LMFDB - Embedded newform 287.3.k.a.124.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(124,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("287.124");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.15
Character	$\chi$	$=$	287.124
Dual form			287.3.k.a.206.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07150 + 1.85589i) q^{2} +(4.93694 - 2.85034i) q^{3} +(-0.296226 - 0.513078i) q^{4} +(-2.71530 - 1.56768i) q^{5} +12.2166i q^{6} +(-3.44147 - 6.09559i) q^{7} -7.30238 q^{8} +(11.7489 - 20.3497i) q^{9} +O(q^{10})$	\(q+(-1.07150 + 1.85589i) q^{2} +(4.93694 - 2.85034i) q^{3} +(-0.296226 - 0.513078i) q^{4} +(-2.71530 - 1.56768i) q^{5} +12.2166i q^{6} +(-3.44147 - 6.09559i) q^{7} -7.30238 q^{8} +(11.7489 - 20.3497i) q^{9} +(5.81889 - 3.35954i) q^{10} +(-0.00185030 - 0.00320482i) q^{11} +(-2.92490 - 1.68869i) q^{12} -9.78880i q^{13} +(15.0003 + 0.144429i) q^{14} -17.8737 q^{15} +(9.00940 - 15.6047i) q^{16} +(14.7019 - 8.48815i) q^{17} +(25.1780 + 43.6095i) q^{18} +(28.9231 + 16.6988i) q^{19} +1.85755i q^{20} +(-34.3649 - 20.2842i) q^{21} +0.00793041 q^{22} +(-3.36401 + 5.82663i) q^{23} +(-36.0514 + 20.8143i) q^{24} +(-7.58477 - 13.1372i) q^{25} +(18.1670 + 10.4887i) q^{26} -82.6478i q^{27} +(-2.10806 + 3.57141i) q^{28} -51.9824 q^{29} +(19.1517 - 33.1717i) q^{30} +(39.5886 - 22.8565i) q^{31} +(4.70240 + 8.14479i) q^{32} +(-0.0182697 - 0.0105480i) q^{33} +36.3802i q^{34} +(-0.211310 + 21.9465i) q^{35} -13.9213 q^{36} +(-23.2460 + 40.2633i) q^{37} +(-61.9822 + 35.7855i) q^{38} +(-27.9015 - 48.3268i) q^{39} +(19.8281 + 11.4478i) q^{40} -6.40312i q^{41} +(74.4673 - 42.0430i) q^{42} -4.99902 q^{43} +(-0.00109622 + 0.00189870i) q^{44} +(-63.8037 + 36.8371i) q^{45} +(-7.20907 - 12.4865i) q^{46} +(70.1293 + 40.4892i) q^{47} -102.720i q^{48} +(-25.3126 + 41.9556i) q^{49} +32.5083 q^{50} +(48.3883 - 83.8110i) q^{51} +(-5.02242 + 2.89969i) q^{52} +(27.7266 + 48.0239i) q^{53} +(153.386 + 88.5572i) q^{54} +0.0116027i q^{55} +(25.1309 + 44.5123i) q^{56} +190.389 q^{57} +(55.6992 - 96.4738i) q^{58} +(-37.2437 + 21.5027i) q^{59} +(5.29465 + 9.17060i) q^{60} +(-55.2987 - 31.9267i) q^{61} +97.9629i q^{62} +(-164.477 - 1.58366i) q^{63} +51.9207 q^{64} +(-15.3457 + 26.5795i) q^{65} +(0.0391520 - 0.0226044i) q^{66} +(42.5117 + 73.6324i) q^{67} +(-8.71016 - 5.02881i) q^{68} +38.3543i q^{69} +(-40.5039 - 23.9078i) q^{70} +13.6818 q^{71} +(-85.7952 + 148.602i) q^{72} +(65.4915 - 37.8116i) q^{73} +(-49.8162 - 86.2842i) q^{74} +(-74.8911 - 43.2384i) q^{75} -19.7864i q^{76} +(-0.0131675 + 0.0223080i) q^{77} +119.586 q^{78} +(13.8020 - 23.9058i) q^{79} +(-48.9265 + 28.2477i) q^{80} +(-129.834 - 224.880i) q^{81} +(11.8835 + 6.86095i) q^{82} +30.6056i q^{83} +(-0.227621 + 23.6406i) q^{84} -53.2267 q^{85} +(5.35645 - 9.27765i) q^{86} +(-256.634 + 148.168i) q^{87} +(0.0135116 + 0.0234028i) q^{88} +(-10.7820 - 6.22501i) q^{89} -157.884i q^{90} +(-59.6686 + 33.6879i) q^{91} +3.98602 q^{92} +(130.298 - 225.682i) q^{93} +(-150.287 + 86.7683i) q^{94} +(-52.3566 - 90.6843i) q^{95} +(46.4309 + 26.8069i) q^{96} -73.6918i q^{97} +(-50.7427 - 91.9328i) q^{98} -0.0869564 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 2 q^{2} - 6 q^{3} - 106 q^{4} - 6 q^{5} - 4 q^{7} - 4 q^{8} + 164 q^{9}+O(q^{10}) $ 108 * q - 2 * q^2 - 6 * q^3 - 106 * q^4 - 6 * q^5 - 4 * q^7 - 4 * q^8 + 164 * q^9	$ 108 q - 2 q^{2} - 6 q^{3} - 106 q^{4} - 6 q^{5} - 4 q^{7} - 4 q^{8} + 164 q^{9} + 48 q^{10} + 6 q^{11} + 18 q^{12} + 38 q^{14} - 56 q^{15} - 202 q^{16} + 48 q^{17} + 32 q^{18} - 78 q^{19} - 104 q^{21} - 48 q^{22} - 16 q^{23} + 248 q^{25} + 144 q^{26} + 168 q^{29} - 64 q^{30} + 30 q^{31} - 104 q^{32} + 24 q^{33} - 54 q^{35} - 524 q^{36} + 76 q^{37} - 24 q^{38} - 34 q^{39} - 288 q^{40} + 190 q^{42} - 112 q^{43} + 102 q^{44} + 6 q^{45} - 68 q^{46} + 294 q^{47} + 68 q^{49} - 264 q^{50} - 36 q^{51} - 306 q^{52} + 152 q^{53} + 102 q^{54} - 438 q^{56} + 256 q^{57} - 164 q^{58} - 138 q^{59} + 280 q^{60} + 282 q^{61} + 442 q^{63} + 796 q^{64} + 76 q^{65} - 240 q^{66} - 158 q^{67} - 738 q^{68} - 82 q^{70} - 48 q^{71} - 374 q^{72} + 48 q^{73} + 34 q^{74} - 258 q^{75} - 184 q^{77} + 432 q^{78} + 128 q^{79} + 12 q^{80} - 262 q^{81} + 628 q^{84} - 196 q^{85} + 316 q^{86} + 438 q^{87} + 76 q^{88} - 24 q^{89} + 370 q^{91} - 592 q^{92} - 90 q^{93} - 264 q^{94} - 250 q^{95} - 102 q^{96} - 100 q^{98} + 168 q^{99}+O(q^{100}) $ 108 * q - 2 * q^2 - 6 * q^3 - 106 * q^4 - 6 * q^5 - 4 * q^7 - 4 * q^8 + 164 * q^9 + 48 * q^10 + 6 * q^11 + 18 * q^12 + 38 * q^14 - 56 * q^15 - 202 * q^16 + 48 * q^17 + 32 * q^18 - 78 * q^19 - 104 * q^21 - 48 * q^22 - 16 * q^23 + 248 * q^25 + 144 * q^26 + 168 * q^29 - 64 * q^30 + 30 * q^31 - 104 * q^32 + 24 * q^33 - 54 * q^35 - 524 * q^36 + 76 * q^37 - 24 * q^38 - 34 * q^39 - 288 * q^40 + 190 * q^42 - 112 * q^43 + 102 * q^44 + 6 * q^45 - 68 * q^46 + 294 * q^47 + 68 * q^49 - 264 * q^50 - 36 * q^51 - 306 * q^52 + 152 * q^53 + 102 * q^54 - 438 * q^56 + 256 * q^57 - 164 * q^58 - 138 * q^59 + 280 * q^60 + 282 * q^61 + 442 * q^63 + 796 * q^64 + 76 * q^65 - 240 * q^66 - 158 * q^67 - 738 * q^68 - 82 * q^70 - 48 * q^71 - 374 * q^72 + 48 * q^73 + 34 * q^74 - 258 * q^75 - 184 * q^77 + 432 * q^78 + 128 * q^79 + 12 * q^80 - 262 * q^81 + 628 * q^84 - 196 * q^85 + 316 * q^86 + 438 * q^87 + 76 * q^88 - 24 * q^89 + 370 * q^91 - 592 * q^92 - 90 * q^93 - 264 * q^94 - 250 * q^95 - 102 * q^96 - 100 * q^98 + 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.07150	+	1.85589i	−0.535750	+	0.927946i	0.463377	+	0.886162i	$0.346638\pi$
$2$	−1.07150	+	1.85589i	−0.535750	+	0.927946i	−0.999127	+	0.0417849i	$0.986696\pi$
$3$	4.93694	−	2.85034i	1.64565	−	0.950115i	0.666874	−	0.745171i	$-0.267632\pi$
$3$	4.93694	−	2.85034i	1.64565	−	0.950115i	0.978774	−	0.204944i	$-0.0657013\pi$
$4$	−0.296226	−	0.513078i	−0.0740564	−	0.128269i
$5$	−2.71530	−	1.56768i	−0.543060	−	0.313536i	0.203258	−	0.979125i	$-0.434847\pi$
$5$	−2.71530	−	1.56768i	−0.543060	−	0.313536i	−0.746318	+	0.665589i	$0.768180\pi$
$6$			12.2166i			2.03610i
$7$	−3.44147	−	6.09559i	−0.491639	−	0.870799i
$7$	−3.44147	−	6.09559i	−0.491639	−	0.870799i
$8$	−7.30238			−0.912797
$9$	11.7489	−	20.3497i	1.30544	−	2.26108i
$10$	5.81889	−	3.35954i	0.581889	−	0.335954i
$11$	−0.00185030	−	0.00320482i	−0.000168210	−	0.000291347i	0.865941	−	0.500146i	$-0.166720\pi$
$11$	−0.00185030	−	0.00320482i	−0.000168210	−	0.000291347i	−0.866109	+	0.499854i	$0.833387\pi$
$12$	−2.92490	−	1.68869i	−0.243741	−	0.140724i
$13$		−	9.78880i		−	0.752985i	−0.926420	−	0.376492i	$-0.877130\pi$
$13$		−	9.78880i		−	0.752985i	0.926420	−	0.376492i	$-0.122870\pi$
$14$	15.0003	+	0.144429i	1.07145	+	0.0103164i
$15$	−17.8737			−1.19158
$16$	9.00940	−	15.6047i	0.563088	−	0.975296i
$17$	14.7019	−	8.48815i	0.864818	−	0.499303i	−0.000805028	−	1.00000i	$-0.500256\pi$
$17$	14.7019	−	8.48815i	0.864818	−	0.499303i	0.865623	+	0.500697i	$0.166923\pi$
$18$	25.1780	+	43.6095i	1.39878	+	2.42275i
$19$	28.9231	+	16.6988i	1.52227	+	0.878882i	0.999654	+	0.0263133i	$0.00837676\pi$
$19$	28.9231	+	16.6988i	1.52227	+	0.878882i	0.522615	+	0.852569i	$0.324957\pi$
$20$			1.85755i			0.0928773i
$21$	−34.3649	−	20.2842i	−1.63642	−	0.965915i
$22$	0.00793041			0.000360473
$23$	−3.36401	+	5.82663i	−0.146261	+	0.253332i	−0.929843	−	0.367957i	$-0.880057\pi$
$23$	−3.36401	+	5.82663i	−0.146261	+	0.253332i	0.783582	+	0.621289i	$0.213391\pi$
$24$	−36.0514	+	20.8143i	−1.50214	+	0.867262i
$25$	−7.58477	−	13.1372i	−0.303391	−	0.525488i
$26$	18.1670	+	10.4887i	0.698730	+	0.403412i
$27$		−	82.6478i		−	3.06103i
$28$	−2.10806	+	3.57141i	−0.0752879	+	0.127550i
$29$	−51.9824			−1.79250			−0.896248	−	0.443553i	$-0.853718\pi$
$29$	−51.9824			−1.79250			−0.896248	+	0.443553i	$0.853718\pi$
$30$	19.1517	−	33.1717i	0.638389	−	1.10572i
$31$	39.5886	−	22.8565i	1.27705	−	0.737306i	0.300746	−	0.953704i	$-0.402764\pi$
$31$	39.5886	−	22.8565i	1.27705	−	0.737306i	0.976305	+	0.216399i	$0.0694311\pi$
$32$	4.70240	+	8.14479i	0.146950	+	0.254525i
$33$	−0.0182697	−	0.0105480i	−0.000553627	−	0.000319637i
$34$			36.3802i			1.07001i
$35$	−0.211310	+	21.9465i	−0.00603743	+	0.627042i
$36$	−13.9213			−0.386704
$37$	−23.2460	+	40.2633i	−0.628270	+	1.08820i	0.359628	+	0.933096i	$0.382903\pi$
$37$	−23.2460	+	40.2633i	−0.628270	+	1.08820i	−0.987899	+	0.155100i	$0.950430\pi$
$38$	−61.9822	+	35.7855i	−1.63111	+	0.941723i
$39$	−27.9015	−	48.3268i	−0.715422	−	1.23915i
$40$	19.8281	+	11.4478i	0.495704	+	0.286195i
$41$		−	6.40312i		−	0.156174i
$41$		−	6.40312i		−	0.156174i
$42$	74.4673	−	42.0430i	1.77303	−	1.00102i
$43$	−4.99902			−0.116256			−0.0581282	−	0.998309i	$-0.518513\pi$
$43$	−4.99902			−0.116256			−0.0581282	+	0.998309i	$0.518513\pi$
$44$	−0.00109622	+	0.00189870i	−2.49140e−5	+	4.31523e-5i
$45$	−63.8037	+	36.8371i	−1.41786	+	0.818602i
$46$	−7.20907	−	12.4865i	−0.156719	−	0.271445i
$47$	70.1293	+	40.4892i	1.49211	+	0.861472i	0.999959	−	0.00903687i	$-0.00287656\pi$
$47$	70.1293	+	40.4892i	1.49211	+	0.861472i	0.492153	+	0.870508i	$0.336210\pi$
$48$		−	102.720i		−	2.13999i
$49$	−25.3126	+	41.9556i	−0.516583	+	0.856237i
$50$	32.5083			0.650166
$51$	48.3883	−	83.8110i	0.948790	−	1.64335i
$52$	−5.02242	+	2.89969i	−0.0965849	+	0.0557633i
$53$	27.7266	+	48.0239i	0.523143	+	0.906110i	0.999637	+	0.0269328i	$0.00857401\pi$
$53$	27.7266	+	48.0239i	0.523143	+	0.906110i	−0.476494	+	0.879178i	$0.658093\pi$
$54$	153.386	+	88.5572i	2.84047	+	1.63995i
$55$			0.0116027i			0.000210959i
$56$	25.1309	+	44.5123i	0.448767	+	0.794863i
$57$	190.389			3.34016
$58$	55.6992	−	96.4738i	0.960330	−	1.66334i
$59$	−37.2437	+	21.5027i	−0.631250	+	0.364452i	−0.781236	−	0.624236i	$-0.785410\pi$
$59$	−37.2437	+	21.5027i	−0.631250	+	0.364452i	0.149986	+	0.988688i	$0.452077\pi$
$60$	5.29465	+	9.17060i	0.0882441	+	0.152843i
$61$	−55.2987	−	31.9267i	−0.906536	−	0.523389i	−0.0272211	−	0.999629i	$-0.508666\pi$
$61$	−55.2987	−	31.9267i	−0.906536	−	0.523389i	−0.879315	+	0.476241i	$0.841999\pi$
$62$			97.9629i			1.58005i
$63$	−164.477	−	1.58366i	−2.61075	−	0.0251374i
$64$	51.9207			0.811262
$65$	−15.3457	+	26.5795i	−0.236088	+	0.408916i
$66$	0.0391520	−	0.0226044i	0.000593212	−	0.000342491i
$67$	42.5117	+	73.6324i	0.634503	+	1.09899i	0.986620	+	0.163035i	$0.0521285\pi$
$67$	42.5117	+	73.6324i	0.634503	+	1.09899i	−0.352117	+	0.935956i	$0.614538\pi$
$68$	−8.71016	−	5.02881i	−0.128091	−	0.0739531i
$69$			38.3543i			0.555860i
$70$	−40.5039	−	23.9078i	−0.578627	−	0.341540i
$71$	13.6818			0.192701			0.0963507	−	0.995347i	$-0.469283\pi$
$71$	13.6818			0.192701			0.0963507	+	0.995347i	$0.469283\pi$
$72$	−85.7952	+	148.602i	−1.19160	+	2.06391i
$73$	65.4915	−	37.8116i	0.897144	−	0.517966i	0.0208717	−	0.999782i	$-0.493356\pi$
$73$	65.4915	−	37.8116i	0.897144	−	0.517966i	0.876273	+	0.481816i	$0.160023\pi$
$74$	−49.8162	−	86.2842i	−0.673192	−	1.16600i
$75$	−74.8911	−	43.2384i	−0.998548	−	0.576512i
$76$		−	19.7864i		−	0.260347i
$77$	−0.0131675	+	0.0223080i	−0.000171007	+	0.000289714i
$78$	119.586			1.53315
$79$	13.8020	−	23.9058i	0.174709	−	0.302605i	−0.765352	−	0.643612i	$-0.777435\pi$
$79$	13.8020	−	23.9058i	0.174709	−	0.302605i	0.940061	+	0.341008i	$0.110768\pi$
$80$	−48.9265	+	28.2477i	−0.611581	+	0.353096i
$81$	−129.834	−	224.880i	−1.60289	−	2.77629i
$82$	11.8835	+	6.86095i	0.144921	+	0.0836701i
$83$			30.6056i			0.368743i	0.982857	+	0.184371i	$0.0590249\pi$
$83$			30.6056i			0.368743i	−0.982857	+	0.184371i	$0.940975\pi$
$84$	−0.227621	+	23.6406i	−0.00270978	+	0.281435i
$85$	−53.2267			−0.626197
$86$	5.35645	−	9.27765i	0.0622843	−	0.107880i
$87$	−256.634	+	148.168i	−2.94982	+	1.70308i
$88$	0.0135116	+	0.0234028i	0.000153541	+	0.000265941i
$89$	−10.7820	−	6.22501i	−0.121147	−	0.0699440i	0.438202	−	0.898876i	$-0.355615\pi$
$89$	−10.7820	−	6.22501i	−0.121147	−	0.0699440i	−0.559349	+	0.828932i	$0.688949\pi$
$90$		−	157.884i		−	1.75427i
$91$	−59.6686	+	33.6879i	−0.655699	+	0.370197i
$92$	3.98602			0.0433263
$93$	130.298	−	225.682i	1.40105	−	2.42669i
$94$	−150.287	+	86.7683i	−1.59880	+	0.923067i
$95$	−52.3566	−	90.6843i	−0.551122	−	0.954571i
$96$	46.4309	+	26.8069i	0.483656	+	0.279239i
$97$		−	73.6918i		−	0.759710i	−0.925046	−	0.379855i	$-0.875974\pi$
$97$		−	73.6918i		−	0.759710i	0.925046	−	0.379855i	$-0.124026\pi$
$98$	−50.7427	−	91.9328i	−0.517783	−	0.938090i
$99$	−0.0869564			−0.000878348
$100$	−4.49360	+	7.78315i	−0.0449360	+	0.0778315i
$101$	−146.081	+	84.3398i	−1.44635	+	0.835048i	−0.998261	−	0.0589438i	$-0.981227\pi$
$101$	−146.081	+	84.3398i	−1.44635	+	0.835048i	−0.448084	+	0.893992i	$0.647893\pi$
$102$	103.696	+	179.607i	1.01663	+	1.76085i
$103$	50.3785	+	29.0860i	0.489111	+	0.282389i	0.724206	−	0.689584i	$-0.242207\pi$
$103$	50.3785	+	29.0860i	0.489111	+	0.282389i	−0.235094	+	0.971973i	$0.575540\pi$
$104$			71.4815i			0.687323i
$105$	61.5118	+	108.951i	0.585827	+	1.03763i
$106$	−118.836			−1.12110
$107$	8.97244	−	15.5407i	0.0838545	−	0.145240i	−0.821048	−	0.570859i	$-0.806610\pi$
$107$	8.97244	−	15.5407i	0.0838545	−	0.145240i	0.904903	+	0.425619i	$0.139944\pi$
$108$	−42.4048	+	24.4824i	−0.392637	+	0.226689i
$109$	35.1613	+	60.9012i	0.322581	+	0.558727i	0.981020	−	0.193907i	$-0.0621161\pi$
$109$	35.1613	+	60.9012i	0.322581	+	0.558727i	−0.658439	+	0.752634i	$0.728783\pi$
$110$	−0.0215334	−	0.0124323i	−0.000195758	−	0.000113021i
$111$			265.036i			2.38772i
$112$	−126.126	−	1.21439i	−1.12612	−	0.0108428i
$113$	54.4262			0.481648			0.240824	−	0.970569i	$-0.422582\pi$
$113$	54.4262			0.481648			0.240824	+	0.970569i	$0.422582\pi$
$114$	−204.002	+	353.341i	−1.78949	+	3.09949i
$115$	18.2686	−	10.5474i	0.158857	−	0.0917162i
$116$	15.3985	+	26.6710i	0.132746	+	0.229923i
$117$	−199.200	−	115.008i	−1.70256	−	0.982974i
$118$		−	92.1605i		−	0.781021i
$119$	−102.336	−	60.4051i	−0.859970	−	0.507606i
$120$	130.521			1.08767
$121$	60.5000	−	104.789i	0.500000	−	0.866025i
$122$	118.505	−	68.4190i	0.971354	−	0.560811i
$123$	−18.2511	−	31.6119i	−0.148383	−	0.257007i
$124$	−23.4543	−	13.5413i	−0.189148	−	0.109204i
$125$			125.946i			1.00757i
$126$	179.177	−	303.556i	1.42204	−	2.40917i
$127$	11.1292			0.0876314			0.0438157	−	0.999040i	$-0.486049\pi$
$127$	11.1292			0.0876314			0.0438157	+	0.999040i	$0.486049\pi$
$128$	−74.4427	+	128.939i	−0.581583	+	1.00733i
$129$	−24.6799	+	14.2489i	−0.191317	+	0.110457i
$130$	−32.8858	−	56.9599i	−0.252968	−	0.438153i
$131$	24.1676	+	13.9531i	0.184485	+	0.106513i	0.589398	−	0.807843i	$-0.299365\pi$
$131$	24.1676	+	13.9531i	0.184485	+	0.106513i	−0.404913	+	0.914355i	$0.632698\pi$
$132$			0.0124984i			9.46846e-5i
$133$	2.25085	−	233.772i	0.0169237	−	1.75768i
$134$	−182.205			−1.35974
$135$	−129.565	+	224.414i	−0.959743	+	1.66232i
$136$	−107.359	+	61.9837i	−0.789403	+	0.455762i
$137$	72.7287	+	125.970i	0.530867	+	0.919488i	0.999351	+	0.0360165i	$0.0114669\pi$
$137$	72.7287	+	125.970i	0.530867	+	0.919488i	−0.468484	+	0.883472i	$0.655200\pi$
$138$	−71.1815	−	41.0967i	−0.515808	−	0.297802i
$139$			36.7513i			0.264398i	0.991223	+	0.132199i	$0.0422037\pi$
$139$			36.7513i			0.264398i	−0.991223	+	0.132199i	$0.957796\pi$
$140$	11.3228	−	6.39269i	0.0808775	−	0.0456621i
$141$	461.632			3.27399
$142$	−14.6601	+	25.3920i	−0.103240	+	0.178817i
$143$	−0.0313714	+	0.0181123i	−0.000219380	+	0.000126659i
$144$	−211.702	−	366.678i	−1.47015	−	2.54638i
$145$	141.148	+	81.4917i	0.973433	+	0.562012i
$146$			162.060i			1.11000i
$147$	−5.37859	+	279.282i	−0.0365890	+	1.89988i
$148$	27.5442			0.186110
$149$	−62.2282	+	107.782i	−0.417639	+	0.723372i	−0.995701	−	0.0926205i	$-0.970476\pi$
$149$	−62.2282	+	107.782i	−0.417639	+	0.723372i	0.578062	+	0.815993i	$0.303809\pi$
$150$	160.492	−	92.6599i	1.06994	−	0.617733i
$151$	48.3227	+	83.6973i	0.320018	+	0.554287i	0.980491	−	0.196562i	$-0.0629778\pi$
$151$	48.3227	+	83.6973i	0.320018	+	0.554287i	−0.660474	+	0.750849i	$0.729644\pi$
$152$	−211.207	−	121.941i	−1.38952	−	0.802241i
$153$		−	398.907i		−	2.60723i
$154$	−0.0272923	−	0.0483406i	−0.000177223	−	0.000313900i
$155$	−143.326			−0.924687
$156$	−16.5303	+	28.6312i	−0.105963	+	0.183534i
$157$	48.9958	−	28.2877i	0.312075	−	0.180177i	−0.335780	−	0.941941i	$-0.609000\pi$
$157$	48.9958	−	28.2877i	0.312075	−	0.180177i	0.647855	+	0.761764i	$0.275666\pi$
$158$	29.5777	+	51.2301i	0.187201	+	0.324241i
$159$	273.769	+	158.061i	1.72182	+	0.994092i
$160$		−	29.4874i		−	0.184296i
$161$	47.0939	+	0.453440i	0.292509	+	0.00281640i
$162$	556.471			3.43500
$163$	133.527	−	231.276i	0.819184	−	1.41887i	−0.0871001	−	0.996200i	$-0.527760\pi$
$163$	133.527	−	231.276i	0.819184	−	1.41887i	0.906284	−	0.422669i	$-0.138907\pi$
$164$	−3.28530	+	1.89677i	−0.0200323	+	0.0115657i
$165$	0.0330718	+	0.0572820i	0.000200435	+	0.000347164i
$166$	−56.8008	−	32.7939i	−0.342173	−	0.197554i
$167$			4.14271i			0.0248066i	0.999923	+	0.0124033i	$0.00394820\pi$
$167$			4.14271i			0.0248066i	−0.999923	+	0.0124033i	$0.996052\pi$
$168$	250.945	+	148.123i	1.49372	+	0.881685i
$169$	73.1793			0.433014
$170$	57.0325	−	98.7831i	0.335485	−	0.581077i
$171$	679.631	−	392.385i	3.97445	−	2.29465i
$172$	1.48084	+	2.56489i	0.00860952	+	0.0149121i
$173$	−102.198	−	59.0040i	−0.590739	−	0.341064i	0.174650	−	0.984631i	$-0.444120\pi$
$173$	−102.198	−	59.0040i	−0.590739	−	0.341064i	−0.765390	+	0.643567i	$0.777454\pi$
$174$		−	635.047i		−	3.64970i
$175$	−53.9763	+	91.4450i	−0.308436	+	0.522543i
$176$	−0.0666806			−0.000378867
$177$	−122.580	+	212.315i	−0.692543	+	1.19952i
$178$	23.1059	−	13.3402i	0.129809	−	0.0749450i
$179$	−29.3279	−	50.7974i	−0.163843	−	0.283785i	0.772401	−	0.635135i	$-0.219056\pi$
$179$	−29.3279	−	50.7974i	−0.163843	−	0.283785i	−0.936244	+	0.351351i	$0.885722\pi$
$180$	37.8006	+	21.8242i	0.210003	+	0.121245i
$181$		−	170.115i		−	0.939863i	−0.882703	−	0.469932i	$-0.844279\pi$
$181$		−	170.115i		−	0.939863i	0.882703	−	0.469932i	$-0.155721\pi$
$182$	1.41379	−	146.835i	0.00776808	−	0.806786i
$183$	−364.009			−1.98912
$184$	24.5653	−	42.5483i	0.133507	−	0.231241i
$185$	126.240	−	72.8845i	0.682377	−	0.393970i
$186$	279.228	+	483.637i	1.50123	+	2.60020i
$187$	−0.0544060	−	0.0314113i	−0.000290941	−	0.000167975i
$188$		−	47.9757i		−	0.255190i
$189$	−503.788	+	284.430i	−2.66554	+	1.50492i
$190$	224.400			1.18105
$191$	−88.1786	+	152.730i	−0.461668	+	0.799633i	−0.999044	−	0.0437100i	$-0.986082\pi$
$191$	−88.1786	+	152.730i	−0.461668	+	0.799633i	0.537376	+	0.843343i	$0.319416\pi$
$192$	256.330	−	147.992i	1.33505	−	0.770792i
$193$	57.2375	+	99.1383i	0.296567	+	0.513670i	0.975348	−	0.220671i	$-0.0708247\pi$
$193$	57.2375	+	99.1383i	0.296567	+	0.513670i	−0.678781	+	0.734341i	$0.737491\pi$
$194$	136.764	+	78.9608i	0.704970	+	0.407014i
$195$			174.962i			0.897242i
$196$	29.0247	+	0.558976i	0.148085	+	0.00285192i
$197$	91.4952			0.464443			0.232221	−	0.972663i	$-0.425401\pi$
$197$	91.4952			0.464443			0.232221	+	0.972663i	$0.425401\pi$
$198$	0.0931738	−	0.161382i	0.000470575	−	0.000815060i
$199$	−101.581	+	58.6479i	−0.510458	+	0.294713i	−0.733022	−	0.680205i	$-0.761891\pi$
$199$	−101.581	+	58.6479i	−0.510458	+	0.294713i	0.222564	+	0.974918i	$0.428557\pi$
$200$	55.3868	+	95.9328i	0.276934	+	0.479664i
$201$	419.756	+	242.346i	2.08834	+	1.20570i
$202$		−	361.481i		−	1.78951i
$203$	178.896	+	316.864i	0.881261	+	1.56090i
$204$	−57.3354			−0.281056
$205$	−10.0380	+	17.3864i	−0.0489661	+	0.0848117i
$206$	−107.961	+	62.3314i	−0.524083	+	0.302579i
$207$	79.0470	+	136.913i	0.381870	+	0.661417i
$208$	−152.752	−	88.1913i	−0.734383	−	0.423996i
$209$		−	0.123591i		−	0.000591345i
$210$	−268.111	−	2.58149i	−1.27672	−	0.0122928i
$211$	−306.218			−1.45127			−0.725634	−	0.688080i	$-0.758454\pi$
$211$	−306.218			−1.45127			−0.725634	+	0.688080i	$0.758454\pi$
$212$	16.4266	−	28.4518i	0.0774842	−	0.134207i
$213$	67.5463	−	38.9979i	0.317119	−	0.183089i
$214$	19.2279	+	33.3038i	0.0898502	+	0.155625i
$215$	13.5738	+	7.83686i	0.0631341	+	0.0364505i
$216$			603.526i			2.79410i
$217$	−275.567	−	162.656i	−1.26989	−	0.749567i
$218$	−150.702			−0.691292
$219$	215.552	−	373.347i	0.984255	−	1.70478i
$220$	0.00595310	−	0.00343703i	2.70596e−5	−	1.56228e-5i
$221$	−83.0888	−	143.914i	−0.375967	−	0.651195i
$222$	−491.879	−	283.987i	−2.21567	−	1.27922i
$223$		−	248.931i		−	1.11628i	−0.829746	−	0.558142i	$-0.811515\pi$
$223$		−	248.931i		−	1.11628i	0.829746	−	0.558142i	$-0.188485\pi$
$224$	33.4642	−	56.6940i	0.149394	−	0.253098i
$225$	−356.452			−1.58423
$226$	−58.3177	+	101.009i	−0.258043	+	0.446944i
$227$	−129.085	+	74.5274i	−0.568658	+	0.328315i	−0.756613	−	0.653863i	$-0.773147\pi$
$227$	−129.085	+	74.5274i	−0.568658	+	0.328315i	0.187955	+	0.982178i	$0.439814\pi$
$228$	−56.3981	−	97.6843i	−0.247360	−	0.428440i
$229$	62.2128	+	35.9186i	0.271672	+	0.156850i	0.629647	−	0.776881i	$-0.283200\pi$
$229$	62.2128	+	35.9186i	0.271672	+	0.156850i	−0.357975	+	0.933731i	$0.616533\pi$
$230$			45.2060i			0.196548i
$231$	−0.00142178	+	0.147665i	−6.15491e−6	+	0.000639244i
$232$	379.595			1.63619
$233$	69.9411	−	121.142i	0.300176	−	0.519921i	−0.675999	−	0.736902i	$-0.736288\pi$
$233$	69.9411	−	121.142i	0.300176	−	0.519921i	0.976176	+	0.216981i	$0.0696211\pi$
$234$	426.885	−	246.462i	1.82429	−	1.05326i
$235$	−126.948	−	219.880i	−0.540204	−	0.935661i
$236$	22.0651	+	12.7393i	0.0934962	+	0.0539800i
$237$		−	157.362i		−	0.663974i
$238$	221.759	−	125.201i	0.931760	−	0.526056i
$239$	54.8774			0.229613			0.114806	−	0.993388i	$-0.463375\pi$
$239$	54.8774			0.229613			0.114806	+	0.993388i	$0.463375\pi$
$240$	−161.031	+	278.915i	−0.670964	+	1.16214i
$241$	−10.4283	+	6.02078i	−0.0432709	+	0.0249825i	−0.521479	−	0.853264i	$-0.674620\pi$
$241$	−10.4283	+	6.02078i	−0.0432709	+	0.0249825i	0.478208	+	0.878246i	$0.341286\pi$
$242$	129.652	+	224.563i	0.535750	+	0.927946i
$243$	−637.794	−	368.231i	−2.62467	−	1.51535i
$244$			37.8300i			0.155041i
$245$	134.504	−	74.2401i	0.548996	−	0.303021i
$246$	78.2243			0.317985
$247$	163.461	−	283.123i	0.661785	−	1.14625i
$248$	−289.091	+	166.907i	−1.16569	+	0.673011i
$249$	87.2366	+	151.098i	0.350348	+	0.606820i
$250$	−233.742	−	134.951i	−0.934968	−	0.539804i
$251$		−	154.499i		−	0.615536i	−0.951462	−	0.307768i	$-0.900418\pi$
$251$		−	154.499i		−	0.615536i	0.951462	−	0.307768i	$-0.0995820\pi$
$252$	47.9099	+	84.8588i	0.190119	+	0.336741i
$253$	0.0248978			9.84101e−5
$254$	−11.9249	+	20.6546i	−0.0469485	+	0.0813173i
$255$	−262.777	+	151.715i	−1.03050	+	0.594959i
$256$	−55.6892	−	96.4566i	−0.217536	−	0.376783i
$257$	360.660	+	208.227i	1.40335	+	0.810222i	0.994734	−	0.102487i	$-0.0326800\pi$
$257$	360.660	+	208.227i	1.40335	+	0.810222i	0.408611	+	0.912709i	$0.366013\pi$
$258$		−	61.0710i		−	0.236709i
$259$	325.429	+	3.13337i	1.25648	+	0.0120979i
$260$	18.1832			0.0699352
$261$	−610.738	+	1057.83i	−2.33999	+	4.05298i
$262$	−51.7911	+	29.9016i	−0.197676	+	0.114128i
$263$	−124.267	−	215.237i	−0.472498	−	0.818391i	0.527006	−	0.849861i	$-0.323314\pi$
$263$	−124.267	−	215.237i	−0.472498	−	0.818391i	−0.999505	+	0.0314701i	$0.989981\pi$
$264$	0.133412	+	0.0770256i	0.000505349	+	0.000291764i
$265$		−	173.866i		−	0.656096i
$266$	431.444	+	254.664i	1.62197	+	0.957383i
$267$	−70.9738			−0.265819
$268$	25.1861	−	43.6236i	0.0939780	−	0.162775i
$269$	58.3340	−	33.6792i	0.216855	−	0.125201i	−0.387638	−	0.921812i	$-0.626709\pi$
$269$	58.3340	−	33.6792i	0.216855	−	0.125201i	0.604493	+	0.796610i	$0.293376\pi$
$270$	−277.658	−	480.918i	−1.02836	−	1.78118i
$271$	30.4797	+	17.5975i	0.112471	+	0.0649354i	0.555180	−	0.831730i	$-0.312649\pi$
$271$	30.4797	+	17.5975i	0.112471	+	0.0649354i	−0.442709	+	0.896665i	$0.645983\pi$
$272$		−	305.892i		−	1.12460i
$273$	−198.558	+	336.391i	−0.727319	+	1.23220i
$274$	−311.715			−1.13765
$275$	−0.0280683	+	0.0486156i	−0.000102066	+	0.000176784i
$276$	19.6788	−	11.3615i	0.0712998	−	0.0411650i
$277$	145.530	+	252.065i	0.525379	+	0.909983i	0.999563	+	0.0295570i	$0.00940965\pi$
$277$	145.530	+	252.065i	0.525379	+	0.909983i	−0.474184	+	0.880426i	$0.657257\pi$
$278$	−68.2064	−	39.3790i	−0.245347	−	0.141651i
$279$		−	1074.16i		−	3.85002i
$280$	1.54307	−	160.262i	0.00551095	−	0.572363i
$281$	140.884			0.501367			0.250684	−	0.968069i	$-0.419345\pi$
$281$	140.884			0.501367			0.250684	+	0.968069i	$0.419345\pi$
$282$	−494.639	+	856.740i	−1.75404	+	3.03809i
$283$	−283.561	+	163.714i	−1.00198	+	0.578496i	−0.908835	−	0.417156i	$-0.863027\pi$
$283$	−283.561	+	163.714i	−1.00198	+	0.578496i	−0.0931494	+	0.995652i	$0.529693\pi$
$284$	−4.05290	−	7.01983i	−0.0142708	−	0.0247177i
$285$	−516.963	−	298.469i	−1.81390	−	1.04726i
$286$		−	0.0776292i		−	0.000271431i
$287$	−39.0309	+	22.0362i	−0.135996	+	0.0767811i
$288$	220.993			0.767335
$289$	−0.402780	+	0.697635i	−0.00139370	+	0.00241396i
$290$	−302.480	+	174.637i	−1.04303	+	0.602196i
$291$	−210.047	−	363.812i	−0.721811	−	1.25021i
$292$	−38.8005	−	22.4015i	−0.132879	−	0.0767175i
$293$		−	320.006i		−	1.09217i	−0.837729	−	0.546086i	$-0.816117\pi$
$293$		−	320.006i		−	1.09217i	0.837729	−	0.546086i	$-0.183883\pi$
$294$	−512.554	−	309.233i	−1.74338	−	1.05181i
$295$	134.837			0.457075
$296$	169.751	−	294.018i	0.573483	−	0.993302i
$297$	−0.264872	+	0.152924i	−0.000891823	+	0.000514895i
$298$	−133.355	−	230.978i	−0.447500	−	0.775093i
$299$	57.0358	+	32.9296i	0.190755	+	0.110132i
$300$			51.2333i			0.170778i
$301$	17.2040	+	30.4720i	0.0571561	+	0.101236i
$302$	−207.111			−0.685798
$303$	−480.795	+	832.762i	−1.58678	+	2.74839i
$304$	521.160	−	300.892i	1.71434	−	0.989776i
$305$	100.102	+	173.381i	0.328202	+	0.568463i
$306$	740.328	+	427.429i	2.41937	+	1.39683i
$307$			409.977i			1.33543i	0.744417	+	0.667715i	$0.232728\pi$
$307$			409.977i			1.33543i	−0.744417	+	0.667715i	$0.767272\pi$
$308$	0.0153463		0.000147761i	4.98257e−5		4.79742e-7i
$309$	331.621			1.07321
$310$	153.574	−	265.999i	0.495401	−	0.858060i
$311$	195.359	−	112.791i	0.628165	−	0.362671i	−0.151876	−	0.988400i	$-0.548531\pi$
$311$	195.359	−	112.791i	0.628165	−	0.362671i	0.780041	+	0.625728i	$0.215198\pi$
$312$	203.747	+	352.900i	0.653035	+	1.13109i
$313$	139.176	+	80.3534i	0.444652	+	0.256720i	0.705569	−	0.708641i	$-0.250691\pi$
$313$	139.176	+	80.3534i	0.444652	+	0.256720i	−0.260917	+	0.965361i	$0.584025\pi$
$314$			121.241i			0.386119i
$315$	444.123	+	262.148i	1.40991	+	0.832215i
$316$	−16.3540			−0.0517533
$317$	299.967	−	519.558i	0.946268	−	1.63898i	0.193075	−	0.981184i	$-0.438154\pi$
$317$	299.967	−	519.558i	0.946268	−	1.63898i	0.753192	−	0.657800i	$-0.228513\pi$
$318$	−586.687	+	338.724i	−1.84493	+	1.06517i
$319$	0.0961833	+	0.166594i	0.000301515	+	0.000522239i
$320$	−140.980	−	81.3950i	−0.440564	−	0.254360i
$321$		−	102.298i		−	0.318686i
$322$	−51.3027	+	86.9154i	−0.159325	+	0.269924i
$323$	566.966			1.75531
$324$	−76.9206	+	133.230i	−0.237409	+	0.411205i
$325$	−128.597	+	74.2458i	−0.395685	+	0.228449i
$326$	286.148	+	495.624i	0.877756	+	1.52032i
$327$	347.179	+	200.444i	1.06171	+	0.612978i
$328$			46.7580i			0.142555i
$329$	5.45760	−	566.822i	0.0165885	−	1.72286i
$330$	−0.141746			−0.000429533
$331$	62.1623	−	107.668i	0.187801	−	0.325282i	−0.756715	−	0.653744i	$-0.773197\pi$
$331$	62.1623	−	107.668i	0.187801	−	0.325282i	0.944517	+	0.328463i	$0.106531\pi$
$332$	15.7031	−	9.06617i	0.0472984	−	0.0273077i
$333$	546.231	+	946.100i	1.64033	+	2.84114i
$334$	−7.68842	−	4.43891i	−0.0230192	−	0.0132902i
$335$		−	266.579i		−	0.795757i
$336$	−626.137	+	353.507i	−1.86350	+	1.05210i
$337$	249.447			0.740198			0.370099	−	0.928992i	$-0.379324\pi$
$337$	249.447			0.740198			0.370099	+	0.928992i	$0.379324\pi$
$338$	−78.4117	+	135.813i	−0.231987	+	0.401814i
$339$	268.699	−	155.134i	0.792623	−	0.457621i
$340$	15.7671	+	27.3095i	0.0463739	+	0.0803219i
$341$	−0.146502	−	0.0845829i	−0.000429624	−	0.000248044i
$342$			1681.76i			4.91744i
$343$	342.857	+	9.90596i	0.999583	+	0.0288804i
$344$	36.5048			0.106118
$345$	60.1273	−	104.143i	0.174282	−	0.301865i
$346$	219.010	−	126.446i	0.632977	−	0.365450i
$347$	28.4701	+	49.3116i	0.0820463	+	0.142108i	0.904129	−	0.427260i	$-0.140521\pi$
$347$	28.4701	+	49.3116i	0.0820463	+	0.142108i	−0.822082	+	0.569368i	$0.807188\pi$
$348$	152.043	+	87.7822i	0.436906	+	0.252248i
$349$		−	49.5237i		−	0.141902i	−0.997480	−	0.0709509i	$-0.977397\pi$
$349$		−	49.5237i		−	0.141902i	0.997480	−	0.0709509i	$-0.0226034\pi$
$350$	−111.876	−	198.158i	−0.319647	−	0.566164i
$351$	−809.023			−2.30491
$352$	0.0174017	−	0.0301407i	4.94368e−5	−	8.56270e-5i
$353$	−317.379	+	183.239i	−0.899090	+	0.519090i	−0.876905	−	0.480664i	$-0.840396\pi$
$353$	−317.379	+	183.239i	−0.899090	+	0.519090i	−0.0221853	+	0.999754i	$0.507062\pi$
$354$	−262.689	−	454.991i	−0.742060	−	1.28529i
$355$	−37.1502	−	21.4487i	−0.104648	−	0.0604188i
$356$			7.37603i			0.0207192i
$357$	−677.405	−	6.52234i	−1.89749	−	0.0182699i
$358$	125.699			0.351116
$359$	166.034	−	287.579i	0.462490	−	0.801057i	−0.536594	−	0.843840i	$-0.680289\pi$
$359$	166.034	−	287.579i	0.462490	−	0.801057i	0.999084	+	0.0427839i	$0.0136227\pi$
$360$	465.919	−	268.998i	1.29422	−	0.747218i
$361$	377.197	+	653.325i	1.04487	+	1.80976i
$362$	315.716	+	182.278i	0.872143	+	0.503532i
$363$		−	689.783i		−	1.90023i
$364$	34.9599	+	20.6354i	0.0960436	+	0.0566907i
$365$	−237.105			−0.649604
$366$	390.035	−	675.561i	1.06567	−	1.84580i
$367$	453.181	−	261.644i	1.23483	−	0.712927i	0.266794	−	0.963754i	$-0.414036\pi$
$367$	453.181	−	261.644i	1.23483	−	0.712927i	0.968032	+	0.250826i	$0.0807024\pi$
$368$	60.6154	+	104.989i	0.164716	+	0.285296i
$369$	−130.302	−	75.2299i	−0.353122	−	0.203875i
$370$			312.383i			0.844279i
$371$	197.314	−	334.283i	0.531843	−	0.901032i
$372$	−154.390			−0.415027
$373$	161.590	−	279.882i	0.433218	−	0.750355i	−0.563931	−	0.825822i	$-0.690712\pi$
$373$	161.590	−	279.882i	0.433218	−	0.750355i	0.997148	+	0.0754673i	$0.0240448\pi$
$374$	0.116592	−	0.0673145i	0.000311743	−	0.000179985i
$375$	358.989	+	621.787i	0.957304	+	1.65810i
$376$	−512.111	−	295.667i	−1.36200	−	0.786349i
$377$			508.845i			1.34972i
$378$	11.9368	−	1239.74i	0.0315788	−	3.27974i
$379$	−353.839			−0.933613			−0.466807	−	0.884359i	$-0.654596\pi$
$379$	−353.839			−0.933613			−0.466807	+	0.884359i	$0.654596\pi$
$380$	−31.0187	+	53.7260i	−0.0816282	+	0.141384i
$381$	54.9442	−	31.7220i	0.144210	−	0.0832599i
$382$	−188.967	−	327.300i	−0.494678	−	0.856807i
$383$	−90.2476	−	52.1045i	−0.235633	−	0.136043i	0.377535	−	0.925995i	$-0.376772\pi$
$383$	−90.2476	−	52.1045i	−0.235633	−	0.136043i	−0.613168	+	0.789952i	$0.710105\pi$
$384$			848.749i			2.21028i
$385$	0.0707256	−	0.0399305i	0.000183703	−	0.000103716i
$386$	−245.320			−0.635544
$387$	−58.7332	+	101.729i	−0.151765	+	0.262865i
$388$	−37.8096	+	21.8294i	−0.0974475	+	0.0562614i
$389$	−34.1825	−	59.2058i	−0.0878727	−	0.152200i	0.818739	−	0.574166i	$-0.194674\pi$
$389$	−34.1825	−	59.2058i	−0.0878727	−	0.152200i	−0.906612	+	0.421966i	$0.861340\pi$
$390$	−324.711	−	187.472i	−0.832592	−	0.480697i
$391$			114.217i			0.292114i
$392$	184.842	−	306.376i	0.471535	−	0.781571i
$393$	159.085			0.404797
$394$	−98.0371	+	169.805i	−0.248825	+	0.430978i
$395$	−74.9532	+	43.2742i	−0.189755	+	0.109555i
$396$	0.0257587	+	0.0446154i	6.50473e−5	+	0.000112665i
$397$	−290.566	−	167.758i	−0.731905	−	0.422565i	0.0872139	−	0.996190i	$-0.472204\pi$
$397$	−290.566	−	167.758i	−0.731905	−	0.422565i	−0.819119	+	0.573624i	$0.805537\pi$
$398$		−	251.365i		−	0.631570i
$399$	−655.218	−	1160.53i	−1.64215	−	2.90861i
$400$	−273.337			−0.683342
$401$	−63.2959	+	109.632i	−0.157845	+	0.273396i	−0.934091	−	0.357034i	$-0.883788\pi$
$401$	−63.2959	+	109.632i	−0.157845	+	0.273396i	0.776246	+	0.630430i	$0.217121\pi$
$402$	−899.536	+	519.348i	−2.23765	+	1.29191i
$403$	−223.738	−	387.525i	−0.555180	−	0.961600i
$404$	86.5458	+	49.9672i	0.214222	+	0.123681i
$405$			814.155i			2.01026i
$406$	−779.752	−	7.50778i	−1.92057	−	0.0184921i
$407$	0.172049			0.000422724
$408$	−353.350	+	612.019i	−0.866053	+	1.50005i
$409$	−613.236	+	354.052i	−1.49935	+	0.865652i	−1.00000		0.000745490i	$-0.999763\pi$
$409$	−613.236	+	354.052i	−1.49935	+	0.865652i	−0.499354	+	0.866398i	$0.666429\pi$
$410$	−21.5115	−	37.2591i	−0.0524671	−	0.0908758i
$411$	718.115	+	414.604i	1.74724	+	1.00877i
$412$		−	34.4641i		−	0.0836507i
$413$	259.245	+	153.022i	0.627712	+	0.370513i
$414$	−338.796			−0.818347
$415$	47.9798	−	83.1035i	0.115614	−	0.200249i
$416$	79.7278	−	46.0308i	0.191653	−	0.110651i
$417$	104.754	+	181.439i	0.251208	+	0.435105i
$418$	0.229372	+	0.132428i	0.000548737	+	0.000316813i
$419$			187.128i			0.446605i	0.974749	+	0.223303i	$0.0716838\pi$
$419$			187.128i			0.446605i	−0.974749	+	0.223303i	$0.928316\pi$
$420$	37.6789	−	63.8344i	0.0897116	−	0.151987i
$421$	−443.718			−1.05396			−0.526981	−	0.849877i	$-0.676676\pi$
$421$	−443.718			−1.05396			−0.526981	+	0.849877i	$0.676676\pi$
$422$	328.112	−	568.307i	0.777517	−	1.34670i
$423$	1647.89	−	951.409i	3.89572	−	2.24919i
$424$	−202.470	−	350.688i	−0.477524	−	0.827095i
$425$	−223.021	−	128.761i	−0.524755	−	0.302968i
$426$			167.145i			0.392359i
$427$	−4.30346	+	446.953i	−0.0100784	+	1.04673i
$428$	−10.6315			−0.0248399
$429$	−0.103252	+	0.178838i	−0.000240682	+	0.000416873i
$430$	−29.0887	+	16.7944i	−0.0676483	+	0.0390567i
$431$	−321.221	−	556.371i	−0.745292	−	1.29088i	−0.950058	−	0.312072i	$-0.898977\pi$
$431$	−321.221	−	556.371i	−0.745292	−	1.29088i	0.204767	−	0.978811i	$-0.434356\pi$
$432$	−1289.70	−	744.608i	−2.98541	−	1.72363i
$433$			848.864i			1.96042i	0.197950	+	0.980212i	$0.436572\pi$
$433$			848.864i			1.96042i	−0.197950	+	0.980212i	$0.563428\pi$
$434$	597.142	−	337.136i	1.37590	−	0.776812i
$435$	929.118			2.13590
$436$	20.8314	−	36.0810i	0.0477784	−	0.0827546i
$437$	−194.595	+	112.350i	−0.445298	+	0.257093i
$438$	461.928	+	800.083i	1.05463	+	1.82667i
$439$	−330.643	−	190.897i	−0.753172	−	0.434844i	0.0736668	−	0.997283i	$-0.476530\pi$
$439$	−330.643	−	190.897i	−0.753172	−	0.434844i	−0.826839	+	0.562439i	$0.809863\pi$
$440$		−	0.0847276i		−	0.000192563i
$441$	556.391	+	1008.04i	1.26166	+	2.28580i
$442$	356.119			0.805698
$443$	24.0443	−	41.6459i	0.0542760	−	0.0940088i	−0.837611	−	0.546267i	$-0.816048\pi$
$443$	24.0443	−	41.6459i	0.0542760	−	0.0940088i	0.891887	+	0.452259i	$0.149382\pi$
$444$	135.984	−	78.5106i	0.306271	−	0.176826i
$445$	19.5176	+	33.8056i	0.0438599	+	0.0759675i
$446$	461.990	+	266.730i	1.03585	+	0.598049i
$447$			709.488i			1.58722i
$448$	−178.684	−	316.488i	−0.398848	−	0.706446i
$449$	−800.605			−1.78309			−0.891543	−	0.452937i	$-0.850376\pi$
$449$	−800.605			−1.78309			−0.891543	+	0.452937i	$0.850376\pi$
$450$	381.938	−	661.536i	0.848751	−	1.47008i
$451$	−0.0205209	+	0.0118477i	−4.55008e−5	+	2.62699e-5i
$452$	−16.1224	−	27.9249i	−0.0356691	−	0.0617807i
$453$	477.132	+	275.473i	1.05327	+	0.608107i
$454$		−	319.425i		−	0.703579i
$455$	214.830	+	2.06847i	0.472153	+	0.00454609i
$456$	−1390.29			−3.04889
$457$	46.0932	−	79.8357i	0.100860	−	0.174695i	−0.811179	−	0.584798i	$-0.801174\pi$
$457$	46.0932	−	79.8357i	0.100860	−	0.174695i	0.912039	+	0.410103i	$0.134507\pi$
$458$	−133.322	+	76.9735i	−0.291096	+	0.168065i
$459$	−701.527	−	1215.08i	−1.52838	−	2.64723i
$460$	−10.8232	−	6.24880i	−0.0235288	−	0.0135843i
$461$			565.589i			1.22687i	0.789744	+	0.613437i	$0.210213\pi$
$461$			565.589i			1.22687i	−0.789744	+	0.613437i	$0.789787\pi$
$462$	−0.272528	−	0.160862i	−0.000589887	−	0.000348186i
$463$	−749.686			−1.61919			−0.809596	−	0.586987i	$-0.800314\pi$
$463$	−749.686			−1.61919			−0.809596	+	0.586987i	$0.800314\pi$
$464$	−468.330	+	811.172i	−1.00933	+	1.74822i
$465$	−707.594	+	408.530i	−1.52171	+	0.878559i
$466$	149.884	+	259.606i	0.321639	+	0.557095i
$467$	553.894	+	319.791i	1.18607	+	0.684777i	0.957410	−	0.288730i	$-0.0932331\pi$
$467$	553.894	+	319.791i	1.18607	+	0.684777i	0.228657	+	0.973507i	$0.426566\pi$
$468$			136.273i			0.291182i
$469$	302.531	−	512.538i	0.645055	−	1.09283i
$470$	544.099			1.15766
$471$	161.260	−	279.310i	0.342377	−	0.593014i
$472$	271.968	−	157.021i	0.576203	−	0.332671i
$473$	0.00924971	+	0.0160210i	1.95554e−5	+	3.38710e-5i
$474$	292.047	+	168.613i	0.616133	+	0.355724i
$475$		−	506.625i		−	1.06658i
$476$	−0.677842	+	70.4001i	−0.00142404	+	0.147899i
$477$	1303.03			2.73172
$478$	−58.8011	+	101.847i	−0.123015	+	0.213068i
$479$	−624.722	+	360.684i	−1.30422	+	0.752993i	−0.981125	−	0.193373i	$-0.938057\pi$
$479$	−624.722	+	360.684i	−1.30422	+	0.752993i	−0.323097	+	0.946366i	$0.604724\pi$
$480$	−84.0492	−	145.578i	−0.175103	−	0.303287i
$481$	394.129	+	227.551i	0.819395	+	0.473078i
$482$		−	25.8051i		−	0.0535375i
$483$	233.792	−	131.995i	0.484042	−	0.273282i
$484$	−71.6866			−0.148113
$485$	−115.525	+	200.095i	−0.238196	+	0.412568i
$486$	1366.79	−	789.118i	2.81233	−	1.62370i
$487$	404.916	+	701.335i	0.831450	+	1.44011i	0.896889	+	0.442257i	$0.145822\pi$
$487$	404.916	+	701.335i	0.831450	+	1.44011i	−0.0654388	+	0.997857i	$0.520845\pi$
$488$	403.812	+	233.141i	0.827484	+	0.477748i
$489$		−	1522.39i		−	3.11328i
$490$	−6.33943	+	329.174i	−0.0129376	+	0.671783i
$491$	−203.382			−0.414219			−0.207110	−	0.978318i	$-0.566406\pi$
$491$	−203.382			−0.414219			−0.207110	+	0.978318i	$0.566406\pi$
$492$	−10.8129	+	18.7285i	−0.0219774	+	0.0380660i
$493$	−764.240	+	441.234i	−1.55018	+	0.894998i
$494$	350.297	+	606.732i	0.709103	+	1.22820i
$495$	0.236113	+	0.136320i	0.000476995	+	0.000275393i
$496$		−	823.693i		−	1.66067i
$497$	−47.0855	−	83.3987i	−0.0947395	−	0.167804i
$498$	−373.896			−0.750796
$499$	−41.2168	+	71.3895i	−0.0825987	+	0.143065i	−0.904365	−	0.426759i	$-0.859655\pi$
$499$	−41.2168	+	71.3895i	−0.0825987	+	0.143065i	0.821767	+	0.569824i	$0.192989\pi$
$500$	64.6200	−	37.3084i	0.129240	−	0.0746168i
$501$	11.8081	+	20.4523i	0.0235691	+	0.0408230i
$502$	286.734	+	165.546i	0.571184	+	0.329773i
$503$			522.555i			1.03888i	0.854508	+	0.519438i	$0.173859\pi$
$503$			522.555i			1.03888i	−0.854508	+	0.519438i	$0.826141\pi$
$504$	1201.08	+	11.5645i	2.38309	+	0.0229454i
$505$	528.871			1.04727
$506$	−0.0266780	+	0.0462076i	−5.27232e−5	+	9.13193e-5i
$507$	361.282	−	208.586i	0.712588	−	0.411413i
$508$	−3.29675	−	5.71014i	−0.00648967	−	0.0112404i
$509$	289.193	+	166.966i	0.568160	+	0.328027i	0.756414	−	0.654093i	$-0.226950\pi$
$509$	289.193	+	166.966i	0.568160	+	0.328027i	−0.188254	+	0.982120i	$0.560283\pi$
$510$		−	650.249i		−	1.27500i
$511$	−455.871	−	269.082i	−0.892116	−	0.526580i
$512$	−356.857			−0.696987
$513$	1380.12	−	2390.43i	2.69029	−	4.65971i
$514$	−772.894	+	446.230i	−1.50368	+	0.868153i
$515$	−91.1951	−	157.955i	−0.177078	−	0.306708i
$516$	14.6216	+	8.44180i	0.0283365	+	0.0163601i
$517$		−	0.299669i		−	0.000579631i
$518$	−354.512	+	600.604i	−0.684387	+	1.15947i
$519$	−672.727			−1.29620
$520$	112.060	−	194.094i	0.215500	−	0.373257i
$521$	611.104	−	352.821i	1.17294	−	0.677199i	0.218572	−	0.975821i	$-0.429860\pi$
$521$	611.104	−	352.821i	1.17294	−	0.677199i	0.954372	+	0.298621i	$0.0965268\pi$
$522$	−1308.81	−	2266.93i	−2.50730	−	4.34277i
$523$	−337.982	−	195.134i	−0.646237	−	0.373105i	0.140776	−	0.990042i	$-0.455040\pi$
$523$	−337.982	−	195.134i	−0.646237	−	0.373105i	−0.787013	+	0.616936i	$0.788374\pi$
$524$		−	16.5331i		−	0.0315517i
$525$	−5.82818	+	605.310i	−0.0111013	+	1.15297i
$526$	532.609			1.01256
$527$	388.018	−	672.067i	0.736277	−	1.27527i
$528$	−0.329198	+	0.190063i	−0.000623481	+	0.000359967i
$529$	241.867	+	418.926i	0.457215	+	0.791920i
$530$	322.676	+	186.297i	0.608822	+	0.351504i
$531$			1010.53i			1.90308i
$532$	−120.610	+	68.0943i	−0.226710	+	0.127997i
$533$	−62.6789			−0.117596
$534$	76.0484	−	131.720i	0.142413	−	0.246666i
$535$	−48.7257	+	28.1318i	−0.0910761	+	0.0525828i
$536$	−310.437	−	537.692i	−0.579173	−	1.00316i
$537$	−289.580	−	167.189i	−0.539256	−	0.311340i
$538$			144.349i			0.268307i
$539$	0.181296	+	0.00349152i	0.000336357	+	6.47777e-6i
$540$	153.522			0.284300
$541$	−261.897	+	453.620i	−0.484099	+	0.838484i	−0.999833	−	0.0182649i	$-0.994186\pi$
$541$	−261.897	+	453.620i	−0.484099	+	0.838484i	0.515734	+	0.856749i	$0.327519\pi$
$542$	−65.3181	+	37.7114i	−0.120513	+	0.0695783i
$543$	−484.887	−	839.849i	−0.892978	−	1.54668i
$544$	138.268	+	79.8293i	0.254170	+	0.146745i
$545$		−	220.487i		−	0.404563i
$546$	−411.551	−	728.946i	−0.753756	−	1.33507i
$547$	−127.268			−0.232665			−0.116333	−	0.993210i	$-0.537114\pi$
$547$	−127.268			−0.232665			−0.116333	+	0.993210i	$0.537114\pi$
$548$	43.0882	−	74.6310i	0.0786282	−	0.136188i
$549$	−1299.40	+	750.210i	−2.36685	+	1.36650i
$550$	−0.0601503	−	0.104183i	−0.000109364	−	0.000189424i
$551$	−1503.49	−	868.042i	−2.72866	−	1.57539i
$552$		−	280.078i		−	0.507387i
$553$	−193.219	−	1.86040i	−0.349402	−	0.00336419i
$554$	−623.741			−1.12589
$555$	415.492	−	719.653i	0.748634	−	1.29667i
$556$	18.8563	−	10.8867i	0.0339141	−	0.0195803i
$557$	43.2231	+	74.8645i	0.0775997	+	0.134407i	0.902214	−	0.431289i	$-0.141941\pi$
$557$	43.2231	+	74.8645i	0.0775997	+	0.134407i	−0.824614	+	0.565696i	$0.808608\pi$
$558$	1993.52	+	1150.96i	3.57262	+	2.06265i
$559$			48.9344i			0.0875393i
$560$	340.566	+	201.022i	0.608153	+	0.358968i
$561$	−0.358132			−0.000638382
$562$	−150.957	+	261.466i	−0.268608	+	0.465242i
$563$	907.452	−	523.918i	1.61182	−	0.930582i	0.622867	−	0.782328i	$-0.285968\pi$
$563$	907.452	−	523.918i	1.61182	−	0.930582i	0.988949	−	0.148254i	$-0.0473654\pi$
$564$	−136.747	−	236.853i	−0.242460	−	0.419953i
$565$	−147.783	−	85.3228i	−0.261564	−	0.151014i
$566$		−	701.680i		−	1.23972i
$567$	−923.955	+	1565.34i	−1.62955	+	2.76073i
$568$	−99.9097			−0.175897
$569$	272.501	−	471.986i	0.478913	−	0.829501i	−0.520795	−	0.853682i	$-0.674364\pi$
$569$	272.501	−	471.986i	0.478913	−	0.829501i	0.999708	+	0.0241809i	$0.00769777\pi$
$570$	1107.85	−	639.619i	1.94360	−	1.12214i
$571$	274.441	+	475.346i	0.480632	+	0.832480i	0.999753	−	0.0222212i	$-0.00707382\pi$
$571$	274.441	+	475.346i	0.480632	+	0.832480i	−0.519121	+	0.854701i	$0.673740\pi$
$572$	0.0185860	+	0.0107306i	3.24930e−5	+	1.87598e-5i
$573$			1005.36i			1.75455i
$574$	0.924799	−	96.0488i	0.00161115	−	0.167332i
$575$	102.061			0.177497
$576$	610.013	−	1056.57i	1.05905	−	1.83433i
$577$	−511.901	+	295.546i	−0.887177	+	0.512212i	−0.873018	−	0.487688i	$-0.837840\pi$
$577$	−511.901	+	295.546i	−0.887177	+	0.512212i	−0.0141592	+	0.999900i	$0.504507\pi$
$578$	−0.863157	−	1.49503i	−0.00149335	−	0.00258656i
$579$	565.157	+	326.293i	0.976091	+	0.563546i
$580$		−	96.5597i		−	0.166482i
$581$	186.560	−	105.328i	0.321101	−	0.181288i
$582$	900.262			1.54684
$583$	0.102605	−	0.177718i	0.000175995	−	0.000304833i
$584$	−478.244	+	276.114i	−0.818911	+	0.472798i
$585$	360.591	+	624.562i	0.616395	+	1.06763i
$586$	593.897	+	342.887i	1.01348	+	0.585131i
$587$			788.554i			1.34336i	0.740840	+	0.671681i	$0.234427\pi$
$587$			788.554i			1.34336i	−0.740840	+	0.671681i	$0.765573\pi$
$588$	144.887	−	79.9708i	0.246406	−	0.136005i
$589$	1526.70			2.59202
$590$	−144.478	+	250.243i	−0.244878	+	0.424141i
$591$	451.707	−	260.793i	0.764309	−	0.441274i
$592$	418.865	+	725.496i	0.707543	+	1.22550i
$593$	−207.732	−	119.934i	−0.350307	−	0.202250i	0.314513	−	0.949253i	$-0.398159\pi$
$593$	−207.732	−	119.934i	−0.350307	−	0.202250i	−0.664820	+	0.747003i	$0.731492\pi$
$594$		−	0.655431i		−	0.00110342i
$595$	183.178	+	324.449i	0.307863	+	0.545292i
$596$	73.7344			0.123715
$597$	−334.333	+	579.082i	−0.560022	+	0.969987i
$598$	−122.228	+	70.5682i	−0.204394	+	0.118007i
$599$	−482.542	−	835.787i	−0.805580	−	1.39530i	−0.915899	−	0.401409i	$-0.868521\pi$
$599$	−482.542	−	835.787i	−0.805580	−	1.39530i	0.110320	−	0.993896i	$-0.464813\pi$
$600$	546.883	+	315.743i	0.911472	+	0.526239i
$601$		−	469.730i		−	0.781581i	−0.920480	−	0.390791i	$-0.872202\pi$
$601$		−	469.730i		−	0.781581i	0.920480	−	0.390791i	$-0.127798\pi$
$602$	−74.9869	−	0.722005i	−0.124563	−	0.00119934i
$603$	1997.87			3.31321
$604$	28.6288	−	49.5866i	0.0473987	−	0.0820970i
$605$	−328.551	+	189.689i	−0.543060	+	0.313536i
$606$	−1030.34	−	1784.61i	−1.70024	−	2.94490i
$607$	−502.845	−	290.318i	−0.828410	−	0.478283i	0.0248982	−	0.999690i	$-0.492074\pi$
$607$	−502.845	−	290.318i	−0.828410	−	0.478283i	−0.853308	+	0.521407i	$0.825407\pi$
$608$			314.097i			0.516607i
$609$	1786.37	+	1054.42i	2.93328	+	1.73140i
$610$	−429.036			−0.703338
$611$	396.340	−	686.482i	0.648675	−	1.12354i
$612$	−204.670	+	118.166i	−0.334428	+	0.193082i
$613$	358.191	+	620.404i	0.584324	+	1.01208i	0.994959	+	0.100279i	$0.0319736\pi$
$613$	358.191	+	620.404i	0.584324	+	1.01208i	−0.410635	+	0.911800i	$0.634693\pi$
$614$	−760.874	−	439.291i	−1.23921	−	0.715457i
$615$			114.448i			0.186094i
$616$	0.0961542	−	0.162902i	0.000156095	−	0.000264451i
$617$	−221.171			−0.358462			−0.179231	−	0.983807i	$-0.557361\pi$
$617$	−221.171			−0.358462			−0.179231	+	0.983807i	$0.557361\pi$
$618$	−355.332	+	615.453i	−0.574971	+	0.995878i
$619$	−226.992	+	131.054i	−0.366708	+	0.211719i	−0.672019	−	0.740534i	$-0.734573\pi$
$619$	−226.992	+	131.054i	−0.366708	+	0.211719i	0.305311	+	0.952253i	$0.401239\pi$
$620$	42.4570	+	73.5376i	0.0684790	+	0.118609i
$621$	481.559	+	278.028i	0.775457	+	0.447710i
$622$			483.421i			0.777205i
$623$	−0.839080	+	87.1462i	−0.00134684	+	0.139881i
$624$	−1005.50			−1.61138
$625$	7.82346	−	13.5506i	0.0125175	−	0.0216810i
$626$	−298.255	+	172.197i	−0.476445	+	0.275076i
$627$	−0.352278	−	0.610163i	−0.000561846	−	0.000973146i
$628$	−29.0276	−	16.7591i	−0.0462223	−	0.0266865i
$629$			789.262i			1.25479i
$630$	−962.396	+	543.353i	−1.52761	+	0.862465i
$631$	−535.037			−0.847920			−0.423960	−	0.905681i	$-0.639360\pi$
$631$	−535.037			−0.847920			−0.423960	+	0.905681i	$0.639360\pi$
$632$	−100.787	+	174.569i	−0.159474	+	0.276217i
$633$	−1511.78	+	872.826i	−2.38828	+	1.37887i
$634$	642.829	+	1113.41i	1.01393	+	1.75617i
$635$	−30.2191	−	17.4470i	−0.0475891	−	0.0274756i
$636$		−	187.286i		−	0.294476i
$637$	410.695	+	247.780i	0.644734	+	0.388979i
$638$	−0.412242			−0.000646147
$639$	160.747	−	278.421i	0.251560	−	0.435714i
$640$	404.268	−	233.404i	0.631669	−	0.364694i
$641$	−264.493	−	458.115i	−0.412626	−	0.714689i	0.582550	−	0.812795i	$-0.302055\pi$
$641$	−264.493	−	458.115i	−0.412626	−	0.714689i	−0.995176	+	0.0981061i	$0.968722\pi$
$642$	189.854	+	109.613i	0.295723	+	0.170736i
$643$		−	372.920i		−	0.579969i	−0.957031	−	0.289985i	$-0.906350\pi$
$643$		−	372.920i		−	0.579969i	0.957031	−	0.289985i	$-0.0936502\pi$
$644$	−13.7178	−	24.2972i	−0.0213009	−	0.0377285i
$645$	89.3510			0.138529
$646$	−607.504	+	1052.23i	−0.940409	+	1.62884i
$647$	363.262	−	209.729i	0.561455	−	0.324156i	−0.192274	−	0.981341i	$-0.561586\pi$
$647$	363.262	−	209.729i	0.561455	−	0.324156i	0.753729	+	0.657185i	$0.228253\pi$
$648$	948.100	+	1642.16i	1.46312	+	2.53419i
$649$	0.137825	+	0.0795730i	0.000212364	+	0.000122609i
$650$		−	318.218i		−	0.489565i
$651$	−1824.08	−	17.5630i	−2.80197	−	0.0269786i
$652$	−158.216			−0.242663
$653$	−57.3373	+	99.3110i	−0.0878059	+	0.152084i	−0.906583	−	0.422027i	$-0.861319\pi$
$653$	−57.3373	+	99.3110i	−0.0878059	+	0.152084i	0.818778	+	0.574111i	$0.194652\pi$
$654$	−744.005	+	429.551i	−1.13762	+	0.656807i
$655$	−43.7481	−	75.7739i	−0.0667910	−	0.115685i
$656$	−99.9191	−	57.6883i	−0.152316	−	0.0879395i
$657$		−	1776.98i		−	2.70469i
$658$	1046.11	+	617.479i	1.58984	+	0.938417i
$659$	511.802			0.776634			0.388317	−	0.921526i	$-0.373057\pi$
$659$	511.802			0.776634			0.388317	+	0.921526i	$0.373057\pi$
$660$	0.0195934	−	0.0339368i	2.96870e−5	−	5.14194e-5i
$661$	999.895	−	577.290i	1.51270	−	0.873358i	0.512811	−	0.858502i	$-0.328604\pi$
$661$	999.895	−	577.290i	1.51270	−	0.873358i	0.999890	−	0.0148564i	$-0.00472912\pi$
$662$	133.214	+	230.733i	0.201229	+	0.348539i
$663$	−820.409	−	473.663i	−1.23742	−	0.714424i
$664$		−	223.494i		−	0.336587i
$665$	−372.591	+	631.232i	−0.560287	+	0.949221i
$666$	−2341.15			−3.51524
$667$	174.869	−	302.882i	0.262173	−	0.454096i
$668$	2.12553	−	1.22718i	0.00318193	−	0.00183709i
$669$	−709.540	−	1228.96i	−1.06060	−	1.83701i
$670$	494.742	+	285.639i	0.738420	+	0.426327i
$671$			0.236297i			0.000352156i
$672$	3.61335	−	375.279i	0.00537701	−	0.558451i
$673$	−776.690			−1.15407			−0.577036	−	0.816719i	$-0.695791\pi$
$673$	−776.690			−1.15407			−0.577036	+	0.816719i	$0.695791\pi$
$674$	−267.282	+	462.946i	−0.396561	+	0.686864i
$675$	−1085.76	+	626.865i	−1.60854	+	0.928688i
$676$	−21.6776	−	37.5467i	−0.0320674	−	0.0555424i
$677$	−948.927	−	547.863i	−1.40166	−	0.809251i	−0.407101	−	0.913383i	$-0.633460\pi$
$677$	−948.927	−	547.863i	−1.40166	−	0.809251i	−0.994563	+	0.104132i	$0.966794\pi$
$678$			664.902i			0.980682i
$679$	−449.196	+	253.608i	−0.661555	+	0.373503i
$680$	388.682			0.571591
$681$	−424.858	+	735.875i	−0.623873	+	1.08058i
$682$	0.313954	−	0.181261i	0.000460343	−	0.000265779i
$683$	−465.868	−	806.908i	−0.682091	−	1.18142i	−0.974341	−	0.225075i	$-0.927737\pi$
$683$	−465.868	−	806.908i	−0.682091	−	1.18142i	0.292250	−	0.956342i	$-0.405596\pi$
$684$	−402.648	−	232.469i	−0.588667	−	0.339867i
$685$		−	456.061i		−	0.665783i
$686$	−385.756	+	625.691i	−0.562326	+	0.912087i
$687$	409.521			0.596101
$688$	−45.0382	+	78.0085i	−0.0654625	+	0.113384i
$689$	470.096	−	271.410i	0.682287	−	0.393919i
$690$	128.853	+	223.180i	0.186743	+	0.323449i
$691$	−446.911	−	258.024i	−0.646760	−	0.373407i	0.140454	−	0.990087i	$-0.455144\pi$
$691$	−446.911	−	258.024i	−0.646760	−	0.373407i	−0.787214	+	0.616680i	$0.788477\pi$
$692$			69.9140i			0.101032i
$693$	0.299258	+	0.530051i	0.000431830	+	0.000764864i
$694$	−122.023			−0.175825
$695$	57.6142	−	99.7907i	0.0828981	−	0.143584i
$696$	1874.04	−	1081.98i	2.69259	−	1.55456i
$697$	−54.3506	−	94.1381i	−0.0779780	−	0.135062i
$698$	91.9108	+	53.0647i	0.131677	+	0.0760239i
$699$		−	797.425i		−	1.14081i
$700$	62.9075	+	0.605700i	0.0898679	+	0.000865286i
$701$	−821.456			−1.17183			−0.585917	−	0.810371i	$-0.699266\pi$
$701$	−821.456			−1.17183			−0.585917	+	0.810371i	$0.699266\pi$
$702$	866.869	−	1501.46i	1.23486	−	2.13883i
$703$	−1344.69	+	776.359i	−1.91279	+	1.10435i
$704$	−0.0960692	−	0.166397i	−0.000136462	−	0.000236359i
$705$	−1253.47	−	723.691i	−1.77797	−	1.02651i
$706$		−	785.362i		−	1.11241i
$707$	1016.83	+	600.197i	1.43824	+	0.848934i
$708$	145.245			0.205149
$709$	220.002	−	381.055i	0.310300	−	0.537455i	−0.668128	−	0.744047i	$-0.732904\pi$
$709$	220.002	−	381.055i	0.310300	−	0.537455i	0.978427	+	0.206592i	$0.0662373\pi$
$710$	79.6129	−	45.9645i	0.112131	−	0.0647388i
$711$	−324.318	−	561.735i	−0.456143	−	0.790063i
$712$	78.7345	+	45.4574i	0.110582	+	0.0638447i
$713$			307.557i			0.431357i
$714$	737.944	−	1250.20i	1.03353	−	1.75098i
$715$	0.113577			0.000158849
$716$	−17.3754	+	30.0950i	−0.0242673	+	0.0420321i
$717$	270.927	−	156.420i	0.377861	−	0.218158i
$718$	355.811	+	616.283i	0.495558	+	0.858332i
$719$	824.743	+	476.166i	1.14707	+	0.662261i	0.948172	−	0.317759i	$-0.102930\pi$
$719$	824.743	+	476.166i	1.14707	+	0.662261i	0.198898	+	0.980020i	$0.436264\pi$
$720$			1327.52i			1.84378i
$721$	3.92055	−	407.186i	0.00543766	−	0.564751i
$722$	−1616.67			−2.23915
$723$	−34.3226	+	59.4485i	−0.0474725	+	0.0822247i
$724$	−87.2823	+	50.3925i	−0.120556	+	0.0696029i
$725$	394.274	+	682.903i	0.543827	+	0.941936i
$726$	1280.16	+	739.103i	1.76331	+	1.01805i
$727$		−	77.2878i		−	0.106311i	−0.998586	−	0.0531553i	$-0.983072\pi$
$727$		−	77.2878i		−	0.106311i	0.998586	−	0.0531553i	$-0.0169278\pi$
$728$	435.723	−	246.002i	0.598520	−	0.337914i
$729$	−1861.32			−2.55325
$730$	254.059	−	440.042i	0.348025	−	0.602798i
$731$	−73.4951	+	42.4324i	−0.100541	+	0.0580471i
$732$	107.829	+	186.765i	0.147307	+	0.255143i
$733$	815.975	+	471.104i	1.11320	+	0.642706i	0.939656	−	0.342120i	$-0.111145\pi$
$733$	815.975	+	471.104i	1.11320	+	0.642706i	0.173544	+	0.984826i	$0.444478\pi$
$734$			1121.41i			1.52780i
$735$	452.429	−	749.902i	0.615550	−	1.02028i
$736$	−63.2756			−0.0859723
$737$	0.157319	−	0.272485i	0.000213459	−	0.000369722i
$738$	279.237	−	161.218i	0.378370	−	0.218452i
$739$	−16.3192	−	28.2657i	−0.0220829	−	0.0382486i	0.854773	−	0.519002i	$-0.173696\pi$
$739$	−16.3192	−	28.2657i	−0.0220829	−	0.0382486i	−0.876856	+	0.480754i	$0.840363\pi$
$740$	−74.7909	−	43.1805i	−0.101069	−	0.0583521i
$741$		−	1863.68i		−	2.51509i
$742$	408.971	+	724.377i	0.551174	+	0.976250i
$743$	241.943			0.325630			0.162815	−	0.986657i	$-0.447943\pi$
$743$	241.943			0.325630			0.162815	+	0.986657i	$0.447943\pi$
$744$	−951.483	+	1648.02i	−1.27888	+	2.21508i
$745$	337.936	−	195.108i	0.453606	−	0.261890i
$746$	346.288	+	599.788i	0.464193	+	0.804005i
$747$	622.817	+	359.584i	0.833758	+	0.481370i
$748$			0.0372193i			4.97585e-5i
$749$	−125.608	−	1.20941i	−0.167701	−	0.00161470i
$750$	−1538.63			−2.05150
$751$	−523.265	+	906.322i	−0.696758	+	1.20682i	0.272827	+	0.962063i	$0.412041\pi$
$751$	−523.265	+	906.322i	−0.696758	+	1.20682i	−0.969584	+	0.244757i	$0.921292\pi$
$752$	1263.65	−	729.566i	1.68038	−	0.970168i
$753$	−440.377	−	762.755i	−0.584830	−	1.01295i
$754$	−944.363	−	545.228i	−1.25247	−	0.723114i
$755$		−	303.018i		−	0.401348i
$756$	295.170	+	174.227i	0.390436	+	0.230459i
$757$	−236.729			−0.312720			−0.156360	−	0.987700i	$-0.549976\pi$
$757$	−236.729			−0.312720			−0.156360	+	0.987700i	$0.549976\pi$
$758$	379.139	−	656.688i	0.500183	−	0.866343i
$759$	0.122919	−	0.0709672i	0.000161948	−	9.35009e-5i
$760$	382.328	+	662.211i	0.503063	+	0.871330i
$761$	−963.608	−	556.339i	−1.26624	−	0.731063i	−0.291965	−	0.956429i	$-0.594309\pi$
$761$	−963.608	−	556.339i	−1.26624	−	0.731063i	−0.974274	+	0.225366i	$0.927642\pi$
$762$			135.961i			0.178426i
$763$	250.223	−	423.919i	0.327946	−	0.555595i
$764$	104.483			0.136758
$765$	−625.357	+	1083.15i	−0.817461	+	1.41588i
$766$	193.401	−	111.660i	0.252481	−	0.145770i
$767$	210.486	+	364.572i	0.274427	+	0.475322i
$768$	−549.869	−	317.467i	−0.715975	−	0.413368i
$769$			237.237i			0.308501i	0.988032	+	0.154250i	$0.0492963\pi$
$769$			237.237i			0.308501i	−0.988032	+	0.154250i	$0.950704\pi$
$770$	−0.00167577	+	0.174045i	−2.17633e−6	+	0.000226032i
$771$	2374.07			3.07921
$772$	33.9104	−	58.7346i	0.0439254	−	0.0760811i
$773$	−532.100	+	307.208i	−0.688357	+	0.397423i	−0.802996	−	0.595984i	$-0.796762\pi$
$773$	−532.100	+	307.208i	−0.688357	+	0.397423i	0.114639	+	0.993407i	$0.463429\pi$
$774$	−125.865	−	218.005i	−0.162617	−	0.281660i
$775$	−600.540	−	346.722i	−0.774891	−	0.447383i
$776$			538.126i			0.693461i
$777$	1615.55	−	912.115i	2.07922	−	1.17389i
$778$	146.506			0.188311
$779$	106.924	−	185.198i	0.137258	−	0.237738i
$780$	89.7692	−	51.8283i	0.115089	−	0.0664465i
$781$	−0.0253155	−	0.0438477i	−3.24142e−5	−	5.61431e-5i
$782$	−211.974	−	122.383i	−0.271067	−	0.156500i
$783$			4296.23i			5.48689i
$784$	426.656	+	772.991i	0.544204	+	0.985958i
$785$	−177.384			−0.225967
$786$	−170.460	+	295.245i	−0.216870	+	0.375630i
$787$	−725.927	+	419.114i	−0.922398	+	0.532546i	−0.884399	−	0.466731i	$-0.845432\pi$
$787$	−725.927	+	419.114i	−0.922398	+	0.532546i	−0.0379984	+	0.999278i	$0.512098\pi$
$788$	−27.1032	−	46.9442i	−0.0343949	−	0.0595738i
$789$	−1227.00	−	708.408i	−1.55513	−	0.897856i
$790$		−	185.473i		−	0.234776i
$791$	−187.306	−	331.760i	−0.236797	−	0.419419i
$792$	0.634989			0.000801753
$793$	−312.524	+	541.308i	−0.394104	+	0.682608i
$794$	622.683	−	359.506i	0.784236	−	0.452779i
$795$	−495.577	−	858.364i	−0.623367	−	1.07970i
$796$	60.1818	+	34.7460i	0.0756053	+	0.0436508i
$797$			202.783i			0.254433i	0.991875	+	0.127216i	$0.0406043\pi$
$797$			202.783i			0.254433i	−0.991875	+	0.127216i	$0.959396\pi$
$798$	2855.89	+	27.4977i	3.57881	+	0.0344583i
$799$	1374.71			1.72054
$800$	71.3332	−	123.553i	0.0891665	−	0.154441i
$801$	−253.355	+	146.275i	−0.316298	+	0.182615i
$802$	−135.643	−	234.941i	−0.169131	−	0.292944i
$803$	−0.242359	−	0.139926i	−0.000301816	−	0.000174254i
$804$		−	287.156i		−	0.357160i
$805$	−127.163	−	75.0594i	−0.157967	−	0.0932415i
$806$	958.939			1.18975
$807$	191.994	−	332.544i	0.237911	−	0.412075i
$808$	1066.74	−	615.881i	1.32022	−	0.762229i
$809$	−328.557	−	569.077i	−0.406127	−	0.703432i	0.588325	−	0.808625i	$-0.299788\pi$
$809$	−328.557	−	569.077i	−0.406127	−	0.703432i	−0.994452	+	0.105192i	$0.966454\pi$
$810$	−1510.98	−	872.367i	−1.86541	−	1.07700i
$811$			906.387i			1.11762i	0.829297	+	0.558808i	$0.188741\pi$
$811$			906.387i			1.11762i	−0.829297	+	0.558808i	$0.811259\pi$
$812$	109.582	−	185.651i	0.134953	−	0.228634i
$813$	200.636			0.246784
$814$	−0.184350	+	0.319304i	−0.000226475	+	0.000392265i
$815$	−725.132	+	418.655i	−0.889732	+	0.513687i
$816$	−871.899	−	1510.17i	−1.06850	−	1.85070i
$817$	−144.587	−	83.4775i	−0.176973	−	0.102176i
$818$		−	1517.47i		−	1.85509i
$819$	−15.5021	+	1610.04i	−0.0189281	+	1.96586i
$820$	11.8941			0.0145050
$821$	−354.458	+	613.940i	−0.431740	+	0.747795i	−0.997023	−	0.0771015i	$-0.975433\pi$
$821$	−354.458	+	613.940i	−0.431740	+	0.747795i	0.565283	+	0.824897i	$0.308767\pi$
$822$	−1538.92	+	888.497i	−1.87217	+	1.08090i
$823$	692.180	+	1198.89i	0.841045	+	1.45673i	0.889012	+	0.457883i	$0.151392\pi$
$823$	692.180	+	1198.89i	0.841045	+	1.45673i	−0.0479676	+	0.998849i	$0.515274\pi$
$824$	−367.883	−	212.397i	−0.446460	−	0.257764i
$825$			0.320017i			0.000387899i
$826$	−561.773	+	317.168i	−0.680113	+	0.383980i
$827$	559.086			0.676041			0.338021	−	0.941139i	$-0.390243\pi$
$827$	559.086			0.676041			0.338021	+	0.941139i	$0.390243\pi$
$828$	46.8315	−	81.1145i	0.0565598	−	0.0979644i
$829$	−545.657	+	315.035i	−0.658211	+	0.380018i	−0.791595	−	0.611046i	$-0.790749\pi$
$829$	−545.657	+	315.035i	−0.658211	+	0.380018i	0.133384	+	0.991064i	$0.457416\pi$
$830$	102.821	+	178.091i	0.123880	+	0.214567i
$831$	1436.95	+	829.621i	1.72918	+	0.998340i
$832$		−	508.242i		−	0.610868i
$833$	−16.0171	+	831.684i	−0.0192282	+	0.998420i
$834$	−448.975			−0.538339
$835$	6.49443	−	11.2487i	0.00777776	−	0.0134715i
$836$	−0.0634119	+	0.0366109i	−7.58515e−5	+	4.37929e-5i
$837$	−1889.04	−	3271.91i	−2.25692	−	3.90909i
$838$	−347.289	−	200.507i	−0.414426	−	0.239269i
$839$			99.3261i			0.118386i	0.998247	+	0.0591931i	$0.0188528\pi$
$839$			99.3261i			0.118386i	−0.998247	+	0.0591931i	$0.981147\pi$
$840$	−449.183	−	795.600i	−0.534741	−	0.947143i
$841$	1861.17			2.21304
$842$	475.444	−	823.494i	0.564661	−	0.978021i
$843$	695.537	−	401.569i	0.825074	−	0.476357i
$844$	90.7095	+	157.113i	0.107476	+	0.186153i
$845$	−198.704	−	114.722i	−0.235152	−	0.135765i
$846$			4077.74i			4.82002i
$847$	−846.961	−	8.15489i	−0.999954	−	0.00962797i
$848$	999.200			1.17830
$849$	−933.284	+	1616.50i	−1.09928	+	1.90400i
$850$	477.934	−	275.935i	0.562275	−	0.324630i
$851$	−156.399	−	270.892i	−0.183783	−	0.318322i
$852$	−40.0179	−	23.1043i	−0.0469693	−	0.0271178i
$853$		−	859.885i		−	1.00807i	−0.863683	−	0.504036i	$-0.831848\pi$
$853$		−	859.885i		−	1.00807i	0.863683	−	0.504036i	$-0.168152\pi$
$854$	−824.886	−	486.897i	−0.965909	−	0.570137i
$855$	−2460.54			−2.87782
$856$	−65.5201	+	113.484i	−0.0765422	+	0.132575i
$857$	680.675	−	392.988i	0.794253	−	0.458562i	−0.0472045	−	0.998885i	$-0.515031\pi$
$857$	680.675	−	392.988i	0.794253	−	0.458562i	0.841458	+	0.540323i	$0.181698\pi$
$858$	−0.221270	−	0.383251i	−0.000257890	−	0.000446679i
$859$	−65.6437	−	37.8994i	−0.0764187	−	0.0441204i	0.461304	−	0.887242i	$-0.347382\pi$
$859$	−65.6437	−	37.8994i	−0.0764187	−	0.0441204i	−0.537722	+	0.843122i	$0.680715\pi$
$860$		−	9.28591i		−	0.0107976i
$861$	−129.882	+	220.043i	−0.150851	+	0.255566i
$862$	1376.75			1.59716
$863$	−299.064	+	517.993i	−0.346539	+	0.600224i	−0.985632	−	0.168906i	$-0.945977\pi$
$863$	−299.064	+	517.993i	−0.346539	+	0.600224i	0.639093	+	0.769130i	$0.279310\pi$
$864$	673.149	−	388.643i	0.779108	−	0.449818i
$865$	184.999	+	320.427i	0.213871	+	0.370436i
$866$	−1575.40	−	909.558i	−1.81917	−	1.05030i
$867$			4.59224i			0.00529671i
$868$	−1.82526	+	189.570i	−0.00210283	+	0.218399i
$869$	−0.102152			−0.000117551
$870$	−995.550	+	1724.34i	−1.14431	+	1.98200i
$871$	720.773	−	416.139i	0.827524	−	0.477771i
$872$	−256.761	−	444.724i	−0.294451	−	0.510005i
$873$	−1499.61	−	865.800i	−1.71777	−	0.991753i
$874$		−	481.530i		−	0.550950i
$875$	767.715	−	433.439i	0.877388	−	0.495359i
$876$	−255.408			−0.291562
$877$	163.165	−	282.611i	0.186049	−	0.322247i	−0.757880	−	0.652394i	$-0.773765\pi$
$877$	163.165	−	282.611i	0.186049	−	0.322247i	0.943930	+	0.330147i	$0.107098\pi$
$878$	708.567	−	409.091i	0.807024	−	0.465936i
$879$	−912.128	−	1579.85i	−1.03769	−	1.79733i
$880$	0.181058	+	0.104534i	0.000205747	+	0.000118788i
$881$		−	1471.47i		−	1.67023i	−0.550075	−	0.835115i	$-0.685401\pi$
$881$		−	1471.47i		−	1.67023i	0.550075	−	0.835115i	$-0.314599\pi$
$882$	−2466.98	−	47.5107i	−2.79703	−	0.0538670i
$883$	155.693			0.176323			0.0881614	−	0.996106i	$-0.471901\pi$
$883$	155.693			0.176323			0.0881614	+	0.996106i	$0.471901\pi$
$884$	−49.2260	+	85.2620i	−0.0556856	+	0.0964502i
$885$	665.683	−	384.333i	0.752185	−	0.434274i
$886$	51.5269	+	89.2472i	0.0581568	+	0.100730i
$887$	237.095	+	136.887i	0.267300	+	0.154326i	0.627660	−	0.778488i	$-0.284013\pi$
$887$	237.095	+	136.887i	0.267300	+	0.154326i	−0.360360	+	0.932813i	$0.617346\pi$
$888$		−	1935.40i		−	2.17950i
$889$	−38.3008	−	67.8390i	−0.0430830	−	0.0763094i
$890$	−83.6526			−0.0939917
$891$	−0.480467	+	0.832192i	−0.000539244	+	0.000933998i
$892$	−127.721	+	73.7398i	−0.143185	+	0.0826679i
$893$	1352.24	+	2342.14i	1.51426	+	2.62278i
$894$	−1316.73	−	760.216i	−1.47286	−	0.850354i
$895$			183.907i			0.205483i
$896$	1042.15	+	10.0343i	1.16311	+	0.0111989i
$897$	375.443			0.418554
$898$	857.849	−	1485.84i	0.955288	−	1.65461i
$899$	−2057.91	+	1188.13i	−2.28911	+	1.32162i
$900$	105.590	+	182.887i	0.117322	+	0.203208i
$901$	815.267	+	470.695i	0.904847	+	0.522413i
$902$		−	0.0507794i		−	5.62964e-5i
$903$	171.791	+	101.401i	0.190245	+	0.112294i
$904$	−397.441			−0.439647
$905$	−266.686	+	461.914i	−0.294681	+	0.510402i
$906$	−1022.49	+	590.338i	−1.12858	+	0.651587i
$907$	−688.038	−	1191.72i	−0.758586	−	1.31391i	−0.943571	−	0.331169i	$-0.892557\pi$
$907$	−688.038	−	1191.72i	−0.758586	−	1.31391i	0.184985	−	0.982741i	$-0.440776\pi$
$908$	76.4767	+	44.1539i	0.0842255	+	0.0486276i
$909$			3963.61i			4.36041i
$910$	−234.029	+	396.485i	−0.257175	+	0.435698i
$911$	−339.157			−0.372291			−0.186146	−	0.982522i	$-0.559600\pi$
$911$	−339.157			−0.372291			−0.186146	+	0.982522i	$0.559600\pi$
$912$	1715.29	−	2970.97i	1.88080	−	3.25764i
$913$	0.0980856	−	0.0566297i	0.000107432	−	6.20260e-5i
$914$	98.7777	+	171.088i	0.108072	+	0.187186i
$915$	988.392	+	570.649i	1.08021	+	0.623660i
$916$		−	42.5600i		−	0.0464629i
$917$	1.88077	−	195.335i	0.00205100	−	0.213015i
$918$	3006.74			3.27532
$919$	−46.3750	+	80.3238i	−0.0504624	+	0.0874035i	−0.890153	−	0.455661i	$-0.849403\pi$
$919$	−46.3750	+	80.3238i	−0.0504624	+	0.0874035i	0.839691	+	0.543065i	$0.182736\pi$
$920$	−133.404	+	77.0209i	−0.145004	+	0.0837183i
$921$	1168.58	+	2024.03i	1.26881	+	2.19765i
$922$	−1049.67	−	606.028i	−1.13847	−	0.657298i
$923$		−	133.928i		−	0.145101i
$924$	0.0761850	−	0.0430128i	8.24513e−5	−	4.65506e-5i
$925$	705.262			0.762445
$926$	803.289	−	1391.34i	0.867483	−	1.50252i
$927$	1183.79	−	683.460i	1.27701	−	0.737281i
$928$	−244.442	−	423.386i	−0.263407	−	0.456235i
$929$	−919.711	−	530.995i	−0.990001	−	0.571577i	−0.0847265	−	0.996404i	$-0.527002\pi$
$929$	−919.711	−	530.995i	−0.990001	−	0.571577i	−0.905275	+	0.424827i	$0.860335\pi$
$930$		−	1750.96i		−	1.88275i
$931$	−1432.72	+	790.799i	−1.53891	+	0.849408i
$932$	−82.8734			−0.0889200
$933$	642.985	−	1113.68i	0.689159	−	1.19366i
$934$	−1186.99	+	685.312i	−1.27087	+	0.733738i
$935$	0.0984857	+	0.170582i	0.000105332	+	0.000182441i
$936$	1454.63	+	839.832i	1.55409	+	0.897256i
$937$			1472.04i			1.57102i	0.618852	+	0.785508i	$0.287598\pi$
$937$			1472.04i			1.57102i	−0.618852	+	0.785508i	$0.712402\pi$
$938$	627.054	+	1110.65i	0.668501	+	1.18406i
$939$	916.140			0.975655
$940$	−75.2105	+	130.268i	−0.0800112	+	0.138583i
$941$	−425.914	+	245.901i	−0.452618	+	0.261319i	−0.708935	−	0.705274i	$-0.750824\pi$
$941$	−425.914	+	245.901i	−0.452618	+	0.261319i	0.256317	+	0.966593i	$0.417491\pi$
$942$	345.579	+	598.561i	0.366857	+	0.635415i
$943$	37.3086	+	21.5402i	0.0395638	+	0.0228422i
$944$			774.905i			0.820874i
$945$	1813.83	+	17.4643i	1.91940	+	0.0184808i
$946$	−0.0396443			−4.19073e−5
$947$	78.5617	−	136.073i	0.0829585	−	0.143688i	−0.821561	−	0.570121i	$-0.806896\pi$
$947$	78.5617	−	136.073i	0.0829585	−	0.143688i	0.904519	+	0.426432i	$0.140230\pi$
$948$	−80.7389	+	46.6146i	−0.0851676	+	0.0491716i
$949$	−370.130	−	641.084i	−0.390021	−	0.675536i
$950$	940.241	+	542.849i	0.989728	+	0.571420i
$951$		−	3420.04i		−	3.59625i
$952$	747.300	+	441.101i	0.784979	+	0.463341i
$953$	−1073.87			−1.12683			−0.563417	−	0.826173i	$-0.690514\pi$
$953$	−1073.87			−1.12683			−0.563417	+	0.826173i	$0.690514\pi$
$954$	−1396.20	+	2418.29i	−1.46352	+	2.53489i
$955$	478.863	−	276.471i	0.501427	−	0.289499i
$956$	−16.2561	−	28.1564i	−0.0170043	−	0.0294523i
$957$	0.949703	+	0.548311i	0.000992375	+	0.000572948i
$958$		−	1545.89i		−	1.61366i
$959$	517.567	−	876.847i	0.539695	−	0.914334i
$960$	−928.016			−0.966683
$961$	564.337	−	977.461i	0.587240	−	1.01713i
$962$	−844.619	+	487.641i	−0.877982	+	0.506903i
$963$	−210.833	−	365.174i	−0.218934	−	0.379204i
$964$	6.17825	+	3.56702i	0.00640898	+	0.00370022i
$965$		−	358.920i		−	0.371938i
$966$	−5.53949	+	575.327i	−0.00573446	+	0.595576i
$967$	−787.449			−0.814321			−0.407161	−	0.913357i	$-0.633481\pi$
$967$	−787.449			−0.814321			−0.407161	+	0.913357i	$0.633481\pi$
$968$	−441.794	+	765.209i	−0.456399	+	0.790506i
$969$	2799.08	−	1616.05i	2.88863	−	1.66775i
$970$	−247.570	−	428.804i	−0.255227	−	0.442066i
$971$	−1011.38	−	583.918i	−1.04158	−	0.601358i	−0.121301	−	0.992616i	$-0.538707\pi$
$971$	−1011.38	−	583.918i	−1.04158	−	0.601358i	−0.920281	+	0.391258i	$0.872040\pi$
$972$			436.317i			0.448886i
$973$	224.021	−	126.478i	0.230237	−	0.129988i
$974$	−1735.47			−1.78180
$975$	−423.252	+	733.094i	−0.434105	+	0.751892i
$976$	−996.417	+	575.281i	−1.02092	+	0.589428i
$977$	143.680	+	248.861i	0.147063	+	0.254720i	0.930141	−	0.367204i	$-0.119685\pi$
$977$	143.680	+	248.861i	0.147063	+	0.254720i	−0.783078	+	0.621924i	$0.786351\pi$
$978$	2825.40	+	1631.24i	2.88895	+	1.66794i
$979$			0.0460727i			4.70610e-5i
$980$	−77.9345	−	47.0192i	−0.0795250	−	0.0479788i
$981$	1652.43			1.68444
$982$	217.923	−	377.455i	0.221918	−	0.384373i
$983$	453.408	−	261.775i	0.461250	−	0.266303i	−0.251320	−	0.967904i	$-0.580865\pi$
$983$	453.408	−	261.775i	0.461250	−	0.266303i	0.712570	+	0.701602i	$0.247531\pi$
$984$	133.277	+	230.842i	0.135444	+	0.234595i
$985$	−248.437	−	143.435i	−0.252220	−	0.145619i
$986$		−	1891.13i		−	1.91798i
$987$	−1588.69	−	2813.92i	−1.60962	−	2.85099i
$988$	−193.685			−0.196038
$989$	16.8167	−	29.1275i	0.0170038	−	0.0294514i
$990$	−0.505990	+	0.292133i	−0.000511101	+	0.000295084i
$991$	47.6021	+	82.4492i	0.0480344	+	0.0831980i	0.889043	−	0.457824i	$-0.151371\pi$
$991$	47.6021	+	82.4492i	0.0480344	+	0.0831980i	−0.841009	+	0.541022i	$0.818038\pi$
$992$	372.323	+	214.961i	0.375325	+	0.216694i
$993$		−	708.736i		−	0.713732i
$994$	205.231	+	1.97605i	0.206470	+	0.00198798i
$995$	367.764			0.369612
$996$	51.6834	−	89.5183i	0.0518910	−	0.0898778i
$997$	−478.838	+	276.457i	−0.480279	+	0.277289i	−0.720533	−	0.693421i	$-0.756103\pi$
$997$	−478.838	+	276.457i	−0.480279	+	0.277289i	0.240254	+	0.970710i	$0.422769\pi$
$998$	−88.3275	−	152.988i	−0.0885045	−	0.153294i
$999$	3327.67	+	1921.23i	3.33100	+	1.92315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.k.a.124.15	✓	108
7.3	odd	6	inner	287.3.k.a.206.15	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.k.a.124.15	✓	108	1.1	even	1	trivial
287.3.k.a.206.15	yes	108	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07150 + 1.85589i) q^{2} +(4.93694 - 2.85034i) q^{3} +(-0.296226 - 0.513078i) q^{4} +(-2.71530 - 1.56768i) q^{5} +12.2166i q^{6} +(-3.44147 - 6.09559i) q^{7} -7.30238 q^{8} +(11.7489 - 20.3497i) q^{9} +O(q^{10})\)	\(q+(-1.07150 + 1.85589i) q^{2} +(4.93694 - 2.85034i) q^{3} +(-0.296226 - 0.513078i) q^{4} +(-2.71530 - 1.56768i) q^{5} +12.2166i q^{6} +(-3.44147 - 6.09559i) q^{7} -7.30238 q^{8} +(11.7489 - 20.3497i) q^{9} +(5.81889 - 3.35954i) q^{10} +(-0.00185030 - 0.00320482i) q^{11} +(-2.92490 - 1.68869i) q^{12} -9.78880i q^{13} +(15.0003 + 0.144429i) q^{14} -17.8737 q^{15} +(9.00940 - 15.6047i) q^{16} +(14.7019 - 8.48815i) q^{17} +(25.1780 + 43.6095i) q^{18} +(28.9231 + 16.6988i) q^{19} +1.85755i q^{20} +(-34.3649 - 20.2842i) q^{21} +0.00793041 q^{22} +(-3.36401 + 5.82663i) q^{23} +(-36.0514 + 20.8143i) q^{24} +(-7.58477 - 13.1372i) q^{25} +(18.1670 + 10.4887i) q^{26} -82.6478i q^{27} +(-2.10806 + 3.57141i) q^{28} -51.9824 q^{29} +(19.1517 - 33.1717i) q^{30} +(39.5886 - 22.8565i) q^{31} +(4.70240 + 8.14479i) q^{32} +(-0.0182697 - 0.0105480i) q^{33} +36.3802i q^{34} +(-0.211310 + 21.9465i) q^{35} -13.9213 q^{36} +(-23.2460 + 40.2633i) q^{37} +(-61.9822 + 35.7855i) q^{38} +(-27.9015 - 48.3268i) q^{39} +(19.8281 + 11.4478i) q^{40} -6.40312i q^{41} +(74.4673 - 42.0430i) q^{42} -4.99902 q^{43} +(-0.00109622 + 0.00189870i) q^{44} +(-63.8037 + 36.8371i) q^{45} +(-7.20907 - 12.4865i) q^{46} +(70.1293 + 40.4892i) q^{47} -102.720i q^{48} +(-25.3126 + 41.9556i) q^{49} +32.5083 q^{50} +(48.3883 - 83.8110i) q^{51} +(-5.02242 + 2.89969i) q^{52} +(27.7266 + 48.0239i) q^{53} +(153.386 + 88.5572i) q^{54} +0.0116027i q^{55} +(25.1309 + 44.5123i) q^{56} +190.389 q^{57} +(55.6992 - 96.4738i) q^{58} +(-37.2437 + 21.5027i) q^{59} +(5.29465 + 9.17060i) q^{60} +(-55.2987 - 31.9267i) q^{61} +97.9629i q^{62} +(-164.477 - 1.58366i) q^{63} +51.9207 q^{64} +(-15.3457 + 26.5795i) q^{65} +(0.0391520 - 0.0226044i) q^{66} +(42.5117 + 73.6324i) q^{67} +(-8.71016 - 5.02881i) q^{68} +38.3543i q^{69} +(-40.5039 - 23.9078i) q^{70} +13.6818 q^{71} +(-85.7952 + 148.602i) q^{72} +(65.4915 - 37.8116i) q^{73} +(-49.8162 - 86.2842i) q^{74} +(-74.8911 - 43.2384i) q^{75} -19.7864i q^{76} +(-0.0131675 + 0.0223080i) q^{77} +119.586 q^{78} +(13.8020 - 23.9058i) q^{79} +(-48.9265 + 28.2477i) q^{80} +(-129.834 - 224.880i) q^{81} +(11.8835 + 6.86095i) q^{82} +30.6056i q^{83} +(-0.227621 + 23.6406i) q^{84} -53.2267 q^{85} +(5.35645 - 9.27765i) q^{86} +(-256.634 + 148.168i) q^{87} +(0.0135116 + 0.0234028i) q^{88} +(-10.7820 - 6.22501i) q^{89} -157.884i q^{90} +(-59.6686 + 33.6879i) q^{91} +3.98602 q^{92} +(130.298 - 225.682i) q^{93} +(-150.287 + 86.7683i) q^{94} +(-52.3566 - 90.6843i) q^{95} +(46.4309 + 26.8069i) q^{96} -73.6918i q^{97} +(-50.7427 - 91.9328i) q^{98} -0.0869564 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{2} - 6 q^{3} - 106 q^{4} - 6 q^{5} - 4 q^{7} - 4 q^{8} + 164 q^{9}+O(q^{10}) \) 108 * q - 2 * q^2 - 6 * q^3 - 106 * q^4 - 6 * q^5 - 4 * q^7 - 4 * q^8 + 164 * q^9	\( 108 q - 2 q^{2} - 6 q^{3} - 106 q^{4} - 6 q^{5} - 4 q^{7} - 4 q^{8} + 164 q^{9} + 48 q^{10} + 6 q^{11} + 18 q^{12} + 38 q^{14} - 56 q^{15} - 202 q^{16} + 48 q^{17} + 32 q^{18} - 78 q^{19} - 104 q^{21} - 48 q^{22} - 16 q^{23} + 248 q^{25} + 144 q^{26} + 168 q^{29} - 64 q^{30} + 30 q^{31} - 104 q^{32} + 24 q^{33} - 54 q^{35} - 524 q^{36} + 76 q^{37} - 24 q^{38} - 34 q^{39} - 288 q^{40} + 190 q^{42} - 112 q^{43} + 102 q^{44} + 6 q^{45} - 68 q^{46} + 294 q^{47} + 68 q^{49} - 264 q^{50} - 36 q^{51} - 306 q^{52} + 152 q^{53} + 102 q^{54} - 438 q^{56} + 256 q^{57} - 164 q^{58} - 138 q^{59} + 280 q^{60} + 282 q^{61} + 442 q^{63} + 796 q^{64} + 76 q^{65} - 240 q^{66} - 158 q^{67} - 738 q^{68} - 82 q^{70} - 48 q^{71} - 374 q^{72} + 48 q^{73} + 34 q^{74} - 258 q^{75} - 184 q^{77} + 432 q^{78} + 128 q^{79} + 12 q^{80} - 262 q^{81} + 628 q^{84} - 196 q^{85} + 316 q^{86} + 438 q^{87} + 76 q^{88} - 24 q^{89} + 370 q^{91} - 592 q^{92} - 90 q^{93} - 264 q^{94} - 250 q^{95} - 102 q^{96} - 100 q^{98} + 168 q^{99}+O(q^{100}) \) 108 * q - 2 * q^2 - 6 * q^3 - 106 * q^4 - 6 * q^5 - 4 * q^7 - 4 * q^8 + 164 * q^9 + 48 * q^10 + 6 * q^11 + 18 * q^12 + 38 * q^14 - 56 * q^15 - 202 * q^16 + 48 * q^17 + 32 * q^18 - 78 * q^19 - 104 * q^21 - 48 * q^22 - 16 * q^23 + 248 * q^25 + 144 * q^26 + 168 * q^29 - 64 * q^30 + 30 * q^31 - 104 * q^32 + 24 * q^33 - 54 * q^35 - 524 * q^36 + 76 * q^37 - 24 * q^38 - 34 * q^39 - 288 * q^40 + 190 * q^42 - 112 * q^43 + 102 * q^44 + 6 * q^45 - 68 * q^46 + 294 * q^47 + 68 * q^49 - 264 * q^50 - 36 * q^51 - 306 * q^52 + 152 * q^53 + 102 * q^54 - 438 * q^56 + 256 * q^57 - 164 * q^58 - 138 * q^59 + 280 * q^60 + 282 * q^61 + 442 * q^63 + 796 * q^64 + 76 * q^65 - 240 * q^66 - 158 * q^67 - 738 * q^68 - 82 * q^70 - 48 * q^71 - 374 * q^72 + 48 * q^73 + 34 * q^74 - 258 * q^75 - 184 * q^77 + 432 * q^78 + 128 * q^79 + 12 * q^80 - 262 * q^81 + 628 * q^84 - 196 * q^85 + 316 * q^86 + 438 * q^87 + 76 * q^88 - 24 * q^89 + 370 * q^91 - 592 * q^92 - 90 * q^93 - 264 * q^94 - 250 * q^95 - 102 * q^96 - 100 * q^98 + 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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