LMFDB - Embedded newform 72.3.p.b.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(43,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("72.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.p (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:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.7
Character	$\chi$	$=$	72.43
Dual form			72.3.p.b.67.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45504 + 1.37217i) q^{2} +(2.66358 + 1.38035i) q^{3} +(0.234289 - 3.99313i) q^{4} +(8.07964 - 4.66478i) q^{5} +(-5.76969 + 1.64642i) q^{6} +(-4.91220 - 2.83606i) q^{7} +(5.13836 + 6.13166i) q^{8} +(5.18928 + 7.35333i) q^{9} +O(q^{10})$	\(q+(-1.45504 + 1.37217i) q^{2} +(2.66358 + 1.38035i) q^{3} +(0.234289 - 3.99313i) q^{4} +(8.07964 - 4.66478i) q^{5} +(-5.76969 + 1.64642i) q^{6} +(-4.91220 - 2.83606i) q^{7} +(5.13836 + 6.13166i) q^{8} +(5.18928 + 7.35333i) q^{9} +(-5.35532 + 17.8741i) q^{10} +(-1.85519 + 3.21328i) q^{11} +(6.13596 - 10.3126i) q^{12} +(-11.0919 + 6.40390i) q^{13} +(11.0390 - 2.61380i) q^{14} +(27.9598 - 1.27229i) q^{15} +(-15.8902 - 1.87110i) q^{16} +11.1817 q^{17} +(-17.6406 - 3.57881i) q^{18} -13.1532 q^{19} +(-16.7341 - 33.3560i) q^{20} +(-9.16928 - 14.3346i) q^{21} +(-1.70980 - 7.22109i) q^{22} +(-20.2104 + 11.6685i) q^{23} +(5.22260 + 23.4249i) q^{24} +(31.0204 - 53.7288i) q^{25} +(7.35189 - 24.5379i) q^{26} +(3.67189 + 26.7492i) q^{27} +(-12.4757 + 18.9506i) q^{28} +(-14.6837 - 8.47767i) q^{29} +(-38.9368 + 40.2168i) q^{30} +(3.32057 - 1.91713i) q^{31} +(25.6884 - 19.0816i) q^{32} +(-9.37688 + 5.99801i) q^{33} +(-16.2699 + 15.3433i) q^{34} -52.9184 q^{35} +(30.5786 - 18.9987i) q^{36} -13.8029i q^{37} +(19.1384 - 18.0484i) q^{38} +(-38.3837 + 1.74662i) q^{39} +(70.1190 + 25.5722i) q^{40} +(3.05861 + 5.29766i) q^{41} +(33.0112 + 8.27564i) q^{42} +(-11.3997 + 19.7448i) q^{43} +(12.3964 + 8.16085i) q^{44} +(76.2291 + 35.2054i) q^{45} +(13.3958 - 44.7103i) q^{46} +(49.8977 + 28.8084i) q^{47} +(-39.7420 - 26.9178i) q^{48} +(-8.41350 - 14.5726i) q^{49} +(28.5893 + 120.743i) q^{50} +(29.7834 + 15.4347i) q^{51} +(22.9729 + 45.7917i) q^{52} +60.0402i q^{53} +(-42.0472 - 33.8827i) q^{54} +34.6162i q^{55} +(-7.85093 - 44.6927i) q^{56} +(-35.0344 - 18.1559i) q^{57} +(32.9983 - 7.81327i) q^{58} +(-55.3504 - 95.8696i) q^{59} +(1.47026 - 111.945i) q^{60} +(-73.2932 - 42.3159i) q^{61} +(-2.20093 + 7.34589i) q^{62} +(-4.63630 - 50.8382i) q^{63} +(-11.1944 + 63.0134i) q^{64} +(-59.7456 + 103.482i) q^{65} +(5.41345 - 21.5940i) q^{66} +(16.0918 + 27.8718i) q^{67} +(2.61976 - 44.6502i) q^{68} +(-69.9385 + 3.18250i) q^{69} +(76.9985 - 72.6132i) q^{70} -38.7881i q^{71} +(-18.4237 + 69.6029i) q^{72} -13.6313 q^{73} +(18.9400 + 20.0838i) q^{74} +(156.790 - 100.292i) q^{75} +(-3.08164 + 52.5223i) q^{76} +(18.2261 - 10.5229i) q^{77} +(53.4532 - 55.2104i) q^{78} +(4.14976 + 2.39586i) q^{79} +(-137.115 + 59.0066i) q^{80} +(-27.1428 + 76.3169i) q^{81} +(-11.7197 - 3.51138i) q^{82} +(-2.70708 + 4.68879i) q^{83} +(-59.3883 + 33.2557i) q^{84} +(90.3444 - 52.1604i) q^{85} +(-10.5063 - 44.3718i) q^{86} +(-27.4092 - 42.8496i) q^{87} +(-29.2354 + 5.13562i) q^{88} +98.2333 q^{89} +(-159.224 + 53.3742i) q^{90} +72.6474 q^{91} +(41.8587 + 83.4366i) q^{92} +(11.4909 - 0.522884i) q^{93} +(-112.133 + 26.5507i) q^{94} +(-106.273 + 61.3566i) q^{95} +(94.7622 - 15.3663i) q^{96} +(42.1665 - 73.0345i) q^{97} +(32.2381 + 9.65898i) q^{98} +(-33.2554 + 3.03280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 + 46 * q^8 - 18 * q^9	$ 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9} - 12 q^{10} - 16 q^{11} - 12 q^{12} + 6 q^{14} + 31 q^{16} - 4 q^{17} - 114 q^{18} - 76 q^{19} - 12 q^{20} + 35 q^{22} + 39 q^{24} + 118 q^{25} - 72 q^{26} - 144 q^{27} - 36 q^{28} - 90 q^{30} - 5 q^{32} + 156 q^{33} + 5 q^{34} - 108 q^{35} + 51 q^{36} - 169 q^{38} - 6 q^{40} + 20 q^{41} - 42 q^{42} - 16 q^{43} + 362 q^{44} - 96 q^{46} + 183 q^{48} + 166 q^{49} + 73 q^{50} + 330 q^{51} - 24 q^{52} + 57 q^{54} + 186 q^{56} - 258 q^{57} + 36 q^{58} - 64 q^{59} + 150 q^{60} + 384 q^{62} - 518 q^{64} - 102 q^{65} + 486 q^{66} - 64 q^{67} - 295 q^{68} - 6 q^{70} - 225 q^{72} - 292 q^{73} + 318 q^{74} + 138 q^{75} + 197 q^{76} + 174 q^{78} - 720 q^{80} - 42 q^{81} + 386 q^{82} + 554 q^{83} - 720 q^{84} - 295 q^{86} + 59 q^{88} - 688 q^{89} - 696 q^{90} - 204 q^{91} - 378 q^{92} - 66 q^{94} - 222 q^{96} + 92 q^{97} - 614 q^{98} + 90 q^{99}+O(q^{100}) $ 40 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 + 46 * q^8 - 18 * q^9 - 12 * q^10 - 16 * q^11 - 12 * q^12 + 6 * q^14 + 31 * q^16 - 4 * q^17 - 114 * q^18 - 76 * q^19 - 12 * q^20 + 35 * q^22 + 39 * q^24 + 118 * q^25 - 72 * q^26 - 144 * q^27 - 36 * q^28 - 90 * q^30 - 5 * q^32 + 156 * q^33 + 5 * q^34 - 108 * q^35 + 51 * q^36 - 169 * q^38 - 6 * q^40 + 20 * q^41 - 42 * q^42 - 16 * q^43 + 362 * q^44 - 96 * q^46 + 183 * q^48 + 166 * q^49 + 73 * q^50 + 330 * q^51 - 24 * q^52 + 57 * q^54 + 186 * q^56 - 258 * q^57 + 36 * q^58 - 64 * q^59 + 150 * q^60 + 384 * q^62 - 518 * q^64 - 102 * q^65 + 486 * q^66 - 64 * q^67 - 295 * q^68 - 6 * q^70 - 225 * q^72 - 292 * q^73 + 318 * q^74 + 138 * q^75 + 197 * q^76 + 174 * q^78 - 720 * q^80 - 42 * q^81 + 386 * q^82 + 554 * q^83 - 720 * q^84 - 295 * q^86 + 59 * q^88 - 688 * q^89 - 696 * q^90 - 204 * q^91 - 378 * q^92 - 66 * q^94 - 222 * q^96 + 92 * q^97 - 614 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.45504	+	1.37217i	−0.727521	+	0.686086i
$2$	−1.45504	+	1.37217i	−0.727521	+	0.686086i
$3$	2.66358	+	1.38035i	0.887859	+	0.460116i
$3$	2.66358	+	1.38035i	0.887859	+	0.460116i
$4$	0.234289	−	3.99313i	0.0585723	−	0.998283i
$5$	8.07964	−	4.66478i	1.61593	−	0.932956i	0.627969	−	0.778239i	$-0.283887\pi$
$5$	8.07964	−	4.66478i	1.61593	−	0.932956i	0.987959	−	0.154718i	$-0.0494468\pi$
$6$	−5.76969	+	1.64642i	−0.961615	+	0.274403i
$7$	−4.91220	−	2.83606i	−0.701744	−	0.405152i	0.106253	−	0.994339i	$-0.466115\pi$
$7$	−4.91220	−	2.83606i	−0.701744	−	0.405152i	−0.807996	+	0.589187i	$0.799448\pi$
$8$	5.13836	+	6.13166i	0.642295	+	0.766457i
$9$	5.18928	+	7.35333i	0.576586	+	0.817036i
$10$	−5.35532	+	17.8741i	−0.535532	+	1.78741i
$11$	−1.85519	+	3.21328i	−0.168654	+	0.292116i	−0.937947	−	0.346779i	$-0.887275\pi$
$11$	−1.85519	+	3.21328i	−0.168654	+	0.292116i	0.769293	+	0.638896i	$0.220609\pi$
$12$	6.13596	−	10.3126i	0.511330	−	0.859384i
$13$	−11.0919	+	6.40390i	−0.853221	+	0.492608i	−0.861736	−	0.507356i	$-0.830623\pi$
$13$	−11.0919	+	6.40390i	−0.853221	+	0.492608i	0.00851505	+	0.999964i	$0.497290\pi$
$14$	11.0390	−	2.61380i	0.788502	−	0.186700i
$15$	27.9598	−	1.27229i	1.86398	−	0.0848191i
$16$	−15.8902	−	1.87110i	−0.993139	−	0.116944i
$17$	11.1817			0.657749			0.328875	−	0.944374i	$-0.393331\pi$
$17$	11.1817			0.657749			0.328875	+	0.944374i	$0.393331\pi$
$18$	−17.6406	−	3.57881i	−0.980035	−	0.198823i
$19$	−13.1532			−0.692271			−0.346136	−	0.938185i	$-0.612506\pi$
$19$	−13.1532			−0.692271			−0.346136	+	0.938185i	$0.612506\pi$
$20$	−16.7341	−	33.3560i	−0.836706	−	1.66780i
$21$	−9.16928	−	14.3346i	−0.436632	−	0.682601i
$22$	−1.70980	−	7.22109i	−0.0777181	−	0.328232i
$23$	−20.2104	+	11.6685i	−0.878713	+	0.507325i	−0.870234	−	0.492639i	$-0.836032\pi$
$23$	−20.2104	+	11.6685i	−0.878713	+	0.507325i	−0.00847922	+	0.999964i	$0.502699\pi$
$24$	5.22260	+	23.4249i	0.217608	+	0.976036i
$25$	31.0204	−	53.7288i	1.24081	−	2.14915i
$26$	7.35189	−	24.5379i	0.282765	−	0.943765i
$27$	3.67189	+	26.7492i	0.135996	+	0.990709i
$28$	−12.4757	+	18.9506i	−0.445559	+	0.676808i
$29$	−14.6837	−	8.47767i	−0.506336	−	0.292333i	0.224990	−	0.974361i	$-0.427765\pi$
$29$	−14.6837	−	8.47767i	−0.506336	−	0.292333i	−0.731326	+	0.682028i	$0.761098\pi$
$30$	−38.9368	+	40.2168i	−1.29789	+	1.34056i
$31$	3.32057	−	1.91713i	0.107115	−	0.0618429i	−0.445485	−	0.895289i	$-0.646969\pi$
$31$	3.32057	−	1.91713i	0.107115	−	0.0618429i	0.552600	+	0.833446i	$0.313636\pi$
$32$	25.6884	−	19.0816i	0.802762	−	0.596299i
$33$	−9.37688	+	5.99801i	−0.284148	+	0.181758i
$34$	−16.2699	+	15.3433i	−0.478526	+	0.451272i
$35$	−52.9184			−1.51196
$36$	30.5786	−	18.9987i	0.849405	−	0.527741i
$37$		−	13.8029i		−	0.373052i	−0.982450	−	0.186526i	$-0.940277\pi$
$37$		−	13.8029i		−	0.373052i	0.982450	−	0.186526i	$-0.0597229\pi$
$38$	19.1384	−	18.0484i	0.503641	−	0.474957i
$39$	−38.3837	+	1.74662i	−0.984197	+	0.0447851i
$40$	70.1190	+	25.5722i	1.75297	+	0.639306i
$41$	3.05861	+	5.29766i	0.0746001	+	0.129211i	0.900912	−	0.434001i	$-0.142899\pi$
$41$	3.05861	+	5.29766i	0.0746001	+	0.129211i	−0.826312	+	0.563212i	$0.809565\pi$
$42$	33.0112	+	8.27564i	0.785982	+	0.197039i
$43$	−11.3997	+	19.7448i	−0.265109	+	0.459182i	−0.967592	−	0.252518i	$-0.918741\pi$
$43$	−11.3997	+	19.7448i	−0.265109	+	0.459182i	0.702483	+	0.711700i	$0.252074\pi$
$44$	12.3964	+	8.16085i	0.281737	+	0.185474i
$45$	76.2291	+	35.2054i	1.69398	+	0.782341i
$46$	13.3958	−	44.7103i	0.291213	−	0.971962i
$47$	49.8977	+	28.8084i	1.06165	+	0.612945i	0.925889	−	0.377796i	$-0.123318\pi$
$47$	49.8977	+	28.8084i	1.06165	+	0.612945i	0.135764	+	0.990741i	$0.456651\pi$
$48$	−39.7420	−	26.9178i	−0.827959	−	0.560788i
$49$	−8.41350	−	14.5726i	−0.171704	−	0.297400i
$50$	28.5893	+	120.743i	0.571786	+	2.41486i
$51$	29.7834	+	15.4347i	0.583988	+	0.302641i
$52$	22.9729	+	45.7917i	0.441787	+	0.880610i
$53$			60.0402i			1.13283i	0.824119	+	0.566417i	$0.191671\pi$
$53$			60.0402i			1.13283i	−0.824119	+	0.566417i	$0.808329\pi$
$54$	−42.0472	−	33.8827i	−0.778651	−	0.627457i
$55$			34.6162i			0.629385i
$56$	−7.85093	−	44.6927i	−0.140195	−	0.798084i
$57$	−35.0344	−	18.1559i	−0.614639	−	0.318525i
$58$	32.9983	−	7.81327i	0.568936	−	0.134712i
$59$	−55.3504	−	95.8696i	−0.938142	−	1.62491i	−0.768933	−	0.639329i	$-0.779212\pi$
$59$	−55.3504	−	95.8696i	−0.938142	−	1.62491i	−0.169208	−	0.985580i	$-0.554121\pi$
$60$	1.47026	−	111.945i	0.0245044	−	1.86575i
$61$	−73.2932	−	42.3159i	−1.20153	−	0.693703i	−0.240633	−	0.970616i	$-0.577355\pi$
$61$	−73.2932	−	42.3159i	−1.20153	−	0.693703i	−0.960895	+	0.276913i	$0.910688\pi$
$62$	−2.20093	+	7.34589i	−0.0354989	+	0.118482i
$63$	−4.63630	−	50.8382i	−0.0735921	−	0.806955i
$64$	−11.1944	+	63.0134i	−0.174913	+	0.984584i
$65$	−59.7456	+	103.482i	−0.919163	+	1.59204i
$66$	5.41345	−	21.5940i	0.0820219	−	0.327183i
$67$	16.0918	+	27.8718i	0.240176	+	0.415997i	0.960764	−	0.277366i	$-0.0894616\pi$
$67$	16.0918	+	27.8718i	0.240176	+	0.415997i	−0.720588	+	0.693363i	$0.756128\pi$
$68$	2.61976	−	44.6502i	0.0385259	−	0.656620i
$69$	−69.9385	+	3.18250i	−1.01360	+	0.0461231i
$70$	76.9985	−	72.6132i	1.09998	−	1.03733i
$71$		−	38.7881i		−	0.546311i	−0.961970	−	0.273156i	$-0.911933\pi$
$71$		−	38.7881i		−	0.546311i	0.961970	−	0.273156i	$-0.0880674\pi$
$72$	−18.4237	+	69.6029i	−0.255884	+	0.966707i
$73$	−13.6313			−0.186730			−0.0933652	−	0.995632i	$-0.529762\pi$
$73$	−13.6313			−0.186730			−0.0933652	+	0.995632i	$0.529762\pi$
$74$	18.9400	+	20.0838i	0.255946	+	0.271403i
$75$	156.790	−	100.292i	2.09053	−	1.33723i
$76$	−3.08164	+	52.5223i	−0.0405479	+	0.691083i
$77$	18.2261	−	10.5229i	0.236703	−	0.136661i
$78$	53.4532	−	55.2104i	0.685297	−	0.707826i
$79$	4.14976	+	2.39586i	0.0525286	+	0.0303274i	0.526034	−	0.850463i	$-0.323678\pi$
$79$	4.14976	+	2.39586i	0.0525286	+	0.0303274i	−0.473506	+	0.880791i	$0.657012\pi$
$80$	−137.115	+	59.0066i	−1.71394	+	0.737582i
$81$	−27.1428	+	76.3169i	−0.335096	+	0.942184i
$82$	−11.7197	−	3.51138i	−0.142923	−	0.0428217i
$83$	−2.70708	+	4.68879i	−0.0326154	+	0.0564915i	−0.881872	−	0.471488i	$-0.843717\pi$
$83$	−2.70708	+	4.68879i	−0.0326154	+	0.0564915i	0.849257	+	0.527980i	$0.177050\pi$
$84$	−59.3883	+	33.2557i	−0.707004	+	0.395901i
$85$	90.3444	−	52.1604i	1.06288	−	0.613651i
$86$	−10.5063	−	44.3718i	−0.122166	−	0.515951i
$87$	−27.4092	−	42.8496i	−0.315048	−	0.492524i
$88$	−29.2354	+	5.13562i	−0.332220	+	0.0583594i
$89$	98.2333			1.10374			0.551872	−	0.833929i	$-0.313914\pi$
$89$	98.2333			1.10374			0.551872	+	0.833929i	$0.313914\pi$
$90$	−159.224	+	53.3742i	−1.76916	+	0.593047i
$91$	72.6474			0.798323
$92$	41.8587	+	83.4366i	0.454986	+	0.906920i
$93$	11.4909	−	0.522884i	0.123558	−	0.00562241i
$94$	−112.133	+	26.5507i	−1.19291	+	0.282454i
$95$	−106.273	+	61.3566i	−1.11866	+	0.645859i
$96$	94.7622	−	15.3663i	0.987106	−	0.160066i
$97$	42.1665	−	73.0345i	0.434706	−	0.752932i	−0.562566	−	0.826753i	$-0.690186\pi$
$97$	42.1665	−	73.0345i	0.434706	−	0.752932i	0.997272	+	0.0738200i	$0.0235190\pi$
$98$	32.2381	+	9.65898i	0.328960	+	0.0985610i
$99$	−33.2554	+	3.03280i	−0.335913	+	0.0306343i
$100$	−207.279	−	136.457i	−2.07279	−	1.36457i
$101$	92.9603	+	53.6706i	0.920399	+	0.531393i	0.883762	−	0.467936i	$-0.155002\pi$
$101$	92.9603	+	53.6706i	0.920399	+	0.531393i	0.0366366	+	0.999329i	$0.488336\pi$
$102$	−64.5151	+	18.4098i	−0.632501	+	0.180489i
$103$	75.2912	−	43.4694i	0.730983	−	0.422033i	−0.0877989	−	0.996138i	$-0.527983\pi$
$103$	75.2912	−	43.4694i	0.730983	−	0.422033i	0.818782	+	0.574105i	$0.194650\pi$
$104$	−96.2606	−	35.1060i	−0.925583	−	0.337558i
$105$	−140.952	−	73.0459i	−1.34240	−	0.695675i
$106$	−82.3854	−	87.3609i	−0.777221	−	0.824160i
$107$	168.670			1.57636			0.788179	−	0.615446i	$-0.211024\pi$
$107$	168.670			1.57636			0.788179	+	0.615446i	$0.211024\pi$
$108$	107.673	−	8.39529i	0.996974	−	0.0777341i
$109$			162.909i			1.49458i	0.664497	+	0.747291i	$0.268646\pi$
$109$			162.909i			1.49458i	−0.664497	+	0.747291i	$0.731354\pi$
$110$	−47.4994	−	50.3680i	−0.431812	−	0.457891i
$111$	19.0528	−	36.7651i	0.171647	−	0.331218i
$112$	72.7494	+	54.2569i	0.649549	+	0.484436i
$113$	30.8328	+	53.4040i	0.272857	+	0.472602i	0.969592	−	0.244727i	$-0.0786982\pi$
$113$	30.8328	+	53.4040i	0.272857	+	0.472602i	−0.696736	+	0.717328i	$0.745365\pi$
$114$	75.8896	−	21.6556i	0.665698	−	0.189962i
$115$	−108.862	+	188.554i	−0.946624	+	1.63960i
$116$	−37.2927	+	56.6479i	−0.321489	+	0.488344i
$117$	−104.649	−	48.3306i	−0.894434	−	0.413082i
$118$	212.087	+	63.5441i	1.79734	+	0.538509i
$119$	−54.9270	−	31.7121i	−0.461571	−	0.266488i
$120$	151.469	+	164.902i	1.26224	+	1.37418i
$121$	53.6166	+	92.8666i	0.443112	+	0.767492i
$122$	164.709	−	38.9996i	1.35008	−	0.319669i
$123$	0.834213	+	18.3327i	0.00678222	+	0.149046i
$124$	−6.87738	−	13.7086i	−0.0554628	−	0.110553i
$125$		−	345.574i		−	2.76459i
$126$	76.5047	+	67.6098i	0.607180	+	0.536586i
$127$		−	108.522i		−	0.854507i	−0.904132	−	0.427254i	$-0.859481\pi$
$127$		−	108.522i		−	0.854507i	0.904132	−	0.427254i	$-0.140519\pi$
$128$	−70.1768	−	107.048i	−0.548256	−	0.836311i
$129$	−57.6186	+	36.8563i	−0.446656	+	0.285708i
$130$	−55.0633	−	232.552i	−0.423564	−	1.78886i
$131$	−32.6404	−	56.5348i	−0.249163	−	0.431563i	0.714131	−	0.700012i	$-0.246822\pi$
$131$	−32.6404	−	56.5348i	−0.249163	−	0.431563i	−0.963294	+	0.268449i	$0.913489\pi$
$132$	21.7540	+	38.8484i	0.164803	+	0.294306i
$133$	64.6110	+	37.3032i	0.485797	+	0.280475i
$134$	−61.6591	−	18.4739i	−0.460142	−	0.137865i
$135$	154.446	+	198.995i	1.14405	+	1.47404i
$136$	57.4558	+	68.5626i	0.422469	+	0.504137i
$137$	35.6297	−	61.7125i	0.260071	−	0.450456i	−0.706190	−	0.708023i	$-0.749587\pi$
$137$	35.6297	−	61.7125i	0.260071	−	0.450456i	0.966261	+	0.257567i	$0.0829207\pi$
$138$	97.3965	−	100.598i	0.705772	−	0.728973i
$139$	−38.9742	−	67.5054i	−0.280390	−	0.485650i	0.691091	−	0.722768i	$-0.257131\pi$
$139$	−38.9742	−	67.5054i	−0.280390	−	0.485650i	−0.971481	+	0.237118i	$0.923797\pi$
$140$	−12.3982	+	211.310i	−0.0885588	+	1.50936i
$141$	93.1406	+	145.610i	0.660572	+	1.03269i
$142$	53.2239	+	56.4383i	0.374816	+	0.397453i
$143$		−	47.5218i		−	0.332320i
$144$	−68.7000	−	126.556i	−0.477083	−	0.878858i
$145$	−158.186			−1.09094
$146$	19.8341	−	18.7045i	0.135850	−	0.128113i
$147$	−2.29472	−	50.4288i	−0.0156104	−	0.343053i
$148$	−55.1169	−	3.23388i	−0.372412	−	0.0218505i
$149$	−127.047	+	73.3505i	−0.852664	+	0.492286i	−0.861549	−	0.507675i	$-0.830505\pi$
$149$	−127.047	+	73.3505i	−0.852664	+	0.492286i	0.00888514	+	0.999961i	$0.497172\pi$
$150$	−90.5175	+	361.071i	−0.603450	+	2.40714i
$151$	91.4191	+	52.7808i	0.605424	+	0.349542i	0.771173	−	0.636626i	$-0.219671\pi$
$151$	91.4191	+	52.7808i	0.605424	+	0.349542i	−0.165748	+	0.986168i	$0.553004\pi$
$152$	−67.5857	−	80.6506i	−0.444643	−	0.530596i
$153$	58.0251	+	82.2230i	0.379249	+	0.537405i
$154$	−12.0806	+	40.3206i	−0.0784454	+	0.261822i
$155$	17.8860	−	30.9794i	0.115393	−	0.199867i
$156$	−2.01841	+	153.680i	−0.0129385	+	0.985130i
$157$	−148.874	+	85.9525i	−0.948243	+	0.547468i	−0.892535	−	0.450979i	$-0.851075\pi$
$157$	−148.874	+	85.9525i	−0.948243	+	0.547468i	−0.0557082	+	0.998447i	$0.517742\pi$
$158$	−9.32561	+	2.20810i	−0.0590228	+	0.0139753i
$159$	−82.8764	+	159.922i	−0.521235	+	1.00580i
$160$	118.541	−	274.003i	0.740884	−	1.71252i
$161$	132.370			0.822175
$162$	−65.2260	−	148.289i	−0.402630	−	0.915363i
$163$	−83.1474			−0.510107			−0.255053	−	0.966927i	$-0.582093\pi$
$163$	−83.1474			−0.510107			−0.255053	+	0.966927i	$0.582093\pi$
$164$	21.8709	−	10.9722i	0.133359	−	0.0669039i
$165$	−47.7824	+	92.2029i	−0.289590	+	0.558805i
$166$	−2.49492	−	10.5370i	−0.0150297	−	0.0634757i
$167$	202.139	−	116.705i	1.21041	−	0.698831i	0.247562	−	0.968872i	$-0.420370\pi$
$167$	202.139	−	116.705i	1.21041	−	0.698831i	0.962849	+	0.270041i	$0.0870371\pi$
$168$	40.7799	−	129.879i	0.242738	−	0.773091i
$169$	−2.48015	+	4.29575i	−0.0146755	+	0.0254186i
$170$	−59.8818	+	199.863i	−0.352246	+	1.17567i
$171$	−68.2554	−	96.7194i	−0.399154	−	0.565611i
$172$	76.1728	+	50.1464i	0.442865	+	0.291549i
$173$	38.5845	+	22.2768i	0.223032	+	0.128767i	0.607353	−	0.794432i	$-0.292231\pi$
$173$	38.5845	+	22.2768i	0.223032	+	0.128767i	−0.384322	+	0.923199i	$0.625565\pi$
$174$	98.6785	+	24.7379i	0.567118	+	0.142172i
$175$	−304.757	+	175.951i	−1.74147	+	1.00544i
$176$	35.4917	−	47.5885i	0.201657	−	0.270389i
$177$	−15.0964	−	331.759i	−0.0852905	−	1.87434i
$178$	−142.933	+	134.793i	−0.802997	+	0.757264i
$179$	−15.3758			−0.0858984			−0.0429492	−	0.999077i	$-0.513675\pi$
$179$	−15.3758			−0.0858984			−0.0429492	+	0.999077i	$0.513675\pi$
$180$	158.439	−	296.145i	0.880219	−	1.64525i
$181$		−	240.627i		−	1.32943i	−0.747096	−	0.664716i	$-0.768553\pi$
$181$		−	240.627i		−	1.32943i	0.747096	−	0.664716i	$-0.231447\pi$
$182$	−105.705	+	99.6848i	−0.580797	+	0.547718i
$183$	−136.811	−	213.882i	−0.747604	−	1.16875i
$184$	−175.396	−	63.9664i	−0.953236	−	0.347643i
$185$	−64.3876	−	111.523i	−0.348041	−	0.602825i
$186$	−16.0022	+	16.5283i	−0.0860335	+	0.0888618i
$187$	−20.7442	+	35.9301i	−0.110932	+	0.192139i
$188$	126.726	−	192.499i	0.674077	−	1.02393i
$189$	57.8252	−	141.811i	0.305954	−	0.750323i
$190$	70.4394	−	235.101i	0.370734	−	1.23737i
$191$	−68.8601	−	39.7564i	−0.360524	−	0.208149i	0.308787	−	0.951131i	$-0.400077\pi$
$191$	−68.8601	−	39.7564i	−0.360524	−	0.208149i	−0.669311	+	0.742983i	$0.733410\pi$
$192$	−116.798	+	152.389i	−0.608321	+	0.793691i
$193$	16.7549	+	29.0203i	0.0868128	+	0.150364i	0.906162	−	0.422930i	$-0.138998\pi$
$193$	16.7549	+	29.0203i	0.0868128	+	0.150364i	−0.819349	+	0.573294i	$0.805665\pi$
$194$	38.8619	+	164.128i	0.200319	+	0.846019i
$195$	−301.979	+	193.163i	−1.54861	+	0.990582i
$196$	−60.1615	+	30.1820i	−0.306947	+	0.153990i
$197$			183.151i			0.929699i	0.885390	+	0.464849i	$0.153892\pi$
$197$			183.151i			0.929699i	−0.885390	+	0.464849i	$0.846108\pi$
$198$	44.2264	−	50.0450i	0.223366	−	0.252752i
$199$			86.2656i			0.433496i	0.976228	+	0.216748i	$0.0695449\pi$
$199$			86.2656i			0.433496i	−0.976228	+	0.216748i	$0.930455\pi$
$200$	488.841	−	85.8721i	2.44420	−	0.429360i
$201$	4.38892	+	96.4509i	0.0218354	+	0.479855i
$202$	−208.906	+	49.4645i	−1.03419	+	0.244874i
$203$	48.0864	+	83.2881i	0.236879	+	0.410286i
$204$	68.6107	−	115.313i	0.336327	−	0.565259i
$205$	49.4249	+	28.5355i	0.241097	+	0.139197i
$206$	−49.9043	+	166.562i	−0.242254	+	0.808555i
$207$	−190.680	−	88.0627i	−0.921157	−	0.425424i
$208$	188.235	−	81.0054i	0.904974	−	0.389449i
$209$	24.4016	−	42.2648i	0.116754	−	0.202224i
$210$	305.323	−	87.1260i	1.45392	−	0.414886i
$211$	−115.005	−	199.195i	−0.545049	−	0.944053i	−0.998604	−	0.0528247i	$-0.983178\pi$
$211$	−115.005	−	199.195i	−0.545049	−	0.944053i	0.453554	−	0.891229i	$-0.350156\pi$
$212$	239.748	+	14.0668i	1.13089	+	0.0663527i
$213$	53.5411	−	103.315i	0.251367	−	0.485047i
$214$	−245.422	+	231.445i	−1.14683	+	1.08152i
$215$			212.708i			0.989339i
$216$	−145.149	+	159.962i	−0.671987	+	0.740563i
$217$	−21.7484			−0.100223
$218$	−223.540	−	237.040i	−1.02541	−	1.08734i
$219$	−36.3081	−	18.8160i	−0.165790	−	0.0859176i
$220$	138.227	+	8.11021i	0.628305	+	0.0368646i
$221$	−124.026	+	71.6067i	−0.561206	+	0.324012i
$222$	22.7254	+	79.6386i	0.102367	+	0.358732i
$223$	327.758	+	189.231i	1.46977	+	0.848570i	0.999425	−	0.0339138i	$-0.0107972\pi$
$223$	327.758	+	189.231i	1.46977	+	0.848570i	0.470342	+	0.882484i	$0.344131\pi$
$224$	−180.303	+	20.8788i	−0.804925	+	0.0932088i
$225$	556.059	−	50.7110i	2.47137	−	0.225382i
$226$	−118.142	−	35.3971i	−0.522754	−	0.156624i
$227$	−208.237	+	360.677i	−0.917343	+	1.58889i	−0.113910	+	0.993491i	$0.536337\pi$
$227$	−208.237	+	360.677i	−0.917343	+	1.58889i	−0.803434	+	0.595394i	$0.796996\pi$
$228$	−80.7072	+	135.643i	−0.353979	+	0.594927i
$229$	153.319	−	88.5187i	0.669515	−	0.386545i	−0.126378	−	0.991982i	$-0.540335\pi$
$229$	153.319	−	88.5187i	0.669515	−	0.386545i	0.795893	+	0.605438i	$0.207002\pi$
$230$	−100.330	−	423.731i	−0.436219	−	1.84231i
$231$	63.0719	−	2.87004i	0.273039	−	0.0124244i
$232$	−23.4683	−	133.597i	−0.101156	−	0.575849i
$233$	−144.457			−0.619987			−0.309993	−	0.950739i	$-0.600327\pi$
$233$	−144.457			−0.619987			−0.309993	+	0.950739i	$0.600327\pi$
$234$	218.586	−	73.2731i	0.934129	−	0.313133i
$235$	537.540			2.28740
$236$	−395.788	+	198.560i	−1.67707	+	0.841356i
$237$	7.74607	+	12.1097i	0.0326839	+	0.0510957i
$238$	123.435	−	29.2268i	0.518636	−	0.122802i
$239$	157.611	−	90.9966i	0.659459	−	0.380739i	−0.132612	−	0.991168i	$-0.542336\pi$
$239$	157.611	−	90.9966i	0.659459	−	0.380739i	0.792071	+	0.610429i	$0.209003\pi$
$240$	−446.667	−	32.0985i	−1.86111	−	0.133744i
$241$	70.3168	−	121.792i	0.291771	−	0.505362i	−0.682458	−	0.730925i	$-0.739089\pi$
$241$	70.3168	−	121.792i	0.291771	−	0.505362i	0.974229	+	0.225563i	$0.0724222\pi$
$242$	−205.443	−	61.5536i	−0.848939	−	0.254354i
$243$	−177.641	+	165.809i	−0.731032	+	0.682343i
$244$	−186.145	+	282.755i	−0.762888	+	1.15883i
$245$	−135.956	−	78.4942i	−0.554922	−	0.320385i
$246$	−26.3694	−	25.5301i	−0.107193	−	0.103781i
$247$	145.893	−	84.2315i	0.590661	−	0.341018i
$248$	28.8175	+	10.5097i	0.116199	+	0.0423777i
$249$	−13.6827	+	8.75225i	−0.0549505	+	0.0351496i
$250$	474.186	+	502.824i	1.89675	+	2.01130i
$251$	38.7781			0.154494			0.0772471	−	0.997012i	$-0.475387\pi$
$251$	38.7781			0.154494			0.0772471	+	0.997012i	$0.475387\pi$
$252$	−204.090	+	6.60252i	−0.809880	+	0.0262005i
$253$		−	86.5889i		−	0.342249i
$254$	148.911	+	157.905i	0.586265	+	0.621671i
$255$	312.639	−	14.2264i	1.22603	−	0.0557897i
$256$	248.998	+	59.4643i	0.972648	+	0.232282i
$257$	−74.9268	−	129.777i	−0.291544	−	0.504969i	0.682631	−	0.730763i	$-0.260836\pi$
$257$	−74.9268	−	129.777i	−0.291544	−	0.504969i	−0.974175	+	0.225794i	$0.927502\pi$
$258$	33.2643	−	132.690i	0.128931	−	0.514303i
$259$	−39.1460	+	67.8028i	−0.151143	+	0.261787i
$260$	399.221	+	262.817i	1.53547	+	1.01083i
$261$	−13.8590	−	151.967i	−0.0530996	−	0.582250i
$262$	125.069	+	37.4722i	0.477361	+	0.143024i
$263$	67.5653	+	39.0088i	0.256902	+	0.148323i	0.622921	−	0.782285i	$-0.285946\pi$
$263$	67.5653	+	39.0088i	0.256902	+	0.148323i	−0.366018	+	0.930608i	$0.619279\pi$
$264$	−84.9596	−	26.6759i	−0.321817	−	0.101045i
$265$	280.074	+	485.103i	1.05688	+	1.83058i
$266$	−145.198	+	34.3797i	−0.545857	+	0.129247i
$267$	261.652	+	135.596i	0.979969	+	0.507851i
$268$	115.066	−	57.7265i	0.429350	−	0.215398i
$269$			240.267i			0.893187i	0.894737	+	0.446594i	$0.147363\pi$
$269$			240.267i			0.893187i	−0.894737	+	0.446594i	$0.852637\pi$
$270$	−497.781	−	77.6187i	−1.84363	−	0.287477i
$271$		−	440.449i		−	1.62527i	−0.582772	−	0.812636i	$-0.698032\pi$
$271$		−	440.449i		−	1.62527i	0.582772	−	0.812636i	$-0.301968\pi$
$272$	−177.680	−	20.9221i	−0.653236	−	0.0769195i
$273$	193.502	+	100.279i	0.708799	+	0.367321i
$274$	32.8374	+	138.684i	0.119845	+	0.506147i
$275$	115.097	+	199.354i	0.418535	+	0.724925i
$276$	−3.67772	+	280.019i	−0.0133251	+	1.01456i
$277$	−111.638	−	64.4543i	−0.403026	−	0.232687i	0.284763	−	0.958598i	$-0.408085\pi$
$277$	−111.638	−	64.4543i	−0.403026	−	0.232687i	−0.687789	+	0.725911i	$0.741418\pi$
$278$	149.338	+	44.7437i	0.537187	+	0.160949i
$279$	31.3286	+	14.4687i	0.112289	+	0.0518591i
$280$	−271.914	−	324.478i	−0.971122	−	1.15885i
$281$	70.2020	−	121.593i	0.249829	−	0.432717i	−0.713649	−	0.700503i	$-0.752959\pi$
$281$	70.2020	−	121.593i	0.249829	−	0.432717i	0.963478	+	0.267787i	$0.0862922\pi$
$282$	−335.325	−	84.0631i	−1.18909	−	0.298096i
$283$	−209.786	−	363.361i	−0.741295	−	1.28396i	−0.951906	−	0.306390i	$-0.900879\pi$
$283$	−209.786	−	363.361i	−0.741295	−	1.28396i	0.210611	−	0.977570i	$-0.432455\pi$
$284$	−154.886	−	9.08764i	−0.545373	−	0.0319987i
$285$	−367.759	+	16.7346i	−1.29038	+	0.0587178i
$286$	65.2080	+	69.1461i	0.228000	+	0.241770i
$287$		−	34.6976i		−	0.120898i
$288$	273.617	+	89.8754i	0.950060	+	0.312067i
$289$	−163.969			−0.567366
$290$	230.167	−	217.058i	0.793679	−	0.748476i
$291$	213.127	−	136.328i	0.732394	−	0.468483i
$292$	−3.19367	+	54.4317i	−0.0109372	+	0.186410i
$293$	329.166	−	190.044i	1.12343	−	0.648615i	0.181158	−	0.983454i	$-0.442015\pi$
$293$	329.166	−	190.044i	1.12343	−	0.648615i	0.942275	+	0.334839i	$0.108682\pi$
$294$	72.5359	+	70.2272i	0.246721	+	0.238868i
$295$	−894.422	−	516.395i	−3.03194	−	1.75049i
$296$	84.6348	−	70.9244i	0.285928	−	0.239610i
$297$	−92.7646	−	37.8259i	−0.312339	−	0.127360i
$298$	84.2089	−	281.058i	0.282580	−	0.943148i
$299$	149.448	−	258.851i	0.499825	−	0.865722i
$300$	−363.745	−	649.579i	−1.21248	−	2.16526i
$301$	111.995	−	64.6604i	0.372077	−	0.214819i
$302$	−205.443	+	48.6444i	−0.680274	+	0.161074i
$303$	173.523	+	271.273i	0.572682	+	0.895292i
$304$	209.006	+	24.6108i	0.687521	+	0.0809567i
$305$	−789.577			−2.58878
$306$	−197.253	−	40.0173i	−0.644618	−	0.130776i
$307$	306.165			0.997281			0.498640	−	0.866809i	$-0.333833\pi$
$307$	306.165			0.997281			0.498640	+	0.866809i	$0.333833\pi$
$308$	−37.7490	−	75.2448i	−0.122562	−	0.244301i
$309$	260.547	−	11.8560i	0.843194	−	0.0383689i
$310$	16.4843	+	69.6190i	0.0531751	+	0.224577i
$311$	−492.156	+	284.146i	−1.58249	+	0.913654i	−0.588000	+	0.808861i	$0.700085\pi$
$311$	−492.156	+	284.146i	−1.58249	+	0.913654i	−0.994494	+	0.104793i	$0.966582\pi$
$312$	−207.939	−	226.381i	−0.666471	−	0.725579i
$313$	−156.683	+	271.382i	−0.500583	+	0.867036i	0.499417	+	0.866362i	$0.333548\pi$
$313$	−156.683	+	271.382i	−0.500583	+	0.867036i	−1.00000		0.000673622i	$0.999786\pi$
$314$	98.6764	−	329.345i	0.314256	−	1.04887i
$315$	−274.608	−	389.127i	−0.871773	−	1.23532i
$316$	10.5393	−	16.0092i	0.0333521	−	0.0506621i
$317$	133.136	+	76.8660i	0.419987	+	0.242480i	0.695072	−	0.718940i	$-0.255373\pi$
$317$	133.136	+	76.8660i	0.419987	+	0.242480i	−0.275085	+	0.961420i	$0.588706\pi$
$318$	−98.8514	−	346.413i	−0.310853	−	1.08935i
$319$	54.4822	−	31.4553i	0.170791	−	0.0986061i
$320$	203.496	+	561.345i	0.635926	+	1.75420i
$321$	449.266	+	232.824i	1.39958	+	0.725308i
$322$	−192.604	+	181.635i	−0.598149	+	0.564083i
$323$	−147.075			−0.455341
$324$	298.384	+	126.265i	0.920939	+	0.389707i
$325$			794.605i			2.44494i
$326$	120.983	−	114.092i	0.371113	−	0.349977i
$327$	−224.872	+	433.922i	−0.687681	+	1.32698i
$328$	−16.7672	+	45.9756i	−0.0511196	+	0.140170i
$329$	−163.405	−	283.026i	−0.496672	−	0.860261i
$330$	−56.9928	−	199.725i	−0.172706	−	0.605226i
$331$	306.335	−	530.588i	0.925484	−	1.60299i	0.134704	−	0.990886i	$-0.456992\pi$
$331$	306.335	−	530.588i	0.925484	−	1.60299i	0.790780	−	0.612100i	$-0.209675\pi$
$332$	18.0887	+	11.9082i	0.0544841	+	0.0358682i
$333$	101.497	−	71.6272i	0.304797	−	0.215097i
$334$	−133.981	+	447.179i	−0.401141	+	1.33886i
$335$	260.031	+	150.129i	0.776213	+	0.448147i
$336$	118.880	+	244.937i	0.353811	+	0.728979i
$337$	−233.237	−	403.978i	−0.692098	−	1.19875i	−0.971149	−	0.238473i	$-0.923353\pi$
$337$	−233.237	−	403.978i	−0.692098	−	1.19875i	0.279051	−	0.960276i	$-0.409980\pi$
$338$	−2.28578	−	9.65369i	−0.00676267	−	0.0285612i
$339$	8.40943	+	184.806i	0.0248066	+	0.545149i
$340$	−187.116	−	372.978i	−0.550343	−	1.09699i
$341$			14.2266i			0.0417201i
$342$	232.030	+	47.0726i	0.678450	+	0.137639i
$343$			373.379i			1.08857i
$344$	−179.644	+	31.5571i	−0.522221	+	0.0917358i
$345$	−550.232	+	351.961i	−1.59488	+	1.02018i
$346$	−86.7095	+	20.5309i	−0.250606	+	0.0593379i
$347$	178.207	+	308.664i	0.513565	+	0.889520i	0.999876	+	0.0157348i	$0.00500876\pi$
$347$	178.207	+	308.664i	0.513565	+	0.889520i	−0.486311	+	0.873786i	$0.661658\pi$
$348$	−177.526	+	99.4092i	−0.510132	+	0.285659i
$349$	125.660	+	72.5496i	0.360056	+	0.207878i	0.669105	−	0.743168i	$-0.266677\pi$
$349$	125.660	+	72.5496i	0.360056	+	0.207878i	−0.309049	+	0.951046i	$0.600011\pi$
$350$	201.998	−	674.195i	0.577137	−	1.92627i
$351$	−212.027	−	273.184i	−0.604066	−	0.778302i
$352$	13.6577	+	117.944i	0.0388002	+	0.335068i
$353$	−209.033	+	362.055i	−0.592160	+	1.02565i	0.401780	+	0.915736i	$0.368392\pi$
$353$	−209.033	+	362.055i	−0.592160	+	1.02565i	−0.993941	+	0.109916i	$0.964942\pi$
$354$	477.196	+	462.008i	1.34801	+	1.30511i
$355$	−180.938	−	313.394i	−0.509684	−	0.882799i
$356$	23.0150	−	392.258i	0.0646489	−	1.10185i
$357$	−102.528	−	160.286i	−0.287195	−	0.448980i
$358$	22.3724	−	21.0983i	0.0624929	−	0.0589337i
$359$		−	291.137i		−	0.810968i	−0.914102	−	0.405484i	$-0.867103\pi$
$359$		−	291.137i		−	0.810968i	0.914102	−	0.405484i	$-0.132897\pi$
$360$	175.826	+	648.309i	0.488405	+	1.80086i
$361$	−187.995			−0.520761
$362$	330.182	+	350.122i	0.912104	+	0.967189i
$363$	14.6235	+	321.367i	0.0402852	+	0.885308i
$364$	17.0205	−	290.091i	0.0467597	−	0.796953i
$365$	−110.136	+	63.5871i	−0.301743	+	0.174211i
$366$	492.549	+	123.478i	1.34576	+	0.337371i
$367$	321.962	+	185.885i	0.877281	+	0.506499i	0.869761	−	0.493473i	$-0.164273\pi$
$367$	321.962	+	185.885i	0.877281	+	0.506499i	0.00752022	+	0.999972i	$0.497606\pi$
$368$	342.981	−	147.599i	0.932012	−	0.401084i
$369$	−23.0835	+	49.9820i	−0.0625568	+	0.135452i
$370$	246.715	+	73.9191i	0.666797	+	0.199781i
$371$	170.278	−	294.930i	0.458970	−	0.794959i
$372$	0.604249	−	46.0072i	0.00162433	−	0.123675i
$373$	−424.454	+	245.059i	−1.13795	+	0.656994i	−0.945921	−	0.324396i	$-0.894839\pi$
$373$	−424.454	+	245.059i	−1.13795	+	0.656994i	−0.192025	+	0.981390i	$0.561506\pi$
$374$	−19.1185	−	80.7444i	−0.0511190	−	0.215894i
$375$	477.012	−	920.462i	1.27203	−	2.45457i
$376$	79.7489	+	453.984i	0.212098	+	1.20740i
$377$	217.160			0.576022
$378$	110.451	+	285.687i	0.292198	+	0.755786i
$379$	−249.848			−0.659230			−0.329615	−	0.944115i	$-0.606919\pi$
$379$	−249.848			−0.659230			−0.329615	+	0.944115i	$0.606919\pi$
$380$	220.106	+	438.736i	0.579227	+	1.15457i
$381$	149.799	−	289.058i	0.393172	−	0.758682i
$382$	154.747	−	36.6407i	0.405096	−	0.0959180i
$383$	42.3609	−	24.4571i	0.110603	−	0.0638566i	−0.443678	−	0.896186i	$-0.646327\pi$
$383$	42.3609	−	24.4571i	0.110603	−	0.0638566i	0.554281	+	0.832330i	$0.312993\pi$
$384$	−39.1580	−	381.998i	−0.101974	−	0.994787i
$385$	98.1737	−	170.042i	0.254997	−	0.441667i
$386$	−64.1998	−	19.2351i	−0.166321	−	0.0498320i
$387$	−204.346	+	18.6358i	−0.528026	+	0.0481545i
$388$	−281.757	−	185.487i	−0.726178	−	0.478060i
$389$	−446.299	−	257.671i	−1.14730	−	0.662393i	−0.199071	−	0.979985i	$-0.563792\pi$
$389$	−446.299	−	257.671i	−1.14730	−	0.662393i	−0.948228	+	0.317592i	$0.897126\pi$
$390$	174.338	−	695.427i	0.447020	−	1.78315i
$391$	−225.987	+	130.474i	−0.577973	+	0.333693i
$392$	46.1226	−	126.468i	0.117660	−	0.322622i
$393$	−8.90243	−	195.640i	−0.0226525	−	0.497811i
$394$	−251.314	−	266.492i	−0.637853	−	0.676375i
$395$	44.7047			0.113177
$396$	4.31899	+	133.504i	0.0109065	+	0.337131i
$397$		−	560.274i		−	1.41127i	−0.708576	−	0.705634i	$-0.750662\pi$
$397$		−	560.274i		−	1.41127i	0.708576	−	0.705634i	$-0.249338\pi$
$398$	−118.371	−	125.520i	−0.297415	−	0.315377i
$399$	120.605	+	188.545i	0.302268	+	0.472545i
$400$	−593.452	+	795.721i	−1.48363	+	1.98930i
$401$	226.974	+	393.131i	0.566021	+	0.980377i	0.996954	+	0.0779928i	$0.0248511\pi$
$401$	226.974	+	393.131i	0.566021	+	0.980377i	−0.430933	+	0.902384i	$0.641816\pi$
$402$	−138.733	−	134.318i	−0.345107	−	0.334123i
$403$	−24.5542	+	42.5292i	−0.0609286	+	0.105531i
$404$	236.094	−	358.628i	0.584390	−	0.887694i
$405$	136.698	+	743.228i	0.337525	+	1.83513i
$406$	−184.253	−	55.2048i	−0.453826	−	0.135972i
$407$	44.3527	+	25.6070i	0.108975	+	0.0629165i
$408$	58.3977	+	261.931i	0.143132	+	0.641987i
$409$	233.772	+	404.905i	0.571570	+	0.989988i	0.996405	+	0.0847172i	$0.0269987\pi$
$409$	233.772	+	404.905i	0.571570	+	0.989988i	−0.424835	+	0.905271i	$0.639668\pi$
$410$	−111.071	+	26.2991i	−0.270904	+	0.0641442i
$411$	180.087	−	115.194i	0.438168	−	0.280278i
$412$	−155.939	−	310.832i	−0.378493	−	0.754447i
$413$			627.908i			1.52036i
$414$	398.284	−	133.510i	0.962038	−	0.322488i
$415$			50.5117i			0.121715i
$416$	−162.736	+	376.156i	−0.391192	+	0.904222i
$417$	−10.6300	−	233.604i	−0.0254915	−	0.560201i
$418$	22.4892	+	94.9801i	0.0538020	+	0.227225i
$419$	92.4411	+	160.113i	0.220623	+	0.382131i	0.954997	−	0.296614i	$-0.0958575\pi$
$419$	92.4411	+	160.113i	0.220623	+	0.382131i	−0.734374	+	0.678745i	$0.762524\pi$
$420$	−324.706	+	545.727i	−0.773108	+	1.29935i
$421$	−326.113	−	188.282i	−0.774616	−	0.447225i	0.0599029	−	0.998204i	$-0.480921\pi$
$421$	−326.113	−	188.282i	−0.774616	−	0.447225i	−0.834519	+	0.550980i	$0.814254\pi$
$422$	440.668	+	132.030i	1.04424	+	0.312867i
$423$	47.0951	+	516.409i	0.111336	+	1.22082i
$424$	−368.146	+	308.508i	−0.868269	+	0.727614i
$425$	346.862	−	600.782i	0.816145	−	1.41360i
$426$	63.8615	+	223.795i	0.149910	+	0.525341i
$427$	240.021	+	415.728i	0.562110	+	0.973603i
$428$	39.5177	−	673.523i	0.0923310	−	1.57365i
$429$	65.5966	−	126.578i	0.152906	−	0.295053i
$430$	−291.872	−	309.499i	−0.678772	−	0.719765i
$431$		−	300.981i		−	0.698332i	−0.937061	−	0.349166i	$-0.886465\pi$
$431$		−	300.981i		−	0.698332i	0.937061	−	0.349166i	$-0.113535\pi$
$432$	−8.29680	−	431.920i	−0.0192056	−	0.999816i
$433$	−670.846			−1.54930			−0.774649	−	0.632391i	$-0.782074\pi$
$433$	−670.846			−1.54930			−0.774649	+	0.632391i	$0.782074\pi$
$434$	31.6448	−	29.8426i	0.0729144	−	0.0687617i
$435$	−421.340	−	218.352i	−0.968598	−	0.501958i
$436$	650.519	+	38.1680i	1.49202	+	0.0875412i
$437$	265.830	−	153.477i	0.608308	−	0.351207i
$438$	78.6484	−	22.4429i	0.179563	−	0.0512395i
$439$	513.168	+	296.277i	1.16895	+	0.674892i	0.953432	−	0.301609i	$-0.0975237\pi$
$439$	513.168	+	296.277i	1.16895	+	0.674892i	0.215515	+	0.976501i	$0.430857\pi$
$440$	−212.255	+	177.871i	−0.482397	+	0.404251i
$441$	63.4971	−	137.488i	0.143984	−	0.311765i
$442$	82.2069	−	274.376i	0.185988	−	0.620761i
$443$	−106.548	+	184.547i	−0.240515	+	0.416584i	−0.960861	−	0.277031i	$-0.910650\pi$
$443$	−106.548	+	184.547i	−0.240515	+	0.416584i	0.720346	+	0.693615i	$0.243983\pi$
$444$	−142.344	−	84.6942i	−0.320595	−	0.190753i
$445$	793.689	−	458.237i	1.78357	−	1.02975i
$446$	−736.559	+	174.401i	−1.65148	+	0.391034i
$447$	−439.648	+	20.0058i	−0.983553	+	0.0447558i
$448$	233.699	−	277.786i	0.521650	−	0.620059i
$449$	574.593			1.27972			0.639858	−	0.768493i	$-0.278993\pi$
$449$	574.593			1.27972			0.639858	+	0.768493i	$0.278993\pi$
$450$	−739.504	+	836.795i	−1.64334	+	1.85954i
$451$	−22.6972			−0.0503263
$452$	220.473	−	110.607i	0.487772	−	0.244707i
$453$	170.646	+	266.776i	0.376701	+	0.588909i
$454$	−191.917	−	810.537i	−0.422726	−	1.78532i
$455$	586.965	−	338.884i	1.29003	−	0.744801i
$456$	−68.6936	−	308.111i	−0.150644	−	0.675682i
$457$	200.997	−	348.138i	0.439819	−	0.761789i	−0.557856	−	0.829938i	$-0.688376\pi$
$457$	200.997	−	348.138i	0.439819	−	0.761789i	0.997675	+	0.0681485i	$0.0217092\pi$
$458$	−101.622	+	339.178i	−0.221883	+	0.740564i
$459$	41.0581	+	299.102i	0.0894511	+	0.651638i
$460$	727.417	+	478.876i	1.58134	+	1.04103i
$461$	−126.646	−	73.1191i	−0.274720	−	0.158610i	0.356311	−	0.934368i	$-0.384034\pi$
$461$	−126.646	−	73.1191i	−0.274720	−	0.158610i	−0.631031	+	0.775758i	$0.717368\pi$
$462$	−87.8340	+	90.7215i	−0.190117	+	0.196367i
$463$	−443.882	+	256.275i	−0.958708	+	0.553510i	−0.895775	−	0.444508i	$-0.853379\pi$
$463$	−443.882	+	256.275i	−0.958708	+	0.553510i	−0.0629326	+	0.998018i	$0.520045\pi$
$464$	217.465	+	162.187i	0.468675	+	0.349540i
$465$	90.4031	−	57.8272i	0.194415	−	0.124360i
$466$	210.191	−	198.220i	0.451053	−	0.425364i
$467$	−294.463			−0.630543			−0.315271	−	0.949002i	$-0.602096\pi$
$467$	−294.463			−0.630543			−0.315271	+	0.949002i	$0.602096\pi$
$468$	−217.509	+	406.553i	−0.464762	+	0.868703i
$469$		−	182.549i		−	0.389231i
$470$	−782.143	+	737.597i	−1.66413	+	1.56936i
$471$	−515.182	+	23.4429i	−1.09380	+	0.0497727i
$472$	303.430	−	832.003i	0.642859	−	1.76272i
$473$	−42.2971	−	73.2607i	−0.0894230	−	0.154885i
$474$	−27.8874	−	6.99114i	−0.0588342	−	0.0147492i
$475$	−408.016	+	706.704i	−0.858980	+	1.48780i
$476$	−139.499	+	211.901i	−0.293066	+	0.445170i
$477$	−441.495	+	311.565i	−0.925566	+	0.653176i
$478$	−104.467	+	348.673i	−0.218550	+	0.729441i
$479$	−648.588	−	374.462i	−1.35405	−	0.781758i	−0.365232	−	0.930917i	$-0.619010\pi$
$479$	−648.588	−	374.462i	−1.35405	−	0.781758i	−0.988813	+	0.149158i	$0.952344\pi$
$480$	693.964	−	566.199i	1.44576	−	1.17958i
$481$	88.3925	+	153.100i	0.183768	+	0.318296i
$482$	64.8060	+	273.699i	0.134452	+	0.567841i
$483$	352.578	+	182.717i	0.729975	+	0.378296i
$484$	383.390	−	192.340i	0.792129	−	0.397397i
$485$		−	786.789i		−	1.62225i
$486$	30.9558	−	485.013i	0.0636950	−	0.997969i
$487$		−	81.6059i		−	0.167569i	−0.996484	−	0.0837843i	$-0.973299\pi$
$487$		−	81.6059i		−	0.167569i	0.996484	−	0.0837843i	$-0.0267007\pi$
$488$	−117.141	−	666.843i	−0.240043	−	1.36648i
$489$	−221.469	−	114.772i	−0.452903	−	0.234708i
$490$	305.529	−	72.3426i	0.623529	−	0.147638i
$491$	−345.383	−	598.220i	−0.703427	−	1.21837i	−0.967256	−	0.253802i	$-0.918319\pi$
$491$	−345.383	−	598.220i	−0.703427	−	1.21837i	0.263829	−	0.964569i	$-0.415014\pi$
$492$	73.4002	+	0.964024i	0.149187	+	0.00195940i
$493$	−164.190	−	94.7950i	−0.333042	−	0.192282i
$494$	−96.7005	+	322.751i	−0.195750	+	0.653341i
$495$	−254.544	+	179.633i	−0.514231	+	0.362895i
$496$	−56.3517	+	24.2505i	−0.113612	+	0.0488922i
$497$	−110.005	+	190.535i	−0.221339	+	0.383370i
$498$	7.89926	−	31.5099i	0.0158620	−	0.0632728i
$499$	432.927	+	749.851i	0.867588	+	1.50271i	0.864454	+	0.502712i	$0.167664\pi$
$499$	432.927	+	749.851i	0.867588	+	1.50271i	0.00313444	+	0.999995i	$0.499002\pi$
$500$	−1379.92	−	80.9643i	−2.75984	−	0.161929i
$501$	699.505	−	31.8304i	1.39622	−	0.0635338i
$502$	−56.4237	+	53.2102i	−0.112398	+	0.105996i
$503$			349.624i			0.695077i	0.937666	+	0.347539i	$0.112982\pi$
$503$			349.624i			0.695077i	−0.937666	+	0.347539i	$0.887018\pi$
$504$	287.899	−	289.653i	0.571229	−	0.574709i
$505$	1001.45			1.98306
$506$	118.815	+	125.990i	0.234812	+	0.248993i
$507$	−12.5357	+	8.01858i	−0.0247253	+	0.0158157i
$508$	−433.344	−	25.4256i	−0.853040	−	0.0500505i
$509$	12.5795	−	7.26280i	0.0247142	−	0.0142688i	−0.487592	−	0.873072i	$-0.662125\pi$
$509$	12.5795	−	7.26280i	0.0247142	−	0.0142688i	0.512306	+	0.858803i	$0.328791\pi$
$510$	−435.381	+	449.694i	−0.853688	+	0.881753i
$511$	66.9598	+	38.6593i	0.131037	+	0.0756542i
$512$	−443.898	+	255.145i	−0.866987	+	0.498330i
$513$	−48.2969	−	351.836i	−0.0941460	−	0.685840i
$514$	287.098	+	86.0185i	0.558556	+	0.167351i
$515$	405.550	−	702.434i	0.787477	−	1.36395i
$516$	133.673	+	238.714i	0.259056	+	0.462624i
$517$	−185.139	+	106.890i	−0.358103	+	0.206751i
$518$	−36.0781	−	152.371i	−0.0696488	−	0.294152i
$519$	72.0230	+	112.596i	0.138773	+	0.216948i
$520$	−941.513	+	165.391i	−1.81060	+	0.318059i
$521$	219.308			0.420936			0.210468	−	0.977601i	$-0.432501\pi$
$521$	219.308			0.420936			0.210468	+	0.977601i	$0.432501\pi$
$522$	228.691	+	202.102i	0.438105	+	0.387168i
$523$	−802.128			−1.53371			−0.766853	−	0.641823i	$-0.778179\pi$
$523$	−802.128			−1.53371			−0.766853	+	0.641823i	$0.778179\pi$
$524$	−233.398	+	117.092i	−0.445416	+	0.223458i
$525$	−1054.62	+	47.9895i	−2.00879	+	0.0914086i
$526$	−151.837	+	35.9517i	−0.288664	+	0.0683492i
$527$	37.1297	−	21.4369i	0.0704549	−	0.0406771i
$528$	160.224	−	77.7647i	0.303454	−	0.147282i
$529$	7.80688	−	13.5219i	0.0147578	−	0.0255613i
$530$	−1073.16	−	321.535i	−2.02484	−	0.606669i
$531$	417.732	−	904.503i	0.786690	−	1.70340i
$532$	164.094	−	249.260i	0.308448	−	0.468535i
$533$	−67.8514	−	39.1740i	−0.127301	−	0.0734972i
$534$	−566.775	+	161.733i	−1.06138	+	0.302871i
$535$	1362.80	−	786.810i	2.54728	−	1.47067i
$536$	−88.2148	+	241.885i	−0.164580	+	0.451277i
$537$	−40.9547	−	21.2240i	−0.0762656	−	0.0395232i
$538$	−329.688	−	349.599i	−0.612803	−	0.649812i
$539$	62.4345			0.115834
$540$	830.798	−	570.103i	1.53852	−	1.05575i
$541$			780.008i			1.44179i	0.693045	+	0.720895i	$0.256269\pi$
$541$			780.008i			1.44179i	−0.693045	+	0.720895i	$0.743731\pi$
$542$	604.371	+	640.871i	1.11508	+	1.18242i
$543$	332.149	−	640.929i	0.611693	−	1.18035i
$544$	287.241	−	213.365i	0.528016	−	0.392216i
$545$	759.937	+	1316.25i	1.39438	+	2.41514i
$546$	−419.153	+	119.608i	−0.767680	+	0.219063i
$547$	−19.8872	+	34.4456i	−0.0363568	+	0.0629718i	−0.883631	−	0.468184i	$-0.844909\pi$
$547$	−19.8872	+	34.4456i	−0.0363568	+	0.0629718i	0.847274	+	0.531155i	$0.178242\pi$
$548$	−238.078	−	156.733i	−0.434450	−	0.286009i
$549$	−69.1766	−	758.538i	−0.126005	−	1.38167i
$550$	−441.020	−	132.135i	−0.801854	−	0.240246i
$551$	193.138	+	111.508i	0.350522	+	0.202374i
$552$	−378.883	−	412.486i	−0.686383	−	0.747258i
$553$	−13.5896	−	23.5380i	−0.0245744	−	0.0425641i
$554$	250.881	−	59.4031i	0.452853	−	0.107226i
$555$	−17.5613	−	385.926i	−0.0316419	−	0.695363i
$556$	−278.689	+	139.814i	−0.501240	+	0.251463i
$557$		−	87.9243i		−	0.157853i	−0.996880	−	0.0789266i	$-0.974851\pi$
$557$		−	87.9243i		−	0.157853i	0.996880	−	0.0789266i	$-0.0251493\pi$
$558$	−65.4380	+	21.9357i	−0.117272	+	0.0393113i
$559$		−	292.009i		−	0.522378i
$560$	840.886	+	99.0156i	1.50158	+	0.176813i
$561$	−104.850	+	67.0682i	−0.186898	+	0.119551i
$562$	64.7003	+	273.253i	0.115125	+	0.486215i
$563$	263.524	+	456.436i	0.468071	+	0.810722i	0.999334	−	0.0364845i	$-0.0116160\pi$
$563$	263.524	+	456.436i	0.468071	+	0.810722i	−0.531264	+	0.847207i	$0.678283\pi$
$564$	603.260	−	337.808i	1.06961	−	0.598950i
$565$	498.236	+	287.656i	0.881833	+	0.509127i
$566$	803.841	+	240.842i	1.42021	+	0.425516i
$567$	349.770	−	297.906i	0.616879	−	0.525407i
$568$	237.835	−	199.307i	0.418724	−	0.350893i
$569$	464.624	−	804.752i	0.816562	−	1.41433i	−0.0916393	−	0.995792i	$-0.529211\pi$
$569$	464.624	−	804.752i	0.816562	−	1.41433i	0.908201	−	0.418534i	$-0.137456\pi$
$570$	512.142	−	528.978i	0.898494	−	0.928031i
$571$	198.535	+	343.873i	0.347698	+	0.602230i	0.985840	−	0.167688i	$-0.0536302\pi$
$571$	198.535	+	343.873i	0.347698	+	0.602230i	−0.638142	+	0.769918i	$0.720297\pi$
$572$	−189.761	−	11.1338i	−0.331749	−	0.0194648i
$573$	−128.536	−	200.945i	−0.224322	−	0.350689i
$574$	47.6111	+	50.4864i	0.0829461	+	0.0879554i
$575$			1447.84i			2.51799i
$576$	−521.449	+	244.677i	−0.905293	+	0.424787i
$577$	351.123			0.608531			0.304266	−	0.952587i	$-0.401589\pi$
$577$	351.123			0.608531			0.304266	+	0.952587i	$0.401589\pi$
$578$	238.581	−	224.993i	0.412770	−	0.389262i
$579$	4.56977	+	100.425i	0.00789253	+	0.173446i
$580$	−37.0613	+	631.657i	−0.0638987	+	1.08906i
$581$	26.5954	−	15.3549i	0.0457753	−	0.0264284i
$582$	−123.042	+	490.810i	−0.211412	+	0.843316i
$583$	−192.926	−	111.386i	−0.330919	−	0.191056i
$584$	−70.0427	−	83.5826i	−0.119936	−	0.143121i
$585$	−1070.98	+	97.6701i	−1.83073	+	0.166957i
$586$	−218.177	+	728.194i	−0.372316	+	1.24265i
$587$	−466.965	+	808.807i	−0.795511	+	1.37787i	0.127003	+	0.991902i	$0.459464\pi$
$587$	−466.965	+	808.807i	−0.795511	+	1.37787i	−0.922514	+	0.385964i	$0.873869\pi$
$588$	−201.907	−	2.65180i	−0.343378	−	0.00450986i
$589$	−43.6759	+	25.2163i	−0.0741527	+	0.0428121i
$590$	2010.00	−	475.925i	3.40678	−	0.806652i
$591$	−252.812	+	487.836i	−0.427769	+	0.825441i
$592$	−25.8266	+	219.331i	−0.0436260	+	0.370492i
$593$	−743.820			−1.25433			−0.627167	−	0.778885i	$-0.715786\pi$
$593$	−743.820			−1.25433			−0.627167	+	0.778885i	$0.715786\pi$
$594$	186.880	−	72.2507i	0.314613	−	0.121634i
$595$	−591.720			−0.994488
$596$	263.133	+	524.500i	0.441498	+	0.880034i
$597$	−119.077	+	229.775i	−0.199458	+	0.384883i
$598$	137.735	+	581.706i	0.230327	+	0.972753i
$599$	−519.915	+	300.173i	−0.867971	+	0.501124i	−0.866674	−	0.498876i	$-0.833746\pi$
$599$	−519.915	+	300.173i	−0.867971	+	0.501124i	−0.00129781	+	0.999999i	$0.500413\pi$
$600$	1420.60	+	446.044i	2.36766	+	0.743406i
$601$	−47.0344	+	81.4660i	−0.0782603	+	0.135551i	−0.902499	−	0.430691i	$-0.858270\pi$
$601$	−47.0344	+	81.4660i	−0.0782603	+	0.135551i	0.824239	+	0.566242i	$0.191603\pi$
$602$	−74.2323	+	247.760i	−0.123309	+	0.411561i
$603$	−121.446	+	262.962i	−0.201402	+	0.436090i
$604$	232.179	−	352.683i	0.384403	−	0.583911i
$605$	866.405	+	500.219i	1.43207	+	0.826808i
$606$	−624.716	−	156.611i	−1.03089	−	0.258434i
$607$	−107.746	+	62.2074i	−0.177506	+	0.102483i	−0.586121	−	0.810224i	$-0.699346\pi$
$607$	−107.746	+	62.2074i	−0.177506	+	0.102483i	0.408614	+	0.912707i	$0.366012\pi$
$608$	−337.883	+	250.983i	−0.555729	+	0.412801i
$609$	13.1152	+	288.220i	0.0215357	+	0.473268i
$610$	1148.87	−	1083.44i	1.88339	−	1.77612i
$611$	−737.945			−1.20777
$612$	341.922	−	212.438i	0.558696	−	0.347121i
$613$		−	196.037i		−	0.319799i	−0.987133	−	0.159899i	$-0.948883\pi$
$613$		−	196.037i		−	0.319799i	0.987133	−	0.159899i	$-0.0511170\pi$
$614$	−445.483	+	420.111i	−0.725542	+	0.684220i
$615$	92.2580	+	144.230i	0.150013	+	0.234520i
$616$	158.175	+	57.6861i	0.256778	+	0.0936463i
$617$	−21.0476	−	36.4555i	−0.0341128	−	0.0590850i	0.848465	−	0.529252i	$-0.177527\pi$
$617$	−21.0476	−	36.4555i	−0.0341128	−	0.0590850i	−0.882578	+	0.470166i	$0.844194\pi$
$618$	−362.838	+	374.766i	−0.587116	+	0.606417i
$619$	−304.862	+	528.036i	−0.492507	+	0.853047i	−0.999963	−	0.00863088i	$-0.997253\pi$
$619$	−304.862	+	528.036i	−0.492507	+	0.853047i	0.507456	+	0.861678i	$0.330586\pi$
$620$	−119.515	−	78.6793i	−0.192765	−	0.126902i
$621$	−386.332	−	497.766i	−0.622113	−	0.801555i
$622$	326.209	−	1088.77i	0.524452	−	1.75043i
$623$	−482.542	−	278.596i	−0.774546	−	0.447184i
$624$	613.193	+	44.0654i	0.982681	+	0.0706177i
$625$	−836.517	−	1448.89i	−1.33843	−	2.31822i
$626$	−144.403	−	609.868i	−0.230676	−	0.974229i
$627$	123.336	−	78.8928i	0.196707	−	0.125826i
$628$	308.340	+	614.612i	0.490988	+	0.978681i
$629$		−	154.341i		−	0.245375i
$630$	933.515	+	189.385i	1.48177	+	0.300611i
$631$			897.433i			1.42224i	0.703071	+	0.711120i	$0.251812\pi$
$631$			897.433i			1.42224i	−0.703071	+	0.711120i	$0.748188\pi$
$632$	6.63235	+	37.7557i	0.0104942	+	0.0597401i
$633$	−31.3669	−	689.319i	−0.0495528	−	1.08897i
$634$	−299.191	+	70.8420i	−0.471911	+	0.111738i
$635$	−506.233	−	876.822i	−0.797218	−	1.38082i
$636$	619.171	+	368.404i	0.973540	+	0.579252i
$637$	186.643	+	107.758i	0.293003	+	0.169165i
$638$	−36.1118	+	120.528i	−0.0566015	+	0.188915i
$639$	285.221	−	201.282i	0.446356	−	0.314996i
$640$	−1066.36	−	537.548i	−1.66618	−	0.839918i
$641$	−478.777	+	829.266i	−0.746922	+	1.29371i	0.202370	+	0.979309i	$0.435136\pi$
$641$	−478.777	+	829.266i	−0.746922	+	1.29371i	−0.949292	+	0.314397i	$0.898198\pi$
$642$	−973.175	+	277.702i	−1.51585	+	0.432558i
$643$	−96.6408	−	167.387i	−0.150297	−	0.260321i	0.781040	−	0.624481i	$-0.214690\pi$
$643$	−96.6408	−	167.387i	−0.150297	−	0.260321i	−0.931337	+	0.364160i	$0.881356\pi$
$644$	31.0129	−	528.572i	0.0481567	−	0.820763i
$645$	−293.611	+	566.564i	−0.455211	+	0.878393i
$646$	214.000	−	201.812i	0.331270	−	0.312403i
$647$		−	462.896i		−	0.715450i	−0.933827	−	0.357725i	$-0.883553\pi$
$647$		−	462.896i		−	0.715450i	0.933827	−	0.357725i	$-0.116447\pi$
$648$	−607.419	+	225.714i	−0.937374	+	0.348323i
$649$	410.741			0.632884
$650$	−1090.33	−	1156.18i	−1.67744	−	1.77874i
$651$	−57.9286	−	30.0204i	−0.0889840	−	0.0461143i
$652$	−19.4805	+	332.019i	−0.0298781	+	0.509231i
$653$	175.738	−	101.463i	0.269125	−	0.155379i	−0.359365	−	0.933197i	$-0.617007\pi$
$653$	175.738	−	101.463i	0.269125	−	0.155379i	0.628490	+	0.777818i	$0.283673\pi$
$654$	−268.218	−	939.937i	−0.410119	−	1.43721i
$655$	−527.445	−	304.520i	−0.805259	−	0.464917i
$656$	−38.6895	−	89.9039i	−0.0589779	−	0.137049i
$657$	−70.7367	−	100.236i	−0.107666	−	0.152565i
$658$	626.121	+	187.594i	0.951552	+	0.285098i
$659$	423.773	−	733.996i	0.643054	−	1.11380i	−0.341693	−	0.939812i	$-0.611000\pi$
$659$	423.773	−	733.996i	0.643054	−	1.11380i	0.984747	−	0.173991i	$-0.0556663\pi$
$660$	356.983	+	212.404i	0.540884	+	0.321824i
$661$	−552.689	+	319.095i	−0.836141	+	0.482746i	−0.855951	−	0.517058i	$-0.827027\pi$
$661$	−552.689	+	319.095i	−0.836141	+	0.482746i	0.0198096	+	0.999804i	$0.493694\pi$
$662$	282.328	+	1192.37i	0.426477	+	1.80117i
$663$	−429.196	+	19.5302i	−0.647355	+	0.0294574i
$664$	−42.6600	+	7.49386i	−0.0642470	+	0.0112859i
$665$	696.044			1.04668
$666$	−49.3981	+	243.492i	−0.0741713	+	0.365604i
$667$	395.686			0.593232
$668$	−418.659	−	834.509i	−0.626735	−	1.24927i
$669$	611.804	+	956.452i	0.914505	+	1.42967i
$670$	−584.360	+	138.364i	−0.872178	+	0.206513i
$671$	271.946	−	157.008i	0.405284	−	0.233991i
$672$	−509.071	−	193.269i	−0.757546	−	0.287603i
$673$	216.850	−	375.595i	0.322214	−	0.558091i	−0.658730	−	0.752379i	$-0.728906\pi$
$673$	216.850	−	375.595i	0.322214	−	0.558091i	0.980945	+	0.194288i	$0.0622396\pi$
$674$	893.697	+	267.764i	1.32596	+	0.397276i
$675$	1551.10	+	632.482i	2.29793	+	0.937011i
$676$	16.5724	+	10.9100i	0.0245154	+	0.0161391i
$677$	304.392	+	175.741i	0.449619	+	0.259588i	0.707669	−	0.706544i	$-0.249747\pi$
$677$	304.392	+	175.741i	0.449619	+	0.259588i	−0.258050	+	0.966131i	$0.583080\pi$
$678$	−265.821	−	257.361i	−0.392066	−	0.379588i
$679$	−414.261	+	239.173i	−0.610104	+	0.352244i
$680$	784.052	+	285.942i	1.15302	+	0.420503i
$681$	−1052.51	+	673.251i	−1.54554	+	0.988621i
$682$	−19.5213	−	20.7002i	−0.0286236	−	0.0303522i
$683$	174.129			0.254948			0.127474	−	0.991842i	$-0.459313\pi$
$683$	174.129			0.254948			0.127474	+	0.991842i	$0.459313\pi$
$684$	−402.205	+	249.892i	−0.588019	+	0.365340i
$685$		−	664.819i		−	0.970539i
$686$	−512.340	−	543.282i	−0.746851	−	0.791956i
$687$	530.563	−	24.1429i	0.772290	−	0.0351424i
$688$	218.088	−	292.419i	0.316988	−	0.425028i
$689$	−384.491	−	665.958i	−0.558043	−	0.966558i
$690$	317.659	−	1267.13i	0.460376	−	1.83642i
$691$	147.131	−	254.838i	0.212925	−	0.368796i	−0.739704	−	0.672932i	$-0.765034\pi$
$691$	147.131	−	254.838i	0.212925	−	0.368796i	0.952629	+	0.304136i	$0.0983678\pi$
$692$	97.9940	−	148.854i	0.141610	−	0.215107i
$693$	171.958	+	79.4166i	0.248136	+	0.114598i
$694$	−682.838	−	204.588i	−0.983916	−	0.294795i
$695$	−629.796	−	363.613i	−0.906181	−	0.523184i
$696$	121.901	−	388.240i	0.175145	−	0.557817i
$697$	34.2005	+	59.2370i	0.0490682	+	0.0849886i
$698$	−282.390	+	66.8639i	−0.404571	+	0.0957935i
$699$	−384.772	−	199.401i	−0.550461	−	0.285266i
$700$	631.196	+	1258.16i	0.901708	+	1.79737i
$701$		−	579.128i		−	0.826146i	−0.910698	−	0.413073i	$-0.864455\pi$
$701$		−	579.128i		−	0.826146i	0.910698	−	0.413073i	$-0.135545\pi$
$702$	683.363	+	106.556i	0.973452	+	0.151790i
$703$			181.552i			0.258253i
$704$	−181.712	−	152.873i	−0.258113	−	0.217149i
$705$	1431.78	+	741.993i	2.03089	+	1.05247i
$706$	−192.651	−	813.634i	−0.272876	−	1.15246i
$707$	−304.427	−	527.282i	−0.430589	−	0.745803i
$708$	−1328.29	−	17.4456i	−1.87612	−	0.0246406i
$709$	−702.992	−	405.872i	−0.991526	−	0.572458i	−0.0857956	−	0.996313i	$-0.527343\pi$
$709$	−702.992	−	405.872i	−0.991526	−	0.572458i	−0.905730	+	0.423855i	$0.860677\pi$
$710$	693.302	+	207.723i	0.976482	+	0.292567i
$711$	3.91668	+	42.9473i	0.00550869	+	0.0604041i
$712$	504.758	+	602.333i	0.708930	+	0.845973i
$713$	−44.7400	+	77.4920i	−0.0627490	+	0.108684i
$714$	369.123	+	92.5360i	0.516979	+	0.129602i
$715$	−221.679	−	383.959i	−0.310040	−	0.537005i
$716$	−3.60239	+	61.3977i	−0.00503127	+	0.0857509i
$717$	545.415	−	24.8187i	0.760690	−	0.0346146i
$718$	399.490	+	423.617i	0.556393	+	0.589996i
$719$		−	441.412i		−	0.613924i	−0.951722	−	0.306962i	$-0.900687\pi$
$719$		−	441.412i		−	0.613924i	0.951722	−	0.306962i	$-0.0993125\pi$
$720$	−1145.42	−	702.053i	−1.59087	−	0.975074i
$721$	−493.128			−0.683950
$722$	273.540	−	257.961i	0.378864	−	0.357287i
$723$	355.410	−	227.341i	0.491576	−	0.314442i
$724$	−960.856	−	56.3764i	−1.32715	−	0.0778679i
$725$	−910.990	+	525.961i	−1.25654	+	0.725463i
$726$	−462.248	−	447.536i	−0.636706	−	0.616441i
$727$	−30.1778	−	17.4232i	−0.0415101	−	0.0239658i	0.479101	−	0.877760i	$-0.340963\pi$
$727$	−30.1778	−	17.4232i	−0.0415101	−	0.0239658i	−0.520611	+	0.853794i	$0.674296\pi$
$728$	373.289	+	445.449i	0.512760	+	0.611881i
$729$	−702.035	+	196.440i	−0.963010	+	0.269465i
$730$	73.0001	−	243.648i	0.100000	−	0.333764i
$731$	−127.468	+	220.781i	−0.174375	+	0.302026i
$732$	−886.112	+	496.196i	−1.21053	+	0.677864i
$733$	−889.135	+	513.342i	−1.21301	+	0.700331i	−0.963413	−	0.268020i	$-0.913631\pi$
$733$	−889.135	+	513.342i	−1.21301	+	0.700331i	−0.249595	+	0.968350i	$0.580297\pi$
$734$	−723.534	+	171.317i	−0.985742	+	0.233402i
$735$	−253.780	−	396.742i	−0.345279	−	0.539785i
$736$	−296.520	+	685.391i	−0.402880	+	0.931238i
$737$	−119.413			−0.162026
$738$	−34.9964	−	104.400i	−0.0474206	−	0.141464i
$739$	1155.74			1.56393			0.781963	−	0.623324i	$-0.214218\pi$
$739$	1155.74			1.56393			0.781963	+	0.623324i	$0.214218\pi$
$740$	−460.410	+	230.980i	−0.622176	+	0.312135i
$741$	504.866	−	22.9735i	0.681331	−	0.0310034i
$742$	156.933	+	662.785i	0.211500	+	0.893241i
$743$	703.173	−	405.977i	0.946397	−	0.546403i	0.0544372	−	0.998517i	$-0.482664\pi$
$743$	703.173	−	405.977i	0.946397	−	0.546403i	0.891960	+	0.452115i	$0.149330\pi$
$744$	62.2505	+	67.7715i	0.0836701	+	0.0910907i
$745$	−684.328	+	1185.29i	−0.918562	+	1.59100i
$746$	281.336	−	938.994i	0.377125	−	1.25871i
$747$	−48.5260	+	4.42544i	−0.0649612	+	0.00592428i
$748$	138.613	+	91.2525i	0.185312	+	0.121995i
$749$	−828.543	−	478.360i	−1.10620	−	0.638665i
$750$	568.960	+	1993.85i	0.758613	+	2.65847i
$751$	189.525	−	109.422i	0.252363	−	0.145702i	−0.368483	−	0.929635i	$-0.620123\pi$
$751$	189.525	−	109.422i	0.252363	−	0.145702i	0.620846	+	0.783933i	$0.286789\pi$
$752$	−738.981	−	551.136i	−0.982688	−	0.732893i
$753$	103.288	+	53.5272i	0.137169	+	0.0710853i
$754$	−315.977	+	297.981i	−0.419068	+	0.395201i
$755$	984.844			1.30443
$756$	−552.722	−	264.129i	−0.731114	−	0.349376i
$757$		−	985.851i		−	1.30231i	−0.758944	−	0.651156i	$-0.774284\pi$
$757$		−	985.851i		−	1.30231i	0.758944	−	0.651156i	$-0.225716\pi$
$758$	363.539	−	342.834i	0.479603	−	0.452288i
$759$	119.523	−	230.636i	0.157474	−	0.303869i
$760$	−922.285	−	336.355i	−1.21353	−	0.442573i
$761$	216.932	+	375.738i	0.285062	+	0.493742i	0.972624	−	0.232384i	$-0.0746525\pi$
$761$	216.932	+	375.738i	0.285062	+	0.493742i	−0.687562	+	0.726125i	$0.741319\pi$
$762$	178.674	+	626.140i	0.234480	+	0.821706i
$763$	462.022	−	800.245i	0.605533	−	1.04881i
$764$	−174.886	+	265.653i	−0.228908	+	0.347713i
$765$	852.374	+	393.657i	1.11421	+	0.514584i
$766$	−28.0775	+	93.7125i	−0.0366548	+	0.122340i
$767$	1227.88	+	708.916i	1.60089	+	0.924272i
$768$	581.144	+	502.092i	0.756698	+	0.653765i
$769$	−318.366	−	551.425i	−0.414000	−	0.717068i	0.581323	−	0.813673i	$-0.302535\pi$
$769$	−318.366	−	551.425i	−0.414000	−	0.717068i	−0.995323	+	0.0966044i	$0.969202\pi$
$770$	90.4798	+	382.129i	0.117506	+	0.496271i
$771$	−20.4358	−	449.096i	−0.0265055	−	0.582485i
$772$	119.807	−	60.1053i	0.155191	−	0.0778565i
$773$			815.596i			1.05510i	0.849523	+	0.527552i	$0.176890\pi$
$773$			815.596i			1.05510i	−0.849523	+	0.527552i	$0.823110\pi$
$774$	271.760	−	307.514i	0.351112	−	0.397305i
$775$		−	237.880i		−	0.306942i
$776$	664.489	−	116.727i	0.856300	−	0.150422i
$777$	−197.860	+	126.563i	−0.254646	+	0.162887i
$778$	1002.95	−	237.477i	1.28914	−	0.305241i
$779$	−40.2303	−	69.6809i	−0.0516435	−	0.0894492i
$780$	700.577	+	1251.10i	0.898176	+	1.60397i
$781$	124.637	+	71.9592i	0.159586	+	0.0921373i
$782$	149.788	−	499.938i	0.191545	−	0.639307i
$783$	172.853	−	423.907i	0.220758	−	0.541388i
$784$	106.426	+	247.304i	0.135747	+	0.315439i
$785$	−801.899	+	1388.93i	−1.02153	+	1.76934i
$786$	281.405	+	272.448i	0.358021	+	0.346626i
$787$	22.2735	+	38.5788i	0.0283017	+	0.0490201i	0.879829	−	0.475290i	$-0.157657\pi$
$787$	22.2735	+	38.5788i	0.0283017	+	0.0490201i	−0.851528	+	0.524310i	$0.824323\pi$
$788$	731.345	+	42.9103i	0.928103	+	0.0544546i
$789$	126.119	+	197.167i	0.159847	+	0.249894i
$790$	−65.0472	+	61.3426i	−0.0823383	+	0.0776488i
$791$		−	349.775i		−	0.442193i
$792$	−189.474	−	188.327i	−0.239235	−	0.237787i
$793$	1083.95			1.36689
$794$	768.792	+	815.221i	0.968252	+	1.02673i
$795$	76.3883	+	1678.71i	0.0960859	+	2.11158i
$796$	344.470	+	20.2111i	0.432751	+	0.0253909i
$797$	−131.223	+	75.7614i	−0.164646	+	0.0950582i	−0.580059	−	0.814575i	$-0.696970\pi$
$797$	−131.223	+	75.7614i	−0.164646	+	0.0950582i	0.415413	+	0.909633i	$0.363637\pi$
$798$	−434.202	−	108.851i	−0.544113	−	0.136404i
$799$	557.943	+	322.128i	0.698301	+	0.403164i
$800$	−228.368	−	1972.12i	−0.285460	−	2.46516i
$801$	509.760	+	722.341i	0.636404	+	0.901799i
$802$	−869.700	−	260.574i	−1.08441	−	0.324905i
$803$	25.2887	−	43.8013i	0.0314927	−	0.0545470i
$804$	386.169	+	5.07187i	0.480310	+	0.00630830i
$805$	1069.50	−	617.478i	1.32858	−	0.767053i
$806$	−22.6299	−	95.5743i	−0.0280768	−	0.118579i
$807$	−331.653	+	639.970i	−0.410970	+	0.793024i
$808$	148.574	+	845.780i	0.183878	+	1.04676i
$809$	−214.614			−0.265284			−0.132642	−	0.991164i	$-0.542346\pi$
$809$	−214.614			−0.265284			−0.132642	+	0.991164i	$0.542346\pi$
$810$	−1218.74	−	893.855i	−1.50461	−	1.10352i
$811$	−958.317			−1.18165			−0.590824	−	0.806800i	$-0.701197\pi$
$811$	−958.317			−1.18165			−0.590824	+	0.806800i	$0.701197\pi$
$812$	343.846	−	172.502i	0.423456	−	0.212441i
$813$	607.973	−	1173.17i	0.747814	−	1.44301i
$814$	−99.6722	+	23.6002i	−0.122447	+	0.0289929i
$815$	−671.801	+	387.864i	−0.824295	+	0.475907i
$816$	−444.385	−	300.988i	−0.544590	−	0.368858i
$817$	149.942	−	259.706i	0.183527	−	0.317878i
$818$	−895.747	−	268.378i	−1.09505	−	0.328091i
$819$	376.988	+	534.200i	0.460302	+	0.652259i
$820$	125.526	−	190.674i	0.153080	−	0.232530i
$821$	980.237	+	565.940i	1.19395	+	0.689330i	0.959201	−	0.282725i	$-0.0912383\pi$
$821$	980.237	+	565.940i	1.19395	+	0.689330i	0.234754	+	0.972055i	$0.424572\pi$
$822$	−103.968	+	414.723i	−0.126481	+	0.504529i
$823$	−786.212	+	453.920i	−0.955300	+	0.551543i	−0.894723	−	0.446621i	$-0.852627\pi$
$823$	−786.212	+	453.920i	−0.955300	+	0.551543i	−0.0605770	+	0.998164i	$0.519294\pi$
$824$	653.413	+	238.298i	0.792977	+	0.289197i
$825$	31.3920	+	689.870i	0.0380509	+	0.836206i
$826$	−861.598	−	913.633i	−1.04310	−	1.10609i
$827$	−10.7818			−0.0130373			−0.00651865	−	0.999979i	$-0.502075\pi$
$827$	−10.7818			−0.0130373			−0.00651865	+	0.999979i	$0.502075\pi$
$828$	−396.320	+	740.776i	−0.478648	+	0.894658i
$829$			112.915i			0.136206i	0.997678	+	0.0681030i	$0.0216946\pi$
$829$			112.915i			0.136206i	−0.997678	+	0.0681030i	$0.978305\pi$
$830$	−69.3107	−	73.4965i	−0.0835068	−	0.0885501i
$831$	−208.387	−	325.779i	−0.250767	−	0.392032i
$832$	−279.364	−	770.625i	−0.335774	−	0.926232i
$833$	−94.0775	−	162.947i	−0.112938	−	0.195615i
$834$	336.011	+	325.317i	0.402891	+	0.390068i
$835$	1088.80	−	1885.87i	1.30396	−	2.25852i
$836$	−163.052	−	107.341i	−0.195038	−	0.128398i
$837$	63.4744	+	81.7829i	0.0758356	+	0.0977096i
$838$	−354.208	−	106.126i	−0.422682	−	0.126641i
$839$	257.467	+	148.649i	0.306874	+	0.177174i	0.645527	−	0.763738i	$-0.276638\pi$
$839$	257.467	+	148.649i	0.306874	+	0.177174i	−0.338653	+	0.940911i	$0.609971\pi$
$840$	−276.372	−	1239.61i	−0.329014	−	1.47572i
$841$	−276.758	−	479.360i	−0.329082	−	0.569988i
$842$	732.863	−	173.526i	0.870383	−	0.206088i
$843$	354.830	−	226.970i	0.420913	−	0.269241i
$844$	−822.358	+	412.563i	−0.974357	+	0.488818i
$845$			46.2775i			0.0547662i
$846$	−777.127	−	686.774i	−0.918590	−	0.811789i
$847$		−	608.240i		−	0.718111i
$848$	112.341	−	954.052i	0.132478	−	1.12506i
$849$	−57.2178	−	1257.42i	−0.0673943	−	1.48106i
$850$	319.678	+	1350.12i	0.376092	+	1.58837i
$851$	161.059	+	278.963i	0.189259	+	0.327806i
$852$	−400.007	−	238.002i	−0.469491	−	0.279345i
$853$	1353.97	+	781.714i	1.58730	+	0.916429i	0.993749	+	0.111634i	$0.0356083\pi$
$853$	1353.97	+	781.714i	1.58730	+	0.916429i	0.593552	+	0.804795i	$0.297725\pi$
$854$	−919.691	−	275.552i	−1.07692	−	0.322660i
$855$	−1002.65	−	463.061i	−1.17269	−	0.541592i
$856$	866.690	+	1034.23i	1.01249	+	1.20821i
$857$	14.3592	−	24.8709i	0.0167552	−	0.0290208i	−0.857526	−	0.514440i	$-0.828000\pi$
$857$	14.3592	−	24.8709i	0.0167552	−	0.0290208i	0.874281	+	0.485419i	$0.161333\pi$
$858$	78.2408	+	274.186i	0.0911898	+	0.319564i
$859$	602.824	+	1044.12i	0.701774	+	1.21551i	0.967843	+	0.251555i	$0.0809418\pi$
$859$	602.824	+	1044.12i	0.701774	+	1.21551i	−0.266069	+	0.963954i	$0.585725\pi$
$860$	849.371	+	49.8352i	0.987641	+	0.0579479i
$861$	47.8948	−	92.4197i	0.0556269	−	0.107340i
$862$	412.998	+	437.940i	0.479116	+	0.508051i
$863$		−	740.816i		−	0.858419i	−0.903205	−	0.429210i	$-0.858792\pi$
$863$		−	740.816i		−	0.858419i	0.903205	−	0.429210i	$-0.141208\pi$
$864$	604.741	+	617.077i	0.699932	+	0.714210i
$865$	415.665			0.480537
$866$	976.109	−	920.516i	1.12715	−	1.06295i
$867$	−436.743	−	226.334i	−0.503741	−	0.261054i
$868$	−5.09542	+	86.8443i	−0.00587030	+	0.100051i
$869$	−15.3972	+	8.88956i	−0.0177183	+	0.0102296i
$870$	912.683	−	260.440i	1.04906	−	0.299357i
$871$	−356.976	−	206.100i	−0.409846	−	0.236625i
$872$	−998.905	+	837.088i	−1.14553	+	0.959963i
$873$	755.860	−	68.9323i	0.865819	−	0.0789603i
$874$	−176.197	+	588.081i	−0.201598	+	0.672861i
$875$	−980.069	+	1697.53i	−1.12008	+	1.94003i
$876$	−83.6412	+	140.574i	−0.0954809	+	0.160473i
$877$	−1084.73	+	626.268i	−1.23686	+	0.714102i	−0.968451	−	0.249203i	$-0.919832\pi$
$877$	−1084.73	+	626.268i	−1.23686	+	0.714102i	−0.268410	+	0.963305i	$0.586498\pi$
$878$	−1153.22	+	273.058i	−1.31347	+	0.311000i
$879$	1139.09	−	51.8332i	1.29589	−	0.0589684i
$880$	64.7703	−	550.059i	0.0736026	−	0.625067i
$881$	814.978			0.925060			0.462530	−	0.886604i	$-0.346942\pi$
$881$	814.978			0.925060			0.462530	+	0.886604i	$0.346942\pi$
$882$	96.2668	+	287.180i	0.109146	+	0.325601i
$883$	−895.745			−1.01443			−0.507217	−	0.861819i	$-0.669326\pi$
$883$	−895.745			−1.01443			−0.507217	+	0.861819i	$0.669326\pi$
$884$	256.877	+	512.031i	0.290585	+	0.579220i
$885$	−1669.56	−	2610.07i	−1.88650	−	2.94923i
$886$	−98.1980	−	414.726i	−0.110833	−	0.468088i
$887$	−1453.92	+	839.424i	−1.63915	+	0.946363i	−0.658021	+	0.752999i	$0.728606\pi$
$887$	−1453.92	+	839.424i	−1.63915	+	0.946363i	−0.981127	+	0.193363i	$0.938060\pi$
$888$	323.332	−	72.0872i	0.364112	−	0.0811792i
$889$	−307.776	+	533.084i	−0.346205	+	0.599645i
$890$	−526.071	+	1755.83i	−0.591091	+	1.97284i
$891$	−194.873	−	228.800i	−0.218712	−	0.256790i
$892$	832.415	−	1264.45i	0.933201	−	1.41754i
$893$	−656.312	−	378.922i	−0.734951	−	0.424324i
$894$	612.255	−	632.382i	0.684849	−	0.707363i
$895$	−124.231	+	71.7248i	−0.138806	+	0.0801394i
$896$	41.1286	+	724.866i	0.0459024	+	0.809002i
$897$	755.369	−	483.179i	0.842106	−	0.538661i
$898$	−836.056	+	788.440i	−0.931020	+	0.877995i
$899$	−65.0112			−0.0723150
$900$	−72.2172	−	2232.30i	−0.0802414	−	2.48033i
$901$			671.354i			0.745121i
$902$	33.0253	−	31.1444i	0.0366134	−	0.0345282i
$903$	387.561	−	17.6357i	0.429193	−	0.0195301i
$904$	−169.025	+	463.465i	−0.186974	+	0.512683i
$905$	−1122.47	−	1944.18i	−1.24030	−	2.14827i
$906$	−614.359	−	154.015i	−0.678100	−	0.169994i
$907$	−195.810	+	339.153i	−0.215888	+	0.373928i	−0.953547	−	0.301245i	$-0.902598\pi$
$907$	−195.810	+	339.153i	−0.215888	+	0.373928i	0.737659	+	0.675173i	$0.235931\pi$
$908$	1391.44	+	916.021i	1.53243	+	1.00883i
$909$	87.7390	+	962.079i	0.0965225	+	1.05839i
$910$	−389.051	+	1298.51i	−0.427528	+	1.42693i
$911$	1375.58	+	794.190i	1.50996	+	0.871778i	0.999932	+	0.0116223i	$0.00369956\pi$
$911$	1375.58	+	794.190i	1.50996	+	0.871778i	0.510031	+	0.860156i	$0.329634\pi$
$912$	522.733	+	354.054i	0.573172	+	0.388218i
$913$	−10.0443	−	17.3972i	−0.0110014	−	0.0190550i
$914$	185.245	+	782.358i	0.202675	+	0.855971i
$915$	−2103.10	−	1089.89i	−2.29847	−	1.19114i
$916$	−317.546	−	632.962i	−0.346666	−	0.691006i
$917$			370.281i			0.403796i
$918$	−470.161	−	378.867i	−0.512157	−	0.412709i
$919$		−	995.618i		−	1.08337i	−0.840581	−	0.541686i	$-0.817786\pi$
$919$		−	995.618i		−	1.08337i	0.840581	−	0.541686i	$-0.182214\pi$
$920$	−1715.52	+	301.357i	−1.86470	+	0.327561i
$921$	815.494	+	422.615i	0.885445	+	0.458865i
$922$	284.607	−	67.3887i	0.308684	−	0.0730897i
$923$	248.395	+	430.233i	0.269117	+	0.466124i
$924$	3.31664	−	252.527i	0.00358944	−	0.273298i
$925$	−741.615	−	428.172i	−0.801746	−	0.462888i
$926$	294.212	−	981.973i	0.317724	−	1.06045i
$927$	710.352	+	328.066i	0.766291	+	0.353901i
$928$	−538.969	+	62.4116i	−0.580786	+	0.0672539i
$929$	729.805	−	1264.06i	0.785581	−	1.36067i	−0.143070	−	0.989713i	$-0.545697\pi$
$929$	729.805	−	1264.06i	0.785581	−	1.36067i	0.928651	−	0.370954i	$-0.120969\pi$
$930$	−52.1914	+	208.190i	−0.0561198	+	0.223860i
$931$	110.664	+	191.676i	0.118866	+	0.205881i
$932$	−33.8447	+	576.836i	−0.0363141	+	0.618923i
$933$	−1703.12	+	77.4989i	−1.82542	+	0.0830642i
$934$	428.456	−	404.054i	0.458733	−	0.432606i
$935$			387.069i			0.413978i
$936$	−241.377	−	890.011i	−0.257881	−	0.950866i
$937$	449.372			0.479585			0.239793	−	0.970824i	$-0.422921\pi$
$937$	449.372			0.479585			0.239793	+	0.970824i	$0.422921\pi$
$938$	250.489	+	265.617i	0.267046	+	0.283173i
$939$	−791.938	+	506.571i	−0.843384	+	0.539479i
$940$	125.940	−	2146.47i	0.133979	−	2.28348i
$941$	994.500	−	574.175i	1.05685	−	0.610175i	0.132294	−	0.991211i	$-0.457766\pi$
$941$	994.500	−	574.175i	1.05685	−	0.610175i	0.924561	+	0.381035i	$0.124432\pi$
$942$	717.443	−	741.029i	0.761617	−	0.786655i
$943$	−123.631	−	71.3786i	−0.131104	−	0.0756931i
$944$	700.148	+	1626.96i	0.741682	+	1.72347i
$945$	−194.311	−	1415.52i	−0.205620	−	1.49791i
$946$	162.070	+	48.5585i	0.171322	+	0.0513303i
$947$	162.539	−	281.526i	0.171636	−	0.297282i	−0.767356	−	0.641221i	$-0.778428\pi$
$947$	162.539	−	281.526i	0.171636	−	0.297282i	0.938992	+	0.343939i	$0.111761\pi$
$948$	50.1704	−	28.0939i	0.0529224	−	0.0296349i
$949$	151.197	−	87.2936i	0.159322	−	0.0919848i
$950$	−376.039	−	1588.15i	−0.395831	−	1.67174i
$951$	248.516	+	388.512i	0.261320	+	0.408530i
$952$	−87.7870	−	499.742i	−0.0922132	−	0.524939i
$953$	−1073.20			−1.12613			−0.563064	−	0.826414i	$-0.690377\pi$
$953$	−1073.20			−1.12613			−0.563064	+	0.826414i	$0.690377\pi$
$954$	214.873	−	1059.15i	0.225233	−	1.11022i
$955$	−741.819			−0.776774
$956$	−326.435	−	650.680i	−0.341459	−	0.680627i
$957$	188.537	−	8.57922i	0.197008	−	0.00896471i
$958$	1457.55	−	345.116i	1.52145	−	0.360246i
$959$	−350.041	+	202.096i	−0.365006	+	0.210736i
$960$	−232.823	+	1776.08i	−0.242524	+	1.85008i
$961$	−473.149	+	819.518i	−0.492351	+	0.852777i
$962$	−338.695	−	101.478i	−0.352074	−	0.105486i
$963$	875.277	+	1240.29i	0.908907	+	1.28794i
$964$	−469.858	−	309.319i	−0.487405	−	0.320870i
$965$	270.746	+	156.316i	0.280566	+	0.161985i
$966$	−763.735	+	217.937i	−0.790616	+	0.225608i
$967$	−3.02820	+	1.74833i	−0.00313154	+	0.00180800i	−0.501565	−	0.865120i	$-0.667242\pi$
$967$	−3.02820	+	1.74833i	−0.00313154	+	0.00180800i	0.498433	+	0.866928i	$0.333909\pi$
$968$	−293.925	+	805.941i	−0.303641	+	0.832583i
$969$	−391.746	−	203.015i	−0.404278	−	0.209510i
$970$	1079.61	+	1144.81i	1.11300	+	1.18022i
$971$	−810.426			−0.834630			−0.417315	−	0.908762i	$-0.637029\pi$
$971$	−810.426			−0.834630			−0.417315	+	0.908762i	$0.637029\pi$
$972$	620.479	+	748.191i	0.638353	+	0.769743i
$973$			442.134i			0.454402i
$974$	111.977	+	118.740i	0.114967	+	0.121910i
$975$	−1096.83	+	2116.49i	−1.12496	+	2.17076i
$976$	1085.47	+	809.547i	1.11216	+	0.829454i
$977$	−546.820	−	947.119i	−0.559692	−	0.969416i	−0.997522	−	0.0703577i	$-0.977586\pi$
$977$	−546.820	−	947.119i	−0.559692	−	0.969416i	0.437829	−	0.899058i	$-0.355747\pi$
$978$	479.734	−	136.896i	0.490526	−	0.139975i
$979$	−182.241	+	315.651i	−0.186150	+	0.322422i
$980$	−345.291	+	524.500i	−0.352338	+	0.535204i
$981$	−1197.93	+	845.383i	−1.22113	+	0.861756i
$982$	1323.41	+	396.511i	1.34766	+	0.403779i
$983$	475.171	+	274.340i	0.483389	+	0.279085i	0.721828	−	0.692073i	$-0.243302\pi$
$983$	475.171	+	274.340i	0.483389	+	0.279085i	−0.238439	+	0.971158i	$0.576636\pi$
$984$	−108.123	+	99.3150i	−0.109881	+	0.100930i
$985$	854.358	+	1479.79i	0.867368	+	1.50233i
$986$	368.978	−	87.3660i	0.374217	−	0.0886064i
$987$	−44.5676	−	979.417i	−0.0451546	−	0.992317i
$988$	−302.166	−	602.305i	−0.305836	−	0.609621i
$989$		−	532.067i		−	0.537985i
$990$	123.885	−	610.652i	0.125136	−	0.616820i
$991$			494.677i			0.499169i	0.968353	+	0.249585i	$0.0802941\pi$
$991$			494.677i			0.499169i	−0.968353	+	0.249585i	$0.919706\pi$
$992$	48.7181	−	112.610i	0.0491110	−	0.113518i
$993$	1548.34	−	990.413i	1.55926	−	0.997395i
$994$	−101.384	−	428.183i	−0.101996	−	0.430767i
$995$	402.410	+	696.995i	0.404433	+	0.700498i
$996$	31.7432	+	56.6873i	0.0318707	+	0.0569149i
$997$	−112.086	−	64.7128i	−0.112423	−	0.0649075i	0.442734	−	0.896653i	$-0.354009\pi$
$997$	−112.086	−	64.7128i	−0.112423	−	0.0649075i	−0.555157	+	0.831745i	$0.687342\pi$
$998$	−1658.85	−	497.014i	−1.66217	−	0.498010i
$999$	369.217	−	50.6828i	0.369586	−	0.0507335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.p.b.43.7	✓	40
3.2	odd	2		216.3.p.b.19.14		40
4.3	odd	2		288.3.t.b.79.4		40
8.3	odd	2	inner	72.3.p.b.43.10	yes	40
8.5	even	2		288.3.t.b.79.3		40
9.2	odd	6		648.3.b.e.163.1		20
9.4	even	3	inner	72.3.p.b.67.10	yes	40
9.5	odd	6		216.3.p.b.91.11		40
9.7	even	3		648.3.b.f.163.20		20
12.11	even	2		864.3.t.b.559.1		40
24.5	odd	2		864.3.t.b.559.20		40
24.11	even	2		216.3.p.b.19.11		40
36.7	odd	6		2592.3.b.e.1135.20		20
36.11	even	6		2592.3.b.f.1135.1		20
36.23	even	6		864.3.t.b.847.20		40
36.31	odd	6		288.3.t.b.175.3		40
72.5	odd	6		864.3.t.b.847.1		40
72.11	even	6		648.3.b.e.163.2		20
72.13	even	6		288.3.t.b.175.4		40
72.29	odd	6		2592.3.b.f.1135.20		20
72.43	odd	6		648.3.b.f.163.19		20
72.59	even	6		216.3.p.b.91.14		40
72.61	even	6		2592.3.b.e.1135.1		20
72.67	odd	6	inner	72.3.p.b.67.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.p.b.43.7	✓	40	1.1	even	1	trivial
72.3.p.b.43.10	yes	40	8.3	odd	2	inner
72.3.p.b.67.7	yes	40	72.67	odd	6	inner
72.3.p.b.67.10	yes	40	9.4	even	3	inner
216.3.p.b.19.11		40	24.11	even	2
216.3.p.b.19.14		40	3.2	odd	2
216.3.p.b.91.11		40	9.5	odd	6
216.3.p.b.91.14		40	72.59	even	6
288.3.t.b.79.3		40	8.5	even	2
288.3.t.b.79.4		40	4.3	odd	2
288.3.t.b.175.3		40	36.31	odd	6
288.3.t.b.175.4		40	72.13	even	6
648.3.b.e.163.1		20	9.2	odd	6
648.3.b.e.163.2		20	72.11	even	6
648.3.b.f.163.19		20	72.43	odd	6
648.3.b.f.163.20		20	9.7	even	3
864.3.t.b.559.1		40	12.11	even	2
864.3.t.b.559.20		40	24.5	odd	2
864.3.t.b.847.1		40	72.5	odd	6
864.3.t.b.847.20		40	36.23	even	6
2592.3.b.e.1135.1		20	72.61	even	6
2592.3.b.e.1135.20		20	36.7	odd	6
2592.3.b.f.1135.1		20	36.11	even	6
2592.3.b.f.1135.20		20	72.29	odd	6

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.45504 + 1.37217i) q^{2} +(2.66358 + 1.38035i) q^{3} +(0.234289 - 3.99313i) q^{4} +(8.07964 - 4.66478i) q^{5} +(-5.76969 + 1.64642i) q^{6} +(-4.91220 - 2.83606i) q^{7} +(5.13836 + 6.13166i) q^{8} +(5.18928 + 7.35333i) q^{9} +O(q^{10})\)	\(q+(-1.45504 + 1.37217i) q^{2} +(2.66358 + 1.38035i) q^{3} +(0.234289 - 3.99313i) q^{4} +(8.07964 - 4.66478i) q^{5} +(-5.76969 + 1.64642i) q^{6} +(-4.91220 - 2.83606i) q^{7} +(5.13836 + 6.13166i) q^{8} +(5.18928 + 7.35333i) q^{9} +(-5.35532 + 17.8741i) q^{10} +(-1.85519 + 3.21328i) q^{11} +(6.13596 - 10.3126i) q^{12} +(-11.0919 + 6.40390i) q^{13} +(11.0390 - 2.61380i) q^{14} +(27.9598 - 1.27229i) q^{15} +(-15.8902 - 1.87110i) q^{16} +11.1817 q^{17} +(-17.6406 - 3.57881i) q^{18} -13.1532 q^{19} +(-16.7341 - 33.3560i) q^{20} +(-9.16928 - 14.3346i) q^{21} +(-1.70980 - 7.22109i) q^{22} +(-20.2104 + 11.6685i) q^{23} +(5.22260 + 23.4249i) q^{24} +(31.0204 - 53.7288i) q^{25} +(7.35189 - 24.5379i) q^{26} +(3.67189 + 26.7492i) q^{27} +(-12.4757 + 18.9506i) q^{28} +(-14.6837 - 8.47767i) q^{29} +(-38.9368 + 40.2168i) q^{30} +(3.32057 - 1.91713i) q^{31} +(25.6884 - 19.0816i) q^{32} +(-9.37688 + 5.99801i) q^{33} +(-16.2699 + 15.3433i) q^{34} -52.9184 q^{35} +(30.5786 - 18.9987i) q^{36} -13.8029i q^{37} +(19.1384 - 18.0484i) q^{38} +(-38.3837 + 1.74662i) q^{39} +(70.1190 + 25.5722i) q^{40} +(3.05861 + 5.29766i) q^{41} +(33.0112 + 8.27564i) q^{42} +(-11.3997 + 19.7448i) q^{43} +(12.3964 + 8.16085i) q^{44} +(76.2291 + 35.2054i) q^{45} +(13.3958 - 44.7103i) q^{46} +(49.8977 + 28.8084i) q^{47} +(-39.7420 - 26.9178i) q^{48} +(-8.41350 - 14.5726i) q^{49} +(28.5893 + 120.743i) q^{50} +(29.7834 + 15.4347i) q^{51} +(22.9729 + 45.7917i) q^{52} +60.0402i q^{53} +(-42.0472 - 33.8827i) q^{54} +34.6162i q^{55} +(-7.85093 - 44.6927i) q^{56} +(-35.0344 - 18.1559i) q^{57} +(32.9983 - 7.81327i) q^{58} +(-55.3504 - 95.8696i) q^{59} +(1.47026 - 111.945i) q^{60} +(-73.2932 - 42.3159i) q^{61} +(-2.20093 + 7.34589i) q^{62} +(-4.63630 - 50.8382i) q^{63} +(-11.1944 + 63.0134i) q^{64} +(-59.7456 + 103.482i) q^{65} +(5.41345 - 21.5940i) q^{66} +(16.0918 + 27.8718i) q^{67} +(2.61976 - 44.6502i) q^{68} +(-69.9385 + 3.18250i) q^{69} +(76.9985 - 72.6132i) q^{70} -38.7881i q^{71} +(-18.4237 + 69.6029i) q^{72} -13.6313 q^{73} +(18.9400 + 20.0838i) q^{74} +(156.790 - 100.292i) q^{75} +(-3.08164 + 52.5223i) q^{76} +(18.2261 - 10.5229i) q^{77} +(53.4532 - 55.2104i) q^{78} +(4.14976 + 2.39586i) q^{79} +(-137.115 + 59.0066i) q^{80} +(-27.1428 + 76.3169i) q^{81} +(-11.7197 - 3.51138i) q^{82} +(-2.70708 + 4.68879i) q^{83} +(-59.3883 + 33.2557i) q^{84} +(90.3444 - 52.1604i) q^{85} +(-10.5063 - 44.3718i) q^{86} +(-27.4092 - 42.8496i) q^{87} +(-29.2354 + 5.13562i) q^{88} +98.2333 q^{89} +(-159.224 + 53.3742i) q^{90} +72.6474 q^{91} +(41.8587 + 83.4366i) q^{92} +(11.4909 - 0.522884i) q^{93} +(-112.133 + 26.5507i) q^{94} +(-106.273 + 61.3566i) q^{95} +(94.7622 - 15.3663i) q^{96} +(42.1665 - 73.0345i) q^{97} +(32.2381 + 9.65898i) q^{98} +(-33.2554 + 3.03280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 + 46 * q^8 - 18 * q^9	\( 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9} - 12 q^{10} - 16 q^{11} - 12 q^{12} + 6 q^{14} + 31 q^{16} - 4 q^{17} - 114 q^{18} - 76 q^{19} - 12 q^{20} + 35 q^{22} + 39 q^{24} + 118 q^{25} - 72 q^{26} - 144 q^{27} - 36 q^{28} - 90 q^{30} - 5 q^{32} + 156 q^{33} + 5 q^{34} - 108 q^{35} + 51 q^{36} - 169 q^{38} - 6 q^{40} + 20 q^{41} - 42 q^{42} - 16 q^{43} + 362 q^{44} - 96 q^{46} + 183 q^{48} + 166 q^{49} + 73 q^{50} + 330 q^{51} - 24 q^{52} + 57 q^{54} + 186 q^{56} - 258 q^{57} + 36 q^{58} - 64 q^{59} + 150 q^{60} + 384 q^{62} - 518 q^{64} - 102 q^{65} + 486 q^{66} - 64 q^{67} - 295 q^{68} - 6 q^{70} - 225 q^{72} - 292 q^{73} + 318 q^{74} + 138 q^{75} + 197 q^{76} + 174 q^{78} - 720 q^{80} - 42 q^{81} + 386 q^{82} + 554 q^{83} - 720 q^{84} - 295 q^{86} + 59 q^{88} - 688 q^{89} - 696 q^{90} - 204 q^{91} - 378 q^{92} - 66 q^{94} - 222 q^{96} + 92 q^{97} - 614 q^{98} + 90 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 + 46 * q^8 - 18 * q^9 - 12 * q^10 - 16 * q^11 - 12 * q^12 + 6 * q^14 + 31 * q^16 - 4 * q^17 - 114 * q^18 - 76 * q^19 - 12 * q^20 + 35 * q^22 + 39 * q^24 + 118 * q^25 - 72 * q^26 - 144 * q^27 - 36 * q^28 - 90 * q^30 - 5 * q^32 + 156 * q^33 + 5 * q^34 - 108 * q^35 + 51 * q^36 - 169 * q^38 - 6 * q^40 + 20 * q^41 - 42 * q^42 - 16 * q^43 + 362 * q^44 - 96 * q^46 + 183 * q^48 + 166 * q^49 + 73 * q^50 + 330 * q^51 - 24 * q^52 + 57 * q^54 + 186 * q^56 - 258 * q^57 + 36 * q^58 - 64 * q^59 + 150 * q^60 + 384 * q^62 - 518 * q^64 - 102 * q^65 + 486 * q^66 - 64 * q^67 - 295 * q^68 - 6 * q^70 - 225 * q^72 - 292 * q^73 + 318 * q^74 + 138 * q^75 + 197 * q^76 + 174 * q^78 - 720 * q^80 - 42 * q^81 + 386 * q^82 + 554 * q^83 - 720 * q^84 - 295 * q^86 + 59 * q^88 - 688 * q^89 - 696 * q^90 - 204 * q^91 - 378 * q^92 - 66 * q^94 - 222 * q^96 + 92 * q^97 - 614 * q^98 + 90 * q^99

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