394261\pi$
$317$	−11.6731	+	20.2183i	−0.655624	+	1.13557i	−0.981737	+	0.190243i	$0.939072\pi$
$318$	−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	−0.797868	−	0.602832i	$-0.794039\pi$
$331$	2.24022	−	3.88018i	0.123134	−	0.213274i	0.921002	+	0.389558i	$0.127372\pi$
$332$	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	0.922342	−	0.386373i	$-0.126272\pi$
$337$	2.32337	+	4.02420i	0.126562	+	0.219212i	−0.795780	+	0.605585i	$0.792939\pi$
$338$	−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	0.919284	−	0.393594i	$-0.128769\pi$
$347$	2.21262	+	3.83236i	0.118779	+	0.205732i	−0.800505	+	0.599326i	$0.795435\pi$
$348$	1.87161	+	0.248958i	0.100329	+	0.0133455i
$349$	0.00675754	−	0.0117044i	0.000361723	−	0.000626522i	−0.865844	−	0.500313i	$-0.833218\pi$
$349$	0.00675754	−	0.0117044i	0.000361723	−	0.000626522i	0.866206	+	0.499687i	$0.166552\pi$
$350$	−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	0.135031	+	0.990841i	$0.456887\pi$
$353$	−14.8536	+	25.7272i	−0.790578	+	1.36932i	−0.925609	+	0.378481i	$0.876447\pi$
$354$	−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	−0.902062	−	0.431607i	$-0.857947\pi$
$367$	−1.47986	+	2.56319i	−0.0772481	+	0.133798i	0.824814	+	0.565405i	$0.191280\pi$
$368$	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	0.800874	−	0.598833i	$-0.204369\pi$
$373$	−2.28220	−	3.95289i	−0.118168	−	0.204673i	−0.919042	+	0.394160i	$0.871035\pi$
$374$	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	0.724140	−	0.689653i	$-0.242237\pi$
$383$	−4.60271	−	7.97213i	−0.235187	−	0.407357i	−0.959327	+	0.282297i	$0.908904\pi$
$384$	−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	−0.320945	−	0.947098i	$-0.604000\pi$
$389$	13.0121	−	22.5376i	0.659738	−	1.14270i	0.980683	−	0.195603i	$-0.0626662\pi$
$390$	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	0.855547	−	0.517725i	$-0.173221\pi$
$401$	−0.412295	−	0.714116i	−0.0205890	−	0.0356612i	−0.876136	+	0.482063i	$0.839887\pi$
$402$	−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	−0.969271	−	0.245997i	$-0.920885\pi$
$409$	−14.1096	−	24.4385i	−0.697675	−	1.20841i	0.271596	−	0.962411i	$-0.412449\pi$
$410$	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	−0.991840	−	0.127486i	$-0.959309\pi$
$419$	−12.4112	−	21.4968i	−0.606327	−	1.05019i	0.385514	−	0.922702i	$-0.374024\pi$
$420$	10.3825	+	25.1610i	0.506614	+	1.22773i
$421$	−16.4032	+	28.4112i	−0.799444	+	1.38468i	0.120534	+	0.992709i	$0.461539\pi$
$421$	−16.4032	+	28.4112i	−0.799444	+	1.38468i	−0.919978	+	0.391969i	$0.871794\pi$
$422$	−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	−0.997284	−	0.0736453i	$-0.976537\pi$
$439$	−9.11140	+	15.7814i	−0.434864	+	0.753206i	0.562421	+	0.826851i	$0.309870\pi$
$440$	−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	−0.936711	−	0.350104i	$-0.886146\pi$
$443$	−3.47615	+	6.02087i	−0.165157	+	0.286060i	0.771554	+	0.636164i	$0.219480\pi$
$444$	−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	−0.992952	−	0.118514i	$-0.962187\pi$
$457$	−8.41934	+	14.5827i	−0.393840	+	0.682151i	0.599112	+	0.800665i	$0.295520\pi$
$458$	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	0.112664	−	0.993633i	$-0.464062\pi$
$461$	19.6855	−	34.0962i	0.916844	−	1.58802i	0.804180	−	0.594386i	$-0.202605\pi$
$462$	77.2839	+	10.2802i	3.59557	+	0.478277i
$463$	1.44170	+	2.49710i	0.0670016	+	0.116050i	0.897580	−	0.440851i	$-0.145323\pi$
$463$	1.44170	+	2.49710i	0.0670016	+	0.116050i	−0.830579	+	0.556902i	$0.811990\pi$
$464$	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	−0.999939	−	0.0110508i	$-0.996482\pi$
$479$	−10.7329	+	18.5899i	−0.490399	+	0.849396i	0.509540	+	0.860447i	$0.329816\pi$
$480$	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	0.954741	−	0.297440i	$-0.0961328\pi$
$491$	4.87000	+	8.43508i	0.219780	+	0.380670i	−0.734961	+	0.678110i	$0.762799\pi$
$492$	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	−0.964426	−	0.264352i	$-0.914842\pi$
$499$	−15.8859	−	27.5151i	−0.711149	−	1.23175i	0.253277	−	0.967394i	$-0.418491\pi$
$500$	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	0.960472	−	0.278375i	$-0.0897959\pi$
$509$	5.39561	+	9.34547i	0.239156	+	0.414231i	−0.721316	+	0.692606i	$0.756463\pi$
$510$	−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	−0.826750	−	0.562570i	$-0.809813\pi$
$547$	1.72662	−	2.99059i	0.0738249	−	0.127868i	0.900575	+	0.434701i	$0.143146\pi$
$548$	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	0.997746	+	0.0670966i	$0.0213736\pi$
$563$	13.2158	+	22.8905i	0.556981	+	0.964719i	−0.440766	+	0.897622i	$0.645293\pi$
$564$	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	−0.999370	−	0.0354904i	$-0.988701\pi$
$569$	−11.1862	+	19.3750i	−0.468949	+	0.812244i	0.530421	+	0.847735i	$0.322034\pi$
$570$	−0.508484	−	0.0676375i	−0.0212980	−	0.00283302i
$571$	7.47062	+	12.9395i	0.312636	+	0.541501i	0.978932	−	0.204186i	$-0.0654548\pi$
$571$	7.47062	+	12.9395i	0.312636	+	0.541501i	−0.666297	+	0.745687i	$0.732121\pi$
$572$	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	−0.722645	−	0.691219i	$-0.757074\pi$
$587$	5.74909	−	9.95772i	0.237291	−	0.410999i	0.959936	+	0.280220i	$0.0904073\pi$
$588$	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	0.507153	−	0.861856i	$-0.330698\pi$
$599$	−12.0613	−	20.8909i	−0.492813	−	0.853577i	−0.999966	+	0.00827908i	$0.997365\pi$
$600$	5.15676	−	6.70177i	0.210524	−	0.273599i
$601$	−0.171419	+	0.296906i	−0.00699232	+	0.0121111i	−0.869500	−	0.493932i	$-0.835559\pi$
$601$	−0.171419	+	0.296906i	−0.00699232	+	0.0121111i	0.862508	+	0.506043i	$0.168892\pi$
$602$	−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	0.946515	+	0.322659i	$0.104577\pi$
$607$	18.5443	+	32.1196i	0.752688	+	1.30369i	−0.193827	+	0.981036i	$0.562090\pi$
$608$	−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	0.966246	−	0.257623i	$-0.0829392\pi$
$617$	6.45863	+	11.1867i	0.260015	+	0.450359i	−0.706231	+	0.707982i	$0.749606\pi$
$618$	19.3886	+	2.57903i	0.779923	+	0.103744i
$619$	3.24865	−	5.62683i	0.130574	−	0.226161i	−0.793324	−	0.608800i	$-0.791651\pi$
$619$	3.24865	−	5.62683i	0.130574	−	0.226161i	0.923898	+	0.382639i	$0.124985\pi$
$620$	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	0.0835833	+	0.996501i	$0.473364\pi$
$641$	−20.7912	+	36.0114i	−0.821203	+	1.42237i	−0.904787	+	0.425865i	$0.859970\pi$
$642$	3.82735	−	4.97407i	0.151054	−	0.196311i
$643$	7.24965	+	12.5568i	0.285898	+	0.495190i	0.972827	−	0.231535i	$-0.0743748\pi$
$643$	7.24965	+	12.5568i	0.285898	+	0.495190i	−0.686928	+	0.726725i	$0.741041\pi$
$644$	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	0.743836	−	0.668362i	$-0.233004\pi$
$653$	−5.28711	−	9.15755i	−0.206901	−	0.358362i	−0.950737	+	0.310000i	$0.899671\pi$
$654$	−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	−0.381602	−	0.924327i	$-0.624627\pi$
$659$	15.6513	−	27.1089i	0.609690	−	1.05601i	0.991291	−	0.131687i	$-0.0420393\pi$
$660$	−12.3309	−	29.8827i	−0.479978	−	1.16318i
$661$	6.52034	+	11.2936i	0.253612	+	0.439269i	0.964518	−	0.264019i	$-0.0850480\pi$
$661$	6.52034	+	11.2936i	0.253612	+	0.439269i	−0.710906	+	0.703287i	$0.751715\pi$
$662$	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	−0.723093	−	0.690751i	$-0.757280\pi$
$673$	6.13953	−	10.6340i	0.236661	−	0.409910i	0.959754	+	0.280841i	$0.0906134\pi$
$674$	−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	0.272155	+	0.962253i	$0.412264\pi$
$677$	−18.1421	+	31.4231i	−0.697258	+	1.20769i	−0.969413	+	0.245434i	$0.921070\pi$
$678$	−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	0.135673	−	0.990754i	$-0.456680\pi$
$691$	24.3378	−	42.1543i	0.925854	−	1.60363i	0.790181	−	0.612873i	$-0.209986\pi$
$692$	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	−0.581875	−	0.813278i	$-0.697681\pi$
$709$	11.0072	−	19.0649i	0.413382	−	0.715999i	0.995257	+	0.0972792i	$0.0310140\pi$
$710$	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	−0.418365	−	0.908279i	$-0.637397\pi$
$727$	15.5687	−	26.9657i	0.577410	−	1.00010i	0.995775	−	0.0918250i	$-0.0292700\pi$
$728$	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	0.996933	−	0.0782593i	$-0.0249362\pi$
$733$	11.6605	+	20.1967i	0.430692	+	0.745980i	−0.566241	+	0.824240i	$0.691603\pi$
$734$	−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	−0.957848	−	0.287276i	$-0.907250\pi$
$743$	−19.8360	−	34.3570i	−0.727713	−	1.26044i	0.230135	−	0.973159i	$-0.426083\pi$
$744$	−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	0.991935	−	0.126746i	$-0.0404533\pi$
$751$	10.5836	+	18.3314i	0.386203	+	0.668922i	−0.605733	+	0.795668i	$0.707120\pi$
$752$	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	0.970073	+	0.242815i	$0.0780708\pi$
$761$	19.1813	+	33.2229i	0.695320	+	1.20433i	−0.274752	+	0.961515i	$0.588596\pi$
$762$	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	0.977663	−	0.210180i	$-0.0674049\pi$
$769$	8.50812	+	14.7365i	0.306811	+	0.531412i	−0.670852	+	0.741591i	$0.734072\pi$
$770$	−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	0.905823	−	0.423657i	$-0.139254\pi$
$787$	2.41300	+	4.17944i	0.0860141	+	0.148981i	−0.819809	+	0.572637i	$0.805920\pi$
$788$	−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	0.552720	−	0.833367i	$-0.313590\pi$
$797$	−12.5729	−	21.7770i	−0.445357	−	0.771380i	−0.998077	+	0.0619864i	$0.980256\pi$
$798$	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	−0.989717	−	0.143039i	$-0.954312\pi$
$821$	−10.6298	+	18.4114i	−0.370983	+	0.642561i	0.618734	+	0.785600i	$0.287646\pi$
$822$	11.8549	+	28.7292i	0.413486	+	1.00205i
$823$	6.19775	+	10.7348i	0.216040	+	0.374192i	0.953594	−	0.301096i	$-0.0973525\pi$
$823$	6.19775	+	10.7348i	0.216040	+	0.374192i	−0.737554	+	0.675288i	$0.764019\pi$
$824$	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	−0.397166	−	0.917747i	$-0.630006\pi$
$839$	17.2695	−	29.9116i	0.596209	−	1.03266i	0.993375	−	0.114917i	$-0.0366603\pi$
$840$	−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	−0.513109	−	0.858323i	$-0.671506\pi$
$853$	14.2168	−	24.6243i	0.486775	−	0.843119i	0.999884	+	0.0152040i	$0.00483976\pi$
$854$	−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	−0.989798	−	0.142481i	$-0.954492\pi$
$857$	−10.8757	+	18.8373i	−0.371507	+	0.643468i	0.618291	+	0.785949i	$0.287825\pi$
$858$	−12.0840	+	15.7045i	−0.412542	+	0.536144i
$859$	1.93271	+	3.34755i	0.0659431	+	0.114217i	0.897112	−	0.441803i	$-0.145661\pi$
$859$	1.93271	+	3.34755i	0.0659431	+	0.114217i	−0.831169	+	0.556020i	$0.812328\pi$
$860$	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	0.647944	−	0.761688i	$-0.275629\pi$
$877$	−9.94057	−	17.2176i	−0.335669	−	0.581396i	−0.983613	+	0.180292i	$0.942296\pi$
$878$	−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	0.922450	−	0.386116i	$-0.126184\pi$
$887$	3.77758	+	6.54296i	0.126839	+	0.219691i	−0.795611	+	0.605807i	$0.792850\pi$
$888$	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	0.334391	+	0.942435i	$0.391470\pi$
$907$	−19.5449	+	33.8527i	−0.648977	+	1.12406i	−0.983368	+	0.181627i	$0.941864\pi$
$908$	−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	−0.399816	−	0.916595i	$-0.630926\pi$
$911$	17.9251	−	31.0473i	0.593887	−	1.02864i	0.993703	−	0.112046i	$-0.0357405\pi$
$912$	−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	−0.833062	−	0.553179i	$-0.813415\pi$
$929$	1.90606	−	3.30140i	0.0625359	−	0.108315i	0.895598	+	0.444864i	$0.146748\pi$
$930$	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	0.950187	−	0.311681i	$-0.100892\pi$
$941$	6.29373	+	10.9011i	0.205170	+	0.355365i	−0.745017	+	0.667045i	$0.767559\pi$
$942$	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	−0.413075	−	0.910697i	$-0.635545\pi$
$947$	17.9147	−	31.0292i	0.582149	−	1.00831i	0.995224	−	0.0976150i	$-0.0311214\pi$
$948$	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	0.965737	−	0.259523i	$-0.0835653\pi$
$967$	8.02651	+	13.9023i	0.258115	+	0.447068i	−0.707622	+	0.706591i	$0.750232\pi$
$968$	−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	0.589583	−	0.807708i	$-0.299292\pi$
$977$	−12.6498	−	21.9102i	−0.404704	−	0.700968i	−0.994287	+	0.106740i	$0.965959\pi$
$978$	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	−0.575588	−	0.817740i	$-0.695227\pi$
$983$	13.1804	−	22.8291i	0.420389	−	0.728135i	0.995977	+	0.0896044i	$0.0285603\pi$
$984$	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	−0.377787	−	0.925892i	$-0.623315\pi$
$997$	19.3542	−	33.5224i	0.612953	−	1.06167i	0.990740	−	0.135773i	$-0.0433518\pi$
$998$	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.196.1	✓	16
3.2	odd	2		1755.2.i.f.586.8		16
9.2	odd	6		5265.2.a.ba.1.1		8
9.4	even	3	inner	585.2.i.e.391.1	yes	16
9.5	odd	6		1755.2.i.f.1171.8		16
9.7	even	3		5265.2.a.bf.1.8		8

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