LMFDB - Embedded newform 570.2.m.a.493.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(37,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("570.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 153x^{16} + 6416x^{12} + 78648x^{8} + 19120x^{4} + 16 $ x^20 + 153x^16 + 6416x^12 + 78648x^8 + 19120x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.7
Root			$0.120370 + 0.120370i$ of defining polynomial
Character	$\chi$	$=$	570.493
Dual form			570.2.m.a.37.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-1.66396 - 1.49373i) q^{5} +1.00000 q^{6} +(-0.170229 + 0.170229i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-1.66396 - 1.49373i) q^{5} +1.00000 q^{6} +(-0.170229 + 0.170229i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-0.120370 - 2.23283i) q^{10} +3.43349 q^{11} +(0.707107 + 0.707107i) q^{12} +(4.54030 - 4.54030i) q^{13} -0.240740 q^{14} +(-2.23283 + 0.120370i) q^{15} -1.00000 q^{16} +(0.537531 - 0.537531i) q^{17} +(0.707107 - 0.707107i) q^{18} +(2.42784 - 3.62016i) q^{19} +(1.49373 - 1.66396i) q^{20} +0.240740i q^{21} +(2.42784 + 2.42784i) q^{22} +(5.15769 + 5.15769i) q^{23} +1.00000i q^{24} +(0.537531 + 4.97102i) q^{25} +6.42095 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.170229 - 0.170229i) q^{28} -5.37513 q^{29} +(-1.66396 - 1.49373i) q^{30} -5.37513i q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.42784 - 2.42784i) q^{33} +0.760184 q^{34} +(0.537531 - 0.0289779i) q^{35} +1.00000 q^{36} +(-5.54122 - 5.54122i) q^{37} +(4.27659 - 0.843095i) q^{38} -6.42095i q^{39} +(2.23283 - 0.120370i) q^{40} -3.68222i q^{41} +(-0.170229 + 0.170229i) q^{42} +(2.29224 + 2.29224i) q^{43} +3.43349i q^{44} +(-1.49373 + 1.66396i) q^{45} +7.29408i q^{46} +(-9.57865 + 9.57865i) q^{47} +(-0.707107 + 0.707107i) q^{48} +6.94204i q^{49} +(-3.13495 + 3.89514i) q^{50} -0.760184i q^{51} +(4.54030 + 4.54030i) q^{52} +(-1.93366 + 1.93366i) q^{53} -1.00000i q^{54} +(-5.71319 - 5.12871i) q^{55} -0.240740i q^{56} +(-0.843095 - 4.27659i) q^{57} +(-3.80079 - 3.80079i) q^{58} -4.20166 q^{59} +(-0.120370 - 2.23283i) q^{60} +1.65954 q^{61} +(3.80079 - 3.80079i) q^{62} +(0.170229 + 0.170229i) q^{63} -1.00000i q^{64} +(-14.3369 + 0.772891i) q^{65} +3.43349 q^{66} +(0.481480 + 0.481480i) q^{67} +(0.537531 + 0.537531i) q^{68} +7.29408 q^{69} +(0.400582 + 0.359601i) q^{70} +8.93130i q^{71} +(0.707107 + 0.707107i) q^{72} +(8.74888 + 8.74888i) q^{73} -7.83647i q^{74} +(3.89514 + 3.13495i) q^{75} +(3.62016 + 2.42784i) q^{76} +(-0.584480 + 0.584480i) q^{77} +(4.54030 - 4.54030i) q^{78} +1.15022 q^{79} +(1.66396 + 1.49373i) q^{80} -1.00000 q^{81} +(2.60372 - 2.60372i) q^{82} +(-9.97102 - 9.97102i) q^{83} -0.240740 q^{84} +(-1.69736 + 0.0915034i) q^{85} +3.24172i q^{86} +(-3.80079 + 3.80079i) q^{87} +(-2.42784 + 2.42784i) q^{88} +2.10098 q^{89} +(-2.23283 + 0.120370i) q^{90} +1.54578i q^{91} +(-5.15769 + 5.15769i) q^{92} +(-3.80079 - 3.80079i) q^{93} -13.5463 q^{94} +(-9.44739 + 2.39726i) q^{95} -1.00000 q^{96} +(10.8544 + 10.8544i) q^{97} +(-4.90877 + 4.90877i) q^{98} -3.43349i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5} + 20 q^{6} - 4 q^{7}+O(q^{10}) $ 20 * q - 4 * q^5 + 20 * q^6 - 4 * q^7	$ 20 q - 4 q^{5} + 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} + 4 q^{17} + 44 q^{23} + 4 q^{25} - 8 q^{26} - 4 q^{28} - 4 q^{30} + 4 q^{35} + 20 q^{36} - 4 q^{38} - 4 q^{42} + 52 q^{43} + 4 q^{47} + 16 q^{55} - 4 q^{57} + 8 q^{58} + 32 q^{61} - 8 q^{62} + 4 q^{63} - 8 q^{66} + 4 q^{68} - 20 q^{73} + 20 q^{76} - 24 q^{77} + 4 q^{80} - 20 q^{81} - 24 q^{82} - 116 q^{83} - 60 q^{85} + 8 q^{87} - 44 q^{92} + 8 q^{93} - 32 q^{95} - 20 q^{96}+O(q^{100}) $ 20 * q - 4 * q^5 + 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 + 4 * q^17 + 44 * q^23 + 4 * q^25 - 8 * q^26 - 4 * q^28 - 4 * q^30 + 4 * q^35 + 20 * q^36 - 4 * q^38 - 4 * q^42 + 52 * q^43 + 4 * q^47 + 16 * q^55 - 4 * q^57 + 8 * q^58 + 32 * q^61 - 8 * q^62 + 4 * q^63 - 8 * q^66 + 4 * q^68 - 20 * q^73 + 20 * q^76 - 24 * q^77 + 4 * q^80 - 20 * q^81 - 24 * q^82 - 116 * q^83 - 60 * q^85 + 8 * q^87 - 44 * q^92 + 8 * q^93 - 32 * q^95 - 20 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$			1.00000i			0.500000i
$5$	−1.66396	−	1.49373i	−0.744146	−	0.668017i
$5$	−1.66396	−	1.49373i	−0.744146	−	0.668017i
$6$	1.00000			0.408248
$7$	−0.170229	+	0.170229i	−0.0643405	+	0.0643405i	−0.738545	−	0.674204i	$-0.764487\pi$
$7$	−0.170229	+	0.170229i	−0.0643405	+	0.0643405i	0.674204	+	0.738545i	$0.264487\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	−0.120370	−	2.23283i	−0.0380644	−	0.706082i
$11$	3.43349			1.03524			0.517618	−	0.855612i	$-0.326819\pi$
$11$	3.43349			1.03524			0.517618	+	0.855612i	$0.326819\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	4.54030	−	4.54030i	1.25925	−	1.25925i	0.307803	−	0.951450i	$-0.400406\pi$
$13$	4.54030	−	4.54030i	1.25925	−	1.25925i	0.951450	−	0.307803i	$-0.0995936\pi$
$14$	−0.240740			−0.0643405
$15$	−2.23283	+	0.120370i	−0.576513	+	0.0310794i
$16$	−1.00000			−0.250000
$17$	0.537531	−	0.537531i	0.130370	−	0.130370i	−0.638911	−	0.769281i	$-0.720615\pi$
$17$	0.537531	−	0.537531i	0.130370	−	0.130370i	0.769281	+	0.638911i	$0.220615\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	2.42784	−	3.62016i	0.556986	−	0.830522i
$19$	2.42784	−	3.62016i	0.556986	−	0.830522i
$20$	1.49373	−	1.66396i	0.334009	−	0.372073i
$21$			0.240740i			0.0525338i
$22$	2.42784	+	2.42784i	0.517618	+	0.517618i
$23$	5.15769	+	5.15769i	1.07545	+	1.07545i	0.996911	+	0.0785425i	$0.0250266\pi$
$23$	5.15769	+	5.15769i	1.07545	+	1.07545i	0.0785425	+	0.996911i	$0.474973\pi$
$24$			1.00000i			0.204124i
$25$	0.537531	+	4.97102i	0.107506	+	0.994204i
$26$	6.42095			1.25925
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−0.170229	−	0.170229i	−0.0321703	−	0.0321703i
$29$	−5.37513			−0.998137			−0.499069	−	0.866562i	$-0.666324\pi$
$29$	−5.37513			−0.998137			−0.499069	+	0.866562i	$0.666324\pi$
$30$	−1.66396	−	1.49373i	−0.303796	−	0.272717i
$31$		−	5.37513i		−	0.965402i	−0.875785	−	0.482701i	$-0.839656\pi$
$31$		−	5.37513i		−	0.965402i	0.875785	−	0.482701i	$-0.160344\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	2.42784	−	2.42784i	0.422634	−	0.422634i
$34$	0.760184			0.130370
$35$	0.537531	−	0.0289779i	0.0908593	−	0.00489816i
$36$	1.00000			0.166667
$37$	−5.54122	−	5.54122i	−0.910972	−	0.910972i	0.0853770	−	0.996349i	$-0.472791\pi$
$37$	−5.54122	−	5.54122i	−0.910972	−	0.910972i	−0.996349	+	0.0853770i	$0.972791\pi$
$38$	4.27659	−	0.843095i	0.693754	−	0.136768i
$39$		−	6.42095i		−	1.02818i
$40$	2.23283	−	0.120370i	0.353041	−	0.0190322i
$41$		−	3.68222i		−	0.575066i	−0.957771	−	0.287533i	$-0.907165\pi$
$41$		−	3.68222i		−	0.575066i	0.957771	−	0.287533i	$-0.0928350\pi$
$42$	−0.170229	+	0.170229i	−0.0262669	+	0.0262669i
$43$	2.29224	+	2.29224i	0.349563	+	0.349563i	0.859947	−	0.510384i	$-0.170497\pi$
$43$	2.29224	+	2.29224i	0.349563	+	0.349563i	−0.510384	+	0.859947i	$0.670497\pi$
$44$			3.43349i			0.517618i
$45$	−1.49373	+	1.66396i	−0.222672	+	0.248049i
$46$			7.29408i			1.07545i
$47$	−9.57865	+	9.57865i	−1.39719	+	1.39719i	−0.589208	+	0.807982i	$0.700560\pi$
$47$	−9.57865	+	9.57865i	−1.39719	+	1.39719i	−0.807982	+	0.589208i	$0.799440\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$			6.94204i			0.991721i
$50$	−3.13495	+	3.89514i	−0.443349	+	0.550855i
$51$		−	0.760184i		−	0.106447i
$52$	4.54030	+	4.54030i	0.629626	+	0.629626i
$53$	−1.93366	+	1.93366i	−0.265608	+	0.265608i	−0.827328	−	0.561720i	$-0.810140\pi$
$53$	−1.93366	+	1.93366i	−0.265608	+	0.265608i	0.561720	+	0.827328i	$0.310140\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−5.71319	−	5.12871i	−0.770367	−	0.691556i
$56$		−	0.240740i		−	0.0321703i
$57$	−0.843095	−	4.27659i	−0.111671	−	0.566448i
$58$	−3.80079	−	3.80079i	−0.499069	−	0.499069i
$59$	−4.20166			−0.547010			−0.273505	−	0.961871i	$-0.588183\pi$
$59$	−4.20166			−0.547010			−0.273505	+	0.961871i	$0.588183\pi$
$60$	−0.120370	−	2.23283i	−0.0155397	−	0.288257i
$61$	1.65954			0.212483			0.106241	−	0.994340i	$-0.466118\pi$
$61$	1.65954			0.212483			0.106241	+	0.994340i	$0.466118\pi$
$62$	3.80079	−	3.80079i	0.482701	−	0.482701i
$63$	0.170229	+	0.170229i	0.0214468	+	0.0214468i
$64$		−	1.00000i		−	0.125000i
$65$	−14.3369	+	0.772891i	−1.77827	+	0.0958653i
$66$	3.43349			0.422634
$67$	0.481480	+	0.481480i	0.0588222	+	0.0588222i	0.735906	−	0.677084i	$-0.236757\pi$
$67$	0.481480	+	0.481480i	0.0588222	+	0.0588222i	−0.677084	+	0.735906i	$0.736757\pi$
$68$	0.537531	+	0.537531i	0.0651852	+	0.0651852i
$69$	7.29408			0.878104
$70$	0.400582	+	0.359601i	0.0478787	+	0.0429806i
$71$			8.93130i			1.05995i	0.848013	+	0.529975i	$0.177799\pi$
$71$			8.93130i			1.05995i	−0.848013	+	0.529975i	$0.822201\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	8.74888	+	8.74888i	1.02398	+	1.02398i	0.999705	+	0.0242731i	$0.00772714\pi$
$73$	8.74888	+	8.74888i	1.02398	+	1.02398i	0.0242731	+	0.999705i	$0.492273\pi$
$74$		−	7.83647i		−	0.910972i
$75$	3.89514	+	3.13495i	0.449771	+	0.361993i
$76$	3.62016	+	2.42784i	0.415261	+	0.278493i
$77$	−0.584480	+	0.584480i	−0.0666077	+	0.0666077i
$78$	4.54030	−	4.54030i	0.514088	−	0.514088i
$79$	1.15022			0.129410			0.0647050	−	0.997904i	$-0.479389\pi$
$79$	1.15022			0.129410			0.0647050	+	0.997904i	$0.479389\pi$
$80$	1.66396	+	1.49373i	0.186036	+	0.167004i
$81$	−1.00000			−0.111111
$82$	2.60372	−	2.60372i	0.287533	−	0.287533i
$83$	−9.97102	−	9.97102i	−1.09446	−	1.09446i	−0.995046	−	0.0994159i	$-0.968303\pi$
$83$	−9.97102	−	9.97102i	−1.09446	−	1.09446i	−0.0994159	−	0.995046i	$-0.531697\pi$
$84$	−0.240740			−0.0262669
$85$	−1.69736	+	0.0915034i	−0.184104	+	0.00992494i
$86$			3.24172i			0.349563i
$87$	−3.80079	+	3.80079i	−0.407488	+	0.407488i
$88$	−2.42784	+	2.42784i	−0.258809	+	0.258809i
$89$	2.10098			0.222703			0.111351	−	0.993781i	$-0.464482\pi$
$89$	2.10098			0.222703			0.111351	+	0.993781i	$0.464482\pi$
$90$	−2.23283	+	0.120370i	−0.235361	+	0.0126881i
$91$			1.54578i			0.162042i
$92$	−5.15769	+	5.15769i	−0.537727	+	0.537727i
$93$	−3.80079	−	3.80079i	−0.394124	−	0.394124i
$94$	−13.5463			−1.39719
$95$	−9.44739	+	2.39726i	−0.969282	+	0.245953i
$96$	−1.00000			−0.102062
$97$	10.8544	+	10.8544i	1.10210	+	1.10210i	0.994157	+	0.107942i	$0.0344260\pi$
$97$	10.8544	+	10.8544i	1.10210	+	1.10210i	0.107942	+	0.994157i	$0.465574\pi$
$98$	−4.90877	+	4.90877i	−0.495860	+	0.495860i
$99$		−	3.43349i		−	0.345079i
$100$	−4.97102	+	0.537531i	−0.497102	+	0.0537531i
$101$	8.90870			0.886449			0.443225	−	0.896411i	$-0.353834\pi$
$101$	8.90870			0.886449			0.443225	+	0.896411i	$0.353834\pi$
$102$	0.537531	−	0.537531i	0.0532235	−	0.0532235i
$103$	6.26365	−	6.26365i	0.617176	−	0.617176i	−0.327630	−	0.944806i	$-0.606250\pi$
$103$	6.26365	−	6.26365i	0.617176	−	0.617176i	0.944806	+	0.327630i	$0.106250\pi$
$104$			6.42095i			0.629626i
$105$	0.359601	−	0.400582i	0.0350935	−	0.0390928i
$106$	−2.73460			−0.265608
$107$	5.59814	+	5.59814i	0.541193	+	0.541193i	0.923879	−	0.382686i	$-0.125001\pi$
$107$	5.59814	+	5.59814i	0.541193	+	0.541193i	−0.382686	+	0.923879i	$0.625001\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−10.7123			−1.02605			−0.513026	−	0.858373i	$-0.671476\pi$
$109$	−10.7123			−1.02605			−0.513026	+	0.858373i	$0.671476\pi$
$110$	−0.413290	−	7.66639i	−0.0394056	−	0.730961i
$111$	−7.83647			−0.743805
$112$	0.170229	−	0.170229i	0.0160851	−	0.0160851i
$113$	−6.81260	+	6.81260i	−0.640875	+	0.640875i	−0.950771	−	0.309895i	$-0.899706\pi$
$113$	−6.81260	+	6.81260i	−0.640875	+	0.640875i	0.309895	+	0.950771i	$0.399706\pi$
$114$	2.42784	−	3.62016i	0.227389	−	0.339059i
$115$	−0.877989	−	16.2864i	−0.0818729	−	1.51872i
$116$		−	5.37513i		−	0.499069i
$117$	−4.54030	−	4.54030i	−0.419751	−	0.419751i
$118$	−2.97102	−	2.97102i	−0.273505	−	0.273505i
$119$			0.183007i			0.0167762i
$120$	1.49373	−	1.66396i	0.136358	−	0.151898i
$121$	0.788861			0.0717146
$122$	1.17347	+	1.17347i	0.106241	+	0.106241i
$123$	−2.60372	−	2.60372i	−0.234770	−	0.234770i
$124$	5.37513			0.482701
$125$	6.53094	−	9.07451i	0.584145	−	0.811649i
$126$			0.240740i			0.0214468i
$127$	5.19935	+	5.19935i	0.461368	+	0.461368i	0.899104	−	0.437736i	$-0.144219\pi$
$127$	5.19935	+	5.19935i	0.461368	+	0.461368i	−0.437736	+	0.899104i	$0.644219\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	3.24172			0.285417
$130$	−10.6842	−	9.59118i	−0.937068	−	0.841202i
$131$	2.14729			0.187610			0.0938048	−	0.995591i	$-0.470097\pi$
$131$	2.14729			0.187610			0.0938048	+	0.995591i	$0.470097\pi$
$132$	2.42784	+	2.42784i	0.211317	+	0.211317i
$133$	0.202967	+	1.02955i	0.0175995	+	0.0892730i
$134$			0.680916i			0.0588222i
$135$	0.120370	+	2.23283i	0.0103598	+	0.192171i
$136$			0.760184i			0.0651852i
$137$	−13.5518	+	13.5518i	−1.15781	+	1.15781i	−0.172863	+	0.984946i	$0.555302\pi$
$137$	−13.5518	+	13.5518i	−1.15781	+	1.15781i	−0.984946	+	0.172863i	$0.944698\pi$
$138$	5.15769	+	5.15769i	0.439052	+	0.439052i
$139$		−	10.5015i		−	0.890721i	−0.895351	−	0.445361i	$-0.853075\pi$
$139$		−	10.5015i		−	0.890721i	0.895351	−	0.445361i	$-0.146925\pi$
$140$	0.0289779	+	0.537531i	0.00244908	+	0.0454297i
$141$			13.5463i			1.14080i
$142$	−6.31539	+	6.31539i	−0.529975	+	0.529975i
$143$	15.5891	−	15.5891i	1.30362	−	1.30362i
$144$			1.00000i			0.0833333i
$145$	8.94401	+	8.02901i	0.742760	+	0.666773i
$146$			12.3728i			1.02398i
$147$	4.90877	+	4.90877i	0.404868	+	0.404868i
$148$	5.54122	−	5.54122i	0.455486	−	0.455486i
$149$			1.02035i			0.0835900i	0.999126	+	0.0417950i	$0.0133076\pi$
$149$			1.02035i			0.0835900i	−0.999126	+	0.0417950i	$0.986692\pi$
$150$	0.537531	+	4.97102i	0.0438892	+	0.405882i
$151$		−	19.8394i		−	1.61451i	−0.590204	−	0.807254i	$-0.700953\pi$
$151$		−	19.8394i		−	1.61451i	0.590204	−	0.807254i	$-0.299047\pi$
$152$	0.843095	+	4.27659i	0.0683841	+	0.346877i
$153$	−0.537531	−	0.537531i	−0.0434568	−	0.0434568i
$154$	−0.826579			−0.0666077
$155$	−8.02901	+	8.94401i	−0.644905	+	0.718400i
$156$	6.42095			0.514088
$157$	−13.1863	+	13.1863i	−1.05238	+	1.05238i	−0.0538289	+	0.998550i	$0.517143\pi$
$157$	−13.1863	+	13.1863i	−1.05238	+	1.05238i	−0.998550	+	0.0538289i	$0.982857\pi$
$158$	0.813330	+	0.813330i	0.0647050	+	0.0647050i
$159$			2.73460i			0.216868i
$160$	0.120370	+	2.23283i	0.00951609	+	0.176520i
$161$	−1.75598			−0.138390
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	1.19921	+	1.19921i	0.0939291	+	0.0939291i	0.752510	−	0.658581i	$-0.228843\pi$
$163$	1.19921	+	1.19921i	0.0939291	+	0.0939291i	−0.658581	+	0.752510i	$0.728843\pi$
$164$	3.68222			0.287533
$165$	−7.66639	+	0.413290i	−0.596827	+	0.0321746i
$166$		−	14.1012i		−	1.09446i
$167$	−11.1290	−	11.1290i	−0.861184	−	0.861184i	0.130292	−	0.991476i	$-0.458409\pi$
$167$	−11.1290	−	11.1290i	−0.861184	−	0.861184i	−0.991476	+	0.130292i	$0.958409\pi$
$168$	−0.170229	−	0.170229i	−0.0131335	−	0.0131335i
$169$		−	28.2287i		−	2.17144i
$170$	−1.26492	−	1.13551i	−0.0970146	−	0.0870897i
$171$	−3.62016	−	2.42784i	−0.276841	−	0.185662i
$172$	−2.29224	+	2.29224i	−0.174782	+	0.174782i
$173$	−15.2012	+	15.2012i	−1.15573	+	1.15573i	−0.170341	+	0.985385i	$0.554487\pi$
$173$	−15.2012	+	15.2012i	−1.15573	+	1.15573i	−0.985385	+	0.170341i	$0.945513\pi$
$174$	−5.37513			−0.407488
$175$	−0.937716	−	0.754709i	−0.0708846	−	0.0570506i
$176$	−3.43349			−0.258809
$177$	−2.97102	+	2.97102i	−0.223316	+	0.223316i
$178$	1.48561	+	1.48561i	0.111351	+	0.111351i
$179$	24.9536			1.86512			0.932559	−	0.361019i	$-0.117571\pi$
$179$	24.9536			1.86512			0.932559	+	0.361019i	$0.117571\pi$
$180$	−1.66396	−	1.49373i	−0.124024	−	0.111336i
$181$		−	15.9721i		−	1.18720i	−0.804762	−	0.593598i	$-0.797707\pi$
$181$		−	15.9721i		−	1.18720i	0.804762	−	0.593598i	$-0.202293\pi$
$182$	−1.09303	+	1.09303i	−0.0810210	+	0.0810210i
$183$	1.17347	−	1.17347i	0.0867456	−	0.0867456i
$184$	−7.29408			−0.537727
$185$	0.943277	+	17.4975i	0.0693511	+	1.28644i
$186$		−	5.37513i		−	0.394124i
$187$	1.84561	−	1.84561i	0.134964	−	0.134964i
$188$	−9.57865	−	9.57865i	−0.698595	−	0.698595i
$189$	0.240740			0.0175113
$190$	−8.37543	−	4.98520i	−0.607618	−	0.361664i
$191$	2.91580			0.210980			0.105490	−	0.994420i	$-0.466359\pi$
$191$	2.91580			0.210980			0.105490	+	0.994420i	$0.466359\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−6.67601	+	6.67601i	−0.480550	+	0.480550i	−0.905307	−	0.424758i	$-0.860359\pi$
$193$	−6.67601	+	6.67601i	−0.480550	+	0.480550i	0.424758	+	0.905307i	$0.360359\pi$
$194$			15.3505i			1.10210i
$195$	−9.59118	+	10.6842i	−0.686839	+	0.765113i
$196$	−6.94204			−0.495860
$197$	−4.08263	+	4.08263i	−0.290875	+	0.290875i	−0.837426	−	0.546551i	$-0.815941\pi$
$197$	−4.08263	+	4.08263i	−0.290875	+	0.290875i	0.546551	+	0.837426i	$0.315941\pi$
$198$	2.42784	−	2.42784i	0.172539	−	0.172539i
$199$			8.23662i			0.583879i	0.956437	+	0.291939i	$0.0943006\pi$
$199$			8.23662i			0.583879i	−0.956437	+	0.291939i	$0.905699\pi$
$200$	−3.89514	−	3.13495i	−0.275428	−	0.221675i
$201$	0.680916			0.0480281
$202$	6.29940	+	6.29940i	0.443225	+	0.443225i
$203$	0.915004	−	0.915004i	0.0642207	−	0.0642207i
$204$	0.760184			0.0532235
$205$	−5.50024	+	6.12706i	−0.384154	+	0.427933i
$206$	8.85814			0.617176
$207$	5.15769	−	5.15769i	0.358484	−	0.358484i
$208$	−4.54030	+	4.54030i	−0.314813	+	0.314813i
$209$	8.33598	−	12.4298i	0.576612	−	0.859787i
$210$	0.537531	−	0.0289779i	0.0370932	−	0.00199967i
$211$		−	14.6136i		−	1.00604i	−0.864275	−	0.503020i	$-0.832222\pi$
$211$		−	14.6136i		−	1.00604i	0.864275	−	0.503020i	$-0.167778\pi$
$212$	−1.93366	−	1.93366i	−0.132804	−	0.132804i
$213$	6.31539	+	6.31539i	0.432723	+	0.432723i
$214$			7.91697i			0.541193i
$215$	−0.390206	−	7.23819i	−0.0266118	−	0.493640i
$216$	1.00000			0.0680414
$217$	0.915004	+	0.915004i	0.0621145	+	0.0621145i
$218$	−7.57474	−	7.57474i	−0.513026	−	0.513026i
$219$	12.3728			0.836075
$220$	5.12871	−	5.71319i	0.345778	−	0.385183i
$221$		−	4.88110i		−	0.328339i
$222$	−5.54122	−	5.54122i	−0.371903	−	0.371903i
$223$	−15.9582	+	15.9582i	−1.06864	+	1.06864i	−0.0711734	+	0.997464i	$0.522674\pi$
$223$	−15.9582	+	15.9582i	−1.06864	+	1.06864i	−0.997464	+	0.0711734i	$0.977326\pi$
$224$	0.240740			0.0160851
$225$	4.97102	−	0.537531i	0.331401	−	0.0358354i
$226$	−9.63447			−0.640875
$227$	5.87132	+	5.87132i	0.389694	+	0.389694i	0.874578	−	0.484885i	$-0.161138\pi$
$227$	5.87132	+	5.87132i	0.389694	+	0.389694i	−0.484885	+	0.874578i	$0.661138\pi$
$228$	4.27659	−	0.843095i	0.283224	−	0.0558353i
$229$			10.2825i			0.679487i	0.940518	+	0.339743i	$0.110340\pi$
$229$			10.2825i			0.679487i	−0.940518	+	0.339743i	$0.889660\pi$
$230$	10.8954	−	12.1371i	0.718421	−	0.800294i
$231$			0.826579i			0.0543849i
$232$	3.80079	−	3.80079i	0.249534	−	0.249534i
$233$	14.4725	+	14.4725i	0.948123	+	0.948123i	0.998719	−	0.0505960i	$-0.0161121\pi$
$233$	14.4725	+	14.4725i	0.948123	+	0.948123i	−0.0505960	+	0.998719i	$0.516112\pi$
$234$		−	6.42095i		−	0.419751i
$235$	30.2464	−	1.63056i	1.97306	−	0.106366i
$236$		−	4.20166i		−	0.273505i
$237$	0.813330	−	0.813330i	0.0528314	−	0.0528314i
$238$	−0.129405	+	0.129405i	−0.00838810	+	0.00838810i
$239$		−	21.4459i		−	1.38722i	−0.720352	−	0.693609i	$-0.756020\pi$
$239$		−	21.4459i		−	1.38722i	0.720352	−	0.693609i	$-0.243980\pi$
$240$	2.23283	−	0.120370i	0.144128	−	0.00776986i
$241$		−	1.51636i		−	0.0976773i	−0.998807	−	0.0488387i	$-0.984448\pi$
$241$		−	1.51636i		−	0.0976773i	0.998807	−	0.0488387i	$-0.0155520\pi$
$242$	0.557809	+	0.557809i	0.0358573	+	0.0358573i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$			1.65954i			0.106241i
$245$	10.3696	−	11.5513i	0.662486	−	0.737985i
$246$		−	3.68222i		−	0.234770i
$247$	−5.41348	−	27.4598i	−0.344451	−	1.74722i
$248$	3.80079	+	3.80079i	0.241351	+	0.241351i
$249$	−14.1012			−0.893624
$250$	11.0347	−	1.79858i	0.697897	−	0.113752i
$251$	11.6524			0.735495			0.367748	−	0.929926i	$-0.380129\pi$
$251$	11.6524			0.735495			0.367748	+	0.929926i	$0.380129\pi$
$252$	−0.170229	+	0.170229i	−0.0107234	+	0.0107234i
$253$	17.7089	+	17.7089i	1.11335	+	1.11335i
$254$			7.35299i			0.461368i
$255$	−1.13551	+	1.26492i	−0.0711084	+	0.0792121i
$256$	1.00000			0.0625000
$257$	−1.00645	−	1.00645i	−0.0627804	−	0.0627804i	0.675020	−	0.737800i	$-0.264135\pi$
$257$	−1.00645	−	1.00645i	−0.0627804	−	0.0627804i	−0.737800	+	0.675020i	$0.764135\pi$
$258$	2.29224	+	2.29224i	0.142709	+	0.142709i
$259$	1.88655			0.117225
$260$	−0.772891	−	14.3369i	−0.0479327	−	0.889135i
$261$			5.37513i			0.332712i
$262$	1.51836	+	1.51836i	0.0938048	+	0.0938048i
$263$	0.396280	+	0.396280i	0.0244357	+	0.0244357i	0.719219	−	0.694783i	$-0.244500\pi$
$263$	0.396280	+	0.396280i	0.0244357	+	0.0244357i	−0.694783	+	0.719219i	$0.744500\pi$
$264$			3.43349i			0.211317i
$265$	6.10589	−	0.329165i	0.375082	−	0.0202204i
$266$	−0.584480	+	0.871519i	−0.0358368	+	0.0534362i
$267$	1.48561	−	1.48561i	0.0909181	−	0.0909181i
$268$	−0.481480	+	0.481480i	−0.0294111	+	0.0294111i
$269$	−20.9263			−1.27590			−0.637948	−	0.770079i	$-0.720217\pi$
$269$	−20.9263			−1.27590			−0.637948	+	0.770079i	$0.720217\pi$
$270$	−1.49373	+	1.66396i	−0.0909056	+	0.101265i
$271$	−16.9175			−1.02767			−0.513834	−	0.857890i	$-0.671775\pi$
$271$	−16.9175			−1.02767			−0.513834	+	0.857890i	$0.671775\pi$
$272$	−0.537531	+	0.537531i	−0.0325926	+	0.0325926i
$273$	1.09303	+	1.09303i	0.0661534	+	0.0661534i
$274$	−19.1651			−1.15781
$275$	1.84561	+	17.0680i	0.111294	+	1.02924i
$276$			7.29408i			0.439052i
$277$	15.6769	−	15.6769i	0.941931	−	0.941931i	−0.0564732	−	0.998404i	$-0.517986\pi$
$277$	15.6769	−	15.6769i	0.941931	−	0.941931i	0.998404	+	0.0564732i	$0.0179856\pi$
$278$	7.42565	−	7.42565i	0.445361	−	0.445361i
$279$	−5.37513			−0.321801
$280$	−0.359601	+	0.400582i	−0.0214903	+	0.0239394i
$281$		−	10.3485i		−	0.617342i	−0.951169	−	0.308671i	$-0.900116\pi$
$281$		−	10.3485i		−	0.617342i	0.951169	−	0.308671i	$-0.0998842\pi$
$282$	−9.57865	+	9.57865i	−0.570400	+	0.570400i
$283$	6.03331	+	6.03331i	0.358643	+	0.358643i	0.863313	−	0.504670i	$-0.168386\pi$
$283$	6.03331	+	6.03331i	0.358643	+	0.358643i	−0.504670	+	0.863313i	$0.668386\pi$
$284$	−8.93130			−0.529975
$285$	−4.98520	+	8.37543i	−0.295297	+	0.496118i
$286$	22.0463			1.30362
$287$	0.626820	+	0.626820i	0.0370000	+	0.0370000i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$			16.4221i			0.966007i
$290$	0.647005	+	12.0017i	0.0379935	+	0.704766i
$291$	15.3505			0.899860
$292$	−8.74888	+	8.74888i	−0.511989	+	0.511989i
$293$	6.64005	−	6.64005i	0.387916	−	0.387916i	−0.486028	−	0.873943i	$-0.661555\pi$
$293$	6.64005	−	6.64005i	0.387916	−	0.387916i	0.873943	+	0.486028i	$0.161555\pi$
$294$			6.94204i			0.404868i
$295$	6.99140	+	6.27615i	0.407055	+	0.365412i
$296$	7.83647			0.455486
$297$	−2.42784	−	2.42784i	−0.140878	−	0.140878i
$298$	−0.721494	+	0.721494i	−0.0417950	+	0.0417950i
$299$	46.8349			2.70853
$300$	−3.13495	+	3.89514i	−0.180997	+	0.224886i
$301$	−0.780412			−0.0449822
$302$	14.0286	−	14.0286i	0.807254	−	0.807254i
$303$	6.29940	−	6.29940i	0.361891	−	0.361891i
$304$	−2.42784	+	3.62016i	−0.139246	+	0.207631i
$305$	−2.76141	−	2.47891i	−0.158118	−	0.141942i
$306$		−	0.760184i		−	0.0434568i
$307$	6.21426	+	6.21426i	0.354667	+	0.354667i	0.861843	−	0.507176i	$-0.169311\pi$
$307$	6.21426	+	6.21426i	0.354667	+	0.354667i	−0.507176	+	0.861843i	$0.669311\pi$
$308$	−0.584480	−	0.584480i	−0.0333038	−	0.0333038i
$309$		−	8.85814i		−	0.503922i
$310$	−12.0017	+	0.647005i	−0.681653	+	0.0367474i
$311$	−4.55027			−0.258022			−0.129011	−	0.991643i	$-0.541180\pi$
$311$	−4.55027			−0.258022			−0.129011	+	0.991643i	$0.541180\pi$
$312$	4.54030	+	4.54030i	0.257044	+	0.257044i
$313$	20.0429	+	20.0429i	1.13289	+	1.13289i	0.989694	+	0.143197i	$0.0457382\pi$
$313$	20.0429	+	20.0429i	1.13289	+	1.13289i	0.143197	+	0.989694i	$0.454262\pi$
$314$	−18.6482			−1.05238
$315$	−0.0289779	−	0.537531i	−0.00163272	−	0.0302864i
$316$			1.15022i			0.0647050i
$317$	21.4280	+	21.4280i	1.20351	+	1.20351i	0.973090	+	0.230424i	$0.0740114\pi$
$317$	21.4280	+	21.4280i	1.20351	+	1.20351i	0.230424	+	0.973090i	$0.425989\pi$
$318$	−1.93366	+	1.93366i	−0.108434	+	0.108434i
$319$	−18.4555			−1.03331
$320$	−1.49373	+	1.66396i	−0.0835021	+	0.0930182i
$321$	7.91697			0.441882
$322$	−1.24166	−	1.24166i	−0.0691952	−	0.0691952i
$323$	−0.640907	−	3.25099i	−0.0356610	−	0.180890i
$324$		−	1.00000i		−	0.0555556i
$325$	25.0105	+	20.1294i	1.38733	+	1.11658i
$326$			1.69593i			0.0939291i
$327$	−7.57474	+	7.57474i	−0.418884	+	0.418884i
$328$	2.60372	+	2.60372i	0.143766	+	0.143766i
$329$		−	3.26113i		−	0.179792i
$330$	−5.71319	−	5.12871i	−0.314501	−	0.282326i
$331$			31.9582i			1.75658i	0.478125	+	0.878292i	$0.341317\pi$
$331$			31.9582i			1.75658i	−0.478125	+	0.878292i	$0.658683\pi$
$332$	9.97102	−	9.97102i	0.547231	−	0.547231i
$333$	−5.54122	+	5.54122i	−0.303657	+	0.303657i
$334$		−	15.7387i		−	0.861184i
$335$	−0.0819620	−	1.52037i	−0.00447806	−	0.0830665i
$336$		−	0.240740i		−	0.0131335i
$337$	−6.27191	−	6.27191i	−0.341653	−	0.341653i	0.515336	−	0.856988i	$-0.327667\pi$
$337$	−6.27191	−	6.27191i	−0.341653	−	0.341653i	−0.856988	+	0.515336i	$0.827667\pi$
$338$	19.9607	−	19.9607i	1.08572	−	1.08572i
$339$			9.63447i			0.523273i
$340$	−0.0915034	−	1.69736i	−0.00496247	−	0.0920521i
$341$		−	18.4555i		−	0.999420i
$342$	−0.843095	−	4.27659i	−0.0455894	−	0.231251i
$343$	−2.37334	−	2.37334i	−0.128148	−	0.128148i
$344$	−3.24172			−0.174782
$345$	−12.1371	−	10.8954i	−0.653437	−	0.586588i
$346$	−21.4978			−1.15573
$347$	−9.84922	+	9.84922i	−0.528734	+	0.528734i	−0.920195	−	0.391461i	$-0.871970\pi$
$347$	−9.84922	+	9.84922i	−0.528734	+	0.528734i	0.391461	+	0.920195i	$0.371970\pi$
$348$	−3.80079	−	3.80079i	−0.203744	−	0.203744i
$349$			23.7919i			1.27355i	0.771049	+	0.636776i	$0.219732\pi$
$349$			23.7919i			1.27355i	−0.771049	+	0.636776i	$0.780268\pi$
$350$	−0.129405	−	1.19672i	−0.00691701	−	0.0639676i
$351$	−6.42095			−0.342725
$352$	−2.42784	−	2.42784i	−0.129405	−	0.129405i
$353$	−16.4474	−	16.4474i	−0.875407	−	0.875407i	0.117649	−	0.993055i	$-0.462464\pi$
$353$	−16.4474	−	16.4474i	−0.875407	−	0.875407i	−0.993055	+	0.117649i	$0.962464\pi$
$354$	−4.20166			−0.223316
$355$	13.3410	−	14.8613i	0.708065	−	0.788758i
$356$			2.10098i			0.111351i
$357$	0.129405	+	0.129405i	0.00684886	+	0.00684886i
$358$	17.6448	+	17.6448i	0.932559	+	0.932559i
$359$			9.08979i			0.479741i	0.970805	+	0.239870i	$0.0771050\pi$
$359$			9.08979i			0.479741i	−0.970805	+	0.239870i	$0.922895\pi$
$360$	−0.120370	−	2.23283i	−0.00634406	−	0.117680i
$361$	−7.21114	−	17.5784i	−0.379534	−	0.925178i
$362$	11.2940	−	11.2940i	0.593598	−	0.593598i
$363$	0.557809	−	0.557809i	0.0292774	−	0.0292774i
$364$	−1.54578			−0.0810210
$365$	−1.48931	−	27.6263i	−0.0779542	−	1.44602i
$366$	1.65954			0.0867456
$367$	17.6931	−	17.6931i	0.923570	−	0.923570i	−0.0737098	−	0.997280i	$-0.523484\pi$
$367$	17.6931	−	17.6931i	0.923570	−	0.923570i	0.997280	+	0.0737098i	$0.0234839\pi$
$368$	−5.15769	−	5.15769i	−0.268863	−	0.268863i
$369$	−3.68222			−0.191689
$370$	−11.7056	+	13.0396i	−0.608545	+	0.677896i
$371$		−	0.658329i		−	0.0341787i
$372$	3.80079	−	3.80079i	0.197062	−	0.197062i
$373$	−4.93586	+	4.93586i	−0.255569	+	0.255569i	−0.823249	−	0.567680i	$-0.807841\pi$
$373$	−4.93586	+	4.93586i	−0.255569	+	0.255569i	0.567680	+	0.823249i	$0.307841\pi$
$374$	2.61008			0.134964
$375$	−1.79858	−	11.0347i	−0.0928780	−	0.569831i
$376$		−	13.5463i		−	0.698595i
$377$	−24.4047	+	24.4047i	−1.25691	+	1.25691i
$378$	0.170229	+	0.170229i	0.00875564	+	0.00875564i
$379$	9.44824			0.485324			0.242662	−	0.970111i	$-0.421979\pi$
$379$	9.44824			0.485324			0.242662	+	0.970111i	$0.421979\pi$
$380$	−2.39726	−	9.44739i	−0.122977	−	0.484641i
$381$	7.35299			0.376705
$382$	2.06179	+	2.06179i	0.105490	+	0.105490i
$383$	17.3196	−	17.3196i	0.884991	−	0.884991i	−0.109046	−	0.994037i	$-0.534779\pi$
$383$	17.3196	−	17.3196i	0.884991	−	0.884991i	0.994037	+	0.109046i	$0.0347794\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	1.84561	−	0.0994955i	0.0940609	−	0.00507076i
$386$	−9.44130			−0.480550
$387$	2.29224	−	2.29224i	0.116521	−	0.116521i
$388$	−10.8544	+	10.8544i	−0.551049	+	0.551049i
$389$			20.3705i			1.03283i	0.856340	+	0.516413i	$0.172733\pi$
$389$			20.3705i			1.03283i	−0.856340	+	0.516413i	$0.827267\pi$
$390$	−14.3369	+	0.772891i	−0.725976	+	0.0391369i
$391$	5.54484			0.280415
$392$	−4.90877	−	4.90877i	−0.247930	−	0.247930i
$393$	1.51836	−	1.51836i	0.0765913	−	0.0765913i
$394$	−5.77371			−0.290875
$395$	−1.91392	−	1.71812i	−0.0963000	−	0.0864481i
$396$	3.43349			0.172539
$397$	13.9251	−	13.9251i	0.698883	−	0.698883i	−0.265287	−	0.964170i	$-0.585467\pi$
$397$	13.9251	−	13.9251i	0.698883	−	0.698883i	0.964170	+	0.265287i	$0.0854666\pi$
$398$	−5.82417	+	5.82417i	−0.291939	+	0.291939i
$399$	0.871519	+	0.584480i	0.0436305	+	0.0292606i
$400$	−0.537531	−	4.97102i	−0.0268765	−	0.248551i
$401$		−	0.407767i		−	0.0203629i	−0.999948	−	0.0101815i	$-0.996759\pi$
$401$		−	0.407767i		−	0.0203629i	0.999948	−	0.0101815i	$-0.00324092\pi$
$402$	0.481480	+	0.481480i	0.0240141	+	0.0240141i
$403$	−24.4047	−	24.4047i	−1.21569	−	1.21569i
$404$			8.90870i			0.443225i
$405$	1.66396	+	1.49373i	0.0826829	+	0.0742241i
$406$	1.29401			0.0642207
$407$	−19.0257	−	19.0257i	−0.943071	−	0.943071i
$408$	0.537531	+	0.537531i	0.0266117	+	0.0266117i
$409$	6.82208			0.337330			0.168665	−	0.985673i	$-0.446054\pi$
$409$	6.82208			0.337330			0.168665	+	0.985673i	$0.446054\pi$
$410$	−8.22175	+	0.443229i	−0.406043	+	0.0218895i
$411$			19.1651i			0.945347i
$412$	6.26365	+	6.26365i	0.308588	+	0.308588i
$413$	0.715245	−	0.715245i	0.0351949	−	0.0351949i
$414$	7.29408			0.358484
$415$	1.69736	+	31.4854i	0.0833200	+	1.54556i
$416$	−6.42095			−0.314813
$417$	−7.42565	−	7.42565i	−0.363636	−	0.363636i
$418$	14.6836	−	2.89476i	0.718199	−	0.141587i
$419$		−	30.8811i		−	1.50864i	−0.656507	−	0.754320i	$-0.727967\pi$
$419$		−	30.8811i		−	1.50864i	0.656507	−	0.754320i	$-0.272033\pi$
$420$	0.400582	+	0.359601i	0.0195464	+	0.0175467i
$421$		−	5.62994i		−	0.274386i	−0.990544	−	0.137193i	$-0.956192\pi$
$421$		−	5.62994i		−	0.274386i	0.990544	−	0.137193i	$-0.0438081\pi$
$422$	10.3334	−	10.3334i	0.503020	−	0.503020i
$423$	9.57865	+	9.57865i	0.465730	+	0.465730i
$424$		−	2.73460i		−	0.132804i
$425$	2.96102	+	2.38314i	0.143630	+	0.115599i
$426$			8.93130i			0.432723i
$427$	−0.282502	+	0.282502i	−0.0136712	+	0.0136712i
$428$	−5.59814	+	5.59814i	−0.270597	+	0.270597i
$429$		−	22.0463i		−	1.06440i
$430$	4.84226	−	5.39409i	0.233514	−	0.260126i
$431$		−	8.03322i		−	0.386947i	−0.981106	−	0.193473i	$-0.938025\pi$
$431$		−	8.03322i		−	0.386947i	0.981106	−	0.193473i	$-0.0619753\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−27.5643	+	27.5643i	−1.32466	+	1.32466i	−0.414695	+	0.909960i	$0.636112\pi$
$433$	−27.5643	+	27.5643i	−1.32466	+	1.32466i	−0.909960	+	0.414695i	$0.863888\pi$
$434$			1.29401i			0.0621145i
$435$	12.0017	−	0.647005i	0.575439	−	0.0310215i
$436$		−	10.7123i		−	0.513026i
$437$	31.1938	−	6.14960i	1.49220	−	0.294175i
$438$	8.74888	+	8.74888i	0.418037	+	0.418037i
$439$	−2.72959			−0.130276			−0.0651381	−	0.997876i	$-0.520749\pi$
$439$	−2.72959			−0.130276			−0.0651381	+	0.997876i	$0.520749\pi$
$440$	7.66639	−	0.413290i	0.365481	−	0.0197028i
$441$	6.94204			0.330574
$442$	3.45146	−	3.45146i	0.164169	−	0.164169i
$443$	−21.7450	−	21.7450i	−1.03313	−	1.03313i	−0.999432	−	0.0337029i	$-0.989270\pi$
$443$	−21.7450	−	21.7450i	−1.03313	−	1.03313i	−0.0337029	−	0.999432i	$-0.510730\pi$
$444$		−	7.83647i		−	0.371903i
$445$	−3.49594	−	3.13829i	−0.165723	−	0.148769i
$446$	−22.5682			−1.06864
$447$	0.721494	+	0.721494i	0.0341255	+	0.0341255i
$448$	0.170229	+	0.170229i	0.00804257	+	0.00804257i
$449$	6.33780			0.299099			0.149550	−	0.988754i	$-0.452218\pi$
$449$	6.33780			0.299099			0.149550	+	0.988754i	$0.452218\pi$
$450$	3.89514	+	3.13495i	0.183618	+	0.147783i
$451$		−	12.6429i		−	0.595329i
$452$	−6.81260	−	6.81260i	−0.320438	−	0.320438i
$453$	−14.0286	−	14.0286i	−0.659120	−	0.659120i
$454$			8.30331i			0.389694i
$455$	2.30898	−	2.57212i	0.108247	−	0.120583i
$456$	3.62016	+	2.42784i	0.169530	+	0.113694i
$457$	−14.1287	+	14.1287i	−0.660915	+	0.660915i	−0.955596	−	0.294681i	$-0.904787\pi$
$457$	−14.1287	+	14.1287i	−0.660915	+	0.660915i	0.294681	+	0.955596i	$0.404787\pi$
$458$	−7.27083	+	7.27083i	−0.339743	+	0.339743i
$459$	−0.760184			−0.0354823
$460$	16.2864	−	0.877989i	0.759358	−	0.0409365i
$461$	−10.3701			−0.482984			−0.241492	−	0.970403i	$-0.577637\pi$
$461$	−10.3701			−0.482984			−0.241492	+	0.970403i	$0.577637\pi$
$462$	−0.584480	+	0.584480i	−0.0271925	+	0.0271925i
$463$	−21.5966	−	21.5966i	−1.00368	−	1.00368i	−0.999993	−	0.00368676i	$-0.998826\pi$
$463$	−21.5966	−	21.5966i	−1.00368	−	1.00368i	−0.00368676	−	0.999993i	$-0.501174\pi$
$464$	5.37513			0.249534
$465$	0.647005	+	12.0017i	0.0300042	+	0.556567i
$466$			20.4672i			0.948123i
$467$	5.68112	−	5.68112i	0.262891	−	0.262891i	−0.563337	−	0.826228i	$-0.690483\pi$
$467$	5.68112	−	5.68112i	0.262891	−	0.262891i	0.826228	+	0.563337i	$0.190483\pi$
$468$	4.54030	−	4.54030i	0.209875	−	0.209875i
$469$	−0.163924			−0.00756930
$470$	22.5404	+	20.2345i	1.03971	+	0.933346i
$471$			18.6482i			0.859264i
$472$	2.97102	−	2.97102i	0.136752	−	0.136752i
$473$	7.87039	+	7.87039i	0.361881	+	0.361881i
$474$	1.15022			0.0528314
$475$	19.3009	+	10.1229i	0.885588	+	0.464471i
$476$	−0.183007			−0.00838810
$477$	1.93366	+	1.93366i	0.0885361	+	0.0885361i
$478$	15.1645	−	15.1645i	0.693609	−	0.693609i
$479$		−	18.3301i		−	0.837524i	−0.908096	−	0.418762i	$-0.862464\pi$
$479$		−	18.3301i		−	0.837524i	0.908096	−	0.418762i	$-0.137536\pi$
$480$	1.66396	+	1.49373i	0.0759491	+	0.0681792i
$481$	−50.3176			−2.29429
$482$	1.07223	−	1.07223i	0.0488387	−	0.0488387i
$483$	−1.24166	+	1.24166i	−0.0564977	+	0.0564977i
$484$			0.788861i			0.0358573i
$485$	−1.84774	−	34.2749i	−0.0839014	−	1.55634i
$486$	−1.00000			−0.0453609
$487$	−8.21504	−	8.21504i	−0.372259	−	0.372259i	0.496040	−	0.868299i	$-0.334787\pi$
$487$	−8.21504	−	8.21504i	−0.372259	−	0.372259i	−0.868299	+	0.496040i	$0.834787\pi$
$488$	−1.17347	+	1.17347i	−0.0531206	+	0.0531206i
$489$	1.69593			0.0766928
$490$	15.5004	−	0.835615i	0.700236	−	0.0377492i
$491$	5.85271			0.264129			0.132065	−	0.991241i	$-0.457839\pi$
$491$	5.85271			0.264129			0.132065	+	0.991241i	$0.457839\pi$
$492$	2.60372	−	2.60372i	0.117385	−	0.117385i
$493$	−2.88930	+	2.88930i	−0.130128	+	0.130128i
$494$	15.5891	−	23.2449i	0.701386	−	1.04584i
$495$	−5.12871	+	5.71319i	−0.230519	+	0.256789i
$496$			5.37513i			0.241351i
$497$	−1.52037	−	1.52037i	−0.0681978	−	0.0681978i
$498$	−9.97102	−	9.97102i	−0.446812	−	0.446812i
$499$			24.4054i			1.09254i	0.837610	+	0.546268i	$0.183952\pi$
$499$			24.4054i			1.09254i	−0.837610	+	0.546268i	$0.816048\pi$
$500$	9.07451	+	6.53094i	0.405825	+	0.292073i
$501$	−15.7387			−0.703154
$502$	8.23952	+	8.23952i	0.367748	+	0.367748i
$503$	19.8672	+	19.8672i	0.885836	+	0.885836i	0.994120	−	0.108284i	$-0.0345357\pi$
$503$	19.8672	+	19.8672i	0.885836	+	0.885836i	−0.108284	+	0.994120i	$0.534536\pi$
$504$	−0.240740			−0.0107234
$505$	−14.8237	−	13.3072i	−0.659647	−	0.592163i
$506$			25.0442i			1.11335i
$507$	−19.9607	−	19.9607i	−0.886485	−	0.886485i
$508$	−5.19935	+	5.19935i	−0.230684	+	0.230684i
$509$	−19.2340			−0.852534			−0.426267	−	0.904597i	$-0.640172\pi$
$509$	−19.2340			−0.852534			−0.426267	+	0.904597i	$0.640172\pi$
$510$	−1.69736	+	0.0915034i	−0.0751603	+	0.00405184i
$511$	−2.97863			−0.131767
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.27659	+	0.843095i	−0.188816	+	0.0372236i
$514$		−	1.42333i		−	0.0627804i
$515$	−19.7787	+	1.06626i	−0.871553	+	0.0469848i
$516$			3.24172i			0.142709i
$517$	−32.8882	+	32.8882i	−1.44642	+	1.44642i
$518$	1.33400	+	1.33400i	0.0586124	+	0.0586124i
$519$			21.4978i			0.943647i
$520$	9.59118	−	10.6842i	0.420601	−	0.468534i
$521$		−	19.1370i		−	0.838407i	−0.907892	−	0.419204i	$-0.862309\pi$
$521$		−	19.1370i		−	0.838407i	0.907892	−	0.419204i	$-0.137691\pi$
$522$	−3.80079	+	3.80079i	−0.166356	+	0.166356i
$523$	−13.3664	+	13.3664i	−0.584471	+	0.584471i	−0.936129	−	0.351657i	$-0.885618\pi$
$523$	−13.3664	+	13.3664i	−0.584471	+	0.584471i	0.351657	+	0.936129i	$0.385618\pi$
$524$			2.14729i			0.0938048i
$525$	−1.19672	+	0.129405i	−0.0522294	+	0.00564771i
$526$			0.560424i			0.0244357i
$527$	−2.88930	−	2.88930i	−0.125860	−	0.125860i
$528$	−2.42784	+	2.42784i	−0.105658	+	0.105658i
$529$			30.2036i			1.31320i
$530$	4.55027	+	4.08476i	0.197651	+	0.177431i
$531$			4.20166i			0.182337i
$532$	−1.02955	+	0.202967i	−0.0446365	+	0.00879973i
$533$	−16.7184	−	16.7184i	−0.724153	−	0.724153i
$534$	2.10098			0.0909181
$535$	−0.952967	−	17.6772i	−0.0412003	−	0.764253i
$536$	−0.680916			−0.0294111
$537$	17.6448	−	17.6448i	0.761431	−	0.761431i
$538$	−14.7971	−	14.7971i	−0.637948	−	0.637948i
$539$			23.8354i			1.02667i
$540$	−2.23283	+	0.120370i	−0.0960855	+	0.00517990i
$541$	−36.4227			−1.56593			−0.782967	−	0.622063i	$-0.786295\pi$
$541$	−36.4227			−1.56593			−0.782967	+	0.622063i	$0.786295\pi$
$542$	−11.9625	−	11.9625i	−0.513834	−	0.513834i
$543$	−11.2940	−	11.2940i	−0.484671	−	0.484671i
$544$	−0.760184			−0.0325926
$545$	17.8249	+	16.0013i	0.763533	+	0.685421i
$546$			1.54578i			0.0661534i
$547$	7.49691	+	7.49691i	0.320545	+	0.320545i	0.848976	−	0.528431i	$-0.177220\pi$
$547$	7.49691	+	7.49691i	0.320545	+	0.320545i	−0.528431	+	0.848976i	$0.677220\pi$
$548$	−13.5518	−	13.5518i	−0.578904	−	0.578904i
$549$		−	1.65954i		−	0.0708275i
$550$	−10.7638	+	13.3739i	−0.458971	+	0.570266i
$551$	−13.0500	+	19.4588i	−0.555948	+	0.828975i
$552$	−5.15769	+	5.15769i	−0.219526	+	0.219526i
$553$	−0.195801	+	0.195801i	−0.00832631	+	0.00832631i
$554$	22.1704			0.941931
$555$	13.0396	+	11.7056i	0.553500	+	0.496875i
$556$	10.5015			0.445361
$557$	6.66081	−	6.66081i	0.282228	−	0.282228i	−0.551769	−	0.833997i	$-0.686047\pi$
$557$	6.66081	−	6.66081i	0.282228	−	0.282228i	0.833997	+	0.551769i	$0.186047\pi$
$558$	−3.80079	−	3.80079i	−0.160900	−	0.160900i
$559$	20.8149			0.880377
$560$	−0.537531	+	0.0289779i	−0.0227148	+	0.00122454i
$561$		−	2.61008i		−	0.110198i
$562$	7.31752	−	7.31752i	0.308671	−	0.308671i
$563$	−18.2264	+	18.2264i	−0.768150	+	0.768150i	−0.977781	−	0.209631i	$-0.932774\pi$
$563$	−18.2264	+	18.2264i	−0.768150	+	0.768150i	0.209631	+	0.977781i	$0.432774\pi$
$564$	−13.5463			−0.570400
$565$	21.5121	−	1.15970i	0.905020	−	0.0487890i
$566$			8.53238i			0.358643i
$567$	0.170229	−	0.170229i	0.00714895	−	0.00714895i
$568$	−6.31539	−	6.31539i	−0.264988	−	0.264988i
$569$	12.9797			0.544138			0.272069	−	0.962278i	$-0.412292\pi$
$569$	12.9797			0.544138			0.272069	+	0.962278i	$0.412292\pi$
$570$	−9.44739	+	2.39726i	−0.395708	+	0.100410i
$571$	−4.34400			−0.181791			−0.0908954	−	0.995860i	$-0.528973\pi$
$571$	−4.34400			−0.181791			−0.0908954	+	0.995860i	$0.528973\pi$
$572$	15.5891	+	15.5891i	0.651812	+	0.651812i
$573$	2.06179	−	2.06179i	0.0861323	−	0.0861323i
$574$			0.886458i			0.0370000i
$575$	−22.8666	+	28.4114i	−0.953602	+	1.18484i
$576$	−1.00000			−0.0416667
$577$	22.6630	−	22.6630i	0.943474	−	0.943474i	−0.0550121	−	0.998486i	$-0.517520\pi$
$577$	22.6630	−	22.6630i	0.943474	−	0.943474i	0.998486	+	0.0550121i	$0.0175197\pi$
$578$	−11.6122	+	11.6122i	−0.483004	+	0.483004i
$579$			9.44130i			0.392367i
$580$	−8.02901	+	8.94401i	−0.333386	+	0.371380i
$581$	3.39472			0.140837
$582$	10.8544	+	10.8544i	0.449930	+	0.449930i
$583$	−6.63919	+	6.63919i	−0.274967	+	0.274967i
$584$	−12.3728			−0.511989
$585$	0.772891	+	14.3369i	0.0319551	+	0.592757i
$586$	9.39045			0.387916
$587$	−1.52632	+	1.52632i	−0.0629979	+	0.0629979i	−0.737904	−	0.674906i	$-0.764184\pi$
$587$	−1.52632	+	1.52632i	−0.0629979	+	0.0629979i	0.674906	+	0.737904i	$0.264184\pi$
$588$	−4.90877	+	4.90877i	−0.202434	+	0.202434i
$589$	−19.4588	−	13.0500i	−0.801788	−	0.537715i
$590$	0.505754	+	9.38157i	0.0208216	+	0.386233i
$591$			5.77371i			0.237499i
$592$	5.54122	+	5.54122i	0.227743	+	0.227743i
$593$	2.34436	+	2.34436i	0.0962714	+	0.0962714i	0.753602	−	0.657331i	$-0.228315\pi$
$593$	2.34436	+	2.34436i	0.0962714	+	0.0962714i	−0.657331	+	0.753602i	$0.728315\pi$
$594$		−	3.43349i		−	0.140878i
$595$	0.273363	−	0.304516i	0.0112068	−	0.0124839i
$596$	−1.02035			−0.0417950
$597$	5.82417	+	5.82417i	0.238368	+	0.238368i
$598$	33.1173	+	33.1173i	1.35427	+	1.35427i
$599$	−20.2744			−0.828391			−0.414195	−	0.910188i	$-0.635937\pi$
$599$	−20.2744			−0.828391			−0.414195	+	0.910188i	$0.635937\pi$
$600$	−4.97102	+	0.537531i	−0.202941	+	0.0219446i
$601$			18.2726i			0.745354i	0.927961	+	0.372677i	$0.121560\pi$
$601$			18.2726i			0.745354i	−0.927961	+	0.372677i	$0.878440\pi$
$602$	−0.551834	−	0.551834i	−0.0224911	−	0.0224911i
$603$	0.481480	−	0.481480i	0.0196074	−	0.0196074i
$604$	19.8394			0.807254
$605$	−1.31263	−	1.17835i	−0.0533662	−	0.0479066i
$606$	8.90870			0.361891
$607$	−21.4067	−	21.4067i	−0.868872	−	0.868872i	0.123476	−	0.992348i	$-0.460596\pi$
$607$	−21.4067	−	21.4067i	−0.868872	−	0.868872i	−0.992348	+	0.123476i	$0.960596\pi$
$608$	−4.27659	+	0.843095i	−0.173438	+	0.0341920i
$609$		−	1.29401i		−	0.0524360i
$610$	−0.199759	−	3.70547i	−0.00808802	−	0.150030i
$611$			86.9799i			3.51883i
$612$	0.537531	−	0.537531i	0.0217284	−	0.0217284i
$613$	−21.6012	−	21.6012i	−0.872462	−	0.872462i	0.120278	−	0.992740i	$-0.461621\pi$
$613$	−21.6012	−	21.6012i	−0.872462	−	0.872462i	−0.992740	+	0.120278i	$0.961621\pi$
$614$			8.78829i			0.354667i
$615$	0.443229	+	8.22175i	0.0178727	+	0.331533i
$616$		−	0.826579i		−	0.0333038i
$617$	13.3582	−	13.3582i	0.537782	−	0.537782i	−0.385095	−	0.922877i	$-0.625831\pi$
$617$	13.3582	−	13.3582i	0.537782	−	0.537782i	0.922877	+	0.385095i	$0.125831\pi$
$618$	6.26365	−	6.26365i	0.251961	−	0.251961i
$619$		−	35.7297i		−	1.43610i	−0.695993	−	0.718049i	$-0.745035\pi$
$619$		−	35.7297i		−	1.43610i	0.695993	−	0.718049i	$-0.254965\pi$
$620$	−8.94401	−	8.02901i	−0.359200	−	0.322453i
$621$		−	7.29408i		−	0.292701i
$622$	−3.21753	−	3.21753i	−0.129011	−	0.129011i
$623$	−0.357647	+	0.357647i	−0.0143288	+	0.0143288i
$624$			6.42095i			0.257044i
$625$	−24.4221	+	5.34416i	−0.976885	+	0.213766i
$626$			28.3449i			1.13289i
$627$	−2.89476	−	14.6836i	−0.115606	−	0.586407i
$628$	−13.1863	−	13.1863i	−0.526190	−	0.526190i
$629$	−5.95716			−0.237528
$630$	0.359601	−	0.400582i	0.0143269	−	0.0159596i
$631$	−5.92905			−0.236032			−0.118016	−	0.993012i	$-0.537653\pi$
$631$	−5.92905			−0.236032			−0.118016	+	0.993012i	$0.537653\pi$
$632$	−0.813330	+	0.813330i	−0.0323525	+	0.0323525i
$633$	−10.3334	−	10.3334i	−0.410714	−	0.410714i
$634$			30.3037i			1.20351i
$635$	−0.885081	−	16.4180i	−0.0351234	−	0.651527i
$636$	−2.73460			−0.108434
$637$	31.5190	+	31.5190i	1.24883	+	1.24883i
$638$	−13.0500	−	13.0500i	−0.516654	−	0.516654i
$639$	8.93130			0.353317
$640$	−2.23283	+	0.120370i	−0.0882602	+	0.00475805i
$641$		−	6.60094i		−	0.260721i	−0.991467	−	0.130361i	$-0.958386\pi$
$641$		−	6.60094i		−	0.260721i	0.991467	−	0.130361i	$-0.0416135\pi$
$642$	5.59814	+	5.59814i	0.220941	+	0.220941i
$643$	13.4065	+	13.4065i	0.528700	+	0.528700i	0.920185	−	0.391484i	$-0.128038\pi$
$643$	13.4065	+	13.4065i	0.528700	+	0.528700i	−0.391484	+	0.920185i	$0.628038\pi$
$644$		−	1.75598i		−	0.0691952i
$645$	−5.39409	−	4.84226i	−0.212392	−	0.190664i
$646$	1.84561	−	2.75199i	0.0726145	−	0.108275i
$647$	10.3980	−	10.3980i	0.408788	−	0.408788i	−0.472528	−	0.881316i	$-0.656658\pi$
$647$	10.3980	−	10.3980i	0.408788	−	0.408788i	0.881316	+	0.472528i	$0.156658\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−14.4264			−0.566284
$650$	3.45146	+	31.9187i	0.135377	+	1.25195i
$651$	1.29401			0.0507163
$652$	−1.19921	+	1.19921i	−0.0469646	+	0.0469646i
$653$	−9.88773	−	9.88773i	−0.386937	−	0.386937i	0.486657	−	0.873593i	$-0.338216\pi$
$653$	−9.88773	−	9.88773i	−0.386937	−	0.386937i	−0.873593	+	0.486657i	$0.838216\pi$
$654$	−10.7123			−0.418884
$655$	−3.57301	−	3.20748i	−0.139609	−	0.125326i
$656$			3.68222i			0.143766i
$657$	8.74888	−	8.74888i	0.341326	−	0.341326i
$658$	2.30597	−	2.30597i	0.0898959	−	0.0898959i
$659$	−13.1768			−0.513294			−0.256647	−	0.966505i	$-0.582618\pi$
$659$	−13.1768			−0.513294			−0.256647	+	0.966505i	$0.582618\pi$
$660$	−0.413290	−	7.66639i	−0.0160873	−	0.298414i
$661$		−	27.6493i		−	1.07543i	−0.843126	−	0.537716i	$-0.819287\pi$
$661$		−	27.6493i		−	1.07543i	0.843126	−	0.537716i	$-0.180713\pi$
$662$	−22.5979	+	22.5979i	−0.878292	+	0.878292i
$663$	−3.45146	−	3.45146i	−0.134044	−	0.134044i
$664$	14.1012			0.547231
$665$	1.20014	−	2.01630i	0.0465393	−	0.0781889i
$666$	−7.83647			−0.303657
$667$	−27.7233	−	27.7233i	−1.07345	−	1.07345i
$668$	11.1290	−	11.1290i	0.430592	−	0.430592i
$669$			22.5682i			0.872539i
$670$	1.01711	−	1.13302i	0.0392942	−	0.0437723i
$671$	5.69802			0.219970
$672$	0.170229	−	0.170229i	0.00656673	−	0.00656673i
$673$	15.0414	−	15.0414i	0.579804	−	0.579804i	−0.355045	−	0.934849i	$-0.615535\pi$
$673$	15.0414	−	15.0414i	0.579804	−	0.579804i	0.934849	+	0.355045i	$0.115535\pi$
$674$		−	8.86982i		−	0.341653i
$675$	3.13495	−	3.89514i	0.120664	−	0.149924i
$676$	28.2287			1.08572
$677$	−32.6303	−	32.6303i	−1.25408	−	1.25408i	−0.953873	−	0.300211i	$-0.902943\pi$
$677$	−32.6303	−	32.6303i	−1.25408	−	1.25408i	−0.300211	−	0.953873i	$-0.597057\pi$
$678$	−6.81260	+	6.81260i	−0.261636	+	0.261636i
$679$	−3.69547			−0.141819
$680$	1.13551	−	1.26492i	0.0435448	−	0.0485073i
$681$	8.30331			0.318183
$682$	13.0500	−	13.0500i	0.499710	−	0.499710i
$683$	19.7427	−	19.7427i	0.755435	−	0.755435i	−0.220053	−	0.975488i	$-0.570623\pi$
$683$	19.7427	−	19.7427i	0.755435	−	0.755435i	0.975488	+	0.220053i	$0.0706231\pi$
$684$	2.42784	−	3.62016i	0.0928310	−	0.138420i
$685$	42.7924	−	2.30691i	1.63501	−	0.0881425i
$686$		−	3.35641i		−	0.128148i
$687$	7.27083	+	7.27083i	0.277399	+	0.277399i
$688$	−2.29224	−	2.29224i	−0.0873908	−	0.0873908i
$689$			17.5588i			0.668936i
$690$	−0.877989	−	16.2864i	−0.0334245	−	0.620013i
$691$	−1.07506			−0.0408973			−0.0204486	−	0.999791i	$-0.506509\pi$
$691$	−1.07506			−0.0408973			−0.0204486	+	0.999791i	$0.506509\pi$
$692$	−15.2012	−	15.2012i	−0.577863	−	0.577863i
$693$	0.584480	+	0.584480i	0.0222026	+	0.0222026i
$694$	−13.9289			−0.528734
$695$	−15.6864	+	17.4740i	−0.595017	+	0.662827i
$696$		−	5.37513i		−	0.203744i
$697$	−1.97931	−	1.97931i	−0.0749715	−	0.0749715i
$698$	−16.8234	+	16.8234i	−0.636776	+	0.636776i
$699$	20.4672			0.774139
$700$	0.754709	−	0.937716i	0.0285253	−	0.0354423i
$701$	49.0251			1.85165			0.925827	−	0.377947i	$-0.123370\pi$
$701$	49.0251			1.85165			0.925827	+	0.377947i	$0.123370\pi$
$702$	−4.54030	−	4.54030i	−0.171363	−	0.171363i
$703$	−33.5134	+	6.60689i	−1.26398	+	0.249184i
$704$		−	3.43349i		−	0.129405i
$705$	20.2345	−	22.5404i	0.762074	−	0.848922i
$706$		−	23.2601i		−	0.875407i
$707$	−1.51652	+	1.51652i	−0.0570346	+	0.0570346i
$708$	−2.97102	−	2.97102i	−0.111658	−	0.111658i
$709$			1.20397i			0.0452160i	0.999744	+	0.0226080i	$0.00719696\pi$
$709$			1.20397i			0.0452160i	−0.999744	+	0.0226080i	$0.992803\pi$
$710$	19.9420	−	1.07506i	0.748412	−	0.0403464i
$711$		−	1.15022i		−	0.0431367i
$712$	−1.48561	+	1.48561i	−0.0556757	+	0.0556757i
$713$	27.7233	−	27.7233i	1.03825	−	1.03825i
$714$			0.183007i			0.00684886i
$715$	−49.2255	+	2.65371i	−1.84093	+	0.0992433i
$716$			24.9536i			0.932559i
$717$	−15.1645	−	15.1645i	−0.566329	−	0.566329i
$718$	−6.42745	+	6.42745i	−0.239870	+	0.239870i
$719$			13.0396i			0.486297i	0.969989	+	0.243148i	$0.0781802\pi$
$719$			13.0396i			0.486297i	−0.969989	+	0.243148i	$0.921820\pi$
$720$	1.49373	−	1.66396i	0.0556681	−	0.0620122i
$721$			2.13251i			0.0794189i
$722$	7.33075	−	17.5288i	0.272822	−	0.652356i
$723$	−1.07223	−	1.07223i	−0.0398766	−	0.0398766i
$724$	15.9721			0.593598
$725$	−2.88930	−	26.7199i	−0.107306	−	0.992352i
$726$	0.788861			0.0292774
$727$	−11.3275	+	11.3275i	−0.420115	+	0.420115i	−0.885243	−	0.465129i	$-0.846008\pi$
$727$	−11.3275	+	11.3275i	−0.420115	+	0.420115i	0.465129	+	0.885243i	$0.346008\pi$
$728$	−1.09303	−	1.09303i	−0.0405105	−	0.0405105i
$729$			1.00000i			0.0370370i
$730$	18.4816	−	20.5878i	0.684035	−	0.761989i
$731$	2.46430			0.0911454
$732$	1.17347	+	1.17347i	0.0433728	+	0.0433728i
$733$	30.7800	+	30.7800i	1.13689	+	1.13689i	0.989005	+	0.147882i	$0.0472456\pi$
$733$	30.7800	+	30.7800i	1.13689	+	1.13689i	0.147882	+	0.989005i	$0.452754\pi$
$734$	25.0218			0.923570
$735$	−0.835615	−	15.5004i	−0.0308221	−	0.571740i
$736$		−	7.29408i		−	0.268863i
$737$	1.65316	+	1.65316i	0.0608949	+	0.0608949i
$738$	−2.60372	−	2.60372i	−0.0958443	−	0.0958443i
$739$		−	44.9834i		−	1.65474i	−0.561656	−	0.827371i	$-0.689835\pi$
$739$		−	44.9834i		−	1.65474i	0.561656	−	0.827371i	$-0.310165\pi$
$740$	−17.4975	+	0.943277i	−0.643220	+	0.0346756i
$741$	−23.2449	−	15.5891i	−0.853922	−	0.572679i
$742$	0.465509	−	0.465509i	0.0170894	−	0.0170894i
$743$	16.4071	−	16.4071i	0.601917	−	0.601917i	−0.338904	−	0.940821i	$-0.610056\pi$
$743$	16.4071	−	16.4071i	0.601917	−	0.601917i	0.940821	+	0.338904i	$0.110056\pi$
$744$	5.37513			0.197062
$745$	1.52412	−	1.69782i	0.0558396	−	0.0622032i
$746$	−6.98036			−0.255569
$747$	−9.97102	+	9.97102i	−0.364821	+	0.364821i
$748$	1.84561	+	1.84561i	0.0674821	+	0.0674821i
$749$	−1.90593			−0.0696413
$750$	6.53094	−	9.07451i	0.238476	−	0.331354i
$751$		−	10.0580i		−	0.367021i	−0.983018	−	0.183510i	$-0.941254\pi$
$751$		−	10.0580i		−	0.367021i	0.983018	−	0.183510i	$-0.0587461\pi$
$752$	9.57865	−	9.57865i	0.349297	−	0.349297i
$753$	8.23952	−	8.23952i	0.300265	−	0.300265i
$754$	−34.5135			−1.25691
$755$	−29.6348	+	33.0120i	−1.07852	+	1.20143i
$756$			0.240740i			0.00875564i
$757$	−0.0674583	+	0.0674583i	−0.00245182	+	0.00245182i	−0.708332	−	0.705880i	$-0.750552\pi$
$757$	−0.0674583	+	0.0674583i	−0.00245182	+	0.00245182i	0.705880	+	0.708332i	$0.250552\pi$
$758$	6.68092	+	6.68092i	0.242662	+	0.242662i
$759$	25.0442			0.909045
$760$	4.98520	−	8.37543i	0.180832	−	0.303809i
$761$	15.9170			0.576990			0.288495	−	0.957481i	$-0.406845\pi$
$761$	15.9170			0.576990			0.288495	+	0.957481i	$0.406845\pi$
$762$	5.19935	+	5.19935i	0.188353	+	0.188353i
$763$	1.82355	−	1.82355i	0.0660168	−	0.0660168i
$764$			2.91580i			0.105490i
$765$	0.0915034	+	1.69736i	0.00330831	+	0.0613681i
$766$	24.4936			0.884991
$767$	−19.0768	+	19.0768i	−0.688823	+	0.688823i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$			4.99203i			0.180017i	0.995941	+	0.0900087i	$0.0286895\pi$
$769$			4.99203i			0.180017i	−0.995941	+	0.0900087i	$0.971311\pi$
$770$	1.37540	+	1.23469i	0.0495658	+	0.0444951i
$771$	−1.42333			−0.0512600
$772$	−6.67601	−	6.67601i	−0.240275	−	0.240275i
$773$	−0.387825	+	0.387825i	−0.0139491	+	0.0139491i	−0.714047	−	0.700098i	$-0.753140\pi$
$773$	−0.387825	+	0.387825i	−0.0139491	+	0.0139491i	0.700098	+	0.714047i	$0.253140\pi$
$774$	3.24172			0.116521
$775$	26.7199	−	2.88930i	0.959807	−	0.103787i
$776$	−15.3505			−0.551049
$777$	1.33400	−	1.33400i	0.0478568	−	0.0478568i
$778$	−14.4041	+	14.4041i	−0.516413	+	0.516413i
$779$	−13.3302	−	8.93985i	−0.477605	−	0.320303i
$780$	−10.6842	−	9.59118i	−0.382556	−	0.343419i
$781$			30.6655i			1.09730i
$782$	3.92079	+	3.92079i	0.140207	+	0.140207i
$783$	3.80079	+	3.80079i	0.135829	+	0.135829i
$784$		−	6.94204i		−	0.247930i
$785$	41.6382	−	2.24469i	1.48613	−	0.0801163i
$786$	2.14729			0.0765913
$787$	33.2308	+	33.2308i	1.18455	+	1.18455i	0.978552	+	0.205999i	$0.0660445\pi$
$787$	33.2308	+	33.2308i	1.18455	+	1.18455i	0.205999	+	0.978552i	$0.433956\pi$
$788$	−4.08263	−	4.08263i	−0.145438	−	0.145438i
$789$	0.560424			0.0199516
$790$	−0.138452	−	2.56824i	−0.00492591	−	0.0913740i
$791$		−	2.31940i		−	0.0824685i
$792$	2.42784	+	2.42784i	0.0862697	+	0.0862697i
$793$	7.53482	−	7.53482i	0.267569	−	0.267569i
$794$	19.6931			0.698883
$795$	4.08476	−	4.55027i	0.144872	−	0.161382i
$796$	−8.23662			−0.291939
$797$	12.3179	+	12.3179i	0.436324	+	0.436324i	0.890773	−	0.454449i	$-0.150164\pi$
$797$	12.3179	+	12.3179i	0.436324	+	0.436324i	−0.454449	+	0.890773i	$0.650164\pi$
$798$	0.202967	+	1.02955i	0.00718495	+	0.0364455i
$799$			10.2976i			0.364304i
$800$	3.13495	−	3.89514i	0.110837	−	0.137714i
$801$		−	2.10098i		−	0.0742343i
$802$	0.288335	−	0.288335i	0.0101815	−	0.0101815i
$803$	30.0392	+	30.0392i	1.06006	+	1.06006i
$804$			0.680916i			0.0240141i
$805$	2.92188	+	2.62296i	0.102983	+	0.0924472i
$806$		−	34.5135i		−	1.21569i
$807$	−14.7971	+	14.7971i	−0.520882	+	0.520882i
$808$	−6.29940	+	6.29940i	−0.221612	+	0.221612i
$809$		−	9.46048i		−	0.332613i	−0.986074	−	0.166306i	$-0.946816\pi$
$809$		−	9.46048i		−	0.332613i	0.986074	−	0.166306i	$-0.0531841\pi$
$810$	0.120370	+	2.23283i	0.00422937	+	0.0784535i
$811$			3.82726i			0.134393i	0.997740	+	0.0671967i	$0.0214055\pi$
$811$			3.82726i			0.134393i	−0.997740	+	0.0671967i	$0.978594\pi$
$812$	0.915004	+	0.915004i	0.0321103	+	0.0321103i
$813$	−11.9625	+	11.9625i	−0.419543	+	0.419543i
$814$		−	26.9065i		−	0.943071i
$815$	−0.204140	−	3.78673i	−0.00715071	−	0.132643i
$816$			0.760184i			0.0266117i
$817$	13.8635	−	2.73308i	0.485022	−	0.0956182i
$818$	4.82394	+	4.82394i	0.168665	+	0.168665i
$819$	1.54578			0.0540140
$820$	−6.12706	−	5.50024i	−0.213966	−	0.192077i
$821$	2.99180			0.104415			0.0522073	−	0.998636i	$-0.483374\pi$
$821$	2.99180			0.104415			0.0522073	+	0.998636i	$0.483374\pi$
$822$	−13.5518	+	13.5518i	−0.472673	+	0.472673i
$823$	−32.6466	−	32.6466i	−1.13799	−	1.13799i	−0.988810	−	0.149179i	$-0.952337\pi$
$823$	−32.6466	−	32.6466i	−1.13799	−	1.13799i	−0.149179	−	0.988810i	$-0.547663\pi$
$824$			8.85814i			0.308588i
$825$	13.3739	+	10.7638i	0.465620	+	0.374748i
$826$	1.01151			0.0351949
$827$	−24.8297	−	24.8297i	−0.863413	−	0.863413i	0.128320	−	0.991733i	$-0.459042\pi$
$827$	−24.8297	−	24.8297i	−0.863413	−	0.863413i	−0.991733	+	0.128320i	$0.959042\pi$
$828$	5.15769	+	5.15769i	0.179242	+	0.179242i
$829$	24.2255			0.841388			0.420694	−	0.907203i	$-0.361787\pi$
$829$	24.2255			0.841388			0.420694	+	0.907203i	$0.361787\pi$
$830$	−21.0633	+	23.4638i	−0.731119	+	0.814439i
$831$		−	22.1704i		−	0.769083i
$832$	−4.54030	−	4.54030i	−0.157407	−	0.157407i
$833$	3.73156	+	3.73156i	0.129291	+	0.129291i
$834$		−	10.5015i		−	0.363636i
$835$	1.89447	+	35.1418i	0.0655609	+	1.21613i
$836$	12.4298	+	8.33598i	0.429893	+	0.288306i
$837$	−3.80079	+	3.80079i	−0.131375	+	0.131375i
$838$	21.8362	−	21.8362i	0.754320	−	0.754320i
$839$	14.8623			0.513105			0.256552	−	0.966530i	$-0.417413\pi$
$839$	14.8623			0.513105			0.256552	+	0.966530i	$0.417413\pi$
$840$	0.0289779	+	0.537531i	0.000999834	+	0.0185466i
$841$	−0.107945			−0.00372223
$842$	3.98097	−	3.98097i	0.137193	−	0.137193i
$843$	−7.31752	−	7.31752i	−0.252029	−	0.252029i
$844$	14.6136			0.503020
$845$	−42.1660	+	46.9714i	−1.45056	+	1.61586i
$846$			13.5463i			0.465730i
$847$	−0.134287	+	0.134287i	−0.00461416	+	0.00461416i
$848$	1.93366	−	1.93366i	0.0664021	−	0.0664021i
$849$	8.53238			0.292831
$850$	0.408622	+	3.77889i	0.0140156	+	0.129615i
$851$		−	57.1599i		−	1.95941i
$852$	−6.31539	+	6.31539i	−0.216362	+	0.216362i
$853$	2.50921	+	2.50921i	0.0859138	+	0.0859138i	0.748758	−	0.662844i	$-0.230651\pi$
$853$	2.50921	+	2.50921i	0.0859138	+	0.0859138i	−0.662844	+	0.748758i	$0.730651\pi$
$854$	−0.399518			−0.0136712
$855$	2.39726	+	9.44739i	0.0819845	+	0.323094i
$856$	−7.91697			−0.270597
$857$	−3.30288	−	3.30288i	−0.112824	−	0.112824i	0.648441	−	0.761265i	$-0.275421\pi$
$857$	−3.30288	−	3.30288i	−0.112824	−	0.112824i	−0.761265	+	0.648441i	$0.775421\pi$
$858$	15.5891	−	15.5891i	0.532202	−	0.532202i
$859$			9.52716i			0.325063i	0.986703	+	0.162531i	$0.0519659\pi$
$859$			9.52716i			0.325063i	−0.986703	+	0.162531i	$0.948034\pi$
$860$	7.23819	−	0.390206i	0.246820	−	0.0133059i
$861$	0.886458			0.0302104
$862$	5.68035	−	5.68035i	0.193473	−	0.193473i
$863$	14.4388	−	14.4388i	0.491503	−	0.491503i	−0.417277	−	0.908779i	$-0.637015\pi$
$863$	14.4388	−	14.4388i	0.491503	−	0.491503i	0.908779	+	0.417277i	$0.137015\pi$
$864$			1.00000i			0.0340207i
$865$	48.0007	−	2.58769i	1.63207	−	0.0879840i
$866$	−38.9818			−1.32466
$867$	11.6122	+	11.6122i	0.394371	+	0.394371i
$868$	−0.915004	+	0.915004i	−0.0310573	+	0.0310573i
$869$	3.94928			0.133970
$870$	8.94401	+	8.02901i	0.303230	+	0.272209i
$871$	4.37213			0.148144
$872$	7.57474	−	7.57474i	0.256513	−	0.256513i
$873$	10.8544	−	10.8544i	0.367366	−	0.367366i
$874$	26.4057	+	17.7089i	0.893188	+	0.599012i
$875$	0.432989	+	2.65650i	0.0146377	+	0.0898062i
$876$			12.3728i			0.418037i
$877$	−27.0374	−	27.0374i	−0.912987	−	0.912987i	0.0835187	−	0.996506i	$-0.473384\pi$
$877$	−27.0374	−	27.0374i	−0.912987	−	0.912987i	−0.996506	+	0.0835187i	$0.973384\pi$
$878$	−1.93011	−	1.93011i	−0.0651381	−	0.0651381i
$879$		−	9.39045i		−	0.316732i
$880$	5.71319	+	5.12871i	0.192592	+	0.172889i
$881$	−15.9706			−0.538063			−0.269031	−	0.963131i	$-0.586704\pi$
$881$	−15.9706			−0.538063			−0.269031	+	0.963131i	$0.586704\pi$
$882$	4.90877	+	4.90877i	0.165287	+	0.165287i
$883$	−8.39528	−	8.39528i	−0.282524	−	0.282524i	0.551591	−	0.834115i	$-0.314021\pi$
$883$	−8.39528	−	8.39528i	−0.282524	−	0.282524i	−0.834115	+	0.551591i	$0.814021\pi$
$884$	4.88110			0.164169
$885$	9.38157	−	0.505754i	0.315358	−	0.0170007i
$886$		−	30.7520i		−	1.03313i
$887$	18.4894	+	18.4894i	0.620814	+	0.620814i	0.945740	−	0.324925i	$-0.105339\pi$
$887$	18.4894	+	18.4894i	0.620814	+	0.620814i	−0.324925	+	0.945740i	$0.605339\pi$
$888$	5.54122	−	5.54122i	0.185951	−	0.185951i
$889$	−1.77016			−0.0593693
$890$	−0.252895	−	4.69111i	−0.00847705	−	0.157246i
$891$	−3.43349			−0.115026
$892$	−15.9582	−	15.9582i	−0.534319	−	0.534319i
$893$	11.4208	+	57.9317i	0.382182	+	1.93861i
$894$			1.02035i			0.0341255i
$895$	−41.5218	−	37.2739i	−1.38792	−	1.24593i
$896$			0.240740i			0.00804257i
$897$	33.1173	−	33.1173i	1.10575	−	1.10575i
$898$	4.48150	+	4.48150i	0.149550	+	0.149550i
$899$			28.8921i			0.963604i
$900$	0.537531	+	4.97102i	0.0179177	+	0.165701i
$901$			2.07880i			0.0692549i
$902$	8.93985	−	8.93985i	0.297664	−	0.297664i
$903$	−0.551834	+	0.551834i	−0.0183639	+	0.0183639i
$904$		−	9.63447i		−	0.320438i
$905$	−23.8580	+	26.5769i	−0.793068	+	0.883447i
$906$		−	19.8394i		−	0.659120i
$907$	−15.6355	−	15.6355i	−0.519169	−	0.519169i	0.398151	−	0.917320i	$-0.369652\pi$
$907$	−15.6355	−	15.6355i	−0.519169	−	0.519169i	−0.917320	+	0.398151i	$0.869652\pi$
$908$	−5.87132	+	5.87132i	−0.194847	+	0.194847i
$909$		−	8.90870i		−	0.295483i
$910$	3.45146	−	0.186066i	0.114415	−	0.00616803i
$911$			21.2778i			0.704964i	0.935819	+	0.352482i	$0.114662\pi$
$911$			21.2778i			0.704964i	−0.935819	+	0.352482i	$0.885338\pi$
$912$	0.843095	+	4.27659i	0.0279177	+	0.141612i
$913$	−34.2354	−	34.2354i	−1.13303	−	1.13303i
$914$	−19.9811			−0.660915
$915$	−3.70547	+	0.199759i	−0.122499	+	0.00660384i
$916$	−10.2825			−0.339743
$917$	−0.365531	+	0.365531i	−0.0120709	+	0.0120709i
$918$	−0.537531	−	0.537531i	−0.0177412	−	0.0177412i
$919$			19.7132i			0.650277i	0.945666	+	0.325139i	$0.105411\pi$
$919$			19.7132i			0.650277i	−0.945666	+	0.325139i	$0.894589\pi$
$920$	12.1371	+	10.8954i	0.400147	+	0.359211i
$921$	8.78829			0.289584
$922$	−7.33277	−	7.33277i	−0.241492	−	0.241492i
$923$	40.5508	+	40.5508i	1.33475	+	1.33475i
$924$	−0.826579			−0.0271925
$925$	24.5670	−	30.5241i	0.807757	−	1.00363i
$926$		−	30.5422i		−	1.00368i
$927$	−6.26365	−	6.26365i	−0.205725	−	0.205725i
$928$	3.80079	+	3.80079i	0.124767	+	0.124767i
$929$		−	44.9199i		−	1.47377i	−0.676016	−	0.736887i	$-0.736295\pi$
$929$		−	44.9199i		−	1.47377i	0.676016	−	0.736887i	$-0.263705\pi$
$930$	−8.02901	+	8.94401i	−0.263282	+	0.293286i
$931$	25.1313	+	16.8542i	0.823646	+	0.552374i
$932$	−14.4725	+	14.4725i	−0.474062	+	0.474062i
$933$	−3.21753	+	3.21753i	−0.105337	+	0.105337i
$934$	8.03432			0.262891
$935$	−5.82786	+	0.314176i	−0.190591	+	0.0102747i
$936$	6.42095			0.209875
$937$	11.9641	−	11.9641i	0.390851	−	0.390851i	−0.484140	−	0.874991i	$-0.660867\pi$
$937$	11.9641	−	11.9641i	0.390851	−	0.390851i	0.874991	+	0.484140i	$0.160867\pi$
$938$	−0.115912	−	0.115912i	−0.00378465	−	0.00378465i
$939$	28.3449			0.925002
$940$	1.63056	+	30.2464i	0.0531831	+	0.986530i
$941$			37.3163i			1.21648i	0.793755	+	0.608238i	$0.208123\pi$
$941$			37.3163i			1.21648i	−0.793755	+	0.608238i	$0.791877\pi$
$942$	−13.1863	+	13.1863i	−0.429632	+	0.429632i
$943$	18.9917	−	18.9917i	0.618456	−	0.618456i
$944$	4.20166			0.136752
$945$	−0.400582	−	0.359601i	−0.0130309	−	0.0116978i
$946$			11.1304i			0.361881i
$947$	21.4508	−	21.4508i	0.697057	−	0.697057i	−0.266717	−	0.963775i	$-0.585939\pi$
$947$	21.4508	−	21.4508i	0.697057	−	0.697057i	0.963775	+	0.266717i	$0.0859390\pi$
$948$	0.813330	+	0.813330i	0.0264157	+	0.0264157i
$949$	79.4451			2.57890
$950$	6.48984	+	20.8058i	0.210558	+	0.675030i
$951$	30.3037			0.982665
$952$	−0.129405	−	0.129405i	−0.00419405	−	0.00419405i
$953$	−24.4941	+	24.4941i	−0.793442	+	0.793442i	−0.982052	−	0.188610i	$-0.939602\pi$
$953$	−24.4941	+	24.4941i	−0.793442	+	0.793442i	0.188610	+	0.982052i	$0.439602\pi$
$954$			2.73460i			0.0885361i
$955$	−4.85178	−	4.35543i	−0.157000	−	0.140938i
$956$	21.4459			0.693609
$957$	−13.0500	+	13.0500i	−0.421846	+	0.421846i
$958$	12.9613	−	12.9613i	0.418762	−	0.418762i
$959$		−	4.61382i		−	0.148988i
$960$	0.120370	+	2.23283i	0.00388493	+	0.0720641i
$961$	2.10794			0.0679982
$962$	−35.5799	−	35.5799i	−1.14714	−	1.14714i
$963$	5.59814	−	5.59814i	0.180398	−	0.180398i
$964$	1.51636			0.0488387
$965$	21.0808	−	1.13645i	0.678614	−	0.0365836i
$966$	−1.75598			−0.0564977
$967$	34.3368	−	34.3368i	1.10420	−	1.10420i	0.110299	−	0.993898i	$-0.464819\pi$
$967$	34.3368	−	34.3368i	1.10420	−	1.10420i	0.993898	−	0.110299i	$-0.0351809\pi$
$968$	−0.557809	+	0.557809i	−0.0179287	+	0.0179287i
$969$	−2.75199	−	1.84561i	−0.0884066	−	0.0592895i
$970$	22.9295	−	25.5426i	0.736221	−	0.820122i
$971$			23.0276i			0.738992i	0.929232	+	0.369496i	$0.120470\pi$
$971$			23.0276i			0.738992i	−0.929232	+	0.369496i	$0.879530\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	1.78765	+	1.78765i	0.0573095	+	0.0573095i
$974$		−	11.6178i		−	0.372259i
$975$	31.9187	−	3.45146i	1.02222	−	0.110535i
$976$	−1.65954			−0.0531206
$977$	−32.7527	−	32.7527i	−1.04785	−	1.04785i	−0.998796	−	0.0490563i	$-0.984379\pi$
$977$	−32.7527	−	32.7527i	−1.04785	−	1.04785i	−0.0490563	−	0.998796i	$-0.515621\pi$
$978$	1.19921	+	1.19921i	0.0383464	+	0.0383464i
$979$	7.21368			0.230550
$980$	11.5513	+	10.3696i	0.368992	+	0.331243i
$981$			10.7123i			0.342018i
$982$	4.13849	+	4.13849i	0.132065	+	0.132065i
$983$	−4.11107	+	4.11107i	−0.131123	+	0.131123i	−0.769622	−	0.638499i	$-0.779555\pi$
$983$	−4.11107	+	4.11107i	−0.131123	+	0.131123i	0.638499	+	0.769622i	$0.279555\pi$
$984$	3.68222			0.117385
$985$	12.8917	−	0.694982i	0.410763	−	0.0221440i
$986$	−4.08609			−0.130128
$987$	−2.30597	−	2.30597i	−0.0733997	−	0.0733997i
$988$	27.4598	−	5.41348i	0.873612	−	0.172226i
$989$			23.6453i			0.751878i
$990$	−7.66639	+	0.413290i	−0.243654	+	0.0131352i
$991$			39.6215i			1.25862i	0.777155	+	0.629309i	$0.216662\pi$
$991$			39.6215i			1.25862i	−0.777155	+	0.629309i	$0.783338\pi$
$992$	−3.80079	+	3.80079i	−0.120675	+	0.120675i
$993$	22.5979	+	22.5979i	0.717122	+	0.717122i
$994$		−	2.15012i		−	0.0681978i
$995$	12.3033	−	13.7054i	0.390041	−	0.434491i
$996$		−	14.1012i		−	0.446812i
$997$	23.8300	−	23.8300i	0.754705	−	0.754705i	−0.220649	−	0.975353i	$-0.570817\pi$
$997$	23.8300	−	23.8300i	0.754705	−	0.754705i	0.975353	+	0.220649i	$0.0708174\pi$
$998$	−17.2572	+	17.2572i	−0.546268	+	0.546268i
$999$			7.83647i			0.247935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.m.a.493.7	yes	20
3.2	odd	2		1710.2.p.d.1063.4		20
5.2	odd	4	inner	570.2.m.a.37.2	✓	20
15.2	even	4		1710.2.p.d.37.9		20
19.18	odd	2	inner	570.2.m.a.493.2	yes	20
57.56	even	2		1710.2.p.d.1063.9		20
95.37	even	4	inner	570.2.m.a.37.7	yes	20
285.227	odd	4		1710.2.p.d.37.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.a.37.2	✓	20	5.2	odd	4	inner
570.2.m.a.37.7	yes	20	95.37	even	4	inner
570.2.m.a.493.2	yes	20	19.18	odd	2	inner
570.2.m.a.493.7	yes	20	1.1	even	1	trivial
1710.2.p.d.37.4		20	285.227	odd	4
1710.2.p.d.37.9		20	15.2	even	4
1710.2.p.d.1063.4		20	3.2	odd	2
1710.2.p.d.1063.9		20	57.56	even	2

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-1.66396 - 1.49373i) q^{5} +1.00000 q^{6} +(-0.170229 + 0.170229i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-1.66396 - 1.49373i) q^{5} +1.00000 q^{6} +(-0.170229 + 0.170229i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-0.120370 - 2.23283i) q^{10} +3.43349 q^{11} +(0.707107 + 0.707107i) q^{12} +(4.54030 - 4.54030i) q^{13} -0.240740 q^{14} +(-2.23283 + 0.120370i) q^{15} -1.00000 q^{16} +(0.537531 - 0.537531i) q^{17} +(0.707107 - 0.707107i) q^{18} +(2.42784 - 3.62016i) q^{19} +(1.49373 - 1.66396i) q^{20} +0.240740i q^{21} +(2.42784 + 2.42784i) q^{22} +(5.15769 + 5.15769i) q^{23} +1.00000i q^{24} +(0.537531 + 4.97102i) q^{25} +6.42095 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.170229 - 0.170229i) q^{28} -5.37513 q^{29} +(-1.66396 - 1.49373i) q^{30} -5.37513i q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.42784 - 2.42784i) q^{33} +0.760184 q^{34} +(0.537531 - 0.0289779i) q^{35} +1.00000 q^{36} +(-5.54122 - 5.54122i) q^{37} +(4.27659 - 0.843095i) q^{38} -6.42095i q^{39} +(2.23283 - 0.120370i) q^{40} -3.68222i q^{41} +(-0.170229 + 0.170229i) q^{42} +(2.29224 + 2.29224i) q^{43} +3.43349i q^{44} +(-1.49373 + 1.66396i) q^{45} +7.29408i q^{46} +(-9.57865 + 9.57865i) q^{47} +(-0.707107 + 0.707107i) q^{48} +6.94204i q^{49} +(-3.13495 + 3.89514i) q^{50} -0.760184i q^{51} +(4.54030 + 4.54030i) q^{52} +(-1.93366 + 1.93366i) q^{53} -1.00000i q^{54} +(-5.71319 - 5.12871i) q^{55} -0.240740i q^{56} +(-0.843095 - 4.27659i) q^{57} +(-3.80079 - 3.80079i) q^{58} -4.20166 q^{59} +(-0.120370 - 2.23283i) q^{60} +1.65954 q^{61} +(3.80079 - 3.80079i) q^{62} +(0.170229 + 0.170229i) q^{63} -1.00000i q^{64} +(-14.3369 + 0.772891i) q^{65} +3.43349 q^{66} +(0.481480 + 0.481480i) q^{67} +(0.537531 + 0.537531i) q^{68} +7.29408 q^{69} +(0.400582 + 0.359601i) q^{70} +8.93130i q^{71} +(0.707107 + 0.707107i) q^{72} +(8.74888 + 8.74888i) q^{73} -7.83647i q^{74} +(3.89514 + 3.13495i) q^{75} +(3.62016 + 2.42784i) q^{76} +(-0.584480 + 0.584480i) q^{77} +(4.54030 - 4.54030i) q^{78} +1.15022 q^{79} +(1.66396 + 1.49373i) q^{80} -1.00000 q^{81} +(2.60372 - 2.60372i) q^{82} +(-9.97102 - 9.97102i) q^{83} -0.240740 q^{84} +(-1.69736 + 0.0915034i) q^{85} +3.24172i q^{86} +(-3.80079 + 3.80079i) q^{87} +(-2.42784 + 2.42784i) q^{88} +2.10098 q^{89} +(-2.23283 + 0.120370i) q^{90} +1.54578i q^{91} +(-5.15769 + 5.15769i) q^{92} +(-3.80079 - 3.80079i) q^{93} -13.5463 q^{94} +(-9.44739 + 2.39726i) q^{95} -1.00000 q^{96} +(10.8544 + 10.8544i) q^{97} +(-4.90877 + 4.90877i) q^{98} -3.43349i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5} + 20 q^{6} - 4 q^{7}+O(q^{10}) \) 20 * q - 4 * q^5 + 20 * q^6 - 4 * q^7	\( 20 q - 4 q^{5} + 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} + 4 q^{17} + 44 q^{23} + 4 q^{25} - 8 q^{26} - 4 q^{28} - 4 q^{30} + 4 q^{35} + 20 q^{36} - 4 q^{38} - 4 q^{42} + 52 q^{43} + 4 q^{47} + 16 q^{55} - 4 q^{57} + 8 q^{58} + 32 q^{61} - 8 q^{62} + 4 q^{63} - 8 q^{66} + 4 q^{68} - 20 q^{73} + 20 q^{76} - 24 q^{77} + 4 q^{80} - 20 q^{81} - 24 q^{82} - 116 q^{83} - 60 q^{85} + 8 q^{87} - 44 q^{92} + 8 q^{93} - 32 q^{95} - 20 q^{96}+O(q^{100}) \) 20 * q - 4 * q^5 + 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 + 4 * q^17 + 44 * q^23 + 4 * q^25 - 8 * q^26 - 4 * q^28 - 4 * q^30 + 4 * q^35 + 20 * q^36 - 4 * q^38 - 4 * q^42 + 52 * q^43 + 4 * q^47 + 16 * q^55 - 4 * q^57 + 8 * q^58 + 32 * q^61 - 8 * q^62 + 4 * q^63 - 8 * q^66 + 4 * q^68 - 20 * q^73 + 20 * q^76 - 24 * q^77 + 4 * q^80 - 20 * q^81 - 24 * q^82 - 116 * q^83 - 60 * q^85 + 8 * q^87 - 44 * q^92 + 8 * q^93 - 32 * q^95 - 20 * q^96

Introduction

L-functions

Modular forms

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