LMFDB - Embedded newform 153.3.t.a.22.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(7,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([32, 33])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.t (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$34$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			22.20
Character	$\chi$	$=$	153.22
Dual form			153.3.t.a.7.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.434420 - 0.566147i) q^{2} +(2.71144 - 1.28378i) q^{3} +(0.903474 + 3.37181i) q^{4} +(1.70774 + 1.49765i) q^{5} +(0.451096 - 2.09277i) q^{6} +(-0.856685 + 0.751292i) q^{7} +(4.93860 + 2.04563i) q^{8} +(5.70382 - 6.96178i) q^{9} +(1.58977 - 0.316224i) q^{10} +(-0.488519 + 7.45335i) q^{11} +(6.77838 + 7.98261i) q^{12} +(-5.82278 + 1.56021i) q^{13} +(0.0531810 + 0.811386i) q^{14} +(6.55309 + 1.86842i) q^{15} +(-8.78878 + 5.07421i) q^{16} +(14.4664 - 8.92882i) q^{17} +(-1.46354 - 6.25354i) q^{18} +(-7.99196 - 19.2943i) q^{19} +(-3.50689 + 7.11127i) q^{20} +(-1.35836 + 3.13688i) q^{21} +(4.00747 + 3.51446i) q^{22} +(-7.81315 - 15.8435i) q^{23} +(16.0169 - 0.793456i) q^{24} +(-2.58973 - 19.6709i) q^{25} +(-1.64622 + 3.97434i) q^{26} +(6.52817 - 26.1989i) q^{27} +(-3.30721 - 2.20981i) q^{28} +(9.18788 + 27.0666i) q^{29} +(3.90459 - 2.89833i) q^{30} +(0.862221 + 13.1549i) q^{31} +(-3.73619 + 28.3792i) q^{32} +(8.24387 + 20.8365i) q^{33} +(1.22946 - 12.0690i) q^{34} -2.58817 q^{35} +(28.6271 + 12.9424i) q^{36} +(-30.4113 - 45.5137i) q^{37} +(-14.3953 - 3.85720i) q^{38} +(-13.7852 + 11.7056i) q^{39} +(5.37020 + 10.8897i) q^{40} +(-22.9425 - 7.78793i) q^{41} +(1.18584 + 2.13175i) q^{42} +(-24.4247 + 3.21558i) q^{43} +(-25.5727 + 5.08672i) q^{44} +(20.1670 - 3.34661i) q^{45} +(-12.3639 - 2.45934i) q^{46} +(-10.6642 + 39.7995i) q^{47} +(-17.3161 + 25.0413i) q^{48} +(-6.22631 + 47.2936i) q^{49} +(-12.2617 - 7.07928i) q^{50} +(27.7621 - 42.7816i) q^{51} +(-10.5215 - 18.2237i) q^{52} +(6.58082 + 15.8875i) q^{53} +(-11.9965 - 15.0772i) q^{54} +(-11.9968 + 11.9968i) q^{55} +(-5.76769 + 1.95787i) q^{56} +(-46.4394 - 42.0554i) q^{57} +(19.3151 + 6.55659i) q^{58} +(4.04791 - 3.10607i) q^{59} +(-0.379420 + 23.7839i) q^{60} +(-36.7147 - 41.8650i) q^{61} +(7.82220 + 5.22663i) q^{62} +(0.343961 + 10.2493i) q^{63} +(-14.2603 - 14.2603i) q^{64} +(-12.2804 - 6.05605i) q^{65} +(15.3778 + 4.38453i) q^{66} +(-37.7144 - 21.7744i) q^{67} +(43.1763 + 40.7110i) q^{68} +(-41.5245 - 32.9283i) q^{69} +(-1.12435 + 1.46528i) q^{70} +(12.5470 + 18.7780i) q^{71} +(42.4101 - 22.7135i) q^{72} +(15.7033 - 78.9458i) q^{73} +(-38.9787 - 2.55480i) q^{74} +(-32.2750 - 50.0119i) q^{75} +(57.8362 - 44.3793i) q^{76} +(-5.18114 - 6.75219i) q^{77} +(0.638534 + 12.8896i) q^{78} +(-7.63974 + 116.560i) q^{79} +(-22.6083 - 4.49708i) q^{80} +(-15.9329 - 79.4175i) q^{81} +(-14.3758 + 9.60560i) q^{82} +(95.4387 + 73.2327i) q^{83} +(-11.8042 - 1.74603i) q^{84} +(38.0771 + 6.41745i) q^{85} +(-8.79010 + 15.2249i) q^{86} +(59.6599 + 61.5943i) q^{87} +(-17.6594 + 35.8098i) q^{88} +(-39.2771 + 39.2771i) q^{89} +(6.86625 - 12.8713i) q^{90} +(3.81611 - 5.71122i) q^{91} +(46.3623 - 40.6587i) q^{92} +(19.2259 + 34.5620i) q^{93} +(17.8996 + 23.3272i) q^{94} +(15.2479 - 44.9188i) q^{95} +(26.3021 + 81.7448i) q^{96} +(33.7447 + 99.4087i) q^{97} +(24.0703 + 24.0703i) q^{98} +(49.1022 + 45.9135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) $ 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.434420	−	0.566147i	0.217210	−	0.283074i	−0.672021	−	0.740532i	$-0.734574\pi$
$2$	0.434420	−	0.566147i	0.217210	−	0.283074i	0.889231	+	0.457459i	$0.151240\pi$
$3$	2.71144	−	1.28378i	0.903813	−	0.427927i
$3$	2.71144	−	1.28378i	0.903813	−	0.427927i
$4$	0.903474	+	3.37181i	0.225869	+	0.842953i
$5$	1.70774	+	1.49765i	0.341548	+	0.299530i	0.812886	−	0.582423i	$-0.197895\pi$
$5$	1.70774	+	1.49765i	0.341548	+	0.299530i	−0.471338	+	0.881953i	$0.656229\pi$
$6$	0.451096	−	2.09277i	0.0751826	−	0.348796i
$7$	−0.856685	+	0.751292i	−0.122384	+	0.107327i	−0.718350	−	0.695682i	$-0.755102\pi$
$7$	−0.856685	+	0.751292i	−0.122384	+	0.107327i	0.595967	+	0.803009i	$0.296769\pi$
$8$	4.93860	+	2.04563i	0.617325	+	0.255704i
$9$	5.70382	−	6.96178i	0.633758	−	0.773532i
$10$	1.58977	−	0.316224i	0.158977	−	0.0316224i
$11$	−0.488519	+	7.45335i	−0.0444108	+	0.677578i	0.916381	+	0.400307i	$0.131097\pi$
$11$	−0.488519	+	7.45335i	−0.0444108	+	0.677578i	−0.960792	+	0.277271i	$0.910570\pi$
$12$	6.77838	+	7.98261i	0.564865	+	0.665217i
$13$	−5.82278	+	1.56021i	−0.447906	+	0.120016i	−0.475720	−	0.879597i	$-0.657812\pi$
$13$	−5.82278	+	1.56021i	−0.447906	+	0.120016i	0.0278133	+	0.999613i	$0.491146\pi$
$14$	0.0531810	+	0.811386i	0.00379865	+	0.0579561i
$15$	6.55309	+	1.86842i	0.436873	+	0.124561i
$16$	−8.78878	+	5.07421i	−0.549299	+	0.317138i
$17$	14.4664	−	8.92882i	0.850964	−	0.525225i
$17$	14.4664	−	8.92882i	0.850964	−	0.525225i
$18$	−1.46354	−	6.25354i	−0.0813078	−	0.347419i
$19$	−7.99196	−	19.2943i	−0.420630	−	1.01549i	−0.982162	−	0.188035i	$-0.939788\pi$
$19$	−7.99196	−	19.2943i	−0.420630	−	1.01549i	0.561533	−	0.827455i	$-0.310212\pi$
$20$	−3.50689	+	7.11127i	−0.175344	+	0.355563i
$21$	−1.35836	+	3.13688i	−0.0646836	+	0.149375i
$22$	4.00747	+	3.51446i	0.182158	+	0.159748i
$23$	−7.81315	−	15.8435i	−0.339702	−	0.688848i	0.658251	−	0.752799i	$-0.271297\pi$
$23$	−7.81315	−	15.8435i	−0.339702	−	0.688848i	−0.997953	+	0.0639508i	$0.979630\pi$
$24$	16.0169	−	0.793456i	0.667369	−	0.0330607i
$25$	−2.58973	−	19.6709i	−0.103589	−	0.786837i
$26$	−1.64622	+	3.97434i	−0.0633163	+	0.152859i
$27$	6.52817	−	26.1989i	0.241784	−	0.970330i
$28$	−3.30721	−	2.20981i	−0.118115	−	0.0789217i
$29$	9.18788	+	27.0666i	0.316823	+	0.933331i	0.982365	+	0.186971i	$0.0598671\pi$
$29$	9.18788	+	27.0666i	0.316823	+	0.933331i	−0.665542	+	0.746360i	$0.731800\pi$
$30$	3.90459	−	2.89833i	0.130153	−	0.0966111i
$31$	0.862221	+	13.1549i	0.0278136	+	0.424353i	0.988947	+	0.148269i	$0.0473702\pi$
$31$	0.862221	+	13.1549i	0.0278136	+	0.424353i	−0.961133	+	0.276084i	$0.910963\pi$
$32$	−3.73619	+	28.3792i	−0.116756	+	0.886848i
$33$	8.24387	+	20.8365i	0.249814	+	0.631408i
$34$	1.22946	−	12.0690i	0.0361606	−	0.354969i
$35$	−2.58817			−0.0739476
$36$	28.6271	+	12.9424i	0.795197	+	0.359511i
$37$	−30.4113	−	45.5137i	−0.821927	−	1.23010i	−0.970477	−	0.241195i	$-0.922461\pi$
$37$	−30.4113	−	45.5137i	−0.821927	−	1.23010i	0.148550	−	0.988905i	$-0.452539\pi$
$38$	−14.3953	−	3.85720i	−0.378823	−	0.101505i
$39$	−13.7852	+	11.7056i	−0.353466	+	0.300143i
$40$	5.37020	+	10.8897i	0.134255	+	0.272242i
$41$	−22.9425	−	7.78793i	−0.559573	−	0.189950i	0.0273015	−	0.999627i	$-0.491309\pi$
$41$	−22.9425	−	7.78793i	−0.559573	−	0.189950i	−0.586875	+	0.809678i	$0.699642\pi$
$42$	1.18584	+	2.13175i	0.0282342	+	0.0507560i
$43$	−24.4247	+	3.21558i	−0.568017	+	0.0747809i	−0.409065	−	0.912505i	$-0.634145\pi$
$43$	−24.4247	+	3.21558i	−0.568017	+	0.0747809i	−0.158952	+	0.987286i	$0.550812\pi$
$44$	−25.5727	+	5.08672i	−0.581197	+	0.115607i
$45$	20.1670	−	3.34661i	0.448154	−	0.0743691i
$46$	−12.3639	−	2.45934i	−0.268781	−	0.0534639i
$47$	−10.6642	+	39.7995i	−0.226899	+	0.846798i	0.754736	+	0.656028i	$0.227765\pi$
$47$	−10.6642	+	39.7995i	−0.226899	+	0.846798i	−0.981635	+	0.190769i	$0.938902\pi$
$48$	−17.3161	+	25.0413i	−0.360752	+	0.521693i
$49$	−6.22631	+	47.2936i	−0.127068	+	0.965175i
$50$	−12.2617	−	7.07928i	−0.245233	−	0.141586i
$51$	27.7621	−	42.7816i	0.544355	−	0.838855i
$52$	−10.5215	−	18.2237i	−0.202336	−	0.350456i
$53$	6.58082	+	15.8875i	0.124166	+	0.299764i	0.973724	−	0.227732i	$-0.0731310\pi$
$53$	6.58082	+	15.8875i	0.124166	+	0.299764i	−0.849558	+	0.527496i	$0.823131\pi$
$54$	−11.9965	−	15.0772i	−0.222157	−	0.279208i
$55$	−11.9968	+	11.9968i	−0.218123	+	0.218123i
$56$	−5.76769	+	1.95787i	−0.102994	+	0.0349619i
$57$	−46.4394	−	42.0554i	−0.814726	−	0.737815i
$58$	19.3151	+	6.55659i	0.333019	+	0.113045i
$59$	4.04791	−	3.10607i	0.0686087	−	0.0526453i	−0.573888	−	0.818934i	$-0.694565\pi$
$59$	4.04791	−	3.10607i	0.0686087	−	0.0526453i	0.642496	+	0.766289i	$0.277899\pi$
$60$	−0.379420	+	23.7839i	−0.00632366	+	0.396398i
$61$	−36.7147	−	41.8650i	−0.601880	−	0.686312i	0.368020	−	0.929818i	$-0.380036\pi$
$61$	−36.7147	−	41.8650i	−0.601880	−	0.686312i	−0.969899	+	0.243506i	$0.921702\pi$
$62$	7.82220	+	5.22663i	0.126165	+	0.0843005i
$63$	0.343961	+	10.2493i	0.00545969	+	0.162687i
$64$	−14.2603	−	14.2603i	−0.222818	−	0.222818i
$65$	−12.2804	−	6.05605i	−0.188930	−	0.0931699i
$66$	15.3778	+	4.38453i	0.232997	+	0.0664323i
$67$	−37.7144	−	21.7744i	−0.562901	−	0.324991i	0.191408	−	0.981511i	$-0.438695\pi$
$67$	−37.7144	−	21.7744i	−0.562901	−	0.324991i	−0.754309	+	0.656519i	$0.772028\pi$
$68$	43.1763	+	40.7110i	0.634946	+	0.598691i
$69$	−41.5245	−	32.9283i	−0.601804	−	0.477222i
$70$	−1.12435	+	1.46528i	−0.0160622	+	0.0209326i
$71$	12.5470	+	18.7780i	0.176719	+	0.264479i	0.909246	−	0.416259i	$-0.136659\pi$
$71$	12.5470	+	18.7780i	0.176719	+	0.264479i	−0.732527	+	0.680738i	$0.761659\pi$
$72$	42.4101	−	22.7135i	0.589030	−	0.315466i
$73$	15.7033	−	78.9458i	0.215114	−	1.08145i	−0.710707	−	0.703488i	$-0.751625\pi$
$73$	15.7033	−	78.9458i	0.215114	−	1.08145i	0.925821	−	0.377962i	$-0.123375\pi$
$74$	−38.9787	−	2.55480i	−0.526739	−	0.0345243i
$75$	−32.2750	−	50.0119i	−0.430334	−	0.666826i
$76$	57.8362	−	44.3793i	0.761003	−	0.583938i
$77$	−5.18114	−	6.75219i	−0.0672875	−	0.0876908i
$78$	0.638534	+	12.8896i	0.00818633	+	0.165251i
$79$	−7.63974	+	116.560i	−0.0967056	+	1.47544i	0.623577	+	0.781762i	$0.285679\pi$
$79$	−7.63974	+	116.560i	−0.0967056	+	1.47544i	−0.720283	+	0.693681i	$0.755988\pi$
$80$	−22.6083	−	4.49708i	−0.282604	−	0.0562135i
$81$	−15.9329	−	79.4175i	−0.196702	−	0.980463i
$82$	−14.3758	+	9.60560i	−0.175315	+	0.117141i
$83$	95.4387	+	73.2327i	1.14986	+	0.882321i	0.994417	−	0.105523i	$-0.0336516\pi$
$83$	95.4387	+	73.2327i	1.14986	+	0.882321i	0.155447	+	0.987844i	$0.450318\pi$
$84$	−11.8042	−	1.74603i	−0.140526	−	0.0207861i
$85$	38.0771	+	6.41745i	0.447965	+	0.0754994i
$86$	−8.79010	+	15.2249i	−0.102210	+	0.177034i
$87$	59.6599	+	61.5943i	0.685746	+	0.707980i
$88$	−17.6594	+	35.8098i	−0.200675	+	0.406929i
$89$	−39.2771	+	39.2771i	−0.441316	+	0.441316i	−0.892454	−	0.451138i	$-0.851018\pi$
$89$	−39.2771	+	39.2771i	−0.441316	+	0.441316i	0.451138	+	0.892454i	$0.351018\pi$
$90$	6.86625	−	12.8713i	0.0762917	−	0.143014i
$91$	3.81611	−	5.71122i	0.0419353	−	0.0627606i
$92$	46.3623	−	40.6587i	0.503938	−	0.441942i
$93$	19.2259	+	34.5620i	0.206730	+	0.371634i
$94$	17.8996	+	23.3272i	0.190421	+	0.248162i
$95$	15.2479	−	44.9188i	0.160504	−	0.472830i
$96$	26.3021	+	81.7448i	0.273981	+	0.851509i
$97$	33.7447	+	99.4087i	0.347883	+	1.02483i	0.970250	+	0.242106i	$0.0778381\pi$
$97$	33.7447	+	99.4087i	0.347883	+	1.02483i	−0.622366	+	0.782726i	$0.713829\pi$
$98$	24.0703	+	24.0703i	0.245615	+	0.245615i
$99$	49.1022	+	45.9135i	0.495982	+	0.463773i
$100$	63.9869	−	26.5043i	0.639869	−	0.265043i
$101$	88.0649	−	50.8443i	0.871930	−	0.503409i	0.00394092	−	0.999992i	$-0.498746\pi$
$101$	88.0649	−	50.8443i	0.871930	−	0.503409i	0.867989	+	0.496583i	$0.165412\pi$
$102$	−12.1603	−	34.3026i	−0.119218	−	0.336300i
$103$	11.9203	−	20.6465i	0.115731	−	0.200452i	−0.802341	−	0.596866i	$-0.796412\pi$
$103$	11.9203	−	20.6465i	0.115731	−	0.200452i	0.918072	+	0.396414i	$0.129746\pi$
$104$	−31.9480	−	4.20603i	−0.307192	−	0.0404426i
$105$	−7.01766	+	3.32264i	−0.0668349	+	0.0316442i
$106$	11.8535	+	3.17614i	0.111825	+	0.0299635i
$107$	32.0208	−	160.980i	0.299260	−	1.50448i	−0.479713	−	0.877425i	$-0.659259\pi$
$107$	32.0208	−	160.980i	0.299260	−	1.50448i	0.778973	−	0.627057i	$-0.215741\pi$
$108$	94.2358	−	1.65829i	0.872554	−	0.0153545i
$109$	−7.12601	−	35.8249i	−0.0653763	−	0.328669i	0.934232	−	0.356667i	$-0.116087\pi$
$109$	−7.12601	−	35.8249i	−0.0653763	−	0.328669i	−0.999608	+	0.0279980i	$0.991087\pi$
$110$	1.58030	+	12.0036i	0.0143664	+	0.109123i
$111$	−140.888	−	84.3663i	−1.26926	−	0.760057i
$112$	3.71700	−	10.9499i	0.0331875	−	0.0977673i
$113$	130.217	−	64.2161i	1.15237	−	0.568284i	0.237239	−	0.971451i	$-0.423757\pi$
$113$	130.217	−	64.2161i	1.15237	−	0.568284i	0.915126	+	0.403168i	$0.132091\pi$
$114$	−43.9837	+	8.02179i	−0.385822	+	0.0703666i
$115$	10.3852	−	38.7579i	0.0903057	−	0.337026i
$116$	−82.9625	+	55.4338i	−0.715194	+	0.477877i
$117$	−22.3502	+	49.4361i	−0.191028	+	0.422531i
$118$		−	3.64105i		−	0.0308564i
$119$	−5.68498	+	18.5177i	−0.0477729	+	0.155611i
$120$	28.5410	+	22.6326i	0.237841	+	0.188605i
$121$	64.6510	+	8.51147i	0.534306	+	0.0703427i
$122$	−39.6513	+	2.59889i	−0.325011	+	0.0213023i
$123$	−72.2052	+	8.33661i	−0.587034	+	0.0677773i
$124$	−43.5770	+	14.7924i	−0.351428	+	0.119294i
$125$	56.5858	−	84.6867i	0.452687	−	0.677493i
$126$	5.95203	+	4.25776i	0.0472383	+	0.0337918i
$127$	141.039	+	58.4203i	1.11054	+	0.460002i	0.861125	−	0.508393i	$-0.169760\pi$
$127$	141.039	+	58.4203i	1.11054	+	0.460002i	0.249419	+	0.968396i	$0.419760\pi$
$128$	−127.785	+	16.8232i	−0.998321	+	0.131431i
$129$	−62.0981	+	40.0748i	−0.481381	+	0.310658i
$130$	−8.76348	+	4.32167i	−0.0674114	+	0.0332436i
$131$	23.9965	−	27.3628i	0.183180	−	0.208876i	−0.652961	−	0.757392i	$-0.726473\pi$
$131$	23.9965	−	27.3628i	0.183180	−	0.208876i	0.836141	+	0.548515i	$0.184807\pi$
$132$	−62.8085	+	46.6220i	−0.475822	+	0.353197i
$133$	21.3423	+	10.5248i	0.160468	+	0.0791341i
$134$	−28.7114	+	11.8926i	−0.214264	+	0.0887511i
$135$	50.3852	−	34.9641i	0.373224	−	0.258993i
$136$	89.7087	−	14.5029i	0.659623	−	0.106639i
$137$	−69.5887	−	120.531i	−0.507947	−	0.879789i	−0.999958	−	0.00920030i	$-0.997071\pi$
$137$	−69.5887	−	120.531i	−0.507947	−	0.879789i	0.492011	−	0.870589i	$-0.336262\pi$
$138$	−36.6813	+	9.20422i	−0.265807	+	0.0666972i
$139$	−15.3481	+	1.00597i	−0.110418	+	0.00723719i	−0.120512	−	0.992712i	$-0.538454\pi$
$139$	−15.3481	+	1.00597i	−0.110418	+	0.00723719i	0.0100939	+	0.999949i	$0.496787\pi$
$140$	−2.33834	−	8.72681i	−0.0167024	−	0.0623344i
$141$	22.1783	+	121.604i	0.157293	+	0.862443i
$142$	16.0818	+	1.05406i	0.113252	+	0.00742293i
$143$	−8.78426	−	44.1614i	−0.0614284	−	0.308821i
$144$	−14.8041	+	90.1280i	−0.102806	+	0.625889i
$145$	−24.8458	+	59.9830i	−0.171350	+	0.413676i
$146$	−37.8731	−	43.1860i	−0.259405	−	0.295795i
$147$	43.8322	+	136.227i	0.298178	+	0.926713i
$148$	125.988	−	143.662i	0.851269	−	0.970686i
$149$	−24.0990	+	6.45730i	−0.161738	+	0.0433376i	−0.338779	−	0.940866i	$-0.610014\pi$
$149$	−24.0990	+	6.45730i	−0.161738	+	0.0433376i	0.177041	+	0.984203i	$0.443347\pi$
$150$	−42.3350	−	3.45376i	−0.282233	−	0.0230251i
$151$	−77.2051	−	59.2416i	−0.511292	−	0.392328i	0.320644	−	0.947200i	$-0.396101\pi$
$151$	−77.2051	−	59.2416i	−0.511292	−	0.392328i	−0.831936	+	0.554872i	$0.812767\pi$
$152$		−	111.635i		−	0.734444i
$153$	20.3531	−	151.640i	0.133027	−	0.991112i
$154$	−6.07352			−0.0394385
$155$	−18.2290	+	23.7565i	−0.117607	+	0.153268i
$156$	−51.9236	−	35.9053i	−0.332843	−	0.230162i
$157$	80.3780	+	299.975i	0.511962	+	1.91067i	0.398633	+	0.917111i	$0.369485\pi$
$157$	80.3780	+	299.975i	0.511962	+	1.91067i	0.113329	+	0.993557i	$0.463848\pi$
$158$	62.6712	+	54.9612i	0.396653	+	0.347856i
$159$	38.2395	+	34.6297i	0.240500	+	0.217797i
$160$	−48.8824	+	42.8687i	−0.305515	+	0.267930i
$161$	18.5965	+	7.70292i	0.115506	+	0.0478442i
$162$	−51.8836	−	25.4802i	−0.320269	−	0.157285i
$163$	−180.883	+	35.9799i	−1.10971	+	0.220736i	−0.715726	−	0.698381i	$-0.753904\pi$
$163$	−180.883	+	35.9799i	−1.10971	+	0.220736i	−0.393986	+	0.919116i	$0.628904\pi$
$164$	5.53148	−	84.3940i	0.0337285	−	0.514598i
$165$	−17.1273	+	47.9297i	−0.103802	+	0.290483i
$166$	82.9209	−	22.2186i	0.499524	−	0.133847i
$167$	4.86013	+	74.1513i	0.0291026	+	0.444020i	0.987400	+	0.158246i	$0.0505839\pi$
$167$	4.86013	+	74.1513i	0.0291026	+	0.444020i	−0.958297	+	0.285774i	$0.907749\pi$
$168$	−13.1253	+	12.7131i	−0.0781267	+	0.0756731i
$169$	−114.888	+	66.3305i	−0.679809	+	0.392488i
$170$	20.1747	−	18.7693i	0.118674	−	0.110408i
$171$	−179.908	−	54.4129i	−1.05209	−	0.318204i
$172$	−32.9094	−	79.4504i	−0.191334	−	0.461921i
$173$	98.4300	−	199.596i	0.568960	−	1.15374i	−0.402254	−	0.915528i	$-0.631773\pi$
$173$	98.4300	−	199.596i	0.568960	−	1.15374i	0.971214	−	0.238208i	$-0.0765601\pi$
$174$	60.7889	−	7.01851i	0.349361	−	0.0403363i
$175$	16.9972	+	14.9061i	0.0971268	+	0.0851779i
$176$	−33.5264	−	67.9847i	−0.190491	−	0.386277i
$177$	6.98816	−	13.6186i	0.0394811	−	0.0769410i
$178$	5.17386	+	39.2994i	0.0290667	+	0.220783i
$179$	−134.059	+	323.646i	−0.748931	+	1.80808i	−0.184033	+	0.982920i	$0.558915\pi$
$179$	−134.059	+	323.646i	−0.748931	+	1.80808i	−0.564899	+	0.825160i	$0.691085\pi$
$180$	29.5045	+	64.9756i	0.163914	+	0.360976i
$181$	95.5047	+	63.8142i	0.527650	+	0.352565i	0.790687	−	0.612221i	$-0.209724\pi$
$181$	95.5047	+	63.8142i	0.527650	+	0.352565i	−0.263036	+	0.964786i	$0.584724\pi$
$182$	−1.57559	−	4.64155i	−0.00865711	−	0.0255030i
$183$	−153.295	−	66.3810i	−0.837678	−	0.362738i
$184$	−6.17600	−	94.2275i	−0.0335652	−	0.512106i
$185$	16.2289	−	123.271i	0.0877240	−	0.666330i
$186$	27.9193	+	4.12971i	0.150104	+	0.0222027i
$187$	59.4825	+	112.185i	0.318088	+	0.599920i
$188$	−143.831			−0.765060
$189$	14.0905	+	27.3488i	0.0745527	+	0.144702i
$190$	−18.8067	−	28.1462i	−0.0989825	−	0.148138i
$191$	−225.921	−	60.5352i	−1.18283	−	0.316938i	−0.386782	−	0.922171i	$-0.626413\pi$
$191$	−225.921	−	60.5352i	−1.18283	−	0.316938i	−0.796049	+	0.605233i	$0.793080\pi$
$192$	−56.9732	−	20.3589i	−0.296735	−	0.106036i
$193$	72.6051	+	147.229i	0.376192	+	0.762842i	0.999822	−	0.0188777i	$-0.00600933\pi$
$193$	72.6051	+	147.229i	0.376192	+	0.762842i	−0.623630	+	0.781720i	$0.714343\pi$
$194$	70.9393	+	24.0806i	0.365666	+	0.124127i
$195$	−41.0723	−	0.655220i	−0.210627	−	0.00336010i
$196$	−165.090	+	21.7346i	−0.842297	+	0.110891i
$197$	137.401	−	27.3309i	0.697469	−	0.138735i	0.166393	−	0.986059i	$-0.446788\pi$
$197$	137.401	−	27.3309i	0.697469	−	0.138735i	0.531076	+	0.847324i	$0.321788\pi$
$198$	47.3248	−	7.85332i	0.239014	−	0.0396632i
$199$	37.8302	+	7.52489i	0.190101	+	0.0378135i	0.289223	−	0.957262i	$-0.406603\pi$
$199$	37.8302	+	7.52489i	0.190101	+	0.0378135i	−0.0991214	+	0.995075i	$0.531603\pi$
$200$	27.4499	−	102.444i	0.137250	−	0.512222i
$201$	−130.214	−	10.6231i	−0.647830	−	0.0528510i
$202$	9.47180	−	71.9455i	0.0468901	−	0.356166i
$203$	−28.2060	−	16.2848i	−0.138946	−	0.0802205i
$204$	169.334	+	54.9565i	0.830068	+	0.269395i
$205$	−27.5163	−	47.6596i	−0.134226	−	0.232486i
$206$	−6.51056	−	15.7179i	−0.0316047	−	0.0763004i
$207$	−154.864	−	35.9750i	−0.748134	−	0.173792i
$208$	43.2583	−	43.2583i	0.207973	−	0.207973i
$209$	147.711	−	50.1413i	0.706754	−	0.239910i
$210$	−1.16751	+	5.41645i	−0.00555958	+	0.0257926i
$211$	−123.056	−	41.7719i	−0.583204	−	0.197971i	0.0142168	−	0.999899i	$-0.495474\pi$
$211$	−123.056	−	41.7719i	−0.583204	−	0.197971i	−0.597421	+	0.801928i	$0.703808\pi$
$212$	−47.6241	+	36.5432i	−0.224642	+	0.172374i
$213$	58.1274	+	34.8077i	0.272898	+	0.163417i
$214$	−77.2277	−	88.0613i	−0.360877	−	0.411501i
$215$	−46.5269	−	31.0883i	−0.216404	−	0.144597i
$216$	85.8334	−	116.032i	0.397377	−	0.537184i
$217$	−10.6219	−	10.6219i	−0.0489487	−	0.0489487i
$218$	−23.3778	−	11.5287i	−0.107238	−	0.0528838i
$219$	−58.7705	−	234.216i	−0.268358	−	1.06948i
$220$	−51.2896	−	29.6121i	−0.233135	−	0.134600i
$221$	−70.3038	+	74.5611i	−0.318117	+	0.337381i
$222$	−108.968	+	43.1129i	−0.490848	+	0.194202i
$223$	−222.741	+	290.282i	−0.998841	+	1.30171i	−0.0457746	+	0.998952i	$0.514576\pi$
$223$	−222.741	+	290.282i	−0.998841	+	1.30171i	−0.953066	+	0.302763i	$0.902091\pi$
$224$	−18.1203	−	27.1189i	−0.0808942	−	0.121067i
$225$	−151.716	−	94.1703i	−0.674294	−	0.418535i
$226$	20.2133	−	101.619i	0.0894392	−	0.449641i
$227$	190.244	+	12.4693i	0.838081	+	0.0549307i	0.478397	−	0.878144i	$-0.341218\pi$
$227$	190.244	+	12.4693i	0.838081	+	0.0549307i	0.359684	+	0.933074i	$0.382885\pi$
$228$	99.8463	−	194.581i	0.437922	−	0.853425i
$229$	−14.0065	+	10.7476i	−0.0611637	+	0.0469326i	−0.638891	−	0.769297i	$-0.720606\pi$
$229$	−14.0065	+	10.7476i	−0.0611637	+	0.0469326i	0.577727	+	0.816230i	$0.303940\pi$
$230$	−17.4312	−	22.7168i	−0.0757877	−	0.0987685i
$231$	−22.7167	−	11.6567i	−0.0983406	−	0.0504620i
$232$	−9.99316	+	152.466i	−0.0430740	+	0.657182i
$233$	298.526	+	59.3806i	1.28123	+	0.254852i	0.788340	−	0.615240i	$-0.210941\pi$
$233$	298.526	+	59.3806i	1.28123	+	0.254852i	0.492889	+	0.870092i	$0.335941\pi$
$234$	18.2787	+	34.1296i	0.0781142	+	0.145853i
$235$	−77.8174	+	51.9959i	−0.331138	+	0.221259i
$236$	14.1303	+	10.8425i	0.0598740	+	0.0459430i
$237$	128.923	+	325.853i	0.543977	+	1.37491i
$238$	8.01405	+	11.2630i	0.0336725	+	0.0473234i
$239$	−117.060	+	202.754i	−0.489792	+	0.848344i	−0.999931	−	0.0117474i	$-0.996261\pi$
$239$	−117.060	+	202.754i	−0.489792	+	0.848344i	0.510139	+	0.860092i	$0.329594\pi$
$240$	−67.0744	+	16.8306i	−0.279477	+	0.0701274i
$241$	208.765	−	423.334i	0.866246	−	1.75657i	0.251481	−	0.967862i	$-0.419082\pi$
$241$	208.765	−	423.334i	0.866246	−	1.75657i	0.614765	−	0.788711i	$-0.289251\pi$
$242$	32.9044	−	32.9044i	0.135969	−	0.135969i
$243$	−145.156	−	194.882i	−0.597349	−	0.801982i
$244$	107.990	−	161.619i	0.442583	−	0.662373i
$245$	−81.4621	+	71.4403i	−0.332498	+	0.291593i
$246$	−26.6476	+	44.5004i	−0.108324	+	0.180896i
$247$	76.6386	+	99.8774i	0.310278	+	0.404362i
$248$	−22.6521	+	66.7308i	−0.0913389	+	0.269076i
$249$	352.791	+	76.0438i	1.41683	+	0.305397i
$250$	−23.3631	−	68.8255i	−0.0934524	−	0.275302i
$251$	204.162	+	204.162i	0.813395	+	0.813395i	0.985141	−	0.171746i	$-0.0549409\pi$
$251$	204.162	+	204.162i	0.813395	+	0.813395i	−0.171746	+	0.985141i	$0.554941\pi$
$252$	−34.2479	+	10.4197i	−0.135904	+	0.0413482i
$253$	121.904	−	50.4943i	0.481834	−	0.199582i
$254$	94.3447	−	54.4699i	0.371436	−	0.214448i
$255$	111.482	−	31.4820i	0.437185	−	0.123459i
$256$	−5.65361	+	9.79234i	−0.0220844	+	0.0382513i
$257$	−57.5968	−	7.58276i	−0.224112	−	0.0295049i	0.0176339	−	0.999845i	$-0.494387\pi$
$257$	−57.5968	−	7.58276i	−0.224112	−	0.0295049i	−0.241746	+	0.970340i	$0.577720\pi$
$258$	−4.28842	+	52.5660i	−0.0166218	+	0.203744i
$259$	60.2470	+	16.1431i	0.232614	+	0.0623287i
$260$	9.32478	−	46.8788i	0.0358645	−	0.180303i
$261$	240.838	+	90.4190i	0.922751	+	0.346433i
$262$	−5.06680	−	25.4725i	−0.0193389	−	0.0972234i
$263$	55.1921	+	419.225i	0.209856	+	1.59401i	0.694626	+	0.719371i	$0.255570\pi$
$263$	55.1921	+	419.225i	0.209856	+	1.59401i	−0.484770	+	0.874642i	$0.661097\pi$
$264$	−1.91062	+	119.767i	−0.00723720	+	0.453663i
$265$	−12.5556	+	36.9875i	−0.0473795	+	0.139575i
$266$	15.2301	−	7.51066i	0.0572560	−	0.0282355i
$267$	−56.0744	+	156.921i	−0.210017	+	0.587718i
$268$	39.3452	−	146.838i	0.146811	−	0.547904i
$269$	−7.13264	+	4.76588i	−0.0265154	+	0.0177170i	−0.568757	−	0.822505i	$-0.692576\pi$
$269$	−7.13264	+	4.76588i	−0.0265154	+	0.0177170i	0.542242	+	0.840222i	$0.317576\pi$
$270$	2.09353	−	43.7145i	0.00775382	−	0.161906i
$271$		−	2.78945i		−	0.0102932i	−0.999987	−	0.00514658i	$-0.998362\pi$
$271$		−	2.78945i		−	0.0102932i	0.999987	−	0.00514658i	$-0.00163822\pi$
$272$	−81.8352	+	151.879i	−0.300865	+	0.558378i
$273$	3.01522	−	20.3847i	0.0110448	−	0.0746692i
$274$	−98.4690	−	12.9637i	−0.359376	−	0.0473128i
$275$	147.880	−	9.69254i	0.537744	−	0.0352456i
$276$	73.5119	−	169.763i	0.266348	−	0.615082i
$277$	358.996	−	121.863i	1.29602	−	0.439938i	0.413622	−	0.910449i	$-0.364264\pi$
$277$	358.996	−	121.863i	1.29602	−	0.439938i	0.882394	+	0.470511i	$0.155930\pi$
$278$	−6.09800	+	9.12631i	−0.0219353	+	0.0328284i
$279$	96.4999	+	69.0309i	0.345878	+	0.247422i
$280$	−12.7819	−	5.29444i	−0.0456497	−	0.0189087i
$281$	−143.223	+	18.8557i	−0.509692	+	0.0671022i	−0.380986	−	0.924581i	$-0.624415\pi$
$281$	−143.223	+	18.8557i	−0.509692	+	0.0671022i	−0.128705	+	0.991683i	$0.541082\pi$
$282$	78.4807	+	40.2712i	0.278300	+	0.142806i
$283$	−298.412	+	147.161i	−1.05446	+	0.520002i	−0.885027	−	0.465540i	$-0.845860\pi$
$283$	−298.412	+	147.161i	−1.05446	+	0.520002i	−0.169433	+	0.985542i	$0.554194\pi$
$284$	−51.9799	+	59.2717i	−0.183028	+	0.208703i
$285$	−16.3221	−	141.370i	−0.0572707	−	0.496034i
$286$	−28.8179	−	14.2114i	−0.100762	−	0.0496903i
$287$	25.5055	−	10.5647i	0.0888694	−	0.0368109i
$288$	176.259	+	187.880i	0.612010	+	0.652361i
$289$	129.552	−	258.335i	0.448278	−	0.893894i
$290$	23.1657	+	40.1241i	0.0798817	+	0.138359i
$291$	219.116	+	226.220i	0.752974	+	0.777388i
$292$	280.378	−	18.3769i	0.960199	−	0.0629347i
$293$	−8.15547	−	30.4366i	−0.0278344	−	0.103879i	0.950611	−	0.310384i	$-0.100458\pi$
$293$	−8.15547	−	30.4366i	−0.0278344	−	0.103879i	−0.978446	+	0.206505i	$0.933791\pi$
$294$	96.1660	+	34.3642i	0.327095	+	0.116885i
$295$	11.5646	+	0.757983i	0.0392020	+	0.00256943i
$296$	−57.0847	−	286.984i	−0.192854	−	0.969541i
$297$	192.081	+	61.4554i	0.646736	+	0.206921i
$298$	−6.81329	+	16.4487i	−0.0228634	+	0.0551971i
$299$	70.2134	+	80.0631i	0.234828	+	0.267770i
$300$	139.471	−	154.010i	0.464904	−	0.513366i
$301$	18.5085	−	21.1048i	0.0614899	−	0.0701158i
$302$	−67.0789	+	17.9737i	−0.222116	+	0.0595157i
$303$	173.510	−	250.917i	0.572640	−	0.828110i
$304$	168.143	+	129.021i	0.553102	+	0.424410i
$305$		−	126.480i		−	0.414689i
$306$	−77.0088	−	77.3984i	−0.251663	−	0.252936i
$307$	−195.690			−0.637428			−0.318714	−	0.947851i	$-0.603251\pi$
$307$	−195.690			−0.637428			−0.318714	+	0.947851i	$0.603251\pi$
$308$	18.0861	−	23.5703i	0.0587211	−	0.0765268i
$309$	5.81553	−	71.2848i	0.0188205	−	0.230695i
$310$	5.53064	+	20.6406i	0.0178408	+	0.0665827i
$311$	−61.2445	−	53.7100i	−0.196928	−	0.172701i	0.555203	−	0.831715i	$-0.312641\pi$
$311$	−61.2445	−	53.7100i	−0.196928	−	0.172701i	−0.752131	+	0.659014i	$0.770974\pi$
$312$	−92.0247	+	29.6098i	−0.294951	+	0.0949031i
$313$	−59.6180	+	52.2836i	−0.190473	+	0.167040i	−0.749271	−	0.662263i	$-0.769596\pi$
$313$	−59.6180	+	52.2836i	−0.190473	+	0.167040i	0.558798	+	0.829304i	$0.311263\pi$
$314$	204.748	+	84.8093i	0.652063	+	0.270093i
$315$	−14.7624	+	18.0183i	−0.0468649	+	0.0572008i
$316$	−399.921	+	79.5491i	−1.26557	+	0.251738i
$317$	−32.5153	+	496.087i	−0.102572	+	1.56494i	0.567955	+	0.823060i	$0.307735\pi$
$317$	−32.5153	+	496.087i	−0.102572	+	1.56494i	−0.670527	+	0.741885i	$0.733932\pi$
$318$	36.2175	−	6.60538i	0.113892	−	0.0207716i
$319$	−206.225	+	55.2579i	−0.646475	+	0.173222i
$320$	−2.99599	−	45.7099i	−0.00936246	−	0.142844i
$321$	−119.840	−	477.594i	−0.373333	−	1.48783i
$322$	12.4397	−	7.18205i	0.0386325	−	0.0223045i
$323$	−287.890	−	207.760i	−0.891301	−	0.643220i
$324$	253.386	−	125.474i	0.782056	−	0.387267i
$325$	45.7702	+	110.499i	0.140831	+	0.339997i
$326$	−58.2093	+	118.037i	−0.178556	+	0.362076i
$327$	−65.3130	−	87.9888i	−0.199734	−	0.269079i
$328$	−97.3725	−	85.3934i	−0.296868	−	0.260346i
$329$	−20.7652	−	42.1076i	−0.0631160	−	0.127987i
$330$	19.6948	+	30.5182i	0.0596813	+	0.0924794i
$331$	−70.1778	−	533.053i	−0.212018	−	1.61043i	−0.684446	−	0.729064i	$-0.739956\pi$
$331$	−70.1778	−	533.053i	−0.212018	−	1.61043i	0.472428	−	0.881369i	$-0.343378\pi$
$332$	−160.700	+	387.965i	−0.484037	+	1.16857i
$333$	−490.317	−	47.8851i	−1.47242	−	0.143799i
$334$	44.0919	+	29.4612i	0.132012	+	0.0882073i
$335$	−31.7960	−	93.6679i	−0.0949133	−	0.279606i
$336$	−3.97888	−	34.4619i	−0.0118419	−	0.102565i
$337$	−10.3887	−	158.501i	−0.0308270	−	0.470329i	−0.985166	−	0.171603i	$-0.945105\pi$
$337$	−10.3887	−	158.501i	−0.0308270	−	0.470329i	0.954339	−	0.298725i	$-0.0965614\pi$
$338$	−12.3567	+	93.8586i	−0.0365584	+	0.277688i
$339$	270.637	−	341.288i	0.798340	−	1.00675i
$340$	12.7632	+	134.187i	0.0375389	+	0.394667i
$341$	−98.4697			−0.288767
$342$	−108.961	+	78.2161i	−0.318600	+	0.228702i
$343$	−61.2165	−	91.6170i	−0.178474	−	0.267105i
$344$	−127.202	−	34.0836i	−0.369773	−	0.0990803i
$345$	−21.5979	−	118.422i	−0.0626027	−	0.343253i
$346$	−70.2409	−	142.435i	−0.203008	−	0.411660i
$347$	−177.329	−	60.1950i	−0.511034	−	0.173473i	0.0539988	−	0.998541i	$-0.482803\pi$
$347$	−177.329	−	60.1950i	−0.511034	−	0.173473i	−0.565033	+	0.825068i	$0.691137\pi$
$348$	−153.783	+	256.811i	−0.441906	+	0.737963i
$349$	338.428	−	44.5549i	0.969708	−	0.127664i	0.371001	−	0.928632i	$-0.379015\pi$
$349$	338.428	−	44.5549i	0.969708	−	0.127664i	0.598707	+	0.800968i	$0.295681\pi$
$350$	15.8230	−	3.14739i	0.0452085	−	0.00899254i
$351$	2.86370	+	162.736i	0.00815869	+	0.463635i
$352$	−209.695	−	41.7109i	−0.595723	−	0.118497i
$353$	−54.9582	+	205.107i	−0.155689	+	0.581039i	0.843356	+	0.537355i	$0.180576\pi$
$353$	−54.9582	+	205.107i	−0.155689	+	0.581039i	−0.999045	+	0.0436845i	$0.986090\pi$
$354$	−4.67431	−	9.87250i	−0.0132043	−	0.0278884i
$355$	−6.69571	+	50.8590i	−0.0188612	+	0.143265i
$356$	−167.921	−	96.9492i	−0.471688	−	0.272329i
$357$	8.35812	+	57.5078i	0.0234121	+	0.161086i
$358$	124.994	+	216.495i	0.349144	+	0.604736i
$359$	62.1499	+	150.043i	0.173119	+	0.417947i	0.986495	−	0.163792i	$-0.0523725\pi$
$359$	62.1499	+	150.043i	0.173119	+	0.417947i	−0.813375	+	0.581739i	$0.802372\pi$
$360$	106.442	+	24.7267i	0.295673	+	0.0686852i
$361$	−53.1332	+	53.1332i	−0.147183	+	0.147183i
$362$	77.6174	−	26.3476i	0.214413	−	0.0727833i
$363$	186.224	−	59.9193i	0.513014	−	0.165067i
$364$	22.7049	+	7.70728i	0.0623761	+	0.0211738i
$365$	145.050	−	111.301i	0.397398	−	0.304934i
$366$	−104.176	+	57.9503i	−0.284633	+	0.158334i
$367$	−292.392	−	333.409i	−0.796707	−	0.908470i	0.200757	−	0.979641i	$-0.435660\pi$
$367$	−292.392	−	333.409i	−0.796707	−	0.908470i	−0.997464	+	0.0711707i	$0.977327\pi$
$368$	149.061	+	99.5995i	0.405058	+	0.270651i
$369$	−185.078	+	115.300i	−0.501566	+	0.312466i
$370$	−62.7393	−	62.7393i	−0.169566	−	0.169566i
$371$	−17.5738	−	8.66646i	−0.0473688	−	0.0233597i
$372$	−99.1663	+	96.0520i	−0.266576	+	0.258204i
$373$	−572.285	−	330.409i	−1.53428	−	0.885815i	−0.999158	−	0.0410382i	$-0.986933\pi$
$373$	−572.285	−	330.409i	−1.53428	−	0.885815i	−0.535119	−	0.844777i	$-0.679733\pi$
$374$	89.3536	+	15.0595i	0.238913	+	0.0402661i
$375$	44.7101	−	302.267i	0.119227	−	0.806044i
$376$	−134.082	+	174.739i	−0.356600	+	0.464730i
$377$	−95.7286	−	143.268i	−0.253922	−	0.380021i
$378$	21.6046	+	3.90358i	0.0571550	+	0.0103269i
$379$	−87.5798	+	440.293i	−0.231081	+	1.16172i	0.674737	+	0.738058i	$0.264257\pi$
$379$	−87.5798	+	440.293i	−0.231081	+	1.16172i	−0.905819	+	0.423666i	$0.860743\pi$
$380$	165.234	+	10.8300i	0.434826	+	0.0285000i
$381$	457.418	−	22.6599i	1.20057	−	0.0594749i
$382$	−132.416	+	101.607i	−0.346639	+	0.265986i
$383$	207.612	+	270.565i	0.542068	+	0.706436i	0.981419	−	0.191879i	$-0.0614582\pi$
$383$	207.612	+	270.565i	0.542068	+	0.706436i	−0.439351	+	0.898316i	$0.644792\pi$
$384$	−324.884	+	209.663i	−0.846053	+	0.545997i
$385$	1.26437	−	19.2905i	0.00328407	−	0.0501053i
$386$	114.894	+	22.8539i	0.297653	+	0.0592069i
$387$	−116.928	+	188.381i	−0.302140	+	0.486772i
$388$	−304.700	+	203.594i	−0.785309	+	0.524727i
$389$	−103.960	−	79.7713i	−0.267249	−	0.205068i	0.466440	−	0.884553i	$-0.345536\pi$
$389$	−103.960	−	79.7713i	−0.267249	−	0.205068i	−0.733689	+	0.679485i	$0.762203\pi$
$390$	−18.2136	+	22.9683i	−0.0467015	+	0.0588932i
$391$	−254.492	−	159.436i	−0.650874	−	0.407765i
$392$	−127.495	+	220.827i	−0.325241	+	0.563334i
$393$	29.9374	−	104.999i	0.0761765	−	0.267173i
$394$	44.2167	−	89.6625i	0.112225	−	0.227570i
$395$	−187.613	+	187.613i	−0.474968	+	0.474968i
$396$	−110.449	+	207.045i	−0.278912	+	0.522841i
$397$	−303.849	+	454.742i	−0.765362	+	1.14545i	0.220087	+	0.975480i	$0.429366\pi$
$397$	−303.849	+	454.742i	−0.765362	+	1.14545i	−0.985450	+	0.169966i	$0.945634\pi$
$398$	20.6944	−	18.1485i	0.0519959	−	0.0455992i
$399$	71.3798	+	1.13871i	0.178897	+	0.00285391i
$400$	122.575	+	159.743i	0.306437	+	0.399357i
$401$	191.412	−	563.881i	0.477336	−	1.40619i	−0.395632	−	0.918409i	$-0.629474\pi$
$401$	191.412	−	563.881i	0.477336	−	1.40619i	0.872968	−	0.487778i	$-0.162192\pi$
$402$	−62.5817	+	69.1053i	−0.155676	+	0.171904i
$403$	−25.5450	−	75.2532i	−0.0633871	−	0.186732i
$404$	251.002	+	251.002i	0.621292	+	0.621292i
$405$	91.7303	−	159.486i	0.226495	−	0.393794i
$406$	−21.4728	+	8.89434i	−0.0528888	+	0.0219072i
$407$	354.086	−	204.432i	0.869991	−	0.502289i
$408$	224.621	−	154.490i	0.550543	−	0.378652i
$409$	−40.7262	+	70.5398i	−0.0995750	+	0.172469i	−0.911509	−	0.411281i	$-0.865082\pi$
$409$	−40.7262	+	70.5398i	−0.0995750	+	0.172469i	0.811934	+	0.583749i	$0.198415\pi$
$410$	−38.9359	−	5.12601i	−0.0949657	−	0.0125025i
$411$	−343.421	−	237.476i	−0.835574	−	0.577802i
$412$	80.3859	+	21.5393i	0.195111	+	0.0522799i
$413$	−1.13422	+	5.70209i	−0.00274629	+	0.0138065i
$414$	−87.6431	+	72.0474i	−0.211698	+	0.174028i
$415$	53.3077	+	267.996i	0.128452	+	0.645774i
$416$	−22.5224	−	171.075i	−0.0541405	−	0.411238i
$417$	−40.3241	+	22.4312i	−0.0967004	+	0.0537919i
$418$	35.7815	−	105.409i	0.0856016	−	0.252174i
$419$	−157.113	+	77.4796i	−0.374972	+	0.184916i	−0.620003	−	0.784600i	$-0.712869\pi$
$419$	−157.113	+	77.4796i	−0.374972	+	0.184916i	0.245031	+	0.969515i	$0.421202\pi$
$420$	−17.5436	−	20.6603i	−0.0417704	−	0.0491912i
$421$	155.501	−	580.339i	0.369362	−	1.37848i	−0.492049	−	0.870568i	$-0.663752\pi$
$421$	155.501	−	580.339i	0.369362	−	1.37848i	0.861410	−	0.507909i	$-0.169582\pi$
$422$	−77.1071	+	51.5213i	−0.182718	+	0.122088i
$423$	216.249	+	301.251i	0.511226	+	0.712178i
$424$			91.9239i			0.216802i
$425$	−213.102	−	261.444i	−0.501417	−	0.615162i
$426$	44.9580	−	17.7875i	0.105535	−	0.0417546i
$427$	62.9058	+	8.28170i	0.147320	+	0.0193951i
$428$	571.723	−	37.4727i	1.33580	−	0.0875531i
$429$	−80.5116	−	108.464i	−0.187673	−	0.252830i
$430$	−37.8128	+	12.8357i	−0.0879367	+	0.0298505i
$431$	114.651	−	171.588i	0.266012	−	0.398116i	−0.674284	−	0.738472i	$-0.735548\pi$
$431$	114.651	−	171.588i	0.266012	−	0.398116i	0.940297	+	0.340356i	$0.110548\pi$
$432$	75.5640	+	263.382i	0.174917	+	0.609680i
$433$	330.769	+	137.009i	0.763900	+	0.316418i	0.730399	−	0.683021i	$-0.239334\pi$
$433$	330.769	+	137.009i	0.763900	+	0.316418i	0.0335014	+	0.999439i	$0.489334\pi$
$434$	−10.6279	+	1.39919i	−0.0244882	+	0.00322393i
$435$	9.63712	+	194.537i	0.0221543	+	0.447211i
$436$	114.357	−	56.3944i	0.262286	−	0.129345i
$437$	−243.247	+	277.370i	−0.556629	+	0.634714i
$438$	−158.132	−	68.4756i	−0.361032	−	0.156337i
$439$	206.500	+	101.835i	0.470388	+	0.231970i	0.662004	−	0.749500i	$-0.269706\pi$
$439$	206.500	+	101.835i	0.470388	+	0.231970i	−0.191616	+	0.981470i	$0.561373\pi$
$440$	−83.7882	+	34.7062i	−0.190428	+	0.0788777i
$441$	293.734	+	313.100i	0.666063	+	0.709978i
$442$	11.6712	+	72.1931i	0.0264055	+	0.163333i
$443$	−371.999	−	644.321i	−0.839727	−	1.45445i	−0.890123	−	0.455720i	$-0.849382\pi$
$443$	−371.999	−	644.321i	−0.839727	−	1.45445i	0.0503961	−	0.998729i	$-0.483952\pi$
$444$	157.179	−	551.270i	0.354006	−	1.24160i
$445$	−125.898	+	8.25182i	−0.282918	+	0.0185434i
$446$	67.5792	+	252.209i	0.151523	+	0.565491i
$447$	−57.0532	+	48.4464i	−0.127636	+	0.108381i
$448$	22.9303	+	1.50293i	0.0511837	+	0.00335476i
$449$	−62.9246	−	316.343i	−0.140144	−	0.704551i	−0.985409	−	0.170204i	$-0.945557\pi$
$449$	−62.9246	−	316.343i	−0.140144	−	0.704551i	0.845265	−	0.534347i	$-0.179443\pi$
$450$	−119.223	+	44.9842i	−0.264939	+	0.0999648i
$451$	69.2540	−	167.194i	0.153557	−	0.370719i
$452$	334.172	+	381.051i	0.739320	+	0.843033i
$453$	−285.390	−	61.5156i	−0.630001	−	0.135796i
$454$	89.7054	−	102.289i	0.197589	−	0.225307i
$455$	15.0703	−	4.03808i	0.0331216	−	0.00887491i
$456$	−143.315	−	302.693i	−0.314288	−	0.663800i
$457$	454.457	+	348.717i	0.994435	+	0.763057i	0.971587	−	0.236682i	$-0.0760599\pi$
$457$	454.457	+	348.717i	0.994435	+	0.763057i	0.0228482	+	0.999739i	$0.492727\pi$
$458$			12.5987i			0.0275081i
$459$	−139.486	−	437.292i	−0.303892	−	0.952707i
$460$	140.067			0.304494
$461$	104.273	−	135.891i	0.226189	−	0.294775i	−0.666448	−	0.745551i	$-0.732186\pi$
$461$	104.273	−	135.891i	0.226189	−	0.294775i	0.892637	+	0.450777i	$0.148853\pi$
$462$	−16.4680	+	7.79707i	−0.0356450	+	0.0168768i
$463$	−158.572	−	591.798i	−0.342488	−	1.27818i	−0.895520	−	0.445021i	$-0.853196\pi$
$463$	−158.572	−	591.798i	−0.342488	−	1.27818i	0.553032	−	0.833160i	$-0.313471\pi$
$464$	−218.092	−	191.261i	−0.470025	−	0.412201i
$465$	−18.9288	+	87.8165i	−0.0407071	+	0.188853i
$466$	163.304	−	143.214i	0.350438	−	0.307326i
$467$	−419.399	−	173.721i	−0.898070	−	0.371993i	−0.114592	−	0.993413i	$-0.536556\pi$
$467$	−419.399	−	173.721i	−0.898070	−	0.371993i	−0.783478	+	0.621420i	$0.786556\pi$
$468$	−186.882	−	30.6966i	−0.399321	−	0.0655910i
$469$	48.6683	−	9.68072i	0.103770	−	0.0206412i
$470$	−4.36809	+	66.6442i	−0.00929381	+	0.141796i
$471$	603.042	+	710.176i	1.28034	+	1.50781i
$472$	26.3449	−	7.05909i	0.0558155	−	0.0149557i
$473$	−12.0349	−	183.617i	−0.0254438	−	0.388197i
$474$	240.487	+	68.5679i	0.507357	+	0.144658i
$475$	−358.840	+	207.176i	−0.755452	+	0.436161i
$476$	−67.5743	−	2.43844i	−0.141963	−	0.00512277i
$477$	148.141	+	44.8052i	0.310568	+	0.0939312i
$478$	63.9355	+	154.354i	0.133756	+	0.322916i
$479$	−330.102	+	669.381i	−0.689149	+	1.39746i	0.217707	+	0.976014i	$0.430142\pi$
$479$	−330.102	+	669.381i	−0.689149	+	1.39746i	−0.906856	+	0.421441i	$0.861524\pi$
$480$	−77.5078	+	178.990i	−0.161475	+	0.372896i
$481$	248.089	+	217.568i	0.515778	+	0.452325i
$482$	−148.978	−	302.097i	−0.309082	−	0.626756i
$483$	60.3122	−	2.98779i	0.124870	−	0.00618591i
$484$	29.7115	+	225.681i	0.0613873	+	0.466283i
$485$	−91.2521	+	220.302i	−0.188149	+	0.454231i
$486$	−173.390	−	2.48096i	−0.356770	−	0.00510485i
$487$	348.753	+	233.029i	0.716125	+	0.478500i	0.859478	−	0.511172i	$-0.170788\pi$
$487$	348.753	+	233.029i	0.716125	+	0.478500i	−0.143353	+	0.989672i	$0.545788\pi$
$488$	−95.6783	−	281.859i	−0.196062	−	0.577581i
$489$	−444.264	+	329.772i	−0.908515	+	0.674379i
$490$	5.05698	+	77.1546i	0.0103204	+	0.157458i
$491$	5.23113	−	39.7344i	0.0106540	−	0.0809254i	−0.985292	−	0.170880i	$-0.945339\pi$
$491$	5.23113	−	39.7344i	0.0106540	−	0.0809254i	0.995946	+	0.0899548i	$0.0286722\pi$
$492$	−93.3451	−	235.931i	−0.189726	−	0.479534i
$493$	374.588	+	309.519i	0.759814	+	0.627828i
$494$	89.8386			0.181860
$495$	15.0915	+	151.946i	0.0304879	+	0.306962i
$496$	−74.3288	−	111.241i	−0.149856	−	0.224276i
$497$	−24.8566	−	6.66031i	−0.0500133	−	0.0134010i
$498$	196.311	−	166.697i	0.394200	−	0.334732i
$499$	−278.391	−	564.521i	−0.557898	−	1.13130i	−0.974950	−	0.222422i	$-0.928604\pi$
$499$	−278.391	−	564.521i	−0.557898	−	1.13130i	0.417053	−	0.908882i	$-0.363063\pi$
$500$	336.671	+	114.285i	0.673343	+	0.228569i
$501$	108.372	+	194.817i	0.216311	+	0.388857i
$502$	204.278	−	26.8937i	0.406928	−	0.0535731i
$503$	944.979	−	187.968i	1.87869	−	0.373694i	0.883232	−	0.468936i	$-0.155362\pi$
$503$	944.979	−	187.968i	1.87869	−	0.373694i	0.995454	+	0.0952420i	$0.0303625\pi$
$504$	−19.2676	+	51.3207i	−0.0382294	+	0.101827i
$505$	226.539	+	45.0614i	0.448592	+	0.0892305i
$506$	24.3703	−	90.9514i	0.0481627	−	0.179746i
$507$	−226.358	+	327.342i	−0.446465	+	0.645644i
$508$	−69.5571	+	528.339i	−0.136923	+	1.04004i
$509$	−454.759	−	262.555i	−0.893436	−	0.515825i	−0.0183710	−	0.999831i	$-0.505848\pi$
$509$	−454.759	−	262.555i	−0.893436	−	0.515825i	−0.875065	+	0.484006i	$0.839181\pi$
$510$	30.6067	−	76.7918i	0.0600131	−	0.150572i
$511$	45.8586	+	79.4294i	0.0897429	+	0.155439i
$512$	−194.205	−	468.852i	−0.379306	−	0.915727i
$513$	−557.663	+	83.4243i	−1.08706	+	0.162620i
$514$	−29.3141	+	29.3141i	−0.0570314	+	0.0570314i
$515$	51.2780	−	17.4065i	0.0995689	−	0.0337991i
$516$	−191.229	−	173.177i	−0.370599	−	0.335614i
$517$	−291.430	−	98.9271i	−0.563694	−	0.191348i
$518$	35.3119	−	27.0957i	0.0681696	−	0.0523084i
$519$	10.6494	−	667.556i	0.0205191	−	1.28624i
$520$	−48.2597	−	55.0297i	−0.0928072	−	0.105826i
$521$	−671.218	−	448.494i	−1.28833	−	0.860832i	−0.292879	−	0.956149i	$-0.594613\pi$
$521$	−671.218	−	448.494i	−1.28833	−	0.860832i	−0.995447	+	0.0953174i	$0.969613\pi$
$522$	155.815	−	97.0698i	0.298497	−	0.185958i
$523$	357.329	+	357.329i	0.683229	+	0.683229i	0.960726	−	0.277497i	$-0.0895049\pi$
$523$	357.329	+	357.329i	0.683229	+	0.683229i	−0.277497	+	0.960726i	$0.589505\pi$
$524$	113.943	+	56.1902i	0.217448	+	0.107233i
$525$	65.2231	+	18.5965i	0.124234	+	0.0354218i
$526$	261.320	+	150.873i	0.496806	+	0.286831i
$527$	129.931	+	182.606i	0.246549	+	0.346501i
$528$	−178.182	−	141.296i	−0.337466	−	0.267606i
$529$	132.064	−	172.109i	0.249648	−	0.325347i
$530$	15.4860	+	23.1764i	0.0292188	+	0.0437290i
$531$	1.46475	−	45.8972i	0.00275848	−	0.0864353i
$532$	−16.2056	+	81.4710i	−0.0304616	+	0.153141i
$533$	145.740	+	9.55230i	0.273433	+	0.0179218i
$534$	64.4804	+	99.9159i	0.120750	+	0.187108i
$535$	295.774	−	226.956i	0.552849	−	0.424216i
$536$	−141.714	−	184.685i	−0.264391	−	0.344561i
$537$	51.9984	+	1049.65i	0.0968313	+	1.95466i
$538$	−0.400373	+	6.10852i	−0.000744189	+	0.0113541i
$539$	−349.454	−	69.5107i	−0.648338	−	0.128962i
$540$	163.414	+	138.300i	0.302618	+	0.256112i
$541$	664.116	−	443.748i	1.22757	−	0.820237i	0.239004	−	0.971019i	$-0.423179\pi$
$541$	664.116	−	443.748i	1.22757	−	0.820237i	0.988567	+	0.150782i	$0.0481792\pi$
$542$	−1.57924	−	1.21179i	−0.00291372	−	0.00223578i
$543$	340.879	+	50.4214i	0.627769	+	0.0928571i
$544$	199.343	+	443.903i	0.366440	+	0.815999i
$545$	41.4837	−	71.8519i	0.0761169	−	0.131838i
$546$	−10.2309	−	10.5626i	−0.0187378	−	0.0193454i
$547$	198.397	−	402.310i	0.362700	−	0.735484i	−0.636664	−	0.771142i	$-0.719686\pi$
$547$	198.397	−	402.310i	0.362700	−	0.735484i	0.999364	+	0.0356580i	$0.0113527\pi$
$548$	343.537	−	343.537i	0.626892	−	0.626892i
$549$	−500.869	+	16.8089i	−0.912330	+	0.0306173i
$550$	58.7544	−	87.9322i	0.106826	−	0.159877i
$551$	448.802	−	393.589i	0.814523	−	0.714318i
$552$	−137.713	−	247.564i	−0.249480	−	0.448485i
$553$	−81.0257	−	105.595i	−0.146520	−	0.190949i
$554$	86.9629	−	256.184i	0.156973	−	0.462427i
$555$	−114.249	−	355.076i	−0.205854	−	0.639777i
$556$	−17.2586	−	50.8421i	−0.0310406	−	0.0914427i
$557$	686.583	+	686.583i	1.23264	+	1.23264i	0.962944	+	0.269700i	$0.0869245\pi$
$557$	686.583	+	686.583i	1.23264	+	1.23264i	0.269700	+	0.962944i	$0.413076\pi$
$558$	81.0031	−	24.6447i	0.145167	−	0.0441662i
$559$	137.203	−	56.8313i	0.245444	−	0.101666i
$560$	22.7468	−	13.1329i	0.0406193	−	0.0234516i
$561$	305.304	+	227.820i	0.544214	+	0.406097i
$562$	−51.5440	+	89.2768i	−0.0917152	+	0.158855i
$563$	920.164	+	121.142i	1.63439	+	0.215172i	0.891105	−	0.453798i	$-0.149931\pi$
$563$	920.164	+	121.142i	1.63439	+	0.215172i	0.743289	+	0.668970i	$0.233265\pi$
$564$	−389.990	+	184.648i	−0.691471	+	0.327389i
$565$	318.550	+	85.3553i	0.563806	+	0.151071i
$566$	−46.3216	+	232.875i	−0.0818403	+	0.411439i
$567$	73.3152	+	56.0655i	0.129304	+	0.0988810i
$568$	23.5519	+	118.404i	0.0414647	+	0.208457i
$569$	−58.5089	−	444.419i	−0.102828	−	0.781053i	−0.962705	−	0.270553i	$-0.912794\pi$
$569$	−58.5089	−	444.419i	−0.102828	−	0.781053i	0.859878	−	0.510500i	$-0.170540\pi$
$570$	−87.1267	−	52.1731i	−0.152854	−	0.0915317i
$571$	247.715	−	729.744i	0.433826	−	1.27801i	−0.481907	−	0.876222i	$-0.660056\pi$
$571$	247.715	−	729.744i	0.433826	−	1.27801i	0.915733	−	0.401788i	$-0.131611\pi$
$572$	140.968	−	69.5176i	0.246447	−	0.121534i
$573$	−690.284	+	125.895i	−1.20468	+	0.219711i
$574$	5.09891	−	19.0294i	0.00888312	−	0.0331523i
$575$	−291.422	+	194.722i	−0.506822	+	0.338647i
$576$	−180.616	+	17.9390i	−0.313569	+	0.0311441i
$577$			843.017i			1.46104i	0.682894	+	0.730518i	$0.260721\pi$
$577$			843.017i			1.46104i	−0.682894	+	0.730518i	$0.739279\pi$
$578$	−89.9756	−	185.572i	−0.155667	−	0.321058i
$579$	385.873	+	305.992i	0.666448	+	0.528484i
$580$	−224.699	−	29.5822i	−0.387412	−	0.0510037i
$581$	−136.780	+	8.96503i	−0.235422	+	0.0154304i
$582$	223.262	−	25.7772i	0.383612	−	0.0442907i
$583$	−121.630	+	41.2878i	−0.208628	+	0.0708196i
$584$	239.047	−	357.758i	0.409326	−	0.612600i
$585$	−112.206	+	50.9512i	−0.191806	+	0.0870961i
$586$	−20.7745	−	8.60508i	−0.0354514	−	0.0146844i
$587$	95.5275	−	12.5764i	0.162738	−	0.0214249i	−0.0487166	−	0.998813i	$-0.515513\pi$
$587$	95.5275	−	12.5764i	0.162738	−	0.0214249i	0.211455	+	0.977388i	$0.432180\pi$
$588$	−419.730	+	270.872i	−0.713827	+	0.460666i
$589$	246.925	−	121.770i	0.419227	−	0.206740i
$590$	5.45302	−	6.21797i	0.00924240	−	0.0105389i
$591$	337.469	−	250.499i	0.571014	−	0.423857i
$592$	498.224	+	245.697i	0.841595	+	0.415028i
$593$	−712.341	+	295.061i	−1.20125	+	0.497574i	−0.891403	−	0.453212i	$-0.850278\pi$
$593$	−712.341	+	295.061i	−1.20125	+	0.497574i	−0.309847	+	0.950786i	$0.600278\pi$
$594$	118.236	−	82.0484i	0.199051	−	0.138129i
$595$	−37.4414	+	23.1093i	−0.0629267	+	0.0388391i
$596$	−43.5456	−	75.4232i	−0.0730631	−	0.126549i
$597$	112.235	−	28.1623i	0.187998	−	0.0471730i
$598$	75.8296	−	4.97013i	0.126805	−	0.00831126i
$599$	296.575	+	1106.83i	0.495117	+	1.84780i	0.529376	+	0.848387i	$0.322426\pi$
$599$	296.575	+	1106.83i	0.495117	+	1.84780i	−0.0342595	+	0.999413i	$0.510907\pi$
$600$	−57.0873	−	313.012i	−0.0951455	−	0.521686i
$601$	−484.642	−	31.7651i	−0.806392	−	0.0528538i	−0.343370	−	0.939200i	$-0.611568\pi$
$601$	−484.642	−	31.7651i	−0.806392	−	0.0528538i	−0.463023	+	0.886346i	$0.653235\pi$
$602$	−3.90801	−	19.6469i	−0.00649170	−	0.0326360i
$603$	−366.705	+	138.362i	−0.608134	+	0.229456i
$604$	129.999	−	313.844i	0.215230	−	0.519610i
$605$	97.6600	+	111.360i	0.161421	+	0.184066i
$606$	−66.6799	−	207.236i	−0.110033	−	0.341973i
$607$	−119.612	+	136.392i	−0.197055	+	0.224698i	−0.841926	−	0.539594i	$-0.818578\pi$
$607$	−119.612	+	136.392i	−0.197055	+	0.224698i	0.644871	+	0.764292i	$0.276911\pi$
$608$	577.415	−	154.718i	0.949696	−	0.254470i
$609$	−97.3851	−	7.94483i	−0.159910	−	0.0130457i
$610$	−71.6064	−	54.9455i	−0.117388	−	0.0900747i
$611$		−	248.382i		−	0.406517i
$612$	529.691	−	68.3761i	0.865508	−	0.111726i
$613$	393.271			0.641552			0.320776	−	0.947155i	$-0.396056\pi$
$613$	393.271			0.641552			0.320776	+	0.947155i	$0.396056\pi$
$614$	−85.0118	+	110.790i	−0.138456	+	0.180439i
$615$	−135.793	−	93.9013i	−0.220802	−	0.152685i
$616$	−11.7750	−	43.9451i	−0.0191153	−	0.0713394i
$617$	87.8580	+	77.0494i	0.142396	+	0.124878i	0.727581	−	0.686022i	$-0.240645\pi$
$617$	87.8580	+	77.0494i	0.142396	+	0.124878i	−0.585185	+	0.810900i	$0.698978\pi$
$618$	−37.8313	−	34.2600i	−0.0612157	−	0.0554369i
$619$	−623.235	+	546.562i	−1.00684	+	0.882977i	−0.993140	−	0.116930i	$-0.962695\pi$
$619$	−623.235	+	546.562i	−1.00684	+	0.882977i	−0.0137015	+	0.999906i	$0.504361\pi$
$620$	−96.5721	−	40.0015i	−0.155761	−	0.0645185i
$621$	−466.088	+	101.267i	−0.750544	+	0.163071i
$622$	−57.0136	+	11.3407i	−0.0916617	+	0.0182326i
$623$	4.13951	−	63.1567i	0.00664448	−	0.101375i
$624$	61.7582	−	172.827i	0.0989715	−	0.276966i
$625$	−255.651	+	68.5014i	−0.409041	+	0.109602i
$626$	3.70095	+	56.4656i	0.00591206	+	0.0902006i
$627$	336.141	−	325.584i	0.536109	−	0.519273i
$628$	−938.840	+	542.039i	−1.49497	+	0.863120i
$629$	−846.325	−	386.882i	−1.34551	−	0.615074i
$630$	3.78789	+	16.1852i	0.00601252	+	0.0256908i
$631$	70.7952	+	170.915i	0.112195	+	0.270863i	0.969997	−	0.243118i	$-0.0781702\pi$
$631$	70.7952	+	170.915i	0.112195	+	0.270863i	−0.857802	+	0.513981i	$0.828170\pi$
$632$	−276.169	+	560.015i	−0.436976	+	0.886099i
$633$	−387.285	+	44.7149i	−0.611825	+	0.0706396i
$634$	266.733	+	233.919i	0.420715	+	0.368957i
$635$	153.365	+	310.994i	0.241520	+	0.489754i
$636$	−82.2163	+	160.224i	−0.129271	+	0.251924i
$637$	−37.5334	−	285.094i	−0.0589221	−	0.447558i
$638$	−58.3043	+	140.759i	−0.0913861	+	0.220626i
$639$	202.294	+	19.7564i	0.316580	+	0.0309176i
$640$	−243.419	−	162.647i	−0.380342	−	0.254137i
$641$	37.7069	+	111.081i	0.0588251	+	0.173293i	0.972370	−	0.233444i	$-0.0749997\pi$
$641$	37.7069	+	111.081i	0.0588251	+	0.173293i	−0.913545	+	0.406738i	$0.866666\pi$
$642$	−322.449	−	139.630i	−0.502258	−	0.217492i
$643$	11.1076	+	169.469i	0.0172746	+	0.263559i	0.997756	+	0.0669493i	$0.0213266\pi$
$643$	11.1076	+	169.469i	0.0172746	+	0.263559i	−0.980482	+	0.196610i	$0.937007\pi$
$644$	−9.17135	+	69.6633i	−0.0142412	+	0.108173i
$645$	−166.066	−	24.5637i	−0.257466	−	0.0380833i
$646$	−242.688	+	72.7330i	−0.375678	+	0.112590i
$647$	−371.295			−0.573872			−0.286936	−	0.957950i	$-0.592637\pi$
$647$	−371.295			−0.573872			−0.286936	+	0.957950i	$0.592637\pi$
$648$	83.7730	−	424.804i	0.129279	−	0.655562i
$649$	21.1732	+	31.6879i	0.0326243	+	0.0488257i
$650$	82.4422	+	22.0903i	0.126834	+	0.0339851i
$651$	−42.4367	−	15.1644i	−0.0651869	−	0.0232940i
$652$	−284.741	−	577.397i	−0.436719	−	0.885578i
$653$	−881.295	−	299.159i	−1.34961	−	0.458131i	−0.449300	−	0.893381i	$-0.648327\pi$
$653$	−881.295	−	299.159i	−1.34961	−	0.458131i	−0.900310	+	0.435250i	$0.856660\pi$
$654$	−78.1879	−	1.24732i	−0.119553	−	0.00190721i
$655$	81.9598	−	10.7902i	0.125129	−	0.0164736i
$656$	241.154	−	47.9686i	0.367613	−	0.0731228i
$657$	−460.035	−	559.616i	−0.700206	−	0.851774i
$658$	−32.8599	−	6.53623i	−0.0499390	−	0.00993349i
$659$	205.289	−	766.150i	0.311516	−	1.16259i	−0.615673	−	0.788002i	$-0.711116\pi$
$659$	205.289	−	766.150i	0.311516	−	1.16259i	0.927189	−	0.374593i	$-0.122218\pi$
$660$	−177.084	−	14.4468i	−0.268309	−	0.0218891i
$661$	−135.669	+	1030.51i	−0.205249	+	1.55902i	0.510016	+	0.860165i	$0.329639\pi$
$661$	−135.669	+	1030.51i	−0.205249	+	1.55902i	−0.715265	+	0.698853i	$0.753694\pi$
$662$	−332.273	−	191.838i	−0.501923	−	0.289786i
$663$	−94.9044	+	292.423i	−0.143144	+	0.441060i
$664$	321.526	+	556.899i	0.484226	+	0.838704i
$665$	20.6845	+	49.9369i	0.0311046	+	0.0750931i
$666$	−240.113	+	256.789i	−0.360531	+	0.385569i
$667$	357.044	−	357.044i	0.535298	−	0.535298i
$668$	−245.633	+	83.3812i	−0.367714	+	0.124822i
$669$	−231.292	+	1073.03i	−0.345727	+	1.60394i
$670$	−66.8426	−	22.6900i	−0.0997651	−	0.0338657i
$671$	329.971	−	253.195i	0.491760	−	0.377340i
$672$	−83.9469	−	50.2689i	−0.124921	−	0.0748050i
$673$	−386.485	−	440.701i	−0.574272	−	0.654831i	0.389667	−	0.920956i	$-0.372590\pi$
$673$	−386.485	−	440.701i	−0.574272	−	0.654831i	−0.963939	+	0.266125i	$0.914257\pi$
$674$	−94.2478	−	62.9744i	−0.139834	−	0.0934338i
$675$	−532.263	−	60.5671i	−0.788538	−	0.0897290i
$676$	−327.452	−	327.452i	−0.484397	−	0.484397i
$677$	−531.016	−	261.868i	−0.784367	−	0.386807i	0.00557825	−	0.999984i	$-0.498224\pi$
$677$	−531.016	−	261.868i	−0.784367	−	0.386807i	−0.789945	+	0.613177i	$0.789891\pi$
$678$	−75.6492	−	301.483i	−0.111577	−	0.444665i
$679$	−103.594	−	59.8097i	−0.152568	−	0.0880850i
$680$	174.920	+	109.585i	0.257235	+	0.161154i
$681$	531.844	−	210.422i	0.780975	−	0.308990i
$682$	−42.7772	+	55.7483i	−0.0627232	+	0.0817424i
$683$	477.510	+	714.645i	0.699136	+	1.04633i	0.995818	+	0.0913553i	$0.0291199\pi$
$683$	477.510	+	714.645i	0.699136	+	1.04633i	−0.296682	+	0.954976i	$0.595880\pi$
$684$	20.9283	−	655.775i	0.0305969	−	0.958735i
$685$	61.6738	−	310.055i	0.0900348	−	0.452635i
$686$	−78.4623	−	5.14269i	−0.114377	−	0.00749664i
$687$	−24.1803	+	47.1226i	−0.0351969	+	0.0685919i
$688$	198.347	−	152.197i	0.288295	−	0.221217i
$689$	−63.1065	−	82.2420i	−0.0915914	−	0.119364i
$690$	−76.4269	−	39.2173i	−0.110764	−	0.0568367i
$691$	49.0908	−	748.980i	0.0710431	−	1.08391i	−0.802338	−	0.596870i	$-0.796411\pi$
$691$	49.0908	−	748.980i	0.0710431	−	1.08391i	0.873381	−	0.487038i	$-0.161923\pi$
$692$	761.930	+	151.557i	1.10106	+	0.219014i
$693$	−76.5596	−	2.44331i	−0.110476	−	0.00352570i
$694$	−111.114	+	74.2443i	−0.160107	+	0.106980i
$695$	−27.7172	−	21.2682i	−0.0398809	−	0.0306017i
$696$	168.637	+	426.232i	0.242295	+	0.612402i
$697$	−401.432	+	92.1862i	−0.575943	+	0.132261i
$698$	121.795	−	210.956i	0.174492	−	0.302229i
$699$	885.668	−	222.235i	1.26705	−	0.317933i
$700$	−34.9042	+	70.7787i	−0.0498631	+	0.101112i
$701$	−119.189	+	119.189i	−0.170027	+	0.170027i	−0.786991	−	0.616964i	$-0.788362\pi$
$701$	−119.189	+	119.189i	−0.170027	+	0.170027i	0.616964	+	0.786991i	$0.288362\pi$
$702$	93.3765	+	69.0744i	0.133015	+	0.0983966i
$703$	−635.109	+	950.508i	−0.903427	+	1.35207i
$704$	113.254	−	99.3209i	0.160872	−	0.141081i
$705$	−144.246	+	240.884i	−0.204604	+	0.341680i
$706$	92.2457	+	120.217i	0.130660	+	0.170279i
$707$	−37.2449	+	109.720i	−0.0526802	+	0.155191i
$708$	52.2328	+	11.2587i	0.0737752	+	0.0159022i
$709$	−269.572	−	794.133i	−0.380214	−	1.12007i	−0.953674	−	0.300841i	$-0.902733\pi$
$709$	−269.572	−	794.133i	−0.380214	−	1.12007i	0.573460	−	0.819233i	$-0.305601\pi$
$710$	25.8849	+	25.8849i	0.0364576	+	0.0364576i
$711$	767.890	+	718.023i	1.08001	+	1.00988i
$712$	−274.321	+	113.627i	−0.385282	+	0.159589i
$713$	201.684	−	116.442i	0.282866	−	0.163313i
$714$	36.1888	+	20.2506i	0.0506846	+	0.0283622i
$715$	51.1371	−	88.5720i	0.0715204	−	0.123877i
$716$	−1212.39	−	159.615i	−1.69329	−	0.222925i
$717$	−57.1100	+	700.036i	−0.0796514	+	0.976340i
$718$	111.946	+	29.9957i	0.155913	+	0.0417768i
$719$	−172.497	+	867.200i	−0.239912	+	1.20612i	0.653516	+	0.756913i	$0.273293\pi$
$719$	−172.497	+	867.200i	−0.239912	+	1.20612i	−0.893428	+	0.449206i	$0.851707\pi$
$720$	−160.262	+	131.744i	−0.222585	+	0.182978i
$721$	5.29966	+	26.6432i	0.00735042	+	0.0369531i
$722$	6.99908	+	53.1633i	0.00969402	+	0.0736334i
$723$	22.5869	−	1415.85i	0.0312405	−	1.95830i
$724$	−128.883	+	379.679i	−0.178016	+	0.524418i
$725$	508.631	−	250.829i	0.701560	−	0.345971i
$726$	46.9764	−	131.460i	0.0647057	−	0.181075i
$727$	241.674	−	901.938i	0.332426	−	1.24063i	−0.574207	−	0.818710i	$-0.694690\pi$
$727$	241.674	−	901.938i	0.332426	−	1.24063i	0.906633	−	0.421920i	$-0.138644\pi$
$728$	30.5293	−	20.3990i	0.0419359	−	0.0280207i
$729$	−643.766	−	342.062i	−0.883081	−	0.469221i
$730$		−	130.471i		−	0.178728i
$731$	−324.626	+	264.602i	−0.444085	+	0.361972i
$732$	85.3262	−	576.856i	0.116566	−	0.788054i
$733$	107.950	+	14.2119i	0.147272	+	0.0193887i	0.203802	−	0.979012i	$-0.434670\pi$
$733$	107.950	+	14.2119i	0.147272	+	0.0193887i	−0.0565298	+	0.998401i	$0.518004\pi$
$734$	−315.779	+	20.6973i	−0.430217	+	0.0281979i
$735$	−129.166	+	298.285i	−0.175736	+	0.405831i
$736$	478.816	−	162.536i	0.650566	−	0.220837i
$737$	180.716	−	270.461i	0.245206	−	0.366976i
$738$	−15.1248	+	154.870i	−0.0204943	+	0.209851i
$739$	−1198.60	−	496.476i	−1.62192	−	0.671822i	−0.627629	−	0.778512i	$-0.715975\pi$
$739$	−1198.60	−	496.476i	−1.62192	−	0.671822i	−0.994292	+	0.106690i	$0.965975\pi$
$740$	430.309	−	56.6513i	0.581499	−	0.0765558i
$741$	336.022	+	172.424i	0.453470	+	0.232692i
$742$	−12.5409	+	6.18449i	−0.0169015	+	0.00833490i
$743$	93.5221	−	106.642i	0.125871	−	0.143528i	−0.685472	−	0.728099i	$-0.740404\pi$
$743$	93.5221	−	106.642i	0.125871	−	0.143528i	0.811342	+	0.584571i	$0.198737\pi$
$744$	24.2479	+	210.017i	0.0325913	+	0.282281i
$745$	−50.8256	−	25.0644i	−0.0682222	−	0.0336435i
$746$	−435.672	+	180.461i	−0.584011	+	0.241905i
$747$	1054.20	−	246.718i	1.41124	−	0.330278i
$748$	−324.526	+	301.920i	−0.433858	+	0.403637i
$749$	93.5110	+	161.966i	0.124848	+	0.216243i
$750$	−151.704	−	156.623i	−0.202273	−	0.208831i
$751$	831.779	−	54.5177i	1.10756	−	0.0725934i	0.499374	−	0.866387i	$-0.333563\pi$
$751$	831.779	−	54.5177i	1.10756	−	0.0725934i	0.608188	+	0.793793i	$0.291897\pi$
$752$	−108.225	−	403.902i	−0.143916	−	0.537103i
$753$	815.673	+	291.474i	1.08323	+	0.387084i
$754$	−122.697	−	8.04199i	−0.162728	−	0.0106658i
$755$	−43.1233	−	216.795i	−0.0571169	−	0.287146i
$756$	−79.4845	+	72.2193i	−0.105138	+	0.0955282i
$757$	509.672	−	1230.46i	0.673279	−	1.62544i	−0.102724	−	0.994710i	$-0.532756\pi$
$757$	509.672	−	1230.46i	0.673279	−	1.62544i	0.776003	−	0.630729i	$-0.217244\pi$
$758$	211.224	+	240.855i	0.278660	+	0.317751i
$759$	265.712	−	293.410i	0.350082	−	0.386575i
$760$	167.191	−	190.644i	0.219988	−	0.250848i
$761$	−1461.30	+	391.553i	−1.92023	+	0.514524i	−0.931770	+	0.363050i	$0.881735\pi$
$761$	−1461.30	+	391.553i	−1.92023	+	0.514524i	−0.988461	+	0.151474i	$0.951598\pi$
$762$	185.883	−	268.810i	0.243940	−	0.352769i
$763$	33.0197	+	25.3369i	0.0432761	+	0.0332070i
$764$		−	816.454i		−	1.06866i
$765$	261.862	−	228.480i	0.342303	−	0.298667i
$766$	243.370			0.317716
$767$	−18.7240	+	24.4016i	−0.0244120	+	0.0318143i
$768$	−2.75822	+	33.8093i	−0.00359143	+	0.0440226i
$769$	217.855	+	813.046i	0.283297	+	1.05728i	0.950075	+	0.312021i	$0.101006\pi$
$769$	217.855	+	813.046i	0.283297	+	1.05728i	−0.666778	+	0.745256i	$0.732327\pi$
$770$	−10.3720	−	9.09601i	−0.0134701	−	0.0118130i
$771$	−165.905	+	53.3814i	−0.215181	+	0.0692365i
$772$	−430.830	+	377.828i	−0.558070	+	0.489414i
$773$	915.550	+	379.233i	1.18441	+	0.490600i	0.885931	−	0.463816i	$-0.153520\pi$
$773$	915.550	+	379.233i	1.18441	+	0.490600i	0.298481	+	0.954416i	$0.403520\pi$
$774$	55.8553	+	148.035i	0.0721645	+	0.191260i
$775$	256.537	−	51.0284i	0.331016	−	0.0658431i
$776$	−36.7023	+	559.969i	−0.0472968	+	0.721609i
$777$	184.080	−	33.5727i	0.236912	−	0.0432081i
$778$	−90.3245	+	24.2024i	−0.116098	+	0.0311085i
$779$	33.0929	+	504.901i	0.0424813	+	0.648139i
$780$	−34.8985	−	139.080i	−0.0447417	−	0.178308i
$781$	−146.088	+	84.3442i	−0.187053	+	0.107995i
$782$	−200.820	+	74.8176i	−0.256804	+	0.0956747i
$783$	769.096	−	64.0170i	0.982242	−	0.0817586i
$784$	−185.256	−	447.246i	−0.236295	−	0.570467i
$785$	−311.992	+	632.657i	−0.397442	+	0.805933i
$786$	−46.4394	−	62.5626i	−0.0590832	−	0.0795961i
$787$	168.393	+	147.677i	0.213969	+	0.187645i	0.759621	−	0.650366i	$-0.225385\pi$
$787$	168.393	+	147.677i	0.213969	+	0.187645i	−0.545652	+	0.838012i	$0.683718\pi$
$788$	216.293	+	438.599i	0.274484	+	0.556598i
$789$	687.843	+	1065.85i	0.871791	+	1.35089i
$790$	24.7137	+	187.719i	0.0312831	+	0.237619i
$791$	−63.3101	+	152.844i	−0.0800381	+	0.193229i
$792$	148.574	+	327.194i	0.187593	+	0.413123i
$793$	279.100	+	186.488i	0.351954	+	0.235168i
$794$	125.453	+	369.572i	0.158001	+	0.465456i
$795$	13.4401	+	116.408i	0.0169058	+	0.146425i
$796$	8.80607	+	134.355i	0.0110629	+	0.168787i
$797$	95.3872	−	724.537i	0.119683	−	0.909081i	−0.821269	−	0.570541i	$-0.806734\pi$
$797$	95.3872	−	724.537i	0.119683	−	0.909081i	0.940952	−	0.338540i	$-0.109933\pi$
$798$	31.6535	−	39.9168i	0.0396660	−	0.0500210i
$799$	201.089	+	670.974i	0.251676	+	0.839767i
$800$	567.920			0.709900
$801$	49.4093	+	497.469i	0.0616845	+	0.621059i
$802$	−236.086	−	353.328i	−0.294372	−	0.440559i
$803$	580.740	+	155.609i	0.723213	+	0.193784i
$804$	−81.8259	−	448.654i	−0.101774	−	0.558028i
$805$	20.2217	+	41.0056i	0.0251202	+	0.0509387i
$806$	−53.7016	−	18.2292i	−0.0666273	−	0.0226169i
$807$	−13.2214	+	22.0791i	−0.0163834	+	0.0273595i
$808$	538.926	−	70.9510i	0.666988	−	0.0878106i
$809$	1348.01	−	268.136i	1.66627	−	0.331441i	0.730193	−	0.683241i	$-0.239430\pi$
$809$	1348.01	−	268.136i	1.66627	−	0.331441i	0.936075	+	0.351799i	$0.114430\pi$
$810$	−50.4433	−	121.217i	−0.0622757	−	0.149651i
$811$	−1211.22	−	240.926i	−1.49349	−	0.297073i	−0.620263	−	0.784394i	$-0.712974\pi$
$811$	−1211.22	−	240.926i	−1.49349	−	0.297073i	−0.873223	+	0.487322i	$0.837974\pi$
$812$	29.4257	−	109.818i	0.0362386	−	0.135244i
$813$	−3.58104	−	7.56342i	−0.00440472	−	0.00930310i
$814$	38.0837	−	289.274i	0.0467858	−	0.355374i
$815$	−362.787	−	209.455i	−0.445137	−	0.257000i
$816$	−26.9124	+	516.869i	−0.0329809	+	0.633418i
$817$	257.244	+	445.559i	0.314864	+	0.545360i
$818$	22.2436	+	53.7009i	0.0271927	+	0.0656490i
$819$	−17.9938	−	59.1427i	−0.0219705	−	0.0722133i
$820$	135.839	−	135.839i	0.165657	−	0.165657i
$821$	−839.965	+	285.130i	−1.02310	+	0.347296i	−0.782049	−	0.623217i	$-0.785825\pi$
$821$	−839.965	+	285.130i	−1.02310	+	0.347296i	−0.241051	+	0.970513i	$0.577492\pi$
$822$	−283.635	+	91.2623i	−0.345055	+	0.111025i
$823$	−652.260	−	221.413i	−0.792540	−	0.269031i	−0.104330	−	0.994543i	$-0.533270\pi$
$823$	−652.260	−	221.413i	−0.792540	−	0.269031i	−0.688210	+	0.725512i	$0.741603\pi$
$824$	101.105	−	77.5804i	0.122700	−	0.0941509i
$825$	388.523	−	216.125i	0.470938	−	0.261970i
$826$	2.73549	+	3.11923i	0.00331174	+	0.00377631i
$827$	−993.699	−	663.969i	−1.20157	−	0.802864i	−0.216715	−	0.976235i	$-0.569534\pi$
$827$	−993.699	−	663.969i	−1.20157	−	0.802864i	−0.984857	+	0.173371i	$0.944534\pi$
$828$	−18.6146	−	554.674i	−0.0224814	−	0.669896i
$829$	−415.809	−	415.809i	−0.501579	−	0.501579i	0.410349	−	0.911928i	$-0.365407\pi$
$829$	−415.809	−	415.809i	−0.501579	−	0.501579i	−0.911928	+	0.410349i	$0.865407\pi$
$830$	174.883	+	86.2428i	0.210703	+	0.103907i
$831$	816.952	−	791.296i	0.983095	−	0.952222i
$832$	105.284	+	60.7857i	0.126543	+	0.0730598i
$833$	332.203	+	739.760i	0.398803	+	0.888068i
$834$	−4.81821	+	32.5739i	−0.00577723	+	0.0390575i
$835$	−102.753	+	133.910i	−0.123057	+	0.160371i
$836$	302.521	+	452.754i	0.361867	+	0.541572i
$837$	350.274	+	63.2885i	0.418488	+	0.0756135i
$838$	−24.3882	+	122.608i	−0.0291029	+	0.146310i
$839$	−110.524	−	7.24416i	−0.131734	−	0.00863428i	−0.000606302	−	1.00000i	$-0.500193\pi$
$839$	−110.524	−	7.24416i	−0.131734	−	0.00863428i	−0.131127	+	0.991366i	$0.541860\pi$
$840$	−41.4543	+	2.05360i	−0.0493504	+	0.00244476i
$841$	19.0259	−	14.5991i	0.0226229	−	0.0173592i
$842$	−261.004	−	340.147i	−0.309981	−	0.403976i
$843$	−364.135	+	234.993i	−0.431951	+	0.278758i
$844$	29.6690	−	452.662i	0.0351529	−	0.536329i
$845$	−295.538	−	58.7862i	−0.349749	−	0.0695695i
$846$	264.495	+	8.44104i	0.312642	+	0.00997759i
$847$	−61.7801	+	41.2802i	−0.0729399	+	0.0487369i
$848$	−138.454	−	106.239i	−0.163271	−	0.125282i
$849$	−620.205	+	782.112i	−0.730512	+	0.921216i
$850$	−240.592	+	7.07066i	−0.283049	+	0.00831842i
$851$	−483.488	+	837.426i	−0.568141	+	0.984050i
$852$	−64.8486	+	227.442i	−0.0761133	+	0.266951i
$853$	−178.472	+	361.906i	−0.209229	+	0.424275i	−0.976038	−	0.217601i	$-0.930177\pi$
$853$	−178.472	+	361.906i	−0.209229	+	0.424275i	0.766809	+	0.641876i	$0.221844\pi$
$854$	32.0162	−	32.0162i	0.0374897	−	0.0374897i
$855$	−225.744	−	362.361i	−0.264028	−	0.423814i
$856$	487.443	−	729.511i	0.569443	−	0.852232i
$857$	−590.749	+	518.073i	−0.689322	+	0.604519i	−0.930644	−	0.365926i	$-0.880752\pi$
$857$	−590.749	+	518.073i	−0.689322	+	0.604519i	0.241322	+	0.970445i	$0.422419\pi$
$858$	−96.3824	−	1.53757i	−0.112334	−	0.00179204i
$859$	292.310	+	380.946i	0.340291	+	0.443476i	0.931882	−	0.362763i	$-0.118166\pi$
$859$	292.310	+	380.946i	0.340291	+	0.443476i	−0.591590	+	0.806239i	$0.701500\pi$
$860$	62.7880	−	184.968i	0.0730093	−	0.215079i
$861$	55.5939	−	61.3891i	0.0645690	−	0.0712997i
$862$	−47.3371	−	139.451i	−0.0549155	−	0.161776i
$863$	563.282	+	563.282i	0.652702	+	0.652702i	0.953643	−	0.300941i	$-0.0973007\pi$
$863$	563.282	+	563.282i	0.652702	+	0.652702i	−0.300941	+	0.953643i	$0.597301\pi$
$864$	719.112	+	283.148i	0.832306	+	0.327717i
$865$	467.018	−	193.445i	0.539905	−	0.223636i
$866$	221.260	−	127.744i	0.255496	−	0.147511i
$867$	19.6280	−	866.778i	0.0226390	−	0.999744i
$868$	26.2183	−	45.4115i	0.0302055	−	0.0523174i
$869$	−865.030	−	113.883i	−0.995432	−	0.131051i
$870$	114.323	+	79.0546i	0.131406	+	0.0908673i
$871$	253.575	+	67.9453i	0.291131	+	0.0780083i
$872$	38.0921	−	191.502i	0.0436836	−	0.219612i
$873$	884.535	+	332.086i	1.01321	+	0.380396i
$874$	51.3609	+	258.209i	0.0587653	+	0.295433i
$875$	15.1482	+	115.062i	0.0173123	+	0.131500i
$876$	736.636	−	409.772i	0.840909	−	0.467776i
$877$	464.053	−	1367.06i	0.529137	−	1.55879i	−0.273226	−	0.961950i	$-0.588091\pi$
$877$	464.053	−	1367.06i	0.529137	−	1.55879i	0.802363	−	0.596837i	$-0.203576\pi$
$878$	147.361	−	72.6705i	0.167837	−	0.0827682i
$879$	−61.1870	−	72.0573i	−0.0696098	−	0.0819764i
$880$	44.5629	−	166.311i	0.0506397	−	0.188990i
$881$	1119.17	−	747.806i	1.27034	−	0.848815i	0.276651	−	0.960970i	$-0.410775\pi$
$881$	1119.17	−	747.806i	1.27034	−	0.848815i	0.993691	+	0.112155i	$0.0357754\pi$
$882$	304.865	−	30.2796i	0.345651	−	0.0343306i
$883$			249.005i			0.281999i	0.990010	+	0.141000i	$0.0450317\pi$
$883$			249.005i			0.281999i	−0.990010	+	0.141000i	$0.954968\pi$
$884$	−314.924	−	169.687i	−0.356249	−	0.191954i
$885$	32.3298	−	12.7912i	0.0365308	−	0.0144533i
$886$	−526.384	−	69.2998i	−0.594113	−	0.0782165i
$887$	1546.75	−	101.380i	1.74380	−	0.114295i	0.840094	−	0.542441i	$-0.182500\pi$
$887$	1546.75	−	101.380i	1.74380	−	0.114295i	0.903710	+	0.428146i	$0.140833\pi$
$888$	−523.206	−	704.856i	−0.589196	−	0.793757i
$889$	−164.717	+	55.9138i	−0.185283	+	0.0628952i
$890$	−50.0211	+	74.8618i	−0.0562034	+	0.0841144i
$891$	599.710	−	79.9566i	0.673076	−	0.0897380i
$892$	−1180.02	−	488.780i	−1.32289	−	0.547959i
$893$	853.132	−	112.317i	0.955355	−	0.125775i
$894$	2.64273	+	53.3465i	0.00295607	+	0.0596718i
$895$	−713.646	+	351.931i	−0.797370	+	0.393219i
$896$	96.8323	−	110.416i	0.108072	−	0.123232i
$897$	293.163	+	126.948i	0.326826	+	0.141525i
$898$	−206.433	−	101.801i	−0.229880	−	0.113364i
$899$	−348.138	+	144.203i	−0.387250	+	0.160404i
$900$	180.453	−	596.639i	0.200503	−	0.662932i
$901$	237.057	+	171.076i	0.263105	+	0.189873i
$902$	−64.5711	−	111.840i	−0.0715866	−	0.123992i
$903$	23.0906	−	80.9853i	0.0255710	−	0.0896847i
$904$	774.453	−	50.7604i	0.856696	−	0.0561508i
$905$	67.5261	+	252.011i	0.0746144	+	0.278465i
$906$	−158.806	+	134.849i	−0.175283	+	0.148840i
$907$	−626.378	−	41.0550i	−0.690605	−	0.0452646i	−0.283940	−	0.958842i	$-0.591642\pi$
$907$	−626.378	−	41.0550i	−0.690605	−	0.0452646i	−0.406665	+	0.913577i	$0.633308\pi$
$908$	129.837	+	652.734i	0.142992	+	0.718870i
$909$	148.339	−	903.096i	0.163190	−	0.993505i
$910$	4.26070	−	10.2862i	0.00468209	−	0.0113036i
$911$	1093.08	+	1246.42i	1.19987	+	1.36819i	0.911827	+	0.410575i	$0.134672\pi$
$911$	1093.08	+	1246.42i	1.19987	+	1.36819i	0.288045	+	0.957617i	$0.406995\pi$
$912$	621.543	+	133.973i	0.681517	+	0.146900i
$913$	−592.453	+	675.563i	−0.648908	+	0.739937i
$914$	394.850	−	105.800i	0.432003	−	0.115755i
$915$	−162.373	−	342.944i	−0.177457	−	0.374802i
$916$	−48.8933	−	37.5171i	−0.0533769	−	0.0409575i
$917$			41.4697i			0.0452232i
$918$	−308.167	−	110.999i	−0.335694	−	0.120914i
$919$	83.4376			0.0907917			0.0453959	−	0.998969i	$-0.485545\pi$
$919$	83.4376			0.0907917			0.0453959	+	0.998969i	$0.485545\pi$
$920$	130.573	−	170.166i	0.141927	−	0.184963i
$921$	−530.603	+	251.223i	−0.576116	+	0.272772i
$922$	−31.6361	−	118.068i	−0.0343125	−	0.128056i
$923$	−102.356	−	89.7641i	−0.110895	−	0.0972525i
$924$	18.7804	−	87.1279i	0.0203251	−	0.0942943i
$925$	−816.540	+	716.086i	−0.882746	+	0.774147i
$926$	−403.931	−	167.314i	−0.436211	−	0.180685i
$927$	−75.7456	−	200.750i	−0.0817104	−	0.216559i
$928$	−802.455	+	159.618i	−0.864714	+	0.172002i
$929$	45.5928	−	695.612i	0.0490773	−	0.748775i	−0.900424	−	0.435013i	$-0.856744\pi$
$929$	45.5928	−	695.612i	0.0490773	−	0.748775i	0.949502	−	0.313762i	$-0.101590\pi$
$930$	41.4940	+	48.8657i	0.0446172	+	0.0525438i
$931$	962.257	−	257.836i	1.03357	−	0.276945i
$932$	69.4907	+	1060.22i	0.0745609	+	1.13758i
$933$	−235.013	−	67.0070i	−0.251889	−	0.0718189i
$934$	−280.546	+	161.974i	−0.300371	+	0.173419i
$935$	−66.4329	+	280.667i	−0.0710512	+	0.300178i
$936$	−211.507	+	198.425i	−0.225969	+	0.211992i
$937$	−296.558	−	715.955i	−0.316498	−	0.764093i	−0.999435	−	0.0336161i	$-0.989298\pi$
$937$	−296.558	−	715.955i	−0.316498	−	0.764093i	0.682937	−	0.730477i	$-0.260702\pi$
$938$	15.6618	−	31.7589i	0.0166970	−	0.0338581i
$939$	−94.5300	+	218.300i	−0.100671	+	0.232482i
$940$	−245.627	−	215.409i	−0.261305	−	0.229158i
$941$	−60.2393	−	122.153i	−0.0640163	−	0.129812i	0.862513	−	0.506035i	$-0.168889\pi$
$941$	−60.2393	−	122.153i	−0.0640163	−	0.129812i	−0.926529	+	0.376223i	$0.877223\pi$
$942$	664.038	−	32.8957i	0.704923	−	0.0349211i
$943$	55.8651	+	424.338i	0.0592419	+	0.449987i
$944$	−19.8154	+	47.8385i	−0.0209909	+	0.0506764i
$945$	−16.8960	+	67.8072i	−0.0178794	+	0.0717536i
$946$	−109.182	−	72.9534i	−0.115415	−	0.0771177i
$947$	−54.1314	−	159.466i	−0.0571609	−	0.168391i	0.914599	−	0.404362i	$-0.132506\pi$
$947$	−54.1314	−	159.466i	−0.0571609	−	0.168391i	−0.971760	+	0.235971i	$0.924173\pi$
$948$	−982.237	+	729.103i	−1.03612	+	0.769096i
$949$	31.7351	+	484.185i	0.0334406	+	0.510205i
$950$	−38.5949	+	293.158i	−0.0406263	+	0.308587i
$951$	548.704	+	1386.85i	0.576976	+	1.45831i
$952$	−65.9562	+	79.8219i	−0.0692817	+	0.0838465i
$953$	−132.763			−0.139311			−0.0696553	−	0.997571i	$-0.522190\pi$
$953$	−132.763			−0.139311			−0.0696553	+	0.997571i	$0.522190\pi$
$954$	89.7218	−	64.4054i	0.0940480	−	0.0675109i
$955$	−295.153	−	441.728i	−0.309061	−	0.462543i
$956$	−789.410	−	211.522i	−0.825743	−	0.221257i
$957$	−488.229	+	414.577i	−0.510166	+	0.433204i
$958$	235.565	+	477.679i	0.245893	+	0.498621i
$959$	150.170	+	50.9757i	0.156590	+	0.0531551i
$960$	−66.8049	−	120.094i	−0.0695885	−	0.125098i
$961$	780.469	−	102.751i	0.812143	−	0.106921i
$962$	230.951	−	45.9389i	0.240073	−	0.0477536i
$963$	−938.065	−	1141.12i	−0.974106	−	1.18496i
$964$	1616.02	+	321.446i	1.67637	+	0.333450i
$965$	−96.5059	+	360.165i	−0.100006	+	0.373228i
$966$	24.5093	−	35.4435i	0.0253719	−	0.0366910i
$967$	146.898	−	1115.80i	0.151911	−	1.15388i	−0.730334	−	0.683090i	$-0.760636\pi$
$967$	146.898	−	1115.80i	0.151911	−	1.15388i	0.882245	−	0.470790i	$-0.156031\pi$
$968$	301.874	+	174.287i	0.311853	+	0.180049i
$969$	−1047.31	−	193.741i	−1.08082	−	0.199940i
$970$	85.0816	+	147.366i	0.0877130	+	0.151923i
$971$	−249.313	−	601.894i	−0.256759	−	0.619871i	0.741962	−	0.670442i	$-0.233896\pi$
$971$	−249.313	−	601.894i	−0.256759	−	0.619871i	−0.998720	+	0.0505717i	$0.983896\pi$
$972$	525.960	−	665.508i	0.541111	−	0.684679i
$973$	12.3927	−	12.3927i	0.0127366	−	0.0127366i
$974$	283.434	−	96.2129i	0.291000	−	0.0987812i
$975$	265.960	+	240.853i	0.272779	+	0.247028i
$976$	535.109	+	181.645i	0.548267	+	0.186112i
$977$	−438.288	+	336.310i	−0.448606	+	0.344228i	−0.808227	−	0.588871i	$-0.799573\pi$
$977$	−438.288	+	336.310i	−0.448606	+	0.344228i	0.359621	+	0.933098i	$0.382906\pi$
$978$	−6.29783	+	394.778i	−0.00643949	+	0.403658i
$979$	−273.559	−	311.934i	−0.279427	−	0.318625i
$980$	−314.482	−	210.130i	−0.320900	−	0.214419i
$981$	−290.051	−	154.729i	−0.295668	−	0.157726i
$982$	−20.2230	−	20.2230i	−0.0205937	−	0.0205937i
$983$	−905.966	−	446.773i	−0.921634	−	0.454500i	−0.0813742	−	0.996684i	$-0.525931\pi$
$983$	−905.966	−	446.773i	−0.921634	−	0.454500i	−0.840260	+	0.542184i	$0.817598\pi$
$984$	−373.646	−	106.534i	−0.379722	−	0.108267i
$985$	275.578	+	159.105i	0.279775	+	0.161528i
$986$	337.962	−	77.6107i	0.342760	−	0.0787127i
$987$	−110.360	−	87.5143i	−0.111814	−	0.0886670i
$988$	−267.527	+	348.648i	−0.270776	+	0.352882i
$989$	241.780	+	361.850i	0.244469	+	0.365874i
$990$	92.5800	+	57.4645i	0.0935152	+	0.0580449i
$991$	−44.7221	+	224.833i	−0.0451282	+	0.226875i	−0.996767	−	0.0803436i	$-0.974398\pi$
$991$	−44.7221	+	224.833i	−0.0451282	+	0.226875i	0.951639	+	0.307218i	$0.0993982\pi$
$992$	−376.548	−	24.6802i	−0.379584	−	0.0248793i
$993$	−874.606	−	1355.25i	−0.880771	−	1.36480i
$994$	−14.5689	+	11.1791i	−0.0146569	+	0.0112466i
$995$	53.3345	+	69.5068i	0.0536025	+	0.0698561i
$996$	62.3322	+	1258.25i	0.0625825	+	1.26330i
$997$	−3.44747	+	52.5982i	−0.00345784	+	0.0527565i	−0.999239	−	0.0390020i	$-0.987582\pi$
$997$	−3.44747	+	52.5982i	−0.00345784	+	0.0527565i	0.995781	+	0.0917585i	$0.0292488\pi$
$998$	−440.540	−	87.6289i	−0.441423	−	0.0878046i
$999$	−1390.94	+	499.621i	−1.39233	+	0.500122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.t.a.22.20	yes	544
9.7	even	3	inner	153.3.t.a.124.15	yes	544
17.7	odd	16	inner	153.3.t.a.58.15	yes	544
153.7	odd	48	inner	153.3.t.a.7.20	✓	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.t.a.7.20	✓	544	153.7	odd	48	inner
153.3.t.a.22.20	yes	544	1.1	even	1	trivial
153.3.t.a.58.15	yes	544	17.7	odd	16	inner
153.3.t.a.124.15	yes	544	9.7	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.t (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.434420 - 0.566147i) q^{2} +(2.71144 - 1.28378i) q^{3} +(0.903474 + 3.37181i) q^{4} +(1.70774 + 1.49765i) q^{5} +(0.451096 - 2.09277i) q^{6} +(-0.856685 + 0.751292i) q^{7} +(4.93860 + 2.04563i) q^{8} +(5.70382 - 6.96178i) q^{9} +(1.58977 - 0.316224i) q^{10} +(-0.488519 + 7.45335i) q^{11} +(6.77838 + 7.98261i) q^{12} +(-5.82278 + 1.56021i) q^{13} +(0.0531810 + 0.811386i) q^{14} +(6.55309 + 1.86842i) q^{15} +(-8.78878 + 5.07421i) q^{16} +(14.4664 - 8.92882i) q^{17} +(-1.46354 - 6.25354i) q^{18} +(-7.99196 - 19.2943i) q^{19} +(-3.50689 + 7.11127i) q^{20} +(-1.35836 + 3.13688i) q^{21} +(4.00747 + 3.51446i) q^{22} +(-7.81315 - 15.8435i) q^{23} +(16.0169 - 0.793456i) q^{24} +(-2.58973 - 19.6709i) q^{25} +(-1.64622 + 3.97434i) q^{26} +(6.52817 - 26.1989i) q^{27} +(-3.30721 - 2.20981i) q^{28} +(9.18788 + 27.0666i) q^{29} +(3.90459 - 2.89833i) q^{30} +(0.862221 + 13.1549i) q^{31} +(-3.73619 + 28.3792i) q^{32} +(8.24387 + 20.8365i) q^{33} +(1.22946 - 12.0690i) q^{34} -2.58817 q^{35} +(28.6271 + 12.9424i) q^{36} +(-30.4113 - 45.5137i) q^{37} +(-14.3953 - 3.85720i) q^{38} +(-13.7852 + 11.7056i) q^{39} +(5.37020 + 10.8897i) q^{40} +(-22.9425 - 7.78793i) q^{41} +(1.18584 + 2.13175i) q^{42} +(-24.4247 + 3.21558i) q^{43} +(-25.5727 + 5.08672i) q^{44} +(20.1670 - 3.34661i) q^{45} +(-12.3639 - 2.45934i) q^{46} +(-10.6642 + 39.7995i) q^{47} +(-17.3161 + 25.0413i) q^{48} +(-6.22631 + 47.2936i) q^{49} +(-12.2617 - 7.07928i) q^{50} +(27.7621 - 42.7816i) q^{51} +(-10.5215 - 18.2237i) q^{52} +(6.58082 + 15.8875i) q^{53} +(-11.9965 - 15.0772i) q^{54} +(-11.9968 + 11.9968i) q^{55} +(-5.76769 + 1.95787i) q^{56} +(-46.4394 - 42.0554i) q^{57} +(19.3151 + 6.55659i) q^{58} +(4.04791 - 3.10607i) q^{59} +(-0.379420 + 23.7839i) q^{60} +(-36.7147 - 41.8650i) q^{61} +(7.82220 + 5.22663i) q^{62} +(0.343961 + 10.2493i) q^{63} +(-14.2603 - 14.2603i) q^{64} +(-12.2804 - 6.05605i) q^{65} +(15.3778 + 4.38453i) q^{66} +(-37.7144 - 21.7744i) q^{67} +(43.1763 + 40.7110i) q^{68} +(-41.5245 - 32.9283i) q^{69} +(-1.12435 + 1.46528i) q^{70} +(12.5470 + 18.7780i) q^{71} +(42.4101 - 22.7135i) q^{72} +(15.7033 - 78.9458i) q^{73} +(-38.9787 - 2.55480i) q^{74} +(-32.2750 - 50.0119i) q^{75} +(57.8362 - 44.3793i) q^{76} +(-5.18114 - 6.75219i) q^{77} +(0.638534 + 12.8896i) q^{78} +(-7.63974 + 116.560i) q^{79} +(-22.6083 - 4.49708i) q^{80} +(-15.9329 - 79.4175i) q^{81} +(-14.3758 + 9.60560i) q^{82} +(95.4387 + 73.2327i) q^{83} +(-11.8042 - 1.74603i) q^{84} +(38.0771 + 6.41745i) q^{85} +(-8.79010 + 15.2249i) q^{86} +(59.6599 + 61.5943i) q^{87} +(-17.6594 + 35.8098i) q^{88} +(-39.2771 + 39.2771i) q^{89} +(6.86625 - 12.8713i) q^{90} +(3.81611 - 5.71122i) q^{91} +(46.3623 - 40.6587i) q^{92} +(19.2259 + 34.5620i) q^{93} +(17.8996 + 23.3272i) q^{94} +(15.2479 - 44.9188i) q^{95} +(26.3021 + 81.7448i) q^{96} +(33.7447 + 99.4087i) q^{97} +(24.0703 + 24.0703i) q^{98} +(49.1022 + 45.9135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) \) 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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