LMFDB - Embedded newform 273.3.bo.c.244.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,3,Mod(160,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("273.160");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	273.bo (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.43871121704$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			244.10
Character	$\chi$	$=$	273.244
Dual form			273.3.bo.c.160.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.181190 - 0.104610i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.97811 + 3.42619i) q^{4} +6.37482 q^{5} +(-0.181190 + 0.313831i) q^{6} +(-3.53577 + 6.04139i) q^{7} +1.66461i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.181190 - 0.104610i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.97811 + 3.42619i) q^{4} +6.37482 q^{5} +(-0.181190 + 0.313831i) q^{6} +(-3.53577 + 6.04139i) q^{7} +1.66461i q^{8} +(1.50000 - 2.59808i) q^{9} +(1.15505 - 0.666871i) q^{10} +(10.6304 - 6.13745i) q^{11} -6.85239i q^{12} +(-4.60160 + 12.1583i) q^{13} +(-0.00865587 + 1.46452i) q^{14} +(-9.56223 + 5.52075i) q^{15} +(-7.73832 - 13.4032i) q^{16} +(-21.0081 - 12.1290i) q^{17} -0.627661i q^{18} +(-17.2042 + 29.7986i) q^{19} +(-12.6101 + 21.8414i) q^{20} +(0.0716584 - 12.1241i) q^{21} +(1.28408 - 2.22409i) q^{22} +(16.9205 + 29.3072i) q^{23} +(-1.44159 - 2.49691i) q^{24} +15.6383 q^{25} +(0.438123 + 2.68435i) q^{26} +5.19615i q^{27} +(-13.7048 - 24.0648i) q^{28} +(-10.3996 - 18.0126i) q^{29} +(-1.15505 + 2.00061i) q^{30} +21.1601 q^{31} +(-8.57058 - 4.94822i) q^{32} +(-10.6304 + 18.4123i) q^{33} -5.07528 q^{34} +(-22.5399 + 38.5127i) q^{35} +(5.93434 + 10.2786i) q^{36} +(-43.2927 + 24.9951i) q^{37} +7.19895i q^{38} +(-3.62704 - 22.2226i) q^{39} +10.6116i q^{40} +(25.3016 + 43.8237i) q^{41} +(-1.25533 - 2.20427i) q^{42} +(10.1236 - 17.5346i) q^{43} +48.5623i q^{44} +(9.56223 - 16.5623i) q^{45} +(6.13167 + 3.54012i) q^{46} -42.2799 q^{47} +(23.2150 + 13.4032i) q^{48} +(-23.9967 - 42.7219i) q^{49} +(2.83351 - 1.63593i) q^{50} +42.0162 q^{51} +(-32.5543 - 39.8165i) q^{52} -6.63303 q^{53} +(0.543571 + 0.941492i) q^{54} +(67.7667 - 39.1251i) q^{55} +(-10.0565 - 5.88566i) q^{56} -59.5971i q^{57} +(-3.76861 - 2.17581i) q^{58} +(11.2729 - 19.5252i) q^{59} -43.6827i q^{60} +(56.9807 + 32.8978i) q^{61} +(3.83401 - 2.21357i) q^{62} +(10.3923 + 18.2483i) q^{63} +59.8360 q^{64} +(-29.3343 + 77.5072i) q^{65} +4.44818i q^{66} +(100.700 - 58.1389i) q^{67} +(83.1128 - 47.9852i) q^{68} +(-50.7616 - 29.3072i) q^{69} +(-0.0551796 + 9.33603i) q^{70} +(41.0541 + 23.7026i) q^{71} +(4.32477 + 2.49691i) q^{72} -18.1837 q^{73} +(-5.22948 + 9.05772i) q^{74} +(-23.4574 + 13.5432i) q^{75} +(-68.0638 - 117.890i) q^{76} +(-0.507837 + 85.9227i) q^{77} +(-2.98190 - 3.64709i) q^{78} +85.7191 q^{79} +(-49.3304 - 85.4427i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(9.16882 + 5.29362i) q^{82} +61.5420 q^{83} +(41.3979 + 24.2284i) q^{84} +(-133.923 - 77.3204i) q^{85} -4.23612i q^{86} +(31.1988 + 18.0126i) q^{87} +(10.2164 + 17.6954i) q^{88} +(-37.7304 - 65.3510i) q^{89} -4.00123i q^{90} +(-57.1831 - 70.7891i) q^{91} -133.883 q^{92} +(-31.7402 + 18.3252i) q^{93} +(-7.66071 + 4.42291i) q^{94} +(-109.674 + 189.960i) q^{95} +17.1412 q^{96} +(-29.0020 + 50.2329i) q^{97} +(-8.81711 - 5.23049i) q^{98} -36.8247i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9}+O(q^{10}) $ 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9	$ 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9} + 42 q^{11} - 36 q^{13} + 16 q^{14} + 6 q^{15} - 96 q^{16} - 12 q^{17} + 12 q^{19} - 10 q^{20} - 18 q^{22} + 24 q^{23} + 264 q^{25} + 114 q^{26} - 104 q^{28} + 76 q^{29} - 160 q^{31} - 42 q^{33} - 192 q^{34} - 100 q^{35} - 132 q^{36} + 6 q^{37} + 60 q^{39} + 200 q^{41} + 18 q^{42} + 48 q^{43} - 6 q^{45} + 396 q^{46} + 56 q^{47} + 288 q^{48} - 154 q^{49} - 102 q^{50} + 24 q^{51} - 360 q^{52} + 76 q^{53} + 192 q^{55} - 132 q^{56} - 162 q^{58} + 128 q^{59} - 120 q^{61} + 24 q^{62} - 30 q^{63} - 484 q^{64} - 284 q^{65} - 144 q^{67} + 234 q^{68} - 72 q^{69} + 300 q^{70} - 96 q^{71} + 728 q^{73} - 144 q^{74} - 396 q^{75} - 516 q^{76} - 160 q^{77} - 144 q^{78} + 68 q^{79} - 58 q^{80} - 162 q^{81} + 72 q^{82} + 368 q^{83} + 108 q^{84} - 324 q^{85} - 228 q^{87} + 186 q^{88} + 92 q^{89} + 176 q^{91} - 1044 q^{92} + 240 q^{93} - 336 q^{94} - 2 q^{95} - 72 q^{97} + 234 q^{98}+O(q^{100}) $ 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9 + 42 * q^11 - 36 * q^13 + 16 * q^14 + 6 * q^15 - 96 * q^16 - 12 * q^17 + 12 * q^19 - 10 * q^20 - 18 * q^22 + 24 * q^23 + 264 * q^25 + 114 * q^26 - 104 * q^28 + 76 * q^29 - 160 * q^31 - 42 * q^33 - 192 * q^34 - 100 * q^35 - 132 * q^36 + 6 * q^37 + 60 * q^39 + 200 * q^41 + 18 * q^42 + 48 * q^43 - 6 * q^45 + 396 * q^46 + 56 * q^47 + 288 * q^48 - 154 * q^49 - 102 * q^50 + 24 * q^51 - 360 * q^52 + 76 * q^53 + 192 * q^55 - 132 * q^56 - 162 * q^58 + 128 * q^59 - 120 * q^61 + 24 * q^62 - 30 * q^63 - 484 * q^64 - 284 * q^65 - 144 * q^67 + 234 * q^68 - 72 * q^69 + 300 * q^70 - 96 * q^71 + 728 * q^73 - 144 * q^74 - 396 * q^75 - 516 * q^76 - 160 * q^77 - 144 * q^78 + 68 * q^79 - 58 * q^80 - 162 * q^81 + 72 * q^82 + 368 * q^83 + 108 * q^84 - 324 * q^85 - 228 * q^87 + 186 * q^88 + 92 * q^89 + 176 * q^91 - 1044 * q^92 + 240 * q^93 - 336 * q^94 - 2 * q^95 - 72 * q^97 + 234 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.181190	−	0.104610i	0.0905951	−	0.0523051i	−0.454018	−	0.890992i	$-0.650010\pi$
$2$	0.181190	−	0.104610i	0.0905951	−	0.0523051i	0.544613	+	0.838687i	$0.316676\pi$
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$	−1.97811	+	3.42619i	−0.494528	+	0.856548i
$5$	6.37482			1.27496			0.637482	−	0.770465i	$-0.279976\pi$
$5$	6.37482			1.27496			0.637482	+	0.770465i	$0.279976\pi$
$6$	−0.181190	+	0.313831i	−0.0301984	+	0.0523051i
$7$	−3.53577	+	6.04139i	−0.505110	+	0.863055i
$7$	−3.53577	+	6.04139i	−0.505110	+	0.863055i
$8$			1.66461i			0.208076i
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	1.15505	−	0.666871i	0.115505	−	0.0666871i
$11$	10.6304	−	6.13745i	0.966397	−	0.557950i	0.0682611	−	0.997667i	$-0.478255\pi$
$11$	10.6304	−	6.13745i	0.966397	−	0.557950i	0.898136	+	0.439718i	$0.144922\pi$
$12$		−	6.85239i		−	0.571032i
$13$	−4.60160	+	12.1583i	−0.353969	+	0.935257i
$13$	−4.60160	+	12.1583i	−0.353969	+	0.935257i
$14$	−0.00865587	+	1.46452i	−0.000618276	+	0.104608i
$15$	−9.56223	+	5.52075i	−0.637482	+	0.368050i
$16$	−7.73832	−	13.4032i	−0.483645	−	0.837698i
$17$	−21.0081	−	12.1290i	−1.23577	−	0.713473i	−0.267544	−	0.963546i	$-0.586212\pi$
$17$	−21.0081	−	12.1290i	−1.23577	−	0.713473i	−0.968227	+	0.250073i	$0.919545\pi$
$18$		−	0.627661i		−	0.0348701i
$19$	−17.2042	+	29.7986i	−0.905485	+	1.56835i	−0.0852199	+	0.996362i	$0.527159\pi$
$19$	−17.2042	+	29.7986i	−0.905485	+	1.56835i	−0.820265	+	0.571984i	$0.806174\pi$
$20$	−12.6101	+	21.8414i	−0.630506	+	1.09207i
$21$	0.0716584	−	12.1241i	0.00341231	−	0.577340i
$22$	1.28408	−	2.22409i	0.0583672	−	0.101095i
$23$	16.9205	+	29.3072i	0.735675	+	1.27423i	0.954427	+	0.298446i	$0.0964683\pi$
$23$	16.9205	+	29.3072i	0.735675	+	1.27423i	−0.218751	+	0.975781i	$0.570198\pi$
$24$	−1.44159	−	2.49691i	−0.0600663	−	0.104038i
$25$	15.6383			0.625532
$26$	0.438123	+	2.68435i	0.0168509	+	0.103244i
$27$			5.19615i			0.192450i
$28$	−13.7048	−	24.0648i	−0.489457	−	0.859456i
$29$	−10.3996	−	18.0126i	−0.358607	−	0.621125i	0.629121	−	0.777307i	$-0.283415\pi$
$29$	−10.3996	−	18.0126i	−0.358607	−	0.621125i	−0.987728	+	0.156182i	$0.950081\pi$
$30$	−1.15505	+	2.00061i	−0.0385018	+	0.0666871i
$31$	21.1601			0.682585			0.341292	−	0.939957i	$-0.389135\pi$
$31$	21.1601			0.682585			0.341292	+	0.939957i	$0.389135\pi$
$32$	−8.57058	−	4.94822i	−0.267831	−	0.154632i
$33$	−10.6304	+	18.4123i	−0.322132	+	0.557950i
$34$	−5.07528			−0.149273
$35$	−22.5399	+	38.5127i	−0.643996	+	1.10036i
$36$	5.93434	+	10.2786i	0.164843	+	0.285516i
$37$	−43.2927	+	24.9951i	−1.17007	+	0.675542i	−0.953697	−	0.300768i	$-0.902757\pi$
$37$	−43.2927	+	24.9951i	−1.17007	+	0.675542i	−0.216376	+	0.976310i	$0.569424\pi$
$38$			7.19895i			0.189446i
$39$	−3.62704	−	22.2226i	−0.0930010	−	0.569811i
$40$			10.6116i			0.265289i
$41$	25.3016	+	43.8237i	0.617113	+	1.06887i	0.990010	+	0.140998i	$0.0450312\pi$
$41$	25.3016	+	43.8237i	0.617113	+	1.06887i	−0.372897	+	0.927873i	$0.621635\pi$
$42$	−1.25533	−	2.20427i	−0.0298887	−	0.0524827i
$43$	10.1236	−	17.5346i	0.235432	−	0.407780i	−0.723966	−	0.689836i	$-0.757683\pi$
$43$	10.1236	−	17.5346i	0.235432	−	0.407780i	0.959398	+	0.282055i	$0.0910161\pi$
$44$			48.5623i			1.10369i
$45$	9.56223	−	16.5623i	0.212494	−	0.368050i
$46$	6.13167	+	3.54012i	0.133297	+	0.0769591i
$47$	−42.2799			−0.899573			−0.449787	−	0.893136i	$-0.648500\pi$
$47$	−42.2799			−0.899573			−0.449787	+	0.893136i	$0.648500\pi$
$48$	23.2150	+	13.4032i	0.483645	+	0.279233i
$49$	−23.9967	−	42.7219i	−0.489728	−	0.871875i
$50$	2.83351	−	1.63593i	0.0566701	−	0.0327185i
$51$	42.0162			0.823847
$52$	−32.5543	−	39.8165i	−0.626045	−	0.765703i
$53$	−6.63303			−0.125152			−0.0625758	−	0.998040i	$-0.519932\pi$
$53$	−6.63303			−0.125152			−0.0625758	+	0.998040i	$0.519932\pi$
$54$	0.543571	+	0.941492i	0.0100661	+	0.0174350i
$55$	67.7667	−	39.1251i	1.23212	−	0.711365i
$56$	−10.0565	−	5.88566i	−0.179581	−	0.105101i
$57$		−	59.5971i		−	1.04556i
$58$	−3.76861	−	2.17581i	−0.0649761	−	0.0375139i
$59$	11.2729	−	19.5252i	0.191066	−	0.330936i	−0.754538	−	0.656256i	$-0.772139\pi$
$59$	11.2729	−	19.5252i	0.191066	−	0.330936i	0.945604	+	0.325321i	$0.105472\pi$
$60$		−	43.6827i		−	0.728045i
$61$	56.9807	+	32.8978i	0.934110	+	0.539309i	0.888109	−	0.459633i	$-0.152019\pi$
$61$	56.9807	+	32.8978i	0.934110	+	0.539309i	0.0460008	+	0.998941i	$0.485352\pi$
$62$	3.83401	−	2.21357i	0.0618389	−	0.0357027i
$63$	10.3923	+	18.2483i	0.164958	+	0.289655i
$64$	59.8360			0.934938
$65$	−29.3343	+	77.5072i	−0.451298	+	1.19242i
$66$			4.44818i			0.0673967i
$67$	100.700	−	58.1389i	1.50298	−	0.867746i	0.502985	−	0.864295i	$-0.332235\pi$
$67$	100.700	−	58.1389i	1.50298	−	0.867746i	0.999994	−	0.00345054i	$-0.00109834\pi$
$68$	83.1128	−	47.9852i	1.22225	−	0.705665i
$69$	−50.7616	−	29.3072i	−0.735675	−	0.424742i
$70$	−0.0551796	+	9.33603i	−0.000788280	+	0.133372i
$71$	41.0541	+	23.7026i	0.578227	+	0.333839i	0.760428	−	0.649422i	$-0.224989\pi$
$71$	41.0541	+	23.7026i	0.578227	+	0.333839i	−0.182202	+	0.983261i	$0.558322\pi$
$72$	4.32477	+	2.49691i	0.0600663	+	0.0346793i
$73$	−18.1837			−0.249091			−0.124546	−	0.992214i	$-0.539747\pi$
$73$	−18.1837			−0.249091			−0.124546	+	0.992214i	$0.539747\pi$
$74$	−5.22948	+	9.05772i	−0.0706686	+	0.122402i
$75$	−23.4574	+	13.5432i	−0.312766	+	0.180576i
$76$	−68.0638	−	117.890i	−0.895576	−	1.55118i
$77$	−0.507837	+	85.9227i	−0.00659528	+	1.11588i
$78$	−2.98190	−	3.64709i	−0.0382294	−	0.0467576i
$79$	85.7191			1.08505			0.542526	−	0.840039i	$-0.317468\pi$
$79$	85.7191			1.08505			0.542526	+	0.840039i	$0.317468\pi$
$80$	−49.3304	−	85.4427i	−0.616630	−	1.06803i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	9.16882	+	5.29362i	0.111815	+	0.0645563i
$83$	61.5420			0.741470			0.370735	−	0.928739i	$-0.379106\pi$
$83$	61.5420			0.741470			0.370735	+	0.928739i	$0.379106\pi$
$84$	41.3979	+	24.2284i	0.492832	+	0.288434i
$85$	−133.923	−	77.3204i	−1.57556	−	0.909652i
$86$		−	4.23612i		−	0.0492572i
$87$	31.1988	+	18.0126i	0.358607	+	0.207042i
$88$	10.2164	+	17.6954i	0.116096	+	0.201084i
$89$	−37.7304	−	65.3510i	−0.423937	−	0.734281i	0.572383	−	0.819986i	$-0.306019\pi$
$89$	−37.7304	−	65.3510i	−0.423937	−	0.734281i	−0.996321	+	0.0857052i	$0.972686\pi$
$90$		−	4.00123i		−	0.0444581i
$91$	−57.1831	−	70.7891i	−0.628385	−	0.777902i
$92$	−133.883			−1.45525
$93$	−31.7402	+	18.3252i	−0.341292	+	0.197045i
$94$	−7.66071	+	4.42291i	−0.0814969	+	0.0470523i
$95$	−109.674	+	189.960i	−1.15446	+	1.99958i
$96$	17.1412			0.178554
$97$	−29.0020	+	50.2329i	−0.298989	+	0.517865i	−0.975905	−	0.218196i	$-0.929983\pi$
$97$	−29.0020	+	50.2329i	−0.298989	+	0.517865i	0.676916	+	0.736061i	$0.263316\pi$
$98$	−8.81711	−	5.23049i	−0.0899705	−	0.0533723i
$99$		−	36.8247i		−	0.371966i
$100$	−30.9343	+	53.5798i	−0.309343	+	0.535798i
$101$	149.251	−	86.1701i	1.47773	−	0.853169i	0.478049	−	0.878333i	$-0.341344\pi$
$101$	149.251	−	86.1701i	1.47773	−	0.853169i	0.999683	+	0.0251643i	$0.00801088\pi$
$102$	7.61293	−	4.39532i	0.0746365	−	0.0430914i
$103$		−	59.9556i		−	0.582093i	−0.956709	−	0.291047i	$-0.905997\pi$
$103$		−	59.9556i		−	0.582093i	0.956709	−	0.291047i	$-0.0940034\pi$
$104$	−20.2388	−	7.65984i	−0.194604	−	0.0736523i
$105$	0.456809	−	77.2892i	0.00435057	−	0.736088i
$106$	−1.20184	+	0.693883i	−0.0113381	+	0.00654606i
$107$	35.4068	+	61.3265i	0.330905	+	0.573144i	0.982690	−	0.185260i	$-0.0593127\pi$
$107$	35.4068	+	61.3265i	0.330905	+	0.573144i	−0.651784	+	0.758404i	$0.725979\pi$
$108$	−17.8030	−	10.2786i	−0.164843	−	0.0951720i
$109$			48.3798i			0.443852i	0.975064	+	0.221926i	$0.0712343\pi$
$109$			48.3798i			0.443852i	−0.975064	+	0.221926i	$0.928766\pi$
$110$	8.18577	−	14.1782i	0.0744161	−	0.128892i
$111$	43.2927	−	74.9852i	0.390024	−	0.675542i
$112$	108.335	+	0.640300i	0.967273	+	0.00571696i
$113$	−8.45251	+	14.6402i	−0.0748009	+	0.129559i	−0.901000	−	0.433820i	$-0.857165\pi$
$113$	−8.45251	+	14.6402i	−0.0748009	+	0.129559i	0.826199	+	0.563379i	$0.190499\pi$
$114$	−6.23447	−	10.7984i	−0.0546883	−	0.0947230i
$115$	107.865	+	186.828i	0.937959	+	1.62459i
$116$	82.2863			0.709365
$117$	24.6859	+	30.1928i	0.210991	+	0.258058i
$118$		−	4.71703i		−	0.0399749i
$119$	147.556	−	84.0326i	1.23997	−	0.706156i
$120$	−9.18988	−	15.9173i	−0.0765823	−	0.132644i
$121$	14.8365	−	25.6975i	0.122616	−	0.212376i
$122$	13.7658			0.112834
$123$	−75.9049	−	43.8237i	−0.617113	−	0.356290i
$124$	−41.8571	+	72.4987i	−0.337558	+	0.584667i
$125$	−59.6791			−0.477433
$126$	3.79194	+	2.21926i	0.0300948	+	0.0176132i
$127$	76.1714	+	131.933i	0.599775	+	1.03884i	0.992854	+	0.119336i	$0.0380765\pi$
$127$	76.1714	+	131.933i	0.599775	+	1.03884i	−0.393079	+	0.919505i	$0.628590\pi$
$128$	45.1240	−	26.0524i	0.352531	−	0.203534i
$129$			35.0691i			0.271854i
$130$	2.79295	+	17.1122i	0.0214842	+	0.131632i
$131$		−	20.5925i		−	0.157195i	−0.996906	−	0.0785974i	$-0.974956\pi$
$131$		−	20.5925i		−	0.157195i	0.996906	−	0.0785974i	$-0.0250442\pi$
$132$	−42.0561	−	72.8434i	−0.318607	−	0.551844i
$133$	−119.195	−	209.298i	−0.896200	−	1.57367i
$134$	12.1639	−	21.0684i	0.0907750	−	0.157227i
$135$			33.1245i			0.245367i
$136$	20.1901	−	34.9702i	0.148456	−	0.257134i
$137$	−28.7960	−	16.6254i	−0.210190	−	0.121353i	0.391210	−	0.920302i	$-0.372057\pi$
$137$	−28.7960	−	16.6254i	−0.210190	−	0.121353i	−0.601400	+	0.798948i	$0.705390\pi$
$138$	−12.2633			−0.0888647
$139$	1.01787	+	0.587665i	0.00732277	+	0.00422780i	0.503657	−	0.863904i	$-0.331988\pi$
$139$	1.01787	+	0.587665i	0.00732277	+	0.00422780i	−0.496334	+	0.868132i	$0.665321\pi$
$140$	−87.3656	−	153.409i	−0.624040	−	1.09578i
$141$	63.4199	−	36.6155i	0.449787	−	0.259684i
$142$	9.91814			0.0698460
$143$	25.7045	+	157.490i	0.179752	+	1.10133i
$144$	−46.4299			−0.322430
$145$	−66.2955	−	114.827i	−0.457211	−	0.791912i
$146$	−3.29470	+	1.90220i	−0.0225665	+	0.0130288i
$147$	72.9933	+	43.3011i	0.496553	+	0.294565i
$148$		−	197.772i		−	1.33630i
$149$	249.367	+	143.972i	1.67360	+	0.966255i	0.965595	+	0.260052i	$0.0837397\pi$
$149$	249.367	+	143.972i	1.67360	+	0.966255i	0.708009	+	0.706203i	$0.249594\pi$
$150$	−2.83351	+	4.90778i	−0.0188900	+	0.0327185i
$151$			264.744i			1.75327i	0.481158	+	0.876634i	$0.340216\pi$
$151$			264.744i			1.75327i	−0.481158	+	0.876634i	$0.659784\pi$
$152$	−49.6029	−	28.6382i	−0.326335	−	0.188409i
$153$	−63.0243	+	36.3871i	−0.411924	+	0.237824i
$154$	8.89638	+	15.6215i	0.0577687	+	0.101438i
$155$	134.892			0.870271
$156$	83.3137	+	31.5319i	0.534062	+	0.202128i
$157$			30.3304i			0.193187i	0.995324	+	0.0965935i	$0.0307947\pi$
$157$			30.3304i			0.193187i	−0.995324	+	0.0965935i	$0.969205\pi$
$158$	15.5315	−	8.96709i	0.0983004	−	0.0567538i
$159$	9.94955	−	5.74437i	0.0625758	−	0.0361281i
$160$	−54.6359	−	31.5440i	−0.341474	−	0.197150i
$161$	−236.883	−	1.40007i	−1.47132	−	0.00869610i
$162$	−1.63071	−	0.941492i	−0.0100661	−	0.00581168i
$163$	56.1162	+	32.3987i	0.344271	+	0.198765i	0.662159	−	0.749363i	$-0.269640\pi$
$163$	56.1162	+	32.3987i	0.344271	+	0.198765i	−0.317888	+	0.948128i	$0.602974\pi$
$164$	−200.198			−1.22072
$165$	−67.7667	+	117.375i	−0.410707	+	0.711365i
$166$	11.1508	−	6.43792i	0.0671735	−	0.0387826i
$167$	88.9377	+	154.045i	0.532561	+	0.922422i	0.999277	+	0.0380154i	$0.0121036\pi$
$167$	88.9377	+	154.045i	0.532561	+	0.922422i	−0.466716	+	0.884407i	$0.654563\pi$
$168$	20.1819	+	0.119283i	0.120130	+	0.000710018i
$169$	−126.651	−	111.896i	−0.749412	−	0.662104i
$170$	−32.3540			−0.190318
$171$	51.6126	+	89.3957i	0.301828	+	0.522782i
$172$	40.0512	+	69.3707i	0.232856	+	0.403318i
$173$	128.501	+	74.1902i	0.742782	+	0.428845i	0.823080	−	0.567926i	$-0.192254\pi$
$173$	128.501	+	74.1902i	0.742782	+	0.428845i	−0.0802981	+	0.996771i	$0.525587\pi$
$174$	7.53722			0.0433174
$175$	−55.2934	+	94.4770i	−0.315962	+	0.539869i
$176$	−164.522	−	94.9870i	−0.934786	−	0.539699i
$177$			39.0504i			0.220624i
$178$	−13.6728	−	7.89398i	−0.0768133	−	0.0443482i
$179$	−132.486	−	229.473i	−0.740145	−	1.28197i	−0.952429	−	0.304761i	$-0.901423\pi$
$179$	−132.486	−	229.473i	−0.740145	−	1.28197i	0.212283	−	0.977208i	$-0.431910\pi$
$180$	37.8303	+	65.5241i	0.210169	+	0.364023i
$181$		−	66.5675i		−	0.367776i	−0.982947	−	0.183888i	$-0.941132\pi$
$181$		−	66.5675i		−	0.367776i	0.982947	−	0.183888i	$-0.0588684\pi$
$182$	−17.7663	−	6.84436i	−0.0976169	−	0.0376064i
$183$	−113.961			−0.622740
$184$	−48.7849	+	28.1660i	−0.265136	+	0.153076i
$185$	−275.983	+	159.339i	−1.49180	+	0.861291i
$186$	−3.83401	+	6.64070i	−0.0206130	+	0.0357027i
$187$	−297.765			−1.59233
$188$	83.6345	−	144.859i	0.444865	−	0.770528i
$189$	−31.3920	−	18.3724i	−0.166095	−	0.0972084i
$190$			45.8920i			0.241537i
$191$	−89.2877	+	154.651i	−0.467475	+	0.809690i	−0.999309	−	0.0371581i	$-0.988169\pi$
$191$	−89.2877	+	154.651i	−0.467475	+	0.809690i	0.531835	+	0.846848i	$0.321503\pi$
$192$	−89.7540	+	51.8195i	−0.467469	+	0.269893i
$193$	63.7120	−	36.7841i	0.330114	−	0.190591i	−0.325778	−	0.945446i	$-0.605626\pi$
$193$	63.7120	−	36.7841i	0.330114	−	0.190591i	0.655892	+	0.754855i	$0.272293\pi$
$194$			12.1356i			0.0625547i
$195$	−23.1217	−	141.665i	−0.118573	−	0.726488i
$196$	193.842	+	2.29144i	0.988988	+	0.0116910i
$197$	−48.7718	+	28.1584i	−0.247573	+	0.142936i	−0.618652	−	0.785665i	$-0.712321\pi$
$197$	−48.7718	+	28.1584i	−0.247573	+	0.142936i	0.371080	+	0.928601i	$0.378988\pi$
$198$	−3.85224	−	6.67227i	−0.0194557	−	0.0336983i
$199$	−81.6597	−	47.1462i	−0.410350	−	0.236916i	0.280590	−	0.959828i	$-0.409470\pi$
$199$	−81.6597	−	47.1462i	−0.410350	−	0.236916i	−0.690940	+	0.722912i	$0.742803\pi$
$200$			26.0316i			0.130158i
$201$	−100.700	+	174.417i	−0.500993	+	0.867746i
$202$	18.0285	−	31.2263i	0.0892502	−	0.154586i
$203$	145.592	+	0.860505i	0.717201	+	0.00423894i
$204$	−83.1128	+	143.956i	−0.407416	+	0.705665i
$205$	161.293	+	279.368i	0.786797	+	1.36277i
$206$	−6.27197	−	10.8634i	−0.0304464	−	0.0527348i
$207$	101.523			0.490450
$208$	198.569	−	32.4092i	0.954658	−	0.155813i
$209$			422.360i			2.02086i
$210$	−8.00247	−	14.0518i	−0.0381070	−	0.0669135i
$211$	−108.835	−	188.507i	−0.515804	−	0.893399i	−0.999832	−	0.0183461i	$-0.994160\pi$
$211$	−108.835	−	188.507i	−0.515804	−	0.893399i	0.484028	−	0.875053i	$-0.339173\pi$
$212$	13.1209	−	22.7260i	0.0618910	−	0.107198i
$213$	−82.1082			−0.385485
$214$	12.8307	+	7.40784i	0.0599568	+	0.0346161i
$215$	64.5360	−	111.780i	0.300167	−	0.519905i
$216$	−8.64954			−0.0400442
$217$	−74.8173	+	127.837i	−0.344780	+	0.589108i
$218$	5.06102	+	8.76595i	0.0232157	+	0.0402108i
$219$	27.2755	−	15.7475i	0.124546	−	0.0719065i
$220$			309.576i			1.40716i
$221$	244.140	−	199.611i	1.10470	−	0.903216i
$222$		−	18.1154i		−	0.0816011i
$223$	94.6082	+	163.866i	0.424252	+	0.734826i	0.996350	−	0.0853589i	$-0.0272037\pi$
$223$	94.6082	+	163.866i	0.424252	+	0.734826i	−0.572098	+	0.820185i	$0.693870\pi$
$224$	60.1977	−	34.2824i	0.268740	−	0.153046i
$225$	23.4574	−	40.6295i	0.104255	−	0.180576i
$226$			3.53687i			0.0156499i
$227$	142.800	−	247.336i	0.629073	−	1.08959i	−0.358665	−	0.933466i	$-0.616768\pi$
$227$	142.800	−	247.336i	0.629073	−	1.08959i	0.987738	−	0.156120i	$-0.0498987\pi$
$228$	204.191	+	117.890i	0.895576	+	0.517061i
$229$	−37.5995			−0.164190			−0.0820951	−	0.996625i	$-0.526161\pi$
$229$	−37.5995			−0.164190			−0.0820951	+	0.996625i	$0.526161\pi$
$230$	39.0883	+	22.5676i	0.169949	+	0.0981201i
$231$	−73.6495	−	129.324i	−0.318829	−	0.559844i
$232$	29.9839	−	17.3112i	0.129241	−	0.0746174i
$233$	−71.7358			−0.307879			−0.153939	−	0.988080i	$-0.549196\pi$
$233$	−71.7358			−0.307879			−0.153939	+	0.988080i	$0.549196\pi$
$234$	7.63132	+	2.88824i	0.0326125	+	0.0123429i
$235$	−269.527			−1.14692
$236$	44.5981	+	77.2461i	0.188975	+	0.327314i
$237$	−128.579	+	74.2349i	−0.542526	+	0.313227i
$238$	17.9450	−	30.6617i	0.0753993	−	0.128831i
$239$		−	328.595i		−	1.37487i	−0.726245	−	0.687436i	$-0.758736\pi$
$239$		−	328.595i		−	1.37487i	0.726245	−	0.687436i	$-0.241264\pi$
$240$	147.991	+	85.4427i	0.616630	+	0.356011i
$241$	179.946	−	311.676i	0.746665	−	1.29326i	−0.202748	−	0.979231i	$-0.564987\pi$
$241$	179.946	−	311.676i	0.746665	−	1.29326i	0.949413	−	0.314031i	$-0.101680\pi$
$242$		−	6.20819i		−	0.0256537i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$	−225.429	+	130.151i	−0.923888	+	0.533407i
$245$	−152.975	−	272.344i	−0.624386	−	1.11161i
$246$	−18.3376			−0.0745432
$247$	−283.134	−	346.296i	−1.14629	−	1.40201i
$248$			35.2233i			0.142029i
$249$	−92.3130	+	53.2969i	−0.370735	+	0.214044i
$250$	−10.8133	+	6.24305i	−0.0432531	+	0.0249722i
$251$	136.871	+	79.0228i	0.545305	+	0.314832i	0.747226	−	0.664570i	$-0.231385\pi$
$251$	136.871	+	79.0228i	0.545305	+	0.314832i	−0.201921	+	0.979402i	$0.564719\pi$
$252$	−83.0793	−	0.491031i	−0.329680	−	0.00194854i
$253$	359.743	+	207.698i	1.42191	+	0.820939i
$254$	27.6030	+	15.9366i	0.108673	+	0.0627426i
$255$	267.846			1.05038
$256$	−114.221	+	197.837i	−0.446177	+	0.772801i
$257$	94.3200	−	54.4557i	0.367004	−	0.211890i	−0.305145	−	0.952306i	$-0.598705\pi$
$257$	94.3200	−	54.4557i	0.367004	−	0.211890i	0.672149	+	0.740416i	$0.265372\pi$
$258$	3.66859	+	6.35418i	0.0142193	+	0.0246286i
$259$	2.06819	−	349.925i	0.00798529	−	1.35106i
$260$	−207.528	−	253.823i	−0.798185	−	0.976243i
$261$	−62.3976			−0.239071
$262$	−2.15419	−	3.73116i	−0.00822210	−	0.0142411i
$263$	−26.9878	−	46.7442i	−0.102615	−	0.177734i	0.810146	−	0.586228i	$-0.199388\pi$
$263$	−26.9878	−	46.7442i	−0.102615	−	0.177734i	−0.912761	+	0.408493i	$0.866054\pi$
$264$	−30.6493	−	17.6954i	−0.116096	−	0.0670279i
$265$	−42.2844			−0.159564
$266$	−43.4916	−	25.4538i	−0.163502	−	0.0956910i
$267$	113.191	+	65.3510i	0.423937	+	0.244760i
$268$			460.022i			1.71650i
$269$	−319.242	−	184.315i	−1.18677	−	0.685185i	−0.229203	−	0.973379i	$-0.573612\pi$
$269$	−319.242	−	184.315i	−1.18677	−	0.685185i	−0.957572	+	0.288194i	$0.906945\pi$
$270$	3.46516	+	6.00184i	0.0128339	+	0.0222290i
$271$	127.990	+	221.685i	0.472288	+	0.818027i	0.999497	−	0.0317089i	$-0.0100949\pi$
$271$	127.990	+	221.685i	0.472288	+	0.818027i	−0.527209	+	0.849735i	$0.676762\pi$
$272$			375.433i			1.38027i
$273$	147.080	+	56.6617i	0.538754	+	0.207552i
$274$	−6.95675			−0.0253896
$275$	166.241	−	95.9792i	0.604512	−	0.349015i
$276$	200.824	−	115.946i	0.727624	−	0.420094i
$277$	71.7004	−	124.189i	0.258846	−	0.448335i	−0.707087	−	0.707127i	$-0.749991\pi$
$277$	71.7004	−	124.189i	0.258846	−	0.448335i	0.965933	+	0.258792i	$0.0833244\pi$
$278$	0.245903			0.000884543
$279$	31.7402	−	54.9756i	0.113764	−	0.197045i
$280$	−64.1085	−	37.5200i	−0.228959	−	0.134000i
$281$		−	88.1433i		−	0.313677i	−0.987624	−	0.156839i	$-0.949870\pi$
$281$		−	88.1433i		−	0.313677i	0.987624	−	0.156839i	$-0.0501302\pi$
$282$	7.66071	−	13.2687i	0.0271656	−	0.0470523i
$283$	−238.013	+	137.417i	−0.841036	+	0.485572i	−0.857616	−	0.514290i	$-0.828055\pi$
$283$	−238.013	+	137.417i	−0.841036	+	0.485572i	0.0165804	+	0.999863i	$0.494722\pi$
$284$	−162.419	+	93.7729i	−0.571899	+	0.330186i
$285$		−	379.921i		−	1.33306i
$286$	21.1324	+	25.8466i	0.0738896	+	0.0903729i
$287$	−354.217	−	2.09356i	−1.23420	−	0.00729463i
$288$	−25.7117	+	14.8447i	−0.0892768	+	0.0515440i
$289$	149.727	+	259.335i	0.518086	+	0.897352i
$290$	−24.0242	−	13.8704i	−0.0828421	−	0.0478289i
$291$		−	100.466i		−	0.345243i
$292$	35.9694	−	62.3008i	0.123183	−	0.213359i
$293$	45.8472	−	79.4097i	0.156475	−	0.271023i	−0.777120	−	0.629352i	$-0.783320\pi$
$293$	45.8472	−	79.4097i	0.156475	−	0.271023i	0.933595	+	0.358329i	$0.116654\pi$
$294$	17.7554	+	0.209890i	0.0603925	+	0.000713912i
$295$	71.8625	−	124.470i	0.243602	−	0.421931i
$296$	−41.6069	−	72.0653i	−0.140564	−	0.243464i
$297$	31.8911	+	55.2370i	0.107377	+	0.185983i
$298$	60.2438			0.202160
$299$	−434.189	+	70.8656i	−1.45214	+	0.237009i
$300$		−	107.160i		−	0.357199i
$301$	70.1384	+	123.159i	0.233018	+	0.409165i
$302$	27.6949	+	47.9689i	0.0917049	+	0.158838i
$303$	−149.251	+	258.510i	−0.492577	+	0.853169i
$304$	532.527			1.75173
$305$	363.242	+	209.718i	1.19096	+	0.687599i
$306$	−7.61293	+	13.1860i	−0.0248788	+	0.0430914i
$307$	41.6685			0.135728			0.0678640	−	0.997695i	$-0.478382\pi$
$307$	41.6685			0.135728			0.0678640	+	0.997695i	$0.478382\pi$
$308$	−293.383	−	171.705i	−0.952543	−	0.557483i
$309$	51.9231	+	89.9334i	0.168036	+	0.291047i
$310$	24.4411	−	14.1111i	0.0788423	−	0.0455196i
$311$		−	612.118i		−	1.96823i	−0.177543	−	0.984113i	$-0.556815\pi$
$311$		−	612.118i		−	1.96823i	0.177543	−	0.984113i	$-0.443185\pi$
$312$	36.9919	−	6.03759i	0.118564	−	0.0193512i
$313$		−	446.944i		−	1.42794i	−0.700178	−	0.713968i	$-0.746896\pi$
$313$		−	446.944i		−	1.42794i	0.700178	−	0.713968i	$-0.253104\pi$
$314$	3.17287	+	5.49557i	0.0101047	+	0.0175018i
$315$	66.2492	+	116.329i	0.210315	+	0.369300i
$316$	−169.562	+	293.690i	−0.536589	+	0.929399i
$317$		−	253.982i		−	0.801204i	−0.916252	−	0.400602i	$-0.868801\pi$
$317$		−	253.982i		−	0.801204i	0.916252	−	0.400602i	$-0.131199\pi$
$318$	1.20184	−	2.08165i	0.00377937	−	0.00654606i
$319$	−221.103	−	127.654i	−0.693113	−	0.400169i
$320$	381.444			1.19201
$321$	−106.221	−	61.3265i	−0.330905	−	0.191048i
$322$	−43.0674	+	24.5267i	−0.133750	+	0.0761700i
$323$	722.856	−	417.341i	2.23794	−	1.29208i
$324$	35.6060			0.109895
$325$	−71.9612	+	190.136i	−0.221419	+	0.585033i
$326$	13.5569			0.0415857
$327$	−41.8982	−	72.5697i	−0.128129	−	0.221926i
$328$	−72.9492	+	42.1172i	−0.222406	+	0.128406i
$329$	149.492	−	255.429i	0.454383	−	0.776381i
$330$			28.3563i			0.0859283i
$331$	294.666	+	170.125i	0.890229	+	0.513974i	0.874017	−	0.485895i	$-0.161506\pi$
$331$	294.666	+	170.125i	0.890229	+	0.513974i	0.0162117	+	0.999869i	$0.494839\pi$
$332$	−121.737	+	210.855i	−0.366678	+	0.635104i
$333$			149.970i			0.450361i
$334$	32.2293	+	18.6076i	0.0964948	+	0.0557113i
$335$	641.942	−	370.625i	1.91624	−	1.10634i
$336$	−163.056	+	92.8600i	−0.485287	+	0.276369i
$337$	−374.905			−1.11248			−0.556238	−	0.831023i	$-0.687756\pi$
$337$	−374.905			−1.11248			−0.556238	+	0.831023i	$0.687756\pi$
$338$	−34.6533	−	7.02544i	−0.102524	−	0.0207853i
$339$		−	29.2803i		−	0.0863727i
$340$	529.829	−	305.897i	1.55832	−	0.899697i
$341$	224.940	−	129.869i	0.659648	−	0.380848i
$342$	18.7034	+	10.7984i	0.0546883	+	0.0315743i
$343$	342.946	+	6.08140i	0.999843	+	0.0177300i
$344$	29.1881	+	16.8518i	0.0848492	+	0.0489877i
$345$	−323.596	−	186.828i	−0.937959	−	0.541531i
$346$	31.0442			0.0897232
$347$	−289.783	+	501.919i	−0.835109	+	1.44645i	0.0588322	+	0.998268i	$0.481262\pi$
$347$	−289.783	+	501.919i	−0.835109	+	1.44645i	−0.893941	+	0.448184i	$0.852071\pi$
$348$	−123.430	+	71.2621i	−0.354683	+	0.204776i
$349$	−230.246	−	398.799i	−0.659732	−	1.14269i	−0.980685	−	0.195594i	$-0.937336\pi$
$349$	−230.246	−	398.799i	−0.659732	−	1.14269i	0.320953	−	0.947095i	$-0.395997\pi$
$350$	−0.135363	+	22.9026i	−0.000386752	+	0.0654359i
$351$	−63.1766	−	23.9106i	−0.179990	−	0.0681214i
$352$	−121.478			−0.345108
$353$	7.42699	+	12.8639i	0.0210396	+	0.0364417i	0.876354	−	0.481668i	$-0.159969\pi$
$353$	7.42699	+	12.8639i	0.0210396	+	0.0364417i	−0.855314	+	0.518110i	$0.826636\pi$
$354$	4.08507	+	7.07555i	0.0115397	+	0.0199874i
$355$	261.712	+	151.100i	0.737218	+	0.425633i
$356$	298.540			0.838596
$357$	−148.560	+	253.836i	−0.416133	+	0.711026i
$358$	−48.0103	−	27.7188i	−0.134107	−	0.0774268i
$359$			420.517i			1.17136i	0.810544	+	0.585678i	$0.199172\pi$
$359$			420.517i			1.17136i	−0.810544	+	0.585678i	$0.800828\pi$
$360$	27.5696	+	15.9173i	0.0765823	+	0.0442148i
$361$	−411.470	−	712.687i	−1.13981	−	1.97420i
$362$	−6.96364	−	12.0614i	−0.0192366	−	0.0333187i
$363$			51.3951i			0.141584i
$364$	355.652	−	55.8913i	0.977065	−	0.153548i
$365$	−115.918			−0.317583
$366$	−20.6487	+	11.9215i	−0.0564172	+	0.0325725i
$367$	−225.422	+	130.148i	−0.614229	+	0.354625i	−0.774619	−	0.632428i	$-0.782058\pi$
$367$	−225.422	+	130.148i	−0.614229	+	0.354625i	0.160390	+	0.987054i	$0.448725\pi$
$368$	261.873	−	453.577i	0.711611	−	1.23255i
$369$	151.810			0.411409
$370$	−33.3370	+	57.7413i	−0.0900999	+	0.156058i
$371$	23.4529	−	40.0727i	0.0632153	−	0.108013i
$372$		−	144.997i		−	0.389778i
$373$	−168.412	+	291.698i	−0.451506	+	0.782032i	−0.998480	−	0.0551180i	$-0.982447\pi$
$373$	−168.412	+	291.698i	−0.451506	+	0.782032i	0.546974	+	0.837150i	$0.315780\pi$
$374$	−53.9521	+	31.1493i	−0.144257	+	0.0832868i
$375$	89.5187	−	51.6836i	0.238717	−	0.137823i
$376$		−	70.3794i		−	0.187179i
$377$	266.859	−	43.5550i	0.707848	−	0.115531i
$378$	−7.60986	−	0.0449772i	−0.0201319	−	0.000118987i
$379$	−156.681	+	90.4598i	−0.413406	+	0.238680i	−0.692252	−	0.721656i	$-0.743381\pi$
$379$	−156.681	+	90.4598i	−0.413406	+	0.238680i	0.278846	+	0.960336i	$0.410048\pi$
$380$	−433.894	−	751.527i	−1.14183	−	1.97770i
$381$	−228.514	−	131.933i	−0.599775	−	0.346280i
$382$			37.3616i			0.0978053i
$383$	−136.764	+	236.882i	−0.357086	+	0.618492i	−0.987473	−	0.157790i	$-0.949563\pi$
$383$	−136.764	+	236.882i	−0.357086	+	0.618492i	0.630386	+	0.776282i	$0.282896\pi$
$384$	−45.1240	+	78.1571i	−0.117510	+	0.203534i
$385$	−3.23737	+	547.742i	−0.00840875	+	1.42271i
$386$	7.69599	−	13.3298i	0.0199378	−	0.0345333i
$387$	−30.3707	−	52.6037i	−0.0784774	−	0.135927i
$388$	−114.738	−	198.733i	−0.295717	−	0.512197i
$389$	594.928			1.52938			0.764689	−	0.644399i	$-0.222893\pi$
$389$	594.928			1.52938			0.764689	+	0.644399i	$0.222893\pi$
$390$	−19.0090	−	23.2496i	−0.0487411	−	0.0596143i
$391$		−	820.919i		−	2.09954i
$392$	71.1151	−	39.9450i	0.181416	−	0.101901i
$393$	17.8337	+	30.8888i	0.0453783	+	0.0785974i
$394$	−5.89132	+	10.2041i	−0.0149526	+	0.0258986i
$395$	546.444			1.38340
$396$	126.168	+	72.8434i	0.318607	+	0.183948i
$397$	−252.659	+	437.618i	−0.636420	+	1.10231i	0.349792	+	0.936827i	$0.386252\pi$
$397$	−252.659	+	437.618i	−0.636420	+	1.10231i	−0.986212	+	0.165485i	$0.947081\pi$
$398$	−19.7279			−0.0495676
$399$	360.049	+	210.722i	0.902379	+	0.528125i
$400$	−121.014	−	209.603i	−0.302535	−	0.524007i
$401$	217.031	−	125.303i	0.541224	−	0.312476i	−0.204351	−	0.978898i	$-0.565508\pi$
$401$	217.031	−	125.303i	0.541224	−	0.312476i	0.745575	+	0.666422i	$0.232175\pi$
$402$			42.1368i			0.104818i
$403$	−97.3704	+	257.272i	−0.241614	+	0.638392i
$404$			681.817i			1.68767i
$405$	−28.6867	−	49.6868i	−0.0708313	−	0.122683i
$406$	26.4698	−	15.0745i	0.0651966	−	0.0371293i
$407$	−306.812	+	531.413i	−0.753837	+	1.30568i
$408$			69.9404i			0.171423i
$409$	258.051	−	446.958i	0.630932	−	1.09281i	−0.356429	−	0.934322i	$-0.616006\pi$
$409$	258.051	−	446.958i	0.630932	−	1.09281i	0.987361	−	0.158484i	$-0.0506607\pi$
$410$	58.4495	+	33.7459i	0.142560	+	0.0823070i
$411$	57.5921			0.140127
$412$	205.419	+	118.599i	0.498591	+	0.287862i
$413$	78.1010	+	137.140i	0.189106	+	0.332059i
$414$	18.3950	−	10.6204i	0.0444324	−	0.0256530i
$415$	392.319			0.945347
$416$	99.6006	−	81.4343i	0.239424	−	0.195755i
$417$	−2.03573			−0.00488185
$418$	44.1831	+	76.5274i	0.105701	+	0.183080i
$419$	−427.835	+	247.011i	−1.02109	+	0.589524i	−0.914418	−	0.404771i	$-0.867351\pi$
$419$	−427.835	+	247.011i	−1.02109	+	0.589524i	−0.106667	+	0.994295i	$0.534018\pi$
$420$	263.904	+	154.452i	0.628343	+	0.367743i
$421$			345.660i			0.821045i	0.911850	+	0.410523i	$0.134654\pi$
$421$			345.660i			0.821045i	−0.911850	+	0.410523i	$0.865346\pi$
$422$	−39.4395	−	22.7704i	−0.0934586	−	0.0539584i
$423$	−63.4199	+	109.847i	−0.149929	+	0.259684i
$424$		−	11.0414i		−	0.0260410i
$425$	−328.531	−	189.677i	−0.773014	−	0.446300i
$426$	−14.8772	+	8.58936i	−0.0349230	+	0.0201628i
$427$	−400.219	+	227.923i	−0.937281	+	0.533778i
$428$	−280.155			−0.654568
$429$	−174.947	−	213.974i	−0.407802	−	0.498773i
$430$		−	27.0045i		−	0.0628012i
$431$	−503.430	+	290.655i	−1.16805	+	0.674375i	−0.953220	−	0.302277i	$-0.902253\pi$
$431$	−503.430	+	290.655i	−1.16805	+	0.674375i	−0.214831	+	0.976651i	$0.568920\pi$
$432$	69.6449	−	40.2095i	0.161215	−	0.0930775i
$433$	−343.220	−	198.158i	−0.792656	−	0.457640i	0.0482407	−	0.998836i	$-0.484639\pi$
$433$	−343.220	−	198.158i	−0.792656	−	0.457640i	−0.840897	+	0.541196i	$0.817972\pi$
$434$	−0.183159	+	30.9894i	−0.000422026	+	0.0714041i
$435$	198.887	+	114.827i	0.457211	+	0.263971i
$436$	−165.759	−	95.7008i	−0.380180	−	0.219497i
$437$	−1164.42			−2.66457
$438$	3.29470	−	5.70659i	0.00752216	−	0.0130288i
$439$	129.424	−	74.7228i	0.294815	−	0.170211i	−0.345296	−	0.938494i	$-0.612222\pi$
$439$	129.424	−	74.7228i	0.294815	−	0.170211i	0.640111	+	0.768282i	$0.278888\pi$
$440$	65.1278	+	112.805i	0.148018	+	0.256374i
$441$	−146.990	−	1.73759i	−0.333310	−	0.00394012i
$442$	23.3544	−	61.7070i	0.0528380	−	0.139609i
$443$	−127.510			−0.287833			−0.143916	−	0.989590i	$-0.545970\pi$
$443$	−127.510			−0.287833			−0.143916	+	0.989590i	$0.545970\pi$
$444$	171.276	+	296.658i	0.385756	+	0.668149i
$445$	−240.525	−	416.601i	−0.540505	−	0.936182i
$446$	34.2842	+	19.7940i	0.0768703	+	0.0443811i
$447$	−498.734			−1.11574
$448$	−211.566	+	361.492i	−0.472246	+	0.806903i
$449$	390.594	+	225.510i	0.869921	+	0.502249i	0.867322	−	0.497748i	$-0.165839\pi$
$449$	390.594	+	225.510i	0.869921	+	0.502249i	0.00259896	+	0.999997i	$0.499173\pi$
$450$		−	9.81556i		−	0.0218123i
$451$	537.931	+	310.575i	1.19275	+	0.688636i
$452$	−33.4400	−	57.9198i	−0.0739824	−	0.128141i
$453$	−229.275	−	397.115i	−0.506125	−	0.876634i
$454$		−	59.7532i		−	0.131615i
$455$	−364.532	−	451.268i	−0.801168	−	0.991797i
$456$	99.2057			0.217556
$457$	597.471	−	344.950i	1.30738	−	0.754814i	0.325719	−	0.945467i	$-0.394394\pi$
$457$	597.471	−	344.950i	1.30738	−	0.754814i	0.981658	+	0.190652i	$0.0610603\pi$
$458$	−6.81267	+	3.93330i	−0.0148748	+	0.00858798i
$459$	63.0243	−	109.161i	0.137308	−	0.237824i
$460$	−853.479			−1.85539
$461$	66.1182	−	114.520i	0.143423	−	0.248417i	−0.785360	−	0.619039i	$-0.787522\pi$
$461$	66.1182	−	114.520i	0.143423	−	0.248417i	0.928784	+	0.370622i	$0.120856\pi$
$462$	−26.8732	−	15.7277i	−0.0581670	−	0.0340427i
$463$		−	310.647i		−	0.670944i	−0.942050	−	0.335472i	$-0.891104\pi$
$463$		−	310.647i		−	0.670944i	0.942050	−	0.335472i	$-0.108896\pi$
$464$	−160.951	+	278.775i	−0.346877	+	0.600808i
$465$	−202.338	+	116.820i	−0.435135	+	0.251226i
$466$	−12.9978	+	7.50429i	−0.0278923	+	0.0161036i
$467$			791.961i			1.69585i	0.530117	+	0.847924i	$0.322148\pi$
$467$			791.961i			1.69585i	−0.530117	+	0.847924i	$0.677852\pi$
$468$	−152.278	+	24.8539i	−0.325380	+	0.0531066i
$469$	−4.81065	+	813.931i	−0.0102573	+	1.73546i
$470$	−48.8356	+	28.1953i	−0.103906	+	0.0599899i
$471$	−26.2669	−	45.4956i	−0.0557683	−	0.0965935i
$472$	32.5017	+	18.7649i	0.0688596	+	0.0397561i
$473$		−	248.532i		−	0.525437i
$474$	−15.5315	+	26.9013i	−0.0327668	+	0.0567538i
$475$	−269.045	+	465.999i	−0.566410	+	0.981051i
$476$	−3.97049	+	671.781i	−0.00834136	+	1.41131i
$477$	−9.94955	+	17.2331i	−0.0208586	+	0.0361281i
$478$	−34.3744	−	59.5381i	−0.0719129	−	0.124557i
$479$	129.849	+	224.906i	0.271084	+	0.469531i	0.969140	−	0.246512i	$-0.0792845\pi$
$479$	129.849	+	224.906i	0.271084	+	0.469531i	−0.698056	+	0.716044i	$0.745951\pi$
$480$	109.272			0.227649
$481$	−104.683	−	641.385i	−0.217636	−	1.33344i
$482$		−	75.2969i		−	0.156218i
$483$	356.537	−	203.047i	0.738173	−	0.420387i
$484$	58.6965	+	101.665i	0.121274	+	0.210052i
$485$	−184.882	+	320.225i	−0.381200	+	0.660258i
$486$	3.26142			0.00671075
$487$	312.782	+	180.585i	0.642263	+	0.370811i	0.785486	−	0.618880i	$-0.212413\pi$
$487$	312.782	+	180.585i	0.642263	+	0.370811i	−0.143223	+	0.989690i	$0.545747\pi$
$488$	−54.7619	+	94.8504i	−0.112217	+	0.194365i
$489$	−112.232			−0.229514
$490$	−56.2075	−	33.3434i	−0.114709	−	0.0680478i
$491$	471.038	+	815.861i	0.959344	+	1.66163i	0.724100	+	0.689695i	$0.242256\pi$
$491$	471.038	+	815.861i	0.959344	+	1.66163i	0.235244	+	0.971936i	$0.424411\pi$
$492$	300.297	−	173.377i	0.610360	−	0.352391i
$493$			504.548i			1.02342i
$494$	−87.5273	−	33.1266i	−0.177181	−	0.0670580i
$495$		−	234.751i		−	0.474244i
$496$	−163.744	−	283.613i	−0.330129	−	0.571800i
$497$	−288.354	+	164.217i	−0.580190	+	0.330416i
$498$	−11.1508	+	19.3138i	−0.0223912	+	0.0387826i
$499$		−	751.785i		−	1.50658i	−0.657686	−	0.753292i	$-0.728465\pi$
$499$		−	751.785i		−	1.50658i	0.657686	−	0.753292i	$-0.271535\pi$
$500$	118.052	−	204.472i	0.236104	−	0.408944i
$501$	−266.813	−	154.045i	−0.532561	−	0.307474i
$502$	33.0664			0.0658693
$503$	252.996	+	146.067i	0.502974	+	0.290392i	0.729941	−	0.683510i	$-0.239548\pi$
$503$	252.996	+	146.067i	0.502974	+	0.290392i	−0.226967	+	0.973903i	$0.572881\pi$
$504$	−30.3762	+	17.2991i	−0.0602702	+	0.0343237i
$505$	951.448	−	549.318i	1.88405	−	1.08776i
$506$	86.9092			0.171757
$507$	286.880	+	58.1607i	0.565839	+	0.114715i
$508$	−602.703			−1.18642
$509$	86.4473	+	149.731i	0.169837	+	0.294167i	0.938363	−	0.345652i	$-0.112342\pi$
$509$	86.4473	+	149.731i	0.169837	+	0.294167i	−0.768525	+	0.639820i	$0.779009\pi$
$510$	48.5310	−	28.0194i	0.0951588	−	0.0549400i
$511$	64.2933	−	109.855i	0.125819	−	0.214980i
$512$			256.214i			0.500417i
$513$	−154.838	−	89.3957i	−0.301828	−	0.174261i
$514$	11.3932	−	19.7337i	0.0221658	−	0.0383923i
$515$		−	382.206i		−	0.742147i
$516$	−120.154	−	69.3707i	−0.232856	−	0.134439i
$517$	−449.451	+	259.491i	−0.869345	+	0.501917i
$518$	−36.2310	−	63.6193i	−0.0699439	−	0.122817i
$519$	−257.002			−0.495188
$520$	−129.019	−	48.8301i	−0.248113	−	0.0939040i
$521$		−	98.8137i		−	0.189662i	−0.995493	−	0.0948308i	$-0.969769\pi$
$521$		−	98.8137i		−	0.189662i	0.995493	−	0.0948308i	$-0.0302310\pi$
$522$	−11.3058	+	6.52743i	−0.0216587	+	0.0125046i
$523$	522.163	−	301.471i	0.998399	−	0.576426i	0.0906247	−	0.995885i	$-0.471114\pi$
$523$	522.163	−	301.471i	0.998399	−	0.576426i	0.907774	+	0.419459i	$0.137780\pi$
$524$	70.5540	+	40.7344i	0.134645	+	0.0777373i
$525$	1.12062	−	189.601i	0.00213451	−	0.361145i
$526$	−9.77983	−	5.64639i	−0.0185928	−	0.0107346i
$527$	−444.534	−	256.652i	−0.843519	−	0.487006i
$528$	329.045			0.623191
$529$	−308.108	+	533.659i	−0.582436	+	1.00881i
$530$	−7.66151	+	4.42338i	−0.0144557	+	0.00834599i
$531$	−33.8186	−	58.5756i	−0.0636886	−	0.110312i
$532$	952.876	+	5.63187i	1.79112	+	0.0105862i
$533$	−649.252	+	105.967i	−1.21811	+	0.198812i
$534$	27.3455			0.0512089
$535$	225.712	+	390.945i	0.421892	+	0.730738i
$536$	96.7784	+	167.625i	0.180557	+	0.312733i
$537$	397.458	+	229.473i	0.740145	+	0.427323i
$538$	−77.1248			−0.143355
$539$	−517.297	−	306.871i	−0.959734	−	0.569334i
$540$	−113.491	−	65.5241i	−0.210169	−	0.121341i
$541$		−	986.752i		−	1.82394i	−0.410256	−	0.911970i	$-0.634561\pi$
$541$		−	986.752i		−	1.82394i	0.410256	−	0.911970i	$-0.365439\pi$
$542$	46.3811	+	26.7781i	0.0855739	+	0.0494061i
$543$	57.6492	+	99.8513i	0.106168	+	0.183888i
$544$	120.034	+	207.906i	0.220651	+	0.382179i
$545$			308.413i			0.565895i
$546$	32.5768	−	5.11951i	0.0596645	−	0.00937638i
$547$	310.653			0.567921			0.283961	−	0.958836i	$-0.408351\pi$
$547$	310.653			0.567921			0.283961	+	0.958836i	$0.408351\pi$
$548$	113.924	−	65.7739i	0.207890	−	0.120025i
$549$	170.942	−	98.6935i	0.311370	−	0.179770i
$550$	20.0808	−	34.7810i	0.0365106	−	0.0632382i
$551$	715.668			1.29885
$552$	48.7849	−	84.4980i	0.0883785	−	0.153076i
$553$	−303.083	+	517.862i	−0.548070	+	0.936460i
$554$		−	30.0024i		−	0.0541559i
$555$	275.983	−	478.017i	0.497267	−	0.861291i
$556$	−4.02691	+	2.32494i	−0.00724264	+	0.00418154i
$557$	−525.824	+	303.585i	−0.944029	+	0.545035i	−0.891221	−	0.453569i	$-0.850150\pi$
$557$	−525.824	+	303.585i	−0.944029	+	0.545035i	−0.0528079	+	0.998605i	$0.516817\pi$
$558$		−	13.2814i		−	0.0238018i
$559$	166.607	+	203.773i	0.298044	+	0.364531i
$560$	690.613	+	4.08179i	1.23324	+	0.00728892i
$561$	446.648	−	257.872i	0.796164	−	0.459665i
$562$	−9.22069	−	15.9707i	−0.0164069	−	0.0284176i
$563$	−776.401	−	448.255i	−1.37904	−	0.796190i	−0.386998	−	0.922081i	$-0.626488\pi$
$563$	−776.401	−	448.255i	−1.37904	−	0.796190i	−0.992044	+	0.125890i	$0.959821\pi$
$564$			289.719i			0.513685i
$565$	−53.8832	+	93.3284i	−0.0953685	+	0.165183i
$566$	−28.7504	+	49.7972i	−0.0507958	+	0.0879809i
$567$	62.9989	+	0.372348i	0.111109	+	0.000656699i
$568$	−39.4555	+	68.3389i	−0.0694639	+	0.120315i
$569$	265.703	+	460.212i	0.466966	+	0.808808i	0.999288	−	0.0377336i	$-0.0120138\pi$
$569$	265.703	+	460.212i	0.466966	+	0.808808i	−0.532322	+	0.846542i	$0.678680\pi$
$570$	−39.7436	−	68.8380i	−0.0697256	−	0.120768i
$571$	220.497			0.386160			0.193080	−	0.981183i	$-0.438152\pi$
$571$	220.497			0.386160			0.193080	+	0.981183i	$0.438152\pi$
$572$	−590.437	−	223.464i	−1.03223	−	0.390671i
$573$		−	309.302i		−	0.539793i
$574$	−64.3996	+	36.6753i	−0.112194	+	0.0638943i
$575$	264.608	+	458.315i	0.460188	+	0.797070i
$576$	89.7540	−	155.459i	0.155823	−	0.269893i
$577$	−562.221			−0.974387			−0.487193	−	0.873294i	$-0.661979\pi$
$577$	−562.221			−0.974387			−0.487193	+	0.873294i	$0.661979\pi$
$578$	54.2581	+	31.3259i	0.0938722	+	0.0541971i
$579$	−63.7120	+	110.352i	−0.110038	+	0.190591i
$580$	524.560			0.904415
$581$	−217.598	+	371.799i	−0.374524	+	0.639929i
$582$	−10.5097	−	18.2034i	−0.0180580	−	0.0312773i
$583$	−70.5116	+	40.7099i	−0.120946	+	0.0698283i
$584$		−	30.2686i		−	0.0518299i
$585$	157.368	+	192.474i	0.269005	+	0.329015i
$586$		−	19.1844i		−	0.0327378i
$587$	−68.0209	−	117.816i	−0.115879	−	0.200708i	0.802252	−	0.596986i	$-0.203635\pi$
$587$	−68.0209	−	117.816i	−0.115879	−	0.200708i	−0.918131	+	0.396278i	$0.870302\pi$
$588$	−292.747	+	164.435i	−0.497869	+	0.279651i
$589$	−364.043	+	630.542i	−0.618070	+	1.07053i
$590$		−	30.0702i		−	0.0509665i
$591$	48.7718	−	84.4753i	0.0825243	−	0.142936i
$592$	670.025	+	386.839i	1.13180	+	0.653445i
$593$	−244.516			−0.412338			−0.206169	−	0.978516i	$-0.566100\pi$
$593$	−244.516			−0.412338			−0.206169	+	0.978516i	$0.566100\pi$
$594$	11.5567	+	6.67227i	0.0194557	+	0.0112328i
$595$	940.642	−	535.693i	1.58091	−	0.900324i
$596$	−986.552	+	569.586i	−1.65529	+	0.955681i
$597$	163.319			0.273567
$598$	−71.2575	+	58.2607i	−0.119160	+	0.0974259i
$599$	−19.9180			−0.0332521			−0.0166260	−	0.999862i	$-0.505292\pi$
$599$	−19.9180			−0.0332521			−0.0166260	+	0.999862i	$0.505292\pi$
$600$	−22.5440	−	39.0474i	−0.0375734	−	0.0650790i
$601$	146.951	−	84.8420i	0.244510	−	0.141168i	−0.372738	−	0.927937i	$-0.621581\pi$
$601$	146.951	−	84.8420i	0.244510	−	0.141168i	0.617248	+	0.786769i	$0.288248\pi$
$602$	25.5920	+	14.9779i	0.0425117	+	0.0248803i
$603$		−	348.834i		−	0.578497i
$604$	−907.062	−	523.693i	−1.50176	−	0.867041i
$605$	94.5799	−	163.817i	0.156330	−	0.270772i
$606$			62.4527i			0.103057i
$607$	−55.0848	−	31.8032i	−0.0907492	−	0.0523941i	0.453939	−	0.891033i	$-0.350019\pi$
$607$	−55.0848	−	31.8032i	−0.0907492	−	0.0523941i	−0.544688	+	0.838639i	$0.683352\pi$
$608$	294.900	−	170.261i	0.485033	−	0.280034i
$609$	−219.133	+	124.795i	−0.359824	+	0.204919i
$610$	87.7544			0.143860
$611$	194.555	−	514.054i	0.318421	−	0.841332i
$612$		−	287.911i		−	0.470443i
$613$	−840.641	+	485.344i	−1.37136	+	0.791753i	−0.991099	−	0.133128i	$-0.957498\pi$
$613$	−840.641	+	485.344i	−1.37136	+	0.791753i	−0.380257	+	0.924881i	$0.624165\pi$
$614$	7.54992	−	4.35895i	0.0122963	−	0.00709927i
$615$	−483.880	−	279.368i	−0.786797	−	0.454257i
$616$	−143.027	−	0.845348i	−0.232187	−	0.00137232i
$617$	569.020	+	328.524i	0.922237	+	0.532454i	0.884348	−	0.466828i	$-0.154603\pi$
$617$	569.020	+	328.524i	0.922237	+	0.532454i	0.0378890	+	0.999282i	$0.487937\pi$
$618$	18.8159	+	10.8634i	0.0304464	+	0.0175783i
$619$	−340.384			−0.549894			−0.274947	−	0.961459i	$-0.588660\pi$
$619$	−340.384			−0.549894			−0.274947	+	0.961459i	$0.588660\pi$
$620$	−266.832	+	462.166i	−0.430374	+	0.745429i
$621$	−152.285	+	87.9216i	−0.245225	+	0.141581i
$622$	−64.0338	−	110.910i	−0.102948	−	0.178312i
$623$	528.217	+	3.12197i	0.847860	+	0.00501118i
$624$	−269.786	+	220.579i	−0.432350	+	0.353493i
$625$	−771.401			−1.23424
$626$	−46.7549	−	80.9819i	−0.0746884	−	0.129364i
$627$	−365.774	−	633.540i	−0.583372	−	1.01043i
$628$	−103.918	−	59.9969i	−0.165474	−	0.0955365i
$629$	1212.66			1.92792
$630$	24.1730	+	14.1474i	0.0383698	+	0.0224562i
$631$	−173.581	−	100.217i	−0.275089	−	0.158823i	0.356109	−	0.934444i	$-0.384103\pi$
$631$	−173.581	−	100.217i	−0.275089	−	0.158823i	−0.631198	+	0.775622i	$0.717436\pi$
$632$			142.688i			0.225773i
$633$	326.504	+	188.507i	0.515804	+	0.297800i
$634$	−26.5691	−	46.0190i	−0.0419071	−	0.0725852i
$635$	485.579	+	841.047i	0.764691	+	1.32448i
$636$			45.4521i			0.0714656i
$637$	629.850	−	95.1711i	0.988776	−	0.149405i
$638$	−53.4156			−0.0837236
$639$	123.162	−	71.1078i	0.192742	−	0.111280i
$640$	287.657	−	166.079i	0.449465	−	0.259498i
$641$	−165.454	+	286.575i	−0.258119	+	0.447075i	−0.965738	−	0.259519i	$-0.916436\pi$
$641$	−165.454	+	286.575i	−0.258119	+	0.447075i	0.707619	+	0.706594i	$0.249769\pi$
$642$	−25.6615			−0.0399712
$643$	−426.855	+	739.334i	−0.663849	+	1.14982i	0.315747	+	0.948843i	$0.397745\pi$
$643$	−426.855	+	739.334i	−0.663849	+	1.14982i	−0.979596	+	0.200976i	$0.935589\pi$
$644$	473.379	−	808.838i	0.735060	−	1.25596i
$645$			223.559i			0.346603i
$646$	87.3163	−	151.236i	0.135164	−	0.234112i
$647$	62.6048	−	36.1449i	0.0967617	−	0.0558654i	−0.450838	−	0.892606i	$-0.648875\pi$
$647$	62.6048	−	36.1449i	0.0967617	−	0.0558654i	0.547600	+	0.836740i	$0.315542\pi$
$648$	12.9743	−	7.49072i	0.0200221	−	0.0115598i
$649$		−	276.747i		−	0.426420i
$650$	6.85149	+	41.9786i	0.0105408	+	0.0645825i
$651$	1.51630	−	256.549i	0.00232919	−	0.394084i
$652$	−222.008	+	128.177i	−0.340504	+	0.196590i
$653$	−323.214	−	559.823i	−0.494968	−	0.857310i	0.505015	−	0.863111i	$-0.331487\pi$
$653$	−323.214	−	559.823i	−0.494968	−	0.857310i	−0.999983	+	0.00580060i	$0.998154\pi$
$654$	−15.1831	−	8.76595i	−0.0232157	−	0.0134036i
$655$		−	131.274i		−	0.200418i
$656$	391.584	−	678.244i	0.596927	−	1.03391i
$657$	−27.2755	+	47.2426i	−0.0415152	+	0.0719065i
$658$	0.365970	−	61.9197i	0.000556185	−	0.0941029i
$659$	86.6585	−	150.097i	0.131500	−	0.227765i	−0.792755	−	0.609540i	$-0.791354\pi$
$659$	86.6585	−	150.097i	0.131500	−	0.227765i	0.924255	+	0.381776i	$0.124687\pi$
$660$	−268.100	−	464.363i	−0.406213	−	0.703581i
$661$	−219.448	−	380.095i	−0.331994	−	0.575031i	0.650909	−	0.759156i	$-0.274388\pi$
$661$	−219.448	−	380.095i	−0.331994	−	0.575031i	−0.982903	+	0.184125i	$0.941055\pi$
$662$	71.1874			0.107534
$663$	−193.342	+	510.847i	−0.291616	+	0.770509i
$664$			102.443i			0.154282i
$665$	−759.844	−	1334.24i	−1.14262	−	2.00637i
$666$	15.6884	+	27.1732i	0.0235562	+	0.0408005i
$667$	351.933	−	609.567i	0.527636	−	0.913893i
$668$	−703.715			−1.05347
$669$	−283.825	−	163.866i	−0.424252	−	0.244942i
$670$	77.5424	−	134.307i	0.115735	−	0.200459i
$671$	807.634			1.20363
$672$	−60.6071	+	103.556i	−0.0901892	+	0.154102i
$673$	514.927	+	891.879i	0.765121	+	1.32523i	0.940182	+	0.340672i	$0.110654\pi$
$673$	514.927	+	891.879i	0.765121	+	1.32523i	−0.175061	+	0.984558i	$0.556012\pi$
$674$	−67.9290	+	39.2188i	−0.100785	+	0.0581882i
$675$			81.2590i			0.120384i
$676$	633.905	−	212.587i	0.937729	−	0.314478i
$677$			558.166i			0.824469i	0.911078	+	0.412235i	$0.135252\pi$
$677$			558.166i			0.824469i	−0.911078	+	0.412235i	$0.864748\pi$
$678$	−3.06302	−	5.30531i	−0.00451773	−	0.00782494i
$679$	−200.932	−	352.824i	−0.295923	−	0.519623i
$680$	128.708	−	222.929i	0.189276	−	0.327836i
$681$			494.672i			0.726391i
$682$	27.1713	−	47.0620i	0.0398406	−	0.0690059i
$683$	−242.104	−	139.779i	−0.354472	−	0.204654i	0.312181	−	0.950023i	$-0.398940\pi$
$683$	−242.104	−	139.779i	−0.354472	−	0.204654i	−0.666653	+	0.745368i	$0.732274\pi$
$684$	−408.383			−0.597051
$685$	−183.570	−	105.984i	−0.267985	−	0.154721i
$686$	62.7746	−	34.7738i	0.0915082	−	0.0506906i
$687$	56.3993	−	32.5622i	0.0820951	−	0.0473976i
$688$	−313.358			−0.455462
$689$	30.5225	−	80.6467i	0.0442998	−	0.117049i
$690$	−78.1765			−0.113299
$691$	−378.617	−	655.783i	−0.547926	−	0.949035i	−0.998416	−	0.0562538i	$-0.982084\pi$
$691$	−378.617	−	655.783i	−0.547926	−	0.949035i	0.450491	−	0.892781i	$-0.351249\pi$
$692$	−508.380	+	293.513i	−0.734653	+	0.424152i
$693$	222.472	+	130.204i	0.321028	+	0.187884i
$694$			121.257i			0.174722i
$695$	6.48871	+	3.74626i	0.00933627	+	0.00539030i
$696$	−29.9839	+	51.9337i	−0.0430804	+	0.0746174i
$697$		−	1227.54i		−	1.76117i
$698$	−83.4368	−	48.1723i	−0.119537	−	0.0690147i
$699$	107.604	−	62.1250i	0.153939	−	0.0888770i
$700$	−214.320	−	376.332i	−0.306171	−	0.537617i
$701$	873.187			1.24563			0.622815	−	0.782369i	$-0.285989\pi$
$701$	873.187			1.24563			0.622815	+	0.782369i	$0.285989\pi$
$702$	−13.9483	+	2.27655i	−0.0198693	+	0.00324295i
$703$		−	1720.08i		−	2.44677i
$704$	636.079	−	367.240i	0.903521	−	0.521648i
$705$	404.290	−	233.417i	0.573462	−	0.331088i
$706$	2.69140	+	1.55388i	0.00381218	+	0.00220096i
$707$	−7.13006	+	1206.36i	−0.0100849	+	1.70631i
$708$	−133.794	−	77.2461i	−0.188975	−	0.109105i
$709$	−77.9909	−	45.0281i	−0.110001	−	0.0635093i	0.443990	−	0.896032i	$-0.353563\pi$
$709$	−77.9909	−	45.0281i	−0.110001	−	0.0635093i	−0.553991	+	0.832522i	$0.686896\pi$
$710$	63.2263			0.0890511
$711$	128.579	−	222.705i	0.180842	−	0.313227i
$712$	108.784	−	62.8063i	0.152786	−	0.0882111i
$713$	358.041	+	620.145i	0.502161	+	0.869768i
$714$	−0.363687	+	61.5335i	−0.000509365	+	0.0861813i
$715$	163.862	+	1003.97i	0.229177	+	1.40415i
$716$	1048.29			1.46409
$717$	284.571	+	492.892i	0.396892	+	0.687436i
$718$	43.9904	+	76.1936i	0.0612679	+	0.106119i
$719$	594.811	+	343.414i	0.827275	+	0.477627i	0.852919	−	0.522044i	$-0.174830\pi$
$719$	594.811	+	343.414i	0.827275	+	0.477627i	−0.0256438	+	0.999671i	$0.508164\pi$
$720$	−295.982			−0.411086
$721$	362.215	+	211.989i	0.502378	+	0.294021i
$722$	−149.109	−	86.0879i	−0.206522	−	0.119235i
$723$			623.352i			0.862175i
$724$	228.073	+	131.678i	0.315018	+	0.181876i
$725$	−162.632	−	281.687i	−0.224320	−	0.388534i
$726$	5.37645	+	9.31229i	0.00740558	+	0.0128268i
$727$		−	262.433i		−	0.360981i	−0.983577	−	0.180491i	$-0.942231\pi$
$727$		−	262.433i		−	0.360981i	0.983577	−	0.180491i	$-0.0577685\pi$
$728$	117.836	−	95.1872i	0.161863	−	0.130752i
$729$	−27.0000			−0.0370370
$730$	−21.0031	+	12.1262i	−0.0287714	+	0.0166112i
$731$	−425.355	+	245.579i	−0.581880	+	0.335949i
$732$	225.429	−	390.454i	0.307963	−	0.533407i
$733$	−150.902			−0.205870			−0.102935	−	0.994688i	$-0.532823\pi$
$733$	−150.902			−0.205870			−0.102935	+	0.994688i	$0.532823\pi$
$734$	−27.2295	+	47.1629i	−0.0370974	+	0.0642546i
$735$	465.319	+	276.036i	0.633087	+	0.375560i
$736$		−	334.906i		−	0.455036i
$737$	713.649	−	1236.08i	0.968317	−	1.67717i
$738$	27.5064	−	15.8809i	0.0372716	−	0.0215188i
$739$	703.434	−	406.128i	0.951872	−	0.549564i	0.0582103	−	0.998304i	$-0.481461\pi$
$739$	703.434	−	406.128i	0.951872	−	0.549564i	0.893662	+	0.448741i	$0.148127\pi$
$740$		−	1260.76i		−	1.70373i
$741$	724.603	+	274.242i	0.977871	+	0.370097i
$742$	0.0574147	−	9.71419i	7.73782e−5	−	0.0130919i
$743$	75.0956	−	43.3565i	0.101071	−	0.0583532i	−0.448613	−	0.893726i	$-0.648082\pi$
$743$	75.0956	−	43.3565i	0.101071	−	0.0583532i	0.549683	+	0.835373i	$0.314748\pi$
$744$	−30.5042	−	52.8349i	−0.0410003	−	0.0710147i
$745$	1589.67	+	917.796i	2.13378	+	1.23194i
$746$			70.4704i			0.0944644i
$747$	92.3130	−	159.891i	0.123578	−	0.214044i
$748$	589.013	−	1020.20i	0.787451	−	1.36390i
$749$	−495.687	−	2.92970i	−0.661799	−	0.00391149i
$750$	10.8133	−	18.7291i	0.0144177	−	0.0249722i
$751$	−167.580	−	290.257i	−0.223142	−	0.386493i	0.732618	−	0.680640i	$-0.238298\pi$
$751$	−167.580	−	290.257i	−0.223142	−	0.386493i	−0.955760	+	0.294146i	$0.904965\pi$
$752$	327.176	+	566.685i	0.435074	+	0.753570i
$753$	−273.743			−0.363536
$754$	43.7959	−	35.8079i	0.0580847	−	0.0474905i
$755$			1687.69i			2.23535i
$756$	125.044	−	71.2122i	0.165402	−	0.0941961i
$757$	−110.772	−	191.863i	−0.146331	−	0.253452i	0.783538	−	0.621344i	$-0.213413\pi$
$757$	−110.772	−	191.863i	−0.146331	−	0.253452i	−0.929869	+	0.367892i	$0.880080\pi$
$758$	−18.9260	+	32.7808i	−0.0249684	+	0.0432465i
$759$	−719.486			−0.947939
$760$	−316.209	−	182.563i	−0.416065	−	0.240215i
$761$	327.027	−	566.428i	0.429734	−	0.744321i	−0.567116	−	0.823638i	$-0.691941\pi$
$761$	327.027	−	566.428i	0.429734	−	0.744321i	0.996849	+	0.0793175i	$0.0252741\pi$
$762$	−55.2060			−0.0724489
$763$	−292.281	−	171.060i	−0.383068	−	0.224194i
$764$	−353.242	−	611.834i	−0.462359	−	0.800830i
$765$	−401.768	+	231.961i	−0.525188	+	0.303217i
$766$			57.2277i			0.0747098i
$767$	185.521	+	226.907i	0.241879	+	0.295837i
$768$		−	395.674i		−	0.515201i
$769$	117.280	+	203.134i	0.152509	+	0.264154i	0.932149	−	0.362074i	$-0.117931\pi$
$769$	117.280	+	203.134i	0.152509	+	0.264154i	−0.779640	+	0.626228i	$0.784598\pi$
$770$	56.7128	+	99.5841i	0.0736530	+	0.129330i
$771$	−94.3200	+	163.367i	−0.122335	+	0.211890i
$772$			291.053i			0.377011i
$773$	348.671	−	603.916i	0.451062	−	0.781262i	−0.547390	−	0.836877i	$-0.684379\pi$
$773$	348.671	−	603.916i	0.451062	−	0.781262i	0.998452	+	0.0556152i	$0.0177120\pi$
$774$	−11.0058	−	6.35418i	−0.0142193	−	0.00820954i
$775$	330.909			0.426979
$776$	−83.6179	−	48.2768i	−0.107755	−	0.0622124i
$777$	299.941	+	526.678i	0.386025	+	0.677835i
$778$	107.795	−	62.2356i	0.138554	−	0.0799943i
$779$	−1741.18			−2.23515
$780$	531.109	+	201.010i	0.680909	+	0.257705i
$781$	581.894			0.745062
$782$	−85.8765	−	148.742i	−0.109816	−	0.190208i
$783$	93.5964	−	54.0379i	0.119536	−	0.0690139i
$784$	−386.914	+	652.227i	−0.493513	+	0.831922i
$785$			193.351i			0.246306i
$786$	6.46257	+	3.73116i	0.00822210	+	0.00474703i
$787$	102.189	−	176.996i	0.129846	−	0.224899i	−0.793771	−	0.608217i	$-0.791885\pi$
$787$	102.189	−	176.996i	0.129846	−	0.224899i	0.923617	+	0.383318i	$0.125218\pi$
$788$		−	222.802i		−	0.282744i
$789$	80.9633	+	46.7442i	0.102615	+	0.0592448i
$790$	99.0102	−	57.1636i	0.125329	−	0.0723590i
$791$	−58.5608	−	102.829i	−0.0740339	−	0.129999i
$792$	61.2985			0.0773972
$793$	−662.185	+	541.408i	−0.835038	+	0.682734i
$794$			105.723i			0.133152i
$795$	63.4266	−	36.6193i	0.0797818	−	0.0460621i
$796$	323.064	−	186.521i	0.405860	−	0.234323i
$797$	−415.160	−	239.693i	−0.520903	−	0.300743i	0.216401	−	0.976305i	$-0.430568\pi$
$797$	−415.160	−	239.693i	−0.520903	−	0.300743i	−0.737304	+	0.675561i	$0.763901\pi$
$798$	87.2811	+	0.515865i	0.109375	+	0.000646447i
$799$	888.222	+	512.815i	1.11167	+	0.641821i
$800$	−134.029	−	77.3818i	−0.167537	−	0.0967273i
$801$	−226.383			−0.282625
$802$	26.2159	−	45.4073i	0.0326882	−	0.0566175i
$803$	−193.299	+	111.601i	−0.240721	+	0.138980i
$804$	−398.391	−	690.033i	−0.495511	−	0.858250i
$805$	−1510.09	−	8.92521i	−1.87589	−	0.0110872i
$806$	9.27073	+	56.8011i	0.0115022	+	0.0704729i
$807$	638.485			0.791183
$808$	143.439	+	248.444i	0.177524	+	0.307480i
$809$	143.790	+	249.051i	0.177737	+	0.307850i	0.941105	−	0.338114i	$-0.109789\pi$
$809$	143.790	+	249.051i	0.177737	+	0.307850i	−0.763368	+	0.645964i	$0.776456\pi$
$810$	−10.3955	−	6.00184i	−0.0128339	−	0.00740968i
$811$	76.4238			0.0942340			0.0471170	−	0.998889i	$-0.484997\pi$
$811$	76.4238			0.0942340			0.0471170	+	0.998889i	$0.484997\pi$
$812$	−290.945	+	497.124i	−0.358307	+	0.612221i
$813$	−383.970	−	221.685i	−0.472288	−	0.272676i
$814$			128.383i			0.157718i
$815$	357.730	+	206.536i	0.438933	+	0.253418i
$816$	−325.135	−	563.150i	−0.398450	−	0.690135i
$817$	348.337	+	603.337i	0.426361	+	0.738478i
$818$		−	107.979i		−	0.132004i
$819$	−269.690	+	42.3823i	−0.329292	+	0.0517488i
$820$	−1276.23			−1.55637
$821$	−278.944	+	161.049i	−0.339762	+	0.196162i	−0.660167	−	0.751119i	$-0.729514\pi$
$821$	−278.944	+	161.049i	−0.339762	+	0.196162i	0.320405	+	0.947281i	$0.396181\pi$
$822$	10.4351	−	6.02472i	0.0126948	−	0.00732934i
$823$	−349.019	+	604.519i	−0.424082	+	0.734531i	−0.996334	−	0.0855462i	$-0.972736\pi$
$823$	−349.019	+	604.519i	−0.424082	+	0.734531i	0.572252	+	0.820078i	$0.306070\pi$
$824$	99.8024			0.121119
$825$	−166.241	+	287.938i	−0.201504	+	0.349015i
$826$	28.4974	+	16.6783i	0.0345005	+	0.0201917i
$827$			89.3063i			0.107988i	0.998541	+	0.0539941i	$0.0171952\pi$
$827$			89.3063i			0.107988i	−0.998541	+	0.0539941i	$0.982805\pi$
$828$	−200.824	+	347.838i	−0.242541	+	0.420094i
$829$	−1284.15	+	741.405i	−1.54904	+	0.894336i	−0.550820	+	0.834624i	$0.685685\pi$
$829$	−1284.15	+	741.405i	−1.54904	+	0.894336i	−0.998216	+	0.0597122i	$0.980982\pi$
$830$	71.0843	−	41.0406i	0.0856438	−	0.0494465i
$831$			248.377i			0.298890i
$832$	−275.341	+	727.507i	−0.330939	+	0.874407i
$833$	−14.0502	+	1188.56i	−0.0168670	+	1.42685i
$834$	−0.368854	+	0.212958i	−0.000442272	+	0.000255346i
$835$	566.961	+	982.006i	0.678996	+	1.17606i
$836$	−1447.09	−	835.475i	−1.73096	−	0.999373i
$837$			109.951i			0.131364i
$838$	−51.6797	+	89.5118i	−0.0616702	+	0.106816i
$839$	623.724	−	1080.32i	0.743414	−	1.28763i	−0.207519	−	0.978231i	$-0.566539\pi$
$839$	623.724	−	1080.32i	0.743414	−	1.28763i	0.950932	−	0.309399i	$-0.100128\pi$
$840$	128.656	+	0.760407i	0.153162	+	0.000905247i
$841$	204.197	−	353.679i	0.242802	−	0.420546i
$842$	36.1596	+	62.6302i	0.0429449	+	0.0743827i
$843$	76.3343	+	132.215i	0.0905508	+	0.156839i
$844$	861.149			1.02032
$845$	−807.375	−	713.314i	−0.955473	−	0.844159i
$846$			26.5375i			0.0313682i
$847$	102.790	+	180.493i	0.121358	+	0.213097i
$848$	51.3285	+	88.9036i	0.0605289	+	0.104839i
$849$	238.013	−	412.251i	0.280345	−	0.485572i
$850$	−79.3688			−0.0933751
$851$	−1465.07	−	845.859i	−1.72159	−	0.993959i
$852$	162.419	−	281.319i	0.190633	−	0.330186i
$853$	−604.288			−0.708426			−0.354213	−	0.935165i	$-0.615251\pi$
$853$	−604.288			−0.708426			−0.354213	+	0.935165i	$0.615251\pi$
$854$	−48.6726	+	83.1645i	−0.0569937	+	0.0973823i
$855$	329.021	+	569.881i	0.384820	+	0.666528i
$856$	−102.084	+	58.9384i	−0.119257	+	0.0688533i
$857$			243.151i			0.283724i	0.989886	+	0.141862i	$0.0453089\pi$
$857$			243.151i			0.283724i	−0.989886	+	0.141862i	$0.954691\pi$
$858$	−54.0825	−	20.4687i	−0.0630332	−	0.0238563i
$859$			1183.06i			1.37725i	0.725116	+	0.688627i	$0.241786\pi$
$859$			1183.06i			1.37725i	−0.725116	+	0.688627i	$0.758214\pi$
$860$	255.319	+	442.225i	0.296883	+	0.514216i
$861$	533.138	−	303.620i	0.619208	−	0.352637i
$862$	−60.8111	+	105.328i	−0.0705465	+	0.122190i
$863$		−	857.830i		−	0.994009i	−0.867748	−	0.497005i	$-0.834433\pi$
$863$		−	857.830i		−	0.994009i	0.867748	−	0.497005i	$-0.165567\pi$
$864$	25.7117	−	44.5340i	0.0297589	−	0.0515440i
$865$	819.172	+	472.949i	0.947020	+	0.546762i
$866$	−82.9175			−0.0957477
$867$	−449.181	−	259.335i	−0.518086	−	0.299117i
$868$	−289.995	−	509.214i	−0.334096	−	0.586652i
$869$	911.226	−	526.096i	1.04859	−	0.605404i
$870$	48.0484			0.0552281
$871$	243.494	+	1491.87i	0.279557	+	1.71283i
$872$	−80.5333			−0.0923547
$873$	87.0059	+	150.699i	0.0996631	+	0.172622i
$874$	−210.981	+	121.810i	−0.241397	+	0.139371i
$875$	211.012	−	360.545i	0.241156	−	0.412051i
$876$			124.602i			0.142239i
$877$	−149.704	−	86.4316i	−0.170700	−	0.0985537i	0.412216	−	0.911086i	$-0.364755\pi$
$877$	−149.704	−	86.4316i	−0.170700	−	0.0985537i	−0.582916	+	0.812533i	$0.698088\pi$
$878$	15.6335	−	27.0781i	0.0178059	−	0.0308406i
$879$			158.819i			0.180682i
$880$	−1048.80	−	605.525i	−1.19182	−	0.688097i
$881$	−827.168	+	477.566i	−0.938897	+	0.542072i	−0.889614	−	0.456713i	$-0.849027\pi$
$881$	−827.168	+	477.566i	−0.938897	+	0.542072i	−0.0492824	+	0.998785i	$0.515693\pi$
$882$	−26.8149	+	15.0618i	−0.0304023	+	0.0170769i
$883$	−35.1165			−0.0397695			−0.0198847	−	0.999802i	$-0.506330\pi$
$883$	−35.1165			−0.0397695			−0.0198847	+	0.999802i	$0.506330\pi$
$884$	200.969	+	1231.32i	0.227340	+	1.39290i
$885$			248.939i			0.281287i
$886$	−23.1036	+	13.3388i	−0.0260763	+	0.0150551i
$887$	104.826	−	60.5211i	0.118180	−	0.0682312i	−0.439745	−	0.898123i	$-0.644931\pi$
$887$	104.826	−	60.5211i	0.118180	−	0.0682312i	0.557925	+	0.829892i	$0.311598\pi$
$888$	124.821	+	72.0653i	0.140564	+	0.0811546i
$889$	−1066.38	−	6.30273i	−1.19953	−	0.00708968i
$890$	−87.1614	−	50.3227i	−0.0979342	−	0.0565423i
$891$	−95.6733	−	55.2370i	−0.107377	−	0.0619944i
$892$	−748.583			−0.839219
$893$	727.393	−	1259.88i	0.814550	−	1.41084i
$894$	−90.3657	+	52.1727i	−0.101080	+	0.0583587i
$895$	−844.574	−	1462.85i	−0.943658	−	1.63446i
$896$	−2.15568	+	364.727i	−0.00240589	+	0.407061i
$897$	589.911	−	482.317i	0.657649	−	0.537700i
$898$	94.3625			0.105081
$899$	−220.057	−	381.150i	−0.244780	−	0.423971i
$900$	92.8030	+	160.739i	0.103114	+	0.178599i
$901$	139.347	+	80.4523i	0.154659	+	0.0892922i
$902$	129.957			0.144077
$903$	−211.866	−	123.996i	−0.234625	−	0.137316i
$904$	−24.3701	−	14.0701i	−0.0269581	−	0.0155643i
$905$		−	424.356i		−	0.468901i
$906$	−83.0846	−	47.9689i	−0.0917049	−	0.0529458i
$907$	230.435	+	399.125i	0.254063	+	0.440050i	0.964641	−	0.263569i	$-0.0848997\pi$
$907$	230.435	+	399.125i	0.254063	+	0.440050i	−0.710578	+	0.703619i	$0.751566\pi$
$908$	564.948	+	978.518i	0.622189	+	1.07766i
$909$		−	517.020i		−	0.568779i
$910$	−113.257	−	43.6315i	−0.124458	−	0.0479468i
$911$	−798.221			−0.876203			−0.438101	−	0.898926i	$-0.644349\pi$
$911$	−798.221			−0.876203			−0.438101	+	0.898926i	$0.644349\pi$
$912$	−798.790	+	461.182i	−0.875866	+	0.505682i
$913$	654.214	−	377.711i	0.716554	−	0.413703i
$914$	72.1706	−	125.003i	0.0789613	−	0.136765i
$915$	−726.483			−0.793971
$916$	74.3761	−	128.823i	0.0811967	−	0.140637i
$917$	124.407	+	72.8104i	0.135668	+	0.0794007i
$918$		−	26.3719i		−	0.0287276i
$919$	581.035	−	1006.38i	0.632247	−	1.09508i	−0.354845	−	0.934925i	$-0.615466\pi$
$919$	581.035	−	1006.38i	0.632247	−	1.09508i	0.987091	−	0.160158i	$-0.0512004\pi$
$920$	−310.995	+	179.553i	−0.338038	+	0.195166i
$921$	−62.5027	+	36.0860i	−0.0678640	+	0.0391813i
$922$		−	27.6666i		−	0.0300071i
$923$	−477.099	+	390.080i	−0.516900	+	0.422622i
$924$	588.776	+	3.47989i	0.637203	+	0.00376612i
$925$	−677.024	+	390.880i	−0.731918	+	0.422573i
$926$	−32.4969	−	56.2862i	−0.0350938	−	0.0607843i
$927$	−155.769	−	89.9334i	−0.168036	−	0.0970155i
$928$			205.838i			0.221808i
$929$	30.5711	−	52.9507i	0.0329075	−	0.0569975i	−0.849103	−	0.528228i	$-0.822857\pi$
$929$	30.5711	−	52.9507i	0.0329075	−	0.0569975i	0.882010	+	0.471230i	$0.156190\pi$
$930$	−24.4411	+	42.3332i	−0.0262808	+	0.0455196i
$931$	1685.90	+	19.9293i	1.81084	+	0.0214063i
$932$	141.901	−	245.781i	0.152255	−	0.263713i
$933$	530.110	+	918.178i	0.568178	+	0.984113i
$934$	82.8473	+	143.496i	0.0887016	+	0.153636i
$935$	−1898.20			−2.03016
$936$	−50.2591	+	41.0923i	−0.0536956	+	0.0439020i
$937$			507.924i			0.542075i	0.962569	+	0.271038i	$0.0873667\pi$
$937$			507.924i			0.542075i	−0.962569	+	0.271038i	$0.912633\pi$
$938$	84.2739	+	147.980i	0.0898442	+	0.157761i
$939$	387.065	+	670.416i	0.412210	+	0.713968i
$940$	533.155	−	923.451i	0.567186	−	0.982395i
$941$	1225.78			1.30263			0.651315	−	0.758807i	$-0.274218\pi$
$941$	1225.78			1.30263			0.651315	+	0.758807i	$0.274218\pi$
$942$	−9.51860	−	5.49557i	−0.0101047	−	0.00583393i
$943$	−856.234	+	1483.04i	−0.907989	+	1.57268i
$944$	−348.932			−0.369632
$945$	−200.118	−	117.121i	−0.211765	−	0.123937i
$946$	−25.9990	−	45.0315i	−0.0274830	−	0.0476020i
$947$	−614.624	+	354.853i	−0.649022	+	0.374713i	−0.788081	−	0.615571i	$-0.788925\pi$
$947$	−614.624	+	354.853i	−0.649022	+	0.374713i	0.139059	+	0.990284i	$0.455592\pi$
$948$		−	587.380i		−	0.619599i
$949$	83.6739	−	221.083i	0.0881706	−	0.232965i
$950$			112.579i			0.118505i
$951$	219.955	+	380.972i	0.231288	+	0.400602i
$952$	139.881	+	245.622i	0.146934	+	0.258007i
$953$	713.059	−	1235.05i	0.748225	−	1.29596i	−0.200448	−	0.979704i	$-0.564240\pi$
$953$	713.059	−	1235.05i	0.748225	−	1.29596i	0.948673	−	0.316260i	$-0.102427\pi$
$954$			4.16330i			0.00436404i
$955$	−569.193	+	985.871i	−0.596013	+	1.03233i
$956$	1125.83	+	649.997i	1.17764	+	0.679914i
$957$	442.206			0.462076
$958$	47.0548	+	27.1671i	0.0491178	+	0.0283582i
$959$	202.257	−	115.184i	0.210904	−	0.120109i
$960$	−572.165	+	330.340i	−0.596006	+	0.344104i
$961$	−513.249			−0.534078
$962$	−86.0629	−	105.262i	−0.0894625	−	0.109420i
$963$	212.441			0.220603
$964$	711.908	+	1233.06i	0.738494	+	1.27911i
$965$	406.152	−	234.492i	0.420883	−	0.242997i
$966$	43.3603	−	74.0875i	0.0448864	−	0.0766952i
$967$		−	1222.79i		−	1.26452i	−0.774757	−	0.632259i	$-0.782128\pi$
$967$		−	1222.79i		−	1.26452i	0.774757	−	0.632259i	$-0.217872\pi$
$968$	42.7763	+	24.6969i	0.0441904	+	0.0255133i
$969$	−722.856	+	1252.02i	−0.745981	+	1.29208i
$970$			77.3623i			0.0797549i
$971$	−1247.04	−	719.982i	−1.28429	−	0.741485i	−0.306660	−	0.951819i	$-0.599211\pi$
$971$	−1247.04	−	719.982i	−1.28429	−	0.741485i	−0.977629	+	0.210335i	$0.932545\pi$
$972$	−53.4091	+	30.8357i	−0.0549476	+	0.0317240i
$973$	−7.14925	+	4.07147i	−0.00734763	+	0.00418445i
$974$	75.5640			0.0775811
$975$	−56.7207	−	347.524i	−0.0581751	−	0.356435i
$976$		−	1018.30i		−	1.04334i
$977$	435.559	−	251.470i	0.445812	−	0.257390i	−0.260248	−	0.965542i	$-0.583804\pi$
$977$	435.559	−	251.470i	0.445812	−	0.257390i	0.706060	+	0.708152i	$0.250471\pi$
$978$	−20.3354	+	11.7407i	−0.0207928	+	0.0120048i
$979$	−802.177	−	463.137i	−0.819384	−	0.473071i
$980$	1235.70	+	14.6075i	1.26092	+	0.0149056i
$981$	125.694	+	72.5697i	0.128129	+	0.0739753i
$982$	170.695	+	98.5507i	0.173824	+	0.100357i
$983$	1368.05			1.39171			0.695853	−	0.718184i	$-0.255027\pi$
$983$	1368.05			1.39171			0.695853	+	0.718184i	$0.255027\pi$
$984$	72.9492	−	126.352i	0.0741353	−	0.128406i
$985$	−310.912	+	179.505i	−0.315646	+	0.182238i
$986$	52.7809	+	91.4192i	0.0535303	+	0.0927173i
$987$	−3.02971	+	512.608i	−0.00306962	+	0.519360i
$988$	1746.55	−	285.061i	1.76776	−	0.288523i
$989$	685.185			0.692806
$990$	−24.5573	−	42.5345i	−0.0248054	−	0.0429641i
$991$	985.579	+	1707.07i	0.994529	+	1.72258i	0.587727	+	0.809059i	$0.300023\pi$
$991$	985.579	+	1707.07i	0.994529	+	1.72258i	0.406802	+	0.913516i	$0.366644\pi$
$992$	−181.355	−	104.705i	−0.182817	−	0.105549i
$993$	−589.332			−0.593486
$994$	−35.0682	+	59.9193i	−0.0352799	+	0.0602810i
$995$	−520.566	−	300.549i	−0.523182	−	0.302059i
$996$		−	421.709i		−	0.423403i
$997$	409.941	+	236.680i	0.411175	+	0.237392i	0.691294	−	0.722573i	$-0.257041\pi$
$997$	409.941	+	236.680i	0.411175	+	0.237392i	−0.280120	+	0.959965i	$0.590374\pi$
$998$	−78.6444	−	136.216i	−0.0788020	−	0.136489i
$999$	−129.878	−	224.955i	−0.130008	−	0.225181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.3.bo.c.244.10	yes	36
7.6	odd	2		273.3.bo.d.244.10	yes	36
13.4	even	6		273.3.bo.d.160.10	yes	36
91.69	odd	6	inner	273.3.bo.c.160.10	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.3.bo.c.160.10	✓	36	91.69	odd	6	inner
273.3.bo.c.244.10	yes	36	1.1	even	1	trivial
273.3.bo.d.160.10	yes	36	13.4	even	6
273.3.bo.d.244.10	yes	36	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	273.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.181190 - 0.104610i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.97811 + 3.42619i) q^{4} +6.37482 q^{5} +(-0.181190 + 0.313831i) q^{6} +(-3.53577 + 6.04139i) q^{7} +1.66461i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.181190 - 0.104610i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.97811 + 3.42619i) q^{4} +6.37482 q^{5} +(-0.181190 + 0.313831i) q^{6} +(-3.53577 + 6.04139i) q^{7} +1.66461i q^{8} +(1.50000 - 2.59808i) q^{9} +(1.15505 - 0.666871i) q^{10} +(10.6304 - 6.13745i) q^{11} -6.85239i q^{12} +(-4.60160 + 12.1583i) q^{13} +(-0.00865587 + 1.46452i) q^{14} +(-9.56223 + 5.52075i) q^{15} +(-7.73832 - 13.4032i) q^{16} +(-21.0081 - 12.1290i) q^{17} -0.627661i q^{18} +(-17.2042 + 29.7986i) q^{19} +(-12.6101 + 21.8414i) q^{20} +(0.0716584 - 12.1241i) q^{21} +(1.28408 - 2.22409i) q^{22} +(16.9205 + 29.3072i) q^{23} +(-1.44159 - 2.49691i) q^{24} +15.6383 q^{25} +(0.438123 + 2.68435i) q^{26} +5.19615i q^{27} +(-13.7048 - 24.0648i) q^{28} +(-10.3996 - 18.0126i) q^{29} +(-1.15505 + 2.00061i) q^{30} +21.1601 q^{31} +(-8.57058 - 4.94822i) q^{32} +(-10.6304 + 18.4123i) q^{33} -5.07528 q^{34} +(-22.5399 + 38.5127i) q^{35} +(5.93434 + 10.2786i) q^{36} +(-43.2927 + 24.9951i) q^{37} +7.19895i q^{38} +(-3.62704 - 22.2226i) q^{39} +10.6116i q^{40} +(25.3016 + 43.8237i) q^{41} +(-1.25533 - 2.20427i) q^{42} +(10.1236 - 17.5346i) q^{43} +48.5623i q^{44} +(9.56223 - 16.5623i) q^{45} +(6.13167 + 3.54012i) q^{46} -42.2799 q^{47} +(23.2150 + 13.4032i) q^{48} +(-23.9967 - 42.7219i) q^{49} +(2.83351 - 1.63593i) q^{50} +42.0162 q^{51} +(-32.5543 - 39.8165i) q^{52} -6.63303 q^{53} +(0.543571 + 0.941492i) q^{54} +(67.7667 - 39.1251i) q^{55} +(-10.0565 - 5.88566i) q^{56} -59.5971i q^{57} +(-3.76861 - 2.17581i) q^{58} +(11.2729 - 19.5252i) q^{59} -43.6827i q^{60} +(56.9807 + 32.8978i) q^{61} +(3.83401 - 2.21357i) q^{62} +(10.3923 + 18.2483i) q^{63} +59.8360 q^{64} +(-29.3343 + 77.5072i) q^{65} +4.44818i q^{66} +(100.700 - 58.1389i) q^{67} +(83.1128 - 47.9852i) q^{68} +(-50.7616 - 29.3072i) q^{69} +(-0.0551796 + 9.33603i) q^{70} +(41.0541 + 23.7026i) q^{71} +(4.32477 + 2.49691i) q^{72} -18.1837 q^{73} +(-5.22948 + 9.05772i) q^{74} +(-23.4574 + 13.5432i) q^{75} +(-68.0638 - 117.890i) q^{76} +(-0.507837 + 85.9227i) q^{77} +(-2.98190 - 3.64709i) q^{78} +85.7191 q^{79} +(-49.3304 - 85.4427i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(9.16882 + 5.29362i) q^{82} +61.5420 q^{83} +(41.3979 + 24.2284i) q^{84} +(-133.923 - 77.3204i) q^{85} -4.23612i q^{86} +(31.1988 + 18.0126i) q^{87} +(10.2164 + 17.6954i) q^{88} +(-37.7304 - 65.3510i) q^{89} -4.00123i q^{90} +(-57.1831 - 70.7891i) q^{91} -133.883 q^{92} +(-31.7402 + 18.3252i) q^{93} +(-7.66071 + 4.42291i) q^{94} +(-109.674 + 189.960i) q^{95} +17.1412 q^{96} +(-29.0020 + 50.2329i) q^{97} +(-8.81711 - 5.23049i) q^{98} -36.8247i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9}+O(q^{10}) \) 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9	\( 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9} + 42 q^{11} - 36 q^{13} + 16 q^{14} + 6 q^{15} - 96 q^{16} - 12 q^{17} + 12 q^{19} - 10 q^{20} - 18 q^{22} + 24 q^{23} + 264 q^{25} + 114 q^{26} - 104 q^{28} + 76 q^{29} - 160 q^{31} - 42 q^{33} - 192 q^{34} - 100 q^{35} - 132 q^{36} + 6 q^{37} + 60 q^{39} + 200 q^{41} + 18 q^{42} + 48 q^{43} - 6 q^{45} + 396 q^{46} + 56 q^{47} + 288 q^{48} - 154 q^{49} - 102 q^{50} + 24 q^{51} - 360 q^{52} + 76 q^{53} + 192 q^{55} - 132 q^{56} - 162 q^{58} + 128 q^{59} - 120 q^{61} + 24 q^{62} - 30 q^{63} - 484 q^{64} - 284 q^{65} - 144 q^{67} + 234 q^{68} - 72 q^{69} + 300 q^{70} - 96 q^{71} + 728 q^{73} - 144 q^{74} - 396 q^{75} - 516 q^{76} - 160 q^{77} - 144 q^{78} + 68 q^{79} - 58 q^{80} - 162 q^{81} + 72 q^{82} + 368 q^{83} + 108 q^{84} - 324 q^{85} - 228 q^{87} + 186 q^{88} + 92 q^{89} + 176 q^{91} - 1044 q^{92} + 240 q^{93} - 336 q^{94} - 2 q^{95} - 72 q^{97} + 234 q^{98}+O(q^{100}) \) 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9 + 42 * q^11 - 36 * q^13 + 16 * q^14 + 6 * q^15 - 96 * q^16 - 12 * q^17 + 12 * q^19 - 10 * q^20 - 18 * q^22 + 24 * q^23 + 264 * q^25 + 114 * q^26 - 104 * q^28 + 76 * q^29 - 160 * q^31 - 42 * q^33 - 192 * q^34 - 100 * q^35 - 132 * q^36 + 6 * q^37 + 60 * q^39 + 200 * q^41 + 18 * q^42 + 48 * q^43 - 6 * q^45 + 396 * q^46 + 56 * q^47 + 288 * q^48 - 154 * q^49 - 102 * q^50 + 24 * q^51 - 360 * q^52 + 76 * q^53 + 192 * q^55 - 132 * q^56 - 162 * q^58 + 128 * q^59 - 120 * q^61 + 24 * q^62 - 30 * q^63 - 484 * q^64 - 284 * q^65 - 144 * q^67 + 234 * q^68 - 72 * q^69 + 300 * q^70 - 96 * q^71 + 728 * q^73 - 144 * q^74 - 396 * q^75 - 516 * q^76 - 160 * q^77 - 144 * q^78 + 68 * q^79 - 58 * q^80 - 162 * q^81 + 72 * q^82 + 368 * q^83 + 108 * q^84 - 324 * q^85 - 228 * q^87 + 186 * q^88 + 92 * q^89 + 176 * q^91 - 1044 * q^92 + 240 * q^93 - 336 * q^94 - 2 * q^95 - 72 * q^97 + 234 * q^98

Introduction

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