LMFDB - Embedded newform 45.3.h.a.29.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,3,Mod(14,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.14"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.h (of order $6$, degree $2$, 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:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 19 x^{16} + 66 x^{14} + 109 x^{12} - 813 x^{10} + 981 x^{8} + 5346 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 19x^16 + 66x^14 + 109x^12 - 813x^10 + 981x^8 + 5346x^6 - 13851x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.2
Root			$-0.346576 + 1.69702i$ of defining polynomial
Character	$\chi$	$=$	45.29
Dual form			45.3.h.a.14.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.42081 + 2.46092i) q^{2} +(2.93933 + 0.600288i) q^{3} +(-2.03740 - 3.52889i) q^{4} +(3.58357 + 3.48684i) q^{5} +(-5.65349 + 6.38055i) q^{6} +(-8.42581 - 4.86464i) q^{7} +0.212574 q^{8} +(8.27931 + 3.52889i) q^{9} +(-13.6724 + 3.86473i) q^{10} +(0.370966 + 0.214177i) q^{11} +(-3.87025 - 11.5956i) q^{12} +(16.2396 - 9.37595i) q^{13} +(23.9429 - 13.8235i) q^{14} +(8.44019 + 12.4001i) q^{15} +(7.84759 - 13.5924i) q^{16} -2.85718 q^{17} +(-20.4476 + 15.3608i) q^{18} +0.530568 q^{19} +(5.00347 - 19.7501i) q^{20} +(-21.8460 - 19.3567i) q^{21} +(-1.05414 + 0.608611i) q^{22} +(-10.8863 - 18.8557i) q^{23} +(0.624825 + 0.127606i) q^{24} +(0.683961 + 24.9906i) q^{25} +53.2858i q^{26} +(22.2173 + 15.3425i) q^{27} +39.6450i q^{28} +(-21.0633 - 12.1609i) q^{29} +(-42.5076 + 3.15236i) q^{30} +(6.33163 + 10.9667i) q^{31} +(22.7250 + 39.3609i) q^{32} +(0.961823 + 0.852224i) q^{33} +(4.05951 - 7.03128i) q^{34} +(-13.2323 - 46.8122i) q^{35} +(-4.41525 - 36.4065i) q^{36} -14.5875i q^{37} +(-0.753837 + 1.30568i) q^{38} +(53.3619 - 17.8106i) q^{39} +(0.761774 + 0.741210i) q^{40} +(-33.1200 + 19.1218i) q^{41} +(78.6743 - 26.2591i) q^{42} +(-50.0269 - 28.8831i) q^{43} -1.74546i q^{44} +(17.3648 + 41.5146i) q^{45} +61.8697 q^{46} +(-24.7850 + 42.9289i) q^{47} +(31.2260 - 35.2418i) q^{48} +(22.8295 + 39.5418i) q^{49} +(-62.4716 - 33.8238i) q^{50} +(-8.39819 - 1.71513i) q^{51} +(-66.1734 - 38.2052i) q^{52} +44.5876 q^{53} +(-69.3232 + 32.8760i) q^{54} +(0.582582 + 2.06102i) q^{55} +(-1.79111 - 1.03410i) q^{56} +(1.55951 + 0.318494i) q^{57} +(59.8538 - 34.5566i) q^{58} +(-54.6329 + 31.5423i) q^{59} +(26.5626 - 55.0485i) q^{60} +(11.0823 - 19.1951i) q^{61} -35.9842 q^{62} +(-52.5931 - 70.0096i) q^{63} -66.3710 q^{64} +(90.8883 + 23.0255i) q^{65} +(-3.46382 + 1.15612i) q^{66} +(-28.1839 + 16.2720i) q^{67} +(5.82123 + 10.0827i) q^{68} +(-20.6797 - 61.9581i) q^{69} +(134.001 + 33.9477i) q^{70} -89.8896i q^{71} +(1.75996 + 0.750149i) q^{72} +144.328i q^{73} +(35.8987 + 20.7261i) q^{74} +(-12.9912 + 73.8663i) q^{75} +(-1.08098 - 1.87232i) q^{76} +(-2.08379 - 3.60923i) q^{77} +(-31.9868 + 156.625i) q^{78} +(-25.1240 + 43.5160i) q^{79} +(75.5169 - 21.3462i) q^{80} +(56.0939 + 58.4335i) q^{81} -108.674i q^{82} +(38.2556 - 66.2606i) q^{83} +(-23.7984 + 116.530i) q^{84} +(-10.2389 - 9.96251i) q^{85} +(142.158 - 82.0747i) q^{86} +(-54.6118 - 48.3889i) q^{87} +(0.0788577 + 0.0455285i) q^{88} +28.9588i q^{89} +(-126.836 - 16.2510i) q^{90} -182.443 q^{91} +(-44.3598 + 76.8334i) q^{92} +(12.0276 + 36.0355i) q^{93} +(-70.4296 - 121.988i) q^{94} +(1.90133 + 1.85000i) q^{95} +(43.1684 + 129.336i) q^{96} +(19.9099 + 11.4950i) q^{97} -129.746 q^{98} +(2.31554 + 3.08234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + 4 q^{10} - 24 q^{11} + 30 q^{14} + 24 q^{15} - 26 q^{16} - 8 q^{19} + 144 q^{20} - 96 q^{21} - 102 q^{24} + 2 q^{25} - 114 q^{29} - 48 q^{30} + 28 q^{31}+ \cdots - 468 q^{99}+O(q^{100}) $ 20 * q - 18 * q^4 - 12 * q^5 + 12 * q^6 - 18 * q^9 + 4 * q^10 - 24 * q^11 + 30 * q^14 + 24 * q^15 - 26 * q^16 - 8 * q^19 + 144 * q^20 - 96 * q^21 - 102 * q^24 + 2 * q^25 - 114 * q^29 - 48 * q^30 + 28 * q^31 - 4 * q^34 + 432 * q^36 + 240 * q^39 - 34 * q^40 + 102 * q^41 - 162 * q^45 + 116 * q^46 - 40 * q^49 - 408 * q^50 - 156 * q^51 - 270 * q^54 + 36 * q^55 - 618 * q^56 + 120 * q^59 + 330 * q^60 - 50 * q^61 + 140 * q^64 + 492 * q^65 - 768 * q^66 + 162 * q^69 - 54 * q^70 + 504 * q^74 + 276 * q^75 - 96 * q^76 - 128 * q^79 + 846 * q^81 + 450 * q^84 - 74 * q^85 + 1488 * q^86 - 990 * q^90 - 288 * q^91 + 218 * q^94 - 762 * q^95 - 474 * q^96 - 468 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.42081	+	2.46092i	−0.710405	+	1.23046i	0.254300	+	0.967125i	$0.418155\pi$
$2$	−1.42081	+	2.46092i	−0.710405	+	1.23046i	−0.964705	+	0.263332i	$0.915178\pi$
$3$	2.93933	+	0.600288i	0.979776	+	0.200096i
$3$	2.93933	+	0.600288i	0.979776	+	0.200096i
$4$	−2.03740	−	3.52889i	−0.509351	−	0.882222i
$5$	3.58357	+	3.48684i	0.716714	+	0.697367i
$5$	3.58357	+	3.48684i	0.716714	+	0.697367i
$6$	−5.65349	+	6.38055i	−0.942248	+	1.06342i
$7$	−8.42581	−	4.86464i	−1.20369	−	0.694949i	−0.242314	−	0.970198i	$-0.577906\pi$
$7$	−8.42581	−	4.86464i	−1.20369	−	0.694949i	−0.961373	+	0.275249i	$0.911240\pi$
$8$	0.212574			0.0265717
$9$	8.27931	+	3.52889i	0.919923	+	0.392099i
$10$	−13.6724	+	3.86473i	−1.36724	+	0.386473i
$11$	0.370966	+	0.214177i	0.0337242	+	0.0194707i	0.516767	−	0.856126i	$-0.327135\pi$
$11$	0.370966	+	0.214177i	0.0337242	+	0.0194707i	−0.483043	+	0.875597i	$0.660469\pi$
$12$	−3.87025	−	11.5956i	−0.322521	−	0.966299i
$13$	16.2396	−	9.37595i	1.24920	−	0.721227i	0.278252	−	0.960508i	$-0.410245\pi$
$13$	16.2396	−	9.37595i	1.24920	−	0.721227i	0.970950	+	0.239281i	$0.0769117\pi$
$14$	23.9429	−	13.8235i	1.71021	−	0.987391i
$15$	8.44019	+	12.4001i	0.562679	+	0.826675i
$16$	7.84759	−	13.5924i	0.490474	−	0.849526i
$17$	−2.85718			−0.168069			−0.0840347	−	0.996463i	$-0.526781\pi$
$17$	−2.85718			−0.168069			−0.0840347	+	0.996463i	$0.526781\pi$
$18$	−20.4476	+	15.3608i	−1.13598	+	0.853378i
$19$	0.530568			0.0279246			0.0139623	−	0.999903i	$-0.495556\pi$
$19$	0.530568			0.0279246			0.0139623	+	0.999903i	$0.495556\pi$
$20$	5.00347	−	19.7501i	0.250173	−	0.987505i
$21$	−21.8460	−	19.3567i	−1.04029	−	0.921747i
$22$	−1.05414	+	0.608611i	−0.0479157	+	0.0276641i
$23$	−10.8863	−	18.8557i	−0.473319	−	0.819813i	0.526214	−	0.850352i	$-0.323611\pi$
$23$	−10.8863	−	18.8557i	−0.473319	−	0.819813i	−0.999534	+	0.0305388i	$0.990278\pi$
$24$	0.624825	+	0.127606i	0.0260344	+	0.00531690i
$25$	0.683961	+	24.9906i	0.0273584	+	0.999626i
$26$			53.2858i			2.04945i
$27$	22.2173	+	15.3425i	0.822862	+	0.568242i
$28$			39.6450i			1.41589i
$29$	−21.0633	−	12.1609i	−0.726320	−	0.419341i	0.0907547	−	0.995873i	$-0.471072\pi$
$29$	−21.0633	−	12.1609i	−0.726320	−	0.419341i	−0.817074	+	0.576532i	$0.804405\pi$
$30$	−42.5076	+	3.15236i	−1.41692	+	0.105079i
$31$	6.33163	+	10.9667i	0.204246	+	0.353765i	0.949892	−	0.312577i	$-0.101192\pi$
$31$	6.33163	+	10.9667i	0.204246	+	0.353765i	−0.745646	+	0.666342i	$0.767859\pi$
$32$	22.7250	+	39.3609i	0.710157	+	1.23003i
$33$	0.961823	+	0.852224i	0.0291462	+	0.0258250i
$34$	4.05951	−	7.03128i	0.119397	−	0.206802i
$35$	−13.2323	−	46.8122i	−0.378065	−	1.33749i
$36$	−4.41525	−	36.4065i	−0.122646	−	1.01129i
$37$		−	14.5875i		−	0.394257i	−0.980378	−	0.197129i	$-0.936838\pi$
$37$		−	14.5875i		−	0.394257i	0.980378	−	0.197129i	$-0.0631617\pi$
$38$	−0.753837	+	1.30568i	−0.0198378	+	0.0343601i
$39$	53.3619	−	17.8106i	1.36825	−	0.456681i
$40$	0.761774	+	0.741210i	0.0190443	+	0.0185303i
$41$	−33.1200	+	19.1218i	−0.807804	+	0.466386i	−0.846193	−	0.532877i	$-0.821111\pi$
$41$	−33.1200	+	19.1218i	−0.807804	+	0.466386i	0.0383889	+	0.999263i	$0.487777\pi$
$42$	78.6743	−	26.2591i	1.87320	−	0.625216i
$43$	−50.0269	−	28.8831i	−1.16342	−	0.671699i	−0.211297	−	0.977422i	$-0.567769\pi$
$43$	−50.0269	−	28.8831i	−1.16342	−	0.671699i	−0.952121	+	0.305723i	$0.901102\pi$
$44$		−	1.74546i		−	0.0396696i
$45$	17.3648	+	41.5146i	0.385885	+	0.922547i
$46$	61.8697			1.34499
$47$	−24.7850	+	42.9289i	−0.527341	+	0.913381i	0.472152	+	0.881517i	$0.343478\pi$
$47$	−24.7850	+	42.9289i	−0.527341	+	0.913381i	−0.999492	+	0.0318635i	$0.989856\pi$
$48$	31.2260	−	35.2418i	0.650542	−	0.734204i
$49$	22.8295	+	39.5418i	0.465908	+	0.806976i
$50$	−62.4716	−	33.8238i	−1.24943	−	0.676476i
$51$	−8.39819	−	1.71513i	−0.164670	−	0.0336300i
$52$	−66.1734	−	38.2052i	−1.27256	−	0.734716i
$53$	44.5876			0.841275			0.420637	−	0.907229i	$-0.361807\pi$
$53$	44.5876			0.841275			0.420637	+	0.907229i	$0.361807\pi$
$54$	−69.3232	+	32.8760i	−1.28376	+	0.608815i
$55$	0.582582	+	2.06102i	0.0105924	+	0.0374730i
$56$	−1.79111	−	1.03410i	−0.0319840	−	0.0184660i
$57$	1.55951	+	0.318494i	0.0273599	+	0.00558761i
$58$	59.8538	−	34.5566i	1.03196	−	0.595804i
$59$	−54.6329	+	31.5423i	−0.925981	+	0.534615i	−0.885538	−	0.464567i	$-0.846210\pi$
$59$	−54.6329	+	31.5423i	−0.925981	+	0.534615i	−0.0404426	+	0.999182i	$0.512877\pi$
$60$	26.5626	−	55.0485i	0.442710	−	0.917476i
$61$	11.0823	−	19.1951i	0.181677	−	0.314673i	−0.760775	−	0.649016i	$-0.775181\pi$
$61$	11.0823	−	19.1951i	0.181677	−	0.314673i	0.942452	+	0.334343i	$0.108514\pi$
$62$	−35.9842			−0.580390
$63$	−52.5931	−	70.0096i	−0.834811	−	1.11126i
$64$	−66.3710			−1.03705
$65$	90.8883	+	23.0255i	1.39828	+	0.354239i
$66$	−3.46382	+	1.15612i	−0.0524821	+	0.0175169i
$67$	−28.1839	+	16.2720i	−0.420655	+	0.242866i	−0.695358	−	0.718664i	$-0.744754\pi$
$67$	−28.1839	+	16.2720i	−0.420655	+	0.242866i	0.274702	+	0.961529i	$0.411421\pi$
$68$	5.82123	+	10.0827i	0.0856063	+	0.148274i
$69$	−20.6797	−	61.9581i	−0.299706	−	0.897943i
$70$	134.001	+	33.9477i	1.91431	+	0.484968i
$71$		−	89.8896i		−	1.26605i	−0.774131	−	0.633025i	$-0.781813\pi$
$71$		−	89.8896i		−	1.26605i	0.774131	−	0.633025i	$-0.218187\pi$
$72$	1.75996	+	0.750149i	0.0244440	+	0.0104187i
$73$			144.328i			1.97709i	0.150926	+	0.988545i	$0.451775\pi$
$73$			144.328i			1.97709i	−0.150926	+	0.988545i	$0.548225\pi$
$74$	35.8987	+	20.7261i	0.485117	+	0.280082i
$75$	−12.9912	+	73.8663i	−0.173216	+	0.984884i
$76$	−1.08098	−	1.87232i	−0.0142234	−	0.0246357i
$77$	−2.08379	−	3.60923i	−0.0270622	−	0.0468732i
$78$	−31.9868	+	156.625i	−0.410087	+	2.00801i
$79$	−25.1240	+	43.5160i	−0.318025	+	0.550836i	−0.980076	−	0.198623i	$-0.936353\pi$
$79$	−25.1240	+	43.5160i	−0.318025	+	0.550836i	0.662051	+	0.749459i	$0.269686\pi$
$80$	75.5169	−	21.3462i	0.943961	−	0.266827i
$81$	56.0939	+	58.4335i	0.692518	+	0.721401i
$82$		−	108.674i		−	1.32529i
$83$	38.2556	−	66.2606i	0.460911	−	0.798321i	−0.538096	−	0.842884i	$-0.680856\pi$
$83$	38.2556	−	66.2606i	0.460911	−	0.798321i	0.999007	+	0.0445628i	$0.0141895\pi$
$84$	−23.7984	+	116.530i	−0.283314	+	1.38726i
$85$	−10.2389	−	9.96251i	−0.120458	−	0.117206i
$86$	142.158	−	82.0747i	1.65300	−	0.954357i
$87$	−54.6118	−	48.3889i	−0.627722	−	0.556194i
$88$	0.0788577	+	0.0455285i	0.000896110	+	0.000517369i
$89$			28.9588i			0.325379i	0.986677	+	0.162690i	$0.0520169\pi$
$89$			28.9588i			0.325379i	−0.986677	+	0.162690i	$0.947983\pi$
$90$	−126.836	−	16.2510i	−1.40929	−	0.180566i
$91$	−182.443			−2.00486
$92$	−44.3598	+	76.8334i	−0.482171	+	0.835145i
$93$	12.0276	+	36.0355i	0.129329	+	0.387479i
$94$	−70.4296	−	121.988i	−0.749251	−	1.29774i
$95$	1.90133	+	1.85000i	0.0200140	+	0.0194737i
$96$	43.1684	+	129.336i	0.449671	+	1.34725i
$97$	19.9099	+	11.4950i	0.205257	+	0.118505i	0.599105	−	0.800670i	$-0.295523\pi$
$97$	19.9099	+	11.4950i	0.205257	+	0.118505i	−0.393848	+	0.919175i	$0.628857\pi$
$98$	−129.746			−1.32393
$99$	2.31554	+	3.08234i	0.0233892	+	0.0311347i
$100$	86.7956	−	53.3296i	0.867956	−	0.533296i
$101$	−49.7337	−	28.7138i	−0.492413	−	0.284295i	0.233162	−	0.972438i	$-0.425093\pi$
$101$	−49.7337	−	28.7138i	−0.492413	−	0.284295i	−0.725575	+	0.688143i	$0.758426\pi$
$102$	16.1530	−	18.2304i	0.158363	−	0.178729i
$103$	74.6430	−	43.0952i	0.724689	−	0.418400i	−0.0917868	−	0.995779i	$-0.529258\pi$
$103$	74.6430	−	43.0952i	0.724689	−	0.418400i	0.816476	+	0.577379i	$0.195924\pi$
$104$	3.45212	−	1.99308i	0.0331935	−	0.0191643i
$105$	−10.7932	−	145.540i	−0.102793	−	1.38609i
$106$	−63.3504	+	109.726i	−0.597646	+	1.03515i
$107$	97.0919			0.907401			0.453701	−	0.891154i	$-0.350104\pi$
$107$	97.0919			0.907401			0.453701	+	0.891154i	$0.350104\pi$
$108$	8.87650	−	109.661i	0.0821898	−	1.01538i
$109$	164.495			1.50913			0.754565	−	0.656225i	$-0.227848\pi$
$109$	164.495			1.50913			0.754565	+	0.656225i	$0.227848\pi$
$110$	−5.89973	−	1.49463i	−0.0536339	−	0.0135875i
$111$	8.75671	−	42.8775i	0.0788893	−	0.386284i
$112$	−132.245	+	76.3514i	−1.18075	+	0.681709i
$113$	21.4024	+	37.0700i	0.189401	+	0.328053i	0.945051	−	0.326924i	$-0.106012\pi$
$113$	21.4024	+	37.0700i	0.189401	+	0.328053i	−0.755649	+	0.654976i	$0.772679\pi$
$114$	−2.99956	+	3.38532i	−0.0263119	+	0.0296957i
$115$	26.7347	−	105.530i	0.232476	−	0.917649i
$116$			99.1065i			0.854366i
$117$	167.540	−	20.3186i	1.43196	−	0.173663i
$118$		−	179.262i		−	1.51917i
$119$	24.0740	+	13.8992i	0.202303	+	0.116800i
$120$	1.79416	+	2.63594i	0.0149514	+	0.0219662i
$121$	−60.4083	−	104.630i	−0.499242	−	0.864712i
$122$	31.4916	+	54.5451i	0.258128	+	0.447091i
$123$	−108.829	+	36.3238i	−0.884789	+	0.295315i
$124$	25.8002	−	44.6872i	0.208066	−	0.360381i
$125$	−84.6872	+	91.9406i	−0.677498	+	0.735525i
$126$	247.013	−	29.9568i	1.96042	−	0.237752i
$127$		−	78.7223i		−	0.619861i	−0.950759	−	0.309931i	$-0.899694\pi$
$127$		−	78.7223i		−	0.619861i	0.950759	−	0.309931i	$-0.100306\pi$
$128$	3.40059	−	5.88999i	0.0265671	−	0.0460155i
$129$	−129.707	−	114.927i	−1.00548	−	0.890910i
$130$	−185.799	+	190.953i	−1.42922	+	1.46887i
$131$	158.295	−	91.3914i	1.20836	−	0.697644i	0.245956	−	0.969281i	$-0.420898\pi$
$131$	158.295	−	91.3914i	1.20836	−	0.697644i	0.962400	+	0.271637i	$0.0875649\pi$
$132$	1.04778	−	5.13049i	0.00793773	−	0.0388673i
$133$	−4.47047	−	2.58103i	−0.0336125	−	0.0194062i
$134$		−	92.4776i		−	0.690132i
$135$	26.1203	+	132.449i	0.193484	+	0.981104i
$136$	−0.607362			−0.00446589
$137$	2.78196	−	4.81850i	0.0203063	−	0.0351715i	−0.855694	−	0.517483i	$-0.826869\pi$
$137$	2.78196	−	4.81850i	0.0203063	−	0.0351715i	0.876000	+	0.482311i	$0.160203\pi$
$138$	181.856	+	37.1396i	1.31779	+	0.269128i
$139$	84.9601	+	147.155i	0.611224	+	1.05867i	0.991034	+	0.133607i	$0.0426559\pi$
$139$	84.9601	+	147.155i	0.611224	+	1.05867i	−0.379810	+	0.925064i	$0.624011\pi$
$140$	−138.235	+	142.071i	−0.987396	+	1.01479i
$141$	−98.6210	+	111.304i	−0.699440	+	0.789390i
$142$	221.211	+	127.716i	1.55782	+	0.899409i
$143$	8.03247			0.0561711
$144$	112.939	−	84.8426i	0.784297	−	0.589185i
$145$	−33.0787	−	117.024i	−0.228129	−	0.807059i
$146$	−355.178	−	205.062i	−2.43273	−	1.40454i
$147$	43.3669	+	129.931i	0.295013	+	0.883883i
$148$	−51.4777	+	29.7207i	−0.347822	+	0.200815i
$149$	−69.9180	+	40.3672i	−0.469249	+	0.270921i	−0.715925	−	0.698177i	$-0.753995\pi$
$149$	−69.9180	+	40.3672i	−0.469249	+	0.270921i	0.246677	+	0.969098i	$0.420661\pi$
$150$	−163.321	−	136.920i	−1.08880	−	0.912801i
$151$	−44.1372	+	76.4478i	−0.292299	+	0.506277i	−0.974353	−	0.225025i	$-0.927754\pi$
$151$	−44.1372	+	76.4478i	−0.292299	+	0.506277i	0.682054	+	0.731302i	$0.261087\pi$
$152$	0.112785			0.000742006
$153$	−23.6555	−	10.0827i	−0.154611	−	0.0658998i
$154$	11.8427			0.0769006
$155$	−15.5492	+	61.3773i	−0.100318	+	0.395983i
$156$	−171.571	−	152.021i	−1.09982	−	0.974492i
$157$	54.3401	−	31.3732i	0.346115	−	0.199830i	−0.316858	−	0.948473i	$-0.602628\pi$
$157$	54.3401	−	31.3732i	0.346115	−	0.199830i	0.662973	+	0.748643i	$0.269294\pi$
$158$	−71.3929	−	123.656i	−0.451854	−	0.782633i
$159$	131.057	+	26.7654i	0.824261	+	0.168336i
$160$	−55.8082	+	220.291i	−0.348801	+	1.37682i
$161$			211.833i			1.31573i
$162$	−223.499	+	55.0195i	−1.37962	+	0.339627i
$163$			241.437i			1.48121i	0.671941	+	0.740605i	$0.265461\pi$
$163$			241.437i			1.48121i	−0.671941	+	0.740605i	$0.734539\pi$
$164$	134.957	+	77.9177i	0.822911	+	0.475108i
$165$	0.475197	+	6.40773i	0.00287998	+	0.0388347i
$166$	108.708	+	188.288i	0.654867	+	1.13426i
$167$	−66.5872	−	115.332i	−0.398726	−	0.690613i	0.594843	−	0.803842i	$-0.297214\pi$
$167$	−66.5872	−	115.332i	−0.398726	−	0.690613i	−0.993569	+	0.113229i	$0.963881\pi$
$168$	−4.64390	−	4.11473i	−0.0276422	−	0.0244924i
$169$	91.3170	−	158.166i	0.540338	−	0.935892i
$170$	39.0644	−	11.0422i	0.229791	−	0.0649543i
$171$	4.39274	+	1.87232i	0.0256885	+	0.0109492i
$172$			235.386i			1.36852i
$173$	−33.5211	+	58.0603i	−0.193764	+	0.335609i	−0.946495	−	0.322720i	$-0.895403\pi$
$173$	−33.5211	+	58.0603i	−0.193764	+	0.335609i	0.752731	+	0.658328i	$0.228736\pi$
$174$	196.674	−	65.6437i	1.13031	−	0.377263i
$175$	115.808	−	213.894i	0.661758	−	1.22225i
$176$	5.82238	−	3.36155i	0.0330817	−	0.0190997i
$177$	−179.518	+	59.9177i	−1.01423	+	0.338518i
$178$	−71.2651	−	41.1449i	−0.400366	−	0.231151i
$179$		−	37.9613i		−	0.212074i	−0.994362	−	0.106037i	$-0.966184\pi$
$179$		−	37.9613i		−	0.212074i	0.994362	−	0.106037i	$-0.0338162\pi$
$180$	111.121	−	145.861i	0.617340	−	0.810337i
$181$	278.012			1.53598			0.767990	−	0.640462i	$-0.221257\pi$
$181$	278.012			1.53598			0.767990	+	0.640462i	$0.221257\pi$
$182$	259.216	−	448.976i	1.42427	−	2.46690i
$183$	44.0970	−	49.7681i	0.240967	−	0.271957i
$184$	−2.31415	−	4.00823i	−0.0125769	−	0.0217839i
$185$	50.8643	−	52.2754i	0.274942	−	0.282570i
$186$	−105.769	−	21.6009i	−0.568652	−	0.116134i
$187$	−1.05992	−	0.611943i	−0.00566800	−	0.00327242i
$188$	201.988			1.07441
$189$	−112.563	−	237.352i	−0.595569	−	1.25583i
$190$	−7.25413	+	2.05051i	−0.0381796	+	0.0107921i
$191$	50.4943	+	29.1529i	0.264368	+	0.152633i	0.626326	−	0.779562i	$-0.284558\pi$
$191$	50.4943	+	29.1529i	0.264368	+	0.152633i	−0.361957	+	0.932195i	$0.617891\pi$
$192$	−195.086	−	39.8417i	−1.01607	−	0.207509i
$193$	−109.611	+	63.2837i	−0.567930	+	0.327895i	−0.756322	−	0.654199i	$-0.773006\pi$
$193$	−109.611	+	63.2837i	−0.567930	+	0.327895i	0.188392	+	0.982094i	$0.439672\pi$
$194$	−56.5764	+	32.6644i	−0.291631	+	0.168373i
$195$	253.329	+	122.239i	1.29912	+	0.626865i
$196$	93.0258	−	161.125i	0.474621	−	0.822068i
$197$	−335.557			−1.70333			−0.851667	−	0.524083i	$-0.824408\pi$
$197$	−335.557			−1.70333			−0.851667	+	0.524083i	$0.824408\pi$
$198$	−10.8753	+	1.31892i	−0.0549258	+	0.00666121i
$199$	−127.161			−0.638998			−0.319499	−	0.947587i	$-0.603515\pi$
$199$	−127.161			−0.638998			−0.319499	+	0.947587i	$0.603515\pi$
$200$	0.145392	+	5.31236i	0.000726961	+	0.0265618i
$201$	−92.6097	+	30.9103i	−0.460745	+	0.153782i
$202$	141.324	−	81.5937i	0.699626	−	0.403929i
$203$	118.317	+	204.931i	0.582841	+	1.00951i
$204$	11.0580	+	33.1307i	0.0542059	+	0.162405i
$205$	−185.362	−	46.9594i	−0.904206	−	0.229070i
$206$			244.920i			1.18893i
$207$	−23.5918	−	194.529i	−0.113970	−	0.939753i
$208$		−	294.314i		−	1.41497i
$209$	0.196823	+	0.113636i	0.000941736	+	0.000543712i
$210$	373.496	+	180.223i	1.77855	+	0.858205i
$211$	−48.8580	−	84.6246i	−0.231555	−	0.401064i	0.726711	−	0.686943i	$-0.241048\pi$
$211$	−48.8580	−	84.6246i	−0.231555	−	0.401064i	−0.958266	+	0.285879i	$0.907715\pi$
$212$	−90.8428	−	157.344i	−0.428504	−	0.742191i
$213$	53.9596	−	264.215i	0.253332	−	1.24045i
$214$	−137.949	+	238.935i	−0.644623	+	1.11652i
$215$	−78.5646	−	277.940i	−0.365417	−	1.29275i
$216$	4.72281	+	3.26142i	0.0218649	+	0.0150992i
$217$		−	123.204i		−	0.567762i
$218$	−233.716	+	404.809i	−1.07209	+	1.85692i
$219$	−86.6381	+	424.226i	−0.395608	+	1.93711i
$220$	6.08614	−	6.25499i	0.0276643	−	0.0284318i
$221$	−46.3995	+	26.7888i	−0.209953	+	0.121216i
$222$	93.0763	+	82.4704i	0.419263	+	0.371488i
$223$	−80.9094	−	46.7130i	−0.362822	−	0.209476i	0.307496	−	0.951549i	$-0.400509\pi$
$223$	−80.9094	−	46.7130i	−0.362822	−	0.209476i	−0.670318	+	0.742074i	$0.733842\pi$
$224$		−	442.196i		−	1.97409i
$225$	−82.5264	+	209.319i	−0.366784	+	0.930306i
$226$	−121.635			−0.538207
$227$	−98.9949	+	171.464i	−0.436101	+	0.755349i	−0.997385	−	0.0722743i	$-0.976974\pi$
$227$	−98.9949	+	171.464i	−0.436101	+	0.755349i	0.561284	+	0.827623i	$0.310308\pi$
$228$	−2.05343	−	6.15225i	−0.00900629	−	0.0269836i
$229$	−90.6197	−	156.958i	−0.395719	−	0.685406i	0.597473	−	0.801889i	$-0.296171\pi$
$229$	−90.6197	−	156.958i	−0.395719	−	0.685406i	−0.993193	+	0.116483i	$0.962838\pi$
$230$	221.715	+	215.730i	0.963976	+	0.937955i
$231$	−3.95837	−	11.8596i	−0.0171358	−	0.0513403i
$232$	−4.47750	−	2.58509i	−0.0192996	−	0.0111426i
$233$	178.525			0.766202			0.383101	−	0.923706i	$-0.374856\pi$
$233$	178.525			0.766202			0.383101	+	0.923706i	$0.374856\pi$
$234$	−188.040	+	441.170i	−0.803588	+	1.88534i
$235$	−238.505	+	67.4175i	−1.01491	+	0.286883i
$236$	222.618	+	128.529i	0.943298	+	0.544613i
$237$	−99.9698	+	112.826i	−0.421814	+	0.476060i
$238$	−68.4093	+	39.4961i	−0.287434	+	0.165950i
$239$	13.2157	−	7.63006i	0.0552956	−	0.0319250i	−0.472097	−	0.881546i	$-0.656503\pi$
$239$	13.2157	−	7.63006i	0.0552956	−	0.0319250i	0.527393	+	0.849621i	$0.323170\pi$
$240$	234.783	−	17.4115i	0.978262	−	0.0725479i
$241$	159.583	−	276.406i	0.662170	−	1.14691i	−0.317874	−	0.948133i	$-0.602969\pi$
$241$	159.583	−	276.406i	0.662170	−	1.14691i	0.980044	−	0.198779i	$-0.0636976\pi$
$242$	343.315			1.41866
$243$	129.802	+	205.428i	0.534163	+	0.845382i
$244$	−90.3163			−0.370149
$245$	−56.0648	+	221.304i	−0.228836	+	0.903280i
$246$	65.2356	−	319.428i	0.265185	−	1.29849i
$247$	8.61623	−	4.97458i	0.0348835	−	0.0201400i
$248$	1.34594	+	2.33123i	0.00542717	+	0.00940014i
$249$	152.221	−	171.797i	0.611330	−	0.689950i
$250$	−105.934	−	339.038i	−0.423734	−	1.35615i
$251$			95.3404i			0.379842i	0.981799	+	0.189921i	$0.0608232\pi$
$251$			95.3404i			0.379842i	−0.981799	+	0.189921i	$0.939177\pi$
$252$	−139.903	+	328.233i	−0.555169	+	1.30251i
$253$		−	9.32644i		−	0.0368634i
$254$	193.729	+	111.850i	0.762713	+	0.440352i
$255$	−24.1151	−	35.4294i	−0.0945692	−	0.138939i
$256$	−123.079	−	213.179i	−0.480777	−	0.832730i
$257$	−3.96637	−	6.86996i	−0.0154334	−	0.0267313i	0.858206	−	0.513306i	$-0.171579\pi$
$257$	−3.96637	−	6.86996i	−0.0154334	−	0.0267313i	−0.873639	+	0.486575i	$0.838246\pi$
$258$	467.116	−	155.909i	1.81053	−	0.604299i
$259$	−70.9631	+	122.912i	−0.273989	+	0.474562i
$260$	−103.922	−	367.647i	−0.399699	−	1.41403i
$261$	−131.475	−	175.014i	−0.503735	−	0.670550i
$262$			519.399i			1.98244i
$263$	205.189	−	355.399i	0.780188	−	1.35133i	−0.151644	−	0.988435i	$-0.548457\pi$
$263$	205.189	−	355.399i	0.780188	−	1.35133i	0.931832	−	0.362890i	$-0.118210\pi$
$264$	0.204459	+	0.181161i	0.000774464	+	0.000686214i
$265$	159.783	+	155.469i	0.602953	+	0.586677i
$266$	12.7034	−	7.33429i	0.0477570	−	0.0275725i
$267$	−17.3836	+	85.1193i	−0.0651071	+	0.318799i
$268$	114.844	+	66.3052i	0.428522	+	0.247408i
$269$			201.081i			0.747513i	0.927527	+	0.373757i	$0.121930\pi$
$269$			201.081i			0.747513i	−0.927527	+	0.373757i	$0.878070\pi$
$270$	−363.058	−	123.905i	−1.34466	−	0.458908i
$271$	121.070			0.446751			0.223376	−	0.974732i	$-0.428292\pi$
$271$	121.070			0.446751			0.223376	+	0.974732i	$0.428292\pi$
$272$	−22.4220	+	38.8360i	−0.0824337	+	0.142779i
$273$	−536.259	−	109.518i	−1.96432	−	0.401165i
$274$	7.90527	+	13.6923i	0.0288514	+	0.0499720i
$275$	−5.09870	+	9.41717i	−0.0185407	+	0.0342443i
$276$	−176.510	+	199.210i	−0.639529	+	0.721775i
$277$	290.125	+	167.504i	1.04738	+	0.604707i	0.921916	−	0.387391i	$-0.126624\pi$
$277$	290.125	+	167.504i	1.04738	+	0.604707i	0.125468	+	0.992098i	$0.459957\pi$
$278$	−482.849			−1.73687
$279$	13.7213	+	113.140i	0.0491802	+	0.405521i
$280$	−2.81284	−	9.95105i	−0.0100458	−	0.0355395i
$281$	120.265	+	69.4349i	0.427989	+	0.247099i	0.698489	−	0.715620i	$-0.253856\pi$
$281$	120.265	+	69.4349i	0.427989	+	0.247099i	−0.270501	+	0.962720i	$0.587189\pi$
$282$	−133.788	−	400.840i	−0.474426	−	1.42142i
$283$	83.8352	−	48.4023i	0.296237	−	0.171033i	−0.344514	−	0.938781i	$-0.611956\pi$
$283$	83.8352	−	48.4023i	0.296237	−	0.171033i	0.640751	+	0.767748i	$0.278623\pi$
$284$	−317.210	+	183.141i	−1.11694	+	0.644864i
$285$	4.47810	+	6.57912i	0.0157126	+	0.0230846i
$286$	−11.4126	+	19.7672i	−0.0399042	+	0.0691162i
$287$	372.083			1.29646
$288$	49.2473	+	406.075i	0.170998	+	1.40998i
$289$	−280.837			−0.971753
$290$	334.984	+	84.8643i	1.15512	+	0.292636i
$291$	51.6214	+	45.7392i	0.177393	+	0.157179i
$292$	509.316	−	294.054i	1.74423	−	1.00703i
$293$	−192.539	−	333.488i	−0.657131	−	1.13818i	−0.981355	−	0.192204i	$-0.938437\pi$
$293$	−192.539	−	333.488i	−0.657131	−	1.13818i	0.324224	−	0.945980i	$-0.394897\pi$
$294$	−381.365	−	77.8846i	−1.29716	−	0.264914i
$295$	−305.764	−	77.4617i	−1.03649	−	0.262582i
$296$		−	3.10093i		−	0.0104761i
$297$	4.95583	+	10.4500i	0.0166863	+	0.0351852i
$298$		−	229.417i		−	0.769854i
$299$	−353.580	−	204.140i	−1.18254	−	0.682742i
$300$	287.134	−	104.651i	0.957114	−	0.348837i
$301$	281.012	+	486.726i	0.933593	+	1.61703i
$302$	−125.421	−	217.236i	−0.415302	−	0.719324i
$303$	−128.947	−	114.254i	−0.425569	−	0.377075i
$304$	4.16368	−	7.21171i	0.0136963	−	0.0237227i
$305$	106.644	−	30.1448i	0.349653	−	0.0988354i
$306$	58.4225	−	43.8886i	0.190923	−	0.143427i
$307$			207.311i			0.675281i	0.941275	+	0.337641i	$0.109629\pi$
$307$			207.311i			0.675281i	−0.941275	+	0.337641i	$0.890371\pi$
$308$	−8.49105	+	14.7069i	−0.0275684	+	0.0477498i
$309$	245.270	−	81.8636i	0.793754	−	0.264931i
$310$	−128.952	−	125.471i	−0.415974	−	0.404745i
$311$	140.437	−	81.0816i	0.451567	−	0.260712i	−0.256925	−	0.966431i	$-0.582709\pi$
$311$	140.437	−	81.0816i	0.451567	−	0.260712i	0.708492	+	0.705719i	$0.249376\pi$
$312$	11.3433	−	3.78606i	0.0363569	−	0.0121348i
$313$	196.427	+	113.407i	0.627561	+	0.362322i	0.779807	−	0.626020i	$-0.215317\pi$
$313$	196.427	+	113.407i	0.627561	+	0.362322i	−0.152246	+	0.988343i	$0.548651\pi$
$314$			178.302i			0.567840i
$315$	55.6408	−	434.268i	0.176638	−	1.37863i
$316$	204.751			0.647946
$317$	244.388	−	423.293i	0.770941	−	1.33531i	−0.166108	−	0.986108i	$-0.553120\pi$
$317$	244.388	−	423.293i	0.770941	−	1.33531i	0.937048	−	0.349200i	$-0.113547\pi$
$318$	−252.075	+	284.493i	−0.792689	+	0.894632i
$319$	−5.20917	−	9.02255i	−0.0163297	−	0.0282839i
$320$	−237.845	−	231.425i	−0.743267	−	0.723203i
$321$	285.385	+	58.2831i	0.889050	+	0.181567i
$322$	−521.302	−	300.974i	−1.61895	−	0.934702i
$323$	−1.51593			−0.00469328
$324$	91.9192	−	317.002i	0.283701	−	0.978400i
$325$	245.418	+	399.426i	0.755134	+	1.22900i
$326$	−594.157	−	343.036i	−1.82257	−	1.05226i
$327$	483.505	+	98.7444i	1.47861	+	0.301971i
$328$	−7.04044	+	4.06480i	−0.0214647	+	0.0123927i
$329$	417.667	−	241.140i	1.26951	−	0.732950i
$330$	−16.4440	−	7.93474i	−0.0498304	−	0.0240447i
$331$	−118.823	+	205.808i	−0.358982	+	0.621775i	−0.987791	−	0.155785i	$-0.950209\pi$
$331$	−118.823	+	205.808i	−0.358982	+	0.621775i	0.628809	+	0.777560i	$0.283543\pi$
$332$	−311.768			−0.939061
$333$	51.4777	−	120.775i	0.154588	−	0.362687i
$334$	378.431			1.13303
$335$	−157.737	−	39.9608i	−0.470856	−	0.119286i
$336$	−434.543	+	145.037i	−1.29328	+	0.431658i
$337$	−244.250	+	141.018i	−0.724777	+	0.418450i	−0.816508	−	0.577334i	$-0.804093\pi$
$337$	−244.250	+	141.018i	−0.724777	+	0.418450i	0.0917314	+	0.995784i	$0.470760\pi$
$338$	259.488	+	449.447i	0.767717	+	1.32973i
$339$	40.6559	+	121.808i	0.119929	+	0.359317i
$340$	−14.2958	+	56.4296i	−0.0420465	+	0.165969i
$341$			5.42437i			0.0159072i
$342$	−10.8489	+	8.14996i	−0.0317218	+	0.0238303i
$343$			32.5057i			0.0947688i
$344$	−10.6344	−	6.13979i	−0.0309140	−	0.0178482i
$345$	141.930	−	294.138i	0.411392	−	0.852573i
$346$	−95.2543	−	164.985i	−0.275302	−	0.476836i
$347$	219.985	+	381.026i	0.633963	+	1.09806i	0.986734	+	0.162347i	$0.0519063\pi$
$347$	219.985	+	381.026i	0.633963	+	1.09806i	−0.352771	+	0.935710i	$0.614760\pi$
$348$	−59.4924	+	291.307i	−0.170955	+	0.837088i
$349$	48.6291	−	84.2280i	0.139338	−	0.241341i	−0.787908	−	0.615793i	$-0.788836\pi$
$349$	48.6291	−	84.2280i	0.139338	−	0.241341i	0.927246	+	0.374452i	$0.122169\pi$
$350$	361.833	+	588.895i	1.03381	+	1.68256i
$351$	504.651	+	40.8489i	1.43775	+	0.116379i
$352$			19.4687i			0.0553089i
$353$	49.0978	−	85.0399i	0.139087	−	0.240906i	−0.788064	−	0.615593i	$-0.788916\pi$
$353$	49.0978	−	85.0399i	0.139087	−	0.240906i	0.927151	+	0.374687i	$0.122250\pi$
$354$	107.609	−	526.911i	0.303980	−	1.48845i
$355$	313.430	−	322.126i	0.882902	−	0.907396i
$356$	102.192	−	59.0007i	0.287057	−	0.165732i
$357$	62.4180	+	55.3055i	0.174840	+	0.154917i
$358$	93.4195	+	53.9358i	0.260948	+	0.150659i
$359$			500.068i			1.39295i	0.717582	+	0.696474i	$0.245249\pi$
$359$			500.068i			1.39295i	−0.717582	+	0.696474i	$0.754751\pi$
$360$	3.69131	+	8.82492i	0.0102536	+	0.0245137i
$361$	−360.718			−0.999220
$362$	−395.003	+	684.165i	−1.09117	+	1.88996i
$363$	−114.752	−	343.805i	−0.316120	−	0.947121i
$364$	371.709	+	643.819i	1.02118	+	1.76873i
$365$	−503.246	+	517.208i	−1.37876	+	1.41701i
$366$	59.8215	+	179.230i	0.163447	+	0.489699i
$367$	−296.023	−	170.909i	−0.806603	−	0.465692i	0.0391718	−	0.999232i	$-0.487528\pi$
$367$	−296.023	−	170.909i	−0.806603	−	0.465692i	−0.845775	+	0.533540i	$0.820861\pi$
$368$	−341.726			−0.928604
$369$	−341.689	+	41.4388i	−0.925987	+	0.112300i
$370$	56.3769	+	199.446i	0.152370	+	0.539044i
$371$	−375.686	−	216.902i	−1.01263	−	0.584643i
$372$	102.660	−	115.863i	0.275969	−	0.311459i
$373$	−529.179	+	305.522i	−1.41871	+	0.819093i	−0.996186	−	0.0872584i	$-0.972189\pi$
$373$	−529.179	+	305.522i	−1.41871	+	0.819093i	−0.422525	+	0.906351i	$0.638856\pi$
$374$	3.01188	−	1.73891i	0.00805316	−	0.00464949i
$375$	−304.114	+	219.407i	−0.810972	+	0.585085i
$376$	−5.26865	+	9.12556i	−0.0140124	+	0.0242701i
$377$	−456.080			−1.20976
$378$	744.034	+	60.2257i	1.96834	+	0.159327i
$379$	187.436			0.494555			0.247277	−	0.968945i	$-0.420464\pi$
$379$	187.436			0.494555			0.247277	+	0.968945i	$0.420464\pi$
$380$	2.65468	−	10.4788i	0.00698600	−	0.0275757i
$381$	47.2561	−	231.391i	0.124032	−	0.607325i
$382$	−143.486	+	82.8415i	−0.375617	+	0.216863i
$383$	73.9088	+	128.014i	0.192973	+	0.334240i	0.946234	−	0.323482i	$-0.104854\pi$
$383$	73.9088	+	128.014i	0.192973	+	0.334240i	−0.753261	+	0.657722i	$0.771520\pi$
$384$	13.5311	−	15.2713i	0.0352373	−	0.0397690i
$385$	5.11739	−	20.1998i	0.0132919	−	0.0524670i
$386$		−	359.656i		−	0.931752i
$387$	−312.263	−	415.671i	−0.806882	−	1.07409i
$388$		−	93.6797i		−	0.241442i
$389$	−397.890	−	229.722i	−1.02285	−	0.590545i	−0.107924	−	0.994159i	$-0.534420\pi$
$389$	−397.890	−	229.722i	−1.02285	−	0.590545i	−0.914929	+	0.403615i	$0.867754\pi$
$390$	−660.751	+	449.742i	−1.69423	+	1.15319i
$391$	31.1042	+	53.8741i	0.0795505	+	0.137786i
$392$	4.85295	+	8.40556i	0.0123800	+	0.0214428i
$393$	520.141	−	173.607i	1.32351	−	0.441748i
$394$	476.763	−	825.777i	1.21006	−	2.09588i
$395$	−241.767	+	68.3396i	−0.612068	+	0.173012i
$396$	6.15954	−	14.4512i	0.0155544	−	0.0364930i
$397$		−	718.905i		−	1.81084i	−0.424512	−	0.905422i	$-0.639554\pi$
$397$		−	718.905i		−	1.81084i	0.424512	−	0.905422i	$-0.360446\pi$
$398$	180.671	−	312.932i	0.453948	−	0.786260i
$399$	−11.5908	−	10.2700i	−0.0290497	−	0.0257395i
$400$	345.051	+	186.820i	0.862627	+	0.467049i
$401$	−65.5957	+	37.8717i	−0.163580	+	0.0944431i	−0.579555	−	0.814933i	$-0.696774\pi$
$401$	−65.5957	+	37.8717i	−0.163580	+	0.0944431i	0.415975	+	0.909376i	$0.363440\pi$
$402$	55.5132	−	271.822i	0.138093	−	0.676175i
$403$	205.647	+	118.730i	0.510289	+	0.294616i
$404$			234.006i			0.579223i
$405$	−2.73140	+	404.991i	−0.00674419	+	0.999977i
$406$	−672.422			−1.65621
$407$	3.12432	−	5.41148i	0.00767646	−	0.0132960i
$408$	−1.78524	−	0.364592i	−0.00437558	−	0.000893607i
$409$	−255.035	−	441.733i	−0.623556	−	1.08003i	−0.988818	−	0.149126i	$-0.952354\pi$
$409$	−255.035	−	441.733i	−0.623556	−	1.08003i	0.365262	−	0.930905i	$-0.380979\pi$
$410$	378.928	−	389.441i	0.924214	−	0.949855i
$411$	11.0696	−	12.4932i	0.0269333	−	0.0303970i
$412$	−304.156	−	175.604i	−0.738242	−	0.426224i
$413$	613.768			1.48612
$414$	512.239	+	218.331i	1.23729	+	0.527370i
$415$	368.132	−	104.059i	0.887064	−	0.250744i
$416$	738.092	+	426.137i	1.77426	+	1.02437i
$417$	161.390	+	483.538i	0.387027	+	1.15956i
$418$	−0.559296	+	0.322910i	−0.00133803	+	0.000772511i
$419$	603.768	−	348.586i	1.44097	−	0.831947i	0.443060	−	0.896492i	$-0.353893\pi$
$419$	603.768	−	348.586i	1.44097	−	0.831947i	0.997915	+	0.0645450i	$0.0205596\pi$
$420$	−491.603	+	334.611i	−1.17048	+	0.796693i
$421$	−378.410	+	655.425i	−0.898836	+	1.55683i	−0.0698516	+	0.997557i	$0.522253\pi$
$421$	−378.410	+	655.425i	−0.898836	+	1.55683i	−0.828984	+	0.559272i	$0.811081\pi$
$422$	277.672			0.657990
$423$	−356.694	+	267.958i	−0.843248	+	0.633471i
$424$	9.47815			0.0223541
$425$	−1.95420	−	71.4027i	−0.00459812	−	0.168006i
$426$	573.545	+	508.190i	1.34635	+	1.19293i
$427$	−186.754	+	107.823i	−0.437364	+	0.252512i
$428$	−197.815	−	342.626i	−0.462186	−	0.800529i
$429$	23.6101	+	4.82179i	0.0550351	+	0.0112396i
$430$	795.613	+	201.560i	1.85026	+	0.468743i
$431$		−	497.875i		−	1.15516i	−0.816333	−	0.577581i	$-0.803997\pi$
$431$		−	497.875i		−	1.15516i	0.816333	−	0.577581i	$-0.196003\pi$
$432$	382.894	−	181.585i	0.886329	−	0.420335i
$433$		−	421.645i		−	0.973775i	−0.873465	−	0.486888i	$-0.838132\pi$
$433$		−	421.645i		−	0.973775i	0.873465	−	0.486888i	$-0.161868\pi$
$434$	303.196	+	175.050i	0.698608	+	0.403341i
$435$	−26.9814	−	363.827i	−0.0620263	−	0.836385i
$436$	−335.143	−	580.485i	−0.768677	−	1.33139i
$437$	−5.77595	−	10.0042i	−0.0132173	−	0.0228930i
$438$	−920.889	−	815.954i	−2.10249	−	1.86291i
$439$	−228.743	+	396.195i	−0.521055	+	0.902494i	0.478645	+	0.878009i	$0.341128\pi$
$439$	−228.743	+	396.195i	−0.521055	+	0.902494i	−0.999700	+	0.0244857i	$0.992205\pi$
$440$	0.123842	+	0.438118i	0.000281458	+	0.000995724i
$441$	49.4738	+	407.942i	0.112185	+	0.925038i
$442$		−	152.247i		−	0.344450i
$443$	−116.136	+	201.153i	−0.262157	+	0.454069i	−0.966815	−	0.255478i	$-0.917767\pi$
$443$	−116.136	+	201.153i	−0.262157	+	0.454069i	0.704658	+	0.709547i	$0.251101\pi$
$444$	−169.151	+	56.4574i	−0.380970	+	0.127156i
$445$	−100.974	+	103.776i	−0.226909	+	0.233204i
$446$	229.914	−	132.741i	0.515502	−	0.297625i
$447$	−229.744	+	76.6815i	−0.513969	+	0.171547i
$448$	559.230	+	322.871i	1.24828	+	0.720695i
$449$		−	678.345i		−	1.51079i	−0.655269	−	0.755395i	$-0.727445\pi$
$449$		−	678.345i		−	1.51079i	0.655269	−	0.755395i	$-0.272555\pi$
$450$	−397.862	−	500.493i	−0.884137	−	1.11221i
$451$	−16.3818			−0.0363234
$452$	87.2105	−	151.053i	0.192943	−	0.334188i
$453$	−175.624	+	198.210i	−0.387692	+	0.437550i
$454$	−281.306	−	487.236i	−0.619617	−	1.07321i
$455$	−653.796	−	636.148i	−1.43691	−	1.39813i
$456$	0.331512	+	0.0677034i	0.000727000	+	0.000148472i
$457$	637.008	+	367.777i	1.39389	+	0.804763i	0.993743	−	0.111688i	$-0.0356258\pi$
$457$	637.008	+	367.777i	1.39389	+	0.804763i	0.400147	+	0.916451i	$0.368959\pi$
$458$	515.014			1.12448
$459$	−63.4787	−	43.8364i	−0.138298	−	0.0955040i
$460$	−426.872	+	120.663i	−0.927982	+	0.262310i
$461$	344.752	+	199.043i	0.747835	+	0.431763i	0.824911	−	0.565263i	$-0.191225\pi$
$461$	344.752	+	199.043i	0.747835	+	0.431763i	−0.0770763	+	0.997025i	$0.524559\pi$
$462$	34.8096	+	7.10903i	0.0753454	+	0.0153875i
$463$	−139.076	+	80.2955i	−0.300380	+	0.173424i	−0.642613	−	0.766191i	$-0.722150\pi$
$463$	−139.076	+	80.2955i	−0.300380	+	0.173424i	0.342234	+	0.939615i	$0.388817\pi$
$464$	−330.592	+	190.867i	−0.712482	+	0.411352i
$465$	−82.5484	+	171.074i	−0.177523	+	0.367901i
$466$	−253.650	+	439.335i	−0.544314	+	0.942780i
$467$	−406.660			−0.870792			−0.435396	−	0.900239i	$-0.643392\pi$
$467$	−406.660			−0.870792			−0.435396	+	0.900239i	$0.643392\pi$
$468$	−413.048	−	549.831i	−0.882581	−	1.17485i
$469$	316.630			0.675117
$470$	172.961	−	682.728i	0.368003	−	1.45261i
$471$	178.556	−	59.5966i	0.379100	−	0.126532i
$472$	−11.6135	+	6.70507i	−0.0246049	+	0.0142057i
$473$	−12.3722	−	21.4293i	−0.0261569	−	0.0453050i
$474$	−135.618	−	406.322i	−0.286114	−	0.857220i
$475$	0.362888	+	13.2592i	0.000763975	+	0.0279142i
$476$		−	113.273i		−	0.237968i
$477$	369.154	+	157.344i	0.773908	+	0.329862i
$478$			43.3635i			0.0907186i
$479$	731.450	+	422.303i	1.52704	+	0.881635i	0.999484	+	0.0321123i	$0.0102234\pi$
$479$	731.450	+	422.303i	1.52704	+	0.881635i	0.527552	+	0.849523i	$0.323110\pi$
$480$	−296.277	+	614.006i	−0.617243	+	1.27918i
$481$	−136.772	−	236.896i	−0.284349	−	0.492507i
$482$	453.474	+	785.440i	0.940818	+	1.62954i
$483$	−127.161	+	622.646i	−0.263272	+	1.28912i
$484$	−246.152	+	426.348i	−0.508579	+	0.880884i
$485$	31.2674	+	110.616i	0.0644689	+	0.228073i
$486$	−689.964	+	27.5569i	−1.41968	+	0.0567014i
$487$		−	225.518i		−	0.463075i	−0.972826	−	0.231538i	$-0.925624\pi$
$487$		−	225.518i		−	0.463075i	0.972826	−	0.231538i	$-0.0743757\pi$
$488$	2.35580	−	4.08037i	0.00482746	−	0.00836141i
$489$	−144.932	+	709.663i	−0.296384	+	1.45125i
$490$	−464.952	−	452.401i	−0.948882	−	0.923268i
$491$	−662.639	+	382.575i	−1.34957	+	0.779175i	−0.988189	−	0.153243i	$-0.951028\pi$
$491$	−662.639	+	382.575i	−1.34957	+	0.779175i	−0.361382	+	0.932418i	$0.617695\pi$
$492$	349.911	+	310.039i	0.711202	+	0.630161i
$493$	60.1815	+	34.7458i	0.122072	+	0.0704783i
$494$			28.2718i			0.0572303i
$495$	−2.44972	+	19.1197i	−0.00494893	+	0.0386256i
$496$	198.752			0.400710
$497$	−437.281	+	757.392i	−0.879841	+	1.52393i
$498$	206.501	+	618.695i	0.414662	+	1.24236i
$499$	102.024	+	176.711i	0.204458	+	0.354131i	0.949960	−	0.312372i	$-0.101124\pi$
$499$	102.024	+	176.711i	0.204458	+	0.354131i	−0.745502	+	0.666503i	$0.767790\pi$
$500$	496.990	+	111.532i	0.993980	+	0.223063i
$501$	−126.489	−	378.971i	−0.252473	−	0.756429i
$502$	−234.625	−	135.461i	−0.467380	−	0.269842i
$503$	−585.545			−1.16411			−0.582053	−	0.813151i	$-0.697750\pi$
$503$	−585.545			−1.16411			−0.582053	+	0.813151i	$0.697750\pi$
$504$	−11.1799	−	14.8822i	−0.0221824	−	0.0295282i
$505$	−78.1041	−	276.311i	−0.154662	−	0.547151i
$506$	22.9516	+	13.2511i	0.0453588	+	0.0261879i
$507$	363.356	−	410.085i	0.716678	−	0.808846i
$508$	−277.802	+	160.389i	−0.546855	+	0.315727i
$509$	10.3361	−	5.96756i	0.0203067	−	0.0117241i	−0.489812	−	0.871828i	$-0.662935\pi$
$509$	10.3361	−	5.96756i	0.0203067	−	0.0117241i	0.510119	+	0.860104i	$0.329601\pi$
$510$	121.452	−	9.00686i	0.238141	−	0.0176605i
$511$	702.102	−	1216.08i	1.37398	−	2.37980i
$512$	726.692			1.41932
$513$	11.7878	+	8.14026i	0.0229781	+	0.0158680i
$514$	22.5418			0.0438557
$515$	417.754	+	105.833i	0.811173	+	0.205502i
$516$	−141.299	+	691.877i	−0.273836	+	1.34085i
$517$	−18.3888	+	10.6168i	−0.0355683	+	0.0205354i
$518$	−201.650	−	349.268i	−0.389286	−	0.674263i
$519$	−133.383	+	150.536i	−0.256999	+	0.290050i
$520$	19.3205	+	4.89462i	0.0371548	+	0.00941274i
$521$		−	541.869i		−	1.04006i	−0.854149	−	0.520028i	$-0.825922\pi$
$521$		−	541.869i		−	1.04006i	0.854149	−	0.520028i	$-0.174078\pi$
$522$	617.495	−	74.8876i	1.18294	−	0.143463i
$523$			356.100i			0.680880i	0.940266	+	0.340440i	$0.110576\pi$
$523$			356.100i			0.680880i	−0.940266	+	0.340440i	$0.889424\pi$
$524$	−645.020	−	372.402i	−1.23095	−	0.710692i
$525$	468.794	−	559.186i	0.892942	−	1.06512i
$526$	583.071	+	1009.91i	1.10850	+	1.91998i
$527$	−18.0906	−	31.3338i	−0.0343275	−	0.0594570i
$528$	19.1318	−	6.38560i	0.0362344	−	0.0120939i
$529$	27.4749	−	47.5879i	0.0519374	−	0.0899582i
$530$	−609.618	+	172.319i	−1.15022	+	0.325130i
$531$	−563.632	+	68.3553i	−1.06145	+	0.128729i
$532$			21.0344i			0.0395383i
$533$	−358.571	+	621.062i	−0.672740	+	1.16522i
$534$	−184.773	−	163.718i	−0.346016	−	0.306588i
$535$	347.936	+	338.544i	0.650347	+	0.632792i
$536$	−5.99116	+	3.45900i	−0.0111775	+	0.00645336i
$537$	22.7877	−	111.581i	0.0424352	−	0.207785i
$538$	−494.843	−	285.698i	−0.919783	−	0.531037i
$539$			19.5582i			0.0362862i
$540$	414.180	−	362.028i	0.767000	−	0.670421i
$541$	378.892			0.700355			0.350178	−	0.936683i	$-0.386121\pi$
$541$	378.892			0.700355			0.350178	+	0.936683i	$0.386121\pi$
$542$	−172.017	+	297.942i	−0.317375	+	0.549709i
$543$	817.170	+	166.887i	1.50492	+	0.307343i
$544$	−64.9294	−	112.461i	−0.119356	−	0.206730i
$545$	589.480	+	573.568i	1.08161	+	1.05242i
$546$	1031.44	−	1164.08i	1.88908	−	2.13202i
$547$	−484.407	−	279.673i	−0.885571	−	0.511285i	−0.0130799	−	0.999914i	$-0.504164\pi$
$547$	−484.407	−	279.673i	−0.885571	−	0.511285i	−0.872491	+	0.488630i	$0.837497\pi$
$548$	−22.6719			−0.0413721
$549$	159.491	−	119.814i	0.290511	−	0.218240i
$550$	−15.9306	−	25.9275i	−0.0289647	−	0.0471409i
$551$	−11.1755	−	6.45218i	−0.0202822	−	0.0117099i
$552$	−4.39596	−	13.1707i	−0.00796370	−	0.0238599i
$553$	423.380	−	244.439i	0.765606	−	0.442023i
$554$	−824.426	+	475.982i	−1.48813	+	0.859174i
$555$	180.887	−	123.121i	0.325923	−	0.221840i
$556$	346.196	−	599.629i	0.622655	−	1.07847i
$557$	471.971			0.847345			0.423673	−	0.905815i	$-0.360741\pi$
$557$	471.971			0.847345			0.423673	+	0.905815i	$0.360741\pi$
$558$	−297.924	−	126.984i	−0.533914	−	0.227570i
$559$	−1083.23			−1.93779
$560$	−740.132	−	187.504i	−1.32167	−	0.334829i
$561$	−2.74810	−	2.43496i	−0.00489858	−	0.00434039i
$562$	−341.747	+	197.308i	−0.608090	+	0.351081i
$563$	−247.289	−	428.316i	−0.439234	−	0.760775i	0.558397	−	0.829574i	$-0.311417\pi$
$563$	−247.289	−	428.316i	−0.439234	−	0.760775i	−0.997631	+	0.0687990i	$0.978083\pi$
$564$	593.710	+	121.251i	1.05268	+	0.214984i
$565$	−52.5600	+	207.469i	−0.0930265	+	0.367202i
$566$			275.082i			0.486010i
$567$	−188.379	−	765.226i	−0.332237	−	1.34961i
$568$		−	19.1082i		−	0.0336412i
$569$	143.305	+	82.7370i	0.251853	+	0.145408i	0.620613	−	0.784117i	$-0.286884\pi$
$569$	143.305	+	82.7370i	0.251853	+	0.145408i	−0.368759	+	0.929525i	$0.620217\pi$
$570$	−22.5532	+	1.67254i	−0.0395670	+	0.00293429i
$571$	−25.5302	−	44.2195i	−0.0447113	−	0.0774423i	0.842804	−	0.538221i	$-0.180903\pi$
$571$	−25.5302	−	44.2195i	−0.0447113	−	0.0774423i	−0.887515	+	0.460779i	$0.847570\pi$
$572$	−16.3654	−	28.3457i	−0.0286108	−	0.0495554i
$573$	130.919	+	116.001i	0.228480	+	0.202445i
$574$	−528.660	+	915.665i	−0.921010	+	1.59524i
$575$	463.770	−	284.953i	0.806557	−	0.495571i
$576$	−549.506	−	234.216i	−0.954004	−	0.406625i
$577$		−	707.833i		−	1.22675i	−0.789793	−	0.613373i	$-0.789812\pi$
$577$		−	707.833i		−	1.22675i	0.789793	−	0.613373i	$-0.210188\pi$
$578$	399.015	−	691.115i	0.690338	−	1.19570i
$579$	−360.170	+	120.214i	−0.622055	+	0.207623i
$580$	−345.568	+	355.155i	−0.595807	+	0.612337i
$581$	−644.669	+	372.200i	−1.10958	+	0.640619i
$582$	−185.905	+	62.0492i	−0.319424	+	0.106614i
$583$	16.5405	+	9.54964i	0.0283713	+	0.0163802i
$584$			30.6803i			0.0525347i
$585$	671.238	+	511.370i	1.14741	+	0.874136i
$586$	1094.25			1.86732
$587$	226.251	−	391.878i	0.385436	−	0.667594i	−0.606394	−	0.795164i	$-0.707385\pi$
$587$	226.251	−	391.878i	0.385436	−	0.667594i	0.991830	+	0.127570i	$0.0407179\pi$
$588$	370.155	−	417.758i	0.629515	−	0.710473i
$589$	3.35936	+	5.81859i	0.00570350	+	0.00987875i
$590$	625.059	−	642.400i	1.05942	−	1.08881i
$591$	−986.312	−	201.431i	−1.66889	−	0.340830i
$592$	−198.280	−	114.477i	−0.334932	−	0.193373i
$593$	227.811			0.384168			0.192084	−	0.981379i	$-0.438475\pi$
$593$	227.811			0.384168			0.192084	+	0.981379i	$0.438475\pi$
$594$	−32.7578	−	2.65158i	−0.0551479	−	0.00446394i
$595$	37.8070	+	133.751i	0.0635411	+	0.224791i
$596$	284.903	+	164.489i	0.478024	+	0.275988i
$597$	−373.767	−	76.3330i	−0.626075	−	0.127861i
$598$	1004.74	−	580.088i	1.68017	−	0.970047i
$599$	−484.611	+	279.790i	−0.809033	+	0.467096i	−0.846620	−	0.532198i	$-0.821366\pi$
$599$	−484.611	+	279.790i	−0.809033	+	0.467096i	0.0375869	+	0.999293i	$0.488033\pi$
$600$	−2.76159	+	15.7020i	−0.00460265	+	0.0261701i
$601$	−335.271	+	580.707i	−0.557856	+	0.966235i	0.439819	+	0.898086i	$0.355043\pi$
$601$	−335.271	+	580.707i	−0.557856	+	0.966235i	−0.997675	+	0.0681485i	$0.978291\pi$
$602$	−1597.06			−2.65292
$603$	−290.765	+	35.2630i	−0.482198	+	0.0584793i
$604$	359.701			0.595532
$605$	148.351	−	585.583i	0.245208	−	0.967906i
$606$	464.379	−	154.995i	0.766301	−	0.255768i
$607$	−864.308	+	499.009i	−1.42390	+	0.822090i	−0.996630	−	0.0820329i	$-0.973859\pi$
$607$	−864.308	+	499.009i	−1.42390	+	0.822090i	−0.427272	+	0.904123i	$0.640525\pi$
$608$	12.0572	+	20.8836i	0.0198309	+	0.0343481i
$609$	224.754	+	673.382i	0.369055	+	1.10572i
$610$	−77.3373	+	305.272i	−0.126782	+	0.500446i
$611$			929.533i			1.52133i
$612$	12.6152	+	104.020i	0.0206130	+	0.169967i
$613$			229.314i			0.374086i	0.982352	+	0.187043i	$0.0598903\pi$
$613$			229.314i			0.374086i	−0.982352	+	0.187043i	$0.940110\pi$
$614$	−510.176	−	294.550i	−0.830905	−	0.479723i
$615$	−516.652	−	249.300i	−0.840084	−	0.405366i
$616$	−0.442960	−	0.767229i	−0.000719091	−	0.00124550i
$617$	−248.717	−	430.791i	−0.403108	−	0.698203i	0.590992	−	0.806678i	$-0.298737\pi$
$617$	−248.717	−	430.791i	−0.403108	−	0.698203i	−0.994099	+	0.108475i	$0.965403\pi$
$618$	−147.023	+	719.901i	−0.237901	+	1.16489i
$619$	528.867	−	916.025i	0.854390	−	1.47985i	−0.0228204	−	0.999740i	$-0.507265\pi$
$619$	528.867	−	916.025i	0.854390	−	1.47985i	0.877210	−	0.480107i	$-0.159402\pi$
$620$	248.274	−	70.1788i	0.400441	−	0.113192i
$621$	47.4293	−	585.946i	0.0763757	−	0.943553i
$622$			460.806i			0.740846i
$623$	140.874	−	244.001i	0.226122	−	0.391655i
$624$	176.673	−	865.087i	0.283130	−	1.38636i
$625$	−624.064	+	34.1853i	−0.998503	+	0.0546964i
$626$	−558.170	+	322.259i	−0.891645	+	0.514792i
$627$	0.510313	+	0.452163i	0.000813896	+	0.000721153i
$628$	−221.425	−	127.840i	−0.352588	−	0.203567i
$629$			41.6792i			0.0662626i
$630$	989.641	+	753.940i	1.57086	+	1.19673i
$631$	638.591			1.01203			0.506015	−	0.862524i	$-0.331118\pi$
$631$	638.591			1.01203			0.506015	+	0.862524i	$0.331118\pi$
$632$	−5.34071	+	9.25037i	−0.00845048	+	0.0146367i
$633$	−92.8107	−	278.068i	−0.146620	−	0.439286i
$634$	694.458	+	1202.84i	1.09536	+	1.89722i
$635$	274.492	−	282.107i	0.432271	−	0.444263i
$636$	−172.565	−	517.019i	−0.271329	−	0.812923i
$637$	741.485	+	428.097i	1.16403	+	0.672051i
$638$	29.6050			0.0464028
$639$	317.210	−	744.224i	0.496417	−	1.16467i
$640$	32.7237	−	9.24991i	0.0511307	−	0.0144530i
$641$	765.794	+	442.131i	1.19469	+	0.689753i	0.959366	−	0.282165i	$-0.0910526\pi$
$641$	765.794	+	442.131i	1.19469	+	0.689753i	0.235321	+	0.971918i	$0.424386\pi$
$642$	−548.908	+	619.500i	−0.854997	+	0.964953i
$643$	884.408	−	510.613i	1.37544	−	0.794111i	0.383834	−	0.923402i	$-0.374604\pi$
$643$	884.408	−	510.613i	1.37544	−	0.794111i	0.991607	+	0.129291i	$0.0412702\pi$
$644$	747.534	−	431.589i	1.16077	−	0.670169i
$645$	−64.0831	−	864.119i	−0.0993536	−	1.33972i
$646$	2.15385	−	3.73057i	0.00333413	−	0.00577488i
$647$	488.043			0.754317			0.377159	−	0.926149i	$-0.376901\pi$
$647$	488.043			0.754317			0.377159	+	0.926149i	$0.376901\pi$
$648$	11.9241	+	12.4214i	0.0184014	+	0.0191689i
$649$	−27.0226			−0.0416373
$650$	−1331.65	+	36.4454i	−2.04869	+	0.0560699i
$651$	73.9581	−	362.138i	0.113607	−	0.556280i
$652$	852.005	−	491.905i	1.30676	−	0.754456i
$653$	305.648	+	529.397i	0.468067	+	0.810716i	0.999334	−	0.0364887i	$-0.0116173\pi$
$653$	305.648	+	529.397i	0.468067	+	0.810716i	−0.531267	+	0.847204i	$0.678284\pi$
$654$	−929.971	+	1049.57i	−1.42197	+	1.60485i
$655$	885.927	+	224.439i	1.35256	+	0.342656i
$656$			600.240i			0.915001i
$657$	−509.316	+	1194.93i	−0.775214	+	1.81877i
$658$			1370.46i			2.08276i
$659$	125.687	+	72.5657i	0.190724	+	0.110115i	0.592322	−	0.805702i	$-0.298211\pi$
$659$	125.687	+	72.5657i	0.190724	+	0.110115i	−0.401597	+	0.915816i	$0.631545\pi$
$660$	21.6440	−	14.7320i	0.0327939	−	0.0223213i
$661$	−415.128	−	719.023i	−0.628030	−	1.08778i	−0.987947	−	0.154796i	$-0.950528\pi$
$661$	−415.128	−	719.023i	−0.628030	−	1.08778i	0.359916	−	0.932985i	$-0.382805\pi$
$662$	−337.650	−	584.827i	−0.510045	−	0.883424i
$663$	−152.464	+	50.8880i	−0.229961	+	0.0767541i
$664$	8.13214	−	14.0853i	0.0122472	−	0.0212128i
$665$	−7.02063	−	24.8371i	−0.0105573	−	0.0373490i
$666$	224.076	+	298.280i	0.336451	+	0.447868i
$667$			529.550i			0.793929i
$668$	−271.330	+	469.957i	−0.406182	+	0.703529i
$669$	−209.778	−	185.874i	−0.313569	−	0.277838i
$670$	322.454	−	331.400i	0.481275	−	0.494627i
$671$	8.22230	−	4.74715i	0.0122538	−	0.00707473i
$672$	265.445	−	1299.76i	0.395007	−	1.93417i
$673$	−235.054	−	135.708i	−0.349262	−	0.201647i	0.315098	−	0.949059i	$-0.397963\pi$
$673$	−235.054	−	135.708i	−0.349262	−	0.201647i	−0.664360	+	0.747412i	$0.731296\pi$
$674$		−	801.438i		−	1.18908i
$675$	−368.224	+	565.717i	−0.545517	+	0.838100i
$676$	−744.199			−1.10089
$677$	447.970	−	775.906i	0.661698	−	1.14609i	−0.318471	−	0.947933i	$-0.603169\pi$
$677$	447.970	−	775.906i	0.661698	−	1.14609i	0.980169	−	0.198162i	$-0.0634972\pi$
$678$	−357.524	−	73.0158i	−0.527322	−	0.107693i
$679$	−111.838	−	193.709i	−0.164710	−	0.285286i
$680$	−2.17652	−	2.11777i	−0.00320077	−	0.00311437i
$681$	−393.907	+	444.564i	−0.578424	+	0.652811i
$682$	−13.3489	−	7.70700i	−0.0195732	−	0.0113006i
$683$	−255.548			−0.374155			−0.187078	−	0.982345i	$-0.559902\pi$
$683$	−255.548			−0.374155			−0.187078	+	0.982345i	$0.559902\pi$
$684$	−2.34259	−	19.3161i	−0.00342484	−	0.0282400i
$685$	26.7706	−	7.56719i	0.0390812	−	0.0110470i
$686$	−79.9938	−	46.1844i	−0.116609	−	0.0673242i
$687$	−172.141	−	515.749i	−0.250569	−	0.750726i
$688$	−785.182	+	453.325i	−1.14125	+	0.658902i
$689$	724.085	−	418.051i	1.05092	−	0.606750i
$690$	522.192	+	767.193i	0.756800	+	1.11187i
$691$	−61.2973	+	106.170i	−0.0887081	+	0.153647i	−0.906965	−	0.421205i	$-0.861607\pi$
$691$	−61.2973	+	106.170i	−0.0887081	+	0.153647i	0.818257	+	0.574852i	$0.194940\pi$
$692$	273.184			0.394775
$693$	−4.51578	−	37.2354i	−0.00651628	−	0.0537308i
$694$	−1250.23			−1.80148
$695$	−208.646	+	823.583i	−0.300209	+	1.18501i
$696$	−11.6091	−	10.2862i	−0.0166797	−	0.0147790i
$697$	94.6296	−	54.6344i	0.135767	−	0.0783852i
$698$	138.185	+	239.344i	0.197973	+	0.342900i
$699$	524.744	+	107.166i	0.750707	+	0.153314i
$700$	−990.753	+	27.1156i	−1.41536	+	0.0387366i
$701$		−	595.027i		−	0.848826i	−0.905469	−	0.424413i	$-0.860480\pi$
$701$		−	595.027i		−	0.848826i	0.905469	−	0.424413i	$-0.139520\pi$
$702$	−817.539	+	1183.86i	−1.16459	+	1.68642i
$703$		−	7.73968i		−	0.0110095i
$704$	−24.6214	−	14.2152i	−0.0349736	−	0.0201920i
$705$	−741.514	+	54.9907i	−1.05179	+	0.0780010i
$706$	139.517	+	241.651i	0.197617	+	0.342282i
$707$	279.365	+	483.874i	0.395141	+	0.684404i
$708$	577.194	+	511.423i	0.815246	+	0.722350i
$709$	−280.492	+	485.826i	−0.395616	+	0.685227i	−0.993180	−	0.116594i	$-0.962802\pi$
$709$	−280.492	+	485.826i	−0.395616	+	0.685227i	0.597564	+	0.801822i	$0.296136\pi$
$710$	347.399	+	1229.00i	0.489295	+	1.73099i
$711$	−361.572	+	271.623i	−0.508541	+	0.382030i
$712$			6.15588i			0.00864589i
$713$	137.857	−	238.775i	0.193347	−	0.334887i
$714$	−224.786	+	75.0268i	−0.314827	+	0.105080i
$715$	28.7849	+	28.0079i	0.0402586	+	0.0391719i
$716$	−133.961	+	77.3424i	−0.187096	+	0.108020i
$717$	43.4254	−	14.4941i	0.0605654	−	0.0202149i
$718$	−1230.63	−	710.502i	−1.71396	−	0.989557i
$719$			1218.37i			1.69453i	0.531168	+	0.847266i	$0.321753\pi$
$719$			1218.37i			1.69453i	−0.531168	+	0.847266i	$0.678247\pi$
$720$	700.556	+	89.7592i	0.972995	+	0.124666i
$721$	−838.570			−1.16307
$722$	512.513	−	887.698i	0.709851	−	1.22950i
$723$	634.990	−	716.652i	0.878271	−	0.991220i
$724$	−566.423	−	981.074i	−0.782353	−	1.35507i
$725$	289.502	−	534.702i	0.399313	−	0.737520i
$726$	1009.11	+	206.088i	1.38997	+	0.283867i
$727$	687.921	+	397.172i	0.946247	+	0.546316i	0.891913	−	0.452207i	$-0.149363\pi$
$727$	687.921	+	397.172i	0.946247	+	0.546316i	0.0543338	+	0.998523i	$0.482696\pi$
$728$	−38.7825			−0.0532727
$729$	258.214	+	681.738i	0.354203	+	0.935169i
$730$	−557.788	−	1973.30i	−0.764093	−	2.70315i
$731$	142.936	+	82.5241i	0.195535	+	0.112892i
$732$	−265.469	−	54.2158i	−0.362663	−	0.0740652i
$733$	−681.408	+	393.411i	−0.929615	+	0.536714i	−0.886690	−	0.462365i	$-0.847001\pi$
$733$	−681.408	+	393.411i	−0.929615	+	0.536714i	−0.0429255	+	0.999078i	$0.513668\pi$
$734$	841.186	−	485.659i	1.14603	−	0.661661i
$735$	−297.639	+	616.829i	−0.404951	+	0.839223i
$736$	494.785	−	856.992i	0.672262	−	1.16439i
$737$	−13.9404			−0.0189150
$738$	383.498	−	899.745i	0.519645	−	1.21917i
$739$	1398.66			1.89264			0.946320	−	0.323231i	$-0.104769\pi$
$739$	1398.66			1.89264			0.946320	+	0.323231i	$0.104769\pi$
$740$	−288.105	−	72.9882i	−0.389331	−	0.0986327i
$741$	28.3121	−	9.44972i	0.0382080	−	0.0127527i
$742$	1067.56	−	616.355i	1.43876	−	0.830667i
$743$	274.315	+	475.127i	0.369199	+	0.639471i	0.989440	−	0.144940i	$-0.0462988\pi$
$743$	274.315	+	475.127i	0.369199	+	0.639471i	−0.620242	+	0.784411i	$0.712965\pi$
$744$	2.55675	+	7.66022i	0.00343649	+	0.0102960i
$745$	−391.310	−	99.1340i	−0.525248	−	0.133066i
$746$		−	1736.35i		−	2.32755i
$747$	550.556	−	413.593i	0.737023	−	0.553672i
$748$			4.98710i			0.00666725i
$749$	−818.078	−	472.318i	−1.09223	−	0.630598i
$750$	−107.853	−	1060.14i	−0.143804	−	1.41351i
$751$	133.681	+	231.542i	0.178003	+	0.308311i	0.941197	−	0.337859i	$-0.109703\pi$
$751$	133.681	+	231.542i	0.178003	+	0.308311i	−0.763193	+	0.646170i	$0.776370\pi$
$752$	389.005	+	673.777i	0.517294	+	0.895980i
$753$	−57.2317	+	280.237i	−0.0760049	+	0.372160i
$754$	648.003	−	1122.37i	0.859420	−	1.48856i
$755$	−424.730	+	120.057i	−0.562556	+	0.159016i
$756$	−608.254	+	880.803i	−0.804569	+	1.16508i
$757$			471.386i			0.622703i	0.950295	+	0.311351i	$0.100782\pi$
$757$			471.386i			0.622703i	−0.950295	+	0.311351i	$0.899218\pi$
$758$	−266.311	+	461.265i	−0.351334	+	0.608529i
$759$	5.59855	−	27.4135i	0.00737621	−	0.0361179i
$760$	0.404173	+	0.393263i	0.000531806	+	0.000517451i
$761$	917.999	−	530.007i	1.20631	−	0.696461i	0.244356	−	0.969686i	$-0.421424\pi$
$761$	917.999	−	530.007i	1.20631	−	0.696461i	0.961950	+	0.273225i	$0.0880902\pi$
$762$	502.292	+	445.056i	0.659175	+	0.584063i
$763$	−1386.00	−	800.210i	−1.81652	−	1.04877i
$764$		−	237.585i		−	0.310975i
$765$	−49.6145	−	118.615i	−0.0648555	−	0.155052i
$766$	−420.042			−0.548357
$767$	−591.478	+	1024.47i	−0.771158	+	1.33569i
$768$	−233.801	−	700.486i	−0.304428	−	0.912091i
$769$	−216.513	−	375.012i	−0.281551	−	0.487661i	0.690216	−	0.723604i	$-0.257516\pi$
$769$	−216.513	−	375.012i	−0.281551	−	0.487661i	−0.971767	+	0.235942i	$0.924182\pi$
$770$	42.4391	+	41.2935i	0.0551158	+	0.0536280i
$771$	−7.53452	−	22.5740i	−0.00977240	−	0.0292789i
$772$	446.642	+	257.869i	0.578552	+	0.334027i
$773$	−1088.28			−1.40787			−0.703936	−	0.710264i	$-0.748576\pi$
$773$	−1088.28			−1.40787			−0.703936	+	0.710264i	$0.748576\pi$
$774$	1466.60	−	177.864i	1.89483	−	0.229798i
$775$	−269.734	+	165.732i	−0.348044	+	0.213848i
$776$	4.23232	+	2.44353i	0.00545402	+	0.00314888i
$777$	−282.366	+	318.680i	−0.363406	+	0.410141i
$778$	1130.65	−	652.782i	1.45328	−	0.839052i
$779$	−17.5724	+	10.1454i	−0.0225576	+	0.0130237i
$780$	−84.7662	−	1143.02i	−0.108675	−	1.46541i
$781$	19.2523	−	33.3460i	0.0246509	−	0.0426965i
$782$	−176.773			−0.226052
$783$	−281.390	−	593.345i	−0.359374	−	0.757785i
$784$	716.626			0.914063
$785$	304.125	+	77.0466i	0.387420	+	0.0981485i
$786$	−311.789	+	1526.69i	−0.396678	+	1.94235i
$787$	279.669	−	161.467i	0.355361	−	0.205168i	−0.311683	−	0.950186i	$-0.600893\pi$
$787$	279.669	−	161.467i	0.355361	−	0.205168i	0.667044	+	0.745018i	$0.267559\pi$
$788$	683.665	+	1184.14i	0.867595	+	1.50272i
$789$	816.461	−	921.461i	1.03480	−	1.16788i
$790$	175.327	−	692.065i	0.221933	−	0.876032i
$791$		−	416.459i		−	0.526497i
$792$	0.492222	+	0.655225i	0.000621493	+	0.000827304i
$793$		−	415.628i		−	0.524121i
$794$	1769.17	+	1021.43i	2.22817	+	1.28643i
$795$	376.327	+	552.891i	0.473368	+	0.695461i
$796$	259.078	+	448.736i	0.325474	+	0.563738i
$797$	−722.713	−	1251.78i	−0.906792	−	1.57061i	−0.818494	−	0.574516i	$-0.805190\pi$
$797$	−722.713	−	1251.78i	−0.906792	−	1.57061i	−0.0882984	−	0.996094i	$-0.528143\pi$
$798$	41.7421	−	13.9322i	0.0523084	−	0.0174589i
$799$	70.8152	−	122.656i	0.0886298	−	0.153511i
$800$	−968.111	+	594.834i	−1.21014	+	0.743542i
$801$	−102.192	+	239.759i	−0.127581	+	0.299324i
$802$		−	215.234i		−	0.268372i
$803$	−30.9117	+	53.5406i	−0.0384953	+	0.0666758i
$804$	297.762	+	263.832i	0.370351	+	0.328150i
$805$	−738.626	+	759.118i	−0.917548	+	0.943003i
$806$	−584.370	+	337.386i	−0.725024	+	0.418593i
$807$	−120.706	+	591.043i	−0.149574	+	0.732396i
$808$	−10.5721	−	6.10380i	−0.0130843	−	0.00755421i
$809$			981.839i			1.21365i	0.794837	+	0.606823i	$0.207556\pi$
$809$			981.839i			1.21365i	−0.794837	+	0.606823i	$0.792444\pi$
$810$	−992.767	−	582.137i	−1.22564	−	0.718687i
$811$	−600.049			−0.739888			−0.369944	−	0.929054i	$-0.620623\pi$
$811$	−600.049			−0.739888			−0.369944	+	0.929054i	$0.620623\pi$
$812$	482.118	−	835.052i	0.593741	−	1.02839i
$813$	355.864	+	72.6766i	0.437717	+	0.0893932i
$814$	8.87812	+	15.3774i	0.0109068	+	0.0188911i
$815$	−841.852	+	865.207i	−1.03295	+	1.06160i
$816$	−89.2183	+	100.692i	−0.109336	+	0.123397i
$817$	−26.5427	−	15.3244i	−0.0324880	−	0.0187570i
$818$	1449.42			1.77191
$819$	−1510.50	−	643.819i	−1.84432	−	0.786104i
$820$	211.943	+	749.798i	0.258467	+	0.914388i
$821$	−896.354	−	517.510i	−1.09178	−	0.630342i	−0.157733	−	0.987482i	$-0.550418\pi$
$821$	−896.354	−	517.510i	−1.09178	−	0.630342i	−0.934051	+	0.357140i	$0.883752\pi$
$822$	15.0169	+	44.9917i	0.0182687	+	0.0547344i
$823$	1219.38	−	704.012i	1.48163	−	0.855421i	0.481850	−	0.876254i	$-0.339965\pi$
$823$	1219.38	−	704.012i	1.48163	−	0.855421i	0.999783	+	0.0208322i	$0.00663158\pi$
$824$	15.8672	−	9.16091i	0.0192563	−	0.0111176i
$825$	−20.6398	+	24.6195i	−0.0250179	+	0.0298418i
$826$	−872.048	+	1510.43i	−1.05575	+	1.82861i
$827$	1535.05			1.85617			0.928086	−	0.372367i	$-0.121454\pi$
$827$	1535.05			1.85617			0.928086	+	0.372367i	$0.121454\pi$
$828$	−638.404	+	479.587i	−0.771020	+	0.579211i
$829$	−185.325			−0.223552			−0.111776	−	0.993733i	$-0.535654\pi$
$829$	−185.325			−0.223552			−0.111776	+	0.993733i	$0.535654\pi$
$830$	−266.965	+	1053.79i	−0.321645	+	1.26962i
$831$	752.223	+	666.507i	0.905202	+	0.802055i
$832$	−1077.84	+	622.292i	−1.29548	+	0.747947i
$833$	−65.2280	−	112.978i	−0.0783049	−	0.135628i
$834$	−1419.25	−	289.848i	−1.70174	−	0.347540i
$835$	163.525	−	645.480i	0.195838	−	0.773030i
$836$		−	0.926087i		−	0.00110776i
$837$	−27.5855	+	340.793i	−0.0329575	+	0.407161i
$838$			1981.10i			2.36408i
$839$	−1120.53	−	646.937i	−1.33555	−	0.771081i	−0.349408	−	0.936971i	$-0.613617\pi$
$839$	−1120.53	−	646.937i	−1.33555	−	0.771081i	−0.986144	+	0.165889i	$0.946951\pi$
$840$	−2.29436	−	30.9379i	−0.00273138	−	0.0368309i
$841$	−124.726	−	216.032i	−0.148307	−	0.256875i
$842$	−1075.30	−	1862.47i	−1.27708	−	2.21196i
$843$	311.817	+	276.285i	0.369889	+	0.327741i
$844$	−199.087	+	344.829i	−0.235885	+	0.408565i
$845$	878.739	−	248.391i	1.03993	−	0.293954i
$846$	−152.628	−	1258.51i	−0.180411	−	1.48760i
$847$			1175.46i			1.38779i
$848$	349.905	−	606.053i	0.412623	−	0.714685i
$849$	275.474	−	91.9449i	0.324469	−	0.108298i
$850$	178.493	+	96.6406i	0.209991	+	0.113695i
$851$	−275.058	+	158.805i	−0.323217	+	0.186610i
$852$	−1042.32	+	347.895i	−1.22338	+	0.408328i
$853$	−335.726	−	193.832i	−0.393583	−	0.227235i	0.290128	−	0.956988i	$-0.406302\pi$
$853$	−335.726	−	193.832i	−0.393583	−	0.227235i	−0.683711	+	0.729752i	$0.739635\pi$
$854$		−	612.782i		−	0.717543i
$855$	9.21324	+	22.0263i	0.0107757	+	0.0257618i
$856$	20.6392			0.0241112
$857$	−39.5696	+	68.5365i	−0.0461722	+	0.0799726i	−0.888188	−	0.459480i	$-0.848036\pi$
$857$	−39.5696	+	68.5365i	−0.0461722	+	0.0799726i	0.842016	+	0.539453i	$0.181369\pi$
$858$	−45.4115	+	51.2515i	−0.0529271	+	0.0597337i
$859$	329.529	+	570.761i	0.383620	+	0.664448i	0.991577	−	0.129521i	$-0.0413441\pi$
$859$	329.529	+	570.761i	0.383620	+	0.664448i	−0.607957	+	0.793970i	$0.708011\pi$
$860$	−820.752	+	843.522i	−0.954363	+	0.980840i
$861$	1093.67	+	223.357i	1.27024	+	0.259416i
$862$	1225.23	+	707.386i	1.42138	+	0.820633i
$863$	−1070.61			−1.24057			−0.620286	−	0.784375i	$-0.712984\pi$
$863$	−1070.61			−1.24057			−0.620286	+	0.784375i	$0.712984\pi$
$864$	−99.0077	+	1223.15i	−0.114592	+	1.41568i
$865$	−322.572	+	91.1805i	−0.372916	+	0.105411i
$866$	1037.63	+	599.077i	1.19819	+	0.691775i
$867$	−825.471	−	168.583i	−0.952100	−	0.194444i
$868$	−434.775	+	251.017i	−0.500892	+	0.289190i
$869$	−18.6403	+	10.7620i	−0.0214503	+	0.0123843i
$870$	933.684	+	450.531i	1.07320	+	0.517851i
$871$	−305.131	+	528.502i	−0.350322	+	0.606776i
$872$	34.9674			0.0401002
$873$	124.276	+	165.430i	0.142355	+	0.189496i
$874$	32.8261			0.0375585
$875$	1160.82	−	362.701i	1.32665	−	0.414515i
$876$	1673.56	−	558.584i	1.91046	−	0.637653i
$877$	928.802	−	536.244i	1.05907	−	0.611452i	0.133893	−	0.990996i	$-0.457252\pi$
$877$	928.802	−	536.244i	1.05907	−	0.611452i	0.925174	+	0.379543i	$0.123919\pi$
$878$	−650.002	−	1125.84i	−0.740321	−	1.28227i
$879$	−365.748	−	1095.81i	−0.416095	−	1.24666i
$880$	32.5861	+	8.25531i	0.0370296	+	0.00938104i
$881$		−	1433.62i		−	1.62726i	−0.581381	−	0.813632i	$-0.697487\pi$
$881$		−	1433.62i		−	1.62726i	0.581381	−	0.813632i	$-0.302513\pi$
$882$	−1074.20	−	457.857i	−1.21792	−	0.519112i
$883$		−	731.816i		−	0.828784i	−0.910099	−	0.414392i	$-0.863994\pi$
$883$		−	731.816i		−	0.828784i	0.910099	−	0.414392i	$-0.136006\pi$
$884$	189.069	+	109.159i	0.213879	+	0.123483i
$885$	−852.240	−	411.232i	−0.962983	−	0.464668i
$886$	−330.013	−	571.600i	−0.372475	−	0.645146i
$887$	642.482	+	1112.81i	0.724331	+	1.25458i	0.959249	+	0.282563i	$0.0911846\pi$
$887$	642.482	+	1112.81i	0.724331	+	1.25458i	−0.234918	+	0.972015i	$0.575482\pi$
$888$	1.86145	−	9.11464i	0.00209623	−	0.0102642i
$889$	−382.956	+	663.299i	−0.430772	+	0.746119i
$890$	−111.918	−	395.935i	−0.125750	−	0.444871i
$891$	8.29381	+	33.6909i	0.00930843	+	0.0378124i
$892$			380.693i			0.426786i
$893$	−13.1501	+	22.7767i	−0.0147258	+	0.0255058i
$894$	137.716	−	674.331i	0.154045	−	0.754285i
$895$	132.365	−	136.037i	0.147894	−	0.151997i
$896$	−57.3054	+	33.0853i	−0.0639569	+	0.0369255i
$897$	−916.747	−	812.284i	−1.02201	−	0.905556i
$898$	1669.35	+	963.800i	1.85896	+	1.07327i
$899$		−	307.993i		−	0.342595i
$900$	906.802	−	135.241i	1.00756	−	0.150267i
$901$	−127.395			−0.141392
$902$	23.2755	−	40.3143i	0.0258043	−	0.0446944i
$903$	533.810	+	1599.34i	0.591151	+	1.77114i
$904$	4.54958	+	7.88010i	0.00503272	+	0.00871693i
$905$	996.277	+	969.383i	1.10086	+	1.07114i
$906$	−238.250	−	713.816i	−0.262969	−	0.787877i
$907$	−877.157	−	506.427i	−0.967097	−	0.558353i	−0.0687467	−	0.997634i	$-0.521900\pi$
$907$	−877.157	−	506.427i	−0.967097	−	0.558353i	−0.898350	+	0.439281i	$0.855233\pi$
$908$	806.770			0.888514
$909$	−310.433	−	413.235i	−0.341511	−	0.454604i
$910$	2494.43	−	705.092i	2.74113	−	0.774827i
$911$	551.233	+	318.255i	0.605086	+	0.349347i	0.771040	−	0.636787i	$-0.219737\pi$
$911$	551.233	+	318.255i	0.605086	+	0.349347i	−0.165954	+	0.986134i	$0.553070\pi$
$912$	16.5675	−	18.6982i	0.0181662	−	0.0205024i
$913$	28.3831	−	16.3870i	0.0310877	−	0.0179485i
$914$	−1810.13	+	1045.08i	−1.98045	+	1.14342i
$915$	331.558	−	24.5883i	0.362358	−	0.0268725i
$916$	−369.258	+	639.573i	−0.403120	+	0.698224i
$917$	−1778.35			−1.93931
$918$	198.069	−	93.9326i	0.215761	−	0.102323i
$919$	1142.09			1.24275			0.621377	−	0.783511i	$-0.286573\pi$
$919$	1142.09			1.24275			0.621377	+	0.783511i	$0.286573\pi$
$920$	5.68311	−	22.4328i	0.00617729	−	0.0243835i
$921$	−124.446	+	609.356i	−0.135121	+	0.661625i
$922$	−979.654	+	565.603i	−1.06253	+	0.613453i
$923$	−842.801	−	1459.77i	−0.913110	−	1.58155i
$924$	−33.7864	+	38.1314i	−0.0365654	+	0.0412678i
$925$	364.552	−	9.97730i	0.394110	−	0.0107863i
$926$		−	456.338i		−	0.492806i
$927$	770.071	−	93.3915i	0.830713	−	0.100746i
$928$		−	1105.42i		−	1.19119i
$929$	−681.162	−	393.269i	−0.733221	−	0.423325i	0.0863784	−	0.996262i	$-0.472471\pi$
$929$	−681.162	−	393.269i	−0.733221	−	0.423325i	−0.819599	+	0.572937i	$0.805804\pi$
$930$	−303.713	−	446.208i	−0.326573	−	0.479794i
$931$	12.1126	+	20.9796i	0.0130103	+	0.0225345i
$932$	−363.728	−	629.995i	−0.390266	−	0.675960i
$933$	461.464	−	154.023i	0.494602	−	0.165083i
$934$	577.787	−	1000.76i	0.618615	−	1.07147i
$935$	−1.66454	−	5.88870i	−0.00178026	−	0.00629807i
$936$	35.6145	−	4.31921i	0.0380497	−	0.00461454i
$937$		−	811.089i		−	0.865623i	−0.901484	−	0.432812i	$-0.857522\pi$
$937$		−	811.089i		−	0.865623i	0.901484	−	0.432812i	$-0.142478\pi$
$938$	−449.871	+	779.199i	−0.479606	+	0.830702i
$939$	509.286	+	451.253i	0.542370	+	0.480567i
$940$	723.839	+	704.300i	0.770042	+	0.749255i
$941$	−715.505	+	413.097i	−0.760367	+	0.438998i	−0.829428	−	0.558614i	$-0.811333\pi$
$941$	−715.505	+	413.097i	−0.760367	+	0.438998i	0.0690604	+	0.997612i	$0.478000\pi$
$942$	−107.032	+	524.087i	−0.113622	+	0.556356i
$943$	721.111	+	416.333i	0.764698	+	0.441499i
$944$			990.124i			1.04886i
$945$	424.232	−	1243.06i	0.448923	−	1.31540i
$946$	70.3142			0.0743279
$947$	458.725	−	794.535i	0.484398	−	0.839002i	−0.515441	−	0.856925i	$-0.672372\pi$
$947$	458.725	−	794.535i	0.484398	−	0.839002i	0.999839	+	0.0179227i	$0.00570527\pi$
$948$	601.830	+	122.909i	0.634842	+	0.129651i
$949$	1353.21	+	2343.83i	1.42593	+	2.46979i
$950$	−33.1455	−	17.9458i	−0.0348900	−	0.0188904i
$951$	972.435	−	1097.49i	1.02254	−	1.15404i
$952$	5.11751	+	2.95460i	0.00537554	+	0.00310357i
$953$	192.772			0.202279			0.101140	−	0.994872i	$-0.467751\pi$
$953$	192.772			0.202279			0.101140	+	0.994872i	$0.467751\pi$
$954$	−911.709	+	684.901i	−0.955670	+	0.717925i
$955$	79.2986	+	280.537i	0.0830352	+	0.293756i
$956$	−53.8513	−	31.0910i	−0.0563298	−	0.0325220i
$957$	−9.89534	−	29.6472i	−0.0103400	−	0.0309794i
$958$	−2078.50	+	1200.03i	−2.16963	+	1.25264i
$959$	−46.8805	+	27.0665i	−0.0488848	+	0.0282236i
$960$	−560.184	−	823.009i	−0.583525	−	0.857301i
$961$	400.321	−	693.376i	0.416567	−	0.721515i
$962$	777.308			0.808012
$963$	803.854	+	342.626i	0.834740	+	0.355791i
$964$	−1300.54			−1.34911
$965$	−613.457	−	155.412i	−0.635707	−	0.161049i
$966$	−1351.61	−	1197.59i	−1.39918	−	1.23974i
$967$	−742.787	+	428.848i	−0.768136	+	0.443483i	−0.832209	−	0.554462i	$-0.812924\pi$
$967$	−742.787	+	428.848i	−0.768136	+	0.443483i	0.0640734	+	0.997945i	$0.479591\pi$
$968$	−12.8412	−	22.2416i	−0.0132657	−	0.0229769i
$969$	−4.45581	−	0.909994i	−0.00459836	−	0.000939106i
$970$	−316.641	−	80.2173i	−0.326434	−	0.0826983i
$971$			546.278i			0.562594i	0.959621	+	0.281297i	$0.0907645\pi$
$971$			546.278i			0.562594i	−0.959621	+	0.281297i	$0.909235\pi$
$972$	460.473	−	876.594i	0.473738	−	0.901846i
$973$		−	1653.20i		−	1.69908i
$974$	554.980	+	320.418i	0.569795	+	0.328971i
$975$	481.595	+	1321.37i	0.493943	+	1.35525i
$976$	−173.938	−	301.270i	−0.178215	−	0.308678i
$977$	−397.664	−	688.774i	−0.407025	−	0.704988i	0.587530	−	0.809203i	$-0.300101\pi$
$977$	−397.664	−	688.774i	−0.407025	−	0.704988i	−0.994555	+	0.104214i	$0.966767\pi$
$978$	−1540.50	−	1364.96i	−1.57515	−	1.39567i
$979$	−6.20231	+	10.7427i	−0.00633535	+	0.0109732i
$980$	895.182	−	253.039i	0.913451	−	0.258203i
$981$	1361.91	+	580.485i	1.38828	+	0.591728i
$982$		−	2174.27i		−	2.21412i
$983$	−539.710	+	934.805i	−0.549044	+	0.950972i	0.449297	+	0.893383i	$0.351675\pi$
$983$	−539.710	+	934.805i	−0.549044	+	0.950972i	−0.998340	+	0.0575890i	$0.981659\pi$
$984$	−23.1342	+	7.72149i	−0.0235104	+	0.00784704i
$985$	−1202.49	−	1170.03i	−1.22080	−	1.18785i
$986$	−171.013	+	98.7344i	−0.173441	+	0.100136i
$987$	1372.42	−	458.070i	1.39049	−	0.464104i
$988$	−35.1095	−	20.2705i	−0.0355359	−	0.0205167i
$989$			1257.72i			1.27171i
$990$	−43.5713	−	33.1940i	−0.0440114	−	0.0335293i
$991$	168.017			0.169543			0.0847716	−	0.996400i	$-0.472984\pi$
$991$	168.017			0.169543			0.0847716	+	0.996400i	$0.472984\pi$
$992$	−287.773	+	498.437i	−0.290093	+	0.502457i
$993$	−472.804	+	533.608i	−0.476137	+	0.537370i
$994$	−1242.59	−	2152.22i	−1.25009	−	2.16521i
$995$	−455.689	−	443.388i	−0.457979	−	0.445616i
$996$	−916.390	−	187.151i	−0.920070	−	0.187902i
$997$	−757.109	−	437.117i	−0.759387	−	0.438432i	0.0696887	−	0.997569i	$-0.477799\pi$
$997$	−757.109	−	437.117i	−0.759387	−	0.438432i	−0.829076	+	0.559137i	$0.811133\pi$
$998$	−579.829			−0.580991
$999$	223.809	−	324.095i	0.224033	−	0.324419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.h.a.29.2	yes	20
3.2	odd	2		135.3.h.a.89.9		20
5.2	odd	4		225.3.j.e.101.2		20
5.3	odd	4		225.3.j.e.101.9		20
5.4	even	2	inner	45.3.h.a.29.9	yes	20
9.2	odd	6		405.3.d.a.404.3		20
9.4	even	3		135.3.h.a.44.2		20
9.5	odd	6	inner	45.3.h.a.14.9	yes	20
9.7	even	3		405.3.d.a.404.18		20
15.2	even	4		675.3.j.e.251.9		20
15.8	even	4		675.3.j.e.251.2		20
15.14	odd	2		135.3.h.a.89.2		20
45.4	even	6		135.3.h.a.44.9		20
45.13	odd	12		675.3.j.e.476.2		20
45.14	odd	6	inner	45.3.h.a.14.2	✓	20
45.22	odd	12		675.3.j.e.476.9		20
45.23	even	12		225.3.j.e.176.9		20
45.29	odd	6		405.3.d.a.404.17		20
45.32	even	12		225.3.j.e.176.2		20
45.34	even	6		405.3.d.a.404.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.2	✓	20	45.14	odd	6	inner
45.3.h.a.14.9	yes	20	9.5	odd	6	inner
45.3.h.a.29.2	yes	20	1.1	even	1	trivial
45.3.h.a.29.9	yes	20	5.4	even	2	inner
135.3.h.a.44.2		20	9.4	even	3
135.3.h.a.44.9		20	45.4	even	6
135.3.h.a.89.2		20	15.14	odd	2
135.3.h.a.89.9		20	3.2	odd	2
225.3.j.e.101.2		20	5.2	odd	4
225.3.j.e.101.9		20	5.3	odd	4
225.3.j.e.176.2		20	45.32	even	12
225.3.j.e.176.9		20	45.23	even	12
405.3.d.a.404.3		20	9.2	odd	6
405.3.d.a.404.4		20	45.34	even	6
405.3.d.a.404.17		20	45.29	odd	6
405.3.d.a.404.18		20	9.7	even	3
675.3.j.e.251.2		20	15.8	even	4
675.3.j.e.251.9		20	15.2	even	4
675.3.j.e.476.2		20	45.13	odd	12
675.3.j.e.476.9		20	45.22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42081 + 2.46092i) q^{2} +(2.93933 + 0.600288i) q^{3} +(-2.03740 - 3.52889i) q^{4} +(3.58357 + 3.48684i) q^{5} +(-5.65349 + 6.38055i) q^{6} +(-8.42581 - 4.86464i) q^{7} +0.212574 q^{8} +(8.27931 + 3.52889i) q^{9} +(-13.6724 + 3.86473i) q^{10} +(0.370966 + 0.214177i) q^{11} +(-3.87025 - 11.5956i) q^{12} +(16.2396 - 9.37595i) q^{13} +(23.9429 - 13.8235i) q^{14} +(8.44019 + 12.4001i) q^{15} +(7.84759 - 13.5924i) q^{16} -2.85718 q^{17} +(-20.4476 + 15.3608i) q^{18} +0.530568 q^{19} +(5.00347 - 19.7501i) q^{20} +(-21.8460 - 19.3567i) q^{21} +(-1.05414 + 0.608611i) q^{22} +(-10.8863 - 18.8557i) q^{23} +(0.624825 + 0.127606i) q^{24} +(0.683961 + 24.9906i) q^{25} +53.2858i q^{26} +(22.2173 + 15.3425i) q^{27} +39.6450i q^{28} +(-21.0633 - 12.1609i) q^{29} +(-42.5076 + 3.15236i) q^{30} +(6.33163 + 10.9667i) q^{31} +(22.7250 + 39.3609i) q^{32} +(0.961823 + 0.852224i) q^{33} +(4.05951 - 7.03128i) q^{34} +(-13.2323 - 46.8122i) q^{35} +(-4.41525 - 36.4065i) q^{36} -14.5875i q^{37} +(-0.753837 + 1.30568i) q^{38} +(53.3619 - 17.8106i) q^{39} +(0.761774 + 0.741210i) q^{40} +(-33.1200 + 19.1218i) q^{41} +(78.6743 - 26.2591i) q^{42} +(-50.0269 - 28.8831i) q^{43} -1.74546i q^{44} +(17.3648 + 41.5146i) q^{45} +61.8697 q^{46} +(-24.7850 + 42.9289i) q^{47} +(31.2260 - 35.2418i) q^{48} +(22.8295 + 39.5418i) q^{49} +(-62.4716 - 33.8238i) q^{50} +(-8.39819 - 1.71513i) q^{51} +(-66.1734 - 38.2052i) q^{52} +44.5876 q^{53} +(-69.3232 + 32.8760i) q^{54} +(0.582582 + 2.06102i) q^{55} +(-1.79111 - 1.03410i) q^{56} +(1.55951 + 0.318494i) q^{57} +(59.8538 - 34.5566i) q^{58} +(-54.6329 + 31.5423i) q^{59} +(26.5626 - 55.0485i) q^{60} +(11.0823 - 19.1951i) q^{61} -35.9842 q^{62} +(-52.5931 - 70.0096i) q^{63} -66.3710 q^{64} +(90.8883 + 23.0255i) q^{65} +(-3.46382 + 1.15612i) q^{66} +(-28.1839 + 16.2720i) q^{67} +(5.82123 + 10.0827i) q^{68} +(-20.6797 - 61.9581i) q^{69} +(134.001 + 33.9477i) q^{70} -89.8896i q^{71} +(1.75996 + 0.750149i) q^{72} +144.328i q^{73} +(35.8987 + 20.7261i) q^{74} +(-12.9912 + 73.8663i) q^{75} +(-1.08098 - 1.87232i) q^{76} +(-2.08379 - 3.60923i) q^{77} +(-31.9868 + 156.625i) q^{78} +(-25.1240 + 43.5160i) q^{79} +(75.5169 - 21.3462i) q^{80} +(56.0939 + 58.4335i) q^{81} -108.674i q^{82} +(38.2556 - 66.2606i) q^{83} +(-23.7984 + 116.530i) q^{84} +(-10.2389 - 9.96251i) q^{85} +(142.158 - 82.0747i) q^{86} +(-54.6118 - 48.3889i) q^{87} +(0.0788577 + 0.0455285i) q^{88} +28.9588i q^{89} +(-126.836 - 16.2510i) q^{90} -182.443 q^{91} +(-44.3598 + 76.8334i) q^{92} +(12.0276 + 36.0355i) q^{93} +(-70.4296 - 121.988i) q^{94} +(1.90133 + 1.85000i) q^{95} +(43.1684 + 129.336i) q^{96} +(19.9099 + 11.4950i) q^{97} -129.746 q^{98} +(2.31554 + 3.08234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + 4 q^{10} - 24 q^{11} + 30 q^{14} + 24 q^{15} - 26 q^{16} - 8 q^{19} + 144 q^{20} - 96 q^{21} - 102 q^{24} + 2 q^{25} - 114 q^{29} - 48 q^{30} + 28 q^{31}+ \cdots - 468 q^{99}+O(q^{100}) \) 20 * q - 18 * q^4 - 12 * q^5 + 12 * q^6 - 18 * q^9 + 4 * q^10 - 24 * q^11 + 30 * q^14 + 24 * q^15 - 26 * q^16 - 8 * q^19 + 144 * q^20 - 96 * q^21 - 102 * q^24 + 2 * q^25 - 114 * q^29 - 48 * q^30 + 28 * q^31 - 4 * q^34 + 432 * q^36 + 240 * q^39 - 34 * q^40 + 102 * q^41 - 162 * q^45 + 116 * q^46 - 40 * q^49 - 408 * q^50 - 156 * q^51 - 270 * q^54 + 36 * q^55 - 618 * q^56 + 120 * q^59 + 330 * q^60 - 50 * q^61 + 140 * q^64 + 492 * q^65 - 768 * q^66 + 162 * q^69 - 54 * q^70 + 504 * q^74 + 276 * q^75 - 96 * q^76 - 128 * q^79 + 846 * q^81 + 450 * q^84 - 74 * q^85 + 1488 * q^86 - 990 * q^90 - 288 * q^91 + 218 * q^94 - 762 * q^95 - 474 * q^96 - 468 * q^99

Introduction

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