LMFDB - Embedded newform 663.2.z.d.511.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [663,2,Mod(205,663)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(663, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("663.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 663 = 3 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	663.z (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:	$5.29408165401$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 602x^{10} + 1212x^{8} + 1259x^{6} + 665x^{4} + 168x^{2} + 16 $ x^16 + 20x^14 + 156x^12 + 602x^10 + 1212x^8 + 1259x^6 + 665x^4 + 168*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			511.1
Root			$-2.29812i$ of defining polynomial
Character	$\chi$	$=$	663.511
Dual form			663.2.z.d.205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99023 - 1.14906i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.64068 + 2.84174i) q^{4} -1.20591i q^{5} +(1.99023 - 1.14906i) q^{6} +(-0.421031 + 0.243082i) q^{7} -2.94471i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.99023 - 1.14906i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.64068 + 2.84174i) q^{4} -1.20591i q^{5} +(1.99023 - 1.14906i) q^{6} +(-0.421031 + 0.243082i) q^{7} -2.94471i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.38566 + 2.40004i) q^{10} +(-2.24386 - 1.29549i) q^{11} -3.28136 q^{12} +(3.21667 + 1.62881i) q^{13} +1.11726 q^{14} +(1.04435 + 0.602955i) q^{15} +(-0.102297 + 0.177183i) q^{16} +(-0.500000 - 0.866025i) q^{17} +2.29812i q^{18} +(-5.56094 + 3.21061i) q^{19} +(3.42688 - 1.97851i) q^{20} -0.486164i q^{21} +(2.97719 + 5.15665i) q^{22} +(0.377366 - 0.653617i) q^{23} +(2.55020 + 1.47236i) q^{24} +3.54578 q^{25} +(-4.53032 - 6.93786i) q^{26} +1.00000 q^{27} +(-1.38155 - 0.797640i) q^{28} +(3.11818 - 5.40084i) q^{29} +(-1.38566 - 2.40004i) q^{30} -0.419682i q^{31} +(-4.69321 + 2.70962i) q^{32} +(2.24386 - 1.29549i) q^{33} +2.29812i q^{34} +(0.293135 + 0.507725i) q^{35} +(1.64068 - 2.84174i) q^{36} +(-3.63371 - 2.09792i) q^{37} +14.7567 q^{38} +(-3.01893 + 1.97132i) q^{39} -3.55106 q^{40} +(-5.32460 - 3.07416i) q^{41} +(-0.558632 + 0.967579i) q^{42} +(-4.12082 - 7.13748i) q^{43} -8.50194i q^{44} +(-1.04435 + 0.602955i) q^{45} +(-1.50209 + 0.867233i) q^{46} -8.23540i q^{47} +(-0.102297 - 0.177183i) q^{48} +(-3.38182 + 5.85749i) q^{49} +(-7.05693 - 4.07432i) q^{50} +1.00000 q^{51} +(0.648877 + 11.8133i) q^{52} -2.42998 q^{53} +(-1.99023 - 1.14906i) q^{54} +(-1.56224 + 2.70589i) q^{55} +(0.715808 + 1.23982i) q^{56} -6.42122i q^{57} +(-12.4118 + 7.16595i) q^{58} +(-9.69027 + 5.59468i) q^{59} +3.95702i q^{60} +(-1.48376 - 2.56994i) q^{61} +(-0.482240 + 0.835264i) q^{62} +(0.421031 + 0.243082i) q^{63} +12.8633 q^{64} +(1.96420 - 3.87902i) q^{65} -5.95439 q^{66} +(-8.62064 - 4.97713i) q^{67} +(1.64068 - 2.84174i) q^{68} +(0.377366 + 0.653617i) q^{69} -1.34732i q^{70} +(-6.03964 + 3.48699i) q^{71} +(-2.55020 + 1.47236i) q^{72} -0.786142i q^{73} +(4.82128 + 8.35070i) q^{74} +(-1.77289 + 3.07074i) q^{75} +(-18.2474 - 10.5352i) q^{76} +1.25964 q^{77} +(8.27352 - 0.454445i) q^{78} -14.4922 q^{79} +(0.213667 + 0.123361i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.06479 + 12.2366i) q^{82} -2.78902i q^{83} +(1.38155 - 0.797640i) q^{84} +(-1.04435 + 0.602955i) q^{85} +18.9403i q^{86} +(3.11818 + 5.40084i) q^{87} +(-3.81485 + 6.60752i) q^{88} +(2.44223 + 1.41002i) q^{89} +2.77133 q^{90} +(-1.75025 + 0.0961373i) q^{91} +2.47655 q^{92} +(0.363455 + 0.209841i) q^{93} +(-9.46297 + 16.3903i) q^{94} +(3.87171 + 6.70599i) q^{95} -5.41925i q^{96} +(1.04751 - 0.604779i) q^{97} +(13.4612 - 7.77183i) q^{98} +2.59098i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} - 2 q^{13} - 26 q^{14} - 3 q^{15} - 8 q^{17} + 27 q^{20} + q^{22} - 21 q^{23} + 14 q^{25} + 2 q^{26} + 16 q^{27} - 33 q^{28} + 29 q^{29} + q^{30} - 15 q^{32} - 3 q^{33} + 15 q^{35} + 4 q^{36} - 18 q^{37} + 62 q^{38} + q^{39} + 4 q^{40} + 12 q^{41} + 13 q^{42} - 3 q^{43} + 3 q^{45} - 9 q^{46} + 2 q^{49} - 36 q^{50} + 16 q^{51} - 8 q^{52} - 26 q^{53} + 9 q^{55} - 37 q^{56} + 30 q^{58} - 3 q^{59} + 29 q^{61} - 20 q^{62} + 36 q^{64} - 16 q^{65} - 2 q^{66} + 33 q^{67} + 4 q^{68} - 21 q^{69} + 27 q^{71} + 17 q^{74} - 7 q^{75} - 48 q^{76} - 8 q^{77} - q^{78} - 14 q^{79} - 39 q^{80} - 8 q^{81} - 3 q^{82} + 33 q^{84} + 3 q^{85} + 29 q^{87} - 5 q^{88} - 3 q^{89} - 2 q^{90} - 70 q^{91} - 64 q^{92} - 6 q^{93} - 25 q^{94} - 27 q^{95} + 6 q^{97} + 102 q^{98}+O(q^{100}) $ 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 - 2 * q^13 - 26 * q^14 - 3 * q^15 - 8 * q^17 + 27 * q^20 + q^22 - 21 * q^23 + 14 * q^25 + 2 * q^26 + 16 * q^27 - 33 * q^28 + 29 * q^29 + q^30 - 15 * q^32 - 3 * q^33 + 15 * q^35 + 4 * q^36 - 18 * q^37 + 62 * q^38 + q^39 + 4 * q^40 + 12 * q^41 + 13 * q^42 - 3 * q^43 + 3 * q^45 - 9 * q^46 + 2 * q^49 - 36 * q^50 + 16 * q^51 - 8 * q^52 - 26 * q^53 + 9 * q^55 - 37 * q^56 + 30 * q^58 - 3 * q^59 + 29 * q^61 - 20 * q^62 + 36 * q^64 - 16 * q^65 - 2 * q^66 + 33 * q^67 + 4 * q^68 - 21 * q^69 + 27 * q^71 + 17 * q^74 - 7 * q^75 - 48 * q^76 - 8 * q^77 - q^78 - 14 * q^79 - 39 * q^80 - 8 * q^81 - 3 * q^82 + 33 * q^84 + 3 * q^85 + 29 * q^87 - 5 * q^88 - 3 * q^89 - 2 * q^90 - 70 * q^91 - 64 * q^92 - 6 * q^93 - 25 * q^94 - 27 * q^95 + 6 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/663\mathbb{Z}\right)^\times$.

$n$	$443$	$547$	$613$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.99023	−	1.14906i	−1.40731	−	0.812508i	−0.412178	−	0.911103i	$-0.635232\pi$
$2$	−1.99023	−	1.14906i	−1.40731	−	0.812508i	−0.995128	+	0.0985950i	$0.968565\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.64068	+	2.84174i	0.820339	+	1.42087i
$5$		−	1.20591i		−	0.539299i	−0.962959	−	0.269650i	$-0.913092\pi$
$5$		−	1.20591i		−	0.539299i	0.962959	−	0.269650i	$-0.0869079\pi$
$6$	1.99023	−	1.14906i	0.812508	−	0.469102i
$7$	−0.421031	+	0.243082i	−0.159135	+	0.0918764i	−0.577453	−	0.816424i	$-0.695953\pi$
$7$	−0.421031	+	0.243082i	−0.159135	+	0.0918764i	0.418318	+	0.908301i	$0.362620\pi$
$8$		−	2.94471i		−	1.04111i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.38566	+	2.40004i	−0.438185	+	0.758959i
$11$	−2.24386	−	1.29549i	−0.676548	−	0.390605i	0.122005	−	0.992529i	$-0.461068\pi$
$11$	−2.24386	−	1.29549i	−0.676548	−	0.390605i	−0.798553	+	0.601924i	$0.794401\pi$
$12$	−3.28136			−0.947246
$13$	3.21667	+	1.62881i	0.892144	+	0.451750i
$13$	3.21667	+	1.62881i	0.892144	+	0.451750i
$14$	1.11726			0.298601
$15$	1.04435	+	0.602955i	0.269650	+	0.155682i
$16$	−0.102297	+	0.177183i	−0.0255742	+	0.0442958i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$			2.29812i			0.541672i
$19$	−5.56094	+	3.21061i	−1.27577	+	0.736565i	−0.976067	−	0.217469i	$-0.930220\pi$
$19$	−5.56094	+	3.21061i	−1.27577	+	0.736565i	−0.299700	+	0.954033i	$0.596887\pi$
$20$	3.42688	−	1.97851i	0.766274	−	0.442408i
$21$		−	0.486164i		−	0.106090i
$22$	2.97719	+	5.15665i	0.634740	+	1.09940i
$23$	0.377366	−	0.653617i	0.0786863	−	0.136289i	−0.823997	−	0.566594i	$-0.808261\pi$
$23$	0.377366	−	0.653617i	0.0786863	−	0.136289i	0.902683	+	0.430305i	$0.141594\pi$
$24$	2.55020	+	1.47236i	0.520557	+	0.300544i
$25$	3.54578			0.709156
$26$	−4.53032	−	6.93786i	−0.888469	−	1.36063i
$27$	1.00000			0.192450
$28$	−1.38155	−	0.797640i	−0.261089	−	0.150740i
$29$	3.11818	−	5.40084i	0.579031	−	1.00291i	−0.416559	−	0.909108i	$-0.636764\pi$
$29$	3.11818	−	5.40084i	0.579031	−	1.00291i	0.995591	−	0.0938031i	$-0.0299024\pi$
$30$	−1.38566	−	2.40004i	−0.252986	−	0.438185i
$31$		−	0.419682i		−	0.0753771i	−0.999290	−	0.0376885i	$-0.988001\pi$
$31$		−	0.419682i		−	0.0753771i	0.999290	−	0.0376885i	$-0.0119995\pi$
$32$	−4.69321	+	2.70962i	−0.829650	+	0.478998i
$33$	2.24386	−	1.29549i	0.390605	−	0.225516i
$34$			2.29812i			0.394124i
$35$	0.293135	+	0.507725i	0.0495489	+	0.0858212i
$36$	1.64068	−	2.84174i	0.273446	−	0.473623i
$37$	−3.63371	−	2.09792i	−0.597378	−	0.344896i	0.170631	−	0.985335i	$-0.445419\pi$
$37$	−3.63371	−	2.09792i	−0.597378	−	0.344896i	−0.768009	+	0.640439i	$0.778753\pi$
$38$	14.7567			2.39386
$39$	−3.01893	+	1.97132i	−0.483415	+	0.315663i
$40$	−3.55106			−0.561472
$41$	−5.32460	−	3.07416i	−0.831562	−	0.480103i	0.0228249	−	0.999739i	$-0.492734\pi$
$41$	−5.32460	−	3.07416i	−0.831562	−	0.480103i	−0.854387	+	0.519637i	$0.826067\pi$
$42$	−0.558632	+	0.967579i	−0.0861988	+	0.149301i
$43$	−4.12082	−	7.13748i	−0.628420	−	1.08845i	−0.987869	−	0.155290i	$-0.950369\pi$
$43$	−4.12082	−	7.13748i	−0.628420	−	1.08845i	0.359449	−	0.933165i	$-0.382965\pi$
$44$		−	8.50194i		−	1.28172i
$45$	−1.04435	+	0.602955i	−0.155682	+	0.0898832i
$46$	−1.50209	+	0.867233i	−0.221471	+	0.127866i
$47$		−	8.23540i		−	1.20126i	−0.799528	−	0.600628i	$-0.794917\pi$
$47$		−	8.23540i		−	1.20126i	0.799528	−	0.600628i	$-0.205083\pi$
$48$	−0.102297	−	0.177183i	−0.0147653	−	0.0255742i
$49$	−3.38182	+	5.85749i	−0.483117	+	0.836784i
$50$	−7.05693	−	4.07432i	−0.998000	−	0.576196i
$51$	1.00000			0.140028
$52$	0.648877	+	11.8133i	0.0899830	+	1.63821i
$53$	−2.42998			−0.333783			−0.166891	−	0.985975i	$-0.553373\pi$
$53$	−2.42998			−0.333783			−0.166891	+	0.985975i	$0.553373\pi$
$54$	−1.99023	−	1.14906i	−0.270836	−	0.156367i
$55$	−1.56224	+	2.70589i	−0.210653	+	0.364862i
$56$	0.715808	+	1.23982i	0.0956538	+	0.165677i
$57$		−	6.42122i		−	0.850512i
$58$	−12.4118	+	7.16595i	−1.62975	+	0.940935i
$59$	−9.69027	+	5.59468i	−1.26157	+	0.728365i	−0.973377	−	0.229209i	$-0.926386\pi$
$59$	−9.69027	+	5.59468i	−1.26157	+	0.728365i	−0.288188	+	0.957574i	$0.593053\pi$
$60$			3.95702i			0.510849i
$61$	−1.48376	−	2.56994i	−0.189976	−	0.329047i	0.755266	−	0.655418i	$-0.227508\pi$
$61$	−1.48376	−	2.56994i	−0.189976	−	0.329047i	−0.945242	+	0.326371i	$0.894174\pi$
$62$	−0.482240	+	0.835264i	−0.0612445	+	0.106079i
$63$	0.421031	+	0.243082i	0.0530449	+	0.0306255i
$64$	12.8633			1.60791
$65$	1.96420	−	3.87902i	0.243629	−	0.481133i
$66$	−5.95439			−0.732935
$67$	−8.62064	−	4.97713i	−1.05318	−	0.608053i	−0.129641	−	0.991561i	$-0.541383\pi$
$67$	−8.62064	−	4.97713i	−1.05318	−	0.608053i	−0.923538	+	0.383508i	$0.874716\pi$
$68$	1.64068	−	2.84174i	0.198962	−	0.344612i
$69$	0.377366	+	0.653617i	0.0454295	+	0.0786863i
$70$		−	1.34732i		−	0.161035i
$71$	−6.03964	+	3.48699i	−0.716774	+	0.413829i	−0.813564	−	0.581475i	$-0.802476\pi$
$71$	−6.03964	+	3.48699i	−0.716774	+	0.413829i	0.0967905	+	0.995305i	$0.469142\pi$
$72$	−2.55020	+	1.47236i	−0.300544	+	0.173519i
$73$		−	0.786142i		−	0.0920109i	−0.998941	−	0.0460055i	$-0.985351\pi$
$73$		−	0.786142i		−	0.0920109i	0.998941	−	0.0460055i	$-0.0146492\pi$
$74$	4.82128	+	8.35070i	0.560462	+	0.970749i
$75$	−1.77289	+	3.07074i	−0.204716	+	0.354578i
$76$	−18.2474	−	10.5352i	−2.09313	−	1.20847i
$77$	1.25964			0.143550
$78$	8.27352	−	0.454445i	0.936792	−	0.0514558i
$79$	−14.4922			−1.63050			−0.815249	−	0.579111i	$-0.803400\pi$
$79$	−14.4922			−1.63050			−0.815249	+	0.579111i	$0.803400\pi$
$80$	0.213667	+	0.123361i	0.0238887	+	0.0137921i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	7.06479	+	12.2366i	0.780175	+	1.35130i
$83$		−	2.78902i		−	0.306135i	−0.988216	−	0.153068i	$-0.951085\pi$
$83$		−	2.78902i		−	0.306135i	0.988216	−	0.153068i	$-0.0489152\pi$
$84$	1.38155	−	0.797640i	0.150740	−	0.0870296i
$85$	−1.04435	+	0.602955i	−0.113275	+	0.0653996i
$86$			18.9403i			2.04238i
$87$	3.11818	+	5.40084i	0.334304	+	0.579031i
$88$	−3.81485	+	6.60752i	−0.406665	+	0.704364i
$89$	2.44223	+	1.41002i	0.258876	+	0.149462i	0.623822	−	0.781567i	$-0.285579\pi$
$89$	2.44223	+	1.41002i	0.258876	+	0.149462i	−0.364946	+	0.931029i	$0.618913\pi$
$90$	2.77133			0.292123
$91$	−1.75025	+	0.0961373i	−0.183476	+	0.0100779i
$92$	2.47655			0.258198
$93$	0.363455	+	0.209841i	0.0376885	+	0.0217595i
$94$	−9.46297	+	16.3903i	−0.976031	+	1.69054i
$95$	3.87171	+	6.70599i	0.397229	+	0.688020i
$96$		−	5.41925i		−	0.553100i
$97$	1.04751	−	0.604779i	0.106358	−	0.0614060i	−0.445877	−	0.895094i	$-0.647108\pi$
$97$	1.04751	−	0.604779i	0.106358	−	0.0614060i	0.552236	+	0.833688i	$0.313775\pi$
$98$	13.4612	−	7.77183i	1.35979	−	0.785074i
$99$			2.59098i			0.260403i
$100$	5.81749	+	10.0762i	0.581749	+	1.00762i
$101$	−6.88621	+	11.9273i	−0.685203	+	1.18681i	0.288170	+	0.957579i	$0.406953\pi$
$101$	−6.88621	+	11.9273i	−0.685203	+	1.18681i	−0.973373	+	0.229228i	$0.926380\pi$
$102$	−1.99023	−	1.14906i	−0.197062	−	0.113774i
$103$	11.2173			1.10527			0.552635	−	0.833424i	$-0.313623\pi$
$103$	11.2173			1.10527			0.552635	+	0.833424i	$0.313623\pi$
$104$	4.79638	−	9.47218i	0.470323	−	0.928824i
$105$	−0.586270			−0.0572141
$106$	4.83621	+	2.79219i	0.469734	+	0.271201i
$107$	4.08449	−	7.07455i	0.394863	−	0.683922i	−0.598221	−	0.801331i	$-0.704125\pi$
$107$	4.08449	−	7.07455i	0.394863	−	0.683922i	0.993084	+	0.117409i	$0.0374588\pi$
$108$	1.64068	+	2.84174i	0.157874	+	0.273446i
$109$		−	4.83598i		−	0.463203i	−0.972811	−	0.231601i	$-0.925604\pi$
$109$		−	4.83598i		−	0.463203i	0.972811	−	0.231601i	$-0.0743965\pi$
$110$	6.21846	−	3.59023i	0.592906	−	0.342315i
$111$	3.63371	−	2.09792i	0.344896	−	0.199126i
$112$		−	0.0994661i		−	0.00939866i
$113$	−6.65017	−	11.5184i	−0.625596	−	1.08356i	−0.988425	−	0.151708i	$-0.951523\pi$
$113$	−6.65017	−	11.5184i	−0.625596	−	1.08356i	0.362830	−	0.931856i	$-0.381811\pi$
$114$	−7.37837	+	12.7797i	−0.691048	+	1.19693i
$115$	−0.788203	−	0.455069i	−0.0735003	−	0.0424354i
$116$	20.4637			1.90001
$117$	−0.197746	−	3.60012i	−0.0182817	−	0.332832i
$118$	25.7145			2.36721
$119$	0.421031	+	0.243082i	0.0385958	+	0.0222833i
$120$	1.77553	−	3.07531i	0.162083	−	0.280736i
$121$	−2.14341	−	3.71249i	−0.194855	−	0.337499i
$122$			6.81971i			0.617427i
$123$	5.32460	−	3.07416i	0.480103	−	0.277187i
$124$	1.19263	−	0.688563i	0.107101	−	0.0618348i
$125$		−	10.3054i		−	0.921747i
$126$	−0.558632	−	0.967579i	−0.0497669	−	0.0861988i
$127$	2.97929	−	5.16029i	0.264370	−	0.457901i	−0.703029	−	0.711161i	$-0.748169\pi$
$127$	2.97929	−	5.16029i	0.264370	−	0.457901i	0.967398	+	0.253260i	$0.0815028\pi$
$128$	−16.2145	−	9.36143i	−1.43317	−	0.827441i
$129$	8.24165			0.725637
$130$	−8.36643	+	5.46316i	−0.733784	+	0.479151i
$131$	−11.5949			−1.01305			−0.506527	−	0.862224i	$-0.669071\pi$
$131$	−11.5949			−1.01305			−0.506527	+	0.862224i	$0.669071\pi$
$132$	7.36290	+	4.25097i	0.640858	+	0.369999i
$133$	1.56088	−	2.70353i	0.135346	−	0.234426i
$134$	11.4380	+	19.8113i	0.988097	+	1.71143i
$135$		−	1.20591i		−	0.103788i
$136$	−2.55020	+	1.47236i	−0.218678	+	0.126254i
$137$	−8.35543	+	4.82401i	−0.713853	+	0.412143i	−0.812486	−	0.582981i	$-0.801886\pi$
$137$	−8.35543	+	4.82401i	−0.713853	+	0.412143i	0.0986333	+	0.995124i	$0.468553\pi$
$138$		−	1.73447i		−	0.147648i
$139$	−9.84427	−	17.0508i	−0.834980	−	1.44623i	−0.894047	−	0.447974i	$-0.852146\pi$
$139$	−9.84427	−	17.0508i	−0.834980	−	1.44623i	0.0590668	−	0.998254i	$-0.481188\pi$
$140$	−0.961881	+	1.66603i	−0.0812938	+	0.140805i
$141$	7.13207	+	4.11770i	0.600628	+	0.346773i
$142$	16.0270			1.34496
$143$	−5.10764	−	7.82198i	−0.427123	−	0.654107i
$144$	0.204594			0.0170495
$145$	−6.51293	−	3.76024i	−0.540869	−	0.312271i
$146$	−0.903324	+	1.56460i	−0.0747596	+	0.129487i
$147$	−3.38182	−	5.85749i	−0.278928	−	0.483117i
$148$		−	13.7681i		−	1.13173i
$149$	4.43749	−	2.56199i	0.363534	−	0.209886i	−0.307096	−	0.951679i	$-0.599357\pi$
$149$	4.43749	−	2.56199i	0.363534	−	0.209886i	0.670630	+	0.741792i	$0.266024\pi$
$150$	7.05693	−	4.07432i	0.576196	−	0.332667i
$151$		−	14.5901i		−	1.18733i	−0.804713	−	0.593665i	$-0.797681\pi$
$151$		−	14.5901i		−	1.18733i	0.804713	−	0.593665i	$-0.202319\pi$
$152$	9.45433	+	16.3754i	0.766848	+	1.32822i
$153$	−0.500000	+	0.866025i	−0.0404226	+	0.0700140i
$154$	−2.50698	−	1.44741i	−0.202018	−	0.116635i
$155$	−0.506098			−0.0406508
$156$	−10.5551	−	5.34470i	−0.845081	−	0.427919i
$157$	16.9628			1.35378			0.676891	−	0.736083i	$-0.263327\pi$
$157$	16.9628			1.35378			0.676891	+	0.736083i	$0.263327\pi$
$158$	28.8428	+	16.6524i	2.29461	+	1.32479i
$159$	1.21499	−	2.10442i	0.0963548	−	0.166891i
$160$	3.26756	+	5.65958i	0.258323	+	0.447429i
$161$			0.366924i			0.0289177i
$162$	1.99023	−	1.14906i	0.156367	−	0.0902787i
$163$	20.4158	−	11.7871i	1.59909	−	0.923237i	0.607430	−	0.794373i	$-0.292200\pi$
$163$	20.4158	−	11.7871i	1.59909	−	0.923237i	0.991662	−	0.128864i	$-0.0411329\pi$
$164$		−	20.1748i		−	1.57539i
$165$	−1.56224	−	2.70589i	−0.121621	−	0.210653i
$166$	−3.20476	+	5.55080i	−0.248737	+	0.430826i
$167$	10.5038	+	6.06436i	0.812807	+	0.469275i	0.847930	−	0.530108i	$-0.177849\pi$
$167$	10.5038	+	6.06436i	0.812807	+	0.469275i	−0.0351224	+	0.999383i	$0.511182\pi$
$168$	−1.43162			−0.110452
$169$	7.69396	+	10.4787i	0.591843	+	0.806053i
$170$	2.77133			0.212551
$171$	5.56094	+	3.21061i	0.425256	+	0.245522i
$172$	13.5219	−	23.4206i	1.03103	−	1.78580i
$173$	1.47156	+	2.54881i	0.111881	+	0.193783i	0.916528	−	0.399969i	$-0.130979\pi$
$173$	1.47156	+	2.54881i	0.111881	+	0.193783i	−0.804648	+	0.593752i	$0.797646\pi$
$174$		−	14.3319i		−	1.08650i
$175$	−1.49288	+	0.861917i	−0.112851	+	0.0651548i
$176$	0.459079	−	0.265049i	0.0346043	−	0.0199788i
$177$		−	11.1894i		−	0.841044i
$178$	−3.24040	−	5.61253i	−0.242878	−	0.420677i
$179$	−9.19165	+	15.9204i	−0.687016	+	1.18995i	0.285782	+	0.958295i	$0.407747\pi$
$179$	−9.19165	+	15.9204i	−0.687016	+	1.18995i	−0.972799	+	0.231653i	$0.925587\pi$
$180$	−3.42688	−	1.97851i	−0.255425	−	0.147469i
$181$	4.35344			0.323588			0.161794	−	0.986825i	$-0.448272\pi$
$181$	4.35344			0.323588			0.161794	+	0.986825i	$0.448272\pi$
$182$	3.59387	+	1.81981i	0.266396	+	0.134893i
$183$	2.96751			0.219365
$184$	−1.92472	−	1.11124i	−0.141892	−	0.0819214i
$185$	−2.52990	+	4.38192i	−0.186002	+	0.322165i
$186$	−0.482240	−	0.835264i	−0.0353595	−	0.0612445i
$187$			2.59098i			0.189471i
$188$	23.4029	−	13.5116i	1.70683	−	0.985438i
$189$	−0.421031	+	0.243082i	−0.0306255	+	0.0176816i
$190$		−	17.7953i		−	1.29101i
$191$	−1.30528	−	2.26081i	−0.0944469	−	0.163587i	0.814931	−	0.579558i	$-0.196775\pi$
$191$	−1.30528	−	2.26081i	−0.0944469	−	0.163587i	−0.909378	+	0.415972i	$0.863442\pi$
$192$	−6.43164	+	11.1399i	−0.464163	+	0.803955i
$193$	8.75278	+	5.05342i	0.630039	+	0.363753i	0.780767	−	0.624822i	$-0.214829\pi$
$193$	8.75278	+	5.05342i	0.630039	+	0.363753i	−0.150728	+	0.988575i	$0.548162\pi$
$194$	−2.77971			−0.199572
$195$	2.37723	+	3.64055i	0.170237	+	0.260705i
$196$	−22.1939			−1.58528
$197$	12.4954	+	7.21420i	0.890257	+	0.513990i	0.874027	−	0.485878i	$-0.161500\pi$
$197$	12.4954	+	7.21420i	0.890257	+	0.513990i	0.0162305	+	0.999868i	$0.494833\pi$
$198$	2.97719	−	5.15665i	0.211580	−	0.366467i
$199$	7.79295	+	13.4978i	0.552428	+	0.956833i	0.998099	+	0.0616359i	$0.0196318\pi$
$199$	7.79295	+	13.4978i	0.552428	+	0.956833i	−0.445671	+	0.895197i	$0.647035\pi$
$200$		−	10.4413i		−	0.738313i
$201$	8.62064	−	4.97713i	0.608053	−	0.351060i
$202$	27.4103	−	15.8253i	1.92858	−	1.11347i
$203$			3.03189i			0.212797i
$204$	1.64068	+	2.84174i	0.114871	+	0.198962i
$205$	−3.70716	+	6.42098i	−0.258919	+	0.448461i
$206$	−22.3249	−	12.8893i	−1.55545	−	0.898040i
$207$	−0.754732			−0.0524575
$208$	−0.617653	+	0.403318i	−0.0428265	+	0.0279651i
$209$	16.6373			1.15082
$210$	1.16681	+	0.673660i	0.0805177	+	0.0464869i
$211$	−10.2284	+	17.7161i	−0.704153	+	1.21963i	0.262843	+	0.964839i	$0.415340\pi$
$211$	−10.2284	+	17.7161i	−0.704153	+	1.21963i	−0.966996	+	0.254790i	$0.917993\pi$
$212$	−3.98681	−	6.90536i	−0.273815	−	0.474262i
$213$		−	6.97398i		−	0.477849i
$214$	−16.2582	+	9.38665i	−1.11139	+	0.641659i
$215$	−8.60715	+	4.96934i	−0.587003	+	0.338906i
$216$		−	2.94471i		−	0.200362i
$217$	0.102017	+	0.176699i	0.00692538	+	0.0119951i
$218$	−5.55683	+	9.62471i	−0.376356	+	0.651868i
$219$	0.680819	+	0.393071i	0.0460055	+	0.0265613i
$220$	−10.2526			−0.691228
$221$	−0.197746	−	3.60012i	−0.0133019	−	0.242171i
$222$	−9.64256			−0.647166
$223$	0.163358	+	0.0943150i	0.0109393	+	0.00631580i	0.505460	−	0.862850i	$-0.331323\pi$
$223$	0.163358	+	0.0943150i	0.0109393	+	0.00631580i	−0.494520	+	0.869166i	$0.664656\pi$
$224$	1.31732	−	2.28167i	0.0880173	−	0.152450i
$225$	−1.77289	−	3.07074i	−0.118193	−	0.204716i
$226$			30.5658i			2.03321i
$227$	−12.2350	+	7.06388i	−0.812065	+	0.468846i	−0.847672	−	0.530520i	$-0.821997\pi$
$227$	−12.2350	+	7.06388i	−0.812065	+	0.468846i	0.0356075	+	0.999366i	$0.488663\pi$
$228$	18.2474	−	10.5352i	1.20847	−	0.697708i
$229$		−	9.68190i		−	0.639798i	−0.947452	−	0.319899i	$-0.896351\pi$
$229$		−	9.68190i		−	0.639798i	0.947452	−	0.319899i	$-0.103649\pi$
$230$	1.04580	+	1.81139i	0.0689583	+	0.119439i
$231$	−0.629822	+	1.09088i	−0.0414392	+	0.0717748i
$232$	−15.9039	−	9.18215i	−1.04415	−	0.602837i
$233$	14.0772			0.922225			0.461113	−	0.887342i	$-0.347450\pi$
$233$	14.0772			0.922225			0.461113	+	0.887342i	$0.347450\pi$
$234$	−3.74320	+	7.39230i	−0.244701	+	0.483250i
$235$	−9.93115			−0.647837
$236$	−31.7972	−	18.3581i	−2.06982	−	1.19501i
$237$	7.24609	−	12.5506i	0.470684	−	0.815249i
$238$	−0.558632	−	0.967579i	−0.0362107	−	0.0627188i
$239$			22.5314i			1.45743i	0.684815	+	0.728717i	$0.259883\pi$
$239$			22.5314i			1.45743i	−0.684815	+	0.728717i	$0.740117\pi$
$240$	−0.213667	+	0.123361i	−0.0137921	+	0.00796290i
$241$	12.4006	−	7.15949i	0.798793	−	0.461183i	−0.0442560	−	0.999020i	$-0.514092\pi$
$241$	12.4006	−	7.15949i	0.798793	−	0.461183i	0.843049	+	0.537837i	$0.180758\pi$
$242$			9.85161i			0.633285i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	4.86874	−	8.43290i	0.311689	−	0.539861i
$245$	7.06360	+	4.07817i	0.451277	+	0.260545i
$246$	−14.1296			−0.900869
$247$	−23.1172	+	1.26977i	−1.47091	+	0.0807938i
$248$	−1.23584			−0.0784761
$249$	2.41537	+	1.39451i	0.153068	+	0.0883736i
$250$	−11.8416	+	20.5102i	−0.748927	+	1.29718i
$251$	−4.46627	−	7.73580i	−0.281908	−	0.488279i	0.689946	−	0.723860i	$-0.257634\pi$
$251$	−4.46627	−	7.73580i	−0.281908	−	0.488279i	−0.971855	+	0.235581i	$0.924301\pi$
$252$			1.59528i			0.100493i
$253$	−1.69351	+	0.977749i	−0.106470	+	0.0614705i
$254$	−11.8590	+	6.84678i	−0.744097	+	0.429605i
$255$		−	1.20591i		−	0.0755170i
$256$	8.65042	+	14.9830i	0.540651	+	0.936435i
$257$	−12.6388	+	21.8910i	−0.788386	+	1.36552i	0.138569	+	0.990353i	$0.455750\pi$
$257$	−12.6388	+	21.8910i	−0.788386	+	1.36552i	−0.926955	+	0.375172i	$0.877584\pi$
$258$	−16.4028	−	9.47015i	−1.02119	−	0.589586i
$259$	2.03987			0.126751
$260$	14.2458	−	0.782487i	0.883485	−	0.0485278i
$261$	−6.23636			−0.386021
$262$	23.0766	+	13.3233i	1.42568	+	0.823114i
$263$	8.92495	−	15.4585i	0.550336	−	0.953210i	−0.447914	−	0.894077i	$-0.647833\pi$
$263$	8.92495	−	15.4585i	0.550336	−	0.953210i	0.998250	−	0.0591333i	$-0.0188337\pi$
$264$	−3.81485	−	6.60752i	−0.234788	−	0.406665i
$265$			2.93033i			0.180009i
$266$	−6.21304	+	3.58710i	−0.380946	+	0.219939i
$267$	−2.44223	+	1.41002i	−0.149462	+	0.0862918i
$268$		−	32.6635i		−	1.99524i
$269$	−0.713399	−	1.23564i	−0.0434967	−	0.0753385i	0.843457	−	0.537196i	$-0.180516\pi$
$269$	−0.713399	−	1.23564i	−0.0434967	−	0.0753385i	−0.886954	+	0.461858i	$0.847183\pi$
$270$	−1.38566	+	2.40004i	−0.0843287	+	0.146062i
$271$	−5.80293	−	3.35032i	−0.352503	−	0.203518i	0.313284	−	0.949659i	$-0.398571\pi$
$271$	−5.80293	−	3.35032i	−0.352503	−	0.203518i	−0.665787	+	0.746142i	$0.731904\pi$
$272$	0.204594			0.0124053
$273$	0.791869	−	1.56383i	0.0479261	−	0.0946474i
$274$	22.1723			1.33948
$275$	−7.95623	−	4.59353i	−0.479778	−	0.277000i
$276$	−1.23827	+	2.14475i	−0.0745353	+	0.129099i
$277$	0.136397	+	0.236246i	0.00819529	+	0.0141947i	0.870094	−	0.492886i	$-0.164058\pi$
$277$	0.136397	+	0.236246i	0.00819529	+	0.0141947i	−0.861899	+	0.507081i	$0.830725\pi$
$278$			45.2466i			2.71371i
$279$	−0.363455	+	0.209841i	−0.0217595	+	0.0125628i
$280$	1.49510	−	0.863199i	0.0893496	−	0.0515860i
$281$		−	7.85168i		−	0.468392i	−0.972189	−	0.234196i	$-0.924754\pi$
$281$		−	7.85168i		−	0.468392i	0.972189	−	0.234196i	$-0.0752457\pi$
$282$	−9.46297	−	16.3903i	−0.563512	−	0.976031i
$283$	−5.53886	+	9.59359i	−0.329251	+	0.570280i	−0.982363	−	0.186981i	$-0.940130\pi$
$283$	−5.53886	+	9.59359i	−0.329251	+	0.570280i	0.653112	+	0.757261i	$0.273463\pi$
$284$	−19.8182	−	11.4421i	−1.17600	−	0.678961i
$285$	−7.74341			−0.458680
$286$	1.17746	+	21.4365i	0.0696246	+	1.26757i
$287$	2.98909			0.176441
$288$	4.69321	+	2.70962i	0.276550	+	0.159666i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	8.64149	+	14.9675i	0.507446	+	0.878922i
$291$			1.20956i			0.0709055i
$292$	2.23401	−	1.28981i	0.130735	−	0.0754802i
$293$	−19.2310	+	11.1030i	−1.12349	+	0.648647i	−0.942289	−	0.334800i	$-0.891331\pi$
$293$	−19.2310	+	11.1030i	−1.12349	+	0.648647i	−0.181200	+	0.983446i	$0.557998\pi$
$294$			15.5437i			0.906525i
$295$	6.74668	+	11.6856i	0.392807	+	0.680361i
$296$	−6.17778	+	10.7002i	−0.359076	+	0.621938i
$297$	−2.24386	−	1.29549i	−0.130202	−	0.0751720i
$298$	−11.7755			−0.682137
$299$	2.27848	−	1.48782i	0.131768	−	0.0860426i
$300$	−11.6350			−0.671746
$301$	3.46999	+	2.00340i	0.200007	+	0.115474i
$302$	−16.7650	+	29.0378i	−0.964715	+	1.67094i
$303$	−6.88621	−	11.9273i	−0.395602	−	0.685203i
$304$		−	1.31374i		−	0.0753482i
$305$	−3.09912	+	1.78928i	−0.177455	+	0.102454i
$306$	1.99023	−	1.14906i	0.113774	−	0.0656874i
$307$			11.4336i			0.652547i	0.945275	+	0.326274i	$0.105793\pi$
$307$			11.4336i			0.652547i	−0.945275	+	0.326274i	$0.894207\pi$
$308$	2.06667	+	3.57958i	0.117759	+	0.203965i
$309$	−5.60863	+	9.71443i	−0.319064	+	0.552635i
$310$	1.00725	+	0.581537i	0.0572081	+	0.0330291i
$311$	26.8816			1.52432			0.762159	−	0.647390i	$-0.224139\pi$
$311$	26.8816			1.52432			0.762159	+	0.647390i	$0.224139\pi$
$312$	5.80496	+	8.88988i	0.328641	+	0.503290i
$313$	13.1482			0.743179			0.371590	−	0.928397i	$-0.378813\pi$
$313$	13.1482			0.743179			0.371590	+	0.928397i	$0.378813\pi$
$314$	−33.7600	−	19.4913i	−1.90519	−	1.09996i
$315$	0.293135	−	0.507725i	0.0165163	−	0.0286071i
$316$	−23.7770	−	41.1830i	−1.33756	−	2.31672i
$317$		−	27.7003i		−	1.55581i	−0.628384	−	0.777903i	$-0.716283\pi$
$317$		−	27.7003i		−	1.55581i	0.628384	−	0.777903i	$-0.283717\pi$
$318$	−4.83621	+	2.79219i	−0.271201	+	0.156578i
$319$	−13.9935	+	8.07915i	−0.783485	+	0.452345i
$320$		−	15.5119i		−	0.867144i
$321$	4.08449	+	7.07455i	0.227974	+	0.394863i
$322$	0.421618	−	0.730263i	0.0234958	−	0.0406960i
$323$	5.56094	+	3.21061i	0.309419	+	0.178643i
$324$	−3.28136			−0.182298
$325$	11.4056	+	5.77540i	0.632670	+	0.320362i
$326$	−54.1763			−3.00055
$327$	4.18808	+	2.41799i	0.231601	+	0.133715i
$328$	−9.05252	+	15.6794i	−0.499842	+	0.865751i
$329$	2.00188	+	3.46736i	0.110367	+	0.191162i
$330$			7.18045i			0.395271i
$331$	18.7264	−	10.8117i	1.02930	−	0.594265i	0.112513	−	0.993650i	$-0.464110\pi$
$331$	18.7264	−	10.8117i	1.02930	−	0.594265i	0.916783	+	0.399386i	$0.130777\pi$
$332$	7.92568	−	4.57589i	0.434978	−	0.251135i
$333$			4.19584i			0.229931i
$334$	−13.9366	−	24.1390i	−0.762579	−	1.32083i
$335$	−6.00197	+	10.3957i	−0.327923	+	0.567979i
$336$	0.0861402	+	0.0497330i	0.00469933	+	0.00271316i
$337$	−34.5222			−1.88054			−0.940272	−	0.340424i	$-0.889429\pi$
$337$	−34.5222			−1.88054			−0.940272	+	0.340424i	$0.889429\pi$
$338$	−3.27212	−	29.6958i	−0.177980	−	1.61524i
$339$	13.3003			0.722376
$340$	−3.42688	−	1.97851i	−0.185849	−	0.107300i
$341$	−0.543694	+	0.941706i	−0.0294427	+	0.0509962i
$342$	−7.37837	−	12.7797i	−0.398977	−	0.691048i
$343$		−	6.69139i		−	0.361301i
$344$	−21.0178	+	12.1346i	−1.13321	+	0.654256i
$345$	0.788203	−	0.455069i	0.0424354	−	0.0245001i
$346$		−	6.76364i		−	0.363615i
$347$	9.51378	+	16.4784i	0.510727	+	0.884605i	0.999923	+	0.0124307i	$0.00395692\pi$
$347$	9.51378	+	16.4784i	0.510727	+	0.884605i	−0.489196	+	0.872174i	$0.662710\pi$
$348$	−10.2319	+	17.7221i	−0.548485	+	0.950004i
$349$	−10.8433	−	6.26037i	−0.580428	−	0.335110i	0.180876	−	0.983506i	$-0.442107\pi$
$349$	−10.8433	−	6.26037i	−0.580428	−	0.335110i	−0.761303	+	0.648396i	$0.775440\pi$
$350$	3.96158			0.211755
$351$	3.21667	+	1.62881i	0.171693	+	0.0869394i
$352$	14.0412			0.748397
$353$	6.92977	+	4.00090i	0.368834	+	0.212947i	0.672949	−	0.739689i	$-0.265027\pi$
$353$	6.92977	+	4.00090i	0.368834	+	0.212947i	−0.304115	+	0.952635i	$0.598361\pi$
$354$	−12.8572	+	22.2694i	−0.683355	+	1.18361i
$355$	4.20499	+	7.28326i	0.223178	+	0.386555i
$356$			9.25356i			0.490438i
$357$	−0.421031	+	0.243082i	−0.0222833	+	0.0128653i
$358$	36.5870	−	21.1235i	1.93368	−	1.11641i
$359$			9.19616i			0.485355i	0.970107	+	0.242677i	$0.0780256\pi$
$359$			9.19616i			0.485355i	−0.970107	+	0.242677i	$0.921974\pi$
$360$	1.77553	+	3.07531i	0.0935786	+	0.162083i
$361$	11.1161	−	19.2536i	0.585055	−	1.01335i
$362$	−8.66434	−	5.00236i	−0.455388	−	0.262918i
$363$	4.28681			0.224999
$364$	−3.14480	−	4.81603i	−0.164832	−	0.252429i
$365$	−0.948015			−0.0496214
$366$	−5.90604	−	3.40985i	−0.308714	−	0.178236i
$367$	−11.7116	+	20.2850i	−0.611338	+	1.05887i	0.379677	+	0.925119i	$0.376035\pi$
$367$	−11.7116	+	20.2850i	−0.611338	+	1.05887i	−0.991015	+	0.133749i	$0.957298\pi$
$368$	0.0772067	+	0.133726i	0.00402468	+	0.00697094i
$369$			6.14832i			0.320069i
$370$	10.0702	−	5.81402i	0.523524	−	0.302257i
$371$	1.02309	−	0.590684i	0.0531164	−	0.0306668i
$372$			1.37713i			0.0714007i
$373$	−16.9837	−	29.4167i	−0.879384	−	1.52314i	−0.852018	−	0.523513i	$-0.824621\pi$
$373$	−16.9837	−	29.4167i	−0.879384	−	1.52314i	−0.0273667	−	0.999625i	$-0.508712\pi$
$374$	2.97719	−	5.15665i	0.153947	−	0.266644i
$375$	8.92477	+	5.15272i	0.460873	+	0.266085i
$376$	−24.2509			−1.25064
$377$	18.8271	−	12.2938i	0.969645	−	0.633164i
$378$	1.11726			0.0574659
$379$	−6.76308	−	3.90467i	−0.347396	−	0.200569i	0.316142	−	0.948712i	$-0.397612\pi$
$379$	−6.76308	−	3.90467i	−0.347396	−	0.200569i	−0.663538	+	0.748143i	$0.730946\pi$
$380$	−12.7045	+	22.0048i	−0.651725	+	1.12882i
$381$	2.97929	+	5.16029i	0.152634	+	0.264370i
$382$			5.99939i			0.306955i
$383$	1.80443	−	1.04179i	0.0922022	−	0.0532330i	−0.453190	−	0.891414i	$-0.649714\pi$
$383$	1.80443	−	1.04179i	0.0922022	−	0.0532330i	0.545392	+	0.838181i	$0.316381\pi$
$384$	16.2145	−	9.36143i	0.827441	−	0.477723i
$385$		−	1.51902i		−	0.0774162i
$386$	−11.6134	−	20.1149i	−0.591105	−	1.02382i
$387$	−4.12082	+	7.13748i	−0.209473	+	0.362818i
$388$	3.43725	+	1.98450i	0.174500	+	0.100748i
$389$	8.08401			0.409876			0.204938	−	0.978775i	$-0.434301\pi$
$389$	8.08401			0.409876			0.204938	+	0.978775i	$0.434301\pi$
$390$	−0.548020	−	9.97712i	−0.0277501	−	0.505211i
$391$	−0.754732			−0.0381684
$392$	17.2486	+	9.95850i	0.871187	+	0.502980i
$393$	5.79746	−	10.0415i	0.292443	−	0.506527i
$394$	−16.5791	−	28.7158i	−0.835243	−	1.44668i
$395$			17.4763i			0.879326i
$396$	−7.36290	+	4.25097i	−0.369999	+	0.213619i
$397$	21.8378	−	12.6081i	1.09601	−	0.632781i	0.160839	−	0.986981i	$-0.448580\pi$
$397$	21.8378	−	12.6081i	1.09601	−	0.632781i	0.935170	+	0.354200i	$0.115247\pi$
$398$		−	35.8183i		−	1.79541i
$399$	1.56088	+	2.70353i	0.0781420	+	0.135346i
$400$	−0.362722	+	0.628253i	−0.0181361	+	0.0314127i
$401$	−16.9464	−	9.78400i	−0.846262	−	0.488590i	0.0131258	−	0.999914i	$-0.495822\pi$
$401$	−16.9464	−	9.78400i	−0.846262	−	0.488590i	−0.859388	+	0.511324i	$0.829155\pi$
$402$	−22.8761			−1.14096
$403$	0.683581	−	1.34998i	0.0340516	−	0.0672472i
$404$	−45.1922			−2.24840
$405$	1.04435	+	0.602955i	0.0518941	+	0.0299611i
$406$	3.48383	−	6.03417i	0.172900	−	0.299471i
$407$	5.43568	+	9.41487i	0.269437	+	0.466678i
$408$		−	2.94471i		−	0.145785i
$409$	−6.89784	+	3.98247i	−0.341076	+	0.196920i	−0.660748	−	0.750608i	$-0.729761\pi$
$409$	−6.89784	+	3.98247i	−0.341076	+	0.196920i	0.319672	+	0.947528i	$0.396427\pi$
$410$	14.7562	−	8.51949i	0.728756	−	0.420748i
$411$		−	9.64802i		−	0.475902i
$412$	18.4039	+	31.8765i	0.906696	+	1.57044i
$413$	2.71993	−	4.71106i	0.133839	−	0.231816i
$414$	1.50209	+	0.867233i	0.0738238	+	0.0426222i
$415$	−3.36331			−0.165098
$416$	−19.5100	+	1.07164i	−0.956555	+	0.0525413i
$417$	19.6885			0.964152
$418$	−33.1120	−	19.1172i	−1.61956	−	0.935054i
$419$	11.7795	−	20.4027i	0.575467	−	0.996739i	−0.420523	−	0.907282i	$-0.638153\pi$
$419$	11.7795	−	20.4027i	0.575467	−	0.996739i	0.995991	−	0.0894571i	$-0.0285132\pi$
$420$	−0.961881	−	1.66603i	−0.0469350	−	0.0812938i
$421$			26.4891i			1.29100i	0.763760	+	0.645501i	$0.223351\pi$
$421$			26.4891i			1.29100i	−0.763760	+	0.645501i	$0.776649\pi$
$422$	40.7138	−	23.5061i	1.98192	−	1.14426i
$423$	−7.13207	+	4.11770i	−0.346773	+	0.200209i
$424$			7.15558i			0.347506i
$425$	−1.77289	−	3.07074i	−0.0859979	−	0.148953i
$426$	−8.01352	+	13.8798i	−0.388256	+	0.672480i
$427$	1.24941	+	0.721350i	0.0604634	+	0.0349086i
$428$	26.8054			1.29569
$429$	9.32786	−	0.512357i	0.450353	−	0.0247368i
$430$	22.8403			1.10146
$431$	13.0821	+	7.55296i	0.630143	+	0.363813i	0.780808	−	0.624772i	$-0.214808\pi$
$431$	13.0821	+	7.55296i	0.630143	+	0.363813i	−0.150664	+	0.988585i	$0.548141\pi$
$432$	−0.102297	+	0.177183i	−0.00492176	+	0.00852473i
$433$	−11.6330	−	20.1490i	−0.559047	−	0.968298i	−0.997576	−	0.0695814i	$-0.977834\pi$
$433$	−11.6330	−	20.1490i	−0.559047	−	0.968298i	0.438529	−	0.898717i	$-0.355500\pi$
$434$		−	0.468895i		−	0.0225077i
$435$	6.51293	−	3.76024i	0.312271	−	0.180290i
$436$	13.7426	−	7.93429i	0.658151	−	0.379983i
$437$			4.84630i			0.231830i
$438$	−0.903324	−	1.56460i	−0.0431625	−	0.0747596i
$439$	6.20915	−	10.7546i	0.296346	−	0.513287i	−0.678951	−	0.734184i	$-0.737565\pi$
$439$	6.20915	−	10.7546i	0.296346	−	0.513287i	0.975297	+	0.220897i	$0.0708984\pi$
$440$	7.96807	+	4.60037i	0.379863	+	0.219314i
$441$	6.76364			0.322078
$442$	−3.74320	+	7.39230i	−0.178046	+	0.351616i
$443$	1.31472			0.0624644			0.0312322	−	0.999512i	$-0.490057\pi$
$443$	1.31472			0.0624644			0.0312322	+	0.999512i	$0.490057\pi$
$444$	11.9235	+	6.88403i	0.565864	+	0.326702i
$445$	1.70036	−	2.94510i	0.0806047	−	0.139611i
$446$	−0.216747	−	0.375417i	−0.0102633	−	0.0177765i
$447$			5.12398i			0.242356i
$448$	−5.41583	+	3.12683i	−0.255874	+	0.147729i
$449$	22.8064	−	13.1673i	1.07630	−	0.621402i	0.146404	−	0.989225i	$-0.453230\pi$
$449$	22.8064	−	13.1673i	1.07630	−	0.621402i	0.929896	+	0.367823i	$0.119897\pi$
$450$			8.14864i			0.384130i
$451$	7.96509	+	13.7959i	0.375061	+	0.649625i
$452$	21.8216	−	37.7961i	1.02640	−	1.77778i
$453$	12.6354	+	7.29507i	0.593665	+	0.342752i
$454$	32.4673			1.52376
$455$	0.115933	+	2.11065i	0.00543501	+	0.0989486i
$456$	−18.9087			−0.885480
$457$	−6.88161	−	3.97310i	−0.321908	−	0.185854i	0.330335	−	0.943864i	$-0.392838\pi$
$457$	−6.88161	−	3.97310i	−0.321908	−	0.185854i	−0.652243	+	0.758010i	$0.726172\pi$
$458$	−11.1251	+	19.2692i	−0.519841	+	0.900391i
$459$	−0.500000	−	0.866025i	−0.0233380	−	0.0404226i
$460$		−	2.98649i		−	0.139246i
$461$	−9.37237	+	5.41114i	−0.436515	+	0.252022i	−0.702118	−	0.712060i	$-0.747762\pi$
$461$	−9.37237	+	5.41114i	−0.436515	+	0.252022i	0.265603	+	0.964082i	$0.414429\pi$
$462$	2.50698	−	1.44741i	0.116635	−	0.0673394i
$463$		−	4.43898i		−	0.206297i	−0.994666	−	0.103149i	$-0.967108\pi$
$463$		−	4.43898i		−	0.206297i	0.994666	−	0.103149i	$-0.0328917\pi$
$464$	0.637959	+	1.10498i	0.0296165	+	0.0512973i
$465$	0.253049	−	0.438294i	0.0117349	−	0.0203254i
$466$	−28.0168	−	16.1755i	−1.29785	−	0.749316i
$467$	−13.8174			−0.639395			−0.319697	−	0.947520i	$-0.603581\pi$
$467$	−13.8174			−0.639395			−0.319697	+	0.947520i	$0.603581\pi$
$468$	9.90618	−	6.46859i	0.457913	−	0.299011i
$469$	4.83941			0.223463
$470$	19.7653	+	11.4115i	0.911704	+	0.526373i
$471$	−8.48142	+	14.6903i	−0.390803	+	0.676891i
$472$	16.4747	+	28.5351i	0.758311	+	1.31343i
$473$			21.3540i			0.981856i
$474$	−28.8428	+	16.6524i	−1.32479	+	0.764869i
$475$	−19.7179	+	11.3841i	−0.904719	+	0.522340i
$476$			1.59528i			0.0731195i
$477$	1.21499	+	2.10442i	0.0556305	+	0.0963548i
$478$	25.8899	−	44.8427i	1.18418	−	2.05106i
$479$	−14.6901	−	8.48131i	−0.671206	−	0.387521i	0.125328	−	0.992115i	$-0.460002\pi$
$479$	−14.6901	−	8.48131i	−0.671206	−	0.387521i	−0.796533	+	0.604595i	$0.793335\pi$
$480$	−6.53512			−0.298286
$481$	−8.27133	−	12.6669i	−0.377140	−	0.577563i
$482$	−32.9067			−1.49886
$483$	−0.317765	−	0.183462i	−0.0144588	−	0.00834781i
$484$	7.03328	−	12.1820i	0.319695	−	0.553727i
$485$	−0.729309	−	1.26320i	−0.0331162	−	0.0573589i
$486$			2.29812i			0.104245i
$487$	−10.1985	+	5.88813i	−0.462140	+	0.266817i	−0.712944	−	0.701221i	$-0.752639\pi$
$487$	−10.1985	+	5.88813i	−0.462140	+	0.266817i	0.250803	+	0.968038i	$0.419305\pi$
$488$	−7.56775	+	4.36924i	−0.342576	+	0.197786i
$489$			23.5742i			1.06606i
$490$	−9.37213	−	16.2330i	−0.423390	−	0.733332i
$491$	−16.5024	+	28.5830i	−0.744744	+	1.28993i	0.205570	+	0.978642i	$0.434095\pi$
$491$	−16.5024	+	28.5830i	−0.744744	+	1.28993i	−0.950314	+	0.311292i	$0.899238\pi$
$492$	17.4719	+	10.0874i	0.787695	+	0.454776i
$493$	−6.23636			−0.280871
$494$	47.4676	+	24.0359i	2.13567	+	1.08143i
$495$	3.12449			0.140435
$496$	0.0743606	+	0.0429321i	0.00333889	+	0.00192771i
$497$	1.69525	−	2.93626i	0.0760423	−	0.131709i
$498$	−3.20476	−	5.55080i	−0.143609	−	0.248737i
$499$		−	8.51437i		−	0.381156i	−0.981672	−	0.190578i	$-0.938964\pi$
$499$		−	8.51437i		−	0.381156i	0.981672	−	0.190578i	$-0.0610361\pi$
$500$	29.2854	−	16.9079i	1.30968	−	0.756145i
$501$	−10.5038	+	6.06436i	−0.469275	+	0.270936i
$502$			20.5280i			0.916211i
$503$	5.17057	+	8.95569i	0.230544	+	0.399315i	0.957968	−	0.286874i	$-0.0926160\pi$
$503$	5.17057	+	8.95569i	0.230544	+	0.399315i	−0.727424	+	0.686188i	$0.759283\pi$
$504$	0.715808	−	1.23982i	0.0318846	−	0.0552258i
$505$	14.3832	+	8.30414i	0.640044	+	0.369530i
$506$	4.49397			0.199781
$507$	−12.9218	+	1.42382i	−0.573877	+	0.0632342i
$508$	19.5523			0.867491
$509$	5.85123	+	3.37821i	0.259351	+	0.149737i	0.624039	−	0.781393i	$-0.285491\pi$
$509$	5.85123	+	3.37821i	0.259351	+	0.149737i	−0.364687	+	0.931130i	$0.618824\pi$
$510$	−1.38566	+	2.40004i	−0.0613582	+	0.106275i
$511$	0.191097	+	0.330990i	0.00845363	+	0.0146421i
$512$		−	2.31368i		−	0.102251i
$513$	−5.56094	+	3.21061i	−0.245522	+	0.141752i
$514$	50.3082	−	29.0455i	2.21900	−	1.28114i
$515$		−	13.5270i		−	0.596071i
$516$	13.5219	+	23.4206i	0.595268	+	1.03103i
$517$	−10.6689	+	18.4791i	−0.469217	+	0.812708i
$518$	−4.05981	−	2.34393i	−0.178378	−	0.102987i
$519$	−2.94312			−0.129189
$520$	−11.4226	−	5.78400i	−0.500914	−	0.253645i
$521$	−0.761492			−0.0333616			−0.0166808	−	0.999861i	$-0.505310\pi$
$521$	−0.761492			−0.0333616			−0.0166808	+	0.999861i	$0.505310\pi$
$522$	12.4118	+	7.16595i	0.543249	+	0.313645i
$523$	−11.0350	+	19.1131i	−0.482525	+	0.835759i	−0.999799	−	0.0200616i	$-0.993614\pi$
$523$	−11.0350	+	19.1131i	−0.482525	+	0.835759i	0.517273	+	0.855820i	$0.326947\pi$
$524$	−19.0235	−	32.9497i	−0.831047	−	1.43942i
$525$		−	1.72383i		−	0.0752342i
$526$	−35.5254	+	20.5106i	−1.54898	+	0.894305i
$527$	−0.363455	+	0.209841i	−0.0158324	+	0.00914081i
$528$			0.530098i			0.0230696i
$529$	11.2152	+	19.4253i	0.487617	+	0.844577i
$530$	3.36713	−	5.83203i	0.146259	−	0.253327i
$531$	9.69027	+	5.59468i	0.420522	+	0.242788i
$532$	10.2436			0.444118
$533$	−12.1203	−	18.5613i	−0.524987	−	0.803980i
$534$	6.48079			0.280451
$535$	−8.53126	−	4.92553i	−0.368839	−	0.212949i
$536$	−14.6562	+	25.3853i	−0.633053	+	1.09648i
$537$	−9.19165	−	15.9204i	−0.396649	−	0.687016i
$538$			3.27895i			0.141366i
$539$	15.1766	−	8.76224i	0.653704	−	0.377416i
$540$	3.42688	−	1.97851i	0.147469	−	0.0851415i
$541$		−	3.58513i		−	0.154137i	−0.997026	−	0.0770683i	$-0.975444\pi$
$541$		−	3.58513i		−	0.154137i	0.997026	−	0.0770683i	$-0.0245560\pi$
$542$	7.69945	+	13.3358i	0.330719	+	0.572823i
$543$	−2.17672	+	3.77019i	−0.0934119	+	0.161794i
$544$	4.69321	+	2.70962i	0.201220	+	0.116174i
$545$	−5.83175			−0.249805
$546$	−3.37294	+	2.20248i	−0.144348	+	0.0942575i
$547$	30.9340			1.32264			0.661321	−	0.750103i	$-0.269996\pi$
$547$	30.9340			1.32264			0.661321	+	0.750103i	$0.269996\pi$
$548$	−27.4172	−	15.8293i	−1.17120	−	0.676194i
$549$	−1.48376	+	2.56994i	−0.0633252	+	0.109682i
$550$	10.5565	+	18.2844i	0.450130	+	0.779648i
$551$			40.0450i			1.70598i
$552$	1.92472	−	1.11124i	0.0819214	−	0.0472973i
$553$	6.10165	−	3.52279i	0.259469	−	0.149804i
$554$		−	0.626913i		−	0.0266350i
$555$	−2.52990	−	4.38192i	−0.107388	−	0.186002i
$556$	32.3026	−	55.9497i	1.36993	−	2.37280i
$557$	−37.9104	−	21.8876i	−1.60631	−	0.927406i	−0.990185	−	0.139761i	$-0.955367\pi$
$557$	−37.9104	−	21.8876i	−1.60631	−	0.927406i	−0.616129	−	0.787645i	$-0.711300\pi$
$558$	0.964479			0.0408297
$559$	−1.62976	−	29.6710i	−0.0689313	−	1.25495i
$560$	−0.119947			−0.00506869
$561$	−2.24386	−	1.29549i	−0.0947357	−	0.0546957i
$562$	−9.02205	+	15.6267i	−0.380572	+	0.659170i
$563$	8.88312	+	15.3860i	0.374379	+	0.648443i	0.990234	−	0.139416i	$-0.0445226\pi$
$563$	8.88312	+	15.3860i	0.374379	+	0.648443i	−0.615855	+	0.787860i	$0.711189\pi$
$564$			27.0233i			1.13789i
$565$	−13.8902	+	8.01951i	−0.584365	+	0.337383i
$566$	22.0472	−	12.7290i	0.926714	−	0.535039i
$567$		−	0.486164i		−	0.0204170i
$568$	10.2682	+	17.7850i	0.430844	+	0.746243i
$569$	19.9498	−	34.5541i	0.836341	−	1.44858i	−0.0565931	−	0.998397i	$-0.518024\pi$
$569$	19.9498	−	34.5541i	0.836341	−	1.44858i	0.892934	−	0.450188i	$-0.148643\pi$
$570$	15.4112	+	8.89765i	0.645503	+	0.372681i
$571$	−27.9105			−1.16802			−0.584009	−	0.811747i	$-0.698517\pi$
$571$	−27.9105			−1.16802			−0.584009	+	0.811747i	$0.698517\pi$
$572$	13.8480	−	27.3480i	0.579015	−	1.14348i
$573$	2.61056			0.109058
$574$	−5.94898	−	3.43465i	−0.248306	−	0.143359i
$575$	1.33806	−	2.31758i	0.0558009	−	0.0966500i
$576$	−6.43164	−	11.1399i	−0.267985	−	0.464163i
$577$		−	20.5674i		−	0.856234i	−0.903723	−	0.428117i	$-0.859177\pi$
$577$		−	20.5674i		−	0.856234i	0.903723	−	0.428117i	$-0.140823\pi$
$578$	1.99023	−	1.14906i	0.0827827	−	0.0477946i
$579$	−8.75278	+	5.05342i	−0.363753	+	0.210013i
$580$		−	24.6774i		−	1.02467i
$581$	0.677962	+	1.17426i	0.0281266	+	0.0487167i
$582$	1.38986	−	2.40730i	0.0576113	−	0.0997858i
$583$	5.45252	+	3.14801i	0.225820	+	0.130377i
$584$	−2.31496			−0.0957938
$585$	−4.34142	+	0.238464i	−0.179496	+	0.00985928i
$586$	51.0323			2.10812
$587$	15.9614	+	9.21532i	0.658798	+	0.380357i	0.791819	−	0.610756i	$-0.209134\pi$
$587$	15.9614	+	9.21532i	0.658798	+	0.380357i	−0.133021	+	0.991113i	$0.542468\pi$
$588$	11.0970	−	19.2205i	0.457631	−	0.792641i
$589$	1.34744	+	2.33383i	0.0555201	+	0.0961636i
$590$		−	31.0093i		−	1.27663i
$591$	−12.4954	+	7.21420i	−0.513990	+	0.296752i
$592$	0.743433	−	0.429221i	0.0305549	−	0.0176409i
$593$			6.33357i			0.260089i	0.991508	+	0.130044i	$0.0415120\pi$
$593$			6.33357i			0.260089i	−0.991508	+	0.130044i	$0.958488\pi$
$594$	2.97719	+	5.15665i	0.122156	+	0.211580i
$595$	0.293135	−	0.507725i	0.0120174	−	0.0208147i
$596$	14.5610	+	8.40680i	0.596442	+	0.344356i
$597$	−15.5859			−0.637888
$598$	−6.24429	+	0.342984i	−0.255348	+	0.0140257i
$599$	11.1552			0.455787			0.227894	−	0.973686i	$-0.426816\pi$
$599$	11.1552			0.455787			0.227894	+	0.973686i	$0.426816\pi$
$600$	9.04245	+	5.22066i	0.369156	+	0.213133i
$601$	11.3610	−	19.6779i	0.463426	−	0.802677i	−0.535703	−	0.844406i	$-0.679953\pi$
$601$	11.3610	−	19.6779i	0.463426	−	0.802677i	0.999129	+	0.0417297i	$0.0132868\pi$
$602$	−4.60405	−	7.97445i	−0.187647	−	0.325014i
$603$			9.95426i			0.405369i
$604$	41.4614	−	23.9377i	1.68704	−	0.974013i
$605$	−4.47692	+	2.58475i	−0.182013	+	0.105085i
$606$			31.6507i			1.28572i
$607$	−5.16508	−	8.94618i	−0.209644	−	0.363114i	0.741958	−	0.670446i	$-0.233897\pi$
$607$	−5.16508	−	8.94618i	−0.209644	−	0.363114i	−0.951602	+	0.307332i	$0.900564\pi$
$608$	17.3991	−	30.1361i	0.705627	−	1.22218i
$609$	−2.62570	−	1.51595i	−0.106399	−	0.0614293i
$610$	8.22395			0.332978
$611$	13.4139	−	26.4906i	0.542668	−	1.07169i
$612$	−3.28136			−0.132641
$613$	12.6639	+	7.31150i	0.511489	+	0.295309i	0.733446	−	0.679748i	$-0.237911\pi$
$613$	12.6639	+	7.31150i	0.511489	+	0.295309i	−0.221956	+	0.975057i	$0.571244\pi$
$614$	13.1378	−	22.7554i	0.530200	−	0.918334i
$615$	−3.70716	−	6.42098i	−0.149487	−	0.258919i
$616$		−	3.70929i		−	0.149452i
$617$	34.0572	−	19.6629i	1.37109	−	0.791600i	0.380026	−	0.924976i	$-0.375915\pi$
$617$	34.0572	−	19.6629i	1.37109	−	0.791600i	0.991065	+	0.133376i	$0.0425819\pi$
$618$	22.3249	−	12.8893i	0.898040	−	0.518484i
$619$		−	5.04668i		−	0.202843i	−0.994844	−	0.101422i	$-0.967661\pi$
$619$		−	5.04668i		−	0.202843i	0.994844	−	0.101422i	$-0.0323391\pi$
$620$	−0.830345	−	1.43820i	−0.0333474	−	0.0577595i
$621$	0.377366	−	0.653617i	0.0151432	−	0.0262288i
$622$	−53.5007	−	30.8886i	−2.14518	−	1.23852i
$623$	−1.37100			−0.0549281
$624$	−0.0404576	−	0.736562i	−0.00161960	−	0.0294861i
$625$	5.30148			0.212059
$626$	−26.1679	−	15.1081i	−1.04588	−	0.603839i
$627$	−8.31864	+	14.4083i	−0.332214	+	0.575412i
$628$	27.8306	+	48.2040i	1.11056	+	1.92355i
$629$			4.19584i			0.167299i
$630$	−1.16681	+	0.673660i	−0.0464869	+	0.0268392i
$631$	−39.0183	+	22.5272i	−1.55330	+	0.896795i	−0.555425	+	0.831567i	$0.687444\pi$
$631$	−39.0183	+	22.5272i	−1.55330	+	0.896795i	−0.997870	+	0.0652285i	$0.979222\pi$
$632$			42.6753i			1.69753i
$633$	−10.2284	−	17.7161i	−0.406543	−	0.704153i
$634$	−31.8294	+	55.1301i	−1.26411	+	2.18950i
$635$	−6.22284	−	3.59276i	−0.246946	−	0.142574i
$636$	7.97362			0.316175
$637$	−20.4189	+	13.3333i	−0.809028	+	0.528284i
$638$	37.1337			1.47014
$639$	6.03964	+	3.48699i	0.238925	+	0.137943i
$640$	−11.2890	+	19.5532i	−0.446238	+	0.772907i
$641$	18.9104	+	32.7537i	0.746915	+	1.29369i	0.949295	+	0.314387i	$0.101799\pi$
$641$	18.9104	+	32.7537i	0.746915	+	1.29369i	−0.202380	+	0.979307i	$0.564868\pi$
$642$		−	18.7733i		−	0.740923i
$643$	21.0980	−	12.1810i	0.832026	−	0.480370i	−0.0225201	−	0.999746i	$-0.507169\pi$
$643$	21.0980	−	12.1810i	0.832026	−	0.480370i	0.854546	+	0.519376i	$0.173836\pi$
$644$	−1.04270	+	0.602004i	−0.0410882	+	0.0237223i
$645$		−	9.93868i		−	0.391335i
$646$	−7.37837	−	12.7797i	−0.290298	−	0.502811i
$647$	12.0448	−	20.8622i	0.473529	−	0.820176i	−0.526012	−	0.850477i	$-0.676313\pi$
$647$	12.0448	−	20.8622i	0.473529	−	0.820176i	0.999541	+	0.0303012i	$0.00964666\pi$
$648$	2.55020	+	1.47236i	0.100181	+	0.0578397i
$649$	28.9914			1.13801
$650$	−16.0635	−	24.6001i	−0.630064	−	0.964896i
$651$	−0.204034			−0.00799674
$652$	66.9917	+	38.6777i	2.62360	+	1.51473i
$653$	10.2951	−	17.8316i	0.402878	−	0.697805i	−0.591194	−	0.806529i	$-0.701343\pi$
$653$	10.2951	−	17.8316i	0.402878	−	0.697805i	0.994072	+	0.108725i	$0.0346767\pi$
$654$	−5.55683	−	9.62471i	−0.217289	−	0.376356i
$655$			13.9824i			0.546339i
$656$	1.08938	−	0.628953i	0.0425331	−	0.0245565i
$657$	−0.680819	+	0.393071i	−0.0265613	+	0.0153352i
$658$		−	9.20112i		−	0.358697i
$659$	−2.83645	−	4.91288i	−0.110493	−	0.191379i	0.805476	−	0.592628i	$-0.201910\pi$
$659$	−2.83645	−	4.91288i	−0.110493	−	0.191379i	−0.915969	+	0.401249i	$0.868576\pi$
$660$	5.12628	−	8.87899i	0.199540	−	0.345614i
$661$	2.05709	+	1.18766i	0.0800113	+	0.0461946i	0.539472	−	0.842004i	$-0.318624\pi$
$661$	2.05709	+	1.18766i	0.0800113	+	0.0461946i	−0.459461	+	0.888198i	$0.651957\pi$
$662$	−49.6932			−1.93138
$663$	3.21667	+	1.62881i	0.124925	+	0.0632577i
$664$	−8.21288			−0.318722
$665$	−3.26021	−	1.88229i	−0.126426	−	0.0729919i
$666$	4.82128	−	8.35070i	0.186821	−	0.323583i
$667$	−2.35339	−	4.07619i	−0.0911236	−	0.157831i
$668$			39.7987i			1.53986i
$669$	−0.163358	+	0.0943150i	−0.00631580	+	0.00364643i
$670$	23.8906	−	13.7932i	0.922975	−	0.532880i
$671$			7.68878i			0.296822i
$672$	1.31732	+	2.28167i	0.0508168	+	0.0880173i
$673$	−23.0379	+	39.9028i	−0.888045	+	1.53814i	−0.0458621	+	0.998948i	$0.514603\pi$
$673$	−23.0379	+	39.9028i	−0.888045	+	1.53814i	−0.842183	+	0.539192i	$0.818730\pi$
$674$	68.7071	+	39.6681i	2.64650	+	1.52796i
$675$	3.54578			0.136477
$676$	−17.1544	+	39.0564i	−0.659784	+	1.50217i
$677$	−44.3478			−1.70443			−0.852213	−	0.523195i	$-0.824740\pi$
$677$	−44.3478			−1.70443			−0.852213	+	0.523195i	$0.824740\pi$
$678$	−26.4708	−	15.2829i	−1.01660	−	0.586936i
$679$	−0.294022	+	0.509261i	−0.0112835	+	0.0195436i
$680$	1.77553	+	3.07531i	0.0680885	+	0.117933i
$681$		−	14.1278i		−	0.541377i
$682$	2.16415	−	1.24947i	0.0828697	−	0.0478448i
$683$	20.8002	−	12.0090i	0.795899	−	0.459512i	−0.0461364	−	0.998935i	$-0.514691\pi$
$683$	20.8002	−	12.0090i	0.795899	−	0.459512i	0.842035	+	0.539423i	$0.181358\pi$
$684$			21.0703i			0.805644i
$685$	5.81732	+	10.0759i	0.222268	+	0.384980i
$686$	−7.68881	+	13.3174i	−0.293560	+	0.508461i
$687$	8.38477	+	4.84095i	0.319899	+	0.184694i
$688$	1.68619			0.0642853
$689$	−7.81644	−	3.95797i	−0.297782	−	0.150786i
$690$	−2.09161			−0.0796262
$691$	16.7911	+	9.69437i	0.638765	+	0.368791i	0.784139	−	0.620586i	$-0.213105\pi$
$691$	16.7911	+	9.69437i	0.638765	+	0.368791i	−0.145373	+	0.989377i	$0.546438\pi$
$692$	−4.82871	+	8.36357i	−0.183560	+	0.317935i
$693$	−0.629822	−	1.09088i	−0.0239249	−	0.0414392i
$694$		−	43.7276i		−	1.65988i
$695$	−20.5617	+	11.8713i	−0.779949	+	0.450304i
$696$	15.9039	−	9.18215i	0.602837	−	0.348048i
$697$			6.14832i			0.232884i
$698$	14.3871	+	24.9192i	0.544559	+	0.943204i
$699$	−7.03858	+	12.1912i	−0.266223	+	0.461113i
$700$	−4.89868	−	2.82826i	−0.185153	−	0.106898i
$701$	−39.8642			−1.50565			−0.752826	−	0.658220i	$-0.771310\pi$
$701$	−39.8642			−1.50565			−0.752826	+	0.658220i	$0.771310\pi$
$702$	−4.53032	−	6.93786i	−0.170986	−	0.261852i
$703$	26.9425			1.01615
$704$	−28.8633	−	16.6643i	−1.08783	−	0.628058i
$705$	4.96557	−	8.60062i	0.187014	−	0.323918i
$706$	−9.19456	−	15.9254i	−0.346042	−	0.599362i
$707$		−	6.69566i		−	0.251816i
$708$	31.7972	−	18.3581i	1.19501	−	0.689941i
$709$	−12.8072	+	7.39422i	−0.480983	+	0.277696i	−0.720826	−	0.693116i	$-0.756237\pi$
$709$	−12.8072	+	7.39422i	−0.480983	+	0.277696i	0.239843	+	0.970812i	$0.422904\pi$
$710$		−	19.3272i		−	0.725335i
$711$	7.24609	+	12.5506i	0.271750	+	0.470684i
$712$	4.15211	−	7.19166i	0.155607	−	0.269519i
$713$	−0.274311	−	0.158374i	−0.0102730	−	0.00593114i
$714$	1.11726			0.0418126
$715$	−9.43260	+	6.15936i	−0.352759	+	0.230347i
$716$	−60.3222			−2.25435
$717$	−19.5128	−	11.2657i	−0.728717	−	0.420725i
$718$	10.5669	−	18.3025i	0.394355	−	0.683042i
$719$	−10.5991	−	18.3582i	−0.395280	−	0.684646i	0.597856	−	0.801603i	$-0.296019\pi$
$719$	−10.5991	−	18.3582i	−0.395280	−	0.684646i	−0.993137	+	0.116957i	$0.962686\pi$
$720$		−	0.246721i		−	0.00919476i
$721$	−4.72281	+	2.72672i	−0.175887	+	0.101548i
$722$	−44.2470	+	25.5460i	−1.64670	+	0.950725i
$723$			14.3190i			0.532529i
$724$	7.14259	+	12.3713i	0.265452	+	0.459777i
$725$	11.0564	−	19.1502i	0.410624	−	0.711221i
$726$	−8.53174	−	4.92581i	−0.316643	−	0.182814i
$727$	−14.6739			−0.544223			−0.272112	−	0.962266i	$-0.587722\pi$
$727$	−14.6739			−0.544223			−0.272112	+	0.962266i	$0.587722\pi$
$728$	0.283097	+	5.15399i	0.0104923	+	0.191020i
$729$	1.00000			0.0370370
$730$	1.88677	+	1.08933i	0.0698325	+	0.0403178i
$731$	−4.12082	+	7.13748i	−0.152414	+	0.263989i
$732$	4.86874	+	8.43290i	0.179954	+	0.311689i
$733$			33.5167i			1.23797i	0.785404	+	0.618983i	$0.212455\pi$
$733$			33.5167i			1.23797i	−0.785404	+	0.618983i	$0.787545\pi$
$734$	46.6174	−	26.9146i	1.72068	−	0.993434i
$735$	−7.06360	+	4.07817i	−0.260545	+	0.150426i
$736$			4.09008i			0.150762i
$737$	12.8957	+	22.3359i	0.475018	+	0.822755i
$738$	7.06479	−	12.2366i	0.260058	−	0.450434i
$739$	44.3905	+	25.6289i	1.63293	+	0.942772i	0.983183	+	0.182622i	$0.0584583\pi$
$739$	44.3905	+	25.6289i	1.63293	+	0.942772i	0.649747	+	0.760151i	$0.274875\pi$
$740$	−16.6030			−0.610340
$741$	10.4589	−	20.6550i	0.384219	−	0.758779i
$742$	−2.71492			−0.0996680
$743$	30.7851	+	17.7738i	1.12939	+	0.652056i	0.943783	−	0.330567i	$-0.107240\pi$
$743$	30.7851	+	17.7738i	1.12939	+	0.652056i	0.185612	+	0.982623i	$0.440573\pi$
$744$	0.617922	−	1.07027i	0.0226541	−	0.0392381i
$745$	−3.08953	−	5.35122i	−0.113191	−	0.196053i
$746$			78.0613i			2.85803i
$747$	−2.41537	+	1.39451i	−0.0883736	+	0.0510225i
$748$	−7.36290	+	4.25097i	−0.269214	+	0.155431i
$749$			3.97147i			0.145114i
$750$	−11.8416	−	20.5102i	−0.432393	−	0.748927i
$751$	−12.7091	+	22.0127i	−0.463760	+	0.803257i	−0.999145	−	0.0413520i	$-0.986833\pi$
$751$	−12.7091	+	22.0127i	−0.463760	+	0.803257i	0.535384	+	0.844609i	$0.320167\pi$
$752$	1.45917	+	0.842455i	0.0532106	+	0.0307212i
$753$	8.93253			0.325520
$754$	−51.5966	+	2.83408i	−1.87904	+	0.103211i
$755$	−17.5944			−0.640326
$756$	−1.38155	−	0.797640i	−0.0502466	−	0.0290099i
$757$	−7.02556	+	12.1686i	−0.255348	+	0.442276i	−0.964990	−	0.262286i	$-0.915523\pi$
$757$	−7.02556	+	12.1686i	−0.255348	+	0.442276i	0.709642	+	0.704563i	$0.248857\pi$
$758$	8.97339	+	15.5424i	0.325928	+	0.564524i
$759$		−	1.95550i		−	0.0709801i
$760$	19.7472	−	11.4011i	0.716308	−	0.413560i
$761$	−5.77659	+	3.33511i	−0.209401	+	0.120898i	−0.601033	−	0.799224i	$-0.705244\pi$
$761$	−5.77659	+	3.33511i	−0.209401	+	0.120898i	0.391632	+	0.920122i	$0.371911\pi$
$762$		−	13.6936i		−	0.496065i
$763$	1.17554	+	2.03610i	0.0425574	+	0.0737116i
$764$	4.28310	−	7.41854i	0.154957	−	0.268393i
$765$	1.04435	+	0.602955i	0.0377585	+	0.0217999i
$766$	−4.78832			−0.173009
$767$	−40.2831	+	2.21266i	−1.45454	+	0.0798944i
$768$	−17.3008			−0.624290
$769$	−26.8173	−	15.4830i	−0.967056	−	0.558330i	−0.0687184	−	0.997636i	$-0.521891\pi$
$769$	−26.8173	−	15.4830i	−0.967056	−	0.558330i	−0.898337	+	0.439306i	$0.855224\pi$
$770$	−1.74544	+	3.02319i	−0.0629013	+	0.108948i
$771$	−12.6388	−	21.8910i	−0.455175	−	0.788386i
$772$			33.1641i			1.19360i
$773$	−8.04788	+	4.64644i	−0.289462	+	0.167121i	−0.637699	−	0.770285i	$-0.720114\pi$
$773$	−8.04788	+	4.64644i	−0.289462	+	0.167121i	0.348237	+	0.937406i	$0.386780\pi$
$774$	16.4028	−	9.47015i	0.589586	−	0.340397i
$775$		−	1.48810i		−	0.0534541i
$776$	−1.78090	−	3.08461i	−0.0639306	−	0.110731i
$777$	−1.01994	+	1.76658i	−0.0365900	+	0.0633757i
$778$	−16.0890	−	9.28902i	−0.576820	−	0.333027i
$779$	39.4797			1.41451
$780$	−6.44523	+	12.7284i	−0.230776	+	0.455751i
$781$	18.0694			0.646576
$782$	1.50209	+	0.867233i	0.0537147	+	0.0310122i
$783$	3.11818	−	5.40084i	0.111435	−	0.193010i
$784$	−0.691899	−	1.19840i	−0.0247107	−	0.0428002i
$785$		−	20.4557i		−	0.730094i
$786$	−23.0766	+	13.3233i	−0.823114	+	0.475225i
$787$	−37.1677	+	21.4588i	−1.32489	+	0.764923i	−0.984504	−	0.175364i	$-0.943890\pi$
$787$	−37.1677	+	21.4588i	−1.32489	+	0.764923i	−0.340382	+	0.940287i	$0.610556\pi$
$788$			47.3447i			1.68659i
$789$	8.92495	+	15.4585i	0.317737	+	0.550336i
$790$	20.0813	−	34.7818i	0.714459	−	1.23748i
$791$	5.59985	+	3.23308i	0.199108	+	0.114955i
$792$	7.62970			0.271110
$793$	−0.586815	−	10.6834i	−0.0208384	−	0.379379i
$794$	−57.9497			−2.05656
$795$	−2.53774	−	1.46517i	−0.0900044	−	0.0519641i
$796$	−25.5715	+	44.2911i	−0.906356	+	1.56986i
$797$	−17.7885	−	30.8105i	−0.630100	−	1.09136i	−0.987531	−	0.157425i	$-0.949681\pi$
$797$	−17.7885	−	30.8105i	−0.630100	−	1.09136i	0.357431	−	0.933940i	$-0.383653\pi$
$798$		−	7.17420i		−	0.253964i
$799$	−7.13207	+	4.11770i	−0.252314	+	0.145674i
$800$	−16.6411	+	9.60774i	−0.588351	+	0.339685i
$801$		−	2.82004i		−	0.0996412i
$802$	22.4848	+	38.9448i	0.793966	+	1.37519i
$803$	−1.01844	+	1.76399i	−0.0359399	+	0.0622498i
$804$	28.2874	+	16.3317i	0.997620	+	0.575976i
$805$	0.442477			0.0155953
$806$	−2.91169	+	1.90129i	−0.102560	+	0.0669702i
$807$	1.42680			0.0502257
$808$	35.1224	+	20.2779i	1.23560	+	0.713375i
$809$	9.28988	−	16.0905i	0.326615	−	0.565714i	−0.655223	−	0.755436i	$-0.727425\pi$
$809$	9.28988	−	16.0905i	0.326615	−	0.565714i	0.981838	+	0.189722i	$0.0607587\pi$
$810$	−1.38566	−	2.40004i	−0.0486872	−	0.0843287i
$811$		−	51.3091i		−	1.80171i	−0.434125	−	0.900853i	$-0.642942\pi$
$811$		−	51.3091i		−	1.80171i	0.434125	−	0.900853i	$-0.357058\pi$
$812$	−8.61585	+	4.97437i	−0.302357	+	0.174566i
$813$	5.80293	−	3.35032i	0.203518	−	0.117501i
$814$		−	24.9837i		−	0.875678i
$815$	−14.2142	−	24.6197i	−0.497901	−	0.862389i
$816$	−0.102297	+	0.177183i	−0.00358110	+	0.00620265i
$817$	45.8313	+	26.4607i	1.60344	+	0.925744i
$818$	18.3044			0.639998
$819$	0.958383	+	1.46769i	0.0334886	+	0.0512854i
$820$	−24.3290			−0.849606
$821$	−22.6261	−	13.0632i	−0.789657	−	0.455909i	0.0501848	−	0.998740i	$-0.484019\pi$
$821$	−22.6261	−	13.0632i	−0.789657	−	0.455909i	−0.839842	+	0.542831i	$0.817352\pi$
$822$	−11.0862	+	19.2018i	−0.386674	+	0.669739i
$823$	−21.7872	−	37.7365i	−0.759452	−	1.31541i	−0.943130	−	0.332424i	$-0.892134\pi$
$823$	−21.7872	−	37.7365i	−0.759452	−	1.31541i	0.183678	−	0.982987i	$-0.441200\pi$
$824$		−	33.0316i		−	1.15071i
$825$	7.95623	−	4.59353i	0.277000	−	0.159926i
$826$	−10.8266	+	6.25074i	−0.376705	+	0.217491i
$827$		−	36.2362i		−	1.26006i	−0.776572	−	0.630029i	$-0.783043\pi$
$827$		−	36.2362i		−	1.26006i	0.776572	−	0.630029i	$-0.216957\pi$
$828$	−1.23827	−	2.14475i	−0.0430330	−	0.0745353i
$829$	−13.4753	+	23.3398i	−0.468015	+	0.810626i	−0.999332	−	0.0365472i	$-0.988364\pi$
$829$	−13.4753	+	23.3398i	−0.468015	+	0.810626i	0.531317	+	0.847173i	$0.321697\pi$
$830$	6.69376	+	3.86465i	0.232344	+	0.134144i
$831$	−0.272794			−0.00946311
$832$	41.3769	+	20.9518i	1.43449	+	0.726373i
$833$	6.76364			0.234346
$834$	−39.1847	−	22.6233i	−1.35686	−	0.783381i
$835$	7.31307	−	12.6666i	0.253079	−	0.438346i
$836$	27.2964	+	47.2788i	0.944067	+	1.63517i
$837$		−	0.419682i		−	0.0145063i
$838$	−46.8879	+	27.0708i	−1.61972	+	0.935144i
$839$	−5.30234	+	3.06131i	−0.183057	+	0.105688i	−0.588728	−	0.808331i	$-0.700371\pi$
$839$	−5.30234	+	3.06131i	−0.183057	+	0.105688i	0.405671	+	0.914019i	$0.367038\pi$
$840$			1.72640i			0.0595664i
$841$	−4.94608	−	8.56686i	−0.170554	−	0.295409i
$842$	30.4376	−	52.7195i	1.04895	−	1.81683i
$843$	6.79975	+	3.92584i	0.234196	+	0.135213i
$844$	−67.1262			−2.31058
$845$	12.6364	−	9.27822i	0.434704	−	0.319181i
$846$	18.9259			0.650687
$847$	1.80488	+	1.04205i	0.0620164	+	0.0358052i
$848$	0.248579	−	0.430551i	0.00853623	−	0.0147852i
$849$	−5.53886	−	9.59359i	−0.190093	−	0.329251i
$850$			8.14864i			0.279496i
$851$	−2.74248	+	1.58337i	−0.0940109	+	0.0542772i
$852$	19.8182	−	11.4421i	0.678961	−	0.391998i
$853$			16.7868i			0.574768i	0.957815	+	0.287384i	$0.0927856\pi$
$853$			16.7868i			0.574768i	−0.957815	+	0.287384i	$0.907214\pi$
$854$	−1.65775	−	2.87131i	−0.0567270	−	0.0982541i
$855$	3.87171	−	6.70599i	0.132410	−	0.229340i
$856$	−20.8325	−	12.0277i	−0.712041	−	0.411097i
$857$	32.6888			1.11663			0.558314	−	0.829630i	$-0.311449\pi$
$857$	32.6888			1.11663			0.558314	+	0.829630i	$0.311449\pi$
$858$	−19.1533	−	9.69856i	−0.653884	−	0.331103i
$859$	−21.0184			−0.717139			−0.358569	−	0.933503i	$-0.616735\pi$
$859$	−21.0184			−0.717139			−0.358569	+	0.933503i	$0.616735\pi$
$860$	−28.2431	−	16.3062i	−0.963083	−	0.556036i
$861$	−1.49455	+	2.58863i	−0.0509340	+	0.0882203i
$862$	−17.3576	−	30.0643i	−0.591203	−	1.02399i
$863$			33.4512i			1.13869i	0.822098	+	0.569346i	$0.192803\pi$
$863$			33.4512i			1.13869i	−0.822098	+	0.569346i	$0.807197\pi$
$864$	−4.69321	+	2.70962i	−0.159666	+	0.0921833i
$865$	3.07364	−	1.77457i	0.104507	−	0.0603371i
$866$			53.4682i			1.81692i
$867$	−0.500000	−	0.866025i	−0.0169809	−	0.0294118i
$868$	−0.334755	+	0.579812i	−0.0113623	+	0.0196801i
$869$	32.5184	+	18.7745i	1.10311	+	0.636881i
$870$	−17.2830			−0.585948
$871$	−19.6230	−	30.0512i	−0.664900	−	1.01825i
$872$	−14.2406			−0.482247
$873$	−1.04751	−	0.604779i	−0.0354528	−	0.0204687i
$874$	5.56869	−	9.64526i	0.188364	−	0.326256i
$875$	2.50507	+	4.33891i	0.0846868	+	0.146682i
$876$			2.57961i			0.0871570i
$877$	−19.5467	+	11.2853i	−0.660045	+	0.381077i	−0.792294	−	0.610139i	$-0.791113\pi$
$877$	−19.5467	+	11.2853i	−0.660045	+	0.381077i	0.132249	+	0.991217i	$0.457780\pi$
$878$	−24.7153	+	14.2694i	−0.834100	+	0.481568i
$879$		−	22.2061i		−	0.748993i
$880$	−0.319625	−	0.553607i	−0.0107746	−	0.0186621i
$881$	23.9414	−	41.4678i	0.806607	−	1.39708i	−0.108594	−	0.994086i	$-0.534635\pi$
$881$	23.9414	−	41.4678i	0.806607	−	1.39708i	0.915201	−	0.402998i	$-0.132032\pi$
$882$	−13.4612	−	7.77183i	−0.453263	−	0.261691i
$883$	−24.5847			−0.827342			−0.413671	−	0.910427i	$-0.635754\pi$
$883$	−24.5847			−0.827342			−0.413671	+	0.910427i	$0.635754\pi$
$884$	9.90618	−	6.46859i	0.333181	−	0.217562i
$885$	−13.4934			−0.453574
$886$	−2.61660	−	1.51070i	−0.0879065	−	0.0507529i
$887$	5.40425	−	9.36043i	0.181457	−	0.314292i	−0.760920	−	0.648846i	$-0.775252\pi$
$887$	5.40425	−	9.36043i	0.181457	−	0.314292i	0.942377	+	0.334553i	$0.108585\pi$
$888$	−6.17778	−	10.7002i	−0.207313	−	0.359076i
$889$			2.89685i			0.0971573i
$890$	−6.76821	+	3.90763i	−0.226871	+	0.130984i
$891$	2.24386	−	1.29549i	0.0751720	−	0.0434006i
$892$			0.618962i			0.0207244i
$893$	26.4407	+	45.7966i	0.884803	+	1.53252i
$894$	5.88776	−	10.1979i	0.196916	−	0.341069i
$895$	19.1986	+	11.0843i	0.641737	+	0.370507i
$896$	9.10239			0.304089
$897$	0.149246	+	2.71713i	0.00498316	+	0.0907223i
$898$	−60.5200			−2.01958
$899$	−2.26664	−	1.30864i	−0.0755965	−	0.0436457i
$900$	5.81749	−	10.0762i	0.193916	−	0.335873i
$901$	1.21499	+	2.10442i	0.0404771	+	0.0701084i
$902$		−	36.6095i		−	1.21896i
$903$	−3.46999	+	2.00340i	−0.115474	+	0.0666689i
$904$	−33.9185	+	19.5829i	−1.12811	+	0.651316i
$905$		−	5.24985i		−	0.174511i
$906$	−16.7650	−	29.0378i	−0.556978	−	0.964715i
$907$	17.4807	−	30.2775i	0.580437	−	1.00535i	−0.414990	−	0.909826i	$-0.636215\pi$
$907$	17.4807	−	30.2775i	0.580437	−	1.00535i	0.995427	−	0.0955210i	$-0.0304517\pi$
$908$	−40.1474	−	23.1791i	−1.33234	−	0.769226i
$909$	13.7724			0.456802
$910$	2.19453	−	4.33389i	0.0727478	−	0.143667i
$911$	−1.22605			−0.0406210			−0.0203105	−	0.999794i	$-0.506465\pi$
$911$	−1.22605			−0.0406210			−0.0203105	+	0.999794i	$0.506465\pi$
$912$	1.13773	+	0.656870i	0.0376741	+	0.0217512i
$913$	−3.61316	+	6.25817i	−0.119578	+	0.207115i
$914$	9.13066	+	15.8148i	0.302016	+	0.523106i
$915$		−	3.57855i		−	0.118303i
$916$	27.5134	−	15.8849i	0.909070	−	0.524852i
$917$	4.88182	−	2.81852i	0.161212	−	0.0930757i
$918$			2.29812i			0.0758493i
$919$	−2.96619	−	5.13759i	−0.0978456	−	0.169473i	0.812947	−	0.582338i	$-0.197862\pi$
$919$	−2.96619	−	5.13759i	−0.0978456	−	0.169473i	−0.910793	+	0.412864i	$0.864528\pi$
$920$	−1.34005	+	2.32103i	−0.0441801	+	0.0765222i
$921$	−9.90175	−	5.71678i	−0.326274	−	0.188374i
$922$	24.8709			0.819080
$923$	−25.1072	+	1.37908i	−0.826413	+	0.0453929i
$924$	−4.13334			−0.135977
$925$	−12.8843	−	7.43878i	−0.423634	−	0.244585i
$926$	−5.10066	+	8.83460i	−0.167618	+	0.290323i
$927$	−5.60863	−	9.71443i	−0.184212	−	0.319064i
$928$			33.7964i			1.10942i
$929$	−1.38703	+	0.800805i	−0.0455071	+	0.0262735i	−0.522581	−	0.852590i	$-0.675031\pi$
$929$	−1.38703	+	0.800805i	−0.0455071	+	0.0262735i	0.477074	+	0.878863i	$0.341697\pi$
$930$	−1.00725	+	0.581537i	−0.0330291	+	0.0190694i
$931$		−	43.4309i		−	1.42339i
$932$	23.0961	+	40.0036i	0.756538	+	1.31036i
$933$	−13.4408	+	23.2802i	−0.440033	+	0.762159i
$934$	27.4999	+	15.8771i	0.899824	+	0.519513i
$935$	3.12449			0.102182
$936$	−10.6013	+	0.582307i	−0.346516	+	0.0190333i
$937$	28.1141			0.918448			0.459224	−	0.888320i	$-0.348127\pi$
$937$	28.1141			0.918448			0.459224	+	0.888320i	$0.348127\pi$
$938$	−9.63154	−	5.56077i	−0.314481	−	0.181566i
$939$	−6.57409	+	11.3867i	−0.214537	+	0.371590i
$940$	−16.2938	−	28.2217i	−0.531446	−	0.920491i
$941$		−	19.1039i		−	0.622769i	−0.950284	−	0.311384i	$-0.899207\pi$
$941$		−	19.1039i		−	0.622769i	0.950284	−	0.311384i	$-0.100793\pi$
$942$	33.7600	−	19.4913i	1.09996	−	0.635062i
$943$	−4.01865	+	2.32017i	−0.130865	+	0.0755550i
$944$		−	2.28927i		−	0.0745094i
$945$	0.293135	+	0.507725i	0.00953569	+	0.0165163i
$946$	24.5370	−	42.4993i	0.797766	−	1.38177i
$947$	15.2417	+	8.79978i	0.495287	+	0.285954i	0.726765	−	0.686886i	$-0.241023\pi$
$947$	15.2417	+	8.79978i	0.495287	+	0.285954i	−0.231478	+	0.972840i	$0.574356\pi$
$948$	47.5540			1.54448
$949$	1.28047	−	2.52876i	0.0415660	−	0.0820870i
$950$	52.3242			1.69762
$951$	23.9892	+	13.8502i	0.777903	+	0.449123i
$952$	0.715808	−	1.23982i	0.0231995	−	0.0401826i
$953$	13.7810	+	23.8694i	0.446411	+	0.773207i	0.998149	−	0.0608107i	$-0.0193686\pi$
$953$	13.7810	+	23.8694i	0.446411	+	0.773207i	−0.551738	+	0.834017i	$0.686035\pi$
$954$		−	5.58438i		−	0.180801i
$955$	−2.72634	+	1.57405i	−0.0882222	+	0.0509351i
$956$	−64.0283	+	36.9668i	−2.07082	+	1.19559i
$957$		−	16.1583i		−	0.522323i
$958$	19.4911	+	33.7595i	0.629728	+	1.09072i
$959$	2.34526	−	4.06211i	0.0757325	−	0.131172i
$960$	13.4337	+	7.75597i	0.433572	+	0.250323i
$961$	30.8239			0.994318
$962$	1.90678	+	34.7144i	0.0614771	+	1.11924i
$963$	−8.16898			−0.263242
$964$	40.6908	+	23.4928i	1.31056	+	0.756654i
$965$	6.09396	−	10.5551i	0.196172	−	0.339779i
$966$	0.421618	+	0.730263i	0.0135653	+	0.0234958i
$967$			0.0241650i			0.000777093i	1.00000		0.000388547i	$0.000123678\pi$
$967$			0.0241650i			0.000777093i	−1.00000		0.000388547i	$0.999876\pi$
$968$	−10.9322	+	6.31172i	−0.351375	+	0.202866i
$969$	−5.56094	+	3.21061i	−0.178643	+	0.103140i
$970$			3.35208i			0.107629i
$971$	15.2827	+	26.4705i	0.490447	+	0.849478i	0.999940	−	0.0109965i	$-0.00350037\pi$
$971$	15.2827	+	26.4705i	0.490447	+	0.849478i	−0.509493	+	0.860475i	$0.670167\pi$
$972$	1.64068	−	2.84174i	0.0526248	−	0.0911488i
$973$	8.28948	+	4.78593i	0.265748	+	0.153430i
$974$	27.0633			0.867164
$975$	−10.7045	+	6.98986i	−0.342817	+	0.223855i
$976$	0.607134			0.0194339
$977$	20.0215	+	11.5594i	0.640544	+	0.369818i	0.784824	−	0.619719i	$-0.212753\pi$
$977$	20.0215	+	11.5594i	0.640544	+	0.369818i	−0.144280	+	0.989537i	$0.546087\pi$
$978$	27.0882	−	46.9181i	0.866184	−	1.50027i
$979$	−3.65334	−	6.32777i	−0.116761	−	0.202236i
$980$			26.7639i			0.854941i
$981$	−4.18808	+	2.41799i	−0.133715	+	0.0772005i
$982$	65.6873	−	37.9246i	2.09617	−	1.21022i
$983$			40.6419i			1.29628i	0.761523	+	0.648138i	$0.224452\pi$
$983$			40.6419i			1.29628i	−0.761523	+	0.648138i	$0.775548\pi$
$984$	−9.05252	−	15.6794i	−0.288584	−	0.499842i
$985$	8.69967	−	15.0683i	0.277194	−	0.480115i
$986$	12.4118	+	7.16595i	0.395272	+	0.228210i
$987$	−4.00376			−0.127441
$988$	−41.5363	−	63.6098i	−1.32144	−	2.02370i
$989$	−6.22024			−0.197792
$990$	−6.21846	−	3.59023i	−0.197635	−	0.114105i
$991$	11.9899	−	20.7670i	0.380870	−	0.659687i	−0.610316	−	0.792158i	$-0.708958\pi$
$991$	11.9899	−	20.7670i	0.380870	−	0.659687i	0.991187	+	0.132471i	$0.0422911\pi$
$992$	1.13718	+	1.96965i	0.0361055	+	0.0625366i
$993$			21.6234i			0.686198i
$994$	−6.74788	+	3.89589i	−0.214030	+	0.123570i
$995$	16.2771	−	9.39759i	0.516019	−	0.297924i
$996$			9.15178i			0.289985i
$997$	−16.0871	−	27.8636i	−0.509483	−	0.882450i	−0.999940	−	0.0109849i	$-0.996503\pi$
$997$	−16.0871	−	27.8636i	−0.509483	−	0.882450i	0.490457	−	0.871466i	$-0.336830\pi$
$998$	−9.78352	+	16.9456i	−0.309692	+	0.536402i
$999$	−3.63371	−	2.09792i	−0.114965	−	0.0663753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	663.2.z.d.511.1	yes	16
13.6	odd	12		8619.2.a.bn.1.15		16
13.7	odd	12		8619.2.a.bn.1.2		16
13.10	even	6	inner	663.2.z.d.205.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
663.2.z.d.205.1	✓	16	13.10	even	6	inner
663.2.z.d.511.1	yes	16	1.1	even	1	trivial
8619.2.a.bn.1.2		16	13.7	odd	12
8619.2.a.bn.1.15		16	13.6	odd	12

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:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99023 - 1.14906i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.64068 + 2.84174i) q^{4} -1.20591i q^{5} +(1.99023 - 1.14906i) q^{6} +(-0.421031 + 0.243082i) q^{7} -2.94471i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.99023 - 1.14906i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.64068 + 2.84174i) q^{4} -1.20591i q^{5} +(1.99023 - 1.14906i) q^{6} +(-0.421031 + 0.243082i) q^{7} -2.94471i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.38566 + 2.40004i) q^{10} +(-2.24386 - 1.29549i) q^{11} -3.28136 q^{12} +(3.21667 + 1.62881i) q^{13} +1.11726 q^{14} +(1.04435 + 0.602955i) q^{15} +(-0.102297 + 0.177183i) q^{16} +(-0.500000 - 0.866025i) q^{17} +2.29812i q^{18} +(-5.56094 + 3.21061i) q^{19} +(3.42688 - 1.97851i) q^{20} -0.486164i q^{21} +(2.97719 + 5.15665i) q^{22} +(0.377366 - 0.653617i) q^{23} +(2.55020 + 1.47236i) q^{24} +3.54578 q^{25} +(-4.53032 - 6.93786i) q^{26} +1.00000 q^{27} +(-1.38155 - 0.797640i) q^{28} +(3.11818 - 5.40084i) q^{29} +(-1.38566 - 2.40004i) q^{30} -0.419682i q^{31} +(-4.69321 + 2.70962i) q^{32} +(2.24386 - 1.29549i) q^{33} +2.29812i q^{34} +(0.293135 + 0.507725i) q^{35} +(1.64068 - 2.84174i) q^{36} +(-3.63371 - 2.09792i) q^{37} +14.7567 q^{38} +(-3.01893 + 1.97132i) q^{39} -3.55106 q^{40} +(-5.32460 - 3.07416i) q^{41} +(-0.558632 + 0.967579i) q^{42} +(-4.12082 - 7.13748i) q^{43} -8.50194i q^{44} +(-1.04435 + 0.602955i) q^{45} +(-1.50209 + 0.867233i) q^{46} -8.23540i q^{47} +(-0.102297 - 0.177183i) q^{48} +(-3.38182 + 5.85749i) q^{49} +(-7.05693 - 4.07432i) q^{50} +1.00000 q^{51} +(0.648877 + 11.8133i) q^{52} -2.42998 q^{53} +(-1.99023 - 1.14906i) q^{54} +(-1.56224 + 2.70589i) q^{55} +(0.715808 + 1.23982i) q^{56} -6.42122i q^{57} +(-12.4118 + 7.16595i) q^{58} +(-9.69027 + 5.59468i) q^{59} +3.95702i q^{60} +(-1.48376 - 2.56994i) q^{61} +(-0.482240 + 0.835264i) q^{62} +(0.421031 + 0.243082i) q^{63} +12.8633 q^{64} +(1.96420 - 3.87902i) q^{65} -5.95439 q^{66} +(-8.62064 - 4.97713i) q^{67} +(1.64068 - 2.84174i) q^{68} +(0.377366 + 0.653617i) q^{69} -1.34732i q^{70} +(-6.03964 + 3.48699i) q^{71} +(-2.55020 + 1.47236i) q^{72} -0.786142i q^{73} +(4.82128 + 8.35070i) q^{74} +(-1.77289 + 3.07074i) q^{75} +(-18.2474 - 10.5352i) q^{76} +1.25964 q^{77} +(8.27352 - 0.454445i) q^{78} -14.4922 q^{79} +(0.213667 + 0.123361i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.06479 + 12.2366i) q^{82} -2.78902i q^{83} +(1.38155 - 0.797640i) q^{84} +(-1.04435 + 0.602955i) q^{85} +18.9403i q^{86} +(3.11818 + 5.40084i) q^{87} +(-3.81485 + 6.60752i) q^{88} +(2.44223 + 1.41002i) q^{89} +2.77133 q^{90} +(-1.75025 + 0.0961373i) q^{91} +2.47655 q^{92} +(0.363455 + 0.209841i) q^{93} +(-9.46297 + 16.3903i) q^{94} +(3.87171 + 6.70599i) q^{95} -5.41925i q^{96} +(1.04751 - 0.604779i) q^{97} +(13.4612 - 7.77183i) q^{98} +2.59098i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} - 2 q^{13} - 26 q^{14} - 3 q^{15} - 8 q^{17} + 27 q^{20} + q^{22} - 21 q^{23} + 14 q^{25} + 2 q^{26} + 16 q^{27} - 33 q^{28} + 29 q^{29} + q^{30} - 15 q^{32} - 3 q^{33} + 15 q^{35} + 4 q^{36} - 18 q^{37} + 62 q^{38} + q^{39} + 4 q^{40} + 12 q^{41} + 13 q^{42} - 3 q^{43} + 3 q^{45} - 9 q^{46} + 2 q^{49} - 36 q^{50} + 16 q^{51} - 8 q^{52} - 26 q^{53} + 9 q^{55} - 37 q^{56} + 30 q^{58} - 3 q^{59} + 29 q^{61} - 20 q^{62} + 36 q^{64} - 16 q^{65} - 2 q^{66} + 33 q^{67} + 4 q^{68} - 21 q^{69} + 27 q^{71} + 17 q^{74} - 7 q^{75} - 48 q^{76} - 8 q^{77} - q^{78} - 14 q^{79} - 39 q^{80} - 8 q^{81} - 3 q^{82} + 33 q^{84} + 3 q^{85} + 29 q^{87} - 5 q^{88} - 3 q^{89} - 2 q^{90} - 70 q^{91} - 64 q^{92} - 6 q^{93} - 25 q^{94} - 27 q^{95} + 6 q^{97} + 102 q^{98}+O(q^{100}) \) 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 - 2 * q^13 - 26 * q^14 - 3 * q^15 - 8 * q^17 + 27 * q^20 + q^22 - 21 * q^23 + 14 * q^25 + 2 * q^26 + 16 * q^27 - 33 * q^28 + 29 * q^29 + q^30 - 15 * q^32 - 3 * q^33 + 15 * q^35 + 4 * q^36 - 18 * q^37 + 62 * q^38 + q^39 + 4 * q^40 + 12 * q^41 + 13 * q^42 - 3 * q^43 + 3 * q^45 - 9 * q^46 + 2 * q^49 - 36 * q^50 + 16 * q^51 - 8 * q^52 - 26 * q^53 + 9 * q^55 - 37 * q^56 + 30 * q^58 - 3 * q^59 + 29 * q^61 - 20 * q^62 + 36 * q^64 - 16 * q^65 - 2 * q^66 + 33 * q^67 + 4 * q^68 - 21 * q^69 + 27 * q^71 + 17 * q^74 - 7 * q^75 - 48 * q^76 - 8 * q^77 - q^78 - 14 * q^79 - 39 * q^80 - 8 * q^81 - 3 * q^82 + 33 * q^84 + 3 * q^85 + 29 * q^87 - 5 * q^88 - 3 * q^89 - 2 * q^90 - 70 * q^91 - 64 * q^92 - 6 * q^93 - 25 * q^94 - 27 * q^95 + 6 * q^97 + 102 * q^98

Introduction

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