Properties

Label 43.6.c.a.6.10
Level $43$
Weight $6$
Character 43.6
Analytic conductor $6.897$
Analytic rank $0$
Dimension $34$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 6.10
Character \(\chi\) \(=\) 43.6
Dual form 43.6.c.a.36.10

$q$-expansion

\(f(q)\) \(=\) \(q+1.74361 q^{2} +(7.37567 - 12.7750i) q^{3} -28.9598 q^{4} +(-8.29752 + 14.3717i) q^{5} +(12.8603 - 22.2747i) q^{6} +(-98.7307 - 171.007i) q^{7} -106.290 q^{8} +(12.6989 + 21.9952i) q^{9} +O(q^{10})\) \(q+1.74361 q^{2} +(7.37567 - 12.7750i) q^{3} -28.9598 q^{4} +(-8.29752 + 14.3717i) q^{5} +(12.8603 - 22.2747i) q^{6} +(-98.7307 - 171.007i) q^{7} -106.290 q^{8} +(12.6989 + 21.9952i) q^{9} +(-14.4677 + 25.0587i) q^{10} -376.577 q^{11} +(-213.598 + 369.963i) q^{12} +(-55.5603 - 96.2332i) q^{13} +(-172.148 - 298.169i) q^{14} +(122.400 + 212.002i) q^{15} +741.385 q^{16} +(-786.400 - 1362.08i) q^{17} +(22.1420 + 38.3511i) q^{18} +(444.429 - 769.773i) q^{19} +(240.295 - 416.202i) q^{20} -2912.82 q^{21} -656.604 q^{22} +(428.153 - 741.583i) q^{23} +(-783.963 + 1357.86i) q^{24} +(1424.80 + 2467.83i) q^{25} +(-96.8756 - 167.793i) q^{26} +3959.23 q^{27} +(2859.22 + 4952.32i) q^{28} +(12.2237 + 21.1721i) q^{29} +(213.417 + 369.650i) q^{30} +(2222.35 - 3849.23i) q^{31} +4693.98 q^{32} +(-2777.51 + 4810.78i) q^{33} +(-1371.18 - 2374.95i) q^{34} +3276.88 q^{35} +(-367.758 - 636.976i) q^{36} +(-3154.45 + 5463.66i) q^{37} +(774.912 - 1342.19i) q^{38} -1639.18 q^{39} +(881.946 - 1527.57i) q^{40} +5203.64 q^{41} -5078.83 q^{42} +(3986.93 - 11450.5i) q^{43} +10905.6 q^{44} -421.478 q^{45} +(746.533 - 1293.03i) q^{46} -13328.9 q^{47} +(5468.21 - 9471.22i) q^{48} +(-11092.0 + 19211.9i) q^{49} +(2484.30 + 4302.94i) q^{50} -23200.9 q^{51} +(1609.01 + 2786.90i) q^{52} +(2126.84 - 3683.80i) q^{53} +6903.36 q^{54} +(3124.65 - 5412.05i) q^{55} +(10494.1 + 18176.3i) q^{56} +(-6555.92 - 11355.2i) q^{57} +(21.3134 + 36.9159i) q^{58} -49458.5 q^{59} +(-3544.67 - 6139.54i) q^{60} +(-17027.7 - 29492.8i) q^{61} +(3874.93 - 6711.57i) q^{62} +(2507.55 - 4343.20i) q^{63} -15539.8 q^{64} +1844.05 q^{65} +(-4842.90 + 8388.14i) q^{66} +(21053.3 - 36465.4i) q^{67} +(22774.0 + 39445.7i) q^{68} +(-6315.84 - 10939.3i) q^{69} +5713.61 q^{70} +(-19431.3 - 33656.0i) q^{71} +(-1349.77 - 2337.87i) q^{72} +(-12721.3 - 22034.0i) q^{73} +(-5500.13 + 9526.51i) q^{74} +42035.5 q^{75} +(-12870.6 + 22292.5i) q^{76} +(37179.7 + 64397.1i) q^{77} -2858.09 q^{78} +(47886.5 + 82941.8i) q^{79} +(-6151.65 + 10655.0i) q^{80} +(26116.1 - 45234.5i) q^{81} +9073.14 q^{82} +(-1039.08 + 1799.74i) q^{83} +84354.7 q^{84} +26100.7 q^{85} +(6951.65 - 19965.2i) q^{86} +360.632 q^{87} +40026.5 q^{88} +(-73066.1 + 126554. i) q^{89} -734.895 q^{90} +(-10971.0 + 19002.3i) q^{91} +(-12399.2 + 21476.1i) q^{92} +(-32782.7 - 56781.3i) q^{93} -23240.5 q^{94} +(7375.31 + 12774.4i) q^{95} +(34621.2 - 59965.8i) q^{96} +18998.2 q^{97} +(-19340.1 + 33498.1i) q^{98} +(-4782.12 - 8282.87i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 14q^{2} - 14q^{3} + 454q^{4} + 71q^{5} + 15q^{6} + 225q^{7} - 936q^{8} - 1011q^{9} + O(q^{10}) \) \( 34q - 14q^{2} - 14q^{3} + 454q^{4} + 71q^{5} + 15q^{6} + 225q^{7} - 936q^{8} - 1011q^{9} - 317q^{10} + 1326q^{11} - 648q^{12} + 1006q^{13} - 1272q^{14} + 683q^{15} + 3574q^{16} + 200q^{17} + 1861q^{18} + 3361q^{19} + 3825q^{20} - 1320q^{21} - 8768q^{22} + 560q^{23} - 7382q^{24} - 3232q^{25} - 3201q^{26} - 122q^{27} + 13934q^{28} + 8887q^{29} - 19449q^{30} - 6749q^{31} - 19086q^{32} + 7106q^{33} + 8423q^{34} + 31118q^{35} - 14112q^{36} - 4514q^{37} + 7072q^{38} - 5404q^{39} - 18519q^{40} - 28996q^{41} + 58118q^{42} - 14998q^{43} + 71050q^{44} - 92096q^{45} + 20052q^{46} - 10742q^{47} + 32927q^{48} + 7472q^{49} + 20362q^{50} + 20250q^{51} + 59532q^{52} - 50572q^{53} - 230084q^{54} + 38544q^{55} - 40355q^{56} - 18087q^{57} - 33436q^{58} + 112654q^{59} + 134093q^{60} - 20120q^{61} - 31491q^{62} + 188227q^{63} + 125164q^{64} - 36578q^{65} + 8803q^{66} - 73824q^{67} - 128456q^{68} + 8005q^{69} - 141610q^{70} + 142842q^{71} + 98466q^{72} - 91624q^{73} - 99720q^{74} + 298358q^{75} + 258288q^{76} + 68051q^{77} - 201116q^{78} + 99734q^{79} - 31261q^{80} - 28441q^{81} - 147772q^{82} - 47340q^{83} - 624232q^{84} - 71734q^{85} - 115526q^{86} - 215924q^{87} - 720684q^{88} + 60402q^{89} + 676108q^{90} + 164172q^{91} + 78997q^{92} - 40793q^{93} - 341874q^{94} + 123541q^{95} - 442140q^{96} + 318476q^{97} + 217473q^{98} - 134770q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.74361 0.308230 0.154115 0.988053i \(-0.450747\pi\)
0.154115 + 0.988053i \(0.450747\pi\)
\(3\) 7.37567 12.7750i 0.473150 0.819519i −0.526378 0.850251i \(-0.676450\pi\)
0.999528 + 0.0307315i \(0.00978368\pi\)
\(4\) −28.9598 −0.904994
\(5\) −8.29752 + 14.3717i −0.148430 + 0.257089i −0.930648 0.365917i \(-0.880755\pi\)
0.782217 + 0.623006i \(0.214089\pi\)
\(6\) 12.8603 22.2747i 0.145839 0.252600i
\(7\) −98.7307 171.007i −0.761565 1.31907i −0.942044 0.335490i \(-0.891098\pi\)
0.180479 0.983579i \(-0.442235\pi\)
\(8\) −106.290 −0.587177
\(9\) 12.6989 + 21.9952i 0.0522589 + 0.0905151i
\(10\) −14.4677 + 25.0587i −0.0457507 + 0.0792426i
\(11\) −376.577 −0.938365 −0.469182 0.883101i \(-0.655451\pi\)
−0.469182 + 0.883101i \(0.655451\pi\)
\(12\) −213.598 + 369.963i −0.428198 + 0.741660i
\(13\) −55.5603 96.2332i −0.0911813 0.157931i 0.816827 0.576882i \(-0.195731\pi\)
−0.908008 + 0.418952i \(0.862398\pi\)
\(14\) −172.148 298.169i −0.234737 0.406577i
\(15\) 122.400 + 212.002i 0.140460 + 0.243283i
\(16\) 741.385 0.724009
\(17\) −786.400 1362.08i −0.659965 1.14309i −0.980624 0.195899i \(-0.937238\pi\)
0.320659 0.947195i \(-0.396096\pi\)
\(18\) 22.1420 + 38.3511i 0.0161078 + 0.0278995i
\(19\) 444.429 769.773i 0.282435 0.489191i −0.689549 0.724239i \(-0.742191\pi\)
0.971984 + 0.235048i \(0.0755246\pi\)
\(20\) 240.295 416.202i 0.134329 0.232664i
\(21\) −2912.82 −1.44134
\(22\) −656.604 −0.289232
\(23\) 428.153 741.583i 0.168764 0.292308i −0.769222 0.638982i \(-0.779356\pi\)
0.937986 + 0.346674i \(0.112689\pi\)
\(24\) −783.963 + 1357.86i −0.277822 + 0.481202i
\(25\) 1424.80 + 2467.83i 0.455937 + 0.789706i
\(26\) −96.8756 167.793i −0.0281048 0.0486790i
\(27\) 3959.23 1.04520
\(28\) 2859.22 + 4952.32i 0.689212 + 1.19375i
\(29\) 12.2237 + 21.1721i 0.00269903 + 0.00467486i 0.867372 0.497661i \(-0.165808\pi\)
−0.864673 + 0.502336i \(0.832474\pi\)
\(30\) 213.417 + 369.650i 0.0432939 + 0.0749872i
\(31\) 2222.35 3849.23i 0.415345 0.719399i −0.580119 0.814531i \(-0.696994\pi\)
0.995465 + 0.0951325i \(0.0303275\pi\)
\(32\) 4693.98 0.810338
\(33\) −2777.51 + 4810.78i −0.443987 + 0.769008i
\(34\) −1371.18 2374.95i −0.203421 0.352336i
\(35\) 3276.88 0.452158
\(36\) −367.758 636.976i −0.0472940 0.0819157i
\(37\) −3154.45 + 5463.66i −0.378808 + 0.656114i −0.990889 0.134681i \(-0.956999\pi\)
0.612081 + 0.790795i \(0.290332\pi\)
\(38\) 774.912 1342.19i 0.0870549 0.150784i
\(39\) −1639.18 −0.172570
\(40\) 881.946 1527.57i 0.0871549 0.150957i
\(41\) 5203.64 0.483446 0.241723 0.970345i \(-0.422287\pi\)
0.241723 + 0.970345i \(0.422287\pi\)
\(42\) −5078.83 −0.444263
\(43\) 3986.93 11450.5i 0.328827 0.944390i
\(44\) 10905.6 0.849215
\(45\) −421.478 −0.0310273
\(46\) 746.533 1293.03i 0.0520181 0.0900980i
\(47\) −13328.9 −0.880139 −0.440069 0.897964i \(-0.645046\pi\)
−0.440069 + 0.897964i \(0.645046\pi\)
\(48\) 5468.21 9471.22i 0.342564 0.593339i
\(49\) −11092.0 + 19211.9i −0.659963 + 1.14309i
\(50\) 2484.30 + 4302.94i 0.140533 + 0.243411i
\(51\) −23200.9 −1.24905
\(52\) 1609.01 + 2786.90i 0.0825186 + 0.142926i
\(53\) 2126.84 3683.80i 0.104003 0.180138i −0.809327 0.587358i \(-0.800168\pi\)
0.913330 + 0.407219i \(0.133502\pi\)
\(54\) 6903.36 0.322163
\(55\) 3124.65 5412.05i 0.139282 0.241243i
\(56\) 10494.1 + 18176.3i 0.447173 + 0.774527i
\(57\) −6555.92 11355.2i −0.267268 0.462921i
\(58\) 21.3134 + 36.9159i 0.000831922 + 0.00144093i
\(59\) −49458.5 −1.84974 −0.924871 0.380281i \(-0.875827\pi\)
−0.924871 + 0.380281i \(0.875827\pi\)
\(60\) −3544.67 6139.54i −0.127115 0.220170i
\(61\) −17027.7 29492.8i −0.585910 1.01483i −0.994761 0.102225i \(-0.967404\pi\)
0.408851 0.912601i \(-0.365930\pi\)
\(62\) 3874.93 6711.57i 0.128022 0.221740i
\(63\) 2507.55 4343.20i 0.0795972 0.137866i
\(64\) −15539.8 −0.474238
\(65\) 1844.05 0.0541363
\(66\) −4842.90 + 8388.14i −0.136850 + 0.237031i
\(67\) 21053.3 36465.4i 0.572972 0.992416i −0.423287 0.905996i \(-0.639124\pi\)
0.996259 0.0864206i \(-0.0275429\pi\)
\(68\) 22774.0 + 39445.7i 0.597265 + 1.03449i
\(69\) −6315.84 10939.3i −0.159701 0.276611i
\(70\) 5713.61 0.139369
\(71\) −19431.3 33656.0i −0.457463 0.792349i 0.541363 0.840789i \(-0.317908\pi\)
−0.998826 + 0.0484399i \(0.984575\pi\)
\(72\) −1349.77 2337.87i −0.0306852 0.0531484i
\(73\) −12721.3 22034.0i −0.279400 0.483934i 0.691836 0.722055i \(-0.256802\pi\)
−0.971236 + 0.238120i \(0.923469\pi\)
\(74\) −5500.13 + 9526.51i −0.116760 + 0.202234i
\(75\) 42035.5 0.862905
\(76\) −12870.6 + 22292.5i −0.255602 + 0.442715i
\(77\) 37179.7 + 64397.1i 0.714626 + 1.23777i
\(78\) −2858.09 −0.0531912
\(79\) 47886.5 + 82941.8i 0.863267 + 1.49522i 0.868758 + 0.495237i \(0.164919\pi\)
−0.00549153 + 0.999985i \(0.501748\pi\)
\(80\) −6151.65 + 10655.0i −0.107465 + 0.186135i
\(81\) 26116.1 45234.5i 0.442279 0.766050i
\(82\) 9073.14 0.149013
\(83\) −1039.08 + 1799.74i −0.0165560 + 0.0286758i −0.874185 0.485594i \(-0.838604\pi\)
0.857629 + 0.514269i \(0.171937\pi\)
\(84\) 84354.7 1.30440
\(85\) 26100.7 0.391836
\(86\) 6951.65 19965.2i 0.101354 0.291090i
\(87\) 360.632 0.00510818
\(88\) 40026.5 0.550986
\(89\) −73066.1 + 126554.i −0.977780 + 1.69356i −0.307342 + 0.951599i \(0.599440\pi\)
−0.670438 + 0.741966i \(0.733894\pi\)
\(90\) −734.895 −0.00956354
\(91\) −10971.0 + 19002.3i −0.138881 + 0.240549i
\(92\) −12399.2 + 21476.1i −0.152730 + 0.264537i
\(93\) −32782.7 56781.3i −0.393041 0.680767i
\(94\) −23240.5 −0.271285
\(95\) 7375.31 + 12774.4i 0.0838439 + 0.145222i
\(96\) 34621.2 59965.8i 0.383411 0.664087i
\(97\) 18998.2 0.205014 0.102507 0.994732i \(-0.467314\pi\)
0.102507 + 0.994732i \(0.467314\pi\)
\(98\) −19340.1 + 33498.1i −0.203420 + 0.352334i
\(99\) −4782.12 8282.87i −0.0490379 0.0849362i
\(100\) −41262.0 71467.9i −0.412620 0.714679i
\(101\) 19393.1 + 33589.9i 0.189167 + 0.327646i 0.944973 0.327149i \(-0.106088\pi\)
−0.755806 + 0.654796i \(0.772755\pi\)
\(102\) −40453.4 −0.384995
\(103\) −86224.2 149345.i −0.800823 1.38707i −0.919075 0.394082i \(-0.871063\pi\)
0.118253 0.992984i \(-0.462271\pi\)
\(104\) 5905.52 + 10228.7i 0.0535395 + 0.0927332i
\(105\) 24169.2 41862.2i 0.213938 0.370552i
\(106\) 3708.39 6423.12i 0.0320568 0.0555241i
\(107\) 215412. 1.81891 0.909453 0.415806i \(-0.136500\pi\)
0.909453 + 0.415806i \(0.136500\pi\)
\(108\) −114659. −0.945904
\(109\) −7192.91 + 12458.5i −0.0579880 + 0.100438i −0.893562 0.448940i \(-0.851802\pi\)
0.835574 + 0.549378i \(0.185135\pi\)
\(110\) 5448.18 9436.53i 0.0429309 0.0743585i
\(111\) 46532.3 + 80596.3i 0.358465 + 0.620880i
\(112\) −73197.4 126782.i −0.551380 0.955018i
\(113\) −10848.6 −0.0799242 −0.0399621 0.999201i \(-0.512724\pi\)
−0.0399621 + 0.999201i \(0.512724\pi\)
\(114\) −11431.0 19799.1i −0.0823800 0.142686i
\(115\) 7105.22 + 12306.6i 0.0500994 + 0.0867747i
\(116\) −353.996 613.139i −0.00244261 0.00423072i
\(117\) 1411.11 2444.12i 0.00953008 0.0165066i
\(118\) −86236.5 −0.570146
\(119\) −155284. + 268959.i −1.00521 + 1.74108i
\(120\) −13009.9 22533.8i −0.0824746 0.142850i
\(121\) −19241.0 −0.119472
\(122\) −29689.7 51424.1i −0.180595 0.312800i
\(123\) 38380.4 66476.8i 0.228742 0.396193i
\(124\) −64359.0 + 111473.i −0.375885 + 0.651052i
\(125\) −99148.8 −0.567561
\(126\) 4372.19 7572.86i 0.0245342 0.0424946i
\(127\) 159848. 0.879424 0.439712 0.898139i \(-0.355080\pi\)
0.439712 + 0.898139i \(0.355080\pi\)
\(128\) −177303. −0.956512
\(129\) −116874. 135388.i −0.618362 0.716318i
\(130\) 3215.31 0.0166865
\(131\) 103109. 0.524952 0.262476 0.964938i \(-0.415461\pi\)
0.262476 + 0.964938i \(0.415461\pi\)
\(132\) 80436.1 139319.i 0.401806 0.695948i
\(133\) −175515. −0.860370
\(134\) 36708.8 63581.5i 0.176607 0.305893i
\(135\) −32851.8 + 56900.9i −0.155140 + 0.268711i
\(136\) 83586.7 + 144776.i 0.387516 + 0.671198i
\(137\) 260707. 1.18673 0.593363 0.804935i \(-0.297800\pi\)
0.593363 + 0.804935i \(0.297800\pi\)
\(138\) −11012.4 19074.0i −0.0492247 0.0852597i
\(139\) 156477. 271026.i 0.686932 1.18980i −0.285894 0.958261i \(-0.592290\pi\)
0.972826 0.231539i \(-0.0743762\pi\)
\(140\) −94897.8 −0.409200
\(141\) −98309.9 + 170278.i −0.416437 + 0.721290i
\(142\) −33880.7 58683.0i −0.141004 0.244226i
\(143\) 20922.7 + 36239.2i 0.0855613 + 0.148197i
\(144\) 9414.79 + 16306.9i 0.0378359 + 0.0655337i
\(145\) −405.705 −0.00160247
\(146\) −22181.1 38418.8i −0.0861194 0.149163i
\(147\) 163622. + 283401.i 0.624522 + 1.08170i
\(148\) 91352.2 158227.i 0.342819 0.593780i
\(149\) −16523.6 + 28619.7i −0.0609732 + 0.105609i −0.894901 0.446265i \(-0.852754\pi\)
0.833928 + 0.551874i \(0.186087\pi\)
\(150\) 73293.6 0.265973
\(151\) 171625. 0.612547 0.306273 0.951944i \(-0.400918\pi\)
0.306273 + 0.951944i \(0.400918\pi\)
\(152\) −47238.5 + 81819.5i −0.165839 + 0.287242i
\(153\) 19972.9 34594.0i 0.0689782 0.119474i
\(154\) 64827.0 + 112284.i 0.220269 + 0.381517i
\(155\) 36880.0 + 63878.1i 0.123300 + 0.213561i
\(156\) 47470.3 0.156174
\(157\) −133583. 231373.i −0.432517 0.749142i 0.564572 0.825384i \(-0.309041\pi\)
−0.997089 + 0.0762420i \(0.975708\pi\)
\(158\) 83495.4 + 144618.i 0.266085 + 0.460872i
\(159\) −31373.8 54341.0i −0.0984179 0.170465i
\(160\) −38948.4 + 67460.5i −0.120279 + 0.208329i
\(161\) −169087. −0.514099
\(162\) 45536.4 78871.4i 0.136324 0.236120i
\(163\) 152556. + 264235.i 0.449740 + 0.778972i 0.998369 0.0570939i \(-0.0181835\pi\)
−0.548629 + 0.836066i \(0.684850\pi\)
\(164\) −150697. −0.437516
\(165\) −46092.8 79835.1i −0.131802 0.228288i
\(166\) −1811.76 + 3138.05i −0.00510305 + 0.00883874i
\(167\) −80139.4 + 138805.i −0.222359 + 0.385137i −0.955524 0.294914i \(-0.904709\pi\)
0.733165 + 0.680051i \(0.238042\pi\)
\(168\) 309605. 0.846319
\(169\) 179473. 310856.i 0.483372 0.837225i
\(170\) 45509.5 0.120776
\(171\) 22575.1 0.0590390
\(172\) −115461. + 331603.i −0.297586 + 0.854668i
\(173\) 654616. 1.66292 0.831460 0.555585i \(-0.187506\pi\)
0.831460 + 0.555585i \(0.187506\pi\)
\(174\) 628.802 0.00157449
\(175\) 281343. 487301.i 0.694451 1.20282i
\(176\) −279188. −0.679384
\(177\) −364790. + 631835.i −0.875205 + 1.51590i
\(178\) −127399. + 220662.i −0.301381 + 0.522008i
\(179\) 374942. + 649418.i 0.874643 + 1.51493i 0.857142 + 0.515080i \(0.172238\pi\)
0.0175011 + 0.999847i \(0.494429\pi\)
\(180\) 12205.9 0.0280795
\(181\) −401046. 694632.i −0.909908 1.57601i −0.814190 0.580598i \(-0.802819\pi\)
−0.0957176 0.995409i \(-0.530515\pi\)
\(182\) −19129.2 + 33132.7i −0.0428073 + 0.0741444i
\(183\) −502363. −1.10889
\(184\) −45508.5 + 78823.1i −0.0990942 + 0.171636i
\(185\) −52348.1 90669.6i −0.112453 0.194775i
\(186\) −57160.4 99004.7i −0.121147 0.209833i
\(187\) 296140. + 512929.i 0.619288 + 1.07264i
\(188\) 386004. 0.796520
\(189\) −390897. 677054.i −0.795991 1.37870i
\(190\) 12859.7 + 22273.6i 0.0258432 + 0.0447617i
\(191\) 34284.6 59382.7i 0.0680011 0.117781i −0.830020 0.557733i \(-0.811671\pi\)
0.898021 + 0.439952i \(0.145005\pi\)
\(192\) −114617. + 198522.i −0.224386 + 0.388647i
\(193\) 352076. 0.680367 0.340184 0.940359i \(-0.389511\pi\)
0.340184 + 0.940359i \(0.389511\pi\)
\(194\) 33125.5 0.0631914
\(195\) 13601.1 23557.8i 0.0256146 0.0443658i
\(196\) 321222. 556373.i 0.597262 1.03449i
\(197\) −171254. 296621.i −0.314395 0.544548i 0.664914 0.746920i \(-0.268468\pi\)
−0.979309 + 0.202372i \(0.935135\pi\)
\(198\) −8338.16 14442.1i −0.0151150 0.0261799i
\(199\) −703078. −1.25855 −0.629275 0.777183i \(-0.716648\pi\)
−0.629275 + 0.777183i \(0.716648\pi\)
\(200\) −151443. 262306.i −0.267715 0.463697i
\(201\) −310565. 537914.i −0.542203 0.939123i
\(202\) 33814.1 + 58567.8i 0.0583069 + 0.100990i
\(203\) 2413.71 4180.66i 0.00411097 0.00712041i
\(204\) 671894. 1.13038
\(205\) −43177.3 + 74785.3i −0.0717581 + 0.124289i
\(206\) −150342. 260399.i −0.246838 0.427535i
\(207\) 21748.3 0.0352777
\(208\) −41191.5 71345.8i −0.0660161 0.114343i
\(209\) −167362. + 289879.i −0.265027 + 0.459040i
\(210\) 42141.7 72991.5i 0.0659422 0.114215i
\(211\) −668712. −1.03403 −0.517015 0.855977i \(-0.672957\pi\)
−0.517015 + 0.855977i \(0.672957\pi\)
\(212\) −61593.0 + 106682.i −0.0941221 + 0.163024i
\(213\) −573275. −0.865793
\(214\) 375595. 0.560642
\(215\) 131481. + 152309.i 0.193985 + 0.224714i
\(216\) −420828. −0.613720
\(217\) −877658. −1.26525
\(218\) −12541.7 + 21722.8i −0.0178737 + 0.0309581i
\(219\) −375314. −0.528791
\(220\) −90489.3 + 156732.i −0.126049 + 0.218324i
\(221\) −87385.2 + 151356.i −0.120353 + 0.208458i
\(222\) 81134.4 + 140529.i 0.110490 + 0.191374i
\(223\) 441945. 0.595122 0.297561 0.954703i \(-0.403827\pi\)
0.297561 + 0.954703i \(0.403827\pi\)
\(224\) −463440. 802701.i −0.617125 1.06889i
\(225\) −36186.9 + 62677.6i −0.0476535 + 0.0825384i
\(226\) −18915.8 −0.0246350
\(227\) −458549. + 794230.i −0.590638 + 1.02301i 0.403509 + 0.914976i \(0.367790\pi\)
−0.994147 + 0.108039i \(0.965543\pi\)
\(228\) 189858. + 328844.i 0.241876 + 0.418941i
\(229\) 113484. + 196560.i 0.143003 + 0.247689i 0.928626 0.371017i \(-0.120991\pi\)
−0.785623 + 0.618705i \(0.787657\pi\)
\(230\) 12388.7 + 21457.9i 0.0154422 + 0.0267466i
\(231\) 1.09690e6 1.35250
\(232\) −1299.26 2250.39i −0.00158481 0.00274497i
\(233\) −184877. 320217.i −0.223097 0.386415i 0.732650 0.680606i \(-0.238283\pi\)
−0.955747 + 0.294190i \(0.904950\pi\)
\(234\) 2460.43 4261.59i 0.00293746 0.00508782i
\(235\) 110597. 191560.i 0.130639 0.226274i
\(236\) 1.43231e6 1.67401
\(237\) 1.41278e6 1.63382
\(238\) −270754. + 468961.i −0.309837 + 0.536653i
\(239\) 326490. 565496.i 0.369721 0.640376i −0.619801 0.784759i \(-0.712786\pi\)
0.989522 + 0.144383i \(0.0461198\pi\)
\(240\) 90745.1 + 157175.i 0.101694 + 0.176139i
\(241\) 76516.8 + 132531.i 0.0848622 + 0.146986i 0.905332 0.424704i \(-0.139622\pi\)
−0.820470 + 0.571689i \(0.806288\pi\)
\(242\) −33548.9 −0.0368247
\(243\) 95798.2 + 165927.i 0.104074 + 0.180261i
\(244\) 493119. + 854107.i 0.530245 + 0.918412i
\(245\) −184072. 318822.i −0.195917 0.339338i
\(246\) 66920.5 115910.i 0.0705053 0.122119i
\(247\) −98770.3 −0.103011
\(248\) −236215. + 409136.i −0.243881 + 0.422414i
\(249\) 15327.9 + 26548.6i 0.0156669 + 0.0271359i
\(250\) −172877. −0.174939
\(251\) −321024. 556031.i −0.321628 0.557076i 0.659196 0.751971i \(-0.270897\pi\)
−0.980824 + 0.194895i \(0.937563\pi\)
\(252\) −72618.1 + 125778.i −0.0720350 + 0.124768i
\(253\) −161233. + 279263.i −0.158362 + 0.274291i
\(254\) 278713. 0.271065
\(255\) 192510. 333437.i 0.185397 0.321117i
\(256\) 188127. 0.179412
\(257\) −1.22989e6 −1.16154 −0.580771 0.814067i \(-0.697249\pi\)
−0.580771 + 0.814067i \(0.697249\pi\)
\(258\) −203783. 236064.i −0.190598 0.220791i
\(259\) 1.24576e6 1.15395
\(260\) −53403.3 −0.0489931
\(261\) −310.455 + 537.725i −0.000282097 + 0.000488606i
\(262\) 179783. 0.161806
\(263\) 768545. 1.33116e6i 0.685141 1.18670i −0.288251 0.957555i \(-0.593074\pi\)
0.973392 0.229145i \(-0.0735929\pi\)
\(264\) 295222. 511340.i 0.260699 0.451543i
\(265\) 35295.0 + 61132.8i 0.0308744 + 0.0534760i
\(266\) −306030. −0.265192
\(267\) 1.07782e6 + 1.86685e6i 0.925272 + 1.60262i
\(268\) −609700. + 1.05603e6i −0.518536 + 0.898131i
\(269\) −211417. −0.178139 −0.0890694 0.996025i \(-0.528389\pi\)
−0.0890694 + 0.996025i \(0.528389\pi\)
\(270\) −57280.8 + 99213.2i −0.0478189 + 0.0828247i
\(271\) 371455. + 643378.i 0.307243 + 0.532161i 0.977758 0.209735i \(-0.0672601\pi\)
−0.670515 + 0.741896i \(0.733927\pi\)
\(272\) −583025. 1.00983e6i −0.477821 0.827610i
\(273\) 161837. + 280310.i 0.131423 + 0.227631i
\(274\) 454572. 0.365785
\(275\) −536547. 929327.i −0.427835 0.741032i
\(276\) 182905. + 316801.i 0.144529 + 0.250331i
\(277\) −399396. + 691774.i −0.312755 + 0.541707i −0.978958 0.204063i \(-0.934585\pi\)
0.666203 + 0.745771i \(0.267919\pi\)
\(278\) 272835. 472565.i 0.211733 0.366732i
\(279\) 112886. 0.0868220
\(280\) −348300. −0.265497
\(281\) 584582. 1.01252e6i 0.441651 0.764962i −0.556161 0.831074i \(-0.687726\pi\)
0.997812 + 0.0661124i \(0.0210596\pi\)
\(282\) −171414. + 296899.i −0.128358 + 0.222323i
\(283\) 345423. + 598291.i 0.256381 + 0.444065i 0.965270 0.261256i \(-0.0841365\pi\)
−0.708889 + 0.705320i \(0.750803\pi\)
\(284\) 562727. + 974671.i 0.414001 + 0.717071i
\(285\) 217591. 0.158683
\(286\) 36481.1 + 63187.1i 0.0263726 + 0.0456787i
\(287\) −513759. 889857.i −0.368176 0.637699i
\(288\) 59608.5 + 103245.i 0.0423474 + 0.0733478i
\(289\) −526921. + 912655.i −0.371109 + 0.642779i
\(290\) −707.393 −0.000493930
\(291\) 140124. 242702.i 0.0970021 0.168013i
\(292\) 368408. + 638101.i 0.252855 + 0.437958i
\(293\) −1.22064e6 −0.830652 −0.415326 0.909673i \(-0.636332\pi\)
−0.415326 + 0.909673i \(0.636332\pi\)
\(294\) 285293. + 494142.i 0.192497 + 0.333414i
\(295\) 410383. 710804.i 0.274558 0.475549i
\(296\) 335287. 580734.i 0.222427 0.385255i
\(297\) −1.49095e6 −0.980783
\(298\) −28810.7 + 49901.7i −0.0187938 + 0.0325518i
\(299\) −95153.2 −0.0615525
\(300\) −1.21734e6 −0.780924
\(301\) −2.35173e6 + 448721.i −1.49614 + 0.285470i
\(302\) 299248. 0.188805
\(303\) 572150. 0.358017
\(304\) 329493. 570698.i 0.204485 0.354179i
\(305\) 565150. 0.347868
\(306\) 34824.9 60318.6i 0.0212612 0.0368254i
\(307\) −1.42690e6 + 2.47146e6i −0.864065 + 1.49660i 0.00390831 + 0.999992i \(0.498756\pi\)
−0.867973 + 0.496611i \(0.834577\pi\)
\(308\) −1.07672e6 1.86493e6i −0.646732 1.12017i
\(309\) −2.54385e6 −1.51564
\(310\) 64304.5 + 111379.i 0.0380047 + 0.0658261i
\(311\) 1.29700e6 2.24646e6i 0.760392 1.31704i −0.182256 0.983251i \(-0.558340\pi\)
0.942648 0.333787i \(-0.108327\pi\)
\(312\) 174229. 0.101329
\(313\) 1.14805e6 1.98848e6i 0.662370 1.14726i −0.317622 0.948218i \(-0.602884\pi\)
0.979991 0.199040i \(-0.0637825\pi\)
\(314\) −232918. 403425.i −0.133315 0.230908i
\(315\) 41612.8 + 72075.5i 0.0236293 + 0.0409271i
\(316\) −1.38678e6 2.40198e6i −0.781251 1.35317i
\(317\) 1.00744e6 0.563083 0.281542 0.959549i \(-0.409154\pi\)
0.281542 + 0.959549i \(0.409154\pi\)
\(318\) −54703.7 94749.6i −0.0303354 0.0525424i
\(319\) −4603.16 7972.90i −0.00253267 0.00438672i
\(320\) 128942. 223334.i 0.0703914 0.121921i
\(321\) 1.58881e6 2.75190e6i 0.860615 1.49063i
\(322\) −294823. −0.158461
\(323\) −1.39800e6 −0.745589
\(324\) −756318. + 1.30998e6i −0.400260 + 0.693271i
\(325\) 158325. 274227.i 0.0831458 0.144013i
\(326\) 265999. + 460724.i 0.138623 + 0.240103i
\(327\) 106105. + 183779.i 0.0548740 + 0.0950446i
\(328\) −553097. −0.283868
\(329\) 1.31598e6 + 2.27934e6i 0.670283 + 1.16096i
\(330\) −80368.0 139201.i −0.0406255 0.0703654i
\(331\) −798717. 1.38342e6i −0.400703 0.694038i 0.593108 0.805123i \(-0.297901\pi\)
−0.993811 + 0.111085i \(0.964568\pi\)
\(332\) 30091.6 52120.2i 0.0149831 0.0259514i
\(333\) −160232. −0.0791844
\(334\) −139732. + 242023.i −0.0685378 + 0.118711i
\(335\) 349380. + 605144.i 0.170093 + 0.294610i
\(336\) −2.15952e6 −1.04354
\(337\) 1.84240e6 + 3.19112e6i 0.883707 + 1.53063i 0.847189 + 0.531292i \(0.178293\pi\)
0.0365180 + 0.999333i \(0.488373\pi\)
\(338\) 312931. 542012.i 0.148990 0.258058i
\(339\) −80015.8 + 138591.i −0.0378161 + 0.0654994i
\(340\) −755870. −0.354609
\(341\) −836887. + 1.44953e6i −0.389745 + 0.675059i
\(342\) 39362.2 0.0181976
\(343\) 1.06175e6 0.487288
\(344\) −423772. + 1.21707e6i −0.193079 + 0.554524i
\(345\) 209623. 0.0948181
\(346\) 1.14140e6 0.512562
\(347\) −1.11833e6 + 1.93700e6i −0.498591 + 0.863585i −0.999999 0.00162608i \(-0.999482\pi\)
0.501408 + 0.865211i \(0.332816\pi\)
\(348\) −10443.8 −0.00462287
\(349\) 2.02855e6 3.51354e6i 0.891500 1.54412i 0.0534215 0.998572i \(-0.482987\pi\)
0.838078 0.545550i \(-0.183679\pi\)
\(350\) 490554. 849664.i 0.214051 0.370747i
\(351\) −219976. 381009.i −0.0953031 0.165070i
\(352\) −1.76764e6 −0.760393
\(353\) 1.48821e6 + 2.57765e6i 0.635663 + 1.10100i 0.986374 + 0.164517i \(0.0526064\pi\)
−0.350712 + 0.936484i \(0.614060\pi\)
\(354\) −636052. + 1.10168e6i −0.269764 + 0.467246i
\(355\) 644926. 0.271606
\(356\) 2.11598e6 3.66499e6i 0.884885 1.53267i
\(357\) 2.29064e6 + 3.96751e6i 0.951232 + 1.64758i
\(358\) 653753. + 1.13233e6i 0.269591 + 0.466946i
\(359\) 1.35299e6 + 2.34344e6i 0.554060 + 0.959660i 0.997976 + 0.0635919i \(0.0202556\pi\)
−0.443916 + 0.896069i \(0.646411\pi\)
\(360\) 44799.0 0.0182185
\(361\) 843016. + 1.46015e6i 0.340461 + 0.589696i
\(362\) −699268. 1.21117e6i −0.280461 0.485773i
\(363\) −141915. + 245805.i −0.0565279 + 0.0979092i
\(364\) 317718. 550304.i 0.125687 0.217695i
\(365\) 422222. 0.165886
\(366\) −875926. −0.341794
\(367\) 1.67727e6 2.90511e6i 0.650035 1.12589i −0.333078 0.942899i \(-0.608087\pi\)
0.983114 0.182995i \(-0.0585793\pi\)
\(368\) 317426. 549798.i 0.122187 0.211633i
\(369\) 66080.7 + 114455.i 0.0252644 + 0.0437592i
\(370\) −91274.9 158093.i −0.0346615 0.0600354i
\(371\) −839938. −0.316820
\(372\) 949382. + 1.64438e6i 0.355700 + 0.616090i
\(373\) −1.43111e6 2.47875e6i −0.532599 0.922489i −0.999275 0.0380608i \(-0.987882\pi\)
0.466676 0.884428i \(-0.345451\pi\)
\(374\) 516353. + 894350.i 0.190883 + 0.330620i
\(375\) −731289. + 1.26663e6i −0.268541 + 0.465127i
\(376\) 1.41674e6 0.516797
\(377\) 1358.30 2352.65i 0.000492202 0.000852519i
\(378\) −681574. 1.18052e6i −0.245348 0.424956i
\(379\) 1.41370e6 0.505545 0.252773 0.967526i \(-0.418658\pi\)
0.252773 + 0.967526i \(0.418658\pi\)
\(380\) −213588. 369945.i −0.0758782 0.131425i
\(381\) 1.17899e6 2.04207e6i 0.416099 0.720705i
\(382\) 59779.2 103541.i 0.0209600 0.0363038i
\(383\) −1.02683e6 −0.357685 −0.178843 0.983878i \(-0.557235\pi\)
−0.178843 + 0.983878i \(0.557235\pi\)
\(384\) −1.30773e6 + 2.26505e6i −0.452573 + 0.783880i
\(385\) −1.23400e6 −0.424289
\(386\) 613885. 0.209710
\(387\) 302484. 57715.3i 0.102666 0.0195891i
\(388\) −550184. −0.185536
\(389\) −2.18252e6 −0.731282 −0.365641 0.930756i \(-0.619150\pi\)
−0.365641 + 0.930756i \(0.619150\pi\)
\(390\) 23715.0 41075.7i 0.00789519 0.0136749i
\(391\) −1.34680e6 −0.445513
\(392\) 1.17897e6 2.04204e6i 0.387515 0.671195i
\(393\) 760501. 1.31723e6i 0.248381 0.430208i
\(394\) −298601. 517192.i −0.0969060 0.167846i
\(395\) −1.58935e6 −0.512540
\(396\) 138489. + 239870.i 0.0443791 + 0.0768668i
\(397\) −262158. + 454071.i −0.0834808 + 0.144593i −0.904743 0.425958i \(-0.859937\pi\)
0.821262 + 0.570551i \(0.193270\pi\)
\(398\) −1.22590e6 −0.387923
\(399\) −1.29454e6 + 2.24221e6i −0.407084 + 0.705090i
\(400\) 1.05633e6 + 1.82961e6i 0.330102 + 0.571754i
\(401\) −439508. 761250.i −0.136492 0.236410i 0.789675 0.613526i \(-0.210249\pi\)
−0.926166 + 0.377115i \(0.876916\pi\)
\(402\) −541504. 937913.i −0.167123 0.289466i
\(403\) −493898. −0.151487
\(404\) −561622. 972757.i −0.171195 0.296518i
\(405\) 433398. + 750668.i 0.131295 + 0.227410i
\(406\) 4208.57 7289.46i 0.00126713 0.00219473i
\(407\) 1.18789e6 2.05749e6i 0.355460 0.615674i
\(408\) 2.46603e6 0.733413
\(409\) 4.28678e6 1.26714 0.633568 0.773687i \(-0.281590\pi\)
0.633568 + 0.773687i \(0.281590\pi\)
\(410\) −75284.5 + 130397.i −0.0221180 + 0.0383095i
\(411\) 1.92289e6 3.33054e6i 0.561499 0.972545i
\(412\) 2.49704e6 + 4.32500e6i 0.724740 + 1.25529i
\(413\) 4.88307e6 + 8.45773e6i 1.40870 + 2.43994i
\(414\) 37920.7 0.0108736
\(415\) −17243.6 29866.8i −0.00491482 0.00851272i
\(416\) −260799. 451717.i −0.0738877 0.127977i
\(417\) −2.30825e6 3.99800e6i −0.650043 1.12591i
\(418\) −291814. + 505436.i −0.0816893 + 0.141490i
\(419\) 1.98522e6 0.552424 0.276212 0.961097i \(-0.410921\pi\)
0.276212 + 0.961097i \(0.410921\pi\)
\(420\) −699935. + 1.21232e6i −0.193613 + 0.335347i
\(421\) −3.21855e6 5.57469e6i −0.885024 1.53291i −0.845687 0.533680i \(-0.820809\pi\)
−0.0393371 0.999226i \(-0.512525\pi\)
\(422\) −1.16597e6 −0.318719
\(423\) −169263. 293172.i −0.0459951 0.0796659i
\(424\) −226063. + 391552.i −0.0610681 + 0.105773i
\(425\) 2.24093e6 3.88140e6i 0.601805 1.04236i
\(426\) −999570. −0.266864
\(427\) −3.36231e6 + 5.82369e6i −0.892418 + 1.54571i
\(428\) −6.23829e6 −1.64610
\(429\) 617276. 0.161933
\(430\) 229252. + 265568.i 0.0597919 + 0.0692636i
\(431\) −6.75585e6 −1.75181 −0.875905 0.482483i \(-0.839735\pi\)
−0.875905 + 0.482483i \(0.839735\pi\)
\(432\) 2.93531e6 0.756737
\(433\) 163731. 283591.i 0.0419673 0.0726896i −0.844279 0.535904i \(-0.819971\pi\)
0.886246 + 0.463215i \(0.153304\pi\)
\(434\) −1.53030e6 −0.389988
\(435\) −2992.35 + 5182.90i −0.000758209 + 0.00131326i
\(436\) 208305. 360795.i 0.0524788 0.0908960i
\(437\) −380567. 659162.i −0.0953296 0.165116i
\(438\) −654402. −0.162989
\(439\) −2.10457e6 3.64523e6i −0.521198 0.902742i −0.999696 0.0246529i \(-0.992152\pi\)
0.478498 0.878089i \(-0.341181\pi\)
\(440\) −332120. + 575249.i −0.0817831 + 0.141652i
\(441\) −563425. −0.137956
\(442\) −152366. + 263906.i −0.0370964 + 0.0642529i
\(443\) 1.94880e6 + 3.37542e6i 0.471800 + 0.817182i 0.999479 0.0322618i \(-0.0102710\pi\)
−0.527679 + 0.849444i \(0.676938\pi\)
\(444\) −1.34757e6 2.33406e6i −0.324409 0.561893i
\(445\) −1.21253e6 2.10017e6i −0.290265 0.502753i
\(446\) 770581. 0.183435
\(447\) 243745. + 422179.i 0.0576988 + 0.0999373i
\(448\) 1.53426e6 + 2.65741e6i 0.361163 + 0.625553i
\(449\) −2.93163e6 + 5.07773e6i −0.686268 + 1.18865i 0.286769 + 0.958000i \(0.407419\pi\)
−0.973037 + 0.230651i \(0.925915\pi\)
\(450\) −63096.0 + 109285.i −0.0146883 + 0.0254408i
\(451\) −1.95957e6 −0.453649
\(452\) 314174. 0.0723309
\(453\) 1.26585e6 2.19252e6i 0.289826 0.501994i
\(454\) −799532. + 1.38483e6i −0.182052 + 0.315324i
\(455\) −182064. 315344.i −0.0412283 0.0714096i
\(456\) 696831. + 1.20695e6i 0.156933 + 0.271817i
\(457\) −3.91502e6 −0.876887 −0.438443 0.898759i \(-0.644470\pi\)
−0.438443 + 0.898759i \(0.644470\pi\)
\(458\) 197872. + 342724.i 0.0440779 + 0.0763451i
\(459\) −3.11354e6 5.39281e6i −0.689799 1.19477i
\(460\) −205766. 356397.i −0.0453397 0.0785306i
\(461\) 2.05874e6 3.56585e6i 0.451180 0.781466i −0.547280 0.836950i \(-0.684337\pi\)
0.998460 + 0.0554833i \(0.0176699\pi\)
\(462\) 1.91257e6 0.416881
\(463\) 2.75528e6 4.77229e6i 0.597330 1.03461i −0.395884 0.918301i \(-0.629562\pi\)
0.993214 0.116305i \(-0.0371049\pi\)
\(464\) 9062.46 + 15696.6i 0.00195412 + 0.00338464i
\(465\) 1.08806e6 0.233357
\(466\) −322354. 558334.i −0.0687652 0.119105i
\(467\) 4.17217e6 7.22640e6i 0.885257 1.53331i 0.0398381 0.999206i \(-0.487316\pi\)
0.845419 0.534104i \(-0.179351\pi\)
\(468\) −40865.5 + 70781.1i −0.00862466 + 0.0149384i
\(469\) −8.31443e6 −1.74542
\(470\) 192839. 334006.i 0.0402670 0.0697445i
\(471\) −3.94107e6 −0.818581
\(472\) 5.25696e6 1.08613
\(473\) −1.50138e6 + 4.31197e6i −0.308559 + 0.886183i
\(474\) 2.46334e6 0.503592
\(475\) 2.53289e6 0.515090
\(476\) 4.49698e6 7.78900e6i 0.909712 1.57567i
\(477\) 108034. 0.0217403
\(478\) 569271. 986007.i 0.113959 0.197383i
\(479\) −4.26690e6 + 7.39050e6i −0.849717 + 1.47175i 0.0317445 + 0.999496i \(0.489894\pi\)
−0.881461 + 0.472257i \(0.843440\pi\)
\(480\) 574541. + 995134.i 0.113820 + 0.197142i
\(481\) 701047. 0.138161
\(482\) 133416. + 231083.i 0.0261571 + 0.0453054i
\(483\) −1.24713e6 + 2.16010e6i −0.243246 + 0.421314i
\(484\) 557216. 0.108121
\(485\) −157638. + 273036.i −0.0304303 + 0.0527068i
\(486\) 167035. + 289313.i 0.0320787 + 0.0555619i
\(487\) −2.37754e6 4.11802e6i −0.454261 0.786803i 0.544384 0.838836i \(-0.316763\pi\)
−0.998645 + 0.0520328i \(0.983430\pi\)
\(488\) 1.80988e6 + 3.13480e6i 0.344033 + 0.595882i
\(489\) 4.50082e6 0.851176
\(490\) −320950. 555902.i −0.0603876 0.104594i
\(491\) 2.51600e6 + 4.35785e6i 0.470986 + 0.815771i 0.999449 0.0331848i \(-0.0105650\pi\)
−0.528464 + 0.848956i \(0.677232\pi\)
\(492\) −1.11149e6 + 1.92515e6i −0.207010 + 0.358553i
\(493\) 19225.4 33299.4i 0.00356253 0.00617049i
\(494\) −172217. −0.0317511
\(495\) 158719. 0.0291149
\(496\) 1.64762e6 2.85376e6i 0.300714 0.520851i
\(497\) −3.83693e6 + 6.64576e6i −0.696775 + 1.20685i
\(498\) 26725.8 + 46290.5i 0.00482901 + 0.00836409i
\(499\) 1.89043e6 + 3.27431e6i 0.339866 + 0.588666i 0.984407 0.175904i \(-0.0562848\pi\)
−0.644541 + 0.764570i \(0.722951\pi\)
\(500\) 2.87133e6 0.513639
\(501\) 1.18216e6 + 2.04757e6i 0.210418 + 0.364455i
\(502\) −559742. 969502.i −0.0991354 0.171708i
\(503\) 5.17226e6 + 8.95861e6i 0.911507 + 1.57878i 0.811936 + 0.583746i \(0.198414\pi\)
0.0995708 + 0.995030i \(0.468253\pi\)
\(504\) −266528. + 461640.i −0.0467376 + 0.0809519i
\(505\) −643659. −0.112312
\(506\) −281127. + 486926.i −0.0488120 + 0.0845448i
\(507\) −2.64746e6 4.58554e6i −0.457414 0.792265i
\(508\) −4.62917e6 −0.795874
\(509\) 2.03678e6 + 3.52780e6i 0.348457 + 0.603545i 0.985976 0.166890i \(-0.0533724\pi\)
−0.637519 + 0.770435i \(0.720039\pi\)
\(510\) 335663. 581385.i 0.0571449 0.0989779i
\(511\) −2.51197e6 + 4.35086e6i −0.425562 + 0.737095i
\(512\) 6.00171e6 1.01181
\(513\) 1.75960e6 3.04771e6i 0.295202 0.511305i
\(514\) −2.14446e6 −0.358022
\(515\) 2.86179e6 0.475466
\(516\) 3.38464e6 + 3.92081e6i 0.559614 + 0.648263i
\(517\) 5.01937e6 0.825891
\(518\) 2.17213e6 0.355681
\(519\) 4.82823e6 8.36274e6i 0.786810 1.36279i
\(520\) −196005. −0.0317876
\(521\) −848912. + 1.47036e6i −0.137015 + 0.237317i −0.926365 0.376626i \(-0.877084\pi\)
0.789350 + 0.613943i \(0.210418\pi\)
\(522\) −541.314 + 937.584i −8.69507e−5 + 0.000150603i
\(523\) 522177. + 904436.i 0.0834763 + 0.144585i 0.904741 0.425962i \(-0.140064\pi\)
−0.821265 + 0.570547i \(0.806731\pi\)
\(524\) −2.98603e6 −0.475079
\(525\) −4.15019e6 7.18835e6i −0.657158 1.13823i
\(526\) 1.34005e6 2.32103e6i 0.211181 0.365777i
\(527\) −6.99064e6 −1.09645
\(528\) −2.05920e6 + 3.56664e6i −0.321450 + 0.556768i
\(529\) 2.85154e6 + 4.93901e6i 0.443037 + 0.767363i
\(530\) 61540.8 + 106592.i 0.00951642 + 0.0164829i
\(531\) −628070. 1.08785e6i −0.0966656 0.167430i
\(532\) 5.08288e6 0.778630
\(533\) −289116. 500763.i −0.0440812 0.0763510i
\(534\) 1.87931e6 + 3.25506e6i 0.285197 + 0.493975i
\(535\) −1.78738e6 + 3.09584e6i −0.269981 + 0.467621i
\(536\) −2.23776e6 + 3.87592e6i −0.336436 + 0.582724i
\(537\) 1.10618e7 1.65535
\(538\) −368629. −0.0549077
\(539\) 4.17699e6 7.23475e6i 0.619286 1.07263i
\(540\) 951381. 1.64784e6i 0.140401 0.243182i
\(541\) 3.42182e6 + 5.92676e6i 0.502648 + 0.870611i 0.999995 + 0.00305985i \(0.000973981\pi\)
−0.497348 + 0.867551i \(0.665693\pi\)
\(542\) 647673. + 1.12180e6i 0.0947017 + 0.164028i
\(543\) −1.18319e7 −1.72209
\(544\) −3.69134e6 6.39360e6i −0.534795 0.926292i
\(545\) −119367. 206749.i −0.0172144 0.0298162i
\(546\) 282181. + 488752.i 0.0405085 + 0.0701628i
\(547\) 1.04409e6 1.80841e6i 0.149200 0.258422i −0.781732 0.623615i \(-0.785664\pi\)
0.930932 + 0.365193i \(0.118997\pi\)
\(548\) −7.55002e6 −1.07398
\(549\) 432467. 749054.i 0.0612381 0.106068i
\(550\) −935531. 1.62039e6i −0.131872 0.228408i
\(551\) 21730.2 0.00304920
\(552\) 671312. + 1.16275e6i 0.0937728 + 0.162419i
\(553\) 9.45572e6 1.63778e7i 1.31487 2.27742i
\(554\) −696392. + 1.20619e6i −0.0964005 + 0.166971i
\(555\) −1.54441e6 −0.212829
\(556\) −4.53155e6 + 7.84887e6i −0.621669 + 1.07676i
\(557\) −5.78663e6 −0.790292 −0.395146 0.918618i \(-0.629306\pi\)
−0.395146 + 0.918618i \(0.629306\pi\)
\(558\) 196830. 0.0267612
\(559\) −1.32343e6 + 252516.i −0.179131 + 0.0341789i
\(560\) 2.42943e6 0.327366
\(561\) 8.73692e6 1.17206
\(562\) 1.01928e6 1.76545e6i 0.136130 0.235784i
\(563\) −1.23011e7 −1.63559 −0.817794 0.575511i \(-0.804803\pi\)
−0.817794 + 0.575511i \(0.804803\pi\)
\(564\) 2.84704e6 4.93121e6i 0.376873 0.652764i
\(565\) 90016.5 155913.i 0.0118632 0.0205476i
\(566\) 602285. + 1.04319e6i 0.0790243 + 0.136874i
\(567\) −1.03139e7 −1.34730
\(568\) 2.06536e6 + 3.57731e6i 0.268611 + 0.465249i
\(569\) 228430. 395652.i 0.0295782 0.0512310i −0.850857 0.525397i \(-0.823917\pi\)
0.880436 + 0.474166i \(0.157250\pi\)
\(570\) 379395. 0.0489108
\(571\) 552741. 957376.i 0.0709466 0.122883i −0.828370 0.560182i \(-0.810731\pi\)
0.899316 + 0.437298i \(0.144065\pi\)
\(572\) −605917. 1.04948e6i −0.0774325 0.134117i
\(573\) −505745. 875975.i −0.0643494 0.111456i
\(574\) −895797. 1.55157e6i −0.113483 0.196558i
\(575\) 2.44013e6 0.307783
\(576\) −197339. 341801.i −0.0247832 0.0429257i
\(577\) 5.82894e6 + 1.00960e7i 0.728870 + 1.26244i 0.957361 + 0.288894i \(0.0932877\pi\)
−0.228491 + 0.973546i \(0.573379\pi\)
\(578\) −918747. + 1.59132e6i −0.114387 + 0.198124i
\(579\) 2.59680e6 4.49779e6i 0.321915 0.557574i
\(580\) 11749.1 0.00145023
\(581\) 410357. 0.0504338
\(582\) 244323. 423179.i 0.0298990 0.0517865i
\(583\) −800919. + 1.38723e6i −0.0975927 + 0.169036i
\(584\) 1.35216e6 + 2.34200e6i 0.164057 + 0.284155i
\(585\) 23417.4 + 40560.2i 0.00282911 + 0.00490016i
\(586\) −2.12833e6 −0.256032
\(587\) −4.19450e6 7.26509e6i −0.502441 0.870254i −0.999996 0.00282121i \(-0.999102\pi\)
0.497555 0.867433i \(-0.334231\pi\)
\(588\) −4.73846e6 8.20725e6i −0.565189 0.978936i
\(589\) −1.97536e6 3.42142e6i −0.234616 0.406367i
\(590\) 715549. 1.23937e6i 0.0846271 0.146578i
\(591\) −5.05246e6 −0.595023
\(592\) −2.33866e6 + 4.05068e6i −0.274260 + 0.475032i
\(593\) −3.65226e6 6.32590e6i −0.426506 0.738730i 0.570054 0.821607i \(-0.306922\pi\)
−0.996560 + 0.0828774i \(0.973589\pi\)
\(594\) −2.59965e6 −0.302307
\(595\) −2.57694e6 4.46338e6i −0.298409 0.516859i
\(596\) 478520. 828821.i 0.0551803 0.0955752i
\(597\) −5.18567e6 + 8.98185e6i −0.595483 + 1.03141i
\(598\) −165910. −0.0189723
\(599\) −7.26051e6 + 1.25756e7i −0.826799 + 1.43206i 0.0737373 + 0.997278i \(0.476507\pi\)
−0.900536 + 0.434780i \(0.856826\pi\)
\(600\) −4.46797e6 −0.506678
\(601\) 3.76875e6 0.425609 0.212804 0.977095i \(-0.431740\pi\)
0.212804 + 0.977095i \(0.431740\pi\)
\(602\) −4.10051e6 + 782395.i −0.461155 + 0.0879903i
\(603\) 1.06942e6 0.119772
\(604\) −4.97024e6 −0.554351
\(605\) 159653. 276526.i 0.0177332 0.0307148i
\(606\) 997608. 0.110351
\(607\) 3.15728e6 5.46857e6i 0.347810 0.602424i −0.638050 0.769995i \(-0.720259\pi\)
0.985860 + 0.167570i \(0.0535922\pi\)
\(608\) 2.08614e6 3.61330e6i 0.228868 0.396410i
\(609\) −35605.4 61670.4i −0.00389021 0.00673804i
\(610\) 985403. 0.107223
\(611\) 740559. + 1.28269e6i 0.0802522 + 0.139001i
\(612\) −578410. + 1.00184e6i −0.0624249 + 0.108123i
\(613\) −1.43635e7 −1.54387 −0.771934 0.635703i \(-0.780710\pi\)
−0.771934 + 0.635703i \(0.780710\pi\)
\(614\) −2.48795e6 + 4.30926e6i −0.266331 + 0.461298i
\(615\) 636924. + 1.10318e6i 0.0679047 + 0.117614i
\(616\) −3.95184e6 6.84479e6i −0.419612 0.726789i
\(617\) 9.08559e6 + 1.57367e7i 0.960816 + 1.66418i 0.720459 + 0.693497i \(0.243931\pi\)
0.240357 + 0.970685i \(0.422736\pi\)
\(618\) −4.43548e6 −0.467165
\(619\) −7.21390e6 1.24948e7i −0.756734 1.31070i −0.944508 0.328489i \(-0.893460\pi\)
0.187774 0.982212i \(-0.439873\pi\)
\(620\) −1.06804e6 1.84990e6i −0.111586 0.193272i
\(621\) 1.69516e6 2.93610e6i 0.176393 0.305521i
\(622\) 2.26146e6 3.91696e6i 0.234376 0.405951i
\(623\) 2.88555e7 2.97857
\(624\) −1.21526e6 −0.124942
\(625\) −3.62982e6 + 6.28703e6i −0.371693 + 0.643792i
\(626\) 2.00176e6 3.46715e6i 0.204162 0.353619i
\(627\) 2.46881e6 + 4.27610e6i 0.250795 + 0.434389i
\(628\) 3.86855e6 + 6.70053e6i 0.391426 + 0.677969i
\(629\) 9.92263e6 1.00000
\(630\) 72556.6 + 125672.i 0.00728326 + 0.0126150i
\(631\) −2.42729e6 4.20419e6i −0.242688 0.420348i 0.718791 0.695226i \(-0.244696\pi\)
−0.961479 + 0.274878i \(0.911363\pi\)
\(632\) −5.08987e6 8.81591e6i −0.506890 0.877959i
\(633\) −4.93220e6 + 8.54282e6i −0.489250 + 0.847407i
\(634\) 1.75659e6 0.173559
\(635\) −1.32634e6 + 2.29729e6i −0.130533 + 0.226090i
\(636\) 908579. + 1.57370e6i 0.0890676 + 0.154270i
\(637\) 2.46510e6 0.240705
\(638\) −8026.13 13901.7i −0.000780646 0.00135212i
\(639\) 493513. 854789.i 0.0478130 0.0828146i
\(640\) 1.47117e6 2.54815e6i 0.141976 0.245909i
\(641\) 4.66681e6 0.448617 0.224308 0.974518i \(-0.427988\pi\)
0.224308 + 0.974518i \(0.427988\pi\)
\(642\) 2.77027e6 4.79824e6i 0.265268 0.459457i
\(643\) 1.78877e7 1.70619 0.853094 0.521757i \(-0.174723\pi\)
0.853094 + 0.521757i \(0.174723\pi\)
\(644\) 4.89674e6 0.465256
\(645\) 2.91552e6 556293.i 0.275941 0.0526507i
\(646\) −2.43756e6 −0.229813
\(647\) 9.98853e6 0.938082 0.469041 0.883176i \(-0.344600\pi\)
0.469041 + 0.883176i \(0.344600\pi\)
\(648\) −2.77589e6 + 4.80799e6i −0.259696 + 0.449807i
\(649\) 1.86249e7 1.73573
\(650\) 276057. 478145.i 0.0256281 0.0443891i
\(651\) −6.47332e6 + 1.12121e7i −0.598652 + 1.03690i
\(652\) −4.41800e6 7.65220e6i −0.407012 0.704965i
\(653\) −2.12539e7 −1.95055 −0.975273 0.221004i \(-0.929067\pi\)
−0.975273 + 0.221004i \(0.929067\pi\)
\(654\) 185006. + 320440.i 0.0169138 + 0.0292956i
\(655\) −855551. + 1.48186e6i −0.0779189 + 0.134960i
\(656\) 3.85790e6 0.350019
\(657\) 323095. 559616.i 0.0292022 0.0505798i
\(658\) 2.29455e6 + 3.97428e6i 0.206601 + 0.357844i
\(659\) −8.03176e6 1.39114e7i −0.720439 1.24784i −0.960824 0.277159i \(-0.910607\pi\)
0.240385 0.970678i \(-0.422726\pi\)
\(660\) 1.33484e6 + 2.31201e6i 0.119280 + 0.206600i
\(661\) −837223. −0.0745311 −0.0372656 0.999305i \(-0.511865\pi\)
−0.0372656 + 0.999305i \(0.511865\pi\)
\(662\) −1.39265e6 2.41215e6i −0.123509 0.213924i
\(663\) 1.28905e6 + 2.23270e6i 0.113890 + 0.197263i
\(664\) 110444. 191295.i 0.00972128 0.0168377i
\(665\) 1.45634e6 2.52245e6i 0.127705 0.221192i
\(666\) −279383. −0.0244070
\(667\) 20934.5 0.00182199
\(668\) 2.32082e6 4.01978e6i 0.201234 0.348547i
\(669\) 3.25964e6 5.64587e6i 0.281582 0.487714i
\(670\) 609184. + 1.05514e6i 0.0524278 + 0.0908076i
\(671\) 6.41223e6 + 1.11063e7i 0.549798 + 0.952277i
\(672\) −1.36727e7 −1.16797
\(673\) 6.52897e6 + 1.13085e7i 0.555657 + 0.962427i 0.997852 + 0.0655076i \(0.0208667\pi\)
−0.442195 + 0.896919i \(0.645800\pi\)
\(674\) 3.21243e6 + 5.56408e6i 0.272385 + 0.471785i
\(675\) 5.64112e6 + 9.77071e6i 0.476547 + 0.825404i
\(676\) −5.19749e6 + 9.00232e6i −0.437449 + 0.757684i
\(677\) 1.92168e6 0.161142 0.0805709 0.996749i \(-0.474326\pi\)
0.0805709 + 0.996749i \(0.474326\pi\)
\(678\) −139517. + 241650.i −0.0116561 + 0.0201889i
\(679\) −1.87570e6 3.24881e6i −0.156131 0.270427i
\(680\) −2.77425e6 −0.230077
\(681\) 6.76421e6 + 1.17160e7i 0.558920 + 0.968078i
\(682\) −1.45921e6 + 2.52742e6i −0.120131 + 0.208073i
\(683\) 9.92777e6 1.71954e7i 0.814329 1.41046i −0.0954799 0.995431i \(-0.530439\pi\)
0.909809 0.415028i \(-0.136228\pi\)
\(684\) −653770. −0.0534299
\(685\) −2.16322e6 + 3.74680e6i −0.176146 + 0.305095i
\(686\) 1.85127e6 0.150197
\(687\) 3.34808e6 0.270647
\(688\) 2.95585e6 8.48919e6i 0.238073 0.683747i
\(689\) −472672. −0.0379325
\(690\) 365501. 0.0292258
\(691\) 85129.2 147448.i 0.00678240 0.0117475i −0.862614 0.505862i \(-0.831174\pi\)
0.869397 + 0.494115i \(0.164508\pi\)
\(692\) −1.89576e7 −1.50493
\(693\) −944283. + 1.63555e6i −0.0746912 + 0.129369i
\(694\) −1.94993e6 + 3.37737e6i −0.153681 + 0.266183i
\(695\) 2.59674e6 + 4.49769e6i 0.203923 + 0.353205i
\(696\) −38331.7 −0.00299940
\(697\) −4.09215e6 7.08780e6i −0.319058 0.552624i
\(698\) 3.53700e6 6.12626e6i 0.274787 0.475945i
\(699\) −5.45438e6 −0.422233
\(700\) −8.14765e6 + 1.41121e7i −0.628474 + 1.08855i
\(701\) 4.44955e6 + 7.70684e6i 0.341996 + 0.592354i 0.984803 0.173674i \(-0.0555638\pi\)
−0.642807 + 0.766028i \(0.722230\pi\)
\(702\) −383553. 664333.i −0.0293753 0.0508795i
\(703\) 2.80385e6 + 4.85642e6i 0.213977 + 0.370619i
\(704\) 5.85194e6 0.445008
\(705\) −1.63146e6 2.82576e6i −0.123624 0.214123i
\(706\) 2.59486e6 + 4.49443e6i 0.195930 + 0.339361i
\(707\) 3.82940e6 6.63271e6i 0.288125 0.499048i
\(708\) 1.05642e7 1.82978e7i 0.792055 1.37188i
\(709\) 4.71951e6 0.352599 0.176300 0.984337i \(-0.443587\pi\)
0.176300 + 0.984337i \(0.443587\pi\)
\(710\) 1.12450e6 0.0837171
\(711\) −1.21621e6 + 2.10654e6i −0.0902268 + 0.156277i
\(712\) 7.76622e6 1.34515e7i 0.574130 0.994422i
\(713\) −1.90302e6 3.29612e6i −0.140191 0.242817i
\(714\) 3.99399e6 + 6.91780e6i 0.293199 + 0.507835i
\(715\) −694426. −0.0507996
\(716\) −1.08582e7 1.88070e7i −0.791547 1.37100i
\(717\) −4.81616e6 8.34183e6i −0.349867 0.605987i
\(718\) 2.35908e6 + 4.08605e6i 0.170778 + 0.295796i
\(719\) 2.28570e6 3.95896e6i 0.164891 0.285600i −0.771725 0.635956i \(-0.780606\pi\)
0.936617 + 0.350356i \(0.113939\pi\)
\(720\) −312477. −0.0224640
\(721\) −1.70260e7 + 2.94898e7i −1.21976 + 2.11268i
\(722\) 1.46989e6 + 2.54593e6i 0.104940 + 0.181762i
\(723\) 2.25745e6 0.160610
\(724\) 1.16142e7 + 2.01164e7i 0.823461 + 1.42628i
\(725\) −34832.7 + 60332.0i −0.00246117 + 0.00426288i
\(726\) −247446. + 428588.i −0.0174236 + 0.0301786i
\(727\) −2.14070e7 −1.50217 −0.751087 0.660204i \(-0.770470\pi\)
−0.751087 + 0.660204i \(0.770470\pi\)
\(728\) 1.16611e6 2.01976e6i 0.0815477 0.141245i
\(729\) 1.55187e7 1.08153
\(730\) 736192. 0.0511309
\(731\) −1.87318e7 + 3.57411e6i −1.29654 + 0.247385i
\(732\) 1.45483e7 1.00354
\(733\) 2.49500e6 0.171518 0.0857591 0.996316i \(-0.472668\pi\)
0.0857591 + 0.996316i \(0.472668\pi\)
\(734\) 2.92450e6 5.06539e6i 0.200360 0.347035i
\(735\) −5.43062e6 −0.370792
\(736\) 2.00974e6 3.48098e6i 0.136756 0.236868i
\(737\) −7.92818e6 + 1.37320e7i −0.537657 + 0.931248i
\(738\) 115219. + 199565.i 0.00778724 + 0.0134879i
\(739\) −1.42343e7 −0.958796 −0.479398 0.877598i \(-0.659145\pi\)
−0.479398 + 0.877598i \(0.659145\pi\)
\(740\) 1.51599e6 + 2.62578e6i 0.101770 + 0.176270i
\(741\) −728497. + 1.26179e6i −0.0487397 + 0.0844196i
\(742\) −1.46453e6 −0.0976535
\(743\) 1.12676e7 1.95161e7i 0.748791 1.29694i −0.199612 0.979875i \(-0.563968\pi\)
0.948403 0.317069i \(-0.102699\pi\)
\(744\) 3.48449e6 + 6.03531e6i 0.230784 + 0.399730i
\(745\) −274209. 474945.i −0.0181005 0.0313511i
\(746\) −2.49530e6 4.32199e6i −0.164163 0.284339i
\(747\) −52780.9 −0.00346079
\(748\) −8.57616e6 1.48543e7i −0.560452 0.970732i
\(749\) −2.12678e7 3.68369e7i −1.38522 2.39926i
\(750\) −1.27508e6 + 2.20851e6i −0.0827725 + 0.143366i
\(751\) 9.68188e6 1.67695e7i 0.626412 1.08498i −0.361854 0.932235i \(-0.617856\pi\)
0.988266 0.152742i \(-0.0488104\pi\)
\(752\) −9.88188e6 −0.637228
\(753\) −9.47108e6 −0.608712
\(754\) 2368.36 4102.11i 0.000151711 0.000262772i
\(755\) −1.42407e6 + 2.46655e6i −0.0909206 + 0.157479i
\(756\) 1.13203e7 + 1.96074e7i 0.720367 + 1.24771i
\(757\) −6.66046e6 1.15362e7i −0.422439 0.731686i 0.573738 0.819039i \(-0.305493\pi\)
−0.996177 + 0.0873524i \(0.972159\pi\)
\(758\) 2.46495e6 0.155824
\(759\) 2.37840e6 + 4.11950e6i 0.149858 + 0.259562i
\(760\) −783924. 1.35780e6i −0.0492312 0.0852709i
\(761\) −8.36937e6 1.44962e7i −0.523879 0.907385i −0.999614 0.0277960i \(-0.991151\pi\)
0.475735 0.879589i \(-0.342182\pi\)
\(762\) 2.05570e6 3.56057e6i 0.128254 0.222143i
\(763\) 2.84064e6 0.176647
\(764\) −992877. + 1.71971e6i −0.0615406 + 0.106592i
\(765\) 331450. + 574089.i 0.0204769 + 0.0354671i
\(766\) −1.79039e6 −0.110249
\(767\) 2.74793e6 + 4.75955e6i 0.168662 + 0.292131i
\(768\) 1.38757e6 2.40333e6i 0.0848888 0.147032i
\(769\) 5.74320e6 9.94752e6i 0.350218 0.606595i −0.636070 0.771632i \(-0.719441\pi\)
0.986287 + 0.165037i \(0.0527742\pi\)
\(770\) −2.15161e6 −0.130779
\(771\) −9.07130e6 + 1.57119e7i −0.549583 + 0.951906i
\(772\) −1.01961e7 −0.615728
\(773\) −2.87417e7